Answer:
Step-by-step explanation:
This is a hypothesis testing involving population proportion. The null hypothesis would be that fewer than or 50% of the people would favor spending money for a sewer system. Since she will vote to appropriate funds only if she can be reasonably sure that a majority of the people in her district favor the measure, then the alternative hypothesis which she should test is that more than 50% of the people would favor spending money for a sewer system.
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.
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!
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 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.
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:
Health issues are a concern of managers, especially as they evaluate the cost of medical insurance. A recent study of 150 executives at Elvers Industries, a large insurance and financial firm located in the Southwest, reported the number of pounds by which the executives were overweight. a. Compute the mean and the standard deviation.
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Health issues are a concern of managers, especially as they evaluate the cost of medical insurance. A recent survey of 150 executives at Elvers Industries, a large insurance and financial firm located in the Southwest, reported the number of pounds by which the executives were overweight. Compute the mean and the standard deviation.
Pounds Overweight Frequency
0 up to 6 14
6 up to 12 42
12 up to 18 58
18 up to 24. 28
24 up to 30. 8
Solution:
This is grouped data. We would determine the midpoint or class mark, x of each class by taking their averages.
The table would become
Class. x f fx
0 up to 6 (0+6)/2 = 3 14 42
6 up to 12 (6+12)/2 = 9 42 378
12 up to 18 (12+18)/2 = 15 58 870
18 up to 24 (18+24)/2= 21 28 588
24 up to 30 (24+30)/2 = 27 8 216
Summation f = 14 + 42 + 58 + 28 + 8 = 150
Summation fx = 42 + 378 + 870 + 588 + 216 = 2094
Mean = Summation fx/Summation f
Mean, m = 2094/150 = 13.96
Standard deviation = √summation of f(x - m)²)/(n - 1)
We would create another column on the table
f x x - m f(x - m)²
14 3 - 10.96 1681.7024
42 9 - 4.96 1033.2672
58 15 1.04 62.7328
28 21 7.04 1387.7248
8 27 12.04 1159.6928
Total = 5325.12
Standard deviation = √5325.12/150 - 1)
Standard deviation = 5.98
The following ple chart shows the number of students in a certain school. There
are 2000 students in the school. Answer questions 21, 22 and 23 from the pie
chart.
Grade 1
30%
Grade 3
20%
Grade 4
15%
21. The number of students in grade 1 is
22. The number of students in grade 3 is
23. The number of students in grade 4 is
Answer:
G1 : 0.3(2000) = 600
G2: 0.2(2000) = 400
G3: 0.15(2000) = 300
G4: 2000/15=150
FACTORISE THIS EXPRESSTION AS FULLY AS POSSIBLE 4x2+x3
Step-by-step explanation:
4x2 + x3
Rearrange
x3 + 4x2
x2 (x + 4)
Determine the equation of the inverse of y=2^3x-1
Answer:
f^-1(y) =[ In(x-2) + 1] /3
Step-by-step explanation:
The inverse of this expression is to find x
Now taking In of both sides we have
y=2^3x-1
In y = In2^3x-1
In y = (3x- 1)In 2
(Iny / In2) + 1= 3x
x =[ (Iny / In2) + 1] /3
Therefore the inverse of y is
f^-1(y) =[ (Inx / In2) + 1] /3
f^-1(y) =[ In(x-2) + 1] /3
The equation of the inverse of the provided equation, which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.
What is the inverse of an equation?The inverse of an equation is the reverse of the original equation. The equation and the inverse of it has symmetry in each other.
To find the inverse of equation, we have to interchange the variable of equation to each other.
The given equation is,
[tex]y=2^{3x-1}[/tex]
Taking log both side of the equation,
[tex]\ln y = \ln 2^{3x-1}[/tex]
Use the log of power and simplify the equation further, as,
[tex]\ln y = \ln 2^{3x-1}\\\ln y = (3x-1)\ln 2\\\dfrac{\ln y}{\ln 2} = (3x-1)\\\ln (y-2)= (3x-1)\\\ln (y-2)+1= 3x\\x=\dfrac{\ln (y-2)+1}{3}[/tex]
Interchange the place of x and y,
[tex]y=\dfrac{\ln (x-2)+1}{3}[/tex]
This is the required inverse equation.
Thus, the equation of the inverse of the provided equation which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.
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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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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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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
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?
Keep getting this wrong please help!!!
Answer:
85 + 35=120
Step-by-step explanation:
85 + 35= 120
85 - 35= 50
the difference is fifty
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.
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.
What’s the correct answer for this question?
Answer:
x = 40
Step-by-step explanation:
Given 2 secants to a circle from an external point, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is
8(8 + x) = 12(12 + 20) ← distribute parenthesis on both sides
64 + 8x = 12 × 32 = 384 ( subtract 64 from both sides )
8x = 320 ( divide both sides by 8 )
x = 40
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)
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
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.
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:
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
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
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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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]
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]
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.
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
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 %
F(x)=3x2 +12x +5 what is the discriminant
Answer:
84
Step-by-step explanation:
This is in the form
ax^2 + bx +c
3x^2 +12x +5
a =3 b = 12 c =5
The discriminant is
b^2 - 4ac
12^2 - 4 * 3 *5
144 - 60
84
