An experiment reported in Popular Science compared fuel economies for two types of similarly equipped diesel mini-trucks. Let us suppose that 12 Volkswagen and 10 Toyota trucks were tested in 90- kilometer-per-hour steady-paced trials. If the 12 Volkswagen trucks averaged 16 kilometers per liter with a standard deviation of 1.0 kilometer per liter and the 10 Toyota trucks averaged 11 kilometers per liter with a standard deviation of 0.8 kilometer per liter, construct a 90% confidence interval for the difference between the average kilometers per liter for these two mini-trucks. Assume that the distances per liter for the truck models are approximately normally distributed with equal variances.

Answer: (3,-6) x=3 y=-6

Step-by-step explanation:

Option (d) i.e y = 2x is correct option as this function is satisfying given values of y and x.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. German mathematician Peter Dirichlet initially offered the standard concept of function in 1837.

y and x are coupled in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x).

We need to check by substituting value of y in every equation to check correct option.

(a) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = 3x= 3×3=9

L.H.S≠R.H.S

So, it is not a correct option.

(b) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = x-3= 3-3=0

L.H.S≠R.H.S

So, it is not a correct option.

(c) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = x+2= 3+3=5

L.H.S≠R.H.S

So, it is not a correct option.

(d) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = 2x= 2×3=6

L.H.S=R.H.S

So, it is correct option.

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Answer:29,921.25

Conner and Darian made a profit of $40,021.50 on the first day of their hot chocolate sale. They donated $10,050.25 of that money to their school, which leaves them with $40,021.50 - $10,050.25 = $29,971.25.

Conner and Darian each gave their dad $25.00, which means they gave a total of $25.00 * 2 = $<<25*2=50.00>>50.00 to their dads.

This means that Conner and Darian had $29,971.25 - $50.00 = $29,921.25 left to invest in their hot chocolate shop.

The rate of change of the table of values is calculated as: A. 1/5.

Given the table above, the rate of change can be calculated using the formula below:

Rate of change (m) = change in y / change in x.

Using two pairs of values from the table, (10, 2) and (20, 4):

Change in y = 4 - 2 = 2

Change in x = 20 - 10 = 10

Therefore:

Rate of change (m) = 2/10

m = 1/5

Therefore, the rate of change is determined as: A. 1/5.

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Answer:

Part A: 2 Part B: 2- and 4-Part C: 8 The graph shows at 8 seconds the slope starts to decrease rapidly. Part D: I believe at 14 seconds the water balloon would be o the ground.

Step-by-step explanation:

The correct answer is (D) 2 + 3 = 6. If an organism is homozygous for 3 genes and heterozygous for 2 genes, it can produce a total of 2 + 3 = 5 different gametes.

When an organism is homozygous for a gene, it means that it carries two copies of the same allele for that gene. When an organism is heterozygous for a gene, it means that it carries two different alleles for that gene.

In this case, the organism is homozygous for 3 genes, which means that all its gametes will carry the same alleles for these 3 genes. It is also heterozygous for 2 genes, which means that it can produce gametes that carry either one of the two alleles for these 2 genes.

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The triangle ΔADB is congruent to the triangle ΔCDB by the ASA postulate.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangles are said to be congruent if two points and the contained side among one triangle match two angles and the contained side of another triangle.

In triangles ΔADB and ΔCDB, then we have

∠BAD = ∠BCD          (Given)

∠BDA = ∠BDC          (Given)

    AD = AD               (Common side)

The triangle ΔADB is congruent to the triangle ΔCDB by the ASA postulate.

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Answer:

ive did the math and its r= 4

Step-by-step explanation:

see the attached solution

Answer:

[tex]\dfrac{-2x^4-6}{(x+1)(x-1)(x^2+1)}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{2}{x+1}-\dfrac{2x}{x-1}+\dfrac{4}{x^2+1}[/tex]

The least common multiplier of the denominators is:

[tex](x+1)(x-1)(x^2+1)[/tex]

Adjust the fractions based on the least common multiplier:

[tex]\implies \dfrac{2(x-1)(x^2+1)}{(x+1)(x-1)(x^2+1)}-\dfrac{2x(x+1)(x^2+1)}{(x+1)(x-1)(x^2+1)}+\dfrac{4(x+1)(x-1)}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{a}{c} \pm \dfrac{b}{c}=\dfrac{a \pm b}{c}:[/tex]

[tex]\implies \dfrac{2(x-1)(x^2+1)-2x(x+1)(x^2+1)+4(x+1)(x-1)}{(x+1)(x-1)(x^2+1)}[/tex]

Simplify:

[tex]\implies \dfrac{2(x^3-x^2+x-1)-2x(x^3+x^2+x+1)+4(x^2-1)}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\implies \dfrac{2x^3-2x^2+2x-2-2x^4-2x^3-2x^2-2x+4x^2-4}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\implies \dfrac{-2x^4+2x^3-2x^3-2x^2-2x^2+4x^2+2x-2x-2-4}{(x+1)(x-1)(x^2+1)}[/tex]

[tex]\implies \dfrac{-2x^4-6}{(x+1)(x-1)(x^2+1)}[/tex]

Answer: D

Step-by-step explanation:

(4,16)

For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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The amount of time required for an assembly line worker to complete a repetitive task is measured using a time and motion study.

According to the data, the average time it takes to move apart from the bin to its place on a car's chassis is 11 seconds, while the standard deviation is 2 seconds.

If XX and YY are independent, the property mean and variance are as follows: X 1 = 11; sigma_X_1 = 2, X 1 = 2, mu_X_2 = 20, X 2 = 20, sigma_X_2 = 4, and X 2 = 4.

aX+bY = a X + b Y; sigma_aX+bY = a X + b Y; aX+bY 2 = a 2 X 2 + b 2 Y 2; and finally, we have the following results:

X 1 + X 2 = X 1 + X 2 = 11+20=31 sigma_X_1+X_2=sqrtsigma_X_1+sigma_X_2=sqrtsigma_X_1+sigma_X_2=sqrtsigma_X_2=sqrtsigma_X_2=sqrtsigma_X_2=sqrtsigma_X_1+

The value reduced by the mean and divided by the standard deviation is the z-score:

z=\dfrac{x-\mu} {\sigma} =\dfrac{30-4.4721} \approx - 0.22

z=σx−μ =4.472130−31

≈−0.22

Decide the relating esteem utilizing table A:

P (X_1+X_2 30) = P(Z-0.22) = 0.4129 P (X 1 30) = P(Z-0.22) = 0.4129

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Answer:

Step-by-step explanation:

first things first go back in the lesson or your notes if you wrote down some and if not go right some down and in the notes there would be the answer between pages 1-5 or maybe  6 IDR ( i dont remember )  but look thru those  pages and you will find the answer hope this helped. please mark me brainiest please.

The true statement about the graph include:

1. The y-intercept represents the orders for hot chocolate on a day when the outside temperature was 52°F.

2. Sheryl gets 160 orders for hot chocolate on a day when the outside temperature is 52°F.

It is clearly mentioned on graph above 52 degrees fahrenheit. So y-intercept represents the orders for hot chocolate when the outside temparature was 52 F.

For every 16° increase in temparature above 52°F there is a decrease of 32 orders. Therefore for each degree increase above 52°F decrease in order = 32/16 => 2

So Sheryl gets 2 few orders for each degree decrease in temperature above 52°F. The slope of the line represents the decrease in numbers of order per degree increase in temparature.

As graph starts with 52oF and the number of orders on it is 160; So, Sheryl gets 160 orders when outside temparature is 52°F.

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By using the properties of rectangle, it can be calculated that-

Value of z is 31°

What is a rectangle?

Rectangle is a four sided two dimensional figure which satisfies the properties of a parallelogram and whose every angle is 90°

FH = 2z + 8

EG = 2z + 8 [Diagonals of a rectangle are equal]

EI = 35

EG = [tex]35 \times 2 = 70[/tex] [Diagonals of rectangle bisect each other]

So,

2z + 8 = 70

2z = 70 - 8

2z = 62

z = [tex]\frac{62}{2}[/tex]

z = 31

Value of z is 31°

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The relation between variables is represented by an equation ; y = 2.5x+15

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Alexa joined a program at some coffee shop which offers her $15 per month, after which she will get her coffee at a discount rate which $2.5

We can represent the relationship as ;

y = 2.5x+15

Where, x (number of coffee) is an independent variable because it does not depend on any condition, and y (cost) is a dependent variable because it depends on the value of x.

Hence, the relation is described as y = 2.5x+15

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The correct answer is D. A 95% confidence interval must be wider than an 80% confidence interval in order to be more confident that it captures the true value of the population proportion.

The width of a confidence interval reflects the degree of uncertainty about the estimate of the population parameter. A wider interval indicates a higher degree of uncertainty, while a narrower interval indicates a lower degree of uncertainty.

The confidence level of a confidence interval is the probability that the interval contains the true population parameter. For example, a 95% confidence interval means that there is a 95% probability that the interval contains the true population parameter. Similarly, an 80% confidence interval means that there is an 80% probability that the interval contains the true population parameter

Since a 95% confidence interval is more confident that it captures the true value of the population parameter than an 80% confidence interval, the 95% confidence interval must be wider in order to capture the true value with a higher degree of confidence.

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A fraction of the students who have brown hair is equal to 1/7.

You should shade only one (1) section on the pie chart to show the number of students with brown hair.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.

Based on the information provided in the table (see attachment), we can logically deduce the following parameters about the various hair color;

Number of brown hair = 1 brown hair.

Number of blonde hair = 4 blonde hair.

Number of black hair = 2 black hair.

Therefore, the total number of hairs is equal to 7 hairs.

For the fraction of students with brown hair, we have;

Fraction = 1/7.

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The process by which people are separated from social participation is known as social exclusion.

This term refers to the process in which people or groups are separated or not allowed to participate.

Exclusion is considered a negative process or phenomenon, since:

In this sense, what must be done is to fight to eliminate exclusion and promote inclusion.

¡Hope this helped!

Answer:

To create a proportion using the form %/100 = is/of, we can first write the given information in the form %/100 = is/of. In this case, we know that 1 1/2% represents 15, so we can write:

1 1/2%/100 = 15/of

Next, we need to solve for the "of" value, which is the number we are trying to find. To do this, we can multiply both sides of the equation by 100 and then divide both sides by 1 1/2% to get:

(1 1/2%/100) * 100 = (15/of) * 100

of = (15/1 1/2%) * 100

Finally, we can evaluate the right-hand side of the equation to find the value of "of". Since 1 1/2% is the same as 1.5%, we can substitute 1.5 for 1 1/2% in the equation to get:

of = (15/1.5%) * 100

of = (15/0.015) * 100

of = 1000

Therefore, the number we are trying to find is 1000.

In summary, the proportion that represents the given word problem is:

1 1/2%/100 = 15/1000

Answer:

[tex]\textsf{Proportion}: \quad \sf \dfrac{1.5}{100}=\dfrac{15}{x}[/tex]

[tex]\textsf{Solution}: \quad \sf x=1000[/tex]

Step-by-step explanation:

Given proportion formula:

[tex]\sf \dfrac{\%}{100}=\dfrac{is}{of}[/tex]

Given word problem:

Let the unknown number be x.

Therefore:

Substitute these into the proportion formula to create a proportion to represent the given word problem:

[tex]\sf \dfrac{1.5}{100}=\dfrac{15}{x}[/tex]

To solve the proportion, cross multiply:

[tex]\implies \sf 1.5x=15 \cdot 100[/tex]

[tex]\implies \sf 1.5x=1500[/tex]

Divide both sides by 1.5:

[tex]\implies \sf \dfrac{1.5x}{1.5}=\dfrac{1500}{1.5}[/tex]

[tex]\implies \sf x=1000[/tex]

The option that shows the estimation that Bradley’s change is reasonable is A. Add 11 and 5 and 3 to get $19; $20-$19=$1, which is very close to the amount of change received by Bradley

Estimation is the process of determining an estimate or approximation, which is a value that can be used for a specific purpose even when the input data is incomplete, uncertain, or unstable. Nonetheless, the value is usable because it is based on the best available information.

In this situation, Henri paid $10.75 for a calculator, $4.98 for copier paper, and $3.21 for folders. He paid with a $20 bill and got $1.06 in change.

The correct estimation is option A.

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The value of d for the given angles will be equal to d = 13. The correct option is B.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Complementary angles are formed when the sum of two angles equals 90 degrees. 30 degrees and 60 degrees, for example, are complementary angles.

Given that one angle measures 18° and another angle measures (6d − 6)°.

The value of d will be calculated as,

18 + 6d - 6 = 90

6d + 12 = 90

6d = 90 - 18

6d = 78

d = 78 / 6

d = 13

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Answer:

4y = (1/2)^x -5

Step-by-step explanation:

The first three equations are lines. All the variables have a power of just one (power of one is a math number that is not written) They are actually all written in slope-intercept form even. Line equations are linear function. Yay the words match!

You get a curve (not linear) when you have exponents, square roots or variables in the denominator of a fraction. Or as here, a variable for an exponent!

1/2 is the slope of the following when you simplify

Answer:

y = 1/3x + 6

Step-by-step explanation:

Answer:

you would times them both so 4x543 =2172

Step-by-step explanation:

543 cubic centimeters has 0.543 L approximate displacement.

Engine displacement means the displacement of the piston inside cylinder from Bottom Dead Center into Top Dead Center in one cycle.

Basic formula to calculate engine displacement is =

V = π/4 x D² x H x N

Where :

D = Bore Diameter

H = Length of Stroke

N = Number of Cylinder

Since the question has already stated cubic centimeter, it has already shown the displacement. So, we can ignore above formula and the 4-cylinder engine information.

First, we state what is known. It is the displacement at cubic centimeter.

Cubic centimeter = 543 cc

Next, we change the unit of cubic centimeter (cc) into liter (L)

Displacement = cc / 1000 L

= 543 / 1000 L = 0.543 L

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1) The base rate for the empty bus is $120.

2) The variable cost (slope) for each person on board the bus is $2.

3) An equation to show the cost, c, of a bus with x number of people on it is C = 120 + 2x.

The total charge for taking 30 people aboard = $180

The total charge for taking 50 people on board = $220

The differences in the number of people and charges are 20 and $40, respectively.

Let x = the number of people boarding the bus and n = the fixed rate per bus.

30x + n = 180 ... Equation 1

50x + n = $220  ... Equation 2

Subtract Equation 1 from Equation 2:

20x = $40

x = $2 ($40/20)

The variable cost per person = $2 ($40/20)

The base rate for the empty bus = 30(2) + n = $180, where n is the base rate or fixed cost per bus.

= 60 + n = $180

n = $120

OR:

50(2) + n = $220

100 + n = $220

n = $120

The equation for the cost, c, of a bus with x number of people:

C = 120 + 2x

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When the sequence limn→∞ (1 n! ∫x t = a f(n+1)(t)(x−t)n d t) converges to zero, as seen on the left side equation the Taylor series will accurately converge to f(x). For the Taylor series of f, this side is known as the integral form of the remainder (x).

Rn(x) = f(n+1)(c) (n + 1); thus, (x a)n + Rn(x)! when there is a c between a and x, (x a)n+1. The Taylor formula is the name given to the second equation. The residual of order n or error term for the Pn(x) over I approximation of f is known as the function Rn(x) (x). To integrate a Taylor Series function, expand the Taylor Series as usual before integrating each term. There is a general expression for the new series. Prior to determining the generic phrase, it is essential to avoid simplification.

Assume that f(x) is a real or composite function and that f(x) is a differentiable function of a real or composite neighborhood number. The following power series is then described by the Taylor series: F (x) = F a F ′ a 1! (x−a)+f”(a)2!

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The percentage increase is about 16.66%.

What is a percentage increase?

The percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in the percentage.

The initial amount was $18 and the final amount is $21.60.

By using the percentage increase formula, we can write

        Percentage increase = (final value - initial value)/|Final value| * 100

                                            = ((21.60 - 18)/21.60)*100

                                            = 16.66%

Hence, the percentage increase is about 16.66%.

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The simple interest rate that Levi is being charged, given that he will have to pay back $ 45 and $ 15. 25 in 5 months, is  81.3 %

The simple interest rate can first be found by finding the monthly amount that Levi has to pay in fees which is :

= 15. 25 / 5 months

= $ 3. 05 fee per month

The amount that the fee would have been in a year is :

= 3. 05  x 12

= $ 36. 60

The simple interest rate is therefore :

= 36. 60 / 45

= 81.3 %

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