Answer:
1. $76,000
2. $58,000 + $2,000 * t
Step-by-step explanation:
2. Now, you might be questioning why we are going with the second question first, but this will be useful as it sets up our equation to make the first question easier. So, we will start with Luke's base salary of $58,000. Then, we will add $2,000 for every year he works at the company. If he works for t years and gains $2,000 on his salary per year, our equation will look like this:
$58,000 + $2,000 * t
That is the equation.
1. Now, using our previous equation, $58,000 + $2,000 * t, we will substitute 9 in for t. We get:
$58,000 + $2,000 * 9
Then, we simplify, giving us:
$58,000 + $18,000 = $76,000
You are filling up a water balloon at a rate of 30pi cm^3sec. How fast is the radius of the balloon increasing when the radius is 2cm
The fast of the radius of balloon increasing is 480 cm³ / sec.
How do you calculate speed?If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.When figuring out test problems, the triangle might help you recall the formula more quickly. You may recall the three formulae with the aid of the triangle: Speed is calculated as Distance x Time.The result will be expressed in miles per hour (mph, mi/h), and so on for km/h, m/s, etc., if the distance was measured in miles and the duration in hours.Simple division of time by distance yields the equation for speed. To calculate speed, divide the distance travelled (say, 3 metres) by the passing time (say, three seconds) (one metre per second)Given data :
V = [tex]\frac{4}{3}[/tex] π r³
we know [tex]\frac{dr}{dt}[/tex] = 30 cm/ sec
we want [tex]\frac{dV}{dt}[/tex] when r = 2cm
Differentiate V = [tex]\frac{4}{3}[/tex] π r³ implicitly with respect to t
[tex]\frac{dV}{dt}[/tex] (V) = [tex]\frac{dr}{dt}[/tex] ( [tex]\frac{4}{3}[/tex] π r³ )
[tex]\frac{dV}{dt}[/tex] = [tex]\frac{4}{3}[/tex] π x 3r² [tex]\frac{dr}{dt}[/tex] = 4 π r² [tex]\frac{dr}{dt}[/tex]
Plug in what you know and solve for what you don't know.
[tex]\frac{dV}{dt}[/tex] = 4π ( 2 )² ( 30 / sec ) =
= 120 x 4 .π cm³ / sec
= 480 cm³ / sec
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An object has a mass of 125 g and a volume of 5 cm3.
Find the density of the object in g/cm3.
Answer: 25g/cm3
Step-by-step explanation: The formula for density is mass÷volume. There is no need to convert the mass since it is already in grams.
Solve problems about dilations and write about solution methods. On a coordinate plane, point B is at (1, negative 1). Point B has coordinate B(1, –1). What is the coordinate of B' under a scale factor of 3? (1, –1) (3, –3) (–2, 2) (–6, 6)
Answer:
B' = (3, -3)
Step-by-step explanation:
If the coordinate (a,b) is dilated by a factor of k, the resulting coordinate will be ()ka, ka)
Given the coordinate (1, -1). When dilated by a factor of 3, the resulting coordinate will be;
B' = 3B
B' = 3(1, -1)
B' = (3(1), 3(-1))
B' = (3, -3)
Question 2
In 2007 the US Census Bureau reported that 71.3% of American families owned their
homes. The city council is debating on whether to offer tax breaks to first time
homebuyers, but they only want to do so if there is strong evidence that the rate of
home ownership has increased since 2007 since it will cost the city money to do so.
a) What are the null and alternative hypothesis?
b) Describe a Type I error in context along with the consequence.
c) Describe a Type Il error in context along with the consequence.
d) Which is a more serious error in this context? Justify your answer
e) For each type of error, tell who would be harmed.
(These are questions to answer, not answer choices.)
The answer to all the questions is explained below with justifications.
What is hypothesis testing?In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test. The type of data used and the purpose of the study will determine the methodology the analyst uses.
a) The null hypothesis[tex](H_o)[/tex] is that 71.3% or more of American families owned their homes.
The alternative hypothesis[tex](H_1)[/tex]is less than 71.3% of American families owned their homes.
b) The type I error is the null hypothesis is true but we assumed it to be false that is 71.3% or more of American families owned their homes but the council did not provide tax breaks.
The type II error is the null hypothesis is false and we assumed it to be true
that is less than 71.3% of American families owned their homes and the council provides tax breaks.
c) The consequences of the type II error would be the council will provide tax breaks to more people and it would cost them a large amount of money.
d) Type II error is more serious in this context as the council has to lay off a large amount as compared to individual homeowners who already can afford to buy a house.
e) For type I error house owners will be harmed and for type II error counsel will be harmed.
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If a sample mean is 32, which of the following is most likely the range of
possible values that best describes an estimate for the population mean?
A. (32, 42)
B. (30.38)
C. (34 42)
O D. (28.36)
Answer:
Step-by-step explanation:
It is D, I did this quiz once
Factor the expression completely.
x^4-17x^2+72
Answer:
It's neither:
x =√ 9.000 = 3.00000 or :
x =√ 9.000 = -3.00000 or :
x =√ 8.000 = 2.82843 or :
x =√ 8.000 = -2.82843
Four solutions
Answer:
x^4 - 17x^2 + 72 = (x^2 - 9)(x^2 - 8)
Step-by-step explanation:
First, we need to find two numbers that multiply to give us 72 and whose sum is -17. We can see that 8 and 9 multiply to give us 72, and their sum is 8 + 9 = 17. Since we want the sum to be negative, we need to change one of the signs. So we write -(8 + 9) = -17.
Next, we write the expression as the product of two binomials. We factor out the common factor x^2 from the first two terms: x^4 - 17x^2 + 72 = x^2(x^2 - 17) + 72
Now, we complete the square in the first binomial. To do this, we need to add and subtract (17/2)^2 = (8.5)^2 = 72.25 inside the bracket:
x^2(x^2 - 17) + 72 = x^2(x^2 - 17 + 72.25 - 72.25) + 72 = x^2(x^2 - 17 + 72.25) - 72.25 + 72
Now we can rewrite the square of a binomial :
x^2(x^2 - 17 + 72.25) = x^2((x-8.5)^2)
Finally, we can combine the two binomials
x^2((x-8.5)^2) + 72 = (x^2(x-8.5)^2) + 8(9)
So the expression x^4 - 17x^2 + 72 factors completely as (x^2 - 9)(x^2 - 8)
Hope this helps!
URGENT
Use technology or a z-score table to answer the question.
The amount spent by customers at a grocery store is normally distributed with a mean of $144.05 and a standard deviation of $34.52.
Approximately what percent of customers at the grocery store spend more than $200?
5.3%
8.2%
91.8%
94.7%
Answer:
5.3%
Step-by-step explanation:
The first step is to find the z score corresponding to $200.
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{200-144.05}{34.52}\approx 1.62[/tex]
The next step is to find the area under the standard normal curve to the right of z = 1.62. Some graphing calculators can do this, and there are tables that will help, although many of those show areas to the left of a particular z-score.
Calculator (TI-83/84)
See the attached image.
The command uses 1 x 10^99 as "positive infinity" and calculates the area under the normal curve from 1.62 all the way to the right.
Table
See attached table. This table shows areas to the left of a certain z-score.
Find the entry for 1.62 (it's on page 2 highlighted with a red box). The table says the area to the left of 1.62 is 0.9474.
But the area under the entire curve is 1!
This important fact means that the area to the right of z = 1.62 is 1 - 0.9474 = 0.0536, about 5.3%
(To get the area to the right of z, subtract the area to the left of z from 1.)
What are the zeros of the quadratic 3(x+4)(x − 12) = 0?
Answer:
-4 and 12 are the zeros of the quadratic.
Step-by-step explanation:
What value does X need to be so (x+4) is 0? -4
What value does X need to be so (x-12) is 0? 12
hello please help i’ll give brainliest
Answer:
number 3
Step-by-step explanation:
it helped us try to learn hieroglyphics
which expression is equivalent to
The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics, = [x[tex]^\frac{1}{8}[/tex] . y⁸] is the right answer.
What is defined as an integer exponent?In mathematics, integer exponents are exponents that fall under the integer category. It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many times that base number must be multiplied by itself.
It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many instances the base number must be multiplied by itself.
According to the given information:= [x[tex]^\frac{1}{4}[/tex] . y¹⁶][tex]^\frac{1}{2}[/tex]
= [x[tex]^\frac{1}{8}[/tex] . y⁸]
The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics, = [x[tex]^\frac{1}{8}[/tex] . y⁸] is the right answer.
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What is the length of the short side of one of the 30 60 90 triangles?
Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.
According to the 30-60-90 triangle theorem, the hypotenuse is twice as long as the shorter leg. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].
A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:
You are aware of the short leg (the side across from the 30-degree angle). To find the hypotenuse, multiply the length by two. The long leg can be calculated by multiplying the short side by the square root of 3.You are aware of the hypotenuse. To get the short side, divide the hypotenuse by two. To determine the long leg, multiply this response by the square root of 3.You are aware of the long leg (the side across from the 60-degree angle). To determine the short side, divide this side by the square root of 3. To find the hypotenuse, multiply that amount by two.To know more about the 30 60 90 triangles on brainly : brainly.com/question/11751274
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(NO LINKKKKKKKKKKS)
Pls help me if your good at math I’ll mark brainliest if correct <3333
Answer:
I think its C
Step-by-step explanation:
Can you help me with this
Step-by-step explanation:
to find the equation of any line we have to first find the slope. the slope formula is:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
our slope here would be 8/13
now we input the points in the equation
y = mx + b
then we find b to be -3(7/13)
so the final equation would be:
[tex]y = \frac{8x}{13} - 3( \frac{7}{13} )[/tex]
the sum of the interior angle of a regular polygon is 1080
find the number of sides of the polygon
Answer:
8 sides
Step-by-step explanation:
(n-2)×180=1080
180n-360=1080
180n=1080+360
180n=1440
n=1440/180
n=8 sides
it's an octagon
Answer:
It has 8 sides
Step-by-step explanation:
This is because the formula is 180(n-2) where n is the amount of sides. An octagon has 8 sides so the sum of the angles is 180(8-2)=180(6)=180×6=1080 degrees
Hope that helps :)
Pls help asap
Which quadratic function is represented by the graph?
Answer:
1st option
Step-by-step explanation:
From the graph the zeros are x = - 3 and x = 1 , then the corresponding factors are
(x + 3) and (x - 1) , so
y = a(x + 3)(x - 1) ← a is a multiplier
To find a substitute a point on the graph into the equation
Using (0, - 1.5 ) , then
- 1.5 = a(3)(- 1) = - 3a ( divide both sides by - 3 )
0.5 = a
Then
f(x) = 0.5(x + 3)(x - 1)
helppp is this the right answer ?!!!
Answer:
yup
Step-by-step explanation:
You want to know the mean number of sick days taken by students in your county last year. At each of five schools you randomly survey ten students. Your results are shown. Use all five samples to make one estimate for the mean number sick days taken by students in your county last year.
A: 0, 1, 1, 3, 0, 3, 0, 2, 3, 4
B: 0, 0, 0, 5, 21, 6, 8, 1, 2, 4
C: 11, 8, 1, 1, 0, 0, 4, 4, 4, 6
D: 8, 0, 10, 8, 6, 7, 9, 2, 1, 1
E: 2, 4, 5, 0, 5, 0, 5, 4, 0, 20
___ Days?
Answer:
4
Step-by-step explanation:
Add each sample separately
A.17 B. 47 C. 39 D. 52 E. 45
Then you add them all together which totals 200 sick days
We know that they surveyed 5 schools and 10 students at random from each one. So we want to know the mean of sick days the students took not the schools in all.
So we divide 200/50
And get a mean of 4.
So each student took an average of 4 sick days each in the country.
help asap:( will give brainliest though!
Answer:
∡B = 60°
Step-by-step explanation:
find BC using Pythagorean Theorem:
5² + BC² = 10²
25 + BC² = 100
BC² = 75
BC = [tex]\sqrt{75}[/tex]
BC = [tex]\sqrt{25}[/tex][tex]\sqrt{3}[/tex] which is 5[tex]\sqrt{3}[/tex]
this indicates that ∡B must be 60° because the ratio of sides in a 30-60-90 triangle are 1 : [tex]\sqrt{3}[/tex] : 2
Brian flips a fair coin 3 times.
What is the probability of getting 3 tails?
Answer:
the answer is one over eight
the formula says required outcome divided by sample space
the sample space here is it because we have three coins and the Three coins have two faces each so it becomes 2 x 2 * 2 that is 8 and that is the total sample space we are supposed to get the probability of getting 3 tails and for each coin you have 1/2 x 1/2 x 1/2 and that is 1/8 as your final answer and do probability of getting three tails
Answer:
If a fair coin is flipped 3 times, the probability of getting exactly 3 tails is 1/8
Step-by-step explanation:
1/2 * 1/2 * 1/2 =1/8
6. If 12 out of 20 students in math made an
A on the test, what percentage of the class
made an A?
Answer:
60%
Step-by-step explanation:
Solving right triangles
Find measure of < j.
Answer:
80
Step-by-step explanation:
Because it is more than 45 and the only one that is more that 45 is 80
Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before dying. Test the hypothesis that the highlighters wrote for less than 14 continuous hours. X = 13.6 hours, s = 1.3 hours. Report the test statistic, p-value, null hypothesis, conclusion and round to nearest thousandth.
Answer:
The null hypothesis is [tex]H_0: \mu = 14[/tex]
The alternate hypothesis is [tex]H_a: \mu < 14[/tex]
The test statistic is t = -1.95.
The p-value is of 0.0292. This means that for a level of significance of 0.0292 and higher, there is sufficient evidence to conclude that the highlighters wrote for less than 14 continuous hours.
Step-by-step explanation:
Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours.
At the null hypothesis, we test if the mean is 14 hours, that is:
[tex]H_0: \mu = 14[/tex]
At the alternate hypothesis, we test if the mean is less than 14 hours, that is:
[tex]H_a: \mu < 14[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
14 is tested at the null hypothesis:
This means that [tex]\mu = 14[/tex]
X = 13.6 hours, s = 1.3 hours. Sample of 40:
In addition to the values of X and s given, we have that [tex]n = 40[/tex]
Test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{13.6 - 14}{\frac{1.3}{\sqrt{40}}}[/tex]
[tex]t = -1.95[/tex]
The test statistic is t = -1.95.
P-value:
The p-value of the test is the probability of finding a sample mean lower than 13.6, which is a left tailed test, with t = -1.95 and 40 - 1 = 39 degrees of freedom.
Using a calculator, the p-value is of 0.0292. This means that for a level of significance of 0.0292 and higher, there is sufficient evidence to conclude that the highlighters wrote for less than 14 continuous hours.
What 2D shape is formed by slicing a square pyramid horizontally?
A circle
B rectangle
C triangle
D) square
Answer:
B, Rectangle.
jsjsjsjs help pls shhssjjdjdhdjhdf
Answer:
6.28
Step-by-step explanation:
½ × 3.47²
hey could anyone help?
Answer:
18
Step-by-step explanation:
The ~ indicates that ∠ABC is similar to ∠QRS. In other words, their proportions are the same, even if their size is different.
So AB has the same proportions as QR. 4 can be multiplied by 2.25 to get to 9. So multiply 8 by 2.25 to get n.
8 * 2.25 = 18 so n = 18
pythamgorean theorem
Answer:
What about Pythagorean Theorem?
Find the following expression
Answer:
40/30
Step-by-step explanation:
[tex] \tan(c) = \frac{40}{30} = \frac{4}{3} [/tex]
8. Given the function h(x)=3^x,find the value of x such that h(x)=27
A. 1
B. 3
C. 2
D. 4
Answer:
x=3
Step-by-step explanation:
3 cubed is 27
You have just received your first paycheck of $4,400 from your new job. You visit the dealership with your friend in search of a car. You see a a used car for $4000. The manager tell you that he will give you a discount of 50 percent. When you get home, your parents tell you that they will pay 50 % of the remaining balance.
You are excited when your friend tell you that you will get the car for "free". You will not have to pay any of your own money for the car?
Answer the questions below by showing your work for each question. Answer must be in full sentence.
a) Is your friend correct in assuming that you will not have to pay any of your own money for the car? Why or why not. Proof it.
b) How much if any of your own money will you have to pay for the car?
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Pls answer my question on a page pls because the files don't work on this computer
the swim team trains 4 days every week. Mon, Tues, and Thurs, the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. how many hours per week does the team train?
The number of hours that the team trians per week is 17 hours.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:
( 1 1/4 + 1/2 + 2 1/2) × 4
= 4.25 × 4
= 17 hours.
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