Answer:
The smallest amount is [tex]\£6,911[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=3\ years\\ A=\£8,000\\ r=5\%=5/100=0.05\\n=1[/tex]
substitute in the formula above
[tex]8,000=P(1+\frac{0.05}{1})^{1*3}[/tex]
solve for P
[tex]8,000=P(1.05)^{3}[/tex]
[tex]P=8,000/(1.05)^{3}[/tex]
[tex]P=\£6,910.70[/tex]
Round to the nearest pound she can invest
The smallest amount is [tex]\£6,911[/tex]
A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $22. The total cost to rent 5 chairs and 6 tables is $60. What is the cost to rent each chair and each table?
Answer:
The cost to rent each chair and each table are $1.5 and $8.75 respectively
Step-by-step explanation:
Let x represent 1 chair
Let y represent 1 table
Therefore
3x + 2y = 22 ------------(1)
5x + 6y = 60 ------------(2)
Multiply (1) by 5 and (2) by 3
15x + 10y = 110 ----------(3)
15x + 18y = 180 ------------(4)
Subtract (3) from (4)
8y = 70
Divide through by 8
y = $8.75
Substitute y = 8.75 in (1)
3x + 2y = 22
3x + 2(8.75) = 22
3x + 17.5 = 22
Collect like terms
3x = 22 - 17.5
3x = 4.5
Divide through by 3
x =$1.5
Final answer:
By setting up a system of linear equations based on the given information and solving it, we determined that the cost to rent each chair is $1.50 and the cost to rent each table is $8.75.
Explanation:
To find the cost to rent each chair and each table from the party rental company, we set up a system of linear equations based on the information given:
3 chairs and 2 tables cost $22.5 chairs and 6 tables cost $60.Let C be the cost of one chair and T be the cost of one table. We can write the following equations:
3C + 2T = $225C + 6T = $60Solving this system of equations, we can find the values of C and T. First, multiply the first equation by 3 to eliminate T:
(3C + 2T) * 3 = 22 * 39C + 6T = $66Now we can subtract the second equation from the modified first equation:
9C + 6T - (5C + 6T) = $66 - $604C = $6C = $1.50With the cost of a chair known, we can substitute back into either equation to find the cost of a table:
3(1.50) + 2T = $224.50 + 2T = $222T = $22 - 4.502T = $17.50T = $8.75The cost to rent each chair is $1.50 and the cost to rent each table is $8.75.
f(x) = -x^3+ 6x – 7 at x = 2
Answer:
f(2)= -4
Step-by-step explanation:
f(x)= -x^3 + 6x - 7
f(2) = -2^3 + 6*2 - 7
f(2)= -8 +12 -7
f(2)= 3-7
f(2)= -4
The value of the function f(x)=-x^3+6x-7 at x=2 is -3.
Explanation:To find the value of the function f(x) = -x^3 + 6x - 7 at x = 2, we substitute the value of x into the function.
So, f(2) = -(2)^3 + 6*(2) - 7 = -8 + 12 - 7 = -3.
Thus, the value of the function at x = 2 is -3. This is a simple algebraic operation involving cubes and multiplication, which are basic arithmetic operations.
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A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues, what will be the population of moose after 12 years?
years=x population =y
0,40
1,62
2,96
3,149
4,231
The population of the moose after 12 years is 7692
Step-by-step explanation:
The form of the exponential growth function is [tex]y=a(b)^{x}[/tex] , where
a is the initial valueb is the growth factorThe table:
→ x : y
→ 0 : 40
→ 1 : 62
→ 2 : 96
→ 3 : 149
→ 4 : 231
To find the value of a , b in the equation use the data in the table
∵ At x = 0 , y = 40
- Substitute them in the form of the equation above
∵ [tex]40=a(b)^{0}[/tex]
- Remember any number to the power of zero is 1 (except 0)
∴ 40 = a(1)
∴ a = 40
- Substitute the value of a in the equation
∴ [tex]y=40(b)^{x}[/tex]
∵ At x = 1 , y = 62
- Substitute them in the form of the equation above
∵ [tex]62=40(b)^{1}[/tex]
∴ 62 = 40 b
- Divide both sides by 40
∴ 1.55 ≅ b
∴ The growth factor is about 1.55
- Substitute its value in the equation
∴ The equation of the population is [tex]y=40(1.55)^{x}[/tex]
To find the population of moose after 12 years substitute x by 12 in the equation
∵ [tex]y=40(1.55)^{12}[/tex]
∴ y ≅ 7692
The population of the moose after 12 years is 7692
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According to the graph, what is the solution (ordered pair) of this system of equations?
Answer:
(2, -1)
Step-by-step explanation:
When line 1 intercepts with line 2, they meet at (2, -1). Therefore that's the solution.
A circle is shown that the radius is 16ft
Sarah wants to place a rim around her circular pool with a foam rim. The foam rim is
sold in boxes that will cover the length of 40 feet. How many boxes of foam rim will
Sarah need to place around the rim of the pool?
4 boxes
(A) 3 boxes
(B) 4 boxes
(C) 5 boxes
(D) 6 boxes
Answer:
3 boxes.
Step-by-step explanation:
The circular pool has a radius of 16 feet.
So, the circumference of the pool will be 2πr = [tex]2 \times \frac{22}{7} \times 16 = 100..57[/tex] feet.
Therefore, to place a rim around the circular pool with a foam rim Sarah will need 100.57 feet length of foam rim.
Now, the foam rim is sold in boxes that will cover the length of 40 feet.
Therefore, she will need [tex]\frac{100.57}{40} = 2.51[/tex] ≈ 3 boxes to place around the rim of the pool. (Answer)
The scale of a room in a blueprint is 6in : 13ft. A wall in the same blueprint is 9 inches. How long is the actual wall?
Answer:
Step-by-step explanation:
6 in to 13 ft = 9 in to x ft
6 / 13 = 9 / x.....cross multiply because this is a proportion
(6)(x) = (13)(9)
6x = 117
x = 117/6
x = 19.5 (or 19 1/2) ft <====
The actual length of a soccer field is 500 feet. A broken measuring instrument shows the length to be 493 feet. Find the percent error for the length of the soccer field.
Answer:
Percent error for the length of the soccer field is 1.4 %
Step-by-step explanation:
The actual length of the soccer field = 500 ft
The measured length of he field = 493 ft
ERROR in the measurement = ACTUAL LENGTH - MEASURED LENGTH
= 500 ft - 493 ft = 7 ft
So, there is an error of 7 ft in measuring the length of the field.
[tex]\textrm{ERROR PERCENTAGE} = \frac{\textrm{Error}}{\textrm{Actual Measuement}} \times 100\\= \frac{7}{500} \times 100 = 1.4[/tex]
Hence, percent error for the length of the soccer field is 1.4 %
The percent error for the length of the soccer field is 1.4%.
We are asked to find the percent error for the length of a soccer field when the actual length is 500 feet, but a broken measuring instrument shows it to be 493 feet.
Calculating percent error:
Find the absolute difference: |493 - 500| = 7 feet.
Calculate percent error: (7/500) x 100%
Percent error = 1.4%.
The equation can be used to find the measure of angle LKJ. Triangle L K J is shown. Angle J L K is a right angle. The length of L K is 7.7 centimeters and the length of L J is 8.9 centimeters. Angle L K J is x. What is the measure of angle LKJ? Round to the nearest whole degree. 41° 45° 49° 55°
Answer:
C, 49°.
Step-by-step explanation:
Cause i said so
Answer:
C, 49.
Step-by-step explanation:
A line has a slope of -3/4 and has a y intercept of 3. What is the x intercept of the line
Answer:
The x-intercept is 4
Step-by-step explanation:
We are given;
The slope of a line as -3/4
y-intercept is 3
We are supposed to determine the x-intercept;
We need to know that;
The slope of a line is given by the ratio of the change in y to the change in x
The coordinates of y-intercept are (0, 3)
Taking the x-intercept as a, then the coordinates of x-intercept is (a, 0)
But;
slope = Δ in y ÷ Δ in x
Therefore;
[tex]\frac{0-3}{a-0}= \frac{-3}{4}[/tex]
Solving for a
[tex]-3a = -12 \\ a =4[/tex]
Therefore, the x-intercept is 4
Dudley Greene's charge account statement shows an unpaid balance of $376.00. The monthly finance charge
is 1.85 percent of the unpaid balance. What is the finance charge?
Answer:
The finance charge is $6.96.
Step-by-step explanation:
Given:
Dudley Greene's charge account statement shows an unpaid balance of $376.00.
The monthly finance charge is 1.85 percent of the unpaid balance.
Now, to find the finance charge.
Unpaid balance = $376.00.
Finance charge = 1.85% of unpaid balance.
So, to get the finance charge:
1.85% of $376.00.
[tex]=\frac{1.85}{100} \times 376.00[/tex]
[tex]=0.0185\times 376.00[/tex]
[tex]=\$6.96.[/tex]
Therefore, the finance charge is $6.96.
What is a equal to?
12=2a
Using the balance method, we find a = 15 by isolating the variable a. Substituting a = 15 back into the original equation, we verify the solution.
To solve the equation 12 = 2a - 18 using the balance method, we aim to isolate the variable a on one side of the equation.
Starting with 12 = 2a - 18, we'll first add 18 to both sides to isolate the term with 2a:
[tex]\[12 + 18 = 2a - 18 + 18\]\[30 = 2a\]\\[/tex]
Next, we divide both sides by 2 to solve for a:
[tex]\[\frac{30}{2} = \frac{2a}{2}\]\[15 = a\][/tex]
Now, let's verify the solution by substituting a = 15 back into the original equation:
[tex]\[12 = 2(15) - 18\]\[12 = 30 - 18\]\[12 = 12\][/tex]
Since the left side equals the right side, the solution a = 15 is verified.
Complete Question:
Solve the following equation using balance method and verify 12 = 2a - 18
What is the slope of a line that passes through (5,-5) and (-6, -4)
Answer: m = [tex]\frac{-1}{11}[/tex]
Step-by-step explanation:
The slope of a line is calculated by :
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = 5
[tex]x_{2}[/tex] = -6
[tex]y_{1}[/tex] = -5
[tex]y_{2}[/tex] = -4
substituting the values , we have :
m = [tex]\frac{-4-(-5)}{-6-5}[/tex]
m = [tex]\frac{-4+5}{-11}[/tex]
Therefore :
slope = [tex]\frac{-1}{11}[/tex]
What is the formula for the volume of a cylinder
Answer:
V=πr2h
Step-by-step explanation:
Answer:
V=πr2h
That's the formula for the volume of a cylinder
A committee consisting of 2 faculty members and 3 students is to be formed. Every committee position has the same duties and voting rights. There are 9 faculty members and 14 students eligible to serve on the committee. In how many ways can the committee be formed?
Answer:
13104
Step-by-step explanation:
9C2 x 14C3 = 36 x 364
= 13104
Determine the diameter of a curcle with the radius 12.2
Answer:
24.4
Step-by-step explanation:
diameter=2*radius
=2*12.2
=24.4
Final answer:
The diameter of a circle with a radius of 12.2 is 24.4 units. This is calculated by doubling the radius, using the formula D = 2r.
Explanation:
To determine the diameter of a circle with a radius of 12.2, you simply need to use the relationship between the radius and the diameter of a circle. The diameter is twice the radius, which can be represented by the formula D = 2r, where D is the diameter and r is the radius.
Substituting the value of the radius into the formula gives us:
D = 2 × 12.2
This calculates to:
D = 24.4
Therefore, the diameter of the circle is 24.4 units. Keep in mind that if the radius was given in a specific unit, like meters or centimeters, then the diameter will be in the same unit.
In the next 10 months Colin wants to save $900 for his vacation. He plans to save $75 each for the first eight months. How much must he save each of the last two months in order to meet his goal if he saves the same amount each month
He must save $150 each of the last two months in order to meet his goal.
Step-by-step explanation:
Given,
Amount Colin wants to save = $900
Amount saved each month for 8 months = $75
Amount saved in 8 months = 75*8 = $600
Let,
x be the amount saved each month for remaining two months.
Therefore;
Number of months * Amount saved + Amount saved in 8 months = Total amount to save
[tex]2x+600=900\\2x=900-600\\2x=300[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{300}{2}\\x=150[/tex]
He must save $150 each of the last two months in order to meet his goal.
Keywords: subtraction, division
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the sum of two numbers is 158.if we add 25 to each one of them,then the first becomes the triple of the other.what are these numbers
Answer:
Why is 90 the sum of all factors of 40, including 40? The factors of the number 40 are: 1, 2, 4, 5, 8, 10, 20, 40. If you add them up, you will get the total of 90.
Step-by-step explanation:
2. Given the points A, B, C, D, calculate:
(a) the angle B of the triangle ABC
(b) the area of the triangle ABC
(c) the median BE of the triangle ABC
(d) the height AH of the triangle ABC
(e) the volume of tetrahedron ABCD
(f) the point E so that ABCE is a parallelogram.
A(-1, 2, -3), B(4, -1, 0), C(2, 1, -2), D( 3,4,5)
What is 4 1/2 + 3 1/4
Add the whole numbers 4 + 3 = 7
Add the fractions 1/2 + 1/4
Rewrite 1/2 to have a common denominator with 1/4
1/2 = 2/4
Now add 2/4 + 1/4 = 3/4
The answer would be 7 3/4
Where in the world may a person walk one mile west, and then one mile north and arrive back at the starting point
Answer:
North Pole
Step-by-step explanation:
Answer:
So your walk of 1 mile West is a complete circle. You then walk 1 mile North, which brings you back to your starting point, (1 + 1/(2pi)) miles from the South Pole. The obvious answer is the North Pole. You're either on the North Pole, or somewhere very near (about 840 feet or less) the South Pole.-step explanation:
The track is 3 miles long and it takes between 1 hour and 1 hour 10 minutes for the train to climb to the top. What is the average speed for the train: when the journey takes 1 hour ?
Answer:
3 Miles per hour, or .05 Miles per minute
Step-by-step explanation:
In a survey of 3300 people who owned a certain type of car, 825 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer: 25%
Step-by-step explanation:
Since 825 people said they would buy the car again, it means they were satisfied with the car
Therefore, the percentage of those satisfied with the car is = (825/3300) x 100 = 25%
A pentagon the Measures of four of its angle are shown bellow: what is the value of x?
Answer:
See below.
Step-by-step explanation:
The sum of the measures of the interior angles of an n-sided polygon is
(n - 2)180
A pentagon has 5 sides, so for a pentagon, n = 5.
(n - 2)180 = (5 - 2)180 = 3(180) = 540
The sum of the measures of the angles of a pentagon is 540.
You don't show the measures of the 4 angles that are known, so to answer the question, add the 4 given measures and subtract the sum from 540.
In Tampa, Florida the sun shines about 66% of the year about how many days does the sun shine in Tampa
Answer: 241 days a year
Step-by-step explanation: 365*0.66=240.9 and then you round up to 241
The total number of days in a year the sun shines in Tampa will be equal to 241 days.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the instructions given in the question,
The total number of days in a year is 365 days.
Then, 66% of the total number of days in a year will be,
365 × 66/100 = 240.9 or,
The number of days of sunshine will be 241 days after rounding up the value.
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John deposited $13 in his bank account on Monday. Then, on Friday he withdrew $15. How much money is in John's bank account now?
$2
$28
-$28
-$2
Answer:
-2
Step-by-step explanation:
Answer:
-2 is 100% correct !
Step-by-step explanation:
Which pair of adjacent angles is complementary?
Answer:
Option C
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
In this problem we have
Option C
One angle measure 35 degrees and the other angle measure 55 degrees (90-35=55)
so
[tex]35^o+55^o=90^o[/tex]
therefore
The pair of angles are complementary
Answer:
C.)
Step-by-step explanation:
Select the three equations that pass through the points (-4, -16) and (5,2).
y + 4 = 2(x - 16)
y-2 = 2(x - 5)
y=2x-8
y + 16 = 2(x + 4)
DONE
Answer:
It's B,C,D
Step-by-step explanation:
Answer:
its b,c, and d
Step-by-step explanation:
What is the solution set of the system of inequalities 5x<8+4y and 2y≤6?
Answer:
See the explanation and the image.Step-by-step explanation:
The inequality [tex]2y \leq 6[/tex] means [tex]y \leq 3[/tex].
y = 0, satisfies the above inequality, so the arrows will be towards the x axis.
Now, we need to draw 5x < 8 + 4y.
First, lets draw the equation of 5x = 8 + 4y.
y = 1 gives x = 2.4 & y = 0 gives x = 1.6.
Hence, the above equation passes through (2.4, 1) and (1.6, 0).
The point (0, 0) satisfies the inequality 5x < 8 + 4y. Hence, the arrows will be towards the origin.
The solution will be the area of APQ except any point on PQ, as PQ is nothing but the line 5x = 8 + 4y.
What is the answer for 4/8-2/5
Answer:
4/8 - 2/5 = 1/10
I need help please and thank you
Answer:
58 degrees
Step-by-step explanation:
All triangles measure up to 180 degrees.
180-87-35=58
joshua has only dimes and pennies in his piggy bank. he has a total of $23.00 in his bank. the amount of pennies is 20 more than 10 times the amount of dimes. how many dimes and pennies are there
There are 1160 pennies and 114 dimes in the piggy bank.
Step-by-step explanation:
Given,
Worth of money = $23.00 = 23*100 = 2300 cents
1 penny = 1 cent
1 dime = 10 cents
Let,
x be the number of pennies
y be the number of cents
According to given statement;
x+10y=2300 Eqn 1
x = 10y+20 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]10y+20+10y=2300\\20y=2300-20\\20y=2280[/tex]
Dividing both sides by 20
[tex]\frac{20y}{20}=\frac{2280}{20}\\y=114[/tex]
Putting y=144 in Eqn 2
[tex]x=10(114)+20\\x=1140+20\\x=1160[/tex]
There are 1160 pennies and 114 dimes in the piggy bank.
Keywords: linear equation, substitution method
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Final answer:
Joshua has 114 dimes and 1160 pennies in his piggy bank. This was determined by setting up a system of equations based on the values of the coins and the given relationship between the number of dimes and pennies.
Explanation:
The problem presented is a typical algebraic word problem that requires setting up equations based on the given information about dimes and pennies. We are told that the total value of the coins is $23.00 and that the number of pennies is 20 more than 10 times the number of dimes. To solve the problem, we need to use the fact that the value of a dime is 10 pennies, and then set up a system of linear equations to find the number of each type of coin.
Step-by-Step Explanation
Let's denote the number of dimes as d and the number of pennies as p.The value of the dimes is 10d pennies since each dime is worth 10 pennies.The total value of the dimes and pennies is 23 dollars or 2300 pennies (since 1 dollar equals 100 pennies).According to the problem, p = 10d + 20.The equation representing the total value is thus 10d + p = 2300.Substituting p from the first equation into the second gives us: 10d + (10d + 20) = 2300.Simplifying this equation, we get 20d + 20 = 2300.Subtracting 20 from both sides, we get 20d = 2280.Dividing both sides by 20, we find out that d = 114.Substituting d back into the first equation to find p, p = 10(114) + 20 which gives us p = 1160.Thus, Joshua has 114 dimes and 1160 pennies in his piggy bank.