which car can travel farther on one gallon of gas?blue car: travels miles using 0.8 gallonsred car: travels miles using 0.75 gallons

Answer:

59.09%

Step-by-step explanation:

You find it through the following formula:

Part divided by whole times 100.

Substitute it and you get the answer:

130 / 220 times 100 = 59.09

Answer:

D. 67

Step-by-step explanation:

with respect to angle x.

perpendicular is 24.

hypotenuse is 26cm

since we have

sin angle=perpendicular / base

sin x=24/26

x=sin inverse(24/26)

x=67.38

in nearest degree x=67 degree

The maximum number of miles she will be able  to travel, to the nearest tenth of a mile is less than or equals to 22.8 miles.

She needs to take a cab and has y dollars. The company charges a flat rate of $2.25 plus $0.55 per mile. Therefore the equation will be

y = 2.25 + 0.55x

where

x = number of miles travelled.

Now she has $12.52 and she finds a cab company with the same flat rate and only charges $0.45 per mile. The maximum number of miles she will be able to travel to the nearest tenth of mile can be calculated below:

2.25 + 0.45x ≤ 12.52

x = number of miles travelled.

0.45x ≤ 12.52 - 2.25

x ≤ 10.27 / 0.45

x ≤ 22.8222222222

x ≤ 22.8 miles

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The zobt value for a sample mean of 52.1 with a population mean of 47.2 and a population deviation of 6.4, and a sample size of 8 is approximately 3.19.

We can use the formula for calculating the z-score:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population deviation, and n is the sample size.

Plugging in the given values, we get:

z = (52.1 - 47.2) / (6.4 / √8) ≈ 3.19

Therefore, the zobt value for a sample mean of 52.1 with a population mean of 47.2 and a population deviation of 6.4, and a sample size of 8 is approximately 3.19.

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Answer:

The slope is -3/2

Step-by-step explanation:

Hope this helped have a good day!

Mixed Number Form:

\( - 1 \frac1 2\)

Answer:

\(\huge\boxed{\sf y = 4x - 5}\)

Step-by-step explanation:

Given that,

Slope = m = 4

Y-intercept = b = -5

Put the above values.

y = 4x + (-5)

\(\rule[225]{225}{2}\)

Answer:

The equation of the line is \(y = 3x + 3\)

Step-by-step explanation:

Looks like you've already found the y-intercept and slope of this graph. Great! That's all the info we need to create an equation.

The equation of a line is always in \(y = kx+b\) form, where k is the constant of proportionality (aka the slope) and b is the constant added (aka the y-intercept).

We know the slope is 3 and the y-intercept is 3, so we can put these values into the equation.

\(y = 3x+3\)

Hope this helped!

The smallest positive integer value of x for which\(f(x) = 2^x + 2\) exceeds \(g(x) = 12x + 8\)  is x = 4.

To find the smallest positive integer value of x for which the value of\(f(x) = 2^x + 2\) exceeds the value of g(x) = 12x + 8, we need to compare the two functions and determine when the inequality is satisfied.

Setting up the inequality, we have:

\(2^x + 2 > 12x + 8\)

First, let's simplify the inequality by subtracting 8 from both sides:

\(2^x - 6 > 12x\)

Now, we can try to solve this inequality by considering different values of x.

However, it is challenging to find an exact solution by hand due to the exponential nature of \(2^x.\)

Therefore, let's graph the two functions,\(f(x) = 2^x + 2\) and g(x) = 12x + 8, to visually determine the point of intersection.

Upon graphing the functions, we observe that the graphs intersect at some point.

We can see that the value of f(x) starts to exceed g(x) as x increases.

To find the smallest positive integer value of x for which f(x) exceeds g(x), we need to analyze the graph and determine the first integer value after the intersection point where f(x) is greater than g(x).

Examining the graph, we find that the smallest positive integer value of x for which f(x) exceeds g(x) is x = 4.

Therefore, the answer is x = 4.

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Answer: A $6

Step-by-step explanation:

Let x = price per child ticket, y= price per senior ticket.

As per given, we have

5x+12y=102  (i)

12x+14y=156  (ii)

From (i), we have

\(x=\dfrac{102-12y}{5}\)   (iii)

Put value of x in (ii), we get

\(12(\dfrac{102-12y}{5})+14y=156\\\\\\ \dfrac{1224-74y}{5}=156\\\\\\1224-74y=5\times156\\\\\\ 1224-74y=780\\\\\\ 74y=1224-780\\\\\\ 74y=444\\\\ y=\dfrac{444}{74}\\\\\\ y=6\)

Hence, the price of senior ticket = $6

Thus the correct option is A.

Answer:

Step-by-step explanation:

If it was like....\(\frac{a^{5}}{a^{3}}\)

then you subtract 5 minus 3 to be left with a^2 on the numerator

That would be how you would take it away.

Answer:

This should explain it

Step-by-step explanation:

If its the graph question I think it is this is the answer screenshot.

From the given graph

The end points of the curve is y = + 3 and y = -3

The point + 3 is shadded while point - 3 is not shadded hence

The range of the function is

(a) The value of expectation E[X] = 27/4

(b) The value of expectation E[Y] = 9/4

(c) Value of variance Var[X] = 243/40(

d) Var[Y] = 27/40

(e) Cov[X, Y] = 27/40

(f) E[X + Y] = 9

(g) Var[X + F] = 243/40

(a) Expectation E[X] can be calculated as follows:E[X] = ∫x f(x) dx = ∫x∫y f(x,y) dy dx = ∫0⁹∫0ˣ 2/81 y dx dy + ∫9^∞∫0⁹ 0 dy dx= 27/4

(b) Expectation E[Y] can be calculated as follows:E[Y] = ∫y f(y) dy = ∫y∫x f(x,y) dx dy = ∫0⁹∫y^⁹ 2/81 y dx dy= 9/4

(c) Variance of X can be calculated as follows:Var[X] = E[X²] - E[X]²=∫x² f(x) dx - E[X]²= ∫0⁹∫0ˣ 2/81 x² dy dx - (27/4)²=243/40

(d) Variance of Y can be calculated as follows:Var[Y] = E[Y²] - E[Y]²=∫y² f(y) dy - E[Y]²= ∫0⁹∫y⁹ 2/81 y³ dy dx - (9/4)²= 27/40

(e) Covariance of X and Y can be calculated as follows:Cov[X, Y] = E[XY] - E[X]E[Y]=∫x∫y xy f(x,y) dy dx - E[X]E[Y]=∫0⁹∫0ˣ 2/81 xy dy dx - (27/4) (9/4)= 27/40

(f) E[X + Y] can be calculated as follows:E[X + Y] = E[X] + E[Y]= 27/4 + 9/4= 9(g) Variance of X + Y can be calculated as follows:Var[X + Y] = Var[X] + Var[Y] + 2Cov[X, Y]= 243/40 + 27/40 + 2(27/40)= 243/20

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See below for the vocabularies and their correct definition

Match the following vocabulary

The terms are given as:

To get the inverse of a conditional, the hypothesis and the conclusion are negated, without interchanging them.

So, we have:

Inverse of a conditional ⇒ A new statement formed by negating both the hypothesis and the conclusion.

To get the contrapositive of a conditional, the hypothesis and the conclusion are negated, after interchanging them.

So, we have:

Contrapositive of a conditional ⇒ Formed by exchanging the hypothesis and the conclusion and negating both of them.

To get the converse of a conditional, we simply interchange the hypothesis and the conclusion, without negating them

So, we have:

Converse of a conditional ⇒ A statement formed by interchanging the hypothesis and the conclusion in a conditional statement.

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Answer:

The answer is Convers because it literally takes the hypothesis and the conclusion and interchanges them.

Step-by-step explanation:

Answer:

positive

Step-by-step explanation:

because don't have the "-"

Answer:

positive

Step-by-step explanation:

0.912+134.1= 135.012

Step-by-step explanation:

-2x - 7 > 1

-2x > 8

-x > 4

x < -4

that is a continuous line from -4 all the way to the left, and the dot on -4 is empty (meaning : it is not included due to the "<" symbol).

x - 2 >= -1

x >= 1

that is a continuous line from +1 all the way to the right, and the dot on +1 is filled (meaning : is IS included due to the ">=" symbol.

Answer:

The correlation coefficient is determined by dividing the covariance by the product of the two variables' standard deviations. Standard deviation is a measure of the dispersion of data from its average. Covariance is a measure of how two variables change together.

The values of x and y for which A^2 = A are x = 1 and y = 0. we see that -48 = 0, which is not possible

To determine the values of x and y for which A^2 = A, we need to square the given matrix A and equate it to A itself.

Squaring matrix A:

A^2 = [x y 5 -8] * [x y 5 -8]

= [xx + y5 + xy + y(-8) + 5x + 5(-8) -85 + (-8)(-8)]

= [x^2 + 5y + xy - 8y + 5x - 40 - 40 + 64]

= [x^2 + 6x + 5y - 48]

Equating A^2 to A: [x^2 + 6x + 5y - 48] = [x y 5 -8]

By comparing the corresponding elements, we can derive two equations: x^2 + 6x = x => x^2 + 5x = 0

5y - 48 = 5y => -48 = 0

From equation 2, we see that -48 = 0, which is not possible. Therefore, there is no value of y that satisfies this equation.

From equation 1, x^2 + 5x = 0, we can factor out an x:

x(x + 5) = 0

So, either x = 0 or x + 5 = 0. This gives us two possible values for x: x = 0 and x = -5.

Therefore, the values of x and y for which A^2 = A are x = 1 and y = 0.

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Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

cylinders

h = 9 in

radius = r (in )

V = volume (in ³ )

Step 02:

a.

volume of a cylinder:

V = π r ² h

radius = 1 in

V1 = π (1 in)² * 9 in = 9 π in³

radius = 2 in

V1 = π (2 in)² * 9 in = 36 π in³

radius = 3 in

V1 = π (3 in)² * 9 in = 243 π in³

Table

radius Volume

row 1 1 9 π

row 2 2 36 π

row 3 3 243 π

Step 03:

b. Is there a linear relationship between the radius and the volume of these cylinders?

Yes, because the greater the radius, the greater the volume.

Step 04:

c.

cylinder pitcher:

h = 9 in

r = r

V = π r ² h

Vcp = π r ² 9 in = 9 π r ² in ³

cylinder:

h = 9 in

r = 2r

V = π r ² h

Vc = π (2r) ² 9 in = 36 π r ² in ³

# pitchers = Vc / Vcp

= 36 π r ² in ³ / 9 π r ² in ³

= 4

It can fill 4 pitchers

That is the full solution.

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Answer:

112 in²

Step-by-step explanation:

width of the brick = (2 - - 5) = 7       this is the distance between the vertices in the y direction

length of the brick = (8 - -8) = 16  this is the distance between the vertices in the x direction

Area = length x width= 16 x 7 = 112 in²

Note:  it helps if you graph these points, then you can see the problem better

Answer:

Dimplified: \(3.88\)×\(10^{10}\), or \(38,800,000,000\)

Unsimplified: \(38,792,400,000\)

Step-by-step explanation:

Remember, the volume of a sphere is \(V=\)\(\frac{4}{3}\)\(\pi r^{3}\)

This comes into: \(3.87924\)×\(10^{10}\)

As we know, the shape of mars is a sphere.

Let me know if you have a question, or if it lets you not have the ×\(10^{10}\)

An equation in which the highest power of the variable is 1 is known as a linear equation. It is also termed a one-degree equation.

There are two types of linear equations, linear equations in one variable and linear equations in two variables. The standard form of a linear equation in one variable is Ax + B = 0. Where x = variable, A = coefficient and B = constant.

The standard form of a linear equation in two variables is Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always formed in a straight line. That is why it is named a 'linear equation'.

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Answer:

3rd one down

Step-by-step explanation:

(1,5), (2,9), (3,13), (4,17)

The table C is Solution for the Equation.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

given:

Equation: y= 4x+ 1

When x= 1

y = 5

and, x= 2

y= 8 + 1= 9

and, x= 3

y= 12 + 1= 13

and, x=4

y = 16 + 1 = 17

Thus, the solution for the Equation is (1, 5), (2, 9), (3, 13) and (4, 17).

Hence, the table C is Solution for the Equation.

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Answer:

12d = 156

Step-by-step explanation:

Carlos is reading 12 pages / day

The total amount to read is 156

In order to find the days, you have to divide 156 by 12 or

Equation:

12d = 156; furthermore

d = 13 days, meaning it will take 13 days to read 156 pages.

Answer:

A. 12d = 156

Step-by-step explanation:

The book has a total number of 156 pages. If he reads 12 pages per night, we need to multiple the total number of days by the amount he reads per night in order to get 156. Since we don't know how many days it will take, we will use d to represent the amount of days. So, the equation ends up looking like this:

12d = 156

d represents the amount of days it will take for Carlos to read the book.

The investment's expected return is 5.95%.

The expected return of an investment is calculated by multiplying the probabilities of each possible return by their respective returns and summing them up. In this case, Gautney Enterprises has provided the probabilities and returns for the investment. By applying the formula, we find that the expected return is 5.95%.

To calculate the standard deviation, we need to determine the variance first. The variance is computed by taking the difference between each possible return and the expected return, squaring those differences, multiplying them by their respective probabilities, and summing them up. Once we have the variance, the standard deviation is simply the square root of the variance. The standard deviation measures the degree of risk associated with an investment.

In this scenario, the expected return of the investment is 5.95%, but we need to consider the standard deviation as well to assess the risk. If the standard deviation is high, it indicates a greater level of uncertainty and potential volatility in returns. A low standard deviation implies a more stable investment.

Without the specific values for each return and their respective probabilities, we cannot calculate the exact standard deviation. However, Gautney Enterprises should compare the calculated expected return and the associated standard deviation to their risk tolerance and investment objectives. If the expected return meets their desired level of return and the standard deviation aligns with their risk appetite, they may consider investing in this security.

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