Answer:
Step-by-step explanation:
complementary is 90 degrees
Suppose we want to choose 2 letters, without replacement, from the 3 letters A,B and C How many ways can this be done, if the order of the choices is taken into consideration? How many ways can this be done, if the order of the choices is not taken into consideration? Please help
The number of ways to choose the letters is given as follows:
Order matters: 6 ways.Order does not matter: 3 ways.How to obtain the number of ways to choose the letters?First we must decide which formula to use, depending if the order matters, as follows:
Order matters: permutation formula.Order does not matter: combination formula.The number of possible permutations of x elements from a set of n elements is given by:
[tex]P(n,x) = \frac{n!}{(n-x)!}[/tex]
Hence, if the order matters, the number of ways is given as follows:
P(3,2) = 3!/(3 - 2)! = 6.
The combination formula is given as follows:
[tex]C(n,x) = \frac{n!}x!{(n-x)!}[/tex]
Hence, if the order does not matter, the number of ways is given as follows:
C(3,2) = 3!/(2! x 1!) = 3.
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Which statement correctly compares the function shown on this graph with the function y=-x+4? C 15 10 10 KE IN Tak LII 467 bottlen LI A. The function shown on the graph has the same rate of change, but a higher starting point. B. The function shown on the graph has a greater rate of change, but the same starting point. C. The function shown on the graph has a smaller rate of change, but the same starting point. D. The function shown on the graph has the same rate of change, but a lower starting point.
It can be said that the statement that correctly compares the function shown on this graph with the function y =4x + 2 is
'The expresion indicated on the graph has a smaller rate of change, but a higher starting point.' (Option A)
How is this so?We have the expression - y = mx + c, where m is the slope and
c is known as the y-intercept"
For given question,
We have been given a expresion which states: y = 4x + 2
This function represents a line.
Looking at the above function side by side with slop-intercept form of the line.
We can state that we have slope of the line = 4 and y - intercept = 2
Note that the pace of change of the line is given by the slope.
This means that the required pace of change of function y = 4x + 2 will be 4.
A beginning point of a function is the commencement value in a linear expression .
The beginning point of above function f(x) is 2.
The graph of the line passes via points (-1, 1) and (0, 4)
So using slope formula,
m1 = (4-1)/(0-(-1))
m1 = 3
This means that the pace of change of function shown on the graph is 3.
This means, the pace of change of function shown on the graph is smaller than the pace of change of function y = 4x + 2
The expression of the function shown on the graph would be y = 3x + 4
The point of incetion of the function shown on the graph is 4.
This signifies that the starting point of the graphed function is higher than the starting point of the function y = 4x + 2.
As a result, the accurate statement comparing the function displayed on this graph to the function y=4x + 2 is 'The function shown on the graph has a lesser rate of change, but a higher beginning point.'
The correct answer is option (A)
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Twenty-two people have hair 2.5 inches long and twenty-eight people have hair 5.7 inches long. What is the average hair length of all the people detailed? A. 4.29 B. 5.10 C. 4.92 D. 4.57
Answer:
A. 4.29
Step-by-step explanation:
The average of a set of numbers is the sum of the numbers divided by the total numbers present.
Sum of numbers: Instead of having to write out 2.5 twenty-two times and 5.7 twenty-eight times, we can remember that adding 2.5 twenty-two times is the same as multiplying 2.5 and 22 while adding 5.7 twenty-eight times is the same as multiplying 5.7 and 28. Thus, our numerator for the average is (2.5 * 22) + (5.7 * 28)
Total number of people: We know that there are 50 people in all since 22 + 28 = 50. Thus, our denominator for the average is 50
Average: We divide our numerator by our denominator and simplify to find our average:
Average = ((2.5 * 22 + (5.7 * 28)) / 50
Average = (55 + 159.6) / 50
Average = 214.6 / 50
Average = 4.292
Average = 4.29
Thus, the average and our answer is A. 4.29
Research shows that 14.3% of persons 20–25 years old vote and 59.9% of persons 60–65 years old vote. What is the absolute increase from the younger group to the older group, to the nearest point?
76 points
319 points
-46 points
46 points
The absolute increase from the younger group to the older group is 59.9% - 14.3% = 45.6%. Rounding to the nearest point, the answer is 46 points.
The absolute increase is the difference between two values, regardless of the direction of change. In this case, we want to find the absolute increase in the percentage of people who vote from the younger group (20-25 years old) to the older group (60-65 years old).
To find the absolute increase, we subtract the percentage of people who vote in the younger group from the percentage of people who vote in the older group, taking the absolute value of the result.
So, the absolute increase in the percentage of people who vote from the younger group to the older group is:
|59.9% - 14.3%| = 45.6%
This means that the percentage of people who vote in the older group is 46 percentage points higher than the percentage of people who vote in the younger group.
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A multiple choice question has five Anne’ answer options of which two options are correct what is the probability of randomly choosing the correct pair of answer options
Answer:
1/10
Step-by-step explanation:
2/5 * 1/4 = 2/20 = 1/10
2 right answers, 5 possible choices
Select one right choice = 2/5
After selecting one right choice, there are 4 possible choices with one more right choice left.
Select another right choice = 1/4
gcd of 120 70 and 30 using prime factorisation
The greatest common divisor of 120, 70, and 30 using prime factorization is 10.
How to find the greatest common divisorTo find the greatest common divisor (GCD) of 120, 70, and 30 using prime factorization we need to first express each number as a product of its prime factors.
Prime factorization of 120
2³ × 3 × 5
Prime factorization of 70
= 2 × 5 × 7
Prime factorization of 30
= 2 × 3 × 5
common prime factors among the three numbers
common prime factors
= 2 × 5
= 10
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(1) 6/6 ✓ (2) 4- 12 cm 9 cm The shape below is made from 4 of these triangles. 15 cm, Work out the area of the shape. Diagram NOT accurately drawn 888 Diagram NOT accurately drawn Onk 20 21-1744-8 30x4+2=6 (7+7)+2-
The perimeter of this solid is 72 cm.
How to calculate the perimeter of this triangle?In Mathematics and Geometry, the perimeter of a triangle can be calculated by using this mathematical equation:
P = a + b + c
Where:
P represents the perimeter of a triangle.a, b, and c represents the side lengths of a triangle.Since the shape was formed by combining four (4) of these triangles, we can logically deduce the following side lengths;
Side length = 12 - 9 = 15 - 12
Side length = 3 cm.
Therefore, the perimeter of this solid can be calculated as follows;
Perimeter of solid = 4(15) + 4(3)
Perimeter of solid = 60 + 12
Perimeter of solid = 72 cm.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
COVID Vaccines As of March 2022, in the United States, 127 million people aged 12 years and older have been vaccinated for COVID (the first full sequence plus one booster) and 38 million have not (Source: How to Compare COVID Deaths for Vaccinated and Unvaccinated People - Scientific American). For those vaccinated, there have been an average of 261 deaths per week and for those who have not, there have been an average of 383 deaths per week. Assume that those data are correct for the past week (so the proportion of vaccinated deaths is 261/127,000,000 and unvaccinated is 383/38,000,000).
1. Which group can be considered the placebo group? Why is it important to have a placebo group? What other factors are important in designing a study like this?
2. What are the conditions that must be met to perform a hypothesis test comparing the vaccinated to the placebo group? Were they met?
3. Regardless of your answer in Part 2, test the hypothesis that the vaccine was effective in reducing the number of deaths from COVID. Use = 0.01 and make sure you state your null and alternative hypotheses and write a sentence stating your conclusion
This question involves statistical analysis and hypothesis testing, and the provided information does not contain all the necessary information to answer the questions fully and accurately. However, I can provide some general guidance on hypothesis testing and the factors to consider when designing a study.
It is not appropriate to refer to the vaccinated group as the placebo group. A placebo group is a group that receives a treatment that is inactive or does not contain the active ingredient being tested, while the treatment group receives the active treatment. In the case of the COVID vaccine, the treatment group is the group that received the vaccine, while the control group would be the group that did not receive the vaccine. In this scenario, it is important to have a control group to compare the effectiveness of the vaccine to the effectiveness of no intervention.
Other important factors to consider when designing a study include sample size, randomization, blinding, and the choice of outcome measures. These factors help to reduce bias and ensure that the results are generalizable to the target population.
To perform a hypothesis test comparing the vaccinated group to the control group, the following conditions must typically be met: the samples are independent, the samples are randomly selected from their respective populations, and the samples are normally distributed (or the sample size is large enough, typically n > 30). Additionally, the variances of the two populations should be assumed to be equal unless there is strong evidence to the contrary.
Assuming the conditions for performing a hypothesis test are met, the null hypothesis (H0) is that there is no difference in the number of deaths from COVID between the vaccinated group and the unvaccinated group, while the alternative hypothesis (Ha) is that the vaccine is effective in reducing the number of deaths from COVID. A two-sample t-test can be used to test whether the means of the two groups are significantly different. If the p-value is less than the significance level (alpha) of 0.01, the null hypothesis can be rejected in favor of the alternative hypothesis, and it can be concluded that the vaccine is effective in reducing the number of deaths from COVID.
Once again, please note that the information provided may not be sufficient to provide an accurate analysis of this question, and further information may be necessary to perform an appropriate hypothesis test and draw meaningful conclusions.
Select all the sets of transformations that result in the same image when performed in any order. Select 3 choices.
A. translation, dilation with center (0,0)
B. two translations.
C. vertical translations, reflection over the y-axis.
D. refelction over the y-axis, dilation with center (2,2)
E. two reflections over the x-axis
The commutative sets of transformations are two translations, refelction over the y-axis, dilation with center (2,2) and two reflections over the x-axis. B, D, and E.
The sets of transformations that result in the same image when performed in any order are called "commutative."
A set of transformations is commutative if the order of the transformations doesn't matter;
Performing the transformations in a different order still results in the same final image.
Based on this definition can select the commutative sets of transformations from the given choices:
Translation and dilation with center (0,0) are not commutative.
The order of the transformations matters.
Two translations are commutative.
The order of the transformations doesn't matter.
Vertical translations and reflection over the y-axis are not commutative. The order of the transformations matters.
Reflection over the y-axis and dilation with center (2,2) are commutative.
The order of the transformations doesn't matter.
Two reflections over the x-axis are commutative.
The order of the transformations doesn't matter.
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Graph the line with slope -1 passing through the point (-4,-5) .
The equation of line is y = -x - 9 which passes through the point Z(-4,-5)
Given data ,
To graph the line with a slope of -1 passing through the point (-4, -5), we can use the point-slope form of a linear equation:
Now , the value of A is
Let the line passes through the point P ( -4 , -5 )
The slope which is the rate of change is is m=-1
y-y₁ = m(x-x₁)
On simplifying , we get
y-(-5) = (-1)(x+4)
Expanding the brackets:
y + 5 = -x - 4
y = -x - 9
Now we have the equation in slope-intercept form. To graph the line, we can plot the given point (-4, -5) and use the slope to find additional points.
Hence , the equation of line is y = -x + 1
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Which of the following function pairs are inverses?
Question 3 options:
A)
B)
C)
f (x) = x2 – 16 and g(x) = x – 4
D)
The function pairs that are inverses are:
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
To determine if two functions are inverses, we need to check if applying one function and then the other function will return the original input.
Let's go through each option:
A) f(x) = -2x and g(x) = (1/2)x
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f((1/2)x) = -2(1/2)x = -x
Since f(g(x)) = -x ≠ x, these functions are not inverses.
B) f(x) = 4x² and g(x) = √x
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f(√x) = 4(√x)² = 4x
Since f(g(x)) = 4x = x, these functions are not inverses.
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f((x + 3)/5) = 5((x + 3)/5) - 3 = x + 3 - 3 = x
Since f(g(x)) = x, these functions are inverses.
D) f(x) = x² - 16 and g(x) = x - 4
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f(x - 4) = (x - 4)² - 16 = x² - 8x + 16 - 16 = x² - 8x
Since f(g(x)) = x² - 8x ≠ x, these functions are not inverses.
Based on the analysis above, the function pairs that are inverses are:
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
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The complete question:
Which of the following function pairs are inverses?
A) f(r) = -2x and g(x) = (1/2)x
B) f() = 4x² and g(x) = √x.
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
D) f(x) =x² - 16 and g(x) = x - 4
6) Stacy ran 8 miles. She
recorded how long it took her to run each mile in minutes. How many total minutes did it take Stacy to run the 8 miles?
Answer Options
36 1/2
72 1/2
81
54 1/4
Answer:
72 1/2
Step-by-step explanation:
so, she ran 2 miles in 8 3/4 minutes each.
3 miles in 9 minutes each.
2 miles in 9 1/4 minutes each.
1 mile in 9 1/2 = 9 2/4 minutes.
in total that means
2×(8 3/4) + 3×9 + 2×(9 1/4) + 9 2/4 =
= 16 6/4 + 27 + 18 2/4 + 9 2/4 =
= 16 + 27 + 18 + 9 + 6/4 + 2/4 + 2/4 =
= 70 + 10/4 = 70 + 2 + 2/4 = 72 2/4 = 72 1/2 minutes
Share #5000 in the ratio of #2000 to #3000 among John and chinedu what percentage of the money does each boy Receive.
HELP ME PLEASE I DON’T UNDERSTAND!!
3a. 60
3b. 4
3c. It means that the individual speeds of the trucks are pretty close to the mean.
4. The temperature is not very consistent.
5. The values in the data set are close together, and the mean is pretty consistent.
6. Evelyn and Nova are correct
Pls give brainliest
Answer:
3a. 60
3b. 4
3c. represents the difference in speed from the mean, or data is close to mean
4. The temps are not consistent, data varies a lot
5. It means that the data does not vary much, data is basically exactly the same as the mean.
6. evelyn, nova
the ratio of 2/3 to 8 as a fraction in simplest form
To write the ratio of 2/3 to 8 as a fraction in simplest form, we need to divide the numerator and denominator by their greatest common factor (GCF).The GCF of 2 and 8 is 2.So, we divide both the numerator and denominator by 2:2/3 ÷ 8/1 = (2/3) ÷ (8/1) = 2/3 x 1/8 = (2 x 1) / (3 x 8) = 2/24Now, we can simplify the fraction by dividing the numerator and denominator by their greatest common factor again.The GCF of 2 and 24 is 2.So, we divide both the numerator and denominator by 2:2/24 ÷ 2/2 = (2/24) ÷ (2/2) = 2/24 x 1/2 = (2 x 1) / (24 x 2) = 1/12Therefore, the ratio of 2/3 to 8 as a fraction in simplest form is 1/12.
Answer:
How to find Ratio?
Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10
In order to find the ratio of a certain number to another number or the relation of each other, we also need to know the concept of fraction and percentage.
1/12 or 1 to 12
The ratio is 2/3*8=23⋅8=2/24=1/12
So it is 1 to 12
MARK AS BRAINLIEST!
Will Give Brainliest Please Help!
Answer:
Corresponding angles is the answer to your question
Find the quotient and remainder using synthetic division.
x^4
-
3
x^3
+
9
x
+
6/
x
+
1
The quotient is
The remainder is
what is 1000 - 5000 +7
Answer:
-3993
Step-by-step explanation:
The density in gold is 27.2 grams per cm. A gold gar in the shape of a rectengular prism, has a length of 23.5 and a width of 28 cm. The mass of the entire bar is 43,892.5 grams. What is the height of the bar?
Answer:2.381 cm.
Step-by-step explanation:
The volume of the gold bar can be calculated using the formula for the volume of a rectangular prism:
Volume = Length x Width x Height
We know the length and width of the bar, so we can substitute those values:
Volume = 23.5 cm x 28 cm x Height
We can then solve for the height by rearranging the equation:
Height = Volume / (Length x Width)
To find the volume, we can use the density of gold and the mass of the bar:
Density = Mass / Volume
Volume = Mass / Density
Substituting the values we have:
Volume = 43,892.5 g / 27.2 g/cm³
Volume = 1610.049 cm³
Now we can substitute the volume into the equation we derived earlier to solve for the height:
Height = 1610.049 cm³ / (23.5 cm x 28 cm)
Height = 2.381 cm
Therefore, the height of the gold bar is approximately 2.381 cm.
DO THE MATH: Billie offers a product for $40 with free shipping. But the shipping is in reality $15 per unit of the product sold. What is the actual selling price of the product, not including shipping costs?
$55
$35
$25
$15
factor each expression completely
please help me asap becasue I need this for math home work due today.
8n^2+68n+84
Step-by-step explanation:
Sometimes it is hard to 'see' the factorization....so you can take the HCF out of the three terms to perhaps see it better:
Factor out a '4'
4* ( 2n^2 + 17n + 21 )
4 ( 2n +3 )(n +7 ) DONE.
The probability that a machine will produce
all bolts in a production run within
specification is 0.998. A sample of 8
machines is taken at random then the
probability that 7 or 8 machines is:
Select one:
O
a. 0.9999
b. 0.9841
c. 1
d. 0.8
The probability that 7 or 8 machines will produce all bolts within specification is approximately 0.9841.
Using the binomial distribution formula, we get:
P(X = 7) = (8 choose 7) * (0.002)⁷ * (0.998)¹ ≈ 0.0081
P(X = 8) = (8 choose 8) * (0.002)⁸ * (0.998)⁰ ≈ 0.000003
Therefore, P(X = 7) + P(X = 8) ≈ 0.0081 + 0.000003 ≈ 0.9841.
Probability is a branch of mathematics that deals with the study of the likelihood of occurrence of events or outcomes in situations where there is uncertainty or randomness. It is a measure of the degree of uncertainty of an event, typically expressed as a number between 0 and 1. Probability is used to make predictions and decisions in various fields, including science, engineering, economics, finance, and social sciences.
It is based on the analysis of past events or observations, and it enables us to estimate the likelihood of future events or outcomes. Probability theory provides a mathematical framework for modeling and analyzing random phenomena and helps us understand the laws of chance that govern various natural and artificial systems.
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NEED HELP ASAP!! WILL MARK BRAINLEST!!! PLS DONT GUESS IF YOU DONT KNOW!!
Answer:
it is A
Step-by-step explanation:
def correct! a+ student
Answer: D
Step-by-step explanation:
The answer has to be A or D because they're the only ones that look like real box-and-whisker plots. The mean is the line in the middle of the "box", so calculating the mean should be easy enough.
Add all the numbers together and then divided by the number of numbers.
56+72+75+98+73+86+48+95+69+88+75+92 = 972
There are 12 numbers.
972/12 = 77.25
Only option D represents the proper mean.
an artist made a fine of stainless steel, then sliced it into three pieces. what is the volume of the largest piece? PLEASE HELP I WILL MARK YOU BRAINLIEST
The volume of the largest piece is given as follows:
V = 10603 cm³.
How to obtain the volume?The volume of a cone of radius r and height h is given by the equation presented as follows:
V = πr²h/3.
The dimensions for the largest piece in this problem are given as follows:
r = 15 cm -> as the diameter is of 30 cm and the radius is half the diameter.h = 3 x 15 = 45 cm.Hence the volume of the largest piece is given as follows:
V = π x 15² x 45/3
V = 10603 cm³.
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Express 11.454545... as a ratio of two integers.
Write your answer as a fraction in its simplest form.
Given fraction:- 11.454545... can be expressed as the ratio 1155/100. However, this fraction is not in its simplest form because both the numerator and denominator have a common factor of 5. A ratio of two integers in simplest form is 231/20.
Let x = 11.454545...
Multiplying both sides of this equation by 100 gives:
100x = 1145.454545...
Subtracting x from both sides gives:
99x = 1145
Dividing both sides by 99 gives:
x = 11.55
Therefore, 11.454545... can be expressed as the ratio 1155/100. However, this fraction is not in its simplest form because both the numerator and denominator have a common factor of 5. Dividing both the numerator and denominator by 5 gives the simplest form of the fraction:
1155/100 = 231/20
Hence, 11.454545... as a ratio of two integers in simplest form is 231/20.
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A person buys a phone for $88 and signs up for a single-line phone plan with 2000 monthly anytime minutes. The plan costs $118.96 per month. Write an equation that can be used to determine the total cost
C(t) of this phone plan for t months. Then, find the cost for 22 months, assuming that the number of minutes the person uses does not exceed 2000 per month.
Answer: The total cost will be equal to $2839.16. The expression to calculate the total cost is 119.92(m)+81=C(t).
What is an expression?
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a person buys a phone for $81 and signs up for a single-line phone plan with 2000 monthly anytime minutes. The plan costs $119.92 per month.
The expression will be formed as below:-
119.92(m)+81=C(t)
119.92(23)+81=C(t)
2839.16=C(t)
Therefore, the total cost will be equal to $2839.16.
Ana estimated the mass of an object to be 54 grams. The actual mass of the object was 45 grams. What was the percent error in Ana’s estimate.
Answer:
20%
Step-by-step explanation:
percent error = (estimated value - real value)/(real value) × 100%
percent error = (54 - 45)/(45) × 100%
percent error = 0.2 × 100%
percent error = 20%
Type in the parent function for a quadratic equation to make your parabola go through the points shown
The parent function for the quadratic equation is y = x²
How to determine the parent function for the quadratic equationFrom the question, we have the following parameters that can be used in our computation:
The graph
From the graph, we have the following points
vertex = (0, 0)
Points = (±1, 1) and (±2, 4)
The equation for the quadratic function is represented as
y = a(x - h)² + k
Where vertex = (h, k)
So, we have
y = a(x - 0)² + 0
Evaluate
y = ax²
Using the points, we have
a(1)² = 1
Evaluate
a = 1
So, we have
y = x²
Hence, the parent function for the quadratic equation is y = x²
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HELPPPP I NEED HELP PLEASE IT'S MATH
Answer:
b. 5, 11, 6
Step-by-step explanation:
Let the sides of a triangle be a, b, and c, where a < b < c. Then, we know that a + b > c. If we use this identity to solve this problem, then we can find that answer choice b does not satisfy it. Thus, b does NOT have the lengths of a triangle.
Use the distributive property to remove the parentheses.
-5(- 6w + 2u -5)
The value of solution of the expression is,
⇒ - 5 (- 6w + 2u - 5)
Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Expression is,
⇒ - 5 (- 6w + 2u - 5)
Now, By using distributive property we get;
⇒ - 5 (- 6w + 2u - 5)
⇒ - 5 × - 6w - 5 × 2u - 5 × - 5
⇒ 30w - 10u + 25
Thus, The value of solution of the expression is,
⇒ - 5 (- 6w + 2u - 5)
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