A bookstore had 90 copies of a magazine. Yesterday , it sold 1/3 of them. Today, it sold 1/6 of what remained. How many copies does the bookstore have left?

We have shown that if two lines are parallel, then they have the same slope.

A shape is translated when it is moved up, down, left or right without turning. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

We can prove that parallel lines have the same slope by using the fact that the distance between corresponding points of a figure and its translated image is the same at every point.

Suppose we have two parallel lines, line A and line B, with slopes m₁ and m₂, respectively. Let P be any point on line A, and let Q be the corresponding point on line B such that P and Q are equidistant from the line of intersection of A and B.

Now let us translate line A to a new line A', such that P is mapped to Q. Since the distance between corresponding points of A and A' is the same at every point, we know that the distance between P and the line of intersection of A and B is equal to the distance between Q and the line of intersection of A' and B.

Since A' and B are still parallel, the distance between Q and the line of intersection of A' and B is equal to the distance between any point on line B and the line of intersection of A' and B.

Therefore, the distance between P and the line of intersection of A and B is equal to the distance between any point on line B and the line of intersection of A' and B. This means that the slope of line B, m₂, must be equal to the slope of line A', which is also equal to m₁.

Hence, we have shown that if two lines are parallel, then they have the same slope.

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The complete question is:

A line and its translated image are parallel because the distance between corresponding points of a figure and its translated image is the same at every point. How could you use that information to show that parallel lines have the same slope?

Answer:

To find the horizontal distance the football travels, we need to find the maximum value of the quadratic function y = -16x^2 + 85x, which occurs at the vertex of the parabola.

The x-coordinate of the vertex is given by -b/2a, where a = -16 and b = 85:

x = -b/2a = -85/(2*(-16)) = 2.66

So the football travels a horizontal distance of approximately 2.66 feet when kicked.

To check that this is the maximum distance, we can find the value of y at x = 2.66:

y = -16(2.66)^2 + 85(2.66) = 113.56

So the maximum height reached by the football is approximately 113.56 feet.

Therefore, Dario kicks the football a horizontal distance of approximately 2.66 feet.

Answer:

The volume of the spray can is given by the formula for the volume of a cylinder:

V = πr^2h

where r is the radius of the base (which is half the diameter), and h is the height.

The diameter of the spray can is 7 inches, so the radius is 7/2 = 3.5 inches.

The height of the spray can is 8 inches.

Substituting these values into the formula, we get:

V = π(3.5)^2(8)

V = π(12.25)(8)

V = 98π

Therefore, the volume of the spray can is 98π cubic inches.

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Using one of circle theorems, the value of x in the given circle is 2

From the question, we are to determine the value of x in the given diagram

In the diagram, we have a circle that shows an arc measure of 186°.

From one of circle theorems, we have that

The angle subtended by an arc at the center of the circle is twice the angle subtended at the circumference.

From this, we can write that

186° = 2(36x + 21)

Solve the equation for x

186° = 2(36x + 21)

Divide both side by 2

186/2 = 2(36x + 21) / 2

93 = (36x + 21)

93 = 36x + 21

Subtract 21 from both sides

93 - 21 = 36x

72 = 36x

Divide both sides by 36

72 / 36 = 36x / 36

2 = x

Hence,

The value of x is 2

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The mean is 0.477514 (rounded to 6 decimal places).

The standard deviation is 0.288919 (rounded to 6 decimal places).

To calculate the mean and standard deviation, we will use the following formulas:

Mean = (sum of all values) / (number of values)

Standard deviation = sqrt[(sum of (value - mean)^2) / (number of values)]

Using these formulas, we can calculate the mean and standard deviation for the given set of random numbers:

Mean = (0.937776 + 0.270012 + 0.243785 + 0.590701 + 0.824982 + 0.131805 + 0.879337 + 0.741998 + 0.254683 + 0.080259 + 0.419321 + 0.928220 + 0.958430 + 0.980182 + 0.263900 + 0.063119 + 0.762096 + 0.485612 + 0.662900 + 0.362242 + 0.724796 + 0.307736 + 0.305021 + 0.417052 + 0.054337 + 0.323357 + 0.069662 + 0.843387 + 0.353107 + 0.074262 + 0.735596 + 0.175095 + 0.390508 + 0.668932 + 0.029861 + 0.205228 + 0.387740 + 0.962169 + 0.646565 + 0.423914 + 0.754782 + 0.156719 + 0.773113 + 0.546335 + 0.323573 + 0.649740 + 0.214082 + 0.382383 + 0.383982 + 0.030539) / 50 = 0.477514

Therefore, the mean is 0.477514 (rounded to 6 decimal places).

Now we will calculate the standard deviation:

Standard deviation = sqrt[((0.937776 - 0.477514)^2 + (0.270012 - 0.477514)^2 + (0.243785 - 0.477514)^2 + ... + (0.382383 - 0.477514)^2 + (0.383982 - 0.477514)^2 + (0.030539 - 0.477514)^2) / 50] = 0.288919

Therefore, the standard deviation is 0.288919 (rounded to 6 decimal places).

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The simplified form of the fraction is A = ( 5q - 20 ) / ( 5q - 6 )

Given data ,

Let the fraction be represented as A

Now , the value of A is

A = ( 10q - 40 ) / ( 10q - 12 )

On simplifying , we get

Divide by 2 on both the numerator and denominator of the fraction , we get

A = ( 5q - 20 ) / ( 5q - 6 )

Hence , the fraction is A = ( 5q - 20 ) / ( 5q - 6 )

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Answer: C

Step-by-step explanation: I did this on an exam

C

The vertical asymptotes are at the values of x 2 and 5.

The vertical asymptotes are the values of x that make the denominator equal to zero.

Here the denominator is:

x² - 7x + 10 = 0

We can use the quadratic formula to find the values of x, these are:

[tex]x = \frac{7 \pm \sqrt{(-7)^2 - 4*1*10} }{2} \\\\x = \frac{7 \pm 3}{2}[/tex]

Then the two values of x are:

x+ = (7 + 3)/2 = 10/2 = 5

x- = (7 - 3)/2 = 4/2 = 2

at these values of x we have the two vertical asymptotes.

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Answer:

Add answers

Step-by-step explanation:

...

The sum of 1/5 + 2 1/3 = 38/15 is an improper fraction.

To add fractions, convert the mixed numbers to improper fractions. Find a common denominator for the fractions and make the denominators the same. Now add or subtract the fractions. Simplify the resulting fraction if necessary.

Here we have

1/5 + 2 1/3 =

To add 1/5 and 2 1/3, convert 2 1/3 to an improper fraction:

=> 2 1/3 = 7/3   [ (3 × 2) + 1 = 7 ]

Now, find a common denominator between 5 and 3, which is 15.

1/5 = 1/5 × 3/3 = 3/15

7/3 = 7/3 × 5/5 = 35/15

Now we can add:

3/15 + 35/15 = 38/15

Therefore,

The sum of 1/5 + 2 1/3 = 38/15 is an improper fraction.

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Answer:

Step-by-step explanation:

We can use the Central Limit Theorem to approximate the distribution of the sample mean. Since the sample size is large (n=61), the sample mean will be approximately normally distributed with mean μ = 2.6 feet and standard deviation σ/√n = 0.4/√61 = 0.0517 feet.

To find the probability that the sample mean is less than 2.2 feet, we standardize the sample mean as follows:

z = (x - μ) / (σ/√n) = (2.2 - 2.6) / (0.4/√61) = -3.692

We look up the probability corresponding to z = -3.692 in the standard normal distribution table or use a calculator to find the area under the standard normal curve to the left of z:

P(z < -3.692) ≈ 0.0001 (rounded to 4 decimal places)

Therefore, the probability that the mean of the sample taken is less than 2.2 feet is approximately 0.0001.

The value of 'x' for given problem is 81 degrees.

The intersection of two lines produces vertical angles, which are pairs of angles. Consistently having the same measure, they are congruent. A pair of vertical angles is a pair of non-adjacent, opposing angles that have the same vertex but different sides.

In given Problem, we have two vertical angles:

one measures (x + 3) degrees and

other measures 84 degrees.

As a result of the congruence of vertical angles, we may construct an equation to get the value of x. 84 degrees and (x + 3) degrees are both vertical angles, hence they must be equal to one another:

x + 3 = 84

To solve for x, we can subtract 3 from both sides of the equation:

x + 3 - 3 = 84 - 3

x = 81

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Correct Question: (x+3) degrees and 84 degrees are pair of vertical angles.Find x?

The linear equation that describes this situation is:

y = 2500 + 300*x

A general linear equation is written as:

y = ax + b

where a is the slope and b is the initial value.

Here we know that she starts with 2,500 points in the game, and then she wins 300 points for every minute.

Then the initial value is 2,500, and the slope is 300, then we can write the linear equation:

y = 2500 + 300*x

That is the correct option.

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Answer:

15cm

Step-by-step explanation:

in an isosceles triangle two sides are equal so represent the two sides as p also those two sides are the longer sides and the perimeter equals to 36 that is the sum of the three sides equals to 36 , so our equation will now be : p+p+6=36 ,. 2p+6=36. ,2p=36-6. 2p=30. divide both side by 2 so p =15 so each longer sides measure 15cm

The data points from table A and table B have been plotted in the graph shown below.

In this scenario, the time (in hours) would be plotted on the x-axis (x-coordinate) of the scatter plot while the energy (kWh) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

For table A, we have:

Time (in hours)         Energy (kWh)

0                                  0.0

1                                   0.3

2                                  0.5

3                                  0.7

4                                  0.9

For table B, we have:

Time (in hours)         Energy (kWh)

0                                  0.0

1                                   0.1

2                                  0.2

3                                  0.3

4                                  0.4

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Answer:

The mean of the sample distribution of the sample mean is the same as the population mean, which is 40 dollars. The standard deviation of the sample distribution of the sample mean (also called the standard error) is given by:

standard error = standard deviation / sqrt(sample size) = 8 / sqrt(49) = 8 / 7

To find the probability that the sample mean would be less than 37.4 dollars, we need to standardize the sample mean using the standard error and then look up the probability from a standard normal distribution table. The z-score for a sample mean of 37.4 dollars is:

z = (37.4 - 40) / (8 / 7) = -1.225

Looking up this z-score in a standard normal distribution table, we find that the probability of getting a sample mean less than 37.4 dollars is 0.1103 (rounded to four decimal places). Therefore, the probability that the sample mean would be less than 37.4 dollars is 0.1103.

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Step-by-step explanation:

Answer:1

just like my answer dawg

Step-by-step explanation:

To graph the line with a slope of -4 and a y-intercept of 8, you can start by plotting the y-intercept point on the y-axis, which is (0, 8). Then, use the slope to find additional points on the line. Since the slope is -4, you can move down 4 units and to the right 1 unit to find another point on the line. Plot this point and draw a straight line through both points to complete the graph. The resulting line will be a straight line that slopes downward to the right and passes through the points (0, 8) and (1, 4).

To fill in the deposit slip, you need to insert the figure, $940 into the checks section of the slip or the Bills section. In the Name and Date sections, you will insert your name and the date of the deposit. The sign section will not be filled as cash was not received.

First, we learn that $800 will be deposited into savings and the rest into checking. If we subtract $800 from  $1,740, we will have $940. So, the amount that will be put into the checking account will be $940.

Name and Date will be filled in according to your personal details. The signature will not be signed as cash was not received.

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Answer:

Step-by-step explanation:

To calculate the area of a parallelogram, you need to know the length of the base and the height of the parallelogram.

The formula for the area of a parallelogram is:

Area = base x height

where the base is any side of the parallelogram and the height is the perpendicular distance between that side and the opposite side.

For example, if you have a parallelogram with a base of 8 meters and a height of 5 meters, you can calculate its area as:

Area = 8 meters x 5 meters = 40 square meters

So, the area of the parallelogram is 40 square meters.

Answer:

Option A (1040 x 246)

Step-by-step explanation:

To see if there is a remainder, we can multiply the quotient and the divisor and subtract it from the dividend. If there is no remainder, the result will be zero. If there is a remainder, the result will be a non-zero number.In this case, we have:

1040 x 246 = 255,840

When we subtract this from the dividend, we get:

256,000 - 255,840 = 160

Since the result is not zero, we can conclude that there is a remainder of 160 when 256,000 is divided by 246.

Using mathematical operations involving unit conversions, the greatest number of 16-inch pieces of wood the carpenter can cut from 8 boards is 54.

The four basic mathematical operations are multiplication, division, subtraction, and addition.

In this situation, the units are converted from feet to inches using multiplication, before the greatest number of pieces are determined using division.

The quantity of boards the carpenter wants to cut = 8 boards

The length of each board = 9 feet

The total quantity of the boards in feet = 72 feet (8 x 9)

12 inches = 1 foot

72 feet = 864 inches (72 x 12)

The length of each piece of wood = 16 inches

The greatest number of 16-inch pieces of wood = 54 pieces (864 ÷ 16)

Thus, we can conclude that the carpenter will get 54 pieces of 16-inch wood from the 8 boards of 9 feet each in length.

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Answer:

4300

Step-by-step explanation:

If 171 out of 400 people like pop music, that means that 42.75% of all citizens prefer pop music.

To calculate the amount of citizens that prefer pop music in a sample of 10000 citizens, all we need to do is multiply 10000 by 0.4275=4275 citizens, which is roughly 4300.

The electric company would need a wire that is approximately 4.58 meters long to reach the top of the 5-meter electric pole from a point on the ground 2 meters from the base of the pole.

What is Meter?

The meter was originally defined as one ten-millionth of the distance from the equator to the North Pole along a meridian through Paris, but this definition was later replaced by the current definition based on the speed of light.

To determine the length of the wire required to reach the top of a 5-meter electric pole from a point on the ground 2 meters from the base of the pole, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the pole, the ground, and the wire form a right triangle, where the pole is the hypotenuse, the distance from the base of the pole to the point on the ground is one of the legs, and the length of the wire needed to reach the top of the pole is the other leg.

Therefore, we can use the Pythagorean theorem to solve for the length of the wire as follows:

wire length = sqrt([tex]pole height^{2}[/tex] - [tex]distance from base^{2}[/tex])

= sqrt([tex]5^{2}[/tex] - [tex]2^{2}[/tex])

= sqrt(25 - 4)

= sqrt(21)

≈ 4.58 meters

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Answer:

Match the polynomial to it's correct name.

1. Quadratic trinomial – a. ƒ(x) = 3x² - 5x + 7

2. Quartic trinomial – b. ƒ(x) = x⁴ - 3x³ + 9x²

3. Cubic monomial – c. h(x) = 15x + 2

4. Linear binomial – d. g(x) = -5x³

[tex]\begin{gathered}\end{gathered}[/tex]

Match the polynomial to it's correct name.

1. Quadratic trinomial – a. ƒ(x) = 3x² - 5x + 7

2. Quartic trinomial – b. ƒ(x) = x⁴ - 3x³ + 9x²

3. Cubic monomial – d. g(x) = -5x³

4. Linear binomial – c. h(x) = 15x + 2

Answer: 1.624 gallons

Step-by-step explanation:

It takes 8.12 gallons to paint the full fence. You only need 1/5 of that. You can turn 1/5 into a decimal if it helps. In this case, that would be 0.2

8.12 x 0.2 = 1.624

After answering the presented question, we can conclude that Ty Cobb's performance had already peaked by 1918, and his future potential was questionable.

A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions. The equal sign divides the variables 3x + 5 and 14 in the equation 3x + 5 = 14, for instance. The relationship between the two phrases that appear on opposing sides of a letter is explained by a mathematical formula. Frequently, the symbol and the single variable are identical. as 2x - 4 equals 2, for example.

Ty Cobb had a batting average of.382 and a slugging percentage of.521, while Babe Ruth had a batting average of.300 and a slugging percentage of.555 in 1918. It is tough to make a firm determination on whether to trade Ruth for Cobb based only on this information.

Nonetheless, given the two players' total performance and potential, it would be unwise to deal Babe Ruth for Ty Cobb. Babe Ruth was recognized for his tremendous hitting and pitching ability and would go on to become one of baseball's best players of all time, but Ty Cobb's performance had already peaked by 1918, and his future potential was questionable.

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Answer:

a) since 27% below the target pressure value =target pressure

Step-by-step explanation:

Answer:

y[tex]\leq[/tex]-2x + 6

y[tex]\leq[/tex][tex]\frac{5}{2}[/tex] x + [tex]\frac{1}{2}[/tex]

y [tex]\geq[/tex][tex]\frac{-2}{3}[/tex]x + [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

Put each equation in the slope intercept form of the in line and then look to see if the graph is above or below the line graphed.  Above the line would be greater than and below the line would be less than.

Helping in the name of Jesus.

The value for each greatest integer function is:

[55.9] = 55

[55.001] = 55

[0.65] = 0

[-34.11] = -35

[16(3/14)] = [227/14] = [16.214] = 16

[-8.21] = -9

[19] = 19

[-0.45] = -1

[-8(1/2)] =[-8.05] = -9

[2/3] = [0.67] = 0

We have,

The greatest integer function, denoted as [x] gives the largest integer that is less than or equal to x.

So,

We can create the inequalities as:

55 ≤ 55.9 ≤ 56

[55.9] = 55

55 ≤ 55.001 ≤ 56

[55.001] = 55

0 ≤ 0.65 ≤ 1

[0.65] = 0

-35 ≤ -34.11 ≤ -33

[-34.11] = -35

16 ≤ 16.214 ≤ 17

[16(3/14)] = [227/14] = [16.214] = 16

Similarly,

[-8.21] = -9

[19] = 19

[-0.45] = -1

[-8(1/2)] =[-8.05] = -9

[2/3] = [0.67] = 0

Thus,

The value for each greatest integer function is given above.

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