If the radius of the hole is 3 inches than the volume of the resulting solid is 410.29 in³ .
In the question ,
it is given that ,
the manufacturer drills a hole in the metal sphere that has radius of 5 inches ,
the radius of hole in sphere is 3 inches .
the volume of the metal sphere is = (4/3)×π×r³
= (4/3)×π×5³
= 523.33 in³
the volume of the hole of radius 3 inches is = (4/3)×π×3³
= 113.04 in³
So , the volume of the remaining solid is = 523.33 - 113.04
= 410.29 in³ .
Therefore , the Volume of the resulting solid is 410.29 in³ .
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The volume of a right cylinder is found by the formula V equals pi r squared h. Two cylinders both have a height of 10 centimeters. One has a volume of 2009.6 cubic centimeters. The other has a volume of 196.25 cubic centimeters. What is the radius of each cylinder? (Use 3.14 as an approximation of pi.)
The radii of the cylinders found using the formular for the volume of a cylinder, and the 2009.6 cubic centimeter and 196.25 cubic centimeter volumes of the cylinders, indicates;
The radius of the 2009.6 cm³ cylinder is 8 centimeters
The radius of the 196.25 cm³ cylinder is 2.5 centimeters
What is a cylinder?A cylinder is a solid that has three dimensions, consisting of two circular, parallel bases that enclose a curved pipe like surface in between.
The volume of one cylinder = 2009.6 cubic centimeters
The volume of the other cylinder = 196.25 cubic centimeters
The height of each cylinder, h = 10 centimeters
The formula for finding the volume of a cylinder is; V = π·r²·h
Where;
r = The radius of the cylinder
h = The height of the cylinder
The formula for finding the volume of a cylinder indicates;
r² = V/(π·h)
r = √(V/(π·h))
The radius of the cylinder of volume 2009.6 cubic centimeters, r₁ is therefore;
r = √(2009.6/(3.14 × 10) = 8
The radius of the 2009.6 cubic centimeters volume cylinder is r₁ = 8 cm
The radius, of the 196.25 cubic centimeters cylinder, r₂, is therefore;
r₂ = √(196.25/(3.14×10)) = 2.5
The radius of the 196.25 cubic centimeter volume cylinder, r₂ = 2.5 cm
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3. Students at Polk Middle School are given a fitness test. The results of their tests are shown in the table. Use the table to answer questions a-c. a. Find the time it takes each student to run . Evian:_ Toby:_ Jillian:_ b. Which student is running at the fastest rate? Expl c. Jillian is trying out for the cross country team. To make the team, she must run in less than . Will Jillian make the team? Explain.
The time for each of them to cover 1 mile is; Evian = 10 min, Toby = 9 min and Jillian = 12 min. The fastest is Toby and No, Jillian can't make the team.
What is unit rate?A unit rate means a rate for one of something.
Given that, Students at Polk Middle School are given a fitness test.
The fitness test result is;
Evian can run [tex]1\frac{1}{2}[/tex] miles in 15 minutes, Toby can run 2/3 miles in 6 minutes and Jillian can run 3/4 miles in 9 minutes
a) The rate of running in 1 mile = (total miles covered)/(total time taken)
Evian =
3/2 miles in 15 minutes
1 mile = 15x2/3
1 mile = 10 minutes
Toby =
2/3 mile in 6 minutes
1 mile = 6x3/2
1 mile = 9 minutes
Jillian =
3/4 miles in 9 minutes
1 mile = 9x4/3
1 mile = 12 minutes.
b) Since, Toby is covering 1 mile in the least minutes in comparison with other two, therefore Toby is fastest among them.
c) Jillian's rate = 1 mile in 12 minutes
Speed = 1/9 miles per minute
Therefore, she will cover 7/2 miles in = 12x7/2 = 42 minutes
That means, she can't make the team.
Hence, the answers are a) Evian = 10 min, b) Toby = 9 min and Jillian = 12 min, the fastest one is Toby and Jillian can't make the team.
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Answer it and explain how you got the answer
a. Using the graph, the estimated solution is: (-2, -0.6).
b. Solving algebraically, the exact solution is: (-2, -4/6).
How to Find the Solution of a System of Equations?The solution 0f a system of equations is that point of intersection where the lines of the two equations meet when they are plotted on a graph.
a. Given the graph of the equations, 2x - 3y = -2 and x + 1.5y = -3, the estimated solution, which is the point of the intersection of both lines can be, (-2, -0.5)
b. To get the exact solution, we would solve algebraically as shown below:
2x - 3y = -2 --> eqn. 1
x + 1.5y = -3 --> eqn. 2
Rewrite eqn. 2:
x = -3 - 1.5y --> eqn. 3
Substitute the value of x into eqn. 1:
2(-3 - 1.5y) - 3y = -2
-6 - 3y - 3y = -2
-6 - 6y = -2
-6y = -2 + 6
-6y = 4
y = 4/-6
y = -4/6
Substitute the value of y into eqn. 3:
x = -3 - 1.5(-4/6)
x = -3 + 1
x = -2.
The exact solution is (-2, -4/6).
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An annual pass to the local zoo is
$40.00. The daily pass is $12.00.
What is the least number of times
you can visit the zoo with the
annual pass to make it the better
deal?
The equation obtained from the expressions of the cost of using the daily and annual pass indicates that the least number of times to visit the zoo to make the annual pass the better deal is 4 times
What is an equation?An equation consists of two mathematical expressions linked with an equals to '=' sign.
The cost of the annual pass to the local zoo = $40.00
The daily pass to the zoo = $12.00
The least number of times to visit the annual pass to make it a better deal
Let x represent the number of times of visiting the zoo, at the first visit, we get;
Cost of visiting the zoo using the annual pass = $40.00
Cost of visiting the zoo using the daily pass = $12 ×1 = $12
Therefore, at the very first visit, it cost more using the annual pass to visit the zoo
When the cost of visiting the zoo is the same using the annual and the daily pass, we get;
12 × x = 40.00Where x = The number of days of visiting the zoo
Therefore;
x = 40.00 ÷ 12.00 = 3.[tex]\overline{3}[/tex]
Therefore, after the third visit, or on the fourth visit, it becomes the better deal to make use of the annual pass.
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drag and drop the quantity on the right column with a number from the left column
Answer: 27, 65, 29, 77, 37
Step-by-step explanation:
The number of diagonals of an [tex]n[/tex]-gon is [tex]\frac{n(n-3)}{2}[/tex].
The number of apothems of an [tex]n[/tex]-gon is [tex]n[/tex].
Answer:
Step-by-step explanation:
what is the probability that you will draw 4 kings when you draw 4 cards from a standard 52-card deck?
The probability that we will draw 4 kings from the 52-card deck be 1/270725.
Given, we draw 4 cards from a standard 52-card deck
we have to find the probability that we draw 4 kings
As, we know that the deck of cards contain 4 kings of two red and two black.
we have to choose 4 kings from 4 kings in the deck
Number of ways to choose 4 kings from the deck of cards = C(4 , 4)
Now, total number of ways in which 4 cards can be chosen be,
C(52 , 4)
So, the probability of drawing 4 kings from the deck of cards be,
P(E) = C(4 , 4)/C(52 , 4)
P(E) = 4×3×2 / 52×51×50×49
P(E) = 1 / 13×17×25×49
P(E) = 1/270725
Hence, the required probability be 1/270725
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Multiple choice. Answer
The function g(x) = (x - 5)² has a translation of 5 units to the right.
What are some rules for the transformation of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over x-axis, (-x, y).
-f(x) = Reflection over y-axis, (x, -y).
The parent function is a quadratic f(x) = x².
Now, The transformed function g(x) = (x - 5)² is a horizontal transformation of 5 units to the right.
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Graph the inequality on the axes below
x+ 5y <-30
The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).
What is an inequality?Inequality is defined as a relationship between two expressions or values that are not equal to each other.In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).Here given the inequality.
x + 5y ≤ 30
To find the x-intercepts.
We have to substitute 0 for y and solve x to determine the x-intercepts.
x + 5 × 0 = 30
By solving the equation.
x = 30
( 30, 0 ) is the x-intercepts.
To find the y-intercepts.
By substituting 0 for x and solving y will get the y-intercept(s).
0 + 5y = 30
5y =30
y = 30/5
y = 6
In the point form, y-intercept.
Y-intercept(s): ( 0, 6 )
(30, 0) is the x-intercept.
Y-intercepts at : ( 0, 6 ).
The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).
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Find the perimeter of the triangle XYZ with verticles X (1, 3) , Y(-4, -1) and Z(4, -1). Round your answer to two decimal places
Answer:
The perimeter is approximately 6.40.
Step-by-step explanation:
To find the perimeter of a triangle with vertices X (1, 3), Y (-4, -1), and Z (4, -1), we can first find the distance between each pair of points using the distance formula.The distance between points X and Y is:
$d(X,Y) = \sqrt{((1 - (-4))^2 + (3 - (-1))^2)} = \sqrt{25 + 16} = \sqrt{41}$
The distance between points Y and Z is:$d(Y,Z) =
\sqrt{((-4 - 4)^2 + ((-1) - (-1))^2)} = \sqrt{0 + 0} = 0$
The distance between points X and Z is:
$d(X,Z) = \sqrt{((1 - 4)^2 + (3 - (-1))^2)} = \sqrt{9 + 16} = \sqrt{25}$
We can then find the perimeter of the triangle by adding up the lengths of the sides. In this case, the perimeter is $d(X,Y) + d(Y,Z) + d(X,Z) = \sqrt{41} + 0 + \sqrt{25} = \sqrt{41} + \sqrt{25} = 6.40\ldots$.
Rounded to two decimal places, the perimeter is approximately 6.40.
given the four digits 2, 4, 6, and 7, how many different positive two-digit integers can be formed using these digits if a digit can be repeated in an integer?
There are 12 different positive two digit integers can be formed using these digits if a digit can be repeated in an integer.
Integer:
An integer is zero (0), a positive integer (1, 2, 3, etc.), or a negative integer with a minus sign (-1, -2, -3, etc.). A negative number is the additive reciprocal of the corresponding positive number. In mathematics languages, sets of integers are often denoted by a bold Z or a bold {Z}.
Given the question :
The number of different positive two integer number can be obtained by:
P(4, 2) = 4P2
We know that:
[tex]^nP_r[/tex] = n! / (n - r)!
⁴P₂ = 4! / (4 - 2)!
⁴P₂ = 4! / 2!
⁴P₂ = (4 * 3 * 2 * 1) / ( 2 * 1)
⁴P₂ = 24 / 2
⁴P₂ = 12
Hence, 12 different positive two-digit integers can be formed using these digits if a digit may not be repeated in an integer.
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7 need help
A reflection maps AABC onto AXYZ. List the corresponding congruent pairs of angles of the two triangles.
Answer:
Option C) ∠C ≅ ∠Z, ∠B ≅ ∠Y, ∠A ≅∠X------------------------------------------
ΔABC and ΔXYZ are congruent triangles.
Corresponding angles map as per the order of vertices:
∠A to ∠X, ∠B to ∠Y and ∠C to ∠Z so these are the pairs of congruent angles.The congruent pairs of angles are:
∠A ≅∠X, ∠B ≅ ∠Y and ∠C ≅ ∠ZThis is matching option C.
If M is a centroid of triangle WOR and YR = 11, what is the length of WR?
Answer:
22
Step-by-step explanation:
Y is midpoint of WR.
Hence,
YR = 1÷2 of WR ( Half of WR )
So,
WR = 2YR
= 2×11
= 22
One angle measures 170°, and another angle measures (6k 44)°. if the angles are vertical angles, determine the value of k. k = 12 k = 20 k = 21 k = 126
Answer: the answer is 21
Step-by-step explanation:
If one angle measures 170°, and another angle measures (6k + 44)° and both are vertical angles that means the second angle should be the same as the first angle.
Vertical angles are congruent meaning they have an equal measure.
Now we have to find k
(6k + 44) = 170
subtract 44 - 44 and 170 - 44
(6k) = 126
divide 6 by 6, that leaves with just k on the left.
126 divided by 6 equals to 21
k = 21
Hope this helps!
PLEASE HELP!!!!
Write the quadratic equation whose graph has x-intercepts of -11 and 3 and passes through the point (1, 192)
A: y=8x^2+64x−264
B: y=8x^2−64x−264
C: y=−8x^2+64x+264
D: y=−8x^2−64x+264
The quadratic equation with the given x-intercepts and that passes through the point (1, 192) is the one in option D.
y = -8x^2 -64x + 264
What is the quadratic equation?If a quadratic equation has x-intercepts x₁ and x₂ and a leading coefficient a, we can write the quadratic equation as:
y = a*(x - x₁)*(x - x₂)
Here we know that the x-intercepts are -11 and 3, replacing that in the equation above we will get:
y = a*(x + 11)*(x - 3)
We also know that the line passes through the point (1, 192), replacing the values in the quadratic equation we will get:
192 = a*(1 + 11)*(1 - 3)
192 = a*12*-2
192 = -24*a
192/-24 = a
-8 = a
So the quadratic equation is:
y = -8*(x + 11)*(x - 3)
Expanding this, we will get:
y = -8x^2 -64x + 264
So the correct option is D.
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11. What is the equation of the line that has a slope of 0 and passes through the point (9,-4)?
Answer:
y = 9
Step-by-step explanation:
The line that has a slope of 0: y = 0*x + ?
pass through the point (9,-4): 9 =0*(-4) + ?, we can get 9.
So the answer is y = 9.
Answer: y=0x-4
Step-by-step explanation:
y=mx+b
-4 = (0)(9)+b
b = -4
y = -4
Which of the following shows that polynomials are closed under addition when two polynomials 4x2 - 8x - 7 and -5x + 16 are added?
The statement which shows that polynomials are closed under addition when two polynomials 4x² - 8x - 7 and -5x + 16 are added include the following: C. 4x² - 13x + 9 will be a polynomial
What is a polynomial function?In Mathematics, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as the following:
Multiplication (product)AdditionSubtractionNext, we would add the two (2) given polynomials as follows;
(4x² - 8x - 7) + (-5x + 16)
4x² - 8x - 7 - 5x + 16
Rearranging the given polynomials by combining like terms, we have;
4x² - 8x - 5x + 16 - 7
4x² - 13x + 9
Therefore, the given polynomials are closed under addition.
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Complete Question:
Which of the following shows that polynomials are closed under addition when two polynomials 4x² - 8x - 7 and -5x + 16 are added?
a. 4x^2 - 13x + 9 may or may not be a polynomial
b. 4x^2 + 13x -23 may or may not be a polynomial
c. 4x^2 -13x + 9 will be a polynomial
d. 4x^2 + 13x - 23 will be a polynomial
Question 6 of 10
What is the equation of a circle centered at the origin with radius 20?
OA. x³ + ³ = 400
OB. x³+y³ = 20
OC. x² + y² = 20
OD. x² + y² = 400
Answer:
x^2 + y^2 = 400
Step-by-step explanation:
the general equation of a circle is,
x^2 +y^2 = r^2
where x, y are the coordinates of the circle
r is the radius
To join a health club, a person must pay a $75 one-time fee plus a charge of $30 per month. This situation can be represented by an equation of the form
y
=
m
x
+
b
, where x = the time in months and y = the total cost in dollars. What is the value of m in the equation?
The value of m in the equation is 30.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
It is a relationship between two expressions that is expressed as an equality on either side of the equal to sign. An equation would be 3 = 18, for instance.
In this case, the person must pay a $75 one-time fee plus a charge of $30 per month.
This will be illustrated in the equation as:
y = 75 + 30x
where
x = the time in months and
y = the total cost in dollars.
The value of m is 30.
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help me plsssss
i put the image below
if u can see it
help asap
Answer:
q= 1.09
Step-by-step explanation:
the works there its a little messy tho
You have won a new PS 5 system in a rafflel With a bit of research, you have determined that the cost of a new PS 5 system is $712 with tax. If you know that the value of gaming consoles decreases each year by 12%, based on the previous year's value, what will your PS 5 system be worth after 6 years?
The salvage value of the PS 5 system after 6 years will be $640.
Explain the term depreciation?Depreciation is the estimated decrease in value of fixed assets over the course of a fiscal year. The amount of an asset's value has indeed been used is shown through depreciation. It enables businesses to purchase assets over a predetermined length of time and generate income from those assets.The formula for the depreciation;
Depreciation per year = (cost of asset - salvage value)/ (useful life of assets)
For the stated question-
Cost of new PS 5 system = $712.salvage value to be find.Depreciation per year = 12%useful life of assets = 6 years.12 = (712 - salvage value)/ (6)
salvage value = 712 - 12x6
salvage value = $640.
Thus, the salvage value of the PS 5 system after 6 years will be $640.
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Ed is 5 years older than his wife. The sum of their ages is 59. How old is Ed? How old is his wife? Ed age: Wife age:
Answer:
ede 5 years old er = wife 25 Ed 34
Help pls thanks urgent !!!
Money market accounts allow for the creation of savings for current or upcoming requirements.
What is meant by money market account?Savings for immediate or future needs can be made in money market accounts. To maintain your emergency savings in a convenient and secure location, for instance, you can think about opening a money market account. You desire to earn an APY similar to CDs without locking up your money for months.
You can get instant access to your money using money market accounts almost whenever you need it. A common feature of MMAs is the availability of check writing and debit card cash access. Also, be aware that you can often withdraw funds without being charged a fee, just like you could with a certificate of deposit (CD).
Therefore, the correct answer is option A. want to make numerous transactions and earn interest.
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A student has two options to purchase a laptop.
Option 1: Pay $540 plus 15% sales tax now.
Option 2: Pay exactly $120 now and then $58 each month for 9 months.
What is the approximate percent increase in how much the student pays with Option 2 versus Option 1?
Responses
Approximate percent increase in how much the student pays with Optin 2 versus Option is 20%
How to find Percentage?$540 plus 15% sales tax now.=$515
Pay exactly $120 now and then $58 each month for 9 months=$642
There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any topic are calculated in terms of percentages in academics. Ram, for instance, scored 78% in his final exam. This percentage is determined using Ram's overall grade point average (GPA) across all disciplines. We must apply a different formula, like the one shown below, to determine the percentage of a number.X Equals P% of NumberIf we don't use the percent sign, we must write the calculations above as P/100 * Number = X.To learn more about Percentage refer to:
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Interpret parts of the algebraic expression to describe the real-world scenario.
The value of a comic book in dollars has been found to be 0.20y + 1.50, where y is the number of years since it was released.
By how much is the value of the comic increasing per year?
How much was the initial value of the comic?
The value of a comic book in dollars has been found to be 0.20y + 1.50, where y is the number of years since it was released. is
(a) [tex]0.2$[/tex]
(b) [tex]1.5$[/tex]
[tex]0.2 y+1.5 \longleftarrow \text { initial value }[/tex]
[tex]when $y$ increase one. the value increase $\$ 0.2$[/tex]
Travelling to movies and television programmes. An element of a comic book being in a popular film or television programme is a major factor in its value rising. Characters' comic book appearances have become far more valuable as they are integrated into the Marvel Cinematic Universe.
Marvel's first comic book just sold for $1.26m. Movies have contributed to the enduring popularity of superheroes, bringing in new audiences. The printed comic is still big business, worth over $1bn in North America alone.
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In 2008, Yolanda paid $3,875 in Social Security tax. If the Social Security tax rate was 6.2% to the maximum income of $94,200 that year, what was Yolanda's taxable income
The Yolanda's taxable income is $62,500.
What is income tax?
An income tax is a charge levied against people or organizations in relation to the income or profits they make. In most cases, income tax is calculated as the sum of the tax rate and the amount of taxable income. The type of taxpayer and the type of income are two factors that can affect the tax rate.
Given:
In 2008, Yolanda paid $3,875 in Social Security tax.
The Social Security tax rate was 6.2% to the maximum income of $94,200 that year.
Lets assume Yolanda´s income be `x`.
Now, calculating the taxable income of Yolanda
6.2% x (x) = 3875
[tex]\frac{6.2}{100} (x) = 3875\\x = 3875(\frac{100}{6.2}) \\x = 62500[/tex]
Hence, the Yolanda's taxable income is $62,500.
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There are 24 men and 25 women running a race. What is the ratio of the number of female runners to the total number of runners?
Answer:
5/9 In fraction form. In decimal form 0.51 and in percentage form %51
Step-by-step explanation:
To find the ratio of the number of female runners to the total number of runners, we can divide the number of female runners by the total number of runners and express the result as a fraction. There are 25 female runners, and there are a total of 24 men + 25 women = 49 runners. Therefore, the ratio of the number of female runners to the total number of runners is 25/49. This fraction can be reduced to 5/9.
If the scale factor from A to B is 8/5 Then the scale factor from B to A is...
The scale factor from B to A is 5/8. Since the scale-up and scale-down of A and B are reciprocal to each other. I.e, scaling of geometry can be reversed by the reciprocal of its scale factor.
What is meant by a scale factor and how is it calculated?Scale factor: A number that is multiplied by the components of an object to create an enlargement or reduction of the object.Scale factor = new length/original length There are two kinds of scaling. They are scale-up and scale-down.Scale-up is nothing but enlarging the shape and scale-down means reducing the shape.The scaling of an object or shape is reversed by finding the reciprocal of its scale factor. If the scale factor is greater than 1 then it goes under enlargement and if it is less than 1, then it goes under reduction.Calculation:The scale factor for the given shape to transform from A to B is 8/5.
So, the original shape is A and it is scaled up by the factor 8/5 and named B.
(Scaled up since scale factor (8/5 = 1.6) > 1)
So, the scaling from B to A is the reverse process of scale-up. That means scale-down. For this, the scale factor is reduced by taking its reciprocal. So, that the shape gets reversed.
The scale factor for scaling down from B to A is 1/(8/5) ⇒ 5/8.
Therefore, the scale factor from B to A is 5/8.
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Which of the following can be represented by the equation 3x = 24?(1 point)
Rita bought stickers and divided them among herself and two other friends. Each one received 24 stickers. How many stickers did Rita buy?
A survey was conducted to determine the favorite subject of seventh grade students. One-third of all surveyed, or 24 students, said math is their favorite subject. How many students were surveyed?
Andrew picks three words from a dictionary every week and lists them in his notebook. So far, he has listed 24 words. How many weeks has Andrew been doing this?
The cost of a pair of shoes is three times the cost of a shirt. If the cost of the shirt is $24, how much does the pair of shoes cost?
Answer:
The last answer is correct
Step-by-step explanation:
3x = 24 Divide both sides by 3
x = 8
A pair of shoes cost $8
Solve for x. 2.5x + 1.5
[A.5A] What is the solution to 2(m+6)-5-3(m-2) ?
Answer:
-m + 13
Step-by-step explanation:
