52 over 100 simplified

Answer:

The backpack costs $42.40.

Step-by-step explanation:

Answer: $42.40 is the backpack cost

Step-by-step explanation:

Answer:

28 students

Step-by-step explanation:

Work backwards.

First, subtract 3:

115 - 3 = 112

Then, divide by 4:

112 ÷ 4 = 28

So, there are 28 math students in his class.

Answer:

To determine the possible degree(s) of a function from the graph alone, you need to examine the behavior of the graph at the extremes (far left and far right) and consider the number of turning points or changes in direction. Here's a step-by-step approach:

Look at the far left side of the graph: Determine the behavior of the graph as it approaches negative infinity. Does the graph approach a specific value, such as a horizontal line (asymptote) or the x-axis? If the graph approaches a horizontal line, it suggests a polynomial function of even degree. If the graph approaches the x-axis, it indicates a polynomial function of odd degree or possibly a function with a root of multiplicity greater than one.

Look at the far right side of the graph: Determine the behavior of the graph as it approaches positive infinity. Similar to step 1, observe if the graph approaches a specific value or a horizontal line. The behavior at the far right side should be consistent with the behavior at the far left side. This can help you identify if the function is even or odd degree.

Examine the number of turning points or changes in direction: Count the number of times the graph changes direction. These points are where the slope of the graph changes from positive to negative or vice versa. The number of turning points can provide an indication of the degree of the polynomial. For example, if there are two turning points, it suggests a polynomial function of degree 3.

Remember that this method provides potential degrees, but it may not definitively determine the exact degree of the function. Additional information or analysis might be required for a more accurate determination.

Answer:

A.

Step-by-step explanation:

The graph was shifted (translated) 2 units upward.

This is because the 2 is being added onto the x. If you were to set x to 0, you result with a y of 2, making it the y-intercept.

A more modern explanation would be, "Parallel lines are two lines within a given plane that never intersect."

Two lines on a sphere are an illustration that defies the notion of parallel lines. Meridians are the name given to longitude lines on spheres like the Earth.

Meridians are lines that run parallel to one another from the North Pole to the South Pole. However, if we take into account two meridian lines, they will cross at the North and South Poles. Two lines that are originally parallel will, therefore, eventually intersect at the poles on a sphere, defying the notion of parallel lines.

We can change the original definition of parallel lines to read, "Parallel lines are two lines that do not intersect within a given plane."

This adjustment accounts for the fact that lines can exist in many geometrical contexts, such as on a sphere or in three-dimensional space, where the idea of parallelism may be different. By including the phrase "within a given plane," we restrict the concept to the typical geometry seen in Euclidean geometry, where parallel lines do not meet.

A newer definition may therefore read, "Parallel lines are two lines within a given plane that never intersect." This updated definition makes clear that parallel lines must be taken into account inside a certain plane in order to maintain their validity, while also acknowledging the limitations of the idea.

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The car's speed to feet per minute is  80.67ft per second.

What is speed?

1 mile = 5280 feet 

so 55 miles = 55*5280 = 290,400ft 

there are 60 seconds in 1 minute and 60 minutes in 1 hour 

so 1 hour = 60*60 = 3600 seconds 

55mile/1hour = 290400ft/3600 seconds = 80.67ft per second

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On solving the given system of equations, we found the values of the variables x and y as 4 and 3 respectively.

What is meant by the system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system. A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations.

The given system of equations is:

2x + 2y = 14

4x - 2y = 10

To solve this, we have to first get rid of one variable.

Here the coefficient of variable y is the same.

So adding the equations, we get

6x = 24

x = 4

Now substituting this value of x in any one of the equations we get y.

2*4 + 2y = 14

8 + 2y = 14

2y= 6

y = 3

Therefore on solving the given system of equations, we found the values of the variables x and y as 4 and 3 respectively.

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The margin of error is defined as follows:

M = 1.9z/sqrt(n).

In which:

The bounds of the confidence interval are given as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

The margin of error is then given as follows:

\(M = z\frac{\sigma}{\sqrt{n}}\)

The problem is incomplete, hence the general procedure to obtain the sample size was presented.

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a) The maximum height of the rock is of: 5.50 metres.

b) The time that the rock was in the air is of: 2.12 seconds.

c) The distance which the rock landed is of: 12.72 meters.

The height of the projectile is modeled using a quadratic function, as follows:

y = -4.905t² + v(0)sin(60)ºt + h(0).

The parameters are given as follows:

Considering the values of these parameters, the function is given as follows:

y = -4.905t² + 10.39t.

The coefficients are given as follows:

a = -4.905, b = 10.39, c = 0.

The maximum height is obtained as the y-coordinate of the vertex, as follows:

Hmax = -(10.39² - 4(4.905)(0))/(4(-4.905)) = 5.50.

The rock hits the ground when:

y = 0.

Hence:

-4.905t² + 10.39t = 0

t(-4.905t + 10.39) = 0.

4.905t = 10.39

t = 10.39/4.905

t = 2.12 seconds.

The horizontal distance is given as follows:

x = v(0)cos(60º)t

Hence:

x = 12 x 0.5 x 2.12 = 12.72 meters.

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The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.

To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.

Step 1: Find the median (Q2)

When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:

Median (Q2) = (41 + 46)/2 = 43.5

Step 2: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:

Q1 = (32 + 32)/2 = 32

Step 3: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:

Q3 = (50 + 51)/2 = 50.5

Now we have all the information we need to construct the five-number summary and interquartile range:

Minimum: 29

Lower quartile (Q1): 32

Median (Q2): 43.5

Upper quartile (Q3): 50.5

Maximum: 53

Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5

the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

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Answer:

Step-by-step explanation:

7.18/9 divide 9 and that would equal 2/1 so its 2

8.24/40 divide 8 and that would equal 3/5

9.7/21 divide 7 and that would equal 1/3

10.9/1 stays the same so its 9

Step-by-step explanation:

(2^2x²/xy²) for x=3 and y=2

we have

2^2(3)²/((3)(2²))

2^2(9)/((3)(4))

2^18/12

262144/12

21845.3

The value of  expression \(2^{2} x^{2}/xy^{2}\)  for x=3 and y=2 is, 3

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,  \(2^{2} x^{2}/xy^{2}\)

The value of expression when, x = 3 & y = 2

⇒  2²×3²/3×2²

⇒  3

Hence, The value is 3

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Answer:

Step-by-step explanation:

20 * ((2*20)-6)

20*34

680

Answer:

The equation is 12.5n where n stands for any hour that Phil is riding his bike. I'm using the nth term here though.

Step-by-step explanation:

Answer:

f(x) = 12.5x

Step-by-step explanation:

50 / 4 = 12.5

25 / 2 = 12.5

so...

for 1 hour, there is 12.5 miles traveled

so...

f(x) - 12.5x

Plz mark as brainliest if this helped! Have a nice day!!!

-Lil_G

For Serenity's lemonade recipe, the lemons being used per cup of lemonade is 0.8

Ratio is a comparison of two quantities that are expressed in relation to each other. Ratios are typically expressed in the form of a fraction, with the numerator representing one quantity and the denominator representing the other quantity.

To find the rate at which lemons are being used in lemons per cup of lemonade, we need to calculate the ratio of lemons used to cups of lemonade.

According to the recipe, 4 lemons are required to make 5 cups of lemonade. So the rate of lemons used is:

4 lemons / 5 cups = 0.8 lemons per cup of lemonade

This means that for every cup of lemonade, 0.8 lemons are used.

Alternatively, we can also express this rate as a fraction, which gives us:

0.8 lemons / 1 cup of lemonade

Either way, the rate of lemons used is 0.8 lemons per cup of lemonade.

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Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)

Answer:

low lying areas

Answer: 2500

Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500

The statement that applies to the sample math is:

B. the work shown to remove all fractions is not correct

The given steps are:

y = ¹/₄x + 2

- I first isolate the constant.

- After doing so, I get the equation: -¹/₄x + y = 2

- To remove the fraction, I multiply by –4, giving the equation x - 4y=2, which is the final answer.

The correct steps are as follows:

y = ¹/₄x + 2

First isolate the constant to get: y - ¹/₄x = 2

To remove the fraction, Multiply the obtained equation by –4

So, Equation : x - 4y = -8

On comparing both the work we can see that in the given work the removal of fraction is done incorrectly

They didn't multiply -4 on the right hand side .

Thus, option B applies.

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Answer:

Form the Segment Addition Postulate, we know that the length of BC is simply the sum of the lengths of AB and CA. However, first we need to find the value of x in order to find the lengths of AB and CA, so we set up an equation where AB = CA, and solve for it:

5x - 22 = 2x - 7

3x = 15

x = 5

Now we substitute the value of x into the lengths of AB and CA:

AB = 2(5) - 7 = 3

CA = 5(5) - 22 = 3

Next, we add the lengths of AB and CA together to get the length of BC:

AB + CA = BC

3 + 3 = BC

BC = 6

Step-by-step explanation:

Please support my answer.

Answer:

Step-by-step explanation:

\(P+Q-R=(2x^2+3xy-5y^2)+(-5x^2+2xy+3y^2)-(-3x^2+5xy-2y^2)\)

                  \(=2x^2+3xy-5y^2-5x^2+2xy+3y^2+3x^2-5xy+2y^2\)

                  \(=2x^2-5x^2+3x^2-5y^2+3y^2+2y^2+3xy+2xy-5xy\)

                  \(=0\)

Answer:

To show that P + Q - R = 0, we need to substitute the expressions for P, Q, and R into the equation and simplify.

P + Q - R = (2x² + 3xy - 5y²) + (-5x² + 2xy + 3y²) - (-3x² + 5xy - 2y²)

Simplifying the brackets on the right-hand side:

P + Q - R = 2x² + 3xy - 5y² - 5x² + 2xy + 3y² + 3x² - 5xy + 2y²

Grouping like terms together:

P + Q - R = (2x² - 5x² + 3x²) + (3xy + 2xy - 5xy) + (-5y² + 3y² + 2y²)

Simplifying the expressions in the brackets:

P + Q - R = 0x² + 0xy + 0y²

Therefore, P + Q - R = 0.

Answer:

If x = 0, then f(0) = -15

If f(x) = 27, then x = 3

The rate of the slower hiker is 1.1 mph and the rate of the faster hiker is 6.6 mph

Explanation

One hiker walks 5.5 mph faster than the other.

Suppose, the speed of the slower hiker is (x) mph.

So, the speed of the faster hiker will be:

(x+5.5)mph

Both hikers are walking toward each other and meet in 10 hours.

We know that, Distance = speed * time

So, the distance walked by the slower hiker in 10 hours = 10x miles and the distance walked by the faster hiker in 10 hours = 10(x + 5.5) miles.

Given that, they were 77 miles apart in the beginning. So the equation will be ...

10x + 10(x + 5.5) = 77

10x + 10x + 55 = 77

20x = 77 - 55 = 22

x = 22/20 = 1.1

Thus, the rate of the slower hiker is 1.1 mph and the rate of the faster hiker is (1.1 + 5.5) mph = 6.6 mph

Answer:

Theoretical probability = 50%

Experimental probability varies.

See below for explanation.

Step-by-step explanation:

This is a problem on theoretical and experimental probability. The results obtained would enable you understand their differences.

The theoretical probability is the result that is expected to happen, but it isn't always what eventually happens.

The theoretical probability of a coin landing on heads is ½ or 50%. This is same for tails.

The experimental probability is the probability obtained from carrying out the experiment. As this is the result of what actually happens, the experimental probability could be lesser  or greater than or equal to 50%.

You are required to carry out the experiment. This is because the result would vary from person to person as well as from one experiment to the other.

First, make a table for the number of trials, outcome (head and tail each) and the frequency. Pen down the result for each of the experiment carried out. You can use a tally to make it easy for compilation.

See attachment for table.

Theoretical probability of 10 trials:

Head= 5, tail = 5

Theoretical probability of 30 trials:

Head= 15, tail = 15

Theoretical probability of 100 trials:

Head= 50, tail = 50

It all amount to 50% each

So do your experiment and record the results. Afterwards compare your result  which is the experimental probability

for head and tail with the theoretical theoretical.

Also compare your result with that of your classmate.

Expression for given numerical is: 9+ (2/x)

Given that we have an word equation that is 9 more than the quotient of 2 and  x

A quotient is a quantity produced by the division of two numbers.

Quotient of 2 and x is \(\frac{2}{x}\).

Nine(9) more  than 2/x is = 9+ (2/x)

So we have an expression that is:

              9+ (2/x)                          

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Answer:

y

a= ——

(r + 1 )t

Step-by-step explanation:

divide both sides

The correct expanded form using Laws of exponents is:

Two-thirds times two-thirds times two-thirds times two-thirds

Some of the laws of exponents are:

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

Now, we want to solve the expression given as: (²/₃)⁴

When we expend this, we arrive at:

²/₃ × ²/₃ × ²/₃ × ²/₃

This among the options is Option A which is:

Two-thirds times two-thirds times two-thirds times two-thirds

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