Question 6 The volumes of two similar solids are 729m3 and 125m3 The surface area of the larger solid is 324m2. What is the surface area of the smaller solid

The true statements about the function are:

The complete question is in the image

From the table, the function values do not exceed 0 at the interval 0 to 2.

This means that f(x) ≤ 0 over the interval [0, 2].

Also from the table, the function values exceeds 0 at the intervals greater than -2 but less than 0

This means that f(x)>0 over the interval (-2,0)

Also from the table, the function values are at least 0 at the intervals greater than 2

This means that f(x) ≥ 0 over the interval [2,∞)

Hence, the true statements are (b), (d) and (e)

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The preference is that ✓5 should be left in radical form as an irrational number.

It should be noted that a radical form is illustrated when n is a positive integer that is greater than 1.

Here, a rational number is a number that can be represented in the form of p/q where p and q are integers. In this case, ✓5 will nvwe give a perfect number in decimal form. Hence, it's better to leave it radical form.

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The probability that both sides of the card is red is 0.33

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that both sides of the card is red = total number of cards in which both sides are red / total number of cards

2/6 = 1/3 = 0.33

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#1

y=x+5

#2

y=3/8

#3

Reflection by y axis as x will be negative and shifting 2 units right

#4

y=6x+1

#5

y=x-11

#6

y=8x

Horizontally streched by 1/8 factor

Answer:

1.  Translated 5 units left.

2.  Vertical stretch by a factor of 3/8.

3.  Reflection in the x-axis, then translated 2 units down.

4.  Vertical stretch by a factor of 6, then translated 1 unit up.

5.  Translated 11 units down.

6.  Vertical stretch by a factor of 8.

7.  Vertical stretch by a factor of 1/3, then reflection in the x-axis.

Step-by-step explanation:

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}.[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}.[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.[/tex]

Parent function:

[tex]y=x[/tex]

[tex]\textsf{1.} \quad y=x+5[/tex]

Translated 5 units left.

[tex]\textsf{2.} \quad y=\dfrac{3}{8}x[/tex]

Vertical stretch by a factor of 3/8.

[tex]\textsf{3.} \quad y=-x-2[/tex]

Reflection in the x-axis, then translated 2 units down.

[tex]\textsf{4.} \quad y=6x+1[/tex]

Vertical stretch by a factor of 6, then translated 1 unit up.

[tex]\textsf{5.} \quad y=x-11[/tex]

Translated 11 units down.

[tex]\textsf{6.} \quad y=8x[/tex]

Vertical stretch by a factor of 8.

[tex]\textsf{7.} \quad y=-\dfrac{1}{3}x[/tex]

Vertical stretch by a factor of 1/3, then a reflection in the x-axis.

The percentage of unemployed women from the total percentage of unemployed is 60%

Percentage of the unemployed women from the total unemployed = 15% / 25% × 100

= 0.60 × 100

= 60%

Therefore, the percentage of unemployed women from the total percentage of unemployed is 60%

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Answer: 94

Step-by-step explanation:

The area of each of the top and bottom face is [tex](4)(6)-(2)(2)=20[/tex].

The area of each of the side faces is 12.

The area of each of the faces facing out is 6.

The area of each of the 3 'inner' faces is also 6.

Adding these together,

[tex]20(2)+12(2)+6(2)+6(3)=94[/tex]

These are the expected numbers of spins that is P(N=n)=n−1/n!

According to the statement

Let N is the number of spins AND

Let S is the sums of spins until the sum is greater than one.

we know that the For N=1, P(S) = 0.

The value of expected random variables are

E(X)=μ=∑xP(x).

Put all the integers values in it and integrate.

According to statement condition the expected number of variables become

P(N=n)=P(Sn−1<1≤Sn)

P(N=n)= P(Sn−1 < 1) - P(Sn <1)

P(N=n)=1/(n−1)!−1/n!

P(N=n)=n−1/n!

So, these are the expected numbers of spins that is P(N=n)=n−1/n!

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To calculate the area of a circle, we use the formula : [tex]\pi r^{2}[/tex], where r is radius.

We replace the numebrs : 144[tex]\pi[/tex] = 452,389342.... = 452 (rounded)

So, the area of this circle is 452 (and whatever units)

Answer:

Area of circle = 452 units²

Step-by-step explanation:

We can use the following formula to calculate the area of a circle:

Area = π r²

where r = radius of circle (12 units)

Substituting into the formula:
Area = π × (12)²

        = π × 144

        = 452.39

        = 452 units²       (rounded to the nearest whole number)

The difference between the retail and wholesale unit price is $ 0.99.

The retail price is the price that the item is sold for to the customer.

Here,

Coordinates extracted from the graph;

(4, 1)     (12, 3)

Equation of straight line (Whole sale price)

(y - y₁) = m(x - x₁)                  

where, m = (y₂-y₁)/(x₂-x₁)

then, m = (3-1) / (12-4)

            = 2/8

           = 1/4

Now,   (y - 1) = 1/4 (x - 4)

           4y - 4 = x - 4

            x = 4y

            x - 4y = 0

Now, whole sale price for 24 boxes; x = 24

           24 - 4y = 0

            4y = 24

             y = 24/4

             y = 6

The wholesale price = $ 6

The retail price = $ 6.99

The difference between retail and wholesale = Retail - Wholesale

                                                                            = 6.99 - 6

                                                                            = $ 0.99

Thus, the difference between the retail and wholesale unit price is $ 0.99.

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Answer:

The y-intercept is 25000 . The intercept is the fixed cost of the doughnut selling company.

Step-by-step explanation:

In the question, it is given that the fixed cost is $25000 and the expense to produce each doughnut is $0.25.

It is required to find and identify the y intercept.

To do so, use the equation derived in previous part of the exercise to interpret the slope. Compare the equation with standard equation of the line.

Step 1 of 1

The total cost of the company is the sum of fixed cost and the expenses for the doughnut, C=0.25x+25000.

Compare the equation with general linear equation y=mx+c.

The y-intercept is 25000 .

The intercept is the fixed cost of the doughnut selling company.

Si cada jugador tiene un total de 2 canicas y hay 5 jugadores, se espera que el número total de canicas sea 10.

Multiplica el número de canicas por el de jugadores:

Este factor se puede descomponer así:

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x = -2.5 is a vertical line. The vertical graph of the equation is shown in the image attached below.

The slope of a vertical line is undefined, therefore, the equation of a vertical line is expressed as x = a, where a is the x-intercept.

Given x = -2.5, the equation suggests it is a vertical line, where the line intercepts the x-axis at -2.5, which is the x-intercepts.

Thus, the graph for x = 2.5 is shown in the diagram below.

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Answer:

C

Step-by-step explanation:

The exact point should be (0, 4) if you're looking for the Y intercept. I'm assuming that each square represents one unit. Hope I could help.

Answer:

c)4

Step-by-step explanation:

Hope it helps!!!

y= 4

x= 0

The length of one of the legs says line AC is 58.31.

A figure can be placed in a coordinate plane on the graph by determining the coordinate of the vertices.

For the given isosceles triangle with:

The coordinate of the vertices are:

The length of one leg is calculated as follows:

[tex]\mathbf{AC= \sqrt{(50-0)^2+(30-0)^2}}}[/tex]

AC = [tex]\mathbf{\sqrt{2500+900}}[/tex]

AC = [tex]\mathbf{\sqrt{3400}}[/tex]

AC = 58.31

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The value of a in the exponential function is 4/5.

Given the exponential function is f(x)=a(3/2)ˣ.

An function may be a mathematical relation of the subsequent form: f(x)=aˣ. where x may be a variable, and a could be a constant called the exponential of the function.

When multiplying the any function by a constant, we may expand or shrink the function in the y-direction.

y=a(b)ˣ

If a>1 then the function will enlarge.

If a<1 then the function will shrink.

When a=4/5

Then 4/5<1 means the function would shrink.

When a=5/4

Then 5/4>1 means the function would enlarge.

When a=3/2

Then 3/2>1 means the function would enlarge.

When a=7/4

Then 7/4>1 means the function would enlarge.

Hence, the given function f(x)=a(3/2)ˣ would shrink when a=4/5.

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Answer:

4/5

Step-by-step explanation:

got it right

The complete statements for the angles as in the task content are:

It follows from the task content that the arrangement involves two parallel lines q and s which are cut by transversal line r.

On this note, according to the description in the task content, the angles formed at the intersections are related as follows;

Angles 1 and 5 are congruent because they are

corresponding angles.

Angles 4 and 6 are congruent because they are alternate angles.

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Answer:

D

Step-by-step explanation:

quadratic formula

Answer:

I hope this is helpful. I had done my calculations and got the answer. The last part in orange is the answer. Your going to have to simplify.

the probability of making a Type I error is equal to the significance level of power. To increase the probability of a Type I error, increase the significance level. Changing the sample size has no effect on the probability of a Type I error.

The electricity of a take a look at can be expanded in a number of methods, for example increasing the pattern length, reducing the standard errors, increasing the difference between the pattern statistic and the hypothesized parameter, or growing the alpha degree.

The chance of creating a kind I mistakes is α, that's the extent of importance you put for your hypothesis check. An α of 0.05 indicates which you are inclined to accept a five% chance which you are incorrect whilst you reject the null hypothesis. To lower this risk, you have to use a decrease cost for α

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The length of GX is 13 and the value of ∠ABX is 22.

We know that the point at which the triangle's three interior angle bisectors converge is known as the incenter. It can be thought of as the intersection of the triangle's internal angle bisectors. Due to the junction point of the central axis being the center of the triangle's inscribed circle, this point will be equally spaced from each of the triangle's sides. The center of a triangle's inscribed circle, which is the biggest circle that can fit inside the triangle, is known as the incenter.

Given that EX = 4z + 1 and  XF = 2z + 7.

Since X is the incentre of this triangle ΔABC, EX = XF = GX.

Now, 4z + 1 = 2z + 7

i.e. 4z - 2z = 7 - 1

i.e. 2z = 6

i.e. z = 6/2 = 3

Then GX = 2 * 3 + 7 = 6 + 7 = 13

Also given that ∠ABC = 44°.

Since X is the incentre of this triangle ΔABC, ∠ABX = ∠CBX

Let ∠ABX = ∠CBX = y

Now y + y = 44

i.e. 2y = 44

i.e y = 44/2 = 22

Then ∠ABX = 22°

Therefore, the length of GX is 13 and the value of ∠ABX is 22°.

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The order of steps to solve the equation are;

x^2 − 15 = 2x

(x − 5)(x + 3) = 0

x − 5 = 0 or x + 3 = 0

Potential solutions are −3 and 5

Logarithm expressions are inverse of an exponential function. Given the logarithm expression shown below:

log(x^2 − 15) = log(2x)

Cancel the log on both sides

x^2-15 = 2x

Equate to zero

x^2-2x-15 = 0

Factorize

x^2 -5x + 3x -15 = 0

x(x-5)+3(x-5) = 0

(x-5)(x+3) = 0

Find the solution

x - 5 = 0 or x + 3 = 0

Potential solution are 5 and -3

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We can solve this graphically, we will see that f(x) = g(x) when x = -2, so the solution is x = -2.

We want to solve the system:

f(x) = g(x)

Where:

[tex]f(x) = 2x + 24\\\\g(x) = 5*(0.5)^x[/tex]

Replacing the functions, we get:

[tex]2x + 24 = 5*(0.5)^x[/tex]

Notice that on the left side x is a coefficient, while on the right side, it is an exponent, so this is really hard to solve with algebra.

But what we can do, is graph both functions, and see for which value of x the graphs do intersect.

Below you can see the graphs, the green one is f(x), the blue one is g(x).

There you can see that the graphs intersect at x = -2

This means that f(x) = g(x) only for x = -2.

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Answer:

Step-by-step explanation:

This looks like it is intended to represent two equations. They can be solved as a system in any of the usual ways.

The two equations seem to be ...

Adding 4y to the second equation gives ...

  x -4y +4y = -3y +4y

  x = y . . . . . . . . simplify

Substituting for y in the first equation gives ...

  4x -x = 3

  3x = 3 . . . . simplify

  x = 1 . . . . . divide by 3

  y = 1 . . . . . same as x

The variables x and y both have a value of 1.

__

The attachment shows a graphical solution to these equations.

The required inequality is 3x + 2y > 390 and two possibilities is given by (100,45) and (80,75).

Student Council is selling t-shirts and hats for $21 and $14, respectively. The club needs to raise at least $2730.

Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.

Let x for the number of t-shirts and y for the number of hats.

Now,
equation for to raise at least $2730.
21x + 14y > 2730
3x + 2y > 390

Two possibility can be caroled out from the graph i,e.  (100,45) and (80,75).

Thus, the required inequality is 3x + 2y > 390 and two possibilities is given by (100,45) and (80,75).  

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This distance can be expressed as 3.84× [tex]10^{8}[/tex] m.

What is distance with example?

Given the distance between the earth and the moon is 384000km

Representing in exponential notation,

=384000×1000m  [∵1km=1000m]

=384× [tex]10^{6}[/tex] m

=3.84× [tex]10^{8}[/tex] m

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The correct question is -

The distance between the Earth and the moon is approximately 384000 km.  this distance can be expressed as ____m.

The line with an equation of y = x have a slope of 1 and y intercept of 0.

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard equation of a line is given as:

y = mx + b

Where m is the slope of the line and b is the y intercept.

The line with an equation of y = x have a slope of 1 and y intercept of 0.

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Answer: [tex]g(x)=(x-5)^2[/tex]

Step-by-step explanation:

The graph of g is the graph of f translated 2 units to the right, so its equation is [tex]g(x)=(x-5)^2[/tex]

Answer:

$0.70 per letter, $1.50 flat fee

Step-by-step explanation:

Let x be the flat fee.

Let y be the cost of sending 1 letter.

Lets create 2 equations from those 2 instances.

First Instance: x + 35y = 26 - Equation 1

Second Instance: x + 18y = 14.1 - Equation 2

To find x and y , we can use elimination method in solving simultaneous equations.

Equation 1 - Equation 2

x - x + 35y - 18y = 26 - 14.1

17y = 11.9

y = [tex]\frac{11.9}{17} \\[/tex]

= $0.70

Now we substitute y into equation 1.

x + 35(0.70) = 26

x + 24.50 = 26

x = 26 - 24.50

= $1.50

From the above we know the post charges $0.70 per letter sent and charges $1.50 flat fee.

The value of the 1 mile is equal to 5280 feet

We have given that,

The problem involves a conversion from feet to miles.

We have to determine how many feet are in one mile.

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

1 mile is equal to 5280 feet

Therefore we get,

1mile=5280 feet.

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The intermediate step of x² - 4x = 45 is (x- 2)² = 49

The equation is given as:

x² - 4x = 45

Take the coefficient of x

k = -4

Divide by 2

k/2 = -2

Square both sides

(k/2)^2 = 4

Add 4 to both sides of x² - 4x = 45

x² - 4x + 4= 45 + 4

This gives

x² - 4x + 4= 49

Express as perfect square

(x- 2)² = 49

Hence, the intermediate step of x² - 4x = 45 is (x- 2)² = 49

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