Answer:
375 guests
Step-by-step explanation:
costs: 1500 + 8g
income: 12g
They must be equal
1500+8g = 12g
Subtract 8g from each side
1500 +8g-8g =12g-8g
1500= 4g
Divide by 4
1500/4 = 4g/4
375 = g
A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. A 95% confidence interval for the difference between the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the following do you know for sure:
A: The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
B: The hypothesis µ1 = µ2 would be rejected at the 10% level of significance.
C: The hypothesis µ1 = µ2 would be rejected at the 1% level of significance.
A) A and B
B) A and C
C) A only
D) A, B, and C
Answer:
C) A only
Step-by-step explanation:
In statistics, the null hypothesis is the default hypothesis and the alternative hypothesis is the research hypothesis. The alternative hypothesis usually comes in place to challenge the null hypothesis in order to determine if the test is statistically significant or not.
Similarly,
In hypothesis testing, the confidence interval consist of all reasonable value of the population mean. Values for which the null hypothesis will be rejected [tex]H_o[/tex] .
Given that:
At 95% confidence interval for the difference between the population means is (1.4, 8.7).
The level of significance = 1 - 0.95 = 0.05 = 5%
So , If the hypothesis test is based on the same samples, The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
What is 3 x 10^6 in standard form?
Answer:
3000000
Step-by-step explanation:
3 * 10^6
10^6 means move the decimal point 6 places to the right
3. becomes
3000000
Answer:
3000000
Step-by-step explanation:
3 x 10^6
3 x 10 x 10 x 10 x 10 x 10 x 10
3 x 1000000
3000000
Test the claim that the proportion of people who own cats is significantly different than 80% at the 0.2 significance level. The null and alternative hypothesis would be:______.
A. H0 : μ = 0.8 H 1 : μ ≠ 0.8
B. H0 : p ≤ 0.8 H 1 : p > 0.8
C. H0 : p = 0.8 H 1 : p ≠ 0.8
D. H0 : μ ≤ 0.8 H 1 : μ > 0.8
E. H0 : p ≥ 0.8 H 1 : p < 0.8
F. H0 : μ ≥ 0.8 H 1 : μ < 0.8
The test is:_____.
a. left-tailed
b. right-tailed
c. two-tailed
Based on a sample of 200 people, 79% owned cats.
The test statistic is:______.
The p-value is:_____.
Based on this we:_____.
A. Fail to reject the null hypothesis.
B. Reject the null hypothesis.
Answer:
C. H0 : p = 0.8 H 1 : p ≠ 0.8
The test is:_____.
c. two-tailed
The test statistic is:______p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]
The p-value is:_____. 0.09887
Based on this we:_____.
B. Reject the null hypothesis.
Step-by-step explanation:
We formulate null and alternative hypotheses as proportion of people who own cats is significantly different than 80%.
H0 : p = 0.8 H 1 : p ≠ 0.8
The alternative hypothesis H1 is that the 80% of the proportion is different and null hypothesis is , it is same.
For a two tailed test for significance level = 0.2 we have critical value ± 1.28.
We have alpha equal to 0.2 for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28
The test statistic is
p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]
Where p = 0.8 , q = 1-p= 1-0.8= 0.2
n= 200
Putting the values
0.8 ± 1.28 [tex]\sqrt{\frac{0.8*0.2}{200} }[/tex]
0.8 ± 0.03620
0.8362, 0.7638
As the calculated value of z lies within the critical region we reject the null hypothesis.
A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t3 − 8t2 + 27t
The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.
Answer:
s = 17 units
Step-by-step explanation:
Given f(t) = t³ - 8t² + 27t
Differentiating f(t), we have
f'(t) = 3t² - 16 t + 27
At t = 0
f'(t) = 27
This is the required obtainaible distance, s.
on the same graph draw line 2y-x=10 and y=3x
Answer:
Step-by-step explanation:
In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 35% with a margin of error of 2.5%. Describe the conclusion about p using an absolute value inequality.
Answer:
The conclusion about p using an absolute value inequality is
[tex]0.325 < p < 0.375[/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.35[/tex]
The margin of error is [tex]E = 0.025[/tex]
The confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
=> [tex]0.35 - 0.025 < p < 0.35 + 0.025[/tex]
=> [tex]0.325 < p < 0.375[/tex]
I need help on this question
Answer:
Figure G.
Step-by-step explanation:
Let's check through the values and calculate the radius and area for all the circle.
For circle R
Diameter = 2 feet
Radius= 1 feet
Area= πr²
Area= 3.14*1
Area= 3.14 feet²
CircleS
Diameter= 4 feet
Radius= 2 feet
Area= πr²
Area= 3.14*2²
Area= 12.56 feet²
Circle T
Diameter= 8 feet
Radius= 4 feet
Area = π r²
area= 3.14*4²
Area=50.24 feet²
Circle U
Diameter= 12 feet
Radius= 6 feet
Area = π r²
area= 3.14*6²
Area=113.04 feet²
The values of the radius and Area all match the graph in figure G
Complete the square to evaluate the definite integral
∫dx/x^2-2x+5
Bounds:1-3
[tex]\displaystyle \int_1^3 \frac{\mathrm dx}{x^2-2x+5}[/tex]
Follow the instruction and complete the square in the denominator:
x ² - 2x + 5 = (x ² - 2x + 1) + 4 = (x - 1)² + 4
Then the integral is
[tex]\displaystyle \int_{x=1}^{x=3} \frac{\mathrm dx}{(x-1)^2+4}[/tex]
Substitute y = x - 1 and dy = dx :
[tex]\displaystyle \int_{y+1=1}^{y+1=3} \frac{\mathrm dy}{y^2+4} = \int_{y=0}^{y=2}\frac{\mathrm dy}{y^2+4}[/tex]
Substitute y = 2 tan(z) and dy = 2 sec²(z) dz :
[tex]\displaystyle \int_{2\tan(z)=0}^{2\tan(z)=2}\frac{2\sec^2(z)}{(2\tan(z))^2+4}\,\mathrm dz = \frac12 \int_{z=0}^{z=\pi/4} \frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = \frac12 \int_{z=0}^{z=\pi/4} \frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = \frac12 \int_{z=0}^{z=\pi/4} \mathrm dz = \frac12 z\bigg|_{z=0}^{z=\pi/4} = \frac12 \left(\frac\pi4-0\right) = \boxed{\frac\pi8}[/tex]
Find the domain of the Bessel function of order 0 defined by [infinity]J0(x) = Σ (−1)^nx^2n/ 2^2n(n!)^2 n = 0
Answer:
Following are the given series for all x:
Step-by-step explanation:
Given equation:
[tex]\bold{J_0(x)=\sum_{n=0}^{\infty}\frac{((-1)^{n}(x^{2n}))}{(2^{2n})(n!)^2}}\\[/tex]
Let the value a so, the value of [tex]a_n[/tex] and the value of [tex]a_(n+1)[/tex]is:
[tex]\to a_n=\frac{(-1)^2n x^{2n}}{2^{2n}(n!)^2}[/tex]
[tex]\to a_{(n+1)}=\frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2}[/tex]
To calculates its series we divide the above value:
[tex]\left | \frac{a_(n+1)}{a_n}\right |= \frac{\frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2}}{\frac{(-1)^2n x^{2n}}{2^{2n}(n!)^2}}\\\\[/tex]
[tex]= \left | \frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2} \cdot \frac {2^{2n}(n!)^2}{(-1)^2n x^{2n}} \right |[/tex]
[tex]= \left | \frac{ x^{2n+2}}{2^{2n+2}(n+1)!^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |[/tex]
[tex]= \left | \frac{ x^{2n+2}}{2^{2n+2}(n+1)^2 (n!)^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |\\\\= \left | \frac{x^{2n}\cdot x^2}{2^{2n} \cdot 2^2(n+1)^2 (n!)^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |\\\\[/tex]
[tex]= \frac{x^2}{2^2(n+1)^2}\longrightarrow 0 <1[/tex] for all x
The final value of the converges series for all x.
Find the length of the leg of a right triangle with leg length b= 21.5 inches and the hypotenuse c= 31.9 inches. Use a calculator to estimate the square root to one decimal place.
Answer:
23.6 (approximate value)
Step-by-step explanation:
a*a+b*b=c*c Pythagorean thereom(21.5)^2 + b*b = (31.9)^2b*b= 1017.61 - 462.25√b*b= √555.36b=23.6(approximate value)Answer:
Step-by-step explanation:
23.6
Help Please. I will Give Brainliest.
Answer:
1/2
Step-by-step explanation:
● 1/4 + 4(1/2 - 3/4 )^2
To make it easier convert the fractions to decimal numbers.
● 1/4 = 0.25
● 1/2 = 0.5
● 3/4 = 0.75
So the expression will be:
● 0.25 + 4(0.5 - 0.75)^2
Calculte first 0.5-0.75 (0.5-0.75= -0.25)
● 0.25 + 4 × (-0.25)^2
-0.25^2 is the same as 0.25^2
● 0.25 + 4 × (0.25)^2
0.25^2 is 0.0625
● 0.25 + 4×0.0625
Multiplication has the priority (4 ×0.0625) wich is 0.25
● 0.25 + 0.25
● 0.5
0.5 is 1/2
So the answer 1/2
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}+4(\frac{1}{2}-\frac{3}{4})^2\\\frac{1}{4}+4(\frac{2-3}{4})^2\\\frac{1}{4}+4(\frac{-1}{4})^2\\\frac{1}{4}+4(\frac{1}{16})\\\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]
The perimeter of a rectangular field is 368 yards. If the length of the field is 98 yards, what is its width?
Answer:
86 = w
Step-by-step explanation:
The perimeter of a triangle is
P = 2(l+w)
368 = 2(98+w)
Divide each side by 2
368/2 = 2/2(98+w)
184 = 98+w
Subtract 98 from each side
184-98 = 98+w-98
86 = w
Is speed the rate of change in the velocity of a moving body?
The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side length of 6 centimeters? Do not include units in your answer.
Answer:
36
step by step
given length=6
so area of square is given by s2 i.e 6^2
=6×6
=36 (Ans)
On a map’s coordinate grid, Panthersville is located at (−3, 2), and Heel City is located at (4, 8). Falconton is the midpoint between Panthersville and Heel City. What is the approximate distance from Panthersville to Falconton? (Each unit on the grid represents 1 mile.) A. 3.25 miles B. 4.61 miles C. 5.00 miles D. 9.22 miles
Answer:
B. 4.61 miles
Step-by-step explanation:
midpoint is (-3+4)/2, (2+8)/2 = (1/2, 5)
distance = √(-3-1/2)² + (2 - 5)² = 4.609772299
[tex]f(x) = {x}^{2} + 4x - 5[/tex] ; >-2
Find [tex] \frac{d {f}^{ - 1} }{dx} [/tex] at x=16
Please show solving
The inverse function theorem says
[tex]\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(f^{-1}(16))}[/tex]
We have
[tex]f(x)=x^2+4x-5[/tex]
defined on [tex]x>-2[/tex], for which we get
[tex]f^{-1}(x)=-2+\sqrt{x+9}[/tex]
and
[tex]f^{-1}(16)=-2+\sqrt{16+9}=3[/tex]
The derivative of [tex]f(x)[/tex] is
[tex]f'(x)=2x+4[/tex]
So we end up with
[tex]\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(3)}=\dfrac1{10}[/tex]
What is the length of the line?
Use inductive reasoning to predict the most probable next number in each list.
9, 13, 21, 33, 49, 69, ?
Answer:
93
Step-by-step explanation:
First differences increase by 4 each time. The given numbers are a quadratic sequence that can be described by 2n² -2n +9. The 7th term would be 93.
_____
First differences are ...
13-9 = 4, 21-13 = 8, 33-21 = 12, 49-33 = 16, 69-49 = 20
Second differences are ...
8-4 = 4, 12-8 = 4, 16-12 = 4, 20-16 = 4
When second differences are constant, the sequence can be represented by a second-degree polynomial function. The leading coefficient is half the value of the second differences.
in the diagram,QOS and ROU are straight lines.OT is the bisector of angle UOS. Angle POQ and angle QOR are complementary angles. Find the values of x and y.pleaseeee answer sooonnn
Answer:
x=50° and y=45°
Step-by-step explanation:
x=QU(90°)-QP(40°)
x=50°
y=SU(90°)/2
y=45°
PLEASE HELP
select all the statistical questions.
A what is the typical amount of rainfall for the month of June in the galapagus islands
B how much did it rain yesterday at the Mexico City International airport
C why do you like to listen to music
D how many songs does the class usually listen to each day
E how many songs did you listen to today
F what is the capital of Canada
G how long does it typically take for 2nd graders to walk a lap around the track
The selected statistical questions are as follows:
A what is the typical amount of rainfall for the month of June in the Galapagos islands
D how many songs does the class usually listen to each day
G how long does it typically take for 2nd graders to walk a lap around the track
Statistical questions are known by these two main characteristics:
they are answered by the collection of datathere is always variability in the data collectedThis means that the data vary. They are not the same data. For example, "How old is Monday?" is not a statistical question because it has one answer.
Thus, statistical questions are not answered by a single number or answer, especially when the correct answer is just one.
Learn more examples of statistical questions here: https://brainly.com/question/15729334
Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on an internet website for $330 making a profit , making a profit of $1.50 on each one.how many comic books were in the box? what was the original price of each comic book (assuming they all cost the same amount)?
Answer: There are 75 books.
Price of each book = $4.
Step-by-step explanation:
Let x = Number of books in the box.
Then as per given,
Cost of x books = $300
Cost of one book = [tex]\$(\dfrac{300}x)[/tex]
Books left after giving 15 of them = x-15
Selling price of (x-15) books= $330
Selling price of one book = [tex]\$(\dfrac{330}{x-15})[/tex]
Profit on each book= $1.50
Profit = selling price - cost price
[tex]\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}][/tex]
[tex]\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75[/tex]
Number of books cannot be negative.
So, there are 75 books.
Price of each book = [tex]\dfrac{300}{75}=\$4[/tex]
So price of each book = $4.
For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.
Answer:
The z-score is [tex]z = 0.6[/tex]
The percentile is [tex]p(Z < 0.6) = 72.57\%[/tex]
Step-by-step explanation:
From the question we are told that
The data value is 0.6 standard deviations above the mean i.e [tex]x = \mu + 0.6 \sigma[/tex]
Where [tex]\mu[/tex] is the population mean and [tex]\sigma[/tex] is the standard deviation
Generally the z-score is mathematically represented as
[tex]z = \frac{x - \mu }{\sigma }[/tex]
=> [tex]z = \frac{(\mu + 0.6\sigma ) - \mu }{\sigma }[/tex]
=> [tex]z = 0.6[/tex]
The percentile is obtained from the z-table and the value is
[tex]p(Z < 0.6) = 0.7257[/tex]
=> [tex]p(Z < 0.6) = 72.57\%[/tex]
Following are the outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event.
1st 2nd 3rd
Boy Boy Boy
Boy Boy Girl
Boy Girl Boy
Boy Girl Girl
Girl Boy Boy
Girl Boy Girl
Girl Girl Boy
Girl Girl Girl
a. Among three children, there are exactly 2 boys.
b. Among three children, there are exactly o girls.
c. Among three children, there is exactly 1 girl.
1. What is the probability of exactly 2 boys out of three children?
2. What is the probability of exactly 0 girls out of three children?
3. What is the probability of exactly 1 girl out of three children?
Answer:
a.0.375
b.0.125
c.0.375
1.0.375
2.0.125
3.0.375
Step-by-step explanation:
a.
The total events in a sample space are n(S)=8
The events that contains exactly two boys
Boy Boy Girl,Boy Girl Boy,Girl Boy Boy.
Let A be the event that there are exactly two boys. Thus, n(A)=3.
So, probability of exactly 2 boys is P(A)=n(A)/n(S)=3/8=0.375.
b.
The event that contains exactly 0 girls.
Boy Boy Boy
Let B be the event that contains exactly 0 girls. Thus, n(B)=1.
So, probability of exactly 0 girls is
P(B)=n(B)/n(S)=1/8=0.125.
c.
The events that contains exactly 1 girl.
Boy Boy Girl,Boy Girl Boy,Girl Boy Boy
Let C be the event that contains exactly 1 girl. Thus, n(C)=3.
So, probability of exactly 1 girl is
P(C)=n(C)/n(S)=3/8=0.375.
Q1 is same as part a.
Q2 is same as part b.
Q3. is same as part c
You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?
Answer: You will need 8 cup scales
Step-by-step explanation:
kg=1000 grams
2000/250=8
Answer:
8
Step-by-step explanation:
2000/250=8
I'm not sure about this one please I need someone to help me.
Answer:
The corresponding graph is Graph A.
Step-by-step explanation:
Part 1: Rewriting the inequality and solving for d
To start, the inequality will need simplified.
[tex]9-4d\geq -3\\\\-4d\geq -12\\\\\frac{-4d}{-4} \geq \frac{-12}{-4} \\\\d \leq 3[/tex]
Because simplifying the inequality involved dividing by a negative number, the sign must be flipped.
Part 2: Determining the graph for the inequality
Now, refer to the rules for graphing inequalities.
If the sign is simply < or >, the graph will start at the number that it begins at and the circle will be open.If the sign is ≤ or ≥, the graph will start at the number that it begins at and the circle will be closed.Therefore, because [tex]d \leq 3[/tex], the graph will start at 3 as a closed dot. Then, it will go left because values must be equal to 3 or less than 3.
Therefore, the graph that represents this is Graph A.
Answer:
Graph A
I hope this helps!
Payton took a friend for a birthday dinner. The total bill for dinner was $44.85 (including tax and a tip). If Payton paid a 19.5% tip, what was his bill before adding the tip?
(Round your answer to the nearest cent.)
$
Number
Answer:
The answer closest to 36.10425. So 36.10 or 36.1
Step-by-step explanation:
x = 44.85 ( 1 - 0.195) = 36.10425
If this helps, it would be nice if 5 stars are given, and a brainliest :)
The amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
For this case, we can assume the amount of bill without tip being A.
Then, as given, Payton gave 19.5% tip (tip is given assumingly on A), then:
Total price of the bill = Bill amount before tip + Tip
44.85 = A + (19.5 % of A)
(we don't write symbols like of currency generally in equations, and understand it from context(which is dollars here))
44.85 = A + (19.5 % of A)
or
[tex]44.85 = A + \dfrac{A}{100} \times 19.5\\\\\text{Multiplying 100 on both the sides}\\\\4485 = 100A + 19.5A\\4485 = 119.5A\\\\\text{Dividing both the sides by 119.5}\\\\\dfrac{4485}{119.5} = A\\\\37.53 \approx A\\\\A \approx 37.53 \: \rm \text{(in dollars)}[/tex]
Thus, the amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
Learn more about percent here:
https://brainly.com/question/11549320
Frances has 4 square baking dishes. Each pan is 7 inches × 7 inches × 2 inches. Which expression will give her the total volume of all the pans? A. 7^2 × 2 B. 7 × 2^4 C. (7 × 2 × 2) × 4 D. (7^2 × 2) × 4
Answer:
D. (7^2 X2) x 4
The equation inside the parenthesis finds the volume of one pan and then that is multiplied by 4 which is the total number of pans. This will find the volume of all 4 pans.
Answer: (7^2 × 2) × 4
Step-by-step explanation:
Evaluate this |-2+3|
[tex]\displaystyle \Large \boldsymbol{} |-2+3| =|1|=1[/tex]
please help me!
find x
Answer:
√13 miles
Step-by-step explanation:
Using Pythagorean Theorem,
h^2=p^2+b^2
Here,
h=x
p=2miles( taking the angle opposite to 2miles as reference)
b=3miles
Now,
x^2=2^2+3^2
x=√(4+9)
x=√13 miles
this question confuses me so much helpppppp
Answer:
-11°C or 1°C
Step-by-step explanation:
The question said that, by the noon, the temperature changes by 6°C, but it doesn't tell you if it changes for a hotter or colder temperature, so its possible the temperature at the noon to be:
-5 -6 = -11°C
or
-5 +6 = 1°C
To graph the possible temperatures, you have to draw a dot at the numbers -11 and 1