Answer:
[tex]perimeter=90[/tex]
Step-by-step explanation:
We know that the length is four times the width, so:
[tex]l=4w[/tex]
We also know the area, which is 324 m². The formula for area:
[tex]A=l*w[/tex]
Insert the known values:
[tex]324=(4w)*w[/tex]
Solve for w. Simplify by removing parentheses:
[tex]324=4w*w\\324=4w^2[/tex]
Divide 4 from both sides to isolate the variable:
[tex]\frac{324}{4}=\frac{4w^2}{4} \\\\81=w^2[/tex]
Find the square root of both sides:
[tex]\sqrt{81} =\sqrt{w^2} \\\\w=9[/tex]
The width is 9 m.
We know the width. Now find the length by using the area formula and inserting known values:
[tex]324=l*9[/tex]
Solve for l. Divide both sides by 9:
[tex]\frac{324}{9}=\frac{l*9}{9}\\\\ l=36[/tex]
The length of the rectangle is 36. (You can check: 4 times 9 is 36)
Now find the perimeter:
[tex]P=2l+2w[/tex]
Insert values:
[tex]P=2(36)+2(9)\\\\P=72+18\\\\P=90[/tex]
The perimeter is 90 m.
Each statement describes a transformation of the graph of F(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) - 3?
Answer: B) Shift 3 units down
Recall that y = f(x) as both describe outputs of a function. The same applies for g(x) as well. Saying f(x)-3 means y-3. So we're subtracting 3 from the y coordinate of each point. A point like (1,5) moves to (1,2). Doing this to all points on f(x) will move the entire curve down 3 units.
A number is 9 more than another number. Twice the sum of the two numbers is 10. Find the two numbers.
Answer:
7, -2
Step-by-step explanation:
we call the first number "X" and the second one "Y"
X is 9 more than Y! which means we need to add 9 to Y so it'll be equal to X. so: Y+9=X
also 2×(X+Y)=10
you can also write this down as: 2X+2Y=10
now we have:
X=Y+9
2X+2Y=10
you can now put what equals to X in the second Equation:
2(Y+9)+2Y=10 => 2Y+18+2Y=10 => 4Y=10-18 =>Y= -2
the only thing left to do is to put Y= -2 in the first equation:
X= -2+9 => X=7
An algebraic equation is an equation with unknown variables which can be represented using any number of the alphabet.
The two numbers are 7 and -2
Let's represent the unknown numbers which are the unknown variables with the letters
Let the first number = m
The second number = n
A number is 9 more than another number. This statement is represented by the algebraic equation:
m = 9 + n .......... Equation 1
Twice the sum of the two numbers is 10. This statement is represented by the algebraic equation:
2 (m + n) = 10
2m + 2n = 10...................Equation 2
We substitute 9 + n for "m" in Equation 2
2(9 + n) + 2n = 10
18 + 2n + 2n = 10
Subtract 18 from both sides
18 - 18 + 2n + 2n = 10 - 18
4n = -8
Divide both sides by 4
4n/4 = -8/4
n = -2
We solve for m using Equation 1
m = 9 + n
m = 9 + (-2)
m = 9 - 2
m = 7
Therefore, the two numbers are 7 and -2
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The Distribution of Sample Means expresses the way in which sample means taken from a population and of a given sample size are distributed around the population mean.
a. True
b. False
Answer:
This is true
Step-by-step explanation:
Because a distribution of sample means is as the set of means from all the possible random samples of a specific size, selected from a specific given population.
Sebastian was in a hotel lobby and took the elevator up 7 floors to his room. Then he took the elevator down 9 floors to the parking garage. He described his movement with the expression 9+ (-7). What is Sebastian's error?
Answer:
Sebastian didn't interpret the numbers correctly (See explanation)
Step-by-step explanation:
If you go up an elevator, you are gaining floors, so the number is positive.
If you go down an elevator, you are losing floors, so the number is positive.
Looking at the statement, he went 7 floors up to his room, then 9 floors down to the parking garage this can be represented as [tex]7 - 9[/tex], since the 7 is positive and the 9 is negative.
Sebastian described the movement as [tex]9 + -7[/tex], which is wrong - 9 should be -9 and -7 should be 7.
Hope this helped!
Answer:
Step-by-step explanation:
Let the lobby level be the reference point for Seb's movement.
The following describes his motion: +7 - 9. This puts him 2 floors below the lobby level.
Seb's "9 + (-7)" is incorrect because it indicates an upward trip, whereas the actual direction was downward. Similarly, "-7" indicates a downward trip, whereas the action direction was upward.
Between 9 AM and 10 AM one hundred airplanes departed from Newark Airport. Ten of the airplanes were delayed by an hour each. Of the remaining airplanes, half left on time and half were delayed by an average of 20 minutes. To the nearest whole minute, how long was the average flight delay
Answer:
27 minutes
Step-by-step explanation:
Given that :
Total number of planes = 100
10 planes were delayed by an hour each= 60 minutes;
Total delay time for the 10 planes = (60 * 10) = 600 minutes
Of the 90 remaining :
Half (45) left on time = no delay
(Delay2) : Half (45) experieced a average delay of 20 minutes.
Total delay time for the 45 planes = (45 * 20) = 900
Hence,
Overall delay time = (600 + 900) = 1500 minutes
Number of planes delayed = (10 +45) = 55 planes
Average flight delay :
(Overall delay time / number of planes delayed)
(1500 / 55) = 27.27
= 27 minutes ( to the nearest minute)
Answer:
27
Step-by-step explanation:
How to solve 14x + 2 = 6 (x - 0)
Answer:
Has not solution.
Step-by-step explanation:
14x÷2 = 6(x - 0)
14x÷2 = 6*x + 6*-0
14x÷2 = 6x - 0
14x = 2*6x
14x ≠ 12x
then:
This equation has not solution.
If 3a/b -6= 21, what is the value of a/b?
Answer:
[tex]\Huge \boxed{9}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{3a}{b} -6= 21[/tex]
Add 6 to both sides.
[tex]\displaystyle \frac{3a}{b} =27[/tex]
Dividing both sides by 3.
[tex]\displaystyle \frac{a}{b} = 9[/tex]
Students raised $88 for charities. Their principal gave $35 to charity A and
the rest to charity B. What is the ratio of money given to charity A to the
money given to charity B?
35:53
35: 88
53:35
88:35
The gym has 15 basketballs and 40 footballs. what is the simplified ratio of basketballs to footballs?
15:40
10:40
3:8
8:3
Answer:
35:53
3:8
Step-by-step explanation:
If f(x)= x and g(x) = x + 6, find g(f(o)).
Answer:
6
Step-by-step explanation:
f(x)= x
g(x) = x + 6,
g(f(o))
Let x = 0
f(0) = 0
g(f(0) = g(0) = 0+6 = 6
Abigail is putting juice into cone-shaped containers to make frozen treats. She has approximately one quarter of a gallon, or 58 cubic inches, of juice to make the treats with. Each
container has a height of 3 inches.
Use the information to complete the table indicating the maximum number of treats that Abigail could make with 58 cubic inches of juice.
Answer/Step-by-step explanation:
Maximum number of treats = amount of juice (58 in³) ÷ volume of cone-shaped container to be used
We are given different containers with the same height of 3 in, but different radius. Volume of a cone is given as ⅓*πr²h
Complete the table as follows:
Maximum no. of treats to be made with container of radius (r) 0.5 in, height 3 in:
Take π as 3.14
Volume = ⅓*3.14*0.5²*3 = 0.79 in³
Max no. of treats = 58 ÷ 0.79 = 73.4
73 containers can be filled completely. Therefore, maximum number of treats she could make is 73
Maximum no. of treats to be made with container of radius (r) 1 in, height 3 in:
Take π as 3.14
Volume = ⅓*3.14*1²*3 = 3.14 in³
Max no. of treats = 58 ÷ 3.14 = 18.5
18 containers can be filled completely, therefore, maximum number of treats to be made with this cone is 18 treats.
Maximum no. of treats to be made with container of radius (r) 1.5 in, height 3 in:
Take π as 3.14
Volume = ⅓*3.14*1.5²*3 = 7.07 in³
Max no. of treats = 58 ÷ 7.07 = 8.2
Max no of treats to be made is 8.
Consider the relationship 7r+4t=14. a. Write the relationship as a function r=f(t).
Answer:
7r + 4t = 14
<=> 7r = 14 - 4t
<=> r = (14 - 4t) / 7
Answer: r = f(t)
[tex]r = 2 - \frac{4}{7} t[/tex]
The relationship 7r+4t=14 in terms of t or as a subject r is r = (14 - 4t)/7.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
7r+4t=14
Write the relationship as a function r=f(t).
Make subject as r
7r = 14 - 4t
r = (14 - 4t)/7 = f(t)
Thus, the relationship 7r+4t=14 in terms of t or as a subject r is r = (14 - 4t)/7.
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How many tens and ones equals 4 tens. And 6 ones
Answer: 46
Step-by-step explanation:
How many real solutions are there?
The discriminant is:
[tex]D=4^2-4(1)(2)=8[/tex]
So [tex]D>0[/tex] which means there are two distinct real solutions.
Hope this helps.
Answer:
2 real solutions
Step-by-step explanation:
x^2 +4x+2 =0
This is in the form ax^2 + bx +c
The discriminant is
b^2 -4ac
4^2 - 4*1*2
16 - 8
8
Since this is greater than 0, we have 2 real solutions
Complete the equation for the horizontal line that passes through (5, –7).
Answer:
y = -7.
Step-by-step explanation:
It is horizontal so it will pass through the y axis where y = -7. It is parallel to the x axis so will never pass through it.
X = 1/7y - 9
X + 9 = 1/7
7x + 63 = y
Y = 7x + 63
Answer:
9x
Step-by-step explanation:
X=1/7y-9
X+9=1/7
7x + 63 = y
Y=7x+63
Y-7x=63
Y=63/7x
Y=9x
Solve the following System of Three Equations:
x−3y+z=−15
2x+y−z=−2
x+y+2z=1
Answer:
x = -3 , y = 4 , z = 0
Step-by-step explanation:
Solve the following system:
{x - 3 y + z = -15
2 x + y - z = -2
x + y + 2 z = 1
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for z:
{x - 3 y + z = -15
2 x + y - z = -2
x + y + 2 z = 1
Hint: | Solve for z.
Subtract x - 3 y from both sides:
{z = 3 y + (-x - 15)
2 x + y - z = -2
x + y + 2 z = 1
Hint: | Perform a substitution.
Substitute z = -15 - x + 3 y into the second and third equations:
{z = -15 - x + 3 y
15 + 3 x - 2 y = -2
x + y + 2 (-15 - x + 3 y) = 1
Hint: | Expand the left hand side of the equation x + y + 2 (-15 - x + 3 y) = 1.
x + y + 2 (-15 - x + 3 y) = x + y + (-30 - 2 x + 6 y) = -30 - x + 7 y:
{z = -15 - x + 3 y
15 + 3 x - 2 y = -2
-30 - x + 7 y = 1
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for x:
{z = -15 - x + 3 y
15 + 3 x - 2 y = -2
-30 - x + 7 y = 1
Hint: | Isolate terms with x to the left hand side.
Subtract 15 - 2 y from both sides:
{z = -15 - x + 3 y
3 x = 2 y - 17
-30 - x + 7 y = 1
Hint: | Solve for x.
Divide both sides by 3:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
-30 - x + 7 y = 1
Hint: | Perform a substitution.
Substitute x = (2 y)/3 - 17/3 into the third equation:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
(19 y)/3 - 73/3 = 1
Hint: | Choose an equation and a variable to solve for.
In the third equation, look to solve for y:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
(19 y)/3 - 73/3 = 1
Hint: | Isolate terms with y to the left hand side.
Add 73/3 to both sides:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
(19 y)/3 = 76/3
Hint: | Solve for y.
Multiply both sides by 3/19:
{z = -15 - x + 3 y
x = (2 y)/3 - 17/3
y = 4
Hint: | Perform a back substitution.
Substitute y = 4 into the first and second equations:
{z = -x - 3
x = -3
y = 4
Hint: | Perform a back substitution.
Substitute x = -3 into the first equation:
{z = 0
x = -3
y = 4
Hint: | Sort results.
Collect results in alphabetical order:
Answer: {x = -3 , y = 4 , z = 0
please help me out :)
Answer:
-2
Step-by-step explanation:
So we want to find the value of:
[tex](-6)+(4)[/tex]
Simply add:
[tex](-6)+4=-2[/tex]
Thus, drop the word SUM on -2.
Further notes:
To use the number line to solve, first start by placing your point on -6.
Since we are adding 4 to -6, we move to the right. Thus, move from -6 four spaces to the right.
If you do so correctly, you will end up at -2, the same answer we acquired previously.
Answer:
[tex]\Huge \boxed{-2}[/tex]
Step-by-step explanation:
The sum is the result from adding two or more numbers to each other.
[tex]-6 + 4 = - 2[/tex]
-6 is the starting point on the number line.
4 is added to -6, so an arrow from -6 goes 4 units to the right of the number line.
The arrow stops at -2.
Divide. 19,432 and 56 pls help me
Answer:
347
Step-by-step explanation:
What is the greatest common factor of 25 and 80?
Answer:
GCF of 25 and 80 = 5
Answer:
GCF of 25 and 80 is 5
Step-by-step explanation:
The ratio of men to women working for a company is 5 to 6. If there are 156 women working for the company, what is the total number of employees? employees
Which shape best describes the distribution of the following data? 1, 15, 36, 6 67,68, 68, 68, 69, 69, 69, 69, 70, 70, 70, 70, 70, 71, 71, 72 a. normal b.bimodal c.positively skewed d.negatively skewed
Answer: d.negatively skewed
Step-by-step explanation:
1
15
36
6
67
68
68
68
69
69
69
69
70
70
70
70
70
71
71
72
The distribution with the data above is negativey skewed. This was inferred from the histogram plot generated from the data.The output shows a distribution which has a long tail to the left and peaks to the right. This characteristics describes a distribution which is negatively skewed. Diagram of the obtained histogram for the distribution can be found in the attachment below.
3.5 - (n + 21) - 4n = -45
Answer:
[tex]n = \frac{11}{2} = 5.500[/tex]
a line parallel to y=5x+2
Answer:
Step-by-step explanation:
y=-1/5x+4
----------
The slope of the perpendicular line is always the opposite reciprocal of the original line
For example: the opposite reciprocal of 5 is -1/5
Six friends want to play enough games of chess to be sure every one plays everyone else. How many games will they have to play
Answer: 15 games
Step-by-step explanation:
Given an isosceles right triangle with side 6 m, what is the length of the hypotenuse?
Show work please
Answer: 6√2m or 8.49.
Step-by-step explanation:
Drawing the right angled triangle and label the sides, AC, which is the hypotenuse and the longest, AB , one if the sides, and BC the third sides. Since it is an isosceles right angle triangle with the right angle at B, based on my own diagram here, two of the sides are equal.
AB = BC = 6m
Now to find the hypotenuse, we apply the Pythagoras theorem which states that the square of the sum of the two sides equal the square of the hypotenuse side.That is
AC² = AB² + BC²
AC² = 6² + 6²
= 36. + 36
= 72
AC² = 72, Therefore, AC which is the hypotenuse
AC = √72
= √36 × √2
= 6√2m. or 8.49m
Please help me out! :)
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
the third option
Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of c, the number of cards Isabella sells, and d, the number of dollars she charges?
Answer:
G.
Step-by-step explanation:
cards = 2
dollars = 9
to check that the number of cards with the correct amount d;
use the ratio and proportion.
(3 x 18)/9 = 4
(4 x 31.5)/18 = 7
(7 x 45)/31.5 = 10
therefore, option G. table G. is the correct answer
try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount. (see attached)
What is the cost of x students paying tuition of $2800 each?
Answer:
$2800[tex]x[/tex]
Step-by-step explanation:
Tuition fee per student = $2800/student
if there are [tex]x[/tex] amount of students, then the total costs of tuition that will be generated will be
([tex]x[/tex] students) x ($2800/student) = $2800[tex]x[/tex]
If for example, there are 200 students in this school, then in this case, [tex]x[/tex] = 200 students.
Total cost = (200 students) x ($2800/student) = $560000.
In simple terms, the cost of [tex]x[/tex] students paying tuition of $2800, is [tex]x[/tex] multiplied by the $2800 tuition for each student which is $2800[tex]x[/tex]
Given the word "Nutrition", what is the probability of picking a "t" when randomly
selecting a letter? (decimal rounded to hundredth)
Answer:
0.2 repeating
Step-by-step explanation:
What are geologists able to tell archaeologists about fossils?
A. the beliefs of early people
B.how early people lived
C. how old they are
D. what they were used for
Answer:
C. . how old they are
Step-by-step explanation:
Geologist are people that deal with the internal structure of the earth.
They study Rocks, and it's deposit accumulated millions of years back.
They can also give account of what happened in the past and the types of organisms that existed in the past.
Fossils are traces of event, remains of dead animals and decomposed object.
So geologist can give account of how many years a particular fossil has lived in that particular environment.