A hat contains slips of paper with the letters A-Z printed on them. If you draw one at random, what is the probability that you will get a vowel?

The boat speeds of 15 km/h and 18 km/h, directions, and the time of travel of 45 minutes gives the angle between their paths as approximately 68°.

The given parameters are;

Direction of the first boat = Northeast

Speed of the first boat = 15 km/h

Direction of the second boat = Northwest

Speed of the second boat = 18 km/h

Distance between the boats after 45 minutes = 14.0 km.

45 minutes = 0.75 × 1 hour

Distance traveled by the first boat in 45 minutes, d1, is therefore;

d1 = 15 km/h × 0.75 hr = 11.25 km

For the second boat, we have;

d2 = 18 km/h × 0.75 hr = 13.5 km

Using cosine rule, we have;

14² = 11.25² + 13.5² - 2 × 11.25 × 13.5 × cos(A)

Where A is the angle between the paths of the two boats.

Which gives;

[tex]cos(A) = \frac{361}{972} [/tex]

[tex] A= \mathbf{ arccos\left(\frac{361}{972} \right) }\approx 68^\circ [/tex]

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The volume of wedge is 4/15 by use of Triple integral.

According to the statement

we  have to find the volume of wedge which is bounded by the parabolic cylinder.

So, because of the given shape of z=√y

the plane y=0 is a boundary, in addition to the given x = 0, z = 0.

so we are in the first octant for all of this. and the further constraint is the plane x + y = 1

Triple integrals are 3 successive integrations, used to calculate a volume, or to integrate in a 4th dimension, over 3 other independent dimensions.

but as a triple integral you would write:

∫x=0 ∫y=0∫z=0 dz dy dx

And after put the values in it and solving it we get the

[−4/15(1−x)^5/2] at x=0

Then after that the answer will become 4/15.

So, The volume of wedge is 4/15 by use of Triple integral.

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The reason why the standard deviation of a set of data is always given as a positive number is because the individual values are squared.

The term standard deviation is used to express how much numbers depart from the mean value. Now we know that the standard deviation for each of the data points is the square of the difference between the score and the mean.

Given that the value that is extracted from each data point is squared, the standard deviation of a set of data is always given as a positive number, but data points can have a negative overall standard deviation.

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The area of the convex polygon is 21.5 square units

The vertices are given as:

(0,5), (-1,2), (4,4), (-3,-4) and (2,0)

The area is then calculated as:

A = 0.5 * |x1y2 - x2y1 +x2y3 - x3y2 + ....... |

So, we have:

A = 0.5 * |-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 +2 * -4 - 0 * -3 - 3 * 2 + 4 * 1|

Evaluate

A = 0.5 * |-43|

Remove the absolute bracket

A = 0.5 * 43

This gives

A = 21.5

Hence, the area of the convex polygon is 21.5 square units

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An absolute value inequality for "all numbers less than 7 and greater than -7" is given by |x| < 7.

Based on the information provided, we can logically deduce that the statement describes an intersection of set because the word "and" was used.

This ultimately implies that, we would use the less than (<) symbol to write an absolute value inequality for the given statement:

|x| < 7

Therefore, this can be translated as follows:

-7 < x < 7      or      x < 7  and    x > -7.

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The pounds of pressure needed to reach a fire 50 feet away is 48 pounds

d = 1/2n + 26

where

If d = 50 feet

d = 1/2n + 26

50 = 1/2n + 26

50 - 26 = 1/2n

24 = 1/2n

n = 24 ÷ 1/2

n = 48 pounds

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Answer:

288pi in^3 , which is 904.78 in^3 to nearest hundredth.

Step-by-step explanation:

V = 4/3 pi r^3

  = 4/3 pi * 6*3

   = 288pi in^3

   = 904.7786842 in^3

Answer:

Below in bold.

Step-by-step explanation:

That would be 4/15 * 360   as there are 360 degrees in a circle

= 96 degrees.

Answer:

A)  

[tex]\begin{array}{|c|c|c|}\cline{1-3} t & H(t) & g(t)\\\cline{1-3} 1 & 60 & 20.4\\\cline{1-3} 2 & 76 & 30.8\\\cline{1-3} 3 & 60 & 41.2\\\cline{1-3} 4 & 12 & 51.6\\\cline{1-3} \end{array}[/tex]

Between 3 and 4 seconds.

B)  The baseballs will collide between 3 and 4 seconds.

Step-by-step explanation:

Given functions:

[tex]H(t)=-16t^2+64t+12[/tex]

[tex]g(t)=10+10.4t[/tex]

Substitute the values of t = 1, 2, 3 and 4 into the two functions:

[tex]H(1)=-16(1)^2+64(1)+12=60[/tex]

[tex]H(2)=-16(2)^2+64(2)+12=76[/tex]

[tex]H(3)=-16(3)^2+64(3)+12=60[/tex]

[tex]H(4)=-16(4)^2+64(4)+12=12[/tex]

[tex]g(1)=10+10.4(1)=20.4[/tex]

[tex]g(2)=10+10.4(2)=30.8[/tex]

[tex]g(3)=10+10.4(3)=41.2[/tex]

[tex]g(4)=10+10.4(4)=51.6[/tex]

Create a table with the found values:

[tex]\begin{array}{|c|c|c|}\cline{1-3} t & H(t) & g(t)\\\cline{1-3} 1 & 60 & 20.4\\\cline{1-3} 2 & 76 & 30.8\\\cline{1-3} 3 & 60 & 41.2\\\cline{1-3} 4 & 12 & 51.6\\\cline{1-3} \end{array}[/tex]

The solution to H(t) = g(t) is between 3 and 4 seconds as:

When t = 3, H(t) > g(t)

When t = 4, H(t) < g(t)

To prove this, equate the equations and solve for t:

[tex]\implies -16t^2+64t+12=10+10.4t[/tex]

[tex]\implies -16t^2+53.6t+2=0[/tex]

Using the Quadratic Formula to solve for t:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]\implies t=\dfrac{-53.6 \pm \sqrt{53.6^2-4(-16)(2)} }{2(-16)}[/tex]

[tex]\implies t=\dfrac{53.6 \pm \sqrt{3000.96}}{32}[/tex]

[tex]\implies t=3.39, -0.04\:\:(\sf 2\:d.p.)[/tex]

As time is positive, t = 3.39 s (which is between 3 and 4 seconds).

When the two baseballs are at the same height they will collide.

Therefore, the baseballs will collide between 3 and 4 seconds (when t = 3.39 s).

Answer:

x^3+6x^2+9x

if you are trying to find the original function

if not, and you are trying to find the zeros is

x=-3

x=0

Step-by-step explanation:

multiply x(x+3)

x^2+3x

then multiply that by x+3 and that should give you the answer

Answer:

x = 0 or x = -3 or x = -3

Step-by-step explanation:

set up factors as:

x = 0

x + 3 = 0

x + 3 = 0

the first will remain as x = 0 while the others become x = -3 once subtracted

i hope this helped!

Answer:

C

Step-by-step explanation:

Distribute the negative, (2x^2 + 5) + (-4x+3)

Add like terms, 2x^2 - 4x +(5+3)

2x^2-4x+8

Answer:

D. (4,0) and (-4,0)

C. there is one discontinuity at x=3

Step-by-step explanation:

Roots can be found by setting f(x)=0:

f(x)=(x^2-16)/(x^2-2x-3)

0=(x^2-16)/(x^2-2x-3), multiply both sides by x^2-2x-3 to get rid of the denominator

0=x^2-16, use difference of squares to factor it

0=(x+4)(x-4)

x=4,-4

Therefore the roots are (4,0) and (-4,0)

Discontinuities are when f(x) is undefined, and f(x) is undefined when something is divided by 0

Set the denominator equal to 0:

0=x^2-6x+9, use the form a^2 - 2ab + b^2 to factor

0=(x-3)^2

x=3

Therefore, there is a discontinuity at x=3

Answer:

11

Step-by-step explanation:

if the some of a number is an restrocal is 122 upon 11 find the integers value of x let the number bees two values of x i e 11 and 1 upon 11 are possible hence required in future value of x is 11

We conclude that the odds of hitting the ball are 0.158

The odds (like the probability) are given by the quotient between the number of attempts in which you hit the ball and the total number of attempts.

Here we know that out of 19 attempts, in 3 you hit the ball. Then the odds of hitting the ball are:

P = 3/19 = 0.158

We conclude that the odds of hitting the ball are 0.158

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Answer:

A

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex] , then

[tex]log_{2}[/tex] 8 = 3 ⇒ 2³ = 8

Answer:

A

Step-by-step explanation:

loga(b)=x

a^x=b

since the answer to log2(8)=3

a^3=8

b=8

a=2

so 2^3=8

I hope this helped!

The triangles are similar by SAS principle.

Similar triangles have the same shape but may have different sizes.

In similar triangles, corresponding sides are always in the same ratio.

The corresponding angles are congruent.

Therefore, using SAS ratio,

6 / 8 = 8 × 3 / 32

6 / 8  = 24 / 32 = 3 / 4

Therefore, the corresponding sides are a ratio of each other.

Therefore, the triangles are similar by SAS principles because the two triangles have two pairs of sides in the same ratio and the included angles are also equal

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Answer:

Step-by-step explanation:

Well first you have:

$15.95 for one sweater
$9.00 each for two shirts

You would double the amount $9.00 which would be:

9 + 9 = 18 or Multiply 9 x 2 = 18

So this would total to 15 + 18 = $33

Answer:

There are 24 frames of animation in 1 second of anime.    Step-by-step explanation:    There are 60 seconds in 1 minute, and 60 minutes in 1 hour. 60×60=3600, so there are 3600 seconds in 1 hour.Since 3600 seconds and 1 hour is the same, there are 86400 frames of animation in 3600 seconds of anime. To find out how many frames are in one second of anime, divide 86400 by 3600.86400 ÷ 3600 = 24There are 24 frames of animation in 1 second of anime.

Answer:

x = 55°

Step-by-step explanation:

That square box indicates a right angle.

A right angle is 90°.

We know that angle x and the 35° angle are making up this 90° angle together.

So, the equation to show what this ship looks like is the following:

[tex]x+35=90[/tex]

This is a simple equation, that if we solve, we get:

[tex]x=55[/tex]

So, x is 55°.

Considering the angle of the ray, it is found that the value of x is of x = 55º.

The ray has an angle of 180º. It is composed by:

Hence:

x + 35 + 90 = 180

x = 180 - 125

x = 55º.

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The coefficient of t to the 4th power in the given expansion is -167403915.

Option (c) is the correct answer.

An expansion of a product of sums uses the fact that multiplication distributes across addition to represent it as a sum of products. A polynomial expression can be expanded by repeatedly substituting equivalent sum of products for subexpressions that multiply two other subexpressions, at least one of which is an addition, up until the expression becomes a sum of (repeated) products. Simplifications like grouping similar terms or canceling terms may also be used during the expansion.

Given expansion=[tex](-9t-9)^{7}[/tex]

Coefficient of the 4th power of t in the expansion,

=[tex]_{7} {C} _{7-4} (-9t)^{4}(-9)^{7-4}[/tex]

=[tex]_{7}C_{3}(-9)^{4}t^{4}(-9)^{3}[/tex]

=[tex]_{7}C_{3}(-9)^{7}t^{4}[/tex]

=[tex]35t^{4}(-9)^{7} \\[/tex]

=[tex]35t^{4}(4782969)[/tex]

= -167403915[tex]t^{4}[/tex]

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Answer:

(12,1)

Step-by-step explanation:

We know that ordered pairs are in the format of (x,y).

This means in that (12, __) 12 is our x coordinate. Plugging 12 into the equation as x we get:

[tex]12-3y=9\\-3y=9-12\\-3y=-3\\y=1[/tex]

Therefore our answer is (12,1) as we plug y back into our coordinate (x,y).

Answer:

(12,1)

Step-by-step explanation:

In the ordered pair, x=12

plug 12 back in the equation

12-3y=9

-3y=-3

3y=3

y=1

See below for the solution of each question

The points are given as:

(3,60) and (5, 80)

The equation is calculated as:

[tex]C(n) = \frac{C_2 -C_1}{n_2 -n_1} * (n - n_1) + C_1[/tex]

This gives

[tex]C(n) = \frac{80- 60}{5-3} * (n - 3) + 60[/tex]

Evaluate the quotient

C(n) = 10 * (n - 3) + 60

Expand

C(n) = 10n - 30 + 60

Evaluate

C(n) = 10n + 30

Hence, the relation of total cost, C, and number of hours, n is C(n) = 10n + 30

The point (3, 60) means he paid $60 for 3 hours

Here, we have:
Fixed = $10

Hourly rate = $15

The equation is calculated as:

C(n) = Fixed + Rate * Number of hours

This gives

C(n) = 10 + 15n

Hence, the relation of total cost, C, and number of hours, n is C(n) = 10 + 15n

The equation is represented as:

C(n) = 10 + 15n

See attachment for the graph

This is the point where the two lines intersect.

From the graph, we have the point of intersection to be:

(n, C(n)) = (4, 70)

This means that the charges for Comput-Repair and Data-Fix are the same after 4 hours

Based on the point of intersection, it is best that Jargit uses Compu-Repair because they have a lesser hourly rate

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Answer:

Step-by-step explanation:

9,328 and you would divide that by 98 and the answer would be 95.18367347 boxes

Answer: 102 degrees

Step-by-step explanation:

The remote angle theorem is that two remote angles are equivalent to the exterior angle. Both 51 degrees are remote angles, and angle 4 is the exterior.

51 + 51 = Angle 4

Angle 4 = 102 degrees

[tex]\\ \rm\dashrightarrow B=10log\dfrac{I}{I_o}[/tex]

[tex]\\ \rm\dashrightarrow B=10\log\dfrac{10^{-7}}{10^{-12}}[/tex]

[tex]\\ \rm\dashrightarrow B=10log10^5[/tex]

[tex]\\ \rm\dashrightarrow B=10\times 5log10[/tex]

[tex]\\ \rm\dashrightarrow B=10(5)[/tex]

[tex]\\ \rm\dashrightarrow B=50dB[/tex]

Answer:

50 Db

Step-by-step explanation:

Given:

[tex]L=10 \log \dfrac{I}{I_0}[/tex]

[tex]I_0=10^{-12}[/tex]

where:

To find the approximate loudness of a dinner conversation with a sound intensity of [tex]I=10^{-7}[/tex], substitute the values of I and I₀ into the given equation and solve for L:

[tex]\implies L=10 \log \dfrac{10^{-7}}{10^{-12}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies L=10 \log 10^{-7-(-12)[/tex]

[tex]\implies L=10 \log 10^5[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies L=5 \cdot 10 \log 10[/tex]

[tex]\implies L=50 \log 10[/tex]

As the given log does not have a specified base, assume the base is 10.

[tex]\implies L=50 \log_{10} 10[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies L=50 (1)[/tex]

[tex]\implies L=50\:\:\sf Db[/tex]

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The equation that represents the situation is,

y = x + 15

Given Information

It is given  that the students complete a 15-point extra-credit assignment in order to raise their test scores.

The new test score is 15 more than the old test score.

We have to find an equation for this situation. A mathematical equation is a formula that uses the equals sign to connect two expressions in order to express their equality.

Forming Equation

Original Score = x

New Score = y ................... (1)

Thus, after the test, the score is raised by 15 points.

⇒ New score = x + 15 .................... (2)

The following equation can be deduced from (1) and (2)

y = x + 15

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Answer:

9 weeks.

Step-by-step explanation:

m = 11w + 67

m = 17w + 13

So:

11w + 67 = 17w + 13

67 - 13 = 17w - 11w

54 = 6w

w = 9.

Answer:

y = -1.3x + 10

Step-by-step explanation:

x_avg = (-2 + -1 + 1 + 2 + 3 + 4)/6 = 1.166666...

y-avg = (21 + 8.6 + 1 + 1 + 5 + 14.3) = 8.48333...

x      y       x-x_avg       y-y_avg          (x-x+avg)²           (x-x_avg)(y-y_avg)

-2    21     -3.1666        12.51666       10.02777                    -39.63611

-1    8.6     -2.1666        0.11666        4.69444                     -0.252777

1      1        -0.1666       -7.48333        0.02777                     1.247222

2      1       0.83333     -7.48333         0.69444                    -6.236111

3      5       1.8333        -3.48333        3.3611111                     -6.386111

4     14.3    2.8333        5.81666         8.02777                     16.480555

sum of (x-x_avg)(y-y_avg) = -34.858

sum of (x+x_avg)² = 26.8333

slope = [(x-x_avg)(y-y_avg)/[(x+x_avg)²]

slope = -34.858/26.8333

slope = -1.29907

y = mx + b

y_avg = m(x_avg) + b

8.48333 = -1.3(1.1666) + b

b = 9.9989

y = -1.3x + 10

Answer:

C) 6

Step-by-step explanation:

3 garden rows = 3*5 = 15 feet

we know we need 2 packages per each 15 feet

45/15=3 so 3 15 in 45, we just multiply 3 and 2 to get 6 packages