two dice are thrown. what is the probability that the sum of the numbers appearing on the two dice is 8, if 3 appears on the first?

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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when lines l, m, and n are intersected by two transversal lines and are parallel, the value of x = 12.5 is obtained.

A transversal in geometry is a line that, at two different places, traverses two lines in the same plane. If two or more additional lines in the Euclidean plane are parallel, transversals can help determine this.

Parallel lines l, m, and n are present.

These parallel lines cross two transversal lines.

theorem of intercept

Intercept lengths between parallel lines are proportionate.

[tex]\frac{16}{x} = \frac{23}{18}[/tex]

x = (16 * 18) /23

x = 12.5

when lines l, m, and n are intersected by two transversal lines and are parallel, the value of x = 12.5 is obtained.

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Answer:

Step-by-step explanation:

balls

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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Answer:

52%

Step-by-step explanation:

What percent of 200 is 104?

104/200 = 0.52

0.52 = 52%

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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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:

formula: Tn=a+(n-1)d

Step-by-step explanation:

Tn=2+(n-1)2

Answer:

Step-by-step explanation:

BRO what FACTOR????????????????????????///////////////////////

Answer:

5

Step-by-step explanation:

[tex]\frac{7.5}{1.5}[/tex] = 5

Answer:

48/7

Step-by-step explanation:

8/7/6

= 8 × 1/7/6

= 8× 6/7

48/7

Answer: 6 boxes of 5 markers in each box

Step-by-step explanation:

1. Consider the factors of 30

30: 1, 2, 3, 5, 6, 10, 15 and 30

2. pick any 2 that make 30

5*6=30

3. Therefore buying 6 boxes of 5 markers each should do the trick,

Hope this helps

Answer: 6 boxes of 5 markers in each box

Step-by-step explanation:

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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The area of the given irregular figure is 143 square inches.

What is area of irregular figure?

We divide an irregular shape into its component common shapes before calculating its area. After that, we add the areas of each shape. For instance, if a square and a triangle make up an irregular polygon, the area of the polygon is equal to the sum of their areas.

We have to divide the given irregular figure into known shapes.

That is rectangle and square.

Rectangles with sides '7 in and 10 in' and '12 in and 4 in' and the square of side 5 in.

So, the area of irregular figure is,

Area = Area of rectangle + Area of rectangle + Area of square

= (7 x 10) + (12 x 4) + 5^2

= 70 + 48 + 25

Area = 143

Hence, the area of the given irregular figure is 143 square inches.

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Given a line with the equation -3x+8y=-10, its slope can be calculated using the slope intercept form of the line that is 3/8.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies). The slope of a line in mathematics indicates how steep a line is. It is also referred to as the gradient. The "change in y" over the "change in x" of a line is referred to as the slope.

Here,

-3x+8y=-10

y=mx+c

where m=slope of line

8y=3x-10

y=3x/8-10/8

slope=3/8

The slope of given line whose equation is -3x+8y=-10 is 3/8 using slope intercept form of line.

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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: 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".

The value of a in the quadratic equation x² + 2x +4 = (x + 2)² + a( x + 2) + b is equal to -2.

We shall first expand the right hand side and express it in form of the left hand side of the quadratic equation, and then compare their coefficients to derive the value of the constant as follows;

Left hand side; {open brackets}

(x + 2)² + a( x + 2) + b = x² + 4x + 4 + ax + 2a + b

(x + 2)² + a( x + 2) + b = x² + 4x + ax + 4 + b {group like terms}

(x + 2)² + a( x + 2) + b = x² + (4 + a)x + 4 + b

such that :

x² + 2x +4 = (x + 2)² + a( x + 2) + b, then;

x² + 2x +4 = x² + (4 + a)x + 4 + b

by comparing coefficients, we have that;

4 + a = 2

a = 2 - 4 {subtract 4 from both sides}

a = -2

Therefore, for all values of x, the constant a = -2 for the quadratic equation x² + 2x +4 = (x + 2)² + a( x + 2) + b.

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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

Step-by-step explanation:

Area of rectangle is length x breadth.

Area = (x + 7)(x + 5)

= (x² + 5x + 7x + 35)

= (x² + 12x + 35)

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:

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.

(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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The half of the mentioned number after performing multiplication with 1/2 is 0.9375.

The half of 1.875 can be calculated by multiplying with (1/2). Half refers to two parts of one thing and hence it represented as the fraction 1/2. So, to find the half, we will multiply the mentioned number with 1/2.

Half value = 1.875 × 1/2

Now performing division and multiplication on Right Hand Side of the equation

Half value = 1.875/2

Half value = 0.9375

Thus, based on the division, the half of 1.875 is 0.9375.

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Option 'a' is the correct answer.

Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being greater than that value is 0.05. The value is Z0.05 =1.65.

In a normal distribution, data points are referred to as x, whereas in a z-distribution, they are referred to as z or z scores. A z score is a standard score that indicates how many standard deviations a given number (x) is from the mean:

Every z score has a corresponding p-value that indicates the likelihood that all values below or above that z score will occur.

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Answer:   6^1/3x6^1/4=6^x/y

X= ,y=

Step-by-step explanation:

Answer:

x = 7 , y = 12

edge 2023

This statement best describes the coefficient, 3,700 is "the amount of the initial deposit". which is the correct answer would be option (C).

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The exponential function is given in the question as:

3700(1.05)^4t

This expression is for the amount that will be in the account, in dollars, after t years.

As per the question,

The coefficient, 3,700 represents the amount of the initial deposit in the given exponential function

Thus, the correct answer would be an option (C).

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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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