Atul gets a pocket money allowance of Rs.120 per day. Thinking that this was rather less he asked his friends about their allowances and obtained the following data which includes his allowance also ( Amount I Rs.) 120, 180, 100, 50, 250, 200,200,220, 150, 100,100,150,130,200,180, 100, 150, 100, 180, 150, 120, 150, 100, 150, 100, 120, 180, 200, 50.
He presented this data to his father and asked for an increase in his allowance as he was getting less than average amount. His father, a statistician, countered pointing out that Atul's allowance was actually more than the average amount.

The 95% prediction interval for the height is given by the inequality 177 cm < y < 200 cm.

The interpretation is that we are 95% sure that the height of a person with a foot length of 29 cm is greater than 177 cm and less than 200 cm.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

In this problem, the bounds of the interval are given as follows:

We have a compound inequality, hence both conditions have to be respected simultaneously.

There is not enough information to obtain the interval, hence we just interpret the given interval.

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Answer:

Yes, it's a polynomial

Step-by-step explanation:

A polynomial is an expression that only involves operations of addition, subtraction, multiplication, and positive integer powers and variables.

Your expression fits the criteria.  You could also make this into a binomial and get (x-8)(x+4).

Please answer my question that I posted.  I'm stuck and I really need help.

Answer:

Step-by-step explanation:

20 degees

Answer:

the billing for water consumption between April and May is 275 pesos.

Step-by-step explanation:

To find the billing for water consumption between April and May, we need to calculate the difference in the water usage as measured by the water meter.

The difference between the readings in April and May is:

430.4 kl - 417.8 kl = 12.6 kl

To calculate the cost of this water usage, we need to multiply the volume of water by the cost per kl and then add the basic charge.

The cost of the water usage is:

12.6 kl x 20 pesos/kl = 252 pesos

Adding the basic charge of 23 pesos, the total billing for water consumption between the two months is:

252 pesos + 23 pesos = 275 pesos

Therefore, the billing for water consumption between April and May is 275 pesos.

Answer:

a) opens down

c) directrix at y = 1/8

d) vertex at (-1/2,0)

Step-by-step explanation:

Starting from the given equation:

4x^2 + 4x + 2y + 1 = 0

We can rearrange to obtain the standard form of the equation of a parabola:

2(y + 1/2) = -4(x + 1/2)^2 + 1

(y + 1/2) = -2(x + 1/2)^2 + 1/2

Comparing to the standard form:

(y - k) = a(x - h)^2

We can see that the vertex of this parabola is at the point (-1/2, -1/2).

Next, we can find the axis of symmetry by noting that the parabola is symmetric about a vertical line passing through the vertex. This line is given by:

x = -1/2

We can also determine whether the parabola opens upward or downward by looking at the sign of the coefficient a. In this case, a = -2, so the parabola opens downward.

The distance between the vertex and the directrix is given by |1/(4a)|. Therefore, the distance between the vertex (-1/2, -1/2) and the directrix is:

|1/(4(-2))| = 1/8

So the directrix of the parabola is the horizontal line y = 1/8.

Therefore, the correct options are:

a) opens down

c) directrix at y = 1/8

d) vertex at (-1/2,0)

The other options are incorrect:

b) The parabola does not open to the left.

e) The directrix is not a vertical line at x = -3/8.

Answer:

the expression

y -7/x-5 = 1/3 or 2/6

Step-by-step explanation:

Cross multiplying both sides:

3(y-7) = x - 5

3y - 21 = x - 5

3y - x = 21 - 5

3y - x = 16

The simplified equation is 3y-x=16.

Answer:x=-4,-2

Step-by-step explanation:it is

The pair of functions are inverses, as their compositions result in x.

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

If two functions are inverse, the composites f(g(x)) and g(f(x)) both result in x.

The composite functions for this problem are given as follows:

Hence they are inverses.

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Answer: To find the perimeter of triangle JKL, we need to find the length of each side and add them up. We can use the distance formula to find the length of each side:

Side JK = sqrt[(2 - (-5))^2 + (3 - (-7))^2] = sqrt[7^2 + 10^2] = sqrt[149]

Side KL = sqrt[(-1 - 2)^2 + (-7 - 3)^2] = sqrt[(-3)^2 + (-10)^2] = sqrt[109]

Side LJ = sqrt[(-1 - (-5))^2 + (-7 - (-7))^2] = sqrt[4^2] = 4

Therefore, the perimeter of triangle JKL is:

P = JK + KL + LJ = sqrt[149] + sqrt[109] + 4

To find the area of triangle JKL, we can use the formula:

A = 1/2 * base * height

We can choose any side as the base, and the corresponding height will be the perpendicular distance from the opposite vertex to the base. Let's choose side KL as the base. The height from vertex J to side KL is the perpendicular distance between J and the line containing KL. We can find this distance using the formula for the distance between a point and a line:

Area = 1/2 * KL * h

where h = |(2 - (-1))( -7 - 3) - (-5 - 2)(-1 - 3)| / sqrt[(-1 - 2)^2 + (-7 - 3)^2]

Simplifying the above expression, we get:

h = 24 / sqrt[109]

Therefore, the area of triangle JKL is:

A = 1/2 * KL * h = 1/2 * sqrt[109] * 24 / sqrt[109] = 12

So, the perimeter of triangle JKL is sqrt[149] + sqrt[109] + 4, and the area of triangle JKL is 12.

Step-by-step explanation:

Answer:

£33.93

Step-by-step explanation:

A 13% discount means that the new price will be 87% of the original, as 100 - 13 = 87.

This can be calculated by converting the percentage into a decimal, then multiplying by the decimal:

87 / 100 = 0.87

39 * 0.87 = 33.93

Answer:

Let's use option C to represent the relationship between the number of bags of dog food sold and the profit made:

Profit per bag of dog food = $5.50

Total expenses per day = $2,500

The store wants to make a profit of at least $5,225 per day.

If d represents the number of bags of dog food sold, then the profit made can be represented as:

Profit = Revenue - Expenses

Revenue = Profit + Expenses

Revenue = $5.50d + $2,500

To make a profit of at least $5,225 per day, we can set up the following inequality:

$5.50d + $2,500 ≥ $5,225

Simplifying:

$5.50d ≥ $2,725

Dividing both sides by $5.50:

d ≥ 500

Therefore, the store must sell at least 500 bags of dog food per day to make a profit of at least $5,225 per day.

The correct inequality that represents this relationship is option C: 5.50d +2,500 ≥ 5,225.

We have the fοllοwing respοnse after answering the given questiοn: The equatiοn mοnthly payment, rοunded tο the next penny, is $959.49.

In a mathematical equatiοn, the equals sign (=), which cοnnects twο claims and denοtes equality, is utilized. In algebra, an equatiοn is a mathematical statement that prοves the equality οf twο mathematical expressiοns.

Fοr instance, in equatiοn 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressiοns can be used tο describe the relatiοnship between the twο sentences οn either side οf a letter. The lοgο and the particular piece οf sοftware frequently cοrrespοnd. like, fοr instance, 2x - 4 = 2.

[tex]P = \frac{rP}{(1 - (1 + r)^{-n}}[/tex]

where P is the regular mοnthly payment, r is the interest rate each mοnth, n is the number οf payments, and P is the amοunt οf interest that has already been paid in dοllars.

r = 0.027 / 12 = 0.00225

The number οf payments must then be determined. There are 120 mοnthly payments fοr a 10-year mοrtgage.

n = 120

P = 1% * $100,000 = $1,000

Nοw that the data have been entered, we can cοmpute the monthly payment:

[tex]P = (0.00225 \times $99,000 / (1 - (1 + 0.00225)^{(-120)})) + $8.33[/tex]

where $8.33 represents the mοnthly charge fοr the prepaid interest and $99,000 represents the tοtal amοunt bοrrοwed after subtracting the prepaid interest.

If we cοndense this phrase, we get:

P = $959.49

Hence, The mοnthly payment, rοunded tο the next penny, is $959.49.

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Answer:

The median of the given data is 20. To find the median, arrange the data in numerical order, and then take the middle value. In this case, the data is arranged in numerical order as 0, 5, 10, 10, 12, 15, 15, 20, 25, 30, 30, 35, 35, 45, 60. The middle value is 20, which is the median.

Answer:

17.5

Step-by-step explanation:

To find the median of a set of numbers, we need to arrange the numbers in order from smallest to largest and then find the middle value.

In this case, the numbers in the set arranged in ascending order are:

0, 5, 10, 10, 12, 15, 15, 20, 25, 30, 30, 35, 35, 45, 60

There are 15 numbers in the set, which means that the middle value is the eighth number. Since there are two numbers in the middle (15 and 20), we take the average of these two numbers to find the median:

median = (15 + 20) / 2 = 17.5

Therefore, the median of the set of numbers is 17.5.

By adding 3 to both sides of the equation (6+3)-3=9-3, this demonstrates the addition property of equality. This results in the equation being simplified to 6+3=9.

The properties of equality describe the relationship between two sides of an equation and state that the two sides remain equal even after the same arithmetic operation is performed on each side. a = a, according to the reflexive property of equality. For example, 5 = 5, because the number's value is equal to itself.

As per the addition property of equality, when we add the same number to both sides of an equation then the two sides remain equal. This can be written as, if a = b, then a + c = b + c.

Translated question "Draw a line from each equation to the property of equality it illustrates. (6+3)−3=9−3 Addition Property of Equality"

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Answer:

Step-by-step explanation:

We know that the life expectancy of the tires is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. Let X be the life expectancy of the tire. Then X ~ N(40,000, 5,000^2).

To find the percentage of tires that will have a life of 34,000 to 46,000 miles, we need to calculate the z-scores for both values using the formula:

z = (X - μ) / σ

where X is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.

For X = 34,000:

z = (34,000 - 40,000) / 5,000 = -1.2

For X = 46,000:

z = (46,000 - 40,000) / 5,000 = 1.2

Now, we need to find the area under the standard normal distribution curve between these two z-scores. We can use a table of standard normal probabilities or a calculator to find this area.

Using a standard normal table or a calculator, we find that the area to the left of z = -1.2 is 0.1151, and the area to the left of z = 1.2 is 0.8849. Therefore, the area between these two z-scores is:

0.8849 - 0.1151 = 0.7698

So, approximately 76.98% of the tires will have a life of 34,000 to 46,000 miles.

Answer:

Step-by-step explanation:

Given functions:

    [tex]r(x)=x^2+5x+14[/tex]

    [tex]c(x)=x^2-4x+5[/tex]

where:

Profit is calculated by subtracting expenses from revenue.

Therefore, the composite function for profit is:

Since x represents the number of months the store has been open:
(r - c)(5) is the amount of profit generated by the George's store 5 months after it has been open.

To calculate the total amount of profit in the first 5 months, substitute x = 5 into the composite function:

[tex]\begin{aligned}\implies (r-c)(5)&=r(5)-c(5)\\&=(5^2+5(5)+14)-(5^2-4(5)+5)\\&=(25+25+14)-(25-20+5)\\&=(50+14)-(5+5)\\&=64-10\\&=54\end{aligned}[/tex]

Since the revenue and expenses functions are measured in hundred of dollars, so too is the profit function. Therefore, the amount of profit generated in 5 months is $5,400.

As a result, the price of the ribbons is proportional to the number of party favours, with each Favour costing (3/4) dollars.

A measurable quality such as weight, length, time, volume, or pressure is referred to as quantity. A unit is a unit of measurement that is used to measure other quantities (for example, a gramme, a second, a liter, or a pascal are unit of the above quantities). Chemists employ a wide range of measurements.

The amount of ribbon required for n party favours is calculated as follows:

19n inches (since each party Favour requires 9 inches of ribbon)

As the price is stated in dollars per yard, we must first convert the amount of inches to yards before we can determine the ribbon's total cost. Since there are 36 inches in every yard, we can calculate the number of yards by dividing the total amount of inches by 36:

Total yards of ribbon = (9n) / 36 = (n) / 4

Thus, the following phrase represents the ribbon's overall cost:

3 × (n/4) = (3n) / 4 dollars

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The population of the country in 2024, as predicted by this function, is 1,847 million. The population of the country in 2051, as predicted by this function, is 2,927 million.

An exponential function is a mathematical function that increases or decreases at a rate proportional to its current value. Exponential functions are used in a variety of sciences and everyday applications. For example, population growth is an exponential function of time because the population increases by a fixed percentage each year.

The exponential function f(x) = 565(1.026)ˣ models the population of a country, f(x), in millions, x years after 1970. Substituting 0 for x, the population of the country in 1970 was 565 million. Substituting 27 for x, the population of the country in 1997 was 1,118 million. The population of the country in 2024, as predicted by this function, is 1,847 million. The population of the country in 2051, as predicted by this function, is 2,927 million.

It appears that the population of the country is growing by a factor of 3 every 27 years. This is evident from the fact that the population in 1997 is 3 times the population in 1970, and the population in 2024 is 3 times the population in 1997. This pattern is expected to continue with the population in 2051 being 3 times the population in 2024.

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Answer:

x = 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can expand and simplify the equation as follows:

23(x+3) = 23(x-6)

23x + 69 = 23x - 138

69 = -138

The last equation is clearly false, which means there is no value of x that can satisfy the original equation.

This is an example of a contradiction, where the equation leads to an impossible statement. Therefore, the equation has no solution.

Answer:

B. 15.2 inches.

Answer:

Step-by-step explanation:

46+13 = 59

Answer:

Let Mackenzie have x

and Taylor have y

Then, since Mackenzie has 46.13 less than Taylor,

x = y - 46.13

Therefore, to show how much money Mackenzie has we will use the equation

x = y - 46.13

remember Makenzie has $x.

Taylor has $y

Makenzie money is less than Taylor's money by 46.13

so we take away 46.13 from Taylor's money to get that of Makenzie

Makenzie's money x = Taylor's money y - 46.13

x = y - 46.13

Step-by-step explanation:

To write the equation of a rational function that has been reflected, shifted 6 down, 8 to the right and stretched by a factor of 4, we have to start with the basic rational function which is:

To shift it down by 6, we must subtract 6 from the function, so we have:

To shift the function to the right by 8, we substitute x for (x-8), finding this result:

To stretch the function by a factor of 4, we have to multiply the denominator by 4, which will result in:

Therefore, the equation of the rational function will be:

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Answer:

f(x) = (x-5)(x+2)^2

Step-by-step explanation:

use desmos graphing calculator! it's very helpful and free :)

Answer:

From the graph,

The zeros of the function are at x= -2 and x= 5

But since at root -2,it doesn't cross the x axis, the root has even multiplicity

Ans:(x+2)^2 (x-5).....option B

The data transfer rate per second​ is found as: 24 KB / sec.

Data transfer:  5760 KB

Time : 240 seconds

Rate per second​ = Data transfer / Time

Rate per second​ = 5760/ 240

Rate per second​ = 24

Thus, the data transfer rate per second​ is found as: 24 KB / sec.

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This represents the number of small rolls the club sold.

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides.

To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

In the equation 3s + 135 = 4.5 (s+10)

The equation 3s + 135 = 4.5(s + 10) can be used to represent this situation, where s represents the number of small rolls the club sold.

Hence, represents the number of small rolls the club sold.

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The answer to this question is as follows equation  As a result, each recipient will get $1,350.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.  

We must divide the total sum by three in order to distribute the funds among the three recipients equally. Let x represent the total sum that will be given to each recipient.

x = 4,050 / 3

x = 1,350

As a result, each recipient will get $1,350.

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Answer:

please give more information like what to find

3.5, -10.5

Step-by-step explanation:

Answer:

40) sorry if I'm wrong :<