100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Crowbar: Effort, MA, VR, Efficiency

User

A crow bar of length 1m is pivoted about 20cm from the tip and a load if 400N is lifted by applying an effort at the other end. Calculate the effort, MA, VR and efficiency.

ChatGPT

To calculate the effort, mechanical advantage (MA), velocity ratio (VR), and efficiency of the crowbar system, we need to use the principles of levers.

Given:

Length of the crowbar (L) = 1 m

Distance from the pivot to the load (d₁) = 20 cm = 0.2 m

Load (W) = 400 N

Effort (E) can be calculated using the equation:

E × MA = W × VR

Calculating Effort:

Let's consider the distance from the pivot to the effort (d₂). Since the crowbar is a rigid object, the sum of the moments on both sides of the pivot should be zero.

(E) × (d₂) = (W) × (d₁)

E × (d₂) = W × (d₁)

E × (d₂) = 400 N × 0.2 m

E × (d₂) = 80 N·m

Since we are given the length of the crowbar (L) = 1 m, we can substitute d₂ = L - d₁.

E × (L - d₁) = 80 N·m

E × (1 m - 0.2 m) = 80 N·m

E × 0.8 m = 80 N·m

E = 80 N·m / 0.8 m

E = 100 N

Therefore, the effort required to lift the load is 100 N.

Calculating Mechanical Advantage (MA):

MA = (L - d₁) / d₁

MA = (1 m - 0.2 m) / 0.2 m

MA = 4

The mechanical advantage of the crowbar system is 4.

Calculating Velocity Ratio (VR):

VR = L / d₁

VR = 1 m / 0.2 m

VR = 5

The velocity ratio of the crowbar system is 5.

Calculating Efficiency:

Efficiency (η) = (MA / VR) × 100

η = (4 / 5) × 100

η = 80%

The efficiency of the crowbar system is 80%.

To summarize:

Effort (E) = 100 N

Mechanical Advantage (MA) = 4

Velocity Ratio (VR) = 5

Efficiency (η) = 80%

User

the phsican orders 15mg of tramadol (liq). On hand is 30mg/2ml vials. how many ml will the MA administer

ChatGPT

To calculate the amount of liquid tramadol the physician will administer, we need to determine the volume (in milliliters) of the medication.

Given:

Ordered dose of tramadol = 15 mg

Concentration of tramadol in vials = 30 mg/2 ml

To find out the required volume, we can set up a proportion:

(30 mg / 2 ml) = (15 mg / x ml)

Cross-multiplying, we have:

30 mg * x ml = 15 mg * 2 ml

30x = 30

Dividing both sides by 30:

x = 1

The required volume of liquid tramadol to administer the ordered dose of 15 mg will be 1 ml.

Therefore, the physician will administer 1 ml of tramadol.

Answer:

the MA will administer 1 ml of tramadol liquid.

Step-by-step explanation:

The yield to maturity of the bond is -2.3%

The yield to maturity (YTM) of a bond is the effective annual interest rate that an investor will receive if they hold the bond until maturity. It is calculated by taking into account the bond's coupon rate, the current market price, and the number of years until maturity.

In this case, the bond has a coupon rate of 8.8%, which means that it pays interest of 4.4% (8.8% / 2) per six months. The bond is currently selling for 112% of par value, which means that an investor would pay $1,120 for a bond with a face value of $1,000. The bond has 13 years remaining until maturity, which means that there are 26 six-month periods until maturity.

To calculate the YTM, we can use the following formula:

YTM = (C + (F - P) / n) / 2

Where:

Plugging in the values, we get:

YTM = (4.4% + (1,000 - 1,120) / 26) / 2

YTM = -2.3%

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The combined weight of the 3/4 lb bags is 1 1/2 lb.

To get combined weight of the 3/4 lb bags, we must know number of bags that weigh 3/4 lb to calculate their total weight.

Given the list of bags and weights:

[tex]1/4 lb, 1/4 lb, 3/4 lb, 1/2 lb, 1/4 lb, 3/4 lb[/tex]

There are two bags that weigh 3/4 lb.

We wlll calculate their total weight as follows:

Total weight of 3/4 lb bags:

= 2 * 3/4 lb

= 6/4 lb

= 1 1/2 lb.

Full question:

A Student makes bags of candy for Spring. The amount of candy in each bag is listed below. 1/4 lb, 1/4 lb, 3/4 lb, 1/2 lb, 1/4 lb, 3/4 lb. What is the combined weight of the 1/4 bags?

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Answer:

-5+√2 and -5-√2

Step-by-step explanation:

With the quadratic formula:

[tex]\displaystyle x^2 + 10x + 25 = 2\\\\x^2+10x+23=0\\\\x=\frac{-10\pm\sqrt{10^2-4(1)(23)}}{2(1)}=\frac{-10\pm\sqrt{100-92}}{2}=\frac{-10\pm\sqrt{8}}{2}=\frac{-10\pm2\sqrt{2}}{2}=-5\pm\sqrt{2}[/tex]

We can also complete the square (which is faster):

[tex]x^2+10x+25=2\\(x+5)^2=2\\x+5=\pm\sqrt{2}\\x=-5\pm\sqrt{2}[/tex]

The number with a z-score of -2.2 is given as follows:

X = 1.2.

The z-score formula is defined as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\mu = 10, \sigma = 4[/tex]

Hence the score X is given as follows:

-2.2 = (X - 10)/4

X - 10 = 8.8

X = 1.2.

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The simplified form of the expression -2(-8x+7)-(-3x - 7) is 19x - 7.

To simplify the expression -2(-8x+7)-(-3x - 7), we can start by applying the distributive property and simplifying the terms.

First, we distribute -2 to (-8x+7):

-2*(-8x) + (-2)*7 - (-3x) - (-7)

This simplifies to:

16x - 14 + 3x + 7

Next, we combine like terms:

(16x + 3x) + (-14 + 7)

This simplifies to:

19x - 7

Therefore, the simplified form of the expression -2(-8x+7)-(-3x - 7) is 19x - 7.

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Step-by-step explanation:

At t = 4   bird is at  6 m

at t= 14 bird is at 29 meters

   bird taveled  29 -6 = 23 meters   in 10 seconds

      velocity = 23 m / 10 s = 2.3 m/ s

The expression that is not equivalent to AC is:

c) BC / tan 20°

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

To find the expression which not equivalent to AC, we have to know which expressions are equivalent to AC.

∠C = 180 - 160 = 20° (sum of angles on a straight line)

∠B = 70°

Using trig. ratios, let's find the expressions that are equivalent to AC:

sin 70° = AC / BC

AC = BC sin 70°

tan 70° = AC / BA

AC = BA tan 70°

cos 20° = AC/BC

AC = BC cos 20°

tan 20° = BA /AC

AC = BA / tan 20°

Therefore, BC / tan 20° is the expression that is not equivalent to AC.

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Evaluating the function f(x) = -2x + 5 when x = -1 is 7

Evaluating a function involves calculating the value of the function for a given input or argument. When you evaluate a function, you substitute the input value into the function's expression and perform the necessary computations to determine the corresponding output value.

A function is typically defined by an equation or rule that relates the input value (often represented as x) to the output value (often represented as f(x)). By evaluating the function, you can determine the specific output value corresponding to a particular input

In this problem given, we can evaluate the function by substituting the value for x into it.

f(x) = -2x + 5

f(-1) = -2(-1) + 5

f(-1) = 2 + 5

f(-1) = 7

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The value of the green box is 0.

To solve the equation[tex]{3x-6} +{ x-2}= \frac{3x-6 + x - 2}{1} = 180$[/tex], we first simplify the left side of the equation:

[tex]{3x-6}{x-2} = \frac{(3x-6) + (x-2)}{x-2} = \frac{4x-8}{x-2}$$[/tex]

Now we can rewrite the original equation as:

[tex]\frac{4x-8}{x-2} = 180$$[/tex]

Next, we can multiply both sides of the equation by x-2 to eliminate the denominator:

[tex]$$(4x-8) = 180(x-2)$$[/tex]

Expanding the right side gives:

[tex]$$(4x-8) = 180x - 360$$[/tex]

Simplifying and moving all the terms to the left side gives:

[tex]$$176x - 352 = 0$$[/tex]

Adding 352 to both sides gives:

176x = 352

Finally, dividing both sides by 176 gives:

[tex]x = \frac{352}{176} = 2[/tex]

Therefore,  since there is no constant term on the left side of the equation after combining like terms.

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Answer:

[tex]\frac{2}{3}\ln(x+1)-\frac{1}{x-2} -\frac{2}{3}\ln(x-2)+C[/tex]

Step-by-step explanation:

Integrate the following expression.

[tex]\int \frac{-x+5}{(x^2-4x+4)(x+1)}[/tex]

[tex]\hrulefill[/tex]

In order to integrate this function we are gonna have to use partial fraction decomposition. Start by factoring the the denominator completely.

[tex]\int \frac{-x+5}{(x^2-4x+4)(x+1)}dx\\\\\Longrightarrow \int \frac{-x+5}{(x-2)^2(x+1)}dx[/tex]

Now we can apply partial fractions. Partial fractions allows us to split up complex fractions, in doing so this will make them easier to integrate.

[tex]\frac{-x+5}{(x-2)^2(x+1)}=\frac{A}{x+1}+\frac{B}{(x-2)^2}+\frac{C}{x-2}\\\\\Longrightarrow \frac{-x+5}{(x-2)^2(x+1)}=\frac{A}{x+1}+\frac{B}{(x-2)^2}+\frac{C}{x-2} \Big](x-2)^2(x+1)\\\\\Longrightarrow \boxed{-x+5=A(x-2)^2+B(x+1)+C(x-2)(x+1)}[/tex]

Expand the right-hand-side and use the comparison method to find the values of the undetermined coefficients, A, B, and C.

[tex]-x+5=A(x-2)^2+B(x+1)+C(x-2)(x+1)\\\\\Longrightarrow -x+5=Ax^2-4Ax+4A+Bx+B+Cx^2-Cx-2C\\\\\Longrightarrow \boxed{0x^2-x+5(1)=(A+C)x^2+(-4A+B-C)x+(4A+B-2C)(1)}[/tex]

We can now form a system of equations.

For x^2 terms:

[tex]A+C=0[/tex]

For x terms:

[tex]-4A+B-C=-1[/tex]

For #'s:

[tex]4A+B-2C=5[/tex]

[tex]\Longrightarrow \left\{\begin{array}{ccc}A+C=0\\-4A+B-C=-1\\4A+B-2C=5\end{array}\right[/tex]

You can use any method of choice to solve the system of equations. I am going to put the system in a matrix and use my calculator to row reduce.

[tex]\Longrightarrow \left[\begin{array}{ccc}1&0&1\\-4&1&-1\\4&1&-2\end{array}\right] =\left[\begin{array}{c}0\\-1\\5\end{array}\right]\\\\ \\ \ \ \ \Longrightarrow \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] =\left[\begin{array}{c}\frac{2}{3} \\1\\-\frac{2}{3}\end{array}\right]\\\\\\\therefore \boxed{A=\frac{2}{3}, \ B=1, \ \text{and} \ C=-\frac{2}{3}}[/tex]

Now we can split up the fraction.

[tex]\frac{-x+5}{(x-2)^2(x+1)}=\frac{A}{x+1}+\frac{B}{(x-2)^2}+\frac{C}{x-2}\\\\\Longrightarrow \boxed{\frac{-x+5}{(x-2)^2(x+1)}=\frac{\frac{2}{3} }{x+1}+\frac{1}{(x-2)^2}+\frac{-\frac{2}{3}}{x-2}}[/tex]

We can integrate the three fractions separately.

[tex]\Longrightarrow \int \frac{\frac{2}{3} }{x+1}dx+ \int \frac{1}{(x-2)^2}dx+\int \frac{-\frac{2}{3}}{x-2}dx\\\\\Longrightarrow \boxed{\frac{2}{3}\int \frac{1 }{x+1}dx+ \int \frac{1}{(x-2)^2}dx-\frac{2}{3}\int \frac{1}{x-2}dx}\\\\[/tex]

For the first integral let u=x+1 => du=dx, for the second let v=x-2 => dv=dx, and for the third integral let w=x-2 => dw=dx

[tex]\Longrightarrow \frac{2}{3} \int \frac{1 }{u}du+ \int \frac{1}{v^2}dv-\frac{2}{3}\int \frac{1}{w}dw\\\\\Longrightarrow \boxed{\frac{2}{3} \int \frac{1 }{u}du+ \int v^{-2}dv-\frac{2}{3}\int \frac{1}{w}dw}[/tex]

Use the rules of integration to integrate.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Natural Log Rule:}}\\\\ \int\frac{1}{x}dx=\ln(x) \end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Power Rule:}}\\\\ \int x^ndx=\frac{x^{n+1}}{n+1} \end{array}\right}[/tex]

[tex]\frac{2}{3} \int \frac{1 }{u}du+ \int v^{-2}dv-\frac{2}{3}\int \frac{1}{w}dw\\\\\Longrightarrow \frac{2}{3}\ln(u)-v^{-1}-\frac{2}{3}\ln(w)+C\\\\\Longrightarrow \frac{2}{3}\ln(x+1)-(x-2)^{-1}-\frac{2}{3}\ln(x-2)+C\\\\\Longrightarrow \frac{2}{3}\ln(x+1)-\frac{1}{x-2} -\frac{2}{3}\ln(x-2)+C\\\\\therefore \boxed{\boxed{\int \frac{-x+5}{(x^2-4x+4)(x+1)}=\frac{2}{3}\ln(x+1)-\frac{1}{x-2} -\frac{2}{3}\ln(x-2)+C}}[/tex]

Thus, the given integral is solved where "C" is some arbitrary constant that can be found given an initial condition.

The numeric values for each expressions are given as follows:

From the graph of function f(x), the numeric values are given as follows:

From the graph of function g(x), the numeric values are given as follows:

Hence the numeric values are found replacing the values on the expressions as follows:

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Answer:

85 feet

Step-by-step explanation:

To find the distance traveled by the laser pointer's beam, we can use the Pythagorean theorem. The laser beam forms a right triangle with the tower as one side and the distance traveled as the hypotenuse.

Let's denote the distance traveled by the laser beam as x. We can set up the following equation using the Pythagorean theorem:

x^2 = 40^2 + 75^2

Simplifying this equation:

x^2 = 1600 + 5625

x^2 = 7225

Taking the square root of both sides:

x = √7225

x = 85

Therefore, the laser pointer's beam has traveled approximately 85 feet.

The first four terms of the geometric sequence with a1 = 3 and r = 2 are:

3, 6, 12, 24.

In a geometric sequence, each term is obtained by multiplying the previous term by a common ratio. Given that a1 (the first term) is 3 and the common ratio (r) is 2, we can find the first four terms of the sequence.

The general formula for the nth term of a geometric sequence is given by: an = a1 * , where an represents the nth term.

Let's calculate the first four terms using this formula:

For n = 1:

a1 = 3 * 2^(1-1) = 3 * [tex]2^0[/tex] = 3 * 1 = 3

For n = 2:

a2 = 3 * 2^(2-1) = 3 * [tex]2^1[/tex] = 3 * 2 = 6For n = 3:

a3 = 3 * 2^(3-1) = 3 *[tex]2^2[/tex] = 3 * 4 = 12

For n = 4:

a4 = 3 * 2^(4-1) = 3 * [tex]2^3[/tex] = 3 * 8 = 24

Therefore, the first four terms of the geometric sequence with a1 = 3 and r = 2 are:

3, 6, 12, 24.

These are the correct values for the terms of the sequence. By understanding the concept of a geometric sequence and using the formula correctly, you can confidently determine the first four terms and succeed in your studies.

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The equation of the ellipse that has the center at (0, 0) the vertex at (-8, 0), and the covertex at (0, 4) is; [tex]\frac{x^2}{64} + \frac{y^2}{16} = 1[/tex]

The standard form of the equation of an ellipse is as follows;

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2}=1[/tex]

Where;

a = The semi major axis

b = The semi minor axis

The semi major axis is the distance from the center of the ellipse to the vertex, and the semi minor axis is the distance from the center to the co-vertex.

The coordinate of the center of the ellipse = (0, 0)

The coordinates of the vertex = (-8, 0)

The coordinates of the co-vertex = (0, -4)

The ellipse has an horizontal major axis, therefore;

a = |0 - (-8)| = 8, and b = |0 - 4| = 4

The equation of the ellipse is therefore;

[tex]\frac{x^2}{8^2} + \frac{y^2}{4^2}=\frac{x^2}{64} + \frac{y^2}{16} = 1[/tex]

[tex]\frac{x^2}{64} + \frac{y^2}{16} = 1[/tex]

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The measurement closest to the value of x is 4.8 units.

To find the length of side EF (denoted as x), we can use the trigonometric function tangent (tan). Since we know the angle EDF is 20 degrees and the adjacent side DE is 14 units, we can use the formula:

tan(∠EDF) = opposite/adjacent

tan(20°) = EF/DE

We can rearrange the equation to solve for EF (x):

0EF = DE * tan(∠EDF)

EF = 14 * tan(20°)

Using a calculator to evaluate the tangent of 20 degrees, we find:

EF ≈ 4.809 units

Among the given options, the measurement closest to the value of x is 4.8 units. 4.8 is the closest value.

To further verify this, we can also evaluate the other options:

5.1 units: This is greater than the calculated value of 4.809 units.

13.2 units: This is significantly larger than the calculated value and does

not match the given information.

14.9 units: This is even larger than the length of side DE, which is not possible in a right triangle.

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The square root of 9 by long division method will give an answer of 3.

1: Group the digits of 9 into pairs from right to left. Since 9 is a single-digit number, we can consider it as a pair by itself.

2: Find the largest number whose square is less than or equal to the leftmost pair. In this case, the largest number whose square is less than or equal to 9 is 3.

3: Write 3 as the divisor on the left, and the quotient on the top right.

3 √ 9 |  0

4: Multiply the divisor (3) by the quotient (3), and write the result under the 9.

3 √ 9 |  0

      - 9

5: Subtract the result (9) from the leftmost pair (9), and write the difference (0) below the line.

3 √ 9 |  0

      - 9

       0

6: Bring down the next pair (0) to the right of the difference.

3 √ 9 |  0

      - 9

       0

     -----

7: Double the quotient (3) and write a blank space to the right.

3 √ 9 |  0

      - 9

       0

     -----

       0

      ?

8: Find a digit to fill in the blank space, such that when the new divisor (37) is multiplied by the digit, the result is less than or equal to the current dividend (0). In this case, the largest digit we can use is 0.

9: Write the digit (0) as the new quotient, and write the product of the new divisor (37) and the new quotient (0) below the line.

3 √ 9 |  0

      - 9

       0

     -----

       0

      0

10: Subtract the product (0) from the current dividend (0), and write the difference (0) below the line.

3 √ 9 |  0

      - 9

       0

     -----

       0

      0

      - 0

11: Since there are no more pairs to bring down, we have reached the end of the division. The square root of 9 is 3.

√9 = 3.

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Then 62.5% of the campers at the Wild Outdoors camp this morning will be horseback riding

To find the percentage of campers that will be horseback riding, we need to first add the ratio together to get the total number of parts. In this case, the ratio of horseback riding to canoeing is 5:3, so there are 5 + 3 = 8 parts in total.

To find the percentage of campers that will be horseback riding, we divide the number of parts for horseback riding by the total number of parts, then multiply by 100 to get the percentage.

So, 5 parts out of 8 parts are for horseback riding. This is equivalent to 5/8 or 0.625 as a decimal. To find the percentage, we multiply by 100, which gives us 62.5%.

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The simplified expression is 6x. Simonne simplifies the expression 12 minus 3 times negative 2x plus 4 to 6x by following the order of operations, performing the necessary multiplication and subtraction.

To simplify the expression 12 minus 3 times negative 2x plus 4, Simonne follows the order of operations (also known as PEMDAS) to ensure the correct simplification.

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's break down the steps:

Step 1: Simplify within parentheses

The expression within the parentheses is -2x + 4. Since there is no exponent or multiplication/division to perform within the parentheses, we move to the next step.

Step 2: Apply the multiplication

The multiplication operation is between 3 and the expression within parentheses (-2x + 4). We distribute the 3 to each term within the parentheses by multiplying each term by 3:

3*(-2x) + 3*4

This simplifies to:

-6x + 12

Step 3: Apply subtraction

The original expression is 12 minus the result from Step 2 (-6x + 12):

12 - (-6x + 12)

To subtract a negative, we can rewrite the expression as:

12 + (-1)*(-6x + 12)

Next, we distribute the -1 to each term within the parentheses:

12 + (-1)*(-6x) + (-1)*12

Simplifying, we have:

12 + 6x - 12

The 12 and -12 cancel each other out, leaving us with:

6x.

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5. Area = 63.75 square units

Perimeter = 34 units

Sum of interior angles = 30 degrees

6. Area = 61. 40 square units

7. Length = 58. 2 units

We need to know that formula for calculating the area of a trapezoid is expressed as;

5. Area = a + b/2(h)

Substitute the values, we have;

Area = 6.5 + 10.5/2(7.5)

Add the values

Area = 63.75 square units

Perimeter = a + b+ c + d

Perimeter = 8.5 +6.5 + 10. 5 + 8.5

Add the values

= 34 units

6. Area of a sector is  = (θ/360º) × πr²

= 110/360 × 3.14 × 8²

Find the square and multiply

= 61. 40 square units

7. Length of an Arc = θ × (π/180) × r

Length = 210 × 3.14/180 × 16

Multiply the values

Length = 58. 2 units

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Boone and Greenville are 36 inches apart from each other.

We have the scale

2 inches = 25 miles

So, for 1 inch the scale = 25/2 = 12.5 miles

Boone and Greenville are 450 miles apart.

Then, the measurement of distance between Boone and Greenville on the map

= 450 / 12.5

= 36 inches

Thus, Boone and Greenville are 36 inches apart from each other.

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56

One measure of the center is the mean.

Mean

The mathematical mean of data is also called the average. There are 3 main measures of center: the mean, median, and mode. The most common of these 3 is mean. However, each measurement has its own advantages and disadvantages. Since there are no outliers in this data set, the mean is a good measure of the center.

Finding Mean

In order to find the mean of a data set, we need to add all the terms and divide by the number of terms. In this case, there are 7 terms in the set. The first step is to add all the terms.

Then, divide the sum by 7.

So, the mean of the data set is 56.

The probability of rolling a 3 is: Probability = 1/6. Option D

To determine the probability of rolling a 3 on a fair, six-sided die, we need to consider the total number of possible outcomes and the number of favorable outcomes.

A fair, six-sided die has six faces, numbered from 1 to 6. Each face has an equal chance of appearing when the die is rolled.

In this case, there is only one face with the number 3, so there is only one favorable outcome for rolling a 3.

The total number of possible outcomes when rolling the die is six, corresponding to the numbers 1 to 6 on the faces.

Therefore, the probability of rolling a 3 can be calculated as:

Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the number of favorable outcomes is 1 (rolling a 3), and the total number of possible outcomes is 6.

Thus, the probability of rolling a 3 is:

Probability = 1/6. Option D is correct.

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Answer:

5

Step-by-step explanation:

From the given division, the remainder is 0 and the quotient is 5.

Given that, 200 divided by 40.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Here, 200/40

40)200(5

    200

_______

     0

So, remainder = 0 and quotient = 5

Therefore, from the given division, the remainder is 0 and the quotient is 5.

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In mathematics, the term "difference" is commonly associated with subtraction. Subtraction is an arithmetic operation that involves finding the difference between two numbers or quantities.

When we subtract one number from another, we are essentially finding the difference between them. The result of a subtraction operation is called the difference. For example, in the expression 10 - 5, the difference is 5, indicating that the number 5 is the result of subtracting 5 from 10.

Subtraction is denoted by the minus sign "-" or by using the word "minus" or "subtract" in mathematical expressions. For instance, in the equation 8 - 3, we are subtracting 3 from 8 to find the difference.

The concept of difference is fundamental in various mathematical applications. It allows us to compare quantities, measure distances, determine changes, and solve various problems. For instance, when analyzing data sets, we often calculate the differences between values to understand patterns, trends, or changes over time.

The difference between two numbers can be positive, negative, or zero. If the minuend (the number from which subtraction is performed) is greater than the subtrahend (the number being subtracted), the difference is positive. If the subtrahend is greater, the difference is negative. When both numbers are equal, the difference is zero.

For example, in the subtraction 7 - 3, the difference is 4. In the subtraction 5 - 9, the difference is -4. And in the subtraction 6 - 6, the difference is 0.

Overall, the concept of difference is a crucial aspect of subtraction, providing a measure of the numerical distance between two quantities. It allows us to express the result of a subtraction operation and plays a significant role in various mathematical calculations and analyses.

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The percentage change in Alphabet's annual revenue from 2011 to 2018 was 261%.

The percentage change can be determined by computing the change (difference) in revenue between 2011 and 2018.

The result is divided by the 2011 revenue and multiplied by 100 to express the resulting quotient in percentages.

Alphabet's annual revenue in 2011 = $37,905 million

Alphabet's annual revenue in 2018 = $136,819 million

The increase in revenue = $98,914 ($136,819 - $37,905) million

Percentage change (increase) in revenue = 260.95% ($98,914 ÷ $37,905 x 100)

= 261%

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⇒ 32% of the people who prefer French fries also prefer pizza

⇒ 60% of the people surveyed prefer burgers, and 40% prefer pizza.

To find out what percentage of people who prefer French fries also prefer pizza,

According to the given information.

60% of the people surveyed prefer burgers over pizza, and of those people, 48 prefer french fries over salad.

This means that 40% of the people surveyed prefer pizza over burgers.

Now, we have to find out what percentage of the people who prefer French fries also prefer pizza.

We know that 48 people prefer French fries over salad,

But we don't know how many of those people prefer burgers or pizza. However, we do know that all of the people surveyed fall into one of these categories:

They either prefer pizza or burgers.

Therefore,

Assume that the remaining 52% of the people surveyed prefer burgers over pizza.

To find the percentage of people who prefer French fries and pizza,

Use a proportion:

⇒ 48 / (40% of 75) = x / 100%

Solving for x, we get:

⇒ x = (48 / (40% of 75 ) x 100%

      = 32%

Therefore,

32% of the people who prefer French fries also prefer pizza.

To find out what percentage of people prefer pizza,

We know that 40% of the people surveyed prefer pizza over burgers, and we know that 28 of the people who prefer pizza also prefer salad.

To find the percentage of people who prefer pizza,

Use a proportion:

⇒ (40% of 75) = y / 100%

Solving for y, we get:

⇒ y = (40% of 75) x 100% = 30

Therefore,

30 people prefer pizza.

To find the percentage of people who prefer pizza, we can use another proportion:

⇒ 30 = (100% - z) / 100% x 75

Solving for z, we get:

z = 60%

Therefore, 60% of the people surveyed prefer burgers, and 40% prefer pizza.

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Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

also the rule of exponents/ radicals

[tex]\sqrt[n]{a^{m} }[/tex] = [tex]a^{\frac{m}{n} }[/tex]

let

[tex]log_{5}[/tex][tex]\sqrt[4]{5}[/tex] = n , then

[tex]\sqrt[4]{5}[/tex] = [tex]5^{n}[/tex] , that is

[tex]5^{\frac{1}{4} }[/tex] = [tex]5^{n}[/tex]

since bases on both sides are the same, both 5 , then equate the exponents

n = [tex]\frac{1}{4}[/tex] ( = 0.25 )

The value of the angle S in the parallelogram is 45°.

Given is a parallelogram QRST where angle T = 135° we need to find the value of angle S,

Since the angle S and T are the adjacent angles and we know that the adjacent angles in a parallelogram are supplementary,

So,

∠T + ∠S = 180°

135° + ∠S = 180°

∠S = 45°

Hence the value of the angle S in the parallelogram is 45°.

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