What is the volume of this rectangular prism?
5 cm
3 cm
4 cm

A. 12 cm3
B. 94 cm3
C. 120 cm3
D. 60 cm3

The approximate value of the expression (−4.8)−9 ⋅ (−4.8)9 is 0.99999999735.

To evaluate the expression (−4.8)−9 ⋅ (−4.8)9, we need to follow the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).

Let's break down the expression step by step:

(−4.8)−9 means raising −4.8 to the power of -9.

First, let's calculate (−4.8)−9:

(−4.8)−9 = 1 / (−4.8)9 (since a negative exponent signifies taking the reciprocal of the base)

Now, let's calculate (−4.8)9:

(−4.8)9 ≈ -11084.4720416 (using a calculator or computational tool to perform the exponentiation)

Substituting this value back into the previous step:

(−4.8)−9 = 1 / (−4.8)9 ≈ 1 / (-11084.4720416) ≈ -9.017218987 × \(10^{(-5)\)

Next, let's move on to the second part of the expression:

(−4.8)−9 ⋅ (−4.8)9 = (-9.017218987 × \(10^{(-5)\)) × (-11084.4720416)

Calculating the multiplication:

(-9.017218987 × \(10^{(-5)\)) × (-11084.4720416) ≈ 0.99999999735

Therefore, the approximate value of the expression (−4.8)−9 ⋅ (−4.8)9 is 0.99999999735.

for such more question on expression

https://brainly.com/question/16763767

#SPJ8

The correct answer is Lower Control Limit (LCL) = –0.0135

To find the lower control limit for a process that monitors the level of defects in the television sets produced using the given process data, construct a control chart for p M .The first step is to compute the mean proportion defective:

Using the given process data, the number of defects over the 12 weeks was 64, with 2400 television sets being inspected.

Pbar = (Number of Defects)/(Number of Inspections)

Pbar = 64/2400Pbar = 0.0267

The second step is to compute the standard deviation of the sample proportions:

s = √ [Pbar (1 – Pbar) / n]n = 200s = √ [0.0267 (1 – 0.0267) / 200]s = 0.0134

The third step is to find the limits of control:

LCL = Pbar – 3sLCL = 0.0267 – 3 (0.0134)

LCL = 0.0267 – 0.0402LCL = –0.0135

The LCL for p is –0.0135.  

Learn more about mean proportion defective from:

https://brainly.com/question/32034511

#SPJ11

The actual area of the closet's floor is 3.52 square meters.

To find the actual area of the closet's floor, we first need to convert the dimensions from the scale drawing to their actual dimensions.

According to the given scale, 2 cm on the scale drawing represents 1 meter in reality. Thus, to convert the dimensions from the scale drawing to actual dimensions, we need to multiply each dimension by the conversion factor:

Actual length = 4.4 cm × (1 m / 2 cm) = 2.2 m

Actual width = 3.2 cm × (1 m / 2 cm) = 1.6 m

Now that we have the actual dimensions, we can calculate the actual area of the closet's floor:

Actual area = Actual length × Actual width

= 2.2 m × 1.6 m

= 3.52 square meters

Therefore, the actual area of the closet's floor is 3.52 square meters.

Learn more about area from

https://brainly.com/question/25292087

#SPJ11

The value of angle CFE in the diagram attached is 51 degrees.

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

From the diagram:

∠AFB = ∠CFD; ∠BFC = ∠DFE

Hence:

∠AFC = ∠CFE

∠AFD = ∠AFC + ∠CFD = ∠AFC + ∠AFB

90 = ∠AFC + 31

∠AFC = 51° = ∠CFE

The value of angle CFE in the diagram attached is 51 degrees.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

the mean and the standard deviation is 0.92 and 0.01808 respectively

Step-by-step explanation:

The computation of the mean and the standard deviation is shown below:

The mean is 0.92

And, the standard deviation is

= √0.92 × (1 - 0.92) ÷ √225

= √0.92 × 0.08 ÷ √225

= √0.0736 ÷ √225

= √3.27

= 0.01808

Hence, the mean and the standard deviation is 0.92 and 0.01808 respectively

Answer:

\(80\)° and \(10\)°

Step-by-step explanation:

Complementary angles are a pair of angles whose measures have a sum of \(90\)°. Therefore, if we let the measure of the bigger angle be \(x\), then the measure of the smaller angle will be \(x-70\) because we are given that the difference of the measures of the two angles is \(70\)°. We can write the following equation to solve for \(x\):

\(x+x-70=90\)

Solving for \(x\), we get:

\(x+x-70=90\)

\(2x-70=90\) (Simplify LHS)

\(2x-70+70=90+70\) (Add \(70\) to both sides of the equation to isolate \(x\))

\(2x=160\) (Simplify)

\(\frac{2x}{2}=\frac{160}{2}\) (Divide both sides of the equation by \(2\) to get rid of \(x\)'s coefficient)

\(x=80\) (Simplify)

Therefore, the measure of one angle is \(80\)° and the measure of the other angle is \(x-70=80-70=10\)°. Hope this helps!

We know, sum of complementary angles = 90°

Let, one of the angle = x°

∴ Another angle = (90 - x)°

As per condition,

(x°) - (90 - x)° = 70°

⇒ x° - 90° + x° = 70°

⇒ 2x° = 70° + 90° = 160°

⇒ x° = 80°.

So, angles are:-

Answer:

144cm2

Step-by-step explanation:

I just looked it up and it's 144

Answer:

slope = -3

Step-by-step explanation:

slope is: (delta y)/(delta x)

so slope = (15-3)/(0-4)

               = -3

Answer:

Thus, the dimensions of the metal plate are 10 dm and 8 dm.

Step-by-step explanation:

For a quadratic equation:

\(x^2+bx+c=0\)

The sum of the roots is -b and the product is c. Note the leading coefficient is 1.

We know the perimeter of the rectangular metal plate is 36 dm and its area is 80 dm^2. Being L and W its dimensions, then:

P=2(L+W)=36

A=L.W=80

Note both formulas are closely related to the roots of the quadratic equation, we only need to adjust the data for the perimeter to be exactly the sum of L+W and not double of it.

Thus we use the semi perimeter instead as P/2=L+W=18

The quadratic equation is, then:

\(x^2-18x+80=0\)

Factoring by finding two numbers that add up to 18 and have a product of 80:

\((x-10)(x-8)=0\)

The solutions to the equation are:

x=10, x=8

Thus, the dimensions of the metal plate are 10 dm and 8 dm.

Answer:

100 minutes

Step-by-step explanation:

Sprints = $39.99 +&0.45

Verizon= $44.99+$0.40

Step 1: Equate the values

\(39.99 + 0.45m = 44.99 + 0.40m\)

Step 2 :Collect like terms and simplify

\(0.45m - 0.40m = 44.99 - 39.99 \\ 0.05m = 5\)

Step 3 :Divide both sides of the equation by 0.05

\( \frac{0.05m}{0.05} = \frac{5}{0.05} \)

Step 4 :Simplify

\(m = 100 \\ = 100 \: minutes\)

The smallest number of eggs that could have been in the box is 1134

The problem is to find the smallest number of eggs that could have been in the box, given the remainder when taking them out by different numbers. Here are the moves toward tackling it:

Allow n to be the quantity of eggs in the container. Then we have the accompanying arrangement of congruences:

n ≡ 1 (mod 2)

n ≡ 1 (mod 3)

n ≡ 1 (mod 4)

n ≡ 1 (mod 5)

n ≡ 1 (mod 6)

n ≡ 0 (mod 7)

For this problem, we have k = 6 k = 6, a i = {1,1,1,1,1,0} a_i = {1,1,1,1,1,0}, M i = {1260,840,630,504,420,720} M_i = {1260,840,630,504,420,720}, and y i = {−1,−2,−3,-4,-5,-6} y_i = {-1,-2,-3,-4,-5,-6}.

Plugging these values into the formula and simplifying modulo 5040, we get:

n = (−1260 + −1680 + −1890 + −2016 + −2100 + 0) mod 5040

n = (−8946) mod 5040

n = (−3906) mod 5040

n = 1134 mod 5040

Therefore, the smallest number of eggs that could have been in the box is 1134

to know more about congruences click here:

https://brainly.com/question/30818154

#SPJ4

The equation of Line 1 in the form y=-12x+28

A measurable path between two places is referred to as a line segment. Line segments may make up the sides of any polygon since they have a set length.

Coordinates of Line 2 M(4,5) and N(6,-19)

Slope of Line 2 is =(-19-5)/(6-4)

=-24/2=-12

Slope of line 1 and line 2 are same

Cordinate of Line 1 is D(2,4)

D(2,4) must pass through line 1, so it must satisfy the equation

y=mx+b

4=2(-12)+b

4+24=b

b=28

the equation of Line 1 in the form y=-12x+28

To know more about slope, visit:

https://brainly.com/question/3605446

#SPJ1

Answer:

36 is the answer i was counting middle line oft triangle abc and it was throwing me off

Step-by-step explanation:

Answer:4

Step-by-step explanation: 12 elves have to check 48 stack

So 1 elf will have to check 48/ 12 = 4

Answer:

each elf will have 4 sacks of toys

Step-by-step explanation:

48/12= 4

Answer:

55

Step-by-step explanation:

False. The range of a linear transformation is a subset of the codomain, not the domain.

The domain is the set of inputs to the transformation, while the codomain is the set of possible outputs. The range is the set of actual outputs produced by the transformation. The statement "The range of a linear transformation must be a subset of the domain" is false. The range of a linear transformation is a subset of the codomain, not the domain. The domain is the set of input vectors, while the codomain contains the possible output vectors after applying the linear transformation.

To know more about linear transformation visit:

https://brainly.com/question/13595405

#SPJ11

The area of the parallelogram with vertices (0,0), (3,6), (8,2), and (11,8) is 0 square units.

To find the area of a parallelogram with given vertices, we can use the formula:

Area = |(x1y2 + x2y3 + x3y4 + x4y1) - (y1x2 + y2x3 + y3x4 + y4x1)| / 2

Given the vertices:

A = (0, 0)

B = (3, 6)

C = (8, 2)

D = (11, 8)

We can plug these coordinates into the formula to calculate the area:

Area = |(0*6 + 3*2 + 8*8 + 11*0) - (0*3 + 6*8 + 2*11 + 8*0)| / 2

Area = |(0 + 6 + 64 + 0) - (0 + 48 + 22 + 0)| / 2

Area = |70 - 70| / 2

Area = 0 / 2

Area = 0

Therefore, the area of the parallelogram with vertices (0,0), (3,6), (8,2), and (11,8) is 0 square units.

Learn more about parallelogram here:

https://brainly.com/question/32441125

#SPJ11

Answer:

The coordinates of the vertices of triangle A'B'C' are \(A'(x,y) = (0,-4)\), \(B'(x,y) = (2,-1)\) and \(C'(x,y) = (3,-5)\).

Step-by-step explanation:

According to this statement, triangle ABC must be translated 5 units in the -y direction to form triangle A'B'C'. We need to use the following operations:

\(A'(x,y) = A(x,y) +(0,-5)\) (1)

\(B'(x,y) = B(x,y) +(0,-5)\) (2)

\(C'(x,y) = C(x,y) + (0,-5)\) (3)

If we know that \(A(x,y) = (0,1)\), \(B(x,y) = (2,4)\) and \(C(x,y) = (3,0)\), then the new  vertices of the rectangle are, respectively:

\(A'(x,y) = (0,-4)\), \(B'(x,y) = (2,-1)\), \(C'(x,y) = (3,-5)\)

Answer:

x=10.247

y=52.02

z=37.98

Step-by-step explanation:

For x you use Pythagorean theorem which, in this situation would be 13^2=8^2+x^2 rearranging this we can figure out x by taking the square root of 13^2-8^2.

For y you can use any trig function but I chose to use cos since that uses info we're given, to find y you just do the inverse cos or cos^-1 of 8/13 to find the angle

For z you can use any trig function but I chose to use sin since that uses info we're given, to find z you just do the inverse sin or sin^-1 of 8/13 to find the angle

By proving the explanation, It is established that a positive integer is expressible as the difference between two squares of integers if and only if it is not of form 4n+2, n ∈ ℤ.

To prove that a positive integer is expressible as the difference of two squares of integers if and only if it is not of form 4n+2, n ∈ ℤ, we will demonstrate two separate cases:

Case 1: If a positive integer is expressible as the difference between two squares of integers, then it is not of form 4n+2.

Assume there exists a positive integer, k, that can be expressed as the difference of two squares of integers, i.e., k = m² - n², where m and n are integers.

We can rewrite the expression as k = (m - n)(m + n).

Now, consider the parity of the terms (m - n) and (m + n).

If both (m - n) and (m + n) are even, then k would be divisible by 4, as it would have a factor of 2 from each term.

In this case, k cannot be of the form 4n+2.

If both (m - n) and (m + n) are odd, then their sum (m - n) + (m + n) would be even. In this case, k cannot be of the form 4n+2.

If one of (m - n) or (m + n) is odd and the other is even, their sum (m - n) + (m + n) would be odd. In this case, k cannot be of the form 4n+2.

Thus, in all cases, if k is expressible as the difference between two squares of integers, it cannot be of form 4n+2.

Case 2: If a positive integer is not of the form 4n+2, then it is expressible as the difference of two squares of integers.

Assume a positive integer, k is not of form 4n+2, where n ∈ ℤ.

Consider the two cases of k being odd or k being even:

If k is odd, we can represent k as k = (k+1)/2 - (k-1)/2.

Both (k+1)/2 and (k-1)/2 are integers, so k can be expressed as the difference between two squares of integers.

If k is even, we can represent k as k = (k/2)²- (k/2 - 1)².

Both (k/2)² and (k/2 - 1)² are squares of integers, so k can be expressed as the difference between two squares of integers.

Therefore, if a positive integer is not of form 4n+2, it is expressible as the difference of two squares of integers.

By proving the above explanation, It is established that a positive integer is expressible as the difference between two squares of integers if and only if it is not of form 4n+2, n ∈ ℤ.

Learn more about Integers at

https://brainly.com/question/18380011

#SPJ4

Answer:

x = 3

Step-by-step explanation:

If you move -2 to the right side of the equation, you get:

4x = 12

Divide both sides by 4, and you get:

x = 3.

The clock minutes rotate 270 degrees in 45 minutes.

While rotating, the clock's hands are seen to move at a speed of six degrees per minute.

The number of degrees for a clock minute is solved by

60 minutes  = 360 degrees

1 minute = ?

cross multiplying

60 * ? = 360

? = 360 / 60

? = 6

hence 1 minute is 6 degrees

The formula to use to get the calculation is multiplying the number of minutes by 6

Number of degrees in 45 minutes = 45 * 6

Number of degrees in 45 minutes = 270 degrees

Learn more about clock rotation:

brainly.com/question/28741125

#SPJ1

The difference in fundraising between incumbents and challengers highlights the significant advantages of incumbency in American politics and the challenges that challengers face in trying to unseat an incumbent candidate.

In the 2020 House races, there was a significant difference in the average amounts raised by incumbents and challengers. According to data from the Center for Responsive Politics, the average amount raised by incumbents was $2.9 million, while the average amount raised by challengers was $676,000.
This discrepancy can largely be attributed to the advantages of incumbency. Incumbent candidates already have established networks of donors and supporters, name recognition, and a record of legislative accomplishments that they can leverage to raise funds. Additionally, incumbents are often able to attract larger donations from political action committees (PACs) and other interest groups who are more likely to support the candidate who already holds the office.
Challengers, on the other hand, often struggle to gain traction in fundraising due to their lack of name recognition and the fact that they are not yet seen as viable candidates. They also face more difficulty in attracting larger donations from PACs and interest groups, as these organizations tend to favor incumbents who are seen as more likely to win.
Overall, the difference in fundraising between incumbents and challengers highlights the significant advantages of incumbency in American politics and the challenges that challengers face in trying to unseat an incumbent candidate.

for more questions on incumbents

https://brainly.com/question/13490927

#SPJ11

Answer:

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Step-by-step explanation:

The area of the part of the plane 3x 2y z = 6 that lies in the first octant  is  mathematically given as

A=3 √(4) units ^2

Generally, the equation for is  mathematically given as

The Figure is the x-y plane triangle formed by the shading. The formula for the surface area of a z=f(x, y) surface is as follows:

\(A=\iint_{R_{x y}} \sqrt{f_{x}^{2}+f_{y}^{2}+1} d x d y(1)\)

The partial derivatives of a function are f x and f y.

\(\begin{aligned}&Z=f(x)=6-3 x-2 y \\&=\frac{\partial f(x)}{\partial x}=-3 \\&=\frac{\partial f(y)}{\partial y}=-2\end{aligned}\)

When these numbers are plugged into equation (1) and the integrals are given bounds, we get:

\(&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{(-3)^{2}+(-2)^2+1dxdy} \\\\&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{14} d x d y \\\\&=\sqrt{14} \int_{0}^{2}[y]_{0}^{3-\frac{3}{2} x} d x d y \\\\&=\sqrt{14} \int_{0}^{2}\left[3-\frac{3}{2} x\right] d x \\\\\)

\(&=\sqrt{14}\left[3 x-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3.2-\frac{3}{2} \cdot \frac{1}{2} \cdot 3^{2}\right] \\\\&=3 \sqrt{14} \text { units }{ }^{2}\)

In conclusion,  the area is

A=3 √4 units ^2

Read more about the plane

https://brainly.com/question/1962726

#SPJ4

The greatest number from to which when 7 is added, the sum divides 90,105,224 without leaving a reminder is 8.

We can represent the greatest number  as  x, which implies that the greatest number that  when 7 is added it will divide the givn numbers without remainder, hence x +7 = hcf.

Then we can test for the factors of the given numbers on after the other as;

90  = (2 * 5 * 3 * 3)

105 = (5 * 3 * 7)

120 = (5 * 2 * 3 * 2 * 2)

Hence the hcf here can be expressed as 5 and 3  which is equivalent to 15

Then (x + 7) = 15

x = (15 - 7)

x = 8

Learn more about greatest number at:

https://brainly.com/question/24442480

SPJ1

Answer:

m<1 =83

m<2 =97

The measurement of the angles is m<1 =83, m<2 =97.

An angle is a term used to describe the distance between two parallel lines that start at the same position.

An angle is a measurement of how much one of the lines must be turned to perfectly overlap the other.

A protractor is used to measure angles in degrees (°).

Angles can be measured from 0 to 360 degrees.

Thus, by knowing the angles, he can cut the different colors of plastic.

The angles are m<1 =83, m<2 =97.

Learn more about angles, here:

https://brainly.com/question/20296885

Answer:

y=3x+(0,4.5)

Step-by-step explanation:

i did this in my head, but the difference between -8 and 7 is 15. the difference between 2 and 7 is 5. it's rise over run so (15,5). that simplified is (3,1)/3. that is the slope. now you need a graph to see the y-int. the y-int is around 4.5.