red die and a black die are rolled at the same time. The probability of getting a 6 on the red die is 16, and the probability of getting a 3 on the black die is 16. Given that the two events are independent, what is their combined probability?

Answer:

6 and 1 over 2 ÷ 1 over 4

Step-by-step explanation:

Given,

The total cups in a recipe =  6 and 1 over 2 cups

[tex]=6\frac{1}{2}\text{ cups}[/tex]

Also, the cups in each serving =  1 over 4 cup

[tex]=\frac{1}{4}\text{ cups}[/tex]

Hence, the number of servings = [tex]\frac{\text{total cups in a recipe}}{\text{cups in each serving}}[/tex]

[tex]=\frac{6\frac{1}{2}}{\frac{1}{4}}[/tex]

= 6 and 1 over 2 ÷ 1 over 4

Second option is correct.

Final answer:

The converse of the given conditional statement 'if x=12 then 2x-5=19' is 'if 2x-5=19, then x=12'. To verify its truth, we solve for x when 2x-5 equals 19, resulting in x equaling 12, thus showing that in this instance, the converse is true.

Explanation:

The converse of a conditional statement is formed by swapping the hypothesis and the conclusion of the original statement. For the statement 'if x=12 then 2x-5=19', its converse would be 'if 2x-5=19, then x=12'. To test the validity of the converse, we substitute the value of x back into the equation 2x-5 and check if it equals 19 when x=12.

However, we need to be cautious because the converse of a true conditional statement is not always true. To determine the truth of the converse, one must check if every instance where 2x-5 equals 19 also means that x must be equal to 12. If there is even a single case where 2x-5 is 19 and x is not 12, then the converse is not true.

For instance, let's test the converse: If we solve the equation 2x-5=19 for x, we get:

x = (19+5)/2

x = 24/2

x = 12

Therefore, for this specific case, the original statement and the converse are both true.

Answer: 16 pieces

Step-by-step explanation:

To get the number of pieces, we simply divide 12 1/3 by 3/4

12 1/3 ÷ 3/4

but 12 1/3 = 37/ 4 ( converting to improper fraction)

12 1/3 ÷ 3/4

=37/ 3 ÷ 3/4

= 37/3 × 4/3

= 148/9

= 16. 44444

= 16 approximately

Therefore we can get 16 pieces of yard from the cloth

there are 4 quarters to 1 hour

3 1/6 x 4 =

19/6 * 4 = 76/6 = 12 4/6, reduces to 12 2/3 km per hour

Answer:- The average speed of Harvey the wonder hamster is[tex]12\frac{2}{3}\ km/hour[/tex].

Explanation:-

Given: Distance traveled by Harvey [tex]=3\frac{1}{6}\ km=\frac{19}{6}\ km[/tex]

Time taken[tex]=\frac{1}{4}\ hour[/tex]

[tex]Speed=\frac{Distance}{Time}\\\Rightarrow\ Speed=\frac{\frac{19}{6}}{\frac{1}{4}}\\\\=\frac{19\times4}{6}\\\\=\frac{38}{ 3}\\\\=12\frac{2}{3}\ km/hour[/tex]

Therefore, the average speed of Harvey the wonder hamster is[tex]12\frac{2}{3}\ km/hour[/tex].

70% = 0.70

70 * 0.70 = 49

 so 49 students passed

Answer:

STep by step

Step-by-step explanation:

Option A is correct, x+4 is the binomial factor of the given trinomial x² - 5x - 36

What is Polynomial?

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given trinomial is  x² - 5x - 36

Now we have to factorize the given polynomial.

x² - 9x +4x - 36

x(x-9)+4(x-9)

(x+4)(x-9)

The factorial form of the trinomial  x² - 5x - 36 is (x+4)(x-9)

So x+4 is the binomial factor of the given trinomial.

Hence, Option A is correct, x+4 is the binomial factor of the given trinomial x² - 5x - 36

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Final answer:

To find the area of a square, we use the formula A = s², where A represents the area and s represents the length of a side. Evaluating the options, the area that could not be Jaime's square is C. 50cm².

Explanation:

To find the area of a square, we need to multiply the length of one side by itself. So, the formula for the area of a square is A = s², where A represents the area and s represents the length of a side. We can evaluate the given options using this formula:

Therefore, the answer is C. 50cm².

Answer:

Option A is correct

2x-9

Step-by-step explanation:

Given the functions:

f(x) = 2x + 3

g(x) = x -6

We have to find  [f o g](x).

[tex][fog](x) = f[g(x)][/tex]

Substitute the function g(x),

[tex][fog](x) = f[x-6][/tex]

Replace the value of x with x-6 in f(x) we have;

[tex][fog](x) =2(x-6)+3[/tex]

⇒[tex][fog](x) =2x-12+3[/tex]

⇒[tex][fog](x) =2x-9[/tex]

Therefore, the value of [tex][fog](x)[/tex] is, 2x-9

The arm span of 74- inch tall person is 74 inches and height of person with 66 inches arm span is 66 inch.

Your arm span is the distance between the middle fingertips on each hand when you stretch your arms out as far as they can reach.

arm span= 66 inches

As, height of person= 74 inch

The person who is having 66inch arm span  also being 66inches in height,

which means the if the arm span is of the 74inch

then man would also be 74inch arm span

This is because your arm span equals your height.

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Final answer:

A person with an arm span of 66 inches is likely to be about 66 inches tall, and a 74-inch-tall person likely has an arm span of about 74 inches. The height in meters of a person who is 6 feet 1.0 inch tall is about 1.8542 meters.

Explanation:

Understanding Arm Span and Height Relationships

The relationship between arm span and height is interesting as they tend to be about the same for an individual. For a person with an arm span of 66 inches, we can estimate that the person's height is approximately the same, around 66 inches. However, this relationship can vary slightly based on individual proportions.

Conversion between Inches and Meters

To convert a person's height from feet and inches to meters, we use the conversion factor 1 meter equals 39.37 inches. For a person who is 6 feet 1.0 inch tall (which equals 73 inches in total), their height in meters would be:

Height in meters = (73 inches) / (39.37 inches per meter) = 1.8542 meters (rounded to four decimal places).

Estimates Based on Anthropometric Data

The arm span of a 74-inch-tall person would again typically be close to their height, so around 74 inches. These estimates are part of anthropometric data, which helps in understanding human body measurements in various fields, including ergonomics, clothing design, and health assessments.

Answer:

t = d/r

Step-by-step explanation:

In order to solve an equation for another term from which is initally solved by another term you just have to leave the term you want to solve the equation for, in this case the "t" and to do so since in this formula it is multiplying the "r" we haec to divide both sides of the equation by "r":

[tex]d=rt[/tex]

[tex]\frac{d}{r} =\frac{rt}{r}[/tex]

Now we eliminate the since they are in both sides of the fraction:

[tex]\frac{d}{r} =\frac{rt}{r}[/tex]

And the function is solved for t.

[tex]t=\frac{d}{r}[/tex]

Answer:

Step-by-step explanation:

The answer to this question is answer A.

A point is equidistant from the two sides of an angle, then it is option (C) on the angle bisector is the correct answer.

An angle bisector is a straight line drawn from the vertex of a triangle to its opposite side in such a way, that it divides the angle into two equal or congruent angles.

For the given situation,

Any point that is on the angle bisector is an equal distance ("equidistant") from the two sides of the angle.

A point which is always equidistant from all the sides is the point of intersection of internal angle bisectors.

Hence we can conclude that a point is equidistant from the two sides of an angle, then it is option (C) on the angle bisector is the correct answer.

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Answer:

the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard[tex]y=\frac{x}{2}+4[/tex]

Step-by-step explanation:

          [tex](y-y_1)=m(x_2-x_1)[/tex]

We can easily take two points from given graphs are

(2,5) and (6,7)

The slope of line is;

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{7-5}{6-2}[/tex]

[tex]m=\frac{2}{4}[/tex]

[tex]m=\frac{1}{2}[/tex]

the slope of line is [tex]\frac{1}{2}[/tex]

Now, find the equation of line with the  slope-intercept form

[tex](y-y_1)=m(x-x_1)[/tex]

[tex](y-5)=\frac{1}{2}(x-2)[/tex]

Add both the sides by 5 in above expression,

[tex]y=\frac{1}{2}(x-2)+5[/tex]

[tex]y=\frac{x}{2}-1+5[/tex]

[tex]y=\frac{x}{2}+4[/tex]

Therefore, the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard[tex]y=\frac{x}{2}+4[/tex]

Final answer:

To solve for b in the equation 4a = 2b - 7, you need to add 7 to both sides and then divide by 2. The solution is b = (4a + 7)/2.

Explanation:

To solve the equation 4a = 2b - 7 for b, you want to isolate b on one side of the equation. This means we need to perform operations that will move all other terms away from b.

First, let's add 7 to both sides of the equation to get rid of the -7 that's subtracted from b:

4a + 7 = 2b

Next, we will divide both sides of the equation by 2 to solve for b:

(4a + 7)/2 = b

So, b equals to the expression (4a + 7)/2.