Natalie is 5 years older than Casey. The sum of their ages is 55. How old are Natalie and Casey?

Answer:  The correct option is

(D) {3, 10, 17, 24, …}.

Reasoning:

 We are given to select the sequence that represents the following function with a domain of natural numbers :

The set of natural numbers is {1, 2, 3, 4, . . .}

to find the sequence, we need to substitute x = 1, 2, 3, 4, . . . in equation (i).

From equation (i), we get

Therefore, the sequence that represents the given function is {3, 10, 17, 24, …}.

Thus, option (D) is CORRECT.

Answer:  

Rectangular pyramid  8 edges

Rectangular prism    12 edges

Triangular Prism   9 edges

Triangular Pyramid  6 edges

Step-by-step explanation: Faces connected at edges

Rectangular pyramid    1 Base  and 4  slanted  triangular sides

Rectangular prism    2 top and bottom bases and 4 sides

Triangular Prism   2 top and bottom triangular bases 3 rectangular sides

Triangular Pyramid    1 triangular base, 3 slanted triangular sides

The matching is as follow:

Rectangular pyramid:  8 edges

Rectangular prism:  12 edges

Triangular Prism: 9 edges

Triangular Pyramid: 6 edges

A pyramid is a triangular-sided, single-polygonal base, three-dimensional polyhedron-shaped construction. A prism is a three-dimensional polyhedron with rectangular sides that are perpendicular to the base and two polygonal bases.

Rectangular pyramid have one Base and 4 slanted triangular sides

Rectangular prism have 2 top and bottom bases and 4 sides

Triangular Prism have 2 top and bottom triangular bases 3 rectangular sides.

Triangular Pyramid have 1 triangular base, 3 slanted triangular sides.

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Each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.Option B,E,F.

Each chart has the following three components:

1. B. A center line representing the average: This line is drawn to show the average value or mean of the data being analyzed. It provides a reference point to compare the data points above and below it.

2. E. An upper line representing the maximum acceptable variation upwards: This line is drawn to indicate the upper limit of acceptable variation or deviation from the average. It helps identify if the data points exceed the acceptable range.

3. F. A lower line representing the maximum acceptable variation downwards: This line is drawn to indicate the lower limit of acceptable variation or deviation from the average. It helps identify if the data points fall below the acceptable range.

These three components together create a control chart, which is a graphical representation used in statistical process control. Control charts help monitor and analyze data over time, allowing organizations to identify trends, detect abnormalities, and make data-driven decisions to improve processes and quality.

In summary, each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.

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The number of ways you can select n elements from N elements by using factorial (!) when n=2 and N=10 is 45.

Factorial is a crucial mathematical operation that is used to determine the number of possible arrangements or the ordered set of numbers. Daniel Bernoulli is credited with discovering the factorial function's well-known interpolating feature. Numerous mathematical ideas, including probability, permutations and combinations, sequences and series, etc., use the factorial concept. A factorial function, in essence, multiplies a number by each number below it until it equals 1. For instance, the factorial of 3 is equal to 6 and reflects the multiplication of the integers 3, 2, and 1.

Now,

The number of ways you can select n elements from N elements when n=2 and N=10 is \(\frac{N!}{n!(N-n)!}\)

=\(\frac{10!}{2!(8)!}\)

=\(\frac{10 \times 9 \times \times 8!}{8! \times 2 !}\)

=45

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Answer:

63 Seconds

Step-by-step explanation:

The reason how I got this is I divided 36 by 4 to get 9 seconds per handspring, next I multiplied 7 by 9 to get the answer.

Answer:

63

Step-by-step explanation:

If gymnast can do 4 back handsprings in 36 seconds , then for 1 backspring the gymnast took 36/4 = 9 seconds.

If the gymnast took 9 seconds for 1 back handsprings, Time taken by the gymnast to do 7 backsprings = 9×7 = 63 seconds

The car will cost $ 800 after a depreciation time of approximately 6 years.

Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:

c(t) = c' + m · t

Where:

If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:

m = (12,000 - 36,000) / (4 - 0)

m = - 24,000 / 4

m = - 6,000

800 = 36,000 - 6,000 · t

6,000 · t = 35,200

t = 35,200 / 6,000

t = 5.867

The expected depreciation time is approximately 6 years.

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The letter A represents where the amount of $158.29 should be written.

The letter D represents where the amount of $250 should be written.

This refers to the automated machine that is used to handle cash transactions and also for making calculations.

Hence, we can see that from the complete information, Ivan has a cash register where he records the amount he spends on groceries which is $158.29, and also the transaction of sending $250 to his savings account.

However, in the cash register, Ivan uses the letter A to show where the amount of $158.29 should be written and the letter D represents where the amount of $250 should be written.

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Answer:

A and D

Edge 2022

The cost of one hot dog is given by $2.75 and cost of one soda is given as $ 1.95.

The cost price is the sum of money used to create products or services before any profit is added for the manufacturer or provider. Other names for it include latest cost, average cost, and real cost.

The extra costs associated with production, real estate, materials, electricity, R&D, testing, worker salary, and other expenses are all included in the cost price. The cost price and the selling price of any thing are always used to determine profit and loss.

At concession stand, parker bought 3 hot dogs and 2 sodas for $12.15.

Let the price of a soda be x

a hot dog cost $0.80 more than a soda,

So the price of the hot dogs is = x + 0.8

The total he spend is 12.15 on 3 hot dogs and 2 sodas so the equation will be,

3(x+0.8) + 2x = 12.15

3x + 2.4 + 2x = 12.15

5x = 12.15 - 2.4

5x = 9.75

x = $ 1.95

So the value of 1 soda is $1.95 and the value of a hot dog is $2.75.

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The indefinite integral of \(x^2 + 36x + 36/(x^3 - 4x) is (1/4)x^3 + C.\)

To use partial fractions to find the indefinite integral of the given expression, we first need to factor the denominator. We have:

\(x^3 - 4x = x(x^2 - 4) = x(x - 2)(x + 2)\)

So we can write:

\(x^2 + 36x + 36= (ax + b)/(x - 2) + (cx + d)/(x + 2) + e*x\)

where a, b, c, d, and e are constants that we need to solve for. To do this, we can use the method of equating coefficients. We have:

\(x^2 + 36x + 36 = (ax + b)(x + 2) + (cx + d)(x - 2) + e*x(x - 2)(x + 2)\)

\(= (a + c + e)x^3 + (2a - 2c + e)x^2 + (-4a + 4c - 2e)x + (2b - 2d)\)

Equating coefficients of like powers of x, we get:

a + c + e = 0

2a - 2c + e = 1

-4a + 4c - 2e = 36

2b - 2d = 36

Solving these equations simultaneously, we get:

a = -1/4, c = 1/4, e = 1/4, b = 0, d = 0

So we have:

\(x^2 + 36x + 36 = (-1/4)(x - 2) + (1/4)(x + 2) + (1/4)x(x - 2)*(x + 2)\)

Integrating both sides with respect to x, we get:

\(∫(x^2 + 36x + 36)dx = -1/4∫(x - 2)dx + 1/4∫(x + 2)dx + 1/4∫x(x - 2)(x + 2)dx\)

\(∫(x^2 + 36x + 36)dx = (-1/4)(x^2/2 - 2x) + (1/4)(x^2/2 + 2x) + 1/4∫(x^3 - 4x)dx + C\)

\(= (1/4)x^3 + C\)

where C is the constant of integration. Thus, the indefinite integral of \(x^2 + 36x + 36/(x^3 - 4x) is (1/4)x^3 + C.\)

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The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

Given

In line with the posed question.

Triangle ABC's vertices are A(-2, 3), B(0, 0), and C. (1, 2).

As we are aware,

The x-coordinates of each point must be negative while keeping the y-value constant in order to reflect a triangle over the y axis.

As a result, when triangle ABC is mirrored across the y-axis, its vertices are

A'(2,3)

B'(0, 0)

C'(-1, 2)

The vertices of the triangle will also change when it is dialated by a scale factor of 2.

A'(4, 6)

B'(0, 0)

And, C'(-2, 4)

The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

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A pond contains 100 fish, of which 30 are carp. if 20 fish are caught, what are the mean and variance of the number of carp among the 20. This Statement is based on the assumption that : X follows hyper-geometric distribution with the given information.

According to the Question:

Total fish = 100

Carp = 30

Number of fish caught = 20

Now,

The random variable X follows hyper-geometric distribution.

Mean = 30 *20 / 100

         = 600/100 = 6

Therefore,

Variance = 30*20/100 * ((20-1)*(30-1)/100-1 + 1-30*20/100)

⇒ Variance = 600/100 * 56/99

⇒ Variance = 112/33

⇒ variance = 3.1111 ≈ 3.12

Assumptions:

Is that X follows hyper-geometric distribution with the given information.

Hyper - Geometric Distribution:

In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that yields n draws without replacement for k successes (if the drawn object has a particular property). random draw). From a finite population of size N containing exactly K objects with this property, each draw either succeeds or fails. In contrast, the binomial distribution describes the probability of k successes in n draws with replacement.

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Step-by-step explanation:

\(( {x}^{2})(x + 3) - (x + 3)\)

\((x + 3)( {x}^{2} - 1) \)

\((x - 1)(x + 1)\)

\((x - 1)(x + 1)(x + 3)\)

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

(x+1) (x-1) (x+3)

Step-by-step explanation:

. .....................

The minimum frequency of radiation is 0.603 × 10¹⁵ and the longest wavelength is 4.97 × 10⁻⁷.

Planck's equation is an equation which describes about the amount of spectral radiance radiated by a black body at a certain wavelength in thermal equilibrium.

We have the Planck's Equation,

E = hv,

where E is the energy, h is the Planck's constant = 6.63 x 10⁻³⁴ J and v is the frequency of radiation.

We have in the question E = 4.0×10⁻¹⁹ J

Substituting,

4.0×10⁻¹⁹ = (6.63 x 10⁻³⁴) v

v = (4.0×10⁻¹⁹) / (6.63 x 10⁻³⁴)

  = 0.603 × 10¹⁵

Also we have the equation to find the wavelength,

v = c / λ, where c is the speed of the light = 3 × 10⁸ and λ is the wavelength.

λ = c / v = (3 × 10⁸) / (0.603 × 10¹⁵)

             = 4.97 × 10⁻⁷

Hence the minimum frequency and the longest wavelength of radiation for which the detector registers a response are 0.603 × 10¹⁵ and 4.97 × 10⁻⁷ respectively.

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Find m∠BOC, if m∠MOP = 110°.

Answer:

m∠BOC= 40 degrees

Step-by-step explanation:

A diagram has been drawn and attached below.

Since ∠AOD is a straight line

x+x+y+y+z+z=180 degrees

\(2x+2y+2z=180^\circ\)

We are given that:

m∠MOP = 110°.

From the diagram

∠MOP=x+2y+z

Therefore:

x+2y+z=110°.

Solving simultaneously by subtraction

\(2x+2y+2z=180^\circ\)

x+2y+z=110°.

We obtain:

x+z=70°

Since we are required to find ∠BOC

∠BOC=2y

Therefore from x+2y+z=110° (since x+z=70°)

70+2y=110

2y=110-70

2y=40

Therefore:

m∠BOC= 40 degrees

The probability that a randomly selected finishing time is greater than 87 seconds is 14.08%. This can be calculated using the empirical rule.

The empirical rule states that for any data that is normally distributed, about 68% of the data will fall within one standard deviation of the mean (in this case, within 69 ± 6 seconds). Approximately 95% of the data will fall within two standard deviations (in this case, within 69 ± 12 seconds), and about 99.7% of the data will fall within three standard deviations (in this case, within 69 ± 18 seconds).Given the mean and standard deviation given, we can calculate the probability that a randomly selected finishing time is greater than 87 seconds.

We can do this by subtracting the area under the curve from the mean to the value we are interested in (in this case, 87 seconds). Since the total area under the curve is 1, subtracting the area from the mean to 87 seconds will give us the desired probability.To calculate the area under the curve, we need to calculate the Z-score, which is the number of standard deviations away from the mean a particular value is. In this case, the Z-score is (87 - 69) / 6, which is 2.16. Using a Z-table, the probability of a Z-score of 2.16 or higher is 0.8592. Therefore, the probability that a randomly selected finishing time is greater than 87 seconds is 1 - 0.8592, which is 0.1408. Rounding to two decimal places, this is 14.08%.

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The amount of wood that they need to complete the supports is given as follows:

130.10 cm.

First we must obtain the side lengths of the right triangle.

The equal side lengths of the right triangle are obtained applying the Pythagorean Theorem, hence:

x² + x² = 92²

2x² = 92²

x² = 4232

x = square root of 4232

x = 65.05 cm.

They have two sides of 65.05 cm, hence the amount of wood needed is obtained as follows:

2 x 65.05 = 130.10 cm.

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After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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The total number of groups in the study of one way ANOVA with the given condition of variable and levels is four different groups and number of different factors in one-way ANOVA is equal to one.

In a one-way ANOVA with one independent variable with four levels, there are four different groups in the study.

Each group represents a level of the independent variable.

There is only one factor in a one-way ANOVA.

The factor is the independent variable with the four levels, which is used to classify the groups in the study.

The factor is what the researcher is interested in studying.

And the ANOVA is used to determine if there are any statistically significant differences in the mean scores between the groups.

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Answer:

1/6

Step-by-step explanation:

People who answered less than 1/2 were:  2 +  1 + 3 = 6 people.

There are a total of 36 people.

People who answered their calls before the second ring were only 6/36.

When we simplify the fraction, we get 1/6.

So, the answer is 1/6.

Answer:

\( \sf \: 3x + 12 \)

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ 3(x + 4)

Let's simplify the expression,

→ 3(x + 4)

→ 3(x) + 3(4)

→ (3 × x) + (3 × 4)

→ 3x + 12

Hence, the answer is 3x + 12.

Answer: Scatter Plot 2

Step-by-step explanation: Usually with graphs like this, anything relative to time (age) will be on the x axis because the text messages depends on the age. This immediately knocks out number 1. Then you just have to start graphing points on the scatter plot and whichever one lines up best, which happens to be #2, is the correct answer.

Hope this helps.

The GCD is \(x+1\), so \(x+1\) divides both \(x^2+ax+b\) and \(x^2+bx+c\). For some \(\alpha\) and \(\beta\) we can write

\(x^2 + ax + b = (x + 1) (x - \alpha)\)

\(x^2 + bx + c = (x + 1) (x - \beta)\)

Expanding the right sides, we get

\(x^2 + ax + b = x^2 + (1 - \alpha) x - \alpha\)

\(x^2 + bx + c = x^2 + (1 - \beta) x - \beta\)

\(x+1\) also divides the LCM, so

\(x^3 - 4x^2 + x + 6 = (x + 1) (x - \alpha) (x - \beta)\)

and expanding gives

\(x^3 - 4x^2 + x + 6 = x^3 + (1 - \alpha - \beta) x^2 + (\alpha \beta - \alpha - \beta) x + \alpha \beta\)

Matching up all the coefficients, we have

\(\begin{cases} a = 1 - \alpha \\ b = -\alpha \\ b = 1 - \beta \\ c = -\beta \\ -4 = 1 - \alpha - \beta \\ 1 = \alpha \beta - \alpha - \beta \\ 6 = \alpha \beta \end{cases} \implies \alpha + \beta = 5\)

All the unknowns are integers, and we have the prime factorization 6 = 2×3 that also satisfies 5 = 2 + 3.

• If \(\alpha=2\) and \(\beta=3\), then \(a=-1\), \(b=-2\), and \(c=-3\).

• If \(\alpha=3\) and \(\beta=2\), then there is no solution for \(a,b,c\) since

\(\begin{cases}b = -\alpha \\ b = 1-\beta \end{cases} \implies \alpha = \beta - 1\)

but 3 ≠ 2 - 1 = 1.

It follows that \(a + b + c = -1 - 2 - 3 = \boxed{-6}\).

The value of x, which we get by using an exponent rule is x = 2.80259.

What is an exponent rule?

Exponent is defined as the method of expressing large numbers in terms of powers. That is, exponent refers to how many times a number is multiplied by itself. For example, 6 is multiplied by itself four times, resulting in 6 6 6 6. This can be written as 64. In this case, 4 is the exponent and 6 is the base.

We have,

               \(\frac{2}{3} ^{x} . \frac{3}{2} ^{2x} = \frac{81}{16}\)

By applying the exponent rule:

              \(\left(-1\cdot \:x+2x\right)\ln \left(\frac{3}{2}\right)=\ln \left(\frac{81}{26}\right)\)

By simplifying the equation:

               \(x=\frac{\ln \left(\frac{81}{26}\right)}{\ln \left(\frac{3}{2}\right)}\)

               x = 2.80259

Hence, the value of x = 2.80259

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Answer:

x=9

Step-by-step explanation:

10+5(x−4)=35 Step 1: Simplify both sides of the equation. 10+5(x−4)=35

10+(5)(x)+(5)(−4)=35(Distribute)

10+5x+−20=35

(5x)+(10+−20)=35(Combine Like Terms)

5x+−10=35

5x−10=35

Step 2: Add 10 to both sides.

5x−10+10=35+10

5x=45

Step 3: Divide both sides by 5.

5x/5 = 45/5

x=9

Answer:

x=13

Step-by-step explanation:

10+5(x-4)=35

10+5x+-20=35

5x+-30=35

5x=65

65 divided by 5=13

x=13

See picture above for more thorough steps

Answer:

A.

Step-by-step explanation:

p-9/3 = 2

p-9 = 2×3

p-9 = 6

p = 6+9

... Hope this will help...