Hypertension is when an adult is classified as having high blood pressure (above 130 systolic blood pressure is considered hypertension). Researchers want to know the proportion of adult North Americans (above age of 18) that have hypertension. Based on a study of 3532 adult North Americans, 1219 of them were classified as having hypertension.
a. Researchers want to test if more than a quarter of all North American adults have hypertension (that is to say more than 25% proportion of North American adults). State the null and alternative hypothesis in proper notation.
b. Create a 95% confidence interval for the true proportion of adult North Americans that have hypertension. Interpret this interval in context of the study.c. Say your 95% confidence interval is (0.329 , 0.361). Can you say with a high degree of confidence that more than a quarter of all North Americans have hypertension. Explain in a sentence or two.
d. If we were to decrease our level of confidence, what would we expect to happen to the confidence interval? Get wider/ get narrower/ stay the same ?

Answer:

Step-by-step explanation:

The volume of a cone of height h and circular base of radius r, is [tex] V = \frac{\pi r^2 h}{3}[/tex]. In this case we have that [tex]V=72\pi[/tex].Then, we have that

[tex]72\pi = \frac{\pi r^2 h}{3}[/tex]

multiplying by 3 on both sides and dividing by [tex]\pi[/tex] we have that

[tex]216 = r^2\cdot h[/tex]

Suppose that we know the value of r, then we can find the value of h by solving h, that is

[tex] h = \frac{216}{r^2}[/tex].

So, by choosing any positive value of r, we can find the value for h. Note that if r=6, then [tex]h= \frac{216}{6^2} = 6[/tex]. This means that the amount of credit is infinite :)

Answer:

Step-by-step explanation:

Slope of parallel lines are equal.

1) m = -2/3

(4,-7)

[tex]y-y_{1}=m(x-x_{1})\\\\y-[-7]=\frac{-2}{3}(x-4)\\\\y+7=\frac{-2}{3}*x-\frac{-2}{3}*4\\\\y+7=\frac{-2}{3}x+\frac{8}{3}\\\\y=\frac{-2}{3}x+\frac{8}{3}-7\\\\y=\frac{-2}{3}x+\frac{8}{3}-\frac{7*3}{1*3}\\\\y=\frac{-2}{3}x+\frac{8}{3}-\frac{21}{3}\\\\y=\frac{-2}{3}x-\frac{13}{3}[/tex]

2) 5x + y = 4

  y = -5x + 4

slope m = -5

(-1,4)

y - 4 = -5(x -[-1])

y- 4 = -5(x+1)

y - 4 = -5x - 5

y = -5x - 5 + 4

y = -5x -1

If two lines are perpendicular, m2 = -1/m1

m1 = -4/3

[tex]m_{2}=\frac{-1}{\frac{-4}{3}}=-1*\frac{-3}{4}=\frac{3}{4}\\[/tex]

(5,4)

[tex]y-4=\frac{3}{4}(x - 5)\\\\y-4=\frac{3}{4}x-\frac{3}{4}*5\\\\y-4=\frac{3}{4}x-\frac{15}{4}\\\\y=\frac{3}{4}x-\frac{15}{4}+4\\\\y=\frac{3}{4}x-\frac{15}{4}+\frac{4*4}{1*4}\\\\y=\frac{3}{4}x-\frac{15}{4}+\frac{16}{4}\\\\y=\frac{3}{4}x+\frac{1}{4}[/tex]

Answer:

3.) is y=3/4x+1/4 That's what i got but i hope this helps.

Step-by-step explanation:

Answer:

{x|x[tex]\in R[/tex]}

Step-by-step explanation:

We are given that a function

[tex]f(x)=2x+6[/tex]

We have to find the domain of the function in the correct set notation.

The given function is linear polynomial .

The linear polynomial is  defined for all real  values of x.

Therefore, the given function is defined for values of x.

Domain of f is given  by

{x|x[tex]\in R[/tex]}

Hence, the domain of the function in the correct set notation is given by

{x|x[tex]\in R[/tex]}

Answer:

8

Step-by-step explanation:

24+8=32 32 divided by 4 is 8

Answer: 8

Step-by-step explanation:

Plug in x as 2 and solve.

(12*2 + 8)/4

Start with parenthesis.

(32)/4

Now divide.

8

Answer:

12c-49

Step-by-step explanation:

−8+(4)(c)+(4)(−9)+−5+6c+2c

=−8+4c+−36+−5+6c+2c

Combine Like Terms:

=−8+4c+−36+−5+6c+2c

=(4c+6c+2c)+(−8+−36+−5)

=12c−49

pls mark me brainliest

Answer:

<1=<5(alternative angle)

<3=<6(alternative angle)

<1+<2+<3=180(given)

<5+<2+<6=180(putting <1=<5 and <3=<5)

proved

Answer:

-45

Step-by-step explanation:

-34+15=-19

-29-(-3)= -29+3= -26

-19 + -26 = -45

Answer:

-45

Step-by-step explanation:

-34 + 15 - 29 - (-3)

-34-29 +15+3

-63+18

18-63

-45

Answer:

C. Domain : {Gem, Hesh, Sam}

Range : {Gale, Abby, Beni}

B. The relation in the figure is a function because each element in the range corresponds to exactly one element in the domain.

Step-by-step explanation:

The figure of the mapping is attached below.

From the diagram, the domain for the relation is the set of Fathers:

{Gem, Hesh, Sam}

The range is the set of Sons:

{Gale, Abby, Beni}

The relation is a function. This is because each element in the range corresponds to exactly one element in the domain.

Answer:

The overall image would be 4 units to the right and 3 units down on the coordinate plane.

Step-by-step explanation:

We do not see an image. But that is okay. (x+4,y-3) means that the x value of each coordinate gets increased by 4 and the y value of each coordinate gets decreased by 3. The overall image would be 4 units to the right and 3 units down on the coordinate plane.

The image would be 4 units to the right and 3 units down on the coordinate plane.

In maths, a translation moves a shape left, right, up, or down but does not turn.

Given the translation of quadrilateral ABCD

(x+4,y-3) means that the x value of each coordinate gets increased by 4 and the y value of each coordinate gets decreased by 3.

Hence, The image would be 4 units to the right and 3 units down on the coordinate plane.

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Answer:

[tex]x\in(1.146,\infty)[/tex]

Step-by-step explanation:

We are given an inequality

[tex]e^x>14[/tex]

We have to solve the given inequality.

Taking both side ln of given inequality

Then, we get

[tex]ln(e^x)>ln(14)[/tex]

[tex]xlne>1.146[/tex]

We know that

lne=1

Using the value

[tex]x>1.146[/tex]

[tex]x\in(1.146,\infty)[/tex]

Hence, the value of x is given by

[tex]x\in(1.146,\infty)[/tex]

Answer:

38.11% probability that the mean of her sample will be between 2700 and 2800 calories

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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 question, we have that:

[tex]\mu = 2760, \sigma = 500, n = 25, s = \frac{500}{\sqrt{25}} = 100[/tex]

Find the probability that the mean of her sample will be between 2700 and 2800 calories

This is the pvalue of Z when X = 2800 subtracted by the pvalue of Z when X = 2700.

X = 2800

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

By the Central Limit Theorem

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

[tex]Z = \frac{2800 - 2760}{100}[/tex]

[tex]Z = 0.4[/tex]

[tex]Z = 0.4[/tex] has a pvalue of 0.6554

X = 2700

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

[tex]Z = \frac{2700 - 2760}{100}[/tex]

[tex]Z = -0.6[/tex]

[tex]Z = -0.6[/tex] has a pvalue of 0.2743

0.6554 - 0.2743 = 0.3811

38.11% probability that the mean of her sample will be between 2700 and 2800 calories

Answer:

25 and 36

Step-by-step explanation:

5^2=25

6^2=36

Answer:

Im feeling pretty today so imma go with C

Step-by-step explanation:

lol i took the test like about 2 days ago and i just checked my answers and C was right, good luck

Answer:

[tex]\frac{6}{40}=\frac{3}{20}[/tex]

Step-by-step explanation:

The experimental probability is the number of times the desired result was obtained over the total number of times the experiment was carried out:

[tex]P=\frac{TimesTheEventOccurs}{TotalNumberOfTrials}[/tex]

In this case the Event we are looking for is rolling a 3 on the number cube.

The total number of trials is:

40

because the student rolls the cube 40 times.

and the times that he got the number 3 (the times the desired event occurs) is:

6

because he rolls a 3 on the number cube 6 times.

Thus our experimental probability to roll a 3 is:

[tex]P=\frac{6}{40}[/tex]

Answer:

Step-by-step explanation:

From the given data

we observed that the missile testing program

Y1 and Y2 are variable, they are also independent

We are aware that

[tex](Y_1)^2 and (Y_2)^2[/tex] have [tex]x^2[/tex] distribution with 1 degree of freedom

and [tex]V=(Y_1^2)+(Y_2)^2[/tex] has x^2 with 2 degree of freedom

[tex]F_v(v)=\frac{e^{-\frac{v}{2}}}2[/tex]

Since we have to find the density formula

[tex]U=\sqrt{V}[/tex]

We use method of transformation

[tex]h(V)=\sqrt{U}\\\\=U[/tex]

There inverse function is [tex]h^-^1(U)=U^2[/tex]

We derivate the fuction above with respect to u

[tex]\frac{d}{du} (h^-^1(u))=\frac{d}{du} (u^2)\\\\=2u^2^-^1\\\\=2u[/tex]

Therefore,

[tex]F_v(u)=F_v(h-^1)(u)\frac{dh^-^1}{du} \\\\=\frac{e^-\frac{u^-^}{2} }{2} (2u)\\\\=e^-{\frac{u^2}{2} }U[/tex]

Answer:

Step-by-step explanation:

let radius=r

height=h

dr/dt=1.6 in/s

dh/dt=-2.2 in/s

volume v=1/3 πr²h

dv/dt=1/3 π[h*2r×dr/dt+r²×dh/dt]

when r=135 in

h=135 in

dv/dt=1/3 π[2×135×135×1.6+135²×(-2.2)]

=1/3 π[135²(3.2-2.2)]

=1/3π135²×1

=6075 π in³/s

Answer:

- The probability that a bolt is too large for its nut = 0.00621

- The image of the drawing of this combined distribution is shown in the attached file to this solution.

Step-by-step explanation:

When independent, normal distributions are combined, the combined mean and combined variance are given through the relation

Combined mean = Σ λᵢμᵢ

(summing all of the distributions in the manner that they are combined)

Combined variance = Σ λᵢ²σᵢ²

(summing all of the distributions in the manner that they are combined)

For this question, the first distribution is the size of a nut, with mean 10 mm and a variance of 0.02

Second distribution is the size of a bolt, with mean 9.5 mm and a variance of 0.02.

The combined distribution is [size of nut − size of bolt]

Hence, λ₁ = 1, λ₂ = -1

μ₁ = 10 mm

μ₂ = 9.5 mm

σ₁² = 0.02

σ₂² = 0.02

Combined Mean = (1×10) + (-1×9.5) = 0.5 mm

Combined Variance = [(1)² × 0.02] + [(-1)² × 0.02] = 0.04

So, the combined distribution is also a normal distribution with a Mean of 0.5 mm and a variance of 0.04.

Standard deviation = √variance = √0.04 = 0.2 mm

The probability that a bolt is too large for its nut, [size of nut − size of bolt] ≤ 0, P(X ≤ 0)

To obtain this required probability, we first normalize/standardize 0 mm

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

z = (x - μ)/σ = (0 - 0.5)/0.2 = - 2.50

To determine the required probability

P(x ≤ 0) = P(z ≤ -2.50)

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

P(x ≤ 0) = P(z ≤ -2.50) = 0.00621

The image of the drawing of this combined distribution is shown in the attached file to this solution.

Hope this Helps!!!

Answer:

a) 34.46% probability that her pulse rate is greater than 70 beats per minute.

b) 2.28% probability that they have pulse rates with a mean greater than 70 beats per minute.

c) Because the underlying distribution(female's pulse rate) is normal.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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.

Distribution of females pulse rates:

Here, i suppose there was a typing mistake, since the mean and the standard deviation are lacking.

Also, the question c. only makes sense if the distribution is normal, so i will treat it as being.

I will use [tex]\mu = 68, \sigma = 5[/tex]. I am guessing these values, just using them to explain the question.

a. If 1 adult female is randomly selected, find the probability that her pulse rate is greater than 70 beats per minute.

This is 1 subtracted by the pvalue of Z when X = 70. So

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

[tex]Z = \frac{70 - 68}{5}[/tex]

[tex]Z = 0.4[/tex]

[tex]Z = 0.4[/tex] has a pvalue of 0.6554

1 - 0.6554 = 0.3446

34.46% probability that her pulse rate is greater than 70 beats per minute.

b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean greater than 70 beats per minute.

Now [tex]n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 70. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{70 - 68}{1}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% probability that they have pulse rates with a mean greater than 70 beats per minute.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30

The sample size only has to exceed 30 if the underlying distribution is normal. Here, the distribution of females' pulse rate is normal, so this requirement does not apply.

Answer:

Given:

Body mass index values:

17.7

29.4

19.2

27.5

33.5

25.6

22.1

44.9

26.5

18.3

22.4

32.4

24.9

28.6

37.7

26.1

21.8

21.2

30.7

21.4

Constructing a frequency distribution beginning with a lower class limit of 15.0 and use a class width of 6.0.

we have:

Body Mass Index____ Frequency

15.0 - 20.9__________3( values of 17.7, 18.3, & 19.2 are within this range)

21.0 to 26.9__________8 values are within this range)

27.0 - 32.9____________ 5 values

33.0 - 38.9____________ 2 values

39.0 - 44.9 _____________2 values

The frequency distribution is not a normal distribution. Here, although the frequencies start from the lowest,  increases afterwards and then a decrease is recorded again, it is not normally distributed because it is not symmetric.

The frequency distribution is not a normal distribution because it is not symmetric and this can be obtained through the given data.

Given :

The data represents the body mass index​ (BMI) values for 20 females.

The frequency distribution begins with a lower class limit of 15.0 and uses a class width of 6.0 are as follows:

Body Mass Index                        Frequency

   15 - 20.9                                         3

   21 - 26.9                                         8

   27 - 32.9                                         5

   33 - 38.9                                         2

   39 - 44.9                                         2

The frequency distribution is not a normal distribution because it is not symmetric.

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Answer:

rational

Step-by-step explanation:

rational + rational=rational

Answer:

1 = 130° , 2 =50° , 3 = 85°, 4=45°

Step-by-step explanation:

1 =45 + 85 = 130 { sum of opposite interior angle equals exterior angle}

2 = 180 - 1 { angles on a straight line equals 180}

= 180 -130 = 50°

4 = 180 - 135 = 45° { angles on a straight line equals 180}

3 = 135 -2 { sum of opposite interior angles equals exterior angle; 3 + 2 = 135}

3 = 135-50 = 85°

Note : sum of opposite interior angles equals external exterior angle, let's prove it:

If we look at the triangle at the bottom left, we have :

85, 45 and r { let's denote r as the missing angle}

So 85 + 45 + r = 180° { sum of angles of a triangle}

By simple arithmetic

r = 180 - ( 85+45) = 180 - 130 = 50°

but r + 4 = 180° { sum of angles in a straight line equals 180°}

4 = 180 - 50 = 130°

So you see 4 is the exterior angle of the triangle opposite to 85° and 45° interior angles}

Answer:

2.25km

Step-by-step explanation:

a scale of 1 : 25000 means:

1 cm on map ------> equals 25000 cm on ground  

hence,

9 cm on map ------> equals 25000 x 9 cm = 225,000 cm = 2.25km on ground

Answer:

x=-10

Step-by-step explanation:

x+8=-2

x=-10 (Subtract 8)

Answer:

-10

Step-by-step explanation:

1. Write it out.

x+8=-2

2. Get x by itself.

To do this, we have to move the 8, but to do that that we have to move it to the other side of the equation. Because the opposite of addition is subtraction, we have to subtract 8 by both sides.  x+8=-2

                                                                                        -8  -8

                                                                                      x=-10

And that's the answer! Hope this helped :)

Answer:

F(1) = 0

F(2) = -6 = 0 - 6 x 1 = F(1) - 6 x 1

F(3) = -12 = 0 - 6 x 2 = F(1) - 6 x 2

F(4) = -18 = 0 - 6 x 3 = F(1) - 6 x 3

...

F(n) = F(1) - 6 x (n - 1)

Hope this help!

:)

Answer:

Option D: A hypothesis test regarding the difference between two population proportions from independent samples.

Step-by-step explanation:

A hypothesis test regarding the difference between two population proportions from independent samples. This type of test is used to compare the two population proportions if they are equal or not. It is appropriate under the condition that

The sampling method for each population is simple random sampling.

The samples are independent.

Each sample includes at least 10 successes and 10 failures.

Each population is at least 20 times as big as its sample.

Answer:

d 0.0235

Step-by-step explanation:

We assume that the lifetime of the blenders follows a normal distribution, with mean of 36 months and standard deviation of 6 months.

We have to calculate the probability that the blenders have a lifetime lower than 24 months, and therefore apply the guarantee.

First, we calculate the z-score:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{24-36}{6}=\dfrac{-12}{6}=-2[/tex]

Then, the probability that the blenders lifetime is 24 or less is:

[tex]P(X<24)=P(z<-2)=0.023\\[/tex]

Answer:

(c) Pi/4

Step-by-step explanation:

3pi/4 = (3 x 180) / 4 = 135 degrees

135 degrees is equivalent to (180 degrees - 135 degrees) 45 degrees

45 degrees = Pi/4

Therefore, the reference angle of 3pi/4 is Pi/4

Thus, the correct option is (c) Pi/4

The reference angle for 3π/4 is π/4.

So, the correct answer is c) π/4.

Given is an angle 3π/4, we need to find its reference angle,

The reference angle is the acute angle formed between the terminal side of an angle and the x-axis in the coordinate plane.

To find the reference angle for an angle, you need to consider the position of the terminal side of the angle in the coordinate plane and determine the acute angle formed.

In this case, we are given the angle 3π/4. To find the reference angle, we need to consider the position of the terminal side of this angle.

The angle 3π/4 lies in the second quadrant of the coordinate plane, where both the x-coordinate and y-coordinate are negative.

To find the reference angle, we need to find the acute angle formed by the terminal side with the x-axis. In the second quadrant, this acute angle is formed by the vertical line connecting the terminal side to the x-axis.

If we draw a vertical line from the terminal side of 3π/4, it intersects the x-axis at π/4.

Therefore, the reference angle for 3π/4 is π/4.

So, the correct answer is c) π/4.

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Answer:

The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle.

Answer:

(27.55, 7.22), (-11.3, 3.21).

Step-by-step explanation:

When is the tangent to the curve horizontal?

The tangent curve is horizontal when the derivative is zero.

The derivative is:

[tex]\frac{dy}{dx} = 3t^{2} - 2t - 27[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]3t^{2} - 2t - 27 = 0[/tex]

So

[tex]a = 3, b = -2, c = -27[/tex]

Then

[tex]\bigtriangleup = b^{2} - 4ac = (-2)^{2} - 4*3*(-27) = 328[/tex]

So

[tex]t_{1} = \frac{-(-2) + \sqrt{328}}{2*3} = 3.35[/tex]

[tex]t_{2} = \frac{-(-2) - \sqrt{328}}{2*3} = -2.685[/tex]

Enter your answers as a comma-separated list of ordered pairs.

We found values of t, now we have to replace in the equations for x and y.

t = 3.35

[tex]x = t^{3} - 3t = (3.35)^{3} - 3*3.35 = 27.55[/tex]

[tex]y = t^{2} - 4 = (3.35)^2 - 4 = 7.22[/tex]

The first point is (27.55, 7.22)

t = -2.685

[tex]x = t^{3} - 3t = (-2.685)^3 - 3*(-2.685) = -11.3[/tex]

[tex]y = t^{2} - 4 = (-2.685)^2 - 4 = 3.21[/tex]

The second point is (-11.3, 3.21).

Answer:

240

Step-by-step explanation:

8*10=80ft *3= 240 but thats over budget

The total cost to fence the rectangular garden is $108. Diego has enough money to fence the rectangular garden.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Given that, a rectangular garden needs to be at least 10 feet wide and at least 8 feet long.

Now the perimeter of rectangular garden is

2(8+10)

= 36 feet

Total cost of fencing = 36×3

= $108

Diego's budget is $120

Therefore, Diego has enough money to fence the rectangular garden.

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