A physical therapist claims that 75% of people lose their balance if they close their eyes while standing on one foot. A gymnast feels that the rate is less than 75%. To test this, she randomly selects 100 people and finds that 80 of them lose their balance while standing on one foot. To determine if these data provide convincing evidence that the proportion of people who lose their balance while standing on one foot and closing their eyes is less than 75%, 150 trials of a simulation are conducted. The gymnast is testing the hypotheses: H0: p = 75% and Ha: p < 75%, where p = the true proportion of people who will lose their balance while standing on one foot and closing their eyes. Based on the results of the simulation, what is the estimate of the P-value of the test? A dotplot. A number line labeled simulated sample percentage of people who lose balance goes from 64 to 88 percent. 64, 3; 66, 3; 67, 4; 68, 8; 69, 5; 70, 7; 71, 8; 72, 11; 73, 15; 74, 12; 75, 11; 76, 8; 77, 18; 78, 10; 79, 10; 80, 5; 81, 4; 82, 2; 83, 2; 84, 1; 85, 2; 87, 1. 0.1133 0.17 0.887 0.92

The area of a regular polygon is one-half the product of its apothem and its perimeter. Often the formula is written like this: Area=1/2(ap), where a denotes the length of an apothem, and p denotes the perimeter.

Step-by-step explanation:

#Hopeithelps

Answer:

y = 1/2x - 7/2

Slope: 1/2

Y-intercept: (0, -7/2)

Step-by-step explanation:

We know the slope-intercept form of an equation of a line is y = mx + c where slope is m and y-intercept is c.

So, -4y = (-2)x + 14 [divide both sides by -4]

-4/-4 = -2/-4 + 14/-4

y = 1/2 -7/2

Hence the slope =  1/2 and y-intercept = -7/2.

Answer:

To find the mean of a given data set, add up all the values then divide by how many numbers ...

Step-by-step explanation:

60/4= 15

15 x 3 =45 minutes

Answer: -10

Step-by-step explanation:

10 x 4 is 40 so with 2 negatives, it turns positive, and 40 plus 10 = 50

Answer:

x=-10

Step-by-step explanation:

-4x+10=50

10=50+4x

-50+10=4x

-40=4x

4x=-40

x=-40÷4

x=-10

Answer:

$25.10

Step-by-step explanation:

lunch=$7.52

dinner=$9.74

breakfast=$5.16

money left=$2.68

make total money he began with ‘x’

to find the total money he began with it will be

x-lunch+dinner+breakfast=money left

x-$7.52+$9.74+$5.16=$2.68

x-$22.42=$2.68

x=$2.68+$22.42

x=$25.10

Answer:

b = 5

Step-by-step explanation:

The y intercept is the value when x =0

y = mx+b  where b is the y intercept

b = 5

Answer:

b = 5

Step-by-step explanation:

Slope-Intercept form: y = mx + b

where:

[tex]\sf \textsf{Given:}\ \dfrac{-4x}{3}+5[/tex]

Therefore, the value of b is 5.

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Answer:

First, break the shape into smaller shapes.

Bigger rectangle: 5m, 8m

Thin rectangle: 7m, 3m

Thinner rectangle: 8m, 2m

We will call the bigger rectangle B, the thin rectangle R, and the thinner rectangle r.

Step-by-step explanation:

B = 8 • 5 = 40

R = 7 • 3 = 21

r = 2 • 8 = 16

Add the areas together:

40 + 21 + 16 = 77

Therefore, the area is 77 meters.

Answer: The answer is B.

Step-by-step explanation: An open circle means < or >. A closed circle means lesser or equal to or greater or equal to. The open circle is on 4 and the ray is going right. The closed circle is on 0 and the ray goes left. This is correct.

The water consumption based on the information for three Months will be 22267m³.

The total water consumption for the three months will be:

= 7219 + 7390 + 7658

= 22267m³

In conclusion, the information simply want you to add the values of the water given.

Therefore, the water consumption based on the information for three Months will be 22267m³.

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Answer:

1. 33.6

Step-by-step explanation:

1. Mean = total score/number of tests

         = (23+28+29+30+30+32+33+36+36+40+41+43+45+46+48)/15

         =33.6

I don't know any of the others, but I hope that this will be helpful :)

Answer:

[tex]h(x) = \frac{1}{4} x[/tex]

Step-by-step explanation:

To find the inverse of a function, the steps are:

In this case, since h(x) is the inverse function of f(x), we can replace x with h(x) in step 3.

_____

f(x)= 4x

Let y= f(x) [tex]\textcolor{steelblue}{\text{ - step 1}}[/tex]

y= 4x

Divide both sides by 4:

[tex] \frac{1}{4} y = x[/tex]

[tex]x = \frac{1}{4} y \: \: \: \textcolor{steelblue}{\: \text{ - step 2}}[/tex]

Replace x with h(x) and y with x:

[tex]\bf{h(x) = \frac{1}{4} x} \: \: \: \textcolor{steelblue}{\: \text{ - step 3}}[/tex]

Additional:

For a similar question on inverse functions, do check out the following!

#a

V={Vowels of English alphabets}

#b

C={cube numbers between 0 to 50}

#c

M={y:y is a multiple of 3 less than 20}

Answer:

h=8.0

Step-by-step explanation:

law of sines

sinA/a=sinB/b

b/a=sinB/sinA

b = a times sinB/sinA

b = 10 times sin53/sin90

on a calculator type sin53 in degrees

b = 10 times 0.7986/1

b = 7.986

Answer:

h = x² - 2x - 35

Step-by-step explanation:

Making the factors :

It mentions the zeros are 7 and -5.

Then, the factors are :

⇒ (x - 7)

⇒ (x + 5)

===========================================================

The quadratic function will be :

⇒ h = (x - 7)(x + 5)

⇒ h = x² - 2x - 35

[tex]\textbf{(i)}\\\\\{1^3 +2^3 \} \times \left(\dfrac 13 \right)^2\\\\=(1+8) \left(\dfrac 19 \right)\\\\=9\left(\dfrac 19 \right)\\\\=1\\\\[/tex]

[tex]\textbf{(ii)}\\\\\{5^{-1}\times 4^{-1}\}^2\\\\=\left(5^{-1} \right)^2 \times \left(4^{-1} \right)^2~~~~~~~~~~~;[(ab)^m = a^mb^m]\\\\=5^{-2}\times 4^{-2}~~~~~~~~~~~~~~~~~~~~;[(a^m)^n = a^{mn}]\\\\=\dfrac 1{5^2} \times \dfrac 1{4^2}~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-m} = \dfrac 1{a^m},~ a\neq 0 \right]\\\\=\dfrac{1}{400}\\\\=0.0025\\\\[/tex]

[tex]\textbf{(iii)}\\\\\left\{ \left(\dfrac 13 \right)^{-2} \times \left( \dfrac 12 \right)^{-2}\right\}\div \left(\dfrac 14 \right)^{-3}\\\\\\=\left( \dfrac 13 \times \dfrac 12 \right)^{-2} \div\left(4^{-1}\right)^{-3}\\\\\\=\left(\dfrac 16 \right)^{-2} \div 4^3\\\\\\=\left(6^{-1} \right)^{-2}\div 4^3\\\\\\=6^2 \div 4^3\\\\\\=36\div 64\\\\\\=\dfrac{9}{16}\\\\\\=0.5625[/tex]

Answer:

3/2

Step-by-step explanation:

As AB and ED are parallel, they have the same slope. This means that since lines that are colllinear with parallel segments are parallel, lines l and m are parallel.

Answer:

A a pair of intersecting lines

Step-by-step explanation:

i got it right on the test bub

Answer: a pair of intersecting lines

Step-by-step explanation: i had many people help me know this is right

By using the description of the graph, we conclude that f(0) = -6 only.

The correct option is the second one.

Here we want to know the value of the function when evaluated in 0. Remember that the points on the graph of the function are of the form:

(x, f(x)).

Now, in the description of the graph you say:

"...  and the y-axis at (0, negative 6)."

So we know that the graph passes through (0, -6), which means that when evaluated in 0, the function is equal to -6.

So the correct option is the second one: –6 only

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Answer:

Step-by-step explanation:

Using the binomial distribution, it is found that there is a 0.7447 = 74.47% probability that fewer than 7 of them show up.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, the values of the parameters are given as follows:

p = 0.7, n = 8.

The probability that fewer than 7 of them show up is given by:

[tec]P(X < 7) = 1 - P(X \geq 7)[/tex]

In which:

[tex]P(X \geq 7) = P(X = 7) + P(X = 8)[/tex]

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977[/tex]

[tex]P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576[/tex]

Then:

[tex]P(X \geq 7) = P(X = 7) + P(X = 8) = 0.1977 + 0.0576 = 0.2553[/tex]

[tec]P(X < 7) = 1 - P(X \geq 7) = 1 - 0.2553 = 0.7447[/tex]

0.7447 = 74.47% probability that fewer than 7 of them show up.

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Answer:

D. 3

Step-by-step explanation:

I used exemplar. the mean means add all the numbers and divide it buy how many there are.

5 + 7 + 9 = 21

21/3 = 7

0 3 4 6 6 7 7 7 9

Median = 6  (the middle number)

Mode = 7 (the most common number)

Range = 9 (Biggest number - smallest number)

Hope this helps!

If not then let me know!

Answer:

Yes it is a right angled triangle

Step-by-step explanation:

If its a right triangle it would satisfy the Pythagoras theorem.

29.3^2 = 858.49

28.5^2 = 812.25

6.8^2 =  46.24

Adding the last 2 values:

812.25 + 46.24

= 858.49

So YES.

you have to use intercept theorem, also known as Thales's theorem to slove this problem

Answer:

Step-by-step explanation:

1/2 chance for 1

1/4 for 2

1/8 for 3

1/16 for 4

1/32 for 5

1/64 for 6

1/128 for 7

1/256 for 8

1/512 for 9

1/1024 for 10

The function that is positive for the entire interval [–3, –2] is the graph of the function (b)

See attachment for the proper representation of the available options

For a function to be positive on the interval [-3,-2];

It means that the y values must be in the positive quadrant from x = -3 to x =-2

From the list of options, we have:

The y values from x = -3 to x =-2 is at the positive quadrant for the second graph i.e. option B

Hence, the function that is positive for the entire interval [–3, –2] is the graph of the function (b)

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Answer:

4/6

Step-by-step explanation:

if the pas is a dozen brownies

1/2 of a pan is 6 2/3 of 6 would be 4/6

Answer:

9 and 6

Step-by-step explanation:

You see, 9x2=18 and 6x3=18