6. For each expression, write an equivalent expression by applying the distributive
property.
a. (y + 4)(y + 7)
b. (y + 3)(3-5)
c. (v - 6)²

The total surface area of the given pyramid is: 95 ft²

To get the surface area of the given pyramid, we will find the individual areas of all surfaces and add up to get the total surface area.

Formula for area of a triangle is:

A = ¹/₂bh

where:

b is base

h is height

Formula for area of a rectangle is:

A = Length * Width

Thus:

Total surface area of pyramid = 4(¹/₂ * 5 * 7) + (5 * 5)

Total surface area of pyramid = 70 + 25

Total surface area of pyramid = 95 ft²

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The measure of angle QRS in triangle QRS is 56.8 degrees.

To find the measure of angle QRS in triangle QRS, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.

We know that:

- The measure of angle RSQ is 48.2 degrees

- The measure of angle SQR is 75 degrees

Let x be the measure of angle QRS. Then, we can write:

RSQ + SQR + QRS = 180

Substituting the known values, we get:

48.2 + 75 + x = 180

Simplifying and solving for x, we get:

x = 180 - 48.2 - 75x = 56.8

Therefore, the measure of angle QRS in triangle QRS is 56.8 degrees.

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Answer:

To many questions, and too many numbers

Step-by-step explanation:

Answer:

28 in²

Step-by-step explanation:

Area of parallelogram = base X vertical height

= 7 X 4

= 28 in²

your wrong you divide by 4 60/4=15 there

1. f(x) =  (2x² + 4x + 4) / x³ = 0; as lim x→∞, and lim x→-∞

2. g(x)  = (2x²  +  4x  + 4)/x² = ∞; as lim x→∞, and lim x→-∞]

3.  h(x)  = (2x²  +  4x  + 4)/x = ∞ as lim x→∞, and -∞ as lim x→-∞.

To find the end behavior of each of the functions, we can take the limit as x approaches infinity and negative infinity.

For  f(x)  = (2x²  +  4x  + 4)/x³;

lim x→∞ (2x² + 4x + 4) / x³ = 0

lim x→-∞ (2x² + 4x + 4) / x³ = 0

f(x) approaches zero as x approaches positive or negative infinity.

For  g(x)  = (2x²  +  4x  + 4)/x²;

lim x→∞ (2x² + 4x + 4) / x² = ∞

lim x→-∞ (2x² + 4x + 4) / x² = ∞

g(x) approaches infinity as x approaches positive or negative infinity.

For  h(x)  = (2x²  +  4x  + 4)/x

lim x→∞ (2x² + 4x + 4) / x = ∞

lim x→-∞ (2x² + 4x + 4) / x = -∞

h(x) approaches infinity as x approaches positive infinity, and negative infinity as well, but with a negative sign.

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The interquartile range for the average of 15 cities is 1.8.

a) X ~ N(9.6, 1.3)

b) X bar ~ N(9.6, 0.13)

c) The probability that one randomly selected city's waterway will have less than 9.3 ppm pollutants can be calculated using the z-score formula: P(X < 9.3) = P(Z < (9.3 - 9.6) / 1.3) = 0.338.

d) The probability that the average amount of pollutants is less than 9.3 can be calculated using the z-score formula: P(Xbar < 9.3) = P(Z < (9.3 - 9.6) / 0.13) = 0.819.

e) The assumption that the distribution is normal is indeed necessary for part d.

f) The IQR for the average of 15 cities can be calculated as follows: Q1 = 8.7 and Q3 = 10.5. IQR = 10.5 - 8.7 = 1.8.

Therefore, the interquartile range for the average of 15 cities is 1.8.

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Answer:True

Lower interest rates reuslt in saving more money.

The conic section of the equation 4x² + 9x +4y² - 36y - 125 = 0 is a circle

The given equation is

4x² + 9xy + 4y² - 36y - 125 =0

The above equation is an illustration of a circle equation

The standard form of a circle equation is

(x - a)² + (y - b)² = r²

Where

(a, b) is the center

r is the radius

While the general form of the equation is

ax² + fx + by² + gy + c =0

Where c is a constant

Recall that, we have

4x² + 9x + 4y² - 36y - 125 =0

This is the general form

We can convert to the standard form as follows

Divide through by 4

x² + 2.25x + y² - 9y - 31.25 =0

Next, we complete the square of the x-terms and the y-terms

For the x-terms, we have

x² + 2.25x = x² + 2.25x + (2.25/2)² - (2.25/2)²

x² + 2.25x = (x + 2.25/2)² - (2.25/2)²

For the y-terms, we have

y² - 9y = y² - 9y + (9/2)² - (9/2)²

y² - 9y = (y - 9/2)² - (9/2)²

Substitute the new x and y terms

So, x² + 2.25x + y² - 9y - 31.25 = 0 becomes

(x + 2.25/2)² - (2.25/2)² + (y - 9/2)² - (9/2)²- 31.25 =0

Evaluate the sum of like terms

(x + 2.25/2)² + (y - 9/2)² - 3377/64 = 0

So, we have

(x + 9/8)² + (y - 9/2)² = 3377/64

Using the above as a guide, we can conclude that the conic section of the equation is a circle

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The salary $50,780 per year is lower than the yearly median.

The yearly median earnings for a male with a bachelor's degree are $40,404 higher than those for a male with a high school diploma.

a. As, the median weekly earnings for males with a bachelor's degree are $1,384.

To convert this to yearly earnings, we can multiply by the number of weeks in a year (52):

= $1,384 x 52

= $71,968

So, the salary $50,780 per year is lower than the yearly median earnings for a male with a bachelor's degree.

b. Now, The yearly median earnings for a male with a high school diploma (no college) are $607 per week. Converting this to yearly earnings:

Yearly median earnings for a male with a high school diploma

= $607 x 52 = $31,564

The difference between the yearly median earnings for a male with a bachelor's degree and a male with a high school diploma is:

= $71,968 - $31,564 = $40,404

So, the yearly median earnings for a male with a bachelor's degree are $40,404 higher than those for a male with a high school diploma.

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The diameter of the second pile of phosphate is found to be approximately 62.6 feet.

The volume of a right circular cone is given by the formula,

V = (1/3)πr²h where volume is V, radius of the base is r, height is h, and π is approximately 3.14159. For the first pile of phosphate,

h = 15.3 feet

d = 48.6 feet

r = d/2 = 24.3 feet

Using the formula for the volume of a cone,

V = (1/3)πr²h

V = (1/3)π(24.3)²(15.3)

V = 24,249.8 cubic feet

For the second pile of phosphate,

h = 15.3 - 3.6 = 11.7 feet

r = ? (to be determined)

Using the same formula for the volume of a cone,

V = (1/3)πr²h

V = (1/3)πr²(11.7)

Since the volume of both piles is the same, we can set the two volume formulas equal to each other,

(1/3)π(24.3)²(15.3) = (1/3)πr²(11.7)

Simplifying,

(24.3)²(15.3) = r²(11.7)

r² = (24.3)²(15.3)/11.7

r = 31.3 feet (rounded to the nearest tenth)

Therefore, the diameter of the second pile of phosphate is d = 2r = 62.6 feet (rounded to the nearest tenth).

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Complete question - As phosphate is mined, it moves along a conveyor belt, falling off of the end of the belt into the shape of a right circular cone, as shown.

Height of the cone is 15.3 feet

Diameter of the base of cone is 48.6 feet

A shorter conveyor belt also has phosphate falling off of the end into the shape of a right circular cone. The height of the second pile of phosphate is 3.6 feet shorter than the height of the first. The volume of both piles is the same. To the nearest tenth of a foot, what is the diameter of the second pile of phosphate?

Answer:

[tex]C = 25.1 \text{ cm}[/tex]

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

[tex]C = \pi d[/tex]

Note: This formula can also be written as [tex]C = 2\pi r[/tex] because [tex]2r = d[/tex].

↓ plugging in the given radius

[tex]C = 8\pi \text{ cm}[/tex]

↓ rounding to the nearest tenth

[tex]\boxed{C = 25.1 \text{ cm}}[/tex]

The reflection rule that maps triangle DEF onto triangle D'E'F' is a reflection across the line that passes through (2,2) and (−1.25,2.75).

A translation is a type of transformation that moves all the points of a figure the same distance and in the same direction.

The shape and size of the figure do not change, only its position in the plane.

(3, 6)--->(1,6)

3-x=1

x=-2

(x-2, y)

To find the reflection rule that maps the triangle D(3, 6), E(-4,-3), F(6, 1) onto its image D'(1, 6), E(8, -3), F'(-2, 1), we need to determine the line of reflection.

In triangle the point where the perpendicular bisectors intersect will be the center of the reflection.

We find that the midpoint of DE is (−0.5,1.5), the midpoint of DF is (4.5,3.5), and the midpoint of EF is (1,−1).

The perpendicular bisectors of DE and DF intersect at (2,2), and the perpendicular bisectors of DE and EF intersect at (−1.25,2.75).

Therefore, the reflection rule that maps triangle DEF onto triangle D'E'F' is a reflection across the line that passes through (2,2) and (−1.25,2.75).

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The measure of <BED = 135 degrees

To determine the value, we need to know the following;

From the information given, we have that;

Angle AED + Angle ACD are on a straight line

Now, susbtitute the values, we have that;

135 + ACD = 180

collect like terms

ACD = 180 - 135

subtract the values

ACD = 45

Then, we have that;

<BED = <ACD + <BEC

Substitute the values

<BED = 45 + 90

<BED = 135 degrees

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Step-by-step explanation:

5 P 5 = 120 ways = 5!

Step-by-step explanation:

OK, 'Brainless'....  the triangle side length rule states that any two sides of a triangle must sum to greater than the remaining side length...

42 + 20 > x        then  12 , 20, 22, 32, 42, 50     will work here

42+x > 20            all of the possibles work here

20 + x > 42         32, 42, 50, 62 and 70 work here

   so   32 and 42 are in all of the lists ....that is your answer

The area of the figure is 183.5 ft².

We have,

The figure has two types of shapes.

Two rectangles and one triangle.

Now,

Area of rectangle = Length x Width

Area of triangle = 1/2 x base x height

Now,

Rectangle 1:

Area = 7 x 5 = 35 ft²

Rectangle 2:

Area = 4 x (4 + 5) = 4 x 9 = 36 ft²

Triangle:

Area = 1/2 x (11 + 4) x 15 = 1/2 x 15 x 15 = 112.5 ft²

Now,

The area of the figure.
= 35 + 36 + 112.5

= 183.5 ft²

Thus,

The area of the figure is 183.5 ft².

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Shakira needs to rent a car for one day and she is trying to decide which car rental company to use. Alpha Car Rental offers a Porsche for $29.17 per day, plus 57 cents per mile. Beta Car Rental also offers the same car for $50.23 per day, plus 44 cents per mile.

To determine which car rental is a better deal, Shakira needs to calculate at what number of miles the prices for both Alpha and Beta Car Rental are the same. To do this, she can use the following equation:

The variable of x is the number of miles. This equation simplifies to x = 21.06 miles. Therefore, at 21.06 miles, Alpha and Beta Car Rental will be the same price.

The set of capacity measures related to cubic meter are ordered from the greatest to the least:

5.5 dam³, 5.480 m³, 5 dam³, 5 dam³, 530 m³, 61 m³

In this problem we need to order a group of capacity measures in cubic meters and its related units from the greateast to the least. To make this we need to understand the following relations:

Now we proceed to order the following set of information:

First, write the set of measures:

5 dam³, 530 m³, 5.480 m³, 5.5 dam³, 5 dam³, 61 m³

Second, convert all measures in cubic decameters into cubic meters:

5.000 m³, 530 m³, 5.480 m³, 5.500 m³, 5.000 m³, 61 m³

Third, order all the set from the greatest to the least:

5.500 m³, 5.480 m³, 5.000 m³, 5.000 m³, 530 m³, 61 m³

Fourth, rewrite the set of measures in its original units:

5.5 dam³, 5.480 m³, 5 dam³, 5 dam³, 530 m³, 61 m³

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(a) The distribution of X ~ N(7.08, 2.29)

(b) The probability of a patron's lunch cost is 0.049

(b) The probability of a group patron's lunch cost is 0.049

(d) The assumption of normal distribution is not necessary

Given that

Mean = 7.08

Standard deviation = 2.29

The distribution of X is represented as

X ~ N(Mean , Standard deviation)

So, we have

X ~ N(7.08, 2.29)

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (6.9379  - 7.08)/2.29 and z = (7.2186 - 7.08)/2.29

Evaluate

z = -0.062 and z = 0.061

So, we have

P = P(-0.062 < z < 0.061)

Evaluate

P = 0.049039

Approximate

P = 0.049

This is same as part (b)

i.e. the probability that the average lunch is between $6.9379 and $7.2186 is 0.049

No, the assumption is not necessary

This is because

The distribution has a sample size less than 25 as required by the central limit theorem

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After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.

To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:

Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)

where:

P = the initial loan amount (in this case, $219,000)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)

b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)

First, we need to calculate the monthly interest rate:

r = 4.5% / 12 = 0.00375 = 0.375%

Next, we can plug in the values to get:

Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)

= $145052.36

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There are 35 different committees that can be formed, each consisting of one man and one woman.

To form the committee consisting of one man and one woman, we need to choose one man from the available seven men and one woman from the available five women.

Number of choices for selecting one man = 7

Number of choices for selecting one woman = 5

To find the total number of different committees that can be formed, we multiply these numbers together:

Total number of committees = 7 × 5

Total number of committees = 35

Therefore, there are 35 different committees that can be formed, each consisting of one man and one woman.

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From the calculation, she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.

We know that we have to consider the restriction that the airline has placed. We have been told that the luggage that have to be packed in this case would have to be less than 22.7 kg.

We would now have to look at all the things that Haley would need to pack so as to determine what can be packed and what can not be packed.

Total luggage  that she has to pack;

Mass of empty suitcase + mass of her clothes + mass of 4 gifts

Total luggage = 5.1 Kg + 14.8 Kg + 4(0.87) = 23.38 Kg

This implies that she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.

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Answer:

Hi!, if you need help right away, chat with a tutor!

Step-by-step explanation:

Jeremy is wrong as I explained below.

As we know,

Thus, as we can see from the figure figure 1 is a rectangle and Figure 2 is a square so,

I do not agree with Jeremy.

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Complete question:

Answer:

98 mm²

Step-by-step explanation:

This parallelogram has a base of 7 and height of 14 mm.

The height is the vertical distance between the two bases

The area = b x h = 7 x 14 = 98 mm²

[tex]\huge\mathcal{\fcolorbox{aqua}{azure}{\red{➳Aɳʂɯҽɾ}}}[/tex]

Refer the attachment for clarity:-

[tex] \colorbox{yellow}{\red{Formula\: Base\: x \:Height= Area}}[/tex]

[tex]\sf{\leadsto 7×14}[/tex]

[tex]{ \red{ \sf 98m {m}^{2} }}[/tex]

______________________________

[tex]\bold{Thank ~you~:)}[/tex]