Seth is using a large shoe box to store his baseball cards. The length of the box is 12 inches, and the height is 6 inches. If the volume of Seth's box is 288 cubic inches, how wide is the box?

5cm

Step-by-step explanation:

volume of cube= l³

125 =l³

3root over 125 =l

l = 5

Answer:

So the length of the edge of a cube with a volume of 125 is 5.

Step-by-step explanation:

Answer:

The rate of change is 12ft/s

Step-by-step explanation:

Given

[tex]h(t) = -16t^2 + 20t[/tex]

Required

Rate of change from when she jumps till 1/2s

The time she jumps is represented as: t = 0

So, calculate h(0)

[tex]h(t) = -16t^2 + 20t[/tex]

[tex]h(0) = -16 * 0^2 + 20 * 0 = 0[/tex]

At t = 1/2

[tex]h(t) = -16t^2 + 20t[/tex]

[tex]h(1/2) = -16 * 1/2^2 + 20 * 1/2 = 6[/tex]

Rate of change is calculated as:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

In this case:

[tex]Rate = \frac{h(b) - h(a)}{b - a}[/tex]

Where

[tex](a,b) = (0,1/2)[/tex]

So, we have:

[tex]Rate = \frac{h(b) - h(a)}{b - a}[/tex]

[tex]Rate = \frac{h(1/2) - h(0)}{1/2 - 0}[/tex]

[tex]Rate = \frac{6 - 0}{1/2 - 0}[/tex]

[tex]Rate = \frac{6}{1/2}[/tex]

[tex]Rate =12[/tex]

The rate of change is 12ft/s

Answer:

135

Step-by-step explanation:

Hello There!

The angle that has a measure of 45° and x are supplementary angles meaning that the sum of the two angles is 180

so x can be found by subtracting the given angle (45 in this case) from 180

180 - 45 = 135

so x = 135

Answer:

135

Step-by-step explanation:

When there's a completely straight line the angle is 180 and when u have a angle already there you subtract 180 from the angle in this case 180-45=135

For the vector field f = 2x², −3y², z², Divergence (∇·f) = 4x - 6y² + 2z, Curl (∇×f) = (0, 0, 0).

To compute the divergence (∇·f) and the curl (∇×f) of the vector field f = (2x², -3y², z²), we can use the vector calculus operators. Divergence (∇·f),

In this case, the divergence of f is the partial derivative of each part of the field, for f = (2x², -3y², z²), we have,

∂f₁/∂x = 4x

∂f₂/∂y = ∂(-3y²)/∂y = -6y²

∂f₃/∂z  = 2z

Therefore, the divergence of f is,

∇·f = 4x - 6y² + 2z

Curl (∇×f),

The curl of a vector field f = (f₁, f₂, f₃) is given by the cross product of the curl operator (∇×) and the vector field. In this case, the curl of f is,

∇×f  = (i∂/∂x + j∂/∂y + k∂/∂y) x (i2x², -j3y², kz²)

Basically we can write  (i2x², -j3y², kz²) as (f₁, f₂, f₃)

we have,

∂f₁/∂z = 0

∂f₂/∂x = ∂(-3y²)/∂x = 0

∂f₃/∂y = ∂(z²)/∂y = 0

Therefore, the curl of f is,

∇×f = (0, 0, 0)

In this case, the curl of f is the zero vector, indicating that the vector field f is irrotational.

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Complete question - compute the divergence ∇·f and the curl∇✕f of the vector field. f = 2x², −3y², z².

Answer:

$1159.69

Step-by-step explanation:

A = P (1 + r/n)^nt

A = 1000 (1 + 0.05/2)^2(3)

A = $1159.69

Answer:

(x, y) -- [X-4, Y+6]

Answer: the one in the bottom right

Step-by-step explanation: each month which is the x axis ( the bottom line) the y axis (line on the left) goes up by 5

so when the x axis is 1 the y axis should be at 5

Answer:

The answer is "True".

Step-by-step explanation:

The z-score value shows how often standard deviations were away from the earth. If it is 0, it is on average. The positive Z sign indicates that perhaps the raw mark is greater than the average. While z-score is equivalent to +1, for example, it is a standard deviation of 1 above average. This can be used for implementing series and also for comparing the trend of mortality among various individuals or between various periods and by using the z score we find the curve length, that's why it is correct.

Answer:

4/5=0.8×7=5.6

5.6 is the answer

Hey there!

4/5 × 7

= 4×7/5

= 28/5

= 5.6

Hope it helps ya!

Answer:

the third option

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

they both started at 0 and added 2 and 6 respectively

The number you are is 2.

Let's break down the information provided:

You are a factor of 40 when paired with 15.

Your least common multiple (LCM) with 15 is not equal to 1.

To find the number that satisfies these conditions, let's examine the factors of 40. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. Now, we need to find a number from this list that is a factor of 40 when paired with 15.

To find the LCM of 15 and each factor of 40, we can compare their multiples:

For 15 and 1: LCM = 15

For 15 and 2: LCM = 30

For 15 and 4: LCM = 60

For 15 and 5: LCM = 15 (already the smaller number)

For 15 and 8: LCM = 120

For 15 and 10: LCM = 30 (already the smaller number)

For 15 and 20: LCM = 60 (already the smaller number)

For 15 and 40: LCM = 120 (already the smaller number)

From the list, we can see that the LCM of 15 with 5, 10, 20, and 40 is equal to 15. However, the problem states that the LCM of 15 with the number is not equal to 1. Thus, the number that satisfies both conditions is 2, as the LCM of 15 and 2 is 30, and it is not equal to 1. Therefore, the number you are is 2.

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a/ To find the limit of the expression 2 + 4 + 3i Re(z - i), we need to replace z with the limit point. Therefore, the expression will be:2 + 4 + 3i Re(z - i) = 6 + 3i Re(z - i)

We have to find the limit as z approaches i. Consider the following:

Since Re(z - i) is a real number, the limit can be found by setting Re(z - i) = 0.

Therefore, lim 2+4+3i Re(z - i) = lim 6 + 3i Re(z - i) = 6.Explanation:

b/ Given the limit lim zi / zi, we can simplify the expression by canceling zi in the numerator and the denominator. Therefore, lim zi / zi = lim 1 = 1.

Explanation:

4. Let f(x) = x3 + iy(a) The derivative of f(x) is the function f′(x). To find the derivative of f(x), we need to differentiate the real and imaginary components of f(x) separately.

Therefore, f′(x) = 3x² + iy, since the derivative of i is zero.

Explanation: (b) We must test the Cauchy-Riemann equations to see if f(x) is analytic. f(x) is said to be analytic if it meets the Cauchy-Riemann conditions. Therefore, we need to verify that the following equations are satisfied: ∂u / ∂x = ∂v / ∂y and ∂u / ∂y = -∂v / ∂x. Using the function given above, we can easily obtain its real and imaginary components. u(x, y) = x³ and v(x, y) = y. Therefore, ∂u / ∂x = 3x² and ∂v / ∂y = 1, but 3x² ≠ 1

Therefore, the Cauchy-Riemann equations are not satisfied, so f(x) is not analytic.

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Answer:

When A is less than 0 the parabola flips downward. When A becomes larger than 1, the parabola becomes more narrow. When A becomes smaller, until 0, the parabola widens.

Step-by-step explanation:

Step-by-step explanation:

11. angles 1 and 2 are vertical angles, meaning they are congruent.

angle 2=angle 1=38 degrees

14. angles 1 and 2 are supplementary angles, meaning they add to 180 degrees.

angle 1=180-angle 2=180-67=113 degrees

Answer:

I couldn't really see the height number (that had to doubled) ir really the radius but I saw 7 for the radius and 3 (×2) for the height so I did the math and the answer is 923.63

Step-by-step explanation:

i could be wrong tho, hope this helped

Answer:

923.63

Step-by-step explanation: hope this helps!!

Answer:

You mean how many centimerters are in a meter?

In that case 100.

Step-by-step explanation:

we do not have enough evidence to conclude that cars get better mileage on premium gasoline. Thus, we can conclude that there is no significant difference between the mileages of cars using premium and regular gasoline.

a. What test should be used?

The test that should be used is the Two-sample t-test because we are working with two independent groups.

b. What are the hypotheses?

The null hypothesis is that there is no difference between the mileage of cars using premium and regular gasoline, while the alternative hypothesis is that there is a difference between the two mileages.

Mathematically, this can be stated as follows: Null hypothesis: µ1 = µ2Alternative hypothesis: µ1 > µ2Where µ1 is the population mean for premium gasoline and µ2 is the population mean for regular gasoline.

c. Based on the R outputs, what is your conclusion about hypotheses testing?

From the R outputs, we can see that the p-value is 0.2826. Since this value is greater than the level of significance (α) of 0.05, we fail to reject the null hypothesis. Therefore, we do not have enough evidence to conclude that cars get better mileage on premium gasoline. Thus, we can conclude that there is no significant difference between the mileages of cars using premium and regular gasoline.

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a. The test that should be used is a two-sample t-test.

b. The null hypothesis is "The population mean mileage of cars using regular and premium gasoline are equal."

The alternative hypothesis is "The population mean mileage of cars using premium gasoline is more than the population mean mileage of cars using regular gasoline."

c. We do not have enough evidence to support the claim that cars get better mileage on premium regular gas.

a. To find what test should be used.

The test that should be used is a two-sample t-test.

b. To find the hypotheses.

The null hypothesis is "The population mean mileage of cars using regular and premium gasoline are equal."

The alternative hypothesis is "The population mean mileage of cars using premium gasoline is more than the population mean mileage of cars using regular gasoline."

c. Based on the R outputs, to find the conclusion about hypotheses testing.

The sample mean of the differences in mileage for cars filled with premium and regular gasoline is 0.8. The calculated t-value is -0.59702.

The calculated p-value is 0.2826.The p-value is higher than the significance level of 0.05.

Therefore, we fail to reject the null hypothesis.

We can't conclude that the population mean mileage of cars using premium gasoline is more than the population mean mileage of cars using regular gasoline.

Hence, we do not have enough evidence to support the claim that cars get better mileage on premium regular gas.

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Answer:

Surface area of prism = 1301 cm²

Step-by-step explanation:

A triangular pyramid has 3 rectangular sides and 2 triangular sides.

Now, we are told that the triangular side is isosceles.

This means that two of the rectangular sides which share a side with the equal side of the triangle are equal as well as the 2 triangular sides.

Surface area of prism = 2(area of triangular face) + 2(area of rectangle sharing one side with the equal side of the triangle) + (area of rectangle sharing side with the unequal side of the triangle).

Area of triangle = ½ × base × height

Area of triangle = ½ × 9 × 13 = 58.5 cm²

Since height of prism is 32 cm, then;

area of rectangle sharing one side with the equal side of the triangle = 32 × 14 = 448 cm²

area of rectangle sharing side with the unequal side of the triangle = 32 × 9 = 288 cm²

Thus;

Surface area of prism = 2(58.5) + 2(448) + 288

Surface area of prism = 1301 cm²

Answer:

B.

Step-by-step explanation:

the three sticks of butter were divided among six people

a. The null hypothesis is H₀: μ = 14 and alternative hypothesis is Ha: μ ≠ 14

b. The t-test for the data is 1.11

c. The p-value for the t-test is 0.28

d. We accept the null hypothesis since the p-value is greater than the significance value.

e. The decision to fail to reject the null hypothesis means that we do not have enough evidence to support the claim

(a) The claim is that the mean time it takes smokers to quit smoking permanently is 14 years.

Null hypothesis (H₀): The mean time it takes smokers to quit smoking permanently is 14 years.

H₀: μ = 14

Alternative hypothesis (Ha): The mean time it takes smokers to quit smoking permanently is not 14 years.

Ha: μ ≠ 14

(b) To identify the standardized test statistic, we can use the formula:

t = (x - μ) / (s / √n)

where:

x is the sample mean,

μ is the population mean,

s is the population standard deviation,

n is the sample size.

Given:

Sample mean (x) = 15.29375 (rounded to 5 decimal places)

Population mean (μ) = 14

Population standard deviation (s) = 6.6

Sample size (n) = 32

Using these values, we can calculate the standardized test statistic.

t = (15.29375 - 14) / (6.6 / √32)

t = 1.11

(c) To find the p-value, we need to use the t-distribution table or statistical software. Since using technology is mentioned in the question, we will use it to calculate the p-value.

The p-value for a two-tailed test is approximately 0.28.

(d) We compare the p-value to the significance level α = 0.09.

Since the p-value 0.28 is greater than the significance level (0.09), we fail to reject the null hypothesis.

(e) The decision to fail to reject the null hypothesis means that we do not have enough evidence to support the claim that the mean time it takes smokers to quit smoking permanently is different from 14 years at the 10% level of significance.

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If the estimate being tested is less than the benchmark, you should conduct a left tail one-sample hypothesis test. So, correct option is C.

In hypothesis testing, the null hypothesis typically assumes that there is no significant difference or effect, and the alternative hypothesis proposes that there is a significant difference or effect.

In this case, since the estimate is less than the benchmark, the alternative hypothesis would state that there is a significant difference, and we are specifically interested in detecting a decrease or a lower value.

Therefore, we conduct a left tail test to evaluate the evidence against the null hypothesis and determine if the estimate is significantly lower than the benchmark.

A left tail test focuses on the leftmost portion of the distribution and calculates the probability of observing a value as extreme or more extreme than the estimate, assuming the null hypothesis is true.

By comparing the test statistic with the critical value or p-value associated with the chosen significance level, we can make conclusions about the statistical significance of the estimate being less than the benchmark.

So, correct option is C.

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Ordered pair (0, 6) and  (2, 7)  satisfy both inequalities in the system and are solutions to the system.

To identify the graph that represents the given system of inequalities y > x + 5 and y ≥ 2x + 3, we need to graph the individual inequalities and find the region where they overlap.

When we plot the graph of inequality separately:

    2. y ≥ 2x + 3:

The overlapping shaded region represents the solution to the system of inequalities.

To find two ordered pairs that are solutions to the system, we can choose any points within the overlapping region. Let's select two points:

Ordered pair 1: (0, 6)

Ordered pair 2: (2, 7)

These two points satisfy both inequalities in the system and are solutions to the system.

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The correct question is given below -

Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system.

y > x + 5

y ≥ 2x + 3

Answer:

s

Step-by-step explanation:

Answer:

fourth option) 5/8 lb

Answer:

a) 1/13 (or 13 depending on the factor is being applied to the dog house or applied to the shed. If its being applied to the shed like 117 * scale factor it is 1/13)

b) 10

Step-by-step explanation:

The scale factor is 13 and the height of the dog house is 10 cm.

A scale factor is defined as the ratio between the scale of a given original object and a new object.

Given that, Dave is building a doghouse that is a scale model of his shed in the farmyard, One of the windows on the shed is 117 cm wide and 130 cm high. On the doghouse the window is 9 cm wide,

a) Since, the scale factor = ratio of original scale to scale of the model.

Therefore,

Scale factor = 117 / 9 = 13

b) Since, the scale factor is 13 and the original scale of the window high is 130 cm.

Therefore, height of the doghouse = 130 / 13 = 10 cm

Hence, the scale factor is 13 and height of the dog house is 10 cm.

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Answer:

I’m sorry, but it’s a black screen.

Step-by-step explanation:

Answer:

Consider this option:

1. the equation of given line is y=-x-3 (it is easy to find it using points (0;-3)&(-3;0)).

2. according to the equation of line: y≥-x-3

The answers are =

a) left-skewed

b) Standard Error ≈ 3.146

c) the probability is approximately 0.7867.

d) standard deviation of = 94.094.

e) the probability is approximately 0.8669.

(a) The distribution of students' grades is left-skewed.

(b) If n = 30 students are selected at random, the distribution of the sample mean grade is approximately normal with a mean of 68 and a standard deviation of 3.146.

To calculate the standard deviation of the sample mean, also known as the standard error, you divide the population standard deviation by the square root of the sample size:

Standard Error = σ / √n = 17.2 / √30 ≈ 3.146

(c) To find the probability that the sample mean grade for these 30 students is less than 72.0, we can use the z-score formula and the standard error calculated above:

z = (x - μ) / (σ / √n)

z = (72 - 68) / (17.2 / √30) ≈ 0.7952

Now, we can use a standard normal distribution table or a calculator to find the probability corresponding to this z-score.

From the table or calculator, the probability is approximately 0.7867.

(d) If n = 30 students are selected at random, the distribution of the sample total grade is approximately normal with a mean of 30 × 68 = 2040 and a standard deviation of √(30) × 17.2 = 94.094.

The mean of the sample total grade is the product of the population mean and the sample size (n).

The standard deviation of the sample total grade is the product of the population standard deviation and the square root of the sample size (n).

(e) To find the probability that the total grade for these 30 students is less than 2160.0, we can use the z-score formula and the standard deviation calculated above:

z = (x - μ) / (σ × √n)

z = (2160 - 2040) / (17.2 × √30) ≈ 1.105

Using the standard normal distribution table or a calculator, the probability corresponding to this z-score is approximately 0.8669.

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Answer:

3.84 feets

Step-by-step explanation:

Given that:

θ = 88°

Radius, r = 2.5

The length of section of the wire, L ; Length of an arc

L = θ / 360° * 2πr

L = 88/360 * 2*π*2.5

L = (88/360) * 15.707963

L = 3.8397

Length of section of wire = 3.84 feets