15. There were 150 students who were surveyed
and asked whether they played a sport and
whether they played a musical instrument. The
results are shown in the table.

Answer:

-2 + sqrt(2)

-2 - sqrt(2)

Step-by-step explanation:

3x² + 12x + 6 = 0

x² + 4x + 2 = 0

Use the quadratic formula:

[-4 + sqrt(4² - 4(1)(2))]/2

-2 + sqrt(2)

[-4 + sqrt(4² - 4(1)(2))]/2

-2 - sqrt(2)

sqrt: square root

Answer:

F= (9C+160)/5

Step-by-step explanation:

C=5(F-32)/9

make F the subject of the formula= isolate F

5(F-32)=9C

5F-160=9C

5F=9C+160

F= (9C+160)/5

check: a, b, c are all positive integers (a=9, b=160, c=5)

Answer:

9c+160/5

Step-by-step explanation:

Answer:

x=-8

Step-by-step explanation:

-8x - 8 + 3(x-2) = -3x + 2     Multiply the parentheses by 3

-8x - 8 + 3x -6= -3x +2        Collect all like terms and Calculate

-5x - 14= -3x + 2                   Move the terms

-5x + 3x = 2 + 14                  Collect all the like terms and Calculate the sum

-2x = 16                                Divide both of the sides by -2

x = -8

I hope this is what you were looking for and helps you out.

Answer:

[tex]x=-8[/tex]

Step-by-step explanation:

Given Equation:

           [tex]-8x-8+3(x-2)=-3x+2[/tex]

Solving for 'x' by taking the terms of 'x' to one side and constants to the other side:

         [tex]-8x-8+3(x)-3(2)=-3x+2\\[/tex]

           [tex]-8x-8+3x-6=-3x+2[/tex]

Adding the like terms:

         [tex]-5x-14=-3x+2[/tex]

Adding '[tex]3x[/tex]' both sides:

         [tex]-5x+3x-14=-3x+3x+2[/tex]

         [tex]-5x+3x-14=2\\\\-2x-14=2[/tex]

Adding '[tex]14[/tex]' both sides:

            [tex]-2x-14+14=2+14\\\\-2x=16\\\\x=\frac{16}{-2}[/tex]

            [tex]x=-8[/tex]

Answer:

A) 40

B) 10

Step-by-step explanation:

A) ⅓×pi×2.5²×8 = 50/3 pi

660pi ÷ 50pi/3 = 39.6

So 40 scoops

B) ⅓×pi×5²×8 = 200pi/3

660pi ÷ 200pi/3 = 9.9

So 10 scoops

Answer: Account might need to be reactivated since it is an old account and the sum on the cheque is larger than usual deposit

2) since it is a cheque deposit and the amount is larger than usual deposit, the bank teller will need to make neccessary confirmation from the cheque owner.

Step-by-step explanation:

Funds from a deposited check may not be available on the day of deposit due to processing times for verifying funds, anti-fraud measures for large or irregular deposits, and the clearing process required for checks drawn on different banks.

Funds from a deposited check may not be available on the day of deposit for a number of reasons. One common reason is due to the processing time that is required for the bank to verify the funds from the issuing account. When an individual makes a deposit, the bank needs to ensure that the payer's account has sufficient funds to cover the check. This process can take several business days, especially if the check is drawn on a different bank or financial institution.

Another reason why funds might not be immediately available is due to anti-fraud measures. Banks often hold larger than usual deposits or checks from new accounts for additional scrutiny to prevent fraud. This hold allows the bank to time to confirm the legitimacy of the check before making the funds available to the depositor.

Finally, if both the issuing and receiving account are at the same bank, a simple internal account transfer can occur with no need for an actual movement of physical funds. However, if the banks are different, checks typically go through a clearing process, which might involve an intermediary such as a Clearing House, where the checks are offset against each other and only the net balances are settled. This systematic arrangement usually results in a delay before the deposited funds are available to the account holder.

Answers:

1. 1/12

2. 1/15

3. 16 feet

4. 222 inches

5. 27 feet

hope it helps :0

Answer:

- 8

Step-by-step explanation:

Given

= 4a + 8z ← substitute a = 8 and z = 3 into the expression

= - 4(8) + 8(3)

= - 32 + 24

= - 8

Answer:

-8

Step-by-step explanation:

a = 8

z = 3

-4(8) + 8(3) = -32 + 24 = -8

Answer:

58

Step-by-step explanation:

The sum of the exterior angles ALWAYS measures 360 degrees, meaning that 90+38+3x+x = 360

This means that 128 + 4x =360, meaning that 4x = 232.

That makes x = 58

To find the value of x, we can use the fact that the sum of the exterior angles of any polygon is always 360 degrees. So, solving the equation 90 + 38 + 3x + x = 360 will give us the value of x, which is 58.

To find the value of x, we can use the fact that the sum of the exterior angles of any polygon is always 360 degrees.

So, we have the equation:

90 + 38 + 3x + x = 360

Combine like terms:

4x + 128 = 360

Subtract 128 from both sides:

4x = 232

Divide by 4:

x = 58

Therefore, the value of x is 58.

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Answer:

To the nearest cent, Christopher will earn $ 0.13 in 3 years

Step-by-step explanation:

Let's recall that the formula of the compounded interest is:

A = P * (1 + r/n)^nt, where

A = Future value

P = Initial deposit

r = Interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Replacing with the values we know:

A = P * (1 + r/n)^n

A = 1 * (1 + 0.1/1) ³°¹

A = 1 * 1.1³

A = 1 * 1.1331

A = 1.13

Interest = Future value - Initial deposit

Interest = 1.13 - 1

Interest = 0.13

Answer:

60 ft.

Step-by-step explanation:

We can solve this problem with a simple proportion:

24 / 10  =  h / 25

10h = 24 * 25

600 = 10h

60 ft. = h

The height of the tree would be 60 feet when its shadow 25-foot.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

We have been given that Derek sees that a 24-foot flag pole casts a 10-foot shadow.

Let the height of the tree would be h when its shadow 25-foot.

According to the given question, we can write the proportion as:

24 : 10  =  h : 25

⇒ 24 / 10  =  h / 25

⇒ 10h = 24 × 25

⇒ 600 = 10h

⇒ 60 = h

⇒ h = 60

Therefore, the height of the tree would be 60 feet when its shadow 25-foot.

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Answer:

Enlargement

Factor 2

Step-by-step explanation:

X'Y'/XY = 10/5 = 2

Answer:

The student is wrong, the total area = 16 ft² + 20 ft²

Step-by-step explanation:

See the attached figure.

The shown figure is a composite area of:

1) A rectangle with length of 8 ft and width of 4 ft

2) A triangle of base (8 - 4 = 4ft) and height of ( 6 - 4 = 2 ft)

The area of the rectangle = length x width = 8 * 4 = 32 ft²

The area of the triangle = 0.5 base x height = 0.5 * 4 * 2 = 4 ft²

So, the total area = 32 + 4 = 36 ft²

OR

The figure can be consists of :

1) A square of side length of 4 ft

2) A trapezoid of height (8-4 = 4 ft) and the bases length is (6 and 4 ft)

So,

The area of the square = 4 * 4 = 16 ft²

The area of the trapezoid = 0.5 (6+4) * 4 = 5 * 4 = 20 ft²

So ,the total area = 16 + 20 = 36 ft²

So,

The student is distracted, he finds the area of total rectangle of sides 8 and 6 ft, he should subtract from it the area of the trapezoid of height 2 ft and bases of 4 and 8 ft

So, the student is wrong

The length of each side is 50 inch/ 600 ft

Step-by-step explanation:

Given,

The perimeter of the square park = 12 inches

1 inch = 200 ft

12 inches = 12×200 ft = 2400 ft

To find each side of the park.

Let, each side be 'a' inches

Formula

The perimeter of a square = 4a

According to the problem,

4a = 2400

or, a = 600 ft

= 50 inch

Answer:

2400 feet

Step-by-step explanation:

1 : 200

12 : X

X = 12 × 200 = 2400 feet

Step-by-step explanation:

The money deposited in the bank = 5000

Rate of interest = 6%

Number of years = 18

By simple interest Formula,

Interest = PNR / 100

Where P is the principal amount = 5000

N = no of years = 18

R =rate of interest = 6

Substituting the values in the equation, we get

Interest = (5000 * 18 * 6) / 100

Interest = 5400

total amount present = principal + interest

  = 5000 + 5400 = 10400

First, lets subtract the amount he has after the transaction and the amount he had before the transaction.

249 - 18 = 231

Second, divide by the amount of books Dan bought.

231 / 7 = $33 per book.

Best of Luck!

At 1 pm the ocean was at a hight tide but at 7pm it was at a low tide this means the tide has been decreasex by 2.6 feet

Step-by-step explanation:

Answer:

  41

Step-by-step explanation:

If your equation is what it appears, we can put 3 where x is and do the arithmetic:

  12·3 +5 = 36 +5 = 41

The family spent 41 to attend the game.

Answer:

  C.  18 cm

Step-by-step explanation:

The ratio of the sides of the triangle shown is 12 : 15 = 4 : 5. We know it is a right triangle, so we know the missing side length completes the ratio

  3 : 4 : 5 = 9 : 12 : 15

Half of XY is 9 cm, so the length of the entire chord is 18 cm.

_____

The chord is tangent to the inner circle, so makes a 90° angle with the radius to that tangent point. This tells you that the triangle shown is a right triangle. It also tells you that the short radius bisects the chord. The Pythagorean theorem can be used to find the length of the side not shown (half the chord length).

The unknown side (a) can be found from  ...

  15² = 12² +a²

  225 -144 = a² . . . . . . subtract 12²

  81 = a² . . . . . . . . . . .  simplify

  9 = a . . . . . . . . . . . . . take the square root

The chord length is 2a, so is ...

  2(9 cm) = 18 cm . . . . length of chord XY

Answer:

p-3

Step-by-step explanation:

3 fewer would be -3

So it would be p-3

Answer: 3<p

Step-by-step explanation:

3 is fewer than (<) p

hope it helps please give brainliest!

Answer: 7:4

Step-by-step explanation:

To take this ratio to its simplest form, we have to divide by a value divisible by both sides of the ratio.

8 is a divisible value, therefore,

56/8 = 56 ÷ 8 = 7

32 ÷ 8 = 4

Thus, 56:32 in its simplest form= 7:4

I hope this helps.

Answer:

x+2y=-1 3x+y=1

Step-by-step explanation:

look photo

Answer: x + 2y = -1 and 3x + y = 1

Step-by-step explanation:

Solution:

Given that,

z varies directly with x and inversely with [tex]y^2[/tex]

Which means,

[tex]z \propto \frac{x}{y^2}\\\\z = k \times \frac{x}{y^2}[/tex]

Where, "k" is constant of proportionality

Substitute x = 2 and y = 5, z = 8 in above

[tex]8 = k \times \frac{2}{5^2}\\\\8 = \frac{2k}{25}\\\\k = 25 \times 4\\\\k = 100[/tex]

What is the value of z when x = 4 and y = 9?

Substitute k = 100 , x = 4 and y = 9 in above

[tex]z = 100 \times \frac{4}{9^2}\\\\z = 100 \times \frac{4}{81}\\\\z = 4.938[/tex]

Thus value of z is 4.938

Answer:

[tex]\$675[/tex]

Step-by-step explanation:

Remember that

[tex]100\%-35\%=65\%=65/100=0.65[/tex]

Let

x ----> the total cost of the books

we know that

The total cost of the book multiplied by 0.65 must be equal to $438.75

so

The linear equation that represent this situation is

[tex]0.65x=438.75[/tex]

solve for x

[tex]x=438.75/0.65\\x=\$675[/tex]

Answer:

[tex]x = - 2 \: o r\: 1[/tex]

Step-by-step explanation:

We want to solve the quadratic equation:

[tex]5x + 5{x}^{2} - 10 = 0[/tex]

Rewrite in standard form to get:

[tex]5 {x}^{2} + 5x - 10 = 0[/tex]

Divide through by 5 to get;

[tex]{x}^{2} + x - 2 = 0[/tex]

Factor to get;

[tex](x + 2)(x - 1) = 0[/tex]

Apply zero product property to get:

[tex]x + 2 = 0 \: or \: x - 1 = 0[/tex]

The solutions are:

[tex]x = - 2 \: or \: x = 1[/tex]

Answer:

Step-by-step explanation:

Your answer is correct except for the intercepts.

The x-intercepts are where the graph crosses the x-axis. Those points are (-3, 0) and (3, 0). They can be identified in a list of points by the fact that the y-coordinate is zero (corresponding to the x-axis).

The y-intercepts are where the graph crosses the y-axis. Those points are (0, -5) and (0, 5). They can be identified in a list of points by the fact that the x-coordinate is zero (corresponding to the y-axis).

Answer:$3912.81

Step-by-step explanation:

You can calculate this by finding the cost ofn1 training session and then multiplying by the 167 training sessions

If 86 training sessions =$2015

Then 1training session=2015/86 =$23.43

167 training sessions =$23.43×167= $3912.81

Answer:

6< 5+x

Step-by-step explanation:

sum = addition

sum of 5 and x= add 5 and x

5+x

less than: "<" and it means that the number on the left is less than the number on the right

6 less than= 6 < 5x

The phrase "6 less than the sum of 5 and x" can be represented by the expression:

(5 + x) - 6

Let's break it down to understand how this expression represents the given phrase:

First, we have the sum of 5 and x, which is represented by (5 + x). This part of the expression calculates the sum of 5 and the variable x.

Then, we have "6 less than" which implies subtracting 6 from the sum. This is represented by - 6.

Finally, we combine these two components: (5 + x) - 6.

In this expression, the sum of 5 and x is calculated first, and then 6 is subtracted from that sum, representing the idea of "6 less than the sum of 5 and x."

To simplify further, we can combine the terms:

(5 + x) - 6 = 5 + x - 6 = x - 1

Therefore, the expression "6 less than the sum of 5 and x" can be represented as x - 1.

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For this case we have that, by definition of trigonometric relationships of rectangular triangles, the cosine of an angle is given by the division of the leg adjacent to the angle on the hypotenuse of the triangle. According to the figure we have:

[tex]Cosine (50) = \frac {6} {x}\\x = \frac {6} {cosine (50)}\\x = 9.3343[/tex]

Thus, the value of x is 9.3

Answer:

[tex]x = 9.3[/tex]

Answer:

7/1 - 1/8= 6[tex]\frac{7}{8}[/tex]

Step-by-step explanation:

Answer:

6.87500

Step-by-step explanation: