Answer:
The answer to this problem is 0.0013.
A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 1700 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?
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
If A=(x | x is an even integer), B=(x | x is an odd integer), C=(2, 3, 4, 5), and D=(13, 14, 15, 16), list the element(s) of the following set.
←
A ∩ D
A ∩ D= (Use a comma to separate elements in the set.)
Answer:
A ∩ D = { 14; 16 }======================
A ∩ D means intersection of the two sets or the common elements of A and D.
We observe that:
Set A has all even integers,Set B has even integers 14 and 16.It means the common elements of the two sets are 14 and 16:
A ∩ D = { 14; 16 }Answer:
A ∩ D = {14, 16}
Step-by-step explanation:
Given sets are,
→ A = {x | x is an even integer}
→ D = {13, 14, 15, 16}
Now we have to,
→ find required set of A ∩ D.
Then the answer will be,
→ A ∩ D = {2, 4, 6, 8, ... n} ∩ {13, 14, 15, 16}
→ A ∩ D = {14, 16}
Hence, the required set is {14, 16}.
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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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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The wholesale price for a pair of shoes is $4.50. A certain department store marks up the wholesale price by 50%. Find the price of the pair of shoes in the
department store.
Round your answer to the nearest cent, as necessary.
The price of the pair of shoes in the department store is $7.
The wholesale price for a pair of shoes is $4.50. A certain department store marks up the wholesale price by 50%.
To find out the price of the pair of shoes in the department store:
The price of the pair of shoes in the department store: $7
Given the wholesale price of pair of shoes is $4.50
Department store of wholesale price is 50%
Than whole sale = 1.5 times the whole sale
Price in department store = 1.5*4.5
= $6.75
Rounded to the nearest cent = $7
Hence the answer is the price of the pair of shoes in the department store is $7.
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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 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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solve and graph X + 6 > -1
Answer: x > -7, see attached
Step-by-step explanation:
Given:
x + 6 > -1
Subtract 6 from both sides of the equation:
x > -7
Graph, see attached. We will graph x = -7, and shade to the right.
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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Assume that a simple random sample has been selected from a normally distributed
population. Find the test statistic t.
A local newspaper reported that for the adult population of a town, the mean annual salary is $30,000.
Test the claim that for the adult population of this town, the mean annual salary is greater than
$30,000. Sample data are summarized as n = 17, sample mean = $22,298, and s = $14,200. Use a
significance level of alpha = 0.05.
Find the test statistic t.
a) -2.24
b) -1.57
c) 1.57
d) 2.24
e) 0.05
The test statistic when the a simple random sample has been selected from a normally distributed population is a) -2.24
What is test statistic?The test statistic is a number derived from a statistical test that is used to determine whether your data could have occurred under the null hypothesis.
u = 30000
x = 22298
s = 14200
n = 17
Test statistic = = (x - u) / s / ✓n
x = mean
u = theoretical value
s = standard deviation
{n} = variable set size
= (x - u) / s / ✓n
= (22298 - 30000) / 14200 / ✓17
= -2.24
Test statistic = -2.24
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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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The size P of a certain insect population at time t (in days) obeys the function P(t) = 700e^0.04t
(a) Determine the number of insects at t = 0 days.
(b) What is the growth rate of the insect population?
(c) Graph the function using a graphing utility.
(d) What is the population after 10 days?
(e) When will the insect population reach 1190?
(f) When will the insect population double?
The number of insects at t=0 is 700, the growth rate is 28e^0.04, population of insects after 10 days is 1044, and the graph of the function is attached.
What is function?
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
a) Number of insects at time (t) = 0 days,
Putting t = 0 in given function:
P(t) = 700e^0.04(0) = 700e^0 = 700
Hence, the number of insects at t = 0 days is 700.
b) Growth rate of insect population,
In order to find growth we need to differentiate the given function with respect to t.
So, dP(t)/dt = 700(0.04)e^0.04(0)
= 28e^0.04
Hence, the growth rate is 28e^0.04.
c) Graph the function is attached in the question.
d) The population of the insects after 10 days,
putting t = 10,
= 700e^0.04(10) = 1044
Hence, population of insects after 10 days is 1044.
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The Old Farmer’s Almanac reports that the average person uses 123 gallons of water daily. If the standard deviation is 21 gallons, find the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons. Assume the variable is normally distributed.
The probability that the mean of the sample is between 120 and 126 gallons is 0.4176
How to determine the probability that the mean is between 120 and 126 gallons?The normal distribution describes a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation
Given: population mean (µ) = 123, standard deviation(σ) =21 and number of sample (n) = 15
Let X represent the gallons of water: We want to find:
P(120 ≤ X ≤ 126)
Z-score(Z) = (X-µ) / (σ/√n)
Z₁ = (120-123)/ (21/√15) = -0.55
Z₂ = 126-123/ (21/√15)= 0.55
P(-0.55≤ Z ≤ 0.55) = = 0.7088 - 0.2912 = 0.4176
(Check the image of the table attached)
Therefore, the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons is 0.4176
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Given that M > N determine whether the inequality M/N > N/M always, sometimes, or never true.
if M > N then the inequality M/N > N/M will be always true
What is Linear Inequality?
The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.
As in the question M is always greater N
So, is M is divided by a number that is less than M the answer will always be greater than 1
but on the other hand, if N is divided by a number greater than N then the answer will always be less than 1
Therefore, M/N > N/M will always be True
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Big Drop is twice as long as Little Drop. How long is Little Drop?
Answer:
Half as big as little drop?
Step-by-step explanation:
Jack has 32 quarters on his desk and Molly has q quarters in her purse
Answer:
32+q
Step-by-step explanation:
it doesn't ask for money
Which set is infinite?
Answer:
Q
Step-by-step explanation:
if you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long, how much string do you still have?
If you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long, Then 16.875 is the remaining string.
What is Fraction?A fraction represents a part of a whole.
1 foot =12 inches
2 foot=24 inches.
Given,
if you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long.
Then how much string do you still have
We have to subtract the used strings from 24 inches string.
4 3/4 inches=19/4
2 3/8 inches=19/8
Now we have to subtract 19/4 and 19/8 from 24 inches.
24-19/4-19/8
24-4.75-2.375
16.875
Hence 16.875 is the string left with us.
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Find the value of x.
f(x)= (1/3)x + 5
Has the output value of -15
Answer:
-60
Step-by-step explanation:
-15 = 1/3x + 5 Multiply all the way through by 3
-45 = x + 15 Subtract 15 from both sides of the equation
-60 = x
Answer: -60 = x
Step-by-step explanation:
If the output value is -15, we need to do this equation.
-15 = (1/3)x + 5.
-5 -5
-20 = (1/3)x
x3 x 3
-60 = x.
Now, let's double-check our answer.
f(60) = (1/3)(-60) + 5
f(-60) = -20 + 5
f(-60) = -15.
This means that x = -60 is our correct answer.
Killer whale weight 16200 and calf weighs 1130 how many pounds greater is the mothers weight than the calf.
Answer: 15,070
Step-by-step explanation: subtraction 16200-1130=15,070
what is the solution of the following system?
-3x-2y=-12
9x+6y=-9
(2,1)
no solution
(-2,-1)
infinitely many solution
Answer:
no solution
Step-by-step explanation:
What is the image point of (2, −6) after the transformation R270° ○ D1/2?
The image point of (2, −6) after the transformation R270° is (4,3).
Given:
(2,-6) and R270° and (1,2)
Let (x,y) be the point
First translation (1,2)
(x,y) → (x+1,y+2)
Translation of R270° for translated coordinates
(x+1,y+2) → (-(y+2),x+1)
substitute (2,-6)
= (-(-6+2),2+1)
= (-(-4),3)
= (4,3)
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Think about
A model of a house was built using the scale 5 in:25 ft. If a window in the
model is 1.5 in. wide, how wide is the actual window?
If a window in the model is 1.5 in. wide, then the actual window is 7.5 feet wide.
What is meant by unit ratio?A two-term ratio expressed with a second term of one is referred to as a unit ratio. A unit ratio can be created from any ratio. Example. An illustration of a set of marbles is shown below. The set has eight blue marbles and two red marbles.
Having a denominator of 1, a unit rate is a ratio between two separate units. Divide the numerator by the denominator to obtain the unit rate. The unit rate is the decimal number that results. The price of a good or service is the numerator of a ratio called the unit price, and the quantity is the denominator.
Given,
The scale of the Model =5 in: 25 ft.
Dividing both sides by 5 we get,
[tex]\frac{5in}{5}[/tex] :[tex]\frac{25ft}{5}[/tex]
1 inch:5 feet
If a window on the model is 1.5 inch wide, then from the unit ratio we get,
1 inch × 1.5 : 5 feet × 1.5 feet
1.5 Inch : 7.5 feet
As a result, a window that is 1.5 inches wide in the model will actually be 7.5 feet wide.
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Vocabulary How does a flow proof show
logical steps in the proof of a conditional
statement
Starting with the provided assertions, a flow proof arranges statements in a logical order.
Define the term flow proof?A mathematically formatted proof known as a "flow proof" uses logic to back up a truth assertion.
A proof will always be a series of assertions that ultimately to a conclusion in mathematics. One or more supplied statements are presented to start a proof. Until the intended conclusion is reached, the given statement is followed by subsequent statements. A chain of statements needs to be logically substantiated for each statement. The statements are verified by comparison to mathematical definitions, properties, and theorems.Thus, opening with the provided assertions, a flow proof arranges statements in a logical order. Arrows are being used to show the sequence of the assertions, and each assertion has its justification stated beneath it.
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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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PLEASE HELP ASAP! 2 QUESTIONS
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 80.4° is added to the data, how does the range change?
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 60° is added to the data, how does the median change?
If a value of 80.4° is added to the data, the range does not change.
The range is 48.
If a value of 60° is added to the data, the median change.
The median was 79.5.
The change median is 77.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
The range formula = Highest value - Lowest value
Now,
Highest value = 105
Lowest value = 57
Range = 105 - 57 = 48.
Now,
If the value of 80.4 is added the range remains the same because the range is dependent only on the value of the highest and the lowest value.
We have,
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
The median is the mid value of the given set of data after arranging in ascending order.
Arranging the set in ascending order.
57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105
There are 12 elements in the set.
Median = (77 + 82) / 2 = 79.5
If 60 is added we get 13 elements in the set.
The arrangement becomes,
57, 58, 60, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105
Median = 77
Thus,
If a value of 80.4° is added to the data, the range does not change.
The range is 48.
If a value of 60° is added to the data, the median change.
The median was 79.5.
The change median is 77.
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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)
how many times smaller is 4 than 400?( Hint -4 does not have any zeros, 2-0=2.
Answer:
396
Step-by-step explanation:
400-4=396
Answer:
396
Step-by-step explanation:
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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