Use the definition man f(x)-f(a) = lim to find the slope of the line tangent to the graph off at P. X-a X-a f(x) = -5x + 9, P(4. - 11) II mtan

If a > 1, the graph of y = a|x| will be vertically stretched (or "taller") or if 0 < a < 1, the graph of y = a|x| will be vertically compressed (or "shorter") or If a is negative, the graph of y = a|x| will be a reflection of the graph of y = |x|  than the graph of y = |x| than the graph of y = |x|,

A graph is a visual representation of a set of objects, called vertices or nodes, that are connected by lines or edges. It is used to study relationships and patterns between these objects.

According to the given information :

The graph of the function y = |x| is a V-shaped graph that passes through the origin, with the arms of the V opening upward and downward at a slope of 1. When we introduce a coefficient 'a' to the function, the graph of y = a|x| is stretched or compressed vertically.

Specifically, if a > 1, the graph of y = a|x| will be vertically stretched (or "taller") than the graph of y = |x|, and the arms of the V will be steeper. On the other hand, if 0 < a < 1, the graph of y = a|x| will be vertically compressed (or "shorter") than the graph of y = |x|, and the arms of the V will be less steep.

If a is negative, the graph of y = a|x| will be a reflection of the graph of y = |x| about the x-axis, resulting in the same shape as y = |x| but flipped upside down

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The law of uninhibited growth is express as:

where N(t) is the population at time t, N0 is the initial population, k is the growth rate and t is the time. In this case we know that after one day, t=1, the population is 800 and that the initial population was 500; plugging these values and solving for k we have:

Now that we have the growth rate, we know that the population growth in this case can be express as:

We want to know the time it takes for the population to be 7000, to find it we equate our expression to this value and solve for t:

Therefore, it takes 5.6 days for the population to reach 7000 individuals.

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

Answer:

204 in

Step-by-step explanation:

I can't really explain this other than that you have to add all the sides and the outside of this shape. For the hypotenuse you use the formula \(a^2+b^2=c^2\). Now just fill in what you know.

\(12^2+9^2=x^2\\144+81=x^2\\225=x^2\\x=15\)

So we have:

length: 12in

base: 9in

hypotenuse: 15in

So now we do 12+15+9+15+12+15+9+15+12+15+9+15+12+15+9+15. Once we do all that we get 204 in.

Answer:

2

Step-by-step explanation:

Yeah its 2 I can explain but will be long but if want comment and I will post but most likely its 2

Answer:

12n-5

Step-by-step explanation:

Since each box has 12 cupcakes, we can multiply n by 12 as there is 12 cupcakes for every box.

12n

Now she eats 5 cupcakes, so we subtract 5 from the equation

Hope this helps!

Answer:

73 1/3 %

Step-by-step explanation:

8 pieces were left

30-8 = 22 so 22 were consumed

22/30 is the percent consumed

.7333333

73.333333%

We know .333333333 is 1/3

73 1/3 %

Answer:

see below

Step-by-step explanation:

bh + hr = 25

Factor out an h

h( b+r) = 25

Divide each side by ( b+r)

h( b+r)/( b+r) = 25/( b+r)

h = 25/( b+r)

Now solve for r

bh + hr = 25

Subtract bh from each side

bh -bh+ hr = 25-bh

hr = 25 -bh

Divide by h

hr/h = 25/h -bh/h

r = 25/h -b

There are 2 × 3^n-1 - 2^n-1 n-digit ternary sequences in which at least one pair of consecutive digits are the same.

The number of n-digit ternary sequences in which at least one pair of consecutive digits are the same can be found using the principle of inclusion-exclusion. We first calculate the total number of n-digit ternary sequences, which is 3ⁿ since each digit can take on three possible values (0, 1, or 2). Next, we calculate the number of n-digit ternary sequences in which no pair of consecutive digits are the same.

To do this, we observe that for any such sequence, the first digit can be any of the three possible values. However, each subsequent digit can only be one of the two values that are different from the previous digit. Therefore, there are 3 choices for the first digit and 2 choices for each subsequent digit, resulting in a total of 3 × 2^n-1 sequences with no consecutive equal digits.

Now, we need to subtract the number of sequences with no consecutive equal digits from the total number of sequences. However, this will also subtract the number of sequences in which two pairs of consecutive digits are the same (e.g., 1101). Therefore, we need to add back in the number of sequences with two pairs of consecutive digits that are the same.

To do this, we observe that there are 2^n-2 ways to choose the positions of the two pairs of consecutive equal digits, and there are 2 choices for the digits in each pair (since they must be the same). Therefore, there are a total of 2^n-1 sequences with two pairs of consecutive equal digits.

Using the principle of inclusion-exclusion, the number of n-digit ternary sequences in which at least one pair of consecutive digits are the same is:

3ⁿ - 3 × 2^n-1 + 2^n-1

This can be simplified to:

2 × 3^n-1 - 2^n-1

Therefore, there are 2 × 3^n-1 - 2^n-1 n-digit ternary sequences in which at least one pair of consecutive digits are the same.

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Answer/Step-by-step explanation:

Length of rectangular garden = 12.63 m

Width of rectangular garden = 3.28

Part A: Perimeter of garden if the length and height is rounded to nearest whole number.

12.63 rounded to nearest whole number = 13

3.28 rounded to nearest whole number = 3

Equation that shows her estimate would be: C. 13 + 3 + 13 + 3 = 32 meters

Part B: Perimeter of garden if the length and height is rounded to nearest tenth.

12.63 rounded to nearest tenth = 12.6

3.28 rounded to nearest tenth = 3.3

Equation that shows this estimate would be: B. 12.6 + 3.3 + 12.6 + 3.3 = 31.8 meters

Part C: Exact Perimeter of her garden.

Exact perimeter would be 12.63 + 3.28 + 12.63 + 3.28 = 31.82 meters

Part D:

Difference between 31.82 and the exact perimeter is 0.02, while difference between 32 and the exact perimeter is 0.18.

Therefore:

The numbers rounded to the nearest TENTH are closer because 31.8 meters is closer to the exact perimeter than 32 meters.

Answer: x=3 y=-5

Step-by-step explanation:

Answer:

45 feet

Step-by-step explanation:

The parabola that forms the shape of the satellite dish has its axis of symmetry along the vertical direction, and the vertex at the bottom center of the dish. Let's assume that the vertex of the parabola is at the origin (0,0) of a coordinate system, and the opening of the dish is along the x-axis. Then the equation of the parabola is:

y = a x^2

where "a" is a constant that determines the shape of the parabola. We can find the value of "a" using the given dimensions of the dish.

At the opening of the dish, which has a diameter of 72 feet, the y-coordinate is zero. Therefore, we have:

0 = a (36)^2

Solving for "a", we get:

a = 0

This means that the equation of the parabola is simply y = 0, which is a horizontal line passing through the origin. Clearly, this is not the correct equation for the parabola.

To find the correct equation, we need another point on the parabola. We are given that the depth of the dish at its center, which corresponds to the focus of the parabola, is 9 feet. Using the definition of a parabola, we know that the distance from any point on the parabola to the focus is equal to the distance from that point to the directrix. Since the axis of symmetry is vertical, the directrix is a horizontal line located 9 feet below the vertex.

The equation of the directrix is therefore:

y = -9

We can use this to find another point on the parabola. Consider a point (x,y) on the parabola that is equidistant from the focus (0,9) and the directrix y = -9. The distance from (x,y) to the focus is:

d = sqrt(x^2 + (y-9)^2)

The distance from (x,y) to the directrix is simply y + 9. Therefore, we have:

sqrt(x^2 + (y-9)^2) = y + 9

Squaring both sides and simplifying, we get:

x^2 = 4y(18-y)

This is the equation of the parabola. We can now find the x-coordinate of the receiver, which is located at the focus (0,9). Setting y = 9 in the equation of the parabola, we get:

x^2 = 4(9)(9) = 324

Therefore, the x-coordinate of the receiver is:

x = ±18

Since the dish is 72 feet across at its opening, the receiver should be located at a distance of 36 feet from the center of the dish. Therefore, the receiver should be placed at a height of:

y = 9 + 36 = 45 feet

above the vertex of the parabola.

Answer:

Please provide a question to be answered.

Answer: (not sure)

half of 2/8 is 0.125 and half of 8/16 is 0.25

if you want half of both together it's 0.625

Step-by-step explanation:

The 85% confidence interval in this scenario would be (32.33, 38.87). This is because the confidence interval is a range of values that is likely to include the true mean of the population, based on the sample statistic.

The 85% confidence interval means that if the same sample was taken many times, the true mean would be within the given range 85% of the time. In this case, the sample mean (35.6 minutes) and the standard deviation (8.2 minutes) are used to calculate the confidence interval, of which the lower limit is 32.33 and the upper limit is 38.87. This is the range within which the true mean of the population is likely to lie.

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The average time a customer waits in the system is 9 minutes.

To calculate the average time a customer waits in the system, we need to consider the arrival rate of customers and the service rate. In this case, customers arrive at the post office at an average rate of one every 6 minutes, which corresponds to an arrival rate of λ = 1/6 customers per minute.

The average time it takes to process a customer is 3 minutes, which represents the service rate, μ = 1/3 customers per minute.

In queuing theory, the average time a customer waits in the system can be calculated using the formula:

Average waiting time = 1 / (service rate - arrival rate)

In this scenario, the service rate (μ) is 1/3 customers per minute, and the arrival rate (λ) is 1/6 customers per minute. Plugging these values into the formula, we have:

Average waiting time = 1 / (1/3 - 1/6) = 1 / (2/6) = 3/2 = 1.5 minutes.

Therefore, the average time a customer waits in the system is 1.5 minutes, or 9 minutes.

This calculation takes into account the balance between customer arrivals and the processing time, providing an estimate of the average waiting time a customer can expect in the system.

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The equity of the entity, according to the basic accounting equation, is R6 000. The basic accounting equation is Assets = Liabilities + Equity. To find the equity of the entity, we need to subtract the total liabilities from the total assets.

Bank balance: R5 000

Machinery balance: R3 000

Trade payables: R2 000

Total assets = Bank + Machinery

            = R5 000 + R3 000

            = R8 000

Total liabilities = Trade payables

                 = R2 000

Equity = Total assets - Total liabilities

      = R8 000 - R2 000

      = R6 000

Therefore, the equity of the entity, according to the basic accounting equation, is R6 000.

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Answer: -19 is the temperature. THe temperature is -19 degrees Fahrenheit

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

\((x + y + 2)(y + 1) = \\ xy + x + {y}^{2} + + y + 2y + 2 = \\ xy + x + {y}^{2} + 3y + 2\)

We can be 98% confident that the true mean life of all General Electric transistors lies within the interval [1058.64, 1143.36] hours.

To construct an approximate 98% confidence interval of the mean life of all General Electric transistors, we can use the following formula:

confidence interval = sample mean ± 1.96 * (sample standard deviation / sqrt(sample size))

In this case, the sample mean is 1101 hours, the sample standard deviation is 71 hours, and the sample size is 70. Plugging these values into the formula, we get the following confidence interval:

confidence interval = [1058.64, 1143.36]

confidence interval = 1101 ± 1.96 * (71 / sqrt(70))

To be "98% confident" in this problem means that if we were to repeat this experiment 100 times, we would expect the confidence interval to contain the true mean life of all General Electric transistors 98 times. In other words, there is a 2% chance that the confidence interval would not contain the true mean life.

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This is a right triangle. Use the Pythagorean theorem to solve:

x^2 + 5.8^2 = 15.6^2

x^2 + 33.64 = 243.36

Subtract 33.64 from both sides:

x^2 = 209.72

Take the square root of both sides:

x = 14.48171

Round to 1 decimal place:

x = 14.5 in.

Answer:

x = 14.5 in

Step-by-step explanation:

There is something called pythagoras' theorem. It states that

a^2 + b^2 = c^2,

a, b and c being sides of a right-angled triangle.

C is always the hypotenuse and a and b are any of the other two.

(The hypotenuse is always the longest side, and always opposite to the right angle, which is always the biggest angle of a right-angled triangle.)

So here we know two sides, the hypotenuse and another side. Let's substitute them into the formula:

5.8^2 + x^2 = 15.6^2

x^2 = 15.6^2 - 5.8^2

x^2 = 243.36 - 33.64

x^2 = 209.72

x = sqr209.72

x = 7sqr107/5 = 14.48171261 in

= 14.5 in (if rounded to 3 significant figures)

You could use a shortcut to do all this and find the answer more quickly:

a^2 = c^2 - b^2 or b^2 = c^2 - a^2

also:

a = sqr(c^2 - b^2)

x = Sqr(15.6^2 - 5.8^2)

= 14.5 in

Answer:

15^7/4

Step-by-step explanation:

A=15 b=7 c=4

.......

Answer:

A = 15   C= 7    B=4

Step-by-step explanation:

Okay so as you can see there is \(15^{7}\) so A would be 15 and C would be 7 and B would be  4

LCL and UCL values of both scenarios are (158.61,161.39),(69.65,70.35) respectively.

To calculate the lower confidence limit (LCL) and upper confidence limit (UCL) for each given scenario, you'll need to use the following formula:

LCL = X - (z * (sigma / √n))
UCL = X+ (z * (sigma / √n))

where X is the sample mean, n is the sample size, sigma is the population standard deviation, and z is the z-score corresponding to the desired confidence level (1 - alpha).

First Scenario:
X = 160, n = 436, sigma = 30, alpha = 0.01

1. Find the z-score for the given alpha (0.01).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.005 = 0.995.
The corresponding z-score is 2.576.

2. Calculate LCL and UCL.
LCL = 160 - (2.576 * (30 / √436)) ≈ 158.61
UCL = 160 + (2.576 * (30 / √436)) ≈ 161.39

First Scenario Result:
LCL = 158.61
UCL = 161.39

Second Scenario:
X= 70, n = 323, sigma = 4, alpha = 0.05

1. Find the z-score for the given alpha (0.05).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.025 = 0.975.
The corresponding z-score is 1.96.

2. Calculate LCL and UCL.
LCL = 70 - (1.96 * (4 / √323)) ≈ 69.65
UCL = 70 + (1.96 * (4 / √323)) ≈ 70.35

Second Scenario Result:
LCL = 69.65
UCL = 70.35

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Step-by-step explanation:

5/4+(12/4_1/2)^2

5/4+((12_8)/4)^2

5/4+1

9/4

Answer:

\(\frac{3}{2}\)

Step-by-step explanation:

Given

\(\frac{5}{4}\) + 4 (\(\frac{3}{4}\) - \(\frac{1}{2}\) )²

= \(\frac{5}{4}\) + 4 (\(\frac{1}{4}\) )²

= \(\frac{5}{4}\) + 4 × \(\frac{1}{16}\)

= \(\frac{5}{4}\) + \(\frac{1}{4}\)

= \(\frac{6}{4}\)

= \(\frac{3}{2}\)

Answer:

\(6.25\ units,\ 5.25 \ units\ and\ 5 \ units\)

Step-by-step explanation:

Given:

The scale factor =  1.25 and rotated =45°

Length of side =5 units; , 4.2 units; and , 4 units respectively.

As mention in the question the ∆ABC and ∆PQR are similar it means there sides are equal .

Therefore sides of  the ∆ PQR is  

\(= (5*1.25),(4.2*1.25),(4*1.25)\\=6.25, 5.25, 5\)

Hence the length of the  ∆PQR is \(6.25\ units,\ 5.25 \ units\ and\ 5 \ units\)

Answer:

sinP = 7/25

cosQ = 7/25

tanP = 7/24

cotQ = 7/24

secP = 25/7

cscQ = 25/24

Step-by-step explanation:

sin∅ is opposite over hypotenuse

cos∅ is adjacent over hypotenuse

tan∅ is opposite over adjacent or sin∅/cos∅

csc∅ is hypotenuse over opposite or 1/sin∅

sec∅ is hypotenuse over adjacent or 1/cos∅

cot∅ is adjacent over opposite or cos∅/sin∅

Since triangle RQP is a right triangle, we can use trig and Pythagorean Theorem: a² + b² = c²

The missing side length RQ after we use Pythagorean Theorem would be 7.

From there, we can find the trigonometric values.

Answer:

Step-by-step explanation:

Using the concept of Ratio and Proportion, we got 22.5 inches height and 71.11 inches as width if screen of the left is 40 inches wide and screen on the right is 40 inches tall respectively.

We know very well that if some dependency is given in form of two variables and asking for other variables then ratio and proportion, will be used

We are given if height of television is 9 then width is 16inch

a)We need to tell height when width is 16 inch

Therefore, height of tv is when width is 40 inch=(9×40)/16

                                                                   Height=22.5 inches

b) Here we need to find just converse of above solution, we need to tell width if height is given as 40 inches.

Therefore width of tv is when height is 40 inches=(16×40)/9

                                                                        width=71.11 inches

Hence, height of widescreen Tv is 22.5 inches when width is 40 inches and width of widescreen TV is 71.11 inches when height is 40 inches

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