which one of the following are parametric equations for the tangent line to the curve at the point ( )?

Answer:

b = -9

Step-by-step explanation:

-3 (3b + 6) = 36 - 3b

-9b - 18 = 36 - 3b

-6b - 18 = 36

-6b = 54

b = -9

Let's check

-3(3(-9) + 6) = 36 - 3(-9)

-3( -27 + 6) = 36 + 27

-3( -21) = 63

63 = 63

So, b = -9 is the correct answer.

Step-by-step explanation:

-3(3b+6)=36-3b

-9b-18=36-3b

-9b+3b=36+18

-6b=54

divide both sides by -6

b= -9

Answer:

64.34 feet.

Step-by-step explanation:

To solve this problem, we can use trigonometric ratios, specifically the tangent ratio.

Let's denote the height up the wall that the ladder reaches as "h". We can then set up the following equation:

tan(65°) = h/30

To solve for h, we can multiply both sides by 30:

30 tan(65°) = h

Using a calculator, we can find that tan(65°) is approximately 2.1445. Multiplying this by 30 gives us:

h ≈ 64.34 feet

Therefore, the ladder reaches approximately 64.34 feet up the wall. Rounded to the nearest hundredth of a foot, the answer is 64.34 feet.

Looking at the derivative, we see that it is defined for all values of t, so there are no vertical tangents.

The critical spots where the slope of the curve is zero or undefinable must be located in order to identify the points of horizontal tangency.

Our first step is to determine y's derivative with regard to x:

dy/dx = 3t^2 - 0

In the event that the derivative is set to zero, we obtain:

3t^2 = 0

t = 0

We gain one crucial insight from this at (22, 0).

The places where the derivative is undefinable must be located in order to determine the vertical tangent. There are no perpendicular tangents when looking at the derivative because it is defined for all values of t.

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In the figure, angles ∠5 and ∠1 are complementary angle.

The sum of two or more angle is 90 degree then the angle is called the complementary angle.

Given that;

Angles are shown in figure.

Now, By the figure we have;

⇒ ∠ 1 and ∠ 4 are vertically opposite angles, hence both are equal.

Here, ∠4 and ∠5 are complementary angles.

⇒ ∠4 + ∠5 = 90°

⇒ ∠1 + ∠5 = 90°

Hence,  Angles ∠5 and ∠1 are complementary angle.

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Comparing the z-scores, we can see that Sean's SAT score is slightly higher relative to the mean and standard deviation of the SAT population than his ACT score is relative to the mean and standard deviation of the ACT population.

To find the z-score for Sean's SAT score, we use the formula:

z = (x - μ) / σ

where x is Sean's SAT score, μ is the population mean (1500), and σ is the population standard deviation (250). Substituting the values, we get:

z = (1700 - 1500) / 250 = 0.8

Therefore, Sean's z-score on the SAT is 0.8.

To find the z-score for Sean's ACT score, we use the formula:

z = (x - μ) / σ

where x is Sean's ACT score, μ is the population mean (20.4), and σ is the population standard deviation (4.8). Substituting the values, we get:

z = (24 - 20.4) / 4.8 = 0.75

Therefore, Sean's z-score on the ACT is 0.75.

Comparing the z-scores, we can see that Sean's SAT score is slightly higher relative to the mean and standard deviation of the SAT population than his ACT score is relative to the mean and standard deviation of the ACT population.

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Answer:

Step-by-step explanation:

The equation that models the population of bats, y, after x years can be found using the formula:

y = P(1 + r)^x

where P is the initial population, r is the annual growth rate as a decimal, and x is the number of years.

In this case, the initial population P is 345,000, the annual growth rate r is 1.2% or 0.012 as a decimal, and x is the number of years. Substituting these values into the formula, we get:

y = 345,000(1 + 0.012)^x

Simplifying the expression in the parentheses, we get:

y = 345,000(1.012)^x

Therefore, the equation that models the population of bats, y, after x years is:

y = 345,000(1.012)^x

Step-by-step explanation:

the other answer is correct.

I just want to point out some mechanism used here :

the increase by 1.2%

an increase by x% means adding x% to the original 100%.

so, we end up with (100 + x)%.

"%" just stands for 1/100.

so, if y = 100%, an increase by x% is

y×(100 + x)/100 = y×(1 + x/100)

in our case here that is

345,000 × (1 + 0.012) = 345,000 × 1.012

and since the increase rate of 1.2% applies per year, we multiply the end population of every year by 1.012 for the following year.

so, each year a new factor of 1.012 is being integrated into the calculation.

it goes then

345,000×1.012×1.012×1.012×...×1.012 x times after x years.

and we get

y = 345,000 × (1.012)^x

The flour is needed for a big batch of cookies that uses 24 cups of oatmeal would be 20 cups.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

In order to find out how many groups of 6 cups of oatmeal there are.

So, For every 6 cups of oatmeal = 24 / 6 = 4

Now,

For 5 cups of flour = 4 x 5 = 20

The flour is needed for a big batch of cookies that uses 24 cups of oatmeal would be 20 cups.

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The efficiency of the a and b from the uniform distribution on the interval a:X-1/2 and b:Xn-n/n+1 is x.

The probability distribution known as the uniform distribution comes in two varieties: the discrete case and the continuous case. Both types of uniform distributions, as their names imply, have constant or uniform probabilities for all possible values of the random variable.

The random sample X1,X2,....,Xn is taken from the uniform distribution on the interval (0,θ).

δlog(L(x,θ))/δθ = -n/θ + ∑(xt)/θ² = 0

n/θ = ∑(xt) /θ²

θ = x

Now derivate it again with respect to θ,

∂²log(L(x;θ)) / ∂θ²

=nθ²−2∑t(xt) / θ³<0

Since, the second derivative is less than 0, ^θ is maximum likelihood estimate of θ.

Therefore, the maximum likelihood estimate of θ is ¯x.

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The linear function relationship between the change in the median home value and the year, indicates that we get;

a) The home values increased at a higher rate in Connecticut

b) The median home value in West Virginia in 2010 is $80,721

c) The home values in both states are equal in 1915

A linear function relationship can be expressed in the form; y = m·x + c. Where, m is the slope of the graph of the function and c is the y-intercept.

a) The rate of increase of the home value, where the values of the house change linearly can be found as follows;

Rate of change of home value for West Virginia =  [tex]\frac{72800-33200}{200-1950} = 792[/tex]

The home values in West Virginia increases by about $792 per year

Rate of change of home values for Connecticut = [tex]\frac{166900-71900}{2000-1950} =1900[/tex]

The home values in Connecticut increases by $1900 each year

Therefore;

b) The increase in the home value in West Virginia per year is $792, therefore, the home value in 2010 can be found as follows;

The number of years between 2010 and 2000 = 2010 - 2000 = 10

Home value in 2010 = Home value in 2000 + 792 × 10

Home value in 2010 = $72800 + $792 × 10 = $80720

c) The equation for the median home value for West Virginia can be presented as follows;

y - 33200 = 792×(x - 1950)

y = 792×(x - 1950) + 33200

The equation for the median home value for Connecticut can be presented as follows;

y - 71900 = 1900×(x - 1950)

y = 1900×(x - 1950) + 71900

When the home values in West Virginia is equal to the home value in Connecticut, we get;

792 × (x - 1950) + 33200 = 1900 × (x - 1950) + 71900

1900·x - 792·x = 1900 × 1950 - 792 × 1950 + 33200 - 71900 = 2121900

1108·x = 2121900

x = 2121900/1108 ≈ 1915.07

The year the median value will be the same in both states is about 1915

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The solution is, $1.33, is the cost per quart.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

A drum of oil contains 55 gal and costs $164.80.

now, we know , 1 gal = 4 quart

so, 55 gal =55 * 4

                 = 220 quart

now, the cost per quart= 220/164.80

                                      =$1.33

Hence, The solution is, $1.33, is the cost per quart.

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Measure of angle G is 62.5°.

For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).

In triangle EFG,

Measure of angle E = 55°

Measure of angle F should be less than 180 = x/2°

By the triangle sum theorem, the Sum of measures of all interior angles of triangle = 180°

m(∠E) + m(∠F) + m(∠G) = 180°

55° + x/2° + x/2= 180°

x= 180° - 55°

x = 125

Measure of angle G = 125/2 = 62.5

Therefore, measure of angle G is 62.5°.

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The value of c is 1/15

Joint probability is a statistical measure that calculates the likelihood of two events occurring together and at the same point in time. Joint probability is the probability of event Y occurring at the same time that event X occurs.

To be valid probability functions, the sum of changes across the entire range of x and y variables must equal one

b) In this case, the joint probability could be represented as follows:

                     x = -2                  x = 0                    x = 2

y = -2               0                         2c                        4c

y = 3                5c                       3c                          c

As a consequence, the total likelihood in this case is:

=> c(2 + 4 + 5 + 3 + 1) = 15c

=> 15c = 1

c = 1/15

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The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.

The class width, also known as the class interval, is the difference between the upper and lower boundaries of a class. In this frequency distribution, the class width is 9 since the lower boundary of the first class is 54.5 and the upper boundary of the last class is 90.5. We can calculate the frequency of each class by counting how many numbers fall within the class boundaries. For example, the first class has 72 observations since there are 72 numbers that fall between 54.5 and 63.5. To calculate the relative frequency of each class, we divide the frequency of each class by the total frequency. For example, the relative frequency of the first class is 0.312 since 72/231 = 0.312. Once the frequencies and relative frequencies have been calculated, a histogram can be made to represent the data. The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.

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Answer:28

Step-by-step explanation: because add z and x

The amount of interest that Laura will be paid in the first 5 years is $600.

The simple interest formula is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given that;

Plug the given values into the above formula and solve for interest I.

I = P × r × t

I = $3,000 × 0.04 × 5

I = $3,000 × 0.2

I = $600

Therefore, the amount of interest payable is $600.

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The absolute value of the x-values of the coordinates of A and B = |2 - 5| = 3 units.

The absolute value of the y-values of the coordinates of B and C = |6 - 3| = 3 units.

If two points lie on a coordinate plane, the distance between them represents the length of the segment both points form, which is determined by finding the absolute difference between the values of their coordinates that lie on the same axis.

Given that a square has the points, A (2, 6), B (5, 6), C (5, 3), D (2, 3), its dimensions can be found as explained below:

Length of AB is found by calculating the absolute value of the x-values of the coordinates of A and B, while to find the length of BC, is the absolute value of the y-values of the coordinates of B and C.

Therefore:

AB = |2 - 5| = 3 units

BC = |6 - 3| = 3 units

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To determine how many cakes Lionel makes in one hour, we can use the following formula:

cakes per hour = total cakes / total hours worked

On Monday, Lionel made 7 cakes in some number of hours, so we don't know how many cakes he made per hour that day. However, on Tuesday, he made an additional 6 cakes (13 total cakes - 7 cakes made on Monday), and he worked for 2 hours longer than he did on Monday. Therefore:

cakes per hour on Tuesday = 6 cakes / 2 hours = 3 cakes per hour

So Lionel made 3 cakes per hour on Tuesday. We don't have enough information to determine how many cakes he made per hour on Monday.

Invested in each vehicle is $40,000 if the annual investment income is $944.25.

Let

CD's = x

Bonds = x + 60000

Stocks = y

x + x + 60000 + y = 140000 ----> 2x + y = 80000 .......(1)

Using I = Prt; t = 1; I = Pr

2x + 3.7(x + 60000) + 11.1y = 7800(100× )  × Since I used an exact proportion, the opposite side needs to be multiplied by 100.

5.7x + 11.1y = 558000 .......(2)

Either elimination or substitution;

x = 20000 y = 40000

So CD's = 20000, Bonds = 80000, Stocks = 40000

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The solution of the modulus equation is -

x = 2

x = - 2

Given is a function as -

|2x| = - 4

We can write -

For {x < 0} → {|x| = - x}. We can write the function as -

- 2x = - 4                                

x = 2

For {x > 0} → {|x| = x}. We can write the function as -

2x = - 4

x = - 2

Therefore, the solution of the modulus equation is -

x = 2

x = - 2

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The number of ordered triples (a, b, c) where a, b, and c are positive integers and a is a factor of b, a is a factor of c, and abc=N, is 64.

To find the ordered triplets, Firstly Factorize N into its prime factors.For each prime factor. we can choose its exponent as the value of a, b, and c. The total number of ordered triples (a, b, c) is (number of exponents + 1)^3.

let N = 24. The prime factorization of 24 is 2^3 * 3^1.

The number of possible values of a is 4 (from 0 to 3), so the number of possible values of b and c is also 4.

The number of ordered triples is 4^3 = 64.

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The post-neonatal mortality rate for the year is 1.1×10⁻⁷.

The post-neonatal mortality rate in a year is applicable when the death day lies between 28 and 364. First, divide the number of post-neonatal deaths by the number of live births. Then multiply the obtained value by 1000 to get the post-neonatal mortality rate.

It is known that 1 billion units = 10⁹ units. So, 20 billion live births will be 20×10⁹ live births. Also, the number of post-neonatal deaths is 2200.

So, use the formula, post-neonatal mortality rate = (the number of post-neonatal deaths)/(the number of live births).

post-neonatal mortality rate = 2200/(20×10⁹)

= 110×10⁻⁹

= 1.1×10⁻⁷

Therefore, the obtained answer is 1.1×10⁻⁷.

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Answer:

False.

Step-by-step explanation:

It is not possible to create a regular tessellation with a regular heptagon. A regular tessellation refers to a pattern of repeating shapes that completely covers a flat surface without any gaps or overlaps. The only regular polygon shapes that can form regular tessellations are the equilateral triangle, square, and hexagon. Regular heptagons do not have the symmetry necessary to form a repeating pattern that covers a flat surface without gaps or overlaps.

The solution is, the required probability is p= 1/10.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

from the given information we get,

We have 5 possible parts colored red, green, blue, purple and yellow

The cube for this case have 6 possible numbers 1,2,3,4,5,6

We have the following even numbers: 2,4,6

Then the probability of obtain an even number is:

p1= 3/6= 1/2

Then the probability of obtain a blue color on the spinner is:

p2= 1/5

Then we want this probability:

Obtain an even number AND sppining a blue on the spinner

Then since the events are independent we can do this:

p = 1/2 * 1/5= 1/10

Hence, The solution is, the required probability is p= 1/10.

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area of square 1 is 28 square units and its side length is[tex]$2\sqrt{7}$[/tex] units.

Let the side length of square 1 be x units. Then the areas of squares 1, 2, and 3 are [tex]$x^2$[/tex], 64, and 36 square units, respectively.

Since square 2 has an area of $64$ square units, its side length is [tex]$\sqrt{64}=8$[/tex] units. Similarly, square 3 has a side length of[tex]$\sqrt{36}=6$[/tex]units.

We can now set up an equation based on the fact that the sum of the areas of squares 1 and 3 is equal to the area of square 2:

[tex]$$x^2+36=64$$[/tex]

Solving for x, we get:

[tex]$$x^2=28$$[/tex]

Therefore, the area of square 1 is [tex]$x^2=28$[/tex] square units, and its side length is [tex]$\sqrt{28}=2\sqrt{7}$[/tex] units.

In summary, the area of square 1 is 28 square units and its side length is[tex]$2\sqrt{7}$[/tex] units.

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A is the answer

tbtfhfhfshfgfsghgf

The Triangle ABC has been dilated through point p and scale factor 3 to produce this finished picture.

Having three sides, three angles, and three points, a triangle is indeed a closed, two-dimensional object. A hexagon also includes a triangular. Triangles can be found in a variety of everyday objects, such as sandwiches, traffic signals, clothes hooks, and billiards racks.

Assume point P as origin then.

P has coordinate (0,0).

And point A has coordinate (-4,0).

point B has coordinate (0,-3).

point C has coordinate (-4,-3).

P(0,0), A(-4,0) B(0,-3) C(-4,-3).

Since the triangle goes an dilation with center  at P and scale factor 3.

Then k=scale factor =3.

Now the new coordinate of Triangle is given by A',B' and C', whose coordinate in (x, y) plane is calculated as.

[tex](\mathrm{x}, \mathrm{y}) \rightarrow(\mathrm{kx}, \mathrm{ky})[/tex]

Now calculating the Coordinates on dilated triangle

A'=3(-4,0)=(-12,0)

B'=3(0,-3)=(0,-9)

C'=3(-4,-3)=(-12,-9).

We will calculate the coordinates of dilated triangle assuming the point P as origin

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Divide the 8-digit student ID by the leftmost 3 digits to find q and r using the Quotient Remainder Theorem. If your 8-digit student ID is 12345678, then d = 123, n = 45,678, q = 371, and r = 45.

Suppose your 8-digit understudy ID is 12345678. Then, at that point, we can take the furthest left three digits to get d = 123. Also, we can take the excess 5 digits to get n = 45,678.

To find q and r, we can utilize the condition n = dq + r and address for q and r.

To begin with, we really want to see as the biggest various of d that is not exactly or equivalent to n. We can do this by separating n by d and taking the floor of the outcome:

q = ⌊n/d⌋ = ⌊45,678/123⌋ = 371

Then, we can track down the rest of taking away the result of d and q from n:

r = n - dq = 45,678 - 123 × 371 = 45,678 - 45,633 = 45

Along these lines, in the event that your 8-digit understudy ID is 12345678, d = 123, n = 45,678, q = 371, and r = 45.

The Remainder Leftover portion Hypothesis expresses that for any whole number n and positive whole number d, there exist whole numbers q and r with the end goal that n=dq+r, where q is the remainder and r is the rest of. We can track down q and r by separating n by d and taking the floor of the outcome for q, and deducting the result of d and q from n for r.

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The best definition of the unit rate is how much of something per 1 unit of something else. Hence option D is the correct answer

Unit rate is basically a ratio and it compares something with 1 unit of some other quantity. So they are used for comparing two different things and if we talk about unit rate then the denominator is always 1 or the other value is always 1

So if we talk about an example of unit rate and if we specifically talk about speed, then we say kilometer per hour

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