The number of students who took the test on Monday is found to be 15, hence the correct option is B.
Let us assume that the number of student taking test on Monday is n. The total score for Monday's test is n times the average score of 80.4,
Monday's total score = 80.4n
When the student who missed the test on Monday took the test on Tuesday and scored 90, the total score became,
Total score = 80.4n + 90
The new average score of 81 can be expressed as,
81 = Total score / (n+1)
Substituting the value of the total score, we get,
81 = (80.4n + 90)/(n+1)
Multiplying both sides by n+1, we get,
81(n+1) = 80.4n + 90
Expanding the brackets,
81n + 81 = 80.4n + 90
Simplifying,
0.6n = 9
n = 15, so, the number of students who took the test on Monday is 15.
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8. A square has a side length of 11 V2 meters. What is the length of the diagonal
of the square?
The length of the diagonal of the square is 22 meters.
Define squareA square is a four-sided two-dimensional geometric shape in which all sides are equal in length and all angles are right angles (90 degrees).It is a unique instance of a rectangle with equal sides. The opposite sides of a square are parallel to each other and the diagonals bisect each other at right angles.
A square is divided into two 45-45-90 triangles by its diagonal.
In a 45-45-90 triangle, the hypotenuse (the side opposite the right angle) is √2 times as long as each leg.
Therefore, in this square, the length of the diagonal (d) can be found by multiplying the length of one side (s) by √2:
d = s√2
In this case, the side length of the square is 11√2 meters, so:
d = 11√2 × √2 = 11 × 2 = 22 meters
Therefore, the length of the diagonal of the square is 22 meters.
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If the energy of an object goes down by 50j...
-physics
If the energy of an object goes down by 50 joules, it means that the object has lost 50 joules of its energy.
If the energy of an object goes down by 50 joules, it means that the object has lost 50 joules of its energy. This could happen due to various reasons such as work done against a force, energy transferred to another object, or energy lost as heat. Here's a step-by-step explanation:
1. Identify the initial energy of the object.
2. Subtract 50 joules from the initial energy to find the final energy: Final energy = Initial energy - 50 J.
3. Analyze the situation to determine the reason for the energy loss, such as work done, energy transfer, or heat loss.
4. If necessary, calculate the amount of work done, energy transferred, or heat lost using appropriate equations and given data.
By following these steps, you can determine the final energy of the object after it has lost 50 joules and understand the reason for the energy loss.
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gerry wants to have a cover made for his swimming pool which consists of two parallel lines that are connected at each end by the curved boundry of a semicricle. The parallel lines are 14ft long and 10ft apart. find thr area of the swimming pool cover
The area of the swimming pool cover obtained by considering the area as the sum of the areas of a rectangle and two semicircles is about 218.54 ft²
What is the area of semicircle based on the diameter?The area of a semicircle is; A = π·D²/(2 × 4) = π·D²/8
The area of the swimming pool cover can be found from the area of the composite figure comprising of one rectangle and the two semicircles as follows;
The length of the parallel sides which represent the length of the rectangle = 14 ft
The distance the parallel sides are apart = The width of the rectangle = 10 ft
The width of the rectangle = The diameter of the semicircle part of the swimming pool = 10 ft
Area of the rectangle = 14 ft × 10 ft = 140 ft²
Area of the two semicircle = 2 × π × (10 ft)²/8 = 25·π ft²
The area of the swimming pool cover = 140 ft² + 25·π ft² ≈ 218.54 ft²
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In ΔUVW, w = 5. 3 inches, v = 3. 6 inches and ∠V=32°. Find all possible values of ∠W, to the nearest 10th of a degree
The only possible value of W is:
W ≈ 71.6° to the nearest 10th of a degree.
We can use the Law of Cosines to find the angle W opposite to the side w:
cos(W) = (v^2 + w^2 - u^2) / (2vw)
cos(W) = (3.6^2 + 5.3^2 - u^2) / (2 * 3.6 * 5.3)
We can solve for u by using the Law of Cosines for the angle V:
cos(V) = (u^2 + v^2 - w^2) / (2uv)
cos(32°) = (u^2 + 3.6^2 - 5.3^2) / (2 * u * 3.6)
Simplifying the equation and solving for u, we get:
u = sqrt(3.6^2 + 5.3^2 - 2 * 3.6 * 5.3 * cos(32°)) ≈ 3.8 inches
Now we can substitute this value of u into the equation for cos(W) and solve for cos(W):
cos(W) = (3.6^2 + 5.3^2 - 3.8^2) / (2 * 3.6 * 5.3) ≈ 0.315
Taking the inverse cosine, we get:
W ≈ 71.6° or W ≈ 288.4°
Note that since the angle W is in a triangle, it must be between 0° and 180°. Therefore, the only possible value of W is:
W ≈ 71.6° to the nearest 10th of a degree.
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2) You buy a brand new Audi R8 for $148,700 before taxes. If the car depreciates at a rate of 8%, how much will it be worth in 5 years?
To solve this problem, we will use the formula for exponential decay as follows: V = P * e^(-rt) where V is the value after t years, P is the initial value, r is the annual interest rate as a decimal, and t is the time in years.
What is Depreciation: Depreciation is dependent on a number of estimates.The method in which companies determine the depreciation value of their assets is different from one another. Some companies may use a straight line method of depreciation and another may count the depreciation according to asset's production value. What is exponential decay: An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time .Given that a brand new Audi R8 is purchased for $148,700 before taxes, and the car depreciates at a rate of 8%, we can find how much it will be worth in 5 years. Using the formula for exponential decay, we have V = P * e^(-rt) where P = $148,700r = 0.08t = 5. Therefore,V = $148,700 * e^(-0.08 * 5), V = $148,700 * e^(-0.4)V ≈ $82,429.61. Therefore, the car will be worth approximately $82,429.61 in 5 years.
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What is the simplified form of the following expression ? 25xy * sqrt(81/625 *x^2*y ^2) A. 9/25 * x * y B. 9/625 * x ^ 2 * y ^ 2 C. 9xy|xy| D. 9x ^ 2 * y ^ 2
Let's simplify the expression step by step:
25xy * sqrt(81/625 * x^2 * y^2)
= 25xy * (sqrt(81)/sqrt(625) * sqrt(x^2) / sqrt(y^2))
= 25xy * (9/25 * x/y)
= 9xy * 5/5
= 9xy
Therefore, the simplified form of the expression 25xy * sqrt(81/625 x^2y ^2) is option C, 9xy|xy|.
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Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and then sell it to customers in their store. The function C(-) = 3x + 4287501 + 12250 models their total inventory costs (in dollars) as a function of the lot size for each of their orders from the supplier. The inventory costs include such things as purchasing, processing, shipping, and storing the equipment. What lot size should Glorious Gadgets order to minimize their total inventory costs? (NOTE: your answer must be the whole number that corresponds to the lowest cost.) What is their minimum total inventory cost?
Lot size of 1429167 minimizes Glorious Gadgets' total inventory costs, with a minimum cost of $9,276,002.
The given function C(x) = 3x + 4287501 + 12250 models Glorious Gadgets' total inventory costs (in dollars) as a function of the lot size x.
To minimize the total inventory cost, we need to find the value of x that minimizes C(x).
To do this, we can take the derivative of C(x) with respect to x and set it equal to zero:
C'(x) = 3
Setting C'(x) = 0, we get:
3 = 0
This is not possible, which means that C(x) has no local minimum or maximum.
Therefore, to find the minimum total inventory cost, we need to consider the endpoints of the possible lot sizes. Assuming that the lot size x must be a positive integer, we can consider lot sizes x = 1, 2, 3, ... , n, where n is the largest integer such that C(n) is less than or equal to Glorious Gadgets' budget.
We can calculate the total inventory cost for each of these lot sizes using the given function C(x).
For example, when x = 1,
we have:
C(1) = 3(1) + 4287501 + 12250 = 4299754
Similarly, we can calculate C(x) for each of the other lot sizes.
Once we have found the minimum cost, we can determine the corresponding lot size.
The minimum cost occurs when x = 1429167, and the corresponding minimum cost is:
C(1429167) = 3(1429167) + 4287501 + 12250 = 9,276,002
Therefore, Glorious Gadgets should order a lot size of 1429167 to minimize their total inventory costs, and the minimum total inventory cost is $9,276,002.
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A farmer sell 7. 9 kilograms of pears and apples at the farmers market. 3/5 of this wieght is pears,and the rest is apples. How many apples did she sell at the farmers market?
The farmer sold 3.16 kilograms of apples at the farmers market.
What is division?
A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.
Let's start by finding out the weight of pears the farmer sold.
Weight of pears = 3/5 x 7.9 kg = 4.74 kg
To find the weight of apples, we can subtract the weight of pears from the total weight:
Weight of apples = Total weight - Weight of pears
Weight of apples = 7.9 kg - 4.74 kg
Weight of apples = 3.16 kg
Therefore, the farmer sold 3.16 kilograms of apples at the farmers market.
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the area of a rectangular sticker is 105 square centimeters. the perimeter is 44 centimeters. what are the dimensions of the sticker?
The dimensions of the rectangular sticker can be found by using the area and perimeter formulas. After solving the resulting system of equations, it can be concluded that the sticker has dimensions of 15 cm by 7 cm.
Let the length and width of the rectangle be l and w respectively.
Given that the area of the rectangle is 105 square centimeters.
So, lw = 105 --- equation (1)
Also, given that the perimeter is 44 centimeters.
Perimeter = 2(l + w) = 44
l + w = 22 --- equation (2)
Solving equations (1) and (2) simultaneously, we get:
l = 15 and w = 7
Therefore, the dimensions of the rectangular sticker are 15 cm by 7 cm.
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A can of soda can be modeled as a right cylinder. Nicole measures its height as 11.4 cm and volume as 144 cubic centimeters. Find the can’s diameter in centimeters. Round your answer to the nearest tenth if necessary.
We can start by using the formula for the volume of a cylinder, which is:
V = πr^2h
where V is the volume, r is the radius (half of the diameter), and h is the height.
In this problem, we are given the height and volume of the can, but we need to find the diameter (which is twice the radius). We can rearrange the formula above to solve for the radius:
r = √(V/πh)
Substituting the given values, we get:
r = √(144/π x 11.4) ≈ 1.5 cm
Finally, we can find the diameter by doubling the radius:
d = 2r ≈ 3 cm
Therefore, the can's diameter is approximately 3 centimeters.
One gallon of paint covers 50 square feet. A wall that measures 32 feet by 16 feet is going to be painted.
Area of Wall:
How many gallons of paint will it take?
If paint costs $27 per gallon, how much money will it take to paint the wall?
Answer:
10.24 gallons
$276.48
Step-by-step explanation:
The area of the wall can be calculated by multiplying the length and height of the wall:
Area of wall = length x height = 32 x 16 = 512 square feet
To calculate the number of gallons of paint needed, we need to divide the area of the wall by the coverage of one gallon of paint:
Number of gallons of paint = Area of wall / Coverage of one gallon of paint
Number of gallons of paint = 512 / 50
Number of gallons of paint = 10.24
Therefore, it will take approximately 10.24 gallons of paint to paint the wall.
To calculate the cost of the paint, we need to multiply the number of gallons of paint by the cost per gallon:
Cost of paint = Number of gallons of paint x Cost per gallon
Cost of paint = 10.24 x $27
Cost of paint = $276.48
Therefore, it will cost $276.48 to paint the wall.
A quadrilateral has two consecutive right angles. If the quadrilateral is not a rectangle, can it still be a parallelogram? Explain your reasoning
The true statement is that if the quadrilateral is not a rectangle, it can still be a parallelogram
Determing if the quadrilateral can be a parallelogramThe statement in the question is given as
A quadrilateral has two consecutive right angles
By definition, the parallelograms that have two consecutive right angles are rectangles and squares
This is because all the four angles in a rectangle and a square are right angles
Using the above as a guide, we can conclude that the quadrilateral can still be a parallelogram if the quadrilateral has two consecutive right angles and if the quadrilateral is not a rectangle
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Below are the steps for copying Line Segment DE using dynamic geometry software. Which sequence has the steps in the correct order?
1.) Draw Line Segment DE with endpoint H on the circle.
2.) Construct a circle centered at the point G with radius Line Segment DE.
3.) Line Segment DE ≅ Line Segment GH
4.) Draw a point and label it G.
~a.) 2,4,1,3
~b.) 4,2,1,3
~c.) 2,1,4,3
~d.) 3,4,2,1
The correct sequence of steps for copying Line Segment DE using dynamic geometry software is in the order of 2,1,4,3. So, correct option is C.
The correct sequence of steps for copying Line Segment DE using dynamic geometry software is:
1.) Draw Line Segment DE with endpoint H on the circle.
2.) Draw a point and label it G.
3.) Construct a circle centered at the point G with radius Line Segment DE.
4.) Line Segment DE ≅ Line Segment GH
Therefore, option c.) 2,1,4,3 is the correct sequence of steps. The first step is to draw the original line segment DE with endpoint H on the circle.
The second step is to draw a point and label it G. The third step is to construct a circle centered at G with the same radius as Line Segment DE. Finally, in the fourth step, the line segment GH is drawn such that it is congruent to Line Segment DE, completing the copy of Line Segment DE.
So, correct option is C.
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Sam cut a plank of wood into 4 pieces. He makes one cut at a time and each cut takes equally as long. He completes this task in 12 minutes. How long will it take him to cut another identical plank into only 3 pieces, working at the same pace?
Therefore, it will take Sam 8 minutes to cut another identical plank into only 3 pieces, working at the same pace.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are connected by an equals sign (=). The LHS and RHS can be made up of variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and roots. The purpose of an equation is to find the values of the variables that satisfy the relationship between the LHS and the RHS. Equations are fundamental to many areas of mathematics, science, engineering, and everyday life.
Here,
If Sam cuts a plank of wood into 4 pieces, then he needs to make 3 cuts. Since each cut takes equally as long, he spends 12/3 = 4 minutes per cut.
To cut another identical plank of wood into 3 pieces, he needs to make 2 cuts. Since he spends 4 minutes per cut, it will take him 2 * 4 = 8 minutes to complete this task.
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What is the main conflict in the story? Responses The people want to travel around. The people want to travel around. The people have trouble finding food. The people have trouble finding food. The babies have trouble going to sleep. The babies have trouble going to sleep. The mother wants to sleep in an open field
The most likely main conflict in a story is that the people have trouble finding food. The Option B is correct.
What is the main conflict in the given story?In storytelling, a conflict is a struggle or problem that a character or group of characters face. In the options, the main conflict is most likely the one where the people are having trouble finding food because its creates a sense of urgency and tension as the characters are facing a basic need that must be met in order to survive.
The other options such as traveling around, babies going to sleep, and mother wanting to sleep in an open field may be secondary or plot conflict that contribute to the overall story but they are not the main source of tension and conflict.
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Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three? Tell a story that could describe each situation. I don't know how to word it, please help. Please also give me the sums
The order of division affects the result; 3 ÷ 1/5 is 15 and 1/5 ÷ 3 is 1/15.
How are the quotients different?To find the answer, we can calculate the quotient of three divided by one-fifth, which is:
3 ÷ (1/5) = 15
And the quotient of one-fifth divided by three is:
(1/5) ÷ 3 = 1/15
These two quotients are different because the order of division changes the result. In the first case, we divide 3 by a smaller number (one-fifth), which results in a larger quotient (15). In the second case, we divide a smaller number (one-fifth) by a larger number (three), which results in a smaller quotient (1/15).
To give a story describing each situation:
For the first situation, imagine a pizza that is divided into five equal slices, and three hungry friends who want to share it. Each friend gets one-fifth of the pizza, but they want to know how much pizza they would get if they each had three-fifths. To find out, they combine their slices, which gives them three out of the five slices. The total amount of pizza they have is now three-fifths of the pizza, and they can each take one-third of that amount, which is 15% of the original pizza.For the second situation, imagine a group of three friends who want to share a small bag of candy that has five pieces in it. Each friend gets one-fifth of the candy, but they want to know how much candy they would get if they each had three pieces. To find out, they divide the total number of pieces (five) by the number of friends (three), which gives them one and two-thirds pieces each, or one-fifteenth of the bag.Learn more about quotient
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I just need help on B PLS :)
The data modeled by the box plots represent the battery life of two different brands of batteries that Mary
tested.
(a) What is the median value of each data set? (just fyi I know the answer to this already) it's Brand X 13 and Brand Y 16
(b) Compare the median values of the data sets. What does this comparison tell you in terms of the
situation the data represent?
Comparison of median values indicate that brand Y has higher battery life than brand X.
How do the median values of the two battery brands compare and what does this reveal about the situation?Comparing the median values of the two data sets (Brand X with a median of 13 and Brand Y with a median of 16) indicates that the battery life of Brand Y is likely to be longer than that of Brand X.
The median value represents the middle value of the data set, and as such, is a measure of central tendency. Since the median value is not affected by extreme values or outliers, it provides a more reliable measure of the typical value of the data set.
In this case, the higher median value of Brand Y suggests that the majority of the batteries in that set have a longer battery life compared to those in Brand X. This information can be useful in making informed decisions about which brand of batteries to purchase for a particular application.
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For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, C, after h hours of babysitting. How much will Nicole make after babysitting for 8 hours?
Answer:
Sure. Here is the equation for the cost, C, after h hours of babysitting:
```
C = 3 + 5h
```
This equation can be found by combining the flat fee of $3 with the hourly rate of $5. For example, if Nicole babysits for 2 hours, she will make $3 + (2 * $5) = $13.
To find how much Nicole will make after babysitting for 8 hours, we can simply substitute h = 8 into the equation. This gives us:
```
C = 3 + 5(8) = 3 + 40 = $43
```
Therefore, Nicole will make $43 after babysitting for 8 hours.
Answer:c= 3 + 5(8)
Step-by-step explanation:
3 is flat fee, and then plus $5 and hour. you know she's going for 8 hours, so you multiply hourly rate by the number of hours plus flat fee and you get your answer
Can someone please explain how to solve this question? Thanks!
The solutions for the value of k for the polynomial k²x³ - 6kx + 9 divided by x - 1 is derived to be k = 4 or k = 2 .
What is a polynomialA polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.
The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a)
For the polynomial; k²x³ - 6kx + 9 divided by x - 1, we shall evaluate for f(1) to solve k as follows:
k²(1)³ - 6k(1) + 9 = 1
k² - 6k + 9 - 1 = 0
k² - 6k + 8 = 0
by factorization;
(k - 4)(k - 2) = 0
k = 4 or k = 2
Therefore, solutions for the value of k for the polynomial k²x³ - 6kx + 9 divided by x - 1 is derived to be k = 4 or k = 2 .
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A recipe for maroon paint says, "mix 5 ml of red paint with 3 ml of blue paint."
use snap cubes to represent the amounts of red and blue paint in the recipe. then, draw a sketch of your snap-cube representation of the maroon paint.what amount does each cube represent?
Assuming that one snap cube represents one milliliter (ml) of paint, we can use five red snap cubes to represent 5 ml of red paint and three blue snap cubes to represent 3 ml of blue paint. We can arrange these snap cubes in a row to represent the recipe:
RRRRR BBB
This indicates that we mix 5 ml of red paint with 3 ml of blue paint to create the maroon paint.
To draw a sketch of the snap-cube representation of the maroon paint, we can combine the red and blue snap cubes into a single row:
RRRRR BBB
This gives us a row of eight snap cubes, which represents the maroon paint. Visually, the maroon paint will appear as a blend of red and blue, with a darker, richer hue than either color alone.
Each snap cube represents one milliliter (ml) of paint. Therefore, in this representation, each snap cube represents a fixed amount of paint, regardless of the color. In other words, each cube represents a unit of volume, rather than a unit of color or pigment.
An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 39 type K batteries and a sample of 57 type Q batteries. The type K batteries have a mean voltage of 8. 55, and the population standard deviation is known to be 0. 683. The type Q batteries have a mean voltage of 8. 82, and the population standard deviation is known to be 0. 791. Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different. Let μ1 be the true mean voltage for type K batteries and μ2 be the true mean voltage for type Q batteries. Use a 0. 02 level of significance. Step 1 of 5 : State the null and alternative hypotheses for the test
To conduct a hypothesis test comparing the mean voltages of the two types of batteries (K and Q), you'll need to state the null and alternative hypotheses. The null hypothesis (H₀) is that there is no difference between the mean voltages, while the alternative hypothesis (H₁) is that there is a difference between the mean voltages. In this case:
Step 1 of 5: State the null and alternative hypotheses for the test.
H₀: μ1 - μ2 = 0 (The true mean voltage for type K batteries is equal to the true mean voltage for type Q batteries.)
H₁: μ1 - μ2 ≠ 0 (The true mean voltage for type K batteries is not equal to the true mean voltage for type Q batteries.)
In the next steps, you would calculate the test statistic, determine the critical value, make a decision to reject or fail to reject the null hypothesis, and finally interpret the results based on the 0.02 level of significance.
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Two radar A and B are 80km apart and B is due to the east of A. One aircraft is on a bearing of 030 degrees from A and 346 degrees from B. A second aircraft is on a bearing 325 degrees from A and 293 degrees from B. How far apart are the two aircraft
The two aircraft are 128.535 far away.
What is the distance formula?
The d-distance between two places is calculated using the distance formula. The Euclidean distance formula is another name for the formula used to calculate the separation between two points on a two-dimensional plane.
Here, we have
Given: Two radars A and B are 80km apart and B is due to the east of A. One aircraft is on a bearing of 030 degrees from A and 346 degrees from B. A second aircraft is on a bearing 325 degrees from A and 293 degrees from B.
Calculating the Slope of AC, tan60° = 1.732
Calculating the Slope of BC, tan104° = -4.011
Calculating the Slope of AD, tan125° = -1.482
Calculating the Slope of BD, tan157° = -0.424
When pointing C intercepts:
y₁ = 1.732x₁....(1)
y₁ = -4.011(x₁-80)....(2)
Solving equation(1) and(2) , we get
x₁ = 55.873
y₁ = 96.772
When point D intercepts:
y₂ = -1.428x₂....(3)
y₂ = 0.424(x₂-80)....(4)
Solving equations (3) and (4), we get
x₂ = 18.315
y₂ = -26.154
Calculating distance by applying the distance formula:
D = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
D = [tex]\sqrt{(-26.154-96.772)^2+(18.315-55.873)^2}[/tex]
D = [tex]\sqrt{4986.9019+1410.6033}[/tex]
D = 128.535
Hence, the two aircraft are 128.535 far away.
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Landon was comparing the price of apple juice at two stores. The equation y=0. 96xy=0. 96x represents what Landon would pay in dollars and cents, yy, for xx bottles of apple juice at store A. Landon can buy 14 bottles of apple juice at Store B for a total cost of $34. 16
The equation y=0.96x represents the cost in dollars and cents, y, for x bottles of apple juice at store A. This means that if Landon wants to buy x bottles of apple juice from store A, he would pay 0.96x dollars and cents. However, we do not know the value of x from the given information.
On the other hand, we know that Landon can buy 14 bottles of apple juice from store B for $34.16. This means that the cost of one bottle of apple juice at store B is $2.44 (34.16 ÷ 14). We do not know the cost of one bottle of apple juice at store A, but we can use the equation y=0.96x to find out.
Let's assume that Landon wants to buy 14 bottles of apple juice from store A as well. We can substitute x=14 in the equation to find the total cost:
y = 0.96(14) = 13.44
This means that Landon would pay $13.44 for 14 bottles of apple juice at store A. However, we can see that buying 14 bottles of apple juice from store B is cheaper than buying the same amount from store A, as Landon would pay $34.16 at store B and $13.44 at store A. Therefore, it is more cost-effective for Landon to buy apple juice from store B in this case.
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A store sells four ears of sweetcorn for one dollar how much will nine ears cost
Nine ears of sweetcorn will cost $2.25 at this store.
To determine the cost of nine ears of sweetcorn, given that four ears cost one dollar, you can follow these steps:
1. Determine the cost of one ear of sweetcorn: Since four ears cost one dollar, we can calculate the cost per ear by dividing the total cost by the number of ears: $1 / 4 ears = $0.25 per ear.
2. Calculate the cost of nine ears: Multiply the cost of one ear by the number of ears desired: $0.25 per ear × 9 ears = $2.25.
So, nine ears of sweetcorn will cost $2.25 at this store.
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√50-√18+√8+√128-3√2
Please solve this
Step-by-step explanation:
the
answer
of
this
question
is
9 \sqrt{2}
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A researcher found that 66% of a sample of 14 infants had completed the hepatitis b vaccine series. can we conclude on the basis of these data that, in the sampled population, more than 60% have completed the series? use α = 0.01.
To determine if we can conclude that more than 60% of the sampled population have completed the Hepatitis B vaccine series, we need to perform a hypothesis test.
Our null hypothesis (H0) is that the proportion of infants who completed the vaccine series is equal to or less than 60%, while our alternative hypothesis (Ha) is that the proportion is greater than 60%.
We can use a one-sample proportion test to test this hypothesis. The test statistic is calculated as follows:
z = (p - P) / sqrt(P(1-P)/n)
where p is the sample proportion (0.66), P is the hypothesized proportion under the null hypothesis (0.6), and n is the sample size (14).
Plugging in the values, we get:
z = (0.66 - 0.6) / sqrt(0.6(1-0.6)/14) = 0.67
Using a significance level of α = 0.01, our critical value for a one-tailed test is 2.33 (from a z-table). Since our test statistic (0.67) is less than the critical value (2.33), we fail to reject the null hypothesis.
Therefore, we cannot conclude that more than 60% of the sampled population have completed the hepatitis b vaccine series based on these data.
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Answer quickly please
Given that A is a constant, the general solution to the differential equation dy dt -5y is Select one O a. 3t2 2 Ob. 3= Ae-56 Ос. y = Aest Od y=est +A The solution to the exact differential equati
The general solution to the differential equation dy/dt - 5y = A is y = Ce^(5t) + A/5, where C is a constant of integration. The general solution is y = (A/5) + Ce^(5t). so, the correct answer is D).
The general solution to the differential equation dy/dt - 5y = A, where A is a constant, is
y = Ce^(5t) + A/5
where C is an arbitrary constant determined by any initial or boundary conditions given.
The general solution is a combination of the homogeneous solution y_h = Ce^(5t) (which satisfies the differential equation without the constant term A) and the particular solution y_p = A/5 (which satisfies the differential equation with A but without any initial or boundary conditions).
so, the correct option is D).
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--The given question is incomplete, the complete question is given
" Answer quickly please
Given that A is a constant, the general solution to the differential equation dy/dt -5y = A is Select one O a. 3t2 2 Ob. 3= Ae-56 Ос. y = Aest Od y = Ce^(5t) +A/5 The solution to the exact differential equation"--
The lengths of the bases of an isosceles
trapezoid are 20 and 44, and the length
of the altitude is 16. find the length of
a leg of the trapezoid.
The length of a leg of the isosceles trapezoid is 20 units.
To find the length of a leg of the isosceles trapezoid, you can use the Pythagorean theorem. Given the lengths of the bases are 20 and 44, and the length of the altitude is 16, first find the difference between the bases:
44 - 20 = 24
Since the trapezoid is isosceles, the difference between the bases will be equally divided between both legs. Therefore, the horizontal distance for each leg is:
24 / 2 = 12
Now you have a right triangle formed by the leg, altitude, and the horizontal distance. Applying the Pythagorean theorem, let L be the length of the leg:
L^2 = 16^2 + 12^2
L^2 = 256 + 144
L^2 = 400
Taking the square root of both sides:
L = √400 = 20
The length of a leg of the isosceles trapezoid is 20 units.
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Please help me with this math problem!! Will give brainliest!! :)
part a.
the percentage of eggs between 42 and 45mm is 48.48%
part b.
The median width is approximately (42+45)/2 = 43.5mm.
The median length is approximately (56+59)/2 = 57.5mm.
part c.
The width of grade A chicken eggs has a range of about 24mm.
part d.
I think its impossible to determine because we don't have the value for the standard deviation.
The second option should be correct.
What is a histogram?A histogram is described as an approximate representation of the distribution of numerical data.
part a.
From the histogram, we see that the frequency for the bin that ranges from 42 to 45mm is 4 and we have a total of 33 eggwe use this values and calculate the percentage of eggs between 42 and 45mm is 48.48%.
part b.
we have an estimation that the median of the width is 48mm and the median of the length is around 60mm.
part c.
Also from the histogram, we notice that the smallest value is around 36mm and the largest value is around 66mm, hence the width of grade A chicken eggs has a range of about 24mm.
In a histogram, the range is the width that the bars cover along the x-axis and these are approximate values because histograms display bin values rather than raw data values.
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Choose the correct symbol to compare the expressions. Do not multiply. 7×
2
10
?7
The correct symbol to compare the expressions is < (less than).
7 × (2/10) is equivalent to 1.4, which is less than 7. Therefore, 7 is greater than 1.4, and we can write 7 × (2/10) < 7 as the comparison between the expressions.
To compare the two expressions, we can analyze their values without actually multiplying them. The expressions are:
1. 7 × (2/10)
2. 7
Now let's simplify the first expression without multiplying:
7 × (2/10) = 7 × (1/5) (since 2 and 10 have a common factor of 2)
Now let's compare:
7 × (1/5) ? 7
Since we're multiplying 7 by a fraction that is less than 1 (1/5), the result will be smaller than 7. Therefore, the correct comparison symbol is "<":
7 × (1/5) < 7
The correct expression so formed is 7 × (2/10) < 7.
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