A stone falls from a train trestle. The stone's height in meters above the ground is modeled by the function h(t)=−4.9t2+155 where t is time in seconds. To the nearest tenth of a second, how long does it take the stone to hit the ground? State what strategy you will use to answer the question, and then find the answer.

Answer:

28, 4 or 4, 28 (order doesn't matter, both are true answers)

Step-by-step explanation:

l + w = 32

l*w = 112

l = 112/w

112/w + w = 32

w = 28 or 4

l = 28 or 4

Answer:

4,28

Step-by-step explanation:

So let's look at the sentence to take any necessary information out. It says the length of a rectangle plus it's width is 32. Since we do not know what the length and width are, let's just represent them as L (length) and W (width). Using this information we get the equation: [tex]L + W = 32[/tex] and since we're given the area of the rectangle, we can also define another equation which is: [tex]LW = 112[/tex] since the length * width = area.

So now all we have is a systems of equations. We can solve for L or W in the area equation and plug it into the addition equation. We can also solve for L or W in the addition equation and then plug it into the area equation, either should work, but in this example I'll solve for L in the addition equation:

Original Equation:

[tex]L + W = 32[/tex]

Subtract 32 from both sides

[tex]L = 32-W[/tex]

Now let's use this definition of L to plug into the second equation:

[tex]LW = 112 \implies (32-W)W = 112[/tex]

Distribute the W

[tex]-W^2+32W=112[/tex]

Now if you notice, we simply have a quadratic equation and we can subtract 112 from both sides and then use the quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Subtract 112 from both sides

[tex]-W^2+32W-112=0[/tex]

Use quadratic formula

[tex]W = \frac{-32\pm\sqrt{32^2-4(-1)(-112)}}{2(-1)}[/tex]

Simplify stuff in radical

[tex]W = \frac{-32\pm\sqrt{576}}{-2}[/tex]

Calculate the square root

[tex]W=\frac{-32\pm24}{-2}[/tex]

Use positive sign:

[tex]W=\frac{-32+24}{-2}[/tex]

Simplify numerator

[tex]W = \frac{-8}{-2}[/tex]

Simplify fraction

[tex]W=4[/tex]

Take negative sign
[tex]W = \frac{-32-24}{-2}[/tex]

Simplify numerator

[tex]W=\frac{-56}{-2}[/tex]

W = [tex]28[/tex]

So we have two solutions, and the reason for this is because had we solved for W in the original equation and substituted that into here, there would be no different, it's not bound by some variable name. So these are actually the two sides of the rectangles

4 + 28 = 32

4 * 28 = 112

4, 28

If you select 25 in the Top Values list, Access displays the top 25 records in the query results.

Queries are excellent tools in Microsoft Excel to show information from related tables in a single result set, as the results that you pull from queries aren’t limited to a single table.

The way to create a simple query using the wizard is as follows;

Now, If you select 25 in the top values list, access displays the top 25 records in the query results.

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Answer:

C

Step-by-step explanation:

y=mx+b where m is the slope or weekly payments and b is the y-intercept or initial fee.

300 = 30w + 60 fits this

Answer:

925.5

Step-by-step explanation:

Hope it helps!

<3

The value of X is 1/3 and Y is 1/2 and Z is 1/4.

According to the statement we have given the equations which are

X + Y = 5XY  -(1)

Y + Z = 6YZ  -(2)

Z  + X = 7XZ  -(3)

and we have to find the value of X,Y,Z.

So, solve the equations for the X,Y,Z

From (1) equation

Y = X / (5X-1)  -(4)

From (3) equation

Z = X / (7X-1)  -(5)

Put (4) and (5) in (2) then

X / (5X-1)  + X / (7X-1)  = 6{[X / (5X-1)][X / (7X-1)]}

X(7X-1)  + X(5X-1) =  6{[X / (5X-1)][X / (7X-1)]} /  {[1 / (5X-1)][1 / (7X-1)]}

Then after solving

12(X)^2 -2X = 6(X)^2

6(X)^2 -2X = 0

X (6X-2) = 0

X = 0, X = 1/3

Here X = 0 is neglected.

So, X=1/3  -(6)

Put (6) in (4) and (5) then

From 4

Y = X / (5X-1)

Y = (1/3) / (5(1/3)-1)

Y = (1/3) / (2/3)

Y = 1/2.

From (5) equation

Z = X / (7X-1)

Z = (1/3) / (7(1/3)-1)

Z = (1/3) / (4/3)

Z = 1/4.

So, The value of X is 1/3 and Y is 1/2 and Z is 1/4.

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Answer:

10 units

Step-by-step explanation:

the longest length is from (11, 1) to (3, 7) and can be clearly shown when graphed

now to find the length you must use the pythagorean theorem

the distance between 11 and 3 is 8 and the distance between 1 and 7 is 6 so

8^2 + 6^2 = c^2

64 + 36 = c^2

100 = c^2

c = 10

that is your answer

Answer:

No largest no could be 100

Step-by-step explanation:

Yes, the sum of the three numbers is 200, and the largest number can indeed be 75.

Let's assume the three numbers are:

Smallest number = 25

Middle number = x (unknown)

Largest number = 75

The sum of the three numbers is 200, so we can set up the equation:

25 + x + 75 = 200

Now, let's solve for x:

x = 200 - 25 - 75

x = 100

So, the middle number is 100.

Now, we can check if the largest number (75) is correct:

25 + 100 + 75 = 200

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Using a system of equations, it is found that she earns $5.5 for each hat and $7 for each scarf sold.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

One week she earns $114.00 by selling eight hats and 10 scarves, hence:

8x + 10y = 114.

The following week she sold 12 hats and six scarves and earned $108.00, hence:

12x + 6y = 108

Simplifying by 6:

2x + y = 18

y = 18 - 2x.

Replacing in the first equation:

8x + 10y = 114.

8x + 10(18 - 2x) = 114

12x = 66

x = 66/12

x = 5.5

y = 18 - 2x = 18 - 2 x 5.5 = 7.

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All the events in the sample space that are not part of the specified event are called Complement of Event.

Complement of event:

The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event. The complement of an event A is denoted as A c A^c Ac or A′. An event and its complement are mutually exclusive and exhaustive.

Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less.

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The surface area of the parallelpiped is equal to 800 square units.

The surface area of the parallelpiped seen in the picture is equal to the sum of the areas of its six faces, which are combination of areas of quadrilaterals and triangles. There are four parallelograms and two squares. Thus, the surface area of the solid is:

A = 2 · 8 · 20 + 2 · 7 · 20 + 2 · 10²

A = 800

The surface area of the parallelpiped is equal to 800 square units.

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The modal and mean mark of the frequency distribution is 5 and 4.83 respectively.

Mode refers to a mark which reoccurs most in a frequency distribution.

The total number of students who wrote the test = 2 + 3 + 4 + 6 + 10 + 4 + 3 + 2 + 1 + 1

= 36 students

Mean mark = Total mark / Total students

= (2×1) + (3×2) + (4×3) + (6×4) + (10×5) + (4×6) + (3×7) + (2×8) + (1×9) + (1×10) / 36

= (2+6+12+24+50+24+21+16+9+10 / 36

= 174/36

= 4.83333333333333

Approximately,

Mean mark = 4.83

If 25% of students failed,

Number of students who failed = 25% of 36

= 25/100 × 36

= 0.25 × 36

= 9 students.

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By the definition of similar polygons, the lengths of corresponding sides are proportional.

The proportion for [tex]x=40[/tex].

As it is given in the definition, similar polygons have congruent angles and proportional sides.

Therefore, by the definition of similar polygons, the lengths of corresponding sides are proportional.

Cross multiply and solve the proportion  [tex]x[/tex] as follows:

The blank should be proportional.

[tex]\frac{12}{8} =\frac{20+x}{x}\\ 12x=160+8x\\4x=160\\x=40[/tex]

Therefore, the proportion for [tex]x=40[/tex].

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Answer: 4

Step-by-step explanation:

Slope is rise over run (up over sideways) from two points.

The two points shown are (0,4) and (-2,-4).

By counting, you can find the slope, which is 8/2 = 4.

The goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

Given that the mean number of goals a netball team scores per match in the first 9 matches of a competition is 4.

Thus the average of the goals in 9 matches is 4.

Total number of goals is = 9*4 = 36 goals .

Given that the team scores 3 goals in their next match .

Thus the total number of goals scored in 10 matches is 36 + 3 = 39 goals,

Required mean = Total goals / 10 matches .

∴ Required mean = 39/10 = 3.9 .

Therefore, the goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

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The probability that Ron will get by a pitch exactly once is 0.351912.

Given that out of 596 plate appearance Ron was hit 19 times from pitches.

We have to find the probability that ron was hit by pitches in 22 plate appearances.

The value of probability lies between 0 and 1. The formula of calculating proabability is number of items/ total items.

We can find the required probability through binomial distribution which is

n[tex]C_{r}p^{r} (1-p)^{n-r}[/tex] where n is the number of trials and r is the successes.

Probability that Ron will be hit =19/596

=0.031

Probability that Ron will get hit by a pitch exactly once =P(X=1)

=[tex]22C_{1}(0.031)^{1} (1-0.031)^{21}[/tex]

=22!/1!21!*0.031*[tex](0.969)^{21}[/tex]

=22*0.031*0.516

=22*0.015996

=0.351912

Hence the probability that Ron will get hit by a pitch exactly once is 0.35.

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Answer:

84

Step-by-step explanation:

Total students he surveyed: 27

Amount that found it something OTHER than easy: 14 (11 moderate + 3 difficult)

This means that [tex]\frac{14}{27}[/tex] found it something other than easy

Multiply that by 162 to find the proportion for the larger population:

162 * (14/27), and we get 84.

In Wagnerian music drama, a basic recurring theme representing a person, object, event, or emotion is known as Leitmotif.

What is serious opera called?

What is Wagnerian leitmotif?

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Answer:

C. Best models this relationship

Step-by-step explanation:



Answer:

C: y=1/3x

Step-by-step explanation:

I'll set up an equation for this.

When x = 6, y needs to be 2.

--> 2 = 6 times ___

since 6 times 1/3 is 2, ___ is 1/3.

Now we know that 1/3 is the slope. In a complete equation, this will be shown as y = 1/3 x.

This can be proven by reinserting the value of x and y.

2 = 1/3 (6)

Since this equation works, we can be sure that C: y=1/3 x is correct.

The definition of the piecewise function is given as follows:

A piecewise function is a function that has different definitions, depending on the input.

Researching this problem on the internet, for x equal or greater than -3 and less than -1, the function is a line with a slope of 1 that goes through (-3,0), hence the definition is found as follows:

y = x + b

0 = -3 + b

b = 3

Then:

[tex]f(x) = x + 3, -3 \leq x < 1[/tex].

For x between -1 and 1, inclusive, the function is constant at 5, hence the definition is:

[tex]f(x) = 5, -1 \leq x \leq 1[/tex].

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The extreme drop can be said to most likely represent: b. A reflection of the migratory nature of the birds at the lake.

Bird migration is a natural process which can be described as a the movement of different birds by flight across thousands of kilometers in search of ecological conditions and habitats that favors breeding, feeding, and raising of their young.

Migratory birds have well built physiology and morphology that make them better equip to fly fast and across long distances in search of the best ecological conditions, which is dependent on seasons.

Like in the graph given, like we see that at the beginning of January, number of birds were few in the lake until sudden increase occurred. It can be said that during those period of increase, the ecological conditions favored the survival of the bird until November and December. This extreme drop can be said to most likely represent: b. A reflection of the migratory nature of the birds at the lake.

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Option A is correct. If segment DC bisects segment AB, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. This can be obtained using perpendicular bisector theorem.

Perpendicular bisector theorem : In a plane, if we choose a point, say D, on the perpendicular bisector,say PQ, drawn from segment, say AB, then the point D is equidistant from the endpoints, that is A and B, of the segment.

That is, perpendicular bisector PQ of line segment AB is the line with         Q = 90° and Q is the midpoint of AB ⇒ AQ = BQ. A point on PQ say D is equidistant from A and B ⇒AD and BD.

Thus in the given question we can use perpendicular bisector theorem.

Here DC is the perpendicular bisector of the line segment AB and therefore AD and BD are equal.

Hence it is clear that Option A is correct.

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Answer:

9

Step-by-step explanation:

Let x = # of movies Jamie watches in a month. 5 + 2.25x represents the monthly cost of Amazing Primo, and 15 + x represents the monthly cost of Netflakes.

5 + 2.25x > 15 + x

1.25x > 10

x > 8

Jamie must watch more than 8 movies each month for the Netflakes account to be cheaper overall.

a. circle 2 = 60°

circle 3 = 120°

circle 4 = 180°

circle 5 = 240°

circle 6 = 300°

b. circle 8 = 15°

circle 9 = 75°

circle 10 = 155°

circle 11 =  215°

circle 12 =  265°

From the information given, we have that;

There are six major circles

Six minor circles

a. There are 6 circles at a point

Note that angles at a point sum up to 360 degrees

Now, let's divide their sum by the six parts

= [tex]\frac{360}{6}[/tex]

= [tex]60[/tex] degrees

Then, circle 1

= 0 × 60

= 0

Circle 2

=  1 × 60

=  60°

Circle 3

= 2 × 60

= 120°

Circle 4

= 3 × 60

= 180°

Circle 5

= 4 × 60

= 240°

Circle 6

= 5 × 60

= 300°

b. We have that each of these circles ( circle 7 - 12) radian measure is

= main circle - [tex]\frac{\pi }{12}[/tex]

The relative position or direction of circle 7 - 12 to their corresponding main circles ( 1 - 6) are all the same, we then have;
For circles 8

= 60° - 45°

= 15°

Circle 9

= 120° - 45°

= 75°

Circle 10

= 180° - 45°

= 155°

Circle 11

= 240° - 45°

= 215°

Circle 12

= 300° - 45°

= 265°

They share the relationship of radian of circle 7 - 12 corresponding to circles 6 - 12 minus π/12

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Hello !

[tex](x {}^{a} ) {}^{b} = x {}^{a \times b} [/tex]

[tex](b {}^{5} ) {}^{2} = b {}^{ 5\times 2} = b {}^{10} [/tex]

→ Answer D

Answer:

D

Step-by-step explanation:

using the rule of exponents

[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](b^5)^{2}[/tex] = [tex]b^{5(2)}[/tex] = [tex]b^{10}[/tex]

Answer:

45 numbers

Step-by-step explanation:

The 10-digit numbers are from 10-99. We can manually analyze each tenth digit and see if we can find a pattern from it. First, 10-19 ~ 10 is the only number in the sequence where the tenth digit is greater than the unit digit (because 1 > 0). In every other case, 1 is less than or equal to the unit digit.

Next, 20-29 ~ 20 and 21 are the two numbers where the tenth digit is greater than the unit digit

30-39 ~ 30, 31, 32 follow the property

40-49 ~ 40, 41, 42, 43 follow the property

We can keep going, but we can see that there is a pattern. The number of numbers that correspond with the property for each set of 10 numbers is equal to the value of the tenth digit. We see that for the 40s, there are 4 numbers. For the 20s, on the other hand, there are 2 numbers. This pattern carries through:

50-59 ~ 5 numbers, 60-69 ~ 6 numbers, 70-79 ~ 7 numbers, 80-89 ~ 8 numbers, 90-99 ~ 9 numbers

We need to find how many 2-digit numbers total follow the property. We can just add our results together to get our answer:

1+2+3+4+5+6+7+8+9=45

Answer:

B) 16

Step-by-step explanation:

12/3 = x/4

48 = 3x  Divide both sides by 3

16 = x

Answer:

1. The zeros are at x = 0 and x = –10

2. The zeros are at x = 3 and x = 4

Step-by-step explanation:

1. f(x) = x (x + 10)

Multiplying any number by 0 = 0,
so f(x) = 0 when...

• x = 0

or

• x + 10 = 0 (if you subtract 10 from both sides, you get x = –10)

2. f(x) = x (x - 3) – 4 (x - 3)

Use distributive property to expand

x² – 3x – 4x + 12

Combine like terms

x² – 7x + 12

Factor

(x – 3) (x – 4)

(You could have also just noticed in the original function that both x and –4 were multiplied by (x – 3) and factored then.)

So f(x) = 0 when...

• x – 3 = 0  (add 3 to both sides to get x = 3)

or

• x – 4 = 0 (add 4 to both sides to get x = 4)

I hope that helped!

The statement that can be concluded from the triangle is A. RS/VU=ST/UT and ∠S≅∠U.

The Side-Angle-Side Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

In this problem the included angle is ∠S≅∠U, therefore side RS must be proportional to side VU  and side ST must be proportional to side UT

Hence, RS/VU=ST/UT.

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The function with the greatest rate of change over the interval [0, 2] is: D. a.

In Mathematics, the rate of change of a function over a given interval can be determined by calculating the slope of the straight line which connect its end points.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

For line a, we have:

Points (x, y) = (0, 1) and (2, 4)

Slope = (4 - 1)/(2 - 0)

Slope = 3/2 or 1.5.

For line b, we have:

Points (x, y) = (0, 0) and (2, 2)

Slope = (2 - 0)/(2 - 0)

Slope = 2/2 or 1.0.

For line c, we have:

Points (x, y) = (0, -1) and (2, 0)

Slope = (0 + 1)/(2 - 0)

Slope = 1/2 or 0.5.

For line d, we have:

Points (x, y) = (0, 0.5) and (2, 2.5)

Slope = (2.5 - 0.5)/(2 - 0)

Slope = 2/2 or 1.

In conclusion, we can logically deduce that "function a" has the greatest rate of change over the interval [0, 2].

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