This means that c must be 1/2, since it is the only value in the interval (0,2) where f'(c) = -1/2, which satisfies the equation given by the Mean Value Theorem.
To apply the Mean Value Theorem, we need to check if f(x) is continuous on [0,2] and differentiable on (0,2).
[tex]f(x) = x^3 - 2x^2[/tex] is a polynomial function, so it is continuous and differentiable everywhere.
Now, we can use the Mean Value Theorem, which states that there exists a number c in (0,2) such that:
[tex]f'(c) = (f(2) - f(0))/(2-0)[/tex]
First, let's find f'(x):
[tex]f'(x) = 3x^2 - 4x[/tex]
Now, we can solve for c:
f'(c) = 3c^2 - 4c
f(2) = 2^3 - 2(2^2) = -4
f(0) = 0^3 - 2(0^2) = 0
(f(2) - f(0))/(2-0) = -4/2 = -2
So, we need to solve the equation 3c^2 - 4c = -2 for c.
Rearranging, we get:
3c^2 - 4c + 2 = 0
Using the quadratic formula, we get:
c = (4 ± sqrt(16 - 24))/6
c = (4 ± 2i)/6
Since the interval is [0,2], we only need to consider real solutions.
[tex]f'(c) = 3c^2 - 4c\\f(2) = 2^3 - 2(2^2) = -4\\f(0) = 0^3 - 2(0^2) = 0\\(f(2) - f(0))/(2-0) = -4/2 = -2\\[/tex]
Therefore, c = 4/3 is not a valid solution.
To choose between the remaining options, we can test if f'(c) is positive or negative.
For c = 0, f'(0) = 0 - 0 = 0.
For [tex]c = 1/2, f'(1/2) = 3(1/2)^2 - 4(1/2) = -1/2.[/tex]
For[tex]c = 1, f'(1) = 3(1)^2 - 4(1) = -1.[/tex]
Therefore, f'(c) is negative on the interval [0,1/2] and positive on the interval [1/2,2].
This means that c must be 1/2, since it is the only value in the interval (0,2) where f'(c) = -1/2, which satisfies the equation given by the Mean Value Theorem.
Therefore, the answer is (b) 1/2.
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help what do i put in the box
The value of x, obtained using the property of bisected angles is 10
What are bisected angles?Bisected angles are angles that are split by a line segment in two to create two angles of the same measure.
The specified information indicates;
[tex]\overrightarrow{GI}[/tex] bisects ∠DGH
m∠DGI = x - 3
m∠IGH = 2·x - 13
The angle addition postulate indicates that we get;
m∠DGH = m∠DGI + m∠IGH
The definition of the bisected angle ∠DGH indicates that we get;
∠DGI = ∠IGH
Therefore;
x - 3 = 2·x - 13
2·x - 13 = x - 3
2·x - x = 13 - 3 = 10
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If a student pulls out a jellybean without looking what is the probability that the jellybean will be yellow? 5/11 probability practice
Read this excerpt from "A Visit from the Goon Squad."
Whatever the reason, a swell of approval palpable as rain lifted from the center of the crowd and rolled out toward its edges, where it crashed against buildings and water wall and rolled back at Scotty with redoubled force, lifting him off his stool, onto his feet (the roadies quickly adjusting the microphones), exploding the quavering husk Scotty had appeared to be just moments before and unleashing something strong, charismatic, and fierce. Anyone who was there that day will tell you the concert really started when Scotty stood up.
How does the author portray Scotty in this excerpt?
His confidence is transformed by the crowd’s response.
His musical ability is improving as he performs.
His anger is unleashed by the chaos of the crowd.
His excitement is shown by his moves on stage.
Answer:
His confidence is transformed by the crowd’s response.
Step-by-step explanation:
Scotty is described as being a "quavering husk...just moments before." This shows his lack of confidence and anxiety about being on stage.
the volume of a cylinder is 282.6. the radius measures 3 yards. what is the height of the cylinder rounded to the nearest yard. use pi
Need help completing this
Answer:
a) What is her GROSS pay for a week? 1,400
b) What is her GROSS pay for a year? 67,200
c) What are her TOTAL DEDUCTIONS for a week? 351.39
d) What is her NET pay for a week? 1,048.61
e) What is her NET pay for a year? 50,333.28
f) What does she pay in Income Tax per YEAR? 13,535.52
g) What does she pay in CPP contributions per YEAR? 2,537.28
h) What does she pay in El contributions per YEAR? 793.92
i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%
Step-by-step explanation:
GROSS
without tax or other contributions having been deductedNET
Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.There are 4 weeks in a month, 52 weeks in a year.
a) What is her GROSS pay for a week? 1,400
The amount of money she makes per hour × the amount of hours she works per week35 × 401,400b) What is her GROSS pay for a year? 67,200
The amount of money she earns in a month × 12(The amount of money she makes per week × 4) × 12(1,400 × 4) × 125600 × 1267,200c) What are her TOTAL DEDUCTIONS for a week? 351.39
Income Tax + CPP + El281.99 + 52.86 + 16.54334.85 + 16.54351.39d) What is her NET pay for a week? 1,048.61
Her gross pay for a week - Her total deductions for a week1,400 - 351.391,048.61e) What is her NET pay for a year? 50,333.28
Her gross pay for a year - Her total deductions for a yearHer gross pay for a year - ([Her total deductions for a week × 4] × 12)Her gross pay for a year - ([351.39 × 4] × 12)67,200 - ([351.39 × 4] × 12)67,200 - (1,405.56 × 12)67,200 - 16,866.7250,333.28f) What does she pay in Income Tax per YEAR? 13,535.52
Income tax per month × 12(Income tax per week × 4) × 12(281.99 × 4) × 121,127.96 × 1213,535.52g) What does she pay in CPP contributions per YEAR? 2,537.28
CPP per month × 12(CPP per week × 4) × 12(52.86 × 4) × 12211.44 × 122,537.28h) What does she pay in El contributions per YEAR? 793.92
El per month × 12(El per week × 4) × 12(16.54 × 4) × 1266.16 × 12793.92i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%
(Her yearly Income Tax ÷ Her yearly Gross Pay) × 100(13,535.52 ÷ 67,200) × 1000.20142... × 10020.142...% or 20.14%How could you mathematically prove that the elevation on ramp B is steeper than ramp A? (without using logic)
Elevation on ramp B is more steep than ramp A.
What is elevation?"Elevation" typically refers to the height of a location above sea level. It is often used in geography and topography to describe the height of a mountain or the altitude of a city or other location. Elevation is usually measured in feet or meters, and it can have a significant impact on climate, weather patterns, and other environmental factors.
What is steep?"Steep" can have a few different meanings depending on the context. It can refer to a steep slope or incline, such as a steep hill or mountain. It can also mean a high price or cost, as in "the price is too steep for me." Additionally, "steep" can refer to the act of soaking something in hot water in order to extract flavor, as in steeping a tea bag in hot water.
For RampA:
tanα=36/30
tanα=1.2
For Ramp B:
tanβ=36/20
tanβ=1.8
Therefore for Ramp B angle is more than Ramp A and incase of tangent function value of angle increases with the angle measures.
So β>α.
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assume that you and a friend both enter a race with three prizes (first, second, and third place). you have a 30% chance of winning one of the prizes. your friend has a 20% chance of winning one of the prizes. however, if you win a prize, then your friend has less chance of also winning a prize. your friend has only a 10% chance of winning one of the prizes, given that you win one of the prizes. what is the probability that both you and your friend will win a prize in this contest? group of answer choices
Your friend has only a 10% chance of winning one of the prizes, given that you win one of the prizes. Then the probability that both you and your companion will win a prize in this challenge is 3%.
Let's begin by calculating the likelihood of you winning a prize, which is given as 30% or 0.3. The likelihood of your companion winning a prize is given as 20% or 0.2. In the event that you win a prize, at that point, the likelihood of your companion winning a prize diminishes to 10% or 0.1. Ready to speak to this conditional likelihood as P.
Presently, ready to utilize the equation for conditional likelihood to discover the likelihood of both you and your companion winning a prize.
P(You and Companion both win a prize)
= P(You win a prize) x P(Friend wins a prize|You win a prize)
= 0.3 x 0.1
= 0.03 or 3%.
thus, the likelihood that both you and your companion will win a prize in this challenge is 3%.
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What is the product of 3x – 4 and 5x^2–2x+6. Write your answer in standard form.
Part a: SHOW WORK
Part b: Is the product of 3x – 4 and 5x^2–2x+6 equal to the product of 4 – 3x and 5x^2 – 2x + 6? EXPLAIN.
50 points, please show work. Thanks.
How do you find the hypotenuse of a 45-45-90 triangle if you know the length of the legs?
The length of the hypotenuse of a 45-45-90 triangle is √2x units.
To find the hypotenuse of a 45-45-90 triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).
Let's denote the length of each leg of the triangle as "x". Since the triangle is isosceles, both legs are of equal length. Therefore, we can write:
Leg 1 = Leg 2 = x
To find the length of the hypotenuse (which we'll call "h"), we can use the Pythagorean theorem as follows:
x² + x² = h²
Simplifying this equation, we get:
2x² = h²
To solve for h, we need to take the square root of both sides of the equation:
√(2x²) = √(h²)
√2 * x = h
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Pls answer step by step if possible
From the similar triangle, y=8.7, and x=4
Solving the similar triangleFrom the similar triangle,
First lets find the angle both triangles share
to determine the value , solving on the bigger triangle,
cosθ= adjacent/hypothenus
cosθ= 5/10
cosθ= 0.5
θ= 60
Therefore, to obtain y,
sin 60= y/10
y=10 sin 60
y=8.7
from the smaller triangle,
to determine x
cos 60=2/x
x cos 60=2
x=2/cos60
x= 4.
Therefore, y=8.7, and x=4.
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According to the U. S. Bureau of the Census, in 2000 there were 35. 3 million residents of Hispanic origin living in the United States. By 2010, the number had increased to 50. 5 million. The exponential growth function A = 35. 3ekt describes the U. S. Hispanic population, A, in millions, t years after 2000. A. Find k, correct to three decimals places. B. Use the resulting model to project the Hispanic resident in population in 2015. C. In which year will the Hispanic resident population reach 70 million?
The value of k is approximately 0.034. The projected Hispanic resident population in 2015 is approximately 73.9 million. The Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.
To find k, we can use the fact that A = 35.3 million when t = 0 (i.e., in 2000), and A = 50.5 million when t = 10 (i.e., in 2010). Substituting these values into the exponential growth function, we get
35.3 = 35.3e^0k
50.5 = 35.3e^(10k)
Dividing the second equation by the first equation, we get
50.5/35.3 = e^(10k)
Taking the natural logarithm of both sides, we get
ln(50.5/35.3) = 10k
Solving for k, we get
k ≈ 0.034
Therefore, the exponential growth function is A = 35.3e^(0.034t).
To project the Hispanic resident population in 2015, we need to find A when t = 15 (i.e., 15 years after 2000). Substituting t = 15 into the exponential growth function, we get
A = 35.3e^(0.034*15) ≈ 73.9 million
Therefore, the projected Hispanic resident population in 2015 is approximately 73.9 million.
To find the year in which the Hispanic resident population reaches 70 million, we need to solve the exponential growth function for t when A = 70. Substituting A = 70 into the exponential growth function, we get
70 = 35.3e^(0.034t)
Dividing both sides by 35.3, we get
e^(0.034t) = 70/35.3
Taking the natural logarithm of both sides, we get
0.034t = ln(70/35.3)
Solving for t, we get
t ≈ 24.7
Therefore, the Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.
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Find the value of x and y 45 5
answer is : x 25. y = 20 both y's will cancel . 2x =50.=x=25
2.
(05.02 MC)
Given ΔABC, what is the measure of b? (2 points)
Triangle ABC with angle A measuring 54 degrees and angle C measuring 59 degrees and side BC measuring 11
b = 9.668
b = 11.655
b = 12.516
b = 16.841
The measure of side ‘b’ in the given triangle ABC, with angle A measuring 54 degrees and angle C measuring 59 degrees and side BC measuring 11 is option-c:12.516, which is found using Sine-law.
What is Sine-law?In a scalene or oblique triangle (a non-right triangle), the law of sine describes the relationship between the sides and angles. Trigonometric laws such as the law of sines and law of cosines are crucial when "solving a triangle" by calculating the unknown angles or sides. The ratio of a triangle's side lengths to the sine of each of its opposite angles must be equal in order for the sine rule to apply. Triangle side length ratios to their corresponding opposite angles are connected by the law of sines. All three sides and the diagonal angles maintain the same ratio.
Given that ∠A= 54° ,∠C= 59° & side BC=a=11
We know that ∠A + ∠B + ∠C = 180° {angle sum property}
Consider △ABC,
54° + 59° + ∠B = 180°
113° + ∠B = 180°
∠B = 180°- 113°
∠B = 67°
Applying Sine-Law,
[tex]\frac{A}{sin\ A} =\frac{B}{sin\ B} = \frac{C}{sin\ C}[/tex]
By using,
[tex]\frac{A}{sin\ A} =\frac{B}{sin\ B}[/tex] , we get:
[tex]\frac{11}{sin\ 54} =\frac{B}{sin\ 67}\\ \\\frac{11}{0.80901} =\frac{B}{0.92050} \\\\B=\frac{11}{0.80901} \times 0.92050[/tex]
B = 13.59686 x 0.92050
B = 12.5159
B = 12.516
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Refer to the attachment for the complete question.
Find the equation that represents the proportional relationship in this graph, for y in terms of x.
Answer:
y = [tex]\frac{1}{3}[/tex]x
Step-by-step explanation:
As y increases by 1, x increases by 3.
Helping in the name of Jesus.
To determine the sample size needed to estimate a parameter, you must know the margin of error. (True or False)
The margin of error is an important factor in determining the sample size needed to estimate a parameter, it is not the only factor - False.
Other factors that need to be considered include the level of confidence desired, the variability of the population being sampled, and the size of the population.
The margin of error is the amount of error that is acceptable in the estimate of the parameter. The smaller the margin of error desired, the larger the sample size needed.
A higher level of confidence requires a larger sample size, as there is less room for error in the estimate. The variability of the population being sampled also plays a role in determining the sample size needed.
Finally, the size of the population being sampled also affects the sample size needed.
A smaller population requires a smaller sample size, while a larger population requires a larger sample size to ensure a representative sample.
In summary, while the margin of error is an important factor in determining the sample size needed to estimate a parameter, it is not the only factor.
Other factors that need to be considered include the level of confidence desired, the variability of the population being sampled, and the size of the population.
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Select the correct answer.
Henry's bread recipe calls for 3 cups of flour, with a variation of up to 4 tablespoons depending on the humidity level. There are 16 tablespoons
in 1 cup. Which inequality could be used to find the number of tablespoons of flour actually used in a recipe?
A.
|t+4|<=48
B.
|t+48|<=4
C.
|t-4|>=48
D.
|t-48|<=54
The inequality to find the number of tablespoons of flour actually used in a recipe is |t - 48| <= 4. The correct answer is D.
Since the recipe calls for 3 cups of flour with a variation of up to 4 tablespoons, the total amount of flour used can vary between 3 cups - 4 tablespoons and 3 cups + 4 tablespoons. Converting tablespoons to cups, this becomes 3 cups - 1/4 cup and 3 cups + 1/4 cup.
Thus, the range of cups of flour used is [3 - 1/4, 3 + 1/4], which is [2.75, 3.25]. Multiplying by 16 to convert back to tablespoons, we get the range [44, 52].
So, the inequality that could be used to find the number of tablespoons of flour actually used in the recipe is
|t - 48| <= 4
where t is the number of tablespoons of flour used. So, the correct option is D).
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There are 56 people at the party. Only 14
of them are wearing red. What percent of
people are NOT wearing red?
Answer: 75%
have a good day/night and crush that homework/class!! you are loved
brainliest??
Answer: 75%
Step-by-step explanation: 56 - 14 = 42. So, 42 people are not wearing red. 42/56 is .75, which is the decimal form for 75%. Also, if you simplify 42/56, you get 3/4 which is also 75%
Find the determinant by row reduction to echelon form. 1 5-6 1 6 5 2 8 7 Use row operations to reduce the matrix to echelon form. 1 5 -615-6 1 6 5 0 1 11 2 8 70 0-27 Find the determinant of the given matrix. 1 5 -6 16 5 -27
The determinant of the given matrix is -27
To find the determinant of the given matrix by row reduction to echelon form, follow these steps:
1. Write down the given matrix:
```
| 1 5 -6 |
| 1 6 5 |
| 2 8 7 |
```
2. Use row operations to reduce the matrix to echelon form. First, eliminate the elements below the pivot element (1) in the first column:
```
R2 = R2 - R1
R3 = R3 - 2 * R1
```
Resulting matrix:
```
| 1 5 -6 |
| 0 1 11 |
| 0 -2 -19 |
```
3. Next, eliminate the elements below the pivot element (1) in the second column:
```
R3 = R3 + 2 * R2
```
Resulting matrix:
```
| 1 5 -6 |
| 0 1 11 |
| 0 0 -27 |
```
4. The matrix is now in echelon form:
```
| 1 5 -6 |
| 0 1 11 |
| 0 0 -27 |
```
5. Find the determinant of the echelon form matrix by multiplying the diagonal elements (pivot elements):
```
Determinant = 1 * 1 * -27 = -27
```
Your answer: The determinant of the given matrix is -27.
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Graph the data set. {(0, 0), (−1, −3), (−2, −6), (−3, −9), (−4, −12)} Which kind of model best describes the data?
Answer:
linear
Step-by-step explanation:
i js took the test
The kind of model that best describes the data is a linear relation
Calculating the kind of model best describes the data?From the question, we have the following parameters that can be used in our computation:
{(0, 0), (−1, −3), (−2, −6), (−3, −9), (−4, −12)}
In the above dataset, we can see that
As x increases by -1The values of y increases by -3Using the above as a guide, we have the following:
The relation has a constant rate of -3/-1
Evaluate
The relation has a constant rate of 3
Only linear relations have constant rates
Hence, the kind of model that best describes the data is a linear relation
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How can i do parallelogram shown below has an area of
15
1515 units
2
2
The height of given parallelogram is 5 units.
Given that, the parallelogram shown below has an area of 15 units.
The base is 3 units.
We know that, the area of a parallelogram is Area = Base × Height
Here, Area = 3×Height
15 = 3×Height
Height = 15/3
Height = 5 units
Therefore, the height of given parallelogram is 5 units.
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"Your question is incomplete, probably the complete question/missing part is:"
The parallelogram shown below has an area of 15 units. Find the missing height.
Look at this rectangle:
4 cm
2 cm
If both dimensions are doubled, then which of the following statements about its perimeter
will be true?
The new perimeter will be 2 times the old perimeter.
The new perimeter will be of the old perimeter.
2
The new perimeter will be 3 times the old perimeter.
Submit
The new perimeter will be 4 times the old perimeter.
Answer:
The new perimeter will be 2 times the old perimeter.
Step-by-step explanation:
Both dimensions are doubled doubled: times 2 or x2 or *2
4*2=8
2*2=4
if both measures are doubled, then the result will be doubled too.
Solve for length of segment a.
a
3 cm
4 cm
6 cm
a = [?] cm
If two segments intersect inside
or outside a circle: ab = cd
Enter
The length of segment a in the given chords is determined as 2.
What is the length of segment a?The measure of length a is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, we will have the following equation.
a x 6 = 3 x 4
6a = 12
divide both sides of the equation by 6;
6a/6 = 12/6
a = 2
Thus, the value of a in the given chords is determined by applying chord theorem.
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What would be the appropriate hypotheses for a research company who wants to see if there is a difference in the amount of vitamin D in a brand name multi-vitamin and generic brand multivitamin
The research company can then conduct an appropriate statistical test, such as a t-test or an ANOVA, to analyze the data and determine whether to accept or reject the null hypothesis. If the null hypothesis is rejected, it would imply that there is a significant difference in the amount of vitamin D between the two types of multi-vitamins.
To examine if there is a difference in the amount of vitamin D in a brand name multi-vitamin and generic brand multi-vitamin, the appropriate hypotheses for the research company would be as follows:
Null Hypothesis (H0): There is no significant difference in the amount of vitamin D in the brand name multi-vitamin and the generic brand multi-vitamin. In other words, the mean amount of vitamin D in both types of multi-vitamins is equal.
Alternative Hypothesis (H1): There is a significant difference in the amount of vitamin D in the brand name multi-vitamin and the generic brand multi-vitamin. This means that the mean amount of vitamin D in one type of multi-vitamin is not equal to the other.
The research company can then conduct an appropriate statistical test, such as a t-test or an ANOVA, to analyze the data and determine whether to accept or reject the null hypothesis. If the null hypothesis is rejected, it would imply that there is a significant difference in the amount of vitamin D between the two types of multi-vitamins.
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Do you want to use a Square section of your yard for a garden. Do you have a most 52 feet of fencing to surround the garden. Right and solve inequality to represent the possible length of each side of the garden
The possible lengths of each side of the garden is given by the inequality relation 0 ≤ x ≤ 12
Given data ,
Let's assume that the square garden has sides of length x.
To surround the garden, we will need fencing of length equal to the perimeter of the square, which is 4x
The total amount of fencing is at most 52 feet
So , the inequality is
4x ≤ 52
Dividing both sides by 4, we get:
x ≤ 13
Therefore, the possible length of each side of the garden is less than or equal to 13 feet
And , each side of garden should be more than 0 , so
x > 0
Hence , the full inequality representing the possible length of each side of the garden would be 0 < x ≤ 13
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A scale model of a tower is 24 inches. The scale is 1.5 in. : 10 ft. What is the actual height, in feet, of the tower?
The actual height of the tower is 160 feet.
Given that, a scale model of a tower is 24 inches.
The scale is 1.5 inches:10 feet.
We know that, 1 foot = 12 inches
So, the scale 1.5 inches : 120 inches.
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
1.5/120 = 24/The actual height of the tower
1.5×The actual height of the tower = 24×120
The actual height of the tower=2880/1.5
= 1920 inches
In feet = 1920/12
= 160 feet
Therefore, the actual height of the tower is 160 feet.
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Which is more, 7 yards or 19 feet?
According to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.
What is multiplication?Multiplication is an arithmetic operation that involves combining two or more numbers to get a product. It is a way of repeatedly adding a number to itself a certain number of times. The number being multiplied is called the multiplicand, while the number of times it is being multiplied is called the multiplier. The result of the multiplication operation is called the product.
According to the given information:To compare 7 yards and 19 feet, we need to convert them to the same unit. Since 1 yard is equal to 3 feet, we can convert yards to feet by multiplying by 3, and we can convert feet to yards by dividing by 3.
In the first answer, we converted 7 yards to feet by multiplying by 3, which gave us 21 feet. Then we compared 21 feet to 19 feet, and found that 21 feet is greater than 19 feet. Therefore, we concluded that 7 yards is more than 19 feet.
In the second answer, we converted 19 feet to yards by dividing by 3, which gave us approximately 6.33 yards (rounded to two decimal places). Then we compared 7 yards to 6.33 yards, and found that 7 yards is greater than 6.33 yards. Therefore, we concluded that 7 yards is more than 19 feet.
Therefore, according to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.
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For Exercises 16-18, use the following information. Brian invests $200 in an
account that pays 5% annual interest compounded continuously.
16. Write a function that models the amount y in the account after x years.
17. Write the domain and range using inequalities. Explain their meaning in this context.
18. How much will Brian have in the account after 8 years?
1. The function that models the amount in the account after x years is [tex]y(x) = 200e^{0.05t}[/tex]
2. The domain is [tex]x > = 0[/tex]. The range is [tex]y > = 200[/tex]
3. After 8 years, Brian will have $298.37 in the account.
How much money will Brian have after x years?Function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The formula for continuous compounding is [tex]A = Pe^{rt}[/tex] where the A is the amount, P is the principal, e is Euler's number, r is the annual interest rate and t is the time in years.
Data:
A = ?
P = 200
t = ?
r = 5% = 0.05
Plugging in the values, we get: [tex]A = 200e^{0.05t}[/tex]which is the function.
2. The domain of the function is x >= 0 which means the number of years must be non-negative.
The range of the function is y >= 200 since the amount in the account cannot be negative and it starts with an initial investment of $200.
3. To get amount in the account after 8 years, we will plug in x = 8 into the formula:
[tex]y = 200 * e^{0.05*8}\\y = 200 * 1.49182469764\\y = 298.364939528\\ y = $298.37.[/tex]
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How do you calculate the distance traveled by an object by first calculating when it is stopped?
To calculate the distance traveled by an object by first calculating when it is stopped, you need to follow these steps:
1. Identify the terms
2. Use the given information
3. Determine when the object is stopped
4. Calculate the distance traveled
Identify the terms:
For this question, we are focusing on distance, velocity, time, and acceleration. The object is stopped when its velocity is zero.
Use the given information:
Collect any given values such as initial velocity, final velocity, time, and acceleration.
Determine when the object is stopped:
To find out when the object is stopped, you'll need to use the equation v = u + at, where v is final velocity (0 m/s when stopped), u is initial velocity, a is acceleration, and t is time.
Solve for t (time) when the object is stopped: t = (v - u) / a.
Calculate the distance traveled:
Now that you have the time when the object is stopped, use one of the equations of motion to find the distance traveled.
We can use the equation s = ut + 0.5at²,
where s is the distance, u is initial velocity, t is the time when the object is stopped, and a is acceleration.
By following these steps and using the provided terms, you'll be able to calculate the distance traveled by an object by first calculating when it is stopped.
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If a sphere has a volume of 36π cubic inches, what is its radius?
radius = ___ inches
The radius of the sphere is approximately 3.634 inches.
We have,
The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume of the sphere and r is its radius.
We know that the volume of the sphere is 36π cubic inches.
Substituting this value into the formula, we get:
36π = (4/3)πr³
Multiplying both sides by 3/4π, we get:
r³ = (36π)/(3/4π) = 48
Taking the cube root of both sides.
r = (48)^(1/3)
r = 3.634 inches (rounded to three decimal places)
Therefore,
The radius of the sphere is approximately 3.634 inches.
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Calvin has a gift card which he is using to buy candy (x), and he has been tracking how much money (y) he spends. He noted that after buying 4 pieces of candy (in all) he has $28.00 left on his card and then after buying 10 pieces of candy (in all) he has $25.00 left on his card. Write the equation of the line that represents his spending on candy
Answer:
To write the equation of the line that represents Calvin’s spending on candy, we need to first find the slope and the y-intercept of the line.
We can use the two points given in the problem: (4, 28) and (10, 25)
Slope (m) = (y2 - y1) / (x2 - x1)
= (25 - 28) / (10 - 4)
= -3/6
= -1/2
The slope represents the rate at which Calvin is spending money on candy.
Now, we can use the point-slope form of the equation of a line to find the equation of the line.
y - y1 = m(x - x1)
y - 28 = (-1/2)(x - 4)
y - 28 = (-1/2)x + 2
y = (-1/2)x + 30
Therefore, the equation of the line that represents Calvin’s spending on candy is y = (-1/2)x + 30.
Answer: Equation that represents his spending on candy- y = (³⁄₁₀) x
X = number of candy
Step-by-step explanation:
y = money spend x = number of candy
y = (m)x
cost for 10 pieces of candy = $(28 - 25) = $3
⇛ 3 = (m)x10 (x = 10 & y = 3)
⇛m=(³⁄₁₀)
Therefore the equation representing his spending on candy is
⇛ y = (³⁄₁₀) x