A gas station employee monitored gas sales one day. The data showed that 80% of customers purchased regular gas. Of the customers who purchased regular gas, 10% pald in cash, whereas 20% of the customers who did not purchase regular gas paid in cash. What percentage of the customers paid in cash? O30% O 28% O 14% O 12%​

B. Row reduce the augmented matrix [A e3], where ez is the third column of 13.

The augmented matrix would be:

[ 2  5 | 0 ]
[ 7  3 | 0 ]
[ 1  2 | 1 ]

Then, perform row operations to transform the left side of the matrix into the identity matrix:

[ 1  0 | ? ]
[ 0  1 | ? ]
[ 0  0 | 1 ]

The third column of the resulting matrix will be the third column of A-1:

[ ? ]
[ ? ]
[ 1 ]

Therefore, the third column of A-1 is:

[ -0.4 ]
[  0.2 ]
[  1   ]
To find the third column of A^-1 without computing the other columns, you can use option B. Row reduce the augmented matrix [A|e3], where e3 is the third column of I3 (the 3x3 identity matrix).

First, construct the augmented matrix [A|e3] with A given as:

A = | 2 5 7 |
   | 3 1 2 |

and e3 from the 3x3 identity matrix I3:

e3 = | 0 |
     | 0 |
     | 1 |

Then, perform row reduction on the augmented matrix [A|e3] to obtain the third column of A^-1.

Visit here to learn more about matrix  : https://brainly.com/question/28180105
#SPJ11

Answer:

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

Step-by-step explanation:

Based on the line of best fit being y = −2x − 2, the residual value when x = -2 is -2.

The residual value is found as:
= Actual y - Predicted y

The actual y is shown to be 0 when x = -2.

The predicted value is:

= -2 x (-2) - 2

= 2

Residual value is:

= 0 - 2

= -2

Find out more on residual value at https://brainly.com/question/2732774.

#SPJ2

Answer:

A.) -2

Step-by-step explanation:

got it right on edge 2022

Answer:

The answer is y= -2

Step-by-step explanation:

(Arrange according to the like terms first)

5y-y+42= 34

4y+ 42-34= 0

4y+ 8= 0

4y= -8

∴ y= -8/4=-2

So, y= -2

Hope it will help.

Answer:

y = -2

Step-by-step explanation:

question : 5y + 42 − y = 34

⇒ 5y + 42 − y = 34

•shifting the +42 to the right side :

⇒ 5y - y = 34 - 42

⇒ 4y = -8

•shifting the 4 to the right side :

⇒ y = -8/4

⇒ y = -2 Answer...

hope that helps...

Step-by-step explanation:

37)3511(94

333

________

181

148

________

23

If your question is 37/3511

Then it would remain same ≈ 0.010

Answer:

5600 dollars

Step-by-step explanation:

The first thing we must do is calculate the area of the rectangle since the value is given per unit area.

They give it per square centimeter, therefore we must pass the measurements from meters to centimeters, knowing that 1 meter is 100 centimeters:

4m * 100cm / 1m = 400cm

5m * 100cm / 1m = 500cm

Now the area would be:

A = 400 * 500 = 20000

20000 cm ^ 2 would be the area of the rectangular wall, we calculate the value like this:

20000 * 0.28 = 5600

In other words, it has a value of 5600 dollars.

Three types of rigid transformations are Reflection, Rotation, and Translation. Rigid transformation, also called isometry.

A rigid transformation, also called isometry,  is a transformation that doesn't change the size or shape of a geometric figure. The following are 3 types of rigid transformation:

1. Reflection

→  is the act of shifting an object's coordinates that flip it across a line without changing its shape or size. Horizontal (draw a figure to the left or right) or vertical (draw a figure to the up or down) reflections are possible. The result of reflection is a mirror image of the figure itself.  

The figure is reflected across \(x-\) or \(y-\) axis, and then change \(x-\) or \(y-\) coordinate.

2. Rotation

→ is the non-modification of an object's size or shape by rotating it around an fixed point. A center of rotation is required to rotate an object. And the rotation did by using a degree.

The figure is rotated by a degree (ex: 90°), and then change \(x-\) or \(y-\) coordinate. Meanwhile, a point's center rotation stays at the same.

3. Translation

→ is sliding a figure in any direction without changing its size, shape, or orientation. Translation could be horizontal (make a figure left or right),  or vertical reflections (make a figure up or down).

Vertical translation is shifting the graph along  \(y-\) axis

Horizontal translation is shifting the graph along  \(x-\) axis.

Here to learn more about Rigid Transformation:

https://brainly.com/question/1462871

#SPJ4

A. By the given conditions, the function f has a root in the interval [a, b].

B. The given conditions provide information about the function f and its derivatives.

Let's analyze the conditions step by step:

1. f(a) < 0 and f(b) > 0: This implies that function f takes negative values at the left endpoint a and positive values at the right endpoint b.

In other words, the function changes the sign between a and b.

2. f'(x) > 0 for all x in (a, b): This condition states that the derivative of f, denoted as f'(x), is always positive in the open interval (a, b).

This indicates that the function is increasing within this interval.

3. f''(x) > 0 for all x in (a, b): This condition states that the second derivative of f, denoted as f''(x), is always positive in the open interval (a, b).

This indicates that the function is concave up within this interval.

By combining these conditions, we can conclude that the function f is continuous, increasing, and concave up within the interval (a, b).

Since f(a) < 0 and f(b) > 0, and the function changes sign between a and b, by the Intermediate Value Theorem, there exists at least one root of the function f in the interval [a, b].

Therefore, the main answer is that the function f has a root in the interval [a, b].

Learn more about Intermediate Value Theorem:

brainly.com/question/30403106

#SPJ11

Answer:

The answer is 640

Step-by-step explanation:

Step-by-step explanation:

when two angles opposite to the two sides of the triangle are the same measure, this triangle is isosceles triangle which means that triangle's two sides are same. this sides are opposite to the angles with same measure

so if CD is 20 than CB is 20 too

hope It'll help and hope I'm correct

Answer:

6 feet by 5 feet by 4 feet

7 feet by 6 feet by 4 feet

Step-by-step explanation:

The surface are of rectangular prism = 140 ft²

Surface area of rectangular prism is given by :

A = 2(lw + lh + wh)

Using trial by error method :

6 feet by 2 feet by 3 feet

A = 2(6*2 + 6*3 + 2*3) = 72ft²

6 feet by 5 feet by 4 feet

A = 2(6*5 + 6*4 + 5*4) = 148 ft²

7 feet by 6 feet by 4 feet

A = 2(7*6 + 7*4 + 6*4) = 188ft²

8 feet by 4 feet by 3 feet

A = 2(8*4 + 8*3 + 4*3) = 136ft²

The total area of the figure in this problem is given as follows:

41.3 ft².

The area of the composite figure is given by the sum of the areas of all the parts that compose the figure.

The figure in this problem is composed as follows:

Then the area of the triangle is given as follows:

At = 0.5 x 6 x 3 = 9 ft².

The area of the semicircle is given as follows:

Ac = π x 3² = 28.3 ft².

The area of the square is given as follows:

As = 2² = 4 ft².

Then the total area of the figure is given as follows:

9 + 28.3 + 4 = 41.3 ft².

More can be learned about area of composite figures at brainly.com/question/10254615

#SPJ1

Answer:

10

Step-by-step explanation:

for two books its 3.75

so 13.75×5 = 16

a) X is an unbiased estimator of p. b) The Var(X) is p(1-p)/n. c) The E[X(1-X)] is (n-1)[p(1-p)/n]. d) The value of c is c = 1/(n-1).

(a) To show that X = Y/n is an unbiased estimator of p, we need to show that E[X] = p.

Since Y is a sum of n iid Bern(p) random variables, we have E[Y] = np.

Now, let's find the expected value of X:

E[X] = E[Y/n] = E[Y]/n = np/n = p.

Therefore, X is an unbiased estimator of p.

(b) To find the variance of X, we'll use the fact that Var(aX) = a^2 * Var(X) for any constant a.

Var(X) = Var(Y/n) = Var(Y)/n² = np(1-p)/n² = p(1-p)/n.

(c) To show that E[X(1-X)] = (n-1)[p(1-p)/n], we expand the expression:

E[X(1-X)] = E[X - X²] = E[X] - E[X²].

We already know that E[X] = p from part (a).

Now, let's find E[X²]:

E[X²] = E[(Y/n)²] = E[(Y²)/n²] = Var(Y)/n² + (E[Y]/n)².

Using the formula for the variance of a binomial distribution, Var(Y) = np(1-p), we have:

E[X²] = np(1-p)/n² + (np/n)² = p(1-p)/n + p² = p(1-p)/n + p(1-p) = (1-p)(p + p(1-p))/n = (1-p)(p + p - p²)/n = (1-p)(2p - p²)/n = 2p(1-p)/n - p²(1-p)/n = 2p(1-p)/n - p(1-p)²/n = [2p(1-p) - p(1-p)²]/n = [p(1-p)(2 - (1-p))]/n = [p(1-p)(1+p)]/n = p(1-p)(1+p)/n = p(1-p)/n.

Therefore, E[X(1-X)] = E[X] - E[X²] = p - p(1-p)/n = (n-1)p(1-p)/n = (n-1)[p(1-p)/n].

(d) To find the value of c such that cX(1-X) is an unbiased estimator of p(1-p)/n, we need to have E[cX(1-X)] = p(1-p)/n.

E[cX(1-X)] = cE[X(1-X)] = c[(n-1)[p(1-p)/n]].

For unbiasedness, we want this to be equal to p(1-p)/n:

c[(n-1)[p(1-p)/n]] = p(1-p)/n.

Simplifying, we have:

c(n-1)p(1-p) = p(1-p).

Since this should hold for all values of p, (n-1)c = 1.

Therefore, the value of c is c = 1/(n-1).

To know more about unbiased estimator:

https://brainly.com/question/32063886

#SPJ4

It is 45° because the sum of all the angles of a triangle is 180° so

\(75° +60° +x = 180° \\ x =180° - 75° -60° \\ x = 45°\)

The quadratic spline S(x) that interpolates the data f(0) = 0, f(1) = 1, and f(2) = 2, and satisfies S'(0) = 2 is given On the interval [0,1], S(x) = 2x + c0x² and On the interval [1,2], S(x) = 2x - 1

To determine a quadratic spline S that interpolates the data f(0)=0, f(1)=1, and f(2)=2 while satisfying S'(0)=2, we can follow these steps:

1. Start by defining the quadratic spline function S(x) on the intervals [0,1] and [1,2]. Let's call the coefficients for S(x) on the interval [0,1] as a0, b0, and c0, and the coefficients for S(x) on the interval [1,2] as a1, b1, and c1.

2. Since S(x) is a quadratic function, it can be represented as S(x) = a + bx + cx². Thus, we have:
  - On the interval [0,1], S(x) = a0 + b0(x - 0) + c0(x - 0)² = a0 + b0x + c0x²
  - On the interval [1,2], S(x) = a1 + b1(x - 1) + c1(x - 1)² = a1 + b1(x - 1) + c1(x² - 2x + 1)

3. To determine the coefficients a0, b0, and c0, we use the interpolation conditions S(0) = f(0) and S(1) = f(1). Substituting these values, we get:
  - For S(0) = 0, we have: a0 = 0
  - For S(1) = 1, we have: a0 + b0 + c0 = 1

4. To determine the coefficients a1, b1, and c1, we use the interpolation conditions S(1) = f(1) and S(2) = f(2). Substituting these values, we get:
  - For S(1) = 1, we have: a1 + b1 + c1 = 1
  - For S(2) = 2, we have: a1 + b1 + 3c1 = 2

5. Next, we need to consider the condition S'(0) = 2. The derivative of S(x) is given by S'(x) = b + 2cx. Substituting x = 0 and S'(0) = 2, we get:
  - For S'(0) = 2, we have: b0 = 2

6. Now we have four equations with four unknowns (a0, b0, a1, and b1). We can solve these equations simultaneously to find the values of a0, b0, a1, and b1.

  Substituting the values from step 3 and 4 into the equations, we get:
  - a1 + b1 + c1 = 1
  - a1 + b1 + 3c1 = 2

  Solving these equations, we find:
  - a1 = -1
  - b1 = 2
  - c1 = 0

  Therefore, the coefficients for S(x) on the interval [1,2] are a1 = -1, b1 = 2, and c1 = 0.

7. Finally, we can write the quadratic spline function S(x) as:
  - On the interval [0,1], S(x) = 0 + 2(x - 0) + c0(x - 0)² = 2x + c0x²
  - On the interval [1,2], S(x) = -1 + 2(x - 1) + 0(x² - 2x + 1) = 2x - 1

Therefore, the quadratic spline S(x) that interpolates the data f(0) = 0, f(1) = 1, and f(2) = 2, and satisfies S'(0) = 2 is given by:
  - On the interval [0,1], S(x) = 2x + c0x²
  - On the interval [1,2], S(x) = 2x - 1

To know more about interpolation visit:

https://brainly.com/question/31321449

#SPJ11

Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

Answer:

24.5

Step-by-step explanation:

38.5 / .5π =

Based on the cost of the copy paper and the discount on ink cartridges, the cost of the ink cartridge is $15 each.

First find the amount paid for the ink cartridges:

= Total spent - cost of copy paper

= 175 - 45

= $130

He got a discount of $2 per cartridge. For 10 cartridges he got a discount of:

= 2 x 10

= $20

The cost of each ink cartridge is:

= (Amount spent on ink cartridges + Discount) / Number of cartridges

= (130 + 20) / 10

= $15 each

In conclusion, each cartridge cost $15.

Find out more at https://brainly.com/question/22085332.

Answer:

Step-by-step explanation:

The main answer is: (15 - 4) * (4 + 11) = 51.

The missing operations only using 3 of these /,*,-,+ = (15 - 4) * (4 + 11) = 51.

To fill in the missing operations in the equation 15 _ 4 _ 4 _ 11 = 51 using only the operations of division (/), multiplication (*), subtraction (-), and addition (+), need to determine the appropriate operations to achieve the desired result.

Given that the equation is 15 _ 4 _ 4 _ 11 = 51, we can try different combinations of operations to find a valid solution:

15 + 4 / 4 * 11 = 51

15 - 4 / 4 + 11 = 51

15 * 4 / 4 - 11 = 51

15 / 4 * 4 + 11 = 51

If we insert parentheses as follows: (15 _ 4) _ (4 _ 11) = 51, then we can determine the missing operations:

(15 - 4) * (4 + 11) = 51

Learn more about parentheses here:

https://brainly.com/question/3572440

#SPJ11

The missing operations in 15_4_4_11=51 is multiplication, subraction, and addition to make the equation 15*4-4+11=51 to equal to 51.

The missing operations in 15_4_4_11=51 can be found using basic problem-solving skills and trial-and-error methods. In mathematics, these operations can be solved using the mathematical operations provided which are division (/), multiplication (*), subtraction (-), and addition (+).

https://brainly.com/question/37046762

#SPJ11

Answer:

C. 150

Step-by-step explanation:

The number of people who took the test is unknown, so call it x.

34% of x liked the flavor.

51 people liked the flavor.

That means that 34% of x is equal to 51.

34% of x = 51

0.34x = 51

x = 51/0.34

x = 150

Answer: C. 150

The ratio of a : b : c in the linear equation is 2 : -1 : -1

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

ax + by + c = 0

The points on the line are given as

(2 ,3) and (8 , 15)

A linear equation is represented as

y = mx + c

Where

Slope = m

y-intercept = c

This means that

3 = 2m + c

15 = 8m + c

Subtract the equations

So, we have the following representation

6m = 12

Divide by 6

m = 2

Substitute m = 2 in 3 = 2m + c

3 = 2 * 2 + c

So, we have

c = -1

Substitute m = 2 and c = -1 in y = mx + c

y = 2x - 1

So, we have

2x - y - 1 = 0

Recall that

ax + by + c = 0

This means that

a : b : c = 2 : -1 : -1

Hence, the ratio is 2 : -1 : -1

Read more about linear equations at

https://brainly.com/question/2030026

#SPJ1

Answer:

3x - 2y = 12

Step-by-step explanation:

3x-2y=12 is the standard form of equation y=3/2x - 6

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The equation is y=3/2x - 6

y equal to three by two times of x minus six

y=3/2x - 6

LCM of 1 and 2 is 2

y=(3x-12)/2

Now apply cross multiplication

2y=3x-12

Two times of y equal to three times of x minus twelve

Now take 2y to RHS side

3x-2y-12=0

3x-2y=12

Hence 3x-2y=12 is the standard Form of equation y=3/2x - 6.

To learn more on slope intercept form click:

https://brainly.com/question/9682526

#SPJ2

After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.

A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.

To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:

$98.48 / 6 = $16.41

Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.

It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.

To learn more about Stock split, visit:

https://brainly.com/question/29754813

#SPJ11

Answer:

B) x = √118 mi

Step-by-step explanation:

This is a right triangle, so we can the measure of x using the Pythagorean theorem, which is

a^2 + b^2 = c^2, where

Step 1:  Plug in x and √26 for a and b and 12 for c and simplify:

x^2 + (√26)^2 = 12^2

x^2 + 26 = 144

Step 2:  Subtract 26 from both sides to isolate x^2:

(x^2 + 26 = 144) - 26

x^2 = 118

Step 3:  Take the square root of both sides to isolate x:

√(x^2) = √118

x = √118 mi

Answer:

Mathematics NCERT Grade 7, Chapter 5: Lines and Angles is all about different lines, line segments, and angles.

A line segment has two end points.

A ray has only one end point (its vertex).

A line has no end points on either side.  

This chapter throws light on topics such as related angles, pair of lines. The chapter deals with different types of angles and lines. The types of angles discussed in this chapter are as follows:

Pairs of Angles          Condition

Two complementary angles Measures add up to 90°

Two supplementary angles Measures add up to 180°

Two adjacent angles Have a common vertex and a common arm but no common interior

Linear pair Adjacent and supplementary

A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.

All the types are discussed in detail and are supplemented with examples and short questions.  

Under the topic pair of lines, various sub-sections are discussed namely:

Intersecting lines

Transversal  

Angles made by a transversal

When two lines intersect (looking like the letter X) we have two pairs of opposite angles. They are called vertically opposite angles. They are equal in measure.

A transversal is a line that intersects two or more lines at distinct points.

Six angles discussed in this section:

1. Interior angles

2. Exterior angles

3. Pairs of Corresponding angles

4. Pairs of Alternate interior angles

5. Pairs of Alternate exterior angles

6. Pairs of interior angles on the same side of the transversal

Transversal of parallel lines

Valve guides can be measured for roundness and diameter using a micrometer or a bore gauge. Both of these tools are commonly used in the automotive industry to measure the dimensions of engine parts such as valve guides.

A micrometer is a precision measuring tool that uses a calibrated screw to measure the diameter of an object with high accuracy. It can be used to measure the diameter of the valve guide at different points along its length to check for roundness. A bore gauge, also known as an inside micrometer, is a specialized tool used to measure the inside diameter of a cylinder, such as the bore of an engine block or the valve guide. It consists of a probe that is inserted into the cylinder and expands to take a measurement. A bore gauge is particularly useful for measuring the internal dimensions of complex shapes like valve guides, which can have irregular or non-circular profiles. Both micrometers and bore gauges come in various sizes and types, and the specific tool used will depend on the size and shape of the valve guide being measured.

Learn more about Valve guides here

https://brainly.com/question/28497905

#SPJ11

The value of the triple integral ∭Ex⁶eʸdV over the region E is 0.

To evaluate the triple integral, we need to determine the limits of integration for each variable (x, y, z) based on the given bounds. The region E is bounded by the parabolic cylinder z = 81 - y² and the planes z = 0, x = 9, and x = -9.

The limits of integration for x are from -9 to 9. The limits of integration for y are determined by the parabolic cylinder, which is y² ≤ 81 - z. Since z = 0, the limits for y are -9 ≤ y ≤ 9. The limits of integration for z are from 0 to 81 - y².

Therefore, the triple integral can be expressed as:

∭Ex⁶eʸdV = ∫[-9, 9] ∫[0, 81-y²] ∫[-9, 9] x⁶eʸ dz dy dx

However, when we look at the integrand, Ex⁶eʸ, we see that it is an odd function with respect to x. Since we are integrating over symmetric bounds (-9 to 9) and the integrand is an odd function, the value of the integral will be 0. Hence, the value of the triple integral ∭Ex⁶eʸdV over the region E is 0.

To know more about triple integral, visit,

https://brainly.com/question/31315543

#SPJ4

Complete question - Evaluate the triple integral ∭Ex⁶eʸdV where E is bounded by the parabolic cylinder z=81−y² and the planes z=0,x=9, and x=−9.

Answer:

$1097.46

Step-by-step explanation:

Assume P is the finall price.  The markup of 26% can be written in decimal form as 0.26.  This is in additon to the full price paid for the gold ring, so we can add 1.00 to 0.26 to arrive at the factor 1.26.  Multiply 1.26 times the store cost of $871 to find the amount after 26% markup:

 ($871)*(1.26) = $1097.46