Answer:
[tex]y=\frac{(-\frac{4}{x}+1)^2-3 }{4}[/tex]
Step-by-step explanation:
We are given the following information. y have the point [tex](-2,\frac{3}{2} )[/tex] and [tex]\frac{dy}{dx} =\frac{\sqrt{4y+3} }{x^2}[/tex]
First, we need to separate the variables to their respective sides
[tex]\frac{1}{\sqrt{4y+3} } dy=\frac{1}{x^2} dx[/tex]
Now, we need to integrate each side
[tex]\int \frac{1}{\sqrt{4y+3} } dy=\int\frac{1}{x^2} dx[/tex]
But first, let us rewrite these functions
[tex]\int (4y+3)^{-\frac{1}{2} } dy=\int x^{-2} dx[/tex]
Before we can integrate, we need to have the hook for the first function. When we integrate [tex](4y+3)^{-\frac{1}{2} }[/tex], we must have a lone 4 within the integral as well.
[tex]\frac{1}{4} \int4 (4y+3)^{-\frac{1}{2} } dy=\int x^{-2} dx[/tex]
Now we can integrate each side to get
[tex]\frac{1}{4} \sqrt{4y+3} =-\frac{1}{x} + c[/tex]
Now is the best time to use the given point in order to find the value of c.
[tex]\frac{1}{4} \sqrt{4(\frac{3}{2}) +3} =-\frac{1}{-2} + c\\\\\frac{1}{4}\sqrt{6+3} =\frac{1}{2} +c \\\\\frac{3}{4}=\frac{1}{2} +c\\ \\c=\frac{1}{4}[/tex]
Now we can plug in our value for c and then solve for y
[tex]\frac{1}{4} \sqrt{4y+3} =-\frac{1}{x} + \frac{1}{4} \\\\\sqrt{4y+3}=-\frac{4}{x} +1\\ \\4y+3=(-\frac{4}{x} +1)^2\\\\4y=(-\frac{4}{x} +1)^2-3\\\\y=\frac{(-\frac{4}{x} +1)^2-3}{4}[/tex]
which is composite number?
Answer:
A whole number that can be made by multiplying other whole numbers.
Example: 18 can be made by 3 × 6 so is a composite number.
16 can be made by 4 x 4 so it is a square root and a composite number
14 can be made by 2 x 7 so is is a composite number.
It is not a prime number as all Composite Number have factors other than 1 and itself). The first few composite numbers (sometimes called "composites" for short) are 4, 6, 8, 9, 10, 12, 14, 15, 16,
Answer:
We need to examine the natural numbers.
The natural numbers are the counting numbers,
1, 2, 3, 4, 5, 6, ...
The number 1 is neither prime nor composite.
All natural numbers greater than 1 are either prime or composite.
A prime number is a number that has exactly two factors, itself and 1.
A composite number has more than 2 factors.
A composite number is a natural number greater than 2 that is not a prime number.
Examples:
Prime: 2, 3, 5, 7, 11, ...
Composite: 4, 6, 8, 9, 10, 12, ...
tan 12 = 22/x
Please help !!! Last answer says 4.7
Answer:
103.5
Step-by-step explanation:
Multiply x on both sides
xtan12 = 22
Now divide tan12 to isolate x
x = (22) / (tan(12))
Now we know that calculator should be in degree mode because the answer choices do not have the radian mode answer. When your calculator is in Degree mode and you calculate this value you get approximately 103.5
The value of x if tan 12 = 22/x is 103.5
Given the trigonometric expression:
tan 12 = 22/x
We need to get the value of "x"
Cross multiply
x tan12 = 22
x = 22/tan12
x = 22/0.2126
x = 103.529
Hence the value of x if tan 12 = 22/x is 103.5
Learn more here: https://brainly.com/question/25618616
I wanted to compare my 5 hamsters’ average intelligence to see if they are different from the average intelligence of the 6 hamsters of another faculty member at a different university. Assume α = .01, then the cutoff for my hypothesis testing is ______.
Answer:
Step-by-step explanation:
The test to use is the t-test of independent means.
To determine the cutoff for the study then you need to find the degree of freedom and the alpha level. After the hypothesis testing, the calculated t value is then compared to the critical t value from the t distribution table using the degrees of freedom.
A powerful computer is purchased for $2000, but loses 20% of its value each year. How much will it be worth 4 years from now?
a. Growth or Decay?
b. What is your multiplier?
c. Is $2000 your zero term or first term? term
d. Write the equation. (do not use spaces in your response; example: f(x)=10.2(1.22)^x )
e. Solve
Answer:
(A)Decay
(b)0.8
(c)First Term
(d)[tex]f(t)=2000(0.8)^t[/tex]
(e)$819.20
Step-by-step explanation:
The exponential function for modelling growth or decay is given as:
[tex]A(t)=A_o(1\pm r)^t[/tex],
Where:
Plus indicates growth and minus indicates decay.
[tex]A_o$ is the Initial Value\\r is the growth/decay rate\\t is the time period[/tex]
For a powerful computer that was purchased for $2000, but loses 20% of its value each year.
(a)Since it loses value, it is a decay.
(b)Multiplier
Its value decays by 20%.
Therefore, our multiplier(1-r) =(1-20&)=1-0.2
Multiplier =0.8
(c)$2000 is our First term (or Initial Value [tex]A_o[/tex])
(d)The function for this problem is therefore:
[tex]f(t)=f_o(1- r)^t\\f(t)=2000(1- 0.2)^t\\\\f(t)=2000(0.8)^t[/tex]
(e)Since we require the worth of the computer after 4 years,
t=4 years
[tex]f(4)=2000(0.8)^4\\f(4)=\$819.20[/tex]
I need the answers for 21 and 22
Answer:
21.b
22.c
Step-by-step explanation:
idk how to explain it lol I did mental math
A recent research show that only 40% of the customers are willing to pay more for the service. Now we have selected 10 customers randomly. What are the expected value and standard deviation
Answer:
The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they are willing to pay more for the service, or they are not. Customers are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
40% of the customers are willing to pay more for the service.
This means that [tex]p = 0.4[/tex]
Now we have selected 10 customers randomly.
This means that [tex]n = 10[/tex]
What are the expected value and standard deviation
[tex]E(X) = np = 10*0.4 = 4[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.4*0.6} = 1.55[/tex]
The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.
Find the percent of decrease from $2.00 to $1.25
Answer:
37.5
Step-by-step explanation:z
2.0-1.25=0.75
0.75/2.00 x 100
37.5% decrease
what is the solution set for the equation (x+3)(x-8)=0
Answer:
x = -3 x=8
Step-by-step explanation:
(x+3)(x-8)=0
Using the zero product property
x+3 =0 x -8 = 0
x = -3 x=8
I need help with all three :(
Answer:
1: Glide
2: Reflection
3: Reflection
Step-by-step explanation:
1): The first one is glide because you are just moving the triangle and not changing anything to the angle and the size.
2): The second one is a reflection because you are reflecting across an invisable line. Basicly think of it as a mirror. In the picture below, you can see the line of reflection.
3): The third one is also a reflection for the same reason as the second, (view attached image below for line of reflection.
A bank wants to attract new customers for its credit card. The bank tries two different approaches in the marketing campaign. The first promises a cash back reward; the second promises low interest rates. A sample of 500 people is called the first brochure; of these, 100 get the credit card. A separate sample of 500 people is called the second brochure; 125 get the credit card. The bank wants to know if the two campaigns are equally attractive to customers. What is a 95% confidence interval for the difference in the two proportions
Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the first brochure,
x = 100
n1 = 500
p1 = 100/500 = 0.2
For the second brochure
x = 125
n2 = 500
p2 = 125/500 = 0.25
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, the z score for confidence level of 95% is 1.96
Margin of error = 1.96 × √[0.2(1 - 0.2)/500 + 0.25(1 - 0.25)/500]
= 1.96 × √0.000695
= 0.052
Confidence interval = (0.2 - 0.25) ± 0.052
= - 0.05 ± 0.052
What is the value of d21+d22+d23 given the matrix equation below?
Answer:
B. 8
Step-by-step explanation:
The question lacks the required diagram. Find the diagram in the attachment.
Before we can find d21, d22 and d23, we need to get the matrix D first as shown in the attached solution.
On comparison as shown in the attachment, d21 = 11, d22 = -10 and d23 = 7
Note that d21 refers to element in the second row and first column of the matrix
d22 is the element in the second row and second column of the matrix
d23 is the element in the second row and third column of the matrix
d21+d22+d23 = 11-10+7
d21+d22+d23 = 8
The second option is correct.
In order to understand reasons why consumers visit their store, a local business conducts a survey by asking the next 100 people who visit their store to fill out a short survey. The business finds that 40 of the 100 people state that the main reason they visited the store was because the store is running a sale on coats that week. A confidence interval is constructed for the population proportion of consumers who would visit the store because of the coat sale. Which confidence interval would be the narrowest?
a. 90%
b. 99%
c. 95%
d. 85%
Answer:
d. 85%
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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The higher the confidence level, the higher the value of z, which means that the margin of error will be higher and the interval will be wider,
Which confidence interval would be the narrowest?
The one with the lowest confidence level. So the answer is d.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
G(x) = x^2 -10x +25
Step-by-step explanation:
To translate F(x) 5 units to the right, replace x with (x-5).
G(x) = F(x-5) = (x -5)^2
G(x) = x^2 -10x +25
Q 4.19: To verify whether there are negative consequences of taking a new type of medicine, 3000 tests were conducted. Assume that the null hypothesis is that the new medicine has no negative effects and the alternative hypothesis is that the new medicine is potentially harmful. 31 of these tests gave significant results at a 1% significance level. What can we say about the potential harmfulness of the new medicine
Answer:
The p-value obtained is less than the significance level at which the test was performed at, hence, we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the the new medicine is potentially harmful.
Step-by-step explanation:
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, the null hypothesis is that the new medicine has no negative effects and the alternative hypothesis is that the new medicine is potentially harmful
Mathematically,
The null hypothesis is represented as
H₀: p = 0
The alternative hypothesis is represented as
Hₐ: p > 0
To do this test, we will use the z-distribution because although no information on the population standard deviation is known, the sample size is large enough.
So, we compute the test statistic
z = (x - μ)/σₓ
x = sample proportion = (31/3000) = 0.0103
μ = p₀ = 0
σₓ = standard error = √[p(1-p)/n]
where n = Sample size = 3000
σₓ = √[0.0103×0.9897/3000] = 0.0018462936 = 0.0018463
z = (0.0103 - 0) ÷ 0.0018463
z = 5.60
checking the tables for the p-value of this test statistic
Significance level = 1% = 0.01
The hypothesis test uses a one-tailed condition because we're testing only in one direction.
p-value (for z = 5.60, at 0.01 significance level, with a one tailed condition) = < 0.00001
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.01
p-value = < 0.00001
p-value < 0.00001 < 0.10
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the the new medicine is potentially harmful.
Hope this Helps!!!
A hot dog has about 1/4 the amount of protein as 3 ounces of hamburger. Together, they have about 25 grams of protein. How many grams of protein are in a 3 oz hamburger?
Answer:
(1) protein in hot dog = ¼ * protein in 3 ounces of hamburger
(2) protein in hot dog + protein in 3 ounces of hamburger = 25
So we need to re-arrange (1) and (2) to solve for the protein in 3 ounces of hamburger!
(re-arrange (1)): 4 * protein in hot dog = protein in 3 ounces of hamburger
(re-arrange (2)): protein in hot dog = 25 - protein in 3 ounces of hamburger
(plugging re-arranged (2) into re-arranged (1)):
4 * (25 - protein in 3 ounces of hamburger) = protein in 3 ounces of hamburger ( multiplying )
100- 4 protein in 3 ounces of hamburger = protein in 3 ounces of hamburger
solving for the protein in 3 ounces of hamburger:
5 * protein in 3 ounces of hamburger = 100
protein in 3 ounces of hamburger = 20 gram
The box plots represent the birth weights, in pounds, of
babies born full term at a hospital during one week.
Female Birth Weight
Complete the statements to compare the weights of
female babies with the weights of male babies.
The median female birth weight is
the
median male birth weight.
The range of female birth weight is
the
range of male birth weight.
Which birth weight measure is the same for both
genders?
5
6
7
8
9
10
11
Male Birth Weight
Answer:
Step-by-step explanation:
The median female *less than*
The range of female*less than*
Which birth weight:*minimum*
Answer:
The median female birth weight is
✔ less than
the median male birth weight.
The range of female birth weight is
✔ less than
the range of male birth weight.
Which birth weight measure is the same for both genders?
✔ minimum
Plz help me :(
Prove for any value of y the value of expression y^4−(y^2−9)(y^2+9) is divisible by 9.
PROOF:
[tex]y^4-(y^2-9)(y^2+9)\\=y^4 -(y^4-81)\\=y^4-y^4+81\\=81[/tex]
And 81 is ALWAYS divisible by 9
Answer:
Its 9*9
Step-by-step explanation:
The equation equals 81 and 9*9=81.
Have a great day! :)
Akmal, Bakri and Cadin share their mother medical expenses which cost RM4200. Cadin pays RM2100 while akmal pays three quarters of Bakri amount. Find the ratio of the expenses shared by Akmal to Bakri to Cadin
Answer:
The ratio of the expenses shared by Akmal to Bakri to Cadin is 7 : 4 : 3
Step-by-step explanation:
The 3 of them shares their mother medical expenses which cost RM4200 . There mother medical expenses is RM4200 in total. Cadin pays RM2100 which is half of their mother medical expenses. Then Akmal pays three quarters of Bakri amount.
Let
The amount Bakri pays = a
Akmal pays = 3/4 of a
Akmal pays = 3/4a
Therefore,
a + 3a/4 = 2100
4a + 3a/ 4 = 2100
7a/4 = 2100
cross multiply
7a = 8400
divide both sides by 7
a = 8400/7
a = 1200
Therefore,
Bakri pays =RM 1200
Akmal pays = 3/4 × 1200 =RM 900
The ratio of the expenses shared by AKmal to Bakri to Cadin is expressed as 2100 : 1200 : 900. Divide through by 300
7 : 4 : 3
Which value of k makes 5-k+12=16 a true statement? Choose 1 answer: Choice A) k=1 (Choice B) k=2 (Choice C) k=3 (Choice D) k=4
Answer:
A) k=1
Step-by-step explanation:
5-k+12=16
17-k=16
k=1
Answer:
k=1
Step-by-step explanation:
5-k+12=16
Combine like terms
17 - k = 16
Subtract 17 from each side
17-k-17 = 16-17
-k = -1
Divide by -1
k = 1
how many significant numbers in 34.6209
Answer:
6
Step-by-step explanation:
What is the value of x?
Answer:
x= 70
Step-by-step explanation:
These are supplementary angles
45+2x-5 = 180
Combine like terms
40+2x= 180
Subtract 40 from each side
40+2x-40 =180-40
2x= 140
Divide by 2
2x/2 =140/2
x = 70
What is the solution set up 7x^2+3X=0
Answer:
X=0,X=-3/7
Step-by-step explanation:
7x^2+3x=0
x(7x+3)=0
x=0
7x+3=0
7x=-3
x=-3/7.
Answer:-3/7
Step-by-step explanation:
Firstly add -3x to both sides of equation. 7x^2+3x-3x=0+-3x
7x^2=-3x
Divid both sides by X
7x^2/X=-3/X
7x=-3
Divid both sides by 7
7x/7=-3/7
X=-3/7
Fifteen different Thursday evening programs reported that a commercial cost an average of $169,000 with a standard deviation of $81,000. What is the 95% confidence interval for the true mean
Answer:
The 95% confidence interval for the true mean is between $0 and $342,729
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
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 = 15 - 1 = 14
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448
The margin of error is:
M = T*s = 2.1448*81000 = 173,729.
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 169,000 - 173,729 = -4,... = $0(cannot be negative)
The upper end of the interval is the sample mean added to M. So it is 169,000 + 173,729 = $342,729
The 95% confidence interval for the true mean is between $0 and $342,729
The table below shows the number of e-mails received each day by a company employee for two separate weeks. If the data were represented with a comparative dot plot, which day would have more dots for week 2 than week 1
Answer:
C
Step-by-step explanation:
Hope this helps
Answer:
C
Step-by-step explanation:
Wednesday hope this helps!
a pail holds 3 1/2 gallons of water. How much is it in cups
Answer:
3 1/2 gallons of water is 56 cups
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
1 gallon=4cups
1/2 gallon=2cups
3*4=12
or 4cups+4cups+4cups=12
12+2=14
If this rectangle is dilated using a scale factor of One-half through point B, what is the result? Point B is the bottom left corner of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and point B is at the bottom left corner. Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X and is outside of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and is outside of rectangle X.
Answer:
the first one
Step-by-step explanation:
I just took it on edge.
Answer:
It is B just took the unit quiz
Step-by-step explanation:
ps help me with this its urgent❤
Use the properties of exponents to simplify the expression. (photo attached)
Answer:
y^6/x^2
Step-by-step explanation:
(y^3/2x^-1/2)^4= y^(4*3/2)x^(-1/2*4)=y^6x^-2= y^6/x^2
Please answer this correctly
Answer:
538
Step-by-step explanation:
l x w
7x39
12x20
5x5
538
A cell phone company is offering 2 different monthly plans. Each plan charges a monthly fee plus an additional cost per minute. Plan A: $ 40 fee plus $0.45 per minute Plan B: $70 fee plus $0.35 per minute a) Write an equation to represent the cost of Plan A b) Write an equation to represent the cost of Plan B c) Which plan would be least expensive for a total of 100 minutes?
*Please Show Work*
Answer:
Plan A would be the least expensive
Step-by-step explanation:
Plan A= $0.45x100= 45, 45+40=$85
Plan B= $0.35x100= 35, 35+70= %105
(Each plan is for 100 minutes)
what is 2n+3n +1 +8n+4
Answer:
13n + 5
Step-by-step explanation:
2+3+8 = 13n
1+4 = 5
13n+5