Answer:
-cos^4(x)
Step-by-step explanation:
Step 1: Use the Pythagorean identity : 1=cos^2(x) + sin^2(x)
1-sin^2(x) = cos^2(x)
-1+sin^2(x) = -cos^2(x)
cos^2(x) (-cos^2(x))
Step 2: Factor out common terms cos^2(x)
cos^2(x) (sin^2(x)-1)
Ans: -cos^4(x)
please solve 2 quickly
Answer:
The maximum is ¼the minimum is ⅕Step-by-step explanation:
Have a great day✧◝(⁰▿⁰)◜✧
A size 8 kid shoe measures 9 inches. If 5 pairs of size 8 kids shoes are lined end to end, then how many inches will they cover?
A nutritionist has developed a diet that she claims will help people lose weight. Twelve people were randomly selected to try the diet. Their weights were recorded prior to beginning the diet and again after 6 months. Here are the original weights, in pounds, with the weight after 6 months in parentheses. Before 192 212 171 215 180 207 165 168 190 184 200 196 After 183 196 174 211 160 191 162 175 190 179 189 195 Test the claim that the diet is effective at the 0.05 level of significance.
The diet which is developed by the nutritionist is effective at the 0.05 level of significance. Claim is agreed.
When do we use two-sample t-test?The two-sample t-test is used to determine if two population means are equal.
A nutritionist has developed a diet that she claims will help people lose weight. In this,
Twelve people were randomly selected to try the diet. Their weights were recorded prior to beginning the diet and again after 6 months.Here are the original weights, in pounds, with the weight after 6 months in parentheses.
Before 192 212 171 215 180 207 165 168 190 184 200 196 After 183 196 174 211 160 191 162 175 190 179 189 195The mean of the weights before 6 moths is,
[tex]\overline X_1=\dfrac{192+ 212 +171 +215 +180 +207 +165 +168 +190 +184 +200 +196 }{12}\\\overline X_1=190[/tex]
The mean of the weights after 6 months is,
[tex]\overline X_2=\dfrac{ 183 +196 +174 +211 +160 +191 +162 +175 +190 +179 +189 +195 }{12}\\\overline X_1=183.75[/tex]
Standard deviation of both the data is 16.9 and 14.7.
1. Null and Alternative Hypotheses.
The following null and alternative hypotheses need to be tested:
[tex]\begin{array}{ccl} H_0: \mu_1 & = & \mu_2 \\\\ \\\\ H_a: \mu_1 & > & \mu_2 \end{array}[/tex]
This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.
(2) Rejection RegionBased on the information provided, the significance level is α=0.05 and the degrees of freedom are df = 22. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:
[tex]df_{Total} = df_1 + df_2 = 11 + 11 = 22[/tex]
Hence, it is found that the critical value for this right-tailed test is
[tex]t_c=1.717[/tex], for α=0.05 and df=22
The rejection region for this right-tailed test is,
[tex]R = \{t: t > 1.717\}[/tex]
(3) Test Statistics
Since it is assumed that the population variances are equal, the t-statistic is computed as follows:
[tex]t = \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}(\frac{1}{n_1}+\frac{1}{n_2}) } }[/tex]
[tex]\displaystyle \frac{ 190 - 183.75}{\sqrt{ \frac{(12-1)16.9^2 + (12-1)14.7^2}{ 12+12-2}(\frac{1}{ 12}+\frac{1}{ 12}) } } = 0.967[/tex]
(4) Decision about the null hypothesisSince it is observed that t=0.967≤tc=1.717 it is then concluded that the null hypothesis is not rejected.
Using the P-value approach: The p-value is p=0.1721 and since p=0.1721≥0.05p = 0.1721 it is concluded that the null hypothesis is not rejected.
(5) Conclusion
It is concluded that the null hypothesis H₀ is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1 is greater than μ2, at the α=0.05 significance level.
Confidence Interval
The 95% confidence interval is −7.16<μ<19.66
Thus, the diet which is developed by the nutritionist is effective at the 0.05 level of significance. Claim is agreed.
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Use both the intercepts and end point behavior to explain why the following isn't a graph of f(x)= x^5 - x.
Factor x^5 - x to get x(x^4 - 1) = x(x^2-1)(x^2+1) = x(x-1)(x+1)(x^2+1)
We see that x = 0, x = 1 and x = -1 are the real number roots or x intercepts. Ignore the complex or imaginary roots. Unfortunately, the graph shows the x intercepts as -2, 0 and 2 which don't match up.
So there's no way that the given graph matches with f(x) = x^5-x.
-------------------
As more proof, let's consider the end behavior.
As x gets really large toward positive infinity, x^5 will do the same and so will x^5-x. Overall, f(x) will head off to positive infinity. Visually, moving to the right will have the graph move upward forever. This is the complete opposite of what is shown on the graph.
Likewise, the left endpoint should be aimed down instead of up. This is because x^5-x will approach negative infinity as x heads to the left.
In short, the graph shows a "rises to the left, falls to the right" end behavior. It should show a "falls to the left, rises to the right" pattern if we wanted to have a chance at matching it with x^5-x. Keep in mind that matching end behavior isn't enough to get a 100% match; however, having this contradictory end behavior is proof we can rule out a match.
I recommend using Desmos, GeoGebra, or whatever graphing program you prefer to plot out y = x^5-x. You'll get a bettter idea of what's happening.
Answer:
The answer it attached below :)
Sorry it took so long!
Select the correct answer.
A triangle with vertices at A(0, O), B(O, 4), and C6, 0) is dilated to yield a triangle with vertices at A(0, 0), B(0, 10), and C(15, 0). The origin is
the center of dilation. What is the scale factor of the dilation?
O A. 1.5
O B. 2
O C. 2.5
© D. 3
The scale factor of the dilation is 2.5.
What is scale factor?A scale factor is a number that is used to change the size of shapes in geometry. It is the ratio of the length of a new shape to the length of the original shape.
Given that, a triangle with vertices, A(0, 0), B(0, 4), and C(6, 0) is dilated to yield a triangle with vertices at A(0, 0), B(0, 10), and C(15, 0).
We need to find the scale factor,
Taking the coordinates of B,
B(0, 4) → B(0, 10)
Scale factor = 10/4 = 2.5
Hence, the scale factor of the dilation is 2.5.
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In AWXY, the measure of ZY=90°, XW = 5, YX = 4, and WY = 3. What ratio
represents the cotangent of ZX?
X
5
4.
Y
W
3
Given:
In Δ[tex]WXY,m < Y=90^o,WY=3,XW=5[/tex] and [tex]YX=4[/tex].
To find:
The ratio represents the cosine of ∠[tex]W[/tex].
Solution:
In Δ[tex]WXY,m < Y=90^o[/tex]. It means the opposite side of angle Y, i.e., XW is the hypotenuse of the triangle.
In a right angle triangle,
[tex]cos0=\frac{Base}{Hypotenuse}[/tex]
In the given triangle,
[tex]cosW=\frac{XY}{YW}[/tex]
[tex]cosW=\frac{3}{5}[/tex]
Therefore, the required cosine ratio is [tex]\frac{3}{5}[/tex].
Joseph walks 10 times around the track at a rate of x laps per hour. She runs eight times around the track of a rate of 3X laps per hour. Write and simplify an expression for the total time it takes him to go around the track 18 times
The expression for the total time is:
T = (324/34x).
How to get the expression?He does 18 laps in total.
8 laps at a rate of 3x10 laps at a rate of x.The average rate for the whole 18 laps is the average of the rates (taking in account the number of laps made with each) so we get:
average rate = (8/18)*3x + (10/18)*x = (34x/18)
This means that he does (34x/18) laps per hour.
Then, the time needed to do 18 laps is:
T = (18/(34x/18)) = (324/34x).
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The equation of any line in the coordinate plane can be written in the form Ax+By=C where A, B, C are real numbers. Select all of the equations below that define y as a function of x.
−12x−85y=0
−9x+0y=78
0x+56y=−11
3x−4y=−2
The equations which define y as a function of x are; −12x−85y=0 and 3x−4y=−2.
What are real numbers?Any number that one can think of, except complex numbers, is a real number. Real numbers therefore include rational numbers like positive and negative integers, fractions, and irrational numbers.
On this note, the equations as displayed in the answers provided above define y as a function of x.
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Please show your work, tysm :D
~giving brainliest!~
Answer:
. 0625
Step-by-step explanation:
1/2^4
or
1/16
just doing half life
Can someone write the equation for this graph and explain the steps. Also can you include all the key features of the graph p
Answer:g(x) = f(x) + 1.5g(
Step-by-step explanation:g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5
Determine if x + 3 is a factor of -3x^3+6x^2+6x+9 How do you know
Answer:
x+3 is not a factor
Step-by-step explanation:
A graphing calculator shows the expression has a zero at x=3 and no other real zeros. If x+3 were a factor, there would be a zero at x = -3.
x+3 is not a factor of the expression.
_____
You can check to see if x+3 is a factor by evaluating the expression for x=-3. If (x+3) is a factor, x=-3 will make the function be zero.
3(-x³ +2x² +2x +3) = 3(((-x +2)x +2)x +3) = 3(((-(-3)+2)(-3) +2)(-3) +3)
= 3((-15+2)(-3) +3) = 3(39 +3) = 126 ≠ 0
The expression evaluates to 126 at x=-3, so x+3 is NOT a factor.
HELP PLEASEEEE
The table below shows the
values for the function y = f(x).
The answers are:
Second option, evaluating x=-1
[tex]g(-1)=-2[/tex]
Fifth option, evaluating x=6
[tex]g(6)=\frac{3}{2}[/tex]
Why?We are given a table that shows the values for the given function (f(x), and we are asked to find the solution of an equivalent function (g(x)).
We have that:
[tex]g(x)=\frac{1}{2}f(x)[/tex]
Now, evaluating we have:
For x=-3
[tex]g(-3)=\frac{1}{2}f(-3)=\frac{1}{2}*5=2.5[/tex]
We have the values (-3,2.5) so, it's not part of the solutions to the function g(x).
For x=-1
[tex]g(-1)=\frac{1}{2}f(-3)=\frac{1}{2}*-4=-2[/tex]
We have the values (-1,-2) so, it's part of the solutions to the function g(x).
For x=0
[tex]g(0)=\frac{1}{2}f(0)=\frac{1}{2}*2=1[/tex]
We have the values (0,1) so, it's not part of the solutions to the function g(x).
For x=5
[tex]g(5)=\frac{1}{2}f(5)=\frac{1}{2}*-8=-4[/tex]
We have the values (5,-8) so, it's not part of the solutions to the function g(x).
For x=6
[tex]g(6)=\frac{1}{2}f(6)=\frac{1}{2} *3=\frac{3}{2}[/tex]
We have the values [tex](6,\frac{3}{2})[/tex] so, it's part of the solutions to the function g(x).
Hence, we have that the answers are:
Second option, evaluating x=-1
[tex]g(-1)=-2[/tex]
Fifth option, evaluating x=6
[tex]g(6)=\frac{3}{2}[/tex]
Have a nice day!
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Fill in the chart. (Round to the nearest penny)
=============================================================
Explanation:
If the money is compounded semiannually at a rate of 8%, then this means the multiplier (common ratio) is b = 1+r/n = 1+0.08/2 = 1.04
r = 0.08 = 8% annual interest raten = 2 = compounding twice a year, aka semiannually, aka every 6 months.In short, b = 1.04 is our growth multiplier. It says that the money is growing by 4% each 6 month period. Each time x goes up by 1, y increases by 4%. The starting amount is a = 2100 dollars.
We go from the template of [tex]y = ab^x[/tex] to [tex]y = 2100(1.04)^x[/tex]
Use that equation to fill out the table. For instance, if x = 2 then,
[tex]y = 2100(1.04)^x\\\\y = 2100(1.04)^2\\\\y = 2100(1.0816)\\\\y = 2271.36\\\\[/tex]
Meaning that after 2 semiannual periods (aka 2*6 = 12 months = 1 year), we'd have $2,271.36 in the account.
Repeat this for the other x values mentioned to get the table shown below. To fill out the final column of the first row, you'll look at the very bottom of the table in the previous column. Four semiannual periods is equal to 2 years.
--------------
These steps are repeated for the second row of the table.
This time the growth multiplier is b = 1 + r/n = 1 + 0.14/12 = 1.0116667 approximately. The starting amount is a = 700
So that's how we go from [tex]y = ab^x[/tex] to [tex]y = 700(1.0116667)^x[/tex]
Like before, you'd plug in the various x values to find their paired y counterparts.
Example:
Plug in x = 18
[tex]y = 700(1.0116667)^x\\\\y = 700(1.0116667)^{18}\\\\y = 700(1.2321801)\\\\y = 862.52607\\\\y = 862.53\\\\[/tex]
The values are approximate. After 18 months, aka 18/12 = 1.5 years = 1 yr + 6 months, we'd have about $862.53 in the account.
Can anyone please help me answer this math questionn ?? Soon as possible !!
Jayne works for a company that offers to contribute $0.40 for each dollar an employee contributes to his or her 401(k) plan. If Jayne contributes $5,300 over the course of the year, how much will her employer contribute to her retirement plan?
Answer:
i believe the answer is 13,250
Step-by-step explanation:
all i did was divide the 5400/0.40 because i thiink its correct, maybe not
The employer contribute to her retirement plan is $2120.
What is 401(k) plan?Many American firms provide 401(k) plans, which are retirement savings plans with favourable tax treatment for the saver. It bears a section number from the United States Internal Revenue Code (IRC).
When a worker enrols in a 401(k), they consent to have a portion of each paycheck put directly into an investing account. A portion or the entire contribution may be matched by the employer. The employee has a variety of investing alternatives, most often mutual funds.
Given:
Jayne contributes $5,300
Now, the contribution of $0.40 for each dollar
So, employer contribute to her retirement plan
= 5300 x 0.40
= $2120
Hence, The employer contribute to her retirement plan is $2120.
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5-16 Find the general indefinite integral.
15. [tex]\int \frac{1-\sin ^{3} t}{\sin ^{2} t} d t[/tex]
Simplify the integrand
[tex]\dfrac{1-\sin^2(t)}{\sin^2(t)} = \dfrac{\cos^2(t)}{\sin^2(t)} = \cot^2(t)[/tex]
Recall the derivative of csc(t),
[tex]\dfrac d{dt} \csc(t) = -\cot^2(t)[/tex]
It follows that
[tex]\displaystyle \int \frac{1-\sin^2(t)}{\sin^2(t)} \, dt = \int \cot^2(t) \, dt = \boxed{-\csc(t) + C}[/tex]
A data lists the number of hours each students from finance class studied for midterm. For this data set, the minimum is 3, the median is 6, the third quartile is 9, the interquartile range is 5, and the maximum is 17. Construct a box-and-whisker plot that show the number of hours studied. Begin by first placing the middle dots on the median. Then work on placing the test of the point starting with the ones closest to the median
Answer:
12
Step-by-step explanation:
this question asked us to find the given data points. Given this data set, what we know that the minimum is the smallest value, which is simply gonna be five. We know the media is gonna be the middle about you. We have to middle values seven and nine. Therefore, we couldn't find the average of the sum plus nine divided by two is eight. Now, we're looking for the first quarter mile. We know that we're gonna be averaging the middle values similarly to what we did for the media. So we have 10 plus 11 divide by two, which is 10.5, and then the maximum is simply the largest value, which is 12.
Mac has taken seven maths exams this year. His average mark is 78%. What mark must he get on the eighth exam to raise his average to 80%?
Answer:
94
Step-by-step explanation:
7*78 + x = 8*80
x = 94
Or, think that he was short 2 points on each of 7 tests, so he has to make them all (14) up on the last test.
Can you please help ni
Answer:
0.0833... inches longer or 1/12
Step-by-step explanation:
7/12=0.583
1/2 but multiplied by 6 is 6/12
so 7/12-6/12=1/12 longer or 0.0833-
100 points + brainiest
A pharmacist mixed 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution.
How many grams is the mixture that the pharmacist has now?
Answer:
35 grams of 11.43% solutionStep-by-step explanation:
The end solution has same volume as initial volumes of mixture.
10 + 25 = 35 gThe concentration of solution is calculated as below
10*0.15 + 25*0.1 = 4 g4 / 35*100% = 11.43% (rounded)Answer:
35 grams
Step-by-step explanation:
25+10=30 grams of the mixture
Help me pls I am not sure about this
Answer: the answer is c which is 61 ¾ inches .
Step-by-step explanation: what I did that I made 62 ½ minus ¾ and it gave 61 ¾ inches, to know how many inches did she grew at the beginning of the year . I hope my answer is correct . Please give brainliest . Thanks .
What is the power set of s={1,2,3,4,5}
The power set P(X) of a finite set X is the set of all possible subsets of X. If X has n elements, then it has a total of 2ⁿ subsets.
For the set S = {1, 2, 3, 4, 5}, we have
• subsets with cardinality 0:
{ } (the empty set)
• subsets with cardinality 1:
{1}, {2}, {3}, {4}, {5}
• subsets with card. 2:
{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}, {3, 4}, {4, 5}
• subsets with card. 3:
{1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 3, 4}, {1, 3, 5}, {1, 4, 5}, {2, 3, 4}, {2, 3, 5}, {2, 4, 5}, {3, 4, 5}
• subsets with card. 4:
{1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {1, 3, 4, 5}, {2, 3, 4, 5}
• subsets with card. 5:
{1, 2, 3, 4, 5}
Then P(S) is the set containing all of these sets,
{{}, {1}, {2}, {3}, …, {1, 2, 3, 4, 5}}
2. Find m angle 1
73
88
60
80
Answer:
88°
Step-by-step explanation:
RULES:
angles on a straight line add up to 180 degreesangles in a triangle add up to 180 degreesso.
because of rule 1, we do 180-120 to get 60, to get that right corner angle. Now, we know 2 angles. So, (because of rule 2), we can do 60+32 = 92, and 180-92 = 88
So, 1 = 88
Hope this helps! If it doesn't make sense, feel free to ask me to explain it further.
- profparis
In the figure below, parallelogram STXY is congruent to parallelogram UTWV.
If mTXY = 118°, what is mXTW?
A.
62°
B.
60°
C.
56°
D.
124°
Answer:
The correct answer is C.56.
Hope this helps you czn!!!!
Please Mark me as Brainleast!!!!!!!!
Directions: Solve for x. Round to the nearest tenth.
3.
2
.
48°
17
29
x
х
х
67°
4.
5.
29°
16°
12
X
Х
37
6.
7.
15
х
589
51°
х
22
Answer:
Step-by-step explanation:
4
(Solve by matrix method): 5/x + 3y = 7, 7y -10/x = 12
Step-by-step explanation:
10 x + 6 y = -14 yes
21 x - 6 y = 39 yes
add those two
31 x + 0 = 25
so
x = -25/31 yes
Now go back and use -25/31 in either of the original equations to get y
5 (-25/31) + 3 y = -7
3 y = 125/31 -7
3 y = (125-217)/31
y = - 92/3
Factor out the greatest common factor from the following polynomial.
3 2
15a + 3a + 1
Find the area of the figure.
1.
Answer:
14cm²
Step-by-step explanation:
Add up all the squares and the other bits to get the answer.
What is a formula for the nth term of the given sequence?
-6,0, 6...
Answer:
Step-by-step explanation:
5 Digit Lock - Level One
*
242
For a fixed loan amount, what happens to the monthly payment as the annual rate increases? a. as the annual rate increases, the monthly payment increases c. as the annual rate increases, the monthly payment stays the same b. as the annual rate increases, the monthly payment decreases d. no correlation Please select the best answer from the choices provided A B C D
Answer:
C
Step-by-step explanation:
looked up on Quizlet so yeah
Help I don’t understand