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The value of the identities are;

1. tan θ = 5/12

2. cot θ = √7/3

To determine the value of the identities, we need to take note of the different identities;

From the information given, we need to take note that;

tan θ = opposite/adjacent

cot θ = inverse of tangent identity

cot θ = adjacent/opposite

then,

1. tan θ =

Opposite = 5

Adjacent = 12

tan θ = 5/12

2. cot θ = 4√7/12 = √7/3

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Answer:32 minutes

Step-by-step explanation:

He is running at a rate of 1 mile every 8 minutes. 3 miles in 24 minutes and 4 miles in 32 minutes

The step in simplifying the expression 3x/(x+5) - 3/(x+6) would result in 3x² + 18x - 3x - 15. The two terms that can be combined in the numerator to simplify are -3x and 18x. So, the correct answer is A), B) and D).

When multiplying the terms together in the first step of simplifying, we would get

3x - 3(x + 5)/(x + 6)

Simplifying this expression would lead to

3x² + 15x - 3x - 15/(x + 6)

Therefore, the answer is option (b): 3x² + 18x - 3x - 15

To simplify the numerator, we need to combine like terms.

To simplify the numerator, we need to combine like terms. The given expression is

3x² + 18x - 3x - 15

Here, the terms 18x and -3x have the same variable (x) and the same power (first power), but they have opposite signs. Therefore, we can combine them by subtracting the smaller value from the larger value. In this case, we have

18x - 3x = 15x

So, the expression simplifies to

3x² + 15x - 15

Therefore, the two terms that we would combine in the numerator to simplify are -3x and 18x, which give us 15x. So, the correct option is B) and D).

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The distribution of the sample is approximately normal with a mean of 0. 15 and a standard deviation of 0. 03852.

One can utilize the Central Limit Theorem (CLT) for proportions to detail the dispersion of the sample proportion. Explained by the CLT, if the size of the sample is sufficiently significant enough, then the distribution with respect to the sample proportion will be mostly indistinguishable from a typical distribution.

np ≥ 10

n(1-p) ≥ 10

Given that both conditions are fulfilled, we can essentially posit that the said sample proportion distribution  is almost normal. In light of this knowledge, it would be pertinent to ascertain the mean (μ) and standard deviation (σ) of the sample proportion distribution.

Mean = p = 0.15

Standard deviation:

= √ ( ( 0.15 x ( 1 - 0. 15 ) ) / 86 )

= 0.03852

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2.2 in decimal form.

eleven fifths

The equations to solve the length of the room is

a) y² - 5y = 750

b) 750 - y ( y - 5 ) = 0

c) ( y + 25 ) ( y - 30 ) = 0

Given data ,

Let the area of a rectangular room is 750 square feet.

Let the width of the room is 5 feet less than the length of the room

So , on simplifying , we get

w = l - 5

Area of rectangle = length x width

And , A = l x w

A = l ( l - 5 )

750 = y ( y - 5 )

Therefore , the equation is

a) y² - 5y = 750

b) 750 - y ( y - 5 ) = 0

On simplifying the quadratic equation , we get

c) ( y + 25 ) ( y - 30 ) = 0

Hence , the length of the rectangular room is solved

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The complete question is attached below :

Which equations can be used to solve for y, the length of the room? Select three options.

a) y(y + 5) = 750

b) y² – 5y = 750

c) 750 – y(y – 5) = 0

d) y(y – 5) + 750 = 0

e) (y + 25)(y – 30) = 0

The steepness of the ramp is approximately 56 feet.

You skateboards down a ramp. The ramp starts at a height of 10 feet and runs 55 feet along the ground.

Therefore, let's find how steeped the ramp is.

Hence, using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

55² + 10² = c²

c² = 3025 + 100

c² = 3125

square root both sides of the equation

c = √3125

c = 55.9016994375

c = 56 feet

Therefore,

steepness of the ramp = 56 feet

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The slope of the line that contains the points (-3, -1) and (3, -10) is -3/2.

Given two points.

We have to find the slope of the line.

Slope of a line passing through (x, y) and (x', y') is,

Slope = (y' - y) / Ix' - x)

Here two points are,

(-3, -1) and (3, -10)

Slope = (-10 - -1) / (3 - -3)

         = -9 / 6

         = -3/2

Hence the slope of the line is -3/2.

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The requried, perimeter and area of the parallelogram are 18.4 centimeters and 18 square centimeters respectively.

To find the perimeter of parallelogram EFGH, we need to find the length of all four sides and add them up. The distance formula is used to find the length of each side:

EF = √((2-(-1))² + (8-5)²) = √(3² + 3²) = √(18)

FG =√(20)

GH = √(18)

HE = √(20)

Therefore, the perimeter is:

Perimeter = EF + FG + GH + HE = √(18) + √(20) + √(18) + √(20) ≈ 18.4

Similarly,
The area of the parallelogram is given as,
= 18 square centimeters

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The sample size needed for the scientist to be 95% confident that her estimate is within 0.4 pounds of μ is given as follows:

n = 189 babies.

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is defined as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters are given as follows:

[tex]M = 0.4 \sigma = 2.8[/tex]

Then the sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

0.4sqrt(n) = 1.96 x 2.8

sqrt(n) = (1.96 x 2.8/0.4)

n = (1.96 x 2.8/0.4)²

n = 189 babies. (rounded up).

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Answer:

<4√97,-9√97>

Step-by-step explanation:

First, we need to find the values of A-C and B-D:

A-C = < 3, 6 > - < 7, -3 > = < -4, 9 >

B-D = < 4, -7 > - < 0, 2 > = < 4, -9 >

Next, we need to find the magnitude of A-C, which is denoted by |A-C| and is equal to the square root of the sum of the squares of its components:

|A-C| = √((-4)^2 + 9^2) =√(97)

Now we can substitute all the values into the expression |A-C|(B-D) and evaluate:

|A-C|(B-D) = √(97) * < 4, -9 >

= < 4√(97), -9√(97) >

So the final answer is < 4√(97), -9√(97) >.

The apex angle |‹aed| of the rectangular base pyramid is equal to 14°.

In a rectangular base pyramid, the base is a rectangle and the apex (or top point) is directly above the center of the rectangle.

The apex angle is the angle formed by the edges of the pyramid at the apex. In a rectangular base pyramid, the apex angle depends on the dimensions of the rectangle base and the height of the pyramid. It can be calculated using trigonometric functions.

The apex angles bec and aed formed by the opposite width of the rectangle base are equal.

In conclusion, the apex angle |‹aed| of the rectangular base pyramid is equal to 14°.

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Using the given data, a logarithmic regression equation of the form Bacteria = 447.91 * ln(12) - 1733.1 was found to model the relationship between time and bacteria population. So, the population of bacteria is about 44.1 at 12 hours.

Based on the provided data, we can use a logarithmic regression to model the relationship between time and bacteria population. Here's how to do it using Microsoft Excel

Enter the data into two columns one for time and one for bacteria population. Create a scatter plot of the data. Right-click on one of the data points in the plot and select "Add Trendline."

In the Trendline options, choose "Logarithmic" as the type of trendline. Check the box for "Display Equation on Chart" to show the equation for the trendline.

The resulting equation is

Bacteria = 447.91 * ln(Time) - 1733.1

This equation represents a logarithmic regression of the bacteria population over time.

To use this equation to predict the bacteria population at a specific time, substitute the time value into the equation and solve for the bacteria population. For example, if we want to predict the bacteria population at 12 hours, we can substitute 12 into the equation

Bacteria = 447.91 * ln(12) - 1733.1

Bacteria ≈ 44.1

So we would predict a bacteria population of about 44.1 at 12 hours.

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Answer:

To calculate the minimal cost of logistics from a factory to a warehouse, you would need to consider various factors such as the distance between the factory and the warehouse, the mode of transportation, the weight and volume of the goods being transported, the number of trips required, and any applicable taxes or fees.

To formulate this as a mathematical problem, you could use linear programming, which is a method for optimizing a linear objective function subject to linear equality and inequality constraints.

Let's say we have a factory that produces goods and a warehouse that stores those goods. We want to transport the goods from the factory to the warehouse in a cost-effective way. Let's assume that there are three transportation options available: truck, train, and ship. Each option has a different cost per unit of distance traveled, and a different maximum weight and volume capacity.

Let x1, x2, and x3 be the number of units transported by truck, train, and ship, respectively. Then, the objective function we want to minimize would be:

C = 10x1 + 8x2 + 6x3

where C is the total cost of transportation.

Next, we would need to set up constraints based on the transportation options and the available resources. For example:

Truck capacity: 3x1 <= 15000 (maximum weight capacity of 15000 units for the truck)

Train capacity: 5x2 + 2x1 <= 40000 (maximum weight capacity of 40000 units for the train)

Ship capacity: 2x3 + 3x1 <= 30000 (maximum weight capacity of 30000 units for the ship)

Distance constraint: 2x1 + 3x2 + 5x3 <= 10000 (maximum distance of 10000 units for all transportation modes combined)

The above constraints limit the total weight transported, the capacity of each mode of transport, and the total distance that the goods are transported.

Finally, we would need to add non-negative constraints to ensure that all variables are greater than or equal to zero:

x1 >= 0, x2 >= 0, x3 >= 0

Once we have set up this linear programming problem, we can use optimization techniques to solve for the values of x1, x2, and x3 that minimize the cost of transportation while satisfying all of the constraints.

Step-by-step explanation:

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The key features of the function f(x) = 2log₃(x+7) graphed below include the following:

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this logarithmic function shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-7, ∞].

Range = [-∞, ∞].

In conclusion, we can logically deduce that this logarithmic function has a vertical asymptote is at x equal to negative seven.

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Solving the given word problem systematically, Serene Travel Organization offers 12 diverse vacation packages.

To calculate the overall number of distinctive excursion packages that Quiet Travel Organization offers, we ought to duplicate the number of cities by the number of carriers:

Add up to number of get-away bundles = number of cities x number of airlines

Since the agency has 6 cities and 2 aircrafts to select from, we are able substitute those values within the over equation:

Add up to number of get-away bundles = 6 x 2 = 12

In this manner, Serene Travel Organization offers 12 diverse get-away bundles.

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Answer:

A

Step-by-step explanation:

A

The volume of the sphere with a radius of 5 feet to the nearest cubic foot is 166.67π feet³.

Given a sphere.

Radius of the sphere = 5 feet

The formula to find the volume of the sphere is,

Volume of the sphere = 4/3 πr³,

where r is the radius of the sphere.

Substituting the given radius,

Volume of the sphere = 4/3 × π × (5)³

                                     = 4/3 × π × 125

                                     = 166.67π

Hence the volume of the sphere is 166.67π feet³.

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The value of angle x is determined as 107⁰.

The value of angle x is calculated by applying principle of intersecting chord theorem.

The intersecting chord theorem states that half of the difference between the arc of two intersecting chords is equal to the tangent angle.

Based on the angle of intersecting chord theorem, we will have the following equation.

m∠MNP = ¹/₂( arc MLP - arc MP )

x = ¹/₂ [(360 -73) - (73)]

x = ¹/₂ (287 - 73 )

x = ¹/₂ (214)

x = 107⁰

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Answer:

The equation Qd = 50 - 4Px + 0.5I + 10Py - 2Pz represents the demand function for a certain good X, where Qd is the quantity demanded, Px is the price of X, I is the consumer's income, Py is the price of another good Y, and Pz is the price of another good Z.

To solve for the equilibrium price and quantity, we need to find the point where the quantity demanded equals the quantity supplied. However, without information on the supply function or market conditions, we cannot find the equilibrium price and quantity.

We can use the demand equation to determine the effect of changes in the independent variables on the quantity demanded for the good. For example, an increase in the price of X (Px) would lead to a decrease in the quantity demanded (Qd), while an increase in the price of Y (Py) or a decrease in the price of Z (Pz) would lead to an increase in the quantity demanded (Qd). An increase in income (I) would also lead to an increase in the quantity demanded (Qd).

Note that it is important to understand the context and assumptions underlying the demand function in order to make accurate economic predictions or decisions based on it.

Step-by-step explanation:

Based on the informtaion provided, the two-way table would be,

                                 Music        World Language         Totals

8th Grade                   20                    40                           60

7th Grade                    10                     50                           60

Total                          30                     90                           120

In this situation there were total 120 seventh and eighth grade CAVA students. And there were a total of 60 eighth grade students.

Total number of students = 120

This means that the number of students in 7th grade : 120- 60 = 60

Out of 120 seventh and eighth grade students, 30 students chose Music as their elechive course.

This means that remaining 120 - 30 = 90 students chose World Language as their elechive course.

Here, 40 eighth grade students chose World Language as their elective.

This means that out of total 90 students 90 - 40 = 50 students of 7th Grade  chose World Language as their elective.

Now consider the 8th grade students,

Out of 60 students 40 chose World Language.

So, 60 - 40 = 20 must chose Music as their elective.

Now consider the 7th grade students,

Out of 60 students 50 chose World Language.

So, 60 - 50 = 10 students must chose Music as their elective.

Hence the required two-way table would be,

                                 Music        World Language         Totals

8th Grade                   20                    40                           60

7th Grade                    10                     50                           60

Total                          30                     90                           120

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The area of the rectangle in terms of x can be represented as (L . W)(x) = 24x³ - 30x² + 72x.

Given a rectangle.

Length of the rectangle, L(x) = 6x

Width of the rectangle, W(x) = 4x² − 5x + 12

The formula to find the area of the rectangle is,

Area = Length × Width

Substituting the given length and width,

Area of the rectangle = L(x) . W(x)

                                    = (L . W)(x)

                                    = (6x) (4x² − 5x + 12)

                                    = 24x³ - 30x² + 72x

Hence the area of the rectangle is represented as (L . W)(x) = 24x³ - 30x² + 72x.

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Answer:

(L . W)(x) = 24x³ - 30x² + 72x.

Step-by-step explanation:

The volume of the flower vase, can be found to be 2, 199 cm ³.

The volume of the flower vase can be found by subtracting the volume of the cone from the volume of the rectangular prism.

Volume of rectangular prism :
= Length x Width x Height

= 20 x 12 x 10

= 2, 400 cm ³

The volume of the cone is:

=  π x radius ² x height / 3

= π x 4 ² x 12 / 3

= 201. 06 cm ³

Volume of vase:

= 2, 400 -  201. 06

= 2198.94

= 2, 199 cm ³

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Answer: x=23

Step-by-step explanation:

Answer: 23

Step-by-step explanation:

When you have a value on the x-axis, your y=0

plug in y=0 to find your x-intercept

1x-2(0)=23

1x=23

x=23

We would expect 138 groups in the larger zoo to have 5 or more people based on the relative frequency of group sizes in Julia's data.

To determine how many groups of 5 or more people we would expect to see in a larger zoo with 600 groups of visitors in a day, we need to use the relative frequency of each group size in Julia's data.

To calculate the relative frequency of each group size, we need to divide the frequency of each group size by the total number of groups:

Group Size   Frequency   Relative Frequency

1                          9             9/150 = 0.06

2                         52           52/150 = 0.35

3                         27            27/150 = 0.18

4                         38            38/150 = 0.25

5                         16             16/150 = 0.11

6                          6              6/150 = 0.04

7                          5              5/150 = 0.03

8                          7              7/150 = 0.05

We can see that the relative frequency of groups with 5 or more people is 0.11 + 0.04 + 0.03 + 0.05 = 0.23. This means that we would expect 23% of the 600 groups in the larger zoo to have 5 or more people.

To calculate the actual number of groups with 5 or more people, we multiply the total number of groups by the relative frequency:

Number of groups with 5 or more people = 600 x 0.23 = 138

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Answer:

Let's set up a system of equations to solve for S and L:

S + L = 24 (they sold a total of 24 shirts)

14S + 17L = 378 (the total amount made from selling the shirts was $378)

We can solve for one variable in the first equation and substitute it into the second equation:

S = 24 - L

14(24 - L) + 17L = 378

336 - 14L + 17L = 378

3L = 42

L = 14

So they sold 14 long sleeve shirts. We can substitute this value back into the first equation to solve for S:

S + 14 = 24

S = 10

Therefore, they sold 10 short sleeve shirts and 14 long sleeve shirts.