The probability of no one drawing their own name is 9/24 = 3/8.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.
The probability that no one draws their own name in a randomized gift exchange can be found using derangements. A derangement is a permutation of a set where none of the elements are in their original position.
With three people, there are 3! = 6 possible permutations. There is only one permutation where no one draws their own name, which is a derangement. Therefore, the probability of no one drawing their own name is 1/6.
With four people, there are 4! = 24 possible permutations. There are nine derangements, which can be calculated using the formula for derangements: [tex]D(n) = n!(1/0! - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!).[/tex]
Therefore, the probability of no one drawing their own name is 9/24 = 3/8.
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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.
You have been told that it costs a company R950 to make 100 units of a product and R1 550 to make 200 units of the same product. As one of the financial managers at the company, you have the responsibility of constructing a linear equation from this data. Use this linear equation to determine how much it will cost the company to produce 500 units of this product. (5)
it will cost the company R3 350 to produce 500 units of this product.
How to determine how much it will cost the company to produce 500 units of this product.Let x be the number of units produced and y be the cost to produce those units. We can use the given information to form two data points:
(100, 950) and (200, 1550)
Using these points, we can find the slope of the line:
slope = (1550 - 950)/(200 - 100) = 6
Next, we can use the point-slope form of a line to find the equation of the line:
y - 950 = 6(x - 100)
y - 950 = 6x - 600
y = 6x + 350
Finally, we can use this equation to find the cost of producing 500 units:
y = 6(500) + 350 = 3350
Therefore, it will cost the company R3 350 to produce 500 units of this product.
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Factor each polynomial. Look for a GCF first.
2x²-8k-90
O
2 (x-9) (x - 5)
2 (x + 9) (x + 5)
2 (x − 9) (x + 5)
2 (x + 9) (x - 5)
Answer:
Step-by-step explanation:
First, you could factor 2 out of the whole thing. The result would be 2(x^2-4x-45). Now we find the factors of 45 which are 1, 45, 5, 9, 15, 3. We have to find the pair that adds up to 4, and multiply to get 45. After some guess and check, we can find that 5 and 9 are those numbers. Now we have to get the right signs. Since the result is a negative number for -8k, and -90, the number that is a negative must be less than the other negative. -9<-5, so the answer would be 2(x-9)(x+5)
1 buy 18 packets of cat food in a box. The table shows the different varieties in the box. My cat eats all the packets of tuna. I then take a packet at random from the ones left in the box.
What is the probability that it will be salmon?
Give your answer as a fraction in its simplest form.
Variety. No. of packets
Chicken. 3
Cod. 4
Salmon. 5
Tuna. 6
The probability of taking salmon packet is 5/12.
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
Here Total number of packets = 18
Then the cat eat all tune . Number of tune packets = 6.
Then remaining packet= 18-6 = 12
Now number of salmon packet = 5.
Then probability that it will be salmon is,
=> P = Number of salmon packet/ Total number of remaining packet.
=> P = 5/12.
Hence the probability of taking salmon packet in fraction is 5/12.
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3. Car A drove 168 miles using 8 gallons of gas. Car B drove 144 using 6 gallons of gas. Which car drives more miles per gallon?
Ryan borrowed $200 from a lender that charged simple interest at an annual rate of 6%. When Ryan paid off the loan, he paid $48 in interest. How long was the loan, in years?
The loan was for 4 years.
What is intrest?
Interest is a fee paid by a borrower of money to the lender as compensation for the use of the money over a certain period of time. It is usually expressed as a percentage of the amount borrowed or invested, and the percentage is called the interest rate. The borrower is expected to pay back the principal amount borrowed plus the interest within a specified period of time.
The formula for simple interest is:
I = P * r * t
where I is the interest paid, P is the principal (the amount borrowed), r is the annual interest rate (as a decimal), and t is the time period in years.
We know that Ryan borrowed $200 and paid $48 in interest, and the interest rate is 6%. Plugging these values into the formula, we get:
48 = 200 * 0.06 * t
Solving for t, we get:
t = 48 / (200 * 0.06)
t = 4
Therefore, the loan was for 4 years.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
the two correct representations of the inequality are: x < 5
How to solve the inequalities?
To solve the inequality –3(2x – 5) < 5(2 – x), we need to simplify it first:
–6x + 15 < 10 – 5x
Now, we can move all the x terms to one side and the constant terms to the other side:
–6x + 5x < 10 – 15
–x < –5
Finally, we need to remember that whenever we multiply or divide an inequality by a negative number, we need to reverse the inequality sign. In this case, we multiplied both sides by –1, so we need to flip the sign:
x > 5
Therefore, the two correct representations of the inequality are:
x < 5 (not x > 5 as mentioned above)
–6x + 15 < 10 – 5x
Option 2, –6x – 5 < 10 – x, is not correct because it doesn't represent the inequality we simplified. The correct representation of the inequality on a number line would be an open circle at x=5 with a bold line pointing to the right, indicating that all the values to the right of 5 satisfy the inequality. The number line from –3 to 3 in increments of 1 with an open circle at negative 5 and a bold line pointing to the left does not represent the inequality we just solved.
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Find the formula for the exponential function in the form, y=a(b^x), that passes through the points (0,1500) and (1,2250).
The exponential function in the form y=a(bˣ) that passes through the points (0,1500) and (1,2250) is y = 1500(1.5ˣ).
What is a function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
We are given two points (0,1500) and (1,2250) through which the exponential function passes.
We can substitute these points into the formula y = a(bˣ) to get two equations:
When x=0, y=1500:
1500 = a(b⁰) = a
When x=1, y=2250:
2250 = a(b¹) = ab
We can solve for b by dividing the second equation by the first:
2250/1500 = ab/a
1.5 = b
Now we can substitute b=1.5 and a=1500 into the exponential function equation to get:
y = 1500(1.5ˣ)
Therefore, the exponential function in the form y=a(bˣ) that passes through the points (0,1500) and (1,2250) is y = 1500(1.5ˣ).
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Which function below has the following domain and range?
Domain: (-7,-5,2,6,7)
Range: (0,1,8)
The following functions, for instance, satisfy the given domain and range: (2, 0), (-5, 1), (7, 8), (6, 0), (-7, 8)
How are functions of domain and range determined?Since there are five points in the domain and three points in the range, there is no single function that has the necessary domain and range because there are more points in the domain than in the range.
A function is a collection of ordered pairs where each input belongs to the domain and each output belongs to the range. As a result, a function with the given domain and range must have five ordered pairs, each of which has a number from the domain and a number from the range as the second element.
The following functions, for instance, satisfy the given domain and range: (2, 0), (-5, 1), (7, 8), (6, 0), (-7, 8)
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Find the centroid of the region lying between the graphs of the functions f(x)=x^4
and f(x)=√x over the interval [0,1].
xCM=
yCM=
The centroid of the region is
x CM =1/2 and
y CM=5/12.
What is centroid?
In mathematics the centroid, can be described as geometric center or center of figure, of a plane figure or solid figure. It is the arithmetic mean position of all the points in the surface of the figure.
The centroid of the area is given by the function f(x).
Given that f(x)= x⁴ and f(x)=√x. Here we take the convention for the 2nd function as g(x). i.e. g(x)= √x.
Now the formula for centroid is given by:
x*= [tex]\frac{1}{A} \int\limits^a_b {x(f(x)-g(x))} \, dx[/tex] ---------(1)
and y*= [tex]\frac{1}{2A} \int\limits^a_b {(f(x)+g(x))(f(x)-g(x))} \, dx[/tex]------------(2)
where A= [tex]\int\limits^a_b {(f(x)-g(x))} \, dx[/tex]-------------(3)
Now f(x)-g(x)= x⁴ - √x
At first we will find the value of A.
A= ∫ (x⁴ - √x)dx
= ∫ x⁴ dx - ∫ √x dx
= x⁵/5 - (2/3) [tex]x^{3/2}[/tex]
Taking limit from 0 to 1 we get,
A= (1/5)-(2/3)
= -7/15
Now x*= -15/7 ∫ x( x⁴ - √x)dx [ putting the values in (1)]
=-15/7 [∫ x⁵ dx - ∫ x √x dx]
= -15/7 [ x⁶/6 - (2/5)[tex]x^{5/2}[/tex]]
Taking the limit from 0 to 1 we get,
x*= (-15/7)×(-7/30)
= 1/2
y*= -15/14∫(x⁴+√x)(x⁴-√x) dx [ putting the values in (2)]
= -15/14 ∫ (x⁸ - x)dx
= -15/14 [x⁹/9 - x²/2]
Taking limit from 0 to 1 we get,
y*= (-15/14)×(-7/18)
= 5/12
Hence the centroid is 1/2 and 5/12.
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Raymond has a circular garden with a radius of 9 feet. He wants to build a walkway that is 4 feet wide around the garden.
What will the area of the walkway be in square feet?
A. 16pi
B. 25pi
C. 81pi
D. 88pi
The solution of circle problem to find area of the walkway be in square feet is 88π square feet.
What is circle?A circle is a two-dimensional geometric shape that consists of all points in a plane that are equidistant from a single fixed point called the center.
According to given information:To find the area of the walkway, we need to subtract the area of the original circular garden from the area of the larger circle that includes the walkway. The radius of the larger circle will be 9 + 4 = 13 feet.
The area of the walkway will be:
Area of larger circle - Area of original circle
= π([tex]13^2[/tex]) - π([tex]9^2[/tex])
= π(169 - 81)
= π(88)
So the area of the walkway will be 88π square feet.
Therefore, the answer is D. 88π.
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Need help on this answer with explanation.
The line of reflection is across x and it's -4
What is line of reflection?A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.
Since the two images are kept away with a distance 2, from -5 to -3, this means the line of reflection will be between -5 and -3. The distance between the object and image should be equal.
Therefore, the line of reflection will be across x axis and on -4.
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Factor the polynomial, if possible. If the expression cannot be factored, enter the expression as is.
Answer:
Step-by-step explanation:
Here we have a quadratic polynomial which has a general form:
[tex]ax^2+bx+c[/tex] ;
A quadratic polynomial can be factored into product of two linear polynomials as: [tex](x-a_1)(x-a_2)=x^2-(a_1+a_2)x+a_1\times a_2[/tex] .
In our case [tex]a=1, b=-18, c=-175[/tex].
Which implies that [tex]a_1+a_2=18\ and \ a_1\times a_2=-175[/tex]. Now 25 times -7 is equal to -175 and sum of 25 and -7 is 18 which can perfectly fit our description so we can say that [tex]a_1=-7 \ a_2=25[/tex]. Hence we can factorize our equation as:
[tex](x+7)(x-25)=x^2-18x-175[/tex]
Really need help please. When u finish this one I need help with more
Answer:
Step-by-step explanation:
Similar triangles have the same shape but different sizes.
A is incorrect. We don't know the length of the sides, or if it is equilateral so we can't say that fg/lm=fh/ln
B is correct. FH and LN may be different sizes but they are similar
C is correct. Since the triangles are similar the angles are similar.
D is incorrect. The triangle is the same shape, not neccesarily the same size
E is correct. See C for explanation.
A well-known basketball coach has coached at the same university for 20 years. After what
seems like an infinite number of seasons, he finds that the mean number of points his teams score
is 72. One year he has an exceptionally tall team. The coach wants to know if the taller team
results in a greater number of points scored. Assume 72 to be the population mean with the
population variance unknown. The taller téam's scores are: '80, 88, 74, 82, 89, 90, 68, 95, 96, 72,
73 (it was a short season).
State the null and research hypotheses.
1) Report degrees of freedom (if applicable).:
2) Report the critical value using alpha= .05.:
3) Calculate the test statistics. :
4) In two or three sentences, briefly explain the results
(This includes your decision concerning the null hypothesis). :
Null hypothesis: The mean number of points scored by the taller team is not significantly different from the population mean of 72.
How did we determine the test statistic?Alternative hypothesis: The mean number of points scored by the taller team is significantly greater than the population mean of 72.
Since the population variance is unknown, we will use a t-test. The degrees of freedom for this test will be 9 (n-1), where n is the sample size of the taller team (10).
Using an alpha level of 0.05 and 9 degrees of freedom, the critical t-value is 1.833.
To calculate the test statistic, we first need to find the sample mean and standard deviation of the taller team's scores. The sample mean is 82, and the sample standard deviation is 9.89. Using these values, we can calculate the t-value:
t = (82-72) / (9.89 / sqrt(10)) = 3.19
Since the calculated t-value (3.19) is greater than the critical t-value (1.833), we reject the null hypothesis and conclude that there is a significant difference between the mean number of points scored by the taller team and the population mean of 72. The coach can therefore conclude that having a taller team does result in a greater number of points scored.
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Find the volume of this
The volume of the solid figure compromising of two rectangular prism is derived to be 152 cubic feet.
How to calculate the volume of a cuboidThe volume of a cuboid also known as a rectangular prism can be calculated using the formula:
V = l x w x h
where:
V is the volume of the cuboid
l is the length of the cuboid
w is the width of the cuboid
h is the height of the cuboid
We shall evaluate for the volume of two rectangular prism observed and thus derive the volume of the solid figure by the sum of our results as follows:
Volume of larger cuboid = 5 ft x 4 ft x 4 ft = 80 ft³
Volume of smaller cuboid = 6 ft x 4 ft x ft = 72 ft³
Volume of solid figure = 80 ft³ + 72 ft³ = 152 ft³
Therefore, the volume of the solid figure compromising of two rectangular prism is derived to be 152 cubic feet.
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gym offers multiple exercise classes per day. The number of people in an exercise class this week is represented in the list.
3, 6, 8, 7, 2, 4, 5, 10, 7, 14
What is the value of the mode for this data set?
14
8
7
3
7 is the mode of this dataset since, as we can see, it appears twice.
What is the mode?The most common occurrence of a number, or the one that does so most frequently.
Example: The mode of the digits 4, 2, 4, 3, and 2 is the number 2, which appears three times, more than any other number.
The mode computation is a rather straightforward procedure.
Calculate the frequency with which each number appears in the group after arranging the numbers in the set in any order—from lowest to highest or highest to lowest.
The most frequent mode is the one that appears.
So, we have the dataset:
3, 6, 8, 7, 2, 4, 5, 10, 7, 14
A number of terms repeated:
3 = 1
6 = 1
8 = 1
7 = 2
2 = 1
4 = 1
5 = 1
10 = 1
14 = 1
Since we can see that 7 is repeated twice then, 7 is the mode of this dataset.
Therefore, 7 is the mode of this dataset since, as we can see, it appears twice.
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Correct question:
The gym offers multiple exercise classes per day. The number of people in an exercise class this week is represented in the list.
3, 6, 8, 7, 2, 4, 5, 10, 7, 14
What is the value of the mode for this data set?
A. 14
B. 8
C. 7
D. 3
What is the perimeter of the shape ABCDEF ( each grind interval = one unit )
A - 20 units
B - 14 units
C - 16 units
D - 18 units
Answer:
[tex]\huge\boxed{\sf Perimeter = 18\ units}[/tex]
Step-by-step explanation:
Perimeter:Sum of all sides of a shape is known as the perimeter.Solution:Here, the shape is made up of grids measuring 1 unit.
Let's count grids on each side.
AB = 5 units
BC = 2 units
CD = 2 units
DE = 2 units
EF = 3 units
FA = 4 units
Now,
Perimeter = sum of all sides
Perimeter = 5 + 2 + 2 + 2 + 3 + 4
Perimeter = 18 units[tex]\rule[225]{225}{2}[/tex]
Please help help me to solve this
The function is not one-to-one.
Define one to one functionA one-to-one function, also known as an injective function, is a function where each element in the domain is uniquely mapped to a distinct element in the range. In other words, for every element in the domain, there exists only one corresponding element in the range, and no two elements in the domain can have the same image in the range.
To determine whether the given function is one-to-one, we need to check whether for any two distinct values of x, the function produces two distinct values of y.
We can rewrite the given function in the form:
y = 2(x + 1)² - 4
y = 2(x² + 2x + 1) - 4
y = 2x² + 4x - 2
To check whether the function is one-to-one, we can take two different values of x and check if the corresponding values of y are different.
Let's take x₁ = 1 and x₂ = 2.
When x = 1, y = 2(1 + 1)² - 4 = 8.
When x = 2, y = 2(2 + 1)² - 4 = 18.
Since y₁ = 8 and y₂= 18, and y₁ ≠ y₂, we can conclude that the function is not one-to-one.
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The number of widgets that a manufacturing plant can produce varies jointly as the number o
workers and the time that they have worked.
1) Find the constant of proportionality, k, to 2 decimal places if 640 workers work 11 hours and
produce 3993.6 widgets.
k
2) How many widgets (to the nearest tenth) can be produced by 650 workers in 27 hours?
Widgets =
Add Work
Calculator
Answer:
Step-by-step explanation:
I think that the answer is ................................................................................................................................................Your adopted
1/2+2/3×1/2
identify the learner's misconceptions analyse the answer
I think the answer is 5/6 ohohohohohohohohohohohoh
The measure of an angle is 72. What is the measure of its complementary angle?
The measure of the complementary angle of 72 degrees is 18 degrees
What is the measure of its complementary angle?The sum of complementary angles is 90 degrees.
So, to find the measure of the complementary angle of an angle that measures 72 degrees, we subtract 72 from 90:
Complementary angle = 90 - 72 = 18 degrees
Therefore, the measure of the complementary angle is 18 degrees.
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Help pls i do not understand this
Answer:
175 = 25 +4tcost of a ticket: $37.50Step-by-step explanation:
Given a total expense of $175 for 4 tickets and an included parking fee of $25, you want an equation for the cost of a ticket, and the solution to that equation.
EquationThe total cost is the sum of the items that contribute to that total. Here, the 175 total cost is the sum of 25 and the price of 4 tickets. If we let 't' represent the price of a ticket, we can describe this relation by ...
175 = 25 + 4t . . . . . . equation for the cost of a ticket
SolutionThis is a 2-step linear equation. The two steps to the solution are ...
Step 1: isolate the variable term by subtracting the constant
175 -25 = 25 -25 +4t
150 = 4t
Step 2: find the value of the variable by dividing by its coefficient
150/4 = 4t/4
37.50 = t
This tells us the cost of a ticket is $37.50.
__
Additional comment
"Write an equation that can be used ..." covers a lot of territory. It is simplest to interpret it to mean "describe the given relationships using one or more equations." You are expected to know how costs are added based on your life experience: the total you pay is the sum of the costs of the individual items.
We could write the equation as ...
t + t + t + t + 25 = 175
Some cashiers will add every item separately like this. Others will enter the price once and tell how many times that price is part of the total:
4t +25 = 175
Multiplication was invented for the purpose of simplifying repeated addition.
Need help! Please show step by step explanation:)
a. the equation of the least-squares line is: y = -0.003x + 3884.658
b. the estimated sales for a pizza chain having 4000 stores is 3754.658 million dollars.
c. the estimated number of stores for a pizza chain whose 2013 sales were 2000 million dollars is 295219.333.
How do we calculate?
We will use linear regression to obtain the least-squares line that fits the given data.
Let x be the number of stores and y be the sales in millions of dollars.
mean of x = (6326 + 4986 + 3890 + 3207)/4 = 4602.25
mean of y = (5700 + 3800 + 3025 + 2485)/4 = 3752.5
Σ((x - mean of x)(y - mean of y)) = (6326 - 4602.25)(5700 - 3752.5) + (4986 - 4602.25)(3800 - 3752.5) + (3890 - 4602.25)(3025 - 3752.5) + (3207 - 4602.25)(2485 - 3752.5) = -79470.75
calculating the sum of the squared deviations of x from its mean:
Σ((x - mean of x)^2) = (6326 - 4602.25)^2 + (4986 - 4602.25)^2 + (3890 - 4602.25)^2 + (3207 - 4602.25)^2 = 25994899.5
finding the slope of the least-squares line:
slope = Σ((x - mean of x)(y - mean of y)) / Σ((x - mean of x)^2) = -79470.75 / 25994899.5 ≈ -0.003056
y-intercept = mean of y - slope * mean of x ≈ 3884.658
equation of the least-squares line is: y = -0.003x + 3884.658
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PLEASE HELP, I don't understand this question.
Michael has recently opened a savings account. The banker gave him an equation to predict his balance at any given month, assuming he made no further deposits nor withdrawals. The equation is as follows: b=975(1.003)^m
where "b" is the balance of the account, and "m" represents the number of months the account has been open.
a) How much did Michael deposit when he first opened the account?
b) Is this a case of exponential growth or exponential decay? How do you know?
c) What is the monthly interest rate on the account?
d) What is the account balance after 6 months?
...after 12 months?
e) How many months will it take to have at least $1000 in the account?
Thank you in advance!
Jairo wants to replace the carpet in his office, shown in the diagram below. The carpet will cover the entire office floor.
How many square feet of carpet will Jairo need for his office?
A. 252 ft^2
B. 65 ft^2
C. 324 ft^2
D. 266 ft^2
A) 252 [tex]ft^2[/tex] of carpet will Jairo need for his trapezoid office.
What is area?
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Here the given trapezoid , Base a = 10ft , Base b= 18ft and Height h = 18ft.
Now using area of trapezoid formula then,
=> Area A = [tex]\frac{a+b}{2}\times h[/tex] square unit.
=> A = [tex]\frac{10+18}{2}\times 18[/tex]
=> A = [tex]\frac{28}{2}\times 18[/tex]
=> A = [tex]14\times18[/tex]
=> A = 252 [tex]ft^2[/tex]
Hence A) 252 [tex]ft^2[/tex] of carpet will Jairo need for his office.
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Solve for x using the picture below.
Answer:
X+5
Step-by-step explanation:
you carry 5 to be corresponding to x
and angles on a straight line add
Answer:
x = 7.5
Step-by-step explanation:
Because the two quadrilaterals formed by the two parallel lines are similar, [tex]\frac{4}{6} =\frac{5}{x}[/tex]
Using cross multiplication, [tex]x = \frac{6*5}{4}[/tex]
Thus, x = [tex]\frac{15}{2}[/tex] = 7.5.
A circle inside a square has a side length of 16 ft
Answer:
[tex]4\pi[/tex]
Step-by-step explanation:
the side of the square equals the diameter of the circle inscribed.
So side of the square a is 4! (a^2=16, a=4)
So the radius of the circle is 2!
The area of the circle is 4π!!!!! (πa^2)
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h. A. h(8) = 21 B. h(-3) = -1 C. h(13) = 18 D. h(2) = 16
None of the statements A, B, C, or D can be true for function h. This is because the domain of h is from -3 to 11, which means that the function only exists for x values between -3 and 11.
What is domain?The domain of a function is the set of all possible values of the independent variable or input for which the function is defined. It is the set of values over which the function is defined and takes real values. In simpler terms, it is the set of all possible x-values for which the function is defined.
In the given question,
None of the statements A, B, C, or D can be true for function h. This is because the domain of h is from -3 to 11, which means that the function only exists for x values between -3 and 11. Statement A refers to h(8) = 21, which is not consistent with the given value of h(8) = 19. Statement B refers to h(-3), which is not a valid value since the domain starts at -3. Statement C refers to h(13), which is also not a valid value since the domain ends at 11. Finally, statement D refers to h(2), which is not within the given domain.
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how many 3-digit numbers can be formed using the digits 2,3 and 4 without repetition? with repetition?
please help
The 27 possible 3-digit numbers with repetition are: 222, 223, 224, 232, 233, 234, 242, 243, 244, 322, 323, 324, 332, 333, 334, 342, 343, 344, 422, 423, 424, 432, 433, 434, 442, 443, and 444.
What is repetition?The use of the same element repeatedly in a combination or permutation is referred to as repetition. You can use any of the numbers (1, 2, or 3) more than once to construct a 3-digit number, for instance, if you are asked to pick a 3-digit number using the digits 1, 2, and 3, with repetition permitted.
Without repetition, we can choose the first digit in 3 ways, the second digit in 2 ways (since we cannot repeat the first digit), and the third digit in 1 way (since we cannot repeat the first or second digit). This gives a total of 3 x 2 x 1 = 6 possible 3-digit numbers.
The 6 possible 3-digit numbers without repetition are: 234, 243, 324, 342, 423, and 432.
With repetition, we can choose each of the three digits in 3 ways (since we can repeat any of the three digits). This gives a total of 3 x 3 x 3 = 27 possible 3-digit numbers.
The 27 possible 3-digit numbers with repetition are: 222, 223, 224, 232, 233, 234, 242, 243, 244, 322, 323, 324, 332, 333, 334, 342, 343, 344, 422, 423, 424, 432, 433, 434, 442, 443, and 444.
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