What fraction is equivalent to 1/4

The numbers are: 2,4,6,8,10,12

The surface area of the cylinder to the nearest square meter include the following: C. 160 square meters.

In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):

SA = 2πrh + 2πr²

Where:

By substituting the given parameters into the formula for the surface area (SA) of a cylinder, we have the following;

Surface area = 2πrh + 2πr²

Surface area = 2(3.14)(2.8)(6.3) + 2(3.14)(2.8²)

Surface area = 160 square meters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Therefore , the solution of the given problem of percentage comes out to be  14 gallons of the first brand and 56 gallons of the second brand must be utilised.

In statistics, a figure or metric than may be presented as a percentage or 100 is denoted by the abbreviation "a%". Another unusual spelling is "pct," "pct," and "pc." The percent symbol ("%") is the method that is most usually used for this. Additionally, there are no indications or predetermined ratios of any component to the whole. Numbers are effectively integers since they frequently add up to 100.

Here,

Let's write "x" for the first brand's (35% pure antifreeze) number of gallons and "y" for the second brand's (60% pure antifreeze) number of gallons.

Given:

70 gallons of mixture are required in total.

Desired antifreeze content in the combination is 55%

Based on the information provided, we can construct the following system of equations:

=> Equation 1: x + y = 70

=> Equation 2: 0.5*70 = 0.55x + 0.60y

=> x = 70 - y

=> 0.35(70 - y) + 0.60y = 0.55 * 70

=> 24.5 - 0.35y + 0.60y = 38.5

=> 0.25y = 14

=> y = 56

=> x = 70 - 56

=> x = 14

In order to get 70 gallons of a mixture that contains 55% pure antifreeze, 14 gallons of the first brand and 56 gallons of the second brand must be utilised.

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Every six months, you will receive $21.50 back from your bond.

The 4.3% coupon is the annual interest rate, which is paid semi-annually (twice a year).

To find the amount earned every 6 months, we need to divide the annual interest rate by 2:

(4.3% / 2) = 2.15%

Next, we need to calculate the dollar amount earned every 6 months. To do this, we need to find 2.15% of the bond's face value:

2.15% of $1000 = $21.50

Therefore, you will earn $21.50 off your bond every 6 months.

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The amount (coupon interest) that is earned off the $1,000 bond with 4.3% coupon every 6 months is $21.50.

The coupon interest represents the periodic payment received by a bondholder from the date of issuance until the date of maturity of a bond.

The coupon interest is computed by applying the coupon rate on the face value of the bond.

Face value of the bond = $1,000

Coupon interest rate = 4.3%

Maturity period = 30 years

Coupon (bond) interest for 6 months = $21.50 ($1,000 x 4.3% x 6/12)

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Here we have an exponential growth were the increase is of 26%, and it can be written as.

[tex]y = a*(1 + 0.26)^t[/tex]

Here we want to rewrite the function

[tex]y = a*(2)^{t/3}[/tex]

In the given form for the general exponential, so let's do that.

We can expand the product to get:

[tex]y = a*(2)^{t/3}\\\\y = a*((2)^{1/3})^t\\\\y = a*(1.26)^t\\\\y = a*(1 + 0.26)^t[/tex]

To identify if it is a growth or a decay we need to see the sign of r (the thing we are adding to the 1) in this case is +0.26

When it is positive we have a growth, so here we have a growth.

And to get the percentage multiply that number by 100%, we will get:

0.25*100% = 26%

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On solving the provided question we can say that area of the polygon is 24 cm sq.

A four-sided polygon having four edges and four corners is referred to as a quadrilateral. The word is derived from the Latin words quadri and latus, both of which imply "side". An object with a rectangle's four sides, four vertices, and four corners is a two-dimensional shape. There are essentially two sorts of concave and convex surfaces. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up the two-dimensional shape of a rectangle. There are many different shapes for quadrilaterals, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

Area of this polygon is -

A = 1/2 * 6* 8

A = 24 cm sq.

Hence, area of the polygon is 24 cm sq.

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A simplification of the fractions (-5/8) ÷ (-3/4) is equal to: B. -20/24.

The step in which Johnetta made her error include the following: A. step 1.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, the division can be calculated as follows;

Fraction = (-5/8) ÷ (-3/4)

Fraction = -5/8 × (-4/3)

Fraction = -20/24

For Johnetta, we have:

Fraction = 7/9 ÷ 3/8

Fraction = 7/9 × 8/3

Fraction = 56/27

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Answer:

Yes

Step-by-step explanation:

(-2, 10)

x = -2

y = 10

y = -4x + 2

Substitute or plug in the x and y values

10 = -4(-2) + 2

Multiply(remember a negative times a negative is a positive)

10 = 8 + 2

Add

10 = 10

Because ten is equal to ten (-2, 10) is a solution for this part

Now take your next equation and repeat the same steps

y = -6x - 2

10 = -6(-2) - 2

10 = 12 -2

10 = 10

(-2, 10) is  a solution to this system of equations

The value of the variable is 3/2

A fraction cam simply be described as an expression that is being used to represent the part of a whole number, a whole variable or element.

There are different types of fractions. They are listed as;

From the information given, we have that;

-7 4/5 divided by X = -5 1/5

convert to improper fractions, we have;

-39/5/x = -26/5

Now, cross multiply the values, we have;

-39/5 = -26x/5

cross multiply

-130x = -195

Divide both sides

x = -195/-130

x = 39/26 = 3/2

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Answer:the median is  Q2 aka 105

Step-by-step explanation:

The third quartile  if the distribution is $22.08.

To find the third quartile, we need to find the value of the stock that separates the top 25% of days from the bottom 75%.

Since the distribution is uniform, we can find the third quartile by taking 75% of the range and adding it to the minimum value.

The range of the stock is:

$26.17 - $9.82 = $16.35

75% of the range is:

0.75 x $16.35 = $12.26

Adding this to the minimum value gives us the third quartile:

$9.82 + $12.26 = $22.08

So the third quartile is $22.08.

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The equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

We can observe from the table that the number of books collected increases by 10 for each week.

Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:

b = mw + c

where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).

The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):

10 = 10 * 1 + c

c = 0

Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

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the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).

Weeks (w) Books Collected (b)

1 10

2 20

3 30

4 40

Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?

Answer:

D. 177 ft²

Step-by-step explanation:

the area of a circle is

pi×r²

r is the radius which is half of the diameter, of course.

so, in our case

area = pi×(15/2)² = pi×7.5² = pi×56.25 =

= 176.7145868... ft² ≈ 177 ft²

Answer:

[tex]192[/tex] [tex]cm^2[/tex]

Step-by-step explanation:

Recall that the formula for the area of a parallelogram is:

[tex]A=bh[/tex]

Where b is the length of the base, and h is the length of the height.

We are given that the base is 24 cm.

So, b=24.

We are also given that the height is 8 cm.

So, h=8.

Let's plug these values into the formula:

[tex]A=bh=\\A=(24)(8)=\\A=192[/tex]

Since area is a two-dimensional measure, we need to label our answer using units squared.

Thus, the area is [tex]192[/tex] [tex]cm^2[/tex]

Area of a parallelogram => [tex]A=bh[/tex]

Where, b=24 cm and h=8 cm

Plug in the known values and solve.

[tex]\Longrightarrow A=bh \Longrightarrow A=(24 \ cm)(8 \ cm) \Longrightarrow A= \boxed{192 \ cm^2}[/tex]

Therefore, the volume of Prism B is 727/4 ft³ or 181 3/4 ft³ in mixed number form.

Subtract the denominator from the numerator. The quotient should be expressed as a whole number in step 2. Step 3: Enter the denominator and numerator, respectively, as the remainder and the divisor.

We can write: Using the formula for a prism's volume (V = Bh, where B is the base area):

We must determine Prism B's cross-sectional area in order to get the volume of Prism B. By dividing the height equation of prism A by its volume equation, the following result is obtained:

cross-sectional area of Prism A = (Volume of Prism A) / (height of Prism A) = (872/1 ft³) / (6 ft) = 218/3 ft²

Using the scale factor equation for height, we get:

k = (height of Prism A) / (height of Prism B) = (6 ft) / (31/12 ft) = 24/31

Using the scale factor equation for cross-sectional area, we get:

k² = (cross-sectional area of Prism A) / (cross-sectional area of Prism B) = (218/3 ft²) / (cross-sectional area of Prism B)

Solving for the cross-sectional area of Prism B, we get:

cross-sectional area of Prism B = [tex](218/3 ft^2) / k^2 = (218/3 ft^2) / (24/31)^2 = 59/3 ft^2[/tex]

Finally, substituting the height and cross-sectional area of Prism B into the volume equation of Prism B, we get:

Volume of Prism B = (cross-sectional area of Prism B) * (height of Prism B) = [tex](59/3 ft^2) * (31/12 ft) = 727/4 ft^3.[/tex]

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The statement The product of 3 and the difference of a number and 8 as an expression is 3(x - 8)

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

The product of 3 and the difference of a number and 8

Represent the number with x

So, we have

The product of 3 and the difference of x and 8

The difference of x and 8 means x - 8

So, we have

The product of 3 and x - 8

The product of 3 * (x - 8)

So, we have

3(x - 8)

Hence, the expression is 3(x - 8)

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Answer:f/g=29

Step-by-step explanation:

Answer: (f/g)=29

Hope this helps

Answer:

Yes, it is a polynomial identity (work below).

Step-by-step explanation:

Let's start by expanding the left side of the equation.

[tex](2x^2+y^2)^2=\\4x^4+y^4+4x^2y^2[/tex]

Now, let's expand the second side.

[tex](2x^2-y^2)^2+(2xy\sqrt{2} )^2=\\4x^4+y^4-4x^2y^2+4x^2y^2(2)=\\4x^4+y^4-4x^2y^2+8x^2y^2[/tex]

There are no like terms on the left side, so let's combine the like terms on the right side.

[tex]4x^4+y^4-4x^2y^2+8x^2y^2=\\4x^4+y^4+4x^2y^2[/tex]

Now, let's check if the left and right sides are equal:

[tex]4x^4+y^4+4x^2y^2= 4x^2+y^4+4x^2y^2[/tex]

Both sides are the same. Thus, the equation is a polynomial identity.

Step-by-step explanation:

Steve spends 20% of £200 = 0.2 * £200 = £40 on his football magazine subscription.

The remaining amount he spends on football stickers, sweets, and fizzy drinks in the ratio of 5:2:1, which means that for every 5 parts he spends on football stickers, he spends 2 parts on sweets and 1 part on fizzy drinks.

So, let's call the amount he spends on football stickers "5x". Then, the amount he spends on sweets is "2x" and the amount he spends on fizzy drinks is "x".

The total amount he spends on these items is:

5x + 2x + x = 8x

We know that he has £200 - £40 = £160 left after paying for his magazine subscription. So, we can set up an equation:

8x = £160

Solving for x, we get:

x = £20

Therefore, Steve spends:

5x = 5 * £20 = £100

on football stickers.

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Answer:

5 : 2 : 1 = 100 : 40 : 20

Step-by-step explanation:

10% = 20 (200÷10=20)

20% = 40 (double both sides)

take away £40 from £200 = £160

£160 is left over after buying the magazine subscription

______________________________

add the radio all together = 5:2:1 = 8

divide 8 by 160 = £20

That now means 1 = 20

5 : 2 : 1

we already found 1, now to find 2 and 5

you times 2

1 = 20

2 = 40

and then do the same for 5

1 = 20

5 = 100

To know this is right, 100 + 40 + 20 = 160 the original number for the money left over.

The maximum grazing area for the cow is approximately 53,343.08 square feet.

The maximum grazing area for the cow can be found by imagining a circle with radius equal to the length of the rope (130 feet) centered at the corner of the barn where the cow is tethered. The grazing area is the portion of the circle that lies outside the barn.

Since the barn is 8 feet by 8 feet, it covers a square area of 64 square feet. The radius of the circle is 130 feet, so the area of the circle is π(130)^2 square feet.

To find the maximum grazing area, we need to subtract the area of the barn from the area of the circle.

Area of circle = π(130)^2 square feet = 53,407.08 square feet

Area of barn = 64 square feet

Maximum grazing area = Area of circle - Area of barn

= 53,407.08 - 64

= 53,343.08 square feet (rounded to two decimal places)

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Starting with the original equation:

-2p - 17 = 3(p - 5)

Distributing the 3 on the right side:

-2p - 17 = 3p - 15

Subtracting 3p from both sides:

-5p - 17 = -15

Adding 17 to both sides:

-5p = 2

Dividing by -5:

p = -2/5

Now, we can substitute this value of p back into the original equation and check if it is a solution:

-2(-2/5) - 17 = 3((-2/5) - 5)

4/5 - 17 = 3(-27/5)

-136/5 = -81/5

The left side does not equal the right side, so the supplied value of p = -2/5 is NOT a solution to the equation.

Hope this helps :)

Answer:

x = 4

Step-by-step explanation:

given 2 secants drawn from an external point to the circle, then the product of one secant's external part and that entire secant is equal to the product of the other secant's external part and that entire secant, that is

x(x + 4x) = 8(8 + 2)

x(5x) = 8(10)

5x² = 80 ( divide both sides by 5 )

x² = 16 ( take square root of both sides )

x = [tex]\sqrt{16}[/tex] = 4

Answer:

[tex]5 {a}^{2} b + 15a {b}^{2} = [/tex]

[tex]5ab(a + 3b)[/tex]

there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.

How to solve the question?

The number of ways to draw 7 cards from a standard deck of 52 cards can be calculated using the combination formula, which is:

C(52, 7) = 52! / (7! * (52-7)!)

where "!" represents the factorial function.

To simplify this expression, we can use the property that n! / k! = n * (n-1) * (n-2) * ... * (n-k+1) for positive integers n and k such that k ≤ n.

Using this property, we can rewrite the above expression as:

C(52, 7) = (52 * 51 * 50 * 49 * 48 * 47 * 46) / (7 * 6 * 5 * 4 * 3 * 2 * 1)

Simplifying this expression, we get:

C(52, 7) = 133,784,560

Therefore, there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.

To understand why this is the case, we can think of each draw as a separate event with no replacement. The first card can be drawn in 52 ways, the second card can be drawn in 51 ways (since one card has already been drawn), the third card can be drawn in 50 ways (since two cards have already been drawn), and so on. Therefore, the total number of ways to draw 7 cards is the product of the number of ways to draw each individual card, which is 52 * 51 * 50 * 49 * 48 * 47 * 46. However, since the order in which the cards are drawn does not matter, we need to divide by the number of ways to arrange 7 cards, which is 7 * 6 * 5 * 4 * 3 * 2 * 1 (i.e., 7 factorial). This gives us the final answer of 133,784,560.

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The cube root function represented by the graph is h(x) = ∛(x + 3) - 2.

The parent cube root function is f(x) = ∛x

If we translate the parent cube root function 3 units to the left, this means that we replace x with (x + 3) in the function.

This results in the new function g(x) = ∛(x + 3). So, for any input value of x, the output value of g(x) is the cube root of (x + 3).

Similarly, if we translate the parent cube root function 2 units down, this means that we subtract 2 from the function.

So, the new function h(x) = ∛(x + 3) - 2.

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The restrictions on the polynomial expression [tex]\frac{x^2 - 25}{x - 1} \div \frac{x^2 - x - 30}{x^2 - 4x - 12}[/tex] are at x = -5, -2, 1 and 6

From the question, we have

[tex]\frac{27x^2y^3}{45x^4}[/tex]

Divide the variables

So, we have

[tex]\frac{27y^3}{45x^2}[/tex]

Divide 27 and 45 by 9

So, we have

[tex]\frac{3y^3}{5x^2}[/tex]

Hence, the solution is [tex]\frac{3y^3}{5x^2}[/tex], x ≠ 0

Given that

[tex]\frac{x + 2}{x^2 - 5x - 14}[/tex]

Factorize the numerator

So, we have

[tex]\frac{x + 2}{(x + 2)(x - 7)}[/tex]

Divide

[tex]\frac{1}{x - 7}[/tex]

So, the solution is [tex]\frac{1}{x - 7}[/tex] , where x ≠ 7

The hole is given as (2, 1/3)

This means that the graph is undefined at (2, 1/3)

One possible equation from the list of options is

[tex]f\left(x\right)\:=\:\frac{x\:-\:2}{x^2\:-\:x\:-\:2}[/tex]

The expression is given as

[tex]\frac{x^2 - 25}{x - 1} \div \frac{x^2 - x - 30}{x^2 - 4x - 12}[/tex]

The restrictions on the polynomial is the domain

When solved graphically, we have the restrictions to be at x = -5, -2, 1 and 6

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Answer:

Step-by-step explanation:

(-50, -20), (-60, 40)

(40 + 20)/(-60 + 50) = 60/-10= -6

y - (-20) = -6(x - (-50))

The y-intercept of a graph  y=-3.

Here, we have,

Given the graph of a function, the y-intercept is defined as the y-coordinate of the point(s) where the graph crosses the y-axis.

There might be more than one y-intercepts or even none.

The graph provided in the question is a line with a negative slope, i.e., a decreasing line.

Carefully looking it can be determined the graph touches the y-axis in the point (0,-3), thus the y-intercept of the graph is y=-3

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complete question:

The graph of the linear function is shown on the coordinate grid. * 910X -10 What is the y intercept of the graph of the linear function?