Answer: 3.5 years
Step-by-step explanation: Let A be the salaries earned from company A for x years and B for company B for the same years.
A = 31000 + n*3000
B = 38000 + n*1000
To find the case where A = b, set them to each other and solve for n, the number of years.
31000 + n*3000 = 38000 + n*1000
2000n = 7000
n = (7000/2000) = 3.5 years.
A B
0 31000 38000
1 34000 39000
2 37000 40000
3 40000 41000
4 43000 42000
5 46000 43000
6 49000 44000
7 52000 45000
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet
and the volume of each large box is 13 cubic feet. A total of 19 boxes of paper were
shipped with a combined volume of 156 cubic feet. Determine the number of small
boxes shipped and the number of large boxes shipped.
There were
Submit Answer
small boxes shipped and
large boxes shipped.
There were 13 small boxes shipped and 6 large boxes shipped.
Let's denote the number of small boxes as 's' and the number of large boxes as 'l'.
According to the given information, the volume of each small box is 6 cubic feet, so the total volume of all small boxes can be calculated as 6s cubic feet.
Similarly, the volume of each large box is 13 cubic feet, so the total volume of all large boxes can be calculated as 13l cubic feet.
We are also given that the combined volume of all the boxes is 156 cubic feet, so we can write the equation:
6s + 13l = 156 ...(1)
Additionally, we know that a total of 19 boxes were shipped, so we can write another equation:
s + l = 19 ...(2)
Now, we have a system of equations (equation 1 and equation 2) that we can solve simultaneously to find the values of 's' and 'l'.
To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method here.
From equation 2, we can rewrite it as s = 19 - l.
Substituting this value of s into equation 1, we get:
6(19 - l) + 13l = 156
Simplifying the equation:
114 - 6l + 13l = 156
Combining like terms:
7l = 42
Dividing both sides by 7:
l = 6
Now, we can substitute this value of l back into equation 2 to find the value of s:
s + 6 = 19
s = 13
The number of small boxes shipped is 13, and the number of large boxes shipped is 6.
There were 13 small boxes shipped and 6 large boxes shipped.
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What is the scale factor of the dilation?
One-eighth
One-fourth
4
8
The image of the parallelogram which is larger than the preimage,
indicates that the scale factor is larger than 1.
Correct response:
The scale factor of the dilation is 4Which is the Method used for finding the scale factorThe scale factor is found by finding the ratio of the corresponding sides.
The possible given diagram in the question is a parallelogram FGHJ
dilated to form the similar parallelogram, F'G'H'J'.
The length of side FG = -2 - (-4) = 2
The length of side F'G' = 3 - (-5) = 8
\(The \ scale \ factor = \mathbf{ \dfrac{Length \ of \ F'G'}{Length \ of \ FG} }\)Which gives;
\(The \ scale \ factor = \dfrac{8}{2} = 4\)
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Answer:
C) 4
Step-by-step explanation:
a card is drawn from a standard deck of 52 playing cards. what is the probability that the card will be a spade or a club? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability that the card will be a spade or a club 50%
Probability in math is referred as how likely an event is to occur, or how likely it is that a proposition is true.
Here we have given that a card is drawn from a standard deck of 52 playing cards.
And we need to find the probability that the card will be a spade or a club and we have to express your answer as a fraction or a decimal number rounded to four decimal places.
While we looking into the given question, we have identified the the total number of cards is 52.
And the number of spade cards = 13 and the number of club cards = 13
Therefore, the total number of spade and club cards
=> 13 + 13
=> 26
Therefore, the probability of getting a spade or a club from a single draw is,
=> 26/52
When we simplified this one, then we get,
=> 0.5
When we convert this into percentage then we get
=> 50%.
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I drive from town a to my home and then to town b. the journey time is 50 minutes what is the average speed?
The average speed can be shown as (A + B)/50 miles per minute, where the distance between town A and his home is A miles, and that from his home to town b is B miles, and the total time is 50 minutes.
The average speed of any object is given as the ratio of the total distance traveled by the body, to the total time taken.
Average Speed = Total Distance/Total Time.
In the question, we are informed that the person drove from town a to his home and then to town b, with the total journey time as 50 minutes.
We are asked to find the average speed of the person.
We assume the distance from town a to his home to be A miles.
We assume the distance from his home to town b to be B miles.
Thus, the total distance traveled = A + B miles.
The total time taken by the person is given to be 50 minutes.
We know that the average speed of any object is given as the ratio of the total distance traveled by the body, to the total time taken.
Thus, the average speed of the person can be shown as:
Average Speed = (A + B)/50 miles per minute.
Thus, the average speed can be shown as (A + B)/50 miles per minute, where the distance between town A and his home is A miles, and that from his home to town b is B miles, and the total time is 50 minutes.
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The volume of this prism is 2465cm3. the area of the cross-section is 85cm2. work out x .
The value of x is 29 cm.
To find the value of x, we can use the formula for the volume of a prism, which is V = A * h, where V is the volume, A is the area of the cross-section, and h is the height. In this case, we are given that the volume is 2465 cm^3 and the area of the cross-section is 85 cm^2. We need to solve for the height, h.
Using the formula, we have 2465 = 85 * h. To solve for h, we divide both sides of the equation by 85, giving us h = 2465 / 85 = 29 cm.
Therefore, the value of x is 29 cm.
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Find the derivative, if it exists, of the function at the specified point.() = ^2 − 4 + 3 at = 1
Find the derivate of the expression using the general procedure to find the derivative of a polynomial function. To do it, multiply the term times the exponent of the variable and raise the variable to the original exponent minus 1:
\(\begin{gathered} f(x)=x^2-4x+3 \\ f^{\prime}(x)=2x^{2-1}-4x^{1-1}-0\cdot3 \\ f^{\prime}(x)=2x-4 \end{gathered}\)Now that we have the expression for the derivative of the function, evaluate it at the value of x that is in the question statement, which is 1:
\(f^{\prime}(1)=2(1)-4=2-4=-2\)The derivative of the function is -2 at x=1.
A group of 9 friends go out to dessert and spend $72.45 including tax.
which costs $8 or a fruit salad which costs $5. The tax on the bill was
ice cream sundae and how many ordered a fruit salad?
what is the axis of symmetry of the graph of the function f(x)=3x^2+12x-4
Answer:
Step-by-step explanation:
Use the equation x = -b/2a => x = -12/6 = -2.
which expressions are equivalent to z (z 6)z (z 6)z, plus, (, z, plus, 6, )
The expression is equivalent to "\(z^4 * (z + 6)^2 + (z + 6)\)".
Why are the expressions "z (z + 6)z (z + 6)z + (z + 6)" and "\(z^4 * (z + 6)^2 + (z + 6)\)" equivalent?To clarify, I understand the expression as: "z * (z + 6) * z * (z + 6) * z + (z + 6)". Let's break down the expression and simplify it step by step:
Distribute the multiplication:
z * (z + 6) * z * (z + 6) * z + (z + 6)
becomes
z * z * z * (z + 6) * (z + 6) * z + (z + 6)
Combine like terms:
z * z * z simplifies to \(z^3\)
(z + 6) * (z + 6) simplifies to (z + 6)^2
The expression now becomes:
\(z^3 * (z + 6)^2 * z + (z + 6)\)
Multiply \(z^3\) and z:
\(z^3 * z\) simplifies to \(z^4\)
The expression becomes:
\(z^4 * (z + 6)^2 + (z + 6)\)
So, an equivalent expression to "z (z + 6)z (z + 6)z + (z + 6)" is "\(z^4 * (z + 6)^2 + (z + 6)\)".
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witch expersson is equivalent to 4x-5?
Answer:
Uh where are the other expressions?
Step-by-step explanation:
what fraction of the figure is shaded?
it takes country a 30 minutes to produce a car and 20 minutes to produce a tank. it takes country b 12 minutes to produce a car and 10 min to produce a tank. it is true that
Country B is more efficient than Country A when it comes to producing cars and tanks.
Country A takes twice as long to produce a car (30 minutes) than Country B (12 minutes). However, Country A takes 20 minutes to produce a tank while Country B takes 10 minutes, cutting the amount of time in half.
We can measure the efficiency of each country by calculating the number of cars and tanks each country can produce in an hour. We can do this using the following formula:
Cars per hour = (60 minutes/minutes to produce car)
Tanks per hour = (60 minutes/minutes to produce tank)
For Country A, the number of cars produced in an hour is (60 minutes/30 minutes) = 2 cars per hour and the number of tanks produced in an hour is (60 minutes/20 minutes) = 3 tanks per hour.
For Country B, the number of cars produced in an hour is (60 minutes/12 minutes) = 5 cars per hour and the number of tanks produced in an hour is (60 minutes/10 minutes) = 6 tanks per hour.
Therefore, Country B is more efficient than Country A when it comes to producing cars and tanks.
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find angle u
please include explanation
Check the picture below.
Between which 2 consecutive integers is each number located on a number line?
__ < .99 < __
Answer:
x lies between 0 and 1 on the number line
Step-by-step explanation:
As we move to the left from 0.99, the first integer we reach is 0; as we move to the right from 0.99, the first integer we reach is 1.
Thus, 0 < x > 1: x lies between 0 and 1 on the number line.
Jimmy and Lauren are
organizing transportation for
a field trip from ACIT. Jimmy
found out that his group has
841 students, and he needs 9
vans and 16 buses to
accommodate. While Lauren’s
group has 351 students, and
she needs 8 vans and 5 buses
for them. How many students
fit in a van and a bus for this
field trip? (please include steps)
Step-by-step explanation:
Jimmy's group : has 841 students
Lauren's group: has 351 students
9 vans 16 buses
8 vans 5 buses
Vans: V
Buses: B
9v + 16b = 841
9v + 16b = 841
-16b -16b
9v/ 9 = 841 /9 - 16b/9
8( 841/9 - 16b/9) +5b = 351
v - (841/ 9 - 16b / 9 )
8 (841 / 9 - 16b/9) +5b = 351
6728/9 - 128b / 9 +5b = 351
-128b/9 + 45b/9 = -83/9b
6728/9 -83/9
- 6728/9 +83/9 = 3159/9 - 6728/9
(9)83b / 9 = -3569 (9)/9
-83b = -3564
-83 -83
B = 43 students
8v + 5b = 351
8v + 5 (43) = 351
8v + 215 = 315
-215 -215
8v = 136
8 8
V = 17 students
43 students can fit on a bus and 17 students can fit in a van.
Jonathan's lawn mower has 45 liters of gasoline in it. After mowing the grass, there are 21 liters of gasoline left in the gas tank. How many milliliters of gasoline did Jonathan use cutting the grass?
Quantity of gasoline that Jonathan use cutting the grass is 24,000 milliliters
To calculate the amount of gasoline Jonathan used cutting the grass, we need to find the difference between the initial amount of gasoline and the amount of gasoline left in the tank after mowing the grass.
The initial amount of gasoline is 45 liters, and the amount of gasoline left in the tank is 21 liters
So, the amount of gasoline Jonathan used is
45 - 21 = 24 liters
However, we are asked to express the amount of gasoline used in milliliters. To do this, we can use a conversion factor that relates liters to milliliters.
There are 1000 milliliters in one liter, so we can multiply the amount of gasoline used in liters by 1000 to get the equivalent amount in milliliters.
Therefore, the amount of gasoline Jonathan used cutting the grass is
24 liters x 1000 ml/liter = 24,000 milliliters
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Please help me out, it will be great, you help me out, thank you
Answer:
the answer is 'c' and 'e'
A certain statistic bˆ is being used to estimate a population parameter B . The expected value of bˆ is equal to B . What property does bˆ exhibit? The sampling distribution of bˆ is normal. The sampling distribution of b hat is normal. A The sampling distribution of bˆ is binomial. The sampling distribution of b hat is binomial. B The sampling distribution of bˆ is uniform. The sampling distribution of b hat is uniform. C bˆ is unbiased. B hat is unbiased. D bˆ is biased.
Answer:
C bˆ is unbiased.
Step-by-step explanation:
In statistics, the sampling distribution showcases the distribution of obtained values by the statistics in all possible sample sizes of the same population. A statistic that estimates a population parameter is termed to be an unbiased estimator if the mean of such distribution appears to be equal to the true value of the estimated parameter.
Thus, from the aforementioned, the property exhibited by b- is unbiased.
d is biased
Step-by-step explanation:
The expected value of d is not D
The property where the expected value of d is D is called unbaisedness, hence d is biased
709,9785,906+678,053,985=???
Answer:
7777839891
Step-by-step explanation:
7099785906+678053985
in the marital instability over the life course project, men were asked to indicate the cause of their divorce. what was the most common response from the men (with 19% of men reporting this cause)?
In the Marital Instability Over the Life Course project, when men were asked to indicate the cause of their divorce, the most common response from the men was incompatibility. And the most common response from the women was infidelity.
What is the meaning of Marital Instability?Marital instability is described as including the range of activities from thinking about and discussing divorce to actually filing for either separation or divorce. There are a lot of causes of marital instability, but the most common causes are money problems and lack of intimacy.
Marital Instability Over the Life Course project is a nationwide longitudinal study started in 1980 with funding from the Social Security Administration's Office of Research and Statistics and the National Institute on Aging. This study measures predicting marital instability and divorce and assessing marital quality were developed.
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the height of a projectile at time t is represented by the function h (t)= −4.9 t2 18 t 40 .
The maximum height of the projectile is 56.53 meters.
The height of a projectile at time t is represented by the function h (t)= −4.9 t² +18t + 40, where h(t) is the height in meters and t is the time in seconds.
This is a quadratic function of the form h(t) = at² + bt + c, where a = -4.9, b = 18, and c = 40.
To find the maximum height of the projectile, we need to find the vertex of the parabolic graph of the function h(t).
The vertex of the parabola is at the point (t, h(t)) where t = -b/2a. Substituting the values of a and b, we get t = -18/(2(-4.9)) = 1.8367 seconds.
To find the maximum height, we need to substitute t = 1.8367 seconds into the function h(t). h(1.8367) = -4.9(1.8367)^2 + 18(1.8367) + 40 = 56.53 meters.
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In the diagram below, lines h and s are parallel. If the m∠2 = 70°, what is the angle measurement of m∠3?
A. 70
B. 130
C. 7
D. 110
Answer:
A
Step-by-step explanation:
Geometry
The answer is A, due to 3 and 2 being vertical.
Ferris wheel in London; England It stands 135 meters tall with a The London Eye iS a giant diamederof 120 meters: It takes half an hour to complete one revolution form hlt) = A cos( Br D t0 model the height; h (in meters). Find cosine funclion of the (in minutes). Assume the passenger passenger riding the London Eye as a function of time 0. Sketch the graph of one period on the next page and is at the bottom of the wheel at time use it to help you answer the following questions and create your function What is a rider' height at m = 0 minutes? (Hint: It is not 0 meters) 2. How long does it take for a rider to reach the top? What is the rider's height at that time? What is the period of this function? Use the period to find What is the vertical shift and amplitude of this function? 5 . Find The Equation Of Your Cosine Function, Use your function to find a rider's height at =21minutes. Sketch the graph ofyour function (This helps to answer the previous questions)
The height of a rider on the London Eye Ferris wheel in London can be modeled by the function h(t) = A * cos(B * t), where t represents time in minutes. The Ferris wheel stands 135 meters tall with a diameter of 120 meters. It takes half an hour (30 minutes) to complete one revolution.
1. At t = 0 minutes, the rider is not at the bottom of the wheel but at the midpoint of the wheel's diameter, so the rider's height is equal to the radius of the wheel, which is half of its diameter. Therefore, the rider's height at t = 0 minutes is 120/2 = 60 meters.
2. To determine the time it takes for the rider to reach the top, we need to find the period of the cosine function. The period (T) is the time it takes for one complete cycle of the function. In this case, the period is equal to the time it takes for the Ferris wheel to make a full revolution, which is 30 minutes. So, the rider reaches the top after half of the period, which is T/2 = 30/2 = 15 minutes. At that time, the rider's height is equal to the sum of the radius of the wheel and its height, which is 60 + 135 = 195 meters.
3. The period of the cosine function is T = 30 minutes.
4. The vertical shift of the function represents the average height of the rider throughout one complete cycle. In this case, the average height is the sum of the radius and the height of the Ferris wheel divided by 2, which is (60 + 135)/2 = 97.5 meters. Therefore, the vertical shift of the function is 97.5 meters. The amplitude of the function is half of the vertical distance between the maximum and minimum values, which is (135 - 60)/2 = 37.5 meters.
5. The equation of the cosine function is h(t) = 97.5 + 37.5 * cos((2π/30) * t). To find the rider's height at t = 21 minutes, we substitute t = 21 into the equation: h(21) = 97.5 + 37.5 * cos((2π/30) * 21) ≈ 185.11 meters.
In summary, the rider's height at t = 0 minutes is 60 meters. It takes 15 minutes for the rider to reach the top, at which point their height is 195 meters. The period of the function is 30 minutes. The vertical shift is 97.5 meters, and the amplitude is 37.5 meters. Using the cosine function, the rider's height at t = 21 minutes is approximately 185.11 meters.
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Express in simplest radical form. 48
Answer: 4\(\sqrt{3\\}\)
Step-by-step explanation:
It is because to get rid of radical of 48, because you factor 48 and it comes out to be 12 and 4, factor of 4 is 2 x 2. Factor of 12 is 6 x 2. Simplify the 6 to
3 x 2. You find the pair and the ones that have a pare become one and go outside of the radical sign on the left. 2 has 2 pairs so it is only 2 x 2 = 4. So 4 goes outside of the radical sign. Then the number that is alone with no pair is 3 so you put the number 3 inside the radical sign.
4\(\sqrt{3}\) is your answer.
Hope this helps, sorry if not...
a number is 4 more than 45% of d (11 points bc im new please help quick)
\(x = 0.45d + 4\)
For each combination of sample size and sample proportion, find the approximate margin of error for the 95% confidence level. (Round the answers to three decimal places.)
(a) n = 200, pÌ = 0.52. (b) n = 800, pÌ = 0.52. (c) n = 800, pÌ = 0.10. (d) n = 800, pÌ = 0.70. (e) n = 1200, pÌ = 0.60.
The margin of error is:
a) 0.069
b) 0.035
c) 0.021
d) 0.032
e) 0.028
What is confidence level?
A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.
Given,
Here at 95% CI, the z value is 1.96
a) sample n = 200, p = 0.52
Now, we find the margin of error and we get
Margin of error = z×√(p(1-p)/n)
Now, substitute values of p, n, and z and we get
= 1.96×√(0.52(1-0.52)/200)
= 0.069
b) n = 800 , p = 0.52
Margin of error = z×√(p(1-p)/n)
Now, we substitute values of n, p, and z and we get
= 1.96×√(0.52(1-0.52)/800)
= 0.035
c) n = 800 , p = 0.1
First, we find the margin of error and we get
Margin of error = z×√(p(1-p)/n)
Now, we substitute values and we get
= 1.96×√(0.1(1-0.1)/800)
= 0.021
d) n = 800 , p = 0.7
Margin of error = z×√(p(1-p)/n)
Now, we substitute values and we get
= 1.96×√(0.7(1-0.7)/800)
= 0.032
e) n = 1200 , p = 0.60
First, we find the margin of error and we get
Margin of error = z×√(p(1-p)/n)
After substituting values we get
= 1.96×√(0.6(1-0.6)/1200)
= 0.028
Hence,
The margin of error is:
a) 0.069
b) 0.035
c) 0.021
d) 0.032
e) 0.028
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The total time, measured in units of 100 hours, that a teenager runs her hair dryer over a period of one year is a continuous random variable X that has the density function below. Use the theorem below to evaluate the mean of the random variable Y = 51X2 + 40X, where Y is equal to the number of kilowatt hours expended annually Theorem: The expected value of the sum or difference of two or more functions of a random variable X is the sum or difference of the expected values of the functions, as given by the formula below 0, elsewhere
Answer:
The mean of the random variable Y is (17/2) kilowatt hours.
Step-by-step explanation:
To find the expected value of Y, we can use the formula provided in the theorem:
E(Y) = E(51X^2 + 40X)
Using linearity of expectation, we can break this down into two separate expected values:
E(Y) = 51E(X^2) + 40E(X)
The given probability density function is, f(x) = (1/4)x, 0 ≤ x ≤ 2.
The expected value of a continuous random variable is calculated using the formula shown below, where E(x) is the expected value of x, and f(x) is the probability density function of x.
E(x) = ∫xf(x)dx
The expected value of the random variable X can be calculated as follows:
E(X) = ∫0² (1/4)x dx = (1/8) [x²]₀² = 1
E(X²) = ∫0² (1/4)x² dx = (1/12) [x³]₀² = (1/6)
Now we can substitute these values into our original equation:
E(Y) = E(51X² + 40X) = 51E(X²) + 40E(X) = 51(1/6) + 40(1) = (17/2) kilowatt hours.
Therefore, the mean of the random variable Y is (17/2) kilowatt hours.
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what is the slope of 9x -5y = 4
the general equation of a graph is given by
y = mx + c
where m= slope
c=intercept
the equation given is
9x-5y=4
make y subject of formula
9x-4=5y
5y=9x-4
divide through by 5
y=9/5x-4/5
comparing with the general equation
mx=9/5x
m=slope=9/5
Find the slope of the line that passes through points (4,5) and (3,-4)?
Answer:
slope=9
Step-by-step explanation:
whole equation=y = 9x – 31
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Frank reads at least 24 pages but not more than 36 pages of a book. He reads 12 pages per hour. The number of hours Frank reads p pages is modeled by a function. t(p)=p12 What is the practical range of the function?
all real numbers from 2 to 3, inclusive
all real numbers
all real numbers from 24 to 36, inclusive
all multiples of 12 between 24 and 36, inclusive
Answer:
as practical range of function is 2 to 3 so we have
12(2) = 24
12(3) = 36
i think this is it
Step-by-step explanation:
i don't really know how to explain it but:
12 x 2 = 24and
12 x 3 = 36