Find the solution(s) to 2x2 + 5x – 3 = 0.

Check all that apply.

A.x = – 1/2

x = 2

C.x = 1/2

x = 3

E.x = –3

Answer:

$3735

Step-by-step explanation:

The formula for simple interest is I = Prt, where I is the interest earned, P is the initial investment, r is the interest rate in decimal form, and t is the time in years.  We have everything we need to find the interest, which is the amount your investment earned while it sat there for 7 years.  Once we find that interest amount, we will add it to the intial investment to find the total amount after 7 years that your money has grown to.

I = 3000(.035)(7) so

I = 735

3000 + 735 = 3735

Answer:

$3,630

Step-by-step explanation:

You invest $3,000 in an account at 3.5% per year simple interest.

We have to calculate the amount in the account at the beginning of the 7th year. This means we have to calculate the interest for completed 6 years.

Formula for simple interest

A = P(1+rt)

A = Amount after maturity

P = Principal amount ( 3,000)

r = rate of interest in decimal ( 0.035)

t = time in years ( 6 )

Now we put the values in to formula

A = 3,000(1 + 0.035 × 6)

A = 3,000 ( 1 + 0.021 )

A = 3,000 × 1.21

A = $3,630

The amount would be $3,630 at the beginning of the 7th year.

Answer:2/3

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

one way we can solve this is by making a tree  using H for heads and T for tails

since it can land H or T, we put them down like this. then we can get H or T again because its a coin, so we put that under each letter. finally we do the same thing again to get 8 possibilities. now we can count how many of them was HHH, which is one

         H              T

         /  \            /   \

       H   T         H   T

      /\     /\        /\    /\

    H T H T     H T H T

    ^      this one

or do 2 x 2 x 2 because there are 2 possibilities each three times

The approximate probability that the person will win at least $15 is 0.255.

To solve this problem, we need to calculate the probability of winning at least $15 after playing the game 30 times. Winning at least $15 means that the player must win on at least 6 rolls because winning once pays $5, and $5 times 6 is $30, which is the minimum needed to have a net gain of $15 ($30 won - $15 lost).

First, let's calculate the probability of winning in a single roll. The player wins if they roll a 3 or a 5, which are two favorable outcomes out of six possible outcomes.

[tex]\[ P(\text{win on a single roll}) = \frac{2}{6} = \frac{1}{3} \][/tex]

The probability of losing in a single roll is the complement of the probability of winning:

[tex][ P(\text{lose on a single roll}) = 1 - P(\text{win on a single roll}) = 1 - \frac{1}{3} = \frac{2}{3} \][/tex]

Now, we need to find the probability of winning at least 6 times in 30 rolls. This can be modeled using the binomial probability formula:

[tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \][/tex]

where [tex]\( n \)[/tex]  is the number of trials (30 in this case), [tex]\( k \)[/tex] is the number of successes (at least 6), [tex]\( p \)[/tex] is the probability of success on a single trial [tex](\( \frac{1}{3} \)), and \( \binom{n}{k} \)[/tex]  is the binomial coefficient.

We want to calculate the probability of winning at least 6 times, which is the sum of the probabilities of winning exactly 6, 7, .. up to 30 times:

[tex]\[ P(X \geq 6) = \sum_{k=6}^{30} \binom{30}{k} \left(\frac{1}{3}\right)^k \left(\frac{2}{3}\right)^{30-k} \][/tex]

[tex]\[ P(X \geq 6) \approx 0.255 \][/tex]

Answer:

(3.01%, 14.77%)

Step-by-step explanation:

The confidence interval of a proportion is:

CI = p ± SE × CV,

where p is the proportion, SE is the standard error, and CV is the critical value (either a t-score or a z-score).

We already know the proportion: 8/90.  But we need to find the standard error and the critical value.

The standard error is:

SE = √(p (1-p) / n)

SE = √((8/90) * (82/90) / 90)

SE = 0.03

To find the critical value, we must first find the alpha level and the degrees of freedom.

The alpha level for a 95% confidence interval is:

α = (1 - 0.95) / 2 = 0.025

The degrees of freedom is one less than the sample size:

df = n - 1 = 90 - 1 = 89

Since df > 30, we can approximate this with a normal distribution.

If we look up the alpha level in a z score table, we find the z-score is 1.96.  That's our critical value.  CV = 1.96.

Now we can find the confidence interval:

CI = 8/90 ± 0.03 * 1.96

CI = 0.0889 ± 0.0588

CI = (0.0301, 0.1477)

So we are 95% confident that the percent of patients who had their teeth whitened is between 3.01% and 14.77%.

Answer:

1,800 bricks are needed

Step-by-step explanation:

First convert the Length and width of the sidewalk into inches

Entire Sidewalk: L= 100x12 =1200in and W= 4 x 12 = 48in

Then we know Area = LxW, so we will do this for both the sidewalk and the brick.

Area of sidewalk: 1200 x 48 = 57600

Bricks ( no need to convert since the measurements are already in inches): 8 x 4 = 32

Now we will divide the area of the entire sidewalk by the area of a single brick to find out how many bricks you need to complete the whole sidewalk:

57600/32= 1,800 bricks

ANSWER

[tex](4n - 1)\sqrt{3 n} + 3\sqrt{n}[/tex]

EXPLANATION

The given expression is

[tex] \sqrt{48 {n}^{3} } + \sqrt{9n} - \sqrt{3n} [/tex]

We remove the perfect squares under the radical sign.

[tex]\sqrt{16 {n}^{2} \times3 n} + \sqrt{9n} - \sqrt{3n} [/tex]

We can now take square root of the perfect squares and simplify them further.

[tex] \sqrt{16 {n}^{2}} \times \sqrt{3 n} + \sqrt{9} \times \sqrt{n} - \sqrt{3n} [/tex]

This simplifies to:

[tex]4n\sqrt{3 n} + 3\sqrt{n} - \sqrt{3n} [/tex]

This further simplifies to:

[tex](4n - 1)\sqrt{3 n} + 3\sqrt{n} [/tex]

Answer:

Option B is Correct

Step-by-step explanation:

[tex]\sqrt{48n^3}+\sqrt{9n} - \sqrt{3n}[/tex]

We need to solve the above expression.

48 can be written as: 2x2x2x2x3

9 can be written as : 3x3

Putting values

[tex]\sqrt{2*2*2*2*3*n*n*n} +\sqrt{3*3*n}-\sqrt{3n}[/tex]

2*2 = 2^2 and n*n = n^2 and 3*3 = 3^2

we also know √ = 1/2

so, putting these values we get,

[tex]\sqrt{2^2*2^2*3*n^2*n} +\sqrt{3^2*n}-\sqrt{3n}\\(2^2)^{1/2} * (2^2)^{1/2} * (3)^{1/2} * (n^2)^{1/2} * n ^{1/2} + ((3^2)^{1/2} *n^{1/2}) -(\sqrt{3n})\\2*2*n * (3^{1/2} *n ^{1/2}) +(3 +n^{1/2}) -(\sqrt{3n})\\4n (\sqrt{3n})+(3 \sqrt{n}) -(\sqrt{3n})\\Rearraninging\\4n(\sqrt{3n}) - (\sqrt{3n})+(3 \sqrt{n})\\Taking \,\,\sqrt{3n} \,\,common\,\, from\,\, 1st\,\, and\,\, 2nd\,\, term\\\sqrt{3n}(4n-1)+(3 \sqrt{n})\\or \,\,it\,\,can\,\,be\,\,written\,\,as\,\,\\(4n-1)\sqrt{3n}+(3 \sqrt{n})[/tex]

So, Option B is Correct.

Answer:

A. Lucy Only

Step-by-step explanation:

Got it right on Khan Academy

The possible sample space is: FV, WV, SV, FB, WB, and SB

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes

As, the sample space with all possibilities in which lucy and katy register a sports League.

Now, they have 2 sports and 3 seasons for the Sample space.

Mow let us consider, V is registered for Volleyball and B is registered for basketball .

and, F is registered Fall, W is registered for Winter and S is for Spring.

so, that the sample space is:

FV, WV, SV, FB, WB, and SB

where, FV is the  registered possibility for fall and in volleyball.

WV is the  registered possibility for Winter and in volleyball.

SV is the  registered possibility for Spring and in volleyball.

and so on..

Therefore, the correctly representation for the sample space is the one that has all these possibilities.

Learn more about probability here:

brainly.com/question/21547529

#SPJ2

To determine how many plants Ms. Holmes had, divide the total amount of water she had by the amount of water she gave each plant. The expression that can be used is (2 1/2 gallons) divided by (1/4 gallon per plant). Simplifying the expression gives the answer of 10 plants.

To determine how many plants Ms. Holmes had, we can divide the total amount of water she had (2 1/2 gallons) by the amount of water she gave each plant (1/4 gallon per plant).

So, the expression that can be used is (2 ½ gallons) ÷ (1/4 gallon per plant). To divide a fraction by a fraction, we multiply the first fraction by the reciprocal of the second fraction. Therefore, the expression simplifies to (2 ½ gallons) × (4 gallons per plant).

Simplifying further, we get 10 gallons. This means that Ms. Holmes had 10 plants.

https://brainly.com/question/17021989

#SPJ12

Answer:

Acute

Step-by-step explanation:

7² + 9² ? 11²

49 + 81 ? 121

130 is greater than 121, so it is an acute triangle

Answer:

the first function, y = (x + 1)^2, does pass through the points (1, 4), (2, 9), and (3, 16).

Step-by-step explanation:

Note that 4, 9 and 16 are squares of 2, 3 and 4.  So it's likely that the parent function is of the form f(x) = x^2.  Note that f(1) = 1, f(2) = 4, f(3) = 9 and f(4) = 16.

Let's now determine whether these three points satisfy the first given equation, y = (x + 1)^2:  Does 4 = (1 + 1)^2?  Does 4 = 2^2?  YES.

Does 9 = (2 + 1)^2?  Does 9 = 3^2?  YES

Does 16 = (3 + 1)^2?  YES

So the first function, y = (x + 1)^2, does pass through the points (1, 4), (2, 9), and (3, 16).

Final answer:

The detailed answers cover questions related to functions, sequences, equations of lines, slopes, and graphing lines.

Explanation:

Question 1:

The function that passes through the points (1, 4), (2, 9), and (3, 16) is y = (x + 1)^2.

Question 2:

The equation representing the total number of laps swum y in terms of hours x is y(x) = 10x + 1.

Question 3:

The sequence {4, 2, 0, -2, -4, -6, …} is an arithmetic sequence with a common difference of -2.

Question 5:

The slope of the line containing (3, 5) and (2, 7) is m = -2.

Question 6:

For a line passing through (-3, 2) with a slope of 4, the equation of the line is y = 4x + 14.

Answer:

Step-by-step explanation:

- 5 + (-3) + 3 is the correct option.

Answer:

-5 + (-3) + 3

Step-by-step explanation:

Answer:

50.24

Step-by-step explanation:

area of a circle =pi r^2

diameter = 2 * radius

radius=8/2=4

area=pi 4^2

=pi 16

=50.26

Answer:

1. no like terms

2. x^ 3 − x^ 2 − x + 1

3.x y + x + y + 1

4.x^ 3 + x^ 2 y + x y^ 2 + y^ 3

Lol

Answer:

The mean is equal to the median, so the data is symmetrical

Step-by-step explanation:

Here is the data.

10 5 8 10 12 6

8 10 15 6 12 18

The given data:   10   5   8   10   12   6   8   10   15   6   12   18

For finding the Mean, we will have to add all numbers together and divide it by total number. i.e sum of terms divided by number of terms  

Mean= 10+5+8+10+12+6+8+10+15+6+12+18  ÷ 12

Mean = 120 ÷ 12 = 10        

For finding the Median, first we need to rearrange the data in ascending order

5   6   6   8   8   10   10   10   12   12   15   18

We can see that the middle values are 10 and 10. So, the median will be the average of those two middle values.

Median = 10+10 ÷ 2

Median = 20 ÷ 2 = 10

From the calculation, we can see that both the median and mean are equal so, the data is symmetrical  

Answer:

8 years

Step-by-step explanation:

Answer:

she will be at the company for 8 years.

Step-by-step explanation:

The number of days of vacation for each year = 3

Maryanne is employed up to a maximum of 24 days of vacation time.

We need to find the number of years she will be in the company before she reaches the maximum amount of vacation of time.

The number of years she will be in the company = The number of maximum days of vacation time divided by the number of days of vacation for each year

= [tex]\frac{24}{3}[/tex]

= 8 years

Therefore, she will be at the company for 8 years.

Answer:

•0.5

Step-by-step explanation:

We'll assume the dilation was done at the origin point, so it was done evenly.

Since the k point went from (10,0) to (5,0), we know it was reduced... so the scale factor has to be below 1. A scale factor means the size wasn't changed and a dilation/scale factor larger than 1 means it was enlarged.

So, we take the new X-value (5) and divide it by the original X-value (10).

Scale factor = 5/10 = 1/2... so 0.5

Answer:

35

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

nCk = n!/(k!(n -k)!)

7C3 = 7!/(3!(7-3)!) = 7·6·5/(3·2·1) = 7·5 = 35

_____

It is convenient to use the largest of the factorials in the denominator to cancel as many factors as you can from the numerator, then cancel factors from the remaining numbers. Here after canceling 4! = 4·3·2·1 from the numerator, we are left with 7·6·5 divided by 3! = 3·2·1 = 6. Obviously, this will cancel the 6 in the numerator product, leaving only 7·5 = 35.

Some graphing and/or scientific calculators will have this function built in.

f(x) = 2(x+8)

replace f(x) with 12 and then solve for x:

12 = 2(x +8)

Use the distributive Property on the right side:

12 = 2x +16

Subtract 16 from each side:

-4 - 2x

Divide both sides by 2:

x = -4 / 2

x = -2

Answer:

−2

Step-by-step explanation:

f(x) = 2(x+8)

f(x) = 12

12 = 2(x+8)

Divide each side by 2

12/2 = 2/2(x+8)

6 = x+8

Subtract 8 from each side

6-8 =x+8-8

-2 = x

Answer:

Thehe answer is 75

Step-by-step explanation:

Answer with Step-by-step explanation:

The length of a rectangle is 3 meters more than the width.

If the width is b.

⇒ Length=b+3

The perimeter of the rectangle is 26 meters.

Since, Perimeter=2(Length+width)

⇒ 2(b+3+b)=26

dividing both sides by 2

⇒ b+3+b=13

⇒ 2b=13-3

⇒ 2b=10

dividing both sides by 2

⇒ b=5

⇒ Width=5 meter

and Length=5+3=8 meter

Answer:

see explanation

Step-by-step explanation:

To evaluate the expression for the given values.

Substitute the given values for x into g(x)

a

g(0) = 3(0)² - 4(0) + 3 = 0 - 0 + 3 = 3

b

g(- 1) = 3(- 1)² - 4(- 1) + 3 = 3 + 4 + 3 = 10

c

g(2) = 3(2)² - 4(2) + 3 = 12 - 8 + 3 = 7

d

g(- x) = 3(- x)² - 4(- x) + 3 = 3x² + 4x + 3

e

g(1 - t)

= 3(1 - t)² - 4(1 - t) + 3

= 3(1 - 2t + t²) - 4 + 4t + 3

= 3 - 6t + 3t² - 4 + 4t + 3

= 3t² - 2t + 2

Answer:

16 Boxes

Step-by-step explanation:

Total Bottles:125

Amount of Bottles A Box Is Able To Hold:8

125/8=15.625

Round Up To Nearest Whole Number

16 Boxes Are Needed To Hold 125 Bottles

Answer:

  8√2

Step-by-step explanation:

The hypotenuse of a right triangle is √2 times the leg length, so you have ...

  [tex]x\sqrt{2}=16[/tex]

Dividing by the coefficient of x gives ...

  [tex]x=\dfrac{16}{\sqrt{2}}=\dfrac{16\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}=8\sqrt{2}[/tex]

Each leg has length 8√2.

put simply, the volume of a rectangular prism is just the product of all its 3 dimensions.

[tex]\bf V=\cfrac{2}{3}\cdot \cfrac{1}{3}\cdot \cfrac{2}{3}\implies V=\cfrac{4}{27}[/tex]

Answer: 0 ≤ t ≤ 40

Step-by-step explanation:

0 and 40 are included in all 3 number lines.

Answer:

4.4, 4.4 : 1, 22 : 5

Step-by-step explanation:

There are many ways to solve this, but I'll do it by finding the ratio between V'T' and VT.

That's easy, we're given the lengths of these two. The ratio would be 8.8/2. 8.8/2 = 4.4, or (8.8*5)/(2*5) = 22/5

Answer:

[tex]y=\tan x[/tex]

Step-by-step explanation:

The trigonometric function that needs a domain restriction of [tex][-\frac{\pi}{2},\frac{\pi}{2} ][/tex] to make it invertible is [tex]y=\tan x[/tex].

The function [tex]y=\tan x[/tex] will pass the horizontal line test on this interval therefore making it an invertible function on this interval.

This explains why the inverse tangent function, [tex]y=\tan^{-1} x[/tex] has range [tex][-\frac{\pi}{2},\frac{\pi}{2} ][/tex].

Answer:

A) [tex]f(x)=sin x[/tex]

Step-by-step explanation:

I just did the test and this was the correct answer.  

Answer:

  B. a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft

Step-by-step explanation:

A diagram can be a useful aid to answering this question. At one corner of the shed, 8 ft of rope is no longer available, so the quarter circle has a radius of 18-8 = 10 ft. (That side of the shed is 12 ft, so the area is only a quarter circle.)

At the other corner of the shed, 12 ft of rope is no longer available, so the quarter circle has a radius of 18-12 = 6 ft. (That side of the shed is 8 ft, so the area is only a quarter circle.)

In the attached diagram, the 3/4 circle with radius 18 ft is shown red, and the quarter circles are shown in green.

Answer:

The answer is below

Step-by-step explanation:

Answer:

The residual e=2 when x = 5.

Step-by-step explanation:

A scatter plot containing the point (5, 29), it means the observed value at x=5 it 29.

The given regression equation is

[tex]\hat{y}=5x+2[/tex]

Substitute x=5 in the above regression equation, to find the predicted value at x=-5.

[tex]\hat{y}=5(5)+2=25+2=27[/tex]

The formula to find the residual value e is

e = Observed value - Predicted value

[tex]e=29-27[/tex]

[tex]e=2[/tex]

Therefore the residual e=2 when x = 5.

Answer:

Option A

53.5

Step-by-step explanation:

Answer: the coefficient of 13m is 13.

Answer:

The coefficient of 13 m is 13.

Step-by-step explanation:

Consider the provided expression.

[tex]13m[/tex]

Numbers appear with variables are called coefficients.

Alphabets in an expression are called variables.

Numbers appear without variables are called Constant terms.

Here we need to identity the coefficient.

From the above definition we know the number appear with the variables are coefficients.

Since m is variable, thus the number 13 must be the coefficient.

Hence, the coefficient of 13 m is 13.