1 point
What mathematical property is most obviously demonstrated by the
following equation: 4(x-7) = 4x - 28*
Commutative
Associative
Distributive
Identity
Inverse

Answer: (In order)

25/4 / 6 1/4 = 1

3 1/7 / 2/7 = 11

5/4 / 1/4 = 5

11 1/4 / 9/4 = 5

8 1/4 / 3/4 = 11

3 1/3 / 10/3 = 1

Step-by-step explanation:

Answer:

a) State the random variable

Random variable : x

which refers to a randomly selected student from the college that is left-handed.

b) state population parameter

population parameter : P

which is the percentage of all students from the college that are left handed

c) state the hypotheses

The hypothesis are;

Null hypothesis                H₀ : p = 0.11

Alternative hypothesis    H₁ : p > 0.11

d) State the Type I error in the context of this problem.

Type - I Error: Rejecting that the % of all the students from the college that are left-handed is 11% when actually the % is really 11%

(Reject H₀ when H₀ is true)

e) State the Type 11 error in the context of this problem

Type-II Error: Failing to Reject that the % of all the students from the college that are left-handed is 11% when the % is really higher than that

(Fail to reject H₀ when H₀ is false)

Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

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The radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis is 27\(a^{\frac{3}{2}\).

To find the radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.

When the curve intersects the x-axis, y=0. Therefore, we have:

a⁰ = x³ - a³

x³ = a³

x = a

Next, we need to find the derivative of y with respect to x:

dy/dx = -2x/(3a²√(x³-a³))

At the point where x=a and y=0, we have:

dy/dx = -2a/(3a²√(a³-a³)) = 0

Therefore, the radius of curvature is given by:

R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)

To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:

d/dx(dy/dx) = -2/(3a²(x³-a³\()^{\frac{3}{2}\)) + 4x²/(9a⁴(x³-a³\()^{\frac{1}{2}\))

At x=a, we have:

d/dx(dy/dx) = -2/(3a²(a³-a³\()^{\frac{3}{2}\)) + 4a²/(9a⁴(a³-a³\()^{\frac{1}{2}\)) = -2/27a³

Therefore, the radius of curvature is:

R = (1/|-2/27a³|) = 27\(a^{\frac{3}{2}\)

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The digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number,

A rational number is a number that can be expressed as a ratio or fraction of two integers (a numerator and a non-zero denominator).

We can see that the next three digits in the decimal points are 6, 6 and 6, respectively. Therefore, the decimal equivalent of 22/6 is:

22/6 = 3.666666...

We notice that the digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number, which means that its decimal representation either terminates (ends) or repeats in a pattern. In this case, it repeats in a pattern of 6's.

Each of the digits after the decimal point will be 6 because this number is a rational number and repeating decimal with a repeating digit of 6.

The difference between 40 and the product of these digits and 6 is always 4.

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The probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth is 0.443

Out of 217 visitors who came to Nayeli's website, none of them purchased a costume. Therefore, the number of visitors who may purchase a costume is 217 less than the total number of visitors:

Total visitors - No. of visitors who didn't purchase a costume = 217

Total visitors - 217 = No. of visitors who may purchase a costume

Total visitors = 113 + 217+36 = 336

Out of the remaining visitors, 113 purchased exactly one costume, and 36 purchased more than one costume. Therefore, the number of visitors who purchased one or more costumes is:

No. of visitors who purchased one or more costumes = 113 + 36 = 149

Therefore, the probability that the next person will purchase one or more costumes can be expressed as:

Probability = No. of visitors who purchased one or more costumes / Total visitors

Probability = 149 /336 = 0.443

The probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth is 0.443

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Answer:

Step-by-step explanation:

.44

Answer:

a

Step-by-step explanation:

the perimeter (P) of a square is the sum of the 4 congruent sides.

the area of a square is calculated as

area = s² ( s is the length of a side )

here area is 36 , then

s² = 36 ( take square root of both sides )

s = \(\sqrt{36}\) = 6

then

P = 4s = 4 × 6 = 24 cm

Answer:

-4

Step-by-step explanation:

i jus did this question

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

$14

Step-by-step explanation:

20 x .7 = 14

Answer:

PRT/100.

200*8*5/100

2*8*5

$80

Answer:

6y +52

Step-by-step explanation:

6(2y + 8) - 2(3y - 2)

Distribute

12y + 48 - 6y +4

Combine like terms

6y +52

Use the combination formula.

5 C2 = 5!/5!3! = 10

The answer is 10

Answer:

10

Step-by-step explanation:

Answer:

Random sample, \(np \geq 10\) and \(n(1-p) \geq 10\), so yes, both conditions were satisfied.

Step-by-step explanation:

60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon.

This means that \(p = 0.6\)

A recent survey was conducted from 1000 of these individuals.

This means that \(n = 1000\)

Also, a random sample, so the first condition was satisfied.

The sample size must be large (so that at least 10 or more successes and failures).

\(np = 1000*0.6 = 600 \geq 10\)

\(n(1-p) = 1000*0.4 = 400 \geq 10\)

So yes, both conditions were met.

Answer:

2,4 3,5

Step-by-step explanation:

Answer:

162

Step-by-step explanation:

4.5x9x4

Answer:

y = (5/7)x + (75/7)

Step-by-step explanation:

If you ever find yourself in a math class where you have to write the equation of a line that goes through a certain point and has a certain slope, don't panic. There is a simple formula that can help you out. It's called the point-slope form and it looks like this:

y - y1 = m (x - x1)

It may look scary, but it's actually pretty easy to use. All you have to do is plug in the values that you know and solve for the ones that you don't. For example, let's say you have a line that passes through the point (-1, 10) and has a slope of 5/7. You can use the point-slope form to write the equation of the line like this:

y - 10 = (5/7) (x - (-1))

See? That wasn't so bad. Now you can simplify the equation by distributing the 5/7 and adding 10 to both sides. You get:

y = (5/7)x + (75/7)

And that's it! You have written the equation of the line in slope-intercept form, which is another way of writing the equation of a line. You can check your answer by plugging in the values of x and y from the original point and seeing if they make the equation true. If they do, you're good to go. If not, you made a mistake somewhere and you should go back and fix it.

Congratulations! You have learned how to use the point-slope form to write the equation of a line. Now you can impress your math teacher and your friends with your skills.  Remember, with great power comes great responsibility.

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

Answer: 2

Step-by-step explanation:

SOOO, hold up your fingers righhht

We all have 5 fingers on each hand righttt

close your hand and stick up two fingers

1...

2...

count the number of fingers that ou held up and ya!

Hope this helps!!

Answer:

\(\huge{x = \frac{236164}{9477} = 24 \frac{8716}{9477}} \)

Step-by-step explanation:

\((81) - 4 \div (729)2 - x = \frac{9}{4} x\)

\(81 - \frac{4}{729} \times 2 - x = \frac{9}{4} x\)

\(81 - \frac{8}{729} - x = \frac{9}{4} x\)

\( \frac{59041}{729} - x = \frac{9}{4} x\)

\(236164 - 2916x = 6561x\)

\( - 2916x - 6561x = - 236164\)

\( - 9477x = - 236164\)

\(\boxed{\green{x = \frac{236164}{9477} = 24 \frac{8716}{9477}}} \)

Answer:

15x + 190 >= 400

* >= means greater than or equal to *

at least 14 friends

Step-by-step explanation:

without the inequality it'd be 15x + 190 = 400

but since you want it to be at least 400 you change the = to the greater than or equal to sign

15x + 190 = 400 * subtract 190 from both sides*

15x = 210 *divide both sides by 15*

x = 14

Answer:what

Step-by-step explanation:

Answer:

The graph is attached

Step-by-step explanation:

Answer:

y = -2x - 3

Step-by-step explanation:

**hopefully the picture helps it to make sense**

good luck

i hope this helps

brainliest would be highly appreciated

have a nice day!

A mixed fraction exists one that is represented by both its quotient and remainder.

Product of -2 1/2 and -3 1/3 is  \(8\frac{1}{3}\).

Product of 1 1/3 and -3 1/2  is \(-5\frac{5}{6}\) .

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction exists, for example, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

Product of -2 1/2 and -3 1/3 is  \(8\frac{1}{3}\).

Product of 1 1/3 and -3 1/2  is \(-5\frac{5}{6}\) .

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ANSWER

Yes

EXPLANATION

We want to identify if the given relation is a function.

A relation is regarded as a function if it maps each input to only one output. In other words, each input has only one output.

The given function maps each input to only one output.

Therefore, YES, it is a function.

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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Step-by-step explanation:

7 - (2x + 5) = 7 - 2x - 5 = 2 - 2x

which could be also written as

2(1 - x)

Answer:

The rate of change in the area beneath the ladder is 5.25 ft²/s

Step-by-step explanation:

Area of triangle is given by;

\(A = \frac{1}{2}bh\\\\2A = bh\\\\take \ derivative \ of \ both \ sides \ with \ respect \ to \ "t"\\\\2\frac{dA}{dt} = h\frac{db}{dt} + b\frac{dh}{dt}\\\\divide \ through \ by \ 2\\\\\frac{dA}{dt} = (\frac{h}{2} )\frac{db}{dt} + (\frac{b}{2}) \frac{dh}{dt}\)

where;

b is the base of the triangle, given as 6 ft

h is the height of the triangle, determined  by applying Pythagoras theorem.

h² = 10² - 6²

h² = 100 - 36

h² = 64

h = √64

h = 8 ft

Determine the rate of change of the height;

\(h^2 + b^2 = 10^2\\\\h^2 + b^2 =100\\\\2h\frac{dh}{dt} + 2b\frac{db}{dt} =0\\\\h\frac{dh}{dt} + b\frac{db}{dt} =0\\\\h \frac{dh}{dt} = -b\frac{db}{dt} \\\\\frac{dh}{dt} = (\frac{-b}{h} )\frac{db}{dt}\\\\\frac{dh}{dt} =(\frac{-6}{8})(3)\\\\\frac{dh}{dt} = -\frac{9}{4} \ ft/s\)

Finally, determine the rate of change of area beneath the ladder;

\(\frac{dA}{dt} = (\frac{h}{2} )\frac{db}{dt} + (\frac{b}{2}) \frac{dh}{dt}\\\\\frac{dA}{dt} = (\frac{8}{2} )(3) + (\frac{6}{2}) (\frac{-9}{4})\\\\\frac{dA}{dt} = 12 - \frac{27}{4} \\\\\frac{dA}{dt} = \frac{48-27}{4}\\\\\frac{dA}{dt} = \frac{21}{4} \ ft^2/s\\\\\frac{dA}{dt} = 5.25 \ ft^2/s\)

Therefore, the rate of change in the area beneath the ladder is 5.25 ft²/s

Answer:

18x^2 + 33x - 9

Step-by-step explanation:

to combine, i like using the foil method

3x x 6x = 18x^2

3x x -9 = 27x

1 x 6x = 6x

1 x -9 = -9

and then just combine those together

18x^2 + 27x + 6x -9

and then add the 2 in the middle

18x^2 + 33x - 9