Please help and hurry!

Answer:

[tex](a)\ \cos(180 - x)[/tex] --- Never true

[tex](b)\ \cos(90 -x)[/tex] --- Always true

[tex](c)\ \cos(x)[/tex] ---- Sometimes true

[tex](d)\ \cos(2x)[/tex] ---- Sometimes true

Step-by-step explanation:

Given

[tex]\sin(x )[/tex]

Required

Determine if the following expression is always, sometimes of never true

[tex](a)\ \cos(180 - x)[/tex]

Expand using cosine rule

[tex]\cos(180 - x) = \cos(180)\cos(x) + \sin(180)\sin(x)[/tex]

[tex]\cos(180) = -1\ \ \sin(180) =0[/tex]

So, we have:

[tex]\cos(180 - x) = -1*\cos(x) + 0*\sin(x)[/tex]

[tex]\cos(180 - x) = -\cos(x) + 0[/tex]

[tex]\cos(180 - x) = -\cos(x)[/tex]

[tex]-\cos(x) \ne \sin(x)[/tex]

Hence: (a) is never true

[tex](b)\ \cos(90 -x)[/tex]

Expand using cosine rule

[tex]\cos(90 -x) = \cos(90)\cos(x) + \sin(90)\sin(x)[/tex]

[tex]\cos(90) = 0\ \ \sin(90) =1[/tex]

So, we have:

[tex]\cos(90 -x) = 0*\cos(x) + 1*\sin(x)[/tex]

[tex]\cos(90 -x) = 0+ \sin(x)[/tex]

[tex]\cos(90 -x) = \sin(x)[/tex]

Hence: (b) is always true

[tex](c)\ \cos(x)[/tex]

If

[tex]\sin(x) = \cos(x)[/tex]

Then:

[tex]x + x = 90[/tex]

[tex]2x = 90[/tex]

Divide both sides by 2

[tex]x = 45[/tex]

(c) is only true for [tex]x = 45[/tex]

Hence: (c) is sometimes true

[tex](d)\ \cos(2x)[/tex]

If

[tex]\sin(x) = \cos(2x)[/tex]

Then:

[tex]x + 2x = 90[/tex]

[tex]3x = 90[/tex]

Divide both sides by 2

[tex]x = 30[/tex]

(d) is only true for [tex]x = 30[/tex]

Hence: (d) is sometimes true

Answer:

Y = - 12.55X1 + 276.52

Step-by-step explanation:

Given the data:

Age of child :(X) : 4, 6, 10, 13, 14, 17

Time (seconds) (Y) : 230, 205, 132, 119, 108, 62

Using technology, the linear regression equation obtained using the data Given is :

Y = - 12.55X1 + 276.52

Where :

Slope = - 12.55

Intercept = 276.52

This also indicates that a negative slope is present and hence a negative relationship between age of Child and time in seconds.

Answer:

$700

Step-by-step explanation:

Adam = 250 +300(12)=3850

Mandy = 750+200(12)=3150

3850-3150=700

Answer:

A=49 degree

a=13.5

b=11.7

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

1. 4500/100=45

2. 2700/45=60

The reason why is because 45 is 1%, so the way to find the percent is to divide 2700 by 45

Answer:

Consider a circle of radius 8 centimetres. Recall that the centre angle in a circle is always 360˚ . However, a semi-circle is a circle cut in half.

Step-by-step explanation:

So, the formula for the area of a semicircle is A = pi * r^2/2. Let's use that formula to calculate the area of a semicircle with a radius of 8 inches. We'll use 3.14 as an approximation of pi. So, now we plug the values into the equation.

Answer:

[tex]x=26.67[/tex]

Step-by-step explanation:

From the question we are told that:

Height of Pole [tex]h_p=15 foot[/tex]

Height of Man [tex]h_m =6ft[/tex]

Distance from Pole [tex]d_p=40ft[/tex]

Generally the equation for similar Property is mathematically given by

[tex]\frac{h_p}{h_m}=\frac{d_p+x}{x}[/tex]

[tex]x=\frac{h_m*(d_p+x)}{h_p}[/tex]

[tex]x=\frac{6*(40+x)}{15}[/tex]

[tex]x=\frac{240+6x}{15}[/tex]

[tex]x=16+0.4x\\x-0.4x=16[/tex]

[tex]x=16\0.6[/tex]

[tex]x=26.67[/tex]

Answer:

b

Step-by-step explanation:

the styles of different cars are qualitative because it is not given a number, just the different styles.  

Hope this helps

Answer:

[tex]y=\frac{x}{2} -5[/tex]

Step-by-step explanation:

Linear functions are those whose graph is a straight line.

A linear function has the following form: [tex]y=f(x)=a+bx[/tex]

A linear function has one independent variable and one dependent variable.

The independent variable is x and the dependent variable is y.

The degree of a linear equation must be 0 or 1 for each of its variables.

1. The degree of the variable y is 1 which means it is not linear.

2. The degree of the variable y is 1 and the degree of variable x is 1 so it is linear.

3. The degree of the variable y is 1 and the degree of the variable x is 2 so it is not linear.

4. The degrees of the variable violates the linear equation definition so it is not linear.

Answer:

0.308

Step-by-step explanation:

Given the data:

1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 6

The sample mean and standard deviation :

Sample mean, xbar = (1+1+2+2+2+3+3+3+3+4+4+6) / 12 = 2.833

Sample standard deviation, s = 1.40 ( calculator)

Hypothesis :

H0 : μ = 2.4

H0 : μ ≠ 2.4

The test statistic :

(xbar - μ) ÷ (s/√(n))

(2.833 - 2.40) / (1.40/sqrt(12))

Test statistic = 1.0713

Using the Pvalue from Test score calculator :

df = n - 1 = 12 - 1 = 11

Pvalue(1.071, 11) two - tailed

= 0.3069

= 0.307

Answer:

hundreds

Step-by-step explanation:

Answer:

P(x > 10) = 0.6981.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

In this question:

[tex]n = 14, p = 0.8[/tex]

P(x>10)

[tex]P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 11) = C_{14,11}.(0.8)^{11}.(0.2)^{3} = 0.2501[/tex]

[tex]P(X = 12) = C_{14,12}.(0.8)^{12}.(0.2)^{2} = 0.2501[/tex]

[tex]P(X = 13) = C_{14,13}.(0.8)^{13}.(0.2)^{1} = 0.1539[/tex]

[tex]P(X = 14) = C_{14,14}.(0.8)^{14}.(0.2)^{0} = 0.0440[/tex]

[tex]P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.2501 + 0.2501 + 0.1539 + 0.0440 = 0.6981[/tex]

So P(x > 10) = 0.6981.

Answer:

Step-by-step explanation:

vertex at  (x,y)=(1,−1)

axis of symmetry:  x=1

mark brailiest

Answer:

3 more words per minute

Step-by-step explanation:

So Graham types 260 words / 5 minutes = 52 words per minute

And Clair types 275 words / 5 minutes = 55 words per minute

Thus Clair ypes 55-52 = 3 more words per minute

9514 1404 393

Answer:

  60 cm

Step-by-step explanation:

July and August are 2 of the 12 months in the year. The growth for the year can be expected to be 6 times the growth in a 2-month period, so 60 cm.

_____

You could get down to particulars as to the number of days in those two months versus the total number of days in a year. You would have to specify whether it is a leap year. In a non-leap year, the growth might be ...

  365/(31+31) × 10 cm ≈ 58.9 cm

In a leap year, it would be 59.0 cm.

Answer:

it would be 103/25

Step-by-step explanation:

Answer: 103/25

Step-by-step explanation:

Answer:

s=32

Step-by-step explanation:

1. Move the constant to the right hand side and change it's sign so

s=20+12

2. Than calcuate s=20+12 which equals 32

so the solution is 32

Answer: 3900[tex]\pi[/tex] ft^3

if you use the formula on how to find the volume of a cone

V=[tex]\pi[/tex]r^2*h/3

you will insert 30 where the r is, 13 in where h is, after you just solve that and your answer would be 3900[tex]\pi[/tex] ft^3

The amount paid for the bananas is $0.8775.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s.

If both these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

Bananas are on sale for $0.39 per pound. Mr. Schurter bought 3 x 3 /4 pounds of bananas.

Cost of 1 pound of banana = $0.39

Let x be the cost of 3 × 3/4 pounds of banana.

3 × 3/4 pounds = 9/4 pounds

By proportional concept,

1 : 0.39 = 9/4 : x

1 / 0.39 = 9/4 / x

Cross multiplying, we get,

1 × x = (9/4) × 0.39

x = 3.51 / 4

x = 0.8775

Hence the cost of 3 × 3/4 pounds of banana is $0.8775.

To learn more about Proportions, click :

https://brainly.com/question/26974513

#SPJ2

Answer:

2.6457513110645905905016157536393

Hope that this helps!

Answer:

2m is the answer for the missing leg

Step-by-step explanation:

Answer:

Exactly 4 pitches: 15/100

= 0.15

Answer:

0.36x, [tex]\frac{9}{25}[/tex]x

Step-by-step explanation:

36/100 = 9/25

Answer:

√41

Step-by-step explanation:

The distance formula is expressed as;

D = √(y2-y1)²+(x2-x1)²

D = √(4-9)²+(-1+5)²

D = √(-5)²+4²

D = √25+16

D = √41

Hence the required distance between F and J is √41

Answer:

The first option:

7,10,8,11

Step-by-step explanation:

It's going in a pattern by counting numerically every other number. It's does this starting from 6 and starting from 4. I'm not sure how to explain this well but I hope you get it.

Answer:

Always, always.