4. Candice leaves on a trip driving at 25 miles per hour. Four hours later, her sister
Liz starts from the same location driving at 50 miles per hour. How long after Liz
leaves home will she catch up to Candice?
A 9 hours
B 4 hours
C 8 hours
D 7 hours

Answer:

a. December 16

Step-by-step explanation:

18 June + 180 days = 15 December

Since 2 options given,

a. December 16 is the answer

Answer: 6 1/6

Step-by-step explanation:

6 can go into 37 6 times

6x6=36

with 1 left over

The fraction 37/6 can be changed to the mixed number​ as 6 1/6 if the fraction is 37/6.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The fraction is:

= 37/6

We can write the above number as:

= (36 + 1)/6

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

= 36/6 + 1/6

= 6 + 1/6

Or

= 6 1/6 (mixed fraction)

Thus, the fraction 37/6 can be changed to the mixed number​ as 6 1/6 if the fraction is 37/6.

Learn more about the fraction here:

brainly.com/question/1301963

#SPJ2

Answer:

Step-by-step explanation:

Consider the function of the rate of flow of money in dollar per year is

[tex]f(t)= 400e^{0.03t}[/tex]

The objective is to find the present value of this income over 10 years period an assume an annual interest rate of 8% compounded continuously.

Given that,

[tex]f(t)= 400e^{0.03t}[/tex]

r = 0.08, t = 10

if f(t) is the rate of  continuously money flow at an interest rate r to T year,

the present value is,

[tex]P= \int\limits^T_0 {f}(t)e^{-rt} \, dt[/tex]

Now input the values to get

[tex]p=\int\limits^{10}_0 400e^{0.03t}*e^{-0.08t} dt[/tex]

[tex]=400\int\limits^{10}_0 e^{0.03t}*^{-0.08t} dt[/tex]

[tex]= 400\int\limits^{10}_0 e^{-0.05t} dt[/tex]

[tex]=400(-\frac{e^{-0.05t}}{0.05} )|_0^1^0[/tex]

[tex]=-\frac{400}{0.05} (e^{-0.05*10}-e^{-0.05*0})\\\\=-\frac{400}{0.05} (e^{-0.5}-e^{*0})\\\\=3147.75[/tex]

Answer:

C.

Step-by-step explanation:

Hello!

Given the variable:

X: childhood asthma prevalence

With mean μ= 2.22%

and standard deviation σ= 1.39%

You have to calculate the probability of the sample average of childhood asthma prevalence in a sample of n= 30 cities is greater than 2.5%

We don't know the distribution of the variable, but remember that thanks to the central limit theorem, since the n ≥ 30, we can approximate the sampling distribution to normal:

X[bar]≈N(μ;σ²/n)

And use the standard normal distribution to calculate the asked probability:

P(X[bar]>2.5)= 1 - P(X≤2.5)

Calculate the Z value for the given X[bar] value:

[tex]Z= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } } = \frac{2.5-2.22}{\frac{1.39}{\sqrt{30} } }= 1.10[/tex]

Using the Z-tables you have to look for the value of

P(Z≤1.10)= 0.86433

1 - 0.86433= 0.13567

Then P(X[bar]>2.5)= 1 - P(X≤2.5)= 1 - P(Z≤1.10)= 1 - 0.86433= 0.13567

13.567% of the 30 cities will have a mean childhood asthma prevalence greater than 2.5%

I hope this helps!

[tex]answer = (3x + 1)\\ solution \\ {9x}^{2} + 6x + 1 \\ = {9x}^{2} + (3 + 3)x + 1 \\ = {9x}^{2} + 3x + 3x + 1 \\ = 3x(3x + 1) + 1(3x + 1) \\ = (3x + 1)(3x + 1) \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.  

Minimum cost=2046.16 cents      

Step-by-step explanation:

Given that a rectangular box with a volume of 684 ft³.

The base and the top of the rectangular box is square in shape

Let the length and width of the rectangular box be x.

[since the base is square in shape,  length=width]

and the height of the rectangular box be h.

The volume of rectangular box is = Length ×width × height

                                                      =(x²h) ft³

[tex]x^2h=684\Rightarrow h=\frac{684}{x^2}[/tex]  (1)

The area of the base and top of rectangular box is = x² ft²

The surface area of the sides= 2(length+width) height

                                               =2(x+x)h

                                               =4xh ft²

The total cost to construct the rectangular box is

=[(x²×20)+(x²×15)+(4xh×1.5)] cents  

=(20x²+15x²+6xh) cents

=(25x²+6xh) cents

Total cost= C(x).

C(x) is in cents.

∴C(x)=25x²+6xh

Putting [tex]h=\frac{684}{x^2}[/tex]

[tex]C(x)=25x^2+6x\times\frac{684}{x^2} \Rightarrow C(x)=25x^2+\frac{4104}{x}[/tex]

Differentiating with respect to x

[tex]C'(x)=50x-\frac{4104}{x^2}[/tex]

To find minimum cost, we set C'(x)=0

[tex]\therefore50x-\frac{4104}{x^2}=0\\\Rightarrow50x=\frac{4104}{x^2}\\\Rightarrow x^3=\frac{4104}{50}\Rightarrow x\approx 4.345[/tex] ft.

Putting the value x in equation (1) we get

[tex]h=\frac{684}{(4.345)^2}[/tex]

 ≈36.23 ft.

The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.  

Minimum cost C(x)=[25(4.345)²+10(4.345)(36.23)] cents

                               =2046.16 cents      

Answer:

(a)[tex]x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3[/tex]

(b) 12

(c)[tex]2\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]G$iven A=\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right][/tex]

We are to compute the quadratic form [tex]x^TAx[/tex] for A.

Part A

[tex]x=\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right][/tex]

[tex]x^TAx = \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right][/tex]

[tex]= \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3x_1+2x_2+0x_3\\2x_1+2x_2+1x_3\\0x_1+1x_2+0x_3\end{array}\right][/tex]

[tex]= x_1(3x_1+2x_2+0x_3)+x_2(2x_1+2x_2+1x_3)+x_3(0x_1+1x_2+0x_3)\\= x_1(3x_1+2x_2)+x_2(2x_1+2x_2+x_3)+x_3(x_2)[/tex]

[tex]= 3x_1^2+2x_1x_2+2x_1x_2+2x_2^2+x_2x_3+x_2x_3\\\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3[/tex]

Part B

[tex]x=\left[\begin{array}{ccc}-2\\-1\\5\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(-2)^2+4(-2)(-1)+2(-1)^2+2(-1)(5)\\=3*4+4*2+2-10\\=12+8+2-10\\=12[/tex]

Part C

[tex]x=\left[\begin{array}{ccc}\frac{1}{2}\\\frac{1}{2}\\\frac{1}{2}\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(\frac{1}{2})^2+4(\frac{1}{2})(\frac{1}{2})+2(\frac{1}{2})^2+2(\frac{1}{2})(\frac{1}{2})\\\\=\frac{3}{4}+1+ \frac{1}{2}+\frac{1}{2}\\\\=2\frac{3}{4}[/tex]

Answer:

A 98% confidence interval for the mean age is:

= ( 13.78, 19.10) months

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 16.44 months

Standard deviation r = 9.47 months

Number of samples n = 69

Confidence interval = 98%

z(at 98% confidence) = 2.33

Substituting the values we have;

16.44+/-2.33(9.47/√69)

16.44+/-2.33(1.140054028722)

16.44+/-2.656325886922

16.44+/-2.66

= ( 13.78, 19.10) months

Therefore, A 98% confidence interval for the mean age is:

= ( 13.78, 19.10) months

Answer:

Systematic Sampling

Step-by-step explanation:

Answer:

The expected revenue is $984.6.

Step-by-step explanation:

The tourist operator sells 21 non-refundable tickets, as the tourist may not show up.

The tourist have a probability of 0.02 of not showing up, independent of each other.

The income is the selling of the 21 tickets at $50 each.

[tex]I=21*50=1,050[/tex]

The only cost considered in this problem is the refund if a tourist show up and a seat is not available.

This only happens when the 21 tourists show up. If each tourist has a probability of 0.02 of not showing up, they have a probability of 0.98 of showing up.

For the event that the 21 tourists show up, we have the probability:

[tex]P=0.98^{21}\approx0.654[/tex]

For each of this event, the tour operator has to pay $100, so the expected revenue of the tour operator is:

[tex]E(R)=I-E(C)=1,050-0.654\cdot 100=1,050-65.4=984.6[/tex]

Step-by-step explanation:

We have [tex]\mathrm{dx} / \mathrm{dt}=0.1 \mathrm{ft} / \mathrm{sec},[/tex] and we want

dy/dt.

[tex]x[/tex] and [tex]y[/tex] are related by the Pythagorean Theorem [tex]x^{2}+y^{2}=(13 f t)^{2}[/tex]

Differentiate both sides of this equation with respect to [tex]t[/tex] to get [tex]2 x \frac{d x}{d t}+2 y \frac{d y}{d t}=0[/tex]

[tex]\frac{d y}{d t}=-\frac{x}{y} \frac{d x}{d t}[/tex]

When [tex]x=12 \mathrm{ft},[/tex]  

we have,  

[tex]y=\sqrt{(13 \mathrm{ft})^{2}-(12 \mathrm{ft})^{2}}=5 \mathrm{ft}[/tex]

therefore

[tex]\frac{d y}{d t}=-\frac{12f t}{5 f t} \cdot \frac{1 f}{\sec }=-\frac{12}{5} \frac{f t}{\sec }[/tex]

Answer:

[tex]z=\frac{0.480 -0.42}{\sqrt{\frac{0.42(1-0.42)}{1045}}}=3.930[/tex]  

The p value for this case would be given by:

[tex]p_v =P(z>3.930)=0.0000443[/tex]  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis so then we can conclude that the true proportion is significantly higher than 0.42

Step-by-step explanation:

Information given

n=1045 represent the random sample selected

X=502 represent the college graduates with a mentor

[tex]\hat p=\frac{502}{1045}=0.480[/tex] estimated proportion of college graduates with a mentor

[tex]p_o=0.42[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the true proportion is higher than 0.42, the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.42[/tex]  

Alternative hypothesis:[tex]p > 0.42[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info we got:

[tex]z=\frac{0.480 -0.42}{\sqrt{\frac{0.42(1-0.42)}{1045}}}=3.930[/tex]  

The p value for this case would be given by:

[tex]p_v =P(z>3.930)=0.0000443[/tex]  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis so then we can conclude that the true proportion is significantly higher than 0.42

Answer:

Y=150

Step-by-step explanation:

Just apply the proportionality rulw and solve for k. Then substitute the value of k into the equation.

Answer:

90

Step-by-step explanation:

Let the constant of proportionality be K

So that;

Y= K(x+2)^2

This means

For two corresponding points (x1,y1) and (x2,y2) we have;

Y1/(x1+2)^2= Y2/(x2+2)^2

If we consider x=8 y=250 as point (x1,y1) and y when x=4 as (x2,y2) we have ;

250/(8+2)^2 =y/(4+2)^2

250/(10)^2 = y/(6)^2

250/100 = y/36

250/100 × 36 = y

90= y

y=90

Answer:

28

Step-by-step explanation:

[tex]k(x) = 5x -6\\\therefore k(4) = 5\times 4 -6\\\therefore k(4) = 20 -6\\\therefore k(4) = 14\\\\\because (k+k)(4) = k(4) + k(4)\\\therefore (k+k)(4)= 14+14\\\huge\red{\boxed{\therefore (k+k)(4) = 28}}[/tex]

In this case, the complement would be selecting a number less than or equal to 7; the probability of this occurring is [tex]\boxed{\frac{7}{10}}.[/tex]

Answer:

it is 3/10

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

Based on the following information:

- There are 150 dog lovers

- There are 120 cat lovers

So:

The null hypothesis:

H, there are an equal number of dog lovers and cat lovers, so the expected frequency in each cell will be the same and that is:

f = (150 + 120) / 2

f = 270/2 = 135

then the first option of 135 is correct

Answer:

n = 66 (to the nearest whole number)

66 randomly selected players must be surveyed

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-M.E

M.E = zr/√n

Making n the subject of formula;

n = (zr/M.E)^2 ........1

Given that;

Mean = x

Standard deviation r = 2.7 inches

Number of samples = n

Confidence interval = 95%

z(at 95% confidence) = 1.96

Margin of error M.E = 0.65 inches

Substituting the given values into equation 1;

n = (zr/M.E)^2

n = (1.96×2.7/0.65)^2

n = 66.28464852071

n = 66 (to the nearest whole number)

66 randomly selected players must be surveyed

Answer:

Horizontal shift to the RIGHT of one unit

Step-by-step explanation:

When looking at a square root equation, the transformation form is:

[tex]f(x) = a\sqrt{b(x-h)} +k[/tex]

'h' represents a horizontal shift of the graph. Therefore, in this instance:

[tex]f(x) = \sqrt{x-1}[/tex]

This means that there is a horizontal shift to the RIGHT of one unit.

Answer:

28

Step-by-step explanation:

10=x 4=y

P=2(x+y)

P=2(10+4)

P=2(14)

P=28

Answer:

B. n=36, p=0.98, x=12

Step-by-step explanation:

98% of bottles have the correct amount.

The probability is equal to 0.98

That is p = 0.98

A bottle of water is supposed to have 12 ounces.

That is the expected value is 12

X = 12

36 bottles has all bottles properly filled

The possible sample space is 36

N = 36

Answer:

[tex] x = \frac{12 \pm \sqrt{(-12)^2 -4(5)(-7)}}{2(5)}[/tex]

And we got for the solution:

[tex] x_1= 2.885 , x_2 = -0.485[/tex]

And the value sof y are using the function y =2x-3:

[tex] y_1=2.77, y_2=-3.97[/tex]

Step-by-step explanation:

For this case we have this function given:

[tex] y = 2x-3[/tex]  (1)

And the circle with center the origin and radius 4 is given by;

[tex] x^2 +y^2 = 16[/tex]  (2)

We can solve fro y from the last equation and we got:

[tex] y = \pm \sqrt{16-x^2}[/tex]   (3)

Now we can set equal equations (3) and (1) and we got:

[tex] 2x-3 = \sqrt{16-x^2}[/tex]

[tex] (2x-3)^2=16-x^2[/tex]

[tex] 4x^2 -12x +9 = 16-x^2[/tex]

[tex] 5x^2 -12x -7=0[/tex]

And using the quadratic equation we got:

[tex] x = \frac{12 \pm \sqrt{(-12)^2 -4(5)(-7)}}{2(5)}[/tex]

And we got for the solution:

[tex] x_1= 2.885 , x_2 = -0.485[/tex]

And the value sof y are using the function y =2x-3:

[tex] y_1=2.77, y_2=-3.97[/tex]

Answer:

A) points at which paths intersect : (1,1,1) ; (2,4,8)

B) DNE

Step-by-step explanation:

A) To find the points in which the particle paths intersect, it is necessary to find the values of t for which the three components of both vectors are equal:

[tex]t_1=1+2t_2\\\\t_1^2=1+6t_2\\\\t_1^3=1+14t_2[/tex]

you replace t1 from the first equation in the second equation:

[tex](1+2t_2)^2=1+6t_2\\\\1+4t_2+4t_2^2=1+6t_2\\\\4t_2^2-2t_2=0\\\\t_2(2t_2-1)=0\\\\t_2=0\\\\t_2=\frac{1}{2}[/tex]

Then, for t2 = 0 and t2=1/2 you obtain for t1:

[tex]t_1=1+2(0)=1\\\\t_1=1+2(\frac{1}{2})=2[/tex]

Hence, for t1=1 and t2=0 the paths intersect. Furthermore, for t1=2 and t2=1/2 the paths also intersect.

The points at which the paths  intersect are:

[tex]r_1(1)=(1,1,1)=r_2(0)=(1,1,1)\\\\r_1(2)=(2,4,8)=r_2(\frac{1}{2})=(2,4,8)[/tex]

B) You have the following two trajectories of two independent particles:

[tex]r_1(t)=(t,t^2,t^3)\\\\r_2(t)=(1+2t,1+6t,1+14t)[/tex]

To find the time in which the particles collide, it is necessary that both particles are in the same position on the same time. That is, each component of the vectors must coincide:

[tex]t=1+2t\\\\t^2=1+6t\\\\t^3=1+14t[/tex]

From the first equation you have:

[tex]t=1+2t\\\\t=-1[/tex]

This values does not have a physical meaning, then, the particle do not collide

answer: DNE

Answer:

.

Step-by-step explanation:

Answer:

A : We keep the middle 97% of values by chopping off 1.5% from each tail.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.97}{2} = 0.015[/tex]

This means that for a 97% confidence interval, 1.5% of each tail is removed, while the middle 97% of values are kept.

So the corect answer is:

A : We keep the middle 97% of values by chopping off 1.5% from each tail.

Answer:

The 99% confidence interval for the population mean is between 10.12 minutes and 13.58 minutes.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575*\frac{3}{\sqrt{20}} = 1.73[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 11.85 - 1.73 = 10.12 minutes

The upper end of the interval is the sample mean added to M. So it is 11.85 + 1.73 = 13.58 minutes

The 99% confidence interval for the population mean is between 10.12 minutes and 13.58 minutes.

Theoretical probability formula: Favorable Outcomes/All Possible Outcomes

So let's find the theoretical probability for each option.

"Not picking a square"

So, there are 2 squares out of the 8 total shapes (2 circles + 4 triangles + 2 squares) So do 8-2=6... This is subtracting the number of squares out. So we are now left with 6/8.. Reduce the fraction: GCF is 2, so 6/8 simplifies to 3/4. So, "Not picking a square" is an option!

"Picking a square"

Okay so there are 2 squares (favorable outcome) out of 8 shapes in total (all possible outcomes) so the fraction is 2/8. Now simplify: GCF = 2, so 2/8 = 1/4. "Picking a square" is NOT an option

"Picking a triangle"

There are 4 triangles out of 8 shapes, so the fraction is 4/8 which = 1/2. The theoretical probability of picking a triangle is 1/2 and thus NOT an option.

"Picking a shape that has only straight edges"

So this basically means every shape that's not a circle. So, there are 4 triangles + 2 squares = 6 total shapes with straight edges. So there are 6 shapes with straight edges out of 8 total shapes: 6/8 reduces to 3/4. "Picking a shape that has only straight edges" IS an option! :D

LASTLY!

"Not picking a circle"

There are only 2 circles out of 8 total shapes, so 8-2=6 so the fraction is 6/8. This reduces to 3/4. "Not picking a circle" Is an option!

CORRECT ANSWERS:

Not picking a square

Picking a shape that has only straight edges

Not picking a circle

Have a good day!

Answer:

A, D, and E

Step-by-step explanation:

got it right on edge

Answer:

4y

Step-by-step explanation:

y - -3y

Subtracting a negative is like adding

y+3y

Combine like terms

4y

Answer:

[tex]4y[/tex]

Step-by-step explanation:

[tex]y - ( - 3y) \\ y + 3y \\ = 4y[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

846^% and then to rond it is 850^%

Step-by-step explanation:

e radius of a 10” pizza is 5”. Using A= pi2, what is the area of the 10” pizza? (Round to the nearest tenth)

Answer:

  76.9 million people per year

Step-by-step explanation:

The increase was 3,000 million people in 39 years, so the number per year was ...

  3000/39 ≈ 76.9 . . . . million people per year