Answer:
[tex]6-8cos2x+2cos4x[/tex]
Step-by-step explanation:
We are given that
[tex]16sin^4 x[/tex]
We can write the given expression as
[tex]16(sin^2x \times sin^2 x)[/tex]
[tex]16(\frac{1-cos2x}{2})(\frac{1-cos2x}{2})[/tex]
By using the formula
[tex]sin^2\theta=\frac{1-cos2\theta}{2}[/tex]
[tex]4(1-cos2x)^2[/tex]
[tex]4(1-2cos2x+cos^2(2x)[/tex]
Using the identity
[tex](a-b)^2=a^2+b^2-2ab[/tex]
[tex]4(1-2cos2x+\frac{1+cos4x}{2})[/tex]
[tex]4-8cos2x+2+2cos4x[/tex]
[tex]6-8cos2x+2cos4x[/tex]
This is required expression.
HELP ME PLS! ASAP I NEED IT WILL FULL PROCESS!!
Write each equation in slope-intercept form (if not in that form). Determine the slope and identify the value where the y-axis intersects. Use these two values to graph the linear equation.
1. y= -x+2
2. 5x+15y=30
3. -50x+20y=40
4. f(x)=-2x+1
5. h(x) = -3/4x+2
Answer:
1. slope = -x, Y-intercept = 2
2. slope = -1/3,Y-intercept = 2
3. slope = 5/2, Y-intercept = 2
4. slope = -2, Y-intercept = 1
5. slope = -3/4, Y-intercept = 2
Step-by-step explanation:
To find the slope and y-intercept you have to solve the equation. You only have to solve for 2 and 3. 1, 4, and 5 already have the equations solved. For questions 1, 4, and 5 the first number is the slope and the second number is the y-intercept. For questions 2 and 5 you have to solve the equations. You have to bring the y to the right side of the equation. to do that you subtract the y. Then you have to bring the number that was already on the right side of the equation to the left side. To do this you also have to subtract that number to bring it to the other side. Now you have to get the y by its self, and to do this you divide the equation. You divide both sides of the equation. Then you can get the slope and y-intercept.
The difference between seven times a number and 9 is equal to three times the sum of the number and 2. Find the number
If x represents the number, which equation is correct for solving this problem?
The difference between seven times a number and 9 is equal to three times the sum of the number and 2. Find the number
If x represents the number, which equation is correct for solving this problem?
Answer:
Number:3.75
Equation:7 x-9=3(x+2)
Step-by-step explanation:
Let the number be x.
According to the question,
7 x-9=3(x+2)
7 x-9= 3 x+ 6
7 x- 3 x= 9+6
4 x= 15
x=15/4
x=3.75
If you verify the answer you will get,
11.25=11.25
Thank you!
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. Please no random answers
Answer:
A
Step-by-step explanation:
A is corrects since -13 is in the the domain of g(x) and 20 is in the range of g(x):
-20 < -13 < 5-5 < 20 < 45B is also false since 4 is in the domain of g(x)) and -11 isn't in the range of g(x)
-20 < 4 < 5-11 < -5C is also false since it's mentioned that g(0) = -2
D is false since 7 isn't in the domain of g(x)
Tanya's car will go 45 meters on 7 gallons. Tanya wants to know how fuel efficient the car is. Please help by computing the ratio. (round to 2 decimal places)
Answer:
5 meters : 1 gallon
fuel efficiency of Car is 7 meters per gallons
Step-by-step explanation:
Given Tanya car goes 45 meters on 7 gallons.
In terms of ratio of distance traveled and fuel consumed
45 meters : 7 gallons
since both 45 and 7 are multiple of 7 dividing both side by 7
45/7 meters : 7/7 gallons
5 meters : 1 gallon
Thus, fuel efficiency of Car is 7 meters per gallons.
HELPPPPPP !!!!!!!!!!!!
! 25 ~! points
PLZ HELPpppP! A lawn is in the shape of a trapezoid with a height of 50 feet and bases of 70 feet and 130 feet. How many bags of fertilizer must be purchased to cover the lawn if each bag covers 3000 square feet? Remember that only whole bags of fertilizer can be purchased. [tex](A=\frac{1}{2}h(B+b))[/tex]
Hi,
Lawn area:[tex]A=\frac{base_{1} +base_{2} }{2} *h\\\\A=(base_{1} +base_{2} ) *h *\frac{1}{2} \\\\A=(70ft + 130ft) * 50ft *\frac{1}{2} \\\\A=5000ft^{2}[/tex]
how many bags of fertilizer we need?each bag covers 3000 ft²
[tex]N_{number of bags} = 5000ft^{2} / 3000ft^{2} \\\\N_{number of bags} = 1.6[/tex]
We need to purchase two bags fertilizer, but will use one and a half of them.
Have a good day.
CNNBC recently reported that the mean annual cost of auto insurance is 1048 dollars. Assume the standard deviation is 282 dollars. You take a simple random sample of 55 auto insurance policies. Find the probability that a sample of size n =55 is randomly selected with a mean less than 997 dollars.
Answer: 0.0899.
Step-by-step explanation:
Given: CNNBC recently reported that the mean annual cost of auto insurance is 1048 dollars, the standard deviation is 282 dollars.
Sample size : n= 55
Let [tex]\overline{X}[/tex] be the sample mean.
The probability that a sample of size n =55 is randomly selected with a mean less than 997 dollars:
[tex]P(\overline{X}<997)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{997-1048}{\dfrac{282}{\sqrt{55}}})[/tex]
[tex]=P(Z<-1.3412)\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(Z<1.3412)\\\\=1-0.9101\ \ \ \ [\text{By z-table}]\\\\ =0.0899[/tex]
Hence, the required probability = 0.0899 .
pls pls help i will mark brainliest to whoever can answer it for me.
Answer:
The lateral surface is 120 [tex]in^2[/tex], which agrees with the third answer option of the list.
Step-by-step explanation:
Notice that the prism has 5 equal lateral faces, which are all rectangles of eight 6". The width of the prisms can be obtained by using the fact that the perimeter of the pentagon is 20", which gives a side length of 20/5 = 4 " which is the same as the with of the lateral rectangles.
Then the lateral area of the prism is:
Lateral area= 5 (6" x 4") = 5 (24) = 120 [tex]in^2[/tex]
At a deli counter, there are sandwiches with meat and vegetarian sandwiches. Kira is at the counter buying sandwiches for a picnic. In how many ways can she choose sandwiches if fewer than must be vegetarian sandwiches
Answer:
The number ways to choose between meat and vegetarian sandwiches can be computed using computation technique.
Step-by-step explanation:
There are two types of sandwiches available at the deli counter. The possibility of combinations can be found by computation technique of statistic. It is assumed that order does not matter and sandwiches will be selected at random. The sandwiches can be arranged in any order and number ways can be found by 2Cn.
Assuming that ten (10) candidates are presented in a random order, what is the probability that hire exactly one candidate
Answer:
The probability that only one candidate is hired is 0.10.
Step-by-step explanation:
The probability of event E occurring is the ration of the favorable number of outcomes to the total number of outcomes.
[tex]P(E)=\frac{n(E)}{N}[/tex]
It is provided that N = 10 candidates are presented in a random order.
Compute the probability that only one candidate is hired as follows:
[tex]P(\text{Only 1 Hire})=\frac{1}{10}=0.10[/tex]
Thus, the probability that only one candidate is hired is 0.10.
Solve |y + 2| > 6 im so confused
Answer:
Below
Step-by-step explanation:
● |y+2| > 6
● y+2 > 6 or y+2 < -6
Add -2 in both sides in the two inequality.
● y+2-2 > 6-2 or y+2-2 < -6-2
● y > 4 or y< -8
Paul is saving for a down payment to buy a house. The account earns 13% interest compound quarterly, and he wants to have $15,000 in 4 years. What must his principal be? Round your answer to the nearest cent. Do not round at any point in solving process; only round your answer. Please help ASAP!! Thank you so much!
Answer:
The principal must be = $8991.88
Step-by-step explanation:
Formula for compound interest is:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where A is the amount after 't' years.
P is the principal amount
n is the number of times interest is compounded each year.
r is the rate of interest.
Here, we are given that:
Amount, A = $15000
Rate of interest = 13 % compounded quarterly i.e. 4 times every year
Number of times, interest is compounded each year, n = 4
Time, t = 4 years.
To find, Principal P = ?
Putting all the given values in the formula to find P.
[tex]15000 = P(1 + \frac{13}{400})^{4\times 4}\\\Rightarrow 15000 = P(1 + 0.0325)^{16}\\\Rightarrow 15000 = P(1.0325)^{16} \\\Rightarrow 15000 = P \times 1.66817253\\\Rightarrow P = \dfrac{15000}{1.66817253}\\\Rightarrow P \approx \$8991.88[/tex]
So, the principal must be = $8991.88
The principal required is $ 8993.
Using the formula;
A = P(1 + r/n)^nt
Where;
P = principal = ?
r = rate = 0.13
n = Number of times the interest is compounded = 4
t = time = 4years
Amount = $15,000
15,000 = P(1 + 0.13/4)^4(4)
15,000 = P(1.668)
P = 15,000/1.668
P =$ 8993
Learn more: https://brainly.com/question/7558603
If x-2y=10 and y is three times the value of x, What is the value of x-y? a) -8 b) -4 c) 0 d) 2 e)4
Answer:
a) 4
Step-by-step explanation:
y = 3x
Plug it in: x - 2 (3x) = 10 --> x - 6x = 10 --> -5x = 10 --> x = -2
Therefore: y = 3(-2) --> y = -6
x - y = -2 - (-6) = 4
An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:
418 421 422 422 425 429 431 434 437
439 446 447 449 452 457 461 465
Calculate a two-sided 95% confidence interval for true average degree of polymerization.
Answer:
The 95% confidence interval for true average degree of polymerization is (431, 446).
Step-by-step explanation:
The data provided for the degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range is:
S = {418, 421, 422, 422, 425, 429, 431, 434, 437, 439, 446, 447, 449, 452, 457, 461, 465}
Compute the sample mean and sample standard deviation:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{7}\times 7455=438.5294\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{17-1}\times 3594.2353}=14.988[/tex]
As the population standard deviation is not provided use the t-statistic to compute the two-sided 95% confidence interval for true average degree of polymerization.
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\frac{s}{\sqrt{n}}[/tex]
The critical value of the t is:
[tex]t_{\alpha /2, (n-1)}=t_{0.05/2, (17-1)}=t_{0.025, 16}=2.12[/tex]
*Use a t-table.
Compute the 95% confidence interval for true average as follows:
[tex]CI=438.5294\pm 2.12\cdot\frac{14.988}{\sqrt{17}}[/tex]
[tex]=438.5294\pm 7.7065\\=(430.8229, 446.2359)\\\approx (431, 446)[/tex]
Thus, the 95% confidence interval for true average degree of polymerization is (431, 446).
Consider this quote: "In a recent survey, 65 out of 100 consumers reported that they preferred plastic bags instead of paper bags for their groceries. If there is no difference in the proportions who prefer each type in the population, the chance of such extreme results in a sample of this size is about .03. Because .03 is less than .05, we can conclude that there is a statistically significant difference in preference." Give a numerical value for each of the following.
a. The p-value.
b. The level of significance, α.
c. The sample proportion.
d. The sample size.
e. The null value.
Answer:
Step-by-step explanation:
The p value (probability of obtaining results as extreme the z score if null is true) is usually the value derived to make a conclusion and in this case the p value is 0.03
The level of significance is the value usually compared with the p value which is 0.05
The sample promotion is 65 out of 100 = 65/100 = 0.65
The sample size is the total number of consumers which is 100
The null value is usually the default value. The null value would assume that there is no difference in the proportions who prefer each type in the population. There are two preferences: 100/2 = 50- 0.5 for each preference.
need help thaanlksss
Answer:
Option (3). [tex]m(\widehat{ACB})=220[/tex]
Step-by-step explanation:
Option (1).
Since measure of an inscribed angle = [tex]\frac{1}{2}(\text{measure of the intercepted arc})[/tex]
m∠ABC = [tex]\frac{1}{2}m(\widehat{AC})[/tex]
[tex]m(\widehat{AC})[/tex] = 2(m∠ABC)
= 2(30°)
= 60°
Therefore, this option is not true.
Option (2),
Since, [tex]m(\widehat{AB})+m(\widehat{BC})+m(\widehat{AC})=360[/tex]
[tex]m(\widehat{AB})+160+60=360[/tex]
m(arc AB) = 360 - 220
= 140°
Therefore, this option is not correct.
Option (3),
[tex]m(\widehat{ACB})=m(\widehat{AC})+m(\widehat{BC})[/tex]
= 60° + 160°
= 220°
Option (3) is the correct option.
Option (4),
[tex]m(\widehat{CBA})= 360-m(\widehat{AC})[/tex]
= 360° - 60°
= 300°
Therefore, this option is not correct.
plzzzzz helpp j + 9 - 3 < 8
Answer:
j < 2
Step-by-step explanation:
Simplify both sides of the inequality and isolating the variable would get you the answer
6th grade math help me, please:)))
Step-by-step explanation:
Hi there!!!
The answer is option A.
reason look in picture.
if you want to solve it just cross multiply it,
[tex]60x = 240000 \times 100[/tex]
or,
[tex]x = 24000000 \div 60[/tex]
and the answer would be 400000.
Hope it helps...
A restaurant gat an average of 14 calls in a 2 hr time period. What is the probability that at most 2 calls in 45 min period
Answer:
0.10512
Step-by-step explanation:
Given the following :
Mean number of calls(μ) in 2 hours = 14
2 hours = 60 * 2 = 120 minutes
Average number of calls in 45 minutes :
= (45 / 120) * 14
= 0.375 * 14
= 5.25
Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)
Using the poisson probability formula:
P(x, μ) = [(e^-μ) * (μ^x)] / x!
Where :
e = euler's constant
μ = 5.25
x = 0, 1, 2
Using the online poisson probability calculator :
P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)
P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512
j/2 +7=-12 solve for j
Answer:
j/2+7= -12
(j+14)/2= -12
cross-multiply
j+14= -24
j= -38
Answer:
[tex]\boxed{j=-38}[/tex]
Step-by-step explanation:
[tex]\frac{j}{2} +7=-12[/tex]
Subtract 7 on both sides.
[tex]\frac{j}{2} +7-7=-12-7[/tex]
[tex]\frac{j}{2}=-19[/tex]
Multiply both sides by 2.
[tex]\frac{j}{2}(2)=-19(2)[/tex]
[tex]j=-38[/tex]
a patient is to receive 1500ml over 8 hours. What is the rate in ml per hour?
Answer
187.5 ml/hr
Step-by-step explanation:
1500ml/8hrs=187.5ml/hr
Square root of one million
Answer:
The square root of one million is 1000 because 1000 x 1000 = 1,000,000
pls guys help me pls :c
Answer: A. [tex]x\geq21\dfrac{2}{3}[/tex] .
Step-by-step explanation:
The given inequation: [tex]81-1\dfrac{1}{5}x\leq55[/tex]
[tex]\Rightarrow\ 81-\dfrac{6}{5}x\leq55[/tex]
Multiplying 5 on both the sides, we get
[tex]5(81-\dfrac{6}{5}x)\leq5\times55\\\\\Rightarrow\ 405-6x\leq275\\\\\Rightarrow\ 6x\geq405-275\\\\\Rightarrow\ 6x\geq130\\\\\Rightarrow\ x\geq\dfrac{130}{6}\\\\\Rightarrow\ x\geq\dfrac{65}{3}\\\\\Rightarrow\ x\geq21\dfrac{2}{3}[/tex]
Hence, the inequality for x is [tex]x\geq21\dfrac{2}{3}[/tex] .
So, the correct option is A. [tex]x\geq21\dfrac{2}{3}[/tex] ..
If one termite can destroy 1.2mg of wood per day, how many kilograms of wood can 10 termites destroy in 1 week? *Can someone please explain how to do this*
Answer:
10 termites will destroy 0.000084kg of wood per week
Step-by-step explanation:
Convert milligram to kilogram
1.2mg=(1.2 / 1,000,000)kg
1.2mg=0.0000012kg
1 termite destroys=0.0000012kg per day
10 termites will destroy (per day) =0.0000012×10 termites per day
10 termites in one day will destroy=0.000012kg
There are 7 days in a week
Therefore,
10 termites will destroy=destruction per day × 7 days
=0.000012×7
=0.000084kg per week
A process on a machine has a standard deviation of 0.04 inches. If a product with specifications of +/- 0.07 inches has to be processed on that machine, is the machine capable of performing that job? Group of answer choices
Answer:
c.) No, because Cp < 1
Step-by-step explanation:
Let us assume that there is centered in the process
and, the width is 2 times the specification
So, the width is
[tex]= 2 \times 0.07[/tex]
= 0.14
Now capability index = Cp is
[tex]= \frac{specification\ width}{6 \times standard\ deviation}\\\\= \frac{0.14}{6\times 0.04}[/tex]
= 0.58333
And the capability index should be minimum 1 for the process
And as we can see that Cp is 0.58333 which is less than 1 so the machine is not able to perform the job
Hene, the correct option is c.
Identify the factors of x2 − 4x − 12.
(x + 4)(x − 3)
(x − 4)(x + 3)
(x − 2)(x + 6)
(x + 2)(x − 6)
Answer:
(x + 2)(x - 6)
Step-by-step explanation:
We are given the equation: x² - 4x - 12. Let's factor this.
First, look at the integer factor pairs of -12:
-1, 12
-2, 6
-3, 4
1, -12
2, -6
3, -4
We would like to find a pair whose sum is -4. Inspecting each pair, we realise that only the pair 2, -6 works because 2 + (-6) = -4.
Thus, our factors are:
x + 2 (from the 2)
x - 6 (from the -6)
The factored form of our given quadratic is:
(x + 2)(x - 6)
~ an aesthetics lover
A random sample of 144 observations produced a sample proportion of 0.4. An approximate 90% confidence interval for the population proportion p is between:_______
a) 0.320 and 0.480
b) 0.333 and 0.480
c) 0.333 and 0.467
d) 0.359 and 0.441
e) 0.313 and 0.487
Answer:
CI =(0.333, 0.480)
Step-by-step explanation:
The formula for calculating the confidence interval is expressed as shown;
CI = p±Z * √p(1-p)/n±0.5/n
Z is the z-score at 90% confidence
p is the sample proportion
n is the sample size
Given n = 144, p = 0.4 and z-score at 90% CI = 1.645 (from z table)
Substituting this values;
CI = p ± 1.645*√0.4(1-0.4)/144 ±0.5/n
CI = 0.4 ± 1.645*√0.4(0.6)/144 ± 0.5/144
CI = 0.4 ±1.645 * √0.24/144 ± 0.00347
CI = 0.4 ±1.645 * 0.04087± 0.00347
CI = 0.4±0.06723±0.00347
CI =(0.333, 0.480)
In 2015, the CDC analyzed whether American adults were eating enough fruits and vegetables. Let the mean cups of vegetables adults eat in a day be μ. If the CDC wanted to know if adults were eating, on average, more than the recommended 2 cups of vegetables a day, what are the null and alternative hypothesis? Select the correct answer below: H0: μ=2; Ha: μ>2 H0: μ>2; Ha: μ=2 H0: μ=2; Ha: μ<2 H0: μ=2; Ha: μ≠2
Answer:
H0: μ=2; Ha: μ>2
Step-by-step explanation:
The null hypothesis is the default hypothesis while the alternative hypothesis is the opposite of the null and is always tested against the null hypothesis.
In this case study, the null hypothesis is that adults were eating, on average, the recommended 2 cups of vegetables a day: H0: μ=2 while the alternative hypothesis is adults were eating, on average, more than the recommended 2 cups of vegetables a day Ha: μ>2.
Exhibit 2-4A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. Undergraduate Major Graduate SchoolBusinessEngineeringOtherTotal Yes 35 42 63140 No 91104 65260 Total126146128400Among the students who plan to go to graduate school, what percentage indicated "Other" majors
Answer:
The percentage of college seniors with "Other" majors is 32%.
Step-by-step explanation:
The total number of college seniors surveyed is, N = 400.
The number of college seniors with "Other" majors is, n = 128.
The percentage of a value of x from N total is given as follows:
[tex]\text{Percentage of}\ x=\frac{x}{N}\times 100\%[/tex]
Compute the percentage of college seniors with "Other" majors as follows:
[tex]\text{Others}\%=\frac{n}{N}\times 100\%[/tex]
[tex]=\frac{128}{400}\times 100\%\\\\=32\%[/tex]
Thus, the percentage of college seniors with "Other" majors is 32%.
What is the slope of the line x = 4?
Answer:
slope is undefined
Step-by-step explanation:
x = 4 is the equation of a vertical line parallel to the y- axis.
The slope of a vertical line is undefined
Answer:
Undefined
Step-by-step explanation:
If the line is strait up like x = 4 that means it is undefined.