2/9 • 3/1
Fraction and whole number multiplication! Image attached

Answer:

24

Step-by-step explanation:

4x6=24

Answer:

12:4 ratio simplified is 3:1

Step-by-step explanation:

The proportion is 2 : 3 and the scale model is represented by the Black tabletop color

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the scale of the color tabletop be represented as a : b

Now , the proportion will be

The scale model of the tabletop is given by A : B = 4 inches by 6 inches

So , the proportion is 4/6 = 2 : 3

And , the black tabletop has an original size of 32 inches by 48 inches

Substituting the values in the equation , we get

4 inches by 6 inches is proportional to 32 inches by 48 inches

On simplifying the equation , we get

4/6 = 32/48

2/3 = 16/24

2/3 = 8/12

2/3 = 2/3

Hence , the proportion is 2 : 3

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(-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is y < x+5

First, we have to find the x-intercept which occurs at y = 0

0 < x + 5

x<-5

For y-intercept,

y <  0+ 5

y <5

As a result, the obtained ordered pair is  (-5, 0 ) and (0, 5).

Hence, (-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5

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He travels a total distance of 296 Kilometers.

The amount of space between two locations is defined as distance. It is often measured in metres, kilometres, or miles. Distance may also refer to the length of time it takes to go from one location to another. The length of a path or the size of an item may be measured using distance. Distance may also be used to calculate an object's speed or the time it takes to go a specific distance.

Given :

miles = 185

Since , 5 miles = 8 kilometers

Therefore, on converting , 185 miles into kilometers , we get

185/5 = 37 kilometers

Also , it has given that 37 Km is exactly 8 times , thus

total distance = 37 * 8 = 296

Hence , he travels a total distance of 296 Kilometers.

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The midpoint rule is an overestimate.

This is because the midpoint rule is a form of numerical integration which approximates the area under a curve by summing the areas of rectangles that are divided into equal intervals. These rectangles are centered on the midpoints of the intervals.

Because the rectangles are centered on the midpoints instead of the endpoints of each interval, the midpoint rule overestimates the area under the curve as the rectangles are wider than the intervals.

This means that the midpoint rule produces a larger area than the exact area under the curve. This is why the midpoint rule is an overestimate.

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The midpoint rule is an overestimate of the definite integral. The midpoint rule is a numerical integration method used to approximate the definite integral of a function.

It works by dividing the interval of integration into smaller subintervals and approximating the integral by summing the areas of rectangles whose heights are determined by the function evaluated at the midpoint of each subinterval.

Since the rectangles in the midpoint rule are taller at the midpoint and shorter at the endpoints, this method generally overestimates the true area under the curve. However, if the function is well-behaved and the subintervals are small enough, the error between the midpoint rule approximation and the true definite integral can be made arbitrarily small.

In conclusion, the midpoint rule is an overestimate of the definite integral, but the error can be made small by using smaller subintervals.

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The lateral surface area of the cylinder for the given measurements is equal to 452.16 square inches.

Pipe is in form of cylinder

Diameter of the cylinder = 6 inches

Height of the cylinder 'h' = 24 inches

Radius of the cylinder 'r' = diameter / 2

                                        = 6/ 2

                                        = 3inches

lateral surface area of the cylinder = 2πrh

value of π = 3.14

Substitute the value we get,

⇒lateral surface area of the cylinder =  2 × π × 3 × 24

⇒lateral surface area of the cylinder = 144π square inches

⇒lateral surface area of the cylinder = 144 × 31.4

⇒ lateral surface area of the cylinder = 452.16 square inches

Therefore, the lateral surface area of the cylindrical pipe is equal to 452.16 square inches.

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Answer: 1  7/24

Step-by-step explanation:

The required unit rate is [tex]\frac{3}{4}[/tex] book/ hour

When two different types of quantities with various units are being compared, the ratio of rate is applied. On the other hand, the unit rate shows how many units of one quantity are equivalent to one unit of another. A unit rate is a ratio between two separate units with 1 as the denominator.

Here we have

1/4 book/ 1/3 hour  

We can convert the given fraction into a unit rate as given below

=> 1/4 book/ 1/3 hour  

=>  [tex]\frac{1}{4} \times (\frac{3}{1})[/tex]  book/ hour

=>  [tex]\frac{3}{4}[/tex] book/ hour

Therefore,

The required unit rate is [tex]\frac{3}{4}[/tex] book/ hour

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Answer:x = 1/60

Step-by-step explanation:

(8^x/4+4)=(8^-19x/4)

Apply fraction cross multiply: a/b = c/d  then a*d = c*b

8^x * 4 = (4+4) * 8^-19x

simplify

8^x * 4 = 8 * 8^-19x

Apply exponet rules

xln(8) + ln(4) = (-19x +1) ln(8)

then just solve

x= 1/60

while y = -1/8

By applying Algebraic fractions simplifying concept, it can conclude that the simplified expression is - (9p + 3) / q.

Algebraic fractions simplifying can be done by factoring the quantifier and denominator, then dividing by the common factors of the quantifier and denominator.

We have the following algebraic fraction:

((9p² - 1) / (pq - 2q)) / (1 - 3p) / (3p - 6)

To simplify this expression, we will do the following steps:

First, we apply the division rule: (a/b) / (c/d) = ad / bc:

    ((9p² - 1) / (pq - 2q)) / (1 - 3p) / (3p - 6)

⇔ ((9p² - 1) (3p - 6)) / ((pq - 2q) (1 - 3p))

Then we find the factors of (9p² - 1), that are (3p - 1) (3p + 1):

⇔ ((3p - 1) (3p + 1) (3p - 6)) / ((pq - 2q) (1 - 3p))

Factor other expressions that are not already factored in:

⇔ ((3p - 1) (3p + 1) 3 (p - 2)) / (q (p - 2) (1 - 3p))

Now we cancel the common factor (p - 2), so we have:

⇔ (3 (3p - 1) (3p + 1)) / (-q (3p - 1))

Then we cancel the common factor (3p -1), so we have:

⇔ (3 (3p + 1)) / -q

Finally, we expand the expression:

⇔ - (9p + 3) / q

Thus the simplified expression is - (9p + 3) / q.

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Answer: -0.26666666666

Step-by-step explanation:

The slope of a line containing the points 5,5 and -9,0 is 5/14.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

Given;

The two points 5,5 and -9,0

m= 0-5/-9-5

m=-5/-14

m=5/14

Therefore, the slope will be 5/14.

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It depends on the specific sequence of customer floors you're looking for. Without knowing that sequence, it's not possible to determine the number of floors that would make the probability of that sequence as large as possible.

In general, the probability of a specific sequence of customer floors will depend on several factors, such as the number of floors in the building, the number of customers, and the order in which they press the buttons.

To determine the number of floors that would maximize the probability of a specific sequence, you would need to know the details of the scenario and perform a more in-depth analysis.

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Given that the student did not pass the exam, the probability that they revised is 24%.

Probability refers to the likelihood, odds or chance of an expected outcome given many possible outcomes.

Probability is the quotient of expected outcomes over total outcomes.

The total number of students in the class = 33

The total number of students who revised = 19

The total number of students who revised and failed the exam = 8

The probability that the student revised but failed the exam = 8/33 = 24%

or (8/19 x 19/33)

Thus, the probability that a student chosen at random from the class revised but failed the exam is 24%.

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Answer:

Step-by-step explanation:

The first derivative of the given function y = 10x^9 + 25x^4 + 68 + 6 + 12x^4 is:

dy/dx = 90x^8 + 100x^3 + 48x^3

= 90x^8 + 148x^3

The second derivative of y = 10x^9 + 25x^4 + 68 + 6 + 12x^4 is:

d^2y/dx^2 = 720x^7 + 444x^2

The third derivative of y = 10x^9 + 25x^4 + 68 + 6 + 12x^4 is:

d^3y/dx^3 = 5040x^6 + 888x

The fourth derivative of y = 10x^9 + 25x^4 + 68 + 6 + 12x^4 is:

d^4y/dx^4 = 30240x^5 + 888

Answer:

y = 2x + 5

The slope: 2

Y-intercept: 5

Step-by-step explanation:

Slope-intercept form: y = mx + b

m = the slope

b = y-intercept

Our equation

-4x+2y=10

2y = 4x + 10

y = 2x + 5

The slope: 2

Y-intercept: 5

The length of AB is [tex]2\sqrt{105}[/tex].

An altitude is a line which passes through the vertex of the triangle and meets the opposite side at the right angle. A triangle has three altitudes.

Consider the triangle ABC, with right angle at B,

Let AB = x, BC = y, BD = z.

By pythagoras theorem,

[tex]AC^{2} =AB^{2} +BC^{2}[/tex]⇒[tex]x^{2} +y^{2} = 21^{2}[/tex]----------(1)

From triangle ADB,

[tex]z^{2} +11^{2} =x^{2}[/tex]-------(2)

[tex]z^{2} +10^{2} =y^{2}[/tex]--------(3)

(2)-(3), we get, [tex]x^{2} -y^{2} =21[/tex]-----(4)

subtract (1) and (4) we get,

[tex]x^{2} =420[/tex]

⇒[tex]x=2\sqrt{105}[/tex]

Hence, the length of AB is [tex]2\sqrt{105}[/tex] in simplest radical forms.

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Step-by-step explanation:

Come over here

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The growth factor is 0.85.

Let's call her initial screen time "x". After one week, her screen time was 884 minutes, which is 100% - 15% = 85% of her initial screen time.

So, 884 minutes = 0.85x

Dividing both sides by 0.85, we get:

x = 1040 minutes

So her initial screen time was 1040 minutes.

The growth factor from her initial screen time to her screen time one week later is:

884 minutes / 1040 minutes = 0.85

So, the growth factor is 0.85.

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1. A function that has a V-shaped graph that opens up or down is the absolute value function.

2. The lowest or highest point on the graph of an absolute value function is the vertex.

3. The line that divides the graph of an absolute value function into two sections that are reflections of each other is the line of symmetry.

The absolute value function of vertex (h,k) is given by the equation presented as follows:

y = |x - h| + k.

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The area of the parallelogram is 416.25 cm²

The area of a parallelogram refers to the total number of unit squares that can fit into it and it is measured in square units (like cm², m², in², etc). It is the region enclosed or encompassed by a parallelogram in two-dimensional space.

Given here: The height = 18.25 ft and base=22.5 ft.

Thus the area of the parallelogram is

A=18.25×22.5

A=416.25 cm²

Thus the area of the parallelogram is 416.25 cm²

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The raise amount if the performance of the employee is adequate, would be $ 0. 53

To find the raise amount when the performance by an employee for the period is adequate, the formula is:

= Current pay per hour x Raise percentage for adequate work

Current pay per hour = $ 10. 60 per hour

Raise percentage for adequate work = 5 %

The raise amount is therefore :

= 10. 60 x 5 %

= 10. 60 x 0. 05

= $ 0. 53

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Answer:

your profit is 400

Step-by-step explanation:

50×225

By applying Fundamental counting principle, it can be concluded that there are 2560 different shoe combinations that can be created.

Fundamental counting principle states that if the first event can be done in k₁ different ways, the second event can be done in k₂ different ways, and so on until the [tex]n^{th}[/tex] event, then the number of different ways of all these events is K, where:

K = k₁ x k₂x . . . x kₙ

The following table shows the design components and how many options Lamar has for each:

Design component      Number of options

   Primary color                        8

 Secondary color                     8

      Sole color                           8

      Lace color                          5

Then we can calculate the number of different combinations that can be created as follows:

Number of combinations = number of option₁ x number of option₂ x

                                             number of option₃ x number of option₄

                                          = 8 x 8 x 8 x 5

                                          = 2560

Thus there are 2560 different shoe combinations that can be created.

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Answer: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80…

Step-by-step explanation:

The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80… and so on. It is a sequence where the difference between each next number and the preceding number, i.e. two consecutive results, is 8.

Answer:

371.54 sqr units

Step-by-step explanation:

area of a circle=πr²

area of inner circle=3.142×8×8=201.088 square units.

area of outer circle = 3.142×13.5×13.5=572.6295 square units

572.6295-201.088=371.5415 square units

=371.54 sqr units

Answer:

0.24

Step-by-step explanation:

4.96÷20=0.248

Round to the nearest cent: 0.24

The value of 'x' in the linear pair of angles is 126°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We know the sum of linear pair of angles is 180°.

Therefore, From the given information

(x - 6)° + 60° = 180°.

x + 54° = 180°.

x = 180° - 54°.

x = 126°.

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