Answer:
The 95% confidence interval for the true average number of homes that a person owns in his or her lifetime is (4,6.2).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 50 - 1 = 49
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0096
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0096\frac{3.8}{\sqrt{50}} = 1.1[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 5.1 - 1.1 = 4
The upper end of the interval is the sample mean added to M. So it is 5.1 + 1.1 = 6.2.
The 95% confidence interval for the true average number of homes that a person owns in his or her lifetime is (4,6.2).
can someone please help with answer and explanation
9514 1404 393
Answer:
(x, y) = (3, 12)
Step-by-step explanation:
The first step in any problem solving is to look at the problem. Here, we see that the first equation can be reduced to standard form by dividing it by 2. This would give both terms a coefficient of 1.
We see that the second equation already has a variable with a coefficient of 1.
When solving a system by substitution, it can save some effort if you start by finding a variable with a coefficient of 1 or -1. Since we see that in the second equation, we choose to solve the second equation for y:
y = 4x . . . . . . . add 4x to both sides of the second equation
Now, we have an expression for y that we can substitute into the first equation.
2x +2(4x) = 30 . . . . substitute for y
10x = 30 . . . . . . . . simplify
x = 3 . . . . . . . . . . divde by 10
y = 4(3) = 12 . . . . . find y using y=4x
The solution is (x, y) = (3, 12).
__
Additional comment
I doesn't matter what variable gets substituted. The purpose of the exercise is to reduce the number of variables in the equation. Here, we start with an equation that has 2 variables. Substituting for one of them gives an equation with only one variable, a lot easier to solve.
You don't have to find an expression for the "bare" variable. We could solve the second equation for 2x, for example: 2x = y/2, then substitute for 2x in the first equation: y/2 +2y = 30 ⇒ y = (2/5)(30) = 12. Or, we could solve the first equation for 2x and substitute into the second: 2x=30-2y, y-2(2x) = 0 ⇒ y-2(30-2y) = 0 ⇒ y = 60/5 = 12.
The substitution property of equality says you can make any substitution of equal values anywhere. "butter = margarine" means you can substitute butter for margarine, or vice versa, wherever you may wish.
Can someone please help solve this equation thank you
Answer:
A and B
Step-by-step explanation:
Both points are in the shaded/blue zone
I hope this helps!
pls ❤ and give brainliest pls
Answer:
Yea both A and B are correct.
Step-by-step explanation:
if you can see you can put (-12,0) inside the shaded triangle also for (-10,1)
you can give brainlist to the person above :D
look at the image below plz correct answers Surface area of cones 15 points
Answer:
[tex]A\approx 282.7\ m^2[/tex]
Step-by-step explanation:
1. Approach
The easiest method to solve this problem is to use the Pythagorean theorem to find the height of the cone. Then one can substitute the values given and found on the cone into the formula to find the surface area in order to solve for the surface area of the given cone.
2. Height of the cone
Imagine drawing a line from the tip of the cone down to the center of the base. This line will form a right angle with the base, thus, a right triangle is formed between the line, the radius (the distance from the center to the circumference or outer edge on a circle) of the base, and the incline of the cone. The Pythagorean theorem is a formula that relates the sides of a right triangle. This formula is as follows:
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs or the sides adjacent to the right angle of the right triangle, and (c) is the hypotenuse or the side opposite the right angle of the right triangle. Substitute the given values into the formula and solve for the unknown, or rather the height of the cone:
[tex]a^2+b^2=c^2[/tex]
[tex]a^2+5^2=13^2[/tex]
Simplify,
[tex]a^2+5^2=13^2[/tex]
[tex]a^2+25=169[/tex]
Inverse operations,
[tex]a^2+25=169[/tex]
[tex]a^2=144[/tex]
[tex]a=12[/tex]
[tex]h=12[/tex]
3. Find the surface area of the cone.
The following formula can be used to find the surface area of a cone:
[tex]A=\pi r(r+\sqrt{h^2+r^2})[/tex]
Where ([tex]\pi[/tex]) represents the numerical value (3.1415...), (r) represents the radius of the base, and (h) represents the height of the cone. Substitute the given values into the formula and solve for the surface area:
[tex]A=\pi r(r+\sqrt{h^2+r^2})[/tex]
[tex]A=\pi 5(5+\sqrt{12^2+5^2})[/tex]
Simplify,
[tex]A=\pi 5(5+\sqrt{12^2+5^2})[/tex]
[tex]A=\pi 5(5+\sqrt{144+25})[/tex]
[tex]A=\pi 5(5+\sqrt{169})[/tex]
[tex]A=\pi 5(5+13)[/tex]
[tex]A=\pi 5(18)[/tex]
[tex]A=\pi 90[/tex]
[tex]A\approx 282.743[/tex]
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. Find each measurement indicated. Round your answers to the nearest tenth. Part 3ddd
Answer:
see below
Step-by-step explanation:
7. We can use the law of sines to solve
sin C sin B
-------- = ----------
AB AC
sin 45 sin 32
--------- = ----------
AB 6
Using cross products
6 sin 45 = AB sin 32
6 sin 45 / sin 32 = AB
8.00620 = AB
To the nearest tenth
8.0= AB
9. We can use the law of sines to solve
sin A sin B
-------- = ----------
CB AC
sin A sin 88
-------- = -----------
13 15
Using cross products
15 sin A = 13 sin 88
sin A = 13/15 sin 88
Taking the inverse sin of each side
sin^-1(sin A) = sin ^-1 (13/15 sin88)
A = 60.01298726
To the nearest tenth
A =60.0
Determine what type of model best fits the given situation:
A. linear
B. exponential
O c. quadratic
D. none of these
Reset Selection
if chaka,ada and ese are to share 120 oranges with the ratio of 1:2:3 respectively. How many oranges does ada have?.
Answer:
40
Step-by-step explanation:
1+2+3=6
1/6×120=20
2/6×120=40
3/6×120=60
Quadrilateral JKLM is rotated - 270° about the origin.
Draw the image of this rotation
Need a visual answer please! Thanks!
Answer:
Step-by-step explanation:
When the quadrilateral JKLM is rotated - 270° about the origin then the image of rotated quadrilateral is shown below.
What is rotation?"It is a transformation in which the object is rotated about a fixed point. "
For given question,
Quadrilateral JKLM is rotated - 270° about the origin.
This means, quadrilateral JKLM is rotated 270° clockwise about the origin.
We know, if point P(x, y) is rotated 270° clockwise or 90° anticlockwise then the coordinated of rotated point would be (-y, x).
From figure, the coordinates of the quadrilateral JKLM are:
J = (3, 3)
K = (5, -5)
L = (-3, -7)
M = (3, -3)
After rotating -270° about the origin the coordinates of the quadrilateral would be,
J' = (-3, 3)
K' = (5, 5)
L' = (7, -3)
M' = (3, 3)
And the image of the rotated quadrilateral J'K'L'M' is shown below.
Therefore, when the quadrilateral JKLM is rotated - 270° about the origin then the image of rotated quadrilateral is shown below.
Learn more about rotation here:
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Damaged items are marked down 25% to 40%. A newspaper coupon holder; to an additional 10% markdown of the new price due to the damage. What is the lowest price of a damaged item that was originally marked GHC100?
A GHC 35.60
B GH 5000
C. GHC 18.00
D. GHC 40.80
E GHC 23.40
Markdown is the difference (at sale) between the price an item is placed at for retail sale, and the actual price the item is sold
The correct option is; B. GHC 50.00
The reason for choosing option B is as follows;
The known parameters
The percentage by which damaged items are marked down = 25% to 40%
The percentage markdown offered by the newspaper coupon = 10%
The original marked price of the item = GHC 100
Strategy:
Apply the damaged items and coupon markdown percentages to the original marked price of GHC100 sum the results to find the total markdown
Solution:
Markdown due to damage:
Given that the item is damaged, to have the lowest price, we apply the largest markdown of 40%;
40% is removed from the price to which the item marked down due to damage, as follows;
The markdown due to damage = 40/100 × GHC 100 = GHC 40
Markdown due to Coupon Holder:
The markdown the coupon holder is to get = 10% off the retail price
Given that the damage is not mentioned in the newspaper, we have;
∴ The markdown the coupon holder is to get = 10/100 × GHC 100 = GHC 10
Total markdown:
The total markdown is therefore equal to GHC 40 + GHC 10 = GHC 50
The Lowest Price of A Damaged Items marked GHC100:
The lowest price of the item = Original price - Maximum markdown
The lowest price of the item = GHC 100 - GHC 50 = GHC 50
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For the inequality 4 < -x^2– y, where is the graph shaded and is the curve solid or dotted"
answer=
X<-4
.............................................................
NEED HALP!!! Find the ordered pair $(s,t)$ that satisfies the system
Answer:
(-8/7 ; 5/7)
Step-by-step explanation:
5t + 1/2s = 3 - - - (1)
3t - 6s = 9 - - - - - (2)
Multiply (1) by 12 and (2) by 1
Add the result to eliminate s
60t + 6s = 36
3t - 6s = 9
____________
63t = 45
t = 45 / 63
t = 5/7
Put t = 5/7 in either (1) or (2) to obtain the value of s
3(5/7) - 6s = 9
15/7 - 6s = 9
-6s = 9 - 15/7
-6s = (63 - 15)/7
-6s = 48/7
s = 48/7 * - 1/6
s = - 8/7
The midpoint of has coordinates of (4, -9). The endpoint A has coordinates (-3, -5). What are the coordinates of B?
9514 1404 393
Answer:
(11, -13)
Step-by-step explanation:
If midpoint M is halfway between A and B:
M = (A +B)/2
Then B is ...
B = 2M -A
B = 2(4, -9) -(-3, -5) = (8+3, -18+5)
B = (11, -13)
Answer:
Use the midpoint formula:
[tex]midpoint=(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})[/tex]
Endpoint A = (x₁, y₁) = (-3, -5)Endpoint B = (x₂, y₂)Midpoint = (4, -9)Substitute in the values:
[tex](4, -9)=(\frac{-3+x_{2}}{2} +\frac{-5+y_{2}}{2} )[/tex]
[tex]4=\frac{-3+x_{2}}{2} \\4(2)=-3+x_{2}\\8+3=x_{2}\\x_{2}=11[/tex] [tex]-9=\frac{-5+y_{2}}{2} \\(-9)(2)=-5+y_{2}\\-18+5=y_{2}\\y_{2}=-13[/tex]
Therefore, Point B = (11, -13)
Most of the heat loss for outdoor swimming pools is due to surface
evaporation. So, the greater the area of the surface of the pool, the greater
the heat loss. For a given perimeter, which surface shape would be more
efficient at retaining heat: a circle or a rectangle? Justify your answer.
Answer:
rectangle
Step-by-step explanation:
Perimeter of 20 feet
rectangle (square is technically a rectangle):
sides 5 and 5
5*5 = 25ft²
Circle:
20/(2π) = 3.18309...
3.1809...²π = 31.831ft²
Max area of rectangle (i.e. square) has a smaller area than a circle.
Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] $ y = e^{{\color{red}5}\sqrt{x}} $
Answer:
The answer is "[tex]\frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]".
Step-by-step explanation:
Given:
[tex]y = e^{{\color{\red}5}\sqrt{x}}[/tex]
let
[tex]\to t= 5\sqrt{x}\\\\\frac{dt}{dx}= 5 \frac{1}{2\sqrt{x}}\\\\\frac{dt}{dx}= \frac{5}{2\sqrt{x}}\\\\[/tex]
and
[tex]\to y=e^t\\\\\to \frac{dy}{dt}=e^t\\[/tex]
[tex]\to \frac{dy}{dt}=e^{5\sqrt{x} }\\[/tex]
So,
[tex]\to \frac{dy}{dx}= \frac{dy}{dt} \times \frac{dt}{dx}[/tex]
[tex]=e^{5\sqrt{x} }\times \frac{5}{2\sqrt{x}}\\\\= \frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]
OR
[tex]\to g(x) = 5\sqrt{x} \\\\\to f(x) = e^{(x)}\\\\[/tex]
Derivate:
[tex]\to f''g' = \frac{e^{(5\sqrt{x})}5}{(2\sqrt{x})}[/tex]
Integrate the following. ∫[tex]84dx[/tex]
Answer:
[tex]\displaystyle \int {84} \, dx = 84x + C[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsDefinite/Indefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {84} \, dx[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {84} \, dx = 84\int {} \, dx[/tex][Integral] Reverse Power Rule: [tex]\displaystyle \int {84} \, dx = 84x + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integrations
What is the equation of the following graph?
Answer:
y=0.5x + 5
Step-by-step explanation:
The points are (0,5) and (-10,0)
to find the slope do
0-5/-10-0 = 5/10 = 1/2 = 0.5
next plug one of the points into point slope formula
y-y1=m(x-x1)
lets use the point (-10,0)
y1=0
x1= -10
m= 0.5
y-0=0.5(x- -10)
y = 0.5(x+10)
distribute the 0.5
y=0.5x+5
Alejandro wants to determine how much money he made in the last month after taxes, social security, and Medicare were taken out of his paycheck. What number should he look at on his paystub? O a) Federal tax amount b) Net pay O c) Gross pay O d) Deductions
Answer:
absolutely B
Step-by-step explanation:
A is one type of tax
C) gross pay includes taxes, social security and something else
D) deductions are the type of fee
and B is the amount of money that he received
Alejandro should look at Net pay on his paystubs the answer is Net pay option (b) is correct.
What is the income tax rate?It is defined as the tax rate applied on the solely earned money by a single entity.
It is given that:
Alejandro wants to determine how much money he made in the last month after taxes, social security, and Medicare were taken out of his paycheck.
The options are:
A) Federal tax amount
The Federal tax amount is one type of tax.
C) Gross pay
The gross pay includes taxes, social security, and other charges
D) Deductions
The deductions are the type of fee or negative amounts.
Alejandro should look at Net pay on his paystubs.
Thus, Alejandro should look at Net pay on his paystubs the answer is Net pay option (b) is correct.
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PLEAZE HELPPPPPPPPPP
Quy tắc suy luận nào là cơ sở của suy diễn sau: "Biết rằng: 2 đường thẳng d và d' song song hoặc cắt nhau. Ta đã có d không song song với d'. Vậy d cắt d'
Select one:
a. Luật loại trừ
b. Luật rút gọn
c. Luật phản chứng
d. Luật tách rời
Answer: a
Step-by-step explanation:
construct the truth table (p ∧ q) =⇒ [(q ∧ ¬p) =⇒ (r ∧ q)]
[tex]\begin{array}{c|c|c|c|c|c} p & q & r & p\land q & q\land \neg p & r \land q \\&&&&\\ T & T & T & T & F & T \\ T & T & F & T & F & F \\ T & F & T & F & F & F \\ T & F & F & F & F & F \\ F & T & T & F & T & T \\ F & T & F & F & T & F \\ F & F & T & F & F & F \\ F & F & F & F & F & F\end{array}[/tex]
An implication A => B is true if either A is false, or both A and B are true. So
[tex]\begin{array}{c|c|c}p\land q & (q\land\neg p) \implies (r\land q) & (p\land q) \implies \big[(q\land\neg p) \implies (r\land q)\big] \\&&\\T & T & \mathbf T\\T & T & \mathbf T\\F & T & \mathbf T\\F & T & \mathbf T\\F & T & \mathbf T\\F & F & \mathbf T\\F & T & \mathbf T\\F & T & \mathbf T\end{array}[/tex]
and the given statement is a tautology.
A veggie wrap at David's Deli is composed of 33 different vegetables and 22 different condiments wrapped up in a tortilla. If there are 66 vegetables, 66 condiments, and 55 types of tortilla available, how many different veggie wraps can be made
Answer:
The answer is "[tex]7.21 \times 10^{37}[/tex]".
Step-by-step explanation:
[tex]\to ^{n}_{C_r}=\frac{n!}{r!(n-r)!}[/tex]
[tex]=^{66}_{C_{33}} \times ^{66}_{C_{22}} \times ^{55}_{C_{1}} \\\\=\frac{66!}{33! (66-33)!} \times \frac{66!}{22! (66-22)!} \times \frac{55!}{1! (55-1)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times \frac{55!}{1! (54)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times \frac{55\times 54!}{1! (54)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times 55\\\\= 7219428434016265740 \times 182183167981760400\times 55\\\\[/tex]
[tex]= 7.21 \times 10^{18} \times 1.82\times10^{17}\times 55\\\\= 7.21 \times 10^{35} \times 1.82\times 55\\\\=721.721 \times 10^{35}\\\\=7.21\times 10^{37}[/tex]
An object travels along the x-axis so that its position after t seconds is given by x(t) = 2t2 – 5t – 18 for all times t such that t ≥ 0.
Which inequality describes all times t for which the object is traveling toward the right?
the function is given, and it's value is where the object is ("how far to the right").
so as long as it rises (going more right), this will be apply.
in the screenshot I graphed the function. of course t is graphed as x and "along the x-axis" is graphed as y, but the pattern is the same anyways.
for the first 1.25 seconds the object goes to the left, and after that always to the right.
since we look at t to calculate x, t effectively takes the role of the important variable that is normally given to x. the calculation pattern are just the same. so let's find the lowest point of this function by calculating it out.
x(t) = 2t² – 5t – 18
x'(t) = 4t -5
x'(t) = 0
0 = 4t -5
5 = 4t
1.25 = t
plugging it into the second derivative
x''(t) = 4
x''(1.25) = 4
it's positive, so at t=1.25 there is a low point
(of course the second derivative is constant anyways.)
the object is traveling toward the right
the object is traveling toward the rightfor t > 1.25
The object is moving to the right, for t > 1.25, the object is moving in a rightward direction.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
An object travels along the x-axis so that its position after t seconds is given by:
x(t) = 2t² – 5t – 18
x'(t) = 4t - 5
x'(t) = 0
4t -5 = 0
t = 5/4 = 1.25 seconds
x''(t) = 4
x''(1.25) = 4
x''(1.25) > 0
At t = 1.25 the object travels at a low point.
Thus, the object is moving to the right, for t > 1.25, the object is moving in a rightward direction.
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why is (3, -5) not a solution to -x+4=-15 and -2x-3y=-8
Step-by-step explanation:
-x+4y= -15
-2x-3y=-8
the intersection point isn't (3,-5)
it's approximately (-1.1818 ,3.45455 )
Answer:
see below
Step-by-step explanation:
Check the solution in both equation
-x+4 = -15
-3 +4 = -15
1 does not equal -15 so it is not a solution
-2x-3y = -8
-2(3)+-3(-5) = -8
-6 +15 = -8
9 = -8
It is not a solution to either equation
The surface area of a cube is 27^2. Calculate the length of the sides of the cube
Answer:
Step-by-step explanation:
Do you mean 27 units² ?
A cube has six congruent, square faces. Area of one face = (27/6) units²
Length of one edge = √(27/6)
= √(9/2)
= √9/√2
= 3/√2
= 3√2/2 units
Solve (2x – 1)2 = 9. Question 11 options: A) x = 2, –1 B) x = 2, 1 C) x = –2, –1 D) x = –2, 1
Answer:
(2x – 1)2 = 9
4x-2=9
4x=9+2
4x=11
x=11/4
x=2.75
Cristina is sending out thank you cards for birthday presents. She has pink (P), blue (B), and green (G) cards, and white (W) and yellow (Y) envelopes to send them in. She chooses a card and an envelope at random for each person. What is the sample space for possible combinations? Enter a list of text [more] Enter each outcome as a two-letter "word", with the first letter for the card and the second letter for the envelope. For example, PW would be a pink card in a white envelope. Separate each element by a comma.
Answer:
PW, BW, GW, PY, BY, GY
Step-by-step explanation:
We need to determine the sample space
pink(P), blue (B), and green (G) cards, (W) and yellow (Y) envelopes
Each color card can match with each color envelope
Start with the white envelopes and each color card
and then the yellow envelopes with each color card
PW BW GW
PY BY GY
commission received
Answer:
Commission Received refers to a percentage amount received by the company (or) an individual on the total sales incurred. It is an indirect income/revenue recorded on the credit side of profit and loss account.
Step-by-step explanation:
mark me brainliest if my answer is correct
A box contains 100 tickets labeled with numbers. The average of the labels is 14 and the SD of the labels is 8.2. Eighteen tickets will be drawn independently at random with replacement from the box. The chance that the absolute value of the difference between the sample sum of the labels on the tickets and 252 does not exceed 278.32 is: __________
Answer:
at most
Step-by-step explanation:
The sample drawn from the population is a relative representation not the absolute representation. The box has 100 tickets in it and sample of tickets is selected to identify difference between sample sum and 252. The at most value for the sample sum can be 278.32 and value cannot exceed beyond this.
Help with this please!!!!!!!!!!!!!!
Answer:
A is the correct answer :)
Answer:
A
Step-by-step explanation:
checking if A is correct, if we get x as 76 then it is correct
if 5miles = 8 kilometers
47.5 miles= x
that is
5=8
47.5=x
cross multiply
5x=380
x=380/5
x=76
there fore A is correct
checking if B is correct, if we get x as 86 then it is correct
if 5miles = 8 kilometers
52.5 miles= x
that is
5=8
52.5=x
cross multiply
5x=420
x=420/5
x=84
therefore B is incorrect
checking if C is correct, if we get x as 34 then it is correct
if 5miles = 8 kilometers
22.5 miles=x
that is
5=8
22.5=x
Cross multiply
5x=180
x=180/5
x=36
therefore C is incorrect
checking if D is correct, if we get x as 22 then it is correct
if 5miles = 8 kilometers
12.5miles = x
that is
5=8
12.5=x
5x=100
x=100/5
x= 20
Which of the following theorems verifies that ANPO- AXYZ?
An architect was designing a rectangular room with a length of 16 feet, a width of 14 feet,
and a height of 10 feet.
What is the volume, in cubic feet of the room?
Show your work
cubic feet
Answer
The architect changed his design and added 2 feet to the length and width of the room.
In cubic feet, how much greater is the volume of the room in his new design?
Show your work
cubic feet
Answer
Hurrryyy knowww
Answer:
(1) 16 x 14 x 10 Room: 2240 ft^3.
(2) How much greater the 18 x 16 x 10 Room is: 640 ft^3.
Step-by-step explanation:
To find the volume of a given space, all we need to do is multiply length*width*height. In this case, the values are 16*14*10, which equals 2240 ft^3.
The changed design would have a volume of 18*16*10, which would equal 2880 ft^3.
To find the difference in volume between the two rooms, all we have to do is subtract the smaller room from the bigger room. 2880 - 2240 = 640 ft^3.
