Find the product. (Do not use spaces in your answer.)

d j · d k

Answer:

(a) $ 30000 + 1500 t

(b) $ 52500

Step-by-step explanation:

Initial profit = # 30,000

Profit increases every year by 5 %.

(a) Let the profit after t year is

P = $ 30,000 + 5% of 30,000 t  = $ 30000 + $ 1500 t

(b) t = 15 years

P = $ 30000 + $ 1500 x 15 = $ 52500  

Using exponential function concepts, it is found that:

a) The model is: [tex]A(t) = 30000(1.05)^t[/tex]

b) The prediction for her profits in 15 years is of $62,368.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

Item a:

Then, the model is:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]A(t) = 30000(1 + 0.05)^t[/tex]

[tex]A(t) = 30000(1.05)^t[/tex]

Item b:

In 15 years, the estimate for the profits is of:

[tex]A(15) = 30000(1.05)^{15} = 62368[/tex]

The prediction for her profits in 15 years is of $62,368.

You can learn more about exponential function concepts at https://brainly.com/question/25537936

Answer:

To change a number from scientific notation to standard form, move the decimal point to the left (if the exponent of ten is a negative number), or to the right (if the exponent is positive). You should move the point as many times as the exponent indicates. Do not write the power of ten anymore

Answer:

-72

Step-by-step explanation:

-8×-9

=-72

hope it helps you..

Answer:

same after 3 years

because .............................

Answer:

The populations of orangutans will be same after 3 years

Step-by-step explanation:

Let the populations or orangutans is the same after n years

Decrease in population of oragnutans in the first study

=784-25n=784−25n

Decrease in population of oragnutans in the second study

=817-36n=817−36n

According to the question

784-25n=817-36n784−25n=817−36n

\implies 36n-25n=817-784⟹36n−25n=817−784

\implies 11n=33⟹11n=33

\implies 11n=33⟹11n=33

\implies n=\frac{33}{11}⟹n=

11

33

\implies n=3\text{ years}⟹n=3 years

Therefore, the populations of orangutans will be equal after 3 years

Hope this is helpful.

Answer:

y = 5x + 19

Step-by-step explanation:

y = 5x + b

4 = 5(-3) + b

4 = -15 + b

19 = b

Answer:

I don't understand this

Answer:

0.6

Step-by-step explanation:

cos H = GH/FH

FH^2=20^2+15^2

FH^2=400+225=625

FH=25

cos H= 15/25=3/5=0.6

===========================================================

Explanation:

Before we can apply a trig ratio, we need to find the length of the hypotenuse. Use the pythagorean theorem.

a^2 + b^2 = c^2

c^2 = a^2 + b^2

c = sqrt(a^2 + b^2)

c = sqrt(15^2 + 20^2)

c = 25

The hypotenuse is 25 units long, which is the length of segment FH.

Now we can find the cosine ratio

cos(angle) = adjacent/hypotenuse

cos(H) = GH/FH

cos(H) = 15/25

cos(H) = 3/5

cos(H) = 0.6

Answer:

Step-by-step explanation:

From the picture attached,

ΔDEF is a right triangle with two sides,

EF = 17 units

DF = 20 units

By applying Pythagoras theorem in the given triangle,

DE² = DF² + EF²

(20)² = DF² + (17)²

DF² = 400 - 289

DF = √111

Trigonometric ratios for the ∠F,

sin(F) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}F=\frac{\sqrt{111}}{20}[/tex]

[tex]\text{cosF}=\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\text{cos}F=\frac{17}{20}[/tex]

[tex]\text{tan}F=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\text{tan}F=\frac{\sqrt{111}}{17}[/tex]

Choose the correct option.

Answer:

- [tex]\frac{2\sqrt{3} }{3}[/tex]

Step-by-step explanation:

Using the identity and the exact value

csc x = [tex]\frac{1}{sinx}[/tex]  and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

- 120° is in the third quadrant where sin < 0 , then

csc - 120° = - sin60° , then

csc - 120°

= [tex]\frac{1}{-sin60}[/tex]

= - [tex]\frac{1}{\frac{\sqrt{3} }{2} }[/tex]

= - [tex]\frac{2}{\sqrt{3} }[/tex] ( rationalise the denominator )

= - [tex]\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

= - [tex]\frac{2\sqrt{3} }{3}[/tex]

The equivalent value of the trigonometric relation cosec ( -120 )° = 2√3/3

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

We know that the cosecant function is defined as the reciprocal of the sine function:

cosec (θ) = 1 / sin(θ)

Therefore, to evaluate cosec(-120°), we first need to find sin(-120°).

We know that sine is an odd function, which means that sin(-θ) = -sin(θ). Therefore,

sin(-120°) = -sin(120°)

We can now use the fact that the sine function has a period of 360 degrees, which means that sin(120°) is the same as sin(120° - 360°) = sin(-240°).

Using the same logic as before, we get:

sin(-240°) = -sin(240°)

Now , from the trigonometric relations , we get

Now, we can use the fact that sin(240°) = sin(240° - 360°) = sin(-120°), which means that:

sin(-240°) = -sin(-120°)

Therefore, we have:

sin(-120°) = -sin(120°) = -sin(-240°) = sin(240°)

Now, we can use the unit circle or trigonometric identities to find sin(240°). One way to do this is to draw a 30-60-90 degree triangle in the third quadrant of the unit circle, with the angle of 240° as the reference angle:

In this triangle, the opposite side (O) has a length of √3, the adjacent side (A) has a length of -1, and the hypotenuse (H) has a length of 2.

Therefore, sin(240°) = O/H = (√3)/2.

Finally, we can use the definition of the cosecant function to find cosec(-120°):

cosec(-120°) = 1/sin(-120°) = 1/sin(240°) = 1/((√3)/2) = 2/√3 = (2√3)/3.

Hence , cosec(-120°) is equal to (2√3)/3.

To learn more about trigonometric relations click :

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Answer:

y = 6x + 22

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x - 1 ← is in slope- intercept form

with slope m = 6

Parallel lines have equal slopes, then

y = 6x + c ← is the partial equation

To find c substitute (- 3, 4 ) into the partial equation

4 = - 18 + c ⇒ c = 4 + 18 = 22

y = 6x + 22 ← equation of parallel line

Answer:

Step-by-step explanation:

An angle is cut in half by the bisector.

Since the given angle is 172, its bisector creates 2 equal angles.

2x = 172                 Divide both sides by 2

x = 172/2

x = 86

Answer:

y = 6,2,0,0,2,6

hope this helps

Step-by-step explanation:

Answer:

.324 or 18.9 degrees

Step-by-step explanation:

rule is

sine equals opposite over hypotenuse,

cosine equals adjacent over hypotenuse, and

tangent equals opposite over adjacent

OR

soh cah toa

sine = soh = 12/37 = .324

arcsin(.324) or sin^-1(.324) in DEGREES not radians =

18.9 degrees

Answer:

21/13

Step-by-step explanation:

3 1/2 = 7/2

2 1/6 = 13/6

7/2 divided by 13/6

7/2 X 6/13 = 42/26 = 21/13

Answer:

Step-by-step explanation:

3 1/2 = 7/2 and 2 1/6 = 13/6

7/2 divided by 13/6 = 7/2 x 6/13

42/26

21/13 is your final answer.

Answer:

39.30°

Step-by-step explanation:

In ∆ KLM :-

Answer:

Step-by-step explanation:

The area of a sector has the formula

[tex]A_s=\frac{\theta}{360}*\pi r^2[/tex] Hopefully, this looks somewhat familiar to you. Theta is the central angle given as 75, r is the radius given as 4. Filling in:

[tex]A_s=\frac{75}{360}*(3.14)(4)^2[/tex] and simplifying that a bit to look less threatening, but not by much:

[tex]A_s=\frac{5}{24}(3.14)(16)[/tex] and

[tex]A_s=\frac{251.2}{24}=\frac{157}{15}=10.466666666...[/tex] Not sure how you're supposed to express your answer so I gave both the fraction and its decimal equivalency.

Answer:

-32 shall be multiplied to get the answer.

Step-by-step explanation:

DON'T MIND MY WRITING!!

Answer:

6 x 2 = 8 + 11 = 19 x 3 = 57

Step-by-step explanation:

Answer:

Vmax = 192.33 cm³

Step-by-step explanation: An error in the problem statement. The sides of the box could not be 12 cm. We assume 1.5 cm

Inside dimensions of the box:

Outer dimensions :          12          10         8

 2 *  1.5   =  3                      3            3         3

Inside dimensions:            9            7         5

The volume of a right circular cylinder is:

V(c)  =  π*r²*h              r is the radius of the base and  h the height

By simple inspection is obvious that volume maximum will occur when r is maximum, and r is maximum, only when the base of the cylinder is in the rectangle 12*10. ( Inside  dim  9*7 ) In that case r  =  7/2   r = 3.5 cm

Then the height is 5 cm.

And the maximum volume of the cylinder is:

Vmax = 3.14* ( 3.5)²*5

Vmax = 192.33 cm³

find the DB =[tex]\displaystyle\bf \sqrt{17^2-8^2} =15[/tex]  ; now find AD=AB-DB=21-15=6  .Then                AC=[tex]\displaystyle\bf \sqrt{AD^2+CD^2} =\sqrt{6^2+8^2} =10[/tex]  

Answer:

C

Step-by-step explanation:

Using Pythagoras' identity in both right triangles

To find BD

BD² + CD² = BC²

BD² + 8² = 17²

BD² + 64 = 289 ( subtract 64 from both sides )

BD² = 225 ( take the square root of both sides )

BD = [tex]\sqrt{225}[/tex] = 15

Then

AD = AB - BD = 21 - 15 = 6

To find AC

AC² = AD² + CD²

AC² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )

AC = [tex]\sqrt{100}[/tex] = 10 → C

Step-by-step explanation:

number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Solve the inequality:

The solution set is the space to the right from 3, where 3 is given by an open circle.

Correct choice reflecting the answer is B:

A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Answer:

34

Step-by-step explanation:

You should not expect more than 34 times to be favorable, because favorable outcomes are about 28% of outcomes, and 28% of 100 is 28, which is less than 34.

6/21 outcomes will be favorable.

Here is a list of all possible :

1 - 1

1 - 2

1 - 3

1 - 4

1 - 5

1 - 6

2 - 2

2 - 3

2 - 4

2 - 5

2 - 6

3 - 3

3 - 4

3 - 5

3 - 6

4 - 4

4 - 5

4 - 6

5 - 5

5 - 6outcomes29 out of every 100 outcomes will likely

6 - 6

One or two of the underlined outcomes have a three. The total number of outcomes is 21, and six of them include 3's. Therefore, when we multiply 6/21 by .286, we get 28.6%.  be favorable.

Hope this helps! : )

Answer:

1/9

Step-by-step explanation:

You would multiply 1/3 by 1/3 since both of the spins are out of three for the probability of rolling on the same color two times.

Answer:

5 / 648

Step-by-step explanation:

Given tbe sample space for a pair of dice attached below :

Sample space for a pair of dice = 6² = 36

Rolling a 3 first :

Recall, probability = required outcome / Total possible outcomes

P(rolling a 3). = 2 / 36 = 1 /18

Probability of rolling a 6 (second roll)

P(rolling a 6) = 5 / 36

Hence,

P(3) then P(6) ;

1 / 18 * 5/36 = 5 / 648

Given:

Number of flower pots = 6

To find:

The number of ways of the gardener to arrange the flower pots.

Solution:

Number of ways to arrange n items is n!.

So, the number of ways to arrange 6 pots is:

[tex]6!=6\times 5\times 4\times 3\times 2\times 1[/tex]

[tex]6!=720[/tex]

Therefore, there are total 720 ways of the gardener to arrange the flowerpots.

Answer:

135g

Step-by-step explanation:

[tex]\boxed{mass = density \times volume}[/tex]

Given: density= 5g/cm³, volume= 27cm³

Mass

= 5 ×27

= 135g