Answer:
6/x^2
Step-by-step explanation:
6x^-2
6*x^-2
6*(1/x^2)
6/x^2
Someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi. We think the actual amount is lower than that and want to run the test at an alpha level of 5%. What would our sample size need to be if we want to reject the null hypothesis if the sample mean is at or below 1,997.2956?
Answer:
The sample size must be greater than 37 if we want to reject the null hypothesis.
Step-by-step explanation:
We are given that someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi.
Also, we are given a level of significance of 5%.
Let [tex]\mu[/tex] = mean breaking strength of their climbing rope
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 2,000 psi {means that the mean breaking strength of their climbing rope is 2,000 psi}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 2,000 psi {means that the mean breaking strength of their climbing rope is lower than 2,000 psi}
Now, the test statistics that we will use here is One-sample z-test statistics as we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = ample mean strength = 1,997.2956 psi
[tex]\sigma[/tex] = population standard devaition = 10 psi
n = sample size
Now, at the 5% level of significance, the z table gives a critical value of -1.645 for the left-tailed test.
So, to reject our null hypothesis our test statistics must be less than -1.645 as only then we have sufficient evidence to reject our null hypothesis.
SO, T.S. < -1.645 {then reject null hypothesis}
[tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < -1.645[/tex]
[tex]\frac{1,997.2956-2,000}{\frac{10}{\sqrt{n} } } < -1.645[/tex]
[tex](\frac{1,997.2956-2,000}{10}) \times {\sqrt{n} } } < -1.645[/tex]
[tex]-0.27044 \times \sqrt{n}< -1.645[/tex]
[tex]\sqrt{n}> \frac{-1.645}{-0.27044}[/tex]
[tex]\sqrt{n}>6.083[/tex]
n > 36.99 ≈ 37.
SO, the sample size must be greater than 37 if we want to reject the null hypothesis.
A thermometer shows a temperature of Negative 20 and three-fourths degrees. A chemist recorded this temperature in her notebook using a decimal. Which number did the chemist write in the notebook?
Answer:
20.75
Step-by-step explanation:
Answer:
C. -20.75
Step-by-step explanation:
Section 1: Write the following times in 24-hour clock time:
a) 7:15 a.m -
b) 1:05 am
c) 2:01 p.m
d) 9:22 p.m
e) 12:25 am
Section 2: Write the following times in 12-hour clock time.
a) 1155 hours
b) 1005 hours
c) 1714 hours
d) 0756 hours
e) 1345 hours
Answer:
Section 1:
a) 7:15 a.m - 19:15
b) 1:05 am - 01:05
c) 2:01 p.m - 14:01
d) 9:22 p.m - 21:22
e) 12:25 am- 24:25
Section 2:
a) 1155 hours - 11:55am
b) 1005 hours -10:05am
c) 1714 hours - 5:14pm
d) 0756 hours - 7:56am
e) 1345 hours- 1:45pm
Answer:
12:25 am= 00:25
Step-by-step explanation:
A solid lies between planes perpendicular to the x-axis at xequals=0 and xequals=1212. The cross-sections perpendicular to the axis on the interval 0less than or equals≤xless than or equals≤1212 are squares with diagonals that run from the parabola y equals negative 2 StartRoot x EndRooty=−2x to the parabola y equals 2 StartRoot x EndRooty=2x. Find the volume of the solid.
Question:
A solid lies between planes perpendicular to the x-axis at x=0 and x=12. The cross-sections perpendicular to the axis on the interval 0≤x≤12 are squares with diagonals that run from the parabola y=-2√x to the parabola y=2√x. Find the volume of the solid.
Answer:
576
Step-by-step explanation:
Given:
Length of diagonal square:
[tex] D = 2\sqrt{x} - (-2\sqrt{x}) [/tex]
[tex] D = 4\sqrt{x} [/tex]
Here, the diagonal is the hypotenus of a right angle triangle, with leg S, where the square has a side of length S.
Using Pythagoras theorem:
[tex] S^2 + S^2 = D^2 [/tex]
[tex] S^2 + S^2 = (4\sqrt{x})^2 [/tex]
[tex] 2S^2 = 16x [/tex]
Divide both sides by 2
[tex] S^2 = 8x [/tex]
Thus,
Area, A = S² = 8x
Take differential volume, dx =
dV = Axdx
dV = 8xdx
Where limit of solid= 0≤x≤12
Volume of solid, V:
V =∫₀¹² dV
V = 8 ∫₀¹² xdx
V = [4x²]₀¹²
V = 4 (12)²
V = 12 * 144
= 576
Volume of solid = 576
If 9x+2y^2−3z^2=132 and 9y−2y^2+3z^2=867, then x+y =
Answer:
[tex]x + y = \frac{1000}{9}[/tex]
Step-by-step explanation:
Step 1: Identify the approach:
With this problem, the general solution is to try manipulate given data and transform data into a new form, in which, the desired value [tex](x + y)[/tex] is on the left side and all of other components which do not contain [tex]x[/tex] or [tex]y[/tex] are on the right side.
Step 2: Analyze:
[tex]9x + 2y^{2} - 3z^{2} = 132\\9y - 2y^{2} + 3z^{2} = 867[/tex]
Realize that in both equations, the [tex]2y^{2}[/tex] and [tex]3z^{2}[/tex] are in form of different signs. Then adding up corresponding sides of both equation can help eliminate these undesired components.
Step 3: Perform manipulation:
[tex]9x + 2y^{2} - 3z^{2} + 9y - 2y^{2} - 3z^{2} = 132 + 867[/tex]
Rearrange:
[tex](9x + 9y) + (2y^{2} - 2y^{2}) +(3z^{2} - 3z^{2}) = 132 + 867[/tex]
Simplify:
[tex]9(x + y) + 0 + 0 = 1000[/tex]
Simplify:
[tex]x + y = \frac{1000}{9}[/tex]
Hope this helps!
:)
Noaya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read. Let y represent the number of pages left to read after x hours.
Answer: –55x + 570
Step-by-step explanation:
The person above me completely missed the question so this is the right one
The perimeter of the rectangle is 28 units.
A rectangle with perimeter 28 units is shown. The length of the sides is w, and the length of the top and bottom sides are 2 w minus 1.
What is the value of w?
5 units
7 units
14 units
15 units
Answer:
5 units
Step-by-step explanation:
P=2(w)+2(2w-1)
28=2w+4w-2
30=6w
w=5
Answer:
5
Step-by-step explanation:
The drama club is selling candles for a fundraiser. They spend $100 on the candles and sell them for $4.50 each. How many candles must they sell to make more than $125 profit?
Let x represent the number of candles sold. Which inequality can you use to find x?
So I try to help
Step-by-step explanation:
I don't no sorrry
Answer:
the first one!!
Step-by-step explanation:
Simplify (x2y)3. x 5y 3 x 2y 3 x 6y 3
Answer:
[tex]x^{6} y^{3}[/tex]
Step-by-step explanation:
[tex](x^2y)3[/tex]
[tex]x^{2 \times 3} \times y^3[/tex]
[tex]x^{6} \times y^3[/tex]
Find the radius of a circle given that the area is three times its circumference
Answer:
Radius of the circle = 6 units
Step-by-step explanation:
Let the radius of the circle be r
According to the given condition:
Area of the circle = 3 times the circumference of the circle
[tex]\therefore \pi r^2 =3\times 2\pi r\\\therefore r^2 = \frac{3\times 2\pi r}{\pi}\\\therefore r^2 = 3\times 2r\\\therefore r = 6\: units\\[/tex]
Two airplanes leave an airport at the same time, flying in the same direction. One plane is flying at twice the speed of the other. If after 4 hours they are 1800 km apart, find the speed of each plane.
Answer:
The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.
Step-by-step explanation:
Two planes:
The first one's speed is x
The second is y.
One plane is flying at twice the speed of the other.
I will say that y = 2x.
Two airplanes leave an airport at the same time, flying in the same direction
Same direction, so their relative speed is the subtraction of their speeds. 2x - x = x.
Means that after 1 hour, they will be x miles apart.
If after 4 hours they are 1800 km apart, find the speed of each plane
After 1 hour, x km apart. After 4, 1800. So
1 hour - x km apart
4 hours - 1800 km apart
4x = 1800
x = 1800/4
x = 450
2x = 2*450 = 900
The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.
The sum is type answer as integer proper fraction or mixed number simplify answer
Answer:
[tex]9\dfrac{5}{6}[/tex]
Step-by-step explanation:
[tex]5\dfrac{1}{6}+4\dfrac{2}{3}=\\\\5\dfrac{1}{6}+4\dfrac{4}{6}=\\\\9\dfrac{5}{6}[/tex]
Hope this helps!
Which equation can be used to find mMN
Answer:
Its depending on the angle
Express the following in usual form
Answer:
52300
Step-by-step explanation:
When you multiply by ten the decimal dot moves one space to the right, so here you multiply by ten four times, so you move the dot four spaces to the right and you get 52300
a consumer affairs company is interested in testing at the 5% level of significance that the average weight of a package of butter is less than 16 oz if the p value is 0.003 the conclusion is
Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation. Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths. What is OB'? 1.5 units 3 units 4.5 units 6 units
If the length of OB was ³/₄, then the length of OB' after dilation is; Option B: 3 units.
Dilation of an object simply means enlarging or shrinking of the object by a scale factor.Now, we are told that Triangle ABC was dilated to Triangle A'B'C' using the rule D₀,₄.What this means is that it was enlarged by a scale factor of 4 with point O as the center of dilation.
Now, if the length of OB is 3/4, it means that the new dilated length is gotten from;Scale factor = new dilated length OB'/(³/₄)
new dilated length OB' = ³/₄ × 4
new dilated length OB' = 3 units
Read more on dilation at; https://brainly.com/question/8532602
Answer:
its 4 units trust just answered it
Step-by-step explanation:
The average number of children a Japanese woman has in her lifetime is 1.37. Suppose that one Japanese woman is randomly chosen. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X.X~ _____(_____,_____) d. Find the probability that she has no children. e. Find the probability that she has fewer children than the Japanese average.
Answer:
a. X: amount of children that a Japanese woman has in her lifetime.
b. X can take natural numbers (all positive integers) as values.
c. X~Poi(1.37).
d. P(X=0)=0.2541
e. P(X<1.37)=0.6022
Step-by-step explanation:
a) This can be modeled with a Poisson distribution.
We let the variable X be the amount of children that a Japanese woman has in her lifetime.
The parameter of the Poisson distribution is λ=1.37.
This is also the value of the mean and the standard deviation.
b) X can take all positive integer values.
c) X is modeled as a Poisson variable with λ=1.37.
d) This can be calculated as:
[tex]P(0)=\lambda^ke^{-\lambda}/k!=1.37^{0} \cdot e^{-1.37}/0!=1*0.2541/1=0.2541\\\\[/tex]
e) Having fewer children than the average means that she has one or none children.
This can be calculated as:
[tex]P(X<1.37)=P(0)+P(1)\\\\\\P(0)=1.37^{0} \cdot e^{-1.37}/0!=1*0.2541/1=0.2541\\\\P(1)=1.37^{1} \cdot e^{-1.37}/1!=1.37*0.2541/1=0.3481\\\\\\P(X<1.37)=0.2541+0.3481=0.6022[/tex]
A political analyst believes that a senator's recent decision to support a bill resulted in a drop of approval ratings. To test this claim, he selects random cities in the state that voted the senator in and compares the approval ratings before the decision to the approval ratings after the decision. Suppose that data were collected for a random sample of 8 cities, where each difference is calculated by subtracting the percent approval rating before the decision from the percent approval rating after the decision. Assume that the percentages are normally distributed. What type of test is this hypothesis test?
Answer:
A paired sample t-test
Step-by-step explanation:
A paired sample t-test is most of the time used when in determining the difference between two related dependent variables and in this context; we have
approval ratings before the senator's decision variables and
approval rating after the senator's decision variables for the same subject
These revolves around the senator's decision causing a decrease in approval ratings. Often the two variables are separated by time.
It is used to determine whether the mean of the dependent variable (approval ratings) is the same in the two related groups (the before and after decision groups).
According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints (Consumer fraud and, 2008). (7.1.2)
State the random variable, population parameter, and hypotheses.
Answer:
Random variable: for this case represent the number of complaints in 2007
Population parameter: represent the real proportion of complaints in 2007 p
Hypothesis to verify
We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:
Null hypothesis:[tex]p=0.23[/tex]
Alternative hypothesis:[tex]p \neq 0.23[/tex]
Step-by-step explanation:
Information provided
n=1432 represent the random sample taken
X=321 represent the number of complaints
[tex]\hat p=\frac{321}{1432}=0.224[/tex] estimated proportion of complaints in 2007
[tex]p_o=0.23[/tex] is the value to verify
z would represent the statistic
Random variable: for this case represent the number of complaints in 2007
Population parameter: represent the real proportion of complaints in 2007 p
Hypothesis to verify
We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:
Null hypothesis:[tex]p=0.23[/tex]
Alternative hypothesis:[tex]p \neq 0.23[/tex]
The temperature in a town is −2.7°C. The temperature decreases 3°C. What is the new temperature? Incorrect
Answer:
-5.7° C
Step-by-step explanation:
-2.7 °C (degrees Celsius) - 3 °C (degrees Celsius) = -5.7° C
An animal shelter has a 65% adoption rate for puppies. Of all puppies in the shelter, 75% live to be 7 years or older. Of the puppies who are adopted, 80% live to be 7 years or older. What is the probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
Answer:
52% probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: A puppy is adopted.
Event B: The puppy lives 7 or more years.
An animal shelter has a 65% adoption rate for puppies
This means that [tex]P(A) = 0.65[/tex]
Of the puppies who are adopted, 80% live to be 7 years or older.
This means that [tex]P(B|A) = 0.8[/tex]
What is the probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(A)*P(B|A)[/tex]
[tex]P(A \cap B) = 0.65*0.8[/tex]
[tex]P(A \cap B) = 0.52[/tex]
52% probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
Suppose Carol Danvers invested $1,000 into an account paying 6% annual interest compounded
annually.
How much is in her account at the end of one year?
Answer:
$ 1,060.00
Step-by-step explanation:
A = $ 1,060.00
A = P + I where
P (principal) = $ 1,000.00
I (interest) = $ 60.00
Compound Interest Equation
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
In two sample surveys 125 people were asked about their favorite fruit in the survey 40 people chose apples 64 choose oranges and 21 chose bananas in the second 34 chose apples 63 chose oranges 19 Joe’s banana marine inferred before is this a French trooper by us on the data explain
Answer:
Marianne made an inference that is true based on the data. More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likely that oranges are the favorite fruit of the entire population.
hope it help please mark me as brainliest
n a group of 40 people, 10 people are healthy. The 30 unhealthy people have either high blood pressure, high cholesterol, or both. Suppose 15 have high blood pressure and 25 have high cholesterol. If a person is randomly selected from this group, what is the probability that they have both high blood pressure and high cholesterol
Answer:
If a person is randomly selected from this group, the probability that they have both high blood pressure and high cholesterol is P=0.25.
Step-by-step explanation:
We can calculate the number of people from the sample that has both high blood pressure (HBP) and high cholesterol (HC) using this identity:
[tex]N(\text{HBP or HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP and HC})\\\\\\ N(\text{HBP and HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP or HC})\\\\\\ N(\text{HBP and HC})=15+25-30=10[/tex]
We can calculate the probability that a random person has both high blood pressure and high cholesterol as:
[tex]P(\text{HBP and HC})=\dfrac{10}{40}=0.25[/tex]
A new post-surgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven others (the controls) receive the standard treatment. The recovery times, in days, are given below.
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
Required:
Find a 98% confidence interval for the difference in the mean recovery times between treatment and control.
Answer:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
Step-by-step explanation:
For this case we have the following info given:
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
We can find the sample mean and deviations with the the following formulas:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s =\sqrt{\frac{\sum_{i=1}^n (X_i- \bar X)^2}{n-1}}[/tex]
And repaplacing we got:
[tex] \bar X_T = 17.714[/tex] the sample mean for treatment
[tex] \bar X_C = 28.714[/tex] the sample mean for treatment
[tex] s_T= 4.461[/tex] the sample deviation for treatment
[tex] s_C= 7.387[/tex] the sample deviation for control
[tex]n_T= n_C= 7[/tex] the sample size for each sample
The degrees of freedom are given by:
[tex] df= 7+7-2= 12[/tex]
The confidence interval for the difference of means is given by:
[tex] (\bar X_T -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_T}{n_T} +\frac{s^2_C}{n_C}}[/tex]
The confidence is 98% so then the significance is [tex]\alpha=0.02[/tex] and [tex] \alpha/2 =0.01[/tex]. Then the critical value would be:
[tex] t_{\alpha/2}=2.681[/tex]
And replacing we got:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication a at what time will you need to stop the infusion
Answer:
6 PM
Step-by-step explanation:
125 mg --- 300 mL
500 mg --- x mL
x = 500*300/125 = 1200 mL solution contains 500 mg
rate = 100 mL/h
1200 mL* 1h/100 mL = 12 h
6AM + 12 h = 6 PM
You need to stop infusion at 6 PM
It is found that You need to stop infusion at 6 PM.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication.
125 mg = 300 mL
500 mg = x mL
x = 500*300/125
x = 1200 mL
Here solution contains 500 mg
The rate = 100 mL/h
1200 mL* 1h/100 mL = 12 h
6AM + 12 h = 6 PM
Therefore, You need to stop infusion at 6 PM.
Learn more about the unitary method;
https://brainly.com/question/23423168
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Graph the line that represents this equation. 3x - 4y =8
Answer:
See attachment
Step-by-step explanation:
The solution is given in the image.
Which graph is the graph of the function?The graph of a feature f is the set of all factors in the plane of the form (x, f(x)). We can also outline the graph of f to be the graph of the equation y = f(x). So, the graph of a feature is a special case of the graph of an equation.
What does the axis of a graph constitute?An axis is a line to the aspect or backside of a graph; it's far labeled to give an explanation for the graph's meaning and the devices of measurement. The x-axis, the horizontal line at the lowest of a graph, may be labeled to present facts about what the graph represents.
Learn more about graphs here: brainly.com/question/4025726
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Please help me extra points for 1 math question. Please help before my time is up. Five times a number, added to -3, is 37. Find that number.
Answer:
your number should be 8
Step-by-step explanation:
5x+(-3)=37
5x-3=37
+3 +3
5x=40
÷5 ÷5
x=8
hope this helps
Answer:
The answer is 8.
5x-3=37
5x=37+3
5x=40
x=40/5
x=8
HOPE IT HELPS!!
luke is 5 years younger than 3 times sydenys age, s in this situation what does 3s represent
3s represents three times Sydney's age. Sydney's age is symbolized with an S.
There are 20 pieces of fruit in a bowl and 5 of them are apples. What percent of the fruit are apples?
Step-by-step explanation:
20fruits=100%
5fruits=?
5x100/20 5fruitsx5%
=24%
