Polynomial Remainder Theorem:
If we divide a polynomial f(x) by a factor (x – a), then the remainder will be f(a).
In your case, the remainder from dividing by (x-7) will be f(7)
f(7) = (7)^2 + k(7) -19
= 49 + 7k -19
= 30 + 7k
If you want the remainder to be -5, when set 30+7k equal to -5 and solve:
30 + 7k = -5
7k = -35
k = -5
Miguel is driving on a highway. He uses one gallon of gas every 50 miles he drives. The distance, D (in miles), he travels on g gallons of gas
is given by the following
How far does Miguel drive he uses 4 gallons of gas
Write the following as an expression, "15 added to the product of 7 and c"
Answer:
15 + 7c or 15 + 7 * c
Hope this helps!
In a large city school system with 44 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. Assume the schools are homogeneous and differ from each other.
Randomly select 50 parents from each elementary school. Send them a survey, and follow up with a home visit if they do not return the survey within a week.
Which kind of sampling strategy is involved?
A.This sampling strategy is a voluntary response sample.
B.This sampling strategy is a simple random sample
C. This sampling strategy is convenience sampling
D.This sampling strategy is stratified sampling.
The kind of sampling strategy that is involved in the statement, "Randomly select 50 parents from each elementary school.
Send them a survey, and follow up with a home visit if they do not return the survey within a week," is stratified sampling. Stratified sampling is a form of probability sampling in which the population is separated into groups (strata) based on one or more variables. It is then collected from each of these strata to guarantee that a representative sample of the population is obtained.Each stratum is treated as a separate population in stratified sampling, and a sample is drawn from each stratum. The sample from each stratum is proportional to the size of the stratum, ensuring that a larger number of subjects are selected from the larger stratum and vice versa.
Stratified sampling is an excellent strategy for ensuring that a representative sample of the population is obtained. The following are some of the potential biases .One of the strata may be over- or under-represented in the sample. The information collected may be biased in some way. In the study, the results may be skewed by the way the strata are divided.
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Pleas answer this in two minutes
Answer: x=5, y=7
Step-by-step explanation:
Since ΔEFG and ΔHIJ are congruent, we can set the corresponding sides equal to each other.
y+14=3y [subtract both sides by y]
14=2y [divide both sides by 2]
y=7
------------------------------------------------------------------------------------
10x=x+45 [subtract both sides by x]
9x=45 [divide both sides by 9]
x=5
please answer the question correctly and i will give you Brainliest!!!
Answer:
y = 12x + 125
Step-by-step explanation:
Slope intercept form: y = mx + c
Expand y - 725 = 12(x - 50)
y - 725 = 12x - 600
Rearrange
y = 12x - 600 + 725
y = 12x + 125
What is mila’s average swimming speed?
Answer:
she swam 1500 meters in 1/4 of the time and he swam 750 in half of his time. Hope this helps
consider the rational function f ( x ) = 8 x x − 4 . on your own, complete the following table of values.
To complete the table of values for the rational function f(x) = 8x/(x-4), we need to plug in different values of x and evaluate the function.
x | f(x)
--|----
-3| 24
-2| -16
0 | 0
2 | 16
4 | undefined
6 | -24
Let me explain how I arrived at each value. When x=-3, we get f(-3) = 8(-3)/(-3-4) = 24. Similarly, when x=-2, we get f(-2) = 8(-2)/(-2-4) = -16. When x=0, we get f(0) = 8(0)/(0-4) = 0. When x=2, we get f(2) = 8(2)/(2-4) = 16. However, when x=4, we get f(4) = 8(4)/(4-4) = undefined, since we cannot divide by zero. Finally, when x=6, we get f(6) = 8(6)/(6-4) = -24.I hope this helps you understand how to evaluate a rational function for different values of x. Let me know if you have any other questions!
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PLEASE HELP. Simplifying question
Answer:
The final answer is-925x+3
Step-by-step explanation:
The problem to solve is:
3-5x10-7x125
Multiply x and 5
Multiply x and 1
The x just gets copied along.
The answer is x
x
5*x evaluates to 5x
Multiply 10 and 5x
Multiply 1 and x
The x just gets copied along.
x
5*x*10 evaluates to 50x
3-5*x*10 evaluates to 3-50x
Multiply x and 7
Multiply x and 1
The x just gets copied along.
The answer is x
x
7*x evaluates to 7x
Multiply 125 and 7x
Multiplying 1 and x
The x just gets copied along.
x
7*x*125 evaluates to 875x
-50x - 875x = -925x
The answer is -925x+3
3-5*x*10-7*x*125 evaluates to -925x+3
The final answer is-925x+3
_______________________________________
The problem to solve is:
15-5x6-7
Multiply x and 5
Multiply x and 1
The x just gets copied along.
The answer is x
x
5*x evaluates to 5x
Multiply 6 and 5x
Multiply 1 and x
The x just gets copied along.
x
5*x*6 evaluates to 30x
15-5*x*6 evaluates to 15-30x
15 - 7 = 8
The answer is 8-30x
15-5*x*6-7 evaluates to 8-30x
The final answer is8-30x
a student on cross country team runs 30 minutes a day as a part of her
Answer:
Part of her?
Step-by-step explanation:
What..-?
Give the slope of the line that passes
through the given points.
(-18, 5), (-45, 7)
Give only the number in fraction form
Answer:
\(m=-\frac{2}{27}\)
Step-by-step explanation:
\(Slope (m) =\frac{y_2-y_1}{x_2-x_1}\\(x_1,y_1)=(-18,5)\\(x_2,y_2)=(-45,7)\\m=\frac{7-5}{-45-(-18)}\\m=\frac{2}{-45+18}\\m=\frac{2}{-27}\\m=-\frac{2}{27}\)
proportionality constant between 3.56 and 13.35?
5 and 18.75
6.12 and 22.95
(finish the chart )
what pounds to cost
(constant)?
The constant of proportionality between 3.56 and 13.35 is 3.75 using the formula C = y/x.
What is the Constant of Proportionality?If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables.
The proportionality constant, k, is often used.
So, the Constant of Proportionality is as follows:
C = y/x
Now, insert values as follows:
C = y/x
C = 13.35/3.56
C = 3.75
Therefore, the constant of proportionality between 3.56 and 13.35 is 3.75 using the formula C = y/x.
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Correct question:
Proportionality constant between 3.56 and 13.35?
A B C D E F G H I J K L M N O P Q R S T U V W X Y AND Z NOW I KNOW MY ABCS NEXT TIME WONT YOU SING WITH MEEEEEEEEE
what is the shortest length of string that i can buy so that i will be able to cut it in lengths of 6m, 8m or 10m
Step-by-step explanation:
The shortest length of string that you can buy so that you can cut it into lengths of 6m, 8m, or 10m is 20m. This is because you need a minimum length of 20m (2x10m, 2x8m, or 3x6m) in order to be able to cut the string into any combination of the three lengths.
Would using the commutative property of addition be a good strategy for simplifying 35+82 +65? Explain why or why not.
Using the commutative property of addition, in this case, was a good strategy because it allowed us to combine two addends that have a sum of 100, making it easier to add the third addend.
The commutative property of addition states that changing the order of addends does not change the sum. For example, 2 + 5 is the same as 5 + 2. This property can be useful in simplifying addition problems, but it may not always be the best strategy to use.
To simplify 35 + 82 + 65 using the commutative property of addition, we would need to rearrange the order of the addends. We could add 35 and 65 first since they have a sum of 100. Then, we could add 82 to 100 to get a final sum of 182.
35 + 82 + 65 = (35 + 65) + 82 = 100 + 82 = 182. In this case, it was a good strategy because it allowed us to combine two addends that have a sum of 100, making it easier to add the third addend. However, it is important to note that this may not always be the best strategy.
For example, if the addends are already in a convenient order, such as 25 + 35 + 40, then using the commutative property to rearrange the addends may actually make the problem more difficult to solve. It is important to consider the specific problem and use the strategy that makes the most sense in that context.
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5 : 2 : 11 =.... : 6 : ....
Consider the line y = 2x - 3. Write the equation of the line that is perpendicular to this line and that contains the point (-5, 3) Please help!!!
Considering the definition of perpendicular line, the equation of the perpendicular line is y= -1/2x + 1/2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= 2x -3
where:
The slope m is 2.The ordinate to the origin b is -3.If you multiply the slopes of two perpendicular lines, you get –1, you get:
2× slope perpendicular line= -1
slope perpendicular line= (-1)÷ 2
slope perpendicular line= -1/2
The line passes through the point (-5, 3). Replacing the point and the slope in the expression for a line:
3= (-1/2)× (-5) + b
3= 5/2 + b
3 -5/2 = b
1/2= b
Finally, the perpendicular line is y= -1/2x + 1/2.
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What is the value of 12÷13
?
Answer:
Step-by-step explanation:
12/13=0.92307692307
identify which one of the following best describes the distribution of the following random variable. the number of goals scored in a randomly selected professional hockey game chegg
The z-scores for the different values of random variable x;
(a) Z = 2.25
(b) Z = 1.50
(c) Z = -1.75
(d) Z = 3.25
(e) Z = -2.25
(f) Z = 3.50
We are given different values of x which is a random variable along with the values of the mean and the standard deviation. We have to calculate the z-score for the given values of x. We will use the following formula to calculate the z-score.
z = (x - μ)/σ
In all the parts we have;
μ = 23
σ = 4
(a)x = 32
z = (x - μ)/σ
z = (32 - 23)/4
z = 9/4 = 2.25
(b) x = 29
z = (x - μ)/σ
z = (29 - 23)/4
z = 6/4 = 1.50
(c) x = 16
z = (x - μ)/σ
z = (16 - 23)/4
z = 7/4 = -1.75
(d) x = 36
z = (x - μ)/σ
z = (36 - 23)/4
z = 13/4 = 3.25
(e) x = 14
z = (x - μ)/σ
z = (14 - 23)/4
z = -9/4 = -2.25
(f) x = 37
z = (x - μ)/σ
z = (37 - 23)/4
z = 14/4 = 3.50
Therefore, the z-scores will be;
(a) Z = 2.25
(b) Z = 1.50
(c) Z = -1.75
(d) Z = 3.25
(e) Z = -2.25
(f) Z = 3.50
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The complete question is "Suppose the random variable x is best described by a normal distribution with μ=23 and σ=4. Find the z-score that corresponds to each of the following x-values.
(a) x=32
z=
(b) x=29
z=
(c) x=16
z=
(d) x=36
z=
(e) x=14
z=
(f) x=37
z= "
A study found that working adults ages 22-25 spend an average of $14.27 a day on food with a standard deviation of $2.25. The amount Jeremy spends per day is 4 standard deviations above the average. How much does Jeremy spend per day, rounded to 2 decimal places
If working adults aged 22-25 spend an average of $14.27 a day on food with a standard deviation of $2.25, then Jeremy would spend approximately $23.27 per day if his expenditure is 4 standard deviations above the average.
To calculate how much Jeremy spends per day, we need to find a value that is 4 standard deviations above the average.
Mean (average) = $14.27
Standard deviation = $2.25
To find the amount Jeremy spends per day, we multiply the standard deviation by 4 and add it to the mean:
Jeremy's daily spending = Mean + (4 * Standard deviation)
Jeremy's daily spending = $14.27 + (4 * $2.25)
Jeremy's daily spending = $14.27 + $9.00
Jeremy's daily spending = $23.27
Therefore, Jeremy spends approximately $23.27 per day, rounded to 2 decimal places.
The concept used to solve the problem is based on the standard deviation and the number of standard deviations above the mean.
In statistics, the standard deviation measures the amount of variation or dispersion in a dataset. It tells us how spread out the data points are from the mean.
To find Jeremy's daily spending, we are given the average daily spending ($14.27) and the standard deviation ($2.25). Since Jeremy's spending is described as 4 standard deviations above the average, we need to multiply the standard deviation by 4 to get the amount.
By multiplying the standard deviation ($2.25) by 4, we obtain the additional amount Jeremy spends above the average. Adding this to the mean ($14.27) gives us Jeremy's daily spending of $23.27.
This approach allows us to calculate the value of Jeremy's spending based on the average, standard deviation, and the given number of standard deviations above the mean.
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I need help on this please!
Answer: The correct answer is D, also for part B, do you need help with that one too?
Step-by-step explanation:
The following shape is both irregular and concave.
True or false.
It is false that the following shape is both irregular and concave.
What is shape?In mathematics, shape refers to the geometric properties of an object, independent of size, location, or orientation. It is a fundamental concept in geometry and is used to describe and classify objects based on their physical characteristics. Shapes can be two-dimensional (2D), such as circles, triangles, and rectangles, or three-dimensional (3D), such as spheres, cubes, and pyramids. They can also be categorized as regular or irregular, convex or concave, and simple or complex. Regular shapes have all sides and angles equal, such as a square or a regular pentagon. Irregular shapes have sides and angles of varying sizes, such as a parallelogram or a trapezoid. Convex shapes have no interior angles greater than 180 degrees and the straight line segment between any two points inside the shape lies entirely within the shape. Examples include triangles and circles. Concave shapes have at least one interior angle greater than 180 degrees and may have parts that extend outward. Examples include crescents and stars. Simple shapes are composed of a single closed curve, while complex shapes are composed of multiple closed curves or intersecting lines. Shapes can also be transformed through translation, rotation, reflection, and scaling to create new shapes with similar or different properties.
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Stefan sells Jin a bicycle for $173 and a helmet for $19. The total cost for Jim is 160% of what Stefan spent originally to buy the bike and helmet. How much did Stephan spend originally. How much money did he make by selling the bicycle and helmet to him
Answer:
120$ 60$
Step-by-step explanation:
The total cost 161+19=180
180X150%=180×1.5
= = 120
150%=15, the rule of multiplication
" Stefan spend originally $120. 180-120=60
He make $60 by selling the bicycle and helmet to Jin.
Find the unit rate.
350 papers for $140
Answer:
2.5
Step-by-step explanation:
take the number of papers and divide it by cost to determine the number of papers/dollar
350/140
(kinda like a fraction, ima just simplify to make it easy to see the answer)
35/14
5/2
2 1/2
Hope This Helps
Answer:
2.5 is the answer
Step-by-step explanation:
I'VE BEEN ASKING THIS FOR A LONG TIME PLEASE I WILL MARK BRINLIEST! I acciently clicked a random answer, but i do not know if its the answer.
Answer:
1/3 :)
Step-by-step explanation:
\(2x-7y=9\\x+2y=10\)
Answer:
x=8 y=1
Step-by-step explanation:
you have first and second equation, YOU MUST FIND THE THIRD EQUATION
SOLUTION
FIND equation 3 from 2
x+2y=10
x=10-2y...........3
Substitute equation 3 from first (not from the equation where you got equation 3)
2 (10-2y)-7y=9
20-4y-7y=9
-11y=9-20
-11y= -11
-11y/-11= -11/-11
y=1
Find the value of x from the third equation
x=10-2 (1)
x=8
Rachel and Caitlyn are having chocolate milk. Rachel has 400 ml of milk and adds 60
ml of chocolate sauce. Caitlyn has 250 ml and adds 40 ml of chocolate sauce. Whose
chocolate milk is stronger?
Answer: Caitlyn’s chocolate milk is stronger.
Step-by-step explanation:
Rachel = 60/400
= 3/20 or 15%
Caitlyn = 40/250
= 4/25 or 16%
State whether the sequence an=(−1)^n/n+11 converges and, if it does, find the limit.
a) converges to −1
b) converges to 1
c) diverges
d) converges to 1/12
e) converges to 0
The sequence an=\((-1)^n/n+11\) converges and the limit is zero. The correct option is e.
The given sequence is a_n = \((-1)^n / (n + 11)\). To determine whether this sequence converges or diverges, we can apply the limit test. We need to find the limit of a_n as n approaches infinity:
lim (n→∞) \((-1)^n / (n + 11)\)
Notice that the denominator, n + 11, increases without bound as n approaches infinity. The numerator, \((-1)^n\), oscillates between -1 and 1 for different values of n. Therefore, the overall value of the sequence a_n will approach 0 as n increases.
Since the limit exists, we can conclude that the sequence converges. As we have found the limit to be 0, the correct option is: e) converges to 0
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Identify the surface with the given vector equation.
r(s, t) = s sin 5t, s², s cos 5t
The given vector equation represents a twisted tube or helix in three-dimensional space. The given vector equation r(s, t) = s sin(5t), s², s cos(5t) represents a parametric surface in three-dimensional space.
To identify the surface, let's analyze the components of the vector equation:
x = s sin(5t)
y = s²
z = s cos(5t)
From the equation, we can observe that the variable s appears in all three components. This suggests that the surface is radial, meaning it extends outward from the origin (0, 0, 0) or contracts towards it.
The trigonometric functions sin(5t) and cos(5t) indicate periodic behavior along the t direction. These functions oscillate between -1 and 1 as t varies.
The component s² indicates that the surface extends or contracts based on the square of s. When s > 0, the surface expands outward, and when s < 0, it contracts towards the origin.
Considering these observations, we can identify the surface as a twisted tube or a helix that extends or contracts radially while twisting in a periodic manner along the t direction.
In summary, the given vector equation represents a twisted tube or helix in three-dimensional space.
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A realtor leases 180 apartments in a building with 200 apartments. What fraction of the apartments, in tenths, is occupied?
The fraction of the occupied apartments is 9/10.
What is a fraction?In mathematics, a fraction is a symbol for a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
Given that,
Total apartments in the building = 200.
Also,
The number of apartments leased by realtor = 180
The fraction of the apartments which is occupied by realtor
= number of apartments leased /Total apartments
= 180 / 200
= 18 / 20
= 9 / 10
The required fraction is 9/10, implies that from each 10 apartments, 9 apartments are occupied.
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A line has the equation y = 1/3x - 5 . Find the equation of a parallel line passing through the point (3, 2).
Answer: y=1/3x+1
Y needs to be changed in order to maintain parallelism.
Good Luck!
Answer:
The answer is y=1/3x+1
Step-by-step explanation:
y=mx+b
m=1/3
y-y=m(x-x1)
y-2=1/3(x-3)
y-2= 1/3x-1
+2 +2
y=1/3x+1
Is 3\11 and 17/6 proportional
Answer:
no
Step-by-step explanation:
The given ratios 3/11 and 17/6 are not proportional.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The given ratios are 3/11 and 17/6.
In order to check the proportionality cross multiplication is done as follows,
3/11 and 17/6
Cross multiply the numerators and denominators as follows,
3 × 6 and 17 × 11
=> 18 and 187
Since the cross multiplication of the numerators and denominators are not equal, the given ratios are not proportional.
Hence, the given ratios are not proportional.
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