According to a report on sleep deprivation by the Centers for Disease Control and Prevention, the proportion of California residents who reported insucient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for Oregon residents. These data are based on simple random samples of 11,545 California and 4,691 Oregon residents. Calculate a 95% con dence interval for the di erence between the proportions of Californians and Oregonians who are sleep deprived and interpret it in context of the data.

Answer:

(a) The 80% confidence interval for the population mean nitrate concentration is (0.648, 0.692).

(b) The critical value of t that should be used in constructing the 80% confidence interval is 1.345.

Step-by-step explanation:

Let X = nitrate concentration.

The sample mean nitrate concentration is, [tex]\bar x=0.670[/tex] cc/cubic meter.

The sample standard deviation of the nitrate concentration is, [tex]s=0.0616[/tex].

It assumed that the population is approximately normal.

And since the population standard deviation is not known, we will use a t-interval.

The (1 - α)% confidence interval for population mean (μ) is:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

(a)

The critical value of t for α = 0.20 and degrees of freedom, (n - 1) = 14 is:

[tex]t_{\alpha/2, (n-1)}=t_{0.20/2, (15-1)}=t_{0.10, 14}=1.345[/tex]

*Use a t-table for the critical value.

Compute the 80% confidence interval for the population mean nitrate concentration as follows:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

     [tex]=0.670\pm 1.345\times \frac{0.0616}{\sqrt{15}}[/tex]

     [tex]=0.670\pm 0.022\\=(0.648, 0.692)\\[/tex]

Thus, the 80% confidence interval for the population mean nitrate concentration is (0.648, 0.692).

(b)

The critical value of t for confidence level (1 - α)% and (n - 1) degrees of freedom is:

[tex]t_{\alpha/2, (n-1)}[/tex]

The value of  is:

α = 0.20

And the degrees of freedom is,

(n - 1) = 15 - 1 = 14

Compute the critical value of t for confidence level 80% and 14 degrees of freedom as follows:

[tex]t_{\alpha/2, (n-1)}=t_{0.20/2, (15-1)}[/tex]

               [tex]=t_{0.10, 14}\\=1.345[/tex]

*Use a t-table for the critical value.

Thus, the critical value of t that should be used in constructing the 80% confidence interval is 1.345.

Answer:

d. She should reject the null hypothesis because p < 0.10.

Step-by-step explanation:

We have a t statistic, so let's solve for the P-value on our calculators. (tcdf on a TI-84 calculator is 2nd->VARS->6.)

tcdf(left bound, right bound, degrees of freedom)

tcdf(1.457,999,14) = .084

.084 < P-value of .10, so we reject the null hypothesis.

Lola's conclusion should be "She should reject the null hypothesis because p< 0.10". Option D is correct.

Given information:

Lola is using a one-sample t-test for a population mean, µ, to test the null hypothesis.

[tex]\mu=40[/tex]

Sample random size is, [tex]n=15[/tex].

The value of the one-sample t-statistic is [tex]t=1.457[/tex].

The left bound will be [tex]t=1.457[/tex] and the value of [tex]n-1[/tex] will be 15-1=14.

Now, use the calculator to find the value of p. The found value of p will be,

[tex]p=0.084[/tex]

So, the value of p is less than 0.1.

Therefore, Lola's conclusion should be "She should reject the null hypothesis because p< 0.10". Option D is correct.

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Answer:

B on edge 2020

Step-by-step explanation:

Applying [tex]\[M_f = M_n \cdot M_{n-1} \cdot ... \cdot M_3 \cdot M_2 \cdot M_1\][/tex] final transformation matrix to the pre-image GHJK [tex](\(P\))[/tex], we get the image G'H''J''K''.

To determine the final transformation that maps the pre-image GHJK to the image G'H''J''K'', we need to break down the transformations and apply them in the correct order.

Let's assume there are several transformations involved, such as translations, rotations, reflections, or dilations. Each transformation can be represented by a matrix or a set of rules.

Let's denote the initial pre-image GHJK as [tex]\(P\).[/tex] The series of transformations can be represented as [tex]\(T_1 \cdot T_2 \cdot T_3 \cdot ... \cdot T_n\)[/tex], where [tex]\(T_1\) to \(T_n\)[/tex] are individual transformations.

To find the final transformation, we need to multiply the matrices representing these transformations in the reverse order. If [tex]\(M_1, M_2, M_3, ..., M_n\)[/tex] are the matrices representing [tex]\(T_1, T_2, T_3, ..., T_n\)[/tex]respectively, the final transformation matrix [tex]\(M_f\)[/tex] would be:

[tex]\[M_f = M_n \cdot M_{n-1} \cdot ... \cdot M_3 \cdot M_2 \cdot M_1\][/tex]

Applying this final transformation matrix to the pre-image GHJK [tex](\(P\))[/tex], we get the image G'H''J''K''.

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Answer:

C,H,I..............

Answer:

54

Step-by-step explanation:

6(6)+3(9)-9

=54

Answer:

54

Step-by-step explanation:

First, since it's given the x and y values, you need to plug them in.

6(6) + 3(9) - 9

36 + 27 - 9

63 - 9

54

Answer:

Therefore profit function is increasing on the interval (0,3200)

Step-by-step explanation:

The cost function of the manufacturer C(x) is given as:

[TeX]C(x)= 0.17x^{2}-0.00016x^{3}[/TeX]

The Revenue function is also given as:

[TeX]R(x)= 0.362x^{2}-0.0002x^{3}[/TeX]

Profit=Revenue-Cost

Therefore:

P(x)=R(x)-C(x)

[TeX]= 0.362x^{2}-0.0002x^{3}-[0.17x^{2}-0.00016x^{3}][/TeX]

[TeX]= 0.362x^{2}-0.0002x^{3}-0.17x^{2}+0.00016x^{3}[/TeX]

The Profit Function, [TeX]P(x)= 0.192x^{2}-0.00004x^{3}[/TeX]

To determine the point where the function is increasing, we take the derivative and examine it's critical points.

The derivative of the profit function is:

[TeX]P^{'}(x)= 0.384x-0.00012x^{2}[/TeX]

Set the derivative equal to zero.

[TeX]0.384x-0.00012x^{2}=0[/TeX]

[TeX]x(0.384x-0.00012x)=0[/TeX]

x=0 or [TeX]0.384-0.00012x=0[/TeX]

x=0 or [TeX]0.384=0.00012x[/TeX]

x=0 or x=3200

Now let's choose 2000 and 4000 as test points.

[TeX]P^{'}(2000)= 0.384(2000)-0.00012(2000)^{2}=288[/TeX]

[TeX]P^{'}(4000)= 0.384(4000)-0.00012(4000)^{2}=-384[/TeX]

Therefore profit function is increasing on the interval (0,3200)

Answer:

The is profit function is increasing on (0, 3200).

Step-by-step explanation:

Given

C(x) = 0.17x² - 0.00016x³

R(x) = 0.362x² - 0.0002x³

The profit function is given by

P(x) = R(x) - C(x)

P(x) = (0.362x² - 0.0002x³) - (0.17x² - 0.00016x³)

P(x) = 0.362x² - 0.0002x³ - 0.17x² + 0.00016x³

P(x) = 0.192x² - 0.00004x³

The derivative of the profit function is given by

P'(x) = 0.384x - 0.00012x²

Determine the critical number of P(x) to get interval where the profit function is increasing,

Set P'(x) = 0

0.384x - 0.00012x² = 0

x(0.384 - 0.00012x) = 0

x = 0 or 0.384 - 0.00012x = 0

0.384 - 0.00012x = 0

x = 0.384/0.00012 = 3200

Therefore the is profit function is increasing on (0, 3200)

Answer:

136

Step-by-step explanation:

Take 68 x 2 since the side lengths are equal.

Given the properties of isosceles triangle, where congruent sides have equal opposite angles, and that the given angle ∠SUT = 68°, it implies that ∠TUV also equals 68°.

The question involves the principles of geometry, specifically the properties of angles and congruent lines. Given that ST≅SV and m∠SUT = 68°, it means that these two line segments are equal in length and that the angle of SUT is 68 degrees.

Since ST and SV are congruent in an isosceles triangle, the angles opposite these sides are equal. Hence, the measure of ∠SUT and ∠TUV are equal. We know m∠SUT = 68°, so therefore, m∠TUV = 68°.

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Answer:

[tex]a) \ H_o:\hat p_f=\hat p_m\\\ \ \ H_a:\hat p_f\neq \hat p_m\\\\b) z\ test=2.925, \ p\ value(two-tail)=0.003444\\\\\\[/tex]

c)  Reject  H_o  since there is sufficient evidence to suggest that there is difference between males and females with respect to how they feel about this issue.

d. No. Interval does not include zero

e. [tex]CI=[0.01044<(\hat p_f-\hat p_m)<0.05576[/tex]

We are 95% confident that the proportional difference lies between the [0.010444,0.05576] interval.

Step-by-step explanation:

a. The null hypothesis is that there is no difference between males and females with respect to how they feel about this issue:

[tex]H_o:p_m=p_f[/tex]

-The alternative hypothesis is that there is some difference between males and females with respect to how they feel about this issue:

[tex]H_a:p_m\neq p_f[/tex]

where [tex]p_m, \ p_f[/tex] is the proportion of males and females respectively.

b. The proportion of males and females in the study can be calculated as follows:

[tex]\hat p=\frac{x}{n}\\\\\hat p_f=\frac{1729}{1913}=0.9038\\\\\hat p_m=\frac{1111}{1276}=0.8707[/tex]

[tex]\hat p=\frac{x_f+x_m}{n_m+n_f}=\frac{1111+1729}{1276+1913}=0.8906[/tex]

#We then calculate the test statistic using the formula:

[tex]z=\frac{(\hat p_f-\hat p_m)}{\sqrt{\hat p(1-\hat p)(\frac{1}{n_f}+\frac{1}{n_m})}}\\\\\\=\frac{(0.9038-0.8707)}{\sqrt{(0.8906\times0.1094)(\frac{1}{1913}+\frac{1}{1276})}}\\\\\\=2.9250\\\\\therefore p-value=0.001722\\[/tex]

[tex]\# The \ two \ tail \ p-value \ is\\\\=0.01722\times 2\\\\=0.003444[/tex]

c. Since p<0.05:

[tex]p<0.05\\\\0.00344<0.05\\\\\therefore Reject \ H_o[/tex]

Hence, we Reject the Null Hypothesis since there is sufficient evidence to suggest that there is difference between males and females with respect to how they feel about this issue

d. The 95% confidence interval can be calculated as below:

[tex]CI=(p_f-p_m)\pm z_{\alpha/2}\sqrt{\frac{\hat p_m(1-\hat p_m)}{n_m}+\frac{\hat p_f(1-\hat p_f)}{n_f}}\\\\=(0.9038-0.8707)\pm 1.96\sqrt{0.00008823+0.000045449}\\\\=0.03310\pm 0.02266\\\\=[0.01044,0.05576][/tex]

Hence, the confidence interval does not include  0

e. The 95% confidence interval calculated from above is :

[tex]0.01044<(p_f-p_m)<0.05576[/tex]

Hence, we are 95% confident that the proportional difference will fall between the interval [tex]0.01044<(\hat p_f-\hat p_m)<0.05576[/tex]

There are 12 valid arrangements for Sunhee to line up the four plastic shapes so that the circle is not next to the square.

In how many ways can Sunhee line up four plastic shapes (a square, a circle, and a pentagon) if the circle cannot be next to the square?

To solve this problem, we can count the total number of ways to arrange the shapes and then subtract the cases where the circle is next to the square.

1. Total ways to arrange the shapes:

Answer:

54.98 degrees.

Step-by-step explanation:

In the diagram, the sides of the A-Frame are lengths AB and BC. The width of the cabin is length BC. We are to determine the measure of the angle at B, i.e. the angle between the two sides of the roof.

Using Cosine Rule:

[tex]b^2=a^2+c^2-2acCos B\\Cos B=\dfrac{b^2-a^2-c^2}{-2ac} \\B=arcCos(\dfrac{b^2-a^2-c^2}{-2ac} )\\a=26, b=24, c=26\\B=arcCos(\dfrac{24^2-26^2-26^2}{-2*26*26} )\\=arcCos 0.5739\\B=54.98^0[/tex]

The angle in between the two sides of the roof is 54.98 degrees.

To find the angle between the two sides of the roof of an A-frame cabin, we can use trigonometry and the Pythagorean theorem. The angle is approximately 22.33°.

To determine the angle between the two sides of the roof of an A-frame cabin, we can use trigonometry. Since the sides of the roof are both 26 feet long and the base of the cabin is 24 feet wide, we can consider the A-frame cabin as a right triangle. The roof line forms the hypotenuse of the triangle, and the sides of the triangle represent the rafters of the A-frame roof.

Using the Pythagorean theorem, we can find the height of the triangle (which is the distance from the base of the cabin to the point where the roof meets): h^2 = 26^2 - 12^2 = 676 - 144 = 532.

Taking the square root of both sides gives us h ≈ 23.07 feet.

Now, we can determine the angle by using trigonometric functions.

The sine function relates the opposite side (the height) to the hypotenuse (the roof line). So, sin(θ) = h / 26, where θ is the angle we want to find. Solving for θ gives us θ ≈ 22.33°.

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Answer:

(-8-3)/(-8+10)= -11/2

y - 3 = -11/2(x+10)

y-3=-11/2x-55

y=-11/2x-52

Step-by-step explanation:

Answer:

fernando is 45 inches tall, and jasmine is 40 inches tall

Step-by-step explanatin

60 divided by 3/4 is 45, 45 divided by 8/9 is 40

Fernando is 45 inches tall, and Jasmine is 40 inches tall.

Emily is 60 inches tall. Fernando is 3/4 of Emily's height:

(60 inches x 3/4 = 45 inches).

Jasmine is 8/9 of Fernando's height:

(45 inches x 8/9 = 40 inches).

To solve the equation x - 6 = 14, the first step is to isolate the variable 'x'. You do this by adding 6 to both sides of the equation, which results in x = 14 + 6. Therefore, 'x' equals 20.

The subject of this question is Mathematics, and it is focusing on solving a basic algebraic equation: x - 6 = 14. When you are asked to solve an equation, you're figuring out what numbers you can replace the variable with to make the equation true. In this case, the variable is 'x', and your goal is to find what number 'x' stands for. The first step to solve the equation is to isolate 'x'. This means you want 'x' to stand alone on one side of the equation. To accomplish this, you need to perform the same operation on both sides of the equation to maintain equality. Here, you would add 6 to both sides of the equation (opposite of subtracting 6), which simplifies to: x = 14 + 6. So, 'x' equals 20.

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Answer:

128.86 square cm

Step-by-step explanation:

Area of shaded region = Area of rectangle - Area of circle

[tex] = 11 \times 12 - \pi {r}^{2} \\ = 132 - 3.14 \times {1}^{2} \\ = 132 - 3.14 \\ = 128.86 \: {cm}^{2} \\ [/tex]

Answer:

128.86

Step-by-step explanation:

Answer:

  m = 57

Step-by-step explanation:

If we assume your equation is supposed to be ...

  512 = (m +7)^(3/2)

we can raise both sides to the 2/3 power to get ...

  512^(2/3) = m +7

  64 = m +7

  57 = m . . . . . . subtract 7

Answer:

The 95% CI is (6.93% , 7.47%)

The 99% CI is (6.85% , 7.55%)

Step-by-step explanation:

We have to estimate two confidence intervals (95% and 99%) for the population mean 30-year fixed mortgage rate.

We know that the population standard deviation is 0.7%.

The sample mean is 7.2%. The sample size is n=26.

The z-score for a 95% CI is z=1.96 and for a 99% CI is z=2.58.

The margin of error for a 95% CI is

[tex]E=z\cdot \sigma/\sqrt{n}=1.96*0.7/\sqrt{26}=1.372/5.099=0.27[/tex]

Then, the upper and lower bounds are:

[tex]LL=\bar x-z\cdot\sigma/\sqrt{n}=7.2-0.27=6.93\\\\ UL=\bar x+z\cdot\sigma/\sqrt{n} =7.2+0.27=7.47[/tex]

Then, the 95% CI is

[tex]6.93\leq x\leq 7.47[/tex]

The margin of error for a 99% CI is

[tex]E=z\cdot \sigma/\sqrt{n}=2.58*0.7/\sqrt{26}=1.806/5.099=0.35[/tex]

Then, the upper and lower bounds are:

[tex]LL=\bar x-z\cdot\sigma/\sqrt{n}=7.2-0.35=6.85\\\\ UL=\bar x+z\cdot\sigma/\sqrt{n} =7.2+0.35=7.55[/tex]

Then, the 99% CI is

[tex]6.85\leq x\leq 7.55[/tex]

Answer:

Area = 20 ft²

Step-by-step explanation:

Area of a thrombus

½ × d1 × d2

½ × 5 × 8

20

Answer:

20 ft squared

Step-by-step explanation:

The area of a rhombus can be calculated by multiplying its diagonals by each other and then halving that product: A = [tex]\frac{1}{2} d_1d_2[/tex]

Here, we know that [tex]d_1[/tex] = 5 and [tex]d_2[/tex] = 8. So, we have the equation: A = [tex]\frac{1}{2} *5*8=(1/2)*40=20[/tex]

Thus, the area is 20 ft squared.

Hope this helps!

Answer:

7 jars per box

Step-by-step explanation:

He now has 41 jars. How many did he have before his teacher gave him 6?

Well, 41-6=35. He had 35 jars before his teacher gave him more.

It says there was an equal amount of jars in each box. There are 5 boxes. Divide the total amount of jars (35) by the amount of boxes to find out how many jars are in each box.

35 jars / 5 boxes = 7 jars / box

Answer:

English plz

Step-by -step explanation:

what dose this say

El condenado sobrevivió al destruir una de las 'papeletas de muerte' sin leerla, y utilizar la ley del Sultán a su favor para afirmar que su 'papeleta de muerte' destruida era la 'papeleta de vida'.

El reo aseguró su supervivencia actuando de manera astuta. Sabiendo que ambas papeletas tenían la palabra muerte, decidió escoger una y, sin leerla, la destruyó por completo. Entonces solicitó que se leyera la papeleta restante, si en la papeleta restante dice muerte, entonces es obvio que la papeleta que destruyó debía tener la sentencia de vida, ya que según el Sultán, el Gran Visir hizo dos papeletas diferentes. De esta manera, aunque el Gran Visir deseaba que obtuviera la sentencia de muerte, el reo se salvó por su astucia sin necesidad de revelar el complot del Visir.

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Answer:

[tex]\frac{5}{3}x^3+\frac{9}{2}x^2-7x+8\\[/tex]

Step-by-step explanation:

Integrate your function with respect to x to get the non-differentiated form.

[tex]\int(5x^2+9x-7)dx=\frac{5}{3}x^3+\frac{9}{2}x^2-7x+c\\[/tex]

Plug in your known value of x to get your value for your constant

[tex]f(0) = 8\\ \frac{5}{3}(0^3)+\frac{9}{2}(0^2)-7(0)+c = 8 \\c=8[/tex]

This gives you your function to be

[tex]\frac{5}{3}x^3+\frac{9}{2}x^2-7x+8\\[/tex]

To find f such that f'(x) = 5x² + 9x - 7 and f(0) = 8, integrate the given function and solve for the constant of integration using the given condition. The resulting equation is f(x) = (5/3)x³ + (9/2)x² - 7x + 8.

To find f such that f'(x) = 5x² + 9x - 7 and f(0) = 8, we need to integrate f'(x) to find the equation for f(x). Let's find the antiderivative of 5x² + 9x - 7, which is  (5/3)x³ + (9/2)x² - 7x + C. To determine the value of C, we can use the given condition f(0) = 8. Substituting x = 0 into the equation, we get 8 = (5/3)(0)³ + (9/2)(0)² - 7(0) + C. Solving for C, we find that C = 8. Therefore, the equation for f(x) is f(x) = (5/3)x³ + (9/2)x² - 7x + 8.

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Step-by-step explanation:

I hope this is what you need

PLEASE MAKE ME BRAINLIEST

The solution of the inequality -14.5 < x represents graph which is correct option C

What is inequality?

Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.

-14.5 < x

x > -14.5

A number line going from negative 15 to negative 11. An open circle is at negative 14.5. Everything to the right of the circle is shaded.

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Answer:

a) Binomial distribution, with n=20 and p=0.10.

b) P(x>1) = 0.6082

c) P(3≤X≤5) = 0.3118

d) E(X) = 2

e) σ=1.34

Step-by-step explanation:

a) As we have a constant "defective" rate for each unit, and we take a random sample of fixed size, the appropiate distribution to model this variable X is the binomial distribution.

The parameters of the binomial distribution for X are n=20 and p=0.10.

[tex]X\sim B(0.10,20)[/tex]

b) The probability of k defective surge protectors is calculated as:

[tex]P(x=k) = \binom{n}{k} p^{k}q^{n-k}[/tex]

In this case, we want to know the probability that more than one unit is defective: P(x>1). This can be calculated as:

[tex]P(x>1)=1-(P(0)+P(1))\\\\\\P(x=0) = \binom{20}{0} p^{0}q^{20}=1*1*0.1216=0.1216\\\\P(x=1) = \binom{20}{1} p^{1}q^{19}=20*0.1*0.1351=0.2702\\\\\\ P(x>1)=1-(0.1216+0.2702)=1-0.3918=0.6082[/tex]

c) We have to calculate the probability that the number of defective surge protectors is between three and five: P(3≤X≤5).

[tex]P(3\leq X\leq 5)=P(3)+P(4)+P(5)\\\\\\P(x=3) = \binom{20}{3} p^{3}q^{17}=1140*0.001*0.1668=0.1901\\\\P(x=4) = \binom{20}{4} p^{4}q^{16}=4845*0.0001*0.1853=0.0898\\\\P(x=5) = \binom{20}{5} p^{5}q^{15}=15504*0*0.2059=0.0319\\\\\\P(3\leq X\leq 5)=P(3)+P(4)+P(5)=0.1901+0.0898+0.0319=0.3118[/tex]

d) The expected number of defective surge protectors can be calculated from the mean of the binomial distribution:

[tex]E(X)=\mu_B=np=20*0.10=2[/tex]

e) The standard deviation of this binomial distribution is:

[tex]\sigma=\sqrt{np(1-p)}=\sqrt{20*0.1*0.9}=\sqrt{1.8}=1.34[/tex]

Answer:

She has completed 2/3 of the poster

Explanation:

1/3 of the poster the first day

+

1/3 of the poster the next day

1/3 + 1/3 = 2/3

4x - 2y = 7

x + 2y =  3

5x = 10

x=2 and y=0

Answer:

{x,y} = {2,1/2}

Step-by-step explanation:

Solve by Substitution :

1. Solve equation [2] for the variable  x  

 [2]    x = -2y + 3

2. Plug this in for variable  x  in equation [1]

  [1]    4•(-2y+3) - 2y = 7

  [1]     - 10y = -5

3.Solve equation [1] for the variable  y  

  [1]    10y = 5

  [1]    y = 1/2

By now we know this much :

   x = -2y+3

   y = 1/2

4.Use the  y  value to solve for  x  

   x = -2(1/2)+3 = 2

Solution :

{x,y} = {2,1/2}

Answer:

its a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

Formula:

[tex]a^{2} + b^{2} = c^{2}[/tex]

Answer:

The GPA for this transcript is:

GPA = 2.73

Step-by-step explanation:

A=4, B=3, C=2, D=1, F=0

Sociology: 3cr: A, Biology: 4cr: C, Music 1cr: B, Math 4cr:B, English 3cr: C

Total number of credit hour = 3 + 4 + 1 + 4 + 3 = 15

Product for each course = the number of credit hours for a course * the number assigned to each grade

Sociology = 3 * 4 = 12

Biology = 4 * 2 = 8

Music = 1 * 3 = 3

Math = 4 * 3 = 12

English = 3 * 2 = 6

Total product = 12 + 8 + 3 + 12 + 6 = 41

GPA = Sum of product / Total credit hour

GPA = 41 / 15 = 2.7333333

GPA = 2.73

Answer:

The results is 2.73.

Step-by-step explanation:

First let's make the calculations for each course;

For Sociology, an A (which is 4) for 3 credits equals to 12.

For Biology, a C (which is 2) for 4 credits equals to 8.

For Music, a B (which is 3) for 1 credit equals to 3.

For Math, a B (which is 3) for 4 credits equals to 12.

For English, a C (which is 2) for 3 credits equals to 6.

If we sum them all up, we find the results to be 41 and the total credits to be 15 for the 5 courses.

Lastly we should divide 41/15 which will be equal to 2.73 which is the GPA.

I hope this answer helps.

Answer:

a) The differential equation is:  [tex]\frac{dm}{dt} =r\,m[/tex]

with initial condition: [tex]m(0)=1\,\,kg[/tex]

b) m(t) =\,1\,\,kg\,\,e^{r\,t}

c)  r=-0.22314

d) Same differential equation, but the solution function would have a different value for "r" resultant from dividing by 60:[tex]\frac{ln(0.8)}{60} =r\\r=-0.003719[/tex]

Step-by-step explanation:

Part a)

The differential equation is:  [tex]\frac{dm}{dt} =r\,m[/tex]

with initial condition: [tex]m(0)=1\,\,kg[/tex]

Part b)

The solution for a function whose derivative is a multiple of the function itself, must be associated with exponential of base "e":

[tex]m(t) =\,A\,e^{r\,t}[/tex]   with [tex]A = m(0) = 1\,\,kg[/tex]

So we can write the function as: [tex]m(t) =\,1\,\,kg\,\,e^{r\,t}[/tex]

Part c)

To find the constant "r", we use the information given on the amount of substance left after one hour (0.8 kg) by using t = 1 hour, and solving for "r" in the equation:

[tex]m(t) =\,1\,\,kg\,\,e^{r\,t}\\m(1) =\,1\,\,kg\,\,e^{r\,(1)}\\0.8\,\,kg=\,1\,\,kg\,\,e^{r\,(1)}\\0.8=e^{r\,(1)}\\ln(0.8)=r\\r=-0.22314[/tex]

where we have rounded the answer to the 5th decimal place. Notice that this constant "r" is negative, associated with a typical exponential decay.

Part d)

The differential equation if we measure the time in minutes would be the same, but its solution would have a different constant "r" given by the answer to the amount of substance left after 60 minutes have elapsed:

[tex]m(t) =\,1\,\,kg\,\,e^{r\,t}\\m(1) =\,1\,\,kg\,\,e^{r\,(60)}\\0.8\,\,kg=\,1\,\,kg\,\,e^{r\,(60)}\\0.8=e^{r\,(60)}\\\frac{ln(0.8)}{60} =r\\r=-0.003719[/tex]

Given:

The base of the triangle = 8.6 yd

The height of the triangle = 10.9 yd

To find the area of the triangle.

Formula

The area of a triangle with b as base and h as height is

[tex]A=\frac{1}{2}bh[/tex]

Now,

Taking, b= 8.6 and h = 10.9 we get,

[tex]A=\frac{1}{2}(8.6)(10.9)[/tex] sq yd

or, [tex]A= 46.87[/tex] sq yd

Hence,

The area of the given triangle is 46.87 sq yd.

Answer:

46.87 yd^2

Step-by-step explanation:

The area of the triangle is given by

A = 1/2 bh

A = 1/2 (8.6)(10.9)

A =46.87 yd^2

Answer:

0.62% probability that a ski resort averages more than 3,000 customers per weekday over the course of four weekdays

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 2000, \sigma = 800, n = 4, s = \frac{800}{\sqrt{4}} = 400[/tex]

Trobability a ski resort averages more than 3,000 customers per weekday over the course of four weekdays.

This is 1 subtracted by the pvalue of Z when X = 3000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{3000 - 2000}{400}[/tex]

[tex]Z = 2.5[/tex]

[tex]Z = 2.5[/tex] has a pvalue of 0.9938

1 - 0.9938 = 0.0062

0.62% probability that a ski resort averages more than 3,000 customers per weekday over the course of four weekdays