Abha is climbing a mountain. While covering 20 yards of horizontal distance, Abha’s elevation increases by 40 yards. Consider Abha’s climb as a linear function.


A drawing shows a girl hiking. The vertical distance is forty yards. The horizontal distance is twenty yards.


What is the slope of her climb?

Answer:$10.88

Step-by-step explanation:

36/100 ×8= 2.88

Selling price is 8+2.88

The sum of the numbers written on the faces of the cube is 333.

A vertex, also known as a point, is a fundamental part of a shape or an object. It is the point at which two or more lines, edges, or faces meet. Vertex can also refer to the corner of a polygon, where multiple lines meet. In 3D geometry, a vertex is a point where three or more edges meet. In a 3D object, each vertex is considered to be a corner of the object. Vertices are a crucial part of the structure and design of shapes, and can be used to define a shape's size, shape and dimension.

The sum of the numbers written on the faces of the cube is equal to the sum of the products of the numbers assigned to the vertices of the cube divided by three. Since the sum of the numbers assigned to all the vertices is equal to 1001, the sum of the numbers written on the faces of the cube is equal to 1001/3, which is equal to 333. Therefore, the sum of the numbers written on the faces of the cube is 333.

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Answer:

a,c,d

Step-by-step explanation:

The identities which are true is A,C, and D.

A trigonometric Identity is made of Trigonometric ratios, which help in solving Trigonometric Equations.

The identity

\(\rm= \dfrac{1- tan^2 x}{2tanx} \\\\\\\\rm= \dfrac{ cos^2 x - sin^2 x}{2 sin x cosx} \\\\\\= cos 2x/ sin 2x \\\\= \dfrac{ 1}{tan 2x}\)

Similarly,

sin 8x = 2 sin4x cos 4x

And,

(sin x + sin 5x) / ( cos x +cos 5x) = tan 3x.

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Answer: 15 + b

Step-by-step explanation:

15 is being increased by b and b could be any number so the expression will be  15 + b . Increase means is going up so you will be adding b.

Scarlett was charged $33 when she received her bill at the restaurant. She chose to tip 26% for the service she received. She must multiply the bill amount by 0.26 to determine the tip.

Tip = 0.26 x $33 = $8.58 Thus the total cost of the dinner plus the tip is: Total = $33 + $8.58 = $41.58  before tax for the lunch and tip. It should be noted that tax is not included in this computation. The tip amount may be calculated by multiplying the meal cost by the tip percentage: Tipping rate = 33 * 0.26 = 8.58 Therefore the entire cost of the lunch, including the tip, is: Cost total = 33 + 8.58 = 41.58 As a result, Scarlett's lunch plus tip, before tax, was $41.58.Scarlett was charged $33 when she received her bill at the restaurant. She chose to tip 26% for the service she received. She must multiply the bill amount by 0.26 to determine the tip: Tip = 0.26 x $33 = $8.58 Thus the total cost of the dinner plus the tip is: Total = $33 + $8.58 = $41.58  before tax for the lunch and tip. It should be noted that tax is not included in this computation. The tip amount may be calculated by multiplying the meal cost by the tip percentage: Tipping rate = 33 * 0.26 = 8.58 Therefore the entire cost of the lunch, including the tip, is Cost total = 33 + 8.58 = 41.58 As a result, Scarlett's lunch plus tip, before tax, was $41.58.Scarlett was charged $33 when she received her bill at the restaurant. She chose to tip 26% for the service she received. She must multiply the bill amount by 0.26 to determine the tip. Tip = 0.26 x $33 = $8.58 Thus the total cost of the dinner plus the tip is: Total = $33 + $8.58 = $41.58.

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Answer:

1 : 700 000

Step-by-step explanation:

63 km = 6 300 000 cm

Make it a proportion:

9 cm - 6 300 000 cm

1 cm - x cm

x = \(\frac{6 300 000 * 1}{9}\) = 700 000 cm

Here we get that in map 1 cm represents 700 000 cm in reality, so the scale is 1 : 700 000

The value of y when x = 0 is 10

The equation is given as

y = x² - 7x + 10

So, we have

y = (0)² - 7(0) + 10

Evaluate

y = 10

In (a), we have

x = 0 and y = 10

This means that the graph crosses the y-axis at y = 10

See attachment for graph

We have

x² - 7x + 10 = 0

Expand

x² - 2x - 5x + 10 = 0

Factorize

(x  - 2)(x - 5) = 0

So, we have

x = 2 and x = 5

In (c), we have

x = 2 and x = 5 and y = 0

This means that the graph crosses the x-axis at x = 2 and x = 5

See attachment for graph

See attachment for graph

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Given :

Triangle XYZ is rotated 90° counterclockwise about the origin to produce X'Y'Z'.

To Find :

What are the coordinates of X'Y'Z .

Solution :

Let , the points are \(X(x_1,y_1)\ ,Y(x_2,y_2) \ , Z(x_3,y_3)\).

When any point ( h , k ) is rotated 90° counterclockwise about the origin the new point produced is ( -k , h).

So , applying same concept in XYZ :

\(X'(-y_1,x_1)\ ,Y'(-y_2,x_2) \ , Z'(-y_3,x_3)\) .

Therefore , transformed points are \(X'(-y_1,x_1)\ ,Y'(-y_2,x_2) \ , Z'(-y_3,x_3)\) .

Hence , this is the required solution .

Answer:

(1,4)

Step-by-step explanation:

Answer:

The sales tax is $3.5

The total cost is $53.5

Step-by-step explanation:

To find the sales tax, you have to find the 7 percent of 50 dollars. In decimal form, 7% is 0.07. So you just have to multiply 0.07 to 50.

50 x 0.07 = 3.5

That's why $3.5 is the sales tax.

In order to get the total cost including sales tax. You just have to add $50 to the sales tax which is $3.5.

$50 + $3.5 = $53.5

The effect of increasing the random sample size of Canadian voters in the Gallup poll from 1,500 to 4,000 people is to reduce the margin of error and increase the accuracy of the poll results.

By increasing the sample size, the Gallup poll is able to gather more data points from a diverse group of voters, which improves the representativeness of the sample.

This helps to minimize biases and better capture the opinions of the population as a whole. In turn, the increased sample size leads to a lower margin of error, meaning that the poll results are more likely to accurately represent the true opinions of Canadian voters.

This is particularly important right before an election, as accurate poll results can inform strategies for political parties and provide insights for voters. Ultimately, increasing the sample size of the random sample in the Gallup poll enhances its reliability and validity, making it a more valuable tool in understanding voter sentiment.

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Answer:

E

Step-by-step explanation:

NO

we have the equation

p(x)=5-4x

this is a linear equation

To graph a line we need two points

so

Part A

we have that

the domain is the interval [-2,2]

Find out the points for x=-2 and for x=2

For x=-2

substitute in the equation

p=5-4(-2)

p=5+8=13

the first point is (-2,13)

For x=2

p=5-4(2)

p=-3

the second point is (2,-3)

To graph the line, plot the points and join them

using a graphing tool

A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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The centroid of the region bounded by the curves y = 12x and y = √x is (72,1.88).

To find the centroid of the region bounded by the given curves y = 12x and y = √x, the following steps should be followed.

Step 1: Sketch the region bounded by the two curves to have an idea of what the region looks like.

Step 2: Determine the area of the region bounded by the two curves. The area A can be computed by evaluating the definite integral of the difference between the two functions. \(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx\]\)  We solve for this integral below.\(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = 64 - 1728 + \frac{2}{3}\sqrt{6}\] \[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = -1663.30\]\)

Step 3: To find the centroid of the region, we need to determine the x and y coordinates of the centroid. The x-coordinate of the centroid is given by the formula below.

\(\[x = \frac{1}{A}\int\limits_{a}^{b} \frac{1}{2}(y_1^2-y_2^2)dx\]\)

where A is the area of the region, and y1 and y2 are the upper and lower functions, respectively. Substituting values, we obtain

\(\[x = \frac{1}{-1663.30}\int\limits_{0}^{144} \frac{1}{2}((\sqrt{x})^2-(12x)^2)dx\]  \[x = 72\]\)

 The y-coordinate of the centroid is given by the formula below.

\(\[y = \frac{1}{2A}\int\limits_{a}^{b}(y_1+y_2)\sqrt{(y_1-y_2)^2+4dx}\]\)

 Substituting values, we obtain \(\[y = \frac{1}{2(-1663.30)}\int\limits_{0}^{144}(12x+\sqrt{x})\sqrt{(\sqrt{x}-12x)^2+4dx}\]  \[y = 1.88\]\)

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Expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

As given in the question,

Condition for the expression:

Sally and Anne both went for a movie.

Each one purchased a drink.

Shared one popcorn and one veggie bought by them.

Consider movie ticket price = 9

drink price = 1.35

Popcorn price = 3.50

Veggie price = 1.74

Explanation for different expressions are:

1. one-half (9 + 1. 35 + 3. 50 + 1. 74)

Here sum of all the amount is divided equally, which is not correct as movie ticket and drink they have purchased individually.

2.  9 + 1. 35 + one-half (3. 50 + 1. 74)

This is correct option as it represents :

Movie ticket price = 9

Drink = 1.35

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

3. 18 + 2. 70 + one-half (3. 50 + 1. 74)

As per consideration of price this is not correct option.

Movie ticket price =18

Drink = 2.70

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

4. 9+1. 35+2(3. 50+1. 7)

This is not correct option as popcorn and veggie price is doubled.

Therefore, expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

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1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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Answer:

CE = 3.2 cm

DH = 4.5 cm

Explanation:

Given:

MNPR ≅ CEDH

≅ - means approximately equal

Lengths of the shape:

MN = CE = 3.2 cm

NP = ED = 6.5 cm

PR = DH = 4.5 cm

RM = HC = 9 cm

The probability that a student who can drive is a college student is 0.2771 or 27.7%

It will be sooved using Baye's theorem -

P(college) = P(C) / 1/5 = 0.2

P(high school students) = P(H) = 4/5 = 0.8

P(college drives) = 0.23

P(high school drives) = 0.15

We have to find, probability that a student who drives is a college student.

That is, we have to find P(C/D).

P(C/D) = P(C ∩ S)/P(S)

Since P(C ∩ S) is an independent event.

P(C ∩ S) = P(C) × P(S)

P(C ∩ S) = 0.2 × 0.23

= 0.046

Using bayes's theorem, we will get

P(C/D) = 0.2771 or 27.7%

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Answer:

Daily allowance of Lily's brother is approximately $10.

Step-by-step explanation:

Let L represents Lily's daily allowance and let B represents her brother's daily allowance, we can therefore obtain the following from the question:

L - B = $8 ........................ (1)  => Indicating the difference in their pocket money

(2/3)L = B + $2 ..................... (2) => Indicating Lily's allowance is $2 more than what her brother gets

From equation (1), we find L as follows:

L = $8 + B ...................................... (3)

Substituting L from equation (3) into equation (2) and solve for B as follows:

(2/3)($8 + B) = B + $2

0.67($8 + B) = B + $2

$5.36 + 0.67B = B + $2

$5.36 - $2 = B - 0.67B

$3.36 = 0.33B

B = $3.36 / 0.33

B = 10.18, or $10 approximately.

Therefore, daily allowance of Lily's brother is approximately $10.

Confirmation Note:

Note that this is not part of the answer to the question. It is just meant to assist you in having a deeper understanding of the question and the answer.

The above answer can be confirmed as follows:

Substituting B = $10 into equation (3), we have:

L = $8 + $10 = $18

This implies that Lily's daily allowance is $18.

Substituting for L = $18 and B = $10 into equation (1), we have:

$18 - $10 = $8 => this confirms that the difference in their pocket money is $8.

Also, substituting for L = $18 and B = $10 into equation (2), we have:

(2/3)18 = 10 + $2 => 12 = 12 => since 12 minus 10 is equal to $2, this confirms that 2/3 of lily's allowance is $2 more than what her brother gets.

Answer:

15

Step-by-step explanation:

for every three boys there are five girls

3 groups of 3 boys

3*5=15 girls

To calculate the discharge through the circular channel, we can use Manning's equation, which relates the flow rate (Q) to the channel properties and flow conditions. Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

where:

Q is the discharge (flow rate)

n is Manning's coefficient (0.014 in this case)

A is the cross-sectional area of the channel

R is the hydraulic radius of the channel

S is the slope of the channel bed

First, let's calculate the cross-sectional area (A) of the circular channel. The diameter of the channel is given as 6m, so the radius (r) is half of that, which is 3m. Therefore, the area can be calculated as:

A = π * r^2 = π * (3m)^2 = 9π m^2

Next, let's calculate the hydraulic radius (R) of the channel. For a circular channel, the hydraulic radius is equal to half of the diameter, which is:

R = r = 3m

Now, we can calculate the slope (S) of the channel bed. The given slope is 1 in 600, which means for every 600 units of horizontal distance, there is a 1-unit change in vertical distance. Therefore, the slope can be expressed as:

S = 1/600

Finally, we can substitute these values into Manning's equation to calculate the discharge (Q):

Q = (1/0.014) * (9π m^2) * (3m)^(2/3) * (1/600)^(1/2)

Using a calculator, the discharge can be evaluated to get the final result.

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Answer:

5.625

Step-by-step explanation:

4.5/0.8 = 5.625

Answer:

here's the answer

Step-by-step explanation:

Answer:

answer in picture

Step-by-step explanation:

Answer:

(x,y) ---> (x+9, y+8)

Step-by-step explanation:

you simply take one point (ex point R to R^1) and count the distance from left to right/right to left which is 9 so that is your X and count up which will be your Y in this case is 8.

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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The equation of line r which is parallel to line q and passes through point (5,-4) is y = (-3/5)x - 1.

The slope-intercept form is expressed as;

y  = mx + b

The point-slope formula is expressed as

y - y₁ = m( x - x₁ )

Given the data in the question;

First, determine the slope of the line q using the slope intercept-form.

y = mx + b

3x + 5y = 10

5y = -3x + 10

y = (-3/5)x + 10/5

y = (-3/5)x + 2

Hence;

Slope of line q m = -3/5

Since, line r is parallel to line q, they both have the same slope.

Therefore, slope of line r will be m  = -3/5

Now, plug the point  (5,-4) and and slope m = -3/5 into the point slope formula and solve for y.

y - y₁ = m( x - x₁ )

y - (-4) = (-3/5)( x - 5 )

y + 4 = (-3/5)x + 3

y = (-3/5)x + 3 - 4

y = (-3/5)x - 1

Therefore, the equation of line r is  y = (-3/5)x - 1.

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1. A simplified expression for the volume of the above prism is 15x³ cubic units.

2. Destiny made her mistake in step 1, and the correct solution with steps is shown below.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular prism = 3x × 5x ×  x

Volume of rectangular prism = 15x³ cubic units.

Question 2.

Given the following expression, \(\frac{5(x+2)-(8-x)}{2}\)

Step 1: we would open the bracket;

\(\frac{5x\;+\;10\;-\;8\;+\;x}{2}\)

Step 2: we would collect like-terms and evaluate;

\(\frac{5x\;+\;x\;+\;10\;-\;8}{2}\\\\\frac{6x\;+\;2}{2}\)

Step 3: we would split;

\(\frac{6x}{2}+ \frac{2}{2}\)

Step 4: we would divide;

3x + 1

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The quadratic equation that has (3·x + β) ans (3·x + a) as the roots can be presented as follows;

9·x² - 7.5·x - 3 = 0

A quadratic equation is an equation that can be expressed in the form; y = a·x² + b·x + c, where, a ≠ 0, and a, b, and c are numbers.

The quadratic equation -2·x² - 5·x + 6 = 0, divided by a factor of -1 indicates that we get;

2·x² + 5·x - 6 = 0

The quadratic formula indicates that we get;

x = (-5 ± √(5² - 4 × 2 × (-6))/(2 × 2) = (-5 ± √(73))/4

Let a = (-5 + √(73))/4 and let β =  (-5 - √(73))/4)

(3·x + ((-5 + √(73))/4)) × (3·x + (-5 - √(73))/4) = 9·x² + 3·x·(-5 - √(73))/4) + 3·x·(-5 + √(73))/4) + ((-5 + √(73))/4)) × (-5 - √(73))/4)

9·x² + 3·x·(-5 - √(73))/4) + 3·x·(-5 + √(73))/4) + ((-5 + √(73))/4)) × (-5 - √(73))/4) = 9·x² - 15·x/2 - 3 = 0

Therefore, the equation that has (3·x + β) ans (3·x + a) as roots is the equation

9·x² - 15·x/2 - 3 = 9·x² - 7.5·x - 3 = 0

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Answer:

2/15

Step-by-step explanation: