1. In the rational function: y = (x ^ 2 + 7) / (2x ^ 2 + x - 3) the vertical asymptotes are:

Answer:

d i did the thing

Step-by-step explanation:

In accordance with the exponential model, the current forest area is equal to 2801.149 square kilometers after six years.  

According with statement, the forest area decreases exponentially in time. Then, the exponential model is defined by following model:

n(x) = n' · (1 - r)ˣ

Where:

If we know that n' = 4400 km², r = 0.0725 and x = 6 yr, then the current forest area is:

n(6) = 4400 · (1 - 0.0725)⁶

n(6) = 2801.149

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Step-by-step explanation:

Let x be the number of buses for the trip.

Then (32 - x) is the number of cars for the trip.

We have 27x + 3(32 - x) = 408.

=> 27x + 96 - 3x = 408

=> 24x = 312

=> x = 13

Hence there are 13 buses and (32 - 13) = 19 cars.

According to the problem,Therefore, x = 12714.29 and y = 1285.71. Mitchell invested $12714.29 at 6% and $1285.71 at 7%.

Investment is the process of using money to purchase assets in order to generate income or increase in value. Investing involves the purchase of assets such as stocks, bonds, mutual funds, real estate, commodities, or other investments in order to achieve financial goals. It is a long-term strategy that involves setting aside funds for the future, with the expectation of obtaining a return on the investment. The ultimate goal of investing is to maximize the return on an investment while minimizing the risk of loss.

Let x be the amount invested at 6%, and y be the amount invested at 7%.

We know that x + y = 14,000, as this is the total amount of the advance.

We also know that the total interest each year is $930. We can calculate the interest individually using the formula I = Prt, where P is the principal (the amount invested), r is the interest rate and t is the time (1 year in this case).

For the 6% investment: I = (x)(0.06)(1) = 0.06x

For the 7% investment: I = (y)(0.07)(1) = 0.07y

We now have two equations:

0.06x + 0.07y = 930

x + y = 14,000

We can use substitution to solve for x and y.

Substitute x + y = 14,000 into equation 0.06x + 0.07y = 930 to get 0.06(14,000) + 0.07y = 930.

Simplifying, we get 840 + 0.07y = 930.

Subtract 840 from both sides to get 0.07y = 90.

Divide both sides by 0.07 to get y = 1285.71.

We now know that y = 1285.71.

Substitute y = 1285.71 into x + y = 14,000 to get x = 14,000 - 1285.71 = 12714.29.

Therefore, x = 12714.29 and y = 1285.71. Mitchell invested $12714.29 at 6% and $1285.71 at 7%.

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Answer:

140°

Step-by-step explanation:

ArcDB is a curved piece of a circle. If you know the measures of the "central angles" (angles with their vertex at the center of the circle) then you can find the measure of the arc.

AngleAPB = 40°

AngleBPC = 90°

So AngleCPD must be equal to 50° see image.

ArcDB is equal to AngleBPD (90° + 50°)

ArcDB = 140°

see images.

Answer:

The equation of this line is y = -4.

Answer:

y=-4

Step-by-step explanation:

zero slope m=0

y-y1=m(x-x1)

y-(-4)=0(x-(-9))

y+4=0

y=-4

The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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Answer:

(C) α + β + γ

Step-by-step explanation:

The sum of interior angles of ΔOCB & ΔOCA = 180° x 2 = 360°

α + β + γ + (360°-x) = 360°

x = α + β + γ

Answer:

65

Step-by-step explanation:

5₁=5·5=25 (square area)

5₂=1/2·5·4=10  (triangle area)

5=25+4·10

=25+40

=65

First, let's calculate the average salary by adding them all together, and then dividing the sum by 5:

We have that the average salary is $97,680.

Next, the annual pension is calculated by multiplying the average salary by 1.35% in decimal form:

finally, we have that Michael's annual pension is $1318.68

Step-by-step explanation:

7 √(1/3) - 2 1/3 √(1/3) +3√147

→7(1/√3) - (7/3)(1/√3) +3√(3×7×7)

→ (7/√3) - (7/3√3) +3×7√3

→ (7/√3) - (7/3√3) + 21√3

On Rationalising the denominators then

→ [ 7√3/(√3×√3)]-[7√3/(3×√3×√3) +21√3

The Rationalising factor of√3 =√3

→ (7√3/3)-[7√3/(3×3)]+21√3

→ (7√3/3)-(7√3/9)+21√3

LCM of 3 and 9 = 9

→ [(3×7√3)-(7√3)+(9×21√3)]/9

→ (21√3-7√3+189√3)/9

→[(21-7+189)√3]/9

→ [(210-7)√3]/9

→ 203√3/9 Ans.

Hope this helps.

In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:

In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).

The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22

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Answer:

70+50=120

Step-by-step explanation

therefore x=120

Answer:v=2.5

Step-by-step explanation:

isolate the variable by dividing both sides by 5

v=2.5

The required confidence interval of the random sample of the given data is  (151.5456, 148.4544).

Statisticians use confidence intervals  to gauge vulnerability in an example variable. For instance, a scientist chooses various examples haphazardly from a similar populace and figures a certainty stretch so that each example might be able to perceive how it might address the genuine worth of the populace variable. The subsequent datasets are different where a few stretches incorporate the genuine populace boundary and others don't.

In an random sample of 60 PCs, the mean fix cost was $150, with the populace standard deviation being $36.

Standard deviationσ = $36, μ = $150 , n = 60

Value of z for 99% confidence interval is 2.576

Then,

Confidence interval =  μ±z(σ/n)

Confidence interval = $150 ± 2.576(36/60)

Confidence interval = $150 ± 1.5456

Confidence interval = $150 +1.5456 , $150 - 1.5456

Confidence interval = 151.5456, 148.4544

Thus, required interval is (151.5456, 148.4544).

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Answer:

The appropriate hypotheses for performing a significance test is:

\(H_0: \mu = 51\)

\(H_1: \mu > 51\)

Step-by-step explanation:

Last year, the mean score on the state’s math test was 51. The administrators have trained the teachers in a new method of teaching math hoping to raise the scores on this standardized test this year.

At the null hypothesis, we test if the mean score this year is the same as last year, that is:

\(H_0: \mu = 51\)

At the alternate hypothesis, we test if the mean score improved this year from last, that is:

\(H_1: \mu > 51\)

The appropriate hypotheses for performing a significance test is:

\(H_0: \mu = 51\)

\(H_1: \mu > 51\)

The numerical value of x in the similar pair of triangle is 10.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

From the diagram,

Side A of the small triangle = 10

Side B of the small triangle = x + 2

Side A of the Big triangle = 10 + x

Side B of the big triangle = x + 14

Hence;

Ratio of Side A to Side B of the small triangle = 10 / x + 2

Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14

Since the triangle area similar, equate the two ratio and solve for x.

10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )

Cross multiply

10( x + 14 ) = ( 10 + x )( x + 2 )

Expand using FOIL method

10x + 140 = 10x + 20 + x² + 2x

10x + 140 = x² + 12x + 20

x² + 12x + 20 = 10x + 140

x² + 12x + 20 - 10x - 140 = 0

x² + 2x - 120 = 0

Factor the left side of the equation

( x - 10 )( x + 12 ) = 0

Hence;

x - 10 = 0 and x + 12 = 0

x = 10 and x = -12

Since the dimension of the triangle cannot be negative,

x = 10

Therefore, the value of x is 10.

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A simple path which visits all vertices can be found using a linear-time algorithm.

How to handle visited vertex is the issue.

The time complexity isn't really linear as you follow because of the many visits.

If not, the following straightforward example will show that your algorithm is flawed:

1 --> 2 -----------> 3 --> 4

       \         /

        --> 5 -->

After finding 1-2-3-4 in the initial search, the search returns to 2 and finds 1-2-5-3. Now that number 3 has been visited, the search halts and ultimately fails.

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Answer:

C; Basketball

Step-by-step explanation:

Although Greg Ridley wants to play for the Scorpions when he grows up, he learns along the way that there are things that are more important, hence the use of the term "treasure."

He learns from this that memories, friendships, and family are all that matters and if having to let go of basketball to sustain the aforementioned elements (which may or may not be an easy thing to do), then it is much more of a necessity than a choice.

Hope this helped! :D

Answer:

Student 1 and Student 3

Step-by-step explanation:

For student 1: ✔

\( {x}^{2} = 64 \\ x = \sqrt{64} \\ x = {}^{ + } 8 \: \: and \: \: {}^{ - } 8\)

For student 2: ❎

\( {x}^{3} = 1 \\ x = \sqrt[3]{1} \\ x = {}^{ + } 1\)

For student 3: ✔

\( {x}^{2} = 9 \\ x = \sqrt{9} \\ x = {}^{ + } 3 \: \: and \: \: {}^{ - } 3\)

For student 4: ❎

\( {x}^{3} = 216 \\ x = \sqrt[3]{216} \\ x = {}^{ + } 6\)

About 80 necklaces have more than 28 beads. Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.

P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)

P(x > 28) = P(x - 24 / 4 > 1)

P(x > 28) = 1 - ∅1

P(x > 28) = 1 - 0.8413

P(x > 28) = 0.1587

Multiply both sides by 500, then we have

500 P(x > 28) = 0.1587 × 500

500 P(x > 28) = 79.35

500 P(x > 28) ≈ 80

About 80 necklaces have more than 28 beads. Then the correct option is C.

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The missing options are given below.

A. About 24 devices have more than 28 beads.

B. About 48 necklaces have more than 28 beads.

C. About 80 necklaces have more than 28 beads.

D. About 96 necklaces have more than 28 beads.

The coordinate of the point after transformation is: (3, -4)

The coordinate initially is given as (0, -4).

Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:

(0 - 1, -4)

= (-1, -4)

Moving by 4 units to the right means an addition of 4 units to x coordinate to get:

(-1 + 4, -4)

= (3, -4)

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The Area of the shaded portion is: 72 square inches

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ *  17 * 13 = 110.5 square inches

Area of smaller triangle =  ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

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After simplifying the given equation the answer will be -2tanx.

What is identity?

An equation is referred to as an identity if it has one or more variables and is true for all alternate values of the variables for which both sides of the equation are defined.

Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.

Given: \(\frac{cosx}{1+sinx}-\frac{cosx}{1-sinx}\)

We have to solve this.

Take cross multiplication.

\(= \frac{cosx - cosxsinx-cosx-cosxsinx}{(1-sin^2x)}\\= \frac{-2cosxsinx}{(1-sin^2x)}\)

Since,

\(1-sin^2x=cos^2x\)

\(= \frac{-2sinx}{cosx}\)

Since, \(\frac{sinx}{cosx} = tanx\)

\(= -2tanx\)

Hence, after simplifying the given equation the answer will be -2tanx.

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Answer:

Yes, Yes

Step-by-step explanation: