Step-by-step explanation:
[tex]-2x^2+10x=-14\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x^2}{-2}+\dfrac{10x}{-2}=\dfrac{-14}{-2}\\\\x^2-5x=7\qquad(a-b)^2=a^2-2ab+b^2\qquad(*)\\\\x^2-2(x)(2.5)=7\qquad\text{add}\ 2.5^2\ \text{to both sides}\\\\\underbrace{x^2-2(x)(2.5)+2.5^2}_{(*)}=7+2.5^2\\\\(x-2.5)^2=7+6.25\\\\(x-2.5)^2=13.25[/tex]
[tex]\text{If you want the solution, then:}\\\\(x-2.5)^2=13.25\iff x-2.5=\pm\sqrt{13.25}\\\\x-\dfrac{25}{10}=\pm\sqrt{\dfrac{1325}{100}}\\\\x-\dfrac{25}{10}=\pm\dfrac{\sqrt{1325}}{\sqrt{100}}\\\\x-\dfrac{25}{10}=\pm\dfrac{\sqrt{25\cdot53}}{10}\\\\x-\dfrac{25}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{53}}{10}\\\\x-\dfrac{25}{10}=\pm\dfrac{5\sqrt{53}}{10}\\\\x-\dfrac{5}{2}=\pm\dfrac{\sqrt{53}}{2}\qquad\text{add}\ \dfrac{5}{2}\ \text{to both sides}\\\\x=\dfrac{5}{2}\pm\dfrac{\sqrt{53}}{2}[/tex]
[tex]\huge\boxed{x=\dfrac{5\pm\sqrt{53}}{2}}[/tex]
Whitney bought a watch for $107.50. The finance charge was $11 and she paid for it over 6 months.
Use the formula Approximate APR =(Finance Charge ÷ #Months)(12)Amount Financed to calculate her approximate APR.
Round the answer to the nearest tenth.
Answer:
20.5
Step-by-step explanation:
ur welcome :D
The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?
Complete Question:
The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?
1) The number of vans sold at the dealership last month was between 10 and 20.
2) The number of sedans sold at the dealership last month was less than 10.
Answer:
The total number of vehicles sold = 32
Step-by-step explanation:
Since the ratio of sales is 4:5:7
Let m be a common factor
The number of sedans sold = 4m
The number of trucks sold = 5m
The number of vans sold = 7m
In (1)
Since the number of vans sold was between 10 and 20. i.e 10 ≤ 7m ≤20
The only multiple of 7 between 10 and 20 is 14
Therefore, 7m = 14; m=2
in (2)
The number of sedans sold was less than 10 i.e. 0 < 4m < 10
There are two multiples of 4 between 0 and 10, they are 4 and 8
for 4m = 4; m=1
for 4m = 8; m=2
m = 2 is the only consistent value in (1) and (2)
The number of sedans sold = 4m = 4 *2 = 8
The number of trucks sold = 5m = 5 * 2 = 10
The number of vans sold = 7m = 7*2 = 14
The total number of vehicles sold = 8 + 10 + 14
The total number of vehicles sold = 32
COMPLETE QUESTION
The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?
1) The number of vans sold at the dealership last month was between 10 and 20.
2) The number of sedans sold at the dealership last month was less than 10.
Answer:
32 Vehicles
Step-by-step explanation:
Take a look at the image to see the explanation
The research department at the company took a sample of 25 comparable textbooks and collected information on their prices. This information produces a mean price of $145 for this sample. It is known that the standard deviation of the prices of all such textbooks is $35 and the population of such prices is normal. (a) What is the point estimate of the mean price of all such textbooks? (b) Construct a 90% confidence interval for the mean price of all such college textbooks.
Answer:
a) [tex]\hat \mu = \bar X = 145[/tex]
b) [tex]145-1.64\frac{35}{\sqrt{25}}=133.52[/tex]
[tex]145+1.64\frac{35}{\sqrt{25}}=156.48[/tex]
So on this case the 90% confidence interval would be given by (133.52;156.48)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X=145[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=35[/tex] represent the population standard deviation
n=25 represent the sample size
a) For this case the best point of estimate for the population mean is the sample mean:
[tex]\hat \mu = \bar X = 145[/tex]
b) Calculate the confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Since the confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that [tex]z_{\alpha/2}=1.64[/tex]
Now we have everything in order to replace into formula (1):
[tex]145-1.64\frac{35}{\sqrt{25}}=133.52[/tex]
[tex]145+1.64\frac{35}{\sqrt{25}}=156.48[/tex]
So on this case the 90% confidence interval would be given by (133.52;156.48)
changle. Show all work. Round each length to the nearest tenth and each angle to the
nearest degree.
17.
AC =
mZA =
mZC =
Answer:
Part 1) [tex]BC=12.2\ units[/tex]
Part 2) [tex]m\angle A=55^o[/tex]
Part 3) [tex]m\angle C=35^o[/tex]
Step-by-step explanation:
Part 1) Find AC
we know that
In the right triangle ABC of the figure
Applying the Pythagorean Theorem
[tex]AC^2=AB^2+BC^2[/tex]
substitute the given values
[tex]AC^2=7^2+10^2[/tex]
[tex]AC^2=149\\AC=12.2\ units[/tex]
Part 2) Find the measure of angle A
we know that
In the right triangle ABC
[tex]tan(A)=\frac{BC}{AB}[/tex] ----> by TOA (opposite side divided by the adjacent side)
substitute the values
[tex]tan(A)=\frac{10}{7}[/tex]
using a calculator
[tex]m\angle A=tan^{-1}(\frac{10}{7})=55^o[/tex]
Part 3) Find the measure of angle C
we know that
In the right triangle ABC
[tex]m\angle A+m\angle C=90^o[/tex] ----> by complementary angles
substitute the given value
[tex]55^o+m\angle C=90^o[/tex]
[tex]m\angle C=90^o-55^o=35^o[/tex]
label the sides opposite, adjacent, or hypotenuse, then find the missing side. Round to the nearest tenth for 25, 26, 27, 29, & 30
Answer:
Please see the attached pictures for full solution.
Pencils cost $0.24 each and pens cost 79 each mrs. Trevonne but six pencils and 5 pen how much did she pay for the pencil and pens in dollars and cents?
Answer:
5 dollars and 19 cents
Step-by-step explanation:
hsgd
44 friends evenly divided up an nnn-slice pizza. One of the friends, Harris, ate 111 fewer slice than he received. How many slices of pizza did Harris eat?
Answer:
Harris ate [tex]\dfrac{n-4}{4}[/tex] slices of pizza.
Step-by-step explanation:
If 4 friends evenly divided up an n-slice pizza
Total Slices=n
Number of people sharing=4
Each Friend will receive [tex]\dfrac{n}{4}[/tex] slice of pizza
Harris Ate 1 fewer slice than he received
Harris' Share= [tex]\dfrac{n}{4}[/tex]
Number of Slices Harris Ate ate[tex]\dfrac{n}{4}-1\\=\dfrac{n-4}{4}[/tex]
Answer:
N-4
___
4
Step-by-step explanation:
Eli is a 12.5 pounds of potatoes to make mashed potatoes. She uses one tenth as many pounds of butter as potatoes. How many pounds of butter does Ellie use
Answer:
Eli used 1.25 pounds of butter to make mashed potato.
Step-by-step explanation:
We are given the following in the question:
Amount of potato used by Eli = 12.5 pounds
Amount of butter used =
[tex]\dfrac{1}{10}(\text{Amount of potato used})[/tex]
Thus, pounds of butter used by Eli is:
[tex]\dfrac{1}{2}\times 12.5\\\\=1.25[/tex]
Thus, Eli used 1.25 pounds of butter to make mashed potato.
If an M:N relationship is mandatory on both sides, and if both relations resulting from the entities involved in the relationship each have 3 records, then the resulting bridge relation cannot have less than ________ records.
Answer:
3
Step-by-step explanation:
A mandatory relationship means that for every A there must be a B and vice versa. The excessive is saying that you have a relationship with 3 records each, therefore the bridge relation cannot have less than 3 records otherwise the mandatory aspect will be broke.
I hope you find this information useful and interetsing! Good luck!
A rose garden is going to be built in the city park in the shape of a parallelogram with a rectangular walkway through it. The garden region is shown below. There will not be roses in the walkway. Find the total area where roses will be planted. Show your work.
Answer: the total area where roses will be planted is 1520 feet²
Step-by-step explanation:
The formula for determining the area of a parallelogram is expressed as
Area = base × height
From the information given,
Base = 20 + 40 = 60 feet
Height = 38 feet
Area of the rose garden = 60 × 38 = 2280 feet²
The formula for determining the area of a rectangle is expressed as
Area = length × width
From the information given,
Length = 38 feet
Width = 20 feet
Area of the rectangular walkway is
20 × 38 = 760 feet²
Therefore, the total area where roses will be planted is
2280 - 760 = 1520 feet²
Help please I'm not sure if I got it right, I'm a bit confused. 5th grade math
Answer:
check your math
Step-by-step explanation:
The first subtraction was correct:
36 -7 3/4 = 28 1/4
The second subtraction needs to be revisited.
28 1/4 -6 2/4 = 27 5/4 -6 2/4 = 21 3/4
__
You can do what you did, but you need to pay attention to the signs.
28 1/4 -6 2/4 = (28 -6) +(1/4 -2/4) = 22 - 1/4 = 21 3/4
The result of subtracting 2/4 from 1/4 is -1/4, not +1/4.
_____
The length of the first cut piece was 21 3/4 inches.
Answer:
21 ¾ inches
Step-by-step explanation:
36 - 6½ - 7¾
36 - (6½ + 7¾)
36 - (6 + 7 + ½ + ¾)
36 - (13 + [2+3]/4) lcm:4
36 - (13 + 5/4)
36 - (13 + 1 + ¼)
36 - 14 - ¼
22 - ¼
21¾ inches
PLZZZZZZZZZ COME HELP ME
Answer:
-2/3
Step-by-step explanation:
using rise over run from point B you go up 2 points and then to point A left 3 and since the line is going down the slope will be negative so -2/3
How much must be deposited today into the following account in order to have $30,000 in 7 years for a down payment on a house? Assume no additional deposits are made.
An account with annual compounding and an APR of 8%
Answer: $17505 must be deposited today.
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited.
From the information given,
A = 30000
r = 8% = 8/100 = 0.08
n = 1 because it was compounded once in a year.
t = year
Therefore,.
30000 = P(1 + 0.08/1)^1 × 7
30000 = P(1.08)^7
30000 = 1.7138P
P = 30000/1.7138
P = $17505
Final answer:
To have $30,000 in 7 years for a down payment on a house, approximately $19,882.68 must be deposited today into an account with annual compounding and an APR of 8%.
Explanation:
To calculate the amount that must be deposited today, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money desired, P is the principal amount (the amount to be deposited), r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years. In this case, A = $30,000, r = 0.08 (8% as a decimal), n = 1 (compounded annually), and t = 7 years:
A = P(1 + r/n)^(nt) ⇒ $30,000 = P(1 + 0.08/1)^(1*7)
Now, we can solve the equation for P:
P = $30,000 / (1 + 0.08/1)^(1*7) ≈ $19,882.68
Therefore, approximately $19,882.68 must be deposited today to have $30,000 in 7 years for the down payment on a house.
researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% 40 % of this population prefers the color red. If 14 14 buyers are randomly selected, what is the probability that exactly 2 2 buyers would prefer red? Round your answer to four decimal places.
Answer: the probability that exactly 2 buyers would prefer red is 0.0320
Step-by-step explanation:
We would assume a binomial distribution for the color preferences of new car buyers. The formula is expressed as
P(x = r) = nCr × p^r × q^(n - r)
Where
x represent the number of successes.
p represents the probability of success.
q = (1 - r) represents the probability of failure.
n represents the number of trials or sample.
From the information given,
p = 40% = 40/100 = 0.4
q = 1 - p = 1 - 0.4
q = 0.6
n = 14
x = r = 2
Therefore,
P(x = 2) = 14C2 × 0.4^2 × 0.6^(14 - 2)
P(x = 2) = 91 × 0.16 × 0.0022
P(x = 2) = 0.0320
24 students will be divided into 4 equal size terms. Each stundent will count off, beginning with the number 1 as the first team. If nate is the eleventh student to count off, to which team number will he be addigned?
Answer:
Nate is in Group 2.
Step-by-step explanation:
Total number of students is 24.
These 24 students are divided equally among 4 groups.
Compute the number of students in each group:
Number of students in each group [tex]=\frac{24}{4}=6[/tex]
Thus, there will be 6 groups.
Now the students are numbered with the first student in the first group numbered as 1.
The groups will be:
Group 1: 1, 2, 3, 4, 5, 6
Group 2: 7, 8, 9, 10, 11, 12
Group 3: 13, 14, 15, 16, 17, 18
Group 4: 19, 20, 21, 22, 23, 24
It is provided that Nate is the 11th student.
Then Nate is in group 2.
A falling object travels a distance given by the formula d=4t+16t^2, where t is measured in seconds and d is measured in feet how long will it take for the object to travel 72ft
Answer:
2 seconds.
Step-by-step explanation:
Given [tex]d=4t+16t^{2}[/tex] and d = 72 ft
We need to solve [tex]72=4t+16t^{2}[/tex]
[tex]4t+16t^{2}-72=0[/tex]
[tex]4t^{2}+t-18=0[/tex]
[tex]4t^{2}+9t-8t-18=0[/tex]
[tex]t(4t+9)-2(4t+9)=0[/tex]
[tex](t-2)(4t+9)=0[/tex]
[tex]t-2=0,4t+9=0[/tex]
[tex]t=2,t=-\frac{9}{4}[/tex]
Since, time can not be negative, so the required time is t = 2 seconds.
Final answer:
To find the time it takes for the object to travel 72 feet based on the given distance formula d=4t+16t², you can solve for t by substituting the distance value of 72 feet into the formula and solving for t.
Explanation:
Distance: To find the time it takes for the object to travel 72 feet, we can set the distance formula d = 4t + 16t² equal to 72 feet and solve for t.
Step-by-step explanation:
Given: d = 4t + 16t² and d = 72 feet
Substitute d = 72 into the formula: 72 = 4t + 16t²
Rearrange the equation: 16t² + 4t - 72 = 0
Solve for t using the quadratic formula or factoring.
The solutions for t will give you the time it takes for the object to travel 72 feet.
Do you agree with the message in the graph title? Why or why not?
a. No, the three candidates were only separated by a margin of about 2%.
b. Yes, Roberts had twice as many votes as Johnson and four times as many as Gomez.
c. No, newspapers are always slanted towards the candidate they favor.
d. Yes, the bar for Roberts is a lot taller than the bars for Johnson and Gomez.
Each of the four responses to the question about the graph's title has a different perspective. Some are based on the data presented on the graph, such as the proportions of votes or the relative sizes of the bars representing each candidate. One comment about media bias doesn't directly pertain to the information on the graph.
Explanation:Without the precise context of the graph or its title, it is a bit tricky to answer this question directly. However, based on the details presented, let's analyze each statement:
Learn more about Graph Interpretation here:
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Compare each common trigonometric function with its respective inverse function and explain why these comparisons make sense in the light of the definition of the inverse of a function. Also, explain why you think the domains and ranges of the inverse trigonometric functions make sense in relation to their parent functions.
Final answer:
The trigonometric functions and their inverse functions are related to each other because they undo each other's actions. Inverse trigonometric functions give the angle whose trigonometric ratio is a given value. The domains and ranges of inverse trigonometric functions are restricted to ensure that they are well-defined.
Explanation:
The trigonometric functions and their inverse functions are related to each other because they undo the actions of the other function. Let's take the sine function as an example. The sine function takes an angle as input and gives the ratio of the opposite side to the hypotenuse as output. Its inverse function, arcsine, takes a ratio as input and gives the angle whose sine is that ratio as output.
These comparisons make sense in the light of the definition of the inverse of a function because an inverse function undoes the action of the original function. In the case of trigonometric functions, they represent a ratio between the sides of a right-angled triangle, and their inverses give the corresponding angle.
The domains and ranges of the inverse trigonometric functions make sense in relation to their parent functions because they are restricted to a specific range to ensure that the inverse function is well-defined. For example, the domain of arcsine function is [-1, 1] because the output of sine function is always between -1 and 1. By restricting the domain, we can ensure that the inverse function is a one-to-one mapping and has a well-defined output for each input.
A truck is being filled with cube-shaped packages that have side lengths of 1/4 foot. The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft. What is the greatest number of packages that can fit in the truck?
Answer:
24000 pieces.
Step-by-step explanation:
Given:
Side lengths of cube = [tex]\frac{1}{4} \ foot[/tex]
The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.
Question asked:
What is the greatest number of packages that can fit in the truck?
Solution:
First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.
[tex]Volume\ of\ cube =a^{3}[/tex]
[tex]=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot[/tex]
Length = 8 foot, Breadth = [tex]6\frac{1}{4} =\frac{25}{4} \ foot[/tex], Height =[tex]7\frac{1}{2} =\frac{15}{2} \ foot[/tex]
[tex]Volume\ of\ rectangular\ prism =length\times breadth\times height[/tex]
[tex]=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot[/tex]
The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube
The greatest number of packages that can fit in the truck = [tex]\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube[/tex]
Thus, the greatest number of packages that can fit in the truck is 24000 pieces.
You decide to invest a total of $1500 in a money market account at an annual interest rate of 3.4%.
Find the balance in the account after 8 years if it is compounded quarterly.
Find the balance in the account after 8 years if it is compounded monthly.
Find the balance in the account after 8 years if it is compounded continuously.
PLEASE SHOW WORK
Answer:
1) $1966.62
2) $1968.12
3) $1968.88
Step-by-step explanation:
1) 1500 × (1 + .034/4)³²
= 1966.618592
2) 1500 × (1 + .034/12)⁹⁶
= 1968.123402
3) 1500 × (e^(8×0.0314))
= 1968.880502
Answer:
1968.880502
Step-by-step explanation:
Susie's bank account balance for January through June was -100 300-475-9200 -250 and 500 what is the range of Susie's bank account balance over the six months.
Answer:
The range is 9,100
Step-by-step explanation:
Six different figures for the account balance for the six months are given.
The range of a set of numbers is defined as the difference between the highest and the lowest of the numbers.
In this question, we have;
Highest: 9200
Lowest: 100
Range = Highest - Lowest = 9200 - 100 = 9100
Answer:
There is a typo in your question it's supposed to be 200 not 9200
Step-by-step explanation:
Consider the function f ( x ) = − 5 x 3 f(x)=-5x3. Determine the average rate of change (ARoC) of f f over the following intervals of x x. From x = 3 x=3 to x = 3.5 x=3.5.
The average rate of change of f over intervals of x from x = 3 to = 3.5 is - 159.
Given that the function is,
f (x) = - 5x³
Used the formula for the average rate of change of function f at interval [a, b] is,
f' (x) = [ f (b) - f (a) ] / (b - a)
Here, f (x) = - 5x³
At x = 3;
f (3) = - 5 × 3³
= - 135
At x = 3.5;
f (3.5) = - 5 × (3.5)³
= - 214.4
Hence, the average rate of change of f over intervals of x from x = 3 to = 3.5 is,
f ' (x) = [- 214.5 - (- 135)] / (3.5 - 3)
f ' (x) = [- 79.5] / 0.5
f ' (x) = - 159
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Final answer:
The average rate of change of the function f(x) = -5[tex]x^3[/tex] from x = 3 to x = 3.5 is -158.75.
Explanation:
The average rate of change (ARoC) can be determined using the formula:
ARoC = (f(x2) - f(x1)) / (x2 - x1)
In this case, the given function is f(x) = -5x^3. To find the ARoC from x = 3 to x = 3.5, substitute these values into the formula:
ARoC = (-5[tex](3.5)^3 - (-5(3)^3)[/tex]) / (3.5 - 3)
Simplifying the equation gives:
ARoC = (-5(42.875) - (-5(27))) / (0.5)
ARoC = (-214.375 + 135) / 0.5
ARoC = -79.375 / 0.5
ARoC = -158.75
Therefore, the average rate of change of f(x) from x = 3 to x = 3.5 is -158.75.
During the summer Austin sells tomatoes at his family's produce stand . Every morning he starts with 150 tomatoes on. Sunday Austin sells 45 of the 150 tomatoes. He wants to know what percent of the tomatoes he sold.
Answer:
30%
Step-by-step explanation:
Given:
Every morning he starts with 150 tomatoes.
On Sunday Austin sells 45 of the 150 tomatoes.
Question asked:
What percent of the tomatoes he sold ?
Solution:
As Austin sells 45 tomatoes out of 150 tomatoes, we will find percent of the tomatoes he sold by using :
Percent of the tomatoes he sold = Number of tomatoes he sold divided by total number of tomatoes he starts with.
[tex]Percentage =\frac{45}{150} \times100\\[/tex]
[tex]=\frac{4500}{150} \\ = 30[/tex]
Therefore, 30% of the tomatoes he sold on Sunday.
the answer is 30%
step by step problem
Answer
Suppose the probability density function of the length of computer cables is f(x)= 0.1 from 1200 to 1210 millimeters. A) Determine the mean and standard deviation of the cable length. B) If the length specifications are 1195 < x < 1205 millimeters, what proportion of cables is within specifications?
Answer:
a) Mean = 1205
Standard Deviation = 2.89
b) P( 1195 < x < 1205) = 0.5
50% of the cables lie within the given specification.
Step-by-step explanation:
We are given the following information in the question:
[tex]f(x) = 0.1[/tex]
a = 1200, b = 1210
We are given a uniform distribution.
a) Mean:
[tex]\mu = \displaystyle\frac{a+b}{2}\\\\\mu = \frac{1200+1210}{2} = 1205[/tex]
Standard Deviation:
[tex]\sigma = \sqrt{\displaystyle\frac{(b-a)^2}{12}}\\\\= \sqrt{\displaystyle\frac{(1210-1200)^2}{12}} = \sqrt{8.33} = 2.89[/tex]
b) P( 1195 < x < 1205)
[tex]=\displaystyle\int_{1195}^{1205} f(x) dx\\\\=\displaystyle\int_{1200}^{1205} (0.1) dx\\\\=0.1[x]_{1200}^{1205} = (0.1)(1205-1200) = 0.5[/tex]
50% of the cables lie within the given specification.
Four of the seven students are from Middle Georgia State College. What is the probability that both of the interviewed students are from Middle Georgia State College? Express your answer as a reduced fraction or decimal rounded to at least four decimal places.
The probability that both of the interviewed students are from Middle Georgia State College is 2/7 or 0.2857 rounded to four decimal places.
Explanation:To calculate the probability that both interviewed students are from Middle Georgia State College, one would use the formula for conditional probability, considering the process as two sequential events. The first student being from the college and then the second one, given the first is already from the college. Since there are four students from the college out of a total of seven, the probability of picking one Middle Georgia State College student first is 4/7. After the first student from the college has been picked, there are now three remaining Middle Georgia students out of the remaining six students. Thus, the probability for the second pick is 3/6, which simplifies to 1/2. The total probability is the product of these two probabilities: (4/7) * (1/2) = 2/7, or approximately 0.2857 when rounded to four decimal places.
Which of the following equations is written in the slope-intercept form?
y + b = m + x
x + y = 1/3m
x = mb + y
y = mx + b
Answer:
y = mx + b
Hope I helped!!! :)
~Nuha
help me answer this please
Answer:
y = 4x -3
Step-by-step explanation:
The line perpendicular to the given line can be written as the same equation with the coefficients of x and y swapped, and one of them negated. The constant may be different, so we'll call it "c".
4x -y +c = 0 . . . . . line perpendicular to that given
The y-intercept of the second given line can be found by setting x=0. That gives the equation -y -3 = 0. The perpendicular line with x=0 would have equation ...
-y +c = 0
Comparing these two tells us c = -3.
So, the general form of the perpendicular line we want is ...
4x -y - 3 = 0
We can add y to put this in slope-intercept form:
y = 4x -3
The freezing point of water is 0∘ C. Scientists use positive numbers to show temperatures above the freezing point of water and negative numbers to show temperatures below the freezing point of water. Snowy's Dessert Cart keeps the ice in their snow cones at a temperature of −15∘ C What does −15∘ C represent in this situation?
Answer:
The -15°C temperature of the ice in their snow cones mean that the temperature of that ice is 15° below the freezing point of water.
Step-by-step explanation:
It is explained that Celsius scale was calibrated based on water. The scientists use 0°C to represent the freezing point of water and subsequently use positive numbers to indicate temperatures above the freezing point of water and negative numbers to indicate temperatures lower than the freezing point of water.
So, a temperature of -15°C simply means that the temperature is 15° lower than the freezing point of water.
Hope this Helps!!!
Answer:
Its A
Step-by-step explanation:
You have 555 reindeer, Bloopin, Rudy, Ezekiel, Prancer, and Balthazar, and you want to have 333 fly your sleigh. You always have your reindeer fly in a single-file line.
How many different ways can you arrange your reindeer?
Answer:
60 combinations for single file.
Step-by-step explanation:
Bloopin has 12 combinations where he leads the single file line of 3 only reindeer's at a time including the reindeer that leads the file. This is not a file of five but as the question asks for 3 there are 5 reindeer's that each have a turn of 12 each, to single file 3 reindeer's, it is here we get 12 for each combination.
12 x 5 = 60 combination.
According to the US Census Bureau's American Community Survey, 87, percent of Americans over the age of 25 have earned a high school diploma. Suppose we are going to take a random sample of 200 Americans in this age group and calculate what proportion of the sample has a high school diploma. a) What is the expected number of people in the sample with a high school diploma? b) What is the expected number of people in the sample without a high school diploma? c) Based on the answers in a) and b), Can the sampling distribution be approximated by a normal distribution? d) What is the mean of the sampling distribution ? e) What is the standard deviation of the sampling distribution ? f) What is the probability that the proportion of people in the sample with a high school diploma is less than 85%?
Answer:
B
Step-by-step explanation: pORBABLITY
Using the Central Limit Theorem, it is found that:
a) 174.
b) 26.
c) Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the central limit theorem is applied, and the sampling distribution can be approximated by a normal distribution.
d) 0.87
e) 0.0238
f) 0.2005 = 20.05% probability that the proportion of people in the sample with a high school diploma is less than 85%.
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The Central Limit Theorem establishes that for a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex] , if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
In this problem:
Sample of 200, thus [tex]n = 200[/tex].87% have a diploma, thus [tex]p = 0.87[/tex].Item a:
This is
[tex]np = 200(0.87) = 174[/tex]
Item b:
This is:
[tex]n(1-p) = 200(0.13) = 26[/tex]
Item c:
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the central limit theorem is applied, and the sampling distribution can be approximated by a normal distribution.
Item d:
The mean is:
[tex]\mu = p = 0.87[/tex]
Item e:
The standard deviation is:
[tex]s = \sqrt{\frac{0.87(0.13)}{200}} = 0.0238[/tex]
Item f:
Using z-scores, the probability is the p-value of Z when X = 0.85.
We have that:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.85 - 0.87}{0.0238}[/tex]
[tex]Z = -0.84[/tex]
[tex]Z = -0.84[/tex] has a p-value of 0.2005.
0.2005 = 20.05% probability that the proportion of people in the sample with a high school diploma is less than 85%.
A similar problem is given at https://brainly.com/question/15581844