write the equation of a line that is perpendicular to the given line and that passes through the given point. -3x - 6y = 17; (6, 3)

Answer: choice D

Step-by-step explanation:

The question asks for the probability that the chose card is a king or a queen.

and we have 8 cards that are a either a king or a queen

so

8/52=2/13

or you can think of it in the additive way(most of the time addition is required when you have “or” and multiplication when you have “and”)

4/52+4/52=2/13

Answer:

  see below

Step-by-step explanation:

You can determine the correct function by looking at the function and graph values at x = 1.

For some constant k, the function is ...

  (g·h)(x) = g(x)·h(x) = (-3^x)(kx) = -kx·3^x

For x=1, the graph shows (g·h)(1) = 6. Using this in our expression for (g·h)(x), we have ...

  (g·h)(1) = 6

  -k(1)(3^1) = 6 . . . . use the expression for (g·h), filling in x=1

  k = -2 . . . . . . . . . divide by -3

The function h(x) is ...

  h(x) = -2x

Answer:

B 63 degrees

Step-by-step explanation:

180 - 54 = 126

126 / 2 = 63

Answer:

[tex]F_p = < - \sqrt{3} , -3 >\\\\F_o = < \sqrt{3} , -1 >[/tex]

Step-by-step explanation:

- A plane is oriented in a Cartesian coordinate system such that it makes an angle of ( π / 3 ) with the positive x - axis.

- A force ( F ) is directed along the y-axis as a vector < 0 , - 4 >

- We are to determine the the components of force ( F ) parallel and normal to the defined plane.

- We will denote two unit vectors: ( [tex]u_p[/tex] ) parallel to plane and ( [tex]u_o[/tex] ) orthogonal to the defined plane. We will define the two unit vectors in ( x - y ) plane as follows:

- The unit vector ( [tex]u_p[/tex] ) parallel to the defined plane makes an angle of ( 30° ) with the positive y-axis and an angle of ( π / 3 = 60° ) with the x-axis. We will find the projection of the vector onto the x and y axes as follows:

                         [tex]u_o[/tex] = < cos ( 60° ) , cos ( 30° ) >

                         [tex]u_o = < \frac{1}{2} , \frac{\sqrt{3} }{2} >[/tex]

- Similarly, the unit vector ( [tex]u_o[/tex] ) orthogonal to plane makes an angle of ( π / 3 ) with the positive x - axis and angle of ( π / 6 ) with the y-axis in negative direction. We will find the projection of the vector onto the x and y axes as follows:

                        [tex]u_p = < cos ( \frac{\pi }{6} ) , - cos ( \frac{\pi }{3} ) >\\\\u_p = < \frac{\sqrt{3} }{2} , -\frac{1}{2} >\\[/tex]

- To find the projection of force ( F ) along and normal to the plane we will apply the dot product formulation:

- The Force vector parallel to the plane ( [tex]F_p[/tex] ) would be:

                          [tex]F_p = u_p(F . u_p)\\\\F_p = < \frac{1}{2} , \frac{\sqrt{3} }{2} > [ < 0 , - 4 > . < \frac{1}{2} , \frac{\sqrt{3} }{2} > ]\\\\F_p = < \frac{1}{2} , \frac{\sqrt{3} }{2} > [ -2\sqrt{3} ]\\\\F_p = < -\sqrt{3} , -3 >\\[/tex]

- Similarly, to find the projection of force ( [tex]F_o[/tex] ) normal to the plane we again employ the dot product formulation with normal unit vector (  [tex]u_o[/tex]  ) as follows:

                         [tex]F_o = u_o ( F . u_o )\\\\F_o = < \frac{\sqrt{3} }{2} , - \frac{1}{2} > [ < 0 , - 4 > . < \frac{\sqrt{3} }{2} , - \frac{1}{2} > ] \\\\F_o = < \frac{\sqrt{3} }{2} , - \frac{1}{2} > [ 2 ] \\\\F_o = < \sqrt{3} , - 1 >[/tex]

- To prove that the projected forces ( [tex]F_o[/tex] ) and ( [tex]F_p[/tex] ) are correct we will apply the vector summation of the two orthogonal vector which must equal to the original vector < 0 , - 4 >

                       [tex]F = F_o + F_p\\\\< 0 , - 4 > = < \sqrt{3}, -1 > + < -\sqrt{3}, -3 > \\\\< 0 , - 4 > = < \sqrt{3} - \sqrt{3} , -1 - 3 > \\\\< 0 , - 4 > = < 0 , - 4 >[/tex]  .. proven                    

Answer:

The answer is D

Step-by-step explanation:

D is the answer because they have a common difference

The rest do not have common difference

Answer:

31200 dollars

Step-by-step explanation:

you multiply 13 by 4, because its last week and this week, then find 60 percent of that. Proportion: x/52000=60/100. When solved, it is $31200

The solution is, $31200 should she plan to spend on advertising next week.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

Last week Malia spent $13,000 on advertising.

This week, she plans to spend three times as much.

Next week, she wants to spend 60% of what she spent the previous two weeks.

now, we have,

you multiply 13000 by 4,

i.e.  13000 *4 = 52000

because its last week and this week,

then find 60 percent of that.

let, she plan to spend on advertising next week is x .

Proportion:

x/52000=60/100.

When solved, it is $31200.

Hence, The solution is, $31200 should she plan to spend on advertising next week.

To learn more on percentage click:

brainly.com/question/13450942

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Answer:

The speed of the current is 3 mph.

Step-by-step explanation:

The speed of he boat in calm water is "18 mph", the speed of the stream is "x" mph. When the boat is going downstream its speed is "x + 18", while when it goes upstream it will be "18-x". The time it takes for the boat to travel 21 miles downstream is:

[tex]time = \frac{21}{x + 18}[/tex]

While the time it takes the boat to travel 15 miles upstream:

[tex]time = \frac{15}{18 - x}[/tex]

Since the times are the same, we can make:

[tex]\frac{21}{x + 18} = \frac{15}{18 -x}\\378 - 21x = 15x + 270\\21x + 15x = 378 - 270\\36x = 108\\x = 3 \text{ mph}[/tex]

The speed of the current is 3 mph.

Answer: The current of the water is 1.714 mph.

Answer:

0.7 + 0.4 - 0.2 = 0.9

Step-by-step explanation:

Let's denote the probabilities as following:

The probability that the show had animals is

P(A) = 0.7

The probability that the show aired more than 10 times is

P(B) = 0.4

The probability that the show had animals and aired more than 10 times is

P(A⋂B) = 0.2

The probability that a randomly selected show had animals or aired more than 10 times is P(A⋃B)

The correct form of  addition rule to determine the probability that a randomly selected show had animals or aired more than 10 times is:

P(A⋃B) = P(A) + P(B) - P(A⋂B) = 0.7 + 0.4 - 0.2 = 0.9

=> Option B is correct

Hope this helps!

Answer:

At the end of year 1,

The first age class has 2112 members.

The second age class has 44 members.

The third age class has 132 members.

Step-by-step explanation:

There are currently

176 members in age class 0

176 members in age class 1

176 members in age class 2

They all die off by age class 3

Starting with the members of age class 0. They produce 3 offsprings each during the first year, leading to 3×176 = 528 new members of age class 0 as at the end of the first year.

Then, of the 176 members of age class 0, only 25% make it to the next age class after a year, that is, only 44 of them.

So, from this group, after a year, age class 0 has 528 members, and age class 1 has 44 members.

Age class 1 group now. Population at the start = 176

They produce 6 offsprings each during that 1 year, that is, 6×176 = 1,056 new members of age class 0 at the end of that year.

Then, the survival rate for those in their second year of living is 75%, hence, 132 of them make it to the next age class.

So, from this group, after a year, age class 0 has 1056 members, and age class 2 has 132 members.

Age class 2 group now. Population at the start = 176

They produce 3 offsprings each during that 1 year, that is, 3×176 = 528 new members of age class 0 at the end of that year.

Then, the survival rate for those in their third year of living is 0%, hence, none of them make it to the next age class.

So, from this group, after a year, age class 0 has 528 members, and they all die off at the end of that 1 year.

So, we now calculate the number of members of each age class now at the end of that 1 year.

Age class 0 = 528 + 1056 + 528 = 2112 members

Age class 1 = 44 members

Age class 2 = 132 members.

Hope this Helps!!!

Answer: c(m),coffee=minutes

Step-by-step explanation:

I hope this answers your question

Answer:

b. 16%

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 500

Standard deviation = 100

Percentage of students who scored less than 400:

400 = 500 - 1*100

So 400 is one standard deviation below the mean.

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

Of those who are below, 68% are within 1 standard deviation of the mean, that is, between 400 and 500. So 100-68 = 32% are below 400.

0.5*0.32 = 0.16 = 16%

So the correct answer is:

b. 16%

Answer:

10 (8-x)(8+x)

Step-by-step explanation:

640-10x^2

Factor out 10

10 (64 - x^2)

Notice that inside the parentheses is the difference of squares

10 ( 8^2 - x^2)   and a^2 - b^2 = (a-b) (a+b)

10 (8-x)(8+x)

Answer:

10(8 - x)(8 + x)

Step-by-step explanation:

Given

640 - 10x^2

Solution

Take out 10 on each side of the minus sign

10(64 - x^2)

The expression in the brackets is a difference of squares which factors as

a^2 - b^2 = (a + b)(a - b)

Factor the expression inside the brackets as a difference of squares.

64 = 8*8

x^2 = x*x

10(8 - x)(8 + x)

Corrected Question

Find a number in between 35.76 and 35.8 and make the inequality 35.76<________<35.8 a true statement?

Answer:

One example is 35.77

Step-by-step explanation:

Given the numbers 35.76 and 35.8

To make the inequality [tex]35.76< x <35.8[/tex] a true statement, we look for a value of x such that:

[tex]x>35.76; and\\x<35.8\\$Let x=35.77\\Cearly:$\\35.77 > 35.76;$ and$\\35.77<35.8[/tex]

Therefore:

[tex]35.76< 35.77 <35.8[/tex] is a true statement.

Answer:

[tex] P(42 < \bar X <48)[/tex]

And we can use the z score formula given by:

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

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

[tex] z= \frac{42-44}{\frac{35}{\sqrt{59}}}= -0.4[/tex]

[tex] z= \frac{48-44}{\frac{35}{\sqrt{59}}}= 0.878[/tex]

And we want to find this probability:

[tex] P(-0.4<z<0.878)[/tex]

And we can use the foolowing excel command and we got:

=NORM.DIST(0.878;0;1;TRUE)-NORM.DIST(-0.4;0;1;TRUE)

And we got:

[tex] P(-0.4<z<0.878)=0.4655[/tex]

Step-by-step explanation:

For this case we know the following parameters:

[tex] \mu = 44 ,\sigma =35[/tex]

We select a sample size of n =59. So then the sample size is large enough to use the central limit theorem and the distribution for the sample mean is given by:

[tex] \bar X \sim N(\mu \frac{\sigma}{\sqrt{n}})[/tex]

We want to find the following probability:

[tex] P(42 < \bar X <48)[/tex]

And we can use the z score formula given by:

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

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

[tex] z= \frac{42-44}{\frac{35}{\sqrt{59}}}= -0.4[/tex]

[tex] z= \frac{48-44}{\frac{35}{\sqrt{59}}}= 0.878[/tex]

And we want to find this probability:

[tex] P(-0.4<z<0.878)[/tex]

And we can use the foolowing excel command and we got:

=NORM.DIST(0.878;0;1;TRUE)-NORM.DIST(-0.4;0;1;TRUE)

And we got:

[tex] P(-0.4<z<0.878)=0.4655[/tex]

Answer:

El capicúa es 707.

Step-by-step explanation:

(The following exercise is presented in Spanish and for such reason explanation will be held in that language).

Un capicúa es un número que se lee de la misma manera tanto de derecha a izquierda como de izquierda a derecha. En este caso, el capicúa mencionado en el enunciado es el siguiente:

[tex]x = 700 + 007[/tex]

[tex]x = 707[/tex]

El capicúa es 707.

Answer:

Step-by-step explanation:

here are some of the graph points:

(-2,-2)

(-1,-3)

(0,-4)

(1,-5)

(2,-6)

(3,-7)

(4,-8)

The graph should have a negative slope and the slope should be -1, and the y-intercept should be -4.  The pic you put is not the correct graph.

Answer:

50men working in 5days will lay 100 meters

Step-by-step explanation:

If 20men working for 10days lays 500meters

then, 1 man will lay 10,000 meters in 10 days

also, 1 man will lay 1000 meters in 1 day

If 1 man lays 1000 meters in 1 day,

Then, 50 men will lay (1000 meters / 50 );  20 meters in 1 day

also, the same 50 men will lay (20 meters x 5days); 100 meters in 5 days.

Therefore, 50men working in 5days will lay 100 meters

Answer:

228incubed

Step-by-step explanation:

Area of prism is area of cross section x length.

So, área of trapezium is a plus b times h divided by 2.

Times that by height. Gives you 228

Answer:

Option 3 is correct.

The data do not provide sufficient evidence to reject H0; thus, we cannot conclude that the mean point spread of home games is higher than that of away games.

Step-by-step explanation:

Before anything else, we first give the null and alternative hypothesis for this question.

Null hypothesis would be that there isn't significant evidence to conclude that the mean point spread of home games is higher than that of away games.

H0: µ1 = µ2

And the alternative hypothesis would be that there is significant evidence to conclude that the mean point spread of home games is higher than that of away games.

Ha: μ1 > μ2

The data from the output of the analysis of the hypothesis test is missing from the question. It was obtained online and is attached to this solution of the question.

The table consists of the difference, the sample mean, the standard error of the mean, degree of freedom, the test statistic and most importantly, the p-value. It is the p-value that absolutely gives us the concluding statement of the hypothesis testing.

When the significance level for a test isn't provided, the convention is usually to use 5% significance.

Interpretation of p-value

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.4351

0.4351 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that 'The data do not provide sufficient evidence to reject H0; thus, we cannot conclude that the mean point spread of home games is higher than that of away games'.

Hope this Helps!!!

Answer:

the first and the second answer

Step-by-step explanation:

Answer:

A and B

Step-by-step explanation:

This is correct believe me it is.

Answer:

√2

Step-by-step explanation:

(-5, 0) and (-4, 1)

[tex]d=\sqrt{(x_{2}-x_{1} )^{2}+ {(y_{2}-y_{1} )^{2}}}[/tex]

[tex]d= \sqrt{(-4-(-5))^{2} + (1-0)^{2}} =\sqrt{1+1} =\sqrt{2}[/tex]

Answer:

[tex]\boxed{\sf \ \ \ diagonal \ length \ = \ 41 \ \ \ }[/tex]

Step-by-step explanation:

Thanks to Pythagoras we can say that

l being the length of the diagonal

[tex]l =\sqrt{9^2+40^2}=\sqrt{81+1600}=\sqrt{1681}=41[/tex]

Answer:

25% of students attend classes in the evening.

Step-by-step explanation:

The proportion of evening students is the number of evening students divided by the total number of students.

The percentage is the proportion multiplied by 100.

We have that:

In total, there are 15000 students.

3750 are evening students

3750/15000 = 0.25

0.25*100 = 25%

25% of students attend classes in the evening.

Answer:

5

Step-by-step explanation:

distribute: 2x+6 = 4x-4

subtract 2x from both sides: 6 = 2x-4

add 4 to both sides: 10 = 2x

divide both sides by 2: 5 = x

x = 5

Answer:

D

(5)

Step-by-step explanation:

Edge2020

Answer:

y=3(x+2)^2-5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

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Answer:

The 90​% confidence interval for the population​ mean is between 27.34 months and 39.84 months.

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{1-0.9}{2} = 0.05[/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]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/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 = 1.645*\frac{19}{\sqrt{25}} = 6.25[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 33.59 - 6.25 = 27.34 months

The upper end of the interval is the sample mean added to M. So it is 33.59 + 6.25 = 39.84 months

The 90​% confidence interval for the population​ mean is between 27.34 months and 39.84 months.

Answer:

120yd cube

Step-by-step explanation:

Answer:

  44

Step-by-step explanation:

Put 8 where x is and do the arithmetic.

  f(8) = 6·8 -4 = 48 -4

  f(8) = 44

Answer:

  q = -5

Step-by-step explanation:

For A the midpoint between B and C, we have ...

  A = (B+C)/2

  C = 2A -B

Point A(-1, 1) is the midpoint* between C(q, 4) and B(3, -2), so the point (q, 4) will be ...

  (q, 4) = 2A -B

  (q, 4) = 2(-1, 1) -(3, -2) = (2(-1)-3), 1(1)+2)

  (q, 4) = (-5, 4)

  q = -5

_____

* We know A is the midpoint because we observe the differences in y-values for C-A and A-B are ... 4 -1 = 3, and 1 -(-2) = 3. That is, points C and B are the same distance from A.