Match each expression

The surveyor must test at the slightest 385 voters within the expansive city to build a 95% certainty interim for the extent who bolster the occupant candidate with an edge of blunder no bigger than 0.05.

To discover the test measure required to attain an edge of mistake of no more than 0.05 for a 95% certainty interim, able to utilize the taking after equation:

n = (z[tex]^{2}[/tex] * p * q) / E[tex]^{2}[/tex]

where:

n is the test estimate

z is the z-score related to the specified level of certainty (in this case, 95% corresponds to a z-score of 1.96)

E is the specified edge of blunder (in this case, 0.05)

Substituting the given values, we get:

n = (1.96[tex]^{2}[/tex] * 0.5 * 0.5) / 0.05[tex]^{2}[/tex]

n = 384.16

thus, we get a test measure of 385.

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Answer:

The answer for anle X is 66°

Step-by-step explanation:

Base angles of an isosceles triangle are equal

<x=<y

<x+<y+<w=180

let<x=X

Remember <X=<Y

X+X+48=180

2X+48=180

2X=180-48

2X=132

divide both sides by 2

X=66°

<X=X

<X=66°

the volume of the apple would increase by ΔVtotal over the five-week period

The volume of the apple is directly proportional to the cube of its radius. Therefore, if the radius increases by 1/8 inch per week for five weeks, the total increase in radius would be 5/8 inches.

To calculate the change in volume, we can use the formula V = (4/3)πr^3.

Initially, let's assume the radius of the apple is r.

After the first week, the radius would be r + 1/8 inches. Therefore, the new volume would be:
[tex]V_1 = (4/3)\pi(r + 1/8)^3[/tex]

To calculate the change in volume, we can subtract the initial volume from the new volume:

[tex]\DeltaV_1 = V_1 - V_0[/tex]

where V0 is the initial volume of the apple.

Similarly, after the second week, the radius would be r + 2/8 inches, and the new volume would be:

[tex]V2 = (4/3)\pi(r + 2/8)^3[/tex]

The change in volume after the second week would be:

ΔV2 = V2 - V1

We can repeat this process for the remaining three weeks and find the total change in volume by adding all the individual changes:

ΔVtotal = ΔV1 + ΔV2 + ΔV3 + ΔV4 + ΔV5

By simplifying this equation, we get:

[tex]\Delta V_{total }=  (4/3) \pi r^3[(r + 1/8)^3 + (r + 2/8)^3 + (r + 3/8)^3 + (r + 4/8)^3 + (r + 5/8)^3 - 5r^3][/tex]

Therefore, the volume of the apple would increase by ΔVtotal over the five-week period.

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The volume of the apple will increase by [tex](4/3)π[(r0 + 5/8)^3 - r0^3][/tex] during the five-week period.

Assuming that the apple is a perfect sphere, we can use the formula for the volume of a sphere:

[tex]V = (4/3)πr^3[/tex]

where V is the volume of the sphere and r is the radius of the sphere.

Let's start by finding the initial volume of the apple. We are not given the initial radius, so let's assume it to be r0.

[tex]V0 = (4/3)πr0^3[/tex]

After one week, the radius increases by 1/8 inch, so the new radius is r1 = r0 + 1/8. The new volume is:

[tex]V1 = (4/3)π(r0 + 1/8)^3[/tex]

After two weeks, the radius increases by another 1/8 inch, so the new radius is r2 = r0 + 2/8. The new volume is:

[tex]V2 = (4/3)π(r0 + 2/8)^3[/tex]

Similarly, after three weeks, the new radius is r3 = r0 + 3/8 and the new volume is:

[tex]V3 = (4/3)π(r0 + 3/8)^3[/tex]

After four weeks, the new radius is r4 = r0 + 4/8 and the new volume is:

[tex]V4 = (4/3)π(r0 + 4/8)^3[/tex]

Finally, after five weeks, the new radius is r5 = r0 + 5/8 and the new volume is:

[tex]V5 = (4/3)π(r0 + 5/8)^3[/tex]

To find how the volume changes during the five-week period, we need to subtract the initial volume from the final volume:

ΔV = V5 - V0

[tex]ΔV = (4/3)π(r0 + 5/8)^3 - (4/3)πr0^3[/tex]

Simplifying this expression, we get:

[tex]ΔV = (4/3)π[(r0 + 5/8)^3 - r0^3][/tex]

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Answer:

≈ $26

Step-by-step explanation:

13% = 0.13

199.99 x 0.13 = $25.9987

So, 13% markup is ≈ $26

The proof that Proven AB ≅ CD and BC ≅ DA is given below.

A parallelogram is a quadrilateral with opposite sides parallel.

The Proof: given ABCD is a parallelogram

In parallelogram ABCD, compare triangles ABC and CDA. In these triangles (See attached image)

AC = CA (common side)

∠BAC = ∠DCA (alternate interior angles)

∠BCA = ∠DAC (alternate interior angles)

Hence by the Angle-Side- Angle postulate, both the triangles are congruent and the corresponding sides are equal.

Therefore we have AB = CD, and BC = AD.

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Step-by-step explanation:

let's first sort the data points from low to high :

42, 68, 70, 72, 74, 75, 79, 80, 82, 83, 84, 85, 86, 87, 91, 92, 94, 95, 97, 98

67.

the mean score is the sum of all data points divided by the number of data points :

1634/20 = 81.7

=> BC is correct

68.

the median is the number in the sorted list, what half of the data points are lower, and the other half higher.

in case of an even number of data points, it is the mean value of the 2 central data points.

in our case these are 83 and 84. the mean value between these two numbers is 83.5.

=> BE is correct

69.

the mode is the most frequent number among the data points.

but all scores appear only once.

so, some say, the mode is the set of all data points.

or, others say, there is no mode (like your teacher, apparently)..

=> ABC is correct.

70.

mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean.

so, now we are creating a new data set : the individual distances of the original data points to their mean value :

39.7, 13.7, 11.7, 9.7, 7.7, 6.7, 2.7, 1.7, 0.3, 1.3, 2.3, 3.3, 4.3, 5.3, 9.3, 10.3, 12.3, 13.3, 15.3, 16.3

the man value for these is the MAD of the original data points :

187.2/20 = 9.36

=> B is correct

71.

the range is the difference between the highest and lowest values in a set of numbers.

so, in our case that is

98 - 42 = 56

=> AD is correct

72.

quartiles are the values that divide a list of numbers into quarters (4 equally long parts).

we have here 20 numbers, so all Qs are between 2 numbers.

Q1 is between the 5th and the 6th number (and again, the mean value between these two numbers is the result) :

Q1 = (74 + 75)/2 = 74.5

=> AE is correct

73.

as above, just for Q3 it is between the 15th and 16th number :

Q3 = (91 + 92)/2 = 91.5

=> DE is correct

74.

the interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.

while the range gives you the spread of the whole data set, the interquartile range gives you the range of the middle half of a data set - so, between Q1 and Q3 :

91.5 - 74.5 = 17

=> E is correct

75.

outliers are extreme values that differ from most other data points in a dataset (much lower or higher than the others).

outliers are therefore values at the extreme ends of a dataset.

often we see at least some of them right away, like 42 in our set.

but are there any others ?

there are some guidelines like building an upper and lower "fence" (or limit), and any value beyond these limits are great candidates for being outliers.

upper fence = Q3 + 1.5 × IQR = 91.5 + 1.5×17 = 117

we have no values higher than 117.

lower fence = Q1 - 1.5 × IQR = 74.5 - 1.5×17 = 49

we have one value (as expected) lower than that (42), which makes this a confirmed outlier.

=> AB is correct.

Answer:

-2

Step-by-step explanation:

The explanation is in the picture

The "possible-sources" of in the measurement error of an experiment are Instrument error, Human error, sampling error and environmental factors, these sources "may" or "may-not" be enough to account for the percent differences calculated from the data.

There are several possible sources of "measurement-error" in an experiment which affect the accuracy and precision of the results.

These sources include instrument error, human error, environmental factors, and sampling error.

(i) "Instrument-Error" : is defined as inaccuracies in the measuring instruments used in the experiment. This include issues such as calibration errors, sensitivity of the instruments.

(ii) "Human-Error" can arise from mistakes made by experimenters during data collection or analysis, such as misreading measurements or recording data incorrectly.

(iii) "Environmental-Factors", such as temperature, humidity, or electromagnetic interference, can also cause error into experiment if they affect performance of measuring instruments.

(iv) "Sampling-Error" occur when a subset of the population is used for the experiment, and the results are generalized to the entire population.

Depending on the magnitude of these sources of error, they may or may not be enough to account for the percent differences calculated from the data.

If the measurement errors are small and within an acceptable range for the experiment, they may not significantly impact the results.

If the errors are large or systematic, they can introduce significant bias into the data and affect the percent differences calculated.

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The given question is incomplete, the complete question is

Discuss the possible sources of measurement error in an experiment. Are these sources of error enough to account for the percent differences you calculated from your data? write out your answer in a clear and well supported paragraph.

The value of the given expression -0.4( -6g - 9h ) - 2h - 0.2( -5h + 3g ) in the simplest form  is equal to  1.8g + 2.6h.

The expression is equal to,

-0.4( -6g - 9h ) - 2h - 0.2( -5h + 3g )

Apply distributive law multiplication over addition.

A ( B + C ) = A × B + A × C

Simplify the expression by first distributing the -0.4 and -0.2 coefficients to the terms inside the parentheses,

= (-0.4 × -6g  + 0.4 × 9h ) -2h - ( 0.2 × -5h  + 0.2 × 3g )

= 2.4g + 3.6h - 2h + h - 0.6g

Combine like terms,

= (2.4g - 0.6g) + (3.6h - 2h + h)

= 1.8g + 2.6h

Therefore, the simplest form of the expression is 1.8g + 2.6h.

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The above question is incomplete, the complete question is:

Rewrite in simplest terms:

− 0. 4 ( − 6 g − 9 h ) − 2 h − 0. 2 ( − 5 h + 3 g )

Answer:

Your answer should be A

The parent function which is represented by the given table as required in the task content is; Choice B. f(x) = |x|.

It follows from the task content that the parent function which is represented by the table is to be determined.

On this note, by observation of the function; the values of y represent the positive version of x.

Consequently, it follows that the table represents the absolute value function.

Therefore, Choice B; f(x) = |x| is correct.

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Maybe 9/12? I counted the amount of times 6 or 9 shows up on the graph. :D. Hope that helps.

Applying the Angle Bisector Theorem, the length of the segments are:

AB = 15;    AC = 20.

The Angle Bisector Theorem states that in a triangle, if a line segment bisects an angle of the triangle and intersects the opposite side, then it divides that side into two segments that are proportional to the lengths of the other two sides of the triangle.

Therefore, we would have the following equation based on the angle bisector theorem:

5y/8 = 4y - 1 / 6

Cross multiply:

8(4y - 1) = 6(5y)

32y - 8 = 30y

32y - 30y = 8

2y = 8

y = 4

AB = 4y - 1 = 4(4) - 1 = 15

AC = 5y = 5(4) = 20

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The wheel does 1,184 revolutions in the 1700 meters.

To find the number of revolutions we need to take the quotient between the distance and the circumference of the wheel.

The circumference of a circle of diameter D is:

C = 3.14*D

So here we have:

C = 3.14*18in = 56.52 in

And we know that:

1 meter ≈ 39.3701 inches

Then the circumference in meters is:

C = 56.52/39.3701 m = 1.435m

The number of revolutions is:

1700m/1.435m = 1,184

That is the correct answer.

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Answer:

Step-by-step explanation:

First find the circumference:

π × 18 = 3.14 × 18 = 56.52"

56.52÷ 39.3701 inches in one meter = 1.4356 meters for the circumference.

Divide 1700 meters by 39.3701 = 1184.173

round to 1184 revolutions

The standard deviation of the ACT scores is approximately 4.2.

Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much the data values deviate, on average, from the mean (or average) of the data set. A higher standard deviation indicates greater variability or spread in the data, while a lower standard deviation indicates less variability or spread.

According to the given information:

To find the standard deviation of ACT scores, we can use the given information about the mean and the percentage of scores above a certain threshold.

Given:

Mean (μ) = 21.4

Percentage of scores above 26 = 15%

Since the distribution is approximately normal, we can use the Z-score formula to find the Z-score corresponding to the given percentage. The Z-score is the number of standard deviations a particular value is from the mean in a normal distribution.

Z-score formula:

Z = (X - μ) / σ

Where:

Z = Z-score

X = Value (in this case, 26)

μ = Mean (21.4)

σ = Standard deviation (to be found)

We can rearrange the formula to solve for σ:

σ = (X - μ) / Z

Substituting the given values:

X = 26

μ = 21.4

Z = Z-score corresponding to 15% (which can be found using a standard normal distribution table or a Z-score calculator)

Assuming a standard normal distribution table or calculator gives us a Z-score of approximately 1.04 for a percentage of 15%, we can plug in the values:

σ = (26 - 21.4) / 1.04

σ = 4.4 / 1.04

σ ≈ 4.2 (rounded to the nearest tenth)

So, the standard deviation of the ACT scores is approximately 4.2.

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Answer: question#7 is 7/12

question#8 is 1  3/8

question#5 is 1/2

question#6 is 12

question#9 is 1  1/6

question#10 is 31/40

question#11 is 3/4

Step-by-step explanation: give brainliest

Question #5: Option A, [tex]\frac{1}{2}[/tex]

Question #6: Option A, 12

Question #7: Option A, [tex]\frac{7}{12}[/tex]

Question #8: Option D, [tex]1\frac{3}{8}[/tex]

Question #9: Option D, [tex]1\frac{1}{6}[/tex]

Question #10: [tex]\frac{31}{40}[/tex]

Question #11: [tex]\frac{3}{4}[/tex]

Pls mark brainliest

Answer:

d. 1 7/30...............

Answer:

D

Step-by-step explanation:

2/5 + 5/6

Make the denominator same

(2×6)/30 + (5×5)/30

12+25/30

37/30

1 7/30

A number multiplied by itself.

What is square?

In mathematics, a square is a number that is obtained by multiplying a number by itself. It is also a geometric shape with four equal sides and four right angles. The area of a square is calculated by multiplying the length of one of its sides by itself. The formula for calculating the area of a square is A = s^2, where A is the area and s is the length of one side.

Squares have many important applications in mathematics, including in algebra, geometry, trigonometry, and calculus. They are used in the Pythagorean theorem, which relates to the sides of a right triangle, and they are used to represent variables in algebraic equations. Squares are also important in geometry, where they are used to construct geometric shapes and to calculate their areas and perimeters.

The better definition of squares is:

A number multiplied by itself.

In mathematics, a square refers to the product of a number multiplied by itself. For example, the square of 4 is 16, because 4 multiplied by 4 equals 16. Squares have a variety of important applications in mathematics, including in geometry, algebra, and calculus.

While a result that has been proved to be true is sometimes referred to as a "square" in certain contexts, it is not the primary definition of the term. Similarly, a triangle with a right angle is referred to as a "right triangle" or a "right-angled triangle," but not a square.

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Answer:

p < -2

Step-by-step explanation:

Answer:

The answer is -2

Step-by-step explanation:

4/5-1/2p>9/5

C.L.T

-1/2p>9/5-4/5

-1/2p>5/5

-1/2p=1

-p/2>1

-p=2

p= -2

The expanded form of 2d with an exponent of -5 is 32d⁵

2d with an exponent of -5

[tex] {(2d)}^{ - 5} [/tex]

[tex] = \frac{1}{ {(2d)}^{5} } [/tex]

expand

[tex] = \frac{1}{2d \times2d \times2d \times2d \times2d } [/tex]

[tex] = {32d}^{5} [/tex]

Therefore, 2d with an exponent of -5 is 32d⁵

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Okay, here are the steps:

1) For the new drug group, the mean reduction is 25 points and standard deviation is 3.1.

To get the 90% CI, we calculate:

Mean ± (1.645 * SD)

= 25 ± (1.645 * 3.1)

= 24.584 to 25.416

2) For the placebo group, the mean reduction is 18 points and standard deviation is 2.8.

To get the 90% CI, we calculate:

Mean ± (1.645 * SD)

= 18 ± (1.645 * 2.8)

= 17.624 to 18.376

3) Since the CI for the new drug (24.584 to 25.416) lies above the CI for the placebo (17.624 to 18.376), there is evidence that the drug is working.

The other options are incorrect. The CI for the new drug does not lie below the placebo CI, so there is evidence the drug is working, not not working.

Thekey is to compare the CI ranges for the two groups. If the CI range for the new drug group lies above the CI range for the placebo group, that indicates the new drug is likely more effective in reducing blood sugar levels, providing evidence that the drug is working.

Does this help explain the steps? Let me know if you have any other questions!

Answer:

29 cm

Step-by-step explanation:

We Know

Pinocchio’s nose is 9cm long.

His nose grows by 6cm if he lies.

His nose shortens by 2cm if he tells the truth.

He lies 4 times and truth 2 times.

We Take

9 + (6 x 4) - (2 x 2) = 29 cm

So, Pinocchio's nose now is 29 cm.

Answer:

29 cm

Step-by-step explanation:

(6x4) + 9

(6x4) = 24 cm

24 + 9 = 33 cm

(2x2) - 33

(2x2) = 4 cm

4 - 33 = 29 cm

I hope this helps!

The fireworks will explode after 1.125 seconds of launching Firework B.

Distance = Speed × time

Let time = t

Firework A:

[tex]D(t) = 360t - - - (1)[/tex]

Firework B:

[tex]D(t) = 280(0.25) + 280t[/tex]

[tex]D(t) = 70 + 280t - - - (2)[/tex]

Equate 1 and 2 :

[tex]360t = 280t + 70[/tex]

Collection of like terms

[tex]360t - 280t = 70[/tex]

[tex]80t = 70[/tex]

[tex]t = 70/80[/tex]

[tex]t = 0.875 seconds[/tex]

[tex]0.875 + 0.25 = 1.125 seconds[/tex]

Therefore, the fireworks will explode after 1.125 seconds of launching Firework B.

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Answer: To find the new balance including interest, we need to take into account the interest charged on the current balance and the new purchase.

First, let's calculate the interest charged on the current balance. The monthly interest rate is 18.99% / 12 = 1.5825%.

The interest charged on the current balance is therefore:

interest on current balance = 0.015825 * 9160.00 = 144.98

So the total balance including interest for the current month is:

current balance including interest = 9160.00 + 144.98 = 9304.98

Next, let's calculate the interest charged on the new purchase of $1,098.00. The interest charged on the new purchase is:

interest on new purchase = 0.015825 * 1098.00 = 17.39

So the total balance including interest for the new purchase is:

new balance including interest = 1098.00 + 17.39 = 1115.39

Finally, we add the current balance including interest and the new balance including interest to get the total balance including interest:

total balance including interest = current balance including interest + new balance including interest

total balance including interest = 9304.98 + 1115.39

total balance including interest = 10420.37

Therefore, the new balance including interest is $10,420.37.

Step-by-step explanation:

The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = (5/2)^x - 5, we need to find the minimum and maximum values of y that can be obtained by plugging in all possible x values.

To find the maximum value of f(x), we can take the limit as x approaches infinity:

Answer:

40-m=21

40-40-m=21-40

m=21-40

m=-19

The value of x is approximately 10.57 and the value of y is approximately 15.25.

In mathematics, a chord is a straight line segment that connects two points on a curve. More specifically, a chord is a line segment that has its endpoints on the curve.

The term "chord" is most commonly used in the context of circle geometry, where a chord is a line segment that connects two points on the circumference of a circle. In this context, the length of a chord can be calculated using the Pythagorean theorem, given the lengths of the radii of the circle and the distance between the endpoints of the chord.

In a circle, if four chords are connected to form a quadrilateral, then opposite angles of the quadrilateral are supplementary. Using this property, we can set up the following equation:

105 + (7y + 1) + (7x + 1) + (4y + 14) = 180

Simplifying and solving for x and y, we get:

7x + 4y + 122 = 180

7x + 4y = 58 ......(1)

Also, we know that the opposite angles of a cyclic quadrilateral are supplementary. Therefore, we can set up the following equations:

105 + (4y + 14) = 180 ......(2)

(7y + 1) + (7x + 1) = 180 ......(3)

Simplifying and solving for y in equation (2), we get:

4y + 119 = 180

4y = 61

y = 15.25

Substituting this value of y in equation (3) and solving for x, we get:

(7x + 1) + (7*15.25 + 1) = 180

7x + 106 = 180

7x = 74

x = 10.57

Therefore, the value of x is approximately 10.57 and the value of y is approximately 15.25.

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Thus, the values of x,y, and z for the similar triangles are obtained:

Part A: y = 6.70; z = 13.41 and x = 6.

Part B: z = 17.88 ; y = 35.77 and x = 32.

Congruent triangles and similar triangles are two distinct but closely related concepts. There are two different kinds of similar triangle problems: those that ask you to determine whether a set of triangles is similar and those that ask you to determine the angles and side length of similar triangles that are missing.

Part A: using similarity of the triangle, taking the ratios of corresponding side.

y/15 = x/z = 3/y

Consider

y/15 = 3/y

y² = 15*3

y² = 45

y = 6.70

Now,

applying Pythagorean theorem:

y² = 3² + x²

x² = y² - 3²

x² = 45 - 9

x² = 36

x = 6

And,

z² = 12² + x²

z² = 144 + 36

z² = 180

z = 13.41

Part B:using similarity of the triangle, taking the ratios of corresponding side.

z/(x + 8) = 16/y = 8/x  ... eq 1

applying Pythagorean theorem:

z² = 16² + 8²

z² = 256 + 64

z² = 320

z = 17.88

Now, from eq 1

z² = 8(8 +x)

320 = 64 + 8x

8x = 320 - 64

x = 256/8

x = 32

Now,

applying Pythagorean theorem:

y² = 16² + x²

y² = 256 + 32²

y² = 1280

y = 35.77

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