The theoretical probability of choosing List A is less than the experimental probability of choosing List A.
The theoretical probability of choosing List B is greater than the experimental probability of choosing List A.
How do the experimental probabilities compare to the theoretical probabilities?For a fair coin, the theoretical probability of obtaining a head or tail is 0.5 or 50% each.
Therefore, theoretically, the probability of choosing List A is 0.5, and the probability of choosing List B is also 0.5.
The experimental probability of choosing List A or List B is obtained using the formula below:
Experimental probability of List A or B = number of heads / total number of trialsExperimental probability of List A = 37/70
Experimental probability of List A = 0.529
The experimental probability of choosing List B is:
Experimental probability of List B = 33/70
Experimental probability of List B = 0.471
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I’m giving 20 points
Answer:
12
Step-by-step explanation:
-3(b - 5) + 7a - (9 - a) ^6 a = 7 and b = -4
-3(-4 - 5) + 7(7) - (9 - 7)^6
= -3(-9) + 49 - (2)^6
= 27 + 49 - (64)
= 27 + 49 - 64
= 76 - 64
= 12
The distance between two triangulation points is found to be x miles. That same distance is y kilometres. If the difference between the numbers x and y is 27, find the value of x.
The value of x is approximately 44.31km
Here is how to calculate a missing valueFirstly, we should know that 1 mile is not the same as kilometres, therefore:
1 mile = 1.60934 km.
Since the difference of x and y gives us 27, we represent it as:
x - y = 27 (in km)
But x is given in miles, so we have
1.60934x - y = 27km
Also the question says the distance x is same as y, then we replace y with x in the above equation:
1.60934x - x = 27
0.60934x = 27
x = 27/0.60934
Therefore x = 44.31km
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The medal distribution from the 2021 summer Olympic Games is shown in the table What is the probability that the winner wins a gold medal and is from the United States?
The probability that a winner wins a gold medal and from the US is 0.06349
The probability a winner wins a gold medal and from the USFrom the question, we have the following parameters that can be used in our computation:
The table of values
Gold medal from the US are 48
And the total number of winners of Gold is 48 + 90 + 107 + 114 + 397
So, we have
Total = 756
So, we have
P = 48/756
Evaluate
P = 0.06349
Hence, the probability is 0.06349
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Express the confidence interval using the indicated format.Express the confidence interval 0.27 space less than space pspace less than space 0.55 in the form of p with hat on topplus-or-minus E.
To find E, we take half of the width of the confidence interval, which is (0.55 - 0.27)/2 = 0.14. The confidence interval is p ± E, which is 0.41 ± 0.14.
The confidence interval 0.27 less than p less than 0.55 can be expressed in the form of p with a hat on top plus or minus E as p ± E, where p is the point estimate and E is the margin of error. To find p, we take the average of the upper and lower bounds of the confidence interval, which gives us (0.27 + 0.55)/2 = 0.41. To find E, we take half of the width of the confidence interval, which is (0.55 - 0.27)/2 = 0.14. Therefore, the confidence interval can be expressed as p ± E, or 0.41 ± 0.14.
To express the given confidence interval 0.27 < p < 0.55 in the form of p ± E, follow these steps:
Step 1: Find the midpoint of the interval, which represents the sample proportion p.
Midpoint = (Lower Limit + Upper Limit) / 2
Midpoint = (0.27 + 0.55) / 2 = 0.41
So, p = 0.41.
Step 2: Calculate the margin of error (E) by subtracting the lower limit from the midpoint or the upper limit from the midpoint.
E = Midpoint - Lower Limit = 0.41 - 0.27 = 0.14
Step 3: Express the confidence interval in the desired format.
The confidence interval is p ± E, which is 0.41 ± 0.14.
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note that in actual scientific practice, we only select one single sample and therefore we can only see the one corresponding interval, out of the potential thousands that are displayed using the applet. based on what you've learned from the simulation (the applet), give the best interpretation of a single 95% confidence interval as follows: we are [ select ] confident that our interval is one that [ select ] contain [ select ] .
In scientific practice, we often use statistical inference to make conclusions about a population based on a sample. The use of confidence intervals is one method of making these inferences. A single 95% confidence interval can be interpreted as follows: we are 95% confident that our interval is one that contains the true population parameter.
This means that if we were to repeat the study many times, we would expect the true population parameter to be within our interval 95% of the time.
It is important to note that this interpretation assumes that the sample was selected randomly and that the assumptions for the statistical test used to construct the interval were met. Additionally, it is important to recognize that the interval is not a guarantee of the true population parameter being within it, but rather a range of values that is likely to contain the true parameter.
Overall, a single 95% confidence interval is a useful tool for making inferences about a population based on a sample, and it provides a range of values that we can be reasonably confident contains the true parameter.
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The perimeter of parallelogram ABCD is 78 cm. AD is 9 cm more than twice AB. Find the lengths of all four sides of ABCD.
Answer:
AB = 10
CD = 10
AD = 29
BC = 29
Step-by-step explanation:
perimeter = AD + BC + AB + CD
AD + BC + AB + CD = 78
Let AB = x
Opposite sides of a parallelogram are congruent.
AB = CD = x
AD = BC = 2x + 9
2x + 9 + 2x + 9 + x + x = 78
6x + 18 = 78
6x = 60
x = 10
2x + 9 = 2(10) + 9 = 29
AB = 10
CD = 10
AD = 29
BC = 29
Answer:
AB = 10 CD = 10 AD = 29 BC = 29
Step-by-step explanation:
I did the test
Hope this helps :)
The population of a town in 2000 was 120,000 people. The town grew at a rate of 3% annually. How many people live in the town in 2018?
if i multiply one side of an equality by ten, to maintain the equality, what do i have to do to the other side (3 words)?
You need to multiply one side of an equality by ten and divide the other side by ten.
How to maintain equality?Divide by ten.
To maintain equality, you need to multiply one side of an equality by ten and divide the other side by ten.
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If i multiply one side of an equality by ten, to maintain the equality, i have to divide the other side by ten. o
When you multiply one side of an equality by ten, you are effectively scaling that side by a factor of ten. In order to maintain the equality, you need to apply the same scaling factor to the other side by dividing it by ten. This ensures that the relative relationship between the two sides remains unchanged, and the equality is preserved.
Therefore, to maintain equality, you need to multiply one side of an equality by ten and divide the other side by ten.
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a. The area of the new parking lot is represented by (100-x)(100+2). Find this product.
ft²
b. Does the area of the parking lot increase, decrease, or stay the same?
The area of the parking lot
:: increases
:: decreases
The original area is 10,000 ft², so the new area is the original area
:: stays the same :: increased by ² :: decreased by ²
c. Use the polynomial in part (a) to find the area of the new parking lot when * = 21.
:: left alone
The solution to the questions on algebra word problem are:
a) 10000 - x²
b) The area of the parking lot decreases
c) when x = 21, the area is 9559 ft²
How to solve algebraic word problems?a) Since the area of the new parking lot is expressed as:
(100 - x)(100 + x)
Expanding this gives:
10000 - x²
b) The original area is 10,000 ft²
The new area is 10000 - x²
Thus:
10,000 - (10000 - x²) = x²
Thus, the area of the parking lot decreases
c) when x = 21, we have:
10000 - 21² = 9559 ft²
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39. Find the equation of the line that passes through (2, 5) and (8, 10)
Answer:
5/6
Step-by-step explanation:
y2-y1/x2-x1
10-5/8-2 = 5/6
Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. A = 110^{\circ}, a = 125, b = 200
The value of the angle B is 56. 64 degrees
How to determine the valueUsing the law of sines, we have;
sin A/a = sin B/b
Given that the parameters are;
A and B are the measure of the anglesa and b are the measure of the sides of the triangleNow, substitute the values, we have;
sin 110/225 = sin B/200
cross multiply the values, we get;
sin B = sin 110(200)/225
find the values
sin B = 0.9396(200)/225
Multiply the values
sin B = 187. 93/225
sin B = 0. 8352
Find the inverse
B = 56. 64 degrees
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between 1976 and 2016, the usa olympic team has participated in 10 olympic games (the team usa has missed the moscow 1980 games due to the cold war). the total number of gold medals won in each of the 10 games ranged between 33 and 83. the number of gold medals won in each of the games is listed below: 33 34 83 36 37 44 37 36 46 47 calculate the value, in number of gold medals, at the 69.5th percentile (show work). (2 points)'
To calculate the value at the 69.5th percentile, we first need to find the rank of this percentile.
69.5th percentile = (69.5/100) x 10 = 6.95th rank
Plugging in the values:
value = (6.95 - 6) / (7 - 6) x (44 - 37) + 37
value = 40.7
Therefore, the value at the 69.5th percentile is 40.7 gold medals.
To calculate the value at the 69.5th percentile, follow these steps:
1. Arrange the data in ascending order:
33, 34, 36, 36, 37, 37, 44, 46, 47, 83
2. Determine the position of the 69.5th percentile in the dataset:
Position = (Percentile / 100) * Total number of data points
Position = (69.5 / 100) * 10 = 6.95
Since the position is not a whole number, we'll need to interpolate between the values at positions 6 and 7.
3. Find the values at positions 6 and 7:
Value at position 6 = 37
Value at position 7 = 44
To interpolate between these two values, we use the percentile formula:
value = (rank - rank_ lower) / (rank_ upper - rank_ lower) x (value_ upper - value_ lower) + value_ lower
where:
- rank = 6.95
- rank_ lower = 6
- rank_ upper = 7
- value_ lower = 37
- value_ upper = 44
4. Interpolate between the values at positions 6 and 7:
Value at 69.5th percentile = Value at position 6 + ((Position - Position 6) * (Value at position 7 - Value at position 6))
Value at 69.5th percentile = 37 + ((6.95 - 6) * (44 - 37))
Value at 69.5th percentile = 37 + (0.95 * 7)
Value at 69.5th percentile = 37 + 6.65
Value at 69.5th percentile = 43.65
The value at the 69.5th percentile is approximately 43.65 gold medals.
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help me pls math is too hared
Each angle is 53 degrees, 32 degrees, and 95 degrees.
We know that,
A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees. A triangle is a three-sided polygon with three vertices. The angle produced within the triangle is 180 degrees. It signifies that the total of a triangle's internal angles equals 180°.
Here,
The sum of angles of triangle is 180 degrees.
4x+5+7x+11+2x+8=180
13x+24=180
13x=156
x=12
T=4x+5
=4*12+5
=53 degree
U=2x+8
=2*12+8
=32 degree
V=7x+11
=7*12+11
=95 degree
The measure of each angle is 53 degree, 32 degree and 95 degree.
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Please help me with this homework only the answer
try (-18,-5)
my step by step explanation is you would distrubute the -5 and add it to the -13 and you would do the same thing for the orher side
hopefully this is correct
and may i have brainliest
The RAND() function in Excel returns a pseudo-random number between 0 and 1. If you enter this function into 1000 cells (i.e. enter the formula in one cell and copy it to 999 other cells), approximately how many of these cells will contain values less than or equal to 0.1?
O A number relatively close to 1
O A number relatively close to 10
O A number relatively close to 100
O A number relatively close to 500
O A number relatively close to 1000
Approximately 100 cells will contain values less than or equal to 0.1.
The RAND() function in Excel returns a pseudo-random number between 0 and 1. If you enter this function into 1000 cells, approximately 10% of these cells (0.1 probability) will contain values less than or equal to 0.1. Therefore, a number relatively close to 100 cells will have values less than or equal to 0.1.
The RAND() function is a built-in function in Excel that generates a random decimal number between 0 and 1. Each time the function is used, a new random number is generated.
The syntax for using the RAND() function is: =RAND() The function takes no arguments and simply returns a random decimal number.
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This is the first time i have been introduced to this without any help with my teacher
well, is a kite so it has two congruent triangles above and two congruent triangles below, for the perimeter is simply the hypotenuse of all four right-triangles.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{above}\\ a=\stackrel{adjacent}{4}\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ above=\sqrt{ 4^2 + 3^2}\implies above=\sqrt{ 16 + 9 } \implies above=\sqrt{ 25 }\implies above=5 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{below}\\ a=\stackrel{adjacent}{3}\\ o=\stackrel{opposite}{7} \end{cases} \\\\\\ below=\sqrt{ 3^2 + 7^2}\implies below=\sqrt{ 9 + 49 } \implies below=\sqrt{ 58 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]5~~ + ~~5~~ + ~~\sqrt{58}~~ + ~~\sqrt{58} ~~ \approx ~~ \text{\LARGE 25.2}[/tex]
after calculating the between-group sum of squares and the within-group sum of squares, the next step is to calculate the mean square between and the mean square within. this is achieved by .
You'll obtain the mean square between and the mean square within, which are crucial for further statistical analyses such as the F-test or ANOVA. To calculate the mean square between and the mean square within after finding the between-group sum of squares and the within-group sum of squares, you can follow these steps:
mean squares:
1. Determine the degrees of freedom between groups (df_between):
Subtract 1 from the number of groups.
2. Determine the degrees of freedom within groups (df_within):
Subtract the number of groups from the total number of observations.
3. Calculate the mean square between (MS_between):
Divide the between-group sum of squares by the degrees of freedom between groups (MS_between = between-group sum of squares / df_between).
4. Calculate the mean square within (MS_within):
Divide the within-group sum of squares by the degrees of freedom within groups (MS_within = within-group sum of squares / df_within).
By following these steps, you'll obtain the mean square between and the mean square within, which are crucial for further statistical analyses such as the F-test or ANOVA.
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Please find domain. Will mark brainliest.
Answer:
F. 100 <= u <= 110.
Step-by-step explanation:
The domain of a function is the set of all possible values of the independent variable (u) for which the function is defined.
In this case, the number of uniforms bought (u) must be at least 100 but not more than 110, since there are at least 100 members but not more than 110 members in the marching band.
Therefore, the domain of the function for this situation is:
100 <= u <= 110
So, the answer is F. 100 <= u <= 110.
Answer:
F: 100 [tex]\leq[/tex] u [tex]\leq[/tex] 110
Step-by-step explanation:
Please help me with this homework only the answer
Answer:
[tex]\frac{11}{9}[/tex]
Step-by-step explanation:
[tex]\frac{change in y}{change in x}[/tex]
[tex]\frac{-14-(-3)}{-9-0}[/tex] = [tex]\frac{-14+3}{-9-0}[/tex] = [tex]\frac{-11}{-9}[/tex] = [tex]\frac{11}{9}[/tex]
Helping in the name of Jesus,
In a parallelogram LMNO, the ratio of LM to MN is 4:3. Find LM if the perimeter of LMNO is 28.
We find LM: LM = 4x = 4 * 2 = 8 So, LM is 8 units long. To solve this problem, we need to use the fact that the opposite sides of a parallelogram are equal in length. Let's start by calling the length of LM "4x", since the ratio of LM to MN is 4:3. That means the length of MN is "3x".
The perimeter of LMNO is the sum of the lengths of all four sides, so we can write an equation:
4x + 3x + 4x + 3x = 28
Simplifying this equation, we get:
14x = 28
Dividing both sides by 14, we find that:
x = 2
Now we can substitute this value of x back into our expressions for the lengths of LM and MN:
LM = 4x = 4(2) = 8
MN = 3x = 3(2) = 6
Since the opposite sides of a parallelogram are equal in length, the other two sides must also have lengths of 8 and 6. Therefore, the perimeter of LMNO is:
8 + 6 + 8 + 6 = 28
So we have found that LM has a length of 8.
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The circles in the model represent positive and
negative integers. Write and solve the equation
that represents the model.
The expression that represents the circles in the model is 4x
Solving the equation that represents the model.From the question, we have the following parameters that can be used in our computation:
The circles in the model
Represent each circle with x
Where
Positive = +xNegative = -xUsing the above as a guide, we have the following:
Positive = +9xNegative = -5xWhen the above expressions are combined, we have
+9x - 5x
Evaluating the above expression
So, we have
4x
Hence, the solution is 4x
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2. A Company manager wishes to test a union leader's claim that employee absences occur on the different week days with the same frequencies. Test this claim at the 0.05 level of significance if the following sample data have been compiled. Select the correct conclusion about the null hypothesis.
Day: Mon Tue Wed Thru Fri
Abs: 37 15 12 23 43
A. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection fo the claim that absences occur on the different week days with the same frequency.
B. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that absences occur on different week days with the same frequency,
C. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that absences occur on the different week days with the same frequency.
D. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that absences occur on the different week days with the same frequency.
5. Perform the indicated goodness-of-fit test. Use a significance level of 0.01 to test the claim that workplace accidents are distributed on workdays as follows: Monday: 25% Tuesday: 15% Wednesday: 15% Thursday: 15% and Friday: 30% In a study of 100 workplace accidents, 29 occurred on a monday, 12 occurred on a tuesday, 16 occurred on a wednesday, 15 occurred on a thursday, and 28 occurred on a Friday. Select the correct critical value.
A. Critical value: x^2=9.488
B. Critical value: x^=11.071
C. Critical value: x^=56.214
D. Critical value: x^=13.277
6. Use a Z^2 test to test the claim that in the given contingency table, the row variable and the column variable are independent. Responses to a survey question are borken down according to employment status and the sample results are given below. At the 0.10 significance level, test the claim that response and employment status are independent.
Yes No Undecided
Employed: 30 15 5
Unemployed: 20 25 10
Select the correct conclusion
7. Use a Z^2 test to test the claim that in the given contingency table, the row variable and the column variable are independent. Responses to a survey question are borken down according to employment status and the sample results are given below. At the 0.10 significance level, test the claim that response and employment status are independent.
Yes No Undecided
Employed: 30 15 5
Unemployed: 20 25 10
Select the correct test statistic and critical value.
A. Test statistic: x^2=4.231. Critical Value X^2=7.779
B. Test statistic: x^2=5.942. Critical Value X^2=4.605
C. Test statistic: x^2=5.942. Critical Value X^2=2.706
D. Test statistic: x^2=4.605 Critical Value X^2=2.706
8. Use a Z^2 test to test the claim that in the given contingency table, the row variable and the column variable are independent. Responses to a survey question are broken down according to gender and the sample results are given below. At the 0.05 significance level, test the claim that response and gender are independent.
Yes No Undecided
Male: 25 50 15
Female: 20 30 10
Select the correct conclusion
9. Use a Z^2 test to test the claim that in the given contingency table, the row variable and the column variable are independent. A study of 160 students who were majoring in either math or english were asked a test question, and the researcher recorded whether they answered correctly. The sample results are given below. At the 0.10 significance level, test the claim that response and major are indepedent.
Correct Incorrect
Math 27 53
English 43 37
Select the correct degrees of freedom
A. df=2
B. df=3
C. df=4
D. df=1
10. A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below.
College A College B college C College D
Smoke 17 26 11 34
Don't smoke 83 74 89 66
Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four colleges.
Select the correct test statistic and conclusion.
A. Test statistic: x^2=17.832. Reject the null hypothesis.
B. Test statistic: x^2=11.345. Reject the null hypothesis.
C. Test statistic: x^2=17.832. Fail to reject the null hypothesis.
D. Test statistic: x^2=11.345. Fail to reject the null hypothesis.
The correct conclusion is:
Fail to reject the null hypothesis.
There is not sufficient evidence to warrant rejection of the claim that absences occur on different weekdays with the same frequency.
Option C is the correct answer.
We have,
To test the claim that employee absences occur on different weekdays with the same frequencies, we need to use the chi-squared goodness of fit test.
First, we calculate the expected frequencies for each weekday assuming they have the same frequency.
Since there are 5 weekdays, we divide the total number of absences (130) by 5 to get the expected frequency of 26 for each weekday.
Using the formula for the chi-squared goodness of fit test, we can calculate the test statistic as follows:
χ² = Σ (O - E)² / E
where O is the observed frequency and E is the expected frequency.
Using the sample data, we get:
χ² = [(37-26)^2/26] + [(15-26)^2/26] + [(12-26)^2/26] + [(23-26)^2/26] + [(43-26)^2/26]
χ² = 8.658
The degrees of freedom for this test is (5 - 1) = 4, since we have 5 weekdays and one parameter (the frequency) has been estimated.
Using a chi-squared distribution table with 4 degrees of freedom and a significance level of 0.05, we find the critical value to be 9.488.
Since the test statistic (8.658) is less than the critical value (9.488), we fail to reject the null hypothesis.
Thus,
The correct conclusion is:
Fail to reject the null hypothesis.
There is not sufficient evidence to warrant rejection of the claim that absences occur on different weekdays with the same frequency.
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PLEASE HELP ME ASAP!!!!
SHOW ALL WORK
Answer:
214 inches
Step-by-step explanation:
Arc length = 2πr(∅/360) = 2π(48)(255/360) = 68π = 213.63 ≈ 214 inches
help quick pls i need to get this done
Answer: The best i could come up with was the BLUE figure
Step-by-step explanation:
Sorry if it is wrong
The table represents a quadratic function C(t). t C(t) −2 1 −1 4 0 5 1 4 2 1 What is the equation of C(t)?
The quadratic function is C(t) = - t² + 5.
We know the equation of the parabola will be given as,
y = a(x - h)² + k
From the table, the coordinate of the vertex will be at (0, 5).
So, the equation can be
C(t) = a(t - 0)² + 5
C(t) = at² + 5
Since, the equation is passing through the point (1, 4)
4 = a (1²) + 5
4 = a + 5
a = - 1
Thus, the required equation is C(t) = - t² + 5.
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A cylinder is sliced in such a way that the plane passes through the cylinder in a slanted direction without going through either base, what is the resulting cross section?
When a cylinder is sliced in such a way that the plane passes through the cylinder in a slanted direction without going through either base, the resulting cross section is an elliptical shape.
To visualize this, imagine a cylinder with circular bases. When a plane intersects the cylinder in a slanted direction, it cuts through the curved surface of the cylinder, creating an elliptical cross section.
The exact shape and size of the elliptical cross section will depend on the angle at which the plane intersects the cylinder and the specific orientation of the cylinder. The major axis of the resulting ellipse will be parallel to the slanted direction of the plane, while the minor axis will be perpendicular to it.
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It's a multiple choice question
In 3rd part, option (c) is not a function. In the 4th part, option (b) is not a function. In the 5th part, option (d) is the parent function for the given y.
For 3rd part,
We have to identify that which relation is not a function. A relation is said to be a function if all the elements of one set have a unique image in another set. In our question, as we can see in option (c), element 1 is connected to 2 elements which are 1 and -1. Element 4 is also connected to two elements which are 2 and -1. Therefore, it is not a function. All the other options are functions as each element has a unique image.
For 4th part,
If we observe option (a), we will get one value of y on equating x to any value. In option (b), y = [tex]\pm\sqrt{36 - x^{2}}[/tex], if we equate x to something, we will get two values of y. In options (c) and (d) also, we will get a unique value of y. Therefore, option (b) is not a function as we do not get a unique image for y.
For 5th part,
y = [tex]3\sqrt{x - 2} + 7[/tex]
To identify the parent function, we strip away all the arithmetic values to leave behind one higher-order operation on just x. Therefore, we will first strip away 3 which is a multiple, and 7 which is being added. Then, we will strip away 2. Now, we are left with just one operation on x which is [tex]\sqrt{x}[/tex]. Therefore, option (d) is the parent function for the given function.
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Giving the mid-point as( -4,7 ) and end point 3,8 calculate the other end point justify your answer
The other endpoint of the line segment with mid-point as( -4,7 ) and end point (3,8) is (-11, 6).
What is the other end point?The midpoint formula is expressed as:
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints of the line segment.
Given that the midpoint is (-4, 7) and one endpoint is (3, 8).
Let the other endpoint be (x, y). T
Hence, we can set up two equations:
(x + 3) / 2 = -4 (equation for x-coordinates)
(y + 8) / 2 = 7 (equation for y-coordinates)
Solving for x and y, we get:
x + 3 = -8
x = -8 - 3
x = -11
For y:
y + 8 = 14
y = 14 - 8
y = 6
Therefore, the other endpoint is (-11, 6).
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Five friends are splitting a package of 30 lemon drops if they divide the candy evenly how many lemon drops will each friend get
Answer: Each Friend will get 6 lemon drops.
Step-by-step explanation:
To find the answer we simply just have to divide 30/5 or 30 divided by 5. The answer to 30 divided by 5 is 6, therefor each friend will get 6 lemon drops.
suppose sat writing scores are normally distributed with a mean of 489 and a standard deviation of 112 . a university plans to award scholarships to students whose scores are in the top 6% . what is the minimum score required for the scholarship? round your answer to the nearest whole number, if necessary.
Minimum score required for the scholarship = 605
To find the minimum score required for the scholarship, we need to find the score that corresponds to the top 6% of scores.
First, we need to find the z-score that corresponds to the top 6%. We can use the standard normal distribution table or calculator to find this.
Using the calculator, we can input:
normalcdf(0.94,9999)
This gives us the area under the curve to the right of z=0.94, which is the z-score that corresponds to the top 6%.
We get: 0.1664
This means that the top 6% of scores correspond to z-scores greater than 0.94.
Now we can use the z-score formula:
z = (x - μ) / σ
where x is the score we want to find, μ is the mean (489), and σ is the standard deviation (112).
Rearranging this formula, we get:
x = z * σ + μ
Substituting in the values we have:
x = 0.94 * 112 + 489
x = 605.08
Rounding this to the nearest whole number, we get:
Minimum score required for the scholarship = 605
To find the minimum score required for the scholarship, we will use the given information about the SAT writing scores being normally distributed with a mean (µ) of 489 and a standard deviation (σ) of 112. We need to find the score that corresponds to the top 6%.
Step 1: Convert the percentage to a decimal. Top 6% = 0.06.
Step 2: Find the Z-score that corresponds to the top 6%. This means we want to find the Z-score that has 1 - 0.06 = 0.94 area to the left. Using a Z-table, you can find that the Z-score is approximately 1.555.
Step 3: Use the Z-score formula to find the minimum score (X):
Z = (X - µ) / σ
1.555 = (X - 489) / 112
Step 4: Solve for X:
1.555 * 112 = X - 489
174.16 = X - 489
X = 663.16
Round to the nearest whole number: X = 663.
So, the minimum score required for the scholarship is 663.
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