Here are the cost of rulers at different shops.
Shop A
3 rulers for £1.50
Shop B
5 rulers for £2
What is the cheapest price for 45 rulers?

Answer:

Angle B is 70 degrees.

Step-by-step explanation:

All 3 angles in a triangle add up to 180.

We know that angle A = 40.

So the other two angles combined = 180-40 = 140.

So add up those other 2 angles, set it equal to 140 and solve for x. Then substitute your X back into the provided equation for B. Let's go!

(2x-30) + (x+20) = 140

Combine like terms:

3x -10 = 140

3x = 150

x = 50

Angle B is 2x-30. Substitute x=50 and solve for angle B:

2(50) - 30 = 100-30 = 70

Angle B is 70 degrees.

we know that,

★ Sum of angles of a triangles is 180°

# According To The Question:-

[tex] \sf \: \longrightarrow \: 40 + (2x-30) + (x+20) = 180[/tex]

[tex] \sf \: \longrightarrow \: 40 + 2x-30+ x+20= 180[/tex]

[tex] \sf \: \longrightarrow \: 40 -30+20+ 2x+ x= 180[/tex]

[tex] \sf \: \longrightarrow \: 10+20+ 2x+ x= 180[/tex]

[tex] \sf \: \longrightarrow \: 30+ 2x+ x= 180[/tex]

[tex] \sf \: \longrightarrow \: 30+ 3x= 180[/tex]

[tex] \sf \: \longrightarrow \: 3x= 180-30[/tex]

[tex] \sf \: \longrightarrow \: 3x= 150[/tex]

[tex] \sf \: \longrightarrow \: x=\frac{ 150}{3}[/tex]

[tex] \sf \: \longrightarrow \: x=50\degree[/tex]

_____________________________________

★ Measure of Angle B :-

[tex] \sf \: \longrightarrow \: \angle B = (2x-30)\degree[/tex]

[tex] \sf \: \longrightarrow \: \angle B = 2x-30\degree[/tex]

[tex] \sf \: \longrightarrow \: \angle B = 2(50)-30\degree[/tex]

[tex] \sf \: \longrightarrow \: \angle B = 2\times 50-30\degree[/tex]

[tex] \sf \: \longrightarrow \: \angle B = 100-30\degree[/tex]

[tex] \sf \: \longrightarrow \: \angle B = 70\degree[/tex]

_____________________________________

The height of the flagpole is 9 meters.

On the diagram we can see two similar right triangles. One has cathetus of 5m and 3m, and the other has a base of 15m, and a height of H, which is the height of the flagpole.

Because the two triangles are similar, the quotients between the sides are equal, then we can write:

H/15m = 3m/5m

Solving that equtaion for H we will get.

H = (3/5)*15m

H = 9m

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The upper bound approximation for pi within 0.005 is 3.150 and the lower bound approximation is 3.140.

we can use the fact that pi is approximately equal to 3.14159. To find the upper and lower bound approximations, we need to add or subtract 0.005 from this value.

For the upper bound approximation, we add 0.005 to 3.14159, which gives us 3.14659. Since pi is greater than this value, we need to round up to the nearest hundredth, giving us 3.150.

For the lower bound approximation, we subtract 0.005 from 3.14159, which gives us 3.13659. Since pi is less than this value, we need to round down to the nearest hundredth, giving us 3.140.

the upper and lower bound approximations for pi within 0.005 are 3.150 and 3.140 respectively.

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Abdul had 9 green beads and 12 yellow beads in his bag originally and after giving one green bead to his sister he had 4 yellow beads remaining.

Let's say the total number of beads in Abdul's bag is "x" and the number of green beads is "g".

We know that 3/7 of the beads are green, so:

g = 3/7 × x

Abdul gives a green bead to his sister 2/5 of the remaining beads are green.

This means that 3/5 of the remaining beads are yellow.

So, we can write:

(g - 1) / (3/5) = y / 2/5

Where "y" is the number of remaining yellow beads.

We can simplify this equation by cross-multiplying:

5(g - 1) = 6y

Expanding and simplifying:

5g - 5 = 6y

5g = 6y + 5

Now we can substitute the first equation (g = 3/7 × x) into this equation:

5(3/7 × x) = 6y + 5

Multiplying both sides by 7 to eliminate the fraction:

15x = 42y + 35

We can rearrange this equation to solve for "y":

y = (15x - 35) / 42

To find values of "x" and "y" that are both integers and satisfy the conditions of the problem.

We know that both "x" and "y" have to be greater than or equal to 1 since Abdul must have at least one bead of each color in his bag.

One possible solution is:

x = 21 (so there are 21 beads in the bag)

g = 9 (since 3/7 of 21 is 9)

y = 4 (since (15×21 - 35) / 42 = 4)

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The company's profit if there are no price increases is $120.

We have,

The problem provides a function P(x) that models the profit of a natural sponge company.

The function takes as input the number of $0.15 increases in the price of each sponge, denoted by x.

When the value of x is 0, it means that there are no price increases, and therefore the initial price of each sponge is unchanged.

Now,

If there are no price increases, then the value of x in the function P(x) is 0, since x represents the number of price increases.

Substituting x = 0 into the function, we get.

P(0) = -0.1(0)^2 + 15(0) + 120 = 120

Therefore,

The company's profit if there are no price increases is $120.

We can also see this from the graph of the function, which starts at (0, 120) and represents the profit when there are no price increases.

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The probability that the mean battery life would differ from the population mean by greater than 18.4 minutes is 0.0148. The formula for the standard error of the mean is  SE = σ/√n

To solve this problem, we need to use the Central Limit Theorem (CLT) which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

The formula for the standard error of the mean is:

SE = σ/√n

Where SE is the standard error, σ is the population standard deviation, and n is the sample size.

In this case, we are given that the population standard deviation (σ) is 62 minutes, the population mean is 606 minutes, and the sample size (n) is 99 batteries. Therefore, the standard error of the mean is:

SE = 62/√99 = 6.231

Next, we need to find the z-score associated with the difference between the sample mean and the population mean of 18.4 minutes. The formula for the z-score is:

z = (x - μ) / SE

Where x is the sample mean, μ is the population mean, and SE is the standard error.

Substituting the values we have:

z = (606 + 18.4 - 606) / 6.231 = 2.96

Using a standard normal distribution table, we find that the probability of getting a z-score greater than 2.96 is 0.0148. Therefore, the probability that the mean battery life would differ from the population mean by greater than 18.4 minutes in a sample of 99 batteries is 0.0148, or about 1.48%.

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Health care workers should monitor the patient's pulse and respirations when assisting them to the dangling position.

This is because the dangling position, which involves sitting on the edge of the bed with the legs hanging down, can cause a sudden drop in blood pressure due to the redistribution of blood flow from the upper body to the lower body. This can lead to dizziness, lightheadedness, and even fainting. Monitoring the patient's pulse and respirations can help identify any changes in their cardiovascular status and ensure that they are stable enough to tolerate the position. While range of motion and continuous positive motion are important considerations in patient care, they are not specifically related to the dangling position. Temperature may also be monitored, but this is not directly related to the risks associated with the dangling position.

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Martina used 16 pounds of type A coffee in her blend.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

Let's assume that Martina used x pounds of type A coffee in her blend. Since the blend used four times as many pounds of type B coffee as type A, the amount of type B coffee used would be 4x pounds.

The total cost of the blend is given as the sum of the cost of type A and type B coffee, so we can write:

Cost = Cost of type A + Cost of type B

= x* + 4x*

Simplifying the expression, we get:

Cost = ( + 4) x

We are given that the total cost of the blend is , so we can write:

( + 4) x =

Solving for x, we get:

x = / ( + 4)

Substituting the given values, we get:

x = / ( + 4)

= / ( + 4)

= / ( + 4)

Therefore, Martina used 16 pounds of type A coffee in her blend.

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Integrating the concentration between 0 and 4, we can see that the correct option is A.

We know that the concentration is given by the quadratic equataion:

c(t) = 2t(4 - t)

To find the cardiatic output for the time interval [0,4 ], we need to integrate over that interval, we will get:

[tex]\int\limits^4_0 {2t*(4 - t)} \, dt = [-(2/3)t^3 + 4t^2 + C]^4_0[/tex]

Where C is the constant of integration.

Evaluating that in the given interval, we will get:

[ -(2/3)*4³ + 4*4² - 0] = 21.33

Then we can see that the correct option is A.

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There is not enough evidence to conclude that the average time spent on leisure activities by American adults has changed. Sample standard deviation (s) is 8.984 hours. Sample mean (x') is 19.9 hours per week

To test whether the claim that American adults spend an average of 18 hours per week on leisure activities is true or false, we can conduct a hypothesis test.

First, we need to define the null and alternative hypotheses. Let µ be the population mean time spent on leisure activities by American adults.

Null hypothesis: µ = 18 hours per week

Alternative hypothesis: µ ≠ 18 hours per week

We can then calculate the sample mean and standard deviation from the data given as follows:

Sample mean (x') = (13+4+15+9+21+42+15+34+20+6) / 10 = 19.9 hours per week

Sample standard deviation (s) = 8.984 hours

Next, we can calculate the test statistic (t-value) using the formula:

t = (x' - µ) / (s / √(n))

where n is the sample size (10).

Using a t-distribution with 9 degrees of freedom (n-1), we can find the critical t-value at a 5% significance level to be ±2.306.

We calculate the t-value as:

t = (19.9 - 18) / (8.984 / √(10)) = 0.911

Since the calculated t-value is less than the critical t-value, we fail to reject the null hypothesis.

In other words, the claim that American adults spend an average of 18 hours per week on leisure activities is not contradicted by the sample data.

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Answer:x=4

Step-by-step explanation: subtract the 3x from its self then do it to the 5x and then you cross out the 3x's because the cancel out and then your left with 2x-2=6, then you add the 2 to itself which means they cancel out then you add it to the 6 and that gives you 8 then you are left with 2x=8 now you divide the 2x by its self then the 2 cancels out and then 8 divide by 2 is 4 and then x=4

N(5*-26 + *3*)^

que 5* meno 26 + 3 no se puede resolver

When conducting a bivariate correlational study, it is important to use a random sample to ensure that the results are generalizable to the larger population.

However, if a random sample is not used, it does not necessarily mean that the association should be automatically rejected. There are several reasons why a random sample may not have been used in a correlational study. For example, the researcher may have had limited access to a specific population or may have chosen to use a convenience sample for practical reasons. In these cases, it is important to consider the potential limitations and biases in the sample. Additionally, it is possible to adjust for some of these limitations through statistical techniques such as weighting or stratification. These techniques can help to ensure that the results are more representative of the larger population, even if a random sample was not used. Overall, while a random sample is preferred in bivariate correlational studies, it is not always feasible or practical. As such, it is important to carefully consider the limitations of the sample and to use appropriate statistical techniques to account for any potential biases. Ultimately, the validity of the association should be evaluated based on the strength of the evidence and the quality of the study design, rather than solely on the use of a random sample.

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Dilation is a transformation, which is used to resize the object while scale factor is the ratio of the dimensions of the new object to the ratio of old object.

Dilation Meaning in Math. Dilation is a transformation, which is used to resize the object.

Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.

Scale factor is the ratio of the length of the new shape to the dimensions of the original shape.

For example if the length of a rectangle is 5m and it's dilated to 10 cm , the scale factor is calculated as;

= 10/5 = 2

Therefore the scale factor is 2

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None of these alternatives is correct. The probability of a type ii error (β) is not directly determined by the probability of a type i error (α).

Type i and type ii errors are two types of errors that can occur in hypothesis testing. Type i error occurs when we reject a true null hypothesis, while type ii error occurs when we fail to reject a false null hypothesis.

The probability of a type i error (α) is typically set by the researcher or the significance level chosen for the test. A common value for α is 0.05, which means that there is a 5% chance of rejecting a true null hypothesis. However, the probability of a type ii error (β) depends on various factors such as the sample size, effect size, and the level of significance chosen for the test.

In general, the probability of a type ii error (β) decreases as the sample size increases or as the effect size increases. It also decreases if the level of significance chosen for the test is reduced. However, it is important to note that there is always a trade-off between type i and type ii errors. As the probability of type i error decreases, the probability of type ii error increases, and vice versa.

In conclusion, the probability of a type ii error (β) cannot be determined solely based on the probability of a type i error (α). It depends on several factors and should be considered along with the probability of type i error when making decisions about hypothesis testing.

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Surface area of the square pyramid is 7 square mi.

A square pyramid is a three-dimensional geometric figure which has a square base and four lateral faces, The lateral faces are triangular faces with a common vertex.

Let us consider a square pyramid, whose side length is "a" and slant height is "h".

Then the area of the base, i.e. area of square shaped base = square unit and the area of each triangular face is (1/2 × a × h) square unit.

So, the sum of areas of 4 triangular faces is 4 × (1/2 × a × h)=2ah square unit.

∴ Surface area of a square pyramid = Area of base + Area of 4 side face

[tex]\sf = (a^2+2ah) \ square \ unit[/tex]

Given that, Side length (a) = 1 mi

And Slant height (h) = 3 mi

∴ Surface area of the given square pyramid = [tex]\sf (1)^2+(2\times1\times3) \ square \ mi[/tex]

[tex]\sf = 1+6 \ square \ mi[/tex]

[tex]\sf = 7 \ square \ mi[/tex]

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Without more information about the methodology and context of Lindsay's study or survey, it's difficult to determine the validity of her inference with certainty.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

If Lindsay has conducted a survey or study and found that out of 400 people, 300 would prefer to watch movies in a theater, her inference would be valid based on the data she collected. However, it's important to note that her inference would only be valid within the context of her study or survey.

If Lindsay's study or survey was conducted in a specific geographic location or demographic group, her results may not be generalizable to other populations or locations. Additionally, if her study or survey had any methodological flaws, such as a biased sample or leading questions, her results may not be reliable.

Therefore, without more information about the methodology and context of Lindsay's study or survey, it's difficult to determine the validity of her inference with certainty.

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Answer:

option 4

Step-by-step explanation:

x² - 16 = 0 ( add 16 to both sides )

x² = 16 ( take square root of both sides )

[tex]\sqrt{x^2}[/tex] = ± [tex]\sqrt{16}[/tex]

x = ± 4

To solve the rational equation 2/(x+2) = 9/8 - (5x)/(4x+8), we can begin by finding a common denominator on both sides of the equation, and then simplifying and rearranging terms to solve for x.

2/(x + 2) = 9/8 - (5x)/(4x + 8)   (original equation)

16*2/(8(x+2)) = 2*9/8 - 5x/(4(x+2))   (multiply both sides by 8(x+2) to get a common denominator)

32/(x+2) = 9/4 - 5x/(4(x+2))   (simplify)

32/(x+2) = (9-5x)/(4(x+2))   (combine the fractions)

32 * 4(x+2) = (9-5x)(x+2)   (cross-multiply)

128(x+2) = 9(x+2) - 5x(x+2)   (distribute)

128x + 256 = 9x + 18 - 5x^2 - 10x   (simplify and collect like terms)

5x^2 - 118x - 238 = 0   (rearrange to standard quadratic form)

We can then use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Where a = 5, b = -118, and c = -238. Plugging in these values, we get:

x = (118 ± sqrt(118^2 - 4(5)(-238))) / (2*5)

x = (118 ± sqrt(14084)) / 10

x = (118 ± 118.6) / 10

So our two solutions for x are:

x = 23.72 or x = -9.52

We can check these solutions back in the original equation to confirm they work.

Check the picture below.

[tex]\sin(A )=\cfrac{\stackrel{opposite}{2\sqrt{2}}}{\underset{hypotenuse}{4}}\implies \sin(A )=\cfrac{\sqrt{2}}{2} \\\\\\ \cos(A )=\cfrac{\stackrel{adjacent}{2\sqrt{2}}}{\underset{hypotenuse}{4}}\implies \cos(A )=\cfrac{\sqrt{2}}{2} \\\\\\ \tan(A )=\cfrac{\stackrel{opposite}{2\sqrt{2}}}{\underset{adjacent}{2\sqrt{2}}}\implies \tan(A)=1[/tex]

The composite function k(t(x)) is -2.5 - 7(ln x)^2 + 3(ln x), and its derivative is -14ln x + 3/x.

To find the composite function k(t(x)), we substitute the expression for t(x) into the function k(t) as follows:

k(t(x)) = 4.5 + 3 - 7t(x)^2 + 3t(x) - 4

k(t(x)) = 4.5 + 3 - 7(ln x)^2 + 3(ln x) - 4

Simplifying this expression, we obtain:

k(t(x)) = -2.5 - 7(ln x)^2 + 3(ln x)

To find the derivative of the composite function, we use the chain rule as follows:

k'(t(x)) = k'(t) * t'(x)

where k'(t) is the derivative of the function k(t) with respect to t, and t'(x) is the derivative of the function t(x) with respect to x.

The derivative of k(t) with respect to t is:

k'(t) = -14t + 3

The derivative of t(x) with respect to x is:

t'(x) = 1/x

Substituting these expressions into the chain rule, we obtain:

k'(t(x)) = (-14t(x) + 3) * (1/x)

k'(t(x)) = (-14ln x + 3/x)

Therefore, the composite function k(t(x)) is -2.5 - 7(ln x)^2 + 3(ln x), and its derivative is -14ln x + 3/x.

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Answer: The trapezoid's area is 265 [tex]unit^{2}[/tex]

Definition of a trapezoid - A trapezoid, also known as a trapezium, is a flat closed shape having four straight sides, with one pair of parallel sides.

The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs. A trapezium can also have parallel legs. The parallel sides can be horizontal, vertical, or slanting.

The perpendicular distance between the parallel sides is called the altitude.

The area of trapezium is given as : [tex]\frac{1}{2}[/tex] × sum of the parallel sides × distance between the parallel sides

Given:  the base lengths of trapezoid are 24 unit and 29 unit and height is 10 unit.

The area of trapezoid = [tex]\frac{1}{2}[/tex] × (24+29) × 10 = 265 [tex]unit^{2}[/tex]

Final answer : The area of trapezoid is 265[tex]unit^{2}[/tex]

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Answer: 1/nine.

Step-by-step explanation:To locate the probability of drawing a black marble after which a inexperienced marble, we need to keep in mind the range of approaches we can draw a black marble and then a inexperienced marble, and divide that with the aid of the whole range of methods we are able to draw  marbles with out replacement.

The opportunity of drawing a black marble on the primary draw is two/10, because there are 2 black marbles out of a total of 10 marbles. Then, in view that we draw the second one marble with out alternative, there will be nine marbles left within the bag. If we drew a black marble on the first draw, there could be 1 black marble and five inexperienced marbles left in the bag. So the possibility of drawing a green marble on the second draw, for the reason that a black marble became drawn on the first draw, is five/nine.

The chance of drawing a black marble after which a inexperienced marble is the manufactured from the chance of drawing a black marble on the primary draw and the opportunity of drawing a inexperienced marble on the second draw, given that a black marble turned into drawn on the primary draw. So we multiply 2/10 by five/nine to get 1/nine.

Therefore, the chance of drawing a black marble after which a inexperienced marble is 1/nine.

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a. modulus 6:The possible inverses of x modulo 6 are numbers y such that xy ≡ 1 (mod 6).

We can check each integer between 1 and 5 to see which ones have a multiplicative inverse modulo 6:

1 * 1 ≡ 1 (mod 6), so 1 is its own inverse.
2 * 3 ≡ 0 (mod 6), so 2 and 3 do not have inverses.
4 * 4 ≡ 4 (mod 6), so 4 does not have an inverse.
5 * 5 ≡ 1 (mod 6), so 5 is its own inverse.

Therefore, the least positive inverses congruent to 1 modulo 6 are 1 and 5.

b. modulus 8:

The possible inverses of x modulo 8 are numbers y such that xy ≡ 1 (mod 8).

We can check each integer between 1 and 7 to see which ones have a multiplicative inverse modulo 8:

1 * 1 ≡ 1 (mod 8), so 1 is its own inverse.
2 * 4 ≡ 0 (mod 8), so 2 and 4 do not have inverses.
3 * 3 ≡ 1 (mod 8), so 3 is its own inverse.
5 * 5 ≡ 1 (mod 8), so 5 is its own inverse.
6 * 7 ≡ 2 (mod 8), so 6 and 7 do not have inverses.

Therefore, the least positive inverses congruent to 1 modulo 8 are 1, 3, and 5.

c. modulus 9:

The possible inverses of x modulo 9 are numbers y such that xy ≡ 1 (mod 9).

We can check each integer between 1 and 8 to see which ones have a multiplicative inverse modulo 9:

1 * 1 ≡ 1 (mod 9), so 1 is its own inverse.
2 * 5 ≡ 1 (mod 9), so 2 and 5 are inverses.
3 * 6 ≡ 0 (mod 9), so 3 does not have an inverse.
4 * 7 ≡ 1 (mod 9), so 4 and 7 are inverses.
8 * 8 ≡ 1 (mod 9), so 8 is its own inverse.

Therefore, the least positive inverses congruent to 1 modulo 9 are 1, 4, 5, and 7.

d. modulus 10:

The possible inverses of x modulo 10 are numbers y such that xy ≡ 1 (mod 10).

We can check each integer between 1 and 9 to see which ones have a multiplicative inverse modulo 10:

1 * 1 ≡ 1 (mod 10), so 1 is its own inverse.
2 * 5 ≡ 0 (mod 10), so 2 and 5 do not have inverses.
3 * 7 ≡ 1 (mod 10), so 3 and 7 are inverses.
4 * 3 ≡ 2 (mod 10), so 4 and 9 are inverses.
6 * 1 ≡ 6 (mod 10), so 6 is its own inverse.
8 * 3 ≡ 4 (mod 10), so 8 and 7 are inverses.

Therefore, the least positive inverses congruent to 1 modulo 10 are 1, 3, 7,

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For a given data set, the confidence interval will be wider for a 95% confidence level than for a 90% confidence level.

A confidence interval is a range within which we expect the true population parameter (e.g., mean or proportion) to fall, based on our sample data. The confidence level represents the probability that the confidence interval contains the true population parameter. A higher confidence level means we are more certain that the interval captures the true value. To achieve a higher confidence level (e.g., 95% instead of 90%), we need to include a larger range of values in the confidence interval.

This is because we are trying to be more certain that the interval contains the true population parameter. The width of the confidence interval is determined by the margin of error, which depends on the standard deviation, sample size, and the chosen confidence level (represented by the critical value, often denoted as "z" or "t"). As we increase the confidence level, the critical value increases, resulting in a larger margin of error and a wider confidence interval.

In summary, the confidence interval will be wider for a 95% confidence level than for a 90% confidence level because we need to include more values in the interval to be more certain that it contains the true population parameter.

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The minimum magnitude of force [tex]$p_1$[/tex] required to cause the block to move is approximately 0.55 times the weight of the block.

The minimum magnitude of force [tex]$p_1$[/tex] can be calculated using the formula [tex]$p_1 = \mu N$[/tex], where [tex]$\mu$[/tex] is the coefficient of static friction and [tex]$N$[/tex] is the normal force acting on the block. The normal force [tex]$N$[/tex] can be calculated as [tex]$N = mg\cos\theta$[/tex], where [tex]$m$[/tex] is the mass of the block, [tex]$g$[/tex] is the acceleration due to gravity, and [tex]$\theta$[/tex] is the angle of inclination.

The coefficient of static friction can be found using the formula [tex]$\mu = \tan\phi$[/tex], where [tex]$\phi$[/tex] is the angle of friction. For most surfaces, the angle of friction is related to the angle of inclination as $\phi = \arctan(\theta)$.

Substituting the given values, we get:

[tex]$\phi = \arctan(30^o) \approx 0.54$[/tex]

[tex]$N = mg\cos(30^o) = \frac{\sqrt{3}}{2}mg$[/tex]

[tex]$\mu = \tan(0.54) \approx 0.63$[/tex]

[tex]$p_1 = \mu N = 0.63\times\frac{\sqrt{3}}{2}mg \approx 0.55mg$[/tex]

Therefore, the minimum magnitude of force [tex]$p_1$[/tex] required to cause the block to move is approximately 0.55 times the weight of the block.

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Answer:

4 (g cm³)

Step-by-step explanation:

Volume of a rectangular block (prism) = length X width X height

we have 2 X 3 X 25 = 150 cm³

Formula for density is

density = mass/volume

            = 600/150

            = 4 (g cm³)

The domain of the set of ordered pairs include the following: {1, 2, 3, 4}.

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the set of ordered pairs above, we can reasonably and logically deduce the following domain and range:

Domain = {1, 2, 3, 4}.

Range = {3, 4, 5}.

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The product (k-1) (6k+5) is C, [tex]6k^2 - k - 5.[/tex] therefore, option C, [tex]6k^2 - k - 5.[/tex] is correct.

To find the product of (k-1) and (6k+5), we can use the distributive property of multiplication.

We can multiply each term in the first expression (k-1) by each term in the second expression (6k+5), and then simplify:

[tex](k-1)(6k+5) = k(6k+5) - 1(6k+5)\\(k-1)(6k+5) = 6k^2 + 5k - 6k - 5\\(k-1)(6k+5) = 6k^2 - k - 5[/tex]

Therefore, the answer is C, [tex]6k^2 - k - 5.[/tex]

We can check our answer by multiplying it out using the distributive property, and we should get the original expressions (k-1) and (6k+5) back.

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