A school has two types of tables: round tables with 6
seats and rectangular tables with 8 seats. For a
fundraising event, they filled the gym with 25 tables,
for a total of 190 seats.
. Use x for the number of round tables.
• Use y for the number of rectangular tables.

Write an equation for the number of tables

To calculate the amount of money in Roberto's savings account after 5 years, you can use the formula for simple interest:

I = Prt

Where:

I = Interest earned

P = Principal (original amount of money in the account)

r = Annual interest rate (expressed as a decimal)

t = Number of years

In this case, the principal is $250, the annual interest rate is 5% (or 0.05 as a decimal), and the number of years is 5.

So, you can plug these values into the formula:

I = 250 * 0.05 * 5

To find out the total amount of money in the account after 5 years, you need to add the interest to the principal:

250 + I = 250 + (250 * 0.05 * 5) = 250 + 62.5 = $312.5

Roberto's account will have $312.5 after 5 years.

The functions f and  have the same axis of symmetry and the y-intercept of f is less than the y-intercept of g.

What is a graph ?

Graph can be defined as the visual representation of the given data using ordered pairs.

Graph of f(x)

You can read the y-intercept on the graph. It is the value of y-coordinate when x = 0; so ti is y = 6.

The axis of simmetry is the vertical line that split the graph into two symmetrical forms. That is the same that the vertical line that passes through the vertex. You can see that it is x = 2

2) Table of values of g(x)

The y-intercept is the value of y-coordinate when x = 0, so it is y = 8.

The axis of symmetry is x = 2.

Hence, The functions f and  have the same axis of symmetry and the y-intercept of f is less than the y-intercept of g.

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The required values are A) 5/3, B) 15, C) 20, D) 86°, E) 15°.

Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal. Consequently, if A = X and AB/XY = AC/XZ, then ABC XYZ.

Because of similarity, Corresponding angles are equal and corresponding sides are Proportional.

So,

In ΔABC

∠A = 180 - 60 - 36

∠A = 180 - 96 = 86°

Which is equal to ∠F

So,D) angle ∠F = 86°

A) Scale factor = AB/EF

= 5/3

So Scale factor is 5/3.

We can say length of side ΔABC = 5/3 Side of ΔDEF.

So, For x

25 = 5x/3

x = 15

For y

y = 5(12)/3

y = 20

And value of z,

4z = 60 degree

z = 15 degree.

Thus, required values are A) 5/3, B) 15, C) 20, D) 86°, E) 15°

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The y-intercept for function f(x) has the same value as the x-intercept of f-inverse.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

As

we can see from figure that y-intercept for f(x)=3

and x-intercept for f inverse = 3

Hence,

         The y-intercept for function f(x) has the same value as the x-intercept of f-inverse

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Answer:

x-intercept

domain of f

Step-by-step explanation:

i just did it

The factors of the expression mn-4m-5n+20 are (m-5)(n-4)

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression mn-4m-5n+20, we need to factorize it,

On factorizing the expression, mn-4m-5n+20, we get,

= mn-4m-5n+20

= m·n-4·m-5·n+5·4

= m(n-4)-5(n-4)

= (m-5)(n-4)

Hence, the factors of the expression mn-4m-5n+20 are (m-5)(n-4)

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A whopping 95% of people fall within the IQ ranges of 70 and 130. 99.7% of people in the world have IQs between 55 and 145. Only about 0.3% of people have IQ scores that fall outside of this range (less than 55 or higher than 145).

According to the one-standard-deviation rule, 32 percent of the population has an IQ score that is at least 15 points off from 100: 16 percent have IQs over 115, and 16 percent have IQs below 85.

The equation IQ=mc100, where m is the mental age and c is the chromological age, determines a person's IQ. Find the range of their mental ages if a group of 12-year-old youngsters has an IQ between 80 and 140.

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Answer: 2) x=60

Step-by-step explanation:

The money that a organisation earns in return for their labour or products is referred to as income.She make from each source last year $6000.

The money that a person or organisation earns in return for their labour or products is referred to as income.

Salary, rent, capital gains, company revenue, and income from other sources are a few typical sources of income. Understanding how each type of income is taxed is not always simple, and you may require an income tax calculator to do so.

Let t=teaching income, p=painting income, and b=book sales income.

t=p+6000 b=(t+p)/7 b+t+p=48000 (t+p)/7 +p+6000+p=48000 substitute (2p+6000)/7 + p+6000 + p = 48000 (2p+6000) + 7(p+6000) + 7p = 7*48000 multiply each side by 7 to eliminate the fraction.

substitution (2p+6000)/7 + p+6000 + p = 48000 (2p+6000) + 7(p+6000) + 7p = 7*48000

2p+6000+7p+42000+7p=336000

16p+48000=336000

16p=336000-48000

16p=288000 \s16p/16=288000/16

p=$18,000.

t=18000+6000

t=$24,000.

b=(24000+18000)/7

=42000/7

=$6000.

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       0.0000732 = 7.32 x 10⁻⁵

     145,000 = 1.45 x 10⁵

Now, According to the question:

If the number is given in the decimal notation, move the decimal point to the right side of its original position and place the decimal point after the first non zero digits. The power ten will be the number of places the original decimal point was moved and it will be negative as it was moved towards the right side.

0.0000732 = 7.32 x 10⁻⁵

If the whole number greater than 10 is to be changed into the power of 10, then move the decimal point to the left side of its original position and place the decimal point after the first digit. The power of 10 will be the number of places the original decimal point was moved and it will be positive as it was moved towards the left side.

145,000 = 1.45 x 10⁵

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The missing angle measures in triangle ABC are 35.5° and 54.5°.

We know that,

In the right triangle ABC

∠A +∠B =90°   ( by complementary angles)

We find the measure of angle B.

we know that

[tex]tanB = \frac{opposite side angle B}{adjacent side angle B}[/tex]

According to the question,

Opposite side angle B= 7 in

Adjacent side angle B = 5in

So, [tex]tanB = \frac{7}{5}[/tex]

      [tex]B = arc tan(\frac{7}{5})[/tex]

      B = 54.5°

Then, we find the measure of angle A

A + B = 90°

 A = 90°-B

A = 90° -  54.5° ( using subtraction)

A = 35.5°

So, The angles measured in triangle ABC are 35.5° and 54.5°.

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Answer:

False. This may be true with a trapezoid but not with a square or rectangle, seeing they have 2.

Step-by-step explanation:

Hope it helps! =D

The relationship between x and y can be described based on the value of the sample correlation coefficient.

Sample covariance measures the degree to which two variables are linearly related and the direction of their linear relationship. The formula for sample covariance is:

[tex]Cov(x,y) = (1/(n-1)) * \Sigma(x-\bar x)(y- \bar y)[/tex] where,

The sample correlation coefficient, also known as Pearson's correlation coefficient, measures the degree to which two variables are linearly related and the direction of their linear relationship. It is a normalized version of the sample covariance, with a value between -1 and 1. The formula for the sample correlation coefficient is:

r = Cov(x,y) / (s1 * s2) where,  

To calculate the sample covariance and sample correlation coefficient, we need to have a sample of data containing the variables x and y. Once we have the data, we can calculate the sample means, and sample standard deviations, and then use the formulas above to calculate the sample covariance and sample correlation coefficient.

The relationship between x and y can be described based on the value of the sample correlation coefficient.

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The complete question is:

Given a sample of data containing the variables x and y, calculate the sample covariance and the sample correlation coefficient, and describe the relationship between x and y.

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The solution for the given equations is x = 26, y = 15.

What is the linear equation in two variables?

A linear equation in two variables is an equation that can be written in the form of "ax + by = c", where a, b, and c are constants, and x and y are the variables.

To solve the equation y = x-11 for x, we can add 11 to both sides of the equation, resulting in y+11 = x.

To solve the equation y=15 for x, we can substitute 15 in the place of y in the first equation

15 = x - 11

So, x = 26

Hence, the solution for the given equations is x = 26, y = 15.

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Answer:approximatly -1.63092975357148

Step-by-step explanation:To solve the equation (1/2)^7x+1 = -9, we first need to get all the terms on one side of the equation by subtracting 1 from both sides. This gives us (1/2)^7x = -10.

Next, we need to get x by itself, so we take the log base 2 of both sides.

This gives us log base 2 of (1/2)^7x = log base 2 of -10.

The log base 2 of (1/2)^7 is -7, so we have -7x = log base 2 of -10

Finally, we divide both sides by -7 and get x = log base 2 of -10/-7

Using a calculator we can calculate this value which is approximatly -1.63092975357148

x = log base 2 of -10/-7 = -1.63092975357148

Students can plant seeds in a whole community garden in 5 1/3 h. Hence, Vanessa is not correct.

In the example question, students must plant seeds in 3/8 of a community garden in two hours.

The children will need 4 hours to plant the seeds for the entire garden, according to Vanessa.

We must confirm whether Vanessa is correct.

Within two hours, students plant seeds in 3/8 of the community garden.

Students can therefore plant seeds in 1 community garden in = 2/(3/8) h.

In one of the community gardens, students can sow seeds in = 2/3 * 8 hours.

In one of the communal gardens, students can plant seedlings in 16/3 hours.

In one of the communal gardens, students can sow seeds in 5 1/3 hours.

Students can therefore plant seeds in the entire community garden in 5 1/3 hours. Hence, Vanessa is not correct.

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Answer:

y = -3x + 3

Step-by-step explanation:

the equation of a line in point-slope form is.

y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])
y - (-6) = -3 (x - 3)

y+6 = -3x+9

Answer:

y = -3x+3

Step-by-step explanation:

Remember that y = mx+c

The slope is m aka the gradient and we know that that's -3.

So just chuck it into the equation:

y = -3x + c

We still have to find c (which is the y intercept)

So substitute the point (3,-6) into the equation

We will have: -6 = -3(3) +c

Once you do algebra you'll get 3=c

So substitute that back into the equation (without the point (3,-6) since we only need the equation)

y = -3x + 3

Hand-grip strength is a sign of general toughness and a good indicator of significant consequences.

For grip strength measurements, current, population-specific reference values are required to interpret the results appropriately.

Objectives

To offer grip-strength reference values and formulae based on population for US citizens ages 18 to 85.

Methods

In this cross-sectional study, hand-grip data from 1232 participants, aged 18 to 85, were taken from the database of the 2011 normative phase of the US National Institutes of Health Toolbox project. Equations and descriptive reference values were derived from the data.

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The question is incomplete
the standard deviation for hand grip strength. what Objectives and Methods of the distribution

Answer: If you take 15% off of 84.75, the new amount would be 71.8875. This can be calculated by multiplying 84.75 by 0.15 (15% written as a decimal), and then subtracting that result from 84.75.

The simplification of the addition of two or more fraction with unlike denominator is:

Convert the denominator with like terms and then add the numerators.

Method of simplification of addition of fraction with unlike denominator is:

Therefore, to simplify unlike fractions find least common multiple and add the like fractions.

The given question is incomplete, I answer the question in general according to my knowledge:

Simplification of adding fractions with unlike denominators with  example?

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Answer: Total amount invested:

= 200000

Total amount earned from investements:

0.109x + 0.029y + 0.05z = 11165

Relation of bonds and CDs:

= +20000

Step-by-step explanation:

All the solution of the blank words are given below.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given:

Figure ABCD is the pre-image.

And A'B'C'D' is the image.

The line of the reflection is y = 0.

The coordinates of the output:

A'(3, -6), B;(1, -1), C'(11, - 1) and D'(6, -6)

Therefore, all the blank words are given above.

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The coordinates of the final image are

A'' (3, 2)

B'' (0, 2)

C'' (2, 3)

The coordinates of the preimage are A(2,3), B(2,0), and C(3,2)

The transformation rule for a 90 degrees clockwise rotation is

(x, y) → (y,-x)

hence we have

A(2,3), → (3,-2)

B(2,0) → (0,-2)

C(3,2) → (2,-3)

The transformation rule for reflection in the y axis is

(x, y) → (x,-y)

hence we have

A'(3,-2) → (3, 2)

B'(0,-2) → (0, 2)

C'(2,-3) → (2, 3)

The image is plotted and attached

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For the sum of ages of Adam, Barry, and Charlie is 53 , Barry is 14 years old.

Number of brothers are three.

Adam, Barry and Charlie.

Let us consider 'x' years be the age of Barry.

Adam age is equal to (2x) years.

And Charlie age is equal to ( x - 3 )years.

Sum of their ages = 53

Substitute the value of Adam, Barry and Charlie age we get,

⇒ x + 2x + x - 3 = 53

⇒ 4x = 53 + 3

⇒ 4x = 56

⇒ x = 56 / 4

⇒ x = 14 years

Barry is  14 years old.

Adam = 2(14 )

          = 28 years

Charlie = 14 - 3

            = 11 years

Therefore, as per the information about the ages of Adam, Barry and Charlie , the Barry is 14 years old.

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Answer:

12 dollars

Step-by-step explanation:

she started with 300 and didn't add any money or take any away... sooo she earned $12 in interest

Answer:

20

Step-by-step explanation:

To find the line of best fit, we can use the equation for a linear regression: y = mx + b, where y is the price, x is the weight in ounces, m is the slope of the line, and b is the y-intercept.

To estimate the price when the weight is 48 ounces, we can plug in x = 48 into the equation: y = mx + b, and solve for y.

The correlation coefficient, denoted by r, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.

In this case, the correlation coefficient means that how strong and direction of the relationship between the price and weight of cereal. A correlation coefficient of 1 means that there is a perfect positive correlation between the two variables, which means that as the weight of the cereal increases, so does the price. A correlation coefficient of -1 means that there is a perfect negative correlation between the two variables, which means that as the weight of the cereal increases, the price decreases. A correlation coefficient of 0 means that there is no correlation between the two variables, which means that there is no relationship between the weight of the cereal and the price.

Answer:

14

Step-by-step explanation:

This question can be expressed as the following linear equation:

2x+8=36, where x is our unknown number.

From here,

2x+8=36

2x=28 (-8 both sides)

x=14 (/2 both sides)

Therefore the number is 14

Answer:

$110 is what she started with

Step-by-step explanation:

Answer:

um i don't know.... 99

Step-by-step explanation:

99 +12

Answer: 12.5% is 1/8

Answer: 25/2 would be your answer, as it is already in it's simplest form.  I hope this helps! :)

Step-by-step explanation: