the correct length of the frame is 17 inches.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees. Area of rectangle is A = a*b
Based on the information given, it should be noted that the diagonal will be the longest side. Therefore, we'll use the Pythagoras theorem to solve the question.
This will be:
d² = 15² + 8²
d² = 225 + 64
d² = 289
d = ✓289
d = 17
Therefore, the correct option is 17 inches.
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translate the sentence into an equation.
Three less than the product of 2 and a number is 4 .
Use the variable x for the unknown number.
The answer of the given question based on the the sentence into an equation is , 2x - 3 = 4.
What is Equation?In mathematics, equation is statement that asserts equality of the two mathematical expressions. It typically contains variables, constants, and mathematical operations like addition, subtraction, multiplication, division, exponentiation, and logarithm. An equation usually consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The values of the variables that satisfy the equation are called its solutions.
The sentence be translated into equation are as follows:
2x - 3 = 4
where x is the unknown number.
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Please help!! You don’t have to answer #2 but I’d appreciate it if you did.
We can use factorization method to solve quadratic equation.
And, The value of solution of the quadratic equation is,
⇒ x = 2, 6
We have to given that;
Quadratic equation is,
⇒ x² - 8x = - 12
Now, We can simplify as;
⇒ x² - 8x = - 12
⇒ x² - 8x + 12 = 0
Factorized it as;
⇒ x² - (6 + 2)x + 12 = 0
⇒ x² - 6x - 2x + 12 = 0
⇒ x (x - 6) - 2 (x - 6) = 0
⇒ (x - 2) (x - 6) = 0
⇒ x = 2, 6
Thus, We can use factorization method to solve quadratic equation.
And, The solution is,
⇒ x = 2, 6
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Each week Sanji gives a prize to one employee based on rolling an 8-sided solid with faces numbered 1 through 8. Select all of the true statements. Group of answer choices p(factor of 24) = 6/8 p(odd number) = 1/2 p(number less than 8) = 1 p(multiple of 3) = 1/4 p(even number) = 1/8 P(the number 9) = 0
The true statements are:
p(factor of 24) = 6/8p(odd number) = 1/2p(multiple of 3) = 1/4P(the number 9) = 0How to get the true statementsp(factor of 24) = 6/8: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among these, the numbers 1, 2, 3, 4, 6, and 8 are on the 8-sided die. So, there are 6 favorable outcomes out of 8 possible outcomes. This statement is true.
p(odd number) = 1/2: There are 4 odd numbers (1, 3, 5, 7) on the 8-sided die, so the probability of rolling an odd number is 4/8 = 1/2. This statement is true.
p(number less than 8) = 1: All numbers on the 8-sided die are less than or equal to 8, but not all are less than 8. There are 7 numbers less than 8 (1, 2, 3, 4, 5, 6, 7), so the probability is 7/8, not 1. This statement is false.
p(multiple of 3) = 1/4: There are 2 multiples of 3 on the 8-sided die (3 and 6), so the probability of rolling a multiple of 3 is 2/8 = 1/4. This statement is true.
p(even number) = 1/8: There are 4 even numbers (2, 4, 6, 8) on the 8-sided die, so the probability of rolling an even number is 4/8 = 1/2, not 1/8. This statement is false.
P(the number 9) = 0: The 8-sided die only has numbers 1 through 8, so it is impossible to roll a 9. The probability of rolling a 9 is indeed 0. This statement is true.
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A person invests 4000 dollars in a bank. The bank pays 5.75% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5900 dollars?
Answer:
t = 6.8 years
Step-by-step explanation:
The formula for compound interest is
[tex]A(t)=P(1+r/n)^n^t[/tex], where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.
We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal). We must solve for t and round to the nearest tenth:
[tex]5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t[/tex]
10
11
How many 4-digit numbers can you make using only 7, 2, and 6 if a 7 must
be in the tens place? You can repeat digits 7, 2, and 6. You can draw a
possibility tree.
Answer:
10
Step-by-step explanation:
I do not know how to make a possibility tree, but I can explain it in words. the possibilities could be at lost, 10
Compute the required rate of return on two stocks with beta values of 0.5 and 2 respectively assuming the risk-
free rate of 5% and the market return of 10% using the capital asset pricing model. Please show work. Thank you.
The required rate of return for the stock with a beta of 0.5 is 7.5% and for the stock with a beta of 2 is 15%.
What is Rate of return?Rate of return is the amount of profit or loss earned on an investment over a certain period of time, expressed as a percentage of the initial investment or total asset value.
What is stock?A stock is a type of security that represents ownership in a company. Investors buy stocks to become shareholders and share in the company's profits and losses.
According to the given information:
The Capital Asset Pricing Model (CAPM) is expressed as:
R = Rf + beta*(Rm - Rf)
Where:
R = Required rate of return
Rf = Risk-free rate of return
beta = Beta coefficient (systematic risk)
Rm = Expected market return
Using the given values, we can compute the required rate of return for each stock:
Stock with beta of 0.5:
R = 5% + 0.5*(10% - 5%)
R = 7.5%
Stock with beta of 2:
R = 5% + 2*(10% - 5%)
R = 15%
Therefore, the required rate of return for the stock with beta of 0.5 is 7.5%, and the required rate of return for the stock with beta of 2 is 15%.
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Prove that heat and light usually go together.
Answer:
Step-by-step explanation:
Infra-red waves commonly known as heat waves and light rays are travel in a speed [tex]3*10^{8} ms^{-1}[/tex] in a vacuum.
a circle has a circumerence of 6. it has a arc length of 1. what is the central angle of the arc
the central angle of the arc is π/3 radians.
What is circumference of a circle?
Circumference or perimeter of a circle refers to the measuring of its limits. Contrarily, a circle's radius influences the amount of space it takes up. If a circle is opened up and represented by a straight line, its circumference is equal to its length. It is usually measured in units like centimetres or metres. While utilising the formula, the radius of the circle is taken into account when calculating the circle's circumference. Therefore, we need to know the radius or diameter value to determine the circle's perimeter.
Central angle (in radians) = arc length / radius
In this case, we are not given the radius of the circle directly, but we know that the circumference of the circle is 6. We can use the formula for circumference to find the radius:
Circumference = 2 * pi * radius
6 = 2 * pi * radius
radius = 3 / pi
Now we can use the formula for the central angle:
Central angle (in radians) = arc length / radius
Central angle = 1 / (3/pi) = pi/3
Therefore, the central angle of the arc is π/3 radians.
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What is angle
Enter your answer in the box
Answer:
CAB is 37 degrees
Step-by-step explanation:
90 + 53 = 143
180 - 143 = 37
What is the area of this figure?
3 mi
3 mi
5 mi
5 mi
4mi
8mi
5 mi
5mi
Answer:
180,000 (OR 90,000 if the figure is a triangle)
Step-by-step explanation:
3 x 3 x 5 x 5 x 4 x 8 x 5 x 5 = 180,000
Area = 180,000
IF THE FIGURE IS A TRIANGLE THEN DIVIDE 180,000 BY 2 AND YOU WILL GET 90,000 AS THE AREA
Trees in a landscaping company's warehouse are being sold at a monthly rate of 7.3%. This situation can be modeled by an exponential function. The warehouse initially contained 45,000 trees.
Which function can be used to find the number of trees in the warehouse at the end of m months?
An exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.
What is function?A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, C programming is built around functions. All C programs have at least one function, which is main(). A function is a group of statements that together perform a task. Every C program has at least one function, main(), and all the other functions are called user-defined functions.
The function that can be used to find the number of trees in the warehouse at the end of m months is an exponential function given by:
N(m) = 45,000(1.073)^m
Where N(m) is the number of trees in the warehouse at the end of m months and 45,000 is the initial number of trees in the warehouse. The rate of 7.3% is represented by 1.073, which is the base of the exponential function.
For example, if we want to find the number of trees in the warehouse at the end of 5 months, we can substitute m = 5 into the exponential function and calculate the result. This gives us N(5) = 45,000(1.073)^5 = 60,731. Thus, the warehouse will contain 60,731 trees at the end of 5 months.
In conclusion, an exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.
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An exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.
What is function?
A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, C programming is built around functions. All C programs have at least one function, which is main(). A function is a group of statements that together perform a task. Every C program has at least one function, main(), and all the other functions are called user-defined functions.
The function that can be used to find the number of trees in the warehouse at the end of m months is an exponential function given by:
[tex]N(m) = 45,000(1.073)^m[/tex]
Where N(m) is the number of trees in the warehouse at the end of m months and 45,000 is the initial number of trees in the warehouse. The rate of 7.3% is represented by 1.073, which is the base of the exponential function.
For example, if we want to find the number of trees in the warehouse at the end of 5 months, we can substitute m = 5 into the exponential function and calculate the result. This gives us N(5) = 45,000(1.073)⁵ =60,731.
Thus, the warehouse will contain 60,731 trees at the end of 5 months.
In conclusion, an exponential function can be used to calculate the number of trees in the warehouse at the end of any given number of months. This function uses the initial number of trees in the warehouse and the rate of 7.3% to determine the result.
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Please help!!!!!!!!!
Answer:
a) (2x+9) + (3x-4) + 36 = 180
b) x = 27.8
c) 79.4°
Step-by-step explanation:
a) (2x+9) + (3x-4) + 36 = 180
This is because all 3 angles of a triangle equal to 180 degrees.
b) Firstly add like terms
5x + 41 = 180
Subtract 41 from both sides.
5x = 139
Divide 5 on both sides.
x = 27.8
c) <GTN = 3x-4
Plug in x = 27.8
3(27.8)-4 = 79.4
<GTN is 79.4 degrees
Find the slope and the y-intercept of the equation:
y = 12x+8
a slope 12 and y-intercept = -8
b slope = -12 and y-intercept = 8
c slope = -12 and y-intercept = -8
d slope 12 and y-intercept = 8
Answer:
The answer to this question is D
Step-by-step explanation:
i solved it
1000 ml of lemonade contains 250 ml of lemon juice.
How much lemon juice does 600 ml of lemonade contain?
how do i work this out
By finding the ratio of total volume to lemmon juice, we can see that In 600ml of juice we have 150ml of lemmon juice.
How much lemon juice does 600 ml of lemonade contain?We know that 1000 ml of lemonade contains 250 ml of lemon juice. Then the ratio to total volume to lemon juice is:
R = 250/1000 = 0.25
Then in 600ml of juice, we will have 0.25 times that of lemmon juice, it gives:
0.25*600ml = 150 ml
In 600ml of juice we have 150ml of lemmon juice.
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I would love some help on this
A ) ⅔ x + 6 = 16
→ ⅔ × 15 + 6 = 16
→ 10 + 6 = 16
→ 16 = 16
Proved
LHS = RHSB ) ⅓ x + 4 = 22
→ ⅓ × 15 + 4 = 22
→ 20 = 2
Not Proved
C) 3x + 15 = 30
→ 3×15+15 = 30
→ 3× 30 =30
→ 90= 30
Not Proved
D) x + 25 = 50
→ 15 + 25 = 50
→ 40 = 50
Not Proved
option a is correct answerSolution -210r -24 = 7r + 12
→ 10r - 7r = 12+24
→ 3r = 36
→ r = 12
Option d is correct answerSolution. -33r -2r-8 = -8r + 10
→ 3r - 2r + 8r = 10+8
→ r + 8r = 18
→ 9r = 18
→ r = 2
Option c is correct answerSolution - 4m/3-18 = m + 6
→ 54- m/ 3 = m + 6
→ 54- m = m + 6×3
→ 54- m = m + 18
Here one side m is positive and one side m is negative so both will cancel .→ 18 - 54
→ -36
Based on the line of best fit, which of these statements is true?
A. Each item requires about 12 minutes of production time.
B. The equipment starts producing items after about 25 minutes of
warming up.
C. The equipment starts producing items after about 20 minutes of
warming up.
D. Each item requires about 3 minutes of production time.
The true statement regarding the line of best fit is that C. the equipment starts producing items after about 20 minutes of warming up
What is the like about?The line of best fit may be explained as a straight line which is drawn to pass through a set of plotted data point which gives the best and most approximate relationship between the data points.
The equipment starts producing items after about 25 minutes of warning up. This is false because machine takes 20 minutes to produce the items.
The equipment starts producing items after about 20 minutes of warming up. This is True.
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For the following data set, what is the mode? Data set: A, B, A, B, C, D, E, G, E, A, B
Answer:
A
Step-by-step explanation:
the answer would be a because it is shown more than the others
If every 2 cm on a scale drawing is equal to 7 feet in real life, which lines on the drawing would be greater than 21 feet in real life? Select all that apply. A) 7 cm B) 5 cm C) 9 cm D) 12 cm
The correct answers are A) 7cm, C) 9cm and D) 12cm
Define the Conversion of units?The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.
If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.
Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:
⇒ [tex]\frac{2cm}{7 feet} = \frac{x cm }{yfeet}[/tex]
where y is the length of the line in real life. Solving for y, we get:
⇒ [tex]y = \frac{7 feet} {2cm} *x[/tex]
⇒ [tex]y = 3.5 x feet[/tex]
If we put x = 2cm (given) then, y = 7 feet
For y = 21 feet, the value of x = 6cm.
Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.
So, the lines on the drawing that are greater than 21 feet in real life are:
A) 7cm, C) 9cm, D) 12cm
Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm
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The equation f(t) = -16t2 + 5t +11 represents the motion of a ball being thrown where t is the time after being thrown. What is the maximum height of the ball? Type only a number (rounded to 1/10th if needed)
Answer:
To find the maximum height of the ball, we need to determine the vertex of the parabolic function f(t) = -16t^2 + 5t + 11. The vertex of a parabola is the point where the function reaches its maximum or minimum value.
The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are the coefficients of the quadratic function. In this case, a = -16 and b = 5, so the x-coordinate of the vertex is:
t = -b/2a = -5/(2*(-16)) = 0.15625
To find the y-coordinate of the vertex, we can substitute t = 0.15625 into the function f(t):
f(0.15625) = -16(0.15625)^2 + 5(0.15625) + 11 ≈ 11.36
Therefore, the maximum height of the ball is approximately 11.4 (rounded to 1/10th).
Evaluate log_10^3.
a) 100
b) 1, 000
c) 9
d) 3
Answer:
The answer is d.
Step-by-step explanation:
Let m = a number
Let n = a different number
[tex]log(m^n)=nlog(m)[/tex]
[tex]log(10^3)=3*log(10)[/tex]
[tex]log(10)=1[/tex]
[tex]log(10^3)=3[/tex]
Find the measure of the missing angle in the triangle.
20 + 70 + x = 180
a. 60
b. 65
c. 75
d. 90
Answer: the missing angle has a measure of 90 degrees, which is option (d).
Step-by-step explanation:
20 + 70 + x = 180
We are able include the two known angles and after that subtract the result from 180 to induce the degree of the lost point:
20 + 70 = 90
180 - 90 = 90
what shape is a concave hexagon with two pairs of congruent sides
The shape that is a concave hexagon with two pairs of congruent sides is an irregular hexagon.
What is a hexagon?A hexagon is defined as the type of polygon that is made up of six sides and six angles that sums up to 720° and also have 6 vertices.
A hexagon can be of various irregular shapes such as concave, convex and complex irregular shapes.
The properties of irregular hexagon include the following:
They have sides of different lengths andThey have angles of varying measures.The concave irregular hexagon has two pairs of congruent sides that are equal in measurement.
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Please help!!!!
Find the surface area of the composite figure below to
the nearest tenth.
Answer:
16801.2cm²
Step-by-step explanation:
Cone :
SA = πrl
SA = π · 28 · 45 90-45 = 45
SA = 3958.406744
Cylinder :
SA = 2 · π · r · ( r+h)
SA = 2 · π · 28 ( 28 +45 )
SA = 2 · π · 28 (73)
SA = 12842.83077
12842.83077 + 3958.406744 =
16801.2cm²
PLEASE HELP ON THIS MATH QUESTION WORTH 20 POINTS WILL GIVE YOU A GOOD SCORE FOR HELPING
Answer: 64
Step-by-step explanation:
First you do, 237+192+179 which is 608.
Then you do, 800-608 which is 192.
Lastly, you do 192 divided by 3 which gives you 64 as your final answer. So you have to do 192/3 for the 3 7th grade classes to get an equal amount of the prize money.
[tex]192/3=64 \dollars[/tex]
Hope this helps!
Given the following list of values, is the mean, median, or mode likely to be the best measure of the center for the data set?
33, 33, 33, 31, 31, 34, 32, 31
Select the correct answer below:
The mode, mean, and median are relatively close together (mode=33, mean=32.125, median=32), we can conclude that this data set is symmetric and does not have any significant outliers.
What is statistics?The area of mathematics known as statistics is concerned with the gathering, examination, interpretation, presentation, and arrangement of data.
The mean, median, and mode are all measures of central tendency that describe the center of a data set in different ways.
The mean is calculated by dividing the total number of values in a data collection by their sum.
The median is the median of the data set when the values are ordered. It is not affected by outliers.
The value that appears most frequently in a data collection is the mode.
It may not be unique or exist in a data set.
For the given data set, the mode is likely to be the best measure of center as it is the value that occurs most frequently. In this case, the mode is 33, which occurs three times, whereas all other values occur only once or twice. Therefore, the mode is the most representative value for this data set.
Alternatively, we can also calculate the mean and median to see how they compare with the mode:
The mean is (33+33+33+31+31+34+32+31)/8 = 32.125
The median is the middle value when the values are arranged in order, which is 32.
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A farmer wants to make a rectangular field with a total area of 3000 square meters. It is surrounded by a fence. It is divided into 3 equal areas by fences as shown. Express the total length L of all the fence required in terms of the length x of one of the fences which divide the field.
Antonio has a 1 gallon of milk. He wants to make a recipe for Mexican rice pudding the calls for 1 quart of milk if he tripled the recipe how many cups of milk will Antonio have left over
At the end, Antonio has 4 cups of milk leftover.
How many cups of milk will Antonio have left over?We know that Antonio has 1 gallon of mil, and he needs to use 3 quarts of milk for the recipe.
Then we need to perform a change of units, we know that:
1 gallon = 4 quarts.
Then after he uses 3 quarts, he will have 1 quart remaining, and now we want to know how many cups is that, we know that:
1 quart = 4 cups.
So Antonio has 4 cups leftover.
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A 1-pound box of candy cost $4.00. What was the cost per ounce (1 pound = 16 ounces)?
Answer:
0.25
Step-by-step explanation:
The cost per ounce of candy can be calculated by dividing the total cost of the box by the number of ounces in the box. Since 1 pound equals 16 ounces, the cost per ounce is $4.00 / 16 ounces = $0.25 per ounce.
So the cost per ounce of candy is $0.25.
Answer: 16/1 16x4 = 64/4
Use calculus to find the area A of the triangle with the given vertices. (0, 6), (2, −3), (3, 4)
The area of the triangle with the given vertices is 11.5 square units.
Define the area of triangle by vertices?The area of a triangle can be calculated using the coordinates of its vertices using the following formula.
To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:
A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2
Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:
A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2
A = (0 - 4 + 27)/2
A = 23/2
A = 11.5
Therefore, the area of the triangle with the given vertices is 11.5 square units.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
Step-by-step explanation:
A
