The two rectangles in the figure are similar. What is the value of x?

8 people received a Baseball Cap

12 people received a Coffee Mug

Hope this helped!

The explanatory variable is the car's weight, with fuel efficiency as the response variable; a likely negative association may exist, possibly linear or non-linear; a correlation like r=-0.9 or r=-0.6 is plausible; an 'unusual point' could be an outlier affecting the correlation; removing it might strengthen or weaken the correlation; converting weights to metric tons wouldn't alter the correlation.

(a) In this context, the explanatory variable is the car's weight (in pounds) and the fuel efficiency (in miles per gallon) is the response variable. This is because we are typically interested in determining the effect of a car's weight on its fuel efficiency.

(b) Based on the context, a scatterplot might show a negative association between the car's weight and its fuel efficiency. This would make sense as heavier cars often require more fuel to operate efficiently, leading to lower miles per gallon.

(c) The form of the relationship between car weight and fuel efficiency can vary. For instance, it could be linear (indicating a constant rate of change) or non-linear (indicating a rate of change that varies with weight).

(d) Without viewing the scatterplot it's not possible to definitively answer this, but based on the proposed negative relationship, a correlation of r=-0.9 or r=-0.6 would be plausible. Correlations range from -1 to 1, and a negative sign indicates an inverse relationship.

(e) An 'unusual point’ could be an outlier on the scatterplot that doesn't model the relationship between car weight and fuel efficiency like the rest of the data. This could be due to factors unique to this car, such as a highly efficient engine that gets more miles per gallon despite its weight

(f) Depending on the unique characteristics of the 'unusual point', its removal could either increase or decrease the correlation. If this point were causing the correlation to be weaker, its removal would cause the correlation to strengthen, and vice-versa.

(g) Converting the car weights to metric tons wouldn't change the correlation between weight and fuel efficiency. Correlation is unitless and depends only on the relationship between variables, not the scale they're measured on. Thus, while the specific values for weight would change, the strength, direction, and form of the relationship between weight and fuel efficiency would remain the same.

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Answer:

4

Step-by-step explanation:

Calculate the distance using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = B(0, 0) and (x₂, y₂ ) = ([tex]\frac{\sqrt{6} }{2}[/tex], [tex]\frac{\sqrt{58} }{2}[/tex] )

AB = [tex]\sqrt{((\frac{\sqrt{6} }{2})^2 }[/tex] + [tex]\{(\frac{\sqrt{58} }{2})^2 }[/tex]

= [tex]\sqrt{\frac{6}{4} }[/tex] + [tex]\frac{58}{4}[/tex]

= [tex]\sqrt{\frac{64}{4} }[/tex]

= [tex]\sqrt{16}[/tex]

= 4

Answer:

Step-by-step explanation:

5 * 8y = 40y

8 * 5 = 40

40y - 40 IS equal to 40y - 40

Answer: no they are not

Step-by-step explanation: since the expression is in the parentheses you have to distribute the 8 amount 5y and 8 basically multiply 8 by he two numbers inside the parentheses 8(5y-8)

40y-64 is not equal to 40y -40

Answer:

Step-by-step explanation:

501

Answer:

Roots are complex numbers

Step-by-step explanation:

we know that

In a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex]

The discriminant is equal to  [tex]b^{2} -4ac[/tex]

If [tex]b^{2} -4ac=0[/tex] -----> The equation has only one real root

If [tex]b^{2} -4ac>0[/tex] -----> The equation has two real roots

If [tex]b^{2} -4ac<0[/tex] -----> The equation has complex roots

In this problem the discriminant is -8

so

-8 < 0

therefore

Roots are complex numbers

Answer:

A) There are two complex roots

Step-by-step explanation:

took the test

Answer:

9 ft

Step-by-step explanation:

you multiply side a by side b

so 3x3 = 9 ft

The answers are shown below:

The arithmetic mean of a given data is the sum of all observations divided by the number of observations. For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:

Mean = Sum of all observations/Number of observations

Mean = Sum of all observations/Number of observations

Mean = (12 + 34 + 45 + 50 + 24)/5

Mean = 165/5 = 33

The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.

For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = middle value i.e. 4.

Given data:

0, 40, 60, 70, 75, 80, 85, 95, 95, 100

a)Mean without '0' = 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/9

                            = 700/9

                            = 77.777

Median without '0' = 80

Mean with ' 0' = 0+ 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/10 = 70

Median with '0' = 80

b)standard deviation= 18.121673811445. (without '0')

standard deviation with 0 = 28.982753492379

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Answer:

The legs would be 15 & 8

Step-by-step explanation:

According to the Pythagorean theorem:

17² = a² + b²

289 = a² + b²

289 = 225 + 64

289 = 15² + 8²

The lengths of the two legs are 15 and 8.

Answer:

0

Step-by-step explanation:

clearly this page is not in need of in answer it does not seem like a real equation you need help with.

Answer:

y= -3,1,5

Step-by-step explanation:

actually the question is what are the values of y when x = -3,-1,1

Answer: -1=-1 ,1=1

You just need to plug it in to the graph.

Answer:

factoring c is the best way to solve this

Step-by-step explanation:

S = C ( 1 + R )

C = S/( 1 + R )

The equation after solving is C = S / (1 + R).

To solve for C in the equation S = C + RC, we can factor out C on the right side:

S = C + RC

S = C(1 + R)

Then, we can divide both sides by (1 + R) to isolate C:

S / (1 + R) = C

Therefore, the solution is:

C = S / (1 + R)

For example, if S = 100 and R = 0.1, then C would be:

C = 100 / (1 + 0.1)

C = 100 / 1.1

C = 90.9090909090909

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Answer: -54

All you need to do is add the two together

Answer:

Step-by-step explanation:

-18 + (-36) =  -18-36 = -54

Answer:

[tex]\frac{3}{2}[/tex] c

Step-by-step explanation:

Given

[tex]\frac{3a+3b}{2a-2b}[/tex] ← factor numerator and denominator

= [tex]\frac{3(a+b)}{2(a-b)}[/tex]

= [tex]\frac{3}{2}[/tex] × [tex]\frac{a+b}{a-b}[/tex] = [tex]\frac{3}{2}[/tex] c

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Y(\stackrel{x_1}{-13}~,~\stackrel{y_1}{8})\qquad Z(\stackrel{x_2}{2}~,~\stackrel{y_2}{-10}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{2-13}{2}~~,~~\cfrac{-10+8}{2} \right)\implies \left( \cfrac{-11}{2}~,~\cfrac{-2}{2} \right)\implies \left(-5\frac{1}{2}~,~-1 \right)[/tex]

Answer: (rounded) 7.1 inches.

For this problem, you have to find the square root of 50, since in a square all sides are equal. When you find the square root, you get 7.071067...., but rounded this would be 7.1 .

Answer:

the answer is sevenm point one

Step-by-step explanation:

Answer:

5.24

Step-by-step explanation:

6.99-1.75 is 5.24.

Answer:

$5.24

Step-by-step explanation:

[tex]\begin{array}{rcr}\text{Original cost} & = & 6.99\\\text{Less coupon} & = & -1.75\\\text{Net cost} & = & \mathbf{5.24}\\\end{array}[/tex]

Answer:

C. (5x^3-7)(2x^2+1)

Step-by-step explanation:

Given expression is,

10x^5+5x^3-14x^2-7

=10x^5-14x^2 + 5x^3 - 7  (By the commutative property)

=2x^2(5x^3-7)+5x^3-7     (Taking 2x^3 common from first two terms )

=(5x^3-7)(2x^2+1)      (Taking 5x^3-7 common from both terms)

\implies 10x^5+5x^3-14x^2-7=(5x^3-7)(2x^2+1)

Hence, Option C is correct

Answer:

21.29 milliliters

Step-by-step explanation:

First find how much water is need for 1 gram of stone by dividing both numbers by 263. Then multiplying both numbers by 70.

Grams : Milliliters

263       80

1           : 0.3042 (Rounded to 4 decimal places)

70        : 21.29 (Rounded to 2 decimal places)

The amount of water needed when using 70 grams of dental stone powder is approximately 21.29 milliliters. This is based on the ratio of stone powder to water in the original mixture.

The question is asking for the calculation of the amount of water needed if 70 grams of dental stone powder is used. This can be resolved by determining the ratio of water to dental stone powder in the initial mixture, and then applying this ratio to the lesser quantity of 70 grams. In the original mixture, there are 263 grams of dental stone powder to 80 milliliters of water which simplifies to approximately 1 gram to 0.3042 milliliters of water. Therefore, if you use 70 grams of stone powder, you multiply 70 grams by 0.3042 milliliters/g, which equates to approximately 21.29 milliliters of water.

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Answer:

A is true.

Step-by-step explanation:

Cos θ = adjacent / hypotenuse = x/1 = x.

Cosθ has a period pf 2π.

Answer:

The correct option is A.

Step-by-step explanation:

Draw a perpendicular form point P on x-axis.

Radius of unit circle is 1 . It means in triangle OPA

Hypotenuse = OP = 1 units

Adjacent= OA = x

Perpendicular = PA = y

In a circle angled triangle,

[tex]\cos \theta = \frac{adjacent}{hypotenuse}[/tex]

In triangle OPA,

[tex]\cos \theta = \frac{x}{1}[/tex]

[tex]\cos \theta =x[/tex]

The x-coordinate of P corresponds to cosθ.

The period of a unit circle is 2π.

Therefore, the correct option is A.

Answer:

After 5 years : ( n + 5 ) years !

Before 5 years : ( n - 5 )

Step-by-step explanation:

Given the age of Mary is n years old

After 5 years , She must be 5 years more from now so,

Her age will be ( n + 5 ) years after 5 years from now !

Also, 5 years ago she must be 5 years less than from now ,

So, her age 5 years ago was ( n - 5 ) years !

To represent Mary's age 5 years from now, the expression 'n + 5' is used. To represent her age 5 years ago, the expression 'n - 5' is used.

To represent Mary's age 5 years from now, we can use the expression n + 5. This is because we add 5 to her current age, represented by 'n', to find her age in the future.

To represent Mary's age 5 years ago, we can use the expression n - 5. This is because we subtract 5 from her current age, represented by 'n', to find her age in the past.

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Let g = grade needed

(78 + 85 + 92 + 97 + g)/5 = 90

Solve for g.

Yes, it will! It will be the same because of the Commutative property. Hope this gives you your whole answer!

Answer:

x=-2

Step-by-step explanation:

Distribute the 3 with the parenthesis to make the new equation -2=12x-9+5.

Combine like terms. -2=12x-4.

Move -4 to other side. -6=12x.

Divide by -6. x=-2

Answer:

116,893,148‬

Hope this helps :)

The product of 4127 and 28324 is 116884748.

To find the product of 4127 and 28324:

Write down the numbers vertically aligning the digits:

4127 x 28324

Multiply each digit of the second number by the entire first number, remembering to shift each subsequent multiplication one place to the left:

4127 × 4 = 16508

4127 × 2 = 8254 (shift one place to the left, becomes 82540)

4127 × 3 = 12381 (shift two places to the left, becomes 1238100)

4127 × 8 = 33016 (shift three places to the left, becomes 33016000)

4127 × 2 = 8254 (shift four places to the left, becomes 82540000)

Add all these partial products together:

16508 + 82540 +1238100 +33016000 +82540000

= 116884748

So, the product of 4127 and 28324 is 116884748.

Answer:

81

Step-by-step explanation:

since b is 9

do 9x9 which is 81

Answer:

[tex]F(x)=\frac{x^2+4x+4}{x^3+5x^2}[/tex]

Step-by-step explanation:

Graph the rational function.

Answer:

1) [tex]2,549,786\ people \approx3,000,000\ people[/tex]

2) [tex]3*10^6[/tex]

Step-by-step explanation:

1) To round a number to the nearest million, you must look at the digit located in the hundred thousands place. If this is greater than or equal to 5 you must round up, and if this is less than 5, you must round down.

In this case you know that the city has a population of [tex]2,549,786\ people[/tex].

You can notice that the digit located in the hundred thousands place is 5, therefore, you must round up:

[tex]2,549,786\ people \approx3,000,000\ people[/tex]

2) Scientific notation has the following form:

[tex]a*10^n[/tex]

Where "a" must be a number from 1 to 10 but not including 10 and "n" must be an integer.

To express [tex]3,000,000[/tex] in Scientific notation, the decimal point must be moved 6 places to the left; therefore, the exponent will be positive.

Then:

[tex]=3*10^6[/tex]