Please i need help i dont fully understand it
(05.01)
A scale drawing of a living room is shown below. The scale is 1 : 40.

A rectangle is shown. The length of the rectangle is labeled 6 inches. The width of the rectangle is labeled 4 inches.
Show your work to determine the area of the room in square feet. (5 points)

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

The sum formula for geometric sequence is Sn = a(1 - r^n) / (1 - r)

A unique kind of sequence is a geometric sequence. It is a sequence in which each term aside from the first term and is multiplied by a fixed number to obtain its subsequent term. To obtain the following term in the geometric sequence, one must multiply with a fixed term known as the common ratio, and one need only divide the term by the same common ratio to determine the previous term in the sequence.

There are infinite and finite geometric sequences. The formula for the same is Sn = a(1 - r^n) / (1 - r). Here Sn is the sum of the first n terms of the geometric sequence,  a is the first term of the sequence,  r is the common ratio between consecutive terms in the sequence and n is the number of terms in the sequence

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The equation for the calculation of the score will be 6-x , where x is the number of birdies (negetive score).

Lets suppose the number of birdies that have been scored is "x" . And since birdie is a negetive score, everytime we score a birdie, we need to reduce 1 from the standing score i.e. to say the total number of birdies is needed to be subustracted from the current score.

Score = Initial Score - Number of birdies

Since the initial score here, as per mentioned is 6 over par , so we need to substract the number of birdies from 6 in order to get actual score.

Therefore, in accordance with the current situation, the equation to calculate the score will be 6-x.

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The addition of the polynomials 2x² + 6x + 5  and   3x² - 2x - 1 will be 5x²  +   4x   +   4.

Sums of terms of the form k × x^n, where k is any number and n is a positive integer, make up polynomials.

A polynomial is a mathematical equation made up of exponents, constants, and variables that are mixed using addition, subtraction, multiplication, and division.

Start with: 2x² + 6x + 5   +   3x² − 2x − 1

Place like terms together: 2x² +3x² +   6x−2x + 5−1

Which is: (2+3)x²  +   (6−2)x  +  L(5−1)

Add the like terms: 5x²  +   4x   +   4

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add the polynomials 2x² + 6x + 5   and   3x² - 2x - 1

Answer: (x,y)=(1,-10)

Step-by-step explanation:

y=-7x-3

5x+4y=-35

substitute the value of y

5x+4(-7x-3)=-35

solve the equation

x=1

substitute the value of x

y=-7 x 1-3

solve the equation

y=-10

A possible solution is

(x,y)=(1,-10)

Check the solution

-10=-7 x 1-3

5 x 1+4 x (-10)=-35

simplify

-10=-10

-35=-35

The ordered pair is a solution

(x,y)=(1,-10)

The blueberry muffins made by baker on monday is 40% of the total muffins made by the baker .

A quantity or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. In order to determine the percentage of a number, divide it by its sum and then multiply the result by 100. The proportion thus refers to a component per 100. The word percent indicates a percentage of 100. The word "percent" denotes "per 100." The letter "%" stands for it.

Now in the given question,

Total number of muffins baker made = 90

Blueberry Muffins made by baker on monday = 36

Prcentage of blueberry muffins out of total muffins  [tex]=\frac{36*100}{90} = 40 %[/tex]

So , the Blueberry Muffins were 40% of the total muffins baker made.

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The slope of the line tangent to the parabola's y-intercepty = [tex](x+2)^2-4[/tex] is 4.

We must first get the parabola's y-intercept in order to determine the slope of the line tangent to it.

We enter x=0 into the equation to obtain the y-intercept:

[tex]y = (x + 2)^2 - 4[/tex]

[tex]y = (0 + 2)^2 - 4[/tex]

y = 4 - 4

y = 0

Hence, the parabola's y-intercept is (0, 0).

The derivative of the parabola's equation must then be determined.

[tex]y = (x + 2)^2 - 4\\y = x^2 + 4x + 4 - 4\\y = x^2 + 4x[/tex]

dy/dx = 2x + 4

By adding x=0 to the derivative, we can now get the slope of the tangent line to the y-intercept:

dy/dx = 2x + 4

dy/dx = 2(0) + 4

dy/dx = 4

Hence, the slope of the line tangent to the parabola's y-intercepty = [tex](x+2)^2-4[/tex] is 4.

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There are approximately 29.53 inches in 75 centimeters.

Conversion factor for centimeters to inches is

1 inch = 2.54 centimeters.

To convert 75 cm to inches, you can divide 75 by 2.54:

75 cm ÷ 2.54 = 29.52756 inches

Rounding this to the nearest hundredth gives approximately 29.53 inches. Therefore, there are approximately 29.53 inches in 75 cm.

A conversion factor is a mathematical expression that expresses the relationship between two units of measurement. It is used to convert measurements between units.

Conversion factors are commonly used to convert measurements between different units of measurement in math, science, and engineering. They are a useful tool for performing calculations and comparing data in various units.

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The perimeter of the square is 12 units.

Let's call the side length of the square "s". We can use the Pythagorean theorem to relate the side length of the square to its diagonal:

s² + s² = (3√2)²

2s² = 18

s² = 9

s = √9 = 3

So the side length of the square is 3. Since all sides of a square are equal, the perimeter of the square is 4 times the side length:

Perimeter = 4s = 4(3) = 12

Therefore, the perimeter of the square is 12 units.

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The choice that represents the quotient of the radicals is given as follows:

D. [tex]x\sqrt{2}[/tex]

The quotient of the radicals for this problem is defined as follows:

[tex]\frac{\sqrt{18x^3}}{\sqrt{9x}}[/tex]

As both the numerator and the denominator have the same root(square root), we can apply the quotient and then take the square root, thus:

[tex]\sqrt{\frac{18x^3}{9x}}[/tex]

Then we can simplify the expression inside the square root as follows:

Hence the square root is taken as follows:

[tex]\sqrt{2x^2} = x\sqrt{2}[/tex]

Meaning that option D is the correct option.

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The probability of finding oil (to 1 decimal) is 0.7.

Probability is a statistic that is used to show the possibility or chance that a certain event will occur. Probabilities can be expressed as fractions from 0 to 1, in contrast to percentages from 0% to 100%. The four main types of probability that mathematicians study are axiomatic, classic, empirical, and subjective. Given that the terms potential and probability are interchangeable, you could define probability as the probability that a particular event will take place.

To determine probability the  Preliminary geologic  , we obtain,

P(oil)=0.3+0.4

P(oil)=0.7.

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Answer:Well lets look at the arithmetic of this. Logically we know that all 42 animals have at least 2 feet each so 42 x 2 =84 that means the remaining feet cannot belong to the chickens and therefore 114–84= 30 remaining feet belong to the cows, therefore you divide 30/2 = 15 cows who have 4 legs each, 60 legs in total. 42–15 = 27 chickens who have 2 legs each, 54 legs in total. This adds up to the total of legs of 114, 60 + 54. Therefore out of a total of 42 animals, 15 are cows and 27 are chickens.

Step-by-step explanation:

Answer:

0 triangles can be formed

Step-by-step explanation:

In order to determine the number of distinct triangles that can be formed with the given information, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's start by drawing a rough sketch of the triangle:

     Z

     |\

     | \

     |   \ x

     |     \

     |       \

     X-----Y

      y=2

We know that mZX = 51°, so we can label that angle on our diagram:

     Z

     |\

     | \

     |   \ x

     |     \

     |51°  \

     X-----Y

      y=2

We can use the sine law to find the length of side XY:

sin(51°) = XY / 5

XY = 5 * sin(51°)

XY ≈ 3.95

Now we need to check whether XY is less than the sum of the other two sides, XZ and YZ:

XZ + YZ > XY

2 + √(x² - XY²) > XY

2 + √(5² - 3.95²) > 3.95

2.86 > 3.95 (false)

Since XY is greater than the sum of the other two sides, it is not possible to form a triangle with the given measurements. Therefore, the number of distinct triangles that can be formed is 0.

I hope this helps! And if you could label my answer brainliest that would be awesome.

- Dante

Answer:

blank=9

Step-by-step explanation:

Answer:

35 degrees

Step-by-step explanation:

The direction "North" is parallel to itself, because of the reflexive property of parallel lines. Using the alternate interior angles theorem, the measure of x + 25 must be equal to 60 degrees. 60 - 25 = 35

Answer:

x = 35°

Step-by-step explanation:

The angle made by the directional line from wharf to Shell Cove relative to North is 60° at the point of departure from the wharf

The angle that this same line makes at the point of arrival at Shell Cove must be 60° relative to North since the two North directions are perpendicular and the line connecting the wharf and shell cove is a transversal intersecting these lines

This is because of the property that when two parallel lines are intersected by a transversal, the alternate interior angles must be the same

The angle made by this transversal at Shell Cove = x + 25 degrees

Since (x + 25)° = 60°

x = 60° - 25°

x = 35°

Answer:

4x=>-74

Step-by-step explanation:

x+23=>18

4(x+23)=>18

4x+92=>18

collect like terms

4x=>18-92

4x=>-74

Answer is 4 (x + 23 ) ≥ 18

Step by step

4 times the sum of a number and 23

4(x + 23)

Is at least 18

≥ 18

Your inequality

4 (x + 23 ) ≥ 18

to solve, distribute

4x + 92 ≥ 18

subtract 92 from both sides

4x + 92 - 92 ≥ 18 - 92

simplify

4x ≥ -74

divide both sides by 4 to solve for x

4/4 x ≥ -74/4

x ≥ 18.5

18.5 is equal to or greater than 18 so problem solved

** We used ≥ in this inequality which means at least (equal to) this number or greater

Answer:

the angle measures 59.9°, and its supplementary angle measures 180° - 59.9° = 120.1°.

Step-by-step explanation:

Let x be the measure of the angle we are trying to find.

By definition of supplementary angles, we know that the angle's supplementary angle measures 180° - x.

We are also given that the angle measures 120.2° less than its supplementary angle. This can be written as:

x = (180° - x) - 120.2°

Simplifying the equation, we get:

x = 59.9°

Therefore, the angle measures 59.9°, and its supplementary angle measures 180° - 59.9° = 120.1°.

Answer:

The major axis of the given ellipse is on the y-axis.

Step-by-step explanation:

The general equation of an ellipse is:

[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]

where (h, k) is the center.

The major axis is the longest diameter of an ellipse, and the minor axis is the shortest diameter of an ellipse.

If a > b the ellipse is horizontal, a is the major radius (parallel to the x-axis), and b is the minor radius (parallel to the y-axis).

If b > a the ellipse is vertical, b is the major radius (parallel to the y-axis), and a is the minor radius (parallel to the x-axis).

The given equation is:

[tex]\dfrac{x^2}{49}+\dfrac{y^2}{81}=1[/tex]

Therefore:

As b > a, the ellipse is vertical.

The major axis is 18 units in length and is parallel to the y-axis.

The minor axis is 14 units in length and is parallel to the x-axis.

Both axes pass through the center of the ellipse.

As the center of the ellipse is the origin, the major axis is on the y-axis and the minor axis is on the x-axis.

She practiced with a rate/speed of 17 min/day.

What is the definition of speed?

The following is the definition of speed:

The rate at which the position of an item changes in any direction.

The ratio of distance travelled to time spent travelling is described as speed. Speed is a scalar number since it has just one direction and no magnitude.

Formula for Speed

The speed formula is as follows:

s=d/t

Where,

s denotes the speed in metres per second, d the distance travelled in metres, and t the time in seconds.

Now,

Given Total time she practiced=595 minutes

Total time she practiced=5 weeks=5*7

=35 days

then rate at which she practiced per day=595/35

=17 min/day

hence,

           Brianna practiced with a rate of 17 min/day.

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From the given information provided, the first three common denominators of 7/9 and 2/3 are 9, 18, and 27.

To find the common denominators of 7/9 and 2/3, we need to find the least common multiple (LCM) of their denominators.

The prime factorization of 9 is 3 x 3, and the prime factorization of 3 is 3.

The prime factorization of 2 is 2, and the prime factorization of 3 is 3.

The common factors are 3, so the LCM of 9 and 3 is 9.

Therefore, the common denominator of 7/9 and 2/3 is 9.

To find the next two common denominators, we can continue to find the LCM of the denominators with the added factor of 9.

The prime factorization of 18 (2 x 3 x 3) includes the prime factors of 9, so it is a common denominator.

The prime factorization of 27 (3 x 3 x 3) also includes the prime factors of 9, so it is another common denominator.

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The equivalent value of 5 ft 7 in cm is 170.18 centimeters

In today's world, measurements play a crucial role in almost everything we do. Whether it's measuring ingredients for a recipe or calculating distances for a road trip, we rely on accurate measurements to ensure success. And as we live in a globalized world, it's important to be able to convert measurements from one unit to another. In this article, we will discuss how to convert the height of 5 feet 7 inches into centimeters.

To convert 5 feet 7 inches into centimeters, we need to first understand the conversion factor between feet and centimeters. 1 foot is equal to 30.48 centimeters. Therefore, to convert 5 feet into centimeters, we can multiply 5 by 30.48, which gives us 152.4 centimeters.

Now, we need to convert the 7 inches into centimeters. 1 inch is equal to 2.54 centimeters.

To convert 7 inches into centimeters, we can multiply 7 by 2.54, which gives us 17.78 centimeters.

Finally, to get the total height in centimeters, we can add the two values we obtained in the previous steps. Therefore, the height of 5 feet 7 inches is equal to

=> (152.4 + 17.78) = 170.18 centimeters

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Answer:

to show how much rainfall there is between months in different regions

The rate of growth of the minimum wage in New York State from 1966 to 2015 is approximately 6.41%.

To determine the rate of growth of the minimum wage in New York State from 1966 to 2015, we can use the following formula:

rate of growth = ((final value / initial value)^(1/number of years) - 1) * 100%

where the initial value is the minimum wage in 1966, the final value is the minimum wage in 2015, and the number of years is the difference between the two years.

Plugging in the values, we get:

rate of growth = [tex](($8.75 / $1.25)^{1/(2015-1966)) - 1} * 100%[/tex]

= [tex]((7)^{1/49) - 1} * 100%[/tex]

=[tex](1.0641 - 1) * 100%[/tex]

= 6.41%

Therefore, the rate of growth of the minimum wage in New York State from 1966 to 2015 is approximately 6.41%.

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Answer: -19

Step-by-step explanation: 5 x 3 = 15

9 x 4 = 36

15 - 36 = -21

-21 + 2 = -19

Answer:

Therefore, adding 10 to the numerator is the better option if we want to increase the value of 46/224.

Step-by-step explanation:

To find which option will give a larger final number, we should calculate both the possibilities and compare them ,

Firstly,add 10 to the numerator

Now,

The new rational number will be,

(46 + 10) / 224

= 56 / 224

= 7 / 28

2ndly,

Add 10 to the denominator

The new rational number will be,

46 / (224 + 10)

= 46 / 234

After comparing these two rational numbers and converting them to decimals or simplify them ,

7 / 28

= 0.25

46 / 234

= 0.196581...

Since 0.25 is larger than 0.196581...,

Now,adding 10 to the numerator will result in a larger final number.

Therefore, adding 10 to the numerator is the better option if we want to increase the value of 46/224.

The possible outcomes for flipping a two-sided tile once are:

Toss 1 Toss 2 Toss 3

Black Black Black

Black Black White

Black White White

Black White Black

White White White

White White Black

White Black Black

White Black White

If we flip the tile three times, the sample space will consist of all possible outcomes of the three flips.

Each flip is independent, so the total number of possible outcomes is the product of the number of outcomes for each flip, which is 2.

Therefore, the sample space for flipping the tile three times is:

BBB,

BBW,

BWB,

BWW,

WBB,

WBW,

WWB,

WWW

Where

B = the black side facing up, and

W = the white side facing up.

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You'd would like to convert a set of raw scores into such a set of z-scores so you can compare scores from different distributions, as well as to create a distribution besides a mean of 0 and a standard deviation of 1.

What is the purpose of converting raw scores to z-scores?

We could indeed convert scores obtained to z-scores to determine where those scores fall inside the distribution. Assume we receive a 68 on an exam.

Why is it critical to convert raw marks to z-scores in multiple regression?

Standardizing raw data by converting it to z-scores has the clear benefits: Recognize in which a piece of evidence falls within a distribution. Contrast evaluation from different variables.

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Answer:

127.5

Step-by-step explanation:

you arrange the numbers from least to greatest then divide by 2 If the amount of numbers you have are iuneven add 1 to it for example the first 9 prime numbers. 9 isn't and even number so you add 1 then divide by

The function that satisfies the differential equation y′ = -2 with initial condition y(0) = -8 is y = -2x - 8.

To solve the differential equation y′ = -2 with initial condition y(0) = -8, we need to find the function y(x) that satisfies both the differential equation and the initial condition.

We can start by integrating both sides of the differential equation with respect to x:

∫y′ dx = ∫(-2) dx

y = -2x + C

where C is a constant of integration.

To find the value of C, we can use the initial condition y(0) = -8:

y(0) = -2(0) + C = C = -8

So the solution to the differential equation with initial condition is:

y = -2x - 8

Therefore, the function that satisfies the differential equation y′ = -2 with initial condition y(0) = -8 is y = -2x - 8.

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The cost for children meal is $14 and the cost for adult meal is $40.

A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.

Let cost of adult meal = a

Let cost of child meal = c

Lorenzo plans to have 98 adults and 77 children attend, so the total projected cost of her meals is $4998.This will be:

98a + 77c = 4998 ...... (1)

Ruth has 71 adults and 91 children on her guest list, so he will pay the caterer $4114. This will be;

71a + 91c = 4114 ......    (2)

Multiply (1) by 71 and (2) by 98

6958a + 5467c = 354858      (3)

6958a + 8918c = 403172         (4)

subtract (3) from (4)

3451 c = 48314

c = 14

The cost of children meal is $14.

From equation (1),

98a + 77c = 4998

98a + 77(14) = 4998

98a + 1078 = 4998

Collect like terms

98a = 4998 - 1078

98a = 3920

a = 40

Adult meals is $40.

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