The sun of two integers is 47. The larger is 7 more than three times the smaller number. Find the integers

In summary, the force required to give the wheel an acceleration of 4.46 rad/s2 when using a 9.00-cm-diameter sprocket is 8,550.54 N, and the force required when using a 5.58-cm-diameter sprocket is 13,764.83 N.

To answer (a) and (b), we need to determine the rotational inertia of the wheel, then calculate the torque and force required to accelerate the wheel with a given angular acceleration.
The rotational inertia of a wheel with all its mass concentrated on the outside radius can be calculated using the formula I = mr^2, where m is the mass of the wheel and r is its radius. In this case, the radius of the wheel is 63.8/2 cm (31.9 cm) and its mass is 1.71 kg, so the rotational inertia is I = \(1.71 * (31.9 cm)^2 = 17,214.939 cm^4.\)
To calculate the torque and force required to accelerate the wheel, we use the equation T = I * alpha, where T is the torque, I is the rotational inertia, and alpha is the angular acceleration. Plugging in the values given in the question, we get\(T = 17,214.939 cm^4 * 4.46\) rad/\(s2 = 76,954.848 Nm.\)
To calculate the force required to accelerate the wheel, we use the equation F = T / r, where F is the force, T is the torque, and r is the radius of the sprocket. For the 9.00-cm-diameter sprocket, the force required is F = 76,954.848 Nm / 9 cm = 8,550.54 N. For the 5.58-cm-diameter sprocket, the force required is F = \(76,954.848 Nm / 5.58\) cm = \(13,764.83 N.\)

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Answer:

correct

Step-by-step explanation:

She is correct.

For any integer, n, 5n is a multiple of 5.

5n + 3 is 3 more than a multiple of 5.

Start with 82. Subtract 3. Now you have 79.

79 is not a multiple of 5, so 5n + 3 will not contain the term 82.

Use an inverse trigonometric ratio to find m∠A. You know the lengths of the ... In △PQR, PR = 23 mm, QR = 39 mm, and m∠R = 163°.

Answer:

54.7599

Step-by-step explanation:

On solving the provided question, we can say that Considering that the test statistic inside the lower tail the rejection zone, the null hypothesis should be rejected.

A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.

\(H0:p=0.25\) (null hypothesis)

\(H0:p \neq 0.25\) (alternative hypothesis)

Do not reject the null because the test statistic\((-1.2) is >\) \(the critical value (-1.7531)\)

Considering that the test statistic is inside the lower tail of the rejection zone, the null hypothesis should be rejected.

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Step-by-step explanation:

A higher confidence interval means less power which in turns means a smaller rejection religion.So our confidence interval would become wider.

Answer:

Step-by-step explanation:

1. 7.2

2. 0.8

3. -0.8

4. -7.2

These are the answers i got, come back if they are still wrong.

Answer:

x = 3

Step-by-step explanation:

Jacob has 1/2 of a container of trail mix.

He is filling snack packs that each use about 1/6 of a container

We need to find the number of snack packs can Jacob make. Let he can make x snack packs.

\(\dfrac{1}{6}x=\dfrac{1}{2}\\\\x=3\)

Hence, he can make 3 snack packs.

Answer:

4

Step-by-step explanation:

1 pi is not rationa;

2. sqrt20 is not rationa;

3.sqrt7 is not rational

4 is the answer

Number four is rational

Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1

Answer:the answer is 9

Step-by-step explanation:

Answer:

0.81

Step-by-step explanation:

\(0.01 \times {3}^{4} = 0.01 \times 81 = 0.81\)

The value of the integral \(∫[√3, -√3] √(9e^(arctan(y))/(1 + y^2)) dy\) is \(6 * (e^(π/6) - e^(-π/6)).\) using substitution.

To evaluate the integral ∫[√3, -√3] √(9e^(arctan(y))/(1 + y^2)) dy, we can use a substitution.

Let u = arctan(y), then du = (1/(1 + y^2)) dy.

When y = -√3, u = arctan(-√3) = -π/3,

and when y = √3, u = arctan(√3) = π/3.

The integral becomes:

∫[-π/3, π/3] √(9e^u) du.

Next, we simplify the integrand:

√(9e^u) = 3√e^u.

Now, we can evaluate the integral:

∫[-π/3, π/3] 3√e^u du

= 3∫[-π/3, π/3] e^(u/2) du.

Using the power rule for integration, we have:

= 3 * [2e^(u/2)]|[-π/3, π/3]

= 6 * (e^(π/6) - e^(-π/6)).

Therefore, the value of the integral ∫[√3, -√3] √(9e^(arctan(y))/(1 + y^2)) dy is 6 * (e^(π/6) - e^(-π/6)).

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In equilateral triangles, 7.0 mm is the length of each edge of the diamond.

The equilateral triangle's definition?

An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle.

                                       A triangle with all three sides equal and interior angles of 60 degrees is said to be equilateral. Triangle with an equal number of sides is known as an isosceles triangle.

V = 0.4783 S³  = 161

   S³   =  161/0.47

       = ∛ 161/0.47

       ≈ 7.0 mm

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The experimental probability of the name Grace being​ chosen = 11/108

The theoretical probability of the name Grace being​ chosen = 1/6

We know that formula for the experimental probability of event A is :

P(A) = (Number of occurance of event A) / (Total number of trials)

Here, a name is chosen 108 times and the name Grace is chosen 11 times.

Let event A: the name Grace being​ chosen

the number of occurance of event A = 11

And the Total number of trials = 108

Using above formula the experimental probability would be,

P(A) = 11/108

Here, six different names were put into a hat.

This means that the number of possible outcomes n(S) = 6

And n(A) = 1

So, the theoretical probability would be,

P = n(A)/n(S)

P = 1/6

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Answer:

Density = 4779 grams per liter

Step-by-step explanation:

here we need to convert

pounds to gram

pint to liter

1 pound = 454 grams

1 pint = 0.57 liters

given

density = 6 pounds per pint

now using grams in place of pound and

liter in place of pint we have

density = 6 pounds per pint = 6*454 grams /0.57 liters

density = 2724 pounds/ 0.57 liters = 4778.94 grams / liters

Density when rounded to nearest whole number is 4779 grams / liters

10.............................

Answer:

br uh

Step-by-step explanation:

Answer:

i think your right - it might me d cause woudn't the gravity and the surface cancel out and the force would make it move because there is no opposite force i donkt know tho

The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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Answer:

The maker of a cell phone screen protector would like to estimate the proportion of customers who file a warranty claim. To do so, they select a random sample of 200 customers and determine that the 96% confidence interval for the true proportion of customers who file a warranty claim to be 0.15 to 0.28.

Step-by-step explanation:

Answer:

n = 2

Step-by-step explanation:

14 = n

7       1

cross-multiply:  7n = 14

n = 2

Answer:

8/21    ≈0.381

Explanation:

if you need the explanation message/comment under this answer for it :)

Answer:

184,586.566

Step-by-step explanation:

Just need to multiply 92293.283 by 2

The answer is 184586.566

Hope it helps.

a)The percentage of students will score below 620 in a typical year is 0.5808.

b)The score that the engineering school should set as a comparable standard on the ACT math test is 24 .

What is Probability?

Probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Given that;

\(\mu=480,\\)  \(\sigma=100\)

a) The percentage of students who will score below 620 is a typical year is obtained below:Ф

\(\therefore P(x < 620)\ =\ P\left(\frac{x-\mu}{\sigma} < \frac{x-480}{100}\right)\\\)

                        \(=\ P\left(\left(z\right) < \frac{620-480}{100}\right)\)

                       \(=\ P\left(\left(z\right) < 1.4\right)\)

                       \(=\ 1-P\left(\left(z\right) > 1.4\right)\)

                       \(=1-0.4192\)

                        \(=0.5808\)

\(\therefore\) the percentage of students will score below 620 in a typical year is 0.5808.

b) The average and standard deviation for ACT math score is :

\(\mu=18,\) \(\sigma=6\)

\(\therefore \ P\left(\frac{x-\mu}{\sigma} > \frac{x-18}{6}\right)=1\)

\(=\ P\left(\left(z\right) > \frac{x-18}{6}\right)\)

or  \(\frac{x-18}{6}=1\)

     \(x =\) 6 x 1 + 18

     \(x =\) 24

\(\therefore\) the score that the engineering school should set as a comparable standard on the ACT math test is 24 .

What is Standard deviation?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

What do you mean by average?

An average is defined as the sum of all the values divided by the total number of values in a given set. It is also known as the arithmetic mean.

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After 37 bounces, the ball's height will be less than 1 foot.

The initial height of the ball is 50 feet.

After first bounce, the ball will reach a height of:

= 50 feet * (1 - 10%)

= 45 feet.

After second bounce, it will reach a height of:

= 45 feet * (1 - 10%)

= 40.5 feet.

Height decreases by 10% after each bounce.

We have to set up an equation:

50 feet * (0.9)^n < 1 foot

Simplifying:

0.9^n < 1/50

Taking the logarithm:

n * log(0.9) < log(1/50)

n > log(1/50) / log(0.9)

n > 37.1298771746

n > 37.13.

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A differential equation is a mathematical equation that relates a function to its derivatives. It involves the unknown function and one or more of its derivative. The solution to the differential equation -

xy' − 2y = x^2, x > 0

is y = (1/4)x^3 + C/x.

To solve the differential equation, we will use the method of integrating factors.

The differential equation is: xy' - 2y = x^2

We can rearrange it in the standard form: y' - (2/x)y = x

The integrating factor (IF) is defined as e^∫(2/x) dx. Integrating 2/x with respect to x gives us 2ln|x|.

Therefore, the integrating factor is IF = e^(2ln|x|) = e^(ln(x^2)) = x^2.

Now, multiply the entire equation by the integrating factor x^2:

x^2(y' - (2/x)y) = x^2(x)

x^2y' - 2xy = x^3

Next, we recognize that the left-hand side is the derivative of (xy) with respect to x. Applying this, we get:

d/dx(xy) = x^3

Integrating both sides with respect to x:

∫d(xy) = ∫x^3 dx

xy = (1/4)x^4 + C

Finally, divide both sides by x:

y = (1/4)x^3 + C/x

where C is the constant of integration.

So, the solution to the given differential equation is y = (1/4)x^3 + C/x.

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The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

690.8 in^2

Step-by-step explanation:

First find the area of the three circles, by doing 3.14 r^2

With the innermost circle, 3.14 6^2 --> 113.04

With the second circle, 10 inches + 6 inches (inner circle radius), 3.14 16^2 --> 803.84.

With the outermost circle, you don't need it for the problem.

Then, we do subtraction to find the area of the shaded region, removing the "dount hole".

803.84 - 113.04 = 690.8 in^2

Answer:

18

Step-by-step explanation:

18 can be divided by 18 =1

54 divided by 18 = 3

The greatest common factor of numbers 18 and 54 is,

⇒ GCD = 18

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

We have to given that;

To find the greatest common factor of 18 and 54.

Now, We know that;

Greatest common factor of numbers are that highest number which divides exactly into two more numbers,  

Here, The numbers are,

⇒ 18 , 54

⇒ 18 = 18

⇒ 54 = 18 × 3

Hence, The greatest common factor of numbers 18 and 54 is,

⇒ GCD = 18

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