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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Which of the following is a reasonable estimated answer to the following problem?
989,867 ÷ 999
What is the GCF of 32a and 48b??
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.
Sofia is learning to knit. After her first three stitches, she had to undo the last two. Then she made three more stitches and again, had to undo the last two. If this pattern continues, how many stitches will Sofia have to make before she has six good stitches?
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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Which graph represents the equation y=13x−4 ?
Answer: The correct option is graph (A).
Step-by-step explanation: We are given to select the graph that represents the following linear equation :
[tex]y=\dfrac{1}{3}x-4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Comparing with the slope-intercept form y = mx + c of a straight line, we see that
the slope of the line (i) is [tex]m=\dfrac{1}{3},[/tex] and y-intercept, c = -4.
Also, we know that the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
Graph (A) :
The points (0, -4) and (3, -3) lies on the line. So, its slope will be
[tex]m=\dfrac{-3-(-4)}{3-0}=\dfrac{1}{3},[/tex]
the point where the line crosses the y-axis is (0, -4).
That is, y-intercept, c = -4.
Since the slope and y-intercept of graph (A) is same as that of line (i), so this option is CORRECT.
Graph (B) :
The points (0, -2) and (3, -3) lies on the line. So, its slope will be
[tex]m=\dfrac{-3-(-2)}{3-0}=-\dfrac{1}{3},[/tex]
Since the slope of graph (B) is not same as that of line (i), so this option is NOT CORRECT.
Graph (C) :
The points (0, -4) and (-3, 3) lies on the line. So, its slope will be
[tex]m=\dfrac{3-(-4)}{-3-0}=-\dfrac{7}{3},[/tex]
Since the slope of graph (C) is not same as that of line (i), so this option is NOT CORRECT.
Graph (D) :
The points (-4, 0) and (-3, 3) lies on the line. So, its slope will be
[tex]m=\dfrac{3-0}{-3-(-4)}=\dfrac{3}{1}=3,[/tex]
Since the slope of graph (B) is not same as that of line (i), so this option is NOT CORRECT.
Thus, graph (A) is the correct option.
Identify the corresponding word problem given the equation: x - 9.2 = 12.8 A) Nick ran 9.2 miles less than Perry last week. If Nick ran 22 miles, how many miles did Perry run? B) Nick ran 12.8 miles less than Perry last week. If Nick ran 9.2 miles, how many miles did Perry run? C) Perry ran 9.2 miles less than Perry last week. If Nick ran 12.8 miles, how many miles did Perry run? D) Nick ran 9.2 miles less than Perry last week. If Nick ran 12.8 miles, how many miles did Perry run?
The correct answer is D
Nick ran 9.2 miles less than Perry last week. If Nick ran 12.8 miles, how many miles did Perry run?
x - 9.2 = 12.8
x = 12.8 + 9.2
x = 22
Perry ran 22 miles for the week, 9.2 miles more than Nick.
Answer:
correct answer is D
Step-by-step explanation:
MS Nelson had 5,280 craft sticks. She gave all of the craft sticks to her 22 students. Each student received the same number of craft sticks. I need the answer to part b and c. I already did a and half of b
What is 1/8 of $68.96
What is eight worth in 8.517
Determine if you can use the HL Congruence Theorem to prove the triangles to prove the triangles below are congruent.
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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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:
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A ferry traveled 1/6 of the distance between two ports in 3/7 hour. At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
Two numbers have a distance of 5 units from 0 on a number line. The numbers can be graphed on the number line as points A and B.
Drag and drop the labels to the correct positions on the number line.
Answer:
Point A is labeled at x=-5 and point B is labeled at x=5.
Step-by-step explanation:
It is given that two numbers have a distance of 5 units from 0 on a number line.
Let the unknown number be x.
Case 1: x is 5 units less than 0.
[tex]x=0-5[/tex]
[tex]x=-5[/tex]
The point A is labeled at x=-5.
Case 2: x is 5 units more than 0.
[tex]x=0+5[/tex]
[tex]x=5[/tex]
The point B is labeled at x=5.
Which distributive property represents the area of the rectangle?
(3 x 3) + (3 x 4)
(3 x 3) + (3 x 9)
(9 x 3) + (6 x 9)
(3 x 3) + (3 x 6)
if 234 players are separated into 18 equal teams,how many players will be on each team?
What two integers is 87 between
Answer:
43 and 44
Step-by-step explanation:
im giving 50 points
Solve the equation.
-4(3 - 2x) + 2x = 2x - 8
A) x = 2
B) x = -1
C) x =
1
2
D) x =
1
3
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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The line of best fit drawn on the plot shown is used to predict the number of tickets sold on a certain day. Use the two points shown on the line of best fit to calculate its slope to the nearest tenth.
Slope=
What is the expression in standard form for 4(2a)+7(-4b)+(3*c*5)
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:
The sequence that begins with 3, where each succeeding term is twice the preceding term
Marcia buys a dress that is on sale for 15% off it's original price. She uses a store coupon to obtain an additional 10% off the sale price. Marcia pays $91.80 for the dress. What was the original price of the dress?
Answer:
120$
Step-by-step explanation:
We must calculate the prices with the application of discounts successively
The last discount he got was 10%, so $ 91.80 equals 90% of the price
We calculate the price before this discount by applying with a simple rule of three
[tex]90 \% \longrightarrow 91.80\\100\% \longrightarrow x\\x=\frac{(100)(91.80)}{90}\\ x= 102\$[/tex]
She pays $ 102 with a 15% discount, so this value equals 85% of the original price
We calculate the price before this discount by applying with a simple rule of three
[tex]85\% \longrightarrow 102\\100\% \longrightarrow x\\x=\frac{(100)(102)}{85}\\ x= 120\$[/tex]
Which story problem could be solved using the given equation? 1/5×2/3=m
Lucas needs a wooden strip that is 2/3 yards long for his boat model. He plans to cut the strip into pieces that are each 1/5 yards long. How many pieces can be cut from the 2/3 yard long strip?
Jasmine bought some tiles to put around her patio. Each tile has a length of 2/3 foot and a width of 1/5 foot. What is the area, in square feet, of each tile?
Lucas’s kitten is 23 foot tall. Jake’s kitten is 1/5 foot taller than Lucas’s kitten. How tall is Jake’s kitten?
Karen measured 2/3 cup of milk for a recipe. She then added another 1/5 cup of the milk to the recipe. How much milk did Karen use in the recipe?
The story problem that can be solved using the given equation is about finding the area of a tile with given dimensions.
Explanation:The story problem that can be solved using the given equation 1/5×2/3=m is Jasmine bought some tiles to put around her patio. Each tile has a length of 2/3 foot and a width of 1/5 foot. What is the area, in square feet, of each tile?
To find the area of the tile, we can multiply the length and width of the tile. Plugging in the values from the equation, we have (2/3) * (1/5) = 2/15. Therefore, each tile has an area of 2/15 square feet.
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Graph y=−5/6x−4 . (if you can give me the coordinates)
the slope is -5/6 and y intercept is -4
so the first dot goes on (0,-4)
the next dot would go
-5/6 x 4 = -29/6
(1,-29/6)
A pianist plans to play 6 pieces at a recital from her repertoire of 26 pieces. How many different recital programs are possible?
The number of different recital programs that are possible is 230230 programs
What is combination?Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula:
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time
The information will be illustrated as:
= 26! / (26 - 6)! 6!
= 26! / 20!6!
= 230230
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