Answer:
= 1
Step-by-step explanation:
The demand for that college will be equal to 1 or it can be said as unit elastic demand over the tuition range. This means that the demand for the college would move proportionately with the tuition range of that college, since the change in revenue is due to the change in tuition only.
Hope this helps.
Good luck and cheers.
Answer:
demand for the college is equal to 1
Step-by-step explanation:
- We know that the change in Total Revenue is only the function of change in tuition fee only.
- The change in tution fee is subjected to 15% last year multiplied by the corresponding change in demand for the college will lead to a change in total revenue.
- The relation can be expressed as:
ΔTR = Δ P *ΔD
Where,
ΔTR : Change in Total Revenue
Δ P : Change in tuition fee
ΔD : Change in demand.
- For TR to remain unchanged then ΔTR = 0. Hence,
ΔTR = 0 = Δ P *ΔD
- We are given a change in Δ P = 15%, so that means for ΔTR = 0, the change in demand ΔD = 0.
- ΔD = 0, also means that the elasticity of the demand curve is perfectly elastic or in other words the demand for the college is equal to 1.
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.
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.
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.
A cube has an edge length of 18m. What is its volume, in cubic m?
For this case we have that by definition, the volume of a cube is given by:
[tex]V = l ^ 3[/tex]
Where:
l: It's the side of the cube
According to the statement we have:
[tex]l = 18 \ m[/tex]
Substituting we have:
[tex]V = 18 ^ 3\\V = 5832 \ m ^ 3[/tex]
Thus, the volume of the cube is [tex]5832 \ m ^ 3[/tex]
ANswer:
The volume of the cube is [tex]5832 \ m ^ 3[/tex]
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
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.
Millie is drawing a triangle.One side has a length of 9 units,and another side has a length of 6 units.What could be the length of the third side of the triangle
The possible length of the third side of a triangle with sides of 9 units and 6 units must be more than 3 units and less than 15 units, according to the triangle inequality theorem.
To determine the possible length of the third side of a triangle when two sides are known, we can use the triangle inequality theorem. The theorem states that the length of any side of a triangle must be less than the sum of the other two sides and greater than their difference. In this case, Millie's triangle has sides of 9 units and 6 units.
The sum of these two sides is 9 units + 6 units = 15 units, and their difference is 9 units - 6 units = 3 units. Therefore, the third side of the triangle must be greater than 3 units but less than 15 units.
The third side must be greater than 3 units.
The third side must be less than 15 units.
To summarize, the third side could have any length that is more than 3 units but less than 15 units.
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%.
-------------------------------------
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
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.
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
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:
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 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.
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.
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
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:
The length around the outside of semicircle C from point A to point D to point B is 37 inches. The perimeter of the semicircle is 60.57 inches. Use 3.14 for pi. What is the area
The calculated area of the semicircle is 584.20 square inches
How to determine the area
From the question, we have the following parameters that can be used in our computation:
Length A to D to B = 37 inches
Perimeter of the semicircle = 60.57 inches
The perimeter of the semicircle is calculated using
P = πr
So, we have
πr = 60.57
r = 60.57/π
r = 60.57/3.14
r = 19.29
The area is then calculated as
Area = πr²/2
This gives
Area = π * 19.29²/2
Using 3.14 for π, we have
Area = 3.14 * 19.29²/2
Evaluate
Area = 584.20
Hence, the area of the semicircle is 584.20 square inches
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)
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:
https://brainly.com/question/11624428
#SPJ2
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.
PLLLLLLLLZ HELP I HAVE A DEADLINE Two elevators begin descending from the same height. Elevator A has descended 4 feet after one second, 9 feet after two seconds, 14 feet after three seconds, and so on. Elevator B has descended
3.5 feet after one second, 6.5 feet after two seconds, 9.5 feet after three seconds, and so on.
How many feet would each elevator descend in 10 seconds?
A: 59 ft; B: 36.5 ft
A: 49 ft; B: 30.5 ft
A: 85 ft; B: 72 ft
A: 54 ft; B: 33.5 ft
Answer:
A
Step-by-step explanation:
i took the test. make me branliest please
Answer:
49 ft; B: 30.5 ft
Step-by-step explanation:
Find nth terms and arithmetic means of arithmetic sequences and find sums of n terms of arithmetic series.
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:
Classify the triangle by its sides.
A. none of these
B. equilateral triangle
C. isosceles triangle
D. scalene triangle
It would be C. isosceles triangle.
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]
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
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
At a bake shop, the cost of flour is $2.50 per pound and increases at a rate of $0.07 per month. The cost of cocoa is $6.00 per pound and decreases at a rate of $0.03 per month. If the trends continue, which system of equations can be used to find the number of months, x, when the price, y, is equal for both flour and cocoa?
Answer:
Step-by-step explanation:
We will find two equations for this system, one representing flour and the other representing cocoa. For the flour, we start with $2.50, and the cost goes up .07 per month, x. The equation for that is
y = .07x + 2.50
For the cocoa, the equation is written in the exact same way, but the cost goes down. Down is a negative thing while up is a positive thing. The cost starts at $6.00 and goes down .03 per month, x. The equation for that is
y = -.03x + 6.00
Comparing the first equation to the second, the .07 is positive because the cost goes UP that amount per month and the .03 is negative because the cost goes DOWN that amount per month. Get it?
If y is cost and we are tryong to find out where the cost is the same, we are looking for when y is the same. If the first y is equal to .07x + 2.50 and the second y is equal to -.03x + 6.00, and y is equal to y, then
.07x + 2.50 = -.03x + 6.00 (this is setting the first y equal to the second y). This is the system that describes how to find the number of months x when the cost y is the same. We'll solve it just for practice.
Combining like terms we get
.10x = 3.5 so
x = 35
Now back sub in what x equals to solve for y. If x = 35, then in the first equation,
.07(35) + 2.50 = y and
y = 4.95 (you could have used the second equation and subbed in 35 for x and you will get the exact same y value. Promise!)
What this answer tells us is that 35 months after the start of this pricing, the cost of flour will be the same as the cost of cocoa. But immediately after 35 months, the costs will not be the same anymore. It is only AT 35 months. At 36 months, the costs will be different.
The requried system of equations used to find the number of months is
y = 2.50 + 0.07x and y = 6 -0.03x.
Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Let the number of months, x, when the price, y.
The cost of flour is $2.50 per pound and increases at a rate of $0.07 per month.
Equation ⇒ y = 2.50 + 0.07x - - - - - (1)
The cost of cocoa is $6.00 per pound and decreases at a rate of $0.03 per month.
Equation ⇒ y = 6 -0.03x - - - - - (2)
Solution of the equation 1 and 2 gives the price which would be equal for both flour and cocoa.
Thus, the requried system of equations used to find the number of months is y = 2.50 + 0.07x and y = 6 -0.03x.
Learn more about simultaneous equations here:
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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
Alex is creating an outdoor structure out of two 12 foot boards. The boards must have an angle of elevation
of at least 40! in order for snow to slide off and must have a width of at least 8 feet (from point A to B) in
order to fit his snow blower.
What is the range of heights, h, that Alex's structure can have? Round to the nearest tenth of a foot and show
how you arrived at your range.
Answer:
5.0 ft - 5.6 ft
Step-by-step explanation:
Given that the structure is to be made using two 12 foot boards, then we expect the total perimeter to be equal to (2*12)= 24 ft.
Using the angle of elevation, 40° and the width of 8 ft then you can apply the formula for tangent of a triangle where ;
Tan α = opposite side length/adjacent length
Tan 40°= h/8
h= 8 tan 40° = 6.71 ft
Applying the cosine of an angle formula to find the length of the sliding side
Cosine β = adjacent length /hypotenuse
Cosine 40°= 8/ sliding side length
sliding side length = 8/cosine 40° =10.44 ft
Checking the perimeter = 10.44 +8+6.71= 25.15 ft
This is more than the total lengths of the boards, so you need to adjust the height as;
24 - 18.44 = 5.56 ft ,thus the height should be less or equal to 5.56 ft
h≤ 5.6 ft
The height range for Alex's outdoor structure that ensures snow slides off with a minimum width of 8 feet is approximately 3.4 to 12 feet, calculated using the tangent function in trigonometry for the minimum height and considering the maximum height based on the board length.
To solve this, we employ trigonometry, specifically the tangent function because it relates the angle of elevation to the opposite side (height in this case) over the adjacent side (half the width here, since it's a symmetrical layout).
First, establish the minimum height using the minimum angle of elevation, 40 degrees:
tan(40 degrees) = h / (8/2)
Solving for h gives h = tan(40 degrees) × 4. Calculating this yields approximately 3.4 feet, which is the minimum height.
Next, considering the boards are 12 feet long, to find the maximum height, we can imagine them being placed vertically, thus:
h = 12 feet as the absolute maximum height since any angle of elevation would still allow snow to slide off.
Therefore, the range of heights for the structure is approximately 3.4 to 12 feet.