A rectangle measures 8.5 cm by 10.7 cm both correct to 1 decimal place.
Calculate the upper bound of the perimeter of the rectangle​

Answer:

D. 246 grams

Step-by-step explanation:

invnorm(.95, 240, 3) is around 244 and the question is asking for the least weight of a bag in the top 95%, so the smallest number within

a. 234

b. 240

c. 243

d. 246

e. 248

is d.

The distribution of the mix follows inverse normal distribution

The least weight of a bag in the top 5% is 246 grams

The given parameters are:

\(\mathbf{\mu = 240}\) ---- population mean

\(\mathbf{\sigma = 3}\) ---- population standard deviation

To get the least weight of a bag in the top 5%, we make use of inverse normal distribution.

So, we have:

\(\mathbf{Least = invNorm(p,[\mu,\sigma])}\)

Being in the top 5% means that:

p = 1 - 5%

p = 1 - 0.05

p = 0.95

So, we have:

\(\mathbf{Least = invNorm(0.95,240,3)}\)

From the inverse normal calculator, we have

\(\mathbf{Least = 246}\)

Hence, the least weight is 246 grams

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Explanation:

1) C = 5/9 f + 32

The start value is the constant = 32.

The start value = 32

Growth value = rate of change

Growth value = 5/9

2) y = 4000 - 250x

The start value is the constant = 4000

The start value = 4000

Answer:

Multiply the number by 3 to get the next number.

Step-by-step explanation:

Answer:

Probability = \(\frac{3}{5}\)

Step-by-step explanation:

Length of segment AD = 12 units

Since, AC = CD

Therefore, AC = CD = \(\frac{12}{2}\) = 6 units

Since, AB = BC

Therefore, AB = BC = \(\frac{1}{2}AC\) = 3 units

Number of total segments = 5

Number of segments having measure greater than three = 3

(AC = CD = 6 units and AD = 12 units)

Probability that the measure of a segment is greater than 3

= \(\frac{\text{Number of segments measuring greater than 3}}{\text{Total number of segments}}\)

= \(\frac{3}{5}\)

Answer:

number of students in a van = 8

number of students in a minibus = 22

Step-by-step explanation:

Let

x = number of students in a van

y = number of students in a minibus

8x + 8y = 240 (1)

4x + y = 54 (2)

Multiply (2) by 8 to eliminate y

4x + y = 54 ×8

32x + 8y = 432 (3)

8x + 8y = 240 (1)

32x + 8y = 432 (3)

Subtract (1) from (3)

32x - 8x = 432 - 240

24x = 192

Divide both sides by 24

x = 192 / 24

= 8

x = 8 students

Substitute x = 8 into (2)

4x + y = 54

4(8) + y = 54

32 + y = 54

y = 54 - 32

= 22

y = 22 students

number of students in a van = 8

number of students in a minibus = 22

Based on the information given, it should be noted that the sentences are modified below.

a. Across the hall from the fossils exhibit are the exhibits for insects and spiders.

b. Desperately poor in Japan, Sayuri becomes a successful geisha after growing up.

c. What caused Mount St. Helens to erupt is interesting to consider. Researchers believe that a series of earthquakes in the area was a contributing factor.

d. Ice cream typically contains 10 percent milk fat, but premium ice cream may contain up to 16 percent milk fat and has considerably less air in the product.

e. If home values climb, the economy may recover more quickly than expected.

Looking wearily into the cameras of US government photographers, the Dust Bowl farmers represented the harshest effects of the Great Depression..

The Trans Alaska Pipeline, which was completed in 1977, has moved more than fifteen billion barrels of oil since then.

Habitually, Mr. Guo dresses in loose clothing and canvas shoes for his wushu workout.

Strategically placed throughout a firefighter training maze are a number of obstacles.

Ian McKellen is a British actor. He made his debut in 1961 and was knighted in 1991. He played Gandalf in the movie trilogy The Lord of the Rings.

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B. The statement is true.

Answer:

d

Step-by-step explanation:

Answer:

C. 23

Hope this helps :-D

Answer:

2x^3-5x^2-17x+20

Step-by-step explanation:

Answer: 2x^3 - 5x^2 - 17x + 20

Step-by-step explanation: just simplify it

The height of the cylinder is 3 inches if the cylinder has a volume of 12π cubic inches and a diameter of 4 inches.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

\(\rm V = \pi r^2 h\)

We have:

Volume of the cylinder = 12π cubic inches

Dimeter of the cylinder = 4 inches

Radius of the cylinder = 2 inches

Here no other information is given in the question, Let suppose it is required to find the height of the cylinder

12π = π(2)²h

12  = 4h

h = 3 inches

Thus, the height of the cylinder is 3 inches if the cylinder has a volume of 12π cubic inches and a diameter of 4 inches.

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The piecewise function that describes what the instructor charges is; f(x) = 500x , 0 < x ≤ 10

400x , 10 < x < 25

350x , x ≥ 25

Let x represent the number of participants and let y represent the charge per participant.

Now, y depends on x, and as such we can say that;

f(x) = y

For, 0 < x ≤ 10, the total charges is 500x,

f(x) = 500x , 0 < x ≤ 10

For 10 < x < 25, total charge is 400x,

f(x) = 400x , 10 < x < 25

For x ≥ 25, the total charge is 350

f(x) = 350x x ≥ 25

Therefore, we can say that;

f(x) = 500x , 0 < x ≤ 10

400x , 10 < x < 25

350x , x ≥ 25

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Write the piecewise function that describes what the instructor charges.

Answer: Its B and C

Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 3 x minus 5 = negative 2 x + 10? Select two options.

x = 5

–15 = –5x

5x = 15

–15 = 5x

x = -5

The volume of the Parallelepiped with adjacent edges pq, pr,and ps = 136

Geometrically, the Scalar triple product:

\({\displaystyle \mathbf {a} \cdot (\mathbf {b} \times \mathbf {c} )} \mathbf{a}\cdot(\mathbf{b}\times \mathbf{c})\)

is the (signed) volume of the parallelepiped defined by the three vectors given. Here, the parentheses may be omitted without causing ambiguity, since the dot product cannot be evaluated first. If it were, it would leave the cross product of a scalar and a vector, which is not defined.

Given three vectors, there is a product, called scalar triple product, that gives , the volume of the parallelepiped that has the three vectors as dimensions.

So,

Given : p(-2,1,0) , q(3,4,3), r(1,4,-1), s(3,6,4).

pq =  ( -2-3 ,1-4 ,0-3) = (-5,-3,-3)

pr= (-2-1, 1-4, 0+1) = (-3,-3,1)

ps= ( -2-3, 1-6, 0-4) = (-5,-5,-4)

pq = (-5  ,  -3  , -3)

pr = (-3,  -3,  1)

ps= (-5,  -5,  -4)

The scalar triple product is given by the determinant of the matrix (3×3)

that has in the rows the three components of the three vectors:

\(\left[\begin{array}{ccc}-5&-3&-3\\-3&-3&1\\-5&-5&-4\end{array}\right] \\\\-5(12+5)-3(12+5)-3(15-15)\\-5(17)-3(17)-3(0)\\-85-51\\-136\\\)

So, The volume never be negative then by applying vector

v = |-136|

v= 136

the volume of the parallelepiped with adjacent edges pq, pr,and ps = 136

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Answer:

The two rules we need to use are:

Sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)

cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)

And we also know that:

sin^2(a) + cos^2(a) = 1

To solve the relations, we start with the left side and try to construct the right side.

a) Sin(3*A) = sin (2*A + A) = sin(2*A)*cos(A) + sin(A)*cos(2*A)

sin(A + A)*cos(A) + sin(A)*cos(A + A)

(sin(A)*cos(A) + sin(A)*cos(A))*cos(A) + sin(A)*(cos(A)*cos(A) - sin(A)*sin(A))

sin(A)*cos^2(A) + sin(A)*cos^2(A) + sin(A)*cos^2(A) - sin^3(A)

3*sin(A)*cos^2(A) - sin(A)*sin^2(A)

sin(A)*(3*cos^2(A) - sin^2(A))

Now we can add and subtract 4*sin^3(A)

sin(A)*(3*cos^2(A) - sin^2(A)) + 4*sin^3(A) -  4*sin^3(A)

sin(A)*(3*cos^2(A) + 3*sin^2(A)) - 4*sin^3(A)

sin(A)*3*(cos^2(A) + sin^2(A)) - 4*sin^3(A)

3*sin(A) - 4*sin^3(A)

b) Here we do the same as before:

cos(3*A) = 4*cos^3(A) - 3*cos(A)

We start with:

Cos(2*A + A) =  cos(2*A)*cos(A) - sin(2*A)*sin(A)

= cos(A + A)*cos(A) - sin(A + A)*sin(A)

= (cos(A)*cos(A) - sin(A)*sin(A))*cos(A) - ( sin(A)*cos(A) + sin(A)*cos(A))*sin(A)

= (cos^2(A) - sin^2(A))*cos(A) - sin^2(A)*cos(A) - sin^2(A)*cos(A)

= cos^3(A) - 3*sin^2(A)*cos(A)

=  cos(A)*(cos^2(A) - 3*sin^2(A))

now we subtract and add 4*cos^3(A)

= cos(A)*(cos^2(A) - 3*sin^2(A)) + 4*cos^3(A) - 4*cos^3(A)

= cos(A)*(-3*cos^2(A) - 3*sin^2(A)) + 4*cos^3(A)

= cos(A)*(-3)*(cos^2(A) + sin^2(A)) + 4*cos^3(A)

= -3*cos(A) + 4*cos^3(A)

First, let's convert all of our denominators to 12 so we can make comparing the fractions easier.

1/3 * 4 = 4/12. 2/3 * 4 = 8/12.

Now that both of our fractions have a denominator of 12, we can compare the fractions!

4/12 (1/3) < 7/12.

8/12 (2/3) > 7/12

Now we have our answer

While Brian traveled, the pilot taught him A. how to steer a Cessna 406.

The Cessna 406 is a twin-engine aircraft that is commonly used for various purposes, such as air ambulance services, freight transport, and surveillance operations. Steering the aircraft is an essential skill that any pilot must learn in order to control the aircraft's direction of flight.

Learning how to steer a Cessna 406 would be an important skill for Brian to acquire if he was planning to become a pilot or work in the aviation industry.

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The probability that you draw a sphere given that it is blue is given as follows:

5/7.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The total outcomes in this problem are the blue shapes, hence the number is given as follows:

6 + 15 = 21 shapes.

The desired outcomes are the blue spheres, hence the number is given as follows:

15.

Hence the probability that you draw a sphere given that it is blue is given as follows:

p = 15/21

p = 5/7. (simplify numerator and denominator by 3).

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The correct interpretation of the 90% confidence interval is: c) 90% of the time, Kat can be certain that the calculated interval (22.96, 26.64) accurately represents the real average number of eggs that chickens on this farm lay.

What is confidence interval?

An predicted range of values for the true population parameter is known as a confidence interval.

The calculation for the 90% confidence interval can be done using the formula:

Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √(Sample Size))

Given:

Sample Mean (x) = 24.8 eggs

Standard Deviation (σ) = 6.9 eggs

Sample Size (n) = 40

Confidence Level = 90%

For a 90% confidence level, the critical value is approximately 1.645.

Now, plug in the values into the formula:

Confidence Interval = 24.8 ± (1.645 * 6.9 / √(40))

Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size:

SE = 6.9 / √(40)

Calculate the margin of error by multiplying the critical value with the standard error:

Margin of Error = 1.645 * SE

Finally, calculate the confidence interval:

Confidence Interval = 24.8 ± Margin of Error

Perform the calculations to find the lower and upper bounds of the confidence interval:

Lower Bound = 24.8 - Margin of Error

Upper Bound = 24.8 + Margin of Error

The resulting confidence interval is (22.96, 26.64).In this case, the confidence interval (22.96, 26.64) is constructed based on the sample mean of 24.8 and the standard deviation of 6.9.

Option c correctly states that Kat can be 90% confident that the true mean number of eggs chickens from this farm lay falls within the interval (22.96, 26.64). This means that if we were to repeat the sampling process multiple times and construct confidence intervals, about 90% of those intervals would contain the true mean.

Options a and b are incorrect because they do not accurately describe the interpretation of a confidence interval. Option d is also incorrect as it mentions "repeated sampling" but does not accurately convey the meaning of the confidence interval capturing the true mean.

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Answer:

3.92*10^3mm

Step-by-step explanation:

In the diagram it gives you 7900mm. There is a figure which was given underneath written 900mm. use 7900 to subtract 900 you will get 7000. Then you can use the Pythagoras theorem to solve it, with a= height, b=5800mm and c=7000mm where, a^2+b^2=c^2.

Answer:

3919 mm

Step-by-step explanation:

Length of hypotenuse = 7900 - 900 = 7000 mm

Base = 5800 mm

Let the height of the triangle be h mm

Therefore, by Pythagoras theorem:

\( h = \sqrt{7000^2 - 5800^2} \)

\( h = \sqrt{49000000- 33,640,000} \)

\( h = \sqrt{15,360,000} \)

\( h = 3,919.18359\: mm\)

\( h = 3,919\: mm\)

1. AUB = {a, b, d, e}

2. AUC = {a, b, d, e}

3. BUC = {a, b, d, e}

In each case, the union includes the elements shared between the sets and the unique elements from each set, without repetitions.

To determine the union of the given subsets, we need to combine all the elements without repetition. Let's analyze each case:

1. AUB:

The set A contains the elements {a, b, d}, and the set B contains the elements {b, d, e}. By combining both sets, we obtain the union AUB = {a, b, d, e}. This is the collection of all the elements that appear in either A or B, without duplicates.

2. AUC:

The set A contains the elements {a, b, d}, and the set C contains the elements {a, b, e}. By combining both sets, we obtain the union AUC = {a, b, d, e}. Once again, this set includes all the elements that appear in either A or C, without repetition.

3. BUC:

The set B contains the elements {b, d, e}, and the set C contains the elements {a, b, e}. By combining both sets, we obtain the union BUC = {a, b, d, e}. Similarly, this set represents all the elements that appear in either B or C, without duplicates.

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Answer: \(90\leq 2x-44\leq 95\)

Step-by-step explanation:

Answer:

Length = 18 ft

Width = 4 ft

Step-by-step explanation:

Let the width of the rectangle be x ft

Therefore, length = (x + 14) ft

Area of rectangle = 72 sq ft

\( \therefore \: x(x + 14) = 72 \\ \therefore \: {x}^{2} + 14x - 72 = 0 \\\therefore \: {x}^{2} + 18x - 4x - 72 = 0 \\\therefore \: x(x + 18) - 4(x + 18) = 0 \\ \therefore \:(x + 18)(x - 4) = 0 \\ \therefore \:x + 18 = 0 \: \: or \: \: x - 4 = 0 \\ \therefore \:x = - 18 \: or \: \: x = 4 \\ \because \: dimensions \: of \: a \: rectangle \: \\ cn \: not \: be \: negative \\ \therefore \: x \neq \: - 18 \\ \implies \: x = 4 \\ \therefore \: x + 14 = 4 + 18 = 18 \\ length \: of \:the \: rectangle \: = 18 \: ft \\ width \: of \: the \: rectangle = 4 \: ft\)

Answer:

<RSQ and <WVX

Step-by-step explanation:

suplementary angles are 2 angles who's measures add to 180

Answer:

Emily is solving the following system of equations using substitution:

y = 3x - 4

y = 2x + 1

Part A:

After substituting y's values:

3x - 4 = 2x + 1

What she did:

3x - 4 = 2x + 1

3x + 2x - 4 = 1

5x - 4 = 1

What she should have done:

3x - 4 = 2x + 1

3x - 2x - 4 = 1

x - 4 = 1

Part B:

This rule has not been followed: Sign changes when numbers shift from left to right of ' = 'sign.

Emily did not changed the sign of the number, 2x from + 2x to - 2x when it was moved from the right side to the left.

\(\)

A plasmid used in both yeast and bacteria requires two different selection markers because the same selection may not work for both hosts and bacteria and yeast recognize different promoters.

When using a plasmid in both yeast and bacteria, it is important to have two different selection markers for several reasons. First, the same selection, such as the presence of an antibiotic, may not be effective in both hosts. Different organisms have varying sensitivities to antibiotics, so a marker that works in bacteria may not work in yeast or vice versa. Therefore, two different selection markers are needed to ensure successful selection in both hosts.

Additionally, bacteria and yeast recognize different promoters, which are DNA sequences that control the initiation of gene expression. Promoters are specific to each organism and play a crucial role in regulating gene expression. By incorporating two different selection markers into the plasmid, each marker can be driven by a promoter recognized specifically by the corresponding host. This ensures that the selection marker is effectively expressed in the appropriate host organism, enabling accurate selection and maintenance of the plasmid.

In summary, using two different selection markers in a plasmid intended for both yeast and bacteria is necessary because the same selection may not be effective in both hosts, and different promoters are recognized by bacteria and yeast. This approach allows for successful selection and maintenance of the plasmid in both organisms.

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Answer:

8 boxes approx

Step-by-step explanation:

Step one:

given data

One box contains 48 bars

Required

The number of boxes needed for a total of 338 students if each person is to get at least one bar.

Step two:

this can be gotten by dividing 338 by the number of the bar in a box

= 338/48

=7.04

=8 boxes approx

He needs to purchase at least 8 box

a. {w : w does not contain substring 01}:

This set contains all possible strings that do not have the substring "01". For example, the strings "0", "1", "00", "11", "10", "001", "000", "011", "111", "100", "0001", etc. are in this set, but the strings "01", "101", "010", "0110", etc. are not.

b. {w : every even position of w is a 1}:

This set contains all possible strings where every character at an even position (including the first character, which is at position 0) is a 1. For example, the strings "1", "1111", "10101", "111111", "1000001", etc. are in this set, but the strings "0", "01", "10", "101", "0110", etc. are not.

c. {w : w contains at least one 0 and at least one 1}:

This set contains all possible strings that have at least one 0 and at least one 1. For example, the strings "0", "1", "10", "01", "101", "010", "001", "110", "011", "1001", "1110", "10101", etc. are in this set, but the strings "00", "11", "000", "111", "0000", "1111", etc. are not.

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The correct answer is option b. Burger Quick, because it has a larger mean.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to gather, analyze, and interpret data from various fields, including business, economics, medicine, engineering, psychology, and social sciences. Statistics allows researchers and analysts to draw conclusions and make predictions based on data, and is used in a wide range of applications, from designing experiments and conducting surveys to testing hypotheses and making decisions based on data-driven insights.

Burger Quick typically has more wait time, because it has a larger interquartile range (IQR) and a larger upper whisker on the box plot, indicating that there is more variability in the wait times and some customers have experienced longer wait times. Although the median wait time for Burger Quick is also larger, it is the IQR and upper whisker that provide more evidence for the longer wait times. The mean is not shown on the box plot and therefore cannot be used to determine which drive-thru typically has more wait time.

Therefore, the correct answer is option b. Burger Quick, because it has a larger mean.

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