The number of students participating in the math competition, where they are divided into teams of 3, must be a multiple of 3. These numbers include 3, 6, 9, etc. Any number divisible by 3 without a remainder is possible.
To determine how many students could be participating in the math competition where teams are composed of 3 students each, we must think about multiples of 3. Since teams must be evenly divided, only a total number of students that is a multiple of 3 would be possible. The concept here is similar to the division of a group assignment among students. For instance, if five students are working on an assignment and they divide it into five equal parts, each student will do one part. In the case of the math competition, we can say that 3, 6, 9, and so on are possible numbers of students participating. Simplistically, any number that can be divided by 3 without leaving a remainder is a valid answer.
help on question 32 please
Answer:
90
Step-by-step explanation:
The mean is measured as
mean = [tex]\frac{score}{count}[/tex]
After 5 tests the mean is 84, that is
[tex]\frac{score}{5}[/tex] = 84 ( multiply both sides by 5 )
score = 420
let the sixth test score be x, then
[tex]\frac{420+x}{6}[/tex] = 85 ( multiply both sides by 6 )
420 + x = 510 ( subtract 420 from both sides )
x = 90
Require to score 90 on the sixth test
Reggie knows how to make 5 different entrees, 4 dif-
ferent side dishes, and 6 different desserts. How many
distinct complete meals, each consisting of an entrée, a
side dish, and a dessert, can Reggie make?
F. 16
G. 26
H. 72
J. 120
K. 144
Reggie can make 120 distinct complete meals, each consisting of an entrée, a side dish, and a dessert.
This is a rather simple and straightforward question.
If Reggie can make
5 Entrees
4 Side dishes
6 Desserts,
Then she can make 5 × 4 × 6 different distinct dishes.
5 × 4 × 6 = 120
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A movie cost 3,254, 107 to produce what digit is in th hundred thousands place
Answer:5
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
3 million
2 hundred thousand
5 ten thousand
4 thousand
1 hundred
0 ten
7 one
Solve for n.
d = 4m +7n
Step-by-step explanation:
d = 4m +7n
d - 4m = 7n
(d -4m)/7 = n
d = 4m +7n
We need to isolate n.
d - 4m = 7n
(d - 4m)/7 = n
Done!
The bottom of Ignacio's desktop is 74.5\,\text{cm}74.5cm74, point, 5, space, c, m from the floor. Ignacio sits in his adjustable chair, and the tops of his legs are 49.3\,\text{cm}49.3cm49, point, 3, space, c, m from the floor. Each clockwise rotation of the knob on the chair raises Ignacio's legs by 4.8\,\text{cm}4.8cm4, point, 8, space, c, m.
Write an inequality to determine the number of clockwise rotations, rrr, Ignacio could make with the knob without his legs touching the desk.
Answer:
The inequality is:
49.3+4.8r <74.5
The solution set is r < 5.25
Step-by-step explanation:
Answer:
The solution set is r < 5.25
and The inequality is:
49.3+4.8r <74.5
Step-by-step explanation:
Hi Im FREDDDDD
In the diagram shown below is it given (known) that FB and EH intersect at A and ZEAG is right. Give
two different angles that are both supplementary to ZFAH. What must be true of these two angles?
Answer:
Angle HAB and Angle FAE are congruent angles
Step-by-step explanation:
we know that
Two angles are supplementary if their sum is equal to 180 degrees
In this problem
m∠FAH+m∠HAB=180° ----> by a linear pair
Remember that
A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. A linear pair of angles must add up to 180 degrees
m∠FAH+m∠FAE=180° ----> by a linear pair
therefore
m∠HAB=m∠FAE -----> by vertical angles
Angle HAB and Angle FAE are congruent angles
Answer:
<HAB is congruent with <FAE
NO CAP
In science class, Savannah measures the temperature of a liquid to be
24 Celsius. Her teacher wants her to convert the temperature to degrees Fahrenheit. What is the temperature of Savannah's liquid to the nearest degree Fahrenheit?
Answer:
75.2 °F
Step-by-step explanation:
(24°C × 9/5) + 32 = 75.2°F
A point, beginning at (0,0), undergoes the following composition of translation. Write an ordered pair for the points final position. T<5,-7> and then T<-6,2>
Answer:
(-1,-5)
Step-by-step explanation:
Starting at (0,0), we perform the first translation:
T<5,-7> implies that we move the point 5 units to the right (in the x (horizontal) direction), and 7 units DOWN in the y <vertical) direction.
From there we do the second translation: T<-6,2>
which means: 6 units to the left (in the horizontal direction) which takes us to "-1" for the x value, and 2 units up (vertical) which takes us to -5 for the y value.
Therefore the new location is (-1,-5)
Which of these rational numbers is a repeating decimal? Select all that apply
A.-0347
B.3.611
C.-1.35
D.2.153
E.7.777
Answer:
C
Step-by-step explanation:
From the given options, only option E.7.777 is a repeating decimal because its decimal part '7' repeats indefinitely.
Explanation:In mathematics, a repeating decimal is a decimal fraction that after some place repeats the same sequence of digits indefinitely. From the options given: A.-0347, B.3.611, C.-1.35, D.2.153, and E.7.777, we are looking for which numbers have decimal parts that repeat.
Option A.-0347 is not a repeating decimal because the decimal part '0347' does not repeat indefinitely. Option B.3.611 and Option D.2.153 also do not have repeating decimal parts.
Option C.-1.35 does not have a repeating decimal part either. However, Option E.7.777 is indeed a repeating decimal, as the decimal part '7' repeats indefinitely.
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the formula F=ma means that the force on an object is equal to its mass times the acceleration. Solve F=ma for m
Answer:
Step-by-step explanation:
F = m / a
cross multiply
m = F /a
To solve F=ma for mass, divide both sides by acceleration to get m=F/a. For a wagon of 55 kg accelerating at 0.0255 m/s², the calculated force is 1.4025 newtons.
Explanation:To solve the formula F=ma for mass (m), you need to isolate the variable m. This is done by dividing both sides of the equation by acceleration (a), thus the rearranged formula becomes m = F/a. When we apply this to a practical example, if a wagon with mass 55 kg accelerates at a rate of 0.0255 m/s², the force on the wagon can be calculated using the same formula. By substituting the values into the formula, the force F is found as F = 55 kg × 0.0255 m/s², which equals 1.4025 newtons (N).
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What is the measure of angle RPS?
Answer:
70
Step-by-step explanation: the type of angle it is
Answer:
∠RPS = 70°
Step-by-step explanation:
∠RPT is a right angle and
∠RPS + ∠SPT = ∠RPT ← substitute values
∠RPS + 20° = 90° ( subtract 20° from both sides )
∠RPS = 70°
What is the domain of the function f(x) = 2x + 5?
O A.
all real numbers except 2
O B. all real numbers
O c. all real numbers except 5
OD. all positive real numbers
There is no value that x cannot be for linear equations.
Thus, the domain is ALL REAL NUMBERS.
CHOICE B.
Answer:
B all real numbers
Step-by-step explanation:
Which inequality represents all the solutions of 8(6x − 7) < 5(9x − 4)?
Answer:
The inequality that represents the solution of 8(6x − 7) < 5(9x − 4) is x < 12.
Step-by-step explanation:
Given 8(6x − 7) < 5(9x − 4)⇒ 48x - 56 < 45x - 20⇒ 48x - 45x < -20 + 56
⇒3x< 36 ⇒ x<36/3 ⇒ x<12.
Inequalities help us to compare two unequal expressions. The correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given inequality can be solved as,
8(6x − 7) < 5(9x − 4)
48x − 56 < 45x − 20
48x − 45x < 56 − 20
3x < 36
x < 36/3
x < 12
Hence, the inequality that represents all the solutions of 8(6x − 7) < 5(9x − 4) is x < 12.
The complete question is:
Which inequality represents all the solutions of 8(6x − 7) < 5(9x − 4)? A. x > 12 B. x < 12 C. x > 20 D. x < 20
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A roll of material is (x + 2) metres wide. Annie buys (x + 3) metres of the material and Bronwyn buys 5 metres of the material.
a) Write an expression, in terms of x, for the area of each piece of material purchased.
b) If Annie has bought more material than Bronwyn, write an expression for how much more she has than Bronwyn.
c) Factorise and simplify this expression.
d) Find the width of the material if Annie has 5m^2 more than Bronwyn.
e) How much material does each person have? Explain.
The problem involves determining the area of material purchased, comparing the quantities, and solving for the width given certain conditions. After setting up and solving the equations, it was found that the width of the material is 3 metres and the total amounts of material purchased by Annie and Bronwyn are 4 and 15 square metres respectively.
To solve the problems related to the area of material purchased by Annie and Bronwyn, follow these steps:
Area of material: Given the width of the material is (x + 2) metres, Annie buys (x + 3) metres long and Bronwyn buys 5 metres long. The area for each piece of material purchased is the product of the width and length. So, Annie's material area is (x + 2)(x + 3) square metres, and Bronwyn's material area is 5(x + 2) square metres.
More material: To express how much more material Annie has than Bronwyn, subtract Bronwyn's area from Annie's area, which gives us ((x + 2)(x + 3) - 5(x + 2)) square metres.
Factorisation: The expression for how much more material Annie has than Bronwyn can be factorized as (x + 2)(x - 2) square metres after simplifying.
Width of material: If Annie has 5 square metres more material than Bronwyn, we solve the equation (x + 2)(x - 2) = 5. Solving this quadratic equation gives x = 1, the width of the material is therefore 3 metres.
Total material: With x = 1, Annie purchases 4 square metres (since 3 x 1 + 3) and Bronwyn purchases 15 square metres (since 5 x 3). So, Annie has 4 square metres of material and Bronwyn has 15 square metres.
solve for x: x² - 14x + 49/x² - 49 = 3/17
Answer:
x = 10
Step-by-step explanation:
Begin by factorising the numerator/ denominator of the left side
x² - 14x + 49 = (x - 7)² ← perfect square
x² - 49 = (x - 7)(x + 7) ← difference of squares
Thus left side becomes
[tex]\frac{(x-7)^2}{(x-7)(x+7)}[/tex] → x ≠ ± 7
Cancel (x - 7) on numerator/denominator, leaving
[tex]\frac{x-7}{x+7}[/tex]
Returning to the equation, that is
[tex]\frac{x-7}{x+7}[/tex] = [tex]\frac{3}{17}[/tex] ( cross- multiply )
17(x - 7) = 3(x + 7) ← distribute both sides
17x - 119 = 3x + 21 ( subtract 3x from both sides )
14x - 119 = 21 ( add 119 to both sides )
14x = 140 ( divide both sides by 14 )
x = 10
Trinity is going to the movies with some friends and will pay for her own ticket plus her own and her friends' small popcorns. Her total cost is given by the following expression: 8.5 + 6x What does the 6x represent?
A. The total cost of the small popcorns
B. The amount of small popcorns she is buying
C. The total cost
D. The cost of the ticket
Answer:
A. The total cost of the small popcorns
Step-by-step explanation:
Let us suppose Trinity is going to the movies with [tex]x[/tex] number of friends, we know she will pay for only her own movie ticket hence cost of movie ticket will be a constant (say [tex]a[/tex]) for her expense and cost of popcorn will be price of one popcorn (say [tex]b[/tex]) multiplied by number of friends.
considering the situation, her expense will be given by the function-
[tex]f(x) = a + bx[/tex]
comparing this with the given function [tex]8.5 + 6x[/tex], [tex]6x[/tex] will be the total cost of small popcorns.
Help please fast
Question 17
Answer:
I think the answer may be 12 minutes
Answer:
I think it is 12 mins
A ladder leaning against the side of a building touches the building at a point 12 meters from the ground. If the foot of the ladder is 18 meters from the base of the building, what is the slope of the ladder?
Answer:
The slope of the ladder to the building is 2/3
Step-by-step explanation:
* Lets explain how to find the the slope of the ladder
- A ladder leaning against the side of a building touches the building
at a point 12 meters from the ground
* That means the height of the ladder (h) from the ground is 12 m
- The foot of the ladder is 18 meters from the base of the building
* That means the horizontal distance (d) on the ground between the
ladder and the building is 18 m
- The slope of the ladder (m) , the height of the ladder (h) and the
horizontal distance on the ground from the base of the ladder to
the base of the building (d) can form a right triangle
∵ The slope of the ladder = the vertical distance/horizontal distance
∵ The vertical distance h is 12 meters
∵ the horizontal distance d is 18 meters
∴ The slope of the ladder [tex]m=\frac{12}{18}=\frac{2}{3}[/tex]
∴ The slope of the ladder to the building is 2/3
Answer:
2/3
Step-by-step explanation:
Its just as easy as it looks. Its 12/18, or Rise 12 and Run 18.
Solving would get you 2/3, so your slope is 2/3
Need help please!!!!!!!!!!!!!!
What is the slope of a line that is perpendicular to 8x+4y=2
Answer:
[tex] \frac{1}{2} = m[/tex]
Step-by-step explanation:
8x + 4y = 2
-8x - 8x
____________
4y = -8x + 2
__ _______
4 4
y = -2x + ½
↑
rate of change [slope]
* Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES]:
-2 → ½
I am joyous to assist you anytime.
12. Snowfall At 8:00 A.M., you measure the depth of snow in your backyard to be
4 inches. At 6:00 P.M., you measure the snow depth to be 19 inches. What is the
average rate of change in the snow depth?
10
Answer: The answer would be 1.5
Step-by-step explanation: From 8-6 it is 10 hours. Then you go from 4 inches to 19 inches. So every 10 hours is 15 inches more of snow. If you divide 15 by 10 then it is 1.5
The volume, V, of the right circular cone with radius r.
and height h, shown below, can be found using the
formula V= { ar?h. A cone-shaped paper cup has a
volume of 142 cubic centimeters and a height of
8.5 centimeters. What is the radius, to the nearest
centimeter, of the paper cup?
Answer:
radius^2 = 3 * Volume / (PI * height)
radius^2 = 3 * (142 cc / 3.14159265 * 8.5)
radius^2 = 3 * (142 cc / 26.703537525 )
radius^2 = 15.9529425493
radius = 4.0 cm
Step-by-step explanation:
Final answer:
The radius of a cone-shaped paper cup with a volume of 142 cubic centimeters and height of 8.5 centimeters is approximately 4 centimeters when rounded to the nearest centimeter.
Explanation:
To determine the radius of a paper cup that is a right circular cone with a given volume, we will use the formula for the volume of a cone V = (1/3) πr²h. The volume, V, is provided as 142 cubic centimeters, and the height, h, is 8.5 centimeters.
Rearrange the formula to solve for the radius, r, as follows:
Divide both sides by π and 8.5 to isolate ¹⁄₃r² on one side.
Multiply both sides by 3 to get rid of ¹⁄₃.
Take the square root of both sides to solve for r.
Once we have the value of r, we round it to the nearest centimeter as the question asks for an approximation to the nearest whole number.
Let's perform the calculation:
V = (1/3)πr²(8.5) => 142 = πr²(8.5/3)
142 = (π × 8.5/3)r²
142 / (π × 8.5/3) = r²
r² ≈ 142 / (3.14159 × 8.5/3)
r² ≈ 15.91549431
r ≈ √15.91549431 ≈ 3.99 cm
Round r to the nearest centimeter: r ≈ 4 centimeters
7/10÷2 5/8
Do i have to simplify
let's firstly convert the mixed fraction to improper fraction and then divide.
[tex]\bf \stackrel{mixed}{2\frac{5}{8}}\implies \cfrac{2\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{21}{8}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{7}{10}\div \cfrac{21}{8}\implies \cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{\underset{5}{~~\begin{matrix} 10\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{\stackrel{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{3}{~~\begin{matrix} 21 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{4}{15}[/tex]
[{8 + 113 • 5] - 8 + 11
Answer:
[8 + 113 • 5] - 8 + 11 =
[8 + 565] - 8 + 11 =
573 - 8 + 11 = 576
A volume of Is formed by revolving a plane figure through 360 degrees around a line
Answer:
y
Step-by-step explanation:
Write all the numbers up to 30 that have an equal number of odd and even factors
Answer: 2, 6, 10, 14, 18, 22, 26, 30 have an equal number of odd and even factors.
Step-by-step explanation:
Since they want the same number of even and odd factors for numbers 1-30 then we can list the factors of only even numbers from 1-30
List factors of even numbers 1-30
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
2) 1,2
4) 1,2,4
6) 1, 2, 3 6
And so forth for the rest of the numbers
you will notice that you add 4 each time untill you get to thirty which are numbers that have an equal number of odd and even factors.
Can someone please solve
y = x + 3
-2 x + 12
Answer: y= -x + 15
Step-by-step explanation:
1.) Put the equation in 1 line: y= x + 3 - 2x + 12
2.) Subtract and add the x's together and the whole numbers together. (1x-2x) (3 + 12)
3.) Put the whole equation together again. y= -x + 15
The number of equal parts that something is evenly distributed into is the
Hey there!
The number of equal parts that something is evenly distributed into is the divisor.
Hope this helps!
x+109 and x+89 what is x they need to be the same number when finished
Answer:
DNE (dose not exist)
Step-by-step explanation:
what you would do is just set both functions equal to each other and then solve for x. so set x+109=x+89. then get you numbers on one side and your x's on one side. so subtract x from on side getting x-x+89=109 now you subtract 89 from both sides getting x-x=109-89 getting 0= 20 0 dosen not = 20 so you would have zero there is no value that you could plug in for x to get them both equal
-10 2/7 divided by -4 4/11 I cannot seem to get this question right
Answer:
-2 5/14
Step-by-step explanation:
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{10\frac{2}{7}}\implies \cfrac{10\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{72}{7}}~\hfill \stackrel{mixed}{4\frac{4}{11}}\implies \cfrac{4\cdot 11+4}{11}\implies \stackrel{improper}{\cfrac{48}{11}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf -\cfrac{72}{7}\div -\cfrac{48}{11}\implies \cfrac{-72}{7}\div \cfrac{-48}{11}\implies \cfrac{\stackrel{3}{~~\begin{matrix} -72 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{7}\cdot \cfrac{11}{\underset{2}{~~\begin{matrix} -48 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{33}{14}\implies 2\frac{5}{14}[/tex]