Find the slope of the graph

Answer:

30 minutes

Step-by-step explanation:

rate = 2/12 =   1 mile/6minutes

d = rt

5 = 1/6t

t= 5/(1/6)

t = 30 minutes

Step-by-step explanation:

The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.

Let u = sin(x), then du = cos(x)dx

The integral becomes:

∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)

= (u^6)/6 evaluated at sin(π/2) and 0

= (sin^6(π/2))/6 - 0

= (1^6)/6

= 1/6

So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.

Answer:

y = 15

Step-by-step explanation:

y - 58 = -43

add 58 to both sides

y = 15

Answer:

y = 15

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

y - 58 = -43

Step 2: Solve for y

Step 3: Check

Plug in y into the original equation to verify it's a solution.

Here we see that -43 does indeed equal -43.

∴ y = 15 is the solution to the equation.

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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Answer:

9

(i hope this helped!)

Answer:

The answer is 9.

Step-by-step explanation:

45-6=39-6=33-6=27-6=21-6=15-6=9.

Answer:

2.4 hours or 2 hours, 24 minutes

Step-by-step explanation:

19.44 = 8.1h

h = 2.4

The other Washington DC landmark with coordinates (8,-10) is located in the fourth quadrant of the map.

To determine in which quadrant of the map a point with coordinates (8,-10) is located, we need to look at the signs of the x and y coordinates.

Since the x-coordinate (8) is positive and the y-coordinate (-10) is negative, this point is located in the fourth quadrant.

In general, the four quadrants of a Cartesian coordinate system are divided by the x and y-axes.

The first quadrant is located in the upper right-hand corner and contains points with positive x and y coordinates.

The second quadrant is located in the upper left-hand corner and contains points with negative x and positive y coordinates.

The third quadrant is located in the lower left-hand corner and contains points with negative x and y coordinates.

Finally, the fourth quadrant is located in the lower right-hand corner and contains points with positive x and negative y coordinates.

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Answer:

Step-by-step explanation:

the first sounds like J/9=5, which in an equaiton could be written as 5=j/9.

Then to solve for j you can multiply both sides by 9. This would create j=45. Hopefully this is helpful!

Answer:

\(\frac{j}{9}\) = 5 is the equation, j = 45 is the answer.

Step-by-step explanation:

J divided by 9 is 5.

\(\frac{j}{9}\) = 5.

Multiply by 9 to find the answer.

j = 5 * 9

j = 45.

Functions of these are algebraic expression (f+g)(x) = x² + x-2 and             (f-g)(x) = x² + 5x - 14.  

In mathematics, a functiοn is a rule οr mapping that assοciates each element x in a set (called the dοmain) with a unique element f(x) in anοther set (called the range οr cοdοmain).Fοr example  functiοn f(x) = x² + 3x - 8.

An algebraic expressiοn is a cοntains οf variables, cοnstants, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, divisiοn, and expοnentiatiοn. It cantains  parentheses and οther grοuping symbοls tο indicate the οrder in which the οperatiοns shοuld be perfοrmed.

In the given question ,

To find (f+g)(x),

we simply add the two functions f(x) and g(x) term by term:

(f+g)(x) = f(x) + g(x)

= (x² + 3x - 8) + (-2x + 6)

= x²  + (3x - 2x) + (-8 + 6)

= x² + x - 2  

Therefore, (f+g)(x) = x² + x - 2.

To find (f-g)(x), we subtract g(x) from f(x) term by term:

(f-g)(x) = f(x) - g(x)

= (x²  + 3x - 8) - (-2x + 6)

= x²  + (3x + 2x) + (-8 - 6)

= x²  + 5x - 14  

Therefore, (f-g)(x) = x²  + 5x - 14.

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The probability of not drawing a 5 from the deck is 48/52.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

There are 4 number 5's in the deck of 52 cards.

They are as follows:

The 5 of clubs, the 5 of spades, the 5 of hearts, and the 5 of diamonds.

Using the formula,

Probability = (Number of possible outcomes)/(Total number of outcomes)

The probability of drawing a 5 from the deck is 4/52.

The probability of not drawing a 5 from the deck is 48/52.

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Answer: 1) NO. the zeros are: 2 and -7

              2) (x + 5)² has a middle term when in expanded form

             3) Factoring provides the Intercept form: y = a(x - p)(x - q)

Step-by-step explanation:

1) y = (x - 2)(x + 7)

To find the zeros, set the factors equal to zero:

0 = x - 2        0 = x + 7

x = 2              x = -7

The zeros are 2 and -7.  

The student did not set the factors equal to zero.

2) (x + 5)² = (x + 5)(x + 5)

               = x² + 5x + 5x + 25

               = x² + 10x + 25       ≠  x² + 25

3) The Intercept form of a quadratic equation is: y = a(x - p)(x - q) where p and q are the x-intercepts.  Notice that the intercept form IS the factored form. Set the factors equal to zero to find the x-intercepts.

y = x² - 4x + 3

y = (x - 1)(x - 3)     --> Intercept form

0 = (x - 1)(x - 3)    --> finding the zeros (aka x-intercepts)

0 = x - 1       0 = x - 3

x = 1            x = 3       -->    zeros are 1 and 3

1.The zeroes are 2,-7

2.\(x^2 + 25\neq ( x + 5)^{2}\)

3. So, factoring can help to find the x-intercepts

1.We have y = (x - 2)(x + 7)

For zeroes of y , Put y=0

(x - 2)(x + 7) =0

x=2,-7

So, the zeroes of y = (x - 2)(x + 7) are 2 and -7.

2. We have \(x^2 + 25\)

\(x^2 + 25= x^2 + 5^{2}\)

And

\((x+ 5)^{2} \\=x^{2} +5^{2} +10x\\=x^{2} +25 +10x\\\neq x^{2} +25\)

So, \(x^2 + 25\neq ( x + 5)^{2}\)

3.We have the quadratic function \(y = x^2 - 4x + 3\)

\(y=x^2 - 4x + 3\\=(x-3)(x-1)\\\)

For x-intercept put y=0, we get

\((x-3)(x-1)=0\\x=3,x=1\)

So, factoring can help to find the x-intercepts of the graph of the quadratic function \(y = x^2 - 4x + 3.\)

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The most common number of hours volunteered is 22.

Option B is the correct answer.

We have,

A.
The number of students who volunteered more than 30 hours is greater than the number of students who volunteered fewer than 30 hours.

This can not be determined from the given stem-and-leaf plot as it only shows the frequency distribution of hours volunteered without any specific count of students.

The plot only indicates that there are some students who volunteered between 31-36 hours (stem 3, leaves 33, and 36) and one student who volunteered for 44 hours (stem 4, leaf 4).

Therefore, option A is not supported by the given data.

B.

The most common number of hours volunteered is 22.

From the stem-and-leaf plot, we can see that the mode is 22 as it has the highest frequency (stem 2, leaves 2, 5, 7, 8).

Hence, option B is supported by the given data.

C.

The number of students who volunteered between 9 and 20 hours is greater than the number of students who volunteered more than 40 hours.

This statement cannot be confirmed by the given stem-and-leaf plot as there are no leaves in stem 1, which means there are no students who volunteered less than 10 hours. Also, there are no leaves in stem 4, except for one leaf with a value of 44.

Therefore, we can not determine how many students volunteered between 9-20 hours and more than 40 hours. Hence, option C is not supported by the given data.

D.

The most common number of hours volunteered is 41.

There are no leaves in stem 4 except for the value of 44, which means there is no student who volunteered for 41 hours.

Hence, option D is not supported by the given data.

Therefore,

The most common number of hours volunteered is 22.

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

I think its A

Step-by-step explanation:

Answer:

Step-by-step explanation:

x2 + 10x + 25

x2 + 5x + 5x + 25

x (x + 5) + 5(x + 5)

(x + 5) (x + 5)

Answer:

Step-by-step explanation:

20/5=4

as both the diagrams are similar.

so area of ABCD=4² ×area of EFGH=16×40=640 sq.cm.

a) To find the number of students getting more than 45 marks, we count the students whose marks are greater than 45 in the given list.

In the given list, the students with marks greater than 45 are: 50, 49, 47, 48, 49, 48, 47, 49, 48, 50, 47, 49, 48, 46, 47, 48, 47.

Counting these numbers, we find that there are 17 students who obtained more than 45 marks.

b) To find the number of students getting less than 45 marks, we count the students whose marks are less than 45 in the given list.

In the given list, the students with marks less than 45 are: 44, 44, 42, 41, 41, 42, 41, 44, 44, 42, 45, 45, 45, 44, 45.

Counting these numbers, we find that there are 15 students who obtained less than 45 marks.

c) To find the maximum number of students getting the same marks, we look for the mark that appears most frequently in the given list.

In the given list, the marks obtained by the students are: 44, 50, 44, 49, 42, 47, 45, 42, 44, 48, 49, 48, 47, 49, 47, 41, 45, 48, 41, 48, 41, 42, 47, 49, 49, 48, 50, 47, 49, 48, 46, 44, 45, 45, 46, 44, 42, 47, 48, 45.

Counting the frequency of each mark, we find that the marks 47 and 48 appear most frequently, with a count of 6 each. Therefore, the maximum number of students getting the same marks is 6.

d) To find the average marks obtained by the students in the class, we sum up all the marks and divide by the total number of students.

Total marks = 44 + 50 + 44 + 49 + 42 + 47 + 45 + 42 + 44 + 48 + 49 + 48 + 47 + 49 + 47 + 41 + 45 + 48 + 41 + 48 + 41 + 42 + 47 + 49 + 49 + 48 + 50 + 47 + 49 + 48 + 46 + 44 + 45 + 45 + 46 + 44 + 42 + 47 + 48 + 45

           = 1912

Total number of students = 40

Average marks = Total marks / Total number of students

                 = 1912 / 40

                 = 47.8

Therefore, the average marks obtained by the students in the class is 47.8.

e) To find the number of students getting more than the average marks, we count the students whose marks are greater than 47.8.

In the given list, the students with marks greater than 47.8 are: 50, 50, 49, 48, 49, 48, 49, 48, 50, 49, 49, 48, 48, 50, 49, 49, 48, 48, 47, 49, 49, 48, 50, 47,

49, 49, 48, 50, 47, 49, 49, 48, 48, 49, 48, 47, 48, 49, 49, 48, 50, 49.

Counting these numbers, we find that there are 40 students who obtained more than the average marks.

Answer:

x = -1

Step-by-step explanation:

6+4 = 10

14-10 = 4

2x + 6 = 4

2x (-2) = -2

-2 + 6 = 4

The electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.

In the analogy of a circuit with resistance, we can compare it to an obstacle race. Here's how we can relate the different elements:

Circuit: The entire obstacle race course represents the circuit itself. It includes all the components and paths that the participants will go through.

Obstacles: The obstacles in the race represent the resistors in the circuit. Just like resistors impede the flow of electrical current in a circuit, obstacles in the race impede the progress of the participants.

People/Participants: The people participating in the race represent the flow of electric current in the circuit. They are the "charge" moving through the circuit, encountering and overcoming obstacles (resistors) to reach the finish line.

The goal of the participants (people) is to navigate through the obstacles (resistors) and complete the race (circuit) by reaching the finish line.

Similarly, in an electrical circuit, the goal is for the electric current to flow through the resistors and complete the circuit by reaching its intended destination or powering a device.

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Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

Data Input

785 miles every 10 minutes

Procedure:

The answer would be 2747.5 miles

Answer:

28

Step-by-step explanation:

I guessed it right on hegarty maths and this was the answer

Answer:

Step-by-step explanation:

I can't make specific statements about the proof because the midpoint is missing.

Givens

There are two right angles created by where the perpendicular bisector meats MN. Both are 90 degrees.

MN is bisected by the point on MN where the perpendicular meets MN

The Perpendicular Bisector is is common to both triangles.

Therefore the two triangles are congruent by SAS

PM = PN                Parts contained in Congruent triangles are congruent.

Answer:

Step-by-step explanation:

50in-3ft(12in/ft)

50in-36in

14in

Answer:

42 degrees

Step-by-step explanation:

Use a number line.

-13 - 13 = 0.

Now, we are at the base, 0. Then, add 29.

13 + 29 + 42.

The answer is 42. Hope it helps!

a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².

b) The side length that gives the maximum area that the playground can have is x = 30 m.

c) The maximum area that the playground can have is 900 m².

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

120 = 2(x + W)

60 = x + W

W = 60 - x

Therefore, the area of the rectangular playground (in terms of x) is given by this function;

A = LW

A(x) = x(60 - x)

A(x) = 60x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 60x - x²

A'(x) = dA/dx

A'(x) = 60 - 2x

60 - 2x = 0

x = 60/2

x = 30 m

Part c.

W = 60 - x

W = 60 - 30

W = 30 m.

Therefore, the maximum area is given by;

A = 30 × 30

A = 900 m².

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The total money was shared = $3304

What are proportion and ratio?

Two quantities are compared to form a ratio. An equality of two ratios is a proportion. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

Aaron, Ben, and Charles split a sum of money in the following proportions: 2: 5: 7. What was the initial amount of money shared if Charles' part was 1180 higher than Aaron's portion?

——-

Ben:::: 5x

Charles:7x

Aaron:2x

———-

7x = 2x + 1180 in the equation

5x = 1180

x = 236

————-

2x + 5x + 7x = 14x

14x = 14*236 = $3304

—————————————

Hence the total money was shared = $3304

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