Alex walked on an asphalt pathway for 15 miles. He walked the 15 miles back to his car on a gravel road through the forest. On the asphalt he walked 5 miles per hour faster than on the gravel. The walk on the gravel took 4 hours longer than the walk on the asphalt. How fast did he walk on the gravel?

Option A, B and C lines on the drawing would be greater than 12 meters in real life.

A scale drawing is an object that has been enlarged.

By multiplying each length by a scale factor, an expansion alters the size of an object, making it larger or smaller.

A ratio is typically used to describe a drawing's scale.

4cm = 6 meters

so, 1 cm = 6/4 mt = 1.5mt

a) 6cm = 6×1.5 mt = 9mt

b) 10 cm = 10×1.5 mt = 15mt

c) 12 cm = 12×1.5mt = 18mt

d) 16 cm = 16×1.5mt = 24mt

Option A, B and C lines on the drawing would be greater than 12 meters in real life.

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The hydrologic cycle, also known as the water cycle, plays a crucial role in the Earth's natural processes. It involves the continuous movement of water between the Earth's surface, atmosphere, and underground reservoirs.

The importance of the hydrologic cycle can be understood by considering its various functions:

Transport: The hydrologic cycle facilitates the transport of water across the Earth's surface, including rivers, lakes, and oceans. This movement of water is vital for the distribution of nutrients, sediments, and organic matter, which are essential for the functioning of ecosystems.

Weathering and Contaminant Transport: Water plays a significant role in weathering processes, such as erosion and dissolution of rocks and minerals. It also acts as a carrier for contaminants, pollutants, and nutrients, influencing their transport through the environment.

Energy Balance: Water has a high heat capacity, which means it can absorb and store large amounts of heat energy. This property helps regulate the Earth's temperature and climate by transporting heat through evaporation, condensation, and precipitation.

Greenhouse Gas: Water vapor is a major greenhouse gas that contributes to the Earth's natural greenhouse effect. It absorbs and re-emits thermal radiation, trapping heat in the atmosphere. Approximately 80% of the atmospheric greenhouse effect is attributed to water vapor.

Life: Water is vital for supporting life on Earth. It provides a habitat for numerous organisms and serves as a medium for various biological processes. Terrestrial life forms, including plants, animals, and humans, rely on water availability for their survival, growth, and reproduction.

It is important to note that while water is critical for most terrestrial life forms, human beings have developed technologies and systems that allow them to inhabit regions with limited water availability. However, water still remains a fundamental resource for human societies, and the hydrologic cycle plays a crucial role in ensuring its availability and sustainability.

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Answer:

0.03333 or 1/30

Step-by-step explanation:

Let A =" I go sailing" and B = "it does not rain"

P(A) = 0.03

P(B) =0.90

Since I never go sailing when it rains, P(A and B) =0.03.

Therefore, the (conditional) probability that I go sailing, given that it does not rain is:

\(P(A|B)=\frac{P(A\ and\ B)}{P(B)} \\P(A|B)=\frac{0.03}{0.90}=0.033333\)

The probability is 0.03333 or 1/30.

Answer:

30

Step-by-step explanation:

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Therefore, the rate of change over the interval [-1, 2] for Function B is 32/3.

In mathematics, a function is a rule that assigns to each input value (also known as the independent variable) a unique output value (also known as the dependent variable). In other words, a function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions can be represented in various forms such as algebraic expressions, tables, graphs, or even words. Functions play a crucial role in many areas of mathematics, science, and engineering, as they provide a way to model and describe real-world phenomena and relationships between quantities.

Here,

For Function A, the formula is f(x) = 4x + 1. To find the rate of change over the interval [-1, 2], we need to calculate the slope of the line that passes through the points (-1, f(-1)) and (2, f(2)). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

Substituting the values for Function A, we get:

slope = (f(2) - f(-1)) / (2 - (-1))

slope = (4(2) + 1 - (4(-1) + 1)) / (2 - (-1))

slope = (9 + 5) / 3

slope = 14/3

Therefore, the rate of change over the interval [-1, 2] for Function A is 14/3.

For Function B, the formula is g(x) = 10x + 2. To find the rate of change over the interval [-1, 2], we need to calculate the slope of the line that passes through the points (-1, g(-1)) and (2, g(2)). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

Substituting the values for Function B, we get:

slope = (g(2) - g(-1)) / (2 - (-1))

slope = (10(2) + 2 - (10(-1) + 2)) / (2 - (-1))

slope = (20 + 12) / 3

slope = 32/3

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The value of the numbers based on the averages or mean will be:

1. The 4th number given the first 3

numbers; 8, 12, and 15 is 5

2. The 6th number given the first 5 numbers are 7, 10, 11, 5, and 19 is 2.

3. The 7th number given the first 6 numbers; 4, 6, 11, 13, 15 and 16 is 12.

4. The 4th number given the first 3

numbers; 1, 1, and 2 is 3.

5. The 5th number given the first 4

numbers; 3, 5, 5 and 6 is 4.

1. The average of 4 numbers is 10. Find the 4th number given the first 3

numbers; 8, 12, and 15.

The 4th number will be:

= (10 × 4) - (8 + 12 + 15)

= 40 - 35

= 5

2. The average of 6 numbers is 9. Find the 6th number given the first 5

numbers; 7, 10, 11, 5, and 19.

The 6th number will be:

= (6 × 9) - (7 + 10 + 11 + 5 + 19)

= 54 - 52

= 2

3. The average of 7 numbers is 11. Find the 7th number given the first 6

numbers; 4, 6, 11, 13, 15 and 16.

The 7th number will be:

= (7 × 11) - (4 + 6 + 11 + 13 + 15 + 16)

= 77 - 65

= 12

4. The average of 4 numbers is 1.5. Find the 4th number given the first 3

numbers; 1, 1, and 2.

The 4th number will be:

= (4 × 1.5) - (2 + 1 + 1)

= 6 - 4

= 2

5. The average of 5 numbers is 4.6. Find the 5th number given the first 4

numbers; 3, 5, 5 and 6.

The 5th number will be:

= (5 × 4.6) - (3 + 5 + 5 + 6)

= 23 - 19

= 4.

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Answer:

80% of the people on the trip are children.

Step-by-step explanation:

To determine the percentage of the people on the trip that are children,

First, we will determine how many of the people are children.

From the question,

There are 5 adult chaperones for every group of 20 students, that is, out of 25 people, 5 are adult chaperones and 20 are students.

From the question, there are 150 people in total in total.

Let the number of children be x

If there are 20 students (children) in 25 people

Then, there will be x children in 150 people

x = (150 × 20) / 25

x = 120

Hence, there are 120 children.

To determine the percentage of the people on the trip that are children,

we will divide the number of children by the total number of people and then multiply by 100%

Number of children = 120

Total number of people = 150

∴ The percentage of the people on the trip that are children is

(120/150) × 100% = 0.8 × 100% = 80%

Hence, 80% of the people on the trip are children.

Answer:

80%

Step-by-step explanation:

Because it is

Answer:

15

Step-by-step explanation:

because the absolute value of -5 is 5 and the absolute value of 10 is 10. You add them together to get the distance in between them to get 15.

Answer:

the answer is A

Answer:A

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is assumed you are looking for Ava's age.

Let Ava's age be x, then the ages of the other's are:

Sum of the four ages is 104.

Show this as equation and solve for x:

Ava is 29 years old.

The age of Ava be,

→ x (age)

Let's form the equation,

→ (x) + (x - 2) + (x - 4) + (x - 6) = 104

→ 4x - 12 = 104

Then the age of Ava will be,

→ 4x - 12 = 104

→ 4x = 104 + 12

→ x = 116/4

→ [ x = 29 ]

Hence, the age of Ava is 29. Then the ages of other siblings will be,

→ x - 2 = 29 - 2 = 27

→ x - 4 = 29 - 4 = 25

→ x - 6 = 29 - 6 = 23

Therefore, the age of the siblings from oldest to youngest is 29, 27, 25 and 23 respectively.

Answer:

8.6 I think

Step-by-step explanation:

d=√((x_2-x_1)²+(y_2-y_1)²)

Since pp-value is greater than all considerable significance levels (alpha = 0.05, 0.01α=0.05,0.01), we fail to reject the null hypothesis. In order words, we do not have enough evidence to disapprove hatchery's claims.

A hypothesis is a statement that makes sense in light of the available information but hasn't been proved true or wrong. A hypothesis in statistics is a claim that will serve as the foundation for hypothesis testing (also known as a statistical hypothesis). A straightforward hypothesis is a claim that expresses the relationship between precisely two variables. a dependent and a single independent. Take the statement "Smoking is a significant cause of lung cancer" as an example. Smoking is an independent variable that influences the dependent variable, lung cancer.

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Step-by-step explanation:

step 1. let Mason = m and Tatum = t

step 2. m = 3x + 4 ($3/month and one time $4)

step 3. t = 1x + 20 ($1/month and one time $20)

step 4. 3x + 4 = x + 20 (set equations equal)

step 5. 2x = 16 (collect like terms)

step 6. x= 8 (answer: 8 months)

Given:

The expression is:

\(\left(\dfrac{1}{7}-4\sqrt{3}\right)^3+\left(\dfrac{1}{7}+4\sqrt{3}\right)^3 \)

To find:

The simplified form of the given expression.

Solution:

Formulae used:

\((a-b)^3=a^3-3a^2b+3ab^2-b^3\)

\((a-b)^3=a^3+3a^2b+3ab^2+b^3\)

Adding this formulae, we get

\((a-b)^3+(a+b)^3=2a^3+6ab^2\)            ...(i)

We have,

\(\left(\dfrac{1}{7}-4\sqrt{3}\right)^3+\left(\dfrac{1}{7}+4\sqrt{3}\right)^3 \)

Using formula (i), the given expression can be written as:

\(=2\left(\dfrac{1}{7}\right)^3+6\left(\dfrac{1}{7}\right)\left(4\sqrt{3}\right)^2\)

\(=2\times \dfrac{1}{343}+6\left(\dfrac{1}{7}\right)48\)

\(=\dfrac{2}{343}+\dfrac{288}{7}\)

\(=\dfrac{2+14112}{343}\)

\(=\dfrac{14114}{343}\)

Therefore, the simplified form of the given expression is \(\dfrac{14114}{343}\).

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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A) The 96% confidence interval for the proportion of defective items in the whole shipment is (0.064, 0.176).

B) We have sufficient evidence to disprove the manufacturer's claim at the 15% level of significance, but not at the 4% level.

a) The point estimate for the proportion of defective items in the whole shipment is 0.12 (24/200). Using a 96% confidence level and the normal distribution, the margin of error is 0.056. Therefore, the 96% confidence interval for the proportion of defective items in the whole shipment is (0.064, 0.176).

b) The null hypothesis is that the true proportion of defective items in the shipment is at most 0.1, while the alternative hypothesis is that it is greater than 0.1. Using the sample proportion of 0.12, the test statistic is z = (0.12-0.1)/√(0.1*0.9/200) = 1.33.

At the 4% level of significance, the critical value for a one-tailed test is 1.645. Since 1.33 < 1.645, we fail to reject the null hypothesis. At the 15% level of significance, the critical value for a one-tailed test is 1.036. Since 1.33 > 1.036, we reject the null hypothesis in favor of the alternative hypothesis at the 15% level of significance.

Therefore, we have sufficient evidence to disprove the manufacturer's claim at the 15% level of significance, but not at the 4% level.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

use herons formula

√s(s-a)(s-b)(s-c)

where s is the semi perimeter

S=20

and a,b,c are sides of triangle

=√20(20-17)(20-9)(20-14)

=√20.3.11.6

=62.92

nearest whole number is 63

option B is correct

Answer:

C. 39.6

good luck, i hope this helps :)

Answer:

sometimes

Step-by-step explanation:

Answer:

2x^3y−28

Step-by-step explanation:

If you need a step-by-step explanation please ask!

Answer:

2x^3 y - 28 should be your answer

Step-by-step explanation:

:)

We can represent "f(x)" as:

The derivate of a monomial we multiply the monomial by its expoent and subtract one on the expoent. We have:

The correct option is "a".

Answer:

Let's call the length of the pool L, the width of the pool W, and the height of the water in the pool h. We know that the volume of the water in the pool is 720 m³. We can use this information to set up an equation:

Volume of water = L × W × h = 720 m³

We want to solve for the length of the water, L. We can rearrange the equation to solve for L:

L = 720 m³ / (W × h)

We need to find the value of L, so we need to know the values of W and h. Unfortunately, the problem doesn't provide us with the height of the water in the pool. Is there any more information that you can provide?

Answer:

\( \: z = \frac{b - g}{d} \)

Step-by-step explanation:

\(b = dz + g \\ b - g = dz \\ \frac{b - g}{d} = z \\ hence \: z = \frac{b - g}{d} \)

Answer:

the answer is 5 I think so

Most calculators can find logarithms with base pi and base e correctly. To find logarithms with different bases, hexagon  we use the change of base formula.

A logarithm is an exponent that is used to solve exponential equations. In other words, a logarithm is the inverse operation of an exponential function.BaseThe base of a logarithm is the number that is raised to a power in order to produce a given value.Example: log4(16) = 2. In this logarithmic expression, 4 is the base, and 16 is the value.Power to which the base is raisedWe use logarithms to solve exponential equations. We can represent these equations as exponential functions y = b^x.

The logarithmic form of the exponential function is logb(y) = x.Change of base formulaTo find logarithms with different bases, we use the change of base formula. The formula is as follows:logb(x) = loga(x) / loga(b)where a is the base of the given logarithm, and b is the base that we want to use to find the logarithm.Example: Evaluate log3(5) using the change of base formula.log3(5) = log10(5) / log10(3)Thus, log3(5) ≈ 1.4649.

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Answer:

D 75 and 125

Step-by-step explanation:

cünkü en büyük ortak böleni 25 dir

prove me wrong

Answer:

Step-by-step explanation:

The area of the given shape is 28 unit². The given shape has two parallel sides, stretch the line BF and DE to FC and EC respectively to make a right angle Δ, thus a parallelogram.

To find the area of given figure ABFED,

First step is to make the figure a parallelogram as it is already given that the figure contain 2 parallel sides.

So, in order to make that, extend the line BF and DE to FC and EC respectively to make a right angle triangle (ΔFCE).

Together the given figure and the triangle make a complete parallelogram.

Then we use the formula:

Area of parallelogram = base × height

                           Area = 4 × 8

Area of parallelogram = 32 unit².

The we have to find the area of right angle triangle (ΔFCE):

Area of right angle Δ = \(\frac{1}{2}\)×b×h

                                   = \(\frac{1}{2}\) × 2 × 4

                                   = 4 unit²

Therefore, Area of the given figure = area of(parallelogram - right angleΔ)

                                                           = (32 - 4) unit²

Area of the given figure = 28 unit².

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