After peering into a wishing well, Jocelyn hypothesizes that the distribution of coins is 50% quarters, 20% dimes, 20% nickels, and 10% pennies. To investigate this claim, she reaches in, mixes the coins well, and selects a random sample of 80 coins. She counts how many coins there are of each type. She would like to know if her observed distribution provides convincing evidence that the true distribution of coins in the well is different from what she originally thought. What are the appropriate hypotheses?
Answers
A small p-value (typically less than the chosen significance level, e.g., 0.05) would provide evidence to reject the null hypothesis , the appropriate hypotheses Null hypothesis.
To investigate whether the observed distribution of coins provides convincing evidence that the true distribution in the well is different from Jocelyn's hypothesis, we need to define the appropriate hypotheses.
Let's denote the proportions of each type of coin in the well as follows:
- P(Q): Proportion of quarters
- P(D): Proportion of dimes
- P(N): Proportion of nickels
- P(P): Proportion of pennies
Based on Jocelyn's hypothesis, she believes the distribution to be:
P(Q) = 0.50 (50% quarters)
P(D) = 0.20 (20% dimes)
P(N) = 0.20 (20% nickels)
P(P) = 0.10 (10% pennies)
To test whether her observed distribution is significantly different from her hypothesis, we can set up the following hypotheses:
Null Hypothesis (H0): The observed distribution is consistent with Jocelyn's hypothesis.
Alternative Hypothesis (HA): The observed distribution is different from Jocelyn's hypothesis.
In terms of the proportions, the null and alternative hypotheses can be stated as:
H0: P(Q) = 0.50, P(D) = 0.20, P(N) = 0.20, P(P) = 0.10
HA: At least one of the proportions is different from Jocelyn's hypothesis.
To analyze the data and determine if there is convincing evidence to reject the null hypothesis, Jocelyn can perform a hypothesis test using statistical methods such as chi-square test or binomial test. These tests will compare the observed frequencies of each type of coin in her sample to the expected frequencies based on her hypothesis.
By evaluating the test statistic and calculating the corresponding p-value, Jocelyn can assess whether the observed distribution of coins is significantly different from her initial hypothesis. A small p-value (typically less than the chosen significance level, e.g., 0.05) would provide evidence to reject the null hypothesis and support the alternative hypothesis, indicating that the true distribution of coins in the well is different from what she originally thought.
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Related Questions
Tetsuo has decided to purchase a new car. He decides to put 10% down and finance the remaining balance. The bank
offers Tetsuo a 36 month loan at 6.71%. If the car is valued at $32,000, what will his monthly payments be?
a. $983.93
c. $782.65
b. $885.45
d. $688.88
Please select the best answer from the choices provided
A
B
ОООО
D
Mark this and return
Save and Exit
Next
Submit
Answers
Answer:
885.45
Step-by-step explanation:
Testuo monthly payments will be around 885$
What is InterestIt is a fee paid for borrowing money or other assets.
• the amount borrowed is called the principal.
• the interest is expressed as a percentage rate of the principal
for a given time interval.
It is given that
Value of the car = $32000
Time period of loan repayment = 36 months
T = 3 years
Rate of Interest = 6.71%
10% down amount from 32000 = 3200 $
So the amount he is putting for finance = 32000 - (0.1 × 32000)
= $28800
Rate of interest can be calculated from
I = P x R x T
I = Interest, P = Principle, R = Rate, T = Time
= (6.71 * 28800 * 3)/(100*12)
= $ 483.12
This is total interest for an year
In one month, rate of interest
= 483.12/12
= $40.26
The principal amount that will be payable per month
= 28800/36
= $800
Total amount payable will be
= $ ( 800 + 40.26 )
= $840
Hence, we can conclude, Tetsuo needs to pay $840.26 as monthly installments, so in the options given it is 885$
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Frank weighs 160 pounds and is on a diet to gain 2 pounds a week so that he can make the football team. John weighs 208 pounds and is on a diet to lose 3 pounds a week so that he can be on the wrestling team in a lower weight class. If Frank and John can meet these goals with their diets, when will they weigh the same, and how much will they weigh at that time? (Hint: Solve for x and y and make sure you write a complete sentence for an answer)
Answers
Answer: If Frank and John can meet these goals with their diets , they will weigh same after 9.6 weeks and they will weigh 179.2 pounds.
Step-by-step explanation:
Let x = Number of weeks.
As per given question ,
Weight of Frank after x weeks = 160+2x (pounds)
Weight of John after x weeks = 208-3x (pounds)
When Weight of Frank= Weight of John
Weight of Frank after 9.6 weeks = 160+2(9.6) = 179.2 pounds
Weight of John after 9.6 weeks = 208-3(9.6)=179.2 pounds
Hence, If Frank and John can meet these goals with their diets , they will weigh same after 9.6 weeks and they will weigh 179.2 pounds.
For the rotation 588^{\circ}588 ∘ , find the coterminal angle from 0^{\circ}\leq\theta<360^{\circ}0 ∘ ≤θ<360 ∘ , the quadrant, and the reference angle.
Answers
The coterminal angle is 330°, which lies in Quadrant fourth, with a reference angle of 258 degrees.
We have 588 ° between 0° ≤θ<360
Coterminal angle in [0, 360°) range is 330°, located in the fourth quadrant.
Then for the reference angle will be
588 -330= 258
Thus, the reference angle is 258°
Therefore, we can conclude that coterminal angle is 330°, which lies in Quadrant fourth, with a reference angle of 258 degrees.
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Four people have measured the height of a wall using different methods. Their results are shown in the table. Order their measurements from least to greatest.
Answers
Split £99 in the ratio 1:8
Answers
Answer:
Step-by-step explanation:
https://math.icalculator.info/ratio-divider-calculator.html
total parts is 8+1 so 9
99/9 = 11 so 1 part = £11
then multiply by the ratio which gives you the answer
Felicia opens a chequing account that charges a monthly maintenance fee of $10.75. She starts her account by depositing $500 at the start of January. At the end of March, how much money will she have in her account? Assume that she does not make any deposits or withdrawals over this time period.
Answers
Answer:
467.65
Step-by-step explanation:
Because 10.75+10.75+10.75 is = 32.25
500-32.25=467.5
Calculate the measure of the major arc MPN.
Answers
Answer:
310°
Step-by-step explanation:
The sum of arcs around a circle is 360°.
MPN +MN = 360°
MPN = 360° -MN . . . . . . . . subtract MN
MPN = 360° -50° = 310° . . . fill in the given value
The measure of major arc MPN is 310°.
What is the initial value of the function
Answers
Answer:
initial value = 5
Step-by-step explanation:
the initial value is the value of y when x = 0.
this is the same as the y- intercept.
from the graph at (0, 5 )
that is when x = 0 the initial value is 5
A firm experiences_______ if inputs are doubled and output more than doubles. diminishing marginal rate of technical substitution diminishing marginal product decreasing returns to scale increasing returns to scale
Answers
A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.
When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.
The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.
This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.
The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.
Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.
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A twelve-foot ladder is leaning against a wall. If the ladder reaches ft high on the wall, what is the angle the ladder forms with the ground to the nearest degree?*
Answers
This question is incomplete.
Complete Question
A twelve-foot ladder is leaning against a wall. If the ladder reaches eight ft high on the wall, what is the angle the ladder forms with the ground to the nearest degree?*
Answer:
42°
Step-by-step explanation:
From the question, the diagram that is formed is a right angle triangle.
To solve for this, we would be using the trigonometric function of Sine.
sin θ = Opposite side/ Hypotenuse
From the question, we are told that:
12 foot ladder is leaning against a wall = Hypotenuse
The ladder reaches 8ft high on the wall = Opposite side.
Hence,
sin θ = 8ft/12ft
θ = arc sin (8ft/12ft)
= 41.810314896
Approximately to the nearest degree
θ = 42°
Therefore, the angle the ladder forms with the ground to the nearest degree is 42°
help please!!
\(\text{solve the following equation : }\)
\( \sf\tan^{2}(\theta)-(1+\sqrt{3})\tan(\theta)+\sqrt{3} = 0\)
Answers
tan²( θ ) - (tan (θ) + √3 tan (θ)) + √3 = 0
tan²( θ ) - tan (θ) - √3 tan (θ) + √3 = 0
tan( θ ) ( tan (θ) - 1) - √3 ( tan (θ) - 1 ) = 0
( tan( θ ) - 1 ) ( tan( θ ) - √3 ) = 0
tan( θ ) - 1 = 0
θ = π/₄
tan( θ ) - √3 = 0
θ = π/₃
so θ = π/₄ and θ = π/₃
Answer:
\( \huge \boxed{ \red{ \boxed{\begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} }}}\)
Step-by-step explanation:
to understand thisyou need to know about:trigonometryPEMDASlet's solve:distribute tan(θ):
=>tan²(θ)-(tan(θ)+√3tan(θ))+√3=0
remove parentheses:
=>tan²(θ)-tan(θ)-√3tan(θ)+√3=0
so this equation is now in standard form i.e ax²+bx+c=0
we can solve by factoring as we solve quadratic equation
factor out tanθ:
=>tan(θ)(tan(θ)-1)-√3tan(θ)+√3=0
factor out -√3:
=>tan(θ)(tan(θ)-1)-√3(tan(θ)-1)=0
group:
=>(tan(θ)-√3)(tan(θ)-1)=0
separate it as two different equation:
\( \implies \begin{cases} \tan( \theta) - 1 = 0 \\ \tan( \theta) - \sqrt{3} = 0 \end{cases}\)
add 1 and √3 to both sides to first and second equation respectively:
\( \implies \begin{cases} \tan( \theta) - 1 + 1 = 0 + 1 \\ \tan( \theta) - \sqrt{3} + \sqrt{3} = 0 + \sqrt{3} \end{cases} \)
\( \implies \begin{cases} \tan( \theta) = 1 \\ \tan( \theta) = \sqrt{3} \end{cases} \)
\( \therefore \begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} \)
what are the minimum and maximum temperatures in the house ?
Answers
Answer:
I mean, I think it varies by house and by location but a general range would be:
Min: 64 *F
Max: 74 *F
Help me please I am so sad
Answers
Answer:B 8;45
Step-by-step explanation:
Answer:
Dont be sad :) The answer is B but give brainliest to the other person ʕ •ᴥ•ʔ
Step-by-step explanation:
You are buying mouthwash at your local store. The price of the mouthwash is $4.39. It is currently on sale for 20% off. You also have a store coupon for $1.00 off and a manufacturer's coupon for $1.25 off. What is your subtotal?
Answers
Answer:5.68 dollars amirikan
Step-by-step explanation:
Given that price of the mouthwash is $4.39. It is currently on sale for 20% discount. You also have a store coupon for $1.00 off and a manufacturer's coupon for $1.25 off. The subtotal you need to pay is $1.262.
What is discount?The term discount refers to the amount or percentage deducted from the normal selling price of something. The discount means a reduction in the price of a good or service.
Discount = Marked price - Selling price
The mouthwash is at sale for 20% off.
Cost price = $4.39
Discount = 20% of $4.39 = $0.878
Total discount = 20% off + store coupon + manufacturer's coupon = $0.878 + $1.000 + $1.250 = $3.128
Selling price = Marked price - Discount = $4.39 - $3.128 = $1.262
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1. Refer to the equation 3x − 5y = 15. (a) Create a table of values for at least 4 points. Show your work on how you found the values for each coordinate pair, and validated the points were on the line.
Work for Point 1
Work for Point 2
Work for Point 3
Work for Point 4
Answers
Answer:
(0, 3 ), (5, 0), (10, -3), (15, -6)
Step-by-step explanation:
3x − 5y = 15
-5y = 3x + 15
y = \(-\frac{3}{5} x + 3\)
Point 1: (0, 3 )
y = -3/5(0) + 3
y = 0 + 3
y = 3
Validate:
3 = -3/5(0) + 3
3 = 3
Point 2: (5, 0)
y = -3/5(5) + 3
y = -3 + 3
y = 0
Validate:
0 = -3/5(5) + 3
0 = 0
Point 3: (10, -3)
y = -3/5(10) + 3
y = -6 + 3
y = -3
Validate:
-3 = -3/5(10) + 3
-3 = -3
Point 4: (15, -6)
y = -3/5(15) + 3
y = -9 + 3
y = -6
Validate:
-6 = -3/5(15) + 3
-6 = -6
Answer: For this problem, you cannot go over 10! so remember guys you can graph it however you want for example if you wanted to you could do -3/5(-2) + 3 for the first point but you would have to solve it. the next one would be maybe -3/5(-1) + 3 if you wanted to go up by plus one REMEMBER this is your OWN graph so do whichever number order you want it doesn't matter you can increase by 1 or 2 or 3 but the final point shouldn't be over ten or you will get the problem wrong. Good Luck I hope I get an A and I hope you guys get A's as well. Do ur absolute best on this
Which fraction is not equivalent to 7/8
Answers
Answer:
C. 15/16
Step-by-step explanation:
A. Divide by 3
B. Divide by 5
C. Can't divide by anything.
D. Divide by 4
Answer:
C
Step-by-step explanation:
21/24 = 7/8
35/40 = 7/8
7/8 ≠ 15/16
14/16 ≠ 15/16
28/32 = 7/8
Pls help me with this work
Answers
Answer:
They are similar because they both have like terms in parenthesis.
Step-by-step explanation:
As long as you have like terms, the equation is the same. You never have to worry about the number before the variable being the same. As long as the variable is the same, you have like terms and that is like terms in the equation. TO SUM IT UP: They both have like terms and that is why they are similar.
A job requires 230' of metal conduit. The conduit comes in 8' sections.
How many sections of conduit will you need to complete this job?
Answers
Divide total length needed by length of a piece:
230/8 = 28.75
Round up to 29
They need 29 pieces
given f(x)=3x+2 and g(x)= √x-1, determine the following: g(f(8))=
Answers
The function operation g(f(8) in the given functions f(x) = 3x+2 and g(x) = √(x-1) is 5.
What is the function operation g(f(8) in the given functions?A function is simply a relationship that maps one input to one output.
Given that:
f(x) = 3x + 2g(x) = √( x - 1 )g(f(x)) = ?First, set up the composite result function:
Evaluate g( 3x + 2 ) by substituting in the value of f into g.
g( 3x + 2 ) = √( ( 3x + 2 ) - 1 )
Simplify
g( 3x + 2 ) = √( 3x + 2 - 1 )
g( 3x + 2 ) = √( 3x + 1 )
Evaluate the result function by replacing the x with 8.
g( f(x) ) = √( 3(8) + 1 )
g( f(x) ) = √( 24 + 1 )
g( f(x) ) = √( 25 )
g( f(x) ) = 5
Therefore, the composite result function g( f(x) ) is 5.
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If Bryan had 2 apples and one of them is gone what happen to the other apples
Answers
Answer:
other apples should also be taken by another person and Bryan had no apples left.
Step-by-step explanation:
What are the lower (Q1) and upper quartiles (Q3) for the following scores?
3,5,5,5,6,8,9,10,11,13,13,14,15,17,18,20
A. Q1 = 5 and Q3 = 15
B. Q1 = 5 and Q3 = 14.5
C. Q1 = 5.5 and Q3 = 15
D. Q1 = 5.5 and Q3 = 14.5
Answers
HELPPPPP
what is the period of the function shows in the graph
Answers
Answer:
4
Step-by-step explanation:
the period is from the top minus top, bottom minus bottom, etc..
one point at the top is one and the next is 5.
5-1=4
hope this helps!
. Four times the sum of 3 and a number is 16. Find the
number.
PLEASE A I NEED IT
Answers
Answer:
x=1
Step-by-step explanation:
it is
suppose that for a given least-squares regression, the sum of squares for error is 100 and the sum of squares for regression is 105. find the coefficient of determination.
Answers
51.21% is the coefficient of determination.
What does coefficient of determination mean?
A statistical model's ability to predict a result is indicated by the coefficient of determination (R2), a value between 0 and 1. The proportion of variation in the dependent variable that the statistical model predicts can be understood as the R2 value.SST = SSE + SSR
Here, SSE = 100 and SSR = 105
SST = 100+105 = 205
Coefficient of determination , R^2 = 105/205 = 51.21%
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0.3(4+x)=4.5
Please help me out, I need this answer ASAP,
I give u 10 pts, thank u SOOO much :3
Answers
Answer: x=11
Step-by-step explanation:
Answer:
\( \sf \: x = 11\)
Step-by-step explanation:
Given equation,
→ 0.3(4 + x) = 4.5
Now the value of x will be,
→ 0.3(4 + x) = 4.5
→ 1.2 + 0.3x = 4.5
→ 0.3x = 4.5 - 1.2
→ 0.3x = 3.3
\( \sf \rightarrow \: x = \frac{3.3}{0.3} \)
→ [ x = 11 ]
Hence, the value of x is 11.
a certain statistic dˆ is being used to estimate a population parameter d. the expected value of dˆ is not equal to d. what property does dˆ exhibit?a. The sampling distribution of d hat is normal.b. The sampling distribution of d hat is binomial.c. The sampling distribution of d hat is uniform.d. d hat is unbiased.e. d hat is biased.
Answers
The right answer is: E, according to the Central Limit Theorem for proportionality. The statistic is inaccurate.
In probability theory, the central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
The Central Limit Theorem establishes that for a proportion p in a sample of size n:
The expected value is μ=р
The standard error is s=\(\sqrt{\frac{p(1-p)}{n} }\)
In this problem, the expected value is different of the expected of μ=р , hence, the statistic is biased, and the correct option is E.
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ABC form a triangle where BAC equals 90° a B equals 10.8 mm and C equals 1.6 mm find the length of BC give your answer rounded to one DP
Please really need help it’s for a test
Answers
Answer:
BC = 10.9 mm
Step-by-step explanation:
The computation of the BC is given below:
Here we applied the pythagorus theorem
AB = 10.8 mm
AC = 1.6mm
BC = ?
Now as we know that
AB^2 + AC^2 = BC^2
10.8mm^2 + 1.6mm^2 = BC^2
116.64mm^2 + 2.56mm^2 = BC^2
BC = 10.9 mm
Which transformations are displayed in the graph of g (x) = -(x+3)^2-1 as it relates to the graph of the parent function? Select all that
apply.
A) Reflected over the x-axis
B) Translated 3 units up
C) Translated 3 units left
D) Translated 1 unit up
E) Translated 1 unit down
OF) Horizontally stretched
Answers
Given statement solution :-The correct transformations are:
A) Reflected over the x-axis
B) Translated 3 units up
The function g(x) = \(-(x+3)^2\)- 1 involves the following transformations as it relates to the parent function\((y = x^2):\)
A) Reflected over the x-axis: Yes, the negative sign in front of the function reflects it over the x-axis.
B) Translated 3 units up: Yes, the function is shifted vertically upward by 3 units due to the "-1" term.
C) Translated 3 units left: No, there is no horizontal translation in this function.
D) Translated 1 unit up: No, the function is shifted vertically up by 3 units, not 1 unit.
E) Translated 1 unit down: No, the function is shifted vertically up by 3 units, not down.
OF) Horizontally stretched: No, there is no horizontal stretching in this function.
Therefore, the correct transformations are:
A) Reflected over the x-axis
B) Translated 3 units up
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A rectangle is inscribed in a circle. Find the area of the shaded region. Use 3.14 for .
Answers
Answer:
Find the area of both the square and circle and subtract the circle’s area from the square’s
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
consider the sequence of numbers: $4$, $7$, $1$, $8$, $9$, $7$, $6$, $\ldots$. for $n>2$, the $n$th term of the sequence is the units digit of the sum of the two previous terms. let $s n$ denote the sum of the first $n$ terms of this sequence. what is $s {100}?$
Answers
The sum of the first 100 terms of the sequence is $620$.
\($s_3 = 4 + 7 = 11$\)
\($s_4 = 11 + 1 = 12$\)
\($s_5 = 12 + 8 = 20$\)
\($s_6 = 20 + 9 = 29$\)
\($s_7 = 29 + 7 = 36$\)
\($s_8 = 36 + 6 = 42$\)
\($s_9 = 42 + 4 = 46$\)
\($s_{10} = 46 + 7 = 53$\)
\($s_{100} = 620$\)
The given sequence is 4, 7, 1, 8, 9, 7, 6 and so on. The nth term of the sequence is the units digit of the sum of the two previous terms. To find the sum of the first 100 terms, we need to calculate the sum of the first two terms, 4 and 7. This is 11. The next term is the units digit of 11, 1. The sum of the first three terms is 12. The next term is the units digit of 12, which is 2. This process is repeated until we reach the 100th term. The sum of the first 100 terms is 620.
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