Find the slope of a line perpendicular to the line whose equation is 2y − 6x = 4.

Answer:

-5

Step-by-step explanation:

y=3x+b

M(2,1)

*see attachment for the megaphone being referred to here

Answer:

9%

Step-by-step explanation:

==>Given:

Conical megaphone with the following dimensions:

Slant height (s) = 2.25 ft

Diameter (D) = 1.2 ft (radius r = 0.6 ft)

π = 3.1

Area covered by sticker on one side = area of square = 6 in × 6 in = 0.5 ft × 0.5 ft = 0.25 ft²

==>Required

% of the surface of area of the conical megaphone that is covered by the sticker = area covered by the sticker ÷ surface area of megaphone × 100

==>SOLUTION

Area covered by sticker on both sides = 0.25 ft² + 0.25 ft² = 0.5 ft²

Surface area of the megaphone = surface area of a cone = πrs + πr²

S.A of megaphone = (3.14 × 0.6 × 2.25) + (3.14 × 0.6²)

S.A = 4.239 + 1.1304

S.A = 5.3694 ft²

Therefore, % of the surface of area of the conical megaphone that is covered by the sticker = 0.5 ÷ 5.3694 × 100

= 9.31202741

= 9%

Answer:

Statistics show the megaphone was a success in South Carolina.

Step-by-step explanation:

Answer:

For this case we want to find the probability that a senior is chosen at random not planning to attend college after graduation so then we can use the complement rule given by:

[tex] P(A') = 1-P(A)[/tex]

Where A is the vent of interest and replacing we got:

[tex] P(A') = 1-0.85= 0.15[/tex]

So then the probability that a senior is chosen at random not planning to attend college after graduation is 0.15 or 15%

Step-by-step explanation:

For this case we know that the sample size if n =240 and we also know that the probability that in the Evan's class the any student are planeed to attend collge after graduation is:

[tex] P(A) =0.85[/tex]

For this case we want to find the probability that a senior is chosen at random not planning to attend college after graduation so then we can use the complement rule given by:

[tex] P(A') = 1-P(A)[/tex]

Where A is the vent of interest and replacing we got:

[tex] P(A') = 1-0.85= 0.15[/tex]

So then the probability that a senior is chosen at random not planning to attend college after graduation is 0.15 or 15%

Answer:

$11154.6

Step-by-step explanation:

We have that the interest would be calculated as follows:  

9000 * 0.0475 = 427.5

then this for the amount of time in years:

427.5 * 6 = 2565

Now, we have to pay 16% federal interest tax. So, that would be

2565 * 0.16 = 410.4

Therefore, the money available to us after 6 years would be:

9000 + 2565 - 410.4 = 11154.6

It means that it would be $ 11154.6

Answer:

A AND B

Step-by-step explanation:

TRUST MEEEEE FRENZ:)

If 4 > 3 then - 4 < -3 is true because when additive opposites of numbers are used inequality get reversed.

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given inequality,

4 > 3

If we multiply with -1 on both sides inequality get reversed

-1 × 4 > -1 × 3

-4 < -3.

Hence, the inequality changes from greater than to less than  when opposites of 4 and 3 are used.

Learn more about inequality here:

https://brainly.com/question/30231190.

#SPJ6

Answer:

i need a the data

Step-by-step explanation:

Answer:66.4

Step-by-step explanation:

[tex]A_{semicircle} =\frac{1}{2} \pi r^2=\frac{1}{2} \pi (\frac{13}{2} )^2= 66.36614 \approx66.4[/tex]

Answer:

10 to the 1st power

Step-by-step explanation:

531 x 10 = 5310

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_A-\mu_B[/tex] = 2.0 units  or  [tex]\mu_D[/tex] = 2.0 units

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_A-\mu_B\neq[/tex] 2.0 units  or  [tex]\mu_D\neq[/tex] 2.0 units

Step-by-step explanation:

We are given the following data below and we have test if the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2;

Pair : 1 2 3 4 5 6 7

Sample1 : 5 6 10 3 6 7 8

Sample2 : 4 4 3 5 5 5 3

Let [tex]\mu_A[/tex] = population mean represented by Sample 1

[tex]\mu_B[/tex] = population mean represented by Sample 2

[tex]\mu_D[/tex] = population mean matched-pair differences for Sample 1 - Sample 2

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_A-\mu_B[/tex] = 2.0 units  or  [tex]\mu_D[/tex] = 2.0 units

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_A-\mu_B\neq[/tex] 2.0 units  or  [tex]\mu_D\neq[/tex] 2.0 units

Here null hypothesis states that the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2.

On the other hand, alternate hypothesis states that the population represented by Sample 1 has a mean that is not 2.0 units higher than the population represented by Sample 2.

Answer:

ffhn

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean daily car rental rates for Boston and μ2 be the mean daily car rental rates for Dallas.

The random variable is μ1 - μ2 = difference in the mean daily car rental rates for Boston and the mean daily car rental rates for Dallas

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 > μ2 H1 : μ1 - μ2 > 0

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

μ1 = 47

μ2 = 44

s1 = 3

s2 = 3

n1 = 8

n2 = 9

t = (47 - 44)/√(3²/8 + 3²/9)

t = 1.41

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [3²/8 + 3²/9]²/[(1/8 - 1)(3²/8)² + (1/9 - 1)(3²/9)²] = 4.515625/0.28571428571

df = 16

We would determine the probability value from the t test calculator. It becomes

p value = 0.09

Since alpha, 0.05 < than the p value, 0.09, then we would fail to reject the null hypothesis.

Answer:

y+5 = 3/4(x+8)

Step-by-step explanation:

The point slope form of the equation of a line is

y - y1 = m(x-x1) where m is the slope and ( x1,y1) is a point on the line

The slope is 3/4 and the point is (-8,-5)

y - -5= 3/4( x - -8)

y+5 = 3/4(x+8)

Answer:

The true statements Include

A) The length of a confidence interval can be determined if you know only the margin of error.

B) The margin of error can be determined if you know only the length of the confidence interval.

D) The confidence interval can be obtained if you know only the margin of error and the sample mean.

G) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.

F) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.

The false statements include

C) The confidence interval can be obtained if you know only the margin of error.

E) The margin of error can be determined if you know only the confidence level.

F) The confidence level can be determined if you know only the margin of error.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

The critical value is obtained using the confidence level (and sample size for t-distributions).

Standard Error of the mean = (Standard deviation)/[√(sample size)]

Standard error of the mean = σₓ = (σ/√n)

Taking each of the statements one at a time

a) The length of a confidence interval can be determined if you know only the margin of error.

According to the mathematical expression of the confidence interval, the length of the confidence interval is 2 × Margin of error. Hence, the length of the confidence interval can be truly obtained from only the margin of error.

This statement is true.

b) The margin of error can be determined if you know only the length of the confidence interval.

This is another way of phrasing statement A. The margin of error is half of the length of the confidence interval.

Hence, this statement is also true.

c) The confidence interval can be obtained if you know only the margin of error.

The confidence interval can be obtained from an expression that involves the sample mean and margin of error.

Confidence Interval = (Sample mean) ± (Margin of error)

The confidence interval cannot be obtained from just the margin of error. Hence, this statement is false.

d) The confidence interval can be obtained if you know only the margin of error and the sample mean.

Like o stated in (c) above, the confidence interval can be obtained from an expression that involves the sample mean and margin of error.

Confidence Interval = (Sample mean) ± (Margin of error)

Hence, this statement is true.

e) The margin of error can be determined if you know only the confidence level.

To obtain the margin of error, if the confidence interval isn't used, an expression involving the critical value and the standard error of the mean is used.

Margin of Error = (Critical value) × (standard Error of the mean)

The critical value is obtained using the confidence level, but the margin of error cannot be obtained from just that, we still need the standard error of the mean.

Hence, this statement is false.

f) The confidence level can be determined if you know only the margin of error.

This is another way of phrasing statement E. Hence, this statement too is false.

g) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.

This is true as these is all that is required to obtain the margin of error.

h) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.

This can be a bit stressful to obtain, but it is true. It is easy to see this from all the explanation from the beginning to this point.

Hope this Helps!!!

Answer:

[tex]P(X>50)=P(\frac{X-\mu}{\sigma}>\frac{50-\mu}{\sigma})=P(Z>\frac{50-44}{5})=P(z>1.2)[/tex]

And we can find this probability using the normal standar distribution and with the complement rule we got:

[tex]P(z>1.2)=1-P(z<1.2) =1-0.8849= 0.1151[/tex]

Step-by-step explanation:

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

[tex]X \sim N(44,5)[/tex]  

Where [tex]\mu=44[/tex] and [tex]\sigma=5[/tex]

We are interested on this probability

[tex]P(X>50)[/tex]

And we can use the z score formula given by:

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

And using this formula we got:

[tex]P(X>50)=P(\frac{X-\mu}{\sigma}>\frac{50-\mu}{\sigma})=P(Z>\frac{50-44}{5})=P(z>1.2)[/tex]

And we can find this probability using the normal standar distribution and with the complement rule we got:

[tex]P(z>1.2)=1-P(z<1.2) =1-0.8849= 0.1151[/tex]

Answer:

a) Mean 0.11 and standard deviation 0.0044.

b) Mean 0.11 and standard deviation 0.0099.

c) Mean 0.11 and standard deviation 0.0198

Step-by-step explanation:

Central Limit Theorem:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.11[/tex]

a. For a random sample of size n equals 5000.

Mean:

[tex]\mu = p = 0.11[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{0.11*0.89}{5000}} = 0.0044[/tex]

Mean 0.11 and standard deviation 0.0044.

b. For a random sample of size n equals 1000.

Mean:

[tex]\mu = p = 0.11[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{0.11*0.89}{1000}} = 0.0044[/tex]

Mean 0.11 and standard deviation 0.0099.

c. For a random sample of size n equals 250.

Mean:

[tex]\mu = p = 0.11[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{0.11*0.89}{250}} = 0.0198[/tex]

Mean 0.11 and standard deviation 0.0198

Answer:

b-d

Step-by-step explanation:

At the airport, d airplanes flew away, and b were still there.

We are required to determine how many more airplanes stayed at the airport than flew away.

To do this, we subtract the number of airplanes which flew away from the number which stayed.

Therefore:

Number of more airplanes which stayed than flew away

=Number of airplanes which stayed-Number of airplanes which flew away

= b-d

Answer:

graph starts high and ends high

Answer:

[tex] V = \frac{182.4 mi}{3 hr}= 60.8 \frac{mi}{hr}[/tex]

And then we can find the distance travelled in 11 hours with this formula:

[tex] D = Vt[/tex]

And replacing we got:

[tex] D = 60.8 \frac{mi}{hr} *11 hr =668.8 mi[/tex]

So then after 11 hours she will travel 668.8 mi

Step-by-step explanation:

For this case w eknow that Alicia drove at a constant speed 182.4 mi in 3 hours. We can find the speed with this formula:

[tex] V= \frac{D}{t}[/tex]

Where V is the velocity, D the distance and t the time if we replace we got:

[tex] V = \frac{182.4 mi}{3 hr}= 60.8 \frac{mi}{hr}[/tex]

And then we can find the distance travelled in 11 hours with this formula:

[tex] D = Vt[/tex]

And replacing we got:

[tex] D = 60.8 \frac{mi}{hr} *11 hr =668.8 mi[/tex]

So then after 11 hours she will travel 668.8 mi

Answer:

We want to test if the scouts in her troop sold more cookies than the average in New York City (50), the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 50[/tex]  

Alternative hypothesis:[tex]\mu > 50[/tex]  

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

For this case we have also the p value calculated

[tex]p_v =0.11[/tex]

If we use any significance level lower than 10% we FAIL to reject the null hypothesis (pvalue>significance) and we can conclude that the true mean is not higher than the mean for New York otherwise if we use a significance level higher than 10% the conclusion would be the opposite.

Step-by-step explanation:

Information given

[tex]\bar X=101.1[/tex] represent the sample mean

[tex]s=29.3[/tex] represent the sample standard deviation

[tex]n=50[/tex] sample size  

[tex]\mu_o =50[/tex] represent the value that we want to test

t would represent the statistic

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

System of hypothesis

We want to test if the scouts in her troop sold more cookies than the average in New York City (50), the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 50[/tex]  

Alternative hypothesis:[tex]\mu > 50[/tex]  

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

For this case we have also the p value calculated

[tex]p_v =0.11[/tex]

Conclusion

If we use any significance level lower than 10% we FAIL to reject the null hypothesis (pvalue>significance) and we can conclude that the true mean is not higher than the mean for New York otherwise if we use a significance level higher than 10% the conclusion would be the opposite.

Answer:

a) 71.25 gallons

b) 25 hrs

c) 105 gallons

d) 47.91 hrs

Step-by-step explanation:

Solution:-

- The rate at which the pollution enter the lake is expressed by a function f ( t ) as follows:

                            [tex]f ( t ) = 10*( 1 - e^-^0^.^5^t )[/tex]

- Where, the rate at which pollution is removed from the lake via a filter is expressed by a function g ( t ):

                             [tex]g ( t ) = 0.4t[/tex]

- We will denote ( x ) as the amount of population in lake at time ( t ).

- We will set up a linear first order ODE using rate of change of pollution ( x ) in the lake at any instance ( t ):

                            [tex]\frac{dx}{dt} = ( flow _ i_n ) - ( flow _ o_u_t )[/tex]

- The respective inflow and outflow of pollution from the lake are expressed by the functions f ( t ) and g ( t ). Hence, the ODE becomes:

                           [tex]\frac{dx}{dt} = f ( t ) - g ( t )\\\\\frac{dx}{dt} = 10*( 1 - e^-^0^.^5^t ) - 0.4t\\\\[/tex]

- Separate the variables and integrate from t = 0 to t = 12 hours.

                         [tex]x = \int\limits^1^2_0 [{10*( 1 - e^-^0^.^5^t ) - 0.4t} ] \, dt \\\\x ( 12 ) = [ 10 * ( t + 2e^-^0^.^5^t ) - 0.2t^2 ] \limits^1^2_0\\\\x ( 12 ) = [ 10 * ( 12 + 2e^-^6 ) - 0.2(12)^2 ] - [ 10* ( 0 + 1 ) - 0.2(0)^2 ]\\\\x ( 12 ) = 71.25 galls[/tex]

- We will use the graphing calculator to evaluate the time ( t ) at which the rate of inflow of pollution is equal to the rate at which pollution is removed from the lake. In other words solve the following equation:

                          [tex]f ( t ) = g ( t )\\\\10*( 1 - e^-^0^.^5^t ) = 0.4t[/tex]

- Solving for the above equation the following intersection point was observed:

                          t = 25 hours

- We will perform integration of the previously expressed ODE from t = 0 to t = 25 hrs.

                           [tex]x ( 25 ) = [ 10*(t - 2e^0^.^5^t ) - 0.2t^2 ]\limits^2^5 _ 0\\\\x ( 25 ) = [ 10*(25 - 2e^1^2^.^5 ) - 0.2(25)^2 ] - [ 20 ] \\\\x ( 25 ) = 105 galls[/tex]

- We will evaluated result of the integration from time t = 0 to time t = t set the amount of pollution ( x ) equal to zero:

                          [tex]x ( t ) = [ 10*( t - 2e^-^0^.^5^t ) - 0.2t^2 ]\limits^t_0\\\\x ( t ) = 10 + 20e^-^0^.^5^t - 0.2t^2 - 20[/tex]

- Use the derived result x ( t ) and feed it into the graphing calculator and solve for x ( t ) = 0; hence,

                       10 + 20e^( -0.5*t ) - 0.2t^2 - 20 = 0

- The answer is evaluated as t = 47.91 hr

Answer:

126 inches

Step-by-step explanation:

The rectangle is 75 in.

The square is 16 in.

The parallelogram is 35 in.

I hope this helps :-)

Answer:

0.3745

Step-by-step explanation:

We have to solve the problem by calculating the z-score value that has the following formula:

z <(x - m) / sd

x is the value to evaluate (<80), m is the mean (85) and the standard deviation is sd (12)

replacing:

p (x <80) = z <(80 - 85) / 12

z <-0.416, we look for this value in the normal distribution table and it corresponds to:

p (x <80) = 0.3745

Which means that the proportion of people is 0.3745

Answer:

Step-by-step explanation:

[tex]u_3 = v_3[/tex] and  [tex]u_2 = v_1[/tex]

[tex]u_1= v_1 -7 v_3[/tex]

Replace the first line to the second line, you have [tex]u_1= u_2-7u_3[/tex]

That shows [tex]\{u_1, u_2, u_3,u_4\}[/tex]

is not linear independent.

Answer:

height of the flag from the bottom of the boat ≈ 32 ft (nearest foot)

Step-by-step explanation:

She is on her boat and the angle of elevation to the top of the flag is 58°. Her eyes her 6 ft above the bottom of the boat she is sailing on. The height of the flag from the bottom of the boat is the sum of the height of the flag and the remaining height from the horizontal line of sight upward to the flag top.

A right angle triangle was formed Shianne line of sight. The angle from her line of sight is 58° from the horizontal. Therefore,

the adjacent side of the triangle formed is 16 ft which is the distance from the boat to the flag.

adjacent side = 16 ft

opposite angle = ?

using tangential ratio

tan 58° = opposite/adjacent

tan 58° = h/16

cross multiply

h = 16 × 1.60033452904

h = 25.6053524647

height of the flag from the bottom of the boat = 25.6053524647  + 6 = 31.6053524647

height of the flag from the bottom of the boat ≈ 32 ft(nearest foot)

Answer:

f(-3) = 4

Step-by-step explanation:

There are two ways to do it with the information given to you, you can look at the graph or use the equation.

Equation:

Since x = -3, you would put -3 in for x in the first equation which gives 4. It looks like you were on the right track but forgot that it was negative so you ended up adding 3 instead of subtracting. At least that is where I assume the 10 comes from.

Graphical:

Looking at the graph you can also find the value. You want to find the value of y at x = -3, so you look at the spot where x = -3. You will see that there are two "points" there, one open and one closed. The closed circle one means that the graph includes -3 in its x value. The open circle one means the graph contains every number until x=-3.

So to find the y value at x = -3 you want to look at the y value that corresponds to the closed circle of the graph since it is the part that includes x=-3 and you will see that y = 4 at that spot.

Answer:

  a.  12%

  b.  2/3

Step-by-step explanation:

Given data regarding orders that do and don't include tents and/or mats, you want to find the probabilities of (a) the order includes mats; (b) the order includes a tent given that it includes mats.

The given data is summarized in the attached two-way table. The value in blue is given in the problem statement. The values in purple are computed from values given in the problem:

  40% of the 20% of orders include a tent and mat = 8% of orders

  5% of the 80% of orders with no tent = 4% of orders include a mat

The numbers in black make the totals come out right.

The table shows that 8% +4% = 12% of all orders include sleeping mats.

  P(m) = 12%

8% of the 12% of orders that include mats also include a tent. The probability of an order including a tent given that it includes a mat is ...

  P(t|m) = 8%/12% = 2/3

Answer:

7th-grade: 4.3

8th-grade: 4.5

Step-by-step explanation:

7th-grade  and 8th-Grade samples have 20 data points. The mean is obtained adding the values of the data set and dividing this addition by the amount of values.

Mean total household of the 7th-grade  sample: (5+4+4+4+4+ 7+ 3+ 4+ 2+ 3+  4+4+ 2+ 4+ 3+ 8+ 7+ 5+ 4+5)/20 = 4.3

Mean total household of the 8th-grade  sample: (7+5+5+5+3+ 4+ 5+ 3+ 2+ 8+ 6+5+6+3+3+4+4+5+3+4)/20 = 4.5

Answer:

7th grade: C

8th grade: B

Step-by-step explanation:

100% true

Answer:

Step-by-step explanation:

Diagram : A visual tool representing mathematical ideas to be interpreted.

Postulate : A mathematical statement taken as a fact.

Theorem : A mathematical statement proven using postulates and definitions.

Definition : A formal statement declaring the meaning of a word.

Step-by-step explanation:

Suppose the results obtained are numbers from 1 to 10, then after 10 rolls, the average is

(1+2+3+4+5+6+7+8+9+10)/10

= 55/10

= 5.5

Answer:

5 , 3 , 3.5     C) The average would approach a set value.

Step-by-step explanation:

The first three numbers don't matter it could be anyone 1-6.

The last answer is C