STUVWXYZ is a cuboid. M and N are the mid-points of
ST and WZ respectively.
Find angle
a SYW
b TNX
c ZMY

a. The tree diagram representing the above situation is illustrated below.

b. The percentage of employees hold management positions is 10%

c. The probability that she/he has a graduate degree is 85%.

In this case, the businessman can choose any 3 suits and 4 ties, so the number of combinations is equal to the number of ways of choosing 3 suits multiplied by the number of ways of choosing 4 ties.

This is equal to 6 x 8 = 48.

The records of the company also provide us with some useful information about the probability of holding a management position.

We can see that 20% of the employees have only a high school diploma and 10% of those employees hold management positions.

This means that the probability of holding a management position given that a person has a high school diploma is 10%.

Similarly, of those having bachelor degrees, 60% hold management positions, meaning the probability of holding a management position given that a person has a bachelor degree is 60%.

Lastly, 85% of the employees who have graduate degrees hold management positions, so the probability of holding a management position given that a person has a graduate degree is 85%.

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Answer:

[tex]y = \frac{Pa}{b} - za[/tex]

Step-by-step explanation:

See picture below :)

The square root of 16*4 can be simplified as follows:

Square root of 16*4 = Square root of (16) * Square root of (4) = 4 * 2 = 8

Therefore, the answer is not A, B, or D. The correct answer is C) 32.

Answer:

The square root of 16*4 can be simplified as follows:

Square root of 16*4 = Square root of (16) * Square root of (4) = 4 * 2 = 8

Therefore, the answer is not A, B, or D. The correct answer is C) 32.

Step-by-step explanation:

the height of the swing when θ is 45º is about 3.7 feet. Graph is attached below.

Graphs are a not unusual place technique to visually illustrate relationships within side the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately within side the textual content and in much less space.

Given, The height h (in feet) of a swing above the ground can be modeled by the function h=−8cosθ+10

Where,

the pivot is 10 feet above the ground,

the rope is 8 feet long,

To find the height of the swing when θ is 45º, we can substitute θ = 45º into the function and evaluate:

h(45º) = -8cos45º + 10

Using the fact that cos(45º) = √2/2, we get:

h(45º) = -8(√2/2) + 10

h(45º) = 10 - 4√2

Rounding to the nearest tenth, we get:

h(45º) ≈ 3.7 feet

Therefore, the height of the swing when θ is 45º is about 3.7 feet.

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Answer:

x² + y² = z²

Step-by-step explanation:

The side of the bottom square is y.

The side of the left square is x.

The side of the right square is z.

These sides are also the legs and hypotenuse of the right triangle.

We use the Pythagorean Theorem.

x² + y² = z²

The usual sign for greater than and less than is "<", the pointed side is always towards the smaller quantity.

When we compare two quantities in mathematics we us the sign"<".

Now, let us say that there are two quantities a and b, and a is greater than b. So, we can write the relation as, a > b. So, we see that b is less than as a and a is greater than b.

Now, to remember this, the pointed side of the sign will be always towards the quantity that is smaller.

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The new value of the house will be $453120.

We can write : a% of b as -

a% of b = a/100 x b

a% of b = ab/100

Given is that a house was valued at $384,000. Over several years, the value increased by 18%.

We can write the new value as -

{x} = 384000 + 18% of 384000

{x} = 384000 + 18/100 x 384000

{x} = 384000 + 18 x 3840

{x} = 384000 + 69120

{x} = 453120

Therefore, the new value of the house will be $453120.

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Line a could also be referred to as line EC.

In mathematics, a line can be named in a variety of ways depending on the context. One common way to name a line given a starting point and an ending point is to use the names of the two points.

For example, if the starting point is labeled A and the ending point is labeled B, we can refer to the line as "line AB" or "line BA" (the order doesn't matter, as the line extends in both directions).

In this case therefore, line a can be referred to as line EC which are the letters at the starting and ending points.

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Therefore , the solution of the given problem of linear equation comes out to be the linear equation of the image is y = 3x + 22.

The formula y = mx+b is used to produce a simple regression curve. The slope is B, and the y-intercept is m. The preceding line indicates independent components, yet is commonly referred to as a "math equation combining many variables". In bivariate linear equations, there are just two variables. Application problems involving linear equations have no known solutions. Y=mx+b.

Here,

Let's first find the coordinates of two points on the original line. We can choose any two points, but for simplicity, let's choose (0,4) and (1,7), which lie on the line y=3x+4.

The distance between these two points is:

d = √((1-0)² + (7-4)²) = √(10)

To find the new coordinates of these points after dilation, we multiply the distance by 4 and use the center of dilation (1,1) as the reference point:

New coordinates of (0,4):

x' = 1 + 4(0-1) = -3

y' = 1 + 4(4-1) = 13

New coordinates of (1,7):

x' = 1 + 4(1-1) = 1

y' = 1 + 4(7-1) = 25

So the image of the line y=3x+4 after dilation by scale factor 4 centered at (1,1) is the line passing through the points (-3,13) and (1,25). We can find the equation of this line by finding the slope and the y-intercept.

Slope:

m = (y2-y1)/(x2-x1) = (25-13)/(1-(-3)) = 12/4 = 3

Y-intercept:

y = mx + b

13 = 3(-3) + b

b = 22

Therefore, the linear equation of the image is y = 3x + 22.

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Answer:

x = -2 | y = -6
x = 1 | y = 6
x = 2 | y = 10

Step-by-step explanation:

An equation in slope-intercept form to represent this linear function is y = 65x + 40.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

Let the fee per month = x.

Given that, A membership at Rocky Heights Climbing Gym costs $65 per month plus a $40 initial fee.

y = 65x + 40.

Hence, an equation in slope-intercept form to represent this linear function is y = 65x + 40.

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At the end of the fourth minute, the point 'g' would be at the position of 9605961 on the line segment TS.

As per the question, at the end of the first minute,  g covers 1/100th of the remaining segment, which is 1/100 × 10000000 = 100000 units. Therefore, the position of point g would be at 10000000 - 100000 = 9900000 at the end of first minute.

At the end of second minute, g covers another 1/100th of the remaining segment, which is 1/100 × 9900000 = 99000 units. So, the position of point g would be now 9900000 - 99000 = 9801000.

On the third minute's end ,  g would covers another 1/100th of the remaining segment, which is 1/100 × 9801000 = 98010 units. Therefore, the position of point g would be at 9801000 - 98010 = 9702990.

For fourth minute's end, point g covers another 1/100th of the next remaining segment, which is 1/100 × 9702990 = 97029 units. Therefore, the final position of point g would be at 9702990 - 97029 = 9605961 units.

Therefore, at the end of the fourth minute, point g would be finally at the position of 9605961 on the line segment TS.

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The correct question is :

imagine a line segment ts of length 10000000 and point g moving from t=10000000 toward s=0, so that it cuts 1/100th of the remaining segment each minute. For example, at the the end of first minute g1 is at 99,00,000. Where is g at the end of fouth minute (g4) ?

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The side lengths that cannot form a triangle are: 2 ft, 3 ft, 8 ft.

The given figure has a total area is 64 square inches, which has four triangles and one rectangle.

The area of a rectangle is represented as the product of the length and width.

The figure will have four triangles and one rectangle.

Here combined area of triangles = (1/2 x 4 x 4) x 4 = 32 square inches

The triangles have a combined area of 32 square inches.

The rectangle has an area = 8 x 4 = 32 square inches.

The figure has a total area = 32 + 32 = 64 square inches.

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The missing figure has been attached below.

This type of scientific experiment is commonly used in microbiology and is called a bacterial culture or bacterial colony.

The scientist likely used a sterile nutrient-rich medium in a petri dish to create an environment in which the bacteria could grow and reproduce. By observing the growth and behavior of the bacteria in the colony, the scientist can study various aspects of bacterial biology, such as metabolism, genetics, and response to environmental conditions. Bacterial cultures can also be used in medical and industrial settings to produce antibiotics, vaccines, and other products.

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Answer:

The percent decrease of the sale price of the sofa from the regular price is 17%.

Step-by-step explanation:

Sure! Here are the steps to find the percent decrease:

The percent decrease of the sale price from the regular price is 17%.

Answer:

17% is the percen

a. To find the angle QCP, we can start by finding the coordinates of the points P, Q, and C. Since P and Q are midpoints of the edges FG and GH, respectively, we can find their coordinates as follows:

P = (0, y, z) where y = (3+4)/2 = 3.5 and z = (0+4)/2 = 2

Q = (x, y, 0) where x = (3+4)/2 = 3.5 and y and z are the same as before.

Since C is the center of the cube, we can find its coordinates as:

C = (2, 2, 2)

Now we can use the dot product formula to find the angle QCP:

cos(QCP) = (PC · QC) / (|PC| · |QC|)

where PC and QC are the vectors from P to C and from Q to C, respectively.

PC = C - P = (2, 2 - 3.5, 2 - 2) = (2, -1.5, 0)

QC = C - Q = (2 - 3.5, 2 - 3.5, 0) = (-1.5, -1.5, 0)

|PC| = sqrt(2² + (-1.5)² + 0²) = sqrt(5.25)

|QC| = sqrt((-1.5)² + (-1.5)² + 0²) = sqrt(4.5)

PC · QC = 2(-1.5) + (-1.5)(-1.5) + 0 = -3 + 2.25 = -0.75

cos(QCP) = (-0.75) / (sqrt(5.25) * sqrt(4.5)) = -0.166666...

Therefore, the angle QCP is cos⁻¹(-0.166666...) ≈ 100.53° (rounded to two decimal places).

b. To find the total surface area of the solid remaining after pyramid PGQC is removed, we need to find the area of the four triangular faces and the square base of the pyramid and subtract them from the total surface area of the cube.

The square base of the pyramid has side length PQ = sqrt((3.5 - 3)² + (3.5 - 4)² + 2²) = sqrt(2.5) and area PQ² = 2.5 cm².

Each of the triangular faces has base PQ and height equal to the distance from P or Q to the plane containing the opposite vertex and the center of the cube. This distance is equal to the length of the perpendicular from the vertex to the opposite face, which is half the length of the diagonal of the cube.

The diagonal of the cube is sqrt(3² + 4² + 4²) = sqrt(41), so the height of each triangular face is sqrt(41)/2.

Therefore, the area of each triangular face is (1/2)PQ(sqrt(41)/2) = (sqrt(41)/4) cm².

The total surface area of the cube is 6s², where s is the length of a side of the cube. Since the volume of the cube is 1728 cm³, we have s³ = 1728, or s = 12 cm.

Therefore, the total surface area of the cube is 6(12²) = 864 cm².

The total surface area of the solid remaining after the pyramid is removed is:

864 - 4(sqrt

Answer:

75 degrees

Step-by-step explanation:

since this figure has four sides we can figure out the measure of the interior angles by using the formula, (n-2)*180, where 'n' = number of sides

(4-2)180 = 2(180) = 360

also, we know that since AB is parallel to DC that the figure is a rhombus where adjacent angles are supplementary

therefore, we can find 'x' by writing this equation:

12x - 3 + 9x - 6 = 180

simplify:

21x - 9 = 180

21x = 189

x = 9

also, we know that opposite angles in a rhombus are equal so if we substitute '9' for 'x' in angle C we will know the measure of angle A:

m<A = 9(9)-6

m<A = 81-6

m<A = 75 degrees

The solution is, Alice makes 3 bunches with 2 red balloons and 5 blue balloons.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

We are given that Alice is making balloon bunches from 6 red balloons and 15 blue balloons.

She wants the same number of red balloons and the same number of blue balloons in each bunch.

We have to find the greatest number of balloon bunches that Alice can making from  all the balloons.

We will find the HCF of 6 and 15

6 = 2×3

15 = 3×5

Common factor of 6 and 15 is 3.

Hence, HCF of 6 and 15=3

Therefore, Alice makes 3 bunches with 2 red balloons and 5 blue balloons.

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The GDP deflator reflects only the prices of all goods and services produced domestically, whereas the CPI (Consumer Price Index) reflects the prices of a fixed basket of goods and services purchased by consumers.

The GDP deflator is a measure of the average level of prices of all new, domestically produced, final goods and services in an economy. It measures the ratio of the value of goods and services produced in a given year at current prices to their value at base year prices. In contrast, the CPI measures the average change over time in the prices paid by urban consumers for a fixed basket of goods and services, including food, housing, transportation, and other goods and services. The GDP deflator is often used to adjust nominal GDP (Gross Domestic Product) to real GDP, which is a measure of economic output that takes into account the effects of inflation. The CPI, on the other hand, is used to adjust income and spending data for changes in the cost of living. In summary, while both the CPI and GDP deflator are measures of inflation, they reflect different aspects of the economy. The CPI reflects the prices paid by consumers for a fixed basket of goods and services, while the GDP deflator reflects the prices of all goods and services produced domestically.

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Complete Question

the CPI for this year is calculated by dividing the using by the using and multiplying by 100. however, the GDP deflator reflects only the prices of all goods and services            . Fill in the blanks.

Based on the drawing of AABC, the ratios wrt to the sides are given below:

There are several ways to find the ratios of sides in geometry, depending on the specific situation. Here are a few common methods:

Similar triangles: If you have two triangles that are similar, that is, they have the same shape but possibly different sizes, then the corresponding sides are in proportion. That is, if the sides of one triangle are a, b, and c, and the sides of the other triangle are x, y, and z, and the triangles are similar, then:

a/x = b/y = c/z

You can use this property to find the ratio of any two sides of a triangle if you know the ratio of the corresponding sides of a similar triangle.

Proportions: In some cases, you can use proportions to find the ratio of sides. For example, if you have a rectangle with sides of length a and b, and you know that the ratio of a to b is 2:3, then you can set up the proportion:

a/b = 2/3

and solve for either a or b.

Trigonometry: If you know the angles of a right triangle, you can use trigonometric ratios to find the ratio of sides. For example, in a right triangle with angle A, the ratio of the side opposite A (which we'll call a) to the hypotenuse (which we'll call c) is given by the sine of A:

sin(A) = a/c

You can rearrange this formula to solve for a or c, depending on what you know.

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The negative solution of the statement is -1

From the question, we have the following parameters that can be used in our computation:

6 times a number is 7 less than the square of that number

When represented as an equation, we have

6x = x^2 - 7

So, we have

x^2 - 6x - 7 = 0

Factorize

x^2 + x - 7x - 7 = 0

This gives

(x + 1)(x - 7)

Solve for x

x = -1 and x = 7

So, the negaive solution is -1

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Answer:

m = 3

Explanation:

the slop is 3

The answer is: A. tan P= 3/4, tan Q=5/4

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratio of the lengths of its sides. There are three primary trigonometric ratios, known as sine, cosine, and tangent, and their reciprocal functions, known as cosecant, secant, and cotangent.

The primary trigonometric ratios are defined as follows:

Sine (sin): The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle.

sin θ = opposite/hypotenuse

Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle.

cos θ = adjacent/hypotenuse

Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.

tan θ = opposite/adjacent

The reciprocal trigonometric ratios are defined as follows:

Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of the angle.

csc θ = 1/sin θ

Secant (sec): The secant of an angle is the reciprocal of the cosine of the angle.

sec θ = 1/cos θ

Cotangent (cot): The cotangent of an angle is the reciprocal of the tangent of the angle.

cot θ = 1/tan θ

Trigonometric ratios are widely used in mathematics, science, and engineering to solve problems involving right triangles, as well as to model and analyze periodic phenomena such as sound waves, light waves, and electromagnetic waves.

Since angle R is a right angle, we can use the tangent ratio for angles P and Q as follows:

tan P = RP / RQ = 12 / 16 = 3 / 4

tan Q = PQ / RQ = 20 / 16 = 5 / 4

Therefore, the answer is: A. tan P= 3/4, tan Q=5/4

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The given expression is (2⋅3)2−52. Therefore, the simplified expression is 11.

To simplify this expression, we first need to apply the exponent rule, which states that (a⋅b)c = ac⋅bc. In this case, we have:

(2⋅3)2 = 22⋅32

Next, we need to simplify the exponents. We have:

22⋅32 = 4⋅9 = 36

Finally, we need to subtract 52 from 36. We have:

36−52 = 36−25 = 11

Therefore, the simplified expression is 11.

Answer: 11.

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The IQR measures the spread of the middle 50% of the data.

Without knowing the actual values of the fuel economy ratings or the summary statistics, we cannot provide an exact answer. However, we can make some general observations about the effects of removing an extreme outlier on the standard deviation and the interquartile range (IQR).

First, the standard deviation measures the spread of the data around the mean. Removing an extreme outlier that is far from the mean could potentially decrease the standard deviation, as the remaining values may be more tightly clustered around the mean. However, the effect on the standard deviation will depend on the exact values of the data points and how much they vary from the mean.

Second, the IQR measures the spread of the middle 50% of the data. Removing an extreme outlier that is far from the bulk of the data may not have a significant effect on the IQR, as the remaining.

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Answer:

I don't really understand geo especially proof so I guess u have to ask ur teachers

the new coordinates of the room are Q(2.3125, 4.125), R(7.3125, 4.125), S(7.3125, 6.125), and T(2.3125, 6.125). the dimensions of the new room on the blueprint are 5.78125 inches by 2 inches and in feet 0.48 feet by 0.17 feet.

To find the new coordinates of the room, we can first calculate the dimensions of the original room and then increase them by 25%. The length of the room is the distance between points R and S, which is:

√(7-2)² + (4-4)² = 5 units

The width of the room is the distance between points Q and T, which is:

√(2-2)² + (6-4)² = 2 units

To increase the dimensions of the room by 25%, we can multiply the length and width by 1.25.

The new length is: 5 × 1.25 = 6.25 units

The new width is: 2 × 1.25 = 2.5 units

To find the new coordinates of the room, we can add half of the increase in each dimension to the original coordinates.

The new coordinates of Q are: (2 + 0.625/2, 4 + 0.25/2) = (2.3125, 4.125)

The new coordinates of R are: (7 + 0.625/2, 4 + 0.25/2) = (7.3125, 4.125)

The new coordinates of S are: (7 + 0.625/2, 6 + 0.25/2) = (7.3125, 6.125)

The new coordinates of T are: (2 + 0.625/2, 6 + 0.25/2) = (2.3125, 6.125)

Therefore, the new coordinates of the room are Q(2.3125, 4.125), R(7.3125, 4.125), S(7.3125, 6.125), and T(2.3125, 6.125).

To find the dimensions of the new room in inches on the blueprint, we can use the Pythagorean theorem: The new length is:

√(7.3125-2.3125)² + (4.125-4.125)² = 5.78125 units

The new width is: √(7.3125-7.3125)² + (6.125-4.125)² = 2 units

Therefore, the dimensions of the new room on the blueprint are 5.78125 inches by 2 inches.

To find the dimensions of the new room in feet in the new house, we can convert the dimensions to feet by dividing by 12:

The new length is: 5.78125 inches / 12 inches/ft = 0.48 ft

The new width is: 2 inches / 12 inches/ft = 0.17 ft

Therefore, the dimensions of the new room in the new house are 0.48 feet by 0.17 feet.

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Complete Question

A rectangular room has coordinates Q (2, 4), R(7, 4), 5 (7, 6), and T(2, 6) on the blueprint. The homeowner wants the dimensions of this room to be 25% larger. What are the coordinates of the new room? What are the dimensions of the new room, in inches, on the blueprint? What will the dimensions of the new room be, in feet, in the new house?

The perimeter of the trapezoid is 100

We would have to solve for the perimeter of the trapezoid.

The perimeter p = sum of the four sides = a + b + c+ d

from the question we have

2 (2x + 8) = 7x - 2

4x + 16 = 7x - 2

- 3x = -16 - 2

x = 6

EF = 2x + 8

= 2(6) + 8

= 12 + 8

= 20

AB = 7x - 2

= 42 - 2

= 40

AE = 1/2AC = 1/2AB = 20

BF = 1/2 CB = 1/2 AB = 20

The perimeter would be

20 + 20 + 20 + 40

= 100

The perimeter = 100

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