Find the range from the ordered pair {(1, 2), (2, 3), (3, 4), (4, 5)}
Answer:
Range { 2,3,4,5}
Step-by-step explanation:
The range is the output values
Range { 2,3,4,5}
if the average of b and c is 8, and d=3b-4, what is the average of c and d in terms of b?
[tex] \underline{ \huge \mathcal{ Ànswér} } \huge: - [/tex]
Average of b and c is 8, that is
[tex]➢ \: \: \dfrac{b + c}{2} = 8[/tex]
[tex]➢ \: \: b + c = 16[/tex]
[tex]➢ \: \: c = 16 - b[/tex]
now let's solve for average of c and d :
[tex]➢ \: \: \dfrac{c + d}{2} [/tex]
[tex]➢ \: \: \dfrac{16 - b + 3b - 4}{2} [/tex]
[tex]➢ \: \: \dfrac{12 + 2b}{2} [/tex]
[tex]➢ \: \: \dfrac{2(6 + b)}{2} [/tex]
[tex]➢ \: \: b + 6[/tex]
Therefore, the average of c and d, in terms of b is : -
[tex] \large \boxed{ \boxed{b + 6}}[/tex]
[tex]\mathrm{✌TeeNForeveR✌}[/tex]
Answer:
b+6
Problem:
If the average of b and c is 8, and d=3b-4, what is the average of c and d in terms of b?
Step-by-step explanation:
We are given (b+c)/2=8 and d=3b-4.
We are asked to find (c+d)/2 in terms of variable, b.
We need to first solve (b+c)/2=8 for c.
Multiply both sides by 2: b+c=16.
Subtract b on both sides: c=16-b
Now let's plug in c=16-b and d=3b-4 into (c+d)/2:
([16-b]+[3b-4])/2
Combine like terms:
(12+2b)/2
Divide top and bottom by 2:
(6+1b)/1
Multiplicative identity property applied:
(6+b)/1
Anything divided by 1 is that anything:
(6+b)
6+b
b+6
A trough has ends shaped like isosceles triangles, with width 2 m and height 5 m, and the trough is 18 m long. Water is being pumped into the trough at a rate of 8 m3/min. At what rate (in m/min) does the height of the water change when the water is 2 m deep
9514 1404 393
Answer:
5/9 m/min
Step-by-step explanation:
The depth of the water is 2/5 of the depth of the trough, so the width of the surface will be 2/5 of the width of the trough:
2/5 × 2 m = 4/5 m
Then the surface area of the water is ...
A = LW = (18 m)(4/5 m) = 14.4 m²
The rate of change of height multiplied by the area gives the rate of change of volume:
8 m³/min = (14.4 m²)(h')
h' = (8 m³/min)/(14.4 m²) = 5/9 m/min
Which of the following is the point and slope of the equation y + 14 = 7(x - 18)?
Answer:
y = 7x - 140
The slope is 7
The y-intersept is -140
= (7, -140)
Step-by-step explanation:
y + 14 = 7(x - 18)
y + 14 = 7x - 126
y =7x - 126 - 14
y = 7x - 140
What is the solution to the inequality -6+|2p+3| > 7
Step-by-step explanation:
you're going to have to set up two expressions since it's an absolute value problem
Select the correct answer.
Which is the minimum or maximum value of the given function?
dndnsn
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the function is not given. So, I will make an assumption.
A quadratic function is represented as:
[tex]f(x) = ax^2 + bx + c[/tex]
If [tex]a > 0[/tex], then the function has a minimum x value
E.g. [tex]f(x) = 4x^2 - 5x + 8[/tex] ------ [tex]4 > 0[/tex]
Else, then the function has a maximum x value
E.g. [tex]f(x)= -4x^2 -5x + 8[/tex] ---- [tex]-4 < 0[/tex]
The maximum or minimum x value is calculated using:
[tex]x = -\frac{b}{2a}[/tex]
For instance, the maximum of [tex]f(x)= -4x^2 -5x + 8[/tex] is:
[tex]x = -\frac{-5}{2*-4}[/tex]
[tex]x = -\frac{5}{8}[/tex]
So, the maximum of the function is:
[tex]f(x)= -4x^2 -5x + 8[/tex]
[tex]f(-\frac{5}{8}) = -4 * (-\frac{5}{8})^2 - 5 *(-\frac{5}{8}) +8[/tex]
[tex]f(-\frac{5}{8}) = 9.5625[/tex]
What is the value of the expression (2x + y) (2x - y) when x = 4 and y = -5?
Answer:
39
Step-by-step explanation:
1. (2(4)-5)(2(4)+5)
2.(3)(13)
3.39
Answer:
Step-by-step explanation:
This is a difference of squares question. You should 64 = 25 = 39 Let's see if that happens.
Difference of squares
(2x - y) ( 2x + y) = 4x^2 - y^2
4(4)^2 - (5)^2
64 - 25 = 39
Now do the question exactly as it is written.
(2*4 - -5)(2*4 + -5)
(8 +5)(8 - 5)
3 * 13
39
They really do give the same answer.
Yanni read 24 pages of
a book. 1 of the book is
still left to read. How many
pages are there in the
whole book?
79
Work out the circumference of this circle.
Take a to be 3.142 and write down all the digits given by your calculator.
14 cm
Answer: 43.988
Step-by-step explanation: The formula for the circumference of a circle is the diameter multiplied by pi. Since the diameter is 14 and it is telling us to use 3.142 as pi, we can multiply the two and get the answer.
Michael drove 210 miles in 3 1/2. Jordan drove 330 miles in 6 hours. Which is an accurate comparison of the rates at which the two people drove?
Michael = 210 / 3.5 = 60 miles per hour
Jordan = 330/ 6 =55 miles per hour
Jordan drove 5 miles per hour slower than michael
Find the slope of the line #67
What is the value of y?
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Answer:
(d) 2
Step-by-step explanation:
The parallel lines divide the transversals proportionally, so we have ...
3y/3 = 2y/y
y = 2 . . . . . . . . . simplify (assuming y ≠ 0)
A random sample of n1 = 296 voters registered in the state of California showed that 146 voted in the last general election. A random sample of n2 = 215 registered voters in the state of Colorado showed that 127 voted in the most recent general election. Do these data indicate that the population proportion of voter turnout in Colorado is higher than that in California? Use a 5% level of significance.
Answer:
The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
California:
Sample of 296 voters, 146 voted. This means that:
[tex]p_{Ca} = \frac{146}{296} = 0.4932[/tex]
[tex]s_{Ca} = \sqrt{\frac{0.4932*0.5068}{296}} = 0.0291[/tex]
Colorado:
Sample of 215 voters, 127 voted. This means that:
[tex]p_{Co} = \frac{127}{215} = 0.5907[/tex]
[tex]s_{Co} = \sqrt{\frac{0.5907*0.4093}{215}} = 0.0335[/tex]
Test if the population proportion of voter turnout in Colorado is higher than that in California:
At the null hypothesis, we test if it is not higher, that is, the subtraction of the proportions is at most 0. So
[tex]H_0: p_{Co} - p_{Ca} \leq 0[/tex]
At the alternative hypothesis, we test if it is higher, that is, the subtraction of the proportions is greater than 0. So
[tex]H_1: p_{Co} - p_{Ca} > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples:
[tex]X = p_{Co} - p_{Ca} = 0.5907 - 0.4932 = 0.0975[/tex]
[tex]s = \sqrt{s_{Co}^2+s_{Ca}^2} = \sqrt{0.0291^2+0.0335^2} = 0.0444[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.0975 - 0}{0.0444}[/tex]
[tex]z = 2.2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference above 0.0975, which is 1 subtracted by the p-value of z = 2.2.
Looking at the z-table, z = 2.2 has a p-value of 0.9861.
1 - 0.9861 = 0.0139.
The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.
What is the area of the given triangle? Round to the nearest tenth
Answer:
28.0125 cm^2 rounded to 28.0 cm^2
Step-by-step explanation:
Area = a*b*sin(c)*1/2
Area = 7 * 13 * sin(38) * 1/2
Area = 91/2 * 0.61566...
Area = 28.0125...
Britany wants to read a book. In her room, she has 5 mysteries, 15 historical fictions, 12 modern fantasies, and 7 blographies.
How many different choices are available?
pleaseee
Answer:
39
Step-by-step explanation:
5 + 15 + 12 + 7 = 39
Answer:
39
Step-by-step explanation:
5 + 15 = 20, 12 + 7 = 19, 20 + 19 = 39.
A group of 120 students were surveyed about their interest in a new International Studies program. Interest was measured in terms of high, medium, or low. 30 students responded high interest; 50 students responded medium interest; 40 students responded low interest. What is the relative frequency of students with high interest? A. 30% B. 36.4% C. 25% D. Cannot be determined. Group of answer choices
Answer:
Option C (25%) is the correct answer.
Step-by-step explanation:
Given:
Number of students,
= 120
Students responded high interest,
= 30
Students responded medium interest,
= 50
Students responded low interest,
= 40
Now,
The relative frequency will be:
= [tex]\frac{30}{120}[/tex]
= [tex]0.25[/tex]
or,
= [tex]25[/tex]%
Bill works for a large food service company. In one hour he can make 19 sandwiches or he can make 40 salads. Bill works 7 hours per day. If Bill needs to make 30 sandwiches then how many salads can he make
Answer:
[tex]x=216 salads[/tex]
Step-by-step explanation:
One Hour:
Salad=40
Sandwich=19
Total work time[tex]T=7[/tex]
Generally
Time to make 30 sandwiches is
[tex]T_s=\frac{30}{19}[/tex]
[tex]T-s=1.6hours[/tex]
Therefore
Bill has 7-1.6 hours to make salads and can make x about of salads in
[tex]x=(7-1.6)*40[/tex]
[tex]x=5.4*40[/tex]
[tex]x=216 salads[/tex]
Find the medien: 16,12,10,15,7,9,16
Answer:
12
Step-by-step explanation:
arrange the numbers in ascending order and cross out from either side till you have a middle line
FINAL ANSWER:
12
Step-by-step explanation:
Median is the middle number in the data set.
so first of ... we need to arrange the group of numbers from lower to greater.
16, 12, 10, 15, 7, 9, 16 ⇒ 7, 9, 10, 12, 15, 16, 16
Now that we have arranged the numbers from least to greatest all we need to do is to find the middle number of the data set (data set? they are the group of numbers)
Ok, so what you want to do here is to just count the numbers until you get to the middle number of the data set...
7, 9, 10, 12, 15, 16, 16
the median in the given data set is 12.
I hope this helps you!!! Let me know if my answer is incorrect or not...
HAVE A GREAT DAY AND GOD BLESS YOU ;)!!!
Can someone please help me?
you have to read the bottom link for the answer key
Draw clearly the graph of the linear equation. y=1/2x, where x= (-4 -2, 0, 2, 4)
Answer:
(in attachment)
Step-by-step explanation:
you can find the points by inputting the x-values into the equation to solve for the y-values, then connecting the plotted points to create the line.
When x=-4
y=1/2(-4)
y=-2
(-4,-2)
Repeat for all values.
HELPPPP
what is this
Answer:
Pls be specific with your question
Select the correct statement about what data scientists do during the Data Preparation stage.
a. During the Data Preparation stage, data scientists define the variables to be used in the model.
b. During the Data Preparation stage, data scientists determine the timing of events.
c. During the Data Preparation stage, data scientists aggregate the data and merge them from different sources.
d. During the Data Preparation stage, data scientists identify missing data.
e. All of the above statements are correct.
Answer:
e. All of the above statements are correct.
Option e is correct. All of the above statements are correct.
What is Data science?Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processes, algorithms and systems to extract or extrapolate knowledge and insights from noisy, structured and unstructured data
Data Scientist makes value out of data, he is expert in various tools and technologies like machine learning, deep learning, artificial intelligence and he solve business problems by presenting a model to predict business future.
During data preparation, data scientists and DBAs aggregate the data and merge them from different sources. During data preparation, data scientists and DBAs define the variables to be used in the model.
Hence, All of the above statements are correct, Option e is correct.
To learn more on Data science click:
https://brainly.com/question/20815848
#SPJ5
The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds. For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23. Find the P-value of the test statistic.
Answer:
The p-value of the test statistic is 0.2019.
Step-by-step explanation:
Test if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds.
At the null hypothesis, we test if it relieves pain in at most 384 seconds, that is:
[tex]H_0: \mu \leq 384[/tex]
At the alternative hypothesis, we test if it relieves pain in more than 384 seconds, that is:
[tex]H_1: \mu > 384[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
384 is tested at the null hypothesis:
This means that [tex]\mu = 384[/tex]
For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23.
This means that [tex]n = 41, X = 387, \sigma = 23[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{387 - 384}{\frac{23}{\sqrt{41}}}[/tex]
[tex]z = 0.835[/tex]
P-value of the test:
The p-value of the test is the probability of finding a sample mean above 387, which is 1 subtracted by the p-value of z = 0.835.
Looking at the z-table, z = 0.835 has a p-value of 0.7981.
1 - 0.7981 = 0.2019
The p-value of the test statistic is 0.2019.
Help I’ll mark you!!
Answer:
A.
Step-by-step explanation:
Each mark is worth two. We are inbetween the first mark and 0 on the left. Half of two is one. and since we are in the left quadrant we know it to be negative. Looking down, we see that we are exactly one mark down. As a mark is two, ans that we are going down, this will be a negative two. That leaves us with the answer of (-1, -2)
Answer:
A. (-1,-2)
Step-by-step explanation:
just trust me...I promise it right
57 117find x triangle
Answer:
60
Step-by-step explanation:
x = 180 - [ 57 + ( 180 - 117 ) ]
= 180 - [ 57 + 63 ]
= 180 - 120
x = 60
The wholesale price of 6 oz plastic bottles is 6 cents how many plastic bottles can be purchased for $98.41
Answer:
1640
Step-by-step explanation:
Take the total amount and divide by the amount for one
Make sure to write 6 cent in dollar form (.06)
98.41 / .06
1640.1666
Round down since we need to buy whole bottles
1640
HELPPP PLEASE ASAP!!! I don’t know how to solve this problem nor where to start? Can some please help me out and explain how you got the answer please. Thank you for your time.
Step-by-step explanation:
Count the number of times you have to move the decimal point to the right until it is to the right of the 1st nonzero number.
a) You have to move the decimal point 11 times until it gets to the right of the 1st nonzero number, which is 7. You then rewrite this number as
[tex]7.2×10^{-11}[/tex]
The exponent of 10 is a negative number because you moved the decimal point to the right.
b) Similarly, you have to move the point 9 times to the right so the answer is
[tex]9.5×10^{-9}[/tex]
a study of patients who were overweight found that 53% also had elevated blood pressure. If 3 overweight patients are selected find the probability that all three have elevated blood pressure
Answer:
14.8%
Step-by-step explanation:
53/100*53/100*53/100
Suppose 50.7 liters of water came out of a faucet today. If 2.6 liters of water come out each minute, for how many minutes was the faucet on?
Simplify: 3.5 x 10^-2 + 2.3 x 10^-2
Given:
The given expression is:
[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]
It can be written as:
[tex]=(3.5+2.3)\times 10^{-2}[/tex]
[tex]=5.8\times 10^{-2}[/tex]
Therefore, the simplified form of the given expression is [tex]5.8\times 10^{-2}[/tex].
