factorise (x - 2y)2 -5(x - 2y) + 6
​

Answer:

15 pieces

Step-by-step explanation:

First, 4 goes into twelve 3 times. since it goes in three times, and you have 5 rolls, you would just multiply the two together.

3*5 = 15 pieces

Question #1

First we have to convert feet to inches.

Knowing that 1 foot is 12 inches we just need to multiply our values by 12.

Meaning that 12 feet of a roll of ribbon is basically 144 inches.

That isn't our final answer because he has 5 rolls so we multiply our answer by 5.

12×12 = 144  ← how many inches are in a single roll

144×5 = 720 So in total there are 720 inches in total.

Question #2

Now that we answered one of the questions we can use this information to answer the other question asking us how many 4 inch pieces can he make from the 5 rolls.

As mentioned above we know the 5 rolls are equivalent to 720 inches..

So we will take that number and divide it by 4.

720÷4  = 180

Meaning that 180 4-inch pieces can be made.

Statement

Therefore the dressmaker has 720 inches of ribbon and with that is able to make 180 4 inch pieces from it.

The probability that the T-shirt John picks is dark blue is 2/3.

To find the probability that John picks a dark blue T-shirt, we'll need to consider the total number of blue T-shirts and the number of dark blue T-shirts.
Determine the total number of blue T-shirts.
John has 2 dark blue and 1 light blue T-shirt, so he has a total of 2 + 1 = 3 blue T-shirts.
Determine the number of dark blue T-shirts.
John has 2 dark blue T-shirts.
Calculate the probability.
The probability that John picks a dark blue T-shirt is the number of dark blue T-shirts divided by the total number of blue T-shirts.
Probability = (Number of dark blue T-shirts) / (Total number of blue T-shirts) = 2 / 3.

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Answer:

PLEASE MARK ME BRAINLIEST!!!

Step-by-step explanation:

moddedcraftxdepic

02/28/2021

Mathematics

High School

answered

Y= x^3 + 8x^2 +5x

work out the coordinates of the two turning points 1  

Answer:

Step-by-step explanation:

tan29=32/x

x=32/(tan29)

x=58m

So the boat is 58 meters from the base of the lighthouse.

Step-by-step explanation:

mark as BRAINLY

thanks.............

Answer:

WX = 7.9

Step-by-step explanation:

By applying tangent rule (law of tan) in the given right triangle WXY.

tan(W) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(27)° = \(\frac{\text{XY}}{\text{WX}}\)

0.509525 = \(\frac{4}{\text{WX}}\)

WX = \(\frac{4}{0.509525}\)

WX = 7.85

WX ≈ 7.9

Therefore, length of side WX is 7.9 units.

Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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Answer:

Explanation:

C ∝ √y

C = k√y

If C = 12.8, y = 16

12.8 = k√16

12.8 = k(4)

k = 3.2

So the expression:

C = 3.2√y

solve for C when y = 400

C  = 3.2(√400)

C = 3.2(20)

C = 64

The expression for C in terms of y where C is directly proportional to the square root of y is C=3.2√y and the value of C at y=400 is 64.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

\(p = kq\)

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

\(p \propto q\) where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

C is directly proportional to the square root of y. Thus, the relation can be represented with the proportionality sign as,

\(C\propto \sqrt{y}\)

Let k is the proportionality constant. Thus, the equation can be rewritten as,

\(C=k \sqrt{y}\)

Here, the value of  C is 12.8 and the value of y is 16. Put these values in the above equation as,

\(12.8=k \times\sqrt{16}\\12.8=k \times4\\k=\dfrac{12.8}{4}\\k=3.2\)

Thus, the value of constant is 3.2.

The value of constant is 3.2. Thus, the expression for C in terms of y is given as,

\(C=3.2\sqrt{y}\)

Put the value of y =400 in the above expression.

\(C=3.2\sqrt{400}\\C=3.2\times20\\C=64\)

Thus, the expression for C in terms of y where C is directly proportional to the square root of y is C=3.2√y and the value of C at y=400 is 64.

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Step-by-step explanation:

100*77+72/4

100*77+18

7700+18

7718

Answer:

Step-by-step explanation:

54 ×100=5400

5400+77=5477

5477÷2 = 2738.5

To calculate the car's efficiency in miles per gallon, we need to convert the fuel consumption rate from liters per 100 kilometers to gallons per mile using the given conversion factors. Answer : 19.7 miles per gallon.

1. Start with the fuel consumption rate of the car, which is 12 liters per 100 kilometers.

2. Convert liters to gallons using the conversion factor 1 gallon = 3.7854 liters.

  - Divide 12 liters by 3.7854 to get the fuel consumption rate in gallons: 12/3.7854 = 3.17 gallons.

3. Convert kilometers to miles using the conversion factor 1 mile = 1.6 kilometers.

  - Divide 100 kilometers by 1.6 to get the distance in miles: 100/1.6 = 62.5 miles.

4. Calculate the car's efficiency in miles per gallon by dividing the distance in miles by the fuel consumption in gallons.

  - Divide 62.5 miles by 3.17 gallons to get the efficiency: 62.5/3.17 ≈ 19.7 miles per gallon.

In summary, the car's efficiency is approximately 19.7 miles per gallon. This means that the car can travel approximately 19.7 miles on one gallon of gasoline.

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Answer:

N because it is in the center of k h and I

Answer:

m∠KHI=105°

Step-by-step explanation:

m∠EHG = 105°

∴m∠KHI = 105°(vertically opposite angles)

hope it helps you!

Explanation:

The word "increased" tells us to add a specific number to the addend. Let us take an example to understand the word "increased".

Example: 3 is increased by 4.

⇒ 3 + 4

Notice that the addend (3) is being increased (+) by 4.

Answer:

0.9

Step-by-step explanation:

In order to get halfway between -0.5 and 2.3, first, we need to take their sum:

Sum of digits

Sum =  \({-0.5+2.3}\)

Sum =  \(1.8\)

Take the average of the sum

Average = \(\frac{1.8}{2} = 0.9\)

Hence the halfway between the numbers is 0.9

The peak is at y = 24 feet, the vertex point (h, k) is (16, 24). Plugging these values into the equation, we get:

y = |x - 16| + 24

This equation models the roof line of Terry's house.

To model the roof line of Terry's house, we can use the concept of absolute value. The equation for an absolute value function can be written as:

y = |x - h| + k

where (h, k) represents the vertex of the absolute value graph.

In this case, the peak of the roof line is at 24 feet. Since the width of the house is 32 feet, the vertex of the absolute value graph will be at the midpoint of the width, which is 16 feet. Therefore, h = 16.

Since the peak is at y = 24 feet, the vertex point (h, k) is (16, 24). Plugging these values into the equation, we get:

y = |x - 16| + 24

This equation models the roof line of Terry's house.

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On solving the provided question, we can say that - the volume of the cylinder will be V = 3.14 * 20*20*50 = 62800

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle. Diameter

volume of the cylinder -

V = \(\pi r^2h\)

r = 40/2 = 20

h = 50

V = 3.14 * 20*20*50 = 62800

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The temperature of the steam is 441.7 K.

A 1-m³ tank contains 2.1085 kg of steam at 0.6 MPa.

The gas constant, critical pressure, and critical temperature of steam are

R = 0.4615 kPa.m³/kg.K,

TCr = 647.1 K, and

PCr = 22.06 MPa.

Using data from the steam tables, let's find the temperature of the steam.

According to the steam table, the specific volume of the steam is 0.194 m³/kg at 0.6 MPa and 393.71 K. Since 1 m³ tank contains 2.1085 kg of steam, the total volume of steam is:

V = m/v

= (2.1085 kg)/(0.194 m³/kg)

= 10.8665 m³

The ideal gas equation of state is:

Pv = mRTor

T = PV/mR

Substituting the values we get:

T = (0.6 MPa)(10.8665 m³)/(2.1085 kg)(0.4615 kPa.m³/kg.K)

T = 441.7 K

Therefore, the temperature of the steam is 441.7 K.

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The radius r that produces the minimum surface area is 1.06 cm and the height h is 1.41 cm.

Let r be the radius of the cylinder and h be the height. You can find the equation for the volume of a solid by adding the volumes of the two hemispheres and the cylinder.

Volume = \((2/3)πr^3 + πr^2h\) = 10 cubic centimeters

Now let's find the values ​​of r and h that minimize the surface area of ​​the solid. This area consists of three parts:

Curved surfaces of two hemispheres and sides of a cylinder. This can be expressed as:

surface area = \(2πr^2 + 2πrh\)

To find the values ​​of r and h that minimize this expression, we can use the Lagrangian multiplier method. Given that the volume of the solid is 10 cubic centimeters, we want to minimize the surface area. So it looks like this:

\(f(r, h) = 2πr^2 + 2πrh + λ[(2/3)πr^3 + πr^2h - 10]\)

Taking the partial derivatives for r, h, and λ and setting them to zero gives

\(4πr + 2πh = 2πr^2λ + (4/3)πr^3λ\)

\(2πr = πr^2λ + πrhλ\)

Solving these equations simultaneously gives:

h = 4r/3

λ = 2/(3r)

Substituting these values ​​into the volume equation gives:

\(r^2h = 5/3\)

Substituting h = 4r/3 from above, we get:

\(r^3 = 15/8pi\)

Taking the cube root of both sides gives:

r=1.06cm

Substituting this value for r into the formula for h yields:

h=1.41cm

Therefore, the radius r that produces the minimum surface area is about 1.06 cm and the height h is about 1.41 cm.

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Ensuring that data is collected the same way each time it is collected is an example of data consistency.

Therefore, ensuring that data is collected the same way each time it is collected is an example of data consistency.

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The value of "m" represents the length of side G F in the kite F G H K. The value of "m" is 3.5. Given that sides G F and F K are congruent, we can conclude that their lengths are equal.

We are given that the length of side G H is 5 m 1 and the length of side H K is 3 m 7.

To find the value of "m," we need to find the length of side G F.

Since G F and F K are congruent, we can set up an equation:

5 m 1 = 3 m 7

To solve for "m," we need to subtract 3 m from both sides of the equation:

5 m - 3 m = 3 m - 3 m + 7

This simplifies to:

2 m = 7

Now, we can solve for "m" by dividing both sides of the equation by 2:

m = 7 ÷ 2

m = 3.5

Therefore, the value of "m" is 3.5.

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The area lying outside r=4sinθ and inside r=2 2sinθ is π.

To find the area lying outside r=4sinθ and inside r=2 2sinθ, we need to find the area enclosed by both the curves and then subtract the area enclosed by the inner curve from it.

The curves intersect at θ = 0 and θ = π.

The equation for the inner curve is r = 2 2sinθ, and the equation for the outer curve is r = 4sinθ.

The area enclosed by both the curves is given by:

A1 = ∫[0,π] 1/2 (4sinθ)^2 dθ - ∫[0,π] 1/2 (2 2sinθ)^2 dθ

Simplifying this expression, we get:

A1 = 8∫[0,π] sin^2θ dθ - 2∫[0,π] sin^2θ dθ

A1 = 6∫[0,π] sin^2θ dθ

Using the trigonometric identity sin^2θ = 1/2 (1-cos2θ), we get:

A1 = 6∫[0,π] 1/2 (1-cos2θ) dθ

A1 = 3∫[0,π] (1-cos2θ) dθ

A1 = 3(θ - 1/2 sin2θ)|[0,π]

A1 = 3π

The area enclosed by the inner curve is given by:

A2 = ∫[0,π] 1/2 (2 2sinθ)^2 dθ

Simplifying this expression, we get:

A2 = 8∫[0,π] sin^2θ dθ

Using the same trigonometric identity as before, we get:

A2 = 4∫[0,π] (1-cos2θ) dθ

A2 = 4(θ - 1/2 sin2θ)|[0,π]

A2 = 2π

Therefore, the area lying outside r=4sinθ and inside r=2 2sinθ is:

A = A1 - A2 = 3π - 2π = π

So, the area lying outside r=4sinθ and inside r=2 2sinθ is π.

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Answer:Top= 1

             Bottom= 2 1/2

Step-by-step explanation:

Top= 1/2x2= 1

Bottom= 1/2+2= 2 1/2 (2.5)

The reasonable estimate is; 100 visitors prefer grizzly bears.

Given that a zoo randomly samples a group of 100 visitors, asking what their favorite type of bear is.

There are,

Black bear = 24.  

Grizzly bear = 30.  

Polar bear = 46

Also, the zoo has 300 visitors one weekend.

We need to find the reasonable estimate of the number of tourists that prefer grizzly bears this weekend,

First, average the votes for Grizzly bears.

(24 + 30 + 46)/3 = 100/3

Now the variable x equal to the estimate of the number of people who will prefer Grizzly bear out of the 300 people and set up proportion equation.

x/300 = 100/300

x = 100

Thus, reasonable estimate is; 100 visitors prefer grizzly bears.

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Answer:

\( \frac{303}{0} \\ \sqrt{ - 9} \\ \sqrt{ - 100}\)

Step-by-step explanation:

\( \frac{303}{0} = > cannot \: be \: defined \\ \\ \sqrt{ - 9} \\ = \sqrt{ - 1} \sqrt{9} \\ = 3i \: (complex \: number) \\ \\ \sqrt{ - 100} \\ = \sqrt{ - 1} \sqrt{100} \\ = 10i \: (complex \: number)\)

The chance model asserts that the long-run proportion of an event is equal to the probability of that event. In other words, if we repeatedly conduct an experiment under the same conditions, the proportion of times that the event occurs over the long run should converge to the probability of the event.

For example, if we flip a fair coin many times, the chance model asserts that the proportion of heads should approach 0.5 as the number of coin flips increases. This is because the probability of flipping heads on a fair coin is 0.5, and over the long run, the proportion of heads should converge to this probability.

The chance model is a fundamental principle in probability theory, and it is used to make predictions about the outcomes of random events. It provides a way to quantify the uncertainty associated with an event and to reason about the likely outcomes of an experiment.

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Answer:

we know that,

y-y1=m(x-x1)

or, y-1=-3(x-5)

or, y-1=15-3x

or 3x+y-16=0 is the required equation

The graph of the line with slope -3 passing through the point (5,1) is attached.

The equation of the line in the slope-intercept form is y = -3x + 16.

The equation of the line in the standard form is 3x + y = 16.

The equation of a line is the representation of a line on a coordinate plane (x-y plane), which shows the relation between x and y, for every point on the particular line.

The standard form of a line is ax + by = c, where x and y are variables and a, b, and c are constants.

The slope-intercept form of a line is y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept of the line.

The equation of a line passing through the point (x₁, y₁), having a slope m, is represented by the one-point formula: y - y₁ = m(x - x₁).

We are asked to graph a line with a slope = -3, passing through the point (5, 1).

We use the one-point formula to determine the equation of this line, with slope m = -3, (x₁, y₁) = (5, 1).

Substituting these values in the equation y - y₁ = m(x - x₁), we get

y - 1 = -3(x - 5)

or, y = -3x + 15 + 1

or, y = -3x + 16.

or, 3x + y = 16

The equation of the line in the slope-intercept form is y = -3x + 16.

The equation of the line in the standard form is 3x + y = 16.

To graph this line we plot the points (5, 1) (as it is given that it passes through this point) and (0, 16) (as the y-intercept is at 16, so the line passes through the point (0, 16)). We join these points by a line and extend this line on both sides to get the required line.

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Yes, a reaction occurs when aqueous solutions of barium bromide and zinc sulfate are combined. However, no net ionic equation can be written as there is no formation of insoluble compounds or ions undergoing a chemical change.

The net ionic equation for this reaction can be determined by examining the solubility rules. BaBr2 is soluble in water, while zinc sulfate (ZnSO4) is also soluble.

According to the solubility rules, barium ions (Ba2+) and sulfate ions (SO4^2-) do not form insoluble compounds. Therefore, no precipitation reaction occurs, and the net ionic equation would be:

No net ionic equation can be written for this reaction since there is no formation of an insoluble compound or any ions undergoing a chemical change.

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Answer:

Least : Orange, red, yellow, purple, green : Greatest

O = 7.2

R= 7.5

Y= 7.875

P= 8.25

G= 8.33

Step-by-step explanation:

either convert them all to fractions, or convert them all to decimals

IM VERY SORRY if its wrong tho :(

a. Based on the given statistic that 85% of vehicles use E-Z Pass, we can expect 85% of the 12 cars to also use E-Z Pass.

Expected number of vehicles using E-Z Pass = 0.85 x 12 = 10.2

b. The mode of the distribution is the value that appears most frequently in the data set. In this case, the mode is 10 (since we cannot have a fraction of a car). The probability associated with the mode is not relevant in this context since mode is a measure of central tendency and not a probability measure.

c. To find the probability that seven or more of the sampled vehicles use E-Z Pass, we can use the binomial distribution formula:

P(X ≥ 7) = 1 - P(X < 7)

where X is the number of vehicles that use E-Z Pass and P(X < 7) is the probability that less than seven vehicles use E-Z Pass.

We can use the binomial probability formula to calculate P(X < 7):

P(X < 7) = Σ [(n choose x) p^x (1-p)^(n-x)] where n=12, x=0,1,2,3,4,5,6 and p=0.85

P(X < 7) = 0.0019 + 0.0148 + 0.0662 + 0.1790 + 0.3119 + 0.3248 + 0.1760

P(X < 7) = 1 - P(X ≥ 7) = 1 - 0.6748 = 0.3252

Therefore, the probability that seven or more of the sampled vehicles use E-Z Pass is:

P(X ≥ 7) = 1 - P(X < 7) = 1 - 0.3252 = 0.6748

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