Answer:
[tex]18\frac{1}{24}[/tex] ≅ 18.0416667
Step-by-step explanation:
5 7/8 + 4 1/3 + 7 5/6 = [tex]\frac{433}{24}[/tex]
1.Conversion a mixed number 5 7/8
to an improper fraction: 5 7/8 = 5 7/8
= 5 · 8 + 7/8
= 40 + 7/8
= 47/8
To find a new numerator:
a) Multiply the whole number 5 by the denominator 8. Whole number 5 equally 5 * 8/8 = 40/8
b) Add the answer from the previous step 40 to the numerator 7. New numerator is 40 + 7 = 47
c) Write a previous answer (new numerator 47) over the denominator 8.
Five and seven-eighths is forty-seven eighths.
2. Conversion a mixed number 4 1/3
to an improper fraction: 4 1/3 = 4 1/3 = 4 · 3 + 1/3 = 12 + 1/3 = 13/3
To find a new numerator:
a) Multiply the whole number 4 by the denominator 3. Whole number 4 equally 4 * 3/3 = 12/3
b) Add the answer from the previous step 12 to the numerator 1. New numerator is 12 + 1 = 13
c) Write a previous answer (new numerator 13) over the denominator 3.
Four and one-third are thirteen-thirds.
3. Add: 47/8
+ 13/3
= 47 · 3/8 · 3
+ 13 · 8/3 · 8
= 141/24
+ 104/24
= 141 + 104/24
= 245/24
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - is LCM(8, 3) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 3 = 24. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - forty-seven eighths plus thirteen-thirds is two hundred forty-five twenty-fourths.
4. Conversion a mixed number 7 5/6
to an improper fraction: 7 5/6 = 7 5/6 = 7 · 6 + 5/6 = 42 + 5/6= 47/6
To find a new numerator:
a) Multiply the whole number 7 by the denominator 6. Whole number 7 equally 7 * 6/6= 42/6
b) Add the answer from the previous step 42 to the numerator 5. New numerator is 42 + 5 = 47
c) Write a previous answer (new numerator 47) over the denominator 6.
Seven and five-sixths are forty-seven-sixths.
5.Add: the result of step No. 3 + 47/6= 245/24 + 47/6 = 245/24 + 47 · 4/6 · 4 = 245/24 + 188/24 = 245 + 188/24 = 433/24
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - is LCM(24, 6) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 24 × 6 = 144. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - two hundred forty-five twenty-fourths plus forty-seven sixths are four hundred thirty-three twenty-fourths.
Help please and thank you
The expression (18)(-3)(-3) is not equivalent to others.
-7+(-3) is equivalent of the expression -7 - 3.
What is an expression?
A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical value is referred to as a constant.
Variable: A symbol without a fixed value is referred to as a variable.
Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.
Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.
Take the first option:
(-9)(-3 × -6)
= (-9)(18)
= (18)(-9) [Commutative property]
= -(-18)(-9)
Apply the associative property on (-9)(-3 × -6):
(-9)(-3 × -6)
= (-9× - 3)(-6)
= (27) (-6)
= (-6)(27) [Commutative property]
The given expression is -7 - 3
Rewrite the above expression:
-7+(-3)
To learn more about the property, click on the below link:
https://brainly.com/question/24242989
#SPJ1
What is the highest value assumed by the loop counter in a correct for statement with the following header? for(i = 7; i <= 72; i += 7)
Select one:
a. 7
b. 70
c. 77
d. 72
The highest value assumed by the loop counter in a correct "for statement" with the given header is (b) 70.
The "for-statement" is ⇒for(i = 7; i <= 72; i += 7) ,
The loop starts with i = 7 and increases by 7 in each iteration until i becomes greater than 72.
So we can find the highest value of "i" assumed by the loop counter by solving the inequality i <= 72 for i.
⇒ i <= 72
Starting with i = 7 and increasing by 7 in each iteration,
We have,
⇒ i = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77
The last value of i in the sequence, 77, is greater than 72, so the loop counter stops before reaching 77.
So, the highest value assumed by the loop counter in this for statement is : 70.
Therefore, the highest value assumed by the loop counter is (b) 70.
Learn more about Loop Header here
https://brainly.com/question/30657477
#SPJ4
Math is not my thing help
Answer:
mine either hahahahahaha
SICCA DI DO rower for and question
1. Which of these factors makes it challenging to make a fair comparison between a current NBA star and an NBA star from the 1990s?
O A. There has been a fall in three-point shots, and players tend to score fewer points now.
B. There has been a rise in three-point shots, and players tend to score more points now.
OC. Players are more likely to make free throws now, and free-throw percentages have increased.
D. Players are less likely to make free throws now, and free-throw percentages have decreased.
The correct option for this question is B. There has been a rise in three-point shots, and players tend to score more points now.
Why it is?
The factor that makes it challenging to make a fair comparison between a current NBA star and an NBA star from the 1990s is:
B. There has been a rise in three-point shots, and players tend to score more points now.
The increase in three-point shots has significantly changed the way the game is played and the strategies used by teams, which makes it difficult to compare the performance of players from different eras.
Players in the current NBA tend to score more points because of the increased emphasis on the three-point shot, while players from the 1990s may have had different strengths and styles of play that were more effective in that era. Therefore, it is challenging to make a fair comparison between players from different eras based solely on their statistics.
To know more about percentage related question visit:
https://brainly.com/question/25847723
#SPJ1
Surveying Property A surveyor locating the corners of a triangular piece of property started at one corner and walked 480 ft in the direction of N36°W to reach the next corner. The surveyor turned and walked S21°W to get to the next corner of the property. Finally, the surveyor walked in the direction N82°E to get back to the starting point. What is the area of the property in square feet?
The area of the triangular piece of property is approximately 63,121.75 square feet.
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
Starting at the first corner, the surveyor walks 480 ft in the direction N36°W. We can break this down into its northward and westward components:
Northward component = 480 cos(36°)
≈ 388.75 ft
Westward component = 480 sin(36°)
≈ 295.42 ft
This takes the surveyor to the second corner of the property.
From the second corner, the surveyor walks S21°W to get to the third corner. We can again break this down into its southward and westward components:
Southward component = 480 cos(21°)
≈ 435.89 ft
Westward component = 480 sin(21°)
≈ 168.75 ft
Finally, the surveyor walks N82°E to get back to the starting point.
We can break this down into its northward and eastward components:
Northward component = 388.75 ft
Eastward component = 435.89 sin(82°)
≈ 426.04 ft
Now we have the lengths of all three sides of the triangular property:
Side 1 = 480 ft
Side 2 = √[(295.42 - (-168.75))^2 + (388.75 - 435.89)^2]
≈ 421.66 ft
Side 3 = √[(426.04 - 295.42)^2 + (388.75 - 0)^2]
≈ 296.13 ft
calculate the area of the triangular property, we can use Heron's formula:
Area = √[s(s - a)(s - b)(s - c)]
where s is the semiperimeter (half the perimeter) of the triangle,
and a, b, and c are the lengths of its sides.
s = (480 + 421.66 + 296.13)/2 ≈ 598.40
Area = √[598.40(598.40 - 480)(598.40 - 421.66)(598.40 - 296.13)]
Area ≈ 63,121.75 sq ft
Therefore, the area of the triangular piece of property is approximately 63,121.75 square feet.
Learn more about Area here:
https://brainly.com/question/27683633
#SPJ1
A calculus instructor uses computer aided instruction and allows students to take the m.i.d.t.e.r.m e.x.a.m as many times as needed until a passing grade is obtained. Following is a record of the number of students in a class of 50 who took the test each number of times.
Students Number of Tests
22 1
15 2
8 3
5 4
a. Find the expected value of the number of tests taken. (10 points)
b. Compute the variance and the standard deviation of the number of tests taken.
The expected value of the number of tests taken is 1.92 an the variance of the number of tests taken is 1.5852 and the standard deviation is 1.259.
The expected value, variance, and standard deviation can be calculated using the following formulas:
Expected value (E) = ΣxP(x)
Variance (Var) = Σ(x - E)² P(x)
Standard deviation (SD) = √Var
a. To find the expected value of the number of tests taken, we can use the formula E = ΣxP(x), where x is the number of tests taken and P(x) is the probability of taking x tests.
E = (1)(22/50) + (2)(15/50) + (3)(8/50) + (4)(5/50)
E = 0.44 + 0.6 + 0.48 + 0.4
E = 1.92
b. To find the variance and standard deviation, we can use the formulas Var = Σ(x - E)² P(x) and SD = √Var.
Var = (1 - 1.92)²(22/50) + (2 - 1.92)² (15/50) + (3 - 1.92)² (8/50) + (4 - 1.92)^2 (5/50)
Var = 0.8464 + 0.0104 + 0.2928 + 0.4356
Var = 1.5852
SD = √1.5852
SD = 1.259
Learn more about variance at https://brainly.com/question/14662961
#SPJ11
The bearing of p from q is 312°, what is the bearing of q from p
As per the difference concept, the bearing of Q from P is 132°.
To find the bearing of Q from P, we need to calculate the difference between the bearing of P from Q and 180 degrees. This is because the bearing from P to Q is the opposite direction of the bearing from Q to P.
Let's use some notation to make this clearer. Let the bearing from P to Q be denoted by B(PQ), and the bearing from Q to P be denoted by B(QP). We are given that B(PQ) = 312°. To find B(QP), we use the following formula:
B(QP) = B(PQ) - 180°
We know that B(PQ) is 312°, so we can substitute this value into the formula to get:
B(QP) = 312° - 180°
B(QP) = 132°
To know more about difference here
https://brainly.com/question/30241588
#SPJ4
First, answer Part A. Then, answer Part B. to scive -x^(2)+3x+14=-(1)/(4)x^(2)+5 ystem into the bin labeled System Solutions.
Using quadratic formula we get, Part A: The solutions for x are: x = (3 + √(57))/(3/2) and x = (3 - √(57))/(3/2). Part B: The first system solution is: ((3 + √(57))/(3/2), -(76 + 6√(57))/(9) + 5) and second system solution is: ((3 - √(57))/(3/2), -(76 - 6√(57))/(9) + 5)
Part A: To solve for x, we need to first rearrange the equation so that all terms are on one side of the equal sign. Adding (1/4)x^(2) to both sides of the equation:
-x^(2) + (1/4)x^(2) + 3x + 14 = 5
Next, combining like terms:
-(3/4)x^(2) + 3x + 14 = 5
Now, subtracting 5 from both sides:
-(3/4)x^(2) + 3x + 9 = 0
Finally, using quadratic formula to solve for x:
x = (-3 ± √(3^(2) - 4(-3/4)(9)))/(2(-3/4))
Simplifying:
x = (-3 ± √(57))/(2(-3/4))
x = (-3 ± √(57))/(-3/2)
x = (3 ± √(57))/(3/2)
Part B: To determine the system solutions, we need to plug in the values of x into the original equation and solve for y. For the first solution:
y = -(1/4)((3 + √(57))/(3/2))^(2) + 5
y = -(1/4)((9 + 6√(57) + 57)/(9/4)) + 5
y = -(1/4)((76 + 6√(57))/(9/4)) + 5
y = -(19 + (3/2)√(57))/(9/4) + 5
y = -(76 + 6√(57))/(9) + 5
For the second solution:
y = -(1/4)((3 - √(57))/(3/2))^(2) + 5
y = -(1/4)((9 - 6√(57) + 57)/(9/4)) + 5
y = -(1/4)((76 - 6√(57))/(9/4)) + 5
y = -(19 - (3/2)√(57))/(9/4) + 5
y = -(76 - 6√(57))/(9) + 5
Know more about quadratic formula here:
https://brainly.com/question/1214333
#SPJ11
a bird has a 90-inch cage. How many ft is that?
Answer:
7.5 feet
Step-by-step explanation:
Divide the length value by 12 for your answer
90/12 = 7.5
There are 12 inches in a foot, so to convert inches to feet, you can divide the number of inches by 12.
Therefore, a 90-inch cage is equivalent to:
90 inches ÷ 12 inches/foot = 7.5 feet
So the bird cage is 7.5 ft.
A person places $8290 in an investment account earning an annual rate of 6%, compounded continuously. Using the formula =V=Pe^rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 12 years.
Step-by-step explanation:
Using the formula V = Pe^(rt), where P is the principal initially invested, e is the base of a natural logarithm, r is the rate of interest, and t is the time in years:
V = Pe^(rt)
We are given that P = $8290, r = 0.06 (since the annual interest rate is 6%), and t = 12 (since we want to find the value of the account after 12 years). Therefore, we can plug in these values and solve for V:
V = 8290 * e^(0.06*12)
V = 8290 * e^(0.72)
V = $17,936.34
Therefore, the amount of money in the account after 12 years, to the nearest cent, is $17,936.34.
The measures of the exterior angles of an octagon are
�
°
x°,
2
�
°
2x°,
4
�
°
4x°,
5
�
°
5x°,
6
�
°
6x°,
8
�
°
8x°,
9
�
°
9x°, and
10
�
°
10x°. Solve for
�
x.
Answer:
12xphjzjhsgwghdghehdhhez7uehdyegd
What is the pattern of _15,25,_45,55,65
Answer:
5 and 35
Step-by-step explanation:
It's going up in tens so it must start from 5, therefore the one between 25 and 45 must be 35.
Arthur and Bryony both wrote essays. Arthur worked for 65 minutes and wrote an average of 16 words per minute. Bryony worked for 90 minutes and wrote an average of 14 words per minute.
a) who wrote more words in total?
b) how many more words did this person write?
Using basic arithmetic operations, we concluded that a) Bryony wrote more words in total than Arthur.
b) Bryony wrote 220 more words than Arthur.
What is the basic arithmetic operation?The four basic mathematical operations are addition, subtraction, multiplication, and division.
a) In order to establish who wrote more words overall, we must total the words that each participant wrote. By dividing the typical words per minute by the total number of minutes each person worked, we may determine this:
Arthur: 65 minutes × 16 words/minute = 1040 words
Bryony: 90 minutes × 14 words/minute = 1260 words
Therefore, Bryony wrote more words in total than Arthur.
b) To find out how many more words Bryony wrote than Arthur, we can subtract Arthur's total from Bryony's total:
1260 words - 1040 words = 220 words
Hence, Bryony wrote 220 more words than Arthur.
To learn more about basic arithmetic operation, Visit
https://brainly.com/question/20628271
#SPJ1
Pete cuts 3 feet from a 7-foot length of rope. Then he cuts 18 inches from the rope. How many inches of rope are left? ASAP PLEASEE
Answer:
7 ft is 84 inches, 3ft is 36 inches
84 - 36 = 48
cuts off 18 more inches
48 - 18 = 30 inches of rope remain
Step-by-step explanation:
Please answer the below urgently
Answer:
a) 7
b) 0.1
Step-by-step explanation:
a)
The width must be able to go up to 35.
Each square is 5 units wide.
35/5 = 7
The grid must be at least 7 squares wide.
b)
The highest y-coordinate is 1.7.
The highest point on the grid should be 2.
There are 20 vertical squares on the grid.
2/20 = 0.1
Each vertical square should be 0.1
A = 0.1
ourse for MATH 1530 Builder 4 Question Complete the table of ordered pairs for the linear equation. y=3x-13
The ordered pairs for the linear equation, y=3x-13 is (0,-13), (1,-10), and (2,-7).
To complete the table of ordered pairs for the linear equation y=3x-13, we need to substitute different values of x into the equation and solve for y. This will give us the ordered pairs (x,y) for the equation.
Step 1: Choose a value for x. Let's start with x=0.
Step 2: Substitute the value of x into the equation and solve for y.
y=3(0)-13
y=-13
Step 3: Write the ordered pair (x,y) for this solution. In this case, the ordered pair is (0,-13).
Step 4: Repeat steps 1-3 for different values of x. Let's try x=1 and x=2.
For x=1:
y=3(1)-13
y=-10
The ordered pair is (1,-10).
For x=2:
y=3(2)-13
y=-7
The ordered pair is (2,-7).
Step 5: Complete the table with the ordered pairs that we found.
x y
0 -13
1 -10
2 -7
So, the table of ordered pairs for the linear equation y=3x-13 is:
(0,-13), (1,-10), and (2,-7).
To know more about ordered pairs refer here:
https://brainly.com/question/30132127#
#SPJ11
The following inequality has a solution in the form x. Solve the inequality and place the correct value of A into the box. -12x-5>1+18x
To solve the inequality -12x - 5 > 1 + 18x, we need to isolate the variable x on one side of the inequality. Here are the steps to do so:
1. Add 12x to both sides of the inequality to eliminate the -12x on the left side:
-5 > 1 + 30x
2. Subtract 1 from both sides of the inequality to eliminate the 1 on the right side:
-6 > 30x
3. Divide both sides of the inequality by 30 to isolate the variable x:
-6/30 > x
4. Simplify the fraction on the left side:
-1/5 > x
Therefore, the solution to the inequality is x < -1/5. The correct value of A is -1/5.
Know more about equations
https://brainly.com/question/22688504
#SPJ11
Describe the transformations that would occur to the parent function of f(x)=-(1)/(3)(x-5)^(3)+3. Select all that apply.
The transformations that would occur to the parent function are a vertical translation, a horizontal translation to the right, and a vertical compression with a reflection over the x-axis.
The parent function of f(x)=-(1)/(3)(x-5)^(3)+3 is f(x)=x^(3). There are several transformations that would occur to the parent function in order to obtain the given function.
1. Vertical translation: The "+3" at the end of the given function indicates that the parent function is shifted up 3 units.
2. Horizontal translation: The "(x-5)" inside the parentheses indicates that the parent function is shifted to the right 5 units.
3. Vertical stretch/compression: The "-(1)/(3)" in front of the parentheses indicates that the parent function is vertically compressed by a factor of 1/3 and reflected over the x-axis.
Therefore, the transformations that would occur to the parent function of f(x)=-(1)/(3)(x-5)^(3)+3 are a vertical translation of 3 units up, a horizontal translation of 5 units to the right, and a vertical compression by a factor of 1/3 with a reflection over the x-axis.
Know more about transformations here:
https://brainly.com/question/27996647
#SPJ11
I just asked this question but completely forgot to mention the main focus of the project. I need to solve this word problem using three ways. Substitution, Elimination, and Graphing. "The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and bus."
Answer:
Let's first define our variables:
Let x be the number of students in each van and bus.
Using substitution:
From the problem, we know that:
High School A rented 8 vans and 8 buses, with a total of 240 students. So we can write the equation:
8x + 8x = 240
High School B rented 4 vans and 1 bus, with a total of 54 students. So we can write the equation:
4x + 1x = 54
Now, we can solve for x in one of the equations and then substitute that value into the other equation to solve for the other variable. For example, let's solve for x in the second equation:
5x = 54
x = 10.8
Now, we can substitute this value of x into the first equation to solve for the number of students in each van and bus for High School A:
8x + 8x = 240
8(10.8) + 8(10.8) = 172.8
So each van and bus for High School A has 10.8 students in it.
Using elimination:
We can rewrite the equations we used above in standard form:
8x + 8y = 240
4x + y = 54
We can eliminate y by multiplying the second equation by -8 and adding it to the first equation:
8x + 8y = 240
-32x - 8y = -432
-24x = -192
x = 8
Now, we can substitute this value of x into either equation to solve for y:
4(8) + y = 54
y = 22
So each van and bus for High School A has 8 students in it and each van and bus for High School B has 22 students in it.
Using graphing:
We can graph the two equations on the same coordinate plane and find the point where they intersect, which represents the solution:
8x + 8y = 240
4x + y = 54
To graph these equations, we can first solve for y in each equation:
y = -x + 30
y = -4x + 54
Then, we can plot these two lines on the same coordinate plane and find their intersection:
(6, 24)
So each van and bus for High School A has 6 students in it and each van and bus for High School B has 24 students in it.
True or False and give the explanation
1. The CPI is not just one index, but includes a large number of groups, subgroups and selected items, such as a food index, a medical care index and an entertainment index.
2. An index number is a percent that measures the change in price, quantity, value, or some other item of interest from one time to another.
1. True. The CPI is not just one index, but includes a large number of groups, subgroups and selected items, such as a food index, a medical care index and an entertainment index.
2. True. An index number is a percent that measures the change in price, quantity, value, or some other item of interest from one time to another.
The Consumer Price Index (CPI) is actually a collection of indices that measure the changes in prices of a wide range of goods and services.
The CPI includes several different groups, subgroups, and selected items, such as a food index, a medical care index, and an entertainment index.
Each of these indices is used to track the changes in prices of specific goods and services within that category.
An index number is a statistical measure that is used to compare the changes in prices, quantities, values, or other items of interest from one time period to another.
Index numbers are typically expressed as a percentage, with a base value of 100 representing the initial time period. Any changes in the index number from one time period to another reflect the percentage change in the item of interest over that time period.
Learn more about Consumer Price Index at https://brainly.com/question/29564624
#SPJ11
Zany and Peter are making caramel apples. Zany has 412 bags of apples. Peter has 3 bags of apples. One full bag of apples has 10 apples and each apple weighs 6 ounces. How many more pounds of apples does Zany have than Peter?
In answering the question above, the solution is Zany thus has 1,533.75 expressions pounds more apples than Peter does.
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
There are 412 bags of apples in all, with 10 apples in each bag, at Zany. Zany thus has a total of:
412 bags multiplied by 10 bags is 4,120 apples.
24,720 ounces is equal to 4,120 apples at 6 ounces each.
16,080 pounds divided by 24,720 ounces is 1,545 pounds.
Peter has a total of three bags of apples, or:
30 apples are equal to 3 bags times 10 bags
Each of Peter's apples weighs 6 ounces, making his total apple weight:
30 apples divided by 6 ounces each equal 180 ounces.
160 ounces / 16 ounces per pound equals 11.25 pounds.
After deducting Peter's weight from Zany's weight, we can determine how many pounds more apples Zany possesses than Peter:
11 pounds less than 1,545 pounds is 1,533.75 pounds.
Zany thus has 1,533.75 pounds more apples than Peter does.
To know more about expressions visit :-
https://brainly.com/question/14083225
#SPJ1
Can someone help me with this
Answer:
-2
Step-by-step explanation:
Whenever you see f(x), for any number x, you plug x into the function. In your function, f(x) = -x - 1, you want to find f(1).
So, f(1) = -(1) - 1, which equals -2
Steve measured an Italian restaurant and made a scale drawing. The scale of the drawing
was 8 millimeters: 3 meters. The restaurant's kitchen is 24 millimeters wide in the drawing.
How wide is the actual kitchen?
In linear equation, 24 wide is the actual kitchen .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
We are given that Luther drew a scale drawing of an Italian restaurant. He used a scale on which 8 millimetre equals 3 meters. We need to find the width of the kitchen if in the drawing it is 24 mm wide.
So,
8mm = 3m
24 mm =?
24 mm = 8 * 3
3 mm = 24 m
The actual width of the kitchen is 18 m.
Learn more about linear equation
brainly.com/question/11897796
#SPJ9
Concrete tiles are made using buckets of cement,sand and gravel mixed into the ratio of 1:4:6. How many buckets of gravel are needed for 4 bucket of cement?
24 buckets of gravel are needed for 4 buckets of cement when making concrete tiles using the given ratio.
What is the ratio?
The ratio is a mathematical concept that represents the relationship between two quantities or values. It is defined as the comparison of two numbers by division, where the first number is called the "antecedent" and the second number is called the "consequent."
According to the given ratio, the amount of gravel needed is 6 times the amount of cement, or 6/1.
To find out how many buckets of gravel are needed for 4 buckets of cement, we can set up a proportion:
6/1 = x/4
where x is the number of buckets of gravel needed.
To solve for x, we can cross-multiply:
6 x 4 = 1 x x
24 = x
Hence, 24 buckets of gravel are needed for 4 buckets of cement when making concrete tiles using the given ratio.
To learn more about the ratio, visit:
https://brainly.com/question/2328454
#SPJ1
Sidney measured a summer camp and made a scale drawing. The sand volleyball court is 3 centimeters wide in the drawing. The actual volleyball court is 9 meters wide. What scale did Sidney use for the drawing?
The scale factor that Sidney used for the drawing is approximately 0.00333.
To determine the scale that Sidney utilised for the drawing, we can put up a proportion. The ratio will compare the drawing's shown volleyball court's width to the actual court's width:
Scale factor = width in drawing / real width
The scaling factor will be x. Next, we have:
3 cm / 900 cm = x
By multiplying 9 metres by 100, we may convert them to centimetres:
9 metres equals 9 times 100, or 900 centimetres.
By condensing the proportion, we obtain:
x = 0.00333
Thus, Sidney utilised a scale factor for the drawing that is roughly 0.00333. As a result, each centimetre on the drawing corresponds to 0.00333 metres, or 3.33 millimetres, on the volleyball court in real life.
To know more about Meters Visit:
https://brainly.com/question/29367164
#SPJ1
One year consumers spent an average of $23 on a meal at a restaurant. Assume that the amount spent on a restaurant meal is normally distributed and that the standard deviation is $6. Complete parts (a) through (c) below.
a. What is the probability that a randomly selected person spent more than $28?=0.2033
P(X>$28)=0.2033
b. What is the probability that a randomly selected person spent between $9 and $21?=0.3608
P($9
c. Between what two values will the middle 95% of the amounts of cash spent fall?
The middle 95% of the amounts of cash spent will fall between X= $? and X=$?
(Round to the nearest cent as needed.)
a) The probability that a person spent more than $28 is of: 0.2033 = 20.33%.
b) The probability that a person spent between $9 and $21 is given as follows: 0.3608 = 36.08%.
c) The middle 95% of the amounts falls between $11.24 and $34.76.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the problem are given as follows:
[tex]\mu = 23, \sigma = 6[/tex]
The probability of a person spending more than $28 is one subtracted by the p-value of Z when X = 28, hence:
Z = (28 - 23)/6
Z = 0.83
Z = 0.83 has a p-value of 0.7967
1 - 0.7967 = 0.2033.
The probability of a person spending between $9 and $21 is given by the p-value of Z when X = 21 subtracted by the p-value of Z when X = 9, hence:
Z = (21 - 23)/6
Z = -0.33
Z = -0.33 has a p-value of 0.3707
Z = (9 - 23)/6
Z = -2.33
Z = -2.33 has a p-value of 0.0099.
0.3703 - 0.0099 = 0.3608 = 36.08%.
The middle 95% of amounts is between the 2.5th percentile(Z = -1.96) and the 97.5th percentile, Z = 1.96, hence:
-1.96 = (X - 23)/6
X - 23 = -1.96 x 6
X = 11.24.
1.96 = (X - 23)/6
X - 23 = 1.96 x 6
X = 34.76.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
Show that the given set is an infinite set by placing it in a one-to-one correspondence with a proper subset of itself. (Use n as your variable. ) B = {11, 15, 19, 23, 27, 31, , 4n + 7, } Let F = {15, 19, 23, 27,
Set B, which contains the elements 11, 15, 19, 23, 27, 31, 4n+7 and so on, is an infinite set because there exists a one-to-one correspondence between set B and a proper subset of itself, namely set F, which contains the odd integers greater than or equal to 15.
To expose that set b is infinite, we want to set up a one-to-one correspondence among set B and A proper subset of itself. Allow F to be the set of odd integers greater than or equal to 15, i. E., F = {15, 19, 23, 27, ...}.We are able to outline a characteristic f from set b to set f as follows:
f(11) = 15
f(15) = 19
f(19) = 23
f(23) = 27
f(27) = 31
f(4n+7) = 4(n+2) + 3
the first five factors of set b are mapped to the primary 5 factors of set f. For any detail 4n+7 in set b, the corresponding detail in set f is 4(n+2)+3, which is the next peculiar integer after 4n+7. It may be shown that this function is a one-to-one correspondence between set b and set f.
Consequently, given that set f is a proper subset of set b and there exists a one-to-one correspondence among them, set b should be infinite.
Learn more about the infinite set:
brainly.com/question/1678568
#SPJ4
Daily production in a sample of 30 carpet looms is recorded as follows – Class Frequency
15.2 – 15.4 2
15.5 – 15.7 5
15.8 – 16.0 11
16.1 – 16.3 6
16.4 – 16.6 3
16.7 – 16.9 3
Construct a histogram and cumulative frequency distribution (CFD) on the above data. Make comments on the distribution of the above data
The CFD shows that 17 observations (56.7%) fall between 15.8 and 16.0.
A histogram is a graph that displays the frequency of data in a given range. The cumulative frequency distribution (CFD) is a graph that displays the cumulative total of frequencies. The histogram and CFD of the given data are shown below:
The data shows a skewed distribution with most of the observations falling between 15.8 and 16.0. The data is highest at 16.0, with 11 observations falling in this range.
Learn more about histogram
brainly.com/question/30354484
#SPJ11
or
A snowboard has a price of $800. With sales tax, it will cost $848. What is the sales tax percentage?
As a result, 6% sales tax is applied.
How do the percentages translate?%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage. Percentile in mathematics is a related topic.
The price of the snowboarder with tax compared to the price of the snowboarders without tax is the differential in the sales tax.
Sales tax therefore equals $848 - $800 = $48.
We need to multiply the result by 100 to get the sales percentage of tax, which we can then divide by the price of the snowboard before taxes.
Sales tax percentage = (Sales tax / Cost without tax) x 100
= ($48 / $800) x 100
= 0.06 x 100
= 6%
To know more about Percentage visit:
https://brainly.in/question/200523
#SPJ1
As a result, 6% sales tax is applied.
Hοw dο the percentages translate?%, which is a relative figure used tο denοte hundredths οf any quantity. Since οne percent (symbοlized as 1%) is equal tο οne hundredth οf sοmething, 100 percent stands fοr everything, and 200 percent refers tο twice the amοunt specified. percentage. Percentile in mathematics is a related tοpic.
The price οf the snοwbοarder with tax cοmpared tο the price οf the snοwbοarders withοut tax is the differential in the sales tax.
Sales tax therefοre equals $848 - $800 = $48.
We need tο multiply the result by 100 tο get the sales percentage οf tax, which we can then divide by the price οf the snοwbοard befοre taxes.
Sales tax percentage = (Sales tax / Cοst withοut tax) x 100
= ($48 / $800) x 100
= 0.06 x 100
= 6%
To know more about Percentage visit:
https://brainly.com/question/29306119
#SPJ1
Find all the values of b that will make the trinomial 3x^(2)-bx+12 factorable? Choose one value of b and factor the resulting trinomial.
To find all the values of b that will make the trinomial 3x^(2)-bx+12 factorable, we need to use the discriminant of the quadratic formula. The discriminant is the part of the quadratic formula under the square root: b^(2)-4ac. If the discriminant is a perfect square, then the trinomial will be factorable.
So we plug in the values of a, b, and c from the trinomial: b^(2)-4(3)(12) = b^(2)-144.
We want this to be a perfect square, so we can set it equal to a perfect square and solve for b:
b^(2)-144 = 36
b^(2) = 180
b = sqrt(180)
b = 6sqrt(5)
So one value of b that will make the trinomial factorable is 6sqrt(5).
Now we can plug this value of b back into the trinomial and factor it:
3x^(2)-6sqrt(5)x+12 = 0
(3x-6)(x-sqrt(5)) = 0
So the factors of the trinomial are (3x-6) and (x-sqrt(5)).
To learn more about quadratic formula here:
https://brainly.com/question/30164833#
#SPJ11