Need help will give brainliest and 5 stars! :)
The logarithmic function can be written exponentially as follows.[tex]t = 8^y.[/tex]
What is logarithmic function?Exponents and logarithms are inverse operations of one another. We can rewrite an equation in logarithmic form as log_a(b) = x if it has the form axe = b. A number's logarithm is the exponent that must be raised in order to obtain that number. For instance, since 102 = 100, log_10(100) = 2. Similar to this, we can express an equation in exponential form, such as axe = b, if it is in logarithmic form, such as log_a(b) = x. The inverse function of the logarithmic function is the exponential function. As a result, when we apply a logarithm to an exponential expression, the original exponent is returned, and the opposite is true.
The given logarithmic expression is [tex]log_{8}(t) = y.[/tex]
We know that if we have an equation in the form [tex]a^x = b[/tex], we can rewrite it in logarithmic form as [tex]log_a(b) = x[/tex] and vice versa.
Thus, [tex]log_{8}(t) = y[/tex]
[tex]t = 8^y[/tex]
Hence, the logarithmic function can be written exponentially as follows.[tex]t = 8^y.[/tex]
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Morgan uses 14
1
4
of her supply of raisins to make trail mix and 38
3
8
of her supply of raisins to make cookies. If Morgan uses 5 pounds of raisins, how many pounds of raisins are in her supply?
Morgan's supply of raisins is approximately 4.62 pounds.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
Let's start by setting up an equation based on the given information:
14/48 + 38/48 = 5/x
Here, x represents the total supply of raisins in pounds.
To solve for x, we can first combine the fractions on the left-hand side of the equation:
52/48 = 5/x
Next, we can simplify by cross-multiplying:
52x = 48 x 5
52x = 240
Finally, we can solve for x by dividing both sides by 52:
x = 240/52
x ≈ 4.62
Therefore, Morgan's supply of raisins is approximately 4.62 pounds.
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30m3n4-5m4complete factored form of the polynomial
Factor of polynomial m are 0, 6n⁴.
What is polynomial in maths?
A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.
= 30m³n⁴ - 5m⁴
= 5m³(6n⁴ - m )
let 5m³(6n⁴ - m ) = 0
5m³ = 0
m = 0
6n⁴ - m = 0
m = 6n⁴
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Researchers have determined that a hip roof offers the most protection to a
house during a hurricane.
a. The house has a square base with a side length of 50 feet. The house has
a variation of a hip roof in the shape of a regular pyramid with a square
base. The roof extends 1 foot beyond the walls of the house on all sides.
What is the length of each side of the base of the roof?
b. The slant height of the roof is 35 feet. Find the sum of the areas of the
lateral faces of the pyramid.
c. A metal roof covering offers the most protection to a house during a
hurricane. The cost of installing metal roof covering is $350 for every
100 square feet of roof. What is the cost of installing a metal roof
covering on the house?
45 points to first answer (actually)
A) 52 ft
B) 3640 ft²
C) $12,740
a. The house has a square base with a side length of 50 feet, and the roof extends 1 foot beyond the walls on all sides. To find the length of each side of the base of the roof, we need to add 1 foot on each side of the square base.
Length of each side of the base of the roof = 50 ft + 1 ft + 1 ft = 52 ft
b. The slant height of the roof is 35 feet. To find the sum of the areas of the lateral faces of the pyramid, we can use the formula for the lateral area of a pyramid:
Lateral Area = (Perimeter of the base * Slant Height) / 2;
Since the base of the roof is a square, the perimeter is:
Perimeter = 4 * Side Length = 4 * 52 ft = 208 ft;
Now we can find the lateral area:
Lateral Area = (208 ft * 35 ft) / 2 = 3640 ft²;
c. The cost of installing a metal roof covering is $350 for every 100 square feet of roof. To find the cost of installing a metal roof covering on the house, we can use the following formula:
Cost = (Lateral Area / 100) * Cost per 100 square feet;
Cost = (3640 ft² / 100) * $350 = 36.4 * $350 ≈ $12,740;
The cost of installing a metal roof covering on the house is approximately $12,740.
Please show your work
We can solve the given equation using differentiation techniques.
What is differentiation?Differentiation is a method of finding the derivative of a function.Differentiation in mathematics is a function's derivative with respect to an independent variable. Calculus's concept of differentiation can be used to calculate the function per unit change in the independent variable.
[tex]f(x)=2x^{4}-8e^{x}[/tex]
[tex]f'(x)=2 * (4x^{3} )-8e^{x}[/tex]
=[tex]8x^{3} - 8e^{x}[/tex]
substitute x= 5
[tex]f'(5)= 8 * (5)^{3} -8 e^{5} \\ = 1000 - 8 e^{5}[/tex]
and for f''(x) we have to again derivate the f'(x)
[tex]f''(x)=24 x^{2} - 8 e^{x}\\ sub x=5 \\-- > f''(5)=24 * 5^{2} - 8 e^{5}\\ = 600 - 8 e^{5}\\[/tex]
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HELP MEEEEE PLEASEE PLEASE PLEASE
Answer:
2 Batch Of Cakes
Step-by-step explanation:
See:
Recipe Requirements for 1 Batch:
2 cups of Flour
1/2 cup of Butter
3/4 cup of Sugar
She Has:
8 Cups of Flour
2 Cups of Butter
2 Cups of Sugar
1 batch:
Ingredient : Required - Present
Flour : 2 Cups - 8 Cups
Butter : 50% of 1 Cup - 2 Cups
Sugar : 75% of 1 Cup - 2Cups
Left ingredients:
Flour : 6 Cups
Butter : 1.5 Cups
Sugar : 1.25 Cups
2 batch:
Ingredient : Required - Present
Flour : 2 Cups - 6 Cups
Butter : 50% of 1 Cup - 1.5 Cups
Sugar : 75% of 1 Cup - 1.25 Cups
Left ingredients:
Flour : 4 Cups
Butter : 1 Cup
Sugar : 0.5 ( 1/2 ) Cups
3 Batch:
We Cannot Make The 3rd Batch as There is no sufficient Sugar
why is creativity important in construction scientific questions
Answer:Creativity is important in constructing scientific questions because the obvious questions do not always lead to interesting results. Scientists need to be able to think outside the box and come up with new and original questions to investigate.
Step-by-step explanation:
please help!!
Coach Rick wants to know which of his runners - Nelson or Tyrese - is more likely to finish a race in 120 seconds or less.
Nelson's finish times, in seconds, for a random sample of sessions is shown below.
108, 130, 106, 121, 126, 124, 110, 124, 122
Tyrese's finish times, in seconds, for a random sample of sessions is shown below.
117, 119, 118, 120, 136, 118, 118, 120, 123
The difference between Nelson's mean finish time and Tyrese's mean finish time is
___ seconds.
The difference between Nelson's median finish time and Tyrese's median finish time is
____ seconds.
Based on the data, ____
is more likely to finish the race in 120 seconds or less.
Answer:
Step-by-step explanation:
To find the mean/average of each child: Add all their times and divide by the number of times there are.
Nelson=(108+130+106+121+126+124+110+124+122)/9
=119
Tyrese=(117,119,118, 120, 136, 118, 118,120, 123)/9
=121
Nelson-Tyrese = 119-121 = -2
For median list numbers in order and pick middle number
Nelson
106, 108, 110, 121, 122, 124, 124, 126, 130
Nelson median=122
Tyrese
117, 118, 118, 118, 119, 120, 120, 123, 136
Tyrese median =119
Based on the data Tyrese is more likely to finish 120 or less. Most of his times are under that, even though nelson has a better average.
Please answer my stats question
Based on the tabulated level of significance, the correct answer is:
No, the length of life of both types of bulbs is not the same, because 2.29 > 2.08; option C.What is the difference in the means of the lifetime of the two types of bulbs?A two-sample t-test with is used to test whether the difference in means is significant at a 5% level of significance.
The null hypothesis is that there is no difference in the means.
The test statistic for the two-sample t-test is given as:
t = (x₁ - x₂) / (Sp * √(1/n₁ + 1/n₂))where;
x₁ and x₂ are the sample means,Sp is the pooled standard deviation, and n₁ and n₂ are the sample sizes.Substituting the given values:
t = (1245 - 1208) / (√(1346 * (1/12 + 1/11)))
t = 2.29
The calculated t-value (2.29) is greater than the tabulated t-value at a 5% level of significance for 21 degrees of freedom, hence, we reject the null hypothesis and conclude that the means are different.
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3. Each equation represents a function. For each, find the inverse function.
a. c =w+3
b. y=x-2
c. y = 5x
d. w = D/7
Answer:
a. To find the inverse of the function c = w + 3, we can follow the steps below:
Step 1: Replace c with y.
y = w + 3
Step 2: Swap the positions of w and y.
w = y + 3
Step 3: Solve for y.
y = w - 3
Therefore, the inverse function is w = y - 3.
b. To find the inverse of the function y = x - 2, we can follow the steps below:
Step 1: Replace y with f(x).
f(x) = x - 2
Step 2: Swap the positions of x and f(x).
x = f(x) - 2
Step 3: Solve for f(x).
f(x) = x + 2
Therefore, the inverse function is f(x) = x + 2.
c. To find the inverse of the function y = 5x, we can follow the steps below:
Step 1: Replace y with f(x).
f(x) = 5x
Step 2: Swap the positions of x and f(x).
x = 5f(x)
Step 3: Solve for f(x).
f(x) = x/5
Therefore, the inverse function is f(x) = x/5.
d. To find the inverse of the function w = D/7, we can follow the steps below:
Step 1: Replace w with f(D).
f(D) = D/7
Step 2: Swap the positions of D and f(D).
D = f(D)/7
Step 3: Solve for f(D).
f(D) = 7D
Therefore, the inverse function is f(D) = 7D.
I don’t understand can someone help me please!
Answer: y = -|x| - 3
Step-by-step explanation:
It's an absolute value function that has been shifted down 3 and has been reflected
y = -|x| - 3
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Statements which are always true regarding the diagram are
1. m∠5 + m∠6 = 180° ...........Parallel Pair
2. External angle of a triangle is equal to 2+3 = 6.
3. Triangle Sum Property: m2 + m3 + m5 = 180°
Think of ABC as having outside angles.
∠ 1, ∠ 4 , and ∠ 6
Triangle's exterior angle property:
A triangle's exterior angle equals the sum of its internal angles.
Exterior 1 has the following
The exterior angle of a triangle is given by the formula: 1 = 5 + 3.
Similarly,
Exterior 4 consists of
∠ 4 = ∠ 5 + ∠ 2.................Triangle's Exterior Angle
Similarly,
Exterior 6 consists of
The exterior angle of a triangle is given by the formula: 6 = 2 + 3
Property Triangle Sum:
The total of the angles in a triangle equals 180°.
∴ m∠2 + m∠3 + m∠5 = 180° .....Sum Triangle Property
Linear Pair:
The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
∴ m∠5 + m∠6 = 180° ...........Linear Pair
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alec makes 75 percent of his free throws he wants to know the probability that he makes at least 4 equal sections and lets the numbers 1-3 represent making a free throw
The probability that Alex makes at least four free throws in the next six attempts is 9/15 or 0.6.
What is the probability?The probability is determined from the simulation as follows:
Alec spins a spinner with four equal sections and lets the numbers 1-3 represent making a free throw.
The number of spins that result in Alec making at least four free throws in the next six attempts is given below:
232344: Alec makes 3 free throws, not successful.231342: Alec makes 3 free throws, not successful.121123: Alec makes 4 free throws, successful.441432: Alec makes 4 free throws, successful.311221: Alec makes 3 free throws, not successful.343133: Alec makes 4 free throws, successful.341414: Alec makes 4 free throws, successful.412312: Alec makes 4 free throws, successful.141111: Alec makes 3 free throws, not successful.423131: Alec makes 4 free throws, successful.432234: Alec makes 5 free throws, successful.143132: Alec makes 4 free throws, successful.423233: Alec makes 5 free throws, successful.411332: Alec makes 4 free throws, successful.143314: Alec makes 4 free throws, successful.9 out of the 15 spins resulted in Alec making at least four free throws in the next six attempts.
The probability based on the simulation = 9/15 or 0.6
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Complete question:
Alec makes 75% of his free throws. He wants to know the probability that he makes at least four of his next six free throws. Alec runs a simulation. He spins a spinner with four equal sections and lets the numbers 1-3 represent making a free throw. Based on the simulation, what is the probability that Alec makes at least four of his next free throws? Explain.
232344
231342
121123
441432
311221
343133
341414
412312
141111
423131
432234
143132
423233
411332
143314
Assume a > 0, b > 0 and 1 < ax < bx for all x < 0. Which of the following are true?
a. a < b < 1
b. 1 < a < b
c. a < 1 < b
d. b < a < 1
e. b < 1 < a
Explain how you got to the answer.
Answer:
there is somthing wrong of what you ask
because it is impossible to be thet a>0 and b>0 and x<0 and still ax>1 or bx>1
2a. Find the volume of the model of Saturn.
2
Eliza made sphere-shaped
models of the Earth and Saturn
out of playdough for a science
project. The model of Earth has
a diameter of 4.8 cm and the
model of Saturn has a diameter
of 45.6 cm.
The volume of the model of Saturn is approximately 4,845.6 cm³.
Evaluate and simplify the expression
when x = 5 and z = 3.
2x - 3(x-z)
z - 1
=
[?]
Answer:
The value of the given equation is 2.
Step-by-step explanation:
Evaluate and simplify the expression
when x = 5 and z = 3.
[tex]\longrightarrow{\sf{\dfrac{2x - 3(x - z)}{z - 1}}}[/tex]
substituting the given values in the equation :
[tex]\longrightarrow{\sf{\dfrac{2x - 3(x - z)}{z - 1}}}[/tex]
[tex]\longrightarrow{\sf{\dfrac{2 \times 5 - 3(5 - 3)}{3 - 1}}}[/tex]
[tex]\longrightarrow{\sf{\dfrac{10 - 3(5 - 3)}{3 - 1}}}[/tex]
[tex]\longrightarrow{\sf{\dfrac{7(2)}{2}}}[/tex]
[tex]\longrightarrow{\sf{\dfrac{7 \times 2}{2}}}[/tex]
[tex]\longrightarrow{\sf{\dfrac{7 \times \cancel{2}}{\cancel{2}}}}[/tex]
[tex]\longrightarrow{\sf{\underline{\underline{2}}}}[/tex]
Hence, the value of the given equation is 2.
————————————————please help me find this which one
Answer:
A
Step-by-step explanation:
Self explanatory
Answer: b
Step-by-step explanation: i just did this one on a algebra 1b assignment lol
The diagram shows a triangle.
31° / 6x / x+16°
What is the value of x?
Step-by-step explanation:
31 + 6x + x + 16 = 180
7x + 47 = 180
7x = 180 - 47
x = 133/7
x = 19
1. If K(-9,2) lies on the perpendicular bisector of
JL and J is located at (-5.-8), which point could
represent the location of L?
A. (1.-2)
B. (-1,-12)
C. (-3,-2)
D. (-3,-12)
Answer:
To find the location of point L, we need to use the fact that point K lies on the perpendicular bisector of segment JL.
The perpendicular bisector of a segment is a line that passes through the midpoint of the segment and is perpendicular to the segment.
First, we can find the midpoint of segment JL:
Midpoint of JL = ((-5 + x)/2, (-8 + y)/2)
where (x, y) is the location of point L.
Since point K lies on the perpendicular bisector of JL, the line passing through K and the midpoint of JL will be perpendicular to JL.
The slope of the line passing through K and the midpoint of JL is:
m = (2 - (-8))/(-9 - (-5 + x)/2) = 10/(-9 - (5 - x)/2) = -4/(x - 7)
where we have used the fact that the line passing through K and the midpoint of JL is perpendicular to JL, so its slope is the negative reciprocal of the slope of JL.
Now, we can use the fact that the line passing through K and the midpoint of JL contains point K(-9, 2) to write the equation of the line:
y - 2 = m(x + 9)
Substituting the expression we found for m, we get:
y - 2 = (-4/(x - 7))(x + 9)
Simplifying this equation, we get:
y = -4x/ (x - 7) - 2
Now, we can substitute the x-coordinates of the answer choices to see which one gives us a valid y-coordinate:
A. (1, -2): y = -4(1)/(-6) - 2 = -1 --> Incorrect
B. (-1, -12): y = -4(-1)/(-8) - 2 = 1/2 --> Incorrect
C. (-3, -2): y = -4(-3)/(-10) - 2 = 6/5 --> Incorrect
D. (-3, -12): y = -4(-3)/(-10 - 4) - 2 = -26/7 --> Correct
Therefore, the location of point L is (-3, -12), which is answer choice D.
Carl swam 7/12 of a mile. Olivia swam ⅝ of a mile. Who swam farther?
Olivia swam farther. This is because 5/8 of a mile is greater than 7/12
How the calculate who swam faster among Carl and Olivia ?Carl swam 7/12 of a mile
Olivia swam 5/8 of a mile
= 7/12
= 0.58
= 5/8
= 0.625
From the calculation above, 5/8 is greater than 7/12
Hence Olivia swam faster than Carl because 5/8 of a mile is greater than 7/12 of a mile
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Given the circle below secant kjI and tangent hi find the length of hi round to the nearest tenth if necessary.
The length of the segment HI is 32.9
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate to the some trigonometric functions of an angle in a right-angled triangle.
We know that the equation or formula of secant-tangent;
HI² = KI × JI
Given values:
KI = KJ + JI
KI = 21 + 24 = 45
JI = 24
put the all values in the secant-tangent equation above,
HI² = 45 × 24
HI² = 1080
Take the square root of both sides
HI = 32.9
Hence, the length of the segment HI is 32.9
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Question figure-
Brent is designing a poster that has an area of 1 square foot. He is going to paste a photo collage on a section of the poster that is 1/3 foot wide and 3/5 foot long. What part of a square foot will the photo collage cover?
Show your work.
The part of the foot will the photo collage cover is 1/5 square foot
How to determine the photo collage cover?Recall that an area of a lawn is an area of soil-covered land planted with grasses and other durable plants such as clover which are maintained at a short height with a lawnmower (or sometimes grazing animals) and used for aesthetic and/or recreational purposes
The given parameters are
Area of the Poster =1 sq.ft.
The collage will cover a part of the poster that is
1/5ft wide and 3/5ft long
Area of the Photo Collage Section
=Length X Width
= 1/3 * 3/5
= 3/15 ft = 1/5foot
In conclusion, the photo cover will cover 1/5 of a square foot
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Write (x - 3)(x + 6) in vertex form (y = (x - h)2 + k). Hint: Expand then complete the square.
(x - 3)(x + 6) can be written in vertex form as y = (x - (-3/2))² - 20.25
What is the vertex form?
The vertex form of a quadratic function is a way of writing a quadratic function in form f(x) = a(x - h)² + k where (h, k) is the vertex of the parabola, a is a coefficient that determines the shape and direction of the parabola, and x is the input variable.
Expanding (x - 3)(x + 6), we get:
x² + 6x - 3x - 18 = x² + 3x - 18
To write this expression in vertex form, we need to complete the square. To do this, we add and subtract (3/2)² = 2.25 inside the parentheses:
x² + 3x - 18 + 2.25 - 2.25 = (x² + 3x + 2.25) - 20.25
Now, we can write the expression in vertex form:
y = (x - (-3/2))² - 20.25
Therefore, (x - 3)(x + 6) can be written in vertex form as:
y = (x - (-3/2))² - 20.25
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You have also decided to put a pool in your backyard, and the builder has shown you the blue print below that shows the pool from above.
Thus, the missing side lengths are :x = 9 feet: y = 6 feet:
Explain about the blue print:A blueprint is a collection of two-dimensional drawings that shows exactly how an architect intends a project to look. Typically, a building's dimensions, materials, and precise location of every component are described in the blueprints.
Given that-
The blue print for the pool of the backyard is prepared which is shown in given diagram.
The given figure consists of the different length measured in feet.To find the each of the missing values subtract the common length from the total length.A figure's longest side is its length, its shortest side is its width, and its highest point is its height.
For the given dimensions in the diagram:
x = 11 + 3 - 5 = 9 ft
y = 8 + 4 - 6 = 6 ft
Thus, the missing side lengths are :x = 9 feet: y = 6 feet:
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Complete question:
You have also decided to put a pool in your backyard, and the builder has shown you the blue print below that shows the pool from above.
Determine the missing side lengths:x = __ feet: y = ___feet:
Diagram for the question is attached.
QUICK I’LL MARK YOU BRAINLIEST!! PLEASE HELP ME SOLVE THIS EXAMPLE!
Answer:
Step-by-step explanation
multiply every term by the least common denominator to remove fractions
A normally distributed data set has a mean of 0 and a standard deviation of 0.5. Which is closest to the percent of values between –1 and 1?
34%
50%
68%
95%
As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
For a normally distributed data set with a mean of 0 and a standard deviation of 0.5, the proportion of values between -1 and 1 is most closely related to 68%.
Approximately 68% of the data in a normal distribution lies within one standard deviation of the mean, which explains why. One standard deviation below the mean is -0.5, and one standard deviation above the mean is 0.5 since the mean is 0 and the standard deviation is 0.5. As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.
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Given m \| nm∥n, find the value of x.
Answer:
x = 15
Step-by-step explanation:
Given m||n, the angles indicated with (6x+20) and (8x-10) are alternate angles and their measures are equal.
So, to find the value of x, we can write the following equation:
8x - 10 = 6x + 20
Transfer like terms to the same side of the equation.8x - 6x = 20 + 10
Add/subtract terms.2x = 30
Divide both sides with 2.x = 15
The 9th grade students are taking a field trip. There are 380 ninth graders and a bus can seat up to 60 students. Write a piecewise function to represent the number of buses
needed, y, if x students attend the field trip.
Hence, the piece-wise function to represent the number of buses required to transport 380, 9th graders is :
f(x) = { 1, if 0 < 380 ≤60x
2, if 60x < 380≤120x
3, if 120x < 380≤180x
4, if 180x < 380 ≤ 240x
5, if 240x < 380≤300x
6, if 300x < 380 ≤ 360x
7, if 360x < 380 }
What is the piece-wise function?
In mathematics, a piece-wise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piece-wise definition is actually a way of expressing the function, rather than a characteristic of the function itself.
How do you compute the piece-wise function?Let 'x' be the number of buses required to transport all the 9th graders. We can write the function in two parts, for 1st part when the number of students is less than or equal to 60 ( that is the capacity of one bus) and for 2nd part when it is greater than 60.
For x buses, each with a capacity of 60, we have:
If 0 < 380 ≤ 60 x, then x = 1 bus is needed to transport all students.If 60 x < 380 ≤ 120 x, then x = 2 buses are needed to transport all students.If 120 x < 380≤ 180 x, then x = 3 buses are needed to transport all students.If 180 x < 380≤240 x, then x = 4 buses are needed to transport all students.If 240 x < 380≤300 x, then x = 5 buses are needed to transport all students.If 300 x < 380 ≤ 360 x, then x = 6 buses are needed to transport all students.If 360 x < 380, then x = 7 buses are needed to transport all students.Therefore, the piece-wise function to represent the number of buses required to transport 380, 9th graders is :
f(x) = { 1, if 0 < 380 ≤60x
2, if 60x < 380≤120x
3, if 120x < 380≤180x
4, if 180x < 380 ≤ 240x
5, if 240x < 380≤300x
6, if 300x < 380 ≤ 360x
7, if 360x < 380 }
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What is the effective annual rate of an account that pays interest at the nominal rate of
7% per year, compounded daily? Compounded hourly?
Answer:
To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:
EAR = (1 + r/n)^n - 1
where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.
For daily compounding, n = 365 (since there are 365 days in a year), so we have:
EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%
To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:
EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%
Therefore, the effective annual rate for hourly compounding is approximately 7.27%.
Translate the given statement into a linear equation in the form
ax + by = c using the indicated variable names. Do not try to solve the resulting equation.
The number of new clients (x) is 149% of the number of old clients (y).
On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y
what is a sequence?A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.
The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:
x = 1.49y
-1.49y + x = 0
-149y + 100x = 0
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The linear equation in the required form is: x - 1.49y = 0
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b
Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."
Using this information, we can write:
x = 1.49y
To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.
Subtracting 1.49y from both sides, we get:
x - 1.49y = 0
So the linear equation in the required form is:
x - 1.49y = 0
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