We are given:
f(x) = 3x + 8
g(x) = -x³
__________________________________________________________
The Concept:
We have to find the values of f(g(3)), which means that we have to apply the function g() on 3 and apply the function f() on the value we get.
Finding f(g(3)):
Finding g(3):
g(x) = -x³
g(3) = -(3)³
g(3) = -27
Finding f(g(3)):
f(x) = 3x + 8
f(g(3)) = 3(g(3)) + 8
f(g(3)) = 3(-27) + 8
f(g(3)) = -81 + 8
f(g(3)) = -73
Hence, f(g(3)) = -73
Compute $\sqrt{25^2-7^2}$.
Answer:
24
Step-by-step explanation:
[tex]\sqrt{25^2-7^2}\\\\=\sqrt{(25-7)(25+7)}\\\\=\sqrt{18(32)}\\\\=\sqrt{9*2*2^5}\\\\=\sqrt{3^2\cdot 2^6}\\\\=\sqrt{(3\cdot2^3)^2}\\\\=3\cdot2^3\\\\=3\cdot8\\\\=24[/tex]
Answer:
24
Step-by-step explanation:
First we compute the number under the radical.
We have 25² = 625 and 7² = 49, so 25² - 7² = 625 - 49 = 576.
Thus, √25² - 7² = √576 = √24², which is 24.
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.6 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 160 engines and the mean pressure was 5.7 pounds/square inch. Assume the variance is known to be 0.25. A level of significance of 0.01 will be used. Make a decision to reject or fail to reject the null hypothesis.
Answer:
The decision rule is
Reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 5.6 \ pounds/inch^2[/tex]
The sample size is n = 160
The sample mean is [tex]\= x = 5.7 \ pounds/ inch^2[/tex]
The variance is [tex]\sigma ^2 = 0.25[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = 5.6[/tex]
The alternative hypothesis is [tex]H_a : \mu > 5.6[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\sigma ^2 }[/tex]
=> [tex]\sigma = \sqrt{0.25 }[/tex]
=> [tex]\sigma = 0.5[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{5.7 - 5.6 }{ \frac{0.5 }{\sqrt{ 160 } } }[/tex]
=> [tex]z = 2.53[/tex]
From the z table the area under the normal curve to the left corresponding to 2.53 is
[tex]p-value = P(Z > 2.53 ) =0.0057[/tex]
From the value obtained we see that the [tex]p-value < \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the believe that the valve performs above the specifications is true
2x^2-20x+100 quadratic formula
Answer:10
Step-by-step explanation:
true or false all states have a sale tax
Answer:
False
Step-by-step explanation:
As of 2017, 5 states (Alaska, Delaware, Montana, New Hampshire and Oregon) do not levy a statewide sales tax. California has the highest base sales tax rate, 7.25%. Including county and city sales taxes, the highest total sales tax is in Arab, Alabama, 13.50%.
An average scanned image occupies 0.5 megabytes of memory with a standard deviation of 0.2 megabytes. If you plan to publish 80 images on your web site, what is the probability that their total size is between 49 megabytes and 53 megabytes?
Answer:
Approximately [tex]0.012[/tex] (that's approximately [tex]1.2\%[/tex].)
Step-by-step explanation:
The question did not specify the exact distribution of the size of those images. However, the sample size [tex]n = 80[/tex] is a rather large number. Assume that:
the sizes of these [tex]80[/tex] images follow the same distribution, with mean [tex]\mu = 0.5[/tex] megabytes and standard deviation [tex]\sigma = 0.2[/tex] megabytes.the size of each image is independent of one another.If both assumptions are met, the central limit theorem would apply. This theorem would suggest that the sum of the sizes of these [tex]80[/tex] image (a random variable) will approximately follow a normal distribution. The mean of that sum would be approximately [tex]n\cdot \mu= 80 \times 0.5[/tex]. The standard deviation of that sum would be approximately [tex]\sigma\, \sqrt{n} = 0.2\times \sqrt{80}[/tex].
Let [tex]\displaystyle \Sigma X[/tex] denote the sum of these eighty sizes.
Under these assumption, [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left(n\, \mu,\, \sigma\,\sqrt{n}\right)[/tex].
That is: [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left({80\times 0.5},\, \left(0.2\times \sqrt{80}\right)^2}\right)[/tex].
The question is asking for the probability [tex]P(49 \le \Sigma X \le 53)[/tex]. Therefore, calculate the [tex]z[/tex]-score that corresponding to [tex]\Sigma X = 49[/tex] and [tex]\Sigma X = 53[/tex]:
For [tex]\Sigma X = 49[/tex], the [tex]z[/tex]-score would be [tex]\displaystyle \frac{\sum X - n\, \mu}{\sigma \sqrt{n}} = \frac{49 - 80 \times 0.5}{0.2\times \sqrt{80}} = 2.25[/tex].For [tex]\Sigma X = 53[/tex], the [tex]z[/tex]-score would be [tex]\displaystyle \frac{\sum X - n\, \mu}{\sigma \sqrt{n}} = \frac{53 - 80 \times 0.5}{0.2\times \sqrt{80}} = 3.25[/tex].Make use of a [tex]z[/tex]-table to find these two probabilities:
[tex]P(X \le 49) = P(Z < 2.25) \approx 0.98778[/tex].[tex]P(X \le 53) = P(Z < 3.25) \approx 0.99942[/tex].Calculate the probability that this question is asking for:
[tex]\begin{aligned}& P(49 \le \Sigma X \le 53) \\ &= P(\Sigma X < 53) - P(\Sigma X < 49) \\ & \approx 0.99942 - 0.98778 \approx 0.012 = 1.2\%\end{aligned}[/tex].
what is the answer for this
Answer:
4
Step-by-step explanation:
Which expressions are equivalent to 4• (7 • y)?
Drag and drop the equivalent expressions into the box.
(7• y)• 4
4 • 7 + 4 • Y
(4 7 • y
28 y
4•7•4• y
PLEASE HELP ASAP!!!
50 POINTS AND BRAINLY!!
Answer:
Step-by-step explanation:
4• (7 • y) is equivalent to all of the following:
28 • y
4 · 7y or (4 · 7) · y
(7 · 4) · y
Note that 4 • 7 + 4 • Y is absolutely wrong, since the original expression has no " + " sign
Question 15 (1 point)
The surface area of a sphere varies directly with the square of its radius. A soap bubble with a
0.75 in. radius has a surface area of approximately 7.07 square inches. Find the value of k, and
then find the radius of a seventeenth-century cannonball that has a surface area of 113.1
square inches.
Answer:
The value of k is 12.57Radius of a seventeenth-century cannonball is 2.999 inches which can be rounded off to 3Step-by-step explanation:
Let s be the surface area and r be the radius
Then according to given statement
s∝r²
Removing the proportionality symbol introduces k, the constant of proportionality
[tex]s = kr^2[/tex]
Now
A soap bubble with a 0.75 in. radius has a surface area of approximately 7.07 square inches.
Putting in the equation
[tex]7.07 = k (0.75)^2\\7.07 = k * 0.5625\\k = \frac{7.07}{0.5625}\\k = 12.5688..\\k = 12.57[/tex]
The euqation beomes
[tex]s = 12.57r^2[/tex]
Putting s = 113.1 in the equation
[tex]113.1 = 12.57r^2\\r^2 = \frac{113.1}{12.57}\\r^2 = 8.99761...\\\sqrt{r^2} = \sqrt{8.9976..}\\r = 2.9996..[/tex]
Hence,
The value of k is 12.57Radius of a seventeenth-century cannonball is 2.999 inches which can be rounded off to 3Find the slope and the y-intercept of the line.
5x - 4y= -16
Write your answers in simplest form.
Step-by-step explanation:
Use the slope-intercept form
y=mx+b
to find the slope m and y-intercept b
Slope: 5/4
y-intercept: (0,-4)
The explains why a x b = b x a and a + b = b + a.
Swedish researchers concluded that viewing and discussing art soothes the soul and helps relieve medical conditions such as high blood pressure and constipation. This conclusion was based on a study in which 10 elderly women gathered once a week to discuss different works of art. The study also included a control group of 10 elderly women who met once a week to discuss their hobbies and interests. At the end of 4 months, the art discussion group was found to have a more positive attitude, to have lower blood pressure, and to use fewer laxatives than the control group.(a) Why would it be important to determine if the researchers assigned the women participating in the study at random to one of the two groups?i) Assigning women at random ensures that the two groups are comparable.ii) Assigning women at random satisfies the conditions of a single-blind experiment. iii) Assigning women at random is not important for the study and can be neglected.(b) Explain why you think that the researchers included a control group in this study.i) A control group is absolutely unnecessary hereii) A control group allows the experiment to be conducted once more if the first attempt failed. iii) A control group is used to increase the size of the sampleiv) A control group provides a baseline for comparisons to determine treatment effects.
Answer:
i) Assigning women at random ensures that the two groups are comparable.
iv) A control group provides a baseline for comparisons to determine treatment effects.
Step-by-step explanation:
(a)
It is pertinent that there two comparable groups. In light of the fact that it will help in making better decisions since there will be some people who have blood pressure as a result of uncontrolled physical characteristics such as anger, positive attitude, lower blood pressure. etc Thus, there is a need to consider two equivalent groups.
(b)
A control group is used as a benchmark for determining the cause and effect of a treatment on a given experimental group. This may be in regard to the social aspect of meeting other individuals involved that make up the physical changes.
X = 3/4. Y = -1/2.
What is x + y?
Evaluate: 12/y+9d if y = 5 and d = 7
here's the answer.....I hope it would work
Answer:
3/17
Step-by-step explanation:
Substitute the given values for the variables.
[tex]\frac{12}{5+9(7)}[/tex]
Simplify
[tex]\frac{12}{5+63}[/tex]
[tex]\frac{12}{68}[/tex]
[tex]\frac{3}{17}[/tex]
5/6 - (-2/3)
Steps please
Answer:
9/6
Steps:
5/6 - (-2 x 2)
____. = 9/6
3 x 2
Suzy is ten years older than Belly, and the next year she will be twice as old as Billy. How old are they now? Show solution.
Answer:
I understand there is a typo, so Belly and Billy are the same person. His age is represented as B, and Suzy's as S.
S = 19
B = 9
Step-by-step explanation:
Suzy is ten years older than Belly:
(1) S = B + 10
the next year she will be twice as old as Billy
(2) S + 1 = 2 (B + 1)
solving the system of equation (1) and (2):
Making (2) - (1):
1 = 2 (B + 1) - B - 10 => 1 = 2 B + 2 - B - 10 => 1 = B - 8 => B = 9
replacing in (1) S = 19
An auto-parts store offers a fuel additive that claims to increase a vehicle’s gas mileage. The additive is poured into a vehicle’s gasoline tank after the tank is filled. To measure the claim, 30 taxi drivers receive a bottle of the additive to use the next time they fill their gas tank. The drivers then compare their gas mileage with the additive to their gas mileage before the additive was used.
What is the response variable in this scenario?
the age of the car
the 30 cars used in the study
the use of the additive
the gas mileage after the additive is used
Answer:
The answer is D. the gas mileage after the additive is used
Step-by-step explanation:
I got 100% on edg!
Answer:
d
Step-by-step explanation:
edge2o2o
What is the equation of the line that passes through the points (-1, 3) and (1, 11)? (5 points)
4x - y = 1
x - 4y = -13
4x - y = -7
4x + y = 1
Answer:
4
Step-by-step explanation:
I am pretty sure its that one
2x - 3y = 8
9y - 6x = - 2
Answer:
what?????????????????
Step-by-step explanation:
how do you want me to solve with a fraph or sometging else
If f(x)=6x-2, what is the value of f(4)?
Please explain I don’t understand these questions.
Answer:
I think it might be 16 or 24.
Step-by-step explanation:
Pardon if I'm wrong.
Based on the graph, what does the point (0, 0) represent
Answer:
you didn't post the graph but (0,0) is the origin
Answer:
ok
Step-by-step explanation:
Which of the following represents an inequality statement with a solution of
Please help out I’ll give you brainliest
Answer:
the second to last one
Step-by-step explanation:
Sorry if it is incorrect!
WHAT IS THE ANSWER PLZ HELP ME??? I WILL MARK BRAINLIEST!!!
Answer:
- 5/6
Step-by-step explanation:
turn it into an improper fraction.
1 and 2/3 = 5/3
2 and 1/2 = 5/2
5/3 - 5/2 = 10/6 - 15/6
= -5/6
Answer:
First you have to change both of the mixed numbers to improper fractions. To do this you would multiply the denominator and the whole number then add the numerator.
1 2/3 = 5/3
-2 1/2 = -5/2
Find the least common denominator (LCM). Add the numerator, and keep the denominator the same.
The LCM for these two fractions would be 6 so to get to six you would multiply 5/3 by 2/2 and -5/2 by 3/3.
5/3 = 10/6
-5/2 = -15/6
Add the numerators (10 + -15 = -5), and keep the denominator the same (6). Therefore, the answer would be -5/6.
which is bigger 1.7m or 0.9m
need an answer showing work thax!
Answer:
Option (a) [tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]
Step-by-step explanation:
The given expression is :
[tex]\dfrac{3}{1{\cdot} 2}+\dfrac{3}{2{\cdot} 3}+\dfrac{3}{3{\cdot} 4}+\dfrac{3}{4{\cdot} 5}+....[/tex]
We need to rewrite the sum using sigma notation.
The numerator is 3 in all terms.
At denominator, in first term (1)(2), in second term (2)(3) and so on.
A general term for the denominator is k(k+1).
Sigma notation is :
[tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]
Hence, the correct option is (A).
A bakery needs to make 7 batches of muffins before opening in 4 hours. Each batch of muffins takes 2/3 hour to bake.
Please help and explain how you got the answer. Im giving out brainliest. || Q4
Answer: 32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
Inside the parentheses, we see 5+3, which equals 8. Now, do 8x4, which equals 32!
The prices for a couch, love seat, and chair are $789, $605, and $284. If the total tax paid is $100.68, which amount is closest to the total cost, in dollars, for all three pieces?
Answer:
1778.68 I think
Step-by-step explanation:
Answer:
605
I just got confused sorry.
I need help please and thanks
Answer:
68 degrees
Step-by-step explanation:
1 & 6 have to equal 180. Therefore, if 1 is 112 then you take 180-112. Then you get 68 degrees.
Answer:
Angle 6 would be 68 degrees
Step-by-step explanation:
Angles 1, 3, 5, and 7 all equal 112. you would subtract 112 from 180 to get the measurement for angles 2, 4, 6, and 8
What is the difference between twice twenty-five and twice five and twenty?
I will give brainliest
Find x and y, there is no given info, and the line that is 8 units long is not a midsegment, but it is parallel to the line that is ten units long
Answer:
x = 1.25
y = 1.75
Step-by-step explanation:
Since, the line that is 8 units long is parallel to the line that is ten units long.
Therefore, both the triangles are similar by AA postulate.
Corresponding sides of of the similar triangles are in proportion.
Therefore,
[tex] \frac{5}{x + 5} = \frac{7}{y + 7} = \frac{8}{10} \\ \\ \implies \frac{5}{x + 5} = \frac{8}{10} \\ \\ 5 \times 10 = 8(x + 5) \\ \\ 50 = 8x + 40 \\ \\ 50 - 40 = 8x \\ \\ 10 = 8x \\ \\ \frac{10}{8} = x \\ \\ x = 1.25 \\ \\ \\ \frac{7}{y + 7} = \frac{8}{10} \\ \\ 7 \times 10 = 8(y + 7) \\ \\ 70 = 8y + 56 \\ \\ 70 - 56 = 8y \\ \\ 14 = 8y \\ \\ \frac{14}{8} = y \\ \\ y = 1.75[/tex]