The solution to the system of equations using the substitution method is option (c) (-5,8)
To solve this system of equations using the substitution method, we need to substitute the second equation into the first equation for y, then solve for x.
The substitution method is a way to solve a system of equations by solving one of the equations for one of the variables, and then substituting that expression into the other equation to get an equation with only one variable.
Substitute y = 8 into the first equation
x + y = 3
x + 8 = 3
x = 3 - 8
Subtract the numbers
x = -5
Therefore, the correct option is (c) (-5,8).
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PLEASE HELP AND EXPLAIN AND SHOW WORK ON HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST.
Answer:
Step-by-step explanation:
Find the missing measures.
The value of the missing angles are:
w = 109°
x = 39°
y = 141°
z = 109°
How to find the measure of the missing angles?In geometry, we know that the sum of angles on a straight line is 180 degrees. Thus:
w = 180 - 71
w = 109°
We know that alternate angles are formed when two parallel lines are cut by a transversal. Thus:
x = 39°
y = 180 - 39
y = 141°
Similarly:
z = 180 - 71
z = 109°
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Two functions are shown below.
Function 1: Jay rides the subway each workday for a month. He spends $5.50 each day that he rides the subway.
Function 2: Keisha has a bike share membership. She rides an e-bike to work. The equation E = 8.25 + 1.50d represents Keisha's bike expenses each month, where
d represents the number of days she rides.
Which function has the greatest rate of change?
A. Function 1
B. Function 2
C. The functions have the same rate of change.
D. The rate of change cannot be determined for either function.
Comparing the rates of change, we can see that Function 2 has a greater rate of change than Function 1. Therefore, the answer is (B) Function 2.
What is the rate of change?
The rate of change is the amount of change in the output (dependent variable) for a given change in the input (independent variable).
In this case, the input is the number of days ridden, and the output is the cost of transportation for a month.
For Function 1, the cost is $5.50 per day. Therefore, the rate of change is $5.50 per day.
For Function 2, the equation E = 8.25 + 1.50d represents the cost of transportation for a month, where d is the number of days ridden. The rate of change is the coefficient of d, which is $1.50 per day.
Hence, Comparing the rates of change, we can see that Function 2 has a greater rate of change than Function 1. Therefore, the answer is (B) Function 2.
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URGENT!! Will give brainliest :)
What is the equation for the line of best fit for the following data? Round the slope and -intercept of the line to three decimal places.
A. y=-0.580×+ 10.671
B. y=-10.671 x+ 0.580
C. y= 10.671 x-0.580
D. y= 0.580x - 10.671
To find the equation for the line of best fit, we can use linear regression. Based on the given data:
x: 2, 5, 7, 12, 16
y: 9, 10, 5, 3, 2
The equation for the line of best fit would be in the form: y = mx + b, where m is the slope and b is the y-intercept.
Using a calculator or statistical software, we can calculate the slope and y-intercept for the line of best fit.
The result is:
Slope (m): -0.580 (rounded to three decimal places) Y-intercept (b): 10.671 (rounded to three decimal places)
So, the correct answer is:
A. y = -0.580x + 10.671
The distance between two cities on a map is 17 centimeters. The scale on the map relates 5 centimeters on the map as 30 miles on the road. What is the actual distance, in miles, between the two cities?
Answer: 102 miles.
Step-by-step explanation:
You divide 17 by 5 and then multiply by 30.
How to solve? Answers are side side side, side angle side, angle angle angle, hypotenuse leg, or none)
The given triangles AOB and triangle OCB are proved congruent by using the property - angle side angle congruency.
Explain about the triangle congruency:Of three sides, three angles, plus three vertices, a triangle is a two-dimensional shape. If the matching sides or angles of two or more triangles match, the triangles are said to be congruent. Congruent triangles are identical in terms of their dimensions and shape.
Two triangles belong together if whose corresponding two angles but one included side are equivalent, according to the Angle- Side- Angle rule (ASA).
Given data:
AB || CDCO = OBAs, AB || CD, ∠ABO ≅ ∠OCD (alternate interior angles)
∠AOB ≅ ∠COD (vertically opposite angles)
So,
∠AOB ≅ ∠COD
CO = OB
∠ABO ≅ ∠OCD
By using angle side angle congruence:
ΔAOB ≅ ΔCOD
Thus, the given triangles AOB and triangle OCB are proved congruent by using the property - angle side angle congruency.
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The Monongahela Incline has a slope of 18. 5/25. 8. As you ride up the funicular, you travel a horizontal distance of 516 feet. How high is it at the top? will give brainliest
The total vertical change after travelling horizontal distance 516 feet is equal to 370 feet.
Monongahela Incline slope is equal to = 18.5 / 25.8
This implies that after traveling a horizontal distance of 25.8 it rise upto 18.5.
To ride up the funicular total travelling at the top is equal to,
25.8 Horizontal change = 18.5 vertical change
⇒ 1 horizontal change = ( 18.5 / 25.8 ) vertical change
⇒ 516 feet horizontal change = 516 feet × ( 18.5 / 25.8 ) vertical change
= 370 feet.
Therefore, the total vertical distance while travelling at the top of the funicular is equal to 370 feet.
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a researcher has collected the following sample data. the mean of the sample is 5. 3 5 12 3 2 the coefficient of variation is . a. 81.24% b. 72.66% c. 330% d. 264%
The mean of the sample is 5, 3, 5, 12, 3, 2 the coefficient of variation is 91%. Option A is the correct answer.
To calculate the coefficient of variation, first, we need to calculate the standard deviation and mean of the sample.
The mean of the sample is (3 + 5 + 12 + 3 + 2)/5 = 5.
To find the standard deviation, we first need to calculate the variance. The variance can be found by taking the sum of the squared differences between each data point and the mean, dividing by the sample size minus one, and then taking the square root.
The variance is ((3-5)² + (5-5)² + (12-5)² + (3-5)² + (2-5)²)/4 = 20.5.
The standard deviation is the square root of the variance, which is approximately 4.53.
Finally, we can calculate the coefficient of variation by dividing the standard deviation by the mean and multiplying by 100%.
Coefficient of variation = (4.53/5) x 100% = 90.6%.
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The question is -
A researcher has collected the following sample data. The mean of the sample is 5, 3, 5, 12, 3, 2 the coefficient of variation is?
a. 91%
b. 72.66%
c. 330%
d. 264%
A carpenter is going to install tiles on a kitchen floor.The kitchen floor is in the shape of a rectangle as shown.
The minimum number of tiles required to cover the kitchen floor is approximately 71 tiles.
Why is this so?The dimension of the square tiles are 6inches L and W
Hence the area = 6 x 6 = 36inches
In ft this would be:
36/12 = 3ft
since 1 ft = 12 inches.
The dimension of the rectangular floor is 12.5ft by 17ft
Hence it's area = L x W = 12.5ft x 17ft = 212.5ft
So recall that the area of the tile = 3f, hence the minimum number of tiles required = 212.5ft/3ft
= 70.8333333333
The minimum number of tiles requires is [tex]\approx[/tex] 71 tiles.
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Full Question:
Although part of your question is missing, you might be referring to a similar question:
A carpenter is going to install square tiles on a living room floor. T?he living room florrs is in the shape of a 12.5ft x 17ft rectangle as shown.
The side length of each square tile is 6 inches. What is the minimum number of the tiles the carpenter needs to completely cover the living room?
Figure LMNO is a reflection of HIJK. Which angle is congruent to ZH?
The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.
In this case, we have two figures, LMNO and HIJK, and we know that LMNO is a reflection of HIJK. This means that there is an axis of reflection that maps HIJK onto LMNO.
When a shape is reflected across a line of symmetry, its angles are preserved. That is, if two angles in the original shape are congruent, then their images in the reflected shape are also congruent.
In this case, ZH is an angle in HIJK, and we want to find the angle in LMNO that corresponds to it. To do this, we need to find the line of symmetry that maps HIJK onto LMNO.
Once we have identified this line, we can draw the perpendicular bisector of ZH and find where it intersects the line of symmetry. The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.
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A ball is dropped from a height of 32 m.
With each bounce, the ball reaches a
height that is half the height of
the previous bounce. After
which bounce will the ball
rebound to a maximum
height of 25 cm?
how would you define the actual score and theoretical score on an exam, and how would you calcutre the percent success
To determine the percent success, divide the actual score by the theoretical score, and then multiply the result by 100 to convert the value to a percentage.
We define the actual score, theoretical score, and explain how to calculate the percent success on an exam.
Actual score:
The actual score refers to the number of points a student has earned on an exam.
It represents the student's performance on the test, taking into account the correct and incorrect answers.
Theoretical score:
The theoretical score is the maximum number of points a student can earn on an exam.
This represents a perfect performance, where the student answers all questions correctly.
Calculating percent success:
To determine the percent success, divide the actual score by the theoretical score, and then multiply the result by 100 to convert the value to a percentage.
a. Divide the actual score by the theoretical score: (actual score) / (theoretical score)
b. Multiply the result by 100: (result from step a) * 100
c. The final value is the percent success.
For example, if a student has an actual score of 80 and the theoretical score is 100, the percent success would be calculated as follows:
a. 80 / 100 = 0.8
b. 0.8 * 100 = 80
c. The percent success is 80%.
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Scenario: You are remodeling a kitchen, including the formal dining room and breakfast nook. It is time to purchase flooring for the space. You need to calculate the area of the entire space and then find the cost of the materials that you would like to purchase to make sure you do not go over your budget of $7,500. See the picture for your blueprint.
The total area of the space is given as 1729 sq ft.
We can make use of engineered wood because it fits the budget
What is a Mathematical Model?A mathematical model is a representation of a real-world system, process, or phenomenon using mathematical concepts, equations, and symbols. The purpose of creating a mathematical model is to understand and analyze the behavior of the system under different conditions and to make predictions about its future behavior.
Mathematical models can be used in various fields, including physics, engineering, economics, biology, and social sciences. They can range in complexity from simple algebraic equations to sophisticated computer simulations and can incorporate various factors such as time, space, and multiple variables.
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3x + 18 > 54 solve the inequality? pls help?
Answer:
x > 12
Step-by-step explanation:
3x + 18 > 54
flip a coin three times. you will win $2 for each heads. what is the expected winning (expec- tation of your winning)? a
The expected winning is $2.
To calculate the expected winning, we need to find the probability of each outcome and multiply it by the amount we will win in that outcome.
There are 2 possible outcomes for each coin flip: heads or tails. Therefore, there are 2x2x2=8 possible outcomes for flipping a coin three times.
Here are all the possible outcomes with the number of heads in each outcome:
HHH (3 heads)HHT (2 heads)HTH (2 heads)THH (2 heads)HTT (1 head)THT (1 head)TTH (1 head)TTT (0 heads)The probability of each outcome can be calculated using the formula: probability = (number of favorable outcomes) / (total number of possible outcomes)
For example, the probability of getting 3 heads (HHH) is 1/8 because there is only one favorable outcome out of 8 possible outcomes.
Using this formula, we can calculate the probability and expected winning for each outcome:
HHH: probability = 1/8, expected winning = $6HHT: probability = 1/4, expected winning = $4HTH: probability = 1/4, expected winning = $4THH: probability = 1/4, expected winning = $4HTT: probability = 3/8, expected winning = $2THT: probability = 3/8, expected winning = $2TTH: probability = 3/8, expected winning = $2TTT: probability = 1/8, expected winning = $0To calculate the overall expected winning, we need to add up the expected winning for each outcome multiplied by its probability:
(1/8) x $6 + (1/4) x $4 + (1/4) x $4 + (1/4) x $4 + (3/8) x $2 + (3/8) x $2 + (3/8) x $2 + (1/8) x $0 = $2
Therefore, the expected winning is $2.
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Find the average value of f(x+y)=sin(x+y) over
(a) the rectangle 0 ≤ x ≤ π/3, 0 ≤ y ≤ 5π/3
(b) the rectangle 0 ≤ x ≤ 2π/3, 0 ≤ y ≤ 7π/6
(a) The average value of f is
(b) The average value of f is
The average value of the function f(x,y) = sin(x+y) over the rectangle 0 ≤ x ≤ π/3, 0 ≤ y ≤ 5π/3 is -27√(3) / (40π^2).
To find the average value of the function f(x,y)=sin(x+y) over the given rectangle, we need to integrate the function over the rectangle and then divide by the area of the rectangle.
So, we have:
average value of f(x,y) = (1/Area of rectangle) × double integral of f(x,y) over the rectangle
where the limits of integration are
0 ≤ x ≤ π/3
0 ≤ y ≤ 5π/3
The area of the rectangle is
Area = (π/3 - 0) × (5π/3 - 0) = 5π^2 / 9
Now, we can integrate the function f(x,y) over the rectangle
double integral of f(x,y) over the rectangle = integral from 0 to π/3 of integral from 0 to 5π/3 of sin(x+y) dy dx
= [tex]\int\limits^{\pi /3}_0[/tex] [-cos(x+y)] evaluated from y=0 to y=5π/3 dx
= [tex]\int\limits^{\pi /3}_0[/tex] [-cos(x+5π/3) + cos(x)] dx
= [tex]\int\limits^{\pi /3}_0[/tex] [-1/2cos(x) - 1/2cos(x+π/3)] dx
= [-1/2sin(x) - 1/4sin(x+π/3)] evaluated from x=0 to x=π/3
= [-1/2sin(π/3) - 1/4sin(2π/3)] - [-1/2sin(0) - 1/4sin(π/3)]
= (-√(3)/4) - (1/4 × √(3)/2) = -3sqrt(3)/8
Therefore, the average value of f(x,y) over the rectangle is
average value of f(x,y) = (1/Area of rectangle) × double integral of f(x,y) over the rectangle
= (-3sqrt(3)/8) / (5π^2 / 9)
= -27sqrt(3) / (40π^2)
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The given question is incomplete, the complete question is:
Find the average value of f(x,y)=sin(x+y) over the rectangle 0≤x≤π/3, 0≤y≤5π/3.
g is there effectiveness of a vaccine against the development of coronavirus symptoms different than no vaccination? a researcher has collected the data below: unvaccinated vaccinated total developed covid-19 25 5 30 stayed healthy 44 52 96 total 69 57 126 4. 1 (1 pt) calculate odds of healthy for each vaccination status 4. 2 (1 pt) calculate odds ratio from 4.1 4. 3 (2 pt) interpret odds ratio and answer the research question.
The odds ratio of 5.91 suggests that vaccination significantly increases the likelihood of remaining healthy and not developing COVID-19 symptoms compared to no vaccination.
Does vaccination lower COVID-19 symptom odds compared to being unvaccinated?Calculate the odds of staying healthy for each vaccination status based on the data provided:
Unvaccinated:
Number of individuals who stayed healthy = 44
Number of individuals who developed COVID-19 = 25
Odds of staying healthy = Number of individuals who stayed healthy / Number of individuals who developed COVID-19 = 44/25 = 1.76
Vaccinated:
Number of individuals who stayed healthy = 52
Number of individuals who developed COVID-19 = 5
Odds of staying healthy = Number of individuals who stayed healthy / Number of individuals who developed COVID-19 = 52/5 = 10.4
Next, let's calculate the odds ratio from the odds of staying healthy for each vaccination status:
Odds ratio = Odds of staying healthy for vaccinated / Odds of staying healthy for unvaccinated
= 10.4 / 1.76
= 5.91
Now, let's interpret the odds ratio and answer the research question. An odds ratio of 5.91 indicates that the odds of staying healthy among vaccinated individuals is 5.91 times higher compared to unvaccinated individuals.
This suggests that vaccination is associated with a significantly higher likelihood of staying healthy and not developing COVID-19 symptoms. Therefore, the data collected by the researcher suggests that the vaccine is effective in preventing the development of COVID-19 symptoms.
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Please help!!!
1-) Sani Has at least 68 envelopes to adress. He has address 17 of them. Write and solve an inequality that describes how many more envelopes , at most , Sani has left to address
2-)Nadine can send or reveive a text message for $0. 5 or get an unlimited number for $5. 0. Write and solve an inequality to find how many messages she can send and receive so the unlimited plan is cheaper than paying for each message
The number of envelopes left to address by Sani is at most 51 .
And Messages > 10 to have unlimited plan cheaper than paying for each messages.
At least numbers of envelopes Sani has = 68
Number of envelops he addressed = 17
Let x be the number of envelopes that Sani has left to address.
Then we have,
x ≤ 68 - 17
Simplifying this inequality, we get,
x ≤ 51
Sani has at most 51 envelopes left to address.
Cost per text message send or received by Nadine = $0.5
Cost pf unlimited number of text message send or received = $5
Let m be the number of messages Nadine sends or receives.
Then the cost of paying for each message is,
0.5m
The cost of the unlimited plan is $5.0.
The number of messages m such that,
5.0 ≤ 0.5m
Simplifying this inequality, we get,
⇒ 10 ≤ m
If Nadine sends or receives more than 10 messages, the unlimited plan is cheaper than paying for each message.
So the solution to the inequality is m > 10.
Therefore, number of message Sani left to address is at most 51 envelopes .
And to have unlimited plan cheaper than paying for each messages for Nadine is m > 10.
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- x\3 > 5 solve the inequality
help pls?
it has a line under this >
Answer:
x >-15
Step-by-step explanation:
Please here is it.
where x >-15
x + 3=8.5 what is the solution to the equation
Answer:
5.5
Step-by-step explanation:
x＋3＝8.5
or，x＝5.5
I hope it helped you
Please Mark me brainliest
-4 ≤ x- 4 ≤ 0 graph the conjuntion ?? can someone help
The inequality is simplified as 0 ≤ x ≤ 4
Define inequalityIn mathematics, inequality refers to a mathematical expression that indicates that two values or quantities are unequal. An inequality is represented by the symbols "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
For example, the inequality "x > 5" means that the value of x is greater than 5, and the inequality "y ≤ 10" means that the value of y is less than or equal to 10.
To graph the conjunction, we first need to solve for x:
-4 ≤ x - 4 ≤ 0
Add 4 to all parts of the inequality:
0 ≤ x ≤ 4
Image of graph is attached below.
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A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
The IQR (Interquartile Range) of 13 is the most accurate measure of variability to use for this data since the data is skewed and contains outliers. The IQR is less sensitive to outliers than the range and provides a better representation of the spread of the middle 50% of the data.
What is variability?Variability refers to the extent to which data points in a dataset differ from each other. It is a measure of how spread out or dispersed a set of data is.
According to given information:In statistics, measures of variability are used to describe how spread out or clustered a set of data is. There are several measures of variability, but the two most common ones are the range and the interquartile range (IQR).
The range is the difference between the maximum and minimum values in a set of data. It is a simple measure of variability that gives an idea of how much the data varies. However, it can be affected by outliers, which are values that are much larger or smaller than the other values in the data set.
The IQR is a more robust measure of variability that is less affected by outliers. It is the difference between the third quartile (the value above which 75% of the data falls) and the first quartile (the value below which 25% of the data falls). The IQR describes the range of the middle 50% of the data and gives an idea of how spread out the data is around the median.
In the case of the charity's donations, the data is skewed towards the higher end, with most of the donations falling between $16 and $20. This means that the range of 13 (20-5) would be affected by the outliers at the high end, and would not accurately represent the variability of the data.
On the other hand, the IQR of 13 (the difference between the third quartile at $20 and the first quartile at $7) would give a more accurate representation of the variability of the data, as it is less affected by the outliers.
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A local doctor’s office logged the number of patients seen in one day by the doctor for ten days. Find the mean, median, range, and midrange of the number of patients seen in ten days.
27, 31, 27, 35, 35, 25, 28, 35, 33, 24
Calculate the mean, median, range, and midrange of the number of patients seen in ten days.
Answer:
Step-by-step explanation:
Medium is 28
Mean is 29
Range is 11
Midrange is 29.5
What are the real and complex solutions of the polynomial equation? x 4 – 41 x 2 = – 400 please show work and how you got then answer
All four zeros are real solutions in the polynomial equation.
What are polynomials in equations?
A polynomial is an expression that consists of one or more variables, coefficients, and non-negative integer exponents of the variables. An equation is a mathematical statement with an equal sign between two algebraic expressions with equal values.
x⁴ – 41 x² = – 400
Adding 400 on both sides to get rid 400 from right side and set 0 on right side, we get
x⁴ - 41x² + 400 = -400 + 400
x⁴ - 41x² + 400 = 0
Factoring by product sum rule.
We need product of 400 and sum upto -41.
We can see that 400 = -25 × -16 = 400 and -25-16 = -41.
Therefore,
x⁴ - 25x² - 16x² + 400 = 0
Making it into two groups, we get
(x⁴ - 25x²) + (-16x² + 400) = 0
Factoring out GCF of each group, we get
x²(x² - 25) (x² - 16) = 0
(x² - 25) = x² - 5² = (x - 5) (x + 5)
x² - 16 = x² - 4² = (x - 4)(x + 4)
(x - 5) (x + 5) (x - 4)(x + 4) = 0
Applying zero product rule,
x-5=0
x+5=0
x-4=0 and
x+4=0.
Therefore,
x = -5, -4, 4 and 5.
All four zeros are real solutions.
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What is the area of this figure?
5 mi
2 mi
11 mi
2 mi
2 mi
3 mi
3 mi
7 mi
14 mi
10 mi
2 mi
5 mi
square miles
So, the area of the figure is 54.5 square miles.
What is area?In mathematics, the area is the measurement of the size of a two-dimensional surface or region, usually expressed in square units. It is a quantity that expresses the extent of a two-dimensional shape or figure in a plane. The area of a figure is calculated by multiplying the length and width of the shape, in the case of a rectangle, or by using the appropriate formula for other shapes such as triangles, circles, or irregular polygons.
Here,
The area of rectangle R1 is:
Area of R1 = 5 mi x 2 mi
= 10 square miles
The area of rectangle R2 is:
Area of R2 = 2 mi x 14 mi
= 28 square miles
The area of the triangle TRI is:
Area of TRI = (1/2) x base x height
= (1/2) x 11 mi x 3 mi
= 16.5 square miles
Therefore, the total area of the figure is:
Area of figure = Area of R1 + Area of R2 + Area of TRI
= 10 + 28 + 16.5
= 54.5 square miles
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please help and explain and show your work on how you got the answer. I WILL MARK YOU BRAINLIEST
Answer:
Step-by-step explanation:
it is -2
Answer: -2
Step-by-step explanation:
So this is asking for the cube root of -8.
This is the same as asking what is multiplied by itself 3 times to get -8.
-2 * -2 *-2 = -8
You can also use a calculator.
Another way to solve it is to write -8^(1/3).
Hope this helps!!!
Inverse of the function
Answer:
f -1
Step-by-step explanation:
the inverse of a function (f) is denoted by f -1 and exsists only when f is both one to one and onto function.
a study using the pretest-posttest design was conducted to determine the effect of regular strenuous physical exercise on students' grades. the researchers randomly divided the participants into an experimental and a control group. the study was designed for a period of 12 months with 100 students in each group. after 6 months, only 40 participants remained in the experimental group. the results obtained at the end of the study were faulty. in this scenario, the faulty results can most likely be attributed to
It is important for researchers to carefully consider these factors when designing studies and analyzing data to ensure that their results are accurate and reliable.
Small Sample Size: With only 40 participants remaining in the experimental group after 6 months, the sample size may have been too small to detect any significant differences between the experimental and control groups.
Sampling Error: Even with random assignment to groups, there is always a chance that the groups will differ on some important characteristic that could affect the results.
Statistical Power: The statistical power of a study refers to its ability to detect a true effect if one exists. With a small sample size, the statistical power of the study may have been too low to detect any real differences between the groups.
Data Analysis: The way in which the data was analyzed could have influenced the results. For example, if the researchers used an inappropriate statistical test or did not correct for multiple comparisons, it could have led to faulty results.
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The slope of one line is a, where a is a positive number. A second line is perpendicular to the hirst line. Which word best describes the slope of the second line? Type positive, negative, or zero.
The slope of the second line is also positive, as it is parallel to the first line which has a positive slope.
What is slope?Slope is a measure of how steep a line is, and is defined as the ratio of the change in the y-coordinate (vertical change) to the change in the x-coordinate (horizontal change) between any two points on the line. It represents the rate at which the line is rising or falling as it moves from left to right. Slope can be positive, negative, or zero. A positive slope indicates that the line is increasing as it moves from left to right, a negative slope indicates that the line is decreasing as it moves from left to right, and a zero slope indicates that the line is horizontal.
Here,
When two lines are parallel, they have the same slope. In this case, the first line has a positive slope of "a," which means that it is increasing as it moves from left to right. Since the second line is parallel to the first line, it will also have the same slope as the first line. Therefore, the slope of the second line will also be positive, indicating that it is increasing as it moves from left to right.
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4. A school principal believes that students spend more time each day reading for pleasure in July (1 point)
than in April. She collects data on the mean number of minutes per day that a sample of 10
students spend reading for pleasure. The results are shown in the table.
Student April July
1
2
سا
4
5
6
7
8
9
10
20
42
28
34
37
25
57
45
65
25
44
35
57
40
31
60
46
75
42 46
Difference
(July-April)
5
2
7
23
3
6
3
1
10
4
Which of the following best describes the principal's conclusion, given a significance level of
0.05?
The students do not spend nmore time reading in April than in July
How to solve for the evidenceFind the mean
5 + 2+ 7+23+3+6+3+1+10 / 10
= 64 / 10
= 6.4
standard deviation = √368.4 / 9 = 6.398
test statistic = 6.4 / 6.398/√10
= 3.1633
degree of freedom= 10 - 1
= 9
p v alue = 0.005745
This shows that the students do not spend nmore time reading in April than in July
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