The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y. Simplify completely.
x = 12, y = 3
1
y =
?
x
►
Enter

Remember that for a given angle θ, any point on the unit circle is written as:

(cos(θ), sin(θ)).

And remember that:

cos(45°) = sin(45°) = √2/2

Then the angle θ = 45° is a solution.

To find another positive solution, we just add the period of the circle, which is 360°.

θ = 45° + 360° = 405°

Adding the period again:

θ = 405° + 360° = 765°

So the 3 positive solutions can be:

{45°, 405°, 765°}

To get the negative angles we just subtract the period:

45° - 360° = -315°

We can do that again:

-315° - 360° = -675°

So the two negative angles are:

{-315°, -675°}

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Answer: Peyton

Step-by-step explanation:

Michelle: Greatest common factor is 1

Naomi: Greatest common factor is abc

Olivia: Greatest common factor is 2ab

Peyton: Greatest common factor is ab

In the case above about Samuel, one can say that Samuel's calculator has display option A.  2.5 E (- 13)

The function was  [tex]\frac{5E (-9) }{2E(4) }[/tex] :

We know that, E implies 10 to rise to power.

So, The equation above is Converted from scientific notation into standard form.

 [tex]\frac{5 x 10^-9 }{2 x 10^ 4 }[/tex]

= 5/2  x 10 ⁻⁹⁻⁴

=2.5 x 10⁻¹³

Therefore, In the case above about Samuel, one can say that Samuel's calculator has display option A.  2.5 E (- 13)

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Answer:

  D.  330.6

Step-by-step explanation:

To evaluate the function for a specific value of x, put that value where x is in the function definition, and do the arithmetic.

__

T(x) = x +0.14x . . . . . given function definition

T(290) = 290 +0.14×290 = 290 +40.6 . . . . substitute 290 for x

T(290) = 330.6

The value of T(290) will be 330.6.The relation between them is shown as T(x)  is dependent and x is the independent variable. Option D s correct.

A connection between independent variables and the dependent variable is defined by the function.

Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.

Given relation;

T(x) = x +0.14x

Substitute the value of x we get;

T(290) = 290 +0.14×290

T(290) = 330.6

Hence, option D s correct.

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Answer:

833.25 or 877.59

Step-by-step explanation:

I solved this in two different ways because I wasn't sure on how the question was meant to be read.

Attempt 1:

(833.3/1)-(1+0.00833)^-360

(1+0.00833)^-360 = 0.0505

so:

833.3 - 0.0505 = 833.25

Attempt 2:

833.3/(1-(1+0.00833)^-360)

1- 0.0505 = 0.9495

833.3/0.9495 = 877.59

The conclusion about the relationship is

The complete question is:

Consider the function f(x) = 3x and a translation of f(x) named g(x). Janeen created a table for select values of x. Her table is shown below. What can be concluded about the relationship between the two functions? Check all that apply.

The functions have the same base.

The functions have the same range.

The functions have the same exponent.

The functions have the same domain.

g(x) is a translation left 1 unit.

g(x) is a translation right 2 units.

g(x) is a translation up 2 units.

Given function is:

f(x) = [tex]3^{x}[/tex]

g(x) = [tex]3^{x+1}[/tex]

Firstly, the functions have the same base i.e., base 3.

second, the functions have the same range.

As the range of f are all the values that f can assume. i.e., positive numbers and the range of g are all the values that g can assume. i.e., positive numbers.

third, both functions have the same domain as x = {0,1,2,3}.

Fourth, g(x) = f(x+1). So, g(x) is a translation left 1 unit.

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Answer:

3041.06

Step-by-step explanation:

The formula of a cone is [tex]\pi r^{2} \frac{h}{3}[/tex] , so plugging both the height and radius will result in the answer!

Answer:

My guess would be D

Step-by-step explanation:

Fundamental Trigonometric Identities are listed below:

Fundamental Trigonometric Identities can be defined as the basic identities or variables that can be used to proffer solutions to any problem relating to angles and trigonometry.

In conclusion, A few Fundamental Trigonometric Identities are listed above.

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Answer:

a) [tex]\frac{450}{100}[/tex] x 45 = 202.5g of sugar is in the can

b)[tex]\frac{4}{100}[/tex] x 80 = 3.2L is left

c)[tex]\frac{2400}{100}[/tex] x 70 = 1480 acres were planted with wheat

a. 202.5g

Since 45% of the energy drink is sugar

⇒ 45% of the total 450 grams will be made up of sugar

∴ sugar = [tex]\frac{45}{100}[/tex] * 450

             = 202.5g

Thus, the can contains 202.5g of sugar

b. 3.2L

Since Simon used up 20% of the paint, the paint left in the can will now be 80% of the original 4 liters

∴ paint left = [tex]\frac{80}{100}[/tex] * 4

                  = 3.2L

Thus, the can has 3.2 liters of paint left.

c. 1680 acres

Here, 30% of the farmer's crop is and the rest is wheat

⇒ 70% is wheat

Total acres of land planted= 2400

∴ Acres planted with wheat = [tex]\frac{70}{100}[/tex] *2400

                                              = 1680 acres

Thus 1680 acres is planted with wheat

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The expression for length and breadth of the rectangle garden in terms of the side of the square tomato patch.

l=3x+2

b=x+5

The linear equation is the equation where the highest degree of the variables is 1.

Here given that the garden is rectangular in shape and the tomato patch is square in shape.

the length of the side of the square tomato patch is x.

Asuume the length of the rectangle garden is l

and the breadth of the rectangle garden is b.

Given that

the length of the garden is greater than the 3 times of the length of the rectangular garden by 2 feet.

3 times of the length of the rectangular garden is 3x

2 feet greater than 3 times of the length of the rectangular garden= 3x+2

so from above, it is clear that l=3x+2

similarly, the breadth of the garden is greater than the length of the rectangular garden by 5 feet.

then the breadth of the garden = b= x+5

Therefore the expression for length and breadth of the rectangle garden in terms of the side of the square tomato patch.

l=3x+2

b=x+5

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Answer:

Non-Homogeneous Recurrence Relation and Particular Solutions

A recurrence relation is called non-homogeneous if it is in the form. Fn=AFn−1+BFn−2+f(n) where f(n)≠0.

Substituting into point-slope form,

[tex]y+5=-\frac{5}{3}(x-15)\\\\y+5=-\frac{5}{3}x+25\\\\\boxed{y=-\frac{5}{3}x+20}[/tex]

The decimal value that express the total percent markdown for the given scenerio are 0.5,0.31,0.09.

Given the total percent markdown for the following scenario, after being rounded to the nearest percent:50%, 31%,and 9%

Percentage is a ratio of the numbers expressed as a fraction of 100.

We have to just convert the percentages into decimal number which will be done as under:

To convert percentages into decimals we need to divide the number by 100. In this way the percentages will become:

50%=50/100

=0.5

31%=31/100

=0.31

9%=9/100

=0.09

Hence the decimal value of 50% ,31 % and 9% in percentages are 0.5,0.31,0.09.

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Answer:0.69

Step-by-step explanation:

Finding the percent increase, it is found that the correct option is given by:

C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.

The percent increase is given by the difference between the final and the initial score, divided by the initial score and multiplied by 100%.

Researching the problem on the internet, we have that:

The percent increases are given as follows:

Hence the correct option is given by:

C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.

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Answer:

the first answer y = 20x - 15

Step-by-step explanation:

since the correct tangent line must share the same point with the originated function, only a line function that delivers y = 25 for x = 2 can be correct.

only the first answer option provides this (20×2 - 15 = 25).

so, we know, this line goes through the given point, but does it have the correct slope for the tangent ?

the correct slope we get from the first derivative of the original function.

f(x) = (1 + 2x)² = 1 + 4x + 4x²

f'(x) = 4 + 8x

for x = 2 we get the tangent slope at that point as

4 + 8×2 = 20

and the provided line is again

y = 20x - 15

with the slope being the factor of x (20).

so, it fits, and indeed, answer 1 is correct.

Answer:

a) Cat

b) 4 (unless there is a key that says otherwise)

c) 3 more people

Step-by-step explanation:

a) It has the least number of shapes (only 5)

b) Cat has 1 small square which stands for 1 person and 4 small squares put together make a big square so a big square is 4 people. Unless a key says that a small square is more or less 1, then it should be 4.

c) If one big square is 4 people, then there are 10 people for giraffes and 7 people for dogs. 10 - 7 = 3 more people.

Answer:

D

Step-by-step explanation:

0.0378÷0.21=0.18

this is 18 hundredths

but its 180 thousandths

Explanation:

Now--this is an awfully odd way to word a question.

BUT, it is solvable!

digits have "place values" in numbers, let's focus on after the decimal point:

_ . _ _ _ _ _ '

we know this can go on forever, but we don't need it to (for this problem, that is)

_ . _ _ _

_ . {tenths} {hundredths} {thousandths} ........

we want to know how many thousandths we have:

the answer to this problem (0.0378 / 0.21) is 0.18

{let's consider what we know about place values:}

"10" can be thought of as ten-ones

and "1" can be thought of as ten tenths

{the reason it's always ten __ is that we use a base-ten system, and there are only ten options for each digit [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] }

so, 10 could be thought of as ten ones, which could each be thought of as ten tenths--meaning that 10 is the same thing as 100 tenths

[if you ignore the decimal point, it becomes more clear]:

10.0 [100]

likewise, 10.00 is 1000 hundredths; and 10.000 is 10,000 thousandths

--------

okay, back to our problem:

how many thousandths make up 0.18?

Let's write this out to the thousandths place:

0.180

if we use our tactic of ignoring the decimal, we are left with 0180 [of course, a "0" before a number has no value, so we can rewrite it as 180], or 180

so, 0.18 is really composed of 180 thousandths, which is how option D is the answer

hope this helps!! :)

{let me know if there's anything else you would like me to explain about this!}

Using the Poisson distribution, it is found that:

a) The mean is of 15.63.

b) The probability is of 0.0911 = 9.11%.

c) The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of​ births.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Item a:

The mean is given by:

[tex]\mu = \frac{5705}{365} = 15.63[/tex]

Item b:

The probability is P(X = 17), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 17) = \frac{e^{-15.63}(15.63)^{17}}{(17)!} = 0.0911[/tex]

The probability is of 0.0911 = 9.11%.

Item c:

The probability is P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-15.63}(15.63)^{0}}{(0)!} = e^{-15.63}[/tex]

The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of​ births.

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Using the Poisson distribution, it is found that

a) The mean is 15.63.

b) The probability is[tex]e^{-15.63}[/tex] of 0.0911 = 9.11%.

c) The probability is, which is less than 0.05, hence 0 births in a single day would be a significantly low number of​ births.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P\left(X=x\right)=\frac{e^{-\mu }\mu ^x}{x!}[/tex]

The parameters are

x is the number of successes.

e = 2.71828 is the Euler number.

[tex]\mu[/tex] is the mean in the given interval.

Item a:The mean is given by:

[tex]\:\mu =\frac{5705}{365}[/tex]

Item b: The probability is P(X = 17), hence:

[tex]P\left(X=17\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{17}}{17!}=0.0911[/tex]

The probability is of 0.0911 = 9.11%.

Item c:The probability is P(X = 0), hence:

[tex]P\left(X=0\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{0}}{0!}=e^{-15.63}[/tex]

The probability is,[tex]e^{-15.63}[/tex] which is less than 0.05,

hence 0 births in a single day would be a significantly low number of​ births.

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Answer:

[tex]\boxed{\bf x=7}[/tex]

[tex]\boxed{\bf GH= 52}[/tex]

Step-by-step explanation:

In the line segment..

[tex]\bf 7x+3+3x-5=9x+5[/tex]

Combine like terms.

Add -2 to both sides.

Subtract 9x from both sides.

[tex]\bf GH=7x+3[/tex]

Answer:

1400 units

$26,600

1700 units

$32,300

Step-by-step explanation:

yw :))

Find volume

Density=12g/cm³

We know

mAss=Density ×Volume

Answer:

6032 g

Step-by-step explanation:

The battery can be modeled as a cylinder.

Volume of a cylinder

  [tex]\sf V=\pi r^2 h[/tex]

where:

Given:

Substitute the given values into the formula and solve for v:

[tex]\begin{aligned}\textsf{Volume of a cylinder} & =\sf \pi r^2 h \\ \implies \textsf{Volume of the battery} & = \sf \pi (4)^2(10)\\ v& = \sf 160 \pi\:\:cm^3\end{aligned}[/tex]

Density equation

  [tex]\rho =\dfrac{m}{v}[/tex]

where:

Given:

   [tex]\rho = 12 \dfrac{\text{g}}{\sf cm^3}[/tex]

   [tex]v=160 \pi \sf \:\:cm^3[/tex]

Substitute the given values into the Density equation and solve for m:

[tex]\begin{aligned}\rho & =\dfrac{m}{v}\\\implies 12 \dfrac{\text{g}}{\sf cm^3} & = \dfrac{m}{160 \pi \sf \:\:cm^3}\\m & = 12 \dfrac{\text{g}}{\sf cm^3} \cdot 160 \pi \sf \:\:cm^3\\m & = 12 \cdot 160 \pi \:\text{g}\\ m & = 1920\pi\:\text{g}\\ m & = 6031.857895...\:\text{g}\end{aligned}[/tex]

Therefore, the total mass of the battery to the nearest gram is 6032 g.

Applying the negative exponent, the equivalent expression  [tex]3^{-3}[/tex]  is 1/27.

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

When we have a negative exponent, we use a fraction, with the term with the exponent going to the denominator.

Hence, the equivalent expression is:

[tex]3^{-3} = \dfrac{1}{3^3} = \dfrac{1}{27}[/tex]

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Answer:

Step-by-step explanation:

A. Correct

B. Correct

C. Correct

D. False

2.

A. Correct

B. Correct

C. Correct

D. False

Hope I helped!

Answer:

wrong question please place correctly thanks

The expression given can be written as [tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]

Expression is a mathematical statement consisting of variables , constants and mathematical operators .

It is given in the question to solve the expression

[tex]\rm \dfrac{4x}{7} + \dfrac{5}{4x^2}[/tex]

Taking LCM , LCM = 28x²

[tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]

Therefore the expression given can be written as [tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]

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Using matrix algebra, the material cost of making one of each product at each location is as follows:​

                       Product X    Product Z

Location A        birr 38          birr 50

Location B        birr 38          birr 49.5

Matrix algebra involves the arrangement of numbers in a rectangular array.

Matrices are arranged in columns and rows to express some mathematical values.

                      Steel    Glass    Plastic

Product X         3            1             2

Product Z         4          0.5           3

                      Steel    Glass    Plastic

Location A      10           2           3

Location B       9           3           4

                      Steel    Glass    Plastic   Total

Location A     30           2           6          38

Location B     27           3           8          38

                      Steel    Glass    Plastic   Total

Location A     40          1             9          50

Location B     36          1.5         12         49.5

Thus, Product X costs birr 38 at locations A and B, respectively, while Product Z costs birr 50 and birr 49.5 at locations A and B, respectively.

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Answer:

3

Step-by-step explanation:

Cardinalities are the number of elements in a set.

(A∩B∩C) is the very middle part of the circle, and there are 3 elements there.

The probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

41% of adults say cashews are their favorite kind of nut.

P = 41% = 0.41

Q = 1 - P = 1 - 0.41 = 0.59

n = 2

From the binomial distribution:

[tex]\rm P(X = r) = C(n, r) P^r(1-P)^{n-r}[/tex]

a) Exactly​ three

[tex]P(X=3) = C(12, 3) (0.41)^3(0.59)^9[/tex]

P(X = 3) = 0.131

b) At least​ four:

P(X≥4) = P(X=4)+ P(X=5)+ P(X=6)+..............+ P(X=13)

[tex]\rm P(X\geq 4)=C(12, 4) (0.41)^4(0.59)^9+C(12, 5) (0.41)^5(0.59)^8+...............+C(12, 3)(0.41)^3(0.59)^9[/tex]

P(X ≥ 4) = 0.795

c) At most two:

P(X≤2) =P(X=0)+ P(X=1)+ P(X=2)

[tex]\rm =C(12, 0) (0.41)^0(0.59)^12+C(12, 1) (0.41)^1(0.59)^1^1+C(12, 2)(0.41)^2(0.59)^1^0[/tex]

P(X ≤ 2) = 0.0733

Thus, the probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.

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