79 Points!!! Algebra question. A biologist plotted the data from his latest experiment and connected the points to form the graph shown. He recognizes that the graph is a translation of y=x^2. Write a function f(x) to represent the graph of his data. Photo attached. Thank you!

Answer:

a. Since the half-life of the isotope is 8 hours, we know that the decay rate is exponential and we can use the formula:

A(t) = A0 * (1/2)^(t/8)

where A0 is the initial amount of the substance, t is the time elapsed, and A(t) is the amount of substance remaining after t hours.

Substituting the given values, we get:

A(t) = 7 * (1/2)^(t/8)

b. To find the rate at which the substance is decaying, we need to take the derivative of A(t) with respect to t:

A'(t) = -7/8 * (1/2)^(t/8) * ln(1/2)

Simplifying, we get:

A'(t) = -ln(2) * (7/8) * (1/2)^(t/8)

c. To find the rate of decay at 14 hours, we can plug in t=14 into the equation we found in part b:

A'(14) = -ln(2) * (7/8) * (1/2)^(14/8) ≈ -0.4346 grams per hour (rounded to four decimal places)

no 1) what is the square root of 2? it's about 1.5

no 2) pi is 3.14 blah blahblah so just put somewhere around 3

no 3) do square root of 11, it's about 3.3 so put it a tiny bit after no 2.

all of these will be after the 0, not before because theyre positive

hope this helps x

However, we need to choose the positive value for t, since time cannot equation be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

So we have:

[tex]-16t^2 + 170t + 30 = 20\\-16t^2 + 170t + 10 = 0\\8t^2 - 85t - 5 = 0\\t = (-b + \sqrt(b^2 - 4ac)) / 2a\\t = (-(-85) + \sqrt((-85)^2 - 4(8)(-5))) / 2(8)\\t = (85 + \sqrt(7225 + 160)) / 16\\t = (85 + \sqrt(7385)) / 16[/tex]

However, we need to choose the positive value for t, since time cannot be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.

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Answer:

We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.

We can set up an equation as follows:

S = m^2 + 6m + 8 = 80

Subtracting 80 from both sides, we get:

m^2 + 6m - 72 = 0

We can factor this quadratic equation as:

(m + 12)(m - 6) = 0

This gives us two possible solutions:

m + 12 = 0 or m - 6 = 0

Solving for m in each case, we get:

m = -12 or m = 6

Since we are looking for a number of months, we can discard the negative solution.

Therefore, book sales reach $80,000 in 6 months.

So, the answer is: 6 months.

The highest point of the quadratic equation that opens down can be (-5, 8)

We have a quadratic equation whose graph opens downwards, and we know that it also passes through the points (-2,5) and (-8, 5).

The highest point will be of the form (x, y).

Such that y is larger than 5, and the value of x is right between the two values above:

x = (-2 - 8)/2

x = -5

So the point is of the form (-5, y) where again y  > 5.

From the given options the only of this form is (-5, 8)

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Answer:

$6235 1

' 1 . ' 8

Answer:

Step-by-step explanation:

Based on this estimate, the insurance company's projected value of this probability insurance policy is negative, implying that the insurance company will lose money on this policy.

Probabilistic theory is a branch of mathematics that calculates the chance of an event or a claim being true. A risk is a number between 0 and 1, where 1 represents certainty and a probability of about 0 shows how likely an event appears to be to occur. Probability is a mathematical term for the likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1, or as percentages ranging from 0% to 100%. The proportion of occurrences among equally likely choices that result in a certain event in compared to all possible outcomes.

The total of the potential payouts multiplied by the odds of each payout occurring equals the anticipated value of the insurance policy. In this scenario, the possible compensation is the $1500 insurance payout, and the likelihood of the client being involved in an accident is 3.3%, or 0.033.

Expected value = (Payout if event happens) x (Probability of event happening) - (Annual premium)

($1500) x (0.033) - ($120) = expected value

Value expected = $49.50 - $120

-$70.50 is the expected value.

Based on this estimate, the insurance company's projected value of this insurance policy is negative, implying that the insurance company will lose money on this policy.

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Answer:

For the first 40 hours that Mr. Ed works, he earns his regular rate of pay, which is $15.50 per hour. So, his regular pay for the week is:

40 hours x $15.50 per hour = $620

For the additional 5 hours he works, he earns overtime pay at a rate of time-and-a-half, which is 1.5 times his regular pay rate. So, his overtime pay for the week is:

5 hours x $15.50 per hour x 1.5 = $116.25

Therefore, Mr. Ed's total pay for the week in which he works 45 hours is:

$620 (regular pay) + $116.25 (overtime pay) = $736.25.

Answer:

21

Step-by-step explanation:

9x + 10 = 20

9x = 10

x = 10/9

What is the value of 18x + 1?

18(10/9) + 1

= 20 + 1

= 21

So, the value of 18x + 1 is 21

Therefore, the probability that at least one of the next six births is a girl is 1 - 0.033 = 0.967 (rounded to three decimal places).

Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

To calculate the probability of an event, you divide the number of ways that event can occur by the total number of possible outcomes. For example, if you flip a fair coin, there are two possible outcomes - heads or tails - and each has an equal probability of 0.5 (or 50%) of occurring.

Given by the question.

To find the probability that at least one of the next six births is a girl, we can find the probability that all six of them are boys and subtract it from 1.

The probability that one birth is a girl is 1 - 0.513 = 0.487.

The probability that all six births are boys is. [tex]0.513^{6}[/tex] = 0.033.

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The fraction of learners who do not cycle to school is equal to 9/10.

Given that the total number of learners is 40, 12 of which walk to school and twice of the number of learners who walk, come to school by car or taxi, then the remainder of learners who cycle to school is calculated as;

40 - [12 +2(12)] = 4

The number of learners who do not cycle to school is;

12 + 2(12) = 36

fraction of learners who do not cycle to school = 36/40

by simplification;

fraction of learners who do not cycle to school = 9/10.

Therefore, the fraction of learners who do not cycle to school is equal to 9/10.

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Answer:

I got 28

Step-by-step explanation:

use the formula k=y/x. 6/8=0.75

21/0.75=

Answer: 1050$

Step-by-step explanation:

im a math teacher

Answer:

9 minutes and 25 seconds to 9 in the evening in analogue time is represented as:

8:50:35 PM

Answer: I think its C

Answer:

Step-by-step explanation:

C is false. [tex]\angle BEC = \angle AED=126[/tex]   (vertically opposite).

The rest are correct.

The value of angle Y (m∠Y) in the given parallelogram is determined as 112⁰.

The value of angle Y is determined by applying the principle of a quadrilateral for the given parallelogram as shown below.

The adjacent angles of a parallelogram are supplementary, that is they add up to 180 degrees, while the opposite angles are equal or congruent.

From the given diagram angle W = angle Y (opposite angles)

angle W + angle Z = 180 (adjacent angles )

angle W = 180 - angle Z

angle W = 180 - 68

angle W = 112

Therefore, angle Y (m∠Y) = 112⁰.

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The simplification of the polynomial using factor by substitution is: ((3y - 2)⁴ - 1)/(3y - 2)²

Factoring polynomials simply means separating a polynomial into its component polynomials.

Sometimes, in the event that polynomials are particularly complicated, it is usually easiest to substitute a simple term and factor down.

We have the equation:

(3y - 2)² - (3y - 2)⁻²

Let 3y - 2 be denoted by S and as such we have:

S² - S⁻²

= S² - 1/S²

Using the denominator as factor, we have:

= (S⁴ - 1)/S²

Plugging 3y - 2 for S gives us:

((3y - 2)⁴ - 1)/(3y - 2)²

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You will pay a total of $26.40 including the 20% tip.

To calculate the total amount including the 20% tip, you need to add 20% of the meal cost to the original meal cost:

A gratuity or a small amount of money given to someone for their service, such as a waiter or a hairdresser.

A piece of advice or a suggestion given to someone to help them do something better or more efficiently.

A pointed or tapered end of an object, such as the tip of a pen or a needle.

Tip amount = 20% of $22.00 = 0.2 x $22.00 = $4.40

Total amount including tip = $22.00 + $4.40 = $26.40

Therefore, you will pay a total of $26.40 including the 20% tip.

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Answer:

Temporary Differences Reported First on:     The Income Statement                       The Tax Return   Revenue      Expense                       Revenue              Expense1)       $272)                          $273)                                                                $274)                                                                                            $275)     $22             $276)                         $27                               $227)     $22             $27                                                             $178)     $22             $27                               $12                        $17Taxable Income assuming pretax accounting income is $100 million1)  Pretax Income - Revenue = $100m - $27m = $73m2) Pretax Income + Expense = $100m + $27m = $127m3) Pretax Income + Revenue Return = $100m + $27m = $127m4) Pretax Income - Expense Return = $100m - $27m = $73m5) Pretax Income - Revenue + Expense = $100m - $22m + $27m = $105m6) Pretax Income + Expense + Revenue Return = $100m + $27m + $22m = $149m7) Pretax Income - Revenue + Expense - Expense Return = $100m - $22m + $27m - $17m = $88m8) Pretax Income - Revenue + Expense + Revenue Return - Expense Return = $100m - $22m + $27m + $12m- $17m = $100m

Step-by-step explanation:

First, return is added to differentiate revenue and expense from the tax return from that of the income statement.Temporary difference is defined as the difference between the tax and financial reporting bases of assets and liabilities. These differences can result in taxable or deductible amounts in future years (deferred tax assets or liabilities).For each scenario, temporal difference of revenue reported first in the income statement is deducted from the pretax accounting income while expenses are added back to the pretax accounting income.For temporal differences from the tax return, the revenue is added to the pretax accounting income while expenses are deducted.

Answer:

0.0234

Step-by-step explanation:

please give brainliest

Step-by-step explanation:

The length of the rectangle is 4 feet longer than its width w, which means the length is w + 4

The perimeter of a rectangle is the sum of the lengths of all four sides which can be expressed as:

Perimeter = 2(length + width)

Substituting w + 4 for length and w for width, we get:

Permiter = 2(w + 4 + w)

Simplifying this expression, we get:

Perimeter = 2(2w + 4)

Perimeter = 4w + 8

Therefore, the algebraic expression to find the perimeter of the rectangular box is 4w + 8

Answer: We can use the DuPont Model to calculate the total assets turnover and equity multiplier:

ROE = ROA × Equity Multiplier

Equity Multiplier = Total Assets / Total Equity

Profit Margin = Net Income / Sales

Total Assets Turnover = Sales / Total Assets

Given:

ROA = 12%

Profit Margin = 8%

ROE = 19%

To find the Total Assets Turnover:

Profit Margin = Net Income / Sales

0.08 = Net Income / Sales

Net Income = 0.08 x Sales

ROA = 12%

ROA = Net Income / Total Assets

0.12 = 0.08 x Sales / Total Assets

Total Assets Turnover = Sales / Total Assets = 0.08 / 0.12 = 0.67

Therefore, the total assets turnover is 0.67.

To find the Equity Multiplier:

ROE = ROA x Equity Multiplier

0.19 = 0.12 x Equity Multiplier

Equity Multiplier = 0.19 / 0.12 = 1.58

Therefore, the equity multiplier is 1.58.

Note: The total assets turnover and equity multiplier are related to each other through the DuPont model. The product of these two ratios should be equal to the ROE. In this case, 0.67 x 1.58 = 1.06, which is approximately equal to 1.9 (ROE in decimal form). This confirms that our calculations are correct.

Step-by-step explanation:

After answering the presented question, we can conclude that The vector expression of equal magnitude and opposite direction to  [tex]\vec{PQ}[/tex] is the same arrow but pointing in the opposite direction: QP vector

An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression.

Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form.

They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To find the vector that starts at [tex]P[/tex]  [tex](3,3)[/tex] and ends at  [tex]Q(-2,2)[/tex] , we can subtract the coordinates of the starting point from the coordinates of the ending point:

[tex]$\vec{PQ} = \begin{pmatrix} -2 \ 2 \end{pmatrix} - \begin{pmatrix} 3 \ 3 \end{pmatrix} = \begin{pmatrix} -5 \ -1 \end{pmatrix}$[/tex]

So the vector that starts at P(3,3) and ends at  [tex]Q(-2,2) is $\vec{PQ} = \begin{pmatrix} -5 \ -1 \end{pmatrix}$.[/tex]

To find the vector of equal magnitude and opposite sense to  , we can simply multiply   [tex]$\vec{PQ}$[/tex] by  [tex]-1:[/tex]

[tex]$-\vec{PQ} = -1 \begin{pmatrix} -5 \ -1 \end{pmatrix} = \begin{pmatrix} 5 \ 1 \end{pmatrix}$[/tex]

So the vector of equal magnitude and opposite sense to [tex]$\vec{PQ}$[/tex]   is [tex]$\begin{pmatrix} 5 \ 1 \end{pmatrix}$.[/tex]

Geometrically, we can represent the vectors graphic[tex]$\vec{PQ}$[/tex]ally by drawing them as directed line segments on a coordinate plane. The vector that starts at [tex]P(3,3)[/tex] and ends at [tex]Q(-2,2)[/tex] is represented by the line segment connecting [tex]P[/tex] to  [tex]Q[/tex].

Therefore, The vector of equal magnitude and opposite sense to  [tex]$\vec{PQ}$[/tex][tex]$\vec{PQ}$[/tex] is represented by the line segment starting at  [tex]Q[/tex] and ending at the point R, which is  [tex]5[/tex] units to the right and [tex]1[/tex] unit up from  [tex]Q[/tex].

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Answer:-2,-5

Step-by-step explanation:

7-4=3

You move 3 units up

You land on -2, -2

the higher units you move up, the higher the number gets to.

Answer:

Is D

Step-by-step explanation:

Thus, we should order two large pizzas, that will cost $22, to serve a group of 12.

Costs in accounting are the dollar amounts paid for materials, labor, services, goods, equipment, and other purchases made for use by a company or even other accounting entity. This sum is listed as the price on invoices and is recorded as an expense of asset cost basis in bookkeeping records.

Solution:

Let x be the quantity of pizzas ordered.

12 x 2 = 24 slices are required because a large pizza contains 8 slices per slice.

As a result, the necessary quantity of pizzas is:

[tex]x\geq 3(x-1) \leq x[/tex]

In order to find the best price, we must reduce the total cost, that is determined by:

C(x) = 15x plus 5(x - 1) (x - 1) - 15

Using the cost function's derivative in relation to x, we may calculate:

C'(x) = 20 - 10[tex]/(x-1)^2[/tex]

Finding the critical points by setting the derivative to zero yields the following results:

20 - 10[tex]/(x-1)^2[/tex] = 0

Simplishing, we obtain:

[tex](x-1)^2[/tex]= 2

By solving for x using square root of the both sides, we arrive at:

x = 1 ± √2

The ideal quantity to order is two pizzas because x has to be an integer.

By adding x = 2 to the cost function, we can determine the total cost:

C(2) = 15(2) + 5(2 - 1) - 15 = 22

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The supplementary angle will be 60°.

What are supplementary angles?

Supplementary angles are angles (only two) whose sum is equal to 180 degrees. In other words, if we add two angles together and the result is 180 degrees, those angles are considered supplementary.

For example, if we have angle A that measures 60 degrees, its supplement angle B will measure 120 degrees (180 - 60 = 120). Angles A and B are supplementary angles.

Supplementary angles can be adjacent, meaning they share a common vertex and side, or they can be non-adjacent. In either case, their sum will always be 180 degrees.

Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and triangles.

Now,

Let x = measure of the angle.

Then, the supplement angle is 180 - x.

According to the problem, x is twice less than the supplement angle. In other words, the supplement angle is twice greater than x. We can write this as:

180 - x = 2x

Solving for x, we get:

180 = 3x

x = 60

Therefore, the angle measures 60 degrees.

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Right Question:- The measure of an angle is twice less than that of its supplement angle. find that angle?

Answer:

Null Hypothesis (H0): There is no significant difference in life span for people in the two towns.

Alternative Hypothesis (H1): There is a significant difference in life span for people in the two towns.

Answer:

The null and alternative hypotheses that should be used to test this claim are:

Null hypothesis: There is no significant difference in lifespan for people in the two towns. Symbolically, this can be represented as H0: μ1 = μ2, where μ1 and μ2 are the population mean lifespans of Town A and Town B, respectively.

Alternative hypothesis: There is a significant difference in lifespan for people in the two towns. Symbolically, this can be represented as Ha: μ1 ≠ μ2.

To test this claim, the researcher can conduct a two-sample t-test using the data collected from the two towns. The test statistic can be calculated as:

t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^0.5

where x1 and x2 are the sample mean lifespans of Town A and Town B, respectively, s1 and s2 are the sample standard deviations of Town A and Town B, respectively, and n1 and n2 are the sample sizes of Town A and Town B, respectively.

Using the given data, the test statistic can be calculated as:

t = (78.5 - 74.4) / (11.2^2/20 + 12.3^2/20)^0.5 = 1.02

At a significance level of 0.05 with 38 degrees of freedom (df = n1 + n2 - 2), the critical value for a two-tailed test is ±2.024. Since the calculated t-value (1.02) falls within the acceptance region (-2.024 < t < 2.024), the null hypothesis cannot be rejected. Therefore, we do not have enough evidence to conclude that there is a significant difference in lifespan for people in the two towns.

Step-by-step explanation:

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Solution :

Zoe's ball pool is a cylinder with height 20 cm and diameter 90 cm.

Height = 20 cm

Diameter = 90 cm

Calculate :

(a) The Radius of the pool.

Answer :

We are given with Diameter of pool 90 cm.

We know that,

Radius = Diameter/2

Radius = 90/2 = 45 cm.

(b) The circumference of the pool .

Answer :

Circumference = 2 πr

[tex]2 \times \dfrac{22}{7} \times 45 \\ \\ \dfrac{ 44 \times 45}{7} \\ \\ \frac{1980}{7} \\ \\ 282.8 \: cm[/tex]

(c) The area of the base of the pool.

Answer :

Area of base = πr²

[tex] \dfrac{22}{7} \times {(45)}^{2} \\ \\ \frac{22}{7} \times 2025 \\ \\ 22 \times 289.28 \\ \\ 578.56 \: {cm}^{2} \\ [/tex]

(d) The volume of the pool

Answer :

Volume of cylinder = πr²h

[tex] \dfrac{22}{7} \times {(45)}^{2} \times 20 \\ \\ \dfrac{22}{7} \times 2025 \times 2 \\ \\ \dfrac{22}{7} \times 4050 \\ \\ \frac{89100}{7} \\ \\ 12728.57 \: {cm}^{3} [/tex]

Step-by-step explanation:

It is an ODD  number  due to statement 1

it is a multiple of 5   due to the last statement

5   15   25   35   45  55  65  75    85  95  105   .....

When you divide by 3    there is a R 1

25    55    85    115    145

When you divide by 4  there is a R = 1

25   is the lowest number    next possible number is 145    then another posssible is 265    etc