There are 2 boys for every 3 girls. Today 5 new boys were added making the number of girls and boys the same. How many boys and girls were there originally?

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

Sample mean

Sample variance

Sample proportion

Step-by-step explanation:

By knowing that p and 2/3 are additive inverses, we will see that p = -2/3

So two numbers A and B are additive inverses if:

A + B = 0

Here the two numbers are p and 2/3, so we have:

2/3 + p = 0

Solving this for p gives:

p = -2/3

Then the value of p is just -2/3.

Now, I can't "drag and drop" the labels in the given image, so I will post a little graph of where each point should be:

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The slope of the tangent line is:

a = (df(x1)/dx)

The slope of the normal one is:

a' = -1/(df(x1)/dx)

For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.

So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:

df(x1)/dx

And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:

a*(df(x1)/dx) = -1

a = -1/(df(x1)/dx)

Where df/dx reffers to the derivative of f(x).

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The number of times of Puerto Rico is 5/6

No earthquake released 10³ of Colombia

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

The table of values

On the table of values, we have

Colombia = 6.0M

Puerto Rico = 5.0M

This means that

Number of times = Puerto Rico/Colombia

Substitute the known values in the above equation, so, we have the following representation

Number of times = 5/6

Here, we have

Colombia = 6.0M

So, we have

Earthquake = Colombia * 10³

This gives

Earthquake = 6 * 10³

From the table of values, we have no entries with the readings 6 * 10³

Hence, no earthquake released 10³ of Colombia

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Answer:

the correct answer is -1/16 i believe

The correct option is A, we have a translation of 7 units to the right.-

To find it, we need to analyze two correspondent vertices.

We can see that vertex A is at (1, 5), while the correspondent vertex A' is at (8, 5)

Taking the difference between that, we will get:

A' - A = (8, 5) - (1, 5) = (8 - 1, 5 - 5) = (7, 0)

The first value gives the horizontal translation and the second the vertical one

So,we have a translation of 7 units to the right, the correct option is A.

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I need to deposit $1558.41 to have $2000 in the account in 5 years.

What is compound interest?

The interest charged on a debt or deposit is known as compound interest. It is the idea that we use the most regularly. Compound interest is calculated for a sum based on both the principal and cumulative interest.

    ∴ Compound interest = P(1 + \(\frac{r}{100*12}\))ⁿ  (∵ for monthly interest)

        P = Principal

        r = rate of interest per month

        n = number of months

Given:

r = 5% per month

n = 5 years = 5*12 = 60 months

  CI = P (1+5/(12 * 100))⁶⁰

2000 = P(1.0041)⁶⁰

2000 = P(1.2834)

      P = 1558.41

Therefore, the amount required to deposit is 1558.41 dollars to get 2000 dollars after 5 years with 5 percent interest per month.

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Answer:

1

Step-by-step explanation:

7-6=1

Answer:

1

Step-by-step explanation:

7-x

x=6

7-6=1

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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Answer: I think it is -5, but im not very sure srry

Step-by-step explanation:

9514 1404 393

Answer:

  -2, 3

Step-by-step explanation:

For the product to be negative, exactly one of the two numbers must be negative. For the sum to be positive, the positive number must be larger than the absolute value of the negative number.

One such pair of numbers is -2 and 3.

__

Their product is -6; their sum is +1.

The statement is false, as the PEMDAS order must be respected, that is, parenthesis operations are done first, then exponents, then multiplication/division and finally addition/subtraction.

The precedence of operations is defined by the PEMDAS acronym, with a highest to lowest order of precedence, as follows:

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An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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The indicated value h(-1)  has a value of 0 when evaluated

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

f(x) = - 2x ^ 2

g(x) = x - 3

h(x) = 2f(x) - g(x)

The indicated value of the function is

h(-1)

This means that

h(-1) = 2f(-1) - g(-1)

Calculate g(-1)

So, we have

g(-1) = -1 - 3

g(-1) = -4

Calculate f(-1)

So, we have

f(-1) = -2 * (-1)^2

f(-1) = -2

Recall that

h(-1) = 2f(-1) - g(-1)

Substitute the known values in the above equation, so, we have the following representation

h(-1) = 2 * -2 + 4

Evaluate

h(-1) = 0

Hence, the value is 0

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Answer:

The correct answer is - 178.

Step-by-step explanation:

The standard deviation is a measure of the amount of dispersion in a set of values.

Given:

Mean of a normal distribution (m) = 154

Standard deviation (s) = 15

z-score = 1.6

Solution:

To find: value (x) that has a z-score of 1.6

z-score is given by = x-u/15

1.6*15 = x-154

=> 154+24 = x

x = 178

Answer:

770cents

Step-by-step explanation:

If a report is 81 pages long, 12 copies will be (81 * 12)pages long

12copies = 972 pages long

If 500 pages costs $3.96 each

972 pages will cost $x

Cross multiply

500x = 972 * 3.96

500x = 3,849.12

x = 3,849.12/500

x = 7.69824

Hence the cost of the reports is $7.69824

Convert to cents;

$1 = 100cents

$7.69824 = y

y = 7.69824 * 100

y = 769.824 cents

y ≈ 770 cents (to the nearest cent.)

Hence the paper is going to cost 770cents (to the nearest cent)

Step-by-step explanation:

I don't know what the specific options are to be selected, but I can tell you what the situation is, and you can then pick the fitting options on your screen :

it is not a function, because 5 in set A (the domain) leads to 2 associated (functional result) values in B (the range).

but in order to be a function, every input value must have exactly one resulting output value. which is violated here.

Answer:

12

Step-by-step explanation:

4.18/6  *  5 over 5

72/6 *5 over 5

72/6 * 5 divided by 5

12.5 divided by 5

12 times 5 over 5

60/5

60 divided by 5

Answer: The usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen.

Step-by-step explanation: To find the usual dose of ibuprofen for a child, we need to follow these steps:

Therefore, the usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen. Hope this helps, and have a great day! =)

Answer:

A acute angle is a angle that is less than 90*

Answer:

equally likely

Step-by-step explanation:

The classical approach to probability requires that the outcomes are​ equally likely.

Equally likely means the chance or possibility of selection in the sample is equal for them. None is prioritized over the other, all has the equal chance of being selected in the sample.

Given that we are using the classical approach to probability which is based on an assumption that for any procedure having random set of possible outcomes, the possibility of each outcome is equal.

Thus, the classical approach to probability requires that the outcomes are​ equally likely.

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You graph >7 with an open dot to the right.

The inequalities ≤ and ≥ would have a closed dot on the number line.

a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".

s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".

t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".

Inequality signs are mathematical symbols used to indicate that one quantity is greater than, less than, or equal to another quantity. These inequality signs includes:

These symbols are used in mathematical expressions and equations to compare values and express relationships between them.

Therefore, with a good understanding of inequality signs we conclude that:

On a graph, > 7 is with an open dot to the right.

Only the inequalities ≤ and ≥ would have a closed dot on the number line.

a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".

s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".

t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".

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The  best measure of center for the data shown is the median, and its value is 17.

The median is the best measure of center for the given data set. To find the median, we arrange the numbers in ascending order:

10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

Since the data set has an odd number of values, the median is the middle value, which in this case is 17.

Therefore, the best measure of center for the data shown is the median, and its value is 17.

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To find the value of (f o g)' at a given value, you first need to understand the concept of composite functions and the chain rule of differentiation. Let's break it down step by step.

To find the value of (f o g)' at a given value, you need to evaluate g(x) and f(x), find their derivatives, and use the chain rule to find the derivative of (f o g) at the given value. It is important to understand the concepts of composite functions and the chain rule to be able to solve problems involving these concepts.

What are composite functions? Composite functions are functions that are formed by composing two or more functions. The notation used to denote composite functions is (f o g)(x), which means that the output of function g is used as the input for function f. In other words, we first evaluate g(x), and then use the result as the input for f(x).

What is the chain rule of differentiation? The chain rule of differentiation is a method used to find the derivative of composite functions. It states that if a function is composed of two or more functions, then its derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.

To find the value of (f o g)' at a given value, we need to follow these steps:1. Find g(x) and f(x)2. Find g'(x) and f'(x)3. Evaluate g(x) at the given value4. Use the chain rule to find (f o g)' at the given value

step 1: Find g(x) and f(x)Let's say that we have two functions: g(x) = x^2 + 3x + 1 and f(x) = sqrt(x). To find (f o g)(x), we first need to evaluate g(x) and then use the result as the input for f(x). Therefore, (f o g)(x) = f(g(x)) = sqrt(x^2 + 3x + 1)

Step 2: Find g'(x) and f'(x)To find g'(x), we need to take the derivative of g(x) using the power rule and the sum rule. Therefore, g'(x) = 2x + 3To find f'(x), we need to take the derivative of f(x) using the power rule and the chain rule. Therefore, f'(x) = 1/2(x)^(-1/2)

Step 3: Evaluate g(x) at the given valueSuppose we want to find (f o g)' at x = 2. To do this, we need to first evaluate g(x) at x = 2. Therefore, g(2) = 2^2 + 3(2) + 1 = 11

Step 4: Use the chain rule to find (f o g)' at the given value now we can use the chain rule to find (f o g)' at x = 2. Therefore, (f o g)'(2) = f'(g(2)) * g'(2) = 1/2(11)^(-1/2) * (2)(3) = 3/sqrt(11)

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Step-by-step explanation:

\(b = k + \frac{l}{m} \\ b - k = \frac{l}{m} \\ m = \frac{l}{b - k} \\ thank \: you\)

Answer:

CGE

Step-by-step explanation:

angle CGE is same side interior angle

same side reffers to same side of transversal

interior refers that is between the parallel lines

Answer: CGE because the interior is parallel lignes

Step-by-step explanation:

The scaled triangle will be larger than the initial size by a factor 2.

The scaled square will be smaller than the initial side by a factor 4.

Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.

Dilation involves scaling an object by a certain factor, that might result in  enlarging or reducing its dimensions uniformly in all directions.

Based on the given diagram, the new length and size of the object is calculated as follows;

For the triangle, (measure the length with ruler)

For the square; (measure the length with ruler)

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Solution

Given for 9 troops, the following requirement are needed:

9 pounds chicken

6 tablespoon of garlic

8 tablespoon of oil

12 potatoes

Proportion of pounds of chicken to potatoes to feed 9 troops

= 9 : 12

Proportion of pounds of chicken to potatoes to feed 3 troops

=3 : 4

The correct option is A