Review the following monthly principal and interest factor chart to answer the question:
FICO Score APR 30-Year Term 20-Year Term 15-Year Term
770-789 5.5 $5.68
$6.88
$8.17
750-769 6.0 $6.00
$7.16
$8.44
730-749 6.5 $6.32
$7.46
$8.71
710-729 7.0
$6.65
$7.75
$8.99
690-709 7.5 $6.99
$8.06
$9.27
Calculate the monthly payment for a 15-year term mortgage after a 20% down payment on a $284,500.00 purchase price,
for a household with a 700 credit score. (4 points)
$2,531.45
$2,109.85
O $1,825.64
$2,384.81

Answer:

5m

Step-by-step explanation:

regla de 3:

1m = 3ft

15 pies ÷ 3 = 5m

Answer:

[tex]-8x^3\sqrt{7}[/tex]

Step-by-step explanation:

Step 1:  Let's start by simplifying -4x^2 * (√63x^2) using the following steps:

1.1: Separate √63x^2 into two terms:  

-4x^2 * (√63 * √x^2)

1.2:  Find the largest perfect square that we can factor out of 63.  It's 9 as 3^2 = 9 and 9 * 7 = 63.  Furthermore, √x^2 simplifies to x:

-4x^2 * (√9 * 7 * (x))

-4x^2 * (3√7 * x)

1.3:  We can multiply x and 3:

-4x^2 * (3x√7)

1.4:  We can distribute -4x^2 to 3x√7.  

-12x^3 * √7

Step 2:  Now we can work on simplifying x^3√112 using the following steps:

2.1:  Find the largest perfect square you can factor out of 112.  It's 16 since 4^2 = 16 and 16 * 7 = 112:

x^3 * √16 * 7

x^3 * 4√7

2.2:  Multiply x^3 and 4√7:
4x^3 * √7

Step 3:  Thus, -4x^2 * √63x^2 simplified individually is -12x^3 * √7 and x^3 * √112 simplified individually is 4x^3 * √7

3.1:  Add -12x^3 * √7 + 4x^3 * √7:

-8x^3√7

Optional Step 4:  We can check that we've correctly simplifed the equation by plugging in a number for x in both the radical expression not yet simplified and the simplified radical expression.  If we get the same answer, then we've simplified the expression correctly.  We can plug in 2 for x.

Plugging in 2 for x in -4x^2 * (√63x^2) + x^3 * (√112):

(1.) -4(2)^2 * √63(2)^2 + 2^3 * √112:

(2.) -4(4) * √63(4) + 8 * √112

(3.) -16 * √252 + 8 * √112

(4.) -16 * √36 * 7 + 8 *√16 * 7

(5.) -16 (6 * √7) + 8(4 *√7)

(6.) -96 * √7 + 32 * √7

(7.) -64√7

(8.) -169.3280839

Plugging in 2 for x in -8x^3√7:

(1.) -8(2)^3 * √7

(2.) -8(8) * √7

(3.) -64 * √7

(4.) -169.3280839

Therefore, we've correctly expressed the expression in simplest radical form

Answer:

  -65°

Step-by-step explanation:

You want the angle whose tangent is -2.1.

The inverse tangent function is used to find the angle when the tangent is known. On your calculator, the key for this will likely be labeled tan⁻¹. You need to make sure the calculator mode is set to degrees.

The value of θ is about -65°.

__

Additional comment

The principal branch of the arctangent function extends from -90° to +90°. The tangent function is periodic with period 180°, so adding any integer multiple of 180° to -65° will give you another angle whose tangent is -2.1. One such angle is 115°.

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The minimum amount one will pay making a deposit of notes and coins is R7.25.

To determine the minimum amount one will pay when making a deposit of notes and coins, we need to consider the costs mentioned in Table 2.

According to Table 2, the cost for notes deposit is R2.25 per R100 (or part thereof) deposited, and the cost for coins deposit is R5 per R100 (or part thereof) deposited.

To calculate the minimum amount, we need to determine the lowest possible value for both the notes and coins deposit costs.

For notes deposit:

The minimum value would be R2.25, as it is the cost for depositing less than R100 worth of notes.

For coins deposit:

The minimum value would be R5, as it is the cost for depositing less than R100 worth of coins.

To calculate the total minimum amount, we sum up the costs for notes and coins deposits:

Minimum amount = R2.25 (notes deposit cost) + R5 (coins deposit cost)

Minimum amount = R7.25

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2.1.1: The basic charge in the given context refers to a fixed monthly fee that is charged by the municipality for the provision of water services, regardless of the amount of water consumed by the user.

2.1.2: To calculate the tariff for a particular consumption level during 2017/2018, you need to find the relevant consumption tier and then apply the corresponding rate. For example, if the consumption level is 10,000 litres per month, then the relevant tier is 7-15 kilolitres, and the rate for this tier is R15.95 per kilolitre. Therefore, the cost of water for this consumption level is:

10 kilolitres x R15.95/kilolitre = R159.50

To this cost, the basic charge needs to be added. According to the table, the basic charge for 2017/2018 is R7.46 per month. Therefore, the total cost of water and basic charge for this consumption level is:

R159.50 + R7.46 = R166.96

Therefore, the tariff for a consumption level of 10,000 litres per month during 2017/2018 is R166.96.

2.1.3: To verify if Mr Morake's statement is correct, we need to check if the basic charge was included in the calculation of his water bill. Assuming that Mr Morake's water usage for the month of August 2018 fell within the 7-15 kilolitre tier, we can calculate his bill as follows:

Water usage: 10 kilolitres

Cost of water: 10 kilolitres x R17.39/kilolitre = R173.90

Based on the above calculation, it appears that the basic charge was included in Mr Morake's water bill, as his total bill of R201.27 exceeds the cost of water alone. Therefore, it seems that Mr Morake's statement is incorrect, and the basic charge was indeed included in his water bill.

Answer:

a. Let X be the length of a wooden pole produced for electricity networks in rural areas. The probability of a pole being rejected because it is too short is 0.02, and the probability of a pole being rejected because it is too long is 0.05. The acceptable range is between 6.3 m and 7.5 m. We can find the mean and standard deviation of X as follows:

First, we need to find the z-score corresponding to the lower bound of the acceptable range:

z1 = (6.3 - μ) / σ

Similarly, we need to find the z-score corresponding to the upper bound of the acceptable range:

z2 = (7.5 - μ) / σ

Using a standard normal table, we can find the values of z1 and z2 that correspond to the probabilities of 0.02 and 0.95, respectively:

z1 = -2.05

z2 = 1.64

Solving for μ and σ, we get:

z1 = (6.3 - μ) / σ => μ = 6.3 + 2.05σ

z2 = (7.5 - μ) / σ => σ = (7.5 - 6.3) / 1.64 = 0.74

Therefore, the mean and standard deviation of X are:

μ = 6.3 + 2.05(0.74) = 7.6 m

σ = 0.74 m

b. Let Y be the number of rejected poles in a sample of 20 poles. Y follows a binomial distribution with parameters n = 20 and p = 0.02 + 0.05 = 0.07. The probability of finding 2 rejected poles in a sample of 20 poles is:

P(Y = 2) = (20 choose 2) * 0.07^2 * 0.93^18 = 0.242

The probability of finding 2 rejected poles in a sample of 20 poles is 0.242.

Answer: 2048

Step-by-step explanation: 1. Write the exponential growth model.

The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.

2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048

Therefore, the estimated population of the town in 2023 is 2048.

Hello !

68/17 = 4

=> yes for 68

84/17 = 4.941...

=> no for 84

357/17 = 21

=> yes for 357

1001/17 = 58.882...

=> no for 1001

Answer: a=101 b=79 c=83 d=97

(x + 12)° + (5x)° = 90°

m∠1 = 25° and m∠2 = 65°

We know that the little box represents 90 degrees. We will write an equation using this information.

      (x + 12)° + (5x)° = 90°

Next, we will solve by isolating the x variable with inverse operations and combing like terms.

      (x + 12)° + (5x)° = 90°

      x° + 5x° = 78°

      6x° = 78°

      x = 13°

Lastly, we will find the value of each angle by substituting.

       m∠1 = (x + 12)° = ((13) + 12)° = 25°

       m∠2 = (5x)° = (5(13))° = 65°

Answer:

a is g(x) b is f(x)

Step-by-step explanation:

because a increases faster

The equation that represents the direct variation between a and b in this scenario is: b = -a.

The correct option is (A).

We have,

The number b varies directly with the number a.

This equation states that b is equal to the negative value of a, which reflects the condition that b is located in the opposite direction from 0 compared to a and varies directly with a.

So, the equation cab be stated as b = -a.

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Answer:

The expression 3+4x2 can be simplified using the order of operations, which is a set of rules used to determine the sequence in which operations are performed in an expression. According to the order of operations, we first perform any calculations inside parentheses, then we perform any multiplications or divisions (from left to right), and finally we perform any additions or subtractions (from left to right).

There are no parentheses in this expression, so we move on to the next step, which is to perform any multiplications or divisions. In this case, we have 4x2, which equals 8. So, we can replace 4x2 with 8, and the expression becomes:

3+8

Finally, we perform the addition, and get the final result:

11

Therefore, 3+4x2 is equal to 11.

Step-by-step explanation:

Answer:

2x squared - 5

= 2(x)^2 - 5

= 2(4)^2 - 5

= 2(16) - 5

= 32 - 5

= 27

Answer:

x ≤ 4

Step-by-step explanation:

To solve the inequality x - 3 ≤ 1, we need to isolate x.

Remember that this is a linear inequality, and linear inequalities are solved the same way as a linear equation - the objective is to leave the variable alone on one side (usually the left-hand side or LHS) to find its value −

x - 3 ≤ 1

x ≤ 4

Therefore, x ≤ 4

Answer: 4.5 or A

Step-by-step explanation:

1) Find LCM of 9 and 6, which is 18.

2) Multiply x/9 by 2. (2x/18)

3) Multiply 3/6 by 3. (9/18)

4) Divide by 2 (numberator on both sides)

               x = 4.5

Answer:

The probability that at least one of two independent purchases is a Samsung display can be calculated using the complement rule:

P(at least one Samsung) = 1 - P(neither is a Samsung)

The probability that neither of the two purchases is a Samsung display is:

P(neither is a Samsung) = (1 - 0.29) x (1 - 0.29) = 0.51

Therefore, the probability that at least one of the two purchases is a Samsung display is:

P(at least one Samsung) = 1 - 0.51 = 0.49

The probability that in a collection of two independent purchases, at least one is a Samsung is 0.49.

If p(x) ⊆ p(y), then it means that every element of the power set of x is also an element of the power set of y. This implies that set x is a subset of set y, written as x ⊆ y.

Here,

Let A be the set x and B be the set y. Then the power sets of A and B are p(A) and p(B) respectively.

Suppose p(A) ⊆ p(B). This means that for every element a in p(A), a is also an element of p(B).

Now consider any element a in A. Since a is an element of A, it is also an element of its power set p(A). Thus, if p(A) ⊆ p(B), a must also be an element of p(B). This means that a is an element of B.

Therefore, we have established that every element of A is an element of B. That is, A ⊆ B.

Thus, if p(x) ⊆ p(y), then x ⊆ y.

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The area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

To find the area of a vertical cross section through the center of the base of the cone-shaped paperweight, we need to determine the radius of the base first.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is about 12.56 inches, so we can set up the equation:

12.56 = 2πr

To solve for r, we divide both sides of the equation by 2π:

r = 12.56 / (2π)

Now we can calculate the radius:

r ≈ 12.56 / (2 × 3.14)

r ≈ 12.56 / 6.28

r ≈ 2 inches

The radius of the base is approximately 2 inches.

Since the vertical cross section passes through the center of the base, the shape of the cross section is a circle. The formula for the area of a circle is A = [tex]πr^2[/tex], where A is the area and r is the radius.

Now we can calculate the area of the cross section:

A = [tex]πr^2[/tex]

A ≈ 3.14 × [tex](2^2)[/tex]

A ≈ 3.14 × 4

A ≈ 12.56 square inches

Therefore, the area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

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Answer:

a. q^2 = sqr(225) can be solved.

q^2 = sqr(225) means q^2 = 15^2. So, q can be found by taking the square root of both sides:

q = ±15

Step-by-step explanation:

Answer:

  (c)  x³·∛x

Step-by-step explanation:

You want the simplified form of ∛(x¹⁰).

The first part of the problem tells you how to get there. After you have that expression, you need to bring the x⁹ term from under the radical.

  [tex]\sqrt[3]{x^{10}}=\sqrt[3]{x^9\cdot x}=\sqrt[3]{x^9}\cdot\sqrt[3]{x}=\boxed{x^3\cdot\sqrt[3]{x}}\qquad\text{matches choice C}[/tex]

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From the given information, we have:

PC = 10 (length of segment PC)

∠CBD = x°

∠BCD = x + 54°

We can determine the relationship between angles ∠CBD and ∠BCD by recognizing that they are inscribed angles intercepting the same arc CD. In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. Therefore, we have:

∠BCD = 1/2(arc CD)

Since ∠BCD = x + 54° and arc CD is the diameter, which is 180°, we can set up the following equation:

x + 54 = 1/2(180)

Simplifying the equation:

x + 54 = 90

x = 90 - 54

x = 36

So, the measure of ∠CBD (m∠CBD) is 36°.

Hello !

45min = 3/4h = 0,75h

[tex]\frac{45km}{0,75h} \\\\= \frac{45km*\frac{1}{0,75} }{0,75h*\frac{1}{0,75} } \\\\= \frac{60km}{1h}[/tex]

s = 60km/h

[tex]s=\dfrac{d}{t}\\\\d=45\text{ km}\\t=45\text{ min}=0.75\text{ h}\\\\s=\dfrac{45\text{ km}}{0.75\text{ h}}=60\dfrac{\text{km}}{\text{h}}[/tex]

Answer:

x = 48°

Step-by-step explanation:

[tex]x=(90-42)^{0} =48^{0}[/tex]

Hope this helps

★ The sum of the angles in a triangle is always 180° ...

________________________________

The limit when n approaches infinity for the given expression is the one in option D, 21.

Here we want to take the following limit of n when it tends to infinity in the following rational expression:

[tex]\lim_{n \to \infty} 24 - 3 - \frac{24}{2n} + \frac{40}{n} + \frac{15}{3n^2}[/tex]

Notice that in all the terms where n appears, it is on the denominator. Thus, when n tends slowly to infinity, the denominator will be way larger than the numerator, and thus, all the fractions will tend to zero, then we will get:

[tex]\lim_{n \to \infty} 24 - 3 - \frac{24}{2n} + \frac{40}{n} + \frac{15}{3n^2} = 24 - 3 = 21[/tex]

The correct option is the last one, D.

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Answer:

8/15

Step-by-step explanation:

Assuming that a is in the 1st quadrant, based on sin a = 8/17 you can build a right triangle as in the picture. Third side you compute with Pythagoras [tex]x^2 + 8^2 = 17^2 \implies x = 15[/tex].

At this point the tangent is the ratio of the two segments, or 8/15.

Else, you can calculate cos a  based on the fact that [tex]cos\ a = \sqrt{1-sin^2\ a}[/tex] (under the same assumption as the beginning. Then it's just a matter of plugging numbers.

Answer:

X = 10

Z = 67

Step-by-step explanation:

We see that the angles are formed by the intersection of two lines.

Angles z and  67° are vertically opposite angles and therefore they are equal to each other

z°= 67°

Angles z and (7x + 43) are supplementary angles. The sum of these angles add up to 180°

z + 7x + 43 = 180

67 + 7x + 43 = 180

7x + 110 = 180

7x = 180 -110 = 70

x = 70/7 = 10