Answer:
1- b. False
2 b. We are 95% confident that the true mean is between 76.08 and 83.92.
Step-by-step explanation:
Confidence Interval is the estimated value that is computed from the statistic of data which is observed. The range value is plausible for unknown parameters. To find the critical value the confidence interval value is observed through the t-value table.
Help me please!!!
10pts
Answer:
-7/2
Step-by-step explanation:
To find the y coordinate of the midpoint and the y coordinates together and divide by 2
(2+-9)/2
-7/2
Answer:
2 goes in green box
Step-by-step explanation:
(9,2) (-7,-9)
(x1, y1) (x2,y2)
Midpoint is (x1+x2)/2 , (y1+y2)/2
(9-7)/2= 1
(2-9)/2 = -7/2
if 25% or the person'so salary is $135.75 then what is the amount of his full salary?
Answer:
543
Step-by-step explanation:
let x= total salary
0.25x=135.75
x=543
Answer:
[tex]\$ \: 543.00[/tex]
Step-by-step explanation:
[tex]25\% \times x =135.75[/tex]
[tex]1/4 \times x =135.75[/tex]
[tex]0.25 \times x =135.75[/tex]
[tex]x=135.75 \times 4[/tex]
[tex]x=543[/tex]
Write a system of linear equations for the graph below
Answer:
y = -3x + 3
[tex]y=\frac{1}{3}x-7[/tex]
Step-by-step explanation:
Slope of a line passing through two points ([tex]x_1, y_1[/tex]) and [tex](x_2, y_2)[/tex] is determined by the formula,
Slope = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
If these points are (0, 3) and (3, -6),
Slope of the line passing through these lines = [tex]\frac{3+6}{0-3}[/tex] = (-3)
Equation of the line which passes through (0, 3) and slope = (-3),
y - y' = m(x - x')
y - 3 = (-3)(x- 0)
y - 3 = -3x
y = -3x + 3
Now slope of another line that passes through (3, -6) and (0, -7),
m' = [tex]\frac{(-6+7)}{(3-0)}[/tex]
m' = [tex]\frac{1}{3}[/tex]
Equation of the line that passes through (0, -7) and slope = [tex]\frac{1}{3}[/tex]
y - (-7) = [tex]\frac{1}{3}(x-0)[/tex]
y + 7 = [tex]\frac{1}{3}x[/tex]
y = [tex]\frac{1}{3}x-7[/tex]
Therefore, system of linear equations are,
y = -3x + 3
[tex]y=\frac{1}{3}x-7[/tex]
The British Department of Transportation studied to see if people avoid driving on Friday the 13th. They did a traffic count on a Friday and then again on a Friday the 13th at the same two locations ("Friday the 13th," 2013). The data for each location on the two different dates is in table #9.2.6. Estimate the mean difference in traffic count between the 6th and the 13th using a 90% level. Dates 6th 13th 1990, July 139246 138548 1990, July 134012 132908 1991, September 137055 136018 1991, September 133732 131843 1991, December 123552 121641 1991, December 121139 118723 1992, March 128293 125532 1992, March 124631 120249 1992, November 124609 122770 1992, November 117584 117263
Answer: The mean difference is between 799586.3 and 803257.9.
Step-by-step explanation: To estimate the mean difference for confidence interval:
Find the statistic sample:
d = value of 6th - value of 13th;Sample mean of difference: mean = ∑d / nSample standard deviation: s = ∑(d - mean)² / n - 1;For the traffic count, mean = 1835.8 and s = 1382607.3
The confidence interval is 90%, so:
α = [tex]\frac{1-0.9}{2}[/tex]
α = 0.05
The degrees of dreedom are:
df = n - 1
df = 10 - 1
df = 9
Using a t-ditribution table, the t-score for α = 0.05 and df = 9 is: t = 1.833.
Error will be:
E = [tex]t.\frac{s}{\sqrt{n} }[/tex]
E = 1.833.([tex]\frac{1382607.3}{\sqrt{10} }[/tex])
E = 801422.1
The interval is: mean - E < μ < E + mean
1835.8 - 801422.1 < μ < 1835.8+801422.1
-799586.3 < μ < 803257.9
The estimate mean difference in trafic count between 6th and 13th using 90% level of confidence is between 799586.3 and 803257.9.
Which linear function has the same y-intercept as the one that is represented by the graph? On a coordinate plane, a line goes through points (3, 4) and (5, 0).
Answer:
A linear equation is an equation with two variables whose graph is a line. The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.If you want to graph a linear equation you have to have at least two points, but it's usually a good idea to use more than two points. When choosing your points try to include both positive and negative values as well as zero
Step-by-step explanation:
Answer:
The answer would be C because the y-intercept is when x is equal to 0
please mark me brainliest
A survey shows that 10% of the population is victimized by property crime each year. A random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 12.35%. Are older people more likely to be victimized
Answer:
We conclude that older people are more likely to be victimized.
Step-by-step explanation:
We are given that a survey shows that 10% of the population is victimized by property crime each year.
A random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 12.35%
Let p = population proportion of people who are victimized.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p \leq[/tex] 10% {means that older people are less likely to be victimized or remains same}
Alternate Hypothesis, [tex]H_A[/tex] : p > 10% {means that older people are more likely to be victimized}
The test statistics that would be used here One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of older people who are victimized = 12.35%
n = sample of older citizens = 527
So, the test statistics = [tex]\frac{0.1235-0.10}{\sqrt{\frac{0.10(1-0.10)}{527} } }[/tex]
= 1.798
The value of z-test statistics is 1.798.
Since in the question, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for right-tailed test.
Since our test statistics is more than the critical value of z as 1.798 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that older people are more likely to be victimized.
Which residual plot shows that the model is a good fit for the data?
Answer: the answer is c (the third answer ) ‼️
Step-by-step explanation:
The data in the given residual plot shows that model C has the best fit.
What is a line of fit?A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit.
Given:
The residual plot of the values in the graph,
The points in the first graph are very far from the x-axis and y-axis so, it is not the best fit,
The points in the second graph are very far from the x-axis and y-axis, and they are symmetric to the y-axis but not the best fit.
Most of the points are close to the x-axis, so it is the best fit,
Thus, the third graph is the best line of fit.
To know more about the line of fits:
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Need help with these problems .( Its okay if u dont know all .Just do what you know)
Answer:
40.5 ft
162 ft
16 in
7.2 in
13.9 ft
Step-by-step explanation:
1) V=√32d
d= ?
V=36 ⇒ 36²= 32d ⇒ d= 1296/32=40.5 feet
2) S= 5.5√d
S= 70 mph, d=?
70²= 5.5²d ⇒ d= 4900/ 30.25≈ 162 feet
3) d= 0.25√h
d= 1 mile, h=?
1²= 0.25²h ⇒ h= 1/0.0625= 16 in
4) a= 4, b= 6, c=?
c²= a²+b² ⇒ c= √a²+b²= √4²+6² = √52≈ 7.2 in
5) c= 16 foot, b= 8 feet, a=?
c²= a²+b² ⇒ a= √c² - b²= √16²-8²= √256- 64= √192≈13.9 feet
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X>1), n=4, p=0.6.
Answer:
[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]
[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]
And replacing we got:
[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=4, p=0.6)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
We want to find the following probability:
[tex] P(X >1)[/tex]
And for this case we can use the complement rule and we got:
[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]
[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]
And replacing we got:
[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]
What number should be in the blank in the sequence? 7; 17; 37; 77; ___ ; 317
Answer:
the answer is 157
Step-by-step explanation:
7 +10= 17
17+20=37
37+40=77
77+80=157
157+160=317
At the beginning you add +10. Every sequence, you need to multiply that number x2. For example: 10 x 2=20...
The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. The population is modeled by the function n = f(t) = a 1 + be−0.7t where t is measured in hours. At time t = 0 the population is 30 cells and is increasing at a rate of 18 cells/hour. Find the values of a and b.
Answer:
a = 30
b = 6/7
Step-by-step explanation:
The number of yeast cells after t hours is modeled by the following equation:
[tex]f(t) = a(1 + be^{-0.7t})[/tex]
In which a is the initial number of cells.
At time t = 0 the population is 30 cells
This means that [tex]a = 30[/tex]
So
[tex]f(t) = 30(1 + be^{-0.7t})[/tex]
And increasing at a rate of 18 cells/hour.
This means that f'(0) = 18.
We use this to find b.
[tex]f(t) = 30(1 + be^{-0.7t})[/tex]
So
[tex]f(t) = 30 + 30be^{-0.7t}[/tex]
Then, it's derivative is:
[tex]f'(t) = -30*0.7be^{-0.7t}[/tex]
We have that:
f'(0) = 18
So
[tex]f'(0) = -30*0.7be^{-0.7*0} = -21b[/tex]
Then
[tex]-21b = 18[/tex]
[tex]21b = -18[/tex]
[tex]b = -\frac{18}{21}[/tex]
[tex]b = \frac{6}{7}[/tex]
choose the graph of y less than negative x squared plus 4x + 5
Answer:
The 1st graph
Step-by-step explanation:
The quickest and easiest way is to just graph y < x² + 4x + 5. When you do so you should be able to see your answer.
An ordinary deck of playing cards contains 52 cards, 26 red and 26 black. If a card is dealt to each of 2 players,.
Find in how many different ways this can be done if the following occur.
a. both cards are red. _____ ways
b. both cards are black _____ways
c. one card is black and the other is red. ________way
Answer:
(a)650 ways
(b)650 ways
(c)676 ways
Step-by-step explanation:
There are 26 red and 26 black cards.
If a card is dealt to each of 2 players, we want to find out how many different ways this can be done.
(a)Both cards are red
If both cards are red:
The first red card can be dealt in 26 ways.
The second red card can be dealt in 25 ways.
Therefore: Both Red cards can be dealt in: 26 X 25 = 650 ways
(b)Both cards are black
If both cards are black:
The first black card can be dealt in 26 ways.
The second black card can be dealt in 25 ways.
Therefore: Both black cards can be dealt in: 26 X 25 = 650 ways
(c)One card is black and the other is red.
The red card can be dealt in 26 ways.
The black card can be dealt in 26 ways.
Therefore: Both cards can be dealt in: 26 X 26 = 676 ways
Find the work done in emptying a cylindrical tank filled with water. The water is being pumped out from the 6 top. The tank has a diameter of 4 feet and is 6 feet tall. The tank is on ground level. Water is 62.4 lbs/ft
Answer:
908360.67 lb-ft
Step-by-step explanation:
height of tank= 6 ft
diameter of the tank = 4 ft
density of water p = 62.4 lbs/ft
A is the cross sectional area of the tank
A = [tex]\pi r^{2}[/tex]
where r = diameter/2 = 4/2 = 2 ft
A = 3.142 x [tex]2^{2}[/tex] = 12.568 ft^2
work done = force x distance through which force is moved
work = F x d
Force due to the water = pgAh
where g = acceleration due to gravity = 32.174 ft/s^2
Force = 62.4 x 32.174 x 12.568 x 6 = 151393.44 lb
work done = force x distance moved
work = 151393.44 x 6 = 908360.67 lb-ft
What is the product of 5 and 3?
40
0 -13
13
040
Answer:
15 is the answer to the question
Answer:
15, which for some reason does not seem to be an option.
Step-by-step explanation:
Product means to multiply to numbers, items etc.
5 times 3, as you should know, is 15.
Hope this helps.
For a project in your statistics class you decide to make a histogram of the salary data for players in the National Basketball Association (NBA). Since most of the players in the NBA earn the league minimum based on their years of service and a few superstars earn very high salaries in comparison, which of the following would most likely be a characteristic of your histogram?
a. Skewed-right
b. Skewed-left
c. Symmetric, with a central peak
d. Uniform
Answer:
b. Skewed-left
Step-by-step explanation:
The histogram will be expressed with the x-axis representing the salaries, in growing amount to the right. The y-axis will represent the relative or absolute frequency.
We know that most of the players earn the minimum league wage. Then, we will have a high frequency in the low salaries classes, at the left of the histogram. A few players earn very high salaries, so we will have a right tail with high values for the salaries a little frequency.
There is no symmetry in this histogram and it is not uniform, as there is no representative mean salary.
As most of the data will be close to the left side, we can conclude that the histogram will be skewed-left.
The Histogram of salary data, with most having less salary is RIGHT Skewed
Given : Data of players' salary is concentrated towards towards most players having less ( minimum ) salary.
Right Skewness denotes a distribution where Tail is on the right side. This implies data is highly concentrated toward left side, ie lower independent variable (x - here 'salary') values.
Left Skewness denotes a distribution where Tail is on the left side. This implies data is highly concentrated towards right side, ie higher independent variable (x - here 'salary') values.
In this case : As more players have lower values of independent variable ie salary, so the data will be concentrated at left - having tail at right.
Hence, it will be Skewed Right
To learn more, refer https://brainly.com/question/3907939?referrer=searchResults
It is known that 40% of adult workers have a high school diploma. If a random sample of 10 adult workers is selected, what is the expected number of adult workers with a high school diploma? (That is, what is E(X)?) Round to the whole number. Do not use decimals. Answer:
Answer:
The expected number of adult workers with a high school diploma is 4.
Step-by-step explanation:
This random variable X can be modeled with the binomial distribution, with parameters n=10 (the sample size) and p=0.4 (the probability that a adult worker have a high school diploma).
The expected value of X is then the mean of the binomial distribution with the parameters already mentioned.
This is calculated as:
[tex]E(X)=\mu_b=n\cdot p=10\cdot0.4=4[/tex]
What are the x-intercepts of the graph of the function below?
y = x^2 – 3x - 28
A. (-7,0) and (-4,0)
B. (7,0) and (-4,0)
C. (7,0) and (4,0)
D. (-7,0) and (4.0)
Answer:
The x intercepts are (7,0) and (-4,0)
Step-by-step explanation:
y = x^2 – 3x - 28
Set y=0
0 = x^2 – 3x - 28
Factor. What 2 numbers multiply to -28 and add to -3
-7*4 = -28
-7+4 = -3
0 = (x-7)(x+4)
Using the zero product property
0 = (x-7) 0 = x+4
x=7 x = -4
The x intercepts are (7,0) and (-4,0)
Juan told Sylvia he got a $0.50 raise this week and his new hourly rate will be $10.25 an hour. Sylvia wants to know what Juan’s hourly rate was before his raise. Which equation and solution can be used to solve this problem? r minus 10.25 = 0.50: Add 10.25 to both sides. The answer is $10.75. r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75. r minus 0.50 = 10.25: Subtract .50 from both sides. The answer is $10.75 r + 10.25 = 0.50: Subtract .50 from both sides. The answer is $9.75.
Answer:
The correct answer is:
r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75.
This is because Juan got a $0.50 raise which means that his new rate will be $0.50 more than his original rate (r).
Answer:
$9.75
Step-by-step explanation:
Which of the following expressions is equal to -1?
sec90°
sin180°
csc270°
Answer:
csc 270° is the answer.
Rasheeda sees a garden in a book. She changes the scale because she wants a garden with different dimensions. The figure below shows both scales and a scale drawing of the garden.
Book scale: 1 inch = 2 feet. Rasheeda's Scale: 2 inches = 3 feet. A rectangle with length A of 18 inches and width B of 6 inches.
Which statements about the gardens are true? Select three options.
Answer:
B. Length A of Rasheeda’s garden is 27 ft.
C. Length B of the book’s garden is 12 ft.
E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.
Step-by-step explanation:
step 1
Find the dimension of the book's garden
we know that
Book scale: 1 inch = 2 feet
That means
1 inch in the drawing represent 2 feet in the actual
To find out the actual dimensions, multiply the dimension in the drawing by 2
so
Length A of the book’s garden
Width B of the book’s garden
step 2
Find the dimension of Rasheeda’s garden
we know that
Rasheeda's Scale: 2 inch = 3 feet
That means
2 inch inches the drawing represent 3 feet in the actual
To find out the actual dimensions, multiply the dimension in the drawing by 3 and divided by 2
so
Length A of Rasheeda's garden
Width B of Rasheeda's garden
Verify each statement
A. Length A of the book’s garden is 18 ft.
The statement is false
Because, Length A of the book’s garden is 36 ft (see the explanation)
B. Length A of Rasheeda’s garden is 27 ft.
The statement is true (see the explanation)
C. Length B of the book’s garden is 12 ft
The statement is true (see the explanation)
D. Length B of Rasheeda’s garden is 6 ft.
The statement is false
Because, Length B of Rasheeda’s garden is 9 ft. (see the explanation)
E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.
The statement is true
Because the difference between 36 ft and 27 ft is equal to 9 ft
F. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.
The statement is false
Because, Length B of the book’s garden is 3 ft greater than length B of Rasheeda’s garden.
taffy927x2 and 22 more users found this answer helpful
Answer:
B. Length A of Rasheeda’s garden is 27 ft.
C. Length B of the book’s garden is 12 ft.
E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.
(second, third, and fifth choices)
Explanation: I did the quiz and got it right.
Hope this Helps!
What is the value of X ?
14
17
24
28
Answer:
24
Step-by-step explanation:
Use the Pythagorean theorem.
Where the sum of the two legs squared is equal to the hypotenuse squared.
10² + x² = 26²
100 + x² = 676
x² = 576
x = √576
x = 24
The value of x is 24.
which is the greatest 1/12, 1/32, 1/48 or 1/18
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
The number with the smallest denominator is the larger number and [tex]\frac{1}{12}[/tex] is the number with the smallest denominator out of [tex]\frac{1}{12} , \frac{1}{32} , \frac{1}{48} , \frac{1}{18}[/tex].
Answer:
1/12
Step-by-step explanation:
Start with a number, for example 100.
Now divide 100 by several numbers which are greater and greater:
100/1 = 100
100/2 = 50
100/4 = 25
100/10 = 10
100/100 = 1
As you divide the same number, 100, by a greater number, the result becomes smaller.
As we divide 100 by 1, then by 2, then by 4, etc., we are always dividing 100 by a greater and greater number. The result is smaller and smaller, 100, 50, 25, etc. If you always divide the same number by other numbers, the larger the number you divide by, the smaller the result.
Numbers in order from greatest to smallest:
1/12, 1/18, 1/32, 1/48
Answer: The greatest number is 1/12
Which scenario is the best example of a deus ex machina?
Answer:
D.
Step-by-step explanation:
Deus ex machina is the plot device of using something very improbable to resolve a situation.
Tickets for a raffle cost $19. There were 798 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1300 and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)
Answer:
-17.32
Step-by-step explanation:
(1319- 19*797)/798 = -17.3233
Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer: time = 20 seconds
Step-by-step explanation:
h(t) = -16t² + 316t + 80
The shape of this graph is an upside parabola ∩.
It lands on the ground when height (h) = 0
Set the equation equal to zero, factor, and solve for t.
0 = -16t² + 316t + 80
0 = 4t² - 79t - 20 divided both sides by -4
0 = (4t + 1)(t - 20) factored the equation
t = -1/4 t = 20 Applied Zero Product Property and solved for t
Since we know time cannot be negative, disregard t = -1/4
The only valid solution is: t = 20
Five-thirds divided by one-third =
Answer:
Step-by-step explanation: [tex]\frac{5}{3}[/tex]÷[tex]\frac{1}{3}[/tex] =
(Decimal: 0.555556)
Alex is paid $30/hr at full rate, and $20/hr at a reduced rate. The hours of work are paid at a ratio of 2:1, full rate : reduced rate. For example, if he worked 3 hours, he would be paid 2 hours at full rate and 1 hour at reduced rate. Calculate his pay for 4 hours of work.
Answer:
$106.67
Step-by-step explanation:
Using the example, for 3 hours work, Alex would be paid ...
(2 hr)($30/hr) +(1 hr)($20/hr) = $60 +$20 = $80
At the same rate of pay, for 4 hours work, the pay would be ...
pay/(4 hr) = $80/(3 hr)
pay = $80(4/3) ≈ $106.67
Alex's pay for 4 hours of work is $106.67.
Algebra 1
Function Notation Worksheet Alternate
Name
For #I-8: Evaluate the following expressions given the functions below:
f(x) = x2 – 7
g(x) = -3x - 1
j(x)=2x-9
h(x) = 1
X=
1. g(10) =
2. What is the value of x if g(x) = 16
3. f(3) =
4. What is the value of x if f(x) = 23
X
5. h(-2) =
6. What is the value of x if h(x) = -2
X =
7. |(7) =
8. h(a) =
For #9-12: Translate the following statements into coordinate points:
9. S(-1) = 3
10. g(4) = -1
11. h(2) = 8
12. k(2) = 9
Answer:
None
Step-by-step explanation:
The answers are:
1. g(10) -31
2. x= -17/3
3. f(3)= 2
4.x= √30
5. h(-2)= 1
6. x= 0
7. h(a)= 1
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = x² – 7
g(x) = -3x - 1
j(x)= 2x-9
h(x) = 1
1. g(10)= -3(10) -1 = -30 - 1= -31
2. g(x) = 16
-3x- 1= 16
-3x = 17
x= -17/3
3. f(3)= (3)² – 7 = 9- 7= 2
4. f(x)= 23
x² – 7= 23
x² = 30
x= √30
5. h(-2)= 1
6. x= 0
7. h(a)= 1
8. S(-1) = 3
The value of function s(a) at a=-1 is 3.
10. g(4) = -1
The value of function g(a) at a=4 is -1.
11. h(2) = 8
The value of function h(a) at a=2 is 8.
12. k(2) = 9
The value of function k(a) at a= 2 is 9.
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Which of the following is the correct graph of the compound inequality 4p + 1 > −15 and 6p + 3 < 45?
The graph of the compound inequality can be seen at the end.
How to get the graph of the compound inequality?Here we have two inequalities that depend on p, these are:
4p + 1 > -15
6p + 3 < 45
First, we need to isolate p on both inequalities.
4p + 1 > -15
4p > -15 - 1
p > -16/4
p > - 4
6p + 3 < 45
6p < 45 - 3 = 42
p < 42/6 = 7
So we have the compound inequality:
p > -4
p < 7
or:
-4 < p < 7
Then this represents the set (-4, 7) where the values -4 and 7 are not included, so we should graph them with open circles.
The graph of the inequality is something like the one below.
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