1. There are 50 contestants signed up for a TV show. There are 36 more female contestants than male contestants. How many female contestants have signed up to compete? Show your solution and explain how you plan to explain this to your students.

Answer:

x = 15 & y = 35

Step-by-step explanation:

[tex]y = x + 20[/tex]

[tex]x + y = 50 \\ x + (x + 20) = 50 \\ 2x + 20 = 50 \\ 2x = 50 - 20 \\ 2x = 30 \\ x = \frac{30}{2} = 15[/tex]

[tex]y = x + 20 = (15) + 20 = 35[/tex]

Answer:

Step-by-step explanation:

(4, 2)

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the area of the rectangle is 80. 1  cm²

From the given information, let's say one side of rectangle = a

The other side  =  (36 - 2a)/2  

=  18 - a   cm

The angles between the diagonals of the rectangle is 78°

Then, the angle diagonal has with base will give

=  (180° - 78°)/2

= 102/2

= 51°

We have the angle to be 51 degrees, using the tan ratio

Tan θ = opposite/ adjacent

Opposite of angle 51 degrees = a

Adjacent = 18 - a

Thus,

[tex]tan 51 = \frac{a}{18 - a}[/tex]

[tex]1. 2349 = \frac{a}{18-a }[/tex]

cross multiply

[tex]18 -a ( 1. 2349) = a[/tex]

[tex]22. 23 - 1. 2349a = a[/tex]

collect like terms

[tex]a + 1. 2349a = 22. 23[/tex]

[tex]2. 2349 a = 22. 23[/tex]

[tex]a = \frac{22. 23}{2. 2349}[/tex]

a = 9. 95

If a = 9. 95cm

Then, 18 - a = 18 - 9. 95 = 8. 05cm

The formula of area of a rectangle is given as;

Area = width × length

Area = 9.95 x 8.05

Area = 80. 1  cm²

Thus, the area of the rectangle is 80. 1  cm²

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The height of the right pyramid is 48.53 cm.

A rectangle pyramid is a 3-dimensional shape that is made up of a rectangular base and 4 triangular faces.

Height = ( 3 x Volume of a pyramid) /( area)

Height = (3 x 21452) / 1326 = 48.53 cm

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The final percent of juice is 10%

We initially have one quart that is 40% juice and 60% water.

Then initially we have:

Then we add another 3 quarts of water, so the new mixture has:

So we have 4 quarts of mixture.

The new percentage of juice will be:

P = (0.4 quarts/4 quarts)*100% = 10%

The final percent of juice is 10%

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The total interest is $107,270

What is monthly payment formula?

The formula for monthly payment is:

[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]

We can find total interest as shown below:

Value of property = $475,000

Money available as a deposit = $80,000

P = 475,000-80,000

= 395000

t = 25 year

r = 2% = 0.02

n = 25*12 = 300

[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]

Putting the value of P, t, r, and n in the above formula

[tex]=\frac{395000(\frac{0.02}{12} )(1+\frac{0.02}{12}) }{(1+\frac{0.02}{12})^{300}-1}[/tex]

after solving the above expression

M = $1674.22

Interest = M*n-P

Putting the value of P, n and M

= 1674.22*300-395000

= 502266-395000

= 107,266

Rounding to nearest ten dollar

= $107,270

Hence, the total interest is $107,270.

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Answer:

Step-by-step explanation:

Answer:

slope is -1

Step-by-step explanation:

Slope of the line is changes in y over changes in x. It can also be referred as rise over run.

We can express mathematically as:

[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

where m is slope.

Let (-2,5) be [tex]\displaystyle{(x_2,y_2)}[/tex] and (6,-3) be [tex]\displaystyle{(x_1,y_1)}[/tex]. Hence, apply the slope formula:

[tex]\displaystyle{m=\dfrac{5-(-3)}{-2-6}}\\\\\displaystyle{m=\dfrac{5+3}{-8}}\\\\\displaystyle{m=\dfrac{8}{-8}}\\\\\displaystyle{m=-1}[/tex]

Therefore, the slope is -1

Answer:

3/2y-5

Step-by-step explanation:

The pattern of 324, 256, 196, 144 is the square of the even numbers in a descending order starting from 18.

A sequence is a set of things next to each other in a set order. It is also referred to as a series.

According to this question, the following sequence is given: 324, 256, 196, 144. A careful observation of these numbers shows that each is the square of even numbers.

18² = 324

16² = 256

14² = 196

12² = 144

Therefore, the pattern of 324, 256, 196, 144 is the square of the even numbers in a descending order starting from 18.

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Answer: 5

Step-by-step explanation:

Because there are 35 when you add yourself so u subtract 30 to get 5

There would be 4 people left in the garden.

34 - 30 = 4.

Subtraction is a mathematical operation that involves taking away one number from another to find the difference between them. For the question, At first, there were 34 people in the garden and later 30 people were no longer alive in the garden, so the difference between 30 people and 34 people is 4.

Subtraction is the opposite of addition, and it is used to measure the distance between two values on the number line.

Subtraction is represented by minus Sign (-). For example, subtracting 5 from 10 gives you a difference of 5 (10 - 5 = 5).

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The value of csc theta is [tex]\frac{3. 61}{2}[/tex]

It is important to note that the ratio for cot is given as;

Cot theta = adjacent/opposite

cosec theta = hypotenuse/opposite

If cot theta = 3/2, then

Adjacent = 3

Opposite = 2

Using Pythagoras theorem, we have

Hypotenuse square = opposite + adjacent square

[tex]H = \sqrt{2^2 + 3^2}[/tex]

[tex]H = \sqrt{4 + 9}[/tex]

[tex]H = 3. 61[/tex]

Cosec theta = [tex]\frac{3. 61}{2}[/tex]

Thus, the value of csc theta is [tex]\frac{3. 61}{2}[/tex]

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Answer:

3.16/2

Step-by-step explanation:

Have a great day

Answer:

Step-by-step explanation:

The given relation between length and width can be used with the area formula to write an equation for the dimensions of the rectangle.

Let w represent the width of the rectangle. The length is 3 more than twice that, so is (2w+3). The area is the product of length and width.

  A = LW

  54 = (2w +3)(w)

Rewriting this equation to standard form gives ...

  2w² +3w -54 = 0

  (2w -9)(w +6) = 0 . . . . factored

  w = 9/2, -6 . . . . . . . . . values that make the equation true

Only the positive width makes sense in a geometry problem, so we have ...

  w = 9/2

  length = 2w +3 = 12

The length of the rectangle is 12 meters; its width is 4.5 meters.

If the value of a is negative, the line is reflected across any of the axis

The equation is given as:

y = ax

The new line is given as

y = -ax

The above implies that y = ax is transformed to y = -ax

The transformation can be any of:

Hence, if the value of a is negative, the line is reflected across any of the axis

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The pairs of prime numbers (a,b) between 1 and 10 inclusive such that a^b * b^a+1 is prime are

The expression that is a prime number is given as:

a^b * b^a + 1

The boundary or range of numbers of a and b is not given.

So, we make use of numbers between 1 and 10

i.e. 1 ≤ a ≤ 10 and 1 ≤ b ≤ 10

Using the above range, we have the following program to determine the pairs of prime numbers (a, b).

for a in range(1,11):

   for b in range(1,11):

       num = (a* *b) * (b* *a) + 1

       flg = False

       if num > 1:

           for i in ra nge(2, num):

               if (num % i) == 0:

                   flg = True

                   break

       if not flg:

           print(str(a)+","+str(b))

The output of the above program is:

(1,1), (1,2), (1,4), (1,6), (1,10), (2,1), (2,2), (2,3), (2,4), (3,2), (4,1), (4,2), (4,4) and (4,6)

The above represent all pairs of prime numbers (a,b) such that a^b * b^a+1 is prime

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[tex](2m+1)+(2n+1)=2m+2n+2\\\\=2(m+n+1)[/tex]

From the calculation, we can see that /BC/ is 8 sin 35. Option D

We can see the image of the triangular piece of cloth as shown in the image. This shows that we have to approach the problem by the use of the trigonometric ratios.

Hence;

/AC/ = 8 in

/BC/ = x

<A = 35 degrees

Sin 35 = /BC//8

/BC/ = 8 sin 35

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(a). All four sides are equal and the angles are right-angled (90 degrees).

(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.

(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.

One of the first areas of mathematics is geometry, along with arithmetic. It is focused on spatial characteristics that relate to the proximity, size, shape, and relative placement of objects.

(a). Two features that make the shape square are all four sides equal and the angles are right-angled (90 degrees).

(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.

(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.

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Answer:

C. 3(x+1)(x-1)-4x

Step-by-step explanation:

3(x+1)(x-1)-4x

(x+1)(x-1)=x^2-1

3(x^2-1)-4x

3x^2-4x-3

Answer:  

- 2/3

Step-by-step explanation:

Answer:

Any equation that has the same slope as the line y = -2/3x + 1 but a different y-intercept will be parallel because the lines will never intersect. For example, y = -2/3x + 2 or y = -2/3x + 3.

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The notation for the translation is (x, y) → (x + 2, y + 2)

The translations are given as:

The above implies that we add 2 to the x coordinate and 2 to the y coordinate.

So, we have:

(x, y) → (x + 2, y + 2)

Hence, the notation for the translation is (x, y) → (x + 2, y + 2)

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Linking each equation with its equivalent equation below:

Equivalent equation can be defined as an equation that has the same value with another equation.

Equivalent equation are not directly the same but can be transformed to look like each other.

In conclusion, The equivalent equations have been matched in the list above.

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At 90 degrees, the tangent of x is undefinable.

The domain of y = tan (x):

y = tan(x)

Except for 90, all sets of positive real numbers fall within the domain of y = tan(x).

At 90 degrees, the tangent of x is undefinable.

Due to the exclusion of 90, all sets of positive real numbers are included in the domain of y = tan(x).

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The complete statement is (d) Any rational root of f(x) is a factor of 9 divided by a factor of 12.

The polynomial is given as:

12x^3 - 5x^2 + 6x + 9

The first term in the above equation is 12 i.e. 12x^3, while the last term is 9

To determine the possible rational roots, we divide the factors of the last term i.e. 12 by the factors of the first term i.e. 12

Hence, the complete statement is (d) Any rational root of f(x) is a factor of 9 divided by a factor of 12.

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Answer:

D

Step-by-step explanation:

I took the test

Answer:

slope intercept form: y = mx + b

6x - 4y = 24

4y = 6x - 24

y = 3/2x - 6

slope: 3/2

y intercept: - 6

Answer:

y = 3/2 x -6

The slope is 3/2 and the y intercept is -6

Step-by-step explanation:

6x-4y = 24

The slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

We need to solve the equation for y

6x-4y =24

Subtract 6x from each side

6x-4y-6x =-6x+24

-4y = -6x+24

Divide each side by -4

-4y/-4 = -6x/-4  + 24/-4

y = 3/2 x -6

The slope is 3/2 and the y intercept is -6

Answer:

English (Ingles):
10 Women come to the party.

Spanish (Espanol):

10 Las mujeres vienen a la fiesta.

Step-by-step explanation:

English (Ingles):

We know that there are 16 people there at the start. 25% of those people are women. We can work out by subtracting 100 by 25 that 75% of the p-eople there are men. We need to do 25% of 16 so we can work out how many men and women there are there.

So we find 10% of 16 which is 1.6 then we take off 5% of 1.6 which is 0.08. We then double 1.6 to get 20% which gives us 3.2. We now add on the 5% to make it 25% which gives us 4.

This means 25% of 16 is 4.

This tells us that there are 4 women at the party and 12 men as 16 - 4 = 12.

It now says that more women arrive which makes the percentage for men go down to 60%. We now need to add 5% on to the 25% of women there are which will tell us how many more women there are now and it will let us work out how many women and men there are in total now.

As we can't do this without it giving us 4.8, we know that 25% of people is 4 women which means 50% of people would be 8 women and we make an estimate of how many women have joined which gives us 6 people which means the total amount of women at the party is 10.

Spanish (Espanol):

Sabemos que hay 16 personas allí al principio. El 25% de esas personas son mujeres. Podemos calcular restando 100 por 25 que el 75% de las personas son hombres. Necesitamos hacer el 25% de 16 para poder calcular cuántos hombres y mujeres hay allí.

Así que encontramos el 10 % de 16, que es 1,6, luego quitamos el 5 % de 1,6, que es 0,08. Luego duplicamos 1,6 para obtener el 20%, lo que nos da 3,2. Ahora sumamos el 5% para convertirlo en 25%, lo que nos da 4.

Esto significa que el 25% de 16 es 4.

Esto nos dice que hay 4 mujeres en la fiesta y 12 hombres como 16 - 4 = 12.

Ahora dice que llegan más mujeres lo que hace que el porcentaje de hombres baje al 60%. Ahora necesitamos agregar un 5% al ​​25% de mujeres que hay, lo que nos dirá cuántas mujeres más hay ahora y nos permitirá calcular cuántas mujeres y hombres hay en total ahora.

Como no podemos hacer esto sin que nos dé 4.8, sabemos que el 25% de las personas son 4 mujeres, lo que significa que el 50% de las personas serían 8 mujeres y hacemos una estimación de cuántas mujeres se han unido, lo que nos da 6 personas que significa que la cantidad total de mujeres en la fiesta es 10.

The functions could represent g(x) is B. [tex]g(x) = f(x - 5)[/tex]

Using the general equation [tex]g(x) =f(x)+ b[/tex]

The g(x) has intercept of y=-2,

Then the  y-intercept of f(x) is at y=3

If we find the difference between both y-intercepts, we have

( -2 -3) = -5

Then b=-5

Hence, [tex]g(x) = f(x - 5)[/tex] is correct.

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The distance d is 9 ft and the height is 12ft.

Here we can model the situation with a right triangle, where the length of the wire is the hypotenuse.

The height is one cathetus and the distance is the other catheti.

Let's define:

We know that the height of the tower is 3 ft larger than the distance, then:

h = d + 3ft

Now we can use the Pythagorean theorem, it says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.

Then:

[tex]d^2 + (d + 3ft)^2 = (15ft)^2[/tex]

Now we can solve this equation for d:

[tex]d^2 + d^2 + 6ft*d + 9ft^2 = (15ft)^2\\\\2d^2 + 6ft*d - 216 ft^2 = 0\\\\d^2 + 3ft*d - 108ft^2 = 0[/tex]

Then the solutions are:

[tex]d = \frac{-3ft \pm \sqrt{(3ft)^2 - 4*(-108ft^2)} }{2} \\\\d = \frac{-3ft \pm 21ft }{2}[/tex]

We only take the positive solution:

d = (-3ft + 21ft)/2 = 9ft

And the height is 3 ft more than that, so:

h = 9ft + 3ft = 12ft

The distance d is 9 ft and the height is 12ft.

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The probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The given parameters are:

Mean = 0.8

Variance = 0.0004

Calculate Standard deviation using

σ = √σ²

This gives

σ = √0.0004

Evaluate

σ = 0.2

Calculate the z-score at x = 0.84 using

z = (x - [tex]\bar x[/tex])/σ = √σ²

This gives

z = (0.84 - 0.8)/0.02

Evaluate

z = 2

The probability is then represented as:

P(x > 0.84) = P(z > 2)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.84) = 0.977

Hence, the probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

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The equation in point slope form is given as y+3 = -5/8(x-4)

The formula for calculating the equation of a line in point-slope form is expressed as:

y-y1= m(x-x1)

Given the coordinate point

Slope = 2-(-3)/-2-4
Slope = 5/-8

Determine the equation

y-(-3) =-5/8(x-4)

y+3 = -5/8(x-4)

Hence the equation in point slope form is given as y+3 = -5/8(x-4)

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Answer:

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

As per given, the missing interior angle is corresponding with 40° angle.

Since corresponding angles are equal, the third interior angle of the triangle is 40°.

Sum of three interior angles is 180°:

Apply angle sum property

The answer is 140