In the problem given, the result of the polynomial long division shows that the quotient is 4x - 4 and the remainder is -5.
How to Perform the Division?To perform polynomial long division of (4x²-24x+15) by (x-5), we follow these steps:
4x - 4
--------------
x - 5 | 4x² - 24x + 15
4x² - 20x
------------
-4x + 15
-4x + 20
----------
-5
Therefore, the quotient is 4x - 4 and the remainder is -5.
We can check our answer by verifying that:
(4x - 4) * (x - 5) + (-5) = 4x² - 24x + 15
which is indeed the original polynomial.
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A rocket is launched in the air. Its height in feet is given by h(t)=−16t^2 +24t where
t represents the time in seconds after launch. How long is the rocket in the air?
Taking into account the zeros of a quadratic function, the time of the rocket when it is in the air is equal to 1.5 seconds.
Zeros of a functionThe points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.
The zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.
In a quadratic function that has the form:
f(x)= ax² + bx + c
the zeros or roots are calculated by:
[tex]x1,x2=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
Time of he rocket in the airA rocket launched with height function h(t)= -16t²+ 24t
where
't' represents the time in seconds'h' is the height of rocket.Time for which rocket is in the air given by h(t) = 0, so:
0= -16t²+ 24t
where:
a= -16b= 24c= 0Solving:
[tex]x1=\frac{-24+\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}[/tex]
[tex]x1=\frac{-24+\sqrt{24^{2}} }{2x(-16)}[/tex]
[tex]x1=\frac{-24+24 }{2x(-16)}[/tex]
[tex]x1=\frac{0 }{-32}[/tex]
x₁= 0
and
[tex]x2=\frac{-24-\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}[/tex]
[tex]x2=\frac{-24-\sqrt{24^{2} } }{2x(-16)}[/tex]
[tex]x2=\frac{-24-24}{2x(-16)}[/tex]
[tex]x2=\frac{-48}{-32}[/tex]
x₂= 1.5
Therefore, the time of the rocket in the air is 1.5 seconds.
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Let S be the universal set, where:
S= {1, 2, 3,..., 18, 19, 20}
Let sets A and B be subsets of S, where:
Answer:
Step-by-step explanation:
Therefore, the height of the tower is approximately 121.4 meters.
Suppose 128 ounces of a radioactive substance exponentially decays to 28 ounces in 6 hours. What is the half-life of the substance? The half-life is:
Answer:
half-life ≈ 2.74
Step-by-step explanation:
One formula we can use for half life is,
N(t) = No * (1/2)^(t / t_1/2), where
N(t) is the amount remaining, No is the initial amount,1/2 is the base t is the time, and t_1/2 is the half lifeWe already know that N(t) = 28, No = 128, the base is 1/2, and t is 6. Thus, we must solve for t_1/2 using the following equation:
28 = 128 * (1/2) ^ (6 / t_1/2)
Step 1: Divide both sides by 128 to clear 128 on the right-hand side of the equation:(28 = 128 * (1/2) ^ (6 / t_1/2) / 128
0.21875 = (1/2) ^ (6 / t_1/2)
Step 2: Take the natural log (ln) of both sides:ln (0.21875) = ln (1/2 ^ (6 / t_1/2))
Step 3: According to the rules of logs, since we're taking the natural log of ln (1/2 ^ 6 / t_1/2, we can bring down the 6 / t_1/2 and it will now act like a coefficient:ln (0.21875) = 6 / t_1/2 * ln (1/2)
Step 4: Divide both sides by ln (1/2) to clear ln (1/2) on the right-hand side of the equation:(ln ( 0.21875) = 6 / t_1/2 * ln (1/2)) / ln (1/2)
ln (0.21875) / ln (1/2) = 6 / t_1/2
Step 5: You can cross multiply, which appears easier when you use the vertical fraction form instead of the horizontal fraction form.[tex]\frac{ln(0.21875)}{ln(1/2)}=\frac{6}{t_{1/2} }\\ \\ t_{1/2}*ln(0.21875)=6*ln(1/2)[/tex]
Step 6: Finally, you can now divide both sides by ln (0.21875) to isolate t_1/2 and to find the half-life. I simply rounded to the nearest hundredth, but I'll provide the entire half-life number so you can round as liberally as much as you need or would like(t_1/2 * ln (0.21875) = 6 * ln (1/2)) / ln (0.21875)
t_1/2 = (6 * ln (1/2) / ln (0.21875)
t_1/2 = 2.736420983 hours
t_1/2 = 2.74 hours
The only real difference between the longer number and the rounded number is that the longer answer gives a more exact answer when you plug it in, but the rounded answer seems to make more sense to write:
Result when plugging in exact answer for t_1/2:
N (2.736420983) = 128 (1/2) ^ (6 / 2.736420983) = 28
Result when plugging in rounded answer for t_1/2:
N (2.74) = 128 (1/2) ^ (6 / 2.74) = 28.05564116
Determine the area of the given region.
[tex]\displaystyle \int_{0}^{\frac{\pi }{3}}~\sin(x)dx\implies \left.\cfrac{}{} -\cos(x)\right]_{0}^{\frac{\pi }{3}}\implies\left( -\cfrac{1}{2}\right) ~~ - ~~(-1)\implies \cfrac{1}{2}[/tex]
Find the Missing angle and find the missing side.
The solution of given trigonometric Problem by using formula of sine , cosine , tangent is part A 1)cos-1(12/13) 2)∅=cos-1(2/3) 3)sin-1(4/13)
part B 1)13.75 unit 2) 8.112 unit 3) 5.5 unit
What is trigonometric ?Trigonometry is a branch of mathematics that deals with the study of relationships between angles and sides of triangles. It primarily focuses on the properties and functions of angles, and how they can be used to calculate the measurements of sides and angles in a triangle.
According to given informationPart A
1)In the given ΔACB Right angle at ∠C
for find ∅ we use
cos∅=B/H
cos∅=AC/AB
cos∅=12/13
∅=cos-1(12/13)
2) cos∅= AC/AB
∅=cos-1(6/9)
∅=cos-1(2/3)
3) sin∅=CB/AC
∅=sin-1(4/13)
Part-B
1) cos37°=11/x
4/5=11/x
x=55/4
x=13.75 unit
2) tan32°=x/13
0.624=x/13
x= 8.112 unit
3) cos 60°=x/11
1/2= x/11
x=11/2
x=5.5 unit
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a certain phone call costs 75 cents for the first three minutes plus 15 cents for each additional minute.if the call lasted x minutes and x is an integer greater than 3, which of the following expresses the cost of the call in dollars?
The equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).
What is linear equation?A linear equation has the formula y = mx + b, where x and y are variables, m is the angle of the line's slope, and b denotes the y-intercept (the location where the line crosses the y-axis). On a graph, this equation represents a straight line.
The y-intercept of a linear equation, which is determined by the value of b, is first plotted on a graph. The slope is then used to determine further points along the line. How much y changes for each unit of x is indicated by the slope. For instance, if the slope is 2, then y grows by 2 for every unit increase in x.
Given that, a certain phone call costs 75 cents for the first three minutes plus 15 cents for each additional minute.
Let us suppose number of minutes = x.
Then,
Cost = 0.75 + 0.15(x - 3)
hence, the equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).
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The complete question is:
Use the frequency distribution to complete parts (a) through (e)
For the frequency distribution table;
1. The total number of observation is 24.
2. The width of each class is 11
3. The midpoint of the second class is 26
4. The model class is 65-75
5. The class limits of the next class is 76-86
How do we find the width, model, midpoint and next class limit for the frequency distribution table?For the frequency distribution table,
1. Total observation is the sum of the frequency:
2 + 3 + 5 + 6 + 0 + 8 = 24
2. The width is the first limit lower class - first limit of upper class.
21-10 = 11 or 32-21 = 11
3. The midpoint of class 2 is 21 + 31 = 52/2 = 26
4. The class with the highest frequency is the model class
5. Next class lower limit = 75 + 1 = 76
Next class upper limit = 75 + 11 = 86
Use the frequency distribution to complete parts (a) through (e).
Class Frequency
a) Determine the total number of observations. 10-20 2
b) Determine the width of each class. 21-31 3
c) Determine the midpoint of the second class. 32-42 5
d) Determine the modal class (or classes). 43-53 6
e) Determine the class limits of the next class 54-64 0
if an additional class were to be added. 65-75 8
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i need help (see picture)
Answer:
Please refer to the attachment
Step-by-step explanation:
Substitute x-values in g(x).
Eg. g(x) at x=0 is g(0)
=> -5(0) -5
= (-5)
Expand (x+2y) in ascending powers of x.
Hence, x + 2y is the expansion of (x+2y) in ascending powers of x as that every number raised to the power of zero equals 1.
what is exponents ?Exponents, usually referred to as powers and indices, are a type of mathematical operation that requires increasing a base number to a specific exponent. You can multiply the minimum amount by itself a given number of times using the exponent. For instance, the number 2 raised toward the power of 3 (printed as 23) is equivalent to 2 x 2 x 2, which is 8. Exponents are frequently employed in scientific notation, algebra, and other areas of mathematics to express extremely big or extremely small integers.
given
The distributive property of multiplication is used to multiply out the expression when expanding (x+2y) in ascending powers of x.
[tex](x + 2y) = x + 2yx^0[/tex]
By remembering that every number raised to the power of zero equals 1, we may simplify the second term. We thus have:
(x + 2y) = x + 2y(1) (1)
When we multiply the expression, we get:
(x + 2y) = x + 2y
Hence, x + 2y is the expansion of (x+2y) in ascending powers of x as that every number raised to the power of zero equals 1.
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Find the area of parallelogram VW XY. Round your answer to the nearest tenth if necessary.
Answer:
Step-by-step explanation
A=bh for a parallelogram. The diagram is flipped(turn your paper)
b=9
h=6.7
A=(9)(6.7)=60.3 in²
Let S be the universal set, where: S={1, 2, 3,…, 18, 19, 20}
Let sets A and B be subsets of S, where:
n(A ∪ B ∪ C) = 16
n(A u B u C) = 2.
How to solve for the setTo find the number of elements in the set ( A cup B cup C), we need to find the union of the sets A, B, and C. This can be done by combining all the elements in A, B, and C, and then removing any duplicates.
So, (A ∪ B ∪ C) = {1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 20}
Therefore, n(A ∪ B ∪ C) = 16.
To find the number of elements in the set ( A ∩ B ∩ C), we need to find the intersection of the sets A, B, and C. This can be done by finding the elements that are common to all three sets.
So, (A ∩ B ∩ C) = {8, 20}
Therefore, n(A u B u C) = 2.
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A bus traveled on a level road for 3 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 2 hours. Find the average speed on the level road if the entire trip was 290 miles.
Answer:
Let's call the average speed on the winding road "x". Then, the average speed on the level road is "x + 20".
We know that the bus traveled on the winding road for 2 hours, so the distance traveled on the winding road is:
distance = rate × time = x × 2 = 2x
We also know that the bus traveled on the level road for 3 hours at an average speed of "x + 20", so the distance traveled on the level road is:
distance = rate × time = (x + 20) × 3 = 3x + 60
The total distance traveled is 290 miles, so we can write:
2x + 3x + 60 = 290
Combining like terms and solving for x, we get:
5x + 60 = 290
5x = 230
x = 46
Therefore, the average speed on the winding road is 46 mph, and the average speed on the level road is:
x + 20 = 46 + 20 = 66 mph.
Three car dealerships were surveyed about the percentage of vehicles on their lot with automatic or manual transmission. The results are displayed below.
Because automatic automobile frequency is different from the dealership, there will be an association.
A frequency chart is what?A list of objects is contained in a frequency table together with the frequency of each item.
The quantity of times that an event or value occurs is its frequency.
A frequency table, then, is a table that contains some facts and their frequency.
Considering the dealership's frequency schedule for both manual and automatic.
We can see that whereas manual transmission dealerships all use the same frequencies, automatic transmission dealerships use distinct frequencies. Since there is a relationship between the two, there will be an association.
Because automatic automobile frequency is different from dealership frequency, there will therefore be a link.
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The complete question is:
Three car dealerships were surveyed about the percentage of vehicles on their lot with automatic or manual transmission. The results are displayed below.
Find f. f ″(x) = −2 + 24x − 12x2, f(0) = 2, f ′(0) = 16
[tex]f''(x)=-2+24x-12x^2\hspace{5em}f'(0)=16\hspace{5em}f(0)=2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \displaystyle \int~(-2+24x-12x^2)dx\implies -2x+12x^2 - 4x^3 + C=f'(x) \\\\\\ \stackrel{\textit{since we know that}}{f'(0)=16}\hspace{5em}-2(0)+12(0)^2-4(0)^3+C=16 \\\\\\ C=16\hspace{5em}\stackrel{\textit{so then we know that}}{-2x+12x^2 - 4x^3 + 16=f'(x)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\displaystyle \int~(-2x+12x^2 - 4x^3 + 16)dx\implies -x^2+4x^3-x^4+16x+C=f(x) \\\\\\ \stackrel{\textit{since we know that}}{f(0)=2}\hspace{5em}-(0)^2+4(0)^3+16(0)+C=2 \\\\\\ C=2\hspace{5em}\boxed{-x^2+4x^3-x^4+16x+2=f(x)}[/tex]
in how many ways can the letters of MCHNLRN be arranged
Answer:
2520
Step-by-step explanation:
There are 7 letters in MCHNLRN and they can be arranged into 7 ways:
7! = 5040 ways in total
However, the letter 'N' is repeated so we have to divide it by 2.
5040 ÷ 2 = 2520 ways
Answer:
2,520 ways
Step-by-step explanation:
MCHNLRN has 7 letters with one repetition.
therefore, =7!/2!
=2,520 ways
Toss a fair coin n = 1 time. The distribution of x
the number on the upper face is flat or
uniform
Answer:1
Step-by-step explanation:
➡) Complete the expression to show the total
points Roopesh earns if 2 beanbags land on
the board and 2 beanbags land in the hole.
2.5
2.2 ? ▼
Answer:
Step-by-step explanation:
8 points
Mrs. Sawyer is interested in a particular bracelet. Its original price was $37,260, but it is now marked down by 45%. What is the price of the bracelet now?
Answer: 20,493
Step-by-step explanation:
%45 off of $37,260 is the same as (45 x 45) / 100 which equals to: 16,767
Then do: 37,260 - 16,767 = 20,493
And there you have it! Hope this helps!!
Anna invested $69,000 in an account paying an interest rate of % compounded 8 1/2 % continuously. Hudson invested $69,000 in an account paying an interest rate of 8 3/8 % compounded daily. After 10 years, how much more money would Anna have in her account than Hudson, to the nearest dollar?
The solution of compound interest problem using formula of amount is
Anna have$2,734 more money than Hudson.
what is compound interest ?Compound interest is a type of interest in which the interest gained is added to the principal sum before the interest for the subsequent period is calculated using the updated total sum. In other words, in addition to the initial principal, the accumulated interest from prior periods is also taken into account for calculating interest. As a result, as time passes, the interest earned increases, increasing the total amount earned or due. Savings accounts, loans, and investments frequently use compound interest.
According to given informationFor continuous compounding, the formula is:
A = Pe^(rt)
Where:
A = the amount after t years
P = the principal amount
r = the annual interest rate (as a decimal)
t = the time in years
For daily compounding, the formula is:
A = P(1 + r/n)^(nt)
Where:
A = the amount after t years
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times compounded per year
t = the time in years
Using these formulas, we can calculate the amount that Anna and Hudson will have after 10 years, and then find the difference between them.
For Anna's investment:
r = 8.5% = 0.085 (as a decimal)
t = 10 years
P = $69,000
A = Pe^(rt) = 69000 * e^(0.085*10) = $156,794.63
For Hudson's investment:
r = 8 3/8% = 8.375% = 0.08375 (as a decimal)
n = 365 (daily compounding)
t = 10 years
P = $69,000
A = P(1 + r/n)^(nt) = 69000(1 + 0.08375/365)^(365*10) = $154,060.52
Therefore, the difference between the two amounts is:
$156,794.63 - $154,060.52 = $2,734.11
So Anna will have approximately $2,734 more in her account than Hudson after 10 years.
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Find an expression which represents the difference when (5x + 6y) is subtracted
from (2x + 7y) in simplest terms.
Answer: -3x+y
Step-by-step explanation:
This is a subtraction problem and "from" means it's the 1st number so
(2x+7y) - (5x + 6y) be careful to distribute negative
2x +7y - 5x -6y
-3x+y
To find the simplest expression when (5x + 6y) is subtracted from (2x + 7y), we subtract the coefficients of like terms. This gives us -3x + y as the final result.
Explanation:The expression represents the difference when (5x + 6y) is subtracted from (2x + 7y) can be found using the properties of addition and subtraction for algebraic expressions. We will combine like terms to simplify.
So, Subtract (5x + 6y) from (2x + 7y), it's like saying (2x + 7y) - (5x + 6y) this will give us:
-3x + y is the final expression in the simplest form.
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pleasse help these are the first questions and I am struggling so hard
The solution to the word problems are:
1) ∠JML = 63°
2) The center of the circle is (4, -4) and Radius = 4
3) The required measurement of the table cloth should be:
48 in x 36 in
4) The correct option of the similar triangles is:
UY/UV = UZ/ZW
How to solve algebraic word problems?1) The angle subtended by an arc at the Centre is twice the angle subtended at the circumference . More simply, the angle at the centre is double the angle at the circumference. Thus:
∠JML = 126/2 = 63°
2) The general formula for equation of a circle is expressed as:
(x - h)² + (y - k)² = r²
where:
(h, k) is the coordinate of the center of the circle
r is the radius
We are given the circle equation as:
(x + 4)² + (y - 4)² = 16
This can be rewritten as:
(x + 4)² + (y - 4)² = 4²
Thus:
Coordinates of center = (4, -4)
Radius = 4
3) The required measurement of the table cloth should be:
48 in x 36 in
4) Since both triangles are similar, then it means ratio of corresponding sides will be equal and as such:
UY/UV = UZ/ZW
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A game has a spinner with 8 equal- sized sections. The results of 450 spins are shown in the table. Part Frequency 1 58 2 52 3 39 4 77 5 50 6 43 7 60 8 71
For Which Number is the number difference between the theoretical probability and experimental probability greatest?Explain
The theoretical probability of each section is 1/8, since there are 8 equal-sized sections on the spinner. To find the theoretical frequency, we multiply the theoretical probability by the total number of spins:
Theoretical frequency = (1/8) x 450 = 56.25
We can then calculate the experimental probability for each section by dividing the frequency by the total number of spins:
Experimental probability = Frequency/Total number of spins
Using this formula, we can calculate the experimental probabilities for each section:
Part 1: Experimental probability = 58/450 ≈ 0.129
Part 2: Experimental probability = 52/450 ≈ 0.116
Part 3: Experimental probability = 39/450 ≈ 0.087
Part 4: Experimental probability = 77/450 ≈ 0.171
Part 5: Experimental probability = 50/450 ≈ 0.111
Part 6: Experimental probability = 43/450 ≈ 0.096
Part 7: Experimental probability = 60/450 ≈ 0.133
Part 8: Experimental probability = 71/450 ≈ 0.158
To find the number with the greatest difference between the theoretical and experimental probability, we can calculate the difference between the two probabilities for each section:
Part 1: |0.125 - 0.129| = 0.004
Part 2: |0.125 - 0.116| = 0.009
Part 3: |0.125 - 0.087| = 0.038
Part 4: |0.125 - 0.171| = 0.046
Part 5: |0.125 - 0.111| = 0.014
Part 6: |0.125 - 0.096| = 0.029
Part 7: |0.125 - 0.133| = 0.008
Part 8: |0.125 - 0.158| = 0.033
As we can see, the greatest difference between the theoretical and experimental probability is for Part 4 with a difference of 0.046. This indicates that the experimental frequency for Part 4 is significantly different from the theoretical frequency, which may suggest that the spinner is biased towards that section.
The graph and table each show a proportional relationship between the number of miles traveled and the
advertised number of gallons of gas used for the two car models, A and B, respectively. Based on the
graph and table, car A can travel how many times the distance car B can travel when both cars use
1 gallon of gas? Write your answer as a decimal.
Enter your answer in the box
1.25
To answer this question, we need to compare the ratios of miles traveled to gallons of gas used for car A and car B when they both use 1 gallon of gas.
For car A, we can see from the graph that 50 miles are traveled for every 2 gallons of gas used, or in other words, 25 miles are traveled for every 1 gallon of gas used. Therefore, car A can travel 25 times the distance for 1 gallon of gas.
For car B, we can see from the table that 40 miles are traveled for every 2 gallons of gas used, or in other words, 20 miles are traveled for every 1 gallon of gas used. Therefore, car B can travel 20 times the distance for 1 gallon of gas.
To compare the two ratios, we can divide the ratio of miles traveled to gallons of gas used for car A by the ratio for car B:
25/20 = 1.25
Therefore, car A can travel 1.25 times the distance car B can travel when both cars use 1 gallon of gas.
amber and bethan tries a number of sweets and shares them in the ratio 2:1
The ratio of the number of sweets that Amber has to the number of sweets that Callum has is 16:9.
What is ratio?A quantitative comparison of two or more quantities that shows their relative sizes is called a ratio.
In terms of how many times one is greater or less than the other, it describes the relationship between the two quantities.
Let's assume that Amber and Bethan bought x number of sweets, then Callum and David also bought x number of sweets.
According to the problem, Amber and Bethan share the sweets in the ratio 2:1. Therefore, Amber has (2/3)(x) sweets and Bethan has (1/3)(x) sweets.
Also, Callum and David share the sweets in the ratio 3:5. Therefore, Callum has (3/8)(x) sweets and David has (5/8)(x) sweets.
Now, we can find the ratio of the number of sweets that Amber has to the number of sweets that Callum has as follows:
Amber/Callum = [(2/3)(x)]/[(3/8)(x)] = (16/9)
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Draw a point that belongs to the solution region of this system of inequalities.
y > 1.5 +4
y
+ 6
Drawing Tools
Select
Point
Click on a tool to begin drawing.
-10
-8
-6
-2
10-
8
4
2-
-2
2
Delete
3
Undo
6
8
Reset
10
The point (2, 7) belongs to the solution region of the system of inequalities.
What is inequalities?
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
The system of inequalities given is:
y > 1.5x + 4
y > -x + 6
One point that belongs to the solution region of this system of inequalities is (2, 7).
To check if this point satisfies the system of inequalities, we can substitute the values of x and y into each inequality:
For the first inequality, y > 1.5x + 4, we have:
7 > 1.5(2) + 4
7 > 7
This is true, so the point (2, 7) satisfies the first inequality.
For the second inequality, y > -x + 6, we have:
7 > -(2) + 6
7 > 4
This is also true, so point (2, 7) satisfies the second inequality.
Therefore, points (2, 7) belong to the solution region of the system of inequalities.
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The numbered disks shown are placed in a box and one disk is selected at random. Find the probability
The probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.
What is the calculation for this?1. Let's calculate the probability of selecting a blue disk
We can select a blue disk with number 2, 6 or 8 out of a total of 8 disks, it means that the probability of selecting a blue disk is = 3/8
2. Let's calculate the probability of selecting the blue disk labeled with number 2 =
We can select the blue disk labeled with number 2 out of three blue disks, it means that the probability of selecting the blue disk labeled with number 2 is = 1 /3
3. These are dependent events because the fact that we select the disk labeled with number 2, depends on selecting a blue disk before, thus:
Probability of selecting a 2 given that a blue disk is selected =
3/8 x 1/3 = 3/24 = 1/8
Thus,it is correct to state that the probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.
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Full Question:
See attached image.
What percent larger is 20.49 trillion to 4.00 trillion
20.49 trillion is 412.25% larger than 4.00 trillion.
How to calculate a percentage increase?To calculate the percentage increase of a value from an initial value to a final value, you can use the following formula:
increase in percentage = ((final value - initial value) / initial value) x 100%
Percentage increase is useful in a variety of contexts, including: Finance, Sales, Economics, Science, Education. Percentage increase is a useful tool for measuring growth or change over time and comparing different values.
To find the percentage increase, we first need to calculate the difference between the two numbers:
20.49 trillion - 4.00 trillion = 16.49 trillion
Next, we can divide the difference by the original amount (4.00 trillion) and multiply by 100 to get the percentage increase:
(16.49 trillion / 4.00 trillion) * 100 = 412.25%
Therefore, 20.49 trillion is 412.25% larger than 4.00 trillion.
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Which type of function best models the data in each table? Use differences or ratios. X-0, 1, 2, 3, 4
Y-0,1.5,6,13.5,24
Answer:
To determine the type of function that best models the data in the table, we can observe the differences or ratios between successive values of y.
Using differences:
The first differences between successive values of y are:
1.5 - 0 = 1.5
6 - 1.5 = 4.5
13.5 - 6 = 7.5
24 - 13.5 = 10.5
The second differences between successive values of y are:
4.5 - 1.5 = 3
7.5 - 4.5 = 3
10.5 - 7.5 = 3
Since the second differences are constant, the function that best models the data is a quadratic function.
Using ratios:
The ratios between successive values of y are:
1.5/0 = undefined
6/1.5 = 4
13.5/6 = 2.25
24/13.5 ≈ 1.78
Since the ratios are not constant, the function that best models the data is not an exponential function.
Therefore, the type of function that best models the data in the table is a quadratic function. We can try to find a quadratic function of the form y = ax^2 + bx + c that passes through the given points. Using the first three points, we get the system of equations:
a(0)^2 + b(0) + c = 0
a(1)^2 + b(1) + c = 1.5
a(2)^2 + b(2) + c = 6
Solving this system of equations, we get:
a = 3/2
b = 0
c = 0
Therefore, the quadratic function that best models the data is y = (3/2)x^2.
For the following polynomial [tex]f(x) = 2x^3 - 4x^2 - 3x + C[/tex] find a real number [tex]C[/tex], so that the polynomial has the indicated root of [tex]x= -1[/tex]
x = -1 is a root of the polynomial only if C = 3.
How to find the value of C?We want to have x = -1 as a root of the polynomial, then we just need to solve:
f(-1) = 0
this is:
2(-1)³ - 4(-1)² - 3(-1) + C =0
-2 - 4 + 3 + C = 0
-3 + C = 0
C = 3
Tha must be the value of C.
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14. Joey gets paid $ 4.50 per hour for
babysitting. How much will he
make if he babysits for 6 hours?
(Answer: $__:__)
11
Answer:
$27.00
Step-by-step explanation:
6 × $4.50 = $27.00
Answer:27
Step-by-step explanation:
4.50 x 6 = 27
