We have a class of a total of 267 students.
The professor has a sample of 59 students, where 22 of them did not complete their essays.
This equals a proportion of:
[tex]p=\frac{22}{59}\approx0.373[/tex]If this sample is representative of the class, we can use this proportion to estimate how many students did not complete the essay.
To do that we multiply the total number of students by the proportion we have just calculated:
[tex]X=N\cdot p=267\cdot0.373\approx99.59\approx100[/tex]Answer: it can be estimated that approximately 100 students did not finish their essay.
Find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores.z = 1 and z = 1.81
Since this is a normal distribution, the area between the z-scores z₁ = 1 and z₂ = 1.81 is just the probability that the random variable Z is between z₁ and z₂:
[tex]P(z_1\leq Z\leq z_2)=P(z_1\leq Z)-P(z_2\leq Z_{})=P(1\leq Z)-P(1.81\leq Z)[/tex]Using the values reported on tables for the standardized normal distribution, we know that:
[tex]\begin{gathered} P(1\leq Z)=0.158655 \\ P(1.81\leq Z)=0.035148 \end{gathered}[/tex]Now, using these results:
[tex]P(z_1\leq Z\leq z_2)=0.158655-0.035148=0.123507[/tex]Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.04 and a standard deviation of 1.53. Using the empirical rule, whatpercentage of American women have shoe sizes that are less than 11.1? Please do not round your answer.
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution.
So we have
So we can apply the rule to obtain
There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon. How many milliliters are in 1 quart? Label your answer to the hundredths place and in mL.
During a class election the ratio of students who voted for candidate A compared tocandidate B was 7: 4. If candidate A received 21 votes, what is the combined amount ofvotes candidate A and candidate B received?
Given: Ratio of students that voted for A compared to B is 7:4
A recieved 21 votes so let B recieve x votes.
So as the given ratios,
[tex]\frac{7}{4}=\frac{21}{x}[/tex][tex]x=\frac{21\times4}{7}=12[/tex]Hence, combined votes received by candidate A and B is 12+21=33
(a) Approximate the population mean and standard deviation of age for males And For females.
1) Since we have a table for grouped data, we need to place into that table another column with the middle point of each interval to get the mean.
2) Setting that table with another column we've got:
Age Middlepoint Male Female Male*freq Female*fr
0-9 (0+9)/2 =4.5 10 9 10*4.5=45 9*4.5=40.5
10-19 (10+19)/2=14.5 11 5 159.5 72.5
20-29 (20+29)/2= 24.5 12 13 294 318.5
30-39 (30+39)/2= 34.5 16 19 552 655.5
40-49 (40+49)/2= 44.5 25 21 1112.5 934.5
50-59 (50+59)/2= 54.5 20 24 1090 1308
60-69 (60+69)/2=64.5 18 18 1161 1161
70-79 (70+79)/2= 74.5 15 14 117.5 1043
Now, we can pick the absolute frequency of males and females and multiply by the middle point.
Now we can add the number of males multiplied by the frequency and divide them by the sum of the frequencies, this way:
[tex]\mu=\frac{45+159.5+294+552+1112.5+1090+1161+117.5}{10+11+12+16+25+20+18+15}\approx38.68[/tex]3) Now to find the standard deviation of this population, we can write out the following:
[tex]\begin{gathered} \sigma=\frac{\sqrt[]{(45-38.68)^2+(159.5-38.68)^2+(294-38.68)^2+(552-38.68)^2+(1112.5-38.68)^2+(1090-38.68)^2+(1161-38.68)^2+(117.5-38.68)^2}}{8} \\ \\ \sigma=452.6694 \end{gathered}[/tex]Question 11
11 of 12
Which choice shows 13*07*4) correctly rewritten using the associative property and
then correctly simplified?
O (1347)*4=91*4=364
O 13*(4*7)=13*28=364
o 13*4*7=52*7=364
O (13*74)=962
Question ID: 116141
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The associative property states that the way the factors are grouped in a multiplication does not change the result.
Grouping 7 and 4
13 * (4*7) = 13 *(28 ) = 364
13 and 7
(13*7)*4 = 91*4= 364
13 and 4
(13*4)*7 = 52*7 = 364
So, the correct options are a and b ( the first 2 options)
Marcus hikes at a rate of 2 1/9 miles per hour. If he hikes for 6 hours, how many miles will he hike?
We have the following:
let s is speed, d is distance and t is time, therefore:
[tex]\begin{gathered} s=\frac{d}{t} \\ d=s\cdot t \\ d=2\frac{1}{9}\cdot6 \\ d=\frac{18+1}{9}\cdot6=\frac{19}{9}\cdot6 \\ d=\frac{114}{9}=\frac{38}{3} \\ d=12\frac{2}{3} \end{gathered}[/tex]Therefore, the answer is the third option 12 2/3 miles
in a popular restaurant on a Saturday night three out of every four customers are female. how many customers y are there for x number of total customers
Let y be the number of female customers in the restaurant. Since we know that 3 out of 4 customers are females and that x is the total number of customers, this means that:
[tex]y=\frac{3}{4}x[/tex]what is 6 3/8 written as a demcimal
Answer:
The solution is 6,375
Step-by-step explanation:
[tex] \sf 6 \frac{3}{8} \\ \\ = \sf \frac{6 \times 8 + 3}{8} \\ \\ \sf \frac{48 + 3}{8} \\ \\ = \sf \frac{51}{8} \\ \\ = \sf 51 \div 8 \\ \\ = \sf6.375[/tex]
Tamara's monthly budget shows$490.00 in fixed expenses, $529.50in variable expenses, and anexpected income of $1,250.00.1. Why doesn't Tamara's budgetbalance?
She has an expected income of $1250.
The total expenses are $490 + $529.50 = $1019.50.
She has a superavit that she can save. This amount is $1250 - $1019.50 = $230.50.
Answer: the budget balance does not balance because the income is greater than the expenses.
Identify which of the following graphs is the graph of two equivalent vectors.
By definition, two vector are equivalent when they have the same length, and they point in the same direction. Any two or more vectors will be equal if they are collinear, codirected, and have the same magnitude.
 A scuba diver is swimming at a depth of 70 feet .He descended at a rate of 5 feet every 12 seconds.At this rate ,how many seconds did it take for the diver to reach the depth of 70 feet?
compare a=0.432, b=0.437
So we need to compare two numbers. This means telling which is smaller and which is greater or if they are equal. In this case we have decimal numbers but it's more comfortable to work with integers so I'm going to multiply both by the same number in order to make them integers:
[tex]\begin{gathered} A=0.432\cdot1000=432 \\ B=0.437\cdot1000=437 \end{gathered}[/tex]Since both a and b where multiplied by the same number then the result of the comparison between A and B is the same as that between a and b. So we have 432 and 437. Let's make a substraction:
[tex]A-B=432-437=-5[/tex]The result is a negative number which means that:
[tex]A-B<0[/tex]Then we add B at both sides of this inequality:
[tex]\begin{gathered} A-B+B<0+B \\ AAs I said before the comparison between A and B is the same as that between a and b which means that:[tex]aAnd that last inequality is the answer.Two Step problem:STEP 1: 7x^2 = -4using the standard form ax^2 +bx + c =0 of the given quadratic equation, factor the left hand side of the equation into two linear factors. STEP 2: 7x^2 = -4xsolve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary. PICTURE OF ANSWER BOX ATTACHED: is for step #2
Step 1
x(7x+4)
Step2
x_1=0, x_2 =-4/7
Step 1)
1) Let's factor that incomplete quadratic equation (since c=0):
7x² = -4x Add 4x to both sides
7x² + 4x = 0 Place outside the parenthese the common factor: x
x(7x+4) = 0
Step 2)
Now we can solve that:
x(7x+4)=0 Which number multiplied by x yields 0?
Then we can state that x_1 = 0
Solving that Linear Factor:
(7x +4) = 0 Removing the Parentheses
7x +4 = 0 Subtract 4 from both sides
7x = -4 Divide both sides by 7
x = -4/7
3) Hence, the answers are:
Step 1
x(7x+4)
Step2
x_1=0, x_2 =-4/7
Which set of graphs can be used to find the solution to the equation?
Given
The inequality,
[tex]3e^x>-\frac{1}{2}x[/tex]To find:
Which set of graphs can be used to find the solution to the equation?
Explanation:
It is given that,
[tex]3e^x>-\frac{1}{2}x[/tex]That implies,
The graph representing 3e^x is,
Also, the graph representing y> - ( 1/2) x is,
By combining these two we get,
[tex]3e^x>-\frac{1}{2}x[/tex]Write a sine function that has an amplitude of 5, a midline of 4 and a period of 3/2
Note that in any sine function :
[tex]y=A\sin (B(x+C))+D[/tex]Amplitude = A
Verical Shift or midline = D
Period = (2π)/B
Horizontal or Phase Shift = C
From the given,
since we dont have any horizontal shift, C = 0.
Amplitude = 5, so A = 5
Midline = 4, so D = 4
and
Period = 3/2, so equating it to (2 π)/B
[tex]\frac{3}{2}=\frac{2\pi}{B}[/tex][tex]B=\frac{4\pi}{3}[/tex]Now, substituting the values obtained, the sine function will be :
[tex]y=5\sin (\frac{4\pi}{3}x)+4[/tex]if 15 pizza cost $195. how much will 100 pizza cost?
15 pizza ---> $195
100 pizza --> x
[tex]\begin{gathered} 15\times x=100\times195 \\ 15x=19500 \\ \frac{15x}{15}=\frac{19500}{15} \\ x=13000 \end{gathered}[/tex]answer:
$13000
if f(x) = 3x⁴ + x² + 3 then what is the remainder when f(x) is divided by x + 1
The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-r) is equal to f(r).
Question 8 of 10What should you multiply the first equation (top equation) by in order toeliminate the variable x when the two equations are added together?(3x-y-14-12x+y - 7dar hereISUBMIT
You can multiply the first equation by 4:
3x - y = 1 (*4)
12x-4y=4
Adding both equations:
12x - 4y = 4
+
-12x + y = 7
__________
0x - 3y = 11
so, you eliminate the X.
In order to eliminate the variable x when the two equations are added together, we needed to multiply the first equation by 4.
To eliminate the variable x when adding the two equations:
First, let's write the equations in a form where the x and y terms have opposite coefficients:
3x - y = 1 (Equation 1)
-12x + y = 7 (Equation 2)
To eliminate the x term, we can multiply Equation 1 by 4:
4 (3x - y) = 4 × 1
12x - 4y = 4 (Equation 3)
Now, we can add Equation 2 and Equation 3 together:
(-12x + y) + (12x - 4y) = 7 + 4
-12x + 12x + y - 4y = 11x - 3y = 11
The x term has been eliminated, and we are left with the equation 11x - 3y = 11.
To learn more about the system of equations;
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Which statement describes the product of the expression 5 x 1/2?A, It is less than 1/2B. It is greater than %. C. It is between 5 and 6. D. It is between 1/2 and 5.
we have the expression
[tex]5\cdot\frac{1}{2}=\frac{5}{2}[/tex]so
Verify each statement
A, It is less than 1/2 -----> is not true
B. It is greater than 5 ----> is not true
C. It is between 5 and 6 ----> is not true
D. It is between 1/2 and 5 ----> is true
because
1/2 < 5/2 < 5
therefore
The answer is option D
A gift box for a shirt has a length of 45 centimeters, a width of 30 centimeters, anda height of 8 centimeters. Find the surface area of the gift box
The main values in order to find the surface are the width and the length, therefore, the surface will be the product between them
[tex]45cm\times30cm=1350cm^2[/tex]Because the box cover from a gift box depends on the width and length, the surface area is 1350cm^2.
2/5 x 2/3???????????
hello
to solve this question, we simpply need to multiply both fractions
[tex]\frac{2}{5}\times\frac{2}{3}=\frac{4}{15}[/tex]from the calculation above, the value of answer is 4/15
which domain restrictions apply to the rational expression? 14-2x / x^2-7x
The domain restrictions that apply on the given rational expression are that x can neither be 0 nor 7.
We are given the rational expression:-
[tex]\frac{(14-2x)}{(x^2-7x)}[/tex]
We have to find the domain restrictions that apply on the given expression.
We know that in a fraction, denominator cannot be 0, or else it will make the fraction indefinite.
Hence, by putting the denominator as 0, we will get the domain restrictions of the expression.
[tex]x^2-7x=0[/tex]
x(x - 7) = 0
x = 0 and 7
Hence, the domain restrictions that apply on the given rational expression are that x can neither be 0 nor 7.
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A rectangular piece of metal is 25 in longer than it is wide Squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an openbox. If the volume of the box is 1530 in. What were the original dimensions of the piece of metal?What is the original width? ____in
Given:-
A rectangular piece of metal is 25 in longer than it is wide Squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1530 in.
To find the original width.
The formula for volume of the box is,
[tex]v=l\times b\times h[/tex]The volume given is 1530.
Also we have,
[tex]L=W+25,H=5[/tex]Substiutiting the values. we get,
[tex]\left(W+15\right)*W-10*5=1530[/tex]Divide both sides by 5,
[tex]\left(W+15\right)*W-10=306[/tex]So,
[tex]w^2+5w-150=306[/tex]So now we get,
[tex]w^2+5w-456=0[/tex]Now we solve the quadratic equation,
[tex]\begin{gathered} w=\frac{-5\pm\sqrt{5^2-4\cdot\:1\cdot\left(-456\right)}}{2\cdot\:1} \\ w=\frac{-5\pm\:43}{2\cdot\:1} \\ w=19,-24 \end{gathered}[/tex]So now we skip the negative value and take the positve value 19.
So the required value is 19.
7(1 - 6p) need help please
Find 7•(1-6p)
First eliminate parenthesis
Apply distributive law
a•(b+c) = ab + ac
Then
7•(1-6p) = 7•1 - 7•6p
. = 7 -42p
ANSWER IS
7 - 42p
Nanny using using an app that shows him how many kilometers he has to run to prepare for a Marathon. The app says here an 8.0 45 kilometer who wants to Post online how many miles away Danny ran blank miles.(one mile = 1.609 km)
The conversion for distance in kilometer to miles is as,
[tex]\begin{gathered} 1\text{ mile=1.609 km} \\ 1\text{ km=}\frac{1}{1.609}\text{ miles} \end{gathered}[/tex]Determine the number of miles in 8.045 km.
[tex]\begin{gathered} 8.045\text{ km=8.045}\cdot\frac{1}{1.609}\text{ miles} \\ =5\text{ miles} \end{gathered}[/tex]So Nanny ran 5 miles.
A rectangle's length is 6 inches greater than its width. If the perimeter of the rectangle is 36 inches, find the length.
We will have the following:
First, we are given the following expressions for the rectangle's length and width respectively:
[tex]l=w+6[/tex]&
[tex]w=w[/tex]Now, we calculate the length and width using the perimeter:
[tex]P=2(l+w)\Rightarrow P=2(w+6+w)\Rightarrow P=2(2w+6)\Rightarrow P=4(w+3)[/tex]So:
[tex]36=4(w+3)\Rightarrow w+3=9\Rightarrow w=6[/tex]Then:
[tex]l=(6)+6\Rightarrow l=12[/tex]So, the measurements of the length and the width are respectively 12 units and 6 units.
sunscreen is priced at $10 per bottle, +8% tax. If Tonya purchases a bottle of sunscreen with a $20 bill, then what is her change
Solution
For this case we know that the price is 10$ per bottle with 8% of tax
We can find the tax using this:
[tex]\frac{10}{100}=\frac{x}{8}[/tex]With x= tax value, solving for x we got:
[tex]x=8\cdot\frac{10}{100}=0.8[/tex]Then the total price is: 10+0.8 = 10.8
Then we can find the change like this:
20-10.8= 9.2
A bag of 11 marbles contains 7 marbles with red on them, 6 with blue on them, 6 with green on them, and 3 with red and green on them. What is the probability that a randomly chosen marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
In the case of two not mutually exclusive events, we have that, given events A and B,
[tex]P(A\lor B)=P(A)+P(B)-P(A\cap B)[/tex]Notice that if we only include the first two contributions, we would count the intersection of the two events twice; therefore, we must subtract the probability of its intersection once.
In our case,
[tex]P(R\lor G)=\frac{7}{11}+\frac{6}{11}-\frac{3}{11}=\frac{10}{11}[/tex]Therefore, the answer is 10/11.
write the equation for each sentence below.a) (p) is the product of 7 to the sum of 3 and 9 b) The difference of (T) and 24 is 9 more than 34
(p) is the product of 7 to the sum of 3 and 9
This means we take the sum of "3" and "9" and multiply it with the variable "p". The expression is shown below
[tex]\begin{gathered} p\times(3+9) \\ =p\times12 \\ =12p \end{gathered}[/tex](b)The difference of (T) and 24 is 9 more than 34
The difference of T and 24 means T - 24
is 9 more than 34 means 34 + 9
Writing it together:
[tex]\begin{gathered} T-24=34+9 \\ T-24=43 \end{gathered}[/tex]