A car uses 8 gallons of gasoline to travel 290 miles. Juanita wants to take a trip that is 400 miles. What equation will she need to use to find out how much gas the trip will use?

The expression for the nth term will be 8.2 - 5.8n. Then the correct option is C.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The first five terms in a pattern of numbers are shown. 2.4, -3.4, -9.2, -15, -20.8. Then the equation is given as,

At x = 1, y is 2.4.

2.4 = m + c           ...1

At x = 2, y is -3.4.

-3.4 = 2m + c          ...2

From equations 1 and 2, then we have

m = -3.4 - 2.4

m = - 5.8

Then the value of 'c' is given s,

2.4 = -5.8 + c

c = 8.2

Then the equation is given as,

y = 8.2 - 5.8x

If the pattern continues. Then the expression for the nth term is given as,

y = 8.2 - 5.8n

The expression for the nth term will be 8.2 - 5.8n. Then the correct option is C.

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The missing options are given below.

A   5.8 - 3n

B   -3 - 5.8

C   8.2 - 5.8n

D   5.8 - 8.2n​

The radius of the circle = r = 4 cm.The length of the segment = a = 3.2 cm.The length of the chord = s = 4.7 cm.We need to find the probability that a randomly selected point within the circle falls in the red shaded area.The red shaded area is a segment of the circle.

Let O be the centre of the circle. Join OA and OB.Let the chord AB cut the circle at C. Join OC. Now, ΔOCA and ΔOCB are congruent (RHS congruence) becauseOA = OB (radii of the same circle)AC = BC (length of the chord)OC = OC (common side)Therefore, ∠OCA = ∠OCB = θ (say)Also, ∠OAC = ∠OBC (vertically opposite angles)Now, ∠OCA + ∠OAC = 90° (angle sum property of the triangle) ⇒ θ + ∠OAC = 90°and ∠OCB + ∠OBC = 90° (angle sum property of the triangle) ⇒ θ + ∠OBC = 90°Adding the above two equations, we get,2θ + ∠OAC + ∠OBC = 180°2θ + ∠AOB = 180° (angles in a straight line)θ = (180° - ∠AOB) / 2

Therefore, θ = (180° - ∠AOB) / 2= (180° - 60°) / 2= 60° / 2= 30°Using the formula for the area of the segment of the circle, we have,Area of the segment = (1/2)rsinθArea of the segment = (1/2)×4×7.56×(sin30°)Area of the segment = 6.28 cm2Now, the area of the circle is πr2 = π×42 = 16π cm2.So, the probability that a randomly selected point within the circle falls in the red shaded area is given by the ratio of the area of the segment to the area of the circle.P(red shaded area) = Area of the segment/Area of the circleP(red shaded area) = 6.28/(16π)P(red shaded area) = 0.125 or 12.5%Therefore, the required probability is 12.5%.Hence, the answer is 12.5%.

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The total weight of the 14 packages that Melissa weighed is gotten as; Total weight = 42 pounds

We are given;

Mean weight = 3

Now,formula for mean is;

Mean = total/sample size

We are given;

Sample size = 14

Thus;

3 = total/14

Total = 3 * 14

Total weight = 42 pounds

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The statement describes the incidence measure of occurrence, which refers to the number of new cases of a disease or condition that occur in a defined population over a specific period of time.

This statement describes the incidence rate of flu among students living in Dunedin hostels.
The incidence rate is a measure of occurrence that calculates the number of new cases (in this case, students getting sick with the flu) in a specific population (150 students in Dunedin hostels) over a specific time period (3 months). This rate helps us understand the frequency at which the flu is affecting this particular group of students

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To find the distance Jerimiah walked, we need to determine the perimeter of the rectangular path. Since each unit on the grid represents 1 city block, we can count the number of units in each side of the rectangle.

Let's assume the sides of the rectangle are a and b. If Jerimiah walks twice around the path, he walks along each side twice. Therefore, the perimeter of the rectangle is given by the equation:

Perimeter = 2a + 2b

Since we know that each unit on the grid represents 1 city block, we can count the number of units in each side of the rectangle and substitute the values into the equation.

Once we calculate the perimeter, we will have the total distance Jerimiah walked.

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By finding the lengths of the sides of the rectangular path connecting the four locations on the coordinate grid, we can determine the total distance Jerimiah walks. Each side is multiplied by 2 to account for Jerimiah walking twice around the path.

The rectangular path connecting the four locations can be visualized on the coordinate grid. Since each unit on the grid represents one city block, we can determine the distance Jerimiah walks by finding the perimeter of the rectangular path.

To calculate the perimeter, we need to find the lengths of the sides of the rectangle. We can determine these lengths by finding the differences in the x-coordinates and the y-coordinates of the locations.

Let's assume the four locations are labeled A, B, C, and D. If the x-coordinates of A and B are the same, and the x-coordinates of C and D are the same, we can find the length of the longer side of the rectangle by subtracting the x-coordinate of A from the x-coordinate of C.

Similarly, we can find the length of the shorter side of the rectangle by subtracting the y-coordinate of A from the y-coordinate of B.

Once we have the lengths of the sides, we can multiply them by 2 (since Jerimiah walks twice around the path) and add them together to find the total distance Jerimiah walks.

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Answer:

28.3 units^2

Explanation:

The area A of the circle is given by the formula

where

π = 3.1415..

d = diameter of the circle.

Now, in our case d = 6; therefore,

Rounded to the nearest tenth this is

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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We can write an equation to resemble the problem.

59n = 113

~Divide 59 to both sides

n ≈ 1.92

Best of Luck!

Answer:

59 * 1.92 = 113.28

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine the number of defective computer chips likely to be in a batch of 507 chips, we can use the experimental probability of manufacturing a defective chip.

The experimental probability is given as 5 out of 13 chips, which means that in a sample of 13 chips, on average, 5 of them are defective.

To find the expected number of defective chips in a batch of 507 chips, we can set up a proportion:

5/13 = x/507

Cross-multiplying:

13x = 5 * 507

Simplifying:

13x = 2535

Dividing both sides by 13:

x ≈ 195

Therefore, based on the experimental probability, it is likely that there will be approximately 195 defective computer chips in a batch of 507 chips.

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Answer:

how many up and to the side. thats kinda slope

Step-by-step explanation:

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

85, 91, 83, 78, 79, 64, 81, 97

Ordered data : 78, 79, 81, 83, 85, 91, 97

Mean:

Σx / n =

n = sample size = 8

(64+78+79+81+83+85+91+97) / 8

= 658 / 8

= 82.25

Median = 1/2(n+1)th term

1/2(8+1)th term = 1/2 * 9 = 4.5th term

(4th term + 5th term) /2 = (81 + 83) / 2 = 82

Mode = 85, 91, 83, 78, 79, 64, 81, 97

Outlier:

Lower = Q1 - 1.5(IQR)

Upper = Q3 + 1.5(IQR)

Using a calculator :

Q1 = 78.5 ; Q3 = 88 ;

IQR = (Q3 - Q1)

(88 - 78.5) = 9.5

Outlier :

78.5 - 1.5(9.5) = values < 64.25

88 + 1.5(9.5) = values > 102.5

Hence. Outlier is 64

Removing the Outlier :

Data = 78, 79, 81, 83, 85, 91, 97

Mean = 84.85

Median = 83

Based on the result, the median is the best measure of central tendency for the data:

Answer:

x=9

Step-by-step explanation−4(2x−1)=−6(x+2)−2

(−4)(2x)+(−4)(−1)=(−6)(x)+(−6)(2)+−2(Distribute)

−8x+4=−6x+−12+−2

−8x+4=(−6x)+(−12+−2)(Combine Like Terms)

−8x+4=−6x+−14

−8x+4=−6x−14

Step 2: Add 6x to both sides.

−8x+4+6x=−6x−14+6x

−2x+4=−14

Step 3: Subtract 4 from both sides.

−2x+4−4=−14−4

−2x=−18

Step 4: Divide both sides by -2.

−2x

−2

=

−18

−2

x=9

Answer:

2

Step-by-step explanation:

This is our equation-

-4(2x-1)=-6(x+2)

We are trying to isolate x in a side, but first, we must multiply the numbers in between the brackets. A negative number multiplied by a positive number gives a negative number, and a negative times a negative is positive, so-

-8x·4=-6x+(-12)

Now we have to multiply -8x times 4

-32x=-6x-12

Now we isolate x-

-24x=-12

We divide and get the final result of x=2

x=2

The measure of length of SU is 18.7

Since a tangent to a circle makes a 90º angle to the origin, we can trace radius, and state that this is 13 units long. Therefore we have here two congruent triangles.

Given that OT=8 and OS=17,

We need to find SU.

To write a property that relates a tangent and a secant from one point

So, ST = SU

SU^2 = GF^2 + OG^2

SU^2 = 8^2 + 17^2

SU^2 = 289+ 64

SU^2 = 353

SU= 18.7

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The whole statement says that "for all people x and y who are not Ralph, x trusts y".

Let F(x, y) be the statement x trusts y, where the domain of discourse for both x and y is all people, nobody trusts Ralph.

The logic symbolization of the given statement is:

∀x ∀y [(x ≠ Ralph ∧ y ≠ Ralph ∧ x ≠ y) → F(x, y)]

Here, the universal quantifier ∀ means "for all".

So, ∀x means "for all people x" and ∀y means "for all people y".

The symbol → means "implies" or "if-then".

The statement (x ≠ Ralph ∧ y ≠ Ralph ∧ x ≠ y) means "x is not Ralph, y is not Ralph, and x is not equal to y".

So, the whole statement says that "for all people x and y who are not Ralph, x trusts y".

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\(\frac{325}{520}\) fraction of the workforce kept their jobs

What is the Percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

What is Percentage change?

The percentage increase is calculated by subtracting the original number from the new number, dividing that result by the original number, and multiplying that result by 100.

where growth in number equals new number minus initial number.

Similar to how a percentage increase is calculated, a percentage reduction is calculated by subtracting a new number from the original number, dividing that new number by the original number, and multiplying that result by 100.

decreasing number where original number - new number

In other words, there is a percentage decline if the response is negative.

Here, It is given:

In January 520 workers were employed;

In the end, 195 employees were redundant;

So, The fraction of the workforce who kept their job:-

The fraction of the workforce who kept their job=\(\frac{520-195}{520}\)

The fraction of the workforce who kept their job=\(\frac{325}{520}\)

Hence,

The fraction of the workforce who kept their job=\(\frac{325}{520}\)

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Answer:

4

4in

Step-by-step explanation:

what grade lvl is this???

Have a nice day! :-)

Answer:

10950 feet

Step-by-step explanation:

1 mile is 5280 feet

5280*2=10560

10560+390=10950

:)

Answer:

Your answer would be 10950!

Step-by-step explanation:

Answer: Just Try to Do somthing because i cant tell you the Answer

Step-by-step explanation:

The percentage of the students are between 62 and 69 inches tall is 46.0%

From the question, we have the following parameters that can be used in our computation:

Mean = 69

Standard deviation = 4

Scores = between 62 and 69

So, the z-scores are

z = (62 - 69)/4 = -1,75

z = (69 - 69)/4 = 0

i.e. between a z-score of -1.75 and a z-score of 0

This is represented as

Probability = (-1.75 < z < 0)

Using a graphing calculator, we have

Probability =  0.45994

Approximate

Probability =  46.0%

Hence, the probability is 46.0%

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a) Two equivalent expressions to model the purchase made by Mrs. Singh, who bought 9 folders and 9 notebooks at the cost of each folder $2.50 and each notebook $4.00 respectively, are:

b) The total cost of the purchase by Mrs. Singh is $58.50.

Algebraic expressions involve the combination of variables, numbers, constants, and values using mathematical operands (addition, subtraction, division, and multiplication).

The unit cost of folders = $2.50

The unit cost of notebooks = $4.00

The number of folders bought = 9

The number of notebooks bought = 9

Let the number of folders bought = x

Let the number of notebooks bought = y

Folders: 2.50x

Notebooks: 4.00y

Folders: 2.50x = $22.50 ($2.50 x 9)

Notebooks: 4.00y = $36.00 ($4 x 9)

Total costs = $58.50

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It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).

In the given question, we have to check that it is possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 2 and 3

2 + 3 < 7

5 > 7

Now we add 2 and 7

2 + 7 > 3

9 > 3

Now we add 3 and 7

7 + 3 > 2

10 > 2

It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).

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Answer:

x = 49°

Step-by-step explanation:

Angles in a Triangle

The sum of the internal angles in any triangle adds up to 180°.

The figure shows a triangle that includes two angles with the same tick mark. This means they are congruent, i.e. they measure the same.

The larger triangle has three defined angles: 43°, 39°, and 2x. Since the sum of them is 180°:

43° + 39° + 2x = 180°

Operating:

82° + 2x = 180°

Subtracting 82°:

2x = 180° - 82° = 98°

x = 98°/2 = 49°

x = 49°

Answer:

F^-1 (x) = 3x/2+5/4

Step-by-step explanation:

First, replace f(x) with y

Replace every x with a y and replace every y with an x .

Solve the equation from Step 2 for y  

Replace y with f−1(x) f − 1 ( x )

Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.

Hope this helps!  Stay Safe!

Answer:

2

Step-by-step explanation:

If we know the old and new values of the qualities and the optimal bundle, the price elasticities of demand for each of the commodities in the bundle could be calculated.

Formula for calculating price elasticity of demand is as follows:

Price elasticity of demand = \(\frac{Percentage change in quantity demanded}{Percentage change in quantity demanded}\). i.e.,

Price elasticity of demand = % change in quantity demanded/ % change in price

Price elasticity of demand for items in a bundle is important because it allows businesses and policymakers to understand how price changes affect the quantity wanted of each thing, which may then inform pricing and policy decisions. Demand elasticity is the degree to which demand changes in response to changes in other economic variables such as price, financial position, and the accessibility of alternatives.

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Answer:

-19

Step-by-step explanation:

Input -6 for n and solve: 3(-6)-1

Answer:

-19

Step-by-step explanation:

3 (-6) - 1 = -19

Answer:

18+\(6\sqrt{5}\)

Step-by-step explanation:

Since the helicopter flies east for six miles and north for 12 miles, it flies 18 miles. Then on the way back, it flies an unknown amount of miles. the path the helicopter takes is in the form of a triangle, and the path back is the hypotenuse of the triangle. To find the hypotenuse, we can do \(a^2+b^2=c^2\), where c is the hypotenuse. We do

\(6^2+12^2=c^2\\36+144=c^2\\180=c^2\\\sqrt{180}=c\\ 6\sqrt{5}=c\)Therefore, the total distance flown by the helicopter is 18+\(6\sqrt{5}\).