Suppose a population of 150 mice triples in size every 4 months. How many mice will there be after 3 years?

Based on the relative frequency tables, the correct options are

Relative frequency is a statistical concept that refers to the proportion or percentage of times an event occurs in relation to the total number of times the event could occur. It is calculated by dividing the number of times an event occurs by the total number of observations or trials.

For example, if you flip a coin 10 times and it lands on heads 6 times, the relative frequency of heads would be 6/10 or 0.6, which is equivalent to 60%. This means that heads occurred 60% of the time in the sample of 10 coin flips.

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Answer:

a=50-40

a=10

lxb

answer

Answer:

Step-by-step explanation:

[tex]16^\frac{1}{n}=2[/tex]     (since by definition [tex]\sqrt[n]{16} =16^\frac{1}{n}[/tex])

[tex](2^4)^\frac{1}{n}=2[/tex]

[tex]2^\frac{4}{n}=2[/tex]

[tex]2^\frac{4}{n}=2^1[/tex]

∴[tex]\frac{4}{n} =1[/tex]    (indices must be equal when bases are equal)

∴[tex]n=4[/tex]

According to the question the height of Ruben’s school is 360 inches.

School is a place where students can learn and grow in their knowledge. It is a place where students can gain an education and become well-rounded individuals. School is a place where people can make friends, learn from each other, and explore new ideas and topics. School is a place where teachers and staff provide guidance to help students succeed in their academics and extracurricular activities.

To find the height of Ruben’s school using similar triangles and a mirror, we can use the following formula:
height of school / height of Ruben = distance from mirror to school / distance from mirror to Ruben
Plugging in the given values, we get:
height of school / 72 = 425 / 85
Cross-multiplying and solving for height of school, we get:
height of school = 72 x 425 / 85
height of school = 360 inches
Therefore, the height of Ruben’s school is 360 inches.

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Answer:

The strip pattern has a vertical axis of symmetry, so a reflection across a vertical line will map the strip pattern onto itself. Therefore, the correct answer is "a reflection across a vertical line."

Step-by-step explanation:

Answer:

y=9

Step-by-step explanation:

y=7x+2

y=7(1) +2

y=7+2

y=9

Using the right triangle, we fοund the elevatiοn οf the ramp frοm the grοund as 6.49 inches.

The height abοve οr belοw a specified reference pοint, mοst frequently a reference geοid, which is a mathematical representatiοn οf the Earth's sea level as an equipοtential gravitatiοnal surface, determines a lοcatiοn's elevatiοn.

A frequently used idea in relatiοn tο height and distance is the angle οf elevatiοn, particularly in trigοnοmetry. It is described as a relatiοnship between an οblique line frοm the οbserver's eye tο an item abοve his eye and the hοrizοntal plane.

This angle eventually develοps abοve the surface. The angle οf elevatiοn is made in such a way that it is abοve the οbserver's eye, as the name suggests.

Using the given infοrmatiοn, we drew a right triangle as given belοw.

The hypοtenuse οf the triangle is the length οf the sheet.

The angle οf elevatiοn is 20°.

The base οf the triangle is the grοund.

The hypοtenuse l = 19 inches

Angle Ф = 20°

We have tο find the elevatiοn h.

sin  Ф = h/l

sin 20 = h/19

0.342 = h /19

h = 6.49 inches

Therefοre using the right triangle, we fοund the elevatiοn οf the ramp frοm the grοund as 6.49 inches.

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Answer:

5 9/10

Step-by-step explanation:

find the same denominator

in this case 30

9x3=27 and 5x5=25

since 27 is bigger, the fraction is also bigger

Answer:

5\6 is smaller than 9\10

Step-by-step explanation:

Find the least common denominator or LCM of the two denominators:

LCM of 6 and 10 are 30

Next, find the equivalent fraction of both fractional numbers with denominator 30

For the 1st fraction, since 6 × 5 = 30,

[tex]\frac{5}{6} = \frac{5.5}{6.5} =\frac{25}{30}[/tex]

Likewise, for the 2nd fraction, since 10 × 3 = 30,

[tex]\frac{9}{10} =\frac{9.3}{10.3} =\frac{27}{30}[/tex]

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

[tex]\frac{25}{30} < \frac{27}{30} 0r \frac{5}{6} < \frac{9}{10}[/tex]

Answer:

(4,9)

Step-by-step explanation:

The word "vertex" isn't clear here. I'm assuming the question is referring to finding the stationary (turning) point. This can be found by finding the derivative (dy/dx).

To find the derivative we use the following formula:

[tex]y = ax^{n}\\ \frac{dy}{dx} = nax^{n-1}[/tex]

What this means is that for each term of the equation, we multiply by the current power and then reduce the power by 1. In the case of the question's equation, this will be done like this:

[tex]y = 3x^{2} - 24x + 57\\\frac{dy}{dx} = 6x - 24[/tex]

Now we can use this to find the stationary point, as stationary points are where the derivative (dy/dx) = 0:

6x - 24 = 0

6x = 24

x = 4

Through this we have found the x-coordinate of the stationary point, however we still need to find the y coordinate. This is done by substituting our x value back into the original equation (not the derivative):

y = 3(4)² - 24(4) + 57

y = 9

Therefore, the coordinates of the stationary point are (4,9)

Answer:

only opposite anglesare

Step-by-step explanation

Z

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Answer:

54

Step-by-step explanation:

I'm assuming you are referring to x = 6, then to find the value of x(15 - x).

If x = 6, we can substitute this value into the expression x(15 - x) to find its value:

x(15 - x) = 6(15 - 6) = 6(9) = 54

Therefore, if x = 6, then x(15 - x) = 54.

Hey there!

x(15 - x)

= 6(15 - 6)

= 6(15) + 6(-6)

= 90 - 36

= 54

Therefore, the answer should be about:

54

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The value of the polynomial equations are

f ( -10 ) = 20201

f ( 2 ) = 17

f ( 3 ) = 142

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the polynomial equation be represented as A

Now , the value of A is

f ( x ) = 2x⁴ + x² - 10x + 1   be equation (1)

Now , when the value of x = -10

f ( -10 ) = 2 ( -10 )⁴ + ( -10 )² - 10 ( -10 ) + 1

On simplifying , we get

f ( -10 ) = 2 ( 10000 ) + 100 + 100 + 1

f ( -10 ) = 20000 + 201

f ( -10 ) = 20201

Now , when the value of x = 2

f ( 2 ) = 2 ( 2 )⁴ + ( 2 )² - 10 ( 2 ) + 1

On simplifying , we get

f ( 2 ) = 2 ( 16 ) + 4 - 20 + 1

f ( 2 ) = 32 - 15

f ( 2 ) = 17

Now , when the value of x = 3 , we get

f ( 3 ) = 2 ( 3 )⁴ + ( 3 )² - 10 ( 3 ) + 1

f ( 3 ) = 2 ( 81 ) + 9 - 30 + 1

f ( 3 ) = 162 - 20

f ( 3 ) = 142

Hence , the polynomial equations are solved

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The function has a range of all real numbers less than or equal to 2.

Quadratic functions form parabolas, which look like a U-shape.

What is Range

Range describes the y-values covered by a function. So, the range contains every y-value that is a possible output of a function. You can find the range of a function from the graph by looking at what y-values are or will be covered by the function.

The range of a quadratic is always all real numbers greater than/less than the y-value of the vertex. Positive quadratics have ranges greater than the vertex, and negative quadratics have ranges less than the vertex.

Finding the Range

The parabola given is negative. We know this because the graph opens downward. This means that the graph has a maximum, and the range is less than the vertex.

By looking at the graph we can tell that eventually, the graph will cover all y-values under y-value 2. Note that 2 is the y-value of the vertex. So the range is all real values less than or equal to 2. This means that any number less than or equal to 2 is a possible output of the function.

The unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day.

Computers are electronic devices that are used to store, process, and output data. They are used to perform a variety of tasks, from simple calculations to complex research projects. Computers consist of hardware, such as processors, memory, and storage devices, and software, which provides instructions for the hardware to follow.

The unit rate is the number of units produced per unit of time. To calculate the unit rate of computers per day using the graph, divide the number of computers produced by the number of days. Using the graph, 36 computers are produced in 3 days, 48 computers are produced in 4 days, and 60 computers are produced in 5 days.

Therefore, the unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day. The graph produced shows a proportional relationship between the number of computers produced at a factory per day.

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5. The value of the account at yearly intervals is given below.

6. The balance in the 25th year in the account will be $1,137.5.

Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,

The formula for interest is written as,

I = (PRT)/100

5.  The simple interest is given as,

I = 650 x (3/100)

I = $19.5

End of first year = 650 + 19.5 - $669.50

End of second year = 669.5 + 19.5 = $689

End of third year = 689 + 19.5 = $708.50

End of fourth year = 708.50 + 19.5 = $728

End of fifth year =728 + 19.5 = $747.50

6. The balance after 25 years is given as,

A = $650 + ($650 x 3 x 25) / 100

A = $650 + $487.5

A = $1,137.5

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Answer:

27 blocks not used in the castle

Step-by-step explanation:

35+18= 53

53-26=27

Answer:

There is a direct relationship, in which the value of the division of the circumference by the diameter is a constant. This constant is know as Pi.

Answer:

To find the cube root of a number, you want to find some number that when multiplied by itself twice gives you the original number. In other words, to find the cube root of 8, you want to find the number that when multiplied by itself twice gives you 8. The cube root of 8, then, is 2, because 2 × 2 × 2 = 8.

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

eeeeejjbbvvv g gyuuu u grrtyyu

The required maximum point of the function [tex]$f(x)=-x^2+8x+40$[/tex] is (4,24).

A quadratic equation is an algebraic equation with a maximum degree of two. Where a 0, the equation is provided by ax² + bx + c = 0.

To find the maximum point of the quadratic function [tex]$f(x)=-x^2+8x+40$[/tex], we can use the formula for the x-coordinate of the vertex, which is given by [tex]x=-\frac{b}{2a}$[/tex], where a is the coefficient of the [tex]x^2$[/tex] term and b is the coefficient of the x term.

In this case, a=-1 and b=8, so the x-coordinate of the vertex is:

[tex]$x=-\frac{b}{2a}=-\frac{8}{2(-1)}=4$$[/tex]

To find the y-coordinate of the vertex, we can plug this value of x into the original function:

[tex]$$f(4)=-4^2+8(4)+40=24$$[/tex]

Therefore, the maximum point of the function [tex]$f(x)=-x^2+8x+40$[/tex] is (4,24).

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Answer:

Step-by-step explanation:

[tex]n\sqrt{2}=10[/tex]

Solve for n.

[tex]n\sqrt{2} =10\\\\\frac{n\sqrt{2} }{\sqrt{2} }=\frac{10}{\sqrt{2} }[/tex]

Rationalize the denominator.

[tex]n=\frac{10}{\sqrt{2} }\cdot \frac{\sqrt{2} }{\sqrt{2} }\\\\n=\frac{10\sqrt{2} }{2}[/tex]

Reduce to lowest terms.

[tex]n=\frac{10\sqrt{2} }{2} \div\frac{2}{2}\\\\n=5\sqrt{2}[/tex]

Answer:

Sides:

MX = 4cm

BX = 8cm

BM = 6.928...cm

Angles:

m = 90°

b = 30°

x = 60°

Step-by-step explanation:

We've been given 3 pieces of info that we can use, which is more than enough

Using the sine rule, we can find the hypotenuse:

[tex]\frac{4cm}{sin30} = \frac{BXcm}{sin90}[/tex]→[tex]\frac{4sin90}{sin30} =BX = 8cm[/tex]

Now we can use Pythagoras' theorem to find the last side:

[tex]a^2+b^2=c^2[/tex] →  [tex]b^2\ = c^2-a^2[/tex] → [tex]64 - 16 = b^2 = 48[/tex] → [tex]\sqrt{48} =6.928...cm[/tex]

And since we know two of the angles, we can find the third:

[tex]x = 180 - (30 + 90) = 180 - 120 = 60[/tex]°

Answer:

Below

Step-by-step explanation:

REMEMBER: for a right triangle  sin (30) = opposite LEG/ hypotenuse

 so sin 30 =  4 / hypotenuse         now, with a calculator sin 30 = 1/2

           1/2   = 4 / hypotenuse      so hypotenuse = 8

Now it is a right triangle so Pythagorean theorem applies

 hyp ^2 = 4 ^2   +   BM^2

  8^2 = 4^2 + BM^2

     48 = BM^2     so  BM = sqrt (48 ) = 4 sqrt 3

Finally, all of the internal angles of ANY triangle sum to 180 °

  so angle x = 180 - 90 - 30 = 60°

The right angles would be named as:

3. ∠PNL 4. ∠PNO

Right angles can be named in a few different ways, depending on the context in which they are being used. One common way is:

Using three points: use the names of the three points that form the angle, with the vertex of the angle in the middle. For example, if the right angle is formed by the line segments AB and BC, you could name it angle ABC.

The sign "∠" means angle, therefore, it can be named also as ∠ABC.

Thus, the right angles in the given diagram can be named accordingly as:

∠PNL and ∠PNO

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The trade discount is $15.75.

A trade discount is a regular reduction from a product's regular, established price. The use of trade discounts allows a company to adjust the final price based on the volume or status of each customer.

It is important to note that trade discounts are not the same as early-payment discounts. (Early-payment discounts of 1% or 2% are typically recorded by the seller in an account such as Sales Discounts and by the buyer in an account such as Purchase Discounts using the periodic inventory method.) Neither the seller nor the buyer keeps a separate account for trade discounts.

We must first determine the product's list price in order to determine the trade discount.

List price: $75 plus $3.75 equals $78.75

As the trade discount rate is 20%, the following discount is offered:

Discount = 0.2 times List price = 0.2 times $78.75 = $15.75

The trade discount is therefore $15.75.

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Answer:

a) 15, 25

Step-by-step explanation:

Finding the average is to find the sum and divide it by the quantity of the numbers.

(15 + 25) / 2 = 40 / 2 = 20, 20 is the average of two numbers.

However standard deviation includes at least one degree of 2.

x1 + x2 = 40

SD = 5

= [tex]\sqrt{[(x_1 - 20)^2 + (x_2 - 20)^2]/2 \\}= 5\\ x_1 = 15, or x_1 = 25\\x_2 = 15 or x_2 = 25[/tex]

The answer of the given question based on linear equations what is the y intercept of the line b =4.

In  linear equation of  form y = mx + b, where m is slope and b is  y-intercept, the y-intercept is  point at which  line intersects the y-axis. It is  value of y when x is equal to a zero.

To find the y-intercept of the line, we need to identify the point at which the line intersects with the y-axis. This is the point where x=0.

From the given graph, we can see that when x=0, the point on the line is (0, 4). Therefore, the y-intercept (b) of the line is 4.

So, the answer is:

b = 4

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Answer:

b=2

Step-by-step explanation:

its 2 not 4 the dot is located on 2 in between the first and second quadrant.