Frank has four different credit cards, the balances and interest information of which are outlined in the table below. he would like to consolidate his credit cards to a single credit card with an apr of 18% and pay off the balance in 24 months. what will his monthly credit card payment be? credit card balance apr a $2,380 19% b $4,500 15% c $1,580 17.50% d $900 21% a. $390.00 b. $462.91 c. $467.29 d. $52.00 please select the best answer from the choices provided a b c d

Answer:

x = 3 ft

y = 83

Step-by-step explanation:

DEFG ≅ SPQR

So, corresponding part will be congruent

∠D ≅ ∠S   ; ∠E ≅ ∠P ;  ∠F≅ ∠Q  ;  ∠G ≅ ∠R

DE = SP

x = 3 ft

Sum of interior angles = 360

∠D + ∠E + ∠F + ∠G = 360

∠S + (y+3) + ∠Q + (y +1) = 360

107 + y + 3 + 83 + y+1 = 360

194 + 2y = 360

        2y = 360 - 194

        2y = 166

         y = 166/2

        y = 83

To find a degree 3 polynomial with a coefficient of x³ equal to 1 and zeros at 1, -4i, and 4i, we can use the fact that complex zeros occur in conjugate pairs. The polynomial can be simplified to x³ - 17x + 16.

Since the coefficient of x³ is 1, the polynomial can be written as x³ + bx² + cx + d, where b, c, and d are real numbers. The zeros of the polynomial are 1, -4i, and 4i. Since complex zeros occur in conjugate pairs, we know that the conjugate of -4i is 4i.

Using Vieta's formulas, we can determine that the sum of the zeros is equal to the opposite of the coefficient of x², which is -b. The sum of the zeros 1, -4i, and 4i is 1 + (-4i) + 4i = 1. Therefore, we have -b = 1, which implies b = -1.

The product of the zeros is equal to the constant term, which is d. The product of the zeros 1, -4i, and 4i is 1 * (-4i) * 4i = 16. Hence, d = 16.

Finally, we can write the polynomial with the given information: x³ - x² + cx + 16. The coefficient of x² is -1, and to make it positive, we can multiply the entire polynomial by -1, resulting in -x³ + x² - cx - 16. Since the coefficient of x³ is required to be 1, we can divide the polynomial by -1 to obtain the simplified form: x³ - 17x + 16.

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Answer:

Part 1:    7/3 degrees/hour

Part 2:    28/3 degrees

Step-by-step explanation:

Part 1:

3 1/2 degrees per 1 1/2 hours =

= (3 1/2)/(1 1/2)

= (7/2) / (3/2)

= 7/2 * 2/3

= 7/3 degrees/hour

The rate is 7/3 degree per hour

Part 2:

In 4 hours, the temperature goes up 4 times what it goes up in 1 hour.

4 hours * 7/3 degree/hour = 28/3 degrees

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer:

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle. In the circle, the two chords ¯PR and ¯QS intersect inside the circle. Since vertical angles are congruent, m∠1=m∠3 and m∠2=m∠4.

Answer:

45

Step-by-step explanation: 180- 135

Answer:

<L = 45

<N = 135

Step-by-step explanation:

<L + 135 = 180

<L = 180 - 135

<L = 45

<N = 135 because of vertical angles

9514 1404 393

Answer:

  a.  (1.4, 2.6)

  b.  (3, 2)

Step-by-step explanation:

a. The circumcenter is the intersection point of the perpendicular bisectors of the sides of the triangle.

For points X(a, b) and Y(c, d), the perpendicular bisector of XY can be written as ...

  (c -a)(x -(c+a)/2) +(d -b)(y -(d+b)/2) = 0

Then the equation of the perpendicular bisector of MN is ...

  (-2-4)(x -(-2+4)/2) +(4-0)(y -(4+0)/2) = 0

  -6(x -1) +4(y -2) = 0

  3x -2y = -1 . . . .  divide by -2 and put in standard form

Similarly, the perpendicular bisector of NO is ...

  (0-(-2))(x -(0-2)/2) +(6 -4)(y -(6+4)/2) = 0

  2(x +1) +2(y -5) = 0

   x + y = 4 . . . . divide by 2 and put in standard form

So, the point of intersection is ...

  (3x -2y) +2(x +y) = (-1) +2(4) . . . . . add twice the 2nd equation to the 1st

  5x = 7 . . . . . . simplify

  x = 1.4 . . . . . . divide by 5

  y = 4-1.4 = 2.6 . . . . . find y from the second equation

The coordinates of the circumcenter are (1.4, 2.6).

__

b. The centroid is the average of the vertex coordinates.

  centroid = (A +B +C)/3 = ((1, 2) +(3, 4) +(5, 0))/3 = (1+3+5, 2+4+0)/3 = (9, 6)/3

  centroid = (3, 2)

Answer:

p^3=x q-x

Step-by-step explanation:

Answer:

q - p³

Explanation:

raise p to the 3rd power gets us p³. then we have to subtract that from q, giving us q - p³, which is the answer.

Answer:

12.60.

Step-by-step explanation:

12.00 × 5%=.6

,6 + 12.00= 12.60

Answer:

2.759 x 3.901 ft

Step-by-step explanation:

To subtract 1/2h-1 from 3/4h+4, we can distribute the negative sign to the expression 1/2h-1 and then combine like terms. This gives:

(3/4h + 4) - (1/2h - 1)

= 3/4h + 4 - 1/2h + 1 (distributing the negative sign)

= (3/4h - 1/2h) + (4 + 1) (combining like terms)

= 1/4h + 5

Therefore, the result of subtracting 1/2h-1 from 3/4h+4 is 1/4h+5.

Answer: 913%

Step-by-step explanation:

Based on the concept of payday loans, Barbara's annual percentage rate is 9.125%

The Annual Percentage Rate (APR) is a term that is used to describe the cost paid each year to borrow money, such as fees, expressed as a percentage.

In this case, to get the annual percentage rate (APR) on Barbara's loan calculate the effective interest rate for the 8-day period and then annualize it.

Given that Barbara borrowed $75 and was charged a fee of $15 for an 8-day term the total amount she needs to repay is $75 + $15 = $90.

To calculate the effective interest rate we can use the following formula:

Effective Interest Rate = (Total Interest / Principal) * (365 / Loan Term)

Total Interest = $15 (fee)

Principal = $75 (loan amount)

Loan Term = 8 days

Substituting the values into the formula:

Effective Interest Rate = (15 / 75) * (365 / 8)

Effective Interest Rate = 0.2 * 45.625

Effective Interest Rate = 9.125%

Therefore, APR = Effective Interest Rate * Compounding Frequency

APR = 9.125% * 1

APR = 9.125%

Hence, in this case, it is concluded the approximate annual percentage rate (APR) on Barbara's loan is around 9.125%.

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-0.05 is the average rate of change in median age per year from 1930 to 1960.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  a data set that gives the median age of an American man at the time of his first marriage.

Year                             Median age

1910                              25.1

1920                             24.6

1930                             24.3

1940                             24.3

1950                             22.8

1960                             22.8

1970                             23.2

1980                             24.7

1990                             26.1

2000                             26.8

The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)

The average rate of change from 1930 to 1960 = -0.05

Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.

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Answer: .................................................

how many ways can the seating be arranged?

answer = 128 ways

correct or what???

Answer:

33%

Step-by-step explanation:

50.5 out of 75 is 67% so you need 33 more percent

33% increase in the number of yards he carried.

Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Given that, Nathan had carried the ball for 50.5 yards at end of the first half of a football game. He carried the ball for a total of 75 yards By the end of the game.

We have to determine the percent of the increase in the number of yards he carried.

⇒ (75-50.5) = 24.5

⇒ 24.5/75

⇒ 0.3267

⇒ 32.67

Round to the nearest whole tenth

⇒ 33 %

Therefore, 33% increase in the number of yards he carried.

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A type II error is committed when a true alternative hypothesis is mistakenly rejected.

This means that the null hypothesis is accepted even though it is false.

It is important to note that a type II error can occur when there is not enough power in the study, which can be influenced by factors such as the sample size, effect size, and variability.

It is important to minimize the risk of type II errors by increasing the power of the study through appropriate sample size and statistical methods.

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The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.

The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.

Here, we will solve this system of equations using inverse of the matrix method as follows:

We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].

The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33]  where,

d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,

d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,

d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,

d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,

d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,

d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,

d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,

d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,

d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.

We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]

Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]

Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.

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Answer:

3/5  is the  probability that the fish is NOT black

Step-by-step explanation:

Because the total  number of fish is  5  and the probability of  the fish being black is 2/5 . So the number of fish left are 3   =  equal to the   the  probability that the fish is NOT black

Answer:

6.05 kg, 6050 grams

Step-by-step explanation:

The kilograms were already given in your question, so that's one half done.

1 kilogram is equivalent to 1000 grams. If we multiply 6.05 by 1000, then you get 6050, the measurement in grams.

Answer:

60° option b) is the answer

The width of Rectangle B, given the relationship that it has with Rectangle A, can be found to be 2. 5 cm

The area of Rectangle B is said to be one - half of the area of Rectangle A which means that the area of Rectangle B is :

= 40 / 2

= 20 cm ²

The rectangles have the same length which means that the length of Rectangle B is 8 cm as well.

The width would therefore be :

= Area of Rectangle B / Length of Rectangle B

= 20 / 8

= 2. 5 cm

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√(9/31) is the irrational number

Answer:

  T/V = P/(nR)

Step-by-step explanation:

You want to find T/V from the equation PV = nRT.

T is in the numerator of the ratio you want. V is on the other side of the equation from T, so you can put V in the denominator by dividing both sides of the equation by V:

  \(P=\dfrac{nRT}{V}\)

Now, you can get the ratio T/V by itself by dividing by its coefficient:

  \(\dfrac{P}{nR}=\dfrac{T}{V}\)

Swapping sides gives you the relation you want:

  \(\boxed{\dfrac{T}{V}=\dfrac{P}{nR}}\)

__

Additional comment

Isolating variables and solving equations using the properties of equality should be familiar processes.

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Answer: It will be 10 degrees and 20 degrees

Step-by-step explanation:

always all angles of a triangle is 180 degrees and we already have 150

so just subtract 150 from 180 and ul get 30 but it has to be two sides so its 10 and 20

The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120

Define System of Equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Jane bought 3 shirts and returned 2 pairs of pants

Laura bought 4 shirt and 3 pairs of pants.

Let, s = cost of shirt

and, p = cost of a pair of pants

The equation for Jane is

3s - 2p = $5

Here, -ve sign because Jane returned 2 pairs of pants and then bill was $5.

Now, the equation for Laura is

4s + 3p = $120

Here, +ve sign because Laura bought 4 shirt and 3 pairs of pants and then bill was $120.

So, the system of equation we get

3s - 2p = $5

4s + 3p = $120

After solving  simultaneously we get the values s = 15 and p = 20.

Now, if you want to cross check then put the values of s and p in equations and it should be equal to RHS value like this,

for 1st equation,

3 * 15 - 2 * 20 ⇒ 45 - 40 = 5 (which is correct)

for 2nd equation,

4 * 15 + 3 * 20 ⇒ 60 + 60 = 120 (which is correct)

Hence, The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120.

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Answer:

n<=7 (less than or equal to)

Step-by-step explanation:

42/6=7, so 7 is the max number of laps he will run.

Answer:

1. $0.29/oz

2.$0.26/oz

3.$0.23/oz

4.$0.22/oz

Step-by-step explanation:

So you have to find how much the toothpaste will cost per oz.

1.  10oz = $2.92 So you have to divide. 2.92/10= 0.292 rounded to the nearest cent is 0.29

2. 12oz = $3.10 Divide: 3.10/12 is about 0.26

3. 8oz=1.85 Divide: 1.85/8 is about 0.23

4.16oz=3.52 Divide: 3.52/16 is exactly 0.22

Hope this helps:)

Answer:

120 students

Step-by-step explanation:

12 didnt with the 25 students....now they are asking 250...10x25=250 . so 12x10=120 :)

Answer:

120 students

Step-by-step explanation:

12/ 25 students=.48

.48*250=120

The marginal revenue in the interval between six and seven jet skis is $300.

Here we are given that total revenue from six jet skis is $2,400

and total revenue from seven jet skis is $2,700

Now, marginal revenue is defined as the revenue gained or lost by producing one more additional unit of a good.

Here, the total revenue increases from $2,400 to $2,700 as we go from producing 6 jet skis to 7 jet skis.

Thus, the change in total revenue will be-

2700 - 2400

= 300

This means that the gain in revenue is $300.

Thus, the marginal revenue in the interval between six and seven jet skis is $300.

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