Give an expression that generates all angles coterminal with each angle. Let n represent any interger?
1. 60°
2. 120°
Answer:
The expression to this question can be defined as follows:
Step-by-step explanation:
Given angle:
1. 60°
2. 120°
Formula:
\(\to \bold{\ angle + 360 \ n}\)
The Expression for point 1:
\(\to 60^{\circ} + 360 \ n\\\)
The Expression for point 2:
\(\to 120^{\circ} + 360 \ n\\\)
What is the answer this is a math question
Answer:
1221 - 321 = 900
Step-by-step explanation:
If f(x)={−2x+1x−8ififx<3x≥3, what is f(7)
Evaluating in x = 7 in the second piece of the function, we get:
f(7) = 1.
How to evaluate the piecewise function?
Here we have the piecewise function:
f(x) = -2x + 1 if x < 3
f(x) = x - 8 if x ≥ 3
Where the part in the right defines the domain of each piece of the function.
And we want to evaluate in x = 7, then we need to use the second part (because 7 is larger than 3). Replacing x by 7 we get:
f(7) = 7 - 8 = -1
f(7) = -1
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Dividing the sum of (7/8) (15/4) (1/12) by their multiplication gives _________
The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).
To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.
The sum of the fractions is:
(7/8) + (15/4) + (1/12)
To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:
(7/8) = (21/24)
(15/4) = (90/24)
(1/12) = (2/24)
Now we can add the fractions:
(21/24) + (90/24) + (2/24) = (113/24)
The multiplication of the fractions is:
(7/8) * (15/4) * (1/12)
To multiply fractions, we multiply the numerators and denominators:
(7*15*1) / (8*4*12) = (7/96)
Now we can divide the sum of the fractions by their multiplication:
(113/24) / (7/96)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(113/24) * (96/7) = (2712/168)
Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).
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Approximately 15% of Americans have a blood type of B. The local blood bank has 80 donors stop by on a given day (which can be considered a random sample from the population). What is the probability that between 15% and 20% of the donors on a given day have a blood type of B?
Answer: the probability that between 15% and 20% of the donors on a given day have a blood type of B is 0.3944
Step-by-step explanation:
Given that;
Binomial Distribution
n = 80
p = 0.15
q = 1 - p = 0.85
Mean = μ = np = 80 X 0.15 = 12
SD = σ = √(npq) = √(80 x 0.15 x 0.85) = -3.1937
Now; Assumptions in normal distribution to binomial distribution
- The sample size = n = 80 > 30 . Large sample
- np = 80 × 0.15 = 12 > 10
- nq = 80 × 0.85 = 68 > 10
so
80 × 0.15 = 12
80 × 0.20 = 16
To find P(12 < X < 16):
Z = (16 - 12) / 3.1937
= 4 / 3.1937
= 1.2525
Table of Area Under Standard Normal Curve gives area = 0.3944
Therefore the probability that between 15% and 20% of the donors on a given day have a blood type of B is 0.3944
A student solves the following problem:
Problem: 2(x−3)+3x=19
Step 1: 2x−6+3x=19
Step 2: 6x−6=19
Step 3: 6x−6 + 6=19 + 6
Step 4: 6x=25
Step 5: 6x6=256
Step 6: x≈4.17
Where is the mistake? What did the student do incorrectly?
Responses
Step 3: Student should have subtracted 6 from both sides, not added 6.
Step 5: Student should have subtracted 6 from both sides, not divided by 6
Step 1: Student should have only distributed the 2 to the x and not the x & 3.
Step 2: Student should have added 2x + 3x = 5x, not 2 x 3 = 6x
Answer:
error in Step 2
Step-by-step explanation:
2(x - 3) + 3x = 19
Step 1 : 2x - 6 + 3x = 19 ← simplify left side by collecting like terms
Step 2 : 5x - 6 = 19 ← add 6 to both sides
Step 3 : 5x - 6 + 6 = 19 + 6
Step 4 : 5x = 25 ← divide both sides by 5
Step 5 : x = 5
Error was made by student in Step 2 who should have added 2x and 3x, not multiplied 2 × 3
84.4% of what number is 19.412?
Answer: 22.4402
Step-by-step explanation:
Answer:
84.4% of 23 is 19.412.
Step-by-step explanation:
Let the unknown number be x.
Now, 84.4% of x = 19.412.
∴ (84.4 ÷ 100) × x = 19.412.
By simplifying the equation,
x = (19.412 × 100) ÷ 84.4
x = 1941.2 ÷ 84.4
∴ x = 23
Thus, 84.4% of 23 is 19.412.
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A bag contains 3 blue marbles, 10 green marbles, 4 yellow marbles, and 8 red marbles. A marble is chosen at random, not replaced, then another marble is chosen. What is the probability that it is a red marble, then a blue marble? Write your answer as a fraction in simplest form.
Answer:
There are a total of 25 marbles in the bag.
The probability of choosing a red marble first is 8/25 since there are 8 red marbles out of 25 marbles in the bag.
Since a marble is not replaced after the first selection, there are now 24 marbles in the bag. There are still 3 blue marbles in the bag.
The probability of choosing a blue marble second, after a red marble has already been selected, is 3/24 or 1/8 since there are 3 blue marbles left out of 24 marbles in the bag.
To find the probability of both events occurring together, we multiply their individual probabilities:
8/25 x 1/8 = 1/25
Therefore, the probability that a red marble is chosen first, followed by a blue marble, is 1/25.
Find the Z-scores that separate the middle 61% of the distribution from the area in the tails of the standard normal distribution
Answer:
Z-scores between -0.86 and 0.86 separate the middle 61% of the distribution from the area in the tails of the standard normal distribution
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Middle 61%
Between the 50 - (61/2) = 19.5th percentile and the 50 + (61/2) = 80.5th percentile.
19.5th percentile.
Z with a pvalue of 0.195. So Z = -0.86
80.5th percentile.
Z with a pvalue of 0.805. So Z = 0.86.
Z-scores between -0.86 and 0.86 separate the middle 61% of the distribution from the area in the tails of the standard normal distribution
The stock of company a gained $0.76 throughout the day and ended at a value of $38.76. By what percentage did the stock rise
Answer:
Its either 1.98 percentage or 51.
Step-by-step explanation:
Divison?
Answer:2%
Step-by-step explanation: 38.76-0.76=38
38(1+r)=38.76
__________
38
1+r=1.02
R=0.02 (2%)
John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.50 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 500 units of vitamins, 600 units of minerals, and 1200 calories. How many boxes of each cereal should he buy to minimize his cost?
Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:
10x + 5y ≥ 500 (minimum 500 units of vitamins)
5x + 10y ≥ 600 (minimum 600 units of minerals)
15x + 15y ≥ 1200 (minimum 1200 calories)
We want to minimize the cost, which is given by:
0.5x + 0.4y
This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:
10x + 5y = 500
5x + 10y = 600
15x + 15y = 1200
Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.
Next, we can calculate the value of the cost function at each corner point of the feasible region:
Corner point A: (20, 40) -> Cost = 20
Corner point B: (40, 25) -> Cost = 25
Corner point C: (60, 0) -> Cost = 30
Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.
Please hurry need help, Answer choices-
A.9
B.-2
C.11
D.3
The numerical value of x in angle ABD is 9 as angle ABC is divided into two equal halves.
What is the numerical value of x?An angle bisector divided an angle into two equal halves.
From the diagram:
Line BD divides angle ABC into two equal halves.
Angle ABD = ( 3x - 7 ) degrees
Angle DBC = 20 degrees
Since angle ABD and DBC are equal haves;
Angle ABD = Angle DBC
Plug in the values:
( 3x - 7 ) = 20
Solve for x:
3x - 7 = 20
Add 7 to both sides:
3x - 7 + 7 = 20 + 7
3x = 27
x = 27/3
x = 9
Therefore, the value of x is 9.
Option A)9 is the correct answer.
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Write a word problem that can be solved using 12.25x=49.
5 1/10 x 1/6 pls helppp
Answer:
51/60
Step-by-step explanation:
First, I'll convert 5 1/10 into an improper fraction to make it easier to work with. I get 51/10. Then, I multiply the two fractions like so:
51/10 * 1/6 = 51/60
You multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom) separately.
So the answer is 51/60.
A large automobile insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period.
Single Policyholders Married Policyholders
n1 = 900 n2 = 400
Number making claims = 135 Number making claims = 24
Required:
a. Use a level of significance α = 0.05. Test to determine whether the claim rates differ between single and married male policyholders. Explain your determination.
b. Provide a 95% confidence interval for the difference between the proportions for the two populations.
Answer:
Step-by-step explanation:
Given the following :
Single policy holders (n1) = 900
Number making claims (x1) = 135
Married Policy holders (n2) = 400
Number making claims (x2) = 24
α = 0.05
a. Use a level of significance α = 0.05. Test to determine whether the claim rates differ between single and married male policyholders. Explain your determination.
Null: p1 - p2 = 0
Alternative : p1 - p2 ≠ 0
p = (n1p1 + n2p2) / n1 + n2 ;
p1 = x1/n1 = 135 / 900 = 0.15
p2 = x2/n2 = 24 / 400 = 0.06
p = (900*0.15 + 400*0.06) / (900 + 400)
p = 0.1223076
Test statistic (z):
(p1 - p2) / √p(1-p)(1/n1 + 1/n2)
(0.15 - 0.06) / √0.12231(1-0.12231)(1/900 + 1/400)
= 4.5710979
Decision:
Reject Null if P < α
Obtaining p value from z score using calculator :
P value = 0.0001
0.0001 < 0.05
Hence,
Reject Null
giving brainliest !! *easy*
um here’s the graph
-3(4x-1) + 9x +8x if x = -9
Answer:
-42
Step-by-step explanation:
What is the range of the function on the graph?
Range is the output values which are the y values.
The dot is at y = 2 and the line moves upward to the right off the graph. This means the line will continue to infinity.
The range would be 2 to infinity.
(2, infinity)
HELP
If 10% of x is 20, what is 23% of x?
Answer:
46
Step-by-step explanation:
Answer:
46
According to question,
10% × x = 20
x = 20 ÷ 10%
x = 20 ÷ 0.1
x = 200
Now find 23% of x
23% × 200
0.23 × 200
46
Math Help Please!
1. Given: f(x) = 3x +1
a. f is the_______of the function.
b. x is the input of your function and is AKA________
c. f(x) is the output of your function and is AKA_________
Answer:
1) f is the name of the function
2) x is the argument
3) output is (3x + 1)
Step-by-step explanation:
In function notation, The expression "f (x)" simply means that f is a formula that has an input variable known as "x". It should be noted that f(x) does not imply that we multiply f and x. Hence, f is the name of the function.
Now, the term "x" is an input variable known as the argument of the function.
f(x) is the output of the function and is; 3x + 1
Which number line can be used to find the distance between (4, -1) and (8, -1)?
O
A+
++
-2 -1 0 1 2 3 4 5 6 7 8
+
-2 -1 0 1 2 3 4 5 6 7 8
++
-2 -1 0 1 2 3 4 5 6 7 8
-8 -7 -6 -5 4 -3 -2 -1 0 1 2
Answer:
A
Step-by-step explanation:
is 1 a prime or composite number?
Answer:
Hello friends
Step-by-step explanation:
Hope it's helpful
Answer:
It's neither
Step-by-step explanation:
The only factor of 1 is 1.
A prime number has exactly two factors so 1 isn't prime.
A composite number has more than 2 factors, so 1 isn't composite either.
so... it's a neutral number.
Hope this helps!
Need Help Quick !!!!!!!!
Given:
The graph of a function.
As \(x\to -5^-, f(x)\to \_\_\_\).
As \(x\to -5^+, f(x)\to \_\_\_\)
To find:
The correct values for the given blanks.
Solution:
From the given graph it is clear that the function approaches to infinity as x approaches to -5 from the left side. So,
As \(x\to -5^-, f(x)\to \infty\).
From the given graph it is clear that the function approaches to negative infinity as x approaches to -5 from the right side. So,
As \(x\to -5^+, f(x)\to -\infty\).
Therefore, the correct option (d).
Y varies inversely as x and y =38 when x =26 find y when x =24
In summary in axis when x = 24, y = 41.1667.
Why is it?
If y varies inversely as x, then y = k/x for some constant k. To find k, we can use the initial values given:
y = k/x
38 = k/26
k = 38×26
k = 988
Now we can use k to find y when x = 24:
y = k/x
y = 988/24
y = 41.1667 (rounded to four decimal places)
Therefore, when x = 24, y = 41.1667.
In mathematics, an axis is a straight line that defines a reference direction for a coordinate system. It is used to locate or plot points, and describe geometric shapes in a plane or in space. In a two-dimensional coordinate system, there are two axes: the x-axis, which is horizontal, and the y-axis, which is vertical.
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ag the tiles to the correct boxes to complete the pairs.
Match the subtraction expressions to their correct answers.
Answer:no pic attached
Step-by-step explanation:
Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
Answer:10
Step-by-step explanation:
In the diagram below, side PQ has a length of 26.86 cm and side PR has a length of 40.00 cm.
Determine the measure of angle Q in degrees to one decimal place.
Goodness gracious! The diagram cannot be rendered!
Step-by-step explanation:
what is the answer to 100001/9
you and a friend have created a carnival game for your classmates. you plan to charge $1 for each time a student plays, and the payout for a win is $5. according to your calculations, the probability of a win is .05 what is your expected value for this game?
Answer:
The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.
Step-by-step explanation:
Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing
In this case:
Probability of Winning = 0.05
Payout for Win = $5
Cost of Playing = $1
Expected Value = (0.05 * $5) - $1
Expected Value = $0.25 - $1
Expected Value = -$0.75
What is the length of the longer leg of the right triangle shown below?
Type your answer as an integer.
A right triangle has hypotenuse of length 13 and a side with length 5.
\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{5}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{13^2-5^2}=b\implies \sqrt{144}=b\implies 12=b\)
The population of a town increased from 3800 in 2007 to 6100 in 2010 find the absolute and relative (percent) increase.
The requried population increased by approximately 60.53%.
To find the absolute increase, we subtract the initial population from the final population:
Absolute increase = Final population - Initial population
Absolute increase = 6100 - 3800
Absolute increase = 2300
Therefore, the population increased by 2300 people.
To find the relative increase, we first calculate the percent change:
Percent change = (New value - Old value) / Old value x 100%
Percent change = (6100 - 3800) / 3800 x 100%
Percent change = 2300 / 3800 x 100%
Percent change = 60.53%
Therefore, the population increased by approximately 60.53%.
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