Two trains left the station traveling in opposite directions. The distance Train A traveled is modeled by the function d(t)=81t where d represents distance in miles and t represents time in hours.

Train B traveled a total of 324 miles in 4 hours.

How does the distance Train A traveled in 1 hour compare to the distance Train B traveled in 1 hour?



The distance Train A traveled in 1 h is equal to the distance Train B traveled in 1 h.

The distance Train A traveled in 1 h is greater than the distance Train B traveled in 1 h.

The distance Train A traveled in 1 h is less than the distance Train B traveled in 1 h.

To round 6541 to the nearest thousand, identify the place value and look at the hundreds place. The answer is 6000.

Rounding 6541 to the nearest thousand:

Identify the place value you are rounding to, which is the nearest thousand.

Look at the hundreds place since we are rounding to the nearest thousand. In 6541, the hundreds digits is 5, so the thousands digit remains 6, and all digits after that become 0. Therefore, 6541 rounded to the nearest thousand is 6000.

Information about Laissez-faire's economy is given.

Laissez-faire is a free-market, capitalist economic theory that rejects government interference. The French Physiocrats, who lived in the 18th century, created the laissez-faire ideology. According to proponents of laissez-faire, government involvement in industry and markets hinders economic progress.

Laissez-Faire capitalism allowed businesses to pursue just their financial goals without having to worry about restrictions from the state or taxes. Naturally, this might induce unfavorable externalities and knowledge asymmetries that could enable producers to act badly and get away with it. Laissez-Faire proponents contend that since the market would eliminate such undesirable actors, extensive and expensive regulation is not necessary. However, in practice, negative actors might carry on their operations for a very long time. Without government testing and regulatory oversight to safeguard consumers, for instance, it could not be known if a vitamin manufacturer is putting sawdust in place of herb powder in their capsules.

Therefore, In real world the laissez-faire is a capitalist economy have regulations.

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Your Turn: In the diagram, AB = 12, DX = 2.5, and BX = 5. Find CD. Show all work.

Solution:

In ΔABX and ΔCDX,

∠CDX=∠ABX=90°

Also,∠CXD=∠AXB (as shown in figure)

∠DCX=∠BAX, as two angles of the triangle are equal. The third angle is also equal.

So ΔCDX≈ΔABX

Hence, the ratio of sides must be equal.

[tex] \frac{CD}{AB} =\frac{DX}{BX} =\frac{CX}{AX} [/tex]

Now, using,

[tex] \frac{CD}{AB} =\frac{DX}{BX} [/tex]

[tex] \frac{CD}{AB=12} =\frac{DX=2.5}{BX=5} [/tex]

[tex] \frac{CD}{12} =\frac{2.5}{5} [/tex]

Now, To solve for CD, Let us multiply by 12 on both sides

[tex] \frac{12*CD}{12} =\frac{12*2.5}{5} [/tex]

[tex] \frac{1*CD}{1} =\frac{30}{5} [/tex]

[tex] CD =\frac{6}{1} [/tex]

CD=6 Answer

Answer:15 quarts/1 x 0.95 liter/1 quart

Step-by-step explanation:

Final answer:

In right triangle PQR, sin Q = 9/41. To find cos P, we need to determine the length of the hypotenuse PR. Once we have PR, we can use the cosine function to find cos P.

Explanation:

In a right triangle, the sine of an angle is the length of the side opposite the angle divided by the length of the hypotenuse. So, in triangle PQR, sin Q = opposite/hypotenuse = PQ/PR = 9/41.

Since angles P and Q are complementary, their sum is 90 degrees. Therefore, angle P = 90 - angle Q.

Now, using the Pythagorean theorem for triangle PQR (PQ^2 + QR^2 = PR^2), we can find PR. Since PQ = 9 and QR = 41, we have: 9^2 + 41^2 = PR^2. Solving for PR gives us PR ≈ 41.297.

Now that we have PR, we can find cos P using the cosine function: cos P = adjacent/hypotenuse = QR/PR = 41/41.297 ≈ 0.993.

In a right triangle, sin Q = 9/41. To find cos P, we can use the identity cos(90 - x) = sin(x). So cos P = sin(Q) = 9/41.

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the hypotenuse. In this case, sin Q = 9/41, which means that the length of the side opposite Q is 9 and the length of the hypotenuse is 41. Since P and Q are complementary angles, P = 90 - Q. Therefore, cos P = cos(90 - Q).

Using the identity cos(90 - x) = sin(x), we can substitute the value of Q to find cos P. cos P = sin(Q) = 9/41.

Answer:

Percentage of employees have high satifaction of tthe job = 44.78%

Explanation:

In a company there are 67 employees

after survey only 30 employees give the high satisfaction feedback.

So, percentage of employess have high job satisfaction = [tex] \frac{Survey result}{Total employees} *100
[/tex]

= [tex] \frac{30}{67}*100 [/tex]

= 0.44776*100

= 44.78% Final answer

Answer: the answer is D

Step-by-step explanation:

The simplification of the given expression by the law of indices will be a⁹.

Index (indices) in Maths is the power or exponent which is raised to a number or a variable.

In other words, the mathematics of power or exponent of any number is called indices.

Another example could be 7² = 7³/7 here we divide to obtain power 2.

As per the given expression,

a⁴ × a⁵

By the law of indices that [tex]a^{m} \times a^{n} = a^{m+n}[/tex].

a⁴ × a⁵ = a⁽⁴ ⁺ ⁵⁾ = a⁹

Hence "The simplification of the given expression by the law of indices will be a⁹".

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Hence, the line with a slope [tex]2[/tex] that passes through the point [tex](2,0)[/tex] is

[tex]y=2x-4[/tex]

What is the line of equation?

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

The numerous points which together form a line in the coordinate axis are represented as a set of variables [tex]x, y[/tex] to form an algebraic equation, which is referred to as an equation of a line.

As we know the line of the slope is

[tex]y=mx+b[/tex]

where [tex]m[/tex] is the slope we have [tex]m = 2.[/tex]

So it would be

[tex]y=2x+b[/tex]

Given the point,   [tex](2, 0)[/tex]

Now, we replace [tex]x[/tex] with [tex]2[/tex] and [tex]y[/tex] with [tex]0[/tex].

Now, we solve for [tex]b[/tex].

So,

[tex]0=2(2)+b\\b+4=0\\b=-4[/tex]

Since we get [tex]b = -4[/tex], we replace [tex]b = -4[/tex]

i.e., [tex]2x-4[/tex]

Hence, the line with a slope [tex]2[/tex] that passes through the point [tex](2,0)[/tex] is

[tex]y=2x-4[/tex]

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Answer:

It is easier to visually compare symmetry and skew of the data.

Step-by-step explanation:

Given that the histogram represents the distributions of rain amounts in two cities.

Histogram enables us to have a visual idea easily understandable about the pattern of the distribution.

The important points are whether the distribution is symmetrical or right/left skewed.

Mean, median, std deviations cannot be found easily by justing seeing the histograms.

Hence correct answer is

It is easier to visually compare symmetry and skew of the data.

Kevin is incorrect because 3:5 may be a simplified ratio.

Kevin is incorrect because 3:5 may be a simplified ratio. Option C is correct.

Given that,
The ratio of girls to boys in a classroom is 3:5. Kevin says there must be 8 students in the classroom. Which explains whether Kevin is correct is to be determined,

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here, the ratio of girls to boys is 3:5, Which implies there are 3 girls over 5 boys in the number, This is the simplified ratio of the girls to boys of the students in the class. So, Kevin says there must be 8 students in the classroom which is right, but Kevin does not explain the proportion in his statement,

Thus, Kevin is incorrect because 3:5 may be a simplified ratio. Option C is correct.

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Answer:

screenshot shows the answer but: n^2-6/n^2-2

Step-by-step explanation:

n^4-11n^2+30/n^4-7n^2+10
simplify the numerator
rewrite n^4 as (n^2)^2
and let u substititue for all occurences of n^2
u^2-11y+30/n^4-7n^2+10
factor u^2 - 11u+30 using the AC method.
(u-6)(u-5)/n^4-7n^2+10

(n^2-6)(n^2-5)/(n^2-5(n^2-2)

Cancel the common factor, and n^2-6/n^2-2 is your answer.

Excluded values/restrictions are n= -sqrt5 n= -sqrt2, also n= sqrt5 n= sqrt2

The value of 32% of 18 is equal to 56.25.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that 18 is 32% of the number w. The value of w will be calculated as:-

18 x  32/100 = w

Solve the above equation by mathematical operations to get the value of w,

18 x  32/100 = w

w = 56.25

Therefore, the value of w will be 56.25.

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The required approximate value volume of the cone is v =  1206 `cm³.

Given that the Height of the cone = 8 m

The Radius of the cone =  12 m

We have to find,The approximate volume of the cone .

The volume of a cone is equal to one-third of the volume of a cylinder having the same base radius and height.

Where V is the volume, r is the radius and h is the height.

The volume of the cone

[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]

Where, π = 3.14

[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3\\\\ V = \dfrac{1}{3} \pi (8)^3 (12) \: \rm unit^3[/tex]

V = 1206 cm³

Hence, The required approximate value volume of the cone is v =  1206 `cm³

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Answer:

the answer is (it cannot be determined from the information given)

Answer:

Option d:  6

Step-by-step explanation:

Find f(g(h(x))).

h(x)=2x+5

g(h(x)) = 3(2x+5)^2 -1     (substitute h(x) in)

f(g(h(x)))= -[3(2x+5)^2 -1]^3    (substitute g(h(x)) in)

Since it asks for the degree of the function, that means we must look for the variable with the highest degree. In this case, after distributing and simplifying out the last equation, we will find that the variable x has the highest degree of x^6, or 6.

Final answer:

The expanded form of 59.69 is 50 + 9 + 0.6 + 0.09.

Explanation:

59.69 written in expanded form can be expressed as:

50 + 9 + 0.6 + 0.09

5 * 10 + 9 * 1 + 0.6 * 0.1 + 0.09 * 0.01

5 * 10 + 9 * 1 + 6 * 0.1 + 9 * 0.01

50 + 9 + 0.6 + 0.09

Therefore, the expanded form of 59.69 is 50 + 9 + 0.6 + 0.09.

Final answer:

The number 59.69 written in expanded form is 50 + 9 + 0.6 + 0.09. Each term represents a digit according to its place value, with tens, ones, tenths, and hundredths places accounted for respectively.

Explanation:

Writing the number 59.69 in expanded form means expressing each digit according to its place value. Expanded form is a way of writing numbers to see the math value of individual digits. The number 59.69 would be broken down as follows:

50 + 9 + 0.6 + 0.09

Each term represents a digit in the number: '5' is in the tens place, so it is represented as 50; '9' is in the ones place, so it is simply 9; '6' is in the tenths place, so it is represented as 0.6; '9' is in the hundredths place, so it is represented as 0.09.

When performing calculations, particularly in subjects such as chemistry, scientific notation is often used to express large or tiny numbers efficiently. For example, to enter a number in scientific notation into a calculator, you must know the correct process, which can vary based on the calculator model. Consulting the instructor or the calculator's manual is advisable if there are any doubts.

Furthermore, working with scientific notation involves understanding how to properly write and interpret the exponents, which indicate how many places the decimal point has been moved.