Big Ideas Math:
Q1. The graph of which of the following functions does not belong with the other three?
Answer: f(x) = 3x^2 + 24x - 6

Q2. This is the only function that does not have x-intercepts at x= Response and x= Response and a vertex at (Response, Response).

Comparing the volume of the paints used and analyzing the proportions, The answer is Tina's shade is more blueish and Tyler's shade is more greenish.

A ratio is a way to compare two or more numbers or amounts. It tells you how much bigger or smaller one number is compared to the other. It is often written as two or more numbers separated by a colon, such as "3:5" or "2:4:6". For example, if a recipe calls for 2 cups of sugar to 4 cups of flour, the ratio would be 2:4. This means for every 2 cups of sugar, there are 4 cups of flour. It's a way to express a relationship between values or quantities and it helps to understand the proportion of one value to the other values.

Proportion is a relationship between two or more values or quantities that compares their sizes. It's a way of saying that two or more values are equal in some way. It can be written as an equation, such as "a/b = c/d", which means that the ratio of a to b is equal to the ratio of c to d. In other words, the proportion states that two or more ratios are equal to each other. For example, if a cake recipe calls for 2 cups of sugar to 4 cups of flour, the proportion would be 2/4 = 1/2. This means that for every 2 parts of sugar, there are 4 parts of flour, which can be written as a ratio 2:4 .

Tina's ratio of blue paint to green paint = 777:555

Tyler's favorite shade has a ratio =  555:777.

The ratio for Tina's shade is greater than 1 .

while the ratio for Tyler's shade is less than 1.

So Tina's shade is more blueish and Tyler's shade is more greenish.

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The syntax for using BASE in Excel is "=LN(number,base)" where "number" is the number for which you want to calculate the logarithm and "base" is the base to which the logarithm should be calculated.

For example, if you want to calculate the logarithm of 10 to the base 2, you would use the formula "=LN(10,2)".

The idea is to express the given integer (20) in terms of either the base or the values given (3 and 5).

Next, since we have the multiplication sign, we use the addition law:

The power of the number becomes the product of the log, so we have:

When you have the same base and number, the result is always 1.

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By probability, she will not receive a phone call from any of her grandchildren after 146 days

In those circumstances, probability helps in assessing the likelihood of an event. Probability plays a significant role in daily life. political strategy analysis, blood type determination, sports and gaming strategies, insurance buying or selling, online shopping, and online gaming.

There is a [tex]\frac{2}{3}[/tex] chance that the first child won't call, a [tex]\frac{3}{4}[/tex] chance that the second child won't call, and a [tex]\frac{4}{5}[/tex] chance that the third child won't call on any given day. There is a [tex]\frac{2}{3} *\frac{3}{4} * \frac{4}{5} = \frac{2}{5}[/tex] chance that no child calls her on a randomly selected day.

When we consider a sample of 360 days, in particular, this "unrigorous" reasoning becomes rigorous due to linearity of expectation; over the first 360 days, 360 * 2/5 = 144 days will pass without a phone call. Now, we just check the remaining days. On days $361 and $362, no one calls her. On days 363 and 364, she receives calls from children every three and four days, respectively. On day 365, she receives calls every five days. Therefore, to get our answer of 146, we two more days in  144.

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Answer:

$13

Step-by-step explanation:

The expected payoff for the winner would be the ticket cost, $3, plus the prize money, $10, which totals $13. This is the expected value of playing the game. However, it's important to note that this does not guarantee that the winner will receive exactly $13, as the outcome of the game is dependent on chance and the player's skill. There is always a chance that the player could win more or less than the expected value.

As 200 is not a perfect square it is not possible to increase the dimensions of the park by the same number of miles.

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

We know the area of a rectangle is (length×width).

Given, Park rangers plan to expand the area of the park to 506 square miles.

Currently, the park has an area of (18×17) = 306 square miles.

Therefore, The amount of square miles they need to increase is (506 - 306)

= 200 miles.

Now, They also want to increase the length and the width by the same amount but 200 is not a perfect square so it is not possible to increase the dimensions by the same amount.

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The missing values in the table can be calculated by multiplying the given weights by 0.92 and 0.88 to get the maximum and minimum weights for each size.

Small egg:

Minimum weight = 1.2 * 0.92 = 1.104 ounces;

Maximum weight = 1.2 * 1.08 = 1.296 ounces

Medium egg:

Minimum weight = 1.6 * 0.92 = 1.472 ounces;

Maximum weight = 1.6 * 1.08 = 1.728 ounces

Large egg: Minimum weight = 2 * 0.92 = 1.84 ounces; Maximum weight = 2 * 1.08 = 2.16 ounces

Extra Large egg: Minimum weight = 2.4 * 0.92 = 2.208 ounces; Maximum weight = 2.4 * 1.08 = 2.592 ounces

Yes, it is possible for an egg to be both large and extra large, as long as the weight of the egg is between 1.84 and 2.592 ounces.

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To find the midpoint of two points in a coordinate plane, you can use the midpoint formula.

The midpoint formula is the average of the x-coordinates and the average of the y-coordinates of the two given points.

The midpoint formula is:

((x1 + x2)/2 , (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

For example, if the two points are (3, 4) and (5, 8), the midpoint would be:

((3 + 5)/2 , (4 + 8)/2) = (4, 6)

So the midpoint between (3, 4) and (5, 8) is (4, 6).

It's important to note that this formula is valid for any dimension, not just 2D, and it can be used to find the midpoint of any two points in space, whether it's in 2D, 3D, 4D and so on.

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a) The given relation is function.

b) The function is, $x = 18.5 y

c) The value of (f+ g)(9) is 5.

d) The he original amount of her loan is 6000.

A function with one or two variables and no exponents is referred to as a linear function. It is a function with a straight line as its graph.

Given:

a) The given relation is function because is input have have output, no two outputs have same input.

b) After 8 hours, a person earned $148 in wages.

So, the unit rate change = 148/ 8

                                        = 18.5

So, if y represents the number of hour and $x the wages, then the function is $x = 18.5 y.

c)  Let f(x)=x and g(x)=x-13

(f+ g)(9)

= (x+  x-13) (9)

= 2x -13

= 2(9)- 13

= 5

d) The modeled function. P(m) = 6000 - 300m.

so, the original amount of her loan is 6000.

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Answer: #181000

Step-by-step explanation:

So, to solve the problem, recall these definitions:

payout - withdrawal

pay in - deposits.

Normally, deposits add money to your balance, and withdrawals take out money.

So, there is one cheque for  paying in 14,000, and two cheques for paying out 49,000 and 34,000

So, the balance is 250000 + 14000 - (49000+34000)

The balance is 181,000

Answer: 1/4 pound (lb) is equal to 4 ounces (oz).

This is because there are 16 ounces in one pound, so you can divide a pound into 16 equal parts, and each part is one ounce. Similarly, you can divide a pound into 4 equal parts , and each part is 1/4 pound. So in order to convert 1/4 pound to ounces, you can multiply 1/4 by 16.

1/4 lb * 16 oz/lb = 4 oz

When converting units, you are essentially multiplying or dividing by a conversion factor. In this case, the conversion factor is 16 oz/lb which tells you that there are 16 ounces in one pound. This factor allows you to convert between pounds and ounces by multiplying or dividing by it.

It's important to pay attention to the units in the conversion factor when using them. Here, the numerator and denominator of the conversion factor have the same unit, but it's not always the case. And the conversion factor helps to cancel out the unwanted unit and yield the desired unit in the end.

Step-by-step explanation:

The description of a solution to the problem modeled by the function y = 2x + 8 is given as follows:

The time needed to complete 40 parts  is of 16 minutes.

The function for this problem is defined as follows:

y = 2x + 8.

In which the variables are defined as follows:

Hence, solving the function for x, we are going to obtain the time needed to produce y parts, giving the description of a solution for this problem.

When y = 40, the solution for x is given as follows:

40 = 2x + 8

2x = 32

x = 32/2

x = 16 minutes.

The interpretation of this solution is that a time of 16 minutes is needed to obtain a production of 40 parts.

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Answer:

y = 2x - 1

Step-by-step explanation:

Point 1: (0, -1); Point 2: (1, 1)

           (x₁, y₁)              (x₂, y₂)

y₂ - y₁      1 - (-1)       1 + 1       2

---------- = --------- = -------- = ------ = 2

x₂ - x₁      1 - 0           1          1

y - y₁ = m(x - x₁)

y - (-1) = 2(x - 0)

y + 1 = 2x - 0

   -1          -1

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

y = 2x - 1

I hope this helps!

Answer:

12

Step-by-step explanation:

11, 11, 13, 13, 12, 13, 11, 12, 10, 13

Put the numbers in ascending (increasing) order.

10, 11, 11, 11, 12, 12, 13, 13, 13, 13

If there is an odd number of numbers, the median is the number in the middle.

There are 10 numbers which is an even number of numbers.

For an even number of numbers, the median is the mean of te two middle numbers.

10, 11, 11, 11, 12, 12, 13, 13, 13, 13

The two middle numbers are 12 and 12.

The mean of 12 and 12 is (12 + 12)/2 = 12

Answer: 12

Answer:

third side = 3

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let the third side be x , then

x² + 4² = 5²

x² + 16 = 25 ( subtract 16 from both sides )

x² = 9 ( take square root of both sides )

x = [tex]\sqrt{9}[/tex] = 3

In mathematics, the symbol " σ" is "σ" (sigma) which is commonly used to represent the sum of a set of values.

It is used to indicate that a series of values are to be added together. For example, the notation "Σx" is read as "the sum of x" and it means to add all values of x together. It is often used in mathematical analysis, statistics, and physics.

For instance, in statistics, the symbol "σ" is used to represent population standard deviation, which is a measure of the dispersion of a set of data points from the mean.

In probability theory, the symbol "σ" is also used to represent the standard deviation of a random variable.

In general, the specific meaning of the symbol "σ" depends on the context in which it is used.

It is also known as Summation notation.

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Answer:

2 prime numbers: 31 and 37

Step-by-step explanation:

31 and 37 are the only prime numbers between 30 and 40

Answer:

Conclusion: Straight line upwards from point (0,3) to (3, 5.25)

Step-by-step explanation:

Your part (a) answer is absolutely correct.

Equation is y = 3/4x + 3

For part (b), you are correct to say that the y-intercept of the graph is 3. The implication is that the initial height of the tree is 3 feet tall. (When the tree just starts to grow at time = 0 years)

Your part (c) answer is absolutely correct as well.

For the graph part,

x = years (independent variable)

y = height (dependent variable)

From the equation you have constructed in part (a), the y-intercept of the graph is 3. Hence, a point (0, 3) can be first plotted in the graph.

Secondly, for part (c), you have also obtained the answer (3, 5.25). Plot that point on the graph as well.

Next, we can see that the graph in (a) is a linear graph in the form y = mx + c, where m is the gradient and c is the y-intercept.

Hence, you can easily draw a straight line upwards from (0,3) to (3,5.25) . It is expected as the gradient of the graph is 3/4, which is a positive number.

Answer:

no

Step-by-step explanation:

The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

8+10 is 18

which is less than 19

Answer:

B. 73

Step-by-step explanation:

An explanation is in the picture if you need it.

Answer:51.1

Step-by-step explanation:

The sum of squares of two sides is equal to the square of the third side.

Finding the Third Side of a Triangle with Two Sides

Let's assume that the triangle is right-angled, as the third side of a right-angled triangle can only be found when the other two sides are known.

A right-angle triangle is what?

This particular sort of triangle adheres to the Pythagoras theorem and may be calculated using the trigonometry tool.

We are aware that the right-angled triangle follows Pythagoras' Theorem.

According to the Pythagorean Theorem, the third side's square equals the sum of the first two sides' squares.

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The complete question should be:

What is the length of 3rd side of a triangle?

Answer:

Step-by-step explanation:Its actually 102, not 110

The equation of the line segment is written in the form y = mx + b, where m is the slope and b is the y-intercept. Finally, a directed line segment is two-dimensional.

1. It has a definite starting point and a definite ending point.

2. It has a definite length.

3. It has a definite direction.

4. It has a slope and equation.

5. It divides the plane into two parts.

6. It is symmetric about its mid-point.

7. It is two-dimensional.

A directed line segment is a line segment that has a definite starting point and a definite ending point. Its length is the distance between the two points and it has a direction, given by the vector from the starting point to the ending point. The line segment divides the plane into two parts. It is symmetric about its mid-point, which is the point halfway between the two endpoints. It has a slope and an equation. The slope is the ratio of the change in y-coordinates to the change in x-coordinates. The equation of the line segment is written in the form y = mx + b, where m is the slope and b is the y-intercept. Finally, a directed line segment is two-dimensional.

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22/154=11/77=1/7

1/7 is the lowest form

Answer:

(r + 7)(r - 4) = 0

Step-by-step explanation:

r² + 3r - 28 = 0

(r + 7)(r - 4) = 0

r = -7, 4

Answer:

Mark angles C and F as congruent.

Step-by-step explanation:

Angle-Angle-Side (AAS) Congruence Theorem

If any two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

The given triangles have one corresponding angle and one corresponding side marked as congruent.  

To satisfy AAS congruency, another pair of corresponding angles need to be marked as congruent.  

As an included side is the side between two angles, we cannot mark angles A and P as congruent, as this would not satisfy AAS congruency since sides AB and PD would be the included sides.  

Therefore, to make triangle ABC congruent to triangle PDF by AAS, mark angles C and F as congruent.

Answer:

-30

Step-by-step explanation:

-1x/5 = 6

-x/5 = 6

-x = 30

x = -30

Answer:

X ≥ 49.5

Step-by-step explanation:

X + 15 ≥ 64.5

Subtract 15 from both sides

X ≥ 49.5

So, the answer is X ≥ 49.5