On what interval is the function h(x) = |x − 2| + 5 increasing? A. (2, ∞) B. (5, ∞) C. (-∞, 2) D. (-∞, 5)

In quantitative literacy, the solution involves finding the LCM of the numbers and then squaring it to obtain the smallest square number that satisfies the given conditions.

In quantitative literacy, finding the smallest square number that is divisible by 8, 12, 15, and 20.

To solve the problem, we need to determine the least common multiple (LCM) of these four numbers.

Let's list the multiples of each number until we find a common multiple:

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, ...

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...

Multiples of 20: 20, 40, 60, 80, 100, 120, ...

From the lists above, we can see that 120 is the smallest common multiple of all the numbers. To find the smallest square number, we need to square 120:

120^2 = 14,400

The smallest square number that is divisible by 8, 12, 15, and 20 is 14,400.

In quantitative literacy, the solution involves finding the LCM of the numbers and then squaring it to obtain the smallest square number that satisfies the given conditions.

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Answer:

There are 20 blue fish in the aquarium.

Step-by-step explanation:

If 60% of the fish are red than 40% are blue. That means that 20% fish is 10 fish. 20% = 10 fish. 40% = 20 fish.

Answer:

a. 73°

b. 98°

Step-by-step explanation:

In quadrilateral EFGH

∡E+∡G=180° sum of opposite angle of quadrilateral inside the circle is 180°

substituting value

11x+8+8x+1=180°

19x+9=180°

19x=180=9

19x=171

x=171/19

x=9°

similarly,

∡H+∡F=180° sum of opposite angle of quadrilateral inside the circle is 180°

substituting value

6y-4+5y-3=180°

11y-7=180°

11y=180°+7

11y=187°

y=187/11

y=17°

Now

a. m∡G=8x+1=8*9+1=73°

b. m∡H=6y-4=6*17-4=98°

Based on the Triangle Inequality Theorem the possible lengths of the sides of a triangle are:

The Triangle Inequality Theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, is used to determine if three lengths can be the lengths of the sides of a triangle.

Considering each option:

A. 12cm, 5cm, 17cm:

12 + 5 > 17 (not satisfied)

5 + 17 > 12 (satisfied)

12 + 17 > 5 (satisfied)

B. 10cm, 15cm, 24cm:

10 + 15 > 24 (satisfied)

15 + 24 > 10 (satisfied)

10 + 24 > 15 (satisfied)

C. 9cm, 22cm, 11cm:

9 + 22 > 11 (satisfied)

22 + 11 > 9 (satisfied)

9 + 11 > 22 (not satisfied)

D. 21cm, 7cm, 6cm:

21 + 7 > 6 (satisfied)

7 + 6 > 21 (not satisfied)

21 + 6 > 7 (satisfied)

Hence, option B and D are correct.

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The distance between Martin's house and the school is 5 kilometers.

To find the distance between Martin's house and the school, we can use the Pythagorean theorem.

Let's represent the distance between Martin's house and the school as x kilometers.

According to the given information:

Distance between Martin's house and Hayley's house (hypotenuse) = 13 kilometers

Distance between the school and Hayley's house (one side of the right triangle) = 12 kilometers

Using the Pythagorean theorem, we have:

x[tex]x^2 + 12^2 = 13^2[/tex]

Simplifying the equation:

[tex]x^2 + 144 = 169x^2 = 169 - 144x^2 = 25[/tex]

Taking the square root of both sides:

x = √25

x = 5

Therefore, the distance between Martin's house and the school is 5 kilometers.

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In the figure, applying  perpendicular bisector theorem for chords in a circle, the value of JN = 9 1/2

The perpendicular bisector theorem for chords in a circle states that if a radius of a circle is perpendicular to a chord, then it bisects the chord.

In other words, the radius divides the chord into two equal segments.

This theorem is a direct consequence of the properties of perpendicular lines and congruent triangles.

applying this to the figure

JN = JK/2

JN = 19/2

JN = 9 1/2

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Answer:

Each person will get 2 pounds of candy

Step-by-step explanation:

Nicole + 3 friends = 4 total

8 pounds of candy = total

total candy / total people

8/4 = 2

Answer:

True

Step-by-step explanation:

If the discriminant [tex]D=b^2-4ac < 0[/tex], then there are two complex roots

If the discriminant [tex]D=b^2-4ac > 0[/tex], then there are two real roots

If the discriminant [tex]D=b^2-4ac=0[/tex], then there is only one real root

All the solutions are,

g⁻¹ = { (7, - 7), (- 7, - 6), (6, - 1), (9, 3) }

h⁻¹ (x) = 5x - 13

⇒ (h⁻¹ о h ) (- 3) = 3

We have to given that,

Functions g and f are defined as,

g = {(- 7, 7), (- 6, - 7), (- 1, 6), (3, 9)

And, h (x) = (x + 13) / 5

Now, We can simplify for inverse function as,

For inverse function of g,

g = {(- 7, 7), (- 6, - 7), (- 1, 6), (3, 9)

g⁻¹ = { (7, - 7), (- 7, - 6), (6, - 1), (9, 3) }

And, Inverse function of h is,

h (x) = (x + 13) / 5

y = (x + 13) / 5

Solve for x,

5y = x + 13

x = 5y - 13

h⁻¹ (x) = 5x - 13

So, We get;

⇒ (h⁻¹ о h ) (- 3)

⇒ (h⁻¹ (h (- 3))

⇒ (h⁻¹ (- 3 + 13)/5)

⇒ (h⁻¹ (2))

⇒ 5 (2) - 13

⇒ 10 - 13

⇒ - 3

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Answer:

100°

Step-by-step explanation:

tThe sum of all arc measures that make up that circle is 360 degrees.

QS + RQ + RS = 360

QS = 360 - 120 - 140 = 100

An arc angle is the degree measurement of that angle inside the circle, opposite the arc

m∠R = arc QS = 100°

Answer:

∠ R = 50°

Step-by-step explanation:

the inscribed angle R is half the measure of its intercepted arc QS

the sum of the arcs on a circle is 360° , that is

RQ + QS + SR = 360°

120° + QS + 140° = 360°

QS + 260° = 360° ( subtract 260° from both sides )

QS = 100°

Then

∠ R = [tex]\frac{1}{2}[/tex] × 100° = 50°

Answer:

3.14 seconds

Step-by-step explanation:

The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

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Robert's dimes are anywhere between 17 and 19.

Nickels

are worth 5 cents, and

dimes

are worth 10 cents. Since Robert has 10 nickels, he already has 50 cents. To reach a minimum of $2.20, or 220 cents, Robert needs at least 170 more cents. Because each dime is worth 10 cents, he needs a minimum of 17 dimes. If he has a maximum of 29 coins in total, subtracting the 10 nickels means that he can have up to 19 dimes. So, Robert could have anywhere between 17 and 19 dimes.

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Answer:10

Step-by-step explanation: You plug in 3 for x so you get the equation 2(3)+4

Which becomes 6+4

Which equals 10

Using a trigonometric relation, we can see that the value of x is 10.39

Here we have a right triangle. We can see that we know the measures of the hypotenuse, and the angle opposite to the side x.

Then to get the value of x, we can use the trigonometric relation:

sin(a) = (opposite cathetus)/hypotenuse.

Replacing the values that we know, we will get.

sin(60°) = x/12

solve that for x:

12*sin(60°) = x

10.39 = x

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The probability that the first ball chosen is black and the second ball chosen is red is 24.24%

First, we shall obtain the total balls present in the box. Details below:

Total ball = 4 + 8

Total ball = 12 balls

Next, we shall obtain the probability of chosen a black ball first. Details below:

P(B) = n(B) / n(T)

P(B) = 8 / 12

Next, we shall obtain the probability of chosen red as the 2nd ball. Details below:

P(R | B)= n(R) / n(T)

P(R | B) = 4 / 11

Finally, we shall obtain the probability that the first ball chosen is black and the second ball chosen is red. Details below:

P(B ∩ R) = [P(B) × P(R | B)] × 100

P(B ∩ R) = [(8 / 12) × (3 / 11)] × 100

P(B ∩ R) = 0.2424 × 100

P(B ∩ R) = 24.24%

Thus, the probability that the first ball chosen is black and the second ball chosen is red is 24.24%

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Using the trigonometric ratios:

(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule:

(2). x = √116

(3). x = 90

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

(1). sinA = 5/13 {opposite/hypotenuse}

cosA = 12/13 {adjacent/hypotenuse}

tanA = 5/13 {opposite/adjacent}

By Pythagoras rule

(2). x = √(4² + 10²)

x = √(16 + 100)

x = √116

(3). 106² = x² + 56²

x² = 106² - 56²

x = √(11236 - 3136)

x = √8100

x = 90

Therefore, using trigonometric ratios:

(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule;

(2). x = √116

(3). x = 90

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Answer:
147 floors

Explanation:

To determine the number of floors in the Burj Khalifa, we can use the information provided. We know that Andre stood 1000 meters away from the building and looked up at a 39.62-degree angle using a laser rangefinder. Let's calculate the height of the Burj Khalifa using basic trigonometry.

First, we can find the height of the building using the tangent function:

tan(angle) = height / distance

tan(39.62 degrees) = height / 1000 meters

height = tan(39.62 degrees) * 1000 meters

height ≈ 747.97 meters

Now, let's calculate the number of floors in the Burj Khalifa. We are given that each floor is 5.079 meters tall.

Number of floors = height / height of each floor

Number of floors = 747.97 meters / 5.079 meters

Number of floors ≈ 147.23 floors

Since we cannot have fractional floors, we can round the number down to the nearest whole number.

Therefore, there are approximately 147 floors in the Burj Khalifa.

The notation which is the most appropriate notation when calculating conditional probabilities is option B.

The appropriate notation for calculating conditional probabilities is often denoted using the vertical bar symbol "|". This symbol represents "given" or "conditional on."

In a mathematical expression, the conditional probability of event A given event B is written as P(A | B), where "P" stands for probability. This notation indicates that the probability of event A occurring is being calculated assuming that event B has already occurred.

Thus option B is correct.

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Answer:

A. 144

D. √9 * √16.  

Step-by-step explanation:

The product property of square roots states that for any two numbers (a and b), where both are greater than or equal to 0, the square root of a product is equal to the product of the square root:

[tex]\sqrt{ab}=\sqrt{a} *\sqrt{b}[/tex]

Thus, √(9 * 16) is equivalent to √9 * √16.  

We can see this mathematically if we evaluate the expressions:

[tex]\sqrt{(9*16)}=\sqrt{9}*\sqrt{16}\\ \sqrt{144}=3*4\\ 12=12[/tex]

Thus, the answers are A and D.

If you can only choose one answer, choose D because the question didn't explicitly ask us to evaluate √(9 * 16).

If you can choose multiple answers, choose A and D.

The quotient is 231, and the remainder is 9 or 231 R9.

To perform long division to find the quotient and remainder of 8,325 divided by 36, you would proceed as follows:

         ______

36 | 8,325

        1,125

         45

and,   36 (36 x 1)

          9

The quotient is 231, and the remainder is 9.

Therefore, the correct answer is 231 R9.

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The value of x that makes [tex]5^x = 625[/tex] true is x = 4.

To determine the value of x in the equation [tex]5^x = 625[/tex], we need to find the exponent that results in 625 when applied to the base 5.

Since 625 can be expressed as 5 raised to the power of 4 ([tex]5^4 = 625[/tex]), the value of x that satisfies the equation is 4.

When we substitute x = 4 into the equation, we get [tex]5^4 = 625[/tex], which is true.

Therefore, x = 4 is the solution to the equation, indicating that 5 raised to the power of 4 equals 625.

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The required median is 110- 120 and the upper quartile of the scores is 110-120.

Given that, the data from the histogram is

CI                 |             f

80-90          |            5

90-100,        |            3

100-110,        |            4

110-120,        |            4

120-130,       |             3

130-140,       |             3

140-150,       |             2

150-160        |             2

To find the median and upper quartile of the given scores, make the cumulative frequency table.

The cumulative frequency table is given below.

CI                 |             f               |             cf            

80-90          |            5               |             5

90-100,        |            3               |             8

100-110,        |            4               |            12

110-120,        |            4               |             16

120-130,       |             3               |             19

130-140,       |             3               |             22

140-150,       |             2               |             24

150-160        |             2               |             26

N = 26.

The median is the N/2 th score when N is even.

Median  = 13th score = 110-120 scores

To find the upper quartile, the product of (3/4 and N )th score gives the upper quartile.

Upper quartile = (3/4 x 26)th score.

Upper quartile = 19.5th  score.

The upper quartile score range is 110 - 120.

Therefore,the required median is 110- 120 and the upper quartile of the scores is 110-120.

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The amount that Mark will pay monthly if the house's original price is 15,000,000 pesos for 20 years at 13.75% monthly compounded interest is 183,810.81 pesos.

The monthly payment can be computed using an online finance calculator that incorporates the compound interest system.

The compound interest system charges interest on both the principal and the accumulated interest for each period.

N (# of periods) = 240 months

I/Y (Interest per year) = 13.75%

PV (Present Value) = 15,000,000 pesos

FV (Future Value) = 0

Results:

Monthly Payment (PMT) = 183,810.81 pesos

The sum of all periodic payments = 44,114,593.72 pesos

Total Interest = 29,114,593.72 pesos

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The product of the fractions is 1/[(x - 5)(x + 7)]

From the question, we have the following parameters that can be used in our computation:

Fraction 1 = (x + 1)/(x² - 25)

Also, we have

Fraction 2 = (x + 5)/(x² + 8x + 7)

So, we have

Product = (x + 1)/(x² - 25) * (x + 5)/(x² + 8x + 7)

When factored, we have

Product = (x + 1)/(x - 5)(x + 5) * (x + 5)/(x + 1)(x + 7)

Evaluate the products

Product = 1/(x - 5) * 1/(x + 7)

This gives

Product = 1/[(x - 5)(x + 7)]

Hence, the product of the fractions is 1/[(x - 5)(x + 7)]

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The points that represent this data set are shown in the scatter plot attached below.

In this exercise, we would plot the number sold on the x-coordinates of a scatter plot while the prices ($) would be plotted on the y-coordinate of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot.

Based on the scatter plot shown below, which models the relationship between the number sold and the prices ($), a linear equation for the line of best fit is as follows:

y = 0.23x + 1.00

In conclusion, the slope of the line is 0.23 and the y-intercept is 1.00.

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The surface area of each solid is listed below:

Case A: A = 584.988 ft²

Case B: A = 320π in²

In this problem we must determine the surface area of each of two solids, that is, the sum of the areas of all faces, whose area formulas are introduced below:

Square

A = l²

Where l is the side length.

Triangle

A = 0.5 · w · h

Where:

Circle

A = π · r²

Where r is the radius.

Lateral side of a cylinder

A = 2π · r · h

Where h is the height of the cylinder.

Now we proceed to determine the surface area of each solid:

Case A:

A = (14 ft)² + 4 · 0.5 · (14 ft) · √[(7 ft)² + (12 ft)²]

A = 584.988 ft²

Case B:

A = 2π · (8 in)² + 2π · (8 in) · (12 in)

A = 320π in²

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Answer: There are 240 people inside the auditorium.

Step-by-step explanation:

30 x 8 = 240