A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 14 cm long and 4 cm wide. The diameter of each circle is the width of the rectangle. What is the area of the bookmark? Use 3.14 for π.
_____
The area of the bookmark is_____cm2.

Answer:

a) 0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb

b) No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.

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 normal distributions can be 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.

Assume that weights of males are normally distributed with a mean of 160 lb and a standard deviation of ​35 lb.

This means that [tex]\mu = 160, \sigma = 35[/tex]

Sample of 10:

This means that [tex]n = 10, s = \frac{35}{\sqrt{10}} = 11.07[/tex]

a) Find the probability that it is overloaded because they have a mean weight greater than 158 lb.​

This is 1 subtracted by the pvalue of Z when X = 158. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{158 - 160}{11.07}[/tex]

[tex]Z = -0.18[/tex]

[tex]Z = -0.18[/tex] has a pvalue of 0.4286

1 - 0.4286 = 0.5714

0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb.

b.) Does this elevator appear to be​ safe?

No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.

Answer:

1/5+8/10=1

Step-by-step explanation:

1/5 = 2/10

Answer:

no of science teachers is 20

no of students is 600

ratio=20/600

=20:600

=1:30

pls give me brainliest

Answer:

If Jenny gives her brother 28 marbles, they will have 59 marbles each.

Step-by-step explanation:

The key to finding this answer is a mean, or average. Find it for the number of marbles:

[tex]\text{Mean}=\frac{87+31}{2}= \frac{118}{2}=59 \text{ marbles}[/tex]

So, on average, each one should have 59 marbles.

Finally, to find out how many marbles Jenny should give to her brother, subtract the average (59 marbles) from her count:

[tex]87-59=28 \text{ marbles}[/tex]

This means Jenny would give up 28 of her marbles to her brother.

Answer:

x= 230

Step-by-step explanation:

since a circle is 360 degrees

x + 130 = 360

x= 360 -130

x=230

Answer:

74

Step-by-step explanation:

Answer:

a) Z = 2.33

b) Z = 1.7

c) Z = 1.65.

d) Z = 0.84.

Step-by-step explanation:

Z-score:

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, which is also the area to the left of z. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, which is also the area to the right of z.

A. The area to the right of z is 0.01.

Z has a pvalue of 1 - 0.01 = 0.99. So Z = 2.33.

B. The area to the right of z is 0.045.

Z has a pvalue of 1 - 0.045 = 0.955. So Z = 1.7

C. The area to the right of z is 0.05.

Z has a pvalue of 1 - 0.05 = 0.95. So Z = 1.65.

D. The area to the right of z is 0.2.

Z has a pvalue of 1 - 0.2 = 0.8. So Z = 0.84.

Answer:x= 9

Step-by-step explanation:

-4(x+5) = 16

-4*x= -4x -4*5= -20

16 - -20= 36

-4x/-4= x 36/-4=9

9514 1404 393

Answer:

  (a, b) = (√2/2, √2/2) . . . . . choice C in each case

Step-by-step explanation:

The points on a unit circle will not have coordinate values greater than 1 (eliminates √2). The coordinates will only be 0 or 1 if the point is on one of the axes. The coordinates (a, b) of the point at 45° are ...

  (cos(45°), sin(45°)) = (a, b) = (√2/2, √2/2)

The coordinate of point (a, b) is (√2/2, √2/2)

Note that the points on a unit circle will not have coordinate values greater than 1.

The coordinates will only be 0 or 1 if the point is on one of the axes. The coordinates (a, b) of the point at 45° is given according to the coordinate point (cos45, sin45)

a = cos45 = √2/2

b = sin45 = √2/2

Hence the coordinate of point (a, b) is (√2/2, √2/2)

Learn more on unit circle here: https://brainly.com/question/23989157

Answer is in the file below

tinyurl.com/wpazsebu

Answer:

Step-by-step explanation:

Half of the animals are cats. If they take in 5 cats, then the total number of animals is 2×5 = 10.

If they take in 8 animals, the number of cats is ½ of 8 = 4.

If they take in 6 cats, then the total number of animals is 2×6 = 12.

If they take in 16 animals, the number of cats is ½ of 16 = 8.

Answer:

69.72 inches.

Step-by-step explanation:

The best point estimate for the average height if males in the United States is...

For large samples, as we have here, the best point estimate is the sample mean. In this question, the sample mean is of 69.72 inches, so the answer is 69.72 inches.

Answer:

i cant see the direction sorry :(

Step-by-step explanation:

I assume the given plane has equation

x + 3y + 4z = d

for some constant d ≠ 0.

You want to maximize the function V(x, y, z) = xyz subject to the above constraint. The Lagrangian would be

L(x, y, z, λ) = xyz - λ (x + 3y + 4z - d)

Find its critical points:

∂L/∂x = yz - λ = 0

∂L/∂y = xz - 3λ = 0

∂L/∂z = xy - 4λ = 0

∂L/∂λ = x + 3y + 4z - d = 0

The first three equations tell you that λ = yz = xz/3 = xy/4. Then, for instance,

yz = xz/3   →   3yz - xz = z (3y - x) = 0   →   z = 0   or   3y - x = 0

If z = 0, we get zero volume which is not useful. So 3y = x. Similarly, you would find x = 4z and 3y = 4z, so a critical point occurs when x = 3y = 4z.

In the fourth equation, we get upon substituting

x + 3y + 4z = 3x = d   →   x = d/3, y = d/9, z = d/12

Then the largest volume of this box would be

V(d/3, d/9, d/12) = d ³ / 324

Answer:

0.7

Step-by-step explanation:

2,3,4,6,8,9,10 are the possible choices.

∴P(even no. or multiple of 3)

= 7/10

Answer:

7/10 or 70%

Step-by-step explanation:

1     no

2     yes

3     yes

4     yes

5     no

6     yes

7     no

8     yes

9     yes

10    yes

7/10 are even or multiples of 3, therefore you have a 70% chance of drawing one of them

Answer:

None

Step-by-step explanation:

2(x + 10) - 17 = 2x - 2

simplify:

2x + 20 - 17 = 2x - 2

2x + 3 = 2x - 2

subtract 3 from both sides of the equation:

2x = 3x -5

no solution

Answer:

The coordinates of point A are [tex]A(x,y) = (4,6)[/tex].

Step-by-step explanation:

The location of point A is defined by the vectorial sum of absolute coordinates of point P and coordinates of point A relative to coordinates of point P, that is:

[tex]A(x,y) = P(x,y) + \vec v_{PA}[/tex] (1)

[tex]P(x,y)[/tex] - Absolute coordinates of point P.

[tex]A(x,y)[/tex] - Absolute coordinates of point A.

[tex]\vec v_{PA}[/tex] - Vector to point A relative to point P.

If we know that [tex]P(x,y) =(6,4)[/tex] and [tex]\vec v_{PA} = (-2, 2 )[/tex], then the absolute coordinates of point A are:

[tex]A(x,y) = (6,4) +(-2,2)[/tex]

[tex]A(x,y) = (4,6)[/tex]

The coordinates of point A are [tex]A(x,y) = (4,6)[/tex].

Answer:

It definitely is linear, and it is a straight line

Step-by-step explanation:

Try using desmos, it may help

Answer:

A) it is linear and it is a straight line

Step-by-step explanation:

it is a linear equation. It will be straight

y=mx+b is linear

Answer:

B

Step-by-step explanation:

Both triangles are similar. The similarity ratio between AB and EF is 4, which must mean that FG is BC (60)/4. The area of a rectangle is base x height -> 6.25 x 15 = 93.75 square cm

Hope this helps!

Answer:

Coefficient is your answer

Answer:

3 is a coefficient

Step-by-step explanation:

a constant is a number without a variable and that is unchanging

3 has the variable w attached to it and will change with the value of w

hope this helps <3

Answer:

it takes his dad 3 hours

Step-by-step explanation:

4.5-1.5 =3

Answer: 1224 miles

Step-by-step explanation:

Given

the average speed of a person is 51 mph

If speed is increased to 72 mph, he would have reached 7 hr earlier

Suppose d and t be the distance and time taken

[tex]\Rightarrow t_1=\dfrac{d}{51}[/tex]

If the speed is 72 mph

[tex]\Rightarrow t_2=\dfrac{d}{72}[/tex]

Also, [tex]t_1-t_2=7[/tex]

[tex]\Rightarrow \dfrac{d}{51}-\dfrac{d}{72}=7\\\\\Rightarrow \dfrac{1}{51}-\dfrac{1}{72}=\dfrac{7}{d}\\\\\Rightarrow \dfrac{24-17}{1224}=\dfrac{7}{d}\\\\\Rightarrow \dfrac{7}{1224}=\dfrac{7}{d}\\\\\Rightarrow d=1224\ miles[/tex]

Answer/Step-by-step explanation:

There are actually two methods that can be used to calculate AC (x):

1. Using Pythagorean Theorem

2. Using Trigonometric Function

1. Using Pythagorean Theorem, we have:

x = √(15² + 20²)

x = √625

x = 25 units

2. Using Trigonometric Function:

Reference angle = 37°

Adjacent = 20

Opposite = 15

Hypotenuse = x

Apply SOH:

Sin 37 = Opp/Hyp

Sin 37 = 15/x

x × Sin 37 = 15

x = 15/sin 37

x = 24.9246021 ≈ 25 units (nearest whole number)

Answer:

x+y≤15

Step-by-step explanation:

We need to write an inequality that represents the sum of x and y is at most 15. At most in inequality is defined as less than or equal to i.e. ≤.

Sum of x and y means x+y

The inequality becomes,

x+y≤15

Hence, the correct option is (b).

The inequality which represents the sum of x and y is at most 15 is; Choice (b) x+y_<15

According to question;

In essence, the sum of x and y is either equal to or lesser than 15.

Therefore, the inequality is Choice B; x+y_<15

Read more;

https://brainly.com/question/23382973

Answer:

8

Step by Step Explanation

Answer and Step-by-step explanation:

To find Z, we have to use the trigonometric function of Sine.

The Sine trig function looks like this:

sin(Angle) = [tex]= \frac{opposite.side}{hypotenuse}[/tex]

Plug in the values and solve for z.

[tex]sin(30) = \frac{4}{z} \\\\\\\\\\z = \frac{4}{sin(30)}[/tex]

Plug into a calculator and solve.

We get z to be 8.

#teamtrees #PAW (Plant And Water)

Answer:

A (50)

Step-by-step explanation:

Mean is the total numbers added up divided by the # of numbers.

There are 6 numbers.

51 + 60 + 80 + 32 + 47 + 30 = 300

300/6 = 50

Therefore, the answer is A.

Answer:

A

Step-by-step explanation:

Because to find the mean you add up all the numbers.

51+60+80+32+47+30=300

Then your suppose to divide by the sum.

300/6=50

Answer:

8^(3n+1) = 80/5

8^(3n+1) = 16

(2^3)^(3n+1) = 2^4

2^(3*(3n+1) = 2^4

Having same power so;

9n+3 = 4

9n = 4-3

9n = 1

n = 1/9