At a school for performance art students 25 of the girls study music, 35 of the girls study dance, and 16 of the girls study music and dance. What fraction of those who study music also study dance?

Answer:

Range of the relation is,  {1 , 0, -1}

Step-by-step explanation:

Given: Relation R = {(-4, 1), (-2, 0) , (8, -1)}

To find the range of the relation R;

In the set of ordered pairs, the domain is the set of the  first number in every pair, and the range is the set of the second number of all the pairs.

Then;

Domain of the relation: {-4, -2, 8}

Range of the relation is; {1 , 0, -1}

therefore, the range of the relation is,  {1 , 0, -1}

The range of the given relation is {-1, 0, 1}

The range of a relation refers to the set of all possible output values of the relation. In this case, the relation consists of three ordered pairs: (-4, 1), (-2, 0), and (8, -1). To find the range, we need to determine the set of all possible second values (y-values) in the ordered pairs. The range of the relation is {-1, 0, 1}.

https://brainly.com/question/29503017

#SPJ3

Answer:

-15

Step-by-step explanation:

Given is a polynomial in x

[tex]F (x)= x^4 + 12x^3 + 30x^2 - 12x + 70[/tex]

We have to find the remainder when the above polynomial is divided by x+5

Remainder theorem says that f(x) gives remainder R when divided by polynomial x-a means f(a) = R

Applying the above theorem we can say that value of the function when x =-5

= Remainder when f is divided by x+5

= F(-5)

Substitute the value of -5 in place of x

= (-5)^4 + 12(-5)^3 + 30(-5)^2 - 12(-5) + 70

= 625-1500+750+60+70

= 5

Hence answer is 5

Answer:

[tex]f(-5)=[/tex] 5

Step-by-step explanation:

According to the polynomial remainder theorem, when a polynomial f(x) is divided by a linear polynomial (x - a), the remainder of that division will be equal to f(a).

Therefore, substituting the value of x as -5 in the given function to find its value:

[tex]f(x)[/tex] = [tex]x^4 + 12x^3 + 30x^2 - 12x + 70[/tex]

[tex]f(-5)[/tex] = [tex](-5)^4 + 12(-5)^3 + 30(-5)^2 - 12(-5) + 70[/tex]

[tex]f(-5)[/tex] = [tex]625+(-1500)+750-(-60)+70[/tex]

[tex]f(-5)[/tex] = [tex]5[/tex]

Therefore, the value of the given function when x = -5 is 5.

Answer:

x=-5, y=-2

Step-by-step explanation:

6x+ 28 =y

5x-y=-23

Substitute 6x+28 in for y in the second equation

5 x-(6x+28)=-23

Distribute the negative sign

5x -6x-28 = -23

-x -28 = -23

Add 28 to each side

-x-28+28 = -23+28

-x = 5

Multiply by -1

x = -5

Now we need to solve for y

y = 6x+28

Substitute x=-5

y = 6(-5) + 28

y = -30+28

y = -2

Answer:

30-6=24

Step-by-step explanation:

Subtract the 6 inches from the 30 inches.

AB corresponds to AC. Both are the left diagonal lines of triangle ABE and triangle ACD. Both AB and AC are also the first two letters of ABE and ACD respectively

BE and CD correspond as well. They are the horizontal sides of the two triangles. BE and CD are the last two letters of ABE and ACD.

Set up the proportion below. Then solve for x

AB/AC = BE/CD

AB/(AB+BC) = BE/CD

x/(x+3) = 2/5

5x = 2(x+3)

5x = 2x+6

5x-2x = 6

3x = 6

x = 2

Answer: AB = 2

note how AB = x = 2, so AC = AB+BC = x+3 = 2+3 = 5. This forms the ratio AB/AC = 2/5 which is identical to the ratio BE/CD = 2/5

To find the value of AB in the similar triangles ABE and ACD, use the ratio of the corresponding sides.

Given that ∆ABE is similar to ∆ACD, we can write the ratio of the corresponding sides: AB/AC = AE/AD = BE/CD. Note that corresponding sides of similar triangles are proportional. Therefore, the value of AB can be determined by the ratio AB/AC.

For example, if the length of AC is 10 units and the ratio AB/AC is 3/5, we can find the length of AB by multiplying 10 by 3/5: AB = (3/5) * AC = (3/5) * 10 = 6 units.

So, the value of AB depends on the specific information given about the ratios of the sides of ∆ABE and ∆ACD.

https://brainly.com/question/34830045

#SPJ3

Answer:

86 wpm

Step-by-step explanation:

You need to set up a proportion

Answer:

86 words per minute

Step-by-step explanation:

You would divide 301 by 3 1/2 to find the unit rate. The answer will be 86. So Shelly types 86 words per minute.

Answer:

3x+ 5 = 6 . Correct.

Step-by-step explanation:

Let x = the number.

          The number tripled: 3x

Tripled and increased by : 3x + 5

                                Equals 6: 3x+ 5 = 6

Correct.

Answer:

y = -1/2 x + 6

Step-by-step explanation:

2x + 4y = 10

4y = -2x + 10

y = -1/2 x + 5/2

Parallel lines, slope is the same = -1/2

passes through the point (8, 2) so

y - 2 = -1/2(x - 8)

y - 2 = -1/2 x + 4

y = -1/2 x + 6

Answer:

y = -1/2x + 6

Step-by-step explanation:

We know that the slope intercept form of a line is [tex]y=mx+c[/tex].

Also, if two lines are parallel, they have the same slope. So re-writing the given equation 2x + 4y = 10 in the slope intercept form to find know its slope.

[tex]2x + 4y = 10\\\\4y=-2x+10\\\\y=\frac{-2}{4} +\frac{10}{4}\\ \\y=\frac{-1}{2} +\frac{10}{4}[/tex]

So the slope of the equation will be [tex]-\frac{1}{2}[/tex].

Finding the y-intercept (c):

[tex]y=mx+c\\\\2=-\frac{1}{2} (8)+c\\\\c=6[/tex]

Therefore, the equation of the line n slope intercept form that is parallel to 2x + 4y = 10 and passes through the point (8, 2) is y = -1/2x + 6.

Hello from MrBillDoesMath!

Answer:

No. That problem cited is one of 3 great unsolved problems of antiquity. See  https://en.wikipedia.org/wiki/Angle_trisection for details.

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

Answer:

NO , an angle is not trisected using only a compass and a straight  edge.

Step-by-step explanation:

We are given two tools a compass and a straight edge

We need to tell if an angle is trisected using them or not.

Answer is NO , an angle is not trisected using only a compass and a straight  edge.

When we draw a semicircle by point pointer of compass at vertex of angle and then draw a line using points we get when semicircle intersects the arms of the angle. We get angle Bisection.

We again try to bisect we get four equal angles not Three.

So It is impossible to make odd numbers of equal angles from a given angle using a compass and a straight edge.

For x = -2  expressions yield 1/4 , -1/2 , 1 , -2 , 4 for x^-2 , x^-1 , x^0 , x^ 1 , x^2 .

Evaluating Expressions for x = -2

When we evaluate expressions containing variables, we substitute the given value for the variable into the expression and simplify. In this case, we're asked to evaluate the following expressions for x = -2:

x^-2

x^-1

x^0

x^1

x^2

1. x^-2

x^-2 represents the reciprocal of the square of x. Substituting x = -2, we get:

x^-2 = 1/(-2)^2 = 1/4

2. x^-1

x^-1 represents the reciprocal of x. Substituting x = -2, we get:

x^-1 = 1/-2 = -1/2

3. x^0

Any non-zero number raised to the power of 0 is 1. Therefore:

x^0 = 1

4. x^1

x^1 represents the value of x itself. Substituting x = -2, we get:

x^1 = -2

5. x^2

x^2 represents the square of x. Substituting x = -2, we get:

x^2 = (-2)^2 = 4

Learn more about Expressions here:

https://brainly.com/question/21469837

#SPJ6

The question probable may be:

Match the following items by evaluating the expression for

x = -2

. x^-2

x ^-1

x^0

x^1

x^2

Answer:

The binomial probability formula can not be used for this experiment because it does not state the number of times he expects to draw his favorite suit.  

Step-by-step explanation:

The binomial probability formula is expressed as follows:

P (k success in n trials) = [tex]\left \{ {{n \atop k} \right.[/tex] [tex]p^{k}[/tex][tex]q^{n-k}[/tex]

n = number of trials, k = number of successes, n-k = number of failures, p = probability of success in one trial and q = 1 - p = probability of failure in one trial.  

In the given problem, all of the variables are known except for 'k', the amount of times that the student predicts he will draw his favorite suit.  

Yes, the student's card drawing experiment can be considered a binomial experiment and therefore the binomial probability formula can be applied. This is because there are two possible outcomes for each trial (success or failure), the trials are independent, and the number of trials is fixed.

Yes, the probability of drawing his favorite suit can be found by using the binomial probability formula. This is because the scenario described satisfies the conditions necessary for a binomial experiment.

First, there are only two possible outcomes for each trial - success (drawing his favorite suit) and failure (not drawing his favorite suit). In a standard deck of 52 cards with 4 suits, there are 13 cards of each suit. Therefore, the probability of success, p, is 13 out of 52, or 0.25 and the probability of failure, q, is 1 - p, or 0.75.

Second, the student performs the experiment 30 times. This means there are a fixed number of independent trials (n = 30). This is independent because he returns the card to the deck and shuffles after each draw, so the outcome of one trial does not affect the outcomes of the other trials.

In a binomial experiment, the random variable X represents the number of successes in n independent trials. The mean, µ, can be calculated using the formula µ = np, and the standard deviation, σ, is given by the formula σ = √npq. Thus, you can use the binomial probability formula to calculate the probability of drawing his favorite suit a certain number of times out of the 30 trials.

https://brainly.com/question/39666605

#SPJ11

The formula of a volume os a cylinder:

[tex]V=\pi r^2H[/tex]

r - radius

H - heihgt

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

If a cylinder and a cone have the same radius and height then the volume of a cone is three times smaller than a volume of a cylinder.

Therefore

[tex]V_{cone}=\dfrac{1}{3}V_{cylinder}[/tex]

We have

[tex]V_{cylinder}=72\ in^3[/tex]

Substitute:

[tex]V_{cone}=\dfrac{1}{3}\cdot72=24\ in^3[/tex]

Answer:

Divisable by 4? look at the last two digets If divide by 4, the whole number divides by 4.

4 = 2^2, so if you can divide a number by 2 twice, then the number is divisible by 4.

Solution:

Array means arrangement of numbers in terms of rows and columns.

The conjecture is not True.

So, the conjecture made by chloe that given any two numbers, the greater number can always be arranged into more arrays is not true.

For example ,

1.(2,3)

2→(2×1),(1×2)

3→(3×1),(1×3)

This pair has same number of arrays because both of them are prime.

2. (3,4)

Here, 4>3

3→ (3 × 1),(1×3)

4→(4×1),(1×4),(2×2)

The pair of numbers are Co-prime, one of them is not prime. So Composite number has more number of arrays.

4. (6,11)

6→(1×6),(6×1),(2×3),(3×2)

11→(1×11),(11×1)

The number 6 is smaller, but it has more number of arrays.

5. (6,8)

6→(1×6),(6×1),(2×3),(3×2)

9→(1×9),(9×1),(3×3)

Both the numbers are composite.Smaller number 6 has more arrays.

These examples disprove the Conjecture made by Chloe, which states that given any two numbers, the greater number can always be arranged into more arrays.

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\underline{d}istance of 810 km in 1.5 \underline{h}ours}}{d=kh} \\\\\\ \textit{we know that } \begin{cases} h=1.5\\ d=810 \end{cases}\implies 810=k(1.5)\implies \cfrac{810}{1.5}=k\implies 540=k[/tex]

Answer : The value of constant of variation is, 540

Step-by-step explanation :

As we know that,

[tex]\text{Distance}=\text{Speed}\times \text{Time}[/tex]

That means,

d = s × t

Here,

's' is constant of variation.

Given:

d = distance = 810 km

t = time = 1.5 hr

Now put the values in the above expression, we get:

d = s × t

810 km = s × 1.5 hr

[tex]s=\frac{810km}{1.5hr}=540km/hr[/tex]

Thus, the value of constant of variation is, 540

Answer:

-3

Step-by-step explanation:

Parallel lines have slopes that are the same.

 So if one line has a slope that is -3, any line that is parallel will have the same slope

Answer:

9090 kilograms

Step-by-step explanation:

To find the number of kilograms per dragon, we divide the amount of meat by the number of dragons.

4545/22  kilograms per dragon

Now we can multiply by the 44 dragon that she has.

4545/22 * 44 = 9090 kilograms

Answer:

i believe your answer is 9090

Step-by-step explanation:

4545 =22 dragons each day

22 times 2=44

4545 times 2

9090

Answer:

b

Step-by-step explanation:

b dont want to explain...

Answer:

B would be your correct answer here because you are counting down by negative hope this helps

Step-by-step explan

Final answer:

Bailey spends more time getting dressed, which is 1/2 of an hour (30 minutes), whereas she spends 1/4 of an hour (15 minutes) eating breakfast.

Explanation:

The question is asking which activity Bailey spends more time on in the morning: getting dressed or eating breakfast. Since Bailey has an hour to get ready, 3/6 of an hour is spent getting dressed, and 1/4 of an hour is spent eating breakfast.

First, we simplify the fraction for getting dressed, as 3/6 can be reduced to 1/2. Thus Bailey spends 1/2 hour or 30 minutes getting dressed. To find how much time is spent eating breakfast, we calculate 1/4 of an hour, which is 15 minutes.

Comparing the two, we see that Bailey spends more time getting dressed (30 minutes) than eating breakfast (15 minutes).

Answer:

8 , 20, 50, 125, 625/2           option D

Step-by-step explanation:

Given that,

first term a₁ = 8

common ratio (r) = [tex]\frac{5}{2}[/tex]

We need to find the five  terms of the geometric progression

We know that the nth term formula :

aₙ = a₁rⁿ-¹

where a₁ is first term and r is the common ratio

n is the number of terms

Second term (n=2)

a₂ = 8*[tex](\frac{5}{2} )^{2-1}[/tex] = [tex]\frac{8*5}{2}[/tex] = 20

Third term (n = 3)

a₃ = 8*[tex](\frac{5}{2} )^{3-1} = 8*(\frac{5}{2} )^{2}  = (\frac{8*25}{4} ) = 50[/tex]

Forth term (n=4)

a₄ = [tex]8(\frac{5}{2} )^{4-1} = 8*(\frac{5}{2} )^{3}  = (\frac{8*125}{8} ) = 125[/tex]

Fifth term (n=5)

a₅ = [tex]8(\frac{5}{2} )^{5-1} = 8*(\frac{5}{2} )^{4}  = (\frac{8*625}{16} ) = \frac{625}{2}[/tex]

So, five terms are :

8 , 20, 50, 125, 625/2

Answer:

D right on edg 2020

Step-by-step explanation:

Answer:

a perfect square is when a number is multiplied by itself. For example, 4*4=16.

16 is the perfect square

something like 20 would not be a perfect square because it is 5*4 and they are not the same number.

Step-by-step explanation:

Answer:

The product of a rational number multiplied by itself.

Step-by-step explanation:

9² = 9×9 which equals 81.  81 is the perfect square of 9 which can also be said that 9 is the square root of 81 or √81

Answer:

Approximately 20 complete pieces of 1 3/4 foot of ribbon can be obtained.

Step-by-step explanation:

You have a piece of ribbon 36 feet long that should be divided into pieces of 1 [tex]\frac{3}{4}[/tex] feet. In order to know the quantity of pieces of said measurement, the total length of the ribbon (36 feet) must then be divided by the desired measurement of each of the pieces (1 3/4 feet):

[tex]amount of pieces of ribbon=\frac{36}{1 \frac{3}{4} }[/tex]

1 [tex]\frac{3}{4}[/tex] is a mixed number. A mixed number or mixed fraction consists of a whole part (natural number) and a fractional part. All fractions greater than unity can be expressed as a mixed number.

To be able to make the division stated previously, it is convenient to pass the mixed number to an improper fraction (An improper fraction is a fraction in which the numerator is greater than or equal to the denominator). For this you multiply the denominator by the whole number. To the result, you must add the numerator. Then that number is placed over the original denominator. Expressed in general is:

[tex]a \frac{b}{c} =\frac{a*c+b}{c}[/tex]

In this case:

[tex]1 \frac{3}{4} =\frac{4*1+3}{4}=\frac{7}{4}[/tex]

Then the previously stated division is expressed as:

[tex]\frac{36}{\frac{7}{4} }[/tex]

One way to perform this division is to reverse the SECOND FRACTION, that is, change the denominator to the numerator and change the numerator to the denominator. Then, both numbers are multiplied.

[tex]\frac{36}{\frac{7}{4} } =36*\frac{4}{7}[/tex]

Given that 36 can be expressed as 36/1, the multiplication is done "online." That is, the numerator of the first fraction by the numerator of the second and the denominator of the first fraction by the denominator of the second.

[tex]\frac{36}{1} *\frac{4}{7} =\frac{36*4}{1*7} =\frac{144}{7}[/tex]

Now it will be passed from fraction to mixed number. For that, the numerator is divided by the denominator. The quotient of the division becomes the integer of the mixed number. The rest of the division is the numerator of the fraction. The denominator is the same as that of the fraction, being the divisor of the division.

When dividing 144 by 7 the quotient is 20, the remainder is 4 and the divisor is 7. Then the mixed number formed is [tex]20 \frac{4}{7}[/tex]

This indicates that approximately 20 complete pieces of 1 3/4 foot of ribbon can be obtained.

Answer

about 20 complete pieces can be cut

Step-by-step explanation:

Answer:

x=24

y = 8 sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use sin and cos

sin 30 = opposite/ hypotenuse

sin 30 = y/ 16 sqrt(3)

Multiply each side by 16 sqrt(3)

16 sqrt(3) * sin 30 = y

16 sqrt(3) * 1/2 = y

8 sqrt(3) = y

cos 30 = adjacent/ hypotenuse

            = x/16 sqrt(3)

Multiply each side by 16 sqrt(3)

16 sqrt(3) cos 30 = x

16 sqrt(3) * (sqrt(3)/2) = x

8 * sqrt(3)*sqrt(3)

8 * 3 = x

24 =x

The solution is $ 8.75

The sales tax amount Sandra will owe on the purchase is $ 8.75

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the price of the coat be = $ 49.99

Let the price of one skirt be = $ 24.99

The sales tax percentage of Sandra's purchase = 7 %

So , the price of 3 skirts = 3 x price of one skirt

Substituting the values in the equation , we get

The price of 3 skirts = 3 x 24.99

The price of 3 skirts = $ 74.97

Now , the total price of the purchase of Sandra = price of the coat + price of 3 skirts

Substituting the values in the equation , we get

The total price of the purchase of Sandra = $ 49.99 + $ 74.97

The total price of the purchase of Sandra = $ 124.96

And , the sales tax amount of the purchase by Sandra A = sales tax percentage of Sandra's purchase x total price of the purchase of Sandra

The sales tax amount of the purchase by Sandra A = ( 7/100 ) x 124.96

The sales tax amount of the purchase by Sandra A = 0.07 x 124.96

The sales tax amount of the purchase by Sandra A = $ 8.7472

Therefore , the value of A is $ 8.75

Hence , the sales tax amount of the purchase by Sandra is  $ 8.75

To learn more about percentage click :

https://brainly.com/question/12861068

#SPJ5

Answer:

see explanation

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0 then the vertex is a minimum

• If a < 0 then the vertex is a maximum

f(x) = (x + 1)² - 2 → has a > 0

vertex = (- 1, - 2 ) and is a minimum

g(x) = - (x - 2)² + 1 → has a < 0

vertex = (2, 1 ) and is a maximum

The answer would be  (3/8) (d+2)

The expression 3/8d + 3/4 is factored by first factoring out the common factor of 3, resulting in the factored form 3*(1/8d + 1/4).

The student's question involves the factoring of a linear algebraic expression. The given expression is 3/8d + 3/4, where 'd' is a variable. To factor this expression, we need to look for common factors in each term. Here, both terms contain a factor of 3, which we can factor out. This results in:

Thus, the fully factored expression is 3/8d + 3/4 = 3*(1/8d + 1/4), with the understanding that 1/4 has been converted to 2/8 to have a common denominator.

Answer:

B

Step-by-step explanation:

arc length = circumference × fraction of circle

                 = 84 ×[tex]\frac{90}{360}[/tex] = 21 cm