Statistics question in image

the area of the model on the right is 100 sq cm.So, the answer is (B) 100 sq cm.in   order to solve this use area of rectangle formula

what is  area of rectangle  ?

The area of a rectangle is the amount of space that is enclosed within its boundaries. It is the product of the length and width of the rectangle. The formula for the area of a rectangle is:

Area = length x width

In the given question,

Since the two models are of the same rectangular patio, they have the same length and width. Let the length of the rectangle be L and the width be W.

The area of a rectangle is given by the formula A = L x W.

For the model on the left, we are given that the area is 4 sq cm.

A = L x W = 4

For the model on the right, the length and width are both increased by a factor of 5. Therefore, the new length is 5L and the new width is 5W.

The area of the new rectangle is:

A = (5L) x (5W) = 25LW

We know that LW = 4 from the model on the left. Therefore:

A = 25LW = 25(4) = 100

Therefore, the area of the model on the right is 100 sq cm.

So, the answer is (B) 100 sq cm.

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You have the following algebraic expression:

( 7x³ + 4x² - 2x + 1 )/(x + 1)

In order to simplify the previous expression you proceed as follow:

7x³ + 4x² - 2x + 1 | x + 1

-7x³ - 7x² 7x² - 3x + 1

0 - 3x² - 2x + 1

3x² + 3x

0 x + 1

-x - 1

0

Hence, the quotient of the given algebraic expression is:

( 7x³ + 4x² - 2x + 1 )/(x + 1) = 7x² - 3x + 1

The previous result is also the simplified form of the given expression

Answer:

"The diagonals of the door frame are congruent."

Step-by-step explanation:

The statement that would not give enough information would be "The diagonals of the door frame are congruent." This is because a rectangle does have congruent diagonals but a rhomboid also has congruent angles and has opposing parallel sides. Therefore, this statement does not give sufficient information to prove that the object in question is a rectangle. We would need more information such as the length of the sides or the degree of the angles.

Answer: 104

Step-by-step explanation:

\(f(-8)\) represents \(f(x)\) evaluated at \(x=-8\).

\(f(-8)=3(-8)^2 +9(-8)-16\\\\=192-72-16\\\\=120-16\\\\=104\)

An addition equation that could be used to find the length of the other piece of material is,

38 = 19 + x.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

A piece of material measures 38 inches.

Courtney cuts the piece of material into two pieces.

One piece measures 19 inches.

Let x be the length of other pieces.

An addition equation that could be used to find the length of the other piece of material is,

38 = 19 + x

Therefore, 19 + x = 38 is an addition equation.

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Answer:

0.459 divided by 0.17 equals 2.7

Step-by-step explanation:

Answer:

2.7

Step-by-step explanation:

0.459÷0.17=2.7

here is your answer!

Answer:

15. $8.47

16. $14.68

17. $121.04

18. $60.52

Step-by-step explanation:

15. Sale tax Round to the nearest cent=

8.65% of $97.89 = 0.0865 × $97.89 = $8.47

16. Tips Round to the nearest cent=

15% of $97.89 = 0.15 × $97.89 = $14.68

17. Total =

$97.89 + $8.47 + $14.68 = $121.04

18. Amount each person pays Round to the nearest cent =

$121.04/2 = $60.52

Maya scored 4 points in game 6. The correct answer is A.

The mean, also known as average, is a mathematical concept that expresses central tendency and is defined as the sum of a set of numbers divided by the total number of values in the set. It is one of the most widely applied central tendency measures in statistics.

The data set's values are totaled up to get the mean, which is then divided by the total number of values.

The mean is given by the formula:

Mean = (Sum of all data values) / (Number of data values)

Substituting the value we have:

(8 + 12 + 10 + 6 + 14 + x) / 6 = 9

50 + x = 54

x = 4

Hence, Maya scored 4 points in game 6. The answer is A.

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Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{MN}\\ o=\stackrel{opposite}{18} \end{cases} \\\\\\ MN=\sqrt{ 30^2 - 18^2} \implies MN=\sqrt{ 576 }\implies MN=24 \\\\[-0.35em] ~\dotfill\\\\ \cos(M )=\cfrac{\stackrel{adjacent}{24}}{\underset{hypotenuse}{30}} \implies \cos(M)=\cfrac{4}{5}\)

Answer:

Step-by-step explanation:

Comment

Since you make no other restrictions, the numbers can have duplicates.

9 + 9 + 2  is one possibility.

9 + 7 + 4   is another

9 + 8 + 3

and another 33 possibilities. Surely you are not expected to list them all. Three should be enough.

The volume of the figure, by splitting it into two cuboids comes to be 3300 ft³.

The volume of a cuboid is the product of its three dimensions i.e. length, breadth, and height.

Let us split the given figure into two cuboids

So, the volume of the figure will be the sum of the volume of both the cuboids.

So, the volume of the cuboid with dimensions 20 ft x 25 ft x 5ft

= 20 x 25 x 5

=2500 ft³.

The volume of the cuboid with dimensions  4 ft x 25ft x 8ft

=4 x 25x 8

=800 ft³.

So, the volume of the figure = 2500 + 800 =3300 ft³.

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Answer:

Step-by-step explanation:

The first step in evaluating the expression is to perform the calculations inside the parentheses. This involves subtracting 3.6 from 7.4.

Step 1: Evaluate the expression inside the parentheses.

7.4 - 3.6 = 3.8

After evaluating the expression inside the parentheses, the expression becomes:

12 ÷ 3.8 + 8 - 2

Step 2: Perform the division.

12 ÷ 3.8 = 3.158

After performing the division, the expression becomes:

3.158 + 8 - 2

Step 3: Perform the addition and subtraction from left to right.

3.158 + 8 = 11.158

11.158 - 2 = 9.158

Therefore, the value of the given expression is approximately 9.158.

The first step is:

Work/explanation:

The expression is:

12 ÷ (7.4 − 3.6) + 8 − 2

Let's recall the order of operations first:

So we evaluate

\(\sf{12\div(7.4-3.6)+8-2}\)

\(\sf{12\div3.8+8-2}\)

Next, division:

\(\sf{3.158+8-2}\)

Next, addition & subtraction:

\(\sf{9.158}\)

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-6 - (-4)]^2 + [8 - (-1)]^2}\implies d=\sqrt{(-6+4)^2+(8+1)^2} \\\\\\ d=\sqrt{(-2)^2 + 9^2}\implies d=\sqrt{85}\)

To find the measure of Angle A, we'll need to use a trigonometric function.

Remember: SOH-CAH-TOA

Looking from Angle A, we know the opposite side and the hypotenuse. Therefore, we should use the sine function.

sin(A) = 9 / 18

---To solve for A, you'll need to use the inverse sin function on your calculator. It should look like so: sin^-1()

The inverse sin of 1/2 = 30

Answer: first option, 30 degrees

Hope this helps!

Answer:

A)  48 Kg

B)  8 Kg

C)  40 Kg

Step-by-step explanation:

If 30% of the mass is equal to 24 Kg.

Then 10% of the mass will be equal to 8 Kg. (Divide both values by 3).

You can now use this info to find the other values:

10 x 6 = 8 x 6,    so 60% = 48 Kg.

10 x 1 = 8 x 1,    so 10% = 8 Kg.

10 x 5 = 8 x 5,    so 50% = 40 Kg.

A)  48 Kg

B)  8 Kg

C)  40 Kg

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

Answer:

3/4

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first term

3/4

Check with the third and second terms

9/4 ÷3

9/4 *1/3= 3/4

The common ratio is 3/4

Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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Answer:

m<I=57

m<J=57

m<K=66

Step-by-step explanation:

All the angles in a triangle add up to 180 degrees.

m<I= 3x+18

m<K= 5x+1

m<I is congruent to m<J.

We can plug the information we already know into the equation.

3x+18+3x+18+5x+1=180

11x+37=180

Subtract 37 from both sides.

11x=143

x=13

Now, we can find out what the angles are.

m<I= 3x+18

m<I=3(13)+18

m<I=39+18

m<I=57

We know that m<I=m<J, so they are both equal to 57 degrees.

m<J=57

Now for m<K:

m<K=5x+1

m<K=5(13)+1

m<K=65+1

m<K=66

We know this is correct because 57+57+66=180.

Answer:

114.3 foot

Step-by-step explanation:

Height of building,h=200 foot

Let BC=x

\(tan\theta=\frac{perpendicular\;side}{base}\)

Using the formula

\(tan(58^{\circ} 6')=\frac{200}{CD}\)

\(CD=\frac{200}{tan(58^{\circ} 6')}\)

\(CD=124.5 foot\)

Now,

\(\frac{BC}{CD}=tan(42^{\circ}33')\)

\(\frac{x}{124.5}=0.9179\)

\(x=124.5\times 0.9179\)

\(x=114.3 foot\)

Hence, the distance of woman from the  ground=114.3 foot

The ground is 123.24 ft far from the stranded woman.

Given the total height of the office building is 200 ft.

And the angle of elevation of the top of the building is 58° 6' and the angle of elevation to the stranded woman is 42° 33'.

We know that, from trigonometric ratios,\(tan \theta =\frac{perpendicular}{base}\)

here \(\theta\) is the angle of elevation of the top of the building from the fireman.

Now, \(tan ( 58^{0} 6')\)\(=\frac{200}{base}\)

\(1.488=\frac{200}{base}\)

\(base=\frac{200}{1.488}\)

\(base=134.40\) ft

Now the woman is stranded in the window of the building say at the height of h ft, and the angle of elevation of the woman from the fireman is  42° 33'.

So, \(tan (42^{0} 33')\)\(= \frac{perpendicular}{base}\)

\(tan(42^{0} 33' )= \frac{h}{134.40}\)

\(0.917=\frac{h}{134.40}\)

\(0.917\times134.40=h\)

\(h=123.24 ft\)

Hence the ground is 123.24 ft far from the stranded woman.

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The dimensions of the rectangle are 4 ft by 5 ft.

Given that the length of a rectangle is 3 ft less than twice the width, and the area of the rectangle is 44 sq.ft. We have to find the dimensions of the rectangle. Let's consider the width of the rectangle as x ft.Length of the rectangle = (2x - 3) ftArea of the rectangle = Length x Width44 = (2x - 3) x x44 = 2x^2 - 3x44 = x (2x - 3)2x^2 - 3x - 44 = 0To solve for x, we will factorize the equation by splitting the middle term.2x^2 - 8x + 5x - 20 = 0Factorize2x(x - 4) + 5(x - 4) = 0(x - 4) (2x + 5) = 0x = 4 ft (since the width of a rectangle can't be negative)or 2x = -5This gives us an invalid value, so x = 4 ftNow that we have the width of the rectangle, we can calculate the length as follows:Length of the rectangle = (2x - 3) ftLength of the rectangle = (2 * 4) - 3Length of the rectangle = 8 - 3Length of the rectangle = 5 ft.

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Step-by-step explanation:

I really hope that that will be helpful to you

The total number of choices is 42 if a local department store sells carpets in 4 sizes. Each carpet comes in 3 different qualities. One of the sizes comes in 5 colors.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

It is given that:

A local department store sells carpets in 4 sizes.

Each carpet comes in 3 different qualities.

One of the sizes comes in 5 colors.

The other sizes come in 3 colors.

The number of choices can be found as follows:

= 1x3x5

= 15

= 3x3x3

= 27

Total number of choices = 15 +27

= 42

Thus, the total number of choices is 42 if a local department store sells carpets in 4 sizes. Each carpet comes in 3 different qualities. One of the sizes comes in 5 colors.

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Answer: g(-2) = 17

Step-by-step explanation:

         When finding g(-2), we will substitute all values of x for -2 in the function. First, we will substitute values in. Then, we will simplify by squaring, multiplying, and adding.

g(x) = 3x² -2x + 1

g(-2) = 3(-2)² -2(-2) + 1

g(-2) = 3(4) + 4 + 1

g(-2) = 12 + 4 + 1

g(-2) = 17

Answer:

slope = \(\frac{11}{15}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-x_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (9, 4 ) and (x₂, y₂ ) = (- 6, - 7 )

m = \(\frac{-7-4}{-6-9}\) = \(\frac{-11}{-15}\) = \(\frac{11}{15}\)

Answer:

8:39

Step-by-step explanation:

because when simplified, all the rest are 1:5