Half of the cars on a train are flat cars. The train has half as many coal cars as flat cars and one-fifth as many passenger cars as coal cars. The remaining 28 cars include engines, a caboose, cattle cars, and others. How many cars does the train have?

Answer:

We can replace the 'm' with the value of 'm' on the table to get the value of 't'.

Using the equation \(t=0.5m+15\) from the first part of the question to complete the table:

\(t=0.5(5)+15\\\rightarrow 0.5*5 = 2.5\\t=2.5 + 15\\t=17.5\)

\(t=0.5(15)+15\\\rightarrow 0.5 * 15 = 7.5\\t=7.5+15\\t=22.5\)

Hope this helps.

Solution

The correct answer is 2 triangles

Option C

Answer:

The correct choice is option D. y = 2x -12

Step-by-step explanation:

slope of the points (5,-2) and (8,4) is m = 2

y — intercept of the points (5,-2) and (8,4) is b = -12

Now, put it all together, and you'll get :  y = 2x -12

Reflexive: No, two countries cannot have the same national language ,Symmetric: Yes, if one country has a common national language with another then the other must have a common national language with the former

a. The relationship between countries that "have a shared national language with"

Reflexive: No, two countries cannot have the same national language

Symmetric: Yes, if one country has a common national language with another then the other must have a common national language with the former

Antisymmetric: No, there can be multiple countries that share a common national language

Transitive: Yes, if Country A has a common national language with Country B and Country B has a common national language with Country C, then Country A has a common national language with Country C.

b. The relationship between individuals with computer science bachelor's degrees:

Reflexive: Yes, a person can have a bachelor's degree in computer science

Symmetric: Yes, if one person has a bachelor's degree in computer science, then the other must also have a bachelor's degree in computer science

Antisymmetric: Yes, if two people have a bachelor's degree in computer science then they are the same person

Transitive: No, a person who has a bachelor's degree in computer science does not necessarily have a bachelor's degree in any other subject.

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Answer:

8. 5 i belive hope this he;ps

Step-by-step explanation:

This exercise has to do with the testing of the hypothesis using the level of significance of 0.01. The results show that the null hypothesis must be rejected at

t = (4.1-4.5)/(1.2/√14) = - 1.25.

In science, a hypothesis refers to a tested assertion concerning the relationship between two or more variables or a proposed explanation for a phenomenon that has been observed.

Step 1 - Recall the values given

The Null Hypothesis would be that:

μ ≥ 4.5

The Alternative Hypothesis would be that:

μ < 4.5

The formula is provided by:

t = (X - μ₀)/(x√n)

Inserting the figures, we have:

t =  (4.1-4.5)/(1.2/√14) = - 1.25.

Degrees of Freedom is given as:

dr = n - 1 - 14 - 1 - 13

Value of p is given as:

P\(_{v}\) = P (t₁₃ < -1.25) = 0.117

Because the p-value is more than the significance level, this thus provides enough evidence to reject the null hypothesis and we can state conclusively that the true mean is not significantly less than 4.5 minutes.

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Using the 20% discount code, Gabby's purchase cost is $272 before tax.

A discount code is a special incentive offered to some selected customers to enjoy the purchase of goods at reduced prices.

A discount code is a marketing gimmick to attract new customers and induce repeat purchases.  Discount codes are offered in appreciation of the customer's continued patronage.

Gabby's purchase cost before tax can be determined as follows:

The list price of the clothes = $340

The discount code = 20%

The net price before tax = $340 x (1 - 20%)

= $272 ($340 x 80%)

Thus, Gabby's purchase will cost her $272 before tax because of the discount code.

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Answer:

The maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Step-by-step explanation:

We are given that weight P is inversely proportional to the distance D between the supports of the beam, and for this certain type of wooden beam, we have:

P = 7200/D

To find the distance between supports needed to carry 1600 lb, we can substitute P = 1600 in the above equation and solve for D:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

So the distance between supports needed to carry 1600 lb is 4.5 feet.

To find the maximum distance between supports for the beam to support a weight of 1600 lb, we can use the same equation and solve for P = 1600:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

Therefore, the maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Answer:

3 hours

Step-by-step explanation:

there's 6 parts and it takes them both an hour for each part so alone they would take 6 hours but divide that by 2 and it's 3 hours

Answer: I would say 3 hours if you worked seperatly from each other to complete one task

Step-by-step explanation:

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

False. 1:6 is a ratio inequivalent to 4:3

Step-by-step explanation:

Logic

Answer:

False

Step-by-step explanation:

False, for example 5:9 is not equal to 4:3

- That is a counter argument

The function can be defined as  price = 6x

It will cost $150 to buy 25 reams of paper.

The domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.

The range of the function is all non-negative real numbers, since the price cannot be negative.

Fir 25 items, price = 6(25) = $150

It will cost $150 to buy 25 reams of paper.

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The complete table using the function rule is

-1 = 4

0 = -2

1 = -8

5 = -32

This is further explained below.

Generally, The link between a dependent variable and an independent variable, expressed in the form of an equation, is known as a function rule. The function rule for a certain function provides an explanation of how to compute the value of the dependent variable, denoted by y, in terms of the value of the independent variable, denoted by x.

In conclusion, The table  values

-1 = 4

0 = -2

1 = -8

5 = -32

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Answer:

000000000

Step-by-step explanation:

Answer:

6 cm²

Step-by-step explanation:

\(\frac{1}{2}\) × 4 cm × 3 cm = 6 cm²

The x-intercepts and y-intercepts of the graph are x = 5 and y = 2

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

The graph

The x-intercepts are when y = 0

In this case, it is

x = 5

The y-intercepts are when x = 0

In this case, it is

y = 2

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Answer:

The probability that there is a sporting event with the garage full is:

= 14%

Step-by-step explanation:

Data on college events on evenings:

Academic events = 35%

Sporting events = 20%

No events = 45%

With academic events, the garage fills up 25% of the time

With sporting events, the garage fills up 75% of the time

With no events, the garage fills up 5% of the time

The probability that there is a sporting event with the garage full when Jose comes to campus is given as:

Probability of sporting events x probability of garage filling up

= 20% * 70%

= 0.14

= 14%

Answer:

The answer is below

Step-by-step explanation:

A function shows the relationship that exist between two variables (the independent variable and dependent variable). The independent variable does not depend on any variable and is known as the input while the dependent variable depends on other variable and is known as the output.

The relationship between two variables of a linear function i.e y (dependent variable) and x (independent variable) represented by the points \((x_1,y_1)\ and\ (x_2,y_2)\) is given by:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

a)  Write an expression for q as a linear function of p.

To do this, q is the dependent variable and p is the independent variable. From the table. the variables can be represented by (1, 18) and (2, 12)

Hence:

\(q-18=\frac{12-18}{2-1}(p-1)\\ \\q-18=-6(p-1)\\\\q-18=-6p+6\\\\q=-6p+24\)

b)  Write an expression for p as a linear function of q.

To do this, p is the dependent variable and q is the independent variable. From the table. the variables can be represented by (18, 1) and (12, 2)

Hence:

\(p-1=\frac{2-1}{12-18}(q-18)\\ \\p-1=-\frac{1}{6}(q-18)\\\\p-1=-\frac{1}{6}q+3\\\\p=-\frac{1}{6}q+4\)

a) An expression for q as a linear function of p is; q = 24 -6p

b) An expression for p as a linear function of q is; p = (24-q)/6

We can write an expression for q in terms of p by evaluating the rate of change as follows;

On this note;

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Answer:

R(x) = (460 * 7x)*(20+ x)

Step-by-step explanation:

If exactly 20 people sign up :

Charge per person = $460

For passengers after 20:

At number of passengers = 20 ;

Cost = (fee * discount * number of additional passesengers) * (20 + Number of additional passengers

Let number of additional passengers after 20 = x

R(x) = ($460 * $7x) * (20 + x)

Hence,

R(x) = (460 * 7x)*(20+ x)

Answer:

\(\textsf{a)} \quad f(x)=2x^3+4x^2-26x+20\)

\(\textsf{b)} \quad f(x)=-3x^3+6x^2-27x+54\)

Step-by-step explanation:

If f(x) is a polynomial, and f(c) = 0, then (x – c) is a factor of f(x).

Given information:

According to the factor theorem the polynomial in factored form is:

\(f(x)=a(x-(-5))(x-2)(x-1)\)

\(f(x)=a(x+5)(x-2)(x-1)\)

To find the value of the leading coefficient, a, apply the condition:

\(\begin{aligned}f(3)=a(3+5)(3-2)(3-1)&=32\\a(8)(1)(2)&=32\\16a&=32\\a&=2\end{aligned}\)

Therefore, the factored polynomial is:

\(f(x)=2(x+5)(x-2)(x-1)\)

Expand the polynomial:

\(f(x)=2(x^2+3x-10)(x-1)\)

\(f(x)=2(x^3-x^2+3x^2-3x-10x+10)\)

\(f(x)=2x^3+4x^2-26x+20\)

Given information:

According to the factor theorem the polynomial in factored form is:

\(f(x)=a(x-(-3i))(x-3i)(x-2)\)

\(f(x)=a(x+3i)(x-3i)(x-2)\)

To find the value of the leading coefficient, a, apply the condition:

\(\begin{aligned}f(1)=a(1+3i)(1-3i)(1-2)&=30\\a(1-9i^2)(-1)&=30\\a(1-9(-1))(-1)&=30\\-10a&=30\\a&=-3\end{aligned}\)

Therefore, the factored polynomial is:

\(f(x)=-3(x+3i)(x-3i)(x-2)\)

Expand the polynomial:

\(f(x)=-3(x^2-9i^2)(x-2)\)

\(f(x)=-3(x^2+9)(x-2)\)

\(f(x)=-3(x^3-2x^2+9x-18)\)

\(f(x)=-3x^3+6x^2-27x+54\)

Answer:

B. lie on different lines

Step-by-step explanation:

The answer for blanks in statements are, an x-intercept of 1 , -3, x>1 , increasing , 7.5.

Many mathematical and real-world phenomena are described by functions. Modeling real-world occurrences like population increase, interest rates, or physical motion is frequently done using them. There are many distinct features that functions can have, including continuity, differentiability, and periodicity. Functions can also be linear or nonlinear.

The domain and range of functions are crucial components. The set of all potential input values makes up the domain of a function, whereas the set of all possible output values makes up the range. The behaviour of a function, such as whether it is increasing, decreasing, or constant, can also be used to categorize it. A function's graph shows the relationship between its input and output values graphically.

Function h has an x-intercept of 1 and a y-intercept of -3.  The function is positive for x>1 and increasing on all intervals of x. The average rate of change for the function on the interval [0, 2] is 7.5

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Answer: The definition of a complementary angle is "Either of two angles whose sum is 90°." Thus the complementary angle for 4 is angle 5.

P.S. if you feel this answer is satisfactory I would appreciate it if you would mark it brainiest.

Answer:

1 to 6

Step-by-step explanation:

the ratio is found by dividing 18 by 3 which is 6.

basically, one squirrel per 6 acorns

By using Pythagoras theorem we get the height of the roof of dog house is 21 inches.

The Pythagoras theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. 

This theorem is named after the Greek philosopher Pythagoras, who lived around 570 BC. born. 

According to the question:

Given, Hypotenuse(h) = 29 inches

           Base(b) = 40/2 = 20 inches

Using Pythagoras theorem, we get

h² = b² + p²

⇒ 29² = 20² + p²

⇒ p² = 29² - 20²

⇒ p² = 841 - 400

⇒ p² = 441

⇒ p = √441

⇒ p = 21

∴ The height of the roof of dog house is 21 inches.

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The unit circle has the co-ordinates (-√2/2, -√2/2)

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: The unit circle and the point makes an angle of 225

we know the co-ordinates of any point on the unit circle is given by

x=cost and y=sint where t is the angle that line passing through the origin containing the point makes with x-axis

Thus x=cos225

           =-√2/2

and y=sin225

        =-√2/2

Hence, The required point is given by co-ordinates (-√2/2, -√2/2)

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The location of point A''' after the three transformations would be (-4, 1).

To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.

When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).

When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).

When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).

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