Sno-Cone at the carnival has the shape of a hemisphere on top of an inverted cone. What is the volume of the sno-cone if its radius is 5 cm and the height of the conical portion is 9.6 cm?

Answer:

To solve the system of linear equations:

x_1 + 3x_2 = 1 ...(1)

2x_1 + 5x_2 = 3 ...(2)

We can use the method of elimination to eliminate one of the variables. To do this, we multiply equation (1) by 2, and subtract it from equation (2), as follows:

2(x_1 + 3x_2 = 1) => 2x_1 + 6x_2 = 2 ...(3)

2x_1 + 5x_2 = 3 ...(2)

(2x_1 + 6x_2 = 2) ...(3)

-x_2 = 1

Thus, we have found that x_2 = -1.

We can substitute this value of x_2 into either equation (1) or (2) to solve for x_1. Let's use equation (1):

x_1 + 3(-1) = 1

x_1 - 3 = 1

x_1 = 4

Therefore, the solution to the system of linear equations is x_1 = 4, x_2 = -1.

So the solution set is {(4, -1)}.

The length of CF is solved to be 12

In the figure the value of CF is solved using the vertical angle theorem and sum of angles in a triangle

In triangle GBC

angle C = 180 - 90 - 45

angle C = 45

Using vertical angle theorem

angle DCB = angle DCF

Using trigonometry relation we have

cos 45 = CF / 12√2

CF = cos 45 * 12√2

CF = 12

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The solution to the inequality is x ≤ 1.

Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.

To solve this inequality, we must first perform the operations on the left side of the equation to get an expression equal to 4. We can start by simplifying the fraction on the left side of the equation. We can multiply both the numerator and denominator by x, which will give us 5x - 3 = x + 2x. We can then add 3 to both sides to get 5x = 3 + 2x, which can then be simplified to 3x = 3. Finally, we can divide both sides by 3 to get x = 1. Therefore, the solution to the inequality is x ≤ 1.

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Answer:

X=4.5, or X=4 1/2

Step-by-step explanation:

Answer: el enunciado cinco veces la diferencia de un numero y 3 es 17

Step-by-step explanation:

Answer:

ATQ, 5( x -3 ) = 17

5 x - 15 = 17

5x = 17 + 15

x = 32 /5

x = 6.4 ,

Answer: One foot is equal to 12 inches, and since 1 inch is equal to 2.54 centimeters, we have:

1 foot = 12 inches = 12 x 2.54 cm = 30.48 cm

So the length of the flat bar is 30.48 cm. Multiplying this length by the price per cm, we get:

30.48 cm x 2 pesos/cm = 60.96 pesos

Therefore, we need 60.96 pesos to buy a flat bar of length 1 foot at a price of 2 pesos per cm.

Step-by-step explanation:

The circumference of a circle with a radius of 14 feet is 88 feet.

Every point in the surface of a circle, which is a circular, two-dimensional object, is evenly separated from the centre. All lines that cross the circle join together to produce the line of reflected symmetry. Each angle has axis of symmetry around the centre, in addition. Monitoring a linear interpolation in a surface while keeping a fixed distance from some other point will result in the closed shape of a circle. The English term circle derives from the Greek word curriculum provides students, which also means hoop or ring.

When we find the circumference, we obtain:

The  circumference( C) of a circle is 2πr.

C=2πr

⇒C=2×[tex]\frac{22}{7}[/tex]×14=88 feet.

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Answer:

g(x) = x + 3

Step-by-step explanation:

To see how this works, we can plug g(x) into f to get:

f(g(x)) = f(x + 3) = (x + 3)^3

Then, we can simplify h(x) = (x + 9) as follows:

h(x) = (x + 9) = ((x + 3) + 6) = g(x) + 6

Finally, we can write h(x) in terms of f(g(x)) as:

h(x) = g(x) + 6 = f(g(x)) + 6 = f(x + 3) + 6 = (x + 3)^3 + 6

commission percentage = 2.18%

Percentage is a way of expressing a proportion or a fraction as a fraction of 100. It is denoted by the symbol "%". For example, if there are 50 red marbles out of 100 marbles in a jar, the percentage of red marbles in the jar would be 50%.

To find the salesperson's commission as a percent of the total monthly sales, we first need to calculate the total monthly sales for September and October combined:

Total monthly sales = September sales + October sales

Total monthly sales = $85,460 + $74,570

Total monthly sales = $160,030

Next, we can divide the commission earned by the total monthly sales and multiply by 100 to get the commission as a percentage:

Commission percentage = (Commission earned / Total monthly sales) x 100

Commission percentage = ($3,485 / $160,030) x 100

Commission percentage = 2.18%

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Answer:

f/ 3 4 5 6

b/ 8 10 12 14

Step-by-step explanation:

the 4th wall has 6×3-4=14

so the relationship is

f/ 3 4 5 6

b/ 8 10 12 14

The solution is, the required z-score is, 0.25.

In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.

here, we have,

Given that :

Mean score, μ = 69

Standard deviation, σ = 4

Score, x = 64

The standardized score, Zscore can be obtained using the formular :

Zscore = (x - μ) / σ

Zscore = (69 - 68) / 4

Zscore = 1 / 4

Zscore = 0.25

Hence, The solution is, the required z-score is, 0.25.

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Answer:

x = -7.8

Step-by-step explanation:

Solve for x:

[tex]x-(-3.9)=-3.9[/tex]

Simplify

[tex]x+3.9=-3.9[/tex]

Subtract 3.9 on both sides

[tex]x=-7.8[/tex]

Point-slope form: y - (-2) = -4(x - 2)

Slope-intercept form: y = -4x - 6

Own integers:

Point-slope form: y - 2 = -2(x - 4)

Slope-intercept form: y = -2x - 6

Point slope form is a type of linear equation that describes the relationship between two points on a line. It is written in the form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Point slope form is used to find the equation of a line when given its slope and one point on the line. It can also be used to find the slope of the line when given two points on the line.

For example, if the point (2, 3) is given and the slope is 4, the point-slope form of the equation would be y - 3 = 4(x - 2).

The point-slope form of an equation of a line is an equation of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this equation, (x1, y1) = (2, -2) and m = -4, so the point-slope form of the equation is y - (-2) = -4(x - 2).

The slope-intercept form of an equation of a line is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept of the line. In this equation, m = -4 and b = -6, so the slope-intercept form of the equation is y = -4x - 6.

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From the arithmetic sequence, the last row has 47 seats, and the auditorium has 15 rows.

We can solve this problem by recognizing that the number of seats in each row forms an arithmetic sequence. Let's call the first term of the sequence (the number of seats in the first row) "a" and the common difference between terms (the number of seats added for each subsequent row) "d".

Using this notation, we have:

a = 8

a + d = 11

a + 2d = 14

We can solve for a and d by subtracting the first equation from the second and the second equation from the third:

d = 3

a = 5

Therefore, the arithmetic sequence that describes the number of seats in each row is:

5, 8, 11, 14, ...

To find the number of seats in the last row, we need to find the nth term of this sequence, where n is the number of rows in the auditorium. We can use the formula for the nth term of an arithmetic sequence:

an = a + (n - 1)d

Since we don't know n, we need to find it first. We can use the formula for the sum of an arithmetic sequence to find the number of rows:

Sn = n/2(2a + (n - 1)d)

We know that there are 435 seats in total, so we can set Sn equal to 435 and solve for n:

435 = n/2(2(5) + (n - 1)(3))

435 = n/2(3n + 7)

870 = n(3n + 7)

3n^2 + 7n - 870 = 0

(n - 15)(3n + 58) = 0

Since n cannot be negative, we have n = 15.

Now that we know there are 15 rows, we can find the number of seats in the last row by plugging n = 15 into the formula for the nth term:

an = a + (n - 1)d

a15 = 5 + (15 - 1)(3)

a15 = 5 + 42

a15 = 47

Therefore, the last row has 47 seats, and the auditorium has 15 rows.

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Translation:

Inside an auditorium there are 435 seats, in such a way that in the first row there are 8 seats, in the second row there are 11, in the third there are 14, and so on, an arithmetic sequence is formed. How many chairs are in the last row? How many rows does that auditorium have?

Answer:

15. x = -3.

16. x = -2.

17 x = 2.

Step-by-step explanation:

To solve the equation 7x + 5 = 12x - 10, we want to isolate the variable x on one side of the equation. We can do this by adding or subtracting terms from both sides of the equation until we have x by itself.

First, let's simplify both sides of the equation by combining like terms:

7x + 5 = 12x - 10

-7x -7x (subtracting 7x from both sides)

5x + 5 = -10

Next, let's isolate the term with x by subtracting 5 from both sides of the equation:

5x + 5 = -10

-5 -5 (subtracting 5 from both sides)

5x = -15

Finally, let's solve for x by dividing both sides of the equation by 5:

5x = -15

x = -3

Therefore, the solution to the equation 7x + 5 = 12x - 10 is x = -3.

26 = 24 - x

-24 -24 (subtracting 24 from both sides)

2 = -x

Next, let's isolate the variable x by multiplying both sides of the equation by -1:

2 = -x

-1 -1 (multiplying both sides by -1)

-2 = x

Therefore, the solution to the equation 26 = 24 - x is x = -2.

2(6x - 7) = 10

12x - 14 = 10

Next, let's isolate the term with x by adding 14 to both sides of the equation:

12x - 14 = 10

+14 +14 (adding 14 to both sides)

12x = 24

Finally, let's solve for x by dividing both sides of the equation by 12:

12x = 24

x = 2

Therefore, the solution to the equation 2(6x - 7) = 10 is x = 2.

The amplitude, period and frequency are 1, 2π and 1/2π

From the question, we have the following parameters that can be used in our computation:

f(x) = sin(x - π/2) - 2

A sinusoidal function is represented as

f(x) = Asin(B(x + C)) + D

Where

Amplitude = A

Period = 2π/B

So, we have

A = 1

Period = 2π/1

Period = 2π

For the frequency, we have

frequency = 1/Period

frequency  = 1/2π

Hence, the frequency is 1/2π

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Answer:

In the given triangle.

Base= 3

Perpendicular=4

Hypotenuse=5

Step-by-step explanation:

CosB = B/H

=3/5

Sin B = P/H

= 4/5

Tan B = P/B

= 4/3

The value of the equation a - 32 = 47 is a = 79.

The correct option is D.

A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.

Given:

An equation,

a - 32 = 47.

To find the value of a:

We will use some mathematical operations.

Add 32 to both sides of the equation,

we get,

a - 32 + 32 = 47 + 32

a - 0 = 79

a = 79

Therefore, the value of a is 79.

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If x represents the number of apples purchased and y represents the number of mangos we can set up the following:

Kayden has $20, so can spend up to this amount:

He must buy a minimum of 16 apples and mangos altogether:

Also, he must buy no less than 16 apples:

We also need to consider y can't be negative, hence add one more inequality:

Plot all four inequalities and see what is the zone of intersection.

The solution is the set of whole coordinates for x and y within the triangle with vertices at (16, 0), (16, 4) and (26.67, 0).

One possible solution is (20, 2) another one (24, 1).

See attached.

The exponential equation that passes through these two points is:

y = 26.678*(14/11)^x

A general exponential equation is:

y = A*(b)^x

If we know the two points (3, 55) and (4, 70), then we can write  two equations:

55 = A*(b)^3

70 = A*(b)^4

If we take the quotient between the second equation and the first one, then we get:

70/55 = (A*(b)^4)/(A*(b)^3)

70/55 = b

14/11 = b

Then we can write:

55 = A*(14/11)^3

(11/14)^3*55 = A

26.678 = A

Then the exponential equation is:

y = 26.678*(14/11)^x

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The solution of the given problem of Test statistic comes out to be Using a table or calculator with 98 degrees of freedom, we find the value to be approximately 0.06.

The test statistic for anything akin to a Z-test has been the Z-statistic, which shows the ordinary normal neutral hypothesis is correct. Suppose you perform a 2 different X y test with a 0.05 threshold of significance and, based on your data, you obtain a 2.5 R t (also referred as a Z-value). 0.0124 is the value for the this Z-value.

Here,

: un - ud <= 0 (the mean GPA of night students is less than or equal to the mean GPA of day students)

H: un - ud > 0 (the mean GPA of night students is greater than the mean GPA of day students)

We will use a significance level of 0.05.

The test statistic is calculated as:

t = (xn - xd - 0) / √(s²/n + s²/n)

where xn and xd are the sample means, s and s are the sample standard deviations, and n is the sample size.

Plugging in the values from the problem, we get:

t = (2.91 - 2.87 - 0) / √0.08²/50 + 0.06²/50) = 1.57

The degrees of freedom for the t-distribution is

f = n₁ + n₂ - 2 = 50 + 50 - 2 = 98 (assuming equal variances).

Using a table or calculator with 98 degrees of freedom, we find the

value to be approximately 0.06.

Since the value (0.06) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to support the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.05 significance level.

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We can use the formula for compound interest to find the time it will take to reach the target amount:

FV = PV * (1 + r)^t

where FV is the future value (target amount), PV is the present value (amount you have today), r is the interest rate, and t is the time (in years).

Substituting the given values, we get:

230000 = 31000 * (1 + 0.045)^t

Simplifying and solving for t, we get:

t = log(230000/31000) / log(1 + 0.045)

t ≈ 14.09

Therefore, it will take approximately 14.09 years to save enough to buy the Ferrari.

Answer:

Below

Step-by-step explanation:

Definition of density is  mass / volume = 1250 g / (5 x14x7) = 2.55 gm/cm^3

The value of y in the regular dodecagon is 8°

What is Dodecagon?

Dodecagon is is a closed figure that has 12 sides and 12 angles. It has 12 vertices, each of which is connected to two sides.

What is Regular Dodecagon?

Regular Dodecagon is has all 12 sides of equal length and all angles of equal measure. It is a 12-sided polygon that is symmetrical.

To find the interior angle ,

= (n - 2)180° where the sides is 12

= (12-2)180°

= 1800°

= 1800/12  = 150°

i.e, each angle of the dodecagon = 150°

To determine this,

17y + 14° = 150°

17y = 150° - 14°

17y = 136°

y = 136°/17

y = 8°

Therefore, the value of y = 8°

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The answer is option B, 1(1/2) yards.

How to determine the total amount?

We apply the following total sales calculation to get the total sales amount.

Total sales = original price + original price * sales tax rate

To find out how many yards of cloth remain, we need to subtract the amount used for making curtains from the total amount provided:

Total amount of cloth provided = 5(3/4) yards

Amount of cloth used for curtains = 4(1/4) yards

Remaining amount of cloth = Total amount of cloth provided - Amount of cloth used for curtains

= 5(3/4) - 4(1/4) yards

= 5 yards + 0.75 yards - 4 yards - 0.25 yards

= 1(1/2) yards

Therefore, the answer is option B, 1(1/2) yards.

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The solution is, y = 2x + 5+4 when graph would shift by 4 unit.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Given  : y = 2x + 5 .

To find :

If you wanted to shift the graph up what would be equation .

Solution : We have given that y = 2x + 5 .

BY the transformation rule ;

if f(x) +k then graph would shift up by k units .

Then to shift the graph of y = 2x + 5 up we need to add something in 5

Like   y = 2x + 5+4

Then graph would shift by 4 unit.

Therefore,   y = 2x + 5+4 graph would shift by 4 unit.

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Answer:

£750

Step-by-step explanation:

The interest Kay will have to pay can be calculated using the simple interest formula:

interest = principal x rate x time

where the principal is the amount borrowed, the rate is the annual interest rate, and the time is the duration of the loan in years.

In this case, the principal is £5,000, the rate is 15% per year, and the time is 1 year. Substituting these values into the formula, we get:

interest = 5000 x 0.15 x 1 = £750

Therefore, Kay will have to pay £750 in interest over the course of the one-year loan.

Answer:

Step-by-step explanation:

Since the interest rate is 15%, she'll have to pay 15% of the principal per yar, which is £5000 x 15 / 100 = £750. And since she borrows it for only one years, that total amount of interest will be £750 x 1 = £750.

The snowstorm resumes at a consistent rate of 2 inches per hour after 5 hours. Draw a second diagonal line with a slope of 2 as a result. Points 7 and 10 should be the beginning and finish of this line, respectively (14,18).

The resulting graph should include a horizontal line at y=10 from (0,4) to (2,10), a diagonal line with a slope of 2 from (7,10) to (0,4), and a horizontal line at y=3 from (0,4) to (0,10). (14,18).

Graphs are visual representations of data that show how any two variables relate to one another. Without requiring a lot of words, they are frequently used to communicate complex and large amounts of data. A specific amount of data must be gathered through surveys or experiments before a graph may be created.

To create the graph of the snow on the ground over time, we can follow these steps:

Start with a point at (0,4) since at the beginning of the storm there were 4 inches of snow on the ground.

From this starting point, draw a diagonal line with a slope of 3, representing the constant rate of snowfall of 3 inches per hour. This line should have a y-intercept of 4 and an x-intercept of 2 (since 6 inches of snow fell in 2 hours).

After the 6 inches of snow have fallen, the snowstorm stops for 5 hours. During this time, the snow on the ground remains the same. So, draw a horizontal line at the y-value of 10 (since there are 10 inches of snow on the ground after the first 6 inches fall).

After 5 hours, the snowstorm starts again at a constant rate of 2 inches per hour. So, draw another diagonal line with a slope of 2. This line should start at the point (7,10) and end at the point (14,18).

The resulting graph should have a diagonal line with a slope of 3 from (0,4) to (2,10), a horizontal line at y=10 from (2,10) to (7,10), and a diagonal line with a slope of 2 from (7,10) to (14,18).

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