If there are 12 boys and 24 girls in a room, fill out all of the possible ratios of boys to girls that could be made.

Answer: x^2 = 11x - 18

Step-by-step explanation:

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

Step-by-step explanation:

f(x) = a(x-x1) (x-x2)

from the vertex, we get a:

0 = a(4-2)²- 8

4a = 8

a = 2

so, the equation:

f(x) = 2(x-0) (x-4)

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

f(x) = 2x² -8x

Answer:  1 question Solve for x

x=

3

−y−2z−10

​

Solve for y

y=−3x−2z−10

Step-by-step explanation: Steps for Solving Linear Equation

3x+y+2z=−10

Subtract y from both sides.

3x+2z=−10−y

Subtract 2z from both sides.

3x=−10−y−2z

The equation is in standard form.

3x=−y−2z−10

Divide both sides by 3.

3

3x

​

=

3

−y−2z−10

​

Dividing by 3 undoes the multiplication by 3.

x=

3

−y−2z−10

​

Answer:

There are 0.1 mililiters in 5 milimeters saline.

Step-by-step explanation:

A 2 % suspension means that 2 % of the volume of a given substance per each 100 milimeters of saline. That is:

\(r = \frac{V_{sub}}{V_{sal}}\)

\(V_{sub} = r\cdot V_{sal}\)

Where:

\(r\) - Suspension ratio, dimensionless.

\(V_{sal}\) - Saline volume, measured in milimeters.

\(V_{sub}\) - Substance volume, measured in milimeters.

Given that \(r = 0.02\) and \(V_{sal} = 5\,mL\), the volume of the substance is:

\(V_{sub} = 0.02\cdot (5\,mL)\)

\(V_{sub} = 0.1\,mL\)

There are 0.1 mililiters in 5 milimeters saline.

Answer:

112

Step-by-step explanation:

The arrow means multiplying but really you need to Pemdas

Answer:

112

Step-by-step explanation:

Using PEMDAS

1) \((4^2+3+2)\)

= 16 + 3 + 2

= 21

2) \(7^2 + 3\) * 21

= 49 + 3 * 21

= 49 + 63

= 112

The surface area of the base ball to the nearest whole number is 26 in²

A sphere is defined as the set of all points in three-dimensional Euclidean space that are located at a distance.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a sphere is expressed as;

SA = 4πr²

where r is the radius and it's calculated as;

C = 2πr

9 = 2πr

r = 4.5/π =

SA = 4 π × (4.5/π)²

SA = 81/π

SA = 26 in²( nearest whole number)

Therefore the surface area of the sphere is 26 in²

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The circumference (c) is the dependent variable.

The radius (r) is the independent variable.

An independent variable is a variable that does not depend on any other variable for its value

A dependent variable is a variable depend on any other variable for its value.

In the rule c = 6.3r, the circumference (c) of a circle depends on the  radius for its value while the radius (r) does not depend on the circumference for its value.

Thus, the circumference (c) is the dependent variable while the radius (r) is the independent variable

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Answer:

Step-by-step explanation:

Answer:

3

---

8

Step-by-step explanation:

the ratio of cakes to pies will be 3:8 if pies to cakes is 8:3

the fraction is 3/8

The value of the distance across the sea is 302 feet

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Two triangles are said to be similar if the ratio of their corresponding sides are in the same proportion.

Triangle PRE and triangle POC are similar triangles based on the angle - angle similarity. Hence:

PR / PO = RE/OC

substituting:

x/ (x + 135) = 185 / 335

335x = 185x + 45225

150x = 45225

x = 302 feet

The value of PR is 302 feet

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According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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a) The 90% confidence interval to estimate the percentage of yellow peas is (23.09%, 29.03%.)

b) Based on the confidence interval, the results of the experiment do not appear to contradict the expectation that 25% of the offspring peas would be yellow.

Given:

Confidence level,c = 90% = 0.90

Number of successes, x = 153

Sample size,n = 434 + 153 = 587

a) The sample proportion is the number of successes divided by the sample size is,

p = x/n

p = 153/587

p ≅ 0.2606

For confidence level 1 - α = 0.90, determine \(z_{\alpha /2} = z_{0.05}\) utilizing the normal probability table in the appendix

\(z_{\alpha /2} = 1.64\)

The margin of error is calculated as:

\(E = z_{\alpha /2} \sqrt{\frac{p(1-p)}{n} }\)

\(E = 1.64\sqrt{\frac{0.2606(1 -0.2606)}{587} }\)

E ≅ 0.0297

Therefore, the boundaries of the confidence interval are:

p - E = 0.2606 - 0.0297 = 0.2309 = 23.09%

p + E = 0.2606 + 0.0297 = 0.2903 = 29.03%

We are 90% confident that the true percentage of yellow peas is between 23.09% and 29.03%.

b) As 25% is between 23.09% and 29.03%, and 25% of the offspring are expected to be yellow peas and thus the results do not contradict expectations.

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Using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.

So, in September, Lucky weighed = 3.07 pounds

The equation form is:

So, now solve this linear equation and find 'x' as follows:

Therefore, using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.

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Answer:

a1 = 2

a2 = 3* (2) - 1 = 6 - 1 = 5

a3 = 3* (5) - 1 = 15 -1 = 14

a4 = 3* (14) - 1 = 42 -1 = 41

a5 = 3* (41) - 1 = 123 -1 = 122

a6= 3* (122)-1= 366 -1= 365

Hope this helps :-))

Answer:

Step-by-step explanation:

Rewriting the given as factors:

As per Wilson's theorem, if n is prime number, (n - 1)! + 1 is divisible by n

As per above, 13 and 7 are both prime numbers, so the expression is divisible by both 7 and 13:

So correct choice is C

Answer:

625 units²

Explanation:

Given that the area of the figure = 25 square units

On dilation with a scale factor, the new area is obtained using the formula:

Therefore, the new area is:

The new area is 625 square units.

Answer:

No

Step-by-step explanation:

Assuming that you put the wrong sign for the second equation if you plug (2,7) into the two equations it only works for one equation.

=========================================

Explanation:

Ignore the info about how much Margo spent.

Anthony spent $10.24 on lunch, before the tip. Then we add on the $2 tip to get a total of 12.24 dollars spent.

The amount of change is 20-12.24 = 7.76

----------------

Here's how the cashier can mentally figure out how much change to give

Start with the number of cents from $12.24

The jump from 24 cents to 100 cents is 76 cents (24+76 = 100)

This gets us from 12.24 to 13.00

The jump from 13 to 20 is another 7 dollars.

So that's how we get 7 + 0.76 = 7.76 in change

Answer:

\({ \sf{ = 548240}}\)

The value of the given expression 3+4% of 6/2+5 is 8.04

In the above question a mathematical expression is given as follows :

3+4% of 6/2+5

The acronym PEDMAS, which stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction, is sometimes used to refer to the BODMAS. The BODMAS rule states that the brackets must be solved first, then powers or roots (i.e. of), followed by Division, Multiplication, Addition, and finally Subtraction.

We need to solve it using the BODMAS rule, which says first we'll solve the percentage then division, multiplication and then addition

3+4% of 6/2+5?

= 3 + \(\frac{4}{100}\) x \(\frac{6}{2}\) + 5

= 3 + \(\frac{3}{25}\) + 5

= \(\frac{25 . 3 + 1 + 5 .25}{25}\)

= \(\frac{75 + 1 + 125}{25}\)

= \(\frac{201}{25}\)

= 8.04

Hence, the value of the given mathematical expression 3+4% of 6/2+5 is 8.04

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Answer:

Step-by-step explanation:

hope it helps.....

have a great day!!

Answer:

6

Step-by-step explanation:

Step-by-step explanation:

a= c-b pls let me know if it is correct or not

Answer:

y = -1/4x + 2

Step-by-step explanation:

lmk if you want an explanation

Answer:

The formula for finding the area of a circle using its radius is:

The formula for finding the area of a circle using its radius is:A = πr²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14

Step-by-step explanation:

Hope it Helps

The formula for finding the area of a circle using its radius is π * r².

The formula for finding the area of a circle using its diameter is (π/4) * d².

The formula for finding the area of a circle using its radius is:

A = π * r²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

r represents the radius of the circle.

If you have the diameter of the circle instead of the radius, you can use the following formula:

A = (π/4) * d²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

d is the diameter of the circle.

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Answer:

the total number of arrangement is six

Step-by-step explanation:

Part (a) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A and B are next to each other.

Suppose A and B are together and form a group, then no. of groups are .

These groups can be arranged in

A and B can be arranged in .

Therefore, the possible no. of arrangements are .

Part (b) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A is before B.

Total no. of arrangements with six letters

The no. of arrangements in which A is before B

Therefore, the possible no. of arrangements are .

Part (c) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A is before B and B is before C.

Total no. of arrangements with six letters

A, B and C can be arranged in

Out of these 6 arrangements, there is only one arrangement in which A is before B and B is before C.

So, the possible no. of ways =

Therefore, the possible no. of arrangements are .

Part (d) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A is before B and C is before D.

The no. of arrangements in which A is before B

Out of these arrangements, half will be with C before D and half will be with D before C.

Therefore, the possible no. of arrangements are .

Part (e) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that A and B are next to each other and C and D are also next to each other.

If A and B form one group and C and D from another group then there are groups and these groups can be arranged in

A and B can be arranged in

Similarly, C and D can be arranged in

Therefore, the possible no. of arrangements are .

Part (f) Step 1. Find the no. of linear arrangements of the letters A, B, C, D, E, F such that E is not last in line.

The no. of arrangements in which the position of E is fixed at last

The no. of arrangements in which the position of E is not fixed

Therefore, the possible no. of arrangements are

\(\textit{Pythagorean Identities} \\\\ 1+\tan^2(\theta)=\sec^2(\theta)\implies \tan^2(\theta)=\sec^2(\theta)-1 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\stackrel{ \textit{difference of squares} }{[sec(x)+1][sec(x)-1]}}{sin^2(x)}\implies \cfrac{sec(x)^2-1^2}{sin^2(x)}\implies \cfrac{sec(x)^2-1}{sin^2(x)} \\\\\\ \cfrac{tan^2(x)}{sin^2(x)}\implies \cfrac{sin^2(x)}{cos^2(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{1}{cos^2(x)}\implies sec^2(x)\)