5/8 of the staff are male. 5/12 of the staff works part time at the aquarium.What fraction of the staff is female?

Answer:

x = 8

or

x = -4

Step-by-step explanation:

3x² - 12x = 96

Divide both sides by 3

x² - 4x = 32

Add 4 to both sides

x² - 4x + 4 = 32 + 4

(x - 2)² = 6²

Find the square root of both sides

√(x - 2)² = √6²

x - 2 = +/- 6

x - 2 = +6 or -6

x - 2=+6

x=6+2

x=8

x - 2=-6

x=-6+2

x=-4

x = 8

or

x = -4

Answer:

The correct option is;

With the compass point on G, construct an arc that intersect GD←→

Step-by-step explanation:

The steps for constructing a parallel line to a given point is as follows;

1) With the straightedge, a transversal is drawn intersecting the giving line and passing through point G

2) Copy the angle formed between the transversal and the given line and the to the point G starting by constructing an arc with the compass on point G to intersect GD←→ then with the compass opening still the same, place the compass on the point of intersection of the arc constructed from point G on GD and construct another arc to intersect the arc previous arc from G to GD

3) The line drawn from the intersection through is a parallel line to EF

Therefore, the correct option is that with the compass point on G, construct an arc that intersect GD←→.

Answer:

A.  With the compass on point D , construct an arc that intersects EF¯¯¯¯¯ and GD←→.

Step-by-step explanation:

I just took the test!

Answer:

15 mL of the solution with 20% water will be needed.

Step-by-step explanation:

Use the inverse relationship

10 mL * (18-15)% = x mL * (20-18)%

x = 10 mL * (3/2) = 15 mL

Answer: 15mL

Step-by-step explanation:

Create a table. Multiply across and add down. The bottom row (Mixture) creates the equation.

                   Qty     ×     %             =      Total          

Solution A     10         15% → 0.15          10(0.15) = 1.5

Solution B      x          20% → 0.20        x(0.20) = 0.20x

Mixture      10 + x   ×    18% → 0.18   =    1.5 + 0.20x

                                  (10 + x)(0.18) = 1.5 + 0.20x

                                    1.8 + 0.18x  = 1.5 + 0.20x

                                    1.8               = 1.5 + 0.02x

                                    0.3              =          0.02x

                                                15  =  x

Answer:

a

Step-by-step explanation:

there are 4 quarts in a gallon.

4 times $0.79 =$3.16

Answer:

[tex]\frac{7}{12}[/tex] of the cake

Step-by-step explanation:

add [tex]\frac{1}{8}[/tex] and [tex]\frac{1}{6}[/tex] to see the total amount of cake eaten.

a. find the common denominator: 8 x 3 = 24 and 6 x 4 = 24

b. multiply accordingly to get the correct numerator: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex]

c. add: [tex]\frac{3}{24}[/tex] + [tex]\frac{4}{24}[/tex] = [tex]\frac{7}{24}[/tex]

subtract found value from total to find left over cake.

a. 24 - 7 = 14

simplify.

a. [tex]\frac{14}{24}[/tex] = [tex]\frac{7}{12}[/tex]

You are left with [tex]\frac{7}{12}[/tex] of the cake.

Answer:

23/30

Step-by-step explanation:

x/y

(3 5/6)/(3 3/4)

((3*6)+5/6)/((3*4)+ 3/4)

(18+5/6)/(12+3/4)

(23/6)/(15/4)

(23/6)*(4/15)

(23*3)/(6*15)

(69/90)

23/30

Answer:

1 1/45

Step-by-step explanation:

Answer:

X=36.4 or 36.37306696.... and Y=42

Step-by-step explanation:

So you have a 30-60-90 triangle!

Do Not Worry this is a hard subject to understand, but I will try to do my best with helping you. Right now you need to find x and y. All you have is 21.  Under your 60 angle, which is pointing downward, is the 21. And 21 is initially in the spot of x or 1. so 21 is the x(But not the x on the side of 90). I am sorry if this is a bit confusing.

You are then going to take your side which is x, the side that is directly in the path of 90, and it is going to be 21[tex]\sqrt{3[/tex]. Then on the side of your y, which is in the path of your 60, it will be 2 times your x.

The general layout of this is:

x is underneath the side of 90 degrees.

then on the side where 60 degrees and 30 degrees is, is going to be x[tex]\sqrt{3[/tex].

Then the last side, where 30 degrees and 90 degrees lay, will be 2(x).

So all you have to do is plug everything in.

x=36.4 in decimal

y=42(because all you had to do was plug 21 where the x is, because that is where x is in the general layout.)

The value of x = 42 units

The value of y = 21√3 units

The study of the correlation between a right-angled triangle's sides and angles is the focus of one of the most significant branches of mathematics in history: trigonometry. Hipparchus, a Greek mathematician, introduced this idea.

As per the given diagram:

The triangle is a right angle triangle.

Using trigonometric ratios to find x and y:

tan30° = (P/B)

tan30° = (21/y)

(1/√3) = (21/y)

y = 21√3 units

sin30° = (P/H)

(1/2) = (21/x)

x = 2 × 21

x = 42 units

The value of x and y is 42 units and 21√3 units, respectively.

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Answer:

An example of a prism could be a an amazon box to represent a rectangular prism.  As the height, length, or width of the box increases, the volume increases allowing more items to fit within the box.

An example of a cone would be an ice cream cone.  As the height or the radius of the cone increases, the more volume the cone can hold, meaning more ice cream for you.

An example of a cylinder could be a cup.  As the height or the radius of the cup increases, the larger the volume.  More drink for you.

An example of a sphere would be a soccer ball.  As the radius increases, the volume of the ball increases.  Hence, larger soccer balls have a bigger radius than smaller soccer balls.  This allows for different varients of the ball to be created (i.e., youth, highschool, college, pro).

Note, the volume can also be decreased by simply shrinking the measurements instead of increasing them.

Step-by-step explanation:

Let's simply look at the equations of each shape.

Volume of a prism = base * height

Volume of a cone = Pi * r^2 * (height/3)

Volume of a cylinder = Pi * r^2 * height

Volume of a sphere = (4/3) Pi r^3

Notice that the volumes of prisms, cones, and cylinders directly correlate to height.  As height increases, the volume increases.  The sphere is unique in that the height is 2 * radius; however, the volume is related to the cube of the radius.  Consider if you expanded the radius of the sphere, the volume will increase.

Answer:

Increase or decrease the dimensions of objects. See below for an explanation!

Step-by-step explanation:

An amazon box, which is a rectangular prism, is an example of a prism. If you increase the height, length, or width of the box, you can fit more stuff inside.

A cup is an example of a cylinder; by increasing the height or radius of the cup, you can fit more of a drink inside.

An icecream cone is an example of a cone; if the height or radius were increased, you might fit more ice cream inside.

A soccer ball is an example of a sphere; increasing the radius makes it larger, and various sizes are available for different levels.

You may also shrink the dimensions for each of these objects to make them smaller.

Hope this helps!

Answer:

y = [tex]\frac{1}{2} x - 3[/tex]

x + y = 18

Step-by-step explanation:

Let the kitten's weight be y and the cat's weight be x

Condition # 1:

y = [tex]\frac{1}{2} x - 3[/tex]

Condition # 2:

x + y = 18

r = radius

h = r+12 = height, 12 more than the radius

[tex]V = \text{Volume of cone (oblique or not)}\\\\V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*r^2*(r+12)\\\\V = \frac{1}{3}\pi*r^2*r+\frac{1}{3}\pi*r^2*12\\\\V = \frac{1}{3}\pi*r^3+\frac{1}{3}*12\pi*r^2\\\\V = \frac{1}{3}\pi r^3+4\pi r^2\\\\[/tex]

ANSWER: SECOND OPTION

Answer:

3x√5 + 6√10x + 5√3x + 10√6

Step-by-step explanation:

(√3x + √5)(√15x + 2√30)

The above expression can be evaluated as follow:

(√3x + √5)(√15x + 2√30)

Expand

√3x (√15x + 2√30) + √5(√15x + 2√30)

x√45 + 2√90x + √75x + 2√150

Express in the best possible surd form.

x•3√5 + 2•3√10x + 5√3x + 2•5√6

3x√5 + 6√10x + 5√3x + 10√6

We can not simplify further.

Therefore,

(√3x + √5)(√15x + 2√30) =

3x√5 + 6√10x + 5√3x + 10√6

Answer:

-5 ≤ x≤ 3

Step-by-step explanation:

The domain is the values for x

x starts and -5 and includes -5 since the circle is closed

and goes to 3 and  includes 3 since the circle is closed

-5 ≤ x≤ 3

Answer:

first option

Step-by-step explanation:

The domain are the values from the x- axis that can be input into the function.

The closed circles at the ends of the graph indicate that x can equal these values.

left side value of x = - 5 and right hand value of x = 3, thus

domain is - 5 ≤ x ≤ 3

Answer:

See my explanation

Step-by-step explanation:

-2x + (x - 4) = 18

-x - 4 = 18

-x = 22          <- this is wrong in question writing as x = 22

so, x = -22

Answer:

A

Step-by-step explanation:

Using ZPP we get x = 0, 2x + 4 = 0, x + 5 = 0. Solving these, we get x = 0, x = -2, x = -5.

Answer:

23

Step-by-step explanation:

Raise 3 to the power of 3

27 - 4

Subtract 4 from 27

23

Hope this was correct

Answer:

23

Explanation:

step 1 - rewrite the expression with the value of x

[tex]x^3 - 4[/tex]

[tex](3)^3 - 4[/tex]

step 2 - solve the exponent

[tex](3)^3 - 4[/tex]

[tex]27 - 4[/tex]

step 3 - subtract

[tex]27 - 4[/tex]

[tex]23[/tex]

therefore, the value of the expression is 23.

Answer:

  60°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between sides of a right triangle and angles.

  Tan = Opposite/Adjacent

  tan(T) = SU/ST

  tan(T) = (5√51)/(5√17) = √3

Now, the arctangent function is used to find the angle whose tangent is √3.

 T = arctan(√3) = 60°

Answer: THE ANSWER IS A

Step-by-step explanation:

5-(3/2)^3

=13/8

im a math god

Answer:

k= l/3 - 14/3j

Step-by-step explanation:

l = 14j + 3k

Solve for k

l = 14j + 3k

Subtract 14j from both sides

l - 14j =14j + 3k - 14j

l - 14j = 3k

Divide both sides by 3

l - 14j / 3=3k / 3

k= l/3 - 14/3j

Or

1/3(l - 14j) = k

Answer:

Which expression is equivalent to ‐10

k

‐

10

?

Step-by-step explanation:

Answer:

(C) 1809 in.2

Step-by-step explanation:

Took the test on edg :3

Answer:

Step-by-step explanation:

Let the unknown number = x

[tex]x *\frac{-5}{27}=\frac{-10}{9}[/tex]

x = [tex]\frac{-10}{9}[/tex] ÷ [tex]\frac{-5}{27}[/tex]

[tex]x=\frac{-10}{9}*\frac{-27}{5}\\\\\\x=-2* - 3\\x = 6[/tex]

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

Explanation:

The distribution is perfectly symmetrical about the center 6. Notice how the left side is a mirror copy of the right side, due to the heights being the same. Because of this, the mean, median and mode are all the same value and that is 6. The mode is equal to 6 as this is the most frequent value.

The longer way to do this problem is to add up each value shown. We have four copies of '2', six copies of '3', and so on. The total sum you would get is 372. Divide this over 62 because there are 62 smaller green squares. The final result is the mean of 6.

The number closest to the mean of the given distribution is 6. Therefore, option A is the correct answer.

In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).

From the given histogram,

Number         Frequency

    2                      4

    3                      6

    4                      7

    5                      9

    6                     10

    7                      9

    8                      7

    9                      6

   10                      4

Here, the mean = [2(4)+3(6)+4(7)+5(9)+6(10)+7(9)+8(7)+9(6)+10(4)]/[4+6+7+9+10+9+7+6+4]

= [8+18+28+45+60+63+56+54+40]/62

= 372/62

= 6

Therefore, option A is the correct answer.

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Answer:

The divisor and dividend have the same signs.

Step-by-step explanation:

Let's look at all of the possible outcomes of dividing with different signs.

Positive / positive = positive

Positive / negative = negative

Negative / positive = negative

Negative / negative = positive

We can see that whenever the signs are the same, the quotient is positive.

Answer:

73cm²

Step-by-step explanation:

Area of rectangle=½ length×width

=½×18×7

=63cm²

Area of triangle=½b×h

base=18-13= 5cm

height=11-7 =4cm

½×b×h

½×5×4

=10cm²

Area of total=63+10

73cm²

Answer: 73c2

Step-by-step explanation:

Answer:

$24 will be the cost of tennis racquet with weight 25 oz.

Step-by-step explanation:

Given that Price of racquet is inversely proportional to its weight.

i.e.

[tex]Price \propto \dfrac{1}{Weight}[/tex]

We can replace the proportional sign with a constant of proportionality.

[tex]Price = \dfrac{C}{Weight}[/tex]

Where C is a constant named as constant of proportionality.

Given that cost of 20 oz. racquet is $30.00

Putting both the values :

[tex]30 = \dfrac{C}{20}\\\Rightarrow C = 600[/tex]

So, the equation becomes:

[tex]Price = \dfrac{600}{Weight}[/tex]

Now, we have to find the price of 25 oz. racquet.

Putting Weight = 25 oz and finding Price:

[tex]Price = \dfrac{600}{25}\\\Rightarrow Price = \$24[/tex]

So, $24 will be the cost of tennis racquet with weight 25 oz.

Answer:  A) 3.2 ft

Step-by-step explanation:

f(4) = -0.3(4)² + 2(4)

     = -4.8 + 8

     =  3.2

Answer:

3.2 feet

Step-by-step explanation:

Answer:

45°

Step-by-step explanation:

[tex]tan^{-1}(1)[/tex] = 45°

Answer:

[tex]\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}[/tex]

Step-by-step explanation:

[tex]\tan\theta=1[/tex]

[tex]\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o[/tex]

Answer:

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Step-by-step explanation:

Let the present age of Devi be x years.

Therefore, mother's present age = 3x

Five years ago:

Devi's age = (x - 5) years

Mother's age =( 3x - 5) years

According to the given condition:

Five years ago:

Devi's mother's age = 4 times Devi's age

3x - 5 = 4( x - 5)

3x - 5 = 4x - 20

20 - 5 = 4x - 3x

15 = x

x = 15 years

3x = 3* 15 = 45 years

Hence,

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Answer:

1) [tex]\boxed{Option \ 3}[/tex]

2) [tex]\boxed{Option \ 2}[/tex]

Step-by-step explanation:

A) [tex]x^2-5x+6[/tex]

Using mid term break formula

[tex]x^2-6x+x-6\\x(x-6)+1(x-6)\\Taking \ (x+6) \ as \ common\\(x-6)(x+1)[/tex]

B) [tex]\frac{-20p^{-5}qr^6}{16p^{-2}q^{-3}r^4}[/tex]

Solving it using the two rules: => [tex]\frac{a^m}{a^n} = a^{m-n} \ and \ a^m * a^n = a^{m+n}[/tex]

=> [tex]\frac{-5p^{-3}q^4r^2}{4}[/tex]

We need to put p in the denominator to cancel its negative sign

=> [tex]\frac{-5q^4r^2}{4p^3}[/tex]

Answer:

C and b

Step-by-step explanation:

First question:

The polynomial expression we want to factor is x^2-5x-6

Let's calculate the discriminant to find the roots. The discrminant is b^2-4ac

● b= -5

● a = 1

● c = -6

b^2-4ac= (-5)^2-4*1*(-6) = 25+24 = 49>0

So this polynomial expression has two roots since the discriminant is positive

Let x" and x' be the roots:

● x'= (-b-7)/2a = (5-7)/2= -1

● x"= (-b+7)/2a = (5+7)/2 =6

7 is the root square of the discrminant

The factorization of this pulynomial is:

● a(x - x') (x-x")

● 1*(x-(-1)) (x-6)

● (x+1)(x-6)

So the right answer is c

■■■■■■■■■■■■■■■■■■■■■■■■

Second question:

The expression is: (-20*p^(-5)*q*r^(6))/(16*p^(-2)*q^(-3)*r^3)

To make it easier we will simplify the similar terms one by one.

● Constant terms

-20/16 = (-5*4)/(4*4) = -5/4

● terms containing p

-p^(-5)/p^(-2) = p^(-5-(-2)) = p^(-3) =1/p^3

● terms containg q

q/q^(-3)= q(1-(-3)) = q^4

● terms containg r

r^6/r^4 = r^(6-4) = r^2

Multiply all terms together:

● -5/4 *1/p^3 *q^4 *r^2

● (-5*q^4*r^2)/(4p^3)

The right answer is b

Answer:

x-intercept → (-5, 0)

Step-by-step explanation:

Let the equation of the line having pairs given in the table is,

y - y' = m(x - x')

m = slope of the line

(x', y') is a point lying on the line.

From the given table,

Two points (33, -22) and (52, -33) lie on the line.

Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                        m = [tex]\frac{-33+22}{52-33}[/tex]

                        m = [tex]-\frac{11}{19}[/tex]

Equation of the line passing through (33, -22) and slope = [tex]-\frac{11}{19}[/tex] will be,

y + 22 = [tex]-\frac{11}{19}(x - 33)[/tex]

For x-intercept y = 0,

0 + 22 = [tex]-\frac{11}{19}(x-33)[/tex]

-38 = x - 33

x = -38 + 33

x = -5

Therefore, x-intercept of the line is (-5, 0).

Answer:

-5,0

Step-by-step explanation:

khan academy

Answer:

72%

Step-by-step explanation:

First find the number of mangoes

200 -56 = 144

Take the number of mangoes over the total

144/200

.72

Change to percent by multiplying by 100

72%

Answer:

72%

Step-by-step explanation:

If 56 of the 200 fruits were durians, then [tex]200-56[/tex] of the fruits were mangoes. Therefore, 144 of the fruits were mangoes.

Now we can set up a percentage proportion to find what percent of 200 144 is.

[tex]\frac{144}{200} = \frac{x}{100}[/tex]

Multiply the cross values and divide by the value thats diagonal to the variable.

[tex]144\cdot100=14400\\14400\div200=72[/tex]

So, the answer is 72%

Hope this helped!