Which of the following best describes the data distribution of the histogram
below?

Answer:

$36 is the correct answer.

Step-by-step explanation:

Given that:

Adam has $15 of a certain type of rare coin.

$5 of this type of rare coins are equivalent to $12.

To find:

The total worth of $15 of rare coins = ?

If value of each coin is same.

Solution:

We are given that value of each coin is same.

So, We can simply use unitary method to find out the total worth of $15 of rare coins.

i.e. we first find out what is the worth of $1 of rare coins and then we find the worth of total required quantity.

Given that

$5 of rare coins are worthy of = $12

$1 of rare coins are worthy of = [tex]\frac{12}{5}[/tex]

$15 of rare coins are worthy of =

[tex]\\\dfrac{12}{5}\times 15\\\Rightarrow \dfrac{12\times 15}{5}\\\Rightarrow 12\times 3\\\Rightarrow \$36[/tex]

[tex]\therefore[/tex] $15 of rare coins are worth of $36.

Expand everything in the limit:

[tex]\displaystyle\lim_{h\to0}\frac{(-7+h)^2-49}h=\lim_{h\to0}\frac{(49-14h+h^2)-49}h=\lim_{h\to0}\frac{h^2-14h}h[/tex]

We have [tex]h[/tex] approaching 0, and in particular [tex]h\neq0[/tex], so we can cancel a factor in the numerator and denominator:

[tex]\displaystyle\lim_{h\to0}\frac{h^2-14h}h=\lim_{h\to0}(h-14)=\boxed{-14}[/tex]

Alternatively, if you already know about derivatives, consider the function [tex]f(x)=x^2[/tex], whose derivative is [tex]f'(x)=2x[/tex].

Using the limit definition, we have

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h=\lim_{h\to0}\frac{(x+h)^2-x^2}h[/tex]

which is exactly the original limit with [tex]x=-7[/tex]. The derivative is [tex]2x[/tex], so the value of the limit is, again, -14.

Answer: Yes

Step-by-step explanation:

First multiply the first equation by three to get 3x+12y=69

Then subtract 12y from both sides of the second equation

Then add the first system and the second like this:

[tex]3x+12y=69\\-3x-12y=1\\--------\\0+0=70\\0=70[/tex]

Because 0≠70, the system has no solutions

Answer:

Rounded to two decimals the regression curve is:

[tex]y=-0.70\,x^2+2.37\,x+11.96[/tex]

Step-by-step explanation:

The objective of this problem is to have you use a calculator and enter the data in to separate lists: one containing the x-values, and the other the correspondent y-values (following the same order).

Once the data is entered, you need to access the regression tool and request a quadratic form of regression.

You should get and image and resulting function as shown in the attached image.

Answer:

Rounded to two decimals the regression curve is:

Step-by-step explanation:

Your answer is the second option, she should choose the rectangular tiles because the total cost will be $8 less.

To find this answer we need to first find the total cost for using square tiles, and the cost for using rectangular tiles, and compare them. We can do this by finding the area of each tile individually, calculating how many tiles we would need, and multiplying this by the cost for one tile:

Square tiles:

The area of one square tile is 1/2 × 1/2 = 1/4 ft. Therefore we need 40 ÷ 1/4 = 160 tiles. If each tile costs $0.45, this means the total cost will be $0.45 × 160 = $72

Rectangular tiles:

The area of one rectangular tile is 2 × 1/4 = 2/4 = 1/2 ft. Thus we need 40 ÷ 1/2 = 80 tiles. Each tile costs $0.80, so the total cost will be 80 × $0.80 = $64.

This shows us that the rectangular tiles will be cheaper by $8.

I hope this helps! Let me know if you have any questions :)

Answer:

B

Step-by-step explanation:

E2020 : )

Answer:  C) ΔUVW and ΔRST are congruent

Step-by-step explanation:

There are four kinds of rigid transformation.

1) translation 2) reflection 3) rotation 4) glide reflection.

If a series of rigid motions maps ΔUVW onto ΔRST.

Then, ΔUVW and ΔRST must be congruent. (No change in size or shape)

hence, the correct statement is C) ΔUVW and ΔRST are congruent.

Answer:

C) ΔUVW and ΔRST are congruent

Step-by-step explanation:

Answer:

[tex]t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32[/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 =2*P(t_{(9)}>2.32)=0.0455[/tex]    

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

Step-by-step explanation:

Information given

data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0

We can calculate the sample mean and deviation with the following formulas:

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

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

[tex]\bar X=201.77[/tex] represent the sample mean    

[tex]s=2.41[/tex] represent the sample standard deviation    

[tex]n=10[/tex] sample size    

[tex]\mu_o =200[/tex] represent the value that we want to test    

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.    

t would represent the statistic

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

Hypothesis to test

We want to determine if the true mean is equal to 200, the system of hypothesis are :    

Null hypothesis:[tex]\mu = 200[/tex]    

Alternative hypothesis:[tex]\mu = 200[/tex]    

The statistic for this case is given by:

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

The statistic is given by:

[tex]t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32[/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 =2*P(t_{(9)}>2.32)=0.0455[/tex]    

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

Answer: 45,000.

Step-by-step explanation:

The equation of inverse variation is given by:-

[tex]k=xy[/tex]

, where k is the constant of proportionality.

Given: After owning the car for 3 years, its value is $15,000. After owning the car for 5 years, its value is $9,000.

Here,

[tex]x_1=3,\ y_1=15000\\\\x_2=5,\ y_2=9000[/tex]

Then, [tex]k=x_1y_1=3\times15000=45,000[/tex]

or [tex]k=x_2y_2=5\times9000=45,000[/tex]  [answer is same in both cases.]

Hence, the constant of proportionality in this inverse variation is 45,000.

Answer:

a) [tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]

The inverse of given function

[tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]

Step-by-step explanation:

Step(i):-

Given function f(x) = 3 cos (2 x -3) + 1

Let y = f(x) = 3 cos (2 x -3) + 1

     y = 3 cos (2 x -3) + 1

   ⇒ y - 1 =  3 cos (2 x -3)

   ⇒   [tex]cos ( 2 x - 3 ) =\frac{y -1}{3}[/tex]

  ⇒[tex]cos ^{-1} ( cos (2 x - 3)) = Cos^{-1} (\frac{y-1}{3} )[/tex]

We know that inverse trigonometric equations

cos⁻¹(cosθ) = θ

[tex]2 x - 3 = Cos^{-1} (\frac{y-1}{3} )[/tex]

[tex]2 x = Cos^{-1} (\frac{y-1}{3} ) +3[/tex]

[tex]x = \frac{1}{2} Cos^{-1} (\frac{y-1}{3} ) +\frac{3}{2}[/tex]

Step(ii):-

we know that   y= f(x)

The inverse of the given function

                         [tex]x = f^{-1} (y)[/tex]

                    [tex]f^{-1} (y) = \frac{1}{2} Cos^{-1} (\frac{y-1}{3} ) +\frac{3}{2}[/tex]

The inverse of given function in terms of 'x'

                     [tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]

conclusion:-

 The inverse of given function

[tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]

Answer:

See below.

Step-by-step explanation:

[tex]\frac{1+cos(\theta)}{sin(\theta)} +\frac{sin(\theta)}{1+cos(\theta)}=2csc(\theta)[/tex]

[tex]\frac{(1+cos(\theta))(1+cos(\theta))}{sin(\theta)((1+cos(\theta))} +\frac{(sin(\theta))(sin(\theta))}{(1+cos(\theta))(sin(\theta))}=2csc(\theta)[/tex]

[tex]\frac{(1+cos(\theta))(1+cos(\theta))+(sin(\theta))(sin(\theta))}{sin(\theta)((1+cos(\theta))}=2csc(\theta)[/tex]

[tex]\frac{(1+2cos(\theta)+cos^2(\theta)+sin^2(\theta))}{sin(\theta)(1+cos(\theta))} =2csc(\theta)[/tex]

Recall the identities:

[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]

[tex]\frac{1+2cos(\theta)+1}{sin(\theta)(1+cos(\theta))} =2csc(\theta)[/tex]

[tex]\frac{2+2cos(\theta)}{sin(\theta)(1+cos(\theta)}=2csc(\theta)[/tex]

[tex]\frac{2(1+cos(\theta))}{sin(\theta)(1+cos(\theta))} =2csc(\theta)[/tex]

[tex]\frac{2}{sin(\theta)} =2csc(\theta)[/tex]

[tex]2csc(\theta)=2csc(\theta)[/tex]

Answer:

f(n) = 74 + 11(n - 1)

For the 7th term

n = 7

f(7) = 74 + 11(7 - 1)

= 74 + 11(6)

= 74 + 66

For the 8th term

n = 8

f(8) = 74 + 11( 8 - 1)

= 74 + 11(7)

= 74 + 77

Hope this helps you

Answer:

Step-by-step explanation:

x-y=3

-y=3-x

y=x-3

when x=3 y=0

when x=1 y=-2

when x=2 y=-1

Answer:

[tex]\angle n=69^o[/tex]

which agrees with answer C in your list of possible options.

Step-by-step explanation:

Notice that you have a triangle defined by the three intersecting lines, and for which you know the internal angles, since you can use supplementary angle properties as well as the property of addition of all internal angles of a triangle. Please see attached image.

Notice that the angles noted in green are those that were obtained via supplementary angle calculation, while the angle noted on orange was obtained using the addition of all internal angles of a triangle.

[tex]180^o-131^o=49^o\\180^o-160^o=20^o\\180^o-49^o-20^o=111^o[/tex]

[tex]\angle n[/tex] can then be obtained based on supplementary angles as well;

[tex]\angle n=180^o-111^o=69^o[/tex]

Answer:

Step-by-step explanation:

Let x represent the number of friends that Monica asked to a charity raffle ticket. If all but 4 of her friends bought a ticket, it means that only 4 of her friends did not buy the charity raffle ticket. Thus, the number of her friends that bought the charity raffle ticket is

x - 4

If each ticket costs $3 and the total amount that was raised is $18, then algebraic expression representing the number of friends that Monica asked is

3(x - 4) = 18

3x - 12 = 18

3x = 18 + 12 = 30

x = 30/3 = 10

Monica asked 10 friends

Answer:

A = 8h + 20

A = 10h

Step-by-step explanation:

Pizza Place

He makes $8 an hour (8h) as well as $20 for driving expenses (+20).

A = 8h + 20

Hardware Store

He is paid $10 and hour (10h).

A = 10h

The system of equations will be

A = 8h + 20

A = 10h

Answer:

A = x² + 9x + 8

Step-by-step explanation:

Area of Parallelogram Formula: A = bh

We are given b = x + 8 and h = x + 1, so simply plug it in:

A = (x + 8)(x + 1)

A = x² + x + 8x + 8

A = x² + 9x + 8

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▹ Answer

A = x² + 9x + 8

▹ Step-by-Step Explanation

A = bh

A = (x + 8) * (x + 1)

A = x² + 9x + 8

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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The correct answer is Graph B

Explanation:

The purpose of histograms is to display visually the frequency of a variable. Additionally, a higher bar represents a higher frequency.

According to this, the correct histogram is graph B because in this the frequencies for each batting average are displayed correctly. For example, the highest bar is related to the average 0.330-0.339, which has the highest frequency (28), this is followed in height by the bar that represents a frequency of 24 and is related to the average 0.340-0.349.

At the same time, the averages 0.320-0.329 and 0.360-0.369 that have a frequency of 2 are represented through the shortest bars, while the average 0.350-0.359 with a frequency of 4 is related to a bar with exactly the double of heigh than those with a frequency of 2.

Answer:

graph B

Step-by-step explanation:

what happened to your screen

u/4 - 4 = -20

Add 4 to both sides:

u/4 = -16

Multiply both sides by 4:

u = -64

Answer:

u=-64

Step-by-step explanation:

u/4 -4 = -20

First add 4 to both sides.

u/4=-16

Now multiply both sides by 4

u=-64

Answer:

[tex] z=\frac{44257-44111}{\frac{2438}{\sqrt{80}}}= 0.536[/tex]

And if we use the normal standard table we got this:

[tex] P(z<0.536) =0.7040[/tex]

Step-by-step explanation:

For this case we have the following info :

[tex]\mu = 44111[/tex] represent the true mean

[tex]\sigma= \sqrt{5943844}= 2438[/tex] represent the deviation

n= 80 represent the sample size

And we want to find the follwing probability:

[tex] P(\bar X< 44257)[/tex]

For this case since the sample size is larger than 30 we can apply the central limit theorem and we can use the z score formula given by:

[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The distribution for the sample mean would be:

[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]

And if we find the z score for this case we got:

[tex] z=\frac{44257-44111}{\frac{2438}{\sqrt{80}}}= 0.536[/tex]

And if we use the normal standard table we got this:

[tex] P(z<0.536) =0.7040[/tex]

Answer:

3.025

Step-by-step explanation:

3.4-1/2(0.75)

3.4-0.375

3.025

Answer:

3ab

Step-by-step explanation:

area = length * width

width = area/length

width = (12ab^2)/(4b)

width = 3ab

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▹ Answer

(-1, 3)

▹ Step-by-Step Explanation

y - 4x = 7

2y + 4x = 2

Substitute

y - (2 - 2y) = 7

Solve

y = 3

Substitute

4x = 2 - 2 * 3

Solve

x = -1

Final Answer

(x, y) = (-1, 3)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

D: (-1,3)

Edg 2020

Answer:

Step-by-step explanation:

5x(x + 3) + 6(x + 3)

The final answer is

( 5x + 6 ) ( x + 3 )

Hope this helps you

We have

[tex]\displaystyle \sum_{n=1}^\infty \frac{n}{n^2+8} < \int_1^\infty \frac{x}{x^2+8}\,\mathrm dx[/tex]

For the integral, substitute y = x ² + 8 and dy = 2x dx. Then

[tex]\displaystyle \int_1^\infty \frac{x}{x^2+8}\,\mathrm dx = \frac12 \int_9^\infty \frac{\mathrm dy}y = \frac12 \ln(y)\bigg|_{y=9}^{y\to\infty} = \infty[/tex]

The integral diverges, so the sum also diverges by the integral test.

Answer:

2m + 1

Step-by-step explanation:

Simply combine like terms. m terms go with m terms and constants go with constants.

Answer:

2m + 1

Step-by-step explanation:

3m + 1 - m =

= 3m - m + 1

= 2m + 1

Answer:

See Explanation

Step-by-step explanation:

[tex]f(x) = 4 - 6x + 3 {x}^{2}...(1) \\ plug \: x = a \: in \: (1) \\ f(a) = \boxed{ 4 - 6a + 3 {a}^{2} } \\ \\ next \: plug \: x = (a + h) \: in \: (1) \\ f(a + h) = 4 - 6(a + h) + 3 {(a + h)}^{2} \\ = 4 - 6a - 6h + 3( {a}^{2} + {h}^{2} + 2ah) \\ = 4 - 6a - 6h + 3 {a}^{2} + 3{h}^{2} + 6ah \\ f(a + h) = \boxed{3 {a}^{2} + 3{h}^{2} + 6ah - 6a - 6h + 4} \\ \\ now \\ \\ \frac{f(a + h) - f(a)}{h} \\ \\ = \frac{(3 {a}^{2} + 3{h}^{2} + 6ah - 6a - 6h + 4) -(4 - 6a + 3 {a}^{2} ) }{h} \\ \\ = \frac{3 {a}^{2} + 3{h}^{2} + 6ah - 6a - 6h + 4 -4 + 6a - 3 {a}^{2} }{h} \\ \\ = \frac{ 3{h}^{2} + 6ah - 6h }{h} \\ \\ = \frac{3h( {h} + 2a - 2) }{h} \\ \\ \frac{f(a + h) - f(a)}{h} = \boxed{ 3( 2a + h - 2)}[/tex]

Divide the amount off the price by the percentage off:

1.05 / 0.15 = 7

The original price is $7.00

Answer:  x = -10

Step-by-step explanation:

see image

A) congruent sides implies congruent angles A = 64°

B) Use the Triangle Sum Theorem: 64° + 64° + B = 180° --> B = 52°

C) B and C are complimentary angles: 52° + C = 90°  --> C = 38°

D) Use the Triangle Sum Theorem knowing that congruent sides implies congruent angles: 38° + 2D = 180°  --> D = 71°

∠2) D and ∠2 are supplementary angles: 71° + ∠2 = 180°  --> ∠2 = 109°

Solve for x:

109° = x + 119

 -10  = x

Answer:

x = -10

Step-by-step explanation:

Find the measure of angle m∠2

The triangles are isosceles triangles, the base angles are equal.

The other base angle is also 64°.

Using Triangle Sum Theorem.

64 + 64 + y = 180

y = 52

The top angle is 52°.

The whole angle is 90°.

90 - 52 = 38

The second triangle has base angles equal.

Using Triangle Sum Theorem.

38 + z + z = 180

z = 71

The two base angles are 71°.

Angles on a straight line add up to 180°.

71 + m∠2 = 180

m∠2 = 109

The measure of m∠2 is 109°

Find the value of x

m∠2 = x + 119

109 = x + 119

x = 109 - 119

x = -10

Answer:

The right answer is the second option, 9,747.

Step-by-step explanation:

[tex]EG^2 = DG*FG \\ EG^2 = 5*14 \\ EG = \sqrt{70}[/tex]

Now let's find DE (Pythagorean theorem).

[tex]DE^2 = DG^2+EG^2\\ DE = \sqrt{25+70} \\ DE = \sqrt{95}[/tex]

[tex]\sqrt{95} =9,7467... = 9,747[/tex]

Answer:

The relationship between the areas of the three squares is that square A plus square B equals the area of square C.

The sum of the square of a and b is equal to the area of square of c

Data;

This theorem is used to calculated a missing side from a right angle triangle when we have the value of at least two sides.

Given that

[tex]c^2 = a^2 + b^2[/tex]

This indicates a relationship such that the sum of square of two sides is equal to the area of the square of one side. I.e the area of the square of c is equal to the sum of the square of both a and b.

Learn more on Pythagoras Theorem here;

https://brainly.com/question/231802