This table shows the results of a survey on how students get to school.
A circle graph is to be used to display the data.
Calculate the sector angle, to the nearest degree, for each method of transportation.
Transportation Number of Students
Bus 39
Bike 12
Walk 25
Car 24

The temperature on the surface of the planet, based on the equation for the temperature, is 47 degrees Celsius.

The equation given of y = 47 - 5x, is such that every one kilometer that we go from the surface of the planet, the temperature reduces by 5 degrees Celsius.

What this means is that at the surface of the planet the temperature is 47 degrees Celsius because this is the temperature when we have not gone a single kilometer above the surface.

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The rest of the question is:

Note that a change can be an increase or a decrease.

For an increase, use a positive number. For a decrease, use a negative number.

What is the temperature on the surface of the planet?

The Equation x² − 15x + 12 = 0 have two Real solution and 3x² − 6x + 4 = 0 have Imaginary solution.

The discriminant, denoted by the equation b² - 4ac, can be used to ascertain if the solutions are real, repetitive, or complex:

1) If the discriminant is smaller than 0, there are two imaginary roots to the problem (s).

2) The equation has one repeating real solution if the discriminant equals zero (s).

Given:

x² − 15x + 12 = 0

Solving the Quadratic Equation

x² − 15x + 12 = 0

D = b² - 4ac

D = (-15)² - 4(1)(12)

D =  225 - 48

D = 177 >0

So, the Equation will have two Real solution.

b) 3x² − 6x + 4 = 0

Solving the Quadratic Equation

3x² − 6x + 4 = 0

D = b² - 4ac

D = (-6)² - 4(3)(4)

D =  36 - 48

D =  -12 >0

So, the Equation will have Imaginary solution.

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=break your pencil lead while writing, and = feel overly stressed.

=put together a swing set correctly, and =read the directions.

These are independent events because the occurrence of one event does not affect the occurrence of the other event. Breaking a pencil lead while writing and feeling overly stressed may happen at the same time, but one event does not cause the other. Similarly, putting together a swing set correctly and reading the directions are independent events because one action (reading the directions) does not determine the outcome of the other action (assembling the swing set correctly).

=make an error on your income tax return, and =file Form 1040 long.

These are dependent events because the occurrence of one event (making an error on the tax return) affects the occurrence of the other event (filing Form 1040 long). If you make an error on your tax return, you may need to file a longer form to correct it.

=have a salad with dinner, and =work on a home project.

These are also dependent events because one event (having a salad with dinner) does not determine the outcome of the other event (working on a home project). These events may happen at the same time, but one does not cause the other.

Answer:

It will turn on again, just charge it. All phones come with a charger.

The value of x to the nearest integer is $294.

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

We can use the formula for the present value of an increasing annuity to solve this problem:

PV = x/(i-g) × (1 - (1+g)/(1+ i)ⁿ)

where PV is the present value,

x is the first payment,

i is the effective annual interest rate,

g is the annual increase rate of the payments, and

n is the total number of payments.

Substituting the given values, we have:

7229.50 = x/(0.07-0.04) (1 - (1+0.04)/(1+0.07)²⁰)

Simplifying and solving for x, we get:

x = 7229.50×0.03 × (1 - 1/1.07^20) / (1.04 × (1 - 1/1.07²⁰))

x= $294

Therefore, the value of x to the nearest integer is $294.

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Answer:

$3.25 per hotdog

Step-by-step explanation:

This question can be written as a system of equations:

x = price of hotdogs

y = price of drinks

First family:

4x + 4y = 18

Second family

5x + 3y = 20

Multiply each equation so that one of the variables can cancel out:

-3(4x + 4y = 18)

4(5x + 3y = 20)

First equation:

-12x - 12y = -54

Second equation

20x + 12y = 80

Add the equations together

-12x - 12y = -54

20x + 12y = 80

8x = 26

Divide

x = $3.25

Insert the x into one of the original equations to find y:

4(3.25) + 4y = 18

13 + 4y = 18

4y = 5

y = $1.25

Hi there, here's your answer:

Given:

The quotient of twice the difference of five less than a number and six.

Let the number be x.

By this, it is understood that the algebraic equation is in a fractional form, with the numerator being

Twice the difference of five less than a number, i.e.

2(x - 5)

And the denominator is 6.

Therefore, we get the algebraic equation to be:

[tex]\frac{2(x-5)}{6}[/tex]

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The number of ways for which he can choose 7 lures if more than 5 must be jigs is of:

372 ways.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The possible combinations are given as follows:

Hence the number of ways is given as follows:

n = 9!/(6! x 3!) x 4!/(1! x 3!) + 9!/(7! x 2!)

n = 372 ways.

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Answer:

[tex]\textsf{C.} \quad \sin x[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}[/tex]

Rewrite the numerator and denominator of the given rational expression using the following trigonometric identities:

[tex]\boxed{\boxed{\begin{array}{c}\underline{\sf Trigonometric\;Identities}\\\\\boxed{\sec^2 x=\dfrac{1}{\cos^2x}} \qquad \boxed{\csc^2 x=\dfrac{1}{\sin^2 x}}\qquad \boxed{\csc x=\dfrac{1}{\sin x}}\\\\\end{array}}}[/tex]

Therefore:

[tex]=\dfrac{\dfrac{1}{\cos^2x} \cdot \dfrac{1}{\sin x}}{\dfrac{1}{\cos^2x}+\dfrac{1}{\sin^2x}}[/tex]

Multiply the fractions in the numerator, and make the denominators of the fractions in the denominator the same:

[tex]=\dfrac{\dfrac{1}{\sin x\cos^2x}}{\dfrac{\sin^2x}{\sin^2x\cos^2x}+\dfrac{\cos^2x}{\sin^2x\cos^2x}}[/tex]

[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{\sin^2x+\cos^2x}{\sin^2x\cos^2x}\right)}[/tex]

[tex]\textsf{Apply the trigonometric identity}\;\;\boxed{\sin^2x + \cos^2 x = 1}:[/tex]

[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{1}{\sin^2x\cos^2x}\right)}[/tex]

[tex]\textsf{Apply\:the\:fraction\:rule}\;\;\boxed{\dfrac{\frac{a}{b}}{\frac{c}{d}}=\dfrac{ad}{bc}}:[/tex]

[tex]=\dfrac{\sin^2x\cos^2x}{\sin x\cos^2x}[/tex]

Cancel the common factor cos²x:

[tex]=\dfrac{\sin^2x}{\sin x}[/tex]

Simplify:

[tex]= \sin x[/tex]

Therefore:

[tex]\large\textsf{$\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}=$}\;\boxed{\boxed{\sin x}}[/tex]

y-coordinates for x=3, 4.2, 2 are y=3.6, 4.8 and 2.6 respectively.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given equation is y=x+0.6

Find the y value for x=3, 4.2, 2

When x=3

y=3+0.6=3.6

When x=4.2

y=4.2+0.6=4.8

When x=2

y=2+0.6=2.6

Therefore, y-coordinates for x=3, 4.2, 2 are y=3.6, 4.8 and 2.6 respectively.

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The ratio 8.64 : 37.76 as a fraction will be 27/118.

What precisely is ratio?

Ratios and proportions are typically described using fractions. When a fraction is presented as a:b, a ratio is shown, whereas a percentage suggests that two ratios are equal. In this case, a and b can be any two numbers. The ratio and proportion are two essential notions that serve as a foundation for understanding other concepts in mathematics and science.

In our daily lives, we apply the notion of ratio and proportion, such as in business when dealing with money or in cooking.

As a consequence, when b is greater than zero, the ratio specifies the connection between two variables, such as a:b. The 2:4 ratio, for example, is written as 2:4 = 1:2. 

Now,

Given ratio is  8.64 : 37.76

we can write this as 8.64/37.76

=864/3776

=432/1888

=216/944

=54/236

=27/118

Hence,

             The ratio 8.64 : 37.76, as a fraction will be 27/118.

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The GCF of the polynomials are

1. for 15x²+18 , the GCF is 3

2. for -18y⁴+6y³+24y² ,the GCF is 6y²

The GCF stands for the “greatest common factor”. The GCF is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.

The GCF is the highest factor that can be used to divide through 2 or more terms

1. For 15x²+18, 3 is a factor of 15 and 18 and it's the greatest factor, therefore the GCF is 3

2. For -18y⁴+6y³+24y², between 18,6 and 24, 6 is the greatest factor Ang between y⁴ ,y³, y², y² is the greatest factor. Therefore the GCF of the expression is 6y².

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Answer:

[tex]x = -64\\\\y = -63\\\\z = -57[/tex]

Step-by-step explanation:

Diagonally opposite angles of a parallelogram are equal

Therefore

-y - 3 = 60

Add 3 to both sides; -3 terms on left side cancel out

- y = 60 + 3

- y = 63

Multiply both sides by -1

-1(-y) = -1(63)

y = - 63

Another property of a parallelogram is that the angles formed on either end by a side must equal 180°.

Rephrased,

The consecutive or adjacent angles are supplementary which means they add up to 180°

We see that -2z + 6 and 60° are adjacent angles
So

- 2z + 6 + 60 = 180

-2z + 66 = 180

-2z = 180 - 66

-2z = 114

z = 114/-2

z = -57

Similarly

-2x - 8 + 60 = 180

-2x + 52 = 180

-2x = 180 - 52

-2x = 128

x = 128/-2

x = -64

Answer:

126

Step-by-step explanation:

360-97-47-90=126

so 126

Answer: C) 126

Step-by-step explanation: first, you need to use this equation...

m∠A + m∠B + m∠C + m∠D = 360°

=> m∠A + 97° + 47° + 90° = 360°    add all of the numbers...

=> m∠A + 234° = 360°                  subtract both sides by 234

=> m∠A = 360°- 234°

=> m∠A = 126°

Hope you've understood...

Answer:

D

Step-by-step explanation:

ASA = 2 non included angles + 1 included side

by knowing angle c is congruent to angle z we can prove the triangles are congruent by ASA postulate.

The correct statements would need to be congruent to show that

Δ ABC= ΔXYZ by ASA are,

⇒ ∠ B ≅ ∠ Y

⇒ ∠ C ≅ ∠ Z

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

AC = XZ

∠ A = ∠ X

Now, To prove the triangles are congruent by ASA , we get;

AC = XZ

∠ A = ∠ X

⇒ ∠ Z = ∠ C

or, ∠ B = ∠ Y

Thus, The correct statements would need to be congruent to show that

Δ ABC= ΔXYZ by ASA are,

⇒ ∠ B ≅ ∠ Y

⇒ ∠ C ≅ ∠ Z

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Answer:

(-3,-1)

Step-by-step explanation:

The two lines intersect at that point. -3 is in the x axis and -1 is in the y axis.

Faith earned £96 in interest at the end of the 3 years.

Using the  simple interest formula:

I = P x r x t

where

I is the interest earned,

P is the principal or initial amount invested,

r is the interest rate as a decimal, and t is the time period in years.

In this case, Faith invested £800 for 3 years at a simple interest rate of 0.4% per year, or 0.04 as a decimal. Plugging in the values:

I = £800 x 0.04 x 3

= £96

Therefore, Faith earned £96 in interest at the end of the 3 years.

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The slope of the line with the points (6, 3) and (12, 6) is equal to 1/2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (6, 12).

Points on y-axis = (3, 6).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (6 - 3)/(12 - 6)

Slope, m = 3/6

Slope, m = 1/2.

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The practise of extracting information from data to guide better business decisions is known as data analysis. Five iterative phases typically comprise the data analysis process:

Choose the data you want to examine.

gather the data

Clean up the data before analysis.

Study the information

Interpret the analysis' findings

It is common knowledge that data analysts focus on the sample size in order to

To prevent a few outlier responses from distorting the results

ensuring that the data reflects a variety of viewpoints

to prevent making erroneous conclusions due to a tiny sample size

An analyst of data is who?

An individual involved in the handling of data is referred to by this phrase.

Such a person aids in the analysis, retrieval, and drawing of conclusions from the information at hand.

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The median of the following salary list is 29763.

The median is the average in the centre of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. For a small data collection, calculate the number of data points (n) and organize them in ascending order.

The middle score in the group is called the median. Begin by sorting all of the data sets from lowest to highest before calculating the median. The median in an odd-numbered set will be the value that falls exactly in the center of the list. You must determine the average of the two middle integers in a set of even numbers.

Arrange in ascending order

21955, 25963, 27507, 32019, 38850, 43715

Take the two mid terms

27507 and 32019

Median = [tex]\dfrac{27507 + 32019}{2}[/tex]

Median = 29763

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Answer:x^3+x^2-8x-32

Step-by-step explanation:

The expression equivalent to 5x +10y -15 by taking the common factor is 5(x + 2y - 3).

What is taking out common factors?

The takeout of the common factor is the procedure, ab + ac = a(b + c). Think about how the expression 5x + 10 gets factored. The common factor 5, which was previously in front of the brackets, has been removed.

Figuring out what to multiply to create an expression. It is comparable to "splitting" an expression into numerous smaller expressions.

Given, the expression is 5x + 10y -15

So, 5x +10y -15 = 5x + 5*2y - 5*3

                         = 5(x + 2y - 3)

Hence, the required answer is 5(x + 2y - 3).

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Answer:

D

Step-by-step explanation:

why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.

x²

-x²

-x -x

x x x x (clearly that means 4x)

-1 -1 -1

1 1

so, we see it is D.

The solution is, 12 (long division) 924 = 77.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

12 (long division) 924

so, we get,

12 | 924  | 77

     84

----------------

       84

       84

-----------------

       0

Hence, The solution is, 12 (long division) 924 = 77.

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Answer: A lot

Step-by-step explanation:

The equation of the polynomial is P(x) = -4(x + 1)(x - 1)(x - 2)^2

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

The graph

On the graph, we have the following readings:

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

Using the above as a guide, we have the following:

P(x) = a * (x + 1)(x - 1)(x - 2)^2

The y-intercept is -12

So, we have

a * (0 + 1)(0 - 1)(0 - 2)^2 = -12

This gives

a = -4

Hence, the expression is P(x) = -4(x + 1)(x - 1)(x - 2)^2

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Answer:

C

Step-by-step explanation:

An irrational number cannot be shown as a simple fraction. If the number has decimals that are non-repeating (so not 7.85555555... or. 9.121212121...), cannot be shown as fractions (not 1.50000000... as it can be written as 3/2), and does not terminate (aka end).  C is the answer you're looking for, as it cannot be shown as a fraction, the numbers after the decimal go on indefinitely,  and the number's don't follow a noticeable repeatable pattern.

Answer:

Step-by-step explanation:

Answer:

0.89

Step-by-step explanation:

As there is 1 green marble out of 9 total marbles, there's a 1 in 9 chance of selecting the green marble. This means that its complement would be the probability of NOT selecting the green marble would be 8/9, or about 0.89

Answer:0.89

Step-by-step explanation: