A film set designer is using white and colored tiles in a pattern to create paths of different lengths. If x is the length of the path in feet, the number of colored tiles needed to make it is calculated using the rule
(4x2y3)(3x2y2)
where y represents the number of white tiles.
Which simplified expression represents the number of colored tiles used for a path of length x feet?
7x4y5
7x4y6
12x4y5
12x4y6
The simplified algebraic expression for the number of colored tiles used for a path(4x^2y^3)(3x^2y^2), is 12x^4y^5. Hence the correct option is 3,
Given the algebraic rule for determining the number of colored tiles ((4x2y3)(3x2y2)), we simplify this expression by multiplying the coefficients and then by adding the exponents for x and y (since they are the same base).
Multiply the coefficients: 4 x 3 = 12
Add the exponents for x: 2 + 2 = 4 (since x2 x x2 = x2+2)
Add the exponents for y: 3 + 2 = 5 (since y3 x y2 = y3+2)
4/5(2x+5)−4=1
x = 1 1/4
x = 1 2/5
x = 5/8
x = 3 1/5
Heather was asked to graph 3x - y = -4 by using slope and y-intercept. Her graph is shown.
Which choice supports the graph that she has drawn?
A) The slope is positive 3 and the y-intercept is (0,4).
B) The slope is negative 3 and the y-intercept is (0,4).
C) The slope is positive 3 and the y-intercept is (0,-4).
D) The slope is negative 3 and the y-intercept is (0,-4).
The correct choice that supports the graph that Heather has drawn is:
The slope is positive 3 and the y-intercept is (0, 4).
Option A is the correct answer.
We have,
To determine which choice supports the graph that Heather has drawn for the equation 3x - y = -4, we need to consider the slope and y-intercept.
The equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Comparing the given equation to the standard form, we can rearrange it as y = 3x + 4.
From this, we can determine that the slope is positive 3 and the y-intercept is (0, 4).
Therefore,
The correct choice that supports the graph that Heather has drawn is:
The slope is positive 3 and the y-intercept is (0, 4).
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In one weekend,a theatre sells 74,877 tickets to a new movie. Write the values for each of the 7s in 74,877.
Answer:
Given number,
74, 877
Since, the place value chart,
Ones = 1,
Tens = 10,
Hundred = 100,
Thousand = 1000,
Ten thousand = 10,000
Hundred thousands = 100,000
Millions = 1,000,000
Hence, by the above chart,
For the number,
74,877
Place value of 7 at ones place = 7,
Place value of 7 at tens place = 70,
Place value of 7 at ten thousand place = 700,000
Which measure of central tendency best describes this situation: the ages of students in an eighth-grade class?
a) Mean; there likely are no outliers.
b) Mode; the data are not numerical.
c) Median; there likely are outliers.
d) Median; there likely are no outliers.
Answer:
Step-by-step explanation:
Its B=median
the lifetime of a smartphone battery while playing video is described by a normal model. if 95% of batteries last between 8.5 and 11.5 hours, what are the mean and standard deviation of the distribution of battery lifetime while playing videos?
I need help with this asap right now please
what is the volume of 20 grams of an object with a density of 55g/cm^3?
The volume of an object with a mass of 55g/cm³ and a mass of 20 grams is 27.5cm³.
What are mass, volume, and density?Mass is the quantity of matter in a physical body.
The volume shows the amount of 3D space occupied by a closed object.
Density is mass per unit of volume.
Volume is only defined for 3-dimensional objects 2 dimensional objects have no volume.
We know volume is equal to mass/density.
Given an object has a density of 55g/cm³ and a mass is 20 grams.
∴ Volume = (55/20) cm³.
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A sales representative earns a 2.5% commission on sales. Find the commission earned when the total sales are $80,700.
To find the commission earned by a sales representative, multiply the total sales by the commission rate of 2.5%. For total sales of $80,700, the commission earned would be $2,017.50.
Explanation:To find the commission earned by a sales representative, we need to multiply the total sales by the commission rate.
In this case, the total sales are $80,700 and the commission rate is 2.5%.
So, the commission earned can be calculated as:
$80,700 x 0.025 = $2,017.50
Therefore, the sales representative will earn a commission of $2,017.50.
Jeanette and Leslie are trying to solve this problem: A camp counselor has a list of 134 campers who signed up for art class. The counselor can place 8 students in each class. How many classes does the counselor need to have?
*Please Show Work*
Which expression is equivalent? (35 pts)
−3(5x + 8) − 7(5x + 3)
A) 50x + 45
B) 50x − 45
C) −50x + 45
D) −50x − 45
Answer:
-50x-45
Step-by-step explanation:
The solution of the given expression is -50x - 45. The correct option is D.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is −3(5x + 8) − 7(5x + 3). The given expression will be solved as below,
E = −3(5x + 8) − 7(5x + 3)
E = -15x - 24 - 35x -21
E = -50x - 45
Therefore, the solution of the given expression is -50x - 45. The correct option is D.
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Can someone help me on this
Simplify the expression: 5+12 divided by 2x2
Jacob, Kylie, and Manuel each bought a sandwich and drink. The total bill to $21, and each drink cost $2. Of each sandwich cost the same amount, what is the cost of one sandwich?
Jennifer's grandmother buys carrots at the farm stand. She and her 3 grandchildren equally share the carrots. The total weigh of the carrots she buys is 28 kg. How many kilograms of carrots will Jennifer get ?
Answer:
7 kilograms of carrots.
Step-by-step explanation:
Jennifer's grandmother buys carrots at the farm stand.
The total weight of the carrots she buys = 28 kilograms
She and her 3 grandchildren equally shares the carrots.
The number of persons among carrots were distributed = 4 persons
To calculate how many kg of carrot each person will get = [tex]\frac{\text{total weight of carrots}}{\text{total number of persons}}[/tex]
They each will get = [tex]\frac{28}{4}[/tex]
= 7 kilograms.
Jennifer will get 7 kilograms of carrots.
An 8-ounce can of tomatoes costs $1.14.A 12-ounce can costs $1.75.Which can of tomatoes cost the least per ounce
Answer:
8-ounce can tomatoes costs the least per ounce.
Step-by-step explanation:
Cost of an 8-ounce can of tomatoes = $1.14
cost per ounce of tomatoes = [tex]\frac{1.14}{8}[/tex]
= $0.1425 ≈ $0.14 per ounce
Cost of an 12-ounce can of tomatoes = $1.75
cost per ounce of tomatoes = [tex]\frac{1.75}{12}[/tex]
= $0.1458 ≈ $0.15 per ounce
Therefore, 8-ounce can of tomatoes cost the least per ounce.
What is the quotient of 6,559 and 21 ?
Jodi went 54 miles on 3.5 gallons of gas, and she wants to know how far she can go on 9 gallons of gas. Which proportion would be useful to solve the problem?
A)
9
3
=
54
x
B)
9
54
=
x
3
C)
54
3.5
=
x
9
D)
54
9
=
3.5
x
Balu and Pumba shared ½ of a cake. Balu got to eat twice as much cake as Pumba. What fraction of the whole cake did Balu eat?
Answer:
Balu ate [tex]\frac{1}{3}[/tex]fraction of the whole cake
Step-by-step explanation:
Let x be the amount of cake eaten by Pumba
Balu got to eat twice as much cake as Pumba.
Balu eat cake = 2x
Balu and Pumba shared ½ of a cake.
So, [tex]2x+x=\frac{1}{2}[/tex]
[tex]3x=\frac{1}{2}[/tex]
[tex]x=\frac{1}{6}[/tex]
So, Pumba's share = [tex]\frac{1}{6}[/tex]
Balu's share = 2x = [tex]\frac{2}{6}=\frac{1}{3}[/tex]
Hence Balu ate [tex]\frac{1}{3}[/tex]fraction of the whole cake
Which expression shows the result of completely factoring and simplifying 3x+9x ? (A) 12x
(B) 3x(3x+9x)
(C) −6x
(D) 9(x+1)
Which souvenirs cost less than $2.25 per item?
Check all that apply.
tote bags: 25 for $49.00
picture frames: 15 for $32.25
water bottles: 12 for $27.60
mugs: 8 for $15.92
T-shirts: 10 for $25.00
Answer:
tote bags, picture frames, and mugs
Step-by-step explanation:
Your picture of your family crest is 4.5 inches wide. You need a reduced copy for the front page of the family newsletter. The copy must fit in a space 1.8 inches wide. Which scale factor should you use on the copy machine to adjust the size of your pictures of the crest?
A) 2/5
B) 5/2
C) 1/2
D) 1/5
Answer:
The answer is : A 2/5
(I just finished taking the test)
The scale factor would be 2/5 to reduce the width from 4.5 inches to 1.8 inches.
What is a scale factor?A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller). For example, we can enlarge a rectangle with sides of 2 cm and 4 cm by multiplying each side by a number, say 2.
Given that your picture of your family crest is 4.5 inches wide. You need a reduced copy for the front page of the family newsletter. The copy must fit in a space 1.8 inches wide.
The scale factor will be calculated as,
Scale factor = Reduced size / Original size
Scale factor = 1.8 / 4.5
Scale factor = 0.4 or 2/5
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how to find the answer to this
5g=230 HOW DO I FIND THIS PLZ HELP NOW
The volume of a rectangular prism can be computed by using the formula V=lwh. Which equation is solved for w? A. w=v/lh B. w=lh/v C. w=vl/h D. w=vlh
The equation w = V/lh can be used to find the width of the rectangular prism option (A) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The volume of a rectangular prism can be computed by using the formula
V=lwh.
A rectangular prism can be defined as a six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape. It is also called a cuboid.
Solve for w:
w = V/lh
Thus, the equation w = V/lh can be used to find the width of the rectangular prism option (A) is correct.
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Final answer:
The equation solved for w is B. w = lh/v
Explanation:
1. Understand the Formula:
The formula for the volume (V) of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.2. Isolate w:
To solve for w, isolate w on one side of the equation.Divide both sides of the formula by lh: V/lh = w3. Determine the Correct Equation:
Compare the isolated w with the provided answer choices.The correct equation solved for w is w = lh/vTherefore, the correct answer will be B. w=lh/v
Evaluate 12x−3y12x−3y when x=−14x=−14 and y=3y=3.
Answer:
-12
Step-by-step explanation:
I think I got it right on Big Ideas
PLEASE HELP!
Sarah paints a straight line. The line is 13 1/2 ft long. She wants to divide the line into sections that are each 1/8 ft long. How many sections will the line be divided into?
write the numerical expressions in words then solve 10×(2.5+13.5)
Which number is equal to 10 to the 3rd power
Ling uses 21 bananas to make 7 fruit smoothies. What is the unit rate that Ling uses for bananas per each smoothie? What is the unit rate? Explain how to use equivalent fractions to find the answer
Answer:
The unit rate that ling uses for bananas per each smoothie is (3/1) bananas per smoothie
Step-by-step explanation:
Ling uses 21 bananas to make 7 fruit smoothies. Total of bananas B = 21. Total of smoothies S =7.
The unit rate U is the relationships B divided by S.
U = B/S
U = 21 bananas / 7 smoothies
U = 21/7 Bananas per smoothies.
We can use the equivalent fractions to find the unit rate. 21 can be expressed as 7*3. 7 can be expressed as 7*1. We can simplify the number 7 in numerator and denominator.
U = (7*3)/(7*1)
U = 3/1.
Finally, the unit rate is 3/1 bananas per smoothie.
A spider walks about 19 cm each second. About how long would it take the spider to walk around the perimeter of a room that is 3 m wide and 4 m long?
Final answer:
To calculate the time it takes the spider to walk around the perimeter of a 3 m by 4 m room, we first find the perimeter in meters, convert it to centimeters, and then divide by the spider's speed in cm/s. The perimeter of the room is 14 m, which is 1400 cm. Dividing this by the spider's speed, 19 cm/s, gives us approximately 74 seconds.
Explanation:
To find out how long it would take the spider to walk around the perimeter of a room that is 3 m wide and 4 m long, we first need to calculate the perimeter of the room. The formula for perimeter P of a rectangle is P = 2(l + w), where l is the length and w is the width.
So for a room that is 3 m wide and 4 m long, the perimeter is:
P = 2(4 m + 3 m) = 2(7 m) = 14 m
Since the spider walks 19 cm each second and there are 100 cm in a meter, we convert the perimeter to centimeters:
14 m = 1400 cm
Now, we calculate the time t it will take for the spider to walk this distance by dividing the perimeter by the spider's speed:
t = perimeter/speed = 1400 cm / 19 cm/s
Therefore, the time taken for the spider to walk around the perimeter is approximately:
t = 73.68 s
So, the spider would take about 74 seconds to walk around the perimeter of the room.
Final answer:
To determine the time for a spider to walk around a 3 m by 4 m room, calculate the perimeter (14 m), convert it to centimeters (1400 cm), and divide by the spider's speed (19 cm/s), resulting in approximately 73.68 seconds.
Explanation:
To calculate the time it would take for a spider to walk around the perimeter of a 3 m by 4 m room, first, find the perimeter of the room by adding the lengths of all the sides:
Perimeter = 2 × (3 m) + 2 × (4 m) = 6 m + 8 m = 14 m.Next, since the spider walks 19 cm each second, convert the perimeter from meters to centimeters because the units need to match.
Perimeter in centimeters = 14 m × 100 cm/m = 1400 cm.Now, divide the total perimeter by the spider's speed to find the time it takes:
Time = Perimeter / SpeedTime = 1400 cm / 19 cm/sTime ≈ 73.68 secondsTherefore, it would take approximately 73.68 seconds for the spider to walk around the perimeter of the room.