a number that cannot be expressed as a ratio of integers. these numbers have digits that go on forever without repeating.

Answer: 24 cups of sugar

Step-by-step explanation: you multiple the orginal amount neede for one batch by 8

8*3=24

The probability that the resulting integer is divisible by 8 is 1/6

According to the question,

Nancy Rolled a six-sided die twice to generate two-digit integers

Total number of outcome by rolling a die = {1 , 2 , 3 , 4 ,5 ,6 }

If you roll twice then total number of outcomes becomes = 6 × 6

=> 36

We have to find  the probability that the resulting integer is divisible by 8

Number of two - digit integer divisible by 8 = 16 , 24 , 32 , 48 , 56 , 64

that is 6  

So, Probability = Number of favorable outcomes / total number of outcomes

=> 6 / 36

=> 1/6 is required probability

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Answer:   You can buy a 9-pound bag for $8.37.

Step-by-step explanation:

[tex]\frac{5lbs}{4.65} =\frac{p}{8.37}[/tex]    

Then, we cross multiply, and we get:

5(8.37) = 4.65p

  41.85 = 4.65p   [We divided 4.65 by both sides]

         9 = p

(a) Area to the left of 24 is 0.6683.

(b) Area to the left of 17 is 0.284.

(c) Area to the right of 19 is 0.5028.

(d) Area to the right of 25 is 0.1019.

(e) Area between 17 and 30 is 0.0884.

We have given that a variable is normally distributed with mean 21 and standard deviation 7.

(a) We have to find area to the left of 24.

We will use z-formula

i.e Z = (X - μ) / σ

where X is the row score, μ is mean and σ is standard deviation.

Substituting the values we get,

Z = (24 - 21)/ 7

  = 3/7

Z = 0.4285

The p-value for 0.4285 is 0.6683.

Therefore area to the left of 24 is 0.6683.

(b) Now to find area to the left of 17,

Z =(17 - 21)/7

   = - 4/7

Z = -0.5714

The p-value for -0.5714 is  0.284.

The area to the left of 17 is 0.284

(c) To find the area of the the right of 19,

Z = (19 - 21)/ 7

   = -2/7

Z = -0.007

P-value for -0.007 is 0.4972

Area of the right of 19 is , 1 - 0.4972 = 0.5028

(d) The area of the right of 25 is,

Z = (25 - 24)/7

  = 1/7

Z = 0.1428

The p-value for 0.128 is 0.8981.

Area right of 25 is 1 - 0.8981 = 0.1019.

(e) To find area between 17 and 30 first we will find area of 17 and 30 individually.

We know area of 17 is 0.284.

Now area of 30,

Z = (30 - 24)/7

  = 6/7

Z = 0.8571.

P-value for 0.8571 is 0.1956.

Area between 17 and 30 is,

0.284-0.1956 = 0.0884.

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Answer:

52%

Step-by-step explanation:

What percent of 200 is 104?

104/200 = 0.52

0.52 = 52%

2,092.1 is the population of the town after 5 years, and P(t)=2500*(1-0.035)^t is the exponential function.

In mathematics, exponential decay defines the process of diminishing an amount by a consistent percentage rate over a period of time.

It can be stated by the formula y=a(1-b)x wherein y is the total form and is the initial money, b is the decay factor, and x is the quantity of time that has passed.

So, we got:

r = 3.5%/100% = 0.035

We have our exponential function:

P(t) = 2500*(1 - 0.035)^t

The number after 5 years is provided by substituting t = 5, we will get:

P(5) =  2500*(1 - 0.035)^5 = 2,092.1

Therefore, 2,092.1 is the population of the town after 5 years, and P(t) = 2500*(1 - 0.035)^t is the exponential function.

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Correct question:
The population of the town is 2500 and is decreasing at a rate of 3.5% per year. Write an exponential decay function to find the population of the town after 5 years

The smallest unit of matter is an atom. The fundamental building block of an element is an atom, which is made up of protons, neutrons, and electrons. This statement is true.

An atom is made up of a nucleus and one or more electrons that are bound to the nucleus. The nucleus is made up of one or more protons, a significant number of neutrons, and other particles. Only the most common form of hydrogen lacks neutrons.

An atom, which is the smallest part of a material, retains all of its properties. A molecule is made up of protons, neutrons, and electrons, which are the building components of matter. Protons and neutrons, which are the only particles in an atom that contribute to its atomic mass, are found in the nucleus of each atom. These early 20th-century discoveries of particles that  a nuclide itself and chemical components are explained by contemporary atomic theory.

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The unit rate for each size to the nearest hundredth of a dollar is Size A = $0.484, Size B = $0.393, Size C = $0.343 and Size D =$0.359.

What is unit rate?

Unit rate is a rate in which the second term of a ratio is one. Unit rate is a way to compare different quantities in which the second term is a constant of one. Unit rate is determined by dividing one quantity by another, with the second quantity always being one. Unit rate can be used to compare different items, such as prices when shopping, or to measure the speed of an object over a given period of time. Unit rate is often expressed as a whole number or a fraction.

Unit rate for Size A = $0.48, Size B = $0.39, Size C = $0.34 and
Size D =$0.36.
Given:
Size A The 7 1/5 ounce can cost $3.49.
Size B The 16 1/2 ounce can cost $6.49.
Size C The 24 3/4 ounce can cost $8.49.
Size D The 30 2/3 ounce can cost $10.99.
To find the unit rate for each, we take the total price and divide by the total ounce,
Size A = [tex]\frac{3.49}{\frac{36}{5} } =0.484[/tex]
Size B = [tex]\frac{6.49}{\frac{33}{2} } =0.393[/tex]
Size C = [tex]\frac{8.49}{\frac{99}{4} } = 0.343[/tex]
Size D = [tex]\frac{10.99}{\frac{92}{3} } = 0.359[/tex]

Hence, the unit rate for each size to the nearest hundredth of a dollar

is Size A = $0.484, Size B = $0.393, Size C = $0.343 and

Size D =$0.359.

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The value of the x in g(h(x)) = 4 is 4 if the g⁻¹(4) = 2 and at x = 4 h(x) = 2 option (C) is correct.

The correct value of x when g(h(x)) = 4 is,

⇒ x = 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The relation is,

g (h (x)) = 4

Now, Substitute x = 4;

LHS;

g (h (x)) = g (h (4))

            = g (2)

           = 4

Thus, The correct value of x when g(h(x)) = 4 is,

⇒ x = 4

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Answer:

1.1 hectares

Step-by-step explanation:

6.93/6.3 = 1.1

He can plant 1.1 hectares of land.

Answer:

a = [tex]\frac{b-4}{-2y}[/tex]

Step-by-step explanation:

ay + 4 = 3ay - b  Subtract 4 from both sides

ay = 3ay -b - 4  Subtract 3ay from both sides

ay - 3ay = b - 4  Factor out the a

a (y -3y)  = b =4  Combine like terms

a(-2y) = b - 4  Divide both sides by -2y

a = [tex]\frac{b-4}{-2y}[/tex]

Answer: A

Step-by-step explanation:

For II,  when the numerator is expanded, it contains terms of ab and a^2 which makes it a quadratic function, not an algebraic function.

For III, tricky one. The a can be cancelled out in the numerator and denominator and the resulting fraction is (b-3)/3. However, this can be further simplified to 1/3b - 1, which makes it not an algebraic fraction anymore.

This is an example of Systematic sampling.

Here we are drawing out every fifth invoice from the file available. Hence here we create an order where every fifth item is selected.

Hence this is called systematic sampling.

This is a type of probability sampling. In this method, samples are selected by the researcher at regular intervals.

This type of sampling is most suitable when we want to conduct a sampling method similar to simple random sampling but the list of population is unknown to us. However, this can also be used when the list of the same is available to us.

Another important condition is the order os the population, i.e ow it is spread must be random and not in some particular order or sample. Else the reult obtained will lose its credibility.

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Answer:just solve it

Step-by-step explanation:

it is super easy

Answer:   6^1/3x6^1/4=6^x/y

X= ,y=

Step-by-step explanation:

Answer:

x = 7 , y = 12

edge 2023

The angle of elevation is 72.5° and the height at which the ladder will elevate on the building is 19.06 ft.

Here we have to find the angle of elevation of the ladder and the height the ladder will reach on the building if the ladder is leaned against a building.

Data given:

length of the ladder = 20 ft

the base of the ladder = 6ft

we have to find the angle of elevation.

cos Ф = base/ hypotenuse

= 6/20

Ф = [tex]cos^{-1}[/tex] ( 6/20)Ф

    = 72.5°

Now we have to find how high the ladder reaches on the building when leaned against a building.

sin(72.5°) = x/ 20

x = 0.953 ×20

x = 19.06 ft

Therefore the angle of elevation is 72.5° and the ladder will elevate to 19.06.

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Hence, the three side length of two triangles are same so they are congurent.  

What is the congurency?

Two shapes are congruent if they are the same (shape and size)- in other words, if the lengths of the sides and the angles are the same.

It is often useful to know when two triangles are congruent.

Here given coordinates of the triangle [tex]FGH[/tex] and triangle [tex]JKL[/tex] are

[tex]F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)[/tex].

So, the distance formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between [tex]FG[/tex]  is

[tex]d=\sqrt{(-2-(-5))^2+(2-10)^2}\\\\d=\sqrt{(-2+5)^2+(2-10)^2}\\\\d=\sqrt{(3)^2+(-8)^2}\\\\d=\sqrt{9+64}\\\\d=\sqrt{73}[/tex]

Distance between [tex]GH[/tex]  is

[tex]d=\sqrt{(-9-(-2))^2+(10-(-7))^2}\\\\d=\sqrt{(-9+2)^2+(10+7)^2}\\\\d=\sqrt{(-7)^2+(-9)^2}\\\\d=\sqrt{49+81}\\\\d=\sqrt{130}[/tex]

Distance between [tex]HF[/tex]  is

[tex]d=\sqrt{(-5-(-9))^2+(10-(-7))^2}\\\\d=\sqrt{(-5+9)^2+(10+7)^2}\\\\d=\sqrt{(4)^2+(17)^2}\\\\d=\sqrt{16+289}\\\\d=\sqrt{305}[/tex]

Distance between [tex]JK[/tex]  is

[tex]d=\sqrt{(9-0)^2+(2-(-5))^2}\\\\d=\sqrt{(9)^2+(2+5)^2}\\\\d=\sqrt{(9)^2+(7)^2}\\\\d=\sqrt{81+49}\\\\d=\sqrt{130}[/tex]

Distance between [tex]KL[/tex]  is

[tex]d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-17)^2+(-4)^2}\\\\d=\sqrt{289+16}\\\\d=\sqrt{305}[/tex]

Distance between [tex]LJ[/tex]  is

[tex]d=\sqrt{(0-(-8))^2+(-5-(-2))^2}\\\\d=\sqrt{(8)^2+(-5+2)^2}\\\\d=\sqrt{(8)^2+(-3)^2}\\\\d=\sqrt{64+9}\\\\d=\sqrt{73}[/tex]

Since, [tex]FG[/tex]≅[tex]LJ-GH[/tex]≅[tex]JK-HF[/tex]≅[tex]KL[/tex]

Hence, the three side length of two triangles are same so they are congurent.  

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The equation of the circle is x²+y²-x-y+0.25=0

What is a circle?

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge. The line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.

For a circle with radius r and center (h,k), its equation would be (x-h)² + (y-k)² = r²

Given, center is (0.5,0.5) and radius is 0.5, h=0.5, k=0.5, r=0.5

The equation becomes:

(x-0.5)² + (y-0.5)² = 0.5²

⇒x²+0.25-x+y²+0.25-y=0.25

⇒x²+y²-x-y+0.25=0

Thus, the equation of a circle becomes x²+y²-x-y+0.25=0

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Answer: The cost of a ticket for an adult is $12 while for children it is $10.

Step-by-step explanation:

Let's assume that cost for adults is A while for children it is C

Now,

2 adults and 4 children spend $64.

2A + 4C = 64

1 adult and 3 children spend $42.

A + 3C = 42

Multiply by 2

2A + 6C = 84

By subtracting equations

6C - 4C = 84 - 64

2C = 20

C = 10

A = 42 - 3(10)

A = 12

Hence "The cost of a ticket for an adult is $12 while for children it is $10".

We might write [tex]y=x+\frac{1}{5} x[/tex] if the entire amount of money is y and the first week's deposit is x.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

When are given an x and y equation that is [tex]y=x+\frac{1}{5} x[/tex] , and the further discussion can be defined as follows:

We must now imagine a condition that can be represented by the above equation.

Let's calculate the place money in piggy bank over two weeks in a row.

In the first week, I deposit a [tex]\frac{1}{5}[/tex]  of a particular amount of money, and the next week, I deposit a quarter of such previous week's investment.

We must now determine the entire amount of money that I have deposited.

We might write [tex]y=x+\frac{1}{5} x[/tex] if the entire amount of money is y and the first week's deposit is x.

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Answer:

One can of tomatoes needs 4 teaspoons of oregano.

Step-by-step explanation:

[tex]\frac{11}{44}[/tex] = [tex]\frac{1}{x}[/tex]  Cross multiply and solve for x

11x = 44  Divide both sides by 11

x = 4

One can of tomatoes needs 4 teaspoons of oregano.

Dimension of maximize area is, length = 1581 m and breadth = 790.5 m.

Given that a rectangular plot of land adjacent to a river is to be divided into two equal plots. And 3162 ft of fencing to enclose the plot.

Consider the length is L and breadth is B of the plot.

Therefore the perimeter = L + 2B = 3162

⇒ L = 3162 - 2B

We know that area is the product of length into breadth i.e,

Area = L × B

        = (3162 - 2B) × B

Area = 3162B - 2B²

The maximum of the quadratic expression is

ax² + bx + c is at s = [tex]\frac{-b}{2a}[/tex] if a < 0.

Now we will calculate maximum point of the equation,

B = [tex]\frac{-3162}{2(-2)}[/tex]

B = 790.5

Now we will find the value of length,

L = 3162 - 2B

  = 3162 - 2(790.5)

  = 3162 - 1581

L = 1581

Hence the length of the rectangular plot is 1581 m and bredth is 790.5 m.

Therefore the maximize area = 1581 × 790.5 =124978

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We got the answer of the equation 65 X 589 X 653 -65 +36 = 25,000,076 by applying the BODMAS rule in the given equation.

By Applying the BODMAS rule we get the answer of this question. BODMAs rule says that firstly solve the bracket, them solve the off, then do division, after then go to multiplication, then do addition and lastly after the addition do subtraction.

The chain should be followed while solving the question. So in the given question we firstly do the multiplication i.e

65 X 589 X 653 which is equal to  25,000,105

After doing multiplication, we will move forward and do the addition i.e

25,000,105 + 36 which is equal to 25,000,141.

Lastly, we will do the subtraction after doing multiplication and addition i.e.

25,000,141 – 65 which is equal to 25,000,076.

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(a) {2, 3, 4, 5, 6, 7, 8}

(b) {2, 4, 5, 9, 11, 12, 14}

(c) No next largest 7-subset; this is the last one in lexicographic order.

(d) {2, 4, 5, 6, 11, 12, 13}

(e) No next largest 7-subset; this is the last one in lexicographic order.

If all of the items in a set A are also in a set B, then the sets A and B are subsets of one another. To put it another way, the set A is contained within the set B. A and B stand for the subset connection.

For instance, if A represents the set of natural numbers and B represents the set of all whole numbers, then B is a subset of A since the set of whole numbers contains all natural numbers. This is how we may comprehend it: Natural numbers 1, 2, 3, and so on make up the set A. B = A collection of whole numbers, such as "0, 1, 2, 3,..."

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On solving the given question, by the equation, A riding 48 mi at 8 mph takes 6 hours, which indeed is 3 hours longer .A riding 48 mi at 8 mph takes 6 hours, which indeed is 3 hours longer.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

J can ride his bike 8 mph faster than A can ride. It takes A 3 hours longer than J to ride 48 miles. How fast can J ride?

Let r = rate that J rides, in miles per hour.

Then rate that A rides is (r – 8).

distance = rate * time

time = distance/rate

Time taken by J to ride 48 miles = 48/r.

Time taken by A to ride 48 miles = 48/(r – 8).

But A's time is 3 hours more than J's time.

48/(r – 8) = 3 + 48/r

Solve that for r.

48/(r – 8) = 3r/r + 48/r

48/(r – 8) = (3r + 48)/r

Multiply both sides by (r – 8)r.

[tex]48(r) = (3r + 48)(r - 8)\\ 48r = 3r2 -24r + 48r -384\\ 0 = 3r2 - 24r -384\\ 0 = r2 -8r - 128\\ 0 = (r -16)(r + 8)[/tex]

So r = 16 mph or r = –8 mph.

J riding 48 mi at 16 mph takes 3 hours.

A riding 48 mi at 8 mph takes 6 hours, which indeed is 3 hours longer.

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The running area does the dog have is 943 square foot.

What is area of section of a circle?

A segment is essentially the area of a circle between the chord and the arc. A circle is a path that a point equidistant from a single point on the plane can follow; this point is known as the circle's center, and the distance between it and that point is known as the circle's radius. A segment is a section of a circle's interior. A sector is the region that a segment encloses and the angle that a segment occupies. By deducting the triangle produced inside the sector from the sector that contains the segment, one can calculate the area of a circular segment.

The area of a section that made by a circle is ∏ r² × (θ/360).

Given that the radius of the circle is 20 ft.

The angle between two consecutive side of a rectangle is 90⁰.

The angle that made the running area by dog = (360⁰ - 90⁰) = 270⁰.

The area is ∏× 20² × (270⁰/360⁰) = 942.85 square foot

The nearest square foot value of 942.85 square foot is 943 square foot.

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Answer:

48/7

Step-by-step explanation:

8/7/6

= 8 × 1/7/6

= 8× 6/7

48/7

No, The side lengths does not make a right triangle.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The sides of the triangle are;

⇒ 20, 20 and √800

Now,

Since, The sides of the triangle are;

⇒ 20, 20 and √800

Hence, We can apply the Pythagoras theorem as;

⇒ (√800) ² = √ 20² + 20²

⇒ 800 ≠ √800

Thus, The side lengths does not make a right triangle.

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Using Pythagoras theorem the side length of DH is 9cm

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

To find the value of DH, we can use Pythagoras's theorem to find the length of HC

EC² = EH² + HC²

25² = 20² + HC²

HC² = 25² - 20²

HC² = 225

HC = √225

HC = 15

Using Pythagoras's theorem again, we can find DH

HC² = DC² + DH²

15² = 12² + DH²

DH = 9

The length of DH is 9cm

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Answer: a>6

Step-by-step explanation:

-3+21a-2a>111

Collect like terms on the left side

19a-3>111

Add 3 to both sides to solve for a terms

19a-3+3>111+3

19a>114

Divide both sides by 19

19a/19>114/19

a>6

[tex]-3+21a-2a > 111[/tex]

Simplify:

[tex]19a-3 > 111[/tex]

Add 3 to both sides:

[tex]19a-3+3 > 111+3[/tex]

[tex]19a > 114[/tex]

Divide both sides by 19:

[tex]\dfrac{19a}{19} > \dfrac{144}{19}[/tex]

[tex]\fbox{a} > \fbox{6}[/tex]

[tex]a > 6[/tex] on a graph: