Using basic arithmetic operation, the solution to the equation 7/6 + 2/3y = 4/3 is y = 3/4.
What is the basic arithmetic operation?
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To solve this equation for y, we need to isolate the variable y on one side of the equation. We can do this by performing algebraic operations to simplify the equation. Here are the steps:
Subtract 7/6 from both sides:
7/6 + 2/3y - 7/6 = 4/3 - 7/6
2/3y = 1/2
Multiply both sides by the reciprocal of 2/3:
(3/2)(2/3y) = (3/2)(1/2)
y = 3/4
Hence, the solution to the equation 7/6 + 2/3y = 4/3 is y = 3/4.
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Please help, Progress reports for the semester coming out soon!!
(Look at screenshot) <33
Answer:
The graph will be parallel with x-axis and intersects y at -8
Step-by-step explanation:
For the function y = -8, whatever the x is, y is always -8.
x y
-10 8
-9 8
-3 8
-2 8
2 8
The graph will be parallel with x-axis and intersects y at -8
Malcom had some milk chocolates and dark chocolates. He ate an equal amount of milk and dark chocolates. He had 5/7 of the milk chocolates and 2/5 of the dark chocolates left. What fraction of the chocolates did Malcom eat?
Malcom ate 7/10 of the total chocolates.
What is amount?Amount is a term used to describe the quantity of something, usually a numerical value. It can refer to money, a number of people or objects, or a measurement such as weight or volume. Amounts can also be used to represent a value of something abstract, such as time, effort, or emotion. Amounts are typically quantified, meaning they can be easily compared to other amounts.
The fraction of chocolates that Malcom ate is 5/7 of the milk chocolates and 2/5 of the dark chocolates, so the total fraction of chocolates that Malcom ate is (5/7) + (2/5) = 7/10. Therefore, Malcom ate 7/10 of the total chocolates.
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What would be the answer to this?
Which expression uses the commutative property to make it easier to evaluate (-3/4)x1/5x(-16)?
A. (-3/4)x(-16)x1/5
B. (-16)x1/5x(-3/4)
C. (-3/4)x5/1x(-16)
D. (4/3)x(-16)x1/5
The expression which uses the commutative property to make it easier to evaluate (-3/4)x1/5x(-16) is (-3/4)x(-16)x1/5) which is therefore denoted as option A.
What is Commutative property?
This states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.
In the expression (-3/4)x1/5x(-16) , there is the need to arrange them so as to make it easier for them to be reduced to their lowest factor which is why -16 was put close to the (-3/4).
(-3/4)x(-16)x1/5 = 12 × 1/5 = 12/5
This is therefore the reason why option A was chosen as the correct choice.
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Find the lateral area and total surface area of the rectangular prism. 12in, 7in, 5in
Answer:
The lateral area of the prism is 190 square inches and the total surface area is 358 square inches.
Step-by-step explanation:
To find the lateral area and total surface area of a rectangular prism, we need to use the following formulas:
Lateral Area = perimeter of the base x height
Total Surface Area = 2 x base area + lateral area
Where the base area is simply the product of the length and width of the rectangular prism.
Let's apply these formulas to the rectangular prism with dimensions 12in x 7in x 5in:
Lateral Area:
To find the perimeter of the base, we add up the lengths of all four sides of the rectangle:
Perimeter of the base = 2(length + width) = 2(12in + 7in) = 2(19in) = 38in
Now, we multiply the perimeter of the base by the height of the prism:
Lateral Area = 38in x 5in = 190in^2
Therefore, the lateral area of the rectangular prism is 190 square inches.
Total Surface Area:
To find the base area, we simply multiply the length and width of the rectangular prism:
Base Area = length x width = 12in x 7in = 84in^2
Now, we can use the formula for total surface area:
Total Surface Area = 2 x base area + lateral area
Total Surface Area = 2(84in^2) + 190in^2
Total Surface Area = 168in^2 + 190in^2
Total Surface Area = 358in^2
Therefore, the total surface area of the rectangular prism is 358 square inches.
So the lateral area of the prism is 190 square inches and the total surface area is 358 square inches.
A high school track team's long jump record is 22 ft 6 3/4 in. This year, Arthur's best long jump is 22 ft 5 1/2 in. If long jumps are measured to the nearest quarter inch, how much farther must Arthur jump to break the record?
Answer:
To compare Arthur's long jump to the record, we need to convert both measurements to the same unit. Let's convert both measurements to inches:
Record: 22 ft 6 3/4 in = (22 x 12) + 6 + 3/4 = 270 + 6 + 0.75 = 276.75 in
Arthur's jump: 22 ft 5 1/2 in = (22 x 12) + 5 + 1/2 = 270 + 5 + 0.5 = 275.5 in
To determine how much farther Arthur needs to jump to break the record, we subtract Arthur's jump distance from the record distance:
Record distance - Arthur's jump distance = 276.75 in - 275.5 in = 1.25 in
However, we are told that long jumps are measured to the nearest quarter inch. Therefore, we need to round the difference to the nearest quarter inch. Since 1.25 inches is closer to 1.25 than it is to 1.5, we round down to the nearest quarter inch. This gives us:
1.25 in ≈ 1.25/4 = 0.3125 quarters ≈ 0.25 quarters
Therefore, Arthur needs to jump an additional 0.25 quarters (or 1/16 of an inch) to break the record.
HELPPPPPP DUE TONIGHTTT
The scatter plot shows the number of hours worked, x, and the amount of money spent on entertainment, y, by each of 23 students.
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.
(b) Using your equation from part (a), predict the money spent on entertainment for a student who works 10 hours.
Note that you can use the graphing tools to help you approximate the line.
Answer:
Step-by-step explanation:
A is y=x+4
b is y=14
Problem C:
A farmer has potatoes planted in a large garden.
The field is 14 yards long and 10-yards wide.
What is the area of the farmer's potato garden?
-
Answer:
140 square yards
Step-by-step explanation:
To calculate the area of the farmer's potato garden, we need to multiply the length by the width of the garden.
Area of the potato garden = Length x Width
Given that the length of the potato garden is 14 yards and the width is 10 yards, we can substitute the values into the formula and get:
Area of the potato garden = 14 yards x 10 yards
Area of the potato garden = 140 square yards
Therefore, the area of the farmer's potato garden is 140 square yards.
Answer:140[tex]yards^{2}[/tex]
Step-by-step explanation: to find the area you multiply two different lengths of the rectangle together to get 140
Problem 5: Assume \( A, B, C, D \), and \( X \) are \( n \times n \) matrices, and assume invertibility of matrices whereever needed. Then solve the equation \( A X(B+C X)^{-1}=D \) for \( X \).
The solution for \( X \) is \( X = (A - D C)^{-1} D B \).
Assume \( A, B, C, D \), and \( X \) are \( n \times n \) matrices, and assume invertibility of matrices wherever needed. Then, the equation \( A X(B+C X)^{-1}=D \) can be solved for \( X \) by following these steps:
Step 1: Multiply both sides of the equation by \( (B+C X) \) to get rid of the inverse:
\( A X = D(B+C X) \)
Step 2: Distribute the \( D \) on the right side of the equation:
\( A X = D B + D C X \)
Step 3: Rearrange the equation to isolate \( X \) on one side:
\( A X - D C X = D B \)
Step 4: Factor out \( X \) on the left side of the equation:
\( (A - D C) X = D B \)
Step 5: Multiply both sides of the equation by the inverse of \( (A - D C) \) to solve for \( X \):
\( X = (A - D C)^{-1} D B \)
Therefore, the solution for \( X \) is \( X = (A - D C)^{-1} D B \).
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Please help I'll mark brainliest !
Answer:
x = -3 to x = 2
Step-by-step explanation:
The function is decreasing where the slope is negative, seen when the y-values decrease as the x-values increase. Your answer is correct.
Answer:
X is - 3 to x is 2
Step-by-step explanation:
Look at the x axis, the point where the curve slopes down is the decreasing point
Where x is - 3 is a peak point, it begins to slope from there and rises when x is 3
Determine the time taken when distance is 7150km and the speed is 780 km/hr
Answer:
denote the time by T , distance by S , and the speed by V. We have that S = 7150km, V = 780 km/hr , T= ?.. T = S:V = 7150 : 780 = 9.17
Answer is T = 9.17 hour
Kareem has 216 role playing game cards.His goal is to collect all 15 sets of cards.There are 72 cards in a set.How many more cards does Kareem need to reach his goal?
Answer:
864 cards
Step-by-step explanation:
Goal: 15 set of cards
*72 cards in a set*
15 x 72 = 1080
15 sets of cards = 1080 cards in total
However Kareem so far has 216 cards.
To find out how much more cards Kareem need to reach his goal, you do the following:
1080 - 216 = 864
Kareem needs 864 more cards to reach his goal.
hope this helped....
A deli owner has room for 65 containers of shredded Parmesan cheese. He has 5-oz and 10-oz containers, and a total of 400 oz of cheese. If 5-oz containers sell for $7 and 10-oz containers sell for $13, how many of each should he sell to maximize his revenue? What is his maximum revenue?
He should sell 50 5-oz containers and 15 10-oz containers to maximize his revenue.
What is cοntainer?A cοntainer is a standard unit οf sοftware that packages up cοde and all its dependencies sο the applicatiοn runs quickly and reliably frοm οne cοmputing envirοnment tο anοther. Cοntainers are a sοlutiοn tο the prοblem οf hοw tο get sοftware tο run reliably when mοved frοm οne cοmputing envirοnment tο anοther. This cοuld be frοm a develοper’s laptοp tο a test envirοnment, frοm a staging envirοnment intο prοductiοn, and perhaps frοm a physical machine in a data center tο a virtual machine in a private οr public clοud.
Corner point (x, y) Value of 8x+14y
0(0,0) 0
A(65,0) 520
B(50, 15) 610
C(0,40) 560
So, the maximum value is 610
Therefore, the maximum point is B(50, 15)
∴ x = 50, y = 15
So, the maximum value is
Therefore, the maximum point is
Hence, he should sell 50 5-oz containers and 15 10-oz containers to maximize his revenue.
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if anyone can help me with this and its the right answer i will give brainy please i really need this
Question 11
Which values in the data set are outliers? Show all work.
72, 81, 82, 83, 83, 85, 100, 54, 75, 81, 83
List the following (and show work if needed): Q1, Median, Q3, Lower Fence, Upper Fence, and Outliers
The dataset's median, which has a value of 82 and a total of 11 values, is the sixth figure.
what is median ?When a dataset is ordered from smallest to largest, the median, a measure of central tendency, shows the middle value of the dataset. It is frequently used as a more reliable substitute for the mean, which can be vulnerable to anomalies in the data with extremely high or low values. We must first sort the numbers in a dataset from smallest to largest before we can determine the median. The median is just the middle value when the dataset has an odd number of numbers. For instance, the median, or middle number, in the dataset "2, 5, 7, 10, 12" is 7.
given
Values that are noticeably higher or lower than the remainder of the dataset are found using the fences.
Step 1: Sort the information by size, starting from the smallest:
[tex]54, 72, 75, 81, 81, 82, 83, 83, 83, 85, 100[/tex]
Step 2: Calculate the middle
The dataset's median represents its middle number. The median is the sixth number in the dataset, which contains 11 values total:
Average: 82
Step 3: Determine the first and third quartiles (Q1 and Q3, respectively):
The medians for the dataset's lower and upper halves are Q1 for the lower part and Q3 for the upper. We don't use the median value to determine Q1 and Q3 because the dataset has an odd amount of values.
54, 72, 75, 81, 81 in the bottom half.
Top half: 83, 83, 83, 83, 85, and 100
Q1 = 75 for the bottom half's median.
Q3 = 83 for the top half's median.
The dataset's median, which has a value of 82 and a total of 11 values, is the sixth figure.
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Let X be a random variable having the gamma
distribution with shape parameter α and scale parameter γ, where α is
know and γ is unknown. let Y = σ log X. Show that
(i) if σ > 0 is unknown, then the distribution of Y is in a location-scale
family;
(ii) if σ > 0 is known, then the distribution of Y is in an exponential family.
Compulsory both subparts required .
i) If σ > 0 is unknown, then the distribution of Y is in a location-scale family with the parameters: Location parameter: α and Scale parameter: γ
ii) If σ > 0 is known, then the distribution of Y is in an exponential family with the parameters: Shape parameter: α and Scale parameter: σγ
(i) If σ > 0 is unknown, then the distribution of Y is in a location-scale family. This is because the distribution of Y can be expressed as a linear transformation of the distribution of X. Specifically, Y = σ log X = σ(log X - E[log X]) + E[log X], where E[log X] is the expected value of log X. This is the form of a location-scale family, with location parameter E[log X] and scale parameter σ.
(ii) If σ > 0 is known, then the distribution of Y is in an exponential family. This is because the distribution of Y can be expressed as an exponential family distribution with natural parameter -1/σ and sufficient statistic log X. Specifically, the probability density function of Y can be written as f_Y(y) = f_X(e^(y/σ)) * (1/σ) * e^(y/σ) = (1/σ) * e^(-(y-E[log X])/σ) * f_X(e^(E[log X]/σ)), where f_X is the probability density function of X. This is the form of an exponential family distribution, with natural parameter -1/σ and sufficient statistic log X.
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Properties of Rhombi/Rhombus
Please show your work !
The properties of Rhombus are:
Opposite angles are equalConsecutive anglesDiagonals bisect each otherDiagonals are perpendicularSymmetryAreaPerimeterExplain about parallelogram ?
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure.
Properties of a parallelogram:
Opposite sides are parallel.
Opposite sides are equal in length.
Opposite angles are equal in measure.
Consecutive angles are supplementary, i.e. their sum is 180 degrees.
Diagonals bisect each other.
Given by the question:
A rhombus, also called a diamond, is a type of parallelogram in which all four sides are equal in length. A rhombus also has the following properties:
Opposite angles are equal: The opposite angles of a rhombus are equal in measure. This means that if angle A is equal to angle C, and angle B is equal to angle D.Consecutive angles are supplementary: The consecutive angles of a rhombus are supplementary, meaning they add up to 180 degrees. For example, if angle A is equal to 80 degrees, then angle B is equal to 100 degrees.Diagonals bisect each other: The diagonals of a rhombus bisect each other at right angles, dividing the rhombus into four congruent right triangles. In other words, the line segment connecting the midpoint of one side to the midpoint of an adjacent side is perpendicular to the line segment connecting the midpoints of the other two sides.Diagonals are perpendicular: The diagonals of a rhombus are perpendicular bisectors of each other, meaning they cut each other at right angles.Symmetry: A rhombus has two lines of symmetry that run through the opposite vertices and bisect the opposite sides.Area: The area of a rhombus can be found by multiplying the length of one diagonal by the length of the other diagonal and dividing by 2. That is, Area = (d1 x d2)/2, where d1 and d2 are the lengths of the diagonals.Perimeter: The perimeter of a rhombus is equal to four times the length of one of its sides. That is, Perimeter = 4s, where s is the length of one side.To know more about parallelogram visit:
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Find the total surface area of a large round bowl (hollow hemisphere) with outer radius of 12 cm and thickness of 1 cm. 1cm 12cm
The total surface area of the hollow hemisphere is 1736.4 cm²
The total surface area of a large round bowl (hollow hemisphere) can be calculated by finding the surface area of the outer hemisphere and the surface area of the inner hemisphere and area of the ring and adding them together.
The formula for the surface area of a hemisphere is 2πr^2, where r is the radius of the hemisphere.
The outer radius of the bowl is 12 cm, so the surface area of the outer hemisphere is:
Surface area of outer hemisphere = 2π(12)^2 = 2π(144) = 288π
The inner radius of the bowl is the outer radius minus the thickness, which is 12 - 1 = 11 cm. So the surface area of the inner hemisphere is:
Surface area of inner hemisphere = 2π(11)^2 = 2π(121) = 242π
area of the concentric circle joining the outer surface and inner surface is π(12²-11²)= 23π
The total surface area of the bowl is the sum of the surface area of the outer hemisphere and the surface area of the inner hemisphere:
Total surface area = 288π + 242π + 23π = 553π
So the total surface area of the bowl is 530π cm^2.
then we can use the approximation π ≈ 3.14 to find the total surface area:
Total surface area ≈ 553*(3.14) ≈ 1736.4 cm^2
So the total surface area of the bowl is approximately 1736.4 cm^2.
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The length of a radius is three-fourths the height of a cone. The surface area is 3750
square units.
What are the height and the radius of the cone?
The height of the cone is approximately 28.867 units and the radius is approximately 21.65 units.
How to Find the Height and Radius of a Cone?Let's denote the height of the cone as "h" and the radius as "r".
From the problem statement, we know that:
r = (3/4)h ...(1) (given)
The surface area of the cone is given as 3750 square units. The formula for the surface area of a cone is:
Surface Area of Cone = πr(r + l),
where "l" is the slant height of the cone. Since the slant height is not given in the problem, we need to express "l" in terms of "r" and "h" using the Pythagorean theorem:
l² = r² + h²
l² = (3/4)² h² + h²
l² = (9/16)h² + h²
l² = (25/16)h²
l = (5/4)h
Substituting this expression for "l" and the expression for "r" from equation (1) into the surface area formula, we get:
3750 = πr(r + l)
3750 = π[(3/4)h] [(3/4)h + (5/4)h]
3750 = π (9/16 + 15/16) h²
3750 = π (24/16) h²
3750 = (3/2) π h²
h² = (2500/3π)
h ≈ 28.867
Substituting this value of "h" into equation (1), we get:
r = (3/4)h
r ≈ 21.65
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Answer: Radius 37.5 & height 50
Step-by-step explanation: correct in edmuntum/plato
omework: 2.1 tion list Solve the following equation and check. (x)/(7)+(x)/(9)=(9)/(14)
We have that, given the equation (x)/(7)+(x)/(9)=(9)/(14) we will get as an answer x = 567/224
To solve the equation (x)/(7)+(x)/(9)=(9)/(14), we need to find the common denominator of the fractions on the left-hand side of the equation. The common denominator of 7 and 9 is 63, so we can multiply each fraction by the appropriate factor to get the common denominator:
[tex](x)/(7) * (9)/(9) + (x)/(9) * (7)/(7) = (9)/(14)[/tex]
[tex](9x)/(63) + (7x)/(63) = (9)/(14)[/tex]
Now we can combine the numerators on the left-hand side of the equation:
[tex](16x)/(63) = (9)/(14)[/tex]
To isolate the variable x, we can cross-multiply and then divide by the coefficient of x:
[tex](16x)(14) = (9)(63)[/tex]
[tex]224x = 567[/tex]
[tex]x = 567/224[/tex]
To check our answer, we can plug it back into the original equation and simplify:
[tex](567/224)/(7) + (567/224)/(9) = (9)/(14)[/tex]
[tex](567/224) * (1/7) + (567/224) * (1/9) = (9)/(14)(567/1568) + (567/2016) = (9)/(14)(1275752 + 1140480)/(3167232) = (9)/(14)(2416232)/(3167232) = (9)/(14)(9)/(14) = (9)/(14)[/tex]
Since both sides of the equation are equal, our answer is correct.
Answer: [tex]x = 567/224[/tex]
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In 2010, bachelor's degrees conferred by colleges and universities in the United States were 1.2 million. In 2020, the number of bachelor's degrees awarded was 1.7 million.
Assume that the relationship between time and degree conferred is linear.
(a) Find an equation describing the number N bachelor's degrees awarded t years after 2010
(b) If the trend continues, estimate the number of bachelor's degrees to be awarded in 2023.
(c) Write a practical sentence expressing how the number of bachelor's degrees awarded changes yearly.
(d) Graph the number of bachelor's degree line over the time period stated in (a)
The equation that describe the number N bachelor's degrees awarded is N = 0.05t + 1.2 (a). The estimated number of bachelor's degrees to be awarded in 2023 is 1.85 million (b).
The practical sentence is "The number of bachelor's degrees awarded increases by 0.05 million, or 50,000, each year." (c). The graph, see the attachment.
The Explanation to Each Answer(a) To find the equation describing the number N of bachelor's degrees awarded t years after 2010, we can use the formula for a linear equation: N = mt + b, where m is the slope and b is the y-intercept.
We can find the slope by using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. In this case, the two points are (2010, 1.2 million) and (2020, 1.7 million).
The y-intercept is the value of N when t = 0, which is the number of bachelor's degrees awarded in 2010, or 1.2 million. So the equation is:
N = 0.05t + 1.2(b) To estimate the number of bachelor's degrees to be awarded in 2023, we can plug in the value of t = 2023 - 2010 = 13 into the equation:
N = 0.05(13) + 1.2N = 0.65 + 1.2N = 1.85 millionSo the estimated number of bachelor's degrees to be awarded in 2023 is 1.85 million.
(c) A practical sentence expressing how the number of bachelor's degrees awarded changes yearly is: "The number of bachelor's degrees awarded increases by 0.05 million, or 50,000, each year."
(d) To graph the number of bachelor's degree line over the time period stated in (a), we can plot the two points (2010, 1.2) and (2020, 1.7) and draw a line through them.
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please help. Shape Y is an enlargement of shape X by a scale factor of 3. Work out lengths a and b. no
Answer:
a = 3, b = 9
Step-by-step explanation:
What is a scale factor?A scale factor is the number that you multiply each side of a shape to enlarge it. A scale factor of 3 means that each side of the new shape is three times the size of the original.
If the new shape is 3 times the size of the original, then we can take the side lengths (3 and 1) and multiply them by 3.
3 × 1 = 3 (side a)3 × 3 = 9 (side b)Therefore, the length of a is 3, whereas the length of b is 9.
given an "Armfield pump rig" to find the characteristics and efficiency of a pump experimentally. In this context, the pump is an energy converter that converts electrical power into hydraulic power.
the sample points are logged with a constant setting of rotational speed (angular velocity). power data is registered along the way - electric power into the electric motor, pressure from the pump and volume flow during throttling of the water flow out of the pump.
given data from EXCELbelow:
use EXCEL to solve the questions below, and explain step by step procedure
a) Calculate effects and efficiencies for all operating points.
b) Create a graph showing the delivery pressure (Pa) ("Pump 1") as a function of volume flow (Flow Rate Q) in (m3 / s)
c) Create a graph showing motor power (Pump 1) (W) as a function of volume flow (Flow Rate) Q (l / s) on an axis and efficiency (Pump 1 (%) on a secondary axis
To calculate the effect of the pump, use the formula: P = Q * ΔP / η and To calculate the efficiency of the pump, use the formula: η = P / P_e. Use the data provided in the EXCEL file.
To solve the questions, follow these steps:
a) Calculate effects and efficiencies for all operating points:
1. To calculate the effect of the pump, use the formula: P = Q * ΔP / η, where P is the power of the pump, Q is the volume flow rate, ΔP is the pressure difference across the pump, and η is the efficiency of the pump.
2. To calculate the efficiency of the pump, use the formula: η = P / P_e, where P is the power of the pump, and P_e is the electrical power input to the pump.
3. Use the data provided in the EXCEL file to calculate the effects and efficiencies for all operating points.
b) Create a graph showing the delivery pressure (Pa) ("Pump 1") as a function of volume flow (Flow Rate Q) in (m3 / s):
1. Select the data for the delivery pressure (Pa) and volume flow (Flow Rate Q) in the EXCEL file.
2. Click on the "Insert" tab in EXCEL and select the "Scatter" chart option.
3. Choose the "Scatter with Straight Lines" option to create a graph showing the delivery pressure (Pa) as a function of volume flow (Flow Rate Q).
c) Create a graph showing motor power (Pump 1) (W) as a function of volume flow (Flow Rate) Q (l / s) on an axis and efficiency (Pump 1 (%) on a secondary axis:
1. Select the data for the motor power (Pump 1) (W) and volume flow (Flow Rate) Q (l / s) in the EXCEL file.
2. Click on the "Insert" tab in EXCEL and select the "Scatter" chart option.
3. Choose the "Scatter with Straight Lines" option to create a graph showing the motor power (Pump 1) (W) as a function of volume flow (Flow Rate) Q (l / s).
4. Add a secondary axis to the graph by clicking on the "Format" tab in EXCEL and selecting the "Secondary Axis" option.
5. Select the data for the efficiency (Pump 1 (%) and add it to the secondary axis of the graph.
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Natasha wants to average at least 90% in math class. Her test scores so far are 94%, 89%,88%,92%, and 85% What score does she need to earn on her next test to reach her goal
Answer:
Let x be the score Natasha needs to earn on her next test to reach an average of 90%.
To find x, we can use the formula for the average:
average = (sum of scores) / (number of scores)
We know that Natasha has taken 5 tests so far, with scores of 94%, 89%, 88%, 92%, and 85%. We can plug these values into the formula and solve for x:
90% = (94% + 89% + 88% + 92% + 85% + x) / 6
Multiplying both sides by 6, we get:
540% = 448% + x
Subtracting 448% from both sides, we get:
92% = x
Therefore, Natasha needs to earn a score of at least 92% on her next test to reach an average of 90%.
Help please ill give everything and good amount of points , please see the image( solve for the missing angle. Round to the nearest degree
Answer:
Step-by-step explanation:
where is the image don't see
Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?
Which of the following equations could be used to solve the problem?
A.n + 4 n = 210
B.5 n + 100 n = 210
C.n + 4 n = 2.10
D.5 n + 100 n = 2.10
The algebraic equation that could be used to solve the problem is C. n + 4n = 2.10.
What is the algebraic equations?An algebraic equation is a mathematical statement that represents the equality of two expressions, using one or more variables, and mathematical operations such as addition, subtraction, multiplication, and division.
To solve this problem, we can use algebraic equations. Let's use the variable "n" to represent the number of nickels that Peggy has.
From the problem statement, we know that Peggy has four times as many quarters as nickels, which means she has 4n quarters.
We also know that she has a total of $2.10 in all. The value of her nickels is 0.05n dollars each, and the value of her quarters is 0.25(4n) = n dollars each. So we can set up the following equation:
0.05n + 0.25(4n) = 2.10
Simplifying this equation, we get:
0.05n + n = 0.525
1.05n = 2.10
n = 2
Therefore, Peggy has 2 nickels and 4(2) = 8 quarters.
Hence, the equation that could be used to solve the problem is C. n + 4n = 2.10.
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Collins Middle School has 228 sixth grade students. If the sixth grade is 30% of the total school, how many students are in the middle school?
Answer:
760 students
Step-by-step explanation:
divide 228 ÷ 30%
30% = 0.30
228 ÷ 0.30 = 760
A snowboard has a price of $800. With sales tax, it will cost $848. What is the sales tax percentage?
As a result, there is a 6% sales tax.
What do the percentages mean?Percentages is a relative figure used to represent hundredths of a quantity. Because one percent (symbolised as 1%) represents one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage. Percentile is a related topic in mathematics.
The difference in sales tax is the price of the snowboarder with tax versus the price of the snowboarder without tax.
Sales tax therefore equals $848 - $800 = $48.
We need to multiply the result by 100 to get the sales percentage of tax, which we can then divide by the price of the snowboard before taxes.
Sales tax percentage = (Sales tax / Cost without tax) x 100
= ($48 / $800) x 100
= 0.06 x 100
= 6%
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Which of these rules are functions on an appropriate domain? Select all that apply.
$\vspace{.05in}$
$A$ inputs a real number, subtracts $100$, then outputs the square root of the result if it is real.
${}B$ inputs a date, then outputs the name of a person born on that date.
$C$ inputs a real number $x$, then outputs a real number $y$ that is less than $\frac{1}{1000}$ larger than $x$. $\smallskip$
$D$ inputs a real number $x$, then outputs the result of the calculation $\dfrac{x^2-1}{(x-1)(x+1)}$.
$E$ inputs a real number $x$, then a coin is flipped. If the coin flips heads, the output is $x+2$. If the coin flips tails, the output is $x+3$.
$F$ inputs a person, then outputs their birth date.
D and F are functions on an appropriate domain. A, C, and D are functions that take in a real number and output a real number, so they are valid functions on the domain of real numbers.
What is domain?A domain is a set of names or IP addresses that are associated with a particular website or web server. It is what allows users to access a website's content using a web browser. Domains are typically purchased from a domain registrar and can be used to host websites, email accounts, and other services.
B and F are invalid functions because they take in a real number and output something that is not a real number.
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Benjamin's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=8x+57 where y represents the expected quiz score and x represents hours spent on homework that week. What is the meaning of the x-value when y = 98?
When the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours.
What is the linear equation in two variables?
A linear equation in two variables is an equation of the form:
ax + by = c
where x and y are variables, a, b, and c are constants, and a and b are not both zero. The graph of a linear equation in two variables is a straight line, and any point on the line satisfies the equation.
The given equation is:
y = 8x + 57
where y is the quiz score and x is the hours spent on homework.
To find the meaning of the x-value when y = 98, we can substitute y = 98 into the equation and solve for x:
98 = 8x + 57
Subtracting 57 from both sides, we get:
41 = 8x
Dividing both sides by 8, we get:
x = 5.125
when the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours. This suggests that students who spend around 5 hours and 7.5 minutes on homework per week can expect to score around 98 on their weekly quiz.
Therefore, when the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours.
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Problem \# 6: Let R^4 have the Euclidean inner product. Find a unit vector with a positive first component that is orthogonal to all three of the following vectors. u = (1,-1, 7, 0) ; v=(8,1,0,1) ; w=(1,0,6,1)
Problem \#6: Enter your answer symbolically, as in these Enter the four components of your vector, separated with commas.
To find a unit vector with a positive first component that is orthogonal to all three of the given vectors, we need to find a vector x = (x1, x2, x3, x4) that satisfies the following equations:
= 0
= 0
= 0
This means that:
x1 - x2 + 7x3 = 0
8x1 + x2 + x4 = 0
x1 + 6x3 + x4 = 0
We can solve this system of equations to find x. One possible solution is x = (1, -1, 0, 1). However, this is not a unit vector, so we need to divide each component by the length of the vector to get a unit vector:
x = (1, -1, 0, 1) / ||(1, -1, 0, 1)|| = (1/sqrt(3), -1/sqrt(3), 0, 1/sqrt(3))
So, the unit vector with a positive first component that is orthogonal to all three of the given vectors is (1/sqrt(3), -1/sqrt(3), 0, 1/sqrt(3)).
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