50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answer: 17 months

Step-by-step explanation:

Total cost of the bike = $1,867

Down payment = $320

so $1,867 - $320 = $1,547

$91 * 17 = 1,547

(17 = months) so $91 * 17 months = 1,547

Option (D) D. Points Q and R is used to removed to make this relation a function.

To determine which two points could be removed to make the relation a function, we need to check if there are any repeated x-values (inputs) in the given set of points. In a function, each input should have a unique output.

Let's analyze the given options:

A. Points R and S: (R, 3), (S, 5)

B. Points Q and T: (Q, 2), (T, 5)

C. Points P and Q: (P, 1), (Q, 2)

D. Points Q and R: (Q, 2), (R, 3)

In this case, if we remove points Q and R, we eliminate the repeated x-value of 2, which ensures that each input has a unique output. Therefore, the answer is:

D. Points Q and R.

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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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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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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

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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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:

The missing variable θ is equal to (11π)/8.

Step-by-step explanation:

Given:

ω = π/8 radian per min

t = 11 min

Step 1: Identify the formula and the missing variable.

The formula is ω = (θ/t), and we are trying to find the value of θ.

Step 2: Rearrange the formula to solve for the missing variable.

To isolate θ, we can multiply both sides of the equation by t:

ω * t = θ

Step 3: Substitute the given values.

Substituting the given values into the rearranged formula, we have:

θ = (π/8) * 11

Step 4: Simplify the expression.

To multiply fractions, we multiply the numerators and multiply the denominators:

θ = (π * 11) / (8 * 1)

θ = (11π) / 8

Step 5: Finalize the answer.

The value of the missing variable θ is (11π)/8. This is the exact answer unless otherwise indicated.

Therefore, the step-by-step process shows that the missing variable θ is equal to (11π)/8.

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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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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In the excerpt, Li's crush gave his girl   friend a rose. The text states: Li's crush gave his girl   friend a rose. She was so happy!

Li's mother was upset about the gift later because she thought it was too expensive.

The text states: Li's mother was upset when she found out how much the rose cost. She thought it was too much money to spend on a gift.

Li's mother's reaction is understandable. Roses are expensive flowers, and it is possible that Li's mother did not have the money to spend on such a gift. However, it is also important to remember that Li's crush was trying to do something nice for his girl friend, and the rose was a symbol of his love for her. In the end, it is up to Li and his girl friend to decide whether or not the rose was worth the money.

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The image of point A after the reflection is A'(3, -4).

The image of point B after the reflection is B'(2, -3).

To reflect a point in the x-axis, we keep the y-coordinate the same and change the sign of the x-coordinate.

For point A(3, 4):

After reflecting point A in the x-axis, the y-coordinate remains the same (4), and the sign of the x-coordinate changes.

Therefore, the image of point A after the reflection is A'(3, -4).

To reflect a point in the y-axis, we keep the x-coordinate the same and change the sign of the y-coordinate.

For point B(-2, -3):

After reflecting point B in the y-axis, the x-coordinate remains the same (-2), and the sign of the y-coordinate changes.

Therefore, the image of point B after the reflection is B'(2, -3).

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The expression that is undefined in the set of real numbers would be = 0/-4. That is option B.

Real numbers are those numbers that can either be positive or negative and that are rational or irrational numbers which are different from complex numbers.

An expression can be said to be an undefined set of real numbers when it's numerator = 0 as seen in 0/-4.

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Step-by-step explanation:

Cylinder LATERAL  S.A. = circ   X   Height = 132 cm  X  30 cm  = 3960 cm^2

   PLUS the two ends  =  two  X  pi r^2

  the circumference = pi * d = 132 cm

                   then  diameter = 132 / pi   then radius =  1/2  132 / pi = 66/ pi

     so end areas :  two *    pi (66/ pi)^2   = 2773.1

TOTAL = 3960  +  2773.1 =  6733.1 cm^2

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:

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

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

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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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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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: There are 240 people inside the auditorium.

Step-by-step explanation:

30 x 8 = 240

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 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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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:

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°

The triangles are similar because they are both right triangles, so they both have an angle that is equals to 90º. They both share a common vertex, <C. So they are similar by the Angle-Angle criterion.

Two triangles are defined as similar triangles when they share these two features listed as follows:

For this problem, they have two equal angle measures, the right angle and < C, hence the third angle also must be equal, and they are similar by the Angle-Angle criterion.

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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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Answer:

3.14 seconds

Step-by-step explanation:

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.