How do you change a ratio into a fraction baseballs to basketballs

Answer:

Length of the shadow is 11.8 meters.

Step-by-step explanation:

In the figure attached,

AB is a 34 meter tall building casting a shadow BC.

Let the measure of BC = x meters

It is given that the distance between A and C is 36 meters.

To find the length of BC we will apply Pythagoras theorem in the triangle.

AB² + BC² = AC²

(34)² + x² = (36)²

1156 + x² = 1296

x² = 1296 - 1156

x² = 140

x = √140

x = 11.832 meters

  ≈ 11.8 meters

Therefore, length of the shadow will be 11.8 meters.

The correct answer to this is that:

Any irrational number when added to 2 / 5 still produces an irrational number.

For example, if we use π to add to 2/5 or 0.4. As far as we know the decimal digits for π just go on forever and do not have a repeating cycle hence making it an irrational number. Adding a rational number such as 0.4 to the value of π does not really greatly change the value of π. The decimal digits (hundredths place and so on) of the resulting number will still go on forever without a continual repeat.

So 0.4 + π is still irrational.

Answer:

5

Step-by-step explanation:

7 7/20 ounces of chemical should be mixed with 4 1/5 gallons of water.

To determine the amount of chemical to mix with 4 1/5 gallons of water, you need to use the given ratio of 1 3/4 ounces of chemical per gallon of water.

1.)  Convert 4 1/5 gallons to a mixed number:

4 1/5 = 21/5 gallons.

2.)  Multiply the amount of water by the chemical-to-water ratio:

(21/5) gallons * (7/4) ounces = 147/20 ounces.

3.)  Convert 147/20 ounces to a mixed number:

147/20 = 7 7/20 ounces.

Therefore, 7 7/20 ounces of chemical should be mixed with 4 1/5 gallons of water.

Answer:

11.34 years.

Step-by-step explanation:

We have been Vito put some money into a cd that pays 12.7 interest compound quarterly.

Since the rule of 72 states that to find the number of years it will take an amount to double, we need to divide 72 by annual interest rate.

First of all let us find the number of years it will take to double Vito's money by dividing 72 by 12.7.

[tex]\text{Time it will take to double Vito's money}=\frac{72}{12.7}[/tex]

[tex]\text{Time it will take to double Vito's money}=5.66929133858\approx 5.669[/tex]    

Since it will take 5.669 years to double Vito's money, so to find the time it will take Vito to have 4 times the money, we will multiply 5.669 by 2.

[tex]\text{Time it will take to have 4 times Vito's money}=5.669*2[/tex]

[tex]\text{Time it will take to have 4 times Vito's money}=11.338\approx 11.34[/tex]  

Therefore, approximately in 11.34 years Vito will have 4 times the amount of money that he has now.

Answer:

the value of 2xy if x =3 and y= 2 is 12

Step-by-step explanation:

To prove that there are no integers m and n that satisfy 2m + 4n = 7, we can assume the opposite and show that it leads to a contradiction. We can rearrange the equation and analyze the parity of the terms to prove there are no integer solutions.

To prove that there does not exist integers m and n such that 2m + 4n = 7, we can start by assuming that such integers do exist. Let's suppose m and n are integers that satisfy the equation.

Rearranging the equation, we have 2m = 7 - 4n. This means that 2m is an even number and 7 - 4n is an odd number. However, there is no way for an even number and an odd number to be equal. Therefore, our assumption was incorrect, and there are no integers m and n that satisfy the equation 2m + 4n = 7.

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The speed of 70 miles per hour is approximately equivalent to 1.17 miles per minute. This conversion is done by dividing the speed in miles per hour by 60, the number of minutes in an hour.

To calculate the conversion from miles per hour to miles per minute, you divide the speed in mph by 60, as there are 60 minutes in an hour. So if we are given a speed limit of 70 miles per hour, that would convert to approximately 1.17 miles per minute.

This is calculated as 70 miles per hour ÷ 60 minutes per hour = 1.17 miles per minute

It's important to remember to use the correct conversion factor related to time, in this case that there are 60 minutes in an hour, to ensure the accuracy of the conversion.

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Answer: 1800°

Step-by-step explanation: In this problem, we're given that a polygon has 12 sides and we're asked find the sum of the measures of its interior angles.

The formula for finding the sum of the measures of the interior angles of a polygon is 180 (n - 2) where n represents the number of sides.

So here, since our polygon has 12 sides, we can plug a 12 in for the n in our formula and we have 180 (12 - 2) which is our equation.

Simplifying inside the parentheses first, 12 - 2 is 10 so we have 180 (10) which is 1800.

So if a polygon has 12 sides, then the sum of the measures of its interior angles is 1800°.

Answer:  The equation of the ellipse is

[tex]\dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]

Step-by-step explanation:  We are given to find the equation of an ellipse that has a center at the origin, a vertex along the major axis at (13, 0) and a focus at (12, 0).

Since the focus lies on the X-axis, so the standard equation of an ellipse with major axis as X-axis is given by

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

According to given information, we have

a vertex along the major axis, (a, 0) = (13, 0)  

⇒ length of the major axis, a = 13,

co-ordinates of focus, (c, 0) = (12, 0)

⇒ c = 12.

We know that

[tex]c^2=a^2-b^2.[/tex]

Therefore,

[tex]12^2=13^2-b^2\\\\\Rightarrow 144=169-b^2\\\\\Rightarrow b^2=169-144\\\\\Rightarrow b^2=25\\\\\Rightarrow b=5.[/tex]

Thus, from equation (i), we get

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\\\\\\\Rightarrow \dfrac{x^2}{13^2}+\dfrac{y^2}{5^2}=1\\\\\\\Rightarrow \dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]

The equation of the ellipse is

[tex]\dfrac{x^2}{169}+\dfrac{y^2}{25}=1.[/tex]

The equation of the ellipse along the major axis at (13, 0), and a focus at (12, 0) is; x²/169 + y²/25 = 1

The equation of an ellipse whose center is the origin, (0,0) usually takes the form;

The coordinates of the vertex on the major axis is given as; (13,0) and the focus at (12,0)

Hence, the square of the length of the minor axis;

Hence, the equation of the described ellipse is;

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16/7 = 12/y

84/16

84/16 = 5.25

5.25+7 = 12.25

 x = 12.25

According the diagram given the correct statements are: The hypotenuse is LN; The side opposite [tex]\rm \angle L[/tex] is NM and The side opposite to [tex]\rm \angle N[/tex] is ML.

Given :

Triangle LNM.

Acccording to the given triangle (attached below):

Therefore, the correct statements are: The hypotenuse is LN; The side opposite [tex]\rm \angle L[/tex] is NM and The side opposite to [tex]\rm \angle N[/tex] is ML.

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In triangle LNM, the side opposite angle L is NM, and the side opposite angle N is ML. The side adjacent to angle L is NM, and the side adjacent to angle N is ML. The hypotenuse of triangle LNM is LN, not NM.

In triangle LNM, the side opposite angle L is NM, so the statement "The side opposite ∠L is NM" is true.

In triangle LNM, the side opposite angle N is ML, so the statement "The side opposite ∠N is ML" is true.

The hypotenuse of triangle LNM is LN, not NM, so the statement "The hypotenuse is NM" is false.

The side adjacent to angle L is NM, so the statement "The side adjacent ∠L is NM" is true.

The side adjacent to angle N is ML, so the statement "The side adjacent ∠N is ML" is true.

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The value of a in the equation [tex]9=(\frac{1}{27})^{a+3}[/tex] is a = -11/3

The given equation is:

[tex]9=(\frac{1}{27})^{a+3}[/tex]

This can be rewritten as:

[tex]9=27^{-1(a+3)}[/tex]

Which can be further simplified as:

[tex]3^2=3^{-3(a+3)}[/tex]

Since the bases are equal, they cancel out

The equation becomes:

2  =  -3(a  +  3)

2  =  -3a  -  9

2+9  =  -3a

-3a  =  11

a  =  -11/3

Therefore, the value of a in the equation [tex]9=(\frac{1}{27})^{a+3}[/tex] is a = -11/3

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The equation that would be used to determine the value of w is expressed as: C. w² + 5w - 300

Area of a rectangle = (length)(width).

Given the following:

Therefore, equation that would be used to find the value of w is:

(w + 5)(w) = 300

w² + 5w = 300

w² + 5w - 300

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Answer:

Step-by-step explanation:

You could, if you wished, take out the negative sign, obtaining -(8)(3).  That would be -24.

But if you meant exponentiation, it would look like (-8)^3, or (-8)³, and that would be equal to 8*8*8 = 512.