help with this question please and thank you!:)

Step-by-step explanation:

AB=BC

8x+6=6x+18

2x=12

x=6

so

AB= 48+6=54cm

BC=36+18=54cm

AD=CD

8y+20=12y-8

-4y=-28

y=7

so

AD= 84-8=76cm

CD=56+20=76cm

AE=2x+4y

AE=2×6+4×7

AE=40cm

AC=2×40=80cm

The expression 2^n - 5^n is indeed a solution to the recurrence relation an = 7an-1 - 10an-2. To use it as the closed formula for the sequence, the initial conditions need to be specified. The initial values for a0 and a1 would need to be determined based on the sequence being generated. Once the initial conditions are established, the expression 2^n - 5^n can be used to find the nth term of the sequence directly without having to rely on the recurrence relation.

To demonstrate that 2^n - 5^n satisfies the given recurrence relation, we need to substitute it into the relation and verify that it holds true for all n.

Given recurrence relation: an = 7an-1 - 10an-2

Substituting 2^n - 5^n into the recurrence relation:

7(2^(n-1) - 5^(n-1)) - 10(2^(n-2) - 5^(n-2))

Expanding and simplifying the expression:

7 * 2^(n-1) - 7 * 5^(n-1) - 10 * 2^(n-2) + 10 * 5^(n-2)

Rearranging the terms:

2 * 7 * 2^(n-2) - 2 * 7 * 5^(n-2) - 10 * 2^(n-2) + 10 * 5^(n-2)

Combining like terms:

2(7 * 2^(n-2) - 7 * 5^(n-2) - 5 * 2^(n-2) + 5 * 5^(n-2))

Factoring out 2 from the expression:

2(7 * 2^(n-2) - 5 * 2^(n-2) - 7 * 5^(n-2) + 5 * 5^(n-2))

Simplifying further:

2(2^(n-2)(7 - 5) - 5^(n-2)(7 - 5))

The expression simplifies to:

2(2^(n-2)(2) - 5^(n-2)(2))

2 * 2^(n-1) - 2 * 5^(n-1)

Which is equal to 2^n - 5^n.

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Answer:

7/40 is the fraction filled with water

Step-by-step explanation:

Here we start by calculating the volume of the cylindrical tank.

Mathematically, that would be;

V = π * r^2 * h

From the question

r = 80 cm = 80/100 = 0.8 meters

h = 1.4 meters

π = 22/7

Plugging these values into the volume equation, we have;

V = 22/7 * 0.8 * 0.8 * 1.4 = 2.816 m^3

But mathematically;

1 m^3 = 1000 liters

So 2.816 m^3 = 2.816 * 1000 = 2816 liters

So the fraction filled with water will be;

492.8/2816 = 0.175 = 175/1000 = 7/40

Answer: $7.1

Step-by-step explanation:

Since the gallon of gas currently costs $3.17 and the prices are projected to increase 124% by April. Then, the projected cost of a gallon of gas in April will be:

= $3.17 × (100% + 124%)

= $3.17 × 224%

= $3.17 × 2.24

= $7.1

Therefore, the projected cost will be $7.1

The Poisson distribution is a probability distribution that describes the number of independent occurrences of an event in a fixed interval of time or space.

In this case, the random variable is the number of occurrences during an interval. Therefore, the statement "the random variable is the number of occurrences during an interval" applies to the Poisson distribution. Another statement that applies to the Poisson distribution is "the probability of the event is proportional to the interval size". This means that the probability of observing k events in a fixed interval is proportional to the length of the interval. However, the statement "the probability of an individual event occurring is quite large" does not describe the Poisson distribution. In fact, the Poisson distribution assumes that the probability of an individual event occurring is small, but the number of events is large. Finally, the statement "the intervals do not overlap and are independent" is not a defining characteristic of the Poisson distribution, although it is often assumed in practical applications. In summary, the Poisson distribution is a probability distribution that models the number of independent occurrences of an event in a fixed interval. The probability of the event is proportional to the interval size, and the random variable is the number of occurrences during an interval.

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As x approaches both positive and negative infinity, f(x) approaches 4.

If she discard previously tried keys the probability is 1/n

If she doesn't discard previously tried keys the probability is: \(\frac{(n-1)^k}{n^k}\)

If she discard previously tried keys, the probability of open the door in the 1st, 2nd and 3rd try are:

1st try: \(\frac{1}{n}\)

2nd try: \((\frac{n-1}{n}) * (\frac{n}{n-1} ) = \frac{1}{n}\)

3rd try: \((\frac{n-1}{n}) * (\frac{n-2}{n-1} ) * (\frac{1}{n}) = \frac{1}{n}\)

Where, for example, the probability of open the door in the 2nd try is the multiplication of the probability that the woman didn't open the door in the 1st try with the probability that she open the door in the 2nd try.

So, the probability that she open the door in the kth try is: 1/n

On the other hand, if she doesn't discard previously tried keys, the probability to open the door in the 1st, 2nd and 3rd try are:

1st try: \(\frac{1}{n}\)

2nd try: \((\frac{n-1}{n}) *( \frac{1}{n}) = \frac{n-1}{n^2}\)

3rd try: \((\frac{n-1}{n}) * (\frac{n}{n-1} ) * (\frac{1}{n}) = \frac{(n-1)^2}{n^3}\)

So, the probability that she open the door in the kth try is:

\(\frac{(n-1)^k^-^1}{n^k}\)

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Where the above are given,

(a) MLE of β: (nα + y₁ + y₂ + ... + yn)/n

(b) MLE of E(Y): (nα + y₁ + y₂ + ... + yn)/n

Maximum Likelihood Estimation (MLE) is   a statistical method used to estimate the parameters of a probability distribution by maximizing the likelihood function based on observed data.

(a) The MLE of β can be found by   maximizing the likelihood function. The likelihood function for  a gamma distribution is given by  -

L(β;  y₁, y₂, ..., yn) = (1/β^nαΓ(α))ⁿ * exp(-( y₁ + y₂ + ... + yn)/β)

Taking the logarithm of the likelihood function (log-likelihood) to simplify the calculations  -

log L(β;  y₁, y₂, ..., yn) =   n*log(1/β) + nα*log(β) - n*logΓ(α) - ( y₁ + y₂ + ... + yn)/β

To find the MLE of β, we differentiate the log-likelihood with respect to β, set it equal to zero, and solve for β  -

d/dβ(log L(β;  y₁, y₂, ..., yn)) = -n/β + nα/β² + ( y₁ + y₂ + ... + yn)/β² = 0

Simplifying the equation -

-n/β + nα/β^2 + ( y₁ + y₂ + ... + yn)/β² = 0

Multiplying through by β²

-nβ + nα + ( y₁ + y₂ + ... + yn) = 0

Rearranging  whave

nβ = nα + ( y₁ + y₂ + ... + yn)

Finally, solving for β -

β = (nα +  y₁ + y₂ + ... + yn)/n

Therefore, the MLE of β is (nα +  y₁ + y₂ + ... + yn)/n.

(b) The MLE of E(Y), the expected value of Y, is simply the MLE of β.

So, the MLE of E(Y) is (nα +  y₁ + y₂ + ... + yₙ)/n.

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Answer:

The pool is 8 feet deep

Step-by-step explanation:

Holding means the area, and we know that area can be found using;

-> length * width * height

or

-> base * height

     [] The base is length times width

base * height = 1,440

(15 * 12) * height = 1,440

(180) * height = 1,440

height = \(\frac{1440}{180}\)

height = 8 feet

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

Answer:

16000 grams

Step-by-step explanation:

9(1000) + 7(1000) = 16000

As we know that perimeter of a shape is the sum of all it's boundaries. Also , let assume that the missing side be y . So ,here ;

\({:\implies \quad \sf (4x-4)+(3x+1)+y=13x-8}\)

\({:\implies \quad \sf 4x-4+3x+1+y=13x-8}\)

\({:\implies \quad \sf y+7x-3=13x-8}\)

\({:\implies \quad \sf y=13x-8-7x+3}\)

Collecting like terms :

\({:\implies \quad \sf y=(13x-7x)+(-8+3)}\)

\({:\implies \quad \bf \therefore \quad \underline{\underline{y=6x-5}}}\)

Hence , the length of Missing side is 6x-5

Answer:

see below

Step-by-step explanation:

Area = pi r^2     r = radius

  diamter = 94    then radius = 94/2 = 47 cm

area = pi (47)^2 = 2209 pi    or 6939.78  cm^2

Answer:

A ≈ 6,939.8 cm²

Step-by-step explanation:

Given : " the diameter is 94cm "

d = 94

Radius is r = d/2 = 94/2 = 47 cm

Area of a circle is

A= π·r²

A = π·47² ≈ 6,939.8 cm²

The area of triangle A"B"C" is 1/9 of the area of triangle ABC.

In this problem, we are given a triangle ABC and asked to construct a new triangle A'B'C' by taking points on each side of the original triangle such that they divide the sides into thirds. We then repeat this process to create another triangle A"B"C" using points on the sides of A'B'C'. The objective is to show that the sides of triangle A"B"C" are parallel to the corresponding sides of triangle ABC. Additionally, we need to determine the fraction of the area of triangle ABC that is occupied by triangle A"B"C".

Let's start by examining triangle ABC and the construction of triangle A'B'C'. We are given that point A' is located one-third of the way from point B to point C. This means that the distance from B to A' is one-third of the distance from B to C. We can express this mathematically as AB' = (1/3)BC. Similarly, we can determine the other side lengths of triangle A'B'C' as BC' = (1/3)CA and CA' = (1/3)AB.

To demonstrate that the sides of triangle A"B"C" are parallel to the corresponding sides of triangle ABC, we need to show that the ratios of the side lengths are equal. Let's consider one side as an example. We know that AB' = (1/3)BC in triangle A'B'C'. Now, let's examine the corresponding side in triangle A"B"C". Denote the side length in triangle A"B"C" as A"B''. Using a similar logic, we can express A"B'' as (1/3)B"C".

To compare the ratios, we can set up a proportion:

AB' / BC = A"B'' / B"C"

Substituting the values we obtained earlier:

(1/3)BC / BC = (1/3)B"C" / B"C"

Simplifying the equation, we find:

1/3 = 1/3

Since the ratio of the side lengths is the same for all corresponding sides, we can conclude that the sides of triangle A"B"C" are parallel to the sides of triangle ABC.

Now, let's determine the fraction of the area of triangle ABC that is occupied by triangle A"B"C". Since triangle A"B"C" is created by taking one-third of each side length of triangle A'B'C', we can conclude that the ratio of their areas will be the square of the ratio of their side lengths.

The ratio of the side lengths is 1/3, so the ratio of the areas will be (1/3)^2 = 1/9.

Therefore, the area of triangle A"B"C" is 1/9 of the area of triangle ABC.

In summary, we have shown that the sides of triangle A"B"C" are parallel to the sides of triangle ABC, and the area of triangle A"B"C" is 1/9 of the area of triangle ABC.

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Answer:

24 degree Celsius

Step-by-step explanation:

Temperature may be defined as the intensity or the degree of heat that is present in any substance or present in the environment. It is the measure of hotness or coldness of any item or surroundings. Temperature is measured with the help of a comparative scale which shows the how hot or cold the place is or item is.

In the context, Riya uses a comparative scale like the thermometer to measure the temperature of the kitchen. The mercury level on the scale rises and stops at a point indicating the temperature of the kitchen.

Thus the temperature of the kitchen according to the scale is \($24 ^ \circ C$\).

Answer:

Step-by-step explanation:

hi its me addison ray

Answer:

first one is correct

Step-by-step explanation:

length of a rectangle = 2b - 8c

breadth of a rectangle = 10b + 6c

now , formula to calculate the perimeter of rectangle is

p = 2 (l + w)

no substitute the value of l(length) and w(width)

p = 2{(2b - 8c) + (10b + 6c)}

p = 2(2b - 8c + 10b + 6c)

p = 2(12b - 2c)

p = 24b - 4c

The capacity of the mug is given by M = 1 7/8 cups

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the amount of mug filled = ( 1/5 ) of the full amount M

Now , the mug contains 3/8 of a cup of water

So , the equation is

( 1/5 )M = ( 3/8 ) of a cup

Multiply by 5 on both sides , we get

M = 15/8 of a cups

M = 1 7/8 cups

Hence , the capacity of the mug is 1 7/8 cups

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Answer:

C= 2.40g+0

Step-by-step explanation:

The total cost is reliant on how many gallons of gas the customer buys. If the person bought 8 gallons, you'd plug 8 in for g. 8 times 2.40 = $19.20

The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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Answer:

they would be continuous

Step-by-step explanation:

When age is rounded to the nearest year, the data become discrete. This is because rounding to the nearest whole number means that age is being quantized into a specific set of values, rather than being treated as a continuous variable.

For example, if someone is 35.5 years old and their age is rounded to the nearest year, they will be recorded as being either 35 or 36 years old.

A continuous variable is a quantity that can take on any value within a certain range, such as height, weight, or temperature. Rounding age to the nearest year effectively converts it from a continuous variable to a discrete variable, since it can only take on a limited number of values.

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i think it is 1/5

Hope this helped :T

Answer:

2(-3±√120)

Step-by-step explanation:

quadratic formula

The best answer regarding the effects of carbon monoxide is option c, CO results in less oxygen loading hemoglobin but unloading is not changed.

Carbon monoxide binds up more tightly to the hemoglobin as compared to the oxygen molecules. This reduces the oxygen-carrying capacity of the blood and results in less oxygen loading onto hemoglobin.

However, once oxygen is already bound to hemoglobin, CO does not significantly affect its release or unloading. Therefore, option c is the most accurate statement among the given choices.

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The true values of x and y in the system of inequalities are (2/3, 10/3)

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

y ≥ 2

x + y ≤ 4

y ≤ 2x + 2

Express the inequalities as equations

So, we have the following representation

x + y = 4

y = 2x + 2

Substitute y = 2x + 2 in the equation

x + y = 4

So, we have the following representation

x + 2x + 2 = 4

Evaluate the like terms

So, the equation becomes

3x = 2

Divide by 3

x = 2/3

Substitute x = 2/3 in y = 2x + 2

y = 2 x 2/3 + 2

Evaluate

y = 10/3

In y ≥ 2, we have

10/3 ≥ 2

The above inequality is true

Hence, the values of x and y are (2/3, 10/3)

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Answer:

10 and 9 over 25

hop you will like it

Answer:

We can use the given formula to solve for the cost C:

P = R - C

We know that P = $49.32 and R = $81.18, so we can substitute these values into the formula:

$49.32 = $81.18 - C

Next, we can solve for C by isolating it on one side of the equation:

C = $81.18 - $49.32

C = $31.86

Therefore, it cost Zach $31.86 to make the jewelry he sold at the fair.

If a function f is differentiable at a point a and f(a) is not equal to zero, then the absolute value function |f| is also differentiable at that point.

The proof involves considering two cases based on the sign of f(a) and showing that the limit of the difference quotient exists for |f| at point a in both cases. However, it is important to note that |f| is not differentiable at the point where f(a) equals zero.

To prove that if f is differentiable at a, then |f| is also differentiable at a, provided that f(a) ≠ 0, we need to show that the limit of the difference quotient exists for |f| at point a.

Let's consider the function g(x) = |x|. The absolute value function is defined as follows:

g(x) = {

x if x ≥ 0,

-x if x < 0.

Since f(a) ≠ 0, we can conclude that f(a) is either positive or negative. Let's consider two cases:

Case 1: f(a) > 0

In this case, we have g(f(a)) = f(a). Since f is differentiable at a, the limit of the difference quotient exists for f at point a:

lim (x→a) [(f(x) - f(a)) / (x - a)] = f'(a).

Taking the absolute value of both sides, we have:

lim (x→a) |(f(x) - f(a)) / (x - a)| = |f'(a)|.

Since |g(f(x)) - g(f(a))| / |x - a| = |(f(x) - f(a)) / (x - a)| for f(a) > 0, the limit on the left-hand side is equal to the limit on the right-hand side, which means |f| is differentiable at a when f(a) > 0.

Case 2: f(a) < 0

In this case, we have g(f(a)) = -f(a). Similarly, we can use the same reasoning as in Case 1 and conclude that |f| is differentiable at a when f(a) < 0.

Since we have covered both cases, we can conclude that if f is differentiable at a and f(a) ≠ 0, then |f| is also differentiable at a.

Note: It's worth mentioning that at the point where f(a) = 0, |f| is not differentiable. The proof above is valid when f(a) ≠ 0.

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Answer:

im not really good at drawing but Can I ask a question can I help you with other questions?

Step-by-step explanation: