The function is solved and f(x) represents the total number of hours; x represents the number of weeks he exercises this summer
Given data ,
Luke is keeping track of the total number of hours he exercises. He started the summer having already put in 15 hours, and he then exercises 7 hours each week.
So , the function is given by
The function to keep track of his exercise is f(x) = 7x + 15
On simplifying the equation , we get
f(x) represents the total number of hours; x represents the number of weeks he exercises this summer
Hence , the function is f(x) = 7x + 15
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Suppose we want to choose 6 letters, without replacement, from 14 distinct letters. If the order of the choices is taken into consideration, how many ways can this be done?
As per the combination method, there are 2,162,880 ways to choose 6 letters from 14 distinct letters, taking into account the order of the choices.
Since we are choosing 6 letters from 14 distinct letters, the number of ways to do this without taking into account the order is given by the combination formula:
C(14, 6) = 3003.
However, since we are also taking into account the order of the choices, we need to multiply the number of choices by the number of ways to arrange those choices.
The number of ways to arrange 6 letters is given by 6!, which represents the number of permutations of 6 objects.
Therefore, the total number of ways to choose 6 letters, with order taken into account, is given by the product of the number of combinations and the number of permutations:
C(14, 6) x 6! = 3003 x 720 = 2,162,880.
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PLEASE ANSWER I NEED HELP WILL MARK BRAINLIST!!!!!
f(x) = x² and g(x) = 3(x + 1)² have the same minimum y-value and axis of symmetry, but they have different y-values at x = -2.
We have the function:
f(x) = x² and g(x) = 3(x + 1)² are both quadratic functions.
1. Minimum y-value:
For f(x) = x², the minimum y-value occurs at the vertex of the parabola, which is at (0, 0). The minimum y-value is 0.
For g(x) = 3(x + 1)², the minimum y-value occurs at the vertex of the parabola, which is at (-1, 0). The minimum y-value is also 0.
Therefore, both functions have the same minimum y-value.
2. Axis of symmetry:
For f(x) = x², the axis of symmetry is the vertical line that passes through the vertex of the parabola, which is x = 0.
For g(x) = 3(x + 1)², the axis of symmetry is also the vertical line that passes through the vertex of the parabola, which is x = -1.
Therefore, both functions have different equations but share the same axis of symmetry.
3. Y-value at x = -2:
For f(x) = x², the y-value at x = -2 is f(-2) = (-2)² = 4.
For g(x) = 3(x + 1)², the y-value at x = -2 is g(-2) = 3(-2 + 1)² = 3.
Therefore, the two functions have different y-values at x = -2.
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what is a sales discount
Answer: A sales discount is a reduced price offered by a business on a product or service.
Step-by-step explanation:
Answer:
when the original selling price of a product does down. You'll be getting the same product at a lower price
Step-by-step explanation:
you can calculate the discount % by
NEW PRICE MULTIPLIED BY 100 DIVIDED BY OLD PRICE
The area of a square garden is the same as the area of a rectangular garden that is 8 ft long and 2 ft wide. Write and solve an equation to find the side length of the square garden. Show your work.
The side length of the square garden is 4 feet if the area of a square garden is the same as the area of a rectangular garden that is 8 ft long and 2 ft wide.
Length of the rectangular garden = 8 ft
Width of the rectangular garden = 2 ft
Area of rectangular garden = length x width
Area of rectangle = 8 ft x 2 ft
Area of rectangular garden = 16 square feet
It is given that the area of the square garden is the same as the area of the rectangular garden. The area of the square garden is calculated as:
Area of square garden = side length x side length
Area of square garden = side length x side length = 16
To solve the equation, we need to make isolate it on one side of the equation.
Taking root on both sides:
[tex]\sqrt{(side length * side length)}[/tex] = [tex]\sqrt{16}[/tex]
side length = ± [tex]\sqrt{16}[/tex]
We need to take the positive root value:
side length = [tex]\sqrt{16}[/tex]
side length = 4 ft
Therefore, we can conclude that the side length of the square garden is 4 feet.
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What is the range of this function?
74
A.
B.
O C.
all real numbers where 2 + n
all real numbers where
+ nn
(-∞0, ∞0)
21
Answer:
[tex](- \infty, \infty)[/tex]
Third answer choice
Step-by-step explanation:
This is the graph of the function f(x) = tan(x)
We can see that the minimum value of f(x) tends to - ∞ and the maximum value tends to + ∞
So the range of f(x) is [tex](- \infty, \infty)[/tex]
This is the third answer choice (the one that is highlighted in orange)
Which parent function is represented by the graph?
-10
10
-10
A. Quadratic parent function
B. An exponential parent function
O C. Absolute value parent function
OD. Linear parent function
10
SUBM
The requried function represents an absolute value parent function.
A graph is shown,
When we see at the points on the curve,
On x = -10 we have y = 10
simultaneously,
On x = 10 again we have y = 10
This implies that the function is an absolute value parent function.
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What is the inverse of the following statement?
"If the corresponding angles are congruent, then the lines are parallel."
If the corresponding angles are not congruent, then the lines are not parallel.
If the lines are parallel, then the corresponding angles are congruent.
If the lines are not parallel, then the corresponding angles are not congruent.
If the corresponding angles are congruent, then the lines must be parallel.
The true statement is that proves the congruence of both triangles is:
∠ABC ≅ ∠DCB;
alternate interior angles of parallel lines are congruent.
Here, we have
to prove that angles are congruent
From the complete question, we have the following highlights
Angles B and C are alternate interior angles
The triangles are bounded by parallel lines
The above highlights mean that:
Angles ABC and DCB are congruent, by the theorem of alternate interior angles of parallel lines
Hence, the true statement is (c)
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complete question:
Isabelle proves that the triangles are congruent by using the parallel lines to determine a second set of angles are congruent. What statement and reason could she have used? ∠ABC ≅ ∠BAC; corresponding angles of parallel lines are congruent. ∠CAB ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ACD ≅ ∠ABD; corresponding angles of parallel lines are congruent.
Enter the exact values of the trigonometric ratios in the boxes.
sin 45°
cos 30
tan 60
=
The required value of trigonometric ratios is,
sin 45° = 1/[tex]\sqrt{2}[/tex]
cos 30 = [tex]\sqrt{3}[/tex]/2
tan 60 = 1/ √3
We know that,
Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Therefore,
sin 45° = 1/[tex]\sqrt{2}[/tex]
cos 30 = [tex]\sqrt{3}[/tex]/2
tan 60 = 1/ √3
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f(x)=x^2-10x+1 in the form a(x-h)^2+k
Answer:
[tex]\displaystyle{f(x)=(x-5)^2-24}[/tex]
Step-by-step explanation:
Given the function:
[tex]\displaystyle{f(x)=x^2-10x+1}[/tex]
Separate 1 out of the terms:
[tex]\displaystyle{f(x)=(x^2-10x)+1}[/tex]
Convert parentheses-terms to perfect square:
[tex]\displaystyle{f(x)=(x^2-10x+25)+1-25}[/tex]
Evaluate and/or simplify:
[tex]\displaystyle{f(x)=(x-5)^2-24}[/tex]
What is the square root of 64 in exponential notation
Answer: 64 1/2
Step-by-step explanation:
Answer:
2³
Step-by-step explanation:
Square root of 64 = 8
exponential notation = 2×2×2 = 2³
if you answer it i will give you 100 points and brainlist
The correct expression that shows the slope of the line that passes through (3, 6) and (-7, -4) is -4 - 6 / -7 - 3.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
Therefore, the slope of a line is the change in y variable with respect to the change in x variable.
Hence,
m = slope = y₂ - y₁ / x₂ - x₁
Therefore, the line passes through (3, 6) and (-7, -4).
where
x₁ = 3
x₂ = -7
y₁ = 6
y₂ = -4
Therefore, the expression is -4 - 6 / -7 - 3.
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A preformed piece of coal weighs 100 g correct to the nearest 5 g. A bag contains 30 pieces of preformed coal. Complete the sticker to attach to this bag of coal. (4 marks) This bag of coal weighs at least This bag of coal weighs at least kg kg
This coal bag has a minimum weight of 2.925 kilograms.
To find the minimum weight of the bag of coalWe must determine the coal's minimum weight, which is 30 pieces.
One piece of coal weighs 100 g, accurate to the closest 5 g. As a result, the actual weight of a piece of coal may range between 97.5 g to 102.5 g.
We can multiply the minimum weight of one piece of coal (97.5 g) by 30 to determine the minimum weight of 30 pieces of coal:
Minimum weight of 30 pieces of coal = 97.5 g x 30 = 2925 g
Therefore, The sticker can be finished as follows:
This coal bag has a minimum weight of 2.925 kilograms.
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Find the mean of the data set: {8, 10, 12, 15, 15, 18, 19, 20, 23, 27} Give the exact answer.
The mean of the data set is 16.7.
To find the mean of a data set, you add up all the values and divide by the number of values.
Adding up all the values, we get:
8 + 10 + 12 + 15 + 15 + 18 + 19 + 20 + 23 + 27 = 167
There are 10 values in the set, so we divide the sum by 10 to get the mean:
Mean = 167/10 = 16.7
Therefore, the mean of the data set is 16.7.
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Ira’s Craft and Hobby Shoppe sells the items shown below. (AKA the image that I put) London has $7.00. She buys one of each item. How much money does she have left?
A. $4.90
B. $4.10
C. $3.10
D $2.10
Answer:
A. $4.90
Step-by-step explanation:
A $5000 investment pays 3% interest compounded monthly. To the nearest cent, what will be the value of the investment after 10 years?
Answer:
We can use the formula for compound interest to solve this problem. The formula is:
A = P * (1 + r/n)^(n*t)
where:
A = the amount of money after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $5000, r = 0.03, n = 12 (since the interest is compounded monthly), and t = 10. Plugging these values into the formula, we get:
A = 5000 * (1 + 0.03/12)^(12*10)
A = 5000 * (1.0025)^120
A ≈ $6,621.36
So the investment will be worth approximately $6,621.36 after 10 years.
Faith only read 60% of her goal for 1 week. How would the mean, median, and mode have changed if Faith had met her goal? Explain.
If Faith had met her goal, the mean would have increased from 60 to 100, the median would have remained the same at 60, and the mode would have changed from 60 to 100.
If Faith had met her goal, the mean, median, and mode would have changed. Let's assume her goal for the week was to read 100 pages.
Faith read only 60% of her goal, which is equivalent to 60 pages
(100 pages × 0.6).
If she had met her goal, she would have read 100 pages in total.
The mean would have changed from 60 pages to 100 pages.
Since we only have one data point (60), the median would have remained the same at 60.
The mode would be 60 since that is the only value we have.
If Faith had met her goal, the mode would have changed to 100, as 100 pages would appear most frequently.
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Jake spent $55 this week. He spent 10% more this week than last week. How much did he spend last week?
Hi can someone who is great at math please help me with these math questions. I'm struggling with them!!
The value of x will be 18.67 for the given data of the triangle.
We have,
Thale's theorem:
When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.
Given that the sides of the triangle are divided into two parts,
For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.
The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-
x / ( x + 7 ) = 16 / 22
22x = 16x + 112
6x = 112
x = 112 / 6
x = 18.67
Therefore, the value of x will be 18.67.
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complete question;
Find the values of x and y. Find value of x.
Can someone help me with this problem please
Suppose M is a matrix of size 9x10, c is a scalar, and the matrix computation cM is defined. What is the size of matrix cM?
When a scalar quantities is multiplied by a matrix of size 9x10, the resulting matrix will also be of size 9x10.
If we perform the matrix computation cM, where c is a scalar and M is a matrix of size 9x10, the resulting matrix cM will also be of size 9x10.
This is because when we multiply a scalar by a matrix, each element in the matrix is multiplied by the scalar.
Therefore, the resulting matrix has the same dimensions as the original matrix.
To see why this is the case, consider a single element in the resulting matrix cM. Let's say the element is located at row i and column j.
Then, it is given by cM[i,j] = c*M[i,j]. Since M[i,j] is just a single element in the original matrix, multiplying it by the scalar c produces a new scalar.
Therefore, cM[i,j] is also a single element in the resulting matrix cM.
Since each element in the original matrix M is multiplied by the scalar c, the resulting matrix cM will have the same dimensions as the original matrix, i.e., 9x10.
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A flat-screen television has a diagonal length of 40 inches. The length of the screen is 175% of its height. What is the length, in inches, of the screen?
The length of the flat-screen television is approximately 40.01 inches.
Let's assume that the height of the flat-screen television is "h" inches.
From the problem statement, we know that the length of the screen is 175% of its height.
Mathematically, we can write:
Length = 1.75 x Height
We can substitute the value of "h" in this equation to find the length of the screen:
Length = 1.75 x h
Now, we also know that the diagonal length of the screen is 40 inches. Using the Pythagorean, we can write:
(Length)² + (Height)² = (Diagonal)²
Substituting the values we have, we get:
(1.75h)² + h² = (40)²
Expanding and simplifying:
3.0625h² = 1600
Dividing both sides by 3.0625:
h² = 522.24
Taking the square root of both sides (and ignoring the negative root since we're dealing with lengths):
h = 22.86 inches
Now we can use the equation we derived earlier to find the length:
Length = 1.75 x h
Length = 1.75 x 22.86
Length = 40.01 inches (rounded to two decimal places)
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*WILL GIVE BRAINLIEST*
Unit 5 circles unit test
What is mST?
i didnt get what you need but i assume you want the angle so it will be 360-130-80-70 = 80⁰
A human hair was measured to be 8.0•10-4 inch thick. A cat hair is measured to be 4.0•10^-1. How much greater is the thickness of the cat hair than the human hair? Writ this in standard form.
Whoever gets this right I will mark brainiest and 60 points!!
Answer:
500 times
Step-by-step explanation:
Divide the thickness of a cat hair by the thickness of a human hair.
4.0 × 10^-1 / 8.0 × 10^-4 =
= 0.5 × 10^3
= 500
500 times
The product of two numbers is 155952. If one number is 342, find the other
number.
Answer:
456
Step-by-step explanation:
Product means an answer derived from multiplication. Therefore, if the product is 155952, and one value is 342, then the following equation is true:
342x = 155952, or 342 * x = 155952
Divide 155952 by 342 to get: 456.
Check the work in the equation:
342(456) = 155952
155952 = 155952, which is true, so the answer is 456.
If I helped, please make this answer brainliest! ;)
PLEASE HELP ME ANSWER (b) REFER TO PICTURE
The standard deviation of the sampling distribution of p is 0.028284
How to calculate the standard deviationThe mean of the sampling distribution of p can be found using the formula:
μp = p = 0.2
The standard deviation of the sampling distribution of p can be found using the formula.
Plugging in the given values, we get:
σp = ✓[(0.2*(1-0.2))/200 * (25000-200)/(25000-1)]
= ✓[(0.16/200) * (24800/24999)]
= ✓[0.0008 * 0.99204]
= ✓(0.0007936)
= 0.028284
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Which of the following shows that the decimal expansion of 12/44 eventually repeats? What did you do to solve for the answer?
Answer:
answer A
Step-by-step explanation:
since 12/44 = 0.2727272727
Yavonne has $15.90 in her checking account. She needs to buy items that cost $3.18 each. How many of these items can she buy?
a
4
b
5
c
6
d
7
Answer:
5.
Step-by-step explanation:
15.90 / 3.18 =
A group of workers painted a house. They used 1 1/2 gallons of paint per hour and painted
for 3 1/4 hours.
How many gallons of paint did the workers use?
Answer:
4,875 gallons.
Step-by-step explanation:
1.5 gallons/hour
1.5 / 4 = 0.375 gallons/25mins
1.5 * 3 (hours) + 0.375 = 4.875 gallons
What is the sum, in degrees, of the interior angles of a regular icosagon
Please help me show work
Answer:
Part A: 13440ft³
Part B: 2940ft³
Step-by-step explanation:
box volume:
20 x 28 = 560
560 x 24 = 13440ft³
Subtract gift volume:
13440 - 10500 = 2940ft³
Three thousand tickets are sold for $5 each. There is a $500
prize, a $250 prize, a $125 prize and a $50 prize. What is the
expected value for a person that buys a ticket? Round to the
nearest cent.
Step-by-step explanation:
The total amount of money collected from the ticket sales is:
$5/ticket x 3000 tickets = $15,000
The expected value for a person that buys a ticket can be calculated by adding up the probabilities of winning each prize multiplied by the amount of money for each prize:
E(X) = (1/3000) x $500 + (1/3000) x $250 + (1/3000) x $125 + (1/3000) x $50 - (2996/3000) x $5
Simplifying this expression:
E(X) = $0.1666667 + $0.0833333 + $0.0416667 + $0.0166667 - $4.9833333
E(X) = -$4.65
Therefore, the expected value for a person that buys a ticket is -$4.65, which means that on average, a person can expect to lose $4.65 for every ticket they buy.
Answer: $0.31
Step-by-step explanation:
1/3000 tickets will be worth $500.
1/3000 tickets will be worth $250.
1/3000 tickets will be worth $125.
1/3000 tickets will be worth $50.
The remaining 2996/3000 tickets will be worth $0. (Nobody else wins.)
So (1/3000)x500 + (1/3000)x250 + (1/3000)x125 + (1/3000)x50 + (2996/3000)x0 = $0.31.
Please note: This question asks for expected value. Expected value is a measure of what you should expect to get per game. The payoff of a game is the expected value of the game minus the cost.
