Answer:
[tex]f(t) = 1450(1.025)^{t}[/tex]
Step-by-step explanation:
Given
[tex]P =1450[/tex] -- principal
[tex]r = 2.5\%[/tex] --- rate
[tex]n = 1[/tex] --- compounded once a year
Required
Determine the function for compound interest
Compound interest f(t) is calculated as:
[tex]f(t) =P(1 + r/n)^{nt[/tex]
So, we have:
[tex]f(t) = 1450(1 + 2.5\%/1)^{1 * t}[/tex]
[tex]f(t) = 1450(1 + 2.5\%)^{t}[/tex]
[tex]f(t) = 1450(1 + 0.025)^{t}[/tex]
[tex]f(t) = 1450(1.025)^{t}[/tex]
A vending machine that dispenses coffee into cups must fill the cups with 7.8 ounces of liquid. Before selling the machine to a college or business, the company tests the machine to be sure it dispenses an average of 7.8 ounces. A sample of 20 amounts is listed here:
7.78 7.79 7.82 7.82 7.87 7.84 7.80 7.82 7.80 7.78
7.83 7.75 7.85 7.83 7.84 7.73 7.82 7.87 7.81 7.88
(1) Set up the null and the alternative hypotheses to test whether the average amount of coffee dispensed is different from 7.8 ounces.
(2) Complete the remaining hypothesis-testing steps using α= .05.
(3) Find the p value.
(4) Based on the p value what can the company conclude about the average amount of coffee dispensed by the machine.
The null hypothesis states that the average amount of coffee dispensed by the machine is equal to 7.8 ounces, while the alternative hypothesis states that the average amount is different from 7.8 ounces.
In this scenario, the null hypothesis (H0) is that the average amount of coffee dispensed by the machine is 7.8 ounces, while the alternative hypothesis (Ha) is that the average amount differs from 7.8 ounces. To test these hypotheses, the next step is to calculate the test statistic.
Using the given sample of 20 amounts, we can compute the mean of the sample, which is 7.816 ounces. The standard deviation of the sample is 0.044 ounces. With these values, we can calculate the t-test statistic.
The t-test statistic is calculated by subtracting the hypothesized value (7.8) from the sample mean (7.816) and dividing it by the standard deviation (0.044), multiplied by the square root of the sample size (20). The resulting t-value is approximately 1.818.
To determine the p-value associated with this t-value, we compare it to the t-distribution with n-1 degrees of freedom (19 degrees of freedom in this case). Using a statistical table or software, we find that the p-value is approximately 0.085.
Since the p-value (0.085) is greater than the significance level (α = 0.05), we fail to reject the null hypothesis. This means that there is insufficient evidence to conclude that the average amount of coffee dispensed by the machine is different from 7.8 ounces. Therefore, based on the p-value, the company cannot conclude that the average amount of coffee dispensed is significantly different from 7.8 ounces.
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a - 2/3 = 3/5 how much is a?
Answer:
its 1 4/5 or 19/15
they are both the same
Step-by-step explanation:
so first you need to find the same common factor
A-10/15=9/15
then add 10/15 and 9/15 to find a
19/15-10/15=9/15
or
1 4/15-2/3=3/5
yw :)
If one of my angles is 130 degrees, what is the measure of the blue angle that is supplementary to it?
Step-by-step explanation:
[tex]180 - 130 = 50[/tex]
Compare the two functions below in two complete sentences.
Help
Answer:
I guess we have the table:
x f(x)
-4 7
-2 5
0 3
2 1
4 - 1
To find the slope of this, we need to select two different points (x1, y1) and (x2, y2) and use the relation:
slope = (y2 - y1)/(x2 - x1)
let´s use the first two:
(-4,7) and (-2, 5)
Slope = (5 - 7)/(-2 - (-4)) = -2/2 = -1
Now, if we want to be sure that this is a linear equation, we should do the same for other two pairs of points, now use the first and the third:
(-4, 7) and (0,3)
S = (3 - 7)/(0 -(-4)) = -4/4 = -1
Now, for the function g(x) we can see a constant line, that is parallel to the x-axis.
This means that the slope of this function is equal to zero.
This means that the slope of g(x) is bigger than the slope of f(x), because 0 > 1 i guess
E B A G ord Теа F NOTE: Angles not necessarily drawn to scale.
help
Answer: x = 13
angel bge and angle agf are vertical meaning they’re equivalent
77 + 90 + x = 180 (180 because all of them added together are supplementary)
167 + x = 180
x = 13
Answer:
Step-by-step explanation:
X=13
n a contingency table, when all the expected frequencies are equal the oberved frequencies the calculaed chi squared statistic equals zero. True or False
The given statement "When all the expected frequencies are equal the observed frequencies the calculated chi squared statistic equals zero." is true because chi-squared statistic will be zero in this case.
In a contingency table, the expected frequencies are calculated based on certain assumptions and can be different from the observed frequencies. The chi-squared statistic is used to determine whether there is a significant association between the variables in the contingency table.
When all the expected frequencies are equal to the observed frequencies, it means that there is a perfect match between the observed data and what would be expected under the assumption of independence.
In this case, the chi-squared statistic will be zero, indicating no discrepancy between the observed and expected frequencies.
This scenario is highly unlikely to occur in real-world data because observed frequencies typically deviate from the expected frequencies due to sampling variability or factors influencing the relationship between variables.
In most cases, the expected frequencies will differ from the observed frequencies, resulting in a non-zero chi-squared statistic, indicating a significant association or departure from independence between the variables.
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Due soon !!!!!!!...
Answer:
50m^2
Step-by-step explanation:
In the exercise, X is a binomial variable with n = 5 and p = 0.4. Compute the given probability. Check your answer using technology. HINT [See Example 2.] (Round your answer to five decimal places.) P(X ≤ 2)
The probability of P(X ≤ 2) is 0.0135
We have the information available from the question:
Binomial variable is X
the value of n = 5
and, the value of p = 0.4
We are given to compute the probability P(X [tex]\leq[/tex] 2) and round the answer to five decimal places.
The binomial distribution formula is given by:
[tex]P(X)=nCx(p)^x(1-q)^n^-^x[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)!x!}[/tex]
We have to find the probability:
P(X [tex]\leq[/tex] 2) = P(X=1) + P(X=2)
P(X = 1) = [tex]5C1(0.4)^1(1-0.4)^5^-^1[/tex] = 0.0026
P(X= 2) =[tex]5C2(0.4)^2(1-0.4)^5^-^2[/tex] = 0.0109
P(X [tex]\leq[/tex] 2) = P(X=1) + P(X=2)
P(X [tex]\leq[/tex] 2) = 0.0026 + 0.0109
P(X [tex]\leq[/tex] 2) = 0.0135
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does someone know the answer?
Answer:
I think it is the last answer.
Step-by-step explanation:
There can only be one vertex.
write an equivilent expression that is equivilent to 4(w+3)-2
Answer:
4w + 10
Step-by-step explanation:
If you have any questions feel free to ask
answer: 4w+10
explanation:: distribute;
= (4)(w)+(4)(3)+−2
= 4w+12+−2
combine like terms;
= 4w+12+−2
= (4w)+(12+−2)
= 4w+10
You are going to install a 15-metre long fence. If the posts are 3 metres apart, how many fence posts will you need? Select the best way to demonstrate the answer to students
Answer : 6 fence posts. The best way to demonstrate the answer to students is to use the formula
Explanation: To install a 15-metre long fence, the posts are 3 metres apart, how many fence posts will you need? The best way to demonstrate the answer to students is to use the formula: Total number of posts = (Length of fence ÷ Distance between posts) + 1
Where;Length of the fence = 15 metres, Distance between posts = 3 metres
Total number of posts = (15 ÷ 3) + 1 Total number of posts = 5 + 1 = 6 Therefore, you will need 6 fence posts.
The best way to demonstrate the answer to students is to use the formula: Total number of posts = (Length of fence ÷ Distance between posts) + 1
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Please help, GodBless.
Answer:
(A) seems to have the least amount of slope with a slope of -6, compred to all, its the least one.
Step-by-step explanation:
Follow slope formula
(y2-y1) / (x2-x1)
Or calculate using rise over run method
Solve −2|m|= −10.
What is m?
Answer:
|m| : -5Step-by-step explanation:
{ -2|m|= -10= |m| : -5 }
Please help me with the question
Answer: 70
Step-by-step explanation: if you look at it hard enough they both look the same, this is called a vertical angle, I'm down for more questions lol. you keep on getting on my fyp
A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip. Each small car can hold 4 people and each large car can hold 6 people. The students rented twice as many large cars as small cars, which altogether can hold 48 people. Graphically solve a system of equations in order to determine the number of small cars rented, x,x, and the number of large cars rented, yy.
Answer:
The students rented 3 small cars and 6 large cars.
Step-by-step explanation:
Since a group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip, and each small car can hold 4 people and each large car can hold 6 people, and the students rented twice as many large cars as small cars, which altogether can hold 48 people, to determine the number of small cars rented, X, and the number of large cars rented, Y, the following calculation must be performed:
4X + 6Y = 48
4x4 + 6x8 = 16 + 48 = 64
4x3 + 6x6 = 12 + 36 = 48
Thus, the students rented 3 small cars and 6 large cars.
How to solve -3x+1<7
Answer:
x > − 2
Step-by-step explanation:
If your motive was to solve for x thats your answer, if not good luck!
which expression is equivalent to (4^2)(4^5)
Answer: Sorry I don't know the answer but I recommend an app that will help you is called Mathpapa is really helpful and have helped me get A on test and homework
Step-by-step explanation: is htis one https://www.mathpapa.com/algebra-calculator.html
Find the range, median, first and third quartiles, and interquartile range for each data set OF THE NUMBERS 52 72 96 21 58 40 75
Answer:
Range: 75 Median: 58 1Q: 40 3Q: 75 Interquartile: 35
1. An exponential function is shown below.
f (x)= -2(2)
Which key attribute does the function not exhibit?
This question seems extremely odd to me. I don't really even understand what's being asked.
As far as exponential functions go, it's missing an exponent for one. The dependent variable is missing. This essentially saying f(x) = -4 or y = -4. Which is fine, but is definitely not an exponential function and in a very odd and incomplete form to begin with.
what is the ratio of 12
12 to 1
is the ratio :)
What is the answer for |-12| is positive or negative
Answer:
postitive
Step-by-step explanation:
|-a| = a, a>0
20. An airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. The airport and factory are 6.0 miles apart. Their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service road will be constructed from the shopping center to the highway that connects the airport and factory. What is the shortest possible length for the service road? Round to the nearest hundredth
1. Prove that at any party of 31 people, there’s always a person who knows an even number of others. (Assume that acquaintance is mutual: if Alice knows Zelda, then Zelda knows Alice.)
To prove that at any party of 31 people, there's always a person who knows an even number of others, we can use the pigeonhole principle.
The pigeonhole principle states that if we distribute more than "n" objects into "n" boxes, then at least one box must contain more than one object. In this case, the "objects" represent the people at the party, and the "boxes" represent the number of people each person knows.
Let's assume, for the sake of contradiction, that every person at the party knows an odd number of others. This means that each person has an odd number of acquaintances.
Now, let's consider the sum of the number of acquaintances for all 31 people. Since each person knows an odd number of others, the sum of odd numbers is also an odd number.
However, if we count the total number of acquaintances in a group, it must be even since each acquaintance involves two people. This creates a contradiction because we cannot have both an odd and an even sum for the total number of acquaintances.
Therefore, our assumption that every person knows an odd number of others must be false. Hence, there must be at least one person at the party who knows an even number of others.
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Find the coordinates of the endpoint of the image?
Given:
The graph of a line segment.
The line segment AB translated by the following rule:
[tex](x,y)\to (x+4,y-3)[/tex]
To find:
The coordinates of the end points of the line segment A'B'.
Solution:
From the given figure, it is clear that the end points of the line segment AB are A(-2,-3) and B(4,-1).
We have,
[tex](x,y)\to (x+4,y-3)[/tex]
Using this rule, we get
[tex]A(-2,-3)\to A'(-2+4,-3-3)[/tex]
[tex]A(-2,-3)\to A'(2,-6)[/tex]
Similarly,
[tex]B(4,-1)\to B'(4+4,-1-3)[/tex]
[tex]B(4,-1)\to B'(8,-4)[/tex]
Therefore, the endpoint of the line segment A'B' are A'(2,-6) and B'(8,-4).
Which describes the cross section of the square prism that passes through the vertices A, B, C, and D shown below?
A square prism. The front left points are labeled A and D. The back right points are labeled B and C.
a rectangle
a square
a kite
a trapezoid
Answer:
its not that i got it wrong
Step-by-step explanation:
47. Brainliest will be given, need answer asap
Answer:
Look below.
Step-by-step explanation:
45. B
46. D
47. B
Answer:
45.A 46. Bike A 47.C
Step-by-step explanation:
Angela bought a dress that cost $22.50. If the sales tax is 6.5%, how much tax did she pay? I need help with this one
how tall is the building in the picture shown
Answer: just figure out how many 8s are in 36 then multiply that by 66 :):)
Step-by-step explanation:
How many solutions does 4(−5x+8)= 4(−5x+8) have?
Answer:
infinity
Step-by-step explanation:
What is the surface area of this right rectangular prism with dimensions of 8 inches by 4 inches by 14 inches?
Answer:
400 inches
Step-by-step explanation:
Area of all sides and add them