Answer:
SEE BELOWStep-by-step explanation:
to understand thisyou need to know about:quadratic functionPEMDASlet's solve:vertex:(h,k)
therefore
vertex:(-1,4)
axis of symmetry:x=h
therefore
axis of symmetry:x=-1
to find the quadratic equation we need to figure out the vertex form of quadratic equation and then simply it to standard form i.e ax²+bx+c=0vertex form of quadratic equation:
y=a(x-h)²+ktherefore
y=a(x-(-1))²+4y=a(x+1)²+4it's to notice that we don't know what a is
therefore we have to figure it out
the graph crosses y-asix at (0,3) coordinates
so,
3=a(0+1)²+4
simplify parentheses:
[tex]3 = a(1 {)}^{2} + 4[/tex]
simplify exponent:
[tex]3 = a + 4[/tex]
therefore
[tex]a = - 1[/tex]
our vertex form of quadratic equation is
y=-(x+1)²+4let's simplify it to standard form
simplify square:
[tex]y = - ( {x}^{2} + 2x + 1) + 4[/tex]
simplify parentheses:
[tex]y = - {x}^{2} - 2x - 1 + 4[/tex]
simplify addition:
[tex]y = - {x}^{2} - 2x + 3[/tex]
therefore our answer is D)y=-x²-2x+3
the domain of the function
[tex]x\in \mathbb{R}[/tex]
and the range of the function is
[tex]y\leqslant 4[/tex]
zeroes of the function:
[tex] - {x}^{2} - 2x + 3 = 0[/tex]
[tex] \sf divide \: both \: sides \: by \: - 1[/tex]
[tex] {x}^{2} + 2x - 3 = 0[/tex]
[tex] \implies \: {x}^{2} + 3x - x + 3 = 0[/tex]
factor out x and -1 respectively:
[tex] \sf \implies \: x(x + 3) - 1(x + 3 )= 0[/tex]
group:
[tex] \implies \: (x - 1)(x + 3) = 0[/tex]
therefore
[tex] \begin{cases} x_{1} = 1 \\ x_{2} = - 3\end{cases}[/tex]
in a book reading contest students read as many books as they can in one week. the number of books read by each student are given, use the data to make a histogram
2, 10, 5, 4, 1, 3, 2, 6, 4, 8, 1, 3, 5
Answer:
C
Step-by-step explanation:
Process of elimination. A) had the wrong numbers on the bottom. B) has the right information but it's too narrow. D) has the wrong information. I just took the quiz and got this questions right. Hope this helps!
Answer:
C is the approximant answer
How was Franklin D. Roosevelt a lasting impact even on today's society
Answer:
Franklin Delano Roosevelt, often referred to by his initials FDR, was an American politician who served as the 32nd president of the United States from 1933 until his death in 1945. A member of the Democratic Party, he won a record four presidential elections and became a central figure in world events during the first half of the 20th century. Roosevelt directed the federal government during most of the Great Depression, implementing his New Deal domestic agenda in response to the worst economic crisis in U.S. history. As a dominant leader of his party, he built the New Deal Coalition, which defined modern liberalism in the United States throughout the middle third of the 20th century. His third and fourth terms were dominated by World War II, which ended shortly after he died in office.
Step-by-step explanation:
to this ‘Great Man Theory’ it can be said that Franklin Delano Roosevelt upheld his victorious and highly regarded government through means of social, economic and political reforms, as well as ambitious personal and strategic decisions that have successfully remained influential to American society today and maintained his image as a prominent historic leader.
What is the explicit formula for the geometric sequence 15, 3, 0.6,
0.12, ...?
Answer:
A
Step-by-step explanation:
first num is 15
ratio is 0.2
formula is a.r^n-1
Please prove the following trigonometric identity.
[tex]\cos^2(5x)-\sin^2(5x)=\cos(10x)[/tex]
Answer:
See Below.
Step-by-step explanation:
We want to verify the trigonometric identity:
[tex]\cos^2(5x)-\sin^2(5x)=\cos(10x)[/tex]
For simplicity, we can let u = 5x. Therefore, by substitution, we acquire:
[tex]\cos^2(u)-\sin^2(u)[/tex]
Recall the double-angle identity formula(s) for cosine:
[tex]\displaystyle \begin{aligned} \cos(2x)&=\cos^2(x)-\sin^2(x)\\&=2\cos^2(x)-1\\&=1-2\sin^2(x)\end{aligned}[/tex]
Therefore, our identity becomes:
[tex]=\cos(2u)[/tex]
Back-substitute:
[tex]=\cos(2(5x))=\cos(10x)\stackrel{\checkmark}{=}\cos(10x)[/tex]
Hence proven.
cos²A - sin²A = cos2A, this is a general indentity where A can have any random value x/2, y/3, 1/8, 8, 9 etc.
Replacing A with 5x:
=> cos²(5x) - sin²(5x) = cos²(10x)
Moreover,
cos(A + B) = cosAcosB - sinAsinB.
When A = B,
cos(A + A) = cosAcosA - sinAsinA
cos2A = cos²A - sin²A
You can do the same with 5x.
cos(10x) = cos(5x + 5x)
cos(10x) = cos(5x)cos(5x) - sin(5x)sin(5x)
cos(10x) = cos²(5x) - sin²(5x)
A box of ceral contains 10 cups . if each bowl holds 1 1/4 cups of cearal. how many bowls of ceral will you get out of the box
Answer:
8 bowls
Step-by-step explanation:
10=40/4
1 1/4=5/4
40/4 divided by 5/4=160/20
160/20=8/1
Answer: the answer is 8
Step-by-step explanation:
Carol has a choice of an account that compounds quarterly and an account that compounds daily.
If they both have the same interest rate, which will earn more interest?
The account that compounds quarterly.
The account that compounds daily.
They will both earn the same interest
Answer: The account that compounds daily.
Step-by-step explanation: If you reinvest your money more frequently, then you will also be able to earn interest on the interest that you earned the previous day and so on.
A triangle with an area of 37 units? is dilated by a scale factor of . Find the area of
the triangle after dilation. Round your answer to the nearest lenth, if necessary.
Answer:
58 units
Step-by-step explanation:
I decided that one side is 37 units and another is 2 units, since that would make the area 37 units. (you can also use 74 units and 1 unit)
Then I multiplied 37 by 5/4, which equals a new length of 46.25 units, and I also multiplied 2 by 5/4, which equals a new length of 2.5 units.
Finally, I solve for the area of the triangle:
1/2(46.25 x 2.5) ≈ 58 units (rounded to the nearest whole number)
Juan Carlos has been asked to find the distance between two points on a coordinate grid using the distance formula calculate the distance between points (-3,2) and (12,10)
Which statement best describes the values of x and y in the table
Answer:
Answer A
Step-by-step explanation:
As the value of x increases by 2 the value of y increases by 4
EASY Work!! Please look at the picture and yes it’s easy for other people but not me for people asking.
Answer:
7()=11
8()=42
I could barely see the answer for number 9 sorry :(
Step-by-step explanation:
the 7() is 2(3)+5
2(3)=6
6+5=11
Question (8)
c^2+3a x b
c(6)^2+ 3(3) x 2/3
36+9 x 2/3
36+6=42
Answer:
(7)=11
(8)=42
Step-by-step explanation:
here
The table shows the prices for the same cereal, sold in different weights. Which size box is the best buy, in terms of price per ounce?
A. 9 oz
B.18 oz
C.28 oz
D.38 oz
Answer:
c
Step-by-step explanation:
ESPERO TE A YDUE :)
On Triangle ABC, Angle A measures 30 degrees, Angle B measures 90 degrees, and Angle C measures 60 degrees. List the sides of Triangle ABC in order from shortest to longest.
Answer:
A=30 B=90 C=60
Step-by-step explanation:
A=30 C=60 B=90
A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct in
your answer
Answer:
59.5 cm
Step-by-step explanation:
Find the area of the entire rectangle first. Formula is base times height: [tex]9*8[/tex]
=72
Next, find the missing sides by subtracting [tex]8-3[/tex] and [tex]9-4[/tex].
=5 and 5
Then find the area of the triangle. Formula is base times height divided by 2: [tex]\frac{5*5}{2}[/tex]
=12.5
Then subtract to find only the shaded section: [tex]72-12.5[/tex]
=59.5 cm
It is desired to compare the hourly rate of an entry-level job in two fast-food chains. Eight locations for each chain are randomly selected throughout the country, the selections for each chain being independent. The following hourly rates are recorded:
Chain A 4.25 4.75 3.80 4.50 3.90 5.00 4.00 3.80
Chain B 4.60 4.65 3.85 4.00 4.80 4.00 4.50 3.65
Under the assumption of normality and equal variances, can it be concluded at the 5% significance level that chain A pays more than chain B for the job under consideration?
Answer:
It can be concluded that at 5% significance level that there is no difference in the amount paid by chain A and chain B for the job under consideration
Step by Step Solution:
The given data are;
Chain A 4.25, 4.75, 3.80, 4.50, 3.90, 5.00, 4.00, 3.80
Chain B 4.60, 4.65, 3.85, 4.00, 4.80, 4.00, 4.50, 3.65
Using the functions of Microsoft Excel, we get;
The mean hourly rate for fast-food Chain A, [tex]\overline x_1[/tex] = 4.25
The standard deviation hourly rate for fast-food Chain A, s₁ = 0.457478
The mean hourly rate for fast-food Chain B, [tex]\overline x_2[/tex] = 4.25625
The standard deviation hourly rate for fast-food Chain B, s₂ = 0.429649
The significance level, α = 5%
The null hypothesis, H₀: [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]
The alternative hypothesis, Hₐ: [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]
The pooled variance, [tex]S_p^2[/tex], is given as follows;
[tex]S_p^2 = \dfrac{s_1^2 \cdot (n_1 - 1) + s_2^2\cdot (n_2-1)}{(n_1 - 1)+ (n_2 -1)}[/tex]
Therefore, we have;
[tex]S_p^2 = \dfrac{0.457478^2 \cdot (8 - 1) + 0.429649^2\cdot (8-1)}{(8 - 1)+ (8 -1)} \approx 0.19682[/tex]
The test statistic is given as follows;
[tex]t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{S_{p}^{2} \cdot \left(\dfrac{1 }{n_{1}}+\dfrac{1}{n_{2}}\right)}}[/tex]
Therefore, we have;
[tex]t=\dfrac{(4.25-4.25625)}{\sqrt{0.19682 \times \left(\dfrac{1 }{8}+\dfrac{1}{8}\right)}} \approx -0.028176[/tex]
The degrees of freedom, df = n₁ + n₂ - 2 = 8 + 8 - 2 = 14
At 5% significance level, the critical t = 2.145
Therefore, given that the absolute value of the test statistic is less than the critical 't', we fail to reject the null hypothesis and it can be concluded that at 5% significance level that chain A pays the same as chain B for the job under consideration
6) Supplementary Exercise 5.51
A consumer advocate claims that 80 percent of cable television subscribers are not satisfied with their cable service. In an attempt to justify this claim, a randomly selected sample of cable subscribers will be polled on this issue.
(a)
Suppose that the advocate's claim is true, and suppose that a random sample of five cable subscribers is selected. Assuming independence, use an appropriate formula to compute the probability that four or more subscribers in the sample are not satisfied with their service. (Do not round intermediate calculations. Round final answer of p to 1 decimal place. Round other final answers to 4 decimal places.)
The answer for 6(a) is P( Xâ¥4) = P ( x = 4) + P (x = 5) = 5/4 * 0.84 * 0.21 + 5/5 * 0.85 * 0.20 = 0.737
(b)
Suppose that the advocate's claim is true, and suppose that a random sample of 25 cable subscribers is selected. Assuming independence, find each of the following: (Do not round intermediate calculations. Round final answer of p to 1 decimal place. Round other final answers to 4 decimal places.)
1.
The probability that 15 or fewer subscribers in the sample are not satisfied with their service.
The answer for 6(b)1 is P(Yâ¤15) = 1 - P( Y > 20) - X20, i = 16 P ( Y = i) = 1- 0.421 - 0.562 = 0.017
2.
The probability that more than 20 subscribers in the sample are not satisfied with their service.
The answer for 6(b)2 is
3.
The probability that between 20 and 24 (inclusive) subscribers in the sample are not satisfied with their service.
The answer for 6(b)3 is P(20 > Y < 24) = 1 - 0.421 - 0.1867 - 0.1358 - 0.0708 - 0.0236 = 0.1621
4.
The probability that exactly 24 subscribers in the sample are not satisfied with their service.
The answer for 6(b)4 is P( Y = 24) = 0.0236
(c)
Suppose that when we survey 25 randomly selected cable television subscribers, we find that 15 are actually not satisfied with their service. Using a probability you found in this exercise as the basis for your answer, do you believe the consumer advocate's claim? Explain. (Round your answer to 4 decimal places.)
Answer:
[tex]P(X \le 4) = 0.7373[/tex]
[tex]P(x \le 15) = 0.0173[/tex]
[tex]P(x > 20) = 0.4207[/tex]
[tex]P(20\ge x \le 24)= 0.6129[/tex]
[tex]P(x = 24) = 0.0236[/tex]
[tex]P(x = 15) = 1.18\%[/tex]
Step-by-step explanation:
Given
[tex]p = 80\% = 0.8[/tex]
The question illustrates binomial distribution and will be solved using:
[tex]P(X = x) = ^nC_xp^x(1 - p)^{n-x}[/tex]
Solving (a):
Given
[tex]n =5[/tex]
Required
[tex]P(X\ge 4)[/tex]
This is calculated using
[tex]P(X \le 4) = P(x = 4) +P(x=5)[/tex]
This gives:
[tex]P(X \le 4) = ^5C_4 * (0.8)^4*(1 - 0.8)^{5-4} + ^5C_5*0.8^5*(1 - 0.8)^{5-5}[/tex]
[tex]P(X \le 4) = 5 * (0.8)^4*(0.2)^1 + 1*0.8^5*(0.2)^0[/tex]
[tex]P(X \le 4) = 0.4096 + 0.32768[/tex]
[tex]P(X \le 4) = 0.73728[/tex]
[tex]P(X \le 4) = 0.7373[/tex] --- approximated
Solving (b):
Given
[tex]n =25[/tex]
i)
Required
[tex]P(X\le 15)[/tex]
This is calculated as:
[tex]P(X\le 15) = 1 - P(x>15)[/tex] --- Complement rule
[tex]P(x>15) = P(x=16) + P(x=17) + P(x =18) + P(x = 19) + P(x = 20) + P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25)[/tex]
[tex]P(x > 15) = {25}^C_{16} * p^{16}*(1-p)^{25-16} +{25}^C_{17} * p^{17}*(1-p)^{25-17} +{25}^C_{18} * p^{18}*(1-p)^{25-18} +{25}^C_{19} * p^{19}*(1-p)^{25-19} +{25}^C_{20} * p^{20}*(1-p)^{25-20} +{25}^C_{21} * p^{21}*(1-p)^{25-21} +{25}^C_{22} * p^{22}*(1-p)^{25-22} +{25}^C_{23} * p^{23}*(1-p)^{25-23} +{25}^C_{24} * p^{24}*(1-p)^{25-24} +{25}^C_{25} * p^{25}*(1-p)^{25-25}[/tex]
[tex]P(x > 15) = 2042975 * 0.8^{16}*0.2^9 +1081575* 0.8^{17}*0.2^8 +480700 * 0.8^{18}*0.2^7 +177100 * 0.8^{19}*0.2^6 +53130 * 0.8^{20}*0.2^5 +12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1 +1 * 0.8^{25}*0.2^0[/tex]
[tex]P(x > 15) = 0.98266813045[/tex]
So:
[tex]P(X\le 15) = 1 - P(x>15)[/tex]
[tex]P(x \le 15) = 1 - 0.98266813045[/tex]
[tex]P(x \le 15) = 0.01733186955[/tex]
[tex]P(x \le 15) = 0.0173[/tex]
ii)
[tex]P(x>20)[/tex]
This is calculated as:
[tex]P(x>20) = P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25)[/tex]
[tex]P(x > 20) = 12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1 +1 * 0.8^{25}*0.2^0[/tex]
[tex]P(x > 20) = 0.42067430925[/tex]
[tex]P(x > 20) = 0.4207[/tex]
iii)
[tex]P(20\ge x \le 24)[/tex]
This is calculated as:
[tex]P(20\ge x \le 24) = P(x = 20) + P(x = 21) + P(x = 22) + P(x =23) + P(x = 24)[/tex]
[tex]P(20\ge x \le 24)= 53130 * 0.8^{20}*0.2^5 +12650 * 0.8^{21}*0.2^4 +2300 * 0.8^{22}*0.2^3 +300 * 0.8^{23}*0.2^2 +25* 0.8^{24}*0.2^1[/tex]
[tex]P(20\ge x \le 24)= 0.61291151859[/tex]
[tex]P(20\ge x \le 24)= 0.6129[/tex]
iv)
[tex]P(x = 24)[/tex]
This is calculated as:
[tex]P(x = 24) = 25* 0.8^{24}*0.2^1[/tex]
[tex]P(x = 24) = 0.0236[/tex]
Solving (c):
[tex]P(x = 15)[/tex]
This is calculated as:
[tex]P(x = 15) = {25}^C_{15} * 0.8^{15} * 0.2^{10}[/tex]
[tex]P(x = 15) = 3268760 * 0.8^{15} * 0.2^{10}[/tex]
[tex]P(x = 15) = 0.01177694905[/tex]
[tex]P(x = 15) = 0.0118[/tex]
Express as percentage
[tex]P(x = 15) = 1.18\%[/tex]
The calculated probability (1.18%) is way less than the advocate's claim.
Hence, we do not believe the claim.
There is 12 inches in a whole hole how many inches is in a half of a hole?
Answer:
6 is hoing to be your answer
Answer:
6in
Step-by-step explanation:
Rory earned an 84% on his test. He answered 21 questions correctly. How many total questions were on the
test? Round to the nearest tenth if necessary
Answer:
21 is 84% to 25, so there would be 25 total questions on the test
A college student wants to determine if degree of introversion/extroversion is associated satisfaction with life. She has a sample of 68 people take two surveys. The first survey yields a higher score the more extroverted a person is. The second survey yields a higher score the more satisfied a person is with their life. What statistics should you use to determine if scores on these two surveys are related to each other
Answer: Correlation
Step-by-step explanation:
The statistics that should be used to determine if scores on these two surveys are related to each other is referred to as correlation.
Correlation indicates the degree by which the variables that are given are linearly related. Correlation is used in the testing and determination of the strength of association that can be found between two variables.
In this case, since the student wants to determine if degree of introversion or extroversion s associated satisfaction with life, the correlation will be appropriate to use.
The historical U.S. mean unemployment insurance benefit was reported to be $238 per week. A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level. What would be the appropriate alternative hypothesis if he wanted to substantiate his suspicion
Answer:
The appropriate alternative hypothesis if he wanted to substantiate his suspicion would be [tex]H_{a}: \mu > 238[/tex]
Step-by-step explanation:
At the null hypothesis, we test that the mean is equal to a certain value.
At the alternate hypothesis, we test that the mean is different, less than or more than the mean value tested at the null hypothesis.
The historical U.S. mean unemployment insurance benefit was reported to be $238 per week.
This means that the null hypothesis is:
[tex]H_{0}: \mu = 238[/tex]
A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level.
This means that the alternate hypothesis is:
[tex]H_{a}: \mu > 238[/tex]
Victor buys four chairs to place around his dining room table. He pays a total of $88. What is the unit
price?
Complete the table following the linear function rule. I don’t know what to do at all.
Answer:
-2, 1, 4
Step-by-step explanation:
The ratio of cows to chickens on Tweedy's Farm is 2:7. Which farms have a greater ratio of cows to chickens than Tweedy's Farm? Select all that apply.
a Steller Stover's Farm 3 cows for 5 chickens
b Awesome Ansel's Farm 1 cow for every 5 chickens
c Happy Hall's Farm 1 cow for every 3 chicken
d Jumping Jack Jones Farm 3 cows for every 8 chickens
The answer would be B) Awesome Ansel's Farm 1 cow for every 5 chickens.
which is an equation of a line through (7,1) and perpendicular to y=-x+3
Answer:
The answer is y=-1x+8 or you can write it this way y=-x+8 either way will work fine.
Step-by-step explanation:
y=mx+b
m=-1
y-y=m(x-x¹)
y-1=-1(x-7)
y-1=-1x+7
+1 +1
y=-x+8
I hope this helps:)
What is the value of xwhen ik o h)(r)
-1?
OA.
2
OB.
-3
O C. 1
OD.
4
I NEED HELP ASAP
Answer:
4
Step-by-step explanation:
Expand and combine like terms: (2x^3+4x^5)^2=
Answer:
16x^10+16x^8+4x^6
The expanded and simplified form of [tex](2x^3 + 4x^5)^2[/tex] is [tex]4x^6 + 16x^8 + 16x^10[/tex].
when we combine all the like terms.
To expand and combine like terms for the expression [tex](2x^3 + 4x^5)^2,[/tex] we need to square each term inside the parentheses and then combine like terms.
Using the FOIL method (First, Outer, Inner, Last) to multiply the terms, we have:
[tex](2x^3 + 4x^5)^2 = (2x^3)^2 + 2(2x^3)(4x^5) + (4x^5)^2[/tex]
Simplifying each term:
[tex](2x^3)^2 = 4x^6\\2(2x^3)(4x^5) = 16x^8\\(4x^5)^2 = 16x^10[/tex]
Combining like terms, we have:
[tex](2x^3 + 4x^5)^2 = 4x^6 + 16x^8 + 16x^10[/tex]
Therefore, the expanded and simplified form of [tex](2x^3 + 4x^5)^2[/tex] is [tex]4x^6 + 16x^8 + 16x^10.[/tex]
To know more about "expression." here
https://brainly.com/question/1859113
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Full Question
Expand and combine like terms: (2x^3+4x^5)^2 by simplication.
(No graph needed)
Find the missing angle of each triangle.
Answer:
1 is 64
2 is 85
3 is 56 hope this helps
Step-by-step explanation:
also how give brainly i want to give u brainly
A stadium is shaped like a hemisphere with a radius of 150 feet. Last month, the owners of the stadium paid $0.05 per cubic foot to cover the cost of utilities. What was the total cost for utilities last month?
Answer:
353,249 feet cubed
Step-by-step explanation:
V=(4/3)[tex]\pi (3.14)rx^{3}[/tex]/2 times 0.05
I GIVE BRAINLIEST FOR EXPLANATION AND CORRECT ANSWER EXTRA POINTS
Answer:
452.39
Step-by-step explanation:
Show your work: 1/2x = 10
Solve for the length of BA and BC, round your answer to 1 decimal place
Answer:
[tex]BA = 6.0[/tex]
[tex]BC = 13.4[/tex]
Step-by-step explanation:
Given
The attached triangle
Solving (a) BA
Considering the tangent of angle C, we have:
[tex]tan\ C = \frac{BA}{AC}\\[/tex]
This gives:
[tex]tan\ 25 = \frac{BA}{12}[/tex]
Make BA the subject
[tex]BA = 12 * tan\ 25[/tex]
[tex]BA = 12 * 0.4663[/tex]
[tex]BA = 6.0[/tex] --- approximated
Solving (a) BC
Using Pythagoras theorem
[tex]BC^2 = BA^2 + AC^2[/tex]
[tex]BC^2 = 6.0^2 + 12^2[/tex]
[tex]BC^2 = 180[/tex]
Square root of both sides
[tex]BC = \sqrt{180[/tex]
[tex]BC = 13.4[/tex]