How do you find the median with an odd number of values?

To find the area of the surface generated by revolving the curve about the x-axis, you need to evaluate the definite integral of the square of the given function within the specified interval.

Definite integral representing the area:

Given curve: y = 81 - x^2, -5 ≤ x ≤ 5

Revolving this curve about the x-axis generates a surface. The definite integral representing the area is obtained by integrating the square of the function and applying the limits of integration.

The total area of the regions between the curves is 726 square units

Calculating the total area of the regions between the curves

From the question, we have the following parameters that can be used in our computation:

y = 81 - x²

Also, we have the interval to be

−5 ≤ x ≤ 5

So, the area of the regions between the curves is

Area = ∫y dx

This gives

Area = ∫(81 - x²) dx

Integrate

Area =  81x - x³/3

Recall that  −5 ≤ x ≤ 5

So, we have

Area =  |[81(-5) - (-5)³/3] - [81(5) - (5)³/3]|

Evaluate

Area =  726

Hence, the total area of the regions between the curves is 726 square units

The microphone, which is at the focal point of a parabolic microphone, should be placed 5 inches from the vertex of the parabola since the parabola is 40 inches wide and 20 inches deep.

The question deals with a parabolic shape and requires using the properties of a parabola to determine the position of the focal point. In the context of a parabolic microphone, the focal point is where the microphone should be placed to best capture sounds. For a parabola given in the form y = 4px, where p is the distance from the vertex to the focus, and the parabola is 40 inches wide (which is the distance from one end of the parabola to the other at the given depth) and 20 inches deep (which is the distance from the vertex to the directrix), we can find p, using the relationship depth = p. Since the depth is 20 inches, the focus (and thus where the microphone should be placed) is 20/4 = 5 inches from the vertex of the parabola.

Answer:

Step-by-step explanation:

Answer:

110 utensils

Step-by-step explanation:

Set up equal fractions, and cross-multiply.

[tex]\frac{22 forks}{33 spoons} = \frac{44 forks}{x spoons}[/tex]

Solve for spoons.

22x = 44*33

22x = 1452

x = 1452/22 = 66 spoons

Now add forks and spoons to get total utensils:

44 forks + 66 spoons = 110 utensils

Answer:

There would be 73 utensils altogether.

Step-by-step explanation:

We have the ratio 22:33 and x:44

in order to determine x we need to divide 44 by 22 which leaves us with 1.33333 or 1 and 1/3

we then need to multiply 22 by our quotient of 1.333 in which leaves us with 29.

so x=29

We then have to add 44 and 29 which leaves us with 73;)

Answer:

12

Step-by-step explanation:

Answer:

a) If Y is distributed N(1, 4), Pr (Y ≤ 3) = 0.84134

b) If Y is distributed N(3, 9), Pr (Y > 0) = 0.84134

c) If Y is distributed N(50, 25), Pr (40 ≤ Y ≤ 52) = 0.63267

d) If Y is distributed N(5, 2), find Pr (6 ≤ Y ≤ 8) = 0.22185

Step-by-step explanation:

With the logical assumption that all of these distributions are normal distribution,

a) Y is distributed N(1, 4), find Pr ( Y ≤ 3 )

Mean = μ = 1

Standard deviation = √(variance) = √4 = 2

To find the required probability, we first standardize 3

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (y - μ)/σ = (3 - 1)/2 = 1

We'll use data from the normal probability table for these probabilities

The required probability

Pr ( Y ≤ 3 ) = P(z ≤ 1) = 0.84134

b) If Y is distributed N(3, 9), find Pr ( Y > 0 )

Mean = μ = 3

Standard deviation = √(variance) = √9 = 3

To find the required probability, we first standardize 0

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (y - μ)/σ = (0 - 3)/3 = -1

We'll use data from the normal probability table for these probabilities

The required probability

Pr ( Y > 0) = P(z > -1) = 1 - P(z ≤ -1) = 1 - 0.15866 = 0.84134

c) If Y is distributed N(50, 25), find Pr (40 ≤ Y ≤ 52).

Mean = μ = 50

Standard deviation = √(variance) = √25 = 5

To find the required probability, we first standardize 40 and 52.

For 40,

z = (y - μ)/σ = (40 - 50)/5 = -2

For 52,

z = (y - μ)/σ = (52 - 50)/5 = 0.4

We'll use data from the normal probability table for these probabilities

The required probability

Pr (40 ≤ Y ≤ 52) = P(-2.00 ≤ z ≤ 0.40)

= P(z ≤ 0.40) - P(z ≤ -2.00)

= 0.65542 - 0.02275

= 0.63267

d) If Y is distributed N(5, 2), find Pr ( 6 ≤ Y ≤ 8 )

Mean = μ = 5

Standard deviation = √(variance) = √2 = 1.414

To find the required probability, we first standardize 6 and 8.

For 6,

z = (y - μ)/σ = (6 - 5)/1.414 = 0.71

For 8,

z = (y - μ)/σ = (8 - 5)/1.414 = 2.12

We'll use data from the normal probability table for these probabilities

The required probability

Pr (6 ≤ Y ≤ 8) = P(0.71 ≤ z ≤ 2.12)

= P(z ≤ 2.12) - P(z ≤ 0.71)

= 0.983 - 0.76115

= 0.22185

Hope this Helps!!

Answer:

a) The value of N(1, 4) = 0.8413

b) The probability of N(3, 9) = 0.8413

ci) The probability (40≤ Y≤ 52) = 0.4

cii) The probability of N (3, 9) = 0.6236

d) The probability of (6≤Y≤8) = 0.2216

Step-by-step explanation:

Detailed step by step explanation is given in the attached document.

A normal distribution is a bell shaped symmetric distribution. This kind of distribution has a normal probability density function. A standard normal distribution is the one that has a mean 0 and variance of 1. It is often denoted as N (0, 1). If a general variance and mean are given and one has to look up probabilities in a normal probability distribution. The variable is standardized first. Standardizing a variable involves subtracting the general mean from the standard and then dividing the result by 1. In order to find the probabilities, the value of z is located in a normal distribution table.

This problem involves conducting a hypothesis test, stating the null hypothesis as 78% or fewer readers own a personal computer, and the alternative hypothesis as more than 78% own one. A statistical test (like a z-test) is needed to compare the p-value to the 0.01 significance level. The publisher's claim is supported if the p-value is less than 0.01.

In this context, we are conducting a hypothesis test to examine a newsletter publisher's claim about their audience's computer ownership. The null and alternative hypotheses would therefore be set up as follows:

Null Hypothesis (H0): p <= 0.78, meaning 78% or fewer readers own a personal computer.

Alternative Hypothesis (Ha): p > 0.78, meaning more than 78% of readers own a personal computer.

We can conduct a hypothesis test to prove or disprove this using statistical methods such as a z-test and by comparing the p-value to the significance level (0.01 in this case). If the p-value obtained from the test is less than 0.01, we can reject the null hypothesis providing sufficient evidence to support the publisher's claim. If not, we fail to reject the null hypothesis which means the evidence is insufficient.

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Given:

The width of the snack box is [tex]1 \frac{1}{2} \ inches=\frac{3}{2} \ inches[/tex]

The length of the snack box is [tex]2 \frac{1}{2} \ inches=\frac{5}{2} \ inches[/tex]

The height of the snack box is 4 inches.

We need to determine the volume of the hamsta snack box.

Volume of the box:

The volume of the box can be determined using the formula,

[tex]V=L \times W \times H[/tex]

where L is the length, W is the width and H is the height of the box.

Substituting the values, we get;

[tex]V=4 \times \frac{3}{2} \times \frac{5}{2}[/tex]

Simplifying, we get,

[tex]V=\frac{60}{4}[/tex]

[tex]V=15 \ in^3[/tex]

Thus, the volume of the Hamsta snack box is 15 cubic inches.

Answer:

15

Step-by-step explanation:

i did the test and got 100

Answer:

196.6 feet

Step-by-step explanation:

Draw the right triangle formed by the zip-line.  Use SOH-CAH-TOA to write and solve an equation:

tan 11.5° = 40 / x

x = 40 / tan 11.5°

x = 196.6

The horizontal distance between the towers is 196.60 ft.

Distance is the measurement of an object from a specific point in the horizontal direction, and height is the measurement of an object in the vertical direction.

Here, ∅₁ is called the angle of elevation and ∅₂ is called the angle of depression. For one specific type of problem in height and distances, we have a generalized formula. Height = Distance moved / [cot(original angle) – cot(final angle)] => h = d / (cot ∅₁ – cot ∅₂)

Given:

The vertical height of the zip line = 40 ft

The angle of elevation = 11.5°

We know, according to trigonometric values tan n = height / base

∴ tan 11.5 = 40 / base

base = 40/ tan 11.5

base = 40 / 0.203

base = 196. 60 ft

Therefore, the horizontal distance between the towers is 196.60 ft.

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Answer: -4x⁴ + x² + 6

Step-by-step explanation:

Remove parentheses:   (-a) = -a

-4x⁴ + 6x²+3 - (5x²-3)

-4x⁴ + 6x² + 3 - 5x² + 3

Simplify -4x⁴+ 6x² + 3 - 5x² + 3:   -4x⁴ + x² + 6

-4x⁴ + x² + 6

Answer:

9

Step-by-step explanation:

In order to figure this out, I made the proportion:

[tex]\frac{300}{x} =\frac{100}{3}[/tex]

Multiply 3 by 300 and x by 100

300*3=?

x*100=?

900=100x

Divide 900 by 100 to find x

900÷100=9

x=9

Answer:

Check the explanation

Step-by-step explanation:

Given that:

The National Institutes of Health has recommended that the healthy adults are to take at least 50 nmol/L of vitamin D per day. Let’s assume that you are interested in discovering if the BSU students are suffering from vitamin D deficiency or not.

a) Formulate the appropriate null and alternative hypotheses

Null hypothesis

H o : u >= 50

Alternative hypothesis

Ha : u < 50

Answer:

a) The distance from the television camera to the rocket is changing at that moment at a speed of

600 ft/s

b) the camera's angle of elevation is changing at that same moment at a rate of

0.16 rad/s = 9.16°/s

Step-by-step explanation:

This is a trigonometry relation type of problem.

An image of when the rocket is 3000 ft from the ground is presented in the attached image.

Let the angle of elevation be θ

The height of the rocket at any time = h

The distance from the camera to the rocket = d

a) At any time, d, h and the initial distance from the camera to the rocket can be related using the Pythagoras theorem.

d² = h² + 4000²

Take the time derivative of both sides

(d/dt) (d²) = (d/dt) [h² + 4000²]

2d (dd/dt) = 2h (dh/dt) + 0

At a particular instant,

h = 3000 ft,

(dh/dt) = 1000 ft/s

d can be obtained using the same Pythagoras theorem

d² = h² + 4000² (but h = 3000 ft)

d² = 3000² + 4000²

d = 5000 ft

2d (dd/dt) = 2h (dh/dt) + 0

(dd/dt) = (h/d) × (dh/dt)

(dd/dt) = (3000/5000) × (1000)

(dd/dt) = 600 ft/s

b) If the television camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing at that same moment?

At any moment in time, θ, h and the initial distance of the camera from the base of the rocket are related through the trigonometric relation

Tan θ = (h/4000) = 0.00025h

Taking the time derivative of both sides

(d/dt) (Tan θ) = (d/dt) (0.00025h)

(Sec² θ) (dθ/dt) = 0.00025 (dh/dt)

At the point where h = 3000 ft, we can calculate the corresponding θ at that point

Tan θ = (3000/4000)

θ = tan⁻¹ (0.75) = 0.6435 rad

(Sec² θ) (dθ/dt) = 0.00025 (dh/dt)

(Sec² 0.6435) (dθ/dt) = 0.00025 (1000)

1.5625 (dθ/dt) = 0.25

(dθ/dt) = (0.25/1.5625) = 0.16 rad/s

Hope this Helps!!!

The rate of change of the hypotenuse distance and the camera's angle of elevation can be calculated using the principles of trigonometry and differentials. The rates derive from the Pythagorean theorem and the derivatives of trigonometric functions, respectively.

This question relates to the concepts of trigonometry and differential calculus. We can see the camera, the rocket and the launch pad as forming a right triangle: the distance from the camera to the rocket is the hypotenuse, the distance from the camera to the launch pad is one leg (adjacent to the angle of elevation) and the distance that the rocket has risen is the other leg (opposite to the angle of elevation).

(a) To find how fast the distance from the camera to the rocket is changing, we can use the Pythagorean theorem (a² + b² = c²). Here, a = 4000 ft, b = 3000 ft, so, c = sqrt((4000)² + (3000)²). The derivative dc/dt (rate of change of c) when b = 3000 ft and db/dt = 1000 ft/s will provide the answer.

(b) To find how fast the camera's angle of elevation (let's symbolize it by θ) is changing, we use the concept of derivatives of trigonometric functions, specifically the tangent, which is defined as opposite (b) over adjacent (a), or tan(θ) = b/a. Then, we can compute dθ/dt using implicit differentiation when b = 3000 ft and db/dt = 1000 ft/s.

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Answer:

a) [tex]t=\frac{(56.2-64.2)-0}{\sqrt{\frac{18.2^2}{22}+\frac{13.9^2}{11}}}}=-1.40[/tex]  

b) [tex]p_v =2*P(t_{31}<-1.4)=0.171[/tex]  

Step-by-step explanation:

Information given

[tex]\bar X_{1}=56.2[/tex] represent the mean for sample 1  

[tex]\bar X_{2}=64.2[/tex] represent the mean for sample 2  

[tex]s_{1}=18.2[/tex] represent the sample standard deviation for 1  

[tex]s_{2}=13.9[/tex] represent the sample standard deviation for 2  

[tex]n_{1}=22[/tex] sample size for the group 2  

[tex]n_{2}=11[/tex] sample size for the group 2  

t would represent the statistic (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to check if the true means are different, the system of hypothesis would be:  

Null hypothesis:[tex]\mu_{1}-\mu_{2}=0[/tex]  

Alternative hypothesis:[tex]\mu_{1} - \mu_{2}\neq 0[/tex]  

The statistic is given by:

[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}[/tex] (1)  

The degrees of freedom are given by:

[tex]df=n_1 +n_2 -2=22+11-2=31[/tex]  

Part a: Statisitc

Replacing into the formula we got:

[tex]t=\frac{(56.2-64.2)-0}{\sqrt{\frac{18.2^2}{22}+\frac{13.9^2}{11}}}}=-1.40[/tex]  

Part b: P value  

The p value on this case would be:

[tex]p_v =2*P(t_{31}<-1.4)=0.171[/tex]  

Answer-

You should always check the solution is a rational equation. It would be easier to get an answer... Idk if this helps, but thats what I was taught>>>

Step-by-step explanation:

Given:

Length of the wall = 8 ft

Width of the wall = 6 ft

Length of the window = 2 ft

Width of the window = 18 in

To find:

The square feet Jamin planning to paint

Solution:

Area of the wall = length × width

                           = 8 × 6

Area of the wall = 48 ft²

Width of the window = 18 in

Convert inch to feet.

1 feet = 12 inch

18 inch = [tex]\frac{18}{12}=1.5[/tex] ft

Area of the window = length × width

                                 = 2 × 1.5

Area of the window = 3 ft²

Area to be painted = Area of the wall - Area of the window

                                = 48 ft² - 3 ft²

                                = 45 ft²

Therefore Jamin planning to paint 45 ft².

Answer:

45 ft²

Step-by-step explanation:

mark me brainy plz!

Answer:

A 35 pages per hour

Step-by-step explanation:

The rate of change is the slope

(0,150)  (7,400)

m = (y2-y1)/(x2-x1)

    =(400-150)/(7-0)

    =250/7

    =35.7 pages per hour

Approximately 36 pages per hour

Answer:

A

Step-by-step explanation:

Rate = slope

(500-150)/(10-0)

= 350/10

= 35

Answer:

x+9

Step-by-step explanation:

1/3x[8-5]+9=1/3x(3)+9

1/3x(3)+9=x+9

x+9

The final result of the expression 1/3x[8-5]+9 is 10.

To evaluate the expression 1/3x[8-5]+9, we need to perform the operations in the correct order, following the PEMDAS/BODMAS rule. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). BODMAS is similar but is used in some regions with the 'O' representing "Orders" or "Indices" instead of Exponents.

Step 1: Inside the brackets, we solve the expression 8 - 5, which gives us 3.

Step 2: Now, we have 1/3x3 + 9. According to PEMDAS/BODMAS, we must perform multiplication before addition. So, we proceed with 1/3 times 3, which equals 1.

Step 3: The expression now simplifies to 1 + 9.

Step 4: Finally, we perform the addition, which yields 10.

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Answer:

[tex]Lower = 231.134- 3.098=228.036[/tex]

[tex]Upper = 231.134+ 3.098=234.232[/tex]

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n=5 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

And for this case we know that the 95% confidence interval is given by:

[tex] \bar X=\frac{233.002 +229.266}{2}= 231.134[/tex]

And the margin of error is given by:

[tex] ME = \frac{233.002 -229.266}{2}= 1.868[/tex]

And the margin of error is given by:

[tex] ME= t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]

The degrees of freedom are given by:

[tex] df = n-1 = 5-1=4[/tex]

And the critical value for 95% of confidence is [tex] t_{\alpha/2}= 2.776[/tex]

So then we can find the deviation like this:

[tex] s = \frac{ME \sqrt{n}}{t_{\alpha/2}}[/tex]

[tex] s = \frac{1.868* \sqrt{5}}{2.776}= 1.506[/tex]

And for the 99% confidence the critical value is: [tex] t_{\alpha/2}= 4.604[/tex]

And the margin of error would be:

[tex] ME = 4.604 *\frac{1.506}{\sqrt{5}}= 3.098[/tex]

And the interval is given by:

[tex]Lower = 231.134- 3.098=228.036[/tex]

[tex]Upper = 231.134+ 3.098=234.232[/tex]

The limits of the 99% confidence interval (CI) for the true average natural frequency (Hz) of delaminated beams are (228.555, 233.713).

 To find the 99% confidence interval, we need to understand that the width of a confidence interval is determined by the standard deviation of the sample, the sample size, and the confidence level.

The formula for a confidence interval for the mean when the population standard deviation is unknown (which is likely the case here, as it is not specified) is given by:

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

First, we need to find the sample mean which is the center of the given 95% CI.

The width of the CI is the difference between the upper and lower limits. For the 95% CI, the width is:

[tex]\[ \text{Width}_{95\%} = 233.002 - 229.266 = 3.736 \][/tex]

Since the 95% CI is symmetric around the sample mean, the margin of error (MOE) for the 95% CI is half of the width:

[tex]\[ \text{MOE}_{95\%} = \frac{\text{Width}_{95\%}}{2} = \frac{3.736}{2} = 1.868 \][/tex]

The 95% CI can be represented as:

[tex]\[ \text{CI}_{95\%} = \bar{x} \pm \text{MOE}_{95\%} \][/tex]

 Finally, the limits of the 99% CI are found by adding and subtracting this MOE from the sample mean:

[tex]\[ \text{Upper limit}_{99\%} = \bar{x} + \text{MOE}_{99\%} = 231.134 + 3.152 \approx 233.713 \][/tex]

Therefore, the 99% confidence interval for the true average natural frequency (Hz) of delaminated beams is (228.555, 233.713).

Answer:

The solution is shown in the picture attached

Step-by-step explanation:

To verify X as a solution to the system, substitute X into the system and check for equality. X is a vector and X' a matrix. Careful calculations with matrices and trigonometric identities are necessary for the verification.

To verify that the vector X is indeed a solution to the given system, we can substitute X into the system and check if both sides are equal. If they are, then X is a solution to the system.

X in this case is a vector whose elements are trigonometric functions of time t. Likewise, X' represents a matrix multiplying the vector X. After applying the multiplication, we can compare the resulting vector with the original vector.

As this involves calculation with matrices and trigonometric identities, careful execution of these steps is necessary to ensure the accuracy of the result.

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Answer:

40

Step-by-step explanation:

200/5 = 40

Answer:

20$

Step-by-step explanation:

10, five dollar bills make 50 so 20 five dollar bills make 100$

Answer:

0.069 = 6.9% probability that a customer has to wait more than 4 minutes.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

In this problem, we have that:

[tex]m = 1.5[/tex]

So

[tex]\mu = \frac{1}{1.5} = 0.6667[/tex]

[tex]P(X \leq x) = 1 - e^{-0.667x}[/tex]

Find the probability that a customer has to wait more than 4 minutes.

Either the customer has to wait 4 minutes or less, or he has to wait more than 4 minutes. The sum of the probabilities of these events is decimal 1. So

[tex]P(X \leq 4) + P(X > 4) = 1[/tex]

We want P(X > 4). So

[tex]P(X > 4) = 1 - P(X \leq 4) = 1 - (1 - e^{-0.667*4}) = 0.069[/tex]

0.069 = 6.9% probability that a customer has to wait more than 4 minutes.

Answer:

[tex]\$456[/tex]

Step-by-step explanation:

The correct question is

Mr. Hopkins is building a sandbox for his children. It would cost $228 for the sand if he builds a sandbox with dimensions 9 ft by 6 ft. If Mr. Hopkins decides to increase the size to 13 1/2 ft by 8 ft but keep the same depth of sand, how much would the sand cost

step 1

Find the unit rate of the cost per square foot

Divide the total cost by the area

[tex]\frac{228}{9*6}=\$\frac{38}{9}\ per\ square\ foot[/tex]

step 2

Find the area of the increased sandbox

we have

[tex]L=13\frac{1}{2}=13.5\ ft[/tex]

[tex]W=8\ ft[/tex]

The area is equal to

[tex]A=(13.5)(8)=108\ ft^2[/tex]

step 3

Find the cost of the new sandbox

Multiply the area by the cost per square foot

[tex]108(\frac{38}{9})=\$456[/tex]

Answer:

5

Step-by-step explanation:

starts with 16. 6 carrots and 10 cucumbers. 10-5=5

Answer:

17

Step-by-step explanation:

Let x, x +1, x + 2, x + 3 be four consecutive integers.

[tex] \therefore \: x + x +1 + x + 2 + x + 3 = 74 \\ \therefore \: 4x + 6 = 74 \\ \therefore \: 4x = 74 - 6 \\ \therefore \: 4x = 68 \\ \therefore \: x = \frac{68}{4} \\ \huge \red{ \boxed{x = 17}}[/tex]

Hence, first integer is 17.

Answer:

17 is your answer

hope this helps :)

Step-by-step explanation:

Answer:

1:B the ballet club

2.B the ballet club.

Step-by-step explanation:

It is correct on khan :)

The chess club accepts 5 new members each week, and had 37 members after 6 weeks. The club started with 7 members. Without more data, a similar function for the ballet club cannot be determined.

This question requires a bait to understand the concept of linear functions. The chess club at Nahk University accepts 5 new members each week and had 37 members after 6 weeks. We can express this as a linear function, with the number of weeks as the independent variable and the number of members as the dependent variable:

Members = 5 * Weeks + Initial Members

Here, we know from the information given that after 6 weeks, the chess club had 37 members. So if we plug those numbers into the equation:

37 = 5 * 6 + Initial Members

Then solving for the number of initial members gives us 7. Hence, the chess club started with 7 members.

To find a similar function for the ballet club, we would need more specific data to map time (in weeks) to the number of members in the same way.

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Answer:

1000000000

Step-by-step explanation:

20000 times 50000 equals 1000000000

when you multiply 20,000 by 50,000, you get the product of 1,000,000,000 or 1 billion.

The The product of 20,000 multiplied by 50,000 is:

20,000 x 50,000 = 1,000,000,000

Therefore, 20,000 multiplied by 50,000 equals 1 billion. of 20,000 multiplied by 50,000 is:

20,000 x 50,000 = 1,000,000,000

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Answer:

A line is at a degree of 180, so the line 170 is on can give you the degree of the smallest angle: 10. A traingel has a total degree of 180, so 125 + 10 = 135. Take 180 and subtract 135 to get x = 45º

Step-by-step explanation:

Answer:

x = 45°

Step-by-step explanation:

Since it's a triangle, the total degrees of it would be 180

You are given one of the angles measurements and another's' supplementary angle

180 - 125 = 55

Take the 170 and subtract from 180 to get the interior angle of the triangle

180 - 170 = 10

Now subtract 55 and 10 to get x

55 - 10 = 45

Answer:

a) P (Y  less than or equal to 79 ) = 0.226  

b) Z = 1.008  less than or equal to Zc = 1.64

So, it means null hypothesis is not rejected.

Step-by-step explanation:

a) Probability that fewer than 80 patients will recover.

As we have:

p = 88% = 0.88 = population success proportion

n = 93 = Sample size

mean = n x p , mean = 93 x 0.88 , mean = 81.84

So, we need P (Y less than or equal to 79) fewer than 80 patients.

Standard Deviation of the population =

SD of population = [tex]\sqrt{n . p . (1-p)}[/tex] , SD of population = [tex]\sqrt{93 .0.88 .(1-0.88)}[/tex]

SD of population = 3.13

As we know that,

probability in binomial distribution is approximately equal to normal distribution so, we will use normal distribution from here. In addition, due to this shift 79 will be equal to 79.5 in normal distribution.

P(Y less than or equal to 79) ≈ P(Y less than or equal to 79.5)

P([tex]\frac{Y - mean }{SD}[/tex]) , P([tex]\frac{79.5 - 81.84}{3.1336}[/tex]) , P(Z less than or equal to -0.75)

So, when will you check the Z score of -0.75 in the Z table you will get the probability which is :

P (Y less than or equal to 79 ) = 0.226

So, 0.226 is the probability that fewer than 80 patients will recover.

b) Z  test is used in this part to check the claim:

Favorable Cases sample (recovered) = 85 = Y

Sample size = N = 93

Significance level = 0.05

Proportion Sample = p = Y/N = 85/93 = 0.914.

1. Null hypothesis and Alternative Hypothesis:

H1: p less than or equal to 88% or p less than or equal to 0.88

H2: p greater than 88% or p greater than 0.88

2. Rejection Region:

Zc value is = 1.64 for a right tail test.

Rejection region is such that z value must be greater than Zc value i.e 1.64. If it is not greater, it will not lie in rejection region.

3. Statistics Test:

In this we have to calculate value of Z and compare it with value of Zc.

Z = [tex]\frac{P-p1}{\sqrt{p1(1-p1)/n} }[/tex]

Small p1 = 0.88 , Capital P = 0.914  Z = [tex]\frac{0.914-0.88}{\sqrt{0.88.(1-0.88)/93} }[/tex]

Z = 1.008

4. Final Decision about the null hypothesis:

As we can see, Z value is less than Zc value, hence it does not lie in the rejection region.

Z = 1.008  less than or equal to Zc = 1.64

So, it means null hypothesis is not rejected.

H1 is not rejected,  it means there is not sufficient proof to claim that population proportion is larger than population success proportion p1.

a. Estimate the probability that fewer than 80 patients will recover: Approximately 0.2743.

b. Confirm/disprove the director's claim:

The probability of observing more than 85 patients recovering out of 93 treated with the new technique is approximately 0.1515. Therefore, there isn't sufficient evidence to support the director's claim that all hospitals should adopt the new technique based solely on this sample data.

To solve this problem, we'll use the normal approximation to the binomial distribution since the sample size (93) is relatively large.

Let's break it down step by step.

Given:

Probability of traditional medical treatment curing the disorder = 0.88

Number of patients treated with the new technique = 93

a. Estimate the probability that fewer than 80 patients will recover.

To estimate this probability, we'll use the normal approximation to the binomial distribution.

1. Calculate the mean [tex](\(\mu\))[/tex] and standard deviation [tex](\(\sigma\))[/tex] of the binomial distribution:

[tex]\[\mu = np = 93 \times 0.88 = 81.84\][/tex]

[tex]\[\sigma = \sqrt{np(1-p)} = \sqrt{93 \times 0.88 \times 0.12} \approx 3.076\][/tex]

2. Standardize the value of 80 using the z-score formula:

[tex]\[z = \frac{x - \mu}{\sigma} = \frac{80 - 81.84}{3.076} \approx -0.600\][/tex]

3. Use the standard normal distribution table or calculator to find the probability corresponding to z = -0.600.

[tex]\[P(Z < -0.600) \approx 0.2743\][/tex]

So, the estimated probability that fewer than 80 patients will recover is approximately 0.2743.

b. The director of the hospital recommends that all hospitals adopt this new technique since more than 85 patients in the sample have recovered after being treated with the new technique.

Confirm/disprove the director's claim.

To confirm/disprove the director's claim

We'll calculate the probability of observing more than 85 successes (patients recovering) out of 93 trials (patients treated) under the assumption that the success rate is the same as the traditional treatment (0.88).

1. Calculate the mean [tex](\(\mu\))[/tex] and standard deviation [tex](\(\sigma\))[/tex] of the binomial distribution:

[tex]\[\mu = np = 93 \times 0.88 = 81.84\][/tex]

[tex]\[\sigma = \sqrt{np(1-p)} = \sqrt{93 \times 0.88 \times 0.12} \approx 3.076\][/tex]

2. Standardize the value of 85 using the z-score formula:

[tex]\[z = \frac{x - \mu}{\sigma} = \frac{85 - 81.84}{3.076} \approx 1.031\][/tex]

3. Calculate the probability of observing more than 85 successes:

[tex]\[P(Z > 1.031) \approx 1 - P(Z < 1.031) \approx 1 - 0.8485 \approx 0.1515\][/tex]

The probability of observing more than 85 successes out of 93 trials is approximately 0.1515, which means there's about a 15.15% chance of observing this many or more successes if the true success rate is 0.88.

Since [tex]\(15.15\% > 5\%\)[/tex]  (common significance level),

We fail to reject the null hypothesis that the success rate of the new technique is the same as the traditional treatment.

Therefore, there isn't sufficient evidence to support the director's claim that all hospitals should adopt the new technique based solely on this sample data.

The equivalent expression to 2 (three-fourths x + 7) minus 3 (one-half x minus 5) is 29.

To find equivalent expressions to 2 (three-fourths x + 7) minus 3 (one-half x minus 5), we first need to distribute the numbers outside the parentheses inside the parentheses. This simplifies the expression as follows:

Subtracting the second expression from the first, we obtain: (1.5x + 14) - (1.5x - 15), which simplifies to 0x + 29, or simply 29.

Therefore, the only expression equivalent to the given expression is 29.

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Answer:

The answer is B, C, and E

Step-by-step explanation: