45% of c is 72. Find the value of c

Answer:

2x+7

Step-by-step explanation:

this is because if you rearrange the bottom equation to be in y= format, this is the solution you will find

Answer:

(a) 6

(b) 49

Step-by-step explanation:

(a) The largest integer which is a factor of 96 and 294 should be their HCF.

Therefore, 96 = 2 × 2 × 2 × 2 × 2 × 3

294 = 2 × 3 × 7 × 7

Therefore, HCF = 2 × 3 = 6

(b) 96n should be the LCM of 96 and 294.

We know, product of two numbers = HCF × LCM

or, LCM = (96 × 294)/6 = 4704

So, 96n = 4704

or n = 49

Hope it helps.

If you have any query, feel free to ask.

The transformation f(x)↦ 1/8f(x) will shrink the graph of f(x) by 8 times.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) → 1/8 f(x)

This means,

The function f(x) will shrink by 8 times.

Thus,

f(x) ↦ 1/8f(x) will shrink the graph of f(x) by 8 times.

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8639 is the value of 75 U.S. dollars in Japanese yen.

The term "yen," which refers to Chinese round coins, dates back in time (yuan). The yen was first coined in 1869, following the Meiji Restoration, and was formally recognised as the fundamental unit in the 1871 monetary reform.

"Yen" is Japanese for "circle" or "round thing." With the "New Currency Act" of 1871, the Meiji government formally adopted this currency in an effort to stabilise the nation's monetary position at the time.

The difference between US and Japanese interest rates has been a major factor in the decline of the yen. In an effort to combat the growing cost of living, the US Federal Reserve has aggressively increased its key interest rate from 0.25% to 3.25% since March.

As we see from the table that,

1 U.S dollar = 115.19 Japanese Yen

$1 = 115.19 ¥

so, $75 = 115.19 × 75¥

$75 = 8639.25¥  ≈ 8639¥

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The true statement about the functions is that that graphs are perpendicular lines

From the question, we have the following parameters that can be used in our computation:

y = 3/4x + 7

y = -4/3x + 7

A linear equation is represented as

y = mx + c

Where

slope = m

This means that the slopes are

3/4 and -4/3

The above slopes are opposite reciprocal

i.e.

3/4 * -4/3 = -1

Hence, they are perpendicular lines

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The simplest form of the function is f(x) = x2. The graph is a parabola often called the basic parabola.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form.

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.

Solve f{x}=x-2?

f(x)=x-2    x∈R

x≤0

x-2≤2

Range of f(x)=[∞,2)

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The original number of CDs is between 1000 and 1500.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Number of copies of a popular CD left to be sold in the store = 20

According to question, this is between 15 and 1.5% of the original number of copies of the CD in the store.

Let the original number of copies of the CD be 'x'.

Now, 20 is equal to 1% of the original number of copies of the CD,

1% of x = 20

1/100 of x= 20

x= 2000

Or if 15 is equal to 1.5% of the original number

1.25% of x= 20

1.25/100 x = 20

x = 1600

Hence, the CDs is between 1000 and 1500.

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The required maximum amount of money the salesperson earns for the entire year is given as $5400.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let the total amount earned be x,
According to the question,
x = 2400 + 250×12
x = $5400

Thus, the required maximum amount of money the salesperson earns for the entire year is given as $5400.

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The mean of the data be 10.5, median is 10.5 and range be 5.

The numbers are sorted, added, and then divided to determine the mean.

8 + 9 + 10 + 10 + 10 + 11 + 11 + 11 + 12 + 13 = 105

Mean = 105 ÷ 10 = 10.5

Mean = 10.5

In essence, determining the median is locating the value in a data sample that lies physically between the other numbers.

The middle number, please. Your right finger should go on 8, and your left finger should go on 13. Your right finger should be at 11, while your left finger should be at 10.

10.5 is the median because it is the midpoint number.

Subtract the largest number from the smallest number to determine the range.

13 - 8 = 5

Therefore, 5 be the range of the data.

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The mean of the data be 10.5, median is 10.5 and range be 5.

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Answer: It would take a total of 11 hours

Step-by-step explanation: here I am using the universal equation of DST, depending on which elements we have we will use this equation.

if we have D, multiply S*T

If we have S Divide D/T

If we have T Divide D/S

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For the required value of the given complex numbers z₁z₂ = 32(cos 255° + isin 255°).

Complex numbers are those that expand on the idea of real numbers by incorporating an illogical element.

The formula for a complex number is "a + bi," where "a" and "b" are real numbers and "i" is the imaginary unit, which is equal to the square root of -1.

"A" stands for the complex number's real component, and "b" stands for the imaginary component.

We multiply the magnitudes of two complex numbers and add their arguments to determine their product.

Let's compute z₁z₂ with the supplied values.

Given:

z₁ = 8(cos 45° + isin 45°)

z₂ = 4(cos 210° + isin 210°)

We add the arguments and multiply the magnitudes to find z₁z₂:

Magnitude of z₁ = 8

Magnitude of z₂ = 4

Argument of z₁ = 45°

Argument of z₂ = 210°

Now, let's calculate z₁z₂:

Magnitude of z₁z₂ = (Magnitude of z₁) × (Magnitude of z₂) = 8 × 4 = 32

Argument of z₁z₂ = (Argument of z₁) + (Argument of z₂) = 45° + 210° = 255°

Therefore, z₁z₂ = 32(cos 255° + isin 255°).

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The correct question =

Given z₁ = 8(cos 45° + isin 45°) and z₂ = 4(cos 210° + isin 210°), what is z₁z₂?

The area of the rectangular piece of land owned by the rancher is:

13.5

The area of a rectangle is a measure of the size of the rectangular space it encloses.

It is calculated by multiplying the length and the width of the rectangle. In this case, the length of the rectangular piece of land owned by the rancher is 5.4 miles and the width is 2.5 miles. To find the area, we multiply these two values.

The formula for finding the area of a rectangle is:

Substituting the values of length and width into the formula:

So the area of the rectangular piece of land owned by the rancher is 13.5. This means that if we divide the land into unit squares of 1 square mile each, we would have 13.5 such unit squares.

The area of a rectangle is an important metric in geometry and is widely used in many fields, including construction, agriculture, and real estate.

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The possible approximate lengths of b are: 2.3 units and 7.8 units

We know that the law of sines for triangle is:

The ratios of the length of all sides of a triangle to the sine of the respective opposite angles are in proportion.

This means, for triangle ABC,

[tex]\frac{sin~ A}{a} =\frac{sin~B}{b} =\frac{sin~ C}{c}[/tex]

where a is the length of side BC,

b is the length of side AC,

c is the length of side AB.

For triangle ABC consider an equation from sine law,

[tex]\frac{sin~ A}{a} =\frac{sin~ C}{c}[/tex]

here, c = 5.4, a = 3.3, and m∠A = 20°

[tex]\frac{sin~ 20}{3.3} =\frac{sin~ C}{5.4}\\\\\frac{0.3420}{3.3} =\frac{sin~ C}{5.4}[/tex]

0.3420 × 5.4 = 3.3 × sin(C)

sin(C) = 0.5596

∠C = arcsin(0.5596)

∠C = 34.03°  OR 145.9°

∠C ≈ 34° OR 146°

We know that the sum of all angles of triangle is 180 degrees.

so, ∠A + ∠B + ∠C = 180°

when m∠C = 34°,

20° + ∠B + 34.03° = 180°

∠B = 125.97°

m∠B = 126°

when m∠C = 146°,

20° + ∠B + 146° = 180°

m∠B = 14°

Now consider equation,

[tex]\frac{sin~ A}{a} =\frac{sin~ B}{b}\\\\\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 126^{\circ}}{b}[/tex]

b × 0.3420 = 0.8090 × 3.3

b = 7.8 units

when m∠B = 14°,

[tex]\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 14^{\circ}}{b}[/tex]

b × 0.3420 = 0.2419 × 3.3

b = 2.3 units

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The complete question is:

Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction

In ΔABC, c = 5.4, a = 3.3, and measure of angle A = 20 degrees. What are the possible approximate lengths of b? Use the law of sines to find the answer.

2.0 units and 4.6 units

2.1 units and 8.7 units

2.3 units and 7.8 units

2.6 units and 6.6 units

Answer: The slope between the points (0,-5) and (-2,3) is (-3 - (-5)) / (-2 - 0) = -8 / -2 = 4.

Step-by-step explanation:

Yes, the vectors v1 = (0,0,-3), v2 = (0,-3, 9), and v3 = (4,-2,-6) do span ℝ3.  This is because any 3 vectors in ℝ3 will span the entire space, meaning that any vector in ℝ3 can be written as a linear combination of these 3 vectors.

To determine if a set of vectors spans a space, we can create a matrix with the vectors as columns and row reduce it to see if there are any free variables. If there are no free variables, the vectors span the space.

The matrix with v1, v2, and v3 as columns is:

| 0 0 4 |

| 0 -3 -2 |

| -3 9 -6 |

Row reducing this matrix gives us:

| 1 0 0 |

| 0 1 0 |

| 0 0 1 |

Since, there are no free variables, the vectors v1, v2, and v3 do span ℝ3.

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The line of best fit for the given points is as follows:

y = 1.21x + 1.57.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

The points for the data-set in this problem are given as follows:

(1,2), (2,5), (3,7), (4,2), (5,10), (6,10) and (7,9).

Inserting these points into the linear regression calculator, the line of best fit for these points is defined as follows:

y = 1.21x + 1.57.

(rounding the coefficients to two decimal places).

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The first part of the process of investigating a question using data is C. Collecting the data.

The first ideas regarding the questions to ask guide the data exploration process. It continues with planning, data gathering and exploration, and feature reporting. There are many different ways to explain and summarize the procedure.

Data is information that has been transformed into a cycle that is useful for transfer or processing in computing. Data is information that has been transformed into binary digital form for use with modern computers and communication mediums. The topic of data may be used in either the

Therefore, option C is correct.

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missing options:

A. Describing the data

B. Describing the data

C. Collecting the data

D. Rephrasing the question

When converted from active voice to passive voice, the sentences read as follows:

Active Voice refers to a sentence construction where the subject is performing the action described by the verb. It emphasizes the doer of the action.

On the other hand, Passive Voice refers to a sentence construction where the action is performed on the subject, rather than the subject performing the action. It emphasizes the action or the object affected by the action.

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Combinations and sequences are widely used in mathematics to explain and assess situations in which the order or selection of components might influence the final result.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

Here,

A combination is a grouping of things from a bigger set in which the order of the components is irrelevant. A sequence is a collection of elements that are ordered in a precise order. Combinations and sequences are frequently used in mathematics to describe and evaluate situations where the order or selection of components might impact the final outcome, such as in combinatorics, probability, and statistics.

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Complete question:

A combination of values that, when arranged correctly, result in a final value. true/false

The width of the enlargement would be 34.2857 cm.

The distance separating an object's ends is its length. The longest dimension is this one. The width of an object is the separation between its two sides. The shortest dimension is this one.

Initial dimension of shorter side = 10 cm

Initial dimension of longer side = 7 cm

Final dimension of shorter side = 24

Final dimension of longer side = x cm

The enlargement always ensure the aspect ratio = longer side / shorter side

10/7 = x/24

Solving for x, we get

[tex]$\frac{x}{24}=\frac{10}{7}$$[/tex]

simplifying the above equation, we get

[tex]$\frac{24 x}{24}=\frac{10 \cdot 24}{7}$$[/tex]

[tex]$x=\frac{240}{7} cm$$[/tex]

Therefore, the  value of x be 34.2857 cm.

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According to the growth factor, starting value and the number of years passed, the number of people who would have died is 12.94×10⁷.

The number of people who would have died from AIDS in 2005 will be calculated by the formula -

f(t) = a×[tex] {b}^{t} [/tex]. In this formula, f(t) is the number of cases that occured in the mentioned number of years and t is the number of years between the start and year in question. a is strating value and b is growth.

t = 2005 - 1990

Performing subtraction on Right Hand Side of the equation

t = 15 years

Keep the values in formula

f = 1900 × 2.1¹⁵

Calculating the power

f = 1900 × 68,122.32

Performing multiplication on Right Hand Side of the equation

f = 12.94 × 10⁷

Thus 12.94×10⁷ people would have died.

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The range of the new score distribution will be greater than the range of the original score distribution.

The range of a set of scores is the difference between the highest and the lowest scores in the set. Adding 5 bonus points to the 10 highest scores in the original set will increase the highest scores and therefore increase the range of the new score distribution.

The range of the original score distribution represents the spread of scores between the highest and lowest scores in the original set, and increasing the highest scores will increase the spread of scores between the highest and lowest scores in the new set, resulting in a greater range.

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(1) By 1716 different ways can the offices be filled if each person can hold at most one office.

(2) By 132 number of ways Caden can be the chairperson.

(3) By 1320 of the 1716 total ways the offices can be filled,

(1) If each person can hold at most one office, there are 13 people to choose from for the first office, 12 people remaining to choose from for the second office, and 11 people remaining to choose from for the third office.

Therefore, the number of different ways the offices can be filled is:

13 * 12 * 11 = 1716 ways

(2) If Caden is the chairperson, there are 12 people to choose from for the second office and 11 people remaining to choose from for the third office.

Therefore, the number of ways Caden can be the chairperson is:

12 * 11 = 132 ways

(3) If Caden is an officer, there are 12 people to choose from for the first office, 11 people remaining to choose from for the second office, and 10 people remaining to choose from for the third office.

Therefore, the number of ways Caden can be an officer is:

12 * 11 * 10 = 1320 ways

So, in 1320 of the 1716 total ways the offices can be filled, Caden is one of the elected officers.

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the area of the given figure will be 13.8 cm².

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The area of triangle = 1/2 (hb)

The sum of all angle of triangle = 180

A triangle with side 6.9 cm extends to form a second right triangle with a height of 4cm.

So the area will be A = 1/2 *6.9 * 4

A = 13.8 cm²

Hence the area of the given figure will be 13.8 cm².

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Answer:

No

20 inches

Step-by-step explanation:

Area of a triangle = 1/2 × breadth × height

Therefore,

[tex] \frac{1}{2} \times 5 \times 8[/tex]

[tex] = \frac{1}{2} \times 40[/tex]

That mean

[tex] = \frac{40}{2} = 20[/tex]

Answer:

rotation on x axis;

(x, y) 》(x, -y)

So,(-6,5) is the correct answer.

Answer:

(-6,5)

Step-by-step explanation:

(x,y) ------》 (x,-y) {reflection over x-axis}

26x - 52y  is the equivalent expression.

2(13a - 5) is the equivalent expression.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

-13 (-2x + 4y)

= -13 x -2x+ -13 x 4y

= 26x - 52y

Now,

26a - 10

Taking out a common factor.

= 2 (13a - 5)

Thus,

26x - 52y and 2(13a - 5) are the equivalent expression.

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