questions 7 and 8 please HELP!! solving steps would be nice

Answer:

(p • q)(x) =  3x² + 2x + 4

Step-by-step explanation:

(p • q)(x) same as p(q(x)) is the composite function obtained by applying the expression for q(x) in place of x in p(x)

We have
p(x) = x + 4

q(x) = 3x² + 2x

To find (p • q)(x)

wherever there is an x in p(x) substitute with 3x² + 2x

(p • q)(x)   =  x + 4

                =  (3x² + 2x) + 4

                =   3x²  + 2x + 4

Each angle in a regular polygon with 5 sides measures 108 degrees.

A polygon is a closed shape with straight sides. A regular polygon is a polygon where all sides are of equal length and all angles are of equal measure.

To find the measure of each angle in a regular pentagon, we can use the formula:

angle measure = (n-2) x 180 / n

where n is the number of sides.

Substituting n=5 into the formula gives:

angle measure = (5-2) x 180 / 5

Subtract the terms

= 3 x 180 / 5

= 540 / 5

Divide the numbers

= 108 degrees

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Answer:

h = 12 feet

Step-by-step explanation:

using the right triangle shown in the diagram.

the base of the triangle is half the measure of the base of the square side.

then base of triangle = [tex]\frac{1}{2}[/tex] × 32 = 16 feet and hypotenuse = 20 feet

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

h² + 16² = 20²

h² + 256 = 400 ( subtract 256 from both sides )

h² = 144 ( take square root of both sides )

h = [tex]\sqrt{144}[/tex] = 12

the height h of the pyramid is 12 feet

The required coefficient of y in  [tex](3xy + 2)^4[/tex] is 96x.

The binomial expansion is a formula for expanding a binomial expression of the form [tex](a + b)^n\\[/tex], where "a" and "b" are constants and "n" is a positive integer. The expansion gives the coefficients of each term in the expansion.

Here,
We can use the binomial theorem to expand the expression,

[tex](3xy + 2)^4 = C(4,0) (3xy)^4 (2)^0 + C(4,1) (3xy)^3 (2)^1 + C(4,2) (3xy)^2 (2)^2 + C(4,3) (3xy)^1 (2)^3 + C(4,4) (3xy)^0 (2)^4[/tex]

where C(n,k) represents the number of combinations of k objects that can be chosen from a set of n objects.

The coefficient of y in the fourth term is given by the coefficient of ([tex]3xy)^1 (2)^3[/tex]. That is, we need to find the coefficient of y in the term:

[tex]C(4,3) (3xy)^1 (2)^3 = 4 * 3xy * 2^3 = 96xy[/tex]

Therefore, the coefficient of y in  [tex](3xy + 2)^4[/tex] is 96x.

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Answer:

w² + 5w - 7

b = 5

c = -7

Step-by-step explanation:

(10w + 3)(w - 1) - (2 - 3w)² (distribute)

10w² - 10w + 3w - 3 - (2 - 3w)² (combine like terms)

10w² - 7w - 3 - (2 - 3w)² (expand (2 - 3w)²)

10w² - 7w - 3 - ((2 - 3w)(2 - 3w)) (distribute)

10w² - 7w - 3 - (4 - 6w - 6w + 9w²) (combine like terms)

10w² - 7w - 3 - (4 - 12w + 9w²) (distribute the negative)

10w² - 7w - 3 - 4 + 12w - 9w² (combine like terms)

w² + 5w - 7

Therefore, b = 5 and c = -7.

The radius of the circle is solved to be

The radius of the circle is using the formula for length of arc

= theta / 360 * 2πr

For angles in radian we have that

= theta * radius

Form the problem we have that

arc length is 11π/3

theta = 11π/6 radians

hence

11π/3 = 11π/6 * radius

radius = 2

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Answer: c = 54

Step-by-step explanation:

c/6 = 9

c/6*(6) = 9*6

c = 54

Answer: c = 54

Step-by-step explanation:

c/6 = 9

you then multiply c/6 by it's denominator, which in this case 6. What you do on one side, you have to do to the other.

6 · c/6 = 9 · 6

Then you multiply everything, 6 cancels out denominator 6 which leaves C and 9 turns into 54. Meaning c equals 54.

c = 54

To check, you can replace c with 54 in your original equation.

54/6

54÷6 = 9

Answer:

12 feet

Step-by-step explanation:

Let h be the height of the tree. We set up and solve this proportion:

[tex] \frac{h}{24} = \frac{3}{6} [/tex]

[tex]6h = 72[/tex]

[tex]h = 12[/tex]

The probability of drawing an even number and then a diamond out of the deck is 9. 8 %

The probability of drawing an even number out of a standard deck of cards is :

= Number of even numbers / Number of total numbers

= 20 / 52

= 5 / 13

The probability of drawing a diamond, assuming the even picked was not a diamond, is :

= Number of diamond cards / 51 cards

= 13 / 51

The probability of both :

= 5 / 13 x 13 / 51

= 9. 8 %

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Full question is :

What is the probability of drawing an even number then drawing a diamond out of the deck.

Answer:

The probability that the first two chocolates Bob eats will have almonds is 5/51 or 9.8% (nearest tenth).

Step-by-step explanation:

Given that Bob has a box of chocolates containing 6 chocolate covered almonds, 4 chocolate covered peanuts, and 8 plain chocolates, the total number of chocolates in the box is:

[tex]\implies \sf Total=6 + 4 + 8 = 18[/tex]

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

Therefore, the probability that the first chocolate Bob eats will have almonds is:

[tex]\implies \sf P(first\;almond)=\dfrac{6}{18}[/tex]

As Bob has eaten one almond chocolate there are now 5 chocolate covered almonds left and a total of 17 chocolates.  Therefore, the probability that the next chocolate Bob eats will have almonds is:

[tex]\implies \sf P(second\;almond)=\dfrac{5}{17}[/tex]

To find the total probability for two or more events, multiply the probabilities.  Therefore, the probability that the first two chocolates Bob eats will have almonds is:

[tex]\begin{aligned}\implies \sf P(first\;almond)\;and\;P(second\;almond) & =\dfrac{6}{18} \times \dfrac{5}{17}\\\\ &=\dfrac{30}{306}\\\\&=\dfrac{5}{51}\\\\&=0.0980392...\\\\&=9.80392...\%\end{aligned}[/tex]

Therefore, the probability that the first two chocolates Bob eats will have almonds is 5/51 or 9.8% (nearest tenth).

Answer:

Below

Step-by-step explanation:

Since it is a QUADRATIC  it should be

3x^2 - 75 = 0    divide through by 3 to get

x^2 - 25 = 0       then

x^2 = 25

x = ±5

Answer:

67°

Step-by-step explanation:

Sum of the interior angles of a triangle = 180

To find x, set the sum of the supplementary angles to the 3 shown angles (x-6, x+9, x) equal to 180:

180 = (180-x+6) + (180-x-9) + (180-x)

180 = 536 - 3x

-357 = -3x

x = 119

119 - 6 = 113    this is the angle supplementary to ∠LMN, therefore:

m∠LMN = 180 - 113 = 67°

From the given information provided, the total cost of olivia membership fee and her car wash is $82.

The membership fee is a one-time cost of $40.00. To calculate the cost of three car washes, we can simply multiply the cost per car wash by the number of car washes:

3 car washes x $14.00 per car wash = $42.00

So the total cost for Olivia's membership fee and three car washes would be:

$40.00 (membership fee) + $42.00 (cost of three car washes) = $82.00

Question - Olivia likes to go to her local car wash because she is a premier member there. Her membership fee costs $40. 00 and that membership allows her to get her car washed for $14. 00 every visit. What would be the cost of Olivia's membership fee and three car washes?

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Answer:

Therefore, the influencer would earn $52 for a video with 1 million views.

Step-by-step explanation:

The method of paying off the credit card that will take the longest period of time is B. Paying the minimum balance each month.

Paying the minimum balance each month will take the longest period of time to pay off the credit card. The minimum payment is typically a small percentage of the outstanding balance, which means that it will take a longer time to pay off the entire balance.

Additionally, interest charges will continue to accrue on the remaining balance, which can increase the total amount owed over time. Making fixed payments each month and snowballing payments according to the highest interest rate or the lowest balance can help to pay off the credit card more quickly.

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Linear Interpolation Calculator is a free online tool that shows the interpolated point for specific coordinates, also termed as online calculator.

It allows users to interpolate (interpolation is a mathematical technique for estimating any value between two known points) data points between the sets(two sets) of points or coordinates.

Take the two known points and calculate the value of the point that lies between them. This has been used in as many engineering applications as estimating the value of a point on a graph or table. This calculator helps in estimating the value of a point that lies between two known points on a line.

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We can say that a and b are identical in absolute value if a and b are nonzero integers such that a divides b (a | b) and b divides a (b | a). That is to say, a =± b.

The transitive property of divisibility serves as evidence for this. We know that there are numbers k and l such that b = ak and a = bl exist if a | b and b | a. We obtain a = alk by substituting the expression for b into the second equation. We can divide both sides by a to get l = 1/k because an is not zero. Given that k and l are both integers, they must both either be 1 or -1. B Equals ak if k = 1, else then b = ak = a(1) = a, and if k = -1, then b = ak = a(-1) = -a. In either case, we have shown that a = ±b.

So if a and b are nonzero integers such that a divides b and b divides a, then we can conclude that a and b have the same absolute value, but possibly opposite signs.

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Answer:

[tex]y = \frac{Pa}{b} - za[/tex]

Step-by-step explanation:

See picture below :)

The speed of 50 mph is equivalent to 80.47 km/h.

Mph is an abbreviation for miles per hour, and it is a unit of measurement commonly used in the United States. On the other hand, km/h stands for kilometers per hour, and it is a unit of measurement commonly used in most other countries.

To convert 50 mph to km/h, we need to use a conversion factor that relates the two units.

The conversion factor we need to use in this case is 1 mile = 1.60934 kilometers. This means that for every mile covered, there are 1.60934 kilometers covered. To convert 50 mph to km/h, we simply need to multiply 50 by the conversion factor, as shown below:

50 mph x 1.60934 km/mi = 80.47 km/h

Therefore, 50 mph is equivalent to 80.47 km/h. This means that if you were driving at 50 mph in the United States, you would be traveling at a speed of 80.47 km/h if you were to convert to km/h in another country.

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The number of ways two names can be chosen from 76 in a raffle where only one entry is allowed is 3,025.

This can be calculated by using the combination formula: nCr = n!/(r!(n-r)!), where n is the total number of names (76) and r is the number of names to be chosen (2). The calculation for the same is written out below:

nCr = 76!/(2!(76-2)!)

= 76!/(2!*74!)

= 3,025.

This means that there are 3,025 possible combinations of two names that can be chosen from the 76 names if only one entry is allowed per person.

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Answer:

x = 50°

d = 40°

Step-by-step explanation:

  Quadrilaterals are four-sided polygon and the sum of all the interior angles is 360°

      Sum of all angles of quadrilateral = 360°

                    60° + x + 3x + 2x = 360

                                  60 + 6x = 360

Subtract 60 from both sides,

                                          6x = 360 - 60

                                          6x = 300

Divide both sides by 6

                                            x = 300 ÷ 6

                                            x = 50°

b)  120° + 110° + 90° + d= 360°

                       320 + d  = 360

   Subtract 320 from both sides,

                                  d = 360 - 320

                                  d = 40°

The dimensions are as follows

14

x = 21

GK = 167

HJ = 98

HGJ = 159

GKJ = 201

15.

x = 9

AD = 108

BC = 23

DC = 139

DCB = 162

The value of x is solved using the concept of angles in a point and this is 360 degrees

Figure 14

9x - 22 + 61 + 5x - 7 + 34 = 360

collecting like terms

9x + 5x  - 22 + 61  - 7 + 34 = 360

solving for x

14x + 66 = 360

14x = 360 - 66

x = 294 / 14

x = 21

GK = 9x - 22 = 9 * 21 - 22 = 167

HJ = 5x - 7 = 5 * 21 - 7 = 98

HGJ = GH + HJ = 61 + 98 = 159

GKJ = GK + KJ = 167 + 34 = 201

15.

12x + 17x - 14 + 2x + 5 + 90 = 360

collecting like terms

12x + 17x + 2x - 14 + 5 + 90 = 360

solving for x

31x + 89 = 360

31x = 360 - 81

x = 279 / 31

x = 9

AD = 12x = 12 * 9 = 108

BC = 2x + 5 = 2 * 9 + 5 = 23

DC = 17x - 14 = 17 * 9 - 14 = 139

DCB = DC + CB = 23 + 139 = 162

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In reference to the given question, the pairs of polygons that  are congruent is  pairs 1 and 3. Hence, the correct answer is D, pairs 1 and 3.

Congruent polygons are polygons that have the same size and shape.

Pair 1 has two same L-shaped shapes, which are not congruent to any other pair.

Pair 2 has two T-shaped shapes with unequal height, which are not congruent to any other pair.

Pair 3 has two same triangles, which are congruent to each other.

Pair 4 has two unequal triangles, which are not congruent to each other or to any other pair.

Therefore, the only pairs of polygons that are congruent are pair 3, which has two same triangles, and pair 1, which has two L-shaped shapes that are the same. So the correct answer is D, pairs 1 and 3.

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The length of the guy wire is approximately 21 feet

From the question, we are to calculate the length of the guy wire.

To calculate the length of the guy wire,

First, we will determine the height of the tower.

Let the height of the tower be h

From the given diagram, we can write that

h/(9 +4) = 5/4

h/13 = 5/4

h = (13×5)/4

h = 65/4

h = 16.25 feet

Let the length of the guy wire be l

Then,

From the Pythagorean's theorem we can write that

l² = 16.25² + (9+4)²

l² = 264.0625 + 13²

l² = 264.0625 + 169

l² = 433.0625

l = √433.0625

l = 20.81015

l ≈ 21 feet

Hence, the length is approximately 21 feet

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The proportion of sampled smokers that like risky things is 0.555.

The propotion of smokers that like risky things will be obtained by dividing the total number of smokers that like risky things by the total number of boys that were sampled.

To obtain this, we will have

Total number of smokers that like risky things= 45

Total number of smokers that don't like risky things = 36

Total number of smokers = 81

So, 45/81

= 0.555

Since we are asked to keep the result in decimal form, we will divide the figure to obtain 0.555.

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Inches to decimal is the conversion used in converting inches to decimal feet. So 1 inch = 0.0833 decimal feet.

By multiplying or dividing, a conversion factor aids in changing one set of units to another. It is the formula necessary to convert a measurement from one unit system to another unit system of the same measurement.

The conversion of inches to decimals is important in the conversion of feet. To convert inches to decimal of foot, multiply the given inches value by  0.0833. That is 1 inch = 0.0833 decimal feet. For example, 6 inches is converted as 6×0.0833=0.4998 decimal feet.

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Note that the prompt is geared at testing the ability of the to understand certain vocabulary terms. The terms are given as follows:

The completed paragraphs are given below.

The first paragraph is completed as follows:

When Dr. Carter is not fulfilling his duties as the professor of paleontology at Ganton College, he is in the jungles of South America supervising excavations of ancient creatures. During the last dig, Dr. Carter recoiled when a poisonous snake tried to bite him. Now he wears tall boots and gloves to obviate the risk of dangerous animals endemic to the region.

He will definitely elicit the need for such safety measures. Some of the incoming scientists will accuse him of self-aggrandizement despite the fact that the sociable doctor always avoids using too much panache when speaking about safety; he'll flaunt his amazing findings when he returns to the campus at the end of the summer. He can put his bombast to better use in the classroom.

The second paragraph is completed as follows:

Baker deigned to give a semi-friendly nod to his Nazi captors, and he immediately suffered the consequences. Baker then endured the loud paroxysm of his cellmates: "What was that? What, are you working for them, too?"

He understood their paranoia. Just weeks before, a(n) mendacious rebel captive had revealed the escape plan to the guard. The prisoners, including Baker, had to abandon months of secrecy and labor that went into the construction of the tunnel. They had not yet regrouped; most of the saturnine prisoners simply lay in their cells, defeated.

Baker sat against the wall and thought about his capture. He had misused the shibboleth that the Nazis used to identify foreign spies. and the lack of orthography on his forged travel documents instantly signaled that he was not the German officer he claimed to have been. They must need information, he reasoned, or they would have executed him by now.

The definition of terms are given as follows:

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Interval notation is a way of representing a range of values on a number line. It is written using brackets and parentheses to indicate whether the endpoints are included or excluded from the interval.

For example, the interval notation for the range of values between 1 and 5 (inclusive) would be [1, 5]. The square brackets indicate that both 1 and 5 are included in the range.

If the endpoints are excluded, we use parentheses. For instance, the interval notation for the range of values between 1 and 5 (excluding 1 and 5) would be (1, 5).

In general, we use square brackets for closed intervals (where the endpoints are included) and parentheses for open intervals (where the endpoints are excluded).

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