Using the formula for the perimeter and area of rectangle, the dimensions are: Length = 19 m; width = 9 m.
What is the Perimeter and Area of a Rectangular Shape?Perimeter = 2(length + width)
Area = (length)(width).
Let x represent the length and y the width, therefore:
2(x + y) = 56 --> eqn. 1
xy = 171 --> eqn. 2
Rewrote eqn. 1
x + y = 56/2
x = 28 - y
Substitute x = (28 - y) into eqn. 2
171 = (28 - y)y
171 = 28y - y²
171 - 28y + y² = 0
y² - 28y + 171 = 0
Factorize
(y - 9)(y - 19)
y = 9 and y = 19
Therefore, the dimensions are: Length = 19 m; width = 9 m.
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PLEASE HELP ASAP 25 POINTS
Answer:
A) Using Commutative property
Step-by-step explanation:
In step 1, it used distributive property when the number 5 is distributed inside of the equation in the parenthesis.
In Step 4, dividing both sides by 10 to further simplify the equation
In step 2, you combined like terms and it results to the equation in step 3
Please help me answer this question
For the function [tex]A(t)=4000e^0^.^0^4^t[/tex] the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]
The given function is [tex]A(t)=4000e^0^.^0^4^t[/tex] gives the balance after t years.
The initial investment is 8000
4% is the compounded interest.
Now differentiate with respect to t
[tex]A'(t)=0.04(4000)e^0^.^0^4^t[/tex]
[tex]A'(t)=160e^0^.^0^4^t[/tex]
Now let us find the value of A'(8)
Plug in t as 8
[tex]A'(8)=160e^0^.^0^4^(^8^)[/tex]
A'(8)=220.3
Hence, the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]
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Aaron kicked a soccer ball with an initial velocity of 39 feet per second at an angle of 44° with the horizontal. After 0.9 seconds, how far has the ball traveled horizontally? A. 11.4 ft B. 24.4 ft C. 12.3 ft D. 25.2 ft
The ball has traveled approximately 25.24 feet Horizontally.The correct answer is D. 25.2 ft.
The horizontal distance traveled by the soccer ball after 0.9 seconds, we can use the equation:
horizontal distance = initial velocity * time * cos(angle)
Substituting the given values:
initial velocity = 39 ft/s
time = 0.9 s
angle = 44°
horizontal distance = 39 ft/s * 0.9 s * cos(44°)
Calculating:
horizontal distance ≈ 39 ft/s * 0.9 s * 0.71934 ≈ 25.24 ft
Therefore, after 0.9 seconds, the ball has traveled approximately 25.24 feet horizontally.
The correct answer is D. 25.2 ft.
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on a map, 1 inch equals 8.7 miles. If two cities are 2.5 inches apart on the map, how far are they actually apart?
The distance between the cities is ? miles
Answer:
the distance between the cities is 21.75 miles.
Step-by-step explanation:
1 inch = 8.7 miles.
2.5 inches x 8.7 miles/inch = 21.75 miles
100 Points! Geometry question. Identify the similar triangles. Then find each measure. Photo attached. Please show as much work as possible. Thank you!
The triangles ABC and DBE are similar by the SAS similarity theorem
The measure of the side lengths AC is 16 units
How to identify the similar triangles.From the question, we have the following parameters that can be used in our computation:
The triangles ABC and DBE
These triangles have the following measures
Two similar corresponding sidesTwo equal corresponding anglesThis means that the triangles are similar by the SAS similarity theorem
How to find each measureUsing the SAS similarity theorem, we have the following equation
(x + 1)/12 = (x + 5)/15
Cross multiply the equation
15x + 15 = 12x + 60
So, we have
3x = 45
Divide by 3
x = 15
This means that
x + 1 = 15 + 1 = 16
x + 5 = 15 + 5 = 20
Hence, the measure of the side lengths are 16 and 20 units
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Under ideal conditions, the population of a certain species doubles every nine years. If the
population starts with 100 individuals, which of the following expressions would give the
population of the species t years after the start, assuming that the population is living
under ideal conditions?
Select all of the following that are quadratic equations. 5 x 2+ 15 x = 0 6 x - 1 = 4 x + 7 x 2 - 4 x = 4 x + 7 2 x - 1 = 0 3 x 2 + 5 x - 7 = 0 x 3 - 2 x 2 + 1 = 0
Answer:
Options A, C and E-----------------------
Quadratic equation has the form of:
ax² + bx + c = 0Analyze the given equations and see which has the same form:
A) 5x² + 15 x = 0, Yes, quadratic equation;B) 6 x - 1 = 4, No, it is a linear equation;C) x + 7x² - 4 x = 4, Yes, quadratic equation;D) x + 72x - 1 = 0, No, it is a linear equationE) 3x² + 5x - 7 = 0, Yes, quadratic equation;F) x³ - 2x² + 1 = 0, No, it is cubic equationONLY NEED PT 2 1st blank is: -1.5,-1.07,=0.70,-0.67,0.67,0.70,1.07,1.5,4,27,33.
2nd blank is:Means, Medians, modes, Standard deviatins, Ranges.
3rd blakn is Below, Above
4th blank is: Means, Medians, modes, Standard deviatins, Ranges.
The z-score is calculated as z-score.
The score x = 33 is 1.5 standard deviations above the mean of 27.
How to Calculate the z-score?To find the z-score for x = 33 in a normal distribution with a mean of 27 and a standard deviation of 4, we can use the formula for calculating the z-score:
z = (x - μ) / σ
where in this case, x = 33, μ = 27, and σ = 4. Plugging these values into the formula, we can calculate the z-score:
z = (33 - 27) / 4
z = 6 / 4
z = 1.5
The z-score for x = 33 is 1.5.
The z-score represents the number of standard deviations that a given value (x) is away from the mean (μ) in a normal distribution. It indicates how many standard deviations a data point is above or below the mean.
In this context, a z-score of 1.5 for x = 33 means that the value 33 is 1.5 standard deviations above the mean of 27.
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A school asks students what type of sports they play. Complete the two-way table for the survey data. Find the answer for the missing letters and show your work as to how you arrived at each answer.
Answer: b: 58-22=36
A=37 68-22-9
d=99 37+62
c=29 34-9
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. Consider function h. h ( x ) = { 3 x − 4 , x < 0 2 x 2 − 3 x + 10 , 0 ≤ x < 4 2 x , x ≥ 4 What are the values of the function when x = 0 and when x = 4 ?
h(0)=
h(4)=
The value of function h (0) is,
h (0) = 10
And, The value of function h (4) is,
h (4) = 8
Given that;
The function is,
h (x) = { 3x - 4 , x < 0
= {2x² - 3x + 10, 0 ≤ x < 4
= { 2x , x≥ 4
Hence, The value of function h (0) is,
h (x) = 2x² - 3x + 10, 0 ≤ x < 4
h (0) = 2 (0) - 3 (0) + 10
h (0) = 10
The value of function h (4) is,
h (x) = 2x
h (4) = 2 (4)
h (4) = 8
Thus, The value of function h (0) is,
h (0) = 10
And, The value of function h (4) is,
h (4) = 8
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Investor C decided to purchase a home that costs $600,000 with a 40% down payment loan, a 3.00% annually fixed rate for a 30 year term, and one payment per month. What is the monthly payment for this mortgage?
Step-by-step explanation:
To calculate the monthly payment for a mortgage, you can use the formula for a fixed-rate mortgage:
Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Loan amount (in this case, the home cost minus the down payment)
r = Monthly interest rate (annual rate divided by 12 and converted to decimal)
n = Total number of payments (number of years multiplied by 12)
Given:
Home cost = $600,000
Down payment = 40% of the home cost = 0.4 * $600,000 = $240,000
Loan amount = Home cost - Down payment = $600,000 - $240,000 = $360,000
Annual interest rate = 3.00%
Loan term = 30 years
First, calculate the monthly interest rate:
Monthly interest rate = (Annual interest rate / 100) / 12 = (3.00 / 100) / 12 = 0.0025
Next, calculate the total number of payments:
Total number of payments = Loan term * 12 = 30 * 12 = 360
Now, substitute the values into the formula:
Monthly Payment = ($360,000 * 0.0025 * (1 + 0.0025)^360) / ((1 + 0.0025)^360 - 1)
After performing the calculations, the monthly payment for this mortgage is approximately $1,520.06.
I hope I was helpful
x=1
x=3
z=x-25y
print(z)
The output of the program for the variable z is -22 or it returns an error if z = x - 25y
Evaluating the output of the programFrom the question, we have the following parameters that can be used in our computation:
x = 1
x = 3
z = x - 25y
print(z)
The value of the variable y is not given
So, the program would return an error
However, if the complete program is as follows (removing the variable y)
x = 1
x = 3
z = x - 25
print(z)
Using the above as a guide, we have the following:
The final value of x is 3
So, we have
z = 3 - 25
Evaluate
z = -22
This means that the output of the program for z is -22
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Erik has been collecting comic books for the past few years. The number of total comic books in his collection each year is as follows. • 30 comic books the first year • 60 comic books the second year • 90 comic books the third year • 120 comic books the fourth year Write a function that represents the number of comic book as a function of the number of years, t.
The function that represents the number of comic book as a function of the number of years, t is expressed as y = 30x or f(t) = 30t.
How to Write a Linear Function?We can use the given data to create a linear equation of the form y = mx + b, where y represents the number of comic books and x represents the number of years.
To find the equation, we can use any two pairs of (x, y) values. Let's use the first and fourth years:
First year: (1, 30)
Fourth year: (4, 120)
The slope, m, of the line can be calculated using the formula:
m = change in y / change in x = (120 - 30) / (4 - 1)
m = 90 / 3
m = 30
The y-intercept, b, can be found by substituting one of the (x, y) values and the slope into the linear equation, y = mx + b:
30 = 30(1) + b
b = 0
Therefore, the equation that represents the number of comic books, y, as a function of the number of years, x, is:
y = 30x
or
f(t) = 30t [where t represents the number of years.]
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A straw is placed inside a rectangular box that is 10 inches by 6 inches by 7 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Answer these 3 questions if not able to answer all try question 10 thank you
Suppose that 15% of all American use CNN as their primary source of news. A random sample of 200 Americans is selected. What is the probability that is your sample of 200 Americans that proportion that us CNN as their primary news source is at least 0.21?
The probability that in a sample of 200 Americans, the proportion that uses CNN as their primary news source is at least 0.21 is 49.6%.
What is the probability?The probability is determined using the normal approximation to the binomial distribution.
Given that the sample size is large (n = 200) and the probability of success (p = 0.15) is not too close to 0 or 1, the mean (μ) and standard deviation (σ) of the binomial distribution, will be:
μ = n * p
μ = 200 * 0.15
μ = 30
σ = √(n * p * (1 - p))
σ = √(200 * 0.15 * (1 - 0.15))
σ ≈ 4.29
Then, the z-score corresponding to the proportion of 0.21 is:
z = (x - μ) / σ
z = (0.21 - 0.15) / 4.29
z ≈ 0.014
Using a calculator, the probability of a z-score of 0.014 is approximately 0.504.
Hence, the probability of obtaining a proportion at least 0.21, is:
Probability = 1 - 0.504
Probability ≈ 0.496
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3. Solve: 5 x 4+ (1+1) + 5 = *
Your answer
Answer:
27
Step-by-step explanation:
We can solve by using order of operations (PEMDAS), which shows us the order in which we're supposed to perform mathematical operations:
Parentheses,Exponents,Multiplication/DivisionThe / comes from the fact that you do these operations from left to right as multiplication and division have the same level of priority in an equation/operation.
and Addition/Subtraction.Like multiplication/division, the / comes from the fact that you do these operations from left to right as addition and subtraction also have the same level of priority in an equation/operation.
Step 1: Simplify inside the parentheses:
5 * 4 + (1 + 1) + 5
5 * 4 + 2 + 5
Step 2: Multiply 5 and 4:
20 + 2 + 5
Step 3: Add 20 and 2:
22 + 5
Step 4: Add 22 and 5 to get your answer:
27
Thus, 5 *4 + (1 + 1) + 5 = 27
Find the equation of the line passing through the point (–1, 5) and perpendicular to the line y = – 3x + 4.
A) 3y = –x + 16
B) y = –3x + 8
C) y = –3x + 2
D) 3y = x + 16
Answer:
D
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 4 ← is in slope- intercept form
with slope m = - 3
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (- 1, 5 ) into the partial equation
5 = - [tex]\frac{1}{3}[/tex] + c ( add [tex]\frac{1}{3}[/tex] to both sides )
5 [tex]\frac{1}{3}[/tex] = c ⇒ c = [tex]\frac{16}{3}[/tex]
y = [tex]\frac{1}{3}[/tex] x + [tex]\frac{16}{3}[/tex] ( multiply through by 3 to clear the fractions )
3y = x + 16
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Find the regression equation. Round your answer to the nearest hundredth.
The equation shows that the point total in the 10th level is predicted to be 514.4.
How to calculate the valueThe equation given is: y= 48.2x + 32.4
where y is the point total and x is the level.
In order to predict the point total in the 10th level, I will substitute x=10 into the equation:
y=48.2(10) + 32.4 = 482 + 32.4 = 514.4
Therefore, the point total in the 10th level is predicted to be 514.4.
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Please help me find the perpendicular height
The perpendicular height of the pyramid is 83.65 cm
How to find the perpendicular height?To find the perpendicular height we can define a right triangle.
The perpendicular height is one leg, and the other leg will be half of the diagonal of the base.
The base is a square whose sidelength is 23cm, then the diagonal is:
D = √( (23cm)² + (23cm)²)
D = 32.527cm
Half of that is
D/2 = 32.527cm/2 = 16.26cm
Now, we know one side of the right triangle and the angle of 79°, for which the known cathetus is adjacent.
The perpendicular height is the opposite cathetus.
Then we can use the relation:
tan(79°) = H/16.26cm
Solving for H, the heigt, we will get.
H = tan(79°)*16.26cm = 83.65 cm
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100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!
The prove of the statement is described below.
First of all ,
Labeling the given figure
And draw a diagonal,
In the quadrilateral PQRS,
The side PQ is equal to the side RS.
Therefore,
PQ = RS
And also, the side PQ is parallel to the side RS.
Then,
PQ || RS.
Now, draw the diagonal PR.
We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.
By the rule of Side-Angle-Side,
we can show that ∆ PQR ≅ ∆ RSP.
Therefore,
The side QR is parallel to PS
Then,
QR || PS.
Hence,
PQRS is a parallelogram.
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mathmatically indication example with solution
A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.
How to solve the equation ?Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.
The equation would be 3 x + 2 = 14.
So we can solve for the equation to be :
3x + 2 - 2 = 14 - 2
3x = 12
3 x / 3 = 12 / 3
x = 4
In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.
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What’s the value of x?
Answer:
The answer is 8
Step-by-step explanation:
/x/ // /8/
x=8
A box has 6 blue socks and 4 white socks. find the number of ways 2 socks can be drawn from the box where
a) There are no restriction
b) They are different colours
c) They are the same colours
The number of ways to draw the socks in each case is given as follows:
a) 90 ways.
b) 48 ways.
c) 42 ways.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways for one trial and n ways for another trial, then there are m x n ways in which the two trials can happen simultaneously.
This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual trial, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, we have that there are no restrictions, hence there are 10 options for the first sock and 9 for the second, hence:
10 x 9 = 90.
For item b, we need one of each, hence the possible combinations are:
One of six(blue) and then one of four(white).One of four(white) and then one of six(blue).Hence:
6 x 4 + 4 x 6 = 48.
For item c, we can take 6 then five(two blue) or 4 then 3(two white), hence:
6 x 5 + 4 x 3 = 42.
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1. The population of a town was 112 in 2014. The population doubles every year.
(a) Use the exponential growth model to write an equation that estimates the population tyears after
2014.
(b) Estimate the population of the town in 2023. Show your work.
Answer:
The estimated population of the town in 2023 is 57,344.
(a) Let P be the population in t years after 2014.
Since the population doubles every year, we can use the formula :
P = P₀(2)ⁿ, where P₀ is the initial population in 2014.
We have P₀= 112, so the equation is P = 112(2)ⁿ.
(b) To find the population in 2023, we need to find t when t + 2014 = 2023.
So t = 2023 - 2014 = 9.
Substituting t = 9 into the equation from part (a), we get:
P = 112(2)⁹
P ≈ 57,344
Therefore, the estimated population of the town in 2023 is 57,344.
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find the expected value of the given variable with the following probability distribution
The expected value of the given variable with the probability distribution is 7
How to find the expected value of the variableFrom the question, we have the following parameters that can be used in our computation:
The probability distribution on the table of values
The expected value of the variable is calculated as
Expected value = ∑x * P(x)
Using the above as a guide, we have the following:
Expected value = 2 * 1/36 + 3 * 1/18 + 4 * 1/12 + 5 * 1/9 + 6 * 5/36 + 7 * 1/6 + 8 * 5/36 + 9 * 1/9 + 10 * 1/12 + 11 * 1/18 + 12 * 1/36
Evaluate
Expected value = 7
Hence, the expected value of the variable is 7
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Need help with this homework
Answer:
Step-by-step explanation:
use gauth math it helps with maths
3. In a data set, the mode, median, and mean are all equal. Which data set below fits this description? A. 26, 39, 39, 39, 52 B. 26, 27, 28, 28, 39 C. 15.0, 15.5, 16.0, 16.0, 21.5 105, 110, 110, 116, 120
Which expression is equivalent to 4^7/8
4^1/4?
Alex washed 3/10 of his laundry yesterday. What fraction of his laundry does he have left to wash?
Answer:
7/10
Step-by-step explanation:
[tex]1 - \frac{3}{10} \\ = \frac{10}{10} - \frac{3}{10 } \\ = \frac{7}{10} [/tex]
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