$100 is borrowed at 9% interest per year. How much is owed after one year if interest is compounded :
a. annually?
b. monthly?
c. continuously?

(a) The inequality equations for the given shop are x + y ≤ 50 denotes the number of wakeboards and surfboards combined (no more than 50) and 150x + 100y ≥ 3000 denotes the earnings of the shop.

(b) The two possible combinations of wakeboard and surfboard are:

10 surfboards and 40 wakeboards i.e., 10 + 40 ≤ 50 and

30 surfboards and 20 wakeboards i.e., 30 + 20 ≤ 50

An inequality equation is the mathematical representation of two expressions comparatively related to each other. I.e., In the inequality equation, unlike the normal equation, the expressions are not always equal but they are either less or more.

It is given that,

The price for a surfboard is $150 and the price for a wakeboard is $100.

Consider the number of surfboards = x and the number of wakeboards = y.

The shop owner can make no more than 50 wakeboards and surfboards combined.

So, we can write this as

x + y ≤ 50....(1)

He wants to make at least $3000 a month. So, we can write this as

150x + 100y ≥ 3000....(2)

Thus, the two inequality equations form a system of inequalities.

When they graphed, we get the possible combinations of the number of surfboards and the number of wakeboards.

The graph for the obtained inequalities is shown in the figure below.

From the graph, we can choose any of the combinations that are in the intersection of both graphs of the system.

Here, take (10, 40) and (30, 20) coordinates that are considered from the intersecting area of both inequalities.

Here, the first inequality equation x + y ≤ 50 is considered for the first quadrant only I.e., 0 < x + y ≤ 50. This is because the number boards should always be positive values.

Therefore, the possible combinations of surfboards and wakeboards that he need to sell to make at least $3000 are

10 surfboards + 40 wakeboards

or

30 surfboards + 20 wakeboards

(There are some more combinations we can get from the graph).

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Yes, the proof of congruence of two triangles ∆ABC ≅ ∆GHF is possible.

The convergence method which proves this congruence is SSS(side-side-side) congruence.

We have given the sketch of two triangles as seen above. We have to prove ∆ABC ≅ ∆GHF

Now , AB = √(-7+7)² + 5² = 5 in triangle ABC and FG = 5 in triangle FGH,

so, AB ≅ FG

Because AC = 3 in triangle ABC and FH = 3 in triangle FGH,

so, AC ≅ FH

To find the lengths of BC and GH , we can use distance formula.

Length of BC :

BC = √[(x₂ - x₁)² + (y₂ - y₁)²]

(x₁, y₁) = B(-7, 0) and (x₂, y₂) = C(-4, 5).

BC = √[(-4 + 7)² + (5 - 0)²]

= √[32 + 52]

= √[9 + 25]

= √34

Length of GH :

GH = √[(x₂ - x₁)² + (y₂ - y₁)²]

(x₁, y₁) = G(1, 2) and (x₂, y₂) = H(6, 5).

GH = √[(6 - 1)² + (5 - 2)²]

= √[52 + 32]

= √[25 + 9]

= √34

Conclusion :because BC = √34 and GH = √34,

=>BC ≅ GH

All the three sides of one triangle is congruent to the corresponding sides of other triangle.

By SSS congruence postulate,

ΔABC ≅ ΔFGH

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Answer: -1 Is the answer.

Answer:

Step-by-step explanation:

\(2-y+y+3(2+2)\\\\y =2\)

Substitutes; y =2 into the given equation

\(2-2+2+3(2+2)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(2+2\right)\::\quad 4\\=2-2+2+3\times\:4\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:3\cdot \:4\::\quad 12\\=2-2+2+12\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:2-2+2+12\:\\:\quad 14\)

Answer:

is 2 and 17

Step-by-step explanation:

because 2 has one and itself and so does 17

Answer:

C, For every x in the real numbers

Step-by-step explanation:

x - 2x + 12 + x - 12 = 0

x - 2x + x = 0

0=0, For every x!

Answer: I don’t understand

Step-by-step explanation:

The theoretical probability of spinning red is given as follows:

1/3.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the spinner in this problem, 2 out of 6 regions are red, hence the theoretical probability is given as follows:

2/6 = 1/3.

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The amount of paper required to make the model is 94.2 square cm

The given parameters in the question are

Slant height = 7 cm

Diameter = 6 cm

This means that

Radius = Diameter/2 = 6 cm/2

So, we have

Radius = 3 cm

The amount of paper required to make the model is then calculated as

A = πr(r + l)

So, we have

A = 3.14 * 3 * (3 + 7)

Evaluate

A = 94.2

Hence, the amount needed is 94.2 square cm

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Answer:

7 (x-7) or 7x-49

a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

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Answer:

20358489841224558533214578

Answer:

x = 48°

Step-by-step explanation:

Complementary angles

Angles that sum to 90°.

Vertical Angle Theorem

When two straight lines intersect, the vertical angles are congruent (equal).

Therefore, angle x is equal to the angle that is complementary to 42°.

To find x, subtract 42° from 90°:

⇒ x = 90° - 42°

⇒ x = 48°

Answer:

Refer below:

Step-by-step explanation:

To form a frequency distribution table for the number of runs scored by a batsman in 20 matches, we can use class intervals of 20 runs.

The given scores are 16, 41, 13, 39, 45, 28, 48, 51, 67, 12, 89, 30, 0, 28, 35, 27, 38, 32, 64, and 70.

Let's create the frequency distribution table:

Class Interval Frequency

0-19                         1

20-39                 6

40-59                 4

60-79                 5

80-99                 2

In the table, the class intervals represent ranges of scores, and the frequency represents the number of scores falling within each interval.

For example, in the class interval of 0-19, there is one score (0) falling within that range. In the interval of 20-39, there are six scores (16, 13, 28, 30, 28, 27) falling within that range. Similarly, we calculate the frequencies for the remaining intervals.

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-3.5, -3, -2 1/2, -2, 2.5

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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Mila's balance after a year would be 1.077 times the amount she initially invested (m).

To find the balance after a year, we need to calculate the simple interest earned on Mila's investment.

The simple interest is calculated by multiplying the principal amount (the money she invests) by the interest rate (7.7%) and the time period (1 year).

The formula for calculating simple interest is:

\(Interest = Principal \times Rate \times Time\)

In this case, the principal is represented by the variable 'm', the rate is 7.7% (or 0.077 as a decimal), and the time is 1 year.

So the expression representing her balance after a year would be:

\(Balance = m + m \times 0.077 \times 1\)

\(Balance = m + 0.077m\)

\(Balance = 1.077m\)

Therefore, Mila's balance after a year would be 1.077 times the amount she initially invested (m).

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2.82047 is  the point(s) that are guaranteed to exist by the Mean Value Theorem.​

What is the mean value theorem?

 If f(x) is continuous on [a, b] and differentiable on (a,b), at least one c exists such that the slope of the secant line equals the slope of the tangent line.

                                 The following is a promise provided by MVT: The slope at one location (a, b) equals the slope of the secant line on [a, b].

since f(X) is a polynomial.

   f(x) = 7 - x²  is continuous on the interval [-1,2] and differentiable on the interval (-1 , 2 )

 by mean value theorem

        f'(e) = f(b) - f(a)/b - a

    here b = 2    a = -1

       f(2) = 7 - 4 = 3

       f(-1) = 7 + 1 = 8

     f'(c) = 3 - 8/3

            = - 5/3

      f'(x) = 2x

       2x = 1

          x = 1/2

2.  f(x) = In (x - 1 )

       f'(x) = 1/(x - 1)

f(2) = ln (2 -1 ) = 0

In(4) = ln (4 - 1) = ln3

  f'(c) =  ln3 - 0/4 -2

        =  ln3/2

     1/C - 1 = ln3/2

   2 = ln3/2 (C - 1)

    2/ln3/2 = C - 1

  C = 2/ln3/2 + 1.

       = 2.82047

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The required expression is (x / 5) + 9

Given that we have to build an equation for the statement "9 more than the quotient of x and 5,

So,

This expression represents the quotient of x divided by 5, and then adding 9 to the result.

Therefore,

"9 more than the quotient of x and 5" can be written mathematically as:

(x / 5) + 9

Hence the required expression is (x / 5) + 9

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Answer:

So first look at the symbol. It must be less than or equal to 17.

By elimination A is 20.5 which is wrong

B is -16.5 by abs =16.5

C is -17.5 by abs = 17.5

D is 12.5

So B and D are possible solutions..

The area of the sidewalk is 388 square feet.

To find the area of the sidewalk you can find the area of each individual shape and add them together.

Area of the first triangle T = (1/2) x 6 ft x 11 ft = 33 sq. ft.

Area of the second triangle = (1/2) x 6 ft x 18 ft = 54 sq. ft.

Area of the rectangle = 6 ft x 30 ft = 180 sq. ft.

Area of the square = 11 ft x 11 ft = 121 sq. ft.

Therefore, the total area of the sidewalk is:

33 sq. ft. + 54 sq. ft. + 180 sq. ft. + 121 sq. ft. = 388 sq. ft.

So, the area of the sidewalk is 388 square feet.

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Answer:

3 1/3 FT 3

Step-by-step explanation:

im not sure if this right but i tried lol

Answer:

There is not enough info you need to add a picture of the box to measure it.

Step-by-step explanation:

Out of the given options, only √196 is a rational number.

A rational number is a number that can be expressed as the ratio of two integers. In other words, it can be written in the form of p/q where p and q are integers and q is not equal to zero.

√56 cannot be simplified further and has no integer factors that can be canceled out to express it as a ratio of two integers. Therefore, it is an irrational number.

Similarly, √63 and √240 cannot be simplified further and do not have any integer factors that can be canceled out to express them as a ratio of two integers. Therefore, they are also irrational numbers.

On the other hand, √196 simplifies to 14 which is a ratio of two integers (14/1). Hence, it is a rational number.

In summary, only √196 is a rational number out of the given options.

The ways a member can make a selection is 76904685

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

List =40

Choice = 8

The number of ways is calculated as

Ways = C(40, 8)

Apply the combination formula

So, we have the following representation

Ways = 40!/(32! * 8!)

Evaluate

Ways = 76904685

Hence, the number of ways is 76904685

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Answer:

k = 6 and k = -4

Step-by-step explanation:

To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).

Possible p-values:

Possible q-values:

Therefore, all the possible values of p/q are:

\(\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}\)

To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:

\(\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}\)

\(\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}\)

\(\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}\)

\(\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}\)

Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.

Note:

If k = 6, the roots are 1 and -1/6.

If k = -4, the roots are -1 and -1/4.

Answer:

1/12

Step-by-step explanation:

When we roll 2 dice, there are 36 possible rolls

How can we get 4

1and 3, 3 and 1, 2 and2 = 3 different rolls

P( 4) = number of rolls with sum of 4/ total rolls

        = 3/36 = 1/12

Answer:

D. addition property of inequality

Step-by-step explanation:

Michael uses addition to move -8 from one side to the other.

Answer:

D. addition property of inequality  

Step-by-step explanation:

Michael uses addition to move -8 from one side to the other one

Answer:10x6=60

60

0 hundreds 60 tenths 0 oned

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

-9+-9-(-6)

-18+6

-12

Therefore, the answer is-12.

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