Answer:
[tex]\$0.26[/tex] has to be paid more if the coupon is applied first
Step-by-step explanation:
Given: A grocery store has a discount of 13% off hand soap. At the same time the hand soap manufacturer has a coupon for $2.00 off.
To find: how much more would be paid if the coupon is applied first
Solution:
Let $ x denotes cost of hand soap
Case 1:
If the discount is given first,
cost of hand soap = [tex]x-\frac{13}{100} x=\$ \frac{87}{100}x[/tex]
If the coupon for $2.00 off is applied,
Final cost of the hand soap = [tex]\$\,(\frac{87}{100}x-2)[/tex]
Case 2:
If the coupon for $2.00 off is applied first,
cost of hand soap = [tex]\$(x-2)[/tex]
If the discount is given then,
final cost of the hand soap = [tex](x-2)-\frac{13}{100}(x-2)=\frac{87}{100}(x-2)[/tex] = [tex]\frac{87}{100}x-\frac{87}{50}[/tex]
Here,
[tex]\frac{87}{100}x-\frac{87}{50}-\frac{87}{100}x+2=\frac{13}{50}=\$0.26[/tex]
So, [tex]\$0.26[/tex] has to be paid more if the coupon is applied first.
Answer:
$0.26
Step-by-step explanation: I took the test
5 gummy worms. 4 are red, 1 is blue. Two gummy worms are chosen at random and not replaced. What is probability of two red gummy worms.
Answer:
3/5
Step-by-step explanation:
because there are more red than blue and the fraction is 3/5 and the probability to pick a red worm is a lot higher than the blue. well there are 4 red worms and 1 blue so it would be 3 red worms out of 5 in total. this is more than 1 blue over 5. 3/5 is more than 1/5
hope this helped
Answer: 3/5
Step-by-step explanation:
Since 4 red gummies you have four out of 5 chance of getting red gummies. Without replacement there are now 4 gummies left and 3 red gummies. There for 3 out of 4 chance of getting another red gummy. Since at same time multiply. 4/5*3/4 = 12/20
Which can be simplified to 3/5
Flip a fair two sided coin 4 times. Find the probability the first or last flip is a tail.
Answer:
1/4
Step-by-step explanation:
Flip a fair two sided coin 4 times, the probability the first or last flip is a tail is
P = (1/2) x 1 x 1 x (1/2) = 1/4
(The probability of getting tail in first flip = 1/2, in the 2nd and 3rd flip, tail and head are both accepted, the probability of getting tail in last flip = 1/2)
Hope this helps!
8. Nate bought two large pizzas and one small pizza and paid $36. If the difference in cost between a large and small pizza is $5.25, how much does a small pizza cost?
Answer:
$8.5
Step-by-step explanation:
We need to propose a system of equations with the information provided to us.
two large pizzas and one small pizza cost $36:
[tex]2L+S=36[/tex]
where
[tex]L[/tex]: Large pizza
[tex]S:[/tex] Small pizza
and the difference in cost between a large and small pizza is $5.25:
[tex]L-S=5.25[/tex]
our system of equations is:
[tex]2L+S=36[/tex]
[tex]L-S=5.25[/tex]
We are asked for the price of small pizza, so we must manipulate the equations in such a way that adding or subtracting them removes the variable L and we are left with an equation for S.
Multiply the second equation of the system by -2
[tex](-2)(L-S=5.25)\\\\-2L+2S=-10.5[/tex]
and now we sum this with the first equation of the system:
[tex]-2L+2S=-10.5\\+(2L+S=36)\\-------------\\-2L+2L+2S+S=-10.5+36[/tex]
simplifying the result:
[tex]3S=25.5[/tex]
and solving for S (the price of a small pizza)
[tex]S=25.5/3\\S=8.5[/tex]
What is the part to part ratio for gender in a daycare of children in which 16 of them are male
Answer:
16:0
Step-by-step explanation:
What is the solution? X/12+3< or = 7
Answer:
x <= 48
Step-by-step explanation:
Subtract 3 from both sides
x/12 <= 4
Multiply by 12
x <= 48
Pedro owns a shrimp truck near the beach. He sells garlic shrimp for $8 a plate and spicy shrimp for $6 a plate. Each day Pedro stocks enough shrimp to sell at most 120 plates total, but he would like to earn at least $800. Which combination of garlic shrimp plates and spicy shrimp plates can Pedro sell to meet his goal? A. 15 garlic shrimp plates and 110 spicy shrimp plates B. 80 garlic shrimp plates and 20 spicy shrimp plates C. 90 garlic shrimp plates and 25 spicy shrimp plates D. 70 garlic shrimp plates and 55 spicy shrimp plates
Answer:
C
Step-by-step explanation:
You can plug in each combination to see what would work
C is the only combination that satisfies all the constraints: it earns him more than $800 and is less than 120 plates.
The combination of 40 plates of garlic shrimp was sold, and 80 plates of spicy shrimp were sold can Pedro sell to meet his goal.
Given that,
Pedro owns a shrimp truck near the beach.
He sells garlic shrimp for $8 a plate and spicy shrimp for $6 a plate.
Each day Pedro stocks enough shrimp to sell at most 120 plates total, but he would like to earn at least $800.
We have to determine,
Which combination of garlic shrimp plates and spicy shrimp plates can Pedro sell to meet his goal?
According to the question,
Let the x plates of garlic shrimp sold,
And y plates of spicy shrimp sold.
Each day Pedro stocks enough shrimp to sell at most 120 plates,
Then,
Plates of garlic shrimp + Plates of spicy shrimp = Total number of shrimp sell each day.
[tex]\rm x + y =120[/tex]
And He sells garlic shrimp for $8 a plate and spicy shrimp for $6 a plate.
He would like to earn at least $800.
Then,
Cost of garlic shrimp per plate + Cost of spicy shrimp per plate = Total earning,
[tex]\rm 8x + 6y = 800[/tex]
On solving both the equation,
[tex]\rm x+y = 120\\\\8x + 6y = 800[/tex]
From equation 1,
[tex]\rm y= 120-x[/tex]
Substitute the value of x in equation 2,
[tex]\rm 8x +6y = 800\\\\8(120-y) + 6y = 800\\\\960 - 8y + 6y = 800\\\\-2y = 800-960\\\\-2y = -160\\\\y = \dfrac{-160}{-2}\\\\y = 80[/tex]
Substitute the value of y in equation 1,
[tex]\rm x + y =120\\\\x +80=120\\\\x = 120-80\\\\x =40[/tex]
Hence, The combination of 40 plates of garlic shrimp was sold, and 80 plates of spicy shrimp were sold can Pedro sell to meet his goal.
For more details refer to the link given below.
https://brainly.com/question/475594
The present value of a perpetuity paying 1 every two years with first payment due immediately is 7.21 at an annual effective rate of i. Another perpetuity paying R every three years with the first payment due at the beginning of year two has the same present value at an annual effective rate of i + 0.01.
Calculate R.
(A) 1.23
(B) 1.56
(C) 1.60
(D) 1.74
(E) 1.94
Answer:
Step-by-step explanation:
image attached (representing first perpetuity on number line)
Present value is 7.21
[tex]7.21=\frac{1}{1-u^2} \\\\1-\frac{1}{7.21} =u^2\\\\\frac{6.21}{7.21} =(1+i)^{-2}\\\\(1+i)^2=\frac{7.21}{6.21} \\\\(i+1)=\sqrt{\frac{7.21}{6.21} }\\\\ i=\sqrt{\frac{7.21}{6.21} } -1\\\\=0.77511297[/tex]
image attached (representing second perpetuity on number line)
we have ,
[tex]7.21=\frac{Ru}{1-u^3}[/tex]
Here,
[tex]V=\frac{1}{1+i}[/tex]i
i = 0.077511297 + 0.01
[tex]\therefore V =\frac{1}{1.087511295} =(1.087511297)^-^1\\\\7.21=\frac{R(1.087511297)^-^1}{1-(1.087511297)^-^3} \\\\7.21=4.132664645R\\\\R=\frac{7.21}{4.132664645} \\\\R= 1.7446370\approx1.74[/tex]
Therefore, value of R is 1.74
Which of the following real-world problems can be modeled with the inequality 384+2x<6x? Marta charges a flat fee of $384 plus $2 per linear foot to decorate tables for a quinceanera. Carla charges $6 per linear foot to do the same. For what number of linear feet, x, will the cost of both decorators be the same? Shawna has made 384 campaign buttons for the student council election. She plans to make 2 more buttons each hour. Marguerite plans to make 6 campaign buttons per hour. For what number of hours, x, will Shawna have the same amount of campaign buttons as Marguerite? Super Clean house cleaning company charges $384 to power wash a house plus $2 per linear foot. Power Bright charges $6 per linear foot and no flat fee. For what number of linear feet, x, will the cost of Super Clean be more expensive than Power Bright? Mega Gym charges a $384 registration fee and $2 each time the gym is used. Super Gym charges a fee of $6 every time the gym is used. What number of times, x, will Super Gym need to be used to exceed the cost of Mega Gym?
Answer:
Mega Gym charges a $384 registration fee and $2 each time the gym is used. Super Gym charges a fee of $6 every time the gym is used. What number of times, x, will Super Gym need to be used to exceed the cost of Mega Gym?
Step-by-step explanation:
Given: the inequality is [tex]384+2x<6x[/tex]
To find: the correct option
Solution:
Let x denotes number of times gym is used.
As Mega Gym charges a $384 registration fee and $2 each time the gym is used,
Total amount charged by Mega Gym = [tex]\$(384+2x)[/tex]
As Super Gym charges a fee of $6 every time the gym is used,
Total amount charged by Super Gym = [tex]\$\,6x[/tex]
In order to find number of times, x Super Gym is used such that cost of Super Gym exceeds the cost of Mega Gym,
Solve the inequality:
cost of Super Gym > cost of Mega Gym
[tex]6x>384+2x\\384+2x<6x[/tex]
So, the correct option is '' Mega Gym charges a $384 registration fee and $2 each time the gym is used. Super Gym charges a fee of $6 every time the gym is used. What number of times, x, will Super Gym need to be used to exceed the cost of Mega Gym? ''
Determine 6m 9m how much greater the area of the yellow rectangle is than the area of the gree rectangle 2m 5m
Step-by-step explanation:
multiple 6 by 9 then 2 by 5 then subtract them
Answer:
44
Step-by-step explanation:
(6*9) - (2*5)
54 - 10
44
What is the range of the function y = -x ^2 + 1?
A. y ≤ -1
B. y ≥ -1
C. y ≤ 1
D. y ≥ 1
Answer:
C. y ≤ 1
Step-by-step explanation:
The maximum value of the function is 1. So, the range is all values of y less than or equal to that.
y ≤ 1
This Question: 4 pts
1 of 11 (0 complete)
Music Preferences
Students at a high school were polled to determine the type of music they preferred. There were 1960 students who
completed the poll. Their responses are represented in the circle graph.
Rap 916
Alternative 46
Rock and Roll 279
Country 183
Jazz 32
Other 89
About What % of the students who completed the poll preferred rock and roll music.
(Round to one decimal place as needed.)
Answer:
The percentage of the students who completed the poll preferred rock and roll music.
P(RR) = 0.1423 = 14.23 %
Step-by-step explanation:
Explanation:-
Given total number of students n(S) = 1960
Given the Students at a high school were polled to determine the type of music they preferred.
Rap 916
Alternative 46
Rock and Roll 279
Country 183
Jazz 32
Other 89
Let ' RR' be the event of Rock and Roll preferred music
given Rock and Roll = 279
n( RR) = 279
The percentage of the students who completed the poll preferred rock and roll music.
[tex]P(RR) = \frac{n(RR)}{n(s)} = \frac{279}{1960}[/tex]
P(RR) = 0.1423 = 14.23 %
A fluctuating electric current II may be considered a uniformly distributed random variable over the interval (9, 11)(9,11). If this current flows through a 2-ohm resistor, find the probability density function of the power P = 2I^2P=2I 2 .
Answer:
Step-by-step explanation:
A fluctuating electric current II may be considered a uniformly distributed random variable over the interval (9, 11)
[tex]p_1=\{^{\frac{1}{2}:9\leq i\leq 11}_{0:otherwise[/tex]
Now define
[tex]p = 2I^2[/tex]
[tex]\Rightarrow I^2=(\frac{p}{2} )\\\\\Rightarrow I=(\frac{p}{2} )^{\frac{1}{2} }\\\\\Rightarrow h^{-1}(p)=(\frac{p}{2} )^{\frac{1}{2}}[/tex]
[tex]\frac{dh^{-1}}{dp} =\frac{d[h^{-1}(p)]}{dp} \\\\=\frac{d(p/2)^{\frac{1}{2} }}{dp}[/tex]
[tex]=\frac{1}{2} \times \frac{1}{2} (\frac{p}{2} )^{{\frac{1}{2}-1} }\\\\=\frac{1}{4}(\frac{p}{2} )^{{\frac{1}{2}-1} }\\\\=\frac{1}{2}(\frac{2}{p} )^{{\frac{1}{2}} }[/tex]
using the transformation method, we get
[tex]f_p(p)=f_1(h^{-1}(p))|\frac{d[h^{-1}(p)]}{dp} |\\\\=\frac{1}{2} \times \frac{1}{4} (\frac{2}{p} )^{\frac{1}{2} }\\\\=\frac{1}{8} (\frac{2}{p} )^{\frac{1}{2} }[/tex]
[tex]f_p(p)=\{^{\frac{1}{8} (\frac{2}{p} )^{\frac{1}{2} },162\leqp\leq 242} }_{0,otherwise}[/tex]
Find the area of a circle with radius, r = 17cm.
Give your answer rounded to 3 SF. (SF means Significant figures)
Answer:
0.0908 [tex]m^{2}[/tex] (to 3 S.F.)
Step-by-step explanation:
Area = π[tex]r^{2}[/tex]
π * [tex]17^{2}[/tex] = 907.92
= 908 [tex]cm^{2}[/tex]
=0.0908 [tex]m^{2}[/tex]
The length of a rectangle is 4 inches longer than the width. If the area is 390 square inches, find the rectangle's dimensions. Round your answers to the nearest tenth of an inch.
Answer:
17.8 in x 21.8 in
Step-by-step explanation:
Given w=width and l=length
w*l=390
l=w+4, therefore w*(w+4)=390
w^2+4w=390
w^2+4w-390=0
Quadratic equation, solve as such
w=-21.8 or 17.8
Solution can't be negative so w=17.8 in
l=w+4 so l=21.8
Q 4.6: In a survey of 1,000 adults living in a big city, 540 participants said that they prefer to get news from the Internet, 330 prefer to watch news on TV, and 130 are rarely interested in the current news. We want to test if the proportion of people getting the news from the Internet is more than 50%. By generating the randomization distribution, we find that the p-value is 0.0057. Choose the correct statement interpreting the p-value.
Answer:
Option E is correct.Step-by-step explanation:
In a survey of 1,000 adults living in a big city, 540 participants said that they prefer to get news from the Internet, 330 prefer to watch news on TV, and 130 are rarely interested in the current news. We want to test if the proportion of people getting the news from the Internet is more than 50%. By generating the randomization distribution, we find that the p-value is 0.0057. Choose the correct statement interpreting the p-value.
A.If the proportion of people getting the news from the Internet is not equal to 0.5 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.
B. If the proportion of people getting the news from the Internet is not equal to 0.54 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.
C. If the proportion of people getting the news from the Internet is equal to 0.54 then there is a 0.0057 chance of seeing the sample proportion less extreme compared to the survey results. р
D. If the proportion of people getting the news from the Internet is equal to 0.54 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.
E. If the proportion of people getting the news from the Internet is equal to 0.5 then there is a 0.0057 chance of seeing the sample proportion as extreme as the survey results.
The correct interpretation of P value will be:
if the proportion of people getting the news from internet is equal to 0.5 then there is a 0.0057 chance of seeing the sample proportion as extreme as survey results.
Option E is correct.What is the area & perimeter of this figure?
Answer:
The perimeter is
Step-by-step explanation:
perimeter is the whole distance you will go around the shape
Perimeter= 19 +3+(19-5)+(8-3)+5+8
= 19+3+14+5+5+8
= 54
For area, cut the triangle into small and big rectangle
Area = 19 * 3+ (8-3) * 5
= 57 + 25
= 82
6
Cheryl had 160 stickers more than Gareth. If Cheryl gave 185 stickers
to Gareth, Gareth would have 3 times as many stickers as Cheryl
How many stickers did Gareth have at first?
165
Answer:
260 stickers
Step-by-step explanation:
Let Gareth's stickers be x.
Hence Cheryl sticker is 160+x;
If Cheryl gave 185 stickers
to Gareth, it means:
Cheryl has at the moment;
160 + x - 185 = x - 25
At this time when Gareth receives 185 he now has:
x+ 185
Also when he receives x +185, he has 3 times Cherry's meaning:
x+185 =3(x-25)
x + 185 = 3x -75
185 + 75 = 3x-2x
260= x
x = 260.
Hence Gareth has 260 stickers
250cm3 of fresh water of density 1000kgm-3 is mixed with 100cm3 of sea water of density 1030kgm-3. Calculate the density of the mixture. *
Answer:
[tex] m_{fresh}= 1000 \frac{Kg}{m^3} * 2.5x10^{-4} m^3 = 0.25 Kg[/tex]
And we can do a similar procedure for the sea water:
[tex] m_{sea}= \rho_{sea} V_{sea} [/tex]
And after convert the volume to m^3 we got:
[tex] m_{sea}= 1030 \frac{Kg}{m^3} * 1x10^{-4} m^3 = 0.103 Kg[/tex]
And then the density for the mixture would be given by:
[tex] \rho_{mixture}= \frac{m_{fresh} +m_{sea}}{v_{fresh} +v_{sea}}[/tex]
And replacing we got:
[tex] \rho_{mixt}= \frac{0.25 +0.103 Kg}{2.5x10^{-4} m^3 +1x10^{-4} m^3} = 1008.571 \frac{Kg}{m^3}[/tex]
Step-by-step explanation:
For this case we can begin calculating the mass for each type of water:
[tex] m_{fresh}= \rho_{fresh} V_{fresh} [/tex]
And after convert the volume to m^3 we got:
[tex] m_{fresh}= 1000 \frac{Kg}{m^3} * 2.5x10^{-4} m^3 = 0.25 Kg[/tex]
And we can do a similar procedure for the sea water:
[tex] m_{sea}= \rho_{sea} V_{sea} [/tex]
And after convert the volume to m^3 we got:
[tex] m_{sea}= 1030 \frac{Kg}{m^3} * 1x10^{-4} m^3 = 0.103 Kg[/tex]
And then the density for the mixture would be given by:
[tex] \rho_{mixture}= \frac{m_{fresh} +m_{sea}}{v_{fresh} +v_{sea}}[/tex]
And replacing we got:
[tex] \rho_{mixt}= \frac{0.25 +0.103 Kg}{2.5x10^{-4} m^3 +1x10^{-4} m^3} = 1008.571 \frac{Kg}{m^3}[/tex]
b) A man purchased 5 dozen of eggs at Rs 5 each. 10 eggs were broken and he
sold the remaining at Rs 5.70 each. Find
(ii) Profit or loss percent.
(i) his total profit or loss.
Answer:
Dear User,
Answer to your query is provided below
(i) Total Loss = Rs.15
(ii) Loss percent = 5%
Step-by-step explanation:
Eggs purchased = 5x12 = 60
Total Cost = 60x5 = Rs 300
Eggs Broken = 10
Eggs Broken cost = 10x5= Rs. 50
Eggs sold = 60-10 = 50
Egg Sale cost = 50x5.70 = Rs 285
(i) Total Loss = C.p. - S.p. = 300 - 285 = 15
(ii) Loss Percent = (Loss/CP)x100 = (15/300)x100 = 5%
Suppose that a population of people has an average weight of 160 lbs, and standard deviation of 50 lbs, and that weight is normally distributed. A researcher samples 100 people, and measures their weight. Find the probability that the researcher observes an average weight of the 100 people to be between 150 and 170. [Round your answer to four decimal places]
Answer:
0.9544 = 95.44% probability that the researcher observes an average weight of the 100 people to be between 150 and 170.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
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.
In this question, we have that:
[tex]\mu = 160, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5[/tex]
Find the probability that the researcher observes an average weight of the 100 people to be between 150 and 170.
This is the pvalue of Z when X = 170 subtracted by the pvalue of Z when X = 150. So
X = 170
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{170 - 160}{5}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 150
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{150 - 160}{5}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that the researcher observes an average weight of the 100 people to be between 150 and 170.
1.solve for x 3x - 2 = 3 - 4x
Answer:
[tex]x=\frac{5}{7}[/tex]
Step-by-step explanation:
[tex]3x - 2 = 3 - 4x[/tex]
Add [tex]2[/tex] and [tex]4x[/tex] on both sides of the equation.
[tex]3x - 2 +2+4x= 3 - 4x+2+4x[/tex]
[tex]3x+4x=-4x+5+4x[/tex]
[tex]7x=5[/tex]
Divide [tex]7[/tex] on both sides of the equation.
[tex]\frac{7x}{7}=\frac{5}{7}[/tex]
[tex]x=\frac{5}{7}[/tex]
In planning a restaurant, it is estimated that a profit of $8 per seat will be made if the number of seats is no more than 50 inclusive. On the other hand, the profit on each seat will decrease 10 cents for each seat above 50.
a) Find the number of seats that will produce the maximum profit.
b) What is the maximum profit?
Answer:
a. 65 seats
b. $422.50
Step-by-step explanation:
We have the following two functions:
8 * x, {0 <= x <= 50}
x * (8 - 0.1 * (x - 50)), {x> 50}, solving we have:
-0.1 * x ^ 2 + 13 * x, {x> 50}
Now we derive both functions and we are left with:
8, {0 <= x <= 50}
-0.2 * x + 13 {x> 50}
we cannot equal to 0 the first function that is equal to 0, because it would be inconsistent, therefore we equal the second function to 0:
-0.2 * x + 13 = 0
0.2 * x = - 13
x = -13 / -0.2
x = 65
Now, test for increasing and decreasing on the intervals (0.65) and (65, infinity)
p '(60) = -0.2 * (60) + 13 = 1
since this value is positive the profit is increasing on (0.65)
p '(70) = -0.2 * (70) + 13 = -1
becuase this value is negative the profit is decreasing on (65, infinity)
Therefore 65 seats are needed to maximize profit
The maximum value would be:
P (65) = 0.1 * (65 ^ 2) + 13 * 65 = 422.5
That is, the maximum value is $ 422.50
A consumer affairs investigator records the repair cost for 4 randomly selected TVs. A sample mean of $91.78 and standard deviation of $23.13 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the TVs. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
= ( $72.756, $110.804)
Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)
Critical value at 90% confidence = 1.645
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $91.78
Standard deviation r = $23.13
Number of samples n = 4
Confidence interval = 90%
Using the z table;
z(α=0.05) = 1.645
Critical value at 90% confidence = 1.645
Substituting the values we have;
$91.78+/-1.645($23.13/√4)
$91.78+/-1.645($11.565)
$91.78+/-$19.024425
$91.78+/-$19.024
= ( $72.756, $110.804)
Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)
Calculating conditional probability
G
The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom.
Here are the results:
Bride
Groom
29
30
20
1
Given that a randomly selected guest is a friend of the groom, find the probability they are a friend of the bride.
P (bride groom)
Complete Question
Calculating conditional probability
The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom.
Here are the results:
Bride :29
Groom :30
BOTH : 20
Given that a randomly selected guest is a friend of the groom, find the probability they are a friend of the bride.
P (bride | groom)
Answer:
The probability is [tex]P(B|G) = \frac{2}{3}[/tex]
Step-by-step explanation:
The sample size is [tex]n = 80[/tex]
The friend of the groom are [tex]G = 30[/tex]
The friend of the groom are [tex]B = 29[/tex]
The friend of both bride and groom are [tex]Z = 20[/tex]
The probability that a guest is a friend of the bride is mathematically represented as
[tex]P(B) = \frac{29}{80}[/tex]
The probability that a guest is a friend of the groom is mathematically represented as
[tex]P(G) = \frac{30}{80}[/tex]
The probability that a guest is both a friend of the bride and a friend of the groom is mathematically represented as
[tex]P(B \ n \ G) = \frac{20}{80}[/tex]
Now
[tex]P(B|G)[/tex] is mathematically represented as
[tex]P(B|G) = \frac{P(B \ n \ G)}{P(G)}[/tex]
Substituting values
[tex]P(B|G) = \frac{\frac{20}{80} }{\frac{30}{80} }[/tex]
[tex]P(B|G) = \frac{2}{3}[/tex]
Answer:
the answer is 3/5
Step-by-step explanation:
on Khan
Find the term that must be added to the equation x2−2x=3 to make it into a perfect square. A. 1 B. 4 C. -3 D. 2
Answer:
1
Step-by-step explanation:
x^2−2x=3
Take the coefficient of x
-2
Divide by 2
-2/2 =-1
Square it
(-1)^2 = 1
Add this to each side
A car travels 300 miles in 10 hours at a constant rate. If the distance traveled by the car can be represented as a function of
the time spent driving, what is the value of the constant of variation, K?
O 1/30 mph
30 mph
60 mph
3000 mph
Answer:
30 mph
Step-by-step explanation:
Distance travelled=300 miles
Time travelled=10hours
At a constant rate,k
Let distance travelled=d
Time travelled=t
Then,
d=kt
300=k*10
300=10k
k=300/10
=30
k=30mph
30 miles per hour
30 MPH ............................................................................................................
A population of beetles are growing according to a linear growth model. The initial population (week 0) is
P0=6, and the population after 8 weeks is P8=86 Find an explicit formula for the beetle population after n weeks.
After how many weeks will the beetle population reach 236?
Answer:
The number of weeks it will take for the beetle population to reach 236 is 28.75.
Step-by-step explanation:
If a quantity starts at size P₀ and grows by d every time period, then the
quantity after n time periods can be determined using explicit form:
[tex]P_{n} = P_{0} + d \cdot n[/tex]
Here,
d = the common difference, i.e. the amount that the population changes each time n is increased by 1.
In this case it is provided that the original population of beetle was:
P₀ = 6; (week 0)
And the population after 8 weeks was,
P₈ = 86
Compute the value of d as follows:
[tex]P_{8} = P_{0} + d \cdot 8\\86=6+8d\\86-6=8d\\80=8d\\d=10[/tex]
Thus, the explicit formula for the beetle population after n weeks is:
[tex]P_{n}=P_{0}+8n[/tex]
Compute the number of weeks it will take for the beetle population to reach 236 as follows:
[tex]P_{n}=P_{0}+8n\\\\236=6+8n\\\\8n=236-6\\\\8n=230\\\\n=28.75[/tex]
Thus, the number of weeks it will take for the beetle population to reach 236 is 28.75.
Omar has three t shirts: one red, one green and one yellow. He has two pairs of shorts one black and red.
-How many different outfits can Omar put together?
-What is the probability of Omar’s outfits including a red T-shirt or red shorts?
Answer:
Omar can put together 6 outfits.
66.67% probability of Omar’s outfits including a red T-shirt or red shorts
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
-How many different outfits can Omar put together?
For each t-shirt, that are two options of shorts.
There are 3 t-shirts.
3*2 = 6
Omar can put together 6 outfits.
What is the probability of Omar’s outfits including a red T-shirt or red shorts?
Red t-shirt and red shorts
Red t-shirt and black shorts
Green shirt and red shorts
Yellow shirt and red shorts
4 desired outcomes.
4/6 = 0.6667
66.67% probability of Omar’s outfits including a red T-shirt or red shorts
Is (-3,4) a solution of the inequality y> - 2x – 3?
O There is not enough given information to determine this.
O (-3, 4) is a solution.
(-3, 4) would be a solution if the inequality was y > - 2x – 3.
(-3, 4) is not a solution.
Answer:
(-3, 4) is a solution
Step-by-step explanation:
The point (-3, 4) is inside the shaded area of the graph, so is a solution.
You can check in the inequality
y > -2x -3
4 > -2(-3) -3 . . . . substitute for x and y
4 > 3 . . . . . . . true; the given point is a solution
What’s the correct answer for this?
Answer:
(0,2)
Step-by-step explanation:
2:4 means one part is 2/(2+4)=1/3 of AB and the other part is 2/3 of AB
Add 1/3 of the distance from -2 to 4. (1/3)(4+2)=2. -2+2=0 The x coordinate is 0
Subtract 1/3 of the distance from 6 to -6, (1/3)6+6)=4 6-4=2 The y coordinate is 2
The point is (0,2)
