A triangular garden is to be split so that the angle at vertex B is bisected. This diagram was supplied by the landscape architect, but you do not have a way to measure the angles at B. You do have the given side lengths, so what is the length of side that will allow the angle at B to be bisected?

A diagram shows a triangle ABC. BD is a line drawn to the base AC. The length of AB is 5 m, BC is 7 m, AD is x m, DC is 4 m, and AC is 12 m.

The probability that Cynthia's morning porridge will be just right is 15%.

Probability is defined as the likeliness of an event to happen. It can be determined by dividing the total number of the desired outcome by the total number of samples.

The sum of the probabilities in a probability distribution is always 1.

If there are three outcomes: too cold, just right, and too hot, then the sum of their probabilities is equal to 1 or 100%.

P(too cold) + P(just right) + P(too hot) = 100%

35% + P(just right) + 50% = 100%

P(just right) = 100 - (35 + 50)

P(just right) = 100 - 85

P(just right) = 15%

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Answer:

362880 ways

Step-by-step explanation:

Given

10 digits

Required

Number of 10 digits that can be formed if no repetition and 2 must always start;

Since digit 2 must always start and no repetition is allowed, then there are 9 digits left

Digit 2 can only take 1 position

9 digits can be arranged without repetition in 9! ways;

Calculating 9!

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

\(9! = 362880\)

Number of arrangement  = 1 * 362880

Number of arrangement  = 362880 ways

The cross product of vectors \(\(a = \mathbf{i} - \mathbf{j} - \mathbf{k}\)\) and \(\(b = \mathbf{i} + \mathbf{j} + \mathbf{k}\)\) is \(\(a \times b = \mathbf{0}\)\)

and \(\(a \times b\)\) is orthogonal to both \(\(a\)\\\) and \(\(b\)\).

To obtain the cross product \(\(a \times b\)\) of vectors \(\(a = \mathbf{i} - \mathbf{j} - \mathbf{k}\)\) and \(\(b = \mathbf{i} + \mathbf{j} + \mathbf{k}\)\), we can use the determinant formula:

\(\[a \times b = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & -1 & -1 \\ 1 & 1 & 1 \end{vmatrix}\]\)

Expanding the determinant, we have:

\(\[a \times b = (\mathbf{j} \cdot \mathbf{k} - \mathbf{k} \cdot \mathbf{j})\mathbf{i} - (\mathbf{i} \cdot \mathbf{k} - \mathbf{k} \cdot \mathbf{i})\mathbf{j} + (\mathbf{i} \cdot \mathbf{j} - \mathbf{j} \cdot \mathbf{i})\mathbf{k}\]\)

Simplifying further:

\(\[a \times b = (0)\mathbf{i} - (0)\mathbf{j} + (0)\mathbf{k}\]\)

Therefore, \(\(a \times b = \mathbf{0}\)\).

To verify that \(\(a \times b\)\) is orthogonal to both \(\(a\) and \(b\)\), we can take their dot products.

\(\((a \times b) \cdot b = \mathbf{0} \cdot (\mathbf{i} + \mathbf{j} + \mathbf{k}) = 0\)\)\(\((a \times b) \cdot a = \mathbf{0} \cdot (\mathbf{i} - \mathbf{j} - \mathbf{k}) = 0\)\)

Since both dot products are zero, it confirms that \(\(a \times b\)\) is orthogonal to both \(\(a\)\\\) and \(\(b\)\).

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To increase usability in a spreadsheet, you can use comments, descriptive labels, and data validation.

To increase usability in a spreadsheet, you can utilize the following techniques:

1. Comments: Comments allow you to add explanatory notes or instructions within cells. They can provide additional context or clarify the purpose of certain data or formulas. Users can view comments by hovering over the respective cell, making it helpful for collaboration and documentation.

2. Descriptive Labels: Instead of relying solely on cell references or generic labels, use descriptive labels that clearly indicate the purpose of each column, row, or range of cells. This approach enhances readability and makes it easier for users to understand the data and navigate through the spreadsheet.

3. Data Validation: Implement data validation rules to ensure the accuracy and integrity of the data entered into the spreadsheet. Data validation allows you to define constraints or conditions for input, such as numeric ranges, predefined lists, or specific text formats. It helps prevent errors and assists users in entering valid data.

4. Formatting: Properly formatting the cells, columns, and rows can greatly enhance usability. Use consistent formatting for similar types of data, apply color schemes or conditional formatting to highlight important information or trends, and adjust the column widths and row heights to optimize readability.

5. Sheet Organization: Organize the spreadsheet by using multiple sheets if needed. Group related information on separate sheets, and provide clear sheet names that reflect the content or purpose of each sheet. This helps users locate and navigate to specific sections or data within the spreadsheet.

6. Clear Instructions or Documentation: Provide clear instructions or documentation either within the spreadsheet or as separate documentation. Explain the purpose of the spreadsheet, any specific procedures or workflows, and how to interpret the data or use any embedded formulas or macros. This helps users understand the spreadsheet's functionality and ensures consistent usage.

7. Error Handling: Implement error handling mechanisms to provide informative error messages or alerts when users input incorrect or incompatible data. Clear error messages guide users in correcting their input and reduce frustration when dealing with potential errors.

By incorporating comments, descriptive labels, data validation, formatting, sheet organization, clear instructions/documentation, and error handling, you can significantly enhance the usability of your spreadsheet and make it more user-friendly for both yourself and others who interact with it.

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Answer:

3034 grams

Step-by-step explanation:

to find one serving divide the total grams by grams per serving:

106200/35

=3034.28571429=3034(rounded to nearest whole number)

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Brenda's total cost at restaurant is $74.96

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.

Brenda's bill before tax and tip is equal to $58.45

A tip of 20% on the bill before tax is given.

Hence, tip value = 20% of $58.45

= $(20×58.45)/100

= $11.69

Tax levied is 8.25% on bill.

Hence, tax amount = 8.25% of $58.45

= $(8.25×58.45)/100

= $4.82

Hence, total bill is equal to the sum of the original bill with the tip along with tax levied, which is equal to

$(58.45+11.69+4.82)

= $74.96

Brenda's total cost at restaurant is $74.96

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Option (A) 18 = 0.1s

Step-by-step explanation:

Every seventh-grade student at Martin Middle School takes one world language class.

Now we will form the equation as per statement of the question.

Let total students of seventh-grade = s

" one tenth of seventh grade students take  French."

" Students who took French were 18."

So  of s = 18

(0.1)s = 18

therefore, Option (A) 18 = 0.1s is the answer.

Answer

a

Step-by-step explanation:

The value of the function of the quadratic equation is 83 when x=3.

6*(3)^2+7*3+8

=6*9+21+8

=54+21+8

=83

Hence the value is 83.

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Answer: The value of the function at x=3 is 83.

Step-by-step explanation:

To find the value of a function at a point, we have to put the value of the point into the function in place of x. Now in our question, to find the value we evaluate f(3).

f(3)=6* (3)^2 + 7*3 + 8

     = 54+21+8

Answer:

rectangle

Step-by-step explanation:

the question is asking what the shape of the cross section would be if it was perpendicular to the base. imagine a cylinder that you could slide a piece of paper into. what would be inside the cylinder? perpendicular to the base, it would be a rectangle. if it was parallel to the base, you'd then have a circle.

Answer:

No, No, Yes, No, Yes, Yes

Step-by-step explanation:

A graph is a function if it passes the vertical line test (in other words, every vertical line that can be drawn intersects the graph at no more than one point).

This is because for a function, each input must map onto no more than one output.

Answer:

you just multiply the values inside the parentheses. 11 x -4 x 12, so its -44 x 12, being -528

Step-by-step explanation:

Answer:

I think you are in a test..You should do by your own

Answer:

find the number of students who obtained more than 70 mark

Answer:

\( \sf \: 12th \: term = 37\)

Step-by-step explanation:

Common difference (d) is,

→ d = a2 - a1

→ d = -3 - (-7)

→ d = -3 + 7

→ [ d = 4 ]

Now the 12th term will be,

→ a1 + (d × (n - 1))

→ -7 + (4 × (12 - 1))

→ -7 + (4 × 11)

→ -7 + 44

→ 37 => 12th term

Hence, the answer is 37.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.

The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.

The measured distance on the map between Beitbridge and Musina is 1.3 cm.

To find the actual distance, we can set up a proportion using the scale:

1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.

Simplifying the proportion, we have:

1 / 3,000,000 = 1.3 / x.

Cross-multiplying, we get:

x = (1.3 * 3,000,000) / 1.

x = 3,900,000 / 1.

x = 3,900,000 km.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

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answer:

measure of angle 1 is 130°.

step by step:

angle 8 = 50

angle 6 = 50 (because of vertical angles)

angle 4 = 50 (because fo alternate interior angles)

therefore, angle 1 = 130 (because of linear pairs)

angle 1 and angle 4 add up to 180°

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The correct answer is (a) 10-15, 15-20. This is an example of a Discontinuous class.

In the context of statistical data and classification, a class is a group of observations or data points that share certain characteristics. Classes can be either continuous or discontinuous, depending on whether the values or categories they represent are continuous or not.

A discontinuous class is a set of values or categories that are not continuous, meaning there are gaps or breaks between them. In this case, the classes 10-15 and 15-20 are discontinuous because there is a gap between them at 15. In contrast, the classes 5-9 and 10-14 are continuous because there are no gaps between them, and 0-5 and 10-15 are also continuous because the lower bound of the second class is equal to the upper bound of the first class.

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The decision variable in this scenario is the model to be produced, which can be represented by the variables A, B, and C. The output variable is the cost of production for the next month.

To determine the model that should be produced to eliminate the cost for the next month, we need to analyze the cost of production for each model. The decision variable represents the choices available, which are models A, B, and C. Let's denote the decision variable as X, where X can take the values A, B, or C.

The output variable in this case is the cost of production for the next month. It is important to consider the costs associated with the raw materials, as well as other factors like delivery time and availability. To make an informed decision, we need to compare the costs associated with each model.

The decision can be made by evaluating the cost of production for each model based on the data provided in the table. By analyzing the cost for each model and considering other relevant factors, such as delivery time and availability of raw materials from the respective suppliers, we can determine which model should be produced to minimize the cost for the next month.

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Answer:

140

Step-by-step explanation:

The whole circle is 360.

You are given one angle measuring 220.

The remainder is angle ACB.

360-220=140.

Answer:

the correct answer of x is 16

Given:

Number of mails received a day = 55

Spam mails = 12

Alex opens 6 emails at random.

Number of emails that are not spam = 55 - 12 = 43

The probability that none of the emails are spam is:

Solving further, we have:

Therefore, the probabilty that none of the emails are spam is 0.210

ANSWER:

0.210

The locus of the centroid of the tetrahedron OABC is a sphere with radius p/3 and center at (p/3, p/3, p/3).

When a variable plane intersects the coordinate axes at points A, B, and C, and is at a constant distance p from the origin O(0,0,0), we can determine the locus of the centroid of the tetrahedron OABC. The centroid of a tetrahedron is the point of intersection of its medians, and each median divides the tetrahedron into two equal volumes.

Let's consider the coordinate axes as the edges of a cube. Since the plane intersects the axes at A, B, and C, we can visualize these points as the vertices of a triangle on one of the faces of the cube. The plane is equidistant from each vertex of the triangle, which means that it is equidistant from the three edges meeting at the origin O.

Now, if we consider the midpoints of the edges OA, OB, and OC, and connect them, we form the medians of the tetrahedron OABC. The centroid G is the point where these medians intersect. Since the plane is equidistant from the edges OA, OB, and OC, the medians will be perpendicular to these edges and pass through the midpoints.

Therefore, the centroid G will be located at the center of the triangle formed by the midpoints of the edges OA, OB, and OC. This center coincides with the center of the face of the cube on which the triangle is situated. As the plane is equidistant from the vertices A, B, and C, the centroid G will be at the same distance from each vertex.

Considering the distance from the origin O to the centroid G, it will be equal to one-third of the distance between the origin and any of the vertices A, B, or C. Since each vertex is at a distance p from the origin, the distance between O and G will be p/3. Thus, the locus of the centroid of the tetrahedron OABC is a sphere with radius p/3 and center at (p/3, p/3, p/3).

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1. The payment amount and the interest on the loan, we need to use the formula for calculating compound interest. The formula is: A = P(1 + r)^n

Where:
A is the total amount after n years,
P is the principal amount (loan amount),
r is the interest rate per period (in this case, 10% per year),
n is the number of periods (in this case, 2 years).

(a) To find the amount of the payment, we need to calculate the total amount (A) and subtract the principal amount (P):

A = P(1 + r)^n
A = $1,600,000(1 + 0.10)^2
A = $1,600,000(1.10)^2
A = $1,600,000(1.21)
A = $1,936,000

Payment amount = A - P = $1,936,000 - $1,600,000 = $336,000

(b) To find the amount of interest, we subtract the principal amount from the total amount:

Interest = A - P = $1,936,000 - $1,600,000 = $336,000

Therefore, the amount of the payment is $336,000 and the amount of interest is also $336,000.

2. To find the interest rate, we can use the formula for compound interest:

A = P(1 + r)^n

Where:
A is the future amount ($2.42 million),
P is the present amount ($2 million),
r is the interest rate per period (unknown),
n is the number of periods (1 year).

We can rearrange the formula to solve for r:

r = (A/P)^(1/n) - 1
r = ($2.42 million / $2 million)^(1/1) - 1
r = 1.21 - 1
r = 0.21

Therefore, the interest rate is 21%.

3. To find the original loan amount, we can use the formula for calculating the future amount with compound interest:

A = P(1 + r)^n

Where:
A is the total cost of repaying the loan ($82 million),
P is the original loan amount (unknown),
r is the interest rate per period (8% per year),
n is the number of periods (1 year).

We can rearrange the formula to solve for P:

P = A / (1 + r)^n
P = $82 million / (1 + 0.08)^1
P = $82 million / 1.08
P ≈ $75.93 million

Therefore, the amount of the original loan was approximately $75.93 million.

4. To find the number of years required for the investment to reach at least $425,000, we can use the formula for compound interest:

A = P(1 + r)^n

Where:
A is the future amount ($425,000),
P is the initial investment ($280,000),
r is the interest rate per period (15% per year),
n is the number of periods (unknown).

We can rearrange the formula to solve for n:

n = log(A/P) / log(1 + r)
n = log($425,000/$280,000) / log(1 + 0.15)
n ≈ 4.61 years

Therefore, it would take approximately 4.61 years for the investment to cumulate to at least $425,000 at a 15% per year interest rate.

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Answer:

r = 8

Step-by-step explanation:

\(\frac{3.6}{3.15}\) = \(\frac{r}{7}\) ( cross- multiply )

3.15r = 3.6 × 7 = 25.2 ( divide both sides by 3.15 )

r = \(\frac{25.2}{3.15}\) = 8

Answer:

8

Step-by-step explanation:

Check the picture below.

The height of the flagpole is 5.25 ft.

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, You must order a new rope for the flagpole. To find out what length of rope is needed, you observe that the pole casts a shadow of 11.8 feet on the ground. The angle of elevation of the sun is 24°.

The situation create a right triangle,

Let the height of the flagpole be x.

Using formula of height and distance,

tan 24° = x / 11.8

x = tan 24° × 11.8

x = 5.25

Hence, the height of the flagpole is 5.25 ft.

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Answer:

0.0412371134

Step-by-step explanation:

Answer:

24.25 hope that helps

Step-by-step explanation:

Answer:

x= 56 x= 89

Step-by-step explanation:

When a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid.

To understand why this is the case, it is helpful to visualize a rectangular pyramid. A rectangular pyramid is a three-dimensional figure with a rectangular base and four triangular faces that meet at a single point at the top, known as the vertex.

If a plane is passed through the pyramid perpendicular to the base but not through the vertex, it will intersect each of the four triangular faces of the pyramid at a different angle, resulting in a cross section that has four sides.

Since the base of the rectangular pyramid is a rectangle, the two opposite sides of the trapezoid cross section will be parallel, and the other two sides will be non-parallel. The shape and size of the trapezoid cross section will depend on the orientation of the plane with respect to the rectangular pyramid.

In summary, when a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid with two parallel sides and two non-parallel sides.

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