Find the measure of the arc or angle indicated

The scale factor of the given scenario is 7/36.

Given that, the scale of the drawing was 7 inches = 1 yard.

We know that, 1 yard = 36 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.

Here, scale factor = 7/36

Therefore, the scale factor of the given scenario is 7/36.

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Answer:

the second equation (59-31-[]=10)

the answer is 18

The standard form of the equation is 2x^2 + 24y - 35 = 0. To find the standard form of the equation of a parabola with vertex at the origin, we need to use the formula 4p(x^2 + y^2) = (x - h)^2 + (y - k)^2, where (h,k) is the vertex and p is the distance from the vertex to the focus (or directrix, depending on the given information).

For the first characteristic, we have a focus at (-9,0), which is to the left of the vertex at the origin. This means that p = 9 (the distance from the vertex to the focus). Substituting into the formula, we get:
4(9)(x^2 + y^2) = (x - 0)^2 + (y - 0)^2
36x^2 + 36y^2 = x^2 + y^2
35x^2 + 35y^2 = 0
So the standard form of the equation is 35x^2 + 35y^2 = 0. For the second characteristic, we have a focus at (0,1/6), which is above the vertex at the origin. This means that p = 1/6 (the distance from the vertex to the focus). We also know that the directrix is a horizontal line 2 units below the vertex. This means that the equation of the directrix is y = -2. Using the formula and the distance formula between a point and a line, we can write:
4(1/6)(x^2 + y^2) = (y - 0)^2 - 2^2
2x^2 + 24y - 35 = 0

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The order of the subgroup h ∩ k can be found using Lagrange's theorem, which states that the order of a subgroup of a group G must divide the order of G. Therefore, the order of h ∩ k must divide both |h| and |k|.

In this case, we are given that |h| ≤ 12 and |k| ≤ 35. The largest possible order of h ∩ k occurs when h and k have no elements in common, in which case |h ∩ k| = 1. Therefore, the order of h ∩ k must be a divisor of both |h| and |k| that is less than or equal to 1. Since 1 is the only such divisor, we have |h ∩ k| = 1.

More generally, if |h| = m and |k| = n, then the largest possible order of h ∩ k occurs when h and k have no elements in common, in which case |h ∩ k| = 1. The order of h ∩ k must divide both m and n, so the possible orders of h ∩ k are the divisors of gcd(m, n). Therefore, |h ∩ k| ≤ gcd(m, n).

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Using the given fraction we can see that there are 0.175 liters of oil in the container.

We know that 3/4 of the total volume in the container is vinegar, then the remaining fraction must be oil.

The remaining fraction is given by:

1 - 3/4

4/4 - 3/4 = 1/4

Then 1/4 of the total volume is oil (because the mix is only oil and vinegar), and we know that the total volume is 0.7 liters, then the amount of oil is:

(1/4)*0.7 L  =0.175 L

There are 0.175 liters of oil in the mix in the container.

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Answer:

5/9

Step-by-step explanation:

we add all of the values and divide by the total number in this case 9, all of them add to make 5 so we do 5÷9 to get 5/9

Answer:

3:5

Step-by-step explanation:

24:40

24 cars without sunroof

24+16=40

40 total cars

reduce the ratio of 24:40

12:20

6:10

3:5

the answer is 3:5

If a storage facility charges $1 per cubic yard and the storage space is 32 ft. The storage charge is $1999.97.

What is mathematical conversions?

Mathematical conversions refer to the process of changing one unit of measurement to another unit of measurement that is equivalent in value.

First, we need to convert the dimensions from feet to yards, since the rate is given per cubic yard.

32 feet = 10.6667 yards (dividing by 3)

160 feet = 53.3333 yards (dividing by 3)

10 feet = 3.3333 yards (dividing by 3)

Next, we can calculate the volume of the storage space in cubic yards by multiplying the three dimensions:

Volume = 10.6667 yards x 53.3333 yards x 3.3333 yards

Volume = 1999.97 cubic yards (rounded to two decimal places)

Finally, we can calculate the storage charge by multiplying the volume by the rate:

Charge = 1999.97 cubic yards x $1/cubic yard

Charge = $1999.97

Therefore, the storage charge is $1999.97.

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Answer: 0.4

Step-by-step explanation:

The number that occurs the most

The point P where the function f(x, y, z) = xºy$z reaches the maximum value for x, y, z > 0 on the unit sphere is (1/√3, 1/√3, 1/√3).

To find the point P where the function f(x, y, z) = [tex]x^y^z[/tex] reaches the maximum value for x, y, z > 0 on the unit sphere, we can use Lagrange multipliers.

Let g(x, y, z) =  x² + y² + z² - 1 be the equation of the unit sphere. We want to maximize f(x, y, z) subject to the constraint g(x, y, z) = 0.

Using Lagrange multipliers, we set up the system of equations

∂f/∂x = λ∂g/∂x

∂f/∂y = λ∂g/∂y

∂f/∂z = λ∂g/∂z

g(x, y, z) = 0

Taking partial derivatives, we get

[tex]y^z * x^{y-1}[/tex]= 2λx

[tex]x^z * y^{z-1}[/tex] = 2λy

[tex]x^y * z^{y-1}[/tex]* ln(z) = 2λz

Simplifying these equations and dividing them by each other, we get:

y ln(x)/x = x ln(y)/y

y ln(z)/z = z ln(y)/y

x ln(z)/z = z ln(x)/x

From the first equation, we get:

y ln(x) = x ln(y)

Taking the exponential of both sides, we get

[tex]x^y[/tex] = yˣ

Similarly, from the second equation, we get

[tex]y^z[/tex] = [tex]z^y[/tex]

And from the third equation, we get

[tex]x^z[/tex] = zˣ

These equations suggest that x, y, and z should all be equal to each other. To confirm this, we can take the logarithm of both sides of x^y = yˣ to get:

y ln(x) = x ln(y)

ln(x)/x = ln(y)/y

This function has a maximum at x = y, which implies that x = y = z. Furthermore, since we are looking for a point on the unit sphere, we have x² + y² + z² = 1, which gives us:

x = y = z = 1/√3

Therefore, the point P is given by (1/√3, 1/√3, 1/√3).

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After 20 minutes, the temperature of the pan will be approximately 29°F.

Using Newton's Law of Cooling, we can write:

T(t) = To + (T₁ - To)e^(-kt)

where T(t) is the temperature of the pan at time t, To is the temperature of the freezer, T₁ is the initial temperature of the pan, and k is a constant that depends on the properties of the pan and the freezer.

We know that after 15 minutes, the temperature of the pan is 41°F, so we can write: 41 = 0 + (140 - 0)e^(-15k)

Simplifying this expression, we get:

e^(-15k) = 41/140

Taking the natural logarithm of both sides, we get:

-15k = ln(41/140)

Solving for k, we get:

k ≈ 0.056

Now we can use this value of k to find the temperature of the pan after 20 minutes:

T(20) = 0 + (140 - 0)e^(-0.056*20) ≈ 29°F

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After 20 minutes, the temperature of the pan will be approximately 29°F.

Using Newton's Law of Cooling, we can write:

T(t) = To + (T₁ - To)e^(-kt)

where T(t) is the temperature of the pan at time t, To is the temperature of the freezer, T₁ is the initial temperature of the pan, and k is a constant that depends on the properties of the pan and the freezer.

We know that after 15 minutes, the temperature of the pan is 41°F, so we can write: 41 = 0 + (140 - 0)e^(-15k)

Simplifying this expression, we get:

e^(-15k) = 41/140

Taking the natural logarithm of both sides, we get:

-15k = ln(41/140)

Solving for k, we get:

k ≈ 0.056

Now we can use this value of k to find the temperature of the pan after 20 minutes:

T(20) = 0 + (140 - 0)e^(-0.056*20) ≈ 29°F

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Step-by-step explanation:

To find the equation of the tangent plane to the surface at the point (5 cos(π/3), 5 sin(π/3), k), we need to first find the partial derivatives of r with respect to u and v:

ru(u, v) = cos(v) i + sin(v) j

rv(u, v) = -5 sin(v) i + 5 cos(v) j + k k

Then, we can plug in the point (5 cos(π/3), 5 sin(π/3), k) to get the partial derivatives evaluated at that point:

ru(5, π/3) = cos(π/3) i + sin(π/3) j = (1/2) i + (√3/2) j

rv(5, π/3) = -5 sin(π/3) i + 5 cos(π/3) j + k k = -5/2 i + (5√3/2) j + k k

Now we can use the point-normal form of the equation of a plane, where the normal vector is given by the cross product of ru and rv:

⟨ru(5, π/3) × rv(5, π/3)⟩ = ⟨(1/2) i + (√3/2) j, (-5/2) i + (5√3/2) j, k⟩ = (-5/2 - √3/2) i + (-5√3/2 - 1/2) j + k k

Thus the equation of the tangent plane to the surface at (5 cos(π/3), 5 sin(π/3), k) is:

(-5/2 - √3/2)(x - 5 cos(π/3)) + (-5√3/2 - 1/2)(y - 5 sin(π/3)) + (z - k) = 0

Simplifying, we get:

-5√3 x + 5y - 5√3 z + (25/2 + 5/2√3) = 0

So the equation of the tangent plane to the surface at the point (5 cos(π/3), 5 sin(π/3), k) is:

-5√3 x + 5y - 5√3 z + 15.79 = 0.

a) Null Hypothesis is μ ≤ 21.6 and Alternative Hypothesis is μ > 21.6.

b) Point estimate of the difference between mean annual consumption in Webster City and the national mean is 2.5.

c) We can conclude that there is sufficient evidence to suggest that the mean annual consumption of milk in Webster City is higher than the national mean.

A. The hypothesis test to determine whether the mean annual consumption in Webster City is higher than the national mean can be set up as follows:

Null Hypothesis: μ ≤ 21.6

Alternative Hypothesis: μ > 21.6

where μ is the true population mean annual consumption of milk in Webster City.

B. The point estimate of the difference between mean annual consumption in Webster City and the national mean is simply the difference between the sample mean and the national mean:

Point Estimate = x' - μ = 24.1 - 21.6 = 2.5

C. To test for a significant difference at α = 0.05, we need to calculate the test statistic and compare it to the critical value.

t = (x' - μ) / (s / √n) = (24.1 - 21.6) / (4.8 / √16) = 2.083

Using a t-table with 15 degrees of freedom and a significance level of 0.05, we find the critical value to be 1.753. Since our test statistic (2.083) is greater than the critical value (1.753), we reject the null hypothesis.

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The volume of the prism is 259 units³.

The volume of the prism can be calculated as follows:

volume of a prism = base area × height

The prism is a triangular base prism. The area of the base of the prism is 37 units² and the height of the prism is 7 units.

Therefore,

Base area of the prism = 37 units²

height  = 7 units

Hence,

volume of a prism = 37 × 7

volume of a prism = 259 units³

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We are given a function f(x,y) = x/y and a point P(8,1). We need to find the gradient of the function, evaluate it at the point P, and find the rate of change of the function at P in the direction of the vector u = 3/5 i + 4/5 j.

Explanation:

(a) The gradient of a function is a vector that points in the direction of the steepest increase of the function at a point and its magnitude gives the rate of increase. The gradient of the function f(x,y) = x/y can be calculated using partial derivatives as follows:

∇f(x, y) = (∂f/∂x)i + (∂f/∂y)j

= (1/y)i - (x/y^2)j

(b) To evaluate the gradient at the point P(8,1), we substitute x=8 and y=1 in the expression for ∇f(x,y) as follows:

∇f(8, 1) = (1/1)i - (8/1^2)j

= i - 8j

(c) The rate of change of the function f(x,y) at the point P(8,1) in the direction of the vector u = 3/5 i + 4/5 j can be found by taking the dot product of the gradient at P with the unit vector in the direction of u as follows:

Duf(8, 1) = ∇f(8,1) . u/|u|

= (i - 8j) . (3/5 i + 4/5 j)/|(3/5 i + 4/5 j)|

= (3/5) - (32/5)

= -29/5

Therefore, the gradient of f is ∇f(x,y) = (1/y)i - (x/y^2)j, the gradient at P is ∇f(8,1) = i - 8j, and the rate of change of f at P in the direction of u is Duf(8,1) = -29/5.

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Therefore, the critical value for testing the hypothesis at a significance level of 0.005 for a sample of size 30 is -2.756 (rounded to three decimal places).

To find the critical value for testing the hypothesis:

H0: μ = 18.38 (null hypothesis)

Ha: μ < 18.38 (alternative hypothesis)

at a significance level of 0.005 for a sample size of 30, we need to use the t-distribution.

Since the alternative hypothesis is one-tailed (μ < 18.38), we will be looking for the critical value in the left tail of the t-distribution.

The critical value is the value that separates the rejection region from the non-rejection region.

To find the critical value, we can use a t-table or a statistical software. Here, I'll use the t-table.

Since the sample size is 30, the degrees of freedom (df) for this t-test is (n - 1) = (30 - 1) = 29.

Looking up the critical value for a one-tailed test with 29 degrees of freedom and a significance level of 0.005 in the t-table, we find that the critical value is approximately -2.756.

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a) when alpha = 0.01 and n = 10, the critical region (cr) boundary is at x^- ≤^- - 2.76. b) when alpha = 0.05 and n = 10, the cr boundary is at x^- ≤^- - 1.83. c) when alpha = 0.01 and n = 16, the cr boundary is at x^- ≤^- - 2.60. d) when alpha = 0.05 and n = 16, the cr boundary is at x^- ≤^- - 1.74.

In hypothesis testing, the critical region is the set of values of the test statistic that will lead to the rejection of the null hypothesis. The critical region is determined by the level of significance or alpha and the sample size. The level of significance is the probability of rejecting the null hypothesis when it is true. The critical region is located in the tail of the sampling distribution and is determined by the standard deviation and the mean of the sampling distribution.

For scenario a) where alpha is 0.01 and the sample size is 10, the critical region is located at x^- ≤^- - 2.76. This means that if the sample mean falls below this value, the null hypothesis will be rejected. Similarly, for scenario b) where alpha is 0.05 and the sample size is 10, the critical region is located at x^- ≤^- - 1.83. For scenario c) where alpha is 0.01 and the sample size is 16, the critical region is located at x^- ≤^- - 2.60. Finally, for scenario d) where alpha is 0.05 and the sample size is 16, the critical region is located at x^- ≤^- - 1.74.

In summary, the critical region for hypothesis testing is determined by the level of significance and the sample size. The critical region is located in the tail of the sampling distribution and is determined by the standard deviation and the mean of the sampling distribution. The critical region boundaries for different scenarios of alpha and sample size are provided in the answer above.

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Answer: Nominal Scale Level

Step-by-step explanation:

Data that is measured using a nominal scale is qualitative.

colors, names, labels and favorite foods along with yes or no responses are examples of nominal level data.

Answer:

Hi,so since this is a triangle with a right angle and that equals to 90 degrees

so we have found our second number.

The sum of angles in a triangle is 180 degrees

so that would be 27+90+x=180

i.e 117 +x =180

solve equation i.e 180 -117=63

therefore x=63 degrees

hope this was helpful

Answer:

90+27+63=180

so the answer is:

X= 63

The area of the shaded region in this problem is given as follows:

995.44 cm².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, hence it's measure is given as follows:

r = 21 cm.

Then the area of the entire circle is given as follows:

A = π x 21²

A = 1385.44 cm².

The right triangle has two sides of length 39 cm and 20 cm, hence it's area is given as follows:

A = 0.5 x 39 x 10

A = 390 cm².

Then the area of the shaded region is given as follows:

1385.44 - 390 = 995.44 cm².

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The appropriate probability distribution to use to test the null hypothesis in this scenario is the t distribution. This is because the sample size is small (n = 12) and the population standard deviation is unknown. The t distribution allows for estimation of the population mean based on the sample mean and standard deviation.

To test the null hypothesis for this problem, you should use the t-distribution. Here's an explanation of why:
1. You have a small sample size (n = 12), which is less than 30. When you have a small sample size, the t-distribution is more appropriate than the normal distribution.
2. The data consists of paired samples, with each person using the slicer and not using the slicer. This means you are comparing the mean differences within the paired samples.
3. The problem doesn't involve proportions or frequencies, so the chi-square and binomial distributions are not suitable here.

Based on these reasons, the appropriate probability distribution to use for this problem is the t-distribution (option B).

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Answer:

156cm area of rhombus and 144cm for its diagonal

Step-by-step explanation:

Hope this helps

The sample standard deviation for the given score and frequency is equal to 8.150.

The sample standard deviation for the ,

Calculate the sample mean (X).

X = Σ(x × f) / Σf,

where x = score, f = frequency

Mean X

= (35×1 +45×3 +55×6 + 65×11 +75×13 + 85×10 + 95×2) /(1+3+6+11+13+10+2)

= 35 + 135 + 330 + 715 + 975 + 850 + 190 / 46

= 3230 /46

= 70.2

Calculate the deviation of each score from the mean (x - X).

For 35,  (35 - 70.2) = -35.2

For 45, (45 - 70.2) = -25.2

For 55, (55 - 70.2) = -15.2

For 65, (65 - 70.2) = -5.2

For 75, (75 - 70.2) = 4.8

For 85,(85 - 70.2) = 14.8

For 95, (95 - 70.2) = 24.8

Square each deviation ( (x - X)² ).

For 35, (-35.2)² = 1239.04

For 45, (-25.2)²= 635.04

For 55, (-15.2)² = 231.04

For 65,(-5.2)² = 27.04

For 75,(4.8)² = 23.04

For 85, (14.8)² = 219.04

For 95, (24.8)² = 615.04

Calculate the sum of squared deviations.

Σ(x - X)²

= 1239.04 + 635.04 + 231.04 + 27.04+ 23.04 + 219.04 + 615.04

= 2989.28

Calculate the variance (s²).

s² = Σ(x - X)² / (n - 1)

⇒s²  = 2989.28 / 46 -1

⇒s²  =66.428

Calculate the sample standard deviation (s).

s = √(s²)

⇒s = √(66.428)

⇒ s = 8.150 (rounded to three decimal places)

Therefore, the sample standard deviation for the given data is 8.150.

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Answer:

(m-4)(m+4)

Step-by-step explanation:

If you multiply both and open up it becomes [tex]m^2-4m+4m-16[/tex], simplify to [tex]m^2-16[/tex]

The equation that shows the given relationship is:

105*0.3 = x

We want to write an equation that shows the relationship.

30% of 105 is x.

First, remember that if we take a percentage X of a number N, the expression is:

N*(X/100%).

In this case we are taking the 30% of 105, then the expression is:

105*(30%/100%)

105*0.3

And that must be equal to x, then the equation that we want is:

105*0.3 = x

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Using the midpoint rule with m = 3 and n = 2 subdivisions, the estimate of || sin(ay?)da over the rectangle R = [0,3] x [0,4] is approximately 16.219.

The midpoint rule is a numerical integration method that approximates the value of a definite integral by dividing the integration region into smaller subintervals and approximating the integrand by its value at the midpoint of each subinterval. In this case, we are integrating sin(ay?) over the rectangle R = [0,3] x [0,4], which means that we need to divide the rectangle into m*n subrectangles, each with width 3/m and height 4/n. Then, we can approximate the integral by summing up the contributions of the midpoints of each subrectangle.

In this case, we have m = 3 and n = 2, which means that we need to divide the rectangle into 6 subrectangles, each with width 1 and height 2. The midpoints of the subrectangles are then (0.5,1), (1.5,1), (2.5,1), (0.5,3), (1.5,3), and (2.5,3). Evaluating the integrand at each midpoint, we get the values sin(a*0.5)2, sin(a1.5)2, sin(a2.5)2, sin(a0.5)2, sin(a1.5)2, and sin(a2.5)*2. Summing up these values and multiplying by the area of each subrectangle (2), we get the estimate of 16.219.

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The enlarged photograph will be 30 inches in width and a proportional length.

Marine has a rectangular photograph that measures 6 inches in width. If she wants to enlarge the photograph using a scale of 1:5, this means that the size of the photograph will be increased by a factor of 5 in both width and height.

To determine the new width of the photograph, we can multiply the original width of 6 inches by 5, which gives us a width of 30 inches for the enlarged photograph.

It's important to note that while the width of the photograph will increase, the aspect ratio of the photograph will remain the same.

This means that the length of the photograph will also be increased by the same factor of 5.

Therefore, the enlarged photograph will be 30 inches in width and a proportional length.

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Answer: 0.54

Step-by-step explanation:

13/24 is 0.54166.....

So if you round that by a tenth, it would be 0.54 because 1 is ower than five is its the same

Answer:

0.5

Step-by-step explanation:

13/24 = 0.541666...

by rounding it to the nearest tenth, it will be 0.5 since the succeeding number from the tenth is lower than 5