Answer:4536 numbers.
Step-by-step explanation:
Since 1 st digit cannot be zero the first digit can be anything from 1–9 ( total 9)
The second digit ( any 10- 1 above)
The third digit ( any 10–2 above)
The last digit ( any 10–3 above)
Total 9x9x8x7 =
4536
:)
the manager of a firm wants to determine if the average hourly wage for semi-skilled workers is $9 in the capital district. in order to do so, she takes a random sample of 100 hourly wages and finds that the sample mean is $8 and the sample standard deviation is $2. the hypotheses to be tested are: h subscript 0 : mu equals 9 h subscript 1 : mu not equal to 9 assume that the actual average is $8.8. what is the probability of type ii error at the 5% significance level?
The probability of type ii error at the 5% significance level is 49.5%
Probability:
In statistics, the number of possible way of occurring an particular event is referred as probability.
Given,
The manager of a firm wants to determine if the average hourly wage for semi-skilled workers is $9 in the capital district. in order to do so, she takes a random sample of 100 hourly wages and finds that the sample mean is $8 and the sample standard deviation is $2. the hypotheses to be tested are: h subscript 0 : mu equals 9 h subscript 1 : mu not equal to 9 assume that the actual average is $8.8.
Here we need to find the probability of type ii error at the 5% significance level.
While we looking into the give question, we have identified the following,
Semi skilled worker hourly wages = $9
Number of samples = 100
sample mean = $8
Standard deviation = $2
Hypotheses
H₀ : μ = 9
H₁ : μ ≠ 9
Significance level = 5%
Therefore, the type II error is calculated as,
=> P [(100 - 9/(2/√100)) ≥ (9 - 8)/(2/√100))] = 1 - 5
When we simplify this one then we get, the probability as 49.5%.
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A circle with radius of 2 cm sits inside a 7 cm x 11 cm rectangle. What is the area of the shaded region? Round your final answer to the nearest hundredth.
A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?.
6000FT, is the shortest length of fence that the rancher can use.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
Let the rectangular field's length be x.
rectangle field width = y
square feet of a rectangular field's area
Because length is always positive, it is always positive.
Once more, discriminate with respect to x
replace x=1500
Therefore, at x=1 500, fencing is minimal.
Change x to 1 500.
the rectangular field is 1500 feet long.
rectangle field's width is 1000 feet.
Replace the values
shortest used fence length =6000ft
Hence, 6000FT, is the shortest length of fence that the rancher can use.
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how many (non-congruent) isosceles triangles exist which have a perimeter of $10$ and integer side lengths?
As per the Pythagoras theorem, there are totally 4 triangles possible.
Pythagoras theorem:
In geometry, Pythagoras theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs.
Given,
Here we need to find how many (non-congruent) isosceles triangles exist which have a perimeter of 10 and integer side lengths.
As per the Pythagoras theorem, we know that the sum of two sides should be greater than the third.
And here we have the isosceles triangles, then the value of two side of the triangle is equal.
Here the perimeter of the triangle is 10.
Then the values must be the sum of 10,
=> 2, 6, 2
=> 1, 1, 8
=> 3, 3, 4
=> 4, 4, 2
These are the possible combinations.
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Plot the points (2, -1) and (7,-1) and find the slope.
Answer:
slope = 0Step-by-step explanation:
Slope =
[tex] \frac{change \: in \: y}{change \: in \: x} [/tex]
X1=2 X2=7
Y1=-1 Y2=-1
hence
[tex] \frac{ - 1 - ( - 1)}{7 - 2} [/tex]
[tex] \frac{ - 1 + 1}{7 - 2} [/tex]
[tex] \frac{0}{5} [/tex]
[tex]slope = 0[/tex]
from a group of 7 men and 6 women a committee consisting of 4 men and 3 women is to be formed. how many different committees are possible if (a) 2 of the men refuse to serve together?
There are 300 number of ways in which committee can be formed. It can be solved by the fomula of combination.
What is the formula of combination?
Following is the fomula of combination:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Here, n is the total objects available and r is the number of object need to choose from n objects.
Consider no man refuses to serve together. Now, number of ways in which 4 men and 3 women committee can be formed from a group of 7 men and 6 woman.
[tex]^7C_4\times\ ^6C_3[/tex]
Now, consider a goup in which the two persons who do not want to serve togather are togather. Consider these person as a single person. Now, we need to choose 3 men (two individual men and one group of 2 men will make 4 men in the group) from 6 men (7 converts into 6 because group of two person is considerd as 1.).
[tex]\ ^6C_3\times\ ^6C_3[/tex]
Now, subtract [tex]\ ^6C_3\times\ ^6C_3[/tex] from [tex]^7C_4\times\ ^6C_3[/tex] to get the actual answer.
[tex]^7C_4\times\ ^6C_3-\ ^6C_3\times\ ^6C_3\\=\frac{7!}{4!3!}\times \frac{6!}{3!3!}-\frac{6!}{3!3!}\times\frac{6!}{3!3!}\\=35\times20-20\times20\\=20\times15\\=300[/tex]
Hence, there are 300 number of ways in which committee can be formed. It can be solved by the fomula of combination.
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roll a fair die 10 times. (a) compute the probability that at least one number occurs exactly 6 times. (b) compute the probability that at least one number occurs exactly once.
The probability that at least one number occurs exactly 6 times is 0.01303 and the probability that at least one number occurs exactly once is 0.323.
In the given question, roll a fair die 10 times.
(a) We have to compute the probability that at least one number occurs exactly 6 times.
At least one number occurring exactly 6 times.
From Binomial distribution
[tex]P(X=x) = ^nC_x(p)^{x}(q)^{n-x}[/tex]
As we roll a dice 10 times. So n=6
As we know that a dice have six faces. Each faces are mark from the number 1 to 6.
That means if we rolled a dice then there is possibility of coming six numbers.
So the probability of coming number in one time is
p=1/6
The probability of not coming the same number is
q=1-p
q=1-1/6 = 5/6
x=6
Now putting the value
[tex]P(X=6) = 6\times^{10}C_{6}(\frac{1}{6})^{6}(\frac{5}{6})^{10-6}[/tex]
[tex]P(X=6) = 6\times^{10}C_{6}(\frac{1}{6})^{6}(\frac{5}{6})^{4}[/tex]
After solving, at least one number occur exactly 6 times
Probability = 0.01303
(b) We have to compute the probability that at least one number occurs exactly once.
[tex]P(X=1)= ^{10}C_{1}(\frac{1}{6})^{1}(\frac{5}{6})^{10-1}[/tex]
[tex]P(X=1) = ^{10}C_{1}(\frac{1}{6})^{1}(\frac{5}{6})^{9}[/tex]
After solving, the probability that at least one number occurs exactly once is
Probability = 0.323
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Mrs. Smith had 5/6 of a sack of garden soil for
plants. She used 2/3 of it for planting 6 pots
How much garden soil did she use?
Answer:
1/6
Step-by-step explanation:
convert them both to the same denominator (bottom number)
2/3 is 4/6
5/6-4/6 is 1/6
How do I turn 2.1 into a decimal? Please help!!
Answer:
2/10
Step-by-step explanation:
add the numbers and minus
If each quadrilateral below is a rectangle find the missing measure in #4
The missing measures of the angles are as follows:
m∠BCD = 90°m∠ABD = 16°m∠CBE = 74°m∠ADE = 74°m∠AEB = 148°m∠DEA = 32°How to determine the measures of the angles?The figure that completes the question is added as an attachment
From the figure of the rectangle, we have:
m∠BDC = 16°
A rectangle has four (4) interior angles that are 90 degrees each.
This means that
m∠ADE = 90 - 16
m∠ADE = 74°
Also, we have:
m∠ABD = m∠BDC = 16° by the alternate interior angles
By the complementary angle, we have:
m∠CBE = 90 - 16 = 74°
By the alternate interior angles, we have
m∠ADE = m∠CBE = 74°
Solving further, we have the following equations:
m∠AEB = 180 - 2(16)
m∠AEB = 148°
m∠DEA = 180 - m∠AEB
m∠DEA = 180 - 148
m∠DEA = 32°
Hence, the measure of the angle DEA is 32 degrees
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g how many ways are there to choose the exec board so that there is at least one masters student and one phd student? (for any of the 4 positions)
The board has a total of 78960006 options from which to select at least one master's and one PhD candidate.
Given,
Total number of students = 8000
Number of Phd students = 5000
Number of masters students = 3000
Number of members in Student Government Executive Board = 4
We have to find the number of ways to choose the exec board so that there is at least one masters student and one Phd student;
Here,
There are 3,000 different ways to have one Master student on the board.
After choosing a masters student, there are 5,000 different methods to have a PhD student on the board.
The number of possible ways to choose the final two members = 7998!/(7998 - 2)!
That is,
5,000 3,000 + 7998!/(7998 - 2) = 78960006
Therefore,
78960006 is the total number of ways the board can choose at least one masters and one PhD.
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in a survey about a new cleaning product, 75% of respondents report they would buy the product again. the margin of error for the survey is 5%. based on the margin of error, what percentage range reflects the population's true response?
Answer:80% - 70%
Step-by-step explanation:
If the margin for the error is 5% im guessing that means 5% backwards or forwards so i believe that my answer is correct
ps if im right brainliest please
The percentage range that reflects the population's true response, considering the margin of error, is from 70% to 80%.
Given, a margin of error of 5%, we can determine the range that reflects the population's true response.
To find the range, we consider the maximum and minimum values within the margin of error.
Maximum Value: 75% + 5% = 80%
Minimum Value: 75% - 5% = 70%
Therefore, the percentage range that reflects the population's true response, considering the margin of error, is from 70% to 80%.
This means that we can be 95% confident that the actual percentage of people who would buy the product again lies within this range.
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Do you prefer taking tests on paper or online? a college instructor gave identical tests to two randomly sampled groups of 45 students. One group took the test on paper and the other took it online. Those who took the test on paper had an average score of 68. 4 with a standard deviation of 12. 1. Those who took the test online had an average score of 71. 3 with a standard deviation of 14. 2. Can you conclude that the mean scores differ between online and paper tests? find the p-value and state a conclusion
As per the given standard deviation, the mean scores difference between online and paper tests is 2.9 and the p value of the test is 0.2999
Standard deviation:
In statistics, standard deviation is a quantity expressing by how much the members of a group differ from the mean value for the group.
Given,
A college instructor gave identical tests to two randomly sampled groups of 45 students. One group took the test on paper and the other took it online. Those who took the test on paper had an average score of 68.4 with a standard deviation of 12.1. Those who took the test online had an average score of 71.3 with a standard deviation of 14.2.
Here we need to find the mean scores difference between online and paper tests and the p value of the test.
While we looking into the given question we have identified the following values,
Test on paper:
Average score = 68.4
Standard deviation = 12.1
Online test
Average score = 71.3
Standard deviation = 14.2
Total number of students = 45
So, the difference between the mean scores differ between online and paper tests is calculated as,
=> 71.3 - 68.4 = 2.9
And the p - value is 0.2999.
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suppose a random variable has population mean 141 and population standard deviation 8.85. what is the standard error of the sample mean of a sample of 43 observations? (round to 2 decimal places.)
The standard error of the sample mean of a given sample of 43 observations with standard deviation 8.85 is equal to 1.35 ( round to 2 decimal places).
As given in the question,
Population mean of the random variable 'μ' = 141
Standard deviation 'σ' = 8.85
Sample size 'N' = 43 observations
Standard error of the sample mean
= σ / √N
= 8.85 / √43
= 8.85 / 6.56
= 1.349
= 1.35 (round to 2 decimal places )
Therefore, for the given standard deviation and sample size the standard error of the sample mean is equal to 1.35.
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a research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and tested them to end-of-life in a road test. the sample mean and standard deviation are 60,139.7 and 3505.42 kilometers. can you conclude, using ????
There is no sufficient evidence to indicate the true standard deviation is less than 4000.
What is the standard deviation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
given that n = 16
x = 60139.7
s = 3718.06
∝ = 0.05
To test the hypothesis
H0 : = 4000
H1 : < 4000 (claim)
test statistics
x² = ((n-1)s²) / H0²
= (15 * 13823970.16) / (16000000)
= 12.96
P- value = P [x² < 12.96] DF = n-1 = 15
= 0.3946
0.1 < P-value <0.5
Hence, there is no sufficient evidence to indicate the true standard deviation is less than 4000.
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Nth for the leaner sequence 22,18,14,10,6
The nth term of the sequence is aₙ = 26 - 4n.
How to find the nth term of a sequence?A sequence is defined as an arrangement of numbers in a particular order.
The sequence is an arithmetic sequence. Therefore, the nth term of the sequence can be found as follows:
aₙ = a + (n - 1)d
where
a = firs termd = common differencen = number of termTherefore,
a = 22
d = 18 - 22 = -4
n = number of terms
Hence,
aₙ = 22 + (n - 1)-4
aₙ = 22 - 4n + 4
aₙ = 22 + 4 - 4n
aₙ = 26 - 4n
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a spinner has six equal parts labeled from 1 to 6. the spinner is spun twice. what is the probability of getting a 3 twice in a row?
The probability of getting 3 twice in a row is 1/36
A spinner has 6 equal parts labeled from 1 to 6.
The spinner is spun twice.
First time what is the conditions {1,2,3,4,5,6}
Second time choices are
{1,1} {1,2} {1,3} {1,4} {1,5} {1,6}
{2,1} {2,2} {2,3} {2,4} {2,5} {2,6}
{3,1} {3,2} {3,3} {3,4} {3,5} {3,6}
{4,1} {4,2} {4,3} {4,4} {4,5} {4,6}
{5,1} {5,2} {5,3} {5,4} {5,5} {5,6}
{6,1} {6,2} {6,3} {6,4} {6,5} {6,6}
So we have total 6*6 = 36 choices
{3,3} comes only 1 times.
We know the formula for probability:
Probability(Event) = Favorable Outcomes/Total Outcomes.
Favorable Outcomes = 1.
Total Outcomes=36.
So the probability of getting a 3 twice in a row is 1/36.
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ghghghghghghghghghghghghghghghgh circle.
Answer:
yass
queen
Step-by-step explanation:
What is the value of x in the triangle?
Answer:
a I dont have a explanation but its a
beth wants to determine a 90 percent confidence interval for the true proportion of high school students in the area who attend their home basketball games. how large of a sample must she have to get a margin of error less than 0.03?
The size of the sample that she would have to get a margin of error less than 0.03 is 752
How to solve for the sample sizeWe have the margin of error E = 0.03
The confidence interval C I = 90 percent
p = 1 - p = 0.5
z α / 2 = 1.645
The formula for the sample size is given as
(z α / 2 / E)² * p * (1 - p)
(1.645 / 0.03)² * 0.5 * 0.5
= 54.833² * 0.5 *0.5
= 752
Hence n is given as 752. The size of the sample would have to be 752.
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Add 0.75 and 0.18. How many tenths are in the sum?
Answer:
Step-by-step explanation:
EXPLANATIONDETAIL STEPSforward
Based on the given conditions, formulate::
Calculate : :
Thanks (77)
Answer: 2 or 100 tenths
Step-by-step explanation:
0.75 + 0.18
You need to do it in the vertical way yo make it easier here i will show you.
0.75
+ 0.18
______
0.93
YOU MUST ALIGN THE DECIMALS TO GET IT RIGHT
Classify each number according to its value. 2.1 × 10-4 9.2 × 10-4 3.4 × 10-5 2.1 × 10-3 2.8 × 10-7 8.3 × 10-5 7.2 × 10-5
According to the information, the numbers are classified as follows: Greater than 8.2 x 104 = None; between 8.2 x 10⁴ and 8.2 x 10⁻⁶ : 2.1 x 10⁻⁴, 9.2 x 10⁻⁴, 3.4 x 10⁻⁵, 2.1 x 10⁻³, 8.3 x 10⁻⁵, 7.2 x 10⁻⁵; and less than 8.2 x 10⁻⁵: 2.8 x 10⁻⁷.
How to find the classification of numbers?To find the classification of numbers we must know how scientific notation works and know how to classify these numbers. According to its scientific notation, if we want to classify numbers greater than 8.2 x 10⁴ we must take the following into account:
All numbers with a power greater than 10⁴ would be greater than 8.2. Therefore, none of the options would be greater than this number.
In the second case, to find the numbers that are between 8.2 x 10⁴ and 8.2 x 10⁻⁶ we must look at the same element, that is, the numbers that have a power less than 10⁴ and greater than 10⁶ would be in the range of this exercise. So the numbers in this range would be:
2.1 x 10⁻⁴9.2 x 10⁻⁴3.4 x 10⁻⁵2.1 x 10⁻³8.3 x 10⁻⁵7.2 x 10⁻⁵In the third case, to identify the numbers that are less than 8.2 x 10⁻⁵ we must take into account the same element. If power is less than 10⁻⁵, they would classify in this interval. So the values that classify are:
8.2 x 10⁻⁷Note: This question is incomplete because there is some information missing. Here is the complete information:
Greater than 8.2 x 104
Between 8.2 x 104
and 8.2 x 10-6
Less than 8.2 x 10-5
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a student at another business school surveys 100 of 1000 graduates from last year and asks about their salaries. the researcher finds that the average income is $65, 000, with a standard deviation of $8000. if you wanted to be 95% sure that the real mean of all 1000 students is within a range of the sample mean, what would you set your confidence interval lower and upper bounds to be?
As per the given standard deviation, the confidence interval is 495.84, upper bound is $65,495.8 and the lower bound is $64,504.2
Confidence interval
Confidence interval means a range of values, bounded above and below the statistic's mean, that likely would contain an unknown population parameter.
Given,
A student at another business school surveys 100 of 1000 graduates from last year and asks about their salaries. the researcher finds that the average income is $65, 000, with a standard deviation of $8000.
Here we need to find the confidence interval lower and upper bounds if you wanted to be 95% sure that the real mean of all 1000 students is within a range of the sample mean.
While we looking into the given question, we have identified the following values,
standard deviation = $8,000
Average income = $65,000
Sample size = 1000
Confidence level = 95%
Then the value of confidence interval is calculated by the formula,
Then we get the value of
Lower bound = 64504.2
Upper bound = 65495.8
Confidence interval (±) = 495.84
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At top speed, cheetahs can run 80 miles per hour. How fast would that be in meters/second?
Answer:
The top speed of a cheetah is around 69 to 75 mph. However, the cat can only sprint a short distance of around 0.28 miles. A cheetah is about 2.7 times faster than the fastest human runner. A cheetah accelerates very quickly, allowing it to overtake prey at close range. The fastest cheetah on record is Sarah. Sarah lives at the Cinncinati Zoo in Ohio.
Step-by-step explanation:
Answer:
35.7632
Step-by-step explanation:
multiply the value in miles per hour by the conversion factor '0.44704'.=35.7632 meters per second
B is the midpoint of AC. D is the midpoint of CE. DE=5 and AE=18. What is the length of BD?
please help
Using the concept of midpoint of a line segment, the length of BD is 9 units
Midpoint of a Line SegmentA midpoint is a point lying between two points and is in the middle of the line joining the two points. If a line is drawn joining the two points, then the midpoint is a point at the middle of the line and is equidistant from the two points. Given any two points, say A and C, the midpoint is a point B which is located halfway between points A and C. Therefore, to calculate the midpoint, we can simply measure the length of the line segment and divide by 2.
In the question given;
AE = 18, DE = 5
But D is the midpoint of CE
CE = 2DE
CE = 2 * 5 = 10
The line CE IS 10
But AE is the total length of the line segment and it equals 18
AE = AC + CE
AC = AE - CE
AC = 18 - 10
AC = 8
If AC = 8, BC = 1/2(AC)
BC = 1/2 (8)
BC = 4
The line BD = BC + CD
BE = 4 + 5 = 9
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Dear Math Students, I have to divide 5 cups in half for a recipe. Here's what I did: 5÷1/2= 5 x 2/1 =10 I know I did the division correctly, but my answer should be less than 5, not more. Can you explain my mistake and help me fix it? Your friend, Puzzled Penguin
Answer: your first step was right5
Step-by-step explanation:
5/2 =2.5
Help me out please thank you
answers:
-3/4
-4/3
4\3
3/4
Answer:
Slope: -4/3
y-intercept: -9
Step-by-step explanation:
hope it helps!
find the area (in cm2) of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 8 cm if two sides of the rectangle lie along the legs.
The area of the largest rectangle that can be inscribed in the right triangle is calculated to be 6 cm^2
As we know that for a rectangle of width W and length L the area is given as;
A = L × W
Now let's say that L is along the 8 cm side and W is along the 3 cm side, let's find a relation between these two.
When we inscribe the rectangle in the larger triangle the quotient between the catheti of the right triangle must be equal to the quotient of the catheti of the right triangle that is generated.
Therefore that new triangle will have legs equal to the;
8cm - L and W.
Then we have that:
8cm - L / W = 8 cm / 3 cm
L = 8 cm - 8/3 × W
Now we can write L in terms of W so that we can replace that in the area equation to get
A = (8cm - (8/3)×W)×W = 8cm×W - (8/3)×W^2
This is the equation we have to maximize, also this is a quadratic polynomial of negative leading coefficient, which means that the maximum is at the vertex.
As we know the vertex of the general quadratic polynomial;
a × x^2 + b × x + c
is at:
x = -b / 2a
Then, in this scenario, the vertex is at;
W = (-8 cm) / (2 × 8/3) = 1.5 cm
Then the length is given by:
L = 8cm - (8/3) × 1.5cm = 4 cm
Therefore the area of the largest rectangle that can be inscribed in the given right triangle is;
A = 1.5 cm × 4 cm = 6 cm^2
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Hellloooo helpppp meeee
70 + 60 + 8x + 2 = 180
132+8x= 180
8x= 180-132
8x=48
x= 6
plug in x
8(6)+2 = 50
Answer:
x = 6
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180°.
To find the value of x, we can use the following equation:
70 + 60 + 8x + 2 = 180
Add like terms132 + 8x = 180
Subtract 132 from both sides8x = 48
divide both side by 8x = 6
What is the solution to the inequality below? 5−10≥−3+14
Answer:
5≥17
Step-by-step explanation: