Find the angle θ between ???? and ???? if ????⋅????=12‖????‖⋅‖????‖. (Use symbolic notation and fractions where needed. Give your answer in terms of π. )

Answer:

Step-by-step explanation:

M = S+3

W = 2M = 2(S+3) = 2S+6

M+S+W = 89

(S+3)+S+(2S+6) = 89

S = 20

Answer:

20

Step-by-step explanation:

Sarah: 21

Mary: 24

Winifred: 48

No

Sarah: 20

Mary: 23

Winifred: 46

Yes

Answer:

A. reflection.

Step-by-step explanation:

If you were to use the reflection rule, then your answer will be:

B' (Now D): (1 , 2)

A' (Now E): (4 , 2)

C' (Now F): (3 , 5)

In this case, the reflected triangle does not match the given points, therefore it cannot be reflection.

~

Answer:

19.80

Step-by-step explanation:

Given the equation :

y = a (e)^kt

If a = 100, y = 50, and k = -0.035, find t.

50 = 100(e)^(-0.035t)

50/100 = e^(-0.035t)

0.5 = e^-0.035t

Take the In

In(0.5) = - 0.035t

-0.693147 = - 0.035t

-0.693147 / - 0.035 = t

19.8042 = t

Hence, t = 19.80

Answer:

The answer is D, the last one.

9514 1404 393

Answer:

  (d)  opens up, (1, -3), narrower

Step-by-step explanation:

The factor of +2 multiplying the function tells you the graph is expanded vertically by a factor of 2. The parent function opens upward, and the positive sign on this expansion factor does not change that. The expansion means that y-values will be farther from the vertex for the same x-value distance from the vertex. This give the appearance of a narrower graph.

As always, the transformation ...

  f(x -h) +k

moves the vertex from (0, 0) to (h, k). Here, you have (h, k) = (1, -3), so that is the location of the vertex of the transformed function.

[tex]\frac{13}{28}[/tex]

Given:

Blue marbles: 3

Reb marbles: 5

Total marbles: 8

Two marbles are selected at random, one after the other with replacement.

Getting the same colour of marbles from the selection means the two marbles are both red or both blue.

(a) Probability of getting 2 marbles being red in colour

i. Probability of picking a red at the first selection:

Number of red marbles ÷ Total number of marbles

=> 5 ÷ 8 = [tex]\frac{5}{8}[/tex]

ii. Probability of picking a red at the second selection:

Number of remaining red marbles ÷ Total number of remaining marbles

Since after the first pick, the marble is not replaced, the remaining red marbles is 4 while the total number of remaining marbles is 7

=> 4 ÷ 7 = [tex]\frac{4}{7}[/tex]

iii. The probability of getting both marbles being red is the product of i and ii above. i.e

[tex]\frac{5}{8}[/tex] x [tex]\frac{4}{7}[/tex] = [tex]\frac{5}{14}[/tex]

(b) Probability of getting 2 marbles being blue in colour

i. Probability of picking a blue at the first selection:

Number of blue marbles ÷ Total number of marbles

=> 3 ÷ 8 = [tex]\frac{3}{8}[/tex]

ii. Probability of picking a blue at the second selection:

Number of remaining blue marbles ÷ Total number of remaining marbles

Since after the first pick, the marble is not replaced, the remaining blue marbles is 2 while the total number of remaining marbles is 7

=> 2 ÷ 7 = [tex]\frac{2}{7}[/tex]

iii. The probability of getting both marbles being blue is the product of i and ii above. i.e

[tex]\frac{3}{8}[/tex] x [tex]\frac{2}{7}[/tex] = [tex]\frac{3}{28}[/tex]

(c) Probability of getting 2 marbles of the same colour.

The probability of getting 2 marbles of same colour is the sum of the probability of getting both marbles of red colour and the probability of getting both marbles as blue colour. i.e The sum of a(iii) and b(iii)

[tex]\frac{5}{14}[/tex] + [tex]\frac{3}{28}[/tex] = [tex]\frac{13}{28}[/tex]

The probability of getting 2 of the same colour is [tex]\frac{13}{28}[/tex]

Answer:

less than or equal to -26

Answer:

9+c < 15

OR

c < 6

Step-by-step explanation:

"the sum of 9 and c" means: 9+c

"is less than or equal to 15" means: < 15

If you need to simplify it, then subtract 9 from both sides, and you get

c < 6

Answer:

3 units

Step-by-step explanation:

(4,2) (7,2)

Subtract 4 from 7 = 3

Subtract 2 from 2 = 0

This means that (7,2) is 3 units up from (4,2).

:) ur welcome

Answer:

Step-by-step explanation:

D=√(x2-x1)²+(y2-y1)²

D=√(7-4)²+(2-2)²

D=√(3)²+0

D=3²*½

D=3

Answer:

They are both 42 cm

Step-by-step explanation:

Answer:

[tex]\frac{20}{40} \ and \ \frac{4}{8} \ is \ equivalent[/tex]

Step-by-step explanation:

1.

[tex]\frac{2}{3} \ and \ \frac{12}{9} \\\\\frac{2}{3} \ and \ \frac{4}{3}\\\\Not \ equivalent[/tex]

2.

[tex]\frac{20}{40} \ and \ \frac{45}{55}\\\\\frac{1}{2} \ and \ \frac{9}{11}\\\\Not\ equivalent[/tex]

3.

[tex]\frac{20}{40} \ and \ \frac{4}{8}\\\\\frac{1}{2} \ and \ \frac{1}{2} \\\\Equivalent[/tex]

4.

[tex]\frac{5}{5} \ and \ \frac{25}{50} \\\\\frac{1}{1} \ and \ \frac{1}{2} \\\\not \ equivalent[/tex]

Answer:

A and D are the answer.

Step-by-step explanation:

We can factor this by grouping

[tex]2 {x}^{2} + 5x - 3[/tex]

[tex]2 {x}^{2} + 6x - x - 3[/tex]

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

The roots are

[tex](x + 3) = 0[/tex]

and

[tex]2x - 1 = 0[/tex]

Let solve for zero in each roots.

[tex]x = - 3[/tex]

[tex]2x = 1[/tex]

[tex]x = \frac{1}{2} [/tex]

Answer:

Test statistic = - 2.71

Step-by-step explanation:

Table of the sample data is attached below :

Using a dependent sample t test :

H0 : μd = 0

H0 : μd ≠ 0

The difference in the 6th and 13th date data is :

Difference, d = -4, -6, -3, -1, 1, -7

The sample size, n = 6

The mean of d ; μd = Σd/ n = - 3.667

Standard deviation of difference, Sd = 3.011

The test statistic : μd/(Sd/√n)

Test statistic = - 3.33 / (3.011/√6)

Test statistic = - 3.33 / 1.2292356

Test statistic = - 2.709

Test statistic = - 2.71

Answer: Approximately 2.29 cm

Step-by-step explanation:

See a pattern?

Week 9 = [tex]1.67(1.04)^{9-1} =1.67(1.04)^{8} =1.67(1.3686)=2.2855[/tex]

Question

Simplify

[tex]2(12 - \frac{18}{3} + 4)[/tex]

Answer:-

ATQ->

[tex]2(12 - ( \frac{ \cancel{18}^{ \: \: \: 6} }{3} ) + 4 \\ 2(12 - 6 + 4) \\ 2(16 - 6) \\ 2(10) \\ 20 \: \: is \: your \: ans[/tex]

Answer:

Depends on how the 3 and the 18 are positioned in the fractions on the equation.

47/3

4

Step-by-step explanation:

Step 1. To simplify this, you need to know one of the most basic sayings in math which summarizes the Order of Operations: PEMDAS

Using PEMDAS:

P- Parenthesis

E- Exponents

M- Multiply

D- Divide

A- Add

S- Subtract

P- Parenthesis: We start off by preforming the parts of the equation within the parenthesis.

The 2 on the outside of the parenthesis, will not affect anything until we deal with what is inside the parenthesis.

The next part that we do, is to go through the rest of the steps, looking for either exponents, multiplication or division, skipping over the adding and subtracting until those are done.

The next part that we see, is Division.

D- Division

We find the point of division after the 18. The value we get has to be either:

a. 3/18

b. 18/3

depending on what you were asking for.

The equation, 2(12-18\3+4) at the bolded point, states that the division should be 1/6 because of the way of the division symbol.

Now the equation should either be one of the following:

a. 2(12-1/6+4)

b. 2(12-6+4)

A-Addition

Now, we can add the 4 to the number we got before, which should get us either

A. 1/6+4

B. 6+4

which added together gets us either

A. 25/6<=>4+1/6

B. 10

S-Subtraction

Now, we subtract both parts from the value of 12 getting us:

A. 12-(4+1/6)=12-4-1/6=8-1/6=7+5/6<=>47/6

B. 12-10=2

M-multiply:

Now we move on to the 2 we put aside earlier and multiply both of the answers:

A. 2(47/6)=47/3 or 15+2/3

B. 2(2)=4

Thus the answer is either 47/3 or 4

9514 1404 393

Answer:

Step-by-step explanation:

Let c represent the number of messages sent by Chang. Then Keiko sent (c-7) messages, and Abdul sent 4(c-7) messages. The total number sent was ...

  c + (c -7) +4(c -7) = 109

  6c -35 = 109 . . . . . . . . . . simplify

  6c = 144 . . . . . . . . . . . add 35

  c = 24 . . . . . . . . . . . divide by 6

  c-7 = 17

  4(c-7) = 68

Keiko sent 17, Chang sent 24, and Abdul sent 68 text messages.

Answer:

0.2917 = 29.17% probability that a randomly selected female student on campus will have served a mission.

Step-by-step explanation:

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

In this question:

1200 female students, out of them, 350 have served a mission. So

[tex]p = \frac{350}{1200} = 0.2917[/tex]

0.2917 = 29.17% probability that a randomly selected female student on campus will have served a mission.

Answer: [tex]R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}[/tex]

Step-by-step explanation:

Given

Two forces of 9 and 13 lbs acts [tex]38^{\circ}[/tex] angle to each other

The resultant of the two forces is given by

[tex]\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}[/tex]

Insert the values

[tex]\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb[/tex]

Resultant makes an angle of

[tex]\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}[/tex]

So, the resultant makes an angle of [tex]22.57^{\circ}[/tex] with 9 lb force

Angle made with 13 lb force is [tex]38^{\circ}-22.57^{\circ}=15.43^{\circ}[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]4(x+y)^{2} - 9(x-y)^{2}=4[x^{2}+2xy+y^{2}]-9[x^{2}-2xy+y^{2}]\\\\=4x^{2}+4*2xy + 4y^{2}-9x^{2}-2xy*(-9)+y^{2}*(-9)\\\\= 4x^{2}+8xy+4y^{2}-9x^{2}+18xy-9y^{2}\\\\= 4x^{2}-9x^{2} + 8xy + 18xy +4y^{2} - 9y^{2}\\\\= -5x^{2} + 26xy - 5y^{2}[/tex]

= -5x² + 25xy + xy - 5y²

= 5x(-x + 5y) - y(-x +5y)

= (-x + 5y)(5x - y)

Answer:

554 executives should be surveyed.

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 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

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.

Standard deviation of 3 hours.

This means that [tex]\sigma = 3[/tex]

The 95% level of confidence is to be used. How many executives should be surveyed?

n executives should be surveyed, and n is found with [tex]M = 0.25[/tex]. So

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

[tex]0.25 = 1.96\frac{3}{\sqrt{n}}[/tex]

[tex]0.25\sqrt{n} = 1.96*3[/tex]

[tex]\sqrt{n} = \frac{1.96*3}{0.25}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*3}{0.25})^2[/tex]

[tex]n = 553.2[/tex]

Rounding up:

554 executives should be surveyed.

Answer:

[tex] - \frac{ \sqrt{3} }{2} [/tex]

Step-by-step explanation:

Unit circle

Answer:

The rotation rule states that rotation 90° counterclockwise means (x, y) = (-y, x)

The new points would be equal to:

Try graphing it to see if the new points make sense(because I'm not too sure :\)

Answer:

1000

Step-by-step explanation:

Answer:

The answer is true

Step-by-step explanation:

Answer:

1. Tyler

2. 8.33

3. 8.5

4. Tyler

Step-by-step explanation:

this is just playing with the numbers. no complex math concepts.

Tyler's graph shows she reached 1 mile after 8 1/3 minutes (8 minutes and 20 seconds). that is 25/3 minutes.

according to Elena's equation she reached 1 mile (x=1) after 8.5 minutes. that is 8 1/2 minutes or 8 minutes and 30 seconds.

so, we see that Elena took more time (10 seconds longer) to run 1 mile, so Tyler was faster.

to generally compare the 2 we can write also Tyler's graph as function (like for Elena) :

8 1/3 = 8.333333....

y = 8.33x

but that is just FYI (not asked for here).

since Tyler was faster (and her graph also showed a straight line of time and distance up to 10 minutes and beyond, so, she did not slow down after the first mile), she also ran further after 10 minutes. that is the definition of "being faster" - to go further in the same amount of time.

Tyler needed 8.33 minutes per mile.

Elena needed 8.5 minutes per mile.

and so, Tyler was faster.

points 1 and 4 are directly coupled. they both express the same thing.

Answer:

Add equations A and C to eliminate y and add B and C to eliminate y

Step-by-step explanation:

From the equation given, we can see that the coefficient of y in A and C are alternating values 5 and  -5 which cancels out on adding same for B and C. Hence t eliminate y, we will add B and C and A and C

Therefore the correct answer will be to eliminate add equations A and C to eliminate y and add B and C to eliminate y

Answer:

20

Step-by-step explanation:

6 + 2 = 8

8 + 3 = 11

11 + 4 =15

15 + 5 =20

Answer:

20

Step-by-step explanation:

the pattern is increase the number by one more than the increase before. so 6,8=2 greater

8-11=3 greater. 11-15=4 greater. so, 15+5=20 (with this answer being 5 greater continuing the pattern.)

Answer:

[tex]{ \tt{rate \: of \: change \: in \: A = 9}}[/tex]

Rate of change in function A is two times than that in function B