b. Express log2 24 in terms of prime factors and leave answer in the most simplified form using properties of logarithms. (2 Marks)​

Answer: mi = 52 x h or y = 52 times x

distance (mi) = y

time (h) = x

It goes 52 miles per hour!  Hope this helps.

The side length of the leg of the special right triangle is equal to 7√2 / 2 units.

In this problem we find the case of special right triangle known as 45° - 90° - 45° triangle, where internal angles are 45°, 90° and 45° and whose side relationship is shown below:

r = √2 · x = √2 · y

Where:

If we know that r = 7, then the side length of the leg is:

x = y = √2 · r / 2

x = y = √2 · 7 / 2

x = y = 7√2 / 2

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The Shares for the other teams are indeed 12, 9, and 6, respectively,  confirms that the solution is correct,there were 8 red balls.

The problem step by step. We are given the following information:

1. The total number of balls is 35.

2. One team takes all the red balls.

3. The remainder (non-red balls) is shared among the other teams in the ratio 4:3:2.

4. The smallest share is 6 balls.

Let's assume the number of red balls is "r". Therefore, the number of non-red balls is 35 - r.

According to the ratio, the shares for the other teams are:

Team 1: (4/9) * (35 - r)

Team 2: (3/9) * (35 - r)

Team 3: (2/9) * (35 - r)

Given that the smallest share is 6 balls, we can set up the equation:

(2/9) * (35 - r) = 6

To solve this equation, we can simplify and solve for "r":

(35 - r) = (9/2) * 6

35 - r = 27

r = 35 - 27

r = 8

Therefore, there were 8 red balls.

To verify the solution, we can calculate the shares for the other teams:

Team 1: (4/9) * (35 - 8) = 4 * 27/9 = 12

Team 2: (3/9) * (35 - 8) = 3 * 27/9 = 9

Team 3: (2/9) * (35 - 8) = 2 * 27/9 = 6

The shares for the other teams are indeed 12, 9, and 6, respectively, which confirms that the solution is correct.

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The total surface area required to wrap the 15 cubed-shaped gift boxes is 3.6 square meters.

To calculate the total surface area of 15 cubed-shaped gift boxes, we need to find the surface area of one gift box and then multiply it by the total number of boxes.

The surface area of a cube can be calculated using the formula:

Surface Area = 6 * [tex](side length)^2[/tex]

Given that the length of each side of the cube-shaped gift box is 20 cm, we can substitute this value into the formula:

Surface Area of one gift box = 6 * (20 cm)^2

= 6 * [tex](400 cm^2)[/tex]

= 2400 [tex]cm^2[/tex]

Since we have 15 gift boxes, we multiply the surface area of one gift box by 15:

Total Surface Area = Surface Area of one gift box * Number of gift boxes

= 2400 [tex]cm^2 * 15[/tex]

= 36000 [tex]cm^2[/tex]

Now, we need to convert the area from square centimeters [tex](cm^2[/tex]) to square meters [tex](m^2).[/tex] There are 10000 square centimeters in a square meter:

Total Surface Area in square meters = Total Surface Area in square centimeters / 10000

= 36000 [tex]cm^2[/tex] / 10000

= 3.6[tex]m^2[/tex]

Therefore, the total surface area required to wrap the 15 cubed-shaped gift boxes is 3.6 square meters.

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The missing coordinate to complete the ordered pair is (9). The ordered pair is (1, 9).

An ordered pair is a mathematical concept that consists of two elements, typically represented as (x, y), where x is the first element, also known as the x-coordinate, and y is the second element, also known as the y-coordinate.

It is also known as coordinates, the point (x, y) on a graph where x and y are real numbers.

If x + y = 10, then we can find the missing coordinate by substituting the given x-coordinate (1) into the equation, x + y = 10:

[tex]\sf x + y = 10[/tex]

[tex]\sf y = 10 - 1[/tex]

[tex]\sf y = 9[/tex]

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To calculate the amount of money in the account after 1 year, we can use the following formula:

A = P(1 + r/n)^nt

Where:

Plugging in the given values, we get:

A = 500(1 + 0.05/4)^4*1

A = 500(1.0125)^4

A = $515.63

Therefore, after 1 year, the account will have $515.63.

Answer: B. t= 15; s=5

Step-by-step explanation:

We will create a system of equations.

    8t + 12s = 180

    t = 3s

Next, we will substitute this value of t into the first equation and solve for s.

    8t + 12s = 180

    8(3s) + 12s = 180

    24s + 12s = 180

    36s = 180

    s = 5 shirts

Lastly, we will substitute this value of s back into t = 3s and solve for t.

    t = 3s

    t = 3(5)

    t = 15 shirts

Answer:

(a) - [tex]\sin(y)=-3\cos(x)+4[/tex]

(b) - [tex]y=e^{2x-1}[/tex]

Step-by-step explanation:

Given the two part question...

(a) - Solve the following first-order differential equation with the given initial condition.

[tex]y'=\frac{3\sin(x)}{\cos(y)}; \ y(0)=\frac{\pi}{2}[/tex]

(b) - Given that y=f(x) passes through the point (1,e) and has the property that the slope of the tangent line to the graph at any point "P" is equal to twice the y-coordinate of "P." Find f(x).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Part (a) -

The given DE is a separable differential equation and can be solved in the following manner.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Seperable Differential Equation}}\\\frac{dy}{dx}=f(x)g(y) \\ \rightarrow \int\frac{dy}{g(y)}=\int f(x)dx \end{array}\right}[/tex]

[tex]y'=\frac{3\sin(x)}{\cos(y)} \rightarrow \frac{dy}{dx} =\frac{3\sin(x)}{\cos(y)}\\\\\Longrightarrow \cos(y)dy=3\sin(x)dx\\\\\Longrightarrow \int\cos(y)dy=3\int\sin(x)dx\\\\\Longrightarrow \boxed{\sin(y)=-3\cos(x)+C}\\\\\text{Now for the given initial condition to find the arbitrary constant, "C."}\\\text{Initial condition} \longrightarrow y(0)=\frac{\pi}{2} \\\\\Longrightarrow \sin(\frac{\pi}{2})=-3\cos(0)+C\\\\\Longrightarrow 1=-3(1)+C\\\\\Longrightarrow \boxed{C=4}\\\\[/tex]

[tex]\therefore \boxed{\boxed{\sin(y)=-3\cos(x)+4}}[/tex]

Thus, the DE is solved.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Part (b) -

[tex]\text{The slope of the tangent line =} \ \frac{dy}{dx} \\\\\text{According to the question, the slope of the tangent line =} \ 2y\\\\\text{So we can say,}\\\\\longrightarrow \boxed{\frac{dy}{dx}=2y} \ \text{Solve the DE}[/tex]

[tex]\frac{dy}{dx}=2y\\\\\Longrightarrow \frac{dy}{2y}=dx \\\\\Longrightarrow \frac{1}{2} \int\frac{dy}{y}=\int dx\\\\\Longrightarrow \frac{1}{2} \ln(y)=x+C\\\\\Longrightarrow \boxed{\ln(y)=2x+ \bar C}[/tex]

Use the given initial condition to find "C." y(e)=1

[tex]\Longrightarrow \ln(e)=2(1)+ \bar C\\\\\Longrightarrow 1=2+ \bar C\\\\\Longrightarrow \boxed{C=-1}[/tex]

[tex]\Longrightarrow \ln(y)=2x+ \bar C\\\\\Longrightarrow \ln(y)=2x-1\\\\ \therefore \boxed{\boxed{ y=e^{2x-1}}}[/tex]

Thus, f(x) is found.

Answer:

4 pounds

Step-by-step explanation:

First, we can calculate how much money Ivanna spent by subtracting her remaining balance after buying the coffee from the original amount on the gift card.

amount spent = $80 - $47.88 = $32.12

Now, we can calculate how many pounds of coffee she bought by dividing the amount she spent by the price rate of coffee by pound.

[tex]\$32.12 \div \dfrac{\$8.03}{1 \text{ lb}}[/tex]

[tex]= \$32.12 \times \dfrac{1 \text{ lb}}{\$8.03}[/tex]

[tex]= \dfrac{32.12}{8.03} \text{ lb}[/tex]

[tex]= \boxed{4 \text{ lb}}[/tex]

So, Ivanna bought 4 pounds of coffee.

Answer:  Ivanna bought 4 pounds of coffee for an amount of$32.12.

Step-by-step explanation:

According to the question,

Money with Ivanna initially: $80

Money with Ivanna later: $47.88

step 1: here we need to find the difference between the amount initially and later,

Difference between the amount initially and later: $80 - $47.88 = $32.12

Given,

Price of coffee per pound:  $8.03

Step 2: now we divide the amount spent by the price per unit of coffee,

that is: $32.12/$8.03 = 4

so the answer is Ivanna bought 4 pounds of coffee for an amount of$32.12

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Answer:

4(2x - 1) + 3(2x + 5)

Step-by-step explanation:

4(2x - 1) + 3(2x+5)

Multiply 4 with 2x - 1 and multiply 3 with 2x + 5,

8x - 8 + 6x + 15 = 0

Arrange x and constant,

8x + 6x = 8 - 15

14x = - 7

14x = - 7

x = -7/14

x = -1/2

x = -0.5

Hope this helps! Recheck the answers.

The Sample space, a clear set of possible outcomes for choosing one card from the set.

The sample space for choosing one card from a set of 10 labeled cards, where each card is labeled with an expression, would consist of all the possible outcomes of this selection process.

Since there are 10 cards in the set, the sample space would consist of the individual expressions labeled on each card. Let's assume the expressions on the cards are labeled as follows:

Card 1: Expression 1

Card 2: Expression 2

Card 3: Expression 3

...

Card 10: Expression 10

{Expression 1, Expression 2, Expression 3, ..., Expression 10}

This sample space represents all the possible outcomes when selecting one card from the set. Each outcome corresponds to one specific expression labeled on a card.

the sample space only includes the individual expressions and not any particular order or arrangement of the cards. The order of the expressions does not matter in this case, as the focus is solely on the expressions themselves.

the sample space, we establish a clear set of possible outcomes for choosing one card from the set.

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The value of probability P (A or B) is,

⇒ P (A or B) = 48

We have to given that,

The Venn diagram of the probability is shown in image.

Now, By given diagram,

⇒ P (A) = 24 + 14

⇒ P (A) = 38

⇒ P (B) = 24 + 10

⇒ P (B) = 34

⇒ P (A and B) = 24

We have to given that,

The expression is,

P (A or B) = P (A) + P (B) - P (A and B)

Substitute all the values, we get;

P (A or B) = 38 + 34 - 24

P (A or B) = 48

Thus, The value of probability P (A or B) is,

⇒ P (A or B) = 48

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Hey there!

5!

= 5(4)(3)(2)(1)

= 20(3)(2)(1)

= 60(2)(1)

= 120(1)

= 120

Therefore, your answer should be: 120

7!

= 7(6)(5)(4)(3)(2)(1)

= 42(5)(4)(3)(2)(1)

= 210(4)(3)(2)(1)

= 840(3)(2)(1)

= 2,520(2)(1)

= 5,040(1)

= 5,040
Therefore, your answer should be: 5,040

9!
= 9(8)(7)(6)(5)(4)(3)(2)(1)

= 72(7)(6)(5)(4)(3)(2)(1)

= 504(6)(5)(4)(3)(2)(1)

= 3,024(5)(4)(3)(2)(1)

= 15,120(4)(3)(2)(1)

= 60,480(3)(2)(1)

= 181,440(2)(1)

= 362,880(1)

= 362,880

Therefore, your answer should be: 362,880

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The equivalent fraction for 1, using the number line and dividing it into four equal parts, is 1/4.

To find an equivalent fraction using a number line, we need to determine a fraction that represents the same value as the given fraction.

Let's assume the given fraction is 1. On a number line, the fraction 1 can be represented as the distance between 0 and 1. Now, we want to find an equivalent fraction, so let's choose a different representation on the number line.

To find an equivalent fraction that represents the same value, we can divide the number line segment between 0 and 1 into equal parts. Let's say we divide it into 4 equal parts.

Now, we need to determine which of the four equal parts represents the fraction 1. Since we divided the segment into four equal parts, each part represents 1/4 (one-fourth) of the whole segment.

Therefore, the equivalent fraction for 1, using the number line and dividing it into four equal parts, is 1/4.

So, the equivalent fraction for 1 is 1/4.

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Step-by-step explanation:

angle x =   180 - 90 - 60   degrees     ( because the anglse of atriangle add to 180 degrees)

x = 30 degrees

The characteristic of the researcher having direct control over at least one variable to both surveys and Observational .

The option that is not a characteristic of both surveys and observational studies is:

a. The researcher has direct control over at least one variable.

Surveys and observational studies have several characteristics in common, such as collecting data about a population and not proving cause and effect. However, the characteristic of the researcher having direct control over at least one variable is not applicable to both surveys and observational studies.

In a survey, the researcher collects data by asking questions to individuals or groups. They do not have direct control over the variables being studied but rather collect information based on participants' responses. The researcher's role is primarily in designing the survey, selecting the sample, and analyzing the data.

In an observational study, the researcher observes and records data without intervening or manipulating any variables. The researcher does not have control over the variables being observed; instead, they observe and document the existing conditions or behaviors.

the characteristic of the researcher having direct control over at least one variable is not applicable to both surveys and observational studies. Both methods involve data collection about a population and do not establish cause and effect relationships, but control over variables is not a shared characteristic.

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The choice of the best Regression model depends on the specific characteristics of the data and the underlying theory or knowledge about the relationship between the variables.

The regression model best represents the relationship between the total number of bacterial clusters and the number of elapsed days, we need to examine the data and consider different regression models.

There are several types of regression models commonly used, including linear regression, polynomial regression, exponential regression, and logarithmic regression. Each model represents a different functional form and can capture different types of relationships between variables.

Without specific data or context provided, it is challenging to determine the exact regression model that best represents the relationship. However, I can briefly explain the characteristics and typical use cases for each regression model:

1. Linear Regression: This model assumes a linear relationship between the variables, where the dependent variable changes linearly with respect to the independent variable. It is suitable when the relationship appears to be a straight line on a scatter plot.

2. Polynomial Regression: This model captures non-linear relationships by including higher-order terms of the independent variable, such as quadratic (x^2), cubic (x^3), or higher-degree terms. It is suitable when the relationship seems to follow a curve rather than a straight line.

3. Exponential Regression: This model assumes an exponential relationship between the variables, where the dependent variable changes exponentially with respect to the independent variable. It is suitable when the data exhibits rapid growth or decay.

4. Logarithmic Regression: This model assumes a logarithmic relationship between the variables, where the dependent variable changes logarithmically with respect to the independent variable. It is suitable when the relationship shows diminishing returns or saturation.

the best regression model, it is important to visually analyze the data through a scatter plot and assess the linearity or curvature of the relationship. Additionally, statistical measures such as the coefficient of determination (R-squared) and residual analysis can help evaluate the goodness of fit for different models.

the choice of the best regression model depends on the specific characteristics of the data and the underlying theory or knowledge about the relationship between the variables.

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The gravitational force between two planets of equal mass that were abruptly moved from a distance of 1 million miles to a distance of 2 million miles would be only one-fourth as strong as it had been before.

True. The gravitational force between two masses is inversely proportional to the square of their separation, as stated by Newton's law of universal gravitation.

The gravitational attraction between two planets of the same mass would drop by a factor of 1/22 or 1/4 if the distance between them increased from 1 million miles to 2 million miles.

As a result, the gravitational force would be reduced to 1/4 of what it was before.

Therefore, the gravitational attraction between two planets of the same mass would drop by a factor of 1/4 (or 1/22) if their separation doubled (from 1 million miles to 2 million miles).

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The question is referring to two functions: h(x) and g(x).

The specific functions h(x) and g(x) are not given in the information provided, but we are given the equation of g(x) as -x^2 - 2x + 6. Without knowing the equation of h(x) or having a visual comparison of the functions, we cannot directly compare them.

The question is asking for the correct statement regarding the comparison between h(x) and g(x).

The answer choices are discussing the maximum value and the value at x=3 for both h(x) and g(x).

To identify the maximum of h(x) and g(x), we need either the equations of the functions or a visual representation of their graphs. Without this information, we cannot determine the maximum values.

Similarly, without knowing the equations of the functions or having a graph, we cannot identify the values of h(x) and g(x) at x=3.

Based on the lack of information provided to make direct comparisons between h(x) and g(x), it is not possible to determine the correct answer choice.

Based on the given information, the fair conclusion would be:

C. The current stock price is up for the day by 0.38%.

The statement mentions that the stock price is up for the day, which is indicated by the positive change of 0.27 (+0.38%).

The solution is; 10 days for Soccer and, 14 days for Baseball camp, are needed to run each of the camps sessions .

Here, we have,

given that,

The Parks and Recreation Department is planning to host sports camps for students during the summer.

Option 1 is to have 8 Soccer and 1 Baseball camp sessions that would last 94 days altogether.

Option 2 has 3 Soccer and 5 Baseball camp sessions that would last 100 days.

now, let,

x days for Soccer and, y days for Baseball camp, are needed to run each of the camps sessions .

then, we have,

8x + y = 94 .....1

3x+ 5y = 100 .....2

solving we get,

equation 1 => 40x + 5y = 470

now, subtracting, we get,

37x = 370

so, x = 10

now, solving we get,

y = 14

Hence, The solution is; 10 days for Soccer and, 14 days for Baseball camp, are needed to run each of the camps sessions .

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Answer:

9

Step-by-step explanation:

3x^2 + 3x - 9

Substitute x = 2 into the equation.

3(2)^2 + 3(2) - 9

3(4) + 6 - 9

12 + 6 - 9

18 - 9 =

9

The reasoning for the third step of the proof would be "Corresponding parts of congruent triangles are congruent." Let's go through the explanation:

1. Given: Quadrilateral ABCD is a rectangle.

2. Given: AB & CD (Opposite sides of a rectangle are equal).

3. To prove: AC & BD.

To prove that AC is equal to BD, we can utilize the property that opposite sides of a rectangle are equal (step 2). In a rectangle, opposite sides are parallel and congruent. Therefore, we have AB || CD and AB = CD.

Now, we need to show that the triangles ABAD and ACDA are congruent, specifically using the SAS (Side-Angle-Side) congruence theorem. The congruence of these triangles will allow us to establish the equality of their corresponding parts, including AC and BD.

4. Given: AD = AD (Reflexive Property of Equality).

5. By step 2, we know AB = CD. Additionally, AD = AD is given (Reflexive Property of Equality).

6. By step 3, ZBAD = ZCDA.

7. Using SAS triangle congruence theorem, we can conclude that triangles ABAD and ACDA are congruent.

Finally, according to the "Corresponding parts of congruent triangles are congruent" property, we can state that AC = BD. This establishes the equality of the diagonals of the rectangle.

Therefore, the correct reasoning for step 3 is "Corresponding parts of congruent triangles are congruent."

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The equation that satisfies the data in the table is: A. y = 2/15(x) + 2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 - 0)/(0 + 15)

Slope (m) = 2/15

At data point (0, 2) and a slope of 2/15, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 2/15(x - 0)  

y = 2/15(x) + 2.

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Answer: 59/16 or 3 11/16

Step-by-step explanation:

11 4/5 ÷ 3 1/5

= 59/5  ÷ 16/5

= 59/5 x 5/16

= 59 x 5/ 5 x 16

= 295/80

= 295 ÷ 5/ 80 ÷ 5

= 59/16

= 3 11/16

Based on the image you provided, it appears to be a rectangular prism (a box) with given dimensions. To find the volume of the rectangular prism, we can use the formula:

Volume = Length × Width × Height

From the image, we can see the following dimensions:

Length = 6 cm

Width = K cm

Height = 22 cm

To find the volume, we need to know the value of K. Unfortunately, the value of K is not provided in the image or the previous conversation.

If you provide the value of K, I can calculate the volume of the rectangular prism for you.