The expression a⁷- a is divisible by 7 if a is an integer.
Given that,
7 divides a^7−a
To find that if a is an integer, then 7 divides a^7 -a or a⁷- a is divisible by the number 7
We can write, where k is an integer
a^7−a=7k
a(a^6−1)=7k
Now if a=k then
a^6−1=7
a^6=8
and a=±1.414 so a^7−a=9.898
If a is not equal to k then
a(a^6−1)=a(a^3+1)(a^3−1)=7k
since a(a+1)(a−1) is the not product of 3 consecutive integers, the expression is divisible by 7.
Hence, The expression a⁷- a is divisible by 7 if a is an integer.
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The correlation coefficient between two quantitative variables is approximately 0. 2. What does the value of this correlation coefficient indicate about how well the model fits the data?.
As per the concept of correlation coefficient "tell us" that the model in question does not fit the data well, in whose case we need to find another that can do it.
Correlation coefficient:
Correlation coefficient refers the a statistical measure of the strength of a linear relationship between two variables. And its values can range from -1 to 1.
Given,
The correlation coefficient between two quantitative variables is approximately 0. 2.
Here we need to find the value of this correlation coefficient indicate about how well the model fits the data
While we looking into the given question, a correlation coefficient of 0.02 is near to zero. In this case, the correlation coefficient is "telling us" that the two variables do not follow the cases 1 and 2 above described. Instead, it follows the case 3.
Therefore, the model in question does not fit the data well, in whose case we need to find another that can do it.
Therefore, it is important to remember that the correlation coefficient does not tell us anything about that one variable causes the other variable, only behaviors as described above.
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9a-b-2a-10b simplify this expression
A. -7a+11b
B. 11a+9b
C. -11a-9b
D. 7a-11b
please solve with explanation Q^Q
Answer:
9a-b-2a-10b=7a-11b
Step-by-step explanation:
collect the like terms, meaning add or subtract the numbers from the ones with the same variable(in this case a and b are the different variables)
9a-2a=7a
-b-10b=-11b
therefore, the correct answer is D
Step-by-step explanation:
Well , all you have to do is to collect the like terms bringing those with the same unknown together.
=9a-2a-b-10b
=7a-11b
Find the slope of the line
We have that the data is: (x₁ = 2, y₁ = 2) and (x₂ = 6, y₂ = 3).
The formula to calculate the slope of the line is:
m = y₂ - y₁/x₂-x₁
m = 3 - 2/6 - 2 = 1/4
The slope through the points (2,2) and (6,3) is 1/4A supervisor records the repair cost for 17 randomly selected TVs. A sample mean of $94.57 and standard deviation of $20.65 are subsequently computed.
Determine the 80 % confidence interval for the mean repair cost for the TVs. Assume the population is approximately normal.
Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
The 80 % confidence interval for the mean repair cost for the TVs will be [87.873,101.266] and the critical value that should be used in constructing the confidence interval is ±1.337 for 80% interval.
What is confidence interval?An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability.
Here,
df = 17-1=16
critical value = ±1.337 for 80% interval
lower end value,
-1.337=(x-94.57)/[20.65/√17]
x = 87.87
higher end value,
1.337=(x-94.57)/[20.65/√17]
x = 101.27
hence, 80% interval:[87.87 101.27]
The range of values within which the mean repair cost for TVs falls within an 80% confidence interval is [87.873,101.266], and a critical value of ±1.337 should be used to construct the confidence interval.
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Albert spends 2 hours a day on his homework and an hour playing video games. What percent of the day is it?
03:Pretest
CR Algebra 1 A (GP) 22-23/3:Identifying and Using Properties
2. You roll a blue number cube and a green number cube. Find P a number less than 2 on the blue cube and an odd number on the green cube.
The probability P (a number less than 2 on the blue cube and odd number on the green cube) is 1/12.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
For the probability,
The sample space of a die is, S = {1,2,3,4,5,6}
The probability of getting a number less than 2 is P(x < 2) = 1/6
The probability of getting an odd number is P(Odd) = 3/6
The required probability is calculated as:
P = 1/6 * 3/6
P = 1/12
Hence, the value of P (a number less than 2 on the blue cube and odd number on the green cube) is 1/12.
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The square has an area of
196. It contains two
overlapping squares; the larger
of these squares has an area 4
times that of the smaller and the area of their
overlap is 1. What is the total area of the
shaded regions?
The total area of the shaded regions is 72 unit sq.
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = side x side
Given that square has an area of 196.
The region contains two overlapping squares that is the larger of these squares has an area 4 times that of the smaller and the area of their overlap is 1.
We can come up with equations as;
Since the area of their overlap is 1 then the side length is 1 unit.
Let the length of the smaller square is x.
The length of the larger square is 2x.
Therefore,
x + 2x - 1 = 3x - 1
Thus, 3x - 1 = 14
x = 5
The area of larger square = 100
The smaller one is 25
The area of shaded region;
196 - 124 = 72.
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im so confused right now
Answer:
The solution is A. 183
Step-by-step explanation:
112-38×14÷14+109
= 74×1+109
= 74+109
= 183
5. Find TR if PR = 10m and QT=7 m
Explain correctly and will give brainlist
Estimate 210 ÷ 5.2 . 9 3/4 +(-205). Is reasonable answer? Explain your answer
Using PEDMAS, the expression is 188.75
PEDMASBODMAS is an acronym and it stands for parentheses, exponents, division, multiplication, addition, subtraction. In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is used, which is the synonym of BODMAS.
To solve this problem, we just need to apply PEDMAS rule here and evaluate the expression.
210 ÷ 5.2 * 9 3/4 - 205 = 755 / 4 = 188.75
The expression has a value of 188.75
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through: (-4, 1) and (1, -3) how do u write the point slope form of the equation of the line through the given points ?
Answer:
through: (-4, 1) and (1, -3) how do u write the point slope form of the equation of the line through the given points ?
Step-by-step explanation:
to find slope you do delta y over delta x meaning 3 - 1 over 1 - (-4) you get 2/5 that is slope then you do to find b you take one of the points and you plug in for y = mx + b doesn't matter which one so -3 = 2/5 (1) + b
-3 = 2/5 + b
subtract 2/5 from both sides you get
-17/5 = b
so the equation is
y = 2/5x - 17/5
In a concrete mixture, the ratio of cement to sand is 1 to 4. At this ratio, how many shovelfuls of cement would be needed to be mixed with 80 shovelfuls of sand?
Answer: 20 shovelfuls of cement would be needed to be mixed with 80 shovelfuls of sand.
Step-by-step explanation:
First, we'd find out 4 divided by 1. This would equal 4.
Because we knew the amount of sand we had, we'd divide instead.
80 divided by 4
(If we had known the amount of cement we had, we would multiply)
This equals 20. This is how we get our answer, 20 to 80
a production process manufactures items with weights that are normally distributed with mean 17 pounds and standard deviation 0.1 pound. an item is considered to be defective if its weight is less than 16.85 pounds or greater than 17.15 pounds. suppose that these items are currently produced in batches of 500 units. a) (10 points) find the probability that an inspected item is defective. b) (10 points) find the probability that at most 10% of the items in a given batch will be defective. hint: find the probability that an item is defective using normal probabilities. then, you can model number of defectives out of 500 as binomial
The probability that at most 10% of the items in a given batch will be defective = 0.31333
We are aware that the item is broken.
Rate it 17.15 if X is either less than 16.85 or is.
Therefore, we simply found the area of one tail and multiplied it by two as we have seen their identical distance from the Min.
Therefore, let's choose 16.85.
We'll calculate a Z score for that.
Therefore, let's go on to the X value less the mean more than the standard deviation
This may be 16.85 -70, which will be 0.15 divided by.1 negative.
You will have a result of -1.5.
As a result, the Z distribution's region to the left of negative 1.5 will have a value of 0.0668. Divide that amount by two.
Z-score=0.0668/2=0.31333
You will also receive 0.31333.
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Describe the sequence of transformation that maps quadrilateral ABCD onto quadrilateral A'B'C'D'.
The sequence of transformation that maps quadrilateral ABCD onto quadrilateral A'B'C'D' is A'(3,-1) , B'(3,2), C'(4,3) and D'(4,0)
From the graph:
A(-4,5) , B(2,5) , C(4,3) ,D(-2,3)
transformations:
A'(-4+7,5-6)
= A'(3,-1)
B'(2+1,5-3)
= B'(3,2)
C'(4,3)
D'(-2+6,3-3)
= D'(4,0)
Therefore the sequence of transformation that maps quadrilateral ABCD onto quadrilateral A'B'C'D' is A'(3,-1) , B'(3,2), C'(4,3) and D'(4,0).
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What does PEMDAS mean??????
Answer:
My teacher uses:
Please Excuse My Dear Aunt Sally : PEMDAS
Parenthesis, exponents, multiplication, division, addition, subtraction
Step-by-step explanation:
Answer:
parenthesis, exponents, multiplication, division, addition, subtraction
Step-by-step explanation:
The table shows the weights of bunches of
bananas and the price of each bunch. Identify
the constant of proportional
ity. Write an
equation to relate weight, w, to the price, p.
The constant of proportionality is: k = 0.45
The equation is: p = 0.45w.
How to Write the Equation of a Proportional Relationship?The equation that models the proportional relationship between two variables, x and y, can be expressed in slope-intercept form as y = kx, here, the value of k is the constant of proportionality between the two variables x and y.
Thus, constant of proportionality, k = y/x.
In the table given, we can use the coordinates of one point, (3, 1.35), to find the constant of proportionality, k:
Constant of proportionality, k = 1.35/3
Constant of proportionality, k = 0.45
To write the equation of the relationship between weight (w) and price (p), substitute k = 0.45 into p = kw.
p = 0.45w
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Riley has $200 she spends 60 on a video game what percent of her money does Riley spend?
Answer:
30%
Step-by-step explanation:
60/200 = 3/10 = 30%
6th grade math, please solve, 20 points.
-32 - (-5)=___
A. 37
B. 27
C. -27
D. -35
Answer:
-27
Step-by-step explanation:
Answer:
-27
Step-by-step explanation:
Since the problem says that you are subtracting -5 you have to turn everything that is on the right to a positive number like so:
-32 - (-5) ---> -32 + 5
So now all you have to do is add 5 to -32
Therefore equaling -27
So your final answer is C. -27
Rule of x and / is.
If we use a × b, then it means that a is b times more than a and if we use a/b it means that we are making parts of a by the factors of b.
What is meant by multiplication and division?A mathematical expression that specifies the objects to be multiplied, known as a factor, produces a product. The other operations are multiplication, addition, and subtraction. When two natural numbers are divided with a remainder, or in the Euclidean method, the result is an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains after computing the quotient.
Rule of Division and Multiplication of Integers
Multiplication:
Rule 1: A positive integer and a negative integer cannot be added together.
Rule 2: A positive number is the result of two positive integers.
Rule 3: It states that the sum of two negative integers is positive.
Examples:
Rule 1: 1. (+4) x (-2) = -8 2. (-2) x (+5) = -10
Rule 2: 1. (+6) x (+8) = +48 2. (+6) x (+2) = +12
Rule 3: 1. (-6) x (-8) Equals +48 2. (-2) x (-4) = +8
Division:
Rule 1: A positive integer and a negative integer cannot be multiplied together.
Rule 2: A positive number is the quotient of two positive integers.
Rule 3: A positive number is the quotient of two negative integers.
Examples:
Rule 1: 1. (-8) / (+4) = -2 2. (-12) / (+6) = -2
Rule 2: 1. (+6) / (-3) = -2 2. (+24) / (-6) = -4
Rule 3. 1. (+9) / (+3) = +3 2. (+16) / (+4) = +4
Rule 4: 1. (-6) / (-2) = +3 2. (-42) / (-7) = +6
This is the summary of multiplication and division rules.
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You decide to buy a car that costs $19,000. You've heard that the car may
depreciate at a rate of 14% per year. At that rate, what will the car be worth
in six years?
Answer:
$7,686.77744
Step-by-step explanation:
19000-14%=16340
16340-14%=14052.4
14052.4-14%=12085.064
12085.064-14%=10393.155
10393.155-14%=8938.1133
8938.1133-14%=7686.77744
(b) suppose you were going to construct an 89% confidence interval from this population. what critical value should you use? (3 decimal places)
Using the theories of confidence interval, we got that 0.945 is critical value which should we use for constructing an 89% confidence interval from this population.
In statistics, a confidence interval is the range of values that is determined through the use of the observed data, calculated at a desired confidence level that may contains the true value of the parameter being studied.
Assuming this is asymmetrical confidence interval we have the diagram, and dealing with a Normal distribution
from the diagram we see that
P(Z<z)=0.89+0.055=0.945
Hence, if I were going to construct an 89% confidence interval from this population, critical value should use is 0.945
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Laurie works for the Mathville High School. Her weekly paycheck reads "You
worked 4s + 3 hours this week, at a rate of 2s + 4 dollars per hour. You earned
a gross amount of $700." How many hours did Laurie work this week?
The total number of hours that Laurie worked for the week is; 35 hours
How to solve Algebra Word Problems?The parameters given are;
Total number of hours worked for the week = 4s + 3 hours
Rate of earning = 2s + 4 dollars per hour
Gross Amount earned = $700
Thus;
(4s + 3)(2s + 4) = 700
8s² + 6s + 16s + 12 = 700
8s² + 22s + 12 = 700
8s² + 22s - 688 = 0
Solving this with an online quadratic calculator gives;
s = 8
Thus;
Total hours worked = 4(8) + 3 = 35 hours
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Calculate the quotient below and give your answer in scientific notation.
180
9 × 10^-5
=?
It take the speed of 299 m to travel 30 cm .
What is speed?
Speed is what it means. the speed at which an object's position changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed only has a direction and no magnitude, it is a scalar quantity.
Let us convert cm to m for distances
C = 2.998× 10^8 ms
The relationship between distance, speed, and time is
T =1 ×10^6/8
Because in this case you are being asked how long or time it takes, make it the subject.
Rounding the quotient produces.
Adjust it again to fit the scientific notation.
The result is -
d= c×t
d=2.998×10^8 m/s 10^6 m/s
d=2.998
As a mathematical expression, the time taken for light is 2.998
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(t-k=12
3t+2k = 141
The values of the variables t and k are 33 and 21, respectively.
We are given a system of two equations. The equations are linear in nature. Each equation represents a straight line. We need to find the solution to the system of linear equations. The coordinates of the intersection point of the straight lines are the solution. The equations are given below.
t - k = 12
3t + 2k = 141
We will substitute the value of t from the first equation into the second equation.
t = 12 + k
3t + 2k = 141
3(12 + k) + 2k = 141
36 + 3k + 2k = 141
5k = 105
k = 21
We will substitute the value of k into the first equation to find the value of t.
t = 12 + k
t = 12 + 21
t = 33
Hence, the values of t and k are 33 and 21, respectively.
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Find the least common denominator of 1/6 and 11/9
Answer:
LCD is 18
Step-by-step explanation:
1/6 = 3/18
11/9 = 22/18
Hey! i need help please!
The expression [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex] in simplified radical form obtained by using the laws of indices is presented as follows;
[tex]2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5} = 2\cdot t \cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
What are the laws of indices?The laws of indices are a set of rules that can be used to simplify expressions of variables and numbers that consists of powers that have the same base.
The expression is; [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex]
The laws of indices which can be used to evaluate the expression includes;
xᵃ × xᵇ = xᵃ⁺ⁿxᵃ ÷ xᵇ = xᵃ⁻ᵇ(xᵃ)ⁿ = [tex]x^{a\times b}[/tex]x⁻ⁿ = 1/xⁿx⁰ = 1[tex]x^\frac{n}{m} =\sqrt[m]{x^n}[/tex]Expressing the index in terms of 5, we get;
[tex]\sqrt[5]{32\cdot t^6\cdot w^{17}} = \sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2}[/tex]
[tex]\sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2} = 2\cdot t\cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
The expression, [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex] in the simplified form is [tex]2\cdot t\cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
A second method evaluating the expression is presented as follows;
[tex]\sqrt[5]{32\cdot t^6\cdot w^{17}} = \sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2}[/tex]
[tex]\sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2} = 2^\frac{5}{5} \cdot t^\frac{5}{5} \times t\cdot w^{\frac{15}{3} } \times w^\frac{2}{5}[/tex]
[tex]2^\frac{5}{5} \cdot t^\frac{5}{5} \times t^{\frac{1}{5} }\cdot w^{\frac{15}{3} } \times w^\frac{2}{5} = 2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5}[/tex]
[tex]2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5} = 2\cdot t \cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]
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The rate of petrol was RS 120 in January. After three months,rate of petrol was RS 150 Find the percentage increase in its rate
The percentage of increase in rate is 25%
Calculating the Percentage:The percentage is a value that is expressed as a fraction of 100. In simple words, the percentage means, a part per hundred. To calculate the percent of a number, divide the number by the whole and multiply by 100. It is denoted by the symbol “%”.
Here we have
The rate of petrol was Rs. 120
After three months the rate of petrol was Rs.150
The increased rate = Rs.150 - Rs. 120 = 30
The percentage of increase = ( Increased rate/ initial rate) × 100
= [tex]\frac{30}{120} \times 100[/tex] = 25%
Therefore,
The percentage of increase in rate is 25%
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a certain machine can process 6,000 letters in 1 hour. at this rate, how many letters can the machine process in 1/12 hour?
sandeep visited green glen apple orchard yesterday. he picked a basket of fresh apples in the field. he also got 3 pounds of pre-picked apples at the farm stand because they were overripe and perfect for making applesauce. the farm charges $4 a pound for apples, regardless of whether they're fresh or pre-picked. sandeep paid $30 in all. which equation can you use to find f, the number of pounds of fresh apples sandeep picked? how many pounds of fresh apples did sandeep pick? write your answer as a whole number or a decimal.
Sandeep picked up 4.5 pounds of fresh apples from the field
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the standard form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.
Pounds of pre-picked apples picked up by Sandeep = 3 pounds
Charges per pound = $4
The total amount paid by Sandeep = $30
Let x be the pounds of fresh apples picked up by Sandeep
In the formulation of the equation we get the following:
Pounds of pre-picked apples*Charges per pound + Pounds of fresh apple picked*Charges per pound = Total amount paid by Sandeep
= 3*4 + x*4 = 30
12 +4x = 30
4x = 18
x = 4.5
So, fresh apples = 4.5 pounds
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Estimate 76.94 - 44.478 by first rounding each number to the nearest whole number.
Estimating 76.94 - 44.478 by first rounding each number to the nearest whole number gives 33
How to estimate the subtraction problemRounding to the nearest whole numbers the figures are written s follows
rounding to the nearest whole is achieved by checking the number following the decimal.
If the number is up to 5 a number is added to the last number before the decimal as in here
76.94 = 77 (to the nearest whole number)
/when the number following the decimal is less than 5 is number is neglected as in here
44.478 = 44 (to the nearest whole number)
The subtraction is continued as follows
= 77 - 44
= 33
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