What is the value of X in the triangle below? if the answer is not an integer, leave it in simplest radical form

Answer:

58%

Step-by-step explanation:

This is a problem of conditional probability.

Let A represent the event that student has dark hair.

So P(A) = 55% = 0.55

Let B represents the event that student has blue eyes.

So, P(B) = 60% = 0.60

Probability that student has blue eyes and dark hairs = P(A and B) = 35% = 0.35

We are to find the probability that a randomly selected student will have dark hair, given that the student has blue eyes. Using the given formula and values, we get:

[tex]P(A|B)=\frac{P(A \cap B)}{P(B)}\\\\ P(A|B)=\frac{0.35}{0.60}\\\\ P(A|B)=0.58[/tex]

Therefore, there is 0.58 or 58% probability that the student will have dark hairs, given that the student has blue eyes.

Point C must be the center of the circle, since all of the radii connect there.

this is super confusing

what are we supposed to evaluate, here? i dunno what your asking us to do

Answer:

Calculate the Difference Quotient for f(x)=2x^2-3

Find f(x+h) and f(x), and plug these values into the difference quotient formula.

definition is valid since center is exactly 1radius away from any point on the outersurface.

other figures do not fit this defn

Answer:

Step-by-step explanation:

Her definition is valid because the sphere is basically defined by its radius, which is the equidistant points towards a center. If points are not equidistant, then that's not a sphere.

Also, Tabitha is considering "a set of points" referring to infinite points on the surface of the sphere. The single point she mentioned is the center.

Therefore, Tabitha's definition is valid because she's considering all elements that define a sphere.

Answer: 36 toy cars

Step-by-step explanation: If Lori bought gifts for her 3 brothers and 6 cousins then she bought gifts for 9 people (3+6). Since she bought 4 toy cars for each of them she bought 36, which is calculated by multiplying 9 x 4.

9 x 4 = 36

Lori bought a total of 36 gifts for her three brothers and six cousins since she bought four gifts for each of them. This was calculated by multiplying the total number of recipients (3+6) by the number of grants each person got (4).

The question is asking how many gifts Lori bought in total. Since Lori bought four toy cars for each of her three brothers and six cousins, we need to multiply the total number of recipients by the number of gifts per person. This gives us (3 brothers + 6 cousins) * 4 skills = 36. So, Lori bought a total of 36 grants.

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Answer:

[tex]A=2,002.9\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of a regular polygon is equal to

[tex]A=\frac{1}{2}rP[/tex]

where

r is the apothem

P is the perimeter

step 1

Find the perimeter

The perimeter of a regular nonagon is

[tex]P=ns[/tex]

where

n is the number of sides (n=9)

s is the length side (s=18 cm)

substitute

[tex]P=9*18=162\ cm[/tex]

step 2

Find the apothem

The apothem in a regular polygon is equal to

[tex]r=\frac{1}{2}(s)cot(180\°/n)[/tex]

we have

[tex]s=18\ cm[/tex]

[tex]n=9[/tex]

substitute

[tex]r=\frac{1}{2}(18)cot(180\°/9)[/tex]

[tex]r=9cot(20\°)=24.73\ cm[/tex]

step 3

Find the area of the regular nonagon

[tex]A=\frac{1}{2}rP[/tex]

substitute

[tex]A=\frac{1}{2}(24.73)(162)=2,002.9\ cm^{2}[/tex]

perpendicular slopes are those that are flipped and opposite signs to the original slope

Answer:

The area is 48 cm^2

Step-by-step explanation:

The formula for area of a triangle is

A = 1/2 b*h

A = 1/2 * 8cm*12cm

A = 1/2 *96cm^2

A = 48 cm^2

The area is 48 cm^2

Answer:

A = 48 cm^2

Step-by-step explanation:

k12

Answer:

1.

Horizontal Asymptote is y = 0

2.

Vertical Asymptote is x = -4

3.

No Slant Asymptote

4.

Hole at (5, 0.14)

5.

x-intercepts:

x-intercept [tex](-\frac{1}{2},0)[/tex]

y-intercepts:

y-intercept  [tex](0,\frac{1}{16})[/tex]

6.

Domain is [tex]{x|x\neq -4,5}[/tex]

Step-by-step explanation:

1. Horizontal Asymptotes

* If the degree of the numerator is less than the degree of the denominator (this is our case since multiplying will give the numerator a degree of 2 and denominator a degree of 3), then y = 0 is the only horizontal asymptote

Horizontal Asymptote is y = 0

2. Vertical Asymptotes

* To get VA (vertical asymptote), we set the denominator equal to zero.

Before doing this, we see that we can cancel out (x-5) from both numerator and denominator so the denominator becomes (x+4)^2. Now we find VA:

[tex](x+4)^2=0\\x+4=0\\x=-4[/tex]

Vertical Asymptote is x = -4

3. Oblique asymptotes

* If the degree of numerator is less than the degree of the denominator (this is our case as explained above), then there is no slant asymptote.

No Slant Asymptote

4. Holes

There is hole in a rational function if there is the same factor in both numerator and denominator (before simplifying, only after factoring). Set that equal to 0 and solve. Then, cross out the common factor and put the x-value into the function and get the y-value of the hole.

We can see that there is a factor of (x-5) in both the numerator and denominator. We set it equal to 0 and solve for x:

[tex]x-5=0\\x=5[/tex]

Putting x = 5, we get:

Y value of hole = [tex]g(x)=\frac{2x+1}{(x+4)^2}\\g(5)=\frac{2(5)+1}{(5+4)^2}\\g(5)=0.14[/tex]

Hole at (5, 0.14)

5. Intercepts

To get x-intercepts, we set y = 0 (g(x) = 0) and for y-intercepts we set x = 0.

x-intercepts:

[tex]0=\frac{2x+1}{(x+4)^2}\\2x+1=0\\2x=-1\\x=-\frac{1}{2}[/tex]

x-intercept [tex](-\frac{1}{2},0)[/tex]

y-intercepts:

[tex]y=\frac{2x+1}{(x+4)^2}\\y=\frac{2(0)+1}{(0+4)^2}\\y=\frac{1}{16}[/tex]

y-intercept  [tex](0,\frac{1}{16})[/tex]

6. Domain

This is the set of allowed x-values of the function. We simply disregard any value that would make the denominator equal to 0.

So we have:

x - 5 = 0, x = 5

and

(x+4)^2 = 0, x = -4

Domain is the set of all real numbers x EXCEPT x = -4 and x = 5

Domain is [tex]{x|x\neq -4,5}[/tex]

i don't think so.....

sorry

This answer explains how to determine the volume of an open box created by cutting squares from each corner of a piece of cardboard, discussing the relations between variables, volume calculation, domain restrictions, and a guess-and-check method for maximizing volume.

Variables: In the open box scenario, let's assume the size of the square cut from each corner is 'x'.

Relation to Dimensions: After cutting and folding, the length of the box would be (6ft - 2x), the width would be (6ft - 2x), and the height would be 'x'.

Product for Volume: The volume formula is length x width x height. Substituting the expressions, we get V = x(6 - 2x)(6 - 2x).

Domain: The domain for the volume function would be 0 < x < 3 (as the size of the cut cannot exceed half of the side length).

Guess and Check: To find the maximum volume, you can test values within the domain like x = 1, 1.5, 2, 2.5, and 3 to determine the optimal cut size and corresponding dimensions and volume.

Answer:

You will need 7 more pennies.

Step-by-step explanation:

Answer:

7 more pennies.

Step-by-step explanation:

Quarters are .25 each and you have 2 so that is .50.

Dimes are .10 each and you have 12 so that is 1.20

Pennies are .01 each and you have 23 so that is .23.

Added together and you get 1.93. So all you need is 7 pennies to get 2 dollars.

Answer:

the answer would be 6:30 pm

Step-by-step explanation:

if you left work at 5:15 and it took 1 1/4 min to get home

you would

find 1/4 witch would be 15 min because 60/4= 15  

then add 1:15 to 5:15

1:15 + 5:15 = 6:30 pm

you arrived home at 6:30 pm

Mr. Banks would get home at 6:30 PM after leaving work at 5:15 PM and driving for 1 hour and 15 minutes.

The student asked what time Mr. Banks would arrive home if he left work at 5:15 PM and took 1 and 1/4 hours to drive home. To solve this, we need to add the travel time to the departure time. Since 1 and 1/4 hours is the same as 1 hour and 15 minutes, we simply add this to 5:15 PM. Adding 1 hour to 5:15 PM, we get 6:15 PM. Then, adding the remaining 15 minutes, we get 6:30 PM. This means Mr. Banks would arrive home around 6:30 PM.

Answer:

The solution in the attached figure

[tex]sin(A)=\frac{12}{13}[/tex]

[tex]sin(B)=\frac{5}{13}[/tex]

[tex]cos(A)=\frac{5}{13}[/tex]

[tex]cos(B)=\frac{12}{13}[/tex]

[tex]sin(A)=cos(B)[/tex]

[tex]sin(B)=cos(A)[/tex]

Step-by-step explanation:

we know that

In the right triangle ABC

sin(A)=cos(B) and cos(A)=sin(B)

because

[tex]A+B=90\°[/tex] -------> by complementary angles

step 1

Find sin(A)

The function sine of angle A is equal to divide the opposite side angle A by the hypotenuse

[tex]sin(A)=\frac{BC}{AB}[/tex]

substitute the values

[tex]sin(A)=\frac{12}{13}[/tex]

step 2

Find sin(B)

The function sine of angle B is equal to divide the opposite side angle B by the hypotenuse

[tex]sin(B)=\frac{AC}{AB}[/tex]

substitute the values

[tex]sin(B)=\frac{5}{13}[/tex]

step 3

Find cos(A)

The function cosine of angle A is equal to divide the adjacent side angle A by the hypotenuse

[tex]cos(A)=\frac{AC}{AB}[/tex]

substitute the values

[tex]cos(A)=\frac{5}{13}[/tex]

[tex]cos(A)=sin(B)[/tex]

step 4

Find cos(B)

The function cosine of angle B is equal to divide the adjacent side angle B by the hypotenuse

[tex]cos(B)=\frac{BC}{AB}[/tex]

substitute the values

[tex]cos(B)=\frac{12}{13}[/tex]

[tex]cos(B)=sin(A)[/tex]

Answer: 5%

Step-by-step explanation: In order to calculate the sales tax rate you divide the amount of the sales tax by the purchase price.

$2/40 = .05 = 5%

The interest rate is 5%.

Answer:

[tex]cos(0\°)=-\frac{\sqrt{85}}{11}[/tex]

[tex]tan(0\°) = -\frac{6}{\sqrt{85}}\\\\[/tex]

Step-by-step explanation:

We know by definition that:

[tex]cos ^ 2(x) = 1-sin ^2(x)[/tex]

We also know that:

[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]

[tex]sec(x) = \frac{1}{cos(x)}[/tex]

Then we can use these identities to solve the problem

if [tex]sin(0\°) = \frac{6}{11}[/tex] then [tex]cos^2(0\°) = 1-(\frac{6}{11})^2[/tex]

[tex]cos(0\°) = \±\sqrt{\frac{85}{121}}\\\\cos(0\°)=\±\frac{\sqrt{85}}{11}[/tex]

As [tex]sec(x) <0[/tex] then [tex]cos(x) <0[/tex]. Therefore we take the negative root:

[tex]cos(0\°)=-\frac{\sqrt{85}}{11}[/tex]

Now that we know [tex]sin(0\°)[/tex] and [tex]cos(0\°)[/tex] we can find [tex]tan(0\°)[/tex]

[tex]tan(0\°) = \frac{sin(0\°)}{cos(0\°)}\\\\tan(0\°) = \frac{\frac{6}{11}}{\frac{-\sqrt{85}}{11} }\\\\tan(0\°) = -\frac{6}{\sqrt{85}}\\\\[/tex]

To find the sales tax rate, you need to find what percentage of the base price the difference in cost is.

First, subtract 22.99 from 24.10:

24.1-22.99=1.11

Now, divide 1.11 by 22.99:

1.11/22.99=0.0483

Multiply 0.0483 by 100 to convert the decimal to a percentage:

0.0483*100=4.83

The sales tax rate was 4.83%.

Hope this helps!!

Answer:

[tex]304\dfrac{4}{7}\ milliliters[/tex]

Step-by-step explanation:

If there are 3 milliliters of compound A used for every 4 milliliters of compound B, then we can denote that we use 3x milliliters of compound A and 4x milliliters of compound B to get 533 milliliters of the drug. Thus,

[tex]3x+4x=533,\\ \\7x=533,\\ \\x=\dfrac{533}{7}\ milliliters.[/tex]

Hence, a chemist must take

[tex]4\cdot \dfrac{533}{7}=\dfrac{2132}{7}=304\dfrac{4}{7}\ milliliters[/tex]

of compound B.

Answer:

228.43 ml

Step-by-step explanation:

The ratio of compound A to compound B will be; 4: 3

4:3 is the same as 4x:3x where 4x is compound A and 3x is compound B.

We can solve for "x":

If amount of compound A is 4x  and compound B is 3x;

Then; 4x + 3x = 533

            7 x = 533

               x = 533/7

Then amount of compound B is 3x = 3(533/7)

                                                          = 228.43 ml

Answer:

A. [tex]9\sqrt{10}[/tex]

Step-by-step explanation:

The given expression is   [tex]-6\sqrt{10}+5\sqrt{90}[/tex]

Remove the perfect square from the second radical.

[tex]=-6\sqrt{10}+5\sqrt{9\times10}[/tex]

[tex]=-6\sqrt{10}+5\sqrt{9} \times \sqrt{10}[/tex]

This implies

[tex]=-6\sqrt{10}+15\sqrt{10}[/tex]

[tex]=(-6+15)\sqrt{10}[/tex]

[tex]=9\sqrt{10}[/tex]

The correct choice is A

Answer:

x = -12

Step-by-step explanation:

x - 8 = -20

+8        +8

Answer:

The null and alternate hypothesis would be

H0:   pm = pf  

H1:   pm < pf  

Test is left tailed

The test statistic: z = -0.98

The p-value: 0.1365

We fail to reject the null hypothesis

Conclusion:  There is not enough evidence to support the claim that the proportion of men who own cats is less than the proportion of women who own cats

Step-by-step explanation:

The null and alternate hypothesis would be

H0:  pm = pf

Ha:  pm < pf    

because they say that the test claim is the proportion of men is smaller less than the proportion of women.  The null hypothesis always get the statement of equality (the equals sign).  In this case, the alternate hypothesis is the claim.  

The test is left tailed because the alternate hypothesis has a <  sign.  It's strictly less than a value, so it's one tailed, and the < or > sign points to the area of rejection, so in this case, it's pointing left

The test statistic is calculation is attached as a photo  

The p-value is found by looking it up on the chart using z = -0.98

Since 0.1365 > 0.005, we fail to reject the null hypothesis

Because we fail to reject the null, there is not enough evidence to support the claim

We perform a hypothesis test for the difference between two proportions. The null hypothesis states the proportion of men owning cats equals the one of women, while the alternative hypothesis says it's smaller. We do a one-tailed test, and if the p-value<=0.005, we reject the null hypothesis.

In order to test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at a .005 significance level, we need to perform a hypothesis test for the difference between two proportions.

The null hypothesis (H0) is that the proportion of men who own cats (pM) equals the proportion of women who own cats (pF), while the alternative hypothesis (H1) is that pM smaller than pF. So they are:

H0: pM = pF

H1: pM < pF

Basing on the samples, 25% of 40 men and 35% of 40 women owned cats. We are making a one-tailed (left-tailed) test because we want to know if pM is less than pF.

The test statistic and p-value have to be calculated using these formulas or a statistical software. If the p-value is less or equal to .005 (our alpha), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

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Answer:

1/3 of a pie.

Step-by-step explanation:

Givens

There are 3 pies

There are 9 people

Answer

Each person gets 3/9 or 1/3 of a pie

So each pie is cut into thirds.

Answer:

B.) -1/3

Step-by-step explanation:

According to the rational root theorem, rational roots will be of the form ...

±(divisor of the constant)/(divisor of the leading coefficient)

= ±(one of {1, 2, 3, 4, 6, 12})/(one of {1, 2, 4})

You will note that 3 is not among the possible denominators, hence -1/3 is not a possible rational root.

the answer is b cause its is correct

Answer:

B

Step-by-step explanation:

Use the Heron's formula for the area of the triangle:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]

where a, b, c are lengths of triangle's sides and [tex]p=\dfrac{a+b+c}{2}.[/tex]

Since [tex]a=11.5,\ b=13.7,\ c=12.2,[/tex] then

[tex]p=\dfrac{11.5+13.7+12.2}{2}=18.7.[/tex]

Hence,

[tex]A=\sqrt{18.7(18.7-11.5)(18.7-13.7)(18.7-12.2)}=\sqrt{18.7\cdot 7.2\cdot 5\cdot 6.5}=\\ \\=\sqrt{11\cdot 1.7\cdot 9\cdot 4\cdot 0.2\cdot 5\cdot 5\cdot 1.3}=30\sqrt{11\cdot 1.7\cdot 0.2\cdot 1.3}=30\sqrt{4.862}\approx 66.1\ un^2.[/tex]

Answer:

Choice b is correct.

Step-by-step explanation:

We have given the sides of triangle.

a = 11.5, b = 13.7 and c  = 12.2

We have to find the area of the triangle.

The formula to find the area of the triangle when three sides are given is:

A = √p(p-a)(p-b)(p-c)

where p = (a+b+c) / 2

p = (11.5+13.5+12.2)/2

p = 18.7

A = √18.7(18.7-11.5)(18.7-13,7)(18.5-12.2)

A = 30√4.862 units²

A≈ 66.1 units²

Answer:

left 3 units and up 6 units

Step-by-step explanation:

we know that

The rule of the translation is equal to

[tex](x,y)------> (x-3,y+6)[/tex]

That means

(x-3)-----> The figure is moved 3 units to the left, because the number is negative

(y+6)----> The figure is moved 6 units up because the number is positive

Answer:

left 3 units and up 6 units

Step-by-step explanation:

Answer:

40 feet

Step-by-step explanation:

The perimeter of a triangle is the distance around the triangle. It can be found by adding all the sides together. First, find the amount each side is by substituting x = 4 and simplifying.

3x - 4 = 3(4) - 4 = 12 - 4 = 8

x² -1 = (4)² - 1 = 16 - 1 = 15

2x² - 15 = 2(4)² - 15 = 32 - 15 = 17

Add the sides together, 8 + 15 + 17 = 40 feet

Answer:

6 bags

Step-by-step explanation:

Answer:

a.) 0.0825 years of age per year

Step-by-step explanation:

By the given table,

The median age at the time of first marriage on 1950 = 22.8 years,

While, the median age on 1990 = 26.1 years,

Hence, the average rate of change in median age per year from 1950 to 1990

[tex]=\frac{22.8 - 26.1}{1950 - 1990}[/tex]

[tex]=\frac{-3.3}{-40}[/tex]

[tex]=0.0825\text{ years of age per year}[/tex]

That is, OPTION a) is correct.

Answer:

It is D

Step-by-step explanation:

got it right on edge