Answer:
[tex]y = 4(x - 4)^2 - 2[/tex]
or
[tex]y=4x^2 -32x + 62[/tex]
Step-by-step explanation:
Given
[tex]V = (4,-2)[/tex] --- vertex
[tex]P = (2,14)[/tex] --- point
Required
The equation of the parabola
The equation of the parabola is of the form
[tex]y = a(x - h)^2 + k[/tex]
Where
[tex]V (4,-2) = (h,k)[/tex] ---- the vertex
So, we have:
[tex]y = a(x - h)^2 + k[/tex]
[tex]y = a(x - 4)^2 - 2[/tex]
In [tex]P = (2,14)[/tex], we have:
[tex](x,y) = (2,14)[/tex]
Substitute [tex](x,y) = (2,14)[/tex] in [tex]y = a(x - 4)^2 - 2[/tex]
[tex]14 = a(2 - 4)^2 - 2[/tex]
[tex]14 = a(- 2)^2 - 2[/tex]
[tex]14 = a*4 - 2[/tex]
[tex]14 = 4a - 2[/tex]
Collect like terms
[tex]4a = 14 +2[/tex]
[tex]4a = 16[/tex]
Divide both sides by 4
[tex]a= 4[/tex]
So:
[tex]y = a(x - 4)^2 - 2[/tex] becomes
[tex]y = 4(x - 4)^2 - 2[/tex]
Open bracket to express the equation in standard form
[tex]y=4(x^2 -8x + 16) - 2[/tex]
[tex]y=4x^2 -32x + 64 - 2[/tex]
[tex]y=4x^2 -32x + 62[/tex]
the perimeter p of a square is 4 times the length of a side x
Answer:
p = 4x
Step-by-step explanation:
The perimeter p of a square is 4 times the length of a side x
p = 4x
Find the missing angle
Answer and Step-by-step explanation:
First, solve for the angle TRS, so that we can find the missing angle.
Subtract the two angles from 180 (because all triangle's angles add up to 180).
180 - 58 - 60 = 62.
By the vertical angles theorem, 62 is equal to the missing angle.
#teamtrees #PAW (Plant And Water)
what is the circumference of a circle with a diameter of 13 inches? round to the nearest hundredth.
Answer:
40.84 to nearest hundredth.
Step-by-step explanation:
C = pi * d
= pi * 13
= 40.8407
USE TABLE AOR TABLE RFOR
SERVING UP A LARGE FEAST?
96"
42"
A А
B
R=45"
SHOW AN EXPLANATION ON WHICH TABLE YOU CHOOSE!!!
Answer:
use table B
Step-by-step explanation:
the perimeter of table A =
2×(96+42) = 2× 138 = 276 inches
the perimeter of table B =
2×3.14×45 = 282.6 inches
table B > table A
Suppose Diana, an educational researcher at a local university, wants to test the impact of a new Spanish course that integrates cultural-immersion teaching techniques with standard teaching practices. She selects a simple random sample of 64 freshmen and divides them into 32 pairs, matched on IQ and high school GPA. She randomly selects one member of each pair to take the new course, while the other member in the pair takes the traditional course.
Next, Diana records the course grade, tallied on a scale from 0 to 4, for all sample members at the end of the semester, and she computes the difference in grades between the members in each matched pair by subtracting the traditional course grade from the new course grade. She wants to determine if the new Spanish course improves or weakens student performance. She runs a matched-pairs t-test to test the null hypothesis, H0:μ=0, against the alternative hypothesis, H1:μ≠0, where μ is the mean course grade difference for the student population.
The sample statistics for Diana's test are summarized in the table.
Variable description Sample mean Sample standard deviation Standard error estimate
traditional course grade x⎯⎯trad= 3.33496 strad=2.02198 SEtrad=0.33700
new course grade x⎯⎯new=3.45287 snew=2.11043 SEnew=0.35174
difference (new − traditional) x⎯⎯=0.11791 s=0.31452 SE=0.05242
Although Diana does not know the standard deviation of the underlying population of course grade differences, she assumes that the population is normally distributed because the sample data are symmetric, single-peaked, and contain no outliers.
Required:
Compute the t-statistic for Diana's matched-pairs t-test.
Answer:
89yuyyygvghhhhhhnnn76yyyyy
Kelly is making a quilt out or "3 square yards of white fabric and 's square yards of yellow fabric. What is the unit rate of yellow
fabric to white fabric?
СА.
3 square yards of yellow fabric to 1 square yard of white fabric
Ов
of a square yard of yellow fabric to 1 square yard of white fabric
OC
of a square yard of yellow fabric to 1 square yard of white fabric
OD
square yards of yellow fabric to 1 square yard of white fabric
Answer:
c
Step-by-step explanation:
I think it is c
Suppose we want to choose 5 letters without replacement from 16 distinct letters
Answer:
16P5
Step-by-step explanation:
16*15*14*13*12
Which answer choice below best describes the number (22 + 6)
Answer:
You FAILED to include any choices.
Step-by-step explanation:
Tamika works in a shoe store and is paid a 12%
commission on her sales. In January her sales total
was $3740. To the nearest dollar, how much did
Tamika earn in commission for January?
Explain correctly. No nonsense, please.
Thank you
Find the principal.
Annual rate of interest = 6.5 \%=6.5%equals, 6, point, 5, percent
Period = 4=4equals, 4 years
Total interest= 1222=1222equals, 1222 rupees
Answer is : 4700
Other ppl be giving me the wrong answer don't trust them lol
Answer:
im in 6th grade so i have no idea
Step-by-step explanation:
if the vertex of triangle abc is A(2, 3) B(4, 5) C(6, 2) . find the reflection of it through y axis
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
A (2, 3 ) → A' (- 2, 3 )
B (4, 5 ) → B' (- 4, 5 )
C (6, 2 ) → C' (- 6, 2 )
A car company invests $200,000 in developing auto-car software. Each software costs $150 to produce and
sells for $400. How many software must the company sell break-even? Determine the break-even point.
Refer to the Cost and Revenue equation.
Answer:
Break even unit = 800
Break even point = $320,000
Step-by-step explanation:
Given:
Amount invested (Fixed cost) = $200,000
Each software cost (variable cost) = $150
Selling price = $400
Find:
Break even unit
Computation:
Assume;
Break even unit = a
Total Cost = Amount invested (Fixed cost) + [Each software cost][Break even unit]
Total cost = 200,000 + 150a
Total revenue = Selling price[Break even unit]
Total revenue = 400a
So,
400a = 200,000 + 150a
250a = 200,000
Break even unit = 800
Break even point = 400a
Break even point = 400(800)
Break even point = $320,000
Pls help me on this due today plssss!!!
Answer:
Step-by-step explanation:
A+B+C+D=360 degree (being one complete turn)
360 degrees
Step-by-step explanation:
because it a venticular angle you one side(180) and the other side (180) given you 360 degrees
Please someone can help me...
Answer:
C
Step-by-step explanation:
Although I don't see the graph, I will assume it's a graph about the relationship between time and distance walked.
Here's the logic:
If you walk a longer time, your distance increases.
You fllp a fair coln 7 times in a row. Let X be the number of heads that come up. Which of the following cannot be a
possible value of X?
2
0
7
16
Answer:
16
Step-by-step explanation:
Given
A coin
[tex]n = 7[/tex] --- Number of flips
[tex]x \to heads[/tex]
Required
Which can't be the value of x
From the question, we understand that the coin was flipped 7 times.
This means that, the highest occurrence of head is:
[tex]x = 7[/tex]
And the list is:
[tex]x = 0[/tex]
So, the range of x is:
[tex]x = \{0,1,2,....,7\}[/tex]
In the above range, only (16) is out of range.
Hence:
[tex]x \ne 16[/tex] --- Number of heads can't be 16
Help me PLEASEEEEEEEEEEEEE
Answer:
D. 144
Step-by-step explanation:
Find volume of shipping container:
2 2/3 = 8/3
2 x 1 = 2
8/3 x 2/1 = 16/3
Find volume of cube:
1/3 x 1/3 = 1/9 x 1/3 = 1/27
Find how many boxes fit in container:
16/3 ÷ 1/27
16/3 x 27/1
Simplify:
16/1 x 9/1 = 144/1
Answer: 144
Can anyone solve this? I'm kind of stuck! Thank you!
Answer:
B
Step-by-step explanation:
0.25 (2d + 1) = 0.25(2d) + 0.25(1)
= 0.50d + 0.25
Answer:
The expression 0.25(2d+1) is equivalent
equivalent go 0.50d +0.25.
Step-by-step explanation:
If yoy simplify the expression if will be 0.5d+0.25
Help me PLEASEEEEEEEEEEEEE
Answer:
4.0.
Step-by-step explanation:
In sample 1, you do 0.65/1.3 which gets you to 0.5, so then you do the same to the bottom which you also have to divide by 1.3, and 5.2/1.3 is 4.0 or 4.
Answer:
option D. 4.0
Step-by-step explanation:
Mass Volume
Sample 1 0.65 0.5
Sample 2 5.2 x
[tex]\frac{0.65}{5.2} = \frac{0.5}{x}\\\\0.65 \times x = 0.5 \times 5.2\\\\0.65x = 2.6\\\\x =\frac{2.6}{0.65} =4[/tex]
Is ΔABC ~ ΔDEF? Explain. Triangle A B C has angle measures A 18 degrees, B 110 degrees, and C unknown. Triangle D E F has angle measures D 52 degrees, E 18 degrees, and F unknown.
9514 1404 393
Answer:
no
Step-by-step explanation:
Triangle ABC has angle measures ...
A = 18°B = 110°C = 180° -18° -110° = 52°Triangle DEF has angle measures ...
D = 52°E = 18°F = 180° -52° -18° = 110°Using the angle measures in the order 18, 110, 52, we can write the similarity statement as ...
ΔABC ~ ΔEFD
The similarity statement given in the problem is incorrect. ΔABC is not similar to ΔDEF.
Select the values that make the inequality h < 2 true.
(Numbers written in order from least to greatest going across.)
Given:
The inequality is:
[tex]h\leq 2[/tex]
To find:
The values that make the given inequality true.
Solution:
We have,
[tex]h\leq 2[/tex]
It means the value of h must be less than or equal to 2.
In the given options, the list of numbers which are less than or equal to 2 is
-6, -3, -1, 1, 1.9, 1.99, 1.999, 2
The list of numbers which are greater than 2 is
2.001, 2.01, 2.1, 3, 5, 7, 10
Therefore, the first 8 options are correct and the required values are -6, -3, -1, 1, 1.9, 1.99, 1.999, 2.
Answer:
Step-by-step explanation:
Make a box-and-whisker plot for the data:
36, 39, 39, 41, 43, 49, 61, 64
a. smallest value 36
b. Quartile 1: 39
c. Median: 42
d. Quartile 2: 55
e. greatest value: 64
The five number summary you wrote out is correct.
The tip of the left whisker is at 36, since this is the smallest value and we don't have outliers. The tip of the right whisker is at 64 which is the max (we don't have outliers here either).
The left and right edges of the box are Q1 and Q3 respectively. The median is the vertical line inside the box. The vertical line does not have to be at the midpoint as the diagram shows.
The IQR (interquartile range) is found by computing IQR = Q3-Q1 = 55-39 = 16
Note that the lower fence is L = Q1 - 1.5*IQR = 39 - 1.5*16 = 15. Anything below this value of L is an outlier.
The upper fence is U = Q3 + 1.5*IQR = 55 + 1.5*16 = 113.5; anything above this value of U is an outlier. All of the values in the given set are between L and U, meaning we don't have outliers. If we had outliers, then we would have island points outside the main box-and-whisker plot.
I used GeoGebra to create the box-and-whisker plot.
Answer:
The data and 5-number summary is given.
Based on the 5 numbers we have the attached box-and-whisker plot.
SOMEONE PLEASE HELP!!!!
Answer:
D. 9
Step-by-step explanation:
When you add 1 + 4 + 5 + 5 + 5 + 6 + 9 + 10 + 10 + 11 + 12 + 12 + 15 + 15 + 15 = 135. Which is all of the numbers given to you, and since mean is when you add all of the numbers together, and than divide it by the amount of numbers there, you will take that 135 and divide it by 15. 135 / 15 = 9. Which gets you to finally getting an answer of 9. so D. 9 is correct.
Answer:
C. 8.5
Step-by-step explanation:
A password is made up of 4 letters. If the letters can be repeated how many passwords can be created. NO LINKS!!!
Answer:
456,796 passwords
Step-by-step explanation:
Because any letter can be repeated for the 4-letter password, there are 26 possible letters for the first letter of the password, 26 possible letters for the second letter of the password, 26 possible letters for the third letter of the password, and 26 possible letters for the fourth letter of the password. Therefore, the possible number of passwords that can be created is 26*26*26*26 = 26^4 = 456,796 passwords
Solve the formula Ax + By = C for X
Answer:
Step-by-step explanation:
Ax+By=C
Ax=C-By
x=C-By/A
Help!!!!!!!!!!!!!!!!!
Answer:
the answer is one hundred and eight 108
Step-by-step explanation:
108 bro trust me
What is -4.5 need help pls help fast I will give u a brilliant and thank
Answer:
its -4.5??? what is the question you're asking
You weigh a random sample of adult golden retrievers and get the following results: 55, 64, 58, 61, 69, 64, 59, 69, 72, and 65. Which answer gives a 98% confidence interval for the mean of the population
Answer:
The 98% confidence interval for the mean of the population is (59, 68.2).
Step-by-step explanation:
Before building the confidence interval, we need to find the sample mean and the sample standard deviation.
Sample mean:
[tex]\overline{x} = \frac{55+64+58+61+69+64+59+69+72+65}{10} = 63.6[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(55-63.6)^2+(64-63.6)^2+(58-63.6)^2+(61-63.6)^2+(69-63.6)^2+(64-63.6)^2+(59-63.6)^2+(69-63.6)^2+(72-63.6)^2+(65-63.6)^2}{10}} = 5.142[/tex]
Confidence interval:
We have the standard deviation for the sample, and thus, we use the t-distribution.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 10 - 1 = 9
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.821
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.821\frac{5.142}{\sqrt{10}} = 4.6[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 63.6 - 4.6 = 59
The upper end of the interval is the sample mean added to M. So it is 63.6 + 4.6 = 68.2.
The 98% confidence interval for the mean of the population is (59, 68.2).
In a simple random sample of 1500 young Americans 1305 had earned a high school diploma.
a. What is the standard error for this estimate of the percentage of all young Americans who earned a high school diploma?
b. Find the margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma.
c. Report the 95% confidence interval for the percentage of all young Americans who earned a high school diploma.
d. Suppose that in the past, 80% of all young Americans earned high school diplomas. Does the confidence interval you found in part c support or refute the claim that the percentage of young Americans who cam high school diplomas has increased? Explain.
Answer:
a) The standard error for this estimate of the percentage of all young Americans who earned a high school diploma is 0.87%.
b) The margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma is of 1.71%.
c) The 95% confidence interval for the percentage of all young Americans who earned a high school diploma is (85.29%, 88.71%).
d) The lower bound of the confidence interval is above 80%, which means that the confidence interval supports the claim that the percentage of young Americans who cam high school diplomas has increased.
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].
Standard error:
The standard error is:
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Margin of error:
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}} = zs[/tex]
The confidence interval is:
Sample proportion plus/minus margin of error. So
[tex](\pi - M, \pi + M)[/tex]
In a simple random sample of 1500 young Americans 1305 had earned a high school diploma.
This means that [tex]n = 1500, \pi = \frac{1305}{1500} = 0.87[/tex]
a. What is the standard error for this estimate of the percentage of all young Americans who earned a high school diploma?
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.87*0.13}{1500}} = 0.0087[/tex]
0.0087*100% = 0.87%.
The standard error for this estimate of the percentage of all young Americans who earned a high school diploma is 0.87%.
b. Find the margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma.
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Then
[tex]M = zs = 1.96*0.0087 = 0.0171[/tex]
0.0171*100% = 1.71%
The margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma is of 1.71%.
c. Report the 95% confidence interval for the percentage of all young Americans who earned a high school diploma.
87% - 1.71% = 85.29%
87% + 1.71% = 88.71%.
The 95% confidence interval for the percentage of all young Americans who earned a high school diploma is (85.29%, 88.71%).
d. Suppose that in the past, 80% of all young Americans earned high school diplomas. Does the confidence interval you found in part c support or refute the claim that the percentage of young Americans who cam high school diplomas has increased? Explain.
The lower bound of the confidence interval is above 80%, which means that the confidence interval supports the claim that the percentage of young Americans who cam high school diplomas has increased.
help!!!!!!!!!!!!!!!!!!!
Answer:
D. 1/5
Step-by-step explanation:
Because
0.2222...>0.2>0.12
Use the formula C = 2nr and = 3.14 to find the circumference of a circle with a radius of 5 meters
Answer:
31.4
Step-by-step explanation:
C = 2 x 3.14 x 5
C = 10 x 3.14
C = 31.4