The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.
Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:
1/4(4 + x) = 4/3
4 * 1/4(4 + x) = 4 * 4/3
Simplifying:
4 + x = 16/3
Subtract 4 from both sides of the equation:
4 + x - 4 = 16/3 - 4
Simplifying:
x = 16/3 - 12/3
x = 4/3
A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.
Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.
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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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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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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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cos(-180").tan 8.cos 690 sin (8-180) cos² (6-90) (5)
cos(-180°) = -1
tan 8° = 0.1425
cos 690° = 0
sin (8-180°) = - sin 172° = - 0.9997
cos² (6-90°) = cos(-84°) = 0.4997
Therefore, the answer to the expression is -0.4997.
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!
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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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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- 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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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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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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#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
q1.2 (3pts) an automated weight monitor can detect underfilled cans of beverages with probability 0.98. what is the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled can?
The probability that it will fail to detect an underfilled can for the first time when it encounters the 10th underfilled can is approximately 0.005.
Since the probability that an automated weight monitor detects underfilled cans of beverages is 0.98, the probability that it will not detect an underfilled can for the first time when it encounters the 10th underfilled can is given by:
(1 - 0.98)10-1(0.98)
Using the formula above, we will solve for the probability below:
(1 - 0.98)10-1(0.98)≈0.005
Thus, the probability that it will fail to detect an underfilled can for the first time when it encounters the 10th underfilled can is approximately 0.005.
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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°
what is the surface area of the net of this square pyramid?
Answer:
64sq cm
Step-by-step explanation:
To find area of net of square pyramid, you have to find area of the 4 triangles and area of square bottom.
Triangle Area = 1/2bh (times 4 because there are 4 triangles.
Square Area = lw
TA= 4(1/2bh)
4(1/2*4*6)
4(1/2*24)
4(12)
TA= 48 sq cm
SA= lw
4*4
SA= 16 sq cm
48 sq cm + 16 sq cm = 64 sq cm
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:
For her phone service, Leila pays a monthly fee of $27, and she spends an additional $0.06 per minute of use. The least she has been charged in a month is $102.90.
What are the possible numbers of minutes she has used her phone in a month?
Use m for the number of minutes, and solve your inequality for m.
Answer:
Step-by-step explanation:
First Of all, Say the N-word, Now if she said the N-word, shell be given 27 dollars,Now I need to do my Homework, if i made you laugh, mark me the Brainliest
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
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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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
Two cars are driving away from an intersection in perpendicular directions. The first cars velocity isms 7 meters per second and the second cars velocity is 3 meters per second. At a certain instant, the first car is 5 meters from the intersection and the second car is 12 meters from the intersection. What is the rate of change of the distance between the cars at that instant?
The rate of change of the distance between the cars at that instant is 5.46 meters/ second.
The first car's velocity = 7 meters per second
The second car's velocity = 3 meters per second.
Distance from the intersection of first car = 5m
Distance from the intersection of second car = 12m
The rate of change is used to numerically quantify the percentage change in value over a predetermined period of time. It is a measure of a variable's velocity.
Calculating the distance between both cars at the instant
= √(12² + 5²)
= √ 144 + 25
= √169
= 13
Calculating the rate of change of distance -
2d/dt
= d(x² + y²)/dt
= 2x dx/dt + 2ydy/dt
= 2×5×7 + 2×12×3
= 70 + 72
= 142
Therefore, total distance -
dd/dt
= 142/26
= 5.46
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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.
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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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.
Create a Dataset Give a positive integer less than 100 as the last data value in each of the following datasets so that the resulting dataset satisfies the given condition (a) The mean of the numbers is substantially less than the median 51,52,53,54 (b) The mean of the numbers is substantially more than the median 2,3,4,5, (c) The mean and the median are equal. 2,3,4,5
(a) Dataset with mean substantially less than median:
9, 10, 11, 12, 90
The mean of this dataset is (9+10+11+12+90)/5 = 26.4, while the median is 11, which is substantially greater than the mean. The last data value is 90, which is a positive integer less than 100.
(b) Dataset with mean substantially more than median:
98, 99, 100, 101, 200
The mean of this dataset is (98+99+100+101+200)/5 = 119.6, while the median is 100, which is substantially less than the mean. The last data value is 200, which is a positive integer less than 100.
(c) Dataset with mean equal to median:
2, 3, 4, 4, 5
The mean of this dataset is (2+3+4+4+5)/5 = 3.6, which is equal to the median (the middle value of the dataset). The last data value is 5, which is a positive integer less than 100.
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I don't really understand how to do reference angles. I only need the last one, -60 degrees, does anyone know how to figure out it's reference angle?
Answer: 60?
Step-by-step explanation:
The reference angle is the acute angle formed between the terminal side of an angle in standard position and the x-axis. To find the reference angle of an angle, you can follow these steps:
Determine the quadrant in which the angle terminates. For -60 degrees, this would be the fourth quadrant.
Determine the corresponding angle in the first quadrant by finding the angle formed between the terminal side and the x-axis. In the fourth quadrant, this angle is equal to 360 degrees minus the original angle. So for -60 degrees, the corresponding angle in the first quadrant is 360 - 60 = 300 degrees.
Subtract this angle from 360 degrees to find the reference angle. For -60 degrees, the reference angle is 360 - 300 = 60 degrees.
Therefore, the reference angle of -60 degrees is 60 degrees.
GIVING BRAINLIEST! IF TWO OR MORE PEOPLE ANSWER!
Answer:
a. Goron 224
b. Smith 96
Fishman 256
Step-by-step explanation:
a. For Goron: 640 x 0.35 = 224
b. For Smith: 640 x 0.15 = 96
For Fishman: 640 x 0.40 = 256
Given the lengths of two sides of a triangle, write an equality to indicate between which two numbers the length of the third side must fall.
The sides are:
8 and 13
I will award brainliest to the first correct answer with a decent explanation
The length of the third side must fall between 8 and 13. This is because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
Francis has an unpaid balance of $480 on his credit card. The annual percentage rate is 12%. What is the finance charge on his next monthly statement?
Answer:
$4.80
Step-by-step explanation:
You want to know the finance charge on a balance of $480 if the APR is 12%.
Finance chargeThe monthly finance charge is the product of the monthly interest rate and the balance. The monthly interest rate is 1/12 of the annual rate.
finance charge = (1/12 · 12%) · $480 = 0.01 · $480 = $4.80
The finance charge on the next monthly statement is $4.80.
you have spent $2,500 on liquor for your bar. your bar sales have been $12,890. what is your cost of sales for liquor, expressed as a percentage?
The cost of sales for liquor, expressed as a percentage is 19.39%.
What is the cost of sales for liquor in percentage?To compute for the cost of sales for liquor, expressed as a percentage given that you have spent $2,500 on liquor for your bar and your bar sales have been $12,890, you can use the formula:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
where, Cost of Goods Sold (COGS) = Beginning Inventory + Purchases - Ending Inventory (or the total cost of goods sold during the period)
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
Let's compute for the COGS first:
COGS = Beginning Inventory + Purchases - Ending Inventory
= $0 + $2,500 - $0
= $2,500
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
= $12,890 - $0 - $0
= $12,890
Cost of sales is obtained as follows:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
= ($2,500 / $12,890) × 100
= 19.39%.
Therefore, the cost of sales for liquor, expressed as a percentage is 19.39%.
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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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