For every 3 minutes that Ryan runs on the treadmill, he burns 28
calories. How many calories can he expect to burn if he runs for 24
minutes?

The particular solution of the differential equation  y''-5y' 4y=8e^x is A*e^x form.

To find the form of the particular solution for the given differential equation, y'' - 5y' + 4y = 8e^x, we will first identify the terms involved and then determine an appropriate trial function for the particular solution.

Given differential equation: y'' - 5y' + 4y = 8e^x

Here, the left side represents a linear differential equation with constant coefficient and the right side is the non-homogeneous term (8e^x).

To find the form of the particular solution, we'll assume a trial function based on the non-homogeneous term. Since the non-homogeneous term is 8e^x, our trial function will have the form:

Trial function: Y_p(x) = A*e^x

Now, we need to find the derivatives of Y_p(x) and substitute them into the differential equation:

First derivative: Y_p'(x) = A*e^x
Second derivative: Y_p''(x) = A*e^x

Substituting these into the differential equation:

(A*e^x) - 5(A*e^x) + 4(A*e^x) = 8e^x

Simplifying the equation:

(A - 5A + 4A)e^x = 8e^x

Now, we compare the coefficients:

A = 8

So, the form of the particular solution for the given differential equation is Y_p(x) = 8e^x

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The correct option regarding whether the sum of a rational number and an irrational number is always irrational is given by:

Yes. The claim is correct because √ 16 + π = 4 + π , and 4 + π is an irrational number.

The sum of a terminating decimal with a non-terminating decimal always results in a non terminating decimal, that is, the sum of a rational number with an irrational number is always irrational, and the correct option is given by:

Yes. The claim is correct because √ 16 + π = 4 + π , and 4 + π is an irrational number.

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Yes, we can find the probability P(19 < X < 28) by using properties of normal distribution and standardizing the values. sample mean (µ) & standard deviation (σ) can be estimated as the population mean (μ) &SD

A) To find the probability P(19 < X < 28), we need to calculate the probability of X falling between 19 and 28 in the given distribution. Since we know the population mean (μ = 23) and standard deviation (σ = 10), we can standardize the values to find the corresponding z-scores. Then we can use the standard normal distribution to find the probability.

B) The sample mean (µ) and standard deviation (σ) can be estimated as the population mean (μ) and standard deviation (σ), respectively. In this case, the sample mean (µ) would be estimated as 23, and the sample standard deviation (σ) would be estimated as 10.

It's important to note that in practice, the values of the sample mean and standard deviation may vary slightly from the population values due to sampling variability. However, with a large sample size (N = 28), the estimates of the sample mean and standard deviation tend to be closer to the population values.

Therefore, we can find the probability P(19 < X < 28) by standardizing the values using the population mean and standard deviation. Additionally, the values of the sample mean (µ) and standard deviation (σ) can be estimated as the population mean (μ) and standard deviation (σ), respectively.

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\( (x + 3)(x + 5)\) ✅

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\( {x}^{2} + 8x + 15 \\ ={x}^{2} + 5x + 3x + 15 \)

Taking \(x\) as common from first two terms and 3 from last two terms, we have

\( =x(x + 5) + 3(x + 5)\)

Taking the factor \((x+5)\) as common,

\( = (x + 3)(x + 5)\)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}\)

Answer:

Solution given:

For bank A.

rate[R]=6.85%

principal [P]=$5000

time [T]=3years

now since simple interest is given by this bank

we have

Simple interest=PTR/100

=5000×6.85×3/100=$1027.5

For bank B

rate[R]=6.85%

principal [P]=$5000

time [T]=3years

now since compound interest is given by this bank

we have

compound interest=P((1+R/100)^T-1)

=$5000((1+6.85/100)³-1)=$1099.49

since

Bank B gives more interest .more amount is

1099.49-1027.5=$71.99 or $72

Answer:

x=4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

0.75x+3=6(x−3)

0.75x+3=(6)(x)+(6)(−3)(Distribute)

0.75x+3=6x+−18

0.75x+3=6x−18

Step 2: Subtract 6x from both sides.

0.75x+3−6x=6x−18−6x

−5.25x+3=−18

Step 3: Subtract 3 from both sides.

−5.25x+3−3=−18−3

−5.25x=−21

Step 4: Divide both sides by -5.25.

−5.25x/-5.25    =    -21/-5.25

Answer: x=4

The value of x from the given equation is 4.

The given equation is 0.75x + 3 = 6 (x - 3).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solve for x as follows:

0.75x + 3 = 6x - 18

⇒ 6x-0.75x = 3+18

⇒ 5.25x=21

⇒ x=21/5.25

⇒ x=4

Therefore, the value of x from the given equation is 4.

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Answer:

x = -6

Step-by-step explanation:

Answer:

5.385 = 5.4

Step-by-step explanation:

Answer:

5.4

Step-by-step explanation:

x^2+y^2=c^2

4+25=c^2

c^2=104

c=5.4

SOLUTION:

Case: Percentage

Given: Frequency table

Required: To find the percentage of the students in grades 9–10 like rap music

Method:

Step 1: First we find the total number of people in grades 9–10.

We see clearly from the tables that 125 students are in grades 9–10.

Step 2: Next we find the number of people in grades 9–10 who like rap music.

There are 40 students in grades 9–10 who like rap music.

Step 3: We express as this as a percentage of the whole

This is 32% of the students in grades 9-10.

Final answer:

32% of students of the students in grades 9–10 like rap music

This method is effective because it breaks down the percentage into smaller parts that are easier to calculate mentally. By finding 5% and 1% separately and then adding them together, you can quickly find the percentage that you need.To find 7% of $1000, there are various mental math methods that one can use. One of the best methods is to use a combination of the 5% and 1% methods. Here's how to do it:

Step 1: Find 5% of $1000
5% of $1000 is $50

Step 2: Find 1% of $1000
1% of $1000 is $10

Step 3: Add the two values together
$50 + $10 = $60

Step 4: Find 1% of $60
1% of $60 is $0.60

Step 5: Multiply $0.60 by 7 to get the final answer
$0.60 x 7 = $4.20

Therefore, 7% of $1000 is $4.20.

This method is effective because it breaks down the percentage into smaller parts that are easier to calculate mentally. By finding 5% and 1% separately and then adding them together, you can quickly find the percentage that you need.

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Answer: x=5+\(\sqrt{15}\)

Step-by-step explanation:

x² - 10x+10=0

x² - 5x - 5x+10=0

x² - 5x - 5x+25-15=0

(x-5)^2 -15=0

(x-5)^2=15

x-5=\(\sqrt{15}\)

x=5+\(\sqrt{15}\)

Answer:

Step-by-step explanation:

I think 18.5 not sure thou

Using Horner's algorithm, it is found that p(4) = 946.

Horner's algorithm is a method used to evaluate a polynomial at a given value of x. It simplifies the process of calculating the value of the polynomial by reducing the number of calculations needed. To use Horner's algorithm to find p(4), where p(z) = 3z^5 – 7z^4 – 5z^3+z^2- 8z +2, follow these steps:

p(4) = 3(4)^5 – 7(4)^4 – 5(4)^3+(4)^2- 8(4) +2
p(4) = 3(4)^5 – 7(4)^4 – 5(4)^3+(4)^2- 8(4) +2

p(4) = 3(1024) – 7(256)– 5(64) + 16 - 32 +2

p(z) = 3072– 1792 – 320 + 16 - 30

p(z) = 1280 – 320 - 14

p(z) = 960 - 14

p(z) = 946

Therefore, p(4) = 946.

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The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

option C.

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is determined as follows;

The four points include;

A = (1, 2)

B = (2, - 3)

C = (-2, - 2)

D = (-3,  1)

The  ordered pair that can be plotted together with these four points, must fall withing these coordinates. Going by this condition we can see that the only option that meet this criteria is;

(2, - 1)

Thus, the ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

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Yes, an angle in a right-angled triangle is always present.  Without any additional information about the triangle, it is impossible to determine the value of the angle in question.

In a right-angled triangle, one of the angles is a right angle, which measures 90 degrees. The other two angles in the triangle are acute angles and their measures always add up to 90 degrees.

To find the value of the angle in question, we need to know some additional information about the triangle. If we have the lengths of two sides of the triangle, we can use trigonometric ratios to find the measure of the angle.

For example, if we know the length of the side opposite the angle and the length of the hypotenuse (the longest side of the triangle), we can use the sine ratio to find the measure of the angle.

If we know the length of the side adjacent to the angle and the length of the hypotenuse, we can use the cosine ratio.

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Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position

The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.

If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.

The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.

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Answer:

Perpendicular

The probability that the sum of the numbers rolled on the dice is even =1/2.

For the given question,

A fair dice is rolled twice.

Six different results are available with a single roll of the dice (1,2,3,4,5,6)

Therefore, if two dice are rolled, there are a total of 36 possible results, or 6².

Sample space for the sum of even = [(1,1), (1,3), (1,5), (2,2), (2, 4),(2,6), (3, 1), (3,3),(3,5),(4,2),(4,4),(4,6), (5, 1), (5,3),(5,5),(6,2),(6,4),(6,6)]

Total sample space for sum of even = 18

For the probability that the sum of the numbers rolled is even is -

probability (sum is even) = 18 / 36 = 1/2

Thus, the probability that the sum of the numbers rolled is even is 1/2.

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Check the picture below.

Answer:

point c is right answer

Step-by-step explanation:

you can also count after -7 d is at -5 the number and then c is located between -7 and -8 so its -7.75

Answer:

1/8m

Step-by-step explanation:

The algebraic expressions one-eighth of m will be written as (1/8)m.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The algebraic expressions one-eighth of m will be written as below:-

E = (1/8)m.

Therefore, the algebraic expressions one-eighth of m will be written as (1/8)m.

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For X, where n=4 and p=0.5,

the probability distribution is given by\(:B(x) = (4 choose x)0.5x(1-0.5)^(4-x), x = 0, 1, 2, 3, 4\)Here, B(x) represents the probability of obtaining x successes out of four trials.

We can calculate the mean and variance using the following formulae\(:μ = np = 4 × 0.5 = 2 (mean value)σ^2 = np(1 − p) = 4 × 0.5 × 0.5 = 1\) (variance)Now, let's find the distribution function:\(For x = 0, P(X ≤ 0) = B(0) = 1/16For x = 1, P(X ≤ 1) = B(0) + B(1) = 1/16 + 4/16 = 5/16For x = 2, P(X ≤ 2) = B(0) + B(1) + B(2) = 1/16 + 4/16 + 6/16 = 11/16For x = 3, P(X ≤ 3) = B(0) + B(1) + B(2) + B(3) = 1/16 + 4/16 + 6/16 + 4/16 = 15/16For x = 4, P(X ≤ 4) = B(0) + B(1) + B(2) + B(3) + B(4) = 1/16 + 4/16 + 6/16 + 4/16 + 1/16 = 16/16 = 1\)

Therefore, the distribution function is given by:\(F(x) = P(X ≤ x) = {1 if x ≥ 4,15/16 if x = 3,11/16 if x = 2,5/16 if x = 1,1/16 if x = 0}2.\)For Y, where n = 10 and p = 0.4, we have to find the largest number c such that\(P(Y ≥ c) ≥ 0.05.\)We know that the probability distribution is given by:\(B(y) = (10 choose y)0.4y(1 − 0.4)^(10−y), y = 0, 1, 2, 3, ..., 10\)We need to find the smallest value of c such that\(P(Y < c) < 0.05.\)

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The half of the number is 4.5 .

Given in question as  14 is subtracted from 6 times a number.

Let us suppose a number is x.

First find 6 times of a number = 6*x.

6 times can be defined as x + x + x + x + x + x = 6*x.

We have to subtract from 6 times a number.

14 is subtracted from 6 times a number means 6x - 14.

After subtracting 14 is left.

So 6x - 14 = 40.

Add 14 both side of equal sign.

6x-14+14 = 40+14.

6x = 54.

x = 54/6.

x = 9.

Half of the number x is 9/2 = 4.5.

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The equation for x for the given expression -1+√3x-8 = 7 is : 9.24.

In order to solve the equation for x we have to isolate variable x, simplify and solve for x.

Let isolate the variable x on one side of the equation.

-1 + √3x - 8 = 7

Simplify the left side by combining the constants:

-9 + √3x = 7

Isolate √3x by adding 9 to both sides:

√3x = 16

Solve for x by dividing both sides by √3:

x = 16/√3

x= 9.237

x = 9.24 ( Approximately)

Therefore the equation is 9.24.

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Answer:

1.875 hours

Step-by-step explanation:

1/a + 1/b = 1/c  where a and b are the times alone and c is the time together

1/3 + 1/5 = 1/c

Multiply by 15c to clear the fractions

15c(1/3 + 1/5 = 1/c)

5c+3c = 15

8c = 15

Divide by 8

8c/8 = 15/8

c = 1.875 hours

Answer:

12.5%

Step-by-step explanation:

Actual measurement of the window = 24 inches

Measured measurement of the window = 27 inches

We need to find the Rivers percent error. It can be calculated as follows :

% = (|actual value-measured value|)/actual value × 100

\(\%=\dfrac{27-24}{24}\times 100\\\\\%=12.5\%\)

So, River's percent error is 12.5%.

Answer:

Y ≤ X + 6

Step-by-step explanation:

Not sure if this is correct

Answer:

y<1/5x+6

Step-by-step explanation:

< bcs below line

dotted line means not equal(≤)

Answer:

20 feet

Step-by-step explanation:

We can use scale factors to represent the lengths. Since the flagpole's base is 4 times the tree's height, we can also say that the flagpole's height is 4 times the tree's height. Since the tree's height is 5 feet, the flagpole's height is 4 x 5, which is 20.