The function f(x) = 150 - 8x represents the distance, in miles, remaining on a trip
x hours into the trip. What is the value of f(5)?

The approximate length of a side of the rhombus is 10.67 cm.

A rhombus is a quadrilateral with all sides of equal length.

The diagonals of a rhombus bisect each other at right angles.

Let's label the length of one diagonal as d1 and the other diagonal as d2.

In the given rugby-shaped figure, the length of d1 is 14 cm, and the length of d2 is 12 cm.

Since the diagonals of a rhombus bisect each other at right angles, we can divide the figure into four right-angled triangles.

Using the Pythagorean theorem, we can find the length of the sides of these triangles.

In one of the triangles, the hypotenuse is d1/2 (half of the diagonal) and one of the legs is x (the length of a side of the rhombus).

Applying the Pythagorean theorem, we have \((x/2)^2 + (x/2)^2 = (d1/2)^2\).

Simplifying the equation, we get \(x^{2/4} + x^{2/4} = 14^{2/4\).

Combining like terms, we have \(2x^{2/4} = 14^{2/4\).

Further simplifying, we get \(x^2 = (14^{2/4)\) * 4/2.

\(x^2 = 14^2\).

Taking the square root of both sides, we have x = √(\(14^2\)).

Evaluating the square root, we find x ≈ 10.67 cm.

Therefore, the approximate length of a side of the rhombus is 10.67 cm.

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Answer:

King George can feed 6 people.

Step-by-step explanation:

Break down each of the four sandwiches into three parts (it helps to draw this out), then take two thirds from each sandwich, this will leave you with four parts left over, which is then broken down into two portions.

Answer:

12

Step-by-step explanation:

Remember, when you add two same symbols, the outcome will be positive.

- + - = +

- + + = -

+ - + = +

+ - - = -

I think it helps you..............

The simplified expression for G is 8√6 and the simplified expression for H is 6√10.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots.

√32.√12 = √(32*12) (multiplying the numbers inside the square roots)

= √384 (calculating the product of 32 and 12)

= 8√6 (simplifying the square root of 384 by factoring out 16 and leaving the remaining 6 inside the square root)

Therefore, the simplified expression for G is 8√6.

Similarly, for expression H, we can simplify it as follows:

√18.√20 = √(18*20) (multiplying the numbers inside the square roots)

= √360 (calculating the product of 18 and 20)

= 6√10 (simplifying the square root of 360 by factoring out 36 and leaving the remaining 10 inside the square root)

Therefore, the simplified expression for H is 6√10.

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1.) \(8\sqrt{6}\)

2.) \(6\sqrt{10}\)

1.) Multiply numbers with radicals: \(\sqrt{384}\)

Factor and rewrite the radicand in exponential form: \(\sqrt{8^2 x 6}\)

Rewrite the expression using: \(^n\sqrt{ab}\) = \(^n\sqrt{a}\)  .  \(^n\sqrt{b}\) : \(\sqrt{8^2 }\) x \(\sqrt{6}\)

Simplify the radical expression: \(8\sqrt{6}\)

________________________________________________________

2.) Multiply numbers with radicals: \(\sqrt{360}\)

Factor and rewrite the radicand in exponential form: \(\sqrt{6^2 x 10}\)

Rewrite the expression using: \(^n\sqrt{ab}\) = \(^n\sqrt{a}\)  .  \(^n\sqrt{b}\) : \(\sqrt{6^2 }\) x \(\sqrt{10}\)

Simplify the radical expression: \(6\sqrt{10}\)

________________________________________________________

The sampling distribution of difference between means approximates a normal curve whose mean is zero.

The sampling distribution means the probability distribution based on the large number of samples of size n from the given population

Mean is the average of the given numbers and it is calculated by dividing the sum of observation by the number of observation. Here the term observation represents the given data.

Here they used the normal curve, sot its mean value is zero

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The  percentage of each types of s. aureus

Total number of individuals = 1000

Number of individuals susceptible (fs) to methicillin = 900

The percentage = (Number of individuals susceptible (fs) to methicillin / Total number of individuals) × 100

= (900/1000) × 100

= 90%

90 are somewhat susceptible (ss) to methicillin

The percentage = (90 /1000) × 100

= 9%

10 are killed only by a full treatment with methicillin (ft)

The percentage = (10/1000) × 100

= 1%

Therefore, the percentage of each types of s. aureus are 90%, 9% and 1%

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Given the diagram for a wooden deck

The scale used is :

Convert the given dimension to the actual dimensions

so,

So, the actual dimensions are : 16 ft , 12 ft , 8 ft , 12 ft

So, the perimeter will be :

So, the answer is option d. 48 ft

A committee consists of 11 men and 12 women. In 304,920 ways can a subcommittee of 4 men and 6 women be chosen

To solve this problem, we will use the combination formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of people (in this case, 23), r is the number of people we want to choose (4 men and 6 women), and ! means factorial (the product of all positive integers up to that number).

First, we need to find the number of ways we can choose 4 men from the 11 available. This is:

11C4 = 11! / (4! * 7!) = 330

Next, we need to find the number of ways we can choose 6 women from the 12 available. This is:

12C6 = 12! / (6! * 6!) = 924

To find the total number of ways we can choose a subcommittee of 4 men and 6 women, we need to multiply these two numbers:

330 * 924 = 304,920

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Each function, we'll substitute the value of -6 for x. Then, we'll simplify the expression by applying the order of operations.

Function Rule 1: `f(x) = -2x - 5` Substitute -6 for x: `f(-6) = -2(-6) - 5` Simplify using the order of operations: `f(-6) = 12 - 5`The answer is `f(-6) = 7`.Function Rule 2: `g(x) = x^2 + 3x - 4`Substitute -6 for x: `g(-6) = (-6)^2 + 3(-6) - 4`Simplify using the order of operations: `g(-6) = 36 - 18 - 4`The answer is `g(-6) = 14`.Function Rule 3: `h(x) = 5x - 2`Substitute -6 for x: `h(-6) = 5(-6) - 2`Simplify using the order of operations: `h(-6) = -30 - 2`

The answer is `h(-6) = -32`.Function Rule 4: `j(x) = -3x^2 + 2x + 7` Substitute -6 for x: `j(-6) = -3(-6)^2 + 2(-6) + 7`Simplify using the order of operations: `j(-6) = -3(36) - 12 + 7`The answer is `j(-6) = -103`.So, the answer to the question is:`f(-6) = 7``g(-6) = 14``h(-6) = -32``j(-6) = -103`

Hence, the answer is a long answer.

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Answer:

-2

Step-by-step explanation:

At first, you might think that -5 is bigger than -2 because 5 > 2, right? Actually, no, that's not how it works. The "rules" for numbers are flipped when you are dealing with negative numbers, so therefore, -2 is bigger. Basically, what I'm saying is that the smaller the number after the negative sign, the bigger the number is and vice versa.

Answer:

Answer is - 2

Step-by-step explanation:

Because in case of negative numbers the number which is smaller in negative no is bigger in negative

numbers I hope you understand....Mark me as brainliest

The expected value of buying one ticket in this charity raffle is $0.42. This means that, on average, a person can expect to win approximately $0.42 if they purchase a single ticket.

To calculate the expected value, we need to consider the probability of winning each prize multiplied by the value of the prize. Let's break it down:

- There is a 1/5000 chance of winning the $600 prize, so the expected value contribution from this prize is (1/5000) * $600 = $0.12.

- There are 3/5000 chances of winning the $300 prize, so the expected value contribution from these prizes is (3/5000) * $300 = $0.18.

- There are 5/5000 chances of winning the $40 prize, so the expected value contribution from these prizes is (5/5000) * $40 = $0.04.

- Finally, there are 20/5000 chances of winning the $5 prize, so the expected value contribution from these prizes is (20/5000) * $5 = $0.08.

Summing up all the expected value contributions, we get $0.12 + $0.18 + $0.04 + $0.08 = $0.42.

Therefore, if you buy one ticket in this raffle, the expected value of your winnings is $0.42.

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The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters so option (C) is correct.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities.

There could be only two terms, but there could be one hundred, a thousand, or a million.

Here are always an integer number of terms in a summation.

As per the given,

Length of the trench on the first day = 18/20 meters

Length of the trench on the second day = 9/20

Total length of the trench = 18/20 + 9/20

Take LCM as 20

⇒ (18 + 9)/20 = 27/20

⇒ 1.35 which is closest among the given option by 1 1/2 meters.

Hence "The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters".

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Step 1: Calculate the percentage accuracy for both Round 1 and Round 2

For Round 1, the percentage accuracy will be

For round 1, the percentage accuracy is 75%

For Round 2,the percentage accuracy will be

For Round 2, the percentage accuracy is 80%

Therefore, with the calculation above we can conclude that on the comparison,

Sasha threw more accurately in Round 2 because she hit the target on a higher percentage of her throws.

Hence,

The correct answer is OPTION D

Answer:

Sasha threw more accurately in Round 2 because she hit the target on a higher percentage of her throws.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The table is:

Number of washes denoted by x: 0, 8, 12

Amount left on card denoted by y: 30, 18, 12

a.       Write an equation that shows the amount of dollars left on the card

Solution:

18 – 30 divided by 8 – 0 = -12/8

On simplest form is -3/2

The equation is y = -3/2x + 30

b.      Explain the meaning of the negative slope above.

As the number of car washes increase, the dollars left on the card decreases.

c.       What is the maximum value of x?

0 = -3/2x + 30

2/3 x 3/2 x = 30/1 x 2/3

Cancel 2/3 x 3/2 and reduce 30 by 3 we get 10, 10 x 2

x = 20

Answer:

m=10

Step-by-step explanation:

–4.2 = –1.96(m − 10) + –4.2

–4.2=-1.96m+19.6-4.2

-19.6=-1.96m

m=10

Answer:

A

Step-by-step explanation:

Note: "of" is a great indicator of multiplication in math problems.

In option A, Lily eats \(\frac{3}{8}\) of the grapes, and there are 4 grapes, so we know it is

(3/8)*4 or 4*(3/8)

In the other options the "of" is followed by a unit that is not 4, such as a foot, a mile, and an hour.

Answer:

4

Step-by-step explanation:

2 ÷ 1/2 = 4

The probability that the dog is still lost at the end of the second day is 0.41

To solve this problem, we can use Bayes' theorem, which allows us to update the probability of an event based on new information.

Let A be the event that the dog is in forest A, and B be the event that the dog is in forest B. Let F be the event that the dog is found within two days.

We want to calculate P(F'), the probability that the dog is still lost at the end of the second day. We can use the law of total probability to express this as

P(F') = P(F'|A) × P(A) + P(F'|B) × P(B)

where P(F'|A) is the probability of not finding the dog within two days given that the dog is in forest A, P(F'|B) is the probability of not finding the dog within two days given that the dog is in forest B, and P(A) and P(B) are the prior probabilities of the dog being in forest A and forest B, respectively.

Using the information given in the problem, we can calculate

P(F'|A) = 1 - 0.5 = 0.5 (the probability of not finding the dog in forest A within two days is 1 - 0.5 = 0.5)

P(F'|B) = 1 - 0.8 = 0.2 (the probability of not finding the dog in forest B within two days is 1 - 0.8 = 0.2)

P(A) = 0.7 (the prior probability of the dog being in forest A)

P(B) = 0.3 (the prior probability of the dog being in forest B)

Plugging these values into the formula above, we get

P(F') = 0.5 × 0.7 + 0.2 × 0.3 = 0.41

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The given question is incomplete, the complete question is:

Oscar has lost his dog; there is a 70% probability it is in forest A and a 30% chance it is forest B. If the dog is in forest A and Oscar looks there for a day, he has a 50% change of finding the dog. If the dog is in forest B and Oscar looks there for a day, he has an 80% chance of finding the dog. what is the probability that the dog is still lost at the end of the second day?

Answer:

a = −10 is your answer

Step-by-step explanation:

Answer:

B.

y = -2x + 12

Step-by-step explanation:

The solution is Option B.

The equation of line is y = -2x + 12 where the slope of the line m = -2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the point be P = P ( 5 , 2 )

y = -2x + 8   be equation (1)

The equation (1) is parallel to the line passing through the point P ( 5 , 2 )

So , the slope of the line will be equal

Slope m = -2

Now , the equation of line is given by y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 2 = -2 ( x - 5 )

On simplifying the equation , we get

y - 2 = -2x + 10

Adding 2 on both sides of the equation , we get

y = -2x + 12

Hence , the equation of line is -2x + 12

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Answer:

Hello,

Step-by-step explanation:

\(f(n)=4n-5\\\\g(n)=an+b\\\\(gof)(n)=5n+1\\\\f(g(n))=f(an+b)=4*a*n+4b-5=5n+1\\\\4an=5n ==> a=5/4\\4b-5=1 ==> 4b=6 ==> b=3/2\\\\\\\boxed{g(n)=\dfrac{5n}{4} +\dfrac{3}{2} }\\\\\)

Answer:

C

Step-by-step explanation:

4a+10=180

4a=170

a=42.5

42.5*2=85

Answer: C. 85.0 degrees

Step-by-step explanation: First you find a using the equation they gave you. A=42.5. Then you plug it into the measures of the angles. But just by looking at the angles you can tell 2a would be the largest so you just plug a in there and you get your answer!

Answer:

5

Step-by-step explanation:

The whole number obtained as the result of the ratio (10²⁰⁰⁰⁰+10²⁰⁰²) : (10²⁰⁰¹+10²⁰⁰¹) is 5.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers. Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B).

It is given that the ratio is,

(10²⁰⁰⁰⁰+10²⁰⁰²) : (10²⁰⁰¹+10²⁰⁰¹)

We have to apply the arithmetic operation for the given ratio in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

\(=\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}} \\\\ =\frac{10^{2000}(1+100)}{10^{2000}(10+10)} \\\\ =\frac{101}{20} \\\\=5\)

Thus, the whole number obtained as the result of the ratio (10²⁰⁰⁰⁰+10²⁰⁰²) : (10²⁰⁰¹+10²⁰⁰¹) is 5.

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Answer:

Step-by-step explanation:here is a example:Recall that the volume of a regular prism is given by the area of the base times the height.

Given that the base of the prism is a regular pentagon with an apothem of 2.8 centimeters.

The pentagon consist of 5 isosceles triangles with the apothem as the height and the side of the pentagon as the base.

Recall that the are of a triangle is given by 1/2 base times height.

Thus the area of of the pentagon base of the prism is given by

Therefore, the volume of the prism is given by volume=7x(2x+1)=14x2+7x

Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24