Determine the surface area of the trapezoidal prism to nearest whole number (no unit is required)

The product of the matrices ( 5 6 ) and ( 1 7 ) is equal to 47.

The number of columns in the first matrix must equal the number of rows in the second matrix in order for two matrices to be multiplied. In this instance, the 1x2 multiplied by 2x1 matrix satisfies this requirement.

In many disciplines, such as computer graphics, physics, and engineering, matrix multiplication is a key idea in linear algebra. It can be used to transform data, determine eigenvalues and eigenvectors, and solve systems of linear equations.

To get the product of two matrices, we need to perform the dot product of each row in the first matrix with each column in the second matrix.

Given the matrices ( 5 6 ) and ( 1 7 ), we can perform the dot product as follows:

( 5 6 ) ( 1 7 ) = ( (5)(1) + (6)(7) )

= (5 + 42)

= 47

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The value of x is 41

When three line segments cross each other at three non-collinear points, a triangle is formed. A triangle is a three-sided polygon with three sides and three angles.

Using the Angle Bisector Theorem and assuming ED is an angle bisector

⇒ EG/EH = DG/HD

⇒ 49 / 58.8 = 35 / (x + 1)

⇒ 49 (x+1) = 58.8×35 ⇒ 2058

⇒ x + 1 = 2058 /49

⇒ x + 1 = 42

⇒ x = 41

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Complete question-

Assuming ED is an angle bisector and applying the Angle Bisector Theorem.

The value of x is 41

A polygon with three sides and three vertices is called a triangle. It belongs to the basic geometric shapes. A triangle with the parts A, B, and C is referred to as triangle ABC. Any three points that are not collinear in Euclidean geometry result in a separate triangle and a distinct plane. When three line lengths cross each other at three non-collinear points, a triangle is formed. A triangle is a three-sided polygon because it has three sides and three angles.

Assuming ED is an angle bisector and applying the Angle Bisector Theorem

[tex]\frac{EG}{EH} =\frac{DG}{HD} \\\\\frac{49}{58.8} =\frac{35}{(x+1)}[/tex]

49 (x+1) = 58.8×35 ⇒ 2058

x + 1 = 2058 /49

x + 1 = 42

x = 41

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The complete question is,

It takes 105 minutes for the second hose alone to fill the pond.

An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, among others.

Let x be the time it takes for the second hose to fill the pond alone.

The rate at which the first hose fills the pond is 1/42 (ponds/minute).

The rate at which the second hose fills the pond is 1/x (ponds/minute).

The combined rate at which the two hoses fill the pond is 1/30 (ponds/minute).

Since they are filling the same pond, we can add their rates to get the combined rate:

⇒ 1/42 + 1/x = 1/30

To solve for x, we can simplify this equation;

⇒ 30x + 1260 = 42x

Subtracting 30x from both sides gives:

⇒ 1260 = 12x

⇒ x = 105

Therefore, it takes the second hose alone 105 minutes to fill the pond.

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Sofia has a rectangle poster that is 42 inches long and 30 inches wide.  The area of the poster is 1260 square inches.

The area of ​​a rectangle depends on its sides. Basically, the area formula is equal to the product of the length and width of a rectangle. When we talk about the perimeter of a rectangle, it is equal to the sum of its four sides. Therefore, we can say that the area bounded by the perimeter of a rectangle is its area. But in the case of a square, since all sides are equal, the area of ​​the square will be equal to the square of its length.

area of ​​rectangle = length x width

We know that :

Area of rectangle = Length × Breadth

                             = 42 × 30 inches

                             = 1260 square inches.

Therefore, the area of a rectangle is 1260 square inches.

Complete Question:

Sofia has a rectangular poster that is 42 inches long and 30 inches wide. What is the area of the poster in square inches? Do not round your answer. Be sure to include the correct unit in your answer.

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Answer:

Step-by-step explanation:

xy=34

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.02}{12}\right)^{12\cdot 15} \implies A \approx 4048.57[/tex]

As a result, the probability that individuals spend between 24.7 as well as 25.5 minutes per day on average reading books is roughly 0.919, or 91.9%.

The probability that an occurrence will occur is determined by probability: P(A) = f / N. Probability and odds are linked, but probability determines what the percentages are.

Given:

Sample size (n) = 50

Sample mean (x) = 25 minutes

Standard deviation (σ) = 1.5 minutes

Range of interest: 24.7 minutes ≤ x ≤ 25.5 minutes

To find the probability that the mean time spent reading each day is between 24.7 and 25.5 minutes, we need to standardize the sample mean using the Central Limit Theorem and the z-score formula:

z = (x - μ) / (σ / √(n))

where μ is the population mean (unknown), σ is the population standard deviation (known), and √(n) is the square root of the sample size.

We can approximate the population mean with the sample mean since the sample size is large (n ≥ 30) and assume a normal distribution for the sample mean.

First, we standardize the lower bound of the range:

z1 = (24.7 - 25) / (1.5 / √(50)) = -1.76

Then, we standardize the upper bound of the range:

z2 = (25.5 - 25) / (1.5 / √(50)) = 1.76

Using a standard normal distribution table or calculator, we can find the area under the curve between z1 and z2:

P(-1.76 ≤ z ≤ 1.76) ≈ 0.919

Therefore, the probability that the mean time people spend reading books each day is between 24.7 and 25.5 minutes is approximately 0.919 or 91.9%.

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Suav would have run approximately [tex]$970$[/tex] miles in [tex]$25$[/tex] weeks, to the nearest whole number.

What are the whole numbers?

Whole numbers are the set of numbers that include all positive integers (1, 2, 3, ...) as well as zero (0). Whole numbers do not include any negative numbers or fractions. Therefore, the set of whole numbers is {0, 1, 2, 3, ...}.

Suav runs [tex]$20$[/tex] miles the first week. Let's use a formula to calculate the number of miles he runs in subsequent weeks. Let [tex]$m$[/tex] be the number of miles he runs in a particular week, and [tex]$w$[/tex] be the number of weeks elapsed since the first week. Then, we have:

[tex]$$m = 20 \cdot 1.05^{w-1}$$[/tex]

This formula takes into account the [tex]$5%$[/tex] increase in miles each week, starting from the initial [tex]$20$[/tex] miles in the first week.

To find the total number of miles Suav runs over [tex]$25$[/tex] weeks, we can sum up the miles he runs in each week using the formula above. That is,

[tex]$$\text{Total miles} = 20 + m_2 + m_3 + \cdots + m_{25}$$[/tex]

where [tex]$m_2, m_3, \ldots, m_{25}$[/tex] are the number of miles he runs in the second to [tex]25$th[/tex] week, respectively.

We can use the formula for [tex]$m$[/tex] to find each of these values. For example, the number of miles he runs in the second week is:

[tex]$$m_2 = 20 \cdot 1.05^{2-1} = 21$$[/tex]

Similarly, we can find the number of miles he runs in each of the other weeks:

[tex]m_3 &= 20 \cdot 1.05^{3-1} = 22.05[/tex]

[tex]m_4 &= 20 \cdot 1.05^{4-1} = 23.103[/tex]

[tex]&\vdots[/tex]

[tex]m_{25} &= 20 \cdot 1.05^{25-1} = 57.597[/tex]

Now, we can substitute these values into the formula for the total miles and simplify:

[tex]\text{Total miles} &= 20 + 21 + 22.05 + \cdots + 57.597 \&\approx 970[/tex]

Therefore, Suav would have run approximately [tex]$970$[/tex] miles in [tex]$25$[/tex] weeks, to the nearest whole number.

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Answer

well if it is 5% each week, then it would be 20 +1. doing this for 25 weeks means it would be 20 + 25 then.

Sorry if wrong. i don't know if u do 5% after each time or from the main number. it doesn't say weather or not.

Step-by-step explanation:

p lz give me brainliest

Joshua scored 65, 80, 85, and 100 on his math tests. 90 score Joshua has to earn on his fifth test to have a mean score of 85

       To calculate the mean score, add up all of the scores and divide by the total number of tests.

       To figure out what score Joshua needs to get on the fifth test, use the formula:

            Total score = mean score × total number of tests

            Total score = 85 × 5

            Total score = 425

  Joshua's total score on all five tests must be 425. He has already earned 330 points from his first four tests (65 + 80 + 85 + 100).

  Therefore, Joshua must earn 95 points on his fifth test (425 - 330 = 95) to achieve a mean score of 85.

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The fraction that is most often used to approximate pi is 22/7

The fraction 22/7 is often used to approximate pi. This is because 22/7 is a common fraction that is close to the decimal approximation of pi, which is 3.14159265359...

While pi is an irrational number that cannot be expressed as a finite decimal or fraction, 22/7 is a commonly used approximation that is easy to remember and gives a reasonable estimate of pi to two decimal places.

However, it is important to note that there are other fractions that can be used to approximate pi with greater accuracy, such as 355/113, which is accurate to six decimal places.

Nonetheless, 22/7 remains a popular approximation of pi in various contexts, from mathematics and engineering to everyday life.

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The reason for step 2 is as follows:

If parallel lines are cut by a transversal, then the corresponding angles are said to be congruent to each other.

A unique sort of quadrilateral made up of parallel lines is called a parallelogram. Any angle between adjacent sides of a parallelogram is possible, but only if the sides are parallel.

If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Hence, if both sets of opposite sides are parallel and equal, a quadrilateral is referred to as a parallelogram.

Here in the question,

Its already given that AB and DC re parallel and equivalent to each other.

So, the AB and DC are cut by a transversal AC and the corresponding angles that are ∠BAC and ∠DCA are congruent to each other.

Hence, the quadrilateral is a parallelogram.

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Answer:

I hope this helps

y = 5x - 3

Answer: 9 weeks

i hope this helps you

Answer:

ans=8.80inch

Step-by-step explanation:

given,

radius(r)=1.6 inch

height(h=2.5 inch

laternal area of cone = AL=√πrh2+r2

√3.14*2.5^2+1.6^2

8.80 inch

The approximate lateral area of the cone is,

⇒ LSA = 10.5 inches

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

To find the approximate lateral area of the cone, we need to know the height of the cone.

Since we are not given the height, we can use the Pythagorean theorem to find it:

Slant height² = h² + r²

2.5² = h² + 1.6²

6.25 = h² + 2.56

h² = 6.25 - 2.56

h² = 3.69

h = √3.69

h = 1.92 in

We know that;

The lateral surface area of a cone is calculated using the formula,

LSA =πr√(r² + h²) square units.

Substitute all the values, we get;

LSA =πr√(r² + h²) square units.

LSA = 3.14 × 1.4√(1.6² + 1.9²) square units.

LSA = 5 √2.6 + 3.6

LSA = 5 √4.2

LSA = 5 × 2.1

LSA = 10.5 inches

Thus, The approximate lateral area of the cone is,

⇒ LSA = 10.5 inches

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After solving the given equations the value of x and y are -2 and 5 respectively.

An equation is a mathematical statement consisting of two expressions joined by an equal sign.

For example, 3x – 5 = 16 is an equation.

Solving this equation gives the value of the variable x as x = 7.

So, the equations are:

7x+10y = 36 ...(1)

y = 2x +9  ...(2)

Now, insert 2x+9 in equation (1):

7x+10y = 36

7x+10(2x +9) = 36

7x+20x+90 = 36

27x = -54

x = -54/27

x = -2

Then, the value of y:

y = 2x +9

y = 2(-2) +9

y = -4+9

y = 5

Therefore, after solving the given equations the value of x and y are -2 and 5 respectively.

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Answer: I really don't know the answer , and im really good at this math problem but i forgot how to do this

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Answer:

Katelyn needs to mow 3 lawns to have enough money to buy the skateboard.

What are inequalities and their types?

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let, 'x' be the no. of lawns she has to mow.

Given, Katelyn wants to buy a $75.00 skateboard and she has $25.00 saved and she mows lawns to make extra money and earns $20.00 for each lawn he mows.

Therefore the inequality that represents this context is,

20x + 25 ≥ 75.

20x ≥ 75 - 20.

20x ≥ 55.

x ≥ 55/20.

x ≥ 2.75, But she has to mow a lawn completely to get paid so she must mow 3 lawns.

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

To find a fraction equivalent to a percentage we have to simply put the number over 100!

For 25% this would look like [tex]\frac{25}{100}[/tex]

Now to simply this, we have to find the highest common factor in both which is 25! This means that both values (25 and 100) can divide by 25 to give a whole number!

To divide both the numerator and denominator we will get the result [tex]\frac{1}{4}[/tex]

Hope this helps, have a lovely day! :)

A. Investment 1: ROI = 20%, Investment 2: ROI = 18%, Investment 3: ROI = 24%. B. Select Investment 3 with the highest ROI of 24% as it generates the most return for the investment amount.

C. Investment 3 is attractive with positive residual income, but from Brown's perspective, the imputed interest charge may reduce overall profitability.

A. To calculate the ROI for each investment, we can use the following formula:

ROI = (Income / Investment) x 100%

For Investment 1: ROI = (50,000 / 250,000) x 100% = 20%

For Investment 2: ROI = (54,000 / 300,000) x 100% = 18%

For Investment 3: ROI = (96,000 / 400,000) x 100% = 24%

B. If the manager's focus is on Glengarry's divisional performance, he would select Investment 3 because it has the highest ROI of 24%. This investment generates the highest return for the amount invested, which is the primary concern for divisional performance.

C. To calculate the residual income for Investment 3, we need to subtract the imputed interest charge from its profit margin traceable to the division:

Residual Income = Profit margin traceable to the division - (Average asset investment x Imputed interest rate)

Residual Income = 96,000 - (400,000 x 22%) = 96,000 - 88,000 = 8,000

From Glengarry's perspective, Investment 3 is attractive because it generates a positive residual income of $8,000. However, from Brown's perspective, it may not be as attractive because the imputed interest charge reduces the overall profitability of the investment.

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Complete question is in the image attached below

The area of the shaded segment of the circle will be 10.45cm².

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

The area of the segment will be calculated thus:

63°/360° × πr² - (1/2 × 10 × 10 × sin 63°)

= 63/360 × 22/7 ×10² × (1/2 × 10 × 10 × sin 63°)

= 55 - 44.55

= 10.45cm²

Therefore, the area of the shaded segment of the circle will be 10.45cm².

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The height of the pole is 220 centimeters. We can solve it in the following manner.

We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).

Let h be the height of the pole. Then, we have:

h² + 21² = 221²

Simplifying the right side of the equation, we get:

h² + 441 = 48841

Subtracting 441 from both sides, we get:

h² = 48400

Taking the square root of both sides, we get:

h = 220

Therefore, the height of the pole is 220 cm.

So, the answer is 220 centimeters.

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The value of such that the matrix is the augmented matrix of a linear system with The system has an infinite number of solutions if $k=-1$.

To find out the value of $k$ that results in the matrix being the augmented matrix of a linear system with infinitely many solutions, you need to reduce the matrix to row echelon form and check the conditions. If you get a row of all zeroes but the last entry in that row is not zero, then there is no solution. If you get a row of all zeroes including the last entry in that row, then there are infinitely many solutions. Therefore, the value of $k$ that leads to the augmented matrix of a linear system with infinitely many solutions is $k=-1$.

A system of linear equations has an infinite number of solutions if and only if its augmented matrix, after being transformed to row-echelon form, has at least one free variable column.

The matrix in question is given as:

[tex]$$\begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix}$$[/tex]

To find the value of $k$, we need to convert it to a row-echelon form.

[tex]$$ \begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix} \overset{R2\rightarrow R2+\frac{3}{2}R1}{\longrightarrow} \begin{bmatrix}2 & -2 & 4 \\ 0 & 0 & 0 \\ 1 & -1 & k\end{bmatrix} $$[/tex]

Notice that the second row of the matrix is all zeros, so the system either has no solution or has an infinite number of solutions. Therefore, we need to determine the value of $k$ to figure out which of the two cases apply. Since the third row is independent, we can choose to work with it only.

[tex]$$1a - 1b = c \rightarrow c = a - b$$[/tex]

We can also write it as a linear combination of $a$ and $b$:

[tex]$$\begin{aligned} c &= a - b \\ &= a(1) + b(-1) \end{aligned}$$[/tex]

Therefore, it follows that if $k$ equals -1, we can rewrite the last row as a linear combination of the first two rows.

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The equation in standard form with integer coefficients is -5x + 10y = -6.

A coefficient is a numerical or constant multiplier of a variable, term or expression.

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A is positive. To convert the given equation y = (1/2)x - (3/5) into standard form, we can multiply both sides by the common denominator of 2 and 5, which is 10. This gives:

10y = 5x - 6

Rearranging the terms, we get:

5x - 10y = 6

Multiplying both sides by -1 to get the coefficient of x positive, we get:

-5x + 10y = -6

Therefore, the equation in standard form with integer coefficients is -5x + 10y = -6.

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In right angle triangle ΔXYZ  in which ∠XYZ = 90° and ∠XZY i= 25°.

YZ =  33 inch, the length of XZ to the nearest hundredth is approximately 13.99 inches.

A trigonometric function is a mathematical function that relates the angles of a right triangle to the ratios of its sides. Three basic trigonometric functions are sine (sin), cosine (cos), and tangent (tan).

In a right triangle, if one angle is θ (where θ is not the right angle), then we can define the following trigonometric functions:

sine of θ (sin θ): the ratio of the length of the side opposite θ to the length of the hypotenuse

cosine of θ (cos θ): the ratio of the length of the adjacent side to the length of the hypotenuse

tangent of θ (tan θ): the ratio of the length of the side opposite θ to the length of the adjacent side

We can use the trigonometric function sine to relate the lengths of the sides in the right triangle XYZ. In particular, we know that:

sin(25°) = XZ / 33

To solve for XZ, we can multiply both sides by 33 and simplify:

XZ = 33 sin(25°)

XZ ≈ 13.99 (rounded to the nearest hundredth)

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The classification of the angles are:

20° and 70°: complementary angles.

20° and 160°: supplementary angles

20° and 20°: vertical angles

Congruent angles are defined as two or more angles that are identical to each other. Thus, the measure of these angles are equal to each other. These type of angles do not make any difference in the congruence of angles, which tells us that they can be acute, obtuse, exterior, or interior angles.

Complementary angles are defined as two angle that sum up to 90 degrees. Thus: 20° and 70° are complementary angles.

Supplementary angles are defined as two angles that sum up to 180°. Thus: 20° and 160° are supplementary angles

Vertical angles are defined as angles that are opposite of each other when two lines cross. Thus they are congruent. Thus:

20° and 20° are vertical angles

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Answer:

kilometers she has walked his year is 1199.814 km

i hope it helps

have a nice day

Step-by-step explanation:

The correct graph that shows the solution to x - 2y > 9 is B.

What is graph?

In mathematics, graphs can represent functions or equations, such as a line on a coordinate plane or a curve in a three-dimensional space. Graphs can also be used to represent data, such as a bar graph or a scatterplot, which can help to identify trends or correlations between different variables.

To graph the solution to the inequality x - 2y > 9, we can start by graphing the boundary line x - 2y = 9, which is the equation that results from replacing the inequality symbol with an equal sign.

The boundary line can be graphed by plotting two points on the line and connecting them with a straight line. To do this, we can choose any two values for x and y that satisfy the equation x - 2y = 9, such as:

We need to determine which side of the boundary line represents the solution to the inequality x - 2y > 9. To do this, we can choose a test point on one side of the boundary line, such as (0, 0), and substitute its coordinates into the inequality.

Substituting (0, 0) into the inequality x - 2y > 9 gives:

0 - 2(0) > 9

which simplifies to:

0 > 9

The side of the line containing (0, 0) is not the solution. Therefore, the solution to the inequality x - 2y > 9 is the side of the line that does not contain the point (0, 0).

Therefore, the correct graph that shows the solution to x - 2y > 9 is B.

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Answer:

80:3

Step-by-step explanation:

8m = 800cm, so the ratio is 800cm:30cm

This can be divided by 10cm on both sides to get 80:3

regular price is 100%, so if we take off 85% from that, that'd be 100% - 85% = 15%, so the sale price is really 15% of the regular price, well, we know regular price is $15.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 15}}{\left( \cfrac{15}{100} \right)15}\implies \text{\LARGE 2.25}[/tex]

Answer: 6.69 dollars

Step-by-step explanation: 33.45/5 = 6.69

Answer:6.69

Step-by-step explanation:you basically divide 33.45 by 5 and the will get you 6.69 which is the unit price of pairs of socks