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What series of transformations would carry trapezoid ABCD onto itself?


(x + 0, y − 4), 90° clockwise rotation, reflection over the y-axis

(x + 0, y − 4), 180° rotation, reflection over the y-axis

(x + 6, y + 0), 90° clockwise rotation, reflection over the x‐axis

(x + 6, y + 0), 180° rotation, reflection over the x‐axis

Answer:

a. [tex]x-y > 0[/tex]

b. [tex]x+y \leq 50[/tex]

c. x=26; y=24 or (24,26)

Step-by-step explanation:

Let x = number of teachers hired.

Let y = number of tutors hired.

Now solving for part a we get

a. Write an inequality that represents the statement that the number of teachers hired must exceed the number of tutors hired.

[tex]x-y > 0[/tex]

solving for part b we get;

b. Write an inequality that represents the statement that the maximum number of teachers and tutors is 50.

[tex]x+y \leq 50[/tex]

solving for part c we get;

c. Choose a point that satisfies the situation, and explain why you chose that number of tutors and teachers.

Now we know that [tex]x-y > 0[/tex] also [tex]x+y \leq 50[/tex]

x=26; y=24

(24,26)

Explanation: To make number of teacher more than number of tutors this is the maximum value we can achieve for the requirement.

a. The inequality x > y represents the statement that the number of teachers hired must exceed the number of tutors hired. b. The inequality x + y ≤ 50 represents the statement that the maximum number of teachers and tutors is 50. c. The point (25, 10) satisfies both inequalities and represents hiring 25 teachers and 10 tutors.

a. To represent the statement that the number of teachers hired must exceed the number of tutors hired, you can write the inequality x > y. This means that the number of teachers, represented by x, must be greater than the number of tutors, represented by y.

b. To represent the statement that the maximum number of teachers and tutors is 50, you can write the inequality x + y ≤ 50. This means that the total number of teachers and tutors hired, represented by x + y, cannot exceed 50.

c. Let's choose the point (25, 10) which represents hiring 25 teachers and 10 tutors. This point satisfies both inequalities: 25 > 10 and 25 + 10 ≤ 50.

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Answer: option A is the correct answer

Step-by-step explanation:

The given triangle is a right angle triangle. This is because one of the angles is 90 degrees. The sum of the other two angles is 90 degrees. To determine sin C, we will apply trigonometric ratio

From the dimensions given and taking C as the reference angle,

Hypotenuse = AC = 17

Adjacent side = BC = 15

Opposite side = AB = 8

Sin# = opposite side / hypotenuse

Since # = C

SinC = 8/17

The value of angle C can be derived by finding Sin^-1(8/17)

Answer:

5/9 yards

Step-by-step explanation:

Just subtract 2/9 from 5/9 to find the difference, which is the answer.

A) State the chain rule for integration

Ans. The chain rule for integration is also known as "  Integration by substitution "

Integration by substitution is taken in order to make integration solve easily in few steps.

For, [tex]I = \int\limits (x+2)^{2} \,dx[/tex]

Instead of expanding term [tex](x+2)^{2}[/tex]

With substitution of  [tex]u = (x+2) [/tex] and [tex]du= 1 dx [/tex]

We simplified the integration as

[tex]I = \int\limits (u)^{2} \, du[/tex]

[tex]I = \frac{(u)^{3}}{3}+C[/tex]

By replacaing value of u=x+2

[tex]I = \frac{(x+2)^{3}}{3}+C[/tex]

B) State the rule of differentiation for the sine function.

Ans. We know that [tex]\frac{d}{dx}Sinx dx = Cosx [/tex]

C) Find the indefinite integral using substitution.

Ans.

Given, [tex]I = \int\limits {\frac{Cos14x}{Sin14x} } \, dx[/tex]

Take y = Sin14x

Differentiating both side

[tex]dy=14Cos14x dx [/tex]

[tex]\frac{dy}{14} = Cos14x\, dx[/tex]

Substituting values in integration,

[tex]I = \int\limits {\frac{Cos14x}{Sin14x} } \, dx[/tex]

[tex]I = \int\limits {\frac{1}{y} } \,\frac{dy}{14} [/tex]

[tex]I = \frac{1}{14}\int\limits {\frac{1}{y} } \,dy [/tex]

[tex]I = \frac{1}{14} lny + C [/tex]

Replacing values in the integration

[tex]I = \frac{1}{14} ln(14Sin14x) + C [/tex]

D)Check your work by taking a derivative of your answer from part C.

Ans.

Answer for Part C is [tex]I = \frac{1}{14} ln(14Sin14x) + C [/tex]

Differentiating the answer

we get,

[tex]=\frac{1}{14}\frac{d}{dx}[ ln(Sin14x) + C]\\=\frac{1}{14}\frac{1}{Sin14x} \frac{d}{dx}(Sin14x)+ \frac{d}{dx}C\\=\frac{1}{14}\frac{1}{Cos14x}(14Cos14x)\\=\frac{Cos14x}{Sin14x} \\ =I[/tex]

Answer:

  7/11

Step-by-step explanation:

Let d represent the original denominator. Then the original numerator is ...

  2d-15

The new numerator is ...

  (2d-15) +5

and the new denominator is ...

  d+7

The ratio of these is 2/3, so we have ...

  [tex]\dfrac{2d-15+5}{d+7}=\dfrac{2}{3}\\\\3(2d-10)=2(d+7) \quad\text{cross multiply}\\\\4d=44 \quad\text{add 30-2d}\\\\d=11\\\\2d-15=2(11)-15=7[/tex]

The original fraction is 7/11.

Answer:.

Step-by-step explanation:

.

Answer:

The proof with the statement is given below.

Step-by-step explanation:

Given:

Construction of angle bisector i.e SP is the bisector of angle RPQ.

To prove:

Δ PWS ≅ Δ PXS

Proof:

In  Δ PWS  and Δ PXS  

∠ WPS ≅ ∠ XPS    …………..{definition of angle bisector}

SP ≅ SP                .......…….{Reflexive property}

PW ≅ XP              ……....….{definition of ≅}

Δ PWS  ≅ Δ PXS  …...........{Side-Angle-Side test i .e SAS}

Angle bisector: A ray divides angle into two equal measures then the ray is called as angle bisector of the bisected angle.

In the construction SP is the bisector of the angle ∠ RPQ

SAS: This test is to prove the triangle congruent when two sides are congruent and angle between that sides should be congruent. then we can say the triangle is congruent by side angle side test.

Answer:

18.63

Step-by-step explanation:

45*115%= 45*1.15 = 51.75

51.75*0.36 = 18.63

Answer:

18.63 dollars.

Step-by-step explanation:

The selling price was  45 + 15% or 45

= 45 + 0.15*45

= 51.75 dollars.

36% of 51.75

=  0.36 * 51.75

=  18.63 dollars  which he had to spend on books.

Answer:

Jay's bread size is 220% of the original size.

Step-by-step explanation:

The question is incomplete.

The complete question is as follows.

Jay is letting her bread rise. After 3 hours,her bread is at 11/5 of its original size. What percent of its original size is jays bread dough?

Solution:

Let the original bread size be = [tex]100[/tex] units

After 3 hours the bread rises = [tex]\frac{11}{5}[/tex] of the original size

New size of bread =  [tex]\frac{11}{5}\times 100=220[/tex] units

Percent of original size the new bread is

⇒ [tex]\frac{New\ bread\ size}{Original\ bread\ size}\times 100[/tex]

⇒ [tex]\frac{220}{100}\times100[/tex]

⇒ [tex]220\%[/tex]

Answer:

[tex]\displaystyle \boxed{66 \times 7}\:7(60 + 6)[/tex]

[tex]\displaystyle \boxed{97 \times 4}\:4(100 - 3)[/tex]

[tex]\displaystyle \boxed{8(4 + 2)}\:32 + 16 = 48[/tex]

[tex]\displaystyle \boxed{5(9 - 6)}\:(5 \times 9) - (5 \times 6)[/tex]

[tex]\displaystyle \boxed{3(4 + 7)}\:(3 \times 4) + (3 \times 7)[/tex]

Step-by-step explanation:

According to the Order of Operations [GEMS\BOMDAS\PEMDAS etc.], you evaluate everything in parentheses first before preceding with your Division & Multiplication and Subtraction & Addition. When you do this, you will know exactly which expression corresponds with its Distributive Property expression.

I am joyous to assist you anytime.

Answer:

36

Step-by-step explanation:

Given:

Length of the cardboard = 27 inches

Width of the cardboard = 72 inches.

Let "x" be side of the square which is cut in each corner.

Now the height of box = "x" inches.

Now the length of the box = 27 - 2x and width = 72 - 2x

Volume (V) = length × width × height

V = (27 - 2x)(72 - 2x)(x)

[tex]V= (1944 -144x -54x + 4x^2)x\\V = (4x^2 - 198x +1944)x\\V = 4x^3 -198x^2 +1944x[/tex]

Now let's find the derivative

V' = [tex]12x^2 - 396x + 1944[/tex]

Now set the derivative equal to zero and find the critical points.

[tex]12x^2 - 396x + 1944[/tex] = 0

12 ([tex]x^2 - 33x + 162[/tex]) = 0

Solving this equation, we get

x = 6 and x = 27

Here we take x = 6, we ignore x = 27 because we cannot cut 27 inches since the entire length is 27 inches.

So, the area of the square = side × side

= 6 inches × 6 inches

The area of the square = 36 square inches.

Answer:

Omar can fill 28 containers

Step-by-step explanation:

Omar have 7 pounds of cherries, each pound need 4 containers because each one only hold of [tex]\frac{1}{4}\\[/tex] pound, now we multiplicate 7 pounds with 4 container for each one and we get 28 containers.

[tex]Number containers = \frac{7 pounds}{\frac{1}{4}pounds } = 28[/tex]

Answer: Slope is 1/5

Step-by-step explanation:

Slope, m is expressed as

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the graph given, we would pick points for y2 and a corresponding x1 and also pick y1 and a corresponding x1

y2 = 4

y 1 = 3

x2 = 5

x1 = 0

Slope = (4-3)/(5-0) = 1/5

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

→The slope of the line given on the graph is [tex]\frac{1}{5}[/tex].

→You can tell because following the rise over run, the line goes up 1 unit, then to the right, 5 units.

→Since it is going to the right, it stays positive. However, if it were to go left, the 5 would be negative.

Answer:

18,471.6 cubic inches of wax will be needed

Step-by-step explanation:

We want the volume that will be required for 210 candles. We first find the volume of 1 candle by using volume of cylinder formula. Then multiply that answer by 210 to find volume of wax needed to make 210 such candles.

Volume of Cylinder is given by the formula:

[tex]V=\pi r^2 h[/tex]

Where

r is the radius

h is the height

Given,

r = 2 in

h = 7 in

We substitute and find 1 candle volume:

Volume of 1 candle = [tex]\pi r^2 h = \pi (2)^2 (7) = 87.96[/tex]

Hence,

Volume of 210 candles = 87.96 * 210 = 18,471.6 cubic inches

Answer:

18,471.6

Step-by-step explanation:

Answer: Length = 9 meters

Width = 6 meters

Step-by-step explanation:

The diagram of the playground is shown in the attached photo

The width of a small playground 3 meters less than the length of the playground.

Length of playground = L meters

Width of playground = (L-3) meters

The area of the playground is 54 square meters.

Area = L × W

54 = L(L - 3)

54 = L^2 - 3L

L^2 - 3L - 54 = 0

L^2 + 6L - 9L- 54 = 0

L(L+6) - 9(L+6) = 0

(L-9)(L+6) = 0

L -9 = 0. or L+6 = 0

L = 9 or L = -6

L cannot be negative so, the length of the playground is 9 meters

The width of the playground is

L-3 = 9-3 = 6 meters

Answer:

b

Step-by-step explanation:

Answer:

6 of the 8 oz one

Step-by-step explanation:

you need to buy 6 of the first to get 48 oz, and the price would be 9.54. you need 4 for the next with the price at 9.96. you need 3 for 16 oz and the price is 9.89. compare all of them and you get 9.54 as the lowest, which was the 8 oz one

Answer:

Step-by-step explanation:

Given Andrew has $600 for materials and can make 18 pieces of furniture, you want to know the number of each kind that maximizes profit if each bookcase costs $20 and gives $60 profit, while each TV stand costs $40 and gives $100 profit.

If x and y represent the numbers of bookcases and TV stands Andrew builds, respectively, then he wants to ...

  maximize 60x +100y

  subject to ...

The attached graph shows the solution space for these constraints. The profit is maximized at the vertex of the space where the profit function line is farthest from the origin. Andrew maximizes his profit by building ...

Andrew needs to solve a linear programming problem to find how many bookcases and TV stands he should manufacture for optimal profit. This is done by setting up and solving inequalities representing Andrew's time and material cost constraints, graphing the feasible region, and finding the point(s) in this region that yield the highest profit.

This question deals with the topics of linear programming and profit maximisation. Here, Andrew has to decide how much of each type of furniture, bookcases or TV stands, he should produce to maximise profit while considering time and material cost constraints.

From the given conditions, we get two inequalities. The first related to time says that the total number of bookcases and TV stands is less than or equal to 18: let bookcases be x, TV stands be y, thus we have x + y <= 18. The second involving the cost of material says that the total cost spent on materials for both products does not exceed $600: thus, we also have 20x + 40y <= 600.

You can graph these inequalities on the x-y plane to get a visual representation of the possibilities.

Finally, to find the optimal solution (i.e., the highest profit), you calculate the profit function P = 60x + 100y for each point in the feasible region and select the point that provides the highest profit.

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Answer:

The angles formed on line b when cut by the transversal are congruent with ∠2 are [tex]\angle{6}\text{ and }\angle{7}[/tex]

Step-by-step explanation:

Consider the provided information.

If transversal line crossed by two parallel lines, then, the corresponding angles and alternate angles are equal .

The angles on the same corners are called corresponding angle.

Alternate Angles:  Angles that are in opposite positions relative to a transversal intersecting two lines.

∠2 and ∠6 are corresponding angles

Therefore, ∠2 = ∠6

∠2 and ∠7 are alternate exterior angles

Therefore, ∠2 = ∠7

Hence, the angles formed on line b when cut by the transversal are congruent with ∠2 are [tex]\angle{6}\text{ and }\angle{7}[/tex]

Answer: a) 12/51

b) 3/51

Step-by-step explanation:

we are assuming the cards are dealt without replacement

a) given that the first card is heart, we are left with 12 hearts and 51 cards in total

Therefore, the probability that the second card is heart is:

P2 = 12/51

b) probability that the two cards are hearts is given by:

P = 13/52 * 12/51

P = 3/51

(a) The chance that the second card is a heart given the first card is a heart is [tex]\(\frac{12}{51}\)[/tex].

(b) The chance that the first card is a heart and the second card is a heart is [tex]\(\frac{1}{17}\)[/tex].

(a) To find the probability that the second card is a heart given that the first card is a heart, we use conditional probability. There are 13 hearts in a standard deck of 52 cards. Once the first heart is drawn, there are 12 hearts left and the total number of cards left is 51. The probability of drawing a heart as the second card, given that the first card is a heart, is the number of remaining hearts divided by the total number of remaining cards.

[tex]\[ P(\text{second card is a heart | first card is a heart}) = \frac{12}{51} \][/tex]

This simplifies to:

[tex]\[ P(\text{second card is a heart | first card is a heart}) = \frac{4}{17} \][/tex]

(b) To find the probability that both the first and second cards are hearts, we multiply the probability of drawing a heart first by the probability of drawing a heart second given that the first card is a heart. The probability of drawing a heart first is [tex]\(\frac{13}{52}\)[/tex], which simplifies to [tex]\(\frac{1}{4}\)[/tex]. We already calculated the probability of drawing a heart second given a heart first as [tex]\(\frac{12}{51}\) or \(\frac{4}{17}\)[/tex].

[tex]\[ P(\text{first card is a heart and second card is a heart}) = P(\text{first card is a heart}) \times P(\text{second card is a heart | first card is a heart}) \][/tex]

[tex]\[ P(\text{first card is a heart and second card is a heart}) = \frac{1}{4} \times \frac{4}{17} \][/tex]

[tex]\[ P(\text{first card is a heart and second card is a heart}) = \frac{1}{17} \][/tex]

Thus, the probability that the first card is a heart and the second card is a heart is [tex]\(\frac{1}{17}\)[/tex].

Answer:

Step-by-step explanation:

Let x = the number of pounds of oranges in the full box.

On a field trip, students ate 3/10 of a box of oranges. This means that the students ate 3/10 × x = 3x/10 pounds of oranges.

Altogether they ate 6 pounds of oranges. This means that

3x/10 = 6

3x = 6×10

3x = 60

x = 60/3 = 20

The full box contained 20 pounds of oranges

Each tenth of the model is 2 pounds because a tenth of 20 pounds is 20/10 = 2 pounds

Answer:

First you would translate triangle ABC to the right . next you would then translate triangle ABC up . Last you would rotate triangle ABC clockwise and matched angle A with angle D.

Step-by-step explanation:

Answer:

Option C: Probability distribution for a random variable

Step-by-step explanation:

A probability distribution for a random variable describes the range and relative likelihood of all possible values for a random variable.

The probability distribution of a random variable is explained as a list of all the possible values of the variable and their probabilities. These probabilities sum up to 1.

Final answer:

The correct term is ' (c) probability distribution for a random variable,' represented by a probability density function for continuous random variables or a probability distribution function for discrete random variables.

Explanation:

The term that describes the range and relative likelihood of all possible values for a random variable is a (c) probability distribution for a random variable. For a continuous random variable, this is represented by a probability density function (pdf), which shows the likelihood of any given value or range of values. The pdf is depicted graphically, and the area under the curve represents the probability for a given range of values. The total area under the pdf curve is always one, signifying that the sum of all probabilities is one. Also, for a discrete random variable, the probability distribution function (PDF) lists all possible values and their associated probabilities, following the rules that each probability is between zero and one inclusive, and the sum of all probabilities equals one.

Answer:

A. 18x8 is 144 then divided by 2 is 72

Answer:

Step-by-step explanation:

Answer:

a) mean= 158.4 , standard deviation = 3.394

b)  Best option : B. Yes, since the original population is normal, the sampling distribution of the sum will also be approximately normal.

c)  P(X>160) = P(Z>0.471) = 1-P(Z<0.471) = 0.3188

Step-by-step explanation:

1) Notation

n = sample size = 8

[tex] \mu [/tex] = population mean = 19.8

[tex] \sigma [/tex] = population standard deviation = 1.2

2) Definition of the variable of interest

Part a

The variable that we are interested is [tex] \sum x_i  [/tex] and the mean and the deviation for this variable are given by :

E([tex] \sum x_i [/tex]) =  [tex] \sum E(x_i) [/tex] = n [tex] \mu [/tex] = 8x19.8 = 158.4

Var([tex] \sum x_i [/tex]) =  [tex] \sum Var(x_i) [/tex] = n [tex] \sigma^2 [/tex]

Sd([tex] \sum x_i [/tex]) =   [tex] \sqrt{n \sigma^2} [/tex] = [tex] \sqrt(8) [/tex]  x 1.2 = 3.394

Part b

For this case the populations are normal, then the distribution for the sample ([tex] \sum x_i [/tex])  is normal too.

Based on this the distribution for the variable X would be normal, so the best option should be:

B. Yes, since the original population is normal, the sampling distribution of the sum will also be approximately normal.

Part c

From part a we know that the mean = 158.4 and the deviation = 3.394

The z score is defined as

Z = (X -mean)/ deviation = (160-158.4)/ 3.394 = 0.471

Then we can find the probability P(X>160) = P(Z>0.471) = 1-P(Z<0.471) = 0.3188

Answer:

Step-by-step explanation:

Total cost of the two T-shirts that you purchased is $25. The sales tax on the T-shirts is 8%. This means that the additional amount that you will pay on the T shirt is

25/100 × 25 = 0.25 × 25 = $6.25

The new cost of the T shirt would be the sum of the original cost and the value of the sales tax. Therefore,

New cost = 25 + 6.25 = $31.25

You have a $30 gift card from Amazon. The new cost of the shirts is higher than that value of the gift card. So the gift card will not cover the cost of the T shirts

To determine if the gift card will cover the cost of the two T-shirts, calculate the sales tax and subtract it from the total cost. The gift card will cover the cost if the remaining balance is positive.

To determine if your gift card will cover the cost of the two T-shirts, you need to calculate the cost of the sales tax and subtract it from the total cost of the T-shirts. First, convert the sales tax percentage to decimal form by dividing it by 100 (8% becomes 0.08). Then, multiply the total cost of the T-shirts (which is $25) by the sales tax rate to find the amount of sales tax. Multiply $25 by 0.08 to get $2. Next, subtract the sales tax amount from the total cost of the T-shirts: $25 - $2 = $23. Finally, determine if the gift card covers the cost by comparing it to the final cost: $30 - $23 = $7.

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Answer:

  x < -7

Step-by-step explanation:

Eliminate parentheses:

  3x -12 > 5x +2

  -14 > 2x . . . . . . . . . add -2-3x

  -7 > x . . . . . . . . . . . divide by 2

Any value of x less than -7 is in the solution set.

Final answer:

The linear speed of the satellite is approximately 434.71 km/min. In kilometers per hour, it is approximately 26082.6 km/hr. In miles per hour, it is approximately 16206.26 miles/hr.

Explanation:

To find the linear speed of the satellite, we need to calculate the circumference of the circular orbit.

The radius of the orbit is the sum of the radius of the Earth and the altitude of the satellite:
Radius of orbit = Radius of Earth + Altitude of satellite = 6378 km + 1250 km = 7628 km

The circumference of a circle is given by the formula:
Circumference = 2π * Radius

Substituting the radius of the orbit into the formula:
Circumference = 2π * 7628 km ≈ 47818.16 km

In 110 minutes, the satellite completes one revolution around the Earth. Therefore, its linear speed is:
Linear speed = Circumference / Time taken = 47818.16 km / 110 minutes ≈ 434.71 km/min

To convert the linear speed from kilometers per minute to kilometers per hour, multiply by 60:
Linear speed = 434.71 km/min * 60 min/hr ≈ 26082.6 km/hr

To convert the linear speed from kilometers per hour to miles per hour, divide by the conversion factor of 1.60934:
Linear speed = 26082.6 km/hr / 1.60934 ≈ 16206.26 miles/hr

In the given arithmetic sequence, the ratio of the first term to the second term is 1:2.

The problem is based on the properties of the arithmetic sequence. To solve it, we use the formula for the sum of an arithmetic sequence: S = n/2*(a + l), where n is the number of terms, a is the first term, and l is the last term.

From the question, we know that 4 times the sum of the first five terms equals the sum of first ten terms. Therefore, 4 * (5/2 * (a + a + 4d)) = 10/2 * (a + a + 9d), where d is the common difference. Simplifying, we find that the ratio of the first term a to the second term (a + d) is 1:2.

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Answer:

Q=95, P= 52.5

Step-by-step explanation:

The profit maximizing level of output in monopolies is reached when the marginal cost is equal to the marginal revenue. This is also the profit maximizing rule in perfect competition, the difference between both is that is perfect competition the marginal revenue is equal to the price while in monopolies, the demand curve is often above the marginal revenue curve, then the actual price (defined by the demand curve) is often higher than the marginal revenue price.

For this problem the profit maximizing level of output is:

MC=MR

5=100-Q

Q=95

Because monopolies decide the selling price based on the demand curve, you should replace this quantity in the demand curve equation:

95=200-2P

95-200/2=-P

P= 52.5

When output is set so that marginal revenue and marginal cost are equal in this economics dilemma, the monopolist will make the most money. That would be at a manufacturing level of 95 units in this instance.

When establishing output, a monopolist in economics attempts to maximize profit by ensuring that Marginal Cost (MC) and Marginal Revenue (MR) are equal. We must assign MR to MC in this case given that MR = 100 - Q and MC = 5. Therefore, 100 - Q = 5, giving Q=95. In order to maximize its profit, the monopolist should create 95 units of the good.

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Answer:

a. See attachments

B. 163630.2ft

C. 147056.70ft

D. 49205.4ft

Step-by-step explanation:

Check attachments for details

Angle a.. Angle of dep to beginning of runway

Angle b... Angle of del to end of runway

AD... Altitude of plane

DB..... Ground distance before touch down

AC... Air distance travelled until touch down on the near end of runway