we first need to find out how many street name boards can be purchased with a budget of R80,000. We can do this by dividing the budget by the cost of each street name board:
R80,000 ÷ R134 = 597.01
Since we cannot purchase a fraction of a street name board, we round down to the nearest whole number. Therefore, the municipality can purchase 597 new street name boards with a budget of R80,000.
To find out how much money will be left in the budget, we can subtract the cost of the street name boards from the initial budget:
R80,000 - (597 x R134) = R1,598
Therefore, the municipality will have R1,598 left in their budget after purchasing 597 new street name boards.
Street name boards are an important part of any municipality as they help residents navigate and locate specific areas. By budgeting for and installing new street name boards, the municipality is taking a proactive approach to improve their community's infrastructure and ensure the safety and well-being of their residents.
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Correct the error in finding the area of sector XZY when the area of ⊙Z is 255 square feet.
n/360=115/225
n=162. 35
Round to the nearest tenth.
The area should equal ______ft2.
It appears to be setting up a proportion between the central angle of the sector and the ratio of arc length to the circumference of the circle, rather than the ratio of the central angle to the full angle of the circle. Then the area should equal to 126.9 [tex]ft^2.[/tex]
To find the area of sector XZY, we need to know the measure of angle XYZ. However, the given equation n/360 = 115/225 is incorrect, as it appears to be setting up a proportion between the central angle of the sector and the ratio of arc length to the circumference of the circle, rather than the ratio of the central angle to the full angle of the circle.
To find the correct measure of angle XYZ, we need to use the formula:
Area of sector XZY = (n/360) x π[tex]r^2[/tex]
where r is the radius of circle Z.
We know that the area of circle Z is 255 square feet, so we can find the radius as follows:
Area of circle Z = π[tex]r^2[/tex]
255 = π[tex]r^2[/tex]
[tex]r^2[/tex] = 81
r = 9
Now we can solve for n using the given ratio of 115/225:
n/360 = 115/225
n = (115/225) x 360
n = 184.32
Rounding to the nearest tenth, we get:
n ≈ 184.3
Finally, we can find the area of sector XZY as:
Area of sector XZY = (n/360) x π[tex]r^2[/tex]
Area of sector XZY = (184.3/360) x π[tex](9)^2[/tex]
Area of sector XZY ≈ 126.9 [tex]ft^2[/tex]
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Construct angle XYZ in which XY= 8.3 cm, YZ= 11.9 cm ii, Construct M the midpoint of XZ where XYZ= 60o
Holly cuts 6 ribbons into fifths for a craft project.
1
how many --size ribbons does she have?
5
holly has
one-fifth-size ribbons.
If Holly cuts 6 ribbons into fifths for her craft project, after cutting, she has a total of 30 one-fifth-size ribbons (6 ribbons x 5 cuts each).
Holly has cut 6 ribbons into fifths for her craft project. This means that she has a total of 30 ribbons, each with a size of one-fifth. To understand this better, we can break it down into fractions. Each ribbon is one-fifth of a whole ribbon, and since Holly has cut 6 ribbons, she has 6 times one-fifth, which equals 30. So, to answer the question, Holly has 30 ribbons, each with a size of one-fifth. These ribbons can be used for various crafts, such as creating bows, wrapping presents, or decorating cards. The possibilities are endless, and with 30 ribbons, Holly can get creative and make a lot of beautiful crafts.
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Rate of Change of Production Costs The daily total cost C(x) incurred by Trappee and Sons for producing x cases of TexaPep hot sauce is given by the following function. C(x) = 0.000002x^3 + 4x + 300 Calculate the following for h = 1, 0.1, 0.01, 0.001, and 0.0001. (Round your answers to four decimal places.)
C(100+h) – C(100)/h
The instantaneous rate of change of cost with respect to x when x = 100 is 4.
We can begin by calculating C(100+h) and C(100):
C(100+h) = 0.000002(100+h)^3 + 4(100+h) + 300
C(100+h) = 0.000002(1,000,000 + 300h^2 + 30h^2 + h^3) + 400 + 4h + 300
C(100+h) = 0.000002h^3 + 0.0006h^2 + 4h + 700
C(100) = 0.000002(100)^3 + 4(100) + 300
C(100) = 2 + 400 + 300
C(100) = 702
Therefore,
C(100+h) - C(100) = (0.000002h^3 + 0.0006h^2 + 4h + 700) - 702
C(100+h) - C(100) = 0.000002h^3 + 0.0006h^2 + 4h - 2
Now, we can find the rate of change of cost with respect to x by dividing this expression by h and taking the limit as h approaches 0:
(C(100+h) - C(100))/h = (0.000002h^3 + 0.0006h^2 + 4h - 2)/h
(C(100+h) - C(100))/h = 0.000002h^2 + 0.0006h + 4 - (2/h)
As h approaches 0, the term 2/h approaches infinity, which means the rate of change of cost with respect to x is undefined. However, we can calculate the limit of the expression as h approaches 0 from the left and from the right to see if it has a finite value:
limit (h->0+) ((C(100+h) - C(100))/h) = 4
limit (h->0-) ((C(100+h) - C(100))/h) = 4
Since the left and right limits are equal, the overall limit exists and equals 4. Therefore, the instantaneous rate of change of cost with respect to x when x = 100 is 4.
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In a certain triangle, one angle has a measure of 42° and another angle has a measure of 96°. If the triangle is isosceles, then which of the following could be the measure of the third angle?
A.
60°
B.
42°
C.
96°
D.
69°
If the triangle is isosceles, then the measure of the third angle could be 42 degrees
Which could be the measure of the third angle?From the question, we have the following parameters that can be used in our computation:
One angle has a measure of 42° Another angle has a measure of 96°.The sum of angles in a triangle is 180 degrees
If the triangle is isosceles, then we have the following possible sum of angles
Sum 1 = 42 + 96 + 96 = 234 -- false
Sum 1 = 42 + 96 + 42 = 180 -- true
Hence, if the triangle is isosceles, then the measure of the third angle could be 42 degrees
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A medical researcher is studying the effects of a drug on blood pressure. Subjects in the study have their blood pressure taken at the beginning of the study. After being on the medication for 4 weeks, their blood pressure is taken again. The change in blood pressure is recorded and used in doing the hypothesis test.
Change: Final Blood Pressure - Initial Blood Pressure
The researcher wants to know if there is evidence that the drug affects blood pressure. At the end of 4 weeks, 36 subjects in the study had an average change in blood pressure of 2. 4 with a standard deviation of 4. 5.
Find the
p
-value for the hypothesis test
The p-value for the hypothesis test is 0.04. This means that if the null hypothesis is true
To find the p-value, we need to conduct a hypothesis test.
The null hypothesis is that there is no difference in blood pressure before and after taking the medication:
H0: μd = 0
The alternative hypothesis is that there is a difference in blood pressure before and after taking the medication:
Ha: μd ≠ 0
where μd is the population mean difference in blood pressure before and after taking the medication.
We are given that the sample size is n = 36, the sample mean difference is ¯d = 2.4, and the sample standard deviation is s = 4.5.
We can calculate the t-statistic as:
t = (¯d - 0) / (s / sqrt(n)) = (2.4 - 0) / (4.5 / sqrt(36)) = 2.13
Using a t-distribution table with 35 degrees of freedom (df = n - 1), we find that the two-tailed p-value for t = 2.13 is approximately 0.04.
Therefore, the p-value for the hypothesis test is 0.04. This means that if the null hypothesis is true (i.e., if there is really no difference in blood pressure before and after taking the medication), there is a 4% chance of observing a sample mean difference as extreme or more extreme than 2.4. Since this p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence that the drug affects blood pressure.
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6(5-4x) < 54
solve the inequality
i hope this helps you.
TRUE or FALSE:
1. Each exterior angle of a regular hexagon is acute
2. The sum of the interior angles of a polygon is not necessarily a multiple of 180
3. In any polygon, the larger the number of vertices, the smaller the measure of an exterior angle
1. The statement "Each exterior angle of a regular hexagon is acute" is True.
2. The statement "The sum of the interior angles of a polygon is always a multiple of 180" is False.
3. The statement "In any polygon, the larger the number of vertices, the smaller the measure of an exterior angle" is True.
1. TRUE: Each exterior angle of a regular hexagon is acute.
A regular hexagon has six equal sides and six equal interior angles. The sum of the interior angles of a hexagon is (6-2) * 180 = 720 degrees. Since it's a regular hexagon, each interior angle is 720/6 = 120 degrees. The exterior angles are supplementary to the interior angles, so each exterior angle is 180 - 120 = 60 degrees. Since 60 degrees is less than 90 degrees, each exterior angle is acute.
2. FALSE: The sum of the interior angles of a polygon is always a multiple of 180.
The formula for the sum of the interior angles of a polygon is (n-2) * 180, where n is the number of vertices (or sides). As you can see, the result is always a multiple of 180.
3. TRUE: In any polygon, the larger the number of vertices, the smaller the measure of an exterior angle.
For a regular polygon, the measure of an exterior angle can be calculated as 360/n, where n is the number of vertices (or sides). As the number of vertices increases, the measure of an exterior angle decreases, since they are inversely proportional.
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In 2010, Little Elm had 3646 residents. Five years later, they had 17,150 residents. If the population grows at this rate, about how many residents will the town have in 2020? Include explanation.
A. 20,800
B. 27,000
C. 30,700
D. 35,400
PLS DON'T PUT LINKS AND WRITE ANSWER, THX! I WILL MARK BRAINLIEST IF YOU WRITE THE ANSWER!
The answer is option C) 30,700
Why the answer is option C?The problem involves using linear interpolation to estimate the population of Little Elm in 2020 based on the given data from 2010 and 2015.
To start, we need to calculate the annual growth rate of the population between 2010 and 2015. This can be done by taking the difference between the population in 2015 and the population in 2010, and then dividing that difference by the number of years in that time period:
Annual growth rate = (17,150 - 3,646) / 5 = 2,700
This means that, on average, the population of Little Elm grew by 2,700 people per year between 2010 and 2015.
Next, we can use this annual growth rate to estimate the population of Little Elm in 2020. To do this, we need to add 10 years of growth to the initial population of 3,646 (since we want to estimate the population in 2020, which is 10 years after 2010):
Estimated population in 2020 = 3,646 + (2,700 x 10) = 30,646
Therefore, the estimated population of Little Elm in 2020 is approximately 30,700, which corresponds to answer choice C.
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Find the area k of the trianglea = 3, c = 2, b = 135 degrees
The area k of the triangle a = 3, c = 2, b = 135 degrees is approximately 1.06125 square units.
The area k of the triangle, we can use the formula:
k = (1/2) * b * c * sin(A)
where A is the angle opposite side a.
Find A, we can use the fact that the angles in a triangle add up to 180 degrees:
A + B + C = 180
Substituting in the given values, we get:
A + 135 + 180 = 360
A = 45 degrees
Now we can plug in all the values into the area formula:
k = (1/2) * 2 * 3 * sin(45)
k = 1.5 * 0.707
k = 1.06125
Therefore, the area k of the triangle is approximately 1.06125 square units.
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The ratio table shows the costs for different amounts of bird seed. find the unit rate in dollars per pound. the unit rate is $ per pound
The ratio table shows the costs for different amounts of birdseed. So, the unit rate is $2 per pound in this example.
To find the unit rate in dollars per pound, follow these steps:
1. Look at the given ratio table, which shows the costs for different amounts of bird seed.
2. Identify the cost and the corresponding amount (in pounds) of bird seed for any one row in the table.
3. Divide the cost (in dollars) by the amount (in pounds) to calculate the unit rate.
For example, if the table shows that the cost is $6 for 3 pounds of bird seed, the unit rate would be calculated as follows:
Unit rate = Cost / Amount
Unit rate = $6 / 3 pounds
Unit rate = $2 per pound
So, the unit rate is $2 per pound in this example
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30 POINTS!!!!!! I WILL GIVE BRAINLIEST!!!!!!!!
If the measure of arc QR is 40 degrees, what is the measure of angle PQR?
The measure of angle PQR is 20 degrees.
We have,
The measure of angle PQR can be found by using the property that the measure of an inscribed angle is half the measure of its intercepted arc.
Given that the measure of arc QR is 40 degrees, we can conclude that the measure of angle PQR is half of that, which is:
The measure of angle PQR = 1/2 x Measure of arc QR
= 1/2 x 40 degrees
= 20 degrees
Therefore,
The measure of angle PQR is 20 degrees.
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A rectangle with length n is inscribed in a circle of radius 9. Find an expression for the area of the rectangle in terms of n
The expression for the area of the rectangle inscribed in a circle of radius 9, in terms of n, is:
Area = n * √(81 - n^2)
To find an expression for the area of a rectangle inscribed in a circle of radius 9, we need to use the terms "rectangle" and "circle."
First, let's denote the length of the rectangle as "n" and the width as "w." Since the rectangle is inscribed in a circle with a radius of 9, its diagonal is equal to the diameter of the circle, which is 2 * 9 = 18.
Using the Pythagorean theorem for the right triangle formed by half of the diagonal, the length, and the width, we can write the equation:
(1/2 * 18)^2 = n^2 + w^2
81 = n^2 + w^2
Now, we need to express w in terms of n. To do this, we'll isolate w from the equation:
w^2 = 81 - n^2
w = √(81 - n^2)
The area of the rectangle can be calculated as the product of its length and width:
Area = n * w
Area = n * √(81 - n^2)
So, the expression for the area of the rectangle inscribed in a circle of radius 9, in terms of n, is:
Area = n * √(81 - n^2)
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How many sides does a regular n-gon have if one interior angle measures 150°? Show all work!
Answer:
A regular n-gon with one interior angle of 150° has 12 sides.
Step-by-step explanation:
The formula for the measure of each interior angle of a regular n-gon is:
180(n-2)/nwhere:
n is the number of sidesWe are given that one interior angle measures 150°, so we can set up the equation:
180(n-2)/n = 150Multiplying both sides by n, we get:
180(n-2) = 150nDistributing, we get:
180n - 360 = 150nSubtracting 150n from both sides, we get:
30n - 360 = 0Adding 360 to both sides, we get:
30n = 360Dividing both sides by 30, we get:
n = 12Therefore, a regular n-gon with one interior angle of 150° has 12 sides.
How to find the area of this whole figure? Please help me
The area of the whole figure is 31.5 sq. units.
What is the area of a figure?The area of a given figure connotes its expanse in a 2 dimensional plane. The shape and size of a given figure determines how to calculate its area.
From the given question, the figure given can be likened to a rhombus. So that;
area of a rhombus = (diagonal 1 * diagonal 2)/ 2
Then,
area of the figure = (diagonal 1 * diagonal 2)/ 2
where: diagonal 1 = 7.5, and diagonal 2 = 8.4
So that;
area of the figure = (7.5*8.4)/ 2
= 63/ 2
= 31.5
The area of the whole figure is 31.5 sq. units.
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Please help!
An airplane is approaching Seattle International Airport. The pilot begins a 13 degree angle of d scent starting from a height of 500 feet. How far from the airport is the plane? Round to the nearest tenth.
We get that the plane is about 2193.0 feet from the airport, Rounding to the nearest tenth
To solve the problem, we will use trigonometry and the tangent function, which relates the other facet of a right triangle to the adjoining aspect:
tan(theta) = opposite / adjacent
wherein theta is the angle of descent, opposite is the change in height, and adjacent is the space from the airplane to the airport.
Rearranging the formula, we get:
adjacent = contrary / tan(theta)
because the angle of descent is 13 ranges and the alternate in height is from 500 ft, we've got:
contrary = 500 ft
theta = 13 stages
Substituting these values into the formula, we get:
adjacent = 500 ft / tan(13 ranges)
using a calculator, we find that tan(13 stages) is about 0.228, so:
adjacent = 500 feet / 0.228 = 2192.98 feet
Therefore, we get that the plane is about 2193.0 feet from the airport.
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The following graph shows a proportional relationship.
What is the constant of proportionality between
�
yy and
�
xx in the graph?
The constant of proportionality between y and x in the graph is 3
What is the constant of proportionality between y and x in the graph?From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings
(x, y) = (1, 3)
Using the above as a guide, we have the following:
The constant of proportionality between y and x in the graph is
k = y/x
substitute the known values in the above equation, so, we have the following representation
k = 3/1
Evaluate
k = 3
Hence, the constant of proportionality between y and x in the graph is 3
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How do I solve this?
Step-by-step explanation:
you can solve cos(u) by
cos(u) = adjecent / hypotenes...general formula of cos
cos(u) = √44 / 12
cos(u) = 2√11 / 12 ..... √44 = √4×11 = 2√11
cos(u) = √11 / 6
u = cos^-1 ( √11 / 6 ) ..... divided both aide by cos ( multiple by cos invers )
u = 56.442 .... so we get it's angle
Answer:
[tex]cos(U)=\frac{\sqrt{11} }{6}[/tex]
Step-by-step explanation:
In a right triangle, the cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. Therefore, we have:
cos(U) = adjacent/hypotenuse = TU/SU
We are given that TU = sqrt(44) and SU = 12, so:
cos(U) = sqrt(44)/12
To simplify this expression, we can first factor 44 into 4 * 11, since 4 is a perfect square and a factor of 44:
cos(U) = sqrt(4 * 11) / 12
cos(U) = (sqrt (4) * sqrt (11)) / 12
cos (U) = (2 * sqrt (11)) / 12
Simplifying the fraction by dividing both the numerator and denominator by 2, we get:
cos(U) = sqrt(11)/6
Therefore, the exact value of cos(U) in simplest radical form is sqrt(11)/6
Furthermore, if you want another way to write the answer, dividing by 6 is the same as multiplying by 1/6 so you can do cos (U) = 1/6 * sqrt (11)
Although the other individual was correct that you use inverse trig (cos ^ -1) to find the measure of U, getting an exact answer requires us to leave it in simplest radical form since the number is so large and at best will yield an approximation if you don't keep it in simplest radical form.
Solve for 2x+y=10
3x=y
Answer:
x=2
Step-by-step explanation:
2x+y=10
3x=y
2x+3x=10
5x=10
x=2
what two double inequalities define shaded region
The calculated two double inequalities that define shaded region are 1 ≤ y < 5 and -3 < x ≤ 2
Determining the two double inequalities that define shaded regionFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following properties
Shaded region is between y = 1 and y = 5 (exclusive of y = 5)Shaded region is between x = -3 and x = 2 (exclusive of y = 5)Using the above as a guide, we have the following:
1 ≤ y < 5
-3 < x ≤ 2
Hence, the two double inequalities that define shaded region are 1 ≤ y < 5 and -3 < x ≤ 2
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How to get 51 by using all four numbers 8 5 6 7 once.
To get 51 using the numbers 8, 5, 6, and 7 exactly once each, you can use the following mathematical expression:
(8 x 6) - 7 + 5 = 51
How it works:
1. Multiply 8 by 6 to get 48: (8 x 6) = 48
2. Subtract 7 from 48 to get 41: 48 - 7 = 41
3. Add 5 to 41 to get 51: 41 + 5 = 51
Therefore, (8 x 6) - 7 + 5 = 51.
Answer:
Step-by-step explanation:
8 x (7 - 5) + 6 = 51
What is one more solution to the following. i already have the first solution which is x=9 but there is one more.
let f (x) = log3(x) + 3 and g(x) = log3(x3) – 1.
part a: if h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points)
part b: determine the solution to the system of nonlinear equations.
( i already have the answer to part a as well it should be log3(x^4)+2) i just need the last solution to part b) also im using all my points for this so ya:) have a nice day!
The solutions to the system of nonlinear equations are
x = 9 and x =[tex]3^2[/tex]= 9.
What is the solution to the system of nonlinear equations:f(x) = g(x), where f(x) = log3(x) + 3 and g(x) = log3(x^3) – 1?
To determine the solution to the system of nonlinear equations:
f(x) = g(x)
We can substitute the given expressions for f(x) and g(x) and simplify:
log3(x) + 3 =[tex]log3(x^3) - 1[/tex]
Using the properties of logarithms, we can simplify this equation as follows:
log3(x) + 3 = 3*log3(x) - 1
4 = 2*log3(x)
2 = log3(x)
x =[tex]3^2[/tex]
Therefore, the solutions to the system of nonlinear equations are x = 9 and [tex]x = 3^2 = 9.[/tex]
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Triangle PQR has vertices at the following coordinates: P(0, 1), Q(3, 2), and R(5, -4). Determine whether or not triangle PQR is a right triangle. Show all calculations for full credit.
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Triangle PQR is not a right triangle.
To determine whether triangle PQR is a right triangle, we need to check if any of its angles is a right angle (90 degrees). We can use the slope formula to find the slopes of the sides of the triangle and check if any of the slopes are negative reciprocals (perpendicular) to each other.
Let's calculate the slopes of the sides PQ, QR, and RP:
Slope of PQ = (y₂ - y₁) / (x₂ - x₁)
= (2 - 1) / (3 - 0)
= 1 / 3
Slope of QR = (y₂ - y₁) / (x₂ - x₁)
= (-4 - 2) / (5 - 3)
= -6 / 2
= -3
Slope of RP = (y₂ - y₁) / (x₂ - x₁)
= (1 - (-4)) / (0 - 5)
= 5 / (-5)
= -1
Now, let's check if any of the slopes are negative reciprocals of each other. We can compare the products of the slopes:
Product of PQ slope and QR slope = (1/3) * (-3) = -1
Product of QR slope and RP slope = (-3) * (-1) = 3
Product of RP slope and PQ slope = (-1) * (1/3) = -1/3
Since the product of the slopes of QR and RP is not equal to -1, triangle PQR is not a right triangle.
Therefore, triangle PQR is not a right triangle.
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In circle K with \text{m} \angle JKL= 90m∠JKL=90, find the \text{m} \angle JMLm∠JML
The measure of angle JML is 180 degrees because in a circle, an angle formed by two chords intersecting inside the circle.
How to find the measurement of angle?In a circle, the measurement of angle formed by two chords intersecting inside the circle is half the sum of the arcs intercepted by the angle. Using this property, we can find the measure of angle JML.
Since angle JKL is a right angle, its intercepted arc is the diameter of the circle. Therefore, its measure is 180 degrees.
By the same property, we know that angle JML is half the sum of the arcs intercepted by it. The arcs intercepted by angle JML are arcs JL and KM.
Since angle JKL is a right angle, arc JL is also 180 degrees.
Since J, K, L, and M are concyclic, we know that angle JKM is supplementary to angle JLM. Therefore, arc KM is the supplement of arc JL and has measure 360 - 180 = 180 degrees.
Thus, the sum of the intercepted arcs is 180 + 180 = 360 degrees, and angle JML is half of this, so its measure is 180 degrees.
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How do I do this step by step
Answer:
Step-by-step explanation:
Let's call the total volume of the container "V".
We know that the container was originally 15% full, so the amount of water in the container was 0.15V.
When 48 litres of water was added, the new volume of water in the container became 0.15V + 48.
We also know that the container is now 75% full, so the new volume of water in the container must be 0.75V.
We can set up an equation to solve for V:
0.15V + 48 = 0.75V
Subtracting 0.15V from both sides:
48 = 0.6V
Dividing both sides by 0.6:
V = 80
So the container can hold 80 litres of water when it is full.
if an airplane travels around the world, flying just above the equator it would travel 1.25 x 10^4 miles. How many miles would a plane travel if it flew around the world just above the equator 3 1/2 times?
(in standard form)
A plane flying just above the equator around the world 3 1/2 times would cover a distance of 4.375 x 10⁴ miles.
If an airplane travels around the world just above the equator once, it covers a distance of 1.25 x 10⁴ miles. To find how many miles it would cover if it flew around the world 3 1/2 times, we need to multiply this distance by 3.5:
1.25 x 10⁴ miles x 3.5 = 4.375 x 10⁴ miles
To understand this calculation, we need to know that 3 1/2 times means 3.5 times. So, we multiply the distance covered in one round of the world by 3.5 to find the total distance covered in 3 1/2 times around the world.
We use standard form to express the answer in a more compact and convenient way, where 4.375 x 10⁴ represents the number 43,750 in scientific notation.
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First one gets brainlist
the average january surface water temperatures (°c) of lake michigan from 2000 to 2009 were 5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, and 4.34.
the mean value of these temperatures is 4.312.
what is the variance of this data set?
The variance of the data set is 0.318652.
To find the variance of this data set, we need to use the formula:
variance = Σ(x - μ)² / n
Where Σ represents the sum, x is the value of each data point, μ is the mean value, and n is the number of data points.
Using this formula, we can calculate the variance as follows:
Variance = [(5.07 - 4.312)² + (3.57 - 4.312)² + (5.32 - 4.312)² + (3.19 - 4.312)² + (3.49 - 4.312)² + (4.25 - 4.312)² + (4.76 - 4.312)² + (5.19 - 4.312)² + (3.94 - 4.312)² + (4.34 - 4.312)²] / 10
Variance = [0.225769 + 0.449769 + 0.370656 + 1.323856 + 0.716164 + 0.006544 + 0.175684 + 0.382884 + 0.135556 + 0.000484] / 10
Variance = 3.18652 / 10
Variance = 0.318652
Therefore, the variance of the data set is 0.318652.
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A company operates two plants which manufacture the same item and whose total cost functions areC1=6.7+0.03(q1)² and C2=7.9+0.04(q2)²,where q1 and q2 are the quantities produced by each plant. The company is a monopoly. The total quantity demanded, q=q1+q2, is related to the price, p, byp=40−0.04q.How much should each plant produce in order to maximize the company's profit? Q1= Q2=
Each plant should produce 576.92 units and 384.61 units respectively to maximize the company's profit.
To maximize the company's profit, we need to find the quantity that maximizes the difference between the total revenue and the total cost. The total revenue is given by:
TR = pq
= (40 - 0.04q)(q1 + q2)
= 40q1 + 40q2 - 0.04[tex]q1^2[/tex]- 0.04[tex]q2^2[/tex] - 0.04q1q2
The total cost is given by:
TC = C1 + C2
[tex]= 6.7 + 0.03q1^2 + 7.9 + 0.04q2^2= 14.6 + 0.03q1^2 + 0.04q2^2[/tex]
The profit is given by:
π = TR - TC
= [tex]40q1 + 40q2 - 0.04q1^2 - 0.04q2^2 - 0.04q1q2 - 14.6 - 0.03q1^2 - 0.04q2^2[/tex]
Simplifying, we get:
π = [tex]40q1 + 40q2 - 0.04q1^2 - 0.04q2^2 - 0.04q1q2 - 14.6 - 0.03q1^2 - 0.04q2^2[/tex]
= [tex]-0.03q1^2 - 0.04q2^2 - 0.04q1q2 + 40q1 + 40q2 - 14.6[/tex]
To maximize profit, we need to take the partial derivatives of the profit function with respect to q1 and q2 and set them equal to zero:
∂π/∂q1 = -0.06q1 - 0.04q2 + 40 = 0
∂π/∂q2 = -0.08q2 - 0.04q1 + 40 = 0
Solving these equations simultaneously, we get:
q1 = 576.92
q2 = 384.61
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Jenny and Kera are playing a game. Jenny has -10 points and loses 5 more points. How many points does Jenny have now? Kera has 22 points and loses 14 points. How many points does Kera have now? Make sure that you type each name with her current score
The current scores of both Jenna and Kera in the game they were playing are
Jenny's current score is -15.
Kera's current score is 8.
How many points does Jenny have now?In the given problem, we are given two players, Jenny and Kera, playing the game.
Jenny has -10 points, which means she already has negative points. He has since lost 5 more points. So his current score would be:
-10 - 5 = -15
So now Jenny has a score of -15.
Kera, meanwhile, has 22 points and 14 points to lose. So his current score would be:
22 - 14 = 8
So now Kera has 8 points.
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Buy-Rite Pharmacy has purchased a small auto for delivering prescriptions. The auto was purchased for $26,000 and will have a 6-year useful life and a $5,500 salvage value. Delivering prescriptions (which the pharmacy has never done before) should increase gross revenues by at least $33,500 per year. The cost of these prescriptions to the pharmacy will be about $28,000 per year. The pharmacy depreciates all assets using the straight-line method. The payback period for the auto is closest to (Ignore income taxes. ): (Round your answer to 1 decimal place. )
The payback period for the auto is approximately 8 years.
Buy-Rite Pharmacy has purchased an auto for delivering prescriptions. The auto was purchased for $26,000, and it has a useful life of 6 years with a $5,500 salvage value. By delivering prescriptions, the pharmacy aims to increase gross revenues by at least $33,500 per year. The pharmacy will incur a cost of $28,000 per year for these prescriptions.
Using the straight-line method, the annual depreciation of the auto is ($26,000 - $5,500) / 6 = $3,917. This means that the total cost of the auto over 6 years will be $26,000 - $5,500 + ($3,917 x 6) = $43,502.
To calculate the payback period, we need to determine how long it will take for the increased gross revenues to cover the cost of the auto.
The net increase in revenues will be $33,500 - $28,000 = $5,500 per year. Therefore, the payback period is $43,502 / $5,500 = 7.9 years, which is rounded to 8 years.
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