Translate algebraic words to symbols. Traple the product of ab

The function that models the above behavior is given as:

f(x) = ACos(B(x + C)) + 6 ..... .......i

where x = 1 (that is January)

D (Average Snowfall) = 6.

Hence, the amplitude (A) is given as:
A = 6-1

= 5

A mathematical function is a function comprising of different variables that    represent different factors or events and the relationships between them.

Recall that in a year we have 12 months. Hence, P = 12

→ P = (2π) /.B → (2π)/B = 12 → B = π/6

Taking the values of A and B and plugging them in, we ahve:

F(x) = 5 cos (π/6(x + C)) + 6................ii

This means that in July, we'll have

x = 7 and f(x) = 1

Therefore,

1 = 5cos ((π/6) (7 + C) + 6 → 5 Cos  ((π/6) (7 + C) →  -5cos ((π/6) (7 + C)

= -1

→   ((π/6) (7 + C) = π

→ 7 + C = 6

→ C = -1

Taking equation ii, we have

F(x) = 5cos ((π6) (x -1)) + 6

F (x) > 10

Therefore

5cos ((π/6) (x-1) + 6 > 10

→  cos ((π/6) (x-1) + 6 > 4/5

→  (π/6) (x-1)  > Cos⁻¹ (4/5)

(π/6) (x-1)  < 0.6435 and

(π/6) (x-1)  > 5.6397

→ x < 2.23 and x > 11.77

The interpretation is that upwards of ten inches of snow fall in January, February, November, and December.

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Based on the terms given on the population type and the variables, the correct matches are:

The population is total set of items that a sample is drawn from and in this case it all the restaurants. The sample would be the selected items from the population.

The control group is the group that is not manipulated by the explanatory variable which is the organic cleaner. The response variable is what changes as a result of the explanatory variable so it is bacterial growth.

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There are 6! = 720 ways of arranging the lamps.

If the leftmost lamp is red, there are 3 choices of lamp in the leftmost position, and the remaining 5 can be placed in any order, so there are 3×5! = 360 ways of arranging the lamps and the leftmost is red.

Hence there is a 360/720 = 1/2 probability that the leftmost lamp is red.

Ignoring lamp color for the moment, the probability of arranging 3 lit lamps and 3 unlit lamps is the same, 1/2.

Since Ryan arranges the lamps randomly by color, then turns 3 of them on randomly, the two events are independent. So

P(leftmost red AND leftmost lit) = P(red) × P(lit) = 1/2² = 1/4

Answer:

No solutions

Step-by-step explanation:

First  ADD  4 /(X+4)   to both sides of the equation to get

( x+4)/ (x+ 4)  = 3

1 = 3 ????    There are no solutions

[tex]\dfrac{x}{x+4}=3-\dfrac{4}{x+4}\qquad(x\not=-4)\\\\x=3(x+4)-4\\x=3x+12-4\\2x=-8\\x=-4[/tex]

Which contradicts initial assumption, therefore [tex]x\in\emptyset[/tex].

The possible functions for f and g are f(x) = [tex]3^{x}[/tex] and g(x) = [tex](\frac{1}{3} )^{x}[/tex]

An exponential function is a mathematical function of the following form: f ( x ) = [tex]p^{x}[/tex] where x is a variable, and p is a constant called the base of the function. The most commonly encountered exponential function base is the transcendental number e.

Analysis:

If for every value of x being positive and y is a positive whole number and for every x being negative y is a positive fraction, then that exponential function has a whole number base, Other wise it would have a fractional base. From the above explanation, f has (1,3) (positive x and whole number y) and (-1, 1/3) (negative x and positive fraction y). so therefore f has a whole number base and g has a fraction base.

Therefore f(x) = [tex]3^{x}[/tex] and g(x) = [tex](\frac{1}{3} )^{x}[/tex]

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Answer:

D is the right answer.

Hope it helps!

Answer:

[tex]\frac{247}{200}[/tex]

Step-by-step explanation:

1.235

= 1 + 0.235 ( the place value of the 5 is thousandths ) , then

= [tex]\frac{1000}{1000}[/tex] + [tex]\frac{235}{1000}[/tex]

= [tex]\frac{1235}{1000}[/tex] ( divide numerator/denominator by 5 )

= [tex]\frac{247}{200}[/tex] ← in simplest form

Answer:

not determinable

Step-by-step explanation:

you can't determine--think of it like this: let's say I figure out a combination of two lengths that work, I could always scale it up (or down)

Let's say AB = 4, and BC = 9, then the area would be 36

but let's say AB = 8, and BC = 18, then the area would be 144

so, from this information alone, we cannot find the answer

hope this helps! have a lovely day :)

The area of the given parallelogram is that: It cannot be determined from the information given

The formula for the area of a parallelogram is:

Area = Base * Height

Now, we are told that the ratio of AB to BC is 4:9.

The most important point here is that we do not know the altitude of the parallelogram; the area of a parallelogram is altitude times base.

A secondary point would be that we do not know the lengths of AB and BC; we only know the ratio of the two sides.

The actual lengths of the sides could be, for example, 8 and 18

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Complete question is:

If the ratio of AB to BC is 4:9, what is the area of Parallelogram ABCD attached?​

Answer:

um tbh me dont know

Step-by-step explanation:

The solution set of the compound inequality is  (-∞, 9] ∪ [17, ∞) and the correct graphical representation on the number line can be seen in the first option.

The solution set of a compound inequality is the set of values that intersect between the two inequalities and they satisfy the solution to each individual inequality.

The graph of a compound inequality can be illustrated on the number line.

From the given information, we have:

[tex]\mathbf{-\dfrac{1}{3}x+10 \geq 7}[/tex]---- (1)

x - 10 ≥ 7      ----- (2)

From equation (1), the solution to the inequality is:

The solution to the second inequality is:

The solution set of the compound inequality is  (-∞, 9] ∪ [17, ∞) and the correct graphical representation on the number line can be seen in the first option.

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The expression with the same values of (1/x – y) in x and y will be 10 / 7.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The expression x-y equals 0.7.

x - y = 0.7    …1

If x and y have certain values.

Then the expression with the same values of (1/x – y) in x and y will be

Take the reciprocal of equation 1, then we have

1 / (x – y) = 1 / 0.7

1 / (x – y) = 10 / 7.

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Answer:

Thus, a golden retriever should be given 19 teaspoon of medicine.

Step-by-step explanation:

Step 1 of 3

Write the data in mathematical form and simplify.

Let x=the number of teaspoon

If 1  teaspoon medicine is 5  pounds then 85  pounds is how many teaspoon of medicine.

Translate the statement into proportion.

[tex]\begin{aligned}\frac{\text { pounds }}{\text { teaspoon }} &=\frac{\text { pounds }}{\text { teaspoon }} \\\frac{5}{1} &=\frac{85}{x}\end{aligned}[/tex]

Step 2 of 3

Multiply both sides by x and simplify

[tex]$x(5)=\frac{85}{\bcancel{x}}(\bcancel{x})[/tex]

5x=85

Divide by 5,

[tex]x=\frac{85}{5}[/tex]

Simplify, x=19

Step 3 of 3

Check the answer.

Substitute x=19  in original proportion and simplify.

[tex]$$\begin{aligned}\frac{5}{1} &=\frac{85}{x} \\5 &=\frac{85}{19}\end{aligned}$\\ \\ Hence, $5=5$, True[/tex]

8m and 12a

Like terms are terms that can be combined to condense a mathematical expression or equation.

Unlike Terms

Unlike terms are defined as terms that have different variables or powers.

If terms meet either of these requirements, they are unlike. On the other hand, for terms to be like they must have both the same variable and power. The coefficients for the terms are not important.

Final Answer

All of the answer choices are to the first power, so the exponents are not important for this question. However, the last 3 answer choices all share the same variable. This means that they are all like terms.

The first answer choice, 8m and 12a, have different variables. This means that they cannot be combined and are unlike terms.

Answer:

65fghxtt

Step-by-step explanation:

7x+2

Step-by-step explanation:

add all the sides of the pentagon and make it equal to the perimeter of the square which is 4y

sides of the pentagon are

5x+3

2x+3

7x+4

9x-10

5x+8

28x+8=4y

7x+2 = y

7x+2 = answer

gathmath

gathmathier6961

another way :

in a standardized test you may want to use real numbers

make x equal a prime number like 3

so then the sides are

18

9

25

17

23

=

92

then divide by 4

23

then divide by 3

which is 7 remainder of 2

which is

7x+2

Answer:

75%

Step-by-step explanation:

[tex]\frac{108 }{144} = 0.75[/tex]

0.75 * 100 = 75%

Answer:

Yes, it is a function

Step-by-step explanation:

A function has only one output for each input. So a function can have the same output for different input, but one input can only have one output. In this case none of the inputs output more than one output, so it is a function.

Answer:

98/22 or 4.4545

Step-by-step explanation:

Perimeter of a rectangle: 2*width+2*length

4x*2+7x*2 = 98

8x+14x = 98

22x = 98

x = 98/22 or 4.4545

Answer:

60 degrees.

Step-by-step explanation:

A reflection does not alter the size of the angles of the triangle so B = 60 degrees.

36 litres 180 millilitres

Hope this helps!

Answer:

Step-by-step explanation

5+5

Answer:

12

Step-by-step explanation:

we can setup an equation and solve for x: 500-25x = 200, where x stands for the number of weeks she withdraws money.

subtract 500 from both sides to get -25x = -300.

multiply each side by -1 to get 25x = 300

divide each side by 25 to get that x = 12

Answer:

D

Step-by-step explanation:

By observation we just know that one of the angles of two triangles is the same.

There are two sides that are not equal in ability to determine similarity.

a) The growth function has the form:

where:

Considering the values we get the function:

b) Number of years between 2012 and 2018 is:

Find the population, using the above equation:

c) Find the value of x when P(x) = 10 million

d) Find the doubling time:

Answer:

[tex]\textsf{a)} \quad f(x)=6.93(1.0218)^x[/tex]

b)  7.89 million (2 d.p.)

c)  2019

d)  32.14 years (2 d.p.) after 2012

Step-by-step explanation:

Exponential Function

   [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part (a)

If the exponential growth rate was 2.18% per year, then each year there would be 102.18% of the previous year's population.

⇒ b = 1.0218

Given:

Substitute the given values into the formula to create an exponential growth function:

  [tex]f(x)=6.93(1.0218)^x[/tex]

Part (b)

To estimate the population of the city in 2018, determine the value of x:[tex]x = 2018 - 2012 = 6[/tex]

Substitute the found value of x into the found exponential function:

[tex]\implies f(6)=6.93(1.0218)^6=7.89 \: \sf million\:(2\:d.p.)[/tex]

Part (c)

To determine when the population of the city will be 10 million, set the function to 10 and solve for x:

[tex]\implies 6.93(1.0218)^x=10[/tex]

[tex]\implies (1.0218)^x=\dfrac{10}{6.93}[/tex]

[tex]\implies \ln (1.0218)^x= \ln \left(\dfrac{10}{6.93}\right)[/tex]

[tex]\implies x\ln (1.0218)= \ln \left(\dfrac{10}{6.93}\right)[/tex]

[tex]\implies x= \dfrac{\ln \left(\frac{10}{6.93}\right)}{\ln (1.0218)}[/tex]

[tex]\implies x=17.00496413...[/tex]

To find the year, add the found value of x to 2012:

[tex]\implies \sf 2012 + 17.00496413... = 2019[/tex]

Part (d)

To find the doubling time, set the function to double the initial population and solve for x:

[tex]\implies 6.93(1.0218)^x=6.93 \cdot 2[/tex]

[tex]\implies (1.0218)^x=2[/tex]

[tex]\implies \ln (1.0218)^x= \ln (2)[/tex]

[tex]\implies x \ln (1.0218)= \ln (2)[/tex]

[tex]\implies x = \dfrac{\ln (2)}{\ln (1.0218)}[/tex]

[tex]\implies x=32.14107014...[/tex]

Therefore, the doubling time is 32.14 years (2 d.p.) after 2012.

Answer: x=-8

Step-by-step explanation:

Answer:

A 3.5

Step-by-step explanation:

To Break it down there 1 3/4 so to put in halve it would be 1/2 1/2 1/2 1/4 so u have 3 feet because 1/2 in is 3 feet then u have a 1/4 inch so that is half of a feet 1 + 1 + 1 + 1/2 is 3 1/2 converted to decimal is 3.5.

2) [tex]ABCD[/tex] is a rhombus (a parallelogram with perpendicular diagonals is a rhombus)

3) [tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex] (diagonals of a rhombus bisect the angles from which they are drawn)