The circle graph shows how a family budgets its annual income. If the total annual income is $125,000, what amount is budgeted for Clothing?

The spinner has 8 equal-sized sections, each labeled 1, 2, 3, or 4 and correct options are:

a. The spinner landing on 1 - 1 (Likely)

b. The spinner landing on an even number - 2 and 4 (Equally likely to occur or not occur)

c. The spinner landing on the number 8 - Impossible (0)

d. The spinner landing on a number - 1, 2, 3, and 4 (Equally likely to occur or not occur)

e. The spinner landing on the left side of the circle - Unlikely (2)

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.

Here,

a. The spinner landing on 1 - There is only one section labeled 1 on the spinner, out of a total of 8 sections. Therefore, the probability of the spinner landing on 1 is 1/8. On the probability scale provided, this probability would be located closer to "Likely" than to "Equally Likely to Occur or Not Occur", but not as close to "Certain".

b. The spinner landing on an even number - There are 4 sections labeled with even numbers (2 and 4), out of a total of 8 sections. Therefore, the probability of the spinner landing on an even number is 4/8 or 1/2. On the probability scale provided, this probability would be located exactly halfway between "Equally Likely to Occur or Not Occur" and "Certain".

c. The spinner landing on the number 8 - There is no section labeled 8 on the spinner, so this event is impossible. On the probability scale provided, this probability would be located at the very bottom of the scale, labeled "Impossible".

d. The spinner landing on a number - Every section of the spinner is labeled with a number, so this event is certain to occur. On the probability scale provided, this probability would be located at the very top of the scale, labeled "Certain".

e. The spinner landing on the left side of the circle - There are 2 sections labeled with numbers that are on the left side of the circle (1 and 2), out of a total of 8 sections. Therefore, the probability of the spinner landing on the left side of the circle is 2/8 or 1/4. On the probability scale provided, this probability would be located closer to "Unlikely" than to "Equally Likely to Occur or Not Occur", but not as close to "Impossible".

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Answer:

The axis of symmetry is at x = -2.

Step-by-step explanation:

To find the axis of symmetry of a quadratic function in the form of f(x) = ax^2 + bx + c, you can use the formula x = -b / (2a).

In the function f(x) = 2x^2 + 8x − 5, a = 2 and b = 8, so we can plug those values into the formula and get:

x = -b / (2a) = -8 / (2 * 2) = -2

Therefore, the axis of symmetry of the function f(x) = 2x^2 + 8x − 5 is located at x = -2.

This means that the graph of the function is symmetric with respect to the vertical line x = -2. Any point on the graph that is a distance of t from the line x = -2 will have a corresponding point on the graph that is also a distance of t from the line.

1. By simplifying and comparing, the value of x is 4

2. By simplifying and comparing, the value of x is 6

3. By simplifying and comparing, the value of x is 0.53 and the value of y is 4

From the question, we are to simplify the given expressions

1.

(4.2 × 10⁷) / (2 × 10³)

This can be expressed

(4.2 / 2) × (10⁷ / 10³)

Simplifying and applying the division law of indices

= 2.1 × 10⁷⁻³

= 2.1 × 10⁴

By comparison, the value of x is 4

2.

(7.2 × 10⁻⁸) ÷ (1.2 × 10⁻³)

This can be expressed as

(7.2 ÷ 1.2) × (10⁻⁸ ÷ 10⁻³)

Simplifying and applying the division law of indices

6 × 10⁻⁸ ⁻ ⁻³

6 × 10⁻⁸ ⁺ ³

6 × 10⁻⁵

By comparison, the value of x is 6

3.

(4.24 × 10⁶) ÷ (8 × 10²)

This can be expressed as

(4.24 ÷ 8) × (10⁶ ÷ 10²)

Simplifying and applying the division law of indices

= 0.53 × 10⁶ ⁻ ²

= 0.53 × 10⁴

By comparison, the value of x is 0.53 and the value of y is 4

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Therefore, the answer is option B 23 and 4/7 inch² that is at least 23 and 4/7 inch² paper is needed to wrap 6 mini muffins.

Total surface area refers to the sum of the areas of all the faces or surfaces of a three-dimensional object. It includes the areas of the base, top, and lateral faces of the object. For example, the total surface area of a cube is the sum of the areas of all six faces, while the total surface area of a cylinder includes the areas of both circular bases and the lateral surface area.

Here,

The surface area of each mini muffin can be calculated by finding the lateral surface area of the cylinder and adding the surface area of its circular bases. The diameter of each mini muffin is 2 inches, so the radius is 1 inch. The height is 1 and 1/4 inches. The lateral surface area of each mini muffin is given by:

Lateral surface area = height x circumference

Lateral surface area = (5/4) x 2 x πr

Lateral surface area = (5/4) x 2 x (22/7) x 1

Lateral surface area = 11/2 cm²

The surface area of each circular base is given by:

Surface area of base = πr²

Surface area of base = (22/7) x 1²

Surface area of base = 22/7 cm²

The total surface area of each mini muffin is given by:

Total surface area = Lateral surface area + 2 x Surface area of base

Total surface area = (11/2) + 2 x (22/7)

Total surface area = 69/14 cm²

To wrap 6 mini muffins, we need to multiply the surface area of one mini muffin by 6. So the total surface area needed is:

Total surface area = 6 x (69/14)

Total surface area = 207/7 cm² (approx.)

Converting to square inches and simplifying, we get:

Total surface area = 23 and 4/7 inch²

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Answer:

[tex]\large\boxed{\tt y = 115^{\circ}.}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the measure of} \ \tt \angle Y.[/tex]

[tex]\textsf{We are given a shape, but we aren't given what shape it is.}[/tex]

[tex]\large\underline{\textsf{What is a Shape?}}[/tex]

[tex]\textsf{A Shape is a specific outline sometimes dependent of how many sides it has.}[/tex]

[tex]\underline{\textsf{Shapes that depend on outlines;}}[/tex]

[tex]\underline{\textsf{Shapes that depend on the number of sides;}}[/tex]

[tex]\textsf{Mainly the opposite.}[/tex]

[tex]\textsf{Because our shape has 5 sides, it's dependent on the amount of sides it has, which}[/tex]

[tex]\textsf{makes the shape a Polygon.}[/tex]

[tex]\large\underline{\textsf{What is a Polygon?}}[/tex]

[tex]\textsf{A Polygon is a closed shape that classifies as a;}[/tex]

[tex]\textsf{The list goes on forever.}[/tex]

[tex]\textsf{Our shape is a Pentagon, due to the shape having 5 sides.}[/tex]

[tex]\large\underline{\textsf{What is a Pentagon made up of?}}[/tex]

[tex]\textsf{A Pentagon is a polygon that has 5 sides, meaning that it has 5 angles.}[/tex]

[tex]\textsf{The total of the angles is what we should find out with a pattern.}[/tex]

[tex]\underline{\textsf{What is the total of all the angles' measures of a Pentagon?}}[/tex]

[tex]\textsf{A Triangle has 3 sides with 3 angles, which add up to 180}^{\circ}.[/tex]

[tex]\textsf{A Quadrilateral has 4 sides with 4 angles, which add up to 360}^{\circ}.[/tex]

[tex]\textsf{The Pattern is that when an extra side is added, the total measure of the angles}[/tex]

[tex]\textsf{increase by 180}^{\circ}.[/tex]

[tex]\textsf{A Pentagon has 5 sides with 5 angles, which add up to} \ \boxed{\tt 540^{\circ}.}[/tex]

[tex]\textsf{Now that we know the total, we can form an equation.}[/tex]

[tex]\tt 540^{\circ} = 135^{\circ} + 112^{\circ} + 88^{\circ} + y^{\circ} + 90^{\circ}[/tex]

[tex]\textsf{Remember that Right Angles are 90}^{\circ} \ \textsf{angles that are represented with a box}[/tex]

[tex]\textsf{symbol.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{Now that we have our equation, we should \underline{combine like terms}, then use the}[/tex]

[tex]\textsf{\underline{subtraction rule of equality} to find the measure of y.}[/tex]

[tex]\underline{\textsf{Combine Like Terms;}}[/tex]

[tex]\tt 540^{\circ} = \boxed{135^{\circ}} + \boxed{112^{\circ}} + \boxed{88^{\circ}} + y^{\circ} + \boxed{90^{\circ}}[/tex]

[tex]\tt 540^{\circ} = 425^{\circ} + y^{\circ}[/tex]

[tex]\underline{\textsf{Use the Subtraction Rule of Equality;}}[/tex]

[tex]\tt 540^{\circ} - 425^{\circ} = 425^{\circ} - 425^{\circ}+ y^{\circ}[/tex]

[tex]\large\boxed{\tt y = 115^{\circ}.}[/tex]

A one-sample t-test is conducted to determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s. The test results fail to reject the null hypothesis, indicating that recent winners do not appear to be significantly different from those in the 1920s and 1930s.

To determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s, a one-sample t-test can be conducted. Using the given sample, the sample mean BMI is calculated to be 18.5.

The null hypothesis is that the population mean BMI of recent winners is equal to 19.2. The alternative hypothesis is that the population mean BMI of recent winners is different from 19.2.

Assuming a significance level of 0.05 and using a two-tailed test, the calculated t-value is -2.08 and the corresponding p-value is 0.057.

Since the p-value is greater than the significance level, we fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that recent Miss America winners have significantly different BMI compared to winners from the 1920s and 1930s.

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An exit ticket is an informal assessment tool used by educators to gauge student understanding of the content taught during a lesson. It is typically a brief activity, such as a short questionnaire or problem-solving task, that students complete at the end of the class.

This helps the teacher identify areas where students may need additional support or review. Exit tickets provide valuable insights into students' learning progress and inform future instruction.

The base of a pyramid refers to the flat surface on which the pyramid rests. In geometry, a pyramid is a polyhedron composed of a base and triangular faces that converge at a single vertex (the apex). The base can be a variety of shapes, including triangles, squares, rectangles, or other polygons.

The properties of the base, such as its area and perimeter, play a crucial role in determining the volume and surface area of the entire pyramid.

To connect these concepts, you could use an exit ticket to assess students' understanding of pyramids, specifically focusing on the properties and importance of the base. This could include questions related to calculating the area, perimeter, or identifying different types of pyramid bases.

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Answer:

1/9 ≅ 0.11

Step-by-step explanation:

Paragraph - 1: Introduction: A mathematical function called a logarithmic function uses logarithms, which are exponential functions' inverses. A logarithmic function has the generic form f(x) = loga(x).

A mathematical function called a logarithmic function uses logarithms, which are exponential functions' inverses. A logarithmic function has the generic form f(x) = loga(x). An essential mathematical topic, logarithmic functions are employed in many disciplines including physics, chemistry, biology, economics, and engineering. Using the pH scale to determine a solution's acidity and alkalinity is one practical use of logarithms.

Paragraph - 1: Introduction:

A mathematical function called a logarithmic function uses logarithms, which are exponential functions' inverses. A logarithmic function has the generic form f(x) = loga(x), where an is the base of the logarithm. The bases 10 and e are the most popular. The mathematical constant e, sometimes referred to as Euler's number, is roughly equal to 2.71828. A logarithm with base e is the natural logarithm, abbreviated as ln(x). A logarithmic function's parent function is f(x) = loga(x), where an is a real number with a positive sign. When the argument of the logarithm equals 1, the point where the function's graph crosses the x-axis is known as the x-intercept of a logarithmic function. There isn't a y-intercept. The graph of a logarithmic function has a vertical asymptote at x = 0.

Paragraph 2: Characteristics:

Logarithmic function f(x) = -log(x-7)-9 is provided. Any real integers bigger than 7 fall into the domain of the function since the logarithm's argument must be positive. Due to the fact that the logarithm approaches negative infinity as x approaches 7 from the right, the function's range includes any real integers that are less than or equal to -9. The function's final behaviour is that it approaches negative infinity as x approaches 7 from the right. The function's x-intercept is (8, 0), indicating that it crosses the x-axis at x = 8. Since the function approaches negative infinity as x moves away from 7 to the right, it has a vertical asymptote at x = 7.

Paragraph 3: Transformations:

The parent function, f(x) = log(x), which has a vertical asymptote at x = 0 and a y-intercept at 0, is transformed into the supplied function, f(x) = -log(x-7)-9) (1, 0). The provided function is created by taking the negative of the logarithm, moving it 7 units to the right on the horizontal axis, and 9 units downward on the vertical axis. The resulting function would be f(x) = -1/4 * log(1/8(x+3))+11 if we shift the provided function left by 3 units, reflect it over the y-axis, shift it down by 2 units, compress it by a factor of 8, and reflect it over the x-axis.

Paragraph 4: Evaluation:

For f(x) = -log(x-7)-9 let x = 8:

f(x) = -log(1)-9 = -9

For x = 10, f(x) = -log(3)-9 = -7.52288.

Paragraph 5 - conclusion:

An essential mathematical topic, logarithmic functions are employed in many disciplines including physics, chemistry, biology, economics, and engineering. Using the pH scale to determine a solution's acidity and alkalinity is one practical use of logarithms. My favourite aspect of logarithms is how they help us simplify complex calculations by reducing big numerical values into more comprehensible forms. Understanding how to employ logarithmic characteristics to simplify complex statements and solve problems was the most difficult part of studying logarithms.

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There are 20,149 different paths from A to B in the given hexagonal lattice, satisfying the given conditions.

To solve this problem, we can use the Principle of Inclusion-Exclusion (PIE). We start by counting the total number of paths from A to B without any restrictions, which is simply 6!/(3!3!) = 20,160. This is the number of ways to arrange 3 up arrows and 3 right arrows.

Next, we count the number of paths that violate the restriction on the middle segment. There are two cases to consider, The bug travels the middle segment from left to right: There are 3 choices for the path of the bug on the top half of the hexagon and 2 choices for the path on the bottom half, for a total of 3*2 = 6 paths.

The bug travels the middle segment from right to left: This is the same as case 1, so there are another 6 paths. However, we have counted some paths twice, namely those that violate both restrictions on the middle segment. There is only one such path, which is the one that starts with the up arrow, goes left on the top half of the hexagon, and goes right on the bottom half.

Thus, the total number of valid paths is 20,160 - 6 - 6 + 1 = 20,149.

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The correct answer to the given question about mapping quadrilateral ABCD onto quadrilateral HGEF is option D Translation 6 units left and 2 units down

To determine the transformation that maps quadrilateral ABCD onto quadrilateral HGFE, we need to compare the corresponding sides and angles of the two quadrilaterals.

Option 1: Rotation of 180° about the origin

A rotation of 180° about the origin would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, side AB of ABCD would not match side HG of HGFE after the rotation. Therefore, option 1 is incorrect.

Option 2: Reflection across the y-axis

A reflection across the y-axis would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, angle A of ABCD would not match angle H of HGFE after the reflection. Therefore, option 2 is incorrect.

Option 3: Reflection across the x-axis

A reflection across the x-axis would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, side BC of ABCD would not match side GF of HGFE after the reflection. Therefore, option 3 is incorrect.

Option 4: Translation 6 units left and 2 units down

A translation 6 units left and 2 units down would map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are congruent. Each point of ABCD would move left by 6 units and down by 2 units to reach its corresponding point in HGFE. Therefore, option 4 is the correct transformation that maps quadrilateral ABCD onto quadrilateral HGFE.

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Answer:

The remainder is 7.

Step-by-step explanation:

Let's pick 15 and 14. The sum of these two numbers is 29. Multiplying 29 by 3, we have 87. 87 divided by 10 is 8 with a remainder of 7.

Answer:

y = 2x - 7

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 )

here m = 2 , then

y = 2x + c ← is the partial equation

to find c substitute (2, - 3 ) into the partial equation

- 3 = 2(2) + c = 4 + c ( subtract 4 from both sides )

- 7 = c

y = 2x - 7 ← equation of line

Answer: 4(5+3) = 4(5) + 4(3) = 20 + 12 = 32

Step-by-step explanation:

Answer:

32=32 ?

Step-by-step explanation:

The correct statement regarding the transformations is given as follows:

g(x) is stretched vertically by a factor of 5 and translated 3 units to the right.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The transformations to the parent function in this problem are given as follows:

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Answer: 8 meters

Step-by-step explanation:

33x9=297

2376 divided by 297= 8

The height of the swimming pool is approximately 2.6 meters. This can be answered by the concept of Surface Area.

To calculate the height of the swimming pool, we can use the formula for the volume of a rectangular prism, which is V = lwh, where V is the volume, l is the length, w is the width, and h is the height. We know that the volume of the pool is 2,376 m3, the length is 33 meters, and the width is 9 meters.

Plugging these values into the formula, we get 2,376 = 33 x 9 x h. Solving for h, we get h = 2.6 meters.

Therefore, the height of the swimming pool is approximately 2.6 meters, which can be calculated by using the formula for the volume of a rectangular prism and plugging in the known values of length, width, and volume.

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The requried length of the line segment on number line SU is 25 units.

To find the length of the line segment SU, we need to subtract the coordinates of S from the coordinates of U and take the absolute value. So we have:

|SU| = |U - S| = |10 - (-15)| = |25| = 25

Therefore, the length of the line segment on number line SU is 25 units.

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Answer:

13

Step-by-step explanation:

The volume of the pyramid can be calculated using the formula:

Volume = (1/3) * base area * height

The base area of the pyramid is equal to the area of one of the square sides, which is:

Base area = 12 in * 12 in = 144 in^2

Therefore, the volume of the pyramid is:

Volume = (1/3) * 144 in^2 * 14 in = 2,688 in^3

Each wax cube has a volume of:

Volume of a wax cube = 6 in * 6 in * 6 in = 216 in^3

To find out how many wax cubes Josiah needs, we can divide the volume of the pyramid by the volume of each wax cube:

Number of wax cubes = Volume of pyramid / Volume of each wax cube

Number of wax cubes = 2,688 in^3 / 216 in^3 = 12.4444...

Since we can't use a fraction of a wax cube, Josiah will need to use 13 wax cubes to make the candle.

The surface area after larger by scale factor is  11700 [tex]in^2[/tex].

The surface area οf an οbject refers tο the οverall space filled by its surfaces. Many 3D shapes in geοmetry have variοus surface areas, which may be quickly estimated using the fοrmulas we shall learn in this lessοn. Twο categοries are used tο classify the surface area:

Here the given rectangular prism ,

Surface area = 1300 square inches

Here the given prism is larger by scale factor of 3 then,

=> surface area = 1300[tex]\times3^2[/tex] =  1300[tex]\times9[/tex] = 11700 [tex]in^2[/tex].

Hence the surface area after larger by scale factor is  11700 [tex]in^2[/tex].

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The final answer is 1 / 11

Deena has a total of 11 pairs of socks in her sock drawer. One pair of those 11 pairs is navy socks. Therefore, the probability that she will choose a pair of navy socks is 1/11.What is probability? Probability is the numerical measure of the possibility of an event taking place. Probability is calculated by dividing the number of successful outcomes by the total number of possible outcomes.The probability of Deena picking navy socks is calculated as:Probability of selecting navy socks = Number of pairs of navy socks/ Total number of pairs of socks in the drawerNumber of pairs of navy socks = 1Total number of pairs of socks in the drawer = 1 /11Probability of selecting navy socks = 1/11Therefore, the probability that Deena will select a pair of navy socks is 1/11.

Therefore, the answer is 1 / 11.

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Answer:

Step-by-step explanation:

1200x5= it is 6000

Answer:

900=5x + 1200

Step-by-step explanation:

The probability that Xeres arrives first AND Regina arrives last is 3.33%.

Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.

Here The number of possible arrangements of n elements is given by:

[tex]A_n=n![/tex]

In this problem:

6 people are invited, so the number of ways they can arrive is T = [tex]6![/tex]

Xeres first and Regina last, for the middle 4 there are  way D= 4! ways

Then the probability is P = [tex]\frac{D}{T}=\frac{4!}{6!}[/tex] =  0.0333 = 3.33%

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Todd drank 29.17% of the bottles. First, we need to calculate the total number of bottles drank by Lydia, Mitchell, and Alexa.

Lydia = (1/8) x 24 = 3 bottles

Mitchell = (33 1/3%) x 24 = (1/3) x 24 = 8 bottles

Alexa = 0.25 x 24 = 6 bottles

The total number of bottles drank by Lydia, Mitchell, and Alexa is 3 + 8 + 6 = 17 bottles.

Therefore, the number of bottles Todd drank is 24 - 17 = 7 bottles.

To find the percentage of bottles Todd drank, we can use the following formula:

Percentage = (Part/Whole) x 100%

Where the Part is 7 and the Whole is 24.

Percentage = (7/24) x 100% = 29.17%

Therefore, Todd drank 29.17% of the bottles.

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Answer:

The angle measurement will stay the same.

Step-by-step explanation:

When you scale a figure the angle measurements stay the same.

Helping in the name of Jesus.

To prepare the cash flow statement, we can use the indirect method, which involves adjusting the net income figure for non-cash items and changes in working capital to arrive at the net cash flow from operating activities. Then, we can account for cash flows from investing and financing activities to arrive at the net change in cash and cash equivalents.

Here's the cash flow statement for Year II:

Cash flow from operating activities:

Net income: Rs. 30,000 (180,000 - 100,000 - 50,000 - 5,000 - 5,000)

Adjustments for non-cash items:

Depreciation: Rs. 30,000 (230,000 - 200,000)

Changes in working capital:

Increase in stock: Rs. 10,000 (100,000 - 90,000)

Increase in debtors: Rs. 20,000 (60,000 - 40,000)

Increase in creditors: Rs. 10,000 (80,000 - 70,000)

Net cash flow from operating activities: Rs. 100,000

Cash flow from investing activities:

Purchase of fixed assets: Rs. 30,000 (230,000 - 200,000)

Net cash flow from investing activities: Rs. -30,000

Cash flow from financing activities:

Repayment of debentures: Rs. 20,000 (50,000 - 30,000)

Payment of dividends: Rs. 5,000

Net cash flow from financing activities: Rs. -25,000

Net change in cash and cash equivalents: Rs. 45,000 (100,000 - 30,000 - 25,000)

Cash and cash equivalents at the beginning of the year: Rs. 60,000

Cash and cash equivalents at the end of the year: Rs. 105,000

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Answer: [tex]F=30N[/tex]

Step-by-step explanation:

1. You know that the force acting on the object varies directly with the object's acceleration. Then, by definition, you have:

[tex]F=ka[/tex]

Where [tex]F[/tex] is the force acting on the object, [tex]a[/tex] is the object's acceleration and [tex]k[/tex] is the constant of proportionality.

2. Keeping this on mind, you can calculate the constant of proportionality by substituting [tex]F=12[/tex] and [tex]a=4[/tex] into the equation and solving for [tex]k[/tex]:

[tex]12=k4[/tex]

[tex]k=\dfrac{12}{4}[/tex]

[tex]k=3[/tex]

3. Now, you can calculate the force when the acceleration of the object becomes 10 m/s², as following:

[tex]F=3(10)[/tex]

[tex]F=30[/tex]

3. The result is:

[tex]F=30N[/tex]

Answer:

35. Radius= 12 cm

36. (B) 50 cm

Step-by-step explanation:

35.

TSA = 2πr(h+r)

Expanding the brackets, we get:

TSA = 2πrh + 2πr^2

Rearranging the equation, we get:

TSA - 2πrh = 2πr^2

Dividing both sides by 2π, we get:

r^2 = (TSA - 2πrh) / 2π

Taking the square root of both sides, we get:

r = √[(TSA - 2πrh) / 2π]

We need to simplify the given equation to solve for r.

r = √[(905.143) - 2(22/7)r(14)) / 2(22/7)]

r = √[(905.143) - (88/7)r] / (44/7)

Squaring both sides, we get:

r^2 = [(905.143) - (88/7)r] / (44/7)

Multiplying both sides by (44/7) and simplifying:

7r^2 - 88r - 905.143 = 0

Using the quadratic formula:

r = [88 ± √(88^2 - 4(7)(-905.143))] / (2(7))

r ≈ 12.009 or r ≈ -12.892

Since r represents the radius of a circle, which cannot be negative, we ignore the negative solution.

Therefore, the solution is r ≈ 12.009.

36.

We can use the formula for the volume of a cylinder:

volume = πr^2h

where r is the radius and h is the height of the cylinder.

First, we need to find the radius of the drum. The diameter is given as 56 cm, so the radius is half of that, or 28 cm.

Next, we can use the given volume of 123.2 liters. However, we need to convert liters to cubic centimeters (cm^3) since the dimensions are in centimeters.

1 liter = 1000 cm^3

So, 123.2 liters = 123,200 cm^3.

Now we can plug in the values:

123,200 cm^3 = π(28 cm)^2h

Simplifying:

123,200 cm^3 = 2464π cm^2h

Dividing both sides by 2464π cm^2:

50 cm = h

Therefore, the height of the drum is 50 cm.

3

when the line is at the y=ax+b form the gradient is equal to a

It means you would expect to win that amount, and if it's negative, it means you would expect to lose that amount.

To calculate the expected value of this bet, we first need to determine the probability of drawing two hearts and the probability of not drawing two hearts.

There are 52 cards in a standard deck, with 13 cards of each suit (hearts, diamonds, clubs, and spades). To calculate the probability of drawing two hearts without replacement, we consider the following:

1st card: The probability of drawing a heart is 13/52, as there are 13 hearts in the deck and 52 cards total.

2nd card: After drawing one heart, there are 12 hearts left and 51 cards total. The probability of drawing another heart is 12/51.

Thus, the probability of drawing two hearts is (13/52) * (12/51).

Next, we need to find the probability of not drawing two hearts. This can be calculated by subtracting the probability of drawing two hearts from 1.

Probability of not drawing two hearts = 1 - [(13/52) * (12/51)]

Now, we can calculate the expected value of the bet:

Expected value = (probability of winning * winnings) + (probability of losing * losses)

In this case, the winnings are $16, and the losses are $3.

Expected value = [(13/52) * (12/51) * $16] + {1 - [(13/52) * (12/51)]} * (-$3)

Now, let's calculate the expected value for 762 bets.

Expected value for 762 bets = 762 * {[(13/52) * (12/51) * $16] + {1 - [(13/52) * (12/51)]} * (-$3)}

Round the final expected value to two decimal places. If it's a positive value, it means you would expect to win that amount, and if it's negative, it means you would expect to lose that amount.

Know more about Probability here:

https://brainly.com/question/24756209

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