Derrick’s parents are finalizing a budget for his college expenses. His first year of college will cost $8,000, and his expenses will increase by 12% each year. What is the amount they should budget for Derrick’s four-year college education, to the nearest dollar?
$38,235 is needed.
$42,823 is needed.
$32,072 is needed.
$39,200 is needed.
1st year = 8000
2nd year = 8000 * 1.12 = 8960
3rd year = 8960*1.12 = 10035.20
4th year = 10035.20 * 1.12 = 11239.42
8000 + 8960 + 10035.20 + 11239.42 = 38234.62 round to $38,235
Answer:
$38,235 is needed.
Step-by-step explanation:
Given,
The cost of first year of college is $ 8000 and it is increasing by 12 % each year,
So, His first year's cost = $ 8000,
Second year's cost = 12 % more than the first year's cost = 112 % of first year's cost = 112 % of 8000 = 1.12 × 8000 = $ 8960,
Third year's cost = 112 % of second year's cost = 112 % of 8960 = 1.12 × 8960 = $ 10035.2
Fourth year's cost = 112% of third year's cost = 1.12 × 10035.2 = $ 11239.424
Hence, Total cost for four-year college education = 8000 + 8960 + 10035.2 + 11239.424 = $ 38234.624 ≈ $ 38235
⇒ $38,235 is needed.
Last week, Marcus had a balance of - $10 in his savings account. This week, the balance is $10. Which equation would show the change,c, in his savings account...?
A. -10 + c =10
B. c + 10 =10
C. c + -10 =-10
D. -10 - c =-10
Give one example of when would use the friendly numbers strategy to substract. Explain why
Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?
-4/5 and 3/4
-4/5 and -3/4
-1, -4/5, 3/4 and 1
-1. -4/5, -3/4 and 1
Answer:
Option 1 is correct.
Step-by-step explanation:
The given polynomial is
[tex]f(x)=20x^4+x^3+8x^2+x-12[/tex]
we have to find all the rational roots of the polynomial f(x)
The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number i.e in the form of [tex]\frac{p}{q}[/tex]
where p is a factor of constant term and q is the factor of coefficient of leading term.
In the given polynomial the constant is -12 and the leading coefficient is 20.
[tex]\text{All possible factor of -12 are }\pm1,\pm2, \pm3, \pm4,\pm6,\pm12[/tex]
[tex]\text{All possible factor of 20 are }\pm1,\pm2,\pm4,\pm5,\pm10,\pm20[/tex]
So, the all possible rational roots of the given polynomial are,
[tex]\pm1,\pm2, \pm3, \pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5},\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}[/tex]
Now, the rational roots of polynomial satisfy the given polynomial
[tex]f(-\frac{4}{5})=20(-\frac{4}{5})^4+(-\frac{4}{5})^3+8(-\frac{4}{5})^2-\frac{4}{5}-12=\frac{256}{625}\times 20-\frac{64}{125}+\frac{128}{125}-\frac{4}{5}-12[/tex]
[tex]=\frac{1024}{125}-\frac{64}{125}+\frac{128}{25}-\frac{4}{5}-12[/tex]
[tex]=\frac{960}{125}+\frac{128}{25}-\frac{4}{5}-12=12-12=0[/tex]
Hence, rational root.
[tex]f(\frac{3}{4})=20(\frac{3}{4})^4+(\frac{3}{4})^3+8(\frac{3}{4})^2+\frac{3}{4}-12=\frac{405}{64}+\frac{27}{64}+\frac{9}{2}+\frac{3}{4}-12=0[/tex]
rational root
[tex]f(1)=20(1)^4+(1)^3+8(1)^2+1-12=20+1+8-11=18\neq 0[/tex]
not a rational root.
hence, option 1 is correct
Answer:
The first option
Step-by-step explanation:
Right on edg:)
Madison is buying a $3,000 car at 9% simple interest for 2 years. What will be the total amount she pays for the car?
Answer:
3540.00
Step-by-step explanation:
The perimeter of a triangle is 26 centimeters. Side *a* of the triangle is 3 centimeters longer than side *b.* Side *c* is 1 centimeter shorter than twice side *b.* find the length of each side. (Show work)
did 6600 bee come first or did 2500 bce
Enter the values to complete the statement. To determine whether (−1,4) (−1,4) is a solution to the equation 3x+8y=29 3x+8y=29 , substitute for x and and for y
point slope for (3,21) and (6,12)
4 and one half divided by 3
ANSWER ASAP!!
Two weeks ago, Alice came home from vacation and noticed that a bean plant was growing in her garden. Today, the stalk is $452$ centimeters tall, and Alice observed that its height increases by $5\%$ every day. How tall was the plant $2$ weeks ago when she first noticed it growing? Express your answer as a decimal to the nearest tenth.
Answer:
Te plant was 228.29 centimeters tall.
Step-by-step explanation:
To find the size of the plant 14 days (2 weeks ago), we will use a formula called "exponential growth."
[tex]A=P(1+r)^{t}[/tex]
where
A=accumulated amount.
P=initial ammount
r=rate
t=elapsed time.
replacing the values we have
A=452 centimeters
P=variable to find
r=5% = 0.05
t=2 weeks= 14 days
So, we substitute the values in the equation
[tex]452=P(1+0.05)^{14}[/tex]
Then, we clear the variable P
[tex]P=\frac{452}{1.05^{14} }[/tex]
and perform the operations
[tex]P=\frac{452}{1.979931} =228.29centimeters[/tex]
A health food producer has 250 samples of a new snack to distribute in the mall the producer has to keep at least 50 samples for display in the health food store for the product launch how long will the samples last if consumers are taking the samples at a rate of 25 every hour
Final answer:
The 200 samples available for distribution will last for 8 hours at a consumption rate of 25 samples per hour.
Explanation:
The health food producer has 200 samples to distribute (250 total minus 50 for display), and if consumers take samples at a rate of 25 every hour, you would divide the 200 samples by the rate of 25 samples per hour to calculate how long the samples will last.
200 samples ÷ 25 samples/hour = 8 hours.
Therefore, the samples available for distribution at the mall will last for 8 hours before they run out, assuming the rate of consumption is constant at 25 samples per hour.
Round each number to the nearest tenth.
What is the best estimate for the difference of 376.64 – 109.38?
A.
267.2
B.
267.3
C.
268
D.
270
What function is represented below? graph begins in the first quadrant and decreases quickly while crossing the ordered pair 2, 1. Then the graph begins to decrease slowly as it approaches the x axis. f(x) = one fourth to the power of x plus 2 f(x) = one fourth to the power of x + 2 f(x) = one fourth to the power of x minus 2 f(x) = one fourth to the power of x − 2
Answer:
The represented function is :
[tex]f(x)=(\frac{1}{4})^{x-2}[/tex]
Step-by-step explanation:
[tex]1.\thinspace f(x)=(\frac{1}{4})^x +2[/tex]
And the equation must pass through (2,1) as given,
But, f(2) = 2.0625 ≠ 1 so this is not the required function.
[tex]2.\thinspace f(x)=(\frac{1}{4})^{x+2}[/tex]
And the equation must pass through (2,1) as given,
But, f(2) = 0.0039 ≠ 1 so this is not the required function.
[tex]3.\thinspace f(x)=(\frac{1}{4})^x -2[/tex]
And the equation must pass through (2,1) as given,
But, f(2) = -1.94 ≠ 1 so this is not the required function.
[tex]4.\thinspace f(x)=(\frac{1}{4})^{x-2}[/tex]
And the equation must pass through (2,1) as given,
We see, f(2) = 1 so this is the required function and the corresponding graph of the function is attached below :
Hence, The correct option is (4)
What is the rational exponent expression of 3 square root 4n
The world record for the 24 hour run for women on all surfaces is 255.303 kilometers, set by mami kudo of Japan in 2011. What was her average speed?
The average speed of Mami on all surfaces is 10.64 km/hr.
What is average?Average is the mid value of two different higher and lower values. The average can be determined by taking the sum of all data and then dividing it by the number of data or the total value divided by the total no. of values.
Given a runner in 24 hours named Mami can run 255.303 kilometers on all surfaces.
∴ Her average speed is (255.303/24) km/hr.
= 10.64 km/hr.
∴ Her average speed is 10.64 km/hr all surfaces.
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The length of a rectangular garden is 7 feet longer than its width. The garden's perimeter is 202 feet. Find the width of the garden.
When Milo got promoted at work he received a 20% pay raise. He now earns $72,000 a year. What was his annual salary before the raise?
the sum of 5 consecutive integers is 110. what is the fourth number in the sequence
Answer:
23
Step-by-step explanation:
choose the ratio that you would use to convert 5.5 pounds to ounces
Answer:
A. 16 ounces/1 pound
Step-by-step explanation:
Remember that: 1 pound (lb) is equal to 16 Ounces (oz).
Then you have to find a ratio to convert 5.5 pounds to ounces.
If you write: 5.5 pounds, you have to find a ratio that eliminates pounds in order to get ounces:
5.5 pounds*16 ounces/1 pound
In this way pounds in the numerator is eliminated with pounds from the denominator and the result you get is in units of ounces.
5.5 pounds*16 ounces/1 pound=88 ounces
Which choice shows the numbers correctly ordered?
A) 2 < 1.1 < 1.5 < π
B) 1.1 < 2 < 1.5 < π
C) 1.1 < 1.5 < 2 < π
D) 2 < π < 1.1 < 1.5
What is -3 -4 in integers
This is a square pyramid. What is the length of the base? h=3 v=36
volume of square pyramid = S^2*h/3
volume = 36
h = 3
36 = S^2 *3/3
36 = S^2
S = sqrt(36)
S = 6
length of base = 6
Carlene is selling T-shirts for a fundraiser. The T-shirts cost $20.50 each. To date, she has raised $700. Her goal is to raise more than $8,900. How many more T-shirts, x, does Carlene need to sell to reach her goal?
Carlene needs to sell 400 more T-shirts at $20.50 each to reach her goal of raising more than $8,900, after already raising $700.
The question asks us to determine how many more T-shirts, designated as x, Carlene needs to sell to reach her fundraising goal of more than $8,900, given that each T-shirt costs $20.50 and she has already raised $700. To solve for x, we can set up the following equation:
Total goal - Amount already raised = Amount still needed
$8,900 - $700 = $8,200
Next, we divide the amount still needed by the price per T-shirt to find out how many T-shirts need to be sold:
x = Amount still needed / Price per T-shirt
x = $8,200 / $20.50
x = 400
Carlene needs to sell 400 more T-shirts to reach her goal.
Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5. Ann paid a total of $49.10
Write an equation to determine the distance in miles (x) between the airport and Ann's home.
Write an equation to determine the distance in miles (x) between the airport and Ann's home.
HELP THIS IS URGENT 40 POINTS
Josiah, the manager of a pet store, bought 72 oz of water conditioner to use in his fish tanks. His small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner. He made a sketch to show the line representing the different combinations of tanks he could put the water conditioner into. The x-axis represented the number of small tanks and the y-axis represented the number of large tanks. The manager labeled only the intercepts.
Which points did the manager label?
(0, 6) and (2, 0)
(0, 12) and (36, 0)
(6, 0) and (0, 2)
(0, 36) and (12, 0)
factor a number, variable, or expression out of the trinomal shown below
Mary is 19 years old. she drinks the recommended intake of 2.2 liters of water and other beverages a day. about how many cups is this equivalent to?
To convert 2.2 liters to cups, multiply by 4.22675. Rounded, it's approximately 9 cups. So, option C) [tex]$9$[/tex] cups is correct.
To find out how many cups 2.2 liters is equivalent to, we'll first convert liters to cups.
1 liter is approximately equal to 4.22675 cups.
So, to find out how many cups are equivalent to 2.2 liters:
[tex]\[ \text{Number of cups} = 2.2 \, \text{liters} \times 4.22675 \, \text{cups/liter} \][/tex]
[tex]\[ \text{Number of cups} \approx 9.29885 \, \text{cups} \][/tex]
Rounded to the nearest whole number, 2.2 liters of water is approximately equivalent to 9 cups. Therefore, the correct answer is:
C) [tex]$9$[/tex] cups
The correct question is:
Mary is 19 years old. She drinks the recommended intake of 2.2 liters of water and other beverages a day. About how many cups is this equivalent to?
A) 3 cups
B) 6 cups
C) 9 cups
D) 12 cups
Y=(3/5)x -3 and 5y =3x-10 these lines are and the second question?
The given lines Y=(3/5)x -3 and 5y =3x-10 are examples of linear equations which, when solved, are found to be parallel due to their identical slope.
Explanation:The lines given in the question are in the format y = mx + b, where 'm' is the slope and 'b' is the y-intercept. The equations are Y=(3/5)x -3 and 5y =3x-10. By comparing the coefficients, the slope of the first line is 3/5 and the y-intercept is -3. For the second equation, we first need to convert it into the 'y = mx + b' form. Dividing every term by 5 gives us y = (3/5)x - 2. Therefore, the slope of the second line is also 3/5 and the y-intercept is -2. Since both lines have the same slope, they are parallel lines.
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(1 point) find ∬rf(x,y)da∬rf(x,y)da where f(x,y)=xf(x,y)=x and r=[1,6]×[4,5]r=[1,6]×[4,5].
The double integral of the function f(x, y) = x over the rectangle defined by [1, 6] and [4, 5] is calculated through an iterated integral to be 17.5.
Explanation:The problem asks to find double integral of the function f(x, y) = x over the rectangle R defined by the interval [1, 6] for x and [4, 5] for y. To find this, we perform an iterated integral. The integral is setup as follows:
∬Rf(x,y)dA = ∫ from 1 to 6 ∫ from 4 to 5 x dy dx
We first integrate with respect to y which gives us: xy| from 4 to 5 = x(5) - x(4) = x.
Then, we integrate this result with respect to x which gives us: 0.5x²| from 1 to 6 = 0.5(6^2) - 0.5(1^2) = 17.5
So, ∬Rf(x,y)dA equals to 17.5
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