Let the width = x
The length would be 4x-27
Area = length x width
2790 = (4x-27) * x
Expand:
2790 = 4x^2 - 27x
Subtract 2790 from both sides:
4x^2 - 27x - 2790 = 0
Use the quadratic formula to solve for the positive value of x:
X = -(-27) + sqrt(-27^2 -4*4(-2790)) /(2*4)
X = 30
Now replace x with 30 in the lengths:
Width = x = 30 inches
Length = 4x -27 = 4(30) -27 = 120-27 = 93 inches
A community swimming pool is a rectangular prism that is 30 feet long, 12 feet wide, and 5 feet deep. The wading pool is half as long, half as deep, and the same width as the larger pool.
How many times greater is the volume of the swimming pool than the volume of the wading pool?
Will give Brainliest!
Find the period and amplitude of the function.
y = -4cos(4/3 x)
Give the exact values, not decimal approximations.
Answer:
y = d + a · cos(bx - c) ⇒ y = -4cos(4/3x)
a = -4b = 4/3c = 0d = 0Amplitude = |a| = |-4| = 4
Period = [tex]\frac{2\pi }{b} =\frac{2\pi }{\frac{4}{3} } =2\pi *\frac{3}{4} =\frac{3}{2} \pi[/tex]
Which is most likely the correlation coefficient for the
set of data shown?
Answer:
Step-by-step explanation:
It would -.21. Negative because the trend of the line sort of resembles a line with a negative slope, and .21 because the dat points do not even remotely resemble a line. The closer that number is to 1, the closer the dots will be to fitting on the line.
help with summer school
Answer:
19
Step-by-step explanation:
3a -2^3 ÷b
Let a = 7 and b = 4
3*7 -2^3 ÷4
PEMDAS says exponents first
3*7 -8 ÷4
Multiply and divide from left to right
21 - 2
Subtract
19
An investment of $8,120 is earning interest at the rate of 5.8% compounded quarterly over 11 years. How much
interest is earned on the investment? Show your work.
Answer:
5180.56 Dollars...........
Which values of x are solutions to this equation? -1/2x^2 + 5x = 8
A) -2
B) 2
C) -8
D) -1.5
E) 11.5
F) 8
Answer:
2, 8
Step-by-step explanation:
-1/2x^2 + 5x = 8
-x^2 + 10x = 16 (Multiplying both sides of the equation by 2)
-x^2 + 10x - 16 = 0
x^2 - 10x + 16 = 0 (changing the signs)
x^2 -2x -8x +16 = 0
x (x-2) -8 (x-2) = 0
(x-2) (x-8)
x-2 = 0
x = 2
or
x -8 = 0
x = 8
Answer from Gauthmath
The values of x are solutions to this equation that is 2, 8
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We are given that the equation as;
-1/2x² + 5x = 8
-x² + 10x = 16
Now Multiplying both sides of the equation by 2;
-x² + 10x - 16 = 0
Or
x² - 10x + 16 = 0
x² -2x -8x +16 = 0
x (x-2) -8 (x-2) = 0
(x-2) (x-8)
The solution are;
x-2 = 0
x = 2
or
x -8 = 0
x = 8
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From a club of 24 people, in how many ways can a group of four members be selected to attend a conference?
Answer:
255,024
Step-by-step explanation:
24 x 23 x 22 x 21
24 options for the first member
23 options for the second member
22 options for the third member
21 options for the last member
How long will it take for money to double if it is invested at 7% compounded monthly?
In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rate of change. Define a function f to determine the value of your car (in dollars) in terms of the number of years t since 2012.
Answer:
The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:
[tex]f(t) = 10000(0.9407)^t[/tex]
Step-by-step explanation:
Value of the car:
Constant rate of change, so the value of the car in t years after 2012 is given by:
[tex]f(t) = f(0)(1-r)^t[/tex]
In which f(0) is the initial value and r is the decay rate, as a decimal.
In 2012 your car was worth $10,000.
This means that [tex]f(0) = 10000[/tex], thus:
[tex]f(t) = 10000(1-r)^t[/tex]
2014 your car was worth $8,850.
2014 - 2012 = 2, so:
[tex]f(2) = 8850[/tex]
We use this to find 1 - r.
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]8850 = 10000(1-r)^2[/tex]
[tex](1-r)^2 = \frac{8850}{10000}[/tex]
[tex](1-r)^2 = 0.885[/tex]
[tex]\sqrt{(1-r)^2} = \sqrt{0.885}[/tex]
[tex]1 - r = 0.9407[/tex]
Thus
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]f(t) = 10000(0.9407)^t[/tex]
If k(x) = 5x - 6, which expression is equivalent to (k+ k)(4)?
Answer:
3h33j333jj3
Step-by-step explanation:b3n3n3nn3n33
Find f′ in terms of g′
f(x)=x2g(x)
Select one:
f′(x)=2xf′(x)+2xg′(x)
f′(x)=2xg′(x)
f′(x)=2x+g′(x)
f′(x)=x2g(x)+2x2g′(x)
f′(x)=2xg(x)+x2g′(x)
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Answer:
(e) f′(x)=2xg(x)+x²g′(x)
Step-by-step explanation:
The product rule applies.
(uv)' = u'v +uv'
__
Here, we have u=x² and v=g(x). Then u'=2x and v'=g'(x).
f(x) = x²·g(x)
f'(x) = 2x·g(x) +x²·g'(x)
The graph shows the distribution of lengths of songs (in seconds). The distribution is approximately Normal, with a mean of 227 seconds and a standard deviation of 31 seconds.
A graph titled Song length has length (seconds) on the x-axis, going from 103 to 351 in increments of 31. The highest point of the curve is at 227.
What percentage of songs have lengths that are within 31 seconds of the mean?
34%
68%
95%
99.7%
its everything between 196 and 258 seconds (at max 31secs away from the mean). imagine straight upward lines separating this area from the rest.
34% would be way too low, 95 and above way too much.
only 68% is remotely plausible.
Please help, I'll give brainliest to the correct answer <3
A company recently purchased a new set of laser printers.
The value of the laser printers P, in dollars, t years after the purchase can be represented by the function P(t)=1,900(0.82)t.
Interpret the meaning of the function in the context of this situation.(1 point)
The initial value of the laser printers was $1,900, and the value increases by 82% each year.
The initial value of the laser printers was $1,558, and the value decreases by 82% each year.
The initial value of the laser printers was $1,558, and the value decreases by 18% each year.
The initial value of the laser printers was $1,900, and the value decreases by 18% each year.
Answer:
The initial value of the laser printers was $1,900, and the value decreases by 18% each year.
Step-by-step explanation:
Here ya go bestie <3
Use the compound interest formula to find the annual interest rate, r, if in 2 years an investment of 4,000 grows to 4410 The rate is %.
Answer:
5%
Step-by-step explanation:
Bank amount=PA*(1+r/100)^t
4410=4000*(1+x/100)^2
1.05=(1+x/100), x=5%
Family Video stocks 1003 drama movies, 518 science fiction movies and
253 children's movies. How many more drama titles than children's
titles does Family Video have in stock?
Answer:
There are 750 more drama movies that children's movies.
Step-by-step explanation:
There are 1003 drama movies, and 253 children's movies.
1003 - 253 = 750
How does the graph of this function compare with the graph of the parent function, y=1/x? It is shifted right 5 units and up 2 units from the parent function. It is shifted left 5 units and up 2 units from the parent function. It is shifted right 5 units and down 2 units from the parent function. It is shifted left 2 units and down 5 units from the parent function. It is shifted right 2 units and up 5 units from the parent function. It is shifted left 2 units and up 5 units from the parent function.
Answer:
It is shifted left 5 units and up 2 units from the parent function.
Step-by-step explanation:
Given
[tex]y = \frac{1}{x}[/tex]
[tex]y' = \frac{1}{x+5} + 2[/tex]
Required
Compare both functions
First, translate y, 5 units left.
The rule is:
[tex](x,y) \to (x + 5,y)[/tex]
So, we have:
[tex]y = \frac{1}{x}[/tex]
[tex]y_1 = \frac{1}{x + 5}[/tex]
Next, translate y1, 2 units up.
The rule is:
[tex](x,y) \to (x,y+2)[/tex]
So, we have:
[tex]y' = y_1 + 2[/tex]
[tex]y' = \frac{1}{x + 5} + 2[/tex]
Hence, the transformation is:
5 units left and 2 units up
Answer:
b
Step-by-step explanation:
If 64 > x^3, then the greatest possible integer value
of x is
(a) 1
(c) 3
(b) 2
(d) 4
Answer:
C
Step-by-step explanation:
64>x^3, plugging in x=3, we have 64>27 which is TRUE
Solve for Y equals -2 over 3x minus 1
Answer:
y=-\frac{2}{3}\approx -0.666666667
The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.05 ounces and a standard deviation of .18 ounces. Suppose that you draw a random sample of 36 cans.
a. Find the probability that the mean weight of the sample is less than 5.97 ounces.
b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.
Answer:
a) 0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.
b) Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 6.05 ounces and a standard deviation of .18 ounces.
This means that [tex]\mu = 6.05, \sigma = 0.18[/tex]
Sample of 36:
This means that [tex]n = 36, s = \frac{0.18}{\sqrt{36}} = 0.03[/tex]
a. Find the probability that the mean weight of the sample is less than 5.97 ounces.
This is the p-value of z when X = 5.97. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.97 - 6.05}{0.03}[/tex]
[tex]Z = -2.67[/tex]
[tex]Z = -2.67[/tex] has a p-value of 0.0038.
0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.
b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.
Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.
What are the coordinates of the point on the directed line segment from (-2,6) to (3,-9) that partitions the segment into a ratio of 3 to 2?
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Answer:
(1, -3)
Step-by-step explanation:
The point P that partitions AB into the ratio m:n is ...
P = (mB +nA)/(m+n)
The point you're looking for is ...
P = (3(3, -9) +2(-2, 6))/(3+2) = (9-4, -27+12)/5 = (5, -15)/5
P = (1, -3)
Given that 3x-7y=-27 and 5x+9y=17. Find the values of x and y that satisfy both equations, using elimination method.
here's the answer to your question
solve for x
3x-7y=-27
5x+9y=17
multiply 9, 7
27x -63y =-243
35x +63y = 119
add and cancel y out
62x = -124
x = -2
plug in x
-6-7y=-27
-7y=-21
y = 3
answer:
y = 3
x = -2
A hospital director is told that 54% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is under the expected percentage. A sample of 120 patients found that 60 were insured. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
Z -0.879173965
Step-by-step explanation:
Z -0.879173965
ρ 0.5
π 0.54
n 120
The value of the test statistic is the z-score z = -0.88
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the test statistic value be represented as z
Now , the probability of emergency room visitors are insured is q = 0.54
The total number of patients n = 120
The number of patients that were insured = 60
So , the percentage of people that were insured p = 60/120 = 0.5
Now , test statistic value z = ( p - q ) / [ √ ( q ( 1 - q )/n² ]
The value of z score is
z = [ 0.5 - 0.54 ] / √ 0.54 ( 1 - 0.54 ) / 120²
On simplifying the equation , we get
The value of z score is z = -0.88
Hence , the test statistic is z = -0.88
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find the value of x²-6x+13 when x=3+2i
Answer:
18
Step-by-step explanation:
x squared -6 +13
5 squared-6×3+2+13
25-20+13
5+13
=18
ASAP PLSSSSSSSS TYYYYYY
Answer:
20% of students prefer to go to the aquarium
50% of teachers prefer to go to the aquarium
Step-by-step explanation:
1.
8 students prefer the aquarium out of 40 students.
Set up an equation:
Variable x = percentage of students
8/40 = x/100
Cross multiply:
8 × 100 = 40 × x
800 = 40x
20 = x
Divide:
20%
Check your work:
40 students × 20%
Convert percentage into decimal:
40 × 0.20
8
8 students prefered the aquarium so this is correct!
2.
5 teachers prefer the aquarium out of 10 teachers.
Set up an equation:
Variable x = percentage of teachers
5/10 = x/100
5 × 100 = 10 × x
500 = 10x
50 = x
50%
Check your work:
10 × 0.50
5
Correct!
The sum of three numbers is 124
The first number is 10 more than the third.
The second number is 4 times the third. What are the numbers?
Answer:
182/3,3 8/3, 152/3
Step-by-step explanation:
a+b+c=124
a trừ c= 10
4b=c
Answer:
a=29,b=79,c=19
Step-by-step explanation:
a=c+10
b=4c
=> a+b+c=c+10+4c+c=124
=> c=19
=> a= 29, b=79
You measure 40 watermelons' weights, and find they have a mean weight of 67 ounces. Assume the population standard deviation is 11.4 ounces. Based on this, what is the maximal margin of error associated with a 99% confidence interval for the true population mean watermelon weight.
Answer:
[tex]35.36,44.64[/tex]
Step-by-step explanation:
Sample size [tex]n=40[/tex]
Mean weight [tex]\=x =67[/tex]
Standard deviation [tex]\sigma=11.4[/tex]
Confidence Interval [tex]CI=0.99[/tex]
\alpha==0.01
Therefore
[tex]Z_{\frac{\alpha}{2}}=Z_[0.005][/tex]
From table
[tex]Z_{\frac{\alpha}{2}}=2.576[/tex]
Generally, the equation for Margin of error is mathematically given by
[tex]M.E=Z_{\frac{\alpha}{2}}*(\frac{\sigma}{sqrt{n}}[/tex]
[tex]M.E=2.576*(\frac{11.4}{\sqrt{40}}[/tex]
[tex]M.E=4.64[/tex]
Therefore Estimated mean is
[tex]\=x-M.E<\mu <\=x +E[/tex]
[tex]40-4.64<\mu< 40+4.64[/tex]
[tex]35.36<\mu < 44.64[/tex]
[tex]35.36,44.64[/tex]
Your small business spent $40 on food and another $60 on materials. Then, you sold an item for $120, but you had to pay a $90 service fee. Finally, you were given a refund from the Internal Revenue Service (IRS) for $70. If the expression describing these transactions is the following, then how does it evaluate?
Answer:
40$+60$=100$ spent
120$sold
90$ payed
70$ refund
120 (sold) -90 (payed) =30+70 (refund) =100$ (profit)
Step-by-step explanation:
You spent 100$
And you sold and got 120 but you payed 90$ from 120$ money left is 30$
Then they refunded you (pay back the money (give you the money ))
So the money that your left with is 30$ and the refund money is 70$
So add the money that your left with is gives you 100$
A ball is thrown from an initial height of 4 feet with an initial upward velocity of 40 feet per second. The ball's height h (in feet) after t seconds is given by the following. h=4+40t-16t2 Find all values of for which the ball's height is 26 feet.
Answer:
Step-by-step explanation:
To find the times that the height is 26 feet, we set the position equation equal to 26 and solve for t:
[tex]26=-16t^2+40t+4[/tex] and
[tex]0=-16t^2+40t-22[/tex] and factor that however you are factoring in class to solve a problem like this. When you do that you get
t = .86 seconds and t = 1.68 seconds. That means that .86 seconds after the ball is thrown into the air, it reaches a height of 26 feet; it goes up to its max height and then gravity takes over and pulls it back down. When this happens, it will pass 26 feet again on its way back down. This second time is after 1.68 seconds.
solving systems by substitution
how would you you find the answer for
-5x + y = -2
-3x+6y=-12 ? having some issues with how to this
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Answer:
(x, y) = (0, -2)
Step-by-step explanation:
When solving by substitution, you usually want to find an expression for one of the variables in terms of the other. So, the first thing you look for is an equation that has a coefficient of 1 or -1 on one of the variables. Recognizing that the second equation's terms all have a common factor of 3, you basically have two choices.
Substitute for yUsing equation 1, you can write an expression for y:
y = 5x -2 . . . . . . add 5x to both sides
Then substituting this into the original equation 2, you have ...
-3x +6(5x -2) = -12
27x -12 = -12 . . . . . . . simplify
27x = 0 . . . . . . . . . add 12
x = 0 . . . . . . . . . divide by 27
y = 5(0) -2 = -2 . . . . find y using the expression for substitution
The solution is (x, y) = (0, -2).
__
Substitute for xIf you decide you'd rather substitute for x, you can solve the second equation easily for x.
-3x +6y = -12
x -2y = 4 . . . . . . divide by -3
x = 2y +4 . . . . . . add 2y
Substituting for x in the first equation gives ...
-5(2y +4) +y = -2 . . . . substitute for x
-9y -20 = -2 . . . . . . . simplify
-9y = 18 . . . . . . . . . add 20
y = -2 . . . . . . . . . . . divide by -9
x = 2(-2) +4 = 0 . . . . find x using the expression for substitution
The solution is (x, y) = (0, -2).
_____
Additional comment
In some cases, there are no variables that have a coefficient of ±1, so you just need to "bite the bullet" and deal with the resulting fractions.
Example:
solve for y: -5x +2y = -2
2y = 5x -2
y = 5/2x -1 . . . . expression used to substitute for y
Of course, you can multiply the equation after substitution by 2 to eliminate fractions, or just work the problem as is. The point of looking for coefficients of ±1 is to avoid having to do arithmetic with fractions. It can help avoid errors to work with integers, but ultimately the method is the same regardless of the form of the numbers.
__
You don't always have to substitute for the "bare" variable. Sometimes it can save steps to substitute for expressions instead of variables. If our system of equations were ...
-5x +2y = -2-3x +6y = -12You can substitute into the second equation for (2y). In that case, the second equation becomes ...
-3x +3(2y) = -12
-3x +3(5x-2) = -12 . . . . . . where 2y = 5x -2
72a^7/-9 as a monomial
Answer:
− 8 a ^7
Step-by-step explanation:
See picture for steps :)
