The range is { -5, -3, 7 }
How to calculate domain and range ?The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). A function's range is the set of possible values that it can accept. The values that the function outputs when we enter an x value are in this set.
domain = x
range = y
when the domain is -1
y = 2(-1) - 3
y = -2 - 3
y = -5
range is -5
When the domain is 0
y = 2(0) - 3
y = 0 - 3
y = -3
range is -3
when the domain is 5
y = 2(5) - 3
y = 10 - 3
y = 7
range is 7
The range is { -5, -3, 7 }
The complete question is : What is the range of the function y=2x-3 when the domain is {-1,0,5}
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. sand is being dumped from a truck at a rate of 40 cubic feet per minute forming a cone with diameter twice the height. how fast is the height changing when the pile is 5 feet high?
Using synthetic division, if 2 is the zero of x³ -7x+6p (x)
Answer:THe answer is 98.78x
Step-by-step explanation:
2r34 means 567
Someone pls help me with this question
how to determine if a binomial is a factor of a polynomial
A binomial is a factor of a polynomial has been determined by using the
polynomial division method.
To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:
Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.
Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.
Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.
Repeat the division process with the new polynomial obtained from the subtraction step.
Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.
If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.
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\(8x + 5 = 6x + 1\)
Answer:
x = -2
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 5 and 6x from both sides of the equation:
8x (-6x) + 5 (-5) = 6x (-6x) + 1 (-5)
8x - 6x = 1 - 5
2x = -4
Isolate the variable, x. Divide 2 from both sides of the equation:
(2x)/2 = (-4)/2
x = -4/2
x = -2
x = -2 is your answer.
~
which expression is equivalent to 2(a-3)+4a
The expression is equivalent to 2(a -3) + 4a will be 6a - 6. Then the correct option is A.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The expression is given below.
⇒ 2(a -3) + 4a
Simplify the expression, then we have
⇒ 2(a -3) + 4a
⇒ 2a - 6 + 4a
⇒ 6a - 6
The expression is equivalent to 2(a -3) + 4a will be 6a - 6. Then the correct option is A.
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The missing options are given below.
A. 6a - 6
B. 6a - 1
C. a - 6
D. None of the above
Please answer soon (60 points!)
Answer:
3.5
Step-by-step explanation:
We will divide 35 by 10.
35/10 = 3.5
The Smith Family is buying a house for $350,000 with a down payment of $70,000 for a 15-year loan, $66 per month insurance, property tax is $230 per month and HOA is $600 per year. Calculate their total monthly payment
Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.
What is the Monthly Payment?To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.
1. Mortgage Payment:
The loan amount is the house price minus the down payment:
$350,000 - $70,000 = $280,000.
To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).
We can use a mortgage calculator formula to calculate the monthly payment:
M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]
Where:
M = Monthly mortgage payment
P = Loan amount
i = Monthly interest rate
n = Number of months
The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.
i = 4% / 12 = 0.00333 (monthly interest rate)
n = 180 (loan term in months)
Plugging in the values into the formula:
M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]
Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.
2. Insurance:
The monthly insurance payment is given as $66.
3. Property Tax:
The monthly property tax payment is given as $230.
4. HOA Fees:
The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.
Now, let's add up all these expenses:
Mortgage payment: $2,014.99
Insurance: $66
Property tax: $230
HOA fees: $50
Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees
Total monthly payment = $2,014.99 + $66 + $230 + $50
Total monthly payment = $2,360.99
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if MQRS is a rectangle with QR=x+7 and MSMS =15, find x
Answer:
Step-by-step explanation:
x+7=15
x=15-7
x=8
since it is a rectangle the breadth are equal.
Consider the expression (-15) + 8. Describe a situation that could be represented by the expression. Then, find the sum and explain what it means in the context of the situation.
Answer:
it not
Step-by-step explanation:
Aaliyah plays forward for her college soccer team, but with pandemic she would only practice with herself. She practices by shooting the ball thirty meters away from the goal and always scores if she places the ball in the top right quadrant of the goal (where the goalkeeper can’t reach it) and misses if she places it elsewhere.
Her data is the following, where (X) means she didn’t score and (O) means she scored:
X O X X O O X X O O X X O O O O O O X X X O O O X X O O O X
a. what is the probability that she scores (O) on any given shot?
b. What is the probability that she scores given that he has scored in the two previous shots?
c. How many runs does she have?
d. what is the z-statistic for the test ? Does it show evidence of the hot hand?
a ) The probability that she scores on any given shot is 30%.
b) The probability of her scoring given that she has scored on the two previous shots is 3/4 or 75%.
c) The z-statistic is 0, which means that there is no evidence of the hot hand phenomenon in Aaliyah's performance.
a. To calculate the probability that Aaliyah scores on any given shot, we can count the number of shots where she scored (O) and divide it by the total number of shots:
Number of shots where Aaliyah scored = 9
Total number of shots = 30
Probability of scoring on any given shot = 9/30 = 0.3 or 30%
Therefore, the probability that she scores on any given shot is 30%.
b. To calculate the probability that Aaliyah scores given that she has scored on the two previous shots, we need to look at the subset of shots where she scored on the two previous shots and see how many times she scored on the current shot. From the data provided, we can identify the following sequences of three shots where Aaliyah scored on the first two shots:
OOX, OOO, OOX, OOO
Out of these four sequences, Aaliyah also scored on the third shot in three of them. Therefore, the probability of her scoring given that she has scored on the two previous shots is 3/4 or 75%.
c. To calculate the runs that Aaliyah has, we need to count the number of times she scored on consecutive shots. We can identify the following sequences of consecutive shots where she scored:
OO, OO, OOO
Therefore, Aaliyah has a total of 6 runs.
d. To test for evidence of the hot hand phenomenon, we can compute the z-statistic for the proportion of shots Aaliyah scored, assuming that her scoring rate is constant and equal to the observed proportion of 9/30.
The formula for the z-statistic is:
z = (p - P) / sqrt(P(1-P) / n)
where:
p = proportion of shots Aaliyah scored in the sample (9/30)
P = hypothesized proportion of shots she would score if her scoring rate is constant
n = sample size (30)
Assuming that Aaliyah's scoring rate is constant and equal to the observed proportion of 9/30, we can set P = 9/30 and compute the z-statistic as follows:
z = (p - P) / sqrt(P(1-P) / n)
z = (0.3 - 0.3) / sqrt(0.3 * 0.7 / 30)
z = 0
The z-statistic is 0, which means that there is no evidence of the hot hand phenomenon in Aaliyah's performance. This suggests that her scoring rate is consistent with what we would expect based on chance alone, given the small sample size and assuming a constant scoring rate.
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You're making lunches for school and you want to pack chips. You
can purchase Funyuns in a 7 oz bag for $2.49. What is the price per
ounce?
Answer : The price per ounce of funyuns is $0.356.
Step-by-step explanation :
As we are given that the price of 7 ounce bag of funyuns is $2.49.
Now we have to determine the price per ounce.
According to the question,
As, 7 ounce bag of funyuns = $2.49
So, 1 ounce bag of funyuns = \(\frac{1\text{ ounce}}{7\text{ ounce}}\times \$ 2.49\)
= $0.356
Therefore, the price per ounce of funyuns is $0.356.
Can you guys help me please
Find the measures of the unknown angle
Don’t answer if you do not know .
Answer:
Below
Step-by-step explanation:
Angle A= 65 degrees
Angle N= 53 degrees
Angle L= 45
4th image= x=30
2x=60
5th image= x=50
x+30=80
Please tell me if this helps!
right triangle abc is shown. triangle a b c is shown. angle a c b is a right angle and angle c b a is 50 degrees. the length of a c is 3 meters, the length of c b is a, and the length of hypotenuse a b is c. which equation can be used to solve for c? sin(50o)
The equation that can be used to solve for c in the given right triangle is the sine function: c = (3 meters) / sin(50°).
In the given right triangle ABC, we are given that angle ACB is a right angle (90°) and angle CBA is 50°. We also know the length of side AC, which is 3 meters. The length of side CB is denoted by "a," and the length of the hypotenuse AB is denoted by "c." To solve for c, we can use the trigonometric function sine (sin). In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we can use the sine of angle CBA (50°) to find the ratio between side CB (a) and the hypotenuse AB (c).
The equation c = (3 meters) / sin(50°) represents this relationship. By dividing the length of side AC (3 meters) by the sine of angle CBA (50°), we can find the length of the hypotenuse AB (c) in meters. Using the given equation, we can calculate the value of c by evaluating the sine of 50° (approximately 0.766) and dividing 3 meters by this value. The resulting value will give us the length of the hypotenuse AB, completing the solution for the right triangle.
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a car is traveling at 40 m/s when it collides head-on with a sport utility vehicle traveling in the opposite direction. in the collision, the two vehicles come to a halt. at what speed was the sport utility vehicle traveling
The SUV's speed before the collision would be greater than 40 m/s
Let's assume the initial speed of the SUV is denoted by V (the value we're trying to find). The momentum of the car before the collision can be calculated as the product of the car's mass (m₁) and its speed (40 m/s), which is given as 40m1. Similarly, the momentum of the SUV before the collision is given by the product of its mass (m₂) and its speed (V), which is Vm₂.
Since the two vehicles come to a halt, the total momentum after the collision is zero. Therefore, the sum of the momenta of the car and the SUV before the collision must also be zero:
40m₁ + Vm₂ = 0
Since the car's mass (m₁) and the SUV's mass (m₂) are not given, we cannot solve for the actual values. However, we can still determine the relationship between the speeds of the car and the SUV before the collision. By rearranging the equation, we can solve for V:
V = -40m₁/m₂
From the equation, we can see that the speed of the SUV before the collision (V) is directly proportional to the speed of the car (40 m/s) and inversely proportional to the mass ratio of the car (m₁) to the SUV (m₂). The negative sign indicates that the SUV was traveling in the opposite direction to the car.
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Robert has 99 buttons. Jack has b more buttons than Robert. Choose the expression that shows how many buttons Jack has
Solution:
Note that:
Robert + b = JackRobert = 99 buttonsSubstituting the values into the equation:
Robert + b = Jack=> 99 + b = JackThis means that Jack has 99 + b buttons.
Situation:
A hiker in Africa discovers a skull that
contains 51% of its original amount of C-
14.
N=Noekt
No inital amount of C-14 (at time
=
t = 0)
N = amount of C-14 at time t
k = 0.0001
t= time, in years
Find the age of the skull to the nearest year.
Enter the correct answer.
Step-by-step explanation:
To determine the age of the skull, we can use the equation for radioactive decay:
N = N0 * e^(-kt)
where N is the remaining amount of C-14, N0 is the initial amount of C-14, k is the decay constant, and t is the time elapsed.
In this situation, we know that N = 0.51N0 (since the skull contains 51% of its original amount of C-14) and k = 0.0001. Plugging these values in, we get:
0.51N0 = N0 * e^(-0.0001t)
Simplifying, we can divide both sides by N0 to get:
0.51 = e^(-0.0001t)
Taking the natural log of both sides, we get:
ln(0.51) = -0.0001t
Solving for t, we get:
t = -ln(0.51)/0.0001
t ≈ 3,841 years
Therefore, the age of the skull is approximately 3,841 years old.
In 2014, a survey stated that 51% of 650 randomly sampled North Carolina residents planned to set off fireworks on July 4th. a) Determine the margin of error for the 95% confidence interval for the proportion of North Carolina residents that plan to set off fireworks. Give your answer to three decimal places. Margin of Error = _____% b) How many randomly sampled residents do we need to survey if we want the 95% margin of error to be less than 3%? Sample size > _____ People
To find the required sample size for a margin of error less than 3%, we can rearrange the formula for the margin of error:
\(n = (Z^2 * p * (1 - p)) / (E^2)\)
Here, Z represents the critical value, p is the estimated proportion (0.51), and E is the desired margin of error (0.03)
To determine the margin of error for the 95% confidence interval, we need to use the formula:
Margin of Error = Critical value * Standard error
The critical value for a 95% confidence level can be obtained from the standard normal distribution table, which corresponds to 1.96. The standard error can be calculated using the following formula:
Standard error = \(\sqrt{(p * (1 - p) / n)}\)
Given that the proportion of North Carolina residents planning to set off fireworks is estimated to be 51% (0.51) based on the survey, we can substitute the values into the formula. However, the sample size (n) is not provided in the question, so we need to determine it in the next part.
To find the required sample size for a margin of error less than 3%, we can rearrange the formula for the margin of error:
\(n = (Z^2 * p * (1 - p)) / (E^2)\)
Here, Z represents the critical value, p is the estimated proportion (0.51), and E is the desired margin of error (0.03). Substituting these values into the formula, we can solve for the required sample size.
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to calculate mad and summing up the forecasts errors, the value used for ||18−20|| in the calculation is? multiple choice question. either 2 or -2 2 -2 cannot be computed
The sum of forecast errors is also known as total forecast error. Therefore, the correct answer is option A, which is "2."
The absolute error of the given data is calculated by subtracting the actual value from the forecasted value, followed by the absolute value.
The errors are then summed up to get the mean absolute deviation. The value used for ||18−20|| in the calculation of MAD and summing up the forecast errors is 2.
Therefore, the correct answer is option A, which is "2."Formula for calculating MAD:MAD = Σ ( | A_i - F_i | ) / n
Where: MAD is the mean absolute deviation|A_i - F_i| represents the absolute error between the actual value (A) and the forecasted value (F)n is the total number of observations, Sum of forecast errors:Σ ( A_i - F_i )Where: A_i is the actual valueF_i is the forecasted value
The sum of forecast errors is also known as total forecast error.
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Nora went shopping for a new phone because of a sale. The store was offering a 10% discount. If the price on the tag was $24, what would be the price after the discount but before tax, to the nearest dollar and cent?
Answer:
$21.6
Step-by-step explanation:
Given data
Cost of Phone= $24
Discount= 10%
Let us find the amount of the discount
=10/100*24
=0.1*24
=$2.4
Hence the amount paid after the discount
=24-2.4
=$21.6
Answer:
21.6
Step-by-step
BIG BRAIN AND MENTAL MATH
20.7 rounded off to the nearest tens place
Answer:
20
Step-by-step explanation:
a red and a blue die are thrown. both dice are fair. the events a, b, and c are defined as follows: a: the sum on the two dice is even b: the sum on the two dice is at least 10 c: the red die comes up 5 (a) calculate the probability of each individual event. that is, calculate p(a), p(b), and p(c). (b) what is p(a|c)? (c) what is p(b|c)? (d) what is p(a|b)? (e) which pairs of events among a, b, and c are independent? feedback
This question requires estimating the probability of various occurrences related to the roll of two dice, one red, and one blue. The occurrences A, B, and C occur when the sum of the two dice is even, when the sum is at least 10, and when the red die comes up 5, respectively. Calculating the likelihood of each individual event, as well as conditional probabilities, and distinguishing independent pairs of occurrences are all part of the process.
(a) Probability of each individual event is as follows:
P(A) = probability of an even sum = (number of favorable outcomes)/(number of possible outcomes)= 18/36 = 1/2
P(B) = probability of a sum at least 10= (number of favorable outcomes)/(number of possible outcomes) = 3/36= 1/12
P(C) = probability of red die shows 5 = (number of favorable outcomes)/(number of possible outcomes) = 1/6
(b) P(A|C) = probability of getting an even sum on the dice given that the red die shows 5= (number of favorable outcomes)/(number of possible outcomes)
Since we know that the red die shows 5, there are three favorable outcomes to getting an even sum: (4, 1), (4, 3), and (6, 5). The probability of one of these outcomes occurring is P(A|C) = 3/3 = 1
(c) P(B|C) = probability of getting a sum of 10 or more on the dice given that the red die shows 5= (number of favorable outcomes)/(number of possible outcomes). Since we know that the red die shows 5, there are no possible outcomes that will result in a sum of 10 or more. Thus, P(B|C) = 0
(d) P(A|B) = probability of getting an even sum on the dice given that the sum is at least 10 = (number of favorable outcomes)/(number of possible outcomes)We know that the only way to obtain a sum of 10 or more is to get a 5 and a 5 or a 6 and a 4. Out of these two possible outcomes, only one of them has an even sum: (6, 4). Therefore, the probability of getting an even sum given that the sum is at least 10 is: P(A|B) = 1/2
(e) To determine which pairs of events among a, b, and c are independent, we have to determine whether P(A) = P(A|C), P(B) = P(B|C) and P(A)P(B) = P(A∩B).- P(A) = 1/2, P(A|C) = 1, P(A) ≠ P(A|C), so events A and C are not independent.- P(B) = 1/12, P(B|C) = 0, P(B) ≠ P(B|C), so events B and C are not independent.- P(A)P(B) = (1/2)(1/12) = 1/24, P(A∩B) = 1/36 = P((6, 4)), P(A)P(B) ≠ P(A∩B), so events A and B are not independent.
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N. 1 and 7/10 gallons of gasoline were used to drive 25 and 1/2 miles. How many
miles per gallon did the car get?
miles per gallon
Answer:
Similar to the question: They figure that they will drive 792 miles round trip. If their car gets 25 miles per gallon and the current cost of gasoline is $2.35, what will the gas for their trip cost? $74.45 George is taking the same trip to San Antonio (792 miles)
Step-by-step explanation:
Hope it helps :)
please answer for 20 points
Answer:
C
Step-by-step explanation:
whenever you see a (as in ax^2 + bx+c) as a number other than 1, you should see if you can factor that out
2(6x^2 -x -1)
= 2(3x+1) (2x-1)
Answer:
2\(3x+1)(2x-1\)
Step-by-step explanation:
what is the difference between relative frequency and cumlative relative frequency
The difference between relative frequency and cumulative relative frequency is that relative frequency is the ratio of the frequency of a particular value in a dataset to the total number of values, expressed as a percentage. Cumulative relative frequency is the sum of all relative frequencies up to a certain point in the data set.
For example, if a data set has 8 values and 4 are the same, the relative frequency would be 50%. Cumulative relative frequency would be 50% at this point since it is the sum of all relative frequencies up to this point in the data set. If there were another 4 of the same values after this point, the relative frequency would remain at 50%, but the cumulative relative frequency would increase to 100% since it includes all previous relative frequencies.
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You select a marble without looking and then put it back. If you do this 9 times, what is the best prediction possible for the number of times you will pick a green or a pink marble?
The best prediction for the number of times you will pick a green or pink marble out of 9 selections is 2/9.
What is the best prediction for picking green or pink marble out of 9 selections?To find the best prediction, we can assume that the marbles are equally likely to be selected each time.
Since there are two outcomes (green or pink) for each selection, the best prediction for the number of times you will pick a green or pink marble would be:
= 2 / 9
= 4.5.
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a subset of a population used by statisticians to make predictions about a population is called a
A subset of a population used by statisticians to make predictions about a population is called a sample.
a sample is a smaller, representative group selected from the larger population. The sample is used to gather data and make inferences about the entire population. By analyzing the sample, statisticians can make predictions about the characteristics, trends, or behaviors of the population without having to study every individual within it. This method saves time, resources, and effort while still providing accurate results.
A sample is a crucial tool in statistical analysis, allowing statisticians to make informed predictions about a population based on the study of a smaller, representative subset.
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How do you calculate the arc length of a circle?
To calculate the arc length of a circle, you need to use the formula: arc length = (central angle in radians) x (radius)
where the central angle is measured in radians and the radius is the distance from the center of the circle to the edge. To use this formula, first convert the central angle from degrees to radians by multiplying it by π/180. Then, multiply the result by the radius to find the arc length. For example, if you have a circle with a radius of 5 units and a central angle of 45 degrees, you can calculate the arc length as follows: Convert the central angle to radians: 45 x π/180 = 0.7854 radians. Multiply the central angle in radians by the radius: 0.7854 x 5 = 3.927 unit. Therefore, the arc length of a circle with a radius of 5 units and a central angle of 45 degrees is 3.927 units.
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Paul is cutting trim for his living room. He needs to cut 6 pieces that are each 72.8 inches long. How many total inches of trim will he need to cut?
Let:
x = total inches of trim he needs to cut
n = Number of pieces he needs to cut
a = length of the pieces
so:
\(\begin{gathered} x=an \\ x=6\times72.8 \\ x=436.8in \end{gathered}\)in percent the whole of an amount W is measured by the formula W=100N/P where N=part and P=percent solve the formula for P (SAVVAS MATH XL)
The equation of P in the given equation is P = 100N/W
How to solve for P in the equation?The equation is given as:
W = 100N/P
Multiply both sides by P
WP = 100N
Divide both sides by W
P = 100N/W
Hence, the equation of P in the given equation is P = 100N/W
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