Each sum using distributive property is given as follows:
1) 12+20= 3(4+5)
2) 36+15= 3(12+5)
3) 24+18= 6(4+3)
4) 20+50= 10(2+5)
5) 6+22= 2(3+11)
6) 60+25= 5(12+5)
Given, sum to be represented by distributive property.
1)
12+20= 3(4+5)
Factors of 12 = 2 × 2 × 3
Factors of 20 = 2 × 2 × 5
GCF of 12 and 20 = 4
Take 4 common from 12 and 20.
Representing in a(b+c) .
4(3+5)
2)
36+15= 3(12+5)
Factors of 36 = 2 × 2 × 3 × 3
Factors of 15 = 3 × 5
GCF of 36 and 15 = 3
Take 3 common from 36 and 15.
Representing in a(b+c) .
3(12+5)
3)
24+18= 6(4+3)
Factors of 24 = 2 × 2 × 2 × 3
Factors of 18 = 2 × 3 × 3
GCF of 24 and 18 = 4
Take 5 common from 24 and 18.
Representing in a(b+c) .
6(4+3)
4)
20+50= 10(2+5)
Factors of 50 = 2 × 5 × 5
Factors of 20 = 2 × 2 × 5
GCF of 50 and 20 = 10
Take 10 common from 50 and 20.
Representing in a(b+c) .
10(2+5)
5)
6+22= 2(3+11)
Factors of 22 = 2 × 11
Factors of 6 = 2 × 3
GCF of 22 and 6 = 2
Take 2 common from 22 and 6 .
Representing in a(b+c) .
2(3+11)
6)
60+25= 5(12+5)
Factors of 60 = 2 × 2 × 3 × 5
Factors of 25 = 5 × 5
GCF of 60 and 25 = 5
Take 5 common from 60 and 25.
Representing in a(b+c) .
5(12+5)
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A certain group of test subjects had pulse rates with a mean of beats per minute and a standard deviation of beats per minute. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is a pulse rate of beats per minute significantly low or significantly high?.
Answer: is this it?
Step-by-step explanation:
a campus performance series features plays, music groups, dance troops, and stand-up comedy. the committee responsible for selecting the performance groups includes three students chosen at random from a pool of volunteers. this year the volunteers came from a variety of majors. however, the three students for the committee were all music majors. does this fact indicate there was bias in the selection process and that the selection process was not random? explain.
NO , this fact does not indicate that there was bias in the selection process and that the selection process was not random.
This fact does not indicate that there was bias in the selection process and that the selection process was not random unless we know the number of different subject majors among the thirty volunteers.
It is possible that out of 30 volunteers , 20 can be from music majors and the rest 10 are majors from other subjects.
so in this case it is possibility for the process to be random and for the three students in the committee to all end up being music majors.
Therefore , by the given information it can be said that the selection process was random and unbiased.
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Stephen and Paul each purchased a movie ticket at AMC Theatres for $11.00 each. Both bought a drini from the concession stand. Stephen used a $5.00 off coupon that he received in the mail. After using the coupon, their total cost before tax was $29.18. Write an equation that can be used to determine the cost of one drink.
The equation that can be used to determine the cost of one drink is d = $12.8 / $2.
What is the equation?The total amount that is paid by Stephen and Paul is the sum of the total cost of the movie tickets, the cost of the drinks less the cost of the coupon.
Total amount paid = cost of two tickets + cost of the two drinks - coupon
($11 x 2) + ($d x 2) - $5 = $29.18
$22 + $2d - 5 = $29.18
$2d = $29.18 + $5 - $22
$2d = $12.18
d = $12.8 / $2
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Given that Sin A=Cos (A + 20).
Find the value of A
The value of A is 35.
How to solve trigonometry?The given expression is as follows:
sin A = cos (A + 20)
using trigonometric rule,
sin A = cos(90 - A)
Therefore,
cos (A + 20) = cos(90 - A)
divide both sides by cos
Hence,
A + 20 = 90 - A
A + A = 90 - 20
2A = 70
divide both sides by 2
A = 70 / 2
A = 35
Therefore, the value of A is 35.
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a student performed the following steps to find the solution to the equation . where did the student go wrong? step 1. factor the polynomial into (x 8) and (x – 6) step 2. x 8
The student is wrong in the steps of the factorization.
What do you mean by factorization in polynomial?Factorization of polynomials, also known as polynomial factorization, is a mathematical and computer algebraic technique that combines irreducible factors with coefficients in the same domain to produce a polynomial with coefficients in a particular field or in integers. A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization. A polynomial can be expressed as the product of its factors, where the components must have a degree that is less than or equal to the original polynomial.
The equation is given as:
x^2 + 2 x - 48 = 0
Expand the equation
x^2 + 8x - 6x - 48 = 0
Factorize the equation
x(x + 8)- 6(x + 8)
Factor out x + 2
(x + 8)(x - 6) = 0
The above means that the factored equation of x^2 + 2x - 48 = 0 is (x + 8)(x - 6) = 0
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1,889 divided by 4 pls help !!
Answer:
472.25
Step-by-step explanation:
1,889 divided by 4 = 472.25
you need a calculator haha
472.25
In November 2010 the average cost of 5 gallons of regular unleaded gasoline in the U,S. was $14,46. What was the average cost for 16 galions
The average cost for 16 gallons is $46.272
How to calculate the cost of 16 gallons ?The first step is to calculate the price of one gallon
5= 14.46
1= x
cross multiply
5x= 14.46
x= 14.46/5
x= 2.892
The price of 16 gallons can be calculated as follows
= 16 × 2.892
= 46.272
Hence the price of 16 gallons is $46.272
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can anyone solve 2x-2 <6
Answer:
x<4
Step-by-step explanation:
Hello,
[tex]2x - 2 < 6[/tex]
[tex]2x < 6 + 2[/tex]
[tex]2x < 8[/tex]
[tex] \frac{2x}{2} < \frac{8}{2} [/tex]
[tex]x < 4[/tex]
To make a small vase, Elisa uses no more than 4.5 ounces of clay. To make a large vase, she uses at least 12 ounces of clay. Which compound inequality represents the number of ounces of clay, c, that Elisa uses to make one vase of either size? 4.5 < c < 12 4.5 ≤ c ≤ 12 c < 4.5 or c > 12 c ≤ 4.5 or c ≥ 12
The compound inequality that represents the number of ounces of clay, "c", Elisa uses to make one vase of either size is [(c ≤ 4.5) or (c ≥ 12)].
As per the question statement, Elisa uses no more than 4.5 ounces of clay to make a small vase and at least 12 ounces of clay to make a large vase.
We are required to find out the compound inequality that represents the number of ounces of clay, that she uses to make one vase of either size.
Let the number of ounces of clay, that Elisa uses to make one vase of either size be denoted by "c".
Since, Elisa uses no more than 4.5 ounces of clay to make a small vase, The words "no more than" implies maximum, i.e., "either less than or equals to" and hence, for a small vase, "c" must be less than or equal to 4.5 oz, which gives [tex](c \leq 4.5)[/tex] ...(1)
On the other hand, to make a large vase, she uses at least 12 ounces of clay where the words "at least" means minimum, i.e, "either more than or equals to" and hence, for a large vase,
Thus "c" is more than or equal to 12 oz, which gives [tex](c \geq 12)[/tex]...(2)
Now, combining (1) and (2), we get [(c ≤ 4.5) or (c ≥ 12)] which is option "d".
compound inequality: In mathematics, a compound inequality is an inequality that combines or "compounds" two simple inequalities.To know more about compound inequality, click on the link below.
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Find the midpoint of the points
Answer: Midpoint=(-3, -5 1/2)
Step-by-step explanation: Using the midpoint formula (x1+y1)/2, (x2+y2)/2 we can calculate. (-2+-4)/2, (-4+-7)/2 The answer (-3, -5 1/2)
5. Which equation's line is steeper and explain how you know
A. y = 3x + 7
B. y=x+9
Answer:
Step-by-step explanation:
A, because the slope 3 is larger than a slope of 1.
Equation A's line is steeper than equation B's line because it has a higher slope.
To determine which equation's line is steeper, we need to compare their slopes. In both equations, the coefficients of the x term represent the slope of the line.
Let's first rewrite both equations in slope-intercept form, which is of the form y = mx + b, where "m" is the slope and "b" is the y-intercept:
A. y = 3x + 7
B. y = x + 9
In equation A, the coefficient of x is 3, which means the slope of the line is 3.
In equation B, the coefficient of x is 1, which means the slope of the line is 1.
Now, to compare the slopes, we can see that the slope of equation A (3) is greater than the slope of equation B (1).
This means that the line represented by equation A is steeper than the line represented by equation B.
Hence, equation A's line is steeper than equation B's line because it has a higher slope.
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Hello! :) Pls help me with this math question :)) I want 5 halves of a cupcake for myself, 2 halves for my friend and 1 half for our other friend, FrostingTower would be great. Pls help!!! Ty :>
The total cupcakes that are needed will be 9 1/2.
How to calculate the fraction?The fraction needed for yourself = 5 1/2
The fraction needed for your friend = 2 1/2
The fraction needed for your other friend = 1 1/2
The total fraction needed will be:
= 5 1/2 + 2 1/2 + 1 1/2
= 9 1/2
Therefore, the cupcakes that are needed will be 9 1/2.
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I want 5 halves of a cupcake for myself, 2 halves for my friend and 1 half for our other friend. What is the total needed?
negative 3 and 4 over 5 minus 5 and 2 over 3.
Answer:
-6.53333333333 (-6.53)
Step-by-step explanation:
Hope this helps! <3
What is the density? Mass= 42.63g Volume= 49ml. Please put in the ml and g at the end.
The shape is a rectangle.
Step-by-step explanation:
49ml
43.63g
the answer is 29ml
Taylor bought a watch on sale for 60% off the original price, and another 10% off the discounted price. If the watch originally cost $82, What was the final sale price?
Answer: $29.52
Step-by-step explanation: 82x0.6=49.2 82-49.2=32.8 32.8x0.1=3.28
32.80-3.28=29.52
the percent of the observations that are classified as outliers by the 1.5 × iqr rule is the same in any normal distribution. what is this percent? show your method clearly.
In any normal distribution, about 0.7 percent (0.7%) of the data are outliers.
What is an outlier?An outlier is also referred to as anomalous data and it can be defined as a numerical value that is either unusually too small or large (big) in comparison with the overall pattern of the numerical values contained in a data set.
What is an interquartile range?IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.
Mathematically, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):
IQR = Q₃ - Q₁ = 75th percentile - 25th percentile.
The 75th percentile is equal to x when z has a p-value of 0.75, therefore, z is equal to 0.675. Similarly, the 25th percentile is equal to x when z has a p-value of 0.25, therefore, z is equal to -0.675.
Based on the 1.5 × IQR rule for outliers, the lower and upper z-scores are given by:
Zl = -0.675 -1.5(IQR)
Zl = -0.675 -1.5(0.675 + 0.675)
Zl = -0.675 -1.5(1.35)
Zl = -0.675 - 2.025
Zl = -2.7
Zu = 0.675 + 1.5(IQR)
Zu = 0.675 + 1.5(0.675 + 0.675)
Zu = 0.675 + 1.5(1.35)
Zu = 0.675 + 2.025
Zu = 2.7
For the p-value, we have:
P(z<2.7) = 1 - 0.9965
P(z<2.7) = 0.0035.
For the percentage of outliers, we have:
Outliers = 2 × 0.0035 × 100
Outliers = 0.0070 × 100
Outliers = 0.7%.
In this context, we can reasonably infer and logically deduce that about 0.7 percent (0.7%) of the data are outliers in any normal distribution.
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Matthew bought a scale model toy version of the
space ship in his favorite science fiction television
show. If the tov is constructed with the scale
1 inch
= 12 feet and the toy is 1 foot 4 Inches
long, how long is the ship in the television show?
A. 192 feet
B.168 feet
C.60 feet
D. 49 feet
Answer: A. 192 feet
Step-by-step explanation:
1 foot 4 inches=
1 foot+4 inches=
12 inches+4 inches=
16 inches
Hence,
16*12=
16*(10+2)=
(16)(10)+(16)(2)=
160+32
192 feet
Please help! I need help hurry please
Answer:
Step-by-step explanation:
f(x)=x^2+1
f(x^2+1)
f(x^2+1):x^4+2x^2+2
f(f(x))=x^4+2x^2+2
2nd answer
Hope this helps!^^
raise 6 to the 7th power, then multiply j by the results
Answer:
279936j
Step-by-step explanation:
A rectangle has a height of 4x^3 and a width of x3+3x^2+2x.
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
Answer:
area of recatangle= 4x^3(x^3+3x^2+2x) =4x^6+12x^5+8x^4
A central angle has the center as its vertex and its sides contain two radii of the circle.
Answer: A central angle is an angle with its vertex at the center of the circle and its two sides are radii. The sum of all central angles in a circle 360 degrees. The degree of the arc formed by the endpoints of a central angle is equal to the degree of the central angle.
Step-by-step explanation:
Which of the following is not equivalent to -2/5
-2/5
2/-5
-2/-5
Answer:
-2/-5
Step-by-step explanation:
your welcome<3<3<3<3<<3
Use the figure to the right to find the value of PT. T is the midpoint of PQ
PT=5x+7 and TQ=9x-9
======================================================
Explanation:
Since T is the midpoint of PQ, this means the smaller pieces PT and TQ must be equal. In other words, T divides PQ in half.
PT = TQ
5x+7 = 9x-9
5x-9x = -9-7
-4x = -16
x = -16/(-4)
x = 4
Use this to find each segment length.
PT = 5x+7 = 5(4)+7 = 20+7 = 27TQ = 9x-9 = 9(4)-9 = 36-9 = 27Both pieces are 27 units long, which confirms the answer.
I also do need help on this one, Simplify the Radical. Thank you.
The simplified form of the radical is expressed as 6xz²∛4
Simplifying radical expressionsGiven the radical function below expressed as:
2(108x²z⁴)^1/3
Expand to have:
2(108x^2/3z^4/3)
Simplify to have:
2(∛108x^2/3z^4/3) = 6(x)
2(3)(∛4)*x^2/3 * z^4/3
6∛4 * x^2/3 * z^4/3
6xz²∛4
Hence the simplified form of the radical is expressed as 6xz²∛4
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giving away points and marking brainliest
what is 500-60
Thanksss for ur kindness :)
hopefully brainly would not take it down
Answer:440
Step-by-step explanation:
what is the mean of 76,88,100,75,95,100
Answer:89
Step-by-step explanation:add them all together and divide by however many numbers you have
Answer:
Hello, Hope your having a good day
Step-by-step explanation:
your Question; what is the mean of 76,88,100,75,95,100
The mean is 89
Median: 91.5
Mode: 100
What is a mean?
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values.
Hope this helped :)
pls like
Determine whether the statement is true or false if x=8, y=2 , and z=3 .
2 x=3 y z
Given that x = 8, y = 2, and z = 3, the equation 2x = 3yz is false.
An expression is a number, variable or the combination of both put together by operation symbols while an equation is a statement that shows that two expressions are equal and is separated by an equal sign "=".
To check if the equation 2x = 3yz is true when x = 8, y = 2, and z = 3, plug in or substitute the value of each variable to the equation and evaluate.
2x = 3yz
2(8) = 3(2)(3)
16 ≠ 18
Since 16 is not equal to 18, the given values do not satisfy the equation, then the statement is not true.
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0.3. human iq scores are approximately normally distributed with a mean of 100 and a standard deviation of 15. the minimum iq score for the top 10% of the population.
According to the given information The highest 10% of the population's IQ is 0.0179.
Describing Standard deviation:The root of the variability in the given group as well as ungrouped data is referred to as the standard deviation. The standardized value is the value left after subtracting the mean and dividing by the standard deviation.
z = (x- μ) / σ
x denotes the observations (a specific value that you are calculating the z-score for).
Mu(μ) is the mean.
Sigma(σ) denotes the standard deviation.
According to the given data:x = 131.5
μ = 200
σ = 15
So, when humans apply the values to the formula, we obtain,
=> z = 131.5 - 100 /15
=> z = 2 .10
Using table A-2, calculate the corresponding probability:
=> P(Z>2.10) = 1 − P(Z<2.10)
=> 1 − 0.9821
=> 0.0179
The top 10% of the population has a required IQ of 0.0179.
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some aspects of the spline smoothing approach to non-parametric regression curve fitting (with discussion).
Regression without parameters using smoothing splines A scatterplot's data is smoothed by fitting a smooth curve to it. Will initially concentrate on two variable issues: OneX Yand Will eventually include more than two predictors. Our example: Where "1; "1;::: "are independent from me," yi=f(xi) + I.
What is a non-parametric regression?The appealing, adaptable, and widely-used method of non-parametric regression uses cubic splines for curve estimation. Although the fundamental concept was developed many years ago, the approach is maybe not as well recognized or used as it could be. This paper's topics and examples are meant to increase comprehension and broaden the applicability of the spline smoothing technology. The fundamentals of the method, its relationship with moving averages and other smoothing techniques, the automatic selection of the degree of smoothing, and the use of residuals for model adaption and diagnostic testing are just a few of the specific topics covered. A finite-dimensional Bayesian framework is used to address the issue of offering inference areas for curves and for pertinent curve attributes.
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a climate change program surveyed 1263 adults in a recent month and asked them about their attitudes on global climate change. a display of the percentages of respondents choosing each of the major alternatives offered is provided. list the errors in this display.
The error are;
1) The percentages do not sum to 100%
2) Showing the pie chart on a slant violates the area principle.
What are the errors?A pie chart is used to show the relationship between variables. We can use the bar chart to categorize the relationship that exists between different variables. In this case, we are looking at the responses to a climate change survey.
We can see that there are the following errors in the chart;
1) The percentages do not sum to 100%
2) Showing the pie chart on a slant violates the area principle.
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