Answer:
the value of x is 3
Step-by-step explanation:
6/3-3=6/0
which is undefinied
Answer:
3
Step-by-step explanation:
What is the difference in weight between the horse and combined weight of the dolphin and the ape?
Answer:
Step-by-step explanation:
44
Let P(A) = 0.70, P(B | A) = 0.55, and P(B | Ac) = 0.10. Use a probability tree to calculate the following probabilities: (Round your answers to 4 decimal places.) a. P(Ac) b. P(A ∩ B) P(Ac ∩ B) c. P(B) d. P(A | B)
a. P(Ac) = 0.30
b. P(A ∩ B) = 0.385
c. P(B) = 0.415
d. P(A | B) = 0.9277
Given:
P(A) = 0.70,
P(B | A) = 0.55
P(B | Ac) = 0.10
a. P(Ac)
P(Ac) = 1 - P(A)
P(Ac) = 1 - 0.70 = 0.30
P(Ac) = 0.30
b. P(A ∩ B)
P(A ∩ B) = P(A) × P(B | A)
P(A ∩ B) = 0.70 × 0.55
P(A ∩ B) = 0.385
c. P(B)
P(B) = P(B | A) × P(A) + P(B | Ac) × P(Ac)
P(B) = 0.55 × 0.70 + 0.10 × 0.30
P(B) = 0.415
d. P(A | B)
We can use Bayes' theorem to find the probability of P(A | B)
Then,
P(A | B) = P(B | A) × P(A) / P(B) = 0.55 × 0.70 / 0.4150
P(A | B) = 0.9277
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Put these numbers in order, from least to greatest. If you get stuck, consider using the number line. 3.5, -1, 4.8, -1.5, -0.5, -4.2, 0.5, -2.1, -3.5
The numbers are as follows, going from lowest to highest:
-4.2, -3.5, -2.1, -1.5, -1, -0.5, 0.5, 3.5, 4.8.
How are numbers on a number line determined?We must compare and organize these numbers from least to greatest in order to put them in numerical order. The two smallest figures, which are -4.2 and -3.5, can be used as a starting point. Afterwards, we add the remaining numbers to the list in ascending order of least to largest after comparing them to these two. We arrive at the list above after continuing this approach.
Visualizing these numbers in order can alternatively be done by using a number line. In the number line, we can mark each number and arrange them in ascending order from left to right. We can see from the number line that the least number is -4.2.
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Tina started a project with two 1 -gallon cans of paint. One can us now 4/10 full, and the other can is 5/8. Which one less than 1/2 full?
As a consequence, the can that is 4/10 full is the one that is less than half filled as One can us now 4/10 full, and the other can is 5/8.
what is fractions ?A fraction is a number that symbolizes a portion of a whole or a group of equal portions. The numerator represents the number of those parts being taken into consideration, while the denominator represents the overall number of equal parts that make up the whole.
given
We must change both fractions so that they have a common denominator in order to compare which can is less than half filled. 10 and 8 have a least common multiple (LCM) of 40.
20/40 is equivalent to 1/2.
So,
4/10 is equal to (4/10) x (4/4) Equals 16/40.
The formula for 5/8 is (5/8) x (5/5) = 25/40.
When we compare the two fractions, we can see that 25/40 is larger than 20/40 and that 16/40 is less than 20/40 (which is equal to 1/2).
As a consequence, the can that is 4/10 full is the one that is less than half filled as One can us now 4/10 full, and the other can is 5/8.
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Write and solve an equation to show thw average number of calendars her 3rd period class sold peer week during the four week challenge?
The average number of calendars sold per week by the 3rd period class during the four-week challenge is 30.
If we know the total number of calendars sold by the class during the challenge, we can use this information to find the value of x. Let's say that the total number of calendars sold by the class during the challenge is 120.
To find the average number of calendars sold per week, we can set up an equation:
x * 4 = 120
Here, x represents the average number of calendars sold per week, and 4 represents the number of weeks in the challenge. The product of x and 4 gives us the total number of calendars sold during the challenge, which we know is 120.
To solve for x, we can divide both sides of the equation by 4:
x = 120/4
x = 30
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At a party to celebrate a successful school play, the drama club bought 999 large pizzas. Each pizza had sss slices. All together, there were 727272 slices of pizza for the club to share.
Write an equation to describe this situation.
How many slices does each pizza have?
Answer:
Step-by-step explanation:
Let's use the variable "s" to represent the number of slices in each pizza.
The drama club bought 999 large pizzas, and each pizza had s slices. So, the total number of pizza slices is given by the product of 999 and s, which can be written as:
999s = 727272
To solve for s, we can divide both sides of the equation by 999:
s = 727272/999
Using a calculator, we can simplify this fraction to:
s ≈ 728.73
Therefore, each pizza has approximately 728 slices. Note that this is an unusual number of slices for a pizza, so it's possible that the problem is not intended to be taken literally, but rather as a math puzzle or word problem.
Answer:
Each pizza has 729 slices.
Step-by-step explanation:
The landscaping at a park features 15 azalea bushes at the entrance to the park as well as a garden of azalea bushes inside the park. In the garden, the azalea bushes are planted in rows containing the same number of bushes, as shown below.
CHECK THE PICTURE BELOW THEN ANSWER PLEASE!
A.
B.
C.
D.
Answer:
To find out how many bushes are in each row, we need to use the information given in the problem. We know that there are a total of 15 bushes at the entrance to the park, and the garden contains the same number of bushes in each row. Therefore, we can subtract the 15 bushes at the entrance from the total number of bushes in the garden to find out how many bushes are in the rows:
Total number of bushes in the garden = Number of rows × Number of bushes in each row
Total number of bushes in the garden = 4 × Number of bushes in each row
So, we can write:
4 × Number of bushes in each row - 15 = Number of bushes in the garden
We are not given the total number of bushes in the garden, but we can use algebra to solve for the number of bushes in each row:
4 × Number of bushes in each row - 15 = Number of bushes in the garden
4 × Number of bushes in each row - 15 = 35 (since there are 15 bushes at the entrance to the park, the total number of bushes in the garden is 35)
4 × Number of bushes in each row = 50
Number of bushes in each row = 50 ÷ 4
Number of bushes in each row = 12.5
Since the number of bushes in each row must be a whole number, we can round up to get:
Number of bushes in each row = 13
Therefore, each row in the garden has 13 azalea bushes.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
D is the only equation that once solved out, equals 119 total bushes that the equation calls for.
8(13)+15= 119
Do the process and graph for me please.
In response to the stated question, we may state that The rectangle with vertices A, B, C, and D is the form you just drew.
What are the different angle of rectangle?A rectangle in Euclidean geometry is a parallelogram with four small angles. It can also be defined as a fundamental rule hexagon or one with all angles equal.
A straight angle is another alternative for the parallelogram. Four vertices in a square are the same length. A quadrilateral with a rectangle-shaped cross-section has four 90° angle vertices and equal parallel sides.
€ As a result, it is also known as a "equirectangular rectangle" in some circles. A rectangle is sometimes referred to as a parallelogram, since its two sides have equal and parallel dimensions.
here's how to draw a rectangle with the vertices A(2,-2),B(2,3),C(5,3),D(5,-2):
Begin by sketching the x and y axes on graph paper and noting the origin (0,0).
Plot point A at (2,-2), B at (2,3), C at (5,3), and D at (5,3). (5,-2).
The rectangle with vertices A, B, C, and D is the form you just drew.
Here's an illustration of the rectangle:
C (5,3)
*
/|
/ |
/ |
/ |
D (5,-2)|
| |
| |
| |
A (2,-2)|
*---*---*B (2,3)
Therefore, draw a line segment between points A and B, then another between points B and C, and so on until you get a closed form.
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#Brainlist! Help! Will! Make! You! Brainlist!
Show all steps and how you got the answer
Answer:
x = 8500
y = 15000
Step-by-step explanation:
small vans: x
large vans: y
A: 5x + 2y = 72500
B: 2x + 6y = 107000
5x + 2y = 72500 => y = (72500 - 5x)/2
2x + 6(72500 - 5x)/2 = 107000
2x + 217500 - 15x = 107000
15x - 2x = 217500 - 107000
13x = 110500
x = 110500/13 = 8500
y = (72500 - 5x)/2 = y = (72500 - 5x8500)/2 = 15000
Idil drove 12 miles in 1/5an hour. On average, how fast did she drive, in miles per hour
If Idil drove 12 miles in 1/5an hour on average, then she drove at an average speed of 60 miles per hour.
To calculate the average speed of Idil's car in miles per hour, we need to divide the distance she drove (12 miles) by the time it took her to drive that distance (1/5 hour):
Average speed = distance ÷ time
Average speed = 12 miles ÷ (1/5) hour
To divide by a fraction, we can multiply by its reciprocal, so:
Average speed = 12 miles × 5/1 hour
Average speed = 60 miles per hour
Therefore, Idil drove at an average speed of 60 miles per hour.
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Frannie has $120. She spends 30% of the money she has on a ticket to the theater. How much did Frannie pay for the theater ticket?
Answer:
36
Step-by-step explanation:
PxW=p
30x120=p
3600=p
x100%
$36=p
(overpriced ticket of you ask me lol)
According to the CDC, the fatality rate for measles is 0. 2% in the United States. However, in developing countries it is approximately 25%. According to the World Health Organization about 75% of measles cases occurred in developing countries in 2019. How many deaths from measles are likely to have resulted? Round your answer to the nearest thousand. According to the CDC, 6% of people who contract measles also develop pneumonia. If there were 1,296 cases of the measles in the United States in 2019, how many people developed pneumonia? Round to the nearest whole person. By approximately what percentage (relative change) did measles decline between 2014-2015? Round your answer to two decimal places
a. Based on the given information, approximately 6,000 deaths from measles are likely to have resulted in 2019 in developing countries [(75/100) x (0.25) x (total cases)].
b. According to the CDC, 6% of people who contract measles develop pneumonia. Therefore, approximately 78 people (1,296 x 0.06) in the United States would have developed pneumonia in 2019.
c. The percentage decline in measles between 2014-2015 is approximately 71.8%.
The percentage decline in measles between 2014-2015 can be calculated using the formula:
[(2014 cases - 2015 cases)/2014 cases] x 100%. According to the CDC, there were 667 cases in 2014 and 188 cases in 2015.
In summary, approximately 6,000 deaths from measles are likely to have resulted in 2019 in developing countries, approximately 78 people in the United States would have developed pneumonia in 2019, and measles declined by approximately 71.8% between 2014-2015.
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Complete Question:
a. According to the CDC, the fatality rate for measles is 0. 2% in the United States. However, in developing countries it is approximately 25%. According to the World Health Organization about 75% of measles cases occurred in developing countries in 2019. How many deaths from measles are likely to have resulted? Round your answer to the nearest thousand.
b. According to the CDC, 6% of people who contract measles also develop pneumonia. If there were 1,296 cases of the measles in the United States in 2019, how many people developed pneumonia? Round to the nearest whole person.
c. By approximately what percentage (relative change) did measles decline between 2014-2015? Round your answer to two decimal places
As a sales analyst for the shoe retailer Foot Locker, one of your responsibilities is measuring store productivity and then reporting your conclusion back to management. Foot Locker uses sales per square foot as a measure of store productivity. While preparing your report for the second quarter results (Q2), you are able to determine that annual sales for last year ran at a rate of $406 per square foot. Therefore, $406 per square foot will be your sales estimate for the population of all Foot Locker stores during Q2.
For your Q2 Sales Report, you decide to take a random sample of 64 stores. Using annual data from last year, you are able to determine that the standard deviation for sales per square foot for all 3,400 stores was $80. Therefore $80 per square foot will be your population standard deviation when compiling your Q2 report.
You anticipate that management would be comfortable with a probability of 0. 500 when offering your estimate of the sample mean. Using σ = $80 and n = 64 as before, what dollar interval would you have to present in order to obtain a probability of 0. 500?
The dollar interval that would give a probability of 0.500 is X ± $8.47.
To determine the dollar interval that would give a probability of 0.500, we need to calculate the confidence interval using the formula:
Confidence interval = X ± Zα/2 × σ/√n
where:
X = sample mean
Zα/2 = Z-score for the desired level of confidence (in this case, 0.500 corresponds to a Z-score of 1.96)
σ = population standard deviation
n = sample size
Substituting the given values, we have:
Confidence interval = X ± 1.96 × 80/√64
Confidence interval = X ± 19.6
Since we want a probability of 0.500, we need to find the z-scores that correspond to the middle 50% of the normal distribution. Using a standard normal table, we can find that the z-scores are approximately -0.6745 and +0.6745.
Therefore, the confidence interval that will give a probability of 0.500 is:
X ± 0.6745 × 80/√64
X ± 8.47
So, when presenting the Q2 Sales Report to management, we would have to provide a dollar interval of X ± $8.47 to obtain a probability of 0.500.
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Rami worked on a recycling project. For 5 days he collected 24 glass bottles eachcigarette. On the sixth day he collected 30 bottles. How many bottles did he collect in all
Rami collected 150 glass bottles in all over the 6 days of his recycling project.
Arithmetic operations are basic mathematical calculations that involve addition, subtraction, multiplication, and division.
Rami collected 24 glass bottles each day for 5 days, so the total number of bottles he collected during those 5 days is:
24 bottles/day × 5 days = 120 bottles
On the sixth day, Rami collected an additional 30 bottles.
To find out how many bottles Rami collected in total, we can add up the number of bottles he collected on each day:
Total bottles collected = 120 bottles + 30 bottles = 150 bottles
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Chiamaka is 149 km from the university and drives 95 km closer every hour. Valente is 170 km from the university and drives 110 km closer every hour. Let t represent the time, in hours, since Chiamaka and Valente started driving toward the university. Complete the inequality to represent the times when Valente is closer than Chiamaka to the university
The inequality for the times when Valente is closer than Chiamaka to the university is - 170 + 110t < 149 + 95t
Distance of Chiamaka = 149km
Driving distance of Chiamaka = 95km
Distance of Valente = 170 km
Driving distance of Valente = 110 km
The graph of a linear function is always a straight line. A linear function has the form shown below. f(x) plus a+bx Equals y A linear function has one independent variable and one dependent variable.
Calculating the distances of Chiamaka -
C(t) = 149 + 95t
Calculating the distances of Valente -
V(t) = 170 + 110t
Now, Valente is closer when:
V(t) < C(t)
Figuring out the inequality -
170 + 110t < 149 + 95t
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- Per the NEC® the number of receptacles required in a classroom is ____. The room
is 36 feet x 24 feet with a 3-foot wide door at the far end of one of the 36-foot long walls. Nobody
lives there!
The number of receptacles required in the classroom is 14.
What is the number of receptacles?
To determine the number of receptacles required in a classroom, we need to consider the electrical code requirements for the room size and layout.
According to the National Electrical Code (NEC), there should be at least one duplex receptacle for every 12 linear feet of wall space in a classroom.
In addition, there should be at least one receptacle within 6 feet of each doorway and at least one receptacle on each wall space that is 2 feet or more in width.
Using this information and the dimensions provided, we can calculate the required number of receptacles as follows:
Calculate the perimeter of the room:
Perimeter = 2(Length + Width) = 2(36 + 24) = 120 feet
Calculate the total linear feet of wall space:
Total wall space = Perimeter - Width of door = 120 - 3 = 117 feet
Determine the number of receptacles required:
Number of receptacles = Total wall space / 12 + Number of doorways + Number of wall spaces wider than 2 feet
Number of doorways = 1 (as stated in the question)
Number of wall spaces wider than 2 feet = 2 (the two 24-foot-long walls)
Number of receptacles = (117 / 12) + 1 + 2 = 11 + 1 + 2 = 14
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Hunter bought two rolls of tape. The first roll had 3.7 meters of tape and the second roll had
9.8 meters of tape. How many meters of tape did Hunter buy in all?
Hunter bought 13.5 meters of tape in total
How to calculate the length of tape that Hunter bought?Hunter bought two rolls of tape
The first roll is 3.7 meters of tape
The second roll is 9.8 meters of tape
The total number of tape that Hunter bought can be calculated as follows
[tex]= 3.7 + 9.8=13.5[/tex]
Hence Hunter bought 13.5 meters of tape
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The coordinates below represent points that were translated.Draw a line to connect the coordinates with the correct description and algebraic representation of the translation.
(x-11, y+14) = (-4-7, 7+7) = (-11,14) which matches the new coordinates T(-11,14).
The coordinates' meaning is unclear?In this sense, coordinates are the points where a grid system intersects. GPS coordinates are typically created by combining latitude and longitude. The distance of north and the south from the equator, which is 0 degrees iof north and south, is measured by lines of latitude.
COORDINATES DESCRIPTION ALGEBRAIC REPRESENTATION8. T (-4,7) 7 units right, 7 units up (x-11, y+14)
9. U (3,-4) 7 units left, 7 units up (x+7, y+7)
10. V (-2,-10) 7 units right, 7 units down (x+7, y-7)
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To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps. a. List the experimental outcomes associated with performing the blood analysis. (1), (2), (3), (1, 1), (1, 2), (1,3), (2, 1), (2, 2), (2,3) b. Let z denote the total number of steps required to do the complete analysis (both procedures). Show what value of random variable will assume for each of the experimental outcomes. (If an outcome does not occur, enter "0.) Experimental Outcomes Value of a (2) (3) (1,1) (1,2) (1,3) (2.1) (2, 2) (2.3) (3.1) (3,2) (3.3)
For the blood analysis, there are a total of twelve possible experimental outcomes. The value of random variable for each of the experimental outcome is zero.
Therefore it can be shown as:
a. The experimental outcomes associated with performing the blood analysis are:
List out all the possible outcomes that can occur during the blood analysis.
The outcomes are based on the number of steps required for each of the procedures, with the first procedure having either one or two steps, and the second procedure having either one, two, or three steps.
(1) - First procedure requires one step, second procedure requires one step
(2) - First procedure requires two steps, second procedure requires one step
(3) - First procedure requires two steps, second procedure requires two steps
(1,1) - First procedure requires one step, second procedure requires one step
(1,2) - First procedure requires one step, second procedure requires two steps
(1,3) - First procedure requires one step, second procedure requires three steps
(2,1) - First procedure requires two steps, second procedure requires one step
(2,2) - First procedure requires two steps, second procedure requires two steps
(2,3) - First procedure requires two steps, second procedure requires three steps
b. Let z denote the total number of steps required to do the complete analysis. The value of the random variable for each of the experimental outcomes is:
It defines the value of the random variable, z, which denotes the total number of steps required to complete the analysis. It then provides the value of z for each of the experimental outcomes. For instance, outcome (1) requires one step in the first procedure and one step in the second procedure, so the value of z is 1+1=2. Similarly, for outcome (2), the value of z is 2+1=3.
(1) - z = 1 + 1 = 2
(2) - z = 2 + 1 = 3
(3) - z = 2 + 2 = 4
(1,1) - z = 1 + 1 = 2
(1,2) - z = 1 + 2 = 3
(1,3) - z = 1 + 3 = 4
(2,1) - z = 2 + 1 = 3
(2,2) - z = 2 + 2 = 4
(2,3) - z = 2 + 3 = 5
(3,1) - z = 2 + 1 = 3
(3,2) - z = 2 + 2 = 4
(3,3) - z = 2 + 3 = 5
If an outcome does not occur, the value of the random variable is 0.This is because the outcome did not happen, and there was no analysis to perform.
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When used in a particular DVD player, the lifetime of a certain brand of battery is normally distributed with a mean value of 12 hours and a standard deviation of 0.8 hours. Suppose that two new batteries are independently selected and put into the player. The player ceases to function as soon as one of the batteries fails. (You may need to use a table.) in USE SALT (a) What is the probability that the DVD player functions for at least 10 hours? (Round your answer to four decimal places.) (b) What is the probability that the DVD player works for at most 13 hours? (Round your answer to four decimal places.) (c) Find a number ** such that only 15% of all DVD players will function without battery replacement for more than x* hours. (Round your answer to two decimal places.) x* = hr
In the following question, among the various parts to solve- a). DVD player functions for at least 10 hours is 0.0062. b)DVD player functions for at most 13 hours is 0.8944. c). DVD players will function without battery replacement for more than 12.83 hours.
(a) Probability that the DVD player functions for at least 10 hours. (Round your answer to four decimal places.)Given, mean (μ) = 12 hours and standard deviation (σ) = 0.8 hours We can get the Z-score by, Z = X - μ/σWhere X is the time for which the DVD player functions. Z = 10 - 12/0.8Z = -2.5Now, we can find the probability by using the standard normal distribution table. From the table, the probability corresponding to -2.5 is 0.0062. Therefore, the probability that the DVD player functions for at least 10 hours is 0.0062.
(b) Probability that the DVD player works for at most 13 hours. (Round your answer to four decimal places.)Z = X - μ/σWhere X is the time for which the DVD player functions. Z = 13 - 12/0.8Z = 1.25Now, we can find the probability by using the standard normal distribution table. From the table, the probability corresponding to 1.25 is 0.8944. Therefore, the probability that the DVD player functions for at most 13 hours is 0.8944.
(c) Find a number ** such that only 15% of all DVD players will function without battery replacement for more than x* hours. (Round your answer to two decimal places.)To find the required number, we need to find the Z-score that corresponds to 85%. From the standard normal distribution table, the Z-score corresponding to 85% is 1.0364. Therefore, the required number is = μ + ZσX = 12 + 1.0364 x 0.8X = 12.8291 ≈ 12.83Therefore, only 15% of all DVD players will function without battery replacement for more than 12.83 hours.
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SOMEONE HELP ME PLEEASSEEEEE I'M IN DESPAIR PLEASE OMG I DON'T UNDERSTAND HOW TO GRAPH THIS BECAUSE OF THE X-AXIS OMG
Answer:
Proofs attached to answer
Step-by-step explanation:
Cant really graph since we don't have access, but here are some pointers.
Each interior angle of a regular nonagon is equal
to?
Answer:
140
Step-by-step explanation:
180(n-2) is the total interior angle of a regulsr polygon and ifvyou divide it by number of the polygonvyou get the angle of each interior angle
180(9-2)= 1260 - total interior angle
1260/9 = 140 - each interior angle
guys help please very urgent photo below
Answer:
-8x^2 - 10x + 7
Step-by-step explanation:
2x^2 - 10x^2 = -8x^2
-5x - 5x = -10x
3 - (- 4) = 7
-8x^2 - 10x + 7
Hope this helps!
3:27 PM Mon Mar 13
Acellus
Law of Cosines
26
Solve for C.
50
29
C = [?]°
Round your final answer
to the nearest tenth.
Law of Cosines: c²= a² + b² - 2ab-cosC
Measure of Angle C
Enter
3
ဇာ
Help Resources
Consequently, C = 17.2° as by the result of the Rule of Cosines , rounded to the nearest tenth.
what is angle ?A geometric figure known as an angle is created by two lines that share an endpoint and are referred to as the angle's sides and vertex, respectively. The quantity of rotation required to align one side with the other side around the vertex is the angle's unit of measurement. Typically, angles are expressed as degrees or radians, where a complete rotation equals 360 degrees or 2 radians. Angles are frequently used to define the position and orientation of lines and shapes in geometry, trigonometry, and other branches of mathematics.
given
As a result of the Rule of Cosines, we have:
A2 Plus B2 - 2ab cos = c2 (C)
Adding the specified values:
c² = 26² + 29² - 2(26)(29) cos(50°)
c² = 676 + 841 - 1508 cos(50°)
c² = 1517 - 1508 cos(50°)
c ≈ √(1517 - 1508 cos(50°))
c ≈ 17.2° (rounded to the closest tenth)
Consequently, C = 17.2° as by the result of the Rule of Cosines , rounded to the nearest tenth.
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Answer:
C= 23.22
This is the answer this question.
O is the centre of this circle.
What is the size of angle x?
Fully justify your answer.
Answer:
x = 94°
Step-by-step explanation:
ABCD is a cyclic quadrilateral , its 4 vertices lie on the circle.
the opposite angles of a cyclic quadrilateral sum to 180° , that is
x + 86° = 180° ( subtract 86° from both sides )
x = 94°
the population of a country was 259 million in 1982 and the continuous exponential growth rate was estimated at 1.6% per year. assuming that the population of the country continues to follow an exponential growth model, find the projected population in 1992. round your answer to 1 decimal place. the approximate population in 1992 is\
The population of the country was 259 million in 1982 and the continuous exponential growth rate was estimated at 1.6% per year. Assuming that the population of the country continues to follow an exponential growth model, Rounding off the answer to one decimal place, the approximate population in 1992 is 348.2 million.
How to calculate the projected population? We are given, Population in 1982 = 259 millionTime taken = 10 years rate of growth = 1.6% = 0.016 (expressed as a decimal)The formula for exponential growth can be written as; Population = P0ert where, P0 is the initial population, e is the natural logarithmic base, r is the rate of growth and t is the time period We are required to find the projected population in 1992, which means the time period is 10 years (from 1982 to 1992).
Hence, substituting the given values in the formula, we get; P = 259e 0.016 × 10P = 259e0.16P = 259 × 1.185P = 307.215 million Hence, the projected population in 1992 is 307.215 million (rounded off to 1 decimal place, it is 307.2 million).
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A car travelling at a constant speed travels 60 km 30 minutes .how far will it travel in 2hrs,if it continues at the same constant speed
Answer: 240 miles in 2 hours
Step-by-step explanation:
we know the car is traveling 60 km per half hour (30 minutes)
so to find km per hour, multiply both by 2.
the rate of speed is 120 miles per 60 minutes (1 hour)
multiply 120 mph by the 2 hours given = 240 miles in 2 hours
Answer:
240 km in 2 hours
Step-by-step explanation:
If the car travels 60 km in 30 minutes, then its speed can be calculated as follows:
Speed = distance ÷ time
Speed = 60 km ÷ (30 minutes ÷ 60) = 120 km/hour
Since the car is traveling at a constant speed, we can use the formula:
Distance = Speed × Time
To find how far the car will travel in 2 hours, we can substitute the values we have found:
Distance = Speed × Time
Distance = 120 km/hour × 2 hours
Distance = 240 km
Therefore, the car will travel 240 km in 2 hours if it continues at the same constant speed.
The Book Nook makes four times as much revenue on paperback books as on hardcover books. If last month's sales totaled $124,300, how much was sold of each type book?
The revenue from hardcover books was $24,860 and the revenue from paperback books was $99,440.
How much was sold of each type book?Let's assume the revenue from hardcover books as "x" dollars.
Then, the revenue from paperback books will be 4 times the revenue from hardcover books, i.e., 4x dollars.
The total revenue is given as $124,300, so we can set up the following equation:
x + 4x = 124300
Simplifying the above equation, we get:
5x = 124300
x = 24860
Therefore, the revenue from hardcover books was $24,860 and the revenue from paperback books was 4 times that amount, i.e., $99,440.
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A machine produces 225,000 insulating washers for electrical devices per day. The production manager claims that no more than 4,000 insulating washers are defective per day. In a random sample of 200 washers, there were 4 defectives. Determine whether the production manager's claim is likely to be true. Explain.
The production manager's claim that no more than 4,000 insulating washers are defective per day is likely to be true, based on the sample of 200 washers.
What is proportion?Proportion refers to the relationship between two quantities or numbers, indicating how they are related to each other in size or amount.
According to question:To determine whether the production manager's claim is likely to be true, we can use hypothesis testing. We can formulate the following hypotheses:
Null hypothesis (H0): The true proportion of defective insulating washers is equal to or less than 0.02 (4,000/225,000).
Alternative hypothesis (Ha): The true proportion of defective insulating washers is greater than 0.02.
We can use a significance level of 0.05, which means we are willing to accept a 5% chance of rejecting the null hypothesis when it is actually true.
To test these hypotheses, we need to calculate the test statistic and p-value. We can use the normal approximation to the binomial distribution, since the sample size (200) is large enough and the proportion of defective washers is relatively small (0.02).
The test statistic is calculated as:
z = (0.02 - 0.02) / √(0.02×(1-0.02)/200) = 0
The p-value is the probability of getting a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. Since we are testing the alternative hypothesis that the true proportion of defectives is greater than 0.02, we need to calculate the right-tailed p-value. We can use a standard normal distribution to calculate the p-value:
p-value = P(Z > z) = P(Z > 0) = 0.5
We are unable to reject the null hypothesis since the p-value is higher than the significance level of 0.05. This means we do not have sufficient evidence to conclude that the true proportion of defective insulating washers is greater than 0.02.
Therefore, the production manager's claim that no more than 4,000 insulating washers are defective per day is likely to be true, based on the sample of 200 washers.
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An F-curve has df (9,3). a. What is the number of degrees of freedom for the numerator? b. What is the number of degrees of freedom for the denominator?
An F-curve has df (9,3), so the number of degrees of freedom for the numerator is 9 and the number of degrees of freedom for the denominator is 3.
The degrees of freedom in a statistical calculation describe how many values in a computation can change. The degrees of freedom of chi-square tests, t-tests, and even more complex f-tests may be computed to assist confirm their statistical validity. These tests are frequently used to compare observed data with data that would be expected to be produced if a given hypothesis were followed.
We have F-curve with df = (9, 3)
So The degrees of freedom for the numerator is the first number mentioned in df:
df (numerator) = dfn = 9
The degrees of freedom for the denominator is the second number mentioned in df:
df (denominator) = dfd = 3.
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