=====================================================
Explanation:
We'll need the slope first
Pick any two points from the table and plug them into the slope formula.
I'm going to use the first two rows to get the two points.
m = (y2 - y1)/(x2 - x1)
m = (64-44)/(24-16)
m = (20)/(8)
m = 5/2
m = 2.5
The slope is m = 2.5
Use this slope value with any (x,y) pair in the table. I'll use (x,y) = (16,44)
---------------------
Plug m = 2.5, x = 16 and y = 44 into the equation below. Solve for b
y = mx+b
44 = 2.5*16 + b
44 = 40 + b
44-40 = b
4 = b
b = 4
The y intercept is b = 4
As an (x,y) point, we say the y intercept is (0, 4). The x coordinate of the y intercept is always 0 since x = 0 for any point on the y axis.
The equation y = mx+b turns into y = 2.5x + 4
This is the same as saying y = (5/2)x + 4
To check this equation works, plugging x = 16 should lead to y = 44.
Plugging in x = 24 should lead to 64
Finally, plugging in x = 32 should lead to 84.
I'll let you do this part.
Edward constructs several similar rectangles using pieces of balm wood. The similar rectangles are based on a rectangle with a length of 3 feet and a width of 5 feet. Which of the following dimensions would NOT be proportional to any of the new rectangles Edward could build?
F. 6 ft by 10 ft
G. 1 ft by 1 2/3ft
H. 18 ft by 30 ft
J . 1 1/5 ft by 2 1/2 ft
-7x(-2) it's multiply and divide integers
Answer:
14
step by step explanation
-7×(-2)
14
Find the area of the smaller sector formed by NMP. Round your answer to the nearest hundredth.
Solution:
Given:
\(\begin{gathered} \theta=60^0 \\ r=12cm \end{gathered}\)The area of sector is given by;
\(\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ A=\frac{60}{360}\times\pi\times12^2 \\ A=\frac{8640\pi}{360} \\ A=24\pi \\ A=75.398 \\ \\ To\text{ the nearest hundredth,} \\ A=75.40cm^2 \end{gathered}\)Therefore, the area of the smaller sector to the nearest hundredth is 75.40 centimeters square.
Which function does not have a period of 27? A. y = csc x B. y = cos x C. y = tan x D. y = sec x
All the functions a to d have a period of 2π
Which function does not have a period of 2π?From the question, we have the following parameters that can be used in our computation:
The functions
A sinusoidal function is represented as
f(x) = Asin(B(x + C)) + D
Where
Period = 2π/B
In the functions (a to d), we have
B = 1
So, we have
Period = 2π/1
Evaluate
Period = 2π
Hence, all the functions have a period of 2π
Read more about sinusoidal function at
brainly.com/question/21286958
#SPJ1
Which of the following best describes the slope of the line
A: positive
B: negative
C: zero
D: undefined
Pls help
The average daily cell phone usage amount for the past 4 days was (3.4p + 1.5) minutes. Which
algebraic expression represents the total usage for the past 4 days?
(12.6p + 1.5) minutes
(126p + 6) minutes
(13.6p + 1.5) minutes
(13.6p + 6) minutes
Answer:
(13.6p + 6) minutes
Step-by-step explanation:
......
Joe transformed the quadratic parent function f(x) to create h(x) as shown. If f(x) =x^2 and h(x=f(x-c), what is the value of c?
The value of the transformed function is h ( x ) = f ( x - 6 )² , where the value of c is -6
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be represented as f ( x )
Now , the value of f ( x ) = x²
And , when the function is shifted horizontally by a factor of -6 , we get
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c)
Substituting the values in the equation , we get
h ( x ) = f ( x + c )
when c = -6
h ( x ) = f ( x - 6 )²
Hence , the transformed function is h ( x ) = f ( x - 6 )²
To learn more about transformation of functions click :
https://brainly.com/question/26896273
#SPJ1
A store pays $150 for a portable basketball backboard and the markup is 40%. Find the amount of markup.
Answer:
$210
Step-by-step explanation:
150(0.4)= 60
60+150=210
$210
Gabe is the human resources manager for the Advanced Scientific Research Lab. He has to record
the heights (in centimeters) and weights (in pounds) for each of the scientists in the lab.
Height distribution (cm): 178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158
Weight distribution (lbs): 157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168
What is the shape of the height and weight distribution?
Last option: The height and weight distributions, respectively, show positive and negative skews.
We know that,
Graphs are used to represent information in bar charts. To depict values, it makes use of bars that reach various heights. Vertical bars, horizontal bars, clustered bars (multiple bars that compare values within a category), and stacked bars are all possible options for bar charts.
we have,
There isn't a lot of data, but it shows that the weights have a negative skew and the heights have a positive skew, with the long tails pointing in opposite directions.
change/ starting point * 100
2.5 millions of books were sold in 1991.
Millions of books sold in 1992 equaled 3.4.
Change = 0.9 (in millions).
0.9/2.5 * 100
= 36%
The height and weight distributions, respectively, show positive and negative skews.
To know more about bar graphs visit:
brainly.com/question/13298277
#SPJ1
HEY! PLEASE HELP IF YOU CAN!!! THANK YOU!! :))
Answer:
The first option
Step-by-step explanation:
Hope this helps! :)
Answer:
a !
Step-by-step explanation:
if you take the original points, (2, 3), and apply the rule, add 5 to 2 and add -4 to 3 you, get the first option! i hope this helps!
Which equation can be used to find A, they area of the parallelogram shown? A = 5x9 A = 4x9 A = 1/2 x 5 x 9 A + 1/2 x 4 x 9
Answer:
A = 4m*9m = 36m^2
Step-by-step explanation:
After a quick online search, I've found that the image of the parallelogram is the one that can be seen below.
In the image we can see a parallelogram with sides:
S1 = 9m (the base)
S2 = 5m
And an altitude H = 4m
For a parallelogram, the area is given by the base times the altitude
In this case, we know that the base is b = 9m, and the altitude is H = 4m
Then the area of the parallelogram show is:
A = 4m*9m = 36m^2
If M=1,000,P=2.25, and Y=2,000, what is velocity? a. 2.25 b. 4.5 c. 2 d. None of the above is true
Answer:d
Step-by-step explanation:
The answer is d. None of the above is true.
To calculate velocity, we need to use the equation:
Velocity = M * P / Y
Given:
M = 1,000
P = 2.25
Y = 2,000
Plugging in the values:
Velocity = 1,000 * 2.25 / 2,000
Simplifying:
Velocity = 2.25 / 2
The result is:
Velocity = 1.125
Therefore, the correct answer is: d. None of the above is true.
Learn more about velocity
https://brainly.com/question/30559316
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.
What are the values a, b, and c in the following quadratic equation?
−6x2 = −9x + 7
A) a = 9, b = 7, c = 6
B) a = −9, b = 7, c = −6
C) a = −6, b = 9, c = −7
D) a = −6, b = −9, c = 7
The values a, b, and c in the quadratic equation \(-6x^2 = -9x + 7\) are:
a = -6, b = -9, c = 7.
What are the coefficients in the given quadratic equation?To identify the values a, b, and c in a quadratic equation, we need to understand the standard form of a quadratic equation: \(ax^2 + bx + c = 0\). In this case, we have\(-6x^2 = -9x + 7\). By rearranging the equation to match the standard form, we get \(-6x^2 + 9x - 7 = 0\). Comparing the coefficients of \(x^2\), x, and the constant term, we can determine the values of a, b, and c.
In this equation, the coefficient of \(x^2\) is -6, which corresponds to the value of a. The coefficient of x is -9, representing the value of b. Lastly, the constant term is 7, indicating the value of c. Therefore, the values a, b, and c in the quadratic equation are a = -6, b = -9, and c = 7.
Learn more about Quadratic equations
brainly.com/question/30098550
#SPJ11
Answer:
C
Step-by-step explanation:
took the test :)
let p and q be distinct primes. (1) prove that (z/(pq))× has order (p − 1)(q − 1);
The order of a in (z/(pq))× is exactly (p-1)(q-1), as desired.
To prove that (z/(pq))× has order (p − 1)(q − 1), we need to show that the least positive integer n such that (z/(pq))×n = 1 is (p − 1)(q − 1).
First, let's define (z/(pq))× as the set of all integers a such that gcd(a,pq) = 1 (i.e., a is relatively prime to pq) and a mod pq is also relatively prime to pq.
Now, we know that the order of an element a in a group is the smallest positive integer n such that a^n = 1. Therefore, we need to find the order of an arbitrary element a in (z/(pq))×.
Let's assume that a is an arbitrary element in (z/(pq))×. Since gcd(a,pq) = 1, we know that a has a multiplicative inverse modulo pq, denoted by a^-1. Therefore, we can write:
a * a^-1 ≡ 1 (mod pq)
Now, let's consider the order of a. Since gcd(a,pq) = 1, we know that a^(p-1) is congruent to 1 modulo p by Fermat's Little Theorem. Similarly, we can show that a^(q-1) is congruent to 1 modulo q. Therefore, we have:
a^(p-1) ≡ 1 (mod p)
a^(q-1) ≡ 1 (mod q)
Now, we can use the Chinese Remainder Theorem to combine these congruences and get:
a^(p-1)(q-1) ≡ 1 (mod pq)
Therefore, we know that the order of a must divide (p-1)(q-1).
To show that the order of a is exactly (p-1)(q-1), we need to show that a^k is not congruent to 1 modulo pq for any positive integer k such that 1 ≤ k < (p-1)(q-1).
Assume for contradiction that there exists such a k. Then, we have:
a^k ≡ 1 (mod pq)
This means that a^k is a multiple of pq, which implies that gcd(a^k, pq) ≥ pq. However, since gcd(a,pq) = 1, we know that gcd(a^k, pq) = gcd(a,pq)^k = 1. This is a contradiction, and therefore our assumption must be false.
Know more about prime here:
https://brainly.com/question/20532807
#SPJ11
The order of a in (z/(pq))× is exactly (p-1)(q-1), as desired.
To prove that (z/(pq))× has order (p − 1)(q − 1), we need to show that the least positive integer n such that (z/(pq))×n = 1 is (p − 1)(q − 1).
First, let's define (z/(pq))× as the set of all integers a such that gcd(a,pq) = 1 (i.e., a is relatively prime to pq) and a mod pq is also relatively prime to pq.
Now, we know that the order of an element a in a group is the smallest positive integer n such that a^n = 1. Therefore, we need to find the order of an arbitrary element a in (z/(pq))×.
Let's assume that a is an arbitrary element in (z/(pq))×. Since gcd(a,pq) = 1, we know that a has a multiplicative inverse modulo pq, denoted by a^-1. Therefore, we can write:
a * a^-1 ≡ 1 (mod pq)
Now, let's consider the order of a. Since gcd(a,pq) = 1, we know that a^(p-1) is congruent to 1 modulo p by Fermat's Little Theorem. Similarly, we can show that a^(q-1) is congruent to 1 modulo q. Therefore, we have:
a^(p-1) ≡ 1 (mod p)
a^(q-1) ≡ 1 (mod q)
Now, we can use the Chinese Remainder Theorem to combine these congruences and get:
a^(p-1)(q-1) ≡ 1 (mod pq)
Therefore, we know that the order of a must divide (p-1)(q-1).
To show that the order of a is exactly (p-1)(q-1), we need to show that a^k is not congruent to 1 modulo pq for any positive integer k such that 1 ≤ k < (p-1)(q-1).
Assume for contradiction that there exists such a k. Then, we have:
a^k ≡ 1 (mod pq)
This means that a^k is a multiple of pq, which implies that gcd(a^k, pq) ≥ pq. However, since gcd(a,pq) = 1, we know that gcd(a^k, pq) = gcd(a,pq)^k = 1. This is a contradiction, and therefore our assumption must be false.
Know more about prime here:
https://brainly.com/question/20532807
#SPJ11
Let $n$ be a positive integer. Let $r$ be the remainder when $n^2$ is divided by $n 4.$ How many different values can $r$ take on
There are n different values that the remainder r can take on when \(n^2\) is divided by n 4.
We can use the Remainder Theorem to solve this problem. The Remainder Theorem states that when a polynomial f(x) is divided by (x-a), the remainder is f(a).
Using this theorem, we can see that \(n^2\) divided by n 4 leaves a remainder of \(n^2 - kn 4\), where k is some integer. We want to find how many different values r can take on, which is the same as finding how many different values \($n^2 - kn 4$\) can take on.
Let's rewrite \(n^2 - kn 4 as n(n - k 4)\). This expression tells us that n and n - k 4 have the same remainder when divided by n 4. Therefore, n - k 4 can only take on n different values, namely \(0, n, 2n, \ldots, (n-1)n.\)
For each of these n values, we can find a corresponding value of k that satisfies\($n^2 - kn 4 \equiv r \pmod{n 4}$\), namely \(k = (n^2 - r)/(n 4).\) Therefore, there are exactly n different values that r can take on.
for such more question on remainder
https://brainly.com/question/11536181
#SPJ11
x+3y=6
3x+9y=72
cdxddxdxfcfcgcffcffcfchcfcfhxhc
Answer:
No solution
Step-by-step explanation:
1) 3(x+3y=6)
3x+9y=72
2) 3x+9y=18
3x+9y=72
3) 3x+9y=18
-
3x+9y=72
____________
-54
question 7. HELP ME WITH THIS
Reduce the expression, if possible, by cancelling the common factors.
−3 is your answer!
have a nice day! please mark brainliest :)
.
The width of a rectangle measures (2.3a + 9.9) centimeters, and its length
measures (6.3a - 2.6) centimeters. Which expression represents the perimeter, in
centimeters, of the rectangle?
12.2a +3.7
O 7.3 + 8.60
O 17.2a + 14.6
O 7.4 +24.4a
Answer:
17.2a+14.6
Step-by-step explanation:
I need answer asap 30 points
Answer:
1.it is the last one
2. the first one
3.the secound one
Step-by-step explanation:
Solve for X. Round your answer to the nearest tenth.
TRUE OR FALSE Let us observe n coin flips. We record each heads as a 1, and each tails as a 0. If we sum up all of our 1s and 0s, then divide by n (in other words, we calculate the sample mean), we have just calculated the sample proportion p-hat.
TRUE. We can observe n coin flips, record each heads as 1, and each tails as 0. Then, sum up all of our 1s and 0s, divide by n (in other words, we calculate the sample mean), and we have just calculated the sample proportion p-hat. This is a method used to find the probability of an event.
The sample proportion is known as p-hat. The proportion of successes in the sample is denoted by the p-hat symbol. The sample proportion is a statistic that estimates the actual proportion of the population. The proportion of successes in a sample is referred to as the sample proportion.
When sample proportion represents a percentage, it is indicated as a percentage (x%). So, sample proportion p-hat is a statistical term that provides us with an estimate of the actual proportion of the population from the sample proportion.
To know more about the probability, visit:
https://brainly.com/question/33406519
#SPJ11
HI, THIS IS MY 3RD TIME ASKING THIS QUESTION I WOULD LOVE IT IF SOMEONE WOULD ANSWER!!!
!! HELP ME PLEASE I BEG YOU !!
Which of the following is the equation for the graph shown?
A. x squared over 5 plus y squared over 30 equals 1
B. x squared over 5 minus y squared over 30 equals 1
C. x squared over 30 plus y squared over 5 equals 1
D. x squared over 30 plus y squared over 25 equals 1
Answer:A. x squared over 5 plus y squared over 30 equals 1
Step-by-step explanation:
Answer:
i thought it was A as well!!!
Step-by-step explanation:
In general, what is the relationship between the standard deviation and variance?
a. Standard deviation equals the squared variance.
b. Variance is the square root of the standard deviation.
c. Standard deviation is the square root of the variance.
d. These two measures are unrelated.
The relationship between the standard deviation and variance is that the standard deviation is the square root of the variance.
The correct option is -C
Hence, the correct option is (c) Standard deviation is the square root of the variance. Variance is the arithmetic mean of the squared differences from the mean of a set of data. It is a statistical measure that measures the spread of a dataset. The squared difference from the mean value is used to determine the variance of the given data set.
It is represented by the symbol 'σ²'. Standard deviation is the square root of the variance. It is used to calculate how far the data points are from the mean value. It is used to measure the dispersion of a dataset. The symbol 'σ' represents the standard deviation. The formula for standard deviation is:σ = √(Σ(X-M)²/N) Where X is the data point, M is the mean value, and N is the number of data points.
To know more about variance visit:
https://brainly.com/question/14116780
#SPJ11
can someone please help
Answer:
-24xy
Step-by-step explanation:
First:
6x-4= -24
Second Add the variable:
-24xy
Third: Solution
-24xy
1 If f(x)= 11. compute f(2) and f'(2). X f(2)= (Simplify your answer.)
To compute f(2), we simply substitute x = 2 into the function f(x) = 11.
f(2) = 11
To compute f'(2), we need to find the derivative of the function f(x) = 11 and then evaluate it at x = 2.
Since the function f(x) = 11 is a constant function, its derivative is zero.
f'(x) = 0
Therefore, f'(2) = 0.
The value of f(2) is 11, which is obtained by substituting x = 2 into the function. The derivative of f(x) is f'(x) = 0, indicating that the function is constant and has a slope of zero at every point, including x = 2. Thus, the value of f'(2) is also 0.
To know more about function , visit
https://brainly.com/question/11624077
#SPJ11
based on murder rates in the united states, the associated press reported that the probability a newborn child has of eventually being a murder victim is 0.0263 for nonwhite males, 0.0049 for white males, 0.0072 for nonwhite females, and 0.0023 for white females. find the conditional odds ratios between race and whether a murder victim, given gender. interpret.
We are required to determine the conditional odds ratios between race and whether a murder victim, given gender, and interpret the data provided. Here, we are given data on murder rates in the United States, based on which we can calculate the conditional odds ratios. The probability of being a murder victim can be represented by P(MV), and the probability of not being a murder victim can be represented by P(NMV). Also, the probabilities of being a nonwhite or white male or female can be represented by P(NW M), P(W M), P(NW F), and P(W F) respectively.
The conditional odds ratios for murder victims, given gender, and race can be calculated as follows:Conditional odds ratio for nonwhite males:
Odds of being a murder victim for nonwhite males: P(MV | NW M) / P(NMV | NW M)P(MV | NW M) = 0.0263 and
P(NMV | NW M) = 1 - P(MV | NW M) = 0.9737
Therefore, odds of being a murder victim for nonwhite males = P(MV | NW M) / P(NMV | NW M) = 0.0263 / 0.9737 = 0.02705
Odds of being a murder victim for white males: P(MV | W M) / P(NMV | W M)P(MV | W M) = 0.0049 and P(NMV | W M) = 1 - P(MV | W M) = 0.9951
Therefore, odds of being a murder victim for white males = P(MV | W M) / P(NMV | W M) = 0.0049 / 0.9951 = 0.00491
Conditional odds ratio for nonwhite females: Odds of being a murder victim for nonwhite females:
P(MV | NW F) / P(NMV | NW F)P(MV | NW F) = 0.0072 and P(NMV | NW F) = 1 - P(MV | NW F) = 0.9928
Therefore, odds of being a murder victim for nonwhite females = P(MV | NW F) / P(NMV | NW F) = 0.0072 / 0.9928 = 0.00726
Odds of being a murder victim for white females: P(MV | W F) / P(NMV | W F)P(MV | W F) = 0.0023 and P(NMV | W F) = 1 - P(MV | W F) = 0.9977
Therefore, odds of being a murder victim for white females = P(MV | W F) / P(NMV | W F) = 0.0023 / 0.9977 = 0.00231
The odds ratios for males versus females, given race and murder victim status, can be represented as follows: Conditional odds ratio for nonwhite victims: Odds ratio for nonwhite males versus nonwhite females:
0.02705 / 0.00726 = 3.726
Odds ratio for white males versus white females: 0.00491 / 0.00231 = 2.124
Odds ratio for nonwhite males versus nonwhite females: 0.0263 / 0.0072 = 3.653
To know more about probability refer here:
https://brainly.com/question/30034780
#SPJ11
For Questions 16 – 18, refer to the problem below. Consider the following set of simultaneous equations. 3x − 4y = −42 (i)
2x + 6y = 50 (ii)
16. If x is made the subject of the formula in equation (ii), then:
A x = 3y + 25 B x = −3y + 25 C x = −6y + 50 D x = −3y − 25
17. If x is eliminated in equation (i) then:
A −13y = −117 B 13y = −117 C 15y = 124
D 16y = 215
Answer:
Step-by-step explanation:
CAN SOMEONE HELP ME OUT WITH THIS, PLEASE AND THANK YOU
Answer:
60 people
Step-by-step explanation:
Of means to multiply
3/8 * 160
Rewriting
3 * 160/8
3 * 20
60
Answer:
60 students gave their speeches
Step-by-step explanation:
divide 160 by 8 you get 20. Then you multiply the 20 by 3 because 20 is only 1/8 of the 160 students, and you get 60.
Identify the correct term.
When two numbers are not equal, an
relationship
is a sentence that uses the symbols >.<2,5 or to show a relationship
Answer:
Step-by-step explanation:
I think that<,> help show the relationship because you are comparing the 2 numbers by stating which is bigger than or smaller than the other.
HOPE IT HELPED
the answer is >,< because it is saying which number is bigger and which is snaller
Classify the following polynomials by the highest power of each of its terms. Combine any like terms first. -x^2+x-x^2+1,x^2+x+2x^3-x,4x+x+x-2,3x^2+4-3x^2-1
Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.
1. -x² + x - x² + 1
Combine like terms: -x² + x - x² + 1 = -2x² + x + 1
This polynomial has degree 2 because the highest power of the variable is 2.
2. x² + x + 2x³ - x
Rearrange terms: 2x³ + x² + x - x = 2x³ + x²
This polynomial has degree 3 because the highest power of the variable is 3.
3. 4x + x + x - 2
Combine like terms: 4x + x + x - 2 = 6x - 2
This polynomial has degree 1 because the highest power of the variable is 1.
4. 3x² + 4 - 3x² - 1
Combine like terms: 3x² - 3x² + 4 - 1 = 3
This polynomial has degree 0 because there is no variable term.
Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.
For such more question on variable
https://brainly.com/question/28248724
#SPJ8