Knowledge Check
Question 10
Keith purchased a prepaid phone card for $50.75. Calls cost 8 cents a minute using this card. The credit, C (in dollars), left on the card after it is used for x
minutes of calls is given by the following
C=50.75-0.08x
How much credit is left on the card after Keith uses it for 30 minutes of calls

Answer:

-205/69

Step-by-step explanation:

-41/3÷23/5

reciprocate, then the sign changes

-41/3×5/23

=-205/69

The time the airplane will arrive at its destination is; 12:30 pm

The relationship between distance, time and speed is;

Speed = Distance/time

Now, we are given;

Distance = 1375 miles

Speed = 550 miles per hour

Thus;

Time = Distance/Speed

Time taken = 1375/550

Time taken = 2.5 hours

Thus, if he leaves by 10 am, then the time to arrive is;

10 am + 2.5 hours = 12:30 pm

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Answer:

x = 5/44

Step by Step:

First start with -2 = -3/5 x-17, once you do that you see that you need to make the x in -3/5 x-17 make the equation equal -2. Requiring knowledge of basic multiplication in the negatives. Once you find the number to multiply by, in this equation would be 5/44, you multiply.

Answer:

the number 12

Step-by-step explanation:

the number 12 is a multiple of both 3 ans 4. the sum of the 2 digits in 12, is 3, which is a prime number. 12 only has 2 digits

Answer:

12

Step-by-step explanation:

12² is 144/9+3 is 144/12

Answer: Raise 2 to the power of 3

9+3=12

Step-by-step explanation: hope this helps!!!!

-4y-1

Step-by-step explanation:

If you subtract [tex]{ \green{ \tt{8y + 7}}} [/tex]from [tex]{ \red{ \tt{4y - 8}}}[/tex] then the resultant answer will be as follows

[tex] \: \: \: \: \: { \red{ \tt{4y - 8}}} \\ - \ \: { \green{ \tt{8y + 7}}} \\ = -{ \blue{ \tt{ 4y - 1}}}[/tex]

According to the given statement East of the hotel, the bus is four blocks east away.

It is one of the subjects covered on almost all admission tests. Logical and analytical abilities are required to address the issue's queries. Mastering the "Directions" topic will make learning about seating arrangements easier.

When a sightseeing bus picks up a group of visitors at a hotel and travels 2 blocks north, 2 blocks east, 1 block south, 2 blocks east, and 1 block south, the following calculation must be performed to establish where the bus is in respect to the hotel:

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Mean height of the students in the class = 65.7 inches

The mean height of all 12 students in the class is 66.0 inches.

So the Total height of 12 students in the class = 66 × 12

                                                                              = 792 inches

As Danielle's height = 62.1 inches

So the total height of 13 students = 792 + 62.1

                                                        = 854.1 inches

Mean of all 13 students in the class = 854.1 / 13

                                                            = 65.7 inches

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The complete question:

Mr. Zuro finds the mean height of all 12 students in his class to be 66.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 62.1 inches tall. What is the mean of the 13 students in the class?

The amount of snowfall in February 2015 was 36.4 inches and the amount of snowfall in February 2020 was 17.9 inches

From the question, we are to determine the amount of snowfall in February 2015 and in February 2020

Let the amount of snowfall in February 2015 be x

and the amount of snowfall in February 2020 by y

From the given information,

"The snowfall in February 2015 was 0.6 inch more than twice the snowfall in February 2020"

That is,

x = 0.6 + 2y

Also, from the information

"The snowfall in February 2015 was also 8.35 inches fewer than 2.5 times the snowfall in February 2020"

x = 2.5y - 8.35

Now,

Solve the system of equations simultaneously

x = 0.6 + 2y             -------- (1)

x = 2.5y - 8.35        -------- (2)

Equate equations (1) and (2)

0.6 + 2y = 2.5y - 8.35

0.6 + 8.35 = 2.5y - 2y

8.95 = 0.5y

y = 8.95/0.5

y = 17.9

Substitute the value of y into equation (1)

x = 0.6 + 2y

x = 0.6 + 2(17.9)

x = 0.6 + 35.8

x = 36.4

Hence, the amount of snowfall in February 2015 was 36.4 inches and the amount of snowfall in February 2020 was 17.9 inches

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1 drink(s) within a 4 hour time span, regardless of height and weight, can get you a BAC of .01%.

Blood Alcohol Content (BAC) is a measure of alcohol in the blood as a percentage. It is calculated in grams per 100 mL of blood, so a BAC of 0.08 means your blood is 0.08% alcohol by volume.

Here, the BAC = 0.1%

Time span = 4 hours

We know,

BAC is a measure of alcohol in the blood as a percentage

Alcohol leaves the body at an average rate of 0.015 g/100mL/hour

Hence, 1 drink(s) within a 4 hour time span, regardless of height and weight, can get you a BAC of .01%.

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The gradient-intercept form of the equation of the line which has a gradient of 5 and passes through the point (1, 11) is y = 5x + 6

Gradient intercept form Or slope incept form of a linear equation is given by

y = mx + c

where m is the gradient or slope of the equation  and c is the constant

As we are aware that the line passes through a point whose coordinates are (1, 11)

By putting the value of gradient/ slope,  x coordinate in place of x in equation and  y coordinate in place of y in equation we get

11 = 5 (1) +c

11= 5 + c

11-5 = c

6 = c

now, substituting the value of c in the Gradient/ slope intercept form

y = 5x + 6

Hence, The gradient-intercept form of the equation of the line which has a gradient of 5 and passes through the point (1, 11) is y = 5x + 6

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By substituting the value of x as 17 in the function R (x) = 2 x + 3.5, we get the value of R ( 17 ) as 37.5.

We are given a function:

R (x) = 2 x + 3.5

where x represents the number of feet the tide moves x minutes after 4 pm.

Now, we are asked to find R (17)

For this, we need to substitute the value of x as 17 that is we need to put x = 17 in the function that is given to us.

R ( x = 17 ) = 2 ( 17 ) + 3.5

R ( 17 ) = 34 + 3.5

R ( 17 ) =37.5

Therefore, by substituting the value of x as 17, we get the value of R ( 17 ) as 37.5.

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Answer:

185

Step-by-step explanation:

Answer:

Step-by-step explanation:

100 + 70 = 170

7+8= 15

170+15 = 185

170 + 78 +185

Answer:

Absolute value is how many steps it takes to get to 0

Step-by-step explanation:

For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero

Answer:

The magnitude (true distance from zero) of a number or measurement, regardless of sign. Usually the true positive value of a number.

Examples:

|–6| = 6

|4| = 4

|200| = 200

|–5000| = 5000

|0.5| = 0.5

The area swept by the wiper is 860.75 square inches, as calculated by the formula of area of a sector.

Given:

To find: Area swept by the wiper.

Finding:

As area of the sector = [tex]\frac{1}{2}r^{2}\theta[/tex],

Area swept by the wiper will be given by: (Area of the sector made by the top end of the windshield) - (Area of the sector made by the bottom end of the windshield)

=> Area swept by the wiper = [tex]\frac{1}{2}(30)^{2}\frac{3\pi}{4} - \frac{1}{2}(13)^{2}\frac{3\pi}{4}[/tex]

=> Area = [tex]\frac{1}{2}\frac{3\pi}{4}(900 - 169)[/tex]

=> Area = [tex]\frac{1}{2}\frac{3\pi}{4}(731)[/tex] ≈ 860.75 square inches

Hence, the area swept by the wiper is 860.75 square inches, as calculated by the formula of area of a sector.

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The hexadecimal representation for the given question is 1. 0xAD 2. 0x27 and the decimal representation of the given question is 1. 10001110 2. 01011100

The hexadecimal numeral system, usually known as base 16 or just "hex," is a positional numeral system used in mathematics and computing that uses the radix (base) of 16 to represent integers. Hexadecimal uses 16 different symbols as opposed to the decimal system's 10 symbols, with the most common being "0"-"9 to represent values 0 to 9 and "A"-"F" (or alternatively "a"-"f") to represent values 10 to 15. Hexadecimal numbers are frequently used by software engineers and system designers because they offer a human-friendly representation of binary-coded data. For example, an 8-bit byte might have values ranging from 00000000 to 11111111 in binary form, which can be succinctly represented as 00 to FF in hexadecimal. Each hexadecimal digit represents four bits (binary digits), often known as a nibble (or nybble).

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Answer:

Equation: [tex]\sf 3x + x + 14 = 90[/tex]

m∠1 = 57°

m∠2 = 33°

Explanation:

A right angle triangle has 90° angle measure.

Here:

m∠1 + m∠2 = 90°

(a)

Substitute given values:

(3x) + (x + 14) = 90

simplify

4x = 90 - 14

evaluate

4x = 76

divide both sides by 4

x = 19

(b)

m∠1 = 3x = 3(19) = 57°

m∠2 = x + 14 = 19 + 14 = 33°

Answer:

[tex]\textsf{(a)} \quad (3x)^{\circ}+(x+14)^{\circ}=90^{\circ}[/tex]

[tex]\textsf{(b)} \quad m \angle 1=\boxed{57}\:^{\circ}[/tex]

       [tex]m \angle 2=\boxed{33}\:^{\circ}[/tex]

Step-by-step explanation:

From inspection of the given diagram:

A right angle is 90° and is represented by the ∟ symbol.

To find x, equal the sum of the angles to 90° and solve for x:

[tex]\implies m \angle 1+m\angle2=90^{\circ}[/tex]

[tex]\implies (3x)^{\circ}+(x+14)^{\circ}=90^{\circ}[/tex]

[tex]\implies 3x+x+14=90[/tex]

[tex]\implies 4x+14=90[/tex]

[tex]\implies 4x+14-14=90-14[/tex]

[tex]\implies 4x=76[/tex]

[tex]\implies 4x \div 4=76 \div 4[/tex]

[tex]\implies x=19[/tex]

To find the degree measure of each angle, substitute the found value of x into the expression for each angle.

[tex]\implies m \angle 1=(3 \cdot 19)^{\circ}=57^{\circ}[/tex]

[tex]\implies m \angle 2=(19+14)^{\circ}=33^{\circ}[/tex]

In order to cover the entire land area of United States with dollar bills, it would cost 9 × 10¹⁴ dollars.

A conversion factor can be defined as a number that is typically used to convert (change) a number in one (1) set of units to another, either by dividing or multiplying.

Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.

Conversion:

1 mile = 160934 cm

Length of contiguous land = 160934 × 3000 miles = 482,802,000 cm.

Width of contiguous land = 160934 × 1000 miles = 160,934,000 cm.

Mathematically, the area of a rectangle can be calculated by using this formula;

Area of rectangle = length × width

Area of contiguous land = 482,802,000 × 160,934,000

Area of contiguous land = 77,699,257,068,000,000 cm²

Next, we would determine the area of Alaska:

Area of Alaska = 1/5 × 77,699,257,068,000,000

Area of Alaska = 15,539,851,413,600,000 cm²

Total area = Area of Alaska + Area of contiguous land

Total area = 15,539,851,413,600,000 + 77,699,257,068,000,000

Total area = 93,239,108,481,600,000 cm²

Also, the area of a dollar bill is given by:

Area of dollar bill = 6.5 × 15.5

Area of dollar bill = 100.75 cm²

Now, we can determine the cost:

Cost = Total area/Area of dollar bill

Cost = 93,239,108,481,600,000/100.75

Cost = 9 × 10¹⁴ dollars.

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Complete Question:

How much would it cost to cover the entire land area of United States with dollar bills? To answer this question, you may find the following information useful:

The contiguous United States (all of the states minus Alaska and Hawaii) can be approximated as a rectangle that measures 1000 miles north to south and 3000 miles east to west, while Alaska has about one-fifth the area of the contiguous states and Hawaii is small enough to be ignored for this rough calculation. Also, note that a dollar bill measures around 6.5cm × 15.5cm. Express your answer to one significant figure!

If the average salary of several of the groups was close to $51,000 then least likely to be the average salary of another one of the groups are equal to $41,000.

Random groups of teachers are = 30

If the average salary of several of the groups was close to equal to = $51,000

The mean, or average, salary is the amount derived by adding two or more salary values and dividing the sum by the number of values.

So we can write,

The average wage is known to be close to $41,000

$41,000 < $51,000

Therefore,

The average salary of another one of the groups are equal to $41,000.

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Answer:

9514 1404 393

Step-by-step explanation:

Answer:

the area is 88

Step-by-step explanation:

2(wl+hl+hw) <- formula

Answer: Seven trillion i think

Step-by-step explanation:

Answer:

38?

Step-by-step explanation:

I can't tell if you were dividing, but 456/12 is equal to 38. Same goes if you were looking for 456=12*x, which x is also 38.

Answer:

Yes

Step-by-step explanation:

Every x and y coordinate is different. The y-coordinates don't have the same x-coordinate, so the function passes the vertical line test. This function is called a discrete function since it's made up of individual points, not a line or curve.

Answer:

yes

Step-by-step explanation:

Different x and y coordinate

Different gradient of line graph

Therefore,it is a function.

The equation of the polynomial on the graph is P(x) = x^2(x - 2)(x + 2)

Expressions are mathematical statements that are represented by variables, coefficients and operators

The graph represents the given parameter

On the graph, we have the following points

The multiplicities at these points are

Using the above as a guide, the equation of the polynomial is

P(x) = (x - x value)^Multiplicity

So, we have

P(x) = (x - 2)^1 * (x + 2)^1 * (x - 0)^2

The above equation becomes

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

Evaluate

P(x) = x^2(x - 2)(x + 2)

Hence, the equation of the polynomial on the graph is P(x) = x^2(x - 2)(x + 2)

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The functions cosecant and cotangent are undefined when functions sine and tangent are equal to zero.

A function becomes undefined when its denominator becomes zero. In the case of trigonometric functions we know that both sine and tangent of 0° are equal to zero. In addtion, there are two following trigonometric formulas:

csc θ = 1 / sin θ

cot θ = 1 / tan θ

Thus, the functions cosecant and cotangent are undefined when functions sine and tangent are equal to zero.

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Answer:

360 milliliters

Step-by-step explanation:

2 (1,5 x 1,2 m) cm ² (wink wink)

Answer:

S

Step-by-step explanation:

because an acute angle is and angle that is 89 or lower the rest are obtuse or right angle

Answer:

∠S

Step-by-step explanation:

An acute angle is an angle that is <90°, and in this case, angle S's measure is less than 90 or 15 in degrees, which both classify acute angles.

Answer:

3^-2

Step-by-step explanation

Subtract the exponent on the denominator from the exponent on the numerator

5-7=-2

keep the 3 and apply the -2 exponent