It costs $145 for 10 people to attend a concert. How much does it cost a group of 8 people?

perimeter = add all 3 sides 13+13+10 = 36 cm

 for area you need to find the height of the triangle, which is the red dotted line

to do that use the Pythagorean Theorem

a^2 + B^2= c^2

a^2 = height

a^2 +5^2 = 13^2

a^2 +25 = 169

a^2 = 169-25 = 144

a=square root(144) = 12

 so the height is 12

area = 1/2 h x b = 1/2 x 12 x 10 = 1/2x 120 = 60

area = 60 cm^2

 cost is $4 per square cm

 there is 60 square cm in the triangle so multiply 60 x 4 = $240

Answer: 199: 1.

Step-by-step explanation:

The odds against any event is the ratio of the unfavorable outcomes to the favorable outcomes.

Given , The winner of a raffle will receive a​ 21-foot outboard boat.

Total raffle tickets were sold  = 6000

Number of tickets you have = 30

We assume that the lottery was fair , then, the number of possible outcome that you will win = 30

and the number of possible outcomes that one of the others wins = 6000-30= 5970

Then, the odds against your winning the​ boat = Number of possible outcomes that one of the others wins : Number of possible outcome that you will win

= 5970: 30 = 199:1   [∵[tex]\dfrac{5970}{30}=\dfrac{199}{1}[/tex]]

Hence, the odds against your winning the​ boat = 199: 1.

The positive root of the given quadratic function is x = 10.

We have the equation:

[tex]x^2 + 5x = 150[/tex]

First, we rewrite it as:

[tex]x^2 + 5x - 150 = 0[/tex]

Using the Bhaskara's formula, we will get:

[tex]x = \frac{-5 \pm \sqrt{5^2 - 4*(-150)*1} }{2} \\\\x = \frac{-5 \pm 25 }{2}[/tex]

The positive solution is:

x = (-5 + 25)/2 = 10

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Answer: The correct option is B, i.e., "As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞".

Explanation:

From the table it is noticed that the first row represents the value of x and the second row represents the value of f(x).

The value of f(x) is 14 at x = -5, after that the value of f(x) is decreased as the value of x increases.

The value of f(x) remains unchanged when the value of x approaches to 0 from 1.

The value of f(x) is -6 at x = 0, after that the value of f(x) is increased as the value of x increases.

From the table it is noticed that as the value of x approaches to positive infinity the value of f(x) is also approaches to positive infinity.

[tex]f(x)\rightarrow\infty \text{ as }x\rightarrow\infty[/tex]

From the table it is noticed that as the value of x approaches negative infinity the value of f(x) is also approaches to positive infinity.

[tex]f(x)\rightarrow\infty \text{ as }x\rightarrow-\infty[/tex]

These statement are shown in second option, therefore the second option is correct.

Answer:

The end behavior of the graph of the function f(x) is:

f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞,

Step-by-step explanation:

Based on the table we could observe that the function f(x) is increasing to the left of -1 as well to the right of -1 and it attains the minimum value to be -6.

Hence, it can be predicted that the end behavior of the graph of the function f(x) goes to infinity in the left and also it goes to infinity in the right.

Hence, the statement that best describes the end behavior of the graph of f(x)  is:

f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞.

Answer:

2:1

Step-by-step explanation:

The ratio is 2:1 and the new value can also be 8/4= 2/1

Answer:

The answer is Savings account B

Savings account A offers a higher APY because it compounds quarterly, which is more frequent than savings account B which compounds semiannually. More compounding periods per year lead to interest being earned on interest more often, resulting in a higher effective yield.

Annual Percentage Yield (APY) given that both accounts offer the same Annual Percentage Rate (APR) of 7%, but one compound quarterly and the other semiannually. The APY is a measure of how much interest an account will earn in a year, taking into account the effect of compounding.

Compounding more frequently results in a higher yield because interest is earned on interest more often. Account A compounds quarterly, meaning it does so four times a year, while Account B compounds semiannually, meaning it does so twice a year. As the frequency of compounding increases, so does the APY, because the money earns interest on the interest that has been added to the account more frequently.

Therefore, the correct answer is A. Savings account A, because it has more compounding periods per year, which means it will have a higher APY compared to savings account B which compounds less frequently.

A = 1.49/5 =0.298 cents per ounce

B = 3.59/12 = 0.299 cents per ounce

 so A has the lowest unit price

The Golden Ratio is a mathematical relationship that exists in art, shapes, nature and the human body. The golden ratio can be present in your body, from the length of your arms and legs when compared to your torso. Fingers is another example because the length of our fingers, each section from the tip of the base to the wrist is larger than the preceding.

The measurement of the human navel to the floor and to the top of the head to the navel is also the Golden ratio. Plastic surgeons and dental surgeons use it to reconstruct the human face. It also appears in everything around us like in the nature and science. It appears on in flower petals because it is believed that each petal is placed to so that each petal gets the best exposure to sunlight. Dolphins, starfish, sea urchins and honeybees also exhibit the proportion like humans. DNA molecules measures 34 angstroms by 21 angstroms at each full cycle of the double helix spiral, these two number are successive numbers. I think that the Golden Ratio is just a freak coincidence that happened.

270 =60 + 0.50(x-40)

270 =60 + 0.50x -20

210 =0.50x -20

230=0.50x

x=230/0.50 = 460 miles

check:

460-40 = 420

420*0.50=210 +60=270

 she can drive 460 miles total

The equation in standard form is y = x^2 - 8x + 38

The vertex form of the equation is given as':

y = (x - 4)^2 + 22

Expand the equation

y = x^2 - 8x + 16 + 22

Evaluate the sum

y = x^2 - 8x + 38

Hence, the equation in standard form is y = x^2 - 8x + 38

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We are given that:

a x^2 + b x + c = 0

Divide all terms with c/ a:

x^2 + (b / a) x + (c / a) = 0

Subtract c from both sides:

x^2 + (b / a) x + (c / a) – c / a = 0 – c / a

x^2 + (b / a) x = - c / a

Add a constant k to complete the square:

where k = ((b / a) / 2)^2 = (b /2a)^2

x^2 + (b / a) x  + k = - c / a + k

x^2 + (b / a) x + (b/2a)^2 = - c / a + (b /2a)^2

So the perfect square trinomial is:

(x + b/2a)^2 = - c / a + (b /2a)^2

Taking the square root of both sides:

x + b/2a = sqrt [- c / a + (b /2a)^2]

x = sqrt [(-c/a) + (b /2a)^2] – (b/2a)

Answer:

My equation is 3x^2 + 12x + 24 = 0. When I divide all of the terms by 3, the equation becomes x^2 + 4x + 8 = 0. When I subtract both sides by the constant, 8, the equation is x^2 + 4x = -8. When I add a constant to create the perfect square, the equation now becomes x^2 + 12x + 36 = 28. Finally, the equation simplified equals (x + 6)= the square root of 28.

Step-by-step explanation:

The value of the expression x + sqrt(yz) when x = 3, y = 2, and z = -8 is 3 + 4i.

To evaluate the expression x + sqrt(yz), we substitute the given values for x, y, and z. Given x = 3, y = 2, and z = -8:

x + sqrt(yz) = 3 + sqrt(2*-8) = 3 + sqrt(-16) = 3 + 4i

Therefore, the value of the expression is 3 + 4i.

Answer:

x=49,6323º

Step-by-step explanation:

To solve this you just have to use the inverted sin X, remember that Sin=opposite/hyphotenuse

Sinx= 16/21

Sin x=,761904

x=-1Sin,761904

x=49,6323

So the measure of the angle X would be 49,6323.

A binomial distribution is an experiment where there are two outcomes; Success and failure. In here, you are given n = 128 and p = 0.27. The formula for the variance of a binomial distribution is n*p(1 – p) or n*p*q*. They are equivalent because q = 1- p. We will use the first equation.

Variance = n*p*(1 – p)

Variance = 128*0.27*(1 – 0.27)

Variance = 25.23

To get the standard deviation, find the square root of the variance.

Standard deviation = sqrt (Variance)

Standard deviation = sqrt (25.23)

Standard deviation = 5.02

One pepper cost is 0.69.

Selling price is defined as the price that a customer pays to purchase a product.

Let one pepper cost is x,

Three peppers cost is 2.07,

x = ratio of the total cost of peppers to the number of peppers .

x= 2.07/3

x = 0.69

So, the peppers cost 69 cents each.

Hence, one pepper cost is 0.69.

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