line a passes through (0,3) & (-4,8) line b passes through (0,5) & (5,9) lines a & b are?

Answer:

  1/3

Step-by-step explanation:

The ratio is undefined at x=0, so we presume that's where we're interested in the limit. Both numerator and denominator are zero at x=0, so L'Hôpital's rule applies. According to that rule, we replace numerator and denominator with their respective derivatives.

  [tex]\displaystyle\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\lim\limits_{x\to 0}\dfrac{\tan'{(4x)}}{4\tan'{(3x)}}=\lim\limits_{x\to 0}\dfrac{4\sec{(4x)^2}}{12\sec{(3x)^2}}=\dfrac{4}{12}\\\\\boxed{\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\dfrac{1}{3}}[/tex]

Answer:

3 1/3

Step-by-step explanation:

8-5=3=3 1/3.

hope u understand

Answer:

(0.5, 2)

Step-by-step explanation:

Since the y coordinates are the same, the distance is between the x values

4 - -3

4+3 = 7

The distance is 7

1/2 the distance would be the center

7/2 = 3.5

Add this to the left coordinate

The x coordinate of the center is -3 + 3.5 = .5

The y coordinate is 2

Answer:

60.85% probability that the sample mean is between $1.4 million and $1.5 million per year

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 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.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question, we have that:

In millions of dollars.

[tex]\mu = 1.47, \sigma = 0.3, n = 30, s = \frac{0.3}{\sqrt{30}} = 0.0548[/tex]

What is the probability that the sample mean is between $1.4 million and $1.5 million per year?

This is the pvalue of Z when X = 1.5 subtracted by the pvalue of Z when X = 1.4. So

X = 1.5

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

[tex]Z = \frac{1.5 - 1.47}{0.0548}[/tex]

[tex]Z = 0.55[/tex]

[tex]Z = 0.55[/tex] has a pvalue of 0.7088

X = 1.4

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

[tex]Z = \frac{1.4 - 1.47}{0.0548}[/tex]

[tex]Z = -1.28[/tex]

[tex]Z = -1.28[/tex] has a pvalue of 0.1003

0.7088 - 0.1003 = 0.6085

60.85% probability that the sample mean is between $1.4 million and $1.5 million per year

Answer:

[tex] z= \frac{1.4-1.47}{\frac{0.3}{\sqrt{30}}}= -1.278[/tex]

[tex] z= \frac{1.5-1.47}{\frac{0.3}{\sqrt{30}}}= 0.548[/tex]

And we can find the probability with this difference:

[tex] P(-1.278<z<0.548) = P(z<0.548) -P(z<-1.278) =0.708-0.101= 0.607[/tex]

So then the probability that the sample mean is between $1.4 million and $1.5 million per year is 0.607

Step-by-step explanation:

For this case we have the following info given:

[tex] \mu = 1.47[/tex] the true mean for the problem

n =30 represent the sample size

[tex] \sigma = 0.3 millions[/tex] represent the population deviation

And we want to find this probability

[tex] P(1.4< \bar X <1.5)[/tex]

And we can use the z score given by:

[tex] z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z scores for the limits we got:

[tex] z= \frac{1.4-1.47}{\frac{0.3}{\sqrt{30}}}= -1.278[/tex]

[tex] z= \frac{1.5-1.47}{\frac{0.3}{\sqrt{30}}}= 0.548[/tex]

And we can find the probability with this difference:

[tex] P(-1.278<z<0.548) = P(z<0.548) -P(z<-1.278) =0.708-0.101= 0.607[/tex]

So then the probability that the sample mean is between $1.4 million and $1.5 million per year is 0.607

Answer:

38.76% probability that between 13 and 17 of these young adults lived with their parents

Step-by-step explanation:

I am going to use the normal approxiation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]p = 0.142, n = 125[/tex]

So

[tex]\mu = E(X) = np = 125*0.142 = 17.75[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{125*0.142*0.858} = 3.9025[/tex]

What is the probability that between 13 and 17 of these young adults lived with their parents?

Using continuity correction, this is [tex]P(13 - 0.5 \leq X \leq 17 + 0.5) = P(12.5 \leq 17.5)[/tex], which is the pvalue of Z when X = 17.5 subtracted by the pvalue of Z when X = 12.5. So

X = 17.5

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

[tex]Z = \frac{17.5 - 17.75}{3.9025}[/tex]

[tex]Z = -0.06[/tex]

[tex]Z = -0.06[/tex] has a pvalue of 0.4761

X = 12.5

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

[tex]Z = \frac{12.5 - 17.75}{3.9025}[/tex]

[tex]Z = -1.35[/tex]

[tex]Z = -1.35[/tex] has a pvalue of 0.0885

0.4761 - 0.0885 = 0.3876

38.76% probability that between 13 and 17 of these young adults lived with their parents

Answer:

h(x-11)=-5

Step-by-step explanation:

just put the equetion from the top

h(x-11)=-5

They aren't independent since the probability uses all the cards in the deck

So at the first deal we have the chance of 26/52 of getting a red card, at the second deal we have the chance of a 25/51 of getting another red card, so they aren't independent

Answer:

1234567891011121314151617181920

Answer:

Isolate the variable using inverse operations.

You would divide each side by 52.

Answer:

A) periodic rate

Step-by-step explanation:

Because a percentage that is charged or added to the credit card we assume that it is an interest rate, they also tell us that it is charged every month, that is, it has a known collection frequency, which means that it is Newspaper.

therefore, the answer in this case is A) periodic rate since it complies with the premise of the statement

Answer:

105 cm ^ 2 / s

Step-by-step explanation:

We have that the area of a rectangle is given by the following equation:

A = l * w

being the length and w the width, if we derive with respect to time we have:

dA / dt = dl / dt * w + dw / dt * l

We all know these data, l = 15; w = 12; dl / dt = 5; dw / dt = 3, replacing we have:

dA / dt = 5 * 12 + 3 * 15

dA / dt = 105

Which means that the area of the rectangle increases by 105 cm ^ 2 / s

Answer:

The 90% confidence interval for the difference between means is (-161.18, 205.18).

Step-by-step explanation:

Sample mean and standard deviation for Region I:

[tex]M=\dfrac{1}{12}\sum_{i=1}^{12}(438+1013+1127+737+...+1075+500+340)\\\\\\ M=\dfrac{8424}{12}=702[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{12}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{11}\cdot [(438-(702))^2+(1013-(702))^2+...+(500-(702))^2+(340-(702))^2]}\\\\\\[/tex]

[tex]s=\sqrt{\dfrac{1}{11}\cdot [(69696)+(96721)+...+(131044)]}\\\\\\s=\sqrt{\dfrac{1174834}{11}}=\sqrt{106803.1}\\\\\\s=326.8[/tex]

Sample mean and standard deviation for Region II:

[tex]M=\dfrac{1}{15}\sum_{i=1}^{15}(778+464+563+...+479+710+389+826)\\\\\\ M=\dfrac{10204}{15}=680[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{15}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{14}\cdot [(778-(680))^2+(464-(680))^2+...+(389-(680))^2+(826-(680))^2]}\\\\\\[/tex]

[tex]s=\sqrt{\dfrac{1}{14}\cdot [(9551.804)+(46771.271)+...+(84836.27)+(21238.2)]}\\\\\\ s=\sqrt{\dfrac{545975.7}{14}}=\sqrt{38998}\\\\\\s=197.5[/tex]

Now, we have to calculate a 90% confidence level for the difference of means.

The degrees of freedom are:

[tex]df=n1+n2-2=12+15-2=25[/tex]

The critical value for 25 degrees of freedom and a confidence level of 90% is t=1.708

The difference between sample means is Md=22.

[tex]M_d=M_1-M_2=702-680=22[/tex]

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

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{326.8^2}{12}+\dfrac{197.5^2}{15}}\\\\\\s_{M_d}=\sqrt{8899.853+2600.417}=\sqrt{11500.27}=107.24[/tex]

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_{M_d}=1.708 \cdot 107.24=183.18[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = 22-183.18=-161.18\\\\UL=M_d+t \cdot s_{M_d} = 22+183.18=205.18[/tex]

The 90% confidence interval for the difference between means is (-161.18, 205.18).

Answer:

The probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.

Step-by-step explanation:

We have a cube, with the faces painted black, that each side is divided in 5, so we end up with 125 cubes.

We have to calculate the probability that a randomly selected cube is rolled and the face on the top is black.

This probability is equal to the proportion of black area in the total area of the cube.

We can define the side of the original cube as A=5a, being a the side of the small cubes.

The area that is painted black is equal to the sum of 6 squares of side A. In terms of a, that is:

[tex]S_b=6\cdot A^2=6\cdot(5a)^2=6\cdot25a^2=150a^2[/tex]

The total area of the 125 small cubes is:

[tex]S=125(6a^2)=750a^2[/tex]

Then, the ratio of black surface to the total surface is:

[tex]s_b/s=(150a^2)/(750a^2)=0.2[/tex]

Then, we can conclude that the probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.

Answer:

Step-by-step explanation:

9x + 2y = 24  (A)

y = 6x + 19 ------ > y - 6x = 19 * (-2) -------> -2y + 6x = -38 (B)

(A) + (B)

15x = -14

x = -14/15

y = 6 * (-14/15) + 19 = -28/5 + 19 = 67/5

Answer:

A. 9x + 2y = 24  

Answer:

hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to

Answer:  v = 5v + 4u + 1.5sin(3t),

Step-by-step explanation:

u" - 5u' - 4u = 1.5sin(3t)        where u'(1) = 2.5   u(1) = 1

v represents the "velocity function"   i.e   v = u'(t)

As v = u'(t)

u' = v

since u' = v

v' = u"

v'  = 5u' + 4u + 1.5sin(3t)   ( given that u" - 5u' - 4u = 1.5sin(3t) )

    = 5v + 4u + 1.5sin(3t)  ( noting that v = u' )

so v' = 5v + 4u + 1.5sin(3t)

d/dt [tex]\left[\begin{array}{ccc}u&\\v&\\\end{array}\right][/tex]= [tex]\left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}u&\\v&\\\end{array}\right][/tex] + [tex]\left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right][/tex]

Given that u(1) = 1 and u'(1) = 2.5

since v = u'

v(1) = 2.5

note: the initial value for the vector valued function is given as

[tex]\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right][/tex]  = [tex]\left[\begin{array}{ccc}1\\2.5\\\end{array}\right][/tex]

Answer:

210 in²

Step-by-step explanation:

6*2.5+6*6*2+(8+6)*2.5+10*2.5+1/2*6*8*2+6*2.5= 210 in²

Answer:

x = 18°

y = 6

Step-by-step explanation:

in a parallelogram:

Any two opposite sides are congruent

and any two opposites angles are congruent:

then

y + 4 = 10

and 3x = 54

then

y = 6

and x =  54/3 = 18

Answer:

x= 18 , y = 6

Step-by-step explanation:

A parallelogram has two opposite sides equal and parallel hence;

y + 4 = 10

y = 10 -4 = 6

Similarly

54 = 3x( opposite angle of a parallelogram are the same because it's congruent)

3x = 54

x = 54/ 3 = 18°

To be congruent means to have the same shape, size and form but can be flipped.

Answer:

both fireworks will explode 4.5 seconds after  Firework B launches

Step-by-step explanation:

Given;

speed of firework A, [tex]V_A[/tex]= 360 ft/s

speed of firework B, [tex]V_B[/tex] = 340 ft/s

If the two fireworks explodes at the same height, then the height attained by the two fireworks are equal.

let the distance traveled by each firework before explosion = d

Distance = speed x time

Distance A = Distance B

speed A x time = speed B x time

let the time both fireworks explodes after Firework B launches = t

([tex]V_A[/tex]) t = ([tex]V_B[/tex] ) t

360t = 340t

if firework B is launched 0.25 s before Firework A, for the time of the two fireworks to be equal since we are considering time (t) after 0.25 seconds, we will have;

360(t-0.25) = 340t

360t  - 90 = 340t

360 t - 340 t = 90

20 t = 90

t = 90/20

t = 4.5 seconds

Therefore, both fireworks will explode 4.5 seconds after  Firework B launches

Answer:

-7

Step-by-step explanation:

The numerator of a  fraction is 1 more than  twice its denominator.

Let the denominator=x

Therefore, the numerator=2x+1

The fraction is: [tex]\dfrac{2x+1}{x}[/tex]

If 4  is added to both the  numerator and the denominator, the fraction reduces to 3.

Therefore:

[tex]\dfrac{2x+1+4}{x+4} =3[/tex]

First, we solve for x

[tex]\dfrac{2x+5}{x+4} =3[/tex]

Cross multiply

2x+5=3(x+4)

Open the bracket on the right-hand side

2x+5=3x+12

Collect like terms

3x-2x=5-12

x=-7

Therefore, the denominator of the fraction, x=-7

Answer:

[tex]x^2+8[/tex]

Step-by-step explanation:

[tex]f(x)=2x^2+1 \\\\g(x)=x^2-7 \\\\(f-g)(x)= (2x^2+1)-(x^2-7)=x^2+8[/tex]

Hope this helps!

Answer:

14 years 3 months.

Step-by-step explanation:

5 + 8 = 13 years

6 + 9 = 15 months = 1 year 3 months.

Total = 14 years 3 months.

Answer: Tamera invited 21 guests while Adelina invited 26 guest.

Step-by-step explanation:

x + (x-5) = 47  

x + x -5 = 47

2x  -5 =47

        +5   +5

2x= 52

x= 26    

26 -5  = 21

Answer:

C) For each hour worked the dollars earned increases by $5

Step-by-step explanation:

I don't have the context of the problem.

However, we do know that in math, when we have an equation of the form [tex]y=mx+b[/tex], the slope m represents the rate of change. This means, how much one quantity changes in regards to other quantity (from the options I can assume that we are talking about amount earned and hours worked).

Thus, in this case we have [tex]m=5[/tex] and this tells us how much the payment increase in terms of hours worked. Thus, we can say that for each work we work the payment increases by $5.

Thus, the correct answer is c) For each hour worked the dollars earned increases by $5

Answer:

When the are intercepted by other lines (math)

Existing, happening at the same time (definition)

Answer: option (g)

Step-by-step explanation:

So the question says :

The study ran for several weeks during the semester. About a week after it started, the university announced that they would be holding training sessions for faculty and staff about how to handle situations involving a gunman on campus. This shut down the study for several days as the university needed the lab building for training. The study then resumed according to script after the training. The researchers found that those in the experimental group did not differ in their memories regarding the presence of a gun compared to those in the control condition. That is, the mean score that a gun was present was similar for the experimental group (M = 65%, SD = 11.4%) and the control group (M = 63%, SD = 13.26%). a. Maturation b. Regression to the mean c. Selection d. Mortality e. Instrumentation f. Testing g. History h. Interactions i. Diffusion j. No Threat

ANS ⇒  The correct answer to this question is option G.

We can confirm here that History is the biggest threat to internal validity in the study as a significant period of time was allowed to pass between the testing conditions.

cheers i hope this helped !!!

Answer:

Volume = PI * radius^2 * height / 3

Volume = 4,712.39 cubic feet

Lateral Area = PI * radius * slant height

slant height^2 = 20^2 + 15^2

slant height ^2 = 625 slant height = 25

Lateral Area = PI * 15 * 25 = 1,178.1 square feet

Surface Area = PI * radius^2 = 706.86 square feet

Step-by-step explanation:

Answer:

11.62 ounces

Step-by-step explanation:

Answer:

C.  (x + 4)(x + 5).

Step-by-step explanation:

We need 2 numbers whose product is + 20 and whose sum is + 9.

They are + 5 and + 4 , so

x2 + 9x +20

= (x + 4)(x + 5).