George peels and eats 2 whole satsumas.
He then splits another satsuma into 6 equal segments and eats 1 of these segments.
How many satsumas does he eat in total?
Give your answer as an improper fraction.

Answer:

50%

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

Looking at the problem, we can take 25, and divide 50 by it.

25 ÷ 50 = 0.5

0.5 is equal to 5/10, which is also equal to 50%, meaning that 50% of 50 is 25.

The house is located 6.87 miles to the east of the cell tower.

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Given:

Let the center of the town represent the origin (0,0).

Also 1 unit = 1 mile.

Since the cell tower is located 3 miles east and 6 miles north of the center of a small town, it is represented by A(3, 6)

The cell tower has a coverage of radius 4 miles. This can be represented by a circle with equation:

(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius.

Then, (x - 3)² + (y - 6)² = 4²

(x - 3)² + (y - 6)² = 16

b) The house is 7 miles north. It can be represented by y = 5 line.

To find the distance east of the house we have to substitute y = 5 and solve for x,

(x - 3)² + (y - 6)² = 16

(x - 3)² + (5 - 6)² = 16

(x - 3)² + 1 = 16

(x - 3)² = 15

(x - 3) = ±3.87

x= 3 ±3.87

x= 6.87 or 0.87.

Hence, the house is located 6.87 miles to the east.

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The graph representing the given pairs is represented by the equation y = (4/5)x + 40.

        {m} - slope                 {c} - intercept along the y - axis.

Given is that Mr. Hart recorded the ratio of the minutes spent driving to the miles driven while on a road trip.

The given table is as follows -

Number of Minutes {m} :      75         60

Number of Miles {M} :          100        80

The slope of this graph will be -

m = (80 - 60)/(100 - 75)

m = 20/25

m = 4/5

The equation of the line can be written as -

y = (4/5)x + c

For the point (75, 100) as follows -

100 = 4/5 x 75 + c

100 = 4 x 15 + c

c = 100 - 60

c = 40

The equation of the graph will be -

y = (4/5)x + 40

Refer to the graph attached.

Therefore, the graph representing the given pairs is represented by the equation y = (4/5)x + 40.

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Jana, because she has the highest ratio since 56 over 80 is greater than 50 over 80.

The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

In baseball, each time a player attempts to hit the ball, it is recorded.

The ratio of hits compared to total attempts is their batting average.

Each player on the team wants to have the highest batting average to help their team the most.

For the season so far,

Jana has hit the ball 7 times out of 10 attempts.

Tasha has hit the ball 10 times out of 16 attempts.

To find the ratio of batting average:

We must find the same number of attempts.

So,

Jana has ratio 7/10.

So, 56 /80 = 0.7

Tasha has ratio 10/16.

So, 50 / 80 = 0.625

Therefore, Jana has the highest batting average.

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Answer:

  See attached

Step-by-step explanation:

You want the solution to the inequality -12x < -48 shown on a number line.

The solution to the inequality is found by dividing by the x-coefficient

  -12x < -48

  x > 4 . . . . . . . divide by -12

When working with inequalities, you need to know that multiplying or dividing by a negative number reverses the inequality symbol.

The value x=4 is not included in the solution set, so an open circle is plotted at that point. All values of x greater than x=4 are included in the solution set, so the number line is shaded to the right of the open circle.

The graph of the solution is shown in the attachment.

__

Additional comment

Often, you can avoid multiplying or dividing an inequality by a negative number by rearranging it. Here, adding 12x+48 to both sides makes it be ...

  48 < 12x

Now, you can divide by 12 without worrying about the inequality symbol:

  4 < x . . . . . same as above

The value of m in the given equation 4x² -mx +9 will be 13.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.

given an equation 4x² -mx + 9 = 0 and the question states that it has a root that is equal to 1

Since 1 is the root of this quadratic equation it will satisfy the equation

Substituting the values in the equation

4 - m + 9 = 0

m = 13

Therefore, In the given equation 4x² -mx +9 the value of m will be 13.

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Answer: He was 32 years old 8 years ago, than a) x-40 b) x-24 c) 40-x d) 24-x e) 24+x

Step-by-step explanation:

Mario was '40 - x' years old when he was 'x' years old.

If he was 32 years old, 8 years ago, then he is 40 now as (32+8) equals 40.

If he is 40 years old now, then he was '40 - x',  x years ago.

Hence, '40 - x' is the answer to this sum.

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The elements in matrix X is attached below

Matrix is a mathematical construct consisting of an array of numbers, symbols, or expressions, arranged in rows and columns. It is most often used to represent linear relationships between two or more variables. Matrices are commonly used in science and engineering to represent systems of equations and in computer programming for representing data and performing operations on it.

In this problem, we can easily find x by reversing the variables and solve.

A - X = B

X = A - B

The elements in the matrix can be solved easily using an online calculator.

The value of x is attached below

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Answer:

m=10

Step-by-step explanation:

m/5+9=11 subtract 9

m/5 = 2 multiply 5 by both sides

m = 10

Answer:

answers 3

Step-by-step explanation:

took more thinking than it should've tbh (3-2=1) (3+10=13) 1x13=13

Answer: Show the table

Step-by-step explanation:

SHow the table

Answer:

30 clovers

Step-by-step explanation:

If Nathaniel find 2 four-leaf clovers in the first 12 minutes of his search, the rate at which he finds the four-leaf clovers is:

[tex]\implies \sf Rate=\dfrac{2\;clovers}{12\;minutes}=\dfrac{1}{6}\;clovers\;per\;minute[/tex]

To predict the number of four-leaf clovers Nathaniel will find in 180 minutes, multiply the found rate by 180 minutes:

[tex]\implies \sf \dfrac{1}{6} \times 180=30\;clovers[/tex]

Therefore, Nathaniel will find 30 clovers in 180 minutes based on the rate at which he found 2 clovers.

[tex] \sf \longmapsto \: Prediction \: of \: 4 \: leaf \: clovers=2/12×180

\: [/tex]

[tex] \sf \longmapsto \: Prediction \: of \: 4 \: leaf \: clovers=30clovers[/tex]

The cost function is a function that describes the total cost of producing x number of books. The fixed cost of 25000 is a constant cost that does not depend on the number of books produced, so it is not included in the cost function. The cost function is therefore:

Cost function: C(x) = 30x

The profit function is a function that describes the profit made from selling x number of books. The profit is equal to the revenue from selling the books minus the cost of producing the books. The revenue from selling x number of books at a price of 50 each is 50x, so the profit function is:

Profit function: P(x) = 50x - 30x = 20x

This profit function tells you that for every book you sell, you will make a profit of 20.

To simplify this expression, you can first simplify the logarithms by using the properties of logarithms and the simplified expression is -0.00195

A logarithm is a mathematical function that is used to determine the power to which a number must be raised in order to produce a certain value. The logarithm of a number "b" to base "a" is represented as loga(b) or logb. The logarithm of b to base a is equal to the exponent to which we must raise a to get b.

[tex]1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125[/tex]

To simplify this expression, you can first simplify the logarithms by using the properties of logarithms.

[tex]1/2 log10 25/4 - 2 log10 4/5 + log10 320/125[/tex]

=[tex]1/2( log10 25 - log10 4) - 2 (log10 4 - log10 5) + (log10 320 - log10 125)[/tex]

= 1/2(1.397940008672037 - 0.6020599913279624) - 2*(-0.6020599913279624 - 0.6989700043360187) + (2.505149978319906 - 2.0969100130080566)

= 0.397940008672037 - 1.204120018655925 - 1.397940008672037 + 0.40825006983185

= -0.2 - 0.2062 + 0.40825

= -0.00195

So the simplified expression is -0.00195

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Complete question is: simplify the given equation:  1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125

On solving the provided questions, we can say that the congruence of ABC=DEF, where A=D, B=E, and C=F.D because they are equal in length. F

A figure that can be put exactly on another is said to be "matching." When the bread is piled, it is the same size and shape. The term "match" describes things that are precisely the same shape and size. A pair of geometric figures is said to be congruent or to be in a congruent relationship if one of them can be reliably superimposed over the other.

B D and F.

B because they would go together if the statement were put in that particular sequence. ABC=DEF, where A=D, B=E, and C=F.D because they are equal in length. F due to the same cause as B.

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Answer:

Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.

Step-by-step explanation:

•Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.

•The Triangle GHI is not similar to triangle ABC because the measure of angle G does not match the measure of angle A.

•The Triangle MNO is not similar to triangle ABC because the measure of angle N does not match the measure of angle B.

• The Triangle POR is not similar to triangle ABC because the measure of angle R does not match the measure of angle A or B.

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Answer: The answer is 29,446,941,856

Step-by-step explanation:

The total number of employees that this company would be said to have is given as 122424

How to solve for the number of employees in the company

We know that the number of employees in one country is 22400, and that this represents 18.3% of the company's employees in total.

We can use this information to set up a proportion to find the total number of employees in the company.

Employees in one country / Total employees = 18.3 / 100

22400 / X = 18.3/100

To find the total number of employees, we can cross-multiply and divide:

X = (22400 * 100) / 18.3

X = 122424

So the company has a total of 122424 employees.

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A student wants to write an expression for, all the elements which are in set A and all the elements in set B. Then, the expression matches the statement is (A n B), which is read as A intersection B. Thus, option B is correct.

The intersection of two sets A and B, denoted by display by (A ∩ B). It is the set containing all elements of A that also belong to B, or, alternatively, all elements of B that also belong to A. The symbol is sued for the intersection is ∩. This is defined as that the element of A and B are is a single set.

Therefore, option B is correct.

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The solution to the system of equation shown in the graph is (2, 3)

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Given the equation:

y=−x+5   (1)

y=2x−1   (2)

Solving by elimination method. Subtract equation 2 from 1:

0 = -3x + 6

x = 2

Put x = 2 in eqn 1:

y = -(2) + 5 = 3

The solution is (2, 3)

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If Twelve out of Sixty students are trying out for the spring musical, the percentage of students trying out for the musical is , 20%.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

In above question, if Twelve out of Sixty students are trying out for the spring musical, we have,

Number of students trying out for the musical = 12

Total number of students = 60

Percentage of students trying out for the musical is , [tex]\frac{12}{60} *100[/tex] = 20%

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The polynomial that represents the value of Terryl’s investment after the first year if he invested x dollars in the fund with the lesser growth rate is;

p(x) = x(1 + 6/100)

g(x) = (1500 - x)(1 + 3.8/100)

The compound interest is defined as a form of interest whereby the rate of interest is applied on the amount obtained after every given interval of time.

We are given that;

The total amount invested in the two mutual funds = $1500.

The growth rate of the first mutual fund = 6%.

The growth rate of the second mutual fund = 3.8%.

If the amount invested in the first mutual fund is x, then the amount invested in second mutual fund is 1500 - x.

The growth for both mutual funds can then be represented by;

First mutual fund; p(x) = x(1 + 6/100)

The second mutual fund; g(x) = (1500 - x)(1 + 3.8/100)

Thus, the polynomial expression for both the mutual funds are;

p(x) = x(1 + 6/100) and g(x) = (1500 - x)(1 + 3.8/100) respectively.

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For the arithmetic sequence 4 - 2(n - 1), we have that:

For the geometric sequence 6 x 3^(n - 1), we have that:

An arithmetic sequence is a sequence of numbers in which there is a common difference of the numbers, that is, the subtraction between consecutive terms of the sequence is always constant.

The nth term of an arithmetic sequence is given by the equation presented as follows:

[tex]a_n = a_1 + d(n - 1)[/tex]

In which:

The sequence in this problem is defined as follows:

4 - 2(n - 1)

Which has first term 4 and common difference -2, hence the terms are:

4, 2, 0, -2, -4, -6 and so on...

A geometric sequence is a sequence of numbers in which there is a common ratio of the numbers, that is, the quotient between consecutive terms of the sequence is always constant.

The nth term of a geometric sequence is given by the equation presented as follows:

[tex]a_n = a_1 \times q^{n - 1}[/tex]

In which:

The sequence for this problem is given as follows:

6 x 3^(n - 1)

Which has first term of 6 and common ratio of 3, hence the terms are given as follows:

6, 18, 54, and so on...

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Answer:

y = -3/4x + 52

y + 6 = -3/4(x-8)

Step-by-step explanation:

y = mx + c

as long as the number is -3/4x , it represents slope -3/

Answer:

B. y = -3/4x + 52, C. y + 6 = -3/4(x - 8), and F. 3x + 4y = 9

Step-by-step explanation:

A. -3x + 4y = -34

y = 3/4x - 17/2

Slope = 3/4

INCORRECT

B. y = -3/4x + 52

Slope = -3/4

CORRECT

C. y + 6 = -3/4(x - 8)

y = -3/4x

Slope = -3/4

CORRECT

D. 4x + 3y = -22

y = -4/3x - 22/3

Slope = -4/3

INCORRECT

E. 4x - 3y = 48

y = 4/3x - 16

Slope = 4/3

INCORRECT

F. 3x + 4y = 9

y = -3/4x + 9/4

Slope = -3/4

CORRECT

G. y - 6 = 3/4(x - 8)

y = 3/4x

Slope = 3/4

INCORRECT

To find the greatest common factor (GCF) between monomials, take each monomial and write it's prime factorization. Then, identify the factors common to each monomial and multiply those common factors together.

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The solution to the above math arithmetic is 5115.

Finding the sum and difference of two integers are the two main addition and subtraction arithmetic procedures. They are both the other's polar opposite. An ordered group of integers with a shared difference between each word is known as an arithmetic sequence. The common difference, for instance, between the mathematical series 3, 9, 15, 21, and 27 is 6.

This grouping contains percent difficulties, decimal recognition, addition, subtraction, multiplication, and division as well as fraction and percent equivalences and estimate issues.

For instance, 5 + 6 = 11 and 11 - 6 = 5.

5x35 + 65x76=5115

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The maximum value considering DP of a and b is 9.52.

The decimal places of a number are the number of digits to be considered after the decimal point. E.g Round 4.7583 to 2 dp, we have;

4.76 3 dp

The maximum value of a sum of numbers is the highest value obtained when these numbers are added one to each other. The decimal places of each number is put into consideration in the process.

From the given question;

a = 8.7 and b = 0.82

Thus,

a + b = 8.7 + 0.82

        = 9.52

a + b = 9.52

Therefore, the maximum of a + b = 9.52

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120:36 is equivalent to 10:3

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"The trick with ratios is to always multiply or divide the numbers by the same value.

Given here the ratio is 120:36≡10:3

 Hence,  120:36 is equivalent to 10:3                                

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