The simplified form of the algebraic expression is \(\frac{23}{10} p+\frac{6}{5} r\) .
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).
A good example of an algebraic expression is 3x² + 2xy + c.Any expression that can be converted into a rational fraction using the properties of the arithmetic operations is said to be rational (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions). In other terms, a rational expression is one that can be created using only the four arithmetic operations and the variables and constants.Given expression is of the form:
\(\frac{3}{5} (\frac{1}{2}p+2r )+2p\)
Now we will use the distributive property to expand the algebraic expression:
\(or, (\frac{3}{5} \times\frac{1}{2}p+\frac{3}{5} \times2r) +2p\\\\or,\frac{3}{10}p+\frac{6}{5} r+2p\\ \\or,\frac{3+20}{10} p+\frac{6}{5} r\\\\or,\frac{23}{10} p+\frac{6}{5} r\)
Hence the simplified algebraic expression is \(\frac{23}{10} p+\frac{6}{5} r\) .
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Rounding to the nearest ten, which two
numbers round to 40?
48
36
41
32
49
Answer:
48 and 32
Step-by-step explanation:
both numbers get rounded by 8 going up and down rounding it to 40
K - 5 = 12. Solve the equation
Answer:
17 = K
Step-by-step explanation:
Add 5 to both sides to get K = 17
help me solve this problem please.
-11, -6, -7 and -6.1 are the answers
The inequality is r lesser than or equal to -6
After reviewing her driving record for the past 3 years, Cindy's insurance company offers her a good driver discount of 4.5%. Her original policy was based on the premiums listed below. What is her new annual premium including the discount? Cindy's Auto Insurance Policy Type of Insurance Coverage Coverage Limits Bodily Injury $50/100,000 Property Damage $25,000 Collision $500 deductible Comprehensive $100 deductible Annual Premiums $31.75 $120.50 $275.75 $100.00 a $504.24 b. $523.50 C. $528.00 d. $551.76
Answer:
its A
Step-by-step explanation:
I just took the test on EDGE
The new annual premium including the discount is $504.24.
Option A is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To calculate the new annual premium with the discount, we need to find the total premium and then subtract the discount.
The total premium is the sum of the individual premiums:
Total premium.
= $31.75 + $120.50 + $275.75 + $100.00
= $528.00
The discount is 4.5% of the total premium:
So,
Discount = 0.045 × $528.00 = $23.76
The new annual premium including the discount is:
New premium = Total Premium - Discount
= $528.00 - $23.76
= $504.24
Therefore,
The new annual premium including the discount is $504.24.
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Simplify the expression below:
14^2 - 24 / 3(2)
--------------------- (divided by)
|-3 + 2(6)|
Answer:
I got 20 when calculating this
Our basketball team won 60 percent of their games. If they lost 8 games, how many games did they play altogether?
Answer:
they played 20 games together
Step-by-step explanation:
use percentages
Let x be the number of total games.
If 60% is won games then 40% is lost games.
(8/x)*100 = 40
8/x = 4/10
80 = 4x
X = 80/4
Therefore the number of games is 20
Rachel has figured that there is an 85% likelihood that she will pass Math and a 70% likelihood she will pass Biology, she also thinks there is a 59.5% likelihood she will pass both. Based on Rachel's figures, what is the probability that Rachel will pass at least one of the courses
The probability that Rachel will pass at least one of the courses is 0.955 or 95.5%
To calculate the probability that Rachel will pass at least one of the courses, we need to use the formula;P(A or B) = P(A) + P(B) - P(A and B)Where P(A or B) is the probability of passing at least one course, P(A) is the probability of passing Math, P(B) is the probability of passing Biology, and P(A and B) is the probability of passing both Math and Biology.
Using the given information, we have:P(A) = 85% = 0.85P(B) = 70% = 0.7P(A and B) = 59.5% = 0.595Substituting these values into the formula, we get:P(passing at least one course) = 0.85 + 0.7 - 0.595= 0.955
As a result, Rachel has a 0.955 or 95.5% chance of passing at least one of the courses.95.5 percent, or 0.955.
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Consider the economy whose data appear in the table below. Working-age population 100,000 Labor force 60,000 Unemployed 12,000 Instructions: Round your answers to one decimal place.
a. The unemployment rate is ___%.
b. The labor-force participation rate is ___ %.
a. The unemployment rate is 20%.
b. The labor-force participation rate is 60%.
According to the question,
Working age population- 100,000
Labour force - 60,000
Unemployed - 12000 instructions
a) The unemployment rate is the percentage of the labor force that is unemployed and it is calculated as follows:
Unemployment Rate = \(\frac{Number of unemployed People}{Labor force}\) × 100
When an unemployed population is 12,000 and the labor force is 60,000,
the unemployment rate is = \(\frac{12000}{60000}\) × 100 = 20%
b) labor force participation rate is the percentage of working adult population that participates in labor either by actively looking for a job, or working. It is calculated as follows:
Labor Force Participation Rate = \(\frac{Labor force}{working age population}\) × 100
When the labor force is 60,000 and the working-age population is 100,000
Labor Force Participation Rate = \(\frac{60000}{100000}\) × 100 = 60%
So, a. The unemployment rate is 20%.
b. The labor-force participation rate is 60 %.
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John works at a factory and makes $11.25 an hour. This week he worked 45 hours
and last week he worked 39 hours. How much money did John make in the past 2
weeks?
Answer: $945
Step-by-step explanation: 11.25x39 is 438.75 and 11.25x45 is 506.25 and you add them together which is 945
Use the substitution method to solve the system of equations.
3x + 4y = 10
y = x-1
A. (2,3)
B. (2,1)
C. (3,2)
D. (1,2)
Answer:
B
Step-by-step explanation:
3x + 4(x-1) = 10
3x+4x-4=10
7x-4=10
+4 +4
7x=14
/7 /7
x=2
y=(2)-1
y=1
You are an order picker. You are mandated to pick 45 units per hour. You work 8. 5 hours a day (minus a 1/2 hour lunch), monday to friday. How many units should you be picking each week?.
On solving the provided question, we can say that - 45 per hour as for that of 40 hours = \(45x40 = 180 per week\)
What is linear equation ?An algebraic equation of the form y=mx+b, where m denotes the slope and b the y-intercept, is known as a linear equation. When y and x are variables, the aforementioned is referred to as a "linear equation in two variables." Bivariate linear equations are defined as linear equations with two variables. 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples of linear equations.
As we work here for 40 hours per a week, so = \((8.5-.5 x 5 = 8x5=40 hours a week)\)
45 per hour as for that of 40 hours = \(45x40 = 180 per week\)
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Express 9 hours as a percentage of 3 days
total hours in 3 days= 72
total %= 9/72*100
= 100/8
= 12.5% ans.... HOPE IT HELPS
Answer:
total hours in 3 days= 72
total %= 9/72*100
= 100/8
= 12.5% ans.... HOPE IT HELPS =D
Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P. y=x1;P(−5,−51) a. The slope of the curve at P is (Simplify your answer.)
Eequation of the tangent line (b) at the given point P.
y + 5¹/² = (1/2) * (-5)⁻¹/² * (x + 5)
How to calculate tangent line (b) at the given point P.To find the slope of the curve at the given point P, we'll first differentiate the function y with respect to x.
Given function: y = x¹/²
Step 1: Differentiate y with respect to x.
dy/dx = (1/2) * x¹/²
Step 2: Plug in the x-coordinate of the point P into the derivative to find the slope at P.
P = (-5, -5¹/²)
dy/dx at P = (1/2) * (-5)⁻¹/²
Slope (a) = (1/2) * (-5)⁻¹/²
Now, we will find the equation of the tangent line at P.
Step 3: Use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point P.
y - (-5¹/²) = (1/2) * (-5)⁻¹/²(x - (-5))
Step 4: Simplify the equation.
y + 5¹/² = (1/2) * (-5)⁻¹/² * (x + 5)
This is the equation of the tangent line (b) at the given point P.
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the joint density of x and y is given by find c. (b) find the density function of x. (c) find the density function of y. (d) find e[x]. (e) find e[y]. 1
(a) The value of C for joint density of x and y is 1/4
(b) The density function of X is \(\frac{e^{-x} }{4}\)
(c) The density function of Y is \(\frac{1}{2}y^{2}e^{-y}\)
(d) The value of E[X] is -1.
(e) The value of E[Y] is 3.
A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The function is f(x, y) = c(y - x) * e ^ (- y) - y < x < y, 0 < y < ∞
The joint density of X and Y is,
f(x,y)=\ matrix c(y - x) * e ^ (- y) - y < x < y , 0<y< infty \\ 0 matrix
Otherwise
The value of C is,
e ^ (- y) * (integrate (y - x) dx from x = - y to y) dy from y = 0 to ∞ = 1*int y=0 ^ infty e^ -y (xy - (x ^ 2)/2) x=-y ^ y dy=1
c = 1/ 4
(a) The value of C for the function is 1/4
(b) The density function of X is \(\frac{e^{-x} }{4}\)
(c) The density function of Y is \(\frac{1}{2}y^{2}e^{-y}\)
(d) The value of E[X] is -1.
(e) The value of E[Y] is 3.
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PLEASEEE HELP ILL GIVE BRAINLIEST btw there are 2 attachments so u could see all the answer choices
Answer:
1) C
Step-by-step explanation:
Step 1)
First we have to plot ↓
2x ≥ y + 2
And that looks like Image 1
Step 2)
Second we have to plot ↓
2x - 5y ≤ 10
and that looks like Image 2
Which ratio forms a proportion with 16/20?
A. 4/10
B. 32/50
C. 8/12
D. 4/5
Answer:
the required ratio which forms proportion with 16/20 is D.) 4/5
Step-by-step explanation:
when you will simplify the ratio you will get
4/5
Which numbers are prime numbers?
5
14
13
4
9
none of the above
Answer:
5 and 13 are prime numbers
Step-by-step explanation:
Answer: 5, 13,
Step-by-step explanation:
what do I check off
On a map scale of 1:10,000, 5cm would represent what distance?
Answer:
500 m
Step-by-step explanation:
10,000x5 is 50000 cm, that is 5 m
HELPPPPPPP
For each graph below, state whether it represents a function.
Answer:
No, No, Yes, No, Yes, Yes
Step-by-step explanation:
A graph is a function if it passes the vertical line test (in other words, every vertical line that can be drawn intersects the graph at no more than one point).
This is because for a function, each input must map onto no more than one output.
just please type anything I just need it for an achievement
Answer:
Achievement
Step-by-step explanation:
to be reach out there is a achievement
Someone help, please!
The appropriate response will be (A). The first equation of motion gives the link between "velocity and time."
What are the names of equations?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
What are the uses of equations?An equation is a mathematical representation of two equal objects, one on each side of a "equals" sign. We can solve challenges in our daily lives with the aid of equations. Most of the time, we look for help with pre algebra to resolve problems in real life. Pre-algebra concepts contain the fundamentals of mathematics.
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The stem-and-leaf plot shows test scores Charlie received for the year.
What is the total number of test scores recorded on the stem-and-leaf plot?
Also here is a snip.
There are 19 test scores recorded on the stem-and-leaf plot for Charlie's tests throughout the year.
The stem-and-leaf plot consists of two parts: the stem and the leaf. The stem represents the digits of the score that are in the tens place, while the leaf represents the digits in the ones place.
To find the total number of test scores recorded on this plot, we need to count the number of leaves.
Looking at the plot, we can see that there are 9 leaves in the 70s stem, 4 leaves in the 80s stem, and 5 leaves in the 90s stem. There is also 1 leaf in the 100s stem.
Therefore, the total number of test scores recorded is:
9 + 4 + 5 + 1 = 19
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Please help I’ll give brainliest
Answer:
1a) 0.1 cm = 1 mm
When converting centimeters to milimeters, multiply the length value by 10.
1b) 25000 mm = 25 m
When converting milimeters to meters, divide the length value by 1000.
1c) 7g = 0.007 kg
When converting grams to kilograms, divide the mass value by 1000.
1d) 30000 ml = 0.03 kl
When converting milimeters to kilometers, divide the volume value by 1000000.
what is the scale factor
Answer:
1 1/3.
Step-by-step explanation:
Multiply the smaller triangle's amounts by 1 1/3, you get the corresponding bigger triangle's amount for that side.
Write the percent as a decimal.
95%
Answer:
9.5 decimal
espero y te ayude
how many ways are there to arrange $6$ beads of distinct colors in a $2 \times 3$ grid if reflections and rotations are considered the same? (in other words, two arrangements are considered the same if i can rotate and/or reflect one arrangement to get the other. assume that each square gets exactly one bead.)
There are 9 or 10 distinct ways to arrange 6 beads of distinct colors in a 2x3 grid if reflections and rotations are considered the same. We can solve this problem using Burnside's Lemma.
Burnside's Lemma states that for a group action on a set, the number of fixed points is given by the average over the group of the number of fixed points under a particular group element, where the average is taken over all group elements.
In this case, the group action is the action of rotating and reflecting the grid, and the set is the set of all possible bead arrangements in the grid. To use Burnside's Lemma, we need to find the number of fixed points (i.e., bead arrangements that are unchanged) under each group element, and then take the average over all group elements.
There are a total of $4$ rotations and $2$ reflections possible for a 2x3 grid.
The identity transformation keeps the grid in its original position, and thus there are
6!/(2!3!) = 60
The $90 rotation keeps $3 beads in the same place and switches the other $3, and similarly $180 and $270 rotation also keeps $3 beads in the same place and switches the other $3$, thus there are
3! = 6
The reflection on the horizontal axis keeps $3 beads in the same place and switches the other $3, and similarly the reflection on the vertical axis also keeps $3 beads in the same place and switches the other $3, thus there are
3! = 6
So the average number of fixed points is $(6+6+6+60)/8 = \(\frac{78}{8}\) = 9.75$
So, there are 9 or 10 distinct ways to arrange 6 beads of distinct colors in a 2x3 grid if reflections and rotations are considered the same.
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The area of a rectangle is represented by x^2 + 7x - 18. Factor to find binomial expressions representing the length and width. What is the difference between the length and width?
Answer:
x^2 + 7x - 18 = (x + 9)(x - 2)
The difference between length and width is x + 9 - (x - 2) = x + 9 - x + 2 = 11.
Soledad buys 5 ounces of frozen yogurt for $2.25. What is the unit price of the frozen yogurt in dollars per ounce?
Answer:
0.45
Step-by-step explanation:
You divided 2.25 by 5
10 of 10
Work out the area of a rectangle with base, b = 38mm and perimeter, P =
100mm.
b
Let the height of the rectangle = h
2b + 2h = 100
2(38) + 2h = 100
2h = 100 - 76
h = 12mm
area of rectangle = base x height
= 38 x 12
= 456mm²
Answer:
456mm²
Step-by-step explanation:
using formula;
b/2( P - 2b) = A
substitute values