What is the angle of elevation of the sun when a 50-ft
mast casts an 18ft shadow? Round to the nearest
whole number.
Tan O
50
18
Tano= Opposite Leg
Adjacent Leg
0=
✓
Submit
50ft
o
F-18 ft -
Please help me solve this problem

Answer:

1. Many possible solutions, two solutions would be: (-1,0) and (1,0)

2. x  =  −

2

±  i

Step-by-step explanation:

For the first equation, since its linear, there are many possible solutions!

two solutions would be: (-1,0) and (1,0)

For the second one, replace y with 0 and solve

x  =  −2 ±  i

Hope i helped, brainliest would be appreciated

Have a nice day!

  -Aadi x

Answer:

2,800

Step-by-step explanation:

700+900+1200=2800

Answer:

To maximize his earnings, Mr. Trenga must purchase 40 kayaks and 25 canoes.

Step-by-step explanation:

Since Mr. Trenga plans to start a new business called Rivers Explorers, which will rent canoes & kayaks to people to travel 10 miles down the Clarion River in Cook Forest State Park, and he has $ 45,000 to purchase new boats (canoes & kayaks) , and he can buy canoes for $ 600 each & kayaks for $ 750 each, and his facility can hold up to 65 boats, if the canoes will rent for $ 25 per day & the kayaks will rent for $ 30 per day, to determine how many canoes & how many kayaks should he buy to earn the most revenue, the following calculation should be performed:

65 x 750 = 48,750

48,750 - 45,000 = 3,750

750 - 600 = 150

3,750 / 150 = 25

25 x 600 + 40 x 750 = 45,000

25 x 25 + 30 x 40 = 1,825

600 x 5 = 3,000

750 x 4 = 3,000

40 x 30 + 25 x 25 = 1,825

60 x 30 + 0 x 25 = 1,800

56 x 30 + 5 x 25 = 1,805

52 x 30 + 10 x 25 = 1,810

48 x 30 + 15 x 25 = 1,815

44 x 30 + 20 x 25 = 1,820

Thus, to maximize his earnings, Mr. Trenga must purchase 40 kayaks and 25 canoes.

Answer:

7

Step-by-step explanation:

+2($($;$)2:

hope it helps

Answer:

m=17

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

m

=

17

Answer:

12a

3/4

34.8

a = 3.2

Step-by-step explanation:

9a + 6 = 34.8

9a = 28.8

28.8/9 = 3.2

Answer:

0 is a rational number, whole number, integer, and a real number.

Step-by-step explanation:

Answer:

a) -150 feet per minute

b)-11,250 feet

c)240 minutes

Step-by-step explanation:

-3000/20 = -150 ft per minute

b) -150 times 75

c)-36000= -150x

Answer:

The missing side is 14.4

x=14.4

Answer:

Step-by-step explanation:

Answer: $21.99

Step-by-step explanation:

First, we need to solve for the total cost of 4 packs of football cards

We can either do: $3.97+$3.97+$3.97+$3.97

or

$3.97 x 4

This will equal: $15.88

Now we need to add $6.11 to $15.88

$6.11+$15.88

$21.99

Answer:

x = 44

Step-by-step explanation:

x + x + 14 + 2x - 10 = 180

4x + 4 = 180

4x = 180 - 4

4x = 176

x = 176 / 4

x = 44

Hope that helps!

Answer:

if x=4, the answer is -2.

Step-by-step explanation:

4x3-(3+4)2

12-7x2

12-14

= -2

i hope this helps :)

Answer:

$5740

Step-by-step explanation:

get 2.5% of 5600

5600/x=100/2.5

(5600/x)*x=(100/2.5)*x

5600=40*x

5600/40=x

140=x

x=140 <----- 2.5% of 5600

5600 + 140 = $5740

Answer:The answer is (1,-4).

Step-by-step explanation: Please mark this brainliest.

Answer:

where is the graph though?

Answer:

45535

Step-by-step explanation:

Answer:

45415

Step-by-step explanation:

Answer:

I think it's 20

Step-by-step explanation:

10x4÷2 because vase times height,the divide by 1/2 which it 2 so answer is 20

Three times the quotient of 3 and 5 is equivalent to 1.8

The question asked us to convert the word problem to equation and solve.

The quotient of 3 and 5 is expressed as 3/5

Taking the product of the result and 3 will give;

Three times the quotient of 3 and 5 = 3 * 3/5

Three times the quotient of 3 and 5 = 9/5 = 1.8

Hence three times the quotient of 3 and 5 is equivalent to 1.8

Learn more on expressions here: https://brainly.com/question/723406

#SPJ6

Answer:

28 Months

Step-by-step explanation:

(1140-1072)= 68

(1900/68)=27.9 ~ 28

Answer:

A

Step-by-step explanation:

Area = 1/2 * b * h

b = 4 in

h = 2.5 inches

Area = 1/2 * 4 * 2.5

Area = 2 * 2.5

Area = 5 in^2

Answer: 10

Step-by-step explanation:

Simplifying

68 = 4x + -2 + 30

Reorder the terms:

68 = -2 + 30 + 4x

Combine like terms: -2 + 30 = 28

68 = 28 + 4x

Solving

68 = 28 + 4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4x' to each side of the equation.

68 + -4x = 28 + 4x + -4x

Combine like terms: 4x + -4x = 0

68 + -4x = 28 + 0

68 + -4x = 28

Add '-68' to each side of the equation.

68 + -68 + -4x = 28 + -68

Combine like terms: 68 + -68 = 0

0 + -4x = 28 + -68

-4x = 28 + -68

Combine like terms: 28 + -68 = -40

-4x = -40

Divide each side by '-4'.

x = 10

Simplifying

x = 10

Answer:

x = 10, y = 112

Step-by-step explanation:

4x - 2 + 30 and 68 are vertical angles and are congruent , then

4x - 2 + 30 = 68

4x + 28 = 68 ( subtract 28 from both sides )

4x = 40 ( divide both sides by 4 )

x = 10

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

y and 68 lie on a straight line and sum to 180° , then

y + 68 = 180 ( subtract 68 from both sides )

y = 112

Answer:

Hypotenuse= 97

Step-by-step explanation:

H² = B² + P²

H² = (65)² + (72)²

H² = 4225 + 5184

H²= 9409

Taking square root on both sides,

H= 97

Answer:

y=2x+4

Step-by-step explanation:

Answer:

a. 0.1038 = 10.38% probability that the sample mean is more than 59 pounds.

b. 0.6772 = 67.72% probability that the sample mean is more than 56 pounds.

c. 0.2210 = 22.10% probability that the sample mean is between 56 and 57 pounds.

d. 0.0146 = 1.46% probability that the sample mean is less than 53 pounds.

e. 0% probability that the sample mean is less than 49 pounds.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. The population standard deviation of annual usage is 12.3 pounds.

This means that [tex]\mu = 56.8, \sigma = 12.3[/tex]

Sample of 50:

This means that [tex]n = 50, s = \frac{12.3}{\sqrt{50}} = 1.74[/tex]

a. More than 59 pounds

This is 1 subtracted by the pvalue of Z when X = 59.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{59 - 56.8}{1.74}[/tex]

[tex]Z = 1.26[/tex]

[tex]Z = 1.26[/tex] has a pvalue of 0.8962

1 - 0.8962 = 0.1038

0.1038 = 10.38% probability that the sample mean is more than 59 pounds.

b. More than 56 pounds

This is 1 subtracted by the pvalue of Z when X = 56. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{56 - 56.8}{1.74}[/tex]

[tex]Z = -0.46[/tex]

[tex]Z = -0.46[/tex] has a pvalue of 0.3228

1 - 0.3228 = 0.6772

0.6772 = 67.72% probability that the sample mean is more than 56 pounds.

c. Between 56 and 57 pounds

This is the pvalue of Z when X = 57 subtracted by the pvalue of Z when X = 56.

X = 57

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{57 - 56.8}{1.74}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a pvalue of 0.5438

X = 56

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{56 - 56.8}{1.74}[/tex]

[tex]Z = -0.46[/tex]

[tex]Z = -0.46[/tex] has a pvalue of 0.3228

0.5438 - 0.3228 = 0.2210

0.2210 = 22.10% probability that the sample mean is between 56 and 57 pounds.

d. Less than 53 pounds

This is the pvalue of Z when X = 53.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{53 - 56.8}{1.74}[/tex]

[tex]Z = -2.18[/tex]

[tex]Z = -2.18[/tex] has a pvalue of 0.0146

0.0146 = 1.46% probability that the sample mean is less than 53 pounds.

e. Less than 49 pounds

This is the pvalue of Z when X = 49.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{49 - 56.8}{1.74}[/tex]

[tex]Z = -4.48[/tex]

[tex]Z = -4.48[/tex] has a pvalue of 0

0% probability that the sample mean is less than 49 pounds.

Answer:

Step-by-step explanation:

[tex]\text{Show that a differentiable function f decreases most rapidly at x in the }[/tex]

[tex]\text{direction opposite the gradient vector, that is, in the direction of}[/tex] [tex]-\bigtriangledown f(x)[/tex][tex]\text{. Let}\ \theta \ \text{be the angle between} \bigtriangledown f(x) \ \text{and unit vector u. Then } D_u f = \mathbf{|\bigtriangledown f| \ cos \ \theta }}[/tex]

[tex]\text{Since the minimum value of} \ \ \mathbf{cos \ \theta} \ \ is \mathbf{-1} \ \text{occuring \ for \ 0} \le \ \theta \ < 2x, \\ \\ when \ \theta = \mathbf{\pi} , \text{the mnimum value of} \ D_uf \ is} -|\bigtriangledown f|, \text{occuring when the direction of u is } \\ \\ \ \mathbf{the \ opposite \ of} \ \text{the direction of } \ \bigtriangledown f (assuming \ \bigtriangledown f\ is \ not \ zero)[/tex]

b) [tex]\text{From part A:}[/tex]

[tex]If \ f(x,y) = x^4y -x^2y^2 \ \ decreases \ fastest \ at \ the \point \ (2,-5)\\ \\ F(x,y) = x^4y -x^2y^3 \\ \\ f_x = \dfrac{df}{dx}= \dfrac{d}{dx}(x^4y-x^2y^3) \\ \\ f_x = \dfrac{df}{dx}= y4x^3 -2y^3x \\ \\ For(2,-5) \\ \\ f_x = (-5)4(2)^3 -2(-5)^3(2) \\ \\ \mathbf{ f_x = 340}[/tex]

[tex]However; f_y = \dfrac{df}{dy} = \dfrac{d}{dy}(x^4y - x^2y^3) \\ \\ f_y = x^4 -3x^2y^2 \\ \\ Now, for (2, -5)\\ \\f_y = (2)^4 -3(2)^2(-5)^2 \\ \\ f_y = -284[/tex]

[tex]So; \bigtriangledown = < 340,-284> \text{this is the direction of fastest decrease}[/tex]

Answer:

I dont see any options....

But 1/4, 1/5, 1/6, 1/7, 2/7, etc

Step-by-step explanation:

Answer:

a lot but here are a few

Step-by-step explanation:

1/3 3/6 2/6 1/6 7/12 6/12 5/12 4/12 3/12 2/12 1/12 16/24 15/24 14/24 13/24 12/24 11/24 10/24 9/24 8/24 7/24 6/24 5/24 4/24 3/24 2/24 and 1/24