Answer:
Decision rule
Fail to reject the null hypothesis
Conclusion
The sample evidence is not sufficient to conclude that more than three out of four financial institutions that offer online banking facilities are prone to fraud.
Step-by-step explanation:
From the question we are told that
The sample size is n = 214
The sample proportion is p = 0.78
The level of significance is [tex]\alpha = 0.05[/tex]
Generally the population proportion is mathematically represented as
[tex]p = \frac{3}{4} =0.75[/tex] (gotten from the statement ''three out of four'' in the question)
The null hypothesis is [tex]H_o : p = 0.75[/tex]
The alternative hypothesis [tex]H_a : p > 0.75[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\^{p} - p}{ \sqrt{\frac{p(1-p)}{n} } }[/tex]
=> [tex]z = \frac{0.78- 0.75}{ \sqrt{\frac{ 0.75(1-0.75)}{214} } }[/tex]
=> [tex]z = 1.01[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P(Z > z )[/tex]
=> [tex]p-value = P(Z > 1.01 )[/tex]
From the z-table
[tex]P(Z > 1.01 ) = 0.15625[/tex]
So
[tex]p-value = 0.15625 [/tex]
From the obtained values we see that [tex]p-value > \alpha[/tex] hence we fail to reject the null hypothesis
Therefore we can conclude that the sample evidence is not sufficient to conclude that more than three out of four financial institutions that offer online banking facilities are prone to fraud.
An airplane is flying overhead at a constant elevation of 4090 ft. A person is viewing the plane from a position 3010 ft from the base of a radio tower. The airplane is flying horizontally away from the person. If the plane is flying at the rate of 700 ft/s, at what rate is the distance between the person and the plane increasing when the plane passes over the radio tower
Answer:
415 ft/s
Step-by-step explanation:
I've attached a diagram showing the triangle formed between the plane, the person and the radio tower.
From the attached diagram, x represents the position between the person and the position on the ground directly below the airplane while s represents the distance between the person and the plane.
The constant elevation remains 4090 ft while the value of x and s varies with time.
Thus, x varies with respect to time as dx/dt while s varies with respect to time as ds/dt.
Now, we are told that the plane is flying at the rate of 700 ft/s. This means that; dx/dt = 700 ft/s
Now we want to find the rate at which the distance between the person and the plane is increasing when the plane passes over the radio tower.
This means that we want to find ds/dt when x = 3010 ft
From pythagoras theorem if x = 3010 ft and the Elevation remains 4090 ft, we can find s as;
s = √(4090² + 3010²)
s = √25788200
s ≈ 5078.21 ft
Since we want to find ds/dt at x = 3010 ft, from the diagram, we can say from pythagoras theorem that;
x² + 4090² = s²
Differentiating x and s with respect to t, we have;
2x(dx/dt) = 2s(ds/dt)
2 will cancel out to give;
x(dx/dt) = s(ds/dt)
ds/dt = (x/s)(dx/dt)
Plugging in 700 for dx/dt, 3010 for x and 5078.21 for s, we have;
ds/dt = (3010/5078.21) × 700
ds/dt ≈ 415 ft/s
Each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are written on a separate piece of paper and
placed in a hat. One piece of paper is randomly selected from the hat. Use the Venn diagram shown
to help you determine the probability that the number selected is odd or less than 5.
Step-by-step explanation:
i dont see a venn diagram but i think the number is probably more than 5
The probability that the number selected is odd or less than five will be 0.20 or 20%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are written on a separate piece of paper and placed in a hat.
One piece of paper is randomly selected from the hat.
Then the probability that the number selected is odd or less than 5 will be
Total event = 10
Favorable event = 2 {1, 3}
Then the probability will be
[tex]\rm P = \dfrac{2}{10}\\\\P = 0.2 \ or \ 20\%[/tex]
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i need help please help me
Answer:
use a contractor or protractor or whatever theyre called
Step-by-step explanation:
i just need points to ask another question
If cost of 3 kg of sugar is Rs 240. What is rate of cost of sugar
Can u please helppppppp !!!!!!!!!
Answer:
yes i can help you
Step-by-step explanation:
Answer:
The height is the water wheel diameter so if you have 9' of head but are only running a 6 foot diameter wheel the height for this calculation is 6 feet. Most people use 12v batteries to store their electricity and an inverter
Step-by-step explanation:
Sorry if I cant help but that's number 2 answer.
A Cessna 172 plane that is used to transport up to four VIPs is 2 km in the air if the potential energy of the VIP plane with three VIPs on board is 860 J what is the combined mass of the Cessna and passengers
Answer:
0.0438 kg
Step-by-step explanation:
We are given;
Potential energy; U = 860 J
Height; h = 2 km = 2000 m
Formula for potential energy is;
U = mgh
Where g is acceleration due to gravity = 9.81 m/s²
Thus;
860 = m × 9.81 × 2000
m = 860/(9.81 × 2000)
m = 0.0438 kg
simplify 3 · 32 + 8 ÷ 2 − (4 + 3)
Answer:
= 93
Step-by-step explanation:
Calculate within parentheses:
(4+3)
= 7
Simplify:
= 3 * 32 + 8 ÷ 2 - 7
Multiply and divide (left to right):
= 96 + 8 ÷ 2 - 7
Multiply and divide (left to right):
= 96 + 4 - 7
Add and subtract (left to right):
= 93
(5/6) 2 x (1 1/10) 2
Answer:
11/3x
your welcome
Three cats and three dogs, A, B, C, D, E, and F, live on a street in three different-coloured houses. Each house hosts one cat and one dog. One house is red. A is a cat and does not live in the red house. B is a dog and does not live in the same house as C (even though they could). D lives in the blue house. D does not live with A or F (even though it could). E does not live with A and does not live in the yellow house.
Indicate whether each letter correspond to a cat or a dog, and match each cat and each dog with a colored house.
Answer:
1) A is a cat; B is a dog; C is a cat; D is a dog; E is a dog; F is a cat
2) A lives with B in a yellow house; C lives with D in a blue house; E lives with F in a red house.
Step-by-step explanation:
Step 1: First we identify the animals as cats or dogs
A is a cat
B is a Dog
Since B can live with C, C is a cat
Since D can live with A, D is a dog
F is a cat since it can live with D
E is therefore, a dog
Step 2: We then identify the house each two animals live in pairs of a cat and a dog
D lives in a blue house
A lives in a yellow house since it does not live with D or in a red house
C lives with D in a blue house since D does not live with either A or F
E lives in a red house since it does not live with A or in a yellow house
F lives with E in a red house since E does not live with A
Therefore, B lives with A in a yellow house
Deandre pays $15.20 for a pack of 8 towels.
Find the unit price in dollars per towel.
If necessary, round your answer to the nearest cent.
Please help
Answer: Each towel costs $1.90
Step-by-step explanation:
$15.20 divided by 8 = $1.90
The following data represent the high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts (a) through (c).
Temperature Lower Limit Upper Limit Days
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Required:
Approximate the mean and standard deviation for temperature.
Answer:
The mean is [tex]\= x = 79.7 [/tex]
The standard deviation [tex]\sigma =7.81[/tex]
Step-by-step explanation:
From the question we are told that
The data given is
Temperature Lower Limit Upper Limit Days
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Generally the average of each limit is evaluated as
Temperature Lower Limit Upper Limit Average[tex](x_i)[/tex] Days[tex](f_i)[/tex]
50-59 50 59 ( 50 + 59 )/2 =54.5 2
60-69 60 69 (60+69)/2 = 64.5 313
70-79 70 79 (70+79)/2 =74.5 1419
80-89 80 89 (80+89)/2 =84.5 1503
90-99 90 99 (90+99)/2 = 94.5 319
100-109 100 109 (100+109)/2 = 104.5 9
Generally the mean is evaluated as
[tex]\mu = \frac{\sum x_i f_i}{\sum f_i}[/tex]
=> [tex]\mu = \frac{ (54.5 * 2) + (64.5 * 313) +\cdots +(104.5 * 9)}{2 + 313 +\cdots + 9}[/tex]
=> [tex]\= x = 79.7 [/tex]
Generally the standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum[ f_i * ( x_i^2 - \= x^2)] }{\sum f_i}}[/tex]
=> [tex]\sigma =\sqrt{ \frac{[2 * [(54.5)^2) - 79.7^2 ]]+[313 *[ (64.5)^2)-79.7^2] +\cdots +[9 *[ (104.5)^2)- 79.7^2] }{2 + 313 +\cdots + 9}}[/tex]
=> [tex]\sigma =7.81[/tex]
The mean and Standard deviation for the given data would be as follows:
μ [tex]= 79.7[/tex]
б [tex]= 7.81[/tex]
Frequency DistributionGiven that,
Temperature Lower Limit Upper Limit Days([tex]f_{i}[/tex])
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Average([tex]x_{i}[/tex])
[tex]( 50 + 59 )/2 =54.5[/tex]
[tex](60+69)/2 = 64.5[/tex]
[tex](70+79)/2 =74.5[/tex]
[tex](80+89)/2 =84.5[/tex]
[tex](90+99)/2 = 94.5[/tex]
[tex](100+109)/2 = 104.5[/tex]
As we know,
Mean (μ) [tex]=[/tex] ∑[tex](x_{i} f_{i}) /[/tex]∑[tex]f_{i}[/tex]
[tex]= [(54.5[/tex] × [tex]2) + (64.5[/tex] ×[tex]313)+....(104.5[/tex]× [tex]9)][/tex][tex]/(2 + 313 + 1419 + ....9)[/tex]
∵ μ [tex]= 79.7[/tex]
As we know,
Standard Deviation:-
[tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{f_{i} }}}[/tex]
by putting the values, we get
∵ б [tex]= 7.81[/tex]
Thus, μ [tex]= 79.7[/tex] and б [tex]= 7.81[/tex] are the correct answers.
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A table marked at ₹ 15,000 is available for ₹ 14,400. Find the discount given and the discount percentage.
Answer: ₹ 600 and 15% discount rate i believe
Step-by-step explanation:
What is the unit rate for meters per second if a car travels 414 meters in 23 seconds?
Answer:
18 meters per second
Step-by-step explanation:
414/23=18
Not trying to be rude but you should know how to do this with or without a calculator
Sharon invests $2000 in a savings
account with a fixed annual interest rate of
7% compounded monthly. What is the amount in her saving account after 5 years?
Help :(
Answer: 0.07
Step-by-step explanation:
Use the given functions to set up and simplify 5years. 7% = 0.075 years = 0.07
How is 5 represented in 6.75
Answer:
5 is in the hundreths place :))
Step-by-step explanation:
Answer:
0.05
Step-by-step explanation:
since the place value of the five is beyond the decimal point, and it is the second number beyond the decimal point, so it is in the hundredths place.
The number 49 has exactly three factors Since 98 is a multiple of 49, which must be tue of 982
It must have only two factors
tmusthave fewer than three factors
It must have exacty three factors
t must have more than three factors
Answer:
it must have more than 3 factors
Step-by-step explanation:
that factors are 1,2,491,982
An investor wants to save money to purchase real estate. She buys an annuity with monthly payments that earn 5.6% interest, compounded monthly. Payments
will be made at the end of each month, Find the total value of the annuity in 16 years if each monthly payment is $65.
Do not round any intermediate computations, and round your final answer to the nearest cent
Answer:
1040
Step-by-step explanation:
just took 65 and mutiply 65$
Answer:
1040
Step-by-step explanation:
just took 65 and mutiply 65$
Simplify the following expression, 3/8 divided by 1/4
The required simplified product is 3/2.
Given that fractions 3/8 ÷ 1/4.
To divide two fractions by multiplying the first fraction with the reciprocal of the second fraction.
Let a, b, c and d be any real numbers. Consider a/b ÷ c/d that gives
[tex]\frac{a}{b}[/tex] ÷ [tex]\frac{c}{d}[/tex] = [tex]\frac{a}{b}[/tex] × [tex]\frac{c}{d}[/tex].
That implies, [tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{8}[/tex] × [tex]\frac{4}{1}[/tex] = [tex]\frac{3}{2}[/tex].
Hence, the required simplified product is 3/2.
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Please help! Thank you
Answer:
-294
Step-by-step explanation:
The company is interested in which confidence intervals associated with 1 (very satisfied) contain the proportion 0.25, or 25%. Determine which confidence levels satisfy this. (Select all that apply.)
Hi, you've asked an incomplete question. However, I provided a brief explanation about confidence interval and confidence level.
Explanation:
The term confidence interval and confidence level are not the same but they are related. Confidence interval refers to a range of values that makes up part of the statistic's mean data which contains an unknown population parameter.
However, the Confidence level is the level of certainty that the confidence interval would contain the true population parameter if a random sample is drawn.
Find the quotient:
_________________
x - 4 ) x^3 + 2x^2 – 16x - 32
Step-by-step explanation:
x-4)x³+2x²-16x-32(x²+6x+8
x³-4x²
- +
____________
6x²-16x-32
6x²-24x
- +
_________
8x-32
8x-32
- +
_____
X X
______
Hence,
The quotient is x²+6x+8.
Help me plsss! I'll give u 10 points
Answer:
1.02n
Step-by-step explanation:
We just have to simply the expression already given which will give you the equivalent expression.
n + 0.02n since these are like terms because of the variable "n", we can just add them together
n+0.02n
1.02n
The Fashion Store has $6000 available each month for advertising. Newspaper ads cost $200 apiece and no more than 20 can be run per month. Radio ads cost $100 each and no more than 30 can run per month. TV ads cost $800 a piece, with a maximum of 7 available each month. Approximately 1000 women will see each newspaper ad, 800 will hear each radio ad, and 14,000 will see each TV ad. How much of each type of advertising should be used if the store wants to maximize exposure?
9514 1404 393
Answer:
7 TV ads4 radio adsStep-by-step explanation:
The audience per dollar is ...
Newspaper: 1000/$200 = 5/$
Radio: 800/$100 = 8/$
TV: 14000/$800 = 17.5/$
So, TV gives the greatest exposure. As much of the budget as possible should be spent on TV ads. That amount is the lesser of $6000 and ...
(7 ads)($800/ad) = $5600
With $5600 spent on TV ads, the remaining advertising budget is ...
$6000 -5600 = $400
The next most cost-effective medium is radio. The remaining $400 budget allows for ...
$400/($100/ad) = 4 ads
__
To maximize exposure, the advertising budget should be spent this way:
TV: 7 ads for $5600, exposure of 98000Radio: 4 ads for $400, exposure of 3200I mark as brainliest
Answer:
D
Step-by-step explanation:
Its d Reason is if she has 5 and he has 10 he has twice as much
A directed segment ST¯¯¯¯¯ is partitioned from S (−5,0) to T in a 32 ratio at point M (10, 15). What are the coordinates of point T? (20, 25) (15, 20) (7, 3) (5, 15
Answer:
[tex]T = (20,25)[/tex]
Step-by-step explanation:
Given
[tex]S = (-5,0)[/tex]
[tex]M = (10,15)[/tex]
[tex]Ratio = 3:2[/tex]
Required
Determine the coordinate of T
Line division by ratio is calculated using:
[tex]M(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where:
[tex](x_1,y_1) = (-5,0)[/tex]
[tex](x,y) = (10,15)[/tex]
[tex]m:n = 3:2[/tex]
So, we have:
[tex](10,15) = (\frac{3 * x_2 + 2 * -5}{3+2},\frac{3 * y_2 + 2 * 0}{3+2})[/tex]
[tex](10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5})[/tex]
Multiply through by 5
[tex]5 * (10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5}) * 5[/tex]
[tex](50,75) = (3x_2 -10,3y_2)[/tex]
By comparison:
[tex]3x_2 - 10 = 50[/tex]
[tex]3y_2 = 75[/tex]
[tex]3x_2 - 10 = 50[/tex]
[tex]3x_2 = 50 + 10[/tex]
[tex]3x_2 = 60[/tex] --- Divide through by 3
[tex]x_2 = 20[/tex]
[tex]3y_2 = 75[/tex]
[tex]y_2 =75/3[/tex] --- Divide through by 3
[tex]y_2 =25[/tex]
Hence:
The coordinates of T is
[tex]T = (20,25)[/tex]
Restless Leg Syndrome and Fibromyalgia
People with restless leg syndrome have a strong urge to move their legs to stop uncomfortable sensations. People with fibromyalgia suffer pain and tenderness in joints throughout the body. A recent study indicates that people with fibromyalgia are much more likely to have restless leg syndrome than people without the disease. The study indicates that, for people with fibromyalgia, the probability is 0.33 of having restless leg syndrome, while for people without fibromyalgia, the probability is 0.03. About 2% of the population has fibromyalgia. Create a tree diagram from this information and use it to find the probability that a person with restless leg syndrome has fibromyalgia.
Answer:
The probability that a person with restless leg syndrome has fibromyalgia is 0.183.
Step-by-step explanation:
Denote the events as follows:
F = a person with fibromyalgia
R = a person having restless leg syndrome
The information provided is as follows:
P (R | F) = 0.33
P (R | F') = 0.03
P (F) = 0.02
Consider the tree diagram attached below.
Compute the probability that a person with restless leg syndrome has fibromyalgia as follows:
[tex]P(F|R)=\frac{P(R|F)P(F)}{P(R|F)P(F)+P(R|F')P(F')}[/tex]
[tex]=\frac{(0.33\times 0.02)}{(0.33\times 0.02)+(0.03\times 0.98)}\\\\=\frac{0.0066}{0.0066+0.0294}\\\\=0.183333\\\\\approx 0.183[/tex]
Thus, the probability that a person with restless leg syndrome has fibromyalgia is 0.183.
Help me please help
what is 3/7 × 3 3/7?
= 3/4 × 3 3/7
= 3 3/7 as an improper fraction = 24/7
= 3/4 × 24/7
= 3 × 24 / 4 × 7
= 72/28
Let us try to simplify it .
We know that both 72 and 28 is divisible by 4 . Hence ,
72 ÷ 4 / 28 ÷ 4
= 18/7
Therefore , 3/7 × 3 3/7 = 72/78 or 18/7 ( simplest form ) .
Answer: 1²³⁄₄₉
Step-by-step explanation:
Convert any mixed numbers to fractions
3³⁄₇ x ²⁴⁄₇
Applying the fractions formula for multiplication
3 x 24
_____
7 x 7
= ⁷²⁄₄₉
Simplifying fraction
1²³⁄₄₉
A cookbook originally cost $13.00. Yesterday, Marta bought it at 40% off.
Horn
40%
OFF
How much was deducted from the original price? (4 pt.)
А
$0.40
B
$5.20
$7.80
A percentage is a way to describe a part of a whole. The amount paid by Marta for the cookbook is $7.80.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
As it is given that the original price of the cookbook was $13, Marta bought it for 40% off. Therefore, Marta only paid 60% of the original cost,
[tex]\text{Amount paid by Marta} = \text{60\% of the original cost}\\\\\text{Amount paid by Marta} = \dfrac{60}{100} \times \$13\\\\\text{Amount paid by Marta} = \$7.8[/tex]
Thus, the amount paid by Marta for the cookbook is $7.80.
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find an equation for the line that passes through the point (7,1) and is perpendicular to the line x-3y+25=0
Answer:
y + 3x = - 20
Step-by-step explanation:
x - 3y + 25 = 0
- 3y = - 25 - x
3y = 25 + x
y = ( 25 + x )/3
y = ( 1/3 )x + 25/3
Y= mX+ c
m= gradient= 1/3
The perpendicular gradient should be the negative reciprocal of the gradient we have now.
which is : -1÷(1/3) = -3
Now for the perpendicular line equation, we have:
y = 1
x= 7
m= -3
y - y1 = m ( x - x1 )
y - 1 = -3 ( x + 7 )
y-1 = -3x -21
y + 3x = -20