The cost of the apple is expressed as y = 12x + 6, where x is the number of apples. Find the cost of dozen apples.

Answer:

The function is exponential.

The function increases by a factor of 2.5 for each unit increase in x.

The domain of the function is all real numbers

The true statements are:

The function is given as:

[tex]\mathbf{y = 3(2.5)^x}[/tex]

An exponential function is represented as:

[tex]\mathbf{y = ab^x}[/tex]

Where: a represents the initial value, and b represents the rate

This means that:

[tex]\mathbf{y = 3(2.5)^x}[/tex] is an exponential function

By comparison:

[tex]\mathbf{b = 2.5}[/tex]

When b > 0, then the function represents an exponential growth

2.5 is greater than 0.

So, the function represents an exponential growth

Lastly, there is no restriction to the values of x.

So, the domain of the function is the set of all real numbers

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Answer:

No, it doesn't mean that we can say over 50% of all people in the U.S. do not support gay marriage.

Step-by-step explanation:

We are given that a telephone poll is conducted by contacting U.S. citizens via landlines about their view of gay marriage.

Suppose over 50% of those called do not support gay marriage.

Firstly, as we can see here that we have no information about the population and also how many people have been surveyed. This means that we can't say that this poll is a representative sample.

A representative sample is that which incorporates the characteristics of the whole population. As here the U.S. citizens have been contacted through landlines which means this poll does not include people who neither have landlines nor cell phones.

So, by no means, a telephone poll is a representative sample of the whole population of Us.

Hence, we can't say that over 50% of all people in the U.S. do not support gay marriage.

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Translate this sentence into an equation. The product of Holly's height and 3 is 39. Use the variable h to represent Holly's height.

Let holly's savings be h. If the  product of Holly's savings and 3 is 39, this can be represented mathematically as h*3 = 39

To get holly's savings "h', we will divide both sides of the equation by 3

h*3 = 39

h*3/ 3= 39/3

h = 13*3/ 3

h = 13 * 3/3

h = 13*1

h = 13

Holly's savings is 13 and the required equation is 3h =39

Answer:

a). x = 11

b). m∠DMC = 39°

c). m∠MAD = 66°

d). m∠ADM = 36°

e). m∠ADC = 18°

Step-by-step explanation:

a). In the figure attached,

m∠AMC = 3x + 6

and m∠DMC = 6x - 49

Since "in-center" of a triangle is a points where the bisectors of internal angles meet.

Therefore, MC is the angle bisector of angle AMD.

and m∠AMC ≅ m∠DMC

3x + 6 = 8x - 49

8x - 3x = 49 + 6

5x = 55

x = 11

b). m∠DMC = 8x - 49

                   = (8 × 11) - 49

                   = 88 - 49

                   = 39°

c). m∠MAD = 2(m∠DAC)

                   = 2(30)°

                   = 60°

d). Since, m∠AMD + m∠ADM + m∠MAD = 180°

    2(39)° + m∠ADM + 66° = 180°

    78° + m∠ADM + 66° = 180°

    m∠ADM = 180° - 144°

                   = 36°

e). m∠ADC = [tex]\frac{1}{2}(m\angle ADM)[/tex]

                   = [tex]\frac{1}{2}(36)[/tex]

                   = 18°

Answer:

Step-by-step explanation:

If I remember this correctly, if things/trials are independent then the result/outcome of one trial does not interfere or affect the outcome of other trials.

For example if you flip a coin 50 times. Each flip should be theoretically independent i.e. each head and tail should have 1/2 chance of showing up no matter what flip you make. It would not be independent if getting tails will give you heads next round for sure (it could happen by chance) but if one thing is causing another thing to happen it is not independent.  Which means the probability of a coin coming up heads does not depend in any way on previous coin flips. The chance of getting tails on the next coin flip should be 1/2 as well.

[tex]9+(-2)\\9-2\\=7[/tex]

[tex]-6+(-3)\\-6-3\\=-9[/tex]

[tex]4+(-9)\\4-9\\=-5[/tex]

Answer:

see below

Step-by-step explanation:

9 + -2 =

9 -2 = 7

-6 + -3

-6 - 3 =-9

4 + - 9

-9 +4 = -5

Answer:

x=52.5

Step-by-step explanation:

x+3x-30=180

4x-30=180

4x=180+30

4x=210

x=52.5

Answer:

50,000

Step-by-step explanation:

ten thousand  thousand  hundreds   tens ones

4                            7                 5            9       2

When rounding to the ten thousands, we look at the thousands place

If it is 5 or higher we round the ten thousands place up

7 is five or higher so we round the 4 up one place  4 becomes 5 and the rest becomes 0

5 0 0 0 0

Answer:

$50,000

Step-by-step explanation:

=> $47,592

While rounding off to the nearest thousand, we check the thousands place. If the digit in the thousands place is greater than 5, 1 will be added to the T. Th. place while if its less than 5, there will be no change and The digits except the ten thousands place will all become zero.

So,

=> $50,000

Answer:

16cm^3

Step-by-step explanation:

V=1/3BH

V=1/3 (4)(4)(3)

V=16cm^3

The volume of the solid right pyramid with the length of the base edge as 4 cm and the height of the pyramid as 3 cm is 16 cm³.

The amount of three-dimensional space enclosed by a closed surface is expressed as a scalar quantity called volume.

The volume of a pyramid is one-third of the product of the base area and its height. And as given that the length of the edge of the square base is 4 cm while the height is 3 cm. Therefore, the volume of the square right pyramid can be written as,

[tex]\rm \text{Volume of Square base pyramid} = \dfrac13 \times \text{(Area of square base)} \times height[/tex]

                                                  [tex]= \dfrac13 \times (4^2) \times 3\\\\= 16 \rm\ cm^3[/tex]

Hence, the volume of the solid right pyramid with the length of the base edge as 4 cm and the height of the pyramid as 3 cm is 16 cm³.

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Step-by-step explanation:

greater than 18 = 0.3

less than 10 = 0.444444

number greater than 18

The probability of spinning a number greater than 18 will be 0.3, and The probability of spinning a number less than 10 will be 0.44, and We would likely have more to spin a number greater than 18.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The probability of spinning a number greater than 18 will be:

⇒ 0.3

The probability of spinning a number less than 10 will be:

⇒ 4 / 9

Here favorable outcomes = 4 and the total number of outcomes = 9

Apply the division operation to get probability as a decimal form

⇒ 0.44

We would likely have more to spin a number greater than 18.

Hence, the probability of spinning a number greater than 18 will be 0.3, and the probability of spinning a number less than 10 will be 0.44, and We would likely have more to spin a number greater than 18.

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Answer:

[tex] 211600 = 225000 -k*6700[/tex]

[tex] k = \frac{225000-211600}{6700}= 2[/tex]

[tex] 238400 = 225000 +k*6700[/tex]

[tex] k = \frac{238400-225000}{6700}= 2[/tex]

So then the % expected would be:

[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]

So then the answer would be 75%

Step-by-step explanation:

For this case we have the following info given:

[tex] \mu = 225000[/tex] represent the true mean

[tex]\sigma =6700[/tex] represent the true deviation

And for this case we want to find the minimum percentage of sold homes between $211,600 and $238,400.

From the chebysev theorem we know that we have [tex]1 -\frac{1}{k^2}[/tex] % of values within [tex]\mu \pm k\sigma[/tex] if we use this formula and the limit given we have:

[tex] 211600 = 225000 -k*6700[/tex]

[tex] k = \frac{225000-211600}{6700}= 2[/tex]

[tex] 238400 = 225000 +k*6700[/tex]

[tex] k = \frac{238400-225000}{6700}= 2[/tex]

So then the % expected would be:

[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]

So then the answer would be 75%

Answer:

HJ > PK

Step-by-step explanation:

Notice that the side PL in one triangle has the same length as side GJ in the other, and side GH has the same size as side LK of the other triangle. Now what is different is the angle subtended between these sides in the case of the triangle on the lower left, the subtended angle is [tex]90^o[/tex] , which is larger angle than that subtended between equal sides on the other triangle ([tex]85^o[/tex])

Therefore, if the angle subtended by the equivalent sides in the triangle on the left is larger than the angle subtended on the right hand side triangle, then the sides associated with such angle aperture must keep the inequality. That is:

Since [tex]\angle\,G\,\,\,>\,\,\,\angle \,L[/tex], then   HJ > PK

Answer:

a)  y₂ (x) = e ⁵ˣ  

Complementary function

               [tex]y_{C} = C_{1} {e^{-5x} } + C_{2} {e^{5x} }[/tex]

b) particular integral

[tex]P.I = y_{p} = \frac{-4}{25}[/tex]

Step-by-step explanation:

step(i):-

Given differential equation y''-25y= 4

operator form

             ⇒    D²y - 25 y =4

            ⇒     (D² - 25) y =4

       This is the form of f(D)y = ∝(x)

where f(m) = D² - 25     and ∝(x) =4

The auxiliary equation A(m) =0

                         ⇒ m² - 25 =0

                          m² - 5²  =0

                      ⇒ (m+5)(m-5) =0

                     ⇒ m =-5 , 5

Complementary function

               [tex]y_{C} = C_{1} {e^{-5x} } + C_{2} {e^{5x} }[/tex]

This is form of

             [tex]y_{C} = C_{1} y_{1} (x) + C_{2} y_{2} (x)[/tex]

where y₁ (x) = e⁻⁵ˣ   and  y₂ (x) = e ⁵ˣ  

Step(ii):-

Particular integral:-

[tex]P.I = y_{p} = \frac{1}{f(D)} \alpha (x)[/tex]

[tex]P.I = y_{p} = \frac{1}{D^{2} -25} 4[/tex]

      =  [tex]= \frac{1}{D^{2} -25} 4e^{0x}[/tex]

put D = 0

The particular integral

[tex]y_{p} = \frac{1}{ -25} 4[/tex]

[tex]P.I = y_{p} = \frac{-4}{25}[/tex]

Conclusion:-

General solution of given differential equation

[tex]y = y_{C} +y_{P}[/tex]

[tex]y = C_{1} {e^{-5x} } + C_{2} {e^{5x} } -\frac{4}{25}[/tex]

Answer:

6 buildings

Step-by-step explanation:

At least 24 and fewer than 46 makes it 24-45

So,

24-45 => 6 buildings

Answer:

The one above is wrong the real answer is

A: y= -4/3x+120

Answer:

d

Step-by-step explanation:

hope this helps

Answer:

The length of the rectangle is 6.

Step-by-step explanation:

Given: The diagonal of a rectangle is 10 and the height is 8.

Please understand, that a diagonal, divides the rectangle into two tringles.

To find the length of the rectangle, you can use Pythagoras on one of the right sided triangles, because the length of the triangle, is also the length of the rectangle!

EXTRA:

If you know the special 3 4 5 triangle, a so called Pythagorean Triple, then you can "see" the simularity between the numbers.

Instead of 5, a diagonal of 10 is given (factor of 2 bigger).

Instead of 4, the height of 8 is given (factor of 2 bigger). By scaling the Pythagorean Triple 3 4 5 by a factor of 2, you get the numbers 6 8 10. Could it be, that the number we need to find, is six?

Try to verify, by calculating the missing number (which is the length of the rectangle we are looking for).

a² + b² = c²

a = length (and is unknown)

b = height = 8

c = hypothenusa/diagonal = 10

Substitute the numbers given:

a² + 8² = 10²

Subtract 8² left and right of the = sign.

a² +8² -8² = 10² - 8²

a² + 0 = 100 - 64

a² = 36

a = + - √36

a = + - 6

EXTRA:

You can ignore the -√36 = -6 part of the solution, because a length of -6 has no meaning here.

a = 6

So, the length of the triangle is 6 and thus, the length of the rectangle is also 6.

Answer:

[tex]50\%, \: 40\%, \: 10\%[/tex]

Step-by-step explanation:

[tex]150:120:30[/tex]

[tex]5:4:1[/tex]

[tex]\frac{100}{5+4+1}[/tex]

[tex]=\frac{100}{10}[/tex]

[tex]=10[/tex]

[tex]5 \times 10:4\times 10:1\times 10[/tex]

[tex]50:40:10[/tex]

Answer:

Cupcakes: 50%

Cookies: 40%

Cakes: 10%

Step-by-step explanation:

150 + 120 + 30 = 300 (there are 300 baked goods)

150 out of 300 = 50%

120 out of 300 = 40%

30 out of 300 = 10%

Okay, I really want to eat this.

Hope it helps!

Answer:

8p + 2s <= 150

Step-by-step explanation:

Let p = number of a pizza.

Let s = price of a bottle of soda.

The inequality is

8p + 2s <= 150

Answer:

  f^-1(x) = (4x +3)/(1 -x)

Step-by-step explanation:

Solve for y:

  f(y) = x

  (y -3)/(y +4) = x

  y -3 = xy +4x . . . . . . multiply by y+4

  y -xy = 4x +3 . . . . . . add 3-xy

  y(1 -x) = 4x +3 . . . . . factor out y

  y = (4x +3)/(1 -x) . . . divide by the coefficient of y

The inverse function is ...

  f^-1(x) = (4x +3)/(1 -x)

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{d\,arccos(x)}{dx} =-\frac{1}{\sqrt{1-x^2} }[/tex]

See the proof below

Step-by-step explanation:

if  [tex]y=arccos(x)[/tex], then :  [tex]cos(y)=cos(arccos(x))=x[/tex]

We can then apply the derivative to both sides of this last equation and remember to use the chain rule as we encounter the variable "y":

[tex]cos(y)=x\\\frac{d}{dx} cos(y)=\frac{d}{dx} x\\-sin(y)\,\frac{dy}{dx} =1\\\frac{dy}{dx} =-\frac{1}{sin(y)} \\\frac{dy}{dx} =-\frac{1}{\sqrt{1-cos^2(y)} }\\\frac{dy}{dx} =-\frac{1}{\sqrt{1-x^2} }\\\frac{d\,arccos(x)}{dx} =-\frac{1}{\sqrt{1-x^2} }[/tex]

Answer:

The value of the test statistic is t=1.12.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that the mean amount of time required to reach a customer service representative significantly differs between the two hotels.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]

The sample 1, of size n1=20 has a mean of 2.65 and a standard deviation of √2.952=1.72.

The sample 2, of size n2=20 has a mean of 2.01 and a standard deviation of √2.952=1.89.

The difference between sample means is Md=0.64.

[tex]M_d=M_1-M_2=2.65-2.01=0.64[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1.72^2+1.89^2}{20}}\\\\\\s_{M_d}=\sqrt{\dfrac{6.531}{20}}=\sqrt{0.327}=0.571[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.64-0}{0.571}=\dfrac{0.64}{0.571}=1.12[/tex]

The test statistics (t-statistic) value will be:

"1.12".

According to the question,

The null and alternative hypothesis will be:

[tex]H_0[/tex] : μ₁ - μ₂ = 0

[tex]H_a[/tex] : μ₁ - μ₂ [tex]\neq[/tex] 0

Mean = 2.65 and 1.01

Observations = n₁ = n₂ = 20

Now,

The difference between sample mean.

→ [tex]M_d[/tex] = M₁ - M₂

        = 2.65 - 2.01

        = 0.64

The estimated standard error will be:

→ [tex]s_M_d[/tex] = [tex]\sqrt{\frac{\sigma_1^2 + \sigma_2^2}{n} }[/tex]

By substituting the values,

         = [tex]\sqrt{\frac{(1.72)^2 + (1.89)^2}{20} }[/tex]

         = [tex]\sqrt{\frac{6.531}{20} }[/tex]

         = [tex]\sqrt{0.327}[/tex]

         = 0.571

hence,

The test statistic (t) be:

= [tex]\frac{M_d(\mu_1 -\mu_2)}{s_M_d}[/tex]

= [tex]\frac{0.64-0}{0.571}[/tex]

= [tex]\frac{0.64-0}{0.571}[/tex]

= 1.12

Thus the above approach is right.

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Answer:

83.29% probability that at least 2 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrives late, or it does not arrive late. The probability of a flight arriving late is independent of other flights. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

80 % of its flights arriving on time.

So 100 - 80 = 20% arrive late, which means that [tex]p = 0.2[/tex]

15 Southwest flights

This means that [tex]n = 15[/tex]

Find the probability that at least 2 flights arrive late.

Either less than two arrive late, or at least 2 do. The sum of the probabilities of these outcomes is 1. So

[tex]P(X < 2) + P(X \geq 2) = 1[/tex]

We want [tex]P(X \geq 2)[/tex]

Then

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{15,0}.(0.2)^{0}.(0.8)^{15} = 0.0352[/tex]

[tex]P(X = 1) = C_{15,1}.(0.2)^{1}.(0.8)^{14} = 0.1319[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0352 + 0.1319 = 0.1671[/tex]

Then

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1671 = 0.8329[/tex]

83.29% probability that at least 2 flights arrive late.

In this exercise we have to use the knowledge of ordinary equations to determine the linear equations, in this way we find that:

1) Linear

2) Non Linear

3) Linear

4) Non linear

So from the knowledge in topics of ordinary equations we find that:

1) [tex](1-x)y"-4xy'+5y=cosx\\= Second \ order\\= linear[/tex]

2)[tex]t^5 y^4 - t^3 y" + 6y =0 \\= Second \ order\\= non \ linear[/tex]

3) [tex](d^2Y/dx^2) = \sqrt{(1+(dy/dx)^2))}\\= Second \ order\\= Linear[/tex]

4) [tex](Sin\theta)y"'- (cos\theta)y' =2\\= Third \ order\\= Non \ linear[/tex]

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Answer:

1 foot squared

Step-by-step explanation:

Er... a square foot is 1 foot squared

Answer:

centimeters

Step-by-step explanation:

Answer:

Let's solve your equation step-by-step.

[tex]x^7+64x^4=0[/tex]

Step 1: Factor left side of equation.

[tex]x^4(x+4)(x^2-4x+16)=0[/tex]

Step 2: Set factors equal to 0.

[tex]x^4=0[/tex]  or  [tex]x+4=0[/tex]  or  [tex]x^2-4x+16=0[/tex] 

[tex]x^4=0[/tex]  or  [tex]x=0[/tex]  

Answer:

I hope this help you :)

Answer:

[tex] y =y_o e^{kt}[/tex]

Where [tex] y_o = 2[/tex] the relative growth is [tex] k =0.7944[/tex] and t represent the number of days.

For this case we can to find the population after the day 6 so then we need to replace t =6 in our model and we got:

[tex] y(6) =2 e^{0.7944*6} = 234.99 \approx 235[/tex]

And for this case we can conclude that the population of protozoa for the 6 day would be approximately 235

Step-by-step explanation:

We can assume that the following model can be used:

[tex] y =y_o e^{kt}[/tex]

Where [tex] y_o = 2[/tex] the relative growth is [tex] k =0.7944[/tex] and t represent the number of days.

For this case we can to find the population after the day 6 so then we need to replace t =6 in our model and we got:

[tex] y(6) =2 e^{0.7944*6} = 234.99 \approx 235[/tex]

And for this case we can conclude that the population of protozoa for the 6 day would be approximately 235

Answer:

24 picked 2 or more

Step-by-step explanation:

At least 2 means 2 or more

Add up all the x's

2: 7

3: 9

4: 8

total: 24