ASAP PLEASE please please

Step-by-step explanation:

a ∈ (0; π/2) here means that our angle, a must lie between 0 and pi/2, exclusive.

So this mean our angle must be in between 0 and pi/2, but can not be neither 0 and pi/2.

Here we have

[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]

We must find cos.

Using the Pythagorean theorem

[tex]( \sin( \alpha ) ) {}^{2} + ( \cos( \alpha ) ) {}^{2} = 1[/tex]

It is mostly notated as this,

[tex] \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1[/tex]

But they mean the same thing, we know

[tex] \sin( \alpha ) = \frac{3 \sqrt{11} }{10} [/tex]

So we plug that in for sin a.

[tex]( \frac{3 \sqrt{11} }{10} ) {}^{2} + \cos {}^{2} ( \alpha ) = 1[/tex]

[tex] \frac{99}{100} + \cos {}^{2} ( \alpha ) = 1[/tex]

[tex] \cos {}^{2} ( \alpha ) = \frac{100}{100} - \frac{99}{100} [/tex]

[tex] \cos {}^{2} ( \alpha ) = \frac{1}{100} [/tex]

Since cos is Positve over the interval (0; π/2), we take the positive or principal square root.

[tex] \cos( \alpha ) = \frac{1}{10} [/tex]

2. We would get the same work for the second part, the only difference is that cosine is negative over the interval

(π/2, π)

So the answer for 2 is

[tex] \cos( \alpha ) = - \frac{1}{10} [/tex]

Disclaimer: Your work you did was correct, just remember for fractions like

[tex]1 - \frac{99}{100} [/tex]

Convert 1 into a fraction that has a denominator of 100.

[tex] \frac{100}{100} - \frac{99}{100} = \frac{1}{100} [/tex]

The length of the bedroom exists at x = 9 and y = 6.

From the given information, we get

Then  [tex]$\frac{(1/4)}{(9/4)} = \frac{1}{x}[/tex]

Solve this for x.

simplifying the value of x we get

Equate (1/9) to 1/x.

x = 9 (feet).

Convert 1.5 inches to feet using a proportion:

[tex]$\frac{(1/4)}{(1.5)} = \frac{1}{y}[/tex]

Solve this for y.

simplifying the value of y we get

(1/4)y = 3/2

Multiply both sides of the equation by 4.

y = 6

Therefore, the length of the bedroom exists at x = 9 and y = 6.

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Answer:

a. 9m

Step-by-step explanation:

Pi = 3.14 = 22/7

formula :

Area of a Sector of a Circle = (central angle)/360 * πr² =

(central angle)/360 * πr² = Area of a Sector of a Circle

43/360 * Pi * r^2 = 30.39

r^2 = (30.39 * 360) / (Pi * 43)

r^2 = (30.39 * 360) / (22/7 * 43)

r = √ (30.39 * 360 * 7) / (22 * 43)

r = √76582.8/946

r = √80.9543340381

8.99746264444 which is roughly

9

The radius of the sector will be 9m. The correct option is A.

The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc segment by simulating it as a network of connected line segments.

The radius will be calculated as below:-

Area of a Sector of a Circle = (central angle)/360 * πr² =

(Ф)/360 * πr² = Area of a Sector of a Circle

43/360 * Pi * r²= 30.39

r² = (30.39 * 360) / (Pi x 43)

r²= (30.39 x 360) / (22/7 x 43)

r = √ (30.39 x 360 x 7) / (22 x 43)

r = √76582.8/946

r = √80.9543340381

r = 9

Therefore, the radius of the sector will be 9m. The correct option is A.

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Based on the given graphs and their equations, the solutions will be located at points (-2, 7) and (0, 1).

To find the solution to y = -2x+ 3, assume that x is a certain number then solve for y.

Given the options, we can assume that x = -2. Solution is:

= -2(-2) + 3

= 4 + 3

y = 7

Solution point is (-2, 7)

The second equation can be solved by equating x to 0:
y = 0² - 0 + 1

y = 1

Solution point is:

= (0, 1)

In conclusion, the solution points are (-2, 7) and (0,1).

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The graph (C) Y represents the function g(x) = (x 1`)2.

To find which of the graphs below represents the function g(x) = (x 1)2:

Parabola: It's a conic section formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements.

Therefore, the graph (C) Y represents the function g(x) = (x 1)2.

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Answer:

D

Step-by-step explanation:

Let x be the first batch

let y be the second batch

y=2x

His brothers each received 9 rolls from the second batch i.e. 9×4=36

So

2x= 36+ (10÷6)x

2x - (10÷6)x = 36

12x-10x = 216

x=108

and y= 2 × 108= 216

Answer:

there are 54 buffalos in 150 acres

Step-by-step explanation:

1. determine the rate of buffalos per acres

45 buffalos per 125 acres =

45 / 125 =

0.36 buffalos per 1 acre

now we know the rate of buffalos per 1 acre, we can multiply it by the required amount of acres (in this case 150)

buffalos per 1 acre x total acres = total buffalos per total acres

0.36 x 150 = 54 buffalos

therefore, there are 54 buffalos per 150 acres.

hope this helps :)

The distance between two slits is d =2.89*10^-7 m

Distance between slits,   d=2.89*10^-7 m

It is given that,

Wavelength, λ = 410nm= 410*10^-9 m

Angle, θ =45

We need to find the distance between two slits that produces first minimum. The equation for the destructive interference is given by :

dsinθ =(n+1/2) λ

For first minimum, n = 0

dsinθ =(1/2) λ

So, d is the distance between slits

d ={1/2 λ}sinθ

=2.89*10^-7 m

So, the distance between two slits is d =2.89*10^-7 m. Hence, this is the required solution.

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Answer:

a) 175 m

b) 20 cm

Explanation:

scaled size → actual size

1 cm represents 25 m

a)

In the scaled size on the map, the distance from church to village is 7 cm.

Then actual size,

1 cm → 25 m

7 cm → (25 × 7) m

7 cm → 175 m

b)

half a kilometer = 0.5 km = 500 m

Then scaled size,

25 meter → 1 cm

500 meter → 500/25 cm = 20 cm

Answer:

let the angles be 3x,4x&5x

Now,

perimeter (p)=sum of all sides

or, 96=3x+4x+5x

or, 96=12x

or,96/12=x

or,8=x

or,x=8

Then,

3x=3*8

=24

4x=4*8

=32

5x=5*8

=45

[tex] \: \: \: \: \: \: \: y = \frac{ - 7x}{8} + 4 \\ \: \: \: \: \: \: multiply \: all \: by \: 8 \\ \: \: \: \: \: \: \: \: 8y = - 7x + 32 \\ \: \: \: \: \: \: \: \: \: 7x + 8y = 32[/tex]

Answer:

x = 2

Step-by-step explanation:

note that 64 = [tex]2^{6}[/tex]

then

[tex]x^{6}[/tex] = [tex]2^{6}[/tex] , so x = 2

Answer:

x=16

Step-by-step explanation:

6= x/4 + 2

Subtract 2 from both sides.

4= x/4

Multiply 4 to both sides.

x=16

Hope this helps!

Answer:

y = - [tex]\frac{1}{3}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2-y_{1} } }{x_{2-x_{1} } }[/tex]

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (3, 4) ← 2 points on the line

m = [tex]\frac{4-5}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex] = - [tex]\frac{1}{3}[/tex]

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = - [tex]\frac{1}{3}[/tex] x + 5 ← equation of line

Step-by-step explanation:

the highest or greatest or largest common factor is the product of the prime factors the numbers have in common :

540 ÷ 2 = 270

270 ÷ 2 = 135

135 ÷ 2 no

135 ÷ 3 = 45

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 3 no

5 ÷ 5 = 1

540 = 2² × 3³ × 5¹

360 ÷ 2 = 180

180 ÷ 2 = 90

90 ÷ 2 = 45

45 ÷ 2 no

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 3 no

5 ÷ 5 = 1

360 = 2³ × 3² × 5¹

so, the HCF = 2² × 3² × 5¹ = 4×9×5 = 180

(1)

to satisfy the condition max. 180 visitors can be invited.

(2)

540 / 180 = 3

so, every visitor can receive 3 pieces of chicken.

and 360 / 180 = 2 cups of drink.

Answer:

9

Step-by-step explanation:

you have to plug in the numbers and solve it, so it would go as follows:

-(-3^2)- 2(-5)(2) - /2/

-9 + 20 - 2 =

9

i hope this helps

Answer:

b

Step-by-step explanation:

the opposite sides of a parallelogram are parallel and congruent

thus option b is the correct one

Answer:

i) a = 2, b = - 3, c =-6

Step-by-step explanation:

4x² - 12x + 3

4x² - 6x - 6x + 9 - 6

(2x - 3)(2x - 3) - 6

(2x - 3)² - 6

(2x + (- 3) )² - 6

In form of (ax + b)² - 6

a = 2, b = - 3, c =-6

Answer:

B

Step-by-step explanation:

First create the equation that has slope of -1 in the form of y=mx+b. Because the slope is -1, m=-1, so the equation is y=-x+b. Now we see that we are given the point (-3, 8) as an intersection point. Substitute x and y for -3 and 8 in our equation. With this information, our equation becomes 8=3+b. Solving, b=5. Our equation is now y=-x+5.

Simplifying all of the answer choices, we have

A. y=-x-5

B. y=-x+5

C. y=-x-5

D. and E. as what they already show

The only answer that matches is B.

The lower and upper bounds of h - k are 42.31 and 42.49 respectively.

Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.

The upper and lower bounds can be written using error intervals

The lowest value of h is 47.15

The greatest value of h is 47.24

The greatest value of k is 4.84

The lowest value of k is 4.75

Thus upper bound of h -k = 47.24 - 4.75 = 42.49

Thus lower bound of h -k = 47.15 - 4.84 = 42.31

Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively.

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The graph of the given equation is shown below

From the question, we are to determine the graph that represents the given equation

The given equation is

4x - 3y = -1

The graph of the equation is shown below

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#1

The unit is pounds

#2

So

#3

We shall use cups

#4

We should use pints

Answer:

1. pounds (lb)

2. pints (pt)

3. teaspoon (tsp)

4. cups (c)

Step-by-step explanation:

Liquid

128 fl oz = 16 cups = 8 pints = 4 quarts = 1 gallon

Mass

32000 ounces = 2000 pounds = 1 ton

1.  The best US standard unit in which to measure pumpkin with a mass of 1.2 kg would be pounds (lb).

⇒ 1 kg ≈ 2.205 lb

⇒ 1.2 kg ≈ 1.2 × 2.205 = 2.65 lb

2. The best US standard unit in which to measure stock with a volume of 1.5 L would be pints (pt).

⇒ 1 L ≈ 2.133 pt

⇒ 1.5 L ≈ 1.5 × 2.113 = 3.17 pt

3. The best US standard unit in which to measure sugar of 5 mL would be teaspoon (tsp).

⇒ 5 mL = 5 g ≈ 1 teaspoon

4.  The best US standard unit in which to measure yogurt with a volume of 0.25 L would be cups (c).

⇒ 1 L ≈ 4.167 c

⇒ 0.25 L ≈ 0.25 × 4.167 =  1.04 c

The equation of the parabolic shape of the gate is:

(x - 40)² = -64(y - 25)

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

The vertex is at the middle of the parabola, that is, a width of 80/2 = 40 meters and a height of 25 meters, hence h = 40, k = 25, and the equation is:

y = a(x - h)² + k

y = a(x - 40)² + 25

When x = 0, y = 0(start of the arc), hence the leading coefficient is found as follows:

0 = 1600a + 25

a = -25/1600

a = -1/64.

Hence the equation is:

y = -1/64(x - 40)² + 25

(x - 40)² = -64(y - 25)

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Answer:

A function that is positive in the entire interval [-3, -2] is -x2 - 5x - 5.

Answer:

The second function (second graph and choice)

Step-by-step explanation:

If you look at the second function you will see that within the closed interval [-3,-2] the graph y  values are positive

First choice is incorrect since at x = -2  the y value is negative

Third choice incorrect since at x = -2, y value is negative

Fourth choice incorrect since y value is negative for x = -2

The volume of the total chocolate is 80 ml, where as the volume of each chocolate is 13.33 ml.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the volume of each chocolate. Hence:

6 * volume of each chocolate = (380 - 300) ml

6x = 80

Divide both sides of the equation by 6:

x = 13.33 ml

The volume of the total chocolate is 80 ml, where as the volume of each chocolate is 13.33 ml.

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The probability of event A and event B IS  15/91.

What is the probability?

Probability determines the odds that a random event would occur. The odds lie between 0 and 1.

The probability of event A  = number of brown marbles / total number of marbles

= 6/14

The probability of event B = number of orange marbles / total number of marbles -1

= 5/13

P(A and B) =6/14 x 5/13

                 = 30/182

                 = 15/91

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Answer:

B.) 5/13

Step-by-step explanation:

15/3=5

91/7=13

5/13

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The total surface area of the solid object is 2660.925 square cm the answer is 2660.925 square cm.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

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

The surface area of the

= surface area of half sphere + surface area of the cylinder - surface area

  of one circular base

The radius r = (64-50)/2 = 7 cm

= (1/2)[4π(7)²] + 2π(7)(50) + 2π(7)² - π(7)²

= (1/2)[615.75] + 2506.99 - 153.94

= 307.875 + 2506.99 - 153.94

= 2660.925 square cm

Thus, the total surface area of the solid object is 2660.925 square cm the answer is 2660.925 square cm.

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Answer:

Math allows the animator to find the unknowns from a set of equations and to work out the aspects of the geometric figures when dealing with the objects that move and change.

Step-by-step explanation:

To learn more:

weusemath.org/?career=animator

Hope this helps!

Answer: (-4, 0) and (4, 8)

Step-by-step explanation:

Looking at the graph, we can see where the line passes the parabola and can tell the solutions are (-4, 0) and (4, 8)

Using the normal distribution, there is a 0.3228 = 32.28% probability that at least 90 cars pass inspection.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

The parameters for the binomial distribution are given by:

n = 100, p = 0.88.

Hence the mean and the standard deviation for the approximation are:

The probability that at least 90 cars pass inspection, using continuity correction, is P(X > 89.5), which is one subtracted by the p-value of Z when X = 89.5, hence:

Z = (89.5 - 88)/3.25

Z = 0.46

Z = 0.46 has a p-value of 0.6772.

1 - 0.6772 = 0.3228.

0.3228 = 32.28% probability that at least 90 cars pass inspection.

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