Melanie babysits for $14 per hour.
If she earned $91 last week,
how many hours did she work?
Define the variable. Write and
solve the equation.

Answer:

y equals to 4x + 3

subtract 3 on both side

4 - 3 equals to 4x + 3 - 3

divide the equation by 4 on both sides

y-3/4 = 4x/4

X = y-3/4

Answer:

[tex]19\sqrt{3}[/tex]

Step-by-step explanation:

Simple math. You could extrapolate the square roots and simplify the coefficients to easily subtract numbers with the same roots.

Which of the following is untrue: the extreme value theorem, mean value theorem, or intermediate value theorem? All three of the calculus-related theorems—Intermediate Value Theorem, Mean Value Theorem, and Extreme Value Theorem—are valid.

According to the intermediate value theorem, a continuous function must take on the value "c" at some point in the interval if it is defined on a closed interval and the value "c" is between the function's minimum and maximum values.

According to the Mean Value Theorem, if a function can be differentiated on an open interval, then at least one point in the interval has a derivative equal to the function's average slope.

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Complete Question is: Which of the following is false according to calculus: the extreme value theorem, mean value theorem, or intermediate value theorem?

keep the highest averaging do no harm imagine that your instructor chose to use the do no harm scoring method in grade it now mode. so My final score is 5/10

What is Mode?

In statistics, the value that consistently appears in a particular set is referred to as the mode. The mode or modal value in a data set is sometimes referred to as the value or number that occurs most frequently in the data set. In addition to mean and median, it is one of the three measures of central tendency.

For a limited number of observations, the mode is simple to find. There could be one mode, several modes, or none at all for a given collection of values.

When we use highest scoring method in Mode, we keep the Highest will give the highest score if the scores are different.

So that the final score is 5/10

because average of 2/10+3/10+10/10  /3= 5/10

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Answer:

x² + (y + 5)² = 61

Step-by-step explanation:

the equation of a circle in standard form is

(x - a)² + (y - b)² = r²

where (a, b ) are the coordinates of the centre and r is the radius

here (a, b ) = (0, - 5 ) and r has to be found

(x - 0)² + (y - (- 5) )² = r² , that is

x² + (y + 5)² = r²

the radius is the distance from the centre to a point on the circle.

using the distance formula to find r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (0, - 5 ) and (x₂, y₂ ) = (- [tex]\sqrt{60}[/tex] , - 6 )

r = [tex]\sqrt{(-\sqrt{60}-0)^2+(-6-(-5))^2 }[/tex]

 = [tex]\sqrt{(-\sqrt{60})^2+(-1)^2 }[/tex]

  = [tex]\sqrt{60+1}[/tex]

  = [tex]\sqrt{61}[/tex]

then r² = ( [tex]\sqrt{61}[/tex] )² = 61

the equation of the circle is then

x² + (y + 5)² = 61

From the above given options by using app is more accurate and reliable so option b is correct

The question is incomplete the options are not given the options are:

a. Marcus should ask each of his classmates to write down on a piece of paper how many hours of sleep they get per night and hand the paper to him.

b. Marcus should have them download an app that tracks their phone geolocation and activity so he can see when their phones are in their rooms and not being used. From this data he can figure out how long each student sleeps.

given that

Marcus wants to learn about the sleeping habits of students in his class.

Marcus wants to collect data from his classmates to learn how many hours of sleep his classmates get.

He then wants to process this data with a computer and visualize it in a Histogram

survey can be done in different ways:

1. by asking question

2. survey

3. observation

From the above given options by using app is more accurate and reliable so option b is correct

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Answer:

Step-by-step explanation:

Divide 138 by 12.

The answer would be 11.5.

Lets leave the 0.5 right now.

So, there would be 11 teams left and the other people left will be in the small group.

Now, multiply 12 by 11. You get 132. Subtract that from 138 and you get the remainder which is 6.

Hence, the number of people in the small group would be 6.

Thanks

Answer:

11 teams & 6 people in the small group

Step-by-step explanation:

138 = 11.5

12

So we can take it as 11 teams

12 × 11 = 132

138 -132 = 6

Therefore remaining people are added to small group

A triangle with the given measure of side length 8cm, 8cm , and 10cm is an isosceles triangle with two sides of equal measure.

As given in the question,

In the given triangle,

Measure of side length of a triangle is given by :

8cm, 8cm , and 10cm

Longest side = 10cm.

But ( 8)² + (8)² ≠ (10)²

It is not right angled triangle as does not satisfied the Pythagoras theorem.

8cm = 8cm.

Here in the given triangle two side length of the triangle are of same measure.

It represents it is an isosceles triangle.

Therefore, the given triangle side length represents it is an isosceles triangle with two sides of equal measure.

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Solve for x values that satisfy a quadratic inequality to write interval notation. This usually involves factoring the quadratic and putting it equal to zero, then utilizing the inequality sign to select viable solutions. After finding the answers, write (a,b) to indicate the interval of x-values that make the inequality true. The interval notation for -3 and 5 is (-3,5).

Generally, Before you can create an interval notation for a quadratic inequality, you must first solve for the values of x that are compatible with the inequality being satisfied. In most cases, this will require factoring the quadratic expression and fixing it so that it equals zero.

After that, the sign of inequality will be used to decide which solutions are appropriate. After you have determined the solutions, you may indicate the range of x-values that cause the inequality to hold using the notation (a,b), where a and b stand for the solutions, respectively.

As an illustration, the interval notation would look like this if the answers were -3 and 5. (-3,5).

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It is likely to randomly select a chocolate chip cookie from the batch.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
The probability of selecting the chocolate chip is given as 0.75.
Which is more than 50%
So, it is likely to randomly select a chocolate chip cookie from the batch.

Thus, It is likely to randomly select a chocolate chip cookie from the batch.

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Answer: B: Likely

Step-by-step explanation:

Jason's trip was 9 minutes longer than his usual drive to work.

Given that,

Distance from Jason's home to office = 20 miles

Speed of driving from home to office = 50 miles/hour

Total time taken to reach from home to office = distance ÷ speed = 20/50 = 0.4 hours = 24 minutes

Thus, on a normal day, Jason takes 0.4 hours to reach his office from home.

Now, Jason drove for 12 minutes when his car broke down,

The taxi arrived 15 minutes later and drove at 40 miles/hour,

Total time spent to reach office from taxi= distance ÷ speed = 20/40 = 0.5 hours= 30 minutes

Although he already spent 12 minutes driving before the taxi arrived so,

30 - 12 = 18 minutes.

But, he waited for the taxi to arrive for 15 minutes so,

18+15 = 33 minutes.

Thus, today Jason took 33 minutes to reach the office from his home.

Therefore, Jason took (33- 24)minutes which is equal to 9 minutes longer than his usual drive to work.

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Answer:

9:02

Step-by-step explanation:

The least common multiple (LCM) of 8 and 32 is 32.

Therefore, both bells will ring at the same time after 32 minutes, at 9:02.

The required number corn plants are on the farm are 21.

metre stick counting techniques. Count the seedlings for each metre of the row using a metre stick. To calculate plants per square metre, multiply that amount by 100, then divide it by the seed spacing in centimeters.

Let the number of rows be x.

the number of corn plants = x - 4

So,

x(x - 4) = 525

x^2 - 4x - 525 = 0

On solving the above quadratic equation, we get

x = 25, x = -21

Thus, number of corn plants in the row are 52 - 4 = 21

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If store c sells 122,420 products, then store b sells 6121 products.

Let x = number of products store a sells

If store a sells one fifth as many as store c, then we can write this expression as:

x = 1/5(122,420)

Evaluating, we have:

x = 24,484

If store a sells four times as many products as store b, then we can write the expression for the number of products store b sells as:

x = 4(number of products store b sells)

Plug in the value of x, we have:

24,484 = 4(number of products store b sells)

number of products store b sells = 6121

Therefore, store b sells 6121 products.

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The three methods to solve a 3 variable linear system of equations are substitution, elimination, and matrix inversion.

1. Substitution: This method involves isolating one of the variables in one of the equations, then substituting it into the other equations to solve for the other two variables.

2. Elimination: In this method, the coefficients of two of the variables in one of the equations are multiplied by constant values, so that when the two equations are added together, one of the variables is eliminated. The remaining variable can then be solved for, and the other two variables can be found using substitution.

3. Matrix Inversion: This method involves writing the system of equations in matrix form, then inverting the matrix using matrix algebra to solve for the three variables.

The three methods to solve a 3 variable linear system of equations are substitution, elimination, and matrix inversion. Substitution involves isolating one of the variables and substituting it into the other equations, elimination involves multiplying coefficients of two of the variables and adding the equations together to eliminate one of the variables, and matrix inversion involves writing the system of equations in matrix form and inverting the matrix to solve for the three variables.

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Answer:

6.25%

Step-by-step explanation:

17 - 16/16 x 100% = 6.25%

As per the measures of given triangle, the measure of the third side is 65°

The term triangle in math is defined as a three-sided polygon, which has three vertices.

Here we have know that the three sides are connected with each other end to end at a point, which forms the angles of the triangle.

Here we have given that Geoffrey draws a triangle, one of the angles measure 75 and one of the angles measure 40

As we all know that the sum of all three angles of the triangle is equal to 180 degrees.

Then let us consider that the third side is x.

Then it can be calculated as,

=> 75 + 40 + x = 180

=> 115 + x = 180

=> x = 180 - 115

=> x = 65°

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The equation 70 + 9.5x = 184 represents the situation and the number of visits is 12 if Marques has a points card for a movie theater.

Any model that meets the algebraic equation y=mx+b is said to be linear. B is the slope, and m is the y-intercept. Since both y and x are distinct factors, the preceding sentence is commonly referred as a "mathematical model with two variables." Two-variable linear equations are referred to as bivariate equations. There are several applications for linear equations, all of which end in zero.

Here,

It is given that:

Marques has a points card for a movie theater. • He receives 70 rewards points just for signing up

Let x be the number of visits.

The linear equation can be framed as follows:

70 + 9.5x = 184

9.5x = 184 - 70

After solving the above linear equation in one variable:

9.5x = 114

x  = 12

Thus, the equation 70 + 9.5x = 184 represents the situation and the number of visits is 12 if Marques has a points card for a movie theater.

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4, 5 and 6 are quantitative variable

given that

When you collect quantitative data, the numbers you record represent real amounts that can be added, subtracted, divided, etc. There are two types of quantitative variables: discrete and continuous.

When you graph or plot statistical data, make sure you have quantitative data of known units. If you don’t have known units, then you won’t be able to graph it.

Variables whose values result from counting or measuring something.

Examples: height, weight, time in the 100 yard dash, number of items sold to a shopper

answer choices

1. Type of cone

2.Chocolate dipped: yes / no

3.Sprinkles: yes / no

4.Cost of chocolate dip

5.Cost of sprinkles

6.Cost of one cone

4, 5 and 6 are quantitative variable

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Answer: 14.4

Step-by-step explanation:

Pythagorean theorem states that a² + b² = c²

Using this,

8² + 12² = c²

64 + 144 = c²

208 = c²

c = 14.4 when rounded to the nearest tenth

The average thickness of a page in the book= is 0.00393cm

determining the thickness of a page

One page has a thickness of 0.12 mm. Therefore, it's easy; all you have to do is add up the pages and divide that number by two. Then double that result by a page's thickness.

A book has 764 pages in total, including the final page.

3.0 cm is how thick the book is.

Divide across 764 to find the thickness of a page from the book: 3.0/764 = 0.003926701

which is roughly equal to 0.00393 cm

Consequently, 0.00393 cm is the average thickness of a book page.

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Answer:

270 donuts

Step-by-step explanation:

We need to find the number of donuts they make per hour. To find that, take the known number of donuts divided by the known number of hours.

150/10=15, so 15 donuts per hour.

Now, we multiply 18x15 and find they will have made 270 donuts.

If the sample has the same mix of people, in the same proportions, as the population being studied then sociologists know if the sample they are using is representative. So the option c is correct.

No subject is off-limits when sociologists use the sociological lens and start asking questions. Every facet of human behaviour has the potential to be studied. Sociologists cast doubt on the society that people have built and inhabit. They observe behavioral patterns as individuals navigate that world.

Sociologists have uncovered workplace patterns that have revolutionized industries, family patterns that have educated parents, and educational patterns that have supported structural changes in classrooms by using sociological methodologies, methodical research, and a scholarly interpretive approach.

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The complete question is;

How do sociologists know if the sample they are using is representative?

a. If the people in the sample freely volunteered to serve as representatives

b. If the sample has an even number, decided by the researcher, of people from several different categories or backgrounds

c. If the sample has the same mix of people, in the same proportions, as the population being studied

d. If the participants have been interviewed to reveal possible bias.

The probability that a junior bio major who has taken statistics has also taken a computer course is 13.46%.

We are trying to find the probability that a junior bio major who has taken a statistics course has also taken a computer course. This is referred to as the conditional probability, denoted as P(computer | statistics).

To calculate this, we can use the formula:

P(computer | statistics) = P(computer and statistics) / P(statistics)

This formula states that the probability of a junior bio major taking a computer course given that they have taken a statistics course is equal to the probability of them taking both a computer and statistics course divided by the probability of them taking only a statistics course.

The information given in the problem is as follows:

P(statistics) = 52%

P(computer) = 23%

P(computer and statistics) = 7%

So we can plug these values into the formula to calculate the conditional probability:

P(computer | statistics) = P(computer and statistics) / P(statistics) = 7% / 52% = 0.1346153846153846 or 13.46%

Therefore, the probability that a junior bio major who has taken statistics has also taken a computer course is 13.46%.

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The complete Question is:

A university requires its biology majors to take a course called BioRe search. The prerequisite for this course is that students must have taken either a Statistics course or a computer course. By the time they are juniors, 52% of the Biology majors have taken Statistics, 23% have had a computer course , and 7% have done both. What's the probability that a junior bio major who has taken statistics has also taken a computer course?

Answer:

Angle 1 = 34°

Angle 2 = 56°

Step-by-step explanation:

To solve, recall that a right angle equals 90°, then write an equation using the given information equalling 90°.  For this problem, let the second angle equal x.  So,

[tex]x+(\frac{1}{2}x+6)=90\\\frac{3}{2}x+6=90\\\frac{3}{2}x=84\\3x=168\\x=56[/tex]

The angle measure of the second angle is 56°.  To find the angle measure of the first angle, subtract 56° from the given 90°.  The first angle measure is 34°.  To check:

[tex]34=(\frac{1}{2})(56)+6\\34=28+6\\34=34[/tex]

The derived angle measures are correct.

The formula for the area of a triangle is A = bh/2.

If the base increases by 10% from b to b(1+10/100) = b(1.1) and the height increases by 10% from h to h(1+10/100) = h(1.1)

then the new area A' = (b(1.1))(h(1.1))/2

To find the percentage increase in area we can use the formula:

X% = (A'-A)/A * 100%

Plugging in the values we have

X% = (b(1.1)h(1.1))/2 - bh/2 / bh/2 * 100%

Simplifying we get

X% = (bh(1.1)^2 - bh)/(bh/2) * 100% = (1.1)^2 * 100% - 100% = 21%

Therefore, the area A increases by 21%.

I hope this helps :)

Step-by-step explanation:

yer lady friend come wait ♥️

ksks ovq fir

On solving the provided question, we can say that there are 7975/5 - 1595 distinct positive number f(m) less than 1992, 1991-1595 = 396 positive integer.

Zero, a positive integer, or a negative integer denoted by a minus sign are all examples of integers. A negative number is the additive reciprocal of a positive number that it corresponds to. A bold Z or a bold "mathbb Z" is frequently used in mathematical notation to denote a group of integers. A positive, negative, or zero integer—not a fraction—is referred to as an integer (pronounced IN-tuh-jer). The numbers -5, 1, 5, 8, 97, and 3,043 are examples of integers. 1.43, 1 3/4, 3.14, and other numbers are non-integer examples. Integers are a collection of integers and their antipodes. Decimals and fractions are not part of the set of integers.

suppose number of zeroes m! be f(m)

f(m) = m/5 + m/25 + m/125 + m/625 + ...

f(m) = f(m+1) = f(m+2) = f(m+3) = f(m+4)

since, f(m)< m/5 + m/25 + m/125 + m/625 + ... = m/4

f(7975) = 1991

there are 7975/5 - 1595 distinct positive number f(m) less than 1992, 1991-1595 = 396 positive integer

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Answer:1, 2, 3, 5, 6, 10, 15 and 30.

Step-by-step explanation: