The diameter of Mars is roughly 17/32 the size of Earth's diameter. The diameter of Mars is 6800 kilometers.
What is Earth's diameter, in kilometers?

By using Euclidean geometry, the set of side lengths  2.5 cm, 1.8 cm, 4 cm can form a triangle.

The sum of the lengths of any two sides must be greater than the length of the third side.

a + b ≥ c

A triangle is a three-sided polygon with three straight sides. It is a basic geometric shape that is found in many areas of mathematics and geometry.

Using this rule, we can determine which of the given sets of side lengths can form a triangle:

(a) 3 cm, 4 cm, 7 cm: It is not possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (3 cm + 4 cm = 7 cm) is equal to the length of the third side.

(b) 2 cm, 3 cm, 7 cm: It is not possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (2 cm + 3 cm = 5 cm) is less than the length of the third side.

(c) 2.5 cm, 1.8 cm, 4 cm: It is possible to form a triangle with these side lengths, because the sum of the lengths of the first two sides (2.5 cm + 1.8 cm = 4.3 cm) is greater than the length of the third side.

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SOLUTION:

(c)

The area of the drive way;

Dimension of Ford Raptor;

Length = 5.603 m

Width = 2.190 m

Area of Ford Raptor;

The number of the dream car the drive way can fit;

The driveway can accommodate only 3 Ford Raptor.

(d)

The volume of Asphalt needed to repave the drive way;

Volume = Length X width X thickness

The volume of Asphalt needed to repave the drive way is 4.5826 cubic meters.

The inclination of the line represented by the equation y = x + 3 is 1, and the inclination of the line represented by the equation 3x - 2y = 6 is 3/2.

To determine the inclination (or slope) of a straight line, we can examine the coefficients of the variables x and y in the equation of the line.

The inclination represents the ratio of how much y changes with respect to x.

Equation: y = x + 3

In this equation, the coefficient of x is 1, which means that for every increase of 1 in x, y also increases by 1.

This indicates that the inclination of the line is positive, meaning it slopes upwards as x increases.

Since the coefficient of x is 1, the inclination can be expressed as 1/1 or simply 1.

Equation: 3x - 2y = 6

To determine the inclination, we need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope.

First, isolate y:

-2y = -3x + 6

Divide the entire equation by -2 to solve for y:

y = (3/2)x - 3

Now we can observe that the coefficient of x is 3/2.

This indicates that for every increase of 1 in x, y increases by 3/2. Therefore, the inclination of this line is positive, indicating an upward slope.

The inclination can be expressed as 3/2.

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Answer:

To find out how many packs of cardinal flower seeds you bought, you need to divide the total amount you spent ($36) by the cost per pack ($4).

$36 ÷ $4 = 9

Therefore, you bought 9 packs of cardinal flower seeds.

A pack of cardinal flower seeds costs $4. You spend $36 on seeds. The correct answer is 9.

Cardinals love sunflower seeds, particularly black oil sunflower seeds. Their thin shells are quite easy for cardinals to break. These songbirds can also eat hulled and heavier-shelled striped sunflower seeds due to their sturdy beaks.

So, if we spend $36 on seeds. we are going to use 36 and 4 to find are answer:

→ 36/4

→ = 9

Therefore, A pack of cardinal flower seeds costs $4. You spend $36 on seeds. The correct answer is 9.

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A normal distribution has a mean of 50 and a standard deviation of 3 , the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241  option a) 0.025.

In probability theory, normal distribution is also known as Gaussian distribution. It is a probability distribution that is symmetrical, bell-shaped, and a continuous probability distribution. It's also a part of continuous probability distribution that describes real-valued random variables whose probability density function is affected by two parameters: the mean μ and the variance σ².

Let us consider the problem. Suppose a normal distribution has a mean of 50 and a standard deviation of 3. Firstly, we need to standardize the random variable X that is to convert it to the standard normal distribution. We use the following formula for this Z = (X - μ) / σwhere X is the random variable and μ is the mean, σ is the standard deviation of the population.

So in this case, we can write this as Z = (44 - 50) / 3 = -2

We have now obtained the standard score or standard deviation for the random variable X.

Now we need to calculate the probability P(X ≤ 44) = P(Z ≤ -2).

The probability of Z being less than -2 is denoted by the area under the standard normal curve to the left of Z = -2.

Using the standard normal table we look for the probability that corresponds to -2 and the closest we find is 0.0228.

This probability represents the area under the standard normal distribution to the left of Z = -2.

To calculate the area to the left of Z = -2, we add the area to the left of the next integer, which is -3, which we find from the standard normal table as 0.0013, 0.0228 + 0.0013 = 0.0241.

Therefore, the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241 or 0.025 (rounded to three decimal places)Therefore, the answer is option A. 0.025.

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Answer:

a

Step-by-step explanation:

the data is represented in the dot plot

Answer:

answer is 77.67

Step-by-step explanation:

explain by the x axis is 68 to y axis is 84 so the median is 77.67

Answer:

All these rooms are rectangles so to find the

area of the rooms multiply length by width.

Living Room: 5x4 = 20 m^2

Answer:

A: 20m^2

Step-by-step explanation:

a= lw

a= 4(5)

a=20

Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

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The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

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Answer:

A. The teacher conducted an observational study by comparing the performance on the test of those who completed their review worksheets to those who did not complete their review worksheets.

The statement that best describes the method how the teacher likely came to the specified conclusion is: Option A. The teacher conducted an observational study by comparing the performance on the test of those who completed their review worksheets to those who did not complete their review worksheets.

In the case of testing about test scores, teacher can't use random or controlled experiment as the teacher would more likely work with real data of test scores instead of students faking it.

The sample survey is not needed as getting test scores doesn't destroy them, nor the population of students is too high(assuming math class has small number of students (usually under some hundreds) ).

Observational study is best choice here, and this is done on all students by observing how much students achieved in scored in test and relate it with them completing the review worksheets or not.

Thus, the statement that best describes the method how the teacher likely came to the specified conclusion is: Option A. The teacher conducted an observational study by comparing the performance on the test of those who completed their review worksheets to those who did not complete their review worksheets.

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Answer:

(1, 1)

Step-by-step explanation:

((-1) + 3)/2 = 1

so the midpoint is (1, 1)

Answer:

I apologize if I am wrong but I would say the second option.

Step-by-step explanation:

When adding a positive with a negative, the answer will always be negative...

The last row of the table will show the total interest paid, which is approximately $243.11.

The correct option is C.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

To calculate the total interest paid,

we need to first find out how many months it will take to pay off the entire balance.

We can use the following formula to calculate the number of months:

N = -log(1-(r×b/p))/log(1+r)

where N is the number of months, r is the monthly interest rate (which is the annual percentage rate divided by 12), b is the balance, and p is the payment.

In this case,

r = 0.1799/12 = 0.01499 (monthly interest rate), b = $1,800, and p = $125.

Plugging these values into the formula, we get:

N = -log(1-(0.01499 × 1800/125))/log(1+0.01499) ≈ 16.24

So it will take about 16.24 months to pay off the entire balance.

Using a spreadsheet, we can create a table with the following columns:

Month: 1 to 16

Balance: starting with $1,800 and decreasing by $125 each month

Interest: calculated as the monthly interest rate times the balance

Payment: $125

Total Interest: calculated as the sum of the interest for all previous months

The last row of the table will show the total interest paid, which is approximately $243.11.

Therefore, the value is (C) $243.11.

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Answer: Option C is correct $243.11

Step-by-step explanation: I got it right On the test!!!

Answer:

42

Step-by-step explanation:

               |--------------1764------------|

               |                                      |

              2                           |-------882-----------|

                                           |                            |

                                          2               |--------441------|

                                                           |                      |

                                                   |------9-----|        |----49---|

                                                   |               |        |             |

                                                  3              3      7            7

From the factor tree we see that

\( 1764 = 2^2 \times 3^3 \times 7^2 \)

Now we need to find the square root of 1764.

\(\sqrt{1764} = \sqrt{2^2 \times 3^2 \times 7^2} = \sqrt{(2 \times 3 \times 7)^2} = \sqrt{(42)^2} = 42\)

Step-by-step explanation: It is right trust me.

A 95% confidence interval for the proportion who believe immigration is a good thing is; CI = (0.4173, 0.7173)

The formula for the confidence interval of proportions is;

CI = p ± z√(p(1 - p)/n)

where;

p is sample proportion

z is z-score at confidence level

n is sample size

We are given;

Number of success; x = 631

Sample size; n = 1095

Thus;

sample proportion; p = x/n = 631/1095 = 0.5763

The z-score at 95% confidence level is 1.96. Thus;

CI = 0.5673 ± 1.96√(0.5673(1 - 0.5673)/1095)

CI = 0.5673 ± 0.015

CI = (0.5673 - 0.15), (0.5673 + 0.15)

CI = (0.4173, 0.7173)

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Answer:

are you working with ratios, rates, and percents?

Step-by-step explanation:

Answer:

The probability of getting a number greater than two or an odd number :

\(= \frac{5}{6}\)

Step-by-step explanation:

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

• let A be the event “getting a number greater than two“

Then

A = {3 , 4 , 5 , 6}

Then

p(A) = 4/6 = 2/3

• let B be the event “getting an odd number“

Then

B = {1 , 3 , 5}

Then

p(B) = 3/6 = 1/2

We notice that The event “getting a number greater than two or an odd number” is the event A∪B.

Then

p(getting a number greater than two or an odd number)

= p(A∪B)

= p(A) + p(B) − p(A∩B)

Calculating p(A∩B) :

A = {3 , 4 , 5 , 6} and B = {1 , 3 , 5}

Then

A∩B = {3 , 5}

Then

p(A∩B) = 2/6 = 1/3

Conclusion :

p(A∪B)

= p(A) + p(B) − p(A∩B)

= 2÷3  + 1÷2  − 1÷3

= 1÷3 + 1÷2

= 5÷6

The probability of getting a number greater than two or an odd number is 0.8.

We have a roll die.

We have to find the probability of getting a number greater than two or an odd number.

The formula to calculate the probability of occurrence of an event 'A' can be written as -  

P(A)  =  \(\frac{No. \;of\;possible\;outcomes}{Total\;number\;of\;outcomes}\)

According to question -

For getting a number greater than two or an odd number, the total number of possible outcomes are - 5.

For rolling a die, the number of outcomes will be - 6

Hence, the probability of occurrence of Event A will be -

P(A) = \(\frac{5}{6}\) = 0.8

Hence, probability of getting a number greater than two or an odd number is 0.8.

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Answer:

9.99 inches

Step-by-step explanation:

Answer:

4/9 = 1/2 x

Step-by-step explanation:  2.84 sands

Answer:

it would be 1/4 and 0.3

Step-by-step explanation:

The five inequality symbols are greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol ().

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Step-by-step explanation:

so, the 200m winner's average speed was

200m/(60+57)sec = 200/117 m/s

so, 400m with the same speed would need x seconds :

200x/117 = 400

200x = 400×117

x = 2×117 = 234 seconds = 3 minutes and 54 seconds

(after seeing that a minute has 60 seconds, and that then 234/60 = 3 and 54 remainder).

so, she would have reduced her time by 10 seconds (from 4 minutes 4 seconds down to 3 minutes 54 seconds = 4 + 6 = 10).

Answer:

Step-by-step explanation:

Ronald's walking speed is 3 miles per hour, and he walks for 2 hours, so he covers 3 * 2 = 6 miles. In the next hour, he runs at a speed of 6 miles per hour, covering an additional 6 miles. Therefore, Ronald traveled a total of 6 + 6 = 12 miles.

Answer:

Sure what do you need?

Step-by-step explanation:

Carrying value on June 30, 2024  is $176 million, total  Interest revenue  is $12.44 million

To calculate the interest revenue for the first six months, we need to find the carrying value of the bonds on June 30, 2024.

The carrying value is the purchase price plus the accrued interest, which is calculated as follows:

Accrued interest = Face value x Coupon rate x Time

where Time = 6/12 = 0.5 (since interest is paid semiannually)

Accrued interest = $200 million x 6% x 0.5 = $6 million

Carrying value on June 30, 2024 = Purchase price + Accrued interest

= $170 million + $6 million

= $176 million

The interest revenue for the first six months is calculated as follows:

Interest revenue = Carrying value x Market rate x Time

= $176 million x 8% x 0.5

= $7.04 million

For the second six months, the carrying value is the fair value of $180 million, since the bonds were revalued at December 31, 2024.

The interest revenue for the second six months is calculated as follows:

Interest revenue = Carrying value x Coupon rate x Time

= $180 million x 6% x 0.5

= $5.4 million

Total interest revenue = Interest revenue for first six months + Interest revenue for second six months

= $7.04 million + $5.4 million

= $12.44 million

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Answer:

See below

Step-by-step explanation:

40 ÷ 50 =   40/50 = 4/5 = .8  

Answer:

67.5

Step-by-step explanation:

Sum of Interior Angles of Pentagon = 540 (5-2) × 180

148 + 112 + 10 + 2x + 2x = 540

270 + 4x = 540

4x = 540 - 270

4x = 270

x = 270/4

x = 67.5

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