Simplify and explain 6 + (5 + x) (Hurry!)

The cable is 805.4 ft long.

Draw a triangle to represent the situation.

Label the sides of the triangle.

Let x = length of cable
Let 1200 = height of mountain
Let 30 = angle of elevation

Use the Law of Cosines to solve for x.

x² = (1200)² + (1200)² - (2)(1200)(1200)cos(30)

x² = 288000 + 288000 - 1,728,000cos(30)

x² = 576000 - 1,728,000cos(30)

x = √576000 - 1,728,000cos(30)

x = √576000 - 1728000(0.866)

x = √576000 - 1511360

x = √646340

x = 805.4 ft

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a. The function of the bee population is: [tex]f(x) = 5000 * (1.12)^x[/tex]

b. To graph the function, f(x), you can use a graphing calculator or software such as Excel or a Python library like Matplotlib.

c. It will take approximately 7.9 months for Oscar to have 15,000 bees in the colony.

The problem states that Oscar wants to own a bee colony and extract honey from the hive. He starts with a colony of 5,000 bees and the number of bees grows exponentially with a growth factor of 12% each month. To solve this problem, we can use the exponential growth formula to determine the number of bees in the colony based on the month.

The exponential growth formula is [tex]P(t) = P_0 * (1 + r)^t[/tex] where

In this case, [tex]P_0[/tex] = 5000, r = 0.12, and t = x (the number of months). So, the function of the bee population is: [tex]f(x) = 5000 * (1.12)^x[/tex]

In order to get a decent amount of honey, Oscar feels that there should be at least 15,000 bees in the colony. To estimate how many months it will take Oscar until he has 15,000 bees, we can set f(x) = 15,000 and solve for x.

By doing this, we get x = log(15000/5000) / log(1.12) ≈ 7.9 months. This means it will take approximately 7.9 months for Oscar to have 15,000 bees in the colony.

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The complete question is:

Oscar wants to own a bee colony so that he can extract honey from the hive. He starts a colony with 5,000 bees. The number of bees grows exponentially with a growth factor of 12% each month.

a. Write a function, f(x), for the bee population that can be used to determine the number of bees in the colony, based on the month, x.

b. Use technology to graph the function, f(x).

c. Oscar feels that in order to get a decent amount of honey, there should be at least 15,000 bees in the colony. Estimate how many months it will take Oscar until he has 15,000 bees.

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The mean of the first population is not significantly larger than that of the second population. The p-value is 0.093.

Population 1: N = 35,X = 5.3, S = 2.8

Population 2: N = 21, X = 4.9, S = 3.2

We can use the t-test to test if the mean of the first population is larger than that of the second population. The formula for this is:

t = (x1 - x2) / (S√((1/N1) + (1/N2)))

Where x1 is the mean of population 1, x2 is the mean of population 2, S is the pooled standard deviation, and N1 and N2 are the sample sizes of the two populations.

Plugging in our values, we get:

t = (5.3 - 4.9) / (3.2√((1/35) + (1/21))) = 1.68

Using an online calculator, we find that the corresponding p-value is 0.093. Therefore, we fail to reject the null hypothesis that the two populations have the same mean and conclude that the mean of the first population is not significantly larger than that of the second population. The p-value is 0.093.

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According to one of Marvel's teachers, a typical learning-disabled student has an IQ of normal or above. Learning disabilities are not related to IQ, so a learning-disabled student could have an IQ of normal or above.

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Answer: 31

Step-by-step explanation:

Let's find the trapezoid area first:

(8-2 + 4) 3 / 2

= 10*3/2

= 15

And then the rectangle:

2 * 8

= 16

add the two areas together

15+16 = 31

The interest rate on Malik's saving account is 4.62%. This was calculated by finding the total amount after 4 years, subtracting the original deposit, and then dividing the interest earned by the original deposit and multiplying by 100.

1. Calculate the total amount in the account after 4 years: 1050 + 241.50 = 1291.50

2. Calculate the interest earned: 1291.50 - 1050 = 241.50

3. Calculate the interest rate: 241.50 / 1050 x 100 = 4.62%

The interest rate on Malik's saving account is 4.62%. This was calculated by finding the total amount after 4 years, subtracting the original deposit, and then dividing the interest earned by the original deposit and multiplying by 100.

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Answer:

addition

Step-by-step explanation:

there's only one sign + so it means addition

Answer: addition

Step-by-step explanation:

The area of the circle is 26.4 square meters

From the question, we have the following parameters that can be used in our computation:

Diameter, d = 5.8 meters

Start by calculating the radius of the circle

r = 5.8/2

Evaluate

r = 2.9

The area of the circle is then calculated as

A = πr²

Where

r = radius

substitute the known values in the above equation, so, we have the following representation

A = 3.14 * 2.9²

Evaluate

A = 26.4

Hence, the area is 26.4 square meters

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At the bicycle manufacturer, the average cost per bicycle is $77.

To find the average cost per bicycle, we need to find the total cost of making all three bicycles and divide that by the number of bicycles.

The total cost is of the bicycles is given by -

$72 (cost of first bicycle) + $83 (cost of second bicycle) + $77 (cost of third bicycle) = $232

Now to find the average cost per bicycle, we will divide the total cost by the number of bicycles.

Hence, $232 ÷ 3 = $77

Therefore, the average cost per bicycle is $77.

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Answer:

10

Step-by-step explanation:

PEMDAS

Answer: 476.7 feet

Step-by-step explanation:

65 miles = 343200 feet

1 hour = 3600 seconds

(343200/3600) = 476.7 feet in 5 seconds

Answer:

The value equivalent to the expression 2^3 + 3^4 is 19

The perimeter of five square and perimeter of rectangular cake is equal,

So, the perimeter of cakes is 600 cm.

The perimeter of a two-dimensional figure is the distance covered around it. It defines the length of shape, whether it is a triangle, square, rectangle or a circle. Area and perimeter are the two major properties of a 2D shape, which describes them.

We have five square cakes of side 30cm.

the perimeter of one cake is =4a

                                                 =4×30

                                                 =120 cm

So, the perimeter of five cake = 5(120)

                                                    =600 cm

The perimeter of five square and perimeter of rectangular cake is equal,

So, the perimeter of cakes is 600 cm.

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Answer:

15r-40

Step-by-step explanation:

By the Distributive Property, [tex]5(3r-8)=5(3r)+5(-8)=15r-40[/tex]

The equation of the line which passes through the point (0,-4) and has a gradient of 0. 5 is (x-8)/2.

A straight line can be represented by the "Point-Slope" form of the line.

In point-slope form, we can deduce an equation of any line on the Cartesian coordinate system with the help of its slope/gradient "m" and a point through which it passes (x1,y1).

the equation of Point Slope form is,

(y-y1)=m(x-x1),

where, x and y are any general point on the line.

in the given question the value of the slope/gradient (m) is given as 0.5

and it passes across the point (0,-4)

so according to the equation of the point-slope form,

the equation of line must be,

(y-(-4))=0.5(x-(0))

= y+4=0.5x

= 2y+8=x

= 2y = x-8

= y = (x-8)/2

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The Radius r changing with respect to time when volume v is  [tex]\frac{1}{9 \pi} \mathrm{cm} / \mathrm{s}\end{aligned}[/tex].

The volume here depends on the diameter of the radius of the sphere since if we take the cross-section of the sphere, it is a circle. The surface area of sphere is the area or region of its outer surface. To calculate the sphere volume, whose radius is ‘r’ we have the below formula:

Volume of sphere [tex]=\frac{4}{3} \pi r^{3}[/tex]

If you consider a circle and a sphere, both are round. The difference between the two shapes is that a circle is a two-dimensional shape and a sphere is a three-dimensional shape which is the reason that we can measure the Volume and area of a Sphere.

volume is,

[tex]$$\begin{aligned}& V=\frac{4}{3} \pi r^3 \\& \Rightarrow \frac{d V}{d t}=4 \pi r^2 \frac{d r}{d t}\end{aligned}$$[/tex]

given that,

[tex]\frac{dV}{d t}[/tex][tex]=4 \mathrm{~cm}^3 / \mathrm{s}, V=36 \pi \mathrm{cm}^3 \text {. }$$[/tex]

[tex]$$find $\frac{d r}{d t}$ :$$[/tex]

[tex]\begin{aligned}& V=36 \pi \\& \frac{4}{3} \pi r^3=36 \pi \\& r^3=27 \\& \Rightarrow r=3 .\end{aligned}[/tex]

substitute the above values,

[tex]$$\begin{aligned}& \frac{d V}{d t}=4 \pi r^2 \frac{d r}{d t} \\& 4=4 \pi(3)^2 \frac{d r}{d t} \\& \frac{d r}{d t}=\frac{1}{9 \pi} \mathrm{cm} / \mathrm{s}\end{aligned}$$[/tex]

Therefore, the radius r changing with respect to time when the volume v is [tex]\frac{1}{9\pi } cm/s[/tex].

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The equation of line with a gradient of 1 which runs through the point (0,4) is y = x + 4.

The slope-intercept form is expresses as;

y = mx + b

Where m is slope and b is y-intercept.

The point-slope form is expressed as;

y - y₁ = m( x - x₁ )

Given that, the slope of the line m = 1 and it passes through (0,4)

Plug the slope m = 1 and point  ( 0,4 ) into the point-slope form above and simplify.

y - y₁ = m( x - x₁ )

y - 4 = 1( x - 0 )

y - 4 = x - 0

y - 4 = x

Add 4 to both sides

y = x + 4

Therefore, the equation of the line is y = x + 4.

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Answer:

The three side lengths given, 12 ft, 16 ft, and 20 ft can form a right triangle. This is because the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 20^2 = 12^2 + 16^2, so the sides 12 ft, 16 ft and 20 ft can form a right triangle.

Answer:

S = 25

Step-by-step explanation:

Since it's stated as a square, that means all sides equal each other

In other words;

s+50 = 3s

To get S alone, we will first subtract 50 on both sides

s = 3s-50

Let's now subtract 3s from both sides

s-3s = -50, aka -2s = -50

Changing those to positive, 2s = 50

Last step is to divide both sides by 2

s = 25

The missing measures by using the rhombus LMNO graphic is, 90° is the measure of LPM,the PMN measurement is 102°, LN is 10 units in length.

A rhombus is a unique type of quadrilateral with four sides that is similar to a parallelogram. In a rhombus, the opposing sides are parallel and the opposing angles are equal.

LMNO LON = 102° NP = 5 units for a rhombus.

According to the rhombic characteristics, all of the sides are congruent (equal), hence LM = MN = NO = OL and the opposite angles are also equal, and the opposite sides are parallel.

Therefore, LON = 102° = LMN.

Since adjacent angles add up to 180 degrees.

L + M thus equals 180 degrees.

∠M + ∠N = 180°

∠N + ∠O = 180°

∠O + ∠L = 180°

So, ∠N = 180° - ∠O = 180° - 102° =78°

∠L = 180° - ∠O = 180° - 102° =78°

∠M = 180° - ∠L = 180° - 78° =102°

Alternatively, we can say that each of the two diagonals in a rhombus is the perpendicular bisector of the other. Diagonals bisect each other at an angle of 90°.

Thus, LPM = NP0 = MPN = LPO = 90 degrees.

So, 90° is the measure of LPM.

The PMN measurement is 102°.

LN is 10 units in length.

The completre question is,

Rhombus LMNO has mLON = 102° and NP = 5 units.

The Rhombus L M N O is depicted. Drawn as parallel lines, they connect at point P and extend from point L to point N and from point M to point O, respectively. Congruence exists on every side.

You may locate the missing measures by using the rhombus LMNO graphic.

° is how much LPM is measured.

° is used to measure PMN.

 Units are the length of LN

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If x is the point reached by F after t seconds, and y is the point reached by S after t seconds, then x = 3t, y = 2t. 30 seconds after leaving point 0, 30 units far apart are F and S. At 100 seconds, F and S will be 100 units apart.

The speed of F reached 12 units in 4 seconds or 3 units per second.

 x = 3t

The speed of S reached 8 units in 4 seconds or 2 units per second.

 y = 2t

x - y = 3t -2t = t

After 30 seconds, the bugs will be apart by (x -y) = 30 units

x - y = 100 = t

After 100 seconds, The bugs will be 100 units apart.

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The amount of gas used for 140 miles is 3.5 gallons and the inverse equation is g = m/40

From the question, we have the following parameters that can be used in our computation:

m = 40g

The number of miles is given as

m = 140

substitute the known values in the above equation, so, we have the following representation

40g = 140

Divide by 40

g = 3.5

Hence, the amount of gas is 3.5 gallons

Recall that, we have

m = 40g

Divide by 40

g = m/40

Hence, the inverse is g = m/40

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The profit when n = 101/2 hours is $1,842.50.

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The y intercept means that gallons of water in the base year is 10.

Y intercept is a coordinate of y which is the point where the line touches the Y axis.

The x coordinate corresponding to this point will be zero.

Given is a graph which relates the two variables year and the gallons of bottled water per person.

From the graph, it is clear that y intercept is at 10.

It is in the year 1990, which is the base value that we take.

All the other year values are based on the base value.

y intercept means in this context that in the year 1990, which is the initial year, gallons of water per person is 10.

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Answer: m * 4/7 > 12/5

The y intercept has been moved down, and the g(x) graph is less steep than the f(x) graph.

the fundamental duty of a family. Y = x or f(x) = x is the parent function for linear functions. Transformation: Modification of a figure's size or position. Child Function: The parent function is f(x) = x for all linear functions. y = x.

The simplest function in a family of functions that yet preserves the definition (or shape) of the entire family is known as a parent function in mathematics.

When the independent variable (often 'x') varies by a constant amount and the dependent variable (typically expressed by 'y') changes by a constant amount, the function is said to be linear.

Therefore, the correct answer is option C. The graph of g(x) is less steep than the graph of f(x) and the y intercept has been shifted down.

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Answer:

X Y

-1 8

0 3

1 -2

2 -7

Step-by-step explanation:

Using the x values of the table, simply plug in those x values, replacing the x in the equation. For example:

y = -5x + 3

y = -5 * 2 + 3

y = -10 + 3

y = -7