Answer:
the answer is the second option; because 4+(-7) is an equivalent expression the answer Is -3
What is 12 less than 15 times x?
Toby just graduated from four years of college. At the beginning of each year, he took out a Stafford loan with a principal of $6,125. Each loan had a duration of ten years and an interest rate of 5.3%, compounded monthly. All of the loans were subsidized. Toby plans to pay off each loan in monthly installments, starting from his graduation. What is the total lifetime cost for Toby to pay off his 4 loans? Round each loan's calculation to the nearest cent.
a.
$7,904.04
b.
$31,616.16
c.
$10,393.82
d.
$36,490.25
Would appreciate if you could show the work for how this is done.
p.s. I later submitted this question and the answer is B.
The cost that's necessary to pay the loan will be $31,616.16.
How to calculate the cost of the loanFirst, we need to calculate the effective monthly interest rate. This will be:
i = 0.053/12
= 0.0044
The effective annual interest rate will then be:
i = (1 + 0.0044)^12 - 1
I = 0.0543
Next thing will be to calculate the present worth of all the loans which will be:
P = 6125 + 6125 (1 + 0.0543) + 6125 (1 + 0.0543)² + 6125(1 + 0.0543)³
P = $22,671.40
The worth of the loans after four years will be:
P = 22671.40 (1 + 0.0543)⁴
= $31,616.16
In conclusion, the correct option is $31,616.16.
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To calculate the total cost of Toby's 4 Stafford loans, the monthly amount for one loan is first calculated and then multiplied by four and by the number of months. The correct total lifetime cost is approximately $31,569.60.
To determine the total lifetime cost that Toby will pay to pay off his 4 Stafford loans, each with a principal of $6,125, an interest rate of 5.3% compounded monthly, and a loan duration of ten years, we need to calculate the monthly payment for a single loan and then multiply by the number of loans and the duration. The formula for the monthly payment on an installment loan is:
P = P[r(1+r)^n] / [(1+r)^n - 1]
where:
P is Principle Amountr is rate of interestn is time in yearsUsing the data given:
P = $6,125 * [0.004417(1 + 0.004417)^120] / [(1 + 0.004417)^120 - 1]
Calculating this gives us a monthly payment of approximately $65.77 for each loan. Toby took out 4 loans, so his total monthly payment is 4 * $65.77 = $263.08.
The total lifetime cost for a single loan is the monthly payment * number of payments (120), which is:
Total cost for one loan = $65.77 * 120 = $7,892.40
And the total lifetime cost to pay off all 4 loans:
Total cost for all loans = $7,892.40 * 4 ≈ $31,569.60
Therefore, rounding each loan's payment to the nearest cent, the total lifetime cost to pay off all 4 of Toby's loans is roughly $31,569.60, making the answer option b the correct one.
A bag of 29 tulip bulbs contains 10 red tulip bulbs, 11 yellow tulip bulbs, and 8 purple tulip bulbs.
What is the probability that two randomly selected tulip bulbs are both red?
What is the probability that the first bulb selected is red and the second is yellow?
What is the probability that the first bulb selected is yellow and the second is red?
Answer:
The probability that two randomly selected tulip bulbs are both red is 0.11
The probability that the first bulb selected is red and the second is yellow is 0.13
The probability that the first bulb selected is yellow and the second is red is 0.13
Step-by-step explanation:
A bag of 29 tulip bulbs contains:
10 red tulip bulbs
11 yellow tulip bulbs
8 purple tulip bulbs
Part 1:What is the probability that two randomly selected tulip bulbs are both red?
No. of red tulips = 10
So, probability of getting red tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]
= [tex]\frac{10}{29}[/tex]
Since 1 bulb is drawn . So, total no. of bulbs remaining = 28
And that 1 bulb is drawn from red bulbs . So, remaining red bulbs = 9
So, probability of getting red bulb in second draw = [tex]\frac{9}{28}[/tex]
Thus the probability that two randomly selected tulip bulbs are both red:
= [tex]\frac{10}{29}\times\frac{9}{28}[/tex]
= [tex]\frac{45}{406}[/tex]
= [tex]0.11[/tex]
Hence the probability that two randomly selected tulip bulbs are both red is 0.11
Part 2: What is the probability that the first bulb selected is red and the second is yellow?
No. of red tulips = 10
So, probability of getting red tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]
= [tex]\frac{10}{29}[/tex]
Since 1 bulb is drawn . So, total no. of bulbs remaining = 28
No. yellow bulbs =11
So, probability of getting yellow bulb in second draw = [tex]\frac{11}{28}[/tex]
Thus the probability that the first bulb selected is red and the second is yellow
= [tex]\frac{10}{29}\times\frac{11}{28}[/tex]
= [tex]\frac{55}{406}[/tex]
= [tex]0.13[/tex]
Hence the probability that the first bulb selected is red and the second is yellow is 0.13
Part 3: What is the probability that the first bulb selected is yellow and the second is red?
No. of yellow tulips = 11
So, probability of getting yellow tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]
= [tex]\frac{11}{29}[/tex]
Since 1 bulb is drawn . So, total no. of bulbs remaining = 28
No. red bulbs =10
So, probability of getting red bulb in second draw = [tex]\frac{10}{28}[/tex]
Thus the probability that the first bulb selected is red and the second is yellow
= [tex]\frac{11}{29}\times\frac{10}{28}[/tex]
= [tex]\frac{55}{406}[/tex]
= [tex]0.13[/tex]
Hence the probability that the first bulb selected is yellow and the second is red is 0.13
Need help solving for X
Given: line segment AB≅line segment BC
Prove: The base angles of an isosceles triangle are congruent.
The two-column proof with missing statement proves the base angles of an isosceles triangle are congruent.
Statement Reason
1. segment BD is an angle bisector of ∠ABC. 1. by Construction
2. ∠ABD ≅ ∠CBD 2. Definition of an Angle Bisector
3. segment BD ≅ segment BD 3. Reflexive Property
4. 4. Side-Angle-Side (SAS) Postulate
5. ∠BAC ≅ ∠BCA 5. CPCTC
Which statement can be used to fill in the numbered blank space?
A. ΔDAB ≅ ΔDBC
B. ΔABD ≅ ΔABC
C. ΔABC ≅ ΔCBD
D. ΔABD ≅ ΔCBD
In the given two column proof two sides and included angles are equal.
Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles .In the figure sides BD≅BD , AB≅ BC and <ABD ≅,BDD Therefore triangle ABD and triangle CBD are congruent by SAS property of congruence.
The correct option for missing statement is D. ΔABD ≅ ΔCBD .
Answer:
ΔABD ≅ ΔCBD
Step-by-step explanation:
Guys this is the right answer, ΔABD ≅ ΔCBD. I got it right on my test!
what is 2.999 rounded to the nearest hundreth?!!
The perimeters of a rectangle and an equilateral triangle are equal. The length of the rectangle is twice the width, and the side of the triangle is 8 more than the width of the rectangle. Which statements about this scenario are true if we use the variable w to represent the width of the rectangle?
Answer:
for online school people it will be 2,3,4
Step-by-step explanation:
i did the assigment
multiply 3/7 x 14
...?
The simplified product of 3/7 multiplied by 14 is 6.
To multiply 3/7 by 14, you can follow these steps:
Multiply the numerators: 3 x 14 = 42.
Multiply the denominators: 7 x 1 = 7.
Therefore, the product of 3/7 multiplied by 14 is 42/7.
However, we can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 7.
= 42/7
= 6/1
= 6.
So, the simplified product of 3/7 multiplied by 14 is 6.
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Will upvote if you explain on how I solve this problem?!?!
f(x) = 5(2)x
solve 9x + 7 = 7x - 5
The solution of equation 9x + 7 = 7x - 5 is -6.
The equation 9x + 7 = 7x - 5 can be solved by first isolating x on one side. To do this, we subtract 7x from both sides of the equation, which gives us 2x + 7 = -5. Next, we subtract 7 from both sides to get 2x = -12. Finally, we divide both sides by 2 to find that x = -6. This single solution can be checked by substituting x back into the original equation to verify that both sides equal out, confirming it is an identity. Therefore, the correct solution is x=-6.
To validate the result, we substitute -6 back into the original equation:
9(-6) + 7 = 7(-6) - 5
-54 + 7 = -42 - 5
-47 = -47, which is indeed an identity.
3x + 2y = 5
5x + 2y = 7
Based on the given system of equations, which of the following is not true?
What percentage of Anchor Global Insurance Full Time employees are employed in the US?
No. Of Employees
FULL TIME PART TIME
US:1,740 170
South East Asia:670 64
UK:300 30
Europe:250 24
China:380 32
Middle East:135 12
Total Cost (IN $ MILLIONS)
Full Time PART TIME
47.0 2.5
What is the simplified form of each expression?
1. (–5.1)^0
1
0
–5.1
–1
2. 3g^-2 b^2
3b^2 over g^2
3g^2b^-2
3gb^-4
b^2 over 3g^2
Estaban has a big jar of change in his room. he has 600 coins in total, 240 of them are pennies. what percentage of the coins are pennies
NEED HELP I SUCK AT MATH AND LIFE IN GENERAL =)
2 .A relation is plotted as a linear function on the coordinate plane starting at point C (0,−1)(0,−1) and ending at point D (2,−11)(2,−11) .
What is the rate of change for the linear function and what is its initial value?
Select from the drop-down menus to correctly complete the statements.
Options for rate of change: a. -11 b. -5 c. 0 d. 5
options for initial value: a. -11 b. -2 c. -1 d. 0
3. Maria is saving money so she can go to a professional football game. Maria has $25. She saves $5 a week.
Graph a ray to represent the amount she saved over time.
( i am really bad at graphs but you're just graphing this i guess???)
4. The temperature decreases by 0.5 degrees every hour.
5. x −2−2 −1−1 0 1 2
y −6−6 −4−4 −2−2 0 2 how would you put that onto a graph???
9. What is the equation of a line with a slope of 1212 and a point (3, 1) on the line?
Express the equation in the form of y=mx+by=mx+b where m is the slope and b is the y-intercept.
10.What does the initial value mean for this function?
Roberta saves $10 each week.
After 4 weeks, Roberta has $90.
Roberta had $50 before she started to save money each week.
Roberta had no money until she started to save $10 a week.
Dan put's 11 dollars or his allowance in his savings account every week. how much money will he have affter 15 weeks
Choose all correct answers. Which of the following ordered pairs are solutions of the system, y > 3 and y < 2x + 2
A. (0, 2)
B. (2, 4)
C. (3, 5)
D. (-2, 0)
sin2x=(\sqrt(3))/(2)
What is "the ratio of a line's rise over its run?"
Fractions that are equivalent to1/2
Maricella has a bag containing 35 nickles and quarters.The total value of these coins is less than $2.50. What is the maximum number of quarters that meets these conditions?
The graph of a line gets _____ as the absolute value of the slope gets bigger.
A. longer
B. shorter
C. steeper
D. less steep
"What is element a23 in matrix A
"
Answer: The answer is (A) -5.
Step-by-step explanation: We are given to find the element [tex]a_{23}[/tex] in the following matrix:
[tex]A=\begin{bmatrix}8 & -4 & -3\\ 3 & -9 & -5\\ -8 & 8 & 8\end{bmatrix}[/tex]
We know that [tex]a_{mn}[/tex] is an element of a matrix present in the m-th row and n-th column.
So, [tex]a_{23}[/tex] will be the element present in the second row and third column.
Since the element in the second row and third column is - 5, so we have
[tex]a_{23}=-5.[/tex]
Thus, (A) -5 is the correct option.
What is the average rate of change of f(x), represented by the table of values, over the interval [-3, 2]?
What additional information would you need to prove that ΔABC ≅ ΔDEF by ASA
The additional information needed to prove that ΔABC ≅ ΔDEF by ASA is two pairs of congruent angles and the included side between the two pairs of congruent angles.
We are given that;
The two triangles ΔABC and ΔDEF
Now,
To prove that ΔABC ≅ ΔDEF by ASA (Angle-Side-Angle) congruence criterion, we need the following information:
Two pairs of congruent angles.
The included side between the two pairs of congruent angles.
If two angles and one side of one triangle are equal to two angles and one side of another triangle, then they are congruent. For example, in ΔABC and ΔDEF, ∠A = ∠D, ∠B = ∠E and BC= EF then ΔABC ≅ ΔDEF by AAS criteria
Therefore, by congruent triangles answer will be two pairs of congruent angles and the included side between the two pairs of congruent angles.
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At a hockey game a vendor sold a combined total of 145 sodas, the number of hot dogs sold was 33 less of sodas sold, Find the number of Sodas and Hot dogs sold?
The number of sodas sold is 145, and the number of hot dogs sold is 112. (145 sodas, 112 hot dogs)
Let's denote:
- s as the number of sodas sold.
- h as the number of hot dogs sold.
Given that the total number of sodas sold is 145, we have:
[tex]\[ s = 145 \][/tex]
And we know that the number of hot dogs sold is 33 less than the number of sodas sold:
[tex]\[ h = s - 33 \][/tex]
Now, substitute the value of s into the equation for h :
[tex]\[ h = 145 - 33 \]\[ h = 112 \][/tex]
So, the number of hot dogs sold is 112, and the number of sodas sold is 145.
how do you round 17.92 to the tens
1. Which is a minor arc in L? (1 point)
a. AB
b. DB
c. ABD
d. CBD
Arc DB measure less than 180 degrees, is called a minor arc.
Option (b) is correct
Major and minor arc:A minor arc is an arc whose angle is less than 180 degrees.
A major arc is an arc whose angle is greater than 180 degrees .A semicircle, is an arc whose angle is equals to 180 degrees . it divides the circle in two.From given figure, It is observed that, arc DB measure less than 180 degrees is called a minor arc.
Hence, option (b) is correct.
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Which of the following is not equivalent to the other three?
A) 1/6
B) 1.66666666.....
C) .17
D) .16
The shortest known adult woman is about 24 inches tall and tallest known adult woman is about 92 inches tall. Write an absolute value equation that represents the minimum and maximum heights. Use x to represent the heights.
Final answer:
The absolute value equation that represents the minimum and maximum heights of adult women, with heights represented by x, is |x - 58| = 34.
Explanation:
To write an absolute value equation representing the minimum and maximum heights of adult women, where the shortest known adult woman is about 24 inches tall and the tallest known adult woman is about 92 inches tall, we can use the variable x to represent an adult woman's height. The midpoint between the smallest and largest height is (24 + 92) / 2 = 58 inches. The distance from this midpoint to each extreme is 34 inches, because 92 - 58 = 34 and 58 - 24 = 34. So, the absolute value equation would be |x - 58| = 34. This equation represents that the height of an adult woman can deviate from 58 inches by 34 inches to be either at the minimum or maximum height recorded.
Final answer:
The absolute value equation representing the minimum and maximum heights of adult women is |x - 58| = 34, where x is the height in inches.
Explanation:
The objective is to write an absolute value equation to represent the minimum and maximum heights of adults.
Using the heights given for the shortest and tallest known adult women, 24 inches and 92 inches respectively, we set the variable x to represent an unknown height.
To express this as an absolute value equation, we identify the midpoint between these two heights, which is (24 inches + 92 inches) / 2 = 58 inches.
The distance from the midpoint to either extreme is (92 inches - 58 inches) = 34 inches, which is the absolute difference.
Therefore, our absolute value equation is |x - 58| = 34.
This equation tells us that the height x must be either 34 inches above or below 58 inches, which corresponds to the minimum and maximum heights of 24 inches (58 - 34) and 92 inches (58 + 34) respectively.