Question 1 of 10
Find the solutions to x² = 18.
O A. x = +6√3
OB. x = +2√3
X
O C. x = ±3-√2
O D. x = ±3√6

Answer:

Step-by-step explanation:

outer area=

first need to find the circumference of outer diameter

= π×4.8

= 15.079644.... cm

to find the outer curved area you would then do

= 77×15.079644

(ii) =1161.13264 cm²

inner curve area

circumference= π×4

=12.5663706.... cm

77×12.5663706

(i) =967.610537 cm²

total surface area=

as the outer and inner curved areas are already found only the top and bottom surfaces need to be

= area of larger circle

=π×4.8²

=72.382294.... cm²

smaller circle

=π×4²

=50.2654824.... cm²

72.382...-50.265

=22.1168116 x 2

=44.2336232 cm²

total surface area

(iii)= 2172.9768 cm²

(round this to however many decimals you need)

I hope this is understandable and useful!

also how many marks is this for?

Answer:

65mph

Step-by-step explanation:

forget about how far apart the cities are for now instead divide 260/4 because tia has traveled 260M for 4 hours

distance

-------------

  time

260/4=65

Answer:

sp=mp-20%ofmp=0.8mp

mp=cp+30%ofcp=1.3cp

mp=1.3cp

cp=mp/1.3

profit %=?

Step-by-step explanation:

The profit percentage is 4% .

Profit percentage (%) is the amount of profit expressed in terms of percentage. This profit is based on the cost price .

Formula for profit percentage is:

(Profit/Cost Price) × 100

where,

Profit = Selling price - Cost price

According to the question

Let Cost price of the article = 100x

marked price is 30% above the cost price

i.e  marked price = \(\frac{130}{100} * 100x\)

                            = 130 x

selling price of an article is 20% less than its marked price

i.e Selling price of the article = \(130x * \frac{100-20}{100}\)

                                                = \(130x * \frac{80}{100}\)

                                                = 104 x

Now ,

Profit = Selling price - Cost Price

Profit = 104x -100x

Profit = 4x        

Profit percentage =   \(\frac{Profit}{Cost PRice} *100\)

substituting the values in formula

Profit percentage =  \(\frac{4x}{100x} *100\)

Profit percentage =  4%

Hence, the profit percentage is 4% .

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Exact Form:

23

266

Decimal Form:

0.08646616...

Part A: Therefore, the cake weighs 112 ounces. Part B: Therefore, after 20 seconds, the tap will dispense 20 seconds × 1.2 pints/second = 24 pints of water.

Part A:

To convert pounds to ounces, we can use the conversion factor: 1 pound = 16 ounces.

Given that the cake weighs 3 (4/1) pounds, we can calculate the weight in ounces as follows:

3 4/1 pounds = 3 pounds + 4/1 pounds = 3 pounds + 4 pounds = 7 pounds

Converting 7 pounds to ounces: 7 pounds × 16 ounces/pound = 112 ounces

Therefore, the cake weighs 112 ounces.

Part B:

To convert gallons to pints, we can use the conversion factors: 1 gallon = 4 quarts and 1 quart = 2 pints.

Given that the running tap dispenses 0.15 gallons of water every second, we can calculate the amount of water dispensed in pints as follows:

0.15 gallons × 4 quarts/gallon × 2 pints/quart = 0.15 × 4 × 2 = 1.2 pints

Therefore, after 20 seconds, the tap will dispense 20 seconds × 1.2 pints/second = 24 pints of water.

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Answer:

15, 36, 39

Step-by-step explanation:

Use the Pythagorean theorem.

a² + b² = c²

2² + 3² ≠ 13²

4² + 6² ≠ 10²

9² + 12² ≠ 18²

15² + 36² = 39²

Answer:

Step-by-step explanation:

\(Lets -test-using ;\\Pythagoras -Theorem=\\a^2+b^2=c^2\\\\(A.) 2,3,13\\2^2 +3^2 = 13^2\\13 = 169\\WRONG\\\\(B.) =4,6,10\\4^2+ 6^2 =10^2\\16+ 36 = 100\\52 = 100\\WRONG\\(C.) 9,12,18\\9^2+12^2=18^2\\225 = 324\\WRONG\\\\(D.) 15 , 36 ,39\\15^2 +36^2 = 39^2\\1521=1521\\\\CORRECT\)

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The difference in lengths of the trips is given as follows:

0.6 hours.

The difference in lengths is obtained applying the proportions in the context of this problem.

In the morning, she took 12 minutes to arrive at the school, leaving at 7:53 and arriving at 8:05.

On the afternoon, she took 48 minutes to arrive at the school, leaving at 14:23 and arriving at 15:11.

The difference in minutes is then given as follows:

48 - 12 = 36 minutes.

As each hour is composed by 60 minutes, the time in hours is given as follows:

36/60 = 0.6 hours.

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The Linnaean class system provides a framework for understanding the diversity of life on Earth by grouping similar organisms together based on shared characteristics.

By comparing and contrasting the definitions of each class, we can see how different groups of animals are related to each other and how they differ in terms of their biological traits.

The Linnaean class system is a way of organizing living things based on shared characteristics. Let's compare and contrast the definitions of the Linnaean classes using a Venn diagram.

First, we have the class Mammalia, which includes all animals that have hair or fur, produce milk to feed their young, and have specialized teeth. This class overlaps with the class Aves, which includes all birds, because some birds have specialized beaks and feathers that are similar to mammalian hair and teeth. However, birds do not produce milk.

Next, we have the class Reptilia, which includes animals that are cold-blooded, lay eggs, and have scales or plates on their skin. This class overlaps with both Mammalia and Aves in terms of species that lay eggs, such as monotremes (platypus and echidnas) and some birds (ostriches and emus). However, reptiles lack specialized teeth and do not produce milk.

Finally, we have the class Amphibia, which includes animals that are cold-blooded, breathe through their skin, and undergo metamorphosis from a water-dwelling larval stage to a land-dwelling adult stage. This class overlaps with Reptilia in terms of some shared characteristics, but Amphibia also lacks specialized teeth and does not lay eggs with hard shells like reptiles.

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Answer:

Step-by-step explanation:

4 8

Answer:

1,059,052,859,206,986,969,696,900

Step-by-step explanation:

Answer:

The answer is 1

Step-by-step explanation:

combine like terms!

\(8+6x-5x+2+2x=12\\8+2+6x-5x+2x=12\\10+6x-5x+2x=12\\10+x+2x=12\\10+2x=12\\2x=2\\x=1\)

hope this helps!!

Answer:

SA: 456

V: 408

Step-by-step explanation:

To find the volume of this prism, you first need to find the area of the triangular base. The base has dimensions 6 by 8, and since it's a triangle, the area of the base is 6*8/2=24. Multiplying this by the length of the prism, you get a volume of 24*17=408. For the surface area, you need to find and add together the areas of all of the surfaces. We have already determined that the area of the two triangular bases are 24. The rectangle formed by the leg with length 6 has area 6*17=102, the one with length 8 has area 136, and the hypotenuse has area 170. Adding all of this together, you get a surface area of 24+24+102+136+170=456 square centimeters. Hope this helps!

The independent variable in a relationship between two variables is the variable that is used to predict or explain the variation in the other variable.

It is the variable that is manipulated or controlled by the researcher. For example, if we are investigating the relationship between temperature and ice cream sales, temperature would be the independent variable, as we would expect changes in temperature to predict changes in ice cream sales.

On a scatter diagram, the independent variable is typically represented on the horizontal axis (x-axis) and the dependent variable is typically represented on the vertical axis (y-axis). This is because the independent variable is typically plotted along the horizontal axis, with its values placed at regular intervals, and the dependent variable is then plotted along the vertical axis, with its values plotted based on their relationship to the corresponding independent variable values.

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The value for the input when the output is −3 is 6.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given y = f(x)

and f(x) = -2/3x + 1

to find the value of x when f(x) = -3

substitute the value of f(x)

f(x) = -2/3x + 1

-3 = -2/3x + 1

-2/3x = -3 - 1

2/3x = 4

x = 4*3/2

x = 6

Hence the input is 6.

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Answer:

5u-2

-_-_-_-_-_-_-_-_-

Answer:

m∠LPM = 60°

Step-by-step explanation:

The average speed of a falling object during the first 3 seconds of its fall is h(3)-h(0)/3.

The model of the motion of the body is given by, and the function of the motion of the body is given by h(t) = 300 - 16t².

The speed of object after 3 seconds is given by . The falling speed of object during the first 3 seconds of falling is calculated as follows, v = dh(t)/dt = -32t.

So now the average speed of the movement is calculated as follows,

v = h(3)-h(0)/3.

Option d is therefore the correct option.

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Complete question - the height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function . what is the average rate at which the object falls during the first 3 seconds?

A.) h(3) – h(0)

B.) h(3/3)-h(0/3)

C.) h(3)/3

D.) (h(3)-h(0))/3

Step-by-step explanation:

The question posed by Andrea is asking how many bonbons would you have in total if you had three bonbons in one box and then had three boxes with the same amount of bonbons.

To find the total number of bonbons, we need to multiply the number of bonbons in one box by the number of boxes.

Given that there are three bonbons in one box, and you have three boxes, the calculation would be:

3 bonbons/box * 3 boxes = 9 bonbons

Therefore, you would have a total of 9 bonbons altogether.

The curve is smooth for \(t\neq 0\) on the intervals (-∞, 0), (0, ∞)

We have to consider the curve

                                               \(r(t) = 8t^{2}i + 7t^{3}j\)

Now, the objective is to find the open intervals when on which the curve given by the vector valued function is smooth, using the result.

The parametrization of the curve represented by the vector valued function

                                       \(r(t) = f(t)i + g(t)j + h(t)k\)

This equation is smooth on an open interval when f'(t), g'(t), and h'(t) are continuous on \(l\) and r'(t) \(\neq\) 0 for any value of t in the interval.

Now, we know the vector equation:

\(r(t) = 8t^{2}i + 7t^{3}j\)

Differentiating r(t) with respect to r,

\(r'(t) = 16t i + 21t^{2} j\)

At t = 0, equate r'(t) = 0.

\(r'(0) = 16(0) + 21(0)^{2}\)

Therefore, the curve is smooth for all values except 0, as we can see above.

Hence, the curve is smooth for \(t\neq 0\) on the intervals (-∞, 0), (0, ∞).

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Answer:

-42+8+17 = -17 and  37+(-21)+(-16) = 0

Step-by-step explanation:

The inequality relating −2\(e^{(-n/n^2)}\) to 121/\(n^2\) for n ≥ 1 is -2\(e^{(-n/n^2)}\) ≤ 121/\(n^2\).

To derive the inequality, we start by comparing the expressions −2\(e^{(-n/n^2)}\)  and 121/\(n^2\).

Since we want to express the numbers in exact form, we keep them as they are.

The inequality states that −2\(e^{(-n/n^2)}\)  is less than or equal to 121/\(n^2\).

This means that the left-hand side is either less than or equal to the right-hand side.

The exponential function e^x is always positive, so −2\(e^{(-n/n^2)}\)  is negative or zero.

On the other hand, 121/\(n^2\) is positive for n ≥ 1.

Therefore, the inequality −2\(e^{(-n/n^2)}\)  ≤ 121/\(n^2\) holds true for n ≥ 1.

The negative or zero value of −2\(e^{(-n/n^2)}\)  ensures that it will be less than or equal to the positive value of 121/\(n^2\).

In symbolic notation, the inequality can be written as −2\(e^{(-n/n^2)}\)  ≤ 121/\(n^2\) for n ≥ 1.

This representation captures the relationship between the two expressions and establishes the condition that must be satisfied for the inequality to hold.

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Step-by-step explanation:

" role="presentation" style="outline: 0px; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.017px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">√x=5x=5

Answer:

Step-by-step explanation:

" role="presentation" style="outline: 0px; display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.017px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">√x=5x=5

Answer/Step-by-step explanation:

10 is between the perfect squares of 9(3) and 16(4).

This means the square root of 10 is between 3 and 4.

The square root of 10 is about 3.162

So, it is less than 5.

Answer:

f(f(-1)) = 0

Step-by-step explanation:

Ok I'm assuming that's supposed to be a chart of some kind.  So first, you have to find what f(-1) is according to the chart.  

According to the chart, if x = -1, then f(-1) is -5

Now comes the next part of the equation.  So you need to find f(-5)

-5 was already founded by f(-1) bc it's first in the parantheses.

f(-1) is -5

so we need to find f(-5)

According to the chart f(-5) is 0

So ur final answer is gonna be 0

When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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