If Quadrilateral Q is a scaled copy of Quadrilateral P created with a scale factor of 3, what is the perimeter of q?

\(6y^2(y^2+6y+9)\\\\=6y^2(y^2+2\cdot 3 \cdot y + 3^2)\\\\=6y^2(y+3)^2\\\\=6y^2(y+3)(y+3)\)

Answer:

12

Step-by-step explanation:

4+4+4=12

Proportionately, since George is twice as old as Jack and Jack is twice as old as Alex if the total of their ages is 147, George is 84 years.

To determine the different ages of the Williams family, we apply ratios.

Ratios define the relative size of one value or age compared to another.

Proportionately, the sum of ratios and the total ages of the family are equated to define the various ages.

Remember that proportion is the equation of two or more ratios.

Let Alex's age = x

Let Jack's age, who is twice as old as Alex, = 2x

Let George's age, who is twice as old as Jack, = 4x (2 x 2x)

The sum of ratios = 7x (x + 2x + 4x)

The total of their ages = 147

Alex's age = 21 (147/7)

Jack's age = 42 (147/7 x 2)

The age of George = 84 (147/7 x 4)

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Answer: Yes

Step-by-step explanation:  Domain - -1,2,3,6    Range- -2,3,1,-2

Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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Answer:

a= rs 1162.88

Step-by-step explanation:

Find the cost of 10.5kg of rice. if the rate of cost of rice is rs 110.75 per kg.

Use proportionality, the equality between 2 ratios.

In the expression a/b = c/d, a and b are in the same proportion as c and d.

a/10.5kg=110.75/1 kg

a = (10.5 kg * rs 110.75) / 1kg

a = rs 1162.875

a= rs 1162.88

The current temperature is 48°F, in expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.

The current temperature is = 48°F.

It is expected to drop = 1.5°F each hour.

We can assume, temperature = 36°F

Let x hours the temperature will be 36°F.

Temperature is a measure of the average kinetic energy of the particles in an object. When the temperature increases, the motion of these particles also increases. Temperature is measured with a thermometer or a calorimeter.

Then,

48 - 1.5x = 36

It's expected to drop 1.5F per hour,

We can list the equation,

So,

We can write,

48 - 1.5x = 36

48 - 36 = 1.5x

We can sum or difference of the product,

1.5x = 12

x = 12/1.5

We can divide the products,

x = 8 hours

Therefore,

In expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.

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Answer:

The present temperature is 48°F; it is anticipated to decrease by 1.5°F every hour, reaching 36°F in 8 hours.

Step-by-step explanation:

48°F is the current temperature.

An hourly decrease of 1.5°F is anticipated.

We'll assume that it's 36°F.

The temperature will be 36°F in x hours.

The average kinetic energy of the particles in an object is measured by its temperature. The velocity of these particles likewise increases as the temperature rises. A thermometer or a calorimeter is used to determine the temperature.

Then,

48 - 1.5x = 36

It's expected to drop 1.5F per hour,

We can list the equation,

So,

We can write,

48 - 1.5x = 36

48 - 36 = 1.5x

We can sum or difference of the product,

1.5x = 12

x = 12/1.5

We can divide the products,

x = 8 hours

Therefore,

In expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.

Answer:

a) 0.11277

b) 0.83253

c) 0.67364

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

From the question,

Mean = $109.55.

Standard deviation = $21.00.

a) What proportion of bills are greater than $135?

z = (x-μ)/σ

z = 135 - 109.55/21

= 1.2119

Probability value from Z-Table:

P(x<135) = 0.88723

P(x>135) = 1 - P(x<135) = 0.11277

The proportion of bills are greater than $135 = 0.11277

(b) What proportion of bills are between $84 and $143?

For x = $84

z = (x-μ)/σ

z = 84 - 109.55/21

= -1.21667

Probability value from Z-Table:

P(x = 84) = 0.11187

For x = 143

z = (x-μ)/σ

z = 143 - 109.55/21

= 1.59286

Probability value from Z-Table:

P(x = 143) = 0.9444

The proportion of bills are between $84 and $143

= P(x = $143) - P(x = 84)

= 0.9444 - 0.11187

= 0.83253

(c) What is the probability that a randomly selected household had a monthly bill less than $119?

For x = $119

=119 - 109.55/ 21

= 0.45

Probability value from Z-Table:

P(x<119) = 0.67364

The probability that a randomly selected household had a monthly bill less than $119 is 0.67364

Answer:

Step-by-step explanation:

77 for (-7,3)

Answer:

Since this is a straight line the slope is just x = -7.

Answer:

its B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

0.0814 = 8.14% probability that at least one of the women has a Chlamydia infection

Step-by-step explanation:

For each women, there are only two possible outcomes. Either they have a Chlamydia infection, or they do not. The probability of a woman having the infection is independent of any other women. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The Centers for Disease Control and Prevention reports that the rate of Chlamydia infections among U.S. women ages 20 to 24 is 2791.5 per 100,000.

This means that:

\(p = \frac{2791.5}{100000} = 0.027915\)

Take a random sample of three U.S. women in this age group.

This means that \(n = 3\)

What is the probability that at least one of the women has a Chlamydia infection?

This is:

\(P(X \geq 1) = 1 - P(X = 0)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{3,0}.(0.027915)^{0}.(1-0.027915)^{3} = 0.9186\)

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9186 = 0.0814\)

0.0814 = 8.14% probability that at least one of the women has a Chlamydia infection

28. t = I / (Pr)

29. y = -(3x / 5) + (15 / 5)

30. y = -3/5 x + 3

31. y = -3/5 * -1 + 3 = 3 + 3/5 = 3.6

32. 2 tablespoons per serving

33. $0.92 per slice

34. 5 tablespoons

35. 45% (159 / 350 = 0.45 and 0.45 * 100 = 45)

Simple interest is a method of calculating the interest charge on a loan or deposit based on a constant interest rate and the original principal amount. The formula for simple interest is I = Prt, where P is the principal amount, r is the interest rate as a decimal, t is the time period in years, and I is the interest amount. In simple interest, the interest amount is calculated only on the original principal, not on any accumulated interest from prior periods.

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The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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Answer:

2 real roots because the discrimnant is greater than 0

Step-by-step explanation:

Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

Answer:

Step-by-step explanation:

Let x represent the number of tickets sold, and y represent the total amount of money raised. Since each ticket is $2.50, the total amount of money raised is equal to $2.50 times the number of tickets. The equation would be y = 2.50x.

Answer:

2x^3-5x^2-28x+15 -------------------------expanded

2x^3-5x^2-28x+15--------------------simplified

Step-by-step explanation:

\left(2x-1\right)\left(x+3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

simplyfied

\left(2x^2+5x-3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

=2x^3-5x^2-28x+15

Answer:

$56.70 all together

Step-by-step explanation:

$22.14 for the jeans

$34.56 for the jacket

$56.7 all together

Take your tax and move the decimal over to the left by 2 spaces

8. becomes .08

take .08 and multiply it by the price so

20.50 x .08= 1.64

and

32 x .08=2.56

the number you get is how much the tax is, $1.64 is 8% of $20.15

take that number and add it to your price

$1.64+$20.50= $22.14

Answer:

$56.70

Step-by-step explanation:

22.14+34.56=$56.70

Answer:

1,462.50

Step-by-step explanation:

6500

x.045

=292.50 per year

x.         5 years

=1,462.50

Answer:

The answer is simulation

Step-by-step explanation:

A random number generator is used to model the patterns of animals in the wild. This type of study is called a simulation.

Simulation is a way to model random events, such that simulated outcomes closely match real-world outcomes. The way of simulating something first needs that a model be advanced, the model shows the key characteristics and functions of the opted process. By observing simulated outcomes, researchers gain insight on the real world.

A random number generator is used to model the patterns of animals in the wild. This type of study is called a simulation.

Simulation is a technique used to study complex systems by modeling them using a computer.

In this case, a random number generator is used to model the patterns of animals in the wild.

By running simulations, researchers can study the behavior of animals in different environments and conditions, without actually observing them in the wild.

Simulations are useful tools for predicting and understanding the behavior of complex systems, such as ecosystems.

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9514 1404 393

Answer:

  10

Step-by-step explanation:

Maybe you want ...

  \(\displaystyle\lim_{x\to 0}(x^2+10)=0^2+10=\boxed{10}\)

Answer:

2nd Number Line.

Step-by-step explanation:

-6 is going to be left of 0 on the number line.

The opposite of -6, or the absolute value of 6, is 6 (positive).

6 is going to be right of 0 on the number line.

Answer: number line number 2

Step-by-step explanation:

Side a of the oblique triangle is 25.57 units and side b is 9.42 units.

The number of sides of a triangle and how their individual sine angles are equal are determined by the law of sines. Other names for the sine law are sine rule, sine formula, and sine law. The law of sine is used to determine the side or unknown angle of an oblique triangle.

Given:

∠A = 107

∠B = 21

∠C = 52

c = 21

So, using the law of sines

b/sin B = c/ sin C

b/sin 21 = 21/sin 52

b = (21 × sin 21) / sin 52

= (21 × 0.35) / (0.78)

b ≈ 9.42

Similarly, side a of the triangle is given by

a/ sin A = c/ sin C

a/sin 107 = 21/sin 52

a = (21 × sin 107) / sin 52

= (21 × 0.955) / (0.78)

a  ≈ 25.57

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Check the picture below.

\(243=9(r)(r)(r)\implies 243=9r^3\implies \cfrac{243}{9}=r^3\implies \sqrt[3]{\cfrac{243}{9}}=r\implies \boxed{3=r} \\\\[-0.35em] ~\dotfill\)

\(n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\stackrel{\textit{term position}}{5}\\ a_1=\textit{first term}\\ r=\stackrel{\textit{common ratio}}{3} \end{cases}\qquad \implies a_5=a_1\cdot 3^{5-1} \\\\\\ 243=a_1\cdot 3^{5-1}\implies 243=a_1\cdot 3^4\implies 243=a_1\cdot 81 \\\\\\ \cfrac{243}{81}=a_1\implies \boxed{3=a_1}\hspace{12em} {\Large \begin{array}{llll} a_n=3(3^{n-1}) \end{array}}\)

Answer:

anything before -1 is lower than -1.  -1 = -1

Step-by-step explanation:

-10, -9, -8, -7, -6, -5, -4, -3, -2 etc. are in a sense before -1 on a time line and they are all less than -1

Set B represents the set of all the natural numbers less than or equal to -1

\(\rm B=\{-\infty ...........-4,-3,-2,-1\}\)

if we include all the numbers the range of set includes every number from

\(\rm -\infty \; to -1\) so the set is represented by K

\(\rm K = \{ -\infty ,.....-1\}\)

In Mathematics a set is  a collection of objects/elements that are constrained by some particular condition.

Let us consider a situation where "S" is the set and the elements are represented by "x"

A set is always denoted in curly braces. Expression (1) represents the set

\(\rm S =\) { \(\rm x_1.x_2,x_3, x_4,x_5........x_n\)}...........(1)

Set S  has elements that are represented as \(\rm x_1\)\(\rm\\where \; i \; represents\; the\; index\; of \; the \; element\\n = number\; of \; elements \; in \; the \; set \; x\)

The set of all the natural numbers less than or equal to -1 is the set of all the negative integers including  -1.

So let us say B represents the set of all the natural numbers less than or equal to -1 . Then we can write it as follows

\(\rm B=\{-\infty ...........-4,-3,-2,-1\}\)

Set B represents the set of all the natural numbers less than or equal to -1

if we include all the numbers the range of set includes every number from

\(\rm -\infty \; to -1\) so the set becomes  

\(\rm K = \{ -\infty ,.....-1\}\)

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Probability = # of desired options / # of total options

Our desired option is blue and there are 9 blue marbles in the bag.

There are 32 total marbles (options) in the bag.

P(blue) = 9 / 32 = 0.28125 = 28.125%

Hope this helps!

Differentition of \(y=log_{2}x^{3}.(5x^{4}+2)\) is \(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}\)

A differential equation is an equation that contains one or more functions with its derivatives.

Given,

\(y=log_{2}x^{3}.(5x^{4}+2)\)

We have to differentiate with respect to x.

y'=xy'+yx'

\(x=log_{2}x^{3}\)

\(y=5x^{4}+2\)

\(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x^{3}} .3x^{2}\)

\(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}\)

Hence, differentiation of \(y=log_{2}x^{3}.(5x^{4}+2)\) is \(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}\)

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Answer:

36) C, 790 m²

37) D, 625 in²

Step-by-step explanation:

To find the volume of a rectangular prism, we will multiply the length, width, and height together. The dimensions of the aquarium are 22.9×7.5×4.6. Multiply these together.

22.9 · 7.5 · 4.6 = 790.05

The volume is 790.05 m². This rounds down to 790 m², so the answer is C.

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For the next question, the dimensions aren't given. Instead, we need to calculate them from the sidelengths of the unit cubes. Multiply 2.5 by the number of units on the length, width, and height of the prism. So, the dimensions are 10×12.5×5. Find the product of these dimensions.

10 · 12.5 · 5 = 625

The volume is 625 in². The answer is D.

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I hope this helps ^^ Good luck