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1 + 1/3=

Answer: 40 km

Step-by-step explanation:

As corresponding sides of similar triangles are proportional, if we let the distance across Clarence lake be x,

[tex]\frac{x}{8}=\frac{15}{3}\\\\\frac{x}{8}=5\\\\x=\boxed{40 \text{ km}}[/tex]

Answer:

-4*(x+1)

Step-by-step explanation:

Simplify

⇒ 8x2 + 8x/-2x

2:  Pulling out like terms

4.1     Pull out like factors :

  8x2 + 8x  =   8x • (x + 1)

Canceling Out :

4.2    Canceling out x as it appears on both sides of the fraction line

Final result :

 -4 • (x + 1)

Answer:

-4(x+1)

Step-by-step explanation:

factor out -2x

-2x(-6x + 2x - 4) / -2x

the -2x in numerator and denominator cancel out

-6x + 2x - 4

-4x - 1

-4(x+1)

A set is a mathematical model for a collection of items. The set of W' is {5, 20, 30}.

A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.

The complete question is given below.

Q13.

T ∪ V = Data points that are in T or V or both.

T ∪ V = {5, 10, 20, 30}

Q14.

T ∩ W = Data points that are in T and W both.

T ∩ W = {10}

Q15.

W' = Data points that are not in W.

W' = {5, 20, 30}

Hence, the set of W' is {5, 20, 30}.

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Answer:

2x(7x-3) + (x²+1)(7)

Step-by-step explanation: use product rule

(a):112

(b):396

(c):360

(d):30

(e):1664

(f):240

Answer:

25

Step-by-step explanation:

find the greatest common factor (GCF) of the 3 quantities using prime factorisation.

125 = 5 × 5 × 5

150 = 2 × 3 × 5 × 5

225 = 3 × 3 × 5 × 5

Next, identify those prime factors that the 3 numbers have in common and multiply them.

the common factors are 5 × 5 = 25

then

125 ÷ 25 = 5

150 ÷ 25 = 6

225 ÷ 25 = 9

the 25 students each get 5 apples, 6 oranges and 9 mangoes

Answer:

Using the concept of number line, we find that Libby owes more than Daniel.

Step-by-step explanation:

Given that the account balance of Daniel is -$1.25 and of Libby is -$2.00. Sandra has as much savings in her account as the amount Daniel owes the bank. So, her account balance is +$1.25.

The numbers to be plotted on the number line are -2.00, -1.25 and 1.25.

The number line is in the attachment.

These numbers are related as: -2 < -1.25 < 1.25.

From the number line, all the names that come left to the origin owe some amount to the bank while all the names that come right to the origin have some money as savings in their account.

Clearly, Daniel and Libby owe the bank.

But since Libby comes before Daniel, Libby owes more than Daniel.

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The polar coordinates of (-4, 150°) will be  [tex]\sqrt[2]{5629}\\[/tex]  and 5069.09939523°

The formula for this conversion will be:

r = [tex]\sqrt{x^2 + y^2}[/tex]

θ = [tex]tan ^-1 (\frac{y}{x} )[/tex]

[tex]r = \sqrt{(4^2) + (150^0)^2} \\\\θ = tan ^-1 (\frac{y}{x} )\\\\\\r = \sqrt[2]{5629} \\\\ = tan ^-1 (\frac{150}{4} )\\[/tex]

= [tex]\frac{75}{2}[/tex]

the inverse of:  [tex]\frac{75}{2}[/tex] is   θ = 5069.09939523°

Therefore:

[tex]r = \sqrt[2]{5629}\\[/tex]

θ = 5069.09939523°

So the polar coordinates of (-4, 150°) will be [tex]\sqrt[2]{5629}\\[/tex]  and 5069.09939523°

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Answer:

21x²

Step-by-step explanation:

hopefully A is a typo

Answer: A (if it's just a typo)   or   [tex]21x^{2}[/tex]

Step-by-step explanation:

Since it's the same variable and same exponent, you just need to add the whole numbers and put the same variable and exponent.

12 + 9 = 21

[tex]21x^{2}[/tex]

Answer:

y=55x

Step-by-step explanation:

(y1-y2)/(x1-x2)=(165-55)/(3-1)=55

55 is the slope

To find y-intercept:

y=55x+b

substitute 1 for x and 55 for y

55=55(1)+b

b=0

So y= 55x

the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x. To write the equation of the line that passes through the points (3, 165) and (1, 55), you can use the point-slope form of a linear equation, which is: y - y₁ = m(x - x₁)

where (x₁, y₁) is one of the points on the line, m is the slope of the line.

First, calculate the slope (m) using the given points (3, 165) and (1, 55):

m = (y₂ - y₁) / (x₂ - x₁) = (55 - 165) / (1 - 3) = (-110) / (-2) = 55

Now that you have the slope (m = 55) and one of the points (let's use (3, 165)), you can plug them into the point-slope form:

y - 165 = 55(x - 3)

Now, you can simplify and rewrite this equation in slope-intercept form (y = mx + b):

y - 165 = 55x - 165

To isolate y, add 165 to both sides:

y = 55x

So, the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x.

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Answer:

y=5x

Step-by-step explanation:

A product means multiplication, and you need to multiply x by 5 in order to make the product have a factor of 5.

The given differential equation is linear with constant coefficients,

[tex]\dfrac{d^2y}{dx^2} - 49y = 0[/tex]

with characteristic equation

[tex]r^2 - 49 = 0[/tex]

and hence characteristic roots [tex]r=\pm7[/tex]. This means the general solution to the ODE is

[tex]y = C_1 e^{7x} + C_2 e^{-7x}[/tex]

In fact, you're given the solution already,

[tex]y = C_1 e^{kx} + C_2 e^{-kx}[/tex]

and you've determined that

[tex]\dfrac{d^2y}{dx^2} = k^2 (C_1 e^{kx} + C_2 e^{-kx}) = k^2 y[/tex]

Comparing this to the given ODE, it's obvious that [tex]k=7[/tex], so you can just replace [tex]k[/tex] with 7 in the given template solution.

Step-by-step explanation:

sorry sorry ^$£%£$¥#^÷£=₩€%¥=£=;÷¥÷¥9=

Differentiate both sides with respect to [tex]t[/tex], treating both [tex]x[/tex] and [tex]y[/tex] as functions of [tex]t[/tex].

[tex]x^3 + y^3 = 9 \implies 3x^2 \dfrac{dx}{dt} + 3y^2 \dfrac{dy}{dt} = 0[/tex]

Then when [tex]x=1[/tex], [tex]y=2[/tex] and [tex]\frac{dx}{dt}=-3[/tex], we get

[tex]3\times1^2\times(-3) + 3\times2^2\dfrac{dy}{dt} = 0 \implies \dfrac{dy}{dt} = \dfrac9{12} = \boxed{\frac34}[/tex]

Let's take this problem step-by-step:

First let's set up the equation for the cost for one week of renting the car

              [tex]charge = 230[/tex]

              [tex]charge = 230 + 0.25x[/tex]

The total cost was 415, therefore:

             [tex]415 =230 + 0.25x\\185 = 0.25x\\x = 740[/tex]

Therefore, you traveled 740 miles

Answer: 740 miles

Hope that helps!

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The opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

The stock of Company A gained 6% today to $87.45.

Let x be the opening price of the stock in the beginning of the day.

(x + 0.06x) = 87.45  

Because gained 6% today to $87.45

1.06x = 87.45

x = $82.5

Thus, the opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.

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Answer:

Using the formula of geometric progression, we get 5.3333333. After rounding off to the nearest hundredth or to the two digit place after the decimal, we get 5.33.

Step-by-step explanation:

Concept: Given expression means that [tex]4(\frac{1}{4} )^{n-1}[/tex] is a series that starts from n = 1 and ends at n = 10. Or we can say that the given expression is a summation from n = 1 to n = 10. This will make a geometric progression. Use the formula of geometric progression to find the answer.

[tex]4(\frac{1}{4})^{0} + 4(\frac{1}{4})^{1} + 4(\frac{1}{4})^{2} +...+ 4(\frac{1}{4})^{10}\\4\frac{-(\frac{1}{4} )^{11} +1}{-\frac{1}{4} +1} \\4\frac{1}{\frac{3}{4} } \\\frac{16}{3} \\5.33333333\\[/tex]

Now, we want the answer to the nearest hundredth. This means that the answer should have two digits after the point.

The answer, to the nearest hundredth is 5.3333333

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Answer:

4(49v²+25)

Step-by-step explanation:

[tex]196 {v}^{2} + 100[/tex]

[tex]4(49 {v}^{2} + 25)[/tex]

Answer:  24 sq units is the area of triangle.

Step-by-step explanation:

Given , (x1 , y1) = (-1, 1),  (x2 , y2) = (3, 5) ,  (x3, y3) = (5, -5)

Using the Formula :

Area of triangle =  [tex]\[\frac{1}{2}(x1(y2-y3) + x2(y3-y1) + x3(y1 -y2))\][/tex]

    [tex]\[=\frac{1}{2}(-1(5-(-5)) + 3(-5-1) + 5(1-5)) \\=\frac{1}{2}(-10 -1 8 -20) \\=\frac{1}{2}(-48) = -24\][/tex]

Area cannot be negative. We only consider the numerical value of answer. Therefore, area of triangle = 24 sq units.

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Si administran 500 ml. La tasa de goteo requerida en gotas por minuto es de 21 gtt/min.

Usando esta fórmula

Tasa de goteo requerida=(ml administrado×gotas/mL)÷ (Número de horas×Número de minutos por hora)

Vamos a conectar la fórmula

Tasa de goteo requerida =(500 mL x 20 gtt/mL) ÷ (8 hrs. x 60 min)

Tasa de goteo requerida =10,000÷480

Tasa de goteo requerida = 20.8

Tasa de goteo requerida =21 gtt/min (Aproximadamente)

Por lo tanto, la tasa de goteo requerida en gotas por minuto es de 21 gtt/min.

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Answer:

Step-by-step explanation:

Answer:

130 sq. units

Step-by-step explanation:

Any number multiplied by 10 is the same number with a 0 added at the end.

Answer:

1300

Step-by-step explanation:

1. calculator

2.putreef Iub numbers

3 solve

Answer: Table D

Step-by-step explanation:

The coefficient of x^2 is -9, the coefficient of x is 7, and the constant is 0, so we know a = -9, b = 7, c = 0.

Thus, table D is the answer.

Answer:

that makes no sence at all i read it over 3 times and still font understand a word of it

sorry :(

Answer:

$1710

Step-by-step explanation:

let me know if you want an explanation :))

Answer: [tex]x=5\sqrt{3}[/tex]

Step-by-step explanation:

As the triangle is equilateral, we know that all sides have a length of 10. Thus, if we consider either of the right triangles, we know they have legs of lengths 5 and x (since an altitude of an equilateral triangle bisects the side it is drawn to), and a hypotenuse of 10.

Thus, by the Pythagorean theorem,

[tex]5^{2}+x^{2}=10^{2}\\\\25+x^{2}=100\\\\x^{2}=75\\\\\boxed{x=5\sqrt{3}}[/tex]

Answer:

117

Step-by-step explanation:

The total population is 117 million

Answer:

P(Event) = N(Favorable Outcomes) / N (Total Outcomes)

P(sum of 10 or 11) = 5/36

Step-by-step explanation:

Probability states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.

The higher or lessen the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2.

So,

P(Event) = N(Favorable Outcomes) / N (Total Outcomes)

Sample Space:

All the possible outcomes of an event are called Sample spaces.

Examples-

• If two dice are rolled together then total outcomes will be 36 and

Sample space will be

[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)  

  (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

  (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

  (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

  (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

  (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]

Probability of rolling a sum of 10 or 11 with two dice:

When two dice are rolled together then total outcomes are 36 and

Sample space is

[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

  (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

  (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

  (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)  

 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)  

 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]

So, pairs with sum 10 or 11 are (4, 6) (5, 5) (6, 4) (5,6) (6,5) i.e. total 5 pairs

Total outcomes = 36

Favorable outcomes = 5

Probability of getting the sum of 10 or 11 = Favorable outcomes / Total outcomes

                                                               = 5 / 36

So, P(sum of 10 or 11) = 5/36

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let's name the vertices of the triangle as A B C and D as the image shown above

In triangle ABC

sin 60° = AB/AC

√3/2 = 8√2/ AC

AC = 16√2/√3

In triangle ACD

sin 45° = AC/AD

1/√2 = 16√2/ 3 AD