The gasoline a vehicle uses varies directly to the distance the vehicle travels. A car uses 10 gallons of gasoline to travel 210 miles. How many gallons will the car use to travel 294 miles

Correct option is   -1,3,4,7 ,, More the data , more is the variance. Observe the range of each data set. Range = Maximum - Minimum  So it has largest variance among given data sets.

\(3,5,8,9,10\)

\(mu = (3+5+8+9+10)/5 = 7\)

\(x\\\) \(x-mu = x-7\) \((x-mu)2\)

3        -4                             16

5        -2                              4

8        1                               1

9        2                              4

10        3                              9

35         0                              34

\(Variance = sum of (x - mu)2 / N\)

\(= 34/5\)

\(= 6.8\)

Correct option is

\(6.8\)

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The given triangle ABC and DEF are similar

From the properties of the similar triangle :

The ratio of the corresponding sides of similar traingle are equal and the ratio of perimeter is also equal to the ratio of corresponding sides

In the triangle ABC, AC=9, BC=6, and the angle B is 90 degree

then apply pythagoras to find the third side of triangle:

Pythagoras Theorem: The square of sum of base and perpendicular is equal to the square of Hypotenuse.

Perimeter of Triangle is express as the sum of the length of all the sides of traingle

The scale Factor :

Since the ratio of perimeter of triangle ABC and DEF are same as the ratio of thier corresponding sides

So,

So, Perimeter of triangle DEF = 38.69 unit

The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.

To determine the correct answer, let's analyze the given information.

We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.

Given:

P(D) = 0.6

P(D and E) = 0.18

Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:

P(D and E) = P(D) * P(E)

Substituting the given values:

0.18 = 0.6 * P(E)

To find the value of P(E), we can rearrange the equation:

P(E) = 0.18 / 0.6

P(E) = 0.3

Therefore, the correct answer is A. P(E) = 0.3.

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Answer:

x = 19.5

4x + 12 = 90 degrees

Step-by-step explanation:

We know it is a right angle, meaning 90 degrees.

4x + 12 = 90

4x = 78

x = 19.5

Answer:

Step-by-step explanation:

You want to know the measure of the angle marked (4x+12)° at the transversal crossing parallel lines at right angles.

The □ symbol on the diagram indicates the lines cross at right angles. The measure of a right angle is 90°. This means all of the angles where the transversal crosses the parallel lines have measures of 90°, including the one marked (4x+12)°.

We can solve for x using this relationship:

  4x +12 = 90 . . . . . . . . . answer to the second part

  x +3 = 22.5 . . . . . . . divide by 4

  x = 19.5 . . . . . . . . subtract 3 . . . answer to the first part

Answer:

h = -4

Step-by-step explanation:

7h-5(3h-8) = 72

Distribute

7h - 15h +40 = 72

Combine like terms

-8h +40 = 72

Subtract 40 from each side

-8h+40-40 = 72-40

-8h = 32

Divide each side by -8

-8h/-8 = -32/-8

h = -4

Steps:

Step 1: Simplify both sides of the equation.

7h−5(3h−8)=72

7h+(−5)(3h)+(−5)(−8)=72(Distribute)

7h+−15h+40=72

(7h+−15h)+(40)=72(Combine Like Terms)

−8h+40=72 −8h+40=72

Step 2: Subtract 40 from both sides.

−8h+40−40=72−40

−8h=32

Step 3: Divide both sides by -8

Answer:  h=−4

The answer for this question is h=-4

Please mark me brainliest

Hope this helps.

Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).

Let the given points be,

A = (3, 2), B = (-2, -3) and C = (2, 3)

The formula for the distance between two points:

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by \(D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$\).

Therefore,

A = \((x_{1} , y_{1} )\) = (3, 2), B = \((x_{2} , y_{2} )\) = (-2, -3)

\(& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}\)  units

B = \((x_{1} , y_{1} )\) = (-2, -3), C = \((x_{2} , y_{2} )\) = (2, 3)

\(& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}\)  units

A = \((x_{1} , y_{1} )\) = (3, 2), C = \((x_{2} , y_{2} )\) = (2, 3)

\(& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}\)  units

By using the Pythagorean theorem:

According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

Now, we can see that,

\(& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\\)

\(& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2\)

Therefore, the given triangle is a right angled triangle.

Therefore, option(A) s correct.

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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.

A. right triangle

B. equilateral triangle

C. isosceles triangle

D. none of these

The statement "you should never buy a product from a good salesman" is a subjective statement and cannot be answered as true or false universally.

It depends on various factors such as the product being sold, the sales tactics used by the salesman, and the individual's personal preferences and needs. A good salesman may provide useful information about the product and help the individual make an informed decision, while a bad salesman may use deceitful tactics to pressure the individual into buying something they don't need.

Therefore, it is important to evaluate each situation individually and make a decision based on the specific circumstances.

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Answer:

Step-by-step explanation:

You did not ask for the answer so I will just tell you the steps. First, you have to add 0.12 on both sides. Then you are going to subtract 1.1j from both sides. Finally you are going to divide both sides by 5.6 to get your final answer.

Answer:

Subtract 1.1j from both sides.

Step-by-step explanation:

Answer:

Step-by-step explanation:

  \(\sqrt{x}-3=0\\\\\sqrt{x}=3\qquad\text{add 3 to both sides}\\\\\boxed{x=9}\qquad\text{square both sides}\)

__

The expression ...

  \(\sqrt{|x|+1}\)

is defined for all values of x. The expression makes sense for all real numbers.

_____

Additional comment

The expression in the second question makes sense for all numbers, real or complex. The value of |x| is never negative, so the value under the radical is always positive.

A relationship is said to exist between two variables in a cross-tabulation if the percentage distribution varies across the different categories of the independent variable.

In a cross-tabulation, also known as a contingency table, two variables are compared to understand the relationship between them. The independent variable is typically displayed in the rows or columns of the table, while the dependent variable is displayed in the other dimension.

In order to determine if a relationship exists between the two variables, we examine the percentage distribution of the dependent variable across the different categories or levels of the independent variable. If these percentages vary significantly across the categories of the independent variable, then we can infer that there is a relationship between the two variables.

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Answer:

-1

Step-by-step explanation:

By combining the like terms from the given expression we get 2y-13

what is an algebraic expression ?

Algebraic expression can be defined as the combination of  constants , variables and operators.

Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.

Given ,

The expression ,

=y-9+y-4

=y+y-(9+4)

=2y-13

Hence , By combining the like terms from the given expression we get 2y-13.

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Answer:

x=5, y=41

Step-by-step explanation:

Because both equations are equal to Y, you can set them equal to each other like this:

8x+1=3x+26

From here, solve for x:

1. 5x+1=26

2. 5x=25

3. x=5

Once you have x, plug it back in to one of the original equations:

y=8(5)+1

y=41 and then you have your answer

If this answer was particularly helpful, please feel free to give it brainliest!! I would greatly appreciate it.

Answer:

(x, y) = (5, 41)

Step-by-step explanation:

y = 8x + 1

y = 3x + 26

Substituting the value of y (first equation) into the second equation, we get:

8x + 1 = 3x + 26

5x = 25

x = 5.

So, to get y, all we have to do is to substitute the value of x into the second equation.

y = 3 * 5 + 26

y = 15 + 26

y = 41

Answer:

1

Step-by-step explanation:

If you're given 3 side lengths and 3 measurements of the angles , there's only one triangle that you may draw. You also can draw distinctive  triangles given 3 aspect lengths or  aspect lengths and the blanketed distinctive measure.

Answer:

1

Step-by-step explanation:

if you are given 3 measurements you are kind of stuck making that one triangle, no matter which way you shape it you have to have those three angles so you can't make more than that one triangle

the answer is A,D,B,F

Step-by-step explanation:

I literally just took the quiz and got 90%

The true statements about this histogram are,

The histogram shows there were 22 students in the class.

The histogram is symmetrical.

The histogram has a peak.

The histogram shows the data is evenly distributed.

The frequency distribution of a collection of data reveals how frequently each unique value appears.

The most typical graph for displaying frequency distributions is a histogram. Although it closely resembles a bar chart, there are significant variances.

Given, A histogram titled Science Grades has grades on the x-axis and the number of students on the y-axis.

2 students received a score of 50 to 59;

5 students received a score of 60 to 69;

8 students received a score of 70 to 79;

5 students received a score of 80 to 89;

2 students received a score of 90 to 100.

∴ The statements that are true about this histogram are,

The histogram shows there were 22 students in the class as

(2 + 5 + 8 + 5 + 2) is 22.

The histogram is symmetrical as the order of students remains the same if we rotate it about the y-axis.

The histogram has a peak as 8 students received a score of 70 to 79.

The histogram shows the data is evenly distributed as this data is somehow bell-shaped.

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Answer:

15/10 and 21/14

Step-by-step explanation:

Simplify:

9/5 and 19/10

Simplified; not proportional.

Simplify:

4/6 and 10/16

2/3 and 5/8

Simplified; not proportional.

Simplify:

25/35 and 20/24

5/7 and 5/6

Simplified; not proportional.

Simplify:

15/10 and 21/14

3/2 and 3/2

Simplified; proportional.

The equation of the tangent to the curve at the point corresponding to t = 1, given by the parametric equations x = t - \(t^{(-1)}\) and y = \(3t^2\), is y = 6x + 9.

To find the equation of the tangent line, we need to determine the slope of the tangent at the point corresponding to t = 1. The slope of the tangent can be found by taking the derivative of y with respect to x, which can be expressed using the chain rule:

dy/dx = (dy/dt) / (dx/dt)

Let's calculate the derivatives:

dx/dt = 1 - (-1/\(t^2\)) = 1 + 1 = 2

dy/dt = 6t

Now, we can find the derivative dy/dx:

dy/dx = (dy/dt) / (dx/dt) = (6t) / 2 = 3t

Substituting t = 1 into the derivative, we get the slope of the tangent at the point:

dy/dx = 3(1) = 3

Next, we need to find the y-coordinate at t = 1. Substituting t = 1 into the equation y = \(3t^2\):

y = \(3(1)^2\) = 3

So, the point on the curve corresponding to t = 1 is (1, 3).

Using the slope-intercept form of a line (y = mx + b), where m is the slope, we can substitute the point (1, 3) and the slope 3 into the equation to solve for b:

3 = 3(1) + b

b = 0

Therefore, the equation of the tangent line is y = 3x + 0, which simplifies to y = 3x.

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The two stores at points A and C would serve the residents of Miniville, providing them access to essential goods and services, with residents in the middle mile having the flexibility to choose between the two stores.

If one store is located at point A and the other store is located at point C, it means that the stores are located at the extremes of the 3-mile stretch of Lake Shore Drive in Miniville. Point B would be the midpoint between points A and C.

Given that the 300 residents of Miniville are evenly distributed along the 3 miles of shoreline on the lake, it implies that there are approximately 100 residents per mile.

Therefore, the store located at point A would serve the residents living in the westernmost mile of Lake Shore Drive, while the store located at point C would serve the residents living in the easternmost mile of Lake Shore Drive.

The residents living in the middle mile, between points A and C, would have the option to shop at either store, depending on their preference or convenience.

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Answer:

first one is greater then or equal to and the second one is less then or equal to

Step-by-step explanation:

he wants to buy at least 8 bags of candy so it has to be 8 or more so greater then or equal to and the second one the most he wants to spend is $40 but think about you would want to spend less but would be ok with spending $40 so less then or equal to (at least that’s how I think) hope that helped

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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Answer:

6

Step-by-step explanation:

The height of the prism is 6 units if the volume of the prism is 234 cubic units, option second 6 units is correct.

It is defined as a three-dimensional space enclosed by an object or thing.

We have a volume of the prism is 234 cubic units.

Here some data are missing so we are assuming

a = 8 units

b = 5 units

h = 3 units

Area of two isosceles trapezoids = 2(8+5)(3/2) = 39 square unit

Area of  the hexagon = Area of two isosceles trapezoids

= 39 square units

Area of hexagon = 2× 19.5 = 39 unit square

Volume of the prism = base area×height

234 = 39h

h = 6 units

Thus, the height of the prism is 6 units if the volume of the prism is 234 cubic units.

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a) To solve the differential equation y" + 4y = -2 with initial conditions y(1/8) = 1/2 and y'(1/8) = 2 using the initial value problem (IVP) approach, we follow these steps:

Write the given differential equation in standard form: y" + 4y = -2.

Assume a particular solution of the form y_p(x) = Ax + B, where A and B are constants to be determined.

Calculate y_p' and y_p" and substitute them into the differential equation to find the values of A and B.

The general solution of the homogeneous equation y" + 4y = 0 is y_c(x) = c1cos(2x) + c2sin(2x), where c1 and c2 are arbitrary constants.

The general solution of the complete differential equation is y(x) = y_c(x) + y_p(x).

Apply the initial conditions y(1/8) = 1/2 and y'(1/8) = 2 to determine the values of c1 and c2.

Write the final solution with the determined values of c1 and c2.

b) To solve the differential equation 2y" + 3y' - 2y = 14x^2 - 4x - 11 with initial conditions y(0) = 0 and y'(0) = 0 using the initial value problem (IVP) approach, we follow these steps:

Write the given differential equation in standard form: 2y" + 3y' - 2y = 14x^2 - 4x - 11.

Assume a particular solution of the form y_p(x) = Ax^2 + Bx + C, where A, B, and C are constants to be determined.

Calculate y_p' and y_p" and substitute them into the differential equation to find the values of A, B, and C.

The general solution of the homogeneous equation 2y" + 3y' - 2y = 0 is y_c(x) = c1e^(x/2) + c2e^(-2x), where c1 and c2 are arbitrary constants.

The general solution of the complete differential equation is y(x) = y_c(x) + y_p(x).

Apply the initial conditions y(0) = 0 and y'(0) = 0 to determine the values of c1 and c2.

Write the final solution with the determined values of c1 and c2.

Note: The solution steps provided are general guidelines for solving differential equations using the IVP approach. The specific calculations and algebraic manipulations required may vary based on the complexity of the equations.

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The function file 'mysolve.m' takes two inputs a and b, calculates the area of the right triangle using the given formula A = 0.5 * a * h and returns the area as output.

To calculate the area of a right triangle, we use the formula A = 0.5 * base * height or A = 0.5 * a * b where a is the length of the leg and b is the length of the hypotenuse.

The function file 'mysolve.m' to calculate the area of the right triangle is given below:

function [area] = mysolve(a,b)h = sqrt(b^2-a^2);area = 0.5*a*h;end

Explanation: The given function takes two input parameters a and b which are the length of the leg and hypotenuse respectively. We first calculate the height h of the triangle using the Pythagorean theorem which is h = sqrt(b^2-a^2). We then use the formula A = 0.5 * base * height to calculate the area of the right triangle where base is a and height is h. Finally, we return the calculated area as output from the function file 'mysolve.m'.

Conclusion: Thus, the function file 'mysolve.m' takes two inputs a and b, calculates the area of the right triangle using the given formula A = 0.5 * a * h and returns the area as output.

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Answer: 2 c squared d + d c + 6 c squared d squared

Step-by-step explanation:   I looked it up

J is 83 degrees

M and L are both 97 degrees I believe

I hope this helps you ^-^

Answer:

\(\angle j=83^{o}\)

\(\angle m=97^{o}\)

\(\angle l= 97^{o}\)

Step-by-step explanation:

\(\angle j=\angle k\)

\(\angle j=83^{o}\)

---------

\(\angle m=180-83\)

\(\angle m=97^{o}\)

--------

\(\angle l=\angle m\)

\(\angle l= 97^{o}\)

Hope this helps!

Answer:

C

Step-by-step explanation:

One clockwise rotation of 90 degrees would transform figure A to figure B, but that is the same thing as a counterclockwise rotation of 270.

(360 - 90 = 270)