Given loga(m) = 10 and loga(n) = 20, find loga(mn2). (Enter an exact number.)

Answer:

Step-by-step explanation:

8.5 inches divided by 2 = 4.25 inches which is the base of the triangle with a height of 5.8 inches. Area of that triangle is 1/2 x base x height = 1/2 x 4.25 inches x 5.8 inches = 12.325 inches squared. Two of the triangles make 1 full isoceles triangle= 2 x 12.325 inches squared = 24.65 inces squared. But there are 5 isoceles triangles in a pentagon, so 5 times 24.65 inches squared = 123.25 inches squared.

Using the information from the given diagram, the measure of angle x (m ∠x) is 52°

From the question, we are to determine the measure of angle x.

From the given diagram, we can write that

m ∠A + m ∠H + m ∠I = 180° (Sum of angle in a triangle)

Also,

m ∠K = m ∠I (Corresponding angles theorem)

∴ m ∠I = 62°

Thus,

x° + 66° + 62° = 180°

x° + 128° = 180°

x° = 180° - 128°

x° = 52°

Hence, the measure of ∠x 52°

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Answer:

Step-by-step explanation:

ABC = the draw of the square means that the angle is right

We can now say that the other two angles are acute because the sum of the interior angles of a triangle is 180 degrees

BCA = acute

CAB = acute

The transformation that converts f(x) to g(x), f(x) is contraction by 5 units

Transformations are mathematical operations which change the shape and orientation of an object or function.

The types of transformations include

Since we have the graph of f(x) = -10(x - 2)² into the graph of g(x)= -2(x - 2)².

We see that f(x) = -10(x - 2)²

= 5 × -2(x - 2)²

= 5g(x)

Since f(x) = 5g(x)

⇒g(x) = f(x)/5

So, we converts f(x) to g(x), f(x) is contraction by 5 units

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The first term of the sequence is 12 and the common difference is -3.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

Given that a formula for the nth term. 5th term is 0​; 45th term is -120. The common difference is calculated as,

a₁ + d(5-1) = 0

a₁ + d(45 - 1) = -120

Solve the above equation,

a₁ + 4d = 0

-a₁ - 44d= +120

___________

     -40d = 120

          d = -3

The value of the first term is,

a₁ + 4d = 0

a₁ + 4 x -3 = 0

a₁ = 12

Therefore, the first term of the sequence is 12 and the common difference is -3.

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Answer:

  (x, y) = (1, 3)

Step-by-step explanation:

You want to solve the system of equations x-y= -2; x+y=4 by the addition method.

The addition method seeks to eliminate one of the variables by adding the equations with appropriate multipliers so that one of the coefficients becomes zero.

Here, we observe that the coefficient of y in one equation is the opposite of that in the other equation. This means adding the two equations will cancel the y-terms:

  (x -y) +(x +y) = (-2) +(4)

  2x = 2 . . . . . . . . . . . . . . . . simplify; y-term is eliminated

  x = 1 . . . . . . divide by 2

  1 +y = 4 . . . . . . . substitute for x in the second equation

  y = 3 . . . . . . . . . subtract 1

The solution is (x, y) = (1, 3).

Simplification of the given expression 2cd³ (c - d +5) is given by

2c²d³ − 2cd⁴ + 10cd³.

As given in the question,

Given expression is equal to :

2cd³ (c - d +5)

Law of exponents for multiplication is given by:

mᵃ × mᵇ  =mᵃ⁺ᵇ

Simplification of the given expression by open the parenthesis we have,

= 2cd³ × c - 2cd³ × d + 2cd³ × 5

Apply law of exponents for multiplication we get,

= 2c¹⁺¹d³ -2cd³⁺¹ + (2×5)cd³

= 2c²d³ -2cd⁴ + 10cd³

Therefore, simplification of the given expression 2cd³ (c - d +5) is given by 2c²d³ − 2cd⁴ + 10cd³.

The complete question is:

Simplify : 2cd³ (c - d +5)

a. 2cd³− 2c²d⁴ + 10c²d³

b. 2c²d³ − 2cd⁴ + 10cd³

c. 2cd³ − 2cd³ + 10cd³

d.  2c²d³− 2c²d⁴ + 10cd²

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The employee's new wage per hour is $10.83. The percentage increase of the original wage to his new​ wage is 3%.

A percent increase means how much a percentage has gone up over time. To find this number, one would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease. The formula for percent increase equals to "Increase / original number (value) x 100".

Given data:

First, we find 3% of $10.51 to get new wage per hour

= 0.03$ * $10.51

= $0.32

Then, we add this increase to $10.51.

= $10.51 + $0.32

= $10.83

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The confidence interval that we have for the population mean is given as [869.9 , 890.7]

The confidence interval is the range of values that, if you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time.

We have the following data that we have to solve this problem with

The mean = x¯=880.3 pounds

The standard deviation = 10.4 pounds.

The confidence interval = 68%

To get the confidence interval for the true mean of the population weight we would have

mean ± standard deviation

880.3 ± 10.4

The interval would be written out as

880.3 - 10.4 and 880.3 + 10.4

the confidence interval =

[869.9 , 890.7]

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Answer:

[tex]x= -4[/tex] + [tex]2\sqrt{5}[/tex]   and   [tex]x= -4 -2\sqrt{5}[/tex]

Step-by-step explanation:

[tex]ax^{2}[/tex] + [tex]bx[/tex] - [tex]c = 0[/tex]

For this equation: [tex]a = 2, b = 16, c = -8[/tex]

[tex]2x^{2}[/tex] + [tex]16x[/tex] - [tex]8 = 0[/tex]

Step 1: Use quadratic formula with [tex]a=2, b=16, c=-8[/tex]

[tex]x=\frac{-b + - \sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]x=\frac{-(16) + - \sqrt{16^{2}-4(2)(-8) } }{2(-2)}[/tex]

[tex]x=\frac{-16+- \sqrt{320} }{4}[/tex]

[tex]x= -4[/tex] + [tex]2\sqrt{5}[/tex]  and   [tex]x= -4 -2\sqrt{5}[/tex]

Hope this helps! :)

589 in base five is  [tex]4324_{5}[/tex].

Given number:

589

converting to [tex]589_{5}[/tex].

⇒ 5|589

⇒ 5|117|4

⇒ 5|23|2

⇒ 5|4|3

⇒ 5|4|4

Now we write the last digit from last number to first that is,

= [tex]4324_{5}[/tex].

Hence 589 in base five is  [tex]4324_{5}[/tex].

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The percent increase from 2,500 pounds this week to 2,525 pounds is 1% increase

From the question, we have the following parameters that can be used in our computation:

Initial weight = 2500 pounds

New weight = 2525 pounds

The percentage increment is then calculated as

Percentage = (Final value - Initial value)/Initial value * 100%

Substitute the known values in the above equation

Percentage = (2525 - 2500)/2500 * 100%

Evaluate the difference

So, we have

Percentage = 25/2500 * 100%

Evaluate the quotient

So, we have

Percentage = 0.01 * 100%

Evaluate the product

So, we have

Percentage = 1%

Hence, the percent increase is 1% increase

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The weight of Luna is 82 pounds , the correct option is (d) .

In the question ,

it is given that

Kira has three dogs Luna , Cooper and Daisy .

let the weight of cooper be c .

given Cooper weighs 25 pounds less than Daisy

which is c = daisy - 25

So , daisy = c + 25

and Luna weighs 20 pounds less than three times Cooper ,

which is Luna = 3c - 20

Given the combined weight is = 175 pounds

Cooper + Daisy + Luna = 175

c + c + 25 + 3c - 20 = 175

5c + 5 = 175

5c = 175 - 5

5c = 170

c = 170/5

c = 34

So, Luna = 3c - 20 = 102 - 20 = 82 pounds .

Therefore , The weight of Luna is 82 pounds .

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Answer:

1024

Step-by-step explanation:

8 times 2 to the 7th power

2 by the 7th power 128 times 8 1024

Answer:

I believe there is supposed to be something in the the corner box (Top left).

Step-by-step explanation:

Answer:

220.

Step-by-step explanation:

If you plug in 4 for L and 6 for W, you are left with 25(4) + 20(6), which is equivalent to 100+120 = $220

Answer:

220

Step-by-step explanation:

Perimeter of triangle FBC is 19.24 units

Area of triangle FBC is 100.62 square units

Given,

The triangle with vertices;

F(-3, 5)

B(3, 2)

C(1, -2)

We have to find the perimeter and area of the triangle;

Formula for getting distance from vertices;

D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]

Here,

D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(3 -(-3) )^{2}+(2 -5 )^{2} }[/tex]

= [tex]\sqrt{6^{2} +(-3)^{2} }[/tex]

= [tex]\sqrt{36+9}[/tex]

= √45

D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(1 -3 )^{2}+(-2-2)^{2} }[/tex]

= [tex]\sqrt{(-2)^{2} +(-4)^{2} }[/tex]

= [tex]\sqrt{4+16}[/tex]

= √20

D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]

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

= [tex]\sqrt{4^{2}+(-7)^{2} }[/tex]

= [tex]\sqrt{16+49}[/tex]

= √65

That is,

Now,

Perimeter of triangle FBC = FB + BC + FC

= √45 + √20 + √65

= 19.24 units

Next,

Area of triangle FBC = 1/2 × BC × FB²

= 1/2 × √20 × √45²

= 100.62 square units.

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Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Total socks= 10

White socks= 8

Total T- shirts= 9

White T- shirts = 2

Now, The probability of choosing a white pair of socks is

= 8/10

= 4/5

and, The probability of choosing a white tee shirt is

= 2/9

and, The probability of both being white is

= 4/5 x 2/9

= 8/45

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The value of 2*(3*5) = 68.

The value of (2*3)*5 = 68.

What is multiplication?

A mathematical formula that specifies the objects to be multiplied, known as a factor, produces a product. For instance, the product of 6 and 5 is 30.

Given: The operation * is defined as,

a*b = a + b - 2ab

We have to find the value of 2*(3*5) and (2*3)*5

First to find the value of 2*(3*5).

2*(3*5) = 2*(3 + 5 - 30) = 2*(-22) = 2 + (-22) - 2(-22)(2) = 68.

Now to find the value of (2*3)*5.

(2*3)*5 = (2 + 3 - 12)*5 = -7*5 = (-7) + 5 - 2(-7)(5) = -2 + 70 = 68.

Therefore, 2* (3*5) = 68 and (2*3)*5 = 68.

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The given infinite series is divergent.

Given,

[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\frac{3n^2+n+1}{2n^2-1}}[/tex]

it is in the form,

[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\ a_n[/tex]

If the series is convergent then it satisfies,

i)[tex]b_{n+1}\ \leq\ b_n\ for\ all\ n[/tex]

ii)[tex]\lim_{n \to \infty} a_n =0[/tex]

if any of the above condition dissatisfies then the series is divergent

First check the 2nd condition,

[tex]\lim_{n \to \infty}\frac{3n^2+n+1}{2n^2-1}}\\\\= \lim_{n \to \infty}\frac{n^2(3+\frac{1}{n}+\frac{1}{n^2})}{n^2(2-\frac{1}{n^2})}}\\\\=\frac{3+0+0}{2-0}\\\\=\frac{3}{2}[/tex]

Here, [tex]\lim_{n \to \infty} a_n \neq 0[/tex]

Thus, the given series is divergent.

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The probability that the proportion of airborne viruses in a sample of 533 viruses would differ is 0.0062.

From the information, the scientist claims that 9% of viruses are airborne and the proportion of airborne viruses in a sample is 533 viruses.

The requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.

The mean is 0.09 and the standard deviation is 0.012.

The probability will be:

= 1 - P[Z < (0.12 - 0.09/0.013)]

= 1 - P(Z < 2.5)

= 1 - 0.99379

= 0.0062

This shows the concept of solving probability regarding z values.

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Answer:

[tex]y= \frac 12 x -3\\y=0.5x -3[/tex]

Depending if you can imput fractions, or decimal numbers.

Step-by-step explanation:

The slope can easily calculated as [tex]m=\frac{\Delta y}{\Delta x} = \frac {0-(-3)}{6-0} = \frac 36 = \frac12[/tex]

The y intercept can be easily read from the graph as and is -3

Answer:

Step-by-step explanation:

[tex]\sf (10-x)+(12-x)[/tex]

Simplify:-

[tex]\sf 10-x+12-x[/tex]

Combine like terms:-

[tex]\sf -x-x+10+12[/tex]

[tex]\sf (-x-x)=\bf -2x[/tex]

[tex]\sf (10+12)=\bf 22[/tex]

[tex]\sf -2x+22[/tex]

Hope this helps!

Have a great day!

The credit sale after state and local tax payable is 2562$.

Percentage is a measurement to find value of given number out of hundred.

Given that,

The credit sale before sales taxes = 2800$,

The rate of state sale tax = 6%,

And rate of local sale tax = 2.5%

The sale after state tax = 2800-2800×6/100=2800-168=2632,

The sale after local tax=2800-2800×2.5/100=2800-70=2730

The credit sale after state and local tax= 2800-168-70=2562.

The required credit sale =2562$.

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Answer:

s = 89°

Step-by-step explanation:

Exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles of the triangle.

[tex] \therefore[/tex]

[tex] \rm \implies (v + 1) \degree + (v - 28) \degree = (v + 32) \degree \\ \\ \rm \implies 2v - 27 \degree = (v + 32) \degree \\ \\ \rm \implies 2v -v = 32 \degree + 27 \degree \\ \\ \rm \implies v = 59 \degree [/tex]

Sum of angles in a straight line is equal to 180°

[tex] \therefore[/tex]

[tex]\rm \implies v + 32 \degree + s = 180 \degree \\ \\ \rm \implies 59 \degree + 32 \degree + s = 180 \degree \\ \\ \rm \implies s + 91 \degree = 180 \degree \\ \\ \rm \implies s = 180 \degree - 91 \degree \\ \\ \rm \implies s = 89 \degree[/tex]

Answer:

8.25 % I got this answer right.

The values that match the various trigonometric identity are;

1) sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀ = 1

2) cos 13 cos 47 + sin 13 sin 47 = 0.5

3) sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π = 0

Trigonometric identities are defined as the equations that involves the trigonometric functions that are true for every value of the variables involved.

1) We know that the trigonometric identity sin(A + B) is expressed as;

sin(A + B) = sinAcosB + cosAsinB

We are given;

sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀

Applying the trigonometric identity above, gives us;

sin(²/₅π + π/₁₀)

= sin(5π/10)

= sin(π/2)

= 1

2) We know that the trigonometric identity sin(A + B) is expressed as;

cos(A + B) = cosAcosB − sinAsinB.

We are given;

cos 13 cos 47 + sin 13 sin 47

Applying the trigonometric identity above, gives us;

cos(13 + 47)

= cos 60

= 0.5

3) We know that the trigonometric identity sin(A + B) is expressed as;

sin(A + B) = sinAcosB + cosAsinB

We are given;

sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π

Applying the trigonometric identity above, gives us;

sin(²/₅π + ⁸/₅π)

= sin(¹⁰/₅π)

= sin(2π)

= 0

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