What is the value of the expression shown below?
7 + (10 − 4)2 ÷ 4 × 1 over 2 to the power of 3
A. 8
B. 8 and 1 over 6
C. 8 and 1 over 8
D. 79
The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $3, sales will reach 6000 Fun Noodles per day during the summer. Raising the price to $4 will cause the sales to fall to 5000 Fun Noodles per day.
a. Assume the the relationship between sales price, x, and number of Fun Noodles sold, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pars of the form (sales price, number sold).
The equation is?
b. Predict the daily sales of Fun Noodles if the price is $3.50.
? sales
? sales
(a) The equation in slope-intercept form for describing the relationship between sales price and quantity of the fun noodle is [tex]y=-1000x+9000[/tex].
(b) The daily sales of fun noodles is [tex]5500[/tex] when, the sales price is [tex]\$3.50[/tex].
(a) The general slope-intercept form of writing the equation of a line is [tex]y-y_1=m(x-x_1)[/tex] where, [tex]m[/tex] is the slope of the line.
According to the question,
[tex](x_1,y_1)\rightarrow (3,6000)[/tex] and [tex](x_2,y_2)\rightarrow (4,5000)[/tex]
Evaluate the value of the slope as-
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\m=\dfrac{5000-6000}{4-3}\\m=-1000[/tex]
Now, substitute the parameters in the equation [tex]y-y_1=m(x-x_1)[/tex]-
[tex]y-y_1=m(x-x_1)\\y-6000=-1000(x-3)\\y-6000=-1000x+3000\\y=-1000x+9000[/tex]
Hence, the equation in slope-intercept form for describing the relationship between sales price and quantity of the fun noodle is [tex]y=-1000x+9000[/tex].
(b) Substitute [tex]x=\$3.50[/tex] in the slope-intercept equation [tex]y=-1000x+9000[/tex] to evaluate the daily sales of fun noodles as-
[tex]y=-1000x+9000\\y=-1000(3.50)+9000\\y=-3500+9000\\y=5500[/tex]
Hence, the daily sales of fun noodles is [tex]5500[/tex] when, the sales price is [tex]\$3.50[/tex].
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Which expression is equivalent to 2.25 + 2.25x + 1 - 0.75x + 2x
The fountain is made up of two semicircles and a quarter circle. Find the perimeter and the area of the fountain. Round the perimeter to the nearest tenth of a foot and the area to the nearest square foot.
The perimeter and area of the fountain comprising two semicircles and a quarter circle can be calculated using principles of circle geometry, adding respective perimeter parts for the total perimeter and summing up the areas of each part for the total area. The perimeter calculation includes the semicircles' straight edges, while the area computation combines semicircle and quarter circle areas.
Explanation:To calculate the perimeter and area of a fountain composed of two semicircles and a quarter circle, we first need to acknowledge that all parts of this shape are derived from circles. Therefore, understanding the properties of a circle is crucial. The formula for the perimeter (circumference) of a whole circle is 2πr, and the formula for the area is πr², where r is the radius of the circle.
To find the perimeter of the given shape, add the perimeters of the two semicircles and a quarter circle. Since the perimeter of a semicircle is πr and there are two, their combined perimeter is 2πr. The perimeter of a quarter circle is πr/2. Therefore, the total perimeter of the shape would be 2πr + πr/2. The straight edges that close the semicircles also contribute to the perimeter, which are diameters of the circles (ϐ2r for each semicircle), resulting in an additional 2r + 2r = 4r to the total perimeter.
For the area, sum the areas of two semicircles and a quarter circle. The area of a semicircle is πr²/2, so together, two semicircles have an area of πr². The area of a quarter circle is πr²/4. Thus, the total area of the shape is πr² + πr²/4 = 5πr²/4.
To find the exact values, you would substitute the specific radius (r) of the circles that constitute the fountain, and calculate using π ≈ 3.14. Make sure to round the perimeter to the nearest tenth of a foot and the area to the nearest square foot as instructed.
8.73e16 in simple form
Solution:
we have been asked to write [tex]8.73e^{16}[/tex] in the simplest form.
This can be alternatively written as [tex]8.73*10^{16}[/tex]
And as we know that a number written in scientific notation can be re-written in the simple form by removing the "10 to the power" term by expanding the given number as below
[tex]8.73*10^{16}=8.73*1000,000,000,000,0000[/tex]
It can be further written by removing the decimal as below
[tex]8.73*10^{16}=87,300,000,000,000,000[/tex]
Hence the required simple form is 87,300,000,000,000,000
You brought 1.5 dozen bagels to school. A dozen bagels cost $5.98. You used a coupon that took $1.00 off of the total. How much did you pay for the bagels?
Answer:
You would pay $7.97 for your bagels!
Which of the points listed is the same distance from the x-axis as the point (8, 3.25)?
A- (-8, 4.75) B- (7, -3.25) C- (3.25, 7) D- None of these are correct.
The points listed which has the same distance from the x axis as the point (8, 3.25) is B- (7, -3.25).
What are the Coordinates?Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.
Given is a point in the XY plane with the coordinates (8, 3.25).
We have to find the point in the options which are at a same distance as the given point.
In order for two points to be at a same distance from the x axis, their y coordinates must be same with either same sign or of the opposite sign.
Here the point with the same y coordinate as the given point is B- (7, -3.25)
Hence option B is correct.
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Find all real numbers X such that 18x-9>9 or 2x-4>-10
Let $\mu$ and $\sigma^2$ denote the mean and variance of the random variable x. determine $e[(x-\mu)/\sigma]$ and $e{[((x-\mu)/\sigma)^2]}$
The expectation of (x-µ)/ equals 0, as it's the standardized form of variable X having a mean of 0. The expectation of {[((x-µ)/)]^2} equals 1, as it's the variance of the standardized variable which is always 1.
Explanation:The question pertains to the concepts of expected values, mean and variance in probability and statistics. When we have a random variable X with mean µ and variance ^2, we can determine the expected value of a transformed variable (x-µ)/ and its square (x-µ)/^2.
The expectation of (x-µ)/ is actually 0. This is because when you subtract the mean (µ) from the random variable and divide by the standard deviation (), you are standardizing the variable to have a mean of 0.
For the expectation of {[((x-µ)/)]^2}, we actually get 1. This is because the square of a standardized random variable, like (x-µ)/, is the variance of the standardized variable, which is always 1.
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Choose the correct simplification of (8x4y3)2. (5 points)
Answer:
the person below is correct 64x8y6 is the right answer
Step-by-step explanation:
y=-2x+1
y=-2x-3
solve and graph
Given this arithmetic sequence, find d. 3,_,_,15
Melissa estimated that she would read 250 Pages last week. she read 290 pages. What is the percent error of Melissa's estimate round to the nearest whole percent
Answer:13.79
Step-by-step explanation: I put that answer and gt it wrong an dthe thing told me the answear was 13.79
write an inequality in slope intercept form for the graph below. if necessary use <= or >=
The correct options are:
1. The equation of a given line is y=-x-3 (it is easy to find it using points (0;-3)&(-3;0)).
2. According to the equation of a line: y≥-x-3
What is the inequality in slope-intercept form?You may use the slope-intercept form to graph inequalities. The slope-intercept form is expressed as y = mx + b, where the variable m stands for the slope of the line, and b stands for the y-intercept (or in which the line crosses the y-axis).
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A square rug lies in the middle of a rectangular room. There are 7 feet of uncovered floor on 2 sides of the rug and 2 feet of uncovered floor on the other 2 sides. Find a polynomial expression for the area of the room in terms of x, the side length of the rug.
Polynomial expression of area of room in terms of x is A = x² + 9x + 14.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Area of rectangle(room) = Length × width
So,
A = (x + 7)(x + 2)
A = x² + 20x + 7x + 14
A = x² + 9x + 14
Hence "Polynomial expression of area of room in terms of x is A = x² + 9x + 14".
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Which of the following criteria are necessary conditions for making a statistical inference?
sample size greater than 30, or an approximately normal data set
sample size greater than 100
convenience sample
simple random sample
systematic sample
Answer:
1 and 4 are correct
Step-by-step explanation:
This table shows the weekly rainfall, in inches, for two cities for ten weeks. City A 0.2 0 1.5 1.3 2.5 3 0.4 0.3 0.2 1 City B 0 0 0.4 0.2 0.3 1 1 1 0.1 0.1 Which conclusion can be drawn from the data?
WILL GIVE BRAINLISET
Answer:
During the 10 wk period, the rainfall amount recorded most often for City B was 1 in
Step-by-step explanation:
Explain what a polynomials is and identify the different parts of a polynomial.
Explain the different labels used to categorize polynomials
Explain how addition and subtraction of polynomials is accomplished
When multiplying polynomials, we are taking every term of one polynomial and multiplying them by every term of the second polynomial, then collecting like terms explain how foil helps us to accomplish this and what category of polynomials foil applies to.
There are tow special case products where the product takes on special patterns explain these two cases and when they occur.
For each of the two special cases, illustrate your explanation with an appropriate exercise from the ( a+b)2=a2+2ab+b2 )(a-b)2=a2-2ab+b2 ) showing how the multiplication is performed using the special pattern formula then also showing the same result using foil.
How far does a horse on a Merry-go-round travel in one revolution if he is 6.5 feet from the center? (Use 3 for π)
A) 13 feet
B) 26 feet
C) 39 feet
D) 52 feet
Answer:
41 FEET
Step-by-step explanation:
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If sec(x)=13/12 what is cos(x)?
Find the perimeter of a polygon with sides 11ft, 7ft, 18ft, 22ft, 14ft, and 23.5ft
!100! POINTS PLEASE HELP ME BRAINLIEST!!!!!!!!!!!!
Answer:
y = 11 is your answer
Abigails mom said she will be home from work in 65 minutes its 4:27 pm and abigail has dance practice at 6:00 pm. How much time will abigail have between the time that her mom gets home from work and the beginning of dance practice
The time that her mom gets home from work and the beginning of dance practice is 28 minutes.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, It is 4:27 pm and Abigail's mom said she will be home from work in 65 minutes.
Now 60 minutes from 4:27 pm is 5:27 pm and 5 minutes more is 5:32 pm.
Abigail has dance practice at 6:00 pm, So the time that her mom gets home from work and the beginning of dance practice is 28 minutes seems obvious.
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Melvin has 1/2 of a cake. He shares the cake equally with each of 2 friends and himself. Show me how u got your answer
Melvin and each of his 2 friends get [tex]\( \frac{1}{6} \)[/tex] of the cake each.
Sure! If Melvin has [tex]\( \frac{1}{2} \)[/tex] of a cake and he wants to share it equally with each of his 2 friends and himself, we need to find out how much each person gets.
First, we need to find out how many people are sharing the cake. Melvin himself plus his 2 friends make a total of 3 people.
Now, to divide [tex]\( \frac{1}{2} \)[/tex] of the cake equally among 3 people, we divide [tex]\( \frac{1}{2} \)[/tex] by 3:
[tex]\[ \frac{1/2}{3} = \frac{1}{2} \times \frac{1}{3} \][/tex]
To multiply fractions, we multiply the numerators together and the denominators together:
[tex]\[ = \frac{1 \times 1}{2 \times 3} \][/tex]
[tex]\[ = \frac{1}{6} \][/tex]
So, each person gets [tex]\( \frac{1}{6} \)[/tex] of the cake.
Therefore, Melvin and each of his 2 friends get [tex]\( \frac{1}{6} \)[/tex] of the cake each.
Which of the following are the correct properties of slope A.If two lines have the same slope, then they are the same line. B.The slope of a line that moves up from left to right is positive. C.A steep line has negative slope. D.Some lines have an undefined slope. E.The slope of a line is always positive.
Answer:
B.The slope of a line that moves up from left to right is positive.
Step-by-step explanation:
Slope is the ratio of vertical change to horizontal change. If a line moves up as x-values increase, then the signs of both changes are positive, and the slope is positive. This observation matches selection B.
_____
Comments on other choices
If a line is vertical, it will exhibit a vertical change with no horizontal change. The denominator of the ratio for slope will be zero. Division by zero is undefined, so we say the slope of a vertical line is "undefined."
Lines with the same slope will be parallel, if they're not the same line.
A line that moves down to the right has a negative change in its vertical coordinate for a positive change in its horizontal coordinate. The ratio of changes will have a negative sign. So, the slope of a line that moves down to the right is negative, not positive.
Two buses leave the station traveling in opposite directions one going east and one going west the eastbound bus travels at 40 mph and the west bound bus travels at 65 mph if both buses leave the station at 10 AM at what time will they be 1260 miles apart
Answer:
10 PM
Step-by-step explanation:
The combined speed of the two buses is ...
40 mph + 65 mph = 105 mi/h
The relationship between distance, speed, and time can be written ...
time = distance/speed
so the elapsed time until the buses cover the distance is ...
time = (1260 mi)/(105 mi/h) = 12 h
___
12 hours after 10 AM is 10 PM.
The buses will be 1260 miles apart at 10 PM.
You process paychecks for your company. Paydays are 2 weeks apart, on Fridays. The first payday in one month is on the 12th. The next payday is on the:
Answer:
The next payday is on the: 26th of that month.
Step-by-step explanation:
You process paychecks for your company.
Paydays are 2 weeks apart, on Fridays.
2 weeks apart means 14 days apart.
The first payday in one month is on the 12th.
Therefore, The next payday is on the: [tex]12+14=26[/tex]
26th of that month.
Tom spent 1/3 of his monthly salary for rent and 1/7 of his monthly salary for his credit card bill. If $1320 was left, what was his monthly salary?
the basketball court in the park is rectangle two of the sides are 84 feet long and the other two sides are 50 ft long what is the perimeter of the basketball court
Heights of adult women in the united states are normally distributed with a population mean of μ = 63.5 inches and a population standard deviation of σ = 2.5. a medical researcher is planning to select a large random sample of adult women to participate in a future study. what is the standard value, or z-value, for an adult woman who has a height of 50.4 inches? (calculate to 1 decimal)
For an adult woman with a height of 50.4 inches in the United States, the standard value (z-value) is approximately -5.2, calculated based on a normal distribution with a mean of 63.5 inches and a standard deviation of 2.5 inches.
To find the standard value or z-value for a given height in a normal distribution, you can use the formula:
[tex]\[ Z = \frac{{X - \mu}}{{\sigma}} \][/tex]
where:
- Z is the z-value,
- X is the individual data point (height in this case),
- [tex]\( \mu \)[/tex] is the population mean,
- [tex]\( \sigma \)[/tex] is the population standard deviation.
For the given problem:
- [tex]\( \mu = 63.5 \)[/tex] inches,
- [tex]\( \sigma = 2.5 \)[/tex] inches,
- X = 50.4 inches.
[tex]\[ Z = \frac{{50.4 - 63.5}}{{2.5}} \]\[ Z \approx -5.24 \][/tex]
Rounded to one decimal place, the z-value for an adult woman with a height of 50.4 inches is approximately -5.2.