Assume the account pays a nominal annual interest of r% compounded quarterly, the value of the interest rate (r) is equal to 7.87%.
How to determine the value of r?Mathematically, compound interest can be calculated by using this formula:
A(t) = P(1 + r/n)^{nt}
Where:
A represents the future value.P represents the principal.r represents the interest rate.n represents the number of times compounded.T represents the time measured in years.Substituting the given parameters into the formula, we have;
1.6(3,818) = 3,818(1 + r/8)^{8 × 6}
1.6 = (1 + r/8)^{48}
Taking the 48th root of both sides of the equation, we have:
[tex]\sqrt[48]{1.6} = \sqrt[48]{(1 + \frac{r}{8} )^{48} }[/tex]
1.00983983823726 = 1 + 0.125r
0.125r = 1.00983983823726 - 1
0.125r = 0.00983983823726
Interest rate, r = 0.00983983823726/0.125
Interest rate, r = 0.0787
Interest rate, r = 7.87%
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the area of a rectangle shown is 44m2
3 2/3 m
x?
work out the missing length x
one day is the amount of time it takes for a planet to make one complete rotation. The number of hours in one day is different for each planet. How many days are equal to 1,100 hours on Saturn? What do you need to do to solve the problem
A) 1,100 hours is equal to approximately 104days in Saturn.
B) You need to know how hours make 1day in Saturn. i.e 10 hours 34minutes or 10.567hours.
From the question note that the number of hours in one day is different for each planet.
Hence for Saturn;
1 day = 10hours.34minutes
X day =1,100 hours
Note; 34 minutes in hours will be:
60 minutes =1hour
34/60 =0.567hour
Thus;
10hours.34minutes = 10hours +0.567hour
=10.567hours
To find the number of days in 1,100 hours, we cross multiply;
X day * 10.567hours =1,100 hours * 1 day
X day = 1,100 hours * 1 day
10.567hours
X day =104.1 ≈ 104 days
Therefore, you need to know the number of hours that makes a day in Saturn.i.e 10 hours 34minutes or 10.567hours.
. Again, 1,100 hours is equal to approximately 104days in Saturn.
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Help Please!
Solve the inequality and graph it’s solution.
Answer:
A) m > -13
Step-by-step explanation:
[tex]-112-14m < 70\\-14m < 70+112\\-14m < 182[/tex]
[tex]\frac{-14m}{-14} < \frac{182}{-14}[/tex]
[tex]m > -13[/tex]
Hope this helps
pls answer all the questions FOIL pre calc
Answer for Part I: x² - 3x - 10
Step-by-step explanation:
The FOIL method means to multiply the "First, Outside, Inside, and Last" in order of the terms. See attached for a visual and the work behind the answer.
Using this method, we end up with;
x² - 3x - 10
help me please please please
Answer:
SA = 148 cm²
Step-by-step explanation:
the opposite faces of the cuboid are congruent , then
SA = 2(6 × 5) + 2(4 × 5) + 2(6 × 4)
= 2(30) + 2(20) + 2(24)
= 60 + 40 + 48
= 148 cm²
would appreciate getting the answer
The value of angle 5 is 115°
What are corresponding angles?Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).
angle 2 is 65°
angle 6 = angle 2 = 65°( corresponding angles)
angle 6 + angle 5 = 180( angles on a straight line)
65 + angle 5 = 180
angle 5 = `180 - 65
angle 5 = 115°
In conclusion, angle 5 is 115°
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Order from least to greatest 5.5 7.428, 5.5081, 5.58
Answer:
5.5,5.5081, 5.58, 7.428
Step-by-step explanation:
to look from least to greatest just look at each place value and see which one is slower and any that you can’t see is zero
Hopes this helps please mark brainliest
Find the slope of the line passing through the points (4, -2) and (9, -2).
slope:
Find the slope of the line passing through the points (2, 9) and (2, - 7).
slope:
Answer:
x1 y1 x2 y2
1. 0 - explanation - (4, -2) (9, -2) -2 - -2
4 - 9 (put a fraction bar when you put the y2 and y1 together and put the x2 and y2 in the denominator spot) basically -2 subtract -2 equals 0
2. it would be defined or 0
You-Pick Blueberry Farm sells 6 pounds of blueberries for $16.50.
How much would 9 pounds of blueberries cost?
How much would 5 pounds of blueberries cost?
I will give brainly! worth 23 points! please hurry!
The value of 9 pounds of blueberries is $24.75.
The value of 5 pounds of blueberries is $13.75.
How to calculate the cost?The fact that the Blueberry Farm sells 6 pounds of blueberries for $16.50 implies that the cost per pound will be:
= $16.50 / 6
= $2.75
Therefore, 9 pounds of blueberries cost:
= Cost per pound × 9
= $2.75 × 9
= $24.75
5 pounds of blueberries will cost:
= 5 × $2.75
= $13.75
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find the area of a rhombus whose diagonals are the lengths 36cm and 22.5 cm
Answer:
area of rhombus=1/2*36*22.5
=405cm^2
Step-by-step explanation:
PLEASE HELP ITS DUE IN 20 MINUTES
Answer/Step-by-step explanation:
[tex]-\frac{8}{27} a^{15} = (-\frac{2}{3})^{3} * (a^3)^5 = (-\frac{2}{3} a^{5})^3[/tex]
I hope this helps!
In a recent student government election the ratio of students who voted for the winner to all the students who was 0.70 to the number of students who wrote it was 75 how many votes did the winner get?
The winner received 53 of the 75 votes in the student gov. election according to provided ratio.
What is ratio?
In arithmetic, a magnitude relation shows range times one number contains another.
Main body:
Because the ratio of students who voted for the winner compared to all students who voted is 0.70
we can rewrite this as:
0.70 = 70/100
And, because we know the total number of students who voted is 75 and if we call the number of students who voted for the winner s , we can then write this relationship and solve for s :
[tex]\frac{70}{100} = \frac{s}{75}[/tex]
Multiplying both sides by 75.
75*[tex]\frac{70}{100} = \frac{s}{75}[/tex]*75
s= 75*70/100
s = 5250/100
s = 52.5
s ≈ 53.
Hence ,The winner received 53 of the 75 votes.
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1) What is the slope of the following graph?
Answer:[tex]\frac{3}{-2}[/tex]
Step-by-step explanation:
slope= [tex]\frac{rise}{run}[/tex]
start at (0,1)
go up 3 units
then go left 2 units
slope= [tex]\frac{3}{-2}[/tex]
-7 + 5x = 5x + 9 help me pls
Answer:
solve for x 7 (5x+9)=- (x-9) 7(5x + 9) = −(x − 9) 7 ( 5 x + 9) = - ( x - 9) Simplify 7(5x+9) 7 ( 5 x + 9). Tap for more steps... 35x+63 = −(x−9) 35 x + 63 = - ( x - 9) Simplify −(x−9) - ( x - 9).
Step-by-step explanation:
Rewrite 0+0+7(5x+9)= -(x----9)
Apply the distributive property. 7 (5x) + 7.9= - (x-9)
Can someone please help me with the following problems
The day which has the least change in temperature is Wednesday.
The two consecutive days which showed a drop in temperature is Wednesday and Thursday.The graph which was easier to read is table graph.Table graph illustrate the data because it clearly shows the data representation.How to read and explain graph?The day which has the least change in temperature can be calculated by finding the change in temperature:
Monday = High temperature - low temperature
= 82° - 58°
= 24°
Tuesday = High temperature - low temperature
= 85° - 60°
= 25°
Wednesday = High temperature - low temperature
= 77° - 62°
= 15°
Thursday = High temperature - low temperature
= 68° - 50°
= 18°
Friday = High temperature - low temperature
= 75° - 48°
= 27°
Saturday = High temperature - low temperature
= 70° - 52°
= 22°
Sunday = High temperature - low temperature
= 84° - 56°
= 28°
The day which has the least change in temperature is Wednesday
Which two consecutive days which showed a drop in temperature: Wednesday and Thursday with 77° and 68° respectively.
Unlike line graph, table graph is the graph that is easier to read.
Therefore, the graph which best illustrate the graph is table graph because it represent the data in a clearer way.
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. a trough has ends shaped like isosceles triangles, with width 3 m and height 4 m, and the trough is 10 m long. water is being pumped into the trough at a rate of 5m3/min. at what rate does the height of the water change when the water is 1 m deep?
The rate at which the height of the water changes when the water is 1m deep is; dh/dt = 1.5m/min
We are given;
width; w = 3m
Height; h = 4m
Length of trough; L = 10m
According to similar triangle property; w =3/4h
volume of water; V = 1/2×w×h×L = 1/2 × 3/4h × h × 10 = 15/4 h²
Differentiate using chain rule for both sides with respect to t gives;
dV/dt = (1/2)(15/2)h(dh/dt).
Now, we are given dV/dt = 5m³/min and we want to find the rate at which the height of water changes when the water is 1 m deep.
Thus;
5 = ×dh/dt
At h = 1m; 5 = 15(1)/2 × dh/dt
⇒ dh/dt = 2/3
dh/dt = 1.5 m / min
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 90(1.02)
The exponential equation represents an exponential growth because the rate of decay is 1.02 which is greater than 1.
y = 90(1.02)^x
The general form equation is:
y(x)= a(1+r)^x such that r is the decay percent.
on comparing,
1 + r = 1.02
r = 1.02 - 1
r = 0.02
converting into percent
r = 0.02 * 100
r = 2%.
Hence the exponential growth is 2%.
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The geometric mean of a number and nine times the number is 30. What is the number?
For the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.
As given in the question,
Geometric mean GM = 30
Let us assume the first number is x
and second number i.e. 9 times of the first number is 9x
By the formula GM = [tex]\sqrt{x.y}[/tex]
Now putting the value
30 = [tex]\sqrt{x.9x}[/tex]
30 = [tex]\sqrt{9x^{2} }[/tex]
30 = 3x (∴ square root of 9 is 3 and sq root of x² is x)
10 = x (by dividing both the side by 3)
Therefore, for the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.
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How do you graph this?
Reflection at point y = -6 will have coordinates as
preimage image
Q(0, -9) Q' (0, -6)
R(4, -9) R' (4, -6)
S(6, -8) S' (6, -5)
T(2, -8) T' (2, -5)
How to find the coordinatesThe transformation involve is reflection and this is a type of transformation that produces the mirror image of the preimage
The transformation rule to get the mirror image is (x, y) → (x, y + 3)
The coordinates are applied as follows
Q(0, -9) → (0, -9 + 3) → Q' (0, -6)
R(4, -9) → (4, -9 + 3) → R' (4, 6)
S(6, -8) → (6, -8 + 3) → S' (6, -5)
T(2, -8) → (2, -8 + 3) → T' (2, -5)
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The tape diagram shows that there are 90 teeth on a comb.
Teeth
90
Complete the table to show different percentages of the teeth on the comb.
90
100%
Percentage
% of 90 teeth
% of 90 teeth
The asked percentages are given as
1. 90 is 100% of 90.
2. 9 is 10% of 90.
3. 27 is 30% of 90.
Explain percentage.A percentage is a particular number or fraction in every hundred. The denominator of the fraction is 100, and it is represented by the symbol "%."
The purpose of percentage calculations is to determine the percentage of a whole in terms of 100. A percentage can be determined using one of two methods:
Through the unitary approach.By making 100 the new denominator of the fraction.It should be noted that when the denominator is not a power of 100, the second technique of percentage computation is not used.
Given, a comb has 90 teeth.
1. Find out what percentage of 90 is 90 now.
Let the percentage be x,
(x/100) × 90 = 90
x = (90 × 100)/90
x = 100 %
2. Now, find what percent of 90 is 9.
Let the percentage be x,
(x/100) × 90 = 9
x= (9 × 100)/ 90
x = 10%
3. Now, find what percent of 90 is 27.
Let the percentage be x,
(x/100) × 90 = 27
x= (27 × 100)/ 90
x = 30%
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write the missing number = 1/2 of 18
please help me !!!!
Answer:
a) 9b) 18Step-by-step explanation:
a) 1/2 of 18 = ?
→ 1/2 of 18
→ (1/2) × 18
→ 18/2 = 9
So, answer is 9.
b) 2/3 of 27 = ?
→ 2/3 of 27
→ (2/3) × 27
→ 54/3 = 18
So, answer is 18.
Determine which integer(s) from the set S:{−24, 2, 20, 35} will make the inequality five sixths m minus five is less than one half m plus 3 false.
S:{−24, 2}
S:{35}
S:{−24, 2, 20}
S:{20}
The inequality five-sixths m minus five is less than one-half m plus 3 false is false for 35 option (B) is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The set of integers:
S:{−24, 2, 20, 35}
Plug the value 35 in the inequality:
= 5/6(35 - 5) < 1/2(35 + 3)
= 5/6(30) < 1/2(38)
= 25 < 19 (False)
Thus, the inequality five-sixths m minus five is less than one-half m plus 3 false is false for 35 option (B) is correct.
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Can you explain how you got your answer please
A software company bought 73 laptops and paid a total of $61,274 to buy them. How much money did each laptop cost the company?
Answer:
839.369863
(Might need to round it depending on what the question requests)
Step-by-step explanation:
Step 1: I divided $61,274 by 73.
Step 2: I multiplied 839.369863 by 73, and I got 61,274.
---------------------------------------------------------------
If it asks to explain say this:
"I divided the amount of money spent by the total amount of laptops bought, and i got 839.369863, To make sure it can be multiplied by 73 to get $61,274, I multiplied 839.369863 by 73 to get $61,274."
Hope this helps :)
(THIS FOR A TEST. WILL GIVE BRAINLIEST) 5. A banquet hall has two types of tables, rectangular and round. The rectangular tables can fit 8 people sitting around them. The round tables can fit 6 people sitting around them. The hall will be hosting a banquet for 192 people. Assume all tables will have the maximum number of people seated at the table.
a. Write an equation in standard form showing the relationship between the number of rectangular tables, z, and the number of round tables, y, that are needed to seat 192 people.
b. Find the z-intercept and explain its meaning in the context of the problem.
c. Find the y-intercept and explain its meaning in the context of the problem.
Answer:
its A.
Step-by-step explanation:
Which equation represents a line which is perpendicular to the line y=2x-5y
A. 2x−y=−4
B. 2y−x=4
C. x+2y=-6
D.2x+y=-2
Answer:
c
Step-by-step explanation:
To find a perpendicular line, you must compare the slopes. With the equation y=2x-5, we're looking for the inverse/opposite slope of -1/2.
Option A still has a slope of 2. Option B, when everything is in the format of mx+b = y format is -x-4=-2y. which gives us 1/2 but not -1/2. C when everything is on the right side gives us -2y=x-6. Divide both sides by -2 to get the y by itself and you're left with y = -1/2x+3. Now we found the equation that gives us the -1/2 slope we were looking for.
Alyssa misses 2% of the free throws she attempts in a season. How many total free throws did she attempt if she missed 63?
Answer: 3150
Step-by-step explanation:
We know that 50×2%s is 100%, so 50×63 should result in the total amount of throws she attempts, which is 3150.
4) What type of slope does the following line have?
Answer: zero slope
Step-by-step explanation:
When the slope of a line is zero it creates a horizontal line.
Suav has a loyalty card good for a discount at his local grocery store. The item he wants to buy is priced at $21, before discount and tax. After the discount, and before tax, the price is $19.53. Find the percent discount.
The percent discount given to Suav in the local grocery store is
How to find the the percent discountinformation given in the problem
The item Suav wants to buy in the grocery store is priced at $21
After the discount, and before tax, the price is $19.53
The discount is found by subtraction as follows
discount = price at the store - price before tax
discount = $21 - $19.53
discount = 1.47
Discount in percent
the problem is discount of the price at the store
percentage deals with a fraction hundred and used as follows
= 1.47/21 * 100
= 7/100 * 100
= 7%
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There is a number written on the board.
One student increased the number by 12.
Another student multiplied the number written
on the board by 3. The first student’s result is 2
greater than the second student's result. What
number is written on the board?
The number written on the board is 2 2/5
What are linear equations?A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0. where, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. where, x and y are variables, A and B are coefficients and C is a constant.
represent the number on the board by x, the result of the second student by y , therefore the result of the first student is 2y
solving for the first student, 12+x= 2y
for the second student , 3x= y
substituting 3x for y in first equation
12+ x= 2(3x)
12+x= 6x
collecting like terms
5x= 12
divide both side by5
x= 12/5= 2 2/5.
Therefore the number on the board is 2 2/5
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Use the diagram of AlL where k, S and are midpoints or the sides, RK = 3, KS = 4, and JK
Is perpendicular to KL.
Find the length of RS
Find the length of JK
Find the length of RT
Find the perimeter of JKL
1. The length of RS is 5.
2. The length of JK is 6.
3. The length of RT is 4.
4. The perimeter of triangle JKL is 24.
What do you mean by right angle triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
According to data in the diagram of the given question:
We have :
The ΔJKL, ΔRKS and ΔRTS are right-angle triangle.
The length of RK=3 and KS=4
We are using pythagoras theorem for determine the length of RS,
(RK)²+(KS)²=(RS)²
(3)²+(4)²=(RS)²
9+16=(RS)²
25=(RS)²
(5)²=(RS)²
RS=5
∴ The the length of RS is 5.
Now, we need to find the length of JK,
JK=2(RK)=2(3)=6
JK=6 [Because RK is midpoint of the side JK]
We have given value of KS=4 and the side KS is the opposite side of RT,
So, that's why the value of RT=4.
Now, we will find the perimeter of ΔJKL,
JK=6, KL=8 and we need to find the side JL,
(JK)²+(RL)²=(JL)²
(6)²+(8)²= (JL)²
36+64=(JL)²
100=(JL)²
(10)²=(JL)²
JL=10
The perimeter of the triangle ΔJKL,
Perimeter=6+8+10=24
Therefore, the perimeter of the triangle is 24.
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