a cube is made up of 27 equal sized cubes. if all faces of the large cube are painted, how many small cubes will not have any paint on any of their faces?

Answer:

Angles in a triangle add up to 180⁰. So the answer is 16.

Step-by-step explanation:

48+84+3k= 180

132+3k= 180

3k= 180-132

3k= 48

k= 48÷3

k=16

Answer: She will pay $52.68, including taxes

Step-by-step explanation: One can of tennis ball is $4 and there are no discount on it. Elena bought 3 cans, so:

can = 3 x 4 = 12

One tennis racket is $43 but it has a discount of 15%:

discount = 0.15 x 43 = 6.45

total racket = 43 - 6.45 = 36.55

Elena will have to pay:

pay = 12 + 36.55 = 48.55

She will also have to pay taxes, which are 8.5% over the price she paid:

pay + tax = 48.55 x 0.085 = 4.13

total to pay = 48.55 + 4.13 = 52.68

Buying 3 can of tennins ball and one racket, Elena paid $52.68, including taxes.

Answer:

try math wa y

Step-by-step explanation:

it will give u the answer to most questions the answer is c

The equivalent expression of the logarithmic expression (logₓy)² is log²ₓy

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

(logₓy)²

The above expression is pronounced

log y to the base of x all squared

When the expression is expanded, we have the following

(logₓy)² = (logₓy) * (logₓy)

Evaluating the expression, we have

(logₓy)² = log²ₓy

Hence, the equivalent expression of the expression (logₓy)² is log²ₓy

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Based on the given ratio, the number of teachers at Still Bay Middle School, who have earned their master's degrees, is 18.

The ratio is the relative size of a value compared to another.

Ratios are depicted as percentages, fractions, or decimals, to show that they are fractional values, representing a portion of a whole.

The ratio of teachers who have earned their master's = 3/5

The total number of teachers at the school = 30

The number of teachers with masters = 18 (30 x 3/5)

The number of teachers without masters = 2/5 (1 - 3/5)

= 12 (30 x 2/5)

Thus, since 3 out of 5 teachers at Still Bay Middle School have earned their master's degrees, the number is 18 if there are 30 teachers at the school.

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Answer:

The answer is 48.

Step-by-step explanation:

The formula for discriminant, D = b² - 4ac. Then you have to substitute the following values into the formula :

\(D = {b}^{2} - 4ac\)

\(let \: a = 2 \\ let \: b = \sqrt{32} \\ let \: c = - 2\)

\(D = {( \sqrt{32} )}^{2} - 4(2)( - 2)\)

\(D = 32 + 16\)

\(D = 48\)

The total length of the movie was 120 minutes.

Let's assume the total duration of the movie is represented by 'M' minutes. According to the given information, Newton and his friends watched 30% of the movie before taking a break. This means they watched 0.3M minutes of the movie.

After the break, they watched the remaining portion of the movie, which is 100% - 30% = 70% of the total duration. This can be represented as 0.7M minutes.

We are given that the duration of the remaining portion after the break is 84 minutes. Therefore, we can set up the following equation:

0.7M = 84

To solve for M, we divide both sides of the equation by 0.7:

M = 84 / 0.7

M = 120

Therefore, the total duration of the movie was 120 minutes.

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The value of y that satisfies the equation is 5, in this particular equation, there is only one Real solution, which is y = 5.

To find the solution of the equation y^3 + 15 = 140, we need to isolate the variable y.

First, let's subtract 15 from both sides of the equation:

y^3 = 140 - 15

y^3 = 125

Next, we take the cube root of both sides to eliminate the cube on the left side:

∛(y^3) = ∛125

y = ∛125

The cube root of 125 is 5, since 5 * 5 * 5 = 125. Therefore, the solution to the equation y^3 + 15 = 140 is:

y = 5

Thus, the value of y that satisfies the equation is 5.

in this particular equation, there is only one real solution, which is y = 5. However, for cubic equations in general, it is possible to have multiple real or complex solutions.

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Minimization of  f(x) = |x+3| + x^3 at the endpoints (-2 and 6)  the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}

within the given interval.

To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.

First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:

|x+3| =

x+3 if x+3 >= 0

-(x+3) if x+3 < 0

Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.

Case 1: x+3 >= 0

In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3

Case 2: x+3 < 0

In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3

Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.

Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.

Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.

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Answer:

R18,801 + R3,996 = R22,797 per month.

Step-by-step explanation:

To calculate the amount of money that the tanker driver receives per day during weekdays, we need to consider the number of hours worked on each weekday and the rate per hour. The driver works for 5% days per week, so there are 5 weekdays and 1 half-day on Saturdays.

On weekdays (Monday to Friday), the driver works for 9 hours per day, so the daily pay is:

9 hours x R92.50 per hour = R832.50 per day

On Saturdays, the driver works for a half-day (4.5 hours) and the rate of pay is doubled, so the pay for the half-day is:

4.5 hours x R92.50 per hour x 2 = R832.50

Therefore, the total pay for the 5 weekdays and 1 half-day on Saturday is:

5 x R832.50 + R832.50 = R4,162.50

So, the driver receives R4,162.50 per week for working 5 weekdays and 1 half-day on Saturdays.

To calculate the amount of money that the driver receives per day during weekdays, we divide the weekly pay by the number of weekdays:

R4,162.50 / 5 = R832.50 per day

Therefore, the driver receives R832.50 per day during weekdays.

2.2 To determine the total number of hours that the driver worked in March 2022, we need to know the number of weekdays and Saturdays in March. There are typically 22 weekdays in March, so the driver works for:

22 weekdays x 9 hours per day = 198 hours on weekdays

In addition, there are typically 4 Saturdays in March, so the driver works for:

4 Saturdays x 4.5 hours per half-day x 2 (double pay rate) = 36 hours on Saturdays

Therefore, the total number of hours that the driver worked in March 2022 is:

198 hours on weekdays + 36 hours on Saturdays = 234 hours

2.3 To determine the salary that the tanker driver has received in the month of June 2022 if he worked the entire month, including Saturdays, we need to know the number of weekdays and Saturdays in June. There are typically 22 weekdays in June, so the driver would work for:

22 weekdays x 9 hours per day x R92.50 per hour = R18,801 per month on weekdays

In addition, there are typically 4 Saturdays in June so that the driver would work for:

4 Saturdays x 4.5 hours per half-day x 2 (double pay rate) x R92.50 per hour = R3,996 per month on Saturdays

Therefore, the total salary that the tanker driver would receive in the month of June 2022 if he worked the entire month, including Saturdays would be:

R18,801 + R3,996 = R22,797 per month.

Answer:

X = -6 is the answer

To estimate the average revenue at a given price, we substitute that price into the expression (950p - 5.4p²) / (950 - 5.4p).

To estimate the average revenue when the price is given, we need to calculate the total revenue and divide it by the total quantity sold.

Given the demand functions x1 = 400 - 3p and x2 = 550 - 2.4p, we can find the total quantity sold, X, by adding the quantities of each product: X = x1 + x2.

Substituting the demand functions into X, we have X = (400 - 3p) + (550 - 2.4p), which simplifies to X = 950 - 5.4p.

The total revenue, R, is given by multiplying the price, p, by the total quantity sold, X: R = pX.

Substituting the expression for X, we have R = p(950 - 5.4p), which simplifies to R = 950p - 5.4p².

To estimate the average revenue at a specific price, we divide the total revenue by the total quantity sold: Average Revenue = R / X.

Substituting the expressions for R and X, we have Average Revenue = (950p - 5.4p²) / (950 - 5.4p).

To estimate the average revenue at a given price, we substitute that price into the expression (950p - 5.4p²) / (950 - 5.4p).

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The power series representation for the function f(x) = x sin(4x) can be found as follows:

Firstly, we can find the power series representation of sin(4x) using the formula for the sine function:$

$\sin x = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}x^{2n+1}$$

Substitute 4x for x to obtain:$$\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}(4x)^{2n+1}

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+1}$$

Multiplying this power series by x gives:

$$x\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

Therefore, the power series representation for the function

f(x) = x sin(4x) is:$$f(x)

= x\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

Therefore, the power series representation for the function f(x) = x sin(4x) is:$$f(x) = x\sin 4x = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

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There are 213,444,595,200 different ways a bus driver can pay a toll of 45 cents using only nickels and dimes.

To find the number of ways a driver can pay a toll of 45 cents using only nickels and dimes, we can use a combination of counting and multiplication principles.

First, we can list out all the possible combinations of coins that add up to 45 cents:

- 9 nickels
- 4 nickels and 5 dimes
- 3 nickels and 6 dimes
- 2 nickels and 7 dimes
- 1 nickel and 8 dimes
- 18 dimes
- 15 dimes and 1 nickel
- 12 dimes and 2 nickels
- 9 dimes and 3 nickels
- 6 dimes and 4 nickels
- 3 dimes and 5 nickels

This gives us a total of 11 different combinations.

Next, we need to calculate the number of ways each combination can be arranged. For example, the combination of 9 nickels can be arranged in 9!/(9-9)! = 1 way (since there is only one way to arrange 9 objects in a line). Similarly, the combination of 4 nickels and 5 dimes can be arranged in (4+5)!/(4!5!) = 126 ways, using the formula for permutations with repetition.

Using this method, we can calculate the number of ways each combination can be arranged and then multiply them together to get the total number of ways the driver can pay a toll of 45 cents:

- 9 nickels: 1 way
- 4 nickels and 5 dimes: 126 ways
- 3 nickels and 6 dimes: 84 ways
- 2 nickels and 7 dimes: 36 ways
- 1 nickel and 8 dimes: 9 ways
- 18 dimes: 1 way
- 15 dimes and 1 nickel: 16 ways
- 12 dimes and 2 nickels: 66 ways
- 9 dimes and 3 nickels: 84 ways
- 6 dimes and 4 nickels: 126 ways
- 3 dimes and 5 nickels: 84 ways

Total number of ways: 1 x 126 x 84 x 36 x 9 x 1 x 16 x 66 x 84 x 126 x 84 = 213,444,595,200 ways.

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The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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Answer:

Step-by-step explanation:

Look at the area of a rectangle with length \(l\) and width \(w\):

    \(A=lw\)

If we halve these: length \(\frac{l}{2}\) and width \(\frac{w}{2}\):

    \(A=\frac{l}{2} \times \frac{w}{2}=\frac{1}{4} lw\)

So for all squares and rectangle the new area will be \(\frac{1}{4}\) of the original area.

So the overall surface area of the prism will be \(\frac{1}{4}\) of the original surface area (since it is just the sum of 4 rectangles and 2 squares).

An example is in the diagram. you can see how halving the dimensions causes the area to be quartered.

Answer:

5

Step-by-step explanation:

Simple Interest =25%*p

rate = term = t

from simple interest = ptr/100

term = rate = 5

Answer:

1/4

Step-by-step explanation:

- 1/4 + 1/2

Get a common denominator

-1/4 + 1/2*2/2

-1/4 + 2/4

1/4

Answer:

1/4

Step-by-step explanation:

-(1/4)+1/2

=-1/4+1/2

=1/4

a) The solution for b in the equation 2b × 3 = 6 is b = 1.

b) The solution for b in the equation 32 - 3b = 2 is b = 10.

c) The solution for b in the equation 6 + 7b = 41 is b = 5.

d) The solution for b in the equation 100/5b = 2 is b = 10.

a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.

2b × 3 = 6

(2b × 3) / 2 = 6 / 2

3b = 3

b = 3/3

b = 1

Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.

c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.

6 + 7b - 6 = 41 - 6

7b = 35

b = 35/7

b = 5

Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.

b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.

32 - 3b - 32 = 2 - 32

-3b = -30

b = (-30)/(-3)

b = 10

Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.

d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.

(100/5b) × 5b = 2 × 5b

100 = 10b

b = 100/10

b = 10.

Therefore, the solution for b in the equation 100/5b = 2 is b = 10.

In summary, the solutions for b in the given equations are:

a) b = 1

c) b = 5

b) b = 10

d) b = 10

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The maximum possible length of the repeating section of the decimal representation of 727 1,229 is 7.

The maximum possible length of the repeating section of the decimal representation of 727 1,229 is 7. The repeating section is comprised of 729.

To calculate this, first consider the prime factorization of 727 1,229. 727 1,229 = 17 × 43 × 137.

Since 17, 43 and 137 are all prime numbers, the prime factorization will not yield a power of 10 as a factor. Therefore, the repeating section must have a length of 7 in the decimal representation of 727 1,229.  
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The graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a function:

f(x) = ∛x

The domain of the function will be all real numbers.

x ∈(-∞, ∞)

The graph will be curved.

Plug x = 0, y = 0

x = 1, y = 1

The graph is shown in the attached picture.

Thus, the graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.

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Step-by-step explanation:

Using the remainder theorem when , when the value of x + 2 is substituted into the polynomial if it's a factor it will produce a result of zero else any number will prove that it's not a factor.

So we have

x + 2 = 0

x = - 2

Substitute the value of x into the polynomial

That's

\(p( - 2) = 2 ({ - 2})^{4} + 6( { - 2})^{3} - 5( - 2) - 10 \\ = 2(16) + 6( - 8) + 10 - 10 \\ = 32 - 48 \\ = - 16\)

Since it leaves a remainder of - 16 (x + 2) is not a factor of the polynomial

Hope this helps you

Answer:

2 piece per hour

Step-by-step explanation:

Given data

Quantity= 4 pieces

time= 2 hours

Required

The unit rate

rate= quantity/time

rate= 4/2

rate= 2 piece per hour

Answer:

x=3

Step-by-step explanation:

Because the shape is a rhombus that means that WZ and XY are parallel

This means we can use the co-interior angles rule to conclude that ∠WZY and ∠XYZ add up to 180°

This means that ∠WZY is 44°

Because the shape in a rhombus ZX and WY are perpendicular

This means that ∠ZRY is a right angle (90°)

Because ZX and WY are perpendicular that means that ∠ZYX is split in half which makes ∠ZYW 68°

Because the angles in a triangle add up to 180°

(10x-8)+68+90=180

(10x-8)+158-158=180-158

10x-8+=22+8

10x/10=30/10

x=3

Answer:

Step-by-step explanation:

Let x be the number of 2 coins and y be the number of 5 coins. Let z be the number of 10 coins she exchanged. Then, we have the first equation

\(2x+5y = 10z\)

Since she has one 5 coin less than 2 coins, then y=x-1. So we get the equation

\(2x+5(x-1) = 10z\)

which is equivalent to

\( 7x-5 = 10z\)

If we add 5 on both sides and factor out on the right by 5 we get

\( 7x = 5(2z+1)\)

We can solve for x and get

\( x = \frac{5(2z+1)}{7}\)

Since x represents the number of 2 coins, we must have that x is an integer. That is, we cannot have, for example 1.5 2 coins. Since 7 doesn't divide 5, we must have that 7 divides 2z+1. That is, the value of z is such that the number 2z+1 is multiple of 7. That is 2z+1 = 7p where p is an integer.

If that is the case, then

x = 5p, then y = 5p-1. By having 2z+1 = 7p, we are forcing that p is an odd integer, so we have infinite solutions. For each value of p that is an odd integer, then x=5p and y=5p-1 is a solution to the problem

Answer:

A) a ratio system

B)The 4 lb peanuts and the 1 lb mixture because the 4lb added to the 1lb of mixture give the correct percentages.

Step-by-step explanation:

I hope this helps :)

-ㄚㄩ尺丨

Answer:

less than a mile is the answer