If the probability that a student in school wears contacts is 0.38 and the probability that a student in the same school has a car is 0.42, what is the probability that a student wears contacts and has a car?

Answer:

[tex](a)\ h = d * \tan(\theta)[/tex]

[tex](b)\ h = 30.57m[/tex]

Step-by-step explanation:

Given

[tex]\theta = 17^o[/tex]

[tex]d =100m[/tex]

[tex]h = ??[/tex]

See attachment for illustration

Solving (a): Trigonometry ratio to calculate h.

From the attachment, we have:

[tex]\tan(\theta) = \frac{h}{d}[/tex]

Multiply both sides by d

[tex]d * \tan(\theta) = \frac{h}{d} * d[/tex]

[tex]d * \tan(\theta) = h[/tex]

Rewrite as:

[tex]h = d * \tan(\theta)[/tex]

Solving (b): The value of h

We have:

[tex]\theta = 17^o[/tex]

[tex]d =100m[/tex]

So:

[tex]h = 100m * \tan(17^o)[/tex]

[tex]h = 100m * 0.3057[/tex]

[tex]h = 30.57m[/tex]

Answer:

-5 ; 1/2

Step-by-step explanation:

GIVEN :-

TO FIND :-

GENERAL CONCEPTS TO BE USED IN THIS QUESTION :-

Lets say there's a quadratic polynomial f(x) = ax² + bx + c , whose factors are (x - α) & (x - β). To find the values of x for which f(x) will be zero , equate the factors of f(x) with 0.

⇒ (x - α) = 0 & (x - β) = 0

⇒ x = α & x = β

Hence, it can be concluded that if (x - α) & (x - β) are factors of f(x) , then α & β are the roots of f(x).

SOLUTION :-

Factorise f(x) = 2x² + 9x - 5.

[tex]=> 2x^2 + 10x - x - 5[/tex]

[tex]=> 2x(x + 5) - 1(x + 5)[/tex]

[tex]=> (x + 5)(2x - 1)[/tex]

So , the factors of f(x) are (x + 5) & (2x - 1). Now equate the factors with zero.

⇒ (x + 5) = 0 & (2x - 1) = 0

⇒ x = -5 & x = 1/2

∴ The zeroes of f(x) = 2x² + 9x - 5 are (-5) & (1/2)

VERIFICATION :-

1) Put x = -5 in f(x) = 2x² + 9x - 5

⇒ f(-5) = 2(-5)² + 9×(-5) - 5

           = 50 - 45 - 5

           = 50 - 50  

           = 0

2) Put x = 1/2 in f(x) = 2x² + 9x - 5

[tex]f(\frac{1}{2} ) = 2 \times (\frac{1}{2} )^2 + 9 \times \frac{1}{2} - 5[/tex]

       [tex]= 2 \times \frac{1}{4} + \frac{9}{2} - 5[/tex]

       [tex]= \frac{1}{2} + \frac{9}{2} - 5[/tex]

       [tex]= \frac{ 1 + 9 - 10}{2}[/tex]

       [tex]= \frac{0}{2}[/tex]

       [tex]= 0[/tex]

Answers:

======================================================

Explanation:

The template for a 30-60-90 triangle is that the short leg x leads to hypotenuse 2x, and longer leg x*sqrt(3). If x = 4, then we get the sides 4, 8, 4*sqrt(3) which are the short leg, hypotenuse, and long leg in that order.

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The template for a 45-45-90 triangle is that we have x as the leg length and x*sqrt(2) as the hypotenuse. If x = 6, then we end up with the sides 6, 6, 6*sqrt(2)

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The triangle with sides 6, 8, 10 is a right triangle because a = 6, b = 8, c = 10 makes a^2+b^2 = c^2 true. I'm using the converse of the pythagorean theorem. We don't have a special right triangle because these sides do not fit the templates mentioned in the previous two sections above.

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The triangle with sides a = 7, b = 8, c = 10 on the other hand will not make a^2+b^2 = c^2 true. Note that a^2+b^2 = 7^2+8^2 = 113 which is not the same as 10^2 = 100. However, a triangle is possible because adding any two sides leads to a sum larger than the third side (triangle inequality theorem).

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We cannot form a triangle with sides 7, 12, 19 because the sides 7 and 12 add to 7+12 = 19 but that's not longer than the third side 19.

The triangle inequality theorem says that if you want to form a triangle with sides a,b,c then the following three inequalities must all be true

a+b > c

a+c > b

b+c > a

Answer:

(5, 6, 9)

Step-by-step explanation:

The domain is basically the set of all x values while the range is the set of all y values, in this case, it's the values of f(x). To find the range, we can plug the x values into the equation:

f(-2) = 9

f(-1) = 6

f(0) = 5

f(1) = 6

f(2) = 9

Since we can't have repeats in the range, it would be: (5, 6, 9)

Answer: 3.9047 rounded to the nearest thousandth is 3.9050, or 3.905.

Step-by-step explanation:

You round 47 up to 50, which gets you to 3.9050, which you can then reduce it to 3.905.

Answer:

t  =  2.25 h

Step-by-step explanation:

In the case, I cover distance d in 3 hours

d =  3 * v₁      (1)

In the second case my speed increase by 1/3 then my speed is  

v₁ + (1/3) v₁   =  (3/3  + 1/3  ) *v₁

my new speed is   (4/3) * v₁  and

d  =  (4/3)*v₁ * t    (2)

Dividing (2) by  (1)  we get

1   = (4/3) *v₁*t/ 3*v₁

1  =  (4/9)*t

t = 9/4  h

t  =  2.25 h

Answer:

Area of the composite figure = 42 in²

Step-by-step explanation:

Composite area of the given figure = Area of the rectangle + Area of the right triangle

Area of the rectangle = Length × Width

                                    = 6 × 5

                                    = 30 in²

Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                         = [tex]\frac{1}{2}(4)(6)[/tex]

                                         = 12 in²

Area of the composite figure = 30 + 12

                                                  = 42 in²

Answer:

-3,6

Step-by-step explanation:

Answer:

2.44%

Step-by-step explanation:

[tex]\frac{22}{900} *100%[/tex]= 2.44%

Answer:

The cofunction of [tex]\tan \frac{2\pi}{11}[/tex] is [tex]\cot \frac{7\pi}{22}[/tex].

Step-by-step explanation:

In trigonometry, a function is a cofunction of another if and only if [tex]f(A) = g(B)[/tex], where A and B are complementary angles. In this case, the complementary function of a tangent function must be a cotangent function, this is:

[tex]\tan \frac{2\pi}{11} = \cot \left(\frac{\pi}{2} - \frac{2\pi}{11} \right)[/tex]

[tex]\tan \frac{2\pi}{11} = \cot \frac{7\pi}{22}[/tex]

[tex]\tan \frac{2\pi}{11} = \frac{1}{\tan \frac{7\pi}{22} }[/tex]

[tex]0.642 = \frac{1}{1.556}[/tex]

[tex]0.642 = 0.642[/tex]

Answer: [tex]5\dfrac{1}{4}\ \text{cups of flour}[/tex]

Step-by-step explanation:

Given

Klarissa requires [tex]1\ \frac{3}{4}[/tex] cups of flour to make a recipe

Convert mixed numeral to fraction

[tex]\Rightarrow 1\dfrac{3}{4}=\dfrac{4+3}{4}\\\\\Rightarrow \dfrac{7}{4}[/tex]

If she wants to triple the recipe then,

[tex]\Rightarrow 3\times \dfrac{7}{4}=\dfrac{21}{4}\\\\\Rightarrow \text{or}\ 5\dfrac{1}{4}\ \text{cups of flour}[/tex]

Answer:

Choice 3

Step-by-step explanation:

The third fraction (third refers to the answer number) is incorrect. As written, the cups won't cancel. The correct way to do this is to invert the fraction.

4 tablespoons

===========

1/4 cup

This is an extremely important procedure to know. Make sure you understand what the basis of it is. Often  times in higher physics, you don't have a proper relationships and this method (called dimensional analysis) is the only tool you have to work with.

So each term has at least 1 cancelation that occurs with the prior term. And it is the units that you look to cancel, and that determines which way to put the intermediate steps.

Answer:

Step-by-step explanation:

angle 1=130 degree(being alternate angles)

angle 2=50 degree

angle 2 +130=180 degree(being co interior angle)

angle 2=180-130

angle 2=50 degree

Answer:

m<1 = 50

m<2 = 130

Step-by-step explanation:

From the picture, you can inference that m<1 looks like 130 degrees, and m<2 does not. You can tell because m<1 looks like a wide-angle, while m<2 looks like a closed-angle. So, m<1 is 130 degrees.

To find m<2 subtract 180 by 130 because 180 is the measure of a straight angle.

180 - 130 = 50

So m<1 = 50

Answer and Step-by-step explanation:

THE QUESTION IS NOT FROM A QUIZ, IT IS FROM A HOMEWORK ASSIGNMENT.

The unit rate is D. $4.00 per pound.

This is because we see on the graph that at 1 pound of fudge, the cost is 4 dollars.

When looking at the unit rate, you want to look at y value for when x is 1.

#teamtrees #PAW (Plant And Water)

Answer:

A=h(b)b/2

Step-by-step explanation:

Answer:

C when multiplying negative numbers if you multiply a negative by a negative you get a positive.

Answer:

By the Pythagorean theorem, it follows that the hypotenuse of this triangle has length c = √a2 + b2, the same as the hypotenuse of the first triangle. Since both triangles' sides are the same lengths a, b and c, the triangles are congruent and must have the same angles. ... If a2 + b2 = c2, then the triangle is right.

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

=2.5(6*4)/6

=2.5*4(6 and 6 gets cancel)

=10

Answer: $240

Step-by-step explanation:

Given

Ahmad earns 6 days daily from 9 am to 5 Pm at a rate of $30 per hour

The total no of hours he worked on a single day is 8 hours

So, the amount he earns on daily basis is

[tex]\Rightarrow 8\times 30\\\Rightarrow \$240[/tex]

Answer:

10.7

Step-by-step explanation:

use

a^2+b^2=c^2

...........

Answer:

x ≈ 10.72

Step-by-step explanation:

Use the Pythagorean Theorem, or

a² + b² = c²

to find x.

a² + b² = c²

9² + x² = 14²

81 + x² = 196

Subtract 81 from both sides.

x² = 115

Take the square root.

x = √115

When rounded to the nearest hundredth as a decimal, the answer is

x = 10.72.

Answer:

Step-by-step explanation:

the circumference you make it using the diameter , pi times ( 3.142 times)

C = 13* 3.142 = 40.846

Answer:

6 (24÷3) -2

6 (8) -2

48-2

=46

Brackets of division multiplication add and subtract

Answer:

x=-15.2

Step-by-step explanation:

Answer:

21.42 cloves of garlic

Step-by-step explanation:

50 ÷ 7 = 7.14

7.14 x 3 = 21.42