A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral tris are all 9 feet long, and the height of the equilateral triangle is 7.8 feet. The pyramid's slant heigh feet. What is its surface area?

A-B is equivalent to 5x2 + 11x - 13 as a result as [tex]A = 3x^2 + 5x - 6[/tex] and  [tex]B = -2x^2 - 6x + 7[/tex] .

A mathematical expression is a grouping of digits, variables, operators, and symbols that denotes a mathematical amount or relationship. It can be analyzed or condensed using mathematical operations and rules, and it can be a single word or a group of terms. Numerous mathematical ideas, including equations, variables, functions, and formulas, can be represented by expressions. Standard form, factored form, extended form, and polynomial form are just a few of the different ways they can be expressed in writing.

given

We must deduct the expression B from the expression A in order to obtain A-B. To accomplish this, we subtract the appropriate coefficients from terms of the same degree. Here are the facts:

[tex]A = 3x^2 + 5x - 6\\B = -2x^2 - 6x + 7[/tex]

A - B =[tex](3x^2 + 5x - 6) (-2x^2 - 6x + 7)[/tex]

= 3x2 + (5x - 6) + (2x2 - 6) + (7x - 5x2 + 11x - 13 (distributing the negative sign)

A-B is equivalent to 5x2 + 11x - 13 as a result as [tex]A = 3x^2 + 5x - 6[/tex] and  [tex]B = -2x^2 - 6x + 7[/tex] .

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Answer:

90, 86, and 92 are three options

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The inequality that represents the possible weight of the Maine Coon is 828 ≤ x ≤ 840

Let x be the weight of Linda's Maine Coon in pounds.

Since the difference in weight between the two cats is at least 6 pounds, we can write the following inequality:

|x - 834| ≥ 6

This inequality can be interpreted as "the absolute value of the difference between the weight of the Maine Coon and 834 pounds is greater than or equal to 6".

Simplifying the inequality, we get:

-6 ≤ x - 834 ≤ 6

Adding 834 to each side of the inequality, we get:

828 ≤ x ≤ 840

Therefore, the possible weight of Linda's Maine Coon is between 828 and 840 pounds, inclusive.

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Length of the Sara's rope of 2 1/2 meter in centimeter is 25 centimeters.

To convert 2 1/2 meters to centimeters, we can use the conversion factor 1 meter = 100 centimeters. This means that:

2.5 meters = 2.5 x 100 centimeters

= 250 centimeters

Therefore, the length of the rope is 250 centimeters. It's important to understand and be able to convert between different units of measurement, as this is a common task in many fields such as science, engineering, and finance. For example, in science, it's important to be able to convert between different units of length, mass, and volume when making measurements or analyzing data. Similarly, in finance, it's common to convert between different currencies or units of time when dealing with investments or loans. Being able to make these conversions accurately is essential to avoid errors or misunderstandings. In this case, converting the length of the rope from meters to centimeters allows us to work with a more convenient unit for the task at hand, which is hanging a swing for Sara's sister.

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Answer:

The time will be 1:00pm(13 hours) at which the degree Celsius will drop down to 8degrees Celsius since the temperature at 12noon was 10 degree Celsius and it is dropping at the rate of 2 degree Celsius.

The probability that a student chosen at random likes science given that he or she likes art is 41.4%

In our case, we want to find P(Science|Art), which is the probability of a student liking science given that he or she likes art. Using Bayes' theorem, we have:

P(Science|Art) = P(Art|Science) x P(Science) / P(Art)

We know that P(Art) = 0.35 and P(Science|Art) = 0.22. To find P(Art|Science), we can use the formula:

P(Art|Science) = P(Science|Art) x P(Art) / P(Science)

We don't know P(Science) yet, but we can calculate it using the fact that:

P(Science) = P(Science|Art) x P(Art) + P(Science|Not Art) x P(Not Art)

where P(Not Art) is the probability that a student does not like art, which is 1 - P(Art) = 0.65. We are given that P(Science|Not Art) = 0.15, which is the probability that a student who does not like art likes science. Substituting these values, we get:

P(Science) = 0.22 x 0.35 + 0.15 x 0.65 = 0.1855

Now we can substitute all the values into Bayes' theorem:

P(Science|Art) = 0.22 x 0.35 / 0.1855 = 0.414 or 41.4%

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t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .

An expression in mathematics is a group of digits, variables, and operations that illustrates a mathematical connection or concept. Symbols, words, or a combination of both can be used to write expressions in a variety of ways. Expressions that are examples include: 3x + 4, 2y - 7z , (a + b) ,x2 + y2 = 2 5sin(x) + 3cos(x). Equations, inequalities, functions, formulae, and many other mathematical ideas can all be represented as expressions. Additionally, they can be altered or simplified using algebraic methods like factoring, combining like terms, and solving for a variable.

given

The sum of m and 83.

Forty-two times s.

Nine divided by d.

t decreased by 29.

Two more than g.

Eleven times x.

h divided by twelve.

Five minus k

t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .

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Answer:

C 9:8

Step-by-step explanation:

total students = 36

5+4=9

5:4 = 20:16

20-2=18

ratio for monday = 18:16

=9:8

The most precise classification of the quadrilateral with opposite sides having the same slopes and consecutive sides having slopes that are reciprocals is a Rectangle.

1. Opposite sides with the same slopes imply that these sides are parallel.
2. Consecutive sides with slopes that are reciprocals mean that they are perpendicular.
3. Parallel opposite sides make the quadrilateral a parallelogram.
4. Perpendicular consecutive sides make it a rectangle, as all angles are 90 degrees.

So, the quadrilateral is a Rectangle.

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Answer: 64πa^2-192πa+144

Step-by-step explanation:

Area of a circle: π •r^2

So then the area would be: 4•π(4a-6)^2

FOIL (4a-6)(4a-6) and get 16a^2-48a+36

Plug it in and get 4•π(16a^2-48a+36)

Distribute pi sign and get 4•(16πa^2-48πa+36π)

Distribute the 4 and you get 64πa^2-192πa+144

Answer: 64πa^2-192πa+144

The set of numbers that are possible values for x in the inequality x < -3 is: {-9, -7, -5}. (Option 2)

To find the possible values of x that satisfy the inequality x < -3, we need to look for numbers that are less than -3. Among the given sets of numbers, only {-9, -7, -5} contains numbers that are less than -3, so this is the set of possible values for x.

{-33, -22, -11} are all greater than -3, so they are not possible values for x in the given inequality.

{5, 7, 9} and {-5, 0, 5} are also greater than -3, so they are not possible values for x in the given inequality.

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Complete Question:

Select all the sets of numbers that are possible values for x in the inequality, x<-3.

The magnitude of the resultant force is given by:

|F| = [tex]sqrt((-7)^2 + 0^2) N|F| = 7 N[/tex]The direction of the resultant force is given by:

[tex]θ = tan^-1(0/-7)θ = tan^-1(0) = 0[/tex]

Therefore, the magnitude of the resultant force is 7 N, and its direction is along the negative x-axis.

1. Cartesian vector expression for five forcesThe five forces acting along the edges of a pentagon plate ABC are shown below:Force acting on AB = (6i + 6j) NForce acting on BC = (8i + 4j) NForce acting on CD = (-5i + 10j) NForce acting on DE = (-10i - 8j) NForce acting on EA = (4i - 12j) N2.

Cartesian vector expression of the resultant force of these five forcesThe resultant force acting on the pentagon plate ABC can be determined by finding the vector sum of the five forces. The cartesian vector expression of the resultant force can be found as follows:[tex]F = F1 + F2 + F3 + F4 + F5F = (6i + 6j) N + (8i + 4j) N + (-5i + 10j) N + (-10i - 8j) N + (4i - 12j) N= (-7i + 0j) N[/tex]

Therefore, the cartesian vector expression of the resultant force is (-7i + 0j) N.3. Magnitude and direction of the resultant forceThe magnitude and direction of the resultant force can be determined by using the cartesian vector expression of the resultant force obtained in the previous step.

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Part a: Expression for conventional account: $(5000-x) at 5%pa.

Part b: polynomial model: T =  5250  -  0.01x

Part c: Sum of investments in retirement account: T= $5245.

When they need to raise money, governments and businesses issue bonds.

a. Create an expression to show how much money is invested in the conventional account.

Back $(5000-x) at 5%pa

b. Construct a polynomial model in its simplest form to represent the entire sum of investments made by T. Kent after a year (possibility: thus every account has A + iA dollars, in Which a is the account's initial balance and I is the interest rate).

The bond will increase to after a year to : x + 0.04x

= x(1+0.04)

= 1.04x   ...eq 1

So, after the time of one year this traditional account growth will be-

(5000-x) + 0.05(5000-x)

= 5000 - x  + 0.05*5000  -  0.05x

= 5000  -  x  + 250  -  0.05x

= 5250  -  1.05x  ..eq 2

From eq 1 and eq 2

T = 1.04x + 5250  -  1.05x

T =  5250  -  0.01x

c. If Kent invested $500 in bonds, how much will he have in the retirement account in a year?

x=500

T= 5250  - 0.01*500

T= 5250 - 5

T= $5245

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When a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will shift towards the left side of the body.

Explanation:

The point at which the weight of a body or an object is concentrated, that is, the point at which the mass of the body or the object is focused is known as the center of gravity. The center of gravity (CG) is the point where the weight of the body is supposed to act, which is the point about which the body remains in balance. The body's center of gravity is important because it affects its balance and stability

                             .When a person is standing in a neutral position, the center of gravity is in the midline of the body. When the person flexes their right shoulder and holds their arm horizontally, the center of gravity will shift towards the left side of the body. This is because the weight of the arm is now being supported by the left side of the body. The shift in the center of gravity will cause the person to adjust their posture to maintain balance and stability.

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Answer: natural number=11

                integer= -4

                irrational= pi, 0.1010010001.....,root 5

                 rational= 0.1212...., -3/5,0.3,2 1/4

Step-by-step explanation:

Answer: Assuming the student walks along a rectangular grid and not diagonally, the possible locations the student could end up after walking 4 miles in any direction would be the points that are 4 units away from the starting point in a north, south, east, or west direction.

Using this information, we can determine that the possible locations the student could end up at are:

(-2, 10)

(-6, 14)

(-10, 10)

(-6, 6)

Therefore, the answer is:

All of the above locations are possible endpoints.

Step-by-step explanation:

If the student walks 4 miles north, south, east, or west,  the location at the end of the walk are respectively, (-6, 14). (-6, 6), (-2,10). (-10, 10).

The Cartesian plane, named after the mathematician René Descartes (1596 - 1650), is a plane with a rectangular coordinate system that associates each point in the plane with a pair of numbers.

Given that,

A student starts a walk at (-6, 10)

If the student walks 4 miles north, south, east, or west,

The location at the end of the walk =

Plotting dotted diagram,

                  East

                     |

North --------- |-------------- South

                     |

                  West

Suppose, he goes to north  direction

Then, 4 will be added to y coordinate,

It can be written as,

(-6, 14)

Similarly, for South, (-6, 6),  

East, (-2,10).

West, (-10, -10)

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The bottom of the ladder is moving at a rate of 1.333 ft/sec when the top is 8 ft from the ground

The bottom of the ladder is moving at a rate of 6 ft/sec when the top is 8 ft from the ground. This can be found by using the equation v = d/t, where v is the velocity, d is the distance, and t is the time. The distance is 8 feet (from the top of the ladder to the ground) and the time is 1/6 seconds (since the ladder is sliding down at a rate of 6 ft/sec). Therefore, the velocity of the bottom of the ladder when the top is 8 ft from the ground is 8/1/6 = 8/6 = 4/3 = 1.333 ft/sec.

To understand this concept more clearly, imagine a ball rolling along the ground. Its velocity is constant until it hits a slope and begins to move down the slope. At this point, its velocity increases as it moves further down the slope, and its velocity is higher when it is further down the slope.

This is the same concept as the ladder sliding down the wall; the bottom of the ladder is moving faster than the top, so the velocity of the bottom of the ladder increases as the top of the ladder gets closer to the ground.

In conclusion, the bottom of the ladder is moving at a rate of 1.333 ft/sec when the top is 8 ft from the ground. This can be found using the equation v = d/t, where v is the velocity, d is the distance, and t is the time. The distance is 8 feet and the time is 1/6 seconds since the ladder is sliding down at a rate of 6 ft/sec.

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No, the lines cannot ever match up perfectly because there is always some sort of difference between them. The lines can have the same slope if they have the same change in y-values for a given change in x-values. The lines can also have the same y-intercept if they cross the y-axis at the same point.

No, there will never be a perfect alignment between the lines since there will always be a discrepancy of some kind. However, the lines can have the same slope and y-intercept. This is possible because the slope and y-intercept are determined by the equation of the line, and if two lines have the same equation, then they will have the same slope and y-intercept.

If the lines intersect the y-axis at the same location, they can also have the same y-intercept. This means that the two lines have the same value of b in the equation y = mx + b. This means that the two lines have the same slope and the same y-intercept.

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The tank contains 1050 milliliters of water when full or 1.05 liters.

To calculate the volume of the tank in milliliters, we multiply the length (15 cm), width (7 cm), and height (10 cm) together:

15 cm x 7 cm x 10 cm = 1050 cm³

Since 1 milliliter equals 1 cubic centimeter (cm^3), we know that the tank can hold 1050 milliliters of water.

To convert milliliters to liters, we can divide the volume in milliliters by 1000:

1050 mL ÷ 1000 = 1.05 L

Therefore, when full, the tank can hold 1050 milliliters of water or 1.05 liters.

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Answer: (-4,11)(-2,7)(0,3)(2,-1)

Step-by-step explanation:

Put the function into desmos and create a table.

Rounding the value to 2 decimal places, the geometric mean annual increase for the period is approximately 1.18.

Geometric mean annual increase for the period:

Let A be the initial value and B be the final value of the given data for the geometric mean annual increase for the period in the United States from 2000 to 2014.

A = 40,255,000 and B = 214,014,920.

To find the geometric mean annual increase for the period, we need to use the formula:

Geometric mean = (B/A)^(1/n), where n = the number of years elapsed.

Therefore, n = 2014 - 2000 = 14 years.

Substituting the values of A, B, and n in the above formula, we get:

Geometric mean = (214,014,920/40,255,000)^(1/14) ≈ 1.1802.

Rounding the value to 2 decimal places, the geometric mean annual increase for the period is approximately 1.18.

Answer: 1.18.

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Answer:

The volume of a sphere is given by the formula:

V = (4/3)πr^3

where r is the radius of the sphere.

Since the diameter of Casper's balloon is 6 inches, the radius is 3 inches. Therefore, the volume of Casper's balloon is:

V1 = (4/3)π(3 inches)^3 = 113.1 cubic inches (approx.)

We know that Casper's balloon is seven times the volume of his brother's balloon. Let's call the volume of his brother's balloon V2. We can set up an equation:

V1 = 7V2

Substituting the value of V1, we get:

113.1 cubic inches = 7V2

Dividing both sides by 7, we get:

V2 = 16.2 cubic inches (approx.)

Therefore, the approximate volume of Casper's brother's balloon is 16.2 cubic inches.

Answer:

Step-by-step explanation:

everything is resolved with the expression:

20^2 x 6 = 2400 cm^2

Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50. The problem can be solved using a system of equations.

Let's use a system of equations to solve this problem:

Let x be the number of shirts that Siona bought, and y be the number of pairs of shorts that she bought. Then we have:

Equation 1: x + y = 10 (Siona bought 10 outfits in total)

Equation 2: 3.50x + 4.00y = 36.50 (The total cost of the outfits is $36.50)

To solve for x and y, we can use substitution or elimination. Let's use substitution:

From Equation 1, we can solve for x in terms of y:

x = 10 - y

Substitute this expression for x into Equation 2:

3.50(10 - y) + 4.00y = 36.50

Simplify and solve for y:

35 - 3.50y + 4.00y = 36.50

0.50y = 1.50

y = 3

Now we can substitute y = 3 back into Equation 1 to solve for x:

x + 3 = 10

x = 7

Therefore, Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50.

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I'm sorry, 35 is not a measure of angle and therefore cannot be rounded to the nearest degree. Are you asking for the sine, cosine, or tangent of 35 degrees?

Answer:

There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

the answer is 56

The relationship between t, the number of tickets, and c, the total cost of tickets is: c = 55t

Relation between two variables, i.e, total cost and number of tickets:

The statistical relationship between two variables is called their correlation. The correlation can be positive, which means that the two variables move in the same direction, or negative, which means that when the value of one variable increases, the value of the other variable decreases.

Based n the Question:

Since there is no processing fee and the ticket price remains the same, we know that the fee will be proportional to the number of tickets purchased. The general form of the equation expressing the proportional relationship between the cost (c) and the number of tickets (t) is:

c = kt

where k is the constant of proportionality (the cost per ticket).

We can find k by using any of the data points given in the table. Using the first point, we have :

110 = k·2

Dividing the equation by 2:

110/2 = k = 55

Then using this value for k, the desired equation can be written:

c = 55t

Complete Question:

Total cost (in dollars) Number of concert tickets. the total costs in dollars are 110 275 440. the number in concert tickets are 2, 5, 8 Write an equation to describe the relationship between the total cost in dollars (c), and the number of tickets purchased (t),

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Rounding to the nearest thousandth means rewrite the number and deleting all digits to the right of the rounded number. The percentage value for 165.1% of 384.7 is equals to the 42.917%.

In mathematics, a percentage is a number that represents a fraction of hundred. We have to calculate the value of 165.1% of 384.7. Percentage solution with steps:

Step 1: We make the assumption that 384.7 is 100% since it is our output value.

Step 2: We next represent the value we need with x. From step 1, it follows that 100% = 384.7.

Step 3: In the same sense, x% = 165.1.

Step 5: Now, we have a pair of simple equations:

100% = 384.7 --(1).

x% = 165.1 ---(2).

Step 6: By simply dividing equation (1) by equation 2 and taking note of the fact that both the LHS (left hand side) of both equations have the same unit (%); we have 100% /x% = 384.7/165.1.

Step 7: Taking the inverse or reciprocal in both sides, x% / 100% = 165.1/384.7

=> x = ( 165.1/384.7) × 100

=> x = 42.91655835716 ~ 42.917 (round to the nearest thousandth). Therefore, 165.1 is 42.917% of 384.7.

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