Answer:
First we need to calculate how many buttons there are. There are 10 buttons. So the probability of getting a blue one is 3/10 for 3 buttons. So that means that the answer to the first one is 30%. So if we get that neither is red we know that the probability of getting a red one is 5/10. So there is a 50% chance of getting a red button and 50% of not. Then we multiply them 5/10*5/10 for 2 times. we get 25/100 aka 25%. So the answer to this question is 25%.
Answer to first: 30%Answer to second: 25%At a gas station, 50% of the customers use regular gas, 30% use mid-grade gas and 20% use premium gas. Of those customers using regular gas, only 30% fill their tanks. Of those customers using mid-grade gas, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. What is the probability that the next customer will request mid-grade gas and fill the tank
Answer:
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
Step-by-step explanation:
In order to calculate the probability that the next customer will request mid-grade gas and fill the tank we would have to make the following calculation:
probability that the next customer will request mid-grade gas and fill the tank= percentage of the people using mid-grade gas* percentage of the people using mid-grade gas that fill their tanks
probability that the next customer will request mid-grade gas and fill the tank= 30%*60%
probability that the next customer will request mid-grade gas and fill the tank= 0.1800
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
A (-5,2) B (0,-5) C (5,1) D (7,5)
Answer:
C
Step-by-step explanation:
Some of the stock in a winery has been found to be infected by Brettanomyces. You independently sample 80 barrels from the winery, and find that 28 of them are infected. Carry out a hypothesis test to evaluate the claim that half of the wine barrels are infected. What is closest to the p-value that you obtain
Answer:
Step-by-step explanation:
If half of the wine barrels are infected, it means that the proportion of infected wine is 0.5
We would set up the hypothesis test.
For the null hypothesis,
p = 0.5
For the alternative hypothesis,
p < 0.5
Considering the population proportion, probability of success, p = 0.5
q = probability of failure = 1 - p
q = 1 - 0.5 = 0.5
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 28
n = number of samples = 80
P = 28/80 = 0.35
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.35 - 0.5)/√(0.5 × 0.5)/80 = - 2.68
From the normal distribution table, the area below the test z score in the left tail 0.0037
Therefore,
p value = 0.0037
Assuming a significance level of 0.05, therefore,
Since alpha, 0.05 > than the p value, 0.0037, then we would reject the null hypothesis.
Please help! Will give Brainliest!
Steps 1-4 in attachment (#4 below)
Step 4: Use the equation you wrote in Step 3. Write the equation for the graph of g(x) that has also been shifted right 1 unit.
Answer:
g(x) = 2|x|g(x) = -2|x|g(x) = -2|x| -3g(x) = -2|x-1| -3Step-by-step explanation:
1) Vertical stretch is accomplished by multiplying the function value by the stretch factor. When |x| is stretched by a factor of 2, the stretched function is ...
g(x) = 2|x|
__
2) Reflection over the x-axis means each y-value is replaced by its opposite. This is accomplished by multiplying the function value by -1.
g(x) = -2|x|
__
3) As you know from when you plot a point on a graph, shifting it down 3 units subtracts 3 from the y-value.
g(x) = -2|x| -3
__
4) A right-shift by k units means the argument of the function is replaced by x-k. We want a right shift of 1 unit, so ...
g(x) = -2|x -1| -3
A 48 meter antenna mast is stabilized by a 52 meter guy wire How far from the base of the mast is the guy wire secured to the ground A 20m B 50m C 60m D 100m
Answer:
A) 20m
Step-by-step explanation:
52^2 - 48^2 = b^2
√2704 - √ 2304 = √400
b^2 = √400 = 20
As this is Pythagoras as we do not have any 2nd angle measure.
if it was trigonometry we could use 90 degree as part of the sum
48/ sin(?)x90 = 52
Then try other angle by deducting angle shown from 90
m/sin (?) x 90 = 52 etc.
But to guarantee you would find the base you could use tan.
Find the probability. Enter your answer as a simplified fraction.
Picking a purple marble from a jar with 14 green and 14 purple marbles.
Answer:
1/2
Step-by-step explanation:
14 green and 14 purple marbles = 28 marbles
P( purple) = purple/ total
= 14/28
=1/2
here it is ill mark you as brainliest if the answer is correct.
Answer:
A = 1168.67 cm²
Step-by-step explanation:
[tex]A=2\pi rh+2\pi r^{2}[/tex] Use this equation to find the surface area
[tex]A=2\pi (6)(25)+2\pi (6)^{2}[/tex] Multiply
[tex]A=2\pi (150)+2\pi (36)[/tex] Multiply
A = 942.48 + 226.19 Add
A = 1168.67 cm²
Answer:
1169.14cm2
Step-by-step explanation:
The surface area is that area which you can feel. Now there are two circles one at the top and one at the bottom.
These areas are expressed as;
π×r2 { remember area of a circle}.
Therefore for the two areas we have twice the area of once since they are the same. Hence we have:
2×π×r2.
Secondly, there is still another area we haven't talked about yet. It's the area you feel at the side and this area curls into a circular fashion.
Now let's assume the two circles are the top and bottom are knocked off , we would have a shape that looks like a rectangle.
Now area of a rectangle is the multiplication of both sides. In this case the side would be the height,h and the circumference of the circle since the rectangle forms into a circle when she try to join both edges together.
Hence the area of this Shape would be;
2πr{circumference} × h=2πrh
Hence the total surface area would be;
2πr2 + 2πrh.
Substituting the giving values we have;
Note: to obtain raduis,r ; we divide the diameter by 2.
2 × 22/7 × 6^2 + 2 × 22/7 × 6× 25
2×22/7(36+150)
44/7(186)= 8184/7
=1169.1429cm2
=1169.14cm2{ to 2 decimal place}
What is the area of triangle ABC?
3 square units
0 7 square units
11 square units
15 square units
[tex]the \: answer \: is \: 7 \: square \: units \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
3) If you know the volume of a prism and the area of the base of the prism, what other information
can you find about the prism?
Answer:
I could find out the surface area and it's capacity
if teta is an angle in right angle triangle if tan teta = 3/4 then find sin teta?
Answer:
[tex] \frac{3}{5}[/tex]
Step-by-step explanation:
The adjacent sides are 3 and 4. Thus the hypotenuse is: (by Pythagoras Theorem)
$=\sqrt{3^2+4^2}$
$=\sqrt{25}$
$=5$
Now by definition of $\sin$, we get:
$\sin \theta= \frac{\text{opposite}}{\text{hypotenuse}}=\frac{3}{5}$
3] The population of a
village is 4800. There are
1200 men, 1620 women
480 boys and the rest are
girls.
(a) How many girls are
in the village?
(b) Calculate the
percentage of men in
the village.
Answer:
A) 1500 girls
B) 25% are men
Step-by-step explanation:
I hope this helps
Wyoming fisheries contend that the mean number of cutthroat trout caught during a full day of fly-fishing on the Snake, Buffalo, and other rivers and streams in the Jackson Hole area is 4.0. To make their yearly update, the fishery personal asked a sample of fly-fishermen to keep a count of the number caught during the day. The numbers were: 4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6. At the 0.05 significance level, can we conclude that the mean number caught is greater than 4.0?
Answer:
[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]
The degrees of freedom are given by:
[tex] df =n-1= 12-1=11[/tex]
And the p value would be:
[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4
Step-by-step explanation:
We have the following data given:
4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6
The sample mean and deviation from these data are:
[tex]\bar X=4.5[/tex] represent the sample mean
[tex]s=2.680[/tex] represent the sample deviation
[tex]n=10[/tex] sample size
[tex]\mu_o =4[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to verify
We want to verify if the true mean is equal to 4, the system of hypothesis would be:
Null hypothesis:[tex]\mu =4[/tex]
Alternative hypothesis:[tex]\mu \neq 4[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the the info we got:
[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]
The degrees of freedom are given by:
[tex] df =n-1= 12-1=11[/tex]
And the p value would be:
[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4
The linear function that is represented by which table has the same slope as the graph? On a coordinate plane, a line goes through points (0, negative 3) and (2, 1). A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries negative 9, negative 7, negative 5, negative 3, negative 1. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries 9, 7, 5, 3, 1. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9. A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 3, 5, 7, 9. Column 2 is labeled y with entries negative 9, negative 13, negative 17, negative 21, negative 25.
Answer:
c
step-by-step explanation:
ok the slope of the line is 2
and so by using the formula y1+y2/x1+x2 we can get the ration of each table
the first table is -9+-7/-25+-21
this can be simplified to -16/-46 which is about 0.347
using this formula for each table you can find the answer .
im
too lazy to do the rest
Answer:
It's C
Step-by-step explanation:
I did the quiz, see Arjinoodles for a detailed explanation.
What’s the correct answer for this question?
Answer:
C and E
Step-by-step explanation:
Focus = (-3,2)
So,
Distance to the focus =
√(x+3)²+(y-2)²
Now
Directrix:
y = 4 and p = -4
Distance from the directrix
= y+p
= y-4
Pls help I really need help
Answer:
7. [tex]x \leq 5[/tex]
8. [tex]x\geq 4[/tex]
9. x < 5
10. x < -7
11. x < 45
12. [tex]x\geq -10[/tex]
13. x < -7
14. x < 45
15. [tex]x\leq 50[/tex]
16. [tex]w\geq 16[/tex]
18. q > 4
Step-by-step explanation:
Barry has $30.00 to spend on soft drinks
for a party. A case of soft drinks costs
$4.65. Which inequality can be used to find how many cases (c) of soft drinks
Barry can purchase?
Answer:
30 ≥ 4.65x
Step-by-step explanation:
He cannot purchase more than $30, so the amount that he buys must always be less than 30.
To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of 25.325.3 milligrams and standard deviation of 2.72.7 milligrams for a sample of n equals 9n=9 cigarettes. Construct a 9090% confidence interval for the mean nicotine content of this brand of cigarette.
Answer:
The 90% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.
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 = 9 - 1 = 8
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8595
The margin of error is:
M = T*s = 1.8595*2.7 = 5
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 25.3 - 5 = 20.3 milligrams
The upper end of the interval is the sample mean added to M. So it is 25.3 + 5 = 30.3 milligrams.
The 90% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.
A man driving a car leaves a point A drives up to 32.5 km in a direction of 070. A cyclist leaves the same point in a direction 130 travelling. After some few hours both drivers are 80 km apart. Use this information to answer 3 questions. (1). What is the distance covered by the cyclist at this time in 2 d.p. (2). Find the bearing of Cyclist from the Car. correct to 1 d.p. (3). Find the shortest distance between the car and the line of path of the cyclist, in 2 d.p.
Answer: No 1 is 91.14 km who else could help with the rest of the solution for number 1, 2 & 3.
A bird of species? A, when? diving, can travel six times as fast as a bird of species B top speed. If the total speeds for these two birds is 224 miles per hour
Answer:
Maximum speed of bird A is [tex]192\,\,\frac{mi}{h}[/tex]
Maximum speed of bird B is [tex]32\,\,\frac{mi}{h}[/tex]
Step-by-step explanation:
This is a problem with two unknowns: Max speed of bird A (we name that "A"), and max speed of bird B (we call that "B"). Now we can create two equations with these two unknowns, based on the info provided:
Equation 1): based on the phrase "bird A can travel six times as fast as bird B" we write:
[tex]A=6\,*\, B\\A=6B[/tex]
Equation 2): based on the phrase; "the total speeds for these two birds is 224 miles per hour", we write:
[tex]A+B=224\,\,\frac{mi}{h}[/tex]
Now, we use the first equation to substitute A in the second equation, ad then solve for the unknown B:
[tex]A+B=224\,\,\frac{mi}{h}\\(6B)+B=224\,\,\frac{mi}{h}\\7B=224\,\,\frac{mi}{h}\\B=\frac{224}{7} \,\,\frac{mi}{h}\\B=32\,\,\frac{mi}{h}[/tex]
Now we can solve for the other unknown "A" using the substitution equation and the value of B we just found:
[tex]A=6B\\A=6\,(32\,\,\frac{mi}{h})\\A=192\,\,\frac{mi}{h}[/tex]
9. Hue wants to buy two necklaces, one for
her sister and one for herself. The necklace
for her sister costs $43.25, and the necklace
for herself costs $26.25. The sales tax on the
purchases is 3%. Find the total cost of Hue's
purchases, including sales tax.
A $71.59
© $67.42
0 $2.09
B $69.50
Answer:
$71.59
Step-by-step explanation:
[tex]43.25+26.25[/tex]
[tex]=69.5[/tex]
[tex]69.5*\frac{103}{100}[/tex]
[tex]69.5*1.03[/tex]
[tex]=71.585[/tex]
Which property is illustrated by the expression 5(4+2)=20+10
Answer:
distributive property
Step-by-step explanation:
The distributive property tells you ...
a(b+c) = ab +ac
5(4+2) = 5·4 +5·2 = 20 +10
[tex]\text{It would most likely be the distributive property}\\\\\text{In the equation:}\\\\5(4+2)=20+10\\\\\text{You would see that you can distribute the 5 into the variables inside }\\\text{the parenthesis}\\\\\text{In which it is set up in that particular way in order to do so}[/tex]
A county environmental agency suspects that the fish in a particular polluted lake have elevated mercury levels. To confirm that suspicion, five striped bass in that lake were caught and their tissues tested for the presence of mercury. For the purposes of comparison, four striped bass in an unpolluted lake were also caught and tested. The fish tissue mercury levels in mg/kg are given below. (Note: You may wish to use Excel for this problem.) Sample 1 (polluted lake) Sample 2 (unpolluted lake) 0.580 0.382 0.711 0.276 0.571 0.570 0.666 0.366 0.598a. Construct the 95% confidence interval for the difference in the population means based on these data.b. Test, at the 5% significance level, whether the data provide sufficient evidence to conclude that fish in the polluted lake have elevated levels of mercury in their tissue.c. Do your answers to (a) and (b) agree or disagree? Explain.
Answer:
a. The 95% confidence interval for the difference between means is (0.071, 0.389).
b. There is enough evidence to support the claim that the fish in this particular polluted lake have signficantly elevated mercury levels.
c. They agree. Both conclude that the levels of mercury are significnatly higher compared to a unpolluted lake.
In the case of the confidence interval, we reach this conclusion because the lower bound is greater than 0. This indicates that, with more than 95% confidence, we can tell that the difference in mercury levels is positive.
In the case of the hypothesis test, we conclude that because the P-value indicates there is a little chance we get that samples if there is no significant difference between the mercury levels. This indicates that the values of mercury in the polluted lake are significantly higher than the unpolluted lake.
Step-by-step explanation:
The table with the data is:
Sample 1 Sample 2
0.580 0.382
0.711 0.276
0.571 0.570
0.666 0.366
0.598
The mean and standard deviation for sample 1 are:
[tex]M=\dfrac{1}{5}\sum_{i=1}^{5}(0.58+0.711+0.571+0.666+0.598)\\\\\\ M=\dfrac{3.126}{5}=0.63[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{5}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(0.58-(0.63))^2+...+(0.598-(0.63))^2]}\\\\\\ s=\sqrt{\dfrac{1}{4}\cdot [(0.002)+(0.007)+(0.003)+(0.002)+(0.001)]}\\\\\\ s=\sqrt{\dfrac{0.015}{4}}=\sqrt{0.0037}\\\\\\s=0.061[/tex]
The mean and standard deviation for sample 2 are:
[tex]M=\dfrac{1}{4}\sum_{i=1}^{4}(0.382+0.276+0.57+0.366)\\\\\\ M=\dfrac{1.594}{4}=0.4[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{3}\cdot [(0.382-(0.4))^2+(0.276-(0.4))^2+(0.57-(0.4))^2+(0.366-(0.4))^2]}\\\\\\ s=\sqrt{\dfrac{1}{3}\cdot [(0)+(0.015)+(0.029)+(0.001)]}\\\\\\ s=\sqrt{\dfrac{0.046}{3}}=\sqrt{0.015}\\\\\\s=0.123[/tex]
Confidence interval
We have to calculate a 95% confidence interval for the difference between means.
The sample 1, of size n1=5 has a mean of 0.63 and a standard deviation of 0.061.
The sample 2, of size n2=4 has a mean of 0.4 and a standard deviation of 0.123.
The difference between sample means is Md=0.23.
[tex]M_d=M_1-M_2=0.63-0.4=0.23[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{0.061^2}{5}+\dfrac{0.123^2}{4}}\\\\\\s_{M_d}=\sqrt{0.001+0.004}=\sqrt{0.005}=0.07[/tex]
The critical t-value for a 95% confidence interval is t=2.365.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=2.365 \cdot 0.07=0.159[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 0.23-0.159=0.071\\\\UL=M_d+t \cdot s_{M_d} = 0.23+0.159=0.389[/tex]
The 95% confidence interval for the difference between means is (0.071, 0.389).
Hypothesis test
This is a hypothesis test for the difference between populations means.
The claim is that the fish in this particular polluted lake have signficantly elevated mercury levels.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=5 has a mean of 0.63 and a standard deviation of 0.061.
The sample 2, of size n2=4 has a mean of 0.4 and a standard deviation of 0.123.
The difference between sample means is Md=0.23.
[tex]M_d=M_1-M_2=0.63-0.4=0.23[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{0.061^2}{5}+\dfrac{0.123^2}{4}}\\\\\\s_{M_d}=\sqrt{0.001+0.004}=\sqrt{0.005}=0.07[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.23-0}{0.07}=\dfrac{0.23}{0.07}=3.42[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=5+4-2=7[/tex]
This test is a right-tailed test, with 7 degrees of freedom and t=3.42, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>3.42)=0.006[/tex]
As the P-value (0.006) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the fish in this particular polluted lake have signficantly elevated mercury levels.
c. They agree. Both conclude that the levels of mercury are significnatly higher compared to a unpolluted lake.
In the case of the confidence interval, we reach this conclusion because the lower bound is greater than 0. This indicates that, with more than 95% confidence, we can tell that the difference in mercury levels is positive.
In the case of the hypothesis test, we conclude that because the P-value indicates there is a little chance we get that samples if there is no significant difference between the mercury levels. This indicates that the values of mercury in the polluted lake are significantly higher than the unpolluted lake.
I don’t know how to do this, what’s the area?
Answer:
Hello!
Step-by-step explanation:
To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.
So,you have to multiply.
Hope this helps.
Solve for x in the diagram below.
Answer:
x = 20
Step-by-step explanation:
The three angles form a straight line so they add to 180 degrees
x+ 100 +3x = 180
Combine like terms
100+4x= 180
Subtract 100 from each side
100+4x-100= 180-100
4x= 80
Divide each side by 4
4x/4 = 80/4
x = 20
Answer:
[tex]x = 20 \: \: degrees[/tex]
Step-by-step explanation:
Angles in a straight line = 180 degrees
[tex]x + 3x + 100 = 180 \\ 4x + 100 = 180 \\ 4x = 180 - 100 \\ 4x = 80 \\ \frac{4x}{4} = \frac{80}{4} \\ x = 20 \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Michael has a weekly food budget of $62. If he plans to budget the same amount for each of the 7 days of the week, what is the maximum amount he can spend on food each day?
Answer:
62/7
Step-by-step explanation:
The budget illustrates ratios and proportions.
The maximum amount to spend on food each day is $8
The given parameters are:
[tex]\mathbf{Budget = \$62}[/tex]
[tex]\mathbf{Days = 7}[/tex]
So, the daily budget is:
[tex]\mathbf{Daily = \frac{Budget}{Days}}[/tex]
So, we have:
[tex]\mathbf{Daily = \frac{\$62}{7}}[/tex]
[tex]\mathbf{Daily = \$8.85714285714}[/tex]
Remove decimal parts (do not approximate)
[tex]\mathbf{Daily = \$8}[/tex]
Hence, the maximum to spend each day is $8
Read more about ratios and proportions at:
https://brainly.com/question/13114933
An artist is trying to choose 5 covers for children’s books. There are 10 different covers to choose from. How many ways can the artist choose covers? (It’s a permutation and combination kind of problem)
Answer:
252
Step-by-step explanation:
The order of the books isn't important, so we'll use combinations.
The number of ways to choose 5 books from 10 is:
₁₀C₅ = 10! / (5! (10 − 5)!)
₁₀C₅ = 10! / (5! 5!)
₁₀C₅ = 10×9×8×7×6 / (5×4×3×2×1)
₁₀C₅ = 252
The height of a cylinder is twice the radius of its base.
What expression represents the volume of the cylinder, in
cubic units?
4pix2
2pix3
pix2+2x
2+pix3
Answer:
The answer is 2pix3 or [tex]2\pi x^3\\[/tex]
Step-by-step explanation:
This problem brothers on the mensuration of solid shapes, a cylinder.
we know that the expression for the volume of a cylinder is
[tex]volume= \pi r^2h\\[/tex]
let the radius r of the base be= x
and the height h of the cylinder be = 2x
we can now solve the expression that represents the volume of the cylinder, in cubic units.
[tex]volume= \pi *x^2*2x\\volume= \pi *2x^3\\\\volume= 2\pi x^3\\[/tex]
A division of a multinational retail company prepared a presentation to give at the home office in Paris, France. The presentation includes a scatterplot that shows the relationship between square footage and annual sales in retail outlets owned by the chain. The units in the plot show the size in thousands of square feet and the response in thousands of dollars. A fitted line in the plot is y = 47 + 650x.
(a) Interpret the slope and intercept in the fitted line.
(b) To present the model in Europe, the plot must be shown with sales denominated in euros rather than dollars 1use the exchange rate
$1 = €0.822 and size given in square meters rather than square feet (1 square foot = 0.093 square meter). Find the slope and intercept in these new units.
(c) Would the r2 summary attached to the regression model change along with the slope and intercept when the data are changed into euros and meters?
(d) Would se change with the new scales?
Answer:
(A) Interpretation is below
(B) The slope in the new units is now 60.45
The intercept in the new units is 38.634
(C) yes
(D) yes
Step-by-step explanation:
(A) The intercept here is 47. This means that the minimum response or payment is 47 (thousand dollars).
The slope is 650. This means that the change in Y due to a change in X is 650. In other words, if there is a change of 1(thousand square feet), there will be a resulting increase of 650(thousand dollars). It will result in an increase instead of decrease because the slope is positive or bearing a + sign.
(B) The new units are EUROS and SQUARE METRES.
$1 = €0.822
1s.f. = 0.093s.m.
The new fitted line would be:
0.822Y = 47(0.822) + (0.093)(650)X
0.822Y = 38.634 + 60.45X
The slope in the new units is 60.45 and the intercept on the y-axis is 38.634.
Which equation is equivalent to One-fourth + x =Negative StartFraction 5 over 4 EndFraction? Select all that apply.
Options:
(A)x = StartFraction 6 over 4 EndFraction
(B)x = Negative StartFraction 6 over 4 EndFraction
(C)x minus one-fourth = negative StartFraction 5 over 4 EndFraction
(D)x = negative three-halves
(E)x = negative three-fourths
Answer:
(B)x = Negative StartFraction 6 over 4 EndFraction
[tex]-\dfrac{6}{4}[/tex]
(D)x = negative three-halves
[tex]-\dfrac{3}{2}[/tex]
Step-by-step explanation:
We want to determine which fraction is equivalent to
[tex]\dfrac{1}{4}+x=-\dfrac{5}{4}\\$First, we collect like terms$\\x=-\dfrac{5}{4}-\dfrac{1}{4} \\\\=\dfrac{-5-1}{4}\\=-\dfrac{6}{4}\\x=-\dfrac{6}{4}[/tex]
This value of x is the result in Option B.
Reducing [tex]-\dfrac{6}{4}[/tex] to its lowest form:
[tex]-\dfrac{6}{4}=-\dfrac{3}{2}[/tex] which is Option D.
Therefore, the correct options are: B and D
(x + y )(x 2 - xy + y 2 )
Answer:
[tex]x^3+y^3[/tex]
Step-by-step explanation:
[tex](x+y)(x^2-xy+y^2)= \\\\x(x^2)+x(-xy)+x(y^2)+y(x^2)+y(-xy)+y(y^2)= \\\\x^3-x^2y+xy^2+x^2y-xy^2+y^3= \\\\\boxed{x^3+y^3}[/tex]
Hope this helps!