Determine whether each logarithm is a common logarithm.
C. (log₁₀100)

Answer:

(5, 2)

Step-by-step explanation:

2(5) + 3(2) = 16

10 + 6 = 16

16 = 16

Hope this helps

Answer:

4) (5, 2)

Step-by-step explanation:

We should go through each of the coordinate pairs and substitute them into the line's equation. If the coordinate pair we checked satisfies the equation, it means the line passes through that point (which also means it's a solution to the equation).

1) (11, 1): [tex]2\times11+3\times1 \to 22 + 3\to25 \ne 16[/tex]
It is not equal to 16, therefore, it does not satisfy the equation.

2) (7, 2): [tex]2\times7+3\times2\to14+6\to20 \ne 16[/tex]
It is not equal to 16, therefore, it does not satisfy the equation.

3) (3, 2): [tex]2\times3+3\times2\to6+6\to12 \ne 16[/tex]
It is not equal to 16, therefore, it does not satisfy the equation.

4) (5, 2): [tex]2\times5+3\times2\to10+6\to16=16[/tex]
It is equal to 16, therefore, it does satisfy the equation.

The value of the maximum profit is 680

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The equation of the profit function is given as

P(x) = 230 + 30x - 0.5x^2

Differentiate the function

So, we have

P'(x) = 0 + 30 - x

Evaluate the like terms in the function

So, we have

P'(x) = 30 - x

Set the function to 0

So, we have

30 - x = 0

Evaluate

x = 30

Substitute x = 30 in the equation P(x) = 230 + 30x - 0.5x^2

So, we have

P(30) = 230 + 30 x 30 - 0.5 x 30^2

Evaluate

P(30) = 680

Rewrite as

Pmax = 680

Hence, the value of the maximum profit is 680

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Answer:

I think it's C, I hope this helps!

answer:

0.66666666666

step-by-step explanation:

2/3

2 divided by 3 = 0.66666666666

All the arithmetic progression terms can be solved by the general formula and by it we get the terms as- 1- 22, 2- 288/25, 3- 1682/27, 4- -89.

For any arithmetic progression, the abbreviation is used as a is the first term and d be the common difference which is {n-(n-1)}.

General formula to find nth term- a(n)=a(n) + (n-1)d

As, here, a=1 and d=1/2 ; implies, a(15) = 22

Similarly, here, a= -3/5 and d= {-2/5-(-3/5)} = 1/5 ; implies, a(30) = 288/25

Here, given, a(5) = 7 and d= 2/3 so by putting these values in the nth term formula we'll get, a= 21/58 ; implies, a(30) = 3364/174 or 1682/87

Here, we get the first term as, a= a+3 and a(2) = a-1 which implies d= (a-1) - (a+3) = -4 , therefore, a(24) = -89



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Answer:

The next 2 numbers would be 30 and 42

Step-by-step explanation:

If the last number in the sequence was 20, and the sequence started at 0 with a constant change, we know that since this constant change is +2 every time the input increases. If 12 + 8 was 20, the next number would be 30. If 20 + 10 is 30, then the next output will be 42, because 30 + 12 = 42.

Hope this helps!

Answer: rtrreg

Step-by-step explanation: 1 34erd rr4

Answer:

you don't have an image

Step-by-step explanation:

Answer:  The SD is 5.589

Step-by-step explanation:

Answer:

  No

Step-by-step explanation:

You want to know if baseline FH can be considered to be perpendicular to one of two congruent sides in isosceles triangle EFH.

The base angles of an isosceles triangle are congruent. That means they can never be right angles.

Base line FH cannot be perpendicular to side FE.

__

Additional comment

Angle E can be a right angle in isosceles triangle EFH, but neither of angles F or H can be.

Diagonal FH bisect angles EFG and EHG and the angle FEH is congruent to angle FGH.

Why is the triangle congruent?

1) EFGH is a rectangle.

The above statements is not true in general. EFGH is a quadrilateral with opposites sides are equal, it may be rectangle in some cases but it is not always be a rectangle.

2). EFGH has 4 congruent sides.The above statement is also false. EFGH has two opposite sides are congruent.

3). Diagonal FH bisect angles EFG and EHG.

The above statement is true. Triangle EFH and FGH both are isosceles triangles and hence they both have equal angles for the equal sides. Thus, it is true in all cases.

4). Diagonal FH is perpendicular to side Fe.

The above case is not true in general.

5). Angle FEH is congruent to angle FGH.

Yes, the above statement is the correct one, because both the triangles are congruent to each other.

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The complete question is -

Triangle FGH is the image of isosceles triangle FEH after a reflection across line HF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent

Answer:

The two angles are congruent or estimated to be congruent because of the "≅" that is showed in the statement.

Step-by-step explanation:

Congruent/Congruence: Having the same size and shape or matching in size and shape: congruent figures.

≅ --> Means to be congruent of seen to be congruent

≈ --> About the same, or seems equal

I hope this helped <3

The fractions whose values are between 1/5 and 1/3 include 1/4, 11/50, 7/25 and 13/50.

It should be noted that fractions simply means the numbers that have a numerator as well as a denominator.

It should be noted that 1/5 when changed to percentage will be:

= 1/5 × 100

= 20%

It should be noted that 1/3 when changed to percentage will be:

= 1/3 × 100

= 33.3%

Therefore, the information simply implies that we should find the fractions that will between 20% and 33.3%

Here, 1/4 = 25%

11/50 = 22%

7/25 = 28%

13/50 = 26%

In this case, the fractions whose values are between 1/5 and 1/3 include 1/4, 11/50, 13/25 and 13/50.

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According to the question, the given rational expression can be simplified which is as shown below:

Rational expression = [tex]\frac{2x+12}{3x-9}.\frac{6-2x}{3x+8}[/tex]

To simplify the given rational expression, calculate the factors of numerator as well as denominator. And later divide them from each other. The expressions are also called as polynomial expressions.

Rational expression = [tex]\frac{2(x+6)}{3(x-3)}.\frac{2(3-x)}{3x+8}[/tex]

The final answer of the expression is [tex]\frac{-4(x+6)}{3(3x+8)}[/tex]

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

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Step-by-step explanation:

the standard deviation is first of all based on the squared differences of every data point to the mean value (squared, so that the direction of the difference does not matter, each number is positive).

this number is normalized to the number of data points (divided by "N").

and from that number we calculate the positive square root.

we take the square root to bring things back from the squared dimension of the data differences to the mean value and make it better understandable in size compared to the sizes of the data points. otherwise there is benefit to the squared variance (the whole thing without the last square root).

we have 15 data points (8 + 7).

first we need the mean value, which is the sum of all data points divided by the number of data points :

(7+10+5+5+6+3+5+5+6+5+5+5+9+3+5)/15 = 84/15 =

= 5.6

the standard variance is now the sum of the squares of the difference of each data point to the mean value.

e.g. the squared difference of 7 to 5.6 is

(7-5.6)² =(-1.4)² = 1.96

(1.96+19.36+0.36+0.36+0.16+5.76+0.36+0.36+0.16+0.36+0.36+0.36+11.56+5.76+0.36) / 15

= 47.6 / 15 = 3.173333333...

and the standard deviation is

SD = sqrt(3.173333333...) = 1.781385229... ≈ 1.78

Answer:

[tex]{ \tt{x + 83 = 180}}[/tex]

[ Property of angles on a straight line ]

[tex]{ \tt{x = 180 - 83}} \\ \\ { \boxed{ \tt{x = 97 \degree}}}[/tex]

[tex]{ \tt{(4y - 27) = x}} \\ [/tex]

[ Property of alternate angles ]

[tex]{ \tt{4y - 27 = 97}} \\ { \tt{4y = 124}} \\ { \tt{ \frac{4y}{4} = \frac{124}{4} }} \\ \\ { \boxed{ \tt{y = 31 \degree}}}[/tex]

The exponential decay model of phosphorus-32 is [tex]P=P_0e^{-0.0483t}[/tex] and

the amount of phosphorus-32 remaining after 84 days is 0.85 mg

It is given that half-life of Phosphorus-32 is 14.3 days.

Putting P = 25 , P₀ = 50 and t = 14.3 in equation (1) , we get

       [tex]25=50e^{14.3r}\\\\0.5=e^{14.3r}[/tex]

Taking log on both sides , we get

         [tex]log0.5=log_{10}e^{14.3r}\\\\-0.301=14.3rlog_{10}e\\\\\frac{-0.301}{14.3}=r\times0.434 \\\\\r=\frac{-0.0210}{0.434} \\\\r=-0.0483[/tex]

The exponential decay model of phosphorus-32 is [tex]P=P_0e^{-0.0483t}[/tex]

We have to find the amount after 84 days .

Putting [tex]P_0=50mg , \ r=0.0483 , \ t=84[/tex] in equation (1) , we get      

         [tex]P=50\times e^{(-0.0483\times84)}\\\ P=50\times e^{-4.064}\\P=50\times 0.0171\\P=0.85mg[/tex]

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As per a quadratic equation, the length of the smallest side is 14 centimeters.

This is a problem of quadratic equation,

s (s + 4) = 192. Now, we will simplify the equation, and we will get s²+4s = 192

and now we can write, s² + 4s - 192 = 0

or, s² + 16s - 14s - 192 = 0

or, s ( s + 16 ) - 14( s - 16 ) = 0

or,( s + 16)( s - 14 ) = 0

As we all know if the multiplication of terms or factors is zero then each possible term or factor will be considered zero.

So, s + 16 = 0

or, s = - 16

Length cannot be a negative one, so 16 c.m is not possible.

s - 14 = 0

or, s = 14

14 c.m is the possible value.

So, the length of the smallest side of the triangle is 14 centimeters.

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The shape that has rotational symmetry of 40 degrees is a nonagon.

It should be noted that a nonagon is a nine-sided polygon and it is also called a 9-gon. In other words, it should be noted that a nonagon is a nine sided closed two dimensional figure.

It should be noted that the degree of rotation for a nonagon is 40º. Since 360° of rotation is a full circle. We need to divide 360° by 40°

360/40=9 the shape has 9 sides

The shape is a nonagon, which has 9 sides.

Therefore, the shape that has rotational symmetry of 40 degrees is a nonagon.

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The six trigonometric functions are:

1. sinθ = ₋2/√29

2. cosθ = ₋5/√29

3. tanθ = 2/5

4. cotθ = 5/2

5. secθ =  ₋√29/5

6. cosecθ = ₋√29/2

Given, the point is (-5 , -2).

The angle is in the 3rd quadrant.

Find the length of the hypotenuse by using the Pythagorean Theorem.

c² = a² + b²

the length of side (a) = -5

the length of side (b) = -2

therefore, c² = (⁻5)² + (₋2)²

c² = 25 + 4

c² = 29

c = √29

c = 5.39

Now, values for the six trigonometric functions are:

sinθ = perpendicular/ base = b/c = ₋2/√29

cosθ = Adjacent/hypotenuse = a/c = ₋5/√29

tanθ = perpendicular/ adjacent = b/a = ₋2/₋5 = 2/5

cosecθ = 1/sinθ = 1/₋2/√29 = ₋√29/2

secθ = 1/cosθ = 1/₋5/√29 = ₋√29/5

cotθ = 1/tanθ = 1/2/5 = 5/2

hence we get the values of all the six trigonometric functions.

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The six trigonometric functions are:1. sinθ = ₋2/√29,2. cosθ = ₋5/√29,3. tanθ = 2/5,4. cotθ = 5/2,5. secθ =  ₋√29/5,6. cosecθ = ₋√29/2

Given, the point is (-5 , -2).

The angle is in the 3rd quadrant.

Find the length of the hypotenuse by using the Pythagorean Theorem.

c² = a² + b²

the length of side (a) = -5

the length of side (b) = -2

therefore, c² = (⁻5)² + (₋2)²

c² = 25 + 4

c² = 29

c = √29

c = 5.39

Now, values for the six trigonometric functions are:

sinθ = perpendicular/ base = b/c = ₋2/√29

cosθ = Adjacent/hypotenuse = a/c = ₋5/√29

tanθ = perpendicular/ adjacent = b/a = ₋2/₋5 = 2/5

cosecθ = 1/sinθ = 1/₋2/√29 = ₋√29/2

secθ = 1/cosθ = 1/₋5/√29 = ₋√29/5

cotθ = 1/tanθ = 1/2/5 = 5/2

hence we get the values of all the six trigonometric functions.

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Answer:

y = -x^2/10 + x/5 - 3/5

Step-by-step explanation:

The answer is D: just rearrange

Value of x in given exponential equation is = -1

In, mathematics a exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as  [tex]a^x[/tex] .

where, a is the base of function

           x is the expression

Mathematically, if  [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as  [tex]a^x = N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

Some important formulas of logarithms :

According to given statement,

[tex]5^{3x} = \frac{1}{125}[/tex]

=> [tex]5^{3x}=\frac{1}{5^3}[/tex]

=> [tex]5^{3x}=5^{-3}[/tex]   (as [tex]\frac{1}{a^x} =a^{-x}[/tex])

=> 3x = -3

=> x = -1

Thus solution for this equation is x =-1.

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the complete table is:

zeros: x = -2, x = 0, x = 2.

Increasing: (-∞, -1.25) and (1.25, ∞)

Decreasing: (-1.25, 1.25)

End Behavior:   as x →∞, y →∞

                         as x → -∞, y→ -∞

Let's solve for the first function.

First, we want to find the zeros of the function. The zeros are the values of x such that the function becomes zero (intercepts the horizontal axis)

So we can see that the zeros are:

x = -2, x = 0, x = 2.

Now we want to see when the function is increasing. The function is increasing when it goes (reading from left to right) the function goes upwards.

The function is increasing on the intervals:

(-∞, -1.25) and (1.25, ∞)

And the function is decreasing between these two intervals:

(-1.25, 1.25)

Now we need to look at the end behavior.

When x tends to infinity, (right side) we can see that the function goes upwards, then:

as x →∞, y →∞

In the left side the function goes downwards, so:

as x → -∞, y→ -∞

Then the complete table is:

zeros: x = -2, x = 0, x = 2.

Increasing: (-∞, -1.25) and (1.25, ∞)

Decreasing: (-1.25, 1.25)

End Behavior:   as x →∞, y →∞

                         as x → -∞, y→ -∞

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The value of x that makes line m parallel to line l is 15.

When parallel lines are cut across by a transversal, angle relationships are formed.

The angle relationship form includes corresponding angles, alternate angles, vertically opposite angles etc.

Therefore, for line m to be parallel to line l,

5x - 10 + 8x - 5 = 180

Hence,

5x - 10 + 8x - 5 = 180

5x + 8x - 10 - 5 = 180

13x - 15 = 180

13x = 180 + 15

13x = 195

Therefore, divide both sides by 13

13x / 13 = 195 / 13

x = 15

Therefore, the value of x that makes line m parallel to line l is 15.

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The terms given in US national debt in standard form when converted to scientific notation form will be 2.86 * 10^11, 3.70 * 10^11, 9.07 * 10^11, 3.23 * 10^12, 5.67 * 10^12 and 1.35 * 10^13 respectively.

Scientific notation if the process of conversion of very large numbers which are otherwise inconvenient to read into decimal form raised to some power of 10. During this conversion, the numbers in standard form are written such that only one place value before decimal is left and written as coefficient and all other numbers are then counted and written in the form of base 10 raised to some exponent value. The coefficient value must be such that its value lies between 1 and 9 and less than 10. Thus, the following numbers can be written as follows in scientific form.

286330760848.37 = 2.86 * 10^11

370918706949.93 = 3.70 * 10^11

907701000000.00 = 9.07 * 10^11

3233313451777.25 = 3.23 * 10^12

5674178209886.86 = 5.67 * 10^12

13561623030891.79 = 1.35 * 10^13  

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Answer:

V = 1,005.31ft³

Step-by-step explanation:

V = [tex]\pi[/tex][tex](\frac{d}{2} )^{2}[/tex]h

V = [tex]\pi[/tex][tex](\frac{16}{2} )^{2}[/tex](5)

V = 1,005.30965ft³

Step-by-step explanation:

diameter is 16 feet

height is 5 feet

For you to find the volume you have to know the

formula for finding it

the formula is πr^2h

π=22/7,

r=radius=16/2=8

h=height=5

πr^2h

22/7 x 8^2 x 5

22/7 x 64 x 5

22/7 x 320

=1005.71 feet^3

Answer:

Check the attached image above for solution

Answer:

36

Step-by-step explanation:

1/6 x = 6

multiply right side by 6 to simplify fraction

x = 36

Using ratio and proportion, of the 243 students in the school altogether, 144 students are expected to participate in school clubs, sports, or activities.

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other. On the other hand, proportion is the equality of two ratios, such that a : b = c : d.

If 32 students participate in school clubs, sports, or activities out of the 54 students, then the ratio between the number of students who participate in school clubs, sports, or activities and the total number of students is:

32 : 54

Using proportion, solve for the number of students who are expected to participate in school clubs, sports, or activities out of 243 students.

32 : 54 = n = 243

where n = number of students who are expected to participate in school clubs, sports, or activities out of 243 students

32 : 54 = n = 243

32(243) = 54n

n = 144

Hence, 144 students are expected to participate in school clubs, sports, or activities out of 243 students.

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Answer: m∠B°=43°

Step-by-step explanation:

If < A and < B are vertical angles, hence, m∠A°=m∠B°=43°