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Related Questions
The trip to Australia is in six months how much does she need to save each month to make her go of $2,370.00?
Answers
Answer:
2 370 / 6 = 395
She need to save $395 per monthStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-NO LINKS!!
You are offered two jobs selling textbooks. One company offers an annual salary of $42000 plus a year-end bonus of 1% of your total sales. The other company offers an annual salary of $30000 plus a year-end bonus of 2.5% of your total sales. How much would you have to sell in a year (in dollars) to make the second offer the better offer?
Total sales would need to be greater than $
Answers
Answer:
At $800,000 of sales the offers are equal. Anything over 800,000 makes the second deal a better deal.
Step-by-step explanation:
Let y equal the total money earned.
Let x equal the total sales.
y = .01x + 42000
y = .025x + 30000 Set these two equations equal to each other.
.01x + 42000 = .025x + 30000 Subtract .01x from both sides
.01x -.01x + 42000 = .025x - .01x + 30000
42000 = .015x + 30000 Subtract 30000 from both sides
12000 = .015x Divide both sides by .015
[tex]\frac{12000}{.015}[/tex] = [tex]\frac{.015x}{.015}[/tex]
800,000 = x
Answer:
job 1 , y = 42 000 + 0.01x
job 2 , y = 30 000 + 0.025x
42 000 + 0.01x < 30 000 + 0.025x
42 000 - 30 000 < 0.025x - 0.01x
12 000 < 0.015x
x < 800 000
You need to make total sales of more than $800 000 to make the second offer better.example of u get 900 000 total sales
42 000 + 0.01(900 000) < 30 000 + 0.025(900 000)
42 000 + 9000 < 30 000 + 22 250
51 000 < 52 500
Therefore, you need to make a total sales of more than $800 000.Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Calculate the standard deviation of the following set of numbers. Use the formula for the standard deviation (s) shown, where x represents the values, n is the number of values, and is the summation symbol, which indicates that you should add the values. S = mon-1) (* {x? - (Ex)}) values: Xı = 13,X2 = 16, x3 = 10 Do not round your answers. Step 1. Calculate the square of each data value. Step 2. Determine n times the sum of squares of the three values. 1 Step 3. Calculate the sum of the three values. Step 4. Calculate the square of the sum of the three values. ηΣ x2 = Step 3. Calculate the sum of the three values. Σx= Step 4. Calculate the square of the sum of the three values. Step 5. Calculate the variance. (n-1) (»« - (Ex)")= Step 6. Calculate the standard deviation. 1 nin – 1) (»Ex2 - (2 x)") =
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The standard deviation is 3.
What is standard deviation?Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.
Given, formula for the standard deviation
s = √[1/n(n-1)](n∑x²-(∑x)²)
values: x₁ = 13, x₂ = 16, x₃ = 10
step1: Calculate the square of each data value.
x₁² = 13² = 169
x₂² = 16² = 256
x₃²= 10² = 100
step2: Determine n times the sum of squares of the three values.
n∑x² = n(x₁²+x₂²+x₃²)
=3(169+256+100) = 1575
step3: Calculate the sum of the three values.
∑x = x₁+x₂+x₃
= 13+16+10 =39
step4: Calculate the square of the sum of the three values.
(∑x)² = 1521
step5: Calculate the variance.
[1/n(n-1)](n∑x²-(∑x)²)
=[1/3(3-1)](1575-1521)
=54/6
=9
step6: Calculate the standard deviation.
√[1/n(n-1)](n∑x²-(∑x)²)
= √9
=3
Hence, The standard deviation using the given formula for x₁=13, x₂=16 and x₃=10 is 3.
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I do not understand what is going on for this question
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(x,y,z)=(19,14,3)
What is equation matrix and vector?This means that by dividing the inverse of the A matrix by the B matrix, we may calculate the values of x, y, and z (the X matrix).An arrangement of numbers, occasionally expressions and symbols, in rows and columns is called a matrix. Quantum mechanics, optics, mathematics, and other mathematical functions are all solved using matrix formulas.It's not nearly as difficult as it sounds; all you have to do is multiply the rows by the columns and add up the components.In geology, seismic surveys are carried out using matrix technology. They are employed in the production of graphs, statistics, calculations, and scientific investigations and research in a range of fields.A matrix is a collection of numbers, while a vector is a list of numbers that can be in either a row or a column (one or more rows, one or more columns).To learn more about equation matrix refer to:
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Jim has to choose between two gym membership plans. Plan A: $50 monthly membership fee and $10 per visit. Plan B: $25 one time membership fee and $15 per visit. How many visits must Jim make to make Plan A the cheaper option?
How many visits for them to cost the same?
Answers
Answer:
Plan B is better than Plan A as B is cheaper than A.
Since we have given that
Plan A consist of :
Amount for monthly membership fee = $50
Cost per visit = $10
Equation of total fees would be
Plan B consist of :
Amount for monthly one time membership fee = $25
Cost per visit = 15
Equation of total fees would be
Here , x denotes the number of visits.
Let us suppose x = 1
Then , fees for plan A would be
Fees for plan B would be
Hence, Plan B is better than Plan A as B is cheaper than A.
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.)
Answers
The probability of not selecting any of the correct six integers in a lottery is 0.18. This is calculated by subtracting the probability of selecting all the correct integers from 1, and the probability of selecting all the correct integers is the product of the probabilities of selecting each of the integers.
The probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers is 0.18. To calculate this probability, we must first find the probability of selecting all the correct integers. This is done by calculating the probability of selecting each of the integers individually and multiplying them together. For example, the probability of selecting 6 is 1/5, since there are five positive integers not exceeding 6. The probability of selecting 8 is 2/5, since there are five positive integers not exceeding 8 and two of them are 8. The probability of selecting 9 is 3/5, since there are five positive integers not exceeding 9 and three of them are 9. The probability of selecting 10 is 4/5, since there are five not exceeding 10 and four of them are 10. The probability of selecting 11 is 5/5, since there are five positive integers not exceeding 11 and five of them are 11
Probability of selecting all the correct integer
= (1/5)*(2/5)*(3/5)*(4/5)*(5/5)
= 0.18
Probability of selecting none of the correct integers
= 1 - 0.18 = 0.18
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The complete question is
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.)Given: 6, 8, 9, 10, 11
Suppose line g is the line with the equation y = x. Given A(7, -3), B(7, 3), and C(-1, -7), what are the coordinates of the vertices of ΔA’B’C’ for the reflection?
Answers
Answer:
Below in bold.
Step-by-step explanation:
A reflection in the line y = x is described as;
(x, y) ---> (y, x)
So, A' = (-3, 7)
B' = (3, 7)
C' = (-7, -1).
Mary, Keith, and David sent a total of 149 text messages over their cell phones during the weekend. Keith sent 4 times as many messages as David. David sent 5 fewer messages than Mary. How many messages did they each send?
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The messages sent by each person will be:
David sent 24 message
Keith sent 96 messages
Mary sent 29 messages.
How many messages did they each send?Let David be represented as x.
Keith sent 4 times as many messages as David. This will be 4x.
David sent 5 fewer messages than Mary. Mary has x + 5.
The equation will be:
David + Keith + Mary = 149
x + 4x + x + 5 = 149
6x + 5 = 149
Collect like terms
6x = 149 - 5
6x = 144
Divide
x = 144 / 6
x = 24
David sent 24 message
Keith = 4x
= 4 × 24
= 96 messages
Mary = x + 5
= 24 + 5
= 29 messages.
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A company is painting the exterior walls of a warehouse. find the lateral surface are of the walls in square feet if the walls are 100 ft., 200 ft, and 30 ft
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The lateral surface area of the walls of the warehouse is 18,000 sq ft.
Area is a measure of the size of a surface or the amount of space that a two-dimensional shape occupies. It is typically measured in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length and width of the shape together.
To find the lateral surface area of the walls of the warehouse, you need to find the combined area of all the exterior walls. To do this, you can use the formula for lateral surface area, which is:
Lateral Surface Area = 2 * (l * h + w * h)
where l is the length of the wall, w is the width of the wall, and h is the height of the wall.
Using this formula, we can find the lateral surface area of each wall and add them together to get the total lateral surface area:
Wall 1: Lateral Surface Area = 2 * (100 ft * 30 ft) = 6,000 sq ft
Wall 2: Lateral Surface Area = 2 * (200 ft * 30 ft) = 12,000 sq ft
Total Lateral Surface Area = 6,000 sq ft + 12,000 sq ft = 18,000 sq ft
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Suppose you took a large number of random samples of size n from a large population and calculated the mean of each sample. Then suppose you plotted the distribution of your sample means in a histogram. Now consider the following possible attributes of your collected data and the population from which they were sampled. For which of the following sets of attributes would you not expect your histogram of your sample means to follow a nearly normal distribution?
A) n = 10. The population distribution is unknown, but the distribution of data in each sample is heavily skewed.
B) n = 120. The population distribution is slightly skewed.
C) n = 20. The population distribution is nearly normal.
D) n = 120. The population distribution is unknown, but the distribution of data in each sample is slightly skewed.
Answers
No, because with a sample size of 10, the heavily skewed population distribution will not allow for a nearly normal distribution of sample means.
With a sample size of 10, the heavily skewed population distribution will not allow for a nearly normal distribution of sample means. This is because the sample size is too small and the skewed population distribution will not have enough data to accurately represent the overall population. With a sample size of 10, the sample means will be heavily influenced by outliers and extreme values, which will lead to a histogram that is skewed and not nearly normal. Therefore, no matter how slightly skewed the population distribution is, a sample size of 10 is not large enough to create a normal distribution of sample means.
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When the measure being made consists of judgments or ratings of multiple observers, the degree of agreement among observers can be established by using a statistical measure of _____.
A. concurrent validity
B. margin of error
C. interrater reliability
D. split-half reliability
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The degree of agreement among observers can be established by using a statistical measure of Inter rater reliability (Option c is correct)
Interrater reliability describes how closely two or more people agree.
Because everyone has used it, interrater reliability is the easiest type of reliability to comprehend. For instance, watching a judged event like dog shows or Olympic ice skating depends on human observers upholding a high level of consistency across observers.
Higher values of Kendall's coefficient, which ranges from 0 to 1, suggest more inter-rater reliability. Excellent values are greater than 0.9, and a value of 1 denotes perfect agreement. For the purpose of testing hypotheses, statistical software can compute confidence ranges and p-values.
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Consider the differential equation dy/dx = 1/3x(y-2)^2.
(a) A slope field for the given differential equation is shown below. Sketch the solution curve that passes through the point (0, 2), and sketch the solution curve that passes through the point (1, 0).
(b) Let y = f(x) be the particular solution to the given differential equation with initial condition f(1) = 0. Write an equation for the line tangent to the graph of y = f(x) at x = 1. Use your equation to approximate f(0.7).
(c) Find the particular solution y = f(x) to the given differential equation with initial condition f(1) = 0.
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The graph is given below and the value of the function is -0.4 at x = 0.7.
What is a differential equation?Any equation with a variable difference in it is a difference equation. The following variables affect how different equations are categorized. • The equation's order. The highest order of difference in the equation is represented by the order.
y = Mt (x - 1) + 0
Where Mt = 1/3* 1(0-2)²
Mt = 1/3*4
Mt = 4/3
From equation 1
y = (4/3)(x - 1)
Function at x = 0.7
f(0.7) = 4/3(0.7 -1 )
= 4/3(-0.3)
F(0.7) = -2/5
Let, u = y - 2
du = dy
[tex]\int\limits {1/(y-2)^2} \, dy = \int\limits {x/3} \, dx \\\int\limits{du/ u^2} \, du = 1/3 \int\limits{x} \, dx[/tex]
-1/u = 1/3( x²/2) + c
-1/(y+2) = x²/6 + c
At point(1 , 0 )
c = 2/6
Thus
-1/(y-2) = x²/ 6 - 1/3
y = -6/(x² + 2) + 2
Therefore, value of the function is -0.4 at x = 0.7.and function at x = 1 is
y = -6/(x² + 2) + 2
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-\sqrt(16x^(2)) if x<0
Answers
Therefore , [tex]-4|x|[/tex] is the square root of [tex]-\sqrt{16x^{2} }[/tex]
what is square root?When a number is multiplied by itself, the result is known as the square root of the number. To represent the square root, use the radical symbol. For illustration, [tex]\sqrt[/tex]16 = 4. Another name for the radical sign is the root symbol or surds.
given
- [tex]\sqrt{16x^{2}[/tex] when [tex]x[/tex] < 0,
In order to solve the given expression we will take the square root of the term inside the root.
Perfect squares (squares of integers) make up the word in the square root, thus we can express it as a square of the numbers.
⇒ [tex]-\sqrt{(4x)^{2} }[/tex] [ as [tex](4x)^{2}[/tex] = [tex]16x^{2}[/tex]]
On taking square root the square gets removed. So, we have,
[tex]-|4x|[/tex] =[tex]-4|x|[/tex]
Since , so the value would be negative.
Therefore , [tex]-4|x|[/tex] is the square root of [tex]-\sqrt{16x^{2} }[/tex]
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In the article "Foods, Fortificants, and Supplements: Where Do Americans Get Their Nutrients?" researchers analyze the nutrient and vitamin intake from a random sample of 16,110 U.S. residents. Researchers compare the level of daily vitamin intake for vitamin A, vitamin B-6, vitamin B-12, vitamin C, vitamin D, vitamin E and calcium. Unless otherwise stated, all hypothesis tests in the study are conducted at the 5% significance level.
Researchers conduct a hypothesis test to determine if the proportion of U.S. residents consuming recommended levels of calcium is different among women and men. The p-value is 0.035, and researchers conduct this test at a 5% level of significance. What does a p-value of 0.035 mean?
There is a 3.5% chance that there is no difference in calcium consumption for women and men.
If the calcium consumption rates are different for the women and men, there is a 3.5% chance that future experiments will show the same difference in calcium consumption as observed in this experiment.
If calcium consumption is the same for women and men, there is a 3.5% chance that future studies will show differences in calcium consumption greater than observed in this study.
If calcium consumption is the same for women and men, there is a 3.5% chance that calcium consumption will be different in future experiments.
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There is sufficient evidence from the hypothesis test, with a p-value of 0.035 < 0.05, to say that men and women in the United States consume different amounts of calcium.
Why are there hypotheses and null hypotheses?The evidence for the null and alternative hypotheses, which are two competing statements, are compared using a statistical test. Null hypothesis or population impact does not exist (H0). An alternate hypothesis, or population effect, exists (Ha or H1).
Here,
The proportion between men and women is examined at the null hypothesis as follows:
[tex]H_{0}[/tex] : u1 - u2= 0
If the proportions are different under the alternative hypothesis, then:
[tex]H_{A}[/tex] : u1 - u2 ≠ 0
There is adequate data to determine that men and women in the United States consume different percentages of the necessary calcium levels because the p-value is 0.035 0.05.
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Can anyone help please?
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The side w of the rectangle is 2.5 cm.
How to find the side of a 2 dimensional figure?The triangle and the rectangle have the same area.
Therefore,
area of a triangle = 1 / 2 bh
where
b = base of the triangleh = height of the triangleb = 5 cm
h = 6 cm
area of a triangle = 1 / 2 × 5 × 6
area of a triangle = 30 / 2
area of a triangle = 15 cm²
Therefore,
area of a rectangle = lw
where
l = lengthw = widthHence,
15 = 6w
w = 15 / 6
w = 5 / 2
w = 2.5 cm
Therefore, the side w is 2.5 cm.
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
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Solve the equation I will leave a five star in a heart
Answers
Answer: b is -17, the y -intercept
Step-by-step explanation:
Do you mean question 7?
We can use the equation y = mx + b to model this, where b is the y intercept.
y = 9/15x - 17
y = mx + b ===> this means that -17 is b.
What is the slope of the line that contains these points?
x 12 13 14 15
y -4, 2 8 14
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The slope of the line is 6.
What is a point on a line?
In geometry, a point is a place. It is completely empty, meaning it has no width, length, or depth. A dot indicates a point. A line is described as a collection of points that stretches in both directions indefinitely.
Given table is
x 12 13 14 15
y -4 2 8 14
The points on the lines are (12,-4), (13,2), (14,8), (15,14).
The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
Now consider two points (12,-4), (13,2) to find the slope:
m = (2 - (-4))/(13 - 12)
m = (2 + 4)/1
m = 6/1
m = 6
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What is the common ratio of the geometric sequence?
Number graph ranging from zero to ten on the x axis and zero to twenty-eight on the y axis. Points are plotted on the graph at (one, eight), (two, twelve), (three, eighteen) and (four, twenty-six point five). The points form a general positive trend.
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A geometric series is one in which there is a constant between two successive numbers in the series.
What is geometric progression?When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.
The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
Suppose the series is given as
2,4,8,16,32,64.........
The common difference is defined as the ratio of the next term to the previous term.
From the above series, the common ratio is calculated as,
Common ratio = 4 / 2
Common ratio = 2
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A fisherman is measuring the amount of bait he has remaining, y, in his bucket he puts 20 peices of bait in his bucket at the beginning of his fishing trip and uses 2 pieces every hour, x.
What is the slope for this linear relationship and what does it mean in this situation?
A. -2; the amount of bait decreases by 2 pieces each hour
B. 2; the amount of bait increases by 2 pieces each hour
C. -20; the amount of bait in the bucket when the fishing trip began
D. 20; the amount of bait in the bucket when the fishing trip began
Answers
Answer:
A
Step-by-step explanation:
bait left = 20 - 2x where x = hours slope = -2 answer A
What’s 9.1k in numbers?
Answers
Answer:
9,100
Step-by-step explanation:
"9.1k" is a shortened notation for 9,100, where "k" stands for "kilo," which means thousand.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
The "k" stands for "kilo," which means thousand. Therefore, when you see a number followed by "k," you can assume that the actual number is 1,000 times greater than what is shown.
In this case, "9.1k" means 9.1 times 1,000, which equals 9,100.
This notation is often used in contexts where brevity is important, such as in social media posts or online comments, where character limits may apply.
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Suppose that a random sample of 41 state college students is asked to measure the length of their right foot in centimeters. A 95% confidence interval constructed using the data is (21.709, 25.091). Which is a correct interpretation for the confidence interval?
a. 95% of the time the sample mean foot length is between (21.709, 25.091).
b. 95% of the foot lengths are between (21.709, 25.091).
c. 95% of the time the population mean foot length is between (21.709, 25.091)
d. All of the above.
e. None of the above.
Answers
The correct interpretation for the confidence interval for the given random sample of 41 state college students is option e (i.e. none of the above).
What is Confidence Interval ?
Confidence interval gives a range of estimated value of population parameter. The value that does not lie within the confidence interval tend to not represent the population parameter whereas , if the value lie inside the confidence interval it represent the population parameter with a certain confidence level.
What are random samples ?
A simple random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected, minimising the risk of selection bias.
According to the question , A 95% confidence interval constructed using the data is (21.709, 25.091)
95 % confidence interval is (21.709, 25.091).
Sample size is 41 state college students
Hence , The correct option is E as the confidence interval tend to reflect the population parameter. And also it show that there is certain confidence level that population parameter will lie within the confidence interval. Suppose we take out 100 sample at random that 95% of this will have population foot length mean between 21.709 and 25.091.
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write y=5/12x-1/2 in standard form
Answers
Answer:
1 - (5/6)x = 2y
Step-by-step explanation:
To write the equation y = 5/12x - 1/2 in standard form, we need to first get rid of the fractions by multiplying both sides of the equation by the least common denominator of the fractions, which in this case is 12. This gives us the equation 12y = 5x - 6. Next, we can rearrange the terms on the right-hand side of the equation to get 6 - 5x = 12y. Finally, we can divide both sides of the equation by 6 to get the equation in standard form, which is 1 - (5/6)x = 2y. The standard form of the equation is thus 1 - (5/6)x = 2y.
Answer:
5/12x = y - 6
Step-by-step explanation:
To write the equation y = 5/12x - 1/2 in standard form, we need to first move all the terms that contain x to one side of the equation and all the constants to the other side. This will give us the equation 5/12x - y = -1/2. Next, we need to multiply both sides of the equation by the denominator of the fraction on the right-hand side to eliminate the fraction. This gives us 5/12x - y = -6. Finally, we need to add y to both sides of the equation to obtain the standard form of the equation, which is 5/12x = -6 + y. This can be written more concisely as 5/12x = y - 6. Therefore, the equation y = 5/12x - 1/2 can be written in standard form as 5/12x = y - 6.
The members of the Rough Bikers Club pay per summer season, plus each time they rent a bike. Nonmembers must pay each time they rent a bike.
a) How many times would a member and a non-member have to rent a bike in order to pay the same amount?
b) How much is that same amount?
Members and non-members will pay the same when renting a bike
times.
They will pay $
. Do not write the dollar sign.
Answers
calculations are also used in statistical predictions of the likely election results, these calculations yield ranges of possibilities rather than precise results.
Given,
Member of the club paying for rental bike =
10
non-member of the club paying for rental bike = 15
Also for summer season member had given $100.
Bike taken by members = x
Bike taken by non-members = y
to pay same amount,
100+10x = 15y
1. let's take x=1
110=15y
y!= integer
x can't be 1
2. let's take x=2
120 = 15y
y = 8 i.e. an integer value
So, members will take bike on rent for 2
times and non-members for 8 times.
And the amount is 120.
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Find the measure of triangle ABD from given figure
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A rental car agency charges $15 per day plus 11 cents per mile to rent a certain car. Another agency charges $18 per day plus 8 cents per mile to rent the same car. How many miles will have to be driven for the cost of the car from the first agency to equal the cost of a car from the second agency?
Answers
If a rental car agency charges $15 per day plus 11 cents per mile to rent a certain car. The number of miles you have to be driven for the cost of the car from the first agency to equal the cost of a car from the second agency is 100 miles.
How to find the number of miles:First step is to set the equation that will be used to find the number of miles
Equation
15+.11x=18+.08x
So,
Number of miles
15+.11x=18+.08x
Collect like terms
.03x=3
Divide both side by 0.03
x=3/.03
x =100 miles
Therefore we can conclude that the number of miles is 100 miles.
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What is the product of (-4)(16) (-7)
A-108
B -71
C 57
D 448
Answers
Answer:
D 448
multiply -4×16×-7
= 448
Original: 2.4
New: 0.8
Answers
Answer:
Divide by 3
Step-by-step explanation:
If you know your multiplication tables, you will know that 8·3 = 24. In reverse, that is 24 / 8 = 3. If you move the decimal point—the dot used for decimals always behind the last digit of a whole number—to the left or right, the answer will stay the same. This is why:
8 · 3 = 24, 80 · 3 = 240, 800 · 3 = 2,400, and so on.
Applying this but the decimal moving to the left results in:
0.8 · 3 = 2.4
I hope you understand!
(If you haven't already, learn your multiplication tables. Just some advice)
Find the gradient of the curve
y = 5x − 10/x^2
at the point where the curve crosses the x-axis
Answers
The gradient of a line is computed by dividing the difference between the -coordinates by the difference between the -coordinates.
How to work out the gradient of a straight line graph?The gradient is the amount of vertical movement for each unit of rightward horizontal movement. The slope becomes steeper the higher the grade.From left to right, a positive gradient rises. From left to right, a downward slope may be seen.The steepness of a gradient of 2 and a gradient of -2 are both 2. A gradient of 2 slopes up from left to right, and a gradient of -2 slopes down from left to right.The gradient is identical for parallel lines.The slopes on perpendicular lines are opposite. One has a gradient that is positive, whereas the other has a gradient that is negative. Their gradients have a product of -1.The Complete Question gradient of a line.
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At 2 p.m., two cars leave Eagle River, WI, one headed north and one headed south. If the car headed north averages 45 mph and the car headed south averages 40 mph, when will the cars be 170 miles apart?
Answers
The time at which the two cars will be 170 miles apart is; 1.619 hours
How to solve Algebra Word Problems?Let us write an equation for each car as;
d₁ = r₁*t₁ (northbound)
d₂ = r₂*t₂ (southbound)
They both start at the same time, and will stop them both when they are 170 miles apart. Thus;
t = d₁/r₁
t = d₂/r₂
Thus, the equation to find their times is;
d₁/r₁ = d₂/r₂
d₁ = d₂r₁ /r₂
Thus;
d₁ + d₂ = 170
d₁ = 170 - d₂
Similarly, r₁ = 45 mph and r₂ = 40 mph
170 - d₂ = d₂(45/60)
4(170 - d₂) =3d₂
7d₂ = 680
d₂ = 680/7
d₂ = 97.143 miles
d₁ = 170 - 97.143
d₁ = 72.857 miles
t₁ = d₁/r₁ = 72.857/45 = 1.619 hours
This represents the time that they will be 170 miles apart
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