How will increasing the level of confidence without changing the sample size affect the width of a confidence interval for a population mean?

Answer:

301.189

Step-by-step explanation:

Given the table :

Source of Variation - - SS - - - df - - - MS - - - - F

Regression - - - - - -3177.17 - - -2 - - 1588.6

Residual - - - - - - - - ______ --17 - - -17.717

Total - - - - - - - - - - 3478.36 - - 19

Calculate the SSR, Sum of Square residual

The Sum of Square RESIDUAL (SSR), Mean Square Residual (MSR) and Degree of Freedom RESIDUAL (DFR) are related by the formular :

MSR = SSR / DFR

Hence,

SSR = MSR × DFR

Fr the table ;

MSR = 17.717 ; DFR = 17

SSR = (17.717 × 17)

SSR = 301.189

Answer:

Step-by-step explanation:

2. ∠K≅∠L and ∠M≅∠N

3. Definition of similar triangles

4. ΔJKL ≈ ΔJMN

5. Addition Property

Answer:

$1092.96

Step-by-step explanation:

Based on the given conditions, formulate: 990 × ( 1 + 2 × 5.2% )

Calculate the product or quotient: 990 × ( 1 + 0.104 )

Calculate the sum or difference: 990 × 1.104

Calculate the product or quotient: 1092.96

Round the number: 1092.96

Answer: $1092.96

The equation that represents a quadratic relationship is y = 4x^2. Option A.

A quadratic relationship is a mathematical relationship where the variable y is a function of the variable x raised to the power of 2. In other words, it is an equation in which the highest power of the variable is 2.

Let's analyze the given equations:

1. y = 4x^2: This equation represents a quadratic relationship because the variable x is raised to the power of 2. The term 4x^2 indicates that the relationship between x and y is quadratic.

2. y = 4x^4: This equation represents a quartic relationship, not a quadratic relationship. The variable x is raised to the power of 4, which indicates a higher degree relationship than quadratic.

3. y = 4x^3: This equation represents a cubic relationship, not a quadratic relationship. The variable x is raised to the power of 3, indicating a higher degree relationship.

4. y = 4: This equation represents a linear relationship, not a quadratic relationship. It is a constant equation where y is always equal to 4, regardless of the value of x. In a quadratic relationship, the variable x should have a power of 2. Option A.

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The length of line CE for the given semicircle is found as 5/2 units.

Using the Two Tangent Theorem, let F be the point of tangency.

AE = EF = x, and BC = FC = 2.

DE therefore equals 2x.

Consider the shown figures;

Triangle CDE and the Pythagorean Theorem produce:

DE² + CD² = CE²

(2 - x)² + 2² = (2 + x)²

x ² -4x + 8 = x² + 4x + 4

x = 1/2

Thus,

CE = FC + x

CE = 5/2

Thus, the length of line CE for the given semicircle is found as 5/2 units.

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The correct question is-

Square ABCD has side length 2. A semicircle with diameter line AB is constructed inside the square, and the tangent to the semicircle from C intersects side line AD at E. What is the length of line CE?

Answer:   CB=2/3

Step-by-step explanation:

The triangle's  angles are 30-60-90 degrees. So This is right triangle.

Let the triangle is ABC. B is right angle=90 degr . A=30 degrees, C=60 degrees

The long side of right triangle is hypotenuse AC=4/3 units.

In right triangle with 30 degr the side CB that is opposite to acute angle 30 degrees is twice shorter than hypotenuse AC

So CB=4/3/2=2/3

Finally using Pithagor theorem we find AB= sqrt( AC^2-CB^2)=

=sqrt(16/9-4/9)=sqrt(12/9)= 2*sqrt(3)/3

2*sqrt(3)/3>2/3  so AB>CB

So the shortest leg of ABC is  CB=2/3

The steps Sergey could use to solve the quadratic equation by completing the square is 5(x2 + 4x) = –7

We should know that in completing the square method both sides of the equation are made perfect squares.

The given equation is 5x²+20x-7=0

Solving this equation by completing the square method we have

5(x²+4x+4)=-7

This means that (x+2)=±√27/5

Simplifying further we have

5(x²+4x)=7

Then expanding to make ²HS a perfect square we have

5(x²+4x+4)=7+20

This means that 5(x²+4x)=-7

Therefore the step he could use is 5(x²+4x)=-7\

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Answer:

0.5319 = 53.19% probability that the young man is taller than the young woman by more than 5 inches

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Distribution of the difference in height between men and woman:

Applying the concept above:

\(\mu = 69.3 - 64 = 5.3\)

\(\sigma = \sqrt{2.7^2 + 2.8^2} = 3.89\)

What is the probability that the young man is taller than the young woman by more than 5 inches?

Probability of the difference being more than 5 inches, that is, 1 subtracted by the pvalue of Z when X = 5.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{5 - 5.3}{3.89}\)

\(Z = -0.08\)

\(Z = -0.08\) has a pvalue of 0.4681

1 - 0.4681 = 0.5319

0.5319 = 53.19% probability that the young man is taller than the young woman by more than 5 inches

The volume of the percentage of the 6 cm diameter, 12 cm height cylindrical can filled by the soda that reaches a height of 5 cm when the can is on its side is about 89.05%

A percentage is a fraction expressing the number of times a part of a set of item is present in each 100 units of the item.

The diameter of the cylindrical soda can = 6 cm

Height of the can = 12 cm

Height the soda reaches when the can is placed on its side = 5 cm

The volume of the can, V = π × 6²/4 × 12 = 108·π

The volume of the cylindrical soda can, V = 108·π cm³

The Volume occupied by the soda can be found as follows;

Angle representing the segment above the soda = 2 × (arccos(2/3)) ≈ 1.682 ≈ 96.38°

Cross sectional area of the soda = Cross sectional area of the can - Area of the segment above the soda

Area of the segment above the soda = (1/2) × 3² × (1.682 - sin(1.682)) ≈ 3.0968

Cross sectional area of the soda = π × 6²/4 - 3.0968

Volume of the soda = (π × 6²/4 - 3.0968)× 12

Percentage of the volume filled by the soda is therefore;

(((π × 6²/4 - 3.0968)× 12)/(108·π)) × 100 ≈ 89.05%

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Both the coordinate points are plotted on the graph. The cartesian graph is attached with the answer.

Given are the two coordinates to be plotted on a Cartesian plan -

(5, 4) , (3, 4).

The two given coordinate points are (5, 4) , (3, 4).

Refer to the graph attached. It shows both the points plotted.

Therefore, both the coordinate points are plotted on the cartesian graph.

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The angle x in the parallel line is 123 degrees.

In the diagram, l₁ and l₂ are parallel.

l₃ and l₄ are perpendicular to each other.

Since l₁ and l₂ are parallel lines, the line l₃ is a transversal that cut across the parallel lines.

Angle relationship are formed such as corresponding angles, alternate angles, vertically opposite angle etc.

Therefore,

57 + x  = 180°

x = 180 - 57

Therefore,

x = 123 degrees.

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The mean of the data set is 82.77

If we want to find the mean, we would have to put it at the back of our minds that the mean is the same as the average. As such, we would have to take the sum of all the values that have been listed in the data set and divide by the total number of the data.

The first step is to arrange the data set orderly from smallest to largest;

70, 71,79, 82,88,85,87,91,92

We have nine values in the data set thus the mean is;

70+71+79+82+88+85+87+91+92/9= 745/9= 82.77

Hence the mean of the data set is 82.77

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9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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The least expensive house in the 100,000 range, given the stem and lead plot on house sale prices, is $120, 000.

The stem and leaf plot on the house sale prices is given such that the stem is in hundreds of thousands and the leaf is in ten thousands.

This means that if you have a stem of 0 and a leaf of 2, the house price is:

= 0 + 20,000

= $20,000

A stem of 3 and a leaf of 4 means the house price is:

= 300,000 + 40,000

= $340,000

The cheapest house in the 100,000 range is the leaf value of 2 which means the least expensive house is:
= 100,000 + 20,000

= $120,000

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Answer:

105n-25n^2

Step-by-step explanation:

-5(-16+5n-5)

-5(-21+5n)

=105n-25n^2

Answer:

the answer is -4

Step-by-step explanation:

The relative minimum point is B. Option B is the correct option.

What is the relative minimum?

The function's graph makes it simple to locate relative minima. It is the pivotal point in the function's graph. Relative minima are locations where the function's graph shifts from decreasing to increasing. A point that is lower than the points to its left and right is said to be at its relative minima.

The points of the graph function are A, B, C, D.

The lowest point among the given points on the graph is B.

Thus the relative minimum point is B.

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Answer:

190-140m

Step-by-step explanation:

(10)(19)-(10)(14m)

Step-by-step explanation:

The slope of g(t) as (-2,2) is given by

\(g'(t)=2t+6\)

\(g'(-2)=2(-2)+6=2\)

Since the normal is parallel to the tangent of f(t) at (1, 1/2),

The tangent line of f(t) has a slope of

\(\dfrac{d}{dx}f(t)=n+2mt=2\)

At point (1, 1/2), we know

\(f'(1)=n+2m=2\)

\(f(1)=2+n(1)+m(1)^2=2+n+m=\frac12\)

Solving,

\(n=5, m=-\frac72\)

Answer:

x = 3

Step-by-step explanation:

First, use trigonometric function to find RT.

θ = 60°

Opposite = 2√3

Hypotenuse = RT

Apply SOH:

Sin θ = Opp/Hyp

Plug in the values

Sin 60° = 2√3/RT

RT*Sin 60° = 2√3

Divide both sides by Sin 60°

RT = 2√3/sin 60°

RT = 2√3 × √3/2 (sin 60° = √3/2)

RT = (2√3 × √3)/2

RT = (2 × 3)/2

RT = 3

✔️Find x

θ = 45°

Opposite = x

Adjacent = 3

Apply TOA:

Tan θ = Opp/Adj

Substitute

Tan 45° = x/3

3 × Tan 45° = x

3 × 1 = x (tan 45° = 1)

3 = x

x = 3

Answer:

\(5-14i\)

Step-by-step explanation:

\((12-6i)-(7+8i)\\\\12-6i-7-8i\\\\5-14i\)

The solution to the expression to a + bi form is 5 - 14i

From the question, we have the following parameters that can be used in our computation:

(12 - 6i) - (7 + 8i)

Open the brackets

So, we have

(12 - 6i) - (7 + 8i) = 12 - 6i - 7 - 8i

Evaluate the like terms

So, we have

(12 - 6i) - (7 + 8i) = 5 - 14i

Hence, the solution is 5 - 14i

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Answer:

Step-by-step explanation:

The BAC (Blood Alcohol Concentration) of a person depends on several factors, such as the amount of alcohol consumed, the time over which the alcohol was consumed, and the weight and gender of the person. For this problem, we will assume that the woman has a normal metabolism and that the alcohol is completely absorbed into her bloodstream.

To calculate the BAC at 8 pm, we need to know the amount of alcohol that the woman consumed and the time over which she consumed it. We are given that she had 2 mixed drinks between 7-8 pm, which contained a total of 2 ounces of liquor. We are also given that she had a glass of wine at 10 pm, but we don't need to consider this for the BAC at 8 pm.

Using the Widmark formula, we can calculate the BAC at 8 pm:

BAC = (Alcohol consumed / (Body weight x r)) - (0.015 x Hours since first drink)

where r is the gender constant (0.55 for females) and 0.015 is the rate at which the liver metabolizes alcohol.

Plugging in the values we know, we get:

BAC = (2 oz / (130 lbs x 0.55)) - (0.015 x 1 hour)

BAC = 0.0208 - 0.015

BAC = 0.0058

Therefore, the woman's BAC at 8 pm was approximately 0.0058, which is below the legal limit for driving in most states in the US.

Linear equations are also first-degree equations as it has the highest exponent of variables as 1

example: y=mx+b

Exponential equations: Are of the form-

Quadratic equation:

From the question given

The options that conform to Linear equations are: B, C, F

The options that conform to exponential equations are: A, G, H

The options that conform to quadratic equations are: D, E

Answer:

4

Step-by-step explanation:

The triangle are similar which means the ratio between sides is the same.

In this case the sides on triangle DEF are 5 times the length of the sides on triangle ABC. So the ? is 20/5.

20/5 = 4

Answer: 56

Step-by-step explanation:

The probability that a flight departed on time given that it arrives is 0.92

The conditional probability of event B occurring giving that event A has occurred is expressed as

P(B|A) = P(A and B)/P(A)

Given the following parameters

P(A and B) = The probability that a flight departs and arrives on time = 0.84

P(A) = The probability that an airplane flight departs on time = 0.91

P(B | A) = 0.84/0.91
P(B | A) = 0.92

Hence the probability that a flight departed on time given that it arrives is 0.92

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If he wants an average of 84, he needs to get at least 93 points.

Remember that the average value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

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Answer:

Step-by-step explanation: