Answer:
The interest rate is 3.79% or 3.8%
Step-by-step explanation:
The formula to find how much money A we have at the end of t years if we start with a principal or amount of money P today and the interest is compounded n times in the years is:
A=P(1+ r/n)^(nt) (1)
Here A = $2,976.45 the final amount
t = 11 years
P = $1,963.45.
and n = 4 because the interest is compounded quarterly or 4 times in the year.
We the need to simplify the interest rate r in (1) so:
A=P(1+ r/n)^(nt) (1)
A/P = (1+ r/n)^(nt)
(A/P)^(1/nt) = (1+ r/n)
(A/P)^(1/nt) - 1 = r/n
((A/P)^(1/nt) - 1 ) * n = r
r = ((A/P)^(1/nt) - 1 ) * n
We replace values and solve doing parenthesis exponents first
r = ((2,976.45/1,963.45.)^(1/(4*11)) - 1 ) * 4
r= ((1.51^(1/44)) -1)*4
((1.51^(1/44)) -1)*4
r= (1.009499443 - 1)*4
r= 0.009499443 *4 = 0.037997773
That expressed in percentage multiplying by 100 is 3.79% or 3.8% interest
at the movie theater, at least 60% of the seats must be full to recover operating costs. on Thursday 146 out of 200 seats are occupied. How many seats are occupied? What percentage of the seats are unoccupied?
Sophie and Eleanor are making bouquets using daisies and tulips. Each bouquet will have the same total number of flowers,Eleanor uses fewer daisies in her bouquet. than sophie. Whose bouquet will have the greatet ratio of daisies of total flowers? Explain.
Answer:
Sophie's ratio is greater.
Step-by-step explanation:
Sophie and Eleanor are making bouquets using daisies and tulips. Each bouquet will have the same total number of flowers.
Eleanor uses fewer daisies in her bouquet than Sophie.
Lets say the total flowers used in each bouquet is 15.
Eleanor uses 5 daisies. So, her ratio for daisies to total flowers become = [tex]\frac{5}{15}=\frac{1}{3}[/tex]
Suppose Sophie uses 10 daisies so her ratio becomes = [tex]\frac{10}{15}=\frac{2}{3}[/tex]
Now comparing both ratios, we can see that Sophie's ratio is greater.
Darius flipped a coin 500 times and it landed heads up 300 times. What is the relative frequency of the coin landing heads up based on the results of this experiment?
A bar of copper has a mass of 216 g and a volume of 24 cm. what is the density of copper
The density of copper bar is 9g/cm³
Given that :
Mass of copper bar = 216 g
Volume = 24 cm
Density of copper will be :
Recall :
Density = Mass / Volume
Density = 216 g / 24 cm³
Hence, Density of copper bar = 9 g/cm³
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You deposit $1,600 in a bank account. Find the balance after 3 years if the account pays 2.4% annual interest compounded quarterly.
$1803.34 will be the balance after 3 years if the account pays 2.4% annual interest compounded quarterly
What is Compound interest?Compound interest is the interest on a loan or deposit that accrues on both the initial principal and the accumulated interest from previous periods.
let's call the amount of money A, the initial amount P, the yearly rate r, the number of compounds per year n.
[tex]A = P(1 + \dfrac{r}{n})^{(nt)[/tex]
[tex]A = 1600(1 + \dfrac{.024}{4})^{((4)(5)[/tex]
[tex]A = 1600(1.006)^{(20)[/tex]
[tex]A = \$1803.34[/tex]
Hence $1803.34 will be the balance after 3 years if the account pays 2.4% annual interest compounded quarterly
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It costs a family $216 to refinish a wood floor. They want to refinish floor in a larger room. The ratio of corresponding sides is 3:4. How much would it cost to refinish wood floor in the larger room?
A) $396
B) $384
C) $262
D) $288
The cost for the larger room comes out to be $384. Option B) is the correct answer.
The cost of refinishing a wood floor in a room is related to the area of the floor. Since the ratio of the corresponding sides of the two rooms is 3:4, the ratio of their areas is the square of the ratio of the sides, being 9:16 (since 32 = 9 and 42 = 16). To find the cost to refinish the larger room, we can set up a proportion where $216 corresponds to an area with a 'weight' of 9, and x corresponds to an area with a 'weight' of 16.
Mathematically this can be represented as 216/9 = x/16. Solving for x, we calculate x = (216/9) imes 16 = 24 imes 16 = $384. Therefore, the cost to refinish the wood floor in the larger room would be $384, which corresponds to option B).
It cost to refinish wood floor in the larger room is $384. So option (b) is correct.
To solve this problem, we'll use the concept of ratios to find the cost of refinishing the wood floor in the larger room.
First, let's set up the ratio of the areas of the two rooms. Since the ratio of corresponding sides is 3:4, the ratio of their areas will be 3^2 : 4^2, which is 9:16.
Now, since the cost of refinishing the smaller room is $216, we need to find what portion of the total cost that represents. Since 9 parts represent $216, 1 part represents $216 ÷ 9 = $24.
Next, we'll find the total cost of refinishing the larger room. Since the larger room has 16 parts (as per the ratio), the total cost will be 16 parts × $24/part = $384.
So, the correct answer is B) $384.
Here's the detailed calculation:
Find the ratio of areas of the rooms: [tex]\(3^2 : 4^2 = 9 : 16\)[/tex]
Find the cost per part: (216 ÷ 9 = 24)
Find the total cost for the larger room: [tex]\(16 \times 24 = 384\)[/tex]
a cube has a volume of 8 cubic inches what is the length of each edge of the cubes
Answer:
The formula for the volume of the cube is v=a3 where a is the length of the edge the volume of the cube is 1/8 cube inches v= 1/8 cube inches a3=(1/2)3 cubic inches
Step-by-step explanation:
log4 (x - 7) = 3
solve for x
What is the expression in standard form for 4(2a)+7(-4b)+(3*c*5)
Sean and his sister, Betty equally mow 8/9th the total area of a lawn. What fraction of the total area did each of them mow? (Show ur work plz)
Using the division operation, the fraction of the total area mowed by each person is [tex] \frac{4}{9}[/tex]
Total fraction mowed = [tex] \frac{8}{9}[/tex]
Number of persons who mowed the area = 2
Since, the same amount of area ws mowed by each person, then the area mowed per person can be calculated thus :
Total Area mowed ÷ number of persons[tex] \frac{48}{9} \div 2 = \frac{4}{9}[/tex]
Hence, each person mowed [tex] \frac{4}{9}[/tex]
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8x+4(x-1) simplify the following expression
plz help me on this question
The manager of a plant nursery bought 120 lb of soil to use for potting plants. The manager can put 5 lb into each of the small pots and 12 lb into each of the large pots. The manager made a sketch to show the line representing the different combinations of pots that can be used. The x-axis represented the number of small pots and the y-axis represented the number of large pots. The manager labeled only the intercepts.
Which points did the manager label?
1. (0, 12) and (5, 0)
2. (0, 10) and (24, 0)
3. (0, 24) and (10, 0)
4. (0, 5) and (12, 0)
The points that were labelled by the manager on the graph are (0, 10) and (24, 0). These points are found by dividing the total amount of soil by the amount of soil required by each type of pot.
Explanation:In this Mathematics problem, we need to determine which points were labelled on the graph created by the nursery manager representing combinations of small and large pots. We can find these points, the intercepts, by understanding that these occur when one variable is zero. The x-intercepts happen when all soil is used for large pots (i.e., the y-axis, or number of small pots, is zero), and the y-intercepts occur when all the soil is used for small pots (i.e., the x-axis, or number of large pots, is zero). For the x-intercept, if each large pot requires 12lb of soil, then the manager could fill 120/12 = 10 large pots if no soil is used for small pots. Therefore, the x-intercept is (0, 10). Similarly, the y-intercept would be obtained by dividing the total amount of soil with the amount used for a small pot. That gives us 120/5 = 24. Hence, the y-intercept is (24, 0). So, the points labelled by the manager are option 2: (0, 10) and (24, 0).
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What is the equation of this graphed line (-6,-3) (6,-7)
Answer: [tex]x+3y=-15[/tex]
Step-by-step explanation:
The equation of a line passes through (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Then, the equation of a line that passes through (-6,-3) (6,-7) will be :-
[tex](y-(-3))=\dfrac{-7-(-3)}{6-(-6)}(x-(-6))\\\\\Rightarrow y+3=\dfrac{-7+3}{6+6}(x+6)\\\\\Rightarrow\ y+3=\dfrac{-4}{12}(x+6)\\\\\Rightarrow\ y+3=\dfrac{-1}{3}(x+6)\\\\\Rightarrow\ 3(y+3)=-x-6\\\\\Rightarrow\ 3y+9=-x-6\\\\\Rightarrow\ x+3y=-15.[/tex]
Hence, the required equation is [tex]x+3y=-15[/tex].
Kelly took 12 pictures at school on Tuesday. She took 7 pictures at lunch and 5 pictures at recess. If she randomly selects a picture to put in her locker, what is the probability it is a picture she took at recess?
a 5/7
b 1/6
c 1/5
d 5/12
Determine if you can use the HL Congruence Theorem to prove the triangles to prove the triangles below are congruent.
Please show work ill give brainliest!!!!!!!!!!
Nick and Cathy collected shells on the seashore. In the morning Nick found several shells, while Cathy found 7 shells. In the afternoon, Nick found 15 more shells. Now the ratio of Nick's shells to Cathy's shells in 3:1. How many shells did Nick find in the morning?
Thanks!!!!!!!!!!!!!!
How can you do this problem ?? Plz explain
Mr Durant bought Console B for $20.99 off the advertised price. Find the total amount Mr. Durant paid.
power negative a b to the third power minus AC if a equals -2 and b equals 3 and C equals negative 8
[tex]\(-ab^3 - ac = 38\)[/tex].
To evaluate the expression [tex]\(-ab^3 - ac\)[/tex] given a = -2, b = 3, and c = -8, we substitute the values into the expression:
[tex]-ab^3 - ac = -(-2)(3)^3 - (-2)(-8)\\= -(-2)(27) - (16)\\= 54 - 16 \\= 38[/tex]
What is 1/8 of $68.96
Simplify fully: √18 / √8
Anthony decided to buy two DVDs that were not included in the deal. His price after tax was $21.60. What was the cost of the two DVDs before the sales tax was added?
The cost of the two DVDs before the sales tax was added is $21.60.
To find the cost of the two DVDs before sales tax, let's first calculate the total cost including tax and then backtrack to find the cost before tax.
Calculate Total Cost with Tax:
The total cost including tax is given by: Total Cost = Price + Tax
Calculate Tax Amount:
Tax = Price * Tax Rate
Given that the sales tax rate is 8 percent (0.08 in decimal form), the tax amount is: Tax = 0.08 * $21.60 = $1.728
Calculate Total Cost:
Total Cost = Price + Tax
Total Cost = $21.60 + $1.728 = $23.328
Find Cost of DVDs Before Tax:
Let the cost of the two DVDs before tax be represented by x.
Total Cost = Price of DVDs + Price of DVDs * Tax Rate
$23.328 = x + 0.08x
$23.328 = 1.08x
Solve for x:
Divide both sides by 1.08:
x = $23.328 / 1.08 = $21.60
So, the cost of the two DVDs before the sales tax was added is $21.60.
Complete Question:
Anthony decided to buy two DVDs that we're not included in the deal. His price was $21.60. The sales tax is 8 percent. What was the cost of the two DVDs before the sales tax was added?
A gift box in the shape of a cube has a volume of 216 cm3 . What is the area of the base of the box
The area of the base of a cube with a volume of 216 cm³ is 36 cm², obtained by first calculating the side length as the cube root of the volume and then squaring that length.
The volume of a cube is calculated by raising the length of one of its sides to the third power (Volume = s³), where s is the length of a side. Given that the volume of the gift box is 216 cm³, we can find the length of a side by taking the cube root of the volume. The cube root of 216 cm³ is 6 cm, which is the length of each side of the box.
Since the base of the cube is a square, the area of the base is simply the length of a side squared (Base Area = s²). Hence, the area of the base of the box is 6 cm × 6 cm, which equals 36 cm².
Write these portions as percents.
A) 3 tenths and 6 hundredths.
B) 8 hundredths
C) 17 hundredths
D) 11 tenths.
How much would $200 invested at 7% interest compounded annually be worth after 5 years? Round your answer to the nearest cent.
Answer:
280.51
Step-by-step explanation:
help me please,it will be greatly appreciated
Mr.hollins determines that he gives away $800 each month. If he gives away 16% of his budget, how much is his overall budget ?
Give an example of an area. You would measure in square miles
please help Graph y= –3x+4 .
The graph of the equation of line y = -3x + 4 is plotted
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = -3x + 4
where the equation is in the form of slope intercept
where the y-intercept is given by b = 4
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = -3
So , the slope of -3 indicates that for every 1 unit increase in x, the value of y decreases by 3 units. The negative slope means that the line is decreasing as x increases, sloping downward from left to right.
Hence , the equation of line is plotted on the graph
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