A retired woman has $60,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%. If we let x be the amount the woman invests in the 15% bond, how much in dollars will she be able to invest in her CD?

The probability of getting the king of spades as the top card and the bottom card of a shuffled deck depends on whether the cards are picked with or without replacement.

The probability of getting the king of spades as the top card and the bottom card of a shuffled deck depends on whether the cards are picked with or without replacement. If the cards are picked without replacement, the probability will be different than if they are picked with replacement.

If the cards are picked without replacement, the probability of getting the king of spades as the top card is 1/52. This is because there is only one king of spades in a deck of 52 cards. After the king of spades is picked as the top card, there are 51 cards left in the deck. The probability of getting the king of spades as the bottom card is also 1/51 because there is only one king of spades left in the deck.

If the cards are picked with replacement, the probability of getting the king of spades as the top card is still 1/52, but the probability of getting the king of spades as the bottom card is also 1/52. This is because each card is put back into the deck and reshuffled before the next card is picked, so the probabilities for each card remain the same.

If your equation is ...

[tex]t-122=3t^2-3[/tex]

then it has no real solutions, and certainly no integer solutions.

_____

The attached graph show the left side is never equal to the right side of this equation for any real values of t.

the correct answer is actually 3

i just got done with the quiz and the answer was 3

Answer:

9.65×10¹⁴

Step-by-step explanation:

The 9 of 9.65 has been moved 14 places to the left to get to its position in 965,000,000,000,000. That is, its value has been multiplied by 10¹⁴.

_____

If you were to write 965,000,000,000,000 in expanded form, you would write it as ...

... 9×10¹⁴ +6×10¹³ +5×10¹² +0×10¹¹ +... +0×10⁰ = 9.65×10¹⁴

The first term of this sum is a clue as to how the number is written in scientific notation,

the answer is 9.65×10¹⁴

To find the number of notepads bought, we can set up an equation by subtracting the cost of the magazine from the total cost and equating it to the cost of the notepads. By solving the equation, we find that you bought 4 notepads.

To solve this problem, we can start by setting up an equation. Let's assume the number of notepads bought is 'x'. We know the magazine cost $6, so the cost of the notepads is $18 - $6 = $12. Since each notepad costs $3, the equation becomes 3x = 12. To find the value of 'x', we can divide both sides of the equation by 3. So, x = 12/3 = 4.

Therefore, you bought 4 notepads.

To convert the number 1,340,000 into scientific notation, move the decimal point 6 places to the left to get 1.34, then place this as an exponent on 10 to get 1.34 x 10^6.

In scientific notation, large numbers are simplified by moving the decimal point to the left until we have a number between 1 and 10. We then use an exponent on 10 to indicate how many places the decimal point has been moved. If you take a look at the number 1,340,000, the decimal point is technically at the end of the number right now. In order to express this number in scientific notation, we move the decimal point 6 places to the left, which gives us 1.34. The number of places we moved the decimal point to the left becomes the exponent on 10. Therefore, 1,340,000 in scientific notation is 1.34 x 10^6.

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Answer: 81 children and 92 adults

Step-by-step explanation:

To solve the exercise, check the data we have from the question:

Total people: 173

Adult tickets price: $5

Children tickets price: $3

Total revenue: $703

We need to know how many of each kind of ticket were sold. To do so, we can show the data as two equations:

Equation 1:

[tex]TotalRevenue = Adults*5 + Children*3[/tex]

[tex]703=5a+3c[/tex]

Equation 2:

[tex]a+c=173[/tex]

Where a represents adults who attended the event and c represents children who attended the event. We can replace one of the unknown quantities following:

[tex]a=173-c[/tex]

[tex]703=5(173-c)+3c[/tex]

Solving:

[tex]703=865-5c+3c[/tex]

[tex]5c-3c=865-703[/tex]

[tex]2c=162[/tex]

[tex]c=81[/tex]

Then, we replace c on equation 2:

[tex]a=173-81[/tex]

[tex]a=92[/tex]

Answer:

2W²-W-28 = 0

Step-by-step explanation:

Answer:

The required function -  [tex]g(x)=\frac{1}{2}(3)^{-x}[/tex]

Step-by-step explanation:

Given : Function represents g(x), a reflection of [tex]f(x) =\frac{1}{2}(3)^x[/tex] across the y-axis

To find : Which function represents the g(x)?

Solution :

The function [tex]f(x) =\frac{1}{2}(3)^x[/tex]

The function f(x) reflected across y-axis to form g(x)

The reflection of the point (x,y) across  the y-axis is the point (-x,y).

f(x,y)→f(-x,y) , the graph of f(x) is reflected across y-axis.

Let [tex]y=\frac{1}{2}(3)^x[/tex]

After reflection across y-axis is

[tex]g(x)=\frac{1}{2}(3)^{-x}[/tex]

The required function.

Refer the attached graph below.

We want to get a quadratic equation by knowing its tangent line at a point. Remember that the tangent line is given by the derivative of the equation.

We will find that the parabola is:

y = 3*x^2  - 4*x

We start with the tangent line:

y₂ = 8*x - 12

The slope of this tangent line is equal to the derivative of our parabola evaluated in x = 2.

Our parabola is y = a*x^2 + b*x

Derivating we get:

y' = 2*a*x + b

Then we have:

2*a*2 + b = 8

And we also know that our parabola passes through the point (2, 4), then we must have:

4 = a*2^2 + b*2

Then we have a system of equations:

2*a*2 + b = 8

4 = a*2^2 + b*2

First we can simplify the equations:

4*a + b = 8

4 = 4*a + 2*b

We can isolate 4*a in the first equation to get:

4*a = 8 - b

Now we can replace it in the second equation:

4 = (8 - b) +  2*b

4 = 8 + b

4 - 8 = b

-4 = b

Now that we know the value of b, we can use

4*a  = 8 - b

4*a = 8 + 4 = 12

a = 12/4 = 3

Then the equation of the parabola is:

y = 3*x^2  - 4*x

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Answer:

standard deviation=4.47

Step-by-step explanation:

We have to find the standard deviation of the data set:

13   17    9  21

Now we calculate the mean of the data .

We know that mean is the average of the data values and is calculated as:

[tex]Mean=\dfrac{13+17+9+21}{4}\\ \\Mean=\dfrac{60}{4}\\\\Mean=15[/tex]

Now we find the difference of each data point from the mean as:

Deviation:

13-15=-2

17-15=2

9-15=-6

21-15=6

Now we have to square the above deviations we obtain:

4   4   36   36

now we calculate the mean of the above sets:

[tex]variance=\dfrac{4+4+36+36}{4}\\ \\Variance=\dfrac{80}{4}\\\\Variance=20[/tex]

now standard deviation is the positive square root of variance

so, standard deviation=√(20)=4.47

Final answer:

To find the standard deviation for Omar's work hours, we first calculate the mean of the data, then compute the squared differences from the mean, sum these, divide by the sample size minus one, and take the square root of this result, which is approximately 5.16 hours.

Explanation:

To calculate the standard deviation for Omar's recorded work hours: 13, 17, 9, 21, we follow these steps:

First find the mean (average) of the sample. Mean = (13 + 17 + 9 + 21) / 4 = 60 / 4 = 15 hours.

Next, subtract the mean from each data point and square the result:[tex](13-15)^2[/tex] = 4,[tex](17-15)^2[/tex] = 4, [tex](9-15)^2[/tex]= 36,[tex](21-15)^2[/tex] = 36.

Now, find the sum of these squared differences: 4 + 4 + 36 + 36 = 80.

Since this is a sample (not the full population), we divide by the sample size minus 1, which is 3: 80 / 3 ≈ 26.67.

Finally, take the square root of this quotient to find the standard deviation: √26.67 ≈ 5.16 hours.

Therefore, the standard deviation for the data is roughly 5.16 hours.