Answer:
15 years
Step-by-step explanation:
Given the quadratic regression model:
y = 8x² - 40x+6 ; where
y = Number of people attending graduate school ;
x = number of years
The value of x when y = 1206
The equation becomes :
1206 = 8x² - 40x+6
1206 - 6 = 8x² - 40x
1200 = 8x² - 40x
Divide through by 8
150 = x² - 5x
x² - 5x - 150 = 0
x² - 15x + 10x - 150 = 0
x(x - 15) + 10(x - 15)
x - 15 = 0 or x + 10 = 0
x = 15 or x = - 10
Number of years can't be negative,
Hence, x = 15 years
1
Select the correct answer.
Simplify the following expression.
우
O A.
OB. 12
Oc. 1
OD.
64
Reset
Next
Answer:
1/64
Step-by-step explanation:
4^ (-11/3) ÷ 4 ^ (-2/3)
We know a^b ÷a^c = a^(b-c)
4 ^(-11/3 - - 2/3)
4^(-11/3 +2/3)
4^(-9/3)
4^ -3
We know a^-b = 1/a^b
1/4^3
1/64
I need two examples of Solve a proportion with a mixed number in one of its numerators. SHOW ALL WORK!!!!!!!!!!!!
Answer:
A proportion equation is something like:
[tex]\frac{A}{B} = \frac{x}{C}[/tex]
Where A, B, and C are known numbers, and we want to find the value of x.
Now we want two cases where in one of the numerators we have a mixed number, where a mixed number is something like:
1 and 1/3
which actually should be written as:
1 + 1/3
1) a random problem can be:
[tex]\frac{1 + 1/3}{4} = \frac{x}{5}[/tex]
We can see that the numerator on the left is a mixed number.
First, let's rewrite the numerator then:
1 + 1/3
we need to have the same denominator in both numbers, so we can multiply and divide by 3 the number 1:
(3/3)*1 + 1/3
3/3 + 1/3 = 4/3
now we can rewrite our equation as:
[tex]\frac{4/3}{4} = \frac{x}{5}[/tex]
now we can solve this:
[tex]\frac{4/3}{4} = \frac{4}{3*4} = \frac{x}{5} \\\\\frac{1}{3} = \frac{x}{5}[/tex]
now we can multiply both sides by 5 to get:
[tex]\frac{5}{3} = x[/tex]
Now let's look at another example, this time we will have the variable x in the denominator:
[tex]\frac{7}{12} = \frac{3 + 4/7}{x}[/tex]
We can see that we have a mixed number in one numerator.
Let's rewrite that number as a fraction:
3 + 4/7
let's multiply and divide the 3 by 7.
(7/7)*3 + 4/7
21/7 + 4/7
25/7
Then we can rewrite our equation as
[tex]\frac{7}{12} = \frac{25/7}{x}[/tex]
Now we can multiply both sides by x to get:
[tex]\frac{7}{12}*x = \frac{25}{7}[/tex]
Now we need to multiply both sides by (12/7) to get:
[tex]x = \frac{25}{7}*\frac{12}{7} = 300/49[/tex]
what is the sum of the angles of a triangle?
6. The area of a rectangular sheet of paper is 300 cm squared. The length is 5 cm more than the width
a) If the width of the rectangle is x cm, state an expression for the length of the rectangle.
b) Write and algebraically solve a quadratic equation to determine the length and
width of the rectangle.
Answer:
Step-by-step explanation:
width = x
length= x + 5
a) x + 5
b) x * (x+5) = 300
x^2 + 5x = 300
x^2 + 5x - 300 = 0
Δ = 25 + 1200 = 1225
width = (-5 + 35)/2 = 15 cm
lenght = 15 + 5 = 20 cm
Answer:
a) length = x + 5
b) [tex]x^{2}[/tex] + 5x - 300 = 0
Step-by-step explanation:
x = width
x + 5 = length
(x)(x + 5) = 300
[tex]x^{2}[/tex] + 5x = 300
[tex]x^{2}[/tex] + 5x - 300 = 0
(x+20)(x-15)
x = -20 or x = 15 ( disregard the -20. measurements can't be negative)
width = 15
length = x+ 5 = 15+5 = 20
The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage? b) Assume that a recent survey suggests that about 87% of adults have heard of the brand.
Answer:
He must survey 123 adults.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Assume that a recent survey suggests that about 87% of adults have heard of the brand.
This means that [tex]\pi = 0.87[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
How many adults must he survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage?
This is n for which M = 0.05. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.645\sqrt{\frac{0.87*0.13}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.645\sqrt{0.87*0.13}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.87*0.13}}{0.05}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645\sqrt{0.87*0.13}}{0.05})^2[/tex]
[tex]n = 122.4[/tex]
Rounding up:
He must survey 123 adults.
plot the following points in the number line, -1/4, 1 1/2, 0.75 (PLS ANSWER ASAP)
Answer:
-1/4 is the least, 0.75 is second, and 1 1/2 is the greatest
Step-by-step explanation:
-1/4 is the least already because it is negative.
1 1/2 is really 1.5 so now compare 0.75 and 1.5.
1.5 is bigger therefore the order is :
-1/4, 0.75, 1 1/2
Find the missing side lengths leave your answer as a racials simplest form
Answer:
u = 26
v = 13√3
it's 30-60-90 triangle
Select the correct answer. This table represents a quadratic function. x y 0 -3 1 -3.75 2 -4 3 -3.75 4 -3 5 -1.75
I really need one fast
I give all my points
Answer:
1/4
Step-by-step explanation:
that is the answer
I found the constant which was -3
a = 1/4
b=-1
Answer:
the value of a in the function's equation is 1/4
Step-by-step explanation:
Plato answer
Calculus 3 Problem
7. Determine if the field F(x, y, z) = ye^z i + xe^z j + xy e^z k is conservative. If it is, find a potential function.
Step-by-step explanation:
Given:
[tex]\vec{\textbf{F}}(x, y, z) = ye^z\hat{\textbf{i}} + xe^z\hat{\textbf{j}} + xye^z\hat{\textbf{k}}[/tex]
A vector field is conservative if
[tex]\vec{\nabla}\textbf{×}\vec{\text{F}} = 0[/tex]
Looking at the components,
[tex]\left(\vec{\nabla}\textbf{×}\vec{\text{F}}\right)_x = \left(\dfrac{\partial F_z}{\partial y} - \dfrac{\partial F_y}{\partial z}\right)_x[/tex]
[tex]= xe^z - ye^z \neq 0[/tex]
Since the x- component is not equal to zero, then the field is not conservative so there is no scalar potential [tex]\phi[/tex].
Write the sentence as an inequality. The cost of a ticket t will be no more than $52.
Answer:
t is less than or equal to $52, or t <= $52
Step-by-step explanation:
If you can't have more than $52, then use less than symbol (<). The sentence doesn't state that a ticket shouldn't cost $52, so it's safe to assume that you can have exactly $52.
A road crew must repave a road that is 2/3 miles long. They can repave 1/12 miles each hour. How long will it take the crew to repave the road?
Write your answer in simplest form.
The value of the expression 23 +32–3x4–52-5+(7x4) is
Answer:
24
Explanation:
(23+32)-(3×4)-(52-5)+(7×4)
(55)-(12)-(47)+(28)
55-12=43-47+28= -1943-19=24Evaluate −a2+c2 when c=−4.
Answer:
[tex]a = 4, -4[/tex]
Step-by-step explanation:
Step 1: Plug in -4 for c
[tex]-a^{2} + c^{2}[/tex]
[tex]-a^{2} + (-4)^{2}[/tex]
[tex]-a^{2} + 16[/tex]
Step 2: Solve for a
[tex]-a^{2}+16-16=0-16[/tex]
[tex]-a^{2}/-1 = -16/-1[/tex]
[tex]a^{2} = 16[/tex]
[tex]\sqrt{a^{2}} = \sqrt{16}[/tex]
[tex]a = 4, -4[/tex]
Answer: [tex]a = 4, -4[/tex]
MIN-
Bill is measuring a piece of material for some curtains.
It is 215 cm wide, how many mm is this?
There are 10 mm in 1 cm.
mm
Answer:
2,150 mm
Step-by-step explanation:
If every cm is 10 mm you multiply 215 by 10. I hope this helped!
How do u determine the equation of the line through each pair of points in slope-intercept form (y=mx+b). (3,0) and (2,4) (-6,3) and (2,-2)
Answer:
Y =-4X +12
Y =-0.625X -0.75
Step-by-step explanation:
(3,0) and (2,4)....
x1 y1 x2 y2
3 0 2 4
(Y2-Y1) (4)-(0)= 4 ΔY 4
(X2-X1) (2)-(3)= -1 ΔX -1
slope= -4
B= 12
Y =-4X +12
~~~~~~~~~~~~~~~~~
(-6,3) and (2,-2)
x1 y1 x2 y2
-6 3 2 -2
(Y2-Y1) (-2)-(3)= -5 ΔY -5
(X2-X1) (2)-(-6)= 8 ΔX 8
slope= - 5/8
B= - 3/4
Y =-0.625X -0.75
(a). Find the value of log 216.
Answer:
2.334453751
Step-by-step explanation:
Press log on your Casio calculator (if you have one) and plug in 216, then close the parentheses!
PLEASE ANSWER I WILL GIVE BRAINLIEST FAST
Answer:
E &F
Step-by-step explanation:
The rules of a 30-60-90 Triangle is E, and F is just a different value of numbers (but the same ratio).
Find the perimeter and area of a square with sides 6 inches in length.
Which of the following is NOT equivalent to 22/7?
a) 2 + 8/7
b) 1 + 15/7
c) 3 (7/1) + 1/7
d) 3 (7/7) + 1/7
Answer:
the option c is the answer for this question
What is the squad root of 81
Answer:
[tex]9[/tex]
Step-by-step explanation:
Step 1: Find the square root of 81
[tex]\sqrt{81}[/tex]
[tex]\sqrt{9*9}[/tex]
[tex]\sqrt{9^{2}}[/tex]
[tex]9[/tex]
Answer: [tex]9[/tex]
Answer:
the square root of 81 is 9
The angles in a triangle are 89, 1, and 90 degrees. Classify the triangle by its angles and sides.
A. Right isosceles
B. Right Scalene
C. Obtuse scalene
D. Acute isosceles
E. Acute scalene
F. Obtuse isosceles
Answer: B. Right Scalene
Step-by-step explanation: Right because one of the degrees is 90 and scalene because no of the sides of the triangle are the same length.
Answer:
b
Step-by-step explanation:
A pyramid art installation has a surface area of 24 m2. An artist creates replicas with scale factors of 1/8, 1/10, and 1/12. What is the surface area of each replica?
Answer:
The replicas will have a surface area of 3 m2, 2.4 m2 and 2 m2 respectively.
Step-by-step explanation:
Given that a pyramid art installation has a surface area of 24 m2, and an artist creates replicas with scale factors of 1/8, 1/10, and 1/12, to determine what is the surface area of each replica, the following calculation has to be done:
24 x 1/8 = 3
24 x 1/10 = 2.4
24 x 1/12 = 2
Therefore, the replicas will have a surface area of 3 m2, 2.4 m2 and 2 m2 respectively.
Answer:
1/8 = 0.38 m^2
1/10= 0.24 m^2
1/12= 0.17 m^2
Step-by-step explanation:
A sign on the gas pumps of a chain of gasoline stations encourages customers to have their oil checked with the claim that one out of four cars needs to have oil added. If this is true, what is the probability of the following events?
a. One out of the next four cars needs oil.
b. Two out of the next eight cars needs oil.
c.Three out of the next 12 cars need oil.
Answer:
a) 0.4219 = 42.19% probability that one out of the next four cars needs oil.
b) 0.3115 = 31.15% probability that two out of the next eight cars needs oil.
c) 0.2581 = 25.81% probability that three out of the next 12 cars need oil.
Step-by-step explanation:
For each car, there are only two possible outcomes. Either they need oil, or they do not need it. The probability of a car needing oil is independent of any other car, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One out of four cars needs to have oil added.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
a. One out of the next four cars needs oil.
This is P(X = 1) when n = 4. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.25)^{1}.(0.75)^{3} = 0.4219[/tex]
0.4219 = 42.19% probability that one out of the next four cars needs oil.
b. Two out of the next eight cars needs oil.
This is P(X = 2) when n = 8. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.25)^{2}.(0.75)^{6} = 0.3115[/tex]
0.3115 = 31.15% probability that two out of the next eight cars needs oil.
c.Three out of the next 12 cars need oil.
This is P(X = 3) when n = 12. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{12,3}.(0.25)^{3}.(0.75)^{9} = 0.2581[/tex]
0.2581 = 25.81% probability that three out of the next 12 cars need oil.
At the beginning of an experiment, a scientist has 120 grams of radioactive goo. After 135 minutes, her sample has decayed to 3.75 grams. Find an exponential formula for G ( t ) G(t) , the amount of goo remaining at time t t .
Answer:
[tex]G(t) = 120e^{-0.0257t}[/tex]
Step-by-step explanation:
Amount of substance:
The amount of the substance after t minutes is given by:
[tex]G(t) = G(0)e^{-kt}[/tex]
In which G(0) is the initial amount and k is the decay rate.
At the beginning of an experiment, a scientist has 120 grams of radioactive goo.
This means that [tex]G(0) = 120[/tex], so:
[tex]G(t) = G(0)e^{-kt}[/tex]
[tex]G(t) = 120e^{-kt}[/tex]
After 135 minutes, her sample has decayed to 3.75 grams.
This means that [tex]G(135) = 3.75[/tex].
We use this to find k. So
[tex]G(t) = 120e^{-kt}[/tex]
[tex]3.75 = 120e^{-135k}[/tex]
[tex]e^{-135k} = \frac{3.75}{120}[/tex]
[tex]\ln{e^{-135k}} = \ln{\frac{3.75}{120}}[/tex]
[tex]-135k = \ln{\frac{3.75}{120}}[/tex]
[tex]k = -\frac{\ln{\frac{3.75}{120}}}{135}[/tex]
[tex]k = 0.0257[/tex]
So
[tex]G(t) = 120e^{-0.0257t}[/tex]
Someone help me?????
Step-by-step explanation:
4. b 612 (72/100) x 850)
5. c. 275 (33/100) x 835
6. b. 39% (3.24 - 2.85) x100%)
What is the slope formula?
Answer:
D is your answer
Step-by-step explanation:
Answer:
Here the slope formula m = ( y 2 − y 1 )/( x 2 -x 1 ) = Δy/Δx
Step-by-step explanation:
Which graph represents the function f (x) = StartFraction 5 minus 5 x squared Over x squared EndFraction? On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.
9514 1404 393
Answer:
2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3
Step-by-step explanation:
Technically, the curve is not a hyperbola. A hyperbola is of the form 1/x; this one is of the form 1/x².
The function can be simplified to ...
f(x) = 5/x² -5
which is a "hyperbola" with a vertical asymptote at x=0 and a vertical translation of -5 units to bring parts of it into the 3rd and 4th quadrants.
Avi uses 11 toothpicks to form a row of 5 attached triangles, as shown. Suppose he continues this pattern, using 89 toothpicks in all. What is the total number of triangles formed? (sorry the picture wasn't uplodaing)
Answer:
44
Step-by-step explanation:
Given that Avi used 11 toothpicks to form a row of 5 attached triangles.
Total number of toothpicks used = 89
Let the total number of triangles formed be represented by x, so that:
11 toothpicks = 5 triangles
It would be observed that only the first triangle starting the pattern has 3 toothpicks. So that;
the average number of toothpicks for 1 triangle = [tex]\frac{11}{5}[/tex]
= 2.2
The number of toothpicks per triangle = 2.0
Thus,
x = [tex]\frac{89}{2.0}[/tex]
= 44.5
x = 44
The total number of triangles formed is 44.
Didi invested a total of $16125 in two accounts paying 8.5% and 4% simple interest. If her total return at the end of 2 years was 1740 , how much did she invest in each account?
Answer:
5000 ;
11125
Step-by-step explanation:
Given :
Total principal = 16125
Rates = 8.5% and 4%
Period, t = 2 years
Total interest = 1740
Let :
Principal amount invested at 8.5% = x
Principal amount invested at 4% = 16125 - x
Interest formula :
Interest = principal * rate * time
Hence, mathematically ;
(x * 8.5% * 2) + [(16125 - x) * 4% * 2] = 1740
(0.17x + 1290 - 0.08x ) = 1740
0.09x + 1290 = 1740
0.09x = 1740 - 1290
0.09x = 450
x = 450 / 0.09
x = 5000
Amount invested at 4% :
16125 - 5000 = 11125
Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 28. A pollster draws a sample of 92
people to interview.
Answer:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
Step-by-step explanation:
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 41, standard deviation of 28:
This means that [tex]\mu = 41, \sigma = 28[/tex]
Sample of 92:
This means that [tex]n = 92, s = \frac{28}{\sqrt{92}} = 2.92[/tex]
Distribution of the sample means:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
