Answers
[tex] \longrightarrow \: - 4 + \frac{x + 4}{3} - 2 = 2(x + 1) \\ \longrightarrow \: { -4} + \frac{x}{3} + \frac{4}{3} - {2} = 2x + 2 \\ \longrightarrow \: { - 4}+ \frac{4}{3} - {2} - 2 = 2x - \frac{x}{3} \\ \longrightarrow \: -4 - 2 - 2 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: - 8 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: \frac{ - 20}{3} = \frac{5}{3} x \\ \longrightarrow \:\frac{ - 20}{3} \times \:3\: = 5x \\ \longrightarrow \:-20 = 5x\\\longrightarrow \:\frac{-20}{5} = x \\\longrightarrow \:x = - 4[/tex]
Related Questions
or
Steven measured a county park and made a scale drawing. The scale he used was 5 inches = 1 yard. What scale factor does the drawing use?
Answers
The scale factor used to draw is 7.2
What is scale factor?The size by which the shape is enlarged or reduced is called as its scale factor.
Given:
5 inches = 1 yard
Now, we know that
1 yd = 3 ft
now, to Convert yards to inches
1 yd = 3 x 12
i yards = 36 inches
and, the scale factor is
=36 ÷ 5
= 7 1/5
= 7.2
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jimmy had a balance of -$176 in his bank account. After he deposited $500 into his account, what was Jimmy's new balance
Answers
The new balance in Jimmy's account is 324.
What does account mean in math?An account is a record that records financial transactions concerning a specific asset, liability, equity, revenue, or expense in an accounting system. As the business events take place throughout the course of the accounting period, these records grow and shrink. The general ledger stores each individual account and is used to create financial statements at the end of an accounting period.
ACCORDING TO GIVEN STATEMENT;
Jimmy had a deposited amount of $500
minus $176, per the information provided;
his new balance is $500 minus $176,
= $324.
The new balance in Jimmy's account is 324.
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A store gathers some demographic information from their customers. The following chart summarizes the age-related information they collected:
Age Number of Customers
<20 78
20-30 58
30-40 53
40-50 77
50-60 52
>60 91
One customer is chosen at random for a prize giveaway.
What is the probability that the customer is at least 30 but no older than 60?
What is the probability that the customer is either older than 60 or younger than 40?
What is the probability that the customer is at least 60?
Answers
The probability that the customer is at least 30 but no older than 60 is o.45, that the customer is either older than 60 or younger than 40 is 0.68 and that the customer is at least 60 is 0.22.
We have the data:
Age Number of Customers
< 20 78
20 - 30 58
30 - 40 53
40 - 50 77
50 - 60 52
> 60 91
The probability that the customer is at least 30 but no older than 60 will be:
P = 182 / 409
P = 0.45
The probability that the customer is either older than 60 or younger than 40 will be:
P = 280 / 409
P = 0.68
The probability that the customer is at least 60 will be:
P = 91 / 409
P = 0.22
Therefore we get the probability that the customer is at least 30 but no older than 60 is o.45, that the customer is either older than 60 or younger than 40 is 0.68 and that the customer is at least 60 is 0.22.
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3. Which of the following is not a rational number?
A) 2.4819327451.....
B) √25
C) 9.1
D) V512
Answers
(D) V512 is not a rational number.
What are rational numbers?A rational number is any number that can be written as a fraction and has both the numerator (the top number) and the denominator (the bottom number) being integers and not equal to zero. In other words, a rational number is p/q, where p and q are both integers and q = 0. A rational number is one that has the form p/q, where p and q are integers and q is greater than zero. Some rational number examples include 1/3, 2/4, 1/5, 9/3, and so on.Since, numbers in options (A), (B), and (C) can be written in fractions, then these numbers are rational numbers.
V512 cannot be written in fractions as we don't know what V is.So, V512 is not rational.Therefore, (D) V512 is not a rational number.
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Find the value of x when 5 - x = 12x + 4
Answers
Answer:
5-4=12x+x
1=13x
1/13=×
How do you do number 10? I got it wrong and is the only one I'm stuck on. PLEASE HELP, thanks!
Answers
Answer:
[tex]x=\frac{3\left(-y+6\right)}{7}[/tex]
Step-by-step explanation:
[tex]14x+6y-6y=36-6y\\14x=36-6y\\Divide\\\frac{14x}{14}=\frac{36}{14}-\frac{6y}{14}\\\frac{14x}{14}\\\frac{14}{14}= 1\\\frac{36}{14}-\frac{6y}{14}\\\frac{36-6y}{14}\\36-6y\\6\cdot \:6-6y\\=6\left(6-y\right)\\=\frac{6\left(6-y\right)}{14}\\=\frac{3\left(-y+6\right)}{7}[/tex]
Hope this helps you, and I hope that you get un-stuck! Have a good day.
i hope this helps you
have a nice day
Find slope of the line
Answers
The slope of the line having the points ( -1 , 8 ) and ( 8 , 9 ) is 1 / 9.
We are given the two points:
( -1 , 8 ) and ( 8 , 9 )
We need to find the slope of the line that contains these two points.
We know that the formula for calculating the slope of the line is given by:
m = y₂ - y₁ / x₂ - x₁
Here, we have:
x₁ = - 1 y₁ = 8
x₂ = 8 y₂ = 9
Substituting the values in the formula, we get that:
m = 9 - 8 / 8 + 1
m = 1 / 9
Therefore, the slope of the line having the points ( -1 , 8 ) and ( 8 , 9 ) is 1 / 9.
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Points: 0 of 1
A jet plane traveling at 500 mph overlakes a propeller plane traveling at 150 mph that had a 3-hour head start. How far from the starting point are the planes?
1
The planes are miles from the starting point.
(Simplify your answer. Type an integer, fraction, or mixed number.)
Answers
Answer:39
Step-by-step explanation:
njhhvhj
tell whether -5 is a solution of the inequities
1. b+6 > 1
Answers
Answer: False, not a solution because 1 is not greater than 1.
Step-by-step explanation:
Original Equation: b + 6 > 1
[plug in -5 for b] -5 + 6 > 1
[reduce] 1 > 1
One is not greater than one, therefore, it is false.
A rental truck costs $53.45 for a day plus 69€ per mile.
(a) If x is the number of miles driven, write an expression for the total cost C, in dollars, of renting the truck for a day.
C=
Answers
Total cost is $ 11,369.45
Rental truck costs $53.45 for a day $69 per mile.
a) If x is the number of miles driven
So, c(x)=53.45+69(x)
c=53.45+69x
b) If x=164 miles
c=53.45+164
c=53.45+11,316
c=$11369.45
∴Total cost is $11,369.45
What does number of miles mean?
the aggregate number of miles traveled over in a given time. length, extent, or distance in miles. the number of miles or the average distance that a vehicle can travel on a specified quantity of fuel: the car gets good mileage.
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solve. what would be the points on a coordinate plane
y + 1/3x=4
Answers
The coordinate points on the line plotted satisfy the equation -
y + 1/3x = 4.
We have the equation of a straight line.
We have to find the coordinates that satisfy this equation.
What is the general equation of a straight line ?The general equation of straight line is -
y = mx + c
According to the question -
y + 1/3x=4
y = - (1/3)x + 4
Comparing it with general equation of line, we get -
m = - 1/3 and c = 4
Now, we will plot the line on graph -
All the coordinate points that are present on this line satisfy the equation of line. The graph extends in both the direction along the x - axis.
Hence, the coordinate points on the line plotted satisfy the equation
y + 1/3x = 4.
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PLEASE HELP
OFFERING 20 POINTS
Answers
Answer:
x = -4
Step-by-step explanation:
A perpendicular bisector is a line that divides the existing line or shape evenly and at 90° angles. First, we want to find the center point of our existing line. In this case, the center sits right at x = -4. Since the existing line is y = 3 and it is perfectly horizontal, we don’t need to do anything further. Our perpendicular bisector is x = -4.
*** When the existing line is y = [singular number], the perpendicular bisector will always be x = [midpoint of existing line], and vice versa.
Hope this helps!
Suppose that approximately 273,000,000 people live in the United States. Of these people, 31,200,000 speak a language other than English at home. Of those who speak another language at home, over 50 percent speak Spanish.
• E = speak English at home
• E' = speak another language at home
• S = speak Spanish at home
Finish each probability statement by matching the correct answer.
P(E' )
Part (b)
P(E)
Part (c)
P(S)
Part (d)
P(S | E' )
Answers
The required probability is given by P(E') =4/35 .
Probability is the study of chance. It can also be defined as the ratio of the favorable outcomes to an event to the total number of outcomes of the event.
Given the total number of people in the USA = 273000000
Let E be the number of people who speak English at home.
Therefore the number of people who don't speak English at home is E'.
∴ E' = 31200000
S speak Spanish in their homes.
∴ S = 50% of 31200000 = 15600000
Now let us find the required probabilities.
We know that probability = favorable outcome ÷ total outcome
total outcome = 273000000
a) favorable outcome(E') = 31200000
P(E')=31200000/273000000
P(E') =4/35
b)favorable outcome(E) = 273000000 - 31200000 = 241800000
P(E) = 241800000/273000000
P(E)={31}/{35}
c)favorable outcome = 15600000
P(S)={15600000}/{273000000}
P(S)={2}/{35}
Therefore the required probability is given by P(E') =4/35 , [tex]P(E)=\frac{31}{35}[/tex] P(E)=31/35 and P(E)=2/35and .
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Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation
(-9,-7) y= -3x+5
Answers
Answer:
y = -3x -34
Step-by-step explanation:
m= -3
plug the point in to find b
slope intercept form: y=mx+b
-7 = -3(-9) +b
-7 = 27 = b
-7 -27 = b
b= -34
plug in the m and b you found into the final equation:
y = -3x -34
Answer:
y = -3x -34
Step-by-step explanation:
If x=2 and y =3 what is the value of 2x^3 +5-10
Answers
Answer: 11
2x^3 + 5 - 10 =
2(2)^3 + 5 - 10 =
2(8) - 5=
16-5=11
Step-by-step explanation:
During each shift, there are nurses needed at each ward. If
there are three shifts in a day, each nurse only can be on duty
for one shift each day. How many more nurses does the
hospital need to employ?
Answers
The hospital needs to employ 21 nurses, 7 for each shift.
What are permutations and combinations?Permutations and combinations are the various ways in which objects from a set can be selected, generally without replacement, to form subsets. When the order of selection is a factor, this selection of subsets is called a permutation; when order is not a factor, it is called a combination.So, there are 3 shifts in a day and 7 nurses are needed for each shift.
Then,
7 × 3 = 21Therefore, 21 nurses are needed, 7 for each shift.
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The complete question is given below:
During each shift, there are 7 nurses needed at each ward. If there are three shifts in a day, each nurse only can be on duty for one shift each day. How many more nurses does the hospital need to employ?
Points: 0 of T
Christine went shopping and bought each of her five nephews a gift, either a video costing $14.95 or a CD
costing $16.88. She spent $78.61 on the gifts. How many videos and how many CDs did she buy?
...
Save
Answers
The number of videos will be 3 and the number of CDs will be 2.
What is an expression?Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Christine went shopping and bought each of her five nephews a gift, either a video costing $14.95 or a CD costing $16.88. She spent $78.61 on the gifts.
The number of the videos and CD will be calculated by forming an equation:-
14.95x + 16.88y = 78.61
From heat and trial, we put x = 3 and y = 2 then calculate.
14.95 x ( 3 ) + 16.88 x ( 2 ) = 78.61
44.85 + 33.76 = 78.61
78.61 = 78.61
Therefore, the number of videos will be 3 and the number of CDs will be 2.
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XZ is the angle bisector of angle WXY. Solve for m. Enter a NUMBER only.
Answers
The value of m would be 7 if XZ is the angle bisector of the angle ∠WXY which are the angles ∠WXM and ∠YXZ would be 42°.
What is an angle bisector?An angle bisector is defined as a line that divides an angle into two equal angles. Draw the given angle first, then cut it in half, and then draw the angle's bisector.
We have been given that XZ is the angle bisector of angle WXY.
⇒ ∠WXM = ∠YXZ
Solve for m
⇒ 10m -28 = 5m + 7
⇒ 10m - 5m = 28 + 7
⇒ 5m = 35
⇒ m = 35/5
⇒ m = 7
So ∠WXM = 10(7) -28 = 42
And ∠YXZ = 5(7) + 7 = 42
Therefore, the value of m would be 7.
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Find the standard deviation and variance for the following data. These are the heights (cm) of 5
students from a class of 30.
162, 166, 179, 170, 175.
Answers
The standard deviation is 6.09
The variance is 37.04.
What is the standard deviation and variance?Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.
In order to determine the standard deviation, take the following steps:
Determine the mean of the observation: (162 + 166 + 179 + 170 + 175) / 5 = 170.40Determine the difference between each value and the mean and then square the result:(162 - 170.40)² + (166- 170.40)² + (179 - 170.40)² + (170 - 170.40)² + (175 - 170.40)²
70.56 + 19.36 + 73.96 + 0.16 + 21.16 = 185.20
Determine the mean of the sum of the squared differences and then find the square root of the mean:√185.20 / 5 = 6.09
Variance measures the rate of dispersion of a data point around the dataset. It can be calculated by finding the square of the standard deviation of a dataset.
6.09² = 37.04
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The equation for photon energy, E , is
E=hcλ
where h = 6.626×10^−34 J⋅s (Planck's constant) and c = 2.99×10^8 m/s (the speed of light).
What is the wavelength, λ , of a photon that has an energy of E = 4.26×10^−19 J ?
Answers
The wavelength λ , of a photon that has an energy of E = 4.26×10^−19 J is 21504.29 meter.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now, the given equation for photon energy, E , is
E = hcλ
Here, h = 6.626×10^−34 J⋅s (Planck's constant) and
c = 2.99×10^8 m/s (the speed of light)
Therefore, we have
E = hcλ
⇒ λ = E/hc
Put the values of E, h and c we get,
λ = 4.26×10^−19 / (6.626×10^−34*2.99×10^8)
Solving we get,
λ = 4.26×10^−19 / 19.81×10^(−34+8)
⇒ λ = 4.26×10^−19 / 19.81×10^-26
⇒ λ = (4.26/19.81)*10^(-19+26)
⇒ λ = 0.215042×10^5 meter
⇒ λ = 21504.29 meter
Thus, the wavelength λ , of a photon that has an energy of E = 4.26×10^−19 J is 21504.29 meter.
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A sample of ore is found to be 0.0022% gold and 0.059% diamond. What is the percentage of matter in the ore that is neither gold nor diamond? Round your answer to the nearest ten thousandth.
Answers
The percentage of matter in the ore that is neither gold nor diamond is 99.9388%.
In the question, we are given that a sample of ore is found to be 0.0022% gold and 0.059% diamond.
We are asked for the percentage of matter in the ore that is neither gold nor diamond.
We know that in any quantity, the total is shown as 100%.
If we assume the percentage of matter in the ore that is neither gold nor diamond to be x%, then using the above theory, we can say that;
x% + 0.0022% + 0.059% = 100%.
This can also be shown as:
x + 0.0022 + 0.059 = 100, which can be simplified as:
x + 0.0612 = 100, which can be solved by subtracting 0.0612 from both sides to get:
x = 100 - 0.0612 = 99.9388.
Thus, the percentage of matter in the ore that is neither gold nor diamond is 99.9388%.
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Elimination Method
Use the elimination method to solve the system of equations below.
0.12
x
−
0.09
y
=
0.45
−
0.3
x
+
1.6
y
=
8.5
Choose one • 4 points
x
=
−
15
y
=
7
x
=
5
y
=
7
x
=
9
y
=
5
x
=
9
Answers
The correct option D. x = 9, y = 7; obtained by the elimination method.
What is defined as the elimination method?The elimination method entails the procedure of eliminating a single variables in a system of linear equations by using addition or subtraction methods in combination with variable coefficient multiplication or division.Now, as per the given question;
The equations are-
0.12x − 0.09y = 0.45 (multiply both side with 100)
12x - 9y = 45 ......equation 1
and,
-0.3x + 1.6y = 8.5 (multiply both side with 40)
-12x + 64y = 340 .......equation 2
Add equation 1 and 2;
55y = 385
y = 5
Put y = 5 in equation 1
12x = 45 + 45
x = 9
Thus, the values of the variables are obtained as (x = 9) and ( y = 7).
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The correct question is-
Use the elimination method to solve the system of equations below.
0.12x − 0.09y = 0.45
-0.3x + 1.6y = 8.5
Choose one • 4 points
A. x = −15, y = 7
B. x = 5, y = 7
C. x = 9, y = 5
D. x = 9, y = 7
Beth rode 45,000 feet on her bike, and Cayden rode 2.5 x 104 ft on his bike. Did Beth or Cayden
ride FURTHEST and by how many feet?
Answers
2.5 • 104 = 260 feet
Beth rode her bike farther.
45,000 - 260 = 44,740
Beth rode her bike farther by 44,740 feet.
The graph of function f(x) is shown below. At which value of x is the slope of the tangent line to the curve equal to 0?
Answers
The slope of the tangent is equal to zero when the derivative is equal to zero, in other words when the function attains a local extremum (maximum or minimum)
So we have to ask ourselves, at which "x" value does f(x) admit a maximum or minimum.
From the graph we can tell that it is at the point of abscissa 2
Answer: x=2For the function f, construct and simpli
1) f(x)=9x+2
Pre-Calc
Answers
Answer:
For the function f(x) = 9x f(x + h) - f(x) construct and simplify the difference quotient h 3 1 The difference quotient for f(x) = is 9x
Step-by-step explanation:
The following frequency table summarizes the number of children that dads in Dads Club have.
Number of children Number of members
111 666
222 444
333 888
444 111
555 111
Based on this data, what is a reasonable estimate of the probability that the next dad to join Dads Club has fewer than 333 children?
Answers
The reasonable estimate of the probability that the next dad to join Dads Club has fewer than 333 children is 50%.
How to illustrate the information?Number of children for 333 = 111 members
It should be noted that the total members is illustrated as:
= 666 + 111 + 111 + 888
= 1776
Therefore, the reasonable estimate of the probability that the next dad to join Dads Club has fewer than 333 children:
= 888 / 1776
= 50%.
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calculate the slope between the two points (6, 5) and (2, 13).
A. zero
B. undefined
C. -2
D. 10
Answers
Answer:
M= -2
Step-by-step explanation:
13-5=8
2-6=-4
8/-4= -2
The formula for slope is Y2-Y1/X2-X1.
so in this case it would be 13-5 divided by 2-6.
How many ounces are in 10 pints
Answers
Answer: 160 ounces
Step-by-step explanation:
1 pint=16 ounces
10 pints * 16 ounces/1 pint=
10*16/1=
10*16=160 ounces
Answer:
192.152
Step-by-step explanation:
there in us ounces
Suppose that between the ages of 22 and 40, you contribute $3000 per year to a 401(k) and your employer contributes $1500 per year on your behalf. The interest rate is 8.3% compounded annually.
a.) What is the value of the 401(k) rounded to the nearest dollar after 18 years?
b.)Suppose that after 18 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the 401(k). How much money to the nearest dollar, will you have in the plan when you reach 65?
c.) What is the difference between the amount of money you will have accumulated in the 401(k) and the amount you contributed to the plan?
Answers
The value of the 401(k) after 18 years is $173,526 , the value of the 401(k) at the age of 65 is $1,273,424 and the difference between the amount of money you will have accumulated in the 401(k) and the amount you contributed to the plan is $1,192,724
As per the given information, you contribute $3000 p.a. and your employer contributes $1500 p.a. to a 401(k)
So, the total amount contributed for 401(k) = $3000+$1500 = $4500 p.a.
This is a case of annuity because fixed amount is contributed each year.
Future value of an annuity is given by a formula = a [tex]\frac{(1+i)^{n} -1}{i}[/tex]
Where, a = annuity = $4500
i = rate of interest = 8.3% p.a. or 0.083
n = no. of years or periods = 18
Now, substituting the values in the formula,
FV of Annuity = 4500 [tex]\frac{( 1+ 0.083)^{18}-1 }{0.083}[/tex]
= 4500 [tex]\frac{4.2006 - 1}{0.083}[/tex]
= 4500 × 38.5614
= 173526.3
The future value of 401(K) after 18 years is $173,526
Now, After 40 years no contributions are made to the funds. Therefore, the future value at age 65 (after 25 years):
By applying compound interest formula, the future value = p × [tex](1+i)^{n}[/tex]
Here, p = present value or principal amount = $184,036
i = rate of interest = 8.9% or 0.089
n = no. of years or periods = 25
Substituting the values:
Future value = $173526 × [tex](1+0.083)^{25}[/tex]
= 173526 × 7.34025
= 1273724.22
You will have $1,273,424 in the plan at age 65.
Now, The difference between the amount of money you will have accumulated ate the age of 65 and the amount you
contributed (for 18years) in the plan = $1,550,956 – ($4500×18)
= $1273724 - $81000
= $1,192,724
Hence, the value of the 401(k) after 18 years is $173,526 , the value of the 401(k) at the age of 65 is $1,273,424 and the difference between the amount of money you will have accumulated in the 401(k) and the amount you contributed to the plan is $1,192,724
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Pllzzzzzz help
What number should be placed in the box to help complete the division calculation?
Answers
Answer:
160
Step-by-step explanation:
1 is in 10s place 16x10=160
