help me please........................................................

Answer:

The exact value of the given trigonometric expression is undefined.

Step-by-step explanation:

Given trigonometric expression:

[tex]\dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)[/tex]

To find the exact value of the given  trigonometric expression, begin by finding the exact values of each of the trigonometric functions in the expression

The exact value of cos(2π/3) is:

[tex]\implies \cos\left(\dfrac{2 \pi}{3}\right)=-\dfrac{1}{2}[/tex]

The exact value of tan(-7π/4) is:

[tex]\implies \tan\left(-\dfrac{7 \pi}{4}\right)=1[/tex]

Since the cosecant function is the reciprocal of the sine function, the exact value of csc(π) is:

[tex]\implies \csc (\pi)=\dfrac{1}{\sin(\pi)}=\dfrac{1}{0}=\textsf{unde\:\!fined}[/tex]

Therefore:

[tex]\begin{aligned}\implies \dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)&=\dfrac{-\dfrac{1}{2}}{1}+\dfrac{1}{0}\\&=-\dfrac{1}{2}+\dfrac{1}{0}\\\\&=\textsf{unde\:\!fined}\end{aligned}[/tex]

a. In the sample:i. The average value of birth weight for all mothers is 7.17 pounds.

ii. For mothers who smoke is 6.82 pounds.

iii. For mothers who do not smoke is 7.28 pounds.b. i. The difference in average birth weight for smoking and nonsmoking mothers can be estimated using the sample data. The difference is given by the formula:

Difference = X1 – X2, where X1 is the average birth weight of mothers who smoke and X2 is the average birth weight of mothers who do not smoke.Using the sample data, the estimated difference in average birth weight for smoking and nonsmoking mothers is: 7.28 – 6.82 = 0.46 pounds.ii. The standard error for the estimated difference can be calculated using the formula:SE(Difference) = sqrt[(SE1)^2 + (SE2)^2]where SE1 and SE2 are the standard errors of the two sample means.Using the sample data, the standard error for the estimated difference is:SE(Difference) = sqrt[(0.23)^2 + (0.12)^2] = 0.26 pounds.iii. The 95% confidence interval for the difference in average birth weight for smoking and nonsmoking mothers can be calculated using the formula:CI(Difference) = Difference ± (t-value) × (SE(Difference))where (t-value) is the value from the t-distribution table for a 95% confidence level with n1 + n2 – 2 degrees of freedom (where n1 and n2 are the sample sizes for smoking and nonsmoking mothers).Using the sample data, the 95% confidence interval for the difference in average birth weight is:CI(Difference) = 0.46 ± (2.048) × (0.26) = (0.04, 0.88) pounds.

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By answering the presented question, we may conclude that As a result, expressions Ivanna's average speed is approximately 2.311 miles per hour.

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

We can use the formula:

rate = distance / time

Let's calculate Ivanna's rate for the first part of her journey:

rate = distance divided by time = 12 miles divided by 5 hours = 2.4 miles per hour

Let us now compute Ivanna's rate for the second leg of her journey:

rate = distance divided by time = 20 miles divided by 9 hours = 2.222... miles per hour

As a result, Ivanna's overall rate is the average of these two rates:

rate = (2.4 miles per hour + 2.222... miles per hour) / 2 = 2.311... miles per hour

As a result, Ivanna's average speed is approximately 2.311 miles per hour.

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The city had 20,000 residents. The next year, it went up by 2%. The new population of the city after a 2% increase is 20400.

To find the new population of the city after a 2% increase from 20000, we need to use the following formula:

New population = Old population + (Percentage increase x Old population)

Substituting the given values into the formula, we get:

New population = 20000 + (2/100 x 20000)

New population = 20000 + 400

New population = 20400

It is important to note that this calculation assumes that the increase in population is the only factor affecting the total population. In reality, there may be other factors that affect the population, such as migration, birth rates, and mortality rates.

Additionally, this calculation only gives the estimated population based on the percentage increase, and the actual population may differ due to various factors.

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If x is a positive integer , 4x^1/2 is equivalent to product of 2 and square root of x, wherein it would surely be a positive value greater than 2.

Positive integers are the numbers on the number line which are greater then zero and extend on the right hand side of the number line till infinity. These numbers are also whole numbers in itself such as 1, 2, 3...,∞. When 4x^1/2 is calculated, it is assumed that 4x is raised to power half, which will provide the answer as 2√x.

It is because square root of 4 will be 2 and that of x will be √x. Square roots are the numbers obtained by multiplying a specific number by the number itself. For example: 3×3 = 9 or square root of 9 is 3.

If some positive integer is fixed in the equation, the desired outcome would be obtained as follows:

If x=4, (4×4)^1/2 = 4

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The value of the given expressions are as follows: a. 25 b. 4 c. 1/4 d. 1/3.

In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical object or quantity. Expressions can be written using variables, operations, functions, and mathematical symbols such as parentheses, exponents, and radicals. An expression can represent a value, an equation, or a formula, and can be evaluated or simplified using mathematical rules and properties. Examples of expressions include 2x + 5, sin(θ), and (a + b)².

Here,

a. [tex]125^{2/3}[/tex]

radical form:

[tex]\sqrt{ (125^2)} = 125^{1/2}[/tex]

[tex]125^{1/2}[/tex] = √125

= 5√5

Therefore, [tex]125^{2/3} = (125x^{1/3})^{2}[/tex]

= [tex](5^3)x^{2/3}[/tex]

= [tex]5x^{3*2/3}[/tex]

= 5²

= 25

b. √16

In radical form:

√16 = 4

Therefore, [tex]16x^{-1/2} = \sqrt{16}[/tex]

= 4

c. [tex]16^{1/2}[/tex]

In radical form:

1/√16 = 1/4

Therefore, [tex]16^{-1/2} = 1/\sqrt{16}[/tex]

= 1/4

d.[tex]\sqrt[4]{81}[/tex]

In radical form:

[tex]\sqrt[4]{81}[/tex] = √(√81)

= √9

= 3

Therefore, [tex]\sqrt[4]{81} = 1/\sqrt[4]{81}[/tex]

= 1/3

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The sampling distribution is approximately normal.

The sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414.What is the sampling distribution of their sample mean IQ?The standard deviation is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where σ is the population standard deviation and n is the sample size. So, we have:$${SD} = \frac{20}{\sqrt{200}} = \sqrt{\frac{20^2}{200}} = \sqrt{2} = 1.414$$The sampling distribution of the sample mean is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where $\sigma$ is the population standard deviation and $n$ is the sample size. Therefore, the sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414. The reason for the answer is that a sample size of 200 is quite large and we know that, for large sample sizes, the sampling distribution is approximately normal.

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Answer:

Step-by-step explanation:

Kind of like rema from the song calm down calm down!!

you an find it on youtub

The theorem is Every nonzero element in the ring has an inverse, hence we deduce that Z[i]/(p) is a field. For any prime number p that is irreducible in Z[i], as asserted, Z[i]/(p) is a field.

         Proof of Theorem is Let p be a prime number that is irreducible in Z[i]. We want to show that Z[i]/(p) is a field, where (p) denotes the ideal generated by p.

Suppose that [c] + [d]i is a nonzero element of [tex]Z[i]/(p)[/tex], where [c] and [d] are congruence classes in Zp.

If one of [c] and [d] is [0], then [c] + [d]i is a unit, since the other element is nonzero. So, suppose that [c] and [d] are both nonzero in Zp.

We observe that p cannot divide c + di in Z[i] since p is irreducible in Z[i] and it cannot divide both c and d. Therefore, p and c + di are relatively prime in Z[i].

            By Theorem 16.7, there exist Gaussian integers r and s such that [tex](c + di)r = 1 + ps.[/tex]

Now, suppose that [e] + [f]i is another nonzero element of Z[i]/(p), where [e] and [f] are congruence classes in Zp. We want to show that [e] + [f]i is also a unit.

Since p and c + di are relatively prime, there exist integers u and v such that [tex]pu + (c + di)v = 1[/tex] , by Bezout's identity.

Multiplying both sides by e + fi, we get:

          [tex]pue + (c + di)ve + (ce - df) + (cf + de)i = e + fi[/tex]

Therefore, [tex](e + fi)(ue + vi(c + di)) = (e + fi)(1 - (cf + de)i)[/tex]

Multiplying both sides by the conjugate of (e + fi), we get:

           [tex](e + fi)(e - fi)(ue + vi(c + di)) = (e^2 + f^2)[/tex]

Since p is irreducible in Z[i], it is also prime. Thus, Z[i]/(p) is an integral domain, which means that the product of two nonzero elements is nonzero. Therefore, [tex]e^2 + f^2[/tex] is nonzero in Zp, and

so    [tex](e + fi) (ue + vi(c + di))[/tex] is a unit in Z[i]/(p).

             We conclude that Z[i]/(p) is a field since every nonzero element has an inverse in the ring.

            Therefore, Z[i]/(p) is a field for any prime number p that is irreducible in Z[i], as claimed

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Answer: [tex]c-34=21[/tex]; 55 cups of lemonade.

Step-by-step explanation:

We are given the amount sold and the amount leftover so we need to figure out how many cups were there at the start. Since you are subtracting the amount of cups you sold from the amount you start with and it equals an end amount, the cups can be modeled by the equation [tex]c-34=21[/tex] rather than [tex]21+c=34[/tex].

Now to solve for c

[tex]c-34=21\\[/tex]

add 34 to both sides

[tex]c=55[/tex]

Answer:

0.999

Step-by-step explanation:

If the driver wore a seat belt, that is the only column we have to look at.

The chance the driver survived is number survived / number total.

Plugging in, we get 412,042/412,493, or about 0.999.

Hope this helps!

The value of μV is 40 cm³.

Given,The area of bottom of cylindrical container = 10 cm²The height of container = h = Mean height = 4 cm Standard deviation of height = σ = 0.2 cm We are supposed to find the mean volume of fluid in the container.In order to calculate the mean volume, first we need to calculate the volume of fluid in the container.Volume of a cylindrical container = πr²h Where, r is the radius of the base of the container.So, we need to calculate the value of r.The area of the bottom of the container is given as 10 cm².

We know that the area of the base of a cylinder is given as:Area of base of cylinder = πr² We are given that area of the base is 10 cm². So,10 = πr²r² = 10/πr = √(10/π) We can find the volume of fluid using the values we have.Volume of fluid = πr²h = π(√(10/π))² x 4 = 40 cm³We know that mean volume, μV is given as:μV = πr²μh So, we need to calculate the value of μh. We know that standard deviation σh is given as:σh = 0.2 cm So,μh = h = 4 cm So,μV = πr²μh = π(√(10/π))² x 4 = 40 cm³

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To see if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska, one can use a two-sample t-test. It is okay to perform the inference procedure, but the following assumptions and conditions must be checked.

Assumptions: Independence: The airfares for each coast should be independent of each other. Normality: The populations of airfares for both coasts should be approximately normally distributed .Equal variances: The population variances for both coasts should be equal.

Conditions: Sample sizes: Both samples should be large enough so that the Central Limit Theorem applies. Rule of thumb for t-tests is that the sample size should be at least 30.Random sampling: Both samples should be random .To test if the conditions are met, one can create a boxplot for each coast, check the normal probability plots, perform the F-test to check for equal variances, and check the sample sizes. If the assumptions and conditions are met, a two-sample t-test can be used to determine if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska.

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The sοlutiοns in οrder frοm least tο greatest are:

Lesser x = -4

Greater x = 1

Ascending οrder refers tο the arrangement οf numbers in which the smallest number cοmes befοre the largest.

Tο sοlve fοr x in the equatiοn [tex]x^2 + 3x - 4 = 0[/tex], we can use the quadratic fοrmula:

[tex]x= \frac{(-b+\sqrt{b^{2} -4ac} )}{2a} \\[/tex]

where a, b, and c are the cοefficients οf the quadratic equatiοn[tex]ax^2 + bx + c = 0.[/tex]

In this case, a = 1, b = 3, and c = -4. Substituting these values intο the quadratic fοrmula, we get:

[tex]x = (-3\± \sqrt{(3^2 - 4(1)(-4)))} / 2(1)\\\\x = (-3 \± \sqrt{(25))} / 2\\\\x = (-3 \± 5) / 2[/tex]

This gives twο pοssible sοlutiοns:

x1 = (-3 - 5) / 2 = -4

x2 = (-3 + 5) / 2 = 1

Therefοre, the sοlutiοns in οrder frοm least tο greatest are:

Lesser x = -4

Greater x = 1

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The estimated annual income can be calculated using the equation above. If the data point is used to calculate the slope and y-intercept of the regression line, then the annual income can be estimated using the equation y = m(14) + b.

If the education level is 14 years,

To create a simple linear regression model using education level as the independent variable, you will need to input data for education level and annual income.

This data can be used to estimate the annual income for any given education level. The equation for this linear regression model is y = mx + b, where y represents the annual income, m is the slope of the line, x is the education level, and b is the y-intercept.

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The order from the greatest number of triangles to the smallest is: Condition A, Condition B, Condition C.

According to the Triangle Inequality Theorem, any two triangle sides' sums must be bigger than the length of the third side.

The triangle inequality theorem can be used to determine the order of the greatest to smallest triangle.

Condition A: Under this condition, we have two sides with lengths 5 and 6, and their angle is 50°. Using these requirements, we may create two separate triangles since 5 + 6 = 11, which is more than the third side.

Condition B: This condition results in a right triangle with a third angle that is 90° and two sharp angles that measure 40° and 50°. According to the Pythagorean theorem, the triangle's two legs must be 30 and 40 inches long, respectively, meaning that the hypotenuse must be 50 inches long. We can only create one triangle as a result.

Condition C: This condition provides us with three sides that are 4, 5, and 9 lengths long. Any two sides must have a length total larger than the third side in order for a triangle to be formed. The three sides provided, however, do not satisfy this since 4 + 5 = 9. Hence, under these circumstances, a triangle cannot be formed.

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The probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.

Standard deviation is a statistical measurement that depicts the average deviation of each value in a dataset from the mean value. It tells you how much your data deviates from the mean value. It represents the typical variation between the mean value and the individual data points.

The formula for the probability that a truck drives between 99 and 128 miles in a day is:

[tex]Z = (X - \mu) /\sigma[/tex]

where, X is the number of miles driven per day; μ is the mean of the number of miles driven per day; σ is the standard deviation of the number of miles driven per day. The value of Z for 99 miles driven per day is:

[tex]Z = (99 - 120) / 11 = -1.91[/tex]

The value of Z for 128 miles driven per day is:

[tex]Z = (128 - 120) / 11 = 0.73[/tex]

Using a standard normal distribution table or calculator, the probability of a truck driving between 99 and 128 miles per day is:

[tex]P(-1.91 < Z < 0.73) = 0.7734[/tex]

Therefore, the probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.

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You answer would be mate it would be x=66

In response to the stated question, we may state that The scatter plot indicates a clustering pattern in the data, and as elevation increases, temperature drops.

"Scatter plots are graphs that show the association of two variables in a data collection. It is a two-dimensional plane or a Cartesian system that represents data points. The X-axis represents the independent variable or characteristic, while the Y-axis represents the dependent variable. These plots are sometimes referred to as scatter graphs or scatter diagrams."

"A scatter plot is also known as a scatter chart, scattergram, or XY graph. The scatter diagram plots numerical data pairings, one variable on each axis, to demonstrate their connection."

Because the graph is a scatter plot, the data displays a clustering pattern.

We may deduce from the figure that as height increases, temperature falls.

As a result, C and E are the proper choices.

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The correct question is -

The scatter plot shows the relationship between elevation and temperature on a certain mountain peak in North America. Which statements are correct?

A. The data shows one potential outlier

B. The data shows a linear association

C. The data shows a clustering pattern

D. The data shows a negative association

E. As elevation increases, temperature decreases

Answer:

Below

Step-by-step explanation:

Mass of bouncies + box = 17342     subtract mass of box from both sides

   mass of bouncies  =  17342 - 429 = 16913 g

Unit mass per bouncy = 505 g / 45 bouncy  

Number of Bouncies =  16913 gm / ( 505 g / 45 bouncy )  = 1507.1 bouncies

  With the given info, I am afraid it IS 1507 bouncies in the box

      maybe since the question asks for APPROXIMATE number, the answer is     1510 bouncies    ( rounded answer) ....or 1500

Answer:

Step-by-step explanation:

C(1,2), radius=6

Equation using  [tex](x-h)^2+(y-k)^2=r^2[/tex]:

   [tex](x-1)^2+(y-2)^2=36[/tex]

By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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It will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

First, we need to convert the dimensions of the tank from inches to feet:

68 inches diameter = 68/12 feet = 5.67 feet diameter

24 feet long = 24 feet long

Next, we can calculate the volume of the tank in cubic feet:

Since 1 cubic foot of water weighs 62.4 pounds, we can calculate the weight of the water in the tank in pounds:

To find out how long it will take to fill the tank, we can use the flow rate of the fire hydrant:

Finally, we can divide the volume of the tank by the flow rate to find out how long it will take to fill the tank:

Therefore, it will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

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The dilated figure has the following coordinates: A' (-15, 0), B' (-5, 10), C' (10, 10), D' (15, -5), and E' (5, -10).

In this sense, coordinates are the points where a grid system intersects. Latitude and longitude are the traditional ways to express GPS coordinates. Degrees of separation north and south from the equator, which is 0 degrees, are measured by lines of latitude coordinates.

Just multiply the coordinates of each point by 5 to construct a figure about the origin using a scale factor of 5.

A (-3, 0)

B (-1, 2)

C (2, 2)

D (3, -1)

E (1, -2)

The coordinates of each point are multiplied by 5 to enlarge the image by a scale factor of 5:

A' = (-3 * 5, 0 * 5) = (-15, 0)

B' = (-1 * 5, 2 * 5) = (-5, 10)

C' = (2 * 5, 2 * 5) = (10, 10)

D' = (3 * 5, -1 * 5) = (15, -5)

E' = (1 * 5, -2 * 5) = (5, -10)

The coordinates of the dilated figure are:

A' (-15, 0)

B' (-5, 10)

C' (10, 10)

D' (15, -5)

E' (5, -10)

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From the given information provided, the solution to the given trigonometric inequality is (π/4, 5π/4).

To solve the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians, we can use the following steps:

Rewrite the inequality in terms of tangent:

Divide both sides by cos(x) to get:

tan(x) > 1

Find the solutions of the equation tan(x) = 1:

tan(x) = 1 when x = π/4 or x = 5π/4.

Check the sign of tangent in the intervals between the solutions:

We need to check the sign of tan(x) for x values in the following intervals:

(0, π/4), (π/4, 5π/4), and (5π/4, 2π).

In the interval (0, π/4), tan(x) is positive and less than 1.

In the interval (π/4, 5π/4), tan(x) is positive and greater than 1.

In the interval (5π/4, 2π), tan(x) is negative and less than -1.

Determine the solution set:

Since we are looking for x values that satisfy tan(x) > 1, the only interval that contains such values is (π/4, 5π/4). Therefore, the solution to the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians is:

π/4 < x < 5π/4

In interval notation, we can write:

(π/4, 5π/4)

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The solution to the system of equations is (x, y) = (1, -1) where the given equations are 11x+9y=-20 and x=-5y-6.

The substitution method is a technique used in algebra to solve systems of equations by replacing one variable with an expression containing another variable. The goal is to eliminate one of the variables so that we can solve for the other one.

We are given the following system of two equations with two variables:

11x + 9y = -20 (equation 1)

x = -5y - 6 (equation 2)

To solve the system using the substitution method, we need to solve one of the equations for one of the variables, and then substitute the expression for that variable into the other equation. Let's solve equation 2 for x:

x = -5y - 6

Now we can substitute this expression for x into equation 1, and solve for y:

11x + 9y = -20

11(-5y - 6) + 9y = -20 (substituting x = -5y - 6)

-55y - 66 + 9y = -20

-46y = 46

y = -1

Now that we have found y = -1, we can substitute this value back into equation 2 and solve for x:

x = -5y - 6

x = -5(-1) - 6

x = 1

Therefore, the solution to the system of equations is (x, y) = (1, -1).

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By using addition calculation, we determine that Angela will end up making 42 cards in total.

Angela made 23 cards for her friends, but she wants to make even more to share with others. To determine how many cards she will make in total, we need to add the number of cards she has already made with the number of cards she plans to make.

So, we add 23 (the number of cards she has made) and 19 (the number of cards she plans to make) so in total, she will make:

23 + 19 = 42

Therefore, Angela will make 42 cards in all.

By using simple arithmetic calculation of basic addition, we find that  Angela will make 42 cards in all.

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Answer:

Step-by-step explanation:\Write an expression for the sequence of operations describe below Add C and the quotient of 2 and D do not simplify any part of the expression

Answer:

Step-by-step explanation:

An important math tool is graphing. It can be a straightforward method for introducing more general concepts like most and least, greater than, or less than. It can also be a great way to get your child interested in math and get them excited about it. Using graphs and charts, you can break down a lot of information into easy-to-understand formats that quickly and clearly convey key points.

Given equation 2x + y = 6 we can drive from this equation that at x = 0 y will be 6 and y =0 x will be 3 hence we have two points of the line (0,6) and (3,0)

From the Given equation (2) 6X + 3Y = 12 we can drive from this equation that at x = 0 y will be 4 and y =0 x will be 2 hence we have two points of the line (0,4) and (2,0).

The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).

A) The 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).Explanation:Given,Sample size, n = 123Average surgery time, μ = 136.9 minutesStandard deviation, σ = 24.1 minutesWe know that for a sample of size n, the 95% confidence interval is given by,  (Formula1)Where, z is the z-score, α/2 = 0.05/2 = 0.025  is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula1), we get the 95% confidence interval as(130.82, 142.98)Thus, the 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).B) The 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).Explanation:We know that for a sample of size n, the 99.5% confidence interval is given by, (Formula2)Where, z is the z-score, α/2 = 0.005/2 = 0.0025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula2), we get the 99.5% confidence interval as (127.93, 145.87).Thus, the 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).C) The surgeon's claim that the mean surgery time is between 133.71 and 140.09 minutes is equivalent to the confidence interval (133.71, 140.09). The surgeon's claim falls inside the 95% confidence interval, (130.82, 142.98), therefore we can say that the surgeon's claim can be made with 95% confidence.D) The formula to find the minimum sample size for a 95% confidence interval that will specify the mean to within ±3 minutes is given by (Formula3)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula3), we get the minimum sample size as 424.15.The minimum sample size required to get a 95% confidence interval that will specify the mean to within ±3 minutes is 425 (Rounded up to the nearest integer).F) The formula to find the minimum sample size for a 99% confidence interval that will specify the mean to within ±3 minutes is given by (Formula4)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula4), we get the minimum sample size as 596.73.The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).

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