To assess the accuracy of a laboratory scale, a standard weight known to weigh 1 gram is repeatedly weighed a total of n times How large should n be so that a 95% confidence interval for µ has a margin of error of ± 0.0001?

Answer:

100%

Step-by-step explanation:

The initial price of the paper = 1.99

The final price of the pack of paper = 3.98

We need to find the percentage increase in the price of the product. It can be solved as follows :

\(\%=\dfrac{3.98-1.99}{1.99}\times 100\\\\=100\%\)

So, the percentage increase in the price of the product is 100%.

Answer:

626.71 cm^2

Step-by-step explanation:

Area of figure = area of half circle + Area of half circle + area of a rectangle

here, diameter=15 cm

radius = 15/2=7.5 cm

length=30cm

breadth=15cm

Now

Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth

=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15

=626.71 cm^2

Answer:

-2

Step-by-step explanation:

So we want to find the value of:

\((-6)+(4)\)

Simply add:

\((-6)+4=-2\)

Thus, drop the word SUM on -2.

Further notes:

To use the number line to solve, first start by placing your point on -6.

Since we are adding 4 to -6, we move to the right. Thus, move from -6 four spaces to the right.

If you do so correctly, you will end up at -2, the same answer we acquired previously.

Answer:

\(\Huge \boxed{-2}\)

Step-by-step explanation:

The sum is the result from adding two or more numbers to each other.

\(-6 + 4 = - 2\)

-6 is the starting point on the number line.

4 is added to -6, so an arrow from -6 goes 4 units to the right of the number line.

The arrow stops at -2.

The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.

In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.

The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.

Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°

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Answer:he sales tax is determined by computing a percent of the purchase price. To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price.

Step-by-step explanation:

will this help

Answer : 15.5 pounds

To ship Liam's package using National parcel

The flat fee rate is $15.76

Let x be the weight of the items in pounds

THey charged $1.53 per pound

Total cost = flat rate charge + charge per pounds x the weight in pounds

Total cost = 15.76 + 1.53 * x

Total cost = 15.76 + 1.53x -------------- equation 1

Using Statewide shipping

It charges a flat fee of $19.48 and $1.29 per pound

Total cost = flat rate charge + charge per pounds x the weight in pounds

Total cost = 19.48 + 1.29 * x

Total cost = 19.48 + 1.29x --------------- equation 2

To calculate how many pounds Liam's package weigh for National Parcel's total charge to be the same as Statewide Shipping's total charge, then, we need to equate the both equation

Equate equation 1 and 2

15.76 + 1.53x = 19.48 + 1.29x

Collect the like terms

19.48 - 15.76 = 1.53x - 1.29x

3.72 = 0.24x

Divide both sides by 0.24

x = 3.72 / 0.24

x = 15.5 pounds

The amount of pounds must Liam's package weigh for National Parcel's total charge to be the same as Statewide Shipping's total charge is 15.5 pounds

The term "100 points" usually indicates a high level of achievement or success in a particular area.

The term "100 points" can refer to a number of different things depending on the context. For example, in sports, it could refer to a team scoring 100 points in a game.

In wine tasting, it could refer to a perfect score given to a wine by a critic or judge. In school, it could refer to receiving a perfect score on an exam or assignment worth 100 points.

It's important to note that while a perfect score of 100 points is often seen as the ultimate goal, it's not always necessary or even possible in some situations. In many cases, simply doing your best and striving for improvement is enough to be considered successful.

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Answer:

\(x^2+(y-5)^2=49\)

Step-by-step explanation:

Recall the formula for the graph of a circle:

\((x-h)^2+(y-k)^2=r^2\\\)

Where h is the x-coordinate of the vertex, k is the y-coordinate of the vertex, and r is the radius.

We are given the vertex and the length of the radius.

Substitute the values:

\((x-0)^2+(y-5)^2=7^2=\\x^2+(y-5)^2=49\)

Thus, the standard form is:

\(x^2+(y-5)^2=49\)

The measure of angle ADC in the geometric system is equal to 55°.

In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:

m ∠ CDE + m ∠ EDF = 180°

(2 · x + 1) + (x - 7) = 180°

3 · x - 6 = 180°

3 · x = 186°

x = 62

m ∠ CDE = 2 · x + 1

m ∠ CDE = 2 · 62 + 1

m ∠ CDE = 125°

m ∠ ADC = 180° - 125°

m ∠ ADC = 55°

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The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

We have,

To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:

CI = X ± (Z * (σ/√n))

where:

CI is the confidence interval

X is the sample mean

Z is the critical value corresponding to the desired confidence level (90% confidence level corresponds to Z = 1.645 for a large sample size)

σ is the population standard deviation

n is the sample size

Given that the sample mean X of the net change in LDL cholesterol is 2.7, the standard deviation (σ) is 17.8, and the sample size (n) is 47, we can calculate the confidence interval as follows:

CI = 2.7 ± (1.645 * (17.8/√47))

Calculating the standard error (SE):

SE = σ/√n = 17.8/√47 ≈ 2.587

Substituting the values into the confidence interval formula:

CI = 2.7 ± (1.645 * 2.587)

Calculating the upper and lower bounds of the confidence interval:

Upper bound = 2.7 + (1.645 * 2.587) ≈ 7.199

Lower bound = 2.7 - (1.645 * 2.587) ≈ -1.799

Therefore, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199.

Interpreting the confidence interval:

Since the confidence interval contains both positive and negative values, it suggests that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

The interval includes zero, indicating that there is a possibility that the mean net change in LDL cholesterol after the garlic treatment could be zero (no change).

However, it is important to note that further studies or a larger sample size may be needed to draw more definitive conclusions.

Thus,

The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

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The 90% confidence interval suggests that the true mean net change in LDL cholesterol after the garlic treatment lies between -1.57 and 6.97 mg/dL. Since the interval contains both positive and negative values, it indicates that the garlic treatment may or may not be effective in reducing LDL cholesterol.

To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:

CI = mean ± (Z * (standard deviation / √n))

Here, n represents the sample size (47), Z is the critical value corresponding to a 90% confidence level (Z = 1.645 for a 90% confidence level), and the mean is 2.7 with a standard deviation of 17.8.

Plugging in the values:

CI = 2.7 ± (1.645 * (17.8 / √47))

CI = 2.7 ± (1.645 * (17.8 / 6.856))

CI = 2.7 ± (1.645 * (2.596))

CI = 2.7 ± 4.270

CI = 2.7 + 4.270  ;  CI = 2.7 - 4.270

CI = 6.97             ;  CI = -1.57

Thus, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately (-1.57, 6.97).

The confidence interval suggests that the effectiveness of garlic in reducing LDL cholesterol is inconclusive. The interval spans both positive and negative values, indicating that the true mean change in LDL cholesterol could be anywhere within this range. Further research or a larger sample size might be needed to draw a more definitive conclusion about the effectiveness of garlic in lowering LDL cholesterol.

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Answer:

Answer 120.15 minutes long

Step-by-step explanation:

Answer:

129.00m

Step-by-step explanation:

1h=60m

2.15=x

2.15h×60m=1h×x

129m×h=1h×x divided both side by 1h

129m=x

There are 2518 sets of five marbles that include either the lavender one or exactly one yellow one, but not both.

To solve this problem, we need to find the number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both colors. Here's one way to approach the problem:

Number of sets of five marbles that include the lavender one: There is only one lavender marble, so we can choose any 4 other marbles to go with it.

There are a total of 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 7 x 6 x 5 x 4 = 840 possible sets of five marbles that include the lavender one.

Number of sets of five marbles that include exactly one yellow one: There are two yellow marbles,

So there are 2 possible choices for the yellow marble. For each choice, we can choose any 4 other marbles to go with it.

As before, there are 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 2 x (7 x 6 x 5 x 4) = 1680 possible sets of five marbles that include exactly one yellow one.

Number of sets of five marbles that include both the lavender one and exactly one yellow one:

We need to subtract these sets from the total number of sets that include either the lavender one or exactly one yellow one.

We have already found that there are 840 sets of five marbles that include the lavender one, and 1680 that include exactly one yellow one.

To find the number of sets that include both, we can choose any one yellow marble and the lavender one.

There are 2 choices for the yellow marble and 1 choice for the lavender one,

So there are 2 x 1 = 2 possible sets of five marbles that include both the lavender one and exactly one yellow one.

Number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both:

Finally, we need to subtract the number of sets that include both the lavender one and exactly one yellow one from the total number of sets that include either the lavender one or exactly one yellow one.

The total number of sets that include either the lavender one or exactly one yellow one is 840 + 1680 = 2520. The number of sets that include both is 2,

So the number of sets that include either the lavender one or exactly one yellow one, but not both, is 2520 - 2 = 2518.

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ANSWER

EXPLANATION

Given;

Recall surface area of a box is calculated using;

Answer:

\( \sqrt{55}\)

Step-by-step explanation:

Given is a right angled triangle.

Therefore, by Pythagoras theorem:

\( {x}^{2} = {8}^{2} - {3}^{2} \\ = 64 - 9 \\ = 55 \\ x = \sqrt{55} \)

Answer:

x<= 8  ( Answer  not in the given options)

Step-by-step explanation:

9x <= 9

divide both sides by 9 to get x

9x   <=  72

9           9

x <=  8

Answer:

3/36 or 8.333

Step-by-step explanation:

the way you get it is write all the possibilities and that how you get 3/36

Answer: Approximately 9.33 square units

As a fraction, this is exactly 28/3

=========================================================

Explanation:

Let's say the height of the upper-left smallest rectangle (area 6) has height of 2. This height doesn't matter and can be anything you want, and it won't affect the final answer.

This means its horizontal portion of area 6 is 6/2 = 3 units across.

The horizontal portion of 3 corresponds directly to the horizontal part of the lower left rectangle (area 7) as well. The height of this rectangle is 7/3. We'll come back to this later.

Since the height of area 6 is 2 units, this also the height of area 8. The horizontal portion of area 8 must be 8/2 = 4 units.

Since the horizontal portion of area 8 is 4 units, and the vertical portion of area 7 is 7/3, this makes the area we're after to be 4*(7/3) = 28/3 = 9.33 approximately.

The inequality graphed on the number line can be written as:

-3 ≤ x < 2

Here we can see an inequality graphed on a number line, we can see that we start with a closed circle at x = -3

A closed circle means that x = -3 is a solution.

And we can see that it ends with an open circle at x = 2, the open circle means that the point is not a solution.

Then the inequality thati is shown in the number line is written as:

-3 ≤ x < 2

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Given:

Number of points scored = 25

The score was 3 more than twice the number of points Alex scored.

Let's write an equation that can be used to find the number of points Alex scored.

Let a represent the number of points Alex scored.

Here, we have the statement: 3 more than twice the number of points.

The expression below represents the statement:

2a + 3

Therefore, the equation that can be used to find a is:

2a + 3 = 25

ANSWER:

2a + 3 = 25

9514 1404 393

Explanation:

For this purpose, we define your power function as ...

  f(x) = a·x^n

Most of the description here applies to any function. A "power function" is a special case of a polynomial function in that it only has one term. The parity of the exponent (even, odd) tells you whether the function is even or odd. As with any even or odd function, there will be a certain symmetry:

  f(-x) = f(x) . . . even function; symmetrical about the y-axis

  f(-x) = -f(x) . . . odd function; symmetrical about the origin

__

The coefficient of the function is the vertical scale factor. As with the vertical scale factor of any function, when it is negative, the function graph is reflected in the x-axis. When it increases in magnitude, points on the graph move farther from the x-axis; closer when it decreases.

__

A) The red graphs in the first attachment are graphs of f(x) = ax^2 for different values of 'a'. As described above, the graph is symmetrical about the y-axis.

B) The black graphs in the first attachment are graphs of f(x) = ax^3 for different values of 'a'. As described above, the graph is symmetrical about the origin.

C) As described above, when the coefficient is negative, the graph of the parent function is reflected across the x-axis. The dashed-line graphs in the first attachment are graphs of the function with a negative coefficient.

D) As described above, the coefficient is the vertical scale factor. Changing it stretches or compresses the graph vertically. The dotted red graph in the first attachment shows a vertical expansion; the dashed black graph shows a vertical compression (reduction in the coefficient magnitude).

__

The second attachment shows graphs with negative exponents. Otherwise, the graphs are scaled and reflected the same as they were in Part 1.

A) As described above, the graph is symmetrical about the y-axis.

B) As described above, the graph is symmetrical about the origin.

C) As described above, a negative coefficient causes the graph to be reflected across the x-axis.

D) As described above, the magnitude of the coefficient affects the distance of the graph from the x-axis. Increasing magnitude increases the distance; decreasing magnitude decreases the distance (proportionally).

The value of x in the linear equation −0.28x − 15.3 = 1.92 is -61.5 option (B) -61.5 is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The linear equation one variable is:

−0.28x − 15.3 = 1.92

-0.28x = 1.92 + 15.3

-0.28x = 17.22

x = -17.22/0.28

x = -61.5

Thus, the value of x in the linear equation −0.28x − 15.3 = 1.92 is -61.5 option (B) -61.5 is correct.

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Answer:

its B -61.5

Step-by-step explanation:

i attched pictures to show you

Answer:

(m-6+2root3)(m-6-2root3)

Step-by-step explanation:

m^2 - 12m +36 -12

= (m-6)^2 - 12

= (m-6+2root3)(m-6-2root3)[root 12 = 2root3]

Answer:

slope=0

Step-by-step explanation:

Conceptually, y never changes, which means the line is a straight horizontal line.

Mathematically, slope is the change in y over the change in x. For example, if we use the first 2 points:

\(\frac{2-2}{1-3} =\frac{0}{-2} =0\)

Because 0 divided by anything is still 0.

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

Answer:

D

Step-by-step explanation:

The perimeter is 54.6.

a   +  3a      + b = 54.6.   since a = 8.7,

8.7 + 3(8.7) + b = 54.6

8.7 + 26.1 + b = 54.6

34.8 + b = 54.6

b = 54.6 - 34.8

b = 19.8

They pretty much have the exact same examples in the instruction videos with different numbers; it helps to watch the videos again.

Answer:

15:21 = 5:7

Step-by-step explanation:

21/7 = 3

5 x 3 = 15