The dimensions of the playground are;
Width = 60 feet
Length = 160 feet
How to determine the dimensionsThe formula for calculating perimeter of a rectangle is expressed as;
Perimeter = 2( l + w)
Where;
l is the length of the rectanglew is the width of the rectangleWe have the values as;
Perimeter = 440 feet
Length = 3w - 20
Width = w
Now, substitute the values into the formula, we have;
440 = 2( 3w - 20 + w)
expand the bracket
440 = 2( 4w - 20)
440 = 8w - 40
collect like terms
8w = 480
Make 'w' the subject of formula
w = 60 feet
Length = 3(60) - 20
Length = 180 - 20
Length = 160 feet
Hence, the values are 60feet and 160 feet
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You can tell that is an irrational number because it has a what?
Answer:
Can't be written as fraction
Step-by-step explanation:
Irrational Numbers are Real Numbers which are not rational , which means that it can't be written as fraction
A boat sails 285 miles south and then 132 miles west. What is the magnitude of the boats resultant vector?
The magnitude of the boats resultant vector is 314.1 mi
What is a vector?A vector is a physical quantity that has both magnitude and direction.
What is a resultant vector?A resultant vector is the sum of two or more vectors.
How to find the boats resultant vector?Since the boat sails 285 miles south and then 132 miles west, we have that its first direction vector is r = (285 mi)j. Also, its direction vector west is r' = -(132 mi)i
So, the resultant vector R = r + r'
= (285 mi)j + (132 mi)i
= (132 mi)i + (285 mi)j
So, the magnitude of the resultant vector is R = √(r² + r'²)
So, substituting thevalues of the variables into the equation, we have
R = √(r² + r'²)
R = √((285 mi)² + (132 mi)²)
R = √(81225 mi² + 17424 mi²)
R = √(98649 mi²)
R = 314.08 mi
R ≅ 314.1 mi
So, the resultant vector is 314.1 mi
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Question 5 (1 point)
What is the area of the figure?
5 cm
11.0 cm
20.0 cm
1 cm
2cm
3 cm
The area of the given figure is 25cm².
Area of rectangle
Area = length x width
Perimeter of rectangle
Perimeter = length + length + width + width
Hence, we have
length = 5cm
width = 5cm
then, by applying the Area of the rectangle, we get
Area = length x width
Area = 5 x 5
= 25cm²
Hence, The area of the given figure is 25cm².
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Sophie determine that the function describing the cost of dinner is linear if you order X eggrolls your dinner will cost 1.50x + $10 what is the per egg roll fee?
Sophie determine that the function describing the cost of dinner is linear if you order X eggrolls your dinner will cost 1.50x + $10 what is the per egg roll fee?
1.50x + $10
per egg roll fee is $1.50
(x^2+4)/(x^3+x^2+4x+4)=
The solution is 1/(x+1)
From the question, we have
(x^2+4)/(x^3+x^2+4x+4)
=(x^2+4)/(x^2 (x^3/x^2 +x^2/x^2 )+2^2 ((2^2⋅x)/2^2 +2^2/2^2 ) )
=(x^2+4)/(x^2 (x^(3-2)+1)+2^2 (x+1))
=(x^2+4)/(x^2 (x+1)+2^2 (x+1))
=(x^2+4)/((x+1)((x^2 (x+1))/(x+1)+(2^2 (x+1))/(x+1)) )
=(x^2+4)/((x+1)(x^2+2^2 ) )
=(x^2+4)/((x+1)(x^2+4) )
=1/(x+1)
The solution is 1/(x+1)
Divide:
Split is to divide into two or more equal sections, places, groupings, or divisions in its most basic form. To divide something simply means to provide it to a group in equal quantities or to cut it up into equal pieces. Let's imagine a diagonal divides a square into two triangles with equal areas. An integer may or may not be the result of a division operation. Sometimes the result will be expressed as decimal numbers.
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A cable TV company has 3400 customers paying $130 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue.
The price that yields maximum revenue is equal to $99. Also, the maximum revenue is equal to $490,050.
How to determine the unit price that yields a maximum revenue?In order to determine the price that would yield the maximum revenue, we have to find the derivative of the revenue function R(p) by applying the Power Rule.
Mathematically, the revenue function, R(p) is given by this mathematical expression:
Revenue function, R(p) = NP
Where:
N represents the number of customersP represents the monthly price of the subscriptionLet the variable n represent the number of reductions in the price. Therefore, we have:
N = 3,400 + 50n ....equation 1.
P = 130 - n
n = 130 - P
From equation 1, we have:
N = 3,400 + 50(130 - P)
N = 3,400 + 6,500 - 50P
Next, we would re-write the revenue function R(p) as follows:
Revenue function, R(p) = (3,400 + 6,500 - 50P)P
Revenue function, R(p) = 3,400P + 6,500P - 50P²
Revenue function, R(p) = 9,900P - 50P²
Taking the derivative of R(p), we have:
R'(p) = 9,900 - 100P
100P = 9,900
Price, P = 9,900/100
Price, P = $99
For the the maximum revenue, we have:
Maximum revenue, R(p) = 9,900P - 50P²
Maximum revenue, R(p) = 9,900(99) - 50(99)²
Maximum revenue, R(p) = 980,100 - 490,050
Maximum revenue, R(p) = $490,050.
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Complete Question:
A cable TV company has 3400 customers paying $130 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue. Find the maximum revenue.
The number of computer security breaches is expected to increase at a yearly rate of 86%
Use the exponential growth model to determine the equivalent monthly rate.
Enter the rate, to the nearest tenth of a percent, in the box.
____%
Answer:
The population is expected to grow at a rate of 1.36% each year. What is the population of the town in 2006? Round your answer to the nearest whole number.
Step-by-step explanation:
The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than 4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 528 jawbreakers that weigh more than .4 ounces?
It would be unusual for this sample of 800 to contain 528 jawbreakers that weigh more than .4 ounces, using the binomial distribution, as 528 is more than 2.5 standard deviations above the mean.
What are unusual values in the binomial distribution?The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The mean of the binomial distribution is of:
E(X) = np.
The standard deviation of the binomial distribution is of:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
The unusual measures are the ones that are more than 2.5 standard deviations from the mean.
The values of the parameters in this problem are given as follows:
p = 0.6, n = 800.
Hence the mean and the standard deviation are given as follows:
Mean: 800 x 0.6 = 480.Standard deviation: [tex]\sqrt{800 \times 0.6 \times 0.4} = 13.86[/tex]The upper bound of usual values is of:
480 + 2.5 x 13.86 = 514.65.
528 > 514.65, hence it is an unusual value.
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3/5 - 1/3 simplified
Answer:
4/15
Step-by-step explanation:
[tex]\frac{3}{5}=\frac{9}{15} \\ \\ \frac{1}{3}=\frac{5}{15} \\ \\ \frac{3}{5}-\frac{1}{3}=\frac{9}{15}-\frac{5}{15}=\frac{4}{15}[/tex]
If a=-1+2i and b=5, then find the value of the a^2b in fully simplified form.
The value of the algebraic expression is:
a^2*b = -15 + 20i
How to find the value of the expression?
Here we have the following expression:
a^2*b
And we want to use the values:
a = -1 + 2i
b = 5
Replacing these values in the expression we will get:
(-1 + 2i)^2*5
Expanding the first part we get:
(-1 + 2i)*(-1 + 2i) = (-1)*(-1) + (-1)*(2i) + (2i)*(-1) + (2i)*(2i)
= 1 - 2i - 2i - 4
= -3 + 4i
Replacing that in the expression we get:
(-1 + 2i)^2*5 = (-3 + 4i)*5 = -3*5 + 4i*5 = -15 + 20i
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I’m stuck on this question I’ve tried this question so many times and I just don’t understand so I need help please
Answer:
see explanation
Step-by-step explanation:
(a)
parallel line segments are indicated by arrows on the segments pointing in the same direction.
from the diagram EA and DC are parallel lines.
(b)
equal lines are indicated by a dash through the lines.
from the diagram AB and BC are equal.
(c)
perpendicular lines are at right angles (90° ) to each other, usually indicated by a small box between them.
from the diagram AE and CD are perpendicular to DE
If the shared side between angles 1 and 2 has a measure of 2x+7 and the shared side between angles 3 and 4 has a measure of 7x+3, what is the value of X?
Round your answer to the nearest hundredth.
Answer:
x = 0.8Step-by-step explanation:
Both mentioned sides have equal length as opposite sides of a parallelogram.
Set equation and solve for x:
2x + 7 = 7x + 37x - 2x = 7 - 35x = 4x = 4/5x = 0.8
The number of carbon atoms in a fossil is given by the function y = 51000(0.85), where t represents the number of
years since being discovered. What is the percent of change each year? Explain how you arrived at your answer.
The percent of change each year is 15%.
How to calculate percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
It is given that The number of carbon atoms in a fossil is given by the function y = [tex]51000(0.85)^t[/tex], where t represents the number of years since being discovered.
Here , y = [tex]51000(0.85)^t[/tex]
t = number of years
y = number of carbon atoms in a fossil.
For t = 1 year
y = 51000[tex](0.85)^1= 51000(0.85) = 43350[/tex]
For t = 2 years
y = 51000[tex](0.85)^2= 36847.5[/tex]
For t = 3 years
y = 51000[tex](0.85)^3=31320.375[/tex]
Percentage change in one year = [tex]\frac{36847.5-43350}{43350}[/tex] × 100 = -15%
Percentage change in second year = [tex]\frac{31320.375-36847.5}{36847.5}[/tex] × 100 = -15%
here, negative sign shows decrement. In this way, every year carbon atom in fossil decreases by 15%.
Therefore, the percent of change each year is 15%.
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BD = 3x, CD = x + 16
what does X =
Answer:
x = 8Step-by-step explanation:
from the figure we understand that it is an isosceles triangle, therefore 2 sides and two congruent angles, BD and CD are congruent, therefore 3x = x + 16.
let's solve
3x = x + 16
2x = 16
x = 8
-----------------------------
check
3 × 8 = 8 + 16
24 = 24
thee answer is good
Write a quadratic function h whose only zero is −13.
The quadratic function whose only zero is -13 is h(x) = x² + 26x + 169
Quadratic functionFrom the question, we are to write a quadratic function whole only zero is -13.
Since -13 is the only zero of the function,
Then,
x = -13 twice
This means that (x + 13) is a factor of the function
Since x = -13 twice,
Then,
The quadratic function h is
h(x) = (x + 13)(x + 13)
Expand the quadratic function by distributing
h(x) = x(x + 13) + 13(x + 13)
h(x) = x² + 13x + 13x + 169
h(x) = x² + 26x + 169
Hence, the function is h(x) = x² + 26x + 169
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10. Brock bought a bicycle that cost $40.00 when it was new. If he eventually sold it for 10%
of the original cost, how much was it sold for?
Answer:IT WOULD BE 60.00
Step-by-step explanation:
BC 40 = 60
Write the equation of the line that is perpendicular
to the y-axis and passes through the point (3, 12).
Answer:
[tex]y=12[/tex]
Step-by-step explanation:
The [tex]y[/tex]-axis has equation [tex]x=0[/tex], so the equation of a line perpendicular to the [tex]y[/tex]-axis would be of the form [tex]y=c[/tex].
The equation of this line given the point [tex](3,12)[/tex] is [tex]y=12[/tex].
A university reported that its enrollment increased from 11,937 students in 2005-2006 to 12,256 students in 2006-2007.
a. What is the ratio of the number of students in 2006-2007 to the number of students in 2005-2006?
b. From your result in part a, determine the growth factor. Write it in decimal form to the nearest thousandth.
c. By what percent did the enrollment increase?
a.
The ratio of the number of students in 2006-2007 to the number of students in 2005-2006 is = 12,256 : 11,937
b.
Growth factor = (12256-11937)/11937
= 0.02672.
c.
Increase in percent = 100* (12256 - 11937)/11937
= 100 * 0.02672
= 2.672%
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5 Math on the Spot Robin says, "I can find 6 × 9 by
multiplying 4 X 9 and doubling it." Does her statement
make sense? Justify your answer.
If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.
What is distributive property?
The same outcome will be obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend separately by the number and then adding the resulting products.
A × (B + C) = AB + AC
A (B - C) = AB - AC
Here,
we can write 6 × 9 as,
= 6 × 9 = 6 × (6 + 3) = (6 × 6) + (6 × 3), by applying distributive property
Hence, If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.
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Consider the equation and the following ordered pairs: (1,y) and (x,−3).
6x+3y=15
What is the first step needed to solve 4 over 7 multiplied by x minus 5 equals negative 13 ? (1 point)
Group of answer choices
Add 5 to both sides
Multiply both sides by 4
Subtract 13 from both sides
Divide both sides by 7
Answer:add 5 to both sides
Step-by-step explanation:
A tutor has 21 students in their tutor group. Within this group,
15 students have attended at least one tutorial. Calculate the
percentage of students in this tutor group who have attended at least
one tutorial.
Give your answer correct to the nearest whole number.
The percentage of students in the tutor group that have attended at least one tutorial is 71%
How to find the percentage?The percentage of students who have attended at least a single tutorial in the tutor group can be found by the formula:
= Number of students who attended at least one tutorial / Total number of students in tutor group x 100%
Number of students who attended at least one tutorial = 21 students
Total number of students in tutor group = 15 students
The percentage is therefore:
= 15 / 21 x 100%
= 0.7142857 x 100%
= 71.42%
= 71%
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hellp foo You are considering different investment strategies to save for your retirement.
Option 1: You invest $25/ month at a rate of 3.25% APR compounded monthly for 30 years.
Option 2: You invest $75/ quarter at a rate of 4.00% APR compounded monthly for 30 years.
Option 3: You invest $1,000 at a rate of 6.25% APR compounded monthly for 30 years.
1) Which option was the least amount invested and what was the investment plan?
2) Which option yielded the highest amount at the end of the 30 years and what was the basis of the plan?
3) What is the difference in the principal invested for the highest and lowest final balances? What is the difference in the interest earned?
4) Is it better to invest more money in the beginning or the end of the 30 years?
1) Option 3 had the least amount invested. The investment plan was to invest a certain amount in the beginning and let it grow at an interest of 6.25% APR compounded monthly for 30 years.
2) Option 2 yielded the highest amount at the end of 30 years. The plan was to invest $75/quarterly i.e, $25/monthly at an interest of 4.00% APR compounded monthly for 30 years.
3) Difference in principle is $8000 and the difference is interest is $2976.83
4) It is better to invest more at the end of 30 years.
Define interest.
When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount per year. The loan's interest rate is denoted by this proportion.
Solution Explained:
First, let's calculate the amount after adding the compound interest using
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex], where P is principal, r = interest rate, n = number of times interest is compounded monthly, and t = time
After calculation (For Op 1 and 2, the principal is $9000 and 3 is $1000)
Option 1 has $15275.50
Option 2 has $17467
Option 3 has $6489.17
Interest for Option 1 = $6275.50
Interest for Option 2 = $8466
Interest for Option 3 = $5489.17
After this solving the questions will be easy to understand.
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Answer:
contributions:
1 $25/ month at a rate of 3.25% APR
2 $75/ quarter at a rate of 4.00%
3 $1,000 at a rate of 6.25% APR
total interest rate:
1 $6275.50
2 $8466
3 $5489.17
final balances:
1 $15275.50
2 $17467
3 $6489.17
questions 1-4
1: Option 3 had the least amount invested
2: option 2
3: Difference is $8000 – and interest difference in $2976.83
4: it’s better to invest more at the end of 30 years
Step-by-step explanation:
i did the assignment
Solve for j ??????????????????????????
Answer:
j=24
Step-by-step explanation:
j/8 - 2 = 1
j/8 - 2 + 2 = 1 + 2
j/8 = 3
8 * j/8 = 8 * 3
j=24
Find the product. Simplify your answer
2x² (4x³+2y¹)
12x³y +6
08x5 +4y6
48x5y6
8x5 +8x²y¹
Answer: The answer is D bc i did the test before hope you have a great day:]
Step-by-step explanation:
8
x
5
−
6
x
4
+
12
x
3
What number when multiplied by 1 1/4 has a product of 1
Answer: 4/5 or 0.8
Step-by-step explanation:
[tex]1\frac{1}{4}[/tex] * [tex]\frac{4}{5}[/tex] = [tex]\frac{1}{1}[/tex] = 1
[tex]1\frac{1}{4}[/tex] is also equal to 1.25.
1.25 * 0.8 = 1
Answer:
4/5
Step-by-step explanation:
because 4 is half of a half two fourths are a half and 4/4 are 1 whole
The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. Suppose that V= 70 cm^3 when T = 420 kelvin and P = 18 kg/cm^2 . Find the pressure when T = 140 kelvin and V = 60 cm^3.
In a case where the expression is give as volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P, then the pressure will be 7kg/cm^2.
How can the pressure be calculated?V = k T/ P
and V= 70 cm^3
T = 420 kelvin
P = 18 kg/cm^2
where K is constant of proportionality,
70 =( k * 420) / 18
k = (70 * 18) / 420
k= 3
Then we were given that the pressure=?
T = 140 kelvin
V = 60 cm^3
then V = k T/ P
P= kT/V
P= (3*140)/60
=7
Then the pressure is 7kg/cm^2
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What is the sale price including tax to the nearest cent? $595 refrigerator, 20% discount; 9.25% tax
The sale price including tax for the refrigerator is $520.
How to calculate the price?From the information, the following can be deduced:
Refrigerator = $595
Discount = 20%
Tax = 9.25%
The sales price will be:
= Refrigerator price + Tax - Discount
= $595 + (9.25% × $595) - (20% × 650)
= $595 + $55 - $130
= $520
The price is $520.
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Graph the line with slope 1/3 and y-intercept −2.
4. Two card are down Randomly from well suffled deck of card without Replacement Find the probability by of getting both Face card at two succession tree diagram.
Answer:
[tex]\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]
Step-by-step explanation:
Two cards are drawn randomly from a well-shuffled deck of cards without replacement. Find the probability of getting both face cards in succession.
In a deck of 52 cards, there are three face cards (J, Q, and K) in each of four suits (clubs, diamonds, hearts, and spades). That means there are 12 face cards in total (J♣, Q♣, K♣, J♦, Q♦, K♦, J♥, Q♥, K♥, J♠, Q♠, K♠).
The probability of drawing a face card the first time, then, is 12 out of 52.
There is now one less face card in the deck, as well as one less card in the deck. Therefore, the probability of drawing a face card a second time is 11 out of 51.
The probability, then, of drawing two face cards in succession is:
[tex]\frac{12}{52}\times{\frac{11}{51}}=\frac{132}{2652}=\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]