4)48 Ans: The average height of a group of boys was 145 cm. When 2 boys joined the group, the average height became 148 cm. Given that the average height of the 2 additional boys was 160 cm, find the number of boys in the group at first.​

1. The z-scores corresponding to Kathy's starting salary is -1.5

2. The z-scores corresponding to Linda's starting salary is -2

z = (x - μ) / σ

Where

z = (x - μ) / σ

z = (31500 - 42000) / 7000

z-score for Kathy's starting salary = -1.5

z = (x - μ) / σ

z = (33000 - 45000) / 6000

z-score for Linda's starting salary = -2

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Answer: 19

Step-by-step explanation:

[tex]F(5)=5^2 - 2(5)+4=19[/tex]

Using the formula for the distance between two points, it is found that:

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In this problem, we use the formula to find the lengths for each side of the triangle.

For example, side AB has length given by the distance between (-6,3) and (3,5), hence:

[tex]AB = \sqrt{(-6 - 3)^2 + (3 - 5)^2} = 9.22[/tex]

Side AC has length given by:

[tex]AC = \sqrt{(-6 - 1)^2 + (3 - (-4))^2} = 9.9[/tex]

Side BC has length given by:

[tex]BC = \sqrt{(3 - 1)^2 + (5 - (-4))^2} = 9.22[/tex]

Since sides AB and BC have the same length, which is different of side AC, the triangle is an isosceles triangle.

The area of a triangle is given by half the length of the base multiplied by the height.

The midpoint of side BC, of length of 9.22 units, is of (2,0.5). The height is the distance of this point from point A, hence:

[tex]d = \sqrt{(-6 - 2)^2 + (3 - 0.5)^2} = 8.38[/tex]

Hence the area is:

A = 0.5 x 9.22 x 8.38 = 38.63 units squared.

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The value of x from the given diagram is 100 degrees

From the given diagram, we will use the theorem "angle at the vertex is half that at the centre.

<50 = 1/2 x

Cross multiply

50 * 2 = x

x = 50 * 2

x = 100 degrees

Hence the value of x from the given diagram is 100 degrees

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Answer: 48m2 + 56m

Step-by-step explanation:

Answer:

Answer B

Step-by-step explanation:

The procedure for solving -275+156-(-293)-157 = 17 is to follow bodmas operation

-275+156-(-293)-157 = 17

Using BODMAS

-275+156-(-293)-157 = 17

= -275 + 156 + 293 - 157

= 17

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The description of the corresponding partition is given as follows:
The infinite classes can be defined as:

At equal  distance of x from point [1,2] 

Where x can vary from o to infinity.

The analogous partition, commonly known as "the set of equivalence classes," is the set A/R, the elements of which are the subsets of A satisfying  the following:


For every a∈A there is some B∈A/R such that a∈B.

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See the graph in the attached image.

Answer:

1: r^5, 2: st^2, 3: qr, 4: 1, 5: m, 6: x, 7: 1/z, 8: a, 9: d^4f^2 10: 1, 11: cd^2, 12: b, 13: 1, 14: st^2, 15: 1/mn.

Step-by-step explanation:

1 explanation: Cancel the common factor of r^6 and r.

2 explanation: Simplify the expression.

3 explanation: simplify the expression.

4 explanation: Simplify the expression.

5 explanation: simplify the expression.

6 explanation: Cancel the common factor of x^2 and x.

7 explanation: Cancel the common factor of z^4 and z^5.

8 explanation: Cancel the common factor of a^2 and a.

9 explanation: simplify the expression.

10 explanation: simplify the expression.

11 explanation: simplify the expression.

12 explanation: simplify the expression.

13 explanation: simplify the expression.

14 explanation: simplify the expression.

15: simplify the expression.

We make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z

The expression is given as:

x^y = z

The above expression is an exponential expression.

Start by taking the logarithm of both sides

y log(x) = log(z)

Divide both sides by log(x)

[tex]y = \log_x(z)[/tex]

Hence, we make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z

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An expression which shows the length of this rope is: 10/cos35 ≈ 12.2 feet.

In order to determine the length of this rope, we would apply the law of cosine because both the rope and apple formed an angle that are adjacent in a right triangle:

cos(θ) = Adj/Hyp

Where:

Substituting the given parameters into the formula, we have;

cos(35) = 10/Hyp

Hyp = 10/cos35

Hyp = 12.2 feet.

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Answer:

  HM = 3   or   HM = 15

Step-by-step explanation:

The product of segment lengths is the same for both chords.

  FM·EM = GM·HM

  GM +HM = 18

Substituting for GM, we have ...

  FM·EM = (18 -HM)·HM

  5·9 = (18 -HM)·HM

Effectively, we want two factors of 45 that have a total of 18. Looking at the factors of 45, we have ...

  45 = 1·45 = 3·15 = 5·9

The totals of these pairs are 46, 18, 14. The factor pair we're looking for is 3·15.

Either of these factors could be HM. The other will be GM.

There is nothing in the problem description that suggests the length of HM relative to other lengths on the diagram. (We know the diagram is not to scale.) So, there are two possible solutions:

  HM = 3   or   HM = 15

Answer:

314402 steps

Step-by-step explanation:

10142 x 31

The volume of the cylinder is 602.88 ft³.

The surface area of the cylinder is  301.44 ft²

volume of a cylinder = πr²h

volume of a cylinder = 3.14 × 4² × 12

volume of a cylinder = 3.14 × 16 × 12

volume of a cylinder = 602.88 ft³

Surface are of a cylinder = 2πr(r + h)

Surface are of a cylinder = 2 × 3.14 × 4(4 + 8)

Surface are of a cylinder =  25.12(12)

Surface are of a cylinder = 301.44 ft²

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The solution for the system of lines is defined as follows,

x-Intercept for line a: (4,0)

y-Intercept for line a: (0,2)

x-Intercept for line b: (1.5, -0)

y-Intercept for line b: (0,-2)

Line a and b intersect at (2,1)

Solving the System of Lines:

Line a: x + 2y = 4

Line b: 3x – 2y = 4

From the graph,

Line a intersect x-axis at (4,0) and y-axis at (0,2)

Line b intersect x-axis at (-1.5,0) and y-axis at (0,-2)

x + 2y = 4

x = 4-2y

Since point P lies on bot the lines A and B, it will satisfy the equations of both a and b.

Thus, substituting x = 4-2y in the equation of line b, we get,

3(4-2y) - 2y = 4

12 - 6y - 2y = 4

8y = 8

y = 1

Putting y=1 in the equation of line a, x = 4-2y, we get,

x = 4-2(1)

x = 4-2

x = 2

Hence, point P≡(2,1).

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The transcribe expression is the expression of the equation in words.

The expression can be transcribe as follows;

1. st  = s multiply by t

2. 6 / t - 4 = 6 divided by t minus 4

3. 20 + t² = 20 plus t squared.

4. 50 - x = 50 minus x

5. x - y² = x minus y squared.

6. 24 / 12 + 12 = 24 divided by 12 plus 12

7. xy - 16 = x multiply by y minus 16

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The width of the cooling tower at the base of the structure is 40 meters.

Given equation

x²/400 -(y-90)²/1600=1

Solving for the width

Cooling tower width =2√400

Cooling tower width=2×20

Cooling tower width=40 meters

Therefore the correct option is D. 40 meters.

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Answer:

40

Step-by-step explanation:

The tax that will be withheld is D. $16.48.

From the information, it was stated that Tim Worker is checking his earnings statement and that his weekly earnings are $520.00.

The tax that will be withheld will be:

= 3.16% × $520

= $16.48

In conclusion, the correct option is D.

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Answer:

all real values of x where x < -1

The correct statement is all real values of x where x < -1.

Option A is the correct answer.

We have,

To determine the values for which the graph of the function

f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.

Let's consider the factors individually:

(x - 3): This factor is positive for x > 3 and negative for x < 3.

(x + 1): This factor is positive for x > -1 and negative for x < -1.

To determine the overall sign of the function, we need to consider the signs of both factors together.

When both factors are positive or both factors are negative, the function is positive.

When the factors have opposite signs, the function is negative.

From the above analysis, we can conclude the following:

When x > 3, both factors are positive, so the function is positive.

When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.

When x < -1, both factors are negative, so the function is positive again.

Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).

Thus,

The correct statement is all real values of x where x < -1.

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The value of the expression is 972

The expression is given as:

27(36)

Express 36 as 18 + 18

27(18+ 18)

Expand

486+ 486

Evaluate the sum

972

Hence, the value of the expression is 972

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The width of the rectangle is 3.5 feet

The width of the rectangle = w

The length of the rectangle = l

The perimeter = p

Length of the rectangle is two feet greater than twice it’s width

l  =  2w + 2

p = 2(l + w)

p = 2(2w + 2 + w)

p = 2(3w + 2)

p = 6w + 4

The perimeter of the rectangle is 25 ft

25  =  6w + 4

This can be rewritten as:

6w + 4 = 25

6w = 25 - 4

6w = 21

w = 21/6

w  = 3.5

Therefore, the width of the rectangle is 3.5 feet

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The annual breakeven point is $550157

Given that the Sales price is $ 31.00, Per-unit variable costs: Invoice cost is 17.05, Sales commissions is 4.05, Total per-unit variable costs is $ 21.10, Total annual fixed costs: Advertising is $ 23,100, Rent is 28,200, Salaries is 124,200 and Total fixed costs is $ 175,500.

The break-even point is your total fixed cost divided by the difference between the unit price and the variable cost per unit.

The sales price is $31 and the total variable cost is $21.10.

Now, we will find the Contribution margin by subtracting the Total variable cost from the sales price, we get

Contribution margin= Sales price-Total sales price

Contribution margin=31-21.10

Contribution margin=9.9

Further, we will find the contribution margin ratio by dividing the contribution margin by Sales price, we get

contribution margin ratio=contribution margin/Sales price

contribution margin ratio=9.9/31

contribution margin ratio=0.319

contribution margin ratio=31.9%

Furthermore, we will find the break-even point, we get

Break-even point=Fixed cost/contribution margin

Break-even point=175500/9.9

Break-even point=17727.27

Now, we will find the break-even sales in dollars, we get

Break-even sales=Fixed cost/contribution margin ratio

Break-even sales=(175500/31.9)×100

Break-even sales=550157

Hence, the annual breakeven point in unit sales is calculated to be $550157.

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Answer:

1. Shorter Side: 4

2. Longer Side: 7

3. Hypotenuse: [tex]\sqrt{65}[/tex]

Step-by-step explanation:

[tex]4^{2} +7^{2} =65[/tex]

Answer:

7

Step-by-step explanation:

7x11=77

Answer: [tex]x=\frac{\log (3/5)}{\log 5}[/tex]

Step-by-step explanation:

[tex]3=5^{x+1}\\\\\log_{5} 3=x+1\\\\x=\log_{5} 3-1\\\\x=\log_{5} 3-\log_{5} 5\\\\x=\log_{5} \left(\frac{3}{5} \right)\\\\x=\frac{\log (3/5)}{\log 5}[/tex]

Answer:

yes it's true no problem sir

The average daily balance of the credit card is 2291.94

What is the average daily balance?

The average daily balance can be determined by dividing the total daily balance of month by numbers of days in month.

We can find average daily balance as shown below:

Average daily balance = total balance of the month/total number of days in the month

Total balance = (2500*10) +(2000*10) +(2750*5) +(2050*6)

= 25000+20000+13750+12300

= 71,050

Number of days = 31

Average daily balance = 71,050/31

= 2291.9354

Round to the nearest cent

= 2291.94

Hence, the average daily balance of the credit card is 2291.94

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[tex]f(x) = kx + m \\ f(x - 1) = k(x - 1) + m[/tex]

[tex]f(x - 1) - f(x) = 2 \\ k(x - 1) + m - kx - m = 2 \\ kx - k + m - kx - m = 2 \\ - k = 2 \\ k = 2[/tex]

[tex]f( - 2) = k( - 2) + m = 1 - m \\ k( - 2) + m = 1 - m \\ ( - 2)( - 2) + m = 1 - m \\ 4 + m = 1 - m \\ 2m = - 3 \\ m = \frac{ - 3}{2} [/tex]

[tex]f(x) = - 2x - \frac{3}{2} [/tex]

El pago en el quinto año sera de $7,320.50, y el importe total es de $30,525.50

Sabemos que el importe inicial es $5,000, cada año paga 10% más que el anterior.

Entonces se hacen 5 pagos, y el pago que se hace en cada año esta dado por la ecuación exponencial:

[tex]P(x) = \$5000*(1.10)^{x - 1}[/tex]

Donde x es el número del año.

Entonces en el año número 5, el pago será:

[tex]P(5) = \$5000*(1.10)^{5 - 1} = \$7,320.50[/tex]

¿Cuanto es el importe total?

Está dado por:

[tex]T = P(1) + P(2) + P(3) + P(4) + P(5)\\\\T = \$5000*( 1 + (1.10)^1 + (1.10)^2 + (1.10)^3+ (1.10)^4) = \$30,525.50[/tex]

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Answer:

2/5

Step-by-step explanation:

20 ounces in all - 12 ounces drank = 8 ounces left

8 ounces left/20 ounces in all = 4/10 = 2/5 = 0.4

The portion of water remaining is 2/5 if the client is instructed to drink 20 ounces of water for 1 hour.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

A client is instructed to drink 20 ounces of water for 1 hour. The client has only been able to drink 12 ounces.

The remaining portion =  20 ounces  -  12 ounces drank

The remaining portion = 8 ounces left

As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

The fraction:

= 8 ounces left/20 ounces in all = 4/10 = 2/5 = 0.4

= 8/20

= 2/5

Thus, the portion of water remaining is 2/5 if the client is instructed to drink 20 ounces of water for 1 hour.

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