solve y=x^2+2 for x.

Final answer:

The ratios for the basketball positions in simplest form are guards as 2:5, forwards as 2:5, and the center as 1:5.

Explanation:

The question asks to write ratios for the positions on a basketball team and then to express those ratios in simplest form. There are 5 position players on a starting basketball team, consisting of 2 guards, 2 forwards, and 1 center. To express the relationships between each position, we can write the ratios of guards to the total number of players, forwards to the total number of players, and the center to the total number of players.

The ratio of guards to the total number of players is 2 guards to 5 total players, which simplifies to 2:5.

The ratio of forwards to the total number of players is 2 forwards to 5 total players, simplifying to 2:5.

Lastly, the ratio of the center to the total number of players is 1 center to 5 total players, simplified as 1:5.

The annual growth rate is 41.4% and the monthly growth rate is 3.45%. The continuous growth rate per year is 2.77%.

To determine the annual growth rate, we need to find the growth factor by taking the square root of the doubling factor. Since the population is predicted to double every 25 years, the annual growth rate would be the square root of 2, which is approximately 1.414. To express it as a percentage, we can subtract 1 from the growth factor and multiply by 100, resulting in an annual growth rate of 41.4%.

The monthly growth rate can be calculated by dividing the annual growth rate by 12. In this case, the monthly growth rate would be approximately 3.45%.

To determine the continuous growth rate per year, we use the formula: r = ln(2)/t, where r is the continuous growth rate and t is the doubling time in years. In this case, the continuous growth rate would be ln(2)/25, which is approximately 0.0277. Multiplying this by 100, we get a continuous growth rate per year of 2.77%.

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a coin has a 1/2 probability of landing on heads

 so it should land on heads 1/2 of the time

1/2 of 200 = 100

Final answer:

With a fair coin, theoretical probability suggests that Jo should expect to land on heads roughly 100 times out of 200 flips. Actual results may vary slightly due to random chance, but should approximate 50 percent heads over a large number of trials.

Explanation:

If Jo is flipping a fair coin, on average, we would expect the coin to land on heads 100 times out of 200 flips. This expectation is based on the theoretical probability of getting heads, which is 0.5 or 50% for a fair coin. Therefore, if Jo flips the coin 200 times, the expected number of heads is calculated by multiplying the total number of flips by the probability of getting heads (0.5), which is 200 * 0.5 = 100.

However, it's important to note that while the theoretical probability suggests that Jo should get heads approximately 100 times, the actual result might be slightly more or slightly less due to random chance. The larger the number of flips, the closer the actual results are likely to get to the expected 50 percent heads, as demonstrated by the law of large numbers. But for any finite number of flips, there is always potential for some variation from the expected value.

Final answer:

The correct expression to calculate the remaining budget for food after spending on groceries and meals out is 550 - (67.19 + 55x), which is option A.

Explanation:

The question asks us to determine which expression correctly represents the amount of money left in the budget for food after the family has spent money on groceries and consumed their meals. The original budget for food is $550, and the family spent $67.19 on drinks and snacks. Each meal they plan to eat out is budgeted at $55. Let's denote the number of meals the family will eat out as 'x'.

To calculate the remaining budget after these expenses, we subtract the cost of groceries and the total cost of eating out (which is $55 times the number of meals 'x'), from the original budget for food. The correct mathematical expression for the remaining budget is:

550 - (67.19 + 55x)

This expression is represented by option A. This correctly factors in the initial expenditure on groceries of $67.19 and then subtracts $55 for each meal 'x' from the remaining budget.

Answer:

Step-by-step explanation:

Alright, lets get started.

The function that models the height of the ball is given by :

[tex]f(x)=-10x^2+20x+8[/tex]

When we plug x as 1.5 , we could get the height f(1.5) as :

[tex]f(1.5)=-10(1.5)^2 +20*1.5 +8[/tex]

[tex]f(1.5)=-22.5+30+8[/tex]

[tex]f(1.5)=15.5[/tex]

So the height of the ball after 1.5 second is 15.5 meters.   : Answer

Hope it will help :)

Answer:

It is c on edge just took the test

Step-by-step explanation:

6^2 + 8^2 = x^2

36 + 64 = 100

sqrt(100) = 10

 x = 10

see attached picture:

the vertical change is the Y calculation

The value of f(x) = x²-3x at x = -1.8 is -2.16.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

We have the quadratic function:

f(x) = x²-3x

So, to find the value at x = -1.8:

Substitute the value to the function.

f(-1.8) = (-1.8)²-3(-1.8)

f(-1.8) = 3.24 - 5.4

f(-1.8) = -2.16

Therefore, the value is -2.16.

To learn more about the quadratic function;

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Answer:

The cashier should refund back to the customer $5,04

Step-by-step explanation:

The cashier has to refund the amount the customer paid, which was the price plus the proportional tax.

Refund=price+tax

Price=$4.80

Tax=$4.80 * 0,05= $0,24

Refund=$4.80 +$0,24=$5,04

Answer:

Option: D is correct.

9/2

Step-by-step explanation:

We have to find the multiplicative rate of change of the exponential function shown on the graph.

We know that a general exponential function is given as:

[tex]y=ab^x[/tex]

where b is the multiplicative rate of change.

Now when x=0 we have y=1.

i.e. 1=a

Hence, a=1

and y=b^x

Also,

the graph passes through (1,9/2)

Now when x=1 we have y=9/2

i.e.

9/2=b

Hence, the multiplicative rate of change is:

9/2

The correct answer is A) 2/9. The multiplicative rate of change of the exponential function shown on the graph is A) 2/9.

To determine the multiplicative rate of change of an exponential function from its graph, we need to identify two points on the graph that are one unit apart horizontally (i.e., one unit apart in the x-direction). The multiplicative rate of change is the ratio of the function values (y-values) of these two points.

Let's assume we have two points, (x, y) and (x+1, y'), where y and y' are the corresponding y-values of the exponential function at these x-values. The multiplicative rate of change, r, is given by:

[tex]\[ r = \frac{y'}{y} \][/tex]

From the graph, we can identify two such points. For example, if the function passes through the y-axis at (0, 1) and then at (1, 2/9), we can calculate the multiplicative rate of change as follows:

[tex]\[ r = \frac{2/9}{1} = \frac{2}{9} \][/tex]

This is the multiplicative rate of change of the exponential function. It indicates that for every unit increase in x, the y-value is multiplied by 2/9.

Therefore, the multiplicative rate of change of the exponential function shown on the graph is A) 2/9.

The correct solutions to the given equation are x = 1 and x = 7.

The solutions to the equation x² - 8x + 7 = 0 are x = 1 and x = 7.

To find these solutions, we can factor the quadratic equation by finding two numbers that multiply to 7 (the constant term) and add up to -8 (the coefficient of the x term).

Therefore, the correct solutions to the given equation are x = 1 and x = 7.

Answer: -2,-1

Step-by-step explanation

If a horizontal line passes through the point (5;-1) then the equation if this line: y=-1

Each point (x;-1) is also on this line.

The lower bound estimate and upper bound estimate are found by rounding 764 to 700 and 241 to 200, then subtracting to get 500. However, the mistake in the options seems that both the lower and upper bound estimates are 500. Based on the given options, the right answer should be option C with lower bound 500 and upper bound 600, albeit the upper bound estimate is not correctly represented.

The lower bound and upper bound estimate of a calculation are found by rounding each number involved to the greatest place value then performing the calculation. In the case of the subtraction 764 - 241, the lower bound estimate will be calculated by underestimating both figures, and the upper bound will be calculated by overestimating.

Therefore, both the lower bound estimate and the upper bound estimate are 500 and the correct option is C. lower bound 500 upper bound 600

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180 = 93 +3x +18

180 =111 +3x

3x = 180-111

3x = 69

x = 69/3

x = 23