The solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.
What are the solutions to the given equation?Given the equation in question;
|3x-7| - 7 = x
First, add 7 to both sides.
|3x-7| - 7 + 7 = x + 7
|3x-7| = x + 7
Next, remove the absolute value term, this creates a ± on the right side of the question.
|3x-7| = x + 7
3x-7 = ±( x + 7 )
The complete solution is the result of both the negative and positive portions of the solution.
For the first solution, use the positive of ±.
3x-7 = ( x + 7 )
3x - 7 = x + 7
3x - x = 7 + 7
2x = 14
x - 14/2
x = 7
For the second solution, use the negative of ±.
3x-7 = -( x + 7 )
3x-7 = -x - 7
3x + x = -7 + 7
4x = 0
x = 0/4
x = 0
Therefore, the solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.
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HELP !!! find the surface area of each figure. Round it to the nearest tenth.
Answer:
556
Step-by-step explanation:
Surface area=2*(lb+bh+lh)=2*(110+80+88)=556
How many centimeters are in 7 feet given that 1 inch is 2.5 cm
Answer: 210 cm
Step-by-step explanation:
1 inch=2.5 cm
1 foot=12 inches
1 foot*12 inches*2.5 cm=30 cm
1 foot=30 cm
7 feet=30*7=210 cm
A forecasting method has produced the following over the past five months. What is the mean absolute deviation? 3. 6 3.8 3.2. \( 3.4 \) \( 3.0 \)
The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.
The mean absolute deviation (MAD) measures the average distance between each data point and the mean of the dataset. To find the MAD, you need to follow these steps:
1. Calculate the mean of the dataset by adding up all the numbers and dividing the sum by the total number of data points. In this case, the dataset consists of the following numbers: 3, 6, 3.8, 3.2, and 3.4. Adding them up gives us a sum of 19.4. Dividing this sum by 5 (since there are 5 data points) gives us a mean of 3.88.
2. Find the absolute deviation for each data point by subtracting the mean from each data point and taking the absolute value. For example, for the first data point, 3, the absolute deviation would be |3 - 3.88| = 0.88. Repeat this step for all the data points.
3. Calculate the mean of the absolute deviations by adding up all the absolute deviations and dividing the sum by the total number of data points. In this case, the absolute deviations are: 0.88, 2.12, 0.72, 0.68, and 0.58. Adding them up gives us a sum of 4.98. Dividing this sum by 5 gives us a mean of 0.996.
So, the mean absolute deviation for the given dataset is approximately 0.996.
The mean absolute deviation helps us understand how much each data point varies from the mean of the dataset. By calculating the absolute deviation for each data point and finding the average, we can determine the typical amount of variation in the dataset.
The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.
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Which input value produces the same output value for the two functions on the graph?
x = −1
x = 0
x = 1
x = 2
Answer:
The image of both graphs can be seen below:
Both functions will have the same output for an input x₀ if:
f(x₀) = g(x₀)
This means that, for that particular value of x₀, the functions will intersect each other.
So we just need to look at the graph and find the x-value where the functions intersect. (Remember that the x-values are in the horizontal axis)
We can see that it happens at x = 1.
Then the input value that produces the same output value for the two functions is:
x = 1
Parker and Hailey each made a batch of paint in the Paint Mixer. Hailey's batch was in the ratio 4 red : 6 yellow. Parker wants to have the same color as Hailey, but he added 6 red : 9 yellow. Is their paint the same color or not? Explain how you know.
Answer:
No, Parker has more yellow then red in his batch to match Hailey's batch.
Step-by-step explanation:
If Parker's batch was 7 red : 9 yellow or 6 red : 8 yellow then Parker's batch would be equivalent to Hailey's batch.
Find, in the form x + iy: (-4+7i)². 4 (-4+7i)².
(-4 + 7i)² = 9 + 56i ; Where x + iy is complex form.
To find the square of (-4 + 7i), we can use the formula for squaring a complex number, which states that (a + bi)² = a² + 2abi - b².
In this case, a = -4 and b = 7. Applying the formula, we have:
(-4 + 7i)² = (-4)² + 2(-4)(7i) - (7i)²
= 16 - 56i - 49i²
Since i² is equal to -1, we can substitute -1 for i²:
(-4 + 7i)² = 16 - 56i - 49(-1)
= 16 - 56i + 49
= 65 - 56i
So, (-4 + 7i)² simplifies to 65 - 56i.
If we multiply the result by 4, we get:
4(-4 + 7i)² = 4(65 - 56i)
= 260 - 224i
Therefore, 4(-4 + 7i)² is equal to 260 - 224i.
The square of (-4 + 7i) is 65 - 56i. Multiplying that result by 4 gives us 260 - 224i.
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Fiona is heating water for a science experiment the temperature of the water increases 4/5 of a degree every 2/5 of a minute how much is the temperature of the water increasing per minute.
Answer needed ASAP
thanks
The temperature that water is increasing per minute is 2 degrees.
What is the increase in temperature per minute?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the digit above the line and the denominator is the number below the line. An example of a fraction is 3/7.
The first step is to determine what 2/5 of a minute is equivalent to in seconds.
1 minute = 60 seconds
2/5 x 60 = 24 seconds
The formula that can be used to determine the temperature that water is increasing per minute is :
Temperature increase per minute = (degree it rises to 2/5 of a minute x seconds in a minute) / seconds in 2/4 of a minute
(4/5 x 60) / 24 = 2 degrees
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Little Johnny gets 2 hotdogs every 5 minutes. How much hotdogs will he have in an hour?( I already know the answer lmbo)
Answer:
24 bog ole hotdogs
Step-by-step explanation:
Answer:
12 hot dogs in 30 minutes
Step-by-step explanation:
1. Write it as a fraction
1. 2/5
2. Write what we know of the answer as a fraction
1. ?/30
3. For the denominator to get to 30, we must multiply 5 by 6. However, we also have to multiply the numerator by 6.
1. 2*6=12.
4. Therefore, the answer is 12/30, or he will eat 12 hot dogs in half an hour.
Solve and CHECK the following:
8−(5x−2)=6−2(3x+1)
Answer:
X=6/11
Step-by-step explanation:
8-(5x-2)=6-2(3x+1)
8-5x+2=6-6x-2
10-5x=4-6x
6=11x
x=6/11
Answer:
8-5x-2=6-6x+2
8-2-6-2=5x-6x
-10+8=-x
-2 =-x
x=2 ........×-1
x=2
if 2x-6=0 the x =?
Answer:
x=3
Step-by-step explanation:
Answer:
x=3
Step-by-step explanation:
\(2x-6=0\\2x-6+6=0+6\\2x=6\\x=3\)
Hope this helps plz hit the crown ;D
Which equation, when solved for x, is equivalent to px-r=w?
Answer:
The answer is A
Step-by-step explanation:
The 20th term of the number sequence is 50
Write down the 21st term of the number sequence.
I hope this help too.
Answer:-
The linear sequence 27, 25, 23, 21, 19... is an arithmetic progression with (-2) as the common difference.
The nth term of an arithmetic progression is an=a1+(n−1)da_n=a_1+(n-1)dan=a1+(n−1)d, where ana_nan is the nth term, a1a_1a1 is the first term, d is the common difference.
In our case, n=50,a1=27,d=−2n=50, a_1=27, d=-2n=50,a1=27,d=−2 , hence, we get
a50=27+49⋅(−2);a50=27−98=−71.a_{50}=27+49\cdot(-2);\\ a_{50}= 27-98=-71. a50=27+49⋅(−2);a50=27−98=−71.
The 50th term of this sequence is (-71).
A hypothesis test is to be performed for a population mean. Which of the following does the probability of a type II error not depend on?
options:
The significance level
The sample mean
The sample size
The true (population) mean
When a thesis test is being performed for a population mean, the probability of a type II error isn't dependent on the sample mean. Option B is the right answer.
A type II error occurs when a null thesis isn't rejected despite it being incorrect. It's worth noting that the threat of making a type II error is affected by several factors, including the sample size, the true population mean, the position of significance, and the variability of the data.
As a result, the larger the sample size, the lower the threat of making a type IIerror.The true population mean also has an impact on the liability of a type II error. As the difference between the true mean and the hypothecated mean grows, the threat of a type II error decreases.
The position of significance is also pivotal in determining the threat of a type II error. As the significance position increases, the threat of a type II error decreases.
So, the correct answer is B
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WILL GIVE BRAINLIEST AND 30 POINTS IF SOMEONE HELPS
The variables are x = 1/2 and y = 5/3
How to solve for the variable x and y?From the figure, we have been told 21x = 5x + 8. So let's solve for x.
21x = 5x + 8
21x - 5x = 8
16x = 8
x = 8/16
x = 1/2 = 0.5
Using the Basic Proportionality Theorem or Thales’s Theorem, which states that "If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally". We can say:
(20y-2)/(17y + 3) = (5x+8)/(21x)
Substitute x = 0.5 and solve for y:
(20y-2)/(17y + 3) = (5(0.5) + 8)/(21(0.5))
(20y-2)/(17y + 3) = (10.5)/(10.5)
(20y-2)/(17y + 3) = 1
20y-2 = 17y + 3
20y - 17y = 3 + 2
3y = 5
y = 5/3
Thus, the variables are x = 1/2 and y = 5/3
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A roller skating rink charges a flat rate of $5 to rent skates, plus $2.50 per hour to skate. You rent skates and skate for 3 hours. If you pay with a $20.00 bill, how much change do you get back?
Answer:
$7.50
Step-by-step explanation:
First, you multiply 3 and $2.50 (because you skate for 3 hours and it's $2.50 per HOUR to skate) 3 x 2.50 is $7.50 plus the flat rate of $5 is $12.50. So, your total altogether would be $12.50. So if you pay that total with $20, you have to subtract 12.50 from 20. 20 - 12.50 is $7.50. Your change will be $7.50. I hope this is correct! So sorry if it isn't!
Answer:
7.5
Step-by-step explanation:
First, you multiply 2.50 x 3. The answer to that is 7.50. Add on the renting skates, that is 12.50. Then, you subtract 12.50 from 20.00. The answer is 7.5.
cany anybody give me the awnser to this?
Have a look at the attached image.
20.
60
(x + 20)
Зх
Sum of angle
measures: 180°
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Sum of the interior angles of any triangle equal 180° .
Thus ;
\((x + 20) + 3x + 60 = 180\)
\(4x + 80 = 180\)
Subtract sides 80
\(4x + 80 - 80 = 180 - 80\)
\(4x = 100\)
Divide sides by 4
\( \frac{4}{4} x = \frac{100}{4} \\ \)
\(x = 25\)
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Answer: definitely x=25
Step-by-step explanation:
Solve the following series. Remember to use your formulas and indicate your final answer. Find the sum of the first 13 terms of: 1, 2, 4, 8, 16, ...
Answer
Sum of the first 13 terms = 8191
Explanation
The sum of terms in a geometric term is given as
\(S_n=\frac{a\lbrack r^n-1\rbrack}{r-1}\)where
a = first term = 1
r = common ratio = ratio of consecutive terms = (Second term)/(First term) = (2/1) = 2
n = number of terms = 13
\(\begin{gathered} S_n=\frac{a\lbrack r^n-1\rbrack}{r-1} \\ S_{13}=\frac{1\lbrack2^{13}-1\rbrack}{2-1}=\frac{8192-1}{1}=8191 \end{gathered}\)Hope this Helps!!!
question one, true or false?
Answer:
I think its True but im not sure
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
the value of Q3 is 15
every polynomial function of odd degree with real coefficients will have at least
Every polynomial function of odd degree with real coefficients will have at least one real root or zero.
This statement is known as the Fundamental Theorem of Algebra. It states that a polynomial of degree n, where n is a positive odd integer, will have at least one real root or zero.
The reason behind this is that when a polynomial of odd degree is graphed, it exhibits behavior where the graph crosses the x-axis at least once. This implies the existence of at least one real root.
For example, a polynomial function of degree 3 (cubic polynomial) with real coefficients will always have at least one real root. Similarly, a polynomial function of degree 5 (quintic polynomial) with real coefficients will also have at least one real root.
It's important to note that while a polynomial of odd degree is guaranteed to have at least one real root, it may also have additional complex roots.
The Fundamental Theorem of Algebra ensures the existence of at least one real root but does not specify the total number of roots.
In summary, every polynomial function of odd degree with real coefficients will have at least one real root or zero, as guaranteed by the Fundamental Theorem of Algebra.
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Sonia has two packages of hamburger meat. The first package weighs 1.76 pounds and the second package weighs 2.29 pounds. She mixes the two packages together and forms hamburgers that weigh 0.25 pound each. What is the greatest number of 0.25 -pound hamburgers Sonia can make using the hamburger meat she has?
Answer:
16 hamburgers
Step-by-step explanation:
add the weights of the meats together
1.76 + 2.29 = 4.05 pounds
divide 4.05 by .25
16.2 pounds or 16 burgers
A rhinoceros in Central Park Zoo weighs 2,200 pounds. What are the benchmark numbers you would use to determine about how much 58 rhinoceroses would weigh?
The computation shows that the weight of 58 rhinoceros will be 127600 pounds
How to compute the value?From the information, one rhinoceros in Central Park Zoo weighs 2,200 pounds. and we are to determine about how much 58 rhinoceroses would weigh.
This will be:
= 2200 × 58
= 127600 pounds.
The weight of 58 rhinoceros will be 127600 pounds.
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Answer:
Look at the other guy's explanation
Step-by-step explanation:
its wrong for me but really good
A saw mill cuts boards that are 16 ft long. After they are cut, the boards are inspected and
rejected if the length has a percent error of 1. 5% or more. The saw mill also cuts boards that are 10, 12, and 14 feet long. An inspector rejects a board that
was 2. 3 inches too long. What was the intended length of the board?
Some acceptable board lengths are: 15.8 ft, 16.20 ft and 16.10 feet
Some board lengths to reject are: 14.8 ft, 17.20 ft and 12.10 feetThe intended lengths are 10.19, 12.19 and 14.19 feetNow, According to the question:
Board lengths that should be accepted
From the question, we have the following parameters that can be used in our computation:
Length = 16 ft
Percent error = 1.5%
This means that the acceptable lengths are
Acceptable = Length ± Percent error * Length
Substitute the known values in the above equation, so, we have the following representation
Acceptable = 16 ± 1.5% * 16
So, we have
Acceptable = 16 ± 0.24
Evaluate
Acceptable = 15.76 to 16.24
Some board lengths that should be accepted are 15.8 ft, 16.20 ft and 16.10 feet
Board lengths that should be rejected
In (a), we have
Acceptable = 15.76 to 16.24
Some board lengths that should be rejected are 14.8 ft, 17.20 ft and 12.10 feet
The intended lengths of the boards
Here, we have
Lengths = 10, 12 and 14 feet
Length too long = 2.3 inches
Convert to inches
Length too long = 0.19
So, we have
Intended lengths = (10, 12 and 14 feet) + 0.19
Evaluate
Intended lengths = 10.19, 12.19 and 14.19 feet
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(03.06 LC)
Choose the equation below that represents the line that passes through the point (-2,-1)
and has a slope of 5.
The line that passes through the point (-2,-1) and has a slope of 5. The equation of the line is y + 1 = 5(x + 2).
What is slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
Using the slope and 1 point format: (y- y₁) = m(x - x₁)
where m = slope = 5, and point is (x₁, y₁). In this case point (x₁, y₁) = (-2, -1)
x₁ = -2, y₁ = -1
Using: (y- y₁) = m(x - x₁)
y - -1 = 5(x - -2)
y + 1 = 5(x + 2).
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One car seat is designed for a child up to and including 28 lb. Another car seat is designed for a child between 15 lb and 45 lb. A third car seat is designed for a
child between 28 lb and 90 lb, inclusive. Model those ranges with compound inequalities.
Please help me giving Brainly
Answer: See explanation
Step-by-step explanation:
f=First car seat. s=Second car seat. t=Third car seat
f<=28
15<s<45 ==> Second car seat can hold between 15 and 45 pounds noninclusive.
28<=t<=90 ==> Third car seat can hold between 28 and 90 pounds inclusive.
9x -5y = 16
-3x + 7y = 16
-4x - 2y = 14
10x - 7y = 25
A jar contains 7 red jelly beans, 2 black jelly beans and 6 green jelly beans. You draw ONE jelly bean. What is the probability of drawing a red bean? a. c. 1 b. d.
Answer:
7/15
Step-by-step explanation:
number of favorable outcomes (red jelly beans) = 7
number of total outcomes (total jelly beans) = 7 + 2 + 6 = 15
probability of red = number of favorable outcomes/number of total outcomes = 7/15
The probability of getting a red jelly bean is 7/15
Total number of jelly beans in the jar (sum of all the jelly beans): 7+6+2= 15
Total number of red jelly beans: 7
Therefore, the probability of getting a red jelly bean= number of red jelly beans/ total number of jelly beans
=7/15
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Let R be the region Bounded by the following curves. Find the volume of the solid generated when R is revolved about the y-axis.
y= sin ^-1 (x/13), X=0, y= (pi/12)
The volume if the solid generated is 12.32 cubic units.
The volume of the solid generated by revolving the region bounded by the curves y = sin^-1(x/13), x = 0, and y = pi/12 about the y-axis can be calculated using the method of cylindrical shells.
First, we need to find the limits of integration for y. From the equation y = sin^-1(x/13), we can solve for x to get x = 13 sin(y). Since y ranges from 0 to pi/12, we know that x ranges from 0 to 13 sin(pi/12).
Next, we need to find the height of each cylindrical shell. This is simply the difference between the upper and lower curves, which is pi/12 - sin^-1(x/13).
Finally, we integrate the expression for the volume of a cylindrical shell over the range of y to obtain the total volume:
V = ∫[0, pi/12] 2πx(pi/12 - sin^-1(x/13)) dy
V = π/6 ∫[0, pi/12] (13sin(y))^2 (pi/12 - y) dy
V = π/6 ∫[0, pi/12] 169sin^2(y) (pi/12 - y) dy
V = π/6 [169(1/2)(pi/12)^2 - 169∫[0, pi/12] ysin^2(y) dy]
V ≈ 12.32 cubic units
Therefore, the volume of the solid generated by revolving the region bounded by the curves y = sin^-1(x/13), x = 0, and y = pi/12 about the y-axis is approximately 12.32 cubic units.
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if the inside height of the trailer is 6.5 feet, what is the total volume of the inside of the trailer, to the nearest cubic foot?
The cross sectional area of the cargo trailer floor, which is a composite figure consisting of a square and an isosceles triangle, indicates that the volume of the inside of the trailer is about 3,952 ft³.
What is a composite figure?A composite figure is a figure comprising of two or more regular figures.
The possible cross section of the trailer, obtained from a similar question on the internet, includes a composite figure, which includes a rectangle and an isosceles triangle.
Please find attached the cross section of the Cargo Trailer Floor created with MS Word.
The dimensions of the rectangle are; Width = 6 ft, length = 10 ft
The dimensions of the triangle are; Base length 6 ft, leg length = 4 ft
Height of the triangular cross section = √(4² - (6/2)²) = √(7)
The cross sectional area of the trailer, A = 6 × 10 + (1/2) × 6 × √(7)
A = 60 + 3·√7
Volume of the trailer, V = Cross sectional area × Height
V = (60 + 3·√7) × 6.5 = 3900 + 19.5·√7
Volume of the trailer = (3,900 + 19.5·√(7)) ft³ ≈ 3952 ft³
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can someone help me answer this pls
Answer:
D
bc to figure out if it is a graph or not, you would see if a horizontal line could pass through the line only once and since the line is horizontal, that is not the case.