Answer:
Collin mistake is step 1
correct answer \(\frac{3x - 3}{x^{2} -3x}\)
Step-by-step explanation:
write the english phrase as an algebraic expression. Let x represent the number
The english phrase "Seven less than four times a number" as an algebraic expression is 4x - 7
Writing the english phrase as an algebraic expressionFrom the question, we have the following parameters that can be used in our computation:
seven less than four times a number
Represent the number with x
So:
four times a number means 4x
So, we have
seven less than 4x
seven less than means - 7
So, we have
4x - 7
Hence, the english phrase as an algebraic expression is 4x - 7
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Complete question
write the english phrase as an algebraic expression. Let x represent the number
Seven less than four times a number
A square has sides with lengths of 3. It is dilated by a scale factor of 2. What is the area of the new square?
Answer:
Step-by-step explanation:
The dilation of a scale factor of 2 means the new shape obtained after scaling the original shape is twice the shape of the original shape.
The length of one side of the image of the square after the dilation is 6 units.
What is dilation with a scale factor of 2?
The dilation of a scale factor of 2 means the new shape obtained after scaling the original shape is twice the shape of the original shape.
We have,
Square side length = 3 units.
Dilation = scale factor of 2.
Dilated with a scale factor of 2 means we will multiply 2 with the side length.
The length of one side of the image of the square is:
= 3 units x 2
= 6 units
Thus the length of one side of the image of the square after dilation is 6 units.
The volume of cone A is equal to the volume of cylinder B. In addition, their radii are
equal in length. What is the ratio of the height of cone A to the height of cylinder B?
Answer:
3:1
Step-by-step explanation:
A cone has the same volume formula as a cylinder, except it is 1/3 as much. So to have the same volume, a cone would need to be 3 times as tall.
convert 4/5 into percent
Karen was in a trivia contest and got 18 of the 20
questions correct. What percent of the questions
did she get wrong?
Help
\(\large\bf{\underline{Given:}}\)
Total questions = 20correct one = 18__________________________________________
\(\large\bf{\underline{To\:find:}}\)
Percentage of wrong questions\(\bf{⟹20 -18 = 2 \: questions}\)
\(\bf{Let\:the \:percentage\:of \:wrong\: question\:be\:x}\)
__________________________________________
\(\large\bf{\underline{Therefore:}}\)
\(⟹x\% \: of \: 20 = 2\)
\(⟹ \frac{x}{100} \times 20 = 2\)
\(⟹x = 2 \times \frac{100}{20} \)
\(⟹x = 10\)
__________________________________________
\(\large\bf{\underline{Hence }}\)
\(\bf{⟹10\%\:of \:the \:questions\: she\: get\: wrong}\)
Can someone answer this question please
If
f(x) = 2x² - 5
and
g(x) = 5x + 7
Find
f(g(x)) = [?]x² + [?]x + [?]
Answer:
f(g(x)) = 50x² + 140x + 93
Step-by-step explanation:
f(g(x)) means that within the f(x) equation, you want to replace all of the x variables with the g(x) equation.
So,
f(g(x)) = 2 (5x+7)² -5
= 2 ( 25x²+ 70x + 49) - 5
= 50x² + 140x + 93
:)
The volume of a rectangular prism is 5,890.625 cm3. If the height is 14.5 cm and the length is 25 cm, what is the value of the width?
Answer:
Step-by-step explanation:
The formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
We know that V = 5,890.625 cm^3, h = 14.5 cm, and l = 25 cm.
Substituting these values into the formula, we get:
5,890.625 = 25w(14.5)
5,890.625 = 362.5w
w = 16.25
Therefore, the width of the rectangular prism is 16.25 cm.
Answer:
It's A
Step-by-step explanation:
well all you have to do is divide like 5,890.625 dvided by 14.5 then divide again by 25 them bam you got 16.25
) 65 people were asked on the activities they engage in during their free time. The results showed that 23 visit national parks, 26 engage in cycling while 22 engage in swimming. Furthermore 9 engage in swimming and visit national parks, 9 engage in swimming only while 11 visit national parks only. How many engage in
i. Swimming and cycling
Answer:
Step-by-step explanation:
i am working on the assumption that nobody does all three of them
i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.
the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.
so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4
What is the value of X?
Answer:
11.5
Step-by-step explanation:
4x+14=60
The moon appears red during a lunar eclipse because red is the __________ wavelength of light in the color spectrum present in sunlight.
longest
shortest
brightest
Answer:
Longest
Step-by-step explanation:
The moon appears red during a lunar eclipse because red is the Longest wavelength of light in the color spectrum present in sunlight.
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If an airplane traveled 414 miles how fast did it travel in 3/4 of an hour?
Answer:
The issue needs you to calculate Claire's airplane's speed in miles per hour.
Claire's airplane travels at a speed of 552 miles per hour.
Given:
414 miles total distance traveled
Time allotted = 3/4 hour
Total distance traveled / Total time = Speed
= 414 miles per hour
414 4/3 = 414
= (414 4 / 3)
1656 / 3 =
equals 552 miles per hour
As a result, Claire's airplane's speed in miles per hour is 552 miles per hour.
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Have a nice day :D
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A pair of dice was rolled many times
and the results appear below. Based
upon these results, what is the
experimental probability of rolling a
multiple of 3?
7
8
9
10 11 12
Outcome 23
35 6
Frequency 3 6 8 11 14
16
15
12
9
5 1
Answer:
6%
Step-by-step explanation:
Out of 100 rolls, there were 6 instances of 3. The experimental probability of rolling a 3 is ...
6/100 = 6%
Which of the following could represent the
interval (5, 100]? Select two that apply.
Answer:
5 < x ≤ 100
(this is inequality form)
{x| 5 < x ≤ 100}
(this is set notation form)
(options B and C)
Step-by-step explanation:
In interval notation,
( or ) : does not include value
[ or ] : does include value
{and remember:
< or > : does not include value
≤ or ≥ : does include value}
when we write something in interval notation, the range of values is from (lowest value, highest value)
for this equation, we know that we are looking for : (5, 100]
which means that the range of numbers goes from
5 (does not include 5) to 100 [does include 100]
so, x > 5 (not equal to); x ≤ 100
we can combine these two concepts: 5 < x ≤ 100
(inequality form)
{when {x | ...} is present, it means the same thing as without it, so
{x| 5 < x ≤ 100} is also correct
(set notation)
hope this helps!!
Answer:
B and C
Step-by-step explanation:
from interval notation we are including 100 but not 5,
x > 5 and x ≤ 100
so B and C are correct
Calculate the interest produced by a principal of $ 4,500 at 5% annual simple interest in 8 months.
Answer:
4,500 x 5 = 22,500
4,500 divided by 5 = 900
4,500 plus 5 = 4,505
4,500 minus 5 = 4,495
Step-by-step explanation:
it is either one of those that u have to choose from good luck
Helps please is for now
Answer:
(-3,5) and (2,3). That's the answer. Plug this number and it would be fine
What is the y-value of the solution for this system of equations:
4x - y = 10
x - 4 = y
The required value of y is obtained as -2.
What are the types of a system of equations?The given system of equation can either have a unique solution, more than one solutions or no solution.
On this basis they are divided into two parts consistent and inconsistent.
A consistent system has one or more solutions while for an inconsistent system there are no solutions.
The given system of equations is as below,
4x - y = 10 (1)
x - 4 = y (2)
Substitute the value of y from equation (2) into equation (1) to get,
4x - (x - 4) = 10
=> 3x + 4 = 10
=> 3x = 6
=> x = 2
Then, substitute x = 2 in x - 4 = y to get,
y = 2 - 4 = -2
Hence, the value of y for the given system of equations is -2.
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The cork in a wine bottle should not exceed 8.77KPa of normal stress. If the shear stress induced by the friction of its perimeter with the bottle is 4.98KPa, which is the maximum allowed ratio between the cork length H and the cork radius R?
The maximum allowed ratio for the cord such that the maximum allowable normal stress is 8.77 kilopascals is equal to 2.081.
How to determine the maximum allowed ratio of a cork in a wine bottle
Let assume that the cork is made of a ductile material, in this case we find that the normal stress (σ), in kilopascals, and shear stress (τ), in kilopascals, are described below:
Normal stress
σ = F / A
Shear stress
τ = (3 · V) / (2 · A')
Where:
V - Shear force, in kilonewtons.F - Normal force, in kilonewtons. A - Transversal area, in square meters. A' - Transversal shear area, in square meters.Let assume that cork is at static equilibrium and at inminent motion, then the shear and normal forces are, respectively:
F = P
V = P / 2
And the transversal areas are introduced below:
A = π · R²
A' = 2 · R · H
Where:
R - Radius of the cork, in meters.H - Height of the cork, in meters.If we know that σ = 8.77 kPa and τ = 4.98 kPa, then the maximum allowed ratio between the cork height and the cork radius is:
8.77 = P / (π · R²)
8.77 = [1 / (π · R)] · (P / R)
4.98 = 1.5 · (0.5 · P) / (2 · R · H)
4.98 = [0.75 / (2 · H)] · (P / R)
Then, we eliminate P / R of the two equations:
8.77π · R = 13.24 · H
H / R = 8.77π / 13.24
H / R = 2.081
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Identify the equation in slope-intercept form for the line with the given slope that contains the given point.
Slope =4; (6,−5)
Answer:
The equation would be -5=4(6)+ b
Step-by-step explanation:
Answer:
y = mix + b where m is the slope, and b is the y- intercept. solution
A veterinarian gives 3/8ML of vitamins to a baby animal Every day. The veterinarian wants to know how many days worth of vitamins she has if she has 3 3/4 ML of vitamins. Which division expression represents the situation
Answer:
sup
Step-by-step explanation:
Which statement is true about the function f(x) = 8x^3?
The function is even because f(–x) = f(x).
The function is odd because f(–x) = f(x).
The function is even because f(–x) = –f(x).
The function is odd because f(–x) = –f(x).
The function f(x) = 8x³ satisfies the condition f(-x) = -f(x) and is odd. D.
To determine whether the function f(x) = 8x³ is even or odd, we need to analyze the symmetry of the function with respect to the y-axis and the origin.
Even function:
If a function is even, it satisfies the condition f(-x) = f(x), meaning that the function is symmetric with respect to the y-axis.
Odd function:
If a function is odd, it satisfies the condition f(-x) = -f(x), meaning that the function is symmetric with respect to the origin.
Now, let's analyze the given function, f(x) = 8x³:
Testing for evenness:
If we substitute -x for x in the function, we have f(-x) = 8(-x)³
= -8x³.
This is not equal to f(x) = 8x³.
The function f(x) = 8x³ is not even.
Testing for oddness:
If we substitute -x for x in the function, we have f(-x) = 8(-x)³
= -8x³.
This is equal to -f(x) = -8x³.
The function is odd because f(–x) = –f(x).
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In a class of 80 Students, 30 offered mathematics, 20 offered Accountancy and 40 offered Economics. Those who offered both mathematics and accountancy are more than those who offered both Accountancy and Economics by 2. No student offered all the subjects and none offered both mathematics and Economics. Find the number of students who offered Accountancy only?
The number of students who offered Accountancy only is 10.
Let's represent the number of students who offered Mathematics as M, the number of students who offered Accountancy as A, and the number of students who offered Economics as E.
From the given information:
M = 30 (Number of students who offered Mathematics)
A = 20 (Number of students who offered Accountancy)
E = 40 (Number of students who offered Economics)
We are also given the following conditions:
M ∩ A > A ∩ E by 2
M ∩ E = 0
We know that the total number of students is 80, so:
M + A + E = 80
Now, let's solve for the number of students who offered Accountancy only.
We can start by substituting the given values into the equation:
30 + 20 + 40 = 80
Now, we need to find the value of A ∩ E (Number of students who offered both Accountancy and Economics).
Since none offered both Mathematics and Economics, we can subtract M from A:
A - M = A ∩ E
20 - 30 = A ∩ E
-10 = A ∩ E
Since A ∩ E cannot be a negative number, we know that A ∩ E = 0.
Now, let's use the first condition: M ∩ A > A ∩ E by 2.
Substituting the values, we have:
M ∩ A - A ∩ E = 2
M ∩ A - 0 = 2
M ∩ A = 2
Now, we can substitute the values of M ∩ A and M into the equation M + A + E = 80:
30 + A + 40 = 80
A + 70 = 80
A = 10
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Is the set of rational expressions closed under subtraction? Explain p(x) - r(x) = ______________
q(x) s(x)
2. Is the set of rational expressions closed under multiplication? Explain ( p(x) ) ( r(x) ) = _______________
q(x) s(x)
3. Is the set of rational expressions closed under division? Explain
p(x) ÷ r(x) = ________________ q(x) s(x)
Answer:
so where is the equation
1. Prove ~ (Pvq) <=> (~P^~9).
Algebra of propositional variables
2. P^ q = q^q
P v q = q v p
show that both are commutative
Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.
How to explain the commutative property.It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property
From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.
In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.
Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.
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Un hombre posee 50 acciones con un valor de 30 cada una , la corporación declaró un dividendo del 6% pagadero en acciones ¿cuantas acciones poseía entonces?
el hombre tenía 50 acciones.
La pregunta es, ¿cuántas acciones poseía el hombre si declararon un dividendo del 6% pagadero en acciones y tenía 50 acciones con un valor de $30 cada una?Para calcular cuántas acciones tenía el hombre,
se puede utilizar la siguiente fórmula:Dividendos = Número de acciones * Precio por acción * Tasa de dividendosDe esta fórmula,
podemos despejar el número de acciones. Así, tenemos:Número de acciones = Dividendos / (Precio por acción * Tasa de dividendos)De los datos del problema, se sabe que el hombre tenía 50 acciones con un valor de $30 cada una.
Además, la corporación declaró un dividendo del 6% pagadero en acciones. Por lo tanto, la tasa de dividendos es del 6%.Para resolver el problema, primero debemos calcular el valor del dividendo que se pagará en acciones.
Para ello, se debe multiplicar el valor de las acciones del hombre por la tasa de dividendos.
Así, tenemos:Valor del dividendo = 50 acciones * $30 * 0.06 = $90El valor del dividendo es de $90. Ahora, podemos sustituir este valor en la fórmula para calcular el número de acciones que tenía el hombre.
Así, tenemos:Número de acciones = $90 / ($30 * 0.06) = 50 accionesPor lo tanto,
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If 21% of a number is 27, find 7% of that number.
Answer:
= 9
Step-by-step explanation:
100% corresponds to the original number.
21% = 21/100 = 0.21
7% = 7/100 = 0.07
100% = 100/100 = 1
Then:
27 ⇒ 0.21
A ⇒ 1
A = 27*1/0.21
A = 128.57
The original number is:
128.58
7% of 128.58:
128.58*0.07 = 9
= 9
PLEASE HELP! I'm lost. :(
In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean
µ = 520 and population standard deviation = 115.
What math SAT score is 1.5 standard deviations above the mean? Round answer to a whole number.
Answer:
A math SAT score of 693 is 1.5 standard deviations above the mean
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean µ = 520 and population standard deviation = 115.
This means that \(\mu = 520, \sigma = 115\)
What math SAT score is 1.5 standard deviations above the mean?
This is X when \(Z = 1.5\). So
\(Z = \frac{X - \mu}{\sigma}\)
\(1.5 = \frac{X - 520}{115}\)
\(X - 520 = 1.5*115\)
\(X = 693\)
A math SAT score of 693 is 1.5 standard deviations above the mean
Please help me with some math im stuck
y = - 40
- 40 since theres no letters it gonna be -40.
help me fast rapidly is of khan academy:
Answer:
0 hundreds
0 tens
7 ones
.
4 tenths
0 hundredths
8 thousandths
Standard form=7.408
Step-by-step explanation:
Lets first solve (7x1)+(4x1/10)+(8x1/1000)
7+0.4+0.008
Simplify:
7.408
PLEASE MARK AS BRAINLIESTthe population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 15% in 10 years. what will be the pop ulation in 30 years? how fast is the population growing at t 30?
Using the differential equation, the population after 30 years is 760.44.
What is meant by differential equation?In mathematics, a differential equation is a relationship between the derivatives of one or more unknown functions. Applications frequently involve a function that represents a physical quantity, derivatives that show the rates at a differential equation that forms a relationship between the three, and a function that represents how those values change.A differential equation is one that has one or more functions and their derivatives. The derivatives of a function define how quickly it changes at a given location. It is frequently used in disciplines including physics, engineering, biology, and others.The population P after t years obeys the differential equation:
dP / dt = kPWhere P(0) = 500 is the initial condition and k is a positive constant.
∫ 1/P dP = ∫ kdtln |P| = kt + C|P| = e^ce^ktUsing P(0) = 500 gives 500 = Ae⁰.
A = 500.Thus, P = 500e^ktFurthermore,
P(10) = 500 × 115% = 575sO575 = 500e^10ke^10k = 1.1510 k = ln (1.15)k = In(1.15)/10 ≈ 0.0140Therefore, P = 500e^0.014t.The population after 30 years is:
P = 500e^0.014(30) = 760.44Therefore, using the differential equation, the population after 30 years is 760.44.
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