1. By what factor does organism A's population grow in the first five days? Express your answer as an
exponential expression. (2 points)

From the given decimals which are 0.2, 0.019, 0.12, 0.02, the smallest number is 0.019.

To compare the given decimals, we need to look at the digits to the right of the decimal point. Starting from the left, the first decimal is 0.2, which has one decimal place. The second decimal is 0.019, which has three decimal places. The third decimal is 0.12, which has two decimal places. Finally, the fourth decimal is 0.02, which has two decimal places.

To compare them, we can line them up vertically by decimal place and see which one has the smallest value in the first decimal place. In this case, the smallest value in the first decimal place is 0.019. Therefore, 0.019 is the smallest decimal among the given options.

In summary, the decimals listed from smallest to largest are: 0.019, 0.02, 0.12, 0.2.

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To find the derivative of r(t), we simply take the partial derivative with respect to each variable:

\(r'(t) = 2i t^2j + 4ti tj + 5k\)

To find the norm of the derivative, we take the magnitude of the vector r'(t):

\(r'(t) = 2i t^2j + 4ti tj + 5k\)
To find the derivative r′(t) of the given vector function r(t) = 2ti + t^2j + 5k, you need to find the derivative of each component with respect to t.

\(r′(t) = (d(2t)/dt)i + (d(t^2)/dt)j + (d(5)/dt)k\)

r′(t) = (2)i + (2t)j + (0)k

Now, to find the norm of the derivative, which is the magnitude of r′(t), you can use the formula:

\(||r^{'}(t)|| = √((2)^2 + (2t)^2 + (0)^2)\)

||r′(t)|| = √(4 + 4\(t^2\))

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JK=JH

\(\\ \sf\longmapsto 10t=7t+15\)

\(\\ \sf\longmapsto 10t-7t=15\)

\(\\ \sf\longmapsto 3t=15\)

\(\\ \sf\longmapsto t=15/3=5\)

Answer:

0.375

Step-by-step explanation:

Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30

three two digit numbers and 8 total so 3/8

These steps are often referred to as the principle of mathematical induction or PMI.

The steps for mathematical induction are:

Base Case: Show that the statement holds for some particular value of n, usually n = 1 or n = 0.

Inductive Hypothesis: Assume that the statement holds for some arbitrary value of n = k, where k is a positive integer.

Inductive Step: Using the inductive hypothesis, show that the statement also holds for n = k + 1.

Conclusion: By the principle of mathematical induction, the statement is true for all positive integers n.

These steps are often referred to as the principle of mathematical induction or PMI. They are used to prove statements that involve an infinite set of integers by showing that the statement holds for a base case, assuming that it holds for an arbitrary value, and then showing that it holds for the next integer in the set.

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Answer:

120°

Step-by-step explanation:

In triangle BDC, <CDB = <DCI , because they are alternate interior angles.

Also, <DBC = <BCH , {alternate interior angles}

And <BCD + <CDB + <DBC = 180°

=> 2x + 4x + 3x = 180°

=> 9x = 180°

Divide by 9,

=> x = 20°

<ABF = <BCI

= 2x + 4x

= 6x

= 6*20°

= 120°

Answer:

540

Step-by-step explanation:

If you divide 540 by 100 (100%) you get 5.4 then multiply it by 10 (10%) to get 54 again. THIS WAS TO CHECK TO GET: 10% or 100% is 10 so multiply 54•10=540

Hope this helps! ;-)

Answer:

4566

Step-by-step explanation:

you you get that answer by learning and trying your best like me by

Reflect point C over the y-axis: Among the given points, if the point C is (-3,2), then to reflect the point C over the y-axis, the x-coordinate of the point C will get changed and the y-coordinate will remain the same.

So, the reflected point will be C' (3,2).If the point C is (3,2), then to reflect the point C over the y-axis, the x-coordinate of the point C will get changed and the y-coordinate will remain the same.So, the reflected point will be C' (-3,2).If the point C is (-2,3), then to reflect the point C over the y-axis, the x-coordinate of the point C will get changed and the y-coordinate will remain the same.So, the reflected point will be C' (2,3).If the point C is (2,-3), then to reflect the point C over the y-axis, the x-coordinate of the point C will get changed and the y-coordinate will remain the same.

So, the reflected point will be C' (-2,-3).Thus, the point C’ (-3,2), C’ (2,3) and C’ (-2,-3) are the points that can be obtained on reflecting the given point C over the y-axis.

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Answer:

Quadrilateral

Step-by-step explanation:

I remember learning this in math class. A parallelogram has two dimensions. Each of its four sides has two parallel pairs. The parallel sides have the same length.

The correct sequence of project phases is Definition - Planning  - Performance. The correct answer is B.

This is the typical order of project phases in a traditional project management approach. It starts with the definition phase, where the project's goals, the scope, and the requirements are established.

Then comes the planning phase, where the project plan is developed, including the allocation of resources, scheduling, and budgeting.

Finally, the performance phase begins, during which the project activities are executed, monitored, and controlled to ensure the successful project completion.

Therefore the sequence of project phase is  Definition - Planning  - Performance The correct answer is B.

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The domain of the function f(x) = x² - 10x + 22 is the set of all real numbers

The function is given as:

f(x) = x² - 10x + 22

The above function is a quadratic function.

And all quadratic functions can take any real number as their input

Hence, the domain of the function f(x) = x² - 10x + 22 is the set of all real numbers

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Answer:

slope = - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 5x + 18 ← is in slope- intercept form

with slope m = - 5

If there are n men and n women in the group, we can first arrange the men and women separately in alternate positions. We can treat the men as a single group and arrange them in n! ways, and similarly, we can treat the women as a single group and arrange them in n! ways.

Next, we need to arrange the two groups (men and women) in alternate positions to satisfy the given condition. Since we need to place the youngest person (who could be a man or a woman) at the beginning of the row, we have two cases:

Case 1: The youngest person is a man

In this case, the men must start the arrangement, followed by the women. Since there are n men and n women, there are n! ways to arrange the men and n! ways to arrange the women. We can fix the youngest man at the beginning of the row, so there are (n-1)! ways to arrange the remaining n-1 men. Similarly, there are (n-1)! ways to arrange the n-1 women. Therefore, the total number of arrangements in this case is:

n! * n! * (n-1)! * (n-1)!

Case 2: The youngest person is a woman

In this case, the women must start the arrangement, followed by the men. Since there are n women and n men, there are n! ways to arrange the women and n! ways to arrange the men. We can fix the youngest woman at the beginning of the row, so there are (n-1)! ways to arrange the remaining n-1 women. Similarly, there are (n-1)! ways to arrange the n-1 men. Therefore, the total number of arrangements in this case is:

n! * n! * (n-1)! * (n-1)!

To get the total number of arrangements that satisfy the given condition, we need to add the number of arrangements in Case 1 and Case 2:

n! * n! * (n-1)! * (n-1)! + n! * n! * (n-1)! * (n-1)!

= 2 * n! * n! * (n-1)! * (n-1)!

= 2 * (n!)^2 * (n-1)!

Therefore, the total number of ways to arrange the people in a row with alternating men and women, starting with the youngest person, is 2 * (n!)^2 * (n-1)!.

Exponential smoothing forecast for March is 204.8.

We can use exponential smoothing to forecast the sales for March. Let \(F_t\)be the forecasted value for time t, and \(Y_t\) be the actual value for time t. Then, we can calculate the exponential smoothing forecast as follows:

\(F_t = \alpha Y_t + (1- \alpha ) F_{t-1}\)

where α is the smoothing constant.

We are given that the first forecast value is set to 190, so F_1 = 190. Also, the actual sales data for January, February, and March are 190, 210, and 208, respectively. We are given that α = 0.4.

Using the formula for exponential smoothing, we can calculate the forecast for February as follows:

\(F_2 = 0.4210 + 0.6190 = 202\)

Using the same formula, we can calculate the forecast for March as follows:

\(F_3 = 0.4208 + 0.6202 = 204.8\)

Therefore, the exponential smoothing forecast for March is 204.8.

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Answer:

b

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

6,780.00 is right answer try it

Answer:

y = 90 x = 58

Step-by-step explanation:

y = 90 because if this symbol |_

180 = x + 32 + 90

x= 180 - 32 - 90

x = 90- 32

x = 58

Answer:

y=90,

x=58

Step-by-step explanation:

y=90( It is rectangle)

x=180-y-32

x=180-90-32

x = 58

Answer:

Line

Step-by-step explanation:

Extends in two directions

The geometric term modeled by a bridge support beam is "cylinder."

Given data:

A bridge support beam often takes the form of a cylindrical shape to provide structural integrity and distribute the weight of the bridge and its load evenly. Cylinders have circular cross-sections.

A bridge support beam is often modeled as a "cylindrical" structure in geometry. Cylinders are three-dimensional geometric shapes characterized by their curved lateral surface and two circular bases of the same size and shape. When designing bridge support systems, engineers often opt for cylindrical beams due to their inherent strength and ability to distribute weight efficiently.

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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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Discount of $7.50, which we then subtract from the original price to get the discounted price of $22.50.

The process of calculating the final sale price of a shirt that is subject to two discounts can be a bit confusing. However, by breaking down each discount and calculating the percentage, we can arrive at the correct answer.

In this scenario, the first discount is 25% off the original price of $30. To calculate this discount, we multiply the original price by the percentage discount (0.25). This gives us a discount of $7.50, which we then subtract from the original price to get the discounted price of $22.50.

The second discount is 10% off the discounted price of $22.50. To calculate this discount, we multiply the discounted price by the percentage discount (0.10). This gives us a discount of $2.25, which we then subtract from the discounted price to get the final sale price of $20.25.

It's important to note that the order in which we apply the discounts matters. If we had applied the second discount before the first discount, we would have arrived at a different final sale price. Therefore, it's important to follow the correct order of operations when calculating multiple discounts.

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Given an angle that is positive, less than 360°, and coterminal with 395° is 35°.

Subtract 360° from 395°.

We know that 1 revolution is equal to 360°.

Therefore, a positive angle that is less than 360° and coterminal with 395° is 35°.

When an angle is less than 360° and shares the same terminal side with another angle that is less than 360°, then the angle is referred to as a coterminal angle.

In other words, the two angles have the same initial side and terminal side but can be either positive or negative.

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Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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If the region R bounded by the functions f(x) = 2 and g(x) = x + 1 is rotated around the x axis , then the volume of the resulting solid is (7/3)π cubic units .

The region R is bounded by the functions f(x) = 2 and g(x) = x + 1 , and is between x = 1 and x = 2 .

Region-R between the lines x = 1 and x = 2 is rotated ,  

So , The volume of the solid can be calculated as :

⇒ Volume = π × \(\int\limits^2_1\) (2)² - (x+1)²dx  ;

⇒ Volume = π × \(\int\limits^2_1\) 4 - (x+1)²dx  ;

⇒ Volume = [4x - (x+1)³/3]²₁ × π ,

⇒ Volume = π × [(4×2 - (2+1)³/3) - ((4×1) - (1+1)³/3)]

= [(8 - 27/3) - (4 - 8/3)]π

= [(8 - 9) - (4/3)]π

= [ -1 - 4/3]π  = -7/3π  ,

On taking the modulus of the volume ,

we get , that the Volume is 7/3π cubic units .

Therefore , the volume of the resulting solid is (7/3)π cubic units .

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The given question is incomplete , the complete question is

Define R as the region bounded by the functions f(x) = 2 and g(x) = x + 1 between x=1 and x=2. if R is rotated around the x-axis, what is the volume of the resulting solid?

The equation (t6)(t-14) is identical to tn when n = 8. A mathematical expression is composed of numbers .

You can multiply, divided, add, or take something away in mathematics. An expression is put together as follows: Expression, numeric value, and math operator A mathematical expression is composed of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Contrasting phrases and emotions is possible. An algebraic expression is any mathematical statement that has elements, quantities, and an arithmetic operation. As an illustration, the phrase 4m + 5 consists of the terms 4m and 5, as well as the given equation's variable m, which are all split by the algebraic sign +.

given

(t^6) (t^-14) = t^n

= 6 -14 = n

n = 8

The equation (t6)(t-14) is identical to tn when n = 8.

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Answer:

Pllsssss Pllsssss Pllsssss

Step-by-step explanation:

Pllsssss Pllsssss Pllsssss

FICA tax contribution for an employee, multiply their gross pay by the Social Security and Medicare tax rates.

FICA is a U.S. federal payroll tax. It stands for the Federal Insurance Contributions Act and is deducted from each paycheck. Your nine-digit number helps Social Security accurately record your covered wages or self-employment. As you work and pay FICA taxes, you earn credits for Social Security benefits.

For both of them, the current Social Security and Medicare tax rates are 6.2% and 1.45%, respectively. So each party – employee and employer – pays 7.65% of their income, for a total FICA contribution of 15.3%. To calculate your FICA tax burden, you can multiply your gross pay by 7.65%.

For example, if an employee’s taxable wages are $700 for the week, their social security contribution would be: $700.00 x 6.2% = $43.40. Their Medicare contribution would be: $700.00 x 1.45%= $10.15.

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Answer:

\(circumference \: of \: a \: circle = 154 \\ 2\pi \: r = 154 \\ 2 \times \frac{22}{7} \times r = 154 \\ r = 98 \\ \\ \\ area \: of \: a \: triangle = \pi {r}^{2} \\ \frac{22}{7 } \times 98 \times 98 = 30184cm ^{2} \)

Step-by-step explanation:

please mark me as brainlest

Answer:

The radius of circle is 24.5 cm.

The area of circle is 1886.5 cm².

Step-by-step explanation:

\(\large{\tt{\purple{\underline{\underline{\pink{SOLUTION: -}}}}}}\)

Finding the radius of circle by substituting the values in the formula :

\(\star{\underline{\boxed{\tt{\purple{C_{(Circle)} = 2\pi r}}}}}\)

\(\longrightarrow{\tt{C_{(Circle)} = 2\pi r}}\)

\(\longrightarrow{\tt{154 = 2 \times \dfrac{22}{7} \times r}}\)

\(\longrightarrow{\tt{154 = \dfrac{2 \times 22}{7} \times r}}\)

\(\longrightarrow{\tt{154 = \dfrac{44}{7} \times r}}\)

\(\longrightarrow{\tt{r = 154 \times \dfrac{7}{44}}}\)

\(\longrightarrow{\tt{r =\dfrac{154 \times 7}{44}}}\)

\(\longrightarrow{\tt{r =\dfrac{1078}{44}}}\)

\(\longrightarrow{\tt{r =24.5}}\)

\(\star{\underline{\boxed{\tt{\red{r =24.5 \: cm}}}}}\)

Hence, the radius of circle is 24.5 cm.

\(\begin{gathered}\end{gathered}\)

Finding the area of circle by substituting the values in the formula :

\(\star{\underline{\boxed{\tt{\purple{A_{(Circle)} = \pi{r}^{2} }}}}}\)

\(\longrightarrow{\tt{A_{(Circle)} = \pi{r}^{2} }}\)

\(\longrightarrow{\tt{Area_{(Circle)} = \dfrac{22}{7} \times {(24.5)}^{2} }}\)

\({\longrightarrow{\tt{Area_{(Circle)} = \dfrac{22}{7} \times {(24.5 \times 24.5)}}}}\)

\({\longrightarrow{\tt{Area_{(Circle)} = \dfrac{22}{7} \times {(600.25)}}}}\)

\({\longrightarrow{\tt{Area_{(Circle)} = \dfrac{22}{7} \times 600.25}}}\)

\({\longrightarrow{\tt{Area_{(Circle)} = \dfrac{22}{\cancel{7}} \times \cancel{600.25}}}}\)

\({\longrightarrow{\tt{Area_{(Circle)} = 22 \times 85.75}}}\)

\({\longrightarrow{\tt{Area_{(Circle)} = 1886.5}}}\)

\(\star{\underline{\boxed{\tt{\red{Area_{(Circle)} = 1886.5 \: {cm}^{2}}}}}}\)

Hence, the area of circle is 1886.5 cm².

\(\rule{300}{2.5}\)

Maximum 8A/144 people are allowed to entire the park.

The entire space taken up by the surface of the park is called area.

If the park is rectangular shaped, then the area is the product of length and breadth. If it is square shaped, area can be determined by the square of the side length.

Given, length of unused space = 12 foot

    breadth of unused space = 12 foot

Area of unused space = 12 x 12 = 144 square feet

Maximum 8 people is allowed for every 144 squares feet space

Let, area of the entire park is A square feet

Now maximum number of people allowed = (8 × A)/ 144

hence, 8A/144 people is allowed.

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Step-by-step explanation:

let's first transform these terms into real fractions :

2/5 = 2/5

4 1/8 = (4×8 + 1)/8 = 33/8

2 1/4 = (2×4 + 1)/4 = 9/4

first we need to handle the division (remember the priorities of arithmetic operations) :

-33/8 / -9/4 = (-33×4) / (-9×8) = 33 / (9×2) = 33/18

then we have to calculate

2/5 + 33/18

to do that we have to bring both fractions to the same denominator (must be divisible by 18 and by 5, so in this case it is 5×18 = 90) :

2/5 = 2/5 × 18/18 = 36/90

33/18 = 33/18 × 5/5 = 165/90

so,

36/90 + 165/90 = 201/90 = 67/30 = 2 7/30