Solve the following quadratic equation using the quadratic formula. Separate multiple answers with a comma if necessary.

[tex]−yx^{2} +4y−6=0[/tex]

Answer:

so she saved 82 cents in the interest the month after

Step-by-step explanation:

case 1: payment is $75

interest on 2000 = 0.125/12×2000 = $20.83

so the actual repayment on the balance = (75-20.83) = $54.17

therefore,balance =$(2000-54.7)=$1945.83

interest in the next month = $20.27

case 2: payment is $100

interest on 2000 is still $20.83

repayment = $79.73

balance = $1920.27

interest in the next month = 20.01

so she saved 82 cents in the interest the month after

Answer:

$101

Step-by-step explanation:

Check link explanation.

Answer:

B (2.5, 0)

Step-by-step explanation:

2x - y = 5 (multiply all by 4)

8x- 4y = 20

-8x - 4y = - 20

eliminate the 4y

8x- 4y = 20

-8x - 4y = - 20

-------------------- –

16x = 40

x = 40/16 = 2.5

now we substitute x with 2.5

2x - y = 5

2(2.5) - y = 5

y = 0

Answer:

its B

Step-by-step explanation:

took the test

Answer:

i dont understand the language

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

Step-by-step explanation:

What is P(D), the probability that a student in the class has a dog?

D=66%

What is P(C), the probability that a student in the class has a cat?

C=60%

What is P(D and C), the probability that a student in the class has a dog and a cat?

DC=50%

Starting off, you already know he has 4 daughters and for every daughter there are 4 sons.

So, we take the 4 daughters and add 4 to each one:

1 daughter + 4 sons = 5 children

We complete that equation 4 times for each daughter, and we end up with 20 children as our answer.

Hope this helps you out a bit! Stay safe and stay healthy! :D

Answer:

[tex]P(z<\frac{a-\mu}{\sigma})=0.10[/tex]

and we can set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]

And if we solve for a we got

[tex]a=104.5 -1.282*23.62=74.22[/tex]

And the best answer for this case would be:

b) $74.23

Step-by-step explanation:

Let X the random variable that represent the stocks price of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(104.5,23.62)[/tex]  

Where [tex]\mu=104.5[/tex] and [tex]\sigma=23.62[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.90[/tex]   (a)

[tex]P(X<a)=0.10[/tex]   (b)

As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.282. On this case P(Z<-1.282)=0.10 and P(z>-1.282)=0.90

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.10[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.10[/tex]

and we can set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]

And if we solve for a we got

[tex]a=104.5 -1.282*23.62=74.22[/tex]

And the best answer for this case would be:

b) $74.23

Answer:

3.25 h = 3 h 15 m

Step-by-step explanation:

156 mi * 1h/48 mi = 3.25 h = 3 h 15 m

Answer: 195 min or 3 hr and 15 min

Step-by-step explanation:

We can set up a proportion to solve this problem.

[tex]\frac{48mi}{60 min} =\frac{156 mi}{x}[/tex]

[tex]48x=156*60[/tex]

[tex]48x=9360[/tex]

[tex]x=195 min[/tex]

We can also write this in terms of hours and minutes.

[tex]\frac{60 min}{1 hr} =\frac{195 min}{x}[/tex]

[tex]60x=195[/tex]

[tex]x=3.25[/tex]

3 hr and 15 min

Answer:

$2

Step-by-step explanation:

Because 3/12 is 0.25 and then you multiply it by 8 to get 2.

Answer:

a) Z = 2.86

b) Z = 2

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 23000, \sigma = 3500[/tex]

a. What is a Z score for a car with a price of $33,000?

This is Z when X = 33000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{33000 - 23000}{3500}[/tex]

[tex]Z = 2.86[/tex]

b. What is a Z score for a car with a price of $30,000?

This is Z when X = 30000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30000 - 23000}{3500}[/tex]

[tex]Z = 2[/tex]

Answer:

Race covers 1911 meters.

Step-by-step explanation:

Triangle ABC represents a race path.

Total distance covered by the race = Perimeter of the triangle ABC

We will apply Sine rule in the given triangle to find the unknown sides.

By Sine rule,

[tex]\frac{SinB}{AC}=\frac{SinA}{BC}=\frac{SinC}{AB}[/tex]

[tex]\frac{Sin35}{450}=\frac{Sin85}{AC}=\frac{Sin60}{AB}[/tex]      [Since m∠A = 180° - (85 + 60)° = 35°]

[tex]\frac{Sin35}{450}=\frac{Sin85}{AC}[/tex]

AC = [tex]\frac{450\times \text{Sin85}}{\text{Sin35}}[/tex]

     = 781.57 meters

[tex]\frac{Sin35}{450}=\frac{Sin60}{AB}[/tex]

AB = [tex]\frac{450\times \text{Sin60}}{\text{Sin35}}[/tex]

     = 679.44 meters

Perimeter of the triangle = AB + BC + AC

                                         = 679.44 + 450 + 781.57

                                         = 1911.01

                                         ≈ 1911 meters

Therefore, the race covers 1911 meters.

Answer:

1911

Step-by-step explanation:

yes

Answer:

She would use 136 yards in 4 skirts, 238 yards in 7 skirts, and 306 yards in 9 skirts. Hope this helps

Step-by-step explanation:

Answer:

For the domain since we have a quadratic function then the domain would be all the real numbers:

[tex] D =[x | x \in R][/tex]

And if we want to find the range we can find the vertex:

[tex] v_x = -\frac{b}{2a}= -\frac{-1}{2*2}= \frac{1}{4}[/tex]

And now we can find th coordinate of y of the vertex like this:

[tex] f(V_x) = 2(\frac{1}{4})^2 -(1/4) +3 =2.875[/tex]

And then the range would be:

[tex] R=[x \geq 2.875][/tex]

Step-by-step explanation:

We have the following function given:

[tex] y = 2x^2 -x +3[/tex]

For this case we can plot the function with a calculator and we got the plot in the figure attached.

For the domain since we have a quadratic function then the domain would be all the real numbers:

[tex] D =[x | x \in R][/tex]

And if we want to find the range we can find the vertex:

[tex] v_x = -\frac{b}{2a}= -\frac{-1}{2*2}= \frac{1}{4}[/tex]

And now we can find th coordinate of y of the vertex like this:

[tex] f(V_x) = 2(\frac{1}{4})^2 -(1/4) +3 =2.875[/tex]

And then the range would be:

[tex] R=[x \geq 2.875][/tex]

The "density of probability" is represented by the Y-axis in the normal distribution.It indicates the likelihood of finding values close to comparable places on the X-axis.

Y is the number of trial on which lock is opend so, P(Y=y) be the probability that key opens  the lock on y th trial Lets draw first key

p(1 st key opens the lock) =1-1/5= 4/5

Hence p(1 st key does not open the lock  = 1- 1/5 =4/5

Since  p (Lock is opened on 1 st triual ) = p(1st key opens the lock )

Hence , P(Y =2 ) 1/4 .4/5 = 1/5

p( y = 4) = 1/5

p(y = 5 ) =1/5

To learn more about probability function refer

https://brainly.com/question/28021875

#SPJ2

Answer:

I think it is 310 plus 300 and

320 plus 390

Step-by-step explanation:

Answer:

The probability that the three drivers would wear seat belts is 0.5

Step-by-step explanation:

Given

Percentage of drivers using seat belt = 80%

Number of drivers pulled over = 3

Required

Probability that all three drivers wore seat belt

First, the probability that a driver would wear seat belt has to be calculated.

Let's represent that with P(D)

P(D) is equivalent to the percentage of drivers using seat belt

[tex]P(D) = 80%[/tex]%

[tex]P(D) = \frac{80}{100}[/tex]

[tex]P(D) = 0.8[/tex]

Let the probability that the three drivers would wear seat belts be represented as P(All).

P(All) is calculated as thus;

(Probability that the first driver would wear seat belt) and (Probability that the second driver would wear seat belt) and (Probability that the first driver would wear seat belt).

Mathematically, this means

[tex]P(All) = P(D) * P(D) * P(D)[/tex]

Substitute [tex]P(D) = 0.8[/tex]

[tex]P(All) = 0.8 * 0.8 * 0.8[/tex]

[tex]P(All) = 0.512[/tex]

[tex]P(All) = 0.5[/tex] --- Approximated

Hence, the probability that the three drivers would wear seat belts is 0.5

Answer:

Probability that 32 or more from this sample used Internet Explorer as their browser is 0.9015.

Step-by-step explanation:

We are given that according to Net Market Share, Microsoft's Internet Explorer browser has 53.4% of the global market.

A random sample of 70 users was selected.

Let [tex]\hat p[/tex] = sample proportion of users who used Internet Explorer as their browser.

The z score probability distribution for sample proportion is given by;

                            Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, p = population proportion of users who use internet explorer = 53.4%

           [tex]\hat p[/tex] = sample proportion = [tex]\frac{32}{70}[/tex] = 0.457

           n = sample of users = 70

Now, probability that 32 or more from this sample used Internet Explorer as their browser is given by = P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.457)

      P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.457) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{0.457-0.534}{\sqrt{\frac{0.457(1-0.457)}{70} } }[/tex] ) = P(Z [tex]\geq[/tex] -1.29)

                            = P(Z [tex]\leq[/tex] 1.29) = 0.9015

The above probability is calculated by looking at the value of x = 1.29 in the z table which has an area of 0.9015.

Answer:

Dimensions: 165 feet by 110 feet.

Maximum Area =18,150 Square feet

Step-by-step explanation:

Let the dimension of the playground be x and y.

The rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground.

Let the side parallel to one side of the playground =x

Therefore, the total length of fencing =2x+x+2y

P=3x+2y

Six hundred and sixty feet of fencing is used.

We have: 3x+2y=660

3x=660-2y

[tex]x=\dfrac{660-2y}{3}[/tex]

Area of the Playground A=xy

We write the area in terms of y by substitution of x derived above.

[tex]A(y)=y\left(\dfrac{660-2y}{3}\right )\\A(y)=\dfrac{660y-2y^2}{3}[/tex]

We want to maximize the total enclosed area.

To do this, we first find the derivative of A(y).

[tex]A'(y)=\dfrac{660-4y}{3}[/tex]

Next, we solve A'(y) for its critical point.

[tex]A'(y)=\dfrac{660-4y}{3}=0\\660-4y=0\\660=4y\\y=660 \div 4\\y=165$ feet\\[/tex]

Recall that: [tex]x=\dfrac{660-2y}{3}[/tex]

Therefore:

[tex]x=\dfrac{660-2(165)}{3}=\dfrac{660-330}{3}=\dfrac{330}{3}\\x=110$ feet[/tex]

Therefore, the dimensions of the playground that maximize the total enclosed area is 165 feet by 110 feet.

Maximum Area =165 X 110

=18,150 Square feet

Answer:

Dimensions: 165 feet by 110 feet.

Maximum Area =18,150 Square feet

Maximum Area =165 X 110

=18,150 Square feet

Answer:

Translated 3 units down 2 units left.

Step-by-step explanation:

It looks like the functions are the same, so if you see, it was translated 3 units down and 2 units left.

Answer:

-2x/yz

Step-by-step explanation:

You can cancel out terms using division and properties of exponents. x^a/x^b = x^a-b

Answer:

A trinomial

Step-by-step explanation:

Since there are three terms, x^2, 3x, and 8, it is a trinomial

Answer:

E : x=12

Step-by-step explanation:

ACCORDING TO THE THEOREM

(PD)(PC) = (AP)(PB)

8(3+x)=10x

24+8x=10x

24=10x-8x

24 = 2x

x = 12

Answer:

12

Step-by-step explanation:

PD * PC = AP * PB

= 8 * (3 + x) = 10 * x

= 24 + 8x = 10x

= 10x - 8x = 24

= 2x = 24

= 12

Answer:

4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

Since Z > -2 and Z < 2, this outcome is not considered unusual.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If [tex]Z \leq 2[/tex] or [tex]Z \geq 2[/tex], the outcome X is considered to be unusual.

In this question:

[tex]\mu = 8.21, \sigma = 1.9[/tex]

Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

This is the pvalue of Z when X = 5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 8.21}{1.9}[/tex]

[tex]Z = -1.69[/tex]

[tex]Z = -1.69[/tex] has a pvalue of 0.0455.

4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

Since Z > -2 and Z < 2, this outcome is not considered unusual.

Answer:

A

Step-by-step explanation:

(f-g)(x) means that the 2 functions are being subtracted.

[tex]3^{x}[/tex] +10x -(5x-3) =[tex]3^{x}[/tex] +10x-5x+3

simplify!

[tex]3^{x}[/tex] +5x+3

the answer is A

Answer:

54 9/10

Step-by-step explanation:

The perimeter is the sum of all the sides

13 1/4 + 12 1/5 + 18 1/4 + 11 1/5

Add up the whole numbers

13+12+18+11 = 54

1/4+1/5+1/4+1/5

2/4+2/5

1/2+2/5

Get a common denominator

1/2*5/5 + 2/5*2/2

5/10 +  4/10

9/10

Add them back together

54 9/10

Complete Question

The complete qustion is shown on the first uploaded image

Answer:

The correct option is B

Step-by-step explanation:

From the question we are told that

      The sample size  is  [tex]n = 49[/tex]

       The mean is  [tex]\mu = 17ppb[/tex]

       The standard deviation is [tex]\sigma = 14 ppb[/tex]

Generally the standard error of this measurement is mathematically represented as

       [tex]\sigma_z = \frac{\sigma}{\sqrt{n} }[/tex]      

substituting values

      [tex]\sigma_{\= x} = \frac{14}{\sqrt{49} }[/tex]  

     [tex]\sigma_{\= x} = 2[/tex]ppb

Now the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb represented as P(X < 15 )

Next is to find the z value

    [tex]z = \frac{\mu -\sigma }{\sigma_{\= x}}[/tex]

     [tex]z = \frac{15-17}{2}[/tex]

      [tex]z = -1[/tex]

Now checking the z-table for the z-score of  -1 we have  

      [tex]P(X<15) = P(Z < -1 )= 0.16[/tex]

Using the normal distribution and the central limit theorem, it is found that there is a 0.16 = 16% probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb, hence option B is correct.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

The probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb is the p-value of Z when X = 15, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{15 - 17}{2}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.16

0.16 = 16% probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb, hence option B is correct.

For more on the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Consider the following pair of equations:

y = 3x + 3 ... 1

y = x − 1 ... 2

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form .

From both equations, we will substitute y = 3x+3 in equation 1 into 2 to have;

3x+3 = x-1

collecting the like terms;

3x-x = -1-3

2x = -4

Dividing both sides by 2 will give;

2x/2 = -4/2

x = -2

Substituting x = -2 into equation 1;

y = 3x+3

y = 3(-2)+3

y = -6+3

y = -3

The solution in (x, y) form is (-2, -3)

Answer:

A: Ben has been a member longer because 1 year, 2 weeks, 3 days is longer than 372 days.

B: 10 days longer

Step-by-step explanation:

1 year, 2 weeks, 3 days is 382 days -> 365 + 14 + 3 = 382

Answer:

480 cubic feet

Step-by-step explanation:

The volume of any rectangular prism can be found by multiplying together the length, width and height. In this case, 8*6*10=48*10=480 cubic feet. Hope this helps!

Answer:

[tex]480 {ft}^{3} [/tex]

Step-by-step explanation:

[tex]area \\ = l \times b \times h \\ = 8 \times 6 \times 10 \\ = 48 \times 10 \\ = 480 {ft}^{3} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Step-by-step explanation:

We are told that P(x)  is the profit of saling x blu ray discs. P(1000) is our profit for selling 1000 blu ray discs. So, our profit is 5000. Recall that the derivative P'(x) represents the rate at which the function P(x) is increasing/decreasing (increasing if P'(x) is positive, or decreasing otherwise) by increasing the values of x. In this case P'(1000)=-3, so the profit will decrease -3 if we increase x in one unit.