Answer:
12r-32
Step-by-step explanation:
Distribute the 4 between the different numbers.
3r * 4 = 12r and 8 * 4 = 32
So...you end up with 12r-32
Hi! I hope you're enjoying your day!
Let's recall that the Distributive Property states that
a(b+c)=ab+ac
Where
a, b, and c can be either constants (numbers like 4) or variables (letters like d)
Simplify:
4(3r-8)
4 times 3r is equal to 12r
12r- (4*8)
[tex]\boxed{\boxed{\bold{12r-32}}}[/tex]
Hope everything is clear.
If you have any questions, please comment.
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Researchers conduct a study of obesity in children. They measure body mass index (BMI), which is a measure of weight relative to height. High BMI is an indication of obesity. Data from a study published in the Journal of the American Dietetic Association shows a fairly strong positive linear association between mother’s BMI and daughter’s BMI (r = 0.506). This means that obese mothers tend to have obese daughters. A. Identify explanatory, response, and potential lurking variables in this study. B. Can we conclude from this study that maternal obesity causes obesity in daughters?
Answer:
Step-by-step explanation:
a. The explanatory variables in this case is the mothers BMI on which the child's BMI is determined.
The response variable is the child's BMI which is also the outcome variable that exists if a child has an obese parent.
Other lurking variables may include the diets and exercise plan of either of these two variables.
b. No, this study cannot be used to conclude that maternal obesity causes obesity in daughters if the lurking variables are not dealt with.
A library subscribes to two different weekly news magazines, each of which is supposed to arrive in Wednesday's mail. In actuality, each one may arrive on Wednesday, Thursday, Friday, or Saturday. Suppose the two arrive independently of one another, and for each one P(Wed.) = 0.3, P(Thurs.) = 0.4, P(Fri.) = 0.2, and P(Sat.) = 0.1. Let Y = the number of days beyond Wednesday that it takes for both magazines to arrive (so possible Y values are 0, 1, 2, or 3).
Required:
Compute the pmf of Y.
Answer:
Step-by-step explanation:
Let the events be
W = Wednesday
T = Thursday
F = Friday
S = Saturday
The corresponding probability are
P (W) = 0.3
P (T) = 0.4
P (F) = 0.2
P (S) = 0.1
Let Y = number of days beyond wednesday that takes for both magazines to arrive
(so possible Y values are 0, 1 , 2 ,3)
The possible outcome are 4² = 16
(W,W) (W,T) (W,F) (W,S)
(T,W) (T,T) (T,F) (T,S)
(F,W) (F,T) (F,F) (F, S)
(S,W) (S,T) (S,F) (S,S)
The values associated for each of the following as follows
Y(W,W) =0, Y(W,T) =1, Y(W,F)=2, Y (W,S)=3
Y(T,W)=1, Y (T,T)=1, Y (T,F)=2, Y (T,S)=3
Y(F,W)=2, Y (F,T)=2, Y (F,F)=2, Y (F, S)=3
Y(S,W)=3, Y (S,T)=3, Y (S,F)=3, Y (S,S)=3
The probability mass function of Y is
P(Y=0)=0.3(0.3)=0.9
P(Y=1) = P[(W,T) or (T,W) or (T,T)]
= [0.3(0.4) + 0.3(0.4) + 0.4(0.4)]
=0.4
P(Y = 2) = P[(W,F) or (T,F) or (F,W) or (F,T) or (F,F)]
=0.3(0.2) + 0.4(0.2) + 0.2(0.3) + 0.2(0.4) + 0.2(0.2)]
=0.32
P(Y =3) = P[(W,S) or (T,S) or (F,S) or (S,W) or (S,T) or (S,F) or (S,S)]
= [0.3(0.1) + 0.4(0.1) + 0.2(0.1) + 0.1(0.3) + 0.1(0.4) + 0.1(0.2) + 0.1(0.1)]
= 0.19
Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2, 0.3, and 0.5, respectively. What is the expected number of books a customer will purchase?
Answer:
Expectation number of books a customer will purchase = 1.3
Step-by-step explanation:
x : 0 1 2
p(x) :0.2, 0.3, and 0.5
Expectation
E(X) = ∑x P(x)
= 0 X 0.2 +1 X 0.3+ 2 X 0.5
= 1.3
Expectation E(X) = 1.3
Expectation number of books a customer will purchase = 1.3
The function
R(x) = 80 + 7.440 √ x 0 ≤ x ≤ 15000
indicates that the monthly revenue R (in thousands of dollars) depends on the amount of dollars x spent on advertising each month.
a. By how much would the monthly revenue be expected to change if the monthly expenditure on advertising were to be raised from its current level of $ 6000 to $ 6001 ? (Use the marginal revenue R '(x) and round to the nearest dollar.) $ Incorrect
b. What is the revenue when the amount spent on advertising is $6000 . Round to the nearest dollar. $ Incorrect
Corrected Question
The function is: [tex]R(x)=80+7.440\sqrt{x} , 0\leq x\leq 15000[/tex]
Answer:
(a)$48.02
(b)$656,299.92
Step-by-step explanation:
(a) We are to determine the change in monthly revenue if the monthly expenditure, x is raised from its current level of 6000 to 6001.
[tex]R(x)=80+7.440\sqrt{x}\\R'(x)=\dfrac{d}{dx} (80+7.440\cdot x^{1/2})\\=7.440 \times \frac{1}{2} \times x^{\frac{1}{2}-1}\\=3.72\times x^{-\frac{1}{2}}\\\\R'(x)=\dfrac{3.72}{\sqrt{x} }[/tex]
Therefore, the expected change in monthly revenue
[tex]R'(6000)=\dfrac{3.72}{\sqrt{6000} }=$0.04802 (thousands)[/tex]
=$48.02
(b)When the amount spent on advertising is $6000
[tex]Revenue, R(6000)=80+7.440\sqrt{6000}\\=\$656.29992$ (in thousands)\\=\$656,299.92[/tex]
pls help me to understand TwT ive been struggling oof.
what is surface area of a square pyramid that has a base of 100 ft a base of 40 ft a height of 50 ft and slant height of 60 ft?
Step-by-step explanation:
The surface area of a square pyramid is the area of the square base plus the area of the 4 lateral faces:
A = b² + 4 (½ bl)
A = b² + 2 bl
where b is the width of the base,
and l is the slant height.
Answe The surface area of a square pyramid is the area of the square base plus the area of the 4 lateral faces:
A = b² + 4 (½ bl)
A = b² + 2 bl
where b is the width of the base,
and l is the slant height.:
Step-by-step explanation:
A 170-lb man carries a 20-lb can of paint up a helical staircase that encircles a silo with radius 30 ft. The silo is 90 ft high and the man makes exactly three complete revolutions. Suppose there is a hole in the can of paint and 8 lb of paint leaks steadily out of the can during the man's ascent. How much work is done by the man against gravity in climbing to the top
The work done by the man against gravity in climbing to the top is 16740 lb-ft
What is work done against gravity?The work done against gravity relies on the height of the object and the weight at which the object is changing.
From the given information:
Taking the vertical y-axis when y = 0, then:
The weight of the paint w(y) becomes;w(0) = 20 lb
w(90) = 20 - 8 = 12 lb
Provided that the paint leaks steadily, the function of y i.e. w(y) can be expressed as a linear function in the form:
w(y) = a + by ---- (1)
Thus;
w(0) = a = 20w(90) = 20 + 90b = 12b = (12 - 20)/90b = -4/45From equation (1)
w(y) = 20 - 4y/45
The total weight becomes;
w = w(y) + the man's weight
w = 20 - 4y/45 + 170
w = 190 - 4y/45
Therefore, the work done against gravity is computed as:
W = ∫ w dy
where;
y varies from 0 to 90[tex]\mathbf{W = \int ^{90}_{0}( 190 - \dfrac{4y}{45} )\ dy }[/tex]
W = 16740 lb-ft
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What is the value of x in the solution to this system of linear equations?
Use substitution.
y = -3x + 3
- 2x + 2y = 6
Answer:
Step-by-step explanation:
y = -3x + 3
-2x + 2y = 6
-2x + 2(-3x + 3) = 6
-2x - 6x + 6 = 6
-8x + 6 = 6
-8x = 0
x = 0
y = -3(0) + 3
y = 0+ 3
y = 3
(0, 3)
Please answer this correctly
Answer:
n = 4
Step-by-step explanation:
These triangles are similar, so you can set up a proportion like this:
[tex]\frac{20}{n} =\frac{10}{2}[/tex]
→Cross multiply:
[tex]\frac{40}{10n}[/tex]
→Divide 40 by 10:
n = 4
Let C(q) represent the cost and R(q) represent the revenue, in dollars, of producing q items.
a. If C(50) = 4900 and C'(50) = 27, estimate C(52)
C(52)= $___________________
b. If C'(50) = 27 and R'(50) =37, approximately how much profit is earned by the 51st item?
The profit on the 51st itme is ____________________ dollars.
c. if C' (100) =41 and R'(100)= 37, should the company produce the 101st item?
The company _______________________ produce the 101st item
Answer:
(a)$4954
(b)$10
(c)The company should not produce the 101st item.
Step-by-step explanation:
(a)
[tex]C'(50)=\dfrac{C(52)-C(50)}{52-50} \\\\C(50) = 4900,C'(50) = 27\\\\$Therefore:\\27=\dfrac{C(52)-4900}{52-50}\\C(52)-4900=27*2\\C(52)=4900+54\\C(52)=\$4954[/tex]
(b)If C'(50) = 27 and R'(50) =37
Cost will increase by $27Revenue will increase by $37Therefore, the profit earned on the 51st item
[tex]=R'(50)-C'(50)[/tex]
=37-27
=$10
(c)If C'(100) = 41 and R'(100) =37
Cost will increase by $41Revenue will increase by $37Therefore, the profit earned on the 101st item
Profit [tex]=R'(100)-C'(100)[/tex]
=37-41
=-$4
The company should not produce the 101st item. It would lose $4 if it does.
Kyle's car gets about 30 miles per gallon. About how many miles can KyleKyle drive on 11.1 gallons of gas? At $2.90 a gallon, about how much would that amount of gas cost?
a researcher is testing reaction times between the dominant and non-dominant hand. they randomly start with each hand for 20 subjects and their reaction times in milliseconds are recorded. test to see if the reaction time is faster for the dominant hand using a 5% level of significance. the hypotheses are:
Null hypothesis (H0): The reaction time for the dominant hand is not faster than the non-dominant hand.
Alternative hypothesis (Ha): The reaction time for the dominant hand is faster than the non-dominant hand.
The null and alternative hypotheses for testing if the reaction time is faster for the dominant hand can be formulated as follows:
Null hypothesis (H0): The reaction time for the dominant hand is not faster than the non-dominant hand.
Alternative hypothesis (Ha): The reaction time for the dominant hand is faster than the non-dominant hand.
To test these hypotheses, we can perform a paired t-test because the same subjects are tested with both hands. The paired t-test compares the means of the paired observations and determines if there is a statistically significant difference between them.
Using a 5% level of significance (α = 0.05), we can calculate the test statistic and compare it to the critical value from the t-distribution with (n-1) degrees of freedom, where n is the number of subjects.
If the calculated test statistic falls in the critical region (i.e., the p-value is less than 0.05), we reject the null hypothesis and conclude that there is evidence to suggest that the reaction time for the dominant hand is indeed faster.
If the calculated test statistic does not fall in the critical region (i.e., the p-value is greater than or equal to 0.05), we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest a difference in reaction times between the dominant and non-dominant hand.
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The null and alternate hypothesis tests are:
H₀: μd = μnd
H₁: μd < μnd
Given data:
The hypotheses for testing if the reaction time is faster for the dominant hand can be stated as follows:
Null Hypothesis (H₀): The reaction time is the same for the dominant and non-dominant hand.
Alternative Hypothesis (H₁): The reaction time is faster for the dominant hand.
Mathematically, these can be represented as:
H₀: μd = μnd
H₁: μd < μnd
Where:
μd is the population mean reaction time for the dominant hand.
μnd is the population mean reaction time for the non-dominant hand.
To test these hypotheses, a statistical test such as a paired t-test can be used. The test will compare the means of the paired observations (reaction times for the dominant and non-dominant hand) and determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
The significance level of 5% (0.05) indicates that if the p-value obtained from the test is less than 0.05, we would reject the null hypothesis and conclude that there is evidence to support the claim that the reaction time is faster for the dominant hand.
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Please answer this question !!! 20 points and brainliest !!
Answer:
see below
Step-by-step explanation:
The first answer choice is the only one that has the first sale correctly represented. Each term is the product of the number of pens of the type and the cost of pens of that type.
12 dozen roller-ball pens will have a cost of 12x
5 dozen ballpoint pens will have a cost of 5y
The total cost of these will be 116 (dollars).
The equation is written ...
12x +5y = 116 . . . . . . . this equation is only found in choice A
1/2 of 30 = 1/4 of ??
Answer:60
Step-by-step explanation:
⅟₂ of 30=15
¼ of 60=15
Half of thirty is 15 so u need to know what ¼ of something makes 15 so all u have to do is times 15 by 4 and there got ur answer this will not go for every question thoThe required value is 60.
What is proportion?The size, number, or amount of one thing or group as compared to the size, number, or amount of another is considered as proportion.
Given that, 1/2 of 30 = 1/4 of ??
So, 1/2 of 30 = 15
a/b = c/d
ad = bc
Let the unknown value be x,
Therefore,
30 / 2 = x / 4
2x = 120
x = 60
Hence, the value of unknown element is 60.
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Ifx-10 is a factor of x2 - 8x - 20, what is the other
factor?
x +
Answer:
[tex] f(x) = x^2 -8x -20[/tex]
We know that one factor is (x-10). We know that we need to find two values that added we got -8 and multiplied we got -20. So then we can set the following options:
[tex] a(10) = -20[/tex]
[tex] a-10= -8[/tex]
And solving for a we got:
[tex] a = -8+10=-2[/tex]
And we got:
[tex] a = -2[/tex]
So then the other factor would [tex] x +2[/tex]
Step-by-step explanation:
For this case we have the following expression:
[tex] f(x) = x^2 -8x -20[/tex]
We know that one factor is (x-10). We know that we need to find two values that added we got -8 and multiplied we got -20. So then we can set the following options:
[tex] a(10) = -20[/tex]
[tex] a-10= -8[/tex]
And solving for a we got:
[tex] a = -8+10=-2[/tex]
And we got:
[tex] a = -2[/tex]
So then the other factor would [tex] x +2[/tex]
Answer:
Step-by-step explanation:
cual de las siguientes rectas son perpendiculares a la recta de la ecuación 4x+6y-6=0
Answer:
Ok, i will answer in English.
The first step is to know that when we have a linear equation like:
y = a*x + b
any line with a slope equal to -1/a will be perpendicular to our line.
So first let's write our equation in the standard form:
4x + 6y - 6 = 0
6y = -4x + 6
y = (-2/3)*x + 1
then the slope is (-2/3)
then the slope of the perpendicular line will be:
-(1/(-2/3)) = 3/2
So the only thing any line with the equation:
y = (3/2)*x + c
where c can be any real number, is perpendicular to 4x+6y-6=0
PLEASE HELP ASAP (20 points) Basic Inverse Function Question
*see attachment*
Answer:
D
Step-by-step explanation:
f(x ) = [tex]x^{2} - 1\\[/tex]
inverse ----> f(x) = y = x
x = [tex]y^{2}[/tex] - 1
[tex]y^{2} = x + 1[/tex]
y = ± [tex]\sqrt{x + 1}[/tex]
prove the identity of sin(x+y)-sin(x-y)=2 cos(x) sin(y)
Answer: I dont have one for sure but I can explain why this is true.
Step by Step:
sin(x+y)−sin(x−y)=sinxcosy+sinycosx−(sinxcosy−sinycosx)
=sinxcosy+sinycosx−sinxcosy+sinycosx
=sinxcosy+sinycosx−sinxcosy+sinycosx
=sinycosx+sinycosx
=2sinycosx
henceforth proved.
During a class trip on the bus, the teacher in the row ahead of me silently asked me if I passed gas. Why did she whisper it with a smile?
Answer:
She liked the smell and was turned on slightly.
Step-by-step explanation:
Some people get aroused when smelling a fart. The teacher was most likely trying to get into your pants.
Kelly has $800, which she divides between two savings accounts. One account earns 2% simple interest and the other earns 5%. If she earns $31 in interest between the two accounts, how much is in each?
Answer:
On the first account, she invests $300, earning 0.02*300 = $6.
On the second acount, she invests 800 - 300 = $500, earning $25.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
In this question:
Two acounts, one with 2% interest(I = 0.02) and the other with 5% interest(I = 0.05).
Each account has two earnings, that i will call [tex]E_{1}[/tex] and [tex]E_{2}[/tex]
Two investments adding up to 800. I will call the first investment P and the second is 800 - P.
Time is not given, but for simplicity, i will use 1 year.
First investment:
I at 2%. The earnings are [tex]E_{1}[/tex].
[tex]E_{1} = 0.02P[/tex]
Second Investment:
Earnings [tex]E_{2}[/tex], at 5%. So
[tex]E_{2} = 0.05(800 - P)[/tex]
The earnings add to 31, so [tex]E_{1} + E_{2} = 31[/tex], then
[tex]E_{2} = 31 - E_{1}[/tex]
So
[tex]31 - E_{1} = 0.05(800 - P)[/tex]
[tex]31 - 0.02P = 0.05(800 - P)[/tex]
[tex]31 - 0.02P = 40 - 0.05P[/tex]
[tex]0.03P = 9[/tex]
[tex]P = \frac{9}{0.03}[/tex]
[tex]P = 300[/tex]
So:
On the first account, she invests $300, earning 0.02*300 = $6.
On the second acount, she invests 800 - 300 = $500, earning $25.
In a basket of fruit, 5/6 of the pieces of fruit are apples. There are 20 apples in the display. The equation 5/6f= 20 can be used to find how many pieces of fruit f are the basket. Use words and numbers to explain how to solve the equation to find how many pieces of fruit are in the basket.
Answer:
There are 24 pieces of fruit in the basket.
Step-by-step explanation:
There are 24 pieces of fruit in the basket because to find how many there are you would do [tex]\\ \frac{6}{5\\}\\ \\[/tex] · [tex]\frac{5}{6}[/tex]f = 20 · 6/5 times 5/6 cancels out, and 20 time 6/5 is 24. 20/24 can also simplify to 5/6.
Hope this helps!
(Make sure to stream ON, Black Swan. Boy With Luv, Mic Drop, and etc.!)
What is the value of "h"?
2 + h - 48 = 30
Please answer and I will brainliest to the person who gives me the link to the profile name UsernameCorrupted.
Please I really need to find this person.
Answer:
h = 76
Step-by-step explanation:
2 + h - 48 = 30
h + 2 - 48 = 30
h - 46 = 30
h - 46 + 46 = 30 + 46
h = 76
Answer:
2+h-48=30
2-48+h=30
-46+h=30
h=30+46
∴h=76
Using f(x) = 2x + 7 and g(x) = x - 3, find f(g(x)).
Answer:
2x+1
Step-by-step explanation:
that's a hard question
we know that g(x)= x-3
so f(g(x))= f(x-3)
we put it in the equation :
f(x-3)= 2(x-3) +7 = 2x-6+7 = 2x +1
Please help. What would be the proper proof for this problem? Prove: line BE congruent line BD.
Answer:
line AB is congruent to line CB . proof: given
line AE is congruent to line CD . proof: definition of a rectangle
angle EAB is congruent to angle BCD . proof: definition of a rectangle
triangle ABE is congruent to CBD . proof: SAS
line BE is congruent to line BD . proof: CPCTC
Step-by-step explanation:
Sorry if I'm wrong on this, but I hope you understand the general idea!
The number of students, S, serviced by the school system in the town of Emor, t years from 2000 can be modeled by the function S(t) = 10,000(1.1). The number ...
The question is incomplete. Here is the complete question.
The number of students, S, serviced by the school system in the town of Emor, t years from 2000 can be modeled by the function S(t) = 10000.[tex](1.1)^{t}[/tex]. The number of classrooms, C, in the town of Emor, t years from 2000 can be modeled by the function C(t) = 450 + 40t. Let D be the average number of students per classroom in Emor's school system t years from 2000.
Write a formula for D(t) in terms of S(t) and C(t).
Write a formula in terms of t.
Answer: D(t) = S(t) / C(t)
D(t) = [tex]\frac{10000.(1.1^{t} )}{450+40t}[/tex]
Step-by-step explanation: First, it is asked to write D(t), which is the average number of students per classroom in terms of students, S(t) and classroom, C(t).
Average is the total number of students divided by the total number of classrooms. Therefore:
D(t) = [tex]\frac{S(t)}{C(t)}[/tex]
Second, to write in term of t, which is time in years, for the average number of students per classroom:
D(t) = [tex]\frac{10000.(1.1)^{t} }{450+40t}[/tex]
In this formula it is clear that the average number of students per classroom is dependent of the growth factor of students each year represented by [tex]1.1^{t}[/tex] and the "growth factor" of classroom each year, represented by 40t.
please help!! simplify. Your answer should only contain positive exponents. 2m squared times 2m to the power 3. m to the power 4 times 2m to the power 3
Answer:
A).4m^(+5)
B).2m^ (+7)
Step-by-step explanation:
First let me convert the expression to words for easy simplification and evaluation.
2m squared times 2m to the power 3.
= 2m² * 2m³
m to the power 4 times 2m to the power 3
= m⁴ * 2m³
So to evaluate.
We just multiply and get our answer.
For 2m² * 2m³
= (2*2)(m²*m³)
= 4(m(²+³))
= 4m^(+5)
For m⁴ * 2m³
= 2(m⁴*m³)
= 2m(⁴+³)
= 2m^ (+7)
George is given two circles, Circle O and circle X, as shown. If he wants to prove that the two circles are similar, what would be the correct first step in his proof? Given: The radius of circle O is r, and the radius of circle X is r'. Prove: Circle O is similar to circle X.
Answer:
Circle O is similar to Circle X because they have the same radius
A package states that there are 60 calories in 12 crackers and 75 calories in 15 crackers. Since the relationship is proportional, how many calories are there in 180 crackers? x y 12 60 15 75
Answer:
900
Step-by-step explanation:
We can write the proportion as ...
calories/crackers = 60/12 = y/180
Multiplying by 180, we have ...
180(5) = y = 900
There are 900 calories in 180 crackers.
The perimeter of the triangle shown to the right is 321 meters. Fin the length of each side.
first side: x meters
second side: 3x meters
third side: (4x-3) meters
Answer: First side is 40.5 meters. Second side is 121.5 meters. The third side is 159.
Step-by-step explanation:
x + 3x + 4x -3 = 321
8x - 3 =321
+3 +3
8x = 324
x = 40.5
Second Side: 3(40.5) = 121.5
Third side: 4(40.5) - 3 = 159
Check: 159 + 121.5 + 40.5 = 321
Why do I need to pay to see answers....
I just need like 5 answers and I'm never coming on here again.
Answer:
same problem with me.That's what happened
A book store is having a sale. The book Bart wants was originally priced at $14.99. The book is now $10.04. By what percentage was the price reduced?
Answer:
33.0220147 % reduction
Step-by-step explanation:
Take the original price and subtract the new price
14.99-10.04 = 4.95
Divide by the original price
4.95/14.99 =.330220147
Change to percent form
33.0220147 %
