There is a mistake in the first step. The correct way to add the linear expression is (−3.78b + 12) − (4.82b − 16) = -8.6b + 18
How to correctly write adding linear expression?An expression is used to show the relationship between the variables.
The linear expression to add is as follows: (−3.78b + 12) − (4.82b − 16)
Firstly we open the bracket on the right side by multiplying the negative sign by the numbers in the brackets.
(−3.78b + 12) − (4.82b − 16)
−3.78b + 12 - 4.82b + 16
Combine like terms
−3.78b + 12 - 4.82b + 16
-3.78b - 4.82b + 12 + 16
Add the like terms
-3.78b - 4.82b + 12 + 16
-8.6b + 18
Therefore, she made the mistake in the first step.
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the average age of vehicles registered in the united states is 96 months. assume the population is normally distributed with a standard deviation of 15 months. find the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months?
The probability that the mean age of a sample of 36 vehicles is between 98 and 100 months is 15.71%.
What exactly is the z-score?The Z-score indicates the measure's deviation from the mean.We analyze the z-score table after deciding the Z-score to ascertain the p-value associated with this z-score.This p-value symbolizes the likelihood that the value of the measure is less than X, or even the percentile of X.For the given question;
The data for the vehicles registered in the united states is given as-
mean μ = 196 monthsstandard deviation σ = 15 monthssample mean x = 98 and 100 monthsSample size n = 36 vehicles.The formula for the z score is-
z = (x - μ)/(σ/√n)
Put the values.
√n = √36 = 6
For x = 98 months
z = (98 - 96)/(15/6)
z = 0.8
p(z < 0.8) = 0.7881
For x = 100 months
z = (100 - 96)/(15/6)
z = 1.6
p(z < 1.6) = 0.9452
P(0.8<x<1.6) = 0.9452 - 0.7881
P(0.8<x<1.6) = 0.1571
Thus, the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months is 15.71%.
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What is the answer to -6x - 11 = 19
And how to solve it?
-6x-11=19/+11 <=>
<=> -6x=30/:(-6) <=>
<=> x=-5
A plane flies 1.7 hours at 140 mph on a bearing of 10 degrees. It then turns and flies 9.6 hours at the same speed on a bearing of 100 degrees. How far is the plane from its starting point?
The starting point is 1,365 miles .
Given :
→ initial time of plane = 1.7 hours
→ initial speed = 140 mph
→ final time of plane = 9.6 hours
→ final speed = same = 140 mph
The initial displacement of the plane is :
distance = speed × time
= 1.7 × 140
= 238 miles
The final displacement of the plane is :
distance = 9.6 × 140
= 1,344 miles
The angles between initial and final displacement is :
100° - 10 ° = 90 °
The distance of the plane from its starting point is calculated as follows
d = [tex]\sqrt{238^{2}+ 1344^{2} }[/tex]
d = [tex]\sqrt{56644 + 1806336}[/tex]
= [tex]\sqrt{1862980}[/tex]
= 1364.9 miles ≈ 1,365 miles
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A recipe calls for 4 apples to serve 6 people. If Jack is planning to serve a crowd of 33 people, how many apples should he use?
Answer:
22 apples
Step-by-step explanation:
33/6=5.5*4=22
Pls give brainliest
Answer:
I believe the answer would be 22 apples
We would like to estimate the proportion of uf students who owns a scooter to within 1% of the truth, with 95% confidence. We believe around 20% of students do. How many students should be sampled?.
It is determined that 188 students should be sampled to use the confidence interval for a proportion.
What is mean by the term confidence interval?A confidence interval is indeed the mean of the estimate plus and minus its variation.We get the very next confidence interval of percentages in a sample of n people surveyed with a success probability of π and a confidence level of.π ± z√π(1-π)/n
In which case,
z is indeed the z-score with the p-value of 1+α/2
The error margin is as follows:
M = z√π(1-π)/n
In this case:
z does have a p-value of at 95% confidence, so z = 1.96.Thus p = 0.2, a 20% estimate.Taking into account, this same sample size is n. M = 0.02.Then:
M = z√π(1-π)/n
0.02 = 1.96√0.02(1-0.02)/n
√n = 13.72
n = 188.23
To summarize:
A total of 188 students must be sampled to estimate the proportion of of students who owns a scooter.
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Will give brainly pls help asap
Answer: [tex]\frac{\sqrt{x}^3 }{3}[/tex]
Step-by-step explanation:
Step 1: Insert f(x) in for the x in g(x). This will give you [tex]\sqrt{x^3}[/tex]
Step 2: Insert [tex]\sqrt{x^3}[/tex] into the x in h(x) giving you [tex]\frac{\sqrt{x}^3 }{3}[/tex]
What is the percentage change from 5 to 2?
Answer:
the percentage change is a 60% change.
Step-by-step explanation:
A change from 5 to 2 represents a negative change (decrease) of -60%
Use the formula found below on this webpage to find the percent change by replacing the given values:
Percent change = New - Old
|Old|
× 100%
Percent change = 2 - 5
|5|
× 100% =
-3
5
× 100 = -60% (decrease)
Where: 5 is the old value and 2 is the new value. In this case we have a negative change (decrease) of -60 percent because the new value is smaller than the old value.
Under her cell phone plan, Mei Mei pays a flat cost of $46 per month and $5 per
gigabyte. She wants to keep her bill under $70 per month. Write and solve an
inequality which can be used to determine g, the number of gigabytes Mei Mei can
use while staying within her budget.
The flat cost of the plan = is $46 per month
Cost per gigabyte = $5 per gigabyte
Number of gigabytes = g
The maximum amount Mei Mei wants to spend on the bill = is $70 per month,
So, for each month,
$46 + $5(g) < $70
⇒ $5(g) < $70 - $46
⇒ $5(g) < $24
⇒ g < $24/$5
⇒ g < 4.8
The number of gigabytes to be used per month should be less than or equal to 4.8.
What is Inequality?Inequalities are algebraic expressions that show how one term is less than, less than or equal to, greater than, or greater than or equal to another rather than how both sides of an equation are equal to each other.The collection of all real numbers that satisfy the inequality is its solution. As a result, x can have any value that resolves the inequality.The values indicated by the symbols < (greater than) and > (less than) are not included in the answer.An inequality with terms of the type of ab, where a and b are real positive numbers or variable expressions, is referred to as a "power inequality." They frequently show up in exercises from mathematics Olympiads.To learn more about Inequality, refer to:
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Inequality: 5g+46<70
Answer: g<4.8
Look at the distance vs. elevation graph. Describe the relationship between distance and elevation. Does the relationship support the continental drift theory? Provide at least one piece of support for your answer by referencing your graph
The relationship has no relation to continental drift theory, as it is a relation between distance and time, not distance and elevation.
What is continental drift theory?The continental drift theory states that the world's tectonic plates are in constant motion over time.
This is supported by the fact that some millions of years ago, there was only one continent, named Pangea, and now we have the continents as we know. These continents are also moving a small amount a year.
In this problem, the elevation decreases and the distance increases, however, the continental drift theory should have the distance increasing or decreasing over time, hence the graph relationship has no relation to the continental drift theory.
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300 divided by 2(0.5 +4.5)^2
Answer: 6
Step-by-step explanation:
1. add (0.5 + 4.5) which equals 5, so now you have 2 x 5^2.
2. evaluate the power (5^2) which equals 25 and you end up with 2 x 25 which equals 50.
3. now you have 300 divided by 50.
300 divided by 50 is 6.
The value of the expression 300 divided by 2(0.5 +4.5)²is 6
What is Simplification ?Simplification is reducing the expression/fraction/problem to a simpler form. It makes the problem easy with calculations and solving.
Given an expression, 300 divided by 2(0.5 +4.5)²
300/2(0.5 +4.5)²
= 300/2x5²
= 300/2x25
= 300/50
= 6
Hence, The value of the expression 300 divided by 2(0.5 +4.5)²is 6
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Here are six numbers
-4, -2, -1, 5, 6, 8
Arrange the numbers into two pairs with the same total
Answer: (8,-4), (6,-2), (5,-1)
Alayna is hanging a picture frame in the center of a wall that is 8 feet wide. If the picture frame is 21 1 over 4
inches wide, how far will each side of the picture frame be from the edge of the wall (in inches)? First, estimate the amount and then find the exact measurement. In two or more complete sentences, explain how you solved the problem. You may include a diagram in your explanation if you wish.
8 feet is known to equal 96 inches.
48 inches are divided in half,
and because the image is hung in the middle of the wall,
the subject of the image is that,
11 inches on each side, as well.
This is,
37 inches of wall on each side of 48-11.
How do you figure out a rectangle's area?A rectangle is a closed figure with four equal and opposite sides. Consequently, the length, which is also known as the height, and the width of a rectangle can be used to define it (sometimes called breadth).
The formula for a rectangle's surface area is as follows:
A=lxw
A=l×w
where:
A is the surface area of the rectangle;
L specifies the length of the rectangle.
Usually, it refers to the longest side of the rectangle.
W is the rectangle's width which is rectangle's shortest side.
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The varsity baseball team has won 15 out of their last
16 games. The junior varsity team has won 6 out of their
last 10 games. What is the probability that both teams
win their next game?
If you could give me step by step explanation that would be great.
Answer:
Step-by-step explanation:
please somebody help me I really need help with this
Answer:
54.4 %
Explanation:
The percent change in net sales can be calculated as:
[tex]\text{ \% Change = }\frac{\text{ Final number - Initial number}}{\text{ Initial number}}\times100[/tex]Where the final number is the net sales in quarter 2 and the initial number is the net sales in quarter 1. Replacing the values by 170 and 110, we get:
[tex]\text{ \% Change = }\frac{170-110}{110}\times100=\frac{60}{110}\times100=54.5\text{ \%}[/tex]Therefore, the answer is:
percent change = 54.5 %
What is the slope of the line that passes through the points (10, 4) and
(7, 3)? Write your answer in simplest form.
================================================
Work Shown:
[tex](x_1,y_1) = (10,4) \text{ and } (x_2,y_2) = (7,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - 4}{7 - 10}\\\\m = \frac{-1}{-3}\\\\m = \frac{1}{3}\\\\[/tex]
-----------------
Extra info:
A slope of 1/3 means "go up 1, then to the right 3"
Think of it like this
slope = rise/run = 1/3
rise = 1 = go up 1
run = 3 = go to the right 3
Complete the table of values representing the linear equation 5x - 4y = -8.
Enter your answers as integers or decimals in the spaces provided.
X
-6
0
y
-3
0
Substitution method - the points are (-6, -11/2),(-4,-3), (-8/5,0), (0,2) and (4,7)
what is the substitution method?
To solve many simultaneous linear equations, use the substitution method in algebra. The value of a variable from one equation is substituted in the second equation in this procedure, as the name implies.
we are given the equation,
5x - 4y = -8
case I
when x = -6
5(-6) - 4y = -8
-30 - 4y = -8
-4y = -8 + 30
-4y = 22
y = -(22/4)
y = -11/2
(x,y) = (-6, -11/2)
case II
when y = -3
5x - 4(-3) = -8
5x + 12 = -8
5x = -8 -12
5x = -20
x = -20/5
x = -4
(x,y) = (-4,-3)
case III
when y = 0
5x - 4y = -8
5x - 4(0) = -8
5x = -8
x = -8/5
(x,y) = (-8/5,0)
case III
when x = 0
5(0) - 4y = -8
0 - 4y = - 8
y= 8/4
y = 2
(x,y) = (0,2)
case IV
when x = 4
5(4) - 4y = -8
20 - 4y = -8
-4y = -8-20
-4y = -28
y = 28/4
y = 7
(x,y) = (4,7)
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What is -0.25 as a fraction in its simplest form
Answer:
-1/4
Explanation:
To write the decimal -0.25 as a fraction we need to multiply and divide by 100 as follows:
[tex]-0.25\times\frac{100}{100}=\frac{-0.25\times100}{100}=\frac{-25}{100}[/tex]We multiply by 100 because there are 2 digits after the decimal point.
Then, we need to simplify the fraction, so we can divide the numerator and the denominator by 25 as:
[tex]\frac{-25}{100}=\frac{-25\div25}{100\div25}=-\frac{1}{4}[/tex]So, the fraction in its simplest form is -1/4
a computer randomly selects 800 names from a list of all registered voters. those selected are surveyed to predict who will win the election for mayor.
a computer randomly selects 800 names from a list of all registered voters. Then option C is correct that is Simple random sampling
A simple random sample in statistics, is a subset of individuals chosen from a larger set. Each individual is chosen randomly and entirely by chance, such that each individual has the same probability for the entire larger set.
the complete question is
Identify the sampling method as simple random sampling, systematic sampling, convenience sampling, or stratified sampling. A computer randomly selects 800 names from a list of all registered voters. Those selected are surveyed to predict who will win the election for Mayor.
Choose the correct sampling technique below.
A. Systematic sampling
B. Convenience sampling
C. Simple random sampling
D. Stratified sampling
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a student missed 4 problems on a mathematics test and received a grade of 75%. if all the problems were of equal value, how many problems were on the test?
The problems in the test are 16.
In the given case a student missed four problems on a test.
The test happened to be a mathematics test and the student scored a total percentage of 75%.
It is mentioned that every question has of same score values.
To find out how many problems were actually on the test we need to solve the problem by following the steps.
Let,
Questions not attempted ( x ) = 4
Percentage gained ( y ) = 75%
The percentage lost is 25%
The total questions in the test are;
→ A = (100/25) * 4
A = 16
Therefore, the questions in the test are 16.
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please help!!!! will mark brainliest if correct!!!
The monomial in standard form is 6x¹¹y¹⁸.
The given expression is
[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}[/tex]
We to write the expression as a monomial in standard form
Monomial is an expression having a single term. It can be represented as kxⁿ, where k is any integer often known as the coefficient, x represents the variable/s in the given expression and n denotes the power.
In the expression
[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}[/tex]
we first need to multiply the powers
using the formula
(mn)ˣ = mˣnˣ
[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}\\(-3x^3y^{2.3}) .(-\frac{2}{3}x^{2.4} y^{3.4} )\\(-3x^3y^{6}) .(-\frac{2}{3}x^{8} y^{12} )\\[/tex]
Now, we need to multiply both the terms
The following formula is used
xᵃ . xᵇ = xᵃ+ᵇ
[tex](-3x^3y^{6}) .(-\frac{2}{3}x^{8} y^{12} )\\\\-3(-\frac{2}{3})x^{3+8} y^{6+12} \\\\6x^{11}y^{18}[/tex]
Therefore the monomial in standard form is 6x¹¹y¹⁸.
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-3p-4<6. I rlly need help guys
Answer:
p > -10/3
Step-by-step explanation:
-4<6+3p
-10<3p
p>-10/3
:]
Answer: p > 10/-3
Step-by-step explanation:
1) Remove the whole numbers next to the variable
Add 10 on both sides.
-3p < 10
2) Set x by itself
Divide -3 on both sides. Dividing -3 will flip the operator sign. (Dividing/Multiplying negative number flips the sign)
p > 10/-3
Gino has a debit card. The account pays no interest. He keeps track of his purchases and deposits in this debit card register. Find the missing entries a through f.
SARL
778.19
8/4 Baseball Bat
42.19
8/5 Gas
8/7 Deposit
8/7 Gas
8/7
Dinner at Spooner's
On the Beach
8/11 Books for Fall Semester
a. 92.19
b. 51.00
C. $400.00
d. 25.00
e. 71.12
f. 491.51
**
**
92 19
ST 00
25 00
71 12
491 ST
400 00
a.
b.
C.
d.
e.
The missing entries are (a) $686, (b) $635, (c) $1035, (d) $1010, (e) $938.88 and (f) $447.37.
What is Debit Card?Debit card is a card owned by a person for which the money used for transaction will be withdrawn or added into the account of the holder immediately.
Given is a table showing the transactions of Gino with his debit card.
He has an initial deposit amount of $778.19.
New balance in the account will be the difference of previous balance and the payment amount.
He paid $92.19 for baseball bat.
a = $778.19 - 92.19 = $686
He paid $51.00 for gas.
b = $686 - $51 = $635
He deposited $400.
c = $635 + $400 = $1035
He paid $25 for gas.
d = $1035 - $25 = $1010
He paid $71.12 for dinner at Spooner's on the beach.
e = $1010 - $71.12 = $938.88
He paid $491.51 for the books for all semester.
f = $938.88 - $491.51 = $447.37
Hence the missing entries are found.
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Identify the slope and y intercept
Step-by-step explanation:
the y-intercept (b) is the easiest :
it is the y-value, when x = 0 : -3
the slope (m) is the ratio (y coordinate difference / x coordinate difference) when going from 1 point to another.
so, we need to identify 2 points in the line.
one we have already with b : (0, -3)
another is the x-axis intercept, which is clearly (4, 0)
the difference is not important, but we need to use the same for both (x and y).
I prefer to go from left to right, so from (0, -3) to (4, 0) :
x changes by +4 (from 0 to 4)
y changes by +3 (from -3 to 0)
the slope is +3/+4 = 3/4
Jordan is mixing water and flour to make tortillas. The number of cups of water, w, needed for f cups of flour is described by the equation w=0.75f . What does 0.75 tell us in this situation?
If the number of cups of water w, needed for f cups of flour is described by the equation w = 0.75f, 0.75 represents the number of cups of water needed for one cup of flour
The equation is
w = 0.75f
Where w is the number of cups waters needed for f cups of flour.
Here w is is dependent variable and f is the independent variable
We can see that w is proportional to the f, the 0.75 is the constant.
w = 0.75f
Move the f to left hand side of the equation
w/f = 0.75
Hence, If the number of cups of water w, needed for f cups of flour is described by the equation w = 0.75f, 0.75 represents the number of cups of water needed for one cup of flour
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PLease help it’s due tomorrow morning
Explain the step that is used to solve the equation
Wukong and Nice are playing a soccer match and the probabilities of them scoring are 7/8 and 5/6 respectively. What is the probability that at least one of them will score a goal if they each play the ball once?
Answer:
Step-by-step explanation:
2038
according to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,875. assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $640. (round your z-score computation to 2 decimal places and final answers to 2 decimal places.) a. what percent of the adults spend more than $2,775 per year on reading and entertainment?
According to a government study among adults the percent of the adults spend more than $2,775 per year on reading and entertainment is
7.98%How to determine if the probability that the elevator is overloadedGiven data form the question
the mean amount spent per year on reading and entertainment is $1,875
standard deviation of $640
what percent of the adults spend more than $2,775 per year on reading and entertainment
Definition of variables
mean sample, μ = $1,875
standard deviation, σ = $640
measure X = $2,775
For normal distribution, the z-score of a measure X with mean μ and standard deviation σ is given by as follows:
Z = ( X - μ ) / σ
Z = (2775 - 1875) / 640
Z = 1.40625 gives p-value of 0.0798250014
This is equivalents to 7.98%
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Find the value of “B,” that will make a perfect square trinomial. x² + Bx + 1.
*
Type the answer for B as a whole number.
Using algebraic identities, we found that for B=2 and B= -2 , the trinomial x² + Bx +1 makes a perfect square.
What are algebraic identities?Algebraic identities are the identities which aids in solving products or powers of algebraic expressions. Most common identities are :
(a+ b)² = a² + 2ab + b²
(a- b)² = a² - 2ab + b²
a² -b² = (a+ b) (a- b), where a and b can be variable or constants or algebraic expressions.
Let the perfect square of the trinomial be (x +a)²
x² + Bx +1 = (x+ a)² = x² + 2xa + a² (using identity (a+ b)² = a² + 2ab + b²)
⇒ x² + Bx +1 = x² + 2xa + a²
⇒ Bx = 2xa , a² =1
⇒B = 2a , a =± 1
if a =1 ⇒ B = 2
If a = -1 , B = -2
For B = 2 , x² + Bx +1 = x² + 2(1)x +1² = (x+1)² ( ∵(a+ b)² = a² + 2ab + b²)
For B = -2 , x² + Bx +1 = x² -2x + (-1)² = x² -2x +1 = ( x-1)² (∵(a- b)² = a² -2ab
+ b²)
Thus, the given trinomial x² + Bx +1 is perfect square when B =2 or -2
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For which of the following pairs (x,y)(x,y) does the inequality 12x^2 + 6y^2 \geq 17xy12x2+6y2≥17xy fail?
Answer:
=(3x - 2y( (4x - 3y)
Step-by-step explanation:
We have,
12x2 – 17xy + 6y2
The coefficient of x2 is 12
The coefficient of x is -17y
Constant term is 6y2
So, we express the middle term -17xy as -9xy – 8xy
12x2 -17xy+ 6y2 = 12x2 – 9xy – 8xy + 6y2
= 3x (4x – 3y) – 2y (4x – 3y)
= (3x – 2y) (4x – 3y)
5) The lengths of the fours sides of a quadrilateral are consecutive integers. If the perimeter is 94 meters, find the value
of the shortest of the four side lengths.
The shortest side is 22 meters in the mentioned quadrilateral.
Let us assume the length of first side be x. So, the other three sides of length will be (x + 1), (x + 2) and (x + 3). The perimeter is sum of all sides of the quadrilateral.
Keep the values in the formula of perimeter -
94 = x + x + 1 + x + 2 + x + 3
Performing addition on Right Hand Side of the equation
94 = 4x + 6
Shifting 6 to other side of the equation
4x = 94 - 6
Performing subtraction on Right Hand Side of the equation
4x = 88
Shifting 4 to Right Hand Side of the equation
x = 88 ÷ 4
Performing division
x = 22
Thus, the shortest side of quadrilateral is 22 meters long.
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