Grandma Anni insists that corresponding lines must be congruent for figures
to be similar. Is she wrong explain

The student must score the marks which should be   ≥ 97

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Let x be the marks need to be scored in the next exam

Average = sum of marks/ number of exams

Given:  score must the student earn on the next exam to have an average of at least 90

This means,

Average ≥ 90

sum of marks/ number of exams  ≥ 90  

( 84+ 87 +92+x)/4   ≥ 90  

(263+x)/4   ≥ 90    

=> 263+x ≥ (90 * 4)

=> 263+x ≥ 360

=>  x ≥ 360 - 263

=> x ≥ 97

The student must score the marks which should be   ≥ 97

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Answer: The polynomial P(x) = x³ + 3x² - 2x + 4 is a cubic polynomial with the following properties:

p2 = 2: the coefficient of the x² term in P(x)

p - 2 = -2: the constant term in P(x)

p0 = 4: the coefficient of the x³ term in P(x)

So, p2 = 2, p - 2 = -2, and p0 = 4.

Step-by-step explanation:

This sample proportion is roughly normally distributed for large samples, with a mean of μˆP=p. and a standard deviation of σˆP=√pqn.

An equation that sets two ratios at the same value is known as a percentage. For instance, if there is one boy and three females, you can phrase the ratio as 1: 3 (there are three girls for every one boy), which means that 3 out of every four girls and one out of every four boys are female.

A ratio that links a portion to the whole is a percentage. For instance, there are 80 women and 20 men among the 100 students in the class. Men make up 20% of the population, or 20/100. Women make up 80% of the population.

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Answer:

5

Step-by-step explanation:

First we do the equation in parathesis

4 - 3 = 1

Now we add 4.

1 + 4 = 5

Answer:

5

Step-by-step explanation:

(x - 3) + 4

(4 - 3) + 4

1 + 4

5

The smallest positive integer n for which Sn is an integer is 063.

What is integer?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Let [tex]K=^9E_{i=11}\frac{1}{i}[/tex].

Examining the terms in S1, it can be seen that S1 = K + 1 since each digit n appears once and 1 appears an extra time.

Now consider writing out S2.

Each term of K will appear 10 times in the units place and 10 times in the tens place (plus one extra 1 will appear), so -

S2 = 20K + 1

In general, the equation is -

[tex]S_n=(n10^{n-1})K+1[/tex]

Because each digit will appear [tex]10^{n-1}[/tex] times in each place in the numbers [tex]1,2,......,10^{n-1}[/tex]and there are n total places.

The denominator of K is [tex]$D = 2^3\cdot 3^2\cdot 5\cdot 7$[/tex] .

For Sn to be an integer [tex]n10^{n-1}[/tex] must be divisible by D.

Since, [tex]10^{n-1}[/tex] only contains the factors 2 and 5 (but will contain enough of them when n ≥ 3), we must choose n to be divisible by [tex]$3^2\cdot 7$[/tex] .

The smallest such n, the answer is 063.

Therefore, the integer is 063.

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Answer:

Step-by-step explanation:

Given trains A and B have weights that total 147 tons, with train A being heavier by 65 tons, you want the weight of each.

The relations given in the problem can be expressed as ...

  A + B = 147 . . . . . . the total weight

  A - B = 65 . . . . . . . the difference of weights (A is heavier)

The equations can be added to eliminate the B variable:

  (A +B) +(A -B) = (147) +(65)

  2A = 212 . . . . simplify

  A = 106 . . . . . divide by 2

The other weight can be found any number of ways. One way is to subtract the difference here:

  B = A -65 = 106 -65 = 41

Train A weighs 106 tons; train B weighs 41 tons.

__

Additional comment

You will see "sum and difference" problems in many forms. The solution is always the same: the greater value is half the sum of the given numbers; the lesser value is half their difference.

  A = (147 +65)/2 = 212/2 = 106

  B = (147 -65)/2 = 82/2 = 41

Answer:

Step-by-step explanation:

The distance between two numbers on the real number line is simply the absolute value of their difference. So, to find the distance between the numbers a = 12 and b = 3, we calculate:

distance = |a - b| = |12 - 3| = |9| = 9

Therefore, the distance between the numbers a = 12 and b = 3 on the real number line is 9 units.

Answer:

Step-by-step explanation:

12.1+|-11|=12

On solving the provided question we can say that Area of the base = [tex]pi*r^2 = 70[/tex] => 350 (3/70) = h = 15 m

The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.

[tex]pi * r^2 * h / 3[/tex]

Area of the base = [tex]pi*r^2 = 70[/tex]  

350 = 70 * h / 3  

350 = (70/3) * h    

350 (3/70) = h = 15 m

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Answer:

3 miles

Step-by-step explanation:

The distance between Arati and Ava can be calculated using the Law of Cosines. Let's call the distance between Arati and Ava as "d". We know that:

a = 2 (distance skied by Arati)

b = 3 (distance skied by Ava ) c = d (distance between Arati and Ava) A = 45 (angle between a and b)

Plugging these values into the Law of Cosines formula:

d^2 = 2^2 + 3^2 - 2 * 2 * 3 * cos(45)

d^2 = 4 + 9 - 12 * (√2 / 2)

d^2 = 13 - 12 * √2

d = √(13 - 12 * √2)

To the nearest mile, the distance between Arati and Ava is approximately 3 miles.

So, adjusted to three decimal places, the lacking angles in the triangle are B = 80°24', a = 1.042 cm, and c = 5.852 cm.

The number of important digits is the total number of digits, excluding the decimal point, all leading zeros, and some following zeroes. The number of decimal points is the number to the left of the decimals.

We are given that triangle ABC is a right triangle with C = 90°, A = 9° 36', and b = 5.812 cm.

To find B, we can use the fact that the sum of the angles in a triangle is 180°. Therefore, we have:

B + A + C = 180°

B + 9°36' + 90° = 180°

B = 80°24'

To find a, we can use the trigonometric function tangent.

We have:

tan A = opposite/adjacent

tan 9°36' = a/b

Solving for a, we get:

a = b tan A = 5.812 cm tan 9°36' ≈ 1.042 cm

The Pythagorean theorem, which says that in a right triangle, the square of the hypotenuse equals the total of the squares of the two sides (a and b), can be used to determine c.

We have:

c² = a² + b²

c² = (1.042 cm)² + (5.812 cm)²

c² ≈ 34.235 cm²

c ≈ √34.235 cm²

c ≈ 5.852 cm

Therefore, the missing parts of the triangle are B ≈ 80°24', a ≈ 1.042 cm, and c ≈ 5.852 cm, rounded to three decimal places.

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The shortest distance between the two lines L1 and L2 is 0.

The shortest distance between two lines can be found using the cross product of their direction vectors.

The direction vectors of line L1 and L2 can be found as:

L1 = B - A = (2 - 3, 1 - 2, 0 - 1) = (-1, -1, -1)

L2 = D - C = (3 - 2, 0 - 4, -2 - (-1)) = (1, -4, -3)

The cross product of the direction vectors of L1 and L2 gives the normal vector to the plane formed by the two lines:

cross(L1, L2) = (1 + 4, -1 - 4, 3 + 1) = (5, -5, 4)

The normal vector of the plane formed by the two lines, and a point on line L1 (A = (3, 2, 1)), can be used to find the equation of the plane:

5x - 5y + 4z = d

5 * 3 - 5 * 2 + 4 * 1 = d

15 - 10 + 4 = d

9 = d

So the equation of the plane formed by the two lines is:

5x - 5y + 4z = 9

The shortest distance between the two lines is equal to the distance between a point on line L1 (A = (3, 2, 1)) and the plane formed by the two lines:

d = abs(9 - (5 * 3 - 5 * 2 + 4 * 1)) / sqrt(5^2 + (-5)^2 + 4^2)

d = abs(9 - 9) / sqrt(29)

d = 0 / sqrt(29)

d = 0

Therefore, the shortest distance between the two lines L1 and L2 is 0.

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a) The ratio of red to blue marbles is 1:2.

b) The ratio of white to red marbles is 3:2.

c)  The probability of drawing a white marble from the bag is 33%.

The ratio is the relative size of a value compared to another.

Ratios show the quantity of one variable contained in a larger variable.

On the other hand, the probability is the odds or likelihood that an expected outcome occurs given many possible outcomes.

Both ratios and probabilities can be expressed in fractions, decimals, and percentages because they are fractional values.

The number of red marbles in the bag = 20

The number of white marbles in the bag = 30

The number of blue marbles in the bag = 40

The total number of marbles in the bag = 90

a) The ratio of red to blue marbles = 20:40 = 1:2

b) The ratio of white to red marbles = 30:20 = 3:2

The sum of ratios of all marbles = 9 (2:3:4)

c) The probability of drawing a white marble from the bag = 3/9  = 0.33 or 33%

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The derivative of y relative to x is given as follows:

dy/dx = 8xsin(x)cos(x) + 4x²(cos²(x) - sin²(x)).

The function for this problem is defined as follows:

y = 4x²sin(x)cos(x)

The function is a product of three functions, hence the product rule is applied, as follows:

dy/dx = [4x²]'sin(x)cos(x) + 4x²[sin(x)]'cos(x) + 4x²sin(x)[cos(x)]'.

The derivatives are given as follows:

Hence the derivative of the function is defined as follows:

dy/dx = 8xsin(x)cos(x) + 4x²cos²(x) - 4x²sin²(x)

dy/dx = 8xsin(x)cos(x) + 4x²(cos²(x) - sin²(x)).

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In a case whereby Koji is installing a rectangular window in an office building. The window is 8 2/3 feet wide and 5 3/4 feet high using the  formula for the area of a rectangle is A=bh, the area of the window is 49 5/6.

The concept that will be used here is area of a rectangle. Since window can be seen to be like a  rectangle then area of window  can be take as area of rectangle which can be calculated as

Area = Length × breadth

The Length=82/3 = 26/3

the breadth= 5 3/4 = 23/4

Then Area =( 26/3 * 23/4) = 299/6 = 49 5/6

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Answer: 49 5/6 square feet

Step-by-step explanation: The width/breadth = 8 2/3 = 26/3

the height = 5 3/4 = 23/4

Area = (26/3 * 23/4) = 598/12 = 49 5/6

The radius of the sphere is half of its diameter, so the radius is 30/2 = 15 inches.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.

Substituting the given values, we get:

V = (4/3)π(15)³

V = (4/3)π(3375)

V = 4500π

Therefore, the volume of the sphere is 4500π cubic inches.

The area of the region bounded by the three lines is 4.

The region bounded by the three lines y = 0, y = x and y = 2x is a triangle. To find the area of this region, we need to split the integral into two parts. The first part is the area of the triangle formed by y = 0, y = x and y = 2x. This can be found by integrating y from 0 to x, and x from 0 to 2x. The second part is the area of the triangle formed by y = 0, y = x and y = 0. This can be found by integrating y from 0 to x, and x from 0 to 0.

Therefore, the area of the region bounded by the three lines is given by:

[tex]A = 1/2 ∫x=0 to 2x ∫y=0 to x dy dx + 1/2 ∫x=0 to 0 ∫y=0 to x dy dxA = 1/2[x^2/2]_0^2x + 1/2[x^2/2]_0^0\\A = x^2 \\A = 4[/tex]

The area of the region bounded by the three lines is 4.

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The average weight of carry-on luggage by passengers in airplanes is (15.7, 20.3) pounds.

The margin of error to be used is 2.3 pounds.

where z is the Z-score that corresponds to the desired confidence level (95% confidence corresponds to a Z-score of 1.96), standard deviation is the population standard deviation (7.5 pounds), and sample size is the number of items in the sample (25).

       Margin of Error = 1.96 * (7.5 / sqrt(25)) = 2.3 pounds

        (average weight - margin of error, average weight + margin of error)

         = (18 - 2.3, 18 + 2.3) = (15.7, 20.3) pounds.

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The Formula is [tex]a_n[/tex]= 50 ([tex]2^{n-1[/tex] ).

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite).

Given:

Ernie scores 50 points in Level 1 of a video game.

After II level the points would be

50 x 2 = 100

Then, after III level the points would be

100 x 2 = 200

So, the Recursive formula for the situation is

[tex]a_n[/tex]= a [tex]r^{n-1[/tex] where r is common ratio = 100/50 = 2

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Answer: the right option is (A) II only

Step-by-step explanation:

Answer:

Step-by-step explanation:

11≥2x-5

or

2x-5≤11

2x≤11+5

x≤16/2

x≤8

2x-5>15

2x>15+5

2x>20

x>20/2

x>10

so either x≤8

or

x>10

Answer: x</= 8 and x>10

Not sure what you are specifically asking for here is the answers for both

Step-by-step explanation:

Step 1: Move the terms

Step 2: Calculate

Step 3: Divide both sides

The composite result function (h o g)(x) in the given functions g(x) = 9 + 4x and h(x) = x + 21/5 is 4x + 66/5.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

To find (h o g)(x), first set up the composite result function h(g(x)).

h(x) = x + 21/5

h( g(x) ) = g(x) + 21/5

Plug g(x) = 9 + 4x

h( g(x) ) = ( 9 + 4x ) + 21/5

Simplify

h( g(x) ) = 9 + 4x + 21/5

h( g(x) ) = 4x + 9 + 21/5

h( g(x) ) = 4x + 66/5

Therefore, the composite function h( g(x) ) is 4x + 66/5.

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The degree of this polynomial is 4.

What is the polynomial?

A polynomial is an algebraic expression consisting of variables and coefficients, combined using only addition, subtraction, and multiplication. Polynomials can have constants (numbers), variables (letters), and exponents (powers). A polynomial is named after the degree of its highest-degree term, with the degree being the exponent of the variable.

The degree of a polynomial is the highest exponent in the polynomial. In this case, the polynomial is "K4," which has only one term.

The degree of this polynomial is 4.

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Using the drop-down menu below to write an inequality is V ≥ 10. The number of visits she needs to make in order to get a free movie ticket is 10.

We have,

75 rewards points just for signing up.

earns 13.5 points for each visit to the movie theater

she needs at least 210 points for a free movie ticket

To write the inequality representing v is,

75 + 13.5v ≥  210

13.5v ≥ 210 - 75

13.5 v ≥ 135

v ≥ 10

Therefore, by solving inequality  the number of visits she needs to make in order to get a free movie ticket is 10.

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The global extreme values of the function f(x, y) = x² + 2(y²) on the circle x² + y² = 1 are,

The maximum value of f on the circle x² + y² = 1 is,

⇒ f(0, ±1) = 2

And, the minimum value is,

⇒ f(±1, 0) =  1

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

Function is,

f(x, y) = x² + 2(y²)

And, Equations of circle is,

x² + y² = 1

Hence, The maximum value of f on the circle x² + y² = 1 is,

⇒ f(0, ±1) = 0² + 2(1²) = 2

And, the minimum value is,

⇒ f(±1, 0) = 1² + 2 × 0 = 1

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3.43 liters of Can A, and 4.57 liters of Can B  should be used from each can to obtain 5 liters of paint which is half blue and half yellow.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

From the question,

Can A is 9 parts of blue  1 part yellow= 90% blue, 10% yellow

Can B is 20% blue, 80% yellow.

let

A + B = 8 Liters

90% A + 20% B = 50% (Blue)

10% A + 80% B = 50% (Yellow)

resolving

90% A + 20% B = 10% A + 80% B

80% A = 60% B

Go back to A + B = 8 and solve for one of the variables.

B = 8 - A

80% A = 60% (8 - A)

80% A = 480% - 60% A

140% A = 480%

A = 3 43 liters

B = 8 - A = 4.57 liters

Hence, 3.43 liters of Can A, and 4.57 liters of Can B should be used.

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Answer:

1

Step-by-step explanation:

Because of the Pythagorean Identity [tex]\sin^2\theta+\cos^2\theta=1[/tex], then the answer is simply 1 as the angle does not matter.

1. Using the conversion rate of 1 kilometer = 0.621371 miles, Oskar determine the distance of his trip in miles.

2. Oskar's 165 kilometer trip is equivalent to 101.87995 miles.

3. The difference between kilometers and miles is that a kilometer is a metric unit of length and a mile is an imperial unit of length.

Paragraph 1: To convert kilometers to miles, Oskar will need to use the conversion rate of 1 kilometer = 0.621371 miles.

This conversion rate can be found on any formula sheet, and it will help Oskar determine the distance of his trip in miles.

Paragraph 2: To convert 165 kilometers into miles, Oskar will simply need to multiply 165 by 0.621371.

The result will give him the distance in miles.

For example, 165 * 0.621371 = 101.87995 miles. Therefore, Oskar's 165 kilometer trip is equivalent to 101.87995 miles.

Paragraph 3: Oskar might be traveling in a country where the maps are labeled in kilometers instead of miles. This is common in many countries, including most of Europe and many countries in Asia. The difference between kilometers and miles is that a kilometer is a metric unit of length and a mile is an imperial unit of length. A kilometer is equal to 0.621371 miles, while a mile is equal to 1.60934 kilometers. It's important to be aware of the units used in different countries to ensure accurate navigation.

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Answer:

43 games

Step-by-step explanation:

The number of home games won by the women’s basketball team is 30 * 1/2 = 15.

The number of away games won by the women's basketball team is 42 * 2/3 = 28.

Therefore, the total number of games won by the team is 15 + 28 = 43.

The following currents are present in the circuit: I₁ = 0.492 A, I₂ = -0.428 A, I₃ = 0.920 A. They are found by Kirchoffs law and solving simultaneously.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

Kirchoff's law and Junction Law will be applied given the various resistances and the circuit.

Apply Kirchoff's law to the left side loop as a starting point.

E₁ + E₂ = (r₁ + R₁ + R₄) I₁ + ( R₂ + r₂ ) I₃

18 + 3 = ( 0.5 + 8 + 15 ) I₁ + ( 10 + 0.25 ) I₃

21 = 23.5 I₁ + 10.25 I₃ —- ( 1 ) ( 1 )

Apply Kirchoff's law to the right side loop as the next step.

E3 - E4 - E2 equals (r3 - r4 - R3) I₂ - ( r₂ + R₂ ) I₃

12 - 24 - 3 = ( 0.75 + 0.25 + 12 ) I₂ - ( 0.25 + 10 ) I₃

-15 = 13 I₂ - 10.25 I₃ —- ( 2 ) ( 2 )

Note: I1 = I2 + I3 when using the Law of Junction.

concurrently solve equations (1) and (2)

I1=0.492A, I2=-0.428A, and I3=0.920A

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7319.6 miles is the estimate of the average distance from the earth to the moon

The length along a line or line segment between two points on the line or line segment.

We can use the triangle formed by the earth's center, point A, and the moon to find the distance.

Let us use the law of cosines to find the distance from the earth to the moon.

d = √3960² + 6156² - 2(3960)(6156)cos(90))

The value of cos90 is 0.

d = √3960² + 6156²

d=√15681600+37896336

d=√53577936

d=7319.6 miles.

Hence,7319.6 miles is the estimate of the average distance from the earth to the moon

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