I have attached the screen shot of the problem

The given expression is a logarithm expression. The value of the log expression is -112.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is log (³√c⁵)/(a⁷b⁸).

The value of log a = 7, log b = 11, log c = 15

Applying the quotient formula log(a/b) = log a - log b in the given expression:

= log (³√c⁵) - log (a⁷b⁸)

Again applying the product formula log (ab) = log a + log b:

= log (³√c⁵) - log (a⁷) - log b⁸

Apply the power rule log (a^b) = b log a:

= (5/3) log c - 7log a - 8log b

Now putting the value of log a = 7, log b = 11, log c = 15:

= (5/3) × 15 - 7 × 7 - 8 × 11

= 5×5 - 49 - 88

= -112

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The volume of a rectangular prism is, 108 unit³

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

A rectangular prism has a width of 2, a height of 9, and a depth of 6.

Now, We know that;

Volume of rectangular prism = Length × Width × Height

Substitute all the values, we get;

⇒ Volume of rectangular prism = Length × Width × Height

⇒ Volume of rectangular prism = 2 × 9 × 6

⇒ Volume of rectangular prism = 108 unit³

Thus, The volume of a rectangular prism = 108 unit³

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The end behavior of the polynomial is:

x → ∞, F(X) → ∞

x → -∞, F(X) →-∞

Then the correct option is C.

Here we have the polynomial:

F(x) = x³ + 2x² - 1

And we want to see which ones of the given statements are true. At the end of the answer you can see the graph of the function so you can know how it behaves.

There we can see that there is one relative maximum and one relative minimum, and that the end behavior is:

x → ∞, F(X) → ∞

x → -∞, F(X) →-∞

Then the only correct option is C.

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Answer:

$5.86

Step-by-step explanation:

The total was $36.31

We were given the price of 1, which was $1.15

$36.31-$1.15 = $35.16 remaining

Since the other 6 friends ordered the same meal, they would have paid the same price, so we would divide by 6

$35.16/6 = $5.86

Answer:VROOOOOOM

Step-by-step explanation:

E E E EE

Answer:

...............

Step-by-step explanation:

It will take 5 minutes to paint this cone

Since the area of the base of the cone is doubled, the new base area becomes 2 * 49π in² = 98π in².

The radius of the original cone can be found by using the formula for the area of a circle:

49π = πr^2

r = 7 in

The height of the new cone can be calculated using the same lateral height as the original cone:

h = 8 in

Using the formula for the volume of a cone, we can calculate the volume of the new cone:

V = (1/3)πr^2h = (1/3)π(7^2)(8) = (1/3)π(392)

The surface area of the original cone can be found using the formula for the surface area of a cone:

A = πr^2 + πrs

where s is the slant height of the cone.

s = √(r^2 + h^2) = √(7^2 + 8^2) = √(49 + 64) = √(113)

So, we have

A = πr^2 + πrs = π(7^2) + π(7)(√(113)) = 49π + 7π(√(113))

The surface area of the new cone can be found using the same formula:

A = πr^2 + πrs = π(7^2 * 2^2) + π(7 * 2)(√(113)) = 98π + 14π(√(113))

When the equations are compared, we have

2 * 49π + 7π(√(113)) = 98π + 14π(√(113))

Since the new cone has twice the surface area of the original cone and can be painted at the same rate,

It will take 2.5 * 2 = 5 minutes to paint this cone.

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Answer:

Step-by-step explanation:

I took the test the answer is 4.2

The dimensions of the original piece of rectangular cardboard are 22 in by 40 in

A prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

Given that, Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard, from which she cuts out 9-in squares from each corner. The length of the original piece of cardboard is 18 in more than the width, the volume of the box is 792 in³,

We know that volume of rectangular box = length × width × height

length = x+18-9-9 = x

height = 9

width = x-9-9 = x+18

= (x-18) × x × 9

(x-18)×9x = 792

9x²-162x-792 = 0

x²-18x-88 = 0

Factorizing to find the value of x,

x = 22 and x = -4

Therefore, width of the cardboard = 22 in

Length = 22+18 = 40 in

Hence, the dimensions of the original piece of rectangular cardboard are 22 in by 40 in

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Check the picture below.

Answer:

1.

x = 5√3

y = 10

2.

x = 2√33 in.

3.

y = 11√3

x = 22

4.

x = 7√2

5.

x = 3 m

6.

x = 16

y = 16√3

Step-by-step explanation:

Recall:

30-60-90 triangle ratio of sides:    1 : √3 : 2

45-45-90 triangle ratio of sides:    1 : 1 : √2

Pythagorean theorem: a² + b² = c²

1.

1 : √3 : 2

5 : x : y

1/5 = √3/x

x = 5√3

1/5 = 2/y

y = 10

2.

a² + b² = c²

8² + x² = 14²

64 + x² = 196

x² = 132

x = 2√33 in.

3.

1 : √3 : 2

11 :  y  : x

1/11 = √3/y

y = 11√3

1/11 = 2/x

x = 22

4.

1 : 1 : √2

7 : 7 : x

1/7 = √2/x

x = 7√2

5.

a² + b² = c²

x² + 4² = 5²

x² + 16 = 25

x² = 9

x = 3 m

6.

1 : √3 : 2

x :   y :  32

1/x = 2/32

2x = 32

x = 16

√3/y = 2/32

√3/y = 1/16

y = 16√3

The total number of pieces of pie they eat in all is (1 + b) pieces of pie

Number of pieces of pie eaten each = 1 piece

Number of friends= b

Total pieces of pie eaten by all = (Robert + Number of friends) × Number of pieces of pie eaten each

= (1 + b) × 1

= (1 + b) pieces of pie

Therefore, Robert and his friends are a total of (1 + b) pieces of pie.

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Answer:

  3.5%

Step-by-step explanation:

You want the percent error in a measured value of 4.16 g/cm³ in relation to a handbook value of 4.018 g/cm³.

The percentage error is calculated as ...

  % error = ((measured) - (actual))/actual × 100%

  = (4.16 -4.018)/4.018 × 100%

  = 0.142/4.018 × 100% ≈ 3.5%

The given numbers, 4.16 and 4.018 have 3 and 4 significant figures, respectively. Their difference will have 2 significant decimal places, as does 4.16, so should be considered to be 0.14. This value has 2 significant figures, so the final answer will have 2 significant figures.

You will note that we kept all of the digits available throughout the computation, rounding to 2 significant figures only at the end.

You will also note that taking differences of numbers of approximately the same value can result in a loss of significant figures.

Yes, the triangle can have the angle measures  31[tex]\frac{3}{4}[/tex]°, 53[tex]\frac{1}{2}[/tex]°, 94[tex]\frac{3}{4}[/tex]°.

And the first angle is 31[tex]\frac{3}{4}[/tex]°.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

The angle measures of the triangle,

= x,  53[tex]\frac{1}{2}[/tex]°, 94[tex]\frac{3}{4}[/tex]°

The angle measure of x = 180 -  53[tex]\frac{1}{2}[/tex]° - 94[tex]\frac{3}{4}[/tex]°

x = 31[tex]\frac{3}{4}[/tex]°

And, yes, the triangle can have the angle measures  31[tex]\frac{3}{4}[/tex]°, 53[tex]\frac{1}{2}[/tex]°, 94[tex]\frac{3}{4}[/tex]°.

Therefore, the first angle is 31[tex]\frac{3}{4}[/tex]°.

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The given equation would be, 5(6b-3) - 3b = 0 and b can take infinite number of values to make the equation true.

What equation system has an infinite number of solutions ?

The prerequisite for a situation in which an equation has an endless number of solutions is that the right and left sides of the equation are equal.

The equation is already complete and has infinitely many solutions.

The unknown variable is b, and there are an infinite number of values that b can take to make the equation true.

5(6b-3) - 3b = 0

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If George painted 1/5 of the room and Adam painted 0.35 of the room then the total percentage of the room painted by Adam and George collectively is 55%.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

The amount of room painted by George is = 1/5

The amount of room painted by George is = 0.35

Convert the fraction into percentage -

Percentage = 1/5 × 100

Percentage = 20%

Convert the decimal into percentage -

Percentage = 0.35 × 100

Percentage = 35%

The total percentage of room painted by George and Adam is -

Total % of room painted = % of room painted by George + % of room painted by Adam

Substitute the values into the equation -

Total % of room painted = 20 + 35

Total % of room painted = 55

Therefore, 55% of the room was painted.

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George and Adam painted the game room together. George painted 1/5 of the room, and Adam painted 0.35 of the room.

What is the total percentage of the room painted by Adam and George?

Answer:

40

Step-by-step explanation:

Assign the variable x to Devaughn's age. If Devaughn is 7 years older than Sydney, then Sydney must be 7 years younger than him, so the expression x - 7 can represent Sydney's age.

The sum of their ages would be x + x - 7 or 2x - 7 which is also said to equal  87. Therefore, this can be written as an equation and be solved accordingly:

2x - 7 = 87

2x = 94

x = 47

Therefore, Devaughn is 47 and Sydney, who is 7 years younger, is 40.

Sydney's age is determined by setting up and solving a simple algebraic equation based on the information provided. The equation that represents this situation is S + (S + 7) = 87, which leads to the conclusion that Sydney is 40 years old.

Devaughn is 7 years older than Sydney. Given that the sum of their ages is 87, we can represent this situation with algebra. Let's denote Sydney's age as S.

Considering Devaughn is 7 years older, we can represent his age as S + 7. Given that the sum of their ages is 87, we can write down this equation: S + (S + 7) = 87.

Solving this equation will help us find Sydney's age. First, simplify the left side: 2S + 7 = 87. Then, subtract 7 from both sides: 2S = 80. Finally, divide both sides by 2 to solve for S, yielding Sydney's age: S = 40.

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Answer:

[tex]22212[/tex].

Step-by-step explanation:

In base-10, for a number to be divisible by [tex]4[/tex], the last two digits must also be divisible. Among all the two-digit numbers formed with "[tex]\texttt{1}[/tex]" and "[tex]\texttt{2}[/tex]", only [tex]12[/tex] satisfies the requirements as the last two digits of [tex]N[/tex].

For a number to be divisible by [tex]9[/tex], the sum of all the digits must also be divisible. For [tex]N\!\![/tex] to be as small as possible, its digits should add up to the smallest multiple, [tex]1 \times 9 = 9[/tex], instead of larger ones such as [tex]18[/tex].

Since the last two digits of [tex]N[/tex] is [tex]\texttt{1}[/tex] and [tex]\texttt{2}[/tex], the other digits of [tex]N\![/tex] would need to add up to [tex]9 - 1 - 2 = 6[/tex]. To minimize the value of [tex]N\!\![/tex], these digits should consist solely of [tex]\texttt{2}[/tex]: [tex]2 + 2 + 2 = 6[/tex]. Therefore, the answer should be [tex]22212[/tex].

Answer:

But the 2lbs.

Step-by-step explanation:

Divide $9.19 by 2 and you get 4.595 which would be the cheapest option out of the 3 because the 1lb is $7.05 and the 3lb is $5.13.

You're welcome.

The inequality and graph of the solutions will be x + 0.80y ≤ 20 and any value on the line or below.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Dion is buying a balloon bouquet. His favorite colors are silver and purple. Silver balloons cost $1.00 and purple balloons cost $0.80.

Let 'x' be the number of silver balloons and 'y' be the number of purple balloons. And if he doesn't spend more than $20. Then the inequality is given as,

$1 x + $0.80 y ≤ $20

x + 0.80y ≤ 20

Take any value on the line or below.

The inequality and graph of the solutions will be x + 0.80y ≤ 20 and any value on the line or below.

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Answer:

√121 = 11

diffrence of 164 and 11 = 164 - 11 = 153

number = 153

The values of the ratios of the perimeters and areas of the red figure to the blue figure, which are similar figures, in the simplest form are:

The ratio of their perimeters:  28/16

The ratio of their areas:  (28)²/(16)²

What is the ratio?

A ratio is a relationship between two things when it is expressed in numbers or amounts.

The ratio of the perimeter of similar figures = a side length of one figure / corresponding side length of the other figure

The ratio of the areas of two similar figures = square of the length of one figure/square of the corresponding length of the other

Thus:

The side length of Red-figure = 28

The side length of the Blue figure = 16

Therefore:

The ratio of their perimeter = Side length of the red figure / Side length of the blue figure

The ratio of the perimeter of the red figure to the blue figure = 28/16

The ratio of their areas = Side length of the red figure / Side length of the blue figure

The ratio of the areas of the red figure to the blue figure = (28)²/(16)²

Hence, The values of the ratios of the perimeters and areas of the red figure to the blue figure, which are similar figures, in the simplest form are:

The ratio of their perimeters:  28/16

The ratio of their areas:  (28)²/(16)²

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The total number of outcomes is 24

If a fair 6-sided die is tossed 4 times in a row, there are 6 possible outcomes for each toss.

So, the number of possible outcomes would be:

6 + 6 + 6 + 6 or  6 * 4

Evaluate

Outcomes = 24

Each of the 4 tosses is independent, so there are 6 options for the result of each toss, and the total number of possible outcomes is obtained by adding the number of options for each toss as calculated above

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Answer:

184

Step-by-step explanation:

1. big rectangle area = 10*(6+5+5) =160

2. top & bottom triangle = (2*1/2 bottom * h)= 6*4 = 24

total 160 +24 =184

the Diagram that would support his plan to use ASA is either option A and Option B.

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

The Corresponding portions of Congruent triangles are the complete form of CPCT. Triangles may be shown to be congruent after which the final dimension can be anticipated without actually measuring the triangle's sides and angles. The following are many congruency rules.

Since All triangles given in the options are congruent we need to find which pair of triangles are supposed to be congruent by the property of ASA.

From ASA:

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and the side included between the angles of the second triangle.

Therefore, Either Option A or Option B is the Diagram that would be supportive of his intention to utilize ASA.

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Answer:  C. 120!

Step-by-step explanation:

Okay so, first we need to find out our percentages of course.
I learned this trick that can help us with this question easily!

14% of 500 - 70 - Drama
14 * 5 = 70.

22% of 500 - 110 - Sports
22 * 5 = 110

20% of 500 - 100 - Reality
20 * 5 = 100

20% of 500 - 100 - Sci-fi
20 * 5 = 100

70 + 110 + 100 + 100 = 380

500 - 380 = 120

Therefore, documentaries is labeled as 24% of 500 or 120 out of 500.

Your welcome! ^^

The  inequalities represent the possible lengths for the third side, x is 4 < x < 14, the correct option is D.

Inequality is defined as the relation which makes a non-equal comparison between two given functions. The set of values of the variable involved in the inequality for which the considered inequality holds true is called the solution set for that inequality.

Given;

One side of triangle =5

The other side of triangle=9

Now, the third side is between the difference and the sum of the other two sides;

9-5 < x < 9+5

4 < x < 14

Therefore, the inequality will be 4 < x < 14.

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1600 units were produced , If you spend $3000 on production cost.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The cost of producing X units of a product is 1.25. Per unit plus $1000 in flat production cost.

If you spend $3000 on production cost.

let, x units were produced.

so, we get,

1.25x+1000 = 3000

1.25x= 2000

x= 1600

Hence, 1600 units were produced , If you spend $3000 on production cost.

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The  value of the inequality is 1

In equality is a mathematical statement showing that two or more variables or quantities are not equal.

The given inequality is  6<2y+4

Making y the subject of the relation

6-4<2y

⇒2=2y

Making y the subject of the relation by dividing both sides by 2

therefore, y<1

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