2x + = x + 5
Solve using a mental strategy
The required solution of the given equation is 5.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The given equation is
2x + = x + 5
According to given question we have
Mental Math is an exercise where we solve mathematical equations mentally without the help of a calculator.
To do the bigger or important quantities first. This gives an estimate of the value expected. Such an approach is front end or left to right multiplication.
2x = x + 5
Substract x from both sides we get,
x=5
Therefore, the required solution of the given equation is 5.
Learn more details about equation here:
https://brainly.com/question/10413253
#SPJ1
A+1/6=1/6 solve the equation
Answer:
Step-by-step explanation:
A + 1/6 = 1/6
subtract 1/6 from both sides
A = 0
Evaluate the expression when x= 6 and y= -4.
-x + 6y
Answer:
Step-by-step explanation:
substitute the value for x and y
-6 + 6(-4)
= -6 -24
= -30
Answer:
-30
Step-by-step explanation:
plug in variables
-6 + 6(-4)
-6+ -24
= -30
A small college needs two additional faculty members: a chemist and a statistician. There are five applicants for the chemistry position and seven applicants for the statistics position. In how many ways can the college fill these positions?
By using permutation, the college can fill the position in 7 ways.
What is Permutation?Permutation shows the no. of ways to arrange the objects or elements.
The Formula for the permutation is P(n, r) = [tex]\frac{n!}{(n-r)!}[/tex]
Given data:
The college needs two additional faculty members a chemist and a statistician. There are five applications for the chemistry position and seven applications for the statistics position.
No. of ways the college can fill the position = no. of ways the college can select Statistics + no. of ways the college can select chemist
By using, the permutation method we can find the no. of ways of selection of both chemist and statistician.
No. of ways the college can fill the position =[tex]5p_{1} +7p_{1}[/tex]
= 5 + 7
= 12 ways
The college can fill the position in 12 ways.
To know more about permutation, visit:
https://brainly.com/question/3867157
#SPJ9
Given the lease terms below from a local car dealership, what is the total cash due at
signing if the dealership requires down payment, security deposit, first month's
payment and the acquisition fee at signing?
Length of lease = 24 months
MSRP of the car = $22, 750
Purchase value of the car after lease = $16, 900
Down payment = $1,800
Monthly payment = $425
Security deposit = $375
Acquisition fee = $300
The total cash due at signing if the dealership requires down payment, security deposit, first month's payment and the acquisition fee at signing is 2400 + 375 + 500 = 3275
When you buy a car, you don't make monthly payments at the beginning. Plus, you don't care how much the buyout costs when you close the lease, that's after you've had it for two years.
You must take care of the deposit, this is your good faith commitment to the rental car. In addition, you may have to pay a deposit based on your credit, and the acquisition fee is what you would pay a broker or dealer to get the car to you if you wanted it from somewhere else.
Therefore,
2400 + 375 + 500 = 3275
For more information about dealership, visit https://brainly.com/question/1918419
#SPJ9
blank are numbers or variables that are multiplied together.
powers
bases
factors
radicals
Answer:
bases....................
The difference of 3 times a number and 5 is 13. Write and solve an equation to
find the number.
Answer:
n=8/3
Step-by-step explanation:
3n-5=13
3n=8
n=8/3
what is the image of the point (4, 0) after a rotation of 90 degrees counterclockwise about the origin
When point is rotated 90 degrees counterclockwise about the origin, point (x,y) becomes (-y,x).
Solving the QuestionWe're given
(4,0) rotated 90 degrees counterclockwise about the originMake the y-coordinate negative:
(4,0)
Switch around the coordinates:
(0,4)
Answer(0,4)
What is the conjugate?
a √a-1
Step-by-step explanation:
In maths, Conjugates are defined as a pair of binomials with identical terms but parting opposite arithmetic operators in the middle of these similar terms. For example, p – q is the conjugate of p + q.
complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, the complex conjugate of {\displaystyle a+bi} is equal to {\displaystyle a-bi.}
The math conjugate of a number is a number that when multiplied or added to the given number results in a rational number. For example,
The conjugate of a surd 6 + √2 is 6 - √2.
The conjugate of a complex number 5 - 3i is 5 + 3i.
To manufacture an automobile requires painting, drying, and polishing. Epsilon Motor Company produces three types of cars, the Delta, the Beta, and the Sigma. Each Delta requires 11 hours for painting, 5 hours for drying, and 3 hours for polishing. A Beta requires 17 hours for painting, 8 hours for drying, and 4 hours for polishing, and a Sigma requires 4 hours for painting, 5 hours for drying, and 1 hour for polishing. If the company has 253 hours for painting, 149 hours for drying, and 63 hours for polishing per month, how many of each type of car are produced?
Step-by-step explanation:
d = number of Delta cars
b = number of Beta cars
s = number of Sigma cars
253 = 11d + 17b + 4s
149 = 5d + 8b + 5s
63 = 3d + 4b + 1s
s = 63 - 3d - 4b
149 = 5d + 8b + 5(63 - 3d - 4b) =
= 5d + 8b + 315 - 15d - 20b = -10d - 12b + 315
-166 = -10d - 12b
-83 = -5d - 6b
83 = 5d + 6b
5d = 83 - 6b
d = (83 - 6b)/5
with these 2 "identities" we are going into the 3rd equation and solve for the third variable (b), followed by solving the first 2 identities :
253 = 11((83 - 6b)/5) + 17b + 4(63 - 3((83 - 6b)/5) - 4b)
1265 = 11(83 - 6b) + 85b + 20×63 - 12(83 - 6b) - 80b
1265 = -(83 - 6b) + 5b + 1260
5 = -83 + 6b + 5b
88 = 11b
b = 8
d = (83 - 6b)/5 = (83 - 48)/5 = 35/5 = 7
s = 63 - 3d - 4b = 63 - 3×7 - 4×8 = 63 - 21 - 32 = 10
7 Delta cars
8 Beta cars
10 Sigma cars
were produced.
50 points
A finance magazine did a survey and found that the average American family spends $1,600 on a summer vacation. If the distribution is normal with standard deviation $411, find the amount a family would have spent to be the 80th percentile.
Answer:
$1,945.91
Step-by-step explanation:
To find the amount a family would have spent to be at the 80th percentile, we can use the normal distribution.
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given that the average spending on a summer vacation is $1,600 and the standard deviation is $411:
Mean μ = $1,600Standard deviation σ = $411We need to convert the problem to the standard normal distribution by calculating the z-score.
The z-score represents the number of standard deviations a data point is away from the mean. To find the z-score corresponding to the 80th percentile, we need to find the critical value or z-score that corresponds to an area of 0.80 under the standard normal curve.
Using a standard normal distribution table or a calculator, the z-score corresponding to an area of 0.80 is 0.84162084...
Next, we use the formula for the z-score:
[tex]\boxed{z = \dfrac{x - \mu}{\sigma}}[/tex]
where z is the z-score, x is the data point, μ is the mean, and σ is the standard deviation.
Substitute z = 0.84162084..., μ = 1600, σ = 411 into the z-score formula:
[tex]0.84162084... = \dfrac{x - 1600}{411}[/tex]
Solving for x:
[tex]x=1945.90616...[/tex]
Therefore, a family would have spent approximately $1,945.91 to be at the 80th percentile of spending on a summer vacation.
Answer:
$1,945.03
Step-by-step explanation:
To find the amount a family would have spent to be at the 80th percentile, we need to find the z-score that corresponds to the 80th percentile and then use that z-score to calculate the corresponding amount.
First, we find the z-score using the standard normal distribution table or a calculator:
z = InvNorm(0.8) ≈ 0.8416
Next, we use the formula for transforming a z-score to a raw score:
z = (x - μ) / σ
where x is the raw score, μ is the mean, and σ is the standard deviation.
Substituting the given values and solving for x, we get:
0.8416 = (x - 1600) / 411
x - 1600 = 0.8416 * 411
x - 1600 = 345.0256
x = 1945.0256
Therefore, a family would have spent about $1,945.03 to be at the 80th percentile.
if the midpoint of line AB is (4,4) and the coordinates of A is (2,1) what is the coordinates if B
The required coordinate of b is given as (6, 7 ).
To find out the coordinate of b if M is the midpoint of AB. A(1, -4) and M(-3 ,0).
What is the midpoint?
The midpoint is that point the line whose length from both the ends of the line is equal.
Here,
We have coordinates of two points i.e. A(1, -4) and M(-3, 0).
Definition of midpoint says,
x = [x₁ + x₂] / 2 ; y = [y₁ + y₂] / 2
x₁ = 2, x = 4 , y₁ = -1, y = 4
now,
4 = [2 + x₂] / 2 ; 4 = [1 + y₂] / 2
x₂ = 8 - 2 ; y₂ = 8 - 1
x₂ = 6 : y₂ = 7
Thus, the coordinate of b is given as (8, 7 ).
To learn more about midpoints follow the link below:
brainly.com/question/28224145
#SPJ1
Question Which graph represents the inequality? 2x−3y<6
I think the answer is B, the one with a complete line and shaded to the bottom
If the odds in favor of an event E are a : b, then the probability of event E is?
Probability of event E is = a/c
In the given statement is:
If the odds in favor of an event E are a : b,
To find the probability of event E is
Formula for Probability
The Probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event to happen P(E) = Number of favourable outcomes / total number of outcomes
Now, According to the question:
Here, Number of outcomes in favor of the event = a
Number of outcomes in against the event = b
Total Outcomes => a + b = c
Therefore, Probability of event E is = a/c
Learn more about Probability at:
https://brainly.com/question/28653094
#SPJ1
The base lengths of a trapezoidal coffee table are 6 feet and 8 feet. The height is 5 feet. What is the area of the coffee table?
Answer:
Just multiply 6x8x5
Step-by-step explanation:
Find the average rate of change of the function f(x)=√x from x₁ = 16 to x₂ = 81.
Answer:
1/13
Step-by-step explanation:
[tex]f(x_1)=4 \\ \\ f(x_2)=9 \\ \\ \frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{1}{13}[/tex]
Ji-yoon started the week with a balance of -$90 in her checking
account. She then wrote a check for $130. Write an expression with
addition that can be used to find the new balance.
Answer:
-$90 + $130= $40
Step-by-step explanation:
Im not sure if this is what you were looking for
The figure on the left is reflected using line to form the image on the
right. Use the information in the original figure to find the corresponding parts in
the image.
The required measures of the corresponding parts in the reflection of figure a = 3.2 and b = 46 degrees. Option C is correct.
As given in the question, the figure on the left is reflected using a line to form the image on the right.
Here,
Since the reflection of a figure never changes its dimension so,
in the figure,
b + 143 + 108 + 63 = 360
b = 46
And also in reflection, the measure of the site will not change so the measure of a = 3.2
Thus, the required measures of the corresponding parts in the reflection of figure a = 3.2 and b = 46 degrees. Option C is correct.
Learn more about Angles here:
https://brainly.com/question/13954458
#SPJ1
PVIF8%,5 means that the rate is[blank]
and the time is[blank]
years?
Answer:
Step-by-step explanation:
it means the rate is 8% and the time is 5 years
A company reported total equity of $185,000 at the beginning of the year. The company reported $250,000 in revenues and $185,000 in expenses for the year. Liabilities at the end of the year totaled $112,000. What are the total assets of the company at the end of the year?
Based on the revenue, total equity, and the ending liabilities, the total assets at the end of the year is $362,000.
What is the total assets?First, find the ending equity:
= Opening equity + Revenue - expenses
= 185,000 + 250,000 - 185,000
= $250,000
The total assets by the accounting equation is:
Assets = Liabilities + Equity
= 112,000 + 250,000
= $362,000
Find out more on the accounting equation at https://brainly.com/question/28246336
#SPJ1
Joshua Vermier of Sacramento, California, received a raise after his first year on the job to $45,400 from his initial salary of $42,800. What was Joshua’s raise stated as a percentage? Inflation averaged 2.4 percent for the year. Round your answer to one decimal place.
1. Joshua's raise stated as a percentage is 6.1%.
2. When inflation is factored in, Joshua's raise reduces to 3.7%
What is a percentage?A percentage is the ratio of a variable when compared to the whole.
Percentages are expressed over 100, like ratios, probabilities, and proportions.
Data and Calculations:Initial salary on the job = $42,800
New salary after the raise = $45,400
The salary increase in dollars = $2,600 ($45,400 - $42,800)
The salary increase in percentage = 6.1% ($2,600/$42,800 x 100)
Inflation rate = 2.4%
The real increase in salary = 3.7% (6.1 - 2.4%).
Thus, Joshua’s raise stated as a percentage is 6.1%.
Learn more about percentages at https://brainly.com/question/843074 and https://brainly.com/question/24877689
#SPJ1
What is the least common denominator of 1/6 and 2/3
Answer:
It is 6 since the denominator 3 can be moved to 6 by only multiplying it by 2
William Smith is choosing artisan bonsai trees. She has 15 different variants of bonsai trees and would like
to use 7 of them. How many different selections of the 7 bonsai trees are possible?
There are 6,435 different selections of 7 bonsais that William Smith can choose.
How many different selections of the 7 bonsai trees are possible?If we have a set of N elements, the number of different combinations of K elements (such that K is equal to or smaller than N) of those N elements is given by:
C(N, K) = N!/( (N - K)!*K!)
In this case, we know that she has 15 different variants of bonsai and she wants to use 7, then:
N = 15
K = 7
Replacing these values in the above formula we will get the possible combinations of bonsais.
C(15, 7) = 15!/( (15 - 7)!*7!) = 15!/( 8!*7!) = (15*14*13*12*11*10*9)/(7*6*5*4*3*2*1) = 6,435
There are 6,435 different selections of 7 bonsais.
If you want to learn more about combinations:https://brainly.com/question/11732255
#SPJ1
During an influenza epidemic, we note that in a household of mother, father and two children, the probability that mother gets influenza is 10%. Furthermore, we see that the probability that father get influenza is also 10% while the probability that both mother and father get influenza is 2%. For the children, we assume a probability of 20% that each child will get influenza and a probability of 10% that both children get the disease at the same time. (a) Are the events that mother and father get influenza independent of each other? (b) What is the probability that at least one child will get influenza? (c) What is the conditional probability that the father has influenza given the the mother has influenza? 5 (d) What is the conditional probability that one child has influenza given that the other child does not have influenza?
Answer:
i could only work out (A)
Step-by-step explanation:
Given: P(MOTHER) = 0.10 P(FATHER) = 0.10 P(MOTHER AND FATHER)= 0.02 P(FIRST CHILD) = 0.20 P(SECOND CHILD) = 0.20 P(FIRST CHILD AND SECOND CHILD) = 0.10 So, we get: P(MOTHER) X P(FATHER) = 0.10X 0.10 = 0.01 Since P(MOTHER) X P(FATHER) = 0.01 P(MO
Find the measurement of the angle indicated for each trapezoid.
*
Answer: m∠B=53°
Step-by-step explanation:
A property that is inherent in a trapezoid of any kind: the sum of the angles adjoining a side is equal to 180°
Hence,
(32x-1)+(14x-3)=180
32x-1+14x-3=180
46x-4=180
46x-4+4=180+4
46x=184
Divide both parts of the equation by 46:
x=4
m∠B=14x-3
m∠B=14(4)-3
m∠B=56-3
m∠B=53°
The perimeter of a baseball diamond is 360 ft. If you take 12 laps around the diamond, what is the total distance you run.
Answer:6-lane, 200-meter rubberized track (8 laps = 1 mile)
Step-by-step explanation:
On a day when the speed of sound is 343 m/s you drop a rock into a well and hear it hit the bottom 3s later. How deep is the well?
Answer:
1029
Step-by-step explanation:
d=s*t
s=343m/s
t=3s
=343m/s*3s
= 1029
Find the value of k the diagram is not to scale
○ 80
○ 36
○ 100
○112
Find the value of k the diagram is not to scale
○ 80
○ 36
○ 100
○112
100 is your answer
please help!
given f(x)=3(4-x), what is the value of f(-2)?
Answer:
18
Step-by-step explanation:
f(-2) = 3(4-x)
=3(4+2)
=3*6=
=18
Given the following function, find f(- 5), f(0), and f(5).
f(x) = - 2x + 2
f(- 5) = ?
Answer: A statement, principle, or policy that creates the link between two variables is known as a function.
The function is given below.
f(x) = –3x – 5
The value of the function at x = –5, 0, 2 will be
f(–5) = –3(–5) – 5
f(–5) = 15 – 5
f(–5) = 10
f(0) = –3(0) – 5
f(0) = 0 – 5
f(0) = –5
f(2) = –3(2) – 5
f(2) = –6 – 5
f(2) = –11
