An example of a hypothesis is: a person is innocent until proven guilty.

a. True
b. False

The equation of exponential regression that fits the data is given as follows:

y = 1.5(2.5)^x.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

To obtain the equation of exponential regression, we must insert the points of the data-set into a calculator.

The points are given as follows:

(1, 3.75), (4, 9.375), (3, 23.438), (4, 58.594), (5, 146.484).

Inserting these points into a calculator, the equation is given as follows:

y = 1.5(2.5)^x.

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The molar solubility of Co(OH)2 in a solution buffered at pH = 4.50 is negligible, while in a solution buffered at pH = 11.25, it is approximately 5.41 x 10^-6 M.

To calculate the molar solubility of Co(OH)2 in a buffered solution, we need to consider the effect of pH on the solubility.

(a) Buffered Solution at pH = 4.50:

At pH = 4.50, the solution is acidic. In an acidic solution, Co(OH)2 will undergo hydrolysis and form Co2+ ions according to the following reaction:

Co(OH)2 (s) ⇌ Co2+ (aq) + 2 OH- (aq)

Since the hydroxide ion concentration is determined by the pH of the solution, we can use the following equation to calculate the molar solubility (S) of Co(OH)2:

Ksp = [Co2+][OH-]^2

To determine the molar solubility, we need to find the concentration of OH- ions. Since the solution is buffered at pH = 4.50, we can assume the concentration of OH- ions to be negligible. Therefore, the molar solubility of Co(OH)2 in this buffered solution is considered very low or negligible.

(b) Buffered Solution at pH = 11.25:

At pH = 11.25, the solution is alkaline/basic. In an alkaline solution, the concentration of OH- ions is relatively high. We can assume that the OH- concentration is in excess and will not significantly affect the solubility equilibrium.

Using the same Ksp expression:

Ksp = [Co2+][OH-]^2

Since the concentration of OH- ions is in excess, we can consider it to be constant. Therefore, we can directly calculate the molar solubility of Co(OH)2 using the Ksp value.

Let's denote the molar solubility of Co(OH)2 as x. Then, we have:

Ksp = [Co2+][OH-]^2 = x * (2x)²= 4x³

Given that Ksp = 2.5 x 10^-16, we can solve for x:

4x³ = \(2.5 * 10^{-16\)

x³ = (\(2.5 * 10^{-16\)) / 4

x = \(((2.5 x 10^-16)^{(1/3) }/ 2^{(1/3))}^{(1/3)} / 2^{(1/3)\)

Using a calculator, we find that the molar solubility of Co(OH)2 in this buffered solution at pH = 11.25 is approximately 5.41 x\(10^{-6\) M.

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B) Dilation and rotation is the sequence of transformations would result in a figure that is similar but not congruent to the original figure

What is Dilation and Rotation transformation?

Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.

Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.

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Answer:

A(t) = R -5(t)

t in minuto

Step-by-step explanation:

Nesta questão, estamos preocupados em estabelecer uma lei que forneça a quantidade de água presente no reservatório a qualquer momento, usando a quantidade inicial de água no reservatório e a taxa de perda de água do reservatório.

Agora, sabemos que a taxa de perda de água é de 5 litros por minuto.

Assim, podemos estabelecer a lei da seguinte forma; vamos chamar a quantidade de água a qualquer momento no reservatório A (t);

A lei é assim; A (t) = R -5t onde t representa o tempo que estamos considerando e é em minutos, enquanto R é o volume inicial de água no tanque.

The area in square feet that will be added to the garden is 44 square feet.

Length of square garden = 8 feet

Area of Square garden = \((side)^{2}\) = \((8)^{2}\) = 64 square feet

On enlarging the square to a rectangle, length rectangular garden is (8+4)feet i.e.,12feet and width of rectangular garden is (8+1)feet i.e.,9feet.

Area of rectangular garden = (length × width)

                                              = (12 × 9) square feet

                                              = 108 square feet

The area in square feet that will be added to the garden = (Area of rectangular garden - Area of Square garden)

= (108 square feet - 64 square feet)

= 44 square feet

The area in square feet that will be added to the garden is 44 square feet.

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For the given problem, The correct answer will be option 2: The IQR of 13 is the most accurate to use, since the data is skewed.

The Interquartile Range (IQR) is a measure of variability that compares the 25th percentile (Q1) to the 75th percentile (Q3) of a dataset (Q3). It is frequently used to describe the distribution or variability of data that may contain outliers or is not regularly distributed.

The data in the histogram is not evenly distributed in this example because there are many donations at the higher end of the scale (16 to 20), resulting in a positively skewed distribution. Using a range of 20, which indicates the difference between the greatest and lowest value in the dataset, may not adequately depict the data's variability since it is significantly impacted by outliers at the extremes.

For the given dataset, IQR can be calculated as:

Arrange the dataset in ascending order:

\(5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20\)

Find the median (Q2), i.e. the middle value of given dataset:

Median (Q2) = 15

Find the lower quartile (Q1), which is the median of the lower half of the dataset:

\(Q1 = Median of (5, 5, 6, 8, 10) = 6\)

Find the upper quartile (Q3) i.e. median of the upper half of dataset:

\(Q3 = Median \;of (15, 18, 20, 20, 20, 20, 20) = 19\)

\(IQR = Q3 - Q1 = 19 - 6 = 13\)

Utilizing the IQR of 13, which represents the range between the 25th percentile (Q1 = 6) and the 75th percentile (Q3 = 19), would provide a more accurate measure of variability that is less impacted by outliers at the higher end of the data. It would also offer a better indication of the organization's typical donations because it captures the middle 50% of the data.

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You were on the right track. Here are two ways to go about it.

• By definition of conditional probability,

Pr[A | B] = Pr[A and B] / Pr[B]

Out of the total 100 participants in the survey, there are 18 people that both have a positive attitude and are over 35, so

Pr[positive and over 35] = 18/100

Out of the 100 pariticipants, 40 are over 35, so

Pr[over 35] = 40/100

Then the conditional probability you want is (18/100) / (40/100) = 18/40 = 9/20.

• There are 40 people over 35 in the survey. You want the probability that someone randomly chosen from this group has a positive attitude, of which there are 18. Hence the probability is 18/40 = 9/20.

Answer:

[-6 , 0]

Step-by-step explanation:

If the absolute value of an expression is equal to a number, that means that the expression itself could be equal to either the negative equivalent to that number or the positive equivalent.

for example, if my inequality is |x| > -3

x could either be:

-3 or 3

So,

| 2(x - 1) + 8 |  ≤  6

can be separated into two separate inequalities:

      2(x - 1) + 8  ≤   6

or,  2(x - 1) + 8  ≥ - 6

we solve these inequalities separately.

2(x - 1) + 8 ≤ 6

2x - 2 + 8  ≤ 6               [distribute 2]

2x  ≤ 0              [add 2 to both sides, subtract 8 from both sides]

x ≤  0   [finalize isolating x by dividing both sides of the equation by 2]

expressed as [in interval notation]:

(-∞, 0]

now, let's solve for the other inequality.

2(x - 1) + 8  ≥  - 6

2x - 2 +  8   ≥  - 6         [distribute 2]

2x  ≥  -12                   [add 2 to both sides, subtract 8 from both]

x  ≥  -6          [divide both by 2 to isolate x]

expressed as [in interval notation]:

[-6 , ∞)

So, our answer for x is going to be

-6 ≤ x ≤ 0

or, expressed in interval notation:

[-6 , 0]

*[ includes number]

*( is not equal to number)

Answer:

100

Step-by-step explanation:

To solve for y in the equation Y/1/5=20, we can multiply both sides of the equation by 1/5 to isolate y on one side of the equation. This gives us:

Y/1/5 * 1/5 = 20 * 1/5

Simplifying this expression gives us:

Y = 100

Therefore, the value of y is one hundred.

Answer:

Y = 4

Step-by-step explanation:

Now we have to,

→ Find the required value of Y.

The equation is,

→ Y/(1/5) = 20

Then the value of Y will be,

→ Y/(1/5) = 20

Simplifying the left hand side:

→ Y × (5/1) = 20

→ 5Y/1 = 20

→ 5Y = 20

Dividing 20 by the number 5:

→ Y = 20/5

→ [ Y = 4 ]

Hence, the value of Y is 4.

Answer:

(9x+7)(9x-7)

value of a =9x

              b = 7

Answer:

See photo below

I hope this helps!

Answer:

\( \frac{2}{5} (d - 10) - \frac{2}{3} (d + 6) \\ = \frac{2d}{5} - \frac{20}{5} - \frac{2d}{3} - \frac{12}{3} \\ = \frac{2d}{5} - \frac{2d}{3} - \frac{20}{5} - \frac{12}{3} \\ = \frac{6d - 10d}{15} - 4 - 4 \\ = \frac{ - 4d}{15} - 8 \\ = \frac{ - 4d - 120}{15 } \\ = - ( \frac{4d + 120}{15} )\)

Thank you ☺️☺️

Answer:

$13.44

Step-by-step explanation:

$4.00 x 12 (comic books) = $48

$48 x 28% = 13.44

Step-by-step explanation:

\(2\mathbf{u}=\langle 10,6 \rangle \\ \\ 3\mathbf{v}=\langle -12, 0 \rangle \\ \\ 2\mathbf{u}-3\mathbf{v}=\langle 10,6 \rangle -\langle -12,0 \rangle =\langle 22,6 \rangle\)

Answer: 190 miles

Solution:

=4 x 95 / 2

=(cross out the common factor)

=2 x 95 = 190

The composition (h ∘ f)(1) simplifies to 512, which is the result of evaluating h at the value of f(1).

To find (h ∘ f)(1), we need to evaluate the composition of functions h and f at x = 1.

First, we evaluate f(1):

f(x) = 4x + 4

f(1) = 4(1) + 4

f(1) = 4 + 4

f(1) = 8

Next, we evaluate h(f(1)):

h(x) = x^3

h(f(1)) = (f(1))^3

h(f(1)) = 8^3

h(f(1)) = 512

Therefore, (h ∘ f)(1) = 512

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Answer:

0.32 ounces of chocolate per mold

Step-by-step explanation:

Answer:

The Triangle

Step-by-step explanation:

Answer:

b and c

Step-by-step explanation:

The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

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Answer:

Its -5/96 in fraction form and −0.052083 repeating in decimal form.

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

when the cake is cut into \(2\) ounce pieces instead of \(3\) pieces it yields \(180\) pieces.

How to find large cake pieces ?

Given in the question when cake cuts into piece that each weight is \(3\) ounce it yields \(120\)

So original large cake weight is

\(w=120*3\\\\w=360\)

So we can find cake pieces when cake cuts into weight \(2\) each piece

\(pieces=\frac{360}{2}\\=180\)

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a) The probability that a person is willing to commute between 10 and 20 miles to work is 0.338. b) 53% of people are willing to commute at least 13.2 miles to work.
a) We are given that the mean of the exponential random variable is 17 miles, so the rate parameter is α = 1/17. We can use the R code provided to find the probability that a person is willing to commute between 10 and 20 miles to work:
pexp(20, 1/17) - pexp(10, 1/17)
This gives us a probability of 0.338, so the answer is 0.338 (rounded to three decimal places).
b) We are given that 53% of people are willing to commute at least a certain distance to work. We can use the R code provided to find this distance:
qexp(0.53, 1/17, lower.tail = FALSE)
This gives us a distance of 13.2 miles, so the answer is 13.2 (rounded to one decimal place).

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The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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Answer:

Explanation:

Here, we want to solve the given equation for L

What that means is that we want to make L the formula subject. Hence, we are to simply isolate L on one side of the equation

To do this, we have to divide both sides by the values attached to L:

112.8 is the the total sound power, when three drill presses are operating

A relation is a function if it has only One y-value for each x-value.

Given that a function P(n) = 108 + 10 log(n) gives the total sound power in decibels when n drill presses are operating in a factory.

We need to find the total sound power, to the nearest decibel, when three drill presses are operating

We have to consider n as 3

P(3) = 108 + 10 log(3)

=108+10×0.477

=108+4.77

=112.77

Hence, 112.8 is the the total sound power when three drill presses are operating

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When an electric field is applied to a charged particle. Since the pressure applied on particles accelerates it, it meets Newton's second law.

The third law asserts that there's an identical and diametrically opposed response to every activity (force) in nature. If object A applies a force to object B, object B applies an opposite force of equal magnitude to object A. In other words, direct impact on the growth energies. In addition, the current injected in the coil becomes proportional to its area.

\(F = ma = qe\)

so \(q e = ma\)

\(F_{12}\) = \(- F_{21}\)

First Law: An object in motion remains in motion until it is acted with by an imbalanced force. Second Law: Force equals an object's mass multiplied by its acceleration (F=ma). Third Law: For any force operating on an item.

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The equation of the linear function is y = -1/2x - 6

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

The graph

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

y = mx - 6

From the graph, we have

A unit increment in x gives an decrement of 1/2 in y

This means that

m = -1/2

So, we have

y = -1/2x - 6

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