In a class of 32 students
The mean height of the 14 boys is 1.56 meters
The mean of all students is 1.515 meters

Work out the mean height for the girls

Answer:

1)5n: not balanced

2)1n: Balanced

4)8n: not balaned

Step-by-step explanation:

1) The equation that determines the number of hours worked by the plumber at Jerald's house is A. 50x + 35 = 190; x = 3.1 hours.

2) The equation that represents, "twenty-four equals the sum of 10.5 and the quotient of a number and 4.5" is B. 24 = 10.5 + 4.5m; m = 3.

3) An equation representing 'five more than three times a number equals 21' is A. 3x + 5 = 21.

4) The cost of the jalapeno is B. $9.24.

5) The equations for the mathematics statements are:

a) 1/3(30 - y) = 3/4

b) 30(1/3) - y = 3/4

c) 1/3y - 30 = 3/4

d) 30(1/3) - y = 3/4

6A) The equation to determine the length (x) of each of the five pieces is x = (4.5 - 0.7) ÷ 5.

6B) The above equation is correct because it can be solved to get the length of each of the five pieces.

6C) The solution and steps of the equation in Part A are as follows:

x = (4.5 - 0.7) ÷ 5

x = 3.8 ÷ 5

x = 0.76 feet

1) Jerald:

Plumber's fixed charge = $35

Plumber's variable charge per hour = $50

Total charges by plumber = $190

The number of hours worked = 3.1 hours ($190 - $35)/$50

2) 24 = 10.5 + 4.5m; m = 3

24 = 10.5 + 4.5 x 3

24 = 10.5 + 13.5

24 = 24

3) 3x + 5 = 21

3x = 21 - 5

3x = 16

x = 5.333

4) The total amount paid by the three friends = $29.19 ($9.73)

The cost of nachos, including tax and tip = $19.95

The cost of jalapeno, including tax and tip = $9.24 ($29.19 - $19.95)

a) 1/3(30 - y) = 3/4

b) 30(1/3) - y = 3/4

c) 1/3y - 30 = 3/4

d) 30(1/3) - y = 3/4

6) Length of wood = 4.5 feet

The number of equal pieces = 5

Remainder = 0.7 feet

The cut length of the wood = 3.8 feet (4.5 - 0.7)

Length of each cut piece = 0.76 feet

The equation and its solution to determine the length of each of the five pieces are:

x = (4.5 - 0.7) ÷ 5

x = 3.8 ÷ 5

x = 0.76 feet

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Answer:

x = 29

Step-by-step explanation:

Not sure if they meant actually 61 different numbers or just 2 numbers to make up 61, but I determined that -29 and 29 make up 61 because a negative plus a positive is always positive.

Answer:

(B+6)- 3

is it correct?

Answer:

[tex] \sf \: r = \sqrt{V/2πh³} [/tex]

Step-by-step explanation:

V=2πr²h³

Divide both sides by 2πh³

V/2πh³= 2πr²h³/2πh³

V/2πh³ = r²

Flip equation

r² = V/2πh³

Take square root of both sides

√r² = √V/2πh³

∴ r = √V/2πh³

Answer:

Fill in the blanks to declare sum equal to a + b (int _ = a __b)An integer data type can hold decimal values.

Answer:

See below

Step-by-step explanation:

See attached pic

Degree refers to the highest exponent

-nomial refers to the number of terms

Answers:

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

Explanation:

The domain is the set of possible x values. The left-most point occurs when x = -2, while the right-most point is when x = 2. Therefore, x is between -2 and 2 in which we write [tex]-2 \le \text{x} \le 2[/tex]. Both endpoints are included.

-----------

The range is the set of possible y values. The possible y values are in the interval [tex]-2 \le \text{y} \le 2[/tex] since y = -2 is the smallest y can get, and y = 2 is the largest it can get. Visually we look at the lowest and highest points respectively to find the span of y values.

-----------

This relation is not a function because it fails the vertical line test.

It is possible to pass a single vertical line through more than one point on the curve. For example, the vertical line through x = -1 goes through the points (-1,1) and (-1,-1)

Phrased another way: The input x = -1 leads to more than one output.

A function is only possible if each input in the domain leads to exactly one output.

The solution of the linear equation is x = -9

A linear equation is an equation in which the highest power of the unknown is one.

To solve a linear equation, we collect the like terms and them perform operations of addition, subtraction, multiplication and division to simplify the results and get the answer.

Since we have 8 - x = 26 + x

To solve the linear equation, we add + x to both sides. So,

8 - x + x = 26 + x + x

8 + 0 = 26 + 2x

8 = 26 + 2x

Next, we subtract 26 from both sides.

8 - 26 = 26 - 26 + 2x

-18 = 0 + 2x

-18 = 2x

Next, we divide both sides by 2. So, we have

2x = -18

x = -18/2

x = -9

So, the solution of the linear equation is x = -9

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Given data,

Live Fund are selling their holdings at $5,000 per share

Sale price of Live Fund holding = 5000 dollar

To find:

Amount that Live Fund will get if they sell half of their holding in Marks Brothers.

Assume the total number of shares held by Live Fund in Marks Brothers as A

Therefore, half the holdings (or half the number of shares) of Live Fund will be.

                            = A/2

Thus, if each share is valued at  $5000,

Then the total value of the number of shares sold will be as follows,

                             = 5000 × A/2  dollars

                             =  [tex]\frac{5000*A}{2}[/tex] dollars

                             = 2500 A dollars

Hence, Live Fund will receive  $2500 A

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Answer: C - 290 kg

700-410=290

the weight  of the moose is 290kg greater than the weight of a polar bear

The per cent of students who have college careers lasting between 2 and 9 years is 95%.

Given that, the normally distributed with a mean length of 5.5 years and a standard deviation of 1.75 years.

The normal distribution is a continuous probability distribution that is symmetrical around its mean with most values near the central peak.

Let x be the length of student's college careers.

\mu = 5.5 years

\sigma = 1.75 years

A percentage of students have college careers lasting between 2 and 9  years.

P(2<=x<=9)=P (2-5.5<=x-5.5<=9-5.5)

P(2<=x<=9)=P (-3.5<=x-5.5<=3.5)

=P (-3.5/1.75<=(x-5.5)/1.75<=3.5/1.75)

We know if x =-=N (4.6^2)

Then x-\mu/\sigma =-= Z (0.1)

=P(-2<=Z<=2)

=0.95

Percentage = P(-2<=Z<=2)*100

=95%

Therefore, the per cent of students who have college careers lasting between 2 and 9 years is 95%.

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An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. The expression x3+7x+2 value is 24 when x=2. So option A is correct.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

The given expression is x^3+7x+2

Now we have to plug in x value as 2

=(2)^3+7*2+2

The value of 2^3 is 8 and 7*2 is 14

=8+14+2

Add 8, 14 and 2 to get the required solution.

=24

Therefore the expression x3+7x+2 value is 24 when x=2.

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Answer:

y

=

x

−

3

5

Explanation:

Replace

f

(

x

)

with

y

.

y

=

5

x

+

3

Swap

x

and

y

.

x

=

5

y

+

3

Solve for

y

.

x

−

3

=

5

y

x

−

3

5

=

y

Step-by-step explanation:

I assume the equation is

[tex]x \, dy - (y^2 - 4y) \, dx = 0[/tex]

since separating variables leads to

[tex]x\,dy = y(y-4) \, dx[/tex]

[tex]\dfrac{dy}{y(y-4)} = \dfrac{dx}x[/tex]

for which the condition that [tex]x>0[/tex] is actually relevant, as opposed to the simpler differential equation

[tex]x \, dx - (y^2-4y)\, dy = 0 \implies y(y-4) \, dy = x \, dx[/tex]

(though it's a bit more work to solve for [tex]y(x)[/tex] in this case)

That the slope [tex]\frac{dy}{dx}[/tex] is non-zero tells us that

[tex]\dfrac{dy}{dx} = \dfrac{y(y-4)}x \neq 0 \implies y\neq0 \text{ and } y \neq 4[/tex]

Integrate both sides.

[tex]\displaystyle \int \frac{dy}{y(y-4)} = \int \frac{dx}x[/tex]

On the left, expand into partial fractions.

[tex]\displaystyle \frac14 \int \left(\frac1{y-4} - \frac1y\right) \, dy = \int \frac{dx}x[/tex]

[tex]\dfrac14 (\ln|y-4| - \ln|y|) = \ln|x| + C[/tex]

With the given initial value, we find

[tex]y(1) = 2 \implies \dfrac14 (\ln|2-4| - \ln|2|) = \ln|1| + C \implies C = 0[/tex]

so the particular solution is

[tex]\dfrac14 (\ln|y-4| - \ln|y|) = \ln|x|[/tex]

By definition of absolute value, with the initial condition of [tex]0 < y=2 < 4[/tex] and the condition [tex]x>0[/tex], we can remove the absolute values.

[tex]\dfrac14 (\ln(4-y) - \ln(y)) = \ln(x)[/tex]

Solve for [tex]y[/tex].

[tex]\ln\left(\dfrac{4-y}y\right) = 4 \ln(x) = \ln\left(x^4\right)[/tex]

[tex]\dfrac{4-y}y = \dfrac4y - 1 = x^4[/tex]

[tex]\implies y(x) = \dfrac4{1 + x^4}[/tex]

Then

[tex]10y\left(\sqrt2\right) = \dfrac{40}{1 + \left(\sqrt2\right)^4} = \boxed{8}[/tex]

On the off-chance you meant the other equation I suggested, we find

[tex]\displaystyle \int y(y-4) \, dy = \int x \, dx[/tex]

[tex]\displaystyle \frac{y^3}3 - 2y^2 = \frac{x^2}2 + C[/tex]

[tex]y(1) = 2 \implies \dfrac83 - 2\cdot4 = \dfrac12 + C \implies C = -\dfrac{35}6[/tex]

Solving for [tex]y(x)[/tex] involves picking the right branch of the cube root that agrees with [tex]y(1)=2[/tex]. With the cube root formula, we find

[tex]y(x) = 2 - \xi(1 - i\sqrt3) - \dfrac1\xi (1+i\sqrt3)[/tex]

where

[tex]\xi = \dfrac{2\sqrt[3]{4}}{\sqrt[3]{3x^2 - 3 + \sqrt{9x^4 - 18x^2 - 1015}}}[/tex]

With a calculator, we find

[tex]10y\left(\sqrt2\right) \approx 18.748[/tex]

The additive inverse are;

For expression;

a) 3-5

Additive inverse = - 3 - (-5)

For expression;

b) 5 - 3

Additive inverse = - 5 - (-3)

What is additive inverse?

The Property of Additive Inverse states that the summation of a number and it's Additive inverse is zero.

The expressions are;

3 - 5 and 5 - 3

Now, The Property of Additive Inverse states that the summation of a number and it's Additive inverse = 0

And, An Additive inverse of a positive integer is a negative integer and vice versa.

For example: 7 - 7 = 0

Here, The additive inverse of 7 = -7

Since, For the question above, we are asked to use the additive inverses and their properties to find the equivalent expressions.

a) 3 - 5

Hence, Additive inverse = - 3 - (-5)

                                      = -3 + 5

                                      = 2

b) 5 - 3

Hence, Additive inverse = - 5 - (-3)

                                      = - 5 + 3

                                      = - 2

So, The additive inverse are;

For expression;

a) 3-5

Additive inverse = - 3 - (-5)

For expression;

b) 5 - 3

Additive inverse = - 5 - (-3)

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Answer:

3-5:

3+(-5)

-5+3

5-3:

-3+5

5+(-3)

Step-by-step explanation:

hope this helps ya (⁠☆⁠▽⁠☆⁠)

Answer:

Step-by-step explanation:

the answer is 7

The liters of the 5% and the 40% solutions that she should mix to get the solution she needs are 5.7 liters and 4.3 liters respectively.

Let x be the of volume of the 40% solution, then the volume of 5% would be:

10 L = 40% solution volume+ 5% solution volume

10 L= x + 5% solution volume

5% solution volume = 10l-x

Then the volume calculation would be:

10 liter × 20% = x liter × 40% + (10- x) liter × 5% 10l * 20%

= x liter * 35% + 10 liter*5%

x liter *35

= 10l * 20 - 10l *5

= 10l*m × 15x liter

= 10l *15/35

= 4.28 L= 4.3L

The volume of 40% solution= 4.3L

The volume of 5% solution will be:

= 10L- 4.3L

= 5.7L

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Complete question :

A cooler contains 4 L of water. The cooler has marks on it at every 0.2 L. Water bottles are filled with water from the cooler, and each bottle holds approximately 4/9L. After 4 water bottles are filled, between which two marks is the water level in the cooler? Show your work.

Answer:

2.2 - 2.4 Litre

Step-by-step explanation:

Capacity of cooler = 4L

Marking on cooler = every 0.2L

Capacity of bottle = 4/9 L

Number of bottles filled = 4

Total volume filled = (4/9) * 4 = 16/9 L = 1.78L

Volume of water left in tank :

(4 - 1.78)Litre

= 2.22 litres

Since, the tank is marked at 0.2 L interval ; the water level will be between 2.20 to 2.40 litres

Answer:

105,342

Step-by-step explanation:

It is valid.

Answer: The following expression: (-5)(-3)(4) = 60

Step-by-step explanation:

Given that,

The following expression is : (-5)(-3)(4)

Let us assume,

These values represented by X1, X2, X3    

Let us assume,       X1 = -5

                                X2 = -3

                                X3 = 4

So, the following expression is: (X1)(X2)(X3)    

                                                    (-5)(-3)(4)

This values using by multiplication,

So, we can write,

                                  = (X1)(X2)

                                  = (-5)(-3)                    [sign (-) (-) = (+)]

                                  = 15

Therefore, X1X2 values = 15

We can solve X3 value,

                                = (X1)(X2)(X3)

                                = 15 (X3)

 Replace X3 value,

                                = 15(X3)

                                = 15 (4)

                                 = 60

Therefore, (X1)(X2)(X3) = 60

The following expression: (-5)(-3)(4) = 60

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2(x-3)-17=13-3(x+20)

2x-6-17=13-3x-60

2x-23=-3x-47

5x-23=-47

5x= -24

Answer:

x = -4.8

Step-by-step explanation:

The ratio of oranges to the fruits is 2 : 9 in the simplest form.

We are given that we have:

4 strawberries

3 blueberries

7 bananas

and  4 oranges.

So, the total fruits we have are:

Total fruits = 4 + 3 + 7 + 4

Total fruits = 7 + 11

Total fruits = 18 fruits

Now, we need to find the ratio of oranges in these fruits.

Ratio refers to the representation of one number with respect to the other number.

So, the ratio will be:

Ratio = 4 : 18

Simplifying the ratio, we get that:

Ratio = 2 : 9

Therefore, the ratio of oranges to the fruits is 2 : 9 in the simplest form.

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Answer: Simplify the expression ( 7 a 5 b 6 ) 4 is = 2401 [tex]a^{20}[/tex] [tex]b^{24}[/tex]

Step-by-step explanation:

Given data,

Expression is = (7 a 5 b 6) 4

So, we can write,

Expression is = (7a^(5)b^(6))^(4)

                       = [tex][7a^{5} b^{6} ]^{4}[/tex]

Use the power rule [tex](ab)^{n}[/tex] = [tex]a^{n} b^{n}[/tex] to distribute the exponent.

We can use this formula,

Apply the product rule to  [tex][7a^{5} b^{6} ]^{4}[/tex]

                                      = [tex][7a^{5} ]^{4}[/tex] [tex][b^{6} ]^{4}[/tex]

Apply the product rule to  [tex]7a^{5}[/tex]

                                       = [tex]7^{4} [a^{5} ]^{4} [b^{6} ]^{4}[/tex]

Raise 7 to the power of 4,

                                        =  2401 [tex][a^{5} ]^{4} [b^{6}]^{4}[/tex]

Multiply the exponents in [tex][a^{5} ]^{4}[/tex]

Apply the power rule and multiply exponents,   [tex][a^{m} ]^{n}[/tex] = [tex]a^{mn}[/tex]

                                        = 2401 [tex]a^{5*4}[/tex] [tex][b^{6} ]^{4}[/tex]

Multiply 5 by 4,

we can write,

                                        = 2401 [tex]a^{20}[/tex] [tex][b^{6} ]^{4}[/tex]

Multiply the exponents in  [tex][b^{6} ]^{4}[/tex]

Apply the power rule and multiply exponents,  [tex][a^{m} ]^{n}[/tex] = [tex]a^{mn}[/tex]

                                        = 2401 [tex]a^{20}[/tex] [tex]b^{6*4}[/tex]

Multiply 6 by 4,

we can write,

                                       = 2401 [tex]a^{20}[/tex] [tex]b^{24}[/tex]

Therefore,

Simplify the expression ( 7 a 5 b 6 ) 4 is = 2401 [tex]a^{20}[/tex] [tex]b^{24}[/tex].

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Answer:

No

Step-by-step explanation:

This is an irrational number... Hope this helps!!

The final solution which Dr. I.M. smart made is 80 ml with 50% acid concentration.

Concentration determine how much percentage of a certain type of liquid is there in the whole mix of two or more than two liquids.

According to the given question Dr. I.M smart mixes 30ml of acid in 50ml of 20% acid solution.

Let us assume that in  50ml of 20% acid solution x ml is acid

∴ (20/100)×50 = x.

(1000/100) = x

x = 10ml.

Now he adds 30 ml of acid into this so total acid in this concentration is (10+30) ml = 40 ml  and remaining concertation has 40 ml of other quantity.

∴ The total solution is now of 80 ml.

So the final solution is 80ml with 50% acid and 50% other concentration.

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I assume you mean

[tex]|2x + 1| \ge -7[/tex]

The absolute value function is non-negative, so

[tex]|2x+1| \ge0 > -7[/tex]

is true for all [tex]x[/tex]; any value of [tex]x[/tex] is a solution to this inequality. (infinitely many solutions)

Check the picture below.

Maxwell is faster than Hayley by 0.5 miles per hour

The first step is to calculate the average speed of Hayley

Average= distance/time

3/4÷1/6

= 3/4 × 6/1

= 9/2

= 4.5

The next step is to calculate the average speed of Maxwell

= 2/3 ÷ 2/15

= 2/3 × 15/2

= 5

The difference between the average speed of both individuals

= 5-4.5

= 0.5

Hence Maxwell is faster than Hayley by 0.5 miles per hour

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