Answer:
17 inches.
Step-by-step explanation:
If the area of a rectangle is the product of its length and width, then;
Area of a rectangle = Length × Width
Given that the width of the poster is greater than 10 inches and is prime, this means and W>10
Area of the rectangle = 204in²
On substituting the values in the formula;
A = LW
204 = LW
Since W is greater than 10 and is prime, it can be between the prime numbers 11, 13 and 17. Note that L must be a whole number as well for any number to be the right answer we seek.
Let's test each values of the prime width that will give a length that is a whole number.
If W = 11
204 = 11×L
L = 204/11
L = 18.54
Since the length didn't give us a whole number, this means our width is not 11.
If W = 13
204 = L × 13
L = 204/13
L = 15.69
Also, we can see that the length is not also a whole number for the value of 13 as the prime width.
If W = 17
204 = L × 17
L = 204/17
L = 12
It can be seen that the length of the rectangle gave us a whole number when we used the prime width of 17, hence the width of the poster that is greater than 10 inches and is prime that makes both length and width to be a whole number is 17 inches.
Answer:17 inches
Step-by-step explanation:
Using Euler's relation, derive the following relationships:a. Cosθ=½(e^jθ+e^−jθ)b. Sinθ=½(e^jθ−e(^−jθ)
Answer:
a. cosθ = ¹/₂[e^jθ + e^(-jθ)] b. sinθ = ¹/₂[e^jθ - e^(-jθ)]
Step-by-step explanation:
a.We know that
e^jθ = cosθ + jsinθ and
e^(-jθ) = cosθ - jsinθ
Adding both equations, we have
e^jθ = cosθ + jsinθ
+
e^(-jθ) = cosθ - jsinθ
e^jθ + e^(-jθ) = cosθ + cosθ + jsinθ - jsinθ
Simplifying, we have
e^jθ + e^(-jθ) = 2cosθ
dividing through by 2 we have
cosθ = ¹/₂[e^jθ + e^(-jθ)]
b. We know that
e^jθ = cosθ + jsinθ and
e^(-jθ) = cosθ - jsinθ
Subtracting both equations, we have
e^jθ = cosθ + jsinθ
-
e^(-jθ) = cosθ - jsinθ
e^jθ + e^(-jθ) = cosθ - cosθ + jsinθ - (-jsinθ)
Simplifying, we have
e^jθ - e^(-jθ) = 2jsinθ
dividing through by 2 we have
sinθ = ¹/₂[e^jθ - e^(-jθ)]
A rectangular athletic field is twice as long as it is wide. If the perimeter of the athletic field is 270 yards what are it’s dimensions?
Answer:
Step-by-step explanation:45x90
4x + 3 x - 6 equals 29 what is X
Rewrite the equation of a straight line in a slope - intercept form x + 2y + 1 = 0
Answer:
y = -x/2 -1/2
Step-by-step explanation:
[tex]x + 2y + 1 = 0\\[/tex]
Write in the y=mx+b form
[tex]2y =-x-1+0\\2y =-x-1[/tex]
Divide both sides by 2
[tex]\frac{2y}{2} =\frac{-1x}{2} -\frac{1}{2} \\\\y = -\frac{x}{2} -\frac{1}{2}[/tex]
6x+2=-8+3x+25 whats the answer to x?
Answer:
x = 5
Step-by-step explanation:
To find the value of x make sure to get it on one side
First subtract 3x from each side. This makes the equation now
3x + 2 = -8 + 25
Now see what 25 subtract by 8 is (17)
3x + 2 = 17
Next subtract 2 from both sides
3x = 15
Lastly, divide 15 by 3, making x equal 5
x = 5
g if cot=-1/3 and sin<0 find each function value only using the appropriate trigonometric identites
Answer:
Step-by-step explanation:
Other trigonometry identities that we have includes cosθ, sinθ, tanθ, secθ, cosecθ
cosecθ = 1/sinθ
Given cotθ=-1/3 and sinθ<0, this means that θ falls in the 4th quadrant.
cotθ= 1/tanθ = -1/3
tanθ = -3/1
Since tanθ = opposite/adjacent = -3/1
opposite = -3
adjacent = 1
Using pythagoras theorem to get the hypotenuse, hyp² = opp²+adj²
hyp² = (-3)²+1²
hyp = √9+1
hyp = √10
cosθ = adjacent/hypotenuse = 1/√10
sinθ = opp/hyp = -3/√10
cosecθ = 1/sinθ = 1/(-3/√10)
cosecθ = -√10/3
secθ = 1/cosθ
secθ = 1/(1/√10)
secθ = 1*√10/1
secθ = √10
The population of a city has increased by 27% since it was last measured. If the current population is 25400, what was the previous population
Answer:6858
Step-by-step explanation:
If angle EFH(5x+1)’ angle HFG(62 degrees) and angle EFG (18x+11) find each measurement
Answer:
∠EFH = 21°
∠HFG = 62°
∠EFG = 83°
Step-by-step explanation:
The diagram showing the angles has been attached to this response.
From the diagram, it can be deduced that;
Angle EFG = angle EFH + angle HFG
=> ∠EFG = ∠EFH + ∠HFG -------------------(i)
From the question:
∠EFH = (5x + 1)° -------------(ii)
∠HFG = 62° -------------(iii)
∠EFG = (18x + 11)° -------------(iv)
Substitute these values into equation (i) as follows;
(18x + 11) = (5x + 1) + 62
=> 18x + 11 = 5x + 1 + 62
Collect like terms and solve for x
18x - 5x = 1 + 62 - 11
13x = 52
x = 4
Now, to get each measurement, substitute x = 4 into each of equations (ii) - (iv)
∠EFH = (5x + 1)°
∠EFH = (5(4) + 1)°
∠EFH = (20 + 1)°
∠EFH = 21°
∠HFG = 62° [Does not depend on x]
∠EFG = (18x + 11)°
∠EFG = (18(4) + 11)°
∠EFG = (72 + 11)°
∠EFG = 83°
Conclusion:
∠EFH = 21°
∠HFG = 62°
∠EFG = 83°
for the right triangle shown, which equation is correct?
Answer: A) sin 59° = cos 31°
Step-by-step explanation:
Based on the angle and the sides provided, we can establish that
tan 31° = 17/x
Since no hypotenuse is provided and we cannot solve for it, we can rule out options B, C, and D.
We know that the sum of the angles of a triangle is 180°. In a right triangle, we know that one of the angles is 90°, so the other two angles are complimentary --> sin Ф = cos (90 - Ф).
Therefore, option A is true.
Two numbers are independently selected from the set of positive integers less than or equal to 5. What is the probability that the sum of the two numbers is less than their product? Express your answer as a common fraction.
Answer: P = 15/25
Step-by-step explanation:
The set of numbers that we have here is:
{1, 2, 3, 4, 5}
We select independently two numbers of that set (so the numbers can be repeated.
We want to find the probability where the sum of the numbers is less than the product.
if one of the selected numbers is 1, then always the sum will be larger than the product, because:
1*1 = 1 and 1 + 1 = 2
1*2 = 2 and 1 + 2 = 3.
and so on.
if both numbers are 2, the sum is equal to the product:
2*2 = 4 = 2 + 2.
if else, the product will be larger than the product.
The first step now is to calculate the total number of possible combinations of 2 numbers:
For the first number, we have 5 options.
for the second number, we have 5 options.
The total number of combinations is equal to the product of the number of options in each case:
C = 5*5 = 25
Now, the combinations where the product is LESS OR EQUAL than the sum are:
1 and 1
1 and 2
1 and 3
1 and 4
1 and 5.
2 and 1
3 and 1
4 and 1
5 and 1
2 and 2.
10 combinations.
Then the combinations where the product is larger than the sum is:
25 - 10 = 15.
Then the probability that we are looking for is:
P = 15/25
You have a choice between going to an in-state college where you would pay $5500 per year for tuition and an out-of-state college where the tuition is $7000 per year. The cost of Iiving is much higher at the in-state college, where you can expect to pay $1000 per month in rent, compared to $750 per month at the other college Assuming all other factors are equal, which is the less expensive choice on an annual (12-month) basis? The yearly expense of the in-state college is $_____and the yearly expense of the out-of-state college is $______. Thus on an annual basis, the less expensive choice is the (1)_______college. (Simplify your answers.) in-state out-of-state
The yearly expense of the in-state college is $16000.
We are given that;
An out-of-state college where the tuition = $7000 per year.
Now,
The yearly expense of the in-state college is:
=5500+12⋅1000
=5500+12000
=17500
By solving;
The yearly expense of the out-of-state college is:
=7000+12⋅750
=7000+9000
=16000
So, on an annual basis, the less expensive choice is the out-of-state college.
Therefore, by algebra the answer will be 16000.
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Which of the following expressions means "five factors of 3"?
Options: 3^5
5^3
5 divided by 3
I know it's definitely not the third option. Please explain your answer so I understand, thank you!
Answer:
3^5
Step-by-step explanation:
five factors of 3"
This means we have 3 multiplied 5 times
3 *3*3*3*3
3^5
After he bought a new car, Nelson purchased car insurance. He must pay $75 each month for the plan.Later that month, Nelson caused a car accident when he lost control of his vehicle. He was required to pay the first $500 of his repair costs, and then the insurance company covered the rest.
Read the passage about Nelson’s car insurance.
What is the $75 payment Nelson must make each month?
premium
co-payment
deductible
payout
Answer:
Premium
Step-by-step explanation:
took the test on Edge
The $75 payment that Nelson must make each month after buying the Car is called; A: Premium
What is Insurance Premium?
Insurance Premium is defined as the amount of money that one will have to pay for an insurance contract. The insurance premium simply represents the income of the insurance company concerned.
Now, the amount of premium paid for different insurance policies usually differs depending on a number of factors. However, the greater the risks associated with an insurance policy, the higher the premium that will be paid.
Since Nelson must make $75 payment each month, then that is referred to as the Premium.
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What is the solution to the system of linear equations? Please show steps 4x + 5y = 9
−11x − 9y = −20
Step-by-step explanation:
4x + 5y = 9
-11x - 9y = -20
solution
5y = 4x - 9
divide both side by 5
5y = 4x - 9
5 5
5 cancel at the L.H.S
y = 4x-9
5
insert the value of y in equation ii above
-11x -9(4x-9) = -20
5
-11x - 36x-81 = -20
5
cross multiply at the RHS
-11x- 36x-81 = -100
-47x-81 = -100
-47x = -100+81
-47x = -19
divide both side by -47
-47x = -19
-47 -47
x =
Which angle is supplementary to 65 degrees
Answer:
115°
Step-by-step explanation:
Supplementary angles equal 180.
180-65=115°
Answer:
[tex]\boxed{115}[/tex]
Step-by-step explanation:
Hey there!
Supplementary angles add up to 180º, so we can set up the following.
x = 180 - 65
x = 115º
Hope this helps :)
7 plus another is 20
Answer:
27
Step-by-step explanation:
Answer:
the answer would 13
Step-by-step explanation:
For the third week of July, Susan Gray worked 43 hours. Susan earns $17.70 an hour. Her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours. Calculate the following for the third week of July (round your responses to the nearest cent if necessary
Answer: $787.65
explanation:
(17.70)(40) = $708
17.70 x 1.5 = 26.55
(3)(26.55) = $79.65
$708 + $79.65 = 787.65
What is the range of the following numbers: 12,8,17,12,15,18,30
Answer: 22
Step-by-step explanation: The range is the difference between the greatest number in the data set and the least numbe rin the data set.
In this case, thats 30 - 8 or 22.
Answer:
22
Step-by-step explanation:
30 - 8 = 22
highest number - lowest number
PLEASE HELP!!! Which expression is equivelent to 32 + 16 1. 8(4+2) 2. 8(24+8) 3. 4(2+7) 4. 7(24+8)
Answer is
1. 8(4+2)
8 × 6 = 48
1
10 points
Simplify the expression by combining like terms.
7a - 2a - a - 13
type your answer...
Answer:
4a - 13
Step-by-step explanation:
● 7a - 2a - a - 13
● (7a - 2a - a) -13
● (5a-a) -13
● 4a -13
8+9t-3+4 please help me
Answer:
t = -1
Step-by-step explanation:
8 + 9t - 3 + 4
Combine like terms
(8 - 3 + 4) + 9t
9 + 9t
9t + 9
Get t by itself
9t + 9 = 0
-9 -9
9t = -9
Divide both sides by 9 to find t
t = -1
Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/6 and the common ratio is 1/4?
Answer:
[tex] a_n = 16(\frac{1}{4})^{n - 1} [/tex]
Step-by-step explanation:
Given:
Fifth term of a geometric sequence = [tex] \frac{1}{16} [/tex]
Common ratio (r) = ¼
Required:
Formula for the nth term of the geometric sequence
Solution:
Step 1: find the first term of the sequence
Formula for nth term of a geometric sequence = [tex] ar^{n - 1} [/tex], where:
a = first term
r = common ratio = ¼
Thus, we are given the 5th term to be ¹/16, so n here = 5.
Input all these values into the formula to find a, the first term.
[tex] \frac{1}{16} = a*\frac{1}{4}^{5 - 1} [/tex]
[tex] \frac{1}{16} = a*\frac{1}{4}^{4} [/tex]
[tex] \frac{1}{16} = a*\frac{1}{256} [/tex]
[tex] \frac{1}{16} = \frac{a}{256} [/tex]
Cross multiply
[tex] 1*256 = a*16 [/tex]
Divide both sides by 16
[tex] \frac{256}{16} = \frac{16a}{16} [/tex]
[tex] 16 = a [/tex]
[tex] a = 16 [/tex]
Step 2: input the value of a and r to find the nth term formula of the sequence
nth term = [tex] ar^{n - 1} [/tex]
nth term = [tex] 16*\frac{1}{4}^{n - 1} [/tex]
[tex] a_n = 16(\frac{1}{4})^{n - 1} [/tex]
What is the product of the binomials below?
(2x +5)(3x+4)
O A. 6x² +23x +20
O B. 5x2 +23x +9
O C. 6x2 + 23x +9
O D. 5x2 +23x+20
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{6 {x}^{2} + 23x + 20}}}}}[/tex]
Option A is the correct option.
Step-by-step explanation:
[tex] \sf{(2x + 5)(3x + 4)}[/tex]
Use the distributive property to multiply each term of the first binomial by each term of the second binomial
⇒[tex] \sf{2x(3x + 4) + 5(3x + 4)}[/tex]
⇒[tex] \sf{6 {x}^{2} + 8x + 15x + 20}[/tex]
Collect like terms
⇒[tex] \sf{6 {x}^{2} + 23x + 20}[/tex]
Hope I helped !
Best regards!!
For each of the following studies, identify the source(s) of sampling bias and describe (i) how it might affect the study conclusions and (ii) how you might alter the sampling method to avoid the bias.
(a) To study the size distribution of rock cod (Epinephelus puscus) off the coast of southeastern Australia, scientists recorded the lengths and weights for all cod captured by a commercial fishing vessel on one day (using standard hook-and-line fishing methods).
(b) A nutritionist is interested in the eating habits of college students and observes what each student who enters a dining hall between 8:00 A.M. and 8:30 A.M. chooses for breakfast on a Monday morning.
(c) To study how fast an experimental painkiller relieves headache pain residents of a nursing home who complain of headaches are given the painkiller and are later asked how quickly their headaches subsided.
Answer:
Answer:
A first of all because the sample involves only rock cods that voluntarily get hooked to the fishing rod, this is a major source of bias as the sample does not represent the whole general population.
Rather adopt stratified sampling stratified basing on Geographical location can be suggested for this study.
II. Because convenient sampling is adopted here data is only gotten from students that eat in the hall in a given period of time so this is a source of bias
Also one study center that is the Hall of only one school is used this is also biased and may affect the result of the study
To avoid this bias a simple random sampling where each student have an equal chance of being selected in the study should be adopted
Iii. this study is using convenient samples. and the effect of head ache medicine may be affected by other medicines too so the headache medicine cannot be the only reason for painrelief so it is better to sample rando amongst patients with headache
0.4 is one tenth of what number
Answer:
.4 is in the 10th place in a number so .4 is one tenth of 1
The given decimal is equivalent to the one tenth of 4.
What is a Decimal number?A decimal number is the representation of a number in whole and a part. The whole is represented by an integer while the part is equivalent to a number divided by the order of 10.
The given number in decimal form is 0.4.
In order to convert it in fraction, it can be written in the form of p/q as follows,
0.4 = 0.4/1
Multiply the numerator and denominator by 10 to obtain,
(0.4 × 10)/(1 × 10) = 4/10
Hence, the given number is one tenth of 4.
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Rewrite this number in appropriate scientific notation of 4,770,000
Ana is a hard-working college junior. One Saturday, she decides to work nonstop until she has answered 200 practice problems for her chemistry course. She starts work at 8:00 AM and uses a table to keep track of her progress throughout the day. She notices that as she gets tired, it takes her longer to solve each problem. Time Total Problems Answered 8:00 AM 0 9:00 AM 80 10:00 AM 140 11:00 AM 180 Noon 200 The marginal, or additional, gain from Ana’s second hour of work, from 9:00 AM to 10:00 AM, is ? problems. The marginal gain from Ana’s fourth hour of work, from 11:00 AM to noon, is ? problems. Later, the teaching assistant in Ana’s chemistry course gives her some advice. The teaching assistant says, “Based on past experience, working on 70 problems raises a student’s exam score by about the same amount as reading the textbook for 1 hour.” For simplicity, assume students always cover the same number of pages during each hour they spend reading. Given this information, in order to use her 4 hours of study time to get the best exam score possible, how many hours should she have spent working on problems and how many should she have spent reading? A. 0 hours working on problems, 4 hours reading B. 1 hour working on problems, 3 hours reading C. 3 hours working on problems, 1 hour reading D. 4 hours working on problems, 0 hours reading
Answer:
60 ; 20
B.) 1 hour working on problems, 3 hours reading
Step-by-step explanation:
Given the information :
Time - - - Total problems Answered
8am: - - - - 0
9am: - - - - 80
10am: - - - - 140
11am: - - - - -180
noon: - - - - 200
The marginal, or additional, gain from Ana’s second hour of work, from 9:00 AM to 10:00 AM, is ?
(Total problem answered at 10 a.m - Total problems Answered at 9a.m)
(140 - 80) = 60
The marginal gain from Ana’s fourth hour of work, from 11:00 AM to noon, is ?
(Total problem answered at Noon - Total problems Answered at 11a.m)
(200 - 180) = 20
In other to get the best possible exam score,
Since it is assumed that
Solving 70 problems is equivalent to 1 hour of reading in terms of score improvement
Also, it is assumed that the same number of pages is covered for every hour spent whine reading.
Hence it is only during the first hour, that is (8:00 - 9:00) that she was able to solve above 70 questions (80 - 0). Number of questions solved during subsequent hours were not up to 70, hence it would have been more rewarding if they had been used for reading.
Hence, she should have spent 1 hour working on problems and 3 hours reading
Determine whether the underlined number is a statistic or a parameter. a sample of seniors selected and it is found that 25% own a computer
Answer: Statistic.
Step-by-step explanation: Statistic are used to refer to numerical measurement pertaining to a sample. A sample refers to a subset of members chosen from a population, which means a smaller representation of the larger group. Hence, in the scenario above, the population is the entire seniors which makes up the group. While the sample is the subset of seniors drawn from the whole. Hence, statistical measures calculated or derived from the sample is called statistic. Hence, the 25% obtained is a statistic.
Solve the following equation using the zero product property (x+9)(4x-1)=0 LAST TRY !!!!!
Answer:
x=-9, x=1/4
Step-by-step explanation:
Split it into x+9=0 and 4x-1=0.
x+9=0; x=-9
4x-1=0; 4x=1; x=1/4
The combined (verbal + quantitative reasoning) score on the GRE (Graduate Record Exam) is normally distributed with mean 1049 and standard deviation 189. Suppose n = 16 randomly selected students take the GRE on the same day.
a. What is the probability that one randomly selected student scores above 1100 on the GRE?
b. Describe the sampling distribution of the sample mean for the 16 students (description should include mean, standard deviation and shape).
c. What is the probability that a random sample of 16 students has a mean GRE score that is less than 1100?
d. What is the probability that a random sample of 16 students has a mean score that is more than 1100?
e. If the sample size in (d) above was increased to 64, what affect would it have on the probability (more, less, the same, can't tell) and why?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Normal distribution :
Mean (m) = 1049
Standard deviation (sd) = 189
Number of samples (n) = 16
A) What is the probability that one randomly selected student scores above 1100 on the GRE?
Obtain the z score
Zscore = (x - m) / sd
Zscore = (1100 - 1049) / 189
Zscore = 51 / 189 = 0.2698412 = 0.27
Using the z-table
P(X > 100) = 1 - P(X < 100) = 1 - 0.6064 = 0.3936
B) The sample mean = population mean
Hence sample mean = 1049
The sample standard deviation = standard error
Standard Error (SE) = sd / sqrt(n)
SE = 189/4 = 47.25
Hence shape = normal, standard deviation = 47.25, mean = 1049
C.) P(X < 1100)
Zscore = (x - m) / SE
Zscore = (1100 - 1049) / 47.25
Zscore = 51 / 47.25 = 1.0793650 = 1.08
Using the z-table :
P(X < 1100) = 0.8599
D.) P(X > 1100)
Zscore = (x - m) / SE
Zscore = (1100 - 1049) / 47.25
Zscore = 51 / 47.25 = 1.0793650 = 1.08
Using the z-table :
P(X > 1100) = 1 - P(X < 1100) = (1 - 0.8599) = 0.1401
E) if n = 64
SE = 189 / sqrt(64) = 189 / 8 = 23.625
P(X > 1100)
Zscore = (x - m) / SE
Zscore = (1100 - 1049) / 23.625
Zscore = 51 / 47.25 = 2.1587301 = 2.16
Using the z-table :
P(X > 1100) = 1 - P(X < 1100) = (1 - 0.9846) = 0.0154
The probability decreases as the same distribution hinges towards a Boal distribution with increasing sample size.