2. A cannon launches a ball across the battlefield. An arms engineer is calculating its
trajectory using a quadratic function. The point where the ball is first launched from the
cannon is best represented by which of the following key features? (1 pt)
a) Vertex
b) The zeros
c) y-intercept
d) Axis of symmetry

Answer:

8/25 of the people in the stadium are children.

Step-by-step explanation:

45 + 23 = 68

100 - 68 = 32%

32/100 simplified is 8/25

Answer:

424,752.7 cm³

Step-by-step explanation:

Since you need to convert from English units to Metric units, you can do that first.

Convert each measurement to centimeters instead of feet since your final answer is in cubic centimeters.

1 foot = 30.48 centimeters

Length = 3 ft    30.48cm

              -----  x ------------    =  91.44 cm

                1            1 ft

Width =  2 ft       30.48cm

            -------  x  -------------  =   60.96 cm

                1             1 ft

Height = 2.5 ft      30.48cm

              --------  x  ------------  =  76.2 cm

                  1            1 ft

The volume is equal to L x W x H

91.44cm x 60.96cm x 76.2cm = 424,752.7 cubic centimeters

Let the number be x

We use addiition sign

The expression is x+15

The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with

Two dots at 0

One dot at 2

Two dots at 3

Four dots each at 4, 5, and 6

One dot at 7

A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.

The data can be presented as follows;

2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6

The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.

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The inequality that models this is:

x  ≥ $30

The situation is "I have no less than $30 in my wallet."

So let's define the variable x = amount of money on my wallet.

Then x must be equal to or more than $30 (so we need to use the symbol ≥), then we can write the inequality:

x  ≥ $30

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The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

Step-by-step explanation:

If 11 flights were sampled with an 85% on-time arrival rate, the number of flights from the sample that arrived on time would be estimated to be 9.35, which would round to 9 flights.

This can be solved by:

(0.85x11)= 9.35

Since there can't be .35 of a flight, we would round to the nearest whole number, which would just be 9.

The final answer= 9 flights

The size he should bring more of is small and is denoted as option C.

This is a term which refers to the number of goods sold within a given period of time.

Given that, a vendor is thinking about changing the number of sweatshirts he brings to an event.

To make sure he doesn't run out, he plans to bring more of the size most likely to be sold.

we need to determine that which size should he bring more of,

So, here according to the table,

Small size has the smallest remaining which is 9 when the difference between the number sold and number put up for sale is calculated.

This is therefore why bringing more of small size will ensure he doesn't run out of stock in the next event as more people prefer it.

Hence, the size he should bring more of is small and is denoted as option C.

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Approximately 99.7% of housing prices are between a low price of $108,000 and a high price of $162,000.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

As we want the interval with a percentage of 99.7%, the bounds within three standard deviations of the mean are given as follows:

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Answer:

A=5

B=3

C=5.83

A^2+B^2=C^2

Answer:

5.83

Step-by-step explanation:

u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D

The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answer:

Dessert 1 is 10 million

Step-by-step explanation:

Do 12 million divided by six and you get 2 million. Then do 2 million times 5 and you get 10 million and this works because 10 million is five times more than 2 million and they add up to get 12 million.

Please give me brainliest

Answer:

Step-by-step explanation:

Let x, y, z represent the amounts invested in the first, second, and third accounts. The given relations are ...

  x + y + z = 1,000,000

  .05x +.02y +.03z = 36,250

  x - 4z = 0

__

Your calculator can tell you the solution to these equations is ...

  x = $500,000 . . . amount invested at 5%

  y = $375,000 . . . amount invested at 2%

  z = $125,000 . . . amount invested at 3%

_____

The attached graphing calculator screenshot shows one way this can be solved using a system of 2 equations in x and y. (X- and y-values are in thousands.)

An equally good substitution would be for x: x = 4z. Then you would have two equations in y and z:

  y + 5z = 1,000,000

  0.02y +0.23z = 36,250

The solution to these by any of your favorite methods is ...

  (y, z) = (375000, 125000) and x=4z = 500000

The volume for the given figure can be calculated as,

Hence, the volume of the given figure is 152 cubic cm.

lmk is anything is unclear. This would also work with cosine but it would have to be set up a little differently.

The solution to the question is mathematically given as

1)

H0: M \(\geqslant\) 300

H0: M \(\geqslant\) 300

2)

Z distribution.

3)

z=-2.4

4)

P=0.0082

5)

"H0" is rejected as a hypothesis with a level of significance of 0.05.

Generally, the equation for is mathematically given as

Solutions

we have, \($u=300$$$\begin{aligned}& \sigma=150 \text { dollars } \\N &=64 \text { individuals } \\\bar{x} &=255 \text { dollare. } \\a=& 0.05 .\end{aligned}\)

(1):

H0: M \(\geqslant\) 300 dollars;  customers save at least 300 dollars per year by switching to them.

H0: M \(\geqslant\) 300 dollars:

(This is a left-tailed test)

(2):

when \(\sigma\) is known, we use the Z test. we use Z distribution.

(3):

\(\begin{gathered}z=\frac{\bar{x}-\mu}{6 / \sqrt{n}}=\frac{255-300}{150 / \sqrt{64}}=\frac{-45}{18.75}=-2.4 \\z=-2.4\end{gathered}\)

(4):

\(Pvalue $=P(z < -2 \cdot 4)$ $=0.0082 \quad\{$ wing $z$ tables $\}$ \\\\\text { Pvalue }=0.0082\)

(5):

In conclusion, Since p-value = 0·0082 <0.05

This is statistically significant at the 0.05 level.

We thus "Refect H0" using a threshold of significance of 0.05.

"H0" is rejected as a hypothesis with a level of significance of 0.05.

There is not enough data to support the assertion that consumers may save at least $300 annually by switching insurance providers.

Therefore, we would not consider making the transition to this firm.

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Answer:

If two vectors are perpendicular, then their dot-product is equal to zero. The cross-product of two vectors is defined to be A×B = (a2_b3 - a3_b2, a3_b1 - a1_b3, a1_b2 - a2*b1). The cross product of two non-parallel vectors is a vector that is perpendicular to both of them.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the complete factorization of x³ +4x² -4x -16.

Pairing terms of the given polynomial, we have ...

  (x³ +4x²) -(4x +16)

Factoring each pair gives ...

  x²(x +4) -4(x +4)

  = (x² -4)(x +4)

The factorization of x² -4 is found using the form for factoring the difference of squares:

  a² -b² = (a +b)(a -b)

  x² -4 = (x +2)(x -2)

Note that x+2 is a factor here.

The complete factorization of the given polynomial is ...

  x³ +4x² -4x -16 = (x +4)(x +2)(x -2)

This is confirmed by the graph, which shows zeros at x = -4, -2, 2.

Answer:

A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:

1/p + 1/7 = 1/5

Multiplying both sides by 35p, we get:

35 + 5p = 7p

Simplifying and rearranging, we get:

2p = 35

Therefore, the distance from the lens to the object, p, is:

p = 35/2 cm

B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:

1/q = 1/f - 1/p

Substituting f = 5 cm, we get:

1/q = 1/5 - 1/p

Multiplying both sides by 5qp, we get:

5p = qp - 5q

Simplifying and rearranging, we get:

q = 5p / (p - 5)

Therefore, the expression that gives q as a function of p is:

q = 5p / (p - 5)

C. Here is a sketch of the graph of q(p):

The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.

D. Taking the limit of q as p approaches infinity, we get:

lim q(p) = 5

This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.

Taking the limit of q as p approaches 5 from the positive side, we get:

lim q(p) = -infinity

This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.

In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.

Answer:

Step-by-step explanation:

\(-\frac{\sqrt{5} }{4} =r cos \theta\\-\frac{\sqrt{11} }{4} =rsin \theta\\divide \\\frac{r~sin~\theta}{r ~cos ~\theta} =\frac{-\frac{\sqrt{11} }{4} }{-\frac{\sqrt{5} }{4} } \\tan~\theta=\frac{11}{5} \\\theta=tan^{-1} (\frac{11}{5} )=65.56^\circ,(65.56+180)^\circ=65.56^\circ,245.56^\circ\)

∵ x,y are both negative.

Hence θ lies in third quadrant.

so θ≈245.56°≈246°

Answer:

300

Step-by-step explanation:

A percentage is a unit of proportion that represents a ratio.

For this question let the unknown number be represented by the variable x. We know that 75 is 50% of x, or half of x. This means that we can find the unknown number by doubling 75.

This means that x is 150. Next, we need to find 200% of 150. 200% of any number is that number times 2. So, to find the final answer we must once again double 150.

So, the final answer is 300.

Answer:

Step-by-step explanation:

270

50% equals to 1/2 so 1/2x=75. Times 2 on both sides you get x=135.

So 135 is x and you multiply 135 by 200%. Which get you 270.

Answer:

d(t)=-10t-520

Step-by-step explanation:

First you have to find the gradient (m) using the formula \(m=\frac{d(t)2-d(t)1}{t2-t1}\)

using the two points you have been given: 1(3,-550) and 2(8,-600)

so you substitute these points into the equation \(m=\frac{-600+500}{8-3}\)

m=-10

Now that you have found the m-value you need to find the b-value by using one of the points you already have, I will use Point 2 (8,-600), and substitute it into the equation and solve

d(t)=-10t+b

-600=-10*8+b

-600=-80+b

-520=b

Therefore, the equation is d(t)=-10t-520

Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

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Answer:

6

Step-by-step explanation:

1. re-write the given system:

cx+3y=c-3; => y= -cx/3 +(c-3)/3

12x+cy=c; => y= -12x/c+c/12

2. according the condition the rule for the parallel graphs is:

-c/3= -12/c

3. to calculate the unknown 'c':

c²=36; ⇔c=±6

Answer:

6

Step-by-step explanation:

The system of equations:

cx + 3y = c - 3 ... (i)

12x + cy = c ... (ii)

Multiplying (i) by c and (ii) by 3 gives;

c²x + 3cy = c² - 3c ... (i)

36x + 3cy = 3c ... (ii)

(i) - (ii) gives;

c²x - 36x + 0 = c² - 3c - 3c

c²x - 36x = c²

c²x - c² = 36x

c²(x - 1) = 36x

c² = \(\frac{36x}{x - 1}\)

If  c = -2 then;

(-2)² = 4 = \(\frac{36x}{x - 1}\) , 4x - 4 = 36x , 32x = -4 , x = \(-\frac{1}{8}\)

If c = 2  then;

2² = \(4 = \frac{36x}{x - 1} , 4x - 4 = 36x , 32x = -4 , x = -\frac{1}{8}\)

If c = 6 then;

6² = 36 = \(\frac{36x}{x - 1}\) , 36x - 36 = 36x, 36x - 36x = 36 , x (36 - 36) = 36 , x(0) = 36 , x =   \(\frac{36}{0}\) = undefined or infinitely many solutions.

Hence the system of equations given above will have infinitely many solutions if the value of c is 6.

The addition property of equality was applied in the step 2 of the equation.

The addition property of equality states that if the same number or value is added to both sides of an equation, then the equality still remains true after the addition.

Therefore, let's see where the addition property theorem is applied.

2 / 3 x - 9 = -13

2 / 3 x - 9 + 9 = -13 + 9

2 / 3 x  = -4

2 / 3 x  × 3 / 2  = -4 × 3 / 2

x = -12 / 2

x = -6

Therefore, the addition property of equality was applied in step 2.

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Answer:

47.6 cm

Step-by-step explanation:

Since the triangle is equilateral then the 2 inclined sides = 7.2 cm

Perimeter is then the sum of the 5 sides

P = 13 + 7.2 + 13 + 7.2 + 7.2 = 47.6 cm

Answer:

B

Step-by-step explanation:

\([(8+15) \times 3] \div 3\\= \frac{(8+15) \times 3}{3}\\= \frac{8 + 15}{1}\\= 8 + 15 = 23\)