If F(a, b, c, d) = a^b + c \times d, what is the value of x such that F(2, x, 4, 11) = 300?

Answer:

Step-by-step explanation:

This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is

[tex]y=a(b)^x[/tex] where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then

a = 5000

If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So

b = 1.035

Our function is

[tex]y=5000(1.035)^x[/tex] where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.

[tex]7300=5000(1.035)^x[/tex] and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.

Begin by dividing both sides by 5000 to get

[tex]1.46=1.035^x[/tex] and take the natural log of both sides:

[tex]ln(1.46)=ln(1.035)^x[/tex]

The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:

[tex]ln(1.46)=xln(1.035)[/tex] To solve for x, we now divide both sides by ln(1.035):

[tex]\frac{ln(1.46)}{ln(1.035)}=x[/tex]

Do that division on your calculator and get that

x = 11.0 years.

That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)

Answer:

you combine like terms by adding them up

Step-by-step explanation:

Answer:

[tex]\frac{8}{27}[/tex] is the probability that a player draws out two tiles of the same color assuming they are drawing one tile from each bag.

Step-by-step explanation:

In each bag there are red, green, and blue tiles, meaning that no matter which color is pulled out first there is always some probability that the second tile will be the same color. So, we can set up three possible outcomes:

Red: The player pulls out a red tile first. This has a [tex]\frac{1}{9}[/tex] probability of happening. Then in order to succeed for the problem, the next tile also needs to be red which has a [tex]\frac{6}{12}[/tex] probability attached to it. [tex]\frac{1}{9}[/tex] × [tex]\frac{6}{12}[/tex]=[tex]\frac{1}{18}[/tex] probability of happening.

Green: There is a [tex]\frac{5}{9}[/tex] probability of the player pulling out a green tile first. In this case we want to calculate the probability of the second tile being green, which would be [tex]\frac{4}{12}[/tex]. [tex]\frac{5}{9}[/tex]×[tex]\frac{4}{12}[/tex]=[tex]\frac{5}{27}[/tex].

Blue: There is a [tex]\frac{3}{9}[/tex] probability of the first tile being blue in which case we are hoping for the second tile to be blue as well. The probability of the second tile being blue is [tex]\frac{2}{12}[/tex] on its own, and them both being blue is  [tex]\frac{3}{9}[/tex]×[tex]\frac{2}{12}[/tex]=[tex]\frac{1}{18}[/tex]

Adding [tex]\frac{1}{18}[/tex]+[tex]\frac{1}{18}[/tex]+[tex]\frac{5}{27}[/tex] we get the answer [tex]\frac{8}{27}[/tex].

Answer:

x = 19

Step-by-step explanation:

Since CD = DE then Δ CDE is isosceles and the base angles are congruent.

∠ DCE = ∠ DEC = 38° , thus

∠ CDE = 180° - (2 × 38)° = 180° - 76° = 104°

The consecutive angles of a parallelogram are supplementary, thus

∠ BAE + ∠ CDE = 180, that is

4x + 104 = 180 ( subtract 104 from both sides )

4x = 76 ( divide both sides by 4 )

x = 19

Answer:

Step-by-step explanation:

Quadrilaterals are four sided shapes. A parallelogram is a quadrilateral with equal and parallel opposite sides. The sum of the interior angles of any quadrilateral is always 360 degrees

Considering the question being asked, the correct option is

1) The sum of the interior angles will still be 360°. This will always remain the same no matter what type of quadrilateral is formed.

For the other options, some will remain the same and this depends on the type of quadrilateral that is formed.

Answer:

Its 1 and 3

Step-by-step explanation:

Answer:

(x+7)(x+6)

Step-by-step explanation:

x²+13x+42

x²+6x+7x+42

x(x+6)+7(x+6)

(x+6)(x+7)

Answer:

a) (x+7) (x+6)

Step-by-step explanation:

That is the correct answer because you get it when you factor the current equation.

Hope it helps

Answer:

Do it your self

Step-by-step explanation:

Answer:

1.2^2

Step-by-step explanation:

1 11/25=36/25

square rout of 36/25=1.2

Answer:

1 11/25 is the same as 36/25. Since 36 and 25 are 6² and 5² respectively the answer is (6 / 5)².

Answer:

The third option: 48 degrees.

Step-by-step explanation:

Angle GFH is congruent to angle CFE, which is congruent to ACB, therefore, all are congruent and equal to 48.

Answer:

x = 48

Step-by-step explanation:

∠x ≅ ∠C (vertical angles)

∠C ≅ ∠CFG (corresponding angles)

∠CFG ≅ ∠HFG ≅ 48° (vertical angle)

So

∠x ≅ 48 (Transitive property of equality)

Answer:

Length = 7 cm

Width = 2 cm

Step-by-step explanation:

Perimeter of rectangle = 18 cm

Let length of rectangle = [tex]l[/tex] cm

Let width of rectangle =  [tex]w[/tex] cm

As per given statement, length is 3 cm more than the twice of its width:

Writing equation:

[tex]l = 2\times w +3 ....... (1)[/tex]

Formula for perimeter of a rectangle is given as:

[tex]P = 2 \times (Length + Width)[/tex]

OR

[tex]P = 2 \times (l + w)[/tex]

Putting values of P as given and [tex]l[/tex] by using equation (1):

[tex]18 = 2 \times (2w +3 + w)\\\Rightarrow \dfrac{18}2 = 3w +3 \\\Rightarrow 9 = 3w +3\\\Rightarrow 3w = 9 -3\\\Rightarrow w = \dfrac{6}{3}\\\Rightarrow w = 2\ cm[/tex]

Putting value of [tex]w[/tex] in equation (1):

[tex]l = 2\times 2 +3 \\\Rightarrow l = 4+3\\\Rightarrow l = 7\ cm[/tex]

So, the dimensions are:

Length = 7 cm

Width = 2 cm

Answer:

0.08 minutes for a kilometer.

Step-by-step explanation:

If the track is 25 kilometers, and he runs 25 kilometers in 2 minutes, he runs a kilometer in 2÷25 minutes or 0.08 minutes which is 4.8 seconds.

I'm pretty sure the track isn't 25 kilometer or he can't run a lap in 2 minutes. But if so, the answer is 0.08 minutes.

Answer: 3/2

Step-by-step explanation:

Just take the length of 1 side, for example LP, and count the length in units.

LP = 8 units

Now, L’P’ = 12 units, so divide the length of L’P’ by LP to get the factor of dilation.

12/8 = 3/2

Answer:

D.

[tex] {4}^{x + 7} [/tex]

Step-by-step explanation:

since it is an exponential graph shifted 7units to the left would be

[tex] {4}^{x + 7} [/tex]

Answer:

The weight in ounces of one box = 15ounces

Step-by-step explanation:

We are told the relationship between the number of boxes and the weight of the crackers in the boxes is given as 11boxes and 165ounces respectively.

In order words, 11boxes weigh 165ounces.

To determine the weight, in ounces, of one box, we would divide the weight of the 11boxes by the number of boxes.

Weight of the 11boxes = 165ounces

Number of boxes that gives that weight = 11

The weight of one box = 165/11

The weight of one box = 15ounces

Answer:

(C)

Step-by-step explanation:

I took the quiz

Answer:

35 cm

Step-by-step explanation:

As shown in the image attached, the A large rectangle is made by joining three identical small rectangles,

The width of one small rectangle is x cm and the length of one small rectangle is 2x cm. Therefore the perimeter of the small rectangle is given as:

2(length + width) = Perimeter

2(2x + x) = 21

2(3x) = 21

6x = 21

x = 21/6 = 3.5 cm

x = 3.5 cm

From the image attached, the width of the large rectangle is 2x (x + x) and the length is 3x (2x + x). Therefore, the perimeter of the large rectangle is:

2(length + width) = Perimeter

2(3x + 2x) = Perimeter

Perimeter = 2(5x)

Perimeter = 10x

Perimeter = 10(3.5)

Perimeter = 35 cm

Answer:

d

Step-by-step explanation:

To construct an angle bisector with a compass  D. Place the compass needle on the vertex of the angle, and draw an arc across both legs of the angle.

An angle bisector is a line segment that divides angle into two equal parts.

According to the given statements to construct an angle bisector using a compass span any width of radius in a compass pace in onto the vertex of the angle cut the two arc on the two lines then without changing the radius draw two arcs where the previous arcs have intersected the two lines.

learn more about angle bisector here :

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Answer:

Step-by-step explanation:

correct one is b

Answer:

1060

Step-by-step explanation:

Given:

No. of boys = 870

No. of girls = 800

Probability that a boy chosen studies Spanish = [tex]\dfrac{2}{3}[/tex]

Probability that a girl chosen studies Spanish = [tex]\dfrac{3}{5}[/tex]

the number of boys in the school who study Spanish :

[tex]\dfrac{2}{3}\times 870=290\times 2=580[/tex]

the number of girls in the school who study Spanish :

[tex]\dfrac{3}{5}\times 800 \\=3\times 160\\\\=480[/tex]

Therefore, total number of students who study Spanish would be :

480+580=1060

Answer:

Zeroes: (-1.45, 0) and (3.45, 0)

Step-by-step explanation:

I plugged the equation into a graphing calc and located the x-values when graphing.

Answer:

It moves 8 to the right

Step-by-step explanation:

This is in the y axis so it will move 8 on the x axis

I'm thinking line 2 and 3 are Parallel

Answer:

C. Lines 2 and 4 are perpendicular

Step-by-step explanation:

If you just graph them all, none of them are parallel. But lines 2 and 4 are perpendicular and so are the lines 1 and 3.

Out of the options, C. Lines 2 and 4 are perpendicular, is the only correct answer in the choices given.

The last 2 shapes.

When you rotate both of them 360 degrees only at 180 and back at 360 it looks same.

Answer:

The 3rd one I took the quiz.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

i did the test for you to see if it was correct. i got a 100.

Answer:

[tex]\frac{13}{24}[/tex]

Step-by-step explanation:

=> [tex]\frac{3}{8} +\frac{1}{6}[/tex]

LCM = 24

=> [tex]\frac{9+4}{24}[/tex]

=> [tex]\frac{13}{24}[/tex]

Answer:

[tex]\frac{13}{24}[/tex]

Step-by-step explanation:

[tex]\frac{3}{8} +\frac{1}{6}[/tex]

[tex]\frac{3 \times 6}{8\times 6} +\frac{1\times8}{6\times8}[/tex]

[tex]\frac{18}{48} +\frac{8}{48}[/tex]

[tex]\frac{18+8}{48}[/tex]

[tex]\frac{26}{48}[/tex]

[tex]\frac{13}{24}=0.54166...[/tex]

Answer:

4.92*10^5

Step-by-step explanation

The annual flow of the Mississippi River would fit in the Atlantic Ocean approximately 4.92 x 10⁵ times.

The space occupied by an object in three-dimensional space is called the volume of an object. In simple words, space is taken by an object.

To find out how many times the annual flow of the Mississippi River would fit in the Atlantic Ocean, we need to divide the volume of the Atlantic Ocean by the annual flow of the Mississippi River:

number of times = (volume of Atlantic Ocean) / (annual flow of Mississippi River)

= (3.1 x 10¹⁷ cubic meters) / (6.3 x 10¹¹ cubic meters)

= 4.92 x 10⁵

Rounding to two decimal places, the final answer is approximately 4.92 x 10⁵. Therefore, the annual flow of the Mississippi River would fit in the Atlantic Ocean approximately 492,000 times.

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Answer:

[tex] - \frac{2}{3} (x - y + 6)[/tex]

[tex] - \frac{2}{3} x - \frac{2}{3} x( - y) - \frac{2}{3} \times 6[/tex]

[tex] - \frac{2}{ 3} x + \frac{2}{3} y - 2 \times 2[/tex]

[tex] - \frac{2}{3} x + \frac{2}{3} y - 4[/tex]

Answer:

x^2-6x+9

Step-by-step explanation:

(x-3)^2

(x-3)(x-3)

x^2-3x-3x+9

x^2-6x+9

Answer:

y=34, x=17 root 3

Step-by-step explanation:

30 60 90 triangle.

Shortest side is x, hypotenuse is 2x, bottom length is x root 3

Answer:

Using the Leg Opposite to 30° Theorem we derive that y = 34 and from the Pythagorean Theorem, x = 17√3.

Answer:

6 : 1

Step-by-step explanation:

Given the ratio

12 : 2 ( divide both parts by 2 )

= 6 : 1 ← in the form n : 1