The number of ways to choose the letters is given as follows:
Order matters: 6 ways.Order does not matter: 3 ways.How to obtain the number of ways to choose the letters?First we must decide which formula to use, depending if the order matters, as follows:
Order matters: permutation formula.Order does not matter: combination formula.The number of possible permutations of x elements from a set of n elements is given by:
[tex]P(n,x) = \frac{n!}{(n-x)!}[/tex]
Hence, if the order matters, the number of ways is given as follows:
P(3,2) = 3!/(3 - 2)! = 6.
The combination formula is given as follows:
[tex]C(n,x) = \frac{n!}x!{(n-x)!}[/tex]
Hence, if the order does not matter, the number of ways is given as follows:
C(3,2) = 3!/(2! x 1!) = 3.
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What is the area of this figure? 4 ft 13 ft 4 ft 4 ft 13 ft 9 ft 8 ft 4 ft 24 ft 7 ft 5 ft 15 ft Write your answer using decimals, if necessary.
The area of the figure is 183.5 ft².
We have,
The figure has two types of shapes.
Two rectangles and one triangle.
Now,
Area of rectangle = Length x Width
Area of triangle = 1/2 x base x height
Now,
Rectangle 1:
Area = 7 x 5 = 35 ft²
Rectangle 2:
Area = 4 x (4 + 5) = 4 x 9 = 36 ft²
Triangle:
Area = 1/2 x (11 + 4) x 15 = 1/2 x 15 x 15 = 112.5 ft²
Now,
The area of the figure.
= 35 + 36 + 112.5
= 183.5 ft²
Thus,
The area of the figure is 183.5 ft².
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If the relationship is proportional, what is the missing value from the table? x y –3 9 –5 ? –7 21 –18 –15 15 18If the relationship is proportional, what is the missing value from the table? x y –3 9 –5 ? –7 21 –18 –15 15 18
If two variables are directly proportional, this means that the ratio of the two variables is constant. In other words, if x and y are directly proportional, then there exists some constant k such that:
y = kx
To find the missing value in the table, we can first calculate the value of k using any set of corresponding values for x and y. For example, we can use the first row of the table:
y = kx 9 = k(-3) k = -3
Now that we know k, we can use it to find the missing value for the second row:
y = kx y = (-3)(-5) y = 15
Therefore, the missing value in the table is 15.
At the end of the week, a paper company in Scranton, PA, determines whether they broke even, made a profit, or made a loss. The likelihood of making a profit is 0.75, whereas the probability of breaking even is 0.21. What is the likelihood that for two consecutive weeks, the company makes a profit and then makes a loss? A. 0.32 B. 0.06 C. 0.03 D. 0.16
The likelihood of profit and loss in the following week is 18.75%. The Option D is correct.
What is the probability?A probability means the branch of math which deals with finding out the likelihood of the occurrence of an event. Its measures the chance of an event happening.
To get probability of the company making a profit and then making a loss in two consecutive weeks, we need to multiply the probabilities of each event occurring.
The probability of making a profit in one week is 0.75
The probability of making a loss in the following week will be:
= 1 - 0.75
= 0.25.
So, probability of the company making a profit in one week and then making a loss in the following week is:
= 0.75 * 0.25
= 0.1875
= 18.75%.
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in how many different ways can 7 floats line up for the homecoming parade
Step-by-step explanation:
7! = 7 P 7 = 5040 ways
7 choices for first
6 choices for 2nd
5 choices for 3rd
4 chouces for 4th
3
2
1
7 x 6 x 5 x 4 x 3 x 2 x 1 = 7!
Find the direction angle of w = 8j
Round your answer to the nearest tenth of a degree
Rounding to the nearest tenth of a degree, the direction angle of w = 8j is 90.0 degrees.
To find the direction angle of a vector, we can use the formula:
θ = arctan(y/x)
In this case, the vector w is given as w = 0 + 8j, which means its x-component is 0 and its y-component is 8.
Plugging the values into the formula, we get:
θ = arctan(8/0)
However, the division by zero is undefined, indicating that the x-component of the vector is zero, and thus the vector lies along the y-axis.
When a vector lies along the y-axis, its direction angle is either 90 degrees or -90 degrees.
In this case, since the vector is pointing upwards (in the positive y-direction), the direction angle is 90 degrees.
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The coordinates of point A' are (4,1) in the given rectangle.
According to the shown figure, the coordinate of the given rectangle can be written as:
The coordinates of vertice A are (4, 3)
As we know that the x-coordinate of the reflected point will be the same as the x-coordinate of the original point.
Therefore, the x-coordinate of point A' will be:
x-coordinate of A' = 4
Here, the y-coordinate of point A is 3, which is 1 unit above the line y = 2. So, the reflection of point A across the line y = 2 will be 1 unit below the line y = 2.
So, the y-coordinate of point A' will be:
y-coordinate of A' = 2 - 1 = 1
Therefore, the coordinates of point A' are (4,1).
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There are 8 strawberry plants in each row. Each plant has 11 strawberries on it. What equation could you use to find how many strawberries there are in 7 rows?
8 + 11 x 7 = ___
8 x 11 + 7 = ___
8 x 11 x 7 = ___
8 x 11 ÷ 7 = ___
help asap and brainliest!!!!!!!!!!!!!!!!!!!!!!!!
The box plots display data collected when two teachers asked their classes how many sheets of paper they used in a week.
A box plot uses a number line from 5 to 49 with tick marks every one unit. The box extends from 8 to 12 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Howard's Class, and the line is labeled Sheets Of Paper.
A box plot uses a number line from 2 to 52 with tick marks every one unit. The box extends from 8 to 25 on the number line. A line in the box is at 16. The lines outside the box end at 5 and 50. The graph is titled Mrs. Potter's Class, and the line is labeled Sheets Of Paper.
Which class used the most paper overall based on the data displayed?
Mrs. Potter's class; it has a larger median value of 16 pieces of paper
Mr. Howard's class; it has a larger median of 11 pieces of paper
Mrs. Potter's class; it has a narrow spread in the data
Mr. Howard's class; it has a wide spread in the data
The spread of the data is not relevant to determining which class used the most paper overall.
Mrs. Potter's class used the most paper overall based on the data displayed because it has a larger median value of 16 pieces of paper. The median value of Mr. Howard's class is 11 pieces of paper.
The spread of the data is not relevant to determining which class used the most paper overall.
Therefore, the correct answer is Mrs. Potter's class; it has a larger median value of 16 pieces of paper.
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You take out a 45-day loan for $2600. At the end of the loan, you owe $70.52 in interest. What is the annual percentage rate? Round your answer to the nearest tenth of a percent.
Expand each logarithm.
1. Log 2^8XYZ
2. Log 9^8lx/y
3. Log 5^5x^3
4. Log 6 3√x
The logarithmic expressions when expanded are
1. [tex]\log2^{8yz}[/tex] = 8xyz log(2)
2. [tex]\log9^{81x/y}[/tex] = 81x/y log(9)
3. [tex]\log5^{x^3}[/tex] = x³ log(5)
4. [tex]\log6^{\sqrt[3]{x}}[/tex] = ∛x log(6)
How to expand the logarithmic expressionFrom the question, we have the following parameters that can be used in our computation:
The logarithmic expressions
The logarithmic expressions can be expanded using power rule of logarithm which states that
logaᵇ = b log(a)
Using the above as a guide, we have the following:
[tex]\log2^{8yz}[/tex] = 8xyz log(2)
[tex]\log9^{81x/y}[/tex] = 81x/y log(9)
[tex]\log5^{x^3}[/tex] = x³ log(5)
[tex]\log6^{\sqrt[3]{x}}[/tex] = ∛x log(6)
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Find the solution of the exponential equation
5^-x/16=5
in terms of logarithms, or correct to four decimal places.
x= ------------
here is the picture if you need to see it more clear.
The solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex] in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.
An exponential function is a mathematical function in the form of [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is a variable. The value of the function at a particular value of "x" is found by raising "a" to the power of "x". Exponential functions are characterized by their rapid growth or decay.
We can solve for x by taking the logarithm of both sides with base 5:
[tex]5^{(\frac{-x}{16})} = 5[/tex]
[tex]log_5(5^{(\frac{-x}{16}))} = log_5(5)[/tex]
(-x/16)log₅(5) = 1
-x/16 = 1/log₅(5)
x = -16/log₅(5)
Using a calculator, we get:
x ≈ -4.4431
Therefore, the solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex] in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.
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What is the square root of 25*25*64*221?
Adam wants to plant flowers in a triangular plot. He has three lengths of plastic edging that measures 8 feet, 15 feet, and 17 feet. Determine whether these pieces fit for a right triangle. Explain.
Using the Pythagorean triple formula the numbers 8, 15 and 17 are Pythagorean triple and as such will form a right-angle triangle.
What is Pythagorean triple?Pythagorean triples are x² = y² + z² where x, y and z are the three positive integers. These triples are represented as (x, y, z). Here, y is the perpendicular, z is the base and x is the hypotenuse of the right-angled triangle.
In this problem, to determine if the given numbers will form a right-angle triangle, we have to check if the numbers are Pythagorean triple.
In doing so, we would use the previous formula given as;
x² = y² + z²
In a Pythagorean triple, the largest side is the hypothenuse.
17² = 8² + 15²
289 = 64 + 225
289 = 289
The numbers are equal and they're Pythagorean triple.
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tamikas math teachers plots student grades on their weekly quizzes against the number of hours yhe say they study on the pair of coordinate axes and then draws the lines of best fits. what is the meaning of the x-value on the line when y = 100
The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.
We have,
Assuming that the line of best fit represents the trend between the number of hours students study and their quiz grades,
The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.
In other words,
If a student studies for this amount of time, they are predicted to achieve a quiz score of 100 based on the trend shown by the line of best fit.
Thus,
The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.
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If trapezoid JKLM is translated using the rule (x, y) → (x + 3, y − 3) and then translated using the rule (x, y) → (x − 1, y + 1) to create trapezoid J″K″L″M″, what is the location of L″?
The location of L″ is (-5, 0).
To find the location of L″, we first need to apply the first translation rule to the coordinates of trapezoid JKLM:
J': (x, y) → (x + 3, y - 3) => J'(-2+3, 1-3) = J(1, -2)
K': (x, y) → (x + 3, y - 3) => K'(1+3, 1-3) = K(4, -2)
L': (x, y) → (x + 3, y - 3) => L'(3+3, -2-3) = L(6, -5)
M': (x, y) → (x + 3, y - 3) => M'(-4+3, 2-3) = M(-1, -1)
Now, we need to apply the second translation rule to the coordinates of J', K', L', and M':
J'': (x, y) → (x - 1, y + 1) => J''(1-1, -2+1) = J''(0, -1)
K'': (x, y) → (x - 1, y + 1) => K''(4-1, -2+1) = K''(3, -1)
L'': (x, y) → (x - 1, y + 1) => L''(6-1, -5+1) = L''(5, -4)
M'': (x, y) → (x - 1, y + 1) => M''(-1-1, -1+1) = M''(-2, 0)
Therefore, the location of L″ is (-5, 0).
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Answer:
(5,-4)
Step-by-step explanation:
How to right 0.76 in standard decimal form math
Answer:
3/4
Step-by-step explanation:
(75 divided by 25 / 100 divided by 25) = 3/4
Simplify:
-$4500 + $3000 + (-$800)
what is the addictive inverse of 36
Answer:
Step-by-step explanation: -36
Mr. Beachy's grade distribution over the past 3 years in Algebra 1 class is shown in the table below. Answer the following questions based on this table in simplest fraction form.
Grade # Students
A
41
B
183
C
265
D
96
F
85
Incomplete
2
How many total students are there?
If Sharon plans on taking Algebra 1 with Mr. Beachy, what is the empirical probability that she will receive an A?
If Cody plans on taking Algebra 1 with Mr. Beachy, what is the empirical probability that he will receive a B?
a.) The number of students that took the Algebra 1 for the whole three years = 672
b.) The empirical probability that Sharon will receive an A would be =0.061
How to calculate the number of students that took the Algebra 1?For question a.)
To calculate the total number of students that took the Algebra 1 for the 3 years, the students that got the various grades are being added up. That is;
Grade A= 41
Grade B =183
Grade C =265
Grade D =96
Grade F =85
Incomplete = 2
Total = 41+183+265+96+85+2 = 672
For b.)
The probability = possible outcome/sample space
possible outcome = 41/672=0.061
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How do I show a example of using tomato sauce and spaghetti as a ratio? I have to make a math problem with it and show calculations on how I did it. Any advices?
Answer:
Step-by-step explanation:
Sure! Here's an example of using tomato sauce and spaghetti as a ratio in a math problem:
Problem: Jane is making spaghetti and tomato sauce for dinner. She wants to mix the tomato sauce and spaghetti in a ratio of 1:4. If she uses 2 cups of tomato sauce, how many cups of spaghetti should she use?
Solution:
To solve this problem, we can set up a proportion using the given ratio:
Tomato sauce : Spaghetti = 1 : 4
Let's assign the variable 'x' to represent the number of cups of spaghetti.
Therefore, the proportion becomes: 1/4 = 2/x
To solve for 'x', we can cross-multiply and solve for 'x':
1 * x = 4 * 2
x = 8
Therefore, Jane should use 8 cups of spaghetti to maintain a ratio of 1:4 with 2 cups of tomato sauce.
You can include these calculations and steps to show how you arrived at the answer.
Step-by-step explanation: Here's an example of using tomato sauce and spaghetti as a ratio in a math problem:
Problem: Jannay has tomato sauce and spaghetti in a ratio of 1:4. If she uses 2 cups of tomato sauce, how many cups of spaghetti should she use?
Solution:
To solve this problem,
Tomato sauce : Spaghetti = 1 : 4
Assign the variable 'x' to represent the number of cups of spaghetti.
The proportion becomes: 1/4 = 2/x
To solve for 'x', cross-multiply and solve for 'x':
1 * x = 4 * 2
x = 8
Therefore, Jannay should use 8 cups of spaghetti to maintain a ratio of 1:4 with 2 cups of tomato sauce.
Need help in this question please
a. The values of k for which points A, B, and C are collinear are k = 3 and k = -2.
b. The value of k for which AB is parallel to CD is k = 13.
How to calculate the valuea. slope AB = (k+4-9)/(k+1-0) = (k-5)/(k+1)
The slope of AC is:
slope AC = (k+3-9)/(2k-0) = (k-6)/(2k)
Since A, B, and C are collinear, slope AB = slope AC. Therefore, we have:
(k-5)/(k+1) = (k-6)/(2k)
2k(k-5) = (k+1)(k-6)
2k^2 - 10k = k² - 5k - 6
k = 3 or k = -2
(b) The slope of AB is:
= (k+4-9)/(k+1-0) = (k-5)/(k+1)
The slope of CD is:
= (k+6-k-3)/(2k+2-2k) = 3/2
Since AB is parallel to CD, slope AB = slope CD. Therefore, we have:
(k-5)/(k+1) = 3/2
2(k-5) = 3(k+1)
k = 13
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Help me find the following measure for this figure
Answer:
A = 36π units²
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( r is the radius )
here r = 6 , then
A = π × 6² = 36π units²
What is the equation of the line shown in the coordinate plane below?
a=y=6x
b=y=-6x
c=y=1/6x
d=y=-1/6 x
Please show your work.
Answer:
your answer is c=y=1/6x
Daniela has a three-season acting contract for a new TV show. Her pay for Season 1 iscp dollars. Then, her pay will increase by 5 percent from Season 1 to Season 2 and by 10 percent from Season 2 to Season 3. Which of the following represents Daniela's Season 3 pay in terms of p?
1.15p is the expression which represents Daniela's Season 3 pay in terms of p
To find Daniela's Season 3 pay in terms of p, we need to calculate the pay increase for each season.
In Season 2, her pay increases by 5 percent, which means she will receive 105 percent (or 1.05) of her Season 1 pay.
In Season 3, her pay increases by 10 percent from Season 2, so she will receive 110 percent (or 1.10) of her Season 2 pay.
To express Daniela's Season 3 pay in terms of p, we multiply the Season 1 pay (p) by the pay increase factors for Season 2 and Season 3:
Season 2 pay = 1.05p
Season 3 pay = 1.10(1.05p) = (1.10)(1.05)p
Simplifying the expression, we get:
Season 3 pay = 1.155p
Therefore, 1.15p is the expression which represents Daniela's Season 3 pay in terms of p
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The angles that we can determine their measure are ∠1, ∠5, ∠6, and ∠7.
option A is the correct answer.
What is the measure of the angles of the polygon?
The measure of the angles of the polygon is calculated as follows;
The following angles were given;
angle 3 = 60⁰
angle 8 = 135⁰
The following angles can be determined as follows;
angle 5 = 180 - 60⁰ ( sum of angles on a straight line )
angle 5 = 120⁰
angle 7 = angle 3 = 60⁰ (corresponding angles )
angle 5 = angle 1 = 120⁰ (corresponding angles )
The value of angle 6 is calculated as;
∠5 + ∠6 + ∠7 + ∠8 = 360 (sum of angles in quadrilateral)
120 + ∠6 + 60 + 135 = 360
315 + ∠6 = 360
∠6 = 360 - 315
∠6 = 45⁰
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Answer the question fom the image
Area of the figure is 402.8 ft².
We have,
Rectangle area = Length x Width
Area of sector = π r² x angle / 360
Now,
There are two rectangles and one sector.
So,
Area of one rectangle.
= 8 x 2
= 16 ft²
Area of another rectangle.
= 5 x 2
= 10 ft²
Area of the sector.
= π x r² x {360 - (150 + 90 + 90)}
= 3.14 x 2² x 30
= 376.8 ft²
Now,
The area of the figure.
= 16 + 10 + 376.8
= 402.8 ft²
Thus,
The area of the figure is 402.8 ft².
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A student wants to get some furniture for his room.
He plans to buy this bed. 190cm 90cm
Scale 1: 50
He needs to know where it can fit in his room.
The room is 3m long and 2.5m wide.
He draws the scale floor plan shown below.
Space for working
Add a scale plan of the bed to the floor plan showing where it can fit in the room.
Answer:
Step-by-step explanation:
You first do 190cm x 90cm then we divide each dimension by 50
190cm ÷ 50 = 3.8cm
90cm ÷ 50 = 1.8cm
So the scaled size is 3.8cm x 1.8cm
By converting the real measurements of the bed and room into a 1:50 scale, we can draw a floor plan and visualize the possibilities of where the bed can fit.
Explanation:This question is about scale drawing and understanding measurements in everyday situations. Given the size of the bed (190cm x 90cm) and the scale of the plan (1:50), we first need to translate the actual measurements into the scale for the drawing.
A ratio of 1:50 means that 1cm on the drawing represents 50cm in real life. So, for the bed which is 190cm long and 90cm wide, we have to divide each value by 50. That gives us a bed representation of 3.8cm (190cm/50) by 1.8cm (90cm/50) on the drawing.
Then, we can use the same technique to draw a floor plan. With the room being 3m (300cm) long and 2.5m (250cm) wide, it translates to a drawing of 6cm (300cm/50) by 5cm (250cm/50). By comparing these dimensions, we can see different possibilities of where the bed can fit into the room on the floor plan.
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5) Use the figure to answer the
following question.
Which expression can be used to find the volume of the figure below?
2 cm
Choose 1 answer:
A
B
8 cm
7 cm 1 cm
6 cm
cm x 7 cm x 1 cm) + (1 cm x 6 cm x 8 cm)
cm x 8 cm x 7 cm) + (1 cm x 6 cm x 8 cm)
cm x 7 cm) + (8 cm x 6 cm)
Option A above
O Option B above
O Option C above
*
1 point
An expression that can be used to find the volume of the figure include the following: B. (2 cm × 8 cm × 7 cm) + (1 cm × 6 cm × 8 cm).
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;
Volume of figure = (2 cm × 8 cm × 7 cm) + (1 cm × 6 cm × 8 cm)
Volume of figure = 112 cm³ + 48 cm³
Volume of figure = 160 cm³
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caculate the circumference of a circle whose diameter is 28cm.
Answer: about 87.96459430051421
Step-by-step explanation: 28 x 3.14 = the answer
angles c and d are complementary. the measure of angle d is 15 degrees greater than the measure of angle. what is the measure of each angle.
The measure of the angles is c = 37. 5 degrees
d = 15 + 37.5 = 52. 5 degrees
How to determine the anglesTo determine the value, we need to know what complementary angles are;
Complementary angles are defined as pair of angles whose sum is equal to 90 degrees
From the information given, we have that;
Angle c and d are both complementary angles
Also, the measure of angle d is 15 degrees greater than the measure of angle c
Then, we have;
d = 15 + c
Substitute the values
c + 15 +c = 90
collect like terms
2c = 90 - 15
2c = 75
Divide both sides by the coefficient
c = 37. 5 degrees
Substitute the value for angles d
d = 15 + 37.5 = 52. 5 degrees
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