The derivative of the equation g(x) = 8x^2 – 4; h(x) = 1.6^x is f'(x) = 40.96x · 1.6^x - 15.040128 · 1.6^x
To find the derivative of f(x) = g(x) · h(x), we use the product rule of derivatives, which states that if f(x) = u(x) · v(x), then f'(x) = u'(x) · v(x) + u(x) · v'(x).
Using this rule, we can find the derivative of f(x) = g(x) · h(x) as follows:
f(x) = g(x) · h(x) = (8x^2 – 4) · (1.6^x)
f'(x) = g'(x) · h(x) + g(x) · h'(x) [applying the product rule]
To find g'(x), we take the derivative of g(x) = 8x^2 – 4, which is:
g'(x) = 16x
To find h'(x), we take the derivative of h(x) = 1.6^x, which is:
h'(x) = ln(1.6) · 1.6^x [using the chain rule and the fact that the derivative of a^x is ln(a) · a^x]
h'(x) ≈ 0.470004 · 1.6^x
Now we substitute these values into the product rule formula:
f'(x) = (16x) · (1.6^x) + (8x^2 – 4) ·0.470004 · 1.6^x
Simplifying this expression, we get:
f'(x) = 25.6^x + (12.8x^2 – 6.4) ·0.470004 · 1.6^x
f'(x) = 40.96x · 1.6^x - 15.040128 · 1.6^x
Therefore, the derivative of f(x) = g(x) · h(x) is:
f'(x) = 40.96x · 1.6^x - 15.040128 · 1.6^x
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A system of linear equations is shown on the graph.
The graph shows a line that passes through negative 10 comma 10, negative 5 comma 9, and 0 comma 8. The graph also shows another line that passes through negative 8 comma 12, negative 5 comma 9, and 0 comma 4.
What is the solution to the system of equations?
There are infinitely many solutions.
There is no solution.
There is one unique solution (−5, 9).
There is one unique solution (0, 8).
The correct statement regarding the solution to the system of equations is given as follows:
There is one unique solution (−5, 9).
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.For the first line, the points are given as follows:
(-10, 10) and (0,8).
Hence the equation is:
y = -0.2x + 8.
For the second line, the points are given as follows:
(-8, 12) and (0,4).
Hence the equation is:
y = -x + 4.
Then the x-coordinate of the solution is obtained as follows:
-0.2x + 8 = -x + 4
0.8x = -4
x = -5.
The y-coordinate is given as follows:
y = -(-5) + 4 = 9.
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What is the answer? I don't understand.
The required height of the trapezoid is 4 ft.
What is trapezoid?In geometry, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American, Canadian, and British English. In Euclidean geometry, a trapezoid is inevitably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases.
According to question:Given data;
a= 3 ft, b = 7 ft, height = h, Area = 20 sq, ft
So,
Area = (a + b)h/2
20 = (3 + 7)h/2
20 = 10h/2
2 = h/2
h = 4 ft
Thus, required height of the trapezoid is 4 ft.
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An art studio offers classes for painting and pottery. Each painting class is 1
hour long. Each pottery class is 1. 5 hours long. The art studio is only open
for classes a maximum of 40 hours per week, and only one class is offered at
a time. Each class costs $35, and the art studio earns a minimum of $1,000
per week from all classes. Let x be the number of painting classes offered per
week, and let y be the number of pottery classes offered per week.
The art studio can offer a maximum of 8 painting classes and 5 pottery classes per week, while still meeting the time constraint and earning at least $1000 per week.
To find the maximum number of classes the art studio can offer per week, we need to set up an equation based on the time constraint.
Let's assume that the studio offers x painting classes and y pottery classes per week. Since each painting class is 1 hour long and each pottery class is 1.5 hours long, the total time spent on classes can be represented by the equation:
1x + 1.5y ≤ 40
This equation states that the total number of hours spent on painting classes (1x) plus the total number of hours spent on pottery classes (1.5y) must be less than or equal to 40 hours per week.
To find the minimum revenue the art studio can earn per week, we can set up another equation based on the cost of each class and the minimum revenue requirement.
Let's assume that each painting or pottery class costs $35. Then the total revenue earned per week can be represented by the equation:
35x + 35y ≥ 1000
This equation states that the total revenue earned from painting classes (35x) plus the total revenue earned from pottery classes (35y) must be greater than or equal to $1000 per week.
Now we have two equations:
1x + 1.5y ≤ 40
35x + 35y ≥ 1000
We can use these equations to find the maximum number of classes the art studio can offer per week.
To do this, we can graph the two equations on the same coordinate plane and find the point where they intersect.
When we do this, we get the point (x, y) = (8, 16/3).
This means that the art studio can offer a maximum of 8 painting classes and 16/3 (or approximately 5.33) pottery classes per week, while still meeting the time constraint and earning at least $1000 per week.
Note that since the studio can only offer one class at a time, they would need to round down the number of pottery classes to 5 in order to offer a whole number of classes per week.
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Veronica has a goal of saving $12,000 for a car. She is given $3000 by her grandfather to start a savings account, and she saves an additional $500 each month. Which equation can be used to find the number of months n it will take Veronica to save for the car?
Answer:
m= month 12k - 3500= 950 she needs to save for 2 in a half months to get her car
Step-by-step explanation:
Meena is going to see a movie and is taking her 2 kids. each movie ticket costs $14 and there are an assortment of snacks available to purchase for $5 each. how much total money would meena have to pay for her family if she were to buy 3 snacks for everybody to share? how much would meena have to pay if she bought xx snacks for everybody to share?
Meena would have to pay a total of $57 for her family if she were to buy 3 snacks for everybody to share.
Meena would have to pay a total of $42 + 5xx for her family if she bought xx snacks for everybody to share.
To calculate the total money Meena would have to pay for her family, including movie tickets and snacks, we'll first look at the scenario with 3 snacks to share.
1. Calculate the cost of movie tickets: Meena + 2 kids = 3 tickets at $14 each.
3 tickets * $14 = $42
2. Calculate the cost of 3 snacks at $5 each.
3 snacks * $5 = $15
3. Add the cost of movie tickets and snacks.
$42 + $15 = $57
Meena would have to pay a total of $57 for her family if she were to buy 3 snacks for everybody to share.
For the scenario where she buys xx snacks:
1. Calculate the cost of movie tickets (same as before):
3 tickets * $14 = $42
2. Calculate the cost of xx snacks at $5 each.
xx snacks * $5 = 5xx
3. Add the cost of movie tickets and snacks.
$42 + 5xx = $42 + 5xx
Meena would have to pay a total of $42 + 5xx for her family if she bought xx snacks for everybody to share.
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A rectangle has vertices located at the points: A(-1 1/4,3 1/2), B(2 2/3,3 1/2), C(2 2/3,-1 3/4), D(-1 1/4,-1 3/4). Find the length of BC
The length of BC is 5.25 units. when the rectangle has vertices located at the points: B is ( 2 2/3,3 1/2) and C is (2 2/3,-1 3/4).
We need to find the length of BC. The length of a line segment BC can be calculated using the distance formula. The formula to find the distance between two points (x1, y1) and (x2, y2) is given as :
d = √(x2−x1)²+(y2−y1)²
Given data:
A = (-1 1/4,3 1/2)
B = ( 2 2/3,3 1/2)
C = (2 2/3,-1 3/4)
D = (-1 1/4,-1 3/4)
We need to Convert the B and C mixed numbers to improper fractions, we get,
B = (2+2/3), (3 + 1/2)
= (8/3, 7/2)
C = (2+2/3) , (-1 + 3/4)
= (8/3, -7/4).
Substituting the B and C values into the distance formula, we get:
= √(8/3 − 8/3)² + ( −7/4 − 7/2 )²
= √0 + ( − 21 / 4 )²
= √441/16
[tex]= 21/4[/tex]
[tex]= 5.25[/tex]
Therefore, the length of BC is 5.25 units.
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Toad and Toadette just had their first little toadstool! Toad's family is known to be purebred dominant for red spots on their white cap. Everyone was shocked when Little Toad was born with a white cap with white spots instead of red. Toadette is very upset as she thinks the Mushroom Kingdom Hospital accidentally switched babies. Is this true? Did the hospital really switch babies? Choose either "yes" or "no" and defend your answer.
No, it is not necessarily true that the hospital switched babies.
What happened there?Even though Toad's family is known for having exceptionally dominant red patches on their white heads, this does not mean that all of their offspring will carry the trait.
In reality, if Toadette carries a recessive gene for white spots and transferred this gene to her baby, Little Toad might have a white head with white spots.
A spontaneous genetic mutation that occurred during the development of an offspring could account for the unexpected white cap with white patches.
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Maryam scored 86. 7% on a test with 30 questions on
it. How many questions did Maryam get wrong?
Help!
Maryam answered 26 questions correctly and got 4 questions wrong on the test with 30 questions.
How many questions did Maryam answer incorrectly?To find how many questions Maryam got wrong, we need to first determine how many questions she got right. Since she scored 86.7%, we can multiply the total number of questions by the percentage to get the number of questions she answered correctly.
86.7% of 30 questions is (86.7/100) * 30 = 26.01 questions.
Since Maryam cannot have answered a fractional number of questions correctly, we round down to the nearest whole number. Thus, she answered 26 questions correctly.
To find out how many questions she got wrong, we can simply subtract the number of questions she got right from the total number of questions. Therefore, Maryam got 30 - 26 = 4 questions wrong.
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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 449 gram setting. It is believed that the machine is underfilling the bags. A 24 bag sample had a mean of 445 grams with a variance of 196. A level of significance of 0. 1 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places
The decision rule for rejecting the null hypothesis in this scenario is to reject the null hypothesis if the sample mean falls below a critical value determined by the level of significance and the population parameters.
How to determine the decision rule for rejecting the null hypothesis in a chocolate chip bag filling machine test at the 449 gram setting?To determine the decision rule for rejecting the null hypothesis, we need to conduct a hypothesis test. In this case, the null hypothesis (H0) is that the bag filling machine works correctly at the 449 gram setting. The alternative hypothesis (Ha) is that the machine is underfilling the bags.
Since the sample size is 24 and the population variance is unknown, we can use the t-distribution for the hypothesis test. With a level of significance of 0.1 (or 10%), the critical t-value can be obtained from the t-distribution table.
Using the sample mean of 445 grams, the sample variance of 196, and the sample size of 24, we can calculate the t-value. The decision rule is to reject the null hypothesis if the calculated t-value is less than the critical t-value or greater than the negative of the critical t-value.
To obtain the specific critical t-value, we need the degrees of freedom, which is (sample size - 1). In this case, it is 24 - 1 = 23. Consulting the t-distribution table or using statistical software, we can find the critical t-value corresponding to a 10% significance level and 23 degrees of freedom.
Finally, we compare the calculated t-value to the critical t-value to determine whether to reject the null hypothesis or not.
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How much more popcorn does the bigger box hold than the smaller box?
\text{cm}^3cm 3
start text, c, m, end text, cubed
\text{Amanda's popcorn container:}Amanda’s popcorn container:start text, A, m, a, n, d, a, apostrophe, s, space, p, o, p, c, o, r, n, space, c, o, n, t, a, i, n, e, r, colon, end text
\text{Mary's popcorn container:}Mary’s popcorn container:start text, M, a, r, y, apostrophe, s, space, p, o, p, c, o, r, n, space, c, o, n, t, a, i, n, e, r, colon, end text
The amount of popcorn the bigger box holds than the smaller box depends on the dimensions of the two containers, so it cannot be determined without additional information.
The difference in the amount of popcorn the two containers hold depends on the volume of each container. Let's assume the volume of Amanda's popcorn container is V1 and the volume of Mary's popcorn container is V2.
If we know the dimensions of both containers, we can calculate their volumes using the formula V = l × w × h, where l is the length, w is the width, and h is the height of the container. Then, we can find the difference in the volumes of the two containers by subtracting V1 from V2.
However, the question does not provide any information about the dimensions of the two containers, so we cannot determine the difference in their volumes. Therefore, the main answer is that the amount of popcorn the bigger box holds than the smaller box cannot be determined without additional information.
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Given: AB=CD, AD|| BC, BF=HD, CGE=AHF and AE=FC.
Prove: BAE=DCF
The ∠BAE ≅ ∠DCF by SAS congruence of triangles. The solution has been obtained by using the congruence of triangles.
What is congruence of triangles?
If all three corresponding sides and all three corresponding angles of two triangles have the same size, the triangles are said to be congruent. These triangles can be moved, flipped, twisted, and turned to achieve the same result. They are parallel to one another when moved.
We are given the following:
AB ≅ CD
AD || BC
BG ≅ HD
∠CGE ≅ ∠AHF
AE ≅ FC
Now,
EF ≅ EF as it is the common side
Since, AD || BC so,
∠BCA ≅ ∠CAD as they are alternate interior angles
From this we get that triangle BAC ≅ triangle ACD.
So, the ∠BAE ≅ ∠DCF.
Hence, the ∠BAE ≅ ∠DCF by SAS congruence of triangles.
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Here is a triangular prism. 4 cm 5 cm 5 cm 10 cm 6 cm answer numerically. units have been provided a. what is the volume of the prism, in cubic centimeters? cm3 b. what is the surface area of the prism, in square centimeters? cm²
A triangular prism is a three-dimensional shape with two parallel triangular bases and three rectangular faces. In this case, the triangular bases have sides of 4 cm, 5 cm, and 5 cm, while the rectangular faces have a length of 10 cm and a height of 6 cm.
To find the volume of the prism, we can use the formula V = Bh, where B is the area of the base and h is the height. The area of a triangle can be found using the formula A = 1/2bh, where b is the base and h is the height.
So, for the triangular base of this prism, we have:
A = 1/2(4 cm)(3 cm) = 6 cm²
The height of the prism is 5 cm, so:
V = Bh = (6 cm²)(5 cm) = 30 cm³
Therefore, the volume of the prism is 30 cubic centimeters.
To find the surface area of the prism, we need to calculate the area of each face and add them up.
The two triangular faces each have an area of:
A = 1/2(4 cm)(5 cm) = 10 cm²
And the three rectangular faces each have an area of:
A = (10 cm)(6 cm) = 60 cm²
So, the total surface area is:
SA = 2(10 cm²) + 3(60 cm²) = 200 cm²
Therefore, the surface area of the prism is 200 square centimeters.
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Ayana played Super Star Quest, a video game that involves collecting stars and spending them on power-ups. At the end of each level, the game showed Ayana how many stars she had. Ayana created a line of best fit relating the level, x, to the number of stars, y. The equation for the line of best fit is y= 3 2 x–1. How many stars does this equation predict Ayana will have at the end of level 10?
There would be 14 stars that this equation predicts Ayana will have at the end of level 10.
In this question, we are given an equation for the line of best fit relating the level, x, to the number of stars, y. The equation is y = (3/2)x - 1.
To find the predicted number of stars at the end of level 10, we need to substitute x = 10 into the equation and solve for y.
y = (3/2)x - 1
y = (3/2)(10) - 1
y = 15 - 1
y = 14
Therefore, the equation predicts that Ayana will have 14 stars at the end of level 10.
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What is one more solution to the following. i already have the first solution which is x=9 but there is one more.
let f (x) = log3(x) + 3 and g(x) = log3(x3) – 1.
part a: if h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points)
part b: determine the solution to the system of nonlinear equations.
( i already have the answer to part a as well it should be log3(x^4)+2) i just need the last solution to part b) also im using all my points for this so ya:) have a nice day!
The solutions to the system of nonlinear equations are
x = 9 and x =[tex]3^2[/tex]= 9.
What is the solution to the system of nonlinear equations:f(x) = g(x), where f(x) = log3(x) + 3 and g(x) = log3(x^3) – 1?
To determine the solution to the system of nonlinear equations:
f(x) = g(x)
We can substitute the given expressions for f(x) and g(x) and simplify:
log3(x) + 3 =[tex]log3(x^3) - 1[/tex]
Using the properties of logarithms, we can simplify this equation as follows:
log3(x) + 3 = 3*log3(x) - 1
4 = 2*log3(x)
2 = log3(x)
x =[tex]3^2[/tex]
Therefore, the solutions to the system of nonlinear equations are x = 9 and [tex]x = 3^2 = 9.[/tex]
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D. Larry has a new plan. Whenever his need for the car exceeds the number of slots he has rented the car for, he returns the car on time to avoid the fine, and uses his bicycle for the remaining deliveries. Unfortunately, bike deliveries take 3 times longer than car deliveries. Suppose he rents the car for 5 slots (75 minutes). If he needs 7 slots, then he uses the car for 5 slots, and the remaining 2 slots are done by bicycle, which take 6 slots (1. 5 hours). How much time does he expect to bicycle on average (in terms of slots)
Larry uses the car for the first 5 slots (75 minutes) and returns it on time to avoid any fine. He then uses his bike for the remaining 2 slots, which takes 6 slots (3 times longer than using the car).
Therefore, in total, Larry uses the car for 5 slots and the bike for 6 slots, for a total of 11 slots.
On average, Larry expects to use the bike for (6/11) of his total slots. Since each bike delivery takes 3 times longer than a car delivery, we can say that Larry expects to spend 3 times as much time on the bike as he would in the car. Therefore, the average time he expects to spend on the bike (in terms of slots) is:
(6/11) * 3 = 1.636 slots
So, Larry expects to spend an average of 1.636 slots (or about 24.5 minutes) on the bike for each delivery.
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An angle measure 94 less than the measure of its supplementary angle. What is the measure of each angle?
The angle measures 43 degrees and its supplementary angle measures 180 - 43 = 137 degrees.
What is the supplementary angle?In geometry, the supplementary angle of an angle is the angle that, when added to the given angle, results in a sum of 180 degrees. In other words, two angles are supplementary if their sum is 180 degrees.
For example, if an angle measures 60 degrees, its supplementary angle would measure 120 degrees, since 60 degrees + 120 degrees = 180 degrees.
According to the given informationLet x be the measure of the angle in degrees.
By definition, the supplementary angle of x measures 180 - x degrees.
We are given that the angle measures 94 degrees less than its supplementary angle, so we can write:
x = (180 - x) - 94
Simplifying and solving for x, we get:
2x = 180 - 94
2x = 86
x = 43
Therefore, the angle measures 43 degrees and its supplementary angle measures 180 - 43 = 137 degrees.
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To the nearest hundredth, what is the relative frequency of boys who want to go to the water park
To find the relative frequency of boys who want to go to the water park, we need to divide the number of boys who want to go to the water park by the total number of boys in the sample:
Relative frequency = Number of boys who want to go to the water park / Total number of boys
Assuming you have the necessary data, you can compute this value by dividing the number of boys who want to go to the water park by the total number of boys and rounding the result to the nearest hundredth.
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In the mid-nineteenth century, explorers used the boiling point of water to estimate altitude. The boiling temperature of water T (in °F) can be approximated by the model T = -1. 83a + 212, where a is the altitude in thousands of feet. Two campers hiking in Colorado boil water for tea. If the water boils at 196°F, approximate the altitude of the campers. Give the result to the nearest hundred feet
The Colorado hikers are at an altitude of 8753.1694 feet.
Here we have been given the equation T = -1. 83a + 212.
Here, T is the boiling point in Fahrenheit of water, while a is the altitude of the place.
We know that the campers in hiing in Colorado boil water for ea. The water boils at a temperature of 196°F, we need to find the altitude.
Here we are going to clearly take T = 196°F
Substituting the value in the above equation will give us
196 = - 1.83a + 212
Taking the variable to the Right Hand Side will give us
196 + 1.83a = 212
Taking 196 to LHS to separate the constant and variable will give us
1.83a = 212 - 196
Solving LHS gives us
1.83a = 16
Taking 1.83 to the other side will give us
a = 16/1.83
or, a = 8.7431694 thousands feet
= 8753.1694 feet
Hence, the Colorado hikers are at an altitude of 8753.1694 feet.
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For the function f(x) = x^2e^7x find the critical numbers and use the First Derivative Test to find the local
maximum and minimum values and where they occur. Enter exact answers in fraction form.
For the function f(x) = x^2e^7x the critical numbers are 0 and -2/7 and using the First Derivative Test local minima at x = 0 and -2/7.
The function f(x) = x²e⁷ˣ
Differentiate the function f(x) with respect to x
f'(x) = 2xe⁷ˣ + 7x²e⁷ˣ
f'(x) = xe⁷ˣ(2 + 7x)
Now put f'(x) = 0 for critical points.
xe⁷ˣ(2 + 7x) = 0
x = 0 2 + 7x = 0 e⁷ˣ ≠ 0
x = 0 x = -2/7 e⁷ˣ ≠ 0
Hence, 0 and -2/7 are the critical points.
f'(x) = 2xe⁷ˣ + 14x²e⁷ˣ
Now f''(x) = 2e⁷ˣ + 14xe⁷ˣ + 28xe⁷ˣ + 98x²e⁷ˣ
f''(x) = 2e⁷ˣ + 42xe⁷ˣ + 98x²e⁷ˣ
f''(x) = 2e⁷ˣ(1 + 21x + 49x²)
Now f''(x) at x = 0
f''(0) = 2e⁷⁽⁰⁾(1 + 21(0) + 49(0)²)
f''(0) = 2(1 + 0 + 0)
f''(0) = 2 > 0
So f(x) has minima at x = 0
Local minima at x = 0 and y = 0.
Now f''(x) at x = -2/7
f''(0) = 2e⁻²(1 + 21(-2/7) + 49(-2/7)²)
f''(0) = 2e⁻²(1 - 6 + 4)
f''(0) = -2e⁻² < 0
f(x) has local minima at x = -2/7
Now y at x = -2/7 is
y = f(-2/7)
y = (-2/7)² e⁻²
y = 4/49e²
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The mathematical phrase 5 + 2 × 18 is an example of a(n)
The mathematical phrase 5 + 2 × 18 is an example of an arithmetic expression.
To solve this expression, follow the order of operations (PEMDAS/BODMAS):
1. Parentheses/Brackets (P/B)
2. Exponents/Orders (E/O)
3. Multiplication and Division (M/D)
4. Addition and Subtraction (A/S)
Your expression: 5 + 2 × 18
Step 1: No parentheses/brackets to solve.
Step 2: No exponents/orders to solve.
Step 3: Solve multiplication: 2 × 18 = 36
Step 4: Solve addition: 5 + 36 = 41
So, the value of the expression 5 + 2 × 18 is 41.
It is important to follow the order of operations when evaluating arithmetic expressions to ensure the correct value is obtained.
An arithmetic expression is a combination of numbers, operators (such as addition, subtraction, multiplication, and division), and parentheses that represents a mathematical calculation. In the given expression, the multiplication operation takes precedence over addition.
According to the order of operations (PEMDAS/BODMAS), multiplication is performed before addition. So, 2 × 18 is evaluated first, resulting in 36, and then 5 + 36 is computed, resulting in 41.
Therefore, the value of the expression is 41. Understanding the order of operations is crucial in correctly evaluating mathematical expressions to obtain accurate results.
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Mike has some candies. he gave some to his friend. then, his mom gave him twice as much as he had in the beginning. how much did he have in the beginning if he has a total of 60 candies now?
According to given question Mike has 25 candies in the beginning.
Let's assume that Mike had "x" candies in the beginning.
After giving 15 candies to his friend, he would have had (x - 15) candies left.
His mom then bought him twice as many candies as he had in the beginning, which would be 2x candies.
So, the total number of candies Mike has now is (x - 15) + 2x = 60.
Combining like terms, we get 3x - 15 = 60.
Adding 15 to both sides, we have 3x = 75.
Finally, dividing both sides by 3, we find that x = 25.
Therefore, Mike had 25 candies in the beginning.
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The complete question is Mike had some candies. He gave 15 of them to his friend. After that, his mom bought him twice as many candies as he had in the beginning. How many candies did Mike have in the beginning if he now has a total of 60 candies?
Here is a list of statistical questions. What data would you collect and analyze to answer each question? For numerical data, include the unit of measurement that you would use.
What is a typical height of female athletes on a team in the most recent international sporting event?
Are most adults in the school football fans?
How long do drivers generally need to wait at a red light in Washington, DC
You can collect data on the heights of all female athletes on a team using recent international sporting event and This data can be gotten by using official event records or by carrying out a survey of the athletes. Heights are said to be measured in centimeters (cm) or feet and inches (ft, in).
Are most adults in the school football fans?To address this question, you can gather information regarding the quantity of school staff members who are passionate about football and compare it against the full count of school staff members. Gathering this information is possible through either conducting a survey or analyzing the number of tickets sold for school football games. The information can be shown using ratio or a percentage.
How long do drivers generally need to wait at a red light in Washington, DC
One can get information on the durations motorists must wait at various traffic signals in Washington, DC. One can ask this information by either installing sensors or cameras at different intersections or by gathering input from drivers through a survey. The duration of waiting periods is commonly quantified in units of seconds (s) or minutes (min).
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Find the value of x
Hellpppp
Explanation is in the image!
A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likel voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0. 014, 0. 064). What was the difference (pre- debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate?
The difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they would vote for this candidate was approximately 0.025.
We are given a confidence interval of (-0.014, 0.064) for the true difference in proportions of likely voters who would vote for the political candidate before and after the debate. This means that we can be 95% confident that the true difference in proportions falls within this interval.
To find the difference in sample proportions, we need to subtract the pre-debate proportion from the post-debate proportion. Let's call the pre-debate proportion "p1" and the post-debate proportion "p2".
We are not given the sample proportions directly, but we can use the midpoint of the confidence interval as an estimate for the true difference in proportions. The midpoint is (-0.014 + 0.064)/2 = 0.025.
So, we can estimate the difference in sample proportions as:
p2 - p1 = 0.025
This means that the post-debate proportion was 0.025 higher than the pre-debate proportion, on average. Note that we don't know the actual values of p1 and p2, just their difference.
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Determine if each root is a rational or irrational number. explain your reasoning. √ 20 3 √ 96
Both √203 and √96 are irrational numbers since the numbers inside the roots are not perfect squares.
To determine whether a root is rational or irrational, we need to know if the number inside the square root is a perfect square or not. If it is not, then the root is irrational.
For √203, we can determine that 203 is not a perfect square, since the last digit is 3, which is not a perfect square. Therefore, √203 is an irrational number.
For √96, we can simplify the expression as follows:
√96 = √(16*6) = √16 * √6 = 4√6
Since 6 is not a perfect square, 4√6 is an irrational number.
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13) a 95 percent confidence interval estimate will have a margin of error that is approximately + or - 47.5 percent of the size of the population mean. true or false
False because the statement "a 95 percent confidence interval estimate will have a margin of error.
How to Calculate 95% confidence interval with margin?A 95% confidence interval (CI) estimate is a range of values that is likely to contain the true population mean with 95% confidence. The margin of error for a confidence interval depends on the sample size, the variability of the data, and the desired level of confidence.
The general formula for the margin of error of a 95% confidence interval for the population mean is:
Margin of error = (z-value) x (standard deviation /√n)
where z-value is the number of standard deviations corresponding to the desired level of confidence (for a 95% CI, this value is 1.96), standard deviation is the standard deviation of the sample data, and n is the sample size.
The margin of error is usually expressed as a percentage of the sample mean, not the population mean. Moreover, the percentage of the margin of error is not fixed, but it varies depending on the data and the sample size.
Therefore, the statement "a 95 percent confidence interval estimate will have a margin of error that is approximately + or - 47.5 percent of the size of the population mean" is not correct.
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Find the equation of the tangent line to the curve (a lemniscate) 2(x^2+y^2) = 25 (z^2-y^2) at the point (-3, -1)
The equation of the tangent line to the lemniscuses 2(x²+y²) = 25 (z²-y²) at the point (-3, -1) is y = (16/25)x + 23/25.
To find the equation of the tangent line to a curve, we need to take the derivative of the equation of the curve and evaluate it at the given point.
First, let's rewrite the equation of the lemniscate in terms of x and y:
2(x² + y²) = 25(z² - y²)
Dividing both sides by 25, we get:
(x² + y²) / (25/2) = (z² - y²) / 12.5
Now, we can take the partial derivatives with respect to x and y:
∂/∂x [(x² + y²) / (25/2)] = (2x) / (25/2) = (4x) / 25
∂/∂y [(x² + y²) / (25/2)] = (2y) / (25/2) = (4y) / 25
Next, we need to find the value of z at the point (-3, -1). To do this, we can substitute x = -3 and y = -1 into the equation of the lemniscate:
2((-3)² + (-1)²) = 25(z² - (-1)²)
20 = 25(z² + 1)
z^2 = 19/25
z = ±sqrt(19)/5
Since we want the tangent line at the point (-3, -1), we'll use z = -sqrt(19)/5.
Now, we can evaluate the partial derivatives at (-3, -1, -sqrt(19)/5):
(4(-3)) / 25 = -12/25
(4(-1)) / 25 = -4/25
So, the slope of the tangent line is:
m = ∂z/∂x × -12/25 + ∂z/∂y × -4/25
m = (2x / (25/2)) × (-12/25) + (2y / (25/2)) × (-4/25)
m = -24x/125 - 8y/125
m = -24(-3)/125 - 8(-1)/125
m = 72/125 + 8/125
m = 80/125
m = 16/25
Finally, we can use the point-slope form of a line to find the equation of the tangent line:
y - (-1) = (16/25)(x - (-3))
y + 1 = (16/25)(x + 3)
y = (16/25)x + 48/25 - 25/25
y = (16/25)x + 23/25
So the equation of the tangent line to the lemniscuses 2(x²+y²) = 25 (z²-y²) at the point (-3, -1) is y = (16/25)x + 23/25.
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Triangle ABC has vertices
A(-3, 3), B(2, 4), and C(-2,
2) and is translated
according to the rule:
(x, y) –> (x+2, y-4).
What are the coordinates
of the vertices of the
translated figure?
The coordinates of the translated triangle A'B'C' are: A'(-1, -1), B'(4, 0), and C'(0, -2).
To find the coordinates of the vertices of the translated figure, we simply apply the given translation rule to each vertex of the original triangle.
For vertex A(-3, 3):
(x, y) --> (x+2, y-4)
(-3, 3) --> (-3+2, 3-4)
(-1, -1)
So, the translated coordinates of vertex A are (-1, -1).
For vertex B(2, 4):
(x, y) --> (x+2, y-4)
(2, 4) --> (2+2, 4-4)
(4, 0)
So, the translated coordinates of vertex B are (4, 0).
For vertex C(-2, 2):
(x, y) --> (x+2, y-4)
(-2, 2) --> (-2+2, 2-4)
(0, -2)
So, the translated coordinates of vertex C are (0, -2).
Therefore, the vertices of the translated triangle are A'(-1, -1), B'(4, 0), and C'(0, -2).
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How many numbers from 2 through 100 can be expressed as p², where p is a prime number?
F. 4
G. 5
H. 7
J. 8
K. 9
Solve for "B" I tried it the way I solved the rest of the equations but I can't get it
Answer:b=30
Step-by-step explanation:
Alternate angles are the same so the angle opposite 30=125
125+30=155.but angles on a straight line=180
So we subtract 180-155 which leaves us with 25 for the top angle in the triangle.Angles in a triangle must add to 180 so we do, 125+25=150
180-150=30
