Adding another 12 to the data set would increase the sum of the values by 12, resulting in a new sum of 239. To find the new mean, we divide the new sum by the total number of values in the set, which is now 8. So the new mean would be 29.875, which is slightly lower than the original mean of 31.6.
To find the new median, we first need to rearrange the values in ascending order: 12, 18, 26, 32, 41, 46, 46, 12. Since there are now an even number of values, we take the average of the middle two, which in this case is (26 + 32) / 2 = 29. So the new median would be 29, which is lower than the original median of 32.
In summary, adding another 12 to the data set would slightly decrease the mean and lower the median.
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The table shows the amount of money raised during a car wash for charity.
Number of Cars Washed Money Raised
3 $43.50
13 $279.50
18 $405.00
Which statement is true?
A. The group raised $14.50 per car.
B. The group raised $21.50 per car.
C. The group raised $22.50 per car.
D. The relationship is not a direct proportion.
Answer:
The correct answer is D. The relationship is not a direct proportion.
We can see that the money raised is not directly proportional to the number of cars washed. For example, when the number of cars washed is doubled from 3 to 13, the money raised is not doubled from $43.50 to $87.00. Instead, it is increased by a factor of 6.5, from $43.50 to $279.50. Similarly, when the number of cars washed is increased by 5 from 13 to 18, the money raised is increased by a factor of 1.4, from $279.50 to $405.00.
This suggests that the amount of money raised is not simply a linear function of the number of cars washed. Instead, it is likely a more complex function that takes into account other factors, such as the time of day, the weather, and the location of the car wash.:
A three digit number is such that twice the hundreds digit is more than the tens digit by 2. The unit digit is thrice the hundred digit. When the digits are reversed the number is increased by 594. Find the number.(5 marks)
Answer:
Step-by-step explanation:
Let the three-digit number be represented as $abc$, where $a$ is the hundreds digit, $b$ is the tens digit, and $c$ is the units digit.
From the problem, we have two equations:
Equation 1: $2a=b+2$
Equation 2: $c=3a$
We can use these equations to solve for $a$, $b$, and $c$.
Starting with Equation 1, we can isolate $b$ to get $b=2a-2$.
Next, we can substitute Equation 2 into Equation 1 to get $2a=3a-6+2$, which simplifies to $a=8$.
Using this value of $a$, we can now find $b$ and $c$. From Equation 2, we have $c=3a=24$. And from Equation 1, we have $b=2a-2=14$.
Thus, the original three-digit number is $abc=824$.
When we reverse the digits to get $cba=428$, we increase the number by 594, so we have $cba=abc+594=824+594=1418$.
Therefore, the answer is $\boxed{824}$.
Tom Jones, a mechanic at Golden Muffler Shop, is able to install new mufflers at an average rate of 3 per hour (exponential distribution). Customers seeking this service, arrive at the rate of 2 per hour (Poisson distribution). They are served first-in, first-out basis and come from a large (infinite population). Tom only has one service bay.
a. Find the probability that there are no cars in the system.
b. Find the average number of cars in the system.
c. Find the average time spent in the system.
d. Find the probability that there are exactly two cars in the system
a. To find the probability that there are no cars in the system, we need to use the formula for the steady-state probability distribution of the M/M/1 queue:
P(0) = (1 - λ/μ)
where λ is the arrival rate (2 per hour) and μ is the service rate (3 per hour).
P(0) = (1 - 2/3) = 1/3 or 0.3333
Therefore, the probability that there are no cars in the system is 0.3333.
b. To find the average number of cars in the system, we can use Little's Law:
L = λW
where L is the average number of cars in the system, λ is the arrival rate (2 per hour), and W is the average time spent in the system.
We can solve for W by using the formula:
W = 1/(μ - λ)
W = 1/(3 - 2) = 1 hour
Therefore, the average number of cars in the system is:
L = λW = 2 x 1 = 2 cars
c. To find the average time spent in the system, we already calculated W in part b:
W = 1 hour
d. To find the probability that there are exactly two cars in the system, we need to use the formula for the steady-state probability distribution:
P(n) = P(0) * (λ/μ)^n / n!
where n is the number of cars in the system.
P(2) = P(0) * (λ/μ)^2 / 2!
P(2) = 0.3333 * (2/3)^2 / 2
P(2) = 0.1111 or 11.11%
Therefore, the probability that there are exactly two cars in the system is 11.11%.
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Under her cell phone plan Yaritza pays a flat cost of $41 and 50 Cent per month and five dollars per gigabyte she wants to keep her bill under $60 per month which inequality can be used to determine ask the minimum number of gigabytes Yahritza can use while staying within her budget
Answer:3 gigabytes of storage.
Step-by-step explanation: Because you start at $41.50 and add 5 is $46.60 and then add 5 again and you get $51.50 then add 5 more you get $56.50.
Which system of equations is represented by the graph?
Answer:
Absoblute value Reflection
Step-by-step explanation:
You can tell it's absolbute value because of the parbolas, and it's reflected acroos the two points. Give brainliest please!
How many different simple random samples of size 4 can be obtained from a population whose size is 50?
The number of random samples, obtained using the formula for combination are 230,300 random samples
What is a random sample?A random sample is a subset of the population, such that each member of the subset have the same chance of being selected.
The formula for combinations indicates that we get;
nCr = n!/(r!*(n - r)!), where;
n = The size of the population
r = The sample size
The number of different simple random samples of size 4 that can be obtained from a population of size 50 therefore can be obtained using the above equation by plugging in r = 4, and n = 50, therefore, we get;
nCr = 50!/(4!*(50 - 4)!) = 230300
The number of different ways and therefore, the number of random samples of size 4 that can be selected from a population of 50 therefore is 230,300 random samples.
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Find the volume of the solid generated by revolving the region enclosed by x= v5y2, x = 0, y = - 4, and y = 4 about the y-axis.
To find the volume of the solid generated by revolving the given region about the y-axis, we can use the method of cylindrical shells.
First, we need to sketch the region and the axis of rotation to visualize the solid. The region is a parabolic shape that extends from y = -4 to y = 4, and the axis of rotation is the y-axis.
Next, we need to set up the integral that represents the volume of the solid. We can slice the solid into thin cylindrical shells, each with radius r = x and height h = dy. The volume of each shell is given by:
dV = 2πrh dy
where the factor of 2π accounts for the full revolution around the y-axis. To express r in terms of y, we can solve the equation x = v5y2 for x:
x = v5y2
r = x = v5y2
Now we can integrate this expression for r over the range of y = -4 to y = 4:
V = ∫-4^4 2πr h dy
= ∫-4^4 2π(v5y2)(dy)
= 80πv5
Therefore, the volume of the solid generated by revolving the given region about the y-axis is 80πv5 cubic units.
To find the volume of the solid generated by revolving the region enclosed by x = √(5y²), x = 0, y = -4, and y = 4 about the y-axis, we can use the disk method.
The disk method involves integrating the area of each circular disk formed when the region is revolved around the y-axis. The area of each disk is A(y) = πR², where R is the radius of the disk.
In this case, the radius is the distance from the y-axis to the curve x = √(5y²), which is simply R(y) = √(5y²).
So the area of each disk is A(y) = π(√(5y²))² = 5πy²
Now, we can find the volume by integrating A(y) from y = -4 to y = 4:
Volume = ∫[A(y) dy] from -4 to 4 = ∫[5πy² dy] from -4 to 4
= 5π∫[y²2 dy] from -4 to 4
= 5π[(1/3)y³] from -4 to 4
= 5π[(1/3)(4³) - (1/3)(-4³)]
= 5π[(1/3)(64 + 64)]
= 5π[(1/3)(128)]
= (5/3)π(128)
= 213.67π cubic units
The volume of the solid generated by revolving the region enclosed by x = √(5y²), x = 0, y = -4, and y = 4 about the y-axis is approximately 213.67π cubic units.
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A track has the dimensions shown.
36.5 m
ISTAN
SAMANT
men komm
84.4 m
Ta
inside of track
outside of track
. The track has 8 lanes
• Each lane is 2.1 meters wide
36.5 m
O
TI
16. To the nearest tenth of a meter, what is
the perimeter of the outside of the
track?
Byp
*REQUIRED
ANA
1
√x
Sign out
Answer:
Step-by-step explanation:
Find two acute angles that satisfy the equation sin(3x + 9) = cos(x + 5). check that your answers make sense.
The equation sin(3x + 9) = cos(x + 5) has no solutions in the set of acute angles.
What are the acute angles that satisfy sin(3x + 9) = cos(x + 5)?To find two acute angles that satisfy the equation sin(3x + 9) = cos(x + 5), we can use the trigonometric identity cos(x) = sin(π/2 - x) to rewrite the right-hand side of the equation as follows:
sin(3x + 9) = cos(x + 5)sin(3x + 9) = sin(π/2 - x - 5)3x + 9 = π/2 - x - 5 + 2πn or 3x + 9 = x + 5 + 2πn + π (where n is an integer)4x = -4 - 2πn or 2x = -2πn - 4 or 2x = π - 2πn - 4Dividing both sides of the equation by 4, we get:
x = -(1/2)πn - 1
So the solutions are given by:
x = -(1/2)π - 1 and x = -(3/2)π - 1
To check that these solutions make sense, we need to ensure that they are acute angles, i.e., angles that measure less than 90 degrees.
The first solution, x = -(1/2)π - 1, can be written in degrees as:
x ≈ -106.26 degrees
This angle is not acute, so it is not a valid solution.
The second solution, x = -(3/2)π - 1, can be written in degrees as:
x ≈ -286.87 degrees
This angle is also not acute, so it is not a valid solution.
Therefore, there are no acute angles that satisfy the equation sin(3x + 9) = cos(x + 5).
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one serving of almonds is 1/3 cup. booker bought 2 and 2/3 cups of almonds how many servings of almonds did booker buy
Booker bought 8 servings of almonds.
How many servings of almonds did Booker buy if he purchased 2 and 2/3 cups of almonds, and one serving of almonds is 1/3 cup?
One serving of almonds is equal to 1/3 cup.
To find how many servings of almonds Booker bought, we can divide the total amount of almonds he purchased by the amount in one serving:
2 and 2/3 cups of almonds = 8/3 cups of almonds
Number of servings = (total amount of almonds purchased) / (amount in one serving)
Number of servings = (8/3) / (1/3)
Number of servings = 8/3 x 3/1
Number of servings = 8
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Mr. Lance designed a class banner shaped like a polygon shown what is the name of the polygon
Step 1: Answer
The point (2, 8) is the point (x1, y1) identified from the equation y - 8 = 3(x - 2).
Step 2: Explanation
The equation y - 8 = 3(x - 2) is in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope of the line. In this case, the slope of the line is 3, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.
Comparing the given equation with the point-slope form, we can see that x1 = 2 and y1 = 8. Therefore, the point (2, 8) is the point identified from the equation.
I need help! Solve for X
25. a state study on labor reported that one-third of full-time teachers in the state also worked part time at another job. for those teachers, the average number of hours worked per week at the part-time job was 13. after an increase in state teacher salaries, a random sample of 400 teachers who worked part time at another job was selected. the average number of hours worked per week at the part-time job for the teachers in the sample was 12. 5 with standard deviation 6. 5 hours. is there convincing statistical evidence at the level of 0. 05, that the average number of hours worked per week at part-time jobs decreased after the salary increase? (a) no. the p-value of the appropriate test is greater than 0. 5. (b) no. the p-value of the appropriate test is less than 0. 5. (c) yes. the p-value of the appropriate test is greater than 0. 5. (d) yes. the p-value of the appropriate test is less than 0. 5. (e) not enough information is given to determine whether there is convincing statistical evidence
From the solution to the question that we have here, the answer is A. There is no solid proof that the number of hours worked dropped after the income rise.
Let μ be the population mean number of hours worked per week by teachers who work part-time jobs, after the salary increase. Here are the alternate and null hypotheses:
H0: μ = 13
H1: μ < 13
n = 400
[tex]\bar{X}=12.5[/tex]
μ = 13
Formula for the t-test statistics is
[tex]t = \frac{\bar{X}-\mu}{s/\sqrt{n} }[/tex]
t = (12.5 - 13)/(6.5/√400)
t = (- 0.5)/(6.5/20)
t = - 10/6.5
= -1.5388
Degree of freedom is 400 -1 = 399
α = 0.05
The p-value is p(t < -1.5385) = 0.062
The p-value exceeds the level of significance. Therefore, we unable to reject the null hypothesis.
Hence, option a is correct.
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Edro, Lena, Harriet, and Yermin each plot a point to approximate StartRoot 0. 50 EndRoot.
Pedro A number line going from 0 to 0. 9 in increments of 0. 1. A point is between 0. 2 and 0. 3.
Lena A number line going from 0 to 0. 9 in increments of 0. 1. A point is between 0. 4 and 0. 5.
Harriet A number line going from 0 to 0. 9 in increments of 0. 1. A point is at 0. 5.
Yermin A number line going from 0 to 0. 9 in increments of 0. 1. A point is just to the right of 0. 7.
Whose point is the best approximation of StartRoot 0. 50 EndRoot?
Pedro
Lena
Harriet
Yermin
Yermin's point is the best approximation of the square root of 0.50.
To know whose point is the best approximation of the square root of 0.50 on a number line. We have the points plotted by Pedro, Lena, Harriet, and Yermin.
Step 1: Calculate the square root of 0.50.
[tex]\sqrt{0.50} = 0.707[/tex]
Step 2: Compare the plotted points to the calculated square root value.
Pedro: Between 0.2 and 0.3
Lena: Between 0.4 and 0.5
Harriet: At 0.5
Yermin: Just to the right of 0.7
Step 3: Determine the closest approximation.
Yermin's point (just to the right of 0.7) is the closest to the calculated value of 0.707.
Your answer: Yermin's point is the best approximation of the square root of 0.50.
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Marsha is considering purchasing 3 points on a $350,000 home mortgage for 20 years. If she
purchases the 3 points, at a cost of 1 percent per point, her monthly mortgage would be
approximately $1,878.63. If she decides not to purchase any points, Mercedes' monthly
payment would be approximately $1,987.13. How much money will Mercedes save over the life
of the loan if she purchases the 3 points?
Marsha would save $26,040 over the life of the loan if she purchases the 3 points.
First, let's calculate the monthly payment if Marsha doesn't purchase any points. We can use a mortgage calculator or the PMT function in Excel to find;
PMT = $1,987.13
Now, let's calculate the monthly payment if Marsha purchases 3 points;
Loan amount = $350,000
Points cost = 3 points × 1% × $350,000 = $10,500
Effective loan amount = $350,000 - $10,500 = $339,500
Interest rate = 4.5% / 12 = 0.375%
Number of payments=20 years × 12 = 240
Using the PMT function, we get;
PMT = $1,878.63
So, by purchasing 3 points, Marsha can save;
$1,987.13 - $1,878.63 = $108.50 per month
Over the life of the loan, which is 20 years or 240 months, the total savings would be;
$108.50 × 240 = $26,040
Therefore, Marsha would save $26,040 amount of money.
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Lourdes could choose to pay an ATM fee to get cash or use a credit card to pay for groceries
that cost $48. The credit card charges interest if the balance is not paid at the end of the month.
Should she use the debit card or credit card? Justify your choice.
Keep in mind that if Lourdes is able to pay off her credit card balance at the end of the month, she won't be charged any interest, making the credit card the better option in that case.
To determine whether Lourdes should use a debit card or credit card, we need to consider the ATM fee and the potential interest charges from the credit card.
Step 1: Determine the ATM fee
Find out how much Lourdes would be charged for using the ATM to withdraw cash.
Step 2: Determine the interest rate on the credit card
Check the credit card's terms and conditions to find the annual percentage rate (APR). This will help us calculate the potential interest charges.
Step 3: Calculate the potential interest charges
Assuming Lourdes doesn't pay off the credit card balance by the end of the month, divide the APR by 12 to get the monthly interest rate. Multiply this rate by the $48 grocery cost to find the potential interest charges.
Step 4: Compare costs
Compare the ATM fee and potential interest charges to determine the cheaper option. If the ATM fee is less than the potential interest charges, Lourdes should use her debit card. If the potential interest charges are less than the ATM fee, she should use her credit card.
Keep in mind that if Lourdes is able to pay off her credit card balance at the end of the month, she won't be charged any interest, making the credit card the better option in that case.
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Earthworm Rivals are building the set for
their new music video. There is a tower made
of 9 glowing bricks that stands 5. 4 meters tall. If each of the bricks is the same exact size,
how tall is each brick?
Since each of the bricks is the same exact size, then each brick is 0.6 meters tall.
To determine the height of each glowing brick, we need to divide the total height of the tower (5.4 meters) by the number of bricks (9). This gives us the average height of each brick.
Using the formula for division, we can write this as:
Height of each brick = Total height of tower / Number of bricks
Plugging in the given values, we get:
Height of each brick = 5.4 meters / 9 bricks
Simplifying this expression, we can cancel out the units of "bricks" to get:
Height of each brick = 0.6 meters
Therefore, each glowing brick in the tower is 0.6 meters tall.
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Tim made his mother a quilt. The width is 6 5 /7 ft and the length is 7 3 /5 ft. What is the area of the quilt?
The quilt's area is approximately 60.74 square feet.
How to calculate the quilt's area?To calculate the area of the quilt, we need to multiply the width by the length.
First, we need to convert the mixed numbers to improper fractions:
Width: 6 5/7 ft = (7 x 6 + 5)/7 = 47/7 ft
Length: 7 3/5 ft = (5 x 7 + 3)/5 = 38/5 ft
Now, we can multiply the width by the length:
Area = width x length
Area = (47/7) ft x (38/5) ft
Area = 2126/35 sq ft
Area ≈ 60.74 sq ft
Therefore, the area of the quilt is approximately 60.74 square feet.
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Find the length of the midsegment of the trapezoid
2n-2
N+12
4n+6
Answer: To find the length of the midsegment of a trapezoid, you need to add the lengths of the two bases together and divide by 2.
The length of the top base is 2n-2 and the length of the bottom base is 4n+6.
Adding the two bases together gives:
(2n-2) + (4n+6) = 6n + 4
Dividing by 2 gives:
(6n + 4) / 2 = 3n + 2
Therefore, the length of the midsegment of the trapezoid is 3n + 2.
If the mean weight of 4 backfield members on the football team is 234 lb and the mean weight of the 7 other players is 192 lb, what is the mean weight of the 11-person team?
The mean weight of the team is approximately ___ pounds.
(Round to the nearest tenth.)
Answer: The mean weight of the 11-person team is 207.3 pounds
Step-by-step explanation:
According to the question,
The mean weight of 4 backfield members = 234 lb
Therefore, the total weight of 4 backfield members = 4 × 234 = 936 lb
Similarly,
The mean weight of the 7 players = 192 lb
And the total weight of 7 players = 7 × 192 = 1344 lb
∴ Total weight of 11 players = (936 + 1344) lb = 2280 lb
We know that,
Mean = [tex]\frac{Total Sum}{Total number of variables}[/tex]
∴ To find the mean weight of the 11 players we need to divide the total weight by 11 :
Mean = [tex]\frac{2280}{11} = 207.27[/tex]
Rounding off to the nearest tenth we get,
Mean = 207.3
Hence, the mean weight of the team is approximately 207.3 pounds
£4500 is shared between 4 charities.
the donation to charity b is 5/6 of the donation to charity d
charity d's donation is twice the donation to charity c.
the ratio of donations for charity c to charity a is 3:4.
work out the donation to charity b.
If the donation to charity b is 5/6 of the donation to charity d, charity d's donation is twice the donation to charity c and the ratio of donations for charity c to charity a is 3:4 then the donation to charity b is £1250.
Let's denote the donation to charity a as x. Then the donation to charity c is (3/4)x, and the donation to charity d is 2(3/4)x = (3/2)x.
We know that the donation to charity b is 5/6 of the donation to charity d, so:
donation to charity b = (5/6)(3/2)x = (5/4)x
We also know that the total donation is £4500, so we can set up an equation:
x + (3/4)x + (3/2)x + (5/4)x = £4500
Multiplying through by 4 to get rid of the fractions, we have:
4x + 3x + 6x + 5x = £18,000
18x = £18,000
x = £1000
So the donation to charity b is: (5/4)x = (5/4)(£1000) = £1250
Therefore, the donation to charity b is £1250.
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Albert and Makayla are each renting a car for one day. Albert’s rental agreement states that the car costs $35 per day and $0. 15 per mile driven. Makayla’s agreement states that the car she is renting costs $45 per day and $0. 10 per mile driven. Write an equation to determine the number of miles, m, Albert and Makayla drive if they spend the same amount of money on their rentals
To determine the number of miles, m, Albert and Makayla drive if they spend the same amount of money on their rentals, we can write an equation using the given information:
Albert's cost = $35 per day + $0.15 per mile driven
Makayla's cost = $45 per day + $0.10 per mile driven
Since they spend the same amount of money, we can set the costs equal to each other:
35 + 0.15m = 45 + 0.10m
Now, we need to solve the equation form, the number of miles driven:
1. Subtract 0.10m from both sides:
35 + 0.05m = 45
2. Subtract 35 from both sides:
0.05m = 10
3. Divide both sides by 0.05:
m = 200
So, if Albert and Makayla spend the same amount of money on their rentals, they both drive 200 miles.
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Which number produces a rational number when multiplied by 1?
O A. TI
O в. -3
• C. Т
O D. -1. 41421356
Number that produces a rational number when multiplied by 1 is option B, -3.
To determine which number produces a rational number when multiplied by 1,
We need to examine each of the given.
Here, options: A. TI , B. -3, C. T, D. -1.41421356
We know,
A rational number can be expressed as a fraction (a/b) where both a and b are integers and b is not equal to 0. When multiplying by 1, the result remains the same. Option B: -3 multiplied by 1 = -3 which is a rational number because it can be expressed as a fraction (-3/1).
Option D: here given number -1.41421356 multiplied by 1 = -1.41421356 and we cannot be easily expressed as a fraction.
Therefore,it's not a rational number.
Thus, the number that produces a rational number when multiplied by 1 is option B, -3.
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Selika give her garden a makeover. She spends money on plant,materials, and labour in the ratio of 1:5:12. She spends £848. 75. How much money does she spend on labour costs
Selika spends £565.85 on labour costs.
Given, Selika spends money on plants, materials, and labor in the ratio of 1:5:12 and spends a total of £848.75. We have to find how much money she spends on labor costs.
Let the amount of money Selika spends on plants be x. Then, the amount of money she spends on materials is 5x, and the amount of money she spends on labor is 12x.
The total amount of money she spends is £848. 75
x + 5x + 12x = 848.75
18x = 848.75
x = 848.75/18
x = 47.15
She spend on labour 12x = 12 × 47.15
= 565.85
Therefore, Selika spends £565.85 on labour costs.
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Here is an inequality: -2x > 10.
1. List some values for x that would make this inequality true.
2. How are the solutions to the inequality -2x [tex]\geq[/tex] 10 different fomt the solutions to -2x > 10? Explain your reasoning.
Therefore , the solution of the given problem of inequality comes out to be the solutions x = -6 or x = -10 would be acceptable.
What exactly is an inequality?Algebra, which lacking a symbol for this difference, can represent it using a pair or group of numbers. Equity usually comes after equilibrium. Inequality is bred by the persistent gap of standards. Equality and disparity are not the same thing. As was my least preferred symbol, notwithstanding knowing that the pieces are often not connected or close to one another. (). No matter how small the variations, they all affect value.
Here,
Finding values of x that cause the left side of the inequality to be bigger than the right side is necessary to make the inequality -2x > 10 true. Divide both sides by -2 and invert the inequality sign to achieve this:
=> -2x > 10
=> x < -5
The inequality is therefore true for any value of x that is less than -5. For instance, the solutions x = -6 or x = -10 would be acceptable.
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 A customer is comparing the size of oil funnels in a store. The funnels are cone shaped. One funnel has a base with a diameter of 8 in. And a slant height of 12 in. What is the height of the funnel? Round your answer to the nearest hundredth. 
The height of the funnel is 11.31, under the condition that one funnel has a base with a diameter of 8 in. And a slant height of 12 in.
Here we have to apply the Pythagorean theorem to evaluate the height of the funnel. The Pythagorean theorem projects that the square of the hypotenuse (the slant height) is equal to the sum of the squares of the other two sides (the radius and height).
Now, we have a cone that has a base diameter of 8 inches which says that the radius is 4 inches. The slant height is 12 inches. Then the height is
h² + r² = l²
h² + 4² = 12²
h² = 144 - 16
h² = 128
h = √(128)
h ≈ 11.31
Hence, 11.31 inches is the approximate height of the funnel after rounding to the nearest hundredth.
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Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. If the rectangular frame's diagonal is 50 inches and forms a 36.87° angle with the bottom of the frame, what is its height? Round your answer to the nearest inch.
The height of the rectangular frame is 30 inches.
How to find the height of the frame?Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. The rectangular frame's diagonal is 50 inches and forms a 36.87° angle with the bottom of the frame.
Hence, the height of the frame can be represented as follows:
using trigonometric ratios,
sin 36.87 = opposite / hypotenuse
sin 36.87 = h / 50
cross multiply
h = 50 sin 36.87
h = 50 × 0.60000142913
h = 30.0000714566
Therefore,
height of the frame = 30 inches
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The bike sarah wants to buy is now 40% off. the original price is $150. decide if you are missing the percent, part or whole. then use the appropriate formula to find the discount amount
The discount amount of the bike Sarah wants to buy is $60. The calculation was done by using the formula: Discount = Original price x Percent off.
To find the discount amount of the bike, we need to use the formula
Discount = Original Price x Discount Rate
where Discount Rate = Percent Off / 100
We know that the original price of the bike is $150 and it is now 40% off. So, the discount rate is
Discount Rate = 40 / 100 = 0.4
Substituting these values in the formula, we get:
Discount = $150 x 0.4 = $60
Therefore, the discount amount of the bike is $60.
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Brainliest if correct!_A particle is projected vertically upwards from a fixed point O. The speed of projection is u m/s. The particle returns to O 4 seconds later. Find:
a) the value of u
b) the greatest height reached by the particle
c) the total time of which the particle is at a height greater than half its greatest height
Thank you so much!
The value of the velocity, u is 19.6 m/s.
The greatest height reached by the particle is 19.6 m.
The total time during which the particle is at a height greater than half its greatest height is 2.33 s.
What is the value of the velocity, u?a) To find the value of the velocity, u, we can use the formula for the time of flight of a vertically projected particle:
t = 2u/g
Since the particle returns to the same point after 4 seconds, we have:
2t = 4
Substituting the value of t in the first equation, we get:
u = gt/2 = 9.8 x 2
u = 19.6 m/s
b) To find the greatest height reached by the particle, we can use the formula for the maximum height reached by a vertically projected particle:
h = u^2/2g
Substituting the value of u, we get:
h = 19.6^2/(2 x 9.8)
h = 19.6 m
c) To find the total time during which the particle is at a height greater than half its greatest height, we can first find the height at which the particle is at half its greatest height:
h/2 = (u^2/2g)/2 = u^2/4g
Substituting the value of u, we get:
h/2 = 19.6^2/(4 x 9.8) = 24.01 m
So, the particle is at a height greater than half its greatest height when it is above 24.01 m.
Next, we can find the time taken by the particle to reach this height:
h = ut - (1/2)gt^2
24.01 = 19.6t - (1/2)9.8t^2
Solving this quadratic equation, we get:
t = 2.33 s or t = 4.10 s
The particle takes 2.33 s to reach a height of 24.01 m, and it takes another 1.67 s (4 - 2.33) to return to the ground.
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10 foot ladder is leaning against a vertical wall when Jack begins
pulling the foot of the ladder away from the wall at a rate of 0.5
fr/s. how fast is the top of the ladder sliding down the wall?
We can use the Pythagorean theorem to relate the distances between the ladder, wall, and ground. Let's call the distance from the foot of the ladder to the wall "x", and the distance from the top of the ladder to the ground "y". Then, we know that:
x^2 + y^2 = 10^2
We can differentiate this equation with respect to time to get:
2x(dx/dt) + 2y(dy/dt) = 0
We're interested in finding dy/dt, the rate at which the top of the ladder is sliding down the wall. We know that dx/dt = 0.5 ft/s, so we can plug in these values and solve for dy/dt:
2x(dx/dt) + 2y(dy/dt) = 0
2(8)(0.5) + 2y(dy/dt) = 0 (since x = 8 based on the Pythagorean theorem)
dy/dt = -4 ft/s
So the top of the ladder is sliding down the wall at a rate of 4 ft/s.
When the 10-foot ladder is leaning against a vertical wall, it forms a right-angled triangle with the wall and the ground. As Jack pulls the foot of the ladder away from the wall at a rate of 0.5 ft/s, the top of the ladder slides down the wall. To find the rate at which the top of the ladder slides down, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a is the distance from the foot of the ladder to the wall, b is the height of the ladder's top from the ground, and c is the length of the ladder (10 feet).
Differentiating both sides with respect to time (t), we get:
2a(da/dt) + 2b(db/dt) = 0
We know that da/dt = 0.5 ft/s. We need to find db/dt, which is the rate at which the top of the ladder slides down the wall. To do this, we need to find the values of a and b at a given moment. Since the problem doesn't provide this information, it's not possible to determine the exact value of db/dt. However, if you have the values of a and b, you can plug them into the equation and solve for db/dt.
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