Answer:
Step-by-step explanation:
if we shift 13 units right and 6 units down we get the reqd. graph.
Answer:
see explanation
Step-by-step explanation:
Given the graph of f(x) then f(x + k) is a horizontal translation of f(x)
• If k > 0 then shift left by k units
• If k < 0 then shift right by k units
Thus y = (x - 13)² represents a shift to the right of 13 units
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then shift up by c units
• If c < 0 then shift down by c units
Thus
y = (x - 13)² + 6 is the graph of y = x² translated 13 units right and 6 units up
Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pianist, the other as the alternate.
What is the probability that the pianist will be a boy and the alternate will be a girl? Express your answer as a percent.
30%
40%
50%
60%
Answer:
30% is the correct answer.
Step-by-step explanation:
Total number of boys = 2
Total number of girls = 3
Total number of students = 5
To find:
Probability that the pianist will be a boy and the alternate will be a girl?
Solution:
Here we have to make 2 choices.
1st choice has to be boy (pianist) and 2nd choice has to be girl (alternate).
[tex]\bold{\text{Required probability }= P(\text{boy as pianist first}) \times P(\text{girl as alternate})}[/tex]
Formula for probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
For [tex]P(\text{boy as pianist})[/tex], number of favorable cases are 2 (total number of boys).
Total number of cases = Total number of students i.e. 5
So, [tex]P(\text{boy as pianist})[/tex] is:
[tex]P(\text{boy as pianist}) = \dfrac{2}{5}[/tex]
For [tex]P(\text{girl as alternate})[/tex], number of favorable cases are 3 (total number of girls).
Now, one boy is already chosen as pianist so Total number of cases = Total number of students left i.e. (5 - 1) = 4
[tex]P(\text{girl as alternate}) = \dfrac{3}{4}[/tex]
So, the required probability is:
[tex]\text{Required probability } = \dfrac{2}{5}\times \dfrac{3}{4} = \dfrac{3}{10} = \bold{30\%}[/tex]
Answer:
30% A
Step-by-step explanation:
I drive 13 miles each way to work every day. It sometimes takes me 20 minutes to get to work, and sometimes it takes me 30 minutes. If Distance = Rate x Time, at what rate am I going if it takes me 20 minutes to get to work? At 30 minutes?
Answer:
39 mph
26 mph
Step-by-step explanation:
distance = rate * time
20 minutes:
13 miles = rate * 20 minutes
rate = (13 miles)/(20 minutes) * (60 minutes)/(hour)
rate = 39 mph
30 minutes:
13 miles = rate * 30 minutes
rate = (13 miles)/(30 minutes) * (60 minutes)/(hour)
rate = 26 mph
6. If x + 2 is the only factor of the polynomial P(x),then P(2) is:
Options:
A. Cannot be determined
B. Not Zero
C. R(2)
D. Zero
Answer:
P(x) = x + 2p(2) = 2 + 2 p(2) = 4So option B is the answer.
If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) is Not Zero. Therefore, the option B is the correct answer.
What is standard form of a polynomial?Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.
Given information;
If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) :
P(x) = x + 2
p(2) = 2 + 2
p(2) = 4
The P(2) is Not Zero.
Therefore, the option B is the correct answer.
Learn more about standard form of a polynomial here:
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Working together, it takes two computers 10 minutes to send out a company's email. If it takes the slower computer 50 minutes to do the job on its own, how long will it take the faster computer to do the job on its own? don't round
Answer:
12.5 minutes
Step-by-step explanation:
When working together,It takes two computers 10 minutes to send out an email
It takes the slower computer 50 minutes to send out an email
Let x represent the time taken by the faster computer to do the job in its own
Therefore, the time required by the faster computer can be calculated as follows
1/x + 1/50= 1/10
Collect the like terms
1/x= 1/10-1/50
1/x= 4/50
Cross multiply both sides
4 × x = 50×1
4x=50
Divide both sides by the coefficient of x which is 4
4x/4=50/4
x= 12.5
Hence the time taken by the faster computer to finish the job on its own is 12.5 minutes
In a recent year, a sample of grade 8 Washington State public school students taking a mathematics assessment test had a mean score of 281 with a standard deviation of 34.4. Possible test scores could range from 0 to 500. Assume that the scores are normally distributed. Question 9 (2.5 points) If 2000 students are randomly selected, how many would you expect to have a score between 250 and 305?
Answer:
The number is [tex]N =1147[/tex] students
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 281[/tex]
The standard deviation is [tex]\sigma = 34.4[/tex]
The sample size is n = 2000
percentage of the would you expect to have a score between 250 and 305 is mathematically represented as
[tex]P(250 < X < 305 ) = P(\frac{ 250 - 281}{34.4 } < \frac{X - \mu }{\sigma } < \frac{ 305 - 281}{34.4 } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (Standardized \ value \ of \ X )[/tex]
So
[tex]P(250 < X < 305 ) = P(-0.9012< Z<0.698 )[/tex]
[tex]P(250 < X < 305 ) = P(z_2 < 0.698 ) - P(z_1 < -0.9012)[/tex]
From the z table the value of [tex]P( z_2 < 0.698) = 0.75741[/tex]
and [tex]P(z_1 < -0.9012) = 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.75741 - 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.57[/tex]
The percentage is [tex]P(250 < X < 305 ) = 57\%[/tex]
The number of students that will get this score is
[tex]N = 2000 * 0.57[/tex]
[tex]N =1147[/tex]
Factor the following
9t^2-42t+49
Answer:
(3t -7)²
Step-by-step explanation:
We know that the square of a binomial is ...
(a -b)² = a² -2ab +b²
So, when we see the first and last terms are both perfect squares, we suspect that the trinomial is a perfect square trinomial.
9t² = (3t)²
49 = 7²
-42t = -2(3t)(7) . . . . confirming we have a perfect square
The factorization is ...
(3t -7)²
Please help me I need it!
What is the error in this problem?
Answer:
wrong position of tan 64
last year a football game scored a total of 427 points, so far this year, they have scored 154 points. They have eight more regular season games. How many points do they need to score each game to beat their record last year?
Answer:
35 points
Step-by-step explanation:
See photo
renea is going to the lake to visit some freinds if the lake is 60 miles away and renae is driving at 40 miles per hour the entire time how long will it take her to get to the lake
Answer:
1.5 hours
Step-by-step explanation:
Set up a proportion:
[tex]\frac{40 miles}{1 hour}[/tex] = [tex]\frac{60 miles}{x}[/tex]
Cross multiply:
40x = 60
x = 1.5
= 1.5 hours
Josephine has a rectangular garden with an area of 2x2 + x – 6 square feet. A rectangle labeled 2 x squared + x minus 6 Which expressions can represent the length and width of the garden? length = x2 – 3 feet; width = 2 feet length = 2x + 3 feet; width = x – 2 feet length = 2x + 2 feet; width = x – 3 feet length = 2x – 3 feet; width = x + 2 feet
Answer:
2x^2 + x - 6 = rectangular garden: length = 2x – 3 feet; width = x + 2 feet
Step-by-step explanation:
(2x - 3)(x + 2) = 2x^2 + x - 6 =
2x^2 + 4x - 3x - 6 = 2x^2 + x - 6 =
2x^2 + x - 6
You get the original equation from the two sides multiplied. :)
Hope this helps, have a good day.
The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The area is 2x² + x – 6 square feet. Then the factor of the equation is given as,
A = 2x² + x – 6
A = 2x² + 4x – 3x – 6
A = 2x(x + 2) – 3(x + 2)
L × W = (2x – 3)(x + 2)
The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.
More about the area of the rectangle link is given below.
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If triangle ABC has one angle measuring 90o and one angle measuring 45o, which of the following is true?
ABC is a right angle
Third angle 45°
Its a isoceles Right Triangle because base angles are equal then two sides are also equal.
Must click thanks and mark brainliest
Sketch a graph to envision the following scenario. Place time on the x-axis. A rock climber is 25 feet above sea level. After 8 seconds he is at sea level. (He did not fall). What is the slope of the line depicted (no units)
Answer:
Please refer to the attached graph.
Slope = -3.125
Step-by-step explanation:
Given
Time is placed on x axis.
Initially, height of rock climber is 25 feet above sea level.
[tex]t_1 =0\ sec[/tex]
[tex]h_1[/tex] = 25 feet
After 8 seconds, he is at sea level.
[tex]t_2 =8\ sec[/tex]
[tex]h_2[/tex] = 0 feet
To find:
Graph of the given points and Slope of the line depicted.
Solution:
Kindly refer to the attached graph.
Here, we have been given two points to be plotted on the xy coordinate plane.
1st point is (0, 25): Time is 0 and height above sea level is 25 ft
2nd point is (8, 0): Time is 8 seconds and height above sea level is 0 ft (i.e. he comes to sea level)
First of all, mark these points and join them with a straight line.
Please refer to attached graph.
Slope of a line is given as:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex]y_2 = 0\\y_1 = 25\\x_2 = 8\\x_1 = 0[/tex]
Using the formula:
[tex]m=\dfrac{0-25}{8-0}\\\Rightarrow m=-\dfrac{25}{8} = \bold{-3.125}[/tex]
omplete the following multiplication problems.
a. 0.34 × 6
b. 0.11 × 4
c. 17 × 0.07
d. 28 × 0.003
e. 3.8 × 5
f. 5.931 × 7
g. 14.07 × 13
h. 3.005 × 32
i. 0.8 × 0.3
j. 0.45 × 0.05
k. 0.09 × 0.02
l. 0.074 × 0.08
m. 2.3 × 0.9
n. 7.25 × 0.3
o. 4.53 × .003
p. 53.67 × 0.056
q. 1.1 × 3.7
r. 3.76 × 18.9
s. 4.57 × 6.1
t. 24.13 × 1.48
Anna is paid $14.75 per hour. She works a
12 hour shift, the last 4 hours being at a double
time pay rate. What is Anna's wage before
tax?
HELP
Answer:
$336
Step-by-step explanation:
$14.75(8) + $14.75(2)(4) - (8 hours of normal shift) + (double pay rate)(for 4 hours)
= $118 + $118 - Add
= $336
You have a $5,000 limit on your credit card. What is the largest balance you should carry on this card to maintain an acceptable debt ratio? Recall that your debt ratio should never exceed 50% of your limit
Answer:
Amount of balance maintain = $2,500
Step-by-step explanation:
Given:
Limit of credit card = $5,000
Debt ratio = 50%
Find:
Amount of balance to maintain
Computation:
Amount of balance to maintain = Limit of credit card × Debt ratio
Amount of balance to maintain = $5,000 × 50%
Amount of balance to maintain = $2,500
Consider the following.
3^5x − 1 = 7
(a) Find the exact solution of the exponential equation in terms of logarithms.
(b) Use a calculator to find an approximation to the solution rounded to six decimal places.
Answer:
Step-by-step explanation:
You've typed the equation incorrectly. 3^5x-1 = 3⁵x-1.
It needs to be typed as 3^(5x-1) = 7.
Which of the following is NOT a requirement of testing a claim about two population means when 1 and 2 are unknown and not assumed to be equal? Choose the correct answer below. A. The two samples are dependent. B. Both samples are simple random samples. C. Either the two sample sizes are large (30 and 30) or both samples come from populations having normal distributions, or both of these conditions are satisfied. D. The two samples are independent.
Answer:
b
Step-by-step explanation:
The sum of triple a number
and nineteen.
Answer:
3x+19
Step-by-step explanation:
Let x be the unknown number
triple means 3 times
sum means add
3x+19
Hey! i've been working on these questions but I have no idea how to solve this one, could anybody help me? Thanks in advance!
Answer:
1) [tex]\boxed{p(x) = x^3-x^2+x-1}[/tex]
2) [tex]\boxed{p(x) = x^2+x-2}[/tex]
3) [tex]\boxed{p(x) =- 2x^2+2x+4}[/tex]
4) [tex]\boxed{p(x) = 2x^2+x-4}[/tex]
Step-by-step explanation:
Part (1)
[tex]p(x) = x^3-x^2+x-1[/tex]
As we have to determine it by ourselves, this is the polynomial having a degree of 3. p(x) with a degree of 3 means that the highest degree/exponent of x should be 3.
Part (2)
[tex]p(x) = x^2+x-2[/tex]
This can be the polynomial having the factor x-1 because if we put:
x - 1 = 0 => x = 1 in the above polynomial, it gives us a result of zero which shows us that (x-1) "is" a factor of the polynomial.
Part (3)
[tex]p(x) = -2x^2+2x+4[/tex]
This can be the polynomial for which p(0) = 4 and p(-1) = 0
Let's check:
[tex]p(0) =- 2(0)^2+2(0)+4\\p(0) = 0 + 0+4\\p(0) = 4[/tex]
[tex]p(-1)= -2(-1)^2+2(-1)+4\\p(-1) = -2(1)-2+4\\p(-1) = -2-2+4\\p(-1) = 0[/tex]
So, this is the required polynomial determined by "myself".
Part (4):
[tex]p(x) = 2x^2+x-4[/tex]
This is the polynomial having a remainder 6 when divided by (x-2)
Let's check:
Let x - 2 = 0 => x = 2
Putting in the above polynomial
[tex]p(x) = 2(2)^2+(2)-4\\Given \ that \ Remainder = 6\\6 = 2(4) +2-4\\6 = 8+2-4\\6 = 10-4\\6 = 6[/tex]
So, Proved that it has a remainder of 6 when divided by (x-2)
Let
A ={1,2,6,7,8,13,15} and B= {1,2,5,6,8,12,15, 18, 20}
Find the following:
LIST the elements in the set
A∪B :
A∪B = { }
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE
LIST the elements in the set
A∩B :
A∩B= { }
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE
Answer:
AUB=(1,2,5,6,7,8,12,13,15, 18,20)
AnB={1,2,6,7,8}
Answer:
Hello,
Step-by-step explanation:
[tex]A =\{1,2,6,7,8,13,15\} \\B= \{1,2,5,6,8,12,15, 18, 20\}\\\\A\ \bigcup\ B=\{1,2,5,6,7,8,12,13,15,18,20\}\\\\A\ \bigcap\ B=\{ 1,2,6,8,15\}\\[/tex]
Suppose that 200 students are randomly selected from a local college campus to investigate the use of cell phones in classrooms. When asked if they are allowed to use cell phones in at least one of their classes, 40% of students responded yes. Using these results, with 95% confidence, the margin of error is 0.068. How would the margin of error change if the sample size increased from 200 to 400 students?
Answer:
It would change to 0.04802
Step-by-step explanation:
from this question we have that n became 400
40% of 400
= 160
p* = 160/400
= 0.4
1 - p* =
= 1 - 0.4
= 0.6
at confidence level,
1 - 0.95
= 0.05
alpha/2 = 0.025
z= 1.96
margin of error. E
= 1.96 x √[(0.4 x 0.6)/400]
= 1.96 x 0.0245
= 0.04802
M.E = 0.04802
URGENT, PLEASE HELP! (1/5) -50 POINTS- !please no wrong answers for the points.! A) [tex]y = 6x - \frac{11}{8}[/tex] B) [tex]y = -6x - 2[/tex] C) [tex]y = \frac{3}{2} x - \frac{1}{8}[/tex] D) [tex]y = -3x + 9[/tex]
Answer:
C y = 3/2x - 1/8
Step-by-step explanation:
We know that the line has a positive slope, because it goes up from the lower left to upper right
We can eliminate B and D
For y = 6x - 11/8
A slope of 6 is very steep
Putting in 6
y = 6*6 -approximately 1 = 35 so the value at 3 would be 35
This is too big
Checking C
y = 3/2(6) - 0 = 9 or 9 This would be about right
What the answer for this question
Answer:
I think the Correct answer is no A.
what is empowerment and radication please that is not from google
Answer:
In MATH:
Empowerment - Gaining the skills required in language and practices to fully understand math.
Radication - The process of extracting a number's root.
In ENGLISH:
Empowerment - The process of gaining more power over anything, including yourself, others, society, government, and corporations.
Ex - In the spirit of empowerment, the company has implemented a new system that asks employees to nominate one another for bonuses.
Radication - The process of establishing, fixing, or creating.
Ex - The high prestige of the premier is radicated in the hearts of the people.
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive
Complete Question
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive
Answer:
Yes the company conclude that the correlation is positive
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The correlation is r = 0.65
The null hypothesis is [tex]H_o : r < 0[/tex]
The alternative hypothesis is [tex]H_1 : r > 0[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]Sr = \sqrt{1- r}[/tex]
[tex]Sr = \sqrt{1- 0.65}[/tex]
[tex]Sr = 0.616[/tex]
The degree of freedom for the one-tail test is
[tex]df = n- 2[/tex]
[tex]df = 14- 2[/tex]
[tex]df = 12[/tex]
The standard error is evaluated as
[tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]
[tex]SE =0.1779[/tex]
The test statistics is evaluated as
[tex]t = \frac{r }{SE}[/tex]
[tex]t = \frac{0.65 }{0.1779}[/tex]
[tex]t = 3.654[/tex]
The p-value of of t is obtained from the z table, the value is
[tex]p-value = P(t < 3.654) = 0.00012909[/tex]
Given that [tex]p-value < \alpha[/tex] then we reject the null hypothesis
Hence the company can conclude that the correlation is positive
Mike has 18 goldfish and 24 silver fish in his aquarium what is the ratio of silverfish to total fish in the aquarium aquarium
Answer:
4:7
Step-by-step explanation:
18+24=total number of fish=42
silver fish amount= 24
therefore, ratio is 24:42=12:21=4:7
In designing an experiment involving a treatment applied to 4 test subjects, researchers plan to use a simple random sample of 4 subjects selected from a pool of 31 available subjects. (Recall that with a simple random sample, all samples of the same size have the same chance of being selected.) Answer the question below.
What is the probability of each simple random sample in thiscase?
Answer:
The probability is [tex]p(n ) = 3.18*10^{-5}[/tex]
Step-by-step explanation:
From the question we are told that
The population size is N = 31
The sample size n = 4
Generally the number of way by which the n can be selected from N is mathematically represented as
[tex]\left N} \atop {}} \right. C_n = \frac{N! }{(N-n)!n!}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{31! }{(31-4)!4!}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{31 * 30 * 29 * 28* 27! }{27! * 4*3 * 2 * 1 }[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{ 755160 }{ 24}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = 31465[/tex]
The number of ways of selecting a particular sample size is is [tex]k = 1[/tex]
Therefore the probability of each simple random sample in this case is mathematically evaluated as
[tex]p(n ) = \frac{1}{31465}[/tex]
[tex]p(n ) = 3.18*10^{-5}[/tex]
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 18% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Required:a. Find the probability that both generators fail during a power outage.b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital?c. Is that probability high enough for the hospital?
Answer:
a. 0.36
b. 0.1296
c. No.
Step-by-step explanation:
1. Note the probability of emergency backup generators to fail when they are needed = 18% or 0.18. Thus,
a. Probability of both emergency backup generators failing = P (G1 and G2 fails) where G represents the generators.
= P (G1 falls) x P ( G2 fails)
= 0.18 x 0.18
= 0.36
b. The probability of having a working generator in the event of a power outage = G1 fails x G2 works + G2 works x G2 fails
= 0.36 x 0.18 + 0.18 x 0.36
= 0.1296
c. Looking at the probability of any of the generators working, it is not meeting safety standards as lives could be lost if the backup generators needed to perform an emergency surgery operation fails.
PLEASE HELP
2/3x =10
Show your work in details if you can, I have a hard time understanding this.
[tex]\\ \sf\longmapsto \dfrac{2}{3}x=10[/tex]
[tex]\\ \sf\longmapsto \dfrac{2x}{3}=10[/tex]
[tex]\\ \sf\longmapsto 2x=3(10)[/tex]
[tex]\\ \sf\longmapsto 2x=30[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{30}{2}[/tex]
[tex]\\ \sf\longmapsto x=15[/tex]
[tex] \begin{cases}\large\bf{\red{ \implies}} \tt \frac{2}{3} x \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt \frac{2x}{3} \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 3 \: \times \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 30 \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \:\frac{ \cancel{30} \: \: ^{15} }{ \cancel{2}} \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \: 15 \end{cases}[/tex]