Null hypothesis: : The population mean number of miles driven annually by cars under the new contracts is 13,680 miles.
Alternative hypothesis:: The population mean number of miles driven annually by cars under the new contracts is less than 13,680 miles.
This is a lower-tailed or left-tailed test. (One-tailed test)
How to explain the hypothesisHere, we have to use one-sample z-test for the population mean, because we are given a value for the population standard deviation and sample size is adequate (n≥30).
The test statistic formula is given as below:
From given information, we have
Z = (13100 - 13680)/[2520/sqrt(90)]
Z = -2.1835
Test statistic = -2.1835
Given test is a lower-tailed test.
From above test statistic value, we have
P-value = 0.0145
We have P-value < α = 0.05
So, we reject the null hypothesis
There is sufficient evidence to conclude that the population mean number of miles driven annually by cars under the new contracts is less than 13,680 miles.
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Which of the following are geometric sequences? Select all correct answers.
Answer:
A, B, E
Step-by-step explanation:
Notice that A, B, and E all maintain their common ratios, while C and D do not.
In right triangle XYZ, X and Z are complementary angles and cos(X) is What is sin(Z)?
A.√20/11
B. 9/11
C. √20/9
D. 11/9
I think the answer is letter A
Need help with question #4
Question:
If n=8 and p=0.8, find P(r=7)
Answer:
0.33554
What is the absolute value of -8.35
Answer:
8.35
Step-by-step explanation:
To get absolute value, just make it the opposite
Answer: |-8.35| = 8.35
Step-by-step explanation: |-8.35| = 8.35
Two different students decide to compare their businesses. Scooter makes his own t-shirts,
while Karissa does computer repairs. For both models, x represents the number of sales made
each month and f(x) represents total money for each individual. The two functions below model
their respective businesses:
Scooter: f(x) = 200 + 15x
Karissa: f(x) = 80 + 35x
a. Describe what the slope and y intercept represent for both models based on the context.
Compare the two functions. What is one statement you could say about each?
b.
C.
In one month, Scooter sells 20 shirts. That same month, Karissa does 12 repairs. Who had
the better month?
a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.
How to Describe what the slope and y intercept represent for both models based on the contexta) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.
In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.
Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.
b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.
For Scooter, with x = 20 (number of shirts sold):
f(x) = 200 + 15x
f(20) = 200 + 15 * 20
f(20) = 200 + 300
f(20) = 500
For Karissa, with x = 12 (number of repairs):
f(x) = 80 + 35x
f(12) = 80 + 35 * 12
f(12) = 80 + 420
f(12) = 500
Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.
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tanx(1+cos2x)=sin2x prove the identity
Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).
What is the prove of the given identity?To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.
Starting with the left-hand side (LHS):
tan(x)(1 + cos(2x))
We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:
LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))
Next, we can simplify the expression by expanding and combining like terms:
LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)
Simplifying further:
LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)
Now, let's work on the right-hand side (RHS):
sin(2x)
Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).
Now, let's compare the LHS and RHS expressions:
LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)
RHS = 2sin(x)cos(x)
To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:
LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)
Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:
LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)
= [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)
= 2sin(x) - 2sin³(x) / cos(x)
Now, using the identity 2sin(x) = sin(2x), we can simplify further:
LHS = sin(2x) - 2sin³(x) / cos(x)
Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.
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2. The diagram above shows a wooden structure in the form of a cone mounted on hemispherical base. The vertical height of the cone is 24cm and the base 7cm. Calculate correct to 3 significant figures the surface area of the structure. (Take π= 22/7)
The surface area of the wooden structure is approximately 1012 cm².
To calculate the surface area of the wooden structure, we need to find the surface area of the cone and the surface area of the hemispherical base, and then add them together.
Surface Area of the Cone:
The surface area of a cone is given by the formula:
A_{cone = \(\pi \times r_{cone} \times (r_{cone} + s_{cone})\), \(r_{cone\) is the radius of the base of the cone and \(s_{cone\) is the slant height of the cone.
The vertical height of the cone is 24 cm, and the base radius is 7 cm, we can calculate the slant height using the Pythagorean theorem:
\(s_{cone\) = \(\sqrt{(r_{cone}^2 + h_{cone}^2).\)
Using the given measurements:
\(s_{cone\) = √(7² + 24²) cm
\(s_{cone\) ≈ √(49 + 576) cm
\(s_{cone\) ≈ √625 cm
\(s_{cone\) ≈ 25 cm
Now, we can calculate the surface area of the cone:
\(A_{cone\) = π × 7 cm × (7 cm + 25 cm)
\(A_{cone\) = (22/7) × 7 cm × 32 cm
\(A_{cone\) = 704 cm²
Surface Area of the Hemispherical Base:
The surface area of a hemisphere is given by the formula:
\(A_{hemisphere\) = \(2 \times \pi \times r_{base}^2\), \(r_{base\) is the radius of the base of the hemisphere.
Given that the base radius is 7 cm, we can calculate the surface area of the hemispherical base:
\(A_{hemisphere\) = 2 × (22/7) × (7 cm)²
\(A_{hemisphere\) = (22/7) × 2 × 49 cm²
\(A_{hemisphere\) = 308 cm²
Total Surface Area:
To calculate the total surface area, we add the surface area of the cone and the surface area of the hemispherical base:
Total Surface Area = \(A_{cone} + A_{hemisphere}\)
Total Surface Area = 704 cm² + 308 cm²
Total Surface Area = 1012 cm²
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g(x)
12 fy
10
88
8
6
4
4-3-2-12
-8
10
-1²1
f(x)
4 5 6 x
Which statement is true regarding the functions on the
graph?
Of(6) = g(3)
f(3) = g(3)
f(3) = g(6)
f(6) = g(6)
PLEASE HURRY IM TIMED!!!!
Answer: f(3) = g(6)
Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer
Dominique is selling merchandise for a school fundraiser. she is selling calendars for $7 each and coffee mugs for $11 each. she must sell at least $700 of merchandise, including at least 50 mugs, to meet her goals. if x represents the number of calendars and y represents the number of mugs, which system of inequalities represents this scenario? a. 7x + 11y > 700 and y > 50 b. 7x + 11y > 700 and x > 50 c. 7x + 11y ≥ 700 and y ≥ 50 d. 7x + 11y ≥ 700 and x ≥ 50
Answer:
Step-by-step explanation:
The goal of Dominique's fundraiser is to sell at least $700 of merchandise, which means she needs to earn at least $700 from the sale of calendars and coffee mugs. This requirement can be represented by the inequality 7x + 11y ≥ 700, where x is the number of calendars sold and y is the number of coffee mugs sold. The "≥ 700" part of the inequality means that the total sales (7x + 11y) must be greater than or equal to $700.
In addition to selling at least $700 of merchandise, Dominique must also sell at least 50 coffee mugs. This requirement can be represented by the inequality y ≥ 50, which means that the number of coffee mugs sold must be greater than or equal to 50.
So, the system of inequalities that represents this scenario is:
7x + 11y ≥ 700 and y ≥ 50
This system of inequalities describes the conditions that Dominique needs to meet in order to reach her fundraising goals.
The system of inequalities which represents this scenario is,
⇒ 7x + 11y ≥ 700 and y ≥ 50
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Dominique is selling calendars for $7 each and coffee mugs for $11 each. And, she must sell at least $700 of merchandise, including at least 50 mugs, to meet her goals.
Now, Let x represents the number of calendars and y represents the number of mugs.
Hence, The correct inequality for this scenario is,
⇒ 7x + 11y ≥ 700 and y ≥ 50
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the population full-time equivalent number of students (ftes) at lake tahoe community college for 2005-2006 through 2010-2011 was given in an updated report. the data are reported here. year 2005-06 2006-07 2007-08 2008-09 2009-10 2010-11 total ftes 1,585 1,690 1,735 1,935 2,021 1,890 calculate the mean, median, standard deviation, the first quartile, the third quartile and the iqr. round to one decimal place. mean _____
median _____
Standard deviation ______
first quartile _____
third quartile ____
IQR _____
The correct answer for the required values is 1825.5, 1,812.5, 165.2, 1,690, 1,935, and 245 respectively.
To find the mean, median, standard deviation, first quartile, third quartile, and interquartile range (IQR) of the full-time equivalent number of students (FTES) at Lake Tahoe Community College for the given years, we can solve it using the following formulas for various aspects:
Mean: μ = (Σx)/n
Median: Middle value of the data set
Standard deviation: σ = sqrt[Σ(x-μ)²/n]
First quartile (Q1): Median of the lower half of the data set
Third quartile (Q3): Median of the upper half of the data set
IQR: Q3 - Q1
Year FTES
2005-06 1,585
2006-07 1,690
2007-08 1,735
2008-09 1,935
2009-10 2,021
2010-11 1,890
1. μ = (Σx)/n = (1,585 + 1,690 + 1,735 + 1,935 + 2,021 + 1,890)/6 = 1,825.2
Therefore the mean is 1,825.2
2. To find the median, arrange the data in ascending order:
1,585, 1,690, 1,735, 1,890, 1,935, 2,021
Since there are an even number of values, the median is the average of the two middle values, which are 1,812.5 and 1,812.5. So, the median is:
Median = (1,812.5 + 1,812.5)/2 = 1,812.5
3. σ = sqrt[Σ(x-μ)²/n]
= sqrt[((1,585-1,825.2)² + (1,690-1,825.2)² + (1,735-1,825.2)² + (1,935-1,825.2)² + (2,021-1,825.2)² + (1,890-1,825.2)²)/6]
= 165.2
4. To find the first quartile (Q1), find the median of the lower half of the data set, which consists of the values 1,585, 1,690, and 1,735.
Since there are an odd number of values, the median is the middle value, which is 1,690. Therefore, Q1 = 1,690.
5. To find the third quartile (Q3), we need to find the median of the upper half of the data set, which consists of the values 1,890, 1,935, and 2,021.
Since there are an odd number of values, the median is the middle value, which is 1,935. Therefore, Q3 = 1,935
6. IQR = Q3 - Q1
Substituting the calculated values in the equation
IQR = 1935 - 1690
= 245
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The three steps below were used to find the value of the expression [(-10 + 2) - 1] + (2 + 3). Step 1: ? Step 2: -9 + 2 + 3 Step 3: -7 + 3 Which expression is missing from Step 1? Question 3 options: [-10 + -1 + 2] + (2 + 3) [-8 - 1] + (2 + 3) [-10 + 1] + (2 + 3) [8 + 1] + (2 + 3)
Therefore, the missing expression in Step 1 is [-8 - 1] + (2 + 3).
In order to find the missing expression in Step 1, let's analyze the given steps and the final expression.
Step 1: ?
Step 2: -9 + 2 + 3
Step 3: -7 + 3
To find the missing expression in Step 1, we need to work backwards from Step 3 to Step 1.
In Step 3, the expression "-7 + 3" gives us a result of -4.
In Step 2, the expression "-9 + 2 + 3" gives us a result of -4.
So, the missing expression in Step 1 should also evaluate to -4 when performed correctly.
Let's check the available options:
[-10 + -1 + 2] + (2 + 3) = -11 + 2 + 5 = -4
[-8 - 1] + (2 + 3) = -9 + 5 = -4
[-10 + 1] + (2 + 3) = -9 + 5 = -4
[8 + 1] + (2 + 3) = 9 + 5 = 14
Out of the given options, only option 2, [-8 - 1] + (2 + 3), correctly evaluates to -4. Therefore, the missing expression in Step 1 is [-8 - 1] + (2 + 3).
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help me to do this
math question
help me to do it with step by step
Step-by-step explanation:
b.solution
we should add q to get p+q
c.solution
we should subtract 7a to get 5a
d.solution
we should subtract 2y to get 3x-2y
Q should be added to P to get p+q
7a should be subtracted from 12a to get 5a
2y should be subtracted from 3x to get 3x-2y
can someone help me on 5 or 6. (find the area and perimeter)
Answer:
the answer is 6 trust. poopoo
Answer this question.
Answer:
B. y = -2x + 5
Step-by-step explanation:
By looking at the table of values, as x increases by 1, y decreases by 2. This means the slope is -2. By process of elimination, this leaves with answer B.
yes or no?????!!!!!!!!
Answer:
Yes they are similar
Step-by-step explanation:
They have the same angle measurements.
Answer:
yes they are similar
Step-by-step explanation:
I need this please help me
Answer:
78
Step-by-step explanation:
m<6 is an alternate exterior angle from m<3 so that means they are equal
Hope this helped!
Find the unknown angle
Answer:
V=70° P=110° U=70° T=70° S=110° R=70°
Step-by-step explanation:
Adjacent Angles equal the same thing (The ones on opposite sides). A straight line must equal 180°.
180°-110° makes V° equal 70°.
Answer:
there are two p. so, i had made upper p as a.
In a recent survey, 1200 people were interviewed. 2 1/2 % of those surveyed earned more than $60,000 a year. How many people who were surveyed earned more than $60,000
30
846
2250
3000
Answer: 30 people who were surveyed earned more than $60,000
Step-by-step explanation:
Set up a proportion
x/1200=2.5/100
Cross multiply
100x=3000
x=30
Three friends went to get gas at three different stations.Adrianna paid $36.00 for 12 gallons of gas. Jason paid $56.00 for 20 gallons of gas. Tom paid $49.50 for 18 gallons of gas. Who got the Best Buy per gallon of gas? Who paid the most and got less savings per gallon of gas?
Answer:
Tom got the best buy per gallon of gas as he paid $2.75 for each gallon.
Adrianna paid more and got less savings per gallon as she paid $3.00 for each gallon.
Step-by-step explanation:
Given that:
Adrianna paid $36.00 for 12 gallons of gas.
Price per gallon = \(\frac{Total\ price}{total\ gallons\ bought}\)
Price per gallon = \(\frac{36.00}{12}=\$3.00\)
Jason paid $56.00 for 20 gallons of gas.
Price per gallon = \(\frac{56.00}{20}\)
Price per gallon = $2.80
Tom paid $49.50 for 18 gallons of gas.
Price per gallon = \(\frac{49.50}{18}\)
Price per gallon = $2.75
We will compare the prices of per gallon gas.
Hence,
Tom got the best buy per gallon of gas as he paid $2.75 for each gallon.
Adrianna paid more and got less savings per gallon as she paid $3.00 for each gallon.
HELP PLEASE
at big 5, the percent of sales tax is 6 percent. you want to buy a skateboard that costs 98 dollars. you have 100 dollars to spend. do you have enough money? if you don't, how much more money would you need in order to buy the skateboard.
You would need an additional $3.88 to buy the skateboard.
To find out if you have enough money to buy the skateboardWe need to calculate the total cost, including sales tax.
The sales tax rate is 6%, so the tax on a skateboard costing $98 would be as follows:
tax = 0.06 x $98 = $5.88
Consequently, the skateboard would have a total cost of:
total cost = $98 + $5.88 = $103.88
Since you have $100 to spend, you do not have enough money to buy the skateboard. You would need:
additional money = $103.88 - $100 = $3.88
Therefore, you would need an additional $3.88 to buy the skateboard.
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Astronomers believe that the radius of a variable star increases and decreases with the brightness of the star. Suppose a variable star has an average radius of 20 million miles and changes by a maximum of 1.6 million miles from this average during a single pulsation, and that the time between periods of maximum brightness is 5.2 days. Find an equation that describes the radius of this star as a function of time. (Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing.) R(t) =
Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then R(t) = 20 + 1.6sin(2πt/5.2).
The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.
In this case, the amplitude is 1.6.
Since the radius changes by a maximum of 1.6 million miles.
The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)
The phase shift is 0, since when t = 0 the radius is increasing.
The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)
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i flip a coin three times and then another three times if the number of heads is the same the first and second time i win is this game worth playing
I flip a coin three times, and then another three times. If the number of heads is the same the first and second time, I win. If the number of heads is different, then I win. If I win, you pay me one dollar. If you win, I give you 3 dollars. This is worth playing game.
Let's assume that player A wins if both sets of coins are fair and have an equal number of heads.
The likelihood of this = (1/8)^2 + (3/8)^2 + (3/8)^2 + (1/8)^2
The likelihood of this = 1/64 + 9/64 + 9/64 + 1/64
The likelihood of this = (1 + 9 + 9 + 1)/64
The likelihood of this = 20/64
The likelihood of this = 5/16
If the two sets are different, let's say B triumphs.
The likelihood of this = 1 - 5/16 = 11/16
Therefore, if A wins 3 dollars and loses 1 dollar, then A's predicted net gain is
= 3 × 5/16 - 1 × 11/16
= 15/16 - 11/16
= (15 - 11)/16
= 4/16
So this game is defiantly worth playing game.
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The complete question is:
I flip a coin three times, and then another three times. If the number of heads is the same the first and second time, I win. If the number of heads is different, then I win. If I win, you pay me one dollar. If you win, I give you 3 dollars. Is this game worth playing?
Paige Inc. has a division that makes paint and another division that constructs houses. The paint division incurs the following costs for one litre of paint: Direct materials R1.10 Direct labour R1.45 Variable overhead R0.90 Fixed overhead R1.15 Total R4.60 The Paint Division can make 1 000 000 litres per year, and is operating at capacity. The Construction Division currently buys paint from an outside supplier for R5.20 per litre (the same price that the Paint Division receives). What is the minimum transfer price?
The solution is, $85,500 are the total cost savings for Leather Stuff.
Explanation:
In this case, we need to calculate the saving per zipper which is external price minus agreed transfer price.
Then, we will multiply the saving per zipper by the quantity of zipper required by Leather Stuff, which is 90,000 zippers.
Cost saving per zipper
= External price - Agreed transfer price
= $3.50 - $3.25
= $0.25
Total cost saving
= $0.95 x 90,000 zippers
= $85,500
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complete question:
Quinn Inc. has a number of divisions. One division, Style, makes zippers that are used in the manufacture of boots. Another division, LeatherStuff, makes boots that use the zippers and needs 90,000 zippers per year. Style incurs the following costs for one zipper: Direct materials $0.23 Direct labor 0.20 Variable overhead 0.95 Fixed overhead 1.32 Total $2.70 Quinn has capacity to make 950,000 zippers per year, but due to a soft market, only plans to produce and sell 620,000 zippers next year. LeatherStuff currently buys zippers from an outside supplier for $3.50 each (the same price that Style receives). Assume that Style and LeatherStuff have agreed on a transfer price of $3.25. What are the total cost savings for LeatherStuff?
Which expressions are equivalent to the one below? Check all that apply.9xA.32 • 3xB.3• 3xC.(3 • 3)xD.32xE.3 • 32xF.3x • 3x
We are given the expression:
\(9^x\)It can be rewritten as:
\(9^x=(3^2)^x=3^{2x}\)It can also be converted to the following equivalent expression by using 9 = 3 x 3:
\(9^x=(3\cdot3)^x\)We can elaborate on the first equivalent expression:
\(3^{2x}=3^{x+x}=3^x\cdot3^x\)Thus, the equivalent expressions are: C, D, and F
What is the answer to 156 x 13
Answer:
2028
Step-by-step explanation:
156 x 13 = 2028
Find the quotient of z₁ by z2. Express your answer in
trigonometric
form.
² - 3 (0 (4) + (*))
Z₁ cos
+/sin
Z₂
²2 = 7 (cos(377)+
COS
8
O A. 7 (cos (577) + i sin (5/77))
8
B.
21(cos(577)+isin (577))
8
OC. 21 cos
21(cos(-7)+ i sin(-77))
O D. 7 (cos(-7) + + sin(-7))
i
+/sin
37T
8
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.
Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.
We have:
z₁ = 7(cos(577°) + i sin(577°))
Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.
From the given information, we have:
z₂ = 21(cos(-7°) + i sin(-77°))
To find the quotient, we divide z₁ by z₂:
z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]
Substituting the given values, we have:
z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]
= (7/21) * [cos(584°) + i sin(584°)]
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.
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Which of the numbers, 285, 627, 5490, 7295, 15780, 43695, are divisible by 5 but not 3?
(BTW I NEED ANSWERS BY TOMORROW 11/28)
Answer:7295
Step-by-step explanation:
the ratio of shorts to pants is 1/2 if there are 8 shorts how many pants are there
A.16
B.4
C.6
D.8
What is the monthly payment for a $14,000 loan for 6 years with an annual interest rate of 3.1%?
Answer:
Calculate the monthly and total repayment cost of your personal loan using the ... 1 year, 2 years, 3 years, 4 years, 5 years, 6 years, 7 years, 8 years, 9 years ... annual interest rates (APRs), you can see how your monthly loan repayments ... We compare loans that can be paid back over terms of between one and 25 years.
Help me with this question please
Answer: C
Step-by-step explanation:
Y=2x-4
8=2(6)-4
8=12-4
8=8 Correct