Part 1: Given cosine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,∞).

Part 2: Given θ = 495°, convert the value of θ to radians and find sec θ.

The estimate of the percentage expression 66 2/3% of 2,600 is 1733.33

The expression is given as:

66 2/3% of 2,600

Rewrite as:

66 2/3% * 2,600

Express the fraction as an improper fraction

200/3% * 2,600

Remove the percentage sign

200/300 * 2,600

Evaluate the product

1733.33

Hence, the estimate of the percentage expression 66 2/3% of 2,600 is 1733.33

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Step-by-step explanation:

First expression ...

[tex] = {ax}^{3} y[/tex]

[tex] = a \times x \times x \times x \times y[/tex]

Second expression.....

[tex] = b {x}^{4} {y}^{3} [/tex]

[tex] = b \times x \times x \times x \times x \times y \times y \times y[/tex]

HCF = common factor...

[tex] = x \times x \times x \times y[/tex]

[tex] = {x}^{3} y[/tex]

[tex]hence \: {x}^{3} y \: is \: the \: answer....[/tex]

Answer: HCF =

x³y

Step-by-step explanation:

HCF of ax³y and bx⁴y³

ax³y = a . x . x . x . y

bx⁴y³ = b . x . x . x . x . y . y . y

Common Factors = x . x . x . y

HCF = x . x . x . y

HCF = x³y Answer

therefore, the HCF of ax³y and bx⁴y³ is x³y.

hope that helps...



note: the dot (.) represents multiplication.

Answer:

The probability of scoring fewer than 5 runs when they win is P = 0.19

How to find the probability?

We know that:

The probability of winning a game is p = 0.53

The probability of scoring 5 or more runs is q = 0.59

The probability of winning and scoring 5 or more runs is k = 0.43

Notice that the joint probability is different than the product of the individual probabilities, this means that the events are not independent.

So, we know that the probability of winning is 0.53

Now, given that they win, the probability of scoring 5 or more times will be q' such that:

0.53*q' = 0.43

q' = 0.811

This means that when they win, the probability of scoring more than 5 times is 0.81

Then the probability of scoring less than 5 times when they win is 1 minus the above probability:

P = 1 - 0.81 = 0.19

The probability of scoring fewer than 5 runs when they win is P = 0.19

Answer:

I believe that the answer is A

Hi student, let me help you out! :)

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We are asked to find the slope of this graph; we are provided with two points:

[tex]\star~\mathrm{(6,0)}[/tex]

[tex]\star~\mathrm{(0,-5)}[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Here's the formula:

[tex]\star~\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}[/tex]

Where

y2 and y1 are y-coordinates

x2 and x1 are x-coordinates

Substitute the values:

[tex]\star~\mathrm{\cfrac{-5-0}{0-6}}}[/tex]

Simplify!

[tex]\star~\mathrm{\cfrac{-5}{-6}}}[/tex]

Simplify more!

[tex]\star~\mathrm{\cfrac{5}{6}}[/tex]

Hope it helps you out! :D

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Answer:

m∠A = 90°

Step-by-step explanation:

In isosceles triangle base angles are congruent. That means we can equate measurments of angle B and angle C and solve for x!

m∠B = m∠C

11x - 10 = 7x + 10

4x - 10 = 10

4x = 20

x = 5

Now let's insert x back in the expressions for angles.

m∠B = (11x − 10)° = (11(5) − 10)° = 45°

m∠C = (7x + 10)° = (7(5) + 10)° = 45°

Sum of all angles in the triangle is 180°. Let's make an equation.

m∠A + m∠B + m∠C = 180°

m∠A + 45°+ 45° = 180°

m∠A  = 90°

The closest to the maximum number of cups the punch bowl can hold is 30

The given parameters are:

1 cup = 15 cubic inches

Diameter of bowl, d = 12 inches

The radius is the half of the diameter.

So, we have:

r = 6

The volume of the bowl is then calculated using:

[tex]V = \frac{2}{3}\pi r^3[/tex]

This gives

[tex]V = \frac{2}{3}\pi * 6^3[/tex]

Evaluate

V = 452.16

The maximum number of cups is then calculated using:

Cups = 452.16/15

Evaluate

Cups = 30.1444

Approximate

Cups = 30

Hence, the closest to the maximum number of cups the punch bowl can hold is 30

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The 48 flies of them will live longer than 21 days if there are 300 houseflies in the study.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have mean u = 18 days

SD = 3 days

X = 21 days

From the formula:

Z = (X - u)/SD

Z = (21 - 18)/3 = 1

P(x<21) = 0.84134

P(x>21) = 1 - P(x<21) = 0.15866

Number of flies = 300×0.15866 = 47.59 ≈ 48 flies

Thus, the 48 flies of them will live longer than 21 days if there are 300 houseflies in the study.

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Omar ran 950 meters farther than Paula. Option A is correct.

The total number of centimeters they both ran is 745000 centimeters. Option D is correct.

The distance between two objects can be determined by finding their difference.

From the given information:

The way to solve this is by converting all the distances to meters.

The total number of centimeters they both ran is:

= (420000+325000) centimeters

= 745,000 centimeters

Therefore, we can conclude that Omar ran 950 meters farther than Paula. The total number of centimeters they both ran is 745000 centimeters.

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Answer:

Omar ran 950 meters farther than Paula. Option A is correct.

The total number of centimeters they both ran is 745000 centimeters. Option D is correct.

How do we determine the distance between two objects?

The distance between two objects can be determined by finding their difference.

From the given information:

Paula ran 3 1/4 kilometers

Omar ran 4200 meters

The way to solve this is by converting all the distances to meters.

Paula = 3250 meters

Omar = 4200 meters

Difference in their distance = (4200 - 3250) meters

Difference in their distance = 950 meters.

The total number of centimeters they both ran is:

= (420000+325000) centimeters

= 745,000 centimeters

Therefore, we can conclude that Omar ran 950 meters farther than Paula. The total number of centimeters they both ran is 745000 centimeters.

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Step-by-step explanation:

Answer:

the last one 1/6

Step-by-step explanation:

1/2 x 1/3 = 1/6

The length of side of triangle portion CE is 16.

When two triangles forms on the same base, has its other two sides in proportional with each other, the triangles are known as the similar triangles.

Given, the dimensions AD = 24, DB = 27 and EB = 18.

In the given diagram of two similar triangles, ABC and DBE

DB/AD = EB/CE

Substitute the values, we get

27/24 = 18/CE

CE= 16

Thus, the value of CE = 16

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The slope of the line is the negative 4/3 and y-intercept will be the negative 1.

The correct equation is given below.

−4x − 3y = 3

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equation of the line will be

−4x − 3y = 3

Then the equation of a line can be written as

4x + 3y = −3

       3y = −4x − 3

         y = −(4/3)x − 1

Then the slope of the line is the negative 4/3 and y-intercept will be the negative 1.

The graph is given below.

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The true statement about the quadratic function is that it has two distinct real zeros

The given parameters are:

The first highlight above means that, the function can be represented as:

y = a(x - x1)(x -x2)

Where x1 and x2 are the x-intercepts

This also means that the quadratic function has two distinct real zeros

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The cost of the ice needed to make 50 snow cones is $54.50.

The first step is to determine the volume of the snow cone.

Volume of the snow cone =volume of a cone + volume of the hemisphere

Volume of the cone = 1/3πr²h

1/3 x 3.14 x 10.2 x (8.3/2)² = 183.87 cm³

Volume of the hemisphere = 2/3πr³

2/3 x 3.14 x (8.3 / 2)³ = 224.43 cm³

Total volume = 224.43 cm³ + 183.87 cm³ = 408.30 cm³

Volume of 50 snow cones =  408.30 cm³ x 50 = 20,414.82

Total grams of ice needed = density x volume

0.697 x 20,414.82 = 14,229.13 grams

Convert gram to 1kg

1kg = 1000g

= 14,229.13 grams  / 1000 = 14.23kg

Cost of the ice = 14.13 x 3.83 = $54.50

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Answer:

let numbers be=x -3=3-x × 4(3-x) x=8 hence 12 -4x=8 = 12-8

Answer:

Step-by-step explanation:

1) Let the unknown angle = x

   x +  43 + 90 = 180

            x + 133 = 180

                      x = 180 -133

                     [tex]\sf \boxed{\bf x = 47^\circ}[/tex]

2) x + 88 + 30 = 180

            x + 118 =180

                   x  = 180 - 118

                  [tex]\sf \boxed{\bf x = 62^\circ}[/tex]

3) x + 98 + 40 = 180

            x + 138 = 180

                    x  = 180 - 138

                    [tex]\sf \boxed{\bf x = 42^\circ}[/tex]

The value of the quotient of 0.378 ÷ 0.3 is 1.26

The quotient of 0.378 ÷ 0.3 is

The expression is given as:

0.378 ÷ 0.3

Rewrite as a fraction

0.378/0.3

Multiply the fraction by 1

Express 1 as 1000/1000

0.378/0.3 * 1000/1000

Evaluate the product

378/300

Divide 378 by 300

1.26

Hence, the quotient of 0.378 ÷ 0.3 is 1.26

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Answer:

f(3) = - 10

Step-by-step explanation:

given

f(n) = f(n - 2) + f(n - 1) , then

f(3) = f(3 - 2) + f(3 - 1) = f(1) + f(2) = - 6 + (- 4) = - 6 - 4 = - 10

[tex]f(3)=f(1)+f(2)=-6+(-4)=-10[/tex]

Answer:

1.64

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

6.6^2 + x^2 = 6.8^2

43.56+x^2=46.24

Subtract 43.56 from each side

x^2 = 46.24-43.56

x^2 =2.68

Take the square root of each side

sqrt(x^2) = sqrt(2.68)

x =1.637080554

To 3 significant digits

x = 1.64

Answer:

Step-by-step explanation:

       x = 1.637 mm

        We can use Pythagorean theorem, to find the unknown side for a right angled triangle.

The side opposite to 90 is the longest side and it is the hypotenuse.

Base² + altitude² = hypotenuse²

 x²     + 6.6²        = 6.8²

      x²  +  43.56  = 46.24

                     x²   = 46.24 - 43.56

                    x²    = 2.68

                      x   = √2.68

                      [tex]\sf \boxed{\bf x = 1.637 \ mm }[/tex]

Step-by-step explanation:

Hopefully this is helpful?

Answer:

[tex]\textsf{x = 45}[/tex]

Here, the given 2 angles are complementary angles. The sum is 90 degrees as indicated by the right angle symbol.

[tex]\textsf {Solving :}[/tex]

[tex]\implies \textsf{x - 2 + 47 = 90}[/tex]

[tex]\implies \textsf{x + 45 = 90}[/tex]

[tex]\implies \textsf{x = 45}[/tex]

Answer:

$ 4.50

Step-by-step explanation:

2% of the price = 9 cents

.02 x   = 9

x = 9 / .02 = 450 cents     or  $4.50

Answer:

2 × 2 × 2 × 3 × 7

Step-by-step explanation:

Answer:

The last option y= -2x-3

Step-by-step explanation:

this equation passes through the point (-2,1)

Answer:

The data is spread out from 1 to 10 pounds of trash

Step-by-step explanation:

Because you see the X's on all the numbers through 1-10, there is none on 0. The other answer options are incorrect

Answer:

False

Step-by-step explanation:

Here's a simple little trick to tell wether a system of inequalities has any solutions or not, just by looking at it:

By following this logic, since the system given has different slopes, it only has one solution. Therefore your answer is false.

Hope this helps you.

Answer:

D where the funds to start and operate your business.........

Answer:

THE ANSWER IS C

Step-by-step explanation:

just add it it and find it 0.007

The probability of getting two red chips is:

P = 1/21.

The probability of getting a red chip is equal to the quotient between the number of red chips and the total number of chips.

There are 4 blue chips and 3 red chips, for a total of 7 chips.

For the first draw, the probability of getting a red one is:

p = 3/7.

For the second draw, now there are 2 red chips and 6 chips in total, so now the probability is:

q = 2/6 = 1/3

Then the joint probability, given by the product between the two individual probabilities, is:

P = q*p = (3/7)*(1/3) = 1/21.

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