the net of a cylinder with a radius of 3cm and a height of 14cm is drawn below. work out the surface area of the cylinder.

Answer:

x = -8

Step-by-step explanation:

3x + 15 - 8 - 9x = 55

(3x+−9x)+(15+−8)=55(Combine Like Terms)

−6x+7=55

−6x=48

x=−8

Let's define the following variables.

x = amount of $8 sparkling water

y = amount of $3 sparkling water

z = amount of $4.50 sparkling water

If we want to create 200 gals of sparkling water then we can form the equation below:

"She must use twice as much of the $4.50 water as the $3.00 water" means the amount of z must be twice to equate to y.

Using the value of y, we can rewrite equation 1 as:

Then, applying the cost per gallon in each type of sparkling water, we have another equation:

To summarize, we have:

Equation 1: x + 3y = 200

Equation 2: 8x + 12y = 1000

Graphing these two equations, we get:

The intersection of the two equations is at (50, 50)c

Therefore, the value of x = 50 gallons and the value of y = 50 gallons.

Now, since z = 2y, ten xz = 2(50) = 100 gallons. z = 100 gallons

In conclusion,

50 gallons of $8.00 sparkling water

50 gallons of $3.00 sparkling water

100 gallons of $4.50 sparkling water

By solving simultaneous linear equation, it can be calculated that

The two numbers are 82 and 48

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Let the numbers be x and y

The sum of two numbers is 130

so, x + y = 130 .... (1)

The difference of two numbers is 34

so, x - y = 34 ..... (2)

Adding  (1) and (2),

2x = 164

\(x = \frac{164}{2}\\x = 82\)

Putting the value of x in (1)

82 + y = 130

y = 130 - 82

y = 48

The two numbers are 82 and 48

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Answer:  It is 0.81

Step-by-step explanation:

I wont give an explanation this time sorry I don't feel like it but just so you know I got this answer right so trust me.

The missing side length of the triangle is s = 10 units

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔXYZ

Now , the triangles are similar

where ΔABC ≅ ΔXYZ

And , corresponding sides of similar triangles are in the same ratio

So , AB / BC = XY / YZ

3 / 5 = 6 / s

Multiply by s on both sides , we get

s ( 3/5 ) = 6

Divide by ( 3/5 ) on both sides , we get

s = 10

Hence , the length of s is s = 10 units

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You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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The equation of the line of best fit using two points on the line is y = 2х + 2. Option B is the answer.

Using thе slоpe-interсept form оf а lineаr еquаtion: y = mх + b, where m is thе slоpe оf thе line аnd b is thе y-interceрt.

Тo find thе slоpe, we cаn use thе formulа:

m = (y2 - y1)/(х2 - х1)

where (х1, y1) аnd (х2, y2) аre two pоints on thе line.

Using thе pоints (4, 10) аnd (6, 14), we get:

m = (14 - 10)/(6 - 4) = 2

So thе slоpe оf thе line is 2.

Тo find thе y-interceрt, we cаn use one оf thе pоints аnd thе slоpe. Let's use thе рoint (4, 10):

y = mх + b 10 = 2(4) + b 10 = 8 + b b = 2

So thе y-interceрt is 2.

Рutting it аll togethеr, we get thе еquаtion оf thе line оf bеst fit:

y = 2х + 2

Therefore, thе аnswer is В. y = 2х + 2.

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Answer:

16)  7⁻²

17) -1⁻²

Step-by-step explanation:

plug in the x=, y=, and n= into the equation.

Answer:

60.2 grams is remaining after 7 minutes.

Step-by-step explanation:

Exponential equation for amount of substance:

The exponential equation for the amount of a substance is given by:

\(A(t) = A(0)(1-r)^t\)

In which A(0) is the initial amount and r is the decay rate, as a decimal, and t is the time measure.

An element with mass 510 grams decays by 26.3% per minute.

This means that \(A(0) = 510, r = 0.263\)

So

\(A(t) = A(0)(1-r)^t\)

\(A(t) = 510(1-0.263)^t\)

\(A(t) = 510(0.737)^t\)

How much of the element is remaining after 7 minutes?

This is A(7). So

\(A(7) = 510(0.737)^7 = 60.2\)

60.2 grams is remaining after 7 minutes.

Yes. Hope this helps!

Step-by-step explanation:

Greetings !

Given fraction

\(4 \frac{5}{6} \)

convert mixed fraction to improper fraction

\(a \frac{b}{c} = \frac{a.c + b}{c} \)

\(4 \frac{5}{6} = \frac{4.6 + 5}{6} = \frac{29}{6} \)

Hope it helps!

A fully inflated professional basketball has a circumference of 78 centimetres, hence the football's radius is 12.42 cm.

A circle is created when almost every point there in plane that is a specific distance away from another point does so (center). As a conclusion, it is a curve made up of segments that are spaced from each other in the plane. It is rotationally homogeneous about the centre in anyway angles. All pair of points in the grid that make up a circle are evenly spaced away from the "centre" and create a closed, two-dimensional object. A specular parity line is generated by a line that passes through circle. It is rotationally symmetric about just the centre at all angles.

given

The football's circumference is 12.42 cm.

Football's circumference is 78 cm.

The formula for the football's circumference is C = 2pir

= 78 r

= 78/2pi r

= 12.42 cm.

A fully inflated professional basketball has a circumference of 78 centimetres, hence the football's radius is 12.42 cm.

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Answer:

483960

Step-by-step explanation:

484848

-     888

______

483960

The two circles, A and B have different diameters. The diiameter of circle A is 5 units while the diameter of circle B is 4 units. This means that circle B is smaller than circle A. This means that there is a dilation and it is a reduction. Thus, we can say that B is 4/5 * A

4/5 * 5 = 4

The image was then translated 12 units down. The correct option is the third one

Answer:

-2/12, -0.1, 1/9

Step-by-step explanation:

Answer:

Least to greatest: -2/12 , -0.1 , 1/9

Greatest to least: 1/9, -0.1, -2/12

Step-by-step explanation:

Change all of the numbers so that they are either fractions or decimals. Usually it is easier to change all the numbers to decimal.

Divide:

1/9 = ~0.111 (rounded)

-0.1 = -0.1

-2/12 = - ~0.167 (rounded)

Put the numbers in number order:

-~0.167 , -0.1 , ~0.111

-2/12 , -0.1 , 1/9

~

Answer:

There are 3 two topping sundaes possible.

Step-by-step explanation:

The order in which the toppings are chosen is not important. For example, chocolate and caramel topping is the same as a caramel and chocolate topping. So we use the combinations formula to solve this question.

Combinations Formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

How many 2 topping sundaes are possible?

2 toppings from a set of 3(chocolate, caramel and strawberry). So

\(C_{3,2} = \frac{3!}{2!(3-2)!} = 3\)

There are 3 two topping sundaes possible.

Answer:

Step-by-step explanation:

the figure is formed by two rectangles, we find the area of ​​both and we add

34 * 8 + 12 * 20 =   (remember pemdas)

272 + 240 =

512 ft²

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Commutativity justifies the statement, of If n is a multiple of 8, then n is even. However, n is not even. Therefore, n is not a multiple of 8.

Commutativity is used in Maths equations and describes sums that can be moved around and will still give the same answer.

'Commutative' comes from the word 'commute' which means to move and travel around, so equations that are commutative have numbers that can be moved within the equation.

commutative law, in mathematics, is either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba.

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Answer:

Step-by-step explanation:108 divided by 12 equals 9 so nine feet next to 108 inches.

and nine divided by 3 is 3 so nine yards in the row with 108 inches.

360 divided by 12 which is 30 so 30 feet in the row with 360 inches.

90 feet divided by three so 30 so 30 yards in the row with 360 inches.

24 inches equals 2 feet

double this length is 48 inches or 4 feet

so in all he cut 6 yards and since he only had three yards you will still have  3 yards left over.

The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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Answer:

a)  963g

b) 17

Step-by-step explanation:

i) Now we must first find the common difference of the AP

d = 7.8 -6 = 1.8

Now the sum of the AP gives the total amount of chemical used for 30 experiments

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

n= 30, a = 6, d= 1.8

Sn = 30/2[2(6) + (30-1) (1.8)]

Sn = 15[12 + 52.2]

Sn = 963g

ii)For the G.P the common ration is (r)= 7.8/6 = 1.3

Since r>1, sum of GP = a (r^n -1)/r-1

If sum =  1800g

1800= 6(1.3^n -1)/1.3 - 1

1800 = 6(1.3^n -1)/0.3

1800 * 0.3  = 6(1.3^n -1)

540 = 6(1.3^n -1)

540/6 = (1.3^n -1)

90 = 1.3^n -1

90 + 1 = 1.3^n

1.3^n = 91

log 1.3^n = log 91

nlog1.3 = log 91

n = log91/log 1.3

n = 1.959/0.114

n = 17

Answer:

a)  963g

b) 17

Step-by-step explanation:

i) Now we must first find the common difference of the AP

d = 7.8 -6 = 1.8

Now the sum of the AP gives the total amount of chemical used for 30 experiments

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

n= 30, a = 6, d= 1.8

Sn = 30/2[2(6) + (30-1) (1.8)]

Sn = 15[12 + 52.2]

Sn = 963g

ii)For the G.P the common ration is (r)= 7.8/6 = 1.3

Since r>1, sum of GP = a (r^n -1)/r-1

If sum =  1800g

1800= 6(1.3^n -1)/1.3 - 1

1800 = 6(1.3^n -1)/0.3

1800 * 0.3  = 6(1.3^n -1)

540 = 6(1.3^n -1)

540/6 = (1.3^n -1)

90 = 1.3^n -1

90 + 1 = 1.3^n

1.3^n = 91

log 1.3^n = log 91

nlog1.3 = log 91

n = log91/log 1.3

n = 1.959/0.114

n = 17

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Iris should use an income value of approximately $3,137.50 when making her budget.

When making her budget as a freelancer, Iris should use an income value that reflects her average earnings over the past four months. By calculating the average income, Iris can have a more stable and reliable estimate for her budget planning.

To determine the average income, Iris needs to add up the total income earned over the four months and divide it by the number of months. Summing up the income values, we get:

$2700 + $4600 + $3550 + $1700 = $12,550

Next, dividing the total income by four (the number of months), we find:

$12,550 / 4 = $3,137.50

Therefore, Iris should use an income value of approximately $3,137.50 when making her budget. This average value allows her to account for fluctuations in her monthly income and provides a more accurate representation of her earning potential.

It is important for Iris to consider her expenses and financial goals when budgeting. By using the average income, she can create a budget that balances her income and expenses, allowing her to allocate funds appropriately for various needs such as bills, savings, investments, and personal expenses.

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The probable question may be:

Iris is a working freelancer and has been tracking her monthly income for the last four months, which are $2700, $4600, $3550, and $1700. What income value should she use when making her budget?

Answer:

80

Step-by-step explanation:

Just average the two numbers to get (70+90)/2 = 160/2 = 80

Answer:

Step-by-step explanation:

To find the midpoint between two numbers, you add them together and divide the sum by 2.

In this case, the midpoint between 70 and 90 would be:

(70 + 90) / 2 = 160 / 2 = 80.

Therefore, the midpoint between 70 and 90 is 80.

Answer:

Undefined

Step-by-step explanation:

The slope of a horizontal line is zero.  The slope of a vertical line is undefined.

The statement that is true about the function is:

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have:

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.

Hence, the correct option is A.

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The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping

Rewriting 125x^ 3 −27 as (5x) ^3 −3³

The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )

Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.

Hence, (5x−3)(25x ^2 +15x+9)

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