I had 13 dollars. My mom gave me 10 dollars. My dad gave me 30 dollars. My Aunt, My Uncle, and Grandma gave me 100 dollars. I had another 7 dollars. How much did I have?

The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

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The probability that at least one of the shirts you draw will be pink 46/51.

What is probability?

The likelihood of an event happening is determined by probability. There are many instances in real life where we may need to make predictions about how something will turn out combination . The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence. By simply dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. The likelihood of an event occurring might range from 0 to 1.

Here the number of pink shirts=8

Number of green shirts=6

Number of red shirts=4

Here if you draw 2 shirts random then,

P(neither the shirt is blue) = \(\frac{6}{18} *\frac{5}{17}\) = \(\frac{5}{51}\)

Now the at least one of the shirt is pink then,

=> P( at least one shirt is pink)= 1-\(\frac{5}{51}\) = \(\frac{51-5}{51}\) = \(\frac{46}{51}\)

Hence the probability that at least one of the shirts you draw will be pink 46/51.

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Answer:

\(D=565.6m\)

Step-by-step explanation:

From the question we are told that:

Diameter \(d=36m\)

Number of times jogged \(N=5\)

Generally the equation for Distance traveled is mathematically given by

D=Circumference of Park * Number of times jogged

Where

Circumference of Park c is mathematically give as

 \(c=2\pi r\)

 \(c=2 3.142*\frac{36}{2}\)

 \(c=113.1\)

Therefore

 \(D=c*N\)

 \(D=113.1*5\)

 \(D=565.6m\)

Answer:

In geometry, postulates are statements that are accepted as true without proof. The three postulates for congruent triangles are ASA, SSS, and SAS. These postulates are used to prove that two triangles are congruent.

ASA Postulate:

ASA stands for "Angle, Side, Angle." This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have ∠A ≅ ∠D, ∠B ≅ ∠E, and AB ≅ DE. Therefore, we can conclude that ΔABC ≅ ΔDEF by ASA postulate.

SSS Postulate:

SSS stands for "Side, Side, Side." This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, we can conclude that ΔABC ≅ ΔDEF by SSS postulate.

SAS Postulate:

SAS stands for "Side, Angle, Side." This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and ∠B ≅ ∠E. Therefore, we can conclude that ΔABC ≅ ΔDEF by SAS postulate.

Overall, the ASA, SSS, and SAS postulates are important tools in proving the congruence of triangles in geometry. They allow us to make logical deductions about the properties of triangles based on their corresponding angles and sides.

Answer:

They are different because ASA means that the two triangles have two angles and the side between the angles congruent. SAS means that two sides and the angle in between them are congruent

Step-by-step explanation:

and sss If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

Answer:

the median would be 260.5

Answer: The answer is 3

Step-by-step explanation:

The constant of proportionality of the relationship shown in the graph is 3 and this can be determined by using the two-point slope form of the line.

Given :

The graph of a straight line is given.

The following steps can be used in order to determine the constant of proportionality of the relationship shown in the graph:

Step 1 - The two-point slope form of the line can be used in order to determine the constant of proportionality of the relationship shown in the graph.

Step 2 - The two-point slope form of the line is given below:

y - y1 / x - x1 = y2 - y1 / x2 - x1

where (x1, y1)  and (x2, y2)  points on the line.

Step 3 - So, substitute (1,3) and (2,6) in the above equation.

y - 3 / x - 1 = 6 - 3 / 2 - 1

Step 4 - Simplify the above equation.

(y - 3) = 3(x - 1)

y - 3 = 3x - 3

y = 3x

So, the constant of proportionality of the relationship shown in the graph is 3. Therefore, the correct option is B).

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~"Gamer"~

The slope of the tangent line to the curve xy² + 5tan(xy) - 2yx = 4 at point (4, 5) is : -0.01017

Given that the curve is xy² + 5tan(xy) - 2yx = 4.

To find the slope of the tangent line, we differentiate both sides of the curve with respect to x using the product rule and chain rule as shown below;

y^2 + 2xy \frac{dy}{dx} + 5\sec^2(xy) \frac{dy}{dx} + 5x\sec^2(xy) y \frac{dy}{dx} -2y - 2x \frac{dy}{dx} = 0\frac{dy}{dx}(2xy + 5\sec^2(xy) + 5xy\sec^2(xy) - 2x)

                                                                                                                                                                   = 2y - y^2\frac{dy}{dx}                      = \frac{2y - y^2}{2xy + 5\sec^2(xy) + 5xy\sec^2(xy) - 2x}

When x = 4,

then the slope of the tangent line to the curve is given by\frac{dy}{dx}|_{x=4} = \frac{2y - y^2}{8y + 5\sec^2(4y) + 20y\sec^2(4y) - 8}

For y = 5, then the slope of the tangent line is given by;

\frac{dy}{dx}|_{x=4, y=5} = \frac{2(5) - 5^2}{8(5) + 5\sec^2(20) + 20(5)\sec^2(20) - 8}

Hence, the slope of the tangent line is;

\frac{dy}{dx}|_{x=4, y=5} = \frac{10 - 25}{40 + 5\sec^2(20) + 100\sec^2(20) - 8}

                                       = \frac{-15}{1472.58}

                                       = -0.01017

Therefore, the slope of the tangent line to the curve xy² + 5tan(xy) - 2yx = 4 at point (4, 5) is -0.01017.

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The relationship between the cost of books and pens is an illustration of linear equation.

The linear equation is (a) \(x - 2y - 10 =0\)

From the question, we have:

x exceeds 2 times y by 10

Rewrite as:

x exceeds 2y by 10

Exceed means plus (+)

So, we have:

\(x = 2y + 10\)

Equate the above equation to 0

\(x - 2y - 10 =0\)

Hence, the required equation is (a) \(x - 2y - 10 =0\)

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Therefore, the final result of the integral is \(-1/2(xcos^2(x)) + 4/(1cos(x)sin(x)) + 4/(1x) + C\), where C is the constant of integration.

To evaluate the integral ∫xsin(x)cos(x)dx, we can use the product-to-sum identities for trigonometric functions. The product-to-sum identities state that sin(x)cos(x) = 1/2*sin(2x).

Applying this identity, the integral becomes ∫x * (1/2*sin(2x)) dx.

We can simplify further by using the power rule of integration, which states that the integral of \(x^n dx\) is \((1/(n+1)) * x^{(n+1)} + C\).

In this case, n = 1, so the integral becomes (1/2) * ∫sin(2x) dx.

Now, we can integrate sin(2x) using the substitution method. Let u = 2x, then du = 2 dx. Rearranging, dx = (1/2) du.

Substituting these values back into the integral, we have (1/2) * ∫sin(2x) dx = (1/2) * ∫sin(u) * (1/2) du = (1/4) * ∫sin(u) du.

The integral of sin(u) du is -cos(u) + C. Substituting back u = 2x, we have -(1/4)*cos(2x) + C.

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Scott can then proceed with the subsequent steps, which involve using a compass and a straightedge to construct the perpendicular line.

To construct a line perpendicular to line l from a point P, not on the line, Scott's first step should be to draw a line segment from point P that intersects line l.

This line segment should be of any length and can be drawn in any direction. This is the initial step in constructing a perpendicular line.

Scott can then proceed with the subsequent steps, which involve using a compass and a straightedge to construct the perpendicular line.

However, it is important to note that the first step specifically involves drawing a line segment from point P to intersect line l.

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Interior angle of a polygon = (n-2) * 180 / n

Exterior angle of a polygon = 360 / n

To translate coordinates in a two-dimensional plane, you need to know the translation vector. A translation vector is a pair of numbers (a, b) that indicates the amount of movement in the x-direction and y-direction.

To translate a point (x, y) by the translation vector (a, b), you can use the following formulas:

x' = x + a

y' = y + b

Where x' and y' are the new coordinates of the point after the translation.

A translation is a transformation that moves a figure a certain distance in a certain direction without rotating or reflecting it. In this case, we are asked to translate the triangle EFG 2 units down. This means that we need to move the triangle down 2 units on the y-axis.

To translate a point (x, y) down 2 units, we can add -2 to the y-coordinate. The new coordinates of the point will be (x, y - 2).

The coordinates of E are (-4, 1), so the coordinates of E' after the translation are (-4, 1-2) = (-4,-1)

The coordinates of F are (-3,-2), so the coordinates of F' after the translation are (-3,-2-2) = (-3,-4)

The coordinates of G are (2, 1), so the coordinates of G' after the translation are (2,1-2) = (2,-1)

So the new coordinates for the triangle EFG' after the translation are:

E'(-4,-1)

F'(-3,-4)

G'(2,-1)

It's important to notice that the x-coordinates didn't change because we are only translating the triangle down, on the y-axis.

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To determine how many miles Theden needs to hike on the third day to finish the trail, we can subtract the distance he hiked on the first two days from the total trail distance:

Total trail distance = 40 miles

Distance hiked on first day = 12.8 miles

Distance hiked on second day = 16.9 miles

Total distance hiked on first two days = 12.8 + 16.9 = 29.7 miles

Distance left to hike on the third day = 40 - 29.7 = 10.3 miles

Therefore, Theden needs to hike 10.3 miles on the third day to finish the trail.

Answer: The correct option is B.

Step-by-step explanation:

The equation of any circle with a given radius \(r\) and coordinates of centre (\(\alpha\),\(\beta\)) is given by:

\((x-\alpha )^{2} +(x-\beta )^{2} =r^{2}\)

Here \(r=16\) ;

\((\alpha ,\beta )\)=\((5,-1)\)

Plugging in the values in the given equation,

We get:

\((x-5)^{2} +(x+1 )^{2} =16^{2}=256\)

Answer:

22.5° and 67.5°

Step-by-step explanation:

The sum of complementary angles equal 90°.

Given that one of the complementary angles is 3 times larger than the other, let "x" represent the other angle.

Thus, the following expression can be written to represent this case:

\( x + 3x = 90 \)

Solve for x

\( 4x = 90 \)

Divide both sides by 4

\( \frac{4x}{4} = \frac{90}{4} \)

\( x = 22.5 \)

The measure of the complementary angles are:

x = 22.5°

3x = 3(22.5) = 67.5°

Answer:

12 is the slope.

Step-by-step explanation:

This is because in the equation y = mx + b, m is the slope.

Hope this helps!

The equivalent expression of 4b+13/2 is (8b+13)/2.

Given an expression be 4b+13/2.

We are required to find the equivalent of the expression 4b+13/2.

Expression is combination of numbers, symbols, fractions, coefficients, determinants, indeterminants. In an expression we do not find any equal to sign. It shows some relationship. In this expression b is the only variable that exists. If we have been given some value of th expression at some point then we can get the value of variable.

The expression is 4b+13/2.

Taking LCM first.

The LCM of any two numbers is basically the value that is evenly divisible by the two given numbers.

=(8b+13)/2

Hence the equivalent expression of 4b+13/2 is (8b+13)/2.

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\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \:x = -3 \)

____________________________________

\( \large \tt Solution \: : \)

\(\qquad \tt \rightarrow \: CD + DE = CE\)

\(\qquad \tt \rightarrow \: x + 10 + x + 4 = 8\)

\(\qquad \tt \rightarrow \: 2x + 14 = 8\)

\(\qquad \tt \rightarrow \: 2x =8 - 14\)

\(\qquad \tt \rightarrow \: 2x = - 6\)

\(\qquad \tt \rightarrow \: x = - 3\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

\(\huge \boxed{\sf x=-3}\\\\\\\displaystyle \sf CD+DE=8 \\\\x+10+x+4=8\\\\2x+14=8\\\\Subtracting\ 14\ from\ each\ side\\\\ 2x+14-14=8-14\\\\2x=-6\\\\ Dividing\ each\ side\ by\ 2 \\\\ \frac{2x}{2} =\frac{-6}{2} \\\\x=-3\)

A bit is a unit of information in computing that can have two values, typically represented as 0 and 1. A bit string of length 9 is a sequence of 9 digits, each of which is either 0 or 1.

(a) How many bit strings of length 9 or less are there?

To find the number of bit strings of length 9 or less, we can sum the number of bit strings of each length from 0 to 9.

For a bit string of length 0, there is only one possible string - the empty string.

For a bit string of length 1, there are two possible strings - 0 or 1.

For a bit string of length 2, there are four possible strings - 00, 01, 10, or 11.

For a bit string of length 3, there are eight possible strings - 000, 001, 010, 011, 100, 101, 110, or 111.

And so on, up to length 9.

That is:

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256= 511.

There are 511 bit strings of length 9 or less.

(b) How many bit strings of length 9 or less are there, including the empty string of length zero?

To find the number of bit strings of length 9 or less, we can use the same method as above, but exclude the strings of length 10:

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256= 511

There are 511 bit strings of length 9 or less, including empty string.

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Answer:

BDA=52 angles at the centre is equal to 2× angles at circumference

Without specific data on the number of students who prefer each option, we cannot calculate the probability.

To determine the probability that a student prefers the zoo or the water park, we need to know the total number of students and the number of students who prefer each option. Without this information, it is not possible to calculate the probability accurately.

To calculate the probability, we would need to divide the number of students who prefer the zoo or the water park by the total number of students. For example, if there are 50 students in total and 30 prefer the zoo and 20 prefer the water park, the probability would be:

P(prefer zoo or water park) = (30 + 20) / 50 = 50 / 50 = 1

However, without specific data on the number of students who prefer each option, we cannot calculate the probability.

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Using a trigonometric identity, considering the given value of the tangent of theta, the secant of the same angle is given by:

\(\sec{\theta} = \pm \sqrt{\frac{11}{8}}\)

According to the following identity:

\(\sec^2{\theta} = 1 + \tan^2{\theta}\)

In this problem, the tangent squared is given as follows:

\(\tan^2{\theta} = \frac{3}{8}\)

Hence the secant is given by:

\(\sec^{2}{\theta} = 1 + \tan^2{\theta}\)

\(\sec^{2}{\theta} = 1 + \frac{3}{8}\)

\(\sec^{2}{\theta} = \frac{11}{8}\)

\(\sec{\theta} = \pm \sqrt{\frac{11}{8}}\)

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Answer:

Plus-or-minus StartRoot eleven-eighths EndFraction

Step-by-step explanation:

The answer above is correct.

Answer:

256

Step-by-step explanation:

I) Solve exponents first:

2^2 x 8^2

= 4 x 64

II) Multiply:

4 x 64

= 256

Answer:

Step-by-step explanation:

To find the surface area of a square pyramid, we need to add the area of the base to the sum of the areas of the four triangular faces.

The area of the base of the pyramid is:

Area of square base = (base length)^2

Area of square base = 3^2

Area of square base = 9 square inches

To find the area of each triangular face, we need to first find the length of each side. Since the base is a square, all sides are equal to 3 inches. The slant height is given as 7 inches, which is the height of each triangular face.

Using the Pythagorean theorem, we can find the length of each side of the triangular face:

(side length)^2 + (height)^2 = (slant height)^2

(side length)^2 + 7^2 = 7^2

(side length)^2 = 7^2 - 7^2

(side length)^2 = 24.5

side length ≈ 4.95

The area of each triangular face is:

Area of triangular face = (1/2) × (base length) × (height)

Area of triangular face = (1/2) × 3 × 7

Area of triangular face = 10.5 square inches

Therefore, the total surface area of the square pyramid is:

Total surface area = Area of base + Sum of areas of four triangular faces

Total surface area = 9 + 4(10.5)

Total surface area = 42 square inches

Hence, the surface area of this square pyramid is 42 square inches.

Answer:

7/8,5/6

Step-by-step explanation:

Two fractions are equivalent when their division is equal to one.

When we are dividing fractions, we multiply the numerator by the inverse of the denominator.

1/9,2/18

7/8,5/6

The division is not 1, so this par of fractions is not equivalent.

3/16, 9/48

6/15, 4/10​

Answer:

Answer is – 3

Step-by-step explanation:

expand the expression using ( a – b) ( a + b) = a² –b²

( 3 ) ² – ( 6) ² *remember to place your square roots inside the brackets my phone doesn't have one*

then simplify the radical

3–6 = – 3

Answer:

The Horizontal Asymptote is at x=3

Step-by-step explanation:

Here is a way to remember this

One way to remember this is the following pnemonic device: BOBO BOTN EATS DC

EABOBO -Exponents are bigger on bottom, y=0

EABOTN -Exponents are bigger on top, none

EATS DC - Exponents are the same, divide coefficients

3/x-2 the exponents are the same, divide leading coefficients

3/1 = 3 the horizontal asymtote is at x=3

The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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Answer:

41 ft 2 in

Step-by-step explanation:

Since the two triangles in question, that means that the triangles have the same proportions. We know that GH = 16 ft 7 in = 199 in (16x12+7) and HN = 6 ft 3 in = 75 in (6x12+3). GH/HN is 199/75. This is the same ratio that GO/AN will have as well. GO is unknown so we will denote it as x and AN = 15 ft 6 in = 186 in (15x12+6). We know that these two fractions are equal. 199/75 = x/186 solving for x, we get x = 493.52 in and converting that into feet we get 41 ft 1.52 in which rounds to 41 ft 2 in.