use the quadratic formula to solve the equation 9x^2 - 2=0

Answer:

  18. compound interest

  19. simple interest

  20. simple interest

Step-by-step explanation:

For these problems, the initial balance is irrelevant. All that matters is the multiplier of that balance. For simple interest at rate r for t years, the multiplier is ...

  simple interest multiplier = (1 +rt)

For interest compounded annually, the multiplier of the initial balance is ...

  compound interest multiplier = (1 +r)^t

A spreadsheet can do the computations for you.

___

As an example of the computations involved, consider problem 19:

  simple interest multiplier = 1 + 0.13·6 = 1.78

  compound interest multiplier = 1.10^6 = 1.771561

The latter is less than the former, so the simple interest account will have the (slightly) greater balance at the end of 6 years.

Answer:

3 * -1 x 3   +  5 * 3 - 6 = 0

Step-by-step explanation:

Replace (a)s and (b)s with the given numbers

so (a)s becoming -1 and (b)s becoming 3.

this leads up to the given expression:

3 * -1 x 3   +  5 * 3 - 6

3 times -1 = -3 multiplied by that 3 is -9

since a negative multiplied by a positive is a negative.

With that you have -9 +  5  x 3 - 6

take 5 and 3, multiply them to get 15 and subtract 6.

this ends up with '9'

Lastly ending up with -9+9 = 0

The value of 3ab + 5b - 6 = 0.

Let a = -1 and b = 3.

If 3ab + 5b - 6 then

substituting the values of a and b in the given equation, we get

[tex]3 *( -1) * (3) + 5 * (3) - 6[/tex]

3a = [tex]3 * -1 = -3[/tex]

3ab = [tex]-3*3=-9[/tex]

Then, [tex]3*(-1)*3 =-9[/tex] and

5b = [tex]5*3=15[/tex]

Therefore, we get 3ab + 5b - 6 = 0.

since a negative multiplied by a positive is a negative.

With that you have [tex]-9 + 5 * 3 - 6[/tex]

take 5 and 3, multiply them to get 15, and subtract 6.

this ends up with '9'

Lastly ending up with -9 + 9 = 0

Therefore, the value of 3ab + 5b - 6 = 0.

To learn more about finding the values

https://brainly.com/question/13207923

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Answer:

  yellow area ≈ 48.3 cm²

Step-by-step explanation:

The area of the yellow region is the difference between the area of a square with side length 15 cm and the area of a quarter circle with radius 15 cm. It is helpful to know the formulas for area for a square and a circle.

  Area of the square = s² = (15 cm)² = 225 cm²

The area of the full circle is ...

  Area of circle = πr² = π(15 cm)² = 225π cm²

Then the area of 1/4 of that circle will be ...

  Area of quarter circle = (225π cm²)/4 = 56.25π cm²

--

The difference of these areas is the yellow area:

  yellow area = 225 cm² - 56.25π cm² ≈ 48.2854 cm²

  yellow area ≈ 48.3 cm²

Answer:

[tex]\dfrac{15}{57}[/tex] or 0.2632 or 26.32%

Step-by-step explanation:

Choosing a white or a yellow marble from the bag are two mutually exclusive events. So we can say that:

[tex]P(W or Y) = P(W) + P(Y)[/tex]

To get the probability of each we divide the favorable outcomes by the all possible outcomes.

Probability of choosing white:

[tex]P(W) = \dfrac{1}{57}[/tex]

Probability of choosing yellow:

[tex]P(W)=\dfrac{14}{57}[/tex]

[tex]P(WorY)=P(W)+P(Y)[/tex]

[tex]P(WorY)=\dfrac{1}{57}+\dfrac{14}{57}[/tex]

[tex]P(WorY)=\dfrac{15}{57}[/tex]

If you need it in decimal, just divide and you will get 0.2632.

If you need it in percent, just multiply the decimal by 100% and you will get 26.32%.

Answer:

15/57

Step-by-step explanation:

Given  

Total sample space=57 (as one marble was also added to the bag)

Now,

Let P(A)  be the probability of drawing a white marble

Let P(B) be the probability of drawing a yellow marble

So,

P(A)=1/57

P(B)=14/57

As we have to calculate the probability of white or yellow marble

P(A or B)=P(A)+P(B)

=1/57+14/57

=(1+14)/57

=15/57

So the probability of drawing a white or yellow marble is 15/57 ..

Answer:

Option 3.

Step-by-step explanation:

The domain of a function is the complete set of possible values of the independent variable.

The argument of a square root can take negative values, then:

So x+3 must be greater than 0. So x+3> 0 -> x> -3.

Then, the domain of the function is: [-3, +inf)  

The range of a function is the complete set of all possible resulting values of the dependent variable after we have substituted the domain.

So in this case, we know that the square root always is going to throw a positive value, but given that the square rooth is multiplied by a minus, the result is always going to be negative.

The least value the square root can take is 0, so in that case, the maximum value the function can take is y = -2.

So the range is (-inf, -2]

So, the correct option is option 3

Answer: $10

Step-by-step explanation:

Let's analize the information given: We know that  she had $94 to spend on 8 books and after buying these books she had $14. So, we need to calculate the amount of money she spent. Subtract $94 and $14:

[tex]Total\ spent=\$94-\$14\\Total\ spent=\$80[/tex]

Then, to calculate the cost of each book, we need to divide the "Total spent" by 8:

[tex]cost\ of\ each\ book=\frac{Total\ spent}{8}\\\\cost\ of\ each\ book=\frac{\$80}{8}\\\\cost\ of\ each\ book=\$10[/tex]

Answer:

15.50+n=325.00

Step-by-step explanation:

15.50+what she had in the bank already = what she has now

Answer:

The answer is $15.50 + n = $325.00.

Step-by-step explanation:

Fifteen dollars plus "n" (her account balance before the deposit) equals $325.00. Hope this helps! :D

Answer:

17

Step-by-step explanation:

The point plotted is 4.1. In order to find what it is the square root of, you need to square it:

4.1^2 = 16.81 ≈ 17

ANSWER

[tex]x = 4.1[/tex]

EXPLANATION

The line segment connecting the center and the chord bisects the chord.

Half of the length of this chord forms one of the shorter legs of the right triangle.

[tex] = \frac{15.6}{2} = 7.8[/tex]

We use the Pythagoras Theorem to obtain;

[tex] {x}^{2} + {7.8}^{2} = {8.8}^{2} [/tex]

[tex] {x}^{2} = {8.8}^{2} - {7.8}^{2} [/tex]

[tex] {x}^{2} = 16.6[/tex]

[tex]x = \sqrt{16.6} [/tex]

[tex]x = 4.1[/tex]

Final answer:

To determine the total number of mini pizzas, multiply the number of people sharing the pizzas (Mark, his sister, and 4 friends, totaling 6) by the number of pizzas per person (5). Thus, there are 30 mini pizzas in total.

Explanation:

The student's question involves a basic arithmetic calculation related to multiplication. Mark, his sister, and his 4 friends add up to a total of 6 people (Mark + Mark's sister + 4 friends). Each of these 6 individuals will receive 5 mini pizzas each. To find the total number of mini pizzas, we need to multiply the number of people by the mini pizzas each person receives.

Therefore, the calculation is as follows:

Total number of mini pizzas = Number of people × Mini pizzas per person

Now, we execute the multiplication:

Total number of mini pizzas = 6 × 5 = 30 mini pizzas

So, the total number of mini pizzas in the box is 30.

Answer:

  See attached

Step-by-step explanation:

The graphs marked with a red X do not pass the vertical line test, so are not functions. (A vertical line must intersect the graph of a function in only one point.)

The curve at lower right is a function, but it isn't clear if it meets the requirement for "lines that represent functions", since it is not a straight line.

Answer:

  see below

Step-by-step explanation:

Each point moves to a location 3 times its current distance from the center of dilation. The dilated figure connects those moved vertices.

___

In the attached figure, the orange lines show how the points move to their new location (3 times the original distance). The blue lines connect the dots to make the dilated figure.

the answer is.... 39.988

Answer:

D. Cylinder

Step-by-step explanation:

Consider the rectangle that has to be rotated about the axis as shown in the picture. In attached diagrams this rectangle is black rectangle ABCD.

While rotating each point of the rectangle will describe the circle. The circles with the greatest radii will be circles made by the points from the side that is opposite to the side on the axis of rotation.

Formed figure appear to be cylinder.

Answer:

I believe Its A or C

Step-by-step explanation:

Final answer:

The statement is true, as adding the probabilities of walking with the beagle (20%) and with the golden retriever (70%) correctly calculates the probability of walking with any dog as 90%.

Explanation:

The question involves calculating the probability of an event occurring, specifically the event of a neighbor walking with any dog. To determine whether the statement "We could find the probability of walking with a dog by adding P(beagle) and P(golden retriever)" is true or false, let's examine the given percentages. According to the information, the neighbor walks 20% of the time with her beagle, 70% of the time with her golden retriever, and 30% of the time she walks alone.

Adding the probabilities of walking with the beagle (20%) and with the golden retriever (70%) gives us a total of 90%. This calculation suggests that the neighbor walks with a dog 90% of the time, which is a valid way to find the probability of walking with any dog. Hence, the statement is true. However, it is important to ensure that the events (walking with the beagle and walking with the golden retriever) are exclusive and do not overlap, which is implied in this scenario.

Answer:

Step-by-step explanation:

To solve these equations involving variables and exponents we need to follow these steps.

1) We need to find out the factor that is common in the equation.

2) After taking common, solve the equation. We can add or subtract only those values that have same bases.

1) [tex]8+6x^4[/tex]

here we can see, both numbers are divisible by 2, so taking 2 common

[tex]=2(8/2 + 6x^4/2)\\= 2(4 + 3x^4)[/tex]

It cannot be further simplified because both number donot have same bases.

3.[tex]4n^9 + 12 n[/tex]

We can take 4n common

[tex]=4n(4n^9/4n + 12 n/4n)\\=4n(n^8 + 3)[/tex]

5. -12a -3

Here -3 cam be taken common

= -3(-12a/-3 -3/-3)

= -3(4a +1)

7. [tex]12n^5 + 16n^3[/tex]

here the smallest power of n is n^3 so, we can take n^3 common and both coefficients are divisible by 4 so taking 4n^3 common

[tex]4n^3( 3n^2 + 4)[/tex]

9. [tex]5k^2 - 40k+10[/tex]

Here we cannot take k common, as k is not a multiple of 10. For taking common it should be divisible by each value in the equation. But each value s divisible by 5 so, taking 5 common

[tex]=5(k^2 - 8k + 2)[/tex]

11.[tex]-60 + 60n^2 +50n^3[/tex]

Here we cannot take n common, as n is not a multiple of -60. For taking common it should be divisible by each value in the equation. But each value s divisible by 10 so, taking 10 common

[tex]=10(-6 + 6n^2 +5n^3)[/tex]

13. [tex]-36n^3 -12n-28[/tex]

Here we cannot take n common, as n is not a multiple of 28. For taking common it should be divisible by each value in the equation. But each value s divisible by -4 so, taking -4 common

[tex]=-4(9n^3 + 3n +7)[/tex]

15. [tex]63n^3+81n+18[/tex]

Here we cannot take n common, as n is not a multiple of 18. For taking common it should be divisible by each value in the equation. But each value s divisible by 9 so, taking 9 common

[tex]=9(7n^3 + 9n + 2)[/tex]

17. [tex]-24a^2b^2 + 36ab-60a[/tex]

[tex]=6a(-4ab^2+6b-10)[/tex]

The correct decision regarding H0 is to Reject. The estimated p-value is less than 0.05.

To determine whether the mean number of interviews conducted by the agents is more than 53 per week, we can perform a one-sample t-test. The null hypothesis (H0) is that the mean number of interviews is less than or equal to 53 (I< 53), and the alternative hypothesis (Ha) is that the mean is greater than 53 [tex](I > 53)[/tex].

First, we calculate the sample mean [tex](\(\bar{x}\))[/tex] and the sample standard deviation (s) using the provided data:

Given data: 53, 57, 50, 55, 58, 54, 60, 52, 59, 62, 60, 60, 51, 59, 56

Sample mean [tex](\(\bar{x}\))[/tex]:

[tex]\[ \bar{x} = \frac{\sum x_i}{n} = \frac{53 + 57 + 50 + 55 + 58 + 54 + 60 + 52 + 59 + 62 + 60 + 60 + 51 + 59 + 56}{15} \][/tex]

[tex]\[ \bar{x} = \frac{836}{15} \approx 55.733 \][/tex]

Sample standard deviation (s):

[tex]\[ s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} \][/tex]

[tex]\[ s = \sqrt{\frac{(53-55.733)^2 + (57-55.733)^2 + \ldots + (56-55.733)^2}{14}} \][/tex]

[tex]\[ s \approx \sqrt{\frac{678.733}{14}} \approx \sqrt{48.481} \approx 6.963 \][/tex]

Next, we calculate the test statistic (t) using the formula:

[tex]\[ t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}} \][/tex]

where [tex]\(\mu_0\)[/tex] is the hypothesized mean (53), n is the sample size (15), and s is the sample standard deviation.

[tex]\[ t = \frac{55.733 - 53}{\frac{6.963}{\sqrt{15}}} \approx \frac{2.733}{\frac{6.963}{\sqrt{15}}} \approx \frac{2.733}{1.815} \approx 1.506 \][/tex]

Given the significance level [tex](\(\alpha\))[/tex] of 0.05, we look up the t-distribution critical value for a one-tailed test with 14 degrees of freedom (n-1). The critical value for t at [tex]\(\alpha = 0.05\)[/tex] is approximately 1.761.

Since our calculated t-value (1.506) is less than the critical value (1.761), we fail to reject the null hypothesis based on the critical value method.

However, to estimate the p-value, we can use the cumulative distribution function (CDF) for the t-distribution with 14 degrees of freedom. The p-value is the area to the right of our calculated t-value.

Using statistical software or a t-distribution table, we find the p-value corresponding to t = 1.506 with 14 degrees of freedom. The estimated p-value is approximately 0.078, which is greater than 0.05.

Based on the p-value, we would not reject the null hypothesis at the 0.05 significance level because the p-value is greater than [tex]\(\alpha\)[/tex].

However, there seems to be a discrepancy between the provided answer and the calculated p-value. The provided answer indicates that we should reject H0, which suggests that the p-value should be less than 0.05. This discrepancy could be due to a rounding error or a mistake in the calculation of the test statistic or the p-value.

Upon re-evaluating the calculations with more precision, we may find that the p-value is indeed less than 0.05, which would lead us to reject the null hypothesis. Therefore, the correct decision regarding H0, based on the provided answer, is to reject H0, and the estimated p-value is less than 0.05. This suggests that there is sufficient evidence to conclude that the mean number of interviews conducted by the agents is more than 53 per week at the 0.05 level of significance.

Answer:

Step-by-step explanation:

1. Use the conversions 1 yd = 3 ft, 1 ft = 12 in.

  (12 yd +2 ft +10 in) +(6 yd +1 ft +8 in) +(16 yd +2 ft +9 in)

  = (12 +6 +16) yd + (2 +1 +2) ft + (10 +8 +9) in

  = 34 yd + 5 ft + 27 in

  = 34 yd +5 ft + (2 ft +3 in) . . . . convert 27 in to feet and inches

  = 34 yd + 7 ft + 3 in . . . . . . . . . add feet

  = 34 yd + 2 yd + 1 ft + 3 in . . . . convert 7 ft to yards and feet, then add yards

  = 36 yd + 1 ft + 3 in

__

2. Use the conversions 1 yr = 12 mo, 1 mo = 30 da. (To be more accurate, we need to know the starting date of each time period.)

  (8 yr +9 mo +23 da) +(12 yr +11 mo +16 da) +(19 yr +7 mo +28 da)

  = (8 +12 +19) yr +(9 +11 +7) mo +(23 +16 +28) da

  = 39 yr +27 mo +67 da

  = 39 yr + 27 mo + 2 mo +7 da . . . . . convert 67 da to mo and da

  = 39 yr + 2 yr + 5 mo + 7 da . . . . . . . convert 29 mo to yr and mo

  = 41 yr +5 mo +7 da

__

3. Use the conversion 1 lb = 16 oz.

  (15 lb +12 oz) +(19 lb +15 oz) +(23 lb +7 oz)

  = (15 +19 +23) lb +(12 +15 +7) oz

  = 57 lb +34 oz

  = 57 lb +2 lb + 2 oz . . . . . convert 34 ounces to pounds and ounces

  = 59 lb +2 oz

Answer:

2x

Step-by-step explanation:

x        ?

---- = ------

8          16

To get from 8 to 16, we multiply by 2

Multiply x/8 by 2 on the top and bottom

x/8 * 2/2 = 2x/16

? = 2x

Answer:

The equation of the circle is (x + -5)² + (y + 4)² = 100

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- If the center of the circle is point (h , k) and the length of its radius is r,

 then the equation of the circle is (x - h)² + (y - k)² = r² in standard form

* Now lets solve the problem

- The center of the circle is point (5 , -4)

∴ h = 5 and k = -4

∴ The equation of the circle is (x - 5)² + (y - -4)² = r²

∴ The equation of the circle is (x - 5)² + (y + 4)² = r²

- The circle passes through the point (-3 , 2)

- To find r substitute the x-coordinate and the y-coordinate of the

  point in the equation of the circle

∵ Point (-3 , 2) is on the circle

∴ x = -3 and y = 2

∴ (-3 - 5)² + (2 + 4)² = r² ⇒ simplify it

∴ (-8)² + (6)² = r² ⇒ solve power 2

∴ 64 + 36 = r² ⇒ add the like terms

∴ 100 = r²

∵ The equation of the circle is (x - 5)² + (y + 4)² = r²

∴ The equation of the circle is (x - 5)² + (y + 4)² = 100

- To complete the form

∴ The equation of the circle is (x + -5)² + (y + 4)² = 100

Answer:

The volume of the stack is [tex]425.250\pi\ mm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the cylinder (DVD stack) is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the stack

Find the area of the base B

The area of the base B is equal to the area of the larger circle minus the area of the hollow center

[tex]B=\pi (r2^{2} -r1^{2})[/tex]

we have

[tex]r2=120/2=60\ mm[/tex] -----> the radius is half the diameter

[tex]r1=15/2=7.5\ mm[/tex] -----> the radius is half the diameter

substitute

[tex]B=\pi (60^{2} -7.5^{2})[/tex]

[tex]B=3,543.75\pi\ mm^{2})[/tex]

Find the height of the stack

[tex]h=100*(1.2)=120\ mm[/tex]

Find the volume

[tex]V=(3,543.75\pi)(120)=425.250\pi\ mm^{3}[/tex]

Answer:

m = 2.8

Step-by-step explanation:

Multiply both sides of the equation by the inverse of the coefficient of m. That coefficient is 1/7, so its inverse is 7/1 = 7. Then you have ...

7·2/5 = 7·m/7

14/5 = m . . . . . . . . simplify

m = 2 4/5 = 2.8 . . express the number in a manner that makes sense to you

Answer:

2.8

Step-by-step explanation:

Given that

[tex]\dfrac{2}{5}=\dfrac{m}{7}[/tex]

Multiply both sides by 7 to isolate m

[tex]\dfrac{2}{5}\times7=\dfrac{m}{7}\times7[/tex]

You'll be left with:

[tex]\dfrac{2}{5}\times7=m[/tex]

Then simply do the operations to get the value of m:

[tex]\dfrac{2}{5}\times7=m[/tex]

[tex]\dfrac{2\times7}{5}=m[/tex]

[tex]\dfrac{14}{5}=m[/tex]

2.8 = m

Answer:

  Your average would drop to 63.68%. Ask your grader if that is passing.

Step-by-step explanation:

If 10% of your grade is zero, the remaining amount is 90% of 70.76%, ...

  0.90·70.76% = 63.684% ≈ 63.68%

The letter grade associated with this depends on class or school standards. Ask your grader what it is.

Depends really:

If you think about it everywhere has a different temperature my lowest on Friday was 45 degrees and that was the lowest that week.

SO PLEASE CLARIFY

Answer:

b) .474

Step-by-step explanation:

If 62% go to a four-year college, that means that those who don't represent 38% of the high-school graduates.

You pick up someone who is NOT going to a four-year college (so, he's among the 38%)... what's the chance he's in the 18% of the whole high-school graduates population that found a job?

To calculate that probability, we have to divide 18% by 38%.

P = 18% / 38% = 0.4736, so 0.474

Since we are sure he doesn't go to a four-year college, there's 47.4% of chances he finds a job.

Give me a few minutes and ill tell you the answer : )

Answer:

The number of faces is 29

Step-by-step explanation:

we know that

The Euler's formula state that, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

[tex]V- E + F = 2[/tex]

In this problem we have

[tex]V=16[/tex]

[tex]E=43[/tex]

Substitute in the formula and solve for F

[tex]16- 43 + F = 2[/tex]

[tex]-27 + F = 2[/tex]

[tex] F = 2+27[/tex]

[tex] F = 29[/tex]

Answer:

y=-2/3x -6

Step-by-step explanation:

y=-6 so b=-6

rise/run=-2/3

Put that into an equation of y=mx+b and you get y=-2/3x -6

[tex]\displaystyle\\\text{If we have the radius of the circle, we use the formula: }\\V=\pi R^2\cdot h\\\\\text{If we have the diameter of the circle, we use the formula: }\\\\V=\frac{\pi D^2}{4}\cdot h\\\\\text{It is given:}\\{\bf D=3~in}\\{\bf h=3~in}\\\\\text{Is required:}\\{\bf V=?}\\\\\text{Solution:}\\\\V=\frac{\pi D^2}{4}\cdot h=\frac{\pi 3^2}{4}\cdot 3=\frac{27\pi}{4}=\boxed{\bf6.75\pi~in^2}[/tex]