A number cube is rolled 500 times. Here are the results: Outcome Rolled 1 2 3 4 5 6 Calculate the following probabilities to the nearest thousandth. The theoretical probability of rolling a 5 or 6 The experimental probability of rolling a 5 or 6 [Choose ] Number of Rolls 81 95 79 89 80 76 [Choose]​

The missing side of the right triangle is √57

To find the missing side of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Let's assume the missing side is represented by the variable x.

According to the Pythagorean theorem:

(2√6[tex])^2 + x^2 = 9^2[/tex]

Simplifying, we have:

[tex]4 \times 6 + x^2 = 81\\24 + x^2 = 81\\x^2 = 81 - 24\\x^2 = 57[/tex]

Taking the square root of both sides, we get:

x = √57

Thus, the missing side of the right triangle is √57

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Answer:

a set of numbers in order of least to greatest

The quadratic equation in standard form that corresponds to the graph shown above is f(x) = x² + 2x - 8

In Mathematics and Geometry, the standard form of a quadratic function can be modeled and represented by using the following mathematical expression;

y = ax² + bx + c

Where:

In this scenario and exercise, we would write a quadratic function that represent f(x) in standard form and with a leading coefficient of 1 by using the roots (-4, 0) and (2, 0) as follows;

f(x) = (x + 4)(x - 2)

f(x) = x² - 2x + 4x - 8

f(x) = x² + 2x - 8

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The slope of the line that is perpendicular to the line y = 3x - 8 is -1/3.

The given line has an equation in slope-intercept form, which is y = 3x - 8. In this form, the coefficient of x represents the slope of the line.

Therefore, the slope of the given line is 3.

To find the slope of a line perpendicular to the given line, we need to take the negative reciprocal of the slope.

The negative reciprocal of 3 is -1/3.

Therefore, the slope of the line that is perpendicular to the line y = 3x - 8 is -1/3.

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Answer:

-3.8 > -4.5

Step-by-step explanation:

Convert the fraction to decimal and then compare.

[tex]\sf -4\dfrac{1}{2}=\dfrac{-9}{2}[/tex]

          = -4.5

Now compare (-3.8) & (-4.5)

-3.8 > -4.5

Answer:

0.168 ft aprox

Step-by-step explanation:

To solve this problem, we can use similar triangles and proportions. Let's denote the distance ahead of the car where the light beam hits the ground as "x" (in feet).

According to the given information, the light beam drops 2 inches for every 26 feet horizontally. We can set up the following proportion:

2 inches / 26 feet = x inches / x + 26 feet

To solve for x, we can cross-multiply and solve the resulting equation. Let's convert inches to feet to maintain consistent units:

2 inches = 2/12 feet = 1/6 feet

1/6 feet / 26 feet = x feet / x + 26 feet

1/6 * (x + 26) = 26 * x

x/6 + 26/6 = 26x

x + 26 = 156x

156x - x = 26

155x = 26

x = 26 / 155 ≈ 0.168 ft

Therefore, the headlights will hit the ground approximately 0.168 feet (or 2.016 inches) ahead of the car.

Answer:

Step-by-step explanation:

The value of the given expression is,

[tex]4^{- 5/2[/tex] =  1/32

[tex](1/16) ^ {- 3/2[/tex] = 64

We have to given that,

Expressions to solve are,

⇒ [tex]4^{- 5/2[/tex]

And, [tex](1/16) ^ {- 3/2[/tex]

We  know that,

Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself

Now, We can simplify the given expression,

By using law of exponents

We get,

⇒ [tex]4^{- 5/2}[/tex]

⇒ [tex]2^{2(- 5/2)}[/tex]

⇒ 2⁻⁵

⇒ 1/2⁵

⇒ 1/32

Thus,

The value of   [tex]4^{- 5/2[/tex] =  1/32

The given expression is,

⇒[tex](1/16) ^ {- 3/2[/tex]

By using law of exponents

We get,

⇒ [tex]16 ^{3/2}[/tex]

⇒ [tex](4^2)^{3/2}[/tex]

⇒ 4³

⇒ 64

The value of  [tex](1/16) ^ {- 3/2[/tex] = 64

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Using a trigonometric relation, we can see that the value of x is 10.39

Here we have a right triangle. We can see that we know the measures of the hypotenuse, and the angle opposite to the side x.

Then to get the value of x, we can use the trigonometric relation:

sin(a) = (opposite cathetus)/hypotenuse.

Replacing the values that we know, we will get.

sin(60°) = x/12

solve that for x:

12*sin(60°) = x

10.39 = x

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Answer: z=3

Step-by-step explanation:

The zeros of this expression are irrational, so it cannot be factored using integers.

When factoring a quadratic expression, we are trying to express it as the product of two binomial factors.

In some cases, such as when the quadratic has irrational zeros, it may not be possible to factor it using integers.

In the case of the quadratic expression x² - 12x + 13, the discriminant (b^2 - 4ac) is equal to (-12)² - 4(1)(13)

= 144 - 52

= 92.

Since the discriminant is positive and not a perfect square, the zeros of the quadratic are irrational.

This means that the expression cannot be factored into two binomial factors with integer coefficients.

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The solution to the system of equations is  x = 5.4 and y = -1.4

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

-x=y-4 y=4x+9

So, we have

-x = y - 4

y = 4x + 9

Rewrite the equation as

x = -y + 4

y = 4x + 9

So, we have

y = 4(-y + 4) + 9

Open the bracket and evaluate

5y = 9 - 16

So, we have

y = -1.4

Recall that

x = -y + 4

So, we have

x = 1.4 + 4

Evaluate

x = 5.4

Hence, the solution is  x = 5.4 and y = -1.4

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Step-by-step explanation:

ln 54.60 = 4         e^x both sides

e ^ (ln 54.60) = e^4

         54.60 = e^4                 Done.

Answer:

Step-by-step explanation:

Area of parallelograph = bh

b=20  h =42

A=(20)(42) = 840 mm²

Answer:

[a] 12 units

Step-by-step explanation:

The answer is (D) 44 units

1. The formula for the area of a rhombus is A= [tex]\frac{d_{1} d_{2}}{2}[/tex]

2. Fill in the information we know:

3. Now work backward:

4. Solve it:

Hence 44 units (D) is your answer

The number of combinations of the 5 white balls and 1 red ball are possible is 1.

We are given that;

White balls=5

Red ball=1

Now,

To find the number of combinations of 5 white balls and 1 red ball, we can use the combinations formula12:

[tex]nCr = n! / (r! (n-r)!)[/tex]

where n is the total number of objects, r is the number of objects to be selected, and ! is the factorial operator.

we can plug in these values into the formula:

[tex]6C6 = 6! / (6! (6-6)!) 6C6 = 6! / (6! 0!) 6C6 = 1 / (1 1) 6C6 = 1[/tex]

So, there is only one combination of 5 white balls and 1 red ball. This makes sense because the order of selection does not matter in a combination. No matter how we arrange the balls, we will always have the same group of 5 white balls and 1 red ball.

Therefore, by combinations and permutations the answer will be 1.

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The reflections are described below.

We know that,

There are two types of reflection:

Reflection with respect to X-axis:

The x-coordinates of a point stay constant when it is mirrored across the X-axis. However, the Y-coordinates are changed into their inverse signs.

As a result, the X-axis reflection of the point (x, y) is (x, -y).

Reflection with respect to Y- axis:

The Y-coordinates of a point stay constant when it is mirrored across the Y-axis. However, the X-coordinates are changed into their inverse signs.

As a result, the Y-axis reflection of the point (x, y) is (-x, y).

Now the reflection is as following:

The point (x, y) when reflected across the x-axis becomes (x', y') = (x, -y)

The point (x, y) when reflected across the y-axis becomes (x', y') = (-x, y)

The point (x, y) when reflected across the line y = x becomes (x', y') = (y, x)

The point (x, y) when reflected across the line y = -x becomes (x', y') = (-y, x)

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Answer: 49.4 thats the answer i devided it

Answer:

solution:  (0,3)

Step-by-step explanation:

You can find the solution when the two lines intersect.

The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is

B) C=360 degrees s over A

The relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:

s = A / 360 * C

Make C the subject of the formula

s = AC / 360

360s = AC

rearranging

AC = 360s

C = 360 degrees s / A

C = (s / A) * 360°

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Answer:

[tex]\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}[/tex]

Step-by-step explanation:

In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.

This is because:

Therefore, this can be expressed as:

[tex]\dfrac{s}{C}=\dfrac{A}{360^{\circ}}[/tex]

Cross multiply:

[tex]360^{\circ} \cdot s=C \cdot A[/tex]

Now, divide both sides by A to isolate C:

[tex]\dfrac{360^{\circ} \cdot s}{A}=C[/tex]

Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:

[tex]\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}[/tex]

In the equation [tex]y = -2(0.5)^x[/tex], the initial amount (a) is -2, and the growth/decay factor (b) is 0.5.

In the given equation, [tex]y = -2(0.5)^x[/tex], we can identify the initial amount and the growth/decay factor.

The equation is in the form of exponential decay, as the base (0.5) is between 0 and 1, resulting in the function decreasing as x increases.

The initial amount, denoted as "a," is the coefficient in front of the exponential term. In this case, the initial amount is -2. This means that when x = 0, y = -2.

The growth/decay factor, denoted as "b," is the base of the exponential term. In this equation, the base is 0.5. The value of the base determines how quickly the function decreases or decays.

To summarize:

Initial amount (a) = -2

Growth/decay factor (b) = 0.5

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The amount of fabric required is 400.551 ft².

We have,

CB= 8 feet

CF= 13 feet

AM = 8 feet

Using Pythagoras

AC² = AM² + CM²

AC = √64+16 = √80 = 4√5 feet

Now, the formula for Triangular prism is

= (Sum of three sides of triangle face)l + base area

= (4√5 + 4√5 + 8)13 + 8 x 8

= 104√5 + 104 + 64

= 104√5 + 168

= 232.551 + 168

= 400.551 ft²

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Fred will pay $43.05 in sales tax if he buys the new refrigerator.

To calculate the sales tax Fred will pay for the new refrigerator, we first need to find the amount of the sales tax.

The cost of the new refrigerator is $615.

To calculate the sales tax, we multiply the cost by the tax rate of 7%:

So, Sales tax = 7% of $615

Sales tax = (7/100) x $615

Sales tax = $43.05

Therefore, Fred will pay $43.05 in sales tax if he buys the new refrigerator.

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The solution of the given equations is: (3,-1).

Here, we have,

from the given graph we get,

1st line passes through ( 0,2 ) and (2,0)

so, equation: y = -x+2 .....1

2nd line passes through ( 0,-4 ) and (4,0)

so, equation: y = x-4 .....2

now, from 1 and 2 we get,

-x + 2 = x -4

or, 2x = 6

or, x = 3

so, we have, y = -1

so, the point of intersection is (3, -1)

Hence, The solution of the given equations is: (3,-1).

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Answer:

45/49

Step-by-step explanation:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

9/14 * 10/7 = 90/98

divide the numerator and the denominator by 2.

90 * 2 = 45

98 * 2 = 49

45/49

The relationship between angles 8 and 7 is that they are supplementary. option B is correct.

Given that a quadrilateral, with three parallel lines, we need to find the relation between angles 8 and 7,

We know that the adjacent angles between the parallel lines are supplementary,

We know that,

Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that are supplementary, the sum of their measures will always be 180 degrees.

So,

The relation between the angles is that they are Supplementary angles.

Hence the option B is correct.

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Answer:

A. 16.7%

B. 89.5%

Step-by-step explanation:

A) Inside the Square

length:4

The square has an area of 16 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being in the square is:

(area of square)/(area of rectangle)

= 16/96

= 0.16666666666666666

This is equal to 16.7%.

B) Outside the right angles Triangle

base:4 height 5

The triangle has an area of 10 square units. The rectangle has an area of 96 square units. The probability of a point chosen randomly inside the rectangle being outside the triangle is:

(area of rectangle - area of triangle)/(area of rectangle)

= (96 - 10)/96

= 0.8958333333

This is equal to 89.5%.