A car is traveling at a speed of 61 kilometers per hour. What is the car's speed in kilometers per minute? How many kilometers will the car travel in 20 minutes? Do not round your answers.

A dilation or combination of stiff movements and dilations constitutes a similarity transformation.

Similar figures don't always have to have the same size but share the same form.

A transition called a dilation keeps shape but not size. So a dilatation is a motion that is not rigid. A dilation or combination of stiff movements and dilations constitutes a similarity transformation. If and only if a similarity transformation translates one of the geometric figures onto the other, then two figures are said to be similar. Similar figures don't always have to have the same size but share the same form.

Similarity transformations include translation, reflection, rotation, and dilation. Rotation, reflection, and translation retain both size and form since they are rigid movements, whereas dilation just makes sure that the shape is preserved.

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Victoria has 37 dimes and 28 quarters in total.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is that Victoria has a total of 65 dimes and quarters worth $10.70.

We can write the system of equations as -

x + y = 65

(1/10)x + (1/4)y = 10.70

Refer to the graph attached. On solving the equation graphically, we get-

x = 37, y = 28

Therefore, Victoria has 37 dimes and 28 quarters in total.

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Answer: $95.76

Step-by-step explanation:

If the 15 is referencing 15%.

15% of 638.40 can be found by making 15% a decimal by moving the decimal to the left twice.

.15 X 638.40= 95.76

As per the conditions given by the question, the 95% confidence interval of the true proportion who said that they would take a ride in a self-driving car is (53.3856%, 62.6144%).

Now, According to the question:

What is confidence interval?

A confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

To find the 95% confidence interval of the true proportion, we need to use the following formula:

point estimate +/- (margin of error * z-score)

The point estimate in this case is the sample proportion, which is 58%. The margin of error is 2.4%, and the z-score for a 95% confidence interval is 1.96.

Plugging these values into the formula, we get:

58% +/- (2.4% * 1.96)

This simplifies to:

58% +/- 4.6144%

So the 95% confidence interval is:

(53.3856%, 62.6144%)

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The value of x in the shape we have here is given as 18.7 cm

In this question we are to find the value of x using the values that we already have in the shape.

The base of the diagram has its length as 40 cm.

The shape is made up of two right angled triangles.

since the top of the shape is 26 m, the triangles would be gotten by

40 - 26 = 14

14 / 2 = 7cm

each rectangular base is therefore 7 cm

we have to solve for the value of x using the Pythagorean theorem

hence we would have:

7² + x² = 20²

49 + x² = 400

x² = 400 - 49

x² = 351

x = 18.7 cm

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The formula to find the side of a geometric shape depends on the shape itself. Few details like area or perimeter of a shape or surface area or volume of a solid with few other parameters should be known.

Few examples :

For a square, the formula to find the side (s) is:

s = √(A)

where A is the area of the square.

For a rectangle, the formula to find the length (l) and width (w) are:

l = A/w and w = A/l

where A is the area of the rectangle.

For a triangle, the formula to find the base (b) and height (h) are:

A = (b*h)/2

where A is the area of the triangle.

For a cube, the formula to find the side (s) is:

V = s^3

where V is the volume of the cube.

Keep in mind that these are a few examples of formulas that can be used to find the side of a geometric shape. Depending on the specific problem, different formulas may be required.

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Using the linear function given, the tree will have a height of 5.25 feet in 3 years

Linear functions are mathematical functions where the output values are in direct proportion to the input values. A linear function has the form

y = mx + c, where m is the slope of the line and c is the y-intercept.

In this problem, the function given already models y = mx + c

Since y = 3/4x + 3;

The height of the tree in 3 years can be solved as;

y = 3/4(3) + 3

y = 9/4 + 3

y = 5.25

The height of the tree in 3 years is 5.25 feet

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With a mass of 50 kg, Becky used 588 watts power to sprint up a 3.0 m high set of stairs in 2. 5 seconds. She is able to run up a 4.5 m high flight of stairs in 3.75 s.

Work (in joules) equals your weight (in newtons) x the height of the stairs (in meters.) The power you now possess is equal to the sum of your labor times the duration of that labor, or: Work (measured in joules) divided by time equals power, measured in watts (in seconds.)

Given that mass of Becky is 50 Kg

gravity of earth is 9.8 m/s²

height of stairs is 3.0 m

time taken to run up in stairs is 2.5 s

Power = work done/ time taken

P = (50*9.8*3.0)/2.5

P = 1470/2.5

P = 588 watt

Becky is able to run up a 3.0 m high flight of stairs in 2.5 s

She is able to run up a 4.5 m high flight of stairs in t =  (2.5 * 4.5)/3

t = 11.25/3

t = 3.75 s

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Answer:

9.75

Step-by-step explanation:

3/4 |1/3x+2| < 6

you can turn the < into a =

then subtract 3/4 from 6 which leaves you with 5.25. And since you know 2 will always be positive because it's in an absolute value bracket 5.25-2=3.25. Which leaves you with

|1/3x| = 3.25

then do 3.25/(1/3) which leaves you with 9.75

:)

The y-intercept of the sine function is -3

We know that the standard form of the sine function is, y = a sin(bx + c) + d

where, amplitude = |a|

period = 2π/b

phase shift = -c/b

and vertical shift = d

Here, a sine function has an amplitude of 3, a period of π, and a phase shift of π/4

a = 3,

So, 2π/b = π

⇒ b = 2

And phase shift -c/b = π/4

⇒ -c/2 = π/4

⇒ -c = π/2

⇒ c = -π/2

So, a sine function would be,

y = 3 sin(2x + -π/2) + 0

y = 3 sin(2x + -π/2)

When x = 0,

y = 3 sin(0+ -π/2)

y = 3 sin(-π/2)

y = 3 × (-1)

y = -3

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If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

If p(x) is a polynomial function with p ( 3/4 ) = 0

Then we need to find which of the given statements are true.

A. The function has a factor of (4x + 3).

If x=3/4 then 4(3/4)+3 which is not equal to zero

B. The function has a factor of (4x – 3).

If x=3/4 then 4(3/4)-3 which is equal to zero

C. The function has a factor of (3x + 4).

If x=3/4 then 3(3/4)+4 which is not equal to zero

D. The function has a factor of (3x – 4).

If x=3/4 then 3(3/4)-4 which is not equal to zero

Hence, If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).

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Answer:

$260

Step-by-step explanation:

$273 - 5% = $260
5% commission = $13

Answer:

260

Step-by-step explanation:

273-5%=260

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.

Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.

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The symbol ∑ (sigma) is used to represent the sum of a set of numbers. This is very important notation in statistics.

If a hypothesis is correct, a set of data's standard deviation serves as a gauge of how rare it is. Standard deviations are expressed in units called sigma, or, by physicists. The findings are progressively inconsistent with the hypothesis as the number of sigma increases. The word's derivation is derived from the Greek letter "sigma," which is used in statistics to measure how much a process deviates from its mean or goal.

To express the total of a set of data or the total of a function over a specified range, it is frequently used in statistics and probability. For instance, if X is a collection of numbers, the term ∑X would stand for the collection's total. The symbol is typically followed by a variable, such as I indicating the range of the sum, for example, ∑i=1 to n for the summing from i=1 to i=n. The index I is frequently used to identify the individual components of the set.

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The log value of log2 is 1Log2 is defined as the logarithm base 2. This means that the logarithm of any number x is equal to the power to which the base 2 must be raised to produce x.

In other words, log2(x) = y, where 2^y = x.

Therefore, when x = 2, 2^y = 2. This means that the logarithm of 2 is equal to 1, since 2^1 = 2.

Therefore, the log value of log2 is 1.

Log2 is an important mathematical concept that is used to calculate the logarithm of a number. Logarithms are used in a variety of fields, including mathematics, physics, engineering, and computer science. Log2 is the logarithm with a base of 2, which means that the logarithm of any number x is equal to the power to which the base 2 must be raised to produce x. To calculate log2 of a number, the formula is log2(x) = y, where 2^y = x. This means that the logarithm of 2 is equal to 1, since 2^1 = 2. Therefore, the log value of log2 is 1. Log2 is often used to calculate logarithms of numbers that are not powers of 2, such as log2(3) = 1.5849. Log2 can also be used to calculate logarithms of numbers with decimals, such as log2(1.5) = 0.5849. Log2 can also be used to calculate exponents, such as 2^3 = 8.

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The complete maze pattern is shown below.

Given is an exponent maze.

We can complete the maze as -

START HERE →→ 3³ → → 9 →→ 1³ →→ 1 →→ 9² →→ 81 →→ 4³ →→ 64 →→ 2⁵ →→ 32 →→ 11² →→ 121 →→ 8² →→ 64 →→ 15³ →→ 3375 →→ 13² →→ 169 →→ 2⁴ →→ 16 →→ 10² →→ 100 →→ 2³ →→ 8 →→ 6⁴ →→ 1296 →→ 12² →→ 144 →→ 3³ →→ 27 →→ YOU MADE IT.

Therefore, the complete maze pattern is shown above.

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Therefore , the solution of the given problem of long division is Quotient is 131 and the Remainder is 5

Synthetic division is another way to divide a polynomial but by binary x - c, while c is a constant. The divisor frequently assumes the form of (x a). In synthetic division, you are just interested in the coefficients of the polynomials, unlike long division.

Here,

The given Divisor = 6 and Dividend = 791

Step 1: Take the first digit of the dividend from the left. ...

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It is the most common method used to solve problems based on division.

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$b+$12 is the equation that will determine the amount of the original bill

percentage, a relative value indicating hundredth parts of any quantity.

Given that The friend told the waiter to remove the $12 dessert from Stan’s bill.

Stan tipped the waiter 20% on the reduced bill, which was a $15 tip

We need to write an equation that will determine the amount of the original bill b.

Let us find what 20% of amount will be 15

20/100×b=15

0.2x=15

b=15/0.2=75

The reduced bill is $75.

As before $12 is removed

$b+$12=$87

$87 is the original bill and 15 is the tip.

Hence, $87 is the original bill.

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Hello there!

Answer:

[tex]V = 18432\pi[/tex] or approximately 57876.48

Step-by-step explanation:

[tex]V = \frac{4}{3} \pi R^{3}[/tex]

R = 24

[tex]V = \frac{4}{3} \pi *24^{3} = 18432\pi[/tex]

if [tex]\pi =3.14[/tex] then:

[tex]V = 57 876.48[/tex]

The answer is :6.5g

The inequality is x 26 and asks for the values of x where the perimeter of the rectangle is smaller than 112.

In mathematics, a link between two terms or values that isn't comparable is referred to as an inequality. As a result, imbalance leads to inequality. A mathematical inequality is a relationship between two non-equal expression . Egality is distinct from inequality. The not common basic is frequently used to denote that two values aren't actually equal (). Various inequalities are used to contrast the values, no matter how small or large. Many simple inequalities can be resolved by switching the two aspects until the variables are the only thing remaining. But a number of things encourage inequality: Values that are negative are divided or added along either side.

Here,

given

A rectangle's perimeter is determined by its length, width, and height.

rectangle's perimeter is calculated as length + length + width + width.

(x +4) + (x+4) + x + x < 112

x + 4 + x + 4 + x + x < 112

4x + 8 < 112

4x < 104

x < 26

In order to find the x value that occur when the rectangle's boundary is less than 112, the inequality is x 26.

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Answer:

2.35 + 0.55 × 15 = 10.6

Therefore, she can go 10.6 miles.

Answer:

10.6

Step-by-step explanation:

2.35 + 0.55 x 15 = 10.6

Answer: No rectangle can make this shape

Step-by-step explanation:

Real numbers are every  number that exists in the real line, The four types of real numbers are rational, irrational, Natural and Integers.

In mathematics, a real number is a value that can be represented on the number line. The set of real numbers includes both rational numbers (such as integers, fractions, and decimals) and irrational numbers (such as √2 and π). Real numbers also include positive numbers, negative numbers, and zero. The set of real numbers is usually represented by the symbol R, and it has the properties of being closed under the operations of addition, subtraction, multiplication, and division (except for division by zero).

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

Rational number = 3/4, -6/2, or 0.5.

Irrational number = √2, π, or e.

Natural number = 1,2,3,4....

Integers = -4, -1, 0, 1, 4.

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Answer:

Undecidable Problems

Step-by-step explanation:

Yes, 6/8 and 9/12 are equal. After simplifying both the fractions we got that both are equal and their value is 3/4.

Let's first try to understand what is a fraction.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

A fraction would be 5/10, for instance.

Here, the numerator is 5 and the denominator is 10.

6/8 is a fraction.

6/8 can be simplified further.

6/8 = 3/4

9/12 is also a fraction.

9/12 can be simplified further.

9/12 = 3/4

To compare 2 fractions first we try to make the same denominator.

we have the same value. so they are equivalent.

Given question is incomplete complete the question here:

Are 6/8 and 9/12 equivalent?

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Yes, 9 is a positive number because 9 is a natural number and also we use 9 in our daily life counting problems also.

Let's first attempt to understand what numbers are.

A number is an arithmetic value that is computed and used to represent a quantity. Numbers are represented in writing by symbols like "3," which are numerical symbols. A number system is a methodical way of employing digits or other symbols to represent numbers. The numerical system is a useful set of numbers that reflects the mathematical and algebraic structure of the number. provides a typical illustration.

Positive numbers Any number that represents something other than zero is considered to be positive. When referring to the amount of money in your bank account, a positive figure would undoubtedly make you feel good as well.

So 9 is a positive number.

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