Directions: Determine whether the ordered palr is a solution to the given equation. Show your work and write "yes" or "no" on the blank line. 1. Equation: 6x - 3y = 21 Ordered Pair: (3,-1) 2. Equation: 7x - 6y = 38 Ordered pair: (2,-4) 3. Equation: 4x - 7y = 13 Ordered pair: (5,12) 2. A 4. Equation: 9x - 8y = 54 Ordered pair: (0,6) B c с C

Solving a system of equations we will see that the song was used on 5 movies and 7 commercials

The variables we will use are:

We know that:

x = y + 2

and:

x*$30 + y*$110 = $760

So the system of equations is:

x = y + 2

x*$30 + y*$110 = $760

Replacing the first equation in the second one:

(y + 2)*$30 + y*$110 = $760

$60 + y*$30 + y*$110 = $760

y*$140 = $760 - $60

y*$140 = $700

y = $700/$140 = 5

Then the value of x is:

x = y + 2 = 5 + 2 = 7

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B) down

its a negative

I hope that helps

Answer:

6936 pints and 1156 cups

Step-by-step explanation:

Answer:

7514 pints

Step-by-step explanation:

i rechecked and this was correct?

Answer:

this would 5 x + 2

Step-by-step explanation:

Answer: (4x2 + 4x - 5) • (x - 1)

Step-by-step explanation: The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  4  and the Trailing Constant is  5.

The factor(s) are:

of the Leading Coefficient :  1,2 ,4

of the Trailing Constant :  1 ,5

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

  4x3-9x+5

can be divided with  x-1

2.2    Polynomial Long Division

Dividing :  4x3-9x+5

                             ("Dividend")

By         :    x-1    ("Divisor")

dividend     4x3      -  9x  +  5

- divisor  * 4x2     4x3  -  4x2        

remainder         4x2  -  9x  +  5

- divisor  * 4x1         4x2  -  4x    

remainder          -  5x  +  5

- divisor  * -5x0          -  5x  +  5

remainder                0

Quotient :  4x2+4x-5  Remainder:  0

2.3     Factoring  4x2+4x-5

The first term is,  4x2  its coefficient is  4 .

The middle term is,  +4x  its coefficient is  4 .

The last term, "the constant", is  -5

Step-1 : Multiply the coefficient of the first term by the constant   4 • -5 = -20

Step-2 : Find two factors of  -20  whose sum equals the coefficient of the middle term, which is   4 .

     -20    +    1    =    -19

     -10    +    2    =    -8

     -5    +    4    =    -1

     -4    +    5    =    1

     -2    +    10    =    8

     -1    +    20    =    19

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

The number 2/5 is both a ratio and a fraction.

The number 2/5 is both a ratio and a fraction. Fractions are meant to signify the numerator and denominator in an expression. in the above expression, we have the denominator as 5 and the numerator as 2.

The expression is also a ratio because it indicates the quantitative relationship between the figures.

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Answer:

21 and 10.5 respectively

Step-by-step explanation:

Remember circumference of a circle is given as;

C= 2×π×r; r is raduis

r = C / 2×π

=65.98/(2×3.142)= 10.50

D= 2× r = 2× 10.50= 21.0( D represent diameter)

Note π = 3.142 a known constant

This distribution of snowfall amounts is skewed to the right

Data is said to be skewed to the right or positively skewed, when the tail of the distribution extends more towards the right side of the data. This means that there are a few larger values or outliers that pull the mean or median towards the higher end of the scale, resulting in a longer tail on the right side of the distribution.

In a positively skewed distribution majority of the data is concentrated towards the lower values.

Considering the stemplot the majority of the data is in the lower values

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Answer:

to the second part

18.7 inches

Answer:

a. increasing n decreases E

Step-by-step explanation:

The sample size refers to the number (n) of units or observations taken from a population for a study. The results obtained from this sample size can be used to make generalizations about the entire population. The margin of error (E) is a measure of the sampling error or the percentage of the difference between the results obtained from the study and the true population value. The relationship between the sample size (n), and the Margin of error (E) is an inverse. That means

Sample size (n) ∝ 1/E

So, as the sample size increases, the margin of error decreases. This would be even more true if the accurate procedures for the experiment are followed.

Answer:

We reject the Null and conclude that the mean costs of a meal at fast food restaurants in two different cities are different.

Step-by-step explanation:

Given :

City n x s

A 26 $4.05 $0.55

B 32 $5.15 $0.85

H0 : μ1 - μ2 = 0

H0 : μ1 - μ2 ≠ 0

n1 = 26 ; x1 = 4.05 ; s1 = 0.55

n2 = 32 ; x2 = 5.15 ; s2 = 0.85

Tstatistic :

(x1 - x2) / √(s1²/n1 + s2²/n2)

(4.05 - 5.15) / √(0.55²/26 + 0.85²/32)

-1.1 / 0.1849668

= - 5.947

Using the smaller n;

df = n - 1 ; 26 - 1 = 25

Pvalue = (-5.947, 24)

Pvalue = 0.000001

Since Pvalue < α ; We reject the Null and conclude that the mean costs of a meal at fast food restaurants in two different cities are different.

Answer:

A) 90

B) The individuals in the survey will be 11, 101, 191,...., 2621.

Step-by-step explanation:

Tenemos lo siguiente a partir del enuciado:

A) let, a consider a department has an alphabetical list of all 2708 employees at company and wants to conduct a systematic sample. Substitute the value as:

k = N/n

reemplanzado nos queda:

k = 2708/30 = 90.26

Lo que quiere decir que el valor de k es de aproximadamente 90 B) Randomly select the number between I and 90, Suppose the randomly selected sumber is 11. The individuals in the survey will be; need to find 30th team, hence by using the airthmetic perogression nth term formula:

30th term = 11+ (30 - 1) *90

30th term = 2621

The individuals in the survey will be 11, 101, 191,...., 2621.

The random sample is obtained

By using the box plot, the top 25 percent of the cars have a typical gas mileage of at least 30 miles per gallon.

To find the value of the typical gas mileage for the top 25 percent of cars, we need to look at the upper quartile (Q3) of the box plot. The upper quartile is the point that separates the highest 25 percent of the data from the lowest 75 percent.

In the box plot, the upper quartile (Q3) is represented by the top of the box (the horizontal line inside the box) and the vertical line extending from the top of the box (the "whisker" above the box). We can estimate the value of Q3 by looking at the scale on the vertical axis and reading off the approximate value at the top of the box and the end of the whisker.

Assuming the scale on the vertical axis is in miles per gallon, we can estimate that Q3 is around 30 miles per gallon. Therefore, we can conclude that the top 25 percent of the cars have a typical gas mileage of at least 30 miles per gallon.

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Answer:

x<6

Step-by-step explanation:

x is less than six thats what the answer means

Answer:

5,4,3,2,1

Step-by-step explanation:

Answer:

That is, two objects are congruent if we can move one of the objects, without changing its shape or size, in such a way that it fits exactly over the other image, and we call these movements congruence transformations.

Yes, because for each input there is exactly one output. Therefore, the relation represented by the mapping diagram is a function.

To determine if the relation represented by the given mapping diagram is a function, we need to check if each input (x value) has exactly one output (y value) associated with it.

From the given mapping diagram, we can see that:

The input value -3 is associated with the output value 0.

The input value -1 is associated with the output value 2.

The input value 1 is associated with the output value 0.

The input value 3 is associated with the output value 2.

The input value 5 is associated with the output value 5.

As we can see, each input value has exactly one output value associated with it. Therefore, the relation represented by the mapping diagram is a function.

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The average cost price of 2000 printed tennis balls will be $1500.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that a local college's service organization purchased 2,000 tennis balls with the school's logo on them. Tennis balls cost $.50 each from Sports Depot, and a one-time stamp costing $500 was added on top of that.

Total cost = ( 2000 x 0.5 ) + 500

Total cost = 1000 + 500

Total cost = $1500

Therefore, the average cost price of 2000 printed tennis balls will be $1500.

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Step-by-step explanation:

Cost of 5 books = $ 36.25

Cost of 1 book = $36.25 / 5 = $ 7.25

The unit price is $ 7.25

Hope it will help :)

9514 1404 393

Answer:

  -195 degrees

Step-by-step explanation:

The angle is shown as being measured CW, so in the reverse of the positive direction. The angle's terminal ray seems to be above the -x axis, making its measure more than 180°. Of the choices offered, the best seems to be ...

  -195 degrees

Answer:

(3x+2)(x-5)

Step-by-step explanation:

Factor by grouping

\(3x^2-13x-10\\=3x^2-15x+2x-10\\=3x(x-5)+2(x-5)\\=(3x+2)(x-5)\)

Using the Empirical Rule, it is found that 99.7% of the weights are between 180 g and 480 g.

It states that, for a normally distributed random variable:

Hence, the bounds of the interval containing 99.7% of the weights is given by:

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500ppm = 0.05%

Now, express the percentage as a fraction:

0.05/100 = 1/2000

Therefore:

To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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Answer:

To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.

To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.

Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.

We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds

Step-by-step explanation:

The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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Answer:

Step-by-step explanation:

To solve the inequalities 2x - 15 < -0.8 and 2x - 15 > 0.8, we will solve them separately and then combine the solutions.

First, let's solve the inequality 2x - 15 < -0.8:

2x - 15 < -0.8

Add 15 to both sides:

2x < 14.2

Divide both sides by 2 (since the coefficient of x is 2 and it is positive, we don't need to flip the inequality symbol):

x < 7.1

Now, let's solve the inequality 2x - 15 > 0.8:

2x - 15 > 0.8

Add 15 to both sides:

2x > 15.8

Divide both sides by 2:

x > 7.9

So, the solutions to the inequalities are:

x < 7.1 and x > 7.9

To write these solutions in interval notation, we can express them as separate intervals and then combine them using the union symbol (∪):

Interval 1: (-∞, 7.1)

Interval 2: (7.9, +∞)

Combining these intervals, the solution in interval notation is:

(-∞, 7.1) ∪ (7.9, +∞)

f(1) = 10

Given f(x) = 3x + 7

To find f(1), replace x by 1 in the equation above

f(1) = 3(1) + 7

= 3 + 7

= 10

Answer:

Distance = 3√13

Step-by-step explanation:

\((-1 ,0)=(x_1 ,y_1)\\(8,6)=(x_2 , y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ \\d = \sqrt{(8-(-1))^2+(6-0)^2}\\ \\d = \sqrt{(8+1)^2 +(6-0)^2}\\ \\d = \sqrt{(9)^2 +(6)^2}\\ \\d = \sqrt{81+36}\\ \\d = \sqrt{117} \\\\d= 3\sqrt{13}\)

The slope in the equation p = 52 + 0.04w represents the rate of change in the water bill payment for each additional unit of water consumed.

Specifically, the slope of 0.04 indicates that for every increase of one unit in the number of water units (w), the water bill payment (p) will increase by 0.04 dollars.

This means that the slope represents the incremental cost of each additional unit of water.

In practical terms, the slope of 0.04 implies that for every additional unit of water consumed, the water bill will increase by $0.04.

This indicates a constant rate of increase in the water bill for each additional unit of water used.

It's important to note that the slope remains constant throughout the equation, suggesting a linear relationship between the amount of water consumed and the corresponding bill payment.

Therefore, The slope, in this case, is the coefficient of the variable w, which is 0.04.

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The probable question may be:

What is the meaning of the slope in the equation p = 52 + 0.04w, which models the relationship between the water bill payment p in dollars and the number of units of water w ?

The length of line segment AB is 5 units.To find the length of line segment AB, we can use the distance formula, which is based on the Pythagorean theorem.

The distance formula calculates the distance between two points (x1, y1) and (x2, y2) in a coordinate plane.

Let's calculate the length of AB using the given coordinates for points A and B:

Coordinates of point A: A = (4, -5)

Coordinates of point B: B = (7, -9)

The distance formula is given by:

\(d = [(x2 - x1)^2 + (y2 - y1)^2]\)

Substituting the coordinates of A and B into the formula:

\(d = [(7 - 4)^2 + (-9 - (-5))^2]\\d =[(3)^2 + (-4)^2]\)

d = √[9 + 16]

d = √25

d = 5

Therefore, the length of line segment AB is 5 units.

The distance formula calculates the straight-line distance between two points in a two-dimensional space. In this case, it determines the distance between points A and B in the coordinate plane. By applying the formula and substituting the given coordinates, we find that the length of AB is 5 units.

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