Write an inequality.
You need to buy several pencils and an eraser. You can spend no more than $7. The eraser costs $.75 and
pencils cost $.25.

As per unitary method, it will take 9 years for the man to be three times as old as his son.

The unitary method is a mathematical technique that involves finding the value of a single unit, and then using that unit to find the value of a larger quantity.

First, let's define our variables:

Let the man's age be M

Let the son's age be S

According to the problem, we know that:

M = 42

S = 12

We want to find out how many years it will take for the man's age (M) to be three times his son's age (S). Let's call this number of years "y".

Using the unitary method, we can set up the following equation:

M + y = 3(S + y)

Here's what this equation means:

M + y represents the man's age after y years

S + y represents the son's age after y years

3(S + y) represents three times the son's age after y years

We can simplify this equation by distributing the 3:

M + y = 3S + 3y

Next, we can isolate the variable y (which represents the number of years we're trying to find) by moving all the other terms to the opposite side of the equation:

y - 3y = 3S - M

Simplifying this, we get:

-2y = 3S - M

Finally, we can solve for y by dividing both sides by -2:

y = (M - 3S) / -2

Plugging in the values we know, we get:

y = (42 - 3(12)) / -2

y = 9

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Complete Question:

A man's age is 42 years and his son's age is 12 years. After how many years will the man be thrice as old as his son?

Answer:

20% reduction in price

Step-by-step explanation:

Let the original price of each box be P and original quantity be Q. The unit rate is P/Q

Jack's approach

increase quantity by 25% = 0.25Q

New quantity = Q + 0.25Q = Q(1  +0.25) = 1.25Q

Unit rate = P/1.25Q

Sadia's approach

Reduce price and keep quantity same

Let price reduction be d% = d/100

Let us denote d/100 as r. This will be a decimal value. For example, a reduction of 10% means that the price is reduced by 0.10

Price reduction = P x r = Pr

New price = P - Pr = P(1-r)

Unit rate by this method =P(1-r) /Q

Both unit rates have to be the same if both values are the same

So
[tex]\dfrac{P}{1.25Q} = \dfrac{P(1-r)}{Q}\\\\\dfrac{P}{Q} \cdot \dfrac{1}{1.25} = \dfrac{P}{Q} \cdot (1-r)\\\\[/tex]

Eliminate [tex]\displaystyle {\dfrac{P}{Q}}[/tex]   common factor from both sides to get

[tex]\dfrac{1}{1.25} = 1- r[/tex]

[tex]\dfrac{1}{1.25} = 0.8\\\\[/tex]

So we get
[tex]1 - r = 0.8\\\\\implies r = 1 - 0.8 = 0.2\\\\[/tex]

0.2 works out to 0.2 x 100 = 20%

So for Sadia's idea to have the same value as Jack's idea, the price should be reduced by 20%

Answer:

e

Step-by-step explanation:

The rule of the sides of a triangle is that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This rule is also known as the triangle inequality theorem.

Whitney drank a total of 2.15 liters of liquid.

Liquids are those substances that can flow or be poured, are incomprehensible, and are more rigid than gases.

From the given table we can say that the drinks Whitney takes over a day, which are juice, milk, and water, all come in the liquid category.

Therefore, the total amount of liquid that Whitney drinks today will be the sum of the volume of all of the above

which is 250 ml + 400 ml + 1,500 ml

=2,150 ml

For converting ml in liters we can divide the given volume by 1000 after which we get,

2,150/1000 = 2.15 Litres.

The complete question that you might be looking for is given below -

From the given table, What is the total amount of liquid in liters that Whitney drinks today?

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The rectangular prism's volume can be represented by a cube whose dimensions are 6 inches.

A right rectangular prism is what?

The right rectangular prism has two simultaneous end panels that are orthogonal to each of the bases, two adjacent lateral faces, and four rectangle-shaped lateral faces. The faces of an oblique prism, a non-right oblong prism, are parallelograms. Alternative name for a right rectangular prism is a cuboid.

To begin, determine the rectangular prism's volume. To calculate this, multiply the length by the breadth by the height, which equals 9 ×4 ×6. 216 cubic inches make up this.

The side length of a cube with a 216 cubic inch capacity must now be determined. The recipe for A cube's volume is equal to its side length raised to the third power (cubed). You are now attempting to determine where s³= 216 This can also be expressed as s = ∛216.

The only thing left to do is to discover the number that, when multiplied by itself three times, equals 216, or its cubic root. It is quite easy to determine that 6× 6× 6, sometimes known as 6 cubed, equals 216. This indicates that the cube's side length is 6 inches.

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Answer:

-2+5/-4+1= -1

Step-by-step explanation:

put y2 minus y1 over x2 minus x1

The cost per minute is $0.04.

Unit rates are defined as rates that are expressed as multiples of 1, such as 2 feet per second or 5 miles per hour.

Given:

Sahalin cellphone plan costs $30 a month.

In a month of may she used cellphone 12.5 hours.

First convert 12.5 hours in minute.

As we know 1 hour = 60 minutes

So, 12.5 hours = 12.5 x 60

                       = 750 minutes

and, the cost per minute

= 30/750

= 0.04

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The total surface area is π[(4/3)x]² + π(4/3)x². The area of the base is greater than the lateral area.

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

Given the cone. The surface area (SA) is given by the equation:

SA = πr² + πrs

where r is the radius of the cone and s is the slant height.

Given that the slant height is x and the radius of the cone is 4/3 the slant height = (4/3)x

Hence:

SA = πr² + πrs

The base area =  πr²; Lateral area = πrs

substituting:

The base area = π[(4/3)x]², the lateral area =  π(4/3)x²

Hence:

SA = π[(4/3)x]² + π(4/3)x²

The area of the base is greater than the lateral area.

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The unknown angles are as follows:

m∠1 = 117°

m∠3 = 68°

m∠4 = 22°

m∠5 = 90°

When lines intersect angle relationships are formed such as linear angles, vertically opposite angles etc.

Therefore,

m∠1 = 180 - 63(sum of angles on a straight line)

m∠1 = 117 degrees

Hence,

m∠3 = 68 degrees(vertical angles)

Vertically opposite angles are congruent.

Hence,

m∠4 = 90 - 68

m∠4 = 22 degrees

Hence,

m∠5 = 90 degrees(right angle)

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The number of possible outcomes in the sample space of a wireless garage door opener with 16 switches can be determined using the concept of combination is 1.

Combination is a mathematical concept that refers to the number of ways that a set of objects can be selected from a larger set without regard to their order.

To determine the number of possible outcomes in the sample space, we can use the concept of combination. In this case, the objects are the 16 switches, and the larger set is the set of all possible settings for these switches (up or down).

To calculate the number of possible combinations, we can use the formula for combination, which is:

ⁿCₓ = n! / (x! * (n - x)!)

where n is the total number of objects (16 switches), and x is the number of objects selected (in this case, also 16 switches). The exclamation mark (!) represents the factorial function, which is the product of all positive integers up to and including the given integer.

Using this formula, we can calculate the number of possible combinations as follows:

=> 16! / (16! x (16 - 16)!)

=> 16! / (16! x 0!)

=> 1

Therefore, the sample space of possible codes for a wireless garage door opener with 16 switches is 1.

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Answer:

Let's call Akanksha's present age "x". After 42 years, her age will be "x + 42". And, as stated in the problem, her age after 42 years will be 4 times her present age, so:

x + 42 = 4x

Solving for x, we can isolate x on one side of the equation:

x + 42 = 4x

3x = 42

x = 14

So Akanksha's present age is 14 years old.

Answer:

Step-by-step explanation:

Difference means subtract or minus (-)

So we always switch 29 and x into x and 29

Can't really explain that much more but it's the correct answer though, trust me! :)

Answer:

Find the indicated side of the

triangle.

b

30°

12

a = -

Step-by-step explanation:

An elevation of negative 25 feet is less than an elevation of 0 feet: True.

An elevation of negative 25 feet is greater than an elevation of 5 feet: False.

An elevation of negative 25 feet is less than an elevation of negative 5 feet: True.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In this context, we can reasonably infer and logically deduce that all numerical values (numbers) to the left are always less than numerical values (numbers) located to the right of a number line such as the following:

-25 < 0.

-25 < 5.

-25 < -5.

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The probability of selecting a credit card customer at random and finding the customer charged between $70 and $83 is 0.4750.

The probability of selecting a credit card customer at random and finding the customer charged between $70 and $83 is 0.4750. This probability can be calculated using the normal distribution. The normal distribution is a probability distribution that is symmetrical and bell-shaped, with the mean (in this case, $70) in the middle of the distribution and the standard deviation (in this case, $10) as the measure of spread.The probability that a customer is charged between $70 and $83 can be calculated using the cumulative distribution function (CDF), which is the probability that a random variable is less than or equal to a given value. To calculate the probability of selecting a customer at random and finding their charge between $70 and $83, we use the CDF to calculate the area between the lower bound of $70 and the upper bound of $83. This area is equal to 0.4750.In conclusion, the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83 is 0.4750. This probability was calculated using the normal distribution and the cumulative distribution function.

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Smaller sample size results in smaller sampling variation of the OLS estimator for the slope coefficient in the sample regression model due to the fact that it reduces the amount of variability in the data. Smaller error variance also reduces sampling variation as it reduces the amount of overall variation in the data.

The sampling variation of the OLS estimator for the slope coefficient in the sample regression model is affected by a variety of factors. A smaller sample size will result in smaller sampling variation because it reduces the amount of variability in the data. This is due to the fact that a smaller sample size will contain less variation in the independent variable, and therefore the estimated slope coefficient will have less variation. Additionally, a smaller error variance will also reduce the sampling variation as it reduces the amount of overall variation in the data. Finally, smaller variation in the independent variable in the sample will also lead to smaller sampling variation of the OLS estimator. This is because the slope coefficient is estimated by minimizing the sum of squared residuals, which is a function of the variation in the independent variable. Thus, if the variation in the independent variable is reduced, the slope coefficient will have less variation. In conclusion, all three factors can lead to reduction in the sampling variation of the OLS estimator for the slope coefficient in the sample regression model.

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The mean score of all the ninth graders in the city is equal to 81.84 ( round to two decimal places )

Number of schools in the city = 3

Result of the mean score of the ninth grade students are

Glenwood     78       269

Central City   93       321

Lincoln High  66       161

Given mean score by PR manager = 81

Correct mean score is calculated as

= ( 78 × 269 + 93 × 321 + 66 × 161 ) / ( 269 + 321 + 161 )

= ( 20982 + 29853 + 10626 ) / 751

= 61461 / 751

= 81.84 ( round to two decimal places )

Therefore, the mean score of the ninth grade students of all the schools in the city is given by 81.84 ( round to two decimal places ).

The above question is incomplete , the complete question is:

In a city with three high schools, all the ninth graders took a Standardized Test, with these results: High School Mean score on test Number of ninth graders

Glenwood     78       269

Central City   93       321

Lincoln High  66       161

The city's PR manager, who never took statistics, claimed the mean score of all ninth graders in the city was 81 . Of course, that is incorrect.

a. What is the mean score for all ninth graders in the city? Round to two decimal places.

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The given statement is True.

What is developing logarithms?

The emergence of logarithms was predicted by comparing arithmetic and geometric series.

True. John Napier is credited with developing logarithms and Henry Briggs is known for working with Napier to advance the concept and promote its use.

Together, they created the logarithmic tables that became a powerful tool in mathematics and science.

Therefore, The given statement is True.

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Answer:

Option B

Step-by-step explanation:

The green graph represents the percentage of calls with the Chicago service center.
For December 1993, the percentage of calls is coming out to at least 95 percent. In addition, the graph is increasing as months go by. Based on these two analysis, the estimate percentage of calls within 10 seconds in January of 1994 is:

Option B: 98

Answer:

56 is 40% of the original number

Step-by-step explanation:

Let [tex]n[/tex] represent the original number

We are given that  

30% of number is 42

70% of the same number is 98

Lets convert the precents to decimals

30% as a decimal is [tex]0.3[/tex]

70% as a decimal is [tex]0.7[/tex]

We can create an equation for each scenario

[tex]0.3n=42\\0.7n=98[/tex]

We can choose either one to evaluate [tex]n[/tex].

[tex]0.3n=42[/tex]

Lets solve for [tex]n[/tex].

Divide both sides by [tex]0.3[/tex].

[tex]n=\frac{42}{0.3}[/tex]

Evaluate [tex]\frac{42}{0.3}[/tex].

[tex]n=140[/tex]

Now that we know what the original number is we can calculate what 40% of the number is.

40% as a decimal is [tex]0.4[/tex].

[tex]140*0.4=56[/tex]

The equation that describes the graphed function is -

g(x) = - f(x) - 3.

A root function in mathematics is given as -

y = [tex]$\sqrt[n]{x}[/tex]

We can further write the function as -

y = [tex]$x^{\frac{1}{n} }[/tex]

Given is the graph of the function as shown in the image attached.

We can write the function f(x) as -

f(x) = √x

Inverting the f(x) across the {x} axis, we can write -

- f(x) = - √x

After downward translation, we can write g(x) as -

g(x) = - f(x) - 3

Therefore, the equation that describes the graphed function is -

g(x) = - f(x) - 3.

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The mean, median, range, and standard deviation are all measures that can be used to calculate information about a set of numbers, such as the ages of ten randomly selected students.

The mean is the result of totaling the ages of ten randomly selected students and then dividing by ten. This calculation is also known as the average. To calculate the mean, first add up all of the ages, which gives us the sum. Then divide the sum by the number of students, which in this case is 10. The result is the mean, or the average age of the group.

The median is the middle value of a group of numbers. To calculate the median, first put the ages in order from least to greatest. Then find the middle value. If there is an even number of values, then the median is the average of the two middle values.

The range is the difference between the highest and lowest values. To calculate the range, just subtract the smallest number from the largest.

The standard deviation is a measure of variation in a set of numbers. To calculate standard deviation, first subtract the mean from each value, then square each of those differences. Add up these squared differences and divide by the number of values. Then take the square root of that number. The result is the standard deviation.

The mean, median, range, and standard deviation are all measures that can be used to calculate information about a set of numbers, such as the ages of ten randomly selected students.

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Answer: 1 [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Make it a mixed number then simplify if you can. I hope this helps.

The value off ARU based on the information will be 35°.

We know, the incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle.

A)By property, AR is angle bisector of angle KRU.

Therefore m(<ARU) = m(<ARK) = 40°

m<ARU= 40°

B) The angle bisectors in a triangle are always concurrent and the point of intersection is known as the incenter of the triangle.

AU = AT = 20

Therefore,

AU = 20

C) AP is angle bisector of <QPR,

By definition of angle bisector

m<QPA = m<APR

3x+2 = 4x-9

4x-3x = 9+2

x =11

m<QPA = 3(11) +2 = 35°

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Answer:

3 liters

Step-by-step explanation:

If he took the 2 fullest containers, he took the two dots that are at 4 1/2, which is also 4.5

Now since there are two, we multiply by 2.

4.5 = 9 liters

It then says he will divide the milk evenly between 3 containers. So now we divide.

9/3 = 3

The solution of the quadratic equation for y is given as follows:

y = 0.17 and y = 1.69.

The quadratic equation for this problem is defined as follows:

7y² - 13y + 2 = 0.

The coefficients are given as follows:

a = 7, b = -13 and c = 2.

Hence the discriminant is of:

D = (-13)² - 4 x 7 x 2

D = 113.

The first root is of:

y = (13 + sqrt(113))/14

y = 1.69.

The second root is of:

y = (13 - sqrt(113))/14

y = 0.17.

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The number of ways the letters can be permutated in the word SPEECHLESS is 100800.

What is meant by permutation?

An arrangement of items in a specific order is referred to as a permutation. A set can be permuted by arranging its components in a linear or sequential order, or by rearrangement of its components if the set is already ordered. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

The  number of letters in SPEECHLESS = 10

The letter E repeats 3 times

The letter S repeats 3 times

The letters P,C,H,L repeats one time.

When there are repeating letters in a word, the total number of distinct ways the letters in the words can be permutated is:

[tex]N= \frac{n!}{r_1!r_2!.....r_m!}[/tex]

where N = number of arrangements

 n = number of letters

r = total number of times one letter is repeated in the word

For SPEECHLESS,

Therefore the number of ways the letters can be permutated  is:

[tex]N= \frac{10!}{3!3!}[/tex] = 100800

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Answer:

34 miles per gallon

Step-by-step explanation:

850/25 = 34

Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

The formula for Percent Decrease is: Decreased Value = (Original Value – New Value)/Original Value.

The computation of our Percent Decrease:

= (64 - 21)/61 * 100

= 70.49%

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Answer:

Rs 3520 is divided in the ratio 11:12:17 as rs 968, rs 1056, and rs 1469

Step-by-step explanation:

According to the question, we have to divide rs 3520 in the ratio 11:12:17

let the common ratio be x

so, total share= (11+12+17)x = 40 x

for the first person, share would be (11x/40x)*(Rs 3520)

=Rs 968

for the second person, share would be (12x/40x)*(Rs 3520)

=Rs 1056

for the third person, share would be (17x/40x)*(Rs 3520)

=Rs 1496

The shares are Rs 968, Rs 1056, and Rs 1469

hope this helps :)