5th grade math problem for my sister. Very confused on what it is asking. Assuming it’s 1/4

Answer: x = 1 In4

Step-by-step explanation:

Sorry if I’m wrong

Answer: 165 square cm

Step-by-step explanation:

The height of the main cable 20 meters from the center is 16 meters above the road.

To find the equation of the parabola, we need to use the information given about the height of the cables at the towers and the center of the bridge. We know that the main cables are 20 meters above the road at the towers, so we can use this information to find the distance between the towers, which is

distance between towers = 80 meters - 2(20 meters) = 40 meters

We also know that the main cables are 4 meters above the road at the center, so we can use this information to find the height of the vertex of the parabola, which is

vertex height = 4 meters + 20 meters = 24 meters

We can now use the vertex form of a parabola to write the equation

y = a(x - h)^2 + k

where (h, k) is the vertex and a is a constant that determines the shape of the parabola.

Substituting the values we found for the vertex height and the distance between the towers, we get

y = a(x - 40)^2 + 24

We now need to find the value of a. To do this, we can use the fact that the vertical cables are spaced every 10 meters. This means that the distance between the vertex of the parabola and a point on the main cable 10 meters from the center of the bridge is

distance = 10 meters

Substituting x = 50 (since the center of the bridge is at x = 40 + 10 = 50) and y = 14 (since the cable is 4 meters above the road at this point), we get

14 = a(50 - 40)^2 + 24

-10 = 100a

a = -0.1

Substituting this value of a into the equation we found earlier, we get

y = -0.1(x - 40)^2 + 24

To find the height of the main cable 20 meters from the center, we can substitute x = 60 (since the center of the bridge is at x = 50 and we want to go 20 meters to the right) into the equation

y = -0.1(60 - 40)^2 + 24

y = -0.1(20)^2 + 24

y = -0.1(400) + 24

y = -40 + 24

y = -16

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Answer:

i) 42 candidates passed Mathematics, 33 candidates passed Science.

ii) There is a 75% chance that a candidate passed exactly one subject.

Step-by-step explanation:

So we know that in total there are 60 candidates, and 15 passed both.

That leaves us with 45 candidates that passed either science or math. Since 9 more passed math than science, we see that out of those 45, 27 candidates passed math and 18 passed science. We add the 15 that got through both to each number, which means in total 42 candidates passed Mathematics, 33 candidates passed Science.

To see the probability, we know that 45 out of 60 only passed one subject. Simplified is 3/4 or 75%.

Answer:

9 boys, 27 girls

Step-by-step explanation:

2 boys : 6 girls = 1 boy : 3 girls

Let b = number of boys and g = number of girls.

[tex] \frac{1}{3} = \frac{b}{g} [/tex]

[tex]g = 3b[/tex]

[tex]b + 3b = 4b = 36[/tex]

[tex]b = 9[/tex]

[tex]g = 27[/tex]

The reflection's rule is described below. The right response is x-axis (x, y) = (x, -y).

When we gaze at our own reflection in a mirror, we naturally think of a reflection as a mirror image.

In maths, the concept of reflection and a mirror image are comparable.

The rules for reflection across the y-axis and x-axis are fundamental transformations in geometry. The rule for reflection across the y-axis is (x, y) → (-x, y), which means that every point's x-coordinate is negated while the y-coordinate remains the same. This transformation has the effect of reflecting the object or figure across the y-axis.    

Similarly, the rule for reflection across the x-axis is (x, y) → (x, -y), which means that every point's y-coordinate is negated while the x-coordinate remains the same. This transformation has the effect of reflecting the object or figure across the x-axis. These transformations are important in many areas of mathematics and science, including computer graphics and physics.

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Answer:

x=2

Step-by-step explanation:

x=7-5

x=2

Thank you for your question

The two lines will be parallel and won't overlap anywhere if they have separate intercepts but the same slope.

given

It appears from the graph that the two lines cross at the location (10, 0). But it's possible that the system has a solution that can't be seen from this part of the coordinate plane.

We would need further information about the slopes and intercepts of the two lines in order to establish whether there is a solution that we cannot see in this region of the coordinate plane.

We have already located the spot on the graph where the two lines will intersect if their slopes and intercepts are different.

The two lines will be parallel and won't overlap anywhere if they have separate intercepts but the same slope.

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Part A: The total distance that the both friends covered with their bicycle = 7n + 7

Part B: The difference between the miles ridden by Jackson and the miles ridden by Ayanna would be =n-3.

The distance that was covered by;

Jackson = 4n + 2

Ayanna = 3n + 5

Total distance = 4n + 2+3n + 5

= 7n + 7

The difference between the both distance = (4n + 2)- 3n + 5

= 4n+2-3n-5

= n -3

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The reasons that completes the proof to show that WX ≅ ZY are:

2. Given; 3. Alternate Interior Angles Theorem 4. Reflexive Property of Congruence 5. AAS 6. CPCTC.

Given that WX║ZY and <X ≅ <Z, we can prove that WX ≅ ZY as shown below in the proof.

Statements                        Reasons                                          

1. WX║ZY                          1. Given

2. <X ≅ <Z                         2. Given

3. <XWY ≅ <ZYW              3.  Alternate Interior Angles Theorem

4. WY ≅ WY                      4. Reflexive Property of Congruence

5. ΔWZY ≅ ΔYXW            5. AAS

6. WX ≅ ZY                       6. CPCTC

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The patient value-added percentage is 17%. The doctor and the waiting are the two separate activities that happened one after another in the hospital. The value-added time is the time that creates value for the customers or patients.

Patient value-added percentage refers to the percentage of time that adds value to the patient.

The patient value-added percentage can be calculated using the following formula,

Value-added percentage = Value-added time ÷ Total time

The given values are,Waiting time = 25 minutes

Visit time = 5 minutes

Total time = Waiting time + Visit time= 25 + 5= 30 minutes

The value-added time is the time that creates value for the customers or patients.

The visit time is the value-added time in this case.

Value-added time = Visit time= 5 minutes

Putting the values in the formula,

Value-added percentage = Value-added time ÷ Total time= 5 ÷ 30= 1 ÷ 6= 0.1666...

The value-added percentage is 16.66… which is approximately 17%.Therefore, the patient value-added percentage is 17%.

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Answer:

292

Step-by-step explanation:

To find the 41st term of the sequence 12, 19, 26, we need to first find the common difference, d, between consecutive terms. We can do this by subtracting the first term from the second term (or the second term from the third term). So the common difference is 7. Now we can use the formula for the nth term of an arithmetic sequence. where an is the nth term, a1 is the first term, d is the common difference, and n is the term we want to find. Substituting the given values, you get the 41st sequence is 292.

Answer:

Step-by-step explanation:

The rectangle ABCD have measures of angle a and b derived to be 69° and 138° respectively to the nearest degree.

Considering the right triangle ADC,

tan ACD = 6/16 {opposite/adjacent}

ACD = tan⁻¹(6/16)

ACD = 20.5560

ACD = 21° to the nearest degree

Angle ACD = Angle ABD, and ABD and a are complementary angles, so;

a + ABD = 90°

a + 21 = 90°

a = 90 - 21

a = 69

The angle b forms an isosceles triangle with the angles C and D, so;

b = 180 - 2(21) {sum of interior angles of a triangle}

b = 180 - 42

b = 138°

Therefore, the rectangle ABCD have measures of angle a and b derived to be 69° and 138° respectively to the nearest degree.

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By determining in triangle MPQ,  NR || PQ, if QM= 31, RM= 21 and PM= 4PN , [tex]\frac{PN}{NM} \neq \frac{QR}{RM}[/tex] , So correct option is A.

A triangle is a three-sided polygon that consists of three line segments, or sides, that intersect at three points, or vertices. Triangles are one of the fundamental shapes in geometry and have numerous properties and applications in mathematics, science, and engineering.

Triangles can be classified based on the lengths of their sides and the measures of their angles. Triangles with three equal sides are called equilateral triangles, while triangles with two equal sides are called isosceles triangles. Triangles with no equal sides are called scalene triangles. Triangles can also be classified based on the measures of their angles, with acute triangles having all angles less than 90 degrees, obtuse triangles having one angle greater than 90 degrees, and right triangles having one angle equal to 90 degrees.

The Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, is a fundamental concept in trigonometry and has numerous practical applications.

Overall, triangles are an important shape in mathematics and have many practical applications in fields such as engineering, architecture, and physics.

As shown in the question:

QM= 31, RM= 21, PM= 4PN

So RQ= 31-21= 10

[tex]\frac{PN}{NM} = \frac{1}{3}\\[/tex]

[tex]\frac{QR}{RM}= \frac{10}{21}[/tex]

So, [tex]\frac{PN}{NM} \neq \frac{QR}{RM}[/tex]

NR and PQ are not parallel .

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The complete question is:

Answer:

-7

Step-by-step explanation:

We dont know the starting temperature so we will just put x for the starting temperature

The temp is first doubled so x*2

Then the temp drops by 10 so 2x-10

After that the temp increases by 40 so 2x-10+40

2x-10+40=16

2x+30=16

2x=16-30

2x=-14

x= -14/2

x=-7

The length that Sarah should make the box in order to minimize the cost of the materials used, is 18 cm.

We know that each can holds 450 cubic centimeters of soda and is 12 centimeters tall. Let's first find the radius of the soda can.

The volume of a cylinder is given by the formula:

V = πr²h

Plugging in the given values:

r = √(450 / (π x 12))

r ≈ 1.77 cm

Now, we know that the box must hold 15 soda cans, and they fit in the box in rows of 3. This means there are 3 rows along the width and 5 rows along the length of the box.

Width: 3 cans x diameter = 3 x 2 x 1.77 ≈ 10.62 cm (since the diameter is twice the radius)

Length: 5 cans * diameter = 5 x 2 x 1.77 = 18 cm

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Answer:

See attached.

Step-by-step explanation:

Helping in the name of Jesus.

This is not a line of best fit because it does not pass through two of the data points. Option D

The line of best fit is a straight line that is used to represent the general trend in a scatter plot or a set of data points. It is also known as the regression line, as it is often used in regression analysis to model the relationship between two variables.

The line of best fit is chosen to minimize the distance between the line and the data points, typically by minimizing the sum of the squared errors (the differences between the actual y-values and the predicted y-values on the line).

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5(7+y)*z

y = 0.4 and z = 1.6

5(7+y)*z

(35 + 5y)*1.6

[35 + 5(0.4)]*(1.6)

(35 + 2)*1.6

37 * 1.6

59.2

Thus, the answer is a) 59.2

there are 9 office suites in company C and the total number of office suites in the three companies is 75.   To solve this problem, we first need to find out how many office suites company A and company B have. Let's represent the total number of office suites in the three companies as x.

Company A has 1/3 of the computers, which means they have 1/3 of the office suites as well. So the number of office suites in company A is:

1/3 * x = x/3

Company B has 2/5 of the computers, which means they have 2/5 of the office suites as well. So the number of office suites in company B is:

2/5 * x = 2x/5

To find out how many office suites are in company C, we can use the fact that the total number of office suites is 60. So we can write an equation:

x/3 + 2x/5 + C = 60

We can simplify this equation by finding a common denominator for the first two terms:

5x/15 + 6x/15 + C = 60

11x/15 + C = 60

Now we can solve for C by isolating it on one side of the equation:

C = 60 - 11x/15

To find the value of x, we can use the fact that the total number of office suites is 60:

x/3 + 2x/5 + (60 - 11x/15) = 60

Multiplying both sides by 15 to eliminate the denominator, we get:

5x + 6x + 900 - 11x = 900

Simplifying, we get:

x = 75

So the total number of office suites in the three companies is 75. To find out how many are in company C, we can substitute x into the equation we found for C:

C = 60 - 11x/15 = 60 - 11(75)/15 = 9

Therefore, there are 9 office suites in company C.

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There are 60 office suites company a has 1/3 of computers company b has 2/5 of computers how many are in company c buildingservice the computers?

. Company A services the computers at 1/3 of the office suites A.16

. Company B services the computers at 2/5 of the office suites B.20

. Company C services the computers at x of the office suites C. 24

D. 28

The table of values of the equation y = -4x is

x y

-2 8

-1 4

0 0

1 -4

Given that

y = -4x

To find the values that complete the table for the given equation y=-4x, we substitute each value of x and evaluate y.

When x = -2, y = -4x = -4(-2) = 8

When x = -1, y = -4x = -4(-1) = 4

When x = 0, y = -4x = -4(0) = 0

When x = 1, y = -4x = -4(1) = -4

So the completed table is:

x y

-2 8

-1 4

0 0

1 -4

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A mathematical process called subtraction reflects the elimination of items from a collection. There are 14 pupils that enjoy pink polka dots.

A mathematical process called subtraction reflects the elimination of items from a collection.

Subtraction is symbolised by the negative sign.

Considering that there were 50 students in the sample as a whole, the number of pupils who enjoy pink polka dots is as follows:

50 students divided by (4+9+11+9+3) yields 14 students.

Thus, there are 14 students that enjoy pink polka dots.

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The complete question is:

A sample of 50 11th graders was asked to select a favorite pattern out of 6 choices. the following display shows what their favorite color patterns were.

blue on grey 4

green 9

pink polka dots?

purple 11

red and orange stripes 9

yellow 3

The counts have been recorded in the accompanying table according to pattern and the number of students who selected the pattern. what is the missing value in the table?

Answer:

82 square feet

Step-by-step explanation:

The surface area of this pyramid:

[tex]5(4) + 2(\frac{1}{2} (4)(7) + \frac{1}{2} (5)(6.8))[/tex]

[tex]20 + 2(14 + 17)[/tex]

[tex]20 + 2(31) = 20 + 62 = 82[/tex]

Answer:

height ≈ 17.0 m

Step-by-step explanation:

consider the right triangle with angle 29° , opposite side x and adjacent side of 28 m

using the tangent ratio in the right triangle

tan29° =[tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{28}[/tex] ( multiply both sides by 28 )

28 × tan29° = x , then

x ≈ 15.5 m ( to the nearest tenth )

now add on the 1.5 m

height of tree = 15.5 + 1.5 = 17.0 m

The car is depreciating by about 0.68% every quarter.

Quarterly rate is a financial term that refers to the interest rate applied to a loan or investment that compounds every quarter, or every three months.

Let f(t) represent the car's worth after t years. We can write a function to represent the value of the car after t years as follows:

f(t) = 10000(1 - 0.18/4)[tex]^(4t)[/tex]

In this function, the quarterly rate of change is 0.18/4 = 0.045. The value of the car is depreciating by 4.5% every quarter.

To determine the percentage rate of change per quarter to the nearest hundredth of a percent, we can use the formula:

r = [tex](1 - q)^4[/tex] - 1

where q is the quarterly rate of change (0.045 in this case) and r is the percentage rate of change per quarter.

Plugging in the values, we get:

r = [tex](1 - 0.045)^4[/tex] - 1

r ≈ -0.68%

So the car is depreciating by about 0.68% every quarter.

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The length of the edge of the square is increasing at a rate of 12/13 cm/min when the area is 169 cm^2, given that the area of the square is increasing at a rate of 24 cm^2/min.

Let's assume that the side length of the square is represented by "x" and the area of square is represented by "A". Then we have:

A = x^2

Differentiating both sides with respect to time "t", we get:

dA/dt = 2x(dx/dt)

Given that dA/dt = 24 cm^2/min, we can find dx/dt when A = 169 cm^2 (which is the area of a square with side length of 13 cm):

24 = 2(13)(dx/dt)

Simplifying this expression, we get:

dx/dt = 24/(26) = 12/13

Therefore, the length of the edge of the square is increasing at a rate of 12/13 cm/min when the area is 169 cm^2.

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_____The given question is incomplete, the complete question is given below:

The area of a square is increasing at a rate of 24 cm^2/min

How fast is the length of the edge increasing when the area = 64 cm^2

Answer:

The mean is 25 and the median is 23

The average rate of change of the function f(x) from x = 2 to x = 6 is 13.

In mathematics, a function is a rule that associates each element of a set (called the domain) with a unique element in another set (called the range). In other words, a function is a relationship between two sets, where each element of the domain is paired with exactly one element in the range.

To find the average rate of change of the function f(x) from x=2 to x=6, we need to calculate the slope of the secant line between the two points.

The formula for the average rate of change of a function f(x) from x=a to x=b is:

average rate of change = (f(b) - f(a)) / (b - a)

In this case, a = 2 and b = 6. So we have:

average rate of change = (f(6) - f(2)) / (6 - 2)

Now, let's substitute the values of f(6) and f(2) in the above equation:

average rate of change = ((6)² + 5(6) - 8 - (2)² - 5(2) + 8) / (6 - 2)

average rate of change = (36 + 30 - 8 - 4 - 10 + 8) / 4

average rate of change = 52 / 4

average rate of change = 13

Therefore, the average rate of change of the function f(x) from x = 2 to x = 6 is 13.

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