A local congressman must decide whether or not to vote for a bill to reduce the speed limit.
Supporters of the bill claim that the gas mileage improves at lower speeds! The congressman was given the data about the Toyota Camry gas usage - presented in the table below. (Picture Attached.)

Note: MPG stands for miles per gallon of gas.

IDENTIFY THE INDEPENDENT VARIABLE FIR THIS DATA AND WHY.

The number of students that took all the three classes is 40

The number of students are in Group 2 is 51 students

(i) To find the number of students who have taken all three classes, we need to subtract the number of students who have taken only two classes from the number of students who have taken at least one class.

Let's call the number of students who have taken all three classes "x".

The number of students who have taken Calculus and Sociology is 15 + x.

The number of students who have taken Calculus and Spanish is 20 + x.

The number of students who have taken Sociology and Spanish is 13 + x.

Adding these three equations, we have:

15 + 78 + 72 = 15 + x + 78 + x + 72 + x

solving for x

165 = 45 + 3x

120 = 3x

isolating x

So, x = 40.

hence, 40 students have taken all three classes.

(ii) To find the number of students in Group 2, we need to add the number of students who have taken at least one class to the number of students who have taken none of the classes.

Let's call the number of students in Group 2 "y".

The number of students who have taken at least one class is

32 + 22 + 16 - 10 - 8 - 11 + 5 = 36.

Therefore, y = 36 + 15 = 51.

So, there are 51 students in Group 2.

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Answer:

1023/4

Step-by-step explanation:

shown in the picture

9514 1404 393

Answer:

  51

Step-by-step explanation:

The rule gives the sequence ...

  75, 69, 63, 57, 51, 45, ...

The 5th number in the sequence is 51.

__

Alternate solution

The equation for the general term of an arithmetic sequence is ...

  an = a1 +d(n -1) . . . . . for first term a1 and common difference d

Your sequence has first term 75 and common difference -6, so the equation is ...

  an = 75 -6(n -1)

Then for n=5, the term is ...

  a5 = 75 -6(5 -4) = 75 -24 = 51

The 5th term is 51.

A possible equation of a rational function for the graph could be:f(x) = (x-2)/(x-1)²

An equation is a mathematical statement that uses an equal sign to describe the relationship between two or more components or variables. It is a way of expressing a condition or a scenario through mathematical terms and symbols. Equations are used to solve problems in a variety of fields, such as physics, chemistry, engineering, economics, and mathematics. In general, an equation has two sides: the left side and the right side, each of which contains numbers and/or variables. The left side is equal to the right side, so if some of the values or variables are known, the unknown values or variables can be determined.

This equation would represent a graph that has a vertical asymptote at x = 1, a hole at x = 2, and an x-intercept of 2. The graph would also have a slant asymptote at y = 1. The graph would also be continuous for all x-values except for x = 1.

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Answer:

sorry i don't know the answer

Answer:

so I know the first answer

Step-by-step explanation:

so total is 40 points but the total is divide by 2 points so we get 20 questions so if u get 6 wrong then you get 20-6=14... therefore the score with 6 wrong is 14

ANSWER

EXPLANATION

We have that the graph of y is:

It is first reflected about the x axis.

A reflection about the x axis is represented as:

y = -f(x)

which means that we find the negative of the function:

Then, it is translated 3 units up (vertical shift) and 4 units right (horizontal shift).

A translation is represented as:

y = f(x - a) + b

where a = horizontal shift; b = vertical shift

So, we have to find:

y = f(x - 4) + 3

That is:

Therefore, that is the equation of the transformed graph.

Part A:

To find out how much leftover pizza Brad had, we need to add up the fractions of each type of pizza:

1/2 cheese pizza + 3/4 sausage pizza + 2/6 pepperoni pizza

We can simplify the fractions by finding a common denominator:

1/2 = 3/6

3/4 = 4.5/6

2/6 = 2/6

Now, we can add the fractions:

3/6 + 4.5/6 + 2/6 = 9.5/6

This means Brad had 9.5/6 of a pizza leftover.

Part B:

Steve had 2/3 of a pizza. To compare this to Brad's leftover pizza, we need to convert Brad's leftover pizza to a fraction with the same denominator as 2/3:

9.5/6 = 9/6 + 0.5/6 = 3/2 + 1/12 = 19/12

Now we can compare:

19/12 - 2/3 = 38/12 - 8/12 = 30/12 = 2.5

This means Brad has 2.5 more pizzas than Steve.

Answer: s is \(> 118 \frac{2}{3}.\)

Step-by-step explanation:

The air balloon will have to fall more than 890 feet for it to reach an elevation below 300 feet. It falls at a rate of 7.5, so 890/7.5=118.6666666666, which is 118 and 2/3. The answer is positive because time can never be negative.

Answer: b)>3

a) for the graph

Step-by-step explanation:

D is the answer.

When f(x) and g(x) are added, the result stays as a polynomial.

Answer:

9x+32

----------

  2

Step-by-step explanation:

Answer:

\(125 \degree\)

Step-by-step explanation:

Let the unknown angle be x

As the interior angles in a triangle are added up to 180°

\(x + 25 + 30 = 180 \\ x + 55 = 180 \\ x = 180 - 55 \\ x = 125 \degree\)

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

Inequality:75x+25_<340

x<_4.2

Step-by-step explanation:

The other guy seemed like a butt. Its okay sometimes we miss something in class and need help. THATS OKAY! Welp hoped this helped. I got this straight from delta so this IS correct. lol no butts its correct!! Hope this helped! ^_~

Answer:

A) Q(t) = 4e^-(0.0079t)

B) t = 115.99 ≈ 116

Therefore scientist will be able to receive data after 116 years

Step-by-step explanation:

a)

to write a function of the form Q(t)= Q₀e⁻^kt to model the quantity Q(t) of ²³⁸Pu left after t-years.

so given that; half-life of ²³⁸Pu is 87.7 years,

∴ t =  87.7 years , Q(t) = 0.5Q₀

Now we substitute these value in the form  Q(t)= Q₀e⁻^kt

Q(t)= Q₀e⁻^kt

0.5Q₀ = Q₀e^ -(87.7k)

0.5 = e^ -(87.7k)

now we take the natural logarithm of both sides

In(0.5) = Ine^ -(87.7k)

Now using the property logₙnᵃ = a

-87.7k = In(0.5)

k = - In(0.5) / 87.7

k = 0.0079

ALSO it was given that Q₀ = 4.0 kg

Therefore , model quality Q(t) of ²³⁸pu left after t years is:

Q(t) = 4e^-(0.0079t)

b)

to find the time left after 1.6kg of ²³⁸pu

we simple substitute  Q(t) = 1.6 into Q(t) = 4e^-(0.0079t)

so we have

1.6 = 4e^-(0.0079t)

e^-(0.0079t) = 1.6/4

e^-(0.0079t) = 0.4

again we take the natural logarithm of both sides,

Ine^-(0.0079t) = In(0.4)

again using the property logₙnᵃ = a

-0.0079t = In(0.4)

t = - in(0.4) / 0.0079

t = 115.99 ≈ 116

Therefore scientist will be able to receive data after 116 years

Answer:

13 coins

Step-by-step explanation:

100% --> 260

1% --> 2.6

5% --> 13

Answer:

13 coins

Step-by-step explanation:

5% of his collection means that we are asking for 5 coins per 100 coins in his current collection. This can be simplified into 5/100 of the collection, which is 1/20. If there are 260 coins in his collection, 1/20 x 260 = 13 coins.

Answer: 13 is in C (the set of complex numbers)

Step-by-step explanation:

13 is in R (the set of real numbers)

13 is in Q (the set of rational number)

13 is in Z (the set of integers)

13 is in N (the set of natural numbers)

Answer:

62.50

Step-by-step explanation:

a) The probability of rolling a 5 or a number greater than 3 is 1/2.

b) The probability of rolling a number less than 4 or an even number is 5/6.

c) The probability of rolling a 4 or an odd number is 2/3.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

In rolling a six-sided die, the total number of outcomes is 6.

The sample space is {1,2,3,4,5,6}

The probability formula is -

Probability = Number of outcomes corresponding to events / total number of outcomes.

(a)  Let A be the event of rolling a 5. Then A = {5}.

Let B be the event of rolling a number greater than 3. Then B = {4,5,6}.

The event of rolling A or B is given by A∪B = {4,5,6}.

So, apply the probability formula -

P(A∪B) = 3/6 = 1/2

Therefore, the probability value is 1/2.

(b)  Let C be the event of rolling a number less than 4. Then C = {1,2,3}.

Let D be the event of rolling an even number. Then D = {2,4,6}.

The event of rolling C or D is given by C∪D = {1,2,3,4,6}.

So, apply the probability formula -

P(C∪D) = 5/6

Therefore, the probability value is 5/6.

(c)  Let E be the event of rolling a 4. Then E = {4}.

Let F be the event of rolling an odd number. Then F = {1,3,5}.

The event of rolling E or F is given by E∪F = {1,3,4,5}.

So, apply the probability formula -

P(E∪F) = 4/6 = 2/3

Therefore, the probability value is 2/3.

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9514 1404 393

Explanation:

1. ∠BAC ≅ ∠BCA, BD ≅ BE, ∆BDA and ∆BEC are right triangles . . . . given

2. ∆ABC is isosceles . . . . definition of isosceles triangle

3. BA ≅ BC . . . . definition of isosceles triangle

4. ∆BDA ≅ ∆BEC . . . . HL theorem

5. AC ≅ CE . . . . CPCTC

Answer:17.2414 percent!

Step-by-step explanation: I've done this before hope this helps

Answer:

5000 g

Step-by-step explanation:

1 kg = 1000 g

5 kg is 5 times 1 kg

5 * 1 kg = 5 * 1000 g

5 kg = 5000 g

Answer:

The equations are:

\(4H + 3P = 13.75\)

\(2H + 5P = 11.25\)

\(Hotdog = 2.50\)

\(Pretzel = 1.25\)

Step-by-step explanation:

Let:

\(H = hot\ dog\)

\(P =Pretzel\)

For Tina:

\(4H + 3P = 13.75\)

For Doug:

\(2H + 5P = 11.25\)

Solving for the price of both items:

We have:

\(4H + 3P = 13.75\) --- (1)

\(2H + 5P = 11.25\) --- (2)

Multiply (2) by 2

2 * (\(2H + 5P = 11.25\))

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

\(4H + 10P = 22.50\) --- (3)

Subtract (3) from (1)

\(4H + 3P = 13.75\)

\(4H + 10P = 22.50\)

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

\(4H - 4H + 3P - 10P = 13.75 - 22.50\)

\(3P - 10P = 13.75 - 22.50\)

\(-7P = -8.75\)

Solve for P

\(P = \frac{-8.75}{-7}\)

\(P = 1.25\)

Substitute 1.25 for P in (2)

\(2H + 5P = 11.25\)

\(2H + 5 * 1.25 = 11.25\)

\(2H + 6.25 = 11.25\)

Collect Like Terms

\(2H = 11.25-6.25\)

\(2H = 5\)

Solve for H

\(H = \frac{5}{2}\)

\(H = 2.50\)

Step-by-step explanation:

This is because when 12 : 3 is simplified it will give you 4 : 1

3 will go into 12 four times and 3 will go into 3 once, leaving 4 : 1

Therefore, 4 : 1 and 12 : 3 are equivalent ratios

The criteria should be used to prove that the pair of triangles are congruent, as mentioned below.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

The angle-Side-Angle congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.

Hence, these above criteria should be used to prove that pair of triangle are congruent.

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Given graph shown a function plotted.

The aim is to determine where the function is strictly decreasing.

The interval where the function is strictly decreasing is given by the union of intervals where the graph is descending from a point.

From the graph, it is clear that the function decreases from

and again from

Therefore, the intervals where the function is strictly decreasing is:

Answer:

1.5

Step-by-step explanation:

The experimental research conducted by the scientist takes into account the following factors:

a)The change in temperature is the independent variable.

b) The effect of temperature on the chimp's act of aggression is the dependent variable.

c)The dependent variable is continuous.

d)The scale of measurement used to measure the dependent variable is interval.

e) The research method being used here is experimental.

In the above experiment the researcher wants to see the change in the aggression of the chimp when there is a change in temperature in the zoo.

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Answer:

1. 49/150

2. 107/300

Step-by-step explanation:

Here is a probability question.

a. The first question asks us to find the probability of getting more than 4.

Now to do this, we look at our possible results when we roll the die, we can see that we can have 1-6.

But within this range, only two numbers are greater than 4, these are 5 and 6

Thus, to calculate the probability of getting either 5 or 6, we look at their frequencies, sum it up, then divide by the total number of times which the die was rolled.

The frequency of 5 is 47, while that of 6 is 51

The probability of getting more than 4 = Probability of getting 5 + Probability of getting 6 = (Frequency of 5 + Frequency of 6)/Total number of trials

= (47 + 51)/300 = 98/300 = 49/150

b. Probability of getting less than 3

Here, we proceed as we did in the first question. The numbers which are less than 3 are 1 and 2.

So the probability of getting less than 3 = Probability of getting 1 + Probability of getting 2 = (Frequency of 1 + Frequency of 2)/Total number of trials

Frequency of 1 = 62 while Frequency of 2 = 45

So, probability of getting less than 3 = (45 + 62)/300 = 107/300

The formula for f : M = 38 + 5f will be f = (M - 38) / 5.

no

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The equation given is:

M = 38 + 5f

We want to make f the subject of the formula

M = 38 + 5f

Subtract 48 from both sides

M - 38 = 5f

Divide through by 5

f = (M - 38) / 5

Therefore, f = (M - 38) / 5

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Let's solve ~

\(\qquad \sf  \dashrightarrow \: 3x + 3 = 2(x + 7)\)

\(\qquad \sf  \dashrightarrow \: 3x + 3 = 2x + 14\)

\(\qquad \sf  \dashrightarrow \: 3x - 2x = 14 - 3\)

\(\qquad \sf  \dashrightarrow \: x = 11\)

Therefore, value of x is 11