In the figure, each cube has a volume of 1 cubic unit. Find the volume of the figure and the area of its base.

A rectangular prism is made up of cubes. The length of the prism is 4 units, width is 3 units, and height is 3 units.

The given series is conditionally convergent.

To determine whether the given series is absolutely convergent, conditionally convergent, or divergent, we can use the following steps:Firstly, let's check the convergence of the given series using the limit comparison test:Since the limit of the ratio of the given series with the p-series is equal to 1, we cannot make any conclusion using the limit comparison test.Now, let's check the absolute convergence of the given series using the comparison test:As the given series is greater than the divergent harmonic series, it diverges. Therefore, the given series is not absolutely convergent.Now, let's check the conditional convergence of the given series using the alternating series test:The terms of the given series are alternating and decreasing in magnitude. Also, the limit of the absolute value of the terms is zero. Hence, by the alternating series test, the given series is conditionally convergent.Therefore, the given series is conditionally convergent.

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Answer:

C

Step-by-step explanation:

Answer:

The answer is C: 56=h−14. Just like jen4755 said.

we have

15!12!(4−1)!

15!12!(3!)=3,758,268,687,305,932,800,000

therefore

the answer is

Answer:

\( \huge{ \boxed{ \bold{ \tt( \: 0 \: ,5 \: )}}}\)

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☞ First, Let's explore about Midpoint :

Midpoint of the segment simply means middle point of a line segment. Formula of Midpoint :

\( \boxed{ \sf{(x _{ \: m \: } ,\: y_{m}) = ( \frac{x_{1} + x_{2}}{2} ,\: \frac{y_{1} + y_{2}}{2} )}}\)

where ,

The Midpoint Formula is used to find the exact center point between two defined points in a line segment.  The Midpoint formula is quite simple , so you should easily be able to remember it. It won't matter which point you pick to be the 'first" point you plug in. Just make sure that you're adding both an x to an x and a y to a y. Hence, keep in mind , in order to find the midpoint of a line segment, the first step is to add both ' x - co-ordinates' and divide it by 2 and then the second step is to add both ' y - co-ordinates ' and divide it by 2.

Now, Let's solve it!

☯ Question :

☯ Step - by - step explanation :

Let P ( x , y ) divide the line joining the points A ( - 2 , 7 ) and B ( 2 , 3 ). Now, let :

Apply midpoint formula , then plug the values and lastly simplify it :

\( \sf{ midpoint \: = \: ( \frac{x _{ \: 1 \: } + x _{ \: 2 \: }}{2} ,  \: \frac{y_{ \: 1 \: } + y _{ \: 2\: }}{2} })\)

➺ \( \sf{midpoint = ( \frac{ - 2 + 2}{2},  \: \frac{7 + 3}{2} )}\)

➺ \( \sf{midpoint = ( \frac{0}{2} ,  \: \frac{10}{2} )}\)

➺ \( \boxed{ \sf{ midpoint = ( \: 0 \: , 5})}\)

Hence , The midpoint of the segment with the end points A ( - 2 , 7 ) and B ( 2 , 3 ) is ( 0 , 5 ) .

Hope I helped!

Have a wonderful time ッ

~TheAnimeGirl ♡

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Answer:

x=9

Step-by-step explanation:

plug in the number 9

-2(9)= -18

-18+3= -15

a) Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))

b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.

Compound interest is a method of calculating interest on a principal amount that includes not only the initial principal but also the accumulated interest from previous periods.

a. The formula for periodic deposits, assuming a fixed interest rate and the same amount of deposit made at the end of each period, is:

Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))

Where:

A = Financial goal

P = Initial deposit (assumed to be 0 in this case)

r = Annual interest rate (as a decimal)

n = Number of compounding periods per year

t = Time (in years)

Substituting the given values, we have:

Periodic Deposit = (210000 - 0*(1 + 0.035/12\()^{(12\times 13)}\) * (12 / ((1 + 0.035/12\()^{(12\times 13)}\) - 1))

= $543.15 (rounded to the nearest cent)

Therefore, the periodic deposit needed to reach the financial goal of $210000, with a 3.5% annual interest rate compounded monthly over 13 years, is $543.15 at the end of each month.

b. To determine how much of the financial goal comes from deposits and how much comes from interest, we can use the following formula for the future value of an annuity:

FV = P * ((1 + r/n)ⁿᵗ - 1) / (r/n) + A * (1 + r/n)ⁿᵗ

Where:

FV = Future value of the annuity (i.e., the financial goal)

P = Initial deposit

A = Periodic deposit

r, n, t = Same as before

Substituting the given values and solving for P, we have:

P = (210000 - 543.15 * (1 + 0.035/12\()^{(12\times 13)}\) ) * (0.035/12) / ((1 + 0.035/12\()^{(12\times 13)}\) - 1)

= $60305.24 (rounded to the nearest cent)

Therefore, the amount of the financial goal that comes from deposits is $60305.24, and the amount that comes from interest is $210000 - $60305.24 = $149694.76.

Hence,

a) Periodic Deposit = (A - P*(1 + r/n)ⁿᵗ) * (n / ((1 + r/n)ⁿᵗ - 1))

b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.

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Answer:

64.8 grams of sugar

Step-by-step explanation:

brainliest plz

Answer:

The CORRECT anser is B and D

Step-by-step explanation:

Hope this helps I just took the quiz!

When sampling without replacement, the standard deviation (SD) of a binomial distribution can be calculated using the following formula:

SD = sqrt((N - n) * p * (1 - p) / (N - 1))

where N is the population size, n is the sample size, and p is the probability of success (in this case, the proportion of echidnas with diets consisting mostly of termites).

Given that the population proportion of echidnas with termite diets is 40% (or 0.4) and the sample size is 20, we can calculate the standard deviation.

SD = sqrt((N - n) * p * (1 - p) / (N - 1))

= sqrt((N - 20) * 0.4 * (1 - 0.4) / (N - 1))

Since we don't have information about the total population size (N), we cannot calculate the exact standard deviation.

However, we can provide an estimation by assuming a large population, which means that the difference between N and N-1 is negligible.

Let's assume N is large, so N - 1 ≈ N:

SD ≈ sqrt((N - 20) * 0.4 * (1 - 0.4) / N)

≈ sqrt(0.24 * (N - 20) / N)

Given the answer choices provided, we can estimate the closest value to the standard deviation.

Let's substitute different values for N and find the closest answer choice.

For N = 100, we have:

SD ≈ sqrt(0.24 * (100 - 20) / 100)

≈ sqrt(0.24 * 80 / 100)

≈ sqrt(0.192)

≈ 0.438

For N = 200, we have:

SD ≈ sqrt(0.24 * (200 - 20) / 200)

≈ sqrt(0.24 * 180 / 200)

≈ sqrt(0.216)

≈ 0.465

Out of the provided answer choices, the closest value to the estimated standard deviation of 0.465 is 0.4.

Therefore, 0.4 is the closest choice to the standard deviation of x.

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Answer:

-48

Step-by-step explanation:

Given:

To Determine: The average rate of change of T with respect to a over the interval of 24000 and 30000

Solution

Let us determine the value of a at the interval given

Let us determine the value of T at the given interval using the values of a

The rate of change would be

Hence, the rate of change of T with respect to a is -46.512 seconds per 1000ft

Answer:

700

Step-by-step explanation:

The ratio of cats to dogs was 3:7

Divide 300 by 3

=100

multiply 100 and 7

=700

Step-by-step explanation:

let common ratio be x

3x + 7x = 300

10 x = 300

x = 300/10= 30

there common ratio x is 30

3 x 30 =90 cats

7 x 30 = 210 dogs

The graph of the parent absolute value function is decreasing over the interval (-∞, 0). The function exhibits a decreasing behavior as x moves from negative infinity towards zero, where the absolute value decreases.

The parent absolute value function is defined as f(x) = |x|. To determine where the graph of this function is decreasing, we need to identify the intervals where the function's slope is negative.

Let's analyze the behavior of the parent absolute value function:

For x < 0, the function can be rewritten as f(x) = -x. In this interval, the function is a linear function with a negative slope of -1. As x decreases, f(x) also decreases, indicating a decreasing behavior.

For x > 0, the function remains f(x) = x. In this interval, the function is a linear function with a positive slope of 1. As x increases, f(x) also increases, indicating an increasing behavior.

At x = 0, the function is not differentiable since the slope changes abruptly from negative to positive. However, it is worth noting that the function does not strictly decrease or increase at x = 0.

Therefore, we can conclude that the graph of the parent absolute value function is decreasing over the interval (-∞, 0).

In this interval, as x moves from negative infinity towards zero, the function values decrease. The farther away x is from zero (in the negative direction), the larger the absolute value, resulting in a decrease in the function values.

On the other hand, the graph of the parent absolute value function is increasing over the interval (0, ∞), as explained earlier.

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Answer

6y² + 2xy + 2x

Explanation

8y² + 7xy - 2y² - 5xy + 2x

We can collect like terms by bringing the expressions that are similar together

8y² - 2y² + 7xy - 5xy + 2x

= 6y² + 2xy + 2x

Hope this Helps!!!

Given:

A line passes through two points are (2,11) and (-8,-19).

To find:

The equation of the line.

Solution:

The line passes through two points are (2,11) and (-8,-19). So, the equation of line is

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

\(y-11=\dfrac{-19-11}{-8-2}(x-2)\)

\(y-11=\dfrac{-30}{-10}(x-2)\)

\(y-11=3(x-2)\)

Using distributive property, we get

\(y-11=3(x)+3(-2)\)

\(y-11=3x-6\)

Adding 11 on both sides, we get

\(y=3x-6+11\)

\(y=3x+5\)

Therefore, the equation of line is \(y=3x+5\). So, the missing values are 3 and 5 respectively.

Answer: 3x+5

Step-by-step explanation:

Answer:

Lesser is -7

Step-by-step explanation:

x(x+4) = 21

Distribute

x^2 + 4x = 21

x^2 + 4x - 21 = 0

x^2 + 7x - 3x -21 = 0

(x+7)(x-3) = 0

x=-7, 3

PLS MARK BRAINLIEST

The solution to the problem is as follows:Given that 80% of teenagers aged 12-17 own smartphones. A random sample of 250 teenagers is drawn.

The probability is calculated by using the Central Limit Theorem and the TI-84 calculator, and the answer is rounded to at least four decimal places.PC <0.11)-0 Х $P(X<0.11)To find the probability of less than 75% of the sampled teenagers owned smartphones, convert the percentage to a proportion.75/100 = 0.75

This means that p = 0.75. To find the sample proportion, use the given formula:p = x/nwhere x is the number of teenagers who own smartphones and n is the sample size.Substituting the values into the formula, we get;$$p = \frac{x}{n}$$$$0.8 = \frac{x}{250}$$$$x = 250 × 0.8$$$$x = 200$$Therefore, the sample proportion is 200/250 = 0.8.To find the probability of less than 75% of the sampled teenagers owned smartphones, we use the standard normal distribution formula, which is:Z = (X - μ)/σwhere X is the random variable, μ is the mean, and σ is the standard deviation.

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We have:

h(x) = f(x) - g(x) = 8x^2 - 3x^4

Taking the derivative, we get:

h'(x) = 16x - 12x^3

Thus, h'(-1) = 16 - 12(-1)^3 = 16 + 12 = 28.

Therefore, h'(-1) = 28.

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Answer:

Step-by-step explanation:

Equation:

-3k = 108

We need to separate -3 from k. So we must do the inverse operation.

Divide both sides by -3

k = -36

Hope this helps :)

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The area A of the region S that lies under the graph of the continuous function f is \(\frac{1}{4}\).

(a)

\(A =\)  \(\int\limits^A_b {f(x)} \, dx\)  

   = \(\lim_{n \to \infty}\)∑ f(xi) Δ x

a = 0, b = 1 → Δ x = \(\frac{1-0}{n}\) = \(\frac{1}{n}\)

x₀ = 0, x₁ = \(\frac{1}{n}\) , x₂ = \(\frac{2}{n}\), x₃ = \(\frac{3}{n}\), ..., xi = \(\frac{i}{n}\)

f(x) = \(x^{3}\)

f(xi) = \([\frac{i}{n} ]^{3}\) = \(\frac{i^{3} }{n^{3} }\)

Then,

A = \(\lim_{n \to \infty}\) ∑(\(\frac{i^{3} }{n^{3} }\)) * \(\frac{1}{n}\)

(b)

A = \(\lim_{n \to \infty}\) [\(\frac{1}{n}\) * ∑ \(\frac{i^{3} }{n^{3} }\) ]

  = \(\lim_{n \to \infty}\) [\(\frac{1}{n}\) * \(\frac{1}{n^{3} }\) ∑ \(i^{3}\)]

  = \(\lim_{n \to \infty}\) [\(\frac{1}{n^{4} }\) * [\(\frac{n(n+1)}{2}\)]^2]

  = \(\lim_{n \to \infty}\) [\(\frac{1}{n^{4} }\) * \(\frac{n^{2}(n+1)^{2} }{4}\)]  

  = \(\lim_{n \to \infty}\) \(\frac{(n+1)^{2} }{4n^{2} }\)

  = \(\frac{1}{4}\) * \(\lim_{n \to \infty}\) \((\frac{n+1}{n} )^{2}\)

  = \(\frac{1}{4}\) * \(1^{2}\)

A = \(\frac{1}{4}\)

Therefore the area A of the region is \(\frac{1}{4}\).

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1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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These steps are often referred to as the principle of mathematical induction or PMI.

The steps for mathematical induction are:

Base Case: Show that the statement holds for some particular value of n, usually n = 1 or n = 0.

Inductive Hypothesis: Assume that the statement holds for some arbitrary value of n = k, where k is a positive integer.

Inductive Step: Using the inductive hypothesis, show that the statement also holds for n = k + 1.

Conclusion: By the principle of mathematical induction, the statement is true for all positive integers n.

These steps are often referred to as the principle of mathematical induction or PMI. They are used to prove statements that involve an infinite set of integers by showing that the statement holds for a base case, assuming that it holds for an arbitrary value, and then showing that it holds for the next integer in the set.

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Answer:

Step-by-step explanation:

0.2 times 0.8 =0.16

2.4 times 0.7 = 1.68

3.9 times 0.4 = 1.56

0.9 times 0.1 = 0.09

0.2 times 1.5= 0.3

0.6 times 0.6= 0.36

pls mark brainliest

Answer:

d≈91.63m

Step-by-step explanation:

d=w2+l2=78.92+46.62≈91.63389m

The given equation, eˣ-z² + 16 sin(x)-5=0, has one unique solution in the interval [0, 1]. The Bisection method can be used to approximate the solution by iteratively narrowing down the interval. After the third iteration, an approximate solution can be found.

To prove that there exists one unique solution in the interval [0, 1], we need to show that the given equation is continuous and changes sign at least once within the interval. Since the exponential function, trigonometric function, and constant term are all continuous, their sum is also continuous.

By evaluating the equation at the endpoints of the interval, we can observe that the equation changes sign from negative to positive, indicating the existence of a root.

To apply the Bisection method, we start with the interval [0, 1] and evaluate the equation at the midpoint of the interval. If the equation evaluates to zero, we have found the solution. Otherwise, we narrow down the interval by selecting the subinterval where the function changes sign. After each iteration, we repeat the process until we reach the desired level of accuracy.

Performing the Bisection method for three iterations will result in a narrower interval where the approximate solution lies. The process involves repeatedly evaluating the equation at the midpoints of the intervals and updating the interval based on the sign change. By the third iteration, we can obtain an approximate solution within the narrowed interval.

The specific value of the approximate solution after the third iteration cannot be determined without performing the actual calculations.

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Answer:

Distance = √(13)

Step-by-step explanation:

Since distance between two points (x, y) and (x', y') on the graph is determined by,

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)

Two points given on the graph are (2, 0) and (5, -2).

Therefore, distance between these points will be

Distance = \(\sqrt{(5-2)^2+(-2-0)^2}\)

               = \(\sqrt{(3)^2+(-2)^2}\)

               = \(\sqrt{13}\)

Therefore, answer will be distance = √(13)

Answer:

Answer is D.

30

Step-by-step explanation:

all angles add up to 180(applys to triangles)