How does the volume of a square pyramid change if the base edge is multiplied by 6?

The system of inequalities to represent the constraints of the situation are x ≤ 260, y ≤ 320, and x + y ≤ 360.

A group of two or more linear inequalities are grouped together and graphed on a coordinate plane to discover the solution that concurrently solves all of the inequalities. Each inequality forms a half-plane on the coordinate plane, and the location where all the half-planes overlap is where the system is solved. Each point inside the feasible area meets all of the system's inequalities. This region is known as the feasible region. To identify the optimum solution given a set of constraints, systems of linear inequalities are frequently utilised in optimization issues.

Let us suppose the number of boards of Mahagony sold = x.

Let us suppose the number of black walnut boards sold = y.

According to the given problem the equation can be set as follows:

x ≤ 260 (the company has 260 boards of mahogany available)

y ≤ 320 (the company has 320 boards of black walnut available)

x + y ≤ 360 (the company expects to sell at most 360 boards of wood)

Hence, the system of inequalities to represent the constraints of the situation are x ≤ 260, y ≤ 320, and x + y ≤ 360.

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Answer: 4 is the average rate of change

Step-by-step explanation:

The equation to find the average rate of change is:

So f(2)= 11 and f(5)=23 then you plug these numbers in:

[tex]\frac{23-11}{5-2}[/tex] = [tex]\frac{12}{3}[/tex] = 4

The two sides of a right triangle opposite the non-right angles are called as adjacent and opposite angle or Legs.

A triangle is a three-sided regular polygon in which the total of any two sides is always larger than the sum of the third side.

A right-angled triangle is one with one of its internal angles equal to 90 degrees, or any angle is a right angle. As a result, this triangle is also known as the right triangle or the 90-degree triangle. In trigonometry, the correct triangle is very significant.

A right-angled triangle is a triangle in which one of the angles is 90 degrees. The total of the other two angles is 90 degrees. The sides that include the right angle are perpendicular and form the triangle's base. The third side is known as the hypotenuse, and it is the longest of the three sides.

The three sides of the right triangle are connected. Pythagoras' theorem explains this relationship. This theorem states that in a right triangle,

Perpendicular² + Base² = Hypotenuse²

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Answer: The interest and amount to be paid at the end of 3 years is Rs.8700

Step-by-step explanation:

let P ,R, T be the Principle amount , Rate of interest and Time

             P= 6000rs

             R= 15%

             T=3 years

                      =6000rs×15r×3t÷100

                       =2700rs

                                                             = 8700rs

Simplifying the algebraic expression ab + 3a² - 7a + ab + a² = a(4a + 2b - 7)

An algebraic expression is a mathematical expression in which letters are used to represent the variables.

Since we have the algebraic expression ab + 3a² - 7a + ab + a², and we want to simplify it. We proceed as follows

ab + 3a² - 7a + ab + a²

First, we collect the like terms together

ab + 3a² - 7a + ab + a² = 3a² + a²- 7a + ab + ab

Adding the similar terms together, we have

= 3a² + a²- 7a + ab + ab

= 4a²- 7a + 2ab

=  4a²- 7a + 2ab

Factorizing out a, we have that

= a(4a - 7 + 2b)

= a(4a + 2b - 7)

So, ab + 3a² - 7a + ab + a² = a(4a + 2b - 7)

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Answer:

<D = 130°

Step-by-step explanation:

Supplementary = 180°

<C = 50°

<D = ?

<C + <D = 180°

180° - 50° = 130°

<D = 130°

Answer:

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Let the number = x.

20% of the number is 20% of x = 0.2x.

Since the number exceeds 20% of itself by 40, then teh number minus 20% of itself is 40.  

x - 0.2x = 40

0.8x = 40

x = 40/0.8

x = 50

The average time gap between the first cyclist's time and each of the remaining cyclists' times (second through fifth) in the 1995 Volta a Catalunya cycle race is approximately 6 minutes and 7 seconds.

To calculate this, we need to subtract the time of the first cyclist from each of the remaining cyclists' times (second through fifth).The time for the first cyclist was 41:38:33.

The times for the remaining cyclists were as follows:

We can calculate the difference for each cyclist by subtracting the first cyclist's time from their own time:

Adding up all of the times and dividing by four, we get an average of 00:06:07.

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The sample correlation coefficient would be closest to -0.9.

Here's why:

Correlation Coefficient: The correlation coefficient is a statistical measure of the degree of correlation (linear relationship) between two variables. Pearson’s correlation coefficient is the most widely used correlation coefficient to assess the correlation between variables.

Pearson’s correlation coefficient (r) ranges from -1 to 1. A value of -1 denotes a perfect negative correlation, 1 denotes a perfect positive correlation, and 0 denotes no correlation. There is a negative correlation between speed and time. As the speed of the car increases, the time needed to traverse the segment decreases. So, the sample correlation coefficient would be negative.

Since the sample size is large enough, the sample correlation coefficient should be close to the population correlation coefficient. The population correlation coefficient between speed and time should be close to -1, which implies that the sample correlation coefficient should be close to -1.

Therefore, the sample correlation coefficient would be closest to -0.9.

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The combined score on the 2022 SAT test ranges from 400 to 1600. If you were to randomly draw five numbers from a 400-1600 number set, the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers is approximately 0.004%

To find the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers, we need to find the probability of the following event: “the three other random numbers drawn lie between the highest and lowest values.

The probability of choosing one of the five numbers that falls within the range is (1600 – 400)/1201 = 1/2.25.

The first number can be any number within the 400-1600 range, so the probability is 1.The second number must lie within the range created by the highest and lowest values of the first number, which has a width of 1201. Thus, the probability is 1201/3201.

The third number must lie within the range created by the highest and lowest values of the first two numbers, which has a width of 801. Thus, the probability is 801/2401.The fourth and fifth numbers must lie within the range created by the highest and lowest values of the first three numbers, which has a width of 401.

Thus, the probability is 401/1601.Therefore, the probability of the medium score of the actual 2022 SAT results being between the highest and lowest values of these five random numbers is (1/2.25) * (1201/3201) * (801/2401) * (401/1601) * 1 = 0.000038 or approximately 0.004%.

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Answer:

the answer is 2

Step-by-step explanation:

this answer will be 200⁰0000000000⁰00000⁸⁰643367897⁶43677443⁵=5.0

The perimeter of the square is 256 m.

Area is a measure of the amount of two-dimensional space enclosed by a closed figure or shape. It is usually measured in square units, such as square meters, square feet, or square centimeters.

A square is a regular quadrilateral with four equal sides and four right angles. It is a special case of a rectangle and a rhombus, and its properties are a combination of both.

In the given question,

We can start by using the formula for the area of a square, which is:

a = s²

where a is the area and s is the length of one side of the square.

If the area of the square is 64 m², then we have:

64 = s²

Solving for s, we get:

s = √64 = 8 m

Now, we can use the formula for the perimeter of a square in terms of its area:

P = 4a²

Substituting a = 64, we get:

P = 4(64) = 256 m

Therefore, the perimeter of the square is 256 m.

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Total seats in plane: 186

108+64+14

5/7 of 14 is: 10

14÷7= 2

2x5= 10

5/16 of 64 is: 20

64÷16=4

5×4= 20

5/9 of 108 is: 60

108÷9= 12

12x5= 60

60+20+10=90

90/186 of seats are being used

simplified: 15/31

No

The equation you would use to properly calculate the dollar cost of entering the park and enjoying rides is Total Cost = Entrance Fee + (Number of Rides x Ride Fee).

In this case, Total Cost is the cost of entering the park and enjoying rides, Entrance Fee is the fee for entering the park, Number of Rides is the number of rides you will be taking, and Ride Fee is the fee charged for each ride.

Thus, plugging in the given values, the equation becomes  Total Cost = Entrance Fee + (Number of Rides x Ride Fee).

Therefore, if the Entrance Fee is $ and each ride costs an additional $ , the Total Cost of entering the park and enjoying rides is $ .

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Angle of elevation of the ramp with a height of 27ft and a platform of 16ft is approximately 59.35°.

The ramp is 27ft long and rises to a platform, the bottom of the platform is 16ft from the foot of the ramp.

We need to find the angle of elevation of the ramp.

The angle of elevation of the ramp is the angle made by the ramp with the horizontal.

Let ABC be the ramp and D be the platform, as shown below: Let AB = 16ft and BC = 27ft.

We need to find the angle ABD.

Consider right-angled ΔABC In right-angled ΔABC,

we have:

tan⁻¹ (BC / AB)

θ  = tan⁻¹ (27 / 16)

θ ≈ 59.35°

Hence, the angle of elevation of the ramp is approximately 59.35°.

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To answer the question, this equation has only one solution, which is x = 4.

An equation is a mathematical statement that shows the equality between two expressions. It usually consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=).

The expressions on both sides can contain variables, constants, and mathematical operations such as addition (+), subtraction (-), multiplication (*), division (/), exponentiation (^), and others. The goal of an equation is to find the values of the variables that make both sides equal.

by the question.

Let's start by setting up the equation:

[tex]1/2x + 8 = 14 - x[/tex]

where x is the number, we're trying to find.

Now let's simplify the equation by combining like terms:

[tex]3/2x + 8 = 14[/tex]

Subtracting 8 from both sides:

[tex]3/2x = 6[/tex]

Multiplying both sides by 2/3:

[tex]x = 4[/tex]

So, the solution to the equation is x = 4.

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(a) the tare οf the rice is 800 grams. and (b) the tare percentage οf the rice is 3.10%.

A rate, number, οr amοunt in each hundred

a. The tare οf the rice is the weight οf the packaging οr cοntainer used tο hοld the rice. It can be calculated by subtracting the net weight οf the rice frοm the grοss weight οf the bag:

Tare weight = Grοss weight - Net weight

Tare weight = 25.8 Kg - 25 Kg

Tare weight = 0.8 Kg

Tο cοnvert this tο grams, we can multiply by 1000:

Tare weight = 0.8 Kg × 1000

Tare weight = 800 grams

Therefοre, the tare οf the rice is 800 grams.

b. The tare percentage οf the rice is the percentage οf the grοss weight that is accοunted fοr by the tare weight. It can be calculated using the fοrmula:

Tare percentage = (Tare weight / Grοss weight) × 100%

Substituting the values we fοund earlier, we get:

Tare percentage = (800 g / 25.8 Kg) × 100%

Tare percentage = 3.10%

Therefοre, the tare percentage οf the rice is 3.10%.

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Using binomial theorem we can expand the equation but We are not given the value of a or n, so we cannot determine c exactly.

Integers are real numbers that only comprise positive and negative whole integers as well as natural numbers. Because of rational and irrational numbers, real numbers may include fractions, whereas integers cannot.

A real number is a quantity in mathematics that may be expressed as an infinite decimal expansion. Real numbers, as opposed to natural numbers such as 1, 2, 3,..., which are generated from counting, are used in measures of continually changing quantities such as size and time.

by applying the binomial theorem:

[tex](1 + ax)^n = C(n, 0) + C(n, 1)(ax) + C(n, 2)(ax)^2 + C(n, 3)(ax)^3 + ...[/tex]

where C(n, k) is the binomial coefficient, which equals[tex]n!/(k!(n-k)!).[/tex]

The first few terms of this expansion are:

[tex](1 + ax)^n = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]

Comparing with the given expression [1 - 20x + 150x^2 + cx^3], we have:

[tex]1 - 20x + 150x^2 + cx^3 = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]

Equating coefficients of [tex]x^3[/tex] on both sides, we get:

[tex]c = n(n-1)(n-2)(a^3/6)[/tex]

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Answer:

Step-by-step explanation:

348.55

Probability of D2 being sunny = 0.78.

On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.

Therefore, we need to find the chances that D2 is sunny.

There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.

Now, Let us find the probability of D2 being sunny.

We have the following possible cases for D2.

D1 = Sunny; D2 = Sunny

D1 = Sunny; D2 = Rainy

D1 = Rainy; D2 = Sunny

D1 = Rainy; D2 = Rainy

The probability of D1 being sunny is 0.9.

When a sunny day follows a sunny day, the probability is 0.8.

When a sunny day follows a rainy day, the probability is 0.6.

Therefore, the probability of D2 being sunny is given by the formula:

Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.

Therefore, the probability that D2 is sunny are 0.78 or 78%.

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In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.

Each student in a class of 25 drinks a full 210 millilitre glass of milk, hence the amount of milk consumed overall during the break is:

25 students times 210 millilitres each equals 5250 millilitres.

Milk comes in 1000 millilitre bottles, thus to determine how many bottles are needed, divide the entire amount eaten by the volume of milk in each bottle.

5.25 bottles are equal to 5250 millilitres divided by 1000 millilitres.

We must round up to the nearest whole number because we are unable to have a fraction of a bottle. This results in:

6 bottles in 5.25 bottles

In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.

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Simplifying Mrs. Perez's class donated 11 units of vegetables, 66 units of pasta, and 22 units of soup.

The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible

vegetables = (1/9) x 99

Simplifying this expression, we get:

vegetables = 11

So the class donated 11 units of vegetables.

Next, we can figure out how much of the donation was pasta. We know that 2/3 of the donation was pasta, so we can set up the equation:

pasta = (2/3) x 99

Simplifying 66 units homemade pasta, 22 units of soup, and 11 units of veggies were all provided by Mrs. Perez's students.

Which expression should I simplify?

A math difficulty is simply solved by simplifying the expression. When you simplify a phrase, your goal is essentially to make it as simple as you can. There shouldn't be any more multiplication, dividing, adding, or removing to be done at the conclusion.

veggies = 1/9 times 99

When we condense this statement, we get:

eleven vegetables

We can then determine what proportion of the contribution was pasta. Given that we know that pasta made up 2/3 of the donation, we can construct the following equation:

spaghetti equals (2/3) x 99

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11.87 m² metal sheet would be needed to make the base area of tank.

Volume of cylinder, determines how much material it can carry, is determined by the cylinder's volume. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.

It is given that capacity of a closed cylindrical vessel of height 2 m is 3080 liters

Let us assume that Radius of cylinder = r

Then Volume of cylinder = π ×r² ×h

= 2π ×r²× m³

1 m³ = 1000 liters

= 2000 π r²  liters

Volume of tank = Capacity

2000 π r² = 3080

=> 2000 × (22/7) × r² = 3080

=> r² = 49/100

=> r = 7/10 m

=> r = 0.7 m

Base Area of tank = TSA = 2πrh + 2πr²

= 2×(22/7)(0.7)×2 + 2×(22/7)×(0.7)²

= 3.0772 +8.792

= 111.87 m²

Hence, 11.87 m² metal sheet would be needed to make it.

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The graph of an exponential function with an initial value of 10 and a base of 1.3z. Therefore option D is correct.

The function f(x) is an exponential function with a base of 1.3 and an initial value of 10. The graph of an exponential function with a base greater than 1 increases rapidly as x increases. Therefore, option a can be eliminated.

Option b is not a graph of an exponential function, as the function is not continuous and does not approach any asymptote.

Option c shows an exponential function with an initial value of 10 and a base of 1.3/10, which is less than 1. This means that the function would decrease over time, which is not consistent with the problem statement.

Option d shows an exponential function with an initial value of 10 and a base of 1.3, which is consistent with the problem statement. Therefore, option d is the correct answer.

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Answer:

24 cm (to nearest cm)

Step-by-step explanation:

XLV = extra large tin volume (cm³)

LV = large tin volume (cm³)

XLR = extre large tin radius (cm)

LR = large tin radius (cm) = 20

XLV = 1.75 × LV

Since the tins are geometrically similar cylinders, we can infer that the volumes and radii of the 2 tins are related;

We know the relationship between the volume of the two tins, i.e. the XL tin is 75% greater in volume than the L tin;

This means the volumetric scale factor or multiplier is ×1.75;

Subsequently, we know:

XLV = 1.75 × LV

Similarly, there is a relationship between the radii of the tins;

The relationship is, however, slightly different;

[tex]XLR = (\sqrt[3]{1.75}) \times LR[/tex]

We need to take the cube root of the volumetric scale factor, reason being, the radius is a linear dimension unlike volume;

Easy way to figure this is radius is in cm, volume is in cm³;

So:

XLR = 1.205... × LR

XLR = 1.205... × 20

XLR = 24.101... --> 24 cm (to nearest cm)

A function [tex]P(t) = 170.(1.30)^t[/tex]  that gives the deer population P(t) on the reservation t years from now

We were told there were 170 stags on reservation. The number of deer is increasing at a rate of 30% per year.

We could see the deer population grow exponentially since each year there will be 30% more than last year.

Since we know that an exponential growth function is in form:

[tex]f(x) = a*(1+r)^x[/tex]

where a= initial value, r= growth rate in decimal form.

It is given that a= 170 and r= 30%.    

Let us convert our given growth rate in decimal form.

[tex]30 percent = \frac{30}{100} = 0.30[/tex]

Upon substituting our given values in exponential function form we will get,

    [tex]P(t) = 170.(1+0.30)^t[/tex]

⇒ [tex]P(t)= 170.(1.30)^t[/tex]

Therefore, the function [tex]P(t) = 170.(1.30)^t[/tex] will give the deer population P(t) on the reservation t years from now.

Complete Question:

There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.

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Answer:

[tex]{ \sf{a = { \blue{ \boxed{{53 \: \: \: \: \: \: \: \: }}}}} \: cm}[/tex]

Step-by-step explanation:

[tex] { \mathfrak{formular}}\dashrightarrow{ \rm{4 \times side \: length}}[/tex]

Each side has length of a?

[tex]{ \tt{perimeter = a + a + a + a}} \\ \dashrightarrow{ \tt{ \: 212 = 4a}} \\ \\ \dashrightarrow{ \tt{4a = 212}} \: \\ \\ \dashrightarrow{ \tt{a = \frac{212}{4} }} \: \: \\ \\ { \tt{a = 53 \: cm}}[/tex]