50 points to whoever can answer this question w/ explanation.

Answer:

12

Step-by-step explanation:

2/3 of 48 is 32, 16 leftover.

1/4 of 16 is 4, 12 leftover

answer=12

Step-by-step explanation:

The potential energy stored in the spring can be calculated using the equation:

PE_spring = 1/2 * k * x^2

where k is the spring constant and x is the displacement of the spring from its rest position. In this case, x = 0.5 m.

The potential energy stored in the rope can be calculated as the gravitational potential energy of the object, which is given by:

PE_rope = m * g * h

where m is the mass of the object (10 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical displacement of the object.

The horizontal and vertical components of the displacement can be calculated using trigonometry:

x = 0.5 * cos(30) = 0.5 * sqrt(3)/2 m

y = 0.5 * sin(30) = 0.5/2 m

The total potential energy stored in the spring and rope is given by the sum of their individual potential energies:

PE = PE_spring + PE_rope = 1/2 * k * x^2 + m * g * h

Substituting in the given values, we find:

PE = 1/2 * k * (0.5 * sqrt(3)/2)^2 + 10 * 9.8 * (0.5/2 + 0.3)

Note: The spring constant (k) is not given, so the answer is given in terms of k.

Answer:

Step-by-step explanation:

The potentpotentialial energy stored in a spring is calculated by 1/2 * k * x^2, where k is the spring constant and x is the displacement from its rest position. The potential energy stored in the rope is calculated as m * g * h, where m is the object's mass, g is acceleration due to gravity and h is the object's vertical displacement. The total potential energy is the sum of these two energies. In this case, the horizontal and vertical components of the displacement can be calculated using trigonometry and then used to find the total potential energy stored in the spring and rope.

The extraneous solutions of the equation is -2 and 15.

ln stands for logarithm and it is a function that returns the power to which a certain number (base) must be raised to obtain a given value. The logarithm is commonly used to simplify mathematical expressions and can be thought of as an inverse operation to exponentiation.

In this equation, we have two logarithmic expressions on the left and right side. To solve for x, we need to find what number raised to the power of the base (ln), will result in x² - 30 and 13x.

So, if we find the height for one triangle, we can find the height for the other triangle. To do this, we will use the logarithmic property:

ln(aᵇ) = b * ln(a)

Where a and b are any positive real numbers.

Applying this property to both logarithmic expressions, we get:

ln(x² - 30) = ln((x² - 30)^(1/ln)) = 1/ln * ln(x² - 30)

Equating the two, we get:

1/ln * ln(x² - 30) = 1/ln * ln(13) + 1/ln * ln(x)

Dividing both sides by 1/ln, we get:

ln(x² - 30) = ln(13) + ln(x)

Using the logarithmic property, we can simplify further:

x² - 30 = 13 * x

Dividing both sides by x, we get:

x²/x - 30/x = 13

x - 30/x = 13

x² - 30 = 13x

x² - 13x - 30 = 0

This is a quadratic equation and can be solved using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Where a = 1, b = -13, c = -30

So,

x = (-(-13) ± √((-13)^2 - 4 * 1 * -30)) / 2 * 1

x = (13 ± √(169 + 120)) / 2

x = (13 ± √289) / 2

x = (13 ± 17) / 2

So,

x = (13 + 17) / 2 = 15 or

x = (13 - 17) / 2 = -2

These are the two solutions to the equation. To check for extraneous solutions, we substitute x = 15 and x = -2 back into the equation and see if it is true.

Complete Question:

Find the solution(s) to[tex]\ln\left(x^2-30\right)=\ln\left(13x\right)\ln ( x^2 - 30 ) = ln( 13 x )[/tex]

Check for extraneous solutions.

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Answer:

14. cross, bounce, cross

15. cross, bounce

16. [tex]x^{4}-12x^{3}+48x^2-64x[/tex]

Step-by-step explanation:

16.

x(x-4)(x-4)(x-4)

x(x-4)(x^2-8x+16)

x^3-8x^2+16x-4x^2+32x-64

x^4-12x^3+48x^2-64x

The solution is Option A.

The dilation scale factor is given by the equation D = 5

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the dilation scale factor be represented as D

Now , the equation will be

The coordinates of the triangle ΔABC is given as

A ( -3 , -3 ) , B ( 3 , 3 ), C ( 0 , 3 )

And , coordinates of the triangle ΔA'B'C' is given as

A′ ( -15 , -15) , B′ ( 15 , 15 ) , C′ ( 0 , 15 )

The dilation factor is given by D = x₂ / x₁ or D = y₂ / y₁

Substituting the values in the equation , we get

D = -15 / -3 = 5

And , D = 15 / 3 = 5

Hence , the dilation factor is 5

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The area of the given shape is  90.4  cm².

The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Given the shape of the boat, which contain, a rectangle and two right triangles,

total area = area of rectangle + area of triangle,

dimensions of the rectangle are,

length = 12 cm width = 5.2 cm

area of rectangle = l*b

area of rectangle = 12*5.2

area of rectangle = 62.4 cm²

area of triangle = 1/2*b*h

height = 8 cm

total base of both triangles = 3 + 4

base = 7 cm

area of triangle = 1/2*8*7

area of triangle = 28 cm²

total area =  62.4 cm² + 28 cm²

total area = 90.4  cm²

Hence the area is 90.4  cm².

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Answer:

32.) Yes

33.) 7

34.) No because 40 is less than 50

Step-by-step explanation:

32.)

Were trying to see is 35 is 3/4ths of 50, so we set up a ratio and solve

[tex] \frac{3}{4} = \frac{x}{50} [/tex]

Next we cross multiply

[tex]4x = 150[/tex]

Lastly divide by 4

[tex]x = 37.5[/tex]

33.) We have to convert 2/5 and 5/6 into a value over 30.

For 2/5, 5 times 6 is 30. 2 times 6 is 12, so we get 12/30 playing Chess.

6 times 5 is 30. 5 times 5 is 25. Making it 25/50 playing Sudoku

[tex] \frac{12}{30} = chess \: \frac{25}{30} = sudoku[/tex]

Since 5 don't play sudoku and 18 don't play chess.

18+5 = 23...

30-23 = 7

34.) The picture to the right shows 20 stamps.

Two sheets of stamps means 20x2 = 40, which is less than 50

To balance a see-saw, the product of the distance of the person's weight from the pivot and their weight must be equal on both sides.

Let's call Daniela's mass "m".

The force on Lucy's side is:

distance * weight = 3.5 meters * 50 kg = 175 kg * meters

The force on Daniela's side is:

distance * weight = d * m

Since the see-saw is balanced, the two forces must be equal:

3.5 * 50 = d * m

Solving for m, we get:

m = 175 / d

Without knowing the distance "d" that Daniela is sitting from the pivot, it is impossible to calculate her weight.

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Answer:

The correct answer is D: Head, head Tail, tail Head, tail Tail, head.

Step-by-step explanation:

When Henry tosses a coin twice, there are four possible outcomes, each with equal probability:

Head, head

Tail, tail

Head, tail

Tail, head

The value of x from the given equation is 7.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is ∛(4x-1)-7=-4.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, ∛(4x-1)-7=-4

∛(4x-1)=3

Cubing on both side of an equation, we get

(∛(4x-1))³=3³

4x-1=27

4x=28

x=7

Therefore, the value of x is 7.

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The measure of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

For the given triangle, let's call the length of the hypotenuse "h". Then, using the Pythagorean theorem:

h^2 = 2^2 + 7^2

h^2 = 4 + 49

h^2 = 53

h = √53

Rounding to the nearest tenth, h = 7.3 cm.

So, the measure of the hypotenuse of the right triangle with legs of length 2 cm and 7 cm is 7.3 cm.

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The flow rates of milk from the bottle are given as follows:

The flow rates are obtained applying the proportions in the context of this problem.

A baby takes 30 min to drink 150 mL of milk from a bottle, hence the rate in mL per minute is given as follows:

150/30 = 5 mL per minute.

Each minute is composed by 60 seconds, hence the rate in mL per second is given as follows:

5/60 = 1/12 mL per second.

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Answer:

C

Step-by-step explanation:

This is a formula - memorize it.

Answer:

the area of each cookie made by Tony is approximately 63.62 square cm.

Step-by-step explanation:

The area of a cookie can be found if we know its radius. To find the radius, we can divide the circumference by 2 times pi (π).

Let's call the radius of the cookie "r".

45 cm / (2 * π) = r

Now that we have the radius, we can find the area using the formula:

π * r^2 = area

So,

π * r^2 = π * (45 / (2 * π))^2 = (45^2) / (4 * π)

Therefore, the area of each cookie made by Tony is approximately 63.62 square cm.

a)  it costs more money to make 100 photocopies

b) you can buy more than 500 photocopies for $40

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

a) In the  graph , 100 photocopies cost $10,

For 101  photocopies, the point on the line comes below of 10 on y axis

So, it costs more money to make 100 photocopies

b)  graph arrow shows line moves on...

so, you can buy more than 500 photocopies for $40

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The sample consists of 4 selected sites, and the corresponding parameter is the population's minimum temperature. The lowest temperature for the sample is 170 °F .

The sampling size is the number of records which used derive estimates for a certain population. A sample size from the population was selected. The amount of subjects the observations that compose up a study is referred to as the "sample size." This number is sometimes referred to as the symbol n. Two statistical traits are influenced by the sample size: 1) The accuracy of our estimations; 2) The power of investigations to draw conclusions. The samples represent the outcomes of random tests. A specific value is selected from a set of possible values when sample a random variable. This particular value is a sample. The potential values and their possibilities are determined by the random variable's posterior distribution.

given

A parameter is a descriptive measure for a population, as opposed to a statistic, which is a descriptive measure for a sample.

170 F is a statistic because it represents the sample minimum temperature and is based on a sample of four randomly selected sites.

The corresponding parameter is changed to the minimum population temperature.

The lowest temperature for the sample is 170F. (F).

Minimum population temperature as a parameter

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Answer: He can have 8 friends.

Step-by-step explanation: 78 minus 42(Private party fee)= 36.

36 divided by 4.5(Per person)= 8

The concept is a Dependent Variable. It's the outgrowth variable of interest that's observed to see whether it's told by a manipulated variable.

The dependent variable is the variable that's being measured or tested in a trial. One way to help identify the dependent variable is to the flashback that it depends on the independent variable.

When experimenters make changes to the independent variable, they also measure any performing changes to the dependent variable. An experimenter might also choose dependent variables grounded on the complexity of their study.

Stability is frequently a good sign of an advanced quality-dependent variable. The dependent variable belongs on the y-axis ( perpendicular line).

Question

What type of variable is the outgrowth of a study?

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Quantitative research is the procedure of gathering and performing a numerical analysis. It can be used to identify trends and averages, formulate hypotheses, examine causality, and extrapolate findings to larger population.

Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings.

Quantitative research collects information from existing and potential customers using sampling methods and sending out online surveys, online polls, and questionnaires, for example. One of the main characteristics of this type of research is that the results can be depicted in numerical form.

An unofficial relationship is mentioned in a theory. If the frequency of winning is correlated with the frequency of purchasing lottery tickets, for instance. "Then" is followed by a forecast of what will happen if you buy lottery tickets more frequently or less frequently.

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The equations can be solved using algebraic methods to find the value of x and y and understand the cost difference between different flowers.

Each system of equations represents the cost of flowers at a florist. By using two equations, we can determine the relationship between the cost of different flowers.

For the first system of equations where red roses cost x dollars and daisies cost y dollars, we can see that 4x + 4y - 36 represents the cost of red roses and x + 2y - 12 represents the cost of daisies. By solving for x and y, we can determine that red roses cost twice as much as daisies.

In the second system of equations where red roses cost x dollars and tulips cost y dollars, we can see that 2x + 3y - 24 represents the cost of red roses and 2x + y - 16 represents the cost of tulips. Solving for x and y, we can determine that red roses cost 50 percent more than tulips.

In the third system of equations where white roses cost x dollars and red roses cost y dollars, we can see that 2x + y - 22 represents the cost of white roses and x + 3y - 26 represents the cost of red roses. Solving for x and y, we can determine that white roses cost twice as much as red roses.

The fourth system of equations where tulips cost x dollars and daisies cost y dollars can be represented by 2x + 3y = 17 and x + y = 7. By solving for x and y, we can determine that tulips cost 50 percent more than daisies.

The fifth system of equations where white roses cost x dollars and tulips cost y dollars can be represented by 3y - 20 and 2x + y = 20. By solving for x and y, we can determine that white roses cost twice as much as tulips.

In the last system of equations where white roses cost x dollars and daisies cost y dollars, we can see that 3x + 2y = 30 represents the cost of white roses and x + y - 11 represents the cost of daisies. By solving for x and y, we can determine the relationship between white roses and daisies.

In conclusion, by using two equations for each system of flowers, we can determine the relationship between their costs.

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Answer:

let 5= a and b = 3^1/3

(a+b) ( a-b)

a^2-b^2

putting the value of a and b we get

(5)^2-(3)^2/2

25-3

22

The volume of the buoy is the sum of volume of hemisphere and volume of cone which is 0.504m³

To calculate the volume of the buoy, we need to find the volume of the hemisphere and the volume of the cone.

The volume of a hemisphere can be calculated using the formula:

V = (2/3) * π * (r^3)

where "r" is the radius of the hemisphere.

So, the volume of a hemisphere with radius "r" is equal to (4/3) times π times the cube of the radius.

The base is 0.95 and the radius is half the length of the base.

radius = 0.95 / 2 = 0.475m

The volume of the hemisphere = 2/3 * 3.14 * 0.475³

volume of hemisphere = 0.224m³

The volume of the cone = 1/3 πr²h

The volume of the cone = 1/3 * 3.14 * 0.475² * 1.2

The volume of the cone = 0.28m³

The volume of buoy = volume of sphere + volume of cone

The volume of buoy = 0.224 + 0.28 = 0.504m³

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Answer:

x = 41

Step-by-step explanation:

Supplementary Angles rule (straight lines in total have the angle of 180):

180 - 147 = 33

Total angles in a triangle equal 180:

180 - 33 - 106 = x

x = 41

The probability that it lands heads at least once is 1.0720.

Probability is the measure of the likelihood of an event occurring. In this case, we are looking at the probability of a coin landing heads at least once after three tosses.

Let's denote the event of the coin landing heads on the first toss as event A, the event of the coin landing heads on the second toss as event B, and the event of the coin landing heads on the third toss as event C.

The probability of landing heads at least once is equal to the sum of the probabilities of each individual event occurring (A, B, or C) minus the probability of all three events occurring (A and B and C).

P(A or B or C) = P(A) + P(B) + P(C) - P(A and B and C)

Since the coin is unfair and has a probability of 0.4 of landing heads, P(A) = P(B) = P(C) = 0.4.

Using the formula for the probability of multiple events happening simultaneously, we find that P(A and B and C) = P(A) * P(B) * P(C) = 0.4 * 0.4 * 0.4 = 0.064.

Plugging in all the values, we get:

P(A or B or C) = 0.4 + 0.4 + 0.4 - 0.064 = 1.136 - 0.064 = 1.072

Rounding to four decimal places, the answer is 1.0720, which means that the probability of the coin landing heads at least once after three tosses is 1.0720.

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Answer:

No it's not!

Pythagorean theorem

15² + 9² = it's not 20

15² + 9² = 17 so

NO

The value of the cubic polynomial evaluated at x = 0.5 is equal to 8.

In this problem we find the case of a cubic polynomial in standard form:

y = a · x³ + b · x² + c · x + d

Where a, b, c, d are real coefficients.

The values of the coefficients must be determined on the knowledge of the leading coefficient (a = 2), the constant term (d = 5) and two values (y(- 1) = 2, f(1) = 14). First, substitute the leading coefficient and the constant term in the definition:

y = 2 · x³ + b · x² + c · x + 5

y - 2 · x³ - 5 = b · x² + c · x

Second, form the system of linear equations by using the given values:

b - c = - 1

b + c = 7

Third, solve the resulting system by numerical methods:

(b, c) = (3, 4)

Fourth, write the resulting polynomial:

y = 2 · x³ + 3 · x² + 4 · x + 5

Fifth, evaluate the polynomial at x = 0.5:

y = 2 · 0.5³ + 3 · 0.5² + 4 · 0.5 + 5

y = 8

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The required value of d in the given arithmetic operation is 9/10.

What are subtraction and addition?

The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction. To add, one must add two or more numbers or values to produce a new number. The inverse of addition is subtraction and vice versa.

For instance, 10 - 1 = 9 if 9 + 1 = 10. That demonstrates that adding 1 produces the number 10 when added to 9, but subtracting 1 from 10 produces the number 9.

Given, -1/3d + 4/5 = 1/2

[tex]\frac{-1}{3} d+\frac{4}{5} =\frac{1}{2} \\\\\frac{-1}{3} d =\frac{1}{2}-\frac{4}{5}\\\\\frac{-1}{3} d = \frac{5-8}{10}\\\\\frac{-1}{3} d = \frac{-3}{10}\\\\\frac{d}{3}=\frac{3}{10}\\\\d = \frac{9}{10}[/tex]

So, the required value of d = 9/10.

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The volume of wheat in the silo is about 1,570 feet and it would take about 63 minutes at the given rate for the silo to empty fully.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these shapes.

The silo is in the shape of cone, so use the formula of volume of a cone to find volume of wheat the tank can hold.

The formula to find volume of a cone is:

V = 1/3 · πr2h -----(1)

Substitute π ≈ 3.14, r = 10 and h = 15 in (1).

V ≈ 1/3 · 3.14 · 102 · 15

V ≈ 1/3 · 3.14 · 100 · 15

V ≈ 1,570

So, the volume of wheat in the silo is about 1,570 feet.

Silo can release wheat from its bottom at the rate of 25 cubic feet per minute.

= 1,570 / 25

= 62.8

≈ 63

Hence, it would take about 63 minutes for the silo to empty fully.

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Answer:

Step-by-step explanation:

Volume is whl.

= 1680 = (14)(12)(x)

= 1680 = 168x

= x = 10

The length is 10ft

Answer: 10 Feet

Step-by-step explanation:

Volume of pool = Length x Width x Depth = LxWxD  

We know  D = 12 feet   W = 14 feet  

So  Lx  14 x 12 = 1680      Solving for L = 10 feet