Answer:
y = 3cos(81x)
Step-by-step explanation:
Hello!
Here is the foundational equation to find sine and cosine:
y = A sin(B(x + C)) + D
Any cosine function can be written as a sine function. y = A sin(Bx) and y = A cos(Bx). The number, A, in front of sine or cosine changes the height of the graph. The value A (in front of sin or cos) affects the amplitude (height). B is the period by which the width of the wavelengths are measrured. C is known as the phase shift, which is positive to the left on graph. D is the vertical shift of function.
The amplitude changes the heaight of the cosine function by 3 units. The period is indicated as 81 and , but usually we must first use the equation that is the usual given: period = [tex]\frac{2\pi }{|B|}[/tex] . B must always have an absolute sign to have a psotive value. In this case, the period was given to us.
So, the final equation looks like this:
y = 3cos(81x)
Hope this helps!
Please help if you can thx :)
Answer:
x = 30
Step-by-step explanation:
All triangle angles add up to 180 so:
x + 3x + 2x = 180
6x = 180
x = 30
The width of a rectangular tank is x cm . It's height is 2/3 it's width and it's length is four times it's height .The volume of the tank in litres is
Answer:
Tank is a tank and a cat is a cat.
Step-by-step explanation:
A bicycle is originally priced at $80 the store owner gives a discount in the bicycle is know priced at $60 enter the percent markdown for the cost of the bicycle
Answer:
25%
Step-by-step explanation:
Since we know that the markdown is $20 by subtracting 80-60 , we find out what percent of 20 is 80. To do that you do 20/80, which is 0.25, or 25 percent.
Out of a total of N students at a school, the number of students who have seen a new television program increases at a rate proportional to the product of the number of students who have seen the program and the number of students who have not seen the program. If S denotes the number of students who have seen the program at time t, which of the following differential equations could be used to model this situation, where k is a positive constant?
a. ds/dt = KS
b. ds/dt = kt(N-t)
c. ds/st = KS(N-S)
d. ds/dt = KS(S-N)
Answer:
ds/dt = kN(N-S)
Step-by-step explanation:
Given
Total number of student = N
number of students who have seen the program = S
Number of students who have not seen the program = N-S
The product of the number of students who have seen the program and the number of students who have not seen the program = N(N-S)
If the rate of number of students who have seen a new television program increases at a rate proportional to the product of the number of students who have seen the program and the number of students who have not seen the program, then:
ds/dt = kN(N-S)
k is the proportionality constant
The price of 4 pounds of grapes is $8.40 What is the price of 1 pound of grapes.
Answer:
$2.10
Step-by-step explanation:
8.40÷4=2.1
Therefore, the price for 1 lb of grapes is $2.10.
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 212 brakes using Compound 1 yields an average brake life of 47,895 miles. A sample of 180 brakes using Compound 2 yields an average brake life of 49,767 miles. Assume that the population standard deviation for Compound 1 is 1590 miles, while the population standard deviation for Compound 2 is 4152 miles.
1. Determine the 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
2. Find the point estimate for the true difference between the population means.
Answer:
1. The 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-2411.84, -1332.16).
2. The point estimate for the true difference between the population means is of -1872.
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of Normal Variables:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
A sample of 212 brakes using Compound 1 yields an average brake life of 47,895 miles. The population standard deviation for Compound 1 is 1590 miles.
This means that [tex]\mu_1 = 47895, \sigma_1 = 1590, n = 212, s_1 = \frac{1590}{\sqrt{212}} = 109.2[/tex]
A sample of 180 brakes using Compound 2 yields an average brake life of 49,767 miles. The population standard deviation for Compound 2 is 4152 miles.
This means that [tex]\mu_2 = 49767, \sigma_2 = 4152, n = 180, s_2 = \frac{4152}{\sqrt{180}} = 309.47[/tex]
True difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
This is the distribution 1 - 2. So
[tex]\mu = \mu_1 - \mu_2 = 47895 - 49767 = -1872[/tex]
This is also the point estimate for the true difference between the population means, which is question 2.
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{109.2^2+309.47^2} = 328.17[/tex]
90% confidence interval
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs = 1.645*328.17 = 539.84[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is -1872 - 539.84 = -2411.84
The upper end of the interval is the sample mean added to M. So it is -1872 + 539.84 = -1332.16.
The 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-2411.84, -1332.16).
2. Use the distributive property to write an expression that is equivalent to 5(-2x-3)
Answer:
-10x-15
Step-by-step explanation:
So first we start off with 5(-2x-3)
Next, we distribute the 5 to the -2x to get -10x.
Next, we distribute the 5 to the -3 to get -15.
Therefore,
-10x-15 is correct
Answer:
-10x-15
Step-by-step explanation:
It's 10x-15, because you just need to simplify it.
It is the same thing as (5 x (-2x)) - (5 x 3), if you use the distributive property.
that is the same as -10x-15
In the spinner below, what is the probability of landing on 5?
A.2/6
B.1/4
C.1/8
D.1/12
You have 15 bottles of coke , you drink 2 bottles a day after a certain amount of days there are 3 bottles left. Which of the following represents the day when you had 3 borrows left
Answer:
15 - 2x = 3
Step-by-step explanation:
Let x be the amount of days that have passed.
15 - 2x gives the amount at any day number x.
15 - 2x = 3 represents the day when you had 3 bottles left.
A major credit card company is investigating whether the distribution of the number of credit cards used by its customers has changed from last year to this year. Customers are classified as using 1 card, 2 cards, or more than 2 cards. The company conducts a chi-square goodness-of-fit test to investigate whether there is a change in the distribution of number of cards used from last year to this year. The value of the chi-square test statistic was
Answer:
C) If the null hypothesis were true, there is a 2 percent chance of obtaining a chi-square value of at least 7.82.
Step-by-step explanation:
The value of the chi-square test statistic was 7.82 and the p- value is 0.02. This means that if the null hypothesis were true there is a 2 percent chance of obtaining a chi square value of at least 7.82
The p- value is defined as obtaining the test statistic under H0 as extreme as observed.
When the p- value is less than 0.05 in the chi square goodness fit test it means that the null hypothesis is rejected.
There fore option C is the best answer.
A)There is a 2 percent chance that the company's claim is correct.
B) There is a 2 percent chance of obtaining a chi-square value of at least 7.82.
C) If the null hypothesis were true, there is a 2 percent chance of obtaining a chi-square value of at least 7.82.
D) If the null hypothesis were true, there is a 2 percent chance that the company's claim is correct.
E) If the null hypothesis were true, there is a 2 percent chance of obtaining a chi-square value of 7.82.
The p-value is defined as obtaining the test statistic under H₀ as extreme as observed. Then the correct option is C.
What are null hypotheses and alternative hypotheses?In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
The value of the chi-square test statistic was 7.82 and the p-value is 0.02. This means that if the null hypothesis were true if there is a 2% chance of obtaining a chi-square value of at least 7.82.
The p-value is defined as obtaining the test statistic under H₀ as extreme as observed.
Thus, the correct option is C.
More about the null hypotheses and the alternative hypotheses link is given below.
https://brainly.com/question/9504281
The soccer team played a total of twenty-four games and won four more games than they lost. What was the team's win-loss record for the season ? wins _____. Losses _____.
Answer:
Wins _16____. Losses _12____.
Step-by-step explanation:
Since they played 24 games, the wins and losses must add to 24.
Wins losses
24 0
23 1
22 2
21 3
20 4
19 5
18 6
17 7
16 8
15 9
14 10
13 11
12 12
11 13
10 14
9 15
They won 4 more than they lost is 16 W and 12 L.
PLEASE HELPPP!!!
The picture is there
Answer:
Its also 30 degrees
Step-by-step explanation:
That shape is a vertical angle. This means that is 2 was 150 degrees, than 4 would also be 150 degrees. This means that if 1 is 30, then 3 is...... eh you get the idea. its 30 degrees.
P.S: Your welcome :)
A textbook store sold a combined total of 402 biology and physics textbooks in a week. The number of physics textbooks
sold was 54 less than the number of biology textbooks sold. How many textbooks of each type were sold?
Number of biology textbooks sold: 0
Number of physics textbooks sold:
0
We have two types of textbooks. Let's use "x" to represent the number of math textbooks and "y" to represent the number of history textbooks.
Altogether, the bookseller sold 240 math and history textbooks. So:
x + y = 240
Now, the number of history textbooks sold was 72 less than the number of math books sold. So:
y = x - 72
Now we can substitute for y in the equation and solve:
x + y = 240
x + (x - 72) = 240
2x - 72 = 240
2x = 312
x = 156
The bookseller sold 156 math textbooks.
Since y = x - 72, he must have sold 84 history textbooks.
Let's check our answers:
x + y = 240
156 + 84 = 240
That is true, so we did get the correct answers.
If The difference of a number and ten is tripled, the result is 4 more than the number. Find the number
Answer:
x=13
Step-by-step explanation:
3(x-10)=x+4
3x-30=x-4
3x=x+26
2x=26
x=13
Find the value of x.
Answer:
x = 113
Step-by-step explanation:
Since the shape is a quadrilateral, the angles add up to 360 so:
x + 87 + 113 + 47 = 360
x + 247 = 360
x = 360 - 247
x = 113
How many solution(s) does the equation x2 - 6x + 6 = -3 have?
Answer:
2 solutions
Step-by-step explanation:
Simplify the expression:
(50 + 4)(2)
Answer:
108
Step-by-step explanation:
50 + 4 = 54
54 x 2 = 108
Write an equation that can be used to find the nth term of the sequence, an.
70, 103, 136, 169, 202, ...
Enter your answer by filling in the boxes.
an = __n + __
Answer:
+12 +1
Step-by-step explanation:
Answer:
an = 33n + 37
Step-by-step explanation:
I took the test.
Please Help with the second one
Answer:
20%
Step-by-step explanation:
Total number of children = 20
Number of children who chose oatmeal = 4
Percentage of children who chose oatmeal :- [tex] \frac{Number \: of \: children \: who \: chose \: oatmeal}{Total \: number \: of \: children} \times 100[/tex]
[tex] = > \frac{4}{20} \times 100 [/tex]
[tex] = > 20\%[/tex]
16. Find the slope and y-intercept of y - y° = m(x – x°) where x° and y°
are constants.
Step-by-step explanation:
Slope = m
y - y° = m(x - x°)
m(x - x°) = y - y°
m = (y - y°)/(x - x°)
y intercept x = 0
... and I don't know :")
Need help will give brainliestttttttttttttttttt
9514 1404 393
Answer:
10π meters
Step-by-step explanation:
The circumference of the island is given by ...
C = πd
For the given diameter, the circumference is ...
C = π(20 m) = 20π m
The penguin swam half that distance, so swam ...
(1/2)(20π m) = 10π m
The penguin swam 10π meters.
A person is holding two drill bits, one is 7/16 and the other is 25/64, and wants to first drill a hole using the smaller bit. To compare, the person expands 7/16 to 64ths. What is the expanded fraction?
Answer:
28/64
Step-by-step explanation:
7/16 = 14/32 = 28/64
Measurement of a circle
(Giving brainliest for the correct answer)
Answer:
A. [tex] \frac{5}{6}\pi x^2 [/tex]
Step-by-step explanation:
Central angle of shaded part
[tex] \theta = 360\degree-60\degree= 300\degree[/tex]
Radius (r) = x unit
Area of the shaded part of [tex] \odot K[/tex]
[tex] = \frac{\theta}{360\degree} \times \pi r^2 [/tex]
[tex] = \frac{300\degree}{360\degree} \times \pi x^2 [/tex]
[tex] = \frac{5}{6}\pi x^2 [/tex]
How many degrees has (triangle)ABC been rotated counterclockwise about the origin?
Answer:
180°
Step-by-step explanation:
180
The total number of degrees in which has the triangle ABC been rotated counterclockwise about the origin is 180 degrees.
What is the rotation of the figure?The transformation of a figure around a point, either clockwise or counterclockwise, is called rotation. A figure's coordinate point changes when it rotates.
About the origin, the triangle ABC has been rotated. The new triangle A'B'C' is created as a result. In the graph below,
The vertex B' points have the same but negative coordinates,
The vertex of B of the original figure points on the same line.
The coordinate point of B is (5,8).
The coordinate points of B' is (-8,-5).
The same will goes for the A and C points of the triangle
Thus the change in coordinate point after the rotation is,
coordinates of B = (5,8)
coordinates of B' = (-5, -8)
The same will follow with A and C
This is the rotation rule of 180 degrees counterclockwise.
Therefore, The triangle ABC has been rotated 180 degrees counterclockwise in all with respect to the origin.
Learn more about the rotation of figures here;
brainly.com/question/26249005
#SPJ2
The area of a playground is 2,400 square yards, and the width is 40 yards. What is the length of the playground? PLEASE HELP
Please answer this hurry up thank you so much!
Write the expression 5^2/3 without using exponents
The expression 5²/3 can be written without exponents as the fraction 25/3 or 8.33 approximately to 2 decimal place.
Whole numbers, exponents and fractionsWhole numbers include all natural numbers and 0 and can be expressed as exponents and fractions. Exponent is the method of expressing numbers in terms of powers while fractions a fraction represents a part of a whole or, more.
The expression 5²/3 having an exponent can be rewritten as follows:
5²/3 = (5 × 5)/3
5²/3 = 25/3
Therefore, without using exponents the fraction 25/3 or 8.33 approximately to 2 decimal place is the same as the expression 5²/3.
Learn more about exponents here: https://brainly.com/question/11975096
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The five members of the Roberts family went to a high school soccer game. The total cost was $44.
They paid $10 less because they used a $10 coupon, how much was the cost per person?
Answer:
%6.8
Step-by-step explanation:
The five members of the Roberts family went to a high school soccer game. The total cost was $44.
They paid $10 less because they used a $10 coupon, how much was the cost per person?
members in the family = 5
total cost = $44
cost per person = 44/5
= $8.8
Now, they got $10 coupon so they paid $10 less.
therefore,
New total cost = $44-$10
= $34
New per person cost = $34/5
= $6.8
Answer:
they paid $8.80 cents per person without coupan but with coupon they paid $6.80
Step-by-step explanation:
i divied 44 by 5 to get $8.80 without cupon but woth coupan is subracted 34 divied by 5 and got $6.80.
what is the value of the expression -5(3+4)?
Answer:
5(3+4) = - 35
Step-by-step explanation:
-5(3 + 4)
-5 × 3 + (-5) × 4
-15 + (- 20)
-15 - 20 = - 35
Thus, The value of the expression
-5(3+4) is - 35
-TheUnknownScientist
Helppppp PLZZZ This is hard
Answer:
100 sq ft
Step-by-step explanation:
triangle has a base of 25 and a height of 8
A = bh/2
A = 8 x 25 / 2
A = 100