Answer:
1728 cm ^ 3.
Step-by-step explanation:
we are given 12 cm
As we know formula of volume of cube = s ^3 ( side * side * side ) So = 12 * 12* 12 = 1728 cm ^ 3.
Find the Volume cylinder (8cm) (12cm) h = 8cm r = 12cm h = 8 cm r = 12 cm. The volume of a cylinder is equal to the area of the base πr2 π r 2 times the height. π⋅(radius)2 ⋅(height) π ⋅ ( r a d i u s) 2 ⋅ ( h e i g h t) Substitute the values of the radius r = 12 r = 12 and height h = 8 h = 8 into the formula to find the volume of the cylinder
P.s hopes this helps
Determine the prime factorization of 350
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define Prime factorization.
Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself. Examples of prime numbers are 2,3,5,7...etc.
STEP 2: Find the prime factors of the given number
Prime factorization of any number means to represent that number as a product of prime numbers.
We start by dividing the number by the lowest possible prime numbers.
STEP 3: Express 350 as a product of its prime factors
[tex]\begin{gathered} \text{Prime factors}=2,5,5,7 \\ \text{Product of prime factors=}2\times5\times5\times7 \\ =2\times5^2\times7 \end{gathered}[/tex]Hence, the prime factorization of 350 is given as:
[tex]2\times5^2\times7[/tex]there are 150 oranges in 10 craftes of each crate has the same amount of oranges how many oranges are in each crate?
Take the total number of oranges and divide by the number of crates
150 orange
----------------
10 crates
15 oranges per crate
Please help this is due tomorrow!!
The expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The given polynomial expression below is:
⇒ 10x⁵y⁷/5x⁵y · 3x⁴y⁸/3x⁻³y¹⁰
Apply the division operation in the constant terms
⇒ 2x⁵y⁷/x⁵y · x⁴y⁸/x⁻³y¹⁰
Apply the arithmetic operation in the Exponents of the same base variables
⇒ 2y⁶ · x⁷y⁻²
⇒ 2y⁶⁻² · x⁷
⇒ 2y⁴ · x⁷
⇒ 2x⁷· y⁴
Therefore, the expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
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Identify each of the following statements as true or false in relation to confidence intervals (CIs).
Let's analyze each sentence to check if it is true or false:
First:
This sentence is true, the confidence interval is an interval where the true mean is likely to be.
Second:
This sentence is true, with a sample size smaller than 30, it is better to use the t-distribution instead of the normal distribution.
Third:
This sentence is true, the confidence interval is not a 100% guarantee that the true mean will be inside it.
Fourth:
Ti s sentence is true, this theorem states that when getting a large enough sample of a distribution with mean and standard deviation, the sample will be approximately normally distributed.
Fifth:
This sentence is false, because the number of degrees of freedom is 1 less than the sample size, so it would be 10.
Therefore the answer is:
True, True, True, True, False.
For the function f(x)=3x2−4x−4,a. Calculate the discriminant.b. Determine whether there are 0, 1, or 2 real solutions to f(x)=0.
Answer:
a) Using the formula for the discriminant we get:
[tex]\begin{gathered} \Delta=(-4)^2-4(3)(-4), \\ \Delta=16+48, \\ \Delta=64. \end{gathered}[/tex]The discriminant is 64.
b) Based on the above result we know that the f(x)=0 has 2 real solutions,
Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4m×3m ?
Given:
Length = 4m
Width= 3m
Height = 2.5 m
Therefore, the surface area of rectangle prism is 2lh+2bh+lb
[tex]\begin{gathered} 4\times2.5\times2+3\times2.5\times2+4\times3=10\times2+5\times3+12 \\ =20+15+12 \\ =47 \end{gathered}[/tex]Hence, the required answer is 47m^2.
¿Por qué NO puede encontrar el punto medio de una línea?
Las líneas en un plano cartesiano son infinitas, no tienen un punto de inicio o final, por lo que no es posible determinar un punto medio para ellas.
The table shows the total cost c for the number of aquarium tickets purchased t. Write an equationthat can be used to find the cost c oft aquarium tickets. Use the equation and complete the table tofind the cost of 7 tickets.7Number of Tickets, tCost, cWrite an equation3$29.2510 12$97.50 $117.00(Use the operation symbols in the math palette as needed. Use integers or decimals for any numbers in the equatioDo not include the $ symbol in your answer.)
We can model the cost and number of tickets by a linear equation of the form
[tex]c=mt+b[/tex]Where c is the cost, t is the number of tickets.
m is the slope of the equation and b is the y-intercept.
First, let us find the slope which is given by
[tex]m=\frac{c_2-c_1}{t_2-t_1}[/tex]You can take any two pairs of values from the table.
[tex]m=\frac{117-97.50}{12-10}=\frac{19.5}{2}=9.75[/tex]The slope is 9.75 and the equation becomes
[tex]c=9.75t+b[/tex]Now we need to find the y-intercept (b)
Choose any one pair of values from the table and substitute them into the above equation and solve for b.
Let's choose (12, 117)
[tex]\begin{gathered} c=9.75t+b \\ 117=9.75(12)+b \\ 117=117+b \\ b=117-117 \\ b=0 \end{gathered}[/tex]The y-intercept is 0 so the equation is
[tex]c=9.75t[/tex]Now to find the cost of 7 tickets, simply substitute t = 7 into the above equation
[tex]\begin{gathered} c=9.75t \\ c=9.75(7) \\ c=68.25 \end{gathered}[/tex]Therefore, the cost of 7 tickets is $68.25
4. Solve the polynomial.
7x³ + 21x² - 63x = 0
After solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}
What is a polynomial?An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² 4x + 7 is an illustration of a polynomial with a single indeterminate x.So, 7x³ + 21x² - 63x = 0:
Now, solve for x as follows:
7x³ + 21x² - 63x = 07x(x² + 3x - 9) = 0Zero factor principal, if ab = 0, then a = 0 and b = 0.
x = 0 and x² + 3x - 9 = 0Now, x² + 3x - 9 = 0:
x = [(-3 ± 3√5)/2]x = 0Therefore, after solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}
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Given a triangle ABC at points A = ( - 2, 2 ) B = ( 2, 5 ) C = ( 2, 0 ), and a first transformation of right 4 and up 3, and a second transformation of left 2 and down 5, what would be the location of the final point B'' ?
Answer
a. (4, 3)
Step-by-step explanation
The translation of a point (x, y) a units to the right and b units up transforms the point into (x + a, y + b).
Considering point B(2, 5), translating it 4 units to the right and 3 units up, we get:
B(2, 5) → (2+4, 5+3) → B'(6, 8)
The translation of a point (x, y) c units to the left and d units down transforms the point into (x - c, y - d).
Considering point B'(6, 8), translating it 2 units to the left and 5 units down, we get:
B'(6, 8) → (6 - 2, 8 - 5) → B''(4, 3)
Answer: The answer would be (4,3)
Step-by-step explanation: because if you started with (2,5), which would be (x,y) x goes left and right, and y goes up and down, and the questions says that you have to go 4 to the right and 3 up, then add 4 to 2, which is 6, and 3 to 5, which is 8, so now you have the point (6,8), then the second translation would be 2 to the left, and down 5, this is negative so you subtract this time, so subtract 2 from 6, which is 4, and 5 from 8, which is 3, so your final answer is (4,3).
Fill in the missing numbers to complete the linear equation that gives the rule for this table.x: 1, 2, 3, 4y: 8, 28, 48, 68Y = ?x + ?
we have a table that describe the line and we need to finde the slope and the intercept with the y axis, so the slope can be found with this equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So I use the numbers in the table to fill the equation so:
[tex]\begin{gathered} m=\frac{28-8}{2-1} \\ m=\frac{20}{1} \\ m=20 \end{gathered}[/tex]now for the intercept we replace x=0 and use the coordinate (1,8) so:
[tex]20=\frac{y-8}{0-1}[/tex]and we solve for y so:
[tex]\begin{gathered} -20=y-8 \\ -20+8=y \\ -12=y \end{gathered}[/tex]So the equation is:
[tex]y=20x+(-12)[/tex]An airplane takes off from an airport that is 144 ft above sea level. The airplane flies at 30,000 ft. To avoid a storm , the airplane goes up to 35,000 ft. Immediately after passing the storm, the airplane returns to its original altitude. Finally , the airplane lands at an airport that is 1,998 ft above sea level . What integer represents the airplanes changes in altitude to avoid the storm ? Immediately after passing the storm ? the integer □ represents the change in altitude to feet to avoid the storm.the integer □ represents the change in altitude in feet immediately after passing the storm.
What integer represents the airplanes changes in altitude to avoid the storm ?
changes = 35000 - 30000
= 5000 ft
the integer 5000 represents the change in altitude to feet to avoid the storm.
the integer -5000 represents the change in altitude in feet immediately after passing the storm.
Abdul will rent a car for a day. The rental company offers two pricing options: Option A and Option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below.
From the graph, we are to determine the following:
(a) We are to find the option that costs less if Abdul drives 300 miles of the rental car and also how much less is it from the other option.
Option A: when x = 300, y = 140
Option B: when x = 300, y = 120
So the difference is:
140 - 120 = 20
So the option that costs less is B
And it costs $20 lesser than option A
(b) For what number of miles does the option costs the same and if Abdul drives less than that amount, what option cost more.
Option A: when x = 100, y = 60
Option B: when x = 100, y = 60
Therefore, the number of miles where the options cost the same is 100 miles.
If Abdul drives less than the amount:
That is x < 100, the B > A,
Which means, if Abdul drives less than 100 miles, Option B, costs more.
ave read 14 pages in 28 minutes how much pages can she read for 50 minutes
Answer:
Step-by-step explanation:
14x2=28
50 divided by 2 = 25 pages
14pages=28mins
page=2mins
so
pages =50/2
=25
The safe load, L, of a wooden beam of width w, height h, and length l, supported at both ends, varies directly as the product of the width and the square of the height, and inversely as the length. A wooden beam 5 inches wide, 8 inches high, and 216 inches long can hold a load of 7670 pounds. What load would a beam 3 inches wide, 5 inches high, and 240 inches long of the same material, support? Round your answer to the nearest integer if necessary.
we know that
L=KW(h^2)/l
we have that
W=5 in
h=8 in
l=216 in
L=7670 pounds
step 1
Find the value of K (constant of proportionality)
substitute the given values in the equation
7670=K(5)(8^2)/216
7670=k(1.4815)
k=5,177.25
step 2
we have the equation
L=(5,177.25)W(h^2)/l
for
W=3 in
h=5 in
l=240 in
substitute in the equation and solve for L
L=(5,177.25)(3)(5^2)/240
L=1,617.89 pounds
Round your answer to the nearest integer
so
L=1,618 pounds
I need help with this questions I don’t. Get it
You will need 275 ml of the 90% solution
Explanation:Let the amount of the 90% alcohol be x
Amount of the 30% alcohol solution = 385 ml
The amount of the mixture = 385 + x
(30% of 385) + (90% of x) = 55% of (385+x)
[tex]\begin{gathered} (\frac{30}{100}\times385)+(\frac{90}{100}\times x)=\frac{55}{100}\times(385+x) \\ \\ (0.3\times385)+(0.9\times x)=0.55(385+x) \\ \\ 115.5+0.9x=211.75+0.55x \\ \\ 0.9x-0.55x=211.75-115.5 \\ \\ 0.35x=96.25 \\ \\ x=\frac{96.25}{0.35} \\ \\ x=275 \\ \\ \end{gathered}[/tex]You will need 275 ml of the 90% solution
Which interval notation represents a function with a domain of all real numbers greater than or equal to 4?A.) -35 D.) y>0 E.) Y<4
If the domain is all real numbers greater than or equal to 4, the interval will be
[tex]x\ge4[/tex]A small college is forming a planning committee from 10 administrators, 16 faculty members, and 9 staff members. In how many ways can a planning committee be formed if there are 3 members from each group?
The number of ways that the planning committee can be formed if there are 3 members from each group is 6545 ways.
What are combinations?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by ⁿCr
The combination formula is illustrated thus:
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time
The number of people will be:
= 10 + 16 + 9
= 35
The number of ways will be:
= ³⁵C₃
= 35! / (35 - 3)! 3!
= 35! / 32! 3!
= 35 × 34 × 33 / 3 × 2
= 6545 ways
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6545 ways can a planning committee be formed if there are 3 members from each group.
What is combination?Combination is a way of selecting items from a collection where the order of selection does not matter.
The formula for combination is ⁿCr = n! / ((n – r)! r!)
Where n is total number of objects and r is number of objects we have to choose.
The committee has 10 administrators, 16 faculty members, and 9 staff members.
The total number of persons
10+16+9
35
Now we need to select 3 persons from 35 persons
n=35 and r=3
³⁵C3 = 35! / ((35 – 3)! 3!)
=35! / ((32)! 3!)
=35×34×33×32! / (32! 3!)
=35×34×33 /6
=6545 ways
Hence in 6545 ways can a planning committee be formed if there are 3 members from each group.
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Nathalie is finishing a workout on the treadmill. She speeds up before slowing down to a stop. Nathalie draws a graph to represent her workout.
As the x-axis increases uniformly the y-axis increase and decreases so the horizontal axis must be labeled with time and the vertical axis with speed so option (A) is correct.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand the behavior of the graph.
The graph of a treadmill workout has been plotted.
We all know that the speed of the treadmill keep fast initially but after some time the speed reduces and it goes to zero lineary.
Therefore,the horizontal axis wich is uniform changes cause to vertical axis with first increase and then decrease shown.
Hence "As the x-axis increases uniformly the y-axis increase and decreases so the horizontal axis must be labeled with time and the vertical axis with speed".
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Let f(t) = 3 + 2, g(x) = -x^2?, andhe) = (x - 2)/5. Find the indicated value:24. h (g(5))
The Solution to Question 24:
Given the function below:
[tex]\begin{gathered} g(x)=-x^2 \\ h(x)=\frac{x-2}{5} \end{gathered}[/tex]We are asked to find the value of h(g(5)).
Step 1:
We shall find g(5) by substituting 5 for x in g(x).
[tex]g(5)=-5^2=-25[/tex]So that:
[tex]h(g(5))=h(-25)[/tex]Similarly, we shall find h(-25) by substituting -25 for x in h(x).
[tex]h(-25)=\frac{-25-2}{5}=\frac{-27}{5}[/tex]Therefore, the correct answer is
[tex]\frac{-27}{5}[/tex]Drag each tile to the correct box. Not all tiles will be used. Arrange the steps to solve the equation x + 3 − 2 x − 1 = - 2 . Simplify to obtain the final radical term on one side of the equation. Raise both sides of the equation to the power of 2. Apply the Zero Product Rule. Use the quadratic formula to find the values of x. Simplify to get a quadratic equation. Raise both sides of the equation to the power of 2 again.
The value of x = 16 + 4[tex]\sqrt{15}[/tex]
Given,
To solve the equations :
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Solve by the given steps :
Now, According to the question:
Step 1: Simplify to obtain the radical form on one side of the equation:
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Step 2: Raise both sides of the equation to the power of 2
[tex](\sqrt{x+3} - \sqrt{x -1})^2 = (-2)^2[/tex]
x + 3 + 2x - 1 -2 [tex]\sqrt{(x+3)(2x -1)}[/tex] = 4
3x - 2 = 2 [tex]\sqrt{(x+3)(2x -1)}[/tex]
[tex](3x - 2)^2 = [2\sqrt{(x+3)(2x -1)}]^2[/tex]
9[tex]x^{2}[/tex] - 12x + 4 = 4 (2[tex]x^{2}[/tex] + 5x -3)
Step 3: Apply the zero product rule, Simplify to get a quadratic equation :
[tex]x^{2}[/tex] - 32x +16 = 0
Step 4: Use the quadratic formula to find the values of x :
[tex]x^{2}[/tex] - 32x + 16 =0
x = 16 + 4[tex]\sqrt{15}[/tex] and x = 16 - 4[tex]\sqrt{15}[/tex]
x = 16 - 4[tex]\sqrt{15}[/tex] (It is rejected)
So, the value of x = 16 + 4[tex]\sqrt{15}[/tex]
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Answer: Raise both sides of the equation to the power of 2
simplify to obtain the final radical term on one side of the equation
raise both sides of the equation to the power of 2 again
simplify to get a quadratic equation
use the quadratic formula to find the xvalues
Step-by-step explanation:
Production has indicated that they can produce widgets at a cost of $16.00 each if they lease new equipment at a cost of $40,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project?
The price/volume option that will allow the firm to avoid losing money on this project is C. 2,300 units at $34.00 each.
How is this option determined?To determine the correct option, we use the cost-volume-profit analysis tool.
The cost-volume-profit (CVP) analysis involves determining how the volume of sales drives profitability.
The CVP technique classifies costs into their variable and fixed cost elements for the purpose of this analysis.
Variable cost per unit = $16
Fixed cost = $40,000
Option A Option B Option C Option D Option E
Sales units 3,000 1,900 2,300 2,500 1,700
Unit selling price $29 $36.50 $34 $31.50 $39
Sales revenue $87,000 $69,350 $78,200 $78,750 $66,300
Variable costs 48,000 30,400 36,800 40,000 27,200
Fixed cost 40,000 40,000 40,000 40,000 40,000
Total costs 88,000 70,400 76,800 80,000 67,200
Thus, the price/volume option that meets the firm's goal is Option C because the sales revenue exceeds the total costs.
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Question Completion with Price/Volume Options:A. 3,000 units at $29.00 each.
B. 1,900 units at $36.50 each.
C. 2,300 units at $34.00 each.
D. 2,500 units at $31.50 each.
E. 1,700 units at $39.00 each.
jessica bought 4 gallons of paint. Jessica needed to use 3/4 of the paint to paint her living room and dining room. How many gallons did she use, write the number of gallons.
Jessica bought 4 gallons of paint. Of that, she used 3/4 to paint. So the ammount she used was
[tex]4\cdot(\frac{3}{4})=\frac{4\cdot3}{4}=3[/tex]So she used 3 gallons of paint.
Number 5 need help I really forgot how to solve this problem
Line Segments and Rays
A line segment has two endpoints. It contains these endpoints and all the points of the line between them,
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.
The figure shows a line that starts in B and goes infinitely to the left side, passing through A, thus the correct choice is B. Ray BA
the Center is (2,0) the circle passes through the point (4.5,0) What is the Radius?
The radius of the circumference would be
x2 = 4.5
x1 = 2
r = x2 - x1
r = 4.5 - 2.0
r = 2.5
The radius would be 2.5
A window washer drops a tool from their platform 155 ft high. The polynomial -16r2 + 155 tells us the height, in feet, of
the tool / seconds after it was dropped. Find the height, in feet, after t = 1.5 seconds.
At t = 1.5 sec the tool is at the height of 119 feet.
Given, A window washer drops a tool from their platform 155 ft high.
The polynomial -16r² + 155 tells us the height, in feet, of the tool / seconds after it was dropped.
we are asked to determine the height, in feet, after t = 1.5 seconds.
we know that h(t) = -16r² + 155
hence at t=1.5 sec, height is = ?
⇒ h(1.5) = -16t² + 155
⇒ h(1.5) = -16(1.5)² + 155
⇒ h(1.5) = -16(2.25) + 155
⇒ h(1.5) = -36 + 155
⇒ h(1.5) = 119
at t=1.5 sec the tool is at the height of 119 feet.
Hence we get the height as 119 feet.
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Answer the questions below about the quadratic function.g(x) = 3x² + 12x+8Does the function have a minimum or maximum value?MinimumMaximumWhere does the minimum or maximum value occur?x =0What is the function's minimum or maximum value?
Plot the function on the graph.
From the graph it can be observed that graph of function opening upwards and it has minimum value at x = -2.
Thus function has minimum value.
The minimum value of the function occurs at x = -2. So mimimum value of function occurs at x = -2.
The value of the function at x = -2 is -4. So function's minimum value is -4.
Question 1. Write the equation of the line that goes through the points (-2,1) and (4,2).
Slope-intercept equation:
y=mx+b
Where:
m= slope
b=y- intercept
Point 1 = (x1,y1) = (-2,1)
Point 2 = (x2,y2)= (4,2)
First, find the slope by applying the formula:
[tex]m=\text{ }\frac{y2-y1}{x2-x1}=\frac{2-1}{4-(-2)}=\frac{1}{6}[/tex]Now we have:
y=1/6x+b
Replace x,y by a point ( for example point 1 (-2,1)) and solve for b:
1 = 1/6 (-2) +b
1= -1/3 +b
1+1/3 = b
b= 4/3
Final equation:
y= 1/6x+4/3
Let p = x^2 + 6.Which equation is equivalent to (22 + 6)^2 – 21 = 4x^2 + 24 in terms of p?Choose 1 answer:А) p^2 + 4p - 21 = 0B) p^2 - 4p - 45 = 0C) p^2 - 4p - 21 = 0D) p^2 + 4p - 45 = 0
Given:
[tex](22+6)^2-21=4x^2+24[/tex][tex]\text{Let p = x}^2+6[/tex]Let's solve the equation in terms of p:
[tex]undefined[/tex]Let set E be defined as follows:
E = {english, math, french, art}
Which of the following are subsets of set
E
The subsets of E is all the above .
What are subsets of set ?If every component present in Set A is also present in Set B, then Set A is said to be a subset of Set B. To put it another way, Set B contains Set A. As an illustration, if set A has the elements X, Y, and set B contains the elements X, Y, and Z, then set A is the subset of set B.
If every element in a set A is also an element in a set B, then the set A is a subset of the set B. The set A is therefore contained within the set B. AB is used to represent the subset connection. For instance, if the sets A and B are equal, AB but BB, respectively.
Let the event E = {english, math, french, art}
The subsets of E is all the above .
null set is also subset of E
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