Determine the nature of the roots: 4x2 + 13x + 6 = 0
a. no real solutions
b. cannot be determined
C. a unique real solution
two distinct real solutions d. two distinct real solutions

Answer:

Bunny Hill Ski Resort:

y = 10x + 35

Diamond Ski Resort:

y = 5x + 40

Point where the cost is the same:

(1, 45)

Step-by-step explanation:

The question tells us that:

$35 and $40 are initial fees

$10 and $5 are hourly fees

This means that x and y will equal:

x = number of hours

y = total cost of ski rental after a number of hours

So we can form these 2 equations:

y = 10x + 35

y = 5x + 40

Now we are going to use System of Equations to find what point the cost of both ski slopes is the same.

Because they both equal y, we can set the equations equal to each other:

10x + 35 = 5x + 40

And we use basic algebra to solve for x:

10x + 35 = 5x + 40

(subtract 5x from both sides)

5x + 35 = 40

(subtract 35 from both sides)

5x = 5

(divide both sides by 5)

x = 1

Remember, x equals the number of hours.

That means when your rent out the skis for 1 hour, you will get the same price of $45 (you find the price by plugging in 1 into both of the equations)

Hope it helps (●'◡'●)

Answer: 3 years

Step-by-step explanation:

Interest is calculated as:

= (P × R × T) / 100

where

P = principal = 150,000

R = rate = 2.5%.

I = interest = 11250

T = time = unknown.

I = (P × R × T) / 100

11250 = (150000 × 2.5 × T)/100

Cross multiply

1125000 = 375000T

T = 1125000/375000

T = 3

The time taken will be 3 years

Answer:

-3a+3bx+2ab

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

4 x 2 x 5 = 40

9 + 2 + 7 + 8 + 4 = 30

40 - 30 = 10

= 10

Answer:

Step-by-step explanation:

Given:

Substitute x= -3:

Step-by-step explanation:

6/10 > _ > 1/3

3/5 > _ > 1/3

½(⅗+⅓)

½(9+5/15)

½(14/5)

=7/15

Answer:

7/15

Step-by-step explanation: 10 and 3 LCM is 30

6/10 x 3 =18/30 and 1/3x 10= 10/30

10/30 and 18/30 average is 14/30 which simplified is 7/15

The answer is 7/15

Hope it helps

Answer:

A. (1, -5), (2, -1), (-1, 7)

Step-by-step explanation:

Reflecting a function over the x-axis:

When a function is reflected over the x-axis, the x-value stays the same, while y changes the signal, so the transformation rule is:

[tex](x,y) \rightarrow (x,-y)[/tex]

To find the range:

We apply the transformation to the points in the domain. Thus:

[tex](1,5) \rightarrow (1,-5)[/tex]

[tex](2,1) \rightarrow (2,-1)[/tex]

[tex](-1,-7) \rightarrow (-1,-(-7)) = (-1, 7)[/tex]

Thus the correct answer is given by option a.

Answer:

It is letter A and please give me brainliest

Step-by-step explanation:

Answer:

0.001831055

Step-by-step explanation:

Here, n = 16, p = 0.5, (1 - p) = 0.5 and x = 14

As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 14)

P(x =14) = 16C14 * 0.5^14 *(1-0.5)^2

               = 120 * 0.5^14 *(1-0.5)^2

= 0.001831055

Answer:

Answer = √(0.301 × 0.699 / 83) ≈ 0.050

A 68 percent confidence interval for the proportion of persons who work less than 40 hours per week is (0.251, 0.351), or equivalently (25.1%, 35.1%)

Step-by-step explanation:

√(0.301 × 0.699 / 83) ≈ 0.050

We have a large sample size of n = 83 respondents. Let p be the true proportion of persons who work less than 40 hours per week. A point estimate of p is  because about 30.1 percent of the sample work less than 40 hours per week. We can estimate the standard deviation of  as . A  confidence interval is given by , then, a 68% confidence interval is , i.e., , i.e., (0.251, 0.351).  is the value that satisfies that there is an area of 0.16 above this and under the standard normal curve.The standard error for a proportion is √(pq/n), where q=1−p.

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

The answer is 40 chocolates in the box in total

Answer:

The responses to these question can be defined as follows:

Step-by-step explanation:

For point a:

[tex]\to P(1) = 0.73[/tex]

For point b:

[tex]\to P(2\ or\ 3) = P(2) + P(3)[/tex]

                    [tex]= 0.27 \times 0.73 + 0.27\times 0.27\times0.73\\\\=0.1971+0.1971\times 0.27\\\\=0.1971+0.053217\\\\=0.250317[/tex]

Answer:

we conclude that population mean is not 11.5

Step-by-step explanation:

The hypothesis :

H0 : μ = 11.5

H1 : μ ≠ 11.5

The test statistic :

(xbar - μ) ÷ (s/√(n))

Test statistic = (12 - 11.5) ÷ (2/√(16))

Test statistic = (0.5) ÷ (2 ÷ 4)

Test statistic = 0.5 / 0.5

Test statistic = 1

The Pvalue from test statistic value, df = n - 1 = 16 - 1 = 15

Pvalue = 0.333

Pvalue > α ; we fail to reject the null ; Hence, we conclude that population mean is not 11.5

Answer:

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set 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]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000.

This means that [tex]\mu = 192723, \sigma = 42000[/tex]

Sample of 75:

This means that [tex]n = 75, s = \frac{42000}{\sqrt{75}}[/tex]

What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009?

1 subtracted by the p-value of Z when X = 190000. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{190000 - 192723}{\frac{42000}{\sqrt{75}}}[/tex]

[tex]Z = -0.56[/tex]

[tex]Z = -0.56[/tex] has a p-value of 0.2877

1 - 0.2877 = 0.7123

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.

Answer:

C

Step-by-step explanation: just C-

Answer: Its not c

Step-by-step explanation: It is A

↦ [tex]\huge\underline{ \underline{Answer:-}}[/tex]

[tex]5x = 3x + 12 \\ 5x - 3x = 12 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Step-by-step explanation:

hope it is h helpful to you

Answer:

X<6 or X>24

Step-by-step explanation:

Answer:

Following are the response to the given choice.

Step-by-step explanation:

Please find the complete question in the attached file.

Subjective opinion = Question of opinion.

Therefore this requires only just opinion and we don't have to do any actual calculations.

Does this seem like a great number of girls, a little number of girls, or a decent number of girls to you but if 1,300 babies were born, 5 of whom were females?

This is a small number of beautiful gals, in my honest opinion. We anticipate boys and girls to be produced about the very same frequency, thus I expect some half of them to be females if there are 1 300 newborns. You should have roughly 650 girls if 50% of the infants are girls, but now we only have five. That appears to me to be considerably low. which is your own opinion.

Answer:

1. +30

2. +64

3. 0

4. -3

5. +24

6. +18

7. -48

8. -64

9. +21

10. -30

11. +12

12. 0

13. -4

14. +56

15. +2

Step-by-step explanation:

When multiplying integers:

two negatives = positive

two positives = positive

one negative x one positive = negative

So, if the signs are the same, the answer is positive.

If you have two different signs, the answer is negative.

You multiply the integers like normal.

Anything multiplied by zero = 0.

Anything multiplied by one = itself (just be careful of the sign).

Explanation:

It's most effective to use a contingency table because we have two variables here: 1) the responses, and 2) the party affiliation.

We can have the responses along the rows and the party affiliation along the columns, or vice versa.

See the example below. The values are completely random simply for the purpose of the example (and not drawn from any real life data source).

As per the given options, the appropriate for the displaying these data will be contingency table. Hence, option D is correct.

A pie chart is a visual depiction of information in the shape of a pie, where the pieces of the pie represent the magnitude of the data. To depict data as a pie chart, you need a list of quantitative variables as well as categorical variables.

As per the given information in the question,

A contingency table in statistics is a particular kind of matrix-style table that shows the frequency of the variables. They are extensively utilized in scientific, engineering, business intelligence, and survey research.

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Answer:

a) f(x,y) = - 1    minimum  at   P ( 0 ; -1 )

b) f (x,y) = 10  maximum at   P ( 3 , 1 ) and   f (x,y) = - 10 minimum at       Q ( - 3 , - 1 )

c)  Max  f ( x , y ) = 2   for points    P ( 1, 2 )  and T ( -1 , -2 )

Min  f ( x , y ) =  -2   for points   Q ( 1 , - 2 )  and R  ( -1 , 2 )

Step-by-step explanation:

A)  f(x,y) = x² - y²         subject to   x² + y² = 1      g(x,y) = x² + y²- 1

δf(x,y)/ δx  = 2*x                                                 δg(x,y)/ δx  =    2*x                      

δf(x,y)/ δy  = - 2*y                                                 δg(x,y)/ δy  =    2*y

δf(x,y)/ δx  = λ* δg(x,y)/ δx

2*x = λ*2*x

δf(x,y)/ δy  = λ* δg(x,y)/ δy

- 2*y = λ*2*y

Then, solving

2*x = λ*2*x           x = λ*x      λ = 1

- 2*y = λ*2*y         y = - 1

x² + y²- 1 = 0         x²  + ( -1)² - 1 = 0      x = 0    

Point  P ( 0 ; -1 )  ; then at that point

f(x,y) = x² - y²             f(x,y) = 0 - ( -1)²     f(x,y) = - 1    minimum

b)  f( x, y ) =  3*x  + y            g ( x , y )  = x² +  y²  = 10

  δf(x,y)/ δx  = 3                   δg(x,y)/ δx  =  2*x

 δf(x,y)/ δy   = 1                   δg(x,y)/ δy  =   2*y

δf(x,y)/ δx  =   λ * δg(x,y)/ δx      ⇒   3 = 2* λ *x    (1)

δf(x,y)/ δy   =  λ *  δg(x,y)/ δy     ⇒    1 = 2*λ * y    (2)

                                                           x² +  y²  - 10 = 0  (3)

Solving that system

From ec (1)     λ  =  3/2*x      From ec (2)     λ  = 1/2*y

Then    (3/2*x )  = 1/2*y          3*y  =  x

x²  +  y²  = 10     ⇒   9y²  + y²  = 10      10*y² = 10

y² = 1       y  ± 1       and    

y  =  1      x  = 3       P  ( 3 , 1  )       y  = - 1    x = -3    Q  ( - 3 , - 1 )

Value of  f( x , y )  at   P   f (x,y) = 3*x + y      f (x,y) =    3*(3) +1  

f (x,y) = 10  maximum at  P ( 3 , 1 )

Value of  f( x , y )  at  Q     f (x,y) = 3*x + y    f (x,y) =  3*(- 3) + ( - 1 )

f (x,y) = - 10 minimum at Q ( - 3 , - 1 )

c)  f( x, y ) =  xy                       g ( x , y )  =  4*x² + y² - 8

δf(x,y)/ δx  = y                         δg(x,y)/ δx  = 8*x

δf(x,y)/ δy = x                          δg(x,y)/ δy  =  2*y

δf(x,y)/ δx  =  λ * δg(x,y)/ δx   ⇒   y  =  λ *8*x    (1)

δf(x,y)/ δy =   λ * δg(x,y)/ δy   ⇒   x  =  λ *2*y    (2)

                                                      4*x² + y² - 8 = 0   (3)

Solving the system

From ec (1)  λ = y/8*x    and From ec (2)      λ = x/2*y        Then    y/8*x  =  x/2*y

2*y² = 8*x²       y² = 4*x²    

Plugging that value in ec (3)

4*x²  +  4*x² - 8 = 0

8*x² = 8     x² = 1        x ± 1      And y² = 4*x²

Then:

for x  = 1      y² =  4     y = ± 2

for x  = -1     y² =  4     y = ± 2

Then we get     P (  1 ; 2 )   Q  ( 1 ; - 2)

                          R ( - 1 ; 2 )  T  ( -1 ; -2)

Plugging that values in f( x , y ) = xy

P (  1 ; 2 )  f( x , y ) = 2            R ( - 1 ; 2 )  f( x , y ) = - 2

Q ( 1 ; - 2)  f( x , y ) = -2           T ( -1 ; -2 )  f( x , y ) = 2

Max  f ( x , y ) = 2   for points    P and T

Min  f ( x , y ) =  -2   for points   Q and R

Answer:

x=2pi/3 +2pi n, 4pi/3 +2pi n for all integar of n.

Step-by-step explanation:

Step-by-step explanation:

[tex]\dfrac{2x^2+x-6}{x+x-6} = \dfrac{(2x-3)(x+2)}{2(x-3)}[/tex]

Answer:

1.125 hours

Step-by-step explanation:

Given :

Ben's speed = 3 mi/hr

Time before Amanda starts = 1.5 hours

Amanda's speed = 7 mi/hr

Time before Amanda catches up with Ben

Recall :

Distance = speed * time

Distance already covered by Ben before Amanda starts :

(3 * 1.5) = 4.5

Hence, we can setup the equation :

Ben's distance = Amanda's distance

Let time taken = x

4.5 + 3x = 7x

4.5 = 7x - 3x

4.5 = 4x

x = 4.5 / 4

x = 1.125 hours

1.125 * 60 = 67. 5 minutes

Answer:

24 .30ms is the answer I think so if the answer is correct plz mark me as brainliest.

The papaya's speed just before it hits the water will be 24.24 m/s.

The rate at which objects moves is called speed. It is given by

[tex]s = \frac{d}{t}[/tex]

An object held above the ground has a potential energy related to the height at which it is held,

PE = mgh

If you drop the object, its potential energy will become the kinetic energy of motion:

KE = ½ mv²

½ mv² = mgh

v  = √(2gh)

v =  √(2*9.8*30)

v =  24.24 m/s

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Answer:

the x-intercepts are at

x = -3

x = 0

x = 1

Step-by-step explanation:

ask the points, where the functional value is 0.

2x³ + 4x² - 6x = 0

we see that every term contains an expression of x. so, we can simplify this

x × (2x² + 4x - 6) = 0

so, one solution is plainly visible : x=0

for the other solutions we need to solve the square equation

2x² + 4x - 6 = 0

or even simpler

x² + 2x - 3 = 0

the solution of a square equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a=1

b=2

c=-3

x = (-2 ± sqrt(2² - 4×1×-3))/(2×1) = (-2 ± sqrt(4 + 12))/2 =

= (-2 ± sqrt(16))/2 = (-2 ± 4)/2 = -1 ± 2

x1 = -1 + 2 = 1

x2 = -1 - 2 = -3

The line in the middle is half the length of the line on the outside. Multiply the middle line by 2 and set it equal to the outside line.

2(x-3) = x + 6

Simplify:

2x -6 p x + 6

Add 6 to both sides

2x = x + 12

Subtract x from both sides:

X = 12

The answer is B) 12

Answer:

A FORMULA is an expression that uses variables to state a rule.

Answer:

x = 4/3

Step-by-step explanation:

Answer:

y=1/2x+1/2

Step-by-step explanation:

In order to find the slope, you can use rise/run, in this case, the slope is 1/2 and the y-intercept is at (0, 0.5)