PLS HELP......!

Fill in the blanks to describe each sequence in words. Then write the missing terms.

• Pyramidal Sequence: Each term in the sequence is the (BLANK) of a perfect square and all perfect squares before it.

1, (BLANK) , 14, 30, (BLANK) , 91, ...
• Fibonacci Sequence: Each term in the sequence is the (BLANK) of the 2 terms before it.

1, 1, 2, 3, (BLANK) , 8, 13, (BLANK) , 34, ...

The sum of the first 10 terms of the geometric progression that is given in the question is 1023.

What is geometric progression ?

Geometric progression, also known as geometric sequence, is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed constant. This fixed constant is called the common ratio.

The given series is a geometric progression, where each term is obtained by multiplying the preceding term by 2. The first term is 1, and the common ratio is 2.

The sum of the first n terms of a geometric progression is given by the formula:

[tex]S_n = a(1 - r^n) / (1 - r)[/tex]

where a is the first term, r is the common ratio, and n is the number of terms.

Using this formula, we can find the sum of the first 10 terms of the given series as:

[tex]S_{10} = 1(1 - 2^{10}) / (1 - 2)[/tex]

[tex]= 1(1 - 1024) / (-1)[/tex]

[tex]= 1023[/tex]

Therefore, the sum of the first 10 terms of the series 1 + 2 + 4 + 8... is 1023.

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Answer:

about 307.08 square feet

Step-by-step explanation:

[tex] \frac{1}{2} (20)(15) + \frac{1}{2} \pi( {10}^{2} ) = 307.08[/tex]

Step-by-step explanation:

p-grams have equal opposite side lengths

soooo  

 5x+7   =  27  

               x = 4

then 22x = 22(4) = 88  units      ( this is also AB length)

The theoretical probability of not picking the silver coin will be 0.38 .

Given,

200 silver coins and 123 gold coins are filled in a bag .

Now,

Total number of coins in a bag = gold + silver coins

Total number of coins in a bag  = 200 + 123

Total number of coins in a bag  = 323

Further ,

Probability of taking silver coin = 200/323

Probability of taking silver coin = 0.619.

probability of taking gold coin = 123/323

probability of taking gold coin  = 0.38

Hence the probability of not selecting silver coin is 0.38 .

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The ticket price that maximizes profit is $2.90.

What is profit and how is it related to revenue and cost?

In business and economics, profit is the amount of money earned after all expenses and costs have been deducted from revenue. Profit is a key metric used to measure the financial success of a company or enterprise. It is calculated as follows:

Profit = Revenue - Cost

Revenue is the total income earned from the sale of goods or services, while cost is the total expense incurred to produce and sell those goods or services. Profit is an important measure of financial performance because it reflects how efficiently a company is using its resources to generate income.

Finding the price that maximizes profit:

We need to find the value of x that corresponds to the maximum value of the revenue function R(x). The price of the tickets can then be determined by adding the value of x to the initial price of $2.

Using the revenue function [tex]R(x)=-30(x-6)^2+320[/tex], we can find the value of x that maximizes the revenue as follows:

Take the derivative of R(x) with respect to x:

[tex]R'(x) = -60(x-6)[/tex]

Set the derivative equal to zero and solve for x:

[tex]R'(x) = 0[/tex]

[tex]-60(x-6) = 0[/tex]

[tex]x = 6[/tex]

Determine the second derivative of R(x) to check that x = 6 corresponds to a maximum:

[tex]R''(x) = -60[/tex]

Since R''(x) is negative, this confirms that x = 6 corresponds to a maximum.

Calculate the corresponding revenue at x = 6:

[tex]R(6) = -30(6-6)^2 + 320[/tex]

[tex]R(6) = 320[/tex]

Determine the ticket price by adding the value of x to the initial price of $2:

Ticket price = $2 + $0.15(x)

Ticket price = $2 + $0.15(6)

Ticket price = $2.90

Therefore, the ticket price that maximizes profit is $2.90.

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Answer:

AB=8.1 and B=29.6

Step-by-step explanation:

1) To find the measure of AB, use the law of cosines

[tex]c^2=4^2+7^2-2(4)(7)cos(90)[/tex]

[tex]c^2 = 16+49 -56cos(90)\\c^2= 65\\c=8.1[/tex]

2) Use law of sines to find the measure of B

[tex]\frac{8.1}{sin(90)} =\frac{4}{sin(B)}[/tex]

B=29.6

The probability that the first three questions have the same answer choice is 1/4, since there are four answer choices and the instructor is randomly selecting the answers according to a discrete uniform distribution. This means that each answer choice has an equal probability of being chosen. Therefore, the probability of all three questions having the same answer is 1/4.

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Answer: 27.50

Step-by-step explanation: 2.50 X 7 =17.50 + 10 = 27.50

Answer:

∠ FZG = 38°

Step-by-step explanation:

∠ HZJ and ∠ FZG are vertically opposite angles and are congruent , then

∠ ZFG = ∠ HZJ = 38°

In the following question, among the given options, The sum of the proportions for all categories of a variable will be (C.) "1.00."

What is proportion? Proportions are usually represented as a decimal numbers between 0 and 1. They can also be represented as a percentage between 0 and 100. Proportions show the relationship between a particular number and a whole group. The total sum of proportions will always be equal to 1.00, which represents the entire group or population. So the answer to the given question is c. 1.00.

ExplanationThe sum of the proportions for all categories of a variable will be 1.00 because of the following: Proportions of a categorical variable are used to analyze data in statistics. A proportion is a fraction of a whole group that represents a part of that group. Proportions are usually represented as a decimal numbers between 0 and 1. They can also be represented as a percentage between 0 and 100. The sum of the proportions for all categories of a variable will be 1.00 representing the whole group or population, which is equal to 100%. This is the same as saying that the proportions for all categories of a variable should add up to 100%.

Therefore, the correct answer to the question is c. 1.00.

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If you know 63 people have swim suits on and 43 have sunglasses, 32 people have swim suits on but not sunglasses.

To find out how many people have swim suits on but not sunglasses, we can use the principle of inclusion-exclusion.

We know that there are 75 people in the park, and 63 of them have swim suits on. We also know that 43 people have sunglasses. However, some people have both swim suits and sunglasses. Let's denote the number of people who have both by x. Then we can use the formula:

total = swim suits + sunglasses - both

Substituting in the given values, we get:

75 = 63 + 43 - x

Simplifying, we get:

x = 31

Therefore, 31 people have both swim suits and sunglasses, and the number of people who have swim suits on but not sunglasses is:

63 - 31 = 32

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Answer:

(15, - 4 ) , (3, - 2 ) , (- 1, 0 )

Step-by-step explanation:

given a point (x, y ) on a function f(x) , then the corresponding point on the inverse function is (y, x )

given the points on g(x) , then the corresponding points on [tex]g^{-1}[/tex] (x) are

(- 4, 15 ) → (15, - 4 )

(- 2, 3 ) → (3, - 2 )

(0, - 1 ) → (- 1, 0 )

The area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence. So the correct answer is d. 7 3/4.

When measuring the area of a shape, we are determining the amount of surface the shape takes up.

To calculate the area enclosed by each fence, we must multiply the length and width of each.

The area enclosed by the wood fence is

6 1/2 x 2 1/4 = 14 7/8 square yards,

and the area enclosed by the metal fence is

2 3/4 x 2 1/2 = 6 7/8 square yards.

To determine how many times greater the area enclosed by the wood fence is than the area enclosed by the metal fence, we must divide the area of the wood fence by the area of the metal fence:

14 7/8 / 6 7/8 = 7 3/4.

This means the area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence.

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The MCAT scores variable can predict some of the variation in the response variable.

The logistic regression model is a type of regression analysis that is widely used in various fields. A logistic model can be fitted using the glm() function in R. Now fit a logistic model with a single explanatory variable, MCAT scores.In logistic regression, the null deviance is the deviance for a model that has only the intercept. The null deviance will always be equal to the residual deviance if the model has only the intercept.The null deviance is calculated based on the difference between the saturated and null models' likelihoods. It is the amount of variation in the response variable that cannot be explained by the model when no predictor variables are used. When the single predictor variable MCAT scores is added to the null model, it reduces the null deviance by 11.59. This is significant because it indicates that the MCAT scores variable can predict some of the variation in the response variable.

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In total, there are 126 cans in the showcase.

We will use the method for the sum of an arithmetic sequence to solve this problem. The formulation is:

S = (n/2)(a + l)

Wherein S is the sum of the sequence, n is the range of terms, a is the first term, and l is the last term.

In this example, the primary time period is 20, and the closing term is 4. The common difference among the terms is -2, given that we are subtracting 2 cans from each row. we will discover the number of terms using the formulation:

l = a + (n-1)d

Wherein d is the common distinction. solving for n, we get:

n = (l - a)/d + 1

n = (4 - 20)/(-2) + 1

n = 9

Now we can plug within the values for a, l, and n into the system for the sum:

S = (n/2)(a + l)

S = (9/2)(20 + 4)

S = 126

Thus, there are 126 cans in the display in total.

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Let (x1, y1) = (9,7) and (x2, y2) = (6,3)

By distance formula,

d = (x2 - x1)² + (y2 - y1)²

d = (6 - 9)² + (3 - 7)²

d = (-3)² + (-4)²

d = 9 + 16

d = 25 units

Answer:49 = 7×7; 64 = 8×8; Difference Square is the answer. where a =7u; b = 8v. Hope that you carry out the rest Bianca,.. Jung Tran

Step-by-step explanation:

The answer is option a: a survey in which people are asked to indicate how much they trust a number of different politicians using a scale of 1-5, with 1 being the least amount of trust. This is an example of quantitative research.

Quantitative research requires participants to quantify their feelings and opinions using numerical values. It involves measuring variables and collecting numerical data, which can then be analyzed statistically. In this case, the survey data can be analyzed to measure the amount of trust people have in politicians.

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After dividing and simplifying we get (x-3)/(x+3)

One of the four fundamental operations of arithmetic, or how numbers are combined to create new numbers, is division. The additional operations are addition, subtraction, and multiplication.

At a fundamental level, counting the instances in which one number is contained within another is one interpretation of the division of two natural numbers. There is no requirement that this quantity be an integer. For instance, if there are 20 apples and they are divided equally among four people, each person will get 5 apples (see picture).

The integer quotient, which is the quantity of times the second number is entirely contained in the first number, and the remainder are both produced by the division with remainder or Euclidean division of two natural numbers.

1/(x+4) divide by  [tex](x-3)/(x^2 + 7x +12)[/tex]

Simplify : [tex]x^2 +7x +12[/tex]

[tex]x^2 + (3+4)x + 12[/tex]

[tex]x^2 + 3x +4x + 12[/tex]

[tex]x(x + 3) + 4(x + 3)[/tex]

[tex](x+3)(x+4)[/tex]

[tex]1/(x + 4) x (x-3)/(x+3)(x-4)[/tex]

After dividing and simplifying we get the following answer;

[tex]= (x-3)/(x+3)[/tex]

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The median of a normal distribution with a mean of $\mu$ and standard deviation of $\sigma$ is simply equal to the mean $\mu$. Therefore, for a normal distribution with a mean of 61 and a standard deviation of 14, the median is also 61.

This is because the normal distribution is a symmetric distribution, with the mean, median, and mode all located at the same point on the horizontal axis. The mean represents the center of the distribution and is also the balance point for the distribution, so half of the observations will be less than the mean and half will be greater than the mean.

Therefore, for a normal distribution with a given mean and standard deviation, we can use the mean as an estimate of the median. In this case, the mean is exactly equal to the median, so the median is 61.

It is worth noting that this property of normal distributions only holds for normal distributions, and not necessarily for other types of distributions. For example, in a skewed distribution, the mean and median may be quite different from each other.

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Answer:

  5240 kg/m³

Step-by-step explanation:

You want the average density of a planet with radius 6052 km and mass 4.87×10^27 g.

The mass is given in grams, and the corresponding unit in the desired answer is kilograms. There are 1000 g in 1 kg, so 4.87×10^27 g = 4.87×10^24 kg.

The radius is given in km, and the corresponding unit in the desired answer is meters. There are 1000 meters in 1 km, so 6052 km = 6052×10^3 m. (We could adjust the decimal point, but we choose to let the calculator do that.)

The units of density tell you it is computed by dividing the mass by the volume:

  ρ = mass/volume

The volume of the sphere is found using the given formula, so the density is ...

  ρ = (4.87×10^24 kg)/(4/3π(6052×10^3 m)^3)

  ρ ≈ 5240 kg/m³

The average density of the planet is about 5240 kg/m³.

__

Additional comment

This is comparable to the average density of Earth, which is about 5520 kg/m³.

Answer:

The statement that describes the graph of the polynomial function f (x) = x^5 - 6x^4 + 9x^3 is that it has a local maximum at x = 0 and a local minimum at x = 2. The degree of the polynomial is 5, which means it has five zeros or x-intercepts. The leading coefficient is positive, which indicates that the graph will rise to the left and right. The function has a point of inflection at x = 1.5, where the concavity changes from up to down. Overall, the graph of this polynomial function has a typical "upside-down U" shape with local extrema and a point of inflection.

In the following question, among the conditions given, There are 26^4 x 10^5 possible license plates that can be issued using this condition.

Hence, This is because the license plates consist of 4 letters and 5 digits. There are 26 possible letters that can be used in the first four places, so the total possible combinations of 4 letters is 26^4. There are 10 possible digits that can be used in the last five places, so the total possible combinations of 5 digits is 10^5. Multiplying these two together gives the total number of possible license plates: 26^4 x 10^5.

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There are a total of $26^4 × 10^5$ possibilities, which simplifies to 26,000,000,000 (twenty-six billion) possibilities. Therefore, with this condition, twenty-six billion license plates can be issued.

A state's license plates consist of 4 letters followed by 5 digits.

How many possible license plates can be issued using this condition?

When designing a license plate, the condition provided in the question suggests that a license plate should consist of 4 letters followed by 5 digits.

Therefore, we can count the total number of license plates in two phases.

The number of choices for each segment must be taken into account separately for the letters and the numbers.

When considering the letter possibilities, there are 26 options for each position since there are 26 letters in the alphabet.

For the first 4 positions, there are a total of $26^4$ = 456,976 possibilities.

Similarly, for the last 5 positions,

there are 10 options for each position since there are 10 digits.

There are $10^5$ = 100,000 possibilities for the last 5 positions.

The entire plate's total number of combinations is obtained by multiplying these numbers.

There are a total of $26^4 × 10^5$ possibilities

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Answer:

16 represents the hours available to sew gloves.

2 represents the cost of producing gloves for a small pair.

Step-by-step explanation:

Answer:

[tex]26 > n + 15[/tex]

[tex]11 > n[/tex]

[tex]n < 11[/tex]

The value of ∠FDE is 36°

An angle is a geometric figure formed by two rays, or lines that extend infinitely in opposite directions, that share a common endpoint called the vertex. The measure of an angle is determined by the amount of rotation between the two rays.

Here given a right angle ∠CDE = 90°

So, we can say that,

∠CDF + ∠FDE = ∠CDE

(2x)° + (x+9)° = 90°

(3x + 9)° = 90°

Simplify it, x = 27°

So, the value of ∠FDE = (x+9)° = (27+9)° = 36°

Therefore, the value of ∠FDE is 36°

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The angle FDE is 36°. The required answer for the given question is option (A). 36°.

Trigonometry angles are the angles provided by the trigonometric function ratios. Trigonometry is the study of the connection between angles and triangle sides. Angle values vary from 0 to 360 degrees.

An angle is a shape in geometry made by two rays or lines that stretch indefinitely in opposite directions and have a common endpoint known as the vertex. The quantity of rotation among the two rays determines the size of an angle.

From the given figure,

∠CDF + ∠FDE = 90

Thus,

(2x)+(x+9) = 90

3x + 9 = 90

3x = 81

x = 27

Then we will have that the angle FDE is:

∠FDE = (27) + 9

∠FDE = 36

The angle of FDE is 36°

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Answer: 1.26 × 10 to the 10th power

Step-by-step explanation:

Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading.

We will take a random sample of 20 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is a binomial distribution.

A binomial distribution is a statistical distribution that represents the likelihood of one of two outcomes in a sequence of independent trials. Binomial distributions can be used to model a variety of phenomena, including flipping coins, rolling dice, and performing multiple independent experiments.

The probability of getting k successes in n trials in a binomial distribution with probability of success p and probability of failure q is given by the following formula:P (k) = nCk * p^k * q^(n-k)Where nCk is the binomial coefficient, which represents the number of ways to select k items from a set of n items without regard to order.

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