Answer:
8
Step-by-step explanation:
The definition of an average can be used with the given values to write an equation for the number of boys.
SetupThe average is the total divided by the number. If there were n original boys, the total was T, where ...
T/n = 145 ⇒ T = 145n
Adding two boys with an average of 160 cm height, the new total became (T +2(160)) and the new average became ...
(T +2(160))/(n +2) = 148 ⇒ T = 148(n +2) -320
Equating the values of T, we have ...
T = 145n = 148(n +2) -320
SolutionSolving for n, we find ...
0 = 3n -24 . . . . . . . . . . . . subtract 145n and simplify
0 = n -8 . . . . . . . . . . . divide by 3
8 = n . . . . . . . . . . . add 8
The number of boys in the group at first was 8.
If a cylinder has a height of 12 feet and a radius of 4 feet, what is its surface area (in square feet)? What is its volume (in cubic feet)? (Round your answers to two decimal places.)
The volume of the cylinder is 602.88 ft³.
The surface area of the cylinder is 301.44 ft²
How to find the volume and surface area of a cylinder?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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For each of the following equivalence relations, describe the corre-
sponding partition. Your description of each partition should have no redundancy,
and should not refer to the name of the relation.
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.
What is a corresponding partition?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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Determine the function f(x)= kx+m if f(x-1)-f(x)=2 and f(-2)=1-m
[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]
Triangle abc has vertices at A(-6, 3) , B(3, 5) and C(1, -4). Show that triangle abc is isosceles and find the area of this triangle.
Using the formula for the distance between two points, it is found that:
Since sides AB and BC have the same length, which is different of side AC, the triangle is an isosceles triangle.The area is of 38.63 units squared.What is the distance between two points?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.
What is the area of a 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 length of a rectangle is two feet greater than twice it’s width. If the perimeter is 25 feet, find the width.” Which of the following translations is correct
The width of the rectangle is 3.5 feet
Solving for the missing sides of a rectangle
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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Tom has 7 hamsters. If each hamster weighs 11 pounds, how much weight is there in total?
Answer:
7
Step-by-step explanation:
7x11=77
For problems 13-19, transcribe the following expressions: (Write it out.)
Example: z + 4 = z plus 4
13. st
14. 6/t - 4
15. 20 + t 2
16. 50 - x
17. x - y 2
18. 24/12 + 12
19. xy - 16
The transcribe expression is the expression of the equation in words.
How to transcribe expression?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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Tom's Sports Wear is a retailer of sports hats located in Atlanta, Georgia. Although Tom's carries numerous styles of sports hats, each hat has approximately the same price and invoice purchase cost, as shown below. Sales personnel receive large commissions to encourage them to be more aggressive in their sales efforts. Currently the economy of Atlanta is really humming, and sales growth at Tom's has been great. However, the business is very competitive, and Tom has relied on its knowledgeable and courteous staff to attract and retain customers, who otherwise might go to other sports wear stores. Also, because of the rapid growth in sales, Tom is finding it more difficult to manage certain aspects of the business, such as restocking of inventory and hiring and training new salespeople.
Sales price $ 31.00
Per-unit variable costs:
Invoice cost 17.05
Sales commissions 4.05
Total per-unit variable costs $ 21.10
Total annual fixed costs:
Advertising $ 23,100
Rent 28,200
Salaries 124,200
Total fixed costs $ 175,500
The annual breakeven point in unit sales is calculated to be:
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 $550157.
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una persona compra un terreno a crédito pagadero en 5 año. El primer año paga 5000$. Si cada año paga 10% más que el anterior; calcula cuanto pagará en el quinto año y cual es el importe del terreno
El pago en el quinto año sera de $7,320.50, y el importe total es de $30,525.50
¿Cual es el importe en el quinto año?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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Using the table, what is the average daily balance of the credit card for the July 1 - July 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00.
Day 1112126 Activity − Payment Purchase Payment Adjustment −−500+750−700 Closing Balance 2500200027502050
To solve, multiply each closing balance by the number of days at that balance, add all of these together and then divide by the total number of days in the billing period.
($2500×10)+($2000×10)+($2750×5)+($2050×6)31≈$2291.94
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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in the diagram , what is the value of x
The value of x from the given diagram is 100 degrees
Sum of interior angleFrom 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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If x^y = z is there any way to find y if you know x and z?
We make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z
How to solve for y?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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Question 3
Show work and solve 3 = 5*+1 using change of base formula.
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]
A -foot pole is supporting a tent and has a rope attached to the top. The rope is pulled straight and the other end is attached to a peg one foot above the ground. The rope and the pole form an angle that measures , as shown below. The pole, the rope, and an imaginary line that runs across the ground from the top of the peg to the pole form a right triangle. The hypotenuse is unknown. The pole is adjacent to the 35-degree angle, and it is labeled 10 feet. The 10 foot measurement includes the height of the 1 foot peg. The imaginary line that runs across the ground is opposite the 35-degree angle, and it is not labeled. Which expression shows the length of the rope?
An expression which shows the length of this rope is: 10/cos35 ≈ 12.2 feet.
How to determine the length of this rope?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:
Adj is the adjacent side of a right triangle.Hyp is the hypotenuse of a right triangle.θ is the angle.Substituting the given parameters into the formula, we have;
cos(35) = 10/Hyp
Hyp = 10/cos35
Hyp = 12.2 feet.
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please help me i included the images of the questions, ill give brainliest
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.
Tim Worker is checking his earnings statement. His weekly earnings are $520.00. If he claims two exemptions, how much tax is withheld? 18.73 15.40 17.65 16.48
The tax that will be withheld is D. $16.48.
How to calculate the tax?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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Need help with defining this question.
Answer: 19
Step-by-step explanation:
[tex]F(5)=5^2 - 2(5)+4=19[/tex]
-275+156-(-293)-157 = 17
ME PUEDEN DAR EL PROCEDIMIENTO
PLIS
The procedure for solving -275+156-(-293)-157 = 17 is to follow bodmas operation
Evaluation-275+156-(-293)-157 = 17
Using BODMAS
b - bracketo - offd - divisionm - multiplicationa - additions - subtraction-275+156-(-293)-157 = 17
= -275 + 156 + 293 - 157
= 17
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Shawn averages 10,142 steps every day. If there were 31 days in the month, about how many steps did he take in that month.
Answer:
314402 steps
Step-by-step explanation:
10142 x 31
Multiply –8m(–6m – 7).
–14m2 – 15m
48m2 + 56m
–14m – 15
48m + 56
Answer: 48m2 + 56m
Step-by-step explanation:
Answer:
Answer B
Step-by-step explanation:
Number graph ranging from negative one to seven on the x axis and negative four to four on the y axis. Two lines that are perpendicular to each other intersect at (two, one). The line with a positive slope is labeled a and the line with a negative slope is labeled b. Use the graph to state the solution for the system. x + 2y = 4 (line a) 3x – 2y = 4 (line b) (2, –1) (2, –1) (2, 1) (2, 1) (–2, 1)
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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Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 400 minus quantity y minus 110 end quantity squared over 2304 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
100 meters
50 meters
48 meters
40 meters
The width of the cooling tower at the base of the structure is 40 meters.
Width of the cooling towerGiven 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:
Construct a right angled traiangle ,choosing whole numbers of centimeters for the lengths of the two shorter sides, such that the hypotenuse will be √65 long.Check the accuracy of your drawing by measuring the hypotrnuse and by calculating √65.
Please give me a correct answer.
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]
find HM if HG=18, FM=5, and EM=9
Answer:
HM = 3 or HM = 15
Step-by-step explanation:
The product of segment lengths is the same for both chords.
SetupFM·EM = GM·HM
GM +HM = 18
Substituting for GM, we have ...
FM·EM = (18 -HM)·HM
5·9 = (18 -HM)·HM
SolutionEffectively, 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
Kathy and Linda both accepted new jobs at different companies. Kathy's starting salary is $31,500 and Linda's starting salary is $33,000. They are curious to know who has the better starting salary, when compared to the salary distributions of their new employers. A website that collects salary information from a sample of employees for a number of major employers reports that Kathy's company offers a mean salary of $42,000 with a standard deviation of $7,000. Linda's company offers a mean salary of $45,000 with a standard deviation of $6,000. Find the z-scores corresponding to each woman's starting salary.
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-scorez = (x - μ) / σ
Where
z is the s-scorex is the scoreμ is the mean σ is the standard deviation1. How to determine the z-score for Kathy's starting salaryStarting salary (x) = $ 31500Mean salary (μ) = $ 42000Standard deviation (σ) = $ 7000z-score for Kathy's starting salary (z) =?z = (x - μ) / σ
z = (31500 - 42000) / 7000
z-score for Kathy's starting salary = -1.5
2. How to determine the z-score for Linda's starting salaryStarting salary (x) = $ 33000Mean salary (μ) = $ 45000Standard deviation (σ) = $ 6000z-score for Linda's starting salary (z) =?z = (x - μ) / σ
z = (33000 - 45000) / 6000
z-score for Linda's starting salary = -2
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The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
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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A client is instructed to drink 20 ounces of water with 1 hour. The client has only been able to drink 12 ounces. What portion of water remains? (express your answer as a fraction reduced to lowest terms)
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.
What is a fraction?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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evaluate the expression 27 (36)
The value of the expression is 972
How to evaluate the expression?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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Which is the graph of f(x) = (4)×?
See the graph in the attached image.
that any pair of congruent triangles is similar True or false.
Answer:
yes it's true no problem sir