Find the area of the figure below

Answer:

y = 4x + 40

Step-by-step explanation:

At sunrise, 0 hours have passed, meaning x = 0.

When x = 0, the temperature is 40, meaning that 40 is the y-intercept.

And every x hours the temperature rises by 4 degrees F

The mean amount of coffee to be dispensed should be set at μ + 0.0525 ounce, where μ represents the original mean amount of coffee. This ensures that the cup overfills only 4% of the time.

To determine the mean amount of coffee to be dispensed, we need to find the value that corresponds to the 96th percentile of the normal distribution. This value represents the amount of coffee that should not be exceeded 96% of the time.

Using a standard normal distribution table or a calculator, we find that the z-score corresponding to the 96th percentile is approximately 1.75.

Since the standard deviation is given as 0.03 ounce, we can set up the equation:

1.75 = (x - μ) / 0.03

Solving for x, the mean amount of coffee to be dispensed, we get:

x - μ = 1.75 * 0.03

x - μ = 0.0525

x = μ + 0.0525

Therefore, the mean amount of coffee to be dispensed should be set at μ + 0.0525 ounce to ensure that the cup overfills only 4% of the time.

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TheThe general solution to the wave equation utt = 4 (uxx + Uyy) is given by the D’Alembert’s formula. Therefore, the solution to the given problem is obtained by finding the specific form of the initial conditions u (x, y, 0) = f (x, y) and ut (x, y, 0) = g (x, y) and then use these values to find u (x, y, t) using the D’Alembert’s formula.

Let us find the form of the wave u(x,y,t) that satisfies the wave equation utt = 4 (uxx + Uyy) given the initial displacement f(x,y) = -3sin(5x)sin(6y) + 11sin(6x)sin(9y) and g(x,y) = 0.

Solution:
The D’Alembert’s formula for the wave equation is given by:

`u(x,y,t) = (1/2) [f(x+ct,y) + f(x-ct,y)] + (1/(2c)) ∫_((x-ct))^(x+ct)∫_((y-c(t-s)))^(y+c(t-s)) g(s,r) dr ds`

where c is the speed of the wave. Comparing with the wave equation `utt = c^2(uxx + uyy)` we have `c = 2`

Therefore, the solution to the wave equation is given by:

`u(x,y,t) = (1/2) [-3sin(5(x+2t))sin(6y) -3sin(5(x-2t))sin(6y) +11sin(6(x+2t))sin(9y) +11sin(6(x-2t))sin(9y)]`

Hence, the solution is:

`u(x,y,t) = (1/2) [-3sin(5(x+2t))sin(6y) -3sin(5(x-2t))sin(6y) +11sin(6(x+2t))sin(9y) +11sin(6(x-2t))sin(9y)]`

So, this is the required solution.

Answer:

B. x=6

Step-by-step explanation:

substitute -7 into 2y to get -14. your new equation should be 4x-14=10. add 14 to both sides to get 4x=24, divide both sides by 4 to get x=6.

Answer:

B. 6

Step-by-step explanation:

y = -7

4x + 2(-7) = 10

4x + (-14) = 10

4x = 10 - (-14)

4x = 24

x = 6

There is a significant relationship between y and both x1 and x2.

MSR = 306.625, MSE = 30.844b. F = 9.939 and p-value = 0.007. At a = 0.05, the overall model is significant.

tB₁ = 7.301 and p-value = 0.0009. At a = 0.05, there is a significant relationship between y and x1. d. tB₂ = 4.771 and p-value = 0.0008. At a = 0.05, there is a significant relationship between y and x2.

In a regression model, the F-test is used to determine whether the regression coefficient as a whole is statistically significant or not.

The p-value of the F-test is compared to the significance level (α) to determine statistical significance.

If the p-value is less than α, the regression coefficient as a whole is considered statistically significant. If it is greater than α, then it is not statistically significant.

t-test is used to determine whether each individual regression coefficient is statistically significant or not.

The p-value of the t-test is compared to the significance level (α) to determine statistical significance.

If the p-value is less than α, the regression coefficient is considered statistically significant.

If it is greater than α, then it is not statistically significant.

In this question, the F-test is significant at a = 0.05, and the t-test for both x1 and x2 is significant at a = 0.05.

Therefore, there is a significant relationship between y and both x1 and x2.

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The integration is ∫∫(q · dS) = ∫[0 to √6] ∫[0 to √6] (-45y - 45z) dy dz.

The rate of heat flow inward across the cylindrical surface y² + z² = 6, 0 ≤ x ≤ 3 can be determined by calculating the flux of the heat vector field through the surface.

To find the rate of heat flow, we need to calculate the surface integral of the heat flux vector across the given cylindrical surface. The heat flux vector is given by q = -K∇u, where K is the conductivity and ∇u is the gradient of the temperature function u(x, y, z).

First, we find the gradient of u:

∇u = (∂u/∂x)i + (∂u/∂y)j + (∂u/∂z)k

= 0i + (6y)j + (6z)k

Then, we calculate the heat flux vector:

q = -K(∇u)

= -7.5(0i + (6y)j + (6z)k)

= -45yj - 45zk

Next, we calculate the surface area element vector, dS, of the cylindrical surface. Since the surface is defined by y² + z² = 6, we can parameterize it as r(y,z) = yi + zk. Taking the cross product of the partial derivatives, we obtain dS = (∂r/∂y) x (∂r/∂z) dy dz = (-j -k) dy dz.

Finally, we can calculate the surface integral by integrating the dot product of q and dS over the given cylindrical surface:

∫∫(q · dS) = ∫∫(-45yj - 45zk) · (-j -k) dy dz

To find the limits of integration, we note that the surface extends from y² + z² = 6 to the origin, which corresponds to 0 ≤ y² + z² ≤ 6. Since the surface is symmetric, we can integrate over a quarter of the surface, from y = 0 to y = √6 and z = 0 to z = √6.

Performing the integration, we get:

∫∫(q · dS) = ∫[0 to √6] ∫[0 to √6] (-45y - 45z) dy dz

Evaluating this double integral will give us the rate of heat flow inward across the cylindrical surface.

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Complete question :

An online store sold a gift basket at five different prices and recorded the number of gift baskets that were sold at each price. The results are shown in the scatterplot.

Which statement is correct based on the scatterplot?

There is no relationship between price and gift baskets sold because the points do not form a straight line.

There is no relationship between price and gift baskets sold because there are multiple prices at which 80 gift baskets were sold.

There is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold increases.

There is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold decreases.

Answer:

There is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold decreases.

Step-by-step explanation:

From the scatterplot provided, it could be observed thatbthere is a linear trend in the plot created. This shows that there is a relationship between the price of gifts and the number if gift basket sold.

Furthermore, the slope of the linear trend line that could be drawn from the plotted data is negative, A negative slope Indicates a negative relationship, that is an increase in x leads to corresponding decrease in y. He ce, as price increases the number sold decreases

Answer:

d and/ or the other dude

Step-by-step explanation:

Answer:

NO

Step-by-step explanation:

From the graph attached,

Equation of the line parallel to x-axis is y = 3.

Since, the line is dotted line, equation will be an inequality (having sign of < or >)

Now shaded region is below the line so equation of the inequality will be,

y < 3

Any point below the dotted line will be the solution of the given inequality.

Therefore, blue dot on the dotted line represented by y = 3 will not be the solution of the inequality.

Answer is NO.

Given:

The data point is (3,10.5).

The prediction equation is [tex]y=-6.1x+12.5[/tex].

To find:

The value of the residual for this data point.

Step-by-step explanation:

The data point is (3,10.5). So, the actual value is 10.5 at [tex]x=3[/tex].

Prediction equation is

[tex]y=-6.1x+12.5[/tex]

Putting [tex]x=3[/tex], we get

[tex]y=-6.1(3)+12.5[/tex]

[tex]y=-18.3+12.5[/tex]

[tex]y=-5.8[/tex]

The formula for residual is:

Residual = Actual value - Expected value

[tex]Residual=10.5-(-5.8)[/tex]

[tex]Residual=10.5+5.8[/tex]

[tex]Residual=16.3[/tex]

Therefore, the residual for the given data point is 16.3.

I had this one before. I'm pretty sure it is 1.61

Answer:

1.61

Step-by-step explanation:

It just makes since.

Answer:

b = -3.

Step-by-step explanation:

If the 3 points are collinear then:

Slope of AB = Slope  of BC and so

(0-2)/(b + 6) = (-4-0)/( 3 - b)

-4(b + 6) = -2(3 - b)

-4b - 24 = -6 + 2b

-24 + 6 = 2b + 4b

6b = -18

b = -3.

Answer:

[tex] cos^{-1}(cos\frac{ 7π}{6})=cos^{-1}(cos\frac{7*180}{6})[/tex]

[tex] cos^{-1}(cos{210})[/tex]

[tex] cos^{-}(cos(180+30))[/tex]

[since in third quadrant cos 30=-[tex] \frac{\sqrt{3}}{2}][/tex]

[tex] cos^{-}(- \frac{\sqrt{3}}{2})[/tex]

:150°or [tex] \frac{5π}{6}[/tex]

150°or [tex] \frac{5π}{6}[/tex]is a required answer.

The appropriate measure of variability for the given data is the IQR, and its value is 16.

Based on the given stem-and-leaf plot, which represents the scores earned in a flower-growing competition, we can determine the appropriate measure of variability for the data.

The stem-and-leaf plot shows the individual scores, and to measure the spread or variability of the data, we have two commonly used measures: the range and the interquartile range (IQR).

The range is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest value is 20, and the largest value is 65. Therefore, the range is 65 - 20 = 45.

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Looking at the stem-and-leaf plot, we can identify the quartiles. The first quartile (Q1) is 25, and the third quartile (Q3) is 41. Therefore, the IQR is 41 - 25 = 16.

In this case, both the range and the IQR are measures of variability, but the IQR is generally preferred when there are potential outliers in the data. It focuses on the central portion of the dataset and is less affected by extreme values. Therefore, the appropriate measure of variability for the given data is the IQR, and its value is 16.

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Answer:

divide 460/60

Step-by-step explanation:  

60 rep one hour and you will find your answer

Answer:

cubes have 6 numbers

3 odd, 3 even

Step-by-step explanation:

probablity=desiredoutcome/totalpossibleoutcomes

there are 6 total desired outcomes (3 on each cube)

total possible, there are 6*6 or 36 total possible outcomes

so 6/36 or 1/6 chance

Answer: 8(8u-5)

Step-by-step explanation:

Find a number that goes into both 64 and 40 the GCF of both is 8 so 8 goes on the outside of the new factor 8u-5 because if we distribute back we should arrive at the original equation

8(8u-5)

Answer:

8%

Step-by-step explanation:

71 citizens should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

We need to find out the sample size of citizens that should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

The formula for the Margin of error is

E: E = Zc/2 * (σ/√n)

Where E is the margin of error Zc/2 is the Z-value for the level of confidence cσ is the population standard deviation is the sample size.

So the formula for the sample size n is: n = (Zc/2 / E)² * σ²

We have Zc/2 = Z0.02/2 = Z0.01 = 2.33 (using z-table) σ = 22 years

E = 3 years

n = (2.33 / 3)² * 22²

n ≈ 70.36 ≈ 71 (rounded up)

Therefore, 71 citizens should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

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Answer:

42.78cm2

Step-by-step explanation:

Area =100°/360 * 22/7 * 7^2

=42.78cm2

The value of area of hexagon is,

A = 672 cm²

Given that;

In a hexagon;

Apothem of the hexagon = 14 cm

And, perimeter of the hexagon: 96 cm

Since, We know that,

Area of the hexagon = [(3√3) / 2] a²    

where, a is the measure of the side

Since, hexagon has 6 sides.

Perimeter = 6a

96 cm = 6a

96 cm / 6 = a

16 = a

We can also use the area of a triangle to approximate the area of the hexagon. There are 6 triangles in the hexagon .

Area of a triangle = (height x base) / 2

A = (14 cm x 16 cm) / 2

A = 224 / 2

A = 112 cm²

So, Area of hexagon is,

A = 112 cm²  x  6 triangles

A = 672 cm²

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Complete question is,

A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm.

What is the approximate area of the hexagon?

224 cm2

336 cm2

448 cm2

672 cm2

Answer:

$ 45,600

Step-by-step explanation:

Answer:

mean: 5

Step-by-step explanation:

(9 + 3 + 1 + 8 + 3 + 6) / 6 = 5

a. The name of the theory used to predict molecular geometries is the VSEPR (Valence Shell Electron Pair Repulsion) theory.

b. The name of the molecular shape for a molecule consisting of a central atom bonded to 2 outer atoms with two lone pairs on the central atom is "bent" or "angular." This molecular shape is also sometimes referred to as "V-shaped" due to its characteristic angular structure.

c. The name of the molecular shape for a molecule consisting of a central atom bonded to 4 outer atoms with no lone pairs on the central atom is "tetrahedral." This molecular shape is characterized by a central atom at the center with four symmetrically arranged outer atoms, forming a three-dimensional tetrahedron-like structure.

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Answer:

Maybe try explaining that if you narrow it down and simplify the numbers by dividing them by 8 or somewhere around there.

Answer: 16.28?

Step-by-step explanation:

Answer:

i think the answer would be A

The correct description of the fraction 2/5 is,

⇒ 2 is the part, 5 is the whole, and the fraction is equivalent to 40%.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

The fraction is,

⇒ 2/5

Now, We can change into percent as;

⇒ 2/5 × 100%

⇒ 2 × 20%

⇒ 40%

Thus, The correct description of the fraction 2/5 is,

⇒ 2 is the part, 5 is the whole, and the fraction is equivalent to 40%.

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Answer:

x < 6.5

Step-by-step explanation:

3(2x - 7) < 4x - 8

6x - 21 < 4x - 8

6x - 4x < -8 + 21

2x < 13

x < 6.5

[tex]c+20=55\\c=55-20\\c=35[/tex]