Find the unknown side length of the rectangle if its area is 11 m

Answer:

Step-by-step explanation:

We first have to find cos 275 and sin 275 and then put them into the formula:

cos 275 = .0872

sin 275 = -.9962

Therefore,

24(.0872 - .9962i) distributes to

2.1 - 23.9i

Answer:

x=26

Step-by-step explanation:

5x=3x+52

5x-3x=52

2x=52

2x/2=52/2

x=52/2

x=26

The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

Given equation :

y=(x−2)2−8

y = 2x - 4 - 8

= 2x - 12

The final equation is y = 2x - 12.

Compare this equation with slope and y-intercept formula :

y = mx+c

So that c = -12

The value of y-intercept according to the solution is -12.

To find the vertex. Let's assume x=0; Substitute in the equation

y = 2(0) -12

y = -12

The first vertex will be (0, -12)

If x = 1; y = 2(1) -12

y = -10

Then the second vertex will be (1, -10).

Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

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The probability that none of the 4 lightbulbs in the sample are defective is 805/1763 as a reduced fraction.

Let's first calculate the total number of ways to choose 4 lightbulbs from 24:

24 choose 4 = (24!)/(4! * 20!) = 10,626

Probability that all 4 lightbulbs in the sample are defective:

There are 4 defective lightbulbs in the shipment, so the number of ways to choose all 4 from the 24 is:

4 choose 4 = 1

So, the probability that all 4 lightbulbs in the sample are defective is:

1/10,626 = 1/5313

Therefore, the probability that all 4 lightbulbs in the sample are defective is 1/5313 as a reduced fraction.

Probability that none of the 4 lightbulbs in the sample are defective:

There are 4 defective lightbulbs in the shipment, so the number of ways to choose 4 non-defective bulbs from the remaining 20 is:

20 choose 4 = (20!)/(4! * 16!) = 4,845

So, the probability that none of the 4 lightbulbs in the sample are defective is:

4,845/10,626 = 805/1763

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For given trapezoid, the measures of angles A, B, and D are 40 degrees and 50 degrees, respectively.

A trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The legs may be of equal length, or they may be different lengths.

Since trapezoid ABCD has two parallel sides, we know that angle A + angle D = 180 degrees. Similarly, angle B + angle C = 180 degrees.

Therefore, we can write:

angle A + angle B + angle C + angle D = 360 degrees

Substituting angle A = angle B and angle C = angle D, we get:

2(angle A) + 2(angle C) = 360 degrees

Simplifying:

2(angle A) + 2(50)= 180 degrees

2(angle A) = 180 degree-100 degree

2(angle A) = 80 degree

angle A= 80 degree/2

angle A = 40 degree

Since we know that angle A = angle B

angle B= 40 degree

Therefore,

angle A = angle B = 40 degrees

angle D = angle C = 50 degrees

So the measures of angles A, B, and D are 40 degrees and 50 degrees, respectively.

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The standard form equation of a circle whose diameter endpoints are  (-3,4) (2,1) is [tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5

The general form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius. This equation is derived using the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. By setting (x - h)² and (y - k)² equal to r² and then combining the two equations, we get the standard form equation of a circle.

The center of the circle lies in the middle of the diameter, so we find the midpoint of the end points:

[tex](\frac{-3+2}{2} , \frac{4+1}{2} )[/tex] = (-0.5, 2.5)

And radius of the circle is half of the diameter, which is:

[tex]\frac{\sqrt{( 2-(-3))^2 + (1-4)^2 )}}{2}[/tex] = [tex]\frac{\sqrt{26}}{2}[/tex]

Therefore, the circle equation is:

[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = [tex](\frac{\sqrt{26} }{2} )^2[/tex] = 26/4 = 6.5

[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5

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in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.

Let's start by setting up an equation based on the given information.

Let Leah's current age be represented by "x". Then, we know that:

x = 3(x-4)

Expanding the right side of the equation:

x = 3x - 12

Bringing the "x" term to the left side and simplifying:

2x = 12

x = 6

So Leah is currently 6 years old. Now we want to find out how many years it will take for her to be exactly twice as old as she was four years ago. Let's represent this number of years as "y". Then we can set up another equation:

6 + y = 2(6 - 4 + y)

Simplifying:

6 + y = 2(2 + y)

6 + y = 4 + 2y

2 = y

So in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.

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Answer:

We can estimate that 900 people in attendance would prefer mustard on a hot dog.

Step-by-step explanation:

What is proportion?

Proportion is a mathematical concept that refers to the relationship between two quantities, expressed as a ratio or a fraction. It represents the size of one quantity relative to another quantity, typically within a larger population or sample.

To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.

The proportion of people in the sample who prefer mustard is:

27/150 = 0.18

To estimate the number of people who prefer mustard in the entire population of 5,000 attendees, we can multiply this proportion by the total number of attendees:

0.18 x 5,000 = 900

Therefore, we can estimate that 900 people in attendance would prefer mustard on a hot dog.

Answer:

2000 people prefer mustard on their hot dog.

900 people prefer chili on their hot dog

2100 people prefer ketchup on their hot dog

Step-by-step explanation:

hope this helps

The missing data value in the project is 25.5.

Range is a statistical measure that represents the difference between the highest and lowest values in a dataset. It is calculated by subtracting the smallest value in the dataset from the largest value.

To find the missing data value, we need to use the given range and the known data values.

The range is the difference between the highest and lowest values in the data set. So, if we sort the given data values in increasing order, we have:

11, 15, 15, 22, 29, 31

The range is 33, which means that:

highest value - lowest value = 33

31 - 11 = 33

So, the missing data value must be between 22 and 29 (since those are the values that are next to each other in the sorted list). To find the exact value, we can take the average of 22 and 29:

(22 + 29) / 2 = 25.5

Therefore, the missing data value is 25.5.

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Answer:

I cannot understand the question

According to the information, the surface area of the solid is 758m² and the volume is 594m³

To find the surface area of the solid we have to perform the following procedure:

12m * 11m = 132m²

132m² * 2 = 264m²

16m * 9m = 144m²

144m² - 18m² = 126m²

126m² * 2 = 252m²

16m * 11m = 176m²

176m² - 66m² = 110m²

3m * 11m = 33m²

33m² * 2 = 66m²

6m * 11m = 66m²

264m² + 66m² + 66m² + 110m² +252m² = 758m²

To find the volume we have to perform the following procedure:

8m * 11m * 9m = 792m³

792m³ - 198m³ = 594m³

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Answer:

f(x) = 4(1.095)^x.

Step-by-step explanation:

The function f(x) = 4(1+0.1/0.5)^0.5x can be simplified using the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction).

First, we can simplify 0.1/0.5 to get 0.2.

Next, we can simplify (1 + 0.2) to get 1.2.

Then, we can simplify (1.2)^0.5 to get approximately 1.095.

Finally, we can multiply 4 by 1.095^x to get the simplified function:

Answer:

To differentiate the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x, we will use the chain rule and product rule.

First, we will take the derivative of both sides of the equation with respect to x:

d/dx [sin(y) + x^2y^3 - cos(x)] = d/dx [2y]

Next, we will differentiate each term on the left side of the equation:

cos(x) - 2xy^2 dx/dx + 3x^2y^2 + sin(y) dy/dx = 2 dy/dx

We can simplify this equation by moving all the terms involving dy/dx to the left side:

cos(x) - 2xy^2 - 2 dy/dx sin(y) = dy/dx [2 - sin(y)]

Now we can solve for dy/dx by isolating it on one side of the equation:

dy/dx [2 - sin(y)] = cos(x) - 2xy^2

dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]

Therefore, the derivative of the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x is:

dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]

Answer:

explanation:A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).

Answer:

=10 m

Step-by-step explanation:

PYTHAGOREAN THEOREM

8^2+6^2=64+36=100

=√100m

=10 m

Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is.

[tex]0.1x + 0.2y = 70[/tex]

[tex]y = 3x[/tex]

Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.

Let's define the variables as follows:

Let x be the number of liters of Drink B produced.

Since the company produced 3 times as many liters of Drink A as liters of Drink B, let y be the number of liters of Drink A produced, so y = 3x.

Now, let's write the system of equations:

The total amount of real fruit juice used is 70 liters, so we can write:

[tex]0.1x + 0.2y = 70[/tex]

Substituting y = 3x into the above equation, we get:

[tex]0.1x + 0.2(3x) = 70[/tex]

Simplifying the equation:

[tex]0.1x + 0.6x = 70[/tex]

[tex]0.7x = 70[/tex]

[tex]x = 100[/tex]

So, the company made 100 liters of Drink B and 3 times as many liters of Drink A, or 300 liters of Drink A.

Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is:

[tex]0.1x + 0.2y = 70[/tex]

[tex]y = 3x[/tex]

Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.

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The amount received from loans as a number in millions is 242,700 million rand.

Deducing value A requires computation of collective income sources, for which the following summation suffices:

Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A

In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.

Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:

Total Income - Total Expenditure = B

(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B

Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.

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The data from the distribution shows a symmetric distribution.

The data from a distribution can be described as symmetric when the values of the data are evenly distributed around its center point. This mans that if the data is folded along its center point and the two halves overlap perfectly, then the distribution is said to be symmetric.

In the histogram, we see an example of symmetric data because the center value that has the frequency of 10 ahs even distribution on both sides.

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So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

The slope of the line passing through points A and B can be calculated as follows:

slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1

The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

To find the y-intercept, we can use point A (0,0) and substitute the slope value.

y = mx + b

0 = 1(0) + b

b = 0

Therefore, the equation of the line passing through points A and B is:

y = 1x + 0

Simplifying, we get:

y = x

So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:

y - 0 = 1(x - 0)

y = x

This confirms our earlier answer.

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From the data in the table, we can conclude that when x = 4, then the residual will equal -1.

To determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.

So, Residual = Gven value - Predicted value.

When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.

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Answer:

The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.

Step-by-step explanation:

In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.

If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.

Axis of symmetry: x = 1[tex]\\[/tex]

Vertex: (0,1)

Y-intercept: (0,1)

Min / Max: 0 / infinity

Domain: -infinity ≥ x ≥ infinity

Range: 0 ≥ y ≥ infinity

The true statements are:

1. The radius of the circle is 3 units

2. The standard form of the equation is (x-1)^2+y^2=3

3. The center of the circle lies on X-axis

4. The radius of this circle is the same as the radius of the circle whose equation is x^2+y^2=9

The given equation is: x^2+y^2-2x-8=0

The equation in the standard form of the circle can be written as (x-h)^2+(y-k)^2=r^2, where h= center of the circle and r= radius of the circle

The given equation in standard form can be written as

(x^2-2x+1)+y^2-9=0

(x-1)^2+y^2=3^2

Hence from the above equation, the center of the circle is at (1,0) and the radius is 3 units.

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Answer:

Likely

Step-by-step explanation:

Answer:

The third option:

Points: A, B, C, D

Line segments: AB, AD, AC, DC, BC

Answer:

164 Cakes

Step-by-step explanation:

382 Cakes are made in Week A. This was twice the amount of Week B. 328 divided by two equals 164.

The perimeter of the figure is 20.56 centimetres

Explain perimeter

Perimeter is the distance around the edge of a two-dimensional shape, such as a polygon or a circle. It is calculated by adding the length of all the sides of the shape. Perimeter is a fundamental measure in geometry and is used to determine the amount of material needed to enclose a shape, such as fencing or paving. It is also used to compare the size of different shapes with the same perimeter.

According to the given information

The perimeter of the figure is 4+4 + circumference of the circle with diameter 4= 8+12.56= 20.56

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The cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.

Cost is the value of goods or services measured in money or other forms of exchange. It is the amount that must be given up in exchange for something else. Costs are typically incurred in the production of goods and services, and can include both tangible and intangible elements, such as labor, materials, overhead, and financing.

The total cost for 3 liters of milk and 5 loaves of bread was $11. Therefore, the cost for 1 liter of milk was ($11 / 3) = $3.67. The cost for 1 loaf of bread was ($11 / 5)
= $2.20.
The total cost for 4 liters of milk and 4 loaves of bread was $10. Therefore, the cost for 1 liter of milk was ($10 / 4) = $2.50. The cost for 1 loaf of bread was ($10 / 4)
= $2.50.
Therefore, the cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.

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With given compound interest, it will take approximately 31 years and 5 months to pay off the loan.

What is Compound interest?

Compound interest is computed on both the starting principal and the accrued interest from prior periods. In other words, it is the interest gained not just on the principle amount but also on any past interest earned.

Now,

Using the given formula:

N = (-log(1 - i * A / P)) / (log(1 + i))

where i = 0.0025 (0.25% monthly interest rate), A = $70,000, and P = $250

N = (-log(1 - 0.0025 * 70000 / 250)) / (log(1 + 0.0025))

N = (-log(1 - 175)) / (log(1.0025))

N = (-log(0.9883)) / (0.0025)

N = 376.48

Rounding up to the nearest whole number, it will take 377 months to pay off the loan.

Therefore, it will take approximately 31 years and 5 months to pay off the loan.

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The answer of the given question based on the expression is , the simplified expression for g(x+5) is 3x² + 30x + 73.

An expression is combination of numbers, variables, and operators (such as +, -, ×, ÷) that represents value or quantity. Expressions can be as simple as a single number or variable, or they can be complex with multiple terms and operations. Expressions can be evaluated or simplified by performing the indicated operations according to the rules of arithmetic and algebra.

To find g(x+5), we replace every occurrence of x in the expression for g(x) with x+5:

g(x+5) = 3(x+5)² + 2

Expanding the square and simplifying, we get:

g(x+5) = 3(x² + 10x + 25) + 2

g(x+5) = 3x² + 30x + 73

Therefore, the simplified expression for g(x+5) is 3x² + 30x + 73.

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Answer:

The third choice (the bottom one)

Step-by-step explanation:

By law of sin, an angle over the side opposite of the angle is equal to another angle over side opposite of the angle. If that doesn't make sense, refer to the picture below. The first option is not applicable because y is not opposite the angle measuring 100 degrees. Therefore, law of sin cannot be applied. The second option is not applicable because y is not opposite the angle measuring 46 degrees. The third option is applicable because the side measuring 21 unites is opposite the angle measuring 46 degrees and side y is opposite the angle measuring 34 degrees.