Graph the equation by using the slope intercept method

The maximum number of pages the report can have, using scientific notation, is of:

2 x 10^6.

A number in scientific notation is written as follows:

[tex]a \times 10^b[/tex]

With the base symbolized [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.

For this problem, the maximum number of pages that the report can have is given by the following division:

Maximum number of pages = Total capacity/Size of page.

These variables, from the text, are given as follows:

Hence the number of pages is obtained as follows:

Maximum number of pages = 4 x 10^6 KB / (2 KB/ page) = 2 x 10^6 pages.

When two numbers are divided in scientific notation, the bases are divided(4/2 = 2), while the exponents are subtracted (6 - 0 = 6).

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Answer:

7 is correct.

There are 4 small triangles, 2 medium-sized triangles, and 1 large triangle.

0.57 mi²  = 15,890,688 ft² after converting square miles in square foot.

The given conversion in question is-

0.57 mi²  = __ ft²

We know that

1 mi²  = 27,878,400 ft²

Then, multiply both sides by 0.57

1 x 0.57 mi²  = 27,878,400 x 0.57 ft²

0.57 mi²  = 15,890,688 ft²

Thus, the conversion of 0.57 mi²  = 15,890,688 ft².

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The probability of landing on an even number or a number greater than two is 5/6.

A fair die is rolled. We need to find out the probability of landing on an even number or a number greater than two.

Let the event of landing on an even number be denoted by the variable E1. Let the event of landing on a number greater than two be denoted by the variable E2. We need to calculate P(E1 ∪ E2).

P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)

P(E1 ∪ E2) = (3/6) + (4/6) - (2/6)

P(E1 ∪ E2) = 5/6

Hence, the probability of landing on an even number or a number greater than two is 5/6.

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Answer: y=2x+1

Hope this helps

The length of AC is 17.3 cm

acc to our question,

Hence,The length of AC is 17.3 cm

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The angle RSQ = 105° and angle PQS = 78°

Given,

In the question:

In the figure,

PSR is a straight line .

To find the angle RSQ and angle PQS.

Now, According to the question;

In ΔQRS,

we know that :

Sum of angle of triangle is 180 degree.

Angle (SQR + QRS + RSQ) = 180°

In the figure,

Angle (23° + 52° + RSQ) = 180°

75° + ∠RSQ = 180°

∠RSQ = 180 - 75

∠RSQ = 105°

We have to find the ∠PQS

Now, PSR is a straight line

In Triangle PSQ

Find the ∠S

105 + ∠S = 180° (Linear Pair)

∠S = 75°

In ΔPQS

Angle(SPQ + PQS + QSP) = 180°

Angle(27° + PQS + 75° ) = 180°

∠PQS = 180 - 102

∠PQS = ∠78°

Hence, The angle RSQ = 105° and angle PQS = 78°

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The total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.

Given, Joh rent a kayak at a nearby state park.

He pay a fee of 12.99 plus 3. 75 for each hour that he spend in the water.

We have to find the amount he spend when he was in the water for 4(1/2) hours.

Total amount = 12.99 + hourly amount

Hourly amount = 3.75×4(1/2)

Hourly amount = 3.75×9/2

Hourly amount = 16.875

Total amount = 12.99 + 16.875

Total amount = 29.865

Hence, the total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.

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The distance between the x-intercepts of these two line is 10 units.

Given that,

These two lines' x-intercepts are separated by 10 units.

Equation of the line with slope 2 is

y-30/x-40 = 2

For x intercept put y = 0,

then

-30/x-40 =2

x =25

Equation of the line with slope 6 is

y-30/x-40 =6

For x intercept put y = 0,

then

-30/x-40 =6

x =35

Distance between x-intercepts of these two lines is difference of the two intercepts i.e,

D = 35-25 = 10.

Thus, the distance between the x-intercepts of these two line is 10 units.

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After the use of fractional exponents give us the value 8√(x²y⁴) is 2³(x²y⁴)¹/₂.

Exponent:

Exponent is refers the way of writing the words, "raised to the power". And it is used to show that a number has been raised to a certain power.

Given,

Here we have the expression 8√(x²y⁴).

Now, we need to simplify the fractional exponents.

When we rewritten the expression like the following,

=> 8√(x²y⁴)

While we looking at these expression we know that, the number 8 can be written as the multiple of 2,

So, it can be written as,

=> 8√(x²y⁴) = 2³√(x²y⁴).

So, in the simplified form it can be written as,

=>8√(x²y⁴) =  2³(x²y⁴)¹/₂.

Therefore, the simplified form is 2³(x²y⁴)¹/₂.

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The constant of proportionality for each table are 5, 2/3, 4, 1/5, 3, 2 and 1/2 while that of the equations are 1/8, 1/3 and 3/2

The constant of proportionality is the ratio of the y value to the x value i.e.

constant of proportionality(k) = y/x

To find the constant of proportionality for each table, just pick any non-zero corresponding x and y values on the table and find the ratio:
Using constant of proportionality(k) = y/x

1.  y/x = 5/1 = 5

2.  y/x= 4/6 = 2/3

3. y/x = 2/0.5 = 4

4. y/x= 2/10 = 1/5

5. y/x = 9/3 = 3

6. y/x = 8/4 = 2

7.y/x = 6/12 = 1/2

For the equations, just rewrite the equations in order to make y/x the subject:

8. y =1/8 x

y/x = 1/8

9. 6y = 2x

y/x = 2/6 = 1/3

10. 4y = 6x

y/x = 6/4 = 3/2

Therefore, the constant of proportionality for each table and equation are 5, 2/3, 4, 1/5, 3, 2, 1/2 and 1/8, 1/3, 3/2 respectively

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The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]

Given,

In the question:

A leading coefficient of 1, and zeros of 4 and 3 + i.

To find the polynomial function of least degree having only real coefficients.

Now, According to the question;

The function has 4 and 3 + i .

As, i's roots

So, 3 - i is also its root a leading coefficient of 1 .

So, The function of polynomial is :

f(x) = (x - 4) [tex][(x - 3)^2 + 1][/tex]

To solve the function;

f(x) = [tex]x^3 -10x^2 +34x-40[/tex]

Hence, The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]

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Answer:

Step-by-step explanation:

Given a car's cost of operation is $485 for 500 miles, you want an equation relating cost for m miles, and solutions to that equation for 1200 miles, and for a cost of $820.

The cost per mile is found by dividing the cost by the associated number of miles:

  $485/(500 mi) = $0.97 /mi

The equation for the cost will show the cost as the cost per mile multiplied by the number of miles:

  C = 0.97m . . . . . where C is cost in dollars for m miles driven

The cost for driving $1200 miles will be ...

  C = 0.97(1200) = $1164

The cost of driving 1200 miles is $1164.

The number of miles that can be driven for a cost of $820 is ...

  820 = 0.97m

  m = 820/0.97 = 845.36

About 845 miles are driven for a cost of $820.

Answer:

z = 52°

Step-by-step explanation:

Formula we use,

→ A + B + C = 180°

Then the value of z will be,

→ 81° + 47 ° + z = 180°

→ 128° + z = 180°

→ z = 180° - 128°

→ [ z = 52° ]

Hence, the value of z is 52°.

The quotient of the fraction is 0.05 and the fraction in its simplest form is 1/20

The quotient of a fraction is the whole number that is obtained when you simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction

Given: 1/5÷4

1/5÷4 = 1/5 × 1/4            (Note: If ÷ change to ×, 4 will change to 1/4 )

        = 1/20 = 0.05

Therefore, the quotient of the fraction is 0.05 and 1/20 should be filled in the box

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Answer: z=-2

Step-by-step explanation:

3z+6z-30=-48

9z-30=-48

9z-30=-48+30

9z=-18

z=-2

Answer:

x = 20

Step-by-step explanation:

We know that a straight line is 180 degrees. We also know that the line A and B is a supplementary angle.

We subtract 180 - 110 which will come out to 70 which is the value of angle B

We know that angles D and E are 90 degrees and since D and C is 180 degrees, that means C and E is equal to 90 degrees as well.

Since B is equal to 70 degrees, we subtract 90 - 70 to get 20 degrees which is the value of x

The lessons can a student take if they pay no more than $175 is 25x + 50 < 175.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

In the 12U Softball division, Olivia gets chosen. What is Olivia's age? Olivia's age is unknown to you because the word "equals" is missing. However, since you are aware that she should be under or equal to 12, you can write Olivia's Age 12. This is a real-world example of an inequality.

given:

Per lesson charges= $25

Recital f= $50

Total money can be spend= $175

let the number of lessons taken be x.

So, the inequality is

25x + 50 < 175

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The total number of skittles in the bag will be 65.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that In a pack of Skittles, 20% are red. If 13 are red. The total number of skittles will be calculated as,

N = ( 13 / 20 ) x 100

N = 130 / 2

N = 65

Therefore, the total number of skittles in the bag will be 65.

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The slope of the line of best fit represents: the expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.

A line of best fit simply refers to a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between data points.

A slope is also referred to as the rate of change and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or data points.

In this scenario, the slope for the given data is the change in temperature with respect to a unit change in the number of chirps sold.

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The standard deviation and variance of the distribution's 96% confidence intervals are 9.841 and 5.704, respectively.

A normal distribution sample of size 50 has an expected higher rate of 20 and a sample mean of 5.

n = 50 makes up the sample size.

Furthermore, the sample variance is s² = 20

The following is the formula for both the variance confidence interval:

σ² = [tex](\frac{(n-1)s^2}{X^2_{{n-1};{1-\alpha /2}}}, \frac{(n-1)s^2}{X^2_{{n-1};{\alpha/2}}})[/tex]

Here, [tex]{X^2_{{n-1};{1-\alpha /2}}}[/tex] is the critical value at the status of significance [tex]\alpha[/tex] & degree of freedom n - 1.

The 90% confidence interval's lower bound for variance is stated as,

[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (30.114)

= 32.54

The 90% confidence interval's upper bound for variance is stated as,

[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (10.117)

= 96.86

Consequently, the confidence level for the distribution's variance is (96.86, 32.54).

Additionally, the range of the distribution's standard deviation inside the 90% confidence interval is (√96.86, √32.54), that's the same as (9.841, 5.704).

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Answer:

To do percentages with fractions,

divide the numerator by denominator to get a decimal,

so for example, your question 56/80.

56/80 is 0.7 decimal, and then to make it percent,

we multiply by 100,

how does that work?

you move two places to the right because 100 has two zeros

so 0.7 would be 70,

therefore the percent of 56/80 would be 70%

Good day ml! <3

Considering the figure the unknown angles are

Using the angle in a straight line are supplementary we have

60 + a + 55 = 180

a + 115 = 180

a = 180 - 115

a = 65

applying sum of angles in a triangle equal to 180, b is calculated as follows

a + b + 90 = 180 right angle triangle

substituting for a

65 + b + 90 = 180

b + 155 = 180

b = 180 - 155

b = 25

applying vertical angle theorem

angle c = angle b

angle c = 25

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The level can be attained  by light reflections.

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The value of angle b is 60 degrees. The reason is angle b is a supplementary angle to angle 120 degrees

angle b is equal to angle c the reason id that they form alternate internal angles

A linear pair is a situation where two adjacent angles are on a straight line, hence their sum is 180 degrees.

Linear pair is special cases of supplementary angles involving only two angles that are adjacent

How to solve for angle b

b + 120 = 180

b = 180 -120

b = 60

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Step-by-step explanation:

the equation

y = -8/5 x + 6

tells us 2 things :

-8/5 is the slope of the line, 6 is the y-intercept (the y value when x = 0).

a parallel line has the same slope (just a different y-intercept) : -8/5

a perpendicular line (intercepts at 90°) turns the original slope upside-down and flips the sign : 5/8

we the use the given point as x and y values and calculate the y-intercepts.

parallel :

3 = -8/5 × 5 + y-intercept = -8 + y-intercept

11 = y-intercept

y = -8/5 x + 11

perpendicular :

3 = 5/8 × 5 + y-intercept = 25/8 + y-intercept

(3×8)/8 = 24/8 = 25/8 + y-intercept

-1/8 = y-interceot

y = 5/8 x - 1/8 = 1/8 × (5x - 1)

The balance in Marie saving account in week 20 will be $408  .

In the question ,

it is given that

the amount in Marie's saving account in week 1 is $180 .

amount of money deposited every week is = $12 .

to find the balance in week 20 means , she deposited money for 19 weeks .

the amount deposited in 19 weeks = 19 × 12 = $228

the equation to represent the balance after w weeks = 180 + 12*w

putting w = 19 in the equation , we get

the balance in saving account in week 20 = 180 + 12*19

the balance in week 20 = 180 + 228

= $408

Therefore , The balance in Marie saving account in week 20 will be $408  .

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