Solve 2 ≤ 2x + 4 < 10 for x.

–1 ≤ x < 3
1 < x < 3
–1 < x < 3
1 ≤ x < 3

The scale which Myron used to create the scale drawing of the school library is the scale of reduction and the scale represents 6 feet for 1 inch.

As we are given that Myron created a scale drawing of the school library in his art class. In the scale drawing, the length of the library is 13 inches and the actual length of the actual library is 78 feet.

So, the size of the drawing is less than the size of the actual length of the actual library.

So, it is the scale of reduction.

We can see:

13 inches represent the actual length of 78 feet.

1 inch will represent the actual length of 78 / 13 = 6 feet.

So, the scale represents 6 feet for 1 inch.

Thus, the scale which Myron used to create the scale drawing of the school library is the scale of reduction and the scale represents 6 feet for 1 inch.

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By using algebraic equation, it was found that Hiroshi spends 30 minutes on his math homework.

To find the amount of time Hiroshi spends on his math homework, we can set up an algebraic equation using the information given.

Let's assume Hiroshi spends "x" minutes on his math homework. We know that one-fourth of his total homework time is spent on math. Since he spends 30 minutes on history homework and 60 minutes on English homework, the total homework time is 30 + 60 + x.

Now, we can set up the equation:

1/4 * (30 + 60 + x) = x

To solve this equation, we can start by simplifying the left side:

1/4 * (90 + x) = x

Next, we can distribute 1/4 to the terms inside the parentheses:

(1/4) * 90 + (1/4) * x = x

Simplifying further, we get:

90/4 + x/4 = x

To eliminate the fraction, we can multiply the entire equation by 4:

90 + x = 4x

Now, we can solve for x by bringing all the x terms to one side:

90 = 4x - x

Combining like terms:

90 = 3x

Finally, divide both sides of the equation by 3 to solve for x:

x = 30

So, Hiroshi spends 30 minutes on his math homework.

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Answer:

3f-7

Step-by-step explanation:

The p value of the test when the cell phone user wants to determine what data plan she should get is 0.1324.

The p-value is a figure that, when generated from a statistical test, indicates how likely it is that, if the null hypothesis were true, you would have discovered a certain collection of observations. In order to determine whether to reject the null hypothesis, P-values are utilized in hypothesis testing.

The following can be deduced from the information:

Number = 15

Mean = 11.25

Standard deviation = 2.5

Test statistics = -1.162

This is the left tailed test.

The p value will be:

P(z < -1.162 )

This will be looked at in the distribution table

= 0.1324

P-value = 0.1324

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The standard deviation of the costs is 37 Dhs

The given mean is 173 and 3% of costs exceed 243. We have to calculate the standard deviation of the cost. Therefore, let's first start by calculating the z-score as follows;z-score formula = `(x - μ) / σ`z-score = `243 - 173 / σ`z-score = `70 / σ`We need to find the standard deviation of the costs. Since the z-score formula includes standard deviation, we can first calculate the z-score and then use it to calculate the standard deviation.Using the z-table, we can find the z-score for 3% = -1.88-1.88 = (243 - 173) / σσ = (243 - 173) / -1.88σ = -70 / -1.88σ = 37.23≈ 37The standard deviation of the costs is 37 Dhs. Hence, the correct option is as follows.Option D is the correct option.

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Answer:

1. In order for Pattern B to be linear, the common difference of the number of dots between each step should be constant.  As it is not constant, the pattern is not linear.

2. In order for Pattern B to be exponential, the common ratio of the number of dots between each step should be constant.  As it is not constant, the pattern is not exponential.

3. In order for Pattern B to be quadratic, its sequence of second differences must be constant.

First differences:

\(1 \underset{+1}{\longrightarrow} 2 \underset{+3}{\longrightarrow} 5 \underset{+5}{\longrightarrow} 10\)

Second differences:

\(1 \underset{+2}{\longrightarrow} 3 \underset{+2}{\longrightarrow} 5\)

Therefore, as the sequence of second difference is constant, the patten is quadratic.

The function for pattern B is:  \(f(x)=x^2+1\)

(where x is the step number)

Answer:

the four is product of -

2×2= 4

2 is a prime number.

it this only prime number which product is 4

Step-by-step explanation:

Answer:

75.39822

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

11×14= 154

7×7= 49

154-49= 105

Answer:

105 is ur answer!

you're welcome lol

The function S(t) = -15t^(5/3) + C which we get by integration of S'(t) and the company  will continue to manufacture this computer for approximately 5.47 months.

To find S(t), we need to integrate the given rate of decline, S'(t), with respect to time (t). We have:

S'(t) = -25t^(2/3)

Integrating both sides with respect to t, we get:

S(t) = ∫(-25t^(2/3) dt)

Using the power rule for integration, we obtain:

S(t) = (-25 * (3/5) * t^(5/3)) + C
S(t) = -15t^(5/3) + C

Now, we're given that at t = 0, S(0) = 2,050 computers. We can use this information to find the constant of integration, C:

S(0) = -15(0)^(5/3) + C
2,050 = C

Thus, the function for the monthly sales is:

S(t) = -15t^(5/3) + 2,050

The company will stop manufacturing when S(t) = 1,000 computers. To find when this occurs, we'll set S(t) equal to 1,000 and solve for t:

1,000 = -15t^(5/3) + 2,050
-1,050 = -15t^(5/3)

Now, isolate t^(5/3) and solve for t:

t^(5/3) = 1,050 / 15
t^(5/3) = 70

Take the cube root of both sides:

t^(5/3)^(3/5) = 70^(3/5)
t = 70^(3/5)

Calculating this value, we get approximately:

t ≈ 5.47

So, the company will continue to manufacture this computer for approximately 5.47 months.

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Answer:

\(\frac{100}{w}\)

Step-by-step explanation:

When it asks for the quotient you are dividing/ putting it in a fraction.

A conditional equation is neither an identity nor a contradiction. It is a statement that is only true under certain conditions.

A conditional equation is an equation that expresses a condition. It has two parts: a hypothesis (or antecedent) and a conclusion (or consequent). The hypothesis states that a certain condition must be met in order for the conclusion to be true. For example, the equation "if x = 4, then x + 1 = 5" is a conditional equation. If the condition (x = 4) is true, then the conclusion (x + 1 = 5) is also true. However, if the condition is false, then the conclusion is also false. Therefore, a conditional equation is neither an identity nor a contradiction, but rather a statement that is only true under certain conditions.

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Answer:

x = 2 and (2, 4 )

Step-by-step explanation:

The equation of a parabola in standard form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = 3(x - 2)² + 4 ← is in vertex form

with vertex = (2, 4 )

This is a vertical parabola, opening upwards and is symmetrical about the vertex.

The axis of symmetry is a vertical line with equation x = 2

According to the equation of the parabola, we have that:

The equation of a quadratic function, of vertex (h,k), is given by:

\(y = a(x - h)^2 + k\)

In which a is the leading coefficient.

The axis of symmetry is x = h.

In this problem, the equation is:

\(f(x) = 3(x - 2)^2 + 4\)

Hence h = 2, k = 4, thus:

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We have:

1 box has 6 cups

and 1 serving is 1/5 of 1 cup

Then:

Since there is 1/5 of a cup of oatmeal in a serving, this means that each of the 6cups contains 5 servings.

The total number of servings is seen to be

as there are 6 groups of 5 servings

Answer: 30

The radius of convergence of the series (cn + dn)xn is less than or equal to 1/10 + 1/11, or approximately 0.206.

The radius of convergence of a power series is a measure of how far from the center the series converges. For a power series ∑cnxn, the radius of convergence is denoted as R and is defined as the reciprocal of the limit superior of the absolute values of the coefficients:

\(R = 1 / lim sup |cn|^{(1/n)\)

Given that the series ∑cnxn has a radius of convergence of 10, we have:

\(lim sup |cn|^{(1/n) }= 1/10\)

Similarly, the series ∑dnxn has a radius of convergence of 11, so:

\(lim sup |dn|^{(1/n)} = 1/11\)

Now, let's consider the series ∑(cn + dn)xn. We want to find its radius of convergence, which we'll denote as R'.

Using the same definition, we have:

\(R' = 1 / lim sup |(cn + dn)|^{(1/n)\)

To simplify this expression, we'll use the triangle inequality:

|(cn + dn)| ≤ |cn| + |dn|

Taking the limit superior of both sides, we have:

lim sup |(cn + dn)| ≤ lim sup (|cn| + |dn|)

Now, let's analyze the right-hand side of the inequality:

lim sup (|cn| + |dn|) = lim sup |cn| + lim sup |dn|

Using the properties of the limit superior, we have:

lim sup |cn| + lim sup |dn| ≤ 1/10 + 1/11

Combining these inequalities, we have:

lim sup |(cn + dn)| ≤ 1/10 + 1/11

Therefore, we can conclude that the radius of convergence of the series ∑(cn + dn)xn is less than or equal to 1/10 + 1/11.

To summarize, the radius of convergence of the series (cn + dn)xn is less than or equal to 1/10 + 1/11.

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The complete question is:

Suppose the series ∑cn xn has a radius of convergence of 10 and the series ∑dn xn has a radius of convergence of 11. What is the radius of convergence of the series ∑(cn + dn)xn?

To calculate the price of the video game console we need to calculate the simple interest first:

Simple Interest = (Principal x Rate x Time)

Simple Interest = (2700 x 0.12 x 3) = $972.00

Now we know the interest, we can calculate the price of the video game console by subtracting the interest from the total amount Claudia returned:

Price of the video game console = $3,000.00 - $972.00 = $2,028.00

So, the price of the video game console is $2,028.00

(a) The maturity value of the loan is $15,246.33.

(b) The amount of interest paid on the loan is $7,246.33.

To calculate the maturity value of the loan, we can use the formula for compound interest: A = \(P(1 + r/n)^(nt)\), where A is the maturity value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal amount (P) is $8000, the interest rate (r) is 9%, the loan duration is 9 years, and interest is compounded quarterly, so n = 4. Plugging these values into the formula, we get A = \(8000(1 + 0.09/4)^(4*9)\) = $15,246.33.

To calculate the amount of interest paid on the loan, we subtract the principal amount from the maturity value: Interest = Maturity value - Principal amount = $15,246.33 - $8000 = $7,246.33.

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Answer:

x = 3

Step-by-step explanation:

5x + 9 = 24

5x = 24 - 9

5x = 15

x = 3

Check:

5(3) + 9 = 24

SM = 24,    MT = 24 ✔️

Answer:

Step-by-step explanation:

If M is the midpoint between points S and T, then both sides; SM and ST are equal. This means that 5x + 9 has to equal 24.

5x + 9= 24

5x +9 - 9= 24 - 9

5x= 15

5x / 5 = 15 / 5

x = 3

ANSWER: x = 3

Tommy and Zach will be 16 miles apart after 2.90 hours.

Let the time taken for Tommy and Zach to run until they are 16 miles apart be t hours.

Tommy runs North at a speed of 5 miles per hour.

Therefore, the distance covered by Tommy in t hours is 5 multiplied by t hours:

=5t miles

Zach runs East at a speed of 8 miles per hour.

Zach started running 2 hours later so that he would run for (t - 2) hours.

Distance covered by Zach in (t - 2) hours running at a speed of 8 miles per hour :

=8(t - 2) miles

Since they are now 16 miles apart, Pythagoras's theorem, a²+ b² = c², is applied.

[8(t - 2)]²+ (5t)² = 16²

64(t - 2)² + 25t² = 256

64(t² + 4 - 4t) + 25t² = 256

64t² + 256 - 256t + 25t² = 256

89t² -256t + 256 - 256 = 0

89t² - 256t = 0

t( 89t - 256) = 0

(89t - 256) = 0

9t = 256

= 256÷9

t = 2.90 hours

Therefore, for 2.90 hours, Zach and Tommy will be 16 miles apart.

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Answer: 20, 16, 45

Step-by-step explanation:

I'm not sure if we can use the number 20 but anyways here it is!

Factors:A factor is simply a number that is multiplied to get a product. Factoring a number means taking the number apart to find its factors.Factors are either composite numbers or prime numbers. A prime number has only two factors, one and itself, so it cannot be divided evenly by any other numbers.

I hope this helps!!

Answer:The boat is traveling at a rate of 3 ft/s.

Step-by-step explanation:

The answer are: a. Total outflows: $2,007,901, b. Total inflows: $827,080, c. Net present value: $824,179, d. Should the old issue be refunded with new debt? Yes

To determine whether the old bond issue should be refunded with new debt, we need to calculate the present value of total outflows, the present value of total inflows, and the net present value (NPV). Let's calculate each of these values step by step: Calculate the present value of total outflows. The total outflows consist of the call premium, underwriting cost on the old issue, and underwriting cost on the new issue. Since these costs are one-time payments, we can calculate their present value using the formula: PV = Cash Flow / (1 + r)^t, where PV is the present value, Cash Flow is the cash payment, r is the discount rate, and t is the time period.

Call premium on the old issue: PV_call = (7% of $22 million) / (1 + 0.1)^16, Underwriting cost on the old issue: PV_underwriting_old = $530,000 / (1 + 0.1)^16, Underwriting cost on the new issue: PV_underwriting_new = $680,000 / (1 + 0.1)^16. Total present value of outflows: PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. Calculate the present value of total inflows. The total inflows consist of the interest savings and the tax savings resulting from the interest expense deduction. Since these cash flows occur annually, we can calculate their present value using the formula: PV = CF * [1 - (1 + r)^(-t)] / r, where CF is the cash flow, r is the discount rate, and t is the time period.

Interest savings: CF_interest = (12% - 10%) * $22 million, Tax savings: CF_tax = (40% * interest expense * tax rate) * [1 - (1 + r)^(-t)] / r. Total present value of inflows: PV_inflows = CF_interest + CF_tax.  Calculate the net present value (NPV). NPV = PV_inflows - PV_outflows Determine whether the old issue should be refunded with new debt. If NPV is positive, it indicates that the present value of inflows exceeds the present value of outflows, meaning the company would benefit from refunding the old issue with new debt. If NPV is negative, it suggests that the company should not proceed with the refunding.

Now let's calculate these values: PV_call = (0.07 * $22,000,000) / (1 + 0.1)^16, PV_underwriting_old = $530,000 / (1 + 0.1)^16, PV_underwriting_new = $680,000 / (1 + 0.1)^16, PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. CF_interest = (0.12 - 0.1) * $22,000,000, CF_tax = (0.4 * interest expense * 0.4) * [1 - (1 + 0.1)^(-16)] / 0.1, PV_inflows = CF_interest + CF_tax. NPV = PV_inflows - PV_outflows.  If NPV is positive, the old issue should be refunded with new debt. If NPV is negative, it should not.

Performing the calculations (rounded to the nearest whole dollar): PV_call ≈ $1,708,085, PV_underwriting_old ≈ $130,892, PV_underwriting_new ≈ $168,924, PV_outflows ≈ $2,007,901,

CF_interest ≈ $440,000, CF_tax ≈ $387,080, PV_inflows ≈ $827,080.  NPV ≈ $824,179.  Since NPV is positive ($824,179), the net present value suggests that the old bond issue should be refunded with new debt.

Therefore, the answers are:

a. Total outflows: $2,007,901

b. Total inflows: $827,080

c. Net present value: $824,179

d. Should the old issue be refunded with new debt? Yes

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Refer to the image attached.

Answer: C

Step-by-step explanation:

Answer:

It will take 5.61 seconds for the coin to reach the stream.

Step-by-step explanation:

The height of the coin, after t seconds, is given by the following equation:

\(h(t) = -16t^{2} + 72t + 100\)

How long will it take the coin to reach the stream?

The stream is the ground level.

So the coin reaches the stream when h(t) = 0.

\(h(t) = -16t^{2} + 72t + 100\)

\(-16t^{2} + 72t + 100 = 0\)

Multiplying by (-1)

\(16t^{2} - 72t - 100 = 0\)

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}\)

\(\bigtriangleup = b^{2} - 4ac\)

In this question:

\(16t^{2} - 72t - 100 = 0\)

So

\(a = 16, b = -72, c = -100\)

\(\bigtriangleup = (-72)^{2} - 4*16*(-100) = 11584\)

\(t_{1} = \frac{-(-72) + \sqrt{11584}}{2*16} = 5.61\)

\(t_{2} = \frac{-(-72) - \sqrt{11584}}{2*16} = -1.11\)

Time is a positive measure, so we take the positive value.

It will take 5.61 seconds for the coin to reach the stream.

Answer:

S₁₅ = 127.5

Step-by-step explanation:

the nth term of an arithmetic progression is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₃ = 1 and a₇ = 7 , then

a₁ + 2d = 1 → (1)

a₁ + 6d = 7 → (2)

subtract (1) from (2) term by term to eliminate a₁

0 + 4d = 6

4d = 6 ( divide both sides by 4 )

d = 1.5

substitute d = 1.5 into (1) and solve for a₁

a₁ + 2(1.5) = 1

a₁ + 3 = 1 ( subtract 3 from both sides )

a₁ = - 2

the sum to n terms of an arithmetic progression is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

with a₁ = - 2 and d = 1.5 , then

S₁₅ = \(\frac{15}{2}\) [ (2 × - 2) + (14 × 1.5) ]

     = 7.5(- 4 + 21)

     = 7.5 × 17

     = 127.5

Absolute change is the numerical difference between two values and relative change is the proportional difference between two values expressed as a percentage.

Absolute change is the numerical difference between two values and is typically expressed as a positive number. It tells us the amount by which a value has increased or decreased.

For example, if the temperature increases from 20 degrees Celsius to 25 degrees Celsius, the absolute change in temperature is 5 degrees Celsius.

Relative change, on the other hand, is the proportional difference between two values and is typically expressed as a percentage. It tells us the amount by which a value has increased or decreased relative to its original value.

For example, if the price of a product increases from $10 to $15, the relative change in price is 50%, because the increase of $5 is 50% of the original price of $10.

In summary, absolute change is the numerical difference between two values and relative change is the proportional difference between two values expressed as a percentage.

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Answer:

\(r=2p+3\)

Step-by-step explanation: