The graph below was drawn with output on the vertical axis and input on the horizontal axis. What does
this graph indicate about the relationship between the input and the output?

If Atharv has 10 nickels and dimes in his pocket, and they have a combined value of 70 cents, then he has 1 nickels and 4 dimes.

Let x be the number of nickels and y be the number of dimes. A nickel is worth 5 cents, and a dime is worth 10 cents. Therefore, we can write two equations:

x + y = 10 (since he has 10 coins in total)

5x + 10y = 70 (since the combined value of the coins is 70 cents)

We can simplify the second equation by dividing both sides by 5:

x + 2y = 14

Now we can use the first equation to solve for one of the variables in terms of the other. Let's solve for x:

x + y = 10x = 10 - y

Now we can substitute this expression for x into the second equation:

x + 2y = 14(10 - y) + 2y = 14

Simplifying, we get:

10 + y = 14

y = 4

Therefore, Atharv has 5 - 4 = 1 nickel and 5 - 1 = 4 dimes.

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Answer: K

Step-by-step explanation:

Answer:

Step-by-step explanation:

k

Jasmin, who is 5 feet tall, is standing in the 15-foot lamppost's light. Her shadow is 4 feet long. If she walks 1 feet farther away from the lamppost, her shadow will lengthen by 3/2 feet.

Let ‘x’ be the distance between Jasmin and the base of the lamppost when she is casting a 4-foot shadow. We can use similar triangles to set up a proportion:

15/x = 5/4

Solving for 'x', we get:

X = 15/3

X = 5 feet

This means that Jasmin is standing 5 feet away from the base of the lamppost when she is casting a 4-foot shadow.

Now, let’s find the distance between Jasmin and the base of the lamppost when she walks 1 foot farther away. This will be ‘5+1=6’ feet.

Again, we can use similar triangles to set up a proportion:

15/6 = y/4+z

Where 'y' is the length of Jasmin’s shadow when she is 6 feet away from the lamppost, and 'z' is the additional length of her shadow.

Simplifying this proportion, we get:

Y = 5/2 + 5z/6

We want to find ‘z’, the additional length of Jasmin’s shadow. We can do this by using the fact that when Jasmin is 6 feet away from the lamppost, her shadow is 4+z feet long. Setting up an equation using this information, we get:

4+z=y

Substituting the expression for ‘y’ from the proportion we set up earlier, we get:

4+z = 5/2 + 5z/6

Solving for 'z', we get:

Z = 3/2

Therefore, Jasmin’s shadow will lengthen by 3/2 feet when she walks 1 foot farther away from the lamppost.

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Three strategies that implement to encourage the use of BEVs are incentives, Infrastructure and Regulations. The cost of gasoline per mile for an ICE vehicle is $0.016 per mile.

Incentives: The federal government could offer financial incentives such as tax credits, rebates, or grants to consumers who purchase BEVs. This would make BEVs more affordable and help to offset the higher upfront cost of these vehicles.

Infrastructure development: The federal government could invest in the development of charging infrastructure for BEVs, such as public charging stations. This would help to alleviate range anxiety and make BEVs more convenient and practical for consumers.

Regulations: The federal government could implement regulations that incentivize or require automakers to produce more BEVs. This could include emissions standards that are more favorable to BEVs, or mandates for automakers to produce a certain percentage of their vehicles as electric.

To calculate the cost of gasoline per mile for an ICE vehicle with fuel efficiency of 235 miles per gallon and gasoline cost of $3.75 per gallon, we divide the cost of gasoline by the fuel efficiency:

Cost per mile = $3.75 / 235 miles per gallon

Cost per mile = $0.016 per mile

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Mobile ladder stands with a top step over 10 feet high and 20 inches or more in depth must be equipped with a safety cage or body belt and lanyard to provide protection against a fall.

The cage should be at least 30 inches tall and should be fully enclosed on all four sides. Additionally, the top step should be enclosed and provided with a grab bar. The ladder must be securely supported and stabilized. Non-skid materials should be applied to the steps and platform. Finally, the ladder must meet safety requirements outlined in the Occupational Safety and Health Administration's (OSHA) regulations.

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Answer:B

Step-by-step explanation: x=3;x=6

The probability that the second crayon drawn is blue and the first crayon drawn is blue is 1/28.

To solve this problem, we can use the conditional probability formula:

P(A and B) = P(B|A) * P(A)

where:

P(A and B) is the probability that both events A and B occur

P(B|A) is the probability of event B given that event A has already occurred

P(A) is the probability of event A occurring

In this case, we want to find the probability of selecting a blue crayon on the second draw given that the first crayon selected was blue. So we have:

P(the second crayon is blue and the first crayon is blue) = P(blue on the second draw | blue on the first draw) * P(blue on the first draw)

To find each of these probabilities, we can start by calculating the total number of possible outcomes:

Total number of outcomes = 8 crayons in the box

Next, we need to find the probability of selecting a blue crayon on the first draw:

P(blue on the first draw) = 2/8 = 1/4

After the first blue crayon has been set aside, there are only 7 crayons left in the box, so the probability of selecting a blue crayon on the second draw given that the first crayon was blue is:

P(blue on the second draw | blue on the first draw) = 1/7

Putting it all together:

P(the second crayon is blue and the first crayon is blue) = P(blue on the second draw | blue on the first draw) * P(blue on the first draw)

= (1/7) * (1/4)

= 1/28

Therefore, the probability that the second crayon drawn is blue and the first crayon drawn is blue is 1/28.

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Answer:

There are 2 dimes in the purse that contains $2.20

What is an equation?

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Let quarters be = x

The dimes be = 1/4 * x

25x+10x/4 = 220

(100x + 10x) /4 = 220

110x/4 = 220

110x = 220*4

110x = 880

x = 880/110

x = 8

The dimes be = 1/4 * x

The dimes be = 1/4 * 8

The dimes be = 2

Step-by-step explanation:

Pls ad brainliest!!!

The expression that is equivalent to the following complex fraction is this: B. -2y + 5x/3x -2y.

An equivalent expression is one that produces the same result as the given one when simplified. To get the equivalent expression, we simply need to simplify the expression above and the one underneath.

After finding the lowest common multiples of the figures underneath and the ones above, the next thing to do will be to multiply by the numerators.

-2/x + 5/y = -2y + 5x

Also:

3/y - 2/x = 3x - 2y

So, option B is an equivalent expression of the complex fraction.

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There are 6,354,000 choices for the password.

To generate a password, you need to have 4 letters followed by 2 even digits between 0 and 9, inclusive.

If the characters and digits cannot be used more than once,

Solution: We have to find the number of choices of the password with given conditions.

To find the number of choices, let us follow the following steps:

Step 1: Choose the first letter in 26 ways

Step 2: Choose the second letter in 25 ways (excluding the letter that we have already chosen)

Step 3: Choose the third letter in 24 ways (excluding the 2 letters that we have already chosen)

Step 4: Choose the fourth letter in 23 ways (excluding the 3 letters that we have already chosen)

Step 5: Choose the first even digit in 5 ways (from 0, 2, 4, 6, and 8)

Step 6: Choose the second even digit in 4 ways (excluding the even digit that we have already chosen)

Therefore, the total number of choices for the password with the given conditions is given by:

Total number of choices = 26 × 25 × 24 × 23 × 5 × 4= 6,354,000.

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This shows that TB did not have a game-long advantage but rather needed to recover from a deficit to triumph.

A subfield of mathematics known as probability studies random events and the possibility that they will occur. It entails calculating the probability of an event happening and expressing it as a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty. The possibility of a coin landing heads-up, the chances of winning a game, or the likelihood of a disease spreading throughout a population are just a few examples of real-world occurrences that may be studied and understood using probability.

given

It is most likely that option 1 happened, according to the victory probability chart in the illustration provided: TB came out as the favourite, trailed for the majority of the game, then made a late comeback.

The graph demonstrates that the victory probability for TB initially increased before sharply declining as NO seized the lead and kept it for the most of the game.

The dramatic increase in the win probability for TB towards the end of the chart, however, shows that TB came back and won in the final few minutes of the game.

This shows that TB did not have a game-long advantage but rather needed to recover from a deficit to triumph.

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Answer:10,400

Step-by-step explanation:

The circumference of a circle with a radius of 15 inches is 30π inches, or 94.25 inches

The circumference of a circle can be calculated using the formula:

C = 2πr

where C is the circumference, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.

In this case, the radius is 15 inches. Substituting this value into the formula, we get:

C = 2π(15) = 30π

So the circumference of a circle with a radius of 15 inches is 30π inches, or approximately 94.2478 inches.

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A discrete data random variable is a random variable that can only take on a finite or countable number of values.

Out of the options given, the number of cars finished in a factory each day is a discrete data random variable. This is because the number of cars finished can only take on a finite number of values, such as 0, 1, 2, 3, and so on. It cannot take on any value between these integers, and there are only a finite number of possible values.

In contrast, a person's height and weight are continuous data random variables, as they can take on any value within a certain range (for example, a person's height can take on any value between 4 feet and 7 feet).

Similarly, the volume of water in a swimming pool can take on any value within a certain range, and is also a continuous data random variable.

Therefore, the only discrete data random variable out of the options given is the number of cars finished in a factory each day.

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The period of the Markov chain is 2.

The period of this Markov chain is determined by the number of times you have to go through the probability transition matrix before you return to the same state. The period for this Markov chain is 2, as you can see from the probability transition matrix below:

 P(i,j)   State 0   State 1    State 0   0.5   0.5    State 1   0.3   0.7  


Starting from State 0, the probability of transitioning to State 0 is 0.5, and the probability of transitioning to State 1 is 0.5. If we start from State 1, the probability of transitioning back to State 0 is 0.3, and the probability of transitioning back to State 1 is 0.7.

Therefore, it takes two steps for the chain to return to its original state and the period of this Markov chain is 2.

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Answer:

[tex]y=3cos(3\pi x)+4[/tex]

Step-by-step explanation:

[tex]f(x)=cos(x)\\[/tex]

[tex]A(f(Bx+C)+D)[/tex]

The outside constants, A & D stretch and shift vertically. The inside constants, B & C stretch and shift horizontally. B & C work oppositely, basically multiplying by B stretches by a factor of 1/B and similarly adding C shifts f(x) horizontally to the left.

[tex]f(x)=cos(x) \text{ The function which we are transforming}\\\text{It currently has a amplitude of 1, time period of $2\pi$ and mid line at $y=0$}[/tex]

[tex]A=3 \text{ As we want to stretch it by 3 units vertically.}\\\text {To find B:}\\T' = T*(1/B)\\\text{Where $T'$ is new time period and T is existing time period}\\2/3=2\pi*(1/B)\\B=3\pi\\\text{C is not needed}\\D=4 \text{ To shift function by 4 units up}[/tex]

I hope this helps

The present value that must be invested to get $2500 after 6 years at a simple interest rate of 11.0% is $1509.64.

In this case, we know the final amount that we want to have after 6 years, which is $2500. We also know the interest rate, which is 11.0%. What we need to find is the principal amount, which is the present value that we must invest now to achieve the desired future value.

Using the formula for simple interest, we can rearrange it to solve for the principal:

Principal = Simple Interest / (Rate x Time)

We know that the simple interest is the difference between the final amount and the principal amount. Therefore, we can substitute the values into the formula:

$2500 - Principal = (Principal x 0.11 x 6)

Simplifying the equation, we get:

$2500 = Principal + (0.66 x Principal)

$2500 = 1.66 x Principal

Dividing both sides by 1.66, we get:

Principal = $1509.64

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The length of the reflected line segment is approximately 11.66 units.

The endpoints of the line segment mentioned in the question are (0,5) and (6,5). After the line segment is reflected across the x-axis, the endpoints of the reflected line segment are (0, -5) and (6, -5).To find the length of the reflected line segment, we will use the distance formula.

Using the distance formula:d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (5 - 5)²]d = √[36 + 0]d = √36d = 6 units. So the length of the original line segment is 6 units.Now, let's find the length of the reflected line segment.Using the distance formula :d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (-5 - 5)²]d = √[36 + 100]d = √136d = 11.66 (approx) units. So the length of the reflected line segment is approximately 11.66 units.

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For the following data, the slope of the linear relationship is option D.

A line's direction and steepness are measured by the line's slope. by solving the slope of the line we can determine whether the lines are perpendicular, parallel, or none at all.

from the given data the first two coordinate points are:

(2,5) and (1,2)

The representation of the slope is given by the variable m.

The slope formula is :

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

by substituting the values in the equation

m = (2 .0- 5.0) / (1.0 - 2.0)

m = -3 / -1

m = 3

Therefore, the slope of the linear relationship is m = 3.

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There are 243 ways to distribute five unlabeled balls into three labeled boxes.

Since the balls are unlabeled, we only need to consider the number of balls in each box, rather than which specific ball goes where.

We can use a combination approach to solve this problem. Let's think about distributing the balls one at a time. For the first ball, there are three boxes to choose from. For the second ball, there are also three boxes to choose from. We can continue this process until all five balls have been distributed.

So, for each ball, there are three choices of which box to put it in. Therefore, the total number of ways to distribute the five balls into the three labeled boxes is

3 x 3 x 3 x 3 x 3 = 3^5 = 243

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Answer:

The formula for the area of a circle is A = πr^2, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14159.

If the radius of the circle is 11 inches, then we can substitute this value into the formula:

A = πr^2

A = π(11)^2

A = π(121)

So the area of the circle is 121π square inches, which is approximately 380.1327 square inches when rounded to four decimal places.

In linear equation, 0.76  will purchase one or more costumes as a decimal to the nearest hundredth.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                 The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

from the given information

  the probability that the next person will purchase one or more costumes

                   = 288 + 13/288 + 13 + 95

                   ≈ 0.76

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As a result, the carer will deliver 0.38 mL of methylprednisolone.

Milliliter is what the ml stands for. When pronouncing the characters aloud, the word ml is usually pronounced millilitre. It's good to keep this in mind. Simply imagine to yourself, "l = liquid," whenever you see the small "l".

To determine how many milliliters of methylprednisolone injection the nurse will administer, we need to know the concentration of the medication. Let's assume the concentration is 40 mg/mL.

We can use the following formula to calculate the amount to administer:

Amount (mL) = Dose (mg) / Concentration (mg/mL)

Plugging in the values from the order, we get:

Amount (mL) = 15 mg / 40 mg/mL

Amount (mL) = 0.375 mL

Rounding the answer to the nearest hundredth gives us:

Amount (mL) = 0.38 mL

Therefore, the nurse will administer 0.38 mL of methylprednisolone injection.

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The given angles and measures is given below:

In mathematics and geometry, an angle is a measure of the space between two intersecting lines, rays, or line segments, usually expressed in degrees, radians, or grads. It is the measure of the opening between two lines that intersect at a common point, called the vertex of the angle.

5) tan x = 153 / 41

x = tan^-1 ( 153 / 41 )

75 degrees

6) tan y = 25/25

y = tan^-1 ( 25/25 )

45 degrees

7) sin z = 10/28

z= sin^-1 ( 10/28 )

21 degrees

8) cos a = 47/50

a = cos^-1( 47/50)

20 degrees

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The null and alternative hypotheses for the manufacturer of banana chips can be defined as:

H0: µ = 409 (Null Hypothesis)

Ha: µ < 409 (Alternative Hypothesis)

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 409.0 409.0 gram setting. It is believed that the machine is underfilling the bags. A 38 bag sample had a mean of 406.0 grams. A level of significance of 0.05 will be used. State the hypotheses. Assume the variance is known to be 400.00. Enter the hypotheses.

The null and alternative hypotheses for the manufacturer of banana chips can be defined as:

H0: µ = 409 (Null Hypothesis)

Ha: µ < 409 (Alternative Hypothesis)

Where µ is the population mean of the weight of banana chips in a bag. The level of significance is 0.05. As the population variance is known, the z-test can be performed. To test the above hypotheses, we can calculate the test statistics as shown below :

z = (X - µ) / [σ / √(n)]

Where, X = Sample mean = 406, Population mean = 409, Population standard deviation = 20 (Square root of variance = √400) , Sample size = 38 substituting the given values, we get

= (406 - 409) / [20 / √(38)]z = -1.581

According to the z-distribution table, the probability of getting a value less than or equal to -1.581 is 0.0562. It means the p-value is 0.0562. Since the p-value (0.0562) > α (0.05), we fail to reject the null hypothesis H0.

Therefore, there is not enough statistical evidence to conclude that the bag filling machine is underfilling the bags at the 409-gram setting. Thus, the given statement is false.

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The probability that you catch two random fish from the same species is 0.375, or 37.5%.

This is because the total number of fish in the lake is 2,000, so if you catch two random fish there is a 1 in 2,000 chance of catching two of the same species.

To find the probability, take the number of fish of one species (800 walleye, 800 bass, 400 perch) divided by 2,000.

In this case it would be 800 divided by 2,000 which is 0.4. Multiply 0.4 by itself, which is 0.16, then multiply 0.16 by 100 which gives you 0.375, or 37.5%.

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Answer:

The z-Table gives the area under the standard normal curve to the left of z. What does the t-Table give? The t-Table gives the area under the t-curve with n degrees of freedom to the left of it

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The conclusion of the test is the calculated z-test value of -1.5 falls within the acceptable limits of +/- 2 sigma.

To interpret the results of the run test, we need to compare the calculated z-test value with the acceptable limits for the test. The acceptable limits for the run test are +/- 2 sigma, which means that the process is considered acceptable if the z-test value falls within this range.

Since the z-value of -1.5 falls within the acceptable limits of +/- 2 sigma, we can conclude that the process is acceptable according to the run test. This means that there is no evidence of non-randomness or nonconformity in the process, and the process is functioning as expected.

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