Assume that military aircraft use ejection seats designed for men weighing between 133.8 lb and 208.0 lb. If women’s weights are normally distributed with a mean of 172.6 lb and a standard deviation of 42.4 lb, what percentage of women have weights between the ejection seat’s weight limits (that is, 133.8 to 208.0 lb)? Enter your answer as a percent rounded to one decimal place (do not add a "%"); add a trailing zeros as needed. The percentage of women with weights between 133.8 and 208.0 lb is [EjectPct] percent.

Answer:

5

Step-by-step explanation:

Since the diagonals of a parallelogram bisect each other, the two halves must be equal. Therefore:

[tex]15-x=2x \\\\15=3x \\\\x=5[/tex]

Hope this helps!

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

CE = EB since E is the midpoint of CB (proven by AD intersecting it).

If CE=EB, then:

[tex]2x=15-x\\[/tex]

Add [tex]x[/tex] to both sides

[tex]3x=15\\[/tex]

Divide both sides by 3

[tex]x=5[/tex]

Answer:

(A) P (n,k) = n!/(n-k)! divided by 2

(B) C (n,3) = n!/(12)(n-3)!

(C) C (n,k) = n!/(n-k)!(k!)

Step-by-step explanation:

Permutation deals with order or arrangement or position of objects. Where this does not matter, we use the Combination formula.

We divide by 2 in all cases, because no 2 chosen chairs should be adjacent.

For (B), n=10

C (n,3) = n!/(n-3)!(3!) divided by 2

3! = 3×2×1 = 6

The expression divided by 2 means it will be multiplied by 1/2

Hence 6×2 = 12

And we arrive at

C (n,3) =n!/(12)(n-3)!

Answer:

False.

The null hypothesis failed to be rejected.

At a significance level of 5%, there is not enough evidence to support the claim that the entering class has a mean SAT score that is significantly lower than 1520.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the entering class has a mean SAT score that is significantly lower than 1520.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=1520\\\\H_a:\mu< 1520[/tex]

The significance level is 0.05.

The sample has a size n=20.

The sample mean is M=1501.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=53.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{53}{\sqrt{20}}=11.851[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1501-1520}{11.851}=\dfrac{-19}{11.851}=-1.6[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=20-1=19[/tex]

This test is a left-tailed test, with 19 degrees of freedom and t=-1.6, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.6)=0.063[/tex]

As the P-value (0.063) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the entering class has a mean SAT score that is significantly lower than 1520.

Answer:

5

Step-by-step explanation:

Since this is a right triangle we can use trig functions

sin theta = opp /hyp

sin 30 = x / 10

10 sin 30 = x

10 * 1/2 = x

5 =x

Answer:

Graph D

Step-by-step explanation:

First, look at the x-intercepts (where the graph touches the x-axis): x= -1 and x= 3

This rules out Graph B and C which have x-intercepts at x= -3 and x= -1

Next, look at the y-intercept (where the graph touches the y-axis): y= -3

This rules out Graph A which has a y-intercept at y= 3

Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.

If two angles is said to create a linear pair, the angles are then regarded as supplementary and it is said that their measures often add up to 180°.

Note that Vertical angles are said to be pair of nonadjacent angles created by the crossing or the intersection of any two straight lines.

Since vertical angles are seen if "X" created by two straight lines then when you look at the image attached, you can see that the angle that can from this is Angle EFA.

Therefore, Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.

Learn more about vertical pair from

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Answer:

⬇⬇⬇⬇⬇⬇

⬇⬇⬇⬇⬇⬇

Step-by-step explanation:

1, 3, 4

proof below

(1) The area of the rectangle is 88 square inches

(3) The equation x² – 3x – 88 = 0 can be used to solve for the length of the rectangle.

(4) The triangle has a base of 11 inches and a height of 8 inches.

Area of a rectangle is the sum of the area of two equal right triangle.

Area of rectangle = 2(area of right triangle)

Area of rectangle = 2(44 sq inches) = 88 sq inches

Let the length = x

then the width becomes, x - 3

Area = x(x - 3) = 88

x² - 3x = 88

x² - 3x - 88 = 0

x = 11

width = 11 - 3 = 8

Thus, the statements that are true include;

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Answer:

1085 nuts per day x 17 days = 18,445 nuts in 17 days

Step-by-step explanation:

Answer:

The probability that the event will not happen is [tex]\frac{4}{17}[/tex]

Step-by-step explanation:

The occurrence of an event can be divided into two parts, the event would occur or the event would not occur. But the probability of an event is 1.

From the given question;

The probability of the event = 1

The probability that the event will happen, P = [tex]\frac{13}{17}[/tex]

Thus,

The probability that the event will not happen = probability of the event - probability that the event will happen

                                               = 1 - P

                                               = 1 - [tex]\frac{13}{17}[/tex]

                                               = [tex]\frac{17 - 13}{17}[/tex]

                                               = [tex]\frac{4}{17}[/tex]

Thus, the probability that the event will not happen is [tex]\frac{4}{17}[/tex].

Answer:

[tex]P(170<X<220)=P(\frac{170-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{220-\mu}{\sigma})=P(\frac{170-200}{50}<Z<\frac{220-200}{50})=P(-0.6<z<0.4)[/tex]

And we can find this probability with this difference:

[tex]P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)=0.655-0.274= 0.381 [/tex]

Step-by-step explanation:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(200,50)[/tex]  

Where [tex]\mu=200[/tex] and [tex]\sigma=50[/tex]

We want to find the following probability:

[tex]P(170<X<220)[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

And using this formula we got:

[tex]P(170<X<220)=P(\frac{170-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{220-\mu}{\sigma})=P(\frac{170-200}{50}<Z<\frac{220-200}{50})=P(-0.6<z<0.4)[/tex]

And we can find this probability with this difference:

[tex]P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)=0.655-0.274= 0.381 [/tex]

Answer:

63

Step-by-step explanation: The ratio from planet A to B is 100 to 3. If an elephant weight 2100 is planet a, then we are multiplying 21 to hundred. Whatever you do on the left side you have to do it on the right side and if you multiply 21 and 3 on the right side then you get 63.

Answer:

63 pounds

Step-by-step explanation:

The ratio for Planet A to Planet B is

100 : 3

Creating a proportionality with the unknown as x

=> [tex]\frac{100}{3} = \frac{2100}{x}[/tex]

Isolating x would give

x = [tex]\frac{2100 * 3}{100}[/tex]

x = 21 × 3

x = 63 pounds

Answer:

The line on the graph is y = 4, where no matter what the value of x is, the value of y will always be 4. Therefore, any line parallel to this one will be y = ?. If it passes through (-4, -6), that means that the equation is y = -6.

Answer:

С)))) Y= -6

Step-by-step explanation:

just did on edg. :D

Answer:

what method exactly r u using ????

[tex]answer \\ a. \frac{2}{117} \\ b. 4 \\ solution \\ a. \: \frac{2}{9} \times \frac{1}{13} \\ = \frac{2 \times 1}{9 \times 13} \\ = \frac{2}{117} \\ b. \: \frac{12}{5} \times \frac{35}{21} \\ = divide \: 35 \: by \: 5 \: it \: becomes \\ = 12 \times \frac{7}{21} \\ divide \: 21 \: by \: 7 \: it \: becomes \\ = 12 \times \frac{1}{3} \\ divide \: 12 \: by \: 3 \: it \: becomes \\ = 4 \times 1 \\ = 4 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

[tex](a) \frac{2}{117} [/tex]

[tex](b)4[/tex]

Step-by-step explanation:

[tex](a) \frac{2}{9} \times \frac{1}{13} \\ = \frac{2}{117} [/tex]

[tex](b) \frac{12}{5} \times \frac{35}{21} \\ = \frac{84}{21} \\ = \frac{28}{7} \\ = 4[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

b=30/2=15

peri= 90

Step-by-step explanation:

Answer: The complete question is "A circle has a radius of \blue{3}3start color #6495ed, 3, end color #6495ed. An arc in this circle has a central angle of 20^\circ20 ∘ 20, degrees. What is the length of the arc?"

The length of the arc is 1.06667 units.

Step-by-step explanation:

According to the question the radius of the circle [tex]R=3 \, units[/tex] and central angle of arc is [tex]\Theta =20^{o}[/tex]

As we know that the length of the arc is given as: [tex]L=R\Theta[/tex]

Where R is radius of the circle, L is the length of the arc and  [tex]\Theta[/tex] is central angle in radian.

Now, [tex]\Theta =20^{o}\times \frac{\Pi }{180}=\frac{\Pi }{9} \, rad[/tex]

Therefore, length of the arc is

[tex]L=3\times \frac{\Pi }{9}=\frac{\Pi }{3} =\frac{3.14}{3}=1.0466667 \, units[/tex]

Answer:

7/10=0.7

3+0.7=3.7

3.7

Hope this helps

Step-by-step explanation:

Answer:

[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]  

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55.

Step-by-step explanation:

Information given

We have the following data: 54 55 58 59 59 60 61 61 62 65

The sample mean and deviation can be calculated with the following formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X-i -\bar x)^2}{n-1}}[/tex]

[tex]\bar X=59.4[/tex] represent the sample mean

[tex]s=3.239[/tex] represent the sample standard deviation

[tex]n=10[/tex] sample size  

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic  

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true mean is higher than 55, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 55[/tex]  

Alternative hypothesis:[tex]\mu > 55[/tex]  

Replacing the info given we got:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing the info given we got:

[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]  

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55

Answer:

2

Step-by-step explanation:

-13+3b=-5-b

4b=8

b=2

Answer:

x = 3.6 cm

Step-by-step explanation:

By the theorem of intersecting secants,

"If two secants are drawn from a point outside the circle, product of the lengths of the secant segment and its external segment are equal."

3(3 + y) = 2(2 + 6 + 3)

9 + 3y = 2 × 11

3y = 22 - 9

3y = 13

y = [tex]\frac{13}{3}[/tex] cm = 4.33 cm

Now we will apply theorem of intersecting chords to determine the value of x.

" When two chords intersect each other in a circle, product of their segments are equal"

[tex]x\times 5=6\times 3[/tex]

[tex]x=\frac{18}{5}[/tex]

[tex]x=3.6[/tex] cm

Therefore, x = 3.6 cm and y = 4.33 cm

Answer:

X ≤ 13

Step-by-step explanation:

Part A: X ≤ 13

Part B:  Draw a closed circle from 13 and up on the number line.

Make the arrow look like this >.

The inequality will be x ≥ 13. The age of the person should be greater than or equal to 13.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

“Children under the age of 13 are not allowed to operate a boat.”

Let x be the age of the person.

The inequality to show the age of children who are allowed to operate a boat will be

x ≥ 13

The age of the person should be greater than or equal to 13.

More about the inequality link is given below.

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Answer:

B) ry-axis(x, y) → (–x, y)

Step-by-step explanation:

Got it right on edge2020 you can trust me :D

Answer:

p-value (0.0208) is less than alpha = 0.05 reject H0.

Step-by-step explanation:

we have the following data:

sample size = n = 75

x, the number to evaluate is 45

the sample proportion would be: x / n = 45/75

p * = 0.6

Now, the null and alternative hypotheses are:

H0: P = 0.72

Ha: P no 72

two tailed test

statistic tes = z = (p * - p) / [(p * (1-p) / n)] ^ (1/2)

replacing we have:

z = (0.6 - 0.72) / [(0.72 * (1-0.72) / 75)] ^ (1/2)

z = -2.31

p-vaule = 2 * p (z <-2.31)

using z table, we get:

p-vaule = 2 * (0.0104)

p-vaule = 0.0208

Therefore, p-value (0.0208) is less than alpha = 0.05 reject H0.

Answer:x greater than -9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

The variable is

X: average mass of a sample of rocks collected in the waters of a region. (measured in grams)

Variables can be:

Quantitative: they represent number, any characteristic that can be "counted" is a quantitative variable, the most common examples are weight, volume, temperature, height, etc...

There are two types of quantitative variables:

⇒ Discrete variables: The only take certain values within the interval of definition of the variable, for example "number of sales" or "money in a wallet"

⇒ Continuous variables: They can take any value within an interval, in this example that you are working with mass, depending on the precision of the scale the mass can have infinite decimal values.

Qualitative: they represent characteristics that cannot be counted, meaning, they are not represented by numbers. There are many attributes that are qualitative variables, for example: colors, race of an animal, phenotypes, types of business, etc...

1)

The variable in this example is Quantitative, it takes numerical values, and the correct option is:

D. Quantitative, because numerical values, found by either measuring or counting, are used to describe the data.

2)

The values of mass of the rocks can take any value within the range of definition of the variable, they only depend on the precision of the scale used to weight the rocks.

B. Interval, because the differences in the data can be meaningfully measured, but the data do not have a true zero point.

3)

A standard 52-card deck contains 13 cards for each suit (clubs, diamonds, hearts and spades)

To calculate the probability of choosing a card at random and it being a Diamond, supposing that all cards are equally probable, you have to divide the total number of diamonds by the total number of cards in the deck:

P(diamond)= 13/52= 0.25

For items 4) and 5) the contingency tables are attached.

4)

a. and b. are conditional probabilities, to calculate them you have to apply the following formula: [tex]P(A|B)= \frac{P(AnB)}{P(B)}[/tex]

This means that the probability of the event "A" given that event "B" has occurred is equal to the probability of the intersection between events "A" and "B" divided by the probability of event "B"

a. P(A|C)= [tex]\frac{P(AnC)}{P(C)}[/tex]

To calculate the probability of the intersection P(A∩C) you have to divide the observations where both events cross by the total of observations on the table:

P(A∩C)= 10/50= 0.20

The probability of C is found in the margins of the table, in this case you have to divide the total of observations for event C by the total of observations of the table:

P(C)= 21/50= 0.42

Now you can calculate the asked probability:

[tex]P(A|C)= \frac{0.2}{0.42}= 0.48[/tex]

b. P(C|A)= [tex]\frac{P(AnC)}{P(A)}[/tex]

From item a. we already know that P(A∩C)= 10/50= 0.20

The probability of event A is  in the margin of the table and you calculate it as:

P(A)= 27/50= 0.54

Then:

[tex]P(C|A)= \frac{0.20}{0.54} = 0.37[/tex]

c. P(BE)

This symbolized the probability of the events "B" and "E" occurring at the same time, you can also symbolize it as P(B∩E)

To calculate the probability of B and E happening you have to do as follows:

P(B∩E)= 8/50= 0.16

5)

a. P(C|A)= 0.37 (As calculated in 4b.)

b. P(BE) and c. P(EB) ⇒ Both expressions symbolize the intersection between events "B" and "E", P(B∩E)= P(E∩B)= 0.16 (As calculated in 4c.)

I hope this helps!

Answer:

[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}[/tex]

[tex]C(t) =\dfrac{ r}{k}- e^{ -kt}[/tex]   ,thus, the  function is said to be an increasing function.

Step-by-step explanation:

Given that:

[tex]\dfrac{dC}{dt}= r-kC[/tex]

[tex]\dfrac{dC}{r-kC}= dt[/tex]

Taking integration on both sides ;

[tex]\int\limits\dfrac{dC}{r-kC}= \int\limits \ dt[/tex]

[tex]- \dfrac{1}{k}In (r-kC)= t +D[/tex]

[tex]In(r-kC) = -kt - kD \\ \\ r- kC = e^{-kt - kD} \\ \\ r- kC = e^{-kt} e^{ - kD} \\ \\r- kC = Ae^{-kt} \\ \\ kC = r - Ae^{-kt} \\ \\ C = \dfrac{r}{k} - \dfrac{A}{k}e ^{-kt} \\ \\[/tex]

[tex]C(t) =\frac{ r}{k} - \frac{A}{k}e^{ -kt}[/tex]

here;

A is an integration constant

In order to determine A, we have [tex]C(0) = C0[/tex]

[tex]C(0) =\frac{ r}{k} - \frac{A}{k}e^{0}[/tex]

[tex]C_0 =\frac{r}{k}- \frac{A}{k}[/tex]

[tex]C_{0} =\frac{ r-A}{k}[/tex]

[tex]kC_{0} =r-A[/tex]

[tex]A =r-kC_{0}[/tex]

Thus:

[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}[/tex]

2. Assuming that C0 < r/k, find lim t→[infinity] C(t) and interpret your answer

[tex]C_{0} < \lim_{t \to \infty }C(t) \\ \\C_0 < \dfrac{r}{k} \\ \\kC_0 <r[/tex]

The equation for C(t) can  be rewritten as :

[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}C(t) =\dfrac{ r}{k} - \left (+ve \right )e^{ -kt} \\ \\C(t) =\dfrac{ r}{k}- e^{ -kt}[/tex]

Thus;  the  function is said to be an increasing function.

Answer:

A. The solutions are [tex]x=3i,\:x=-3i[/tex].

B. The factored form of the quadratic expression [tex]x^2+9=(x-3i)(x+3i)[/tex]

Step-by-step explanation:

A. To find the solutions to the quadratic equation [tex]x^2+9=0[/tex] you must:

[tex]\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\x^2+9-9=0-9\\\\\mathrm{Simplify}\\\\x^2=-9\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{-9},\:x=-\sqrt{-9}[/tex]

[tex]x=\sqrt{-9} = \sqrt{-1}\sqrt{9}=\sqrt{9}i=3i\\\\x=-\sqrt{-9}=-\sqrt{-1}\sqrt{9}=-\sqrt{9}i=-3i[/tex]

The solutions are:

[tex]x=3i,\:x=-3i[/tex]

B. Two expressions are equivalent to each other if they represent the same value no matter which values we choose for the variables.

To factor [tex]x^2+9[/tex]:

First, multiply the constant in the polynomial by [tex]i^2[/tex] where [tex]i^2[/tex] is equal to -1.

[tex]x^2+9i^2[/tex]

Since both terms are perfect squares, factor using the difference of squares formula

[tex]a^2-i^2=(a+i)(a-i)[/tex]

[tex]x^2+9=x^2+9i^2=\left(-3i+x\right)\left(3i+x\right)[/tex]

Answer:

90% probability that she has at least one marble of each color

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

What is the probability that she has at least one marble of each color?

Desired outcomes:

Two red(from a set of 2) and one yellow(from a set of 3)

Or

One red(from a set of 2) and two yellows(from a set of 3).

So

[tex]D = C_{2,2}*C_{3,1} + C_{2,1}*C_{3,2} = \frac{2!}{2!(2-2)!}*\frac{3!}{1!(3-1)!} + \frac{2!}{1!(2-1)!}*\frac{3!}{2!(3-2)!} = 3 + 6 = 9[/tex]

Total outcomes:

Three marbles, from a set of 3 + 2 = 5. So

[tex]T = C_{5,3} = \frac{5!}{3!(5-3)!} = 10[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{9}{10} = 0.9[/tex]

90% probability that she has at least one marble of each color

Answer:

x ≥-1

Step-by-step explanation:

-1/2x -3 ≤ -2.5

Add 3 to each side

-1/2x -3+3 ≤ -2.5+3

-1/2x ≤ .5

Multiply each side by -2, remembering to flip the inequality

-2 * -1/2x ≥ 1/2 * -2

x ≥-1

Answer:

105.13ft^2

Step-by-step explanation:

[tex]A=lw\\=10*8\\=80ft^2[/tex]

Rectangle

[tex]A=\frac{1}{2} \pi r^2\\=\frac{1}{2\pi } 4^2\\=25.13[/tex]

Add both together

80+25.13

=105.13

Answer :  105.13

Step-by-step explanation: