a truck costs 40,000. it depreciates in value 5000 dollars per year write a linear model in the form v(t)=mt+b where v(t) represents the current value of the truck after t years of owning it
Clara earns either minimum wage or commission, whichever pay is greater each week . Minimum wage is 15 h. Clara's commission is 5 % of sales. During one week , Clara works 25 h and sells $5800 worth of merchandise
Calculate Clara's pay based on commission:
Clara's pay based on commission is $290.
Given:
Minimum wage is 15 h. Clara's commission is 5 % of sales. During one week ,Clara works 25 h and sells $5800 worth of merchandise.
commission = 5%
Clara's pay = 5800*5%
= 5800*5/100
= 58*5
= $290.
Therefore Clara's pay based on commission is $290.
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(b) Tickets for a raffle are placed in a box. The box contains 25 blue tickets and 20 red
tickets. Tickets are drawn at random from the box, one at a time and are not replaced.
What is the probability that:
(i) the first ticket drawn is red and the second ticket drawn is blue?
2
The probability that a red ticket is drawn first and then the second ticket drawn is blue is 0.253.
What is the probability?Probability determines the odds that a random event would occur. The odds that the random event occurs has a probability value that lies between 0 and 1.
The more likely it is that the event would occur, the closer the probability value would be to 1. The more unlikely it is that the event would not happen, the closer the probability value would be to 0.
The probability that a red ticket is drawn first and then the second ticket drawn is blue = (number of red tickets / total number of tickets) x (number of blue tickets / total number of tickets)
Total number of tickets = number of blue tickets + number of red tickets
25 + 20 = 45
The probability that a red ticket is drawn first and then the second ticket drawn is blue = (20 / 45) x (25 / 44) = 0.253
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Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a z-score of -2
The Z-score of a value is the count of the number of standard deviations between the value and the mean of the set. Hence, the height of a man with a z-score is [tex]25.35inches[/tex]
What is z-sore ?
The z-score of a value is the count of the number of standard deviations between the value and the mean of the set. You can find it by subtracting the value from the mean and dividing the result by the standard deviation.
Here given that,
mean=[tex]69.0 inches[/tex]
standard deviation=[tex]2.8 inches[/tex]
[tex]x=-2[/tex]
The general formula of the z-score is
[tex]z=\frac{x-mean}{standard deviation}[/tex] .......[tex](1)[/tex]
Now, putting the values in the equation [tex](1)[/tex], we get
[tex]z=\frac{-2-69.0}{2.8}\\z=\frac{71}{2.8}\\z=25.35inches[/tex]
Hence, the height of a man with a z-score is [tex]25.35inches[/tex]
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Chase is filing as a single individual for the year 2018 and has a total taxable income of $91,630. If he is in the 24% tax bracket, where the federal income tax owed is $14,089.50 plus 24% of every dollar above $82,500, how much does Chase owe in federal income taxes for 2018? Round your answer to the nearest cent. Do NOT round until you calculate the final answer.
In the year 2018, the amount that Chase owes in federal income taxes is $16, 280.70
How to find the federal income taxes?In 2018, Chase earned $91, 630 which put him in the 24% tax bracket. Here, his tax is $14,089.50 plus 24% of every dollar above $82,500.
The amount that Chase made above $82, 500 is:
= 91, 630 - 82, 500
= $9, 130
The federal income tax that Chase owes is therefore:
= 14, 089.50 + (9, 130 x 24%)
= 14, 089.50 + $2, 191. 20
= $16, 280.70
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Answer: $16,280.70
Step-by-step explanation:
First, find the difference between $91,630 and $82,500 to find the amount that is taxed at the 24% tax rate.
$91,630−$82,500=$9,130
Now, multiply $9,130 by 24% to find the additional amount of tax.
$9,130⋅24%=$2,191.20
Add $2,191.20 to $14,089.50 to find the total amount of federal income taxes Chase owes.
$2,191.20+$14,089.50=$16,280.70
Therefore, Chase owes $16,280.70 in federal income taxes for 2018.
Fill in the blanks
Suppose a person gained three pounds (a negative weight loss). Then z =__. This z-score tells you that x = -3 is__ standard deviations to the (right or left) of the mean.
Suppose a person gained three pounds (a negative weight loss). Then z = -1. This z-score tells you that x = -3 is 1 standard deviation to the left of the mean.
A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values in terms of standard deviations. It is calculated using the formula:
[tex]\\\mathrm {z = \frac{x - \mu}{\sigma} }[/tex]
Where:
z = z-score
x = individual data point (in this case, the weight change in pounds)
μ = mean of the data set (average weight change in pounds)
σ = standard deviation of the data set (a measure of how spread out the data is)
If the person gained three pounds (a negative weight loss), it means the value of x is -3 pounds (x = -3).
To calculate the z-score, we need to know the mean and standard deviation of the weight changes in pounds for the entire group of people.
Let's assume the mean (μ) is 0 pounds (no weight change on average), and the standard deviation (σ) is 3 pounds (for example).
z = (-3 - 0) / 3
z = -1
So, the z-score (z) is -1.
A negative z-score indicates that the data point (in this case, the weight change of -3 pounds) is below the mean.
Since the z-score is -1, this tells us that the weight change of -3 pounds is 1 standard deviation to the left of the mean.
The negative sign indicates it is below the mean, and the absolute value of the z-score (1) indicates it is 1 standard deviation away from the mean.
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A rectangle is made up of green and red tiles. The ratio of green tiles to red tiles is 3 : 4. Which of the following could be the number of green tiles in the rectangle?
The possible number of green tiles in the rectangle can be found to be H. 24.
How to find the number?The number of green tiles and red tiles in the rectangle will need to be expressed as whole number alone.
This means that because the ratio of the green tiles to the red tiles is 3 : 4, number of green tiles should be divisible by 3.
The numbers given are:
= 10 / 3
= 3.33
16:
= 16 / 3
= 5.33
24:
= 24 / 3
= 8
Because 24 is divisible by 3, there must be 24 green tiles in the rectangle.
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Assume that females have pulse rates that are normally distributed with a mean of =76.0 beats per minute and a standard deviation of o=12.5 beats per minute. Complete parts (a) through (c) below.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 83 beats per minute.
The probability is
The required probability for 1 adult female is randomly selected, find the probability that her pulse rate is less than 83 beats per minute is 0.5948.
In statistics, what does a probability mean?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.Statistics is the study of events that follow a probability distribution.Let, X= The female have pulse rate
μ = 7.60 bpm , σ² = 12.5²
a) We find
P[ 1 adult female is randomly selected, her pulse rate is less than 79 bpm]
= P [ X < 79]
= P [ X - μ/ σ < 79 - μ/ σ ]
= P[ X - 76/12.5 < 79 - 76/ 12.5 ]
= P[Z < 0.24]
= 0.5948 (From standard normal cumulative probability table)
Hence, the required probability of 1 adult female is randomly selected, find the probability that her pulse rate is less than 83 beats per minute.is 0.5948.
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someone help tyyyyy its due soon
a teacher gives a test with 15 questions that is worth 35 points It includes multiple choice questions worth 1 point each and short response questions worth 5 points each how many short responses and multiple choice questions are there
There are 10 multiple choice questions and 5 short response.
How to calculate the value?The following can be deduced:
The teacher gives a test with 15 questions that is worth 35 points.
Multiple choice questions = m = 1 point each
Short response questions = s = 5 points
The equation will be:
a + s = 15
a + 5s = 35
Subtract
4s = 20
Divide
s = 20/4
s = 5
Number of short response questions = 5
Number of multiple choice will be:
a + s = 15
a + 5 = 15
a = 15 - 5
a = 10
Multiple choice = 10
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Evaluate the expression when m = -7. m2+4m−4
If our equation is as follows;
[tex]f(m)=m^2+4m-4[/tex]We are given an initial condition. We replace the unknown by [tex]-7[/tex] to get the result.
[tex]f(-7)=(-7)^2+4(-7)-4[/tex][tex]f(-7)=49-28-4[/tex][tex]f(-7)=17[/tex]Adriana just won $500 000 in a lottery. She plans to invest the money in an
account from which regular withdrawals can be made every month for 25 years.
How much is each withdrawal if the interest rate is 5% per year, compounded
monthly?
a. $2549.31 c. $11 079.06
b. $2922.95 d. $5539.53
$5539.53 is each withdrawal if the interest rate is 5% per year, compounded monthly.
What is compounded interest?
Compound interest is the interest earned on savings that are calculated on both the initial principal and the interest earned in previous periods.
We have,
Initial amount - le 5,00,000
Interest = l = 5/100 = 0.05/12 = 0.004167
Time period T = 25 x 12 = 300
[tex]A = P(1 + r)^t[/tex]
where A = total balance after t years,
P = principal amount (the amount invested),
r = interest rate (decimal form), and
t = time in years.
How much money will Jack have after 25 years?
[tex]A = 5,00,000 (1+ 0.05)^{25}[/tex]
A = 1661859
A / 300 = 5643
Therefore, $5539.53 is each withdrawal if the interest rate is 5% per year, compounded monthly.
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Which event has a theoretical probability of exactly Three-fourths? Select three options. not picking a square picking a square picking a triangle picking a shape that has only straight edges not picking a circle
The event that has a theoretical probability of exactly Three-fourths include:
A. not picking a square
D. picking a shape that has only straight edges
E. not picking a circle
What is a theoretical probability?The theoretical probability is defined as the proportion of favorable outcomes to possible outcomes. The theory of probability is the science of probability.
The sample space of an object determines theoretical probability. The probability of rolling a 3 on a fair die, for example, is 1/6. This is because the number 3 represents one of the six possible outcomes of rolling a fair die
Therefore, based on the information given, it should be noted that the correct options are A, D and E.
This equation is written as follows: Theoretical Probability = the number of favorable outcomes divided by the total number of possible outcomes.
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Find the perimeter of the rectangle. length 7 inches and area 35 square inches.
pls help!!!
Step-by-step explanation:
Find the perimeter of the rectangle. length 7 inches and area 35 square inches.
P = 2W + 2L
A = LW
because you know that L = 7:
A = LW
35 = 7W
divide both sides by 7:
35/7 = 7W/7
W = 5
substitute into first equation:
P = 2W + 2L
P = 2(5) + 2(7)
P = 10 + 14
P = 24
the anwer is 5
35 divied by 7 is 5
7 times 5 is 35
An ordinary fair die is a cube with the numbers 1 through 6 on the sides. Imagine that such a die is rolled twice in succession and that the faces of the 2 rolls are added together. This sum is recorded of single trial of a random experiment. Event A: The sum is greater than 8. Event B: the sum is not divisible by 5
The probability of event A is 5/18.
The probability of event B is 29/36.
What are the probabilities?Probability is used to determine how likely it is that a random event would happen. The probability that the random event would happen would lie between 0 and 1.
The probability that the sum is greater than 8 = sample space that have a sum greater than 8 / total number of sample space
sample space that have a sum greater than 8 = (3,6) (4,5) (4,6) (5,4) (5,5) (5,6) (6,3) (6, 4) (6,5) (6,6) = 10
Total number of sample space = 36
The probability that the sum is greater than 8 = 10 / 36 = 5/18
The probability that the number is not divisible by 5 = sample spaces that is not divisible by 5 / total number of sample spaces
= 29 / 36
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Here is the rest of the question:
Write your answers as exact fractions.
P(a)
P(b)
NEED to know today please
Game Station 4: Spinner of 4 equal parts: Red, Purple, Green and Orange - Rules: If the arrow lands in the red quadrant, "Team Y" gets 7 points. If it lands in the other quadrants, both teams lose 1 point
A. "Team Y" spins 5 times. How many of the possible outcomes could have landed in Red exactly 3 times and on purple exactly 2 times?
B. "Team Z" spins 4 times. How many of the possible outcomes could have landed in Red
C. "Team Y" spins 5 times. How many of the possible outcomes could have landed in Red at least once?
use combinations, not probability.
The number of outcomes, using the Fundamental Counting Theorem, is given as follows:
A. Red exactly 3 times and Purple exactly 2: 10.
B. Red at least ounce in 4 spins: 175.
C. Red at least ounce in 5 spins: 781.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Item a is used with the combination formula, as it is an arrangement of five elements with 3 and 2 repetitions, hence the number of outcomes is:
[tex]C_{5,3} = \frac{5!}{3!2!} = 10[/tex]
What is the Fundamental Counting Theorem?The Fundamental Counting Principle states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item b, in four spins, each with four outcomes, the parameters are given as follows:
[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex]
Hence the number of outcomes is:
N = 4^4 = 256.
For no red results, the parameters are as follows:
[tex]n_1 = n_2 = n_3 = n_4 = 3[/tex]
Hence:
N = 3^4 = 81.
Hence the number of outcomes with at least one red is:
256 - 81 = 175.
For item 3, the lone difference is that there are five trials, hence:
Total outcomes: 4^5 = 1024.None red: 3^5 = 243.At least one red: 1024 - 243 = 781.More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/15878751
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Which set is infinite?
Answer:
Q
Step-by-step explanation:
WRITE AS A SIMPLE LOGARITHM.. 2logx-3log(x+2)+3logy
Answer:
log(x^2 y^3/(x+2)^3)
Step-by-step explanation:
Solve the equation for exact solutions. 6 cos^(-1) x = pi
I got √3/2
The exact solutions for the equation cos⁻¹x = π will be x=√3/2.
What is the equation?
An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equation to be solved,
cos⁻¹x = π
[tex]6\arccos \left(x\right)=\pi \quad :\quad x=\frac{\sqrt{3}}{2}[/tex]
Divide by 6 on both the side,
[tex]\frac{6\arccos \left(x\right)}{6}=\frac{\pi }{6}[/tex][tex]\frac{6\arccos \left(x\right)}{6}=\frac{\pi }{6}[/tex]
Simplify,
[tex]\arccos \left(x\right)=\frac{\pi }{6}[/tex]
From the trigonometric inverse principle,
[tex]x=\frac{\sqrt{3}}{2}[/tex]
Thus, the exact solution for the equation cos⁻¹x = π will be x=√3/2.
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How much longer is a stick insect measuring 12 cm than a fly which is 2.5 mm long? Give your answer in millimeters.
The required answer would be the stick insect is 117.5 millimeters long.
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
The stick insect measures 12 cm then a fly which is 2.5 mm long.
According to the given question, the required solution would be as:
⇒ 12 cm - 2.5 mm
Convert the centimeters into millimeters
⇒ 10 × 12 mm - 2.5 mm
⇒ 120 - 2.5
Apply the subtraction operation,
⇒ 117.5 millimeters
Thus, the required answer would be the stick insect is 117.5 millimeters long.
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The quadrilateral below is a parallelogram. Solve for x.
Answer:
x = 16 units
Step-by-step explanation:
supplementary angles = 180°
so
3x + 5 + 9x - 17 = 180
12x - 12 = 180
12x = 180 + 12
12x = 192
x = 192 : 12
x = 16 units
--------------------------------
check
3 * 16 + 5 + 9 * 16 - 17 = 180
180 = 180
the answer is good
Name an angle vertical to LEGH.
Answer:
IGF
Step-by-step explanation:
the two angles have the same vertex and lie on the same lines
Find the slope, of m of the line that passed through the points (-2/3, 3/4) and (5/6, -1/2). Enter your answer as a fraction in simplest form in the box
m = (-1/2 - 3/4) / (5/6 - (-2/3))
= (-2/4 - 3/4) / (5/6 + 4/6)
= (-5/4) / (9/6)
times 24 on top and bottom,
= -30/36
= -5/6
PLEASE HELP I HAVE TO SUBMIT IN 10 MINUTES
Carl began his hike at feet 1,482 above sea level. He then hiked down 2,173 feet, increased his altitude by another 663 feet and then decreased his altitude by 345 feet. What is Carl's final altitude?
The final altitude of Carl is -373 feet
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Carl began his hike at an altitude = 1482 feet
And , Carl hiked down an altitude = 2173 feet
Now , Carl is at an altitude of = 1482 - 2173 feet
= -691 feet
And , Carl increased his altitude by = 663 feet
Now , Carl is at an altitude of = -691 + 663 feet
= -28 feet
And , Carl decreased his altitude by = 345 feet
Now , Carl is at an altitude of = -28 - 345
= -373 feet
The final altitude of Carl is -373 feet
Hence , the final altitude is -373 feet
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Magan went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 350 mg of sodium and each frozen dinner has 650 mg of sodium. Magan purchased a total of 11 cans of soup and frozen dinners which collectively contain 4750 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.
Magan bought 8 cans of soup and 3 cans of frozen dinners.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let x represent the number of cans of soup purchased and y the number of frozen dinners purchased.
Magan purchased a total of 11 cans of soup and frozen dinners.
As per the given information, we can write the equations would be as
x + y = 11 ....(i)
Also:
350x + 650y = 4750
7x +13y =95 ....(ii)
Solving equations (i) and (ii) simultaneously gives the values are:
x = 8, and y = 3
Thus, Magan bought 8 cans of soup and 3 cans of frozen dinners.
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For which pair of triangles could the Angle-Side-Angle Postulate (ASA) be used to prove that △ABC≅△XYZ ? I only have an hour pls help.
The pair that support Angle-Side-Angle Postulate (ASA) be used to prove that △ABC≅△XYZ is option B
What are congruent triangles?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
examples of these rules are
Angle - Side - Angle = ASASide - Side - Side = SSSSide - Angle - Side = SASAngle - Angle - Side = AASHypotenuse and one leg = HLThe problem requires the prove by Angle - Side- Angle = ASA to ensure that the the triangles are congruent
The Angle - Side - Angle = ASA have it that the two triangles being compared should have their two angles and the included side being equal
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Find the measure of the numbered angle.
Answer:
1- 50
2- 130
3- 50
4- 130
5- 40
6- 140
7- 90
8- 140
Step-by-step explanation:
Answer:
m∠1 = 50°
Step-by-step explanation:
From inspection of the given diagram we can see that angle 1, angle 40° and a right angle are the interior angles of a right triangle.
As the interior angles of a triangle sum to 180°:
⇒ m∠1 + 40° + 90° = 180°
⇒ m∠1 + 130° = 180°
⇒ m∠1 + 130° - 130° = 180° - 130°
⇒ m∠1 = 50°
Therefore, the measure of angle 1 is 50°.
What is the value of 10a - 4b when a = 3 and b = 6?
Solve for b.
b - 14 = -10
A. b = -4
B. b = 4
C. b = -24
D. b = 24
The value of b after solution of the expression, b-14 = -10, is 4.
According to the question,
We have the following expression:
b-14 = -10
Now, we will first add 14 on both sides of the above equation:
b = -10+14
We know that when two integers are of different signs then the smaller number is subtracted from the larger number but the sign in the result is of the larger number.
So, in this case, 14 is larger than 10 then the result will be positive.
So, we have the following expression:
b = 4
Hence, the correct option is B.
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Find the compound interest and the total amount after an hour if the interest is compounded
every ten minutes.
Principal = 512
Rate of interest = 5% per minute
The compound interest = $5320
and the total amount = $5832
In this question, we need to find the compound interest and the total amount after an hour if the interest is compounded every ten minutes.
Here, principal P= $512
rate of interest R = 5% per minute
= 5 x 10 (interest for every 10 min)
= 50
Now n = 60 / 10
n = 6
So using compound interest formula the total amount would be,
A = P(1 + R / 100)^n
A = 512 (1 + 50/100)^6
A = 512 (3/2)^6
A = 5.2 (1.5)^6
A= $5832
Now the Compound Interest = A – P
= 5832 – 512
= $5320
Therefore, the compound interest = $5320
and the total amount = $5832
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