Kate intends to give her 12 good friends a treat at the school cafeteria. Her friends can have either a cupcake
or an ice cream cup. A cupcake costs $1.20 and an ice cream cup costs $1.50.
(i) What is the maximum and minimum amount of money Kate may have to spend?
(ii) Kate intends to spend not more than $16 on the treat. If two of her friends insist on having cupcakes,
what is the maximum number of ice cream cups her friends can have?

The number of books to read per month is 3 or more.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

14x ≥ 42

Solve for x.

14x ≥ 42

Divide both sides by 14.

x ≥ 42/14

x ≥ 3

This means,

The number of books to read per month is 3 or more.

Thus,

The number of books to read per month is 3 or more.

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When factoring a tricky trinomial with a leading coefficient greater than 1, and you have more than one pair of factors for a term, it is usually best to try the pair of factors that multiplies to give the constant term first.

This is because when factoring a trinomial with a leading coefficient greater than 1, the first term will always have fewer factors than the last term, and it can be easier to find the correct pair of factors for the constant term than for the first term.

If the correct pair of factors for the constant term is found first, it can be easier to use that information to deduce the correct pair of factors for the first term.

In addition, once you have found one pair of factors for the trinomial, you can use the factoring by grouping technique to factor the trinomial completely. This involves grouping the terms of the trinomial in pairs, factoring out the greatest common factor of each pair, and then factoring out the greatest common factor of the resulting expressions.

Overall, when factoring a tricky trinomial with a leading coefficient greater than 1, it can be helpful to start by trying the pair of factors that multiplies to give the constant term first, and then using the factoring by grouping technique to factor the trinomial completely.

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On solving the provided question, we can say that equation for getting amount spent by Daniel is y + 38 / 3 = x

A mathematical equatiοn is a formula that joins two statements and uses the equal symbοl (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equatiοn in algebra.

For instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the twο sentences οn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbol. for instance, 2x – 4 = 2.

equatiοn for getting amοunt spent by Daniel -

x = y+38 / 3

Tracy then spent (in dοllars) accοrding to the provided descriptiοn (we don't write symbols like $ when writing equations because it is clear from the cοntext what the quantity stands fοr).

y = 3x - 38

y + 3x8 = 3x

y + 38 / 3 = x

equation for getting amοunt spent by Daniel is

y + 38 / 3 = x

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The institution anticipates having 2158 students who can speak three or more languages.

The two ratios given are equivalent to one another, as demonstrated by the proportional equation. The percentage expresses the equality of something like the two ratios as well as fractions.

Comparing two integers that each stand for a component of a whole results in a percentage. In essence, a percentage declares that two fractions are equal, regardless of the difference in amount. For instance, the ratio of half of 10 marbles to half of 50 marbles is 10.

[tex]\frac{x}{32370}=\frac{12}{180}[/tex]

[tex]{x} = \frac{12}{180}\times32370\\{x}=2158[/tex]

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The length of AC from the given triangle ABC is 10 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, in the right triangle ABC below, DE is parallel to AC, and DE is perpendicular to CB at E.

The length of AB is 26 units, the length of DE is 5 units, and the length of BE is 12 units.

Consider ΔABC and ΔBDE

∠BDE=∠BAC=90°

∠ABC=∠DBE (Reflexive property)

By AA similarity, ΔABC is similar to ΔBDE.

By midpoint line segment theorem,

AC=2DE

AC=2×5

AC=10 units

Therefore, the length of AC is 10 units.

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The shark is fed during the feeding at night is 1/6 tons.

What is a proper fraction?

A proper fraction is one that doesn't contain any whole numbers and has a smaller numerator than a denominator. A fraction that represents a number greater than one and has a larger numerator than the denominator is said to be improper.

Given that during the morning feeding, 2/15 of a ton of fish is fed. During the afternoon feeding the weight of the fish fed will be 1/15 of a ton more than the fish fed during the morning.

The shark fed (2/15 + 1/15) ton during the afternoon.

Assume that the shark fed x tons at night.

Therefore, the total fed is 2/15 + (2/15 + 1/15) + x

The equation is:

2/15 + (2/15 + 1/15) + x = 1/2

Add like terms:

5/15 + x = 1/2

1/3 + x = 1/2

Subtract 1/3 from both sides:

x = 1/2 - 1/3

x = (3-2)/6

x = 1/6

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Answer:

[tex]p(3and7)andq(1and9)[/tex]

Step-by-step explanation:

Principal = $2,500

Rate = 3.8%

5A). The interest Yousuff make in one year

Therefore Time = 1 year.

Simple interest

[tex] = \frac{pincipal \times time \times rate}{100 \\ } \\ = \frac{2500 \times 1 \times 3.8}{100} \\ = 25 \times 1 \times 3.8 \\ = 95 .[/tex]

Therefore the interest Yousuff make in one year = $95.

5B). Interest Yousuff make in after 8 years

the time = 8 years

the interest

[tex] = \frac{pincipal \times time \times rate}{100} \\ = \frac{2500 \times 8 \times 3.8}{100} \\ = 25 \times 8 \times 3.8 \\ = 200 \times 3.8 \\ = 760 [/tex]

Therefore the interest Yousuff make after 8 years = $760.

5C). Principal - interest that Yousuff made after 8 years.

$2500 - $ 760

= $ 1,740.

The exponent of g, r, is -65536.

The exponent of y, s, is 1.

The leading coefficient, k, is 4.

Note: The expression 4^65536g³y² √√/65536g³y² is not equal to kg³y³, but instead represents the value of 4 raised to the power of 65536 times g raised to the power of -65536, divided by the square root of 65536 times g raised to the power of -65536 times y squared. The square root symbol is used twice, which is equivalent to taking the square root of the square root, or the fourth root.

Answer: 5[tex]\sqrt{3}[/tex]

Step-by-step explanation:

The 30-60-90 triangle rule states that the hypotenuse is twice the length of the shortest leg (which would be 5) and the longer leg is [tex]\sqrt{3}[/tex] times the length of the shorter leg.

Since we are trying to find x we would use the rule for the longer leg

so 5 * [tex]\sqrt{3}[/tex] would just be 5[tex]\sqrt{3}[/tex]

The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.

The 30°-60°-90° Triangle Theorem states that in such a triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is the product of the length of the hypotenuse and the square root of 3 divided by 2.

here, we have,

Using this theorem, we can write:

y = hypotenuse

Opposite of 30° angle = 5 = hypotenuse/2

Opposite of 60° angle = x = hypotenuse × (√(3)/2)

Solving for the hypotenuse in terms of y from the first equation, we get:

hypotenuse = 5×2 = 10

Substituting this value into the third equation, we get:

x = 10 × (√(3)/2) = 5 × √(3)

Hence, The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.

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The angle formed between the cables is 48.7°.

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

Given: Tugboat A and Tugboat B are pulling a barge. Each tugboat is connected to the barge via a cable. If the length of the cables is 63 meters and 68 meters and the tugboats are 35 meters apart.

a = 68 m

b = 63 m

c = Distance between the tugboats = 35 m

m∠C = Angle between the cables

c² = a² + b² - 2abcosC

m∠C = cos⁻¹(c² - a² - b²)/(-2ab)

m∠C = cos⁻¹(35² - 68² - 63²)/(-2(68)(63))

m∠C = 48.7°

Hence, the angle formed between the cables is 48.7°.

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The given function represents exponential growth, the value of a is 1 and the value of r is 0.45.

The quantity increases slowly after which the rate of change and the rate of growth increases over a period of time rapidly. This increase in growth is calculated by using the exponential growth formula.

The exponential growth formula is [tex]Amount = Initial value(1+\frac{r}{100} )^{\frac{t}{n}}[/tex].

The given exponential function is [tex]x(t)=(1.45)^{\frac{t}{2} }[/tex].

Now, [tex]x(t)=(1+0.45)^{\frac{t}{2} }[/tex]

Compare, [tex]x(t)=(1+0.45)^{\frac{t}{2} }[/tex] with [tex]y=a(1+r)^t[/tex], we get

a=1 and r=0.45

Therefore, the value of a is 1 and the value of r is 0.45.

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Each of the following measurements contain a) 1, b) 4,c) 3,d) 1,e) 2,f) 4,g) 2  significant figures.

Significant digit -Precision refers to the number of digits to which a value can be assigned. Therefore, numbers that can have a value of digits are called significant digits.

Below are the key figures for each value reported.

(a) 2- 1significant digits

(b) 81.640 - 4 significant digits;

(c) 7.03 - 3 Significant Figures

(d) 0.003 - 1significant digits

(e) 0.0086 to 2 significant digits

(f) 3236 - 4 significant digits

(g) 8700 - 2 significant digits

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The correct answer is 45.28°

In order to get that answer, you must set up the arc length formula.

l = m/360 • 2πr

4.9 = m/360 • 12.4π

We are trying to find the angle measure; therefore, we are going to divide.

4.9 = 0.10821m

Flip the equation

0.10821m = 4.9

0.10821m/0.10821 = 4.9/0.10821

m = 45.28°

We can use the formula angle = (arc length / radius) or an online calculator to find the angle of the slice, which is approximately 47 degrees in this case.

To find the measure of the angle of one slice of pizza, we can use the formula:

angle = (arc length / radius)

However, we are not given the radius of the pizza, so we first need to find it. One way to do this is to use the length of one side of the slice and the central angle of the slice. We know that the central angle of the slice is twice the angle at the center of the pizza that the slice occupies, so we can find this angle by:

angle at center = (angle of slice) / 2

We can then use the law of cosines to find the length of the radius:

radius² = (side length / 2)^2 + (side length / 2)² - 2 * (side length / 2) * (side length / 2) * cos(angle at center)

Once we have the radius, we can use the formula above to find the angle of the slice. However, since this calculation can be quite involved, it may be simpler to use an online pizza slice angle calculator. Using this tool with the given values, we find that the angle of one slice of pizza is approximately 47 degrees.

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A step that is not performed in the process of solving n² - 12n - 10 = 0 by completing the square is: C. Factor n² - 12n - 10 = 0.

In order to solve the given quadratic equation, we would use the completing the square method as follows;

n² - 12n - 10 = 0

By keeping x terms on the left-hand side of the quadratic equation, we would move the constant term to the right-hand side of the quadratic equation by adding 10 on both sides as follows;

n² - 12n - 10 + 10 = 0 + 10

n² - 12n = 10

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

n² - 12n + (12/2)² = 10 + (12/2)²

n² - 12n + 36 = 10 + 36

n² - 12n + 36 = 46

(n - 6)² = 46

By taking the square root of each side, we have:

n - 6 = ±46

n = 6 ±46

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Complete Question:

Which step is NOT performed in the process of solving n² - 12n - 10 = 0 by completing the square?

Add 10 to each side

Add 36 to each side

Factor n² - 12n - 10 = 0

Take the square root of each side

Answer:

About 54 geckos

The set representing the ordered numbers is given as follows:

0.45, 52%, 10/11, 31.

The numbers for this problem are given as follows:

For the three numbers with an integer part of zero, we order them according to the decimal part, hence:

0.45, 52%, 10/11.

31 has an integer part of 31 and is greater than the other numbers, hence the ordered data-set is given as follows:

0.45, 52%, 10/11, 31.

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The correct size of the distance matrix for a multivariate data set with 25 subjects and 7 variables is 25 x 25.

Understanding the many objectives and histories of the various types of multivariate analysis, as well as how they connect to one another, is the focus of multivariate statistics.

The distance matrix contains the pairwise distances between all pairs of subjects in the dataset, and therefore has the same number of rows and columns as the number of subjects in the dataset. Since there are 25 subjects in this dataset, the distance matrix will have 25 rows and 25 columns.

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The standard deviation of the sampling distribution of x bar (the mean of a sample) is always less than the standard deviation of the population from which it is sampled.

Central Limit Theorem states that as the sample size increases, the sampling distribution of x bar approaches a normal distribution with a mean equal to the population's mean and a standard deviation equal to the population's standard deviation divided by the square root of the sample size.

Standard deviation of the sampling distribution of x = σ / √N,

where:

σ  = standard deviation of the population

N = sample size

As a result, the standard deviation of the sampling distribution of x bar is also less variable than the standard deviation of the population.  

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The value of x in the triangle is 6√5

from the question, we have the following parameters that can be used in our computation:

The triangle

Using the above as a guide, we have the following:

x/20 = 9/x

Cross multiply the equation

so, we have the following representation

x^2 = 180

TAke the square root of hoth sides

This gives

x = 6√5

Hence, the solution of x is  6√5

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The values of f and g based on the given diagram ABCE is 6cm and 8cm respectively.

Area of ABCE = 60cm²

Area of ABCD = 48cm²

Area of ADE = Area of ABCE - Area of ABCD

= 60 cm² - 48 cm²

= 12 cm²

Area of ADE = 1/2 × base × height

12 = 1/2 × 4 × h

12 = 4/2h

12 = 2h

divide both sides by 2

h = 12/2

h = 6 cm

AD = height = BC = 6 cm

Area of ABCD = length × width

48 = l × 6

48 = 6l

l = 48/6

l = 8 cm

In conclusion, f and g are 6cm and 8cm respectively.

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The boat that will cost Stephanie less to buy and use is boat B, and the difference between the cost is $11.7.

Let's calculate first the cost of each boat:

Boat A

cost + repairs + gasoline for 3 years= total cost

2400 + 600 + gasoline cost

gasoline cost = 40 / 15 = 2.66 gallons per month x 36 = 95.76 X 3.89 = 372.5

2400 + 600 + 372.5 = 3,372.5

Boat B

cost + repairs + gasoline for 3 years= total cost

2800 + 250 + gasoline cost

gasoline cost = 40 / 18 = 2.22 gallons per month x 36 = 79.92 X 3.89 = 310.88

2800 + 250 + 310.88 = 3,360.88

Difference: 3,372.5 - 3, 360.88 = 11.7

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For diagram A, the unsimplified equation represents the relationship between x and y is y = x + x/3.

For diagram B, the unsimplified equation represents the relationship between x and y is y = x + 2x/3.

For diagram C, the unsimplified equation represents the relationship between x and y is y = x - x/3.

For diagram D, the unsimplified equation represents the relationship between x and y is y = x - 2x/3.

Performing mathematical operations reduces an unsimplified equation to a simplified equation. A simplified equation is used for convenience.

Diagram A:

The value of x contains 3 congruent colored rectangles. The noncolored rectangle is 1. So, the value of the noncolored rectangle will be x/3.

Clearly, y will be the sum of x and x/3, that is, y = x + x/3.

Therefore, the obtained answer is y = x + x/3.

Diagram B:

The value of x contains 3 congruent colored rectangles. The noncolored congruent rectangles are 2. So, the value of the noncolored rectangles will be 2x/3.

Clearly, y will be the sum of x and 2x/3, that is, y = x + 2x/3.

Therefore, the obtained answer is y = x + 2x/3.

Diagram C:

The value of x contains 3 congruent colored rectangles. So, the value of 1 rectangle will be x/3.

Clearly, y will be the difference between x and x/3, that is, y = x - x/3.

Therefore, the obtained answer is y = x - x/3.

Diagram D:

The value of x contains 3 congruent colored rectangles. So, the value of 2 congruent rectangles will be 2x/3.

Clearly, y will be the difference between x and 2x/3, that is, y = x - 2x/3.

Therefore, the obtained answer is y = x - 2x/3.

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This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.

The interest rate in this situation is 19% compounded monthly. This means that each month, the interest rate is applied to the total balance. The formula to calculate the amount of interest owed is:Interest Owed = Balance x (Interest Rate/12) .In this case, the formula would be:Interest Owed = 16,783 x (0.19/12).This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.

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30 minutes twice a day for 184 days, total 368 gallons of water will be used in each hole.

Assuming that each hole uses one gallon of water per 30 minutes.

1 hole = 1 gallon of water

The total amount of water used in each hole over 184 days would be 184 gallons.

So, in 184 days = 184 gallons of water

This is because each hole would be watered twice a day for 184 days, which comes out to 368 separate waterings.

= 184 × 2

= 368 gallons

The total amount of water used would be 368 gallons.

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The complete question is:

How many gallons of water will be used in each hole if 30 minutes is spent twice a day for 184 days?

Answer:

AB = a - 8b

Step-by-step explanation:

AB = AO + OB

    = - OA + OB

     = - (4a + 7b ) + (5a - b )

    = - 4a - 7b + 5a - b ← collect like terms

     = a - 8b

If the presented hypothesis is confirmed, it can be assumed that individuals in the experimental group suffer from headaches more frequently than those in the control group.

The study examines how stress affects headaches. The theory can be stated as follows: People who encounter stress episodes more than twice per day would feel headaches more frequently than people who do not experience stress. This question concerns a cause and effect analysis, which can be done with reliable results when using an experimental investigation. Therefore, it is advised to use an experimental design for dealing with headaches brought on by stress. Stress events are the only unchanging factor in our study, however they do cause changes in the frequency of headaches. The degree of headaches, which fluctuates when the independent variable is changed, can be thought of as the dependent variable. Here, the technique can be applied as follows: Informed consent is obtained from a sample of 400 persons, all of whom fall within the age range of 25 to 40 (to lessen the impact of any auxiliary variables on the results). The volunteers are divided into two groups at random, one of which is the experimental group and the other the control group (double-blind design to avoid any potential biases). Three times a day, participants in the experimental group are exposed to a show that is heavy on the negative feelings that can lead to stress; in contrast, individuals in the control group are not exposed to any of the shows mentioned above. Then, the presence of headaches is assessed in both groups' members.

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Answer:

12 Days

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

To find the ratio of the problem (days: pages) we can use this equation:

pages read ÷ days it took = pages read each day

Fitting the numbers into the equation:

168 ÷ 7 = 24

So, everyday Kelly reads 24 pages.

To find out how many more days Kelly needs to read, if she reads at the same rate, we can use this equation:

(456 - 168) ÷ 24 = days left

We can use this to check our work:

168 + (24 ×?) = 456

Solving for the first equation:

(456 - 168) ÷ 24 = days left

288 ÷ 24 = 12

Now, we can check our work.

168 + (24 ×?) = 456

Inserting 12 into the equation:

168 + (24 × 12) = 456

168 + 288 = 456

Therefore, to complete the book it will take Kelly 12 more days.

The bike has 21 gears, 3 on the front and 7 on the rear cogset, giving a total of 21 average possible gear combinations.

The bike has 3 sprockets on the front and 7 sprockets on the cogset at the rear of the bike. This combination of 3 sprockets on the front and 7 on the rear creates a total of 21 possible gear combinations. This is calculated by multiplying the number of sprockets on the front by the number of sprockets on the rear. When you change the gear on the bike, you are changing the combination of the front and rear sprockets. By doing this, you can adjust the gearing of the bike to make it easier or harder to pedal depending on the terrain. Having a wide range of gears helps you to climb hills, accelerate and maintain speed on flat roads, as well as descend hills. Having 21 gears gives you a lot of options to make your ride as comfortable and efficient as possible.

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