log₂ 3+ log₂ (x-4)= 4

If Nick spends $4.89 and Riley spends 3 times as much as Nick and Clay spends $12.73 more than Riley , then the total amount spent by Clay is $27.4 .

The amount Nick spends to buy School Supplies is = $4.89 ,

the amount spent by Riley is 3 times of amount spent by Nick ,

that means , Riley spent = 3 × 4.89 = $14.67 ,

the amount spent by Clay is $12.73 more than the amount spent by Riley , which means ;

Clay spent is = $14.67 + $12.73 = $27.4 .

Therefore , Clay spent $27.4 to buy school supplies .

The given question is incomplete , the complete question is

Some friends go to the store to buy school supplies. Nick spends $4.89  Riley spends 3 times as much as Nick. Clay spends $12.73 more than Riley. How much did Clay spend ?

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Violet's money tripled Dylan's money to triple= 23,249.95.

Dylan invested $6,100 in an account paying an interest rate of 2% compound.

Violet invested $6,100 in an account paying an interest rate of 2%

compound.

The formula for compound amounts is A = P(1 + r/n)^(nt),

where n is the number of compounding periods per year, t is the number of years, P is the initial amount invested and r is the annual interest rate as a decimal fraction.

Here,

A = ($6100)(1 + 0.02/4)^(12*4)

Evaluating this we get:

A = ($6100)(1.005)^48, or

A  = ($6100)(`1.2704)

A = $7,749.98

Violet's money to triple than for Dylan's money to triple

=3(A)=3*7749.98=23249.95.

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Varun takes 4 rotis per meal and Rosa takes 2 per meal

Varun wastes 40 rotis in 20 days

Let's call the number of rotis Varun takes per meal "V".

We know that Rosa takes half the amount of rotis as Varun, so Rosa takes V/2 rotis per meal.

Together, they take V + V/2 = 1.5V rotis per meal.

If they consume 120 rotis in 20 days, that means the amount they consume is

Amount = 120/20 = 6 rotis per day.

So, 1.5V = 6, and V = 4.

Varun takes 4 rotis per meal and wastes 4/2 = 2 rotis per meal.

Over 20 days, Varun would waste 2 * 20 = 40 rotis.

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In triangle UVT, the missing length, i.e., UV is 37. It is applicable in the case when triangle UVT ≈ triangle DEF.

Two triangles that are identical in size and shape are said to be congruent triangles. They share the same number of vertices, angles, and sides—three. The matching sides and angles of the two triangles must match in size for them to be considered congruent. In other words, when the two triangles are positioned next to one another, they must match.

The Pythagorean theorem may be used to determine the length that is lacking if the other three lengths are known. According to the Pythagorean theorem, the square of the longest side of a right triangle is equal to the sum of the squares of the two shorter sides. By computing the square root of the sum of the squares of the other three lengths, it is possible to determine the missing length.

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Step-by-step explanation:

a = 16

b = 3

because only the factor 3 gets repeatedly added every year (x).

the rest (the starting value that gets tripled and then tripled and then tripled ... every year) is constant.

f(x) = 16×3^x

as you know, exponents have the higher priority to multiplications.

if you want to be save you can use brackets like

f(x) = 16×(3^x)

Answer:The mathematical expression -4(-3t-10t-7)-t can be simplified to -4( -13t - 7 ) - t . This can be simplified even further by combining like terms to -4( -13t - 7) - 1t .

Step-by-step explanation:

The price for a children's ticket is $2.50

Now, According to the question:

A fundraising dinner was held on two consecutive nights.

Let the number of children's tickets be x.

Let the number of adults' tickets be y.

The total number of tickets sold is 937.50

On the first night, 100 adult tickets and 175 children's tickets

Therefore,

100x + 175y = $937.50

On the second night, 200 adult tickets and 316 children's tickets were sold for a total of $1790.

200x + 316y = $1790

Now, we have two simultaneous equations:

100x + 175y = $937.50 ----(1)

200x + 316y = $1790----(2)

Divide by 2 equation (2)

100x + 158y = $895----(3)

From the first equation, make y the subject of the formula:

100x = 937.50 - 175y

Put the value of 100x in equation (3)

937.50 -175y + 158y = $895

937.50 - 17y = $895

-17y = -42.5

y = 2.50

Hence, the price for a children's ticket is $2.50

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Plans for what to do after high school and three ways to protect yourself from the effects of inflation are mentioned below.

To take into account a recovering economy with scarce jobs and low salaries when making plans for after high school, one could consider the following:

To protect oneself from the effects of inflation, one could consider the following:

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Answer: He can buy 4 pants for $120 and 4 shirts for $80

Answer: Roger wants to buy at least 6 items, so he needs to buy at least 6 pants or 6 shirts or a combination of both.

Step-by-step explanation:

The cost of 6 pants is $30 x 6 = $180.

The cost of 6 shirts is $20 x 6 = $120.

If Roger wants to buy both pants and shirts, he can buy 3 pants and 6 shirts for a total cost of $90 + $120 = $210.

Another option would be 4 pants and 5 shirts for a total cost of $120 + $100 = $220.

Thus, Roger can buy either 6 pants, 6 shirts or a combination of 3 pants and 6 shirts or 4 pants and 5 shirts with his $200.

Answer: Solving a compound inequality in compact form is similar to solving a simple inequality in the sense that both involve isolating the variable on one side of the inequality and then using the same rules of inequality to find the solution set. Both compound and simple inequalities can be graphed as a line on a number line or coordinate plane, with the solution set being either all the numbers less than, greater than, or between two values, depending on the inequality sign.

However, solving a compound inequality in compact form is different from solving a simple inequality in that a compound inequality has two or more inequality statements combined using "and" or "or" connectors. When solving a compound inequality, we have to consider both inequalities together to find the final solution set. For example, when solving the inequality 3 < x < 5, we have to consider both 3 < x and x < 5, to find the range of x that satisfies both inequalities. And when we have a compound inequality with "or" connector like 3<x<5 or 6<x<8, we need to find the solution set for each inequality separately and then combine them.

So, the difference between solving a compound inequality and a simple inequality is that a compound inequality has multiple inequality statements that must be considered together to find the final solution set, while a simple inequality has only one inequality statement.

Step-by-step explanation:

This means that if 7 or more teachers attend the training, it will be a good decision, as the cost of sending them will be less than the cost of not sending them.

What is an algebraic manipulation?

Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.

To determine if sending teachers to the summer training on mentor groups is a good decision, the committee needs to calculate the break-even point. This is the point at which the cost of sending the teachers is equal to the cost of not sending them. The break-even point can be calculated by dividing the advanced payment by the difference between the cost at registration and the advanced payment.

In this case, the break-even point is: $1,250 ÷ ($175 - $1,250) = $1,250 ÷ -$1,075 = 7 teachers.

Hence, This means that if 7 or more teachers attend the training, it will be a good decision, as the cost of sending them will be less than the cost of not sending them.

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Answer:

x = 200

Step-by-step explanation:

[tex]\frac{x}{5} = \frac{120}{3}[/tex]

so you cross multiply

5 × 120 = 600

x × 3 = 3x

so

3x = 600

x = 200

Answer:

Step-by-step explanation:

Prime factorization is the process of expressing a number as the product of its prime factors. To find the prime factorization of a number, you can use the following steps:Divide the number by the smallest prime factor (2) and write the result.Divide the quotient from step 1 by the next smallest prime factor (3) and write the result.Repeat step 2 with each successive prime factor until the quotient is 1.For example, to find the prime factorization of 60:60 / 2 = 30 -> 2

30 / 2 = 15 -> 2 * 2 = 4

15 / 3 = 5 -> 4 * 3 = 12

5 / 5 = 1 -> 12 * 5 = 60The prime factorization of 60 is 2 * 2 * 3 * 5To find the greatest common factor (GCF) of two numbers, you can use the following steps:Write the prime factorization of each number.Write the GCF as the product of the prime factors that are common to both numbers, each raised to the lowest power that occurs in both factorizations.For example, to find the GCF of 24 and 40:Prime factorization of 24 = 2^3 * 3

Prime factorization of 40 = 2^3 * 5The GCF is 2^3 = 8To find the least common multiple (LCM) of two numbers, you can use the following steps:Write the prime factorization of each number.Write the LCM as the product of the prime factors of each number, each raised to the highest power that occurs in either factorization.For example, to find the LCM of 24 and 40:Prime factorization of 24 = 2^3 * 3

Prime factorization of 40 = 2^3 * 5The LCM is 2^3 * 3 * 5 = 120Alternatively, you can use the formula LCM(a, b) = (a * b) / GCF(a, b)Please note that this is a method for finding the prime factorization and GCF/LCM of small numbers. For larger numbers, it is more efficient to use a specific algorithm or software.

The money Nicole that he owes by selling the 36 quarts of lemonade is $ 54.

As per the given data, Nicole is selling the lemonade at her stand.

She charges $0.75 per pint.

Mr. Terry buys 36 quarts of lemonade.

Here we have to determine how much money he owes Nicole by selling the 36 quarts of lemonade.

Convert the quantity from quarts to pints.

As we know that 1 quart = 2 pints

1 quart = 2 pints

36 quarts = 2 × 36 pints

36 quarts = 72 pints.

The 36 quarts are equal to 72 pints.

The cost of one pint is $0.75.

We have to find the cost of 72 pints.

1 pint = $0.75

72 pints = ( 0.75 × 72 pints ) $

72 pints = 54 $.

Therefore the money owned by Nicole is $ 54.

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The quadratic equation 3x² + 2x - 5 = 0 is solved to give x = 1 and -5/3

From the information given, we have the quadratic equation as;

3x² + 2x - 5 = 0

Using the factorization method of solving quadratic equation, we have to take the following steps

Multiply the coefficient of x² by the constant -5

Find the pair factors of the product of their multiplication that sums up to 2

The pair factors are +5 and -3

Substitute the values

3x² + 5x - 3x - 5 = 0

Add parentheses

(3x² + 5x) - (3x - 5) =0

factorize the values

x(3x +5) - 1(3x + 5) = 0

The values of x are;

x= 1 and x = -5/3

Thus, the values are 1 and -5/3

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The complete question:

Solve the quadratic equation 3x2 + 2x - 5 = 0 using factorization method

The points G and H is the center of dilation from the points E, F, G, or H

What is Center of Dilation ?

The middle of a dilation is a hard and fast point inside the aircraft about which all points are increased or reduced in size. The middle is the handiest invariant (now not changing) factor below a dilation (k ≠1), and may be positioned inside, outdoor, or on a parent.

Given ,

In the Quadrilateral ABCD and its dilated image A′B′C′D′ are shown in the figure.

The points E, F, G, or H.

So, The center of dilation could be G and H .

Therefore, The points G and H is the center of dilation from the points E, F, G, or H

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[tex]~~~~~~ \stackrel{\textit{\LARGE Bank 1}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$25000\\ r=rate\to 5.25\%\to \frac{5.25}{100}\dotfill &0.0525\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (25000)(0.0525)(3) \implies I = 3937.5 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{\textit{\LARGE Bank 2}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$25000\\ r=rate\to 8.5\%\to \frac{8.5}{100}\dotfill &0.085\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (25000)(0.085)(3) \implies I = 6375 \\\\[-0.35em] ~\dotfill\\\\ 3937.5~~ + ~~6375\implies \text{\LARGE 10312.5}[/tex]

Relative frequencies are calculated by dividing the count by the total count in the column or row.

Joint relative frequencies show the proportion of individuals in a specific category of two variables.

They are calculated by dividing the count of individuals in a specific category by the total number of individuals surveyed.

In a two-way table, they are represented by the cells and give a sense of how the two variables are related to each other.

For example, in the given table, the joint relative frequency of males who plan to go to college is 0.35, which means 35% of the surveyed males plan to go to college.

Joint relative frequencies can be used to identify patterns and relationships between two variables, such as how gender and college plans are related.

joint relative frequencies:

Yes No Total

M 0.35 0.23 0.58

F 0.33 0.19 0.52

1

Marginal relative frequencies:

Yes No Total

M 0.58 0.42 1

F 0.52 0.48 1

1

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She will lay sod over area of 925.02 square feet of 3/4 of circle and triangle.

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

and Area of circle = πr²

Now,

Sod will be laid over=3/4*circle + on triangle

=3/4*πr^2+1/2*base*height

=3/4*3.14*18*18+1/2*18*18

=763.02+162

=925.02 square feet

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The probability that valley 1 is also infected is 15%

The math term probability is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Here we have know that two valleys are sometimes infected with tree rot.

The probability of rotting valley 1 = 35%

The probability of rotting valley 2 = 60%

And the probability that at least one is infected = 80%

When we convert these values into decimal then we get,

The probability of rotting valley 1 = 0.35

The probability of rotting valley 2 = 0.6

And the probability that at least one is infected = 0.8

Then the probability that valley 1 is also infected is

=> P = 0.35 + 0.6 - 0.8

=> P = 0.15

When we convert it into percentage then we get,

=> P = 15%.

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Robel's age will be 15 and Father's age will be 45, which is three times as old as Robel.

Robel's current age = x

Father's current age = 4x

After 5 years,

Robel's age = x + 5

Father's age = 4x + 5

After 5 years, father will be three times a old a Robel

4x + 5 = 3(x + 5)

4x + 5 = 3x + 15

x = 10

Therefore, Robel's current age is 10 years and father's current age is 40 years.

Let x represent the current age of Robel and 4x represent the current age of Robel's father.

We can use the formula 4x + 5 = 3(x + 5) to solve for x.

We rearrange the equation to get x = 10.

Robel's current age is 10 years and father's current age is 40 years.

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The lateral surface area of the cylinder is 357.96[tex]cm^2[/tex]

Now, According to the question:

In two-dimensional geometry, a cylinder has two circles as its bases so that both the bases are parallel and congruent.

In a cylinder, there is a lateral surface that is between the bases.

Let us suppose d is the diameter of the base of a cylinder, and h is the height of the cylinder then:

Radius of the cylinder (r) = [tex]\frac{d}{2}[/tex]

Lateral surface area of the cylinder(S) = [tex]2\pi rh[/tex]

Total surface area(A) = lateral area + total area of the bases

Given that the diameter of the above cylinder is 12cm, and the height of the cylinder is 3.5cm.

d = 12cm

and,

h = 3.5cm

Now the radius of the cylinder:

(r) = [tex]\frac{d}{2}[/tex] = 12/2 = 6cm

Now the total surface area of the cylinder:

A = [tex]2\pi r(h +r)[/tex]

A = [tex]2\pi (6)(3.5+6)[/tex]

A = [tex]12\pi (9.5)[/tex]

A = 114[tex]\pi[/tex]

We use [tex]\pi[/tex] = 3.14

A = 114(3.14)

A = 357.96[tex]cm^2[/tex]

Hence, the lateral surface area of the cylinder is 357.96[tex]cm^2[/tex]

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0.266… is the answer.

I hope this helps even a bit :]

The shortest possible height of the vase rounded to the nearest tenth of a centimetres is 45.650.

The concept of rounding the numbers will be used here to find the answer. Concerning this, we must know, that a number will be rounded to next digit, if the subsequent number if 5 or more than 5.

We know 6 preceedes 7 and the number is rounded to nearest tenth. So, the just possible number will be 45.69. However, as mentioned, it will be rounded to 45.7. The same will happen for till 45.65. Proceeding before this, we get 45.64 which will not be rounded to 45.7. Thus, the smallest possible number is 45.65 centimetres.

Similarly, the 1 at hundredths place will be the smallest number. This is because, rounding off 5 will eventually lead to rounding off to 45.7.

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Statement "B. the median is a negative number" will be correct among these options.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given,  that A set of data contains 10 negative numbers and 4 positive numbers.

Since the value of data is not given it can be any positive or negative numbers

mode:

A mode is described as a value in a group of values that occurs most frequently. The value that appears the most frequently is this one.

Range:

When the sample maximum and minimum are subtracted, the range of a set of data in statistics is the difference between the greatest and lowest values.

Median:

The median is the value that's exactly in the middle of a dataset when it is ordered.

Thus, the Median will be negative.

Therefore, Statement "B. the median is a negative number" will be correct among these options.

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Complete question:

A set of data contains 10 negative numbers and 4 positive numbers. Which one of these statements must be true?

A. The mean is a negative number.

B. The median is a negative number.

C. The mode is a negative number.

D. The range is a negative number.

If there are multiple coins in a row we call them a streak , the expected number of streaks here are 224

Attempt: I interpreted the number of streaks as the number of switch between either H to T or T to H in the sequence + 1.

The problem has a markov chain structure and so we can  obtain the following equations, given S(n)

A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.

number of strike in sequence with n coins:

                 S(n|H) = 0.2s(n-1) + 0.8 (1+s(n-1))

                  S(n|T) = 0.8s(n-1) + 0.2(1+s(n-1))

This implies S(n) = S(n|T)p(T) + S(n|H)p(H)

                           = S(n-1) + 8/25

Therefore,  E[S(700)] = 224.

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1. The probability of getting heads on the first two and then a tail on the third is 1/8.

2. The probability of not getting a clay pot or a cactus is  1/2.

3. The probability of getting the same number twice is 1/36.

4. The probability of getting at least two heads is

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

1. The probability of getting a head P(H) = 1/2 and the probability of getting a tail P(T) = 1/2.

Therefore, The probability of getting heads on the first two and then a tail on the third is,

= (1/2)×(1/2)×(1/2).

= 1/8.

2. The probability of getting a clay pot is 1/4 and the probability of getting a cactus is 1/4.

So, The probability of getting a clay pot or a cactus is 1/4 + 1/4.

= 2/4.

= 1/2.

Therefore, The probability of not getting a clay pot or a cactus is,

= 1 - 1/2.

= 1/2.

3. Suppose we get a number 1 on the first throw and we know its probability is 1/6,

Therefore, The probability of getting 1 again is also 1/6.

So, The probability of getting the same number twice is,

= (1/6)×(1/6).

= 1/36.

4. The probability of getting at least two heads is,

P(HHT) + P(HHH).

= (1/2)×(1/2)×(1/2) + (1/2)×(1/2)×(1/2).

= 1/8 + 1/8.

= 2/8.

= 1/4.

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She buys 15 bags of candy.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.

Given that the number of bags of taffy was 5 more than the number of bags of caramels.

The Taffy bags weigh 8 ounces each, and the caramel bags weigh 16 ounces each.

The total weight of the bags of candy was 400 ounces.

Consider c be the total number of Carmel candy bags and t the total number of taffy bags that Ariel bought.

t = 5 + c

Then, we have:

8t + 16c = 400

8(5 + c) + 16c = 400

40 + 8c + 16c = 400

24c = 360

c = 15.

Hence, she buys 15 bags of candy.

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