What should be subtracted from thrice 13 by 5 to obtain 5 by 13

Answers

Answer 1

The number that should be subtracted from thrice 13 by 5 to obtain 5 by 13 is 130.

What number should be subtracted?

The number that should be subtracted from thrice 13 by 5 to obtain 5 by 13 is calculated as follows;

let the number = n

thrice 13 by 5 = 3 (13) x 5 = 195

5 by 13 = 5 x 13 = 65

The value of the unknown number, n,  is calculated as;

195 - n = 65

n = 195 - 65

n = 130

Thus, when we subtract 130 from thrice 13 by 5, we will obtain 5 by 13 as shown in the calculation above.

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Related Questions

Charlyne deposited $3400 into a savings account that has an annual simple interest rate of 0.2%

Answers

The amount in the savings account after each number of years are as follows

2 years = $3413.6

5 years = $3434

8 years = $3454.4

How to calculate the simple interest and future value?

In Mathematics, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

S.I represents the simple interest.P is the principal or starting amount.R is the interest rate.A is the future value.T represents the time measured in years.

By substituting the given parameters into the simple interest formula, we have;

SI = 3400 × 0.2/100 × 2

SI = $13.6

A = SI + P = 13.6 + 3400 = $3413.6

After 5 years, we have:

SI = 3400 × 0.2/100 × 5

SI = $34

A = SI + P = 34 + 3400 = $3434

After 8 years, we have:

SI = 3400 × 0.2/100 × 8

SI = $54.4

A = SI + P = 54.4 + 3400 = $3454.4

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Complete Question:

Charlyne deposited $3400 into a savings account that has an annual simple interest rate of 0.2%. Find the amount in the savings account after each number of years.

2 years $

5 years $

8 years $

Which expressions are equivalent to 6 +(–x) + 2x + (–7) + 2x? Check all that apply.
A. x + x + 6 – 7 + x
B. 2x + 2 + x
C. 3 – x + 2x – 4 + 2x
D. x – 1
E. x + 1

(The answer is A and C)

Answers

The expressions are equivalent to the given expression are x + x + 6 – 7 + x and 3 – x + 2x – 4 + 2x. Therefore, the options A and C are correct answer.

The given expression is 6+(-x)+2x+(-7)+2x.

If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Here, group the like terms, we get

(-x+2x+2x)+(6-7)

= 3x-1

Therefore, the options A and C are correct answer.

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Answer:

yo

Step-by-step explanation:

the answers are A and C

x + x + 6 – 7 + x and  3 – x + 2x – 4 + 2x

Edge 2023

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln 3x, y = 2, y = 3, x= 0; about the y-axis
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 9x^6, y = 9x, x greaterthanorequalto 0; about the x-axis

Answers

The volume of solid generated by rotating the region bounded by curves y = ln( 3x), y = 2, y = 3, x= 0; about the y-axis is equals to the [tex] \frac{π}{18}({e^6}- e^4)[/tex]. The volume of solid generated by rotating the region bounded by curves = 9x⁶, y = 9x, x ≥0; about x-axis is equals to the [tex]\frac{81π}{13} \\ [/tex].

We have a solid obtained by rotating the region bounded by the curves with equations, y = ln 3x, y = 2, y = 3, x= 0; about the specified line, y-axis. We have to determine the volume, V of that solid. First, see the above diagram where red line, green line, blue line and purple lines represent y = ln 3x, y = 3, y = 2, x= 0 respectively. The volume of shaded region will be determine. Using formula, [tex]V = \int_{y = 2}^{y = 3} πx² dy \\ [/tex]

Now, y = ln( 3x)

taking exponential both sides,

[tex]e^ y = 3x [/tex]

[tex]x = \frac{ e^y}{3}[/tex]

so, [tex]V = \int_{y = 2}^{y = 3} π ( \frac{e^y}{3})² dy \\ [/tex]

[tex]= \int_{y = 2}^{y = 3} π ( \frac{e^{2y}}{9})dy \\ [/tex]

[tex]=[π(\frac{e^{2y}}{9 \times 2})]_{2}^{3} [/tex]

[tex]= π ( \frac{e^6}{18} -\frac{ e^4}{18})[/tex]

[tex]= \frac{π}{18}({e^6}- e^4)[/tex]

Hence, required value is [tex]= \frac{π}{18}({e^6}- e^4)[/tex].

Solid obtained by rotating the region bounded by the curves with equations, y = 9x⁶, y = 9x, x ≥0; about the specified line, x-axis. We have to determine the volume, V of that solid. First we determine the intersection points of y = 9x² and y = 9x

=> 9x = 9x²

=> x = 1

Using the formula, [tex]V = \int_{x= 0}^{x = 1} πy² dx \\ [/tex]

[tex] = \int_{x= 0}^{x = 1} π(9x⁶)² dx \\ [/tex]

[tex] = \int_{x= 0}^{x = 1} 81πx¹² dx \\ [/tex]

[tex] = 81π [ \frac{x¹³}{13}]_{x= 0}^{x = 1} \\ [/tex]

[tex] = 81π [ \frac{1¹³}{13} - 0] \\ [/tex]

[tex] = \frac{81π}{13} \\ [/tex]. Hence, required value is [tex]\frac{81π}{13} \\ [/tex].

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A sail moves 1/50 of a mile in 5/6 of an hour
if a sail continues at that pace, how far, in miles, does it move in one hour?

Answers

The sail would move 3/25 of a mile, or approximately 0.12 miles in one hour.

Let's start by finding the distance traveled by the sail in 1/6 of an hour. We can do this by dividing 5/6 by 5 (the numerator and denominator of 1/6 are obtained by dividing the numerator and denominator of 5/6 by 5).

(5/6) ÷ 5 = 1/6

Now, we know that the sail moves 1/50 of a mile in 1/6 of an hour. To find how far it would move in one hour, we need to multiply 1/50 by the reciprocal of 1/6. The reciprocal of a fraction is obtained by flipping it upside down.

(1/50) × (6/1) = 6/50

Simplifying 6/50, we get 3/25. Therefore, the sail would move 3/25 of a mile in one hour if it continues at the same pace.

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Is it true that If A is n×n and detA = 2, then detA^3 = 6.

Answers

It is not true that if A is an n × n matrix with detA = 2, then detA³ = 6.

det(A³) = det(A × A × A) = det(A) × det(A) × det(A) = (det(A))³ = 2³ = 8

detA³ = 8, not 6.

The determinant of a matrix is a scalar value that encodes various properties of the matrix.

One of the properties is the volume scaling factor that is induced by the matrix transformation.

The determinant has the property that det(kA) = kⁿ × det(A) for any scalar k and n × n matrix A, where n denotes the dimension of the matrix.

Therefore, we have:

det(A³) = det(A × A × A) = det(A) × det(A) × det(A) = (det(A))³ = 2³ = 8

detA³ = 8, not 6.

The determinant of a matrix raised to a power is not simply obtained by raising the determinant to the same power.

The determinant of a matrix raised to a power can be obtained by raising the determinant of the matrix to the power and then multiplying by the scaling factor induced by the matrix transformation.

Specifically, for a matrix A with detA = 2 and an integer k, we have:

[tex]det(A^k) = (det(A))^k \times scaling factor induced by A^k[/tex]

The scaling factor induced by [tex]A^k[/tex] can be computed by considering the effect of [tex]A^k[/tex] on the unit hypercube.

This calculation requires the use of linear algebra and is beyond the scope of this answer.

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For a large sample of blood pressure values, the mean is 120 and the standard deviation is 10. Assuming a bell-shaped curve, which interval is likely to cover about 95% of blood pressures in the sample?

Answers

For a large sample of blood pressure values with a mean of 120 and a standard deviation of 10, the interval that is likely to cover about 95% of the blood pressures in the sample is between 100 and 140.

Based on the given information, we can use the empirical rule to estimate the interval that is likely to cover about 95% of the blood pressures in the sample. The empirical rule states that for a bell-shaped curve, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations of the mean, and nearly all (99.7%) falls within three standard deviations of the mean.

Therefore, for a large sample of blood pressure values with a mean of 120 and a standard deviation of 10, the interval that is likely to cover about 95% of the blood pressures in the sample is between 100 and 140. This is because two standard deviations above and below the mean (2 x 10 = 20) added to and subtracted from the mean (120) gives us a range of 100 to 140.

Based on the given information, for a large sample of blood pressure values with a mean of 120 and a standard deviation of 10, and assuming a bell-shaped curve, the interval likely to cover about 95% of blood pressures in the sample would be within two standard deviations from the mean. This interval can be calculated as follows:

Lower limit: Mean - (2 × Standard Deviation) = 120 - (2 × 10) = 100
Upper limit: Mean + (2 × Standard Deviation) = 120 + (2 × 10) = 140

So, the interval that covers approximately 95% of blood pressures in the sample is 100 to 140.

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how to asses the integer rules

Answers

Gaining a full grasp of the regulations relating to integers requires insight and precision. To get started, here's an overview of some essential tips:

how to asses the integer rules

Comprehending Integers: Essentially, integers are entire numbers (whether negative, positive or zero) that don't encompass any fractions or decimals.

Familiarizing Yourself with Basic Operations: The four primary operations when it comes to maniputating integers include subtraction, addition, multiplication, and division.

Absorbing Diverse Guidelines: There are individual protocols for each operation, such as rules for adding and subtracting integers having disparate signs, as well as guidance for multiplying and dividing integers boasting diverse signs.

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a coach is hosting a cookout for their kick ball team. the coach wants to have two hot dogs for each guest, and 8 extra hot dogs in case some teammates bring friends. the coach writes an equation to determine how many hot dogs are needed for the cookout. which variable is independent?

Answers

The independent variable in this scenario is the number of guests that will be attending the cookout. The number of hot dogs needed is dependent on the number of guests, as the coach plans to provide two hot dogs for each guest and an additional 8 hot dogs for potential extra guests.


. In this situation, the coach needs to determine the number of hot dogs required for the cookout based on the number of guests. Let's represent the number of guests as "g" (independent variable) and the total number of hot dogs needed as "h" (dependent variable).

The coach wants 2 hot dogs for each guest and 8 extra hot dogs. So, the equation would be:

h = 2g + 8

In this equation, the independent variable is "g" (number of guests) because the total number of hot dogs needed (dependent variable "h") depends on how many guests are attending the cookout.

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the probability of winning a certain lotter is 1/51,949. for people who play 560 times, find the standard deviation for the random variable x, the number of wins

Answers

The standard deviation for the random variable X, the number of wins, is approximately 0.10341.

Probability of winning a certain lottery [tex]= 1/51,949[/tex]

560 times were played overall.

Let X represent the random variable that represents the number of victories out of 560 plays.

The probability of winning in one play is [tex]p = 1/51,949[/tex]. The probability of not winning in one play is [tex]q = 1 - p[/tex]

[tex]q = (51,949 - 1) / 51,949[/tex]

[tex]q = 51,948 / 51,949.[/tex]

What X should actually be is:

[tex]E(X) = np[/tex]

[tex]E(X) = 560 * (1/51,949)[/tex]

[tex]E(X) = 0.010793[/tex]

The variance of X is:

[tex]Var(X) = npq[/tex]

[tex]Var(X) = 560 * (1/51,949) * (51,948/51,949)[/tex]

[tex]Var(X) = 0.010699[/tex]

The value of X's standard deviation is

[tex]SD(X) = \sqrt{Var(X)}[/tex]

[tex]SD(X) = \sqrt{0.010699}[/tex]

[tex]SD(X) = 0.10341[/tex](approx)

Therefore, the standard deviation for the random variable X, the number of wins, is approximately 0.10341.

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find the amount (future value) of the ordinary annuity. (round your answer to the nearest cent.) $450/month for 18 years at 5%/year compounded monthly

Answers

The future value of the ordinary annuity is $35,134.71 rounded to the nearest cent.

To find the future value of an annuity, we can use the formula:

FV = PMT x (((1 + r)ⁿ - 1) / r)

Where:

PMT = the amount of the periodic payment (in this case, $450 per month)

r = the interest rate per period (5% / 12 months = 0.004167 per month)

n = the total number of periods (18 years x 12 months per year = 216 months)

Plugging in the numbers, we get:

FV = $450 x (((1 + 0.004167)²¹⁶ - 1) / 0.004167)

FV = $450 x (78.077126)

FV = $35,134.71

Therefore, the future value of the ordinary annuity is $35,134.71 rounded to the nearest cent.

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Julie was assigned to take her statistics class with Professor Fisher, whose final scores follow a normal distribution with mean 75
and a standard deviation of 6
. Her score on the final was 84
.
What is Julie's z-score?

Answers

Julie's z-score is 1.5. This means that her score on the final was 1.5 standard deviations above the mean score of the class.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To calculate Julie's z-score, we need to use the formula:

z = (x - μ) / σ

where:

x is Julie's score on the final (84)

μ is the mean score of the class (75)

σ is the standard deviation of the class (6)

Plugging in the values, we get:

z = (84 - 75) / 6

z = 1.5

Therefore, Julie's z-score is 1.5. This means that her score on the final was 1.5 standard deviations above the mean score of the class.

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in a survey, 75% of household reported to have some kind of board games. out of 10 households, what is the probability that less than 3 households have board games?

Answers

After performing the calculations, you'll find that the probability of less than 3 households having board games out of 10 households is approximately 0.0038 or 0.38%.

To find the probability that less than 3 households have board games, we can use the binomial probability formula. The terms involved in this problem are:

1. n: number of trials (households)
2. k: number of successful outcomes (households with board games)
3. p: probability of success (having board games)
4. q: probability of failure (not having board games)

Given that 75% of households have board games, p = 0.75, and q = 1 - p = 0.25. In this case, n = 10 households. We need to find the probability of k = 0, 1, or 2 households having board games.

The binomial probability formula is:
P(X = k) = C(n, k) * p^k * q^(n-k)

Step 1: Calculate the probability for k = 0, 1, and 2 separately:
P(X = 0) = C(10, 0) * 0.75^0 * 0.25^10
P(X = 1) = C(10, 1) * 0.75^1 * 0.25^9
P(X = 2) = C(10, 2) * 0.75^2 * 0.25^8

Step 2: Add the probabilities for k = 0, 1, and 2 to get the total probability:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

After performing the calculations, you'll find that the probability of less than 3 households having board games out of 10 households is approximately 0.0038 or 0.38%.

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At M3 Consulting, the probability the computer network crashes on any workday equals 0.16.Calculate the probability that during a regular work week (Monday through Friday), the computernetwork crashesa. on both Monday and Tuesday.b. for the first time Thursday.c. every day.d. on at least one day.

Answers

a. The probability that the network crashes on both Monday and Tuesday is 0.1024; b. The probability that the network crashes for the first time on Thursday is 0.1389 ; c. The probability that the network crashes every day is 0.0001; d. The probability that the network crashes on at least one day is 0.3222.

We can approach this problem using the binomial distribution. Let X be the number of days in a week that the network crashes. Then X follows a binomial distribution with parameters n = 5 (number of days in a workweek) and p = 0.16 (probability of a crash on any given day).

a. The probability that the network crashes on both Monday and Tuesday is:

P(X = 2) = (5 choose 2) * (0.16)² * (1-0.16)³

= 0.1024

b. The probability that the network crashes for the first time on Thursday is the probability that it does not crash on Monday, Tuesday, or Wednesday, but does crash on Thursday and/or Friday. So:

P(X = 1) * P(no crashes on Monday, Tuesday, Wednesday) = (5 choose 1) * (0.16) * (1-0.16)⁴ * (0.84)³

= 0.3808 * 0.3652

= 0.1389

c. The probability that the network crashes every day is:

P(X = 5) = (5 choose 5) * (0.16)⁵ * (1-0.16)⁰

= 0.0001

d. The probability that the network crashes on at least one day is the complement of the probability that it does not crash at all during the week:

P(X >= 1) = 1 - P(X = 0)

= 1 - (5 choose 0) * (0.16)⁰ * (1-0.16)⁵

= 1 - 0.6778

= 0.3222

Therefore, a. The probability that the network crashes on both Monday and Tuesday is 0.1024; b. The probability that the network crashes for the first time on Thursday is 0.1389 ; c. The probability that the network crashes every day is 0.0001; d. The probability that the network crashes on at least one day is 0.3222.

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Suppose the Volume of a cube is 27 cubic centimeters. What would be its new volume if
one of its dimensions was quadrupled, a second dimension was halved, and a third
dimension did not change?

Answers

If one dimension was quadrupled, second dimension was halved and third dimension did not change, the volume of a cube would be changed by 27 cubic centimeters to 54 cubic centimeters.

First we identify the original dimensions of the cube. It is given that volume of the cube is 27 cubic centimeters, each side of the cube will be 3 centimeters (3x3x3=27).

According to the question:

One dimension was quadrupled: 3 x 4 = 12cm

Second dimension was halved: 3 / 2 = 1.5cm

Third dimension did not change: 3cm

So, new dimensions are 12cm x 1.5cm x 3 cm

To find the new volume, we will use the formula:

V = product of dimensions

12 cm x 1.5 cm x 3 cm = 54 cubic centimeters

Therefore, the new volume of the cube would be 54 cubic centimeters.

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The polynomial of degree 4, P(x) has a root multiplicity 2 at x=4 and roots multiplicity 1 at x=0 and x=-4 and it goes through the point (5, 18) how do you find a formula for p(x)?

Answers

The polynomial is P(x)= 2/5x(x-4)²(x+4)

What in mathematics is a polynomial?

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. x²- 4x + 7 is an illustration of a polynomial with a single indeterminate x.

If the polynomial has a root of multiplicity 2 at  x=4, the (x−4)² is a factor.

Multiplicity 1 at x=0, then x is a factor.

Multiplicity 1 at x= -4 then (x+4) is a factor.

So P(x) = Ax(x-4)²(x+4)

As it passes through (5,18) so

18 = A.5.(5-4)² . (5+4)

So, A = 18/5 .(1/9)

= 2/5

Therefore, The polynomial is P(x)= 2/5x(x-4)²(x+4)

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The distinction between real variables and nominal variables is known as.

Answers

The distinction between real variables and nominal variables is based on the type of measurement used to represent the variable.

A variable is a characteristic that can take different values or levels. Real variables are measured on a numerical scale and can take any value within a certain range.

On the other hand, nominal variables are categorical variables that represent non-numerical attributes. They are used to classify data into different groups or categories based on their characteristics. Examples of nominal variables include gender, race, nationality, and occupation. These variables cannot be measured using a numerical scale, but they can be represented using labels or codes.

The distinction between real variables and nominal variables is important because they require different methods of analysis. Real variables can be analyzed using statistical methods such as mean, standard deviation, and correlation, while nominal variables require different methods such as frequency tables and chi-square tests.

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What is the simplified form of the following expression? Assume x > 0.

3

2x

4/6x

O2x

√24x3

2x

24x3

16x4

O√12x²

Answers

The simplified form of expression [tex]\sqrt[4]{\frac{3}{2x} }[/tex] is  [tex]\frac{\sqrt[4]{24 x^3}}{2x }[/tex]

The correct answer is an option (B)

Consider an expression [tex]\sqrt[4]{\frac{3}{2x} }[/tex]

Multiply the fraction by an expression to form a perfect square in the denominator.

[tex]\sqrt[4]{\frac{3}{2x} }[/tex]

[tex]=\sqrt[4]{\frac{3\times 2^3\times x^3}{2x\times 2^3\times x^3} }[/tex]

We know that the cube of 2 is 8. So, substitute 2³ = 8

[tex]=\sqrt[4]{\frac{3\times 8\times x^3}{2x\times 8\times x^3} }[/tex]

Now, we multiply the monomials.

[tex]=\sqrt[4]{\frac{24\times x^3}{16\times x^4} }[/tex]

We know that the exponent rule [tex](a\times b)^m=a^m\times b^m[/tex]

[tex]=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{16\times x^4} }[/tex]

We know that 2⁴ = 16

[tex]=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{2^4\times x^4} }\\\\=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{2^4}\times \sqrt[4]{x^4} }[/tex]        ............(using the exponent rule [tex](a\times b)^m=a^m\times b^m[/tex])

[tex]=\frac{\sqrt[4]{24\times x^3}}{2x }[/tex]           .......(Simplify the radical expressions)

Here, [tex]\frac{\sqrt[4]{24 x^3}}{2x }[/tex] is the simplified form of expression.

Therefore, the correct answer is an option (B)

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Find the complete question below.

What is the surface area of the triangular prism.

Answers

Answer:480cm^3

Step-by-step explanation:

Spin a spinner with three equal sections colored red, white, and blue. What is P(yellow)?

33%
0%
100%
66%

Answers

In a case whereby there is a spinner with three equal sections colored red, white, and blue the  P(yellow) is 33%

What is probability?

Probability can be described as trhe act of showing how likely something is to happen it should be noted that this usually comes into play when we were not sure about the outcome of an event,  and the analysis of events governed by probability can be regarded as statistics.

P(yellow) =  1/3

= 0.33

0.33 * 100

= 33 percent

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can density curves occur in other shapes?

Answers

Density curves can occur in a variety of shapes, depending on the distribution of the underlying data.

The normal distribution is the most commonly encountered density curve, other shapes are also possible, including skewed, bimodal, uniform, and multimodal distributions.

A skewed density curve can be either positively skewed, where the tail is longer on the right-hand side, or negatively skewed, where the tail is longer on the left-hand side.

A density curve for income data might be positively skewed, since there are more people with lower incomes than with higher incomes, and the higher incomes have a longer tail to the right.

Another type of density curve is the bimodal distribution, which has two peaks or modes.

This can occur when there are two distinct groups or populations within the data, such as in the case of height data for men and women.

Density curves can also take on other shapes, such as a uniform distribution where all values are equally likely, or a multimodal distribution where there are more than two modes.

Density curves can occur in a variety of shapes depending on the underlying distribution of the data.

The normal distribution is the most commonly encountered density curve, other shapes are also possible, including skewed, bimodal, uniform, and multimodal distributions.

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suppose that a researcher is interested in estimating the mean systolic blood pressure, , of executives of major corporations. he plans to use the blood pressures of a random sample of executives of major corporations to estimate . assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is mm hg, what is the minimum sample size needed for the researcher to be confident that his estimate is within mm hg of ?carry your intermediate computations to at least three decimal places. write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).

Answers

To determine the minimum sample size needed for the researcher to be confident that his estimate is within "mm" hg of the true mean systolic blood pressure, we will use the following formula:

n = (Z * σ / E)²

where:
n = minimum sample size
Z = Z-score corresponding to the desired confidence level
σ = population standard deviation (in this case, "mm" hg)
E = margin of error (in this case, "mm" hg)

1. Determine the Z-score corresponding to the desired confidence level. Common confidence levels include 90%, 95%, and 99%, which correspond to Z-scores of 1.645, 1.960, and 2.576, respectively. Choose the appropriate Z-score based on the desired confidence level.

2. Substitute the given values of σ and E (both in "mm" hg) and the chosen Z-score into the formula: n = (Z * σ / E)²

3. Carry out the calculations, rounding the result up to the nearest whole number. This will ensure that the sample size is the minimum whole number that satisfies the requirements.

4. The result is the minimum sample size needed for the researcher to be confident that his estimate is within "mm" hg of the true mean systolic blood pressure.

Note: Since this question haven't provided specific values for standard deviation, margin of error, and desired confidence level . follow the steps with the specific values you have to find the minimum sample size.

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) two adults are selected at random. find the probability that at least one of the two smokes.round your answer to 4 decimal places.leave your answer in decimal form.

Answers

The probability that at least one of the two adults smokes is approximately 0.4375, or 0.438 rounded to 4 decimal places.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To find the probability that at least one of the two adults smokes, we can calculate the probability that neither of them smokes and then subtract that from 1.

Let's assume that the probability that an adult smokes is p. Then, the probability that an adult does not smoke is (1-p). Since the two adults are selected randomly, the probability that both of them do not smoke is (1-p)*(1-p), or (1-p)².

Therefore, the probability that at least one of the two adults smokes is:

1 - (1-p)²

Simplifying this expression, we get:

1 - (1 - 2p + p²)

= 2p - p²

We don't know the value of p, but we can assume a reasonable value based on smoking rates in the population. Let's say that p is 0.25, or 25%.

Substituting this value into the equation, we get:

2(0.25) - (0.25)²

= 0.5 - 0.0625

= 0.4375

Therefore, the probability that at least one of the two adults smokes is approximately 0.4375, or 0.438 rounded to 4 decimal places.

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An artist bought a set of 10 paintbrushes that contained x small paintbrushes and y large paintbrushes. The number of small paintbrushes in the set was 4 times the number of large paintbrushes in the set.

Answers

The amounts for each type of paintbrush is given as follows:

8 small paintbrushes.2 large paintbrushes.

How to obtain the amounts?

The amounts are obtained by a system of equations, for which the variables are given as follows:

Variable x: number of small paintbrushes.Variable y: number of large paintbrushes.

A total of 10 paintbrushes were purchased, hence:

x + y = 10.

The number of small paintbrushes in the set was 4 times the number of large paintbrushes in the set, hence:

x = 4y.

Replacing into the first equation, the value of y is obtained as follows:

4y + y = 10

5y = 10

y = 2.

Hence the value of x is of:

x = 4 x 2

x = 8.

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Write an expression that can be a rule for the number sequence below.

5, 9, 13, 17, 21, …Write an expression that can be a rule for the number sequence below.

5, 9, 13, 17, 21, …

5n, where n is equal to 0, 1, 2, 3, 4
5 + n, where n is equal to 0, 1, 2, 3, 4
5 + 4n, where n is equal to 0, 1, 2, 3
5n + 4, where n is equal to 1, 2, 3, 4

5n, where n is equal to 0, 1, 2, 3, 4
5 + n, where n is equal to 0, 1, 2, 3, 4
5 + 4n, where n is equal to 0, 1, 2, 3
5n + 4, where n is equal to 1, 2, 3, 4

Answers

The arithmetic sequence is given by the expression A = 5 + 4n

Given data ,

Let the number sequence be represented as A

Now , the value of A is

A = 5 + 9 + 13 + 17 + 21 ...

On simplifying , we get

The first term of the series is a₁ = 5

Let the second term be a₂ = 9

So , the common difference d = a₂ - a₁

d = 9 - 5 = 4

And , let the number of terms be n

So , the expression is

A = 5 + 4n

when n = 4

A = 5 + 4 ( 4 ) = 25

Hence , the arithmetic sequence is A = 5 + 4n

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(Fraction)

(i)
b²-a²
2a²+ab-3b²

(k)
3x-3y
ax-ay-x+y

j)
y²-6y-7
2y²-17y+21

(l)
a²-ab-ac+bc
a²+ab-ac-bc

Answers

Answer:

(i) To simplify (b²-a²) ÷ (2a²+ab-3b²), we can factor the numerator and denominator using the difference of squares formula, which states that a² - b² = (a + b)(a - b).

(b²-a²) = (b + a)(b - a)

(2a²+ab-3b²) = (2a-b)(a+3b)

Thus, we can rewrite the expression as:

(b + a)(b - a) / (2a-b)(a+3b)

(ii) To simplify (3x-3y) ÷ (ax-ay-x+y), we can factor out the common factor of 3 from the numerator and the common factor of (a-1) from the denominator:

3(x-y) / (a-1)(x-y)

We can then cancel the common factor of (x-y) to get the simplified form:

3 / a-1

(iii) To simplify (y²-6y-7) ÷ (2y²-17y+21), we can factor both the numerator and the denominator:

(y-7)(y+1) / (2y-3)(y-7)

We can then cancel out the common factor of (y-7) to get the simplified form:

(y+1) / (2y-3)

(iv) To simplify (a²-ab-ac+bc) ÷ (a²+ab-ac-bc), we can factor out the -1 from the denominator:

(a²-ab-ac+bc) ÷ -1(a²-ab+ac-bc)

We can then factor out the common factor of (a-b) from both the numerator and the denominator:

(a-b)(a-c) ÷ -1(a-b)(a+c)

Cancelling out the common factor of (a-b) gives us the simplified expression:

(c-a) / (a+c)

The article referenced in this lesson also stated that the pig landed on its right side lesson also stated that the pig landed on its right side 4,172 times out of 11,954 tosses. You will construct a 90% confidence interval for the population proportion of tosses of a plg die in which the pig lands on A Are the criteria for approximate normality met? es of a pig die in which the pig lands on its right side. B Find the sample proportion and the critical value: 0571 and Z= C Find the estimated standard error, SA, and compute the margin of error, m. 0349U-2349) = 0,004 11,954 m=2 si: 2x 0,004 -0.008 D Find the 90% confidence interval. Provide an interpretation of the confidence interval in context of this problem. E Would you support the claim that 33% of all tosses have the pig landing on its right side? Explain your reasoning. F What is the best way to decrease the margin of error and create a more precise estimate for the population proportion? Why would you want a smaller margin of error? G If you were to compute the 99% confidence interval, would it be wider or narrower than the 90% confidence interval? Explain briefly.

Answers

To determine if the criteria for approximate normality is met, we need to check if both the sample size and sample proportion are large enough. The sample size is n = 11,954 which is greater than 10.

Additionally, the sample proportion of landing on its right side is p = 0.571 which is also greater than 10. Therefore, the criteria for approximate normality is met.


A 99% confidence interval would be wider than the 90% confidence interval. This is because a higher confidence level requires a larger range to ensure the true population proportion is captured within the interval with a higher degree of certainty.

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determine if the function is an exponential function

f (x) = x^3

Answers

Answer:

Yes, the function is exponential.

Step-by-step explanation:

The "^" represents an exponet. If you want to know, the exponent is 3.

PLS HELP
(Will give the brainliest)

Answers

Answer:

5

Step-by-step explanation:

Given a=12 and c=13,

b = 5

∠α = 67.38° = 67°22'48" = 1.17601 rad

∠β = 22.62° = 22°37'12" = 0.39479 rad

h = 4.61538

area = 30

perimeter = 30

inradius = 2

circumradius = 6.5

Please answer!!! Simplify [tex]\frac{\sqrt 7 + \sqrt 3}{2\sqrt 3 - \sqrt 7}[/tex]

Answers

The simplified rational expression for this problem is given as follows:

[tex]\frac{3\sqrt{21} + 13}{12}[/tex]

How to simplify the rational expression?

The rational expression in the context of this problem is defined as follows:

[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}}[/tex]

The first step in simplifying the expression is removing the root from the denominator, multiplying numerator and denominator by the conjugate, as follows:

[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}} \times \frac{2\sqrt{3} + \sqrt{7}}{2\sqrt{3} + \sqrt{7}}[/tex]

Applying the subtraction of perfect squares, the denominator is given as follows:

2² x 3 - 7 = 12.

The numerator is:

[tex](\sqrt{7} + \sqrt{3})(2\sqrt{3} + \sqrt{7}) = 2\sqrt{21} + 7 + 6 + \sqrt{21} = 3\sqrt{21} + 13[/tex]

Thus the simplified expression is:

[tex]\frac{3\sqrt{21} + 13}{12}[/tex]

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Subtract 1/2h-1 from 3/4h +4

Answers

To subtract 1/2h-1 from 3/4h+4, we can distribute the negative sign to the expression 1/2h-1 and then combine like terms. This gives:

(3/4h + 4) - (1/2h - 1)

= 3/4h + 4 - 1/2h + 1 (distributing the negative sign)

= (3/4h - 1/2h) + (4 + 1) (combining like terms)

= 1/4h + 5

Therefore, the result of subtracting 1/2h-1 from 3/4h+4 is 1/4h+5.

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