five rectangles, and have integer side lengths. rectangle has a width of , rectangle has a width of rectangle has a length of rectangle has a length of and rectangle has a length of if all five rectangles have the same area , what is the least possible value of ?

Answers

Answer 1

All five rectangles have the same area of 60, and the sum of their dimensions is:

2 + 30 + 4 + 15 + 6 + 10 + 8 + 7.5 + 10

Let the width of rectangle 1 be w1, the width of rectangle 2 be w2, and so on. We know that all five rectangles have the same area, so we can set up an equation:

[tex]w1 * l1 = w2 * l2 = w3 * l3 = w4 * l4 = w5 * l5[/tex]

We can simplify this equation by dividing both sides by w1 * l1, which gives:

[tex]1 = (w2 * l2) / (w1 * l1) = (w3 * l3) / (w1 * l1) = (w4 * l4) / (w1 * l1) = (w5 * l5) / (w1 * l1)[/tex]

Let's define a new variable x = w2 * l2 = w3 * l3 = w4 * l4 = w5 * l5. Then we have:

[tex]w1 * l1 = xw2 * l2 = xw3 * l3 = xw4 * l4 = xw5 * l5 = x[/tex]

Now we need to find the least possible value of w1 + l1 + w2 + l2 + w3 + l3 + w4 + l4 + w5 + l5. Since w1 * l1 = x, we can rewrite this as:

[tex]w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x)[/tex]

To find the minimum value of this expression, we can take its derivative with respect to w1, set it equal to zero, and solve for w1:

[tex]d/dw1 (w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x)) = 1 - 2 * sqrt(x) / w1^1.5 + 2 * sqrt(x) / w1^2.5 = 0[/tex]

Solving for w1, we get:

[tex]w1 = 2 * x^(1/4)[/tex]

Substituting this back into our expression for the sum of the rectangle dimensions, we get:

[tex]w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x) = 2 * x^(1/4) + 2 * x^(3/4) + 8 * (x / 2)^(1/4)[/tex]

To find the minimum value of this expression, we can take its derivative with respect to x, set it equal to zero, and solve for x:

[tex]d/dx (2 * x^(1/4) + 2 * x^(3/4) + 8 * (x / 2)^(1/4)) = 1/2 * x^(-3/4) + 3/2 * x^(1/4) + 2 / (2 * x)^(3/4) = 0[/tex]

Solving for x, we get:

x = 4

Therefore, the least possible value of w1 is:

w1 =[tex]2 * x^(1/4) = 2[/tex]

And the dimensions of the rectangles are:

Rectangle 1: 2 x 30

Rectangle 2: 4 x 15

Rectangle 3: 6 x 10

Rectangle 4: 8 x 7.5

Rectangle 5: 10 x 6

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Related Questions

Consider a sequence whose first five terms are:-1.75, -0.5, 0.75, 2, 3.25
Which explicit function (with domain all integers n ≥ 1) could be used to define and continue this sequence?

Answers

Step-by-step explanation:

+ 1.25

every new term is the previous term + 1.25.

with starting value -1.75

f(n) = 1.25n - 1.75

Ms.Lewis is comparing computer at an electronic store. she asks the questions shown below. State whether each questions is statistical or not. Explain. What are the prices of the computers?​

Answers

The question "What are the prices of the computers?" is not a statistical question.

Identifying the type of question

A statistical question is a question that can be answered by collecting and analyzing data. It usually involves some variability or variation in the data, and the answer may vary depending on the sample or population being studied.

In this case, the question is asking for a specific piece of information - the prices of the computers - which can be obtained directly from the store or manufacturer. There is no variability or variation involved, and the answer is not dependent on any data collection or analysis.

Therefore, this question is not a statistical question.

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Find the number of permutations with of the letters in each word 1)CANNON
2)BANANA
3)TOMORROW
4)REFERENCE

Answers

The number of possible letter combinations in the words presented is as follows:

CANNON: 2520

BANANA: 120

TOMORROW: 2520

REFERENCE: 20160

What is permutation?

It is used to determine how many distinct arrangements can be made from a given set of elements.

1) CANNON: CANNON is made up of seven letters, two of which are identical 'N's. So, the following formula can be used to get the total number of permutations for CANNON:

Total number of permutations = 7! / 2!

= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 2520

2) BANANA: BANANA is made up of six letters, three of which are the letter 'A' and are similar. The total amount of BANANA combinations can be calculated using the formula below:

Total number of permutations = 6! / 3!

= (6 x 5 x 4 x 3 x 2 x 1) / 3!

= 120

3) TOMORROW: The word TOMORROW is made up of seven letters, two of which are identical 'O's. Thus, the sum of TOMORROW's permutations can be determined as follows:

Total number of permutations = 7! / 2!

= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 2520

4) REFERENCE: Eight letters make up REFERENCE, two of which are identical 'E's. So, the following formula can be used to determine the total number of permutations for REFERENCE:

Total number of permutations = 8! / 2!

= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 20160

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match the answers to the questions. ⚠️due tmr!

Answers

Below is the correct matching of the questions to the right answers

Mean average deviation - (C) The average deviation of the data from the mean.Range of a data set - (E) The difference between the highest value and the lowest value in a numerical data set.First quartile - (AB) The median in the lower half of the rank-ordered data.Second quartile - (B) The median value in the data set.Third quartile - (A) The median in the upper half of the rank-ordered data.Interquartile range - (D) The distance between the first and third quartiles of the data set.

What you should know about statistical measures

The statistical measures listed in the previous question are often used to describe and analyze statistical variables.

For instance, the range of a data set is a measure of the spread of values in a variable, while the quartiles and interquartile range provide information about the distribution of the variable. Mean average deviation is a measure of the variability of the variable around its mean value.

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1. Mean average deviation - The average deviation of the data from the mean.

2. Range of a data set - The difference between the highest value and the lowest value in a numerical data set.

3. First quartile - The median in the upper half of the rank-ordered data.

4. Second quartile - The median value in the data set.

5. Third quartile - The median in the lower half of the rank-ordered data.

6. Interquartile range - he distance between the first and third quartiles of the data set.

What you should know about statistical measures?

The statistical measures are often used to describe and analyze statistical variables. For instance, the range of a data set is a measure of the spread of values in a variable, while the quartiles and interquartile range provide information about the distribution of the variable. Mean average deviation is a measure of the variability of the variable around its mean value.

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PLEASE ANSWER ASAP
1. How many atoms are present in 8.500 mole of chlorine atoms?
2. Determine the mass (g) of 15.50 mole of oxygen.
3. Determine the number of moles of helium in 1.953 x 108 g of helium.
4. Calculate the number of atoms in 147.82 g of sulfur.
5. Determine the molar mass of Co.
6. Determine the formula mass of Ca3(PO4)2.
IT WOULD BE HELPFUL

Answers

The number of atoms present in 8.500 mole of chlorine atoms can be calculated using Avogadro's number, which is 6.022 x [tex]10^{23}[/tex] atoms per mole. Therefore:

Number of atoms = 8.500 mole x 6.022 x [tex]10^{23}[/tex]atoms/mole

Number of atoms = 5.1177 x [tex]10^{24}[/tex] atoms

Find out the mass (g) of 15.50 mole of oxygen?

The mass of 15.50 mole of oxygen can be calculated using the molar mass of oxygen, which is 16.00 g/mol. Therefore:

Mass = 15.50 mole x 16.00 g/mole

Mass = 248 g

The number of moles of helium in 1.953 x [tex]10^{8}[/tex] g of helium can be calculated using the molar mass of helium, which is 4.00 g/mol. Therefore:

Number of moles = 1.953 x [tex]10^{8}[/tex] g / 4.00 g/mol

Number of moles = 4.883 x [tex]10^{7}[/tex] mol

The number of atoms in 147.82 g of sulfur can be calculated using the molar mass of sulfur, which is 32.06 g/mol, and Avogadro's number. Therefore:

Number of moles = 147.82 g / 32.06 g/mol

Number of moles = 4.608 mol

Number of atoms = 4.608 mol x 6.022 x [tex]10^{23}[/tex] atoms/mol

Number of atoms = 2.773 x [tex]10^{24}[/tex] atoms

The molar mass of Co (cobalt) is 58.93 g/mol.

The formula mass of Ca3(PO4)2 can be calculated by adding the atomic masses of each element in the compound. The atomic masses are:

Ca = 40.08 g/mol

P = 30.97 g/mol

O = 16.00 g/mol

Formula mass = (3 x Ca) + (2 x P) + (8 x O)

Formula mass = (3 x 40.08 g/mol) + (2 x 30.97 g/mol) + (8 x 16.00 g/mol)

Formula mass = 310.18 g/mol

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as part of their quality assurance program, a cell phone manufacturer inspects the display on each phone selected through random sampling to verify that the screen displays all colors with the brilliance their customers have come to expect. each phone in a sample is turned on, run through a self-test procedure, and classified as either acceptable or unacceptable based on its test performance. suppose 30 phones are randomly tested each day for seven days, and the average daily proportion of unacceptable phones is found to be 0.01. what lower and upper control limits should the manufacturer actually use in the resulting control chart?

Answers

The lower and upper control limits that the manufacturer should use in the resulting control chart are LCL = 0.023,UCL = 0.043

To calculate the lower and upper control limits for the control chart, we need to use the following formula:
Lower control limit (LCL) = average proportion of defects - 3 x square root of [(average proportion of defects x (1 - average proportion of defects)) / sample size]
Upper control limit (UCL) = average proportion of defects + 3 x square root of [(average proportion of defects x (1 - average proportion of defects)) / sample size]
Using the given information, we can plug in the values to get:
LCL = 0.01 - 3 x square root of [(0.01 x 0.99) / 30] = -0.023
UCL = 0.01 + 3 x square root of [(0.01 x 0.99) / 30] = 0.043
However, since control limits cannot be negative, the lower control limit should be set to zero.

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The manufacturer should use control limits of 0 for the lower limit and 0.136 for the upper limit in their control chart for monitoring the proportion of unacceptable phones in their quality assurance program.

Determine the lower and upper control limits for the manufacturer's control chart, we first need to calculate the standard deviation of the proportion of unacceptable phones based on the given information.
To do this, we can use the formula:
[tex]Standard deviation = \sqrt(p\times(1-p)/n)[/tex]
p is the proportion of unacceptable phones (0.01), and n is the sample size (30 phones per day for 7 days = 210 total phones).
Plugging in these values, we get:
[tex]Standard deviation = \sqrt(0.01\times(1-0.01)/210) = 0.042[/tex]
Next, we can use this standard deviation to calculate the control limits. The lower control limit (LCL) is given by:
[tex][tex]LCL = p - 3\times\sqrt(p\times(1-p)/n)[/tex][/tex]
and the upper control limit (UCL) is given by:
[tex]UCL = p + 3\times\sqrt(p\times(1-p)/n)[/tex]
Plugging in our values, we get:
[tex]LCL = 0.01 - 3\times0.042 = -0.075[/tex]
[tex]UCL = 0.01 + 3\times0.042 = 0.095[/tex]
Values don't make sense - the proportion of unacceptable phones cannot be negative, and the UCL is above 1, which is also impossible.
To correct for this, we can use the formula:
[tex]LCL = max(0, p - 3\times\sqrt(p\times(1-p)/n))[/tex]
[tex]UCL = min(1, p + 3\times\sqrt(p\times(1-p)/n))[/tex]
This ensures that the control limits are within the range of possible values for the proportion of unacceptable phones.
Plugging in our values with this formula, we get:
[tex]LCL = max(0, 0.01 - 3\times0.042) = 0[/tex]
[tex]UCL = min(1, 0.01 + 3\times0.042) = 0.136[/tex]

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how many atheletes in total were acccused of using performance-enhancing drugs? of these, how many were using and how many were not? what percentage of those accused of using were falsely accused?

Answers

There have been numerous cases of athletes being accused of using performance-enhancing drugs, and the numbers may vary depending on the sport, country, and time period in question.

Additionally, determining how many athletes were using or not using performance-enhancing drugs would require specific information on individual cases.

Regarding the percentage of athletes falsely accused of using performance-enhancing drugs, it is difficult to determine an accurate figure without examining each case in detail. False accusations may occur due to various reasons, such as flawed testing procedures or contaminated supplements, and the percentage of false accusations may vary depending on the situation.

If you have a specific case or sport in mind, I can try to provide you with more information on that topic.

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Claire works at the Sweet Shop, where candy is bagged and sold by its weight. Claire's last 4 sales of gourmet gummy worms are shown in the table.

The cost of the gummy worms is proportional to the amount, in pounds, of gummy worms purchased.
This situation can be represented by an equation in the form y = kx, where k is the constant of proportionality.
Gourmet
Gummy Worms,
x (pounds)

Cost,
y
0.75 $6.30
2.5 $21.00
4 $33.60
7 $58.80
What is the constant of proportionality?

Answers

The constant of proportionality is $8.40

What is constant of proportionality?

The constant of proportionality is a value that relates two quantities that are proportional to each other. It is represented by the letter k and is found by dividing the dependent variable by the independent variable. In this case, the constant of proportionality is $8.40 for the given data set.

According to the given information:

To find the constant of proportionality, we can use any two data points from the table and plug them into the equation y = kx.

Let's use the first and second data points: (0.75, $6.30) and (2.5, $21.00).

We can set up the equation as:

$6.30 = k(0.75)

Solving for k, we get:

k = $6.30/0.75 = $8.40

Now, we can check our work by using another data point. Let's use the third data point: (4, $33.60).

Plugging in the values, we get:

$33.60 = k(4)

k = $33.60/4 = $8.40

Since we get the same value for k, we can be confident that our answer is correct.

Therefore, the constant of proportionality is $8.40.

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Find the nearest 10th the cylinder is 22 inches and 12.5 inches what is the lateral surface ?

Answers

Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².

What is surface area?

Surface area is the total area of the exposed surfaces of a three-dimensional object. It is measured in square units such as square centimeters (cm2) or square meters (m2). Surface area is an important concept in mathematics, science, and engineering, as it is the total area that determines properties such as friction, heat transfer, and fluid dynamics. For example, a larger surface area can increase the rate of heat transfer and allow for more efficient cooling. Similarly, a larger surface area can increase the friction between two objects, allowing them to grip better. Surface area is also important in chemistry, as it affects the amount of gas or liquid that can be absorbed or released by a given object.

The cylinder has a radius of 11 inches and a height of 12.5 inches. To find the lateral surface area of a cylinder, the formula used is A = 2πrℎ, where r is the radius and h is the height of the cylinder. After plugging in the values, the lateral surface area of the cylinder is 821.75 inches². Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².

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3. Soshi's rhombus has a base of 12 in. and a
height of 10 in. Jack's rhombus has base and
height measures that are double those of Soshis
rhombus. Compare the area of Jack's rhombus to
the area of Soshi's rhombus.

Answers

Answer:

The area of Jack's rhombus is four times the area of Soshi's rhombus.

Step-by-step explanation:

First, calculate the area of Soshi's rhombus. Use the formula for the area of a rhombus:

[tex]A = bh=\\A=(12)(10)=\\A=120[/tex]

Now, we have the Soshi's rhombus is 120 [tex]in^2[/tex].

Jack's rhombus' base and height are double those of Soshi's; multiply each value by two.

[tex]12*2=24\\\\10*2=20[/tex]

Now, substitute the values in the formula for the area of a rhombus:

[tex]A = bh=\\A=(24)(20)=\\A=480[/tex]

Notice that 480 is 4 times 120.

This is because area is a two-dimensional measure (measured in units squared, like [tex]in^2[/tex]) while length is a one-dimensional measure (measured in regular units, like cm and in), The one-dimensional measures of Jack's rhombus are double those of Soshi's, and to translate this to the two-dimensional measure of area, square 2 (2 squared is 2 times 2).

2 squared is 4, so:

the area of Jack's rhombus is four times that of Soshi's.

A circle with center O and radius 5 has central angle XOY. X and Y are points on the circle. ​If the measure of arc XY is 90 degrees, what is the length of chord XY?

Answers

The length of chord XY is 5√2.

What is the length of the chord?

It is described as the line segment that connects any two points on the circle's circumference without going through the circle's center. As a result, the diameter is the chord of a particular circle that is the longest and goes through its center. In mathematics, determining the chord's length can be crucial at times.

Here, we have

Given: A circle with center O and radius 5 has a central angle XOY. X and Y are points on the circle. ​If the measure of arc XY is 90 degrees.

We have to find the length of chord XY.

∠XOY = 90°

OX = OY = 5

We draw a perpendicular from the center to chord XY bisect XY at D.

Now, since OD bisects ∠XOY

∠XOD = ∠YOD = 90°/2 = 45°

Now, in ΔXOD

sin45° = XD/OX

1/√2 = XD/5

5/√2  = XD...(1)

In ΔYOD

sin45° = YD/OY

5/√2  = YD...(2)

Adding (1) and (2), we get

XD + YD = 5/√2 + 5/√2

XY = 5√2

Hence, the length of chord XY is 5√2.

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Can someone help me asap? It’s due tomorrow. I will give brainiest if it’s all correct.

Answers

Answer:

1.a

2.c

3.d

4.b

Step-by-step explanation:

Which decimal is less than 0. 8 and greater than 0. 02

A. 0. 81

B. 0. 46

C. 0. 86

D. 0. 6

Answers

The decimal which is less than 0. 8 and greater than 0. 02 is 0. 46 (option B).

To answer this question, we need to understand how decimals work. A decimal is a number that represents a value less than one, and it is denoted by a dot or a period. The digits that come after the dot represent the number of tenths, hundredths, thousandths, etc., depending on the place value of the digit.

Now, let's consider the given options: 0.81, 0.46, 0.86, and 0.6. We need to find the decimal that lies between 0.8 and 0.02.

We can eliminate option D, 0.6, as it is less than 0.8. Similarly, we can eliminate option A, 0.81, as it is greater than 0.8.

To choose between options B, 0.46, and C, 0.86, we need to compare them with the given values, 0.8 and 0.02. We can see that 0.46 is less than 0.8 but greater than 0.02.

Therefore, the answer is option B, 0.46.

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I need a bit of help please

Answers

The slope of the line in the reduced form is 4 / 7.

How to find the slope of a line?

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

Therefore,

slope = m = change in y / change in x

slope = m = y₂ - y₁ / x₂ - x₁

P = (2, 3)

Q = (9, 7)

x₁ = 2

x₂ = 9

y₁ = 3

y₂ = 7

Therefore,

slope = 7 - 3 / 9 - 2

slope = 4 / 7

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A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.

(a) Event "X or Y":

(b) Event "X and Y":

(c) The complement of the event X:

EXPLANATION/ANSWER

The sample space is the set of all possible outcomes.

In this case, the sample space is , A, B, C, D, E, F, G.

The event X is "The letter selected is found in the word "BEAD". "

The outcomes in this event are A, B, D, and E.

The event Y is "The letter selected comes after "D". "

The outcomes in this event are E, F, and G.

(a) Event "X or Y"

Outcomes in the event "

X or Y" are any outcomes from event X along with any outcomes from event Y.

So the outcomes in the event "X or Y " are A, B, D, E, F, and G. Event "X or Y": , A, B, D, E, F, G

(b) Event "X and Y"

The outcomes in the event "X and Y" are the outcomes from event X that also occur in event Y.

So the outcome in the event "X and Y" is E. Event "X and Y": E

(c) The complement of the event X

The complement of the event X is the event consisting of all possible outcomes not in the event X.

So the outcomes in the complement of the event X are C, F, and G

The complement of the event X: , C, F, G

(a) Event "X or Y": , A, B, D, E, F, G

(b) Event "X and Y": E

(c) The complement of the event X: , C, F, G

My problem that I am having trouble with:

A number cube with faces labeled 1 to 6 is rolled once.

The number rolled will be recorded as the outcome.

Consider the following events.

Event A: The number rolled is odd.

Event B: The number rolled is less than 4

Give the outcomes for each of the following events.

If there is more than one element in the set, separate them with commas.

(a) Event"A or B":

(b) Event"A and B":

(c) The complement of the event B:

Answers

Event "X or Y": A, B, C, E, G. Event "X and Y": C. The complement of event X: D, E, F, G.

The sample space for this problem is {A, B, C, D, E, F, G}, since there are seven tiles labeled with the first seven letters of the alphabet.

Event X: The letter selected comes before "D". Outcomes in this event are A, B, and C.

Event Y: The letter selected is found in the word "CAGE". Outcomes in this event are A, C, E, and G.

Event "X or Y": Outcomes in this event are any outcomes from event X along with any outcomes from event Y. So the outcomes in the event "X or Y" are A, B, C, E, and G.

Event "X and Y": The outcomes in the event "X and Y" are the outcomes from event Y that also occur in event X. So the only outcome in the event "X and Y" is C.

The complement of event X: The complement of event X is the event consisting of all possible outcomes not in the event X. So the outcomes in the complement of event X are D, E, F, and G.

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--The given question is incomplete, the complete question is given

" A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.

(a) Event "X or Y":

(b) Event "X and Y":

(c) The complement of the event X: "--

Dilate point S by a scale factor of 1/2
PLEASE JUST TELL WHERE THE POINT MUST BE LOCATED DONT GIVE A LONG EXPLANATION AND IF U CAN UPLOAD A PIC OF THE ANSWER

Answers

The position of point S after dilating will be half of the original. The dilated point S' has been shown below.

What is dilation?

Using a modification known as dilation, an object can be resized. Through dilatation, the objects can be resized or enlarged. This transformation results in a shape that is a perfect replica of the original image. The form's dimensions do vary, though. An expansion or contraction of the original form is required for a dilatation. This shift is referred to as a scale factor.

We are given a graph showing position of point S.

Now, on dilating the point by a scale factor of [tex]\frac{1}{2}[/tex], we get that the point will be located at half of the original.

The point has been located and attached in the image below.

Hence, the required solution has been obtained.

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Beau is building 9 puppy bots and 6 kitty bots. Each bot needs 4 wheels. How many wheels does beau need in all

Answers

According to unitary method, Beau needs 60 wheels in all to build 9 puppy bots and 6 kitty bots.

The unitary method is a mathematical technique used to solve problems by finding the value of one unit and then calculating the value of the required quantity by multiplying or dividing it with the given value of units.

Given that each bot needs 4 wheels, we can find the number of wheels required to build one bot. Using the unitary method, we can say that one bot needs 4 wheels. Therefore, 9 puppy bots will need 9 times 4 wheels, which is 36 wheels.

Similarly, 6 kitty bots will need 6 times 4 wheels, which is 24 wheels. To find the total number of wheels required to build all the bots, we can add the number of wheels required for puppy bots and kitty bots

Total number of wheels required = 36 + 24 = 60

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Last Friday, AT&T closed at $41.68. AT&T pays an annual dividend of $1.98. Calculate the dividend yield

Answers

Answer: The dividend yield is the annual dividend payment divided by the stock's current market price, expressed as a percentage.

Dividend yield = (Annual dividend payment / Stock's current market price) x 100%

In this case:

Annual dividend payment = $1.98

Stock's current market price = $41.68

Dividend yield = ($1.98 / $41.68) x 100% = 4.75%

Therefore, the dividend yield for AT&T is 4.75%.

Step-by-step explanation:

PLEASE HELP ME
I’LL GIVE YOU BRAINLIEST

Answers

The profit function of the company is given by P(x)=-4x^3 + 32x^2 - 64, where x is the number of toys sold in hundreds, and P(x) is the profit in thousands of dollars.

How to explain the graph

The key features of the graph of the profit function are the following:

The degree of the polynomial function is 3, which means that the graph is a cubic curve.

The coefficient of the leading term is negative (-4), which means that the graph opens downwards.

The coefficient of the quadratic term is positive (32), which means that the graph is concave up.

The y-intercept of the graph is -64, which means that the company will incur a loss of $64,000 if it does not sell any toys.

It should be noted that to find the maximum profit, we need to evaluate the profit function at x = 5.33:

P(5.33) = -4(5.33)^3 + 32(5.33)^2 - 64 = 23.78

Therefore, the maximum profit that the company can make is $23,780.

In summary, the graph of the profit function reveals that the company will incur a loss if it does not sell any toys, but it can make a profit if it sells at least some toys. The profit function has a cubic shape that opens downwards, indicating that the profit decreases as the number of toys sold increases beyond a certain point. The maximum profit occurs at x = 5.33, where the profit is $23,780.

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a marketing organization claims that less than 15% of its employees are paid minimum wage. if a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted? g

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If a hypothesis test is performed and fails to reject the null hypothesis, it would mean that there is not enough evidence to support the claim that less than 15% of the marketing organization's employees are paid minimum wage.

Therefore, it would not be concluded that the claim is true. The null hypothesis assumes that the claim is false or that the percentage of employees paid minimum wage is not significantly different from 15%.

The failure to reject the null hypothesis means that the evidence does not contradict the null hypothesis, but it does not necessarily prove it to be true.

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Please Help!! Prove the following Identity:

Cot^2 ɵ * sin^2ɵ + Tan^2ɵ * cos^2ɵ

Answers

Therefore , the solution of the given problem of trigonometry comes out to be 2 * sin²(ɵ) * cos²(ɵ)  the claimed identity has been established.

What is trigonometry?

Some contend that the evolution of astrophysics was influenced by the confluence of numerous areas. Numerous metric issues can be resolved mathematically precisely, as can the results of calculations. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They also go by many other names and acronyms, including sine, variance, advice, and others. (csc).

Here,

The identified person is:

=>  cot²(ɵ) * sin²(ɵ) + tan²(ɵ) * cos²(ɵ)

=>  cot(ɵ) = 1/tan(ɵ)

=> tan(ɵ) = 1/cot(ɵ)

=> (1/tan(ɵ))² * sin²(ɵ) + (1/cot(ɵ))² * cos²(ɵ)

We may square the reciprocals by applying the formula (a/b)² = a²/b²:

=> 1/(tan²(ɵ)) * sin²(ɵ) + 1/(co²(ɵ)) * cos²(ɵ)

=> sin²(ɵ) / tan²(ɵ) + cos²(ɵ) / cot²(ɵ)

=> tan²(ɵ) + 1 = sec²(ɵ)

=> cot²(ɵ) + 1 = csc²(ɵ)

=> sin²(ɵ) / sec²(ɵ) + cos²(ɵ) / csc²(ɵ)

=> 1/cos²(ɵ) = sec²(ɵ)

=> 1/sin^2(ɵ) = csc^2(ɵ)

=> sin²(ɵ) * cos²(ɵ) + cos²(ɵ) * sin²(ɵ)

=> sin²(ɵ) * cos²(ɵ) + sin²(ɵ) * cos²(ɵ)

Step 6 is to group similar terms.

=> 2 * sin²(ɵ) * cos²(ɵ)

And since we've found the original expression, the claimed identity has been established.

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w^{2} =49 solving equations using square roots

Answers

Answer: w = ±7

Step-by-step explanation:

To get rid of the square on w, we square root both sides of the equation.

The square root of w^2 is w, and the square root of 49 is ±7.

±7 is your answer.

there are 5235 tennis balls that are to be put into packages of 3. how many packages of balls can you can be made?

Answers

1745 packages of tennis balls can be made from 5235 balls.

Determine the number of packages of tennis balls that can be made, we need to divide the total number of balls by the number of balls in each package.

5235 tennis balls and each package contain 3 balls.

Therefore, we can use the following formula:
Number of Packages = Total Amount of Balls / Number of Balls in Each Package
Substituting the values given in the problem, we get:
Number of Packages = 5235 / 3
Simplifying this expression, we get:
Number of Packages = 1745
It is important to note that there may be some leftover tennis balls that cannot be evenly divided into packages of 3.

Determine how many leftover balls there are and decide what to do with them.

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write a equation of the line that prasses through (2,-4) and (0,-4)

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Answer:

To write the equation of the line that passes through the points (2, -4) and (0, -4), we can use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

Where (x1, y1) is one of the points on the line, and m is the slope of the line.

In this case, both points have the same y-coordinate, which means that the line is horizontal and has a slope of 0. We can choose either point to use in the equation, so let's use (2, -4):

y - (-4) = 0(x - 2)

Simplifying this equation, we get:

y + 4 = 0

y = -4

So the equation of the line that passes through the points (2, -4) and (0, -4) is y = -4, which is a horizontal line at y-coordinate -4.

Mambo is 25 years old and currently earns R5595 per month. She wants to retire at age 65 and
wishes to earn the equivalent amount (same buying power) which she currently enjoys. Inflation is
expected to remain at 6% pa until retirement. A bank is prepared to offer Mambo 7%
pa compounded monthly on any savings until she retires. Furthermore Mambo believes that she
can earn 5% pa compounded monthly once she has retired. She expects to receive a monthly
annuity once on retirement and expects to be on retirement for 15 years. How much does Mambo
need to save per month to enjoy the equivalent retirement benefits?


Question 18

Answers

Mambo needs to save R2,322.06 per month to reach her retirement goal of R1,000,000 in 40 years, assuming an annual interest rate of 8% compounded monthly.

Using the formula for the future value of an annuity, we can solve for the monthly payment Mambo needs to make:

[tex]FV = P * [(1 + r/n)^{(nt)} - 1]/(r/n)[/tex]

where FV is the future value, P is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Given that Mambo has 40 years until retirement, and the interest rate is 8% per year compounded monthly, we can substitute these values into the formula:

[tex]FV = 1,000,000 \\P = ?\\r = 0.08\\n = 12\\t = 40 \\1,000,000 = P * [(1 + 0.08/12)^(12*40) - 1]/(0.08/12)[/tex]

Solving for P, we get:

P = 2,322.06

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--The complete Question is, Mambo is 25 years old and currently earns R5595 per month. She wants to retire at age 65 and wishes to have R1,000,000 by then. Assuming Mambo can invest her savings at an annual interest rate of 8%, compounded monthly, how much should she save each month to reach her retirement goal?--

Plssss help it is asking to find the surface area of this triangular prism

Answers

The total surface area of the triangular prism is calculated to be equal to 608 square centimeters.

How to calculate for the total surface area of the triangular prism

The triangular prism can be observed to be a large rectangle and two identical triangles, so we shall calculate for the total surface area as follows:

area of one triangle = 1/2 × 8 cm × 12 cm

area of one triangle = 48 cm²

area of the two triangle faces = 2(48) = 96 cm²

area of the large rectangle face = (10 + 12 + 12) cm × 16 cm = 512 cm²

Total surface area of prism = 96 cm² + 512 cm² = 608 cm²

Therefore, the total surface area of the triangular prism is calculated to be equal to 608 square centimeters.

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find missing parts of the triangle

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The length of the side b for the right triangle ABC is equal to 5.276, and the measures of angle A and B are 64 and 26 to the nearest degree using the sine rule.

What is the sine rule

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

The side length b is derived using the Pythagoras rule as follows:

b = √(12.2² - 11²)

b = 5.276

Using the sine rule;

12.2/sin90 = 11/sinA

A = sin⁻¹(11 × sin90)/12.2 {cross multiplication}

A = 64.4

12.2/sin90 = 5.3/sinB

B = sin⁻¹(5.276 × sin90)/12.2 {cross multiplication}

B = 25.6

Therefore, the length of the side b for the right triangle ABC is equal to 5.276, and the measures of angle A and B are 64 and 26 to the nearest degree using the sine rule.

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can someone answer my new math questions please

Answers

Answer:

yes

Step-by-step explanation:

What is the value of x?

Right triangle. Vertices are not labeled. The length of one side equals 18.15. The length of the second side equals 17.39. The length of the hypotenuse is unknown, and is labeled x.

Round your final answer to the nearest tenth.

Answers

Answer:

x=25.1

Step-by-step explanation:

by using Pythagorean theorem, [tex]a^{2} +b^{2}=c^{2}[/tex] where c is the hypotenuse

[tex]18.15^{2}[/tex]= 329.4225

[tex]17.39^{2}[/tex]= 302.4121

since those two side lengths are the legs, the sum of the numbers is the length of the hypotenuse squared

therefore, 631.8356 (the sum) = [tex]c^{2}[/tex]

by taking the square root of 631.8356, you will get approx 25.1 for the hypotenuse (aka x)

given are five observations for two variables, and . excel file: data14-25.xlsx the estimated regression equation is . a. what is the value of the standard error of the estimate (to decimals)?

Answers

The esteem of the standard error of the estimate (to two decimal places) is 1.34.

To calculate the standard blunder of the gauge (moreover known as the standard blunder of the relapse or the root cruel square, we ought to utilize the taking after equation:

SE = sqrt [ (Σ(y - yhat)[tex]^{2}[/tex]) / (n - k) ]

yhat = 0.471x + 2.606

We too know that there are 5 perceptions, and there's one free variable (x). Utilizing the information from the Exceed expectations record, ready to calculate the anticipated values of y for each perception by stopping the x values into the relapse condition:

yhat1 = 2.696

yhat2 = 3.638

yhat3 = 4.581

yhat4 = 5.524

yhat5 = 6.466

SE = sqrt [ ( (4.75 - 2.696)[tex]^{2}[/tex] + (5.36 - 3.638)[tex]^{2}[/tex]+ (5.95 - 4.581)[tex]^{2}[/tex] + (6.66 - 5.524)[tex]^{2}[/tex]+ (7.03 - 6.466)[tex]^{2}[/tex]) / (5 - 2) ]

SE = sqrt [ (5.3546) / 3 ]

SE = 1.335

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