Given the current i = 6 - 3i amperes and resistance r = 7 + 8i ohms, the voltage E of the Circuit, calculated using Ohm's law, is 66 + 27i volts.
To find the voltage (E) of a circuit using Ohm's law, we can substitute the given values of current (i) and resistance (r) into the formula E = i * r.
Given:
i = 6 - 3i (amperes)
r = 7 + 8i (ohms)
Substituting these values into the formula, we have:
E = (6 - 3i) * (7 + 8i)
To multiply these complex numbers, we can use the distributive property and perform the multiplication as follows:
E = 6 * 7 + 6 * 8i - 3i * 7 - 3i * 8i
= 42 + 48i - 21i - 24i^2
Remember that i^2 is defined as -1, so we can simplify further:
E = 42 + 48i - 21i - 24(-1)
= 42 + 48i - 21i + 24
= 66 + 27i
Therefore, the voltage (E) of the circuit is 66 + 27i volts.
Given the current i = 6 - 3i amperes and resistance r = 7 + 8i ohms, the voltage E of the circuit, calculated using Ohm's law, is 66 + 27i volts.
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Find sin ø
Triangle side=16 side =20 base =12
From the given right angled triangle the ratio of sinθ is 16/20. Therefore, the correct answer is option B.
From the given right angle triangle, hypotenuse=20 units, Opposite to angle θ is 16 units and adjacent side = 12 units.
We know that, sinθ= Opposite/hypotenuse
sinθ= 16/20
sinθ= 4/5
Therefore, the correct answer is option B.
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Joseph has 9 business shirts. He needs to take 4 shirts for a work conference. In how many ways can he choose 4 shirts out of 9?
Answer: 3,024
Step-by-step explanation:
This is a probability question. Here, the order does not matter, so a combination of shirts 1, 2, 3, and 4 and 4, 3, 2, and 1 count together as 1. We use the permutation calculator to get 9! / ( 9 - 4 )!. ( 9 - 4 )! is equal to 5! and 9! / 5! = 9x8x7x6, or 3,024
You are a student working toward an associate's degree to become a paramedic. You
just got your midterm grade for the Paramedic Pharmacology class you're taking and
it is a 91.25, which seems a little low, so you decide to double check. Luckily, you
save all of your tests, so you can use them to figure out your average. However,
when you go back through your tests, you notice that one is missing. Based on the
midterm average, what is the grade for the missing test?
Test grades: {90 88 ? 92}
The grade for the missing test is 95.
To determine the grade for the missing test, we can use the information provided.
We know the average of all the tests, including the missing one, is 91.25.
Let's calculate the average using the given test grades: 90, 88, ?, 92.
The sum of the known test grades is: 90 + 88 + 92 = 270.
Since we have four tests in total, including the missing one, we can set up the equation:
(270 + ?) / 4 = 91.25
To find the missing grade, we can solve for the variable "?":
270 + ? = 91.25 x 4
270 + ? = 365
? = 365 - 270
? = 95
Therefore, the grade for the missing test is 95.
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SOMEBODY PLEASE PLEASE HELP ME IM BEGGING YOU
ILL RATE YOU 5 STARS AND GIVE A HEART PLEASE HELP
Answer:
Step-by-step explanation:
bus / walking
mean:105/ 123
median:15/ 20
mode: 14/ 21
range: 46 /3
Answer:
Bus Walking
Mean- 17.5 Mean- 20.5
Medium- 15 Medium- 20.5
Mode- 14,15 Mode- 20,21
Range- 17 Range- 3
Step-by-step explanation:
Bus: 14, 14, 15, 15, 16, 31
Mean- 14+14+15+15+16+31= 105/6= 17.5
All the numbers combined and then divided by how many numbers were added
Medium- 15+15= 30/2= 15
Two middle numbers are added together and then divided by two
Mode- 14, 15
The most frequent number
Range- 31-14= 17
the difference between the lowest and highest values
Walking: 19, 20, 20, 21, 21, 22
Mean- 19+20+20+21+21+22= 123/6= 20.5
All the numbers combined and then divided by how many numbers were added
Medium- 20+21= 41/2= 20.5
Two middle numbers are added together and then divided by two
Mode-20,21
The most frequent number
Range- 22-19= 3
the difference between the lowest and highest values
E. There are three boxes on the table. The mass of box 1 is three times more than the
mass of box 3, The mass of box 2 is two-thirds the mass of box 1. If the mass of box 3
is 150 grams, what is the mass of each of the other boxes?
The mass of Box 1 is 450 grams, the mass of Box 2 is 300 grams, and the mass of Box 3 is 150 grams.
Given that,
The mass of Box 3 = 150 grams
Assume that,
Mass of Box 1 is "x"
And the mass of Box 2 "y".
We know that,
Box 1 has a mass that is three times more than Box 3,
Therefore,
⇒ 3x150 = 450 grams
Then,
⇒ x = 450
Box 2 has a mass that is two-thirds the mass of Box 1,
so its mass is,
⇒ (2/3)x450 = 300 grams.
it means, y = 300
Hence,
Masses are:
Box 1 is 450 grams
Box 2 is 300 grams
Box 3 is 150 grams
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please help will give 5 stars image is attached!
Using the concept of similar triangles, the values of x is 12 units
What are similar triangles?Similar triangles are triangles that have the same shape but possibly different sizes. In other words, they have corresponding angles that are equal, and their corresponding sides are in proportion.
Two triangles are considered similar if and only if:
Their corresponding angles are congruent (equal in measure).The ratios of the lengths of their corresponding sides are equal.x/6 = (18 + 6) / x
x / 6 = 24 / x
cross multiply both sides by x;
x * x = 24 * 6
x² = 144
x = √144
x = 12
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The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Mountain View School Bay Side School
0 5, 6, 8
9, 8, 2, 0 1 0, 2, 4, 5, 6, 8
8, 7, 6, 5, 5, 4, 4, 3, 1, 0 2 0, 0, 2, 3, 5
0 3
4 2
Key: 2 | 1 | 0 means 12 for Mountain View and 10 for Bay Side
Part A: Calculate the measures of center. Show all work. (2 points)
Part B: Calculate the measures of variability. Show all work. (1 point)
Part C: If you are interested in a larger class size, which school is a better choice for you? Explain your reasoning. (1 point)
Part A: The measures of center in Mountain View School, mean = 4.75, median = 4.5 and Bay Side School, mean = 5.5, median = 4.5
Part B: The measures of variability: Mountain View School, Range= 9 IQR= 4, Bay Side School, Range= 10 IQR= 3
Part C: Bay Side School would be the better choice.
Part A: Measures of Center
To calculate the measures of center, we will determine the mean and median for each school.
Mountain View School:
Mean = (0 + 5 + 6 + 8 + 9 + 8 + 2 + 0) / 8 = 38 / 8 = 4.75
Median = (4 + 5) / 2 = 4.5
Bay Side School:
Mean = (10 + 2 + 4 + 5 + 6 + 8 + 8 + 7 + 6 + 5 + 5 + 4 + 4 + 3 + 1 + 0) / 16 = 88 / 16 = 5.5
Median = (4 + 5) / 2 = 4.5
Part B: Measures of Variability
To calculate the measures of variability, we will determine the range and interquartile range (IQR) for each school.
Mountain View School:
Range = 9 - 0 = 9
IQR = (6 - 2) = 4
Bay Side School:
Range = 10 - 0 = 10
IQR = (6 - 3) = 3
Part C: Choice based on Class Size
If you are interested in a larger class size, Bay Side School would be the better choice. The mean class size at Bay Side School is 5.5, while at Mountain View School it is 4.75. The range of class sizes at Bay Side School is also larger (10) compared to Mountain View School (9). This indicates that there is a greater variation in class sizes at Bay Side School, providing a higher likelihood of finding larger class sizes. However, it's important to consider other factors such as teaching quality, resources, and overall educational environment before making a final decision.
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Assistance required urgently.
Answer: B
Step-by-step explanation:
Some of the items on a restaurant menu are vegetarian and some of them are gluten free. There are 29 items on the menu. 21 of the items are not vegetarian and 7 of these are also not gluten free. 6 of the items are vegetarian but not gluten free. a) If a randomly chosen item is gluten free, what is the probability that it is also vegetarian? b) If a randomly chosen item is vegetarian, what is the probability that it is also gluten free? Give each answer as a fraction in its simplest form.
The probability that a arbitrarily chosen thing that's gluten-free is additionally veggie lover is 6/13.
The probability that a haphazardly chosen thing that's veggie lover is additionally gluten-free is 6/19.
How to Solve the Probability?To fathom this issue, let's characterize the taking after occasions:
V = Thing is veggie lover
G = Thing is gluten-free
We are given the following data:
P(V') = 21/29 (21 things are not veggie lover out of 29)
P(V'∩G') = 7/29 (7 things are not vegan and not gluten-free out of 29)
P(V∩G') = 6/29 (6 things are veggie lover but not gluten-free out of 29)
a) We got to discover P(V|G), the likelihood that an item is vegan given that it is gluten-free. Able to utilize Bayes' hypothesis:
P(V|G) = P(V∩G) / P(G)
We know that P(V∩G) = P(G∩V) = P(V∩G') (since V and G are independent occasions), and P(G) = P(G∩V) + P(G∩V'), so:
P(V|G) = P(V∩G') / [P(G∩V) + P(G∩V')]
Substituting the given values:
P(V|G) = (6/29) / [(6/29) + (7/29)]
= 6/13
Subsequently, the probability that a arbitrarily chosen thing that's gluten-free is additionally veggie lover is 6/13.
b) We ought to discover P(G|V), the likelihood that an thing is gluten-free given that it is veggie lover. Once more, utilizing Bayes' hypothesis:
P(G|V) = P(G∩V) / P(V)
We know that P(G∩V) = P(V∩G) = P(V∩G') (since V and G are independent occasions), and P(V) = P(V∩G) + P(V∩G'), so:
P(G|V) = P(V∩G') / [P(V∩G) + P(V∩G')]
Substituting the given values:
P(G|V) = (6/29) / [(6/29) + (7/29) + (6/29)]
= 6/19
Hence, the likelihood that a haphazardly chosen thing that's veggie lover is additionally gluten-free is 6/19.
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Solve by graphing. x2 + 2x – 3 = 0
By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.
To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.
First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.
We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.
1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:
0 = x^2 + 2x - 3.
This quadratic equation can be factored as (x + 3)(x - 1) = 0.
Therefore, x = -3 or x = 1.
2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.
3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).
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Consider the following random sample of 25 students’ answer to the survey question. In a typical day, how many times do you use social networking websites. 7 10 20 10 40 15 10 6 10 50 30 7 10 50 55 10 15 6 20 10 35 10 5 50 10 a) What is the mean, median and mode? What does that tell about the likely shape of the distribution? b) What is the variance and standard deviation?
The Variance is approximately 422.12 and the standard deviation is approximately 20.54. These measures indicate that the data set has a relatively high dispersion or spread.
a) To find the mean, median, and mode of the given data set, we can perform the following calculations:
Mean: The mean is calculated by summing all the values and dividing by the total number of values.
Mean = (7 + 10 + 20 + 10 + 40 + 15 + 10 + 6 + 10 + 50 + 30 + 7 + 10 + 50 + 55 + 10 + 15 + 6 + 20 + 10 + 35 + 10 + 5 + 50 + 10) / 25
Mean = 357 / 25
Mean ≈ 14.28
Median: The median is the middle value of the data set when arranged in ascending order. If there is an even number of values, the median is the average of the two middle values.
Arranging the data set in ascending order: 5, 6, 6, 7, 7, 10, 10, 10, 10, 10, 10, 10, 10, 15, 15, 20, 30, 35, 40, 50, 50, 50, 55
Since there are 25 values, the median is the 13th value, which is 10.
Mode: The mode is the value(s) that appear most frequently in the data set.
In this case, the mode is 10, as it appears the most number of times (8 times)
Based on the mean, median, and mode, we can infer that the distribution of the data set is likely to be positively skewed, as there are some higher values that are pulling the mean towards the right.
b) To find the variance and standard deviation, we can use the following formulas:
Variance: The variance measures the spread of the data set.
Variance = Σ((xi - mean)^2) / n
where Σ represents the sum, xi represents each value, mean is the mean calculated earlier, and n is the total number of values.
Standard Deviation: The standard deviation is the square root of the variance and provides a measure of the dispersion of the data.
Standard Deviation = √Variance
Performing the calculations:
Variance = [(7 - 14.28)^2 + (10 - 14.28)^2 + ... + (10 - 14.28)^2] / 25
Variance ≈ 422.12
Standard Deviation = √Variance
Standard Deviation ≈ √422.12 ≈ 20.54
Therefore, the variance is approximately 422.12 and the standard deviation is approximately 20.54. These measures indicate that the data set has a relatively high dispersion or spread.
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Write a linear equation in slope intercept form that passes through the point (-1,-8) and (1,-2)
choose the slope and y-intercept that correspond with the graph.
Answer:
First Choice: slope: -3/2 y-intercept: 2
Step-by-step explanation:
Take two plotted points, ex: (0, 2) and (2, -1)
Use slope formula: y2- y1 / x2 - x1
(0, 2) - (x1, y1)
(2, -1) - (x2, y2)
-1 - 2 / 2 - 0 = -3 / 2 (slope)
Now for the y-intercept, the line passes through the number "2" on the y-intercept. Therefore, the y-intercept must be "2".
If this was in slope-intercept form, it would look like; y = -3/2x + 2.
The answer to your question is the first choice. Hope this helps!
A rain gutter along the edge of a roof has the shape of a rectangular prism. It is 7 inches high and 18 feet long. It has a volume of 7560 cubic inches How wide is the gutter?
The width of prism is 5 inches.
We have,
height= 7 inch
Length of prism = 18 feet = 18 x 12 = 216 inches
and Volume of prism = 7560 cubic inches
We know the formula for Volume of Rectangular prism
7560 = l w h
7560 = 7 x 216 x width
7560 = 1512 x width
width = 7560/ 1512
width = 5 inches
Thus, the width of prism is 5 inches.
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In a circle, the length of an an arc intercepted by a central angle is 12mm, and the radius of the circle is a 8 mm. What is the measure, in radians, of the angle?
12/8 = 3/2 (radians)
6. What is the formula for the slope of a line passing through points (x₁, y₁) and (x2,Y₂)?
Answer: A
Slope = (difference in y) divided by (difference in x)
Here's a dot plot showing the daily high temperatures in Olivine City in July.
The statement that Brock could use to qualify the distribution is that there is a peak at 22°C.
How to decribe the distributionBrock can describe the distribution by stating that there is a peak of temperatures at 22°C. It is at this peak that the mean of the distributionc an be found.
A normal distribution such as the one shown in the diagram has a bell curve and the sample emans plotted can be used to indicate how close to the actual population the sample size is. So, option B is a way to describe the distribution.
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Evaluate f (-3) for f(x) = x3 + 3x + 17
The output value of f( -3 ) in the function f(x) = x³ + 3x + 17 is -19.
What is the output value of f( -3 ) in the function?Given the function in the question:
f(x) = x³ + 3x + 17
To evaluate f(-3) for the function f(x) = x³ + 3x + 17, we simply substitute -3 for x in the expression and calculate the result.
f(x) = x³ + 3x + 17
Plug in x = -3
f(-3) = (-3)³ + 3(-3) + 17
First, let's calculate (-3)³, which means raising -3 to the power of 3:
(-3)³ = -3 × -3 × -3 = -27
Next, let's calculate 3(-3):
3(-3) = -9
Now, we can substitute these values into the expression:
f(-3) = -27 + (-9) + 17
Simplifying further:
f(-3) = -27 - 9 + 17
f(-3) = -36 + 17
f(-3) = -19
Therefore, the output value of f(-3) is -19.
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How many pairs of parallel sides
does this shape appear to have?
There are three pairs of parallel sides.
We have,
Parallel sides refer to two or more sides of a polygon or a shape that are always equidistant and do not intersect.
In other words, parallel sides are lines that lie in the same plane and never meet or cross each other.
In a polygon, such as a rectangle or a parallelogram, parallel sides are pairs of sides that are opposite to each other.
For example, in a rectangle, the two pairs of opposite sides are parallel to each other.
Similarly, in a parallelogram, both pairs of opposite sides are parallel.
Now,
From the figure,
There are three pairs of parallel sides:
- a and d are parallel
- b and e are parallel
- f and c are parallel
Thus,
There are three pairs of parallel sides.
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SOMEBODY PLEASE PLEASE HELP ME
ILL GIVE YOU 5 STARS, BRAINLIEST AND GIVE A HEART PLEASE HELP
(Please make sure you answer Part B of the question and show your work!!)
From the results, the mode of transportation that was faster for June is Bus.
How to determine the fastest trnasportation modeTo obtain the fastest means of transportation, the mode of the figures will provide a clue. For Bus, the figures are 16, 14, 15, 14, 31, 15 and for walking, the figures are 22, 19, 21, 20, 21, 20.
The highest nmbers in occurence for the first set of figures are 14 and 15 and for the second set of figures, the numbers that appeared most are 20, 21, and 22. So, the bus offered the fastest route for going to school.
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Exponential Data
In this activity, you will graph and write exponential functions to model population data presented in tables. Then you’ll use your models to make predictions and draw a conclusion.
Question 1
A town’s population has been exponentially increasing for the past 10 years. The town council initially recorded the town’s population at 6,000 people and tracked it each year after that. The table represents their data.
Years Town Population
(in thousands)
0 6
1 6.9
2 9
3 10.5
4 13
5 14.2
6 18
7 20.8
8 26
9 31.3
Use the graphing tool to plot the population data and determine the curve of best fit.
Part A
Question
What is the equation of the curve of best fit for the population data?
Enter the correct answer in the box by replacing a and b with the values from the graphing tool. Do not round the values of a and b.
Part B
Question
If the town continues to grow at the same rate, approximately what will be the population, to the nearest 100 people, 25 years after the town council started tracking the population data?
341,100 people
180,000 people
271,200 people
572,400 people
Question 2
Because of the growth in the town’s population, the agricultural department kept track of the town’s native bee population during the same time period. They feared with the increase of people in the town, the bee population would start to decrease, affecting the ecosystem. Their data is shown in the table.
Years Bee Population
(in thousands)
0 320
1 225
2 152.6
3 111.2
4 75
5 56.8
6 36.7
7 26.9
8 17.5
9 13.2
Use the graphing tool to plot the population data and determine the curve of best fit.
Part A
Question
What is the equation of the curve of best fit for the population data?
Enter the correct answer in the box by replacing a and b with the values from the graphing tool. Do not round the values of a and b.
Part B
After several years of recording the data, the agricultural committee requested help from the town council for a grant to boost the bee population. The council denied the request, saying it wouldn’t take any action until the population dropped below 5,000 bees.
In the 12th year after initially recording the bee population, the agricultural committee plans to speak with the board again. Will the committee have a good chance of convincing the board to help support bees this time around? Justify your conclusion using mathematical reasoning.
Answer:
1.The equation of best fit is ŷ = 2.69152X + 3.45818.
Step-by-step explanation:
The decimal point is missing in the quotient below. 100.34/2.9=346. Write and estimate on the line and then place the decimal point in the quotient above.
The quotient with the decimal point placed correctly is 34.6.
Estimating the division of 100.34 by 2.9:
We can round 100.34 to the nearest whole number, which is 100, and round 2.9 to the nearest whole number, which is 3.
Dividing 100 by 3 gives an estimated quotient of 33.
Comparing the estimate to the given quotient:
The given quotient is 346, which is significantly larger than our estimate of 33.
To place the decimal point in the quotient, we need to determine the difference between the given quotient and our estimate. In this case, the difference is four places.
Correcting the quotient:
We can place the decimal point four places to the left in the given quotient 346 to match our estimate of 33. This gives us the corrected quotient:
100.34 ÷ 2.9 ≈ 34.6
So, the quotient with the decimal point placed correctly is 34.6.
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A triangular prism has an approximate surface area of 39.5 square feet. The sides of the equilateral triangular bases are one-third the length of the prism. What are the dimensions of the prism to the nearest foot?
Note that based on the triangular prism problem, the missing items from the blank space are:
1) 2 feet
2) 6 feet.
How is this so?Let the side of the triangular base = x ft
then the length of the prism = 3xft
The side fo the triangular base = 1/3 x the length of the prism.
Hence the surface area:
= 2 * 1/2 * x² * Sin60° + x * (3x) * 3
= √3/2x² + 9x²
The surface area = Area of two equilateral triangles + Areas of three rectangles.
Hence, (√3/2 + 9) X² = 30.5
x = 2ft
Thus, the side fo the triangular base is 2ft and the lenght of the prism is 6ft approximately.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See the attached.
Determine the x- and y- intercepts for the graph defined by the given equation.
y = -8
a. x-intercept is (0, -8)
b.
No y-intercept
No x-intercept
y-intercept is (0, -8)
c. x-intercept is (-8, 0)
No y-intercept
No x-intercept
y-intercept is (-8, 0)
d.
The intercepts of the function y = -8 are given as follows:
No x-intercept.y-intercept is (0,-8).What are the intercepts of a function?The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.The function in this problem is defined as follows:
y = -8.
The function in this problem is a horizontal line at y = -8, meaning that it does not cross the x-axis, hence:
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suppose A and B are independent events. If P(A)=0.25 and P(B)=0.8, what is P(A B)?
If A and B are independent events with P(A) = 0.25 and P(B) = 0.8, the probability of both events occurring together, P(A B), is 0.2. I hope this helps! Let me know if you have any further questions.
Since A and B are independent events, we know that the occurrence of one event does not affect the probability of the other event happening. Therefore, we can use the formula P(A B) = P(A) * P(B).
Substituting the given probabilities, we get P(A B) = 0.25 * 0.8 = 0.2. This means that the probability of both events A and B occurring together is 0.2 or 20%.
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what is the answer for
2[32-(4-1)3]
[tex] \large\sf \longrightarrow \: 2 \: [ \: 32- \: (4-1) \: 3 \: ] \\ [/tex]
[tex] \large\sf \longrightarrow \: 2 \: [ \: 32- \: (3) \: 3 \: ] \\ [/tex]
[tex]\large \sf \longrightarrow \: 2 \: [ \: 32- \: 3 \times \: 3 \: ] \\ [/tex]
[tex]\large \sf \longrightarrow \: 2 \: [ \: 32- \: 9 \: ] \\ [/tex]
[tex] \large\sf \longrightarrow \: 2 \: [ \: 23 \: ] \\ [/tex]
[tex] \large\sf \longrightarrow \: 2 \: \times 23 \\ [/tex]
[tex] \large\sf \longrightarrow \: 46 \\ [/tex]
STATISTICS
1. The senior class president would like to host an after-graduation lock-in. There will be games, gifts, and food! In order to decide if classmates would be willing to buy tickets and aftend, she has decided to conduct a survey. She will select 25 students to meet and hear input on the prizes, food, and ticket price. There are 500 members of the senior class.
a. She selects every tenth student as they get off the bus one morning.
b. She asks her choir director to allow her to survey the choir.
c. She meets with the counselor, who selects every twentieth student on the school roster.
d. She assigns each senior a number and randomly selects 25 numbers.
e. She makes an announcement that people interested should meet in the library after school.
f. A roster of the senior class is printed, and each student's name is put into a hat. The principal selects 25 names.
Answer: Option D, she assigns each senior a number and randomly selects 25 numbers. This method would help ensure that the students selected for the survey are representative of the entire senior class.
if 4x+8x=64 what is 2x
Step-by-step explanation:
4x+8x=64
or, 12x=64
or, X=64/12
X= 5.333
now, 2x= 2 multiply X= 2 multiply 5.333= 10.666
hence,2x= 10.666
What are prime intigers
Whole numbers that are only divisible by 1 and theirselves.
someone please help with my geometry
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