An aeroplane X whose average speed is 50°km/hr leaves kano airport at 7.00am and travels for 2 hours on a bearing 050°. It then changes its course and flies on a bearing 1200 to an airstrip A. Another aeroplane Y leaves kano airport at 10.00am and flies on a straight course to the airstrip A. both planes arrives at the airstrip A at 11.30am. calculate the average speed of Y to three significant figures. the direction of flight Y to the nearest degree

Answer:

E:

Step-by-step explanation:

The equation of circles is

(x-a)²+(y-b)²=r²

Where

Center = (a,b) = (-6,-3) and r = 12

Now

The equation becomes

(x+6)²+(x+3)²=144

Answer:

I'm glad you asked!

Step-by-step explanation:

OK,let's simplify the number for a equivalent expression.

[tex]4+2(1+3x)[/tex]

Distribute:

[tex]=4+(2)(1)+(2)(3x)[/tex]

[tex]= 4+2+6x[/tex]

Combine Like Terms:

[tex]=4+2+6x[/tex]

[tex]=(6x)+(4+2)[/tex]

[tex]=6x+6[/tex]

The Final Answer is : [tex]6x+6[/tex]

The expression that is equivalent to 4+2(1+3x) is 6x+6.

Mathematical expressions that are made up of constants, variables, and coefficients that are combined using algebraic operations such as multiplication, addition, subtraction, and division are called Algebraic expressions.

Given, 4+2(1+3x)

Firstly distribute 2(1+3x) to get 2+6x then,

4+2(1+3x)

=4+2+6x

=6x+6

Thus, 4+2(1+3x)=6x+6

For more simplification visit- https://brainly.com/question/953809?referrer=searchResults

#SPJ2

Answer:

The expected value of profit is -$0.65.

Step-by-step explanation:

The rules of the lottery are as follows:

The probability of winning is, P (W) = 0.001.

Then the probability of losing will be,

P (L) = 1 - P (W)

       = 1 - 0.001

       = 0.999

Let the random variable X represent the amount of profit.

The probability distribution table of the lottery result is as follows:

Result      X        P (X)

Win      +349     0.001

Lose         -1       0.999

The formula to compute the expected value of X is:

[tex]E(X)=\sum X\cdot P(X)[/tex]

Compute the expected value of profit  as follows:

[tex]E(X)=\sum X\cdot P(X)[/tex]

         [tex]=(349\times 0.001)+(-1\times 0.999)\\\\=0.349-0.999\\\\=-0.65[/tex]

Thus, the expected value of profit is -$0.65.

Answer:

3. 72.9%

Step-by-step explanation:

Let's call M the event that the customer is male and C the event that the customer prefer chocolate chips Scones.

So, the probability P(M∪C) that a customer chosen at random will be a male or prefer the Chocolate Chip Scones is calculated as:

P(M∪C) = P(M) + P(C) - P(M∩C)

Then, there are 145 males (317 customer - 172 females = 145 males), so the probability that the customer is a males is:

P(M) = 145/317 = 0.4574

There are 167 customers that prefer chocolate chips Scones ( 317 customers - 150 customers that prefer the Cranberry Walnut Scones = 167), so the probability that a customer prefer chocolate chips Scones is:

P(C) = 167/317 = 0.5268

Finally, 81 customers were males and prefer the Chocolate Chip Scones, so the probability that a customer will be a male and prefer chocolate  chip scones is:

P(M∩C) = 81/317 = 0.2555

Therefore,  P(M∪C) is equal to:

P(M∪C) = 0.4574 + 0.5268 - 0.2555

P(M∪C) = 0.7287

P(M∪C) = 72.9%

Answer:

3. 72.9%

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

Male or prefers the Chocolate Chip Scones. That is, males and females who prefer the Chocolate Chip Scones.

There are 172 female customers and 317-172 = 145 male customers.

150 customers prefer the Cranberry Walnut Scones. So 317 - 150 = 167 customers prefer the Chocolate Chip Scones.

81 of those are male, so 167 - 81 = 86 are female.

So the total of desired outcomes is 86 + 145 = 231

Total outcomes:

317 total customers.

Probability:

231/317 = 0.729

So the correct answer is:

3. 72.9%

The angle of elevation of the sun when a 10-foot tree creates a shadow that is 15 feet long  is 33.69 degrees

To find the angle of elevation of the sun, we can use trigonometry and the concept of similar triangles.

Given that:

The tree's height is 10 feet.

The length of the shadow is 15 feet.

Let's assume that the tree's height is "h"  feet.

Length of its shadow is represented by "s" feet

The angle of elevation of the sun is the angle between the ground and the line from the top of the tree to the tip of its shadow.

The angle can be determined using the tangent function.

[tex]tan\theta[/tex] = [tex]\dfrac{h}{s}[/tex]

Now, substitute the given values:

[tex]tan\theta[/tex]= [tex]\dfrac{10}{15}[/tex]

[tex]tan\theta[/tex] = [tex]\dfrac{2}{3}[/tex]

The angle of elevation can be obtained by  taking the inverse tangent of 2/3

angle of elevation =[tex]\tan^-1\dfrac{2}{3}[/tex]

angle of elevation ≈ 33.66 degrees

So, the angle of elevation of the sun is approximately 33.69 degrees.

Learn more about angle of elevation here:

https://brainly.com/question/31006775

#SPJ4

Answer:

7x+6 = 6x-3

Step-by-step explanation:

2 (x + 3) + 5 x = 3 (2 x - 1)

Distribute

2x+6+5x = 6x-3

Combine like terms

7x+6 = 6x-3

Answer:

7x + 6 = 6x - 3                                  Option A

Step-by-step explanation:

Now Jalesa wants to simplify this equation.

Firstly applying the distributive property

Distribute the 2 over the parenthesis and distribute the over the parenthesis

that is,

2*x + 2*3 + 5x = 3*2x - 3*1

2x + 6 + 5x = 6x - 3

After that combine like terms

2x + 5x + 6 = 6x - 3

7x + 6 = 6x - 3

Result is:

7x + 6 = 6x - 3

That's the final answer.

Answer:

[tex]= 8 \frac{27}{132} = 8\frac{9}{44}\\ [/tex]

Step-by-step explanation:

[tex]15 \frac{5}{11} - 7 \frac{3}{12} \\ \frac{170}{11} - \frac{87}{12} \\ \frac{2040 - 957}{132} \\ = \frac{1083}{132} \\ = 8 \frac{27}{132} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

8 9/44.

Step-by-step explanation:

15 5/11 - 7 3/12

= 15 - 7 + 5/11 - 1/4       The LCD of 4 and 11 is 44 so we have:

15 - 7 + 20/44 - 11/44

= 8 + 9/44

= 8 9/44.

Answer:

a. SST = 1816

SSR = 1511.804

SSE = 465.804

b. Coefficient of determination, R² = 0.832491079

c. The correlation coefficient r = 0.8636

Step-by-step explanation:

y = 23.194 + 0.318·x

Where:

x = Price

y = Overall score

The observed data are given as follows;

Brand                Price  Score

Bose                 180     76

Scullcandy       150      71

Koss                 95       62

Phillips/O'Neill 70       57

Denon              70       30

JVC                   35       34

[tex]SST = \sum \left (y - \bar{y} \right )^{2}[/tex]= 1816

[tex]SSR = \sum \left ({y}'-\bar{y{}'} \right )^{2}[/tex] = 1511.804

[tex]SSE = \sum \left (y - {y}' \right )^{2}[/tex] = 465.804

Coefficient of determination

[tex]Coefficient \, of \, determination = \dfrac{SSR}{SST}[/tex]= 0.832

Coefficient of correlation =

[tex]r = \dfrac{n\left (\sum xy \right )-\left (\sum x \right )\left (\sum y \right )}{\sqrt{\left [n\sum x^{2}-\left (\sum x \right )^{2} \right ]\left [n\sum y^{2}-\left (\sum y \right )^{2} \right ]}}[/tex]

Ʃxy  = 37500

Ʃx =600

Ʃy = 330

Ʃx² = 74950

Ʃy²  = 19966

[tex]r = \dfrac{6 \left (37500 \right )-\left (600 \right )\left (330 \right )}{\sqrt{\left [6\times 74950-\left (600 \right )^{2} \right ]\left [6 \times 19966-\left (330 \right )^{2} \right ]}} = 0.8636[/tex]

Answer:

107 meters

Step-by-step explanation:

Central angle = 123°

In radians

123° = 123π/180

123° = 2.147 radians

Putting in formula

S = r∅

S = (50)(2.147)

S = 107 meters

[tex]z_1z_2=(3+2i)(4+3i)=3\cdot4+2i\cdot4+3\cdot3i+2i\cdot3i[/tex]

[tex]z_1z_2=12+8i+9i+6i^2[/tex]

[tex]i^2=-1[/tex], so

[tex]z_1z_2=12+8i+9i-6=\boxed{6+17i}[/tex]

Answer:

46.7%

Step-by-step explanation:

Given:

Total number of students in Mrs. Verner's class = 15

Number of girls = 8

To find: percentage are boys

Solution:

Percentage of boys = ( Number of boys / Total number of students ) × 100

Number of boys = Total number of students - Number of girls = 15 - 8 = 7

So,

Percentage of boys = [tex]\frac{7}{15}[/tex] × 100 = 46.7%

Answer:

64

Step-by-step explanation:

If the mean is 15, the sum of 5 numbers is:

Minimum value for the first four numbers would be:

Then the fifth number is:

So the maximum difference is:

Answer:

36π

Step-by-step explanation:

area=πr²

=πx6x6

6x6=36

area = 36π

Answer:

The minimum score required for an A grade is 77.

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

[tex]\mu = 67.7, \sigma = 7.8[/tex]

Find the minimum score required for an A grade.

Top 12% of scores get an A.

100-12 = 88th percentile.

The 88th percentile of scores is the minimum required for an A grade. This score is X when Z has a pvalue of 0.88. So X when Z = 1.175.

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

[tex]1.175 = \frac{X - 67.7}{7.8}[/tex]

[tex]X - 67.7 = 7.8*1.175[/tex]

[tex]X = 76.865[/tex]

Rounding to the nearest whole number:

The minimum score required for an A grade is 77.

We have a right triangle and we're given the leg lengths.  

tan X = |YZ| / |XZ| = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

tan X = YZ / XZ = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

Answer:

15

Step-by-step explanation:

Because the two triangles are similar:

[tex]\dfrac{LN}{30}=\dfrac{6}{30-18} \\\\\\\dfrac{LN}{30}=\dfrac{6}{12} \\\\\\LN=30\cdot \dfrac{1}{2}=15[/tex]

Hope this helps!

Answer:

Average waiting time = 4 minutes

Step-by-step explanation:

From this question, we are told that the sky train is supposed to arrive every 8 minutes.

Thus, the waiting time of the passengers for the train = 8 minutes.

Then, the average waiting time is simply the mean or 50th percentile of the total waiting time.

So, average waiting time = 50% × 8

Average waiting time = 4 minutes

Answer:

Step-by-step explanation:

The mean of the reading points is

Mean = (5.8 + 5.9 + 4.9 + 5.2 + 5.0 + 4.9 + 6.2 + 5.1 + 5.7 + 6.1)/10 = 5.48

The process is out of control if the mean salt level of the readings is greater than 5.4

For the null hypothesis,

µ = 5.4

For the alternative hypothesis,

µ > 5.4

This is a right tailed test.

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 5.4

x = 5.48

σ = 0.3

n = 10

z = (5.48 - 5.4)/(0.3/√10) = 0.84

Looking at the normal distribution table, the probability corresponding to the z score is 0.7996

The probability value to the right of the z score is 1 - 0.7996 = 0.2

Assuming a significance level of 0.05

Since alpha, 0.05 < than the p value, 0.2, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the process is not out of control. If we had rejected the null hypothesis, then our conclusion would be that the process is out of control.

Answer:

b. 4.9 × 1011

Step-by-step explanation:

Using scientific notation is similar to expressing in standard form. Given that (7 × 105)2

We open the parenthesis. This may first be expressed as

7² × 10⁽⁵⁾²

Then expand,

= 49 × 10¹⁰

To put in scientific notation, 49 = 4.9 × 10

Hence the expression becomes

= 4.9 × 10 × 10¹⁰

Using the laws of indices

= 4.9 ×  10¹¹ in scientific notation

Answer:

4.9 × 1011

Step-by-step explanation:

I did it in grandpoint

Answer:

[tex]47\frac{5}{8}[/tex]

Step-by-step explanation:

Weight from before + Weight gained

[tex]46\frac{3}{8} +1\frac{1}{4}[/tex]

Convert to improper fractions.

[tex]371/8 + 5/4[/tex]

Find the common denominator.

[tex]371/8 + 10/8[/tex]

Add.

[tex]381/8[/tex]

Convert to a mixed fraction.

[tex]47\frac{5}{8}[/tex]

Answer:

47 5/8 kg

Step-by-step explanation:

Ealier weight + gained weight = Monday's weight

46 3/8 + 1 1/4

= 371/8 + 5/4

= 371/8 + 10/8

= 381/8

= 47 5/8 kg

Answer:

option 2

Step-by-step explanation:

Because (0, 900) is a point on the line it means that it costs $900 to make the commercial. A slope of 110 means that they pay $110 every time it's aired so the answer is Option 2.

Answer:

FALSE

Step-by-step explanation:

Answer: g(x)

Step-by-step explanation:

The graph represented by the degrees Fahrenheit outside is y = 2x - 3 where g ( x ) = 2x - 3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Slope m = 2

Given that it was -3 degrees Fahrenheit outdoors when Janelle woke up. The temperature increased by 2 degrees every hour as the morning went on. It implies,

Temperature at start: -3

Changes occur at a rate of 2 degrees each hour.

A line's slope intercept form is y = 2x - 3

Hence , the equation of line is y = 2x - 3 and the graph depicted is g ( x )

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ7

The complete question is attached below :

When Janelle woke up, it was –3 degrees Fahrenheit outside. As the morning progressed, the temperature rose 2 degrees every hour. Which line on the graph could represent this scenario?

a(x)

f(x)

g(x)

h(x)

Answer:

Jaleel is correct because 2 (x + 2) = 2x - 4

Step-by-step explanation:

To solve 2 (x - 2) + 2:

2 (x - 2) + 2

Distribute

2x - 4 + 2

Combine like terms

2x - 2

Lisa did not distribute correctly :)

Answer:

D

Step-by-step explanation:

Answer:

40 - 59 ⇒ 6

60 - 79 ⇒ 5

Answer:

40-59: 6

60-79: 5

Step-by-step explanation:

If you just added up, you can find all the values.

Answer:

The nearest time is 15 years or 180 months

Answer:

63.45

Step-by-step explanation:

First, it should be noted that the question is incorrect because 64 can't be divided by 11 but assuming that the question is correct, the solution is as follows

Given

LCM = 368

HCF = 11

One number = 64

Required

The other number

Let both numbers be represented by m and n, such that

[tex]m = 64[/tex]

From laws of HCF and LCM

The product of both numbers = Product of HCF and LCM

i.e.

[tex]m * n = HCF * LCM[/tex]

By substituting 68 for m; 368 for LCM and 11 for HCF

[tex]m * n = HCF * LCM[/tex] becomes

[tex]64 * n = 368 * 11[/tex]

[tex]64n = 4048[/tex]

Divide both sides by 64

[tex]\frac{64n}{64} = \frac{4048}{64}[/tex]

[tex]n = \frac{4048}{64}[/tex]

[tex]n = 63.25[/tex]

Answer: 5x-3

Step-by-step explanation:

(f+g)(x) means f(x)+g(x). Knowing this, we add the 2 functions together.

2x-6+3x+9

5x-3

Answer:

40°

Step-by-step explanation:

2x = 3x - 20 add like terms

x = 20 and angle l is equal to 3x minus 20 so 3 × 20 - 20 = 40°