Find the measure for angle b

Answer:

Step-by-step explanation:

The formula to find the angle between 2 vectors is

[tex]cos\theta=\frac{u*v}{|u||v|}[/tex] which is the dot product of u*v over the (magnitude of u times the magnitude of v). We also know that θ = [tex]\frac{\sqrt{2} }{2}[/tex]. Filling in that formula requires us to find the dot product of u and v, which is

u·v = (2×(-6)) + (a×8) so

u·v = -12 + 8a. Then we need the magnitudes of both u and v:

[tex]|u|=\sqrt{2^2+a^2}=\sqrt{4+a^2}[/tex] and

[tex]|v|=\sqrt{(-6)^2+8^2}=\sqrt{100}=10[/tex]

Putting all of together looks like this:

[tex]\frac{\sqrt{2} }{2}=\frac{-12+8a}{10\sqrt{4+a^2} }[/tex] . Cross multiply to get

[tex]10\sqrt{2}(\sqrt{4+a^2})=2(-12+8a)[/tex] which is tricky to simplify. You really need to know the rules for multiplying radicals to do this correctly. The simplification is

[tex]10\sqrt{8+2a^2}=-24+16a[/tex] and we need to solve for a. Begin by squaring both sides to get rid of the square root to get:

100(8 + 2a²) = 256a² - 768a +576 and simplify some more by distributing through the parenthesis to get

800 + 200a² = 256a² -768a + 576. Combine like terms to come up with

0 = 56a² - 768a - 224 and we need to factor that. Assuming since you're this far in math (pre-calc or maybe late algebra 2) you know how to factor, when you do, you get values for a of - .285714... and 14.

Therefore, the value for a is 14. I checked it...it works

Answer:

a = 14, U = (2, 14)

Step-by-step explanation:

the other answer is correct.

just to add the solution path for the quadratic equation

0 = 56a² - 768a - 224

in general, a quadratic equation usually expressed in x

0 = ax² + bx + c

has its solution as

x = (-b ± sqrt(b² - 4ac))/(2a)

for us here this looks like this then

a = (768 ± sqrt(768² - 4×56×-224))/(2×56) =

= (768 ± sqrt(589824 + 4×56×224))/112 =

= (768 ± sqrt(589824 + 50176))/112 =

= (768 ± sqrt(640000))/112 = (768 ± 800)/112

a1 = (768 + 800)/112 = 1568/112 = 14

a2 = (768 - 800)/112 = -32/112 = -0.29

and the negative solution would be for a vector solution in the wrong direction (down instead of up). as V is pointing up left, and the angle is only 45 degrees (pi/4), also U has to point up.

so, 14 is the solution for U.

Answer:

1

Step-by-step explanation:

the answer is in the image above

Answer:

No entiendo

Step-by-step explanation:

Answer:

y = 5

Step-by-step explanation:

    [tex]x \ \alpha \ y[/tex]

[tex]=> x = k \times y\\=> 35 = k \times 7\\=> k = 5[/tex]

    [tex]x = k \times y[/tex]

[tex]=>25 = 5 \times y\\ =>5 = y[/tex]

Answer:

y = 5

Step-by-step explanation:

x = 35, y = 7

x = ?y

35 = ?7

? = 5

x = 25, y = ?

x = ?y

25 = 5y

y = 5

Answer:

1,171,875

Step-by-step explanation:

The sequence is multiplying by 5 every time. It will be 3, 15, 75, 375, 1875, 9375, 46,875, 234,375, and then 1,171,875

Step-by-step explanation:

The relative frequency for a 15% discount is 52.1%.

The relative frequency is the quotient of a particular frequency divided by the total number of frequencies.

Given:

A store is giving out cards labeled 1 through 10 when customers enter the store.

If the card is an even number, you get a 15% discount on your purchase that day.

The subgroup for even numbers = 2, 4, 6, 8, 10

The subgroup frequency = 56 + 50 + 54 + 49 + 54 = 263

The total frequency = 500

The relative frequency = 263/500 = 0.521 = 52.1%

Therefore, 52.1% is the relative frequency.

To learn more about the relative frequency;

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Answer:

Step-by-step explanation:shsjsjdhdbshchdhchfhchdfhehxbehchr hehfhehdhejsjwhd khasa

Answer:

4,398.23

Step-by-step explanation:

Answer:

Step-by-step explanation:

radius=diameter/2

=14/2

=7 mm

volume of cylinder=πr^2h

=3.14*(7)^2*10

=3.14*41*10

=1287.4 mm^3

Answer:

The answer is "Option D"

Step-by-step explanation:

In this question the "choice D" is wrong because [tex]H_a: \mu_d \neq 0[/tex].

Answer:

both apply

Step-by-step explanation:

i guessed just do it

Answer:

answer for this solution is 18π

Step-by-step explanation:

area =πr²

81π = πr²

r² = 81

r = 9

circumference = 2πr

= 2π*9

=18π

Answer:

the value of a rare coin in the beginning of the first year,

t = 0, so f(0) = 4• 2^0 = 4•1 = 4 (y-intercept)

Answer:

the y-intercept is at t=0, so in the model no time has past yet. it's the initial value of the coin

Answer:

24 per day

Step-by-step explanation:

'x' = days, so since 24 is with x, the rate of change is 24

Answer:

Step-by-step explanation:

Equations:

Double the second equation and subtract from the first one:

Find p:

Answer:

Ishaan is correct because snakes with 17 1/4 inches occured most often  in the dot plot. Raj is incorrect because 17 3/4 didnt occur the most often but it was the highest length of the snake. Ishaan is correct.

Step-by-step explanation:

Answer:

0.75

Step-by-step explanation:

Given that the probability of winning a game is 25%

Pr(they don't win) = 1 - Pr(they win)

Pr(they don't win) = 1 - 0.25

Pr(they don't win) = 0.75

Hence the probability that they won is 0.75 or 75%

Answer:

0.5

Step-by-step explanation:

Wanted outcome / possible outcomes = 0.5 in this case.

Answer:

Third table

Step-by-step explanation:

For the relationship to be proportional

y/x = constant

First table y/x = 8/4 = 2    then 7/11 doesn't =2  so it is not

Second table y/x =52/5 = 5    then 49/7 doesn't =5  so it is not

Third table y/x = 3/6=1/2    then 5/10 = 1/2   then 7/14 = 1/2  it is proportional

Last table y/x = 6/3 = 2    then 11/8 doesn't =2  so it is not

Answer:

[tex]( {x}^{2} + 12)(x + 2)[/tex]

Step-by-step explanation:

[tex] {x}^{3} +2 {x}^{2} +12x+24[/tex]

[tex]( {x}^{3}+2 {x}^{2} )+12x+24[/tex]

[tex] {x}^{2} (x+2)+12(x+2)[/tex]

[tex]( {x}^{2} + 12)(x + 2)[/tex]

The population of interest: Male RCCC students.

Sample size: 31.

The sample mean: 69.68 inches.

Median: 69 inches.

Mode: 70 inches.

Range: 11 inches.

Standard deviation: 3.32 (rounded to 2 decimal places).

Variance: 11.02 (rounded to 2 decimal places).

We have,

Mean:

To find the mean, we sum up all the heights and divide by the total number of data points (31 in this case):

Mean = (70 + 70 + 70 + ... + 75) / 31

Mean ≈ 69.68 inches

Median:

The median represents the middle value in the dataset when arranged in ascending order. Since the dataset has an odd number of values (31), the median will be the value in the middle position when ordered:

Median = 69 inches

Mode:

The mode represents the value(s) that occur most frequently in the dataset. In this case, the mode is the height that appears most often:

Mode = 70 inches

Range:

The range is calculated by subtracting the minimum value from the maximum value in the dataset:

Range = Maximum height - Minimum height

Range = 75 - 64 = 11 inches

Standard Deviation (σ):

To find the standard deviation, we can use the formula that involves finding the difference between each value and the mean, squaring those differences, averaging them, and taking the square root:

Standard Deviation (σ) ≈ 3.32 (rounded to 2 decimal places)

Variance (σ²):

The variance is the square of the standard deviation.

We can square the value of the standard deviation to find the variance:

Variance (σ²) ≈ 11.02 (rounded to 2 decimal places)

The height dataset (in inches) for the 31 male RCCC students is as follows:

1 70

2 70

3 70

4 70

5 71

6 64

7 64

8 65

9 65

10 66

11 66

12 67

13 67

14 68

15 68

16 68

17 69

18 72

19 72

20 72

21 72

22 73

23 73

24 73

25 73

26 73

27 73

28 74

29 75

30 75

31 75

32 75

Thus,

The population of interest: Male RCCC students.

Sample size: 31.

The sample mean: 69.68 inches.

Median: 69 inches.

Mode: 70 inches.

Range: 11 inches.

Standard deviation: 3.32 (rounded to 2 decimal places).

Variance: 11.02 (rounded to 2 decimal places).

Learn more about mean here:

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Answer:

Step 1: 180 (straight line)-156(interior angle)=24(exterior angle)

Step 2: 360÷24= 15 sides

Answer:what’s the answer?

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

Cosine = base/ hypotenuse = 6/10 = 3/5

Answer:

The two inequality are : x ≤  100 and x ≥ 60

So the inequality is : 60 ≤ x≤ 100.

Step-by-step explanation:

Answer:

Hi so the answer to this equation is:

60 _< x _< 100

Step-by-step explanation:

Sorry if it looks a little complicated, another way of phrasing it would be 60 less than or equel to x less than or equel to 100. I think this is the answer because she only has 100 braclets so she cant sell more than that, hence less than or equel to 100. and i believe it is 60 because if she sells each braclet for 5 dollars and her goal is 300, 60 would allow her to reach her goal because 5 x 60 = 300. and she needs to earn at least 300 buckaroos for her fundraiser.

Im not super great with algebra but i hope this is right and that it helps you

peace✌

Hope it helps you!

-miraculousfanx-

Answer:

p2 = (-9 , -3)

Step-by-step explanation:

let p2 be (a , b)

given :

p1(-1 , 7) = (x1 , y1)

p2(a , b) = (x2 , y2)

using midpoint formula:

midpoint = (x1 + x2/2 , y1 + y2/2)

(-5 , 2) = (-1 + a/2 , 7 + b/2)

Now , compare corresponding elements

-5 = -1 + a/2

-5*2 = -1 + a

-10 = -1 + a

-10 + 1 = a

-9 = a

2 = 7 + b/2

2*2 = 7 + b

4 = 7 + b

4 - 7 = b

-3 = b

therefore p2 = (-9 , -3)

Answer:

0.5944 = 59.44% probability that the team has at least 2 grade 11 students

Step-by-step explanation:

The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

We have that:

6 + 8 = 14 students, which means that [tex]N = 14[/tex]

6 grade 11 students means that [tex]k = 6[/tex]

Teams of 4 members means that [tex]n = 4[/tex]

What is the probability that the team has at least 2 grade 11 students?

This is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,14,4,6) = \frac{C_{6,0}*C_{8,4}}{C_{14,4}} = 0.0699[/tex]

[tex]P(X = 1) = h(1,14,4,6) = \frac{C_{6,1}*C_{8,3}}{C_{14,4}} = 0.3357[/tex]

Then

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0699 + 0.3357 = 0.4056[/tex]

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.4056 = 0.5944[/tex]

0.5944 = 59.44% probability that the team has at least 2 grade 11 students

Answer:

D. x = 5; x = -5

Step-by-step explanation:

x^2 - 25 = 0

Add 25 to each side

x^2 - 25+25 = 0+25

x^2 = 25

Take the square root of each side

sqrt(x^2) = sqrt(25)

x = ±5