Evaluate the expression

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:

The answer is (c) ⇒ the value is 6.6667

Step-by-step explanation:

∵ [tex]\lim_{x\to \2} _2\frac{x^{5}-32}{x^{3}-8}[/tex]

∵ 32 = 2^5 , 8 = 2³

∴ [tex]\lim_{x \to \2}_2 \frac{x^{5}-2^{5}}{x^{3}-2^{3} }[/tex]

* by using the rule:

[tex]\lim_{x\to\a}_a \frac{x^{n}-a^{n}}{x^{m}-a^{m}}=\frac{n}{m}(a)^{n-m}[/tex]

∴ [tex]\frac{5}{3}(2)^{5-3}=\frac{5}{3}(2)^{2}=\frac{20}{3}[/tex]

∴ 20/3 = 6.6667 ⇒ answer (c)

Answer:

The correct option is c.

Step-by-step explanation:

The given limit is

[tex]lim_{x\rightarrow 2}\frac{x^5-32}{x^3-8}[/tex]

It is can be written as

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}[/tex]

According to the property of limits,

[tex]lim_{x\rightarrow a}\frac{x^n-a^n}{x^m-a^m}=\frac{n}{m}(a)^{n-m}[/tex]

In the given limit, a=2, n=5 and m=3. Using the above property of limits we get

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(2)^{5-3}[/tex]

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(2)^{2}[/tex]

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{5}{3}(4)[/tex]

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=\frac{20}{3}[/tex]

[tex]lim_{x\rightarrow 2}\frac{x^5-2^5}{x^3-2^3}=6.6667[/tex]

Therefore the correct option is c.

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]

Answer:

B

Step-by-step explanation:

Note that the absolute value always returns a positive value, that is

| - 2 | = | 2 | = 2

given

2| u | - | v | with u = - 9 and v = - 2, then

2 | - 9 | - | - 2 |

= 2 × 9 - 2 = 18 - 2 = 16 → B

Answer:

[tex]\large\boxed{A=240\ cm^2}[/tex]

Step-by-step explanation:

Look at the picture.

The formula of an area of a rhombus:

[tex]A+\dfrac{d_1d_2}{2}[/tex]

d₁, d₂ - diagonals

We have d₁ = 30 cm.

Use the Pythagorean theorem to calculate d₂ = 2x.

[tex]x^2+15^2=17^2[/tex]

[tex]x^2+225=289[/tex]             subtract 225 from both sides

[tex]x^2=64\to x=\sqrt{64}\\\\x=8\ cm[/tex]

d₂ = (2)(8) = 16 cm.

Substitute:

[tex]A=\dfrac{(30)(16)}{2}=(30)(8)=240[/tex]

Answer:

The altitude to the base is [tex]5\ units[/tex]

Step-by-step explanation:

we know that

To find the length of the altitude apply the Pythagoras Theorem

Let

h-----> the altitude

[tex]h^{2}=13^{2}-(24/2)^{2}[/tex]

[tex]h^{2}=13^{2}-(12)^{2}[/tex]

[tex]h^{2}=169-144[/tex]

[tex]h^{2}=25[/tex]

[tex]h=5\ units[/tex]

Answer:

The Answer C

Step-by-step explanation:

I just did the test

The answer is C because you multiply 8×8.95 to get your lowest range, and 8×15.79 to get your highest range.

Answer:

Choice D is correct

Step-by-step explanation:

The first step is to write the polar equation of the conic section in standard form by dividing both the numerator and the denominator by 2;

[tex]r=\frac{3}{1-cos(theta)}[/tex]

The eccentricity of this conic section is thus 1, the coefficient of cos θ. Thus, this conic section is a parabola since its eccentricity is 1.

The value of the directrix is determined as;

d = k/e = 3/1 = 3

The denominator of the polar equation of this conic section contains (-cos θ) which implies that this parabola opens towards the right and thus the equation of its directrix is;

x = -3

Thus, the polar equation represents a parabola that opens towards the right with a directrix located at  x = -3. Choice D fits this criteria

Answer:

D

Step-by-step explanation:

edge

Since this is subtraction, everything must be turned negative in the second polynomial.

(6x^2 - 5x) - (2x^2 + 3x - 2)

6x^2 - 5x - 2x^2 - 3x - (-2)

6x^2 - 5x - 2x^2 - 3x + 2

Now, reorder the terms to make it easier.

6x^2 - 2x^2 - 5x - 3x + 2

Now, just combine like terms.

4x^2 - 5x - 3x + 2

4x^2 - 8x + 2

There’s the answer!

Please consider marking this answer as Brainliest to help me advance.

Answer: 2500 years

Step-by-step explanation:

I'm not quite sure if I'm doing this right myself but I'll give it a shot.

We use this formula to find half-life but we can just plug in the numbers we know to find t.

[tex]A(t)=A_{0}(1/2)^t^/^h[/tex]

We know half-life is 5730 years and that the parchment has retained 74% of its Carbon-14. For [tex]A_{0[/tex] let's just assume that there are 100 original  atoms of Carbon-14 and for A(t) let's assume there are 74 Carbon-14 atoms AFTER the amount of time has passed. That way, 74% of the C-14 still remains as 74/100 is 74%. Not quite sure how to explain it but I hope you get it. h is the last variable we need to know and it's just the half-life, which has been given to us already, 5730 years, so now we have this.

[tex]74=100(1/2)^t^/^5^7^3^0[/tex]

Now, solve. First, divide by 100.

[tex]0.74=(0.5)^t^/^5^7^3^0[/tex]

Take the log of everything

[tex]log(0.74)=\frac{t}{5730} log(0.5)[/tex]

Divide the entire equation by log (0.5) and multiply the entire equation by 5730 to isolate the t and get

[tex]5730\frac{log(0.74)}{log(0.5)} =t[/tex]

Use your calculator to solve that giant mess for t and you'll get that t is roughly 2489.128182 years. Round that to the nearest hundred years, and you'll find the hopefully correct answer is 2500 years.

Really hope that all the equations that I wrote came out good and that that's right, this is definitely the longest answer I've ever written.

Answer: P(A or B) = 22/26 or 11/13

Step-by-step explanation:All in all there are 26 pieces of clothing available. The probability of randomly selecting a blue piece is equal to 18/26. Also, the probability of picking up a pants is 14/26. There are 10 blue pants and the probability of picking up one of those is 10/26. The answer can be computed as follows:

               P(A or B) = (18/26) + (14/26) - (10/26) = 22/26 

                           P(A or B) = 22/26 or 11/13

Step-by-step explanation:

[tex]n!=\underbrace{1\cdot2\cdot3\cdot...\cdot n}\\\\6!=1\cdot2\cdot3\cdot4\cdot5\cdot6=720\\=======================\\_nP_r=\dfrac{n!}{(n-r)!}\\\\_8P_5=\dfrac{8!}{(8-5)!}=\dfrac{8!}{3!}=\dfrac{3!\cdot4\cdot5\cdot6\cdot7\cdot8}{3!}=4\cdot5\cdot6\cdot7\cdot8=6,720\\=======================\\_nC_r=\dfrac{n!}{r!(n-r)!}\\\\_{12}C_4=\dfrac{12!}{4!(12-4)!}=\dfrac{4!\cdot5\cdot6\cdot...\cdot12}{4!\cdot8!}=\dfrac{5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11\cdot12}{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8}=495[/tex]

Answer:

[tex]7,561.12\ mm^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of a cone is equal to

[tex]LA=\pi rl[/tex]

where

r is the radius of the base

l is the slant height

we have

[tex]r=80/2=40\ mm[/tex] ----> the radius is half the diameter

[tex]h=45\ mm[/tex]

To find the slant height apply the Pythagoras theorem

[tex]l^{2}=r^{2}+h^{2}[/tex]

substitute the values

[tex]l^{2}=40^{2}+45^{2}[/tex]

[tex]l^{2}=3,625[/tex]

[tex]l=60.2\ mm[/tex]

Find the lateral area

assume [tex]\pi=3.14[/tex]

[tex]LA=(3.14)(40)(60.2)=7,561.12\ mm^{2}[/tex]

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:

x = -12

Step-by-step explanation:

x - 8 = -20

+8        +8

You would need to multiply the quantity of shrubs bought by the price of each one, so 4p and add that to the price of the soil to get the total cost

The equation becomes 4p + 17.50 = 53.50

Now solve for p:

4p +17.50 = 53.50

Subtract 17.50 from both sides:

4p = 36

Divide both sides by 4:

p = 36/4

p = 9

The answer would be: 4p + $17.50 = $53.50; p = $9.00

Answer:

Seven forward, seven opposite. It's like saying a footballer runs from 0 yd line to 50 yd line then turns around and runs 50 yards again, ends up right back at the 0.

Answer:

a

Step-by-step explanation:

got it right on test

Answer:

$87.95

Step-by-step explanation:

1. multiply the stock (92) time 4.4% (or 0.044)

    92*0.044 = 4.048

2. subtract 4.048 from 92

    92-4.048 = 87.952

3. Round to the nearest cent (2 in the thousandth place means the 5 stays the same)

    87.95

Answer:

24

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

it had a 50 &#>#*(@?'ndhdjeke

Your answer’s 5! If not, message me, I’ll be happy to help.

The answer is 5! Hope this helps :)

Answer:

The rectangular 5 x 10 table.

Step-by-step explanation:

To find which table the office manager needs to get so he can sit more people at it is decided by one factor, the perimeter. The rectangular one, which is 5 x 10 the perimeter is (5 x 2) + (10 x 2) = 10 + 20 = 30. The circular one can be calculated by the equation[tex]\pi * d[/tex] where d = 8. Putting [tex]/pi[/tex] x 8 in my calculator and it comes out approximately at 25.132, having a less amount of perimeter space to work with, making the rectangular table the way to go.

The rectangular and circular tables offer roughly the same area, approximately 50 square feet. However, due to space utilization, traditionally, rectangular tables can seat more people as it allows seating around the sides and ends instead of wasting some space at the edges, a common issue with circular tables.

Determining which table can seat more depends on how much space each person needs. However, as a basic comparison, we can calculate the area of each table as a starting point.

The rectangular table is 5 feet wide and 10 feet long. Therefore, its area is 5 * 10 = 50 square feet.

For the circular table, we can use the formula for the area of a circle, which is pi * r^2, where r is the radius. The radius is half the diameter, so it is 4 feet here. Thus, the area is about 3.14 * 4^2 = 50.24 square feet.

Both tables have very similar areas. However, people can sit around both the sides and ends of a rectangular table, while some space might be wasted around the edges of the circular one. Therefore, the office manager might find that the rectangular table can seat more people comfortably.

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Answer:

Step-by-step explanation:

Remarks

They want only the exponential equation, here's the point.

Equation

[tex]\text{Amount the pressure becomes} = \dfrac{101 kpa}{(1+\dfrac{ 1.8}{100} )^\frac{h}{500} }[/tex]

What this gives you is the equation for a rise every  500 feet. To figure out the %

Use

[tex]\text {\% =} \frac{\text{101 - answer from above equation}}{101}*100\%[/tex]

Example

Let h = 1000 feet

101 / (1 + 1.8/100) ^ (1000/500)

101 / (1.018)^2

101 / 1.036324

97.46

Now take this number and use the second formula

% = (101 - 97.46)/101 * 100%

% = 3.54%

The answer should be 3.6% (2 * 1.8%)

This is close enough. The question does say approximately.

1500 feet will give you 5.2% which is close to 5.4 (1.8 * 3). The higher you go, the more it is going to be out, but the results will always be close.

Answer:

6 bags

Step-by-step explanation:

Answer:

[tex]\large\boxed{3x-4y=30}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{2}x-\dfrac{2}{3}y=5\qquad\text{multiply both sides by LCM(2, 3) = 6}\\\\6\!\!\!\!\diagup^3\cdot\dfrac{1}{2\!\!\!\!\diagup_1}x-6\!\!\!\!\diagup^2\cdot\dfrac{2}{3\!\!\!\!\diagup_1}y=6\cdot5\\\\(3)(x)-(2)(2y)=30\\\\3x-4y=30[/tex]

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

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:

Statements                       Reasons

1. 2x + 11 = 15                    1. Given

2. 2x = 4                            2. Subtraction Property of Equality

3. X = 2                              3. Division Property of Equality

Step-by-step explanation:

An equation can be solved and its solution proven using algebraic theorems and properties. To create a proof, form two columns. Label one side Statements and the other Reasons.

Begin your proof listing the any information given to you. List as the reason - Given.

Then list the next step which here would be to subtract by 11 on both side. The reason is Subtraction Property of Equality. Subtraction is the inverse of addition. Inverse axiom is another acceptable reason.

Then divide both sides by 2. The reason is Division Property of Equality or Inverse axiom once again. See the proof below.

Statements                       Reasons

1. 2x + 11 = 15                    1. Given

2. 2x = 4                            2. Subtraction Property of Equality

3. X = 2                              3. Division Property of Equality

Answer:

40

Step-by-step explanation:

You do 480 divided by 12

To find the length of the room Alyssa wants to tile, given its area is 480 square feet and its width is 12 feet, divide the area by the width. The length is found to be 40 feet.

The question asks to find the length of a room given its area is 480 square feet and its width is 12 feet. To find the length, you use the formula for the area of a rectangle, which is Area = Length × Width. Since we're given the area and the width, we can rearrange the formula to solve for the length by dividing the area by the width.

Therefore, Length = Area / Width = 480 sq ft / 12 ft = 40 feet.

This means that the length of the room Alyssa wants to tile is 40 feet.