To find the arithmetic mean (average) of a group of numbers add the numbers and divide by the total number of items we added.
(12+16+10+8+14+15)/6
= 75/6
= 12.5 (answer is already rounded to nearest tenth)
Write 3.278 correct to 1 decimal place.
Answer: 0.3278
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-8b+ 2 + 6b = -3b + 7
Answer:
b = 5
Step-by-step explanation:
Add 8b to both sides :
2+6b = 5b+7
Subtract 5b from both sides :
2+b = 7
Subtract 2 from both sides :
b = 5
Let's check :
-8(5) + 2 +6(5) = -3(5) + 7
-40 + 2 + 30 = -15 + 7
-38 + 30 = -8
-8 = -8
Correct
Hope this helped and have a good day
Answer:
b = 5
Step-by-step explanation:
to solve this you must first combine like terms
-8b + 2 + 6b = -3b + 7
combine (add) -8b and 6b
that makes -2b
-2b + 2 = -3b + 7
now add 3b to both sides to put b on one side
-2b + 2 + 3b = -3b + 3b + 7
b + 2 = 7
now subtract 2 to both side
b + 2 - 2 = 7 - 2
b = 5
that is your answer
Compute the value of the expression C (8,5)
The value of C (8,5) is 56.
What is the combination?A combination is made up of n different items that are taken one at a time without repeating itself.
The given expression is C(8,5).
The expression C (8,5) can be denoted as ₈C₅.
The formula for selecting x thins from n things is:
ₙCₓ = n!/( (n-x)! x!)
Therefore, the value of ₈C₅ is:
₈C₅ = 8!/( (8-5)! 5 !)
= 8!/( 3! ×5!)
= (8×7×6×5!)/( 3! ×5!)
= (8×7×6)/(3!)
= (8×7×6)/(6)
= 8×7
=56
Hence, the value of C (8,5) is 56.
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Graph the linear function w(x)=3/5x+2
The graph of the linear function w(x) = 3/5x + 2 is coordinates or points (0,2), (1,2.6) (2,3.2) (3,3.8)
What is a linear function?
A linear function is a straight line on an x-y coordinate.
Formula
w(x) = 3/5x +2 in each coordinate I have a x so for example 3.
I would rewrite this as 3/5(3) + 2
w(x) = 3/5x +2
w(3) = 3/5(3) + 2
y = 1.8 + 2
y = 3.8
A company gives yearly raises to their employees. The salaries at the company are based on the equation below, where S is the salary before taxes and t is the time since the date of hire in years.
S = $33,113 + $600t
What is the minimum number of years an employee would have to stay to make a salary of over $40,000 per year?
A. 13 years
B. 12 years
C. 11 years
D. 1 year
Based on the equation, the minimum number of years an employee would have to stay to make a salary of over $40,000 per year is B. 12 years.
What is an equation?An equation is a mathematical statement that defines that two or more mathematical expressions are equal or equivalent.
Equations show equality using the equation symbol (=).
When one expression is more or less than, or not equal to another expression, it is an inequality.
If S = $33,113 + $600t
Where S = the salary before taxes
t = the time since the date of hire in years.
For S ≥ $40,000:
$33,113 + $600t ≥ $40,000
$600t ≥ $40,000 - $33,113
$600t ≥ $6,887
t ≥ 11.48
t = 12 years
Thus, using the given equation, an employee needs to stay at the work for 12 years to earn more than $40,000 a year.
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For every pull-up Mark completes, he does 4 push-ups. If he did 48 push-up, how many pull-ups did he do?
Answer:
Mark did 12 pull ups
Step-by-step explanation:
48 / 4 = 12
A cube box is 20 cm x 20 cm x 20 cm. What is the surface area of the largest size sphere that can fit in this box? Leave your answer in terms of pi.
The surface area of the largest size sphere that can fit in this box is 400π
What is the surface area of the sphere?
The surface area of a sphere is the space that the sphere's outer surface occupies. A sphere is a circle in three dimensions. A circle is a two-dimensional (2D) shape, whereas a sphere is a three-dimensional (3D) shape, which is the difference between the two.
Here, we have
The diameter of the biggest sphere will be equal to the side of the sphere.
radius = 20/2
= 10
The surface area of the sphere = 4πr²
=4π(10)²
= 400π
Hence, the surface area of the largest size sphere that can fit in this box is 400π.
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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8. What are the two numbers?
The first number is 3 and the second number is -5.
According to the question,
We have the following information:
There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8.
Now, let's take the first number to be x and the second number to be y.
So, we have the following expressions:
6x+4y = - 2
6x = -2-4y ...(1)
6x+2y = 8
Putting the value of 6x from equation 1:
-2-4y+2y = 8
-2-2y = 8
-2y = 8+2
-2y = 10
y = -10/2
y = -5
Putting this value of y in equation 1:
6x = -2-4y
6x = -2-4*(-5)
6x = -2+20
6x = 18
x = 18/6
x = 3
Hence, the first number is 3 and the second number is -5.
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Question 6
The functions g is defined on the real numbers by g (x) = (x² + 1) (3x - 5). What is the value
of g(4) ?
-51
63
119
175
Answer: 119
Step-by-step explanation:
(4^2+1)(3*4-5)
=(16+1)(12-5)
=17*7
=119
Answer:
g(4) = 119
Step-by-step explanation:
g(x) = (x² + 1) (3x - 5)
Substitute x for 4 in the equation
g(4) = (4² + 1) (3(4) - 5)
g(4) = (16 + 1) (12 - 5)
g(4) = (17) (7)
g(4) = 119
Hence, the value of g(4) is 119
What is the equation of this line in slope intercept form?
2x+3y=−6
A street light is mounted at the top of a 15-ft-tall pole. a man 6 ft tall walks away from the pole with a speed of 6 ft/s along a straight path. How fast is the tip of his shadow moving when he is 50 ft from the pole?
The tip of his shadow moving when he is 50 ft from the pole is 10ft/s
What is meant by differentiation?The practical approach of differentiation may be performed utilizing just algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.
The theory offers the following fundamental guidelines for differentiating the sum, product, or quotient of any two functions f(x) and g(x) whose derivatives are known (where a and b are constants) for functions constructed of combinations of these types of functions
I assume the man and pole are standing straight up, which means the 2 triangles are similar to each other.
(y-x)/y =6/15
15(y-x)=6y
9y=15x
y=(5/3)x
Differentiating both sides with respect to t,
dy/dt=(5/3)dx/dt
We know that, dx/dt= 6 ft/s
((5/3)*6=10 ft/s
Therefore, the tip of his shadow moving when he is 50 ft from the pole is 10ft/s
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Add and simplify.
7/12 + 2/15
how to solve this proportion
Answer:
Hope the picture will help you
5. The diagram shows a rectangular field ABCD has a path of uniform width around it. AB and BC are 6m and 4 m respectively. Given that area PQRS is twice the area of ABCD. Find the length of PQ and QR.
Tthe length of PQ and QR. is 6 and 8 m
Area of rectangular field ABCD is = 4m x 6m = 24m2
Area of rectangular field PQRS (ABCD with uniform path) = (4 + x)(6 + x)
= 24 + 4x + 6x + x²
48 = 24 + 10x + x²
x² + 10x - 24 = 0
x² + 12x - 2x - 24
x(x + 12) - 2(x + 12)
(x - 2)(x + 12) = 0
x - 2 = 0
x = 2
PQ = 4 + 2 = 6
QR = 6 + 2 = 8
Therefore, the length of PQ and QR. is 6 and 8 m
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JMP made a profit of $85,000 last year. If the profit margin increased by 20% this year what is the amount of profit made by JMP
The amount of profit made by JMP is 102000.
Given,
In the question;
JMP made a profit of $85,000 last year.
If the profit margin increased by 20% this year.
To find the amount of profit made by JMP.
Now, According to the question:
Based on the given condition:
Formulate:
= 85000 x (20% + 1)
Calculate;
85000 x (0.2 + 1)
Calculate the sum or difference
85000 x 1.2
= 102000
Hence, The amount of profit made by JMP is 102000.
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Directions - Write an equation in slope-intercept (y = mx + b) form for each line.
The equation in slope intercept form of the line that passes through the graph is y = 2/3x + 2
How to determine the equation of the line?From the graph, we have the points to be given as
(-3,0) and (0,2)
Start by calculating the slope of the points using the following slope equation
m = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (-3,0) and (0,2)
So, we have
m = (2 - 0)/(0 + 3)
Evaluate
m = 2/3
The equation is then calculated as
y = m(x - x₁) + y₁
Where
(x, y) = (0, 2) and m = 2/3
So, we have
y = 2/3(x - 0) + 2
Expand
y = 2/3x + 2
Hence, the equation in slope intercept form of the line is y = 2/3x + 2
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An Olympic-size swimming pool holds approximately 6×105 gallons of water. The capacity of this swimming pool is between which interval?
The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.
What is the capacity?Capacity refers to the product of the length, width, and height of a three-dimensional object or space.
The capacity of an object means the same as its volume.
Olympic-size swimming pools have the following standard dimensions:
Length = 50 m
Width = 25 m
Height = 2 m
Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)
= 660,000 gallons (2,500 x 1,000 ÷ 3.785)
An interval estimate shows the lower and upper limits.
6 x 105 gallons = 630 gallons
Thus, the capacity of the swimming pool is Option B.
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Question Completion with Answer Options:A. 100 gallons to 500 gallons
B. 500 gallons to 1,000 gallons
C. 1,000 gallons to 1,500 gallons
D. 1,500 gallons to 2,000 gallons
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper
Answer:(1) y-intercept exists 490 and the slope is -2/3x.
(2) First, I observe the point (0,490) and plot a point there. Then utilize our slope -2/3 to compute the direction and angle the line moves by measuring 2 down and 3 to the right.
(3) The equation of the function is
The diagram illustrates how many wraps could've been sold for each number of sandwich sales to maintain the identical earnings of $1,470.
(4) The graph of the equation is shown below.
(5) The profits exist the same (slope) but the y-intercept is more increased than the actual diagram.
(6) The equation is
Step-by-step explanation:
(1)
slope-intercept form of a linear equation is where one side includes only "y".
⇒
⇒
Therefore,
.
Hence, the y-intercept exists at 490 and the slope is -2/3x.
(2)
I would graph this line using the slope-intercept method First, I observe the point (0,490) and plot a point there. Then utilize our slope -2/3 to compute the direction and angle the line moves by measuring 2 down and 3 to the right.
(3)
The equation of the function is. The diagram illustrates how many wraps could've been sold for each number of sandwich sales to maintain the identical earnings of $1,470.
(4)
The graph of the function is shown below,
(5)
Therefore,
The profits exist the same (slope) but the y-intercept is more increased than the actual diagram.
(6)
y intercept= 300
The equation will be,
David and Vicky share £36 in the ratio 2:7. How much do they each
receive?
David share is £8
Vicky share is £28
From the question, we have
David and Vicky share £36 in the ratio 2:7.
David share = £36 *2/9 = £8
Vicky share = £36 *7/9 = £28
Multiplication:
The product of the numbers is what is obtained in mathematics when two or more numbers are multiplied. We frequently perform it since it is one of the fundamental mathematical operations. Using multiplication tables is the most straightforward use. In mathematics, adding a number repeatedly in relation to another is represented by multiplying two integers. These figures can be natural figures, whole figures, fractional figures, integer figures, or other figures. When m is multiplied by n, m is either added to itself n times or multiplied by n.
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During the WMS Presidential elections, candidate #1 received 75 votes whereas candidate #2, who
promised better lunches and longer seminar class times received 165 votes. What is the percentage
difference between the WMS Presidential Candidate # 1 and WMS Presidential Candidate # 2's total
number of votes?
Answer: candidate 2 has 90 votes
Step-by-step explanation:
165-75=90
Emory walks one lap on the
track every 7 minutes. Madison
walks one lap on the track every
8 minutes. How many minutes
will pass before they meet on
track at the same time?
Answer: 56 minutes
Step-by-step explanation:
7 = 7, 14, 28, 35, 42, 49, 56
8 = 8, 16, 24, 32, 40, 48, 56
7 and 8 have 56 in common so it would take them 56 minutes
6th grade problem i need help
Answer:
Step-by-step explanation:
1. First multiply to get the number of hours for 5 painters.
5*21= 105 minutes for 5 painters.
2. Divide by 7 for hours taken for the 7 painters!
105/7=15
3. Answer=15 hours
the variables x and y are related such that each time x decreases by 5 , y increases by 2 .if y is a positive value when x=0. which of the following equations could express the relationship between x and y
The linear function that could express the relationship between x and y is given as follows:
y = -0.4x + b, b > 0.
What is a linear function?The slope-intercept representation of a linear function is given by the rule presented below as follows:
y = mx + b
The coefficients of the function, along with their meaning, are listed as follows:
m is the slope of the function, being obtained by the division of the change in y by the change in x.b is the y-intercept of the function, representing the values of the output variable y when the input variable x assumes a value of zero.In the relationship, we have that each time x decreases by 5 , y increases by 2, hence the slope is obtained as follows:
y = -2/5 = -0.4.
The y-intercept is positive, hence the definition of the function is given as follows:
y = -0.4x + b, b > 0.
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Which of the following is the inverse of f(x) =
2x+4/3
By using the concept of function, it can be calculated that
[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here, the function is
[tex]f(x) = 2x + \frac{4}{3}\\[/tex]
Let f(x) = y
[tex]2x + \frac{4}{3} = y\\\frac{6x + 4}{3} = y\\[/tex]
6x + 4 = 3y
6x = 3y - 4
[tex]x = \frac{3y - 4}{6}[/tex]
[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]
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I need answer help please
For given function f(x) = 7/(x² - 5),
f(a + 4) = 7/(a² + 8x + 11)
In this question we have been given a function f(x) = 7/(x² - 5)
We need to evaluate f(a + 4)
Substitute x = a + 4 in given function.
f(a + 4)
= 7/((a + 4)² - 5)
= 7/(a² + 8x + 16 - 5)
= 7/(a² + 8x + 11)
Therefore, for given function f(x) = 7/(x² - 5),
f(a + 4) = 7/(a² + 8x + 11)
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What is the correct answer
Answer: See coordinate graph below.
Step-by-step explanation: The black point is the original point and the red point is the reflected point.
Ordered pair of the reflected point:
A': (1, -4)
Let me know if this is right! :)
The CDC is investigating if the average blood pressure of the US population is
different from 123. A hypothesis test is conducted which returns a sample mean of
128 and a p-value of 0.0037. What is the appropriate conclusion at the 5%
significance level?
Option B. The appropriate conclusion at the 5% significance level is to Reject the null hypothesis, the population mean is significantly different from 123
How to test the hypothesisH0: mean = 123
H1 : mean ≠ 123
We have the p value of the statistics stated already in the question as p value = 0.0037.
The level is significance that we have been given in the question is 5% = 0.05
We are to test here if the true mean is different from 123.
Hence we would be testing the p value against the significance level.
We can see that P value is < level of significance.
0.0037 < 0.05
Hence we would reject the null hypothesis.
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there are three consecutive odd integers such that if the second is subtracted from twice the sum of the first and third,the result is 52 more than the first. find the sum of the first and second
The sum of the first and second integer is 44.
How to illustrate the information?Let the numbers be x, x+2 and x+4.
If the second is subtracted from twice the sum of the first and third,the result is 52 more than the first. This will be:
2(x + 2 + x + 4) - (x + 2) = x + 52
2(2x + 6) - (x + 2) = x + 52
4x + 12 - x - 2 = x + 52
Collect like terms
4x - x - x = 52 - 12 + 2
2x = 42
Divide
x = 42/2
x = 21
Second Integer = x + 2 = 21 + 2 = 23
Third integer = x + 4 = 21 + 4 = 25
Sum = 21 + 23 = 44
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Fill in the table using this function rule. y=-2x-3
Answer:
6
Step-by-step explanation:
the answer is 6
Assume that a hat contains four bills: a $1, a $5, a $10,
and a $20 bill. Two bills are to be selected at random with
replacement. Find the probability that both bills are $20 if
the first selected is a $20 bill?
The probability that both bills are $20 if the first selected is
a $20 bill is
(Simplify your answer. Type an integer or a fraction.)
The probability that both bills are $20 if the first selected is a $20 bill is 1/16.
What is probability ?The probability formula is as defined as the possibility of any event to happen which comes to be equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event to occur P (E) =
[tex]\frac{Number of favourable outcomes}{ Total number of outcomes }[/tex]
Hat contains four bills: a $1, a $5, a $10, and a $20 bill.
Probability(P1) of Getting $20 bill in 1st selection = 1/4 ;
After Replacement,
Probability(P2) of Getting $20 bill in 2nd selection = 1/4 ;
So, the probability that both bills are $20 if the first selected is
a $20 bill = 1/4 * 1/4 = 1/16,
Hence we get 1/16 as the probability of getting both bills of $20.
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