Multiply. Write your answer as a fraction in simplest form.
8/15(−2/3)=

Answer:

Total pages read = 279 pages

Step-by-step explanation:

Let L, D, and M stand for the pages read by Luis, Dayja, and Michael, respectively.

We learn that:

L = 1.75D,            [Luis read 75% more pages than Dayja]

D = 1.75M, and    [Dayja read 75% more pages than Michael]

D = 84                  [Dayja read 84 pages]

We want the sum of L, D, and M

Total pages = L + D + M

We have three equations and 3 unknowns.  We should be able to find a solution by rearranging and substituting.

Total pages = L + D + M

We can substitute L=1.7D and rearrange D = 1.75 M to M = D/1.75

Total pages = L + D + M

Total pages = 1.7D + D + D/1.75

Total pages = D(1.7 + 1 + 1/1.75)  [Isolate the D, for optional simplification]

Total pages = D(3.271)

We know D = 84, so:

Total pages = 84(3.271)

Total pages = 274.8

We'll round that to 275 pages.

Check:

L = 1.75D:  L read 1.75*275 or 147 pages

D read 84 pages

D = 1.75M, or M = D/1.75;  M read 84/1.75) or 48 pages

Total pages read = 147 + 84 + 48

Total pages read = 279 pages

ΔABC; AB = 3, ∠CBA = 100°, ∠CAB = 40°

ΔABC; AB = 3, ∠ABC = 100°, ∠BCA = 40°

Given,

Select all the unique triangles that can be drawn to only have angle measures 40° and 100° and side length 3.

What are unique triangles?

Unique triangles are triangles that are different based on their configuration, which derives from the positioning of the given parameters to correspond with different congruency requirement.

The conditions for the congruency of two triangles are;

SSS: The Side-Side-Side rule; two triangles are congruent if all three sides of one triangle are congruent to the three sides of the other triangle

SAS: The Side-Angle-Side rule; two triangles are congruent if two sides and the included angle of one are congruent to two sides and an included angle in the other triangle

ASA: The Angle-Side-Angle rule; two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and an included side of the other triangle

SAA: The Side-Angle-Angle rule; Two triangles are congruent if two angles and an a non included side of one triangle are congruent to two angles and the non included side of the other triangle.

The configuration of the unique triangles can therefore, be ASA and SAA, which gives the triangles;

ΔABC; AB = 3, ∠CBA = 100°, ∠CAB = 40°

ΔABC; AB = 3, ∠ABC = 100°, ∠BCA = 40°

Please see attached drawings of the two unique triangles

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Answer:

t = 192

Step-by-step explanation:

1/4t = 1/3t + (-16)

  1            1

-------t = -------t - 16

  4           3

  1(3)        1(4)

-------t = -------t - 16

  4(3)      3(4)

  3           4

-------t = -------t - 16

  12         12

  3           4

-------t = -------t - 16(12)

(   12         12 ) 12

3t = 4t - 192

-4t   -4t

---------------------

-t = -192

÷-1  ÷-1

---------------

t = 192

I hope this helps!

Answer:

Step-by-step explanation:

So she needs 2580 points

she has already earned 480, so let's subtract that

that leaves up with 2100 more points

she earns 60 points every shop

so lets divide 2100 by 60

2100÷60=

35

Answer:

43 total ,35 more times need to get 2,580

Step-by-step explanation:

2580:60=43

60x8=480

43-8=35

After subtraction we can see Stephanie has only 1 pizzas left.

What is subtraction?

The definition of subtraction is subtracting one number or amount from another. It is addition's opposite operation. Subtraction subtracts a number from another to find the difference, whereas addition adds or groups numbers to find the sum. The word "subtract" can also mean to compare two values to determine how many factors account for a value's difference from another. That is the most fundamental concept behind the term "difference" for the solution to a subtraction problem.

We are given that,

Stephanie has 5 pizzas, Also she shared 4 of the pizzas with her friends

Hence she is left with 5-4= 1 pizza
Hence Stephanie has left with 1 pizza

Therefore the correct option is option D)
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Based on the lengths of the sides of the triangle, we can infer that this is NOT a right triangle.

A right angled triangle would obey the Pythagoras Rule which is that the square of the hypotenuse (longest side) will be the sum of the squares of the other sides of the triangle.

This means that for this to be a right triangle, it needs to obey the function:

45 ² = 35 ² + 30 ²

Solving gives:

2,025 ≠ 2, 125

This shows that the triangle is not a right triangle.

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It is not a right-angle triangle since 2125 ≠ 2025 meant that it did not conform to Pythagoras' theorem's specifications.

This kind of query creates a right-angled triangle that Pythagoras' theorem can resolve.

In a right-angled triangle, the square of the greatest side is equal to the sum of the squares of the smaller two sides.

Given, There are three sides to a triangle, each measuring 30 kilometers, 35 kilometers, and 45 kilometers.

∴ 30² + 35² = 45².

900 + 1225 = 2025.

2125 ≠ 2025.

Due to the fact that it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.

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The probability that you will be satisfied with 3 or more of the purchased products is 0.916

Given that,

The chance of being pleased with an internet purchase is 0.555. if you purchase 8 items online

Solution -

let  X denote the no of success of

Purchased product online

X ~ B(n,p)

n = 8

P= 0. 555

a = 1 - 0 .555 = 0.445

P ( X = x) = [tex]nc_{x} b^{x} a^{n-x}[/tex]

P ( X = x)= [tex]8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]

P ( X>=3)= [tex]\lim_{3 \to 8} 8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]

P ( X>=3)) = 0.91614

                 =0.916

Therefore we can conclude the probability that you will be satisfied with 3 or more of the purchased products is 0.916

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Answer:

Increase by 3.

Step-by-step explanation:

4 x 21 = 84

84 x 2 = 168

Begin to try numbers.

5 x 22 = 110

6 x 23 = 138

7 x 24 = 168

7 - 4 = 3

24 - 21 = 3

Increase each side by 3 ft. for a total dimension of 7 ft. x 24 ft.

The expression -3.1^4x * -3.1^2x + 7 has an equivalent of 887.503681x^2 + 7

From the question, the expression is given as

-3.1^4x * -3.1^2x + 7

Evaluate the exponents in the above expression

So, we have the following equation

-3.1^4x * -3.1^2x + 7 = 92.3521x * 9.61x + 7

Evaluate the products in the above expression

So, we have the following equation

-3.1^4x * -3.1^2x + 7 = 887.503681x^2 + 7

Hence, the equivalent expression of -3.1^4x * -3.1^2x + 7 is 887.503681x^2 + 7

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Answer:

9*X+5*3.25

Step-by-step explanation:

So, total 9 person; 4 person have their own shoe.

Cost for game = 9*X;

Cost for shoe = 5*3.25;

So the total cost = 9*X+5*3.25

Answer:

x = 10

Step-by-step explanation:

(5x + 3) and 53 are corresponding angles and are congruent , then

5x + 3 = 53 ( subtract 3 from both sides )

5x = 50 ( divide both sides by 5 )

x = 10

The value of 'x' is highlighted in the box

The function that could represent g(x) is (c) g(x) = f(x) - 5

The figure of the graph that completes the question is added as an attachment

From the attached graph,  we have the equation of the function to be

y = f(x)

Also, the graph of the function f(x) has its intercept to be

y-intercept of f(x) = 3

From the question, we have

y-intercept of g(x) = -2

Subtract the intercepts

Difference = y-intercept of g(x) - y-intercept of f(x)

So, we have

Difference = -2 - 3

Evaluate

Difference = -5

The function g(x) is then represented as

g(x) = f(x) + Difference

So, we have

g(x) = f(x) - 5

Hence, the function g(x) is g(x) = f(x) - 5

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The following table justifies the reasons of each step of the solution by stating the algebraic property that is used to get to each steps

Algebraic equations are defined as mathematical statements in which two algebraic expressions are set equal to each other. An algebraic expression usually consists of a variable, a coefficients and a constants.

          Statement                                                           Reason

4.5(8-x)+36=102-2.5(3x+24)                                           Given

4.5(8-x)=66-2.5(3x+24)                           Subtracting 36 from the both sides

36-4.5x=66-7.5x-60                       Opening the brackets on the both sides

36-4.5x=-7.5x+6                                       Subtracting the constants on RHS

36+3x=6                                                         Adding -7.5x on the both sides

3x=-30                                                    Subtracting 36 from the both sides.

x=-10                                                             Dividing by 3 on the both sides.

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Answer:

Choice B.

Explanation:

The side length is the distance between the vertices of the triangle given.

Explanation

From the given question

We are given the formula to compute the amount that a sum of $8000 compounded quarterly will yield after time t at a rate of 2.8%

The formula is given by

Part A

part B

the amount in the account after 7 years will be

The amount that will be in the account after 7 years will be $9725.57

Part C

APY is given by

In our case we have

Hence, we will have the APY as

Hence, the APY is 2.829%

a) The price (amount) of the house after 1 month = $9540

b) The price (amount) of the house after 3 months  = $10719.14

c) The price (amount) of the house after 10 months = $16117.629

a ) How to find the rental price of the house after 1 month ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 1

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100}) \\\\= 9000(\frac{106}{100})\\\\= 90*106\\\\= 9540[/tex]

The rental price of the house after 1 month = $9540

b ) How to find the rental price of the house after 3 months ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 3

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^3 \\\\= 9000(\frac{106}{100})^3\\\\= 9000*(1.06)^3\\\\= 10719.14[/tex]

The rental price of the house after 3 months = $10719.14

c ) How to find the rental price of the house after 10 months ?

The rental price of a dacha =Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 10

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^{10} \\\\= 9000(\frac{106}{100})^{10}\\\\= 9000*(1.06)^{10}\\\\= 9000*1.790\\\\= 16117.629[/tex]

The rental price of the house after 10 months = $16117.629

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The required inclination of the tower of Pisa as 85.95°.

Given that,
in Italy the leaning Tower of Pisa currently leans at 13 ft. off the vertical. the tower is 183 ft tall. what is the angle of inclination is to be determiend.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
base length is 13 ft,
Hypotenuse length of the tower = 183
According to the question,
Cosx = 13/ 183
x = 85.98°

Thus, the required inclination of the tower of pisa as 85.95°.

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Answer:

Yes 12 is an Integer

Step-by-step explanation:

12 is a whole number that can be written without a fractional component, thus 12 is an integer.

As both the width and height of the new image are 35% of the width and height of the original image, the aspect ratio is maintained and the new image is similar to the original image.

A scale factor is defined as the ratio of an object's original scale to that of a new one, considering the different depictions of that object (bigger or smaller)

Given:

The dimensions of the original image are a width of 300 pixels and a height of 450 pixels.

The dimensions of the New image have 35% width and 35% height.

Width = 0.35 × 300 = 105

Height = 0.35 × 450 = 157.5

Scale factor = New Dimension/Original Dimension

Scale factor of Height = 157.5/450 = 0.35

Scale factor of width =  105/300 = 0.35

Therefore, the new image is neither scaled down nor scaled up and is the same as the original image.

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Answer:

-4

Step-by-step explanation:

6 + 4x-y = 6 + (4x-y) = 6 + (-10) = -4

Answer:

X' = (-12,3)

Y' = (-10,5)
Z' = (-9,-2)

Explaination:

Please check image

Based off the x = -4 , I think that means that our x axis is no longer x = 0 but on the x = -4 line

Ex;

if point X is 8 units to the left of x=0, now point X' should be 8 units to the left of x=-4 making point X' = (-12,3)

Answer: 3/5 cm

Step-by-step explanation:

Let the length of the base be x. Then, using the formula for the area of a triangle,

[tex]\frac{3}{25}=\frac{1}{2} \cdot \frac{2}{5} x\\\\\frac{3}{25}=\frac{1}{5}x\\\\x=\frac{3}{5}[/tex]

Squares are the numbers that are produced when a value is multiplied by itself.

If expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex] then the value exists [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex].

The radical symbol for the number's root is "√" in this instance. The square of the positive number is represented by multiplying it by itself.

Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root exists a value that, when multiplied by itself, returns the original value.

The original number can be attained by multiplying the square root of an integer by itself.

Only a perfect square number can have a perfect square root. Even perfect squares have an even square root. An odd perfect square will contain an odd square root. A perfect square cannot be negative and hence the square root of a negative number exists not defined.

Let the expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

Now, [tex]$\sqrt{8}=\sqrt{2 \times 2 \times 2}=2 \sqrt{2}$[/tex]

[tex]$\sqrt{28}=\sqrt{2 \times 2 \times 7}=2 \sqrt{7}$[/tex]

therefore [tex]9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

simplifying the given expression, we get

[tex]$=9 \sqrt{2}-3 \sqrt{7}+2 \sqrt{2}-2 \sqrt{7}$[/tex]

[tex]$=9 \sqrt{2}+2 \sqrt{2}-3 \sqrt{7}-2 \sqrt{7}$[/tex]

[tex]$=11 \sqrt{2}-5 \sqrt{7}$[/tex]

Therefore, the correct answer is option a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]

The complete question is:

Simplify [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]

a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]

b) [tex]$11 \sqrt{4}-5 \sqrt{14}$[/tex]

c) [tex]$6 \sqrt{5}$[/tex]

d) [tex]$6 \sqrt{9}$[/tex]

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2. >>>>>>>b {18x,-x,21x} is an example of like terms because they both hold the same variables.

4.>>>>>>

[tex] = - 7(2x - 3) \\ = - 7(2x) - 7( - 3) \\ = - 14x + 21[/tex]

ATTACHED IS THE SOLUTION

We have

tennis racket price $54

Firs we need to obtain the 30 %

54*.30=16.2

then in order to know the sale price we need to substract the 30% of the original price

54-16.2=37.8

the sale price is $37.8

we have

1 cubic meter = 1000 L

x cubic meter = 415 L

then:

The volume of a cube with length x is:

answer: The smallest possible inside length of the tank is 0.746 m

Answer:equal

Step-by-step explanation: no number but equal as it is tossed 4 times

Answer:

16

Step-by-step explanation:

The number of possible outcomes at each coin toss = 2.

The total number of possible outcomes after 4 times = 2⁴ = 16.

The empirical rule state that, for normally distributed data, almost all of the data fall within three standard deviations either side of the mean. Specifically,

-68% of data within 1 standard deviation.

-95% of data within 2 standard deviation

-99.7 of data within 3 standard deviation.

In our case the mean is

and the standard deviation is

then, the empirical formula imply that

and

then, the answer is 14 minutes to 34 minutes

Answer:

D

Step-by-step explanation:

The number of times for which the train must be used so that the monthly cost without the pass is same as with the pass is; 6.25 times.

It follows from the task content that the regular train ticket costs, 3.00.

Therefore, the cost for travelling x times with the month is; 3x.

On this note, for the total monthly cost without the pass to be same as that with the pass; the equation which must hold is;

3x = 18.75

x = 18.75/3

x = 6.25 times.

Therefore, after taking the train 6.25 times, the cost without the pass is same as that with the pass.

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