HELP PLEASE

Solve the right triangle if the hypotenuse is 5 and one acute angle is 34°. Round answers to two decimal places.

Answer:

The constant of variation is 4

Step-by-step explanation:

We are looking for the constant of variation when t varies directly as the square of s

t = k s^2  where k is the constant of variation

t = 64 and s = 4

64 = k  4^2

64 = k * 16

Divide each side by 16

64/16 = k * 16/16

4 = k

The constant of variation is 4

The solution to the system of equation is (0, 1)

Given the following system of equation as shown below

2^(x)+3^(y)=5,

2^(x+2)+3^(y+1)=18

Rewrite

2^(x)+3^(y)=5,

2^x*2^2 + 3^y*3^1 = 18

___________

2^(x)+3^(y)=5,

4(2^x) + + 3(3^y) = 18

Let a = 2^x and b = 3^y

Substitute

a + b = 5

4a + 3b = 18

a = 5 - b

Substitute

4(5-b) + 3b = 18

20 - 4b + 3b = 18

-b = -2

b = 2

since a = 5 - b

a = 5 - 2

a = 3

Recall that a = 2^x and b = 3^y

2^x = 2

x = 0

Similarly

3^y = 3

y =1

Hence the solution to the system of equation is (0, 1)

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Answer: 2.25 inches

Step-by-step explanation:

The radius of a circle is half the diameter.

The total surface area of the tower composed of a prism with a square base and a pyramid is 3600 + 400√2 m²

Total surface area of the tower = area of the base + 4(area of the rectangular surface) + 4(area of the triangular surface)

Therefore,

area of the base = 20² = 400 m²

4(area of the rectangular surface)  = 4(40 × 20) = 3200 m²

4(area of the triangular surface) = 4(1 / 2 × 10√2 × 20) = 4(100√2) = 400√2 m²

Therefore,

total surface area = 400 + 3200 + 400√2

total surface area = 3600 + 400√2 m²

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Answer:

a)400V2 plus 3,600 m2

Step-by-step explanation:

Answer: The initial population is 18 and 1 year(t=1) later it is 38

Step-by-step explanation:

38 = 18 * e^(1*k), where k is the growth rate

e^(1*k) = 38/18

Take the natural log(ln) of both sides of the = k = ln(38/18) = 0.747

P(t) = 18 * e^(0.747*t), where P(t) is the population affected at time t(years since 1996)

Answer:

(4, 7/2)

Step-by-step explanation:

midpoint = x values/2, y values/2

Answer:

-1.5

Step-by-step explanation:

To work out the gradient of the line, we use this equation:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

Substituting in, we get:

[tex] \frac{5 - ( - 4)}{ - 2 - 4} [/tex]

Which simplifies to:

[tex] \frac{9}{ - 6} = \frac{3}{ - 2} = - \frac{3}{2} = - 1.5[/tex]

Answer:

y = 0.8425   or   y = -0.8425

Step-by-step explanation:

All points in the Cartesian coordinate system have an x and y coordinate, defined by two perpendicular measurements.

If the point is on the unit circle, then the radius of the circle is defined to be 1 unit, and the corresponding right triangle follows the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

For a unit circle:

[tex]x^2+y^2=1^2[/tex]

Substituting the known value for x, and simplifying...

[tex](-0.5387)^2+y^2=(1)^2[/tex]

[tex]0.29019769+y^2=1[/tex]

Subtracting 0.29019769 from both sides to begin to isolate "y"...

[tex]y^2=1-0.29019769[/tex]

[tex]y^2=0.70980231[/tex]

Applying the square root property...

[tex]\sqrt{y^2}=\pm \sqrt{0.70980231}[/tex]

[tex]y=\pm 0.8424976171...[/tex]

So, (to 4 decimal places), the y coordinate could be either 0.8425 or -0.8425.

With only the given information, either result is a valid answer.

The graph that includes the possible values for the number of people who still need to sign up for the team is:

Number line with closed circle on 5 and shading to the right.

Researching this problem on the internet, a team currently has 4 players, and needs at least 9.

When x players are signed, the number of players will be of 4 + x. Since the team needs at least 9 players, the inequality is:

[tex]4 + x \geq 9[/tex]

The solution is:

[tex]x \geq 9 - 4[/tex]

[tex]x \geq 5[/tex]

Which is represented as follows:

Number line with closed circle on 5 and shading to the right.

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The probability that a certain rope will break before being subjected to 120 pounds is 89.4%.

The probability is calculated as follows:

Mean = 100

Standard deviation = 16

The probability is obtained from the z-score.

x = mean + z-score * standard deviation

120 = 100 + z-score * 16

z-score = 20/16

z-score = 1.25

From normal distribution table, the probability with a z-score of 1.25 is 89.4%

In conclusion, the probability is obtained from the z-score.

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The probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.

When a random variable X is normally distributed, with the mean as μ, and standard deviation as σ, then the probability P(X < x) is calculated using the Z-score table, as the probability P(Z < z), where z is calculated using the formula, z = (x - μ)/σ.

In the question, we are asked to find the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12.

We calculate as follows:

P(X < 105)

= P(Z < (105-90)/12)

= P(Z < 1.25)

Now we check the z-score table for the value of z as 1.25.

On the left column we choose the value 1.2.

On the top row, we choose the value .05.

The intersection of these, gives us the value,

P(Z < 1.25) = 0.8944.

Thus, the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.

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Answer:

6.2%, 0.6, 5/8, 2/3

Step-by-step explanation:

For some reason, you have written the same numbers over and over.  It looks like there are only really 4 numbers.

I changed each number into a decimal and then compared them.

6.2% to change a percent to a decimal, move the decimal 2 places to the left so 6.2% equals 0.062.

0.6 is already in decimal form

5/8 you divide 5 by 8.  Put in your calculator 5 the division symbol and then  8 to get  0.625.

2/3 is 0.6 repeating or 0.66666 forever.

Now compare:

62% = 0.62

0.6

5/8 = 0.625

2/3 = 0.66666...

Answer:

53 times per second

Step-by-step explanation:

There are 60 seconds in 1 minute, so divide the 3180 flaps per minute into 60 equal parts.

3180 / 60 = 53

Answer:

40

Step-by-step explanation:

Set up a proportion

Inch/ threads = inch to threads

.1/4 = 1/x  Cross multiple

.1x = 4  Divide both sides by .1

x = 40

Answer:

6

Step-by-step explanation:

no calculator at hand ?

really ? you are using us a simple calculator ?

Answer:

6

Step-by-step explanation:

what is the sum of .74+.19+3.09+1.98=​

0.74+

0.19+

3.09+

1.98=

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

6

The y-values of the two functions f(x) = 3x² -3 and g(x) = 2* - 3 has the minimum y-value of g(x) approaches -3 and f(x) contains the smallest possible y-value.

It exists described as a special kind of relationship and they contain a predefined domain and range according to the function every value in the domain exists connected to just one value in the range.

Given: f(x) = 3x² -3

As we can see in the graph the first term exists 3x² and exists still positive for all x.

The range for f(x) ∈ [-3, ∞)

When x = 0 then f(x) = -3

The above value exists as the smallest possible value on the y-axis.

Given:  [tex]g(x) = 2^x - 3[/tex]

[tex]2^x[/tex] exists also a positive quantity and it exists as an exponential function.

The range for the g(x) ∈ (-3, ∞)

It signifies that g(x) never touches the y-axis at -3.

We can express the minimum value of g(x) approaches -3.

Therefore, the correct answer is option B. The minimum y-value of g(x) approaches -3 and option D. f(x) has the smallest possible y-value.

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Put brackets equal 0

(2x + 1) (x - 1) = 0

(2x + 1) = 0

-1, then ÷2

x = - 1/2 or - 0.5

(x - 1) = 0

+1

x = 1

So, x = - 0.5 & x = 1

Hope this helps!

Answer:

x = -0.5

x = 1

Step-by-step explanation:

Hello!

We can set each factor to 0 and solve for x in both.

There are 2 solutions for x, -0.5 and 1.

The value of (p*q)(5) and (q*p)(5) is 288

The functions are given as:

p(x)=x+1

q(x)=2x^2-2

Calculate p(5) and q(5)

p(5)=5+1 = 6

q(5)=2(5)^2-2 = 48

The functions are then calculated as:

(p*q)(5) = p(5) * q(5)

(p*q)(5) = 6 * 48

(p*q)(5) = 288

Also, we have:

(q*p)(5) = (p*q)(5)

(q*p)(5) = 288

Hence, the value of (p*q)(5) and (q*p)(5) is 288

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Complete question

Suppose that the functions p and q are defined as follows. p(x)=-x-1 q(x)=-2x^2-2 Find the following. (p*q)(5) (q*p)(5)

The domain of a function is the range of its inverse, and vice versa.

So, the domain is [tex]x > 1[/tex] and the range is [tex]y > 3[/tex].

Similar: yes

Similarity statement: [tex]ADCB \sim SVUT[/tex]

Scale factor: 1/3

Answer:

H = 12cm

b

I hope I was able to help

Answer:

7.26

Step-by-step explanation:

Here

Diameter=2m

Length =2.6m

Breadth=4m

Now

Area of circle=(22*2*2*4)/7

=22/7

=3.14m^2

again

Area of rectangle= lb

=2.6m*4m

=10.4m^2

So

Area of the shaded region is 10.4m^2-3.14m^2

=7.26m^2

The answer is 7.26 m².

To find the shaded area, subtract the area of the circle from the area of the rectangle.

The surface area of the closed box in terms of l only, which has the square base is,[tex]2l^2 + \frac{116}{l}[/tex]

The volume of cuboid or box can be given as,

Volume = l × b × h

Here, (l) is the length, (b) is the width of the box and (h) is the height of the box.

A closed box has a square base with side length l feet and height h feet.  Therefore, the length and width will be the same.

Then the volume of the box is 29 cubic feet. Thus,

29 = l × l × h

29 = [tex]l^2 h[/tex]

[tex]h = \frac{l^2}{29}[/tex]

The surface area of the square base box is,

Area = [tex]2l^2 + 4lh[/tex]

Substitute the value of h

Area = [tex]2l^2 + 4l\frac{29}{l^2}[/tex]

Area =  ,[tex]2l^2 + \frac{116}{l}[/tex]

Therefore, the surface area of the closed box in terms of l only, which has the square base is,[tex]2l^2 + \frac{116}{l}[/tex]

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Answer:

The ratios are not equal, so this is not a dilation.

Step-by-step explanation:

4/3 is the first ratio

3/4 is the second ratio

Since these ratios are not equal there is not a dilation.

The probability of selecting from the platter a chocolate cupcake and then a yellow cupcake is  0.10.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of selecting a chocolate cupcake and then a yellow cupcake = (number of chocolate cupcake / total number of cupcakes) x (number of yellow cupcakes / total number of cupcakes - 1)

(13 / 38) x (11 / 37) = 0.10

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{(2,0),(-5,-2),(10,8),(6,0),(-9,-2)} is the correct answer (D)

Answer:

  (d)  {(2, 0), (-5, -2), (10, 8), (6, 0), (-9, -2)}

Step-by-step explanation:

The domain is the list of x-values. The range is the list of y-values. You are looking for the set that matches the given lists.

The list of x-values is {-9, -2}. The list is too short.

The list of x-values is {-9, -5, 2, 6, 10}. This matches the required domain.

The list of y-values is {-2, 0, 8, 5, 9}. The list is too long.

The list of x-values is {-2, 8, 0, -2, 0}. The list does not match the given domain list.

The list of x-values is {2, -5, 10, 6, -9}. This matches the given domain.

The list of y-values is {0, -2, 8, 0, -2}. This matches the given range.

The function of interest is ...

   {(2, 0), (-5, -2), (10, 8), (6, 0), (-9, -2)}