Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5 is given by 24 = 10.5 + x/4.5
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
What is quotient?Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number. As a general rule, the smaller the divisor (denominator) of an expression, the larger would be the quotient.
In order to translate this word problem, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:
Let n represent the unknown number.
Translating the word problem into an algebraic equation, we have;
24 = 10.5 + x/4.5
Read more on quotient here: brainly.com/question/748723
#SPJ1
An entry level web developer's annual pay is $56,940 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its web developers. If the firm cuts the work year to 50 weeks but keeps the same rate of pay, how much should the web developer expect his annual pay to decrease? Round your answer to the nearest dollar.
Based on the first entry level web developer salary paid, and the new work year, the amount the web developer can expect his annual pay to decrease by is $2,190
How to find the decrease in pay?First, find the weekly pay of the web developer in the first salary:
= 56,940 / 52
= $1,095 per week
The new salary of the web developer as a result of the work week becoming 50 weeks is:
= 1,095 x 50
= $54,750
The decrease in this annual pay to the web developer is:
= 56,940 - 54,750
= $2,190
Find out more on decrease in pay at https://brainly.com/question/21090152
#SPJ1
Question 9(Multiple Choice Worth 1 points) (04.05 MC) A company determines an employee's starting salary according to the number of years of experience, as detailed in the table. Years of experience Salary 0 $40,000 1 $42,150 $44,260 $46,785 $48,820 $51,126 2 3 4 5 Use the equation for the line of best fit to predict the salary for an employee with 7 years of experience? (Round your answer to the nearest dollar) O $52,900 O $53,340 O $53,914 O $55,573
By using the equation for the line of best fit, the salary for an employee who has seven (7) years of experience is: D. $55,573.
What is a line of best fit?A line of best fit is a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between a data.
In this scenario, the employee's salary would be plotted on the y-axis of the scatter plot while the years of experience would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the data in the given table, an equation for the line of best fit is given by:
y = 2233.3x + 39940
Next, we would use the above equation for the line of best fit to predict the salary for an employee with 7 years of experience:
y = 2233.3(7) + 39940
y = 15,633.1 + 39940
y = 55,573.1 ≈ $55,573.
Read more on line of best fit here: brainly.com/question/12891189
#SPJ1
make a table of values for the equation. Then graph the equation.
Check the picture below.
Tickets for the school's jazz concert are $4 for students and $8 for all others. if they sold 40 tickets for opening night for a total of $220, how many students were attendance?
• write each answer in simplest form.
1. 1/6 +2/6
2. 2/5 - 1/5
Answer:
1. 1/2
2. 1/5
Step-by-step explanation:
I used a calculator!
Answer:
1.3/6 or 1/2
2.1/5
Step-by-step explanation:
Just write that out, thats all the steps there is, 3/6 simplifies to 1/2 because they're equivalent
−185%−1.7=I do not know the answer
Answer: -1.4
Step-by-step explanation: simply subtract negative 185 by 1.7
400 g of
raspberries
500 g of strawberries cost £4.10
Work out the total cost of 200 g of raspberries and 200 g of strawberries.
and 300g of strawberries cost a total of £7.46
The most appropriate choice for unitary method will be given by
Total cost of 200g raspberries and 200 g strawberries is £4.14
What is unitary method?
It is the method by which we find the value of single unit form the value of multiple unit and value of multiple unit from the value of single unit.
Here,
500 g of strawberries cost £4.10
1 g of strawberries cost £[tex]\frac{4.10}{500}[/tex]
300 g of strawberries cost £[tex]\frac{4.10}{500} \times 300[/tex]
= £2.46
400 g of raspberries 300g of strawberries cost a total of £7.46
Let the cost of 400 g of raspberries be £x
so,
x + 2.46 = 7.46
x = 7.46 - 2.46
x = £5
cost of 400 g of raspberries = £5
cost of 1 g of raspberries = £[tex]\frac{5}{400}[/tex]
cost of 200 g of raspberries = £[tex]\frac{5}{400} \times 200[/tex]
= £2.5
cost of 300 g strawberries = £2.46
cost of 1 g strawberries = £[tex]\frac{2.46}{300}[/tex]
cost of 200 g of strawberries = £[tex]\frac{2.46}{300} \times 200[/tex]
= £1.64
Total cost of 200g raspberries and 200 g strawberries = £(2.5 + 1.64)
= £4.14
To learn more about unitary method, refer to the link:
brainly.com/question/24587372
#SPJ9
Complete question
400 g of raspberries and 300 g of strawberries cost a total of £7.46.
500 g of strawberries cost £4.10.
Work out the total cost of 200 g of raspberries and 200 g of strawberries.
100 people where sampled and their heights were recorded, it was discovered the mean height was 5 feet and 6.3 inches with a standard deviation of 3.75 inches. what is the probability of someone being 5 feet and 4.2 inches tall?
The probability of someone being 5 feet and 4.2 inched tall is 0.2877
Probability:
Probability means the possibility of occurring the specific even across the total number of event.
Given,
100 people where sampled and their heights were recorded, it was discovered the mean height was 5 feet and 6.3 inches with a standard deviation of 3.75 inches.
Here we need to find the the probability of someone being 5 feet and 4.2 inches tall.
From the given details, we know that,
n = 100
mean (ч) = 5 feet and 6.3 inches
standard deviation (σ) = 3.75 inches
We know that the formula to find the probability is,
P = (x - ч)/σ
But here we have used the different measurement for each. So, the first step is convert them into inches.
So,
5 feet and 6.3 inches = 60 + 6.3 inches = 66.3 inches.
Similarly 5 feet and 4.2 inches = 64.2 inches.
So, the probability is,
P (X < 64.2) = (64.2 - 66.3)/3.75
P (X < 64.2) = -0.56
Based on the standard normal table to conclude that:
P (X < 64.2) = -0.56 = 0.2877
Therefore, the probability of someone being 5 feet and 4.2 inches tall is 0.2877.
To know more about Probability here.
https://brainly.com/question/11234923
#SPJ1
Lincoln high school have 75 less than four times as many students as washington high school right in expression to find the number of students at lincoln high school washington high school has w students
Main Answer:
Number of students in Lincoln high school is [tex]4w-75[/tex]
Explanation:
Number of students in Washington high school = w
Number of students in Lincoln high school = 75 less than four times number of students in Washington high school
Therefore, number of students in Lincoln high school = [tex]4w-75[/tex]
Can you please help? Thanks!
If a cylindrical barrel has a radius of 5.7 ft and a height of 8.4 ft, tripling the height of the concerned barrel will triple up its current volume.
As per the question statement, a cylindrical barrel has a radius of 5.7 ft and a height of 8.4 ft.
We are required to determine the dimension or dimensions which on tripling, will triple up the current volume of our question-mentioned barrel.
To solve this question, first we need to know the formula to calculate the volume of a cylinder, which goes as (π * r² * h)
Where [π = (22/7)], (r = radius of the cylinder)
And, (h = height of the cylinder).
Here, (r = 5.7 ft) and (h = 8.4 ft).
Now, considering [V = (π * r² * h)], where, ["V" is the volume]
if we triple our radius "r", our Volume "V₁" will become {π * (3r)² * h}
or, V₁ = 9πr²h
or, V₁ = 9(π * r² * h)
or, V₁ = 9V,
That is, 9 times the current volume. Hence, tripling the radius will not triple up the current volume of our concerned barrel.
Now, considering we triple our height "h", our Volume "V₂" will become {π * r² * 3h}
or, V₂ = 3πr²h
or, V₂ = 3(π * r² * h)
or, V₂ = 3V,
That is, 3 times the current volume. Hence, tripling the height will triple up the current volume of our concerned barrel.
As Proof,
Current Volume of our barrel = [(22/7) * (5.7)²* (8.4)]
= 857.74 ft²
And Volume of our barrel tripling the height = [(22/7) * (5.7)²* (3*8.4)]
= 2573.21 ft²
And, (2573.21/857.74) = 3.
Therefore, tripling the height of the concerned barrel will triple up its current volume, thus Proved.
Volume: In Mathematics and the whole of applied science, volume is defined as the space occupied within the boundaries of a three-dimensional object, or simply, the capacity of a three-dimensional object.To learn more about Volumes, click on the link below.
brainly.com/question/11168779
#SPJ1
You want to cover one wall of your room with neon-color wallpaper that costs $25
for a double roll containing 44 square feet. The wall is 18.5 feet long and 10 feet
high.
a. How much wallpaper will
you need?
b. How much will the wallpaper cost
Answer: You will need 185 square feet of wallpaper. It will cost you $125.
Step-by-step explanation:
18.5 x 10= 185
185/44= 4.2
4.2 is a little over 4 so you would need 5. You will have extra.
$25 x 5 rolls= $125
Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form.
(−2,4) and (7,−8)
The distance between the sides of the right-angled triangle is given as follows:
Recall that a right-angled triangle is one that has at least one side equal to 90°
In the question, we know the endpoints and the line hypothenus. To find the length of the hypothenuse, we can state:
Distance = [tex]\sqrt{(x2 - x1)^{2} +(y2 - y1)^{2} }[/tex]
Recall that the distance between the two points is given as (−2,4) for first point and (7,−8) for the second point.; Hence:
Distance = √[(-2+7)²+ (4+-8)²]
Distance = √(5²) + (-4)²
Distance = √(25+16)
Distance = √41
Hence the third point is (-2-8).
Learn more about right-angled triangles:
https://brainly.com/question/64787
#SPJ1
What is the slope of the line parallel to :y=-4/7x+2
Answer:Two lines are parallel if the have the same slope. To find the slope of the line parallel to the line y=4/7x-2 we need to get the line into slope-intercept form (y = mx + b), but the line is already in that form, so the slope is m = 4/7.
Step-by-step explanation:
Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.
f(x)=6x+5 and g(x)= x-5/6
a. f(g(x))= (Simplify your answer.)
b. g(f(x))= (Simplify your answer.)
Part a
[tex]f(g(x))=6\left(x-\frac{5}{6})+5=6x-5+5=6x[/tex]
Part b
[tex]g(f(x))=g(6x+5)=(6x+5)-\frac{5}{6}=6x+\frac{25}{6}[/tex]
Therefore, the functions are not inverses of each other since [tex](f(g(x)) \neq x[/tex].
find the value of expression when y=4 2y+2y2
The value of the expression 2y + 2y² when y = 4 is 40.
Whet is an expression?It should be noted that in Mathematics, an expression simply means the finite combination that is formed according to a specific rule. It should be noted that an expression must have variables that are connected by the operator.
In this case, the expression given in the question is:
2y + 2y².
where y = 4
We have to put y = 4 into the expression. This will be:
2y + 2y².
2(4) + 2(4)²
= 8 + 32
= 40
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
The area of a trapezoid is 31.5cm. If the parallel sides are of lengths 7.3cm and 5.3cm.Calculate te perpendicular distance between them
The perpendicular distance ( height ) between the parallels sides of the trapezoid is 5cm.
How to calculate the height of a trapezoid?A trapezoid is simply a quadrilateral with at least one pair of parallel sides.
The area of trapezoid is expressed as;
A = h × (a + b)/2
Where a is base a, b is base b and h is height.
Given the data in the question;
Area A = 31.5cm²Base a = 7.3cmBase b = 5.3cmHeight h = ?To determine the height of the trapezoid, plug the given values into the above formula and solve for h.
A = h × (a + b)/2
31.5cm² = h × ( 7.3cm + 5.3cm)/2
31.5cm² = h × ( 12.6cm )/2
31.5cm² = h × 6.3 cm
h = 31.5cm² / 6.3 cm
Height h = 5cm
Therefore, the height of the given trapezoid is 5 centimeters.
Learn more about area of trapezoids here: https://brainly.com/question/12623349
#SPJ1
what is the equation of the least squares regression line that describes the rela- tionship between operating cost per hour and number of passenger seats in the
The relationship between operating cost per hour and the number of passenger seats is shown by the equation of the least squares regression line, where y=1136+14.673x is the expected operating cost per hour and x is the number of passenger seats.
Why do you use the word "square"?a plane figure in geometry with four equal sides and four right angles of 90 degrees. A square is both an equilateral rectangle and a special kind of parallelogram (an equilateral and equiangular one).
the parallelogram in detail.In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. The confronting or opposed sides and the opposing angles of a parallelogram are of equal length.
based on the available facts;
y=1136+14.673x
where
x= number of passenger seat
y=predicted operating cost per hour.
to know more about square visit;
#https://brainly.com/question/9459418
#SPJ9
Suppose that kellogg believes that the average weight for a box of frosted flakes is 18 ounces. As part of a quality control effort, they sample 30 boxes and find that the mean of those 30 boxes is 18. 2 ounces. Historical records show that the standard deviation of the filling process is 0. 32 ounces. How likely is it for the sample mean to have been 18. 2 ounces or larger if the actual mean is 18 ounces and the standard deviation of the filling process is 0. 32 ounces? round your answer to four decimal places.
Probability for the sample mean to have been 18.2 ounces or larger = 0.0003
Sample size, n = 30 boxes
Sample mean, [tex]\bar x[/tex] = 18.2 ounces
Population mean, μ = 18 ounces
Standard deviation of the population, σ = 0.32 ounces
We assume that this follows normal distribution.
Then the z-score, z = [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
= [tex]\frac{18.2-18}{\frac{0.32}{\sqrt{30}} }[/tex]
= 3.42
This z-score follows Standard Normal Distribution with mean = 0 and standard deviation = 1
Probability for the sample mean to have been 18.2 ounces or larger =
P(z ≥ 3.42) = 0.5 - P(0 < z < 3.423)
= 0.5 - 0.4997
= 0.0003
Learn more about standard normal distribution at https://brainly.com/question/27701525
#SPJ9
MUEVE 1 CERILLA PARA ARREGLAR LA ECUACIÓN
Use the figure at the right . If JK=2x+6 and NO=11 what is the value of x
Answer: x=5/2
Step-by-step explanation:
JK=NO
2x+6=11
2x+6-6=11-6
2x=5
x=5/2
of 107 athletes surveyed about what sport they play, some play basket ball. Of those who play basketball, 48 play baseball and the remaining 33 who do not play baseball, Write an equation to find the number of athletes surveyed who do not play basketball.
The equation for the number of athletes who do not play basketball is x = 107 - 81
How to calculate the value?Athletes surveyed = 107 athletes
Athletes who play basketball
Athletes who play baseball = 48 athletes
Athletes who don't play baseball = 33 athletes
Athletes who play basketball will be:
= athletes who play baseball + athletes who don't play baseball
= 48 + 33.
= 81
Total athletes = Athletes who play basketball + Athletes who don't play basketball
107 = 81 + x
x = 107 - 81
x = 26
The value is 26.
Learn more about equations on:
https://brainly.com/question/2972832
#SPJ1
8 squared plus x squared = 17 squared solve for x
Answer:
x ≈ 15
Step-by-step explanation:
using Pythagoras' identity in the right triangle
a² + b² = c²
with a = 8, b = x , c = 17
8² + x² = 17²
64 + x² = 289 ( subtract 64 from both sides )
x² = 225 ( take square root of both sides )
[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{225}[/tex]
x = 15
If u/8 -4 = 7, what does u equal
Answer:
88
Step-by-step explanation:
[tex]\frac{u}{8}-4=7 \\ \\ \frac{u}{8}=11 \\ \\ u=88[/tex]
Answer:u=88
Step-by-step explanation:
what is 40% written as a fraction in its simplest form
Answer:
2/5
Step-by-step explanation:
40%= 40/100 = 4/10 = 2/5
Answer:
2/5
Step-by-step explanation:
Simplest form:
[tex]\sf 40 \%= \dfrac{40}{100}=\dfrac{4}{10}=\dfrac{2}{5}[/tex]
I need help understanding this problem
The solution to the given inequalities is -7 < x ≤ 6. The graph of the inequality is shown below on a number line.
Solving Inequalities and Graphing Number lineFrom the question, we are to solve the given inequalities
The given inequalities are
-3x - 7 < 14 and -25 ≤ -3x - 7
Solving -3x - 7 < 14
-3x - 7 < 14
Add 3x to both sides of the inequality
-3x + 3x - 7 < 14 + 3x
-7 < 14 + 3x
Subtract 14 from both sides
-7 - 14 < 14 - 14 + 3x
-21 < 3x
Divide through by 3
-21/3 < 3x/3
-7 < x
Solving -25 ≤ -3x - 7
-25 ≤ -3x - 7
Add 3x to both sides
-25 + 3x ≤ -3x + 3x - 7
-25 + 3x ≤ - 7
Add 25 to both sides
-25 + 25 + 3x ≤ - 7 + 25
3x ≤ 18
Divide through by 3
3x/3 ≤ 18/3
x ≤ 6
Thus,
The solutions to the inequalities are
-7 < x and x ≤ 6
That is,
-7 < x ≤ 6
The number line is shown below
Learn more on Solving inequalities here: https://brainly.com/question/24372553
#SPJ1
Simplify
8(x + 3)2/ 2(x + 3)
Answer:
4(x+
Step-by-step explanation:
8(x+3)^2/2(x+3)
[8(x + 3)(x + 3)]/2(x + 3)
8 ÷ 2 = 4
(x + 3)(x + 3) ÷ (x + 3) = (x + 3). In other words, we cancel one of the numerator factors.
Answer: 4(x + 3).
Answer:
4(x + 3)
or 4x + 12.
Step-by-step explanation:
8(x + 3)^2/ 2(x + 3)
x + 3 is common to both numerator and denominator of the fraction so they simplify to (x + 3)^2 / (x + 3) = (x+3).
the answer is 8 * (x + 3) / 2
= 4(x+ 3).
What is the quotient? a-3/7 / 3-1/21
The quotient of a-3/7 / 3-1/21 is 3/2(a - 3)
The quotient of a-3/7 / 3-a/21 is -3
Determining the quotient of a division operationFrom the question, we are to determine the quotient of the given division operation.
The given division operation is
a - 3/ 7 / 3 -1 / 21
That is,
a - 3/ 7 ÷ 3 -1 / 21
This becomes
a - 3 / 7 × 21 / 3 -1
a - 3 / 7 × 21 / 2
3(a - 3) / 2
= 3/2(a - 3)
If we are to find the quotient of
a - 3/ 7 / 3 -a / 21
This becomes
a - 3/ 7 ÷ 3 - a / 21
a - 3/ 7 × 21 / 3 - a
21(a -3) / 7(3 - a)
3( a - 3) / (3 -a )
Multiply the numerator and the denominator by -1
-1 × 3( a - 3) / -1 × (3 -a )
-3( a - 3) / (-3 + a)
-3( a - 3) / (a - 3)
= -3
Hence, the quotient is -3
Learn more on Determining quotient here: https://brainly.com/question/12558750
#SPJ1
Which of the following describe 73.222...? Select all that apply.
whole
number
integer
rational
number
Answer:
rational
number
Step-by-step explanation:
because any decimal number that repeats forever can be written as a fraction and any number that can be written as a fraction is rational
a number is any value that has no variables
a whole number is a positive value that is not a decimal
an integer is also any whole value
a rectangle has an area of 35cm2
its width is 5cm
what is its length
Answer: L - 7 because 35/5
Answer:
The length is 7 cm
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
35 = l*5
Divide each side by 5
35/5 = l*5/5
7 = l
The length is 7 cm
The shape of a water tower can partially be modeled by a sphere in which the diameter is 30 feet. A painter needs to calculate the surface area of this part of the water tower to accurately estimate the amount of paint needed for the job. What is the surface area of this portion of the water tower to the nearest square foot? Surface area: square feet
Answer: i believe the answer is 113.1 square feet
Step-by-step explanation: pi times 30