The triangle O'P'Q' is a dilation of the triangle OPQ. What is the scale factor of the dilation?
104
-10 -8 -6
Pr
-4
-2
do
P
6
4
2
O
o
-2
-4
-6
8
6
00
10
10
Simplify your answer and write it as a proper fraction, an improper fraction, or a whole
number.

Answer:

4 Months, and the Total amount is 280

Step-by-step explanation:

60 + 55m = ?

200 + 45m = ?

60 + 55 = 115 + 55 = 170 + 55 = 225 + 55 = 280

200 + 45 = 245 + 45 = 290 + 45 = 235 + 45 = 280

           1                  2                 3                 4

Answer:  \(y = 20\sqrt{15}feet\), \(x = 10\sqrt{15}feet\)

Step-by-step explanation:

given data:

area of the pool = 1800 square feet.

length along the deck = 5- foot

length of side along the deck = 10-foot

Solution:

dimension of  the pool = \(x * y\)

total area \(A = (20+y)(10+x)\)\(...................eqn1\)

since \(xy = 3000\\\)

\(y = \frac{3000}{x}\)\(..............................eqn2\)

insert eqn2 into eqn1

\(A = (\frac{3000}{x} +20)(10+x)\)

\(A = \frac{3000(x+10)}{x^{2} } + \frac{3000}{x} +20\)

\(20 - \frac{30000}{x^{2} } = 0\)

\(x = 10\sqrt{15}\)feet

to solve for y, \(\frac{60000}{x^{3} }\)

\(y = 20\sqrt{15}\)

Answer:

Hindi ko pa po alam solve nyan grade six palang po ako my apologies

Answer:

z = 40°

y = 40°

x = 121°

Step-by-step explanation:

121 + 19 = 140

180 - 140 = 40

z = 40

y = 40

x = 121

40 + 19 = 59

180 - 59 = 121

Maria must cut an additional $70 from her expenses each month in order to save enough money to buy a new TV that costs $420 in 6 months. By allocating this additional amount towards her savings goal, she will be able to reach her target within the desired timeframe. It's important for Maria to review her budget and identify areas where she can reduce expenses in order to make room for the additional savings. This could involve cutting back on discretionary spending, finding ways to save on daily expenses, or exploring opportunities to increase her income.

Maria must cut an additional $70 from her expenses each month.

To determine how much additional money Maria must cut from her expenses each month to afford a new TV that costs $420 in 6 months, we divide the total cost by the number of months.

Additional money per month = Total cost / Number of months

Additional money per month = $420 / 6

Additional money per month = $70

With careful planning and commitment to her budget, Maria can achieve her goal of purchasing a new TV without compromising her financial stability.

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Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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Given that there are 25 observations in a sample taken from a normal distribution having mean 98.6 and standard deviation 17.2.

We are to find \(P(92 < X < 100)\), where X is the random variable with a normal distribution having mean 98.6 and standard deviation 17.2.

We know that the distribution is normal, and we have the mean and standard deviation. Let Z be the standard normal variable such that \(Z = (X - μ) / σ\), where \(μ\) and \(σ\) are the mean and standard deviation of the normal distribution.

The probability that X lies between two given values a and b is the probability that Z lies between the corresponding standard scores.

(ii) To find \(P(X > 105)\), we use the same standard normal variable Z.

\(P(X > 105) = P(Z > (105 - 98.6) / 17.2)= P(Z > 0.372)\). From standard normal tables, the area under the curve to the right of z = 0.372 is 0.3520.

P(X > 105) = 0.3520. This implies that the probability that the value of X is greater than 105 is 0.3520.

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Answer: y-7 =0

Step-by-step explanation: after applying m=y1-y2/x1-x2 you get 0/-7 which means that the slope is 0

Answer:

11=x

Step-by-step explanation:

since the lines are parallel the distances between each section of line is proportional to each other.

5/6=(x-1)/12

multiply both sides by 12

12(5/6)=(x-1)12/12

10=(x-1)

add 1 to both sides

10+1=x-1+1

11=x

I hope that helps :)

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

The point (x,y) on reflection over x-axis, chanes to (x,-y) or x-xoordinate remain same and y-coordinate changes.

So point (4,-3) after reflection over the x-axis changes to (4,3).

Answer: (4,3)

Answer:

16/2 = 8 inches

Step-by-step explanation:

There is enough proof to indicate that the percentage of newsletter readers who possess a Rolls Royce is less than 69%.

The null hypothesis is that p = 0.69, meaning that 69% of the newsletter readers own a Rolls Royce. The alternative hypothesis is that p < 0.69, meaning that less than 69% of the newsletter readers own a Rolls Royce.

We can use a one-tailed z-test to test the hypothesis. Assuming a sample size of n = 100, if we observe fewer than 69 Rolls Royces in our sample, we can reject the null hypothesis.

Using a z-test, we can calculate the z-score by using the formula:

z = (p' - p) / sqrt(p * (1 - p) / n)

where p' is the sample proportion, p is the hypothesized proportion, and n is the sample size.

At a significance level of 0.10, the critical z-value is -1.28. If the calculated z-score is less than -1.28, we can reject the null hypothesis.

If we conduct a survey of 100 newsletter readers and find that 58 of them own a Rolls Royce, the sample proportion would be p' = 0.58. Calculating the z-score, we get:

z = (0.58 - 0.69) / sqrt(0.69 * 0.31 / 100) = -1.83

Since -1.83 is less than -1.28, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that fewer than 69% of the newsletter readers own a Rolls Royce.

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1)

\(\displaystyle\\\frac{1}{3} ;\frac{1\times2}{3\times2} =\frac{2}{6} ;\frac{4}{12} \\\\\frac{2\div2}{4\div2} =\frac{1}{2} ;\frac{2}{4} ;\frac{2\times2}{4\times2} =\frac{4}{8}\)

2)

\(\displaystyle\\\frac{1}{12} ;\frac{1\times2}{12\times2} =\frac{2}{24} ;\frac{3}{36} \\\\\frac{2\div2}{12\div2} =\frac{1}{6} ;\frac{2}{12};\frac{1\times3}{6\times3} =\frac{3}{18} \\\\\frac{1}{4} ;\frac{1\times2}{4\times2}=\frac{2}{8} ;\frac{3}{12}\)

If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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Answer:

Step-by-step explanation: 4.242

The difference of time taken by Rosa and Maya to ran the hurdles is 4.242 seconds .

The correct option is B .

Given, time taken by Rosa and Maya to ran the hurdles.

Time taken by Rosa to ran the hurdle = 58.32 seconds .

Time taken by Maya to ran the hurdle = 54.078 seconds .

Difference between the time taken:

Rosa is taking more time to cover the distance than Maya . Thus the speed of Rosa is less than the speed of Maya .

Relationship between speed, time and distance.

Distance = Speed × Time

Subtract time taken by Rosa to ran the hurdle from time taken by Maya to ran the hurdle.

= 58.32 - 54.078

= 4.242 seconds

Therefore the correct option is B .

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Answer:

Hope it helps you!...............

The number of sides the regular polygon has is: B. 8.

A polygon with an n-side have a sum of interior angles which can be determined using the formula: (n - 2)180, where n is the number of sides of the regular polygon.

Thus, to find the measure of each interior angle of the polygon, we have: interior angle of a polygon = sum of interior angles ÷ number of sides.

Given the following information about the regular polygon:

Interior angle of the regular polygon = 135 degrees.

Plug this into the given formula for finding the interior angle of a polygon:

135 = (n - 2)180/n

Multiply n by both sides of the equation

135 × n = (n - 2)180/n × n

135n = (n - 2)180

Open the bracket

135n = 180n - 360

Subtract both sides by 180n

135n - 180n = 180n - 360 - 180n

-45n = -360

Divide both sides by -45

-45n/-45 = -360/-45

n = 8

Thus, the number of sides that the regular polygon has is: B. 8 sides.

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Answer:

y = 1.1

Step-by-step explanation:

Proportion is a statement that two ratios are equal.

It can be written in two ways:

We can use cross products to find a missing term in it.

Let us solve the question

∵ The proportion statement is \(\frac{7.7}{15.4}\) = \(\frac{y}{2.2}\)

→ Use the  cross multiplication to find y

∵ y × 15.4 = 7.7 × 2.2

∴ 15.4y = 16.94

→ Divide both sides by 15.4 to find y

∵ \(\frac{15.4y}{15.4}\) = \(\frac{16.94}{15.4}\)

∴ y = 1.1

No need to round it to the nearest tenth because the answer has no hundredth to round it to the tenth

The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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Answer:

Negative 3.2 minus (x + 19.1) less-than-or-equal-to 14.2

Step-by-step explanation:

Negative 3.2 minus (x + 19.1) less-than-or-equal-to 14.2

Angle 0 is in the 1st quadrant, its reference angle is 0 radians, and it intersects the unit circle at the point (1, 0).

Define Angle ?

In mathematics, an angle is a geometric figure formed by two rays or lines that share a common endpoint, called the vertex.

a. The angle 0 is measured from the positive x-axis in a counterclockwise direction. In the Cartesian coordinate system, the positive x-axis lies on the right side of the coordinate plane. Since the angle 0 starts from this position, it falls within the 1st quadrant. The 1st quadrant is the region where both x and y coordinates are positive.

b. The reference angle is the positive acute angle between the terminal side of an angle and the x-axis. Since the angle 0 lies entirely on the positive x-axis, the terminal side coincides with the x-axis. In this case, the reference angle for 0 radians is 0 radians itself. The reference angle is always positive and its value is less than or equal to π/2 radians (90 degrees).

c. To find the point where 0 intersects the unit circle, we consider the trigonometric functions cosine and sine. The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system.

For angle 0, the cosine function gives the x-coordinate on the unit circle, and the sine function gives the y-coordinate. Since 0 lies on the positive x-axis, the x-coordinate is 1 (cos(0) = 1), and the y-coordinate is 0 (sin(0) = 0). Therefore, the point of intersection with the unit circle for angle 0 is (1, 0).

In summary, angle 0 is in the 1st quadrant, its reference angle is 0 radians, and it intersects the unit circle at the point (1, 0).

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Answer:

30

Step-by-step explanation:

The sum of interior angles in this shape is equal to 360°

x + x + 5x + 5x = 360

12x = 360 divide both sides by 12

x = 30

Answer:

b

Step-by-step explanation: hope this helps

The rate of change of the area of the square when the side length is 8 inches is 224 inches per hour.

Let s be the side of the given square.

A = s²

dA/dt = d (s²)/dt

dA/dt = 2s × ds/dt

Given ds/dt= 14 inches per hour, s = 8 inches

dA/dt = 2×14×8

dA/dt = 224 inches per hour

The area of the square is s². Since we need to find the rate of change we need to differentiate the area with respect to time which will give us  2s × ds/dt. Once we replace the given values with their respective positions we will get the desired answer. Hence the rate of change in the area of the square is 224 inches per hour.

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The formula to best describe the table is y = 4x - 3  .

Linear equation can represented in different form such as slope intercept form, point slope form, standard form and general form.

The table is a linear table. Therefore, let's represent the formula of the table in slope intercept form.

y = mx + b

where

Therefore, using (0, -3) and (2, 5)

m = 5 + 3/ 2 - 0

m = 8 / 2

m = 4

Therefore, the y-intercept can be calculated as follows:

using (0, -3)

y = 4x + b

-3 = 4(0) + b

b = -3

Therefore, the formula is y = 4x - 3  

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The difference quotient of \(f(x) = x^2 - 6x + 5\) is is 2x - 6 + h.

To find the difference quotient for the function \(f(x) = x^2 - 6x + 5\), we need to evaluate

(f(x + h) - f(x)) / h, where h is not equal to 0.

First, let's find f(x + h):

\(f(x + h) = (x + h)^2 - 6(x + h) + 5\)

\(= x^2 + 2hx + h^2 - 6x - 6h + 5\)

\(= x^2 - 6x + 5 + 2hx - 6h + h^2\)

Now, we can substitute the values of f(x + h) and f(x) into the difference quotient:

\((f(x + h) - f(x)) / h = ((x^2 - 6x + 5 + 2hx - 6h + h^2) - (x^2 - 6x + 5)) / h\)

= (2hx - 6h + h^2) / h

= 2x - 6 + h

Therefore, the difference quotient of \(f(x) = x^2 - 6x + 5\) is 2x - 6 + h.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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