The perimeter of the rectangle is 28 units.
What is the value of w?
5 units
7 units
74 units
15 units

Answer:

9.72 seconds ( approx )

Step-by-step explanation:

Since, the equation that shows the height of the rocket from the ground,

y=-16x^2+143x+121y=−16x

2

+143x+121

Where,

x = time after launch, in seconds,

When the rocket hits the ground,

y = 0,

i.e.

-16x^2 + 143x+12=0−16x

2

+143x+12=0

By the quadratic formula,

x = \frac{-143\pm \sqrt{(143)^2 - 4\times -16\times 12}}{-32}x=

−32

−143±

(143)

2

−4×−16×12

x = \frac{-143\pm \sqrt{20449 + 7744}}{-32}x=

−32

−143±

20449+7744

\implies x = -0.778\text{ or }x=9.716⟹x=−0.778 or x=9.716

∵ Time can not be negative,

So, the time taken to hit the ground = 9.716 seconds ≈ 9.72 seconds.

Step-by-step explanation:

그것이 당신에게 도움이되기를 바랍니다 :)

Answer:

the answer is 24 m3

Answer:

$496

Step-by-step explanation:

Given figure is a parallelogram

To Find

Value of"x"

\(m \angle \: A = m \angle \: C\)

\(2x + 35 = 5x - 22\)

\( \implies 2x - 5x = - 22 - 35 \div \\ \implies - 3x = - 57 \\ \\ \implies x = \frac{ - 57}{ - 3} \\ \\ \implies x = \cancel\frac{ - 57}{ - 3} \\ \\ \implies x = 19\)

\(\therefore \text{Option C= 19 is the correct answer}\)

Answer:

there is no table so we are therefore unable to answer this question

Step-by-step explanation:

sorry

Answer:

11.3, rounded

Step-by-step explanation:

mean = average. Add them all up, then divide by how many entries/data points you have.

12 + 18 + 9 + 14 + 8 + 7 = 68

There are 6 numbers we added, so 68/6 = 11.3333333

Please let me know if you have questions.

The rank of population size from fastest to slowest growth is N = 1250, N = 1500, N = 1000, N = 750, N = 500, and N = 250.

The population growth rate is the measure that helps to determine how much the population size changes over time. The population growth rate shows either logistic growth or exponential growth. The formula for logistic population growth is given by \(\frac{dN}{dt}=r_{\text{max}}N\left(\frac{K-N}{N}\right)\). Here, N is the population size, t is time, r (max) is the maximum rate of increase, and K is the carrying capacity.

The one that grows fast will have a large population size, and the one that grows slowly will have a small population size. To rank the population size, arrange the given population size from the largest to the smallest. As a result, we get,

Fastest growth rate N=1250, N=1500 , N=1000, N= 750, N= 500, N= 250 Slowest growth rate

The complete question is -

Arrange the following population sizes in the order of decreasing growth rate. Rank the population sizes (N) from fastest to slowest growth. If two population sizes have the same growth, overlap them.

N = 1250, N = 1500, N = 1000, N = 750, N = 500, N = 250

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The volume of the solid enclosed by the given paraboloids is 68 cubic units.

To find the volume of the solid enclosed by the paraboloids \(z = 16(x^2 + y^2) and z = 18 - 16(x^2 + y^2),\) we need to determine the limits of integration for x, y, and z.

First, let's set the two equations equal to each other to find the intersection points:

\(16(x^2 + y^2) = 18 - 16(x^2 + y^2)\)

Simplifying the equation:

\(32(x^2 + y^2) = 18\\x^2 + y^2 = 18/32\\x^2 + y^2 = 9/16\)

This equation represents a circle in the xy-plane with a radius of \((9/16)^{1/2} = 3/4.\)

Now, we need to determine the limits of integration for x, y, and z based on the geometry of the solid. Since the paraboloids are symmetric about the z-axis, we can integrate over a quarter of the circle in the xy-plane and multiply the result by 4.

The limits of integration for x will be from -3/4 to 3/4, and for y, it will also be from -3/4 to 3/4.

To find the limits of integration for z, we need to determine the upper and lower surfaces of the solid. The upper surface is given by\(z = 18 - 16(x^2 + y^2), and the lower surface is given by z = 16(x^2 + y^2).\)

Therefore, the limits of integration for z will be from the lower surface \((16(x^2 + y^2))\) to the upper surface \((18 - 16(x^2 + y^2)).\) Substituting the limits of integration for x and y, we have:

\(z = 16(x^2 + y^2) to z = 18 - 16(x^2 + y^2)\)

Now, we can set up the integral to calculate the volume:

\(V = 4 \int\ \int\ \int\ (18 - 16(x^2 + y^2) - 16(x^2 + y^2)) dxdydz\\V = 4 \int\ \int\ \int\ (18 - 32(x^2 + y^2)) dxdydz\)

Since the limits of integration are symmetric, we can simplify the integral by integrating over a quarter of the circle:

\(V = 4 \int\ \int\ \int\(18 - 32(x^2 + y^2)) dx dy dz, where x and y range from 0 to 3/4, and z ranges from 16(x^2 + y^2) to 18 - 16(x^2 + y^2).\)

where the limits of integration are as follows:

x ranges from -3/4 to 3/4,

y ranges from -3/4 to 3/4,

and z ranges from \(16(x^2 + y^2) to 18 - 16(x^2 + y^2).\)

Now, let's evaluate this integral step by step:

\(V = 4 \int\ \int\ \int\ (18 - 32(x^2 + y^2)) dxdydz\)

Using the given limits of integration, we have:

\(V = 4 \int\[y=-3/4 to 3/4] \int\[x=-3/4 to 3/4] \int\[z=16(x^2 + y^2) to 18 - 16(x^2 + y^2)] (18 - 32(x^2 + y^2)) dx dy dz\)

Now, we can perform the innermost integral with respect to x:

\(V = 4 \int\[y=-3/4 to 3/4] \int\[x=-3/4 to 3/4] [(18x - 32x^3/3) - (18y^2x - 32y^2x^3/3)] z=16(x^2 + y^2) to 18 - 16(x^2 + y^2) dy dz\)

Simplifying this expression, we have:

\(V = 4 \int\[y=-3/4 to 3/4] \int\[x=-3/4 to 3/4] [(18 - 32x^2 - 32y^2) - (18 - 32(x^2 + y^2))] dy dz\\V = 4 \int\[y=-3/4 to 3/4] \int\[x=-3/4 to 3/4] (-32x^2 - 32y^2) dy dz\\V = 4 \int\[y=-3/4 to 3/4] [-(32/3)x^2y - (32/3)y^3] x=-3/4 to 3/4 dz\\V = 4 \int\[y=-3/4 to 3/4] [-(64/48)y - (64/48)y^3] dz\\V = 4 \int\[y=-3/4 to 3/4] (-(64/48)y - (64/48)y^3) dz\)

Now, we can integrate with respect to y:

\(V = 4 [-(64/48)(y^2/2) - (64/48)(y^4/4)] y=-3/4 to 3/4 dz\\\\V = 4 (-(64/48)(9/32) - (64/48)(81/1024)) dz\\\\V = 4 (-(576/1536) - (5184/1536)) dz\\\\V = 4 (6288/1536) dz\\\\V = 26112/384\\\\V = 68\)

The volume of the solid enclosed by the given paraboloids is 68 cubic units.

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\(24.9^{\circ}\) and \(65.1^{\circ}\)

Recall that Angles that are complementary to each other add up to \(90^{\circ}\).

Let \(a\) be the measure of the complementary angle.

If an angle is \(40.2^{\circ}\) more than its complementary angle, the measure of that angle is \(a +40.2\). The sum of both angles are expressed \(a +(a +40.2)\) but since the have to add to \(90\) as they are complementary, \(a +(a +40.2) = 90\).

Solving for \(a\):

\(a +(a +40.2) = 90 \\ a +a +40.2 = 90 \\ 2a +40.2 = 90 \\ 2a +40.2 -40.2 = 90 -40.2 \\ 2a = 49.8 \\ \frac{2a}{2} = \frac{49.8}{2} \\ a = 24.9\)

Since the other angle measures \(a +40.2\), we can plug in the value of \(a\) to find the measure of the angle.

Evaluating \(a +40.2\):

\(a +40.2 \\ 24.9 +40.2 \\ 65.1\)

The measure of the angles are \(24.9^{\circ}\) and \(65.1^{\circ}\)

We have proved that AB = CD in the given trapezoid ABCD using the properties of the trapezoid and the circle.

To prove that AB = CD, we will use several properties of the given trapezoid and the circle. Let's start by analyzing the information provided step by step.

AC is the bisector of angle BAD:

This implies that angles BAC and CAD are congruent, denoting them as α.

M is the midpoint of CD:

This means that MC = MD.

The circumcircle of triangle OMD intersects AC again at point K:

Let's denote the center of the circumcircle as P. Since P lies on the perpendicular bisector of segment OM (as it is the center of the circumcircle), we have PM = PO.

BK ⊥ AC:

This states that BK is perpendicular to AC, meaning that angle BKC is a right angle.

Now, let's proceed with the proof:

ΔABK ≅ ΔCDK (By ASA congruence)

We need to prove that ΔABK and ΔCDK are congruent. By construction, we know that BK = DK (as K lies on the perpendicular bisector of CD). Additionally, we have angle ABK = angle CDK (both are right angles due to BK ⊥ AC). Therefore, we can conclude that side AB is congruent to side CD.

Proving that ΔABC and ΔCDA are congruent (By SAS congruence)

We need to prove that ΔABC and ΔCDA are congruent. By construction, we know that AC is common to both triangles. Also, we have AB = CD (from Step 1). Now, we need to prove that angle BAC = angle CDA.

Since AC is the bisector of angle BAD, we have angle BAC = angle CAD (as denoted by α in Step 1). Similarly, we can infer that angle CDA = angle CAD. Therefore, angle BAC = angle CDA.

Finally, we have ΔABC ≅ ΔCDA, which implies that AB = CD.

Proving that AB || CD

Since ΔABC and ΔCDA are congruent (from Step 2), we can conclude that AB || CD (as corresponding sides of congruent triangles are parallel).

Thus, we have proved that AB = CD in the given trapezoid ABCD using the properties of the trapezoid and the circle.

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The range of time values describes the entire interval over which Georgiana would be interpolating is 0 to 30 minutes.

What is the domain and range of a function?

The domain of a function is the set of x values for which it is defined, whereas the range is the set of y values for which it is defined.

As in the table, the minimum time for which the distance is defined is 0 minutes while the maximum time is 30 minutes. Therefore, the range of time values describes the entire interval over which Georgiana would be interpolating is 0 to 30 minutes.

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Answer:

C

Step-by-step explanation:

Labor productivity in this case is equal to 10 baskets.

When eight weavers are employed, and output is 80 baskets, labor productivity is equal to 10 baskets.

A labor productivity measure is a way of estimating the amount of output generated per unit of labor.

The following formula is used to calculate labor productivity:

                               Total output produced / Total number of workers involved in the production.  

Therefore, in this case, labor productivity will be equal to the total output produced divided by the total number of weavers employed.

Mathematically, Labor productivity = Total output produced / Total number of weavers employed

Given,The number of weavers employed, n = 8Output produced, Y = 80 baskets

Substitute the above values into the formula for labor productivity,

                        Labor productivity = Total output produced / Total number of weavers employed

                                                   = 80 / 8= 10

Thus, labor productivity in this case is equal to 10 baskets.

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Answer:

im not sure but i think its e,c,f

Step-by-step explanation:

Answer:

55 °

Here's the way i got my answer :

Complementary angles are two angles that have a sum of 90° ,therefore 35° + X = 90°

X=55° .

to get ∠DBF

180° - 90° = 90 °

to get ∠EBF

∠CBD + ∠DBE + ∠EBF = 180°

35° + 90° + ∠EBF = 180°

∠EBF = 55°

The radius of convergence,R, of the series \(\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \]\) is (1, ∞)

We know that for a power series ∑an (x - p)^n

if |x - p| < R then the series converges,

and if |x - p| > R then the series diverges.

Here, the number R is called the radius of convergence.

We have been given a series \(\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \]\)

We need find the radius of convergence.

We use ratio test.

We know for \($\lim_{x\to\infty}~ | \frac{a_{n+1}}{a_n}|=L\)

if L < 1, then the series converges

and If \($\lim_{x\to\infty}~a_n \neq 0\) then \(\sum a_n\) diverges.

Using ratio test for given series,

\($\lim_{x\to\infty}~ | \frac{9(-1)^{n+1}~ (n+1)x^{n+1}}{9(-1)^n~ nx^n}|\\\\\\\)

= \($\lim_{x\to\infty}~ | \frac{(n+1)x^{n+1}}{nx^n}|\)

= \($\lim_{x\to\infty}~ | \frac{(n+1)x}{n}|\)

\(=|x| $\lim_{x\to\infty}~ | \frac{n+1}{n}|\)

= |x|

This means, the series is convergent for |x| < 1.

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Answer:

4. rise

match the following definition with the correct term:

the vertical distance between two points on a line

1. run

2. rate of run

3. slope

4. rise

Answer:

The answer is 162.5

Step-by-step explanation:

you divide 2 by 3 and then figure out how many examples where given to find the average and multiply by that much and you get the answer.

Answer: 120

Step-by-step explanation:

angle c is 120 degrees and angle a is congruent to angle c which mean angle a is 120. hope this helps.

There is a 4/5 probability of catching a T-shirt that is not a size small.

Simply put, the probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

So, there were 50 shirts thrown into the throng in total.

There were 10 little shirts thrown.

15 medium-sized shirts were hurled.

The quantity of extra-large and big shirts.

= Total shirts - ( 10 + 15)

= 50 - 25 = 25

So, a total of 25 shirts are scattered throughout the large/extra large shirts.

A number of shirts that are NOT SMALL size are now available.

= Total shirts - Shirts with small size = 50 - 10 = 40

Probability of getting a not small t-shirt = The total not small t-shirt/The total number of t-shirts

= 40/50

= 4/5

Therefore, there is a 4/5 probability of catching a T-shirt that is not a size small.

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Answer:

1,

Step-by-step explanation:

now z also a dk4k ak4 smka 4ml 4 LL

Answer:

f(x) = x(x-1)

Step-by-step explanation:

The easy way to do this is to look at it graphically. an inverse function is reflected across the line y=x. f(x)=x(x-1) is an upward opening parabola when reflected, there are two y-values for all positive values of x. A function can only have one y for every x.

Answer:

2nd to the left

Step-by-step explanation:

Answer:

75lbs

Step-by-step explanation:

if the mean of the packages was 15 then all the items averaged to 5 pounds each meaning they had a total of 15*5 or 75lbs

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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Answer:

correct value of x = 5

Step-by-step explanation:

\( \frac{ {( - 2)}^{4x + 2} }{ {( - 2)}^{2x} } = {( - 2)}^{12} \\ = \frac{ {( - 2)}^{4 \times 5 + 2} }{ { ( - 2)}^{2 \times 5 } } \\ = \frac{ {( - 2)}^{22} }{ { ( - 2)}^{10} } \\ = \frac{4194304}{1024} \\ = 4096 = 4096(i.e \: {( - 12)}^{12} = 4096) \\ \)

Answer:

1st is x=15

2nd is x=27

Step-by-step explanation:

Answer:

The perimeter of the shape is (7x²+10x+81) inches.

Step-by-step explanation:

When finding the perimeter of a shape, you have to add up all the side lengths :

\(p = 31 + (4 {x}^{2} + 8x) + (3 {x}^{2} - 5x + 20) + (7x + 30)\)

\(p = 31 + 4 {x}^{2} + 8x + 3 {x}^{2} - 5x + 20 + 7x + 30 \)

\(p =( 7 {x}^{2} + 10x + 81) \: inches\)

Answer:

Step-by-step explanation:

every 10 mph above 60, but below 120, you save 5 seconds a mile. But between the 30-60 area, every ten saves 10 seconds a mile (if I am remembering correctly), and every 10 between 15-30 is 20 seconds.

Answer:

25！=1*2*3*4*5*6*...23*24*25

26= 2*13

28=2*14or 4*7

36=2*18or 3*12 or 4*9

56=7*8

All products above are inside 25! So they are all factors of 25!

But 58=2*29 and 29 is not inside 25! so it's not a factor of 25!

Step-by-step explanation:

hope it helped

Answer:

n=25

Step-by-step explanation:

Let n be the greatest possible integer Jo could be thinking of. We know n<100 and n=8k-1=7l-3 for some positive integers k and l. From this, we see that 7l=8k+2=2(4k+1), so $7l$ is a multiple of 14. List some multiples of 14, in decreasing order: 112, 98, 84, 70, .... Since n<100, 112 is too large, but 98 works: \($7k=98\Rightarrow n=98-3=95=8(12)-1$\). Thus,\($n=\boxed{95}$\).

Hope this helped! :)

Answer:

x1 = 2, x2 =-8

y1=-2, y2 =-2

y2-y1 = |-2+2| =0

x2-x1= |-8-2|= 10

So distance is 10 units

Step-by-step explanation:

The mass of the thin bar is \((\pi/2) - 1\).

To find the mass of the thin bar with the given density function, we need to integrate the density function over the length of the bar.

The length of the bar is given as L = SA - SX = \(\pi/2 - 0 = \pi/2.\)

So, the mass of the bar is given by the integral:

M = ∫(SX to SA) p(x) dx

Substituting the given density function, we get:

M = ∫(0 to \(\pi/2\)) (1 + sin x) dx

Using integration rules, we can integrate this as follows:

M = [x - cos x] from 0 to \(\pi/2\)

M = \((\pi/2) - cos(\pi/2) - 0 + cos(0)\)

\(M = (\pi/2) - 1\)

Therefore, the mass of the thin bar is \((\pi/2) - 1.\)

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