find the missing length indicated ​

Answer:

Step-by-step explanation:

(m-7)(m-7)=0

m=7

The polygon is a parallelogram and rectangle

The polygon is a parallelogram , quadrilateral and a rectangle

The sum of angles of a parallelogram is 360°

The four types are parallelograms, squares, rectangles, and rhombuses

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

The polygon is represented as OPQR

Now , the number of sides of the polygon = 4

So , it is a quadrilateral

Now , the measure of sides of the quadrilateral are

OP = 20 units

PQ = 40 units

QR = 20 units

RO = 40 units

So, it has 2 congruent sides and they are parallel in shape

So, it is a parallelogram

Now, the 2 opposite pairs of sides of the parallelogram are equal

So, it is a rectangle

Hence, the polygon is a parallelogram and rectangle

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For retirement savings, to accumulate $400,000 in 20 years with a 7% annual interest rate, the monthly deposit required is approximately $623, and the interest earned will be approximately $277,914.

(a) to accumulate $530,000 in 5 years with a 6% monthly interest rate, we can use the formula for the future value of a sinking fund:

FV = P * ((1 + r)^n - 1) / r,

where FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of months.

Plugging in the values, we have:

$530,000 = P * ((1 + 0.06/12)^(5*12) - 1) / (0.06/12).

Solving for P, we find that the monthly deposit should be approximately $8,469.

(b) to pay off a $100,000 note in 7 years with a 5% quarterly interest rate, we can use the formula for the sinking fund required:

PV = P * (1 - (1 + r)^(-n)) / r,

where PV is the present value, P is the quarterly deposit, r is the quarterly interest rate, and n is the number of quarters.

Plugging in the values, we have:

$100,000 = P * (1 - (1 + 0.05/4)^(-7*4)) / (0.05/4).

Solving for P, we find that the quarterly deposit should be approximately $3,309.

For retirement savings, to accumulate $400,000 in 20 years with a 7% annual interest rate, we can use the formula for the future value of a sinking fund:

FV = P * ((1 + r)^n - 1) / r,

where FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of months.

Plugging in the values, we have:

$400,000 = P * ((1 + 0.07/12)^(20*12) - 1) / (0.07/12).

Solving for P, we find that the monthly deposit should be approximately $623.

To calculate the interest earned, we subtract the total amount deposited from the final value:

Interest earned = FV - (P * n).

Plugging in the values, we have:

Interest earned = $400,000 - ($623 * 20 * 12).

Calculating this, we find that the interest earned will be approximately $277,914.

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4(3+14c−12d)

=(4)(3+14c+−12d)

=(4)(3)+(4)(14c)+(4)(−12d)

=12+c−2d

=c−2d+12

The statement is true. Trigonometry is indeed highly useful in navigation, and the term "bearing" is commonly used to describe direction in navigation.

In navigation, a bearing refers to the direction of an object or a point relative to a reference point. It is typically measured in degrees clockwise from the north direction. Trigonometric concepts such as angles, triangles, and trigonometric functions (sine, cosine, tangent) are used to determine and calculate bearings.

Bearing can be expressed in two ways:

a. True Bearing: True bearing refers to the direction of an object relative to true north. It is measured with respect to the Earth's geographic north pole.

b. Magnetic Bearing: Magnetic bearing refers to the direction of an object relative to magnetic north. It takes into account the magnetic declination, which is the difference between true north and magnetic north at a specific location.

Trigonometry plays a crucial role in converting between true bearing and magnetic bearing, as well as in various navigation techniques such as triangulation, dead reckoning, and celestial navigation.

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Answer:

y - 1 = -7/2 (x + 3 )

Explanation:

The point-slope form of a line is

where (x_1, y_1) is a point on the line and m is the slope.

Let us first find the slope.

A point on the line we are told is (-3, 1); thereofore, (x_1, y_1) = (-3, 1); hence

The dimensions of the shape allow us to find the length of PR to be 19.8 units.

The shape that is given is an equilateral triangle. This allows us to know that all the sides of the shape are equal.

This means that PR and QR are the same:

PR = QR

Equate both formulas as:

2n + 9 = 7n - 18

You can then solve for the value of n:

7n - 2n = 18 + 9

5n = 27

n = 5.4

The length of PR is therefore:

= 2n + 9

= 2 (5.4) + 9

= 19.8 units

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Answer:

x = -1 and 5

Step-by-step explanation:

Solve:  \(-16x^2+64x+80=0\)

Factor out common value of 16:

\(\implies 16(-x^2+4x+5)=0\)

Divide both sides by 16:  

\(\implies -x^2+4x+5=0\)

Change signs:

\(\implies x^2-4x-5=0\)

Break expression into groups:

\(\implies x^2+x-5x-5=0\)

\(\implies( x^2+x)-(5x+5)=0\)

Factor parentheses:

\(\implies x(x+1)-5(x+1)=0\)

Factor out common term \(x+1\):

\(\implies (x+1)(x-5)=0\)

Therefore,

\(x+1=0\)  and  \(x-5=0\)

So \(x=-1\) and \(x=5\)

\(\\ \tt\hookrightarrow -16x^2+64x+80=0\)

\(\\ \tt\hookrightarrow 16x^2-64x-80=\)

\(\\ \tt\hookrightarrow 16(x^2-4x-5)=0\)

\(\\ \tt\hookrightarrow x^2-4x-5=0\)

\(\\ \tt\hookrightarrow x^2-5x+x-5=0\)

\(\\ \tt\hookrightarrow x(x-5)+1(x-5)=0\)

\(\\ \tt\hookrightarrow (x+1)(x-5)=0\)

The function expressing the amount of money Marsha pays for herself and friends to go to the roller coaster theme park is f(x) = $10x + $15.

Given that Marsha pays $25 for the first ticket purchase to the roller coaster theme park and each ticket after the first is $10.To express the amount of money she pays for herself and friends to go to the roller coaster theme park, we can write a function as follows; Let x be the total number of people in the group.

If Marsha and her friends are 'x' in number, then the total number of tickets they will have to purchase will be 'x'.Then the amount Marsha pays for herself is $25 and the amount Marsha pays for her friends is $10 per person. So, the amount Marsha pays for the friends is (x - 1) * $10Hence, the function can be expressed as:f(x) = $25 + (x - 1) * $10 = $25 + $10x - $10= $10x + $15.

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Answer:

52

Step-by-step explanation:

\(r^{2} -14+8p\)

Substitute values given:

\((8)^{2} -14+8(\frac{1}{4} )\)

Simplify:

64-14+2

50+2

52

Therefore 52 is our answer

Answer:

56

Step-by-step explanation:

if r = 8 than r to the second power is 8 to the second power (or 8x8) which equals 64

64 - 14 + 8p

If p + 1/4 = 2

64 - 14 + 2

54 + 2

56

Answer:

f) 11

g) 75

please correct me if I am wrong

Answer:

the answer is ab

Step-by-step explanation:

you should go to the x axis and go to the four then go up 7 and it should land on the line in between a and b

Let me know if this helps :)

Answer:

y=(-9-2x)/3

Step-by-step explanation:

a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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In polar coordinates, the radial distance "r" is defined as the distance from the origin to a point in the plane. Since distance cannot be negative, we only consider the positive square root of 3 in the range for this problem. So, the correct range for "r" is 0 ≤ r ≤ √3, and negative square root of 3 is not included because it doesn't represent a valid distance in polar coordinates.

To find the volume of the given solid enclosed by the hyperboloid −x2 − y2 + z2 = 6 and the plane z = 3 using polar coordinates, we need to express the equation of the hyperboloid in terms of polar coordinates.

Substituting x = rcosθ and y = rsinθ, we get:

−r2cos2θ − r2sin2θ + z2 = 6

Simplifying, we get:

z2 = 6 - r2

Since the plane z = 3 intersects the hyperboloid, we have:

3 = √(6 - r2)

Solving for r, we get:

r = √3

Hence, the range for r is 0 ≤ r ≤ √3.

In summary, the negative square root of 3 is not included in the range of r because r represents a distance and cannot be negative. The volume of the solid can be found by integrating the function f(r,θ) = √(6 - r2) over the range 0 ≤ r ≤ √3 and 0 ≤ θ ≤ 2π using polar coordinates. The result will be in cubic units and can be obtained by evaluating the integral.

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There are four levels of measurements in statistics, namely nominal, ordinal, interval, ratio. These levels are important when it comes to analyzing data, since it helps us determine the technique that we can use to support or refute our study.

In the nominal level, we can categorize data but they cannot be ranked. An example would be hair color. In an ordinal data, the data can be both categorize and ranked, but doing mathematical calculation may not make sense. Also, the intervals between rankings doesn't necessarily dictate how close or far apart the data are.

A good example is level of education. In an interval level, the data can be categorized, ranked, and measured but they do not have a true zero. An example could be a range of values that does not include zero. Lastly, in the Ratio level the data can be categorized, rank, and measured, and it has a true zero.

So ratio level is most appropriate for ages of children. Note that ages can be categorized, rank, and measured .Moreover, an age equal to zero means that there is no age or the absence of age.  

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Answer:

14.82 km

Step-by-step explanation:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

f(x) = x^3 + x^2 - x

f(4) = ?

Step 02:

If x = 4

f(4) = (4)³ + (4)² - 4

= 64 + 16 - 4

= 76

The answer is:

f(4) = 76

The standard matrix of T is [[1, 1], [1, 1]].

To find the standard matrix of the linear transformation T with respect to the standard basis, we need to determine the images of the standard basis vectors under T.

The standard basis for R² consists of the vectors e₁ = [1, 0] and e₂ = [0, 1]. We will find the images of these vectors under T.

T(e₁) = [1 1; 0 1] * [1; 0] = [1; 0]

T(e₂) = [1 1; 0 1] * [0; 1] = [1; 1]

Now, we can form the matrix by placing the images of the basis vectors as columns:

[1 1; 1 1]

Therefore, the standard matrix of T is [[1, 1], [1, 1]].

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Answer:

(8,-4,-10,-16)

Step-by-step explanation:

Here, we are told to find the range from the given points set

The range are simply the y-values

These are;

(8,-4, -10, -16)

To compute the probabilities and sketch the graphs, we can use technology such as a statistical software or a graphing calculator. The steps involved are as follows:

(a) For X ~ N(3.7, 4.55), to find P(3.0 ≤ X ≤ 4.0), we can use the normal distribution function with the given mean and standard deviation. By inputting the values into the software, it will calculate the probability for us. Similarly, for (b) X ~ N(62, 100), to find P(45 ≤ X ≤ 50), and (c) X ~ N(7.6, 12), to find P(8 ≤ X ≤ 9) and P(X ≥ 45), we can follow the same process.

Once the probabilities are computed, we can plot the corresponding graphs to visualize the probability distributions. Each graph will have the X-axis representing the variable X and the Y-axis representing the probability density. The graphs will show the range of X values and the corresponding probabilities within that range.

By utilizing technology, we can efficiently calculate the probabilities and create accurate graphs to visualize the distributions.

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The probability that the chip drawn from urn II is red is 4/15. Let's call the event that the chip drawn from urn I and transferred to urn II is red "R1", and the event that the chip drawn from urn II is red "R2".

The probability of event R1 is 2/6 = 1/3.

Given that event R1 has occurred, the number of red chips in urn II becomes 4, and the number of total chips becomes 4+1=5. The probability of event R2 is 4/5 = 4/5.

The probability of both events occurring is (1/3) * (4/5) = 4/15.

So, the probability that the chip drawn from urn II is red is 4/15.

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Answer:

7/20

Step-by-step explanation:

35/100

simplify 7/20

Answer:

Hey there!

The point (0,0) represents that 0 dollars are raised at the beginning of the fundraiser.

Let me know if this helps :)

Answer:

B. $0 is expected to be raised in the fundraiser.

Hope this helps!

Answer:

Mr . Li's salary = $ 2950

Step-by-step explanation:

Ratio  = 7 : 8

Total part = 7+8 = 15

Mr. Lim's part = 7/15

Total salary = $ x

Mr. Lim's salary = $ 2450

\(\dfrac{7}{15}*x= 2450\\\\\\x = 2450*\dfrac{15}{7}\\\\\)

x = 370 * 15

x = $ 5550

Mr . Li's salary = \(\dfrac{8}{15}*5550\)

                       = 8 * 370

                       = $ 2950

Answer:

x = 99,53633682

Step-by-step explanation:

sin(34) = x/178

x = sin(34)×178

x = 99,53633682

The equation of the circle with center (9,-5) and passing through (10,2) is \((x - 9)^2 + (y + 5)^2\) = 50.

To decide the condition of a circle with focus (9,- 5) and going through the point (10,2), we can utilize the standard condition of a circle:

\((x - h)^2 + (y - k)^2 = r^2\)

where (h,k) is the focal point of the circle, and r is the span.

Subbing the qualities we know, we have:

\((x - 9)^2 + (y + 5)^2 = r^2\)

To find the worth of r, we can utilize the way that the circle goes through (10,2). Subbing these qualities, we get:

\((10 - 9)^2 + (2 + 5)^2 = r^2\)

Improving on this articulation, we get:

\(r^2 = 50\)

Subbing this worth back into our situation, we get:

\((x - 9)^2 + (y + 5)^2 = 50\)

To track down the situation of a circle with focus (9,- 5) and going through the point (10,2), we utilize the standard condition of a circle. We substitute the qualities we know and utilize the way that the circle goes through (10,2) to track down the worth of the range. Subbing this worth back into our situation, we acquire the condition of the circle, \((x - 9)^2 + (y + 5)^2 = 50.\)

Thusly, the condition of the circle with focus (9,- 5) and going through (10,2) is \((x - 9)^2 + (y + 5)^2 = 50.\)

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We can draw a graph satisfying these conditions. One possible such graph is shown below:graph(400,400,-1,4,-1,4,

circle(0,2,0.2),circle(1,3,0.2),circle(1,1,0.2),circle(2,2,0.2),

arrow(0,2,1,3),arrow(1,3,2,2),

arrow(0,2,1,1),arrow(1,1,2,2),arrow(2,2,1,3)

)

1. Simple digraph with indegrees 0, 1, 2, 4, 5 and outdegrees 0, 3, 3, 3, 3.Answer:We note that the sum of the indegrees is equal to the sum of the outdegrees: $0 + 1 + 2 + 4 + 5 = 3 + 3 + 3 + 3 + 0 = 12$.Therefore, we can draw a graph satisfying these conditions. One possible such graph is shown below:graph(400,400,-1,6,-1,4,

circle(0,2,0.2),circle(1,1,0.2),circle(2,3,0.2),circle(3,3,0.2),circle(4,3,0.2),circle(5,2,0.2),

arrow(0,2,1,1),arrow(1,1,2,3),arrow(2,3,4,3),arrow(3,3,5,2),

arrow(1,1,2,3),arrow(2,3,3,3),arrow(4,3,5,2)

)

2. Simple digraph with indegrees 0, 1, 2, 2 and outdegrees 0, 1, 1, 3.Answer:Again, we note that the sum of the indegrees is equal to the sum of the outdegrees: $0 + 1 + 2 + 2 = 1 + 1 + 3 + 0 = 5$.Therefore, we can draw a graph satisfying these conditions. One possible such graph is shown below:graph(400,400,-1,4,-1,4,

circle(0,2,0.2),circle(1,3,0.2),circle(1,1,0.2),circle(2,2,0.2),

arrow(0,2,1,3),arrow(1,3,2,2),

arrow(0,2,1,1),arrow(1,1,2,2),arrow(2,2,1,3

)

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