The function f(x) is given by the set of ordered pairs.

{(1,0), (–10,2), (0,6), (3,17), (–2,–1)}

The function that models the given situation is; f(x) = 109(0.935)^(t) + 72

We are given that;

Temperature of hot tea = 181°F

Room temperature = 72°F

Rate of the hot tea cooling on a desk in the room = 6.5% every minute

We know that an exponential function is of the form of;

y = A(r)^(x)

where;

A is the initial value.

r is the rate of increase/decrease in decimals.

Thus, our initial value is;

A = 181 - 72 = 109

The rate of increase/decrease in decimals = 1 - (6.5%) = 0.935

Since the room temperature is 72 degrees Fahrenheit, then the function is;

f(x) = 109(0.935)^(t) + 72

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Using the given equation, the missing values in the table are:

x            y

32         14

12          9

0           6

-8          4

-36       -3

Given the equation, y - 6 = x/4, we can rewrite the equation as:

y = x/4 + 6

For x = 12, we have:

y = 12/4 + 6 = 3 + 6

y = 9

For x = 0, we have:

y = 0/4 + 6 = 0 + 6

y = 6

For y = 4, we have:

4 = x/4 + 6

4 - 6 = x/4

-2 = x/4

-8 = x

x = -8

For y = -3, we have:

-3 = x/4 + 6

-3 - 6 = x/4

-9 = x/4

-36 = x

x = -36

Thus, using the given equation, the missing values in the table are:

x            y

32         14

12          9

0           6

-8          4

-36       -3

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your question is wrong to make sure

Answer:

Here in the picture is the prime factorisation of 13824

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Answer:

1) 1/2 × 3/5 = 45/150

2) 5/5 × 3/5 = 90/150

3) 2 2/3 × 3/5 = 1 90/150

Explanation below

Explanation belowHope this helps :)

Step-by-step explanation:

1/2 × 3/5 = 3/10

2 2/3 × 3/5 = 8/3 × 3/5 = 24/15

5/5 × 3/5 = 15/25

We need to find the Least Common Multiple (LCM) to order them from least to greatest.

The LCM is 150.

3/10 = 45/150

24/15 = 1 9/15 = 1 90/150

15/25 = 90/150

So the order from least to greatest is ...

1) 1/2 × 3/5 = 45/150

2) 5/5 × 3/5 = 90/150

3) 2 2/3 × 3/5 = 1 90/150

The solution to the literal equation is y = x - 2.

To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.

From the given information:

4x + 1 = 9 + 4y

To solve for y, we have to switch the sides:

9 + 4y = 4x + 1

Subtract 9 from both sides

9 - 9 + 4y = 4x + 1 - 9

4y = 4x - 8

Divide both sides by 4

[tex]\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}[/tex]

y = x - 2

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The velocity of a particle = i + 2t j

The acceleration of a particle = 2 j

The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]

Here,

The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]

We have to find, the velocity, acceleration, and speed of a particle with the given position function.

What is Velocity of a particle with the given position function?

The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.

Now,

The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]

The velocity of a particle = [tex]\frac{d r(t)}{dt}[/tex]

[tex]r (t ) = ti + t^{2} j +2k[/tex]

[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]

The acceleration of a particle = [tex]\frac{d^{2} r(t)}{dt^{2} }[/tex]

[tex]r (t ) = ti + t^{2} j +2k[/tex]

[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]

[tex]\frac{d^{2} r(t)}{dt^{2} }= 2j[/tex]

The speed of a particle = [tex]| \frac{d r(t)}{dt}| = |v(t)|[/tex]

[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]

[tex]|v(t)|=\sqrt{1 + 4t^{2} }[/tex]

Hence, The velocity of a particle = [tex]i + 2t j[/tex]

The acceleration of a particle = [tex]2 j[/tex]

The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]

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Answer:

Step-by-step explanation:

7(i)

[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=\frac{dx}{dx} *(3x-5)^\frac{5}{3}+x*\frac{d}{dx} \{(3x-5)^\frac{5}{3} \}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=1*(3x-5)^\frac{5}{3} +x*\frac{5}{3}*(3x-5)^{\frac{5}{3} -1}*\frac{d}{dx} \{(3x-5)\}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +\frac{x*5*(3x-5)^{\frac{2}{3}}*3 }{3} \\\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +5x*(3x-5)^\frac{2}{3} \\\\[/tex]

[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3}*((3x-5)^{\frac{5}{3}-\frac{2}{3}} + 5x)\\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5)^\frac{3}{3}+5x) \\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5+5x)\\\ \frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(8x-5)*(3x-5)^\frac{2}{3}[/tex]

7(ii)

[tex]\int\limits {(x*(3x-5)^\frac{2}{3}) } \, dx \\Let\ \sqrt[3]{3x-5} =u\\Hence,\\(\sqrt[3]{3x-5})^3=u^3\\ 3x-5=u^3\\3x-5+5=u^3+5\\3x=u^3+5\\[/tex]

Divide both parts of the equation by 3:

[tex]\displaystyle\\x=\frac{u^3+5}{3}\\\\dx=\frac{d}{du} \{\frac{u^3+5}{3}\} \\dx=\frac{3u^2}{3} du=\\\\dx=u^2du\\Hence,\\\\\int\limits {\frac{u^3+5}{3}* u^2*u^2} \, du =\\\\\int\limits {\frac{u^3+5}{3} *u^4} \, du =\\\\\int\limits {\frac{u^7+5u^4}{3} } \, du =\\\\\frac{1}{3} \int\limits {u^7} \, du +\frac{1}{3}\int\limits {5u^4} \, dxu =\\\\[/tex]

Answer: 18

Step-by-step Explanation:

Subtract: 5 from 41 | 41-5= 36

Divide: by 2 | 36/2= 18

Answer:18

Step-by-step explanation:

SUBTRACT41 FROM 5

THAT GIVES YOU 38

THEN DIVIDE 38/2 AND IT WILL GIVES 18

The relationship between the length of a side and the area is non proportional.

The answer is non proportional because the side length is x,

so is the other side lengths.

The side lengths are all equal and to find area you do x squared or x times x.

So they are not proportional because there will be different numbers for each.

For example. X= 2, area ( x squared ) is 4.

Hence, The relationship between the length of a side and the area is non proportional.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In a square, we need to find the relationship between the length of a side and the area.

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Step-by-step explanation:

did you leave something out ?

(5p + 3)(p + 1) = 5p×p + 5p×1 + 3×p + 3×1 =

= 5p² + 5p + 3p + 3 = 5p² + 8p + 3

at no point do we have 5 terms to sum up. but 4 and then finally 3, yes.

but we always have also additions, not only multiplications (products).

so, none of the 2 options is correct.

we could, of course. start with the initial expression, that shows the product of 2 factors and multiply by 1×1

(5p + 3)(p + 1)×1×1

then we have the expression as product of 4 factors.

in the same way we could bump up the sum scenario by adding one or 2 0s : tadah ! sum of 5 terms.

I strongly suspect there is something missing in the problem description.

Answer:

Neither is correct.

Step-by-step explanation:

One year on Venus is 225 days on Earth.

Multiply that by 9 1/2.
The answer you get is 2137.5

9 1/2 years on Venus years is equivalent to 2137.5 days on Earth.

There are  9 1/2 years on Venus years is equivalent to 2137.5 days on Earth, the answer would be 2137.5 days.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Equivalent to 9 1/2 years on venus.

Let the number of days on earth is x:

One year on Venus is 225 days on Earth.

= (225)(9 1/2)

= (225x19)/2

= 2137.5 days

Thus, there are  9 1/2 years on Venus years is equivalent to 2137.5 days on Earth, the answer would be 2137.5 days.

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Answer:

1st Question:  The answer is the bottom left

2nd Question: The answer is the bottom right

3rd Question: The answer is the top left

4th Question: The answer is the top right.

Step-by-step explanation:

Step-by-step explanation:

You want to demonstrate the identity ...

  (1-tan⁴(A))·cos⁴(A) = 1 -2·sin²(A)

Working with the left side, we have ...

  [tex](1-\tan^4(A))\cos^4(A)=1-2\sin^2(A)\\\\(1-\dfrac{\sin^4(A)}{\cos^4(A)})\cos^4(A)=1-2\sin^2(A)\qquad\text{use tangent identity}\\\\\cos^4(A)-\sin^4(A)=1-2\sin^2(A)\qquad\text{multiply it out}\\\\(\cos^2(A) +\sin^2(A))(\cos^2(A)-\sin^2(A))=1-2\sin^2(A)\qquad\text{factor}\\\\1((1-\sin^2(A))-\sin^2(A)) = 1-2\sin^2(A)\qquad\text{use $\cos^2$ identity}\\\\1-2\sin^2(A)=1-2\sin^2(A)\qquad\text{Q.E.D.}[/tex]

__

Additional comment

The referenced identities are ...

  tan = sin/cos

  cos² = 1 -sin²

and the factorization of the difference of squares:

  a² -b² = (a +b)(a -b).

The perimeter of ABC with vertices A(-4,4), B(2,-2), and C(-4,-2) is 20.848 units.

We are given the vertices:

A(-4,4), B(2,-2), and C(-4,-2).

We need to find the perimeter of ABC.

AB = √ ( 2 + 4)² + (-2 - 4)²

AB = √ 6² + 6²

AB = √72

AB = 6 √2 units

BC = √ (-4 - 2)² + ( -2 + 2)²

BC = √ 6²

BC = 6 units

AC = √ ( -4 + 4)² + (-2 - 4)²

AC = √ 6²

AC = 6 units.

Perimeter = AB + BC + AC

Perimeter = 6 √2 + 6 + 6 units

Perimeter = 12 + 6 √2 units.

Perimeter = 12 + 6(1.414) units

Perimeter = 12 + 8.848 units

Perimeter = 20.848 units

Therefore, the perimeter of ABC with vertices A(-4,4), B(2,-2), and C(-4,-2) is 20.848 units.

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The set of all such points is a sphere center c = ( 23/3 , 19/3 , 3 ) r = 2√83/9

what is the sphere?

The standard form of the equation of a sphere with center (a ,b ,c) and radius r is

( x -a)² + ( y-b)² + ( z - c)² = r²

We let P = ( x, y,z ) be an arbitrary point which satisfies the given conditions. Then

[tex]\sqrt{(x - 1)^{2} + ( y - 5)^{2} + (z - 3)^{2} } = 2 \sqrt({x - 6)^{2} + ( y - 2 )^{2} +( z - 3)^{2} }[/tex]

Squaring both sides of this equation and simplifying yields

( x - 1)² + ( y - 5)² + ( z -3)² = 4 [ (x - 6)² + ( y- 6 )² + ( z - 3)²

( 3x² - 46x + 143 ) + ( 3y² - 38y + 119 ) + ( 3z² - 18z + 27 ) = 0

Next, we complete the square for each variable to obtain

( x - 23/3)²  + ( y - 19/3)² + ( z - 3 )² = 332/9

Thus the set of all such points P forms a sphere, with

center c = ( 23/3 , 19/3 , 3 ) r = 2√83/9

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Answer:

21=1×21 or 3×7

Step-by-step explanation:

21 is a composite number.factors of 21:1,3,7,21.

Prime factorization:21=3×7.

since 3 and 7 are the only prime numbers ...

Thanks!!

Answer:

49

Step-by-step explanation:

The ratio of three numbers = 2:5:7

Then the numbers are 2x,5x and 7x

Given that the LCM of these numbers  = 490

LCM of 2x,5x,7x is 2×5×7×x = 70x

Then, we have 70x = 490

x  = 7

Hence, the numbers are 14, 35 and 49

Largest number = 49

∴The square root of the largest number = 7

A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160feett/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute

Given that 1)A gull can fly at a speed of 22 miles per hour and asked to convert its units to  foot/hour

2)An AMTRAK train travels at 125 miles per hour and is asked to convert its units to  miles/minute

1 mile=5280 feet

22 miles/hour=22 × 5280 foot/hour

22 miles/hour=116,160 foot/hour

1 hour=60 minute

125 miles/hour= 125/60 miles/minutes

125 miles/hour= 2.083 miles/minutes≈ 2.1miles/minutes

Therefore, A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160 feet/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute

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Answer:

11

Step-by-step explanation:

Plug 4 into the x, 6(4) = 24

24 - 13 = 11

Answer:

30 yards

Step-by-step explanation:

9+9+6+6=30yards

The events A and B are not independent.

Given that,

                  P(A|B) = 0.4

                  P(A) = 0.5

                  P(B) = 0.8

Two events A and B are said to be independent, if P(A∩B) = P(A) P(B)

We have, P(A|B) = P(A∩B)/P(B)

Therefore, P(A∩B) = P(A|B) P(B) = 0.4 x 0.8 = 0.32

Now P(A) P(B) = 0.5 x 0.8 = 0.4

So P(A∩B) ≠ P(A)P(B)

Therefore, the events A and B are not independent.

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Answer:

Step-by-step explanation:

no solution

The term in the given expression is -3x − 7(x + 4) (A) -3x.

Term:

Therefore, the term in the given expression is (A) -3x.

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The correct question is given below:
Which choice is a term in this expression? -3x − 7(x + 4)

Ordinal is the answer.

In the given statement is:
A scale that allows one to determine only if there is more, less, or an equal amount of the attribute in comparison to another observation is called a(n) ____ scale.

Ordinal Scale is the 2nd level of measurement that reports the ranking and ordering of the data without actually establishing the degree of variation between them. Ordinal level of measurement is the second of the four measurement scales. "Ordinal" indicates "Order".

Hence, The answer is Ordinal

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Answer:

-15w+9y+6

Step-by-step explanation:

I think that you are asking to simplify the expression.  An equation has an equal sign and I do not see one.

We need to distribute the -3 to everything inside of the parentheses.  

A negative times a negative is a positive.

A negative times a positive is a negative.

-3(5w-3y-2)

-3(5w) -3(-3y) -3(-2)

-15w + 9y + 6

Hi!

To simplify this, use the Distributive Property:

Now, let's simplify the given expression:

[tex]\dashrightarrow\sf{-3(5w-2y-2)}[/tex]

Like the property said, We should distribute -3 so that it's multiplied by each term:

[tex]\bullet\dashrightarrow\sf{-15w+9y+6}[/tex]

Therefore,

[tex]\bullet\dashrightarrow\stackrel{\heartsuit}{\boxed{\boxed{\boldsymbol{-15w+9y+6}}}}}\dashleftarrow\bullet[/tex]

- stargazing :')

Given that sample standard deviation is zero. This indicates that the variance of sample is also zero as square of sample standard deviation is sample Variance. Variance is average of the squared deviations from mean. As shown in below formula

Since Variance = 0 , we substitute in formula and we get the sum of squares of deviations of all data points from mean should be zero. This is only possible if and only if all the data points in the data distribution are same as mean of the data distribution. In the case the variance and standard deviation will be zero.

Variance = Summation n to i = 1 [tex]\frac{(X_{1-X} )^2}{n-1}[/tex]

        0 = Summation n to i = 1[tex]\frac{(X_{1-X} )^2}{n-1}[/tex]

                Summation n to i [tex]{(X_{1-X} )^2[/tex] = 0

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The number of weeks that it will take Jason to have coins from all 195 countries is 24 weeks.

It should be noted that an equation is simply used in Mathematics to show the relationship the exist between different variables.

Let the number of weeks be represented by w.

Therefore, based on the information, the appropriate equation will be:

99 + (4 × w) = 195

99 + 4w = 195

4w = 195 - 99

4w = 96

Divide

w = 96/4

w = 24

Therefore, based on the calculation illustrated above, the number of weeks that it will take Jason to have coins from all 195 countries is 24 weeks.

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Answer:

-6r+5

Step-by-step explanation:

Combining the like terms

⇒-4r-2r+5

⇒-6r+5