What is the distance of the point (- 2 5 from the Y-axis?
Answers
At the position (2,5), the x and y coordinates are 2 and 5.
What is the distance of the point ?The length of the line segment connecting any two points is referred to as their distance. In coordinate geometry, the distance between two points can be computed by measuring the length of the line segment connecting the two points. The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations. A line's point slope form equation is y - y1 = m. (x – x1). Consequently, y - 0 = m(x = 0) is the equation for a line travelling through the origin with a slope of m.In the point (2,5) the x coordinate is 2 and the y coordinate is 5.
The distance if a point from y axis can be determined by the value of the x coordinate i.e., Distance of (2,5) from y axis is 2 units ( which is the x coordinate).
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Related Questions
when a positive integer is expressed in base 7, it is $ab 7$, and when it is expressed in base 5, it is $ba 5$. what is the positive integer in decimal?
Answers
17 is the integer expressed in base 10.
Given that,
The base 7 representation of a positive integer is AB and its base 5 representation is BA, where A and B are digits from 1 to 4, inclusive.
We have to find what is the integer expressed in base 10.
We know that,
Base 7 representation of a positive integer AB.
Can be written as 7A+B in base 10.
Base 5 representation of BA can be written as 5B+A in base 10.
So, 7A+B= 5B+A
6A=4B
A=2/3B
Now, A and B must be in 1 to 4.
The digits between 1 and 4 who are 2/3 of another is 2 and 3.
A=2 and B=3
So,
Base 7 is 23
And Base 5 is 32
Base 7 is 23 is 17 of base 10.
And Base 5 is 32 is 17 of base 10.
A=17
Therefore, 17 is the integer expressed in base 10.
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A bike store sells scooters at a 54%
markup. If the store sells each
scooter for $69.30 then what is their
non-markup price?
Answers
Answer:
$45.00
Step-by-step explanation:
154% → $69.30
100% → $69.30 x 100/154 = $45.00
If a bike store sells scooters at a 54% markup. If the store sells each
scooter for $69.30 then their non-markup price is $45.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
A bike store sells scooters at a 154% markup
154% of non mark up price is equal to the price of each scooter.
Convert 154% to the decimal value by dividing 100
154/100=1.54
Let x be the non mark up price
1.54×x=69.3
Divide both sides by 1.54
x=69.3/1.54
x = 45
Hence $45 is their non-markup price.
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During the holidays,Joseph earns extra money plowing snow from driveways. He plows 3 driveways an hour and has 42 driveways to plow. How long will it take him? PLEASE HELP ! I WILL GIVE BRAINLIEST
Answers
Answer:
14 hours
Step-by-step explanation:
3/hr and has 42 driveways to plow
42/3 = 14
which means he will need 14 hours to plow
Answer:
It will take him 14 hours to plow.
Step-by-step explanation:
42 divided by 3 is 14.
HELP ASAP!!
duskkdkdkdjdjdkddkkffkkkfkgkfkfkkf
Answers
A cone with a volume 1,780.38 and a height of 7. What is the radius
Answers
Answer:
15.585 is the radius of the cone
If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c. True False Question 4 (1 point). A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0. True False Question 5 (1 point) If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = C. True False
Answers
Question 3: True
Question 4: False
Question 5: True
If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.
This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.
Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.
True
When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.
Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.
False
A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.
Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.
True
If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.
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-2) You and your friend went to the movies. Tickets
cost $5.50 each and a popcorn with 2 sodas cost
$6.50. What is the total after 5% sales tax is added?
Answers
Answer:
$18.38
Step-by-step explanation:
The tickets cost $5.50 each. 2 people are going, which means that you are going to buy two tickets, one for each person:
5.50 x 2 = 11
The popcorn and sodas cost $6.50, so you are going to add that to the cost of the tickets:
11 + 6.50 = 17.50
Divide the number you have by a 100:
17.50 ÷ 100 = 0.175
Multiply what you have by 5:
0.175 x 5 = 0.875
Round that off to two decimal places:
0.875 = 0.88
Add to the cost of the tickets, popcorn and sodas:
0.88 + 17.50 = 18.38
Answer:
$18.38
Step-by-step explanation:
Let's build an expression to help answer this problem.
2 tickets + popcorn and sodas + tax =
2(5.50) + 6.50 + T(0.05) where T is equal to the total prior to tax.
Now let's solve for T:
11 + 6.50 = T = 17.50
Now let's find the tax:
17.50(0.05) = 0.875
Total after tax = 17.50 + 0.875 = 18.38 rounding to the nearest cent.
Hope this helped!
Can u help solve this
Answers
Answer:
- 5/3
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -1 -9)/(4 - -2)
= (-1-9)/(4+2)
= -10/6
- 5/3
Answer:
\(slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 1 - 9}{4 - - 2} \\ \frac{ - 10}{6} \\ = - \frac{5}{3} \\ thank \: you\)
A MARAThon runner runs 1620 yards in 9 minutes, how many seconds will it take him to run 351 ft
Answers
Therefore, 1620 yards = 4860 feet
4860 ft in 9 minutes, or 540 seconds
Average speed = distance / time
Average speed = 4860 ft / 540 seconds
Average speed = 9 ft / s
Time = distance / speed
Time = 351 ft / (9ft/s)
Time = 39 seconds!!
A rod is cut into 8 equal pieces.what fraction of the rod does 1 piece represent
Answers
Answer:
1/8
Step-by-step explanation:
you divide 1 by 8 which is 1/8.
if g ( x ) is the f ( x ) = x after a vertical compression by 1 4 , a shift left by 3, and a shift up by 1, c) the vertical intercept of this line is
Answers
If g ( x ) is the f ( x ) = x after a vertical compression by 1 4 , a shift left by 3, and a shift up by 1, c) the vertical intercept of this line is 7/4.
To find the vertical intercept of the line after the given transformations, we need to determine the value of the function when x is equal to 0.
Let's break down the transformations step by step:
Vertical compression by 1/4: This means the vertical coordinates of the points on the graph will be multiplied by 1/4. Since the original function is f(x) = x, the compressed function becomes f(x) = (1/4)x.
Shift left by 3: This means the graph will shift horizontally to the right by 3 units. The function becomes f(x) = (1/4)(x + 3).
Shift up by 1: This means the graph will move vertically upwards by 1 unit. The function becomes f(x) = (1/4)(x + 3) + 1.
Now, to find the vertical intercept, we substitute x = 0 into the function:
g(0) = (1/4)(0 + 3) + 1
g(0) = (1/4)(3) + 1
g(0) = 3/4 + 1
g(0) = 3/4 + 4/4
g(0) = 7/4
Therefore, the vertical intercept of the line after the given transformations is 7/4.
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q(x)=-7x^3+9x^2-8x+2 (a) Possible number(s) of positive real zeros: & (b) Possible number(s) of negative real zeros:
Answers
Possible number(s) of positive real zeros are 1 or 0 and Possible number(s) of negative real zeros: 2 or any even number
To determine the possible number of positive and negative real zeros of the polynomial q(x) = -7x^3 + 9x^2 - 8x + 2, we can use Descartes' rule of signs.
(a) Possible number(s) of positive real zeros:
For the polynomial q(x), we count the number of sign changes in the coefficients when we write them in descending order:
-7x^3 + 9x^2 - 8x + 2
There is only one sign change, from -8x to +2. Thus, there is exactly 1 positive real zero or none at all.
Possible number(s) of negative real zeros:
To determine the possible number of negative real zeros, we substitute -x into the polynomial:
-7(-x)^3 + 9(-x)^2 - 8(-x) + 2
Simplifying the expression:
7x^3 + 9x^2 + 8x + 2
Again, we count the number of sign changes in the coefficients:
7x^3 + 9x^2 + 8x + 2
There are two sign changes, from 7x^3 to 9x^2 and from 9x^2 to 8x. Thus, there are either 2 negative real zeros or any even number of negative real zeros.
In summary:
(a) Possible number(s) of positive real zeros: 1 or 0
(b) Possible number(s) of negative real zeros: 2 or any even number
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Greatest common factor of 18,54, and 72
Greatest common factor of 48 and 60
Greatest common factor of 32 and 52
Answers
Answer:
GCF for 18, 54, 72 is 18
GCF for 48 & 60 is 12
GCF of 32 & 52 is 4
Please show work for problem
Answers
Coin Flip: heads or tails — 2 possible options
So, you multiply 10 (# generator) by 2 (coin flip possibilities)
As a ratio, 1:20
As a percentage, 5%
Hope this helps! If you found my answer helpful, please mark brainliest!
What is the relationship between ∠a and ∠b?Choose 1 answer:A. Vertical anglesB. Complementary anglesC. Supplementary anglesD. None of the above
Answers
Answer:
C. Supplementary angles
Explanation:
Angles a and b are on the straight line AC.
Recall that the sum of angles on a straight line is 180 degrees.
If two angles add up to 180 degrees, they are said to be Supplementary.
Hence angles a and b are Supplementary angles.
Is it a
linear function?
Answers
Answer:
No
Step-by-step explanation:
Well, by looking at the x factors, none of them repeat so it is a function. To determine if it's linear, you can look to see if the change is consistent. From 0 to 2 is +2, and from 10 to 6 is -4. From 2 to 4 is +2, but from 6 to 4 is -2. Since it doesn't go down the table at a set rate, it isn't linear. So, it is a function, but not a linear function
Name That Scenario: Mail Time We've seen many different scenarios, so let's practice identifying our parameter of interest. Write the appropriate symbol for the parameter of interest for each of the following inference procedures. While not required, you may also think about what type of inference procedure (confidence interval or hypothesis test) would be most appropriate. a) A dorm manager would like to estimate the percentage of all mail items received at the dorm that are considered packages, defined as an item that cannot fit in the dorm mailbox. Type Markdown and LaTeX:
α 2
b) A FedEx warehouse manager would like to assess if the average number of packages sent from online retailers to a neighborhood in Champaign is greater than the average number of packages sent from online retailers to a neighborhood in Urbana. Type Markdown and LaTeX:
α 2
c) A bakery sells many products, including cookies \& cakes. The bakery offers both shipping and store pick-up on the products. The bakery manager woulc like to estimate the difference in store pick-up rates between all cookies and all cakes sold by the bakery. Type Markdown and LaTeX:
α 2
d) How long does mail delivery take? In a review of a mail delivery company, the reviewers would like to examine if there is an association between the weight of the package and the delivery time (the time for the package from pickup to delivery). Type Markdown and LaTeX:
α 2
Answers
a) The parameter of interest is the percentage of mail items received at the dorm that are considered packages. This can be denoted as p, where p is the proportion of packages out of all mail items received at the dorm. A confidence interval would be most appropriate for this inference procedure.
b) The parameter of interest is the difference in the average number of packages sent from online retailers to a neighborhood in Champaign and the average number of packages sent from online retailers to a neighborhood in Urbana. This can be denoted as μ1 - μ2, where μ1 is the average number of packages sent to Champaign and μ2 is the average number of packages sent to Urbana. A hypothesis test would be most appropriate for this inference procedure.
c) The parameter of interest is the difference in store pick-up rates between all cookies and all cakes sold by the bakery. This can be denoted as p1 - p2, where p1 is the proportion of cookies that are picked up in store and p2 is the proportion of cakes that are picked up in store. A confidence interval would be most appropriate for this inference procedure.
d) The parameter of interest is the association between the weight of the package and the delivery time. This can be denoted as ρ, where ρ is the correlation coefficient between the weight of the package and the delivery time. A hypothesis test would be most appropriate for this inference procedure.
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Tricia is driving 64 miles per hour on an interstate highway. She must make a quick stop
because there is an emergency vehicle ahead.
a. what is her approximate reaction distance ?
b.what is her approximate braking distance ?
c. what is her total stopping distance ?
Answers
Answer:
the answer is c.
Step-by-step explanation:
ts
Identify as many solutions to the equation below as you can.
x + y = 12
(ex. 1 + 11 = 12, so (1, 11) is a solution)
Answers
Answer:
2+10=12
3+9=12
4+8=12
5+7=12
6+6=12
Karma wants to buy cereal bars from the corner shop or the super market. What is the cost of 10 cereal bars at the cheaper shop? Give answers is pounds
5=4. 2=1. 50
Answers
The cost of 10 cereal bars at the cheaper shop (i.e. at supermarket) = £7.5
We can observe that at corner shop, 5 cereal bars cost 4 pounds.
So, using unitary method, 1 cereal bar costs 5/4 = 0.8 pounds.
And at supermarket, 2 cereal bars cost 1.50 pounds.
so, using unitary method one cereal bar costs 1.5/2 = 0.75 pounds.
This means that supermarket is cheaper than the corner shop.
Now we need to finnd the cost of 10 cereal bars at the cheaper shop i.e., to find the cost of 10 cereal bars at supermarket.
Let us assume that the cost of 10 cereal bars is m pounds.
Using unitary method the cost of 10 cereal bars at supermarket would be:
x = (number of cereal bars) × (cost of each cereal bar)
x = 10 × 0.75
x = 7.5 pounds
Therefore, the cost of 10 cereal bars at the cheaper shop = £7.5
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Find the complete question below.
Karma wants to buy cereal bars from the corner shop or the super market. What is the cost of 10 cereal bars at the cheaper shop?
What percent is 12 of 32 need help quick
Answers
Answer:
37.5%
Step-by-step explanation:
got this question correct
Symplify the expession 71 2/3% helppp
Answers
Answer:
0.71(6)
Step-by-step explanation:
the ending of "6" is forever.
Jada bought an iPhone for $1000 in 2019. An iPhone declines about 9% yearly, How much is the iPhone worth in 2022? ROUND YOUR ANSWER TO
THE NEAREST WHOLE NUMBER.
Answers
Answer:
686
Step-by-step explanation:
1-0.09=0.91
1000
((((1000*0.91)*0.91)*0.91)*0.91)
685.74961
rounded to whole number
686
2. Over the first five years of owning her car, Gina drove about 12. 200 miles the first year, 16,211 miles the second year, 12,050 the third ye and mode of this data. B. Explain which measure of central tendency will best predict how many miles Gina will drive in the sixth year mean = 13. 027; median=12. 200mode=4. 861 the median is the best choice because it is not skewed by the high outlier mean = 12. 2; me * dian = 13. 027 no modethe mean is the best choice because it is representative of the entire data set. Mean = 13. 027; median=12. 200: no mode ; the median is the best choice because it is not skewed by the high outlier mean = 13. 027; me * dian = 12, 200 no mode the mean is the best choice because it is representative of the entire data set
Answers
The median is the best choice to predict how many miles Gina will drive in the sixth year because it is not skewed by the high outlier of 16,211 miles in the second year.
The data for Gina's car mileage is:
12,200 miles in the first year
16,211 miles in the second year
12,050 miles in the third year
To find the mode, we need to identify the value that occurs most frequently in the data set. In this case, there is no mode because no value appears more than once.
To find the median, we need to arrange the data set in order from smallest to largest and identify the middle value. If there is an even number of values, we take the average of the two middle values.
12,050, 12,200, 16,211
The median is 12,200 because it is the middle value when the data set is arranged in order.
To find the mean, we add up all of the values and divide by the number of values.
(12,200 + 16,211 + 12,050) / 3 = 13,027
Therefore, the mean is 13,027.
Based on the given data, the median is the best choice to predict how many miles Gina will drive in the sixth year because it is not skewed by the high outlier of 16,211 miles in the second year. The mean is also a reasonable choice, but it may be influenced by the high value. However, since we do not have any information about any changes in Gina's driving patterns or other relevant factors, it's difficult to accurately predict how many miles she will drive in the sixth year based solely on the given data.
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Find the greatest whole number that will satisfy this inequality: 4x-3 < 2 - x
Answers
Answer:
0
Step-by-step explanation:
First try to find all x. Add x on both sides to get 5x-3<2. Add 3 on both sides to get 5x<5. Divide by 5 on both sides to get x<1. The greatest whole number less than 1 is 0.
Answer:
0
0
0
0
0
0
0
0
0
0
0
0
please help me with 14 and 15 please
Answers
Answer with Step-by-step explanation:
Assuming the two lines are parallel
Angle ABC= Angle BCD [Being alternate interior angles]
Angle BCD=22
Angle BCD+Angle DCE=180 [Angles in a straight line]
22+ Angle DCE=180
Angle DCE=180-22
Angle DCE= 158
Angle DCE= Angle BCF [ Vertically opposite angles]
Angle DCE=158
Angle ECF= Angle BCD [ Vertically opposite angles]
Angle ECF=22
Demand history for the past three years is shown below, along with the seasonal indices for each quarter.
Year Quarter Demand Seasonal Index
Year 1 Q1 319 0.762
Q2 344 0.836
Q3 523 1.309
Q4 435 1.103
Year 2 Q1 327 0.762
Q2 341 0.836
Q3 537 1.309
Q4 506 1.103
Year 3 Q1 307 0.762
Q2 349 0.836
Q3 577 1.309
Q4 438 1.103
Use exponential smoothing with alpha (α) = 0.35 and an initial forecast of 417 along with seasonality to calculate the Year 4, Q1 forecast.
Answers
The Year 4, Q1 forecast using exponential smoothing with α = 0.35 and an initial forecast of 417, along with seasonality, is 335.88.
Exponential smoothing is a forecasting technique that takes into account both the historical demand and the trend of the data. It is calculated using the formula:
Forecast = α * (Demand / Seasonal Index) + (1 - α) * Previous Forecast
Initial forecast (Previous Forecast) = 417
α (Smoothing parameter) = 0.35
Demand for Year 4, Q1 = 307
Seasonal Index for Q1 = 0.762
Using the formula, we can calculate the Year 4, Q1 forecast:
Forecast = 0.35 * (307 / 0.762) + (1 - 0.35) * 417
= 335.88
Therefore, the Year 4, Q1 forecast using exponential smoothing with α = 0.35 and an initial forecast of 417, along with seasonality, is 335.88.
The forecasted demand for Year 4, Q1 using exponential smoothing is 335.88.
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Chi-square distributions that are positively skewed have a research hypothesis that is?
Answers
Answer:
A one tailed test
Step-by-step explanation:
Chi-Square Distributions That Are Positively Skewed Have A Research Hypothesis That Is A One-Tailed Test.
Chi-Square distributions are positively skewed, with the degree of skew decreasing with increasing degrees of freedom.
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One-Tailed Test
In probability theory and statistics, the chi-square distribution with k degrees of freedom is the distribution of the sum of squares of k independent standard normal random variables. The chi-square distribution is a continuous probability distribution. The shape of the chi-square distribution depends on its degrees of freedom k. It is used to describe the distribution of the sum of squares of random variables. The chi-square distribution is positively skewed, with decreasing skewness as the degrees of freedom increase. The chi-squre distribution approaches the normal distribution on increase of degree of freedom.Chi-Square distributions that are positively skewed have a research hypothesis that is a One-Tailed Test.
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A water tank at Camp Newton holds 1200 gallons of water at time t = 0. During the time interval Osts 18 hours, water is pumped into the tank at the rate
W(t) = 95Vt sin^2 (t/6) gallons per hour During the same time interval water is removed from the tank at the rate R(t) = 275 sin^2 (1/3) gallons per hour a. Is the amount of water in the tank increasing at time t = 15? Why or why not?
b. To the nearest whole number, how many gallons of water are in the tank at time t = 18? c. At what time t, for 0 st 18, is the amount of water in the tank at an absolute minimum? Show the work that leads to your conclusion d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(C) until the tank becomes empty. Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.
Answers
(a)The amount of water in the tank is increasing.
(b)Evaluate \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.
(c)Solve part (b) to get the absolute minimum from the critical points.
(d)The equation can be set up as \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.
What is the absolute value of a number?
The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.
To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:
a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.
At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.
Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.
b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:
\(\int\limits^{18}_0(W(t) - R(t)) dt\)
Evaluate this integral to get the number of gallons of water in the tank at t = 18.
c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.
d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.
The equation can be set up as:
\(\int\limits^k_{18}-R(t) dt = 1200\)
Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.
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a math teacher claimed that the average grade of the students in her algebra 2 classes this year would be equal to the average grade of the same students in algebra 1 classes two years ago. the average grade of algebra 1 students two years ago was 92%. in a random sample of 25 current algebra 2 students, the average grade was 87%, with a standard deviation of 7%. is there enough evidence to reject the teacher's claim?
Answers
From the hypothesis test conducted, the calculated t-statistic of -3.57 is less than the lower critical t-value of -2.064. This tells us that the observed sample mean of 87% is significantly different from the claimed population mean of 92% at the 0.05 significance level. Therefore, the null hypothesis can be rejected and conclusions can be made that that there is enough evidence to suggest that the average grade of the students in the Algebra 2 class this year is not equal to the average grade of the same students in the Algebra 1 class two years ago.
How do we conduct a hypothesis test?To determine whether there is enough evidence to reject the teacher's claim, we can conduct a hypothesis test. A one-sample t-test will be us to compare sample mean.
Here are the sample statistics:
Sample size (n) = 25
Sample mean (X) = 87%
Sample standard deviation (s) = 7%
A significance level (α) of 0.05, wil be used
We first calculate the t-statistic, with (X - μ) / (s/√n),
t = (87 - 92) / (7/√25) = -5 / (7/5) = -3.57
Then, we check this value against the critical t-value for a two-tailed test with 24 degrees of freedom (n-1), and α = 0.05.
The critical t-values for a two-tailed test at α = 0.05 and df = 24 are approximately -2.064 and +2.064.
-3.57 t-test is less than the lower critical t-value of -2.064. This means that the observed sample mean of 87% is significantly different from the claimed population mean of 92% at the 0.05 significance level.
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