Use a model to divide 1/3 divided 4

Answer:

x= 6

Step-by-step explanation:

3^3x = 9^9

3^3x = 3^(2×9)

3^3x = 3^18

3x = 18

3x/3 = 18/3

x = 6

Answer:

x = -91 8/35

Step-by-step explanation:

Challenging, but lets take it step by step.  We have two sets each  of complex fractions being multiplied, and then added.  As per PEDMAS, do the multiplication first and then add. [I changed the -71/7 as per your note in the comment section.]

[-7 1/7 * (3 2/5)]    +       [6 3/5*(-7 1/7)]     =  x

Convert the two numbers into fractions.  Eg., 7 1/7 becomes 50/7 and 3 2/5 becomes 17/5.  6 3/5 becomes 33/5 and 7 1/7 becomes 50/7.

[-50/7 * (17/5)]    +       [33/5*(-50/7)]     =  x

Now multiply the numerators and denominators.

[-850/35]    +       [-2343/35]     =  x

Now we can add the two fractions since they have the same denominator.

-(3193/35)  = x

x = -91 8/35

The value of 'x' in similar triangles is 6.9 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, A line segment parallel to one side of the triangle divides the other two sides in the ratio of their respective lengths.

Therefore, The ratio can be formed as,

13/5 = 18/x.

13x = 90.

x = 6.9 units.

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The solution of the equations 3y - 2x = 7 and y = 3x + 7 will be (-2, 1). Then the correct option is B.

The possible value of the variables that satisfy the equation which is known as the solution of the equation.

The equations are given below.

-2x + 3y = 7            ...1

y = 3x + 7               ...2

From equations 1 and 2, then we have

- 2x + 3(3x + 7) = 7

- 2x + 9x + 21 = 7

7x = - 14

x = - 2

Then the value of 'y' is given as,

y = 3(-2) + 7

y = - 6 + 7

y = 1

The solution of the equations 3y - 2x = 7 and y = 3x + 7 will be (-2, 1). Then the correct option is B.

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Using the relationship between speed, distance and time, Jen's average walking speed was approximately 1.75 meters per second over the 20-second window.

To find Jen's average walking speed, we need to first find the total distance that she walked in 20 seconds. We can do this by multiplying the number of strides she took by the distance of each stride, which is given as 140 cm.

From the graph provided, we can see that Jen took 25 strides in the 20-second window. Therefore, the total distance she walked is:

distance = number of strides * distance per stride = 25 * 140 cm = 3500 cm

To convert this to meters, we divide by 100:

distance = 3500 cm / 100 = 35 meters

Finally, we can find Jen's average walking speed by dividing the total distance by the time it took her to walk it, which is 20 seconds:

average speed = distance / time = 35 meters / 20 seconds ≈ 1.75 meters per second

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Answer: 1.33 m/s

Step-by-step explanation:

We need meters per second, not centimeters per second, so convert the stride of 140 cm to meters:

140 cm times 1 m/100 cm = 1.4 meters.

The number of pulses going above the dashed line for the 3 g threshold to

count as strides are 19. Therefore, a total assumed distance of $19 times 1.4 meters  is covered in 20 seconds, making the average speed

19 times 1.4/20 = 19 times 0.07 = 1.33m/s.

The fraction of nine times two thirds is 18/3 (option D)

What is fraction ?

A fraction is a way of representing a part of a whole or a ratio between two numbers. It consists of two numbers written one above the other and separated by a horizontal line called a fraction bar.

The number above the fraction bar is called the numerator, and it represents the part of the whole or the quantity being considered. The number below the fraction bar is called the denominator, and it represents the total number of equal parts into which the whole has been divided.

Given by the question:

Nine times two thirds can be written as:

9 × 2/3 = 18/3=6

Simplifying this fraction, we can divide both the numerator and denominator by their greatest common factor of 3, which gives:

18/3
so the correct option is D.

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Answer:

The answer is 4×7×8 units³

Step-by-step explanation:

This is a really easy question. All you have to do is take a look at the prism and you see the height of 4 units, the width of 8 units, and the length of 7 units. To find the volume of a cube you have to multiply the Length, Width, and Height. Therefore, 7×8×4. Also, it doesn't matter the order of the numbers to multiply. Hope this helps!!

The transformations from the parent cube root function to generate function g(x) are given as follows:

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

For this problem, the transformations are given as follows:

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Jimbo approximately 5.09 minutes to solve the problem by himself.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The amount of time it takes Jimbo to solve the problem by himself = x.

The amount of time Jimmy takes to solve the problem.

= 8 minutes

The amount of time it takes Jimmy to solve the problem by himself.

= 1/8

Jimbo and Jim Bob together can solve the problem in 6 minutes, so their combined rate of work is 1/6 of the problem per minute.

The amount of time it takes Jim Bon to solve the problem by himself.

= 1/14

Now,

We can make an equation:

1/8 + 1/x + 1/14 = 1/6

We can solve for x to find the amount of time it would take Jimbo to solve the problem by himself.

1/8 + 1/x + 1/14 = 1/6

Multiply both sides by 168x.

We get,

21x + 168 + 12x = 28x

33x = 168

x = 168/33

x = 5.09

Thus,

Jimbo approximately 5.09 minutes to solve the problem.

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The measure of angle ∠T found in the triangle  ΔRST found using the law of cosines is 127.3°.

What is meant by the law of cosines?

The law of cosines, commonly referred to as the cosine formula or cosine rule, is a relation in trigonometry that links the lengths of a triangle's sides to the cosine of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.

If ABC is a triangle, then as per the statement of the law of cosines,  we have:

c = [tex]\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}[/tex]

where,

c = length of side c

a = length of side a

b = length of side b

γ = angle opposite c

Given a  triangle,  ΔRST

The length of side r = 530 cm

The length of side s = 530 cm

The length of side t = 950 cm

According to the law of cosines,

t² =s² + r² - 2.s.r . cos T

950²  = 530² + 530² - 2 * 530 * 530  * cos T

902500  =  280900 + 280900 - 561800 * cos T

cos T = -0.6064

m∠T = 127.3°

Therefore the measure of angle ∠T found using the law of cosines is 127.3°.

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Mat must bowl 140 in the next game.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

Matt bowled games of 162, 170, and 148.

Average = 155

let the score on fourth game be x.

So, (162 + 170 + 148 + x)/4 = 155

480 + x= 620

x= 140

Thus, he must bowled 140.

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Answer:

We know that half of the choir members are women, which means:

Number of women = 80/2 = 40

We also know that the number of men is one-quarter of the number of women, which means:

Number of men = 40/4 = 10

Now, we're given that the ratio of children to men in the choir is n:1. Let's call the number of children in the choir "c".

So, we have:

c : 10 = n : 1

We can cross-multiply to get:

c = 10n

Since we know that the total number of people in the choir is 80, we can set up another equation:

40 (women) + 10 (men) + c (children) = 80

Substituting c = 10n, we get:

40 + 10 + 10n = 80

Simplifying the left side, we get:

50 + 10n = 80

Subtracting 50 from both sides, we get:

10n = 30

Dividing both sides by 10, we get:

n = 3

Therefore, the value of n is 3

The required expression is 30 - 10√5 which is in the form a + b√5, where a = 30 and b = -10.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

(5-√5)²

Expanding the above expression,

(5)² + (√5)² - 2 × 5 × √5

25 + 5 - 10√5

30 - 10√5

Compare the above expression to the form a + b√5, and we get

a = 30 and b = -10

Thus, the required expression is 30 - 10√5.

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Answer:

x=10,y= -2).

Step-by-step explanation:

The given system of equations is:

x = 10

3x + 5y = 20

We can use substitution to solve for y. Starting with the first equation:

x = 10

We can substitute the value of x into the second equation:

3x + 5y = 20

3 * 10 + 5y = 20

30 + 5y = 20

5y = 20 - 30

5y = -10

Finally, we can solve for y by dividing both sides of the equation by 5:

y = -10 / 5

y = -2

x=10,y= -2).

Nvm. I got it wrong me self. Srry:(

Ross achieved a higher sales target.

A fraction is a number which represents the part of a whole or collection of objects. It is in the from of [tex]\frac{a}{b}[/tex] where a represents the numerator part and the b represents the denominator parts.

A contact center provides incentives based on the number of sales achieved by its representatives.

Ross made 27 sales in 3 days.

Sales per one day =[tex]\frac{27}{3}=9.[/tex]

Mona secured 49 sales in one week

Sales per day =[tex]\frac{49}{7}=7[/tex]

Therefore, in one day sale of Ross is 9 and sale of Mona is 7.

Hence, Ross achieved a higher sales target.

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we can estimate that 762 adults in Eric's sample use their computer every day.

Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population.

We can use the proportion from the article to estimate the number of adults who use their computer every day in Eric's sample.

The proportion of adults who use their computer every day from the article is:

15/25 = 0.6

This means that 60% of adults use their computer every day.

To estimate the number of adults who use their computer every day in Eric's sample, we can multiply the proportion by the sample size:

0.6 x 1,270 = 762

So we can estimate that 762 adults in Eric's sample use their computer every day.

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Answer:

70

The top line should add up to 180 and both sides other than x are 55 so since 55+55=110  180-110=70

The function to represent a direct variation relationship between y and x is y = kx.

A direct variation relationship is one where the ratio of two quantities is always constant. In mathematical terms, if y varies directly with x, then there is a constant k such that y = kx.

Below is a function to represent a direct variation relationship between y and x:

y = kx

where k is the constant of proportionality.

A real world example of a direct variation relationship is the relationship between the distance traveled by a vehicle and the time it takes to travel that distance.

If a car travels at a constant speed, then the distance it travels is directly proportional to the time it takes to travel that distance. In mathematical terms, we can write:

distance = rate × time

where the constant of proportionality (rate) is the speed of the car.

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Answer:

Step-by-step explanation:

Change in demand refers to a shift in the entire demand curve, either to the right or to the left, resulting in a higher or lower demand for a good or service, respectively. It can be caused by a variety of factors, such as changes in consumer preferences, changes in the price of related goods, changes in income, changes in the population, or changes in consumer expectations.

Change in quantity demanded, on the other hand, refers to a movement along the demand curve, resulting from a change in the price of a good or service, without any change in the underlying demand for the good or service. For example, if the price of a good decreases, the quantity demanded of that good will increase, and vice versa. This relationship between price and quantity demanded is known as the law of demand.

In summary, change in demand represents a shift in the demand curve, while change in quantity demanded represents a movement along the demand curve.

Yes multiplying the matrices shows that it is inverse matrix

The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix.

Using multiplication of matrices product is sort as follows

Row 1 column 1

= 5 * - 5 + 2 * 13 = -25 + 26 = 1

Row 1 column 2

= 5 * -2 + 2 * 5 = -10 + 10 = 0

Row 2 column 1

= 13 * -5 + 5 * 13 = -65 + 65 = 0

Row 2 column 2

= 13 * 2 + 5 * -5 = 26 + -25 = 1

The identity matrix is

Row 1 column 1    Row 1 column 2           1      0

Row 2 column 1   Row 2 column 2           0      1

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Answer:

The marginal cost in this range is $0.50 per bouquet. This can be calculated by finding the difference in total cost of arranging 500 bouquets and 600 bouquets, which is $800, and dividing that by the difference in quantity of bouquets, which is 100. This gives a marginal cost of $0.50 per bouquet.

Answer:

Since the ratio of the altitudes of the two triangles ABC and DEF is 1:3, we can say that the altitude of triangle DEF is three times that of triangle ABC.

Let's assume the altitude of triangle ABC is h, then the altitude of triangle DEF is 3h.

Now, we know that the area of a triangle is given by the formula:

Area = (1/2) * base * height

Let's apply this formula to both triangles:

Area of triangle ABC = (1/2) * base * altitude

= (1/2) * 7cm * h

= 3.5h cm^2

Area of triangle DEF = (1/2) * base * altitude

= (1/2) * 7cm * 3h

= 10.5h cm^2

Since the two triangles are similar, their areas are proportional to the squares of their corresponding sides. That is:

Area of triangle ABC / Area of triangle DEF = (AB / DE)^2

Substituting the values, we get:

3.5h / 10.5h = (AB / DE)^2

1/3 = (AB / DE)^2

Taking the square root of both sides, we get:

AB / DE = 1 / sqrt(3)

AB = (1 / sqrt(3)) * DE

Now, we know that the sides of triangle ABC are 3cm, 5cm, and 7cm.

Let's assume that the sides of triangle DEF are a, b, and c.

Since the sides of the two triangles are proportional, we can write:

a / 3 = b / 5 = c / 7 = 1 / sqrt(3)

Solving for a, b, and c, we get:

a = 3 / sqrt(3) = sqrt(3) cm

b = 5 / sqrt(3) = (5 * sqrt(3)) / 3 cm

c = 7 / sqrt(3) = (7 * sqrt(3)) / sqrt(3) = 7 cm

Therefore, the measures of the sides of triangle DEF are sqrt(3) cm, (5 * sqrt(3)) / 3 cm, and 7 cm.

Answer:

Step-by-step explanation:

5 x 10^3 x 9 x 10^7 can be written as follows in standard form:

5 x 10^3 = 5 x 10^3 x 1 = 5 x 10^3

9 x 10^7 = 9 x 10^7 x 1 = 9 x 10^7

So,

5 x 10^3 x 9 x 10^7 = (5 x 10^3) x (9 x 10^7) = 45 x 10^(3 + 7) = 45 x 10^10 = 4.5 x 10^11

In standard form, the coefficient (45) is written as a number between 1 and 10, and the exponent (10) gives the number of places the decimal point must be moved. So, 4.5 x 10^11 is written in standard form as 4.5 x 10^11.

Answer:

Step-by-step explanation:

45*10^10=4.5*10^11

No, not all fixed costs are considered sunk costs. Sunk costs are costs that have already been incurred and cannot be recovered, regardless of any future actions.

Fixed costs, on the other hand, are costs that do not vary with changes in output or sales, such as rent or salaries. While some fixed costs may be sunk costs (such as a non-refundable deposit for a lease), other fixed costs may still be recoverable or avoidable with different decisions, and therefore are not considered sunk costs. Sunk costs are only relevant in decision making to the extent that they cannot be recovered and should not be factored into future decisions.

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The residual plot tell you about the line of best fit, the closer a data point's residual is to 0, the better the fit.

A residual value is a measure of how much a retrogression line vertically misses a data point. Retrogression lines are the stylish fit of a set of data. You can suppose of the lines as pars; a many data points will fit the line and others will miss.

A residual plot has the Residual Values on the perpendicular axis; the vertical axis displays the independent variable.

A residual plot is generally used to find problems with retrogression. Some data sets aren't good campaigners for retrogression, including

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Answer: 108 degrees.

Step-by-step explanation:

I think this is how you solve it:

A circle has a total of 360 degrees.

Having 5 equally placed sensors with a certain detection angle means that the sensors form a regular pentagon.

Finding the measure of the interior angles of a regular pentagon can be found using the formula

(180(n-2))/n, with n being the number of vertices of the polygon.

180(5-2)/5 ; 180(3)/5 ; 540/5 = 108

I think this means the detection angle is 108 degrees. Hope this helps!

If you get it wrong I'm terribly sorry T-T

Using the geometric mean theorem, the value of x is approximately 8.2.

The right triangle altitude theorem, also known as the geometric mean theorem, is a basic concept in geometry that connects the altitude of a right triangle to the two line segments it creates on the hypotenuse. According to the theorem, the altitude is equal to the geometric mean of the two line segments.

Using the theorem, we have:

14 = √(x * 24)

14² = 24x

196 = 24x

x = 196/24

x ≈ 8.2

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The required  ST² = TW × RT has been proven for the triangle RST where SW is perpendicular from vertex S to RT.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
For the triangle RST where SW is perpendicular from vertex S to RT

Rewrite the equation,
ST² = TW × RT
ST/TW = RT/ST

It implies triangle SWT is similar to triangle RST,

Where,

∠S = ∠W and ∠T = ∠T

So triangle SWT is similar to triangle RST, by AA postulate of similarity.

If triangles are similar,
ST/TW = RT/ST   [became valid statement]

ST² = TW × RT

Thus, ST² = TW × RT hence proved.

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The surface area of the given figure is 200 yd².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Representing the figure as three dimensional, this consists of two triangular bases and three rectangular faces.

Area of triangle = [tex]\frac{1}{2}[/tex] × base × height

                          = [tex]\frac{1}{2}[/tex] × 6 × 4

                          = 12 yards²

Area of two triangular faces = 12 × 2 = 24 yd²

Of the three rectangular faces, two of them have a length of 11 yd and width of 5 yd.

Area of a rectangle = Length × Width

Area of two rectangular faces = 2 × Length × Width

                                                  = 2 × 11 × 5

                                                  = 110 yd²

Area of the third rectangular face = 11 × 6 = 66 yd²

Total surface area = 24 yd² + 110 yd² + 66 yd²

                              = 200 yd²

Hence the total surface area is 200 yd².

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