Fourteen boys and 21 girls will be equally divided into groups. Find the greatest number of groups that can be created if no one is left out.

Answer:

40m

Step-by-step explanation:

to find the area of a triangle you must do bh/2

So you do 10 times 8 which is 80.

Then you do 80 divided by 2 which is 40.

I hope this helps!

Answer:

C

Step-by-step explanation:

The profit (in thousands of dollars) of a company is given by the function:

[tex]\displaystyle P(x) = -8x^2+32x+14[/tex]

And we want to find the maximum profit of the company.

Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex. Recall that the vertex of a quadratic is given by:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

Find the x-coordinate of the vertex. In this case, a = -8, b = 32, and c = 14. Hence:

[tex]\displaystyle x=-\frac{(32)}{2(-8)}=\frac{32}{16}=2[/tex]

To find the maximum profit, substitute this value back into the function. Hence:

[tex]\displaystyle P(2) = -8(2)^2+32(2) + 14 = 46[/tex]

Therefore, the maximum profit of the company is 46 thousand dollars.

Our answer is C.

9514 1404 393

Answer:

  a.  $19817.10

  b.  $21998.87

Step-by-step explanation:

The formula for the future value of an annuity with payments "A" and interest at rate r compounded quarterly for t years is ...

  FV = A((1 +r/4)^(4t) -1)/(r/4)

The attachment shows this evaluated for ...

a. A = 900, r = 0.04, t = 5. FV = $19817.10

b. A = 450, r - 0.04, t = 10. FV = 21,998.87

Answer:

Step-by-step explanation:

If the three points are collinear, the slopes of RS and ST are same:

Since the sloes are equal we have the following equation:

Slopes must be equal

slope of RS

Now

Slope of ST=-2

Answer:

y - 1 = 4x - 20.

The slope of the line y = 4x +1 is the coefficient of x, so the slope is 4. Parallel lines have the same slope, so the slope of the "other" line is also 4. Using the point-slope form of a line, the equation of the line in question is: y - 1 = 4(x - 5). Distributing 4, we get y - 1 = 4x - 20. i dont know correct me if im wrong

a perfect square trinomial, (x + y)² = x² + 2xy + y²

so, if we have the x of the bx, what is left is the b

the expression would have to be (x + 7)², since we have the 49 and the x²

so, what's left: x² + 14x + 49,

b = 14

hope it helps :)

Answer:

The last choice

Step-by-step explanation:

:)

Answer:

See step by step

Step-by-step explanation:

1a.

[tex] \frac{7\pi}{3} [/tex]

Coterminal Angles difference or a full revolution or 2 pi. so it standard position will be

[tex] \frac{7\pi}{3} - \frac{6\pi}{3} = \frac{\pi}{3} [/tex]

The expression will be

[tex] \frac{\pi}{3} + 2\pi \times n[/tex]

where n is the interger number of revolutions.

1b. Instead using radians, we will be using degrees.

Coterminal Angles difference will be 360 degrees. so it standard position within the unit circle will be

[tex] - 100 + 360 = 260[/tex]

The expression is

[tex] - 100 + 360 \times n[/tex]

where n is the interger number of revolutions.

Answer:

C

Step-by-step explanation:

Hypergeometric distribution

[tex]\frac{{6\choose2}}{{12\choose2}}=\frac{15}{66}= \frac{5}{22}[/tex]

Answer:

you can make 3 outfits

Step-by-step explanation:

because,if you just have 3 shoes aotomaticly you just wear 3 shirt and 3 pants.

for the socks, one people wear 2 socks so there you have 3 outfits

Answer:

[tex]810[/tex]

Step-by-step explanation:

For each shirt, there are 6 different pairs of pants to pair with it. For each of these pairs of pants, there are 3 different shoes to pair and so on.

Therefore, there are [tex]5\cdot 6\cdot 3\cdot 9=\boxed{810}[/tex] combinations you can make.

Answer

Step-by-step explanation:

Answer:

115

Step-by-step explanation:

The opposite angles (115degree angle and angle 4) are equal.

Angle 3=65

Angle 4=115

Angle 5=115

Angle 6=65

Angle 7=65

Angle 8=115

Brainliest please~

Answer:

110100

Step-by-step explanation:

Answer:

Dado que el área de un triángulo es igual a la multiplicación de su base por su altura, si la base de un triángulo se duplica, su área se incrementará, con lo cual la afirmación es incorrecta, ya que el área no se reducirá a la mitad. Así, por ejemplo, un triángulo de base 10 y altura 15 tendrá un área de 50 (10 x 5), mientras que si su base se duplica a 20, pasará a tener un área de 100 (20 x 5), con lo cual su área también se duplicará.

9514 1404 393

Answer:

  (c) √49

  (d) 2.544544...(3-digit repeat)

Step-by-step explanation:

Square roots of perfect squares are rational, as are repeating decimals.

The distance AB across the river is approximately 171.4 meters

The known parameters are;

The distance BC laid off on one side of the river = 415 m

The measure of ∠B = 112.2°

The measure of angle ∠C = 18.3°

The unknown parameter;

The distance AB across the river

Strategy;

Taking the points A, B, and C, being the vertices of the triangle, ΔABC, and apply sine rule to find distance AB;

By the angle sum property, the measure of angle, ∠A = 180° - (∠B + ∠C)

∴ ∠A = 180° - (112.2° + 18.3°) = 49.5°

By sine rule, we get;

[tex]\mathbf{\dfrac{a}{sin (\alpha)} = \dfrac{b}{sin (\beta)} = \dfrac{c}{sin (\gamma)}}[/tex]

Therefore;

[tex]\mathbf {a = sin (\alpha) \times \dfrac{b}{sin (\beta)}}[/tex]

Plugging in α = AB, [tex]\alpha[/tex] = ∠C = 18.3°, b = BC = 415, β = ∠A = 49.5°, we get;

[tex]AB = sin (18.3 ^{\circ}) \times \dfrac{415}{sin (49.5^{\circ})} \approx 171.4[/tex]

The distance across the river, AB ≈ 171.4 m

Learn more about sine rule here;

https://brainly.com/question/15018190

Answer: (2)

Step-by-step explanation:

His yearly interest amount would be 20000(0.08).

His quarterly interest amount would be [tex]\frac{20000(0.08)}{4}[/tex], since one year has 4 quarters.

Step-by-step explanation:

here's the answer to your question

Answer:

53.24 in

Step-by-step explanation:

sin(theta) = perpendicular/hypotenuse

sin(33)=29/hypotenuse

hypotenuse=29/sin(33)=53.24 in

9514 1404 393

Answer:

Step-by-step explanation:

The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.

1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)

__

2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)

Answer:

A. 9

Step-by-step explanation:

First find the slope (m) using two given pairs of values form the table, say (1, 6) and (2, 3):

Slope (m) = change in y/change in x

Slope (m) = (3 - 6)/(2 - 1) = -3/1

Slope (m) = -3

Next, substitute (1, 6) = (x, y) and m = -3 into y = mx + b and solve for y-intercept (b).

Thus:

6 = -3(1) + b

6 = -3 + b

Add 3 to both sides

6 + 3 = -3 + b + 3

9 = b

b = 9

y-intercept = 9

Answer:

5√5

Step-by-step explanation:

Answer:

Surface area = 90 cm²

Step-by-step explanation:

Given net of the rectangular prism shows the dimensions as,

Length = 5 cm

Width = 5 cm

Height = 2 cm

`Expression for the surface area of a rectangular prism = 2(lb + bh + hl)

Here, l = length

w = width

h = height

By substituting the values in the expression,

Surface area = 2(5×2 + 5×2 + 5×5)

                      = 2(10 + 10 + 25)

                      = 90 cm²

Answer:

Step-by-step explanation:

Answer:

0.013 = 1.3% probability that fifteen employees must be tested in order to find three positives.

Step-by-step explanation:

For each employee, there are only two possible outcomes. Either they test positive, or they do not. The probability of an employee testing positive is independent of any other employee, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

40% of the employees have positive indications of asbestos in their lungs

This means that [tex]p = 0.4[/tex]

Find the probability that fifteen employees must be tested in order to find three positives.

2 during the first 14(given by P(X = 2) when n = 14).

The 15th is positive, with 0.4 probability. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{14,2}.(0.4)^{2}.(0.6)^{12} = 0.0317[/tex]

0.0317*0.4 = 0.013.

0.013 = 1.3% probability that fifteen employees must be tested in order to find three positives.

Answer:

B, 300,00

3-1st

4-10th

2-100th

1- 1000th

9-10,000th

3-100,000th

Answer:

B. 300,000

Step-by-step explanation:

Answer:

The approximate percentage of cars that remain in service between 36 and 39 months is of 2.35%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 45 months, standard deviation of 3 months.

What is the approximate percentage of cars that remain in service between 36 and 39 months?

36 = 45 - 3(3)

39 = 45 - 2(3)

So within 2 and 3 standard deviations below the mean.

99.7 - 95 = 4.7% of the measures are between 2 and 3 standard deviations of the mean, however, this is two-tailed, considering both above and below the mean.

In this case, both 36 and 39 are below the mean, and due to the symmetry of the normal distribution, this percentage is divided by half, so 4.7/2 = 2.35.

The approximate percentage of cars that remain in service between 36 and 39 months is of 2.35%.

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{15 - 7x = 14}[/tex]

[tex]\large\text{-7x + 15 = 14}[/tex]

[tex]\underline{\large\text{SUBTRACT 15 to BOTH SIDES}}[/tex]

[tex]\large\text{-7x + 15 - 15 = 14 - 15}[/tex]

[tex]\underline{\underline{\large\text{CANCEL out: 15 - 15 because that gives you 0}}}[/tex]

[tex]\underline{\underline{\large\text{KEEP: 14 - 15 because that helps solve for the x-value}}}[/tex]

[tex]\large\text{14 - 15 = \bf -1}[/tex]

[tex]\underline{\underline{\underline{\large\text{NEW EQUATION: -7x = -1}}}}[/tex]

[tex]\underline{\large\text{DIVIDE -7 to BOTH SIDES}}[/tex]

[tex]\mathsf{\dfrac{-7\mathsf{x}}{-7}=\dfrac{-1}{-7}}[/tex]

[tex]\underline{\underline{\large\text{CANCEL out: } \dfrac{-7}{-7} \large\text{ because that gives you 1}}}[/tex]

[tex]\underline{\underline{\large\text{KEEP: }\dfrac{-1}{-7}\large\text{ because helps you get the x-value}}}[/tex]

[tex]\mathsf{x = \dfrac{-1}{-7}}[/tex]

[tex]\mathsf{x = \dfrac{-1\div-1}{-7\div-1}}[/tex]

[tex]\mathsf{x =\bf \dfrac{1}{7}}[/tex]

[tex]\boxed{\boxed{\large\text{Therefore, your answer is: \bf x = }\bf \dfrac{1}{7}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

[tex](f\cdot g)(x) = 2x^3 + 5x^2-x-6[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]f(x)=2x^2+x-3\text{ and } g(x)=x+2[/tex]

And we want to find:

[tex](f \cdot g)(x)[/tex]

Recall that this is equivalent to:

[tex]=f(x)\cdot g(x)[/tex]

Substitute. Hence:

[tex](f\cdot g)(x)= (2x^2+x-3)(x+2)[/tex]

Expand if desired:

[tex]\displaystyle = x(2x^2+x-3)+2(2x^2+x-3) \\ \\ = (2x^3+x^2-3x)+(4x^2+2x-6) \\ \\\ = 2x^3 + 5x^2-x-6[/tex]

Answer:

2x^3+5x^2-x-6

Step-by-step explanation:

f(x) = 2x^2 + x − 3 and g(x) = x + 2.

(f • g)(x) = (2x^2 + x − 3 ) * (x + 2)

Distribute

           =  (2x^2 + x − 3 )*x + (2x^2 + x − 3 )*2

            = 2x^3 +x^2 -3x + 4x^2 +2x -6

Combine like terms

            =2x^3+5x^2-x-6