Answer:
1/6
Step-by-step explanation:
There are 6 CD
P( song from 6th ) = number of CD's that are 6th/ total
= 1/6
4x – 8 + 6x – 12 = 10
Step-by-step explanation:
4x+6x-8-12=10
10x-20=10
10x=10+20
10x=30
x=3
Answer:
x=3
Step-by-step explanation:
to find X first find the like terms
like terms: 4x and 6x
like terms: -12 and -8
combine the like the like terms
4x+6x=10x
-12-8=-20
10x-20=10
add 20 on both sides
10x-20+20=10+20
10x=30
divide both sides by 10
10x/10=30/10
x=3
ANSWER CHECK
substitute the variable
4(3) – 8 + 6(3) – 12 = 10
12-8+18-12
4+18-12
22-12 = 10
10=10
Elena's mother asked her to add a half-cup of water to the beans.
How many ounces of water did Elena add?
Answer:
4 oz
Step-by-step explanation:
one cup is 8 oz
1/2 cup is 8/2 oz which is 4 oz
Answer:
4 fluid ounces
Step-by-step explanation:
One cup is 8 oz so we would have to divide 8 by 2 to get 4 because one half of 8 is 4.
Formulate the situation as a linear programming problem by identifying the variables, the objective function, and the constraints. Be sure to state clearly the meaning of each variable. Determine whether a solution exists, and if it does, find it. State your final answer in terms of the original question. A rancher raises goats and llamas on his 400-acre ranch. Each goat needs 2 acres of land and requires $100 of veterinary care per year, and each llama needs 5 acres of land and requires $80 of veterinary care per year. The rancher can afford no more than $13,200 for veterinary care this year. If the expected profit is $84 for each goat and $126 for each llama, how many of each animal should he raise to obtain the greatest possible profit? The rancher should raise goats and llamas for a maximum profit of $________
Answer:
zero goats and 120 Ilamas to get profit of $15,120
Step-by-step explanation:
Goats: G
Ilamas: l
Explicit constraints:
2G + 5l ≤ 400
100G+ 80l≤ 13,200
Implicit constraints
G≥0
I≥0
P= 84G+ 126l
See attachment for optimal area
substituting coordinats of optimal region in profit equation to get profit
When G= 132, l=0
P=84(132) + 126(0)
P=11,088
When G=0, l=120
P=84(0)+ 126(120)
P = 15120
When G= 100, l=40
P=84(100)+126(40)
P=13440
Dayson is covering a package in the shape of a rectangular prism with wrapping paper. The package is 50 centimeters by 20 centimeters by 18 centimeters. He has 1 square meter of wrapping paper. Can he completely cover the package with wrapping paper? Complete the explanation to show your answer.
Answer:
Yes, Dayson can completely cover the package with wrapping paper.
Step-by-step explanation:
Given: The rectangular prism is 50 centimeters by 20 centimeters by 18 centimeters.
Area of wrapping paper is 1 square meter.
To find: whether he can completely cover the package with wrapping paper
Solution:
Total surface area of the rectangular prism = 2(lb + bh +hl)
where l denotes length, b denotes breadth and h denotes height
Total surface area of the rectangular prism = [tex]2\left [ (50)(20)+(20)(18)+(18)(50) \right ][/tex]
[tex]=2\left ( 1000+360+900 \right )\\=2(2260)\\=4520\,\,cm^2[/tex]
As [tex]1\,m^2=10000\,cm^2[/tex],
Total surface area of the rectangular prism = [tex]4520\,cm^2=0.4520\,m^2[/tex]
As Dayson has [tex]1\,m^2> 0.4520\,m^2[/tex] of wrapping paper, he can completely cover the package with wrapping paper.
You do a study of hypnotherapy to determine how effective it is in increasing the number of hours of sleep subjects get each night. You measure hours of sleep for 12 subjects with the following results. Construct a 95% confidence interval for the mean number of hours slept for the population (assumed normal) from which you took the data AND determine the margin of error EBM.
DATA: 8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5
Answer:
Confidence interval
[tex]8.98-2.2\frac{1.29}{\sqrt{12}}=8.16[/tex]
[tex]8.98+2.2\frac{1.29}{\sqrt{12}}=9.80[/tex]
And the margin of error would be:
[tex] ME=2.2\frac{1.29}{\sqrt{12}}=0.819[/tex]
Step-by-step explanation:
For this case we have the followig dataset:
DATA: 8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5
We can calculate the mean and the deviation with the following formulas:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex] \bar X= 8.98[/tex
[tex]s = 1.29[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=12-1=11[/tex]
The Confidence level is 0.95 or 95%, the value of significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]t_{\alpha/2}=2.20[/tex]
Repplacing the info we got:
[tex]8.98-2.2\frac{1.29}{\sqrt{12}}=8.16[/tex]
[tex]8.98+2.2\frac{1.29}{\sqrt{12}}=9.80[/tex] And the margin of error would be:
[tex] ME=2.2\frac{1.29}{\sqrt{12}}=0.819[/tex]
The 95% confidence interval is [tex]\mathbf{ (8.17,9.79)}[/tex], and the margin of error is 0.81
The dataset is given as:
[tex]\mathbf{x= 8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5}[/tex]
Start by calculating the sample mean
This is calculated as:
[tex]\mathbf{\bar x = \frac{\sum x}{n}}[/tex]
[tex]\mathbf{\bar x= \frac{8.2+ 9.1+ 7.7+ 8.6+ 6.9+11.2+ 10.1+ 9.9+ 8.9+ 9.2+ 7.5+ 10.5}{12}}[/tex]
[tex]\mathbf{\bar x= \frac{107.8}{12}}[/tex]
[tex]\mathbf{\bar x= 8.98}[/tex]
Next, calculate the sample standard deviation
This is calculated as:
[tex]\mathbf{\sigma_x = \sqrt{\frac{\sum (x - \bar x)^2}{n-1}}}[/tex]
[tex]\mathbf{\sigma_x= \sqrt{\frac{(8.2 - 8.89)^2 +.......... + (10.5- 8.89)^2}{12 - 1}}}[/tex]
[tex]\mathbf{\sigma_x= 1.29}[/tex]
Calculate the degrees of freedom
[tex]\mathbf{df = n - 1}[/tex]
[tex]\mathbf{df = 12 - 1}[/tex]
[tex]\mathbf{df = 11}[/tex]
Calculate the significance level
[tex]\mathbf{\alpha /2=\frac{1 - 95\%}2 = 0.025}[/tex]
The critical value at [tex]\mathbf{\alpha/2 = 0.025}[/tex] and df = 11 is:
[tex]\mathbf{t_{\alpha/2} = 2.20}[/tex]
Calculate the margin of error
[tex]\mathbf{E = t_{\alpha/2} \frac{\sigma}{\sqrt n}}[/tex]
So, we have:
[tex]\mathbf{E = 2.20 \times \frac{1.29}{\sqrt{12}}}[/tex]
[tex]\mathbf{E = 0.81}[/tex]
The confidence interval is then calculated as:
[tex]\mathbf{CI =\bar x \pm E}[/tex]
So, we have:
[tex]\mathbf{CI = 8.98 \pm 0.81}}[/tex]
Split
[tex]\mathbf{CI = (8.98 - 0.81,8.98 + 0.81)}[/tex]
[tex]\mathbf{CI = (8.17,9.79)}[/tex]
So, the 95% confidence interval is [tex]\mathbf{ (8.17,9.79)}[/tex], and the margin of error is 0.81
Read more about confidence intervals and margin of errors at:
https://brainly.com/question/19426829
For a statistics class project, a college student randomly samples 75 men who exercise at a gym regularly and 68 women who exercise at a gym regularly. The college student believes that on average men spend more time at the gym each week. The college student records the number of minutes each person exercises in a given week. The college student conducts a hypothesis test at the 5% significance level. Use the summary statistics below to conduct a hypothesis test using your calculator or calculator
Answer:
Step-by-step explanation:
The record of the statistics and the summary statistics which are the missing files in the question are attached below.
From the given information:
The null hypothesis and the alternative hypothesis can be represented by :
[tex]\mathbf{H_o:}[/tex] There is no difference between the average time spend by men and women at gym each week
[tex]\mathbf{H_i:}[/tex] The average time spend by men is greater than the average time spend by women at the gym each week
From the summary statistics in the attached file below:
The p-value = 0.3253
Level of significance = 5% = 0.05
Therefore; it is obvious that the p-value is greater than the level of significance i.e (0.3253 > 0.05)
Hence; there is no enough evidence to reject the null hypothesis
CONCLUSION: We conclude that the mean number of minutes exercised per week is larger for men than women at the this gym.
Please help! Correct answer only, please! Find the product A · A^t A. B. C. D.
Answer: choice A
Step-by-step explanation:
the transposed matrix would be
5 3
2 -1
so
5*5+2*2=29
3*5+2*-1=13
5*3-2*-1=13
3*3+-1*-1=10
which gives us the answer
29 13
13 10
The table below shows the time intervals (hours) it takes people to arrive at a counter at a bus terminal Time (hrs) Number of people 0-0.25 0.25-0.50 0.50-0.75 0.75-1.00 1.00-1.25 1.25-1.50 38 67 50 36 30 29 Use this to answer questions 5 to 8. 5. What is the modal arrival time, correct to 2 decimal places? Answer: hours 6. Find the mean time of arrival in minutes, correct to 3 significant figures? Answer: 7. What is the standard deviation of the data distribution, correct to 2 decimal place? Answer: hours 8. The median time of arrival approximated to 2 decimal places is ... Answer: hours
Answer:
Step-by-step explanation:
5.) here no. of people represent frequencies, so modal group (the group with the highest frequency) is 0.25-0.50.
Estimated Mode = L + (( fm − fm-1) / ( (fm − fm-1) + (fm − fm+1) ) ) × w
where,
L is the lower class boundary of the modal group = 0.25
fm-1 is the frequency of the group before the modal group = 38
fm is the frequency of the modal group = 67
fm+1 is the frequency of the group after the modal group = 50
w is the group width = 0.25
mode= 0.25 + ((67-38)/((67-38)+(67-50)))* 0.25
= 0.25 + (29/ (29+17))*0.25
= 0.25 + 0.63*0.25
= 0.41
6) mean= total(fx) / total(f)
= 166.25/250
= 0.665
7) standard deviation = sqaure root (( total(fx2) - (total(f)* mean2)) / (total(f)-1))
= sqaure root (( 149.906 - 250* 0.6652)/ 249 )
= square root ( (149.906 - 110.556) /249)
= sqaure root (0.158)
= 0.397
8) The median is the middle value, which in our case is the 125 (250/2) , which is in the 0.5 - 0.75 group.
Estimated Median = L + ( ((n/2) − B)/G) × w
where:
L is the lower class boundary of the group containing the median = 0.5
n is the total number of values = 250
B is the cumulative frequency of the groups before the median group = 105
G is the frequency of the median group = 50
w is the group width = 0.25
median = 0.5 + (((250/2)-105)/50)*0.25
= 0.5 + ((125-105)/50)*0.25
= 0.5 + (20/50)*0.25
= 0.6
g(x) = 3x + 3, find g(6).
Answer:
Step-by-step explanation:
g(6) = 3(6) + 3
= 18+3
= 21
What is the midpoint of the line segment with endpoints (3.2,2.5) and (1.6-4.5)?
Answer:
(2.4, -1)
Step-by-step explanation:
To find the midpoints of two points in the format (x,y), we find the mean for the values of x and y.
In this question:
(3.2, 2.5) and (1.6, -4.5)
Mean for the values of x:
(3.2 + 1.6)/2 = 2.4
Mean for the values of y:
(2.5 - 4.5)/2 = -1
Midpoint:
(2.4, -1)
An inlet pipe can fill a tank in 10 minutes. A drain can empty the tank in 12 minutes. If the tank is empty, and both the pipe and drain are open, how long will it take before the tank overflows?
Answer: Total time taken by them would be 60 minutes = 1 hour before the tank overflows.
Step-by-step explanation:
Since we have given that
Time taken by an inlet pipe =10 minutes
Time taken by a drain = 12 minutes
So, if both are open together,
Total work done by them would be
[tex]\dfrac{1}{10}-\dfrac{1}{12}\\\\=\dfrac{6-5}{60}\\\\=\dfrac{1}{60}[/tex]
So, total time taken by them would be 60 minutes = 1 hour before the tank overflows.
verify 10÷(6+4)≠(10÷6)+(10÷4)
Please see attached picture for full solution
Hope it helps
Good luck on your assignment
A loan company charges $30 interest <br />for a one month loan of $500. Find the annual interest they are charging
Answer:
$360
Step-by-step explanation:
If the company charges $30 for $500 in one month.
The interest they will be changing for a year = 30*12 = $360 interest.
It's just simple, multipling the the interest value by 12 to get it's annual interest value.
Natalie is in charge of inspecting frozen pepperoni pizzas. To ensure that the pizzas being produced are roughly 10 inches, she samples 30 pizzas at random every hour starting at 9 am until 4 pm and measures the diameter of these pizzas using a ruler. That means, every work day, she collects 8 samples with 30 pizzas each and inspects these 240 pizzas. Which of the statement(s) is true?
a) n equals 8
b) n equals 30
c) The number of samples is 8
d) The sample size is 30
e) The sample size is 8.
f) Each day she collects a total of 240 observations.
g) n equals 240
h) The sample size is 240.
Answer:
The statements that are true are:
b) n equals 30
c) The number of samples is 8
d) The sample size is 30
f) Each day she collects a total of 240 observations.
Step-by-step explanation:
She takes a sample every hour, so she takes 8 samples during the day.
Each samples consist of 30 individuals (pizzas).
This adds a total of 240 observations during the day.
The statements that are true are:
b) n equals 30
c) The number of samples is 8
d) The sample size is 30
f) Each day she collects a total of 240 observations.
The radius of the earth is approximately 5,000,000 meters write 5,000,000 in scientific notion
Answer:
5 × 10⁶
Step-by-step explanation:
To convert a long number to a scientific notation:
Count the number of zeros in the number
Use the count as the power of 10.
5,000,000 has six zeros
So:
× 10⁶
Now 5 will be left to be added to the notation.
5 × 10⁶
Answer:
5 x 10'6
Step-by-step explanation:
Express the ratio below in its simplest form. 15 : 10
Answer: 3:2
Step-by-step explanation:
Answer:
3/2 = 3:2
Step-by-step explanation:
15:10 = 15 /10 = 3/2. { dividing both numerator and denominator by 5}
help me please I don't understand this one
Answer:
A
Step-by-step explanation:
I'm not sure if it's right though
Complete the statement.
L=234 mL
Answer:
0.234
Step-by-step explanation:
Answer:
0.234
To convert from milliliters to liters, divide by 1,000.
234 ÷ 1,000 = 0.234
Step-by-step explanation:
Complete each statement.
? L = 234 mL
234/1000=0.234
There are 1000 milliliters in a liter, therefore dividing the milliliters by 1000 will give you the amount of liters. Liters = 0.234
RESULT
0.234L
find the distance between (8, -4) and (2, 15). round to the nearest tenth
Answer:
19.9
Step-by-step explanation:
d = sqrt(6^2+19^2) = sqrt( 397) =. 19.9
How do you factor the trinomial 3x^2+18x-21?
Answer:
(3)(x+7)(x-1)
Step-by-step explanation:
3x^2+18x-21
Let's start by taking 3 out of the equation.
3(x^2+6x-7)
Now, when we factor, we need to find two numbers that add up to 6 and multiply to -7.
The numbers would be 7 and -1.
So the factored form of this would be:
(3)(x+7)(x-1)
Suppose you have $200,000 in a bank term account. You earn 5% interest per annum from his account you anticipate that infla
Answer:
Interest= $10000
Step-by-step explanation:
So we are to calculate the interest at 5% annum of $200000.
Ok , we'll use the formula
PRT/100 = interest
Where P = principal
R = rate
T= time
(200000* 5*1)/100 = interest
1000000/100 = interest
10000 = interest
Interest= $10000
Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-half x minus three-halves?
The inverse of the function g(x)=-2x -3.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given function:
f(x) = -1/2 x - 3/2
Since the function is inverse, so
g(f(x)) = a(-1x/2 - 3/2) + b
x = -ax/2 - 3x/2 + b
-a/2 = 1
a = -2
and, -3a/2 + b = 0
b= -3
Hence, the inverse of the function g(x)=-2x -3.
Learn more about Function here:
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Complete each statement so it will result in the truth value F.
If the GCD of 5 and 12 is 1, then _______
-> 12 is even
->12 is less than 5
->5 is less than 12
->5 is prime
The sum of 5 and 12 is 7 if and only if _______
->12 is divisible by 5
-> 12 is greater than 5
-> 5 is even
->the difference between 12 and 5 is -7
Answer:
We want to create sentences that are false (this means that the truth value is F
False ---> true: then the statement is false
true-----> false: then the statement is false.
For the first option we have:
"If the GCD of 5 and 12 is 1,____"
the left side is true, so the right side must be false:
"If the GCD of 5 and 12 is 1, then 12 is less than 5"
this means that the truth value is false, because the left side is true and the right side false.
For the second sentence we have:
The sum of 5 and 12 is 7 if and only if _______
The left side is false, so the right side must be true, the only true option is 12 is greater than 5, so the sentence is:
"The sum of 5 and 12 is 7 if and only if 12 is greater than 5."
Somebody plz help. I’ll rate you Brainalist.
Principal = $5,400, rate = 18%, time = 2 years. What is the simple interest?
Answer:
$1,944.00
Step-by-step explanation:
Interest= Principal x Rate x Time (years)
Rate: 18%= 0.18
Interest= 5,400 x 0.18 x 2= $1,944
The quantities xxx and yyy are proportional. xxx yyy 777 353535 121212 606060 202020 100100100 Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x.
Answer: The constant of proportionality is r = 5.
Step-by-step explanation:
O, we know that x and y are proportional, this means that:
y = r*x
where r is the constant of proportionality.
we also have the table
x y
7 35
12 60
20 100
Now, we can replace those values in our equation and get, for the first pair:
35 = r*7
r = 35/7 = 5
for the second pair:
60 = r*12
60/12 = 5 = r
So we can conclude that the constant of proportionality is 5.
Answer:
5
Step-by-step explanation:
It was right for me on khan
The graph shows the solution for which inequalities?
Answer:
Inequalities are,
y ≥ 4x + 2
y ≥ 2
Step-by-step explanation:
Solid yellow line of the graph attached passes through two points (0, -2) and (1, 2).
Let the equation of this line is,
y = mx + b
Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{2+2}{1-0}[/tex]
m = 4
Y-intercept 'b' = -2
Equation of the line will be,
y = 4x - 2
Since shaded area is on the left side of this solid line so the inequality representing this region will be,
y ≥ 4x - 2
Another line is a solid blue line parallel to the x-axis.
Shaded region (blue) above the line will be represented by,
y ≥ 2
Therefore, the common shaded area of these inequalities will be the solution of the given inequalities.
Determine the number solutions for system x-2y=1 and -4x+8y=-4
Answer:
Hence, the system of equation does not have solution.
Step-by-step explanation:
You have the following 2x2 system:
[tex]x-2y=1\ \ \ \ (1)\\\\-4x+8y=-4\ \ \ \ (2)[/tex]
You can obtain the solution to the system by using substitution method.
You solve the first equation for x:
[tex]x=1+2y[/tex] (3)
Next, you replace (3) in the equation (2), and you solve for y:
[tex]-4(1+2y)+8y=-4\\\\-4-8y+8y=-4\\\\0=0[/tex]
The last result is the trivial solution. This means that the equation (2) is a multiple scale of the first equation. In fact, if you multiply equation (1) by -4, you obtain the equation (2).
Hence, the system of equations does not have solution.
3. The path of an underground stream is given by the function y = 4x² +17x -32. Two
new houses need wells to be dug. On the area plan, these houses lie on a line defined by
the equation y = –15x+10. Determine the coordinates where the two wells need to be
dug.
Answer:
The coordinate of the wells are
[tex] (-4 -\sqrt[]{\frac{53}{2}}, 70+15\sqrt[]{\frac{53}{2}})[/tex]
[tex] (-4 +\sqrt[]{\frac{53}{2}}, 70-15\sqrt[]{\frac{53}{2}})[/tex]
Step-by-step explanation:
The y coordinate of the stream is given by [tex] y = 4x^2+17x-32[/tex]. Also, the y coordinate of the houses are determined by y=-15x+10. We will assume that the houses are goint to be built on the exact position where we build the wells. We want to build the wells at the exat position in which both functions cross each other, so we have the following equation
[tex] 4x^2+17x-32 = -15x+10[/tex]
or equivalently
[tex]4x^2+32x-42=0[/tex] (by summing 15x and substracting 10 on both sides)
Dividing by 2 on both sides, we get
[tex]2x^2+16x-21=0[/tex]
Recall that given the equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
Taking a =2, b = 16 and c = -21, we get the solutions
[tex]x_1 = -4 -\sqrt[]{\frac{53}{2}}[/tex]
[tex]x_2 = -4 +\sqrt[]{\frac{53}{2}}[/tex]
If we replace this values in any of the equations, we get
[tex]y_1 = 70+15\sqrt[]{\frac{53}{2}}[/tex]
[tex]y_2 = 70-15\sqrt[]{\frac{53}{2}}[/tex]
Find the exact value of cos 15º.
Answer:
0.965925826
Step-by-step explanation:
Answer:
(pi6 + pi2)/4
Step-by-step explanation:
