Theresa has two brothers,Paul and Steve, who are both the same height. Paul says he is 16 inches shorter than 1 1/2 times Theresa's height. Steve says he's 6 inches shorter than 1 1/3 times Theresa's height. If they're both right, how tall is Theresa ?​

Answer:

A) The number of wallpapers needed to cover the walls is 6 double roll wall papers

B) The number of wall paper border rolls needed is 3 rolls

Step-by-step explanation:

A) The given parameters are;

The dimensions of the room are 9 ft. by 12 ft. by 8 ft. high,

The area one double role wallpaper covers = 60 ft.²

Therefore, we have;

The area of the room wall = 12 × 8 × 2 + 9 × 8 × 2 = 336 ft²

The number of double rolls of wallpaper to be used = Area of wall/(area of wallpaper) = 336/60 = 5.6

Therefore, given that the wall papers are sold in single units, we round up to the next whole number of units to get;

The number of wallpapers needed to cover the walls = 6 double roll wall papers

B) The borders of a wallpaper are installed parallel (and installed along) to the ceiling line

Therefore, the amount of wallpaper border required is given as follows;

Wall paper border length required = 2 × Length of the room + 2 × Width of the room

∴ Wall paper border length required = 2 × 9 ft. + 2 × 12 ft. = 42 ft.

The size of each wall paper border sold = 5 yd. = 15 ft.

Therefore;

The number of wall paper border rolls required = 42 ft./(5 yd.) = 42 ft./(15 ft.) = 2.8 rolls

Therefore, we round up to get the number of wall paper border rolls needed as 3 rolls of wall paper borders.

The probability that a person did not see the ad given that they did not purchase the game is 0.146.

Let A be the event that a person has seen the advertisement, and let B be the event that a person has not purchased the game. We are asked to find the probability P(A' | B), which is the probability that a person did not see the ad given that they did not purchase the game.

We can use Bayes' theorem to calculate this probability:

P(A' | B) = P(B | A') * P(A') / P(B)

Where

We know that 47% of the market has seen the ad, so the probability of not seeing the ad is 1 - 0.47 = 0.53. We also know that 48% of those who see the ad purchase the game, so 52% of those who see the ad do not purchase the game. Finally, we know that 86% of those who have not seen the ad have not purchased the game.

Putting all of this information together, we can calculate:

P(B | A') = 86%

P(A') = 53%

P(B) = P(B | A') * P(A') + P(B | A) * P(A) = 0.52 * 0.47 + 0.14 * 0.53 = 0.3111

Substituting these values into Bayes' theorem, we get:

P(A' | B) = (0.86 * 0.53) / 0.3111 = 0.146 (rounded to three decimal places)

Therefore, the probability that a person did not see the ad given that they did not purchase the game is 0.146.

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Answer: 2538

Step-by-step explanation:

12*21/2

126

126/1*41/2

2538

Answer:

l*b*h=2583m²

Step-by-step explanation:

note no need units, so no need metre square or m²

Answer:

x > 8

Step-by-step explanation:

-6x + 18 < 2 - 4x

-2x + 18 < 2

-2x < -16

x > 8

The number that will complete the square to solve equation is 1/36.

What is completing the square?

For some values of h and k, completing the square is an elementary algebraic method for changing a quadratic polynomial of the form

ax^2 + bx + c to the form a^2 + k. In other words, the quadratic expression is completed by inserting a perfect square trinomial.

Consider, the given polynomial

3w^2 - w - 24 = 0

Rewrite the polynomial in the form ax^2 + bx = c

Add 24 on both sides,

3w^2 - w - 24 + 24 = 24

⇒ 3w^2 - w = 24

Divide both sides by 3,

\(w^2-\frac{1}{3}w = 8\)

To complete the square x^2 + bx, we add \((\frac{b}{2} )^2\)

Here, b = -1/3

So, \((\frac{b}{2})^2 = (\frac{-1/3}{2})^2 = (-\frac{1}{6})^2 = \frac{1}{36}\)

Adding to both sides of the equation, we have

\(w^2-\frac{1}{3}w+\frac{1}{36} = 8+\frac{1}{36}\)

Hence, the number that will complete the square to solve an equation is 1/36.

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Answer:

y=2x-1

Step-by-step explanation:

y-y sub 1=m(x- xsub1)

y-(-1)=2(x-0)

y+1=2(x-0)

y+1=2x-0

y=2x-1

The value of a is given by the third root of the function.

The function for this problem is defined as follows:

f(x) = x(x - 2)(x - a).

According to the Factor Theorem, the function is defined as a product of it's linear factors, hence the roots of the function are given as follows:

Hence the value of a is the third root of the function, which is the value on the graph at which the function crosses the x-axis along with x = 0 and x = 2.

The problem is incomplete, hence the general procedure to obtain the value of a is presented.

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Fat contributes 90 kilocalories to the total energy value of the candy bar.

To calculate the number of kilocalories contributed by fat, we need to use the fact that each gram of fat provides 9 kilocalories of energy. Therefore, for the 10 grams of fat in the candy bar, we can calculate the energy contribution as follows:

Energy from fat = (10 g) x (9 kcal/g) = 90 kcal

The carbohydrate and protein content of the candy bar are not relevant to this calculation. Therefore, the total energy value of the candy bar can be determined by simply adding the energy contribution from fat to the energy contributions from carbohydrate and protein.

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Answer:

What?

Step-by-step explanation:

The two positive numbers are 6 and 11

From the question, we understand that:

There are two positive numbers

Represent these numbers with x and y

So, we have the following equations

x = y - 5

6x - 3y = 3

Substitute x = y - 5 in 6x - 3y = 3

6(y - 5) - 3y = 3

Open the brackets

6y - 30 - 3y = 3

Evaluate the like terms

3y = 33

Divide by 3

y = 11

Substitute y = 11 in x = y - 5

x = 11 - 5

So, we have

x = 6

hence, the numbers are 6 and 11

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It should be 33.49 sorry if I’m a little off!

Answer:

(3,2)

Step-by-step explanation:

So like the last one we just have to find the distances between x on point a and x on point x and the distances between y on point a and y on point b. 4+2=6 and 3+3=6 and since we are trying to find the point that is 1/6 of the distance from a we do 6/6 and 6/6 which is 1 and 1. Then we subtract 1 from the x and y values of A. So the coordinates 1/6 of the way is (3,2)

The amount of water that flows from the tank during the first 40 minutes is 10,000 liters.

During the first 40 minutes, the rate of water flowing from the tank can be determined by substituting t = 40 into the given equation r(t) = 400 − 8t. This gives us r(40) = 400 − 8(40) = 400 − 320 = 80 liters per minute. To find the total amount of water that flows from the tank during this time period, we need to calculate the integral of r(t) from t = 0 to t = 40.

∫(400 − 8t) dt from 0 to 40 equals ∫(400 − 8t) dt = 400t - 4t^2 evaluated from 0 to 40, which simplifies to (400 * 40 - 4 * 40^2) - (400 * 0 - 4 * 0^2) = 16,000 - 0 = 16,000 liters.

Therefore, the amount of water that flows from the tank during the first 40 minutes is 16,000 liters.

The given equation represents the rate at which water flows from the bottom of the storage tank. By integrating this equation over a specific time interval, we can determine the total amount of water that has flowed during that period. Integration involves finding the antiderivative of the function and evaluating it at the upper and lower limits of the interval.

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Since the dimension of H and V is the same (n), it means that their bases have the same number of linearly independent vectors. Consequently, the basis of H can also serve as a basis for V.

Given that H is an n-dimensional subspace of an n-dimensional vector space V, where n is a natural number, we want to prove that H = V.
Since H is a subspace of V, it must satisfy the following properties:
1. H is closed under addition.
2. H is closed under scalar multiplication.
3. The zero vector (0) is in H.
We know that H is an n-dimensional subspace, which means it has a basis with n linearly independent vectors. Similarly, V is an n-dimensional vector space, so it also has a basis with n linearly independent vectors.
Since H and V share the same basis, they span the same space. Thus, we can conclude that H = V.

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The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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Answer:

b

Step-by-step explanation:

42.75+4=6

Answer:

$1.40/ hour

Step-by-step explanation:

The rate of the deductions is

Full amount minus new amount.  This is the amount taken per hour

$6.50/ hour -$5.2/hour = rate

$1.40/ hour

Answer:

Larger number=21

Smaller number=20

Step-by-step explanation:

20+21=41

21-20=1

Based on the given statement, the correct answer would be:

option A. The statement makes sense. Sally listens to music when she is depressed. If she is listening to music, then Sally must be depressed.

The given statement is discussing a potential relationship between Sally's emotional state of being depressed and her behavior of listening to music. The question asks whether the statement makes sense, is clearly true, or does not make sense, and provides four options to choose from.

Option A states that the statement makes sense and suggests that if Sally is listening to music, then she must be depressed. This option is reasonable because the statement establishes a connection between Sally's depression and her behavior of listening to music. It implies that listening to music is a coping mechanism or an activity she engages in when she experiences depressive feelings.

Therefore, if someone observes Sally listening to music, it can be inferred that she might be in a depressed state at that moment.

On the other hand, options B and C can be eliminated because they make extreme and unsupported claims. Option B suggests that Sally only listens to music when she is depressed, which is not explicitly stated in the given statement. Option C states that if Sally is listening to music, then she must not be depressed, which contradicts the initial connection established between depression and listening to music in the statement.

Option D highlights the incomplete nature of the statement but does not render it entirely senseless. It acknowledges that the statement mentions Sally's behavior of listening to music when she is depressed but does not provide information about other potential reasons she might listen to music.

In summary, option A is the most appropriate choice as it aligns with the established correlation between Sally's depression and her listening to music, while considering the possibility of other reasons for her music listening behavior.

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Answer:

\(A + \frac{B}{x-3} + \frac{C}{(x-3)^{2} }\)

Step-by-step explanation:

First, because the degree of the numerator is the same as the degree of the denominator, this fraction needs simplified further by long division. Upon simplification, the rational expression is \(7+\frac{2x-11}{x^2-6x+9}\).

Next, the denominatior needs factored in order to split up the second part of the simplified expression into two different partial fractions. Such factorization yields us, \((x-3)^{2}\).

Finally, we have all of our necessary information to set up all of our partial fractions.

This gives us \(A + \frac{B}{x-3} + \frac{C}{(x-3)^{2} }\), which is our answer.

Answer:

prt/100

1650*4*1/100 = 66

1800*4*1/100 = 72

then 72-66 = 6

6 = 30 then 1 = 5 ans.

plz give me the brainliest i need it

The value of c can be found by solving the equation yc^2 = -x^2 + 5x.

Square is a two-dimensional shape with four equal sides and four equal angles of 90 degrees each. It is a regular polygon and is one of the most common shapes in mathematics. Squares can be found in nature, architecture, and art. They are used to divide and organize space, and are often used as a form of measurement in areas such as geometry, construction, and engineering.

After rearranging the equation, we can solve for c by using the quadratic formula. c = (x^2 - 5x)/(x^2). Therefore, the value of c is (x^2 - 5x)/(x^2).

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Answer:

1 1/6

Step-by-step explanation:

because if you do 7÷6 that will be your answer

Observe that

5/12 = 1/4 + 1/6

so that

tan(5π/12) = tan(π/4 + π/6)

Then

tan(5π/12) = sin(π/4 + π/6) / cos(π/4 + π/6)

… = (sin(π/4) cos(π/6) + cos(π/4) sin(π/6)) / (cos(π/4) cos(π/6) - sin(π/4) sin(π/6))

… = (cos(π/6) + sin(π/6)) / (cos(π/6) - sin(π/6))

(since sin(π/4) = cos(π/4) = 1/√2)

… = (√3/2 + 1/2) / (√3/2 - 1/2)

… = (√3 + 1) / (√3 - 1)

… = (√3 + 1) / (√3 - 1) × (√3 + 1) / (√3 + 1)

… = (√3 + 1)² / ((√3)² - 1²)

… = ((√3)² + 2√3 + 1²) / (3 - 1)

… = (3 + 2√3 + 1) / 2

… = (4 + 2√3) / 2

… = 2 + √3 … … … (C)

If you insist on using the half-angle identity, recall that

sin²(x) = (1 - cos(2x))/2

cos²(x) = (1 + cos(2x))/2

==>   tan²(x) = (1 - cos(2x)) / (1 + cos(2x))

Let x = 5π/12. The angle x lies in the first quadrant, so we know tan(x) is positive.

==>   tan(x) = +√[(1 - cos(2x)) / (1 + cos(2x))]

We also know

cos(2x) = cos(5π/6) = -√3/2

which means

tan(x) = tan(5π/12) = √[(1 - (-√3/2)) / (1 + (-√3/2))]

… = √[(1 + √3/2) / (1 - √3/2)]

… = √[(2 + √3) / (2 - √3)]

… = √[(2 + √3) / (2 - √3) × (2 + √3) / (2 + √3)]

… = √[(2 + √3)² / (2² - (√3)²)]

… = √[(2 + √3)² / (4 - 3)]

… = √[(2 + √3)²]

… = 2 + √3

The area οf the circle is 30.25π square centimeters

The circumference, which is the perimeter οf a circle οr ellipse in geοmetry, cοmes frοm the Latin circumferens, which means "carrying arοund." The circumference wοuld be the length οf the circle's arc, if the circle were οpened up and straightened οut tο a line segment, in οther wοrds.

The fοrmula fοr the circumference οf a circle is C = 2πr, where C is the circumference and r is the radius. We can rearrange this formula to solve for the radius:

\(r = C / (2\pi)\)

Substituting the given circumference of 11π cm, we get:

\(r = 11\pi / (2\pi) = 5.5\)

Now that we know the radius, we can use the formula for the area of a circle to find the area:

\(A = \pi r^2\)

Substituting the value we found for the radius, we get:

\(A = \pi (5.5)^2 = 30.25\pi\)

Therefore, the area of the circle is 30.25π square centimeters.

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In a course of 12 weeks, Perry will be able to play a total of 25 pieces of the piano Leon.

A total of 18 pieces of piano are learnt by Perry in a course of 9 weeks.

By using simple algebra, we can find the number of pieces that will be played by Perry in one week,

So, we can write, The learing speed,

Number of piano pieces learnt = Weeks

19 pieces = 9 weeks

Learning speed = 19/9 Pieces per week

So, the number of pieces learnt in 12 weeks is,

Number of pieces learnt = 19/9 x 12

Number of pieces learnt = 25.22

Number of pieces learnt = 25

So, Perry will be able to play 25 pieces.

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