EXPLANATION
If the volume of the cone is of V=448m^3 and it is dilated by a scale factor of 1/4, the resulting volume would be as shown as follows:
[tex]\text{Volume}_{\text{dilated}}=448\cdot1\frac{1}{4}=560m^3[/tex]Use the iterative rule to find the 5th term in the sequence:
an = 4x3n-1
972
243
324
81
Answer:
324
Step-by-step explanation:
1) substitute the 5 into the formula
n=5 [tex]a_{n}=4[/tex]×[tex]3^{5-1}[/tex]
2) simplify
5-1 = 4
[tex]3^4[/tex] = 81
4×81 = 324
Hope this helps, have a great day!
Answer:
5th term = 324
Step-by-step explanation:
[tex]a_n \: = \: 4 \: \cdot \: {3}^{n - 1} [/tex]
Where, n = 5
[tex]a_5 \: = \: 4 \: \cdot \: {3}^{5 - 1} [/tex]
[tex]a_5 \: = 4 \: \cdot \: {3}^{4} [/tex]
[tex]a_5 \: = 4 \: \cdot \: 81[/tex]
[tex]a_5 \: = \: 324[/tex]
If x = a/b (with a ≠ b and b ≠ 0), then express a+b/a-b in terms of x.
Using the properties of ratio and proportion we can find the value as [tex]\frac{x+1}{x-1}[/tex] .
A theorem built on the idea of proportions enables a computation procedure that is speedier and requires fewer expansions.
When working with rational functions or fractional equations, it is helpful. Use the componendo and dividendo rule to study ratios and proportions. If the ratio of any two provided numbers is the same as the ratio of the other two numbers, then the ratios of the sum of the denominator and numerator to the difference of the denominator and numerator of the two rational numbers are comparable in nature.The given ratio is of the form x = a /b
This can be written in the form of
[tex]\frac{x}{1} = \frac{a}{b}[/tex]
Now we have to find the value of [tex]\frac{a+b}{a-b}[/tex].
Using the componendo and dividendo rule we get:
Adding the denominator to the numerator to get the new numerator and subtracting the denominator from the numerator to get the new denominator.
Mathematically:
[tex]\frac{a+b}{a-b} = \frac{x+1}{x-1}[/tex]
Therefore this is the required result.
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if angle ab is a right triangle then ab is perpendicular to bc
Answer:
it should be a 90-degree angle or right triangle
Step-by-step explanation:
a-software company is hiring an engineer and a manager. How many ways can these positions be filled if 17 people apply for the position of an engineer and 22 people apply for the position of a manager question
Given:
17 people apply for the position of an engineer.
22 people apply for the position of a manager.
[tex]\begin{gathered} \text{Total number of ways to fill the positions=17}\times22 \\ \text{Total number of ways to fill the positions=}374 \end{gathered}[/tex]Number of ways to fill the positions is 374.
All sixth grade students are asked to bring something for the fall dance. One student brought 1 ½ gallon of apple juice and another student brought 3 ½ gallon of apple juice. Each serving is ⅓ cup. Given this amount, how many students would be able to have some apple juice ?
Based on the gallons of apple juice brought by the students, and the serving per gallon, the number of students that would have some apple juice is 15 students
How to find the number of students?First, find the total amount of juice that the students brought of apple juice:
= 1 ½ + 3 ½
= 3/2 + 7/2
= 10 / 2
= 5 gallons
If each serving is in a 1/2 cup, then the number of students that would be able to get some apple juice is:
= Number of gallons of juice / Number of cups per serving
= 5 ÷ ⅓
= 5 x 3/1
= 15 / 1
= 15 students
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The scale from a garden to drawing is 8 ft to 1 cm the scale from the same garden to another drawing is 2 ft to 1 cm what are the lengtgs of the base snd height of the garden in the other scale drawing?
The lengths of the base and height of the garden in the other scale drawing is 9.6 cm and 14.4 cm
How to calculate the value?The scale from a garden to the illustration is stated as 8 feet to 1 centimeter in the question. The drawing's base and height are each 2.4 cm long and 3.6 cm tall, respectively.
As a result, the lengths of the garden's base and height are, respectively, 2.4*8 ft (19.2 ft) and 3.6*8 ft (28.8 ft).
We now know that the scale is 2 feet to 1 centimeter between the same garden and another drawing.
Thus, the lengths of the base and the height of the other drawing are 19.2/2 cm. = 9.6 cm. and 28.8/2 cm. = 14.4 cm. respectively.
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Elena has 6,492 stickers in her collection. She wants to put them into a book. She can fit 12 stickers on each page. How many pages will she need? (2 points)
541
553
545
549
Answer:
541
Step-by-step explanation:
Divide 6492 by 12
6492/12=541
A student is trying to solve the system of two equations given below:
Equation P: y + z = 6
Equation Q: 8y + 7z = 1
Which of the following is a possible step used in eliminating the y-term?
The possible step used in eliminating the y-term in Equation P: y + z = 6 Equation Q: 8y + 7z = 1 is (y + z = 6) * (−8)
The two equations are :
Equation P: y + z = 6
Equation Q: 8y + 7z = 1
What is simultaneous linear equation?Simultaneous linear equations are the system of two linear equations in two or three variables that are solved together to find a common solution.
A system of simultaneous linear equations is any set of two or more linear equations that share the same unknown variables. Finding values for the unknown variables that simultaneously satisfy all of the equations is required to solve such a system.
Two linear equations in two variables together are known as simultaneous linear equations.
The solution of the system of simultaneous linear equations is the ordered pair (x, y) that satisfies both linear equations.
Based on the given conditions,
Equation P: y + z = 6 ( Equation-1 )
Equation Q: 8y + 7z = 1 ( Equation-2 )
To solve the above simultaneous linear equation multiply the equation-1 with (-8)
So,
We can write,
⇒ ( y + z = 6 ) * (-8)
-8y - 8z = -48 ( Equation-3 )
Now add Equation (3) with Equation (2)
Then,
-8y - 8z = -48
8y + 7z = 1
----------------------------
-z = -47
z = 47
Therefore,
The expression ( y + z = 6 ) * (-8) is a possible step used in eliminating the y-term.
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A construction company charges $15 per hour for debris removal, plus a one-time fee for the use of a trash dumpster. The total fee for 9 hours of service is $195
The trash dumpster fee was 60 dollars.
A linear function has a y-intercept of -12 and a slope of 3/2. What is the
equation of the line?
Answer:
y = (3/2)x - 12
Step-by-step explanation:
The equation of a line is expressed in the form y = mx + c, where m is the gradient (slope) and c is the y-intercept. Simply substitute your values into this form:
y = (3/2)x - 12
How many two digit numbers have an odd number of factors?
There will be 6 two-digit numbers having an odd number of factors.
According to the question,
We have the following information:
There are two-digit numbers.
It means that the list of numbers is from 10 to 99.
Now, we have to find the numbers with the odd number of factors.
We know that odd numbers are the numbers which are not divisible by 2. For example, 1, 3, 5, etc. are odd numbers.
Note that 1 is also included as a factor.
Now, the numbers with odd number of factors will be the perfect squares as 1 will be added to them and the numbers will become odd.
So, the perfect two-digit square numbers are 16, 25, 36, 49, 64 and 81.
Now, we can prove that these numbers satisfy the given conditions by taking factor of any one number.
Let's take 25. The factors of 25 are 1, 5, and 5. So, in total there are 3 factors.
Hence, there are 6 two-digit numbers having an odd number of factors.
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Please help me its do today
The measure of the missing angle is 80 degrees.
What is the measure of the missing angle?The shape of the object formed by GEF is a triangle. A triangle is a polygon that has three sides. The sum of angles in a triangle is 180. A triangle has three vertices.
<EGF = 180 - (28 + 58)
180 - 80
100
<EGF+ <FGT = 180 degrees
This is because angle on straight line is equal to 180 degrees
<FGT = 180 - 100 = 80 degrees
Alternatively, <FGT is equal to80 (28 + 58). This is because the sum of the two interior opposite angles in equal to the exterior angle.
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Which expression shows the result of applying the distributive property to 3 (1/5x - 1/7)
The expression used to show the distributive property is 3/5 x - 3/7 .
The examples that follow show how to apply the distributive law towards the set of real numbers R.
Usually, this kind of multiplication is intended when the word "multiplication" is used in elementary mathematicsFrom an algebraic standpoint, real numbers are a field, ensuring the distributive law's applicability. Real numbers are a field in algebra, guaranteeing the applicability of the distributive law.The distributive principle of binary operations generalizes the distributive law, which asserts that equality holds throughout mathematicsThe law states that p·(q + r) = (p · q) + (q · r).Now the given expression is 3 (1/5x - 1/7)
Therefore it can be broken down into smaller parts by using the distributive property.
therefore:
3 (1/5x - 1/7)
=3×(1/5x) - 3×(1/7)
=3/5x - 3/7
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The perimeter of a square can be found using the equation P=4A√, where A represents the area of the square. If the square has a perimeter of 56 inches, what is the area of the square? Responses 28 square inches 28 square inches 14−−√ inches square root of 14 inches 7 inches 7 inches 196 square inches
The area of square is 196 square inches which is the last option.
Perimeter of square
The perimeter of a square is the distance covered by its four sides. Perimeter surrounds or outlines the shape in a two-dimensional plane.
Given that:-
Perimeter of square = 56 inches
The perimeter of a square can be found using the equation :
[tex]P=4\sqrt{A}[/tex]
Where, A is the area of the square and,
P is the perimeter of the square.
We have to find the area of the square.
Using the given data to find the area of the square, we get,
[tex]56 = 4\sqrt{A}\\\\ \frac{56}{4}=\sqrt{A}\\\\ 14=\sqrt{A}\\\\[/tex]
Squaring the equation, we get,
A = 196 square inches.
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Need help asap, worth 20 points
Answer:
2
Step-by-step explanation:
Solve the equation for x. 2x+y = 7
PLEASE PLEASE HELP
Answer:
x = (7/2) - (y/2)
Step-by-step explanation:
The minimum wage for employees of a company is modeled by the function f(x)=7.25x The company decided to offer a signing bonus of $75. How does adding this amount affect a graph of an employee’s earnings?
After adding bonus amount, the graph of an employee’s earnings is translated upward by 75 units.
In this question, we have been given the minimum wage for employees of a company is modeled by the function f(x)=7.25x
Let h(x) be a function that models how much employee earns after a signing bonus of $75
The wage for the employees after signing the bonus would be 7.25x + 75
so, h(x) = 7.25x + 75 is the required function.
Here x is the number of working days, it can not be negative but must be greater than or equal to zero.
The graph of functions f(x) and h(x) are shown below.
The blue line represents the graph of the function which models an employee’s earnings after a signing a bonus.
The graph of f(x) is translated upward by 75 units.
The initial value of graph of h(x) is (0, 75) This means even if the employee works 0 days, he will get $75
Therefore, after adding bonus amount, the graph of an employee’s earnings is translated upward by 75 units.
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find the first 5 terms and the 25th term of 6n-3n^2
The fifth and the twenty fifth terms of the arithmetic sequence are a5 = - 45 and a25 = - 1725
What is an arithmetic sequence ?A group of integers that are arranged in a particular order and share a difference between each term is known as an arithmetic sequence. For instance, the common difference between the numbers 3, 9, 15, 21, and 27 in mathematics is 6. The term "arithmetic progression" can refer to an arithmetic sequence..
The given expression is [tex]6n - 3n^2[/tex]
The 5th term that is n = 5
thus the given expression will become
[tex]6n-3n^2[/tex]
which is equal 6×5 - 3 (5)²
= 30 - 3 × 25
= 30 - 75
= - 45
The 25th term is n = 25
Thus the given expression that is [tex]6n-3n^2[/tex]
= 6 × 25 - 3× ( 25) ²
= 150 - 3 × 625
= - 1725
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a researcher attempts to study the effects of alcohol on task performance. one factor is alcohol (alcohol treatment, placebo control), and the other factor is task difficulty (easy, difficult. if the researcher uses a repeated measures design with 15 participants per condition, how many participants will he need for the study?
If the researcher employs a repeated measures design with 15 participants per condition, the study will require 15 participants
What is repeated measures?A repeated-measures design takes multiple, or repeated, measurements on each experimental unit. We call an experiment with repeated measures one in which all participants participate in all conditions. For example, you might want to learn whether taking vitamin supplements before an exam improves recall. So, in the first condition, you give a vitamin tablet to each participant. A repeated measures design is a type of research design in which multiple measures of the same variable are taken on the same or matched subjects under different conditions or over two or more time periods. In a longitudinal study, for example, repeated measurements are collected to assess change over time.To learn more about repeated measures, refer to:
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HELP URGENT!!!!! WILL MARK BRAINLIEST!!!! SHOW WORK!!!!!!
Consider P(x) = x^3+3x^2-4, and c=-2. Show the given value of c is a zero of P(x) (this could be done through synthetic division), find all zeros of P(x), and write P(x) in factored form.
Zeros:
Factored form: P(x)=
Answers:
Zeros: -2 and 1
Factored form: P(x) = (x+2)(x+2)(x-1)
====================================================
Explanation:
One way to show that c = -2 is a zero or root of P(x) is to plug it in as the x value and simplify. If we get P(x) = 0, then that input is a root.
P(x) = x^3+3x^2-4
P(-2) = (-2)^3+3(-2)^2-4
P(-2) = -8+3(4)-4
P(-2) = -8+12-4
P(-2) = 4-4
P(-2) = 0
In short, the input x = -2 leads to the output P(x) = 0.
This confirms -2 is a root of P(x). By extension, this tells us that (x+2) is a factor of P(x).
We can determine the other factor using synthetic division as shown in figure 1. See the image below.
The synthetic division table shows us getting a remainder of 0, as highlighted in yellow.
The other stuff in pink represents the coefficients of the quotient.
We have the coefficients 1, 1, -2 which forms 1x^2+1x-2 and that simplifies to x^2+x-2
This further factors to (x-1)(x+2) because we're looking for two numbers that a) multiply to -2 and b) add to 1. Use the FOIL rule to expand (x-1)(x+2) and you should get x^2+x-2 again. This helps confirm the factorization was done correctly.
---------------------
In short, we found that P(x) = (x+2)(x^2+x-2) and it fully factors to P(x) = (x+2)(x+2)(x-1)
Each factor leads to a root.
x+2 = 0 leads to the root x = -2
x-1 = 0 leads to the root x = 1
Visually, each root is an x intercept where the curve either crosses the x axis or touches it before bouncing away. See figure 2 below.
The school athletic director has a storage closet that is 4 and 1/2 ft long and 2 and 2/3 ft deep and 6 ft tall she wants to put carpet in the closet how much carpeting will she need
Answer:
3 ft^2
Step-by-step explanation:
We'll assume the carpet is only for the closet floor. In that case we don't need the closet height.
Area of the floor can be calculated by multiplying the length (4 1/2 feet) and depth (2/3 foot):
Area = (4 1/2 feet)*(2/3 feet)
Area = (9/2 ')*(2/3 ')
Area = (18/6)'
Area = 3 ft^2
how much less than 6 is the sum of 2 3/4 and 2 4/5
Answer:
0.45
Step-by-step explanation:
2.75+ 2.80= 5.55
6-5.55= 0.45
I hope this helps! :) If it does could you please mark me brainliest?
Answer:
Step-by-step explanation:
answer: 9/20
formulate 2 3/4 + 2 4/5 - 6
sorry if im wrong.
Simon feeds each of his dogs 1/8 of a can of food each day. He uses a total of 5/8 of a can of
food each day. How many dogs does Simon have?
you can drive around a NASCAR speedway 40 times for $10 how many times can you go around the track for eight dollars?
draw a picture to solve. Mandi has 8 dog biscuits. She has 7 dog bowls. Each dog bowl gets the same number of dog biscuits. How many dog biscuits are in each bowl?
If Mandi has 8 dog biscuits, she has 7 dog bowls and each dog bowl gets the same number of dog biscuits, then the number of dog biscuits in each bowl is 1.14 biscuits
Number of dog biscuits that Mandi has = 8 dog biscuits
Number of dog bowls that Mandi has = 7 dog bowls
Each dog bowl get the same number of dog biscuits.
To find the number of dog biscuits in each bowl we have to do the division
Number of dog biscuits in each bowl = Number of dog biscuits that Mandi has ÷ Number of dog bowls that Mandi has
Substitute the values in the equation
= 8/7
= 1.14 biscuits
Hence, if Mandi has 8 dog biscuits, she has 7 dog bowls and each dog bowl gets the same number of dog biscuits, then the number of dog biscuits in each bowl is 1.14 biscuits
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What is a polynomial with more than 3 terms read with
A polynomial more than 3 terms is read as trinomial.
What is polynomial?A polynomial is an equation that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates.
Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.
hence, a polynomial more than 3 is trinomial or cubic.
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The maximum speed of a car on a trip is 60 miles per hour. Write and solve an inequality that represents the number of hours the car takes to travel 180 miles.
TEXT ANSWER
Question 8
Point M is the midpoint of PQ. The coordinates of P and M are given below.
M(5,-2) and P(11, - 10)
Based on this information, what are the coordinates of ?
Show all work and provide any necessary descriptions.
Answer:
Q (- 1, 6 )
Step-by-step explanation:
use the midpoint formula to find the coordinates of M then equate the x and y coordinates with the actual coordinates of M
P (11, - 10) and let Q = (x, y ) , then
[tex]\frac{11+x}{2}[/tex] = 5 ( multiply both sides by 2 )
11 + x = 10 ( subtract 11 from both sides )
x = - 1
and
[tex]\frac{-10+y}{2}[/tex] = - 2 ( multiply both sides by 2 )
- 10 + y = - 4 ( add 10 to both sides )
y = 6
coordinates of Q = (- 1, 6 )
how to do 475x64????
Poker is a common game in which players are dealt five cards from a deck of cards. It can be shown that there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in the table below. Find the requested probability. Use a calculator. (Show your answer to nine decimal places.)
P(royal flush)
The requested probability is 0.99974
What is probability ?The likelihood of an event happening is gauged by probability. Many things are impossible to completely predict in advance. Only the likelihood of an event occurring, or how probable it is to happen, can be predicted using probability. Tossing a coin, for instance, has a chance of coming up heads or tails.
TOTAL NUMBER OF POSSIBLE HANDS..
WE HAVE 52 CARDS WITH 4 SUITS AND 13 CARDS PER SUITE.
WHEN WE ARE DEALT A 5 CARDER, DISREGARDING THE ORDER OF DEAL,WE HAVE
C[52,5] TOTAL NUMBER OF POSSIBLE HANDS =52!/[47!×5!]=[52× 51 × 50 ×49× 48× (47!) ]/[5! ×47!]=
=[52× 51× 50× 49×48]/ [5!] = 2598960
ROYAL FLUSH
THIS COULD BE OF ANY SUIT ...
SO WE HAVE 4 POSSIBILITIES
ONCE A SUIT IS CHOSEN THE THEN THE OTHER POSSIBILITY IS TO ONLY GET
A,K,Q,J,10 IN THAT SUIT, OF EACH OF WHICH, THERE IS ONLY ONE CARD IN THE PACK
SO THERE IS ONLY 1*1*1*1*1=1 WAY
SO TOAL NUMBER OF POSSIBILITIES ARE 4^ * 1 = 4 WAYS
SO PROBABILITY = 4/2598960 = 0.00000154 ..........ANSWER
PROBABILITY = 0.00000 ...ANSWER
TWO PAIR OR BETTER
THERE ARE ...4+36+624+3744+5108+10200+54912+123552-198180
HENCE PROBABILITY = 198180/2598960=0.0762536
-0.07625...........ANSWER
WE CAN GET 4 OF A KIND OR BETTER IN 4+36+624= 664 WAYS
SO LOSING HANDS TO 4 OF A KIND ARE =2598960-664-2598296
SO PROBABILITY = 2598296/2598960-0.9997445
=0.99974...........ANSWER
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