A random sample of 17 hotels in Boston had an average nightly room rate of $165.40 with a sample standard deviation of $21.70. The critical value for a 98% confidence interval around this sample mean is ________.
Answer:
153.158 ; 177.642
Step-by-step explanation:
Given the following:
Sample mean (m) = 165.40
Sample standard deviation (s) = 21.70
Sample size (n) = 17
α = 98%
Confidence interval = m ± z(SE)
z at 98% = 2.326
SE = s/√n
SE = 21.70/√17 = 5.2630230
Hence,
Confidence interval = 165.40 ± 2.326(5.2630230)
165.40 - 12.241791498 OR 165.40 + 12.241791498
153.158 ; 177.642
help me please i’ll do anything
Answer:
in the first one, she makes $7.50 per box
Step-by-step explanation:
looking at the graph
What is the value of j
. If BC=46.5 and AC=82.3 Find AB.
Which number has the same absolute value
as 8
Answer:8
Step-by-step explanation:
is 600 : 450 and 4 : 3 equivalent
Answer:
Yes
Step-by-step explanation:
600/150=4
450/150=3
A sphere has a radius of 6 centimeters.
Find the surface area of the sphere.
PLS HELP I'LL GIVE A LOT OF POINTS
Answer:
A sphere with a radius of 6 cm will have a surface area of about 452.39
Step-by-step explanation:
Answer: 452.39 cm^2.
SA = 4πr^2 = 4π(6)^2 ≅ 452.39 cm^2.
∴ the surface area of the sphere is around 452.39 cm^2.
Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?
A.
{-4, 4, 14}
B.
{2, 4, 9}
C.
{-12, -4, 6}
D.
{12, 4, -6}
Answer:
The range is {12, 4, -6} ⇒ D
Step-by-step explanation:
The range of the relation is the values of y corresponding to the values given for x which is the domain of the relation
∵ The relation is 12x + 6y = 24
∵ The domain of the function is {-4, 0, 5}
→ That means x = -4, 0, 5, we need to find their corresponding values of y
∴ Substitute the values of x in the relation
∵ x = -4
∴ 12(-4) + 6y = 24
∴ -48 + 6y = 24
→ Add 48 to both sides
∴ -48 + 48 + 6y = 24 + 48
∴ 6y = 72
→ Divide both sides by 6 to find y
∴ [tex]\frac{6y}{6}=\frac{72}{6}[/tex]
∴ y = 12
∵ x = 0
∴ 12(0) + 6y = 24
∴ 0 + 6y = 24
∴ 6y = 24
→ Divide both sides by 6 to find y
∴ [tex]\frac{6y}{6}=\frac{24}{6}[/tex]
∴ y = 4
∵ x = 5
∴ 12(5) + 6y = 24
∴ 60 + 6y = 24
→ Subtract 60 from both sides
∴ 60 - 60 + 6y = 24 - 60
∴ 6y = -36
→ Divide both sides by 6 to find y
∴ [tex]\frac{6y}{6}=\frac{-36}{6}[/tex]
∴ y = -6
∵ The range is the values of y which corresponding to the domain
∴ The range is {12, 4, -6}
The answer is down below have a good day!!!
A company manufactures and sells x VCRs per month. If the cost and revenue equations are C(x) = 200 + 2x, R(x) = 20x − (x^2/50) , use differentials to estimate the change, ∆P, in profit when the production is increased from 100 to 101.
Answer:
ΔP = 14
Step-by-step explanation:
Given
[tex]C(x) = 200 + 2x[/tex]
[tex]R(x) = 20x - \frac{x^2}{50}[/tex]
Required
Determine the change in profit
First, we need to determine the profit
[tex]P(x) = R(x) - C(x)[/tex]
[tex]P(x) = 20x - \frac{x^2}{50} - 200 - 2x[/tex]
Collect Like Terms
[tex]P(x) = - \frac{x^2}{50} + 20x - 2x- 200[/tex]
[tex]P(x) = - \frac{x^2}{50} + 18x- 200[/tex]
Differentiate wrt x
[tex]P'(x) = -\frac{x}{25} + 18[/tex]
When Profit increases from 100 to 101, the change becomes
ΔP [tex]= -\frac{x}{25} + 18[/tex]Δx
Δx[tex]= (x_2 - x_1)[/tex]
Where
[tex]x_2 = 101[/tex]
[tex]x_1 = x = 100[/tex]
So, the expression: ΔP [tex]= -\frac{x}{25} + 18[/tex]Δx becomes
ΔP [tex]= (-\frac{x}{25} + 18)(x_2 - x_1)[/tex]
ΔP [tex]= (-\frac{100}{25} + 18)(101 - 100)[/tex]
ΔP [tex]= (-4+ 18)(1)[/tex]
ΔP [tex]= (14)(1)[/tex]
ΔP = 14
what are the slopes of the two different lines? are they undefined?
Answer:
m = (y2 -- y1) / (x2 -- x1)
Step-by-step explanation:
There are four blue marbles and 6 red marbles. What is the ratio of blue marbles to red marbles. Write the ratio in simplest form
Answer:
2:3
Step-by-step explanation:
2 is the greatest common factor, so divide both 4 and 6 by 2, which should result as 2:3.
hope this helps :)
Suppose n(t) = -51^2 + 10t + 3 represents the height of a
diver above the water (in meters), 1 seconds after
the diver leaves the springboard. Which of these
statements is true?
(А)
After 1 second, the diver will be 3 feet above
the water.
B
After 5 seconds, the diver will be 25 feet above
the water.
С
After 1 second, the diver will be 8 feet above
the water.
D
After 5 seconds, the diver will be 78 feet above
the water.
Answer:
The correct option is (c).
Step-by-step explanation:
The height of a diver abov the water is given by :
[tex]h(t) = -5t^2 + 10t + 3[/tex] ....(1)
Where h(t) is in meters and t is in seconds
Put t = 1 s, in equation (1) we get :
[tex]h(1) = -5(1)^2 + 10(1) + 3\\\\=8\ \text{feet}[/tex]
Put t = 5 s, in equation (1) we get :
[tex]h(1) = -5(5)^2 + 10(5) + 3\\\\=-72\ \text{feet}[/tex]
Out of the given options, "after 1 second, the diver will be 8 feet above the water is (c)". Hence, the correct option is (c).
In two hours, Christopher can read 150 pages. At this rate, how many pages can Christopher read in three hours?
WILL RECIEVE BRAINLIST AND EXTRA POINTS
what value of x will make the equation f(x)=6 true ?
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]f(x) = 6[/tex]
Required
Solve for x
The question is incomplete as the function f(x) is not given.
However, the following explanation will guide you
As a point of reference, we assume that f(x) is:
[tex]f(x) = 2x + 4[/tex]
To solve further, we substitute 6 for f(x)
[tex]6 = 2x + 4[/tex]
Then, we solve for x
[tex]2x = 6 - 4[/tex]
[tex]2x = 2[/tex]
Divide through by 2
[tex]x = 1[/tex]
So, in your case.
All you need to do is substitute 6 for f(x) then solve for x
In the diagram, bisects ABC. Find mABD and mDBC
Answer:
Angle ABD = 45 degrees
Angle DBC = 45 degrees
Step-by-step explanation:
If the ray BD bisects ABC, then it divides it in two angles of equal measure. The we can write the following equality:
angle ABD = Angle DBC
9 x + 9 = 12 x - 3
solve for x by subtracting 9x from both sides,
9 = 3 x - 3
and adding 3 to both sides:
9 + 3 = 3 x
12 = 3 x
divide both side by 3 to isolate "x":
12/3 = x
x = 4
And now we can find the value of each angle:
Angle ABD = 9 x + 9 = 9 (4) + 9 = 36 + 9 = 45 degrees
Angle DBC = 12 x - 3 = 12 (4) - 3 = 18 - 3 = 45 degrees
most ants can lift 50 times their own weight. If an ant weighs 5 milligrams, how many ants would it take to lift a 500 gram bag of sugar?
Answer:
2000
Step-by-step explanation:
5*50=250 mg
250*4=1000 mg
1000*500=500 m
4*500=2000
It would take 2,000 ants to hoist a 500-gram bag of sugar.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, most ants can lift 50 times their own weight.
also given every ant has 5 mg weight.
So, 1 ant can lift = 5mg * 50 = 250mg
Since 1 gram has 1000 mg
Ant can lift = 1/4 grams
thus,
1/4 gram of sugar can be lifted by = 1 ant
1 gram of sugar can be lifted by = 4 ant
500 grams of sugar can be lifted by = 4 * 500 ant = 2000 ants
Therefore, 2000 ants would it take to lift a 500-gram bag of sugar.
Learn more about proportionalities here:
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1. Which of the following statements best describes the patterns and trends of the Periodic Table?
a. The atomic number and atomic mass decrease from left to right across a period; energy levels
decrease from top to bottom down a group
b. The atomic number and atomic mass increase from left to right across a period; energy levels
decrease from top to bottom down a group.
c. The atomic number and atomic mass increase from left to right across a period; energy levels
increase from top to bottom down a group.
d. The atomic number and atomic mass decrease from left to right across a period; energy levels
increase from top to bottom down a group.
Answer:
Its C
Explanation
c. The atomic number and atomic mass increase from left to right across a period; energy levels
increase from top to bottom down a group.
10/3 = x/ (-5/2) what does x equal
The answer to the equation is [tex]x=-\frac{25}{3}[/tex]
First, you must cross multiply the fractions.
[tex]10*-\frac{5}{2} =x*3[/tex]
[tex]-25=3x[/tex]
Then, you must flip the equation.
[tex]3x=-25[/tex]
Finally, divide 3 on each side
[tex]\frac{3x}{3}=\frac{-25}{3}[/tex]
[tex]x=-\frac{25}{3}[/tex]
Which of the following is equivalent to 7^2•7^5•2^2/7^3•2^6
When you add, you subtract the exponents. When you divide, you subtract the exponents.
When you have multiplication and division in one expression, you do it from left to right.
7^2 times 7^5 = 7^ (2+5) = 7^7
7^7 times 2^2 / 7^3 = 7 ^(7 - 3) times 2^2
7^4 times 2^2 times 2^6 = 7^4 times 2^(2+6) = 7^4 times 2^8
Put it in a calculator.
614656.
That is the answer, but you didn't include the "which of the following", so I guess you'll have to put each value in the calculator to find out!
If the 7^3 times 2^6 is in parenthesis, then the answer is 150.0625.
What is the scale factor of AABC to ADEF?
B
72
359
66
E
-35"
A 80°
12
80*
DS
11
42
65"
A. 6
B.
1
2
1
C.
02
D. 2
so we know that the size of the triangle is decreasing witch means that the scale factor is going to be a fraction. to find this fraction you are going to divide the smaller side by the corisponding longer side.
12/72= 1/6
the correct answer is c 1/6
The scale factor of triangles ABC and DEF is 6.
Option A is the correct answer.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
From the triangles,
The ratio of the corresponding sides of the two triangles must be equal.
The value of the ratio is the scale factor.
So,
AB/DE = BC/EF = AC/DF
This can be written as,
72/12 = 66/11 = 42/7
6 = 6 = 6
Thus,
The scale factor of triangles ABC and DEF is 6.
Learn more about scale factors here:
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Please help me if you know it thank you so much
Answer:
a) 9 beats
b) 9 beats per minute
c) y=9x
d) 180 times
Someone Help Me Please. ?
Answer:
I’m guessing number 3
Step-by-step explanation:
Hey I need help with this question:
6(x-3)^2-26 = 10
Answer:
x = 3 ±sqrt(6)
Step-by-step explanation:
6(x-3)^2-26 = 10
Add 26 to each side
6(x-3)^2-26+26 = 10+26
6(x-3)^2 = 36
Divide by 6
6/6(x-3)^2 = 36/6
(x-3)^2 = 6
Take the square root of each side
sqrt((x-3)^2) = ±sqrt(6)
x-3 = ±sqrt(6)
Add 3 to each side
x-3+3 =3 ±sqrt(6)
x = 3 ±sqrt(6)
Dexter rode his bike 2 kilometers. Then, he walked 955 meters more to go fishing. How many total meters did Dexter travel to go fishing?
Answer:
The Answer is 2955.
Step-by-step explanation:
First convert 2 km to meters. 1 km = 1,000 meters. So, 2 km = 2x1,000. Dexter walked 955 meters. We can add to find out how far he traveled all together. 2,000+955=2,955 meters. Dexter traveled a total of 2,955 meters to fishing.
Answer:
2955
Step-by-step explanation:
Properties of the normal distribution include?
Answer:
Properties of a normal distribution
The mean, mode and median are all equal.
The curve is symmetric at the center (i.e. around the mean, μ).
Exactly half of the values are to the left of center and exactly half the values are to the right.
The total area under the curve is 1.
Step-by-step explanation:
The solution is , given below.
What is normal distribution?A normal distribution is a type of continuous probability distribution in which most data points cluster toward the middle of the range, while the rest taper off symmetrically toward either extreme. The middle of the range is also known as the mean of the distribution.
here, we have,
Properties of a normal distributionThe mean, mode and median are all equal.The curve is symmetric at the center (i.e. around the mean, μ).Exactly half of the values are to the left of center and exactly half the values are to the right.The total area under the curve is 1.To learn more on normal distribution click:
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Is the answer x=6????
Answer:
x=12
Step-by-step explanation:
5x-2 = 58
5x = 60
x = 12
18. Leonardo lives in a 10-storey apartment
building. The building is 121 m tall.
All the storeys have the same height.
How high is each storey?
Answer:
12.1 m tall
Step-by-step explanation:
First you take 121 and divide it by 10 then you take the end number and add a m
Part A
Choose a writing prompt from the following list. Then brainstorm a topic by asking the questions in the table. Fill in the
table with the prompt, topic, and answers to the questions:
Recount a personal achievement that you're proud of.
• Describe a place that has helped make you who you are.
• Identify and describe your role model.
Examine something that you're afraid of..
Describe something that motivates you.
В І у хх,
AAEEE 3
Font Sures
3
5
o
Writing Prompt
Topic
What?
Where?
When?
Who?
Why?
How?
I
I’m
Answer:
Step-by-step explanation:
you pick your topic
the what is what is your topic
where does your topic take place
who is in your topic or who is it talking about
why did you choose this topic
find the value of x. PLEASE HELP.
The answer is 25. Teacher gave us the answer, but I need to show my work.
Answer:
Step-by-step explanation:
2+5x+53=180
55+5x=180
5x=125
x=25
hope this helps :)
1. The assessed value of the Sanchez house is $485,000. The
annual property tax is rate 2.975% of the assessed value.
What is the annual property tax on the Sanchez house?