Answer:
Step-by-step explanation:
Unfortunately, there is no table provided in your question. However, we can still solve the problem based on the given information.
Let's assume that Ronald buys "x" pounds of apples and "y" pounds of peaches. We know that the cost of apples is $5 per pound, and the cost of peaches is $6 per pound.
So, the total cost of apples will be 5x, and the total cost of peaches will be 6y. We also know that Ronald has $60 to spend. Therefore, we can write the following equation:
5x + 6y = 60
This is the equation that represents the total cost of apples and peaches that Ronald can buy with $60.
However, we want to find the function that relates the number of pounds of apples, x, and the number of pounds of peaches, y, that Ronald can purchase. To do this, we need to solve the above equation for y in terms of x:
5x + 6y = 60
6y = 60 - 5x
y = (60 - 5x)/6
This is the function that relates the number of pounds of apples, x, and the number of pounds of peaches, y, that Ronald can purchase with $60.
Need help with these questions!! Person who answers will be marked brainliest
Answer:
1.5 for both
Step-by-step explanation:
Taking each number and multiplying it by 1.5 will get you the dilated coordinates
A 2 yard piece of copper wire costs $9. 72. What is the price per foot
the price per foot of the copper wire is $1.62.
What is the arithmetic operation?
The basic mathematical operations are addition, subtraction, multiplication, and division, which involve manipulating two or more quantities. They are essential to the study of numbers, including the order of operations, and are fundamental to other mathematical areas such as algebra, data management, and geometry. Understanding the rules of arithmetic operations is crucial for solving problems that involve these operations.
There are 3 feet in one yard, so 2 yards of copper wire is equal to 6 feet.
To find the price per foot, we need to divide the total price by the number of feet:
Price per foot = Total price ÷ Number of feet
Price per foot = $9.72 ÷ 6
Price per foot = $1.62
Therefore, the price per foot of the copper wire is $1.62.
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The owner of a company asks a manager, "How many hours does an employee work each week?" a. Is this a statistical question? Explain. The question a statistical question because there. Question 2 b. The manager records the number of hours worked each week by several employees. Display the data in a dot plot. Identify any clusters, peaks, or gaps in the data. Hours worked 40 39 40 39 47 38 41 37 40 41 40 43 40 41 40 38 40 42 40 42 Most of the data are clustered around. There is a peak at and a gap between. Question 3 c. Use the distribution of the data to answer the question. Most employees work about hours each week
This is a statistical question because it involves collecting data. Most employees work around 40 hours each week.
a. This is a statistical question because it involves collecting data on the number of hours worked by employees each week and analyzing the distribution or pattern of the data.
b. Here's a dot plot of the data provided:
37: •
38: ••
39: ••
40: ••••••••
41: •••
42: ••
43: •
47: •
The distribution of the data in the dot plot shows that the majority of employees worked around 40 hours each week, as this is where the data is most heavily clustered. Most of the data are clustered around 40 hours, with a peak at 40 hours. There is a gap between 43 and 47 hours.
c. Based on the distribution of the data, most employees work about 40 hours each week.
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Include all given digits mercury venus earth mars jupiter saturn uranus neptune distance from the sun (au) 0. 39 0. 72 1 1. 52 na 19. 18 30. 06 orbital period (years) 0. 242 0. 0616 1 1. 88 na 84. 0 165
The values of distance and orbital periods of planets Mercury is 0.39AU and 0.242yrs,Venus 0.72AU distance and 0.616yrs,Earth 1AU distance and 1yrs,Mars 1.52AUdistance and 1.88,Jupiter 5.2AUdistance and 1.88 ,Saturn N/Adistance and NA years as infromation is not provided,Uranus 19.18AUdistance and 84yrs,Neptune 30.06AUdistance and165yrs.
Based on the given information, here are some key facts about the planets in our solar system:
- Mercury is the closest planet to the Sun, with a distance from the Sun of 0.39 astronomical units (AU). It has an orbital period of 0.242 years.
- Venus is the second planet from the Sun, with a distance of 0.72 AU. Its orbital period is 0.616 years.
- Earth is the third planet from the Sun, with a distance of 1 AU. Its orbital period is 1 year.
- Mars is the fourth planet from the Sun, with a distance of 1.52 AU. Its orbital period is 1.88 years.
- Jupiter is the fifth planet from the Sun, with a distance of 5.2 AU. Its orbital period is 11.86 years.
- Saturn is the sixth planet from the Sun, with a distance of N/A AU. Its orbital period is N/A.
- Uranus is the seventh planet from the Sun, with a distance of 19.18 AU. Its orbital period is 84 years.
- Neptune is the eighth planet from the Sun, with a distance of 30.06 AU. Its orbital period is 165 years.
Therefore the the distance and orbital periods are in increasing arrangement mercury, venus, earth, mars, jupiter, saturn ,uranus, neptune distance from the sun.
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Sylvia’s car trunk measures 4.25 ft wide by 4 ft deep and 4 1 thirdft high. she has cubic boxes 16 inches wide and smaller rectangular boxes 3 inches wide by 6 inches long and 4 inches high. she has to get as many of the large boxes into her trunk as she can, and after that, she can fill the space up with the smaller boxes. how many large and small boxes can she fit into her trunk?
Sylvia can fit 9 large cubic boxes and 240 small rectangular boxes into her car trunk.
How many boxes can fit in Sylvia's car trunk?We first need to convert all measurements to the same unit. Since the large cubic boxes are given in inches, we need to convert the dimensions of the trunk to inches as well.
The trunk measures 51 inches wide (4.25 ft x 12 in/ft), 48 inches deep (4 ft x 12 in/ft), and 53.33 inches high (4*1/3 ft x 12 in/ft).
Next, we need to determine how many large boxes can fit in the trunk. Since each large box is 16 inches wide,
we can fit 3 boxes across the width of the trunk:
(51 inches ÷ 16 inches = 3.19)
Similarly, we can fit 3 boxes deep and 3 boxes high.
Therefore, the maximum number of large boxes Sylvia can fit in her trunk is:
27 (3 x 3 x 3 = 27)
After fitting as many large boxes as possible, we can calculate the remaining volume of the trunk and use this to determine how many small boxes can fit.
The remaining volume is approximately 59,712 cubic inches (51 in x 48 in x 20 in).
Dividing this by the volume of each small box:
(3 in x 6 in x 4 in = 72 cubic inches)
We can fit 829 small boxes in the remaining space.
Therefore, Sylvia can fit a total of 27 large boxes and 829 small boxes in her trunk.
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1. bona drives tor 3 hours at 44mph. clare drives 144 mies in 4 hours. how
for would bena travel if she drove for 3 hours at the same speed os
claire
2. janet and andrew leave their home at the same time. janet has 60
milles to travel and drives at 40 mph. andrew have 80 miles to travel
and also drives at 40 mph
a) how long does janets journey take?
(b) how much longer does andrew spend driving than janeta
1) Bona can drive 108 miles if she drove for 3 hour at the same speed as Claire.
2) Janet would take 1.5 hour to complete the journey and Andrew spend half hour more driving than Janet.
1) Bona speed is 44mph
Time taken by Bona is 3 hour
distance travelled by Claire is 144 miles
Time taken by Claire is 4 hour
Claire's speed = distance / time
Claire's speed = 144/4
Claire's speed = 36 mph
Distance travelled by Bona = speed × time
Distance travelled by Bona = 36 × 3
Distance travelled by Bona = 108 miles
2) Janet distance = 60 miles
Janet speed = 40 mph
Time taken by Janet = distance / speed
Time taken by Janet = 60/40
Time taken by Janet = 1.5 hour
Janet would take 1.5 hour to complete the journey
Andrew distance = 80 miles
Andrew speed = 40 mph
Time taken by Andrew = distance / speed
Time taken by Andrew = 80/40
Time taken by Andrew= 2 hour
Andrew spend half hour more driving than Janet.
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And 7/8 hours Greg reads 2/3 chapters. What is the unit rate in chapters per hour? Write your answer in simplest form
The unit rate for chapters per hour is calculated as 16/21
How to find the unit rateIn order to find the unit rate for the number of chapters Gregory reads in an hour, we must firstly divide the total amount of chapters read by the amount of hours devoted to the activity:
= 2/3 chapters ÷ 7/8 hours
= 2/3 chapters × 8/7 hours
= 16/21 chapters per hour
Consequently, the unit rate for chapters per hour is calculated as 16/21, which already exists in its most simplified form.
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+ = a) Find a parametrization for the curve of intersection of 9y2 + z2 = 1 and xyz = 1 such that it is defined for all t + b) Same for surfaces x=y_and x2 - y2 =z. c) Same for surfaces x2 + y2 + z =
a) Parametrization for the curve of intersection of 9y2 + z2 = 1 and xyz = 1 is:
x = 1/(z(sqrt((1 - z^2)/9)))
y = ±sqrt((1 - z^2)/9)
z = t
b)Parametrization for the curve of intersection of x=y_and x2 - y2 =z is
x = t
y = t
z = 0
c)Parametrization for the curve of intersection of x2 + y2 + z = is
x = r cos(t)
y = r sin(t)
z = 1 - r
a) To find the curve of intersection of the two surfaces [tex]9y^2 + z^2 = 1[/tex] and xyz = 1:
We can solve for one variable in terms of the others.
For example, we can solve for y in terms of z and x using the first equation:
[tex]9y^2 + z^2 = 1[/tex]
[tex]9y^2 = 1 - z^2[/tex]
[tex]y^2 = (1 - z^2)/9[/tex]
y = ±sqrt([tex](1 - z^2)/9)[/tex]
Substituting this into the second equation, we get:
x(sqrt((1 - [tex]z^2)/9))z = 1[/tex]
x = 1/(z(sqrt((1 - [tex]z^2)/9)))[/tex]
So, a parametrization for the curve of intersection is:
x = 1/(z(sqrt((1 - [tex]z^2)/9)))[/tex]
y = ±sqrt((1 - z^2)/9)
z = t
This is defined for all t except at z = ±1.
b) To find the curve of intersection of the two surfaces x = y and [tex]x^2 - y^2 = z:[/tex]
We can substitute x = y into the second equation:
[tex]x^2 - y^2 = z[/tex]
[tex]y^2 - y^2 = z[/tex]
z = 0
So the curve of intersection is just the x = y line.
A parametrization for this line is:
x = t
y = t
z = 0
c) To find a parametrization for the surface [tex]x^2 + y^2 + z = 1:[/tex]
We can use cylindrical coordinates:
x = r cos(t)
y = r sin(t)
z = 1 - r
where 0 ≤ r ≤ 1 and 0 ≤ t < 2π.
This parameterization covers the surface of a unit cylinder with its top and bottom caps removed.
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Mabel saved up her money and bought a model train. Each of the 8 cars on the train was the same length. When Mabel put all the cars together, the train was 3 feet long. How long was each car?
Each car on Mabel's train is a little less than half a foot long i.e., 3/8 feet long, or 0.375 feet long. This is solved by using simple mathematical operations.
To find the length of each car on Mabel's train, we can use the formula:
Total length of train = length of one car × number of cars
We are given that Mabel's train has 8 cars and is 3 feet long, so we can substitute those values into the formula and solve for the length of one car:
3 = x × 8
where x is the length of one car.
To solve for x, we can divide both sides by 8:
3/8 = x
Therefore, each car on Mabel's train is 3/8 feet long, or 0.375 feet long.
In other words, each car is a little less than half a foot long.
To help visualize this, imagine dividing the 3-foot length of the train into 8 equal parts. Each part would be 3/8 feet long, which is the length of one car. So when Mabel puts all 8 cars together, they form a train that is 3 feet long.
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Identify the measure of arc FE⏜ given the measure of arc FGC⏜ is 220∘
The value of the angle of the arc FE⏜ is calculated as: 20°
How to find the angle at the arc?The angle of an arc is identified by its two endpoints. The measure of an arc angle is found by dividing the arc length by the circle's circumference, then multiplying by 360 degrees. Formulas for calculating arcs and angles vary based on where they are in reference to the circle.
Now, from the given image, we see that:
FGC⏜ = 220°
∠B = 30°
∠OEC = ∠OCE = 30°
CDE⏜ = 220°
Thus:
FE⏜ = 360° - 220° - 120°
FE⏜ = 20°
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The point R(-2, 9) is rotated 90° clockwise around the origin. What are the coordinates of the resulting point, R′?
The coordinates of the resulting point, R′ are R' = (-9, -2)
What are the coordinates of the resulting point, R′?From the question, we have the following parameters that can be used in our computation:
The point R(-2, 9) is rotated 90° clockwise around the origin.
This means thar
R = (-2, 9)
Rotation rule = 90° clockwise around the origin.
The rotation rule of 90° clockwise around the origin is
(x,y) becomes (y,-x)
So, we have
R' = (y, -x)
Substitute the known values in the above equation, so, we have the following representation
R' = (-9, -2)
Hence, the coordinates of the resulting point, R′ are R' = (-9, -2)
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3
33 points
Given the bbjective Function:
Revenue =75x + 85y
and the critical points:
(0,0) (180, 120) (300,0)
Which critical point will yield a maximum revenue?
the (0,0)
the (180, 120)
the (300,0)
Cannot be determined with this information
Can be more than 1 answer
The critical point (180, 120) will yield a maximum revenue of 23,700. So, the correct answer is the (180, 120).
To determine which critical point will yield a maximum revenue, we need to evaluate the objective function at each point and compare the results.
Objective Function: Revenue = 75x + 85y
1. Point (0,0):
Revenue = 75(0) + 85(0) = 0
2. Point (180, 120):
Revenue = 75(180) + 85(120) = 13500 + 10200 = 23700
3. Point (300,0):
Revenue = 75(300) + 85(0) = 22500 + 0 = 22500
Comparing the revenues at each point:
(0,0) - Revenue = 0
(180, 120) - Revenue = 23700
(300,0) - Revenue = 22500
The critical point (180, 120) will yield a maximum revenue of 23,700. So, the correct answer is the (180, 120).
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Simplify 3y(y^2-3y+2)
Step-by-step explanation:
if this factorisation because I think you alr simplified, but here's the answer for factorisation anyways.
you can text me below in the comments section if that's not you want, I will try to answer if I can!!!
Answer:
3y(y - 2)(y - 1)
Step-by-step explanation:
Simplify by factoring
3y(y² - 3y + 2)
= 3y(y - 2)(y - 1)
Tables
Contingency Tables
10. In recent years, concerns have been expressed about adverse health effects from amalgam
dental restorations, which contain mercury. The table shows results from a study in which
some patients were treated with amalgam restorations and others were treated with composite
restorations that do not contain mercury. Use a 0. 01 significance level to find the critical value
needed to test for independence between the type of restoration and sensory disorders.
Adverse health
condition reported
No adverse health
condition reported
01136
Amalgam
36
231
Composite
28
239
(1 poin
The critical value needed to test for independence between the type of restoration and sensory disorders is 6. 635.
How to find the critical value ?To evaluate the correlation between sensory impairments and restoration type, a chi-square test of independence can be used. To determine the critical value for this statistical test, consult the chi-square distribution table at a 0.01 significance level.
The degrees of freedom for a chi-square test of independence :
Degrees of Freedom ( df ) = ( Number of Rows - 1 ) x ( Number of Columns - 1 )
The number of rows from the table = 2
Number of columns is also = 2
The df is therefore:
df = (2 - 1) x (2 - 1) = 1 x 1 = 1
The critical value for χ² with 1 degree of freedom at a 0. 01 significance level can be founding using the Chi - Square table to be approximately 6.635.
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Full question is:
In recent years, concerns have been expressed about adverse health effects from amalgam dental restorations, which contain mercury. The table shows results from a study in which some patients were treated with amalgam restorations and others were treated with composite restorations that do not contain mercury. Use a 0. 01 significance level to find the critical value needed to test for independence between the type of restoration and sensory disorders.
Nine hundred thirty six student's, 65% of the entire student body, attended the football game. find the size of the student body.
The size of the student body is approximately 1440 students.
To determine the size of the student body, we'll use the given information that 936 students represent 65% of the total number of students. We can set up a proportion to solve for the unknown total (let's call it "x"):
(65% of x) = 936
To express the percentage as a decimal, divide 65 by 100, which equals 0.65:
0.65 * x = 936
Next, to find the value of x, divide both sides of the equation by 0.65:
x = 936 / 0.65
x ≈ 1440
So, the size of the student body is approximately 1440 students. In this problem, we used the concept of percentage to find out the total number of students in the student body, knowing that 936 students (65%) attended the football game.
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If KJ=10, find the length of arc HJ
Answer:
Step-by-step explanation:
The arc length formula is
[tex]L=\frac{\theta}{360}*2\pi r[/tex]
Theta is the angle that intersects arc HJ. That measure is 180-122 which is 58 degrees. We put that into the formula along with the radius measure of 10 to get:
[tex]L=\frac{58}{360}*2\pi (10)[/tex] which gives us, rounded to the nearest hundredth,
L = 10.12 units
Using technology, calculate the weighted mean of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst?
The ranking from worst to best is Portfolio 3, Portfolio 2, and Portfolio 1. So, correct option is B.
To calculate the weighted mean of the RORs for each portfolio, we need to first multiply each ROR by the corresponding portfolio value and then sum the products for each portfolio. We then divide the total by the sum of the portfolio values.
The weighted mean for Portfolio 1 = [(10.4% x $700) + (-29.7% x $12,000) + (37.2% x $600) + (7.5% x $4,400) + (6.3% x $250)] / ($700 + $12,000 + $600 + $4,400 + $250) = -16.8%
Similarly, the weighted mean for Portfolio 2 = 3.8% and for Portfolio 3 = 11.2%.
Based on the results, the list that shows a comparison of the overall performance of the portfolios from worst to best is option b) Portfolio 3, Portfolio 2, Portfolio 1. Portfolio 3 has the highest weighted mean return of 11.2%, followed by Portfolio 2 with a return of 3.8%, and Portfolio 1 has the lowest weighted mean return of -16.8%.
Therefore, correct option is B.
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Complete question is:
ROR Portfolio 1 Portfolio 2 Portfolio 3
10.4% $700 $6,000 $3,500
-29.7% $12,000 $9,000 $5,500
37.2% $600 $4,500 $5,750
7.5% $4,400 $2,000 $1,500
6.3% $250 $1,100 $4,500
Calculate the weighted mean of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from worst to best?
a) Portfolio 3, Portfolio 1, Portfolio 2
b) Portfolio 3, Portfolio 2, Portfolio 1
c) Portfolio 1, Portfolio 2, Portfolio 3
d) Portfolio 1, Portfolio 3, Portfolio 2
Jovi's garden is 32 feet long and 8 feet wide. He divides the garden into square sections that are 4 feet long then he plants a different type of vegetable in each section. What is the greatest number of types of vegetables that jovi can play in the garden
Answer:
Step-by-step explanation:
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State the number of complex zeros and the possible rational zeros for the function
show your work
The function f(x) = x² + 12x - 3 has two distinct real roots and no rational or complex roots. The possible rational roots are ±1 and ±3, but they are not actual roots of the equation.
To find the number of complex zeros and possible rational zeros of the function f(x) = x² + 12x - 3 = 0, we can use the same methods as in the previous question.
According to the rational root theorem, any rational root of the polynomial must be of the form p/q, where p is a factor of the constant term (-3) and q is a factor of the leading coefficient (1). The possible rational roots are therefore ±1, ±3.
To determine if there are any complex roots, we can use the quadratic formula. The solutions to the equation f(x) = 0 are given by
x = (-b ± √(b² - 4ac)) / 2a
Plugging in the coefficients of the polynomial, we get
x = (-12 ± √(12² - 4(1)(-3))) / 2(1)
x = (-12 ± √(156)) / 2
x = -6 ± 3√(13)
Since the discriminant (b² - 4ac) is positive, the square root is real, and the roots are two distinct real numbers. Therefore, there are no complex roots.
The possible rational roots we found earlier, ±1 and ±3, are not actual roots of the equation, since plugging them into the equation does not give us zero. Therefore, there are no rational roots either.
In conclusion, the equation f(x) = x² + 12x - 3 = 0 has two distinct real roots and no complex or rational roots.
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--The given question is incomplete, the complete question is given
" State the number of complex zeros and the possible rational zeros for the function f(x) = x² + 12x -3 = 0
show your work"--
The given segment is the diameter of a circle bar cd the coordinates of c are (-3,5) and the coordinates of d are (6,-2) . find the center of the circle
To find the center of the circle, we need to find the midpoint of the diameter segment CD.
Using the midpoint formula, we can find the coordinates of the midpoint M:
Midpoint formula:
M = ( (x1 + x2)/2 , (y1 + y2)/2 )
Plugging in the coordinates of C (-3,5) and D (6,-2):
M = ( (-3 + 6)/2 , (5 - 2)/2 )
M = (1.5, 1.5)
Therefore, the center of the circle is at point M with coordinates (1.5, 1.5).
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The seventh-grade students at Charleston Middle School are choosing one girl and one boy for student council. Their choices for girls are Michaela (M), Candice (C), and Raven (R), and for boys, Neil (N), Barney (B), and Ted (T). The sample space for the combined selection is represented in the table. Complete the table and the sentence beneath it.
Boys
Neil Barney Ted
Girls Michaela N-M
B-M
T-M
Candice N-C
B-C
T-C
Raven N-R
B-R
T-R
If instead of three girls and three boys, there were four girls and four boys to choose from, the new sample size would be ?
If there were four girls and four boys to choose from, the new sample size is one that will be a total of 16 possible combinations.
What is the sample about?When making selections for the student council's representatives, the sample size belongs to the whole of the feasible options.
To know the sample size, we must reason every conceivable permutation involving a single female and a single male.
So, if there were four girls and four boys to choose from, the new sample size would be:
There are:
4 choices for girls
4 choices for boys.
So, for each girl's choice, there would be 4 corresponding choices for boys.
Hence it will be:
4 x 4 = 16
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What is the surface area of this right triangular prism?
The surface area of the triangular prism is 720in²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as
SA = 2B +ph
where p is the perimeter of the base and h is the height of the prism.
Base area = 1/2 bh
= 1/2 × 24 × 5
= 12 × 5
= 60 in²
Perimeter of the base = 24 +13 +13
= 50 in²
the height of the prism = 12 in
therefore SA = 2 × 60+ 12 × 50
= 120 + 600
= 720 in²
Therefore the surface area of the prism is 720 in²
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given m||n, find the value of x
Answer:
Step-by-step explanation:
The value of x is 19 if the lines l and m are parallel.
The lines l and m are parallel
The corresponding angles are equal
We have to find the value of x
6x-9 = 5x+10
Let us take all the variable terms on one side
6x-5x=10+9
x=19
Hence, the value of x is 19 if the lines l and m are parallel.
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what is 88 closer to 64 or 125
Answer:
64
Step-by-step explanation:
Answer:
64...i think
Step-by-step explanation:
125 - 88=37
88-64=24
PLS MARK BRAINLIEST
If f(x) = x2 − 6x − 4 and g(x) = 5x + 3, what is (f + g)(−3)? (1 point)
41
35
11
−35
As per the given information in the question, we can compute that the correct option is C) 11.
According to the question:
[tex]f(x)=x^{2} -6x-4[/tex]
[tex]g(x)=5x+3[/tex]
Therefore,
[tex](f+g)(x)= f(x)+g(x) \\
=x^{2} -6x-4+5x+3 \\
=x^2-x-1[/tex]
Now, to find (f+g)(-3):
substituting x=-3 in the above equation
we get,
[tex](f+g)(-3)= (-3)^2-(-3)-1 \\
= 9+3-1 \\
=11[/tex]
Hence (f+g)(-3)=11
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Use the differential dz to approximate the change that will be
observed in z = f (x, y) = 5/x^2 + y^2 as x changes from −1 to
−0.93 and y changes from 2 to 1.94.
To approximate the change in z = f(x, y) as x changes from −1 to −0.93 and y changes from 2 to 1.94, we can use the differential dz.
First, we need to find the partial derivatives of f with respect to x and y:
∂f/∂x = -10/x³(y²)
∂f/∂y = -10(x²)/y³
Then, we can use the following formula:
dz ≈ ∂f/∂x * Δx + ∂f/∂y * Δy
where Δx and Δy are the changes in x and y, respectively.
Substituting in the given values, we have:
Δx = -0.93 - (-1) = 0.07
Δy = 1.94 - 2 = -0.06
Using the partial derivatives we calculated earlier, we get:
dz ≈ (-10/-1.037³(2²)) * 0.07 + (-10((-1)²)/1.94³) * (-0.06)
dz ≈ -0.031
Therefore, the approximate change observed in z as x changes from −1 to −0.93 and y changes from 2 to 1.94 is -0.031.
To approximate the change in z using the differential dz, we first need to find the partial derivatives of z with respect to x and y. Given z = f(x, y) = 5/(x² + y²):
∂z/∂x = -10x/(x² + y²)²
∂z/∂y = -10y/(x² + y²)²
Now, we need to find the differential dz:
dz = (∂z/∂x)dx + (∂z/∂y)dy
Since x changes from -1 to -0.93, dx = -0.93 - (-1) = 0.07. Similarly, y changes from 2 to 1.94, so dy = 1.94 - 2 = -0.06.
Now, plug in the initial values of x and y (-1, 2):
∂z/∂x = -10(-1)/((-1)² + 2²)² = -10/25
∂z/∂y = -10(2)/((-1)² + 2²)² = -40/25
Now, plug in dx and dy into the dz equation:
dz = (-10/25)(0.07) + (-40/25)(-0.06) = 0.28 - 0.096 = 0.184
So, the approximate change in z when x changes from -1 to -0.93 and y changes from 2 to 1.94 is 0.184.
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A recent survey of fortune 500 firms found that on average, they contribute $332.54 per month for each salaried employee's health insurance. if you are told that almost all salaried employees at fortune 500 firms receive a health insurance contribution between $220.61 and $444.47, and assuming a bell-shaped distribution, what must the standard deviation for this data be
The standard deviation for the data must be approximately $111.93.
How to calculate the standard deviationSince we are given a range of values that encompasses about 95% of the data, we can assume that this range is within two standard deviations of the mean.
Thus, we can set up the following equation:
2σ = $444.47 - $220.61
Simplifying this equation, we get:
2σ = $223.86
σ = $111.93
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Madison swims 2/5 mile in an hour. Declan swims 7/10 mine in 1/5 hour. Who swims faster?
Declan swims faster than Madison, with a speed of 7/2 miles per hour compared to Madison's speed of 2/5 miles per hour.
How to compare swimming speed?Declan swims faster than Madison. While Madison swims 2/5 mile in an hour, which means her speed is 2/5 miles per hour, Declan swims 7/10 mile in 1/5 hour, which means his speed is 7/2 miles per hour. This indicates that Declan's speed is greater than Madison's speed.
In fact, we can see that Declan's speed is almost 4 times faster than Madison's speed. This means that Declan can cover a greater distance in the same amount of time compared to Madison.
Therefore, based on the given information, we can confidently say that Declan swims faster than Madison.
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Julia just lit a new candle and then let it burn all the way down to nothing. The candle burned at a rate of 0.75 inches per hour and its initial length was 9 inches. Write an equation for
L
,
L, in terms of
t
,
t, representing the length of the candle remaining unburned, in inches,
t
t hours after the candle was lit.
The required equation for the length of the candle is L = 9-0.75t.
Given that a 9-inch candle burns at the rate of 0.75 in per hour we need to determine the equation for the length L of the candle when it burns for t hours,
So, if the candle is burning at the rate of 0.75 in per hour so after burning for t hour the length decreases by 0.75t, from the original length i.e 9 in
So, we can write the equation as =
L = 9-0.75t
Hence the required equation for the length of the candle is L = 9-0.75t.
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If y, p and q vary jointly and p is 14 when y and q are equal to 2, determine q when p and y are equal to 7
In the given question, if y, p and q vary jointly and p is 14 when y and q are equal to 2 and p and y are equal to 7, we get q is equal to 14 using the joint variation formula.
To solve this problem, we need to use the formula for joint variation, which states that y, p, and q vary jointly if there exists a constant k such that ypk = kq.
In this case, we know that when y=2 and q=2, p=14. So we can set up the equation: 2*14*k = 2kq
Simplifying this, we get: 28k = 2kq
Dividing both sides by 2k, we get: 14 = q
So when p=7 and y=7, we can use the same equation: 7*14*k = 7kq
Simplifying this, we get: 98k = 7kq
Dividing both sides by 7k, we get: q = 14
Therefore, when p and y are equal to 7, q is equal to 14.
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