The probability that none of the four unrelated Caucasian people in the U.S. have AB- blood is approximately 0.9606 or 96.06%.
The problem states that the probability that a Caucasian person in the U.S. has AB- blood is 1%. This means that the probability of a Caucasian person not having AB- blood is 1 - 0.01 = 0.99.
The problem asks to find the probability that none of the four unrelated Caucasian people have AB- blood. Since we are assuming that the blood types of the four people are independent, we can multiply the probabilities of each person not having AB- blood to find the probability that none of them have AB- blood.
Using the multiplication rule of probability, we can calculate the probability of no AB- blood as:
P(No AB- in 4) = P(Not AB-) * P(Not AB-) * P(Not AB-) * P(Not AB-)
P(No AB- in 4) = 0.99 * 0.99 * 0.99 * 0.99
P(No AB- in 4) = 0.9606
Therefore, the probability that none of the four unrelated Caucasian people in the U.S. have AB- blood is approximately 0.9606 or 96.06%. This means that there is a high likelihood that none of the four people have AB- blood.
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Your company must charge $100 for a software upgrade to make a profit on its development. You must find out if your customers are willing to pay this much. A random sample of 50 customers finds that 17 would pay $100 for the upgrade. If the upgrade is to be profitable, you will need to sell it to more than 20% of your customers. Do the sample data provide good evidence that more than 20% are willing to buy at the 5% level of significance?
a) State the appropriate null and alternative hypotheses. Explain how you decided the alternative.
b) Give the z statistic and its p-value for this test.
c) Should you proceed with plans to develop and market the upgrade? Explain in context of this hypothesis test.
d) Give the 90% confidence interval for the proportion of all customers willing to pay $100.00 for the upgrade. Explain how this supports your hypothesis test conclusion.
e) You company’s overseas division also took a random sample of 50 customers and found that 38 would pay the $100.00 upgrade. Explain why or why not these two populations are different.
a. Hypotheses are: [tex]\rm H_{0}:p=0.20,H_{a}:p > 0.20[/tex]
b. Z-statistics will be 2.47 and p-value = 0.0068
c. you should proceed with plans to develop and market the upgrade.
d. Confidence interval for population proportion will be (0.23, 0.45)
e. The populations are different because they are frοm different regiοns sο prefrences οf peοple may different.
What is Probability?Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.
a. Hypotheses are:
[tex]\rm H_{0}:p=0.20,H_{a}:p > 0.20[/tex]
b) Here we have following information:
[tex]\rm n=50, \hat{p}=\frac{17}{50}=0.34[/tex]
Standard deviation of the proportion is:
[tex]\rm \sigma=\sqrt{\frac{p\left ( 1-p \right )}{n}}=\sqrt{\frac{0.20\left ( 1-0.20 \right )}{50}}=0.0566[/tex]
Test statistics will be:
[tex]$ \rm z=\frac{\hat{p}-p}{\sigma}=\frac{0.34-0.20}{0.0566}=2.47[/tex]
Alternative hypothesis shows that the test is right tailed so p-value of the test is
[tex]\rm p-value = P(z > 2.47) = 1 - P(z \leq 2.47)=1-0.9932=0.0068[/tex]
c. Since p-value of the test is less than 0.05 so we reject the null hypothesis at 0.05 level of significance. So based on this sample, you should proceed with plans to develop and market the upgrade.
d. For 90% confidence interval [tex]\alpha[/tex] = 0.10 so critical value of z will be[tex]\rm z_{c}=z_{\alpha/2}=1.645[/tex]
Confidence interval for population proportion will be
[tex]\rm \hat{p}\pm z_{c}\sqrt{\frac{\hat{p}\left ( 1-\hat{p} \right )}{n}}=0.34\pm 1.645\sqrt{\frac{0.34\left (1-0.34 \right )}{50}}=0.34\pm 0.11 =(0.23, 0.45)[/tex]
e. The populations are different because they are frοm different regiοns sο prefrences οf peοple may different.
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2. (a) Arnold walked a distance of 50km due north. He continued to move 25km due east.
Sketch a diagram to illustrate the Arnold's movement from the starting point.
Find correct to the nearest whole number the distance between where he started the
journey and where he ended the journey
The bearing of his starting point from his end point.
Answer:
Step-by-step explanation:
The sketch is a right-angled triangle.
We can use Pythagoras' theorem.
[tex]z^{2} =x^{2} +y^{2}[/tex]
z=√(50^2+25^2)
z= 25√5
z=25*2.23
z=55.75
z≈56km
the distance between where he started the
journey=56km
tan(90-Θ)=25/50
cotΘ=1/2
tanΘ=2
Θ=[tex]tan^{-1} (2)[/tex]
bearing of his starting point from his end point[tex]tan^{-1} (2)[/tex]
HELP PLSSSSSSSSSSSSSSSSSS NEED THIS ASAP
Answer:
Step-by-step explanation:
First you have to find out how many red were in the original 27 marbles.
If there were 7 Black and 4 Yellow - this is 11 so 27 - 11 = 16 RED.
Removing 3 Black - changes the the can to 24 marbles.
4 Black - 4 Yellow and 16 Red.
So probability the random pick is red after the removal of 3 Black is
16 out of 24. [tex]\frac{16}{24}[/tex]
This reduces to 2/3.
Choice (K)
Answer:
Step-by-step explanation:
There are 27 marbles which include 7 black marbles
4 yellow marbles
Therefore, the number of red marbles=27-(7+4) marbles
=16 red marbles
When 3 black marbles are removed from the can, the total number of marbles become 24, which includes the 4 black marbles,4 yellow marbles and 16 red marbles.
So, the probability of the picking of a random red marble from the can after removing the black marbles = 16÷24
This when reduced gives the result 2÷3.
Hence, the answer is option K which means the probability that it was red is 2/3.
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(5, 5, 6, 9, 9, 11, 13}
This set has two_____
-medians
-means
-modes
Answer:
modes
Step-by-step explanation:
The only one of the three (median, mode, mean) that there can be more than one for a set is the mode, and in fact it has two modes: 5 and 9.
Answer: modes
3.
The formula for converting Fahrenheit temperature to centigrade is °C
=% (°F - 32). What is the difference in centigrade degrees between a
temperature of 60°F and a temperature of 78°F?
25
A. 1°C
B. 5°C
C. 10°C
D. 18°C
The difference in centigrade degrees between a temperature of 60°F and a temperature of 78°F is 10°C.
Calculating the difference between the temperaturesTo convert Fahrenheit (°F) to Celsius (°C), you can use the following formula:
°C = (°F - 32) / 1.8
Using this formula, we can first convert 60°F to Celsius:
°C = (60°F - 32) / 1.8
°C = (28°F) / 1.8
°C = 15.56°C
Similarly, we can convert 78°F to Celsius:
°C = (78°F - 32) / 1.8
°C = (46°F) / 1.8
°C = 25.56°C
The difference in Celsius degrees between these two temperatures is:
Δ°C = 25.56°C - 15.56°C
Δ°C = 10°C
Therefore, the difference in centigrade degrees between a temperature of 60°F and a temperature of 78°F is 10°C.
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A scientist was in a submarine, 52.3 feet below sea level, studying ocean life. Over the next ten minutes, she went down 21.5 feet. How many feet was she now below sea level?
After descending [tex]21.5[/tex] feet, the scientist's new position in the submarine would be [tex]30.8[/tex] feet below sea level.
What is the sea level?The scientist was initially in a submarine, located 52.3 feet below sea level. This means that her position was [tex]52.3[/tex]feet lower than the surface of the sea.
Over the next ten minutes, the scientist descended further into the ocean by [tex]21.5[/tex] feet. This means that she traveled down an additional [tex]21.5[/tex]feet from her initial position.
To calculate her new position below sea level, we can subtract the distance she traveled downward (21.5 feet) from her initial position (52.3 feet below sea level).
[tex]52.3 feet - 21.5 feet = 30.8 feet[/tex]
Therefore, after descending 21.5 feet, the scientist's new position in the submarine would be 30.8 feet below sea level.
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Solve for ∠A
. Round your answer to the nearest tenth.
∠A
= degrees
(60 points)
Answer:
∠A = 48.2
Step-by-step explanation:
Cos^-1(6/9
Use the Cosine with the negative one because you are finding an angle. Then, because Cosine is adjacent/hypotenuse, 6 would be your adjacent side length to theta and 9 would be the hypotenuse as it is across from the right angle.
5.2, 5.2, 4.7, 5.4, 3.9, 3.5, 4.1, 4.2, 5.4, 4.7, 4.8, 4.2, 4.6, 5.1, 3.8, 3.9, 4.6, 5.1, 3.6, 4.6, 4.3, 3.4, 4.9, 4.2, 4.0
A manufacturer of pencils randomly selects 25 pencils and measures their length (in inches). Their data is shown. Create a frequency distribution with 6 classes and a class width of 0.4 inches. What is the shape of the frequency histogram?
The histogram is bimodal.
The histogram is roughly symmetrical.
The histogram is skewed right.
The histogram is uniform.
The histogram is skewed left.
Answer:
A) The histogram is bimodal.
Answer:
To create a frequency distribution, we first need to determine the range of the data. The smallest measurement is 3.4 inches and the largest is 5.4 inches, so the range is 5.4 - 3.4 = 2 inches. To create 6 classes with a width of 0.4 inches, we divide the range by 0.4 and round up to the nearest integer:
Number of classes = (range / class width) rounded up = 2 / 0.4 = 5
So we will use 5 classes with a width of 0.4 inches each. The classes and their corresponding frequency counts are:
Class 1: 3.4 - 3.8 | Frequency: 3
Class 2: 3.9 - 4.3 | Frequency: 8
Class 3: 4.4 - 4.8 | Frequency: 6
Class 4: 4.9 - 5.3 | Frequency: 7
Class 5: 5.4 - 5.8 | Frequency: 1
To create a histogram, we can plot the frequency counts on the y-axis and the class intervals on the x-axis. The shape of the histogram can give us information about the distribution of the data. In this case, the histogram is bimodal, meaning there are two peaks in the data. This suggests that the data may be composed of two separate subpopulations.
2. Using the link on the activity page, cut out each net. Fold and tape each net into a
solid. Your solids do not need to be perfect. (9 points: 3 points for
three-dimensional
each solid)
To fold and tape a net into a solid shape, cut out the net, fold it along the lines, tape the edges together, and flatten the edges
Instructions for Folding and Taping a Net into a Solid ShapeThe net cannot be fold and tape as it is given as a picture, however the general steps to fold and tape a net into a solid shape:
Choose a netCut out the net: Cut out the net along the lines so that you have a flat, two-dimensional shape.Fold along the lines: Fold the net along the lines indicated on the paper. Tape the edges: Use small pieces of clear tape to connect the edges of the net together, forming a solid shape.Flatten the edges: After taping, you may notice that some edges of the solid shape are not lying flat.When the above stapes are followed, some of the nets that can be gotten from the given shape are triangular pyramids and triangles
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Burt ran the length of the trail in his town’s park. There are 9 parts to the trail, and each part is the same length. Burt ran a total of 1.8 kilometers.
There are 9 parts to the trail, and each part is the same length. and hence each part of the trail is 0.2 kilometers long.
What is perimeter of rectangle?The following equation may be used to determine a rectangle's perimeter:
Perimeter is equal to 2 x (length + breadth).
where "length" denotes the rectangle's length and "width" denotes the rectangle's width. In order to account for both sides of the rectangle, we add the length and breadth together and multiply the result by 2, which is the distance around the outside of the rectangle.
The distance ran by Brurt is:
1.8 km ÷ 9 = 0.2 km
Hence, each part of the trail is 0.2 kilometers long.
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Which equation of a circle has the center, C, and radius, r, as shown in the graph?
The equation of a circle given by the graph is (x-3)²+(y+2)²=29,
hence option b is correct.
A circle is a closed curve that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center. A circle with an (h, k) center and a radius of r has the equation:
(x-h)² + (y-k)²= r²
This is the equation's standard form. Hence, we can quickly determine the equation of a circle if we know its radius and center coordinates.
We know that the equation of the circle is -
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h,k) is the center of the circle and r is the radius,
given that,
center of the circle is = (3,-2)
and the radius is=√29
Hence the equation of a circle is
[tex](x-3)^2+(y+2)^2=(\sqrt29)^2\\\\(x-3)^2+(y+2)^2=29[/tex]
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I need help with this please
Answer: 384 cm cubed
Step-by-step explanation: The first thing you will do is 48 square centimeters times 8 cm. Since 48 is squared you have that 2 right above it. Your 8 technically has a 1 above it. So add the 2 and the 1, and you will get cubed. (AKA 3)
Eric had a box of 24 candy bars that he planned to sell for 63 cents each. Unfortunately, his sister ate 7 of his candy bars before he started selling them. In order to bring in the same amount of money as he would have if his sister had not eaten any of the candy bars, what price (in cents) should he charge for each of the remaining candy bars?
The price (in cents) should he charge for each of the remaining candy bars 49
First, we would want to calculate how much the box would sell for before the sister ate some.
We would get 24*63(in cents) and we can further get 1512 cents before the sister ate the candy bars.
The sister ate 7 candy bars leaving us with 31 candy bars. To deduct the price for each candy bar, it would be a situation like the following:
$6 for 3 boxes of 500 cookies (i know that's cheap)
6/3...
$2 per box.
Using our situation we get 1512 cents for 31 candy bars.
1512÷31
=48.77
That does seem unrealistic, so we round to the nearest whole number and we get...
49 cents
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The sum of 1/2 and 2/3 is ______1. a. equal to b. less than c. greater than
Answer:
c. greater than
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] + [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{6}[/tex] + [tex]\frac{4}{6}[/tex] = [tex]\frac{7}{6}[/tex] ≈ 1.167
1.167 > 1
So, the answer is c. greater than
One plumbing job requires 45 meters of PVC pipe, and a second job requires 30 meters. The pipe comes in 6-meter lengths only. How many sections should the plumber buy? How much pipe will be left over, assuming that there are no errors?
a) The plumber should buy 13 sections of 6-meter lengths of PVC pipes.
b) Assuming that there are no errors, the left-over pipe after satisfying Jobs A and B should be 3 meters.
How the quantities are determined:We can use mathematical operations of addition, division, multiplication, and subtraction to determine the two quantities above.
In the first place, the total quantity of PVC pipes required is 75 meters.
This sum is divided by 6 to obtain the sections required, which is approximated to the nearest whole number.
Finally, 75 meters are subtracted from the total quantity bought.
PVC pipes required by Job A = 45 meters
PVC pipes required by Job B = 30 meters
The total quantity of PVC pipes required = 75 meters
The length of each PVC pipe = 6 meters
The number of pipes to buy = 13 sections (75 ÷ 6)
13 sections of pipes = 78 (6 x 13)
Leftover PVC pipes = 3 meters (78 - 75)
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The center of the circle is shown.
9
What is the exact area of the circle?
324n
18n
9r
81n
Answer:
The area is (9^2)π = 81π.
The _______________ is a collection of people and companies where shares in the various companies are bought, sold, and traded.
A. Life Insurance Company
B. Savings Institution
C. Stock Market
D. Bonds
Answer:
C) Stock Market.
Brainly wants me to put at least 20 characters and since I only provided the answer choice and was too lazy to do an explanation I am putting this here.
Answer:
C) Stock Market.
Step-by-step explanation:
The term stock market refers to several exchanges in which shares of publicly held companies are bought and sold.
what is 95.2% confidence interval in z-score
A 95.2% confidence interval in z-score is a range of values that is likely to contain the true population mean with a probability of 95.2%. The z-score for a 95.2% confidence interval is approximately ±1.97.
To calculate the 95.2% confidence interval in z-score, we can use the following formula:
CI = X ± z × (σ/√n)
where X is the sample mean, σ is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution table.
For a 95.2% confidence interval, the area in the tails of the standard normal distribution is 0.024 (0.5 - 0.952/2). Therefore, the critical z-value for a 95.2% confidence interval is approximately ±1.97.
This formula assumes that the sample follows a normal distribution, or that the sample size is large enough to satisfy the central limit theorem.
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In ΔMNO, m ∠ � = ( 4 � − 13 ) ∘ m∠M=(4x−13) ∘ , m ∠ � = ( 2 � − 13 ) ∘ m∠N=(2x−13) ∘ , and m ∠ � = ( 5 � + 19 ) ∘ m∠O=(5x+19) ∘ . Find m ∠ � . m∠N.
The value of m∠N is 21° ,the value of m∠M is 55° and the value m∠O is 106°.
To find the value of x, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore:
m∠M + m∠N + m∠O = 180
Substituting the given angle measures, we get:
(4x-13) + (2x-13) + (5x+19) = 180
Simplifying the equation, we get:
11x - 7 = 180
11x = 187
x = 17
Now that we know the value of x, we can find the measure of each angle. Substituting x = 17, we get:
m∠M = (4x-13) = (417-13) = 59 degrees
m∠N = (2x-13) = (217-13) = 21 degrees
m∠O = (5x+19) = (5*17+19) = 106 degrees
Therefore, the measure of ∠MNO is:
m∠N = 21 degrees
Note: The question also asks for the measure of ∠P, but there is no information given about ∠P in the problem.
In AMNO, m angle M = (4x - 13) deg m angle N = (2x - 13) deg and m angle O = (5x + 19) deg Find m/N.
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A group of people were asked if they had run a red light in the last year. 348 responded "yes", and 400 responded "no".
The probability of people who run red lights is
=0.465
Probability is the measure of the likelihood or chance that an event will occur.
Probability = Possible outcome of an event ÷ Total outcome
Total number of people asked if they had run a red light = number of people that responded 'yes' + number of people that responded 'no'
Total outcome = 348+400
Total outcome = 748
Possible outcome = number of people that responded yes = 394
The probability that if a person is chosen at random, they have run a red light in the last year will be
[tex]=\frac{348}{748}\\\\=0.465[/tex]
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PLEASE HELPPPP GIVNG BRAINLIESt
MNOP is a trapezium. If MN//OP and A is the midpoint of NO prove : Area of triangle MAP = 1/2area of trapezium MNOP
To prove: Area of triangle MAP = 1/2 area of trapezium MNOP
Given: MN//OP and A is the midpoint of NO
Proof:
Let h be the height of trapezium MNOP.
The area of trapezium MNOP is given by:
Area of trapezium MNOP = (1/2) × (MN + OP) × h
Since MN//OP, we have MN = OP.
Therefore, Area of trapezium MNOP = (1/2) × 2MN × h = MN × h
Now, consider triangle MAP.
The base of triangle MAP is MA, which is half of NO.
Therefore, the base of triangle MAP is (1/2) × NO.
The height of triangle MAP is h, which is the same as the height of trapezium MNOP.
Therefore, the area of triangle MAP is given by:
Area of triangle MAP = (1/2) × (base) × (height) = (1/2) × (1/2NO) × h
Substituting NO = 2OA, we get:
Area of triangle MAP = (1/2) × (1/2 × 2OA) × h = (1/2) × OA × h
Since A is the midpoint of NO, we have OA = 1/2NO.
Therefore, Area of triangle MAP = (1/2) × (1/2NO) × h = (1/2) × (base of trapezium MNOP) × h
Hence, Area of triangle MAP = 1/2 Area of trapezium MNOP.
Therefore, the given statement is proved.
Answer: Given that MNOP is a trapezium with MN parallel to OP and A is the midpoint of NO.
To prove that the area of triangle MAP is half the area of trapezium MNOP, we need to use the following theorem:
Theorem: If a line segment joins the midpoint of one side of a triangle to a vertex opposite to that side, then the segment divides the triangle into two equal areas.
Proof:
Since A is the midpoint of NO, we can draw a line segment AP from vertex P to point A on NO as shown in the figure below:
css
Copy code
M _______N
|\ |
| \ |
| \ |
| \|
O--------P
A
We can see that triangle MAP is formed by the line segment AP and side MP of the trapezium.
Also, we can see that triangle MAN is congruent to triangle NOP because they are both right triangles with corresponding sides parallel. Therefore, they have the same area.
Since MNOP is a trapezium, the area of trapezium is given by:
Area of trapezium MNOP = (1/2)(MN+OP) × height
Since MN is parallel to OP, the height of the trapezium is the same as the height of triangle MAN and NOP.
Therefore, the area of trapezium MNOP can be written as:
Area of trapezium MNOP = (1/2)(MN+OP) × height
= (1/2)(MA+AP+OP) × height
= (1/2)(MA+MP) × height (Since AP = NO/2 = height)
So, we have proved that:
Area of trapezium MNOP = (1/2)(MA+MP) × height
Using the theorem, we know that AP divides triangle MAP into two equal areas. Therefore,
Area of triangle MAP = (1/2) × Area of triangle MAP
Substituting the above in the expression for the area of trapezium, we get:
Area of trapezium MNOP = Area of triangle MAP + (1/2) × Area of triangle MAP
= (3/2) × Area of triangle MAP
Therefore, we have:
Area of triangle MAP = (1/2) × Area of trapezium MNOP
Thus, we have proved that the area of triangle MAP is half the area of trapezium MNOP.
Step-by-step explanation:
example of improper sampling in day to day life?
Answer: Sampling is very often used in our daily life. For example, while purchasing fruits from a shop, we usually examine a few to assess the quality. A doctor examines a few drops of blood as a sample and draws a conclusion about the blood constitution of the whole body.
. Ten weeks of data on the Commodity Futures Index are 7.35, 7.40, 7.55, 7.56, 7.60, 7.52,
7.52, 7.70, 7.62, and 7.55.
a. Construct a time series plot. What type of pattern exists in the data?
b. Use trial and error to find a value of the exponential smoothing coefficient that results in a relatively small MSE.
By iterating through different alpha values, you can identify the optimal alpha for this data set that results in the smallest MSE.
How to solvea. To construct a time series plot, you would typically use software like Excel or programming languages like Python or R.
However, I can describe the general trend based on the given data points.
Week 1: 7.35
Week 2: 7.40
Week 3: 7.55
Week 4: 7.56
Week 5: 7.60
Week 6: 7.52
Week 7: 7.52
Week 8: 7.70
Week 9: 7.62
Week 10: 7.55
Based on the data, there seems to be a slight overall upward trend in the Commodity Futures Index over the ten weeks, but there are also small fluctuations up and down throughout the period.
b. To find the best exponential smoothing coefficient (alpha) using the trial and error method, you would typically use software or programming languages to calculate the Mean Squared Error (MSE) for each alpha value.
Choose an initial value for alpha (e.g., 0.1).
Apply the exponential smoothing formula to the data series: St = α * Xt + (1 - α) * St-1, where St is the smoothed value at time t, α is the smoothing coefficient, Xt is the observed value at time t, and St-1 is the smoothed value at time t-1.
Calculate the forecast errors (Et) as the difference between the observed value and the smoothed value for each time period: Et = Xt - St-1.
Compute the Mean Squared Error (MSE) by taking the average of the squared forecast errors.
Repeat steps 2-4 with different values of alpha (e.g., 0.2, 0.3, 0.4, etc.) until you find the alpha value that minimizes the MSE.
By iterating through different alpha values, you can identify the optimal alpha for this data set that results in the smallest MSE.
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What is the probability of getting a even number from the bag
Answer: The actual answer is 7/12, but the closest match is (A) 1/2.
Question 7 of 10
In the triangle below, b=_ If necessary, round your
answer to two decimal places.
A
33.7°
C
Answer here
8
26.4
24
SUBMIT
the length of the missing side is approximately 4.73 units. Rounded to two decimal places, the answer is 4.73.
How to solve the problem?To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.
Let's label the missing side as b, and use sin(A) = opposite/hypotenuse to find the length of the side opposite angle A:
sin(A) = opposite/hypotenuse
sin(33.7°) = b/8
b = 8 × sin(33.7°)
b ≈ 4.726
Therefore, the length of the missing side is approximately 4.73 units. Rounded to two decimal places, the answer is 4.73.
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translate the triangle 3 to the right and 2 down
According to the assumption the translated triangle would have vertices at (4,0), (6,2), and (5,-1).
Given,
To translate a triangle 3 units to the right and 2 units down, we would take each point of the original triangle and add 3 to the x-coordinate and subtract 2 from the y-coordinate.
For example, if the original triangle has vertices at (1,2), (3,4), and (2,1), the translated triangle would have vertices at:
(1+3, 2-2) = (4,0)
(3+3, 4-2) = (6,2)
(2+3, 1-2) = (5,-1)
So, the translated triangle would have vertices at (4,0), (6,2), and (5,-1).
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Find the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55%. P = [?]% Round to the nearest tenth of a percent. Enter
the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55% is 0.29 = 29%
A binomial experiment is an experiment that has the following four properties:
The experiment consists of n repeated trials
Each trial has only two possible outcomes
The probability of success, denoted p, is the same for each trial
Each trial is independent
the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55%
We know that the binomial distribution
[tex]^nc_rp^rq^{n-r[/tex]
Where n is the number of trails
p is the probability of success in each trial
q =1-p which is the probability of failure
Here r=4
n=7
p= 55 % =0.55
then by the formula
[tex]p(4)=^7c_4(o.55)^4(0.45)^3\\\\p(4)=35*0.091*0.091\\p(4)=0.29[/tex]
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Assume the random variable x is normally distributed with mean u=89 and standard deviation o=4. Find the indicated probability. P(x<87)
The random variable x is normally distributed with mean u=89 and standard deviation o=4. The indicated probability, P(x<87)= 0.3085.
Describe Standard Deviation?In statistics, standard deviation is a measure of the amount of variation or dispersion in a set of data. It is a commonly used measure of the spread of a distribution and is calculated as the square root of the variance.
A higher standard deviation indicates that the data points are more spread out from the mean, while a lower standard deviation indicates that the data points are more tightly clustered around the mean.
Standard deviation is an important concept in statistics and is used in many statistical analyses, such as hypothesis testing and confidence interval estimation. It is also used in finance and economics to measure the risk associated with investments and to assess the variability of economic data.
To solve this problem, we need to standardize the value using z-score formula.
z = (x - mu) / sigma
Here, x = 87, mu = 89, and sigma = 4.
z = (87 - 89) / 4 = -0.5
We can look up the corresponding area under the standard normal distribution curve using a table or calculator. The area to the left of z = -0.5 is 0.3085.
Therefore, P(x < 87) = P(z < -0.5) = 0.3085.
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34kg of apples cost $374. how many kilograms of apples can you get with $220
Answer:
20 kilograms.
Step-by-step explanation:
First, we need to find the cost per kilogram.
We can do this by dividing 374 by 34.
That gives us 11. So, our cost per kilogram is $11.
Next, to find how many kilograms we can get with $220 dollars, we need to divide 220 by 11.
That leaves us with a final answer of 20 kilograms.
Bob runs an auto repair shop. Over 6 months, he finds that out of 700 cars that are brought in, 144 require more than one day to repair. Based on this information, what is the probability that the next car brought to his shop can be fixed in a day? Responses 20.6% 20.6% 55.6% 55.6% 79.4% 79.4% 82.9%
The answer to the given question about probability of Bob's shop is option 7) 79.4%.
Out of 700 cars, 144 require more than one day to repair. So the number of cars that can be fixed in one day is
700 - 144 = 556.
The probability that the next car brought to the shop can be fixed in a day is the ratio of the number of cars that can be fixed in a day to the total number of cars:
probability = 556/700
= 0.794 or 79.4%
Therefore, the correct answer is option 7) 79.4%.
Probability is a branch of mathematics that deals with the study of random events or phenomena. It is used to quantify the likelihood of an event occurring, and it is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. Probability theory is widely used in various fields, such as statistics, physics, economics, and finance, to make predictions and decisions based on uncertain or incomplete information. It provides a powerful tool for analyzing and understanding uncertainty, risk, and randomness in real-world situations, and it has numerous practical applications in diverse areas of research and industry
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