1. x - 3 is not a factor
2. The remainder is 32.
1. How to determine if x - 3 is a factor of 2x³ - 4x² - 6?Using the remainder theorem, which states that for a polynomial p(x), if x - a is a factor, then p(a) = 0.
So, p(x) = 2x³ - 4x² - 6 If x - 3 is a factor, then
p(3) = 0
So, substituting x = 3 into the equation, we have
p(3) = 2x³ - 4x² - 6
= 2(3)³ - 4(2)² - 6
= 2(27) - 4(4) - 6
= 54 - 16 - 6
= 54 - 22
= 32
Since p(3) ≠ 0.
x - 3 is not a factor
2. What is the remainder?Since p(3) = 32,
The remainder is 32.
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3. What is true for an image and a preimage in a reflection? (1 point)
The image is larger than the preimage.
The image is smaller than the preimage.
The image and the preimage have the same orientation.
The image and the preimage have different orientations.
Answer: The image and the preimage have the same orientation.
Answer:
The image and the preimage have the different orientation.
Step-by-step explanation:
i
took
the
test
monty takes a cab to work and pays a fare of $12.75, he tips the diver 20% and the tax rate is 8%. how much does he spend on the trip
The cost of the fare based on the information is $16.32.
How to calculate the value?Amount for the fare = $12.75
Tip for the driver = 20% = 20% × $12.75 = $2.55
Tax rate = 8% = 8% × $12.75 = $1.02
Therefore the total amount will be:
= Cost of fare + Tip + Tax
= $12.75 + $2.55 + $1.02
= $16.32
The cost is $16.32. This illustrate the concept of addition.
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1. 3x-4=232. 9-4x=173.6(x-7)=364. 2(x-5)-8= 34
Solving those simple linear equations, by isolating the variable, and combining like terms.
1.3x-4=23
3x -4=23
3x=27
x=9
2) 9-4x=17
-4x =17-9
-4x=8
4x=-8
x=-2
3) 6(x-7)=36 Distributing the factor
6x -42=36
6x=36+42
6x=78
x=13
4) 2(x-5)-8=34 Distributing the factor
2x -10-8=34
2x -18=34
2x=52
x=26
Students A and B have probabilities of failing an exam of 1/2 and 1/5 respectively. The probability of them both failing the examination is 1/10. Determine the probability that at least one of the two students fail.
Answer:
7/5
Step-by-step explanation:
1/2 + 1/5
probability that at least one of the two students fail is 7/5
Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces. how many pieces of fish would there be if jorge divided each fish into tenths.
Answer:
1,730
Step-by-step explanation:
173x10 (pieces)= 1730
3. The following are the sizes in square feet of the seventeen new faculty office in the mathematics department at a college.102123142155104185159124154136113110107119120127155Find the mean square footage. Round your answer to the nearest tenth, if necessary. square feetFind the median square footage. square feet
Given a sample of the size, measured in square feet, of 17 faculty offices.
1) Mean
To calculate the mean of the sample you have to add all observations of the data set and divide it by the sample size:
[tex]\bar{x}=\frac{\Sigma x_i}{n}[/tex][tex]\begin{gathered} \bar{x}=\frac{102+123+142+155+104+185+159+124+154+136+113+110+107+119+120+127+155}{17} \\ \bar{x}=\frac{2235}{17} \\ \bar{x}=131.47\approx131.5ft^2 \end{gathered}[/tex]The mean square footage is 131.5 ft²
2) Median
To determine the median of the data set, first, you have to calculate the position of the median, following the formula:
[tex]\text{PosMe}=\frac{(n+1)}{2}[/tex]The sample size is n=17, then the position of the median is
[tex]\begin{gathered} \text{PosMe}=\frac{17+1}{2} \\ \text{PosMe}=\frac{18}{2} \\ \text{PosMe}=9 \end{gathered}[/tex]The median corresponds to the ninth observation of the data set.
Next, you have to order the data set from least to greatest:
102, 104, 107, 110, 113, 119, 120, 123, 124, 127, 136, 142, 154, 155, 155, 159, 185
Count the ninth observation from the left.
The median of the data set is Me= 124 ft²
The senior class sells hamburgers and hot dogs at a football game and makes a profit of $1.75 on each hamburger and $1.25 on each hot dog. The class would like a profit of at least $280. Let x represent the number of hamburgers and y represent the number of hot dogs sold
Answer:
1.75x + 1.25y >= 280
Step-by-step explanation:
1.75x + 1.25y >= 280
consider the experiment of a worker assembling a product. a. define a random variable that represents the time in minutes required to assemble the product. b. what values may the random variable assume? c. is the random variable discrete or continuous?
(a) Let "X" be the random variable that represents the time in minutes required to assemble the product.
(b) The random variable may assume the values in the interval (0, ∞).
(c) The random variable "X" is continuous in nature.
A random variable is a mathematical representation of a number or object that is affected by random occurrences. It is a mapping or function between probable outcomes in a sample space and a measured space, which is frequently real numbers.A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable might be discrete (with fixed values) or continuous (any value in a continuous range).To learn more about variables, visit :
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Which expression is equivalent to 3 x − 2 − 5 2 − 4 x − 2 ? 2x-8/13-5x -5x-8/2x-8 -5x-4/x-2 13-5x/2x-8
The equivalent expression of the expression given as [tex]\frac{\frac{3}{x - 2} - 5}{2 - \frac{4}{x - 2}}[/tex] is (13 - 5x)/(2x - 8)
How to determine the equivalent expression?From the question, the expression is given as
[tex]\frac{\frac{3}{x - 2} - 5}{2 - \frac{4}{x - 2}}[/tex]
Take the LCM of the fractions in the above expression
So, we have
[tex]\frac{\frac{3 - 5x + 10}{x - 2}}{\frac{2x - 4 - 4}{x - 2}}[/tex]
Evaluate the like terms of the expressions
So, we have
[tex]\frac{\frac{13 - 5x}{x - 2}}{\frac{2x - 8}{x - 2}}[/tex]
Divide the common factor x -2 in the expression
So, we have
[tex]\frac{13 - 5x}{2x - 8}[/tex]
Rewrite as
(13 - 5x)/(2x - 8)
The expression cannot be further simplified
Hence, the solution is (13 - 5x)/(2x - 8)
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on the number line drop box plot for data how many siblings does seventh grade have the number summaries below min:0,q1:1,medium:2,q3:3,max:10
Here, we want to drop a box plot on the number line given the listed numbers
We have the box plot as follows
The listing of the numbers is the actual way the numbers on the box plot will be listed from left to right
We have this as follows;
what is the answer to 20x + 35y
The greatest common factor is 5 .
If you factor it out, the expression becomes 5 (4x + 7y) .
Answer: 55x^1 y^1
Step-by-step explanation:
Add 20+35= 55
x & y can't stand by it's self, so x^1 and y^1
So you take those answers and you got 55x^1 y^1
You must keep it in letters in alphabetic order or it's considered wrong.
two angles are a linear pair, and one has twice the measure of the other. Find the smaller angles measure
Answer:
60°Step-by-step explanation:
two angles are a linear pair, and one has twice the measure of the other. Find the smaller angles measure
linear pair = 180°
180 : 3 = 60° (smaller angle)
60° x 2 = 120° (bigger angle)
120 is twice 60 and the sum is 180°
the answer is good
What is 420÷60 hellllllllppp
Answer:7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
420÷60 is the same as 42÷6.
42 goes into 6, 7 times:
6, 12, 18, 24, 30, 36, 42.
Therefore, 420÷6 is 7.
Please use a calculator next time.
-3x – 10 = 32Help me I need the answer
Answer:
x = - 14
Step-by-step explanation:
-3x – 10 = 32 Help me I need the answer
-3x – 10 = 32
-3x = 32 + 10
-3x = 42
x = 42 :(-3)
x = - 14
-----------------
check
-3 × (-14) - 10 = 32 (remember pemdas)
42 - 10 = 32
32 = 32
the answer is good
A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. Is it a right triangle?
Based on the lengths of the sides of the triangle, we can infer that this is NOT a right triangle.
How to find a right triangle?A right angled triangle would obey the Pythagoras Rule which is that the square of the hypotenuse (longest side) will be the sum of the squares of the other sides of the triangle.
This means that for this to be a right triangle, it needs to obey the function:
45 ² = 35 ² + 30 ²
Solving gives:
2,025 ≠ 2, 125
This shows that the triangle is not a right triangle.
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It is not a right-angle triangle since 2125 ≠ 2025 meant that it did not conform to Pythagoras' theorem's specifications.
This kind of query creates a right-angled triangle that Pythagoras' theorem can resolve.
What is Pythagoras' theorem?In a right-angled triangle, the square of the greatest side is equal to the sum of the squares of the smaller two sides.
Given, There are three sides to a triangle, each measuring 30 kilometers, 35 kilometers, and 45 kilometers.
∴ 30² + 35² = 45².
900 + 1225 = 2025.
2125 ≠ 2025.
Due to the fact that it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.
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an environmentalist wishes to conduct a hypothesis test on the percentage of cars driven in the city that are hybrids. is it sufficient for him to use a simple random sample of 172172 cars if hybrids currently account for 6%6% of the car sales in the country and he claims that the percentage of hybrids in the city is higher than that?
It is enough for him to use a simple random sample of 172 cars.
It is required that there are at least 10 successes and 10 failures to test a hypothesis that involves a proportion p in a sample of size n.
Following conditions are required for it:
1) np ≥ 10
2) n (1-p) ≥ 10
p = 6% = 0.06
n = 172
np = 172x0.06 = 10.322 ≥ 10172 (1-0.06) = 161.68 ≥ 10So, there are at least 10 successes and 10 failures in the 172 cars sample, it is enough for him to use a simple random sample of 172 cars.
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3. What is the probability of rolling a 5 on a fair die, if we know that the roll is odd? 4 Lamino dr
Let:
A = Rolling an odd number
B = Rolling a 5
N = Number of possible outcomes
so:
[tex]\begin{gathered} P(A)=\frac{3}{6}=\frac{1}{2} \\ P(B|A)=\frac{P(B\cap A)}{P(A)} \\ \text{Where:} \\ P(B\cap A)=P(A)\cdot P(B) \\ P(B)=\frac{1}{6} \\ so\colon \\ P(B|A)=\frac{\frac{1}{6}\cdot\frac{1}{2}}{\frac{1}{2}}=\frac{1}{6} \end{gathered}[/tex]Cindy struck out 7, 14, 6, 4, 5, and 6 batters in softball games this season. In discussingher stats with a newspaper reporter, Cindy's coach mentions that the average number ofCindy's strikeouts is 7. Is the coach's statement misleading? Explain why or why not.O No; the mean of her strikeouts is 7.O None of the other answers are correctO Yes, she struck out 7 batters only one time.O No; she typically strikes out 7 batters in a game.O Yes; the median of her strikeouts is 7.
Given that the batters were 7, 14,6,4,5 and 6 then to find the average, you add the batters and divide by their number
[tex]\text{sum}=7+14+6+4+5+6=42[/tex][tex]\text{Average}=\frac{42}{6}=7[/tex]Here you notice that the average is 7, so the coach's statement is true.
Your answer is , No;the mean of her strikeouts is 7
A girl scout troop hiked 6.8 miles southeast in 2 hours. What was the troop’s velocity?
Answer:
1.5 m/s
Step-by-step explanation:
Distance = 6.8×1609.344 = 10943.5392
time=2×60×60 = 7200
velocity= distance/time = 10943.5392/7200= 1.51 m/s
Solve for x. Show each step of the solution.
5(2-x)-10=25-2(3x+40)
Answer:
x=-55Step-by-step explanation:
[tex]5(2-x)-10=25-2(3x+40)\\\\10-5x-10=25-6x-80\\\\-5x=-6x-55\\\\-5x+6x=-55\\\\x= -55 [/tex]
Answer:
x = -55
Step-by-step explanation:
Hello!
We can solve for x by isolating the variable.
Solve for x5(2 - x) - 10 = 25 - 2(3x + 40)5(2) - 5(x) - 10 = 25 - 2(3x) - 2(40)10 - 5x - 10 = 25 - 6x - 80-5x = -55 - 6xx = -55The value of x is -55.
A forest is decreasing in size by 60 hectares every 3 years. In how many years will the forest have decreased by 140 hectares?
A forest is decreasing in size by 60 hectares every 3 years. In 7 years, the forest will have decreased by 140 hectares.
Using the Unitary Method:
∵ In '3' years, a forest decreased in size by '60' hectares
∴ In '1' year, a forest will be decreased in size by '20' hectares
Every year 20 hectares is decreased. Considering a regular trend in the decrement of forest area, the time span of '7' years will diminish 'to 140' hectares.
The 'Unitary Method' is also known as the 'Mango Method'. It establishes a relation between given data. The relation is used to predict results in different conditions. The Unitary Method is always used for regular trends.
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◄) Solve for w.
29 + 17w = 624
W =
Helppp
Answer:
w = 35
Step-by-step explanation:
29 + 17w = 624
subtract 29 from both side
17 w = 595
divide both sides by 17
w = 35
1. 2 ² x 5b³
2. (3a²) ² x 2 (b ²) ³
3. 15d ³ divided by 3d ²
1. 2 ² x 5b³ = 20b³
2. (3a²) ² x 2 (b ²) ³ = 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex] 5d
3. 15d ³ divided by 3d ² = 5d
What is Operations?
An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's acuity is determined by the number of operands.
The given problems are:
1. 2 ² x 5b³
2. (3a²) ² x 2 (b ²) ³
3. 15d ³ divided by 3d ²
1. 2 ² x 5b³
= 4 x 5b³
= 20b³
2. (3a²) ² x 2 (b ²) ³
By the exponent rule:
[tex](x^{n} )^m[/tex] = [tex]x^{n * m}[/tex]
= [tex]x^{nm}[/tex]
∴ 3[tex]a^{2*2}[/tex] x 2[tex]b^{2*3}[/tex]
= 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex]
3. 15d ³ divided by 3d ²
15d ³ ÷ 3d ²
By the exponent rule:
[tex]a^{m}[/tex]÷[tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]
∴ 5[tex]d^{3-2}[/tex] = 5[tex]d^{1}[/tex]
= 5d
Hence, The solutions are 20b³, 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex] and 5d
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a newsletter publisher believes that more than 79y% of their readers own a laptop. is there sufficient evidence at the 0.020.02 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
The Null hypothesis will be expressed as u = 0.79 whereas the Alternative hypothesis will be expressed as. u > 0.79
The null hypothesis (H0) may be used to show that there exists no significant variation between variables or that a single variable is not different than its mean. While an alternative Hypothesis (Ha) is a theory that attempts to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean. According to the question we can say that the
Null hypothesis (H0): u = 0.79
Alternative hypothesis (Ha): u > 0.79
Where u may be called as the proportion of their reader that owns a personal computer.
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Solve 7+y=5(2y-1)+3y. Y=
Answer: y = 1
Step-by-step explanation:
Given
7 + y = 5(2y - 1) + 3y ← distribute and simplify right side
7 + y = 10y - 5 + 3y
7 + y = 13y - 5 ( subtract y from both sides )
7 = 12y - 5 ( add 5 to both sides )
12 = 12y ( divide both sides by 12 )
1 = y
This data can best be modeled withwhich type of function?ху018,250118,730a. Linearb. QuadraticC. Exponential219,210319,690420,170
A linear function is a function in which we add multiple of a constant.
Given data:
We have
[tex]\begin{gathered} y=18,250+480(1)\text{ at x=0} \\ y=18,730=18,250+480(1)\text{ at x=1} \\ y=19,210=18,250+480(2)\text{ at x=2} \\ y=19,690=18,250+480(3)\text{ at x=3} \\ y=20,170=18,250+480(4)\text{ at x=4} \end{gathered}[/tex]Clearly, we have add multiples of 480 to 18,250.
So, the given function represents a linear function.
So, the correct option is (a).
Point (2,11.9),(4,10.5)
(2,8) , (4,7.5)
(2,6) , (4,1.5)
(2,0.5) , (4.-1)
(2,-1) , (4,-1)
(-2.8,-5.0) , (-3.6,-5.9)
rise over run so what's the answer
The slopes formed by each of the pairs of points are given as follows:
(2,11.9),(4,10.5): -0.7.(2,8) , (4,7.5): -0.25.(2,6) , (4,1.5): -2.25.(2,0.5) , (4.-1): -0.75.(2,-1) , (4,-1): 0.(-2.8,-5.0) , (-3.6,-5.9): 0.89.SlopeThe slope is equivalent to the rate of change, hence, given two points, the slope is calculated as the change in y, also called rise, of these two points divided by the change in x, also called run.
For the first case, the points are:
(2, 11.9) and (4, 10.5)
Hence:
The change in x is of 4 - 2 = 2.The change in y is of 10.5 - 11.9 = -1.4.The slope is:
m = -1.4/2 = -0.7.
The other slopes are calculated as follows:
(2,8) , (4,7.5): m = (7.5 - 8)/(4 - 2) = -0.25.(2,6) , (4,1.5): m = (1.5 - 6)/(4 - 2) = -2.25.(2,0.5) , (4.-1): m = (-1 - 0.5)/(4 - 2) = -0.75.(2,-1) , (4,-1): m = (-1 - (-1))/(4 - 2) = 0. (no change in the output).(-2.8,-5.0) , (-3.6,-5.9): m = (-3.6 - (-2.8))/(-5.9 - (-5)) = 0.89.More can be learned about slopes at https://brainly.com/question/28954211
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WILL GIVE BRAINLIEST PLS HELP
Passed exam | Did not pass exam | Row Totals
Completed exam review | 55% | 10% | 65%
Did not complete exam review | 20% | 15% | 35%
Column Totals | 75% | 25% | 100%
Part A: What is the percentage of students who failed the exam, given that they completed the exam review? Round to the nearest percentage. (2 points)
Part B: What is the percentage of students who failed the exam, given that they did not complete the exam review? Round to the nearest percentage. (2 points)
Part C: Is there an association between failing the exam and completing the exam review? Justify your answer. (2 points)
Answer:
A: 15%
B: 43%
C: yes
Step-by-step explanation:
You want the percentages of students who failed the exam, given that they (A) did, or (B) did not complete the exam review. You also want to know if this indicates an association between failing and reviewing.
NotationLet F represent the event "failed the exam." Let R represent the event "completed the exam review." R' will be the event "did not complete the review."
A: P(F|R)The probability is ...
P(F|R) = P(F&R) / P(R)
P(F|R) = 0.10/0.65 = 2/13 ≈ 15%
About 15% failed who completed the review.
B: P(F|R')P(F|R') = P(F&R') / P(R')
P(F|R') = 0.15/0.35 = 3/7 ≈ 43%
About 43% failed who did not complete the review.
C: AssociationIf the events "Failed the exam" and "Completed the review" were independent, then the probability of one would not be conditional upon the other. Here, the probability of failing is clearly different for those who completed the review, so there is an association between failing the exam and completing the exam review.
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what is the rule for this pattern?
17, 20, 19, 22, 21
Answer:
+3, -1
Step-by-step explanation:
17 + 3 = 20
20 - 1 = 19
19 + 3 = 22
22 - 1 = 21
Please mark me brainliest if this helps!
How to solve Y=2x-1 2x+y=3 in solving systems using substitution
Answer:
x = 1, y = 1
Step-by-step explanation:
This Question involves the concept of Solving Simulteanous Equations.
Simulteanous EquationsSimulteanous Equations are 2 sets of equation with 2 unknownes to solve. Methods used are Substitution and Elimination methods, use either to solve unless question specify a method.
Example:
2x + 4y = 67
3x + 9y = 90
ApplicationWe are given the 2 equations:
y = 2x - 1 (Equation 1)
2x + y = 3 (Equation 2)
We are asked to use the Substitution Method.
We first substitute Equation 1 to Equation 2 to find the value of x.
2x + (2x - 1) = 3
2x + 2x - 1 = 3
4x - 1 = 3
4x = 3 + 1
4x = 4
x = 4 ÷ 4 = 1
Now we can substitute x into Equation 1 to find the value of y.
y = 2(1) - 1
y = 2 - 1 = 1