Graph the solution to the inequality on the number line.


|4y+8| <4

The angular speed of the pulley in rad/sec is 7.95 rad/sec, and the linear speed of the chain in cm/sec is 495.6 cm/sec.

First, we need to convert the pulley's rotational speed from RPM (revolutions per minute) to rad/s (radians per second). To do this, we can use the formula:

angular speed (in rad/s) = 2π × rotational speed (in RPM) / 60

Substituting the given values, we get:

angular speed (in rad/s) = 2π × 38 / 60 = 7.95 rad/s

Next, we can use the formula for linear speed of a point on the circumference of a circle:

linear speed = radius × angular speed

Substituting the values we have, we get:

linear speed = 26 cm × 7.95 rad/s = 206.7 cm/s

However, this is the linear speed of the pulley's circumference. Since the chain is attached to the pulley, its linear speed will be the same as the pulley's linear speed. Thus, the final answer for the linear speed of the chain is:

linear speed of chain = 206.7 cm/s × 2.4 = 495.6 cm/s

Here, 2.4 is the gear ratio of the chain to pulley.

For more questions like Speed visit the link below:

https://brainly.com/question/2923987

#SPJ11

The expression written using each base only once is 4¹¹ , the correct option is (a).

The expression 4⁸×4³ can be simplified using the rule of exponents,

The rule of exponents states that when we multiplying two exponential expressions with the same base, the exponents gets added.

which means that, nᵃ×nᵇ = nᵃ⁺ᵇ;

In this case the expression is: 4⁸×4³ , it has common base as "4",

So, by the rule of exponents, the power(exponents) gets added up ;

The expression "4⁸×4³" can be rewritten as 4⁸⁺³, which is equal to 4¹¹,

Therefore, Option(a)4¹¹, is the expression written using each base only once.

Learn more about Expression here

https://brainly.com/question/29122772

#SPJ4

The given question is incomplete, the complete question is

What is the expression written using each base only once? 4⁸×4³

(a) 4¹¹

(b) 12¹¹

(c) 4²⁴

(d) 64¹¹.

The mechanic must mix 12 gallons of a 40% antifreeze solution with 4 gallons of an 80% antifreeze solution to create 16 gallons of a 50% antifreeze solution.

To find out how much of a 40% antifreeze solution must be mixed with an 80% antifreeze solution to create 16 gallons of a 50% antifreeze solution, we can use the following equation:

40% x + 80% y = 50% (16)

Where x is the amount of 40% antifreeze solution and y is the amount of 80% antifreeze solution.

We can also use the fact that the total amount of solution must equal 16 gallons:

x + y = 16

Now we can solve for one variable in terms of the other. Let's solve for x in the second equation:

x = 16 - y

And substitute this value of x into the first equation:

40% (16 - y) + 80% y = 50% (16)

Simplifying:

[tex]6.4 - 0.4y + 0.8y = 8[/tex]

0.4y = 1.6

y = 4

Now we can substitute this value of y back into the equation for x:

x = 16 - 4

x = 12

To learn more about antifreeze solution here:

https://brainly.com/question/28057522#

#SPJ11

The measure of the central angle indicated is 60°.

The central angle of a circle is the angle that an arc takes up in the centre. The radius vectors are what make up the angle's arms.

The formula for calculating a central angle is: Central Angle = Arc length (AB) / Radius (OA) = (s 360°) / 2r, where "s" stands for arc length and "r" for circle radius.

Now here in the given diagram,

Let x equal the desired angle.

The central angle that we need to find is:

Now x = 360-120-(90+90)

⇒ x = 360-300

⇒ x = 60°

To know more about central angle, visit:

https://brainly.com/question/15698342

#SPJ1

The maximum of the sinusoidal function is 4

From the question, we have the following parameters that can be used in our computation:

The graph of the sinusoidal function

In the graph of the sinusoidal function, we can see that

The maximum is at y = 4

Also, we can see that

The minimum is at y = 1

Hence, the maximum is 4

Read more about sinusoidal function at

https://brainly.com/question/27174319

#SPJ1

Answer:

5

Step-by-step explanation:

The difference in price of both the shops is £0.25.  

What is price?

Price is the amount of money one pays for a good or service. It is determined by a variety of factors, such as supply and demand, the cost of production, and the availability of resources. Prices are also affected by government regulations, taxes, inflation, and other economic and market forces. The price of a product or service is an important factor in determining whether consumers will purchase it or not.

Shop A  | Shop B

200 cm | £0.50 | 300 cm | £0.75

The difference in the price of 300cm of ribbon between shop A and shop B is £0.25. Eloise spent £0.50 on 200cm of ribbon at shop A, and £0.75 on 300cm of ribbon at shop B. Therefore, the difference in price is £0.25.

To know more about price

https://brainly.com/question/19104371

#SPJ1

Answer: Using the given functions, we can model the distance, d(t), that the car is from the city as:

d(t) = f(t) + g(t) = 10 + 65t

So, after 2 hours of driving, the distance that the car has traveled from the city is:

d(2) = 10 + 65(2) = 10 + 130 = 140 miles

Therefore, Riordan is incorrect, and the correct distance the car is from the city after 2 hours of driving is 140 miles.

Step-by-step explanation:

Answer:

55/100 and 48/100, in decimal form it will be 0.55 and 0.48

Step-by-step explanation:

11/20 and 12/25

The common denominator in this question will be 100

55/100 and 48/100

So the slope-intercept form of the equation of the line passing through the two given points is:

y = -5x + 26

If an equation is expressed in the form y=mx+b, where m denotes the slope and b the y-intercept, it is said to be linear.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

To find the slope of the line passing through the two given points (5,1) and (2,16), we can use the formula:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) = (5,1) and (x2, y2) = (2,16)

m = (16 - 1)/(2 - 5) = -5

So the slope of the line is -5.

To find the y-intercept b, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Using the point (5,1) and the slope m = -5, we get:

y - 1 = -5(x - 5)

Simplifying this equation, we get:

y = -5x + 26

So the slope-intercept form of the equation of the line passing through the two given points is:

y = -5x + 26

To know more about linear equation visit:

https://brainly.com/question/29739212

#SPJ1

The process to find the scale factor of a shape and the concept of sequence of transformations is explained below.

In order to find the scale factor of a shape, we need to compare the corresponding side lengths of the original shape to the corresponding side lengths of the new shape after a dilation.

The scale factor is the ratio of any two corresponding side lengths.

The sequence of transformations is defined as the order in which different transformations are applied to a shape.

For example, if we have a triangle and we first translate it, then rotate it, and then dilate it, the sequence of transformations would be : translate → rotate → dilate.

Learn more about Scale Factor here

https://brainly.com/question/30948953

#SPJ4

The given question is incomplete, the complete question is

How do you find the scale factor of a shape? And What is the sequence of transformations?

The exponential function that models the percentage as a function of P is given as follows:

P(t) = 100(0.705)^t.

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

The parameters for this problem are given as follows:

Hence the function that models the data in the table is defined as follows:

P(t) = 100(0.705)^t.

More can be learned about exponential functions at brainly.com/question/30113628

#SPJ1

Answer:

80

Step-by-step explanation:

we will write an inequality of 1.50x + 130 =250

We subtract 130 from each side, so we have

1.50x=120

Now we divide by 1.50 on each side

X=80.

42 kilograms are equal to 6.6 stones.

A unit is a common element used to quantify similar physical quantities.

As per the given data:

1 kilogram = 2.2 pounds

1 stone = 14 pounds

For converting 42 kilogram to stones:

42 kilogram = 2.2 × 42 pounds

= 92.4 pounds

1 pound = (1/14) stone

= 92.4 × (1/14) stones

= 6.6 stones

Hence, 42 kilograms are equal to 6.6 stones.

To learn more about the unit, click:

brainly.com/question/11875738

#SPJ1

The polynomial f(x) of degree 3 with real coefficients and the given zeros is f(x) = x³ - x² + 4x + 2.

To find a polynomial f(x) of degree 3 with real coefficients and the given zeros, we need to use the fact that if a polynomial has a complex root, then its conjugate is also a root. This means that if 1-i is a root, then 1+i is also a root.

So, our polynomial f(x) has the following roots: -1, 1-i, 1+i.

We can write the polynomial as the product of its factors:

f(x) = (x - (-1))(x - (1-i))(x - (1+i))

Simplifying the factors:

f(x) = (x + 1)(x - 1 + i)(x - 1 - i)

Multiplying the factors:

f(x) = (x + 1)(x² - 2x + 2)

Expanding the polynomial:

f(x) = x³ - 2x² + 2x + x² - 2x + 2

Simplifying the polynomial:

f(x) = x³ - x² + 4x + 2

To know more about real coefficients click on below link:

https://brainly.com/question/8528053#

#SPJ11

the height of the antenna is approximately 24 meters.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

From the diagram, we see that we need to find the distance d and the height h. We can use the tangent function to find these values.

First, let's find d:

tan(θ) = h / (d + 1.51)

Rearranging, we get:

d = (h / tan(θ)) - 1.51

Next, let's find h:

tan(θ') = h / d

Substituting the expression for d that we found above, we get:

tan(θ') = h / ((h / tan(θ)) - 1.51)

Multiplying both sides by (h/tan(θ1)) - 1.51 and simplifying, we get:

h = (29 * tan(θ') * tan(θ)) / (tan(θ') - tan(θ))

Now we can plug in the values for the angles and solve for h:

h = (29 * tan(31°) * tan(17°)) / (tan(31°) - tan(17°))

h ≈ 24

So the height of the antenna is approximately 24 meters.

Learn more about right-angle triangles here:

https://brainly.com/question/3770177

#SPJ1

Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6

Degree of each term: 7, 4, 3, 1, and 0

Degree of the polynomial: 7

Leading term: -5s^(7)

Leading coefficient: -5

Constant term: -6

The terms of the polynomial are -5s^(7), -8s^(4), 6s^(3), 4s, and -6. The degree of each term is 7, 4, 3, 1, and 0, respectively. The degree of the polynomial is the highest degree of any of its terms, which is 7.

The leading term is the term with the highest degree, which is -5s^(7). The leading coefficient is the coefficient of the leading term, which is -5. The constant term is the term with a degree of 0, which is -6.

So, the terms are -5s^(7), -8s^(4), 6s^(3), 4s, and -6; the degree of each term is 7, 4, 3, 1, and 0; the degree of the polynomial is 7; the leading term is -5s^(7); the leading coefficient is -5; and the constant term is -6.

Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6

Degree of each term: 7, 4, 3, 1, and 0

Degree of the polynomial: 7

Leading term: -5s^(7)

Leading coefficient: -5

Constant term: -6

Learn more about Polynomial

brainly.com/question/11536910

#SPJ11

Answer:

Step-by-step explanation:

jkhnb and then efhrfehnb c3454k3

Answer:

The number is → 56

Step-by-step explanation:

tens digit [tex]\Rightarrow x[/tex]

unit digit [tex]\Rightarrow y[/tex]

"The difference between the digits of a two-digit number is 1...", " ...the unit digit is greater than the tens digit..."

[tex]y-x=1 \qquad \textbf{ec.1}[/tex]

"The number itself is one more (unit) than five times the sum of its digits..."

[tex]10x+y=5(x+y)+1\\ 10x+y= 5x + 5y+1\\5x= 4y+1 \qquad \textbf{ec.2}[/tex]

we clear "y" in equation 1:

[tex]y=1+x \qquad \textbf{ec.3}[/tex]

then we substitute in equation 2:

[tex]5x=4(1+x)+1\\5x=5+4x\\\boxed{x=5}[/tex]

Finally, we substitute in equation 3:

[tex]y=1+5\\\boxed{y=6}[/tex]

With this we have solved the exercise.

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Therefore by increasing  [tex]\alpha[/tex] smoothing characteristics we can achieve minimum MSE which is good for forecasting in exponential smoothing.

Therefore the pattern of the data is a horizontal pattern in time series.

The given data can be summarized as follows:

Week Value

1 24

2 13

3 20

4 12

5 19

6 23

7 15

a) To calculate a two-week moving average, we first need to calculate the average of the first two weeks:

[tex]MA_{1}=\frac{24+13}{2}=18.5[/tex]

Then we can calculate the moving average for the second week as follows:

[tex]MA_{2}=\frac{13+20}{2}=16.5[/tex]

Similarly, we can calculate the moving averages for the rest of the weeks:

Week Value Two-Week Moving Average

1 24

2 13 18.5

3 20 16.5

4 12 16.0

5 19 15.5

6 23 21.0

7 15 19.0

The forecast for the fourth week is the moving average for the second week (16.5), and the forecast for the fifth week is the moving average for the third week (16.0), and so on. The forecast error is the difference between the forecast value and the actual value.

Week Value Two-Week Moving Average Forecast Forecast Error

1 24  

2 13 18.5  

3 20 16.5  

4 12 16.0 16.5 -4.5

5 19 15.5 16.0 3.0

6 23 21.0 15.5 7.5

7 15 19.0 21.0 -6.0

The mean squared error (MSE) is the average of the squared forecast errors:

MSE= [tex]\frac{(-4.5)^{2}+3^{2}+7.5^{2}+(-6)^{2}}{4}=33.375[/tex]

The forecast for the eighth week is the moving average for the seventh week (19.0).

b) To calculate a three-week moving average, we first need to calculate the average of the first three weeks:

[tex]MA_{2}=\frac{24+13+20}{3}=19.0[/tex]

Then we can calculate the moving average for the third week as follows:

[tex]MA_{3}=\frac{13+20+12}{3}=15.0[/tex]

Similarly, we can calculate the moving averages for the rest of the weeks:

Week Value Three-Week Moving Average

1 24

2 13

3 20 19.0

4 12

Read more about time series plot here:

https://brainly.com/question/29654037

#SPJ1

Answer:

4 : 2 : 5

Step-by-step explanation:

To find the ratio of silver to brown to pink counters in simplest form, we need to divide the number of each type of counter by their greatest common factor.

The greatest common factor of 16, 8, and 20 is 4.

So, we divide each of the numbers by 4:

Silver counters: 16 ÷ 4 = 4

Brown counters: 8 ÷ 4 = 2

Pink counters: 20 ÷ 4 = 5

Therefore, the ratio of silver to brown to pink counters in simplest form is:

4 : 2 : 5

or

2 : 1 : 2.5 (if we prefer to express the ratio in decimal form)

Answer: 415

83 = [tex]\frac{y}{5}[/tex]

83(5) = y

415 = y

Answer:

y = 415

Step-by-step explanation:

83 = y/5

83 x 5 = y

415 = y

To write a C++ program that prints a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5, you can use the following code:

This program will print a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5. The table will display x in one decimal place, its square in 2 decimal places and its square root in 4 decimal places, with all numbers being right justified. The columns of the table will have appropriate headings.

Learn more about square

brainly.com/question/28348992

#SPJ11

{18, 36, 24, 48, 39, 72}

In Exercises 1-6, the subgroup generated by the given subset is a set of elements that are all powers of the same element.

1. The subset {2,3} of Z12 generates the subgroup {2, 4, 8, 3, 9, 6, 12}.
2. The subset {4,6} of Z12 generates the subgroup {4, 8, 6, 12}.
3. The subset {8,10} of Z18 generates the subgroup {8, 16, 10, 18}.
4. The subset {12,30} of Z36 generates the subgroup {12, 24, 30, 36}.
5. The subset {12,42} of Z6 generates the subgroup {12, 6}.
6. The subset {18,24,39} of Z generates the subgroup {18, 36, 24, 48, 39, 72}.

Learn more about subsets and subgroups

brainly.com/question/30883522

#SPJ11

The length of the escalator, considering the trigonometric ratios, is of

38.1 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 30º, we have that:

Hence the length of the escalator is obtained with the tangent as follows:

tan(30º) = 22/l

l = 22/tangent of 30 degrees

l = 38.1 ft.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

The solution of the given system of equations is x = -1 and y = 4.

The given system of equations is 4x + 8y = 40 and 6x + 3y = 6.

To solve this system of equations, we need to use elimination method. We can subtract 6x from both sides of the second equation and subtract 4x from both sides of the first equation. We get:

8y = 40 - 4x and 3y = 6 - 6x

We can now divide both sides of the second equation by 3 to obtain y = 2 - 2x.

We can substitute the value of y from the second equation into the first equation to get 4x + 8(2 - 2x) = 40, which simplifies to -8x = 8. We can solve this equation for x by dividing both sides by -8, resulting in x = -1.

Substituting the value of x into either equation, we can obtain y = 4. So, the solution of the given system of equations is x = -1 and y = 4.

To know more about elimination method click on below link:

https://brainly.com/question/12090959#

#SPJ11

The root(s) and multiplicity for each term are:
- Root: x = -3/2, Multiplicity: 4
- Root: x = 10, Multiplicity: 2
- Root: x = -1/2, Multiplicity: 6

The root(s) and multiplicity for each term are as follows:

- The term (2x+3) has a root of x = -3/2 and a multiplicity of 4. This means that the value of x = -3/2 makes the term (2x+3) equal to zero and that this root appears 4 times in the equation.
- The term (x-10) has a root of x = 10 and a multiplicity of 2. This means that the value of x = 10 makes the term (x-10) equal to zero and that this root appears 2 times in the equation.
- The term (2x+1) has a root of x = -1/2 and a multiplicity of 6. This means that the value of x = -1/2 makes the term (2x+1) equal to zero and that this root appears 6 times in the equation.

In summary, the root(s) and multiplicity for each term are:
- Root: x = -3/2, Multiplicity: 4
- Root: x = 10, Multiplicity: 2
- Root: x = -1/2, Multiplicity: 6

Learn more about root(s)

brainly.com/question/30405376

#SPJ11

Answer:

36.9

Step-by-step explanation:

sinJ=[tex]\frac{21}{35}[/tex]

    J= [tex]sin^{-1}[/tex][tex]\frac{21}{35}[/tex]

    J= 36.9

The set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.

The set of vectors {v1, v2, v3} is linearly dependent if there exists a set of real numbers a, b, and c such that a*v1 + b*v2 + c*v3 = 0 and at least one of a, b, or c is not equal to zero. In this case, we can write the equation as:

a*1 + b*2 + c*(-1) = 0

We can rearrange this equation to solve for h:

h = -a - 2*b + c

Now we can plug in the values for v1, v2, and v3:

h = -1 - 2*2 + (-1)*(-1)

h = -4

Therefore, the set of vectors {v1, v2, v3} is linearly dependent when h = -4.

Alternatively, we can also use the determinant of the matrix formed by the vectors to determine when the set is linearly dependent. The determinant of the matrix is given by:

| 1 2 -1 |
| -1 1 3 | = (1)(1)(h) + (2)(3)(-1) + (-1)(-1)(2) - (-1)(1)(-1) - (2)(-1)(1) - (1)(3)(2)
| 2 1 h |

Simplifying this equation gives:

h - 6 - 2 + 1 + 2 - 6 = 0

h - 11 = 0

h = 11

Therefore, the set of vectors {v1, v2, v3} is also linearly dependent when h = 11.

So the set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.

Learn more about linearly dependent

brainly.com/question/30076836

#SPJ11

Answer:

28 and 152 degrees

Step-by-step explanation:

Using sine inverse, the answer is 28 or 152 degrees.

Answer:48.87°

Step-by-step explanation: