The gas tank of a car holds 15.9 gallons. If it required 12.2 gallons to fill the tank, how many gallons were still in the car before it was filled up?

The control limits help to separate common and special causes from each other.

Control lines are the horizontal lines drawn on the control chart. A control chart has several components. It has two control limits. They are represented by dashed lines. The lower one is called the lower control limit (LCL) and the upper one is called the upper control limit (UCL).

The control limits help us mark the highest (by UCL) and lowest (by LCL) error that is bearable. All those errors that occur between UCL and LCL are common errors/variations while the errors that occur above UCL or below LCL are the products with assignable causes variations.

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The statement which is best explained by the alternate exterior angles theorem is ∠1 ≅∠2.

What do you mean by angles?

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

We know that, alternate exterior angles theorem states that, when two parallel lines are cut by a transversal line, the resultant exterior angles are congruent.

∠1 and ∠2 are both alternate exterior angles.

Therefore, the correct answer for the following problem is ∠1 ≅∠2.

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The owner of a sandwich shop surveyed her customers on how often they came in as she also added the quantity this means that she had created marketing demand schedule.

The call for agenda indicates the variety of products customers will purchase at a given fee. An instance of this will be film ticketseconomics, a marketplace call for agenda is a tabulation of the amount of an awesome that each one customers in a marketplace will buy at a given fee. At any given fee, the corresponding cost at the call for agenda is the sum of all customers' portions demanded at that fee.

Demand schedules may be used to are expecting the quantity of cloth important primarily based totally at the fee of a product. If the call for agenda predicts that the amount demanded rises because the fee decreases, the enterprise may also want extra elements to provide extra products.

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The probability is 0.0062. This is calculated using the normal approximation to the binomial distribution, with mean μ = 80 and σ = 9.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

1. Calculate the mean (μ): μ = 80

2. Calculate the standard deviation (σ): σ = 9

3. Calculate the z-score for 90 free throws: z = (90-80)/9 = 1

4. Calculate the probability using the z-score: P(x≥90) = 1 - P(x<90) = 1 - 0.8413 = 0.1587

5. Round the probability to four decimal places: P(x≥90) = 0.0062

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a) The vertical rise per step is of 18.1 feet.

b) The number of steps needed to climb from road level to the 2nd floor is of: 3 steps.

The rise is obtained applying the slope concept, as follows:

Rise = Total elevation x Tangent of Angle.

The parameters are given as follows:

Then the rise per step is calculated as follows:

Rise = 24 x tangent of 37 degrees = 18.1 feet.

The total vertical elevation needed to reach the second floor is given as follows:

24 + 24 = 48 feet.

Then the total number of steps needed to climb to the 2nd floor is found applying the proportion, as follows:

48/18.1 = 2.65 steps.

Rounding up, 3 steps are needed.

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Answer:

D

Step-by-step explanation:

The sum of the length of any 2 sides is greater than the length of any 3rd side

10+8 = 18, so D is not possible

The relationship (comparison) between the measures in the specified angles found using the angle–side triangle inequality shows the following inequalities between the angles

m∠QRW < m∠RWQ

7. m∠RTW < m∠TWR

m∠RST > m∠TRS

9. m∠RWQ  < m∠QRW

The angle–side triangle inequality indicates that in a triangles, the larger the angle of a triangle, the larger is the side opposite the angle.

Similarly, the larger the side length of a side of a triangle, the larger is the angle opposite the specified side.

Based on the angle-side triangle inequality, we get;

∠QRW is the angle opposite to the side of length 45 units, and ∠RWQ is the angle opposite the side of length 47 units.

Therefore; m∠QRW < m∠RWQ

7. In triangle ΔRTW, ∠RTW is the angle opposite to the side of length 34 units, and ∠TWR is the angle opposite the side of length 35 units.

Therefore; m∠RTW < m∠TWR

In triangle ΔRST, ∠RST is the angle opposite to the side of length 35 units, and ∠TRS is the angle opposite the side of length 22 units.

Therefore; m∠RST > m∠TRS

9. In triangle ΔQRW, ∠RWQ is the angle opposite to the 47 unit long side and ∠QRW⇔ is the angle opposite the side of length 45 units.

Therefore; m∠RWQ > m∠QRW

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Answer: 4/5

Message: If this was helpful let me know! :)

Answer:

D) no solution

Step-by-step explanation:

since 4+2= 6 but there no solution s because 8+? might not equal the same number as 4+2

The net worth of the surf shop is  $859,489

We know that a balance sheet is the summary of the assets and liabilities of the legal person.

The balance sheet appears thus:

Assets:                                       $

Building mortgage                109,850

Accounts receivable                10,760  

property value                         182,974

Long term investment             237,000

Owned inventory                       72,980      

cash                                         215,083

Savings account                      128,721

Equipment                                 30,971

Liabilities

Debt                                        35,988

Long term liability                 38,000

Small business loan              62,700

Difference in assets and liabilities = $859,489

Therefore, the net worth of the surf shop is $859,489

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Answer: A. p + (3p – 5) + (4p + 6)

Step-by-step explanation:  Total number of tomato plants that Lauryn, Padma, and Kent grew = 8p + 1

Correct selling price = $10

What is selling price?

The selling price of an item is the price at which it is purchased. For instance, $10 would be regarded as the umbrella's selling price if Neil sold the identical umbrella for that sum. It is referred to as S.P.

Based on given conditions formulate:

= 6(1+67%)

= 6(1.67)

= 10

correct selling price = $10

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The value of x, the distance from the base of the roof to the top of the roof is 8 feet.

What is Pythagorean theorem?

The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

Given: The roof of a patio is in the shape of triangle.

We have to find the distance x from the base of the roof to a top of the roof.

Let the base of the roof is divided into two parts by the line x.

The half distance is 15 feet.

The triangle made is a right angle triangle.

So we can we the Pythagorean theorem to find the value of x.

By the Pythagorean theorem,

x^2 + 15^2 = 17^2

x^2 + 225 =  289

          x^2 = 289 - 225

          x^2 = 64

              x = 8

Hence, the value of x, the distance from the base of the roof to the top of the roof is 8 feet.

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The sample size to meet the error margin is 2185.

What is the error margin?

The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.

Here, we have

The sample size (n) is calculated according to the formula:

n =  p(1 - p) (z²/ e²)

Where:

z = 1.96 for a confidence level (α) of 95%, p = proportion, e = margin of error.

z = 1.96, p = 0.35, e = 0.02

n =  0.35(1 - 0.35) (1.962/ 0.022)

n = (0.2275)(9604)

= 2184.91

n ≈ 2185

Hence, the sample size meets the error margin is 2185.

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Answer:

1 1/4

Step-by-step explanation:

Divide 125 by 100, which gets you 1.25 (also known as 1 1/4)

Henry walked 1.25 miles each day to and from school.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that,

Henry walks to and from school each day.

Distance travelled by Henry in 100 days = 125 miles

In order to find the distance travelled by Henry in 1 day to and from school, divide the total distance by 100.

Distance travelled in 1 day = 125 / 100 = 1.25 miles

Hence the distance Henry walk to and from school is 1.25 miles.

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The coordinate of the triangle after reflection are; A'(0,3),  B'(2,1) , C'(-3,3)

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

We are given that Triangle ABC Has the verties of A(0,-3) B(2,-1) and C(-3,-3).

The transformation for reflection across the x-axis is;

(x, y) ⇒ (x, -y) . . . reflection across the x-axis

Then we have;

 A(0, -3) ⇒ A'(0, 3)

B(2,-1) = B'(2,1)

C(-3,-3) =C'(-3,3)

Therefore, The coordinate of the triangle are;

A'(0,3),  B'(2,1) , C'(-3,3)

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Answer: (8,8)

Step-by-step explanation: because, you just need to do the math

The equation of line is y = ( 3/4 )x + 2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P = P ( 8 , 8 )

Let the second point be Q = Q ( 4 , 5 )

Now , the slope of the line between the two points is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 5 - 8 ) / ( 4 - 8 )

Slope m = -3/-4

Slope m = 3/4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 8 = 3/4 ( x - 8 )

On simplifying the equation , we get

y - 8 = ( 3/4 )x - 6

Adding 8 on both sides of the equation , we get

y = ( 3/4 )x + 2

Therefore , the value of A is y = ( 3/4 )x + 2

Hence , the equation of line is y = ( 3/4 )x + 2

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Answer:

-4

Step-by-step explanation:

Slope is represented by:

Rise/run

So, count up from a point on the line and count across to another point on the graph.

I started from -1, counted up 4 and counted 1 across to point (-1,3)

So your slope is 4/-1, which is the same as -4

The slope of a line from the given graph is -4. Therefore, option D is the correct answer.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

From the given graph,

Rise is (-5-(-1)=-4

Run is 1

So, Slope =Rise/Run

= -4/1

= -4

The slope from the graph is -4. Therefore, option D is the correct answer.

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Answer:

the component form of the resultant vector is (-2, -1).

Step-by-step explanation:

To find the component form of the resultant vector, we need to add the corresponding components of the two input vectors. In this case, the x-component of the resultant vector is equal to the x-component of vector b minus the x-component of vector u, and the y-component of the resultant vector is equal to the y-component of vector b minus the y-component of vector u.

We can therefore write the component form of the resultant vector as follows:

-u + b = (-u_x + b_x, -u_y + b_y) = (-5 + 3, -2 + 1) = (-2, -1)

therefore, the component form of the resultant vector is (-2, -1).

Answer:

Option C is the correct answer.

Step-by-step explanation:

There are two terms in business

So,

In this case, Philippines is doing exporting and Canada is doing Importing.

Thus, The answer is Philippines.

Mathematical equations are essentially relationships. A line equation describes the relationship between x and y values found on a coordinate plane.

Firstly understand the values in the table. The numbers in a table are often the x and y values that are true for the line, which means the x and y values correspond to the coordinates of points on the line.

Then we need to determine the slope. We can do this by taking two points from the table and plugging them into formula.

Next we need to find the y-intercept. To do this, we need one point from the table to plug into our function.

Once you find the value of the slope, plug it into the the slope-intercept form of the line. The result is the function that describes the relationship in the given table of values.

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Answer:

702,653

Step-by-step explanation:

but the real total added up is 945,556

Answer:

PEmDas so -53Step-by-step explanation:

Answer:

-53

Step-by-step explanation:

-9 + (-44)

-9 - 44

- 53

The test statistic under the null hypothesis of is when the sample mean is for a random sample of size 15 from a normal population with unknown variance. The given statement is true.

For a random sample of size 15 from a healthy population with known variation. the statistical measure under test for the null hypothesis.

Even when the population variance is known and the sample size is modest, the Z-test can be used.

The given statement is true.

Hypothesis :

In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.

Complete question:

True or False: For a random sample of size 15 from a normal population with known variance, the test statistic with the null hypothesis of H_o: u =  (i - uo)/n), when i is the sample mean.

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Answer:

In Jewish tradition, Abraham is called Avraham Avinu (אברהם אבינו), "our father Abraham," signifying that he is both the biological progenitor of the Jews and the father of Judaism, the first Jew.

Step-by-step explanation:

The factorised form of given function f(x) is (x + 2)(x +√3)(x-√3)

Describe a polynomial.

A mathematical expression that contains at least two terms with variables or integers is referred to as a polynomial. A polynomial may include several terms.

We have been given the polynomial function:

⇒ x³ + 2x² - 3x -6

Simplify the radical by breaking the radicand up into a product of known factors.

⇒ x³ + 2x² - 3x -6

Add and subtract the second term to the expression and factor by grouping.

⇒ x²(x + 2) - 3(x + 2)

⇒ (x + 2)(x² - 3)

⇒ (x + 2)(x +√3)(x-√3)

Therefore, the factorised form of given function f(x) is (x + 2)(x +√3)(x-√3).

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Answer:

B) on edge

Step-by-step explanation:

The Bus can hold 59 students and van can hold 18 students.

The freshman class rented and filled 1 van and 6 buses with 372 students. This can be illustrated as:

v + 6b = 372 .... i

The sophomore class rented and filled 4 vans and 12 buses with 780 students. This can be illustrated as:

4v + 12b = 780 ... ii

where v = van.

b = bus

v + 6b = 372

4v + 12b = 780

Reduce equation ii by 2. The new equations will be:

v + 6b = 372

2v + 6b = 390

Subtract

v = 18

The van can hold 18 students

Since v + 6b = 372

This will be:

18 + 6b = 372

6b = 354

b = 59.

Bus can hold 59 students.

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