Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. irenes car had 5.7 gallons in the 14-gallon tank on the coldest day of the year irene filled the tank with gas that cost ​ ​$3.80 per gallon. How much did irene spend on​ gas?

Considering that y is between x and z, we have that:

We consider that y is between x and z, hence the length of the segment is given by:

xz = xy + yz

The separate lengths are given as follows:

Hence:

4k + 38 = 3k - 2 + 7k + 4.

4k + 38 = 10k + 2

6k = 36

k = 6.

Hence the length of yz is given by:

yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.

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Option D, which states that all of the above factors would increase the width of a confidence interval for a population mean, is correct.

A confidence interval is a range of values within which we estimate the population parameter, such as the population mean. The width of a confidence interval is influenced by several factors.
First, increasing the level of confidence (option A) leads to a wider interval. A higher confidence level requires a larger range of values to capture the population parameter with a higher degree of certainty.
Second, increasing the sample size (option B) generally results in a narrower interval. With a larger sample size, we have more information about the population, leading to a more precise estimate of the mean.
Third, decreasing the sample standard deviation (option C) also leads to a narrower interval. A smaller standard deviation indicates less variability in the data, resulting in a more precise estimate of the mean.
Therefore, when all of these factors are considered together (option D), it is clear that increasing the level of confidence, increasing the sample size, and decreasing the sample standard deviation would all contribute to an increase in the width of a confidence interval for a population mean.

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The  examples that would constitute a discrete random variable are;

I. Total number of points scored in a football game

III. Number of near collisions of aircraft in a year

A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.

A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.

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If she receives $2 off the regular price, p. by using a coupon. her total cost, including 20% for tax and tip, is $9. then the regular price of the lunch special is $11.

Let's figure out why that is so. Romita gets a sushi lunch special at Yoshi's, with a coupon. Romita received a discount of $2 off the regular price, P.

         Let's assume that the price of lunch before the discount is $P.

 Therefore, after the discount, the cost of the lunch is (P - 2).

 Now, let's determine the total cost of the lunch. The price of the lunch is inclusive of 20% tax and tip. This implies that Romita's total cost is 120% of the final cost of the lunch.

    We can represent this information in the equation below:

             Total cost = 120% of (P - 2)

             Total cost = 1.2(P - 2)

    From the given information, we know that the total cost is $9.

    This means we can solve the equation for P.P = (9/1.2) + 2P = 7.5 + 2P = $11

         The regular price of the lunch special is $11.

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When a transversal cuts two parallel lines, 8 angles are created.

When two lines do not cross one another, they are said to be parallel. In addition, parallel lines are two lines that cross each other at infinity.

A transversal line is one that crosses two other lines at two different locations. Line l meets a and b in the image below at two different locations, P and Q. Line l is the transversal line as a result.

Corresponding angles are those that are created when two parallel lines and a transversal intersect, also known as matching corners or corresponding corners.

∠1 and ∠6

∠4 and ∠8

∠2 and ∠5

∠3 and ∠7

When a transversal connects two coplanar lines, alternate interior angles are created.

∠4 and ∠5

∠3 and ∠6

However, each pair of alternate interior angles is equal if a transversal meets two parallel lines.

∠4 = ∠5

∠3 = ∠6

The pair of angles that are created on the outer side of two lines but on the other side of the transversal are known as alternate exterior angles.

Consecutive interior angles, related angles, and co-interior angles are other names for interior angles that are on the same side of the transversal.

∠3 and ∠5

∠4 and ∠6

When a transversal cuts two parallel lines, 8 angles are created.

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∠1 and ∠6

∠4 and ∠8

∠2 and ∠5

∠3 and ∠7

When a transversal connects two coplanar lines, alternate interior angles are created.

∠4 and ∠5

∠3 and ∠6

However, each pair of alternate interior angles is equal if a transversal meets two parallel lines.

∠4 = ∠5

∠3 = ∠6

Consecutive interior angles, related angles, and co-interior angles are other names for interior angles that are on the same side of the transversal.

∠3 and ∠5

∠4 and ∠6

The value of the given expression will be 3√5.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression c² = 45 will be solved as below:-

c² = 45

Take the square root of the number 45.

c = √45

c = √ 9 x √5

c = 3√5

Therefore, the value of the given expression will be 3√5.

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Answer:

\(\boxed{y=-\frac{1}{2}x+2}\)

Step-by-step explanation:

\(2x+4y=8\\\\2x-2x+4y=8-2x\\\\4y=8-2x\\\\\frac{4y=8-2x}{4}\\\\y=2-\frac{2}{4}x\\\\ y=2-\frac{1}{2}x\\\\\boxed{y=-\frac{1}{2}x+2}\)

Hope this helps.

Answer:

y=4-x/2

Step-by-step explanation:

We are given with an equation and need to find it's solution set also we are given with a condition that m ≠ {0, 1} . So , let's start ;

So we are given with :

\({:\implies \quad \sf \dfrac{6}{m}+2=\dfrac{m+3}{m-1}}\)

First , we will simplify the given Equation and then we will solve it . So , now taking LCM in LHS ;

\({:\implies \quad \sf \dfrac{6+2m}{m}=\dfrac{m+3}{m-1}}\)

Now , Cross Multiplying ;

\({:\implies \quad \sf (m-1)(6+2m)=m(m+3)}\)

\({:\implies \quad \sf m(6+2m)-1(6+2m)=m^{2}+3m}\)

\({:\implies \quad \sf 6m+2m^{2}-6-2m=m^{2}+3m}\)

Now , transposing whole RHS to LHS and collecting like terms ;

\({:\implies \quad \sf (2m^{2}-m^{2})+(6m-2m-3m)-6=0}\)

\({:\implies \quad \sf m^{2}+m-6=0}\)

Now , we will solve this by splitting the Middle term ;

\({:\implies \quad \sf m^{2}+3m-2m-6=0}\)

\({:\implies \quad \sf m(m+3)-2(m+3)=0}\)

\({:\implies \quad \sf (m+3)(m-2)=0}\)

So , now either , m+3 = 0 or m-2 = 0 . On simplification we will get , m = 2 , -3. So m = {-3, 2}

Hence Option 1) {-3, 2} is correct

An equation to model the situation: h = 30000 - 2000t

the altitude of the plane after 5 minutes is  20000 feet

In this question, an airplane 30,000 feet above the ground.

It begins descending at a rate of 2,000 feet per minute.

We need to write an equation to model the situation. Also, we need to find

the altitude of the plane after 5 minutes.

Let h be the altitude of plane after t hours.

So, we get an equation,

h = 30000 - 2000t

For t = 5 minutes,

h = 30000 - 2000(5)

h = 30000 - 10000

h = 20000 feet

Therefore, an equation to model the situation: h = 30000 - 2000t

the altitude of the plane after 5 minutes is  20000 feet

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Answer:show ur homework page I have the same one I think

Step-by-step explanation:

\( \sf \dashrightarrow(x - 4) {}^{2} \)

\( \\ \\ \)

\( \sf \dashrightarrow {x}^{2} + {4}^{2} + 2 \times 4 \times x\)

\( \\ \\ \)

\( \sf \dashrightarrow {x}^{2} + 16 + 8x\)

Bob continues his research because even though there is no linear equation relationship between the number of bedrooms and selling price, there could be another type of relationship.

Bob continues his research because even though the correlation value he calculated between the number of bedrooms and the selling price was only 0.05, this does not necessarily mean that there is no relationship of any kind between these two variables. It simply means that there is no linear relationship between the two. There could still be other types of relationships between the two variables, such as an exponential or quadratic relationship. It is possible that further analysis and exploration of the data set would reveal such a relationship and allow Bob to uncover the relationship between the two variables. Additionally, even if the correlation value is low, it does not necessarily mean that there is no relationship between the two variables. It simply means that the relationship is weak. Therefore, Bob should continue his research in order to uncover any potential relationships between the number of bedrooms and selling price.

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The point on the graph where the tangent plane is parallel is (52, 52, -5382).

What is the tangent plane?

The surface that contains all tangent lines of the curve at a point, $P$, that lies on the surface and passes through the point is represented by the tangent plane. We discovered earlier in our talks of derivatives and tangent lines that we can use tangent lines to mimic the behavior of a graph. We may employ tangent planes for a similar reason now that we're working with multivariable functions and three-dimensional coordinate systems.

Here, we have

Given: Let P be the tangent plane to the graph of g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286). Let f(x, y) = 26 – x² - y².

We have to find the point on the graph where the tangent plane is parallel.

Let P be the tangent plane to the graph z = g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286).

φ(x,y,z) = 13x² + 26y² + z - 26

Δφ = 26xi + 52yj + k

Δφ(4, 2, –286) = 104i + 104j + k

Then,

P: 104(x-4) + 104(y-2)+1(z+286) = 0

104x + 104y + z = 338...(1)

Now, Let

ψ(x,y,z) =  x² + y² + z - 26

Δψ = 2xi + 2yj + k

Let (x₀,y₀,z₀) be the point of the graph z = f(x,y) = 26 – x² - y² where the tangent plane in the plane is parallel to equation (1).

Δψ (x₀,y₀,z₀)  =  (2x₀,2y₀,1)

= 2x₀/104 = 2y₀/104 = 1/1

x₀ = 52 = y₀

Now, z₀ = 26 – x₀² - y₀² = 26 – 52² - 52²= -5382

Hence,  the point on the graph where the tangent plane is parallel is (52, 52, -5382).

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Answer:

1) 3*10^9

2) 6*10^-10

Step-by-step explanation:

To find scientific notation, it's a number between one and ten, times ten to the power of as many zeroes as needed.

Answer:

Step-by-step explanation:

800 J/kgC

What is the specific heat of a material that gains 600 joules of energy when a 0.25 kg object increases in temperature by 3C?

it is 800 J/kgC

average inflation rate of cold drink will be 100%

Inflation is the term used to describe an increase in the price of goods and services that households buy. It is determined by how quickly these prices fluctuate. Prices frequently rise with time, but they can also fall (a situation called deflation).

You will subtract the starting price (A) from the later price (B), and divide it by the starting date (A). Then multiply the result by 100 to get the inflation rate percentage.

FORMULA FOR FINDING AVERAGE INFLATION = ((B-A)/A)*100

            plugging in the values =

∵ given in the question that cost will double in the next 8 years i.e.

                                                                             = Rs. 4.50 * 2

                                                                             = Rs.9.00

∴ when we plug in  the values in the formula we get

                                                 = ((9-4.5)/4.5) * 100

                                                 = 100 % inflation rate

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After 9 years, the amount in Account A is approximately $12,742.16, the amount in Account B is approximately $12,813.51, and the difference in interest earned between Account B and Account A is approximately $71.35.

To calculate the amount in each account after 9 years, we'll use the following formulas:

For Account A (simple interest):

Amount_A = Principal_A * (1 + interest_rate_A * time)

For Account B (compounded interest):

Amount_B = Principal_B * (1 + interest_rate_B/12)* (12 * time)

Given the following values:

Principal_A = $7,617.52

Principal_B = $7,617.52

Interest rate_A = 6.956% = 0.06956

Interest rate_B = 6.956% = 0.06956

Time = 9 years

Calculating the amounts in each account:

Amount_A = $7,617.52 * (1 + 0.06956 * 9)

Amount_B = $7,617.52 * (1 + 0.06956/12)\(^{(12 * 9)\)

Amount_A ≈ $12,742.16

Amount_B ≈ $12,813.51

To calculate the difference in interest earned between Account B and Account A, we subtract the initial principal from each account's total amount and round the result to two decimal places:

Interest_difference = Amount_B - Amount_A

Interest_difference ≈ $12,813.51 - $12,742.16

≈ $71.35

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

The focus (or foci).

Step-by-step explanation:

The focus of a hyperbola are equidistant from the center of the hyperbola. They can be found with the formula c²= a² + b². The points for the foci being

(-c, y) and (c, y).

In this illustration, the foci are the points in blue.

The bearing between Point A (N 1147.8000 E 710.4700) and Point B (N 1489.1700 E 138.5700) is computed as ON 30°49'59"W.

To compute the bearing between Point A and Point B, we need to determine the directions from Point A to Point B. The coordinates for Point A are N 1147.8000 E 710.4700, while the coordinates for Point B are N 1489.1700 E 138.5700. The bearing is given as ON 30°49'59"W, which means the direction from Point A to Point B is approximately 30 degrees, 49 minutes, and 59 seconds west of north. This indicates the angle between the north direction and the line connecting Point A and Point B.

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Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

Answer:

216 m³

Step-by-step explanation:

let's calculate the area of the front face and then multiply it by 4m

11*3 + (11-4)*3

(left and right triangle equal a rectangle area here)

= 33 + 21

= 54

multiplied by 4

-> 216

the last step is like multiplying with height in other exercises and other bodies

pls brainliest

Answer:

A) ±\(6\sqrt{2}\)

Step-by-step explanation:

Formula for the Slope: (y2 - y1) / (x2 - x1)

You can use any two points to find the slope, as long as those two points are on the line.

Point 1 = (-2, 8)

Point 2 = (0, 0)

Slope = (0 - 8) / (0 - - 2)

Slope = -8 / 2

Slope = -4

Hope this helps!

Answer:

-4

Step-by-step explanation:

The formula to find the slope is (change in y)/(change in x). In other words, rise over run.

If we look at the data, we can see that the x and y value changes.

x value: -3 --> -2 --> -1 --> 0 --> 1

y value: 12 --> 8 --> 4 --> 0 --> -4

When y changed from 12 to 8, the x changed from -3 to -2.

y: 12 --> 8

x: -3 --> -2

There was a difference of -4 in the y and a difference of 1 in the x.

At the top, I wrote that the slope was (change in y)/(change in x)

With -4 and 1 we found, we can say that the slope is -4/1.

If we simplify this answer, we end up with -4.

So -4 is the slope of the data.

Answer:

3 9/40 is the answer The decimal form of that is 3.225

Step-by-step explanation:

Explanation is on image, using calculator.

Answer:

it is 3 9/40 or 129/40

Step-by-step explanation:

hope that helps

An equation of the form \(x^2 + bx + c = 0\) that has the solutions x = -4 and x = 6 can be obtained by expanding the equation (x - (-4))(x - 6) = 0. This simplifies to \(x^2 - 2x - 24 = 0.\)

To find an equation of the form \(x^2 + bx + c = 0\) with the given solutions x = -4 and x = 6, we can start by using the fact that the product of the roots of a quadratic equation is equal to the constant term divided by the coefficient of \(x^2\). In this case, the product of the roots is (-4) * 6 = -24.

We can then write the equation as (x - r1)(x - r2) = 0, where r1 and r2 are the roots. Substituting the given values, we have (x - (-4))(x - 6) = 0. Expanding this equation gives \(x^2 - 2x - 24 = 0.\)

Therefore, the equation\(x^2 - 2x - 24 = 0\) has the solutions x = -4 and x = 6. This equation satisfies the form \(x^2 + bx + c = 0\), where b = -2 and c = -24. By rearranging the terms, we can easily identify the coefficients b and c in the equation.

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Answer:

x-3

Step-by-step explanation:

f(x) = 3x - 2

g(x) = 2x + 1,

(f- g)(x) =  3x - 2  - ( 2x+1)

Distribute

            = 3x -2 -2x-1

Combine like terms

             x-3

The difference between a bar graph and a histogram is that of  b. a bar graph displays categorical data, while a histogram displays quantitative data.

A bar graph is majorly used to compare different categories or groups of data. It displays data in separate bars, each representing a different category. A histogram, on the other hand, is used to display the distribution of a continuous quantitative variable. It shows the frequency of different values within a range of values by using bars of different heights. The bars in a histogram are also adjacent to each other, with no space between them.

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The equation that can be used to find x, the number of yards that Aj walks and runs each week is 2x = 400 + 90.

Let's assume that Aj runs x yards each week. Then, the number of yards that Aj walks each week would be (x + 90) yards, since he walks 90 more yards than he runs.

The total distance that Aj covers each week would be the sum of the distance that he runs and the distance that he walks, which is given as 400 yards.

So, we can write an equation as:

Distance covered by Aj = Distance that he runs + Distance that he walks

or,

Simplifying this equation gives:

Therefore, the equation that can be used to find x, the number of yards that Aj walks and runs each week is 2x = 400 + 90.

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