Stephanie puts thirty cubes in a box. The cubes are 1\2 inches on each side. The box holds 2 layers with 15 cubes in each layer. What is the volume of the box?

Answers

Answer 1

If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.

To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.

Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:

30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches

The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.

The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.

Now, we can calculate the volume of the box by multiplying its length, width, and height:

Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.

In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.

To learn more about volume click on,

https://brainly.com/question/9351547

#SPJ4


Related Questions

A friend is building a garden with two side lengths 16 ft and exactly one right angle. What geometric figures could describe how the garden might look?
SELECT ALL THAT APPLY:
A. Kite.
B. Isosceles right triangle
C. Quadrilateral
D. Parallelogram

(Remember it is multiple choice)

Answers

Answer:

B. Isosceles right triangle

C. Quadrilateral

D. Parallelogram

Step-by-step explanation:

Answer:

The geometric figures that could describe how the garden might look are B. Isosceles right triangle and C. Quadrilateral.

What is the next term of 24,30,36,42,48

Answers

Answer:

54

Step-by-step explanation:

Add six each time -> 24 + 6 = 30 + 6 = 36 etc

the probability that deshawn palys basketball after school is 20% the probability that he talks to friends after school is 45% he says the p b or t is 65% explain dans error

Answers

Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.

How do we find the error?

Given:

Probability of Deshawn playing basketball after school = 20%Probability of Deshawn talking to friends after school = 45%Probability of Deshawn doing either basketball or talking to friends after school = 65%

Let’s consider the probability of Deshawn not doing basketball after school:Probability of Deshawn not doing basketball after school = 100% - Probability of Deshawn doing basketball after school= 100% - 20% = 80%

Similarly, let’s consider the probability of Deshawn not talking to friends after school: Probability of Deshawn not talking to friends after school = 100% - Probability of Deshawn talking to friends after school= 100% - 45% = 55% Probability of Deshawn doing neither basketball nor talking to friends after school:Probability of Deshawn not doing basketball after school * Probability of Deshawn not talking to friends after school= 80% * 55% = 44%

The probability of Deshawn doing either basketball or talking to friends after school is 65%, and the probability of Deshawn doing neither basketball nor talking to friends after school is 44%, which is greater than 35% which is Dans mistake. Hence, Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.

See more about probability at: https://brainly.com/question/24756209

#SPJ11

could someone help out?

Answers

Answer:

27.18

Step-by-step explanation:

Firstly, you must label the triangle.

r- opposite

13.85- adjacent

We know that tan θ = opposite/ adjacent so we substitute our numbers into the equation.

tan (63) = r/13.85

Then, times 13.85 on both sides so we only have our unknown on one side.

(x13.85)  tan(63)= r/13.85   (x13.85)

r= tan (63) x 13.85

r=27.18

:)

If the weight of the package is multipled by 5/7 the result is 40. 5. How much does the package weigh

Answers

The weight of the package is 56 using arithmetic operations.

What is multiplication?

Mathematicians use multiplication to calculate the product of two or more integers. It is a fundamental operation in mathematics that is frequently used in everyday living. When we need to combine sets of similar sizes, we use multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are compounded are referred to as the factors. Repeated adding of the same number is made easier by multiplying the numbers.

let weight of package be= x

x*5/7=40

x=(40*7)/5

x=56

To know more about multiplication, visit

https://brainly.com/question/5992872

#SPJ1

Maria purchased 1,000 shares of stock for $35. 50 per share in 2014. She sold them in 2016 for $55. 10 per share. Express her capital gain as a percent, rounded to the nearest tenth of a percent

Answers

Maria's capital gain is 55.21%. Rounded to the nearest tenth of a percent, this is 55.2%.

To determine Maria's capital gain as a percent, we need to calculate the difference between the selling price and the purchase price, and then express this difference as a percentage of the purchase price.

The purchase price for 1,000 shares of stock was:

$35.50 x 1,000 = $35,500

The selling price for 1,000 shares of stock was:

$55.10 x 1,000 = $55,100

The capital gain is the difference between the selling price and the purchase price:

$55,100 - $35,500 = $19,600

To express this gain as a percentage of the purchase price, we divide the capital gain by the purchase price and multiply by 100:

($19,600 / $35,500) x 100 = 55.21%

In summary, to calculate the percent capital gain from the purchase and selling price of a stock, we simply divide the difference between the two prices by the purchase price and multiply by 100.

To learn more about capital gain click on,

https://brainly.com/question/28628208

#SPJ4

consider a completely randomized design with k treatments. assume all pairwise comparisons of treatment means are to be made using a multiple comparisons procedure. determine the total number of pairwise comparisons for k.

Answers

The total number of pairwise comparisons for k is (k*(k-1))/2.

There are (k*(k-1))/2 pairwise comparisons in a completely randomized design with k treatments. For example, if there are 4 treatments, there will be 6 pairwise comparisons (4C2 = 6). Here's the explanation:In a completely randomized design, the treatments are randomly assigned to the experimental units. The main objective of such a design is to determine whether the treatment means are different from each other or not.To compare the treatment means, we use the mean square between treatments (MST) and mean square error (MSE). The test statistic used to compare the means is F = MST/MSE.The ANOVA table for a completely randomized design has the following format:Source of variationSum of SquaresDegrees of freedomMean SquareF-testtreatmentSS(k-1)k-1MST=MSTrMSEResidualSSTn-kMSEReference: https://www.stat.yale.edu/Courses/1997-98/101/anovar.htmNow, we need to compare each pair of treatments using a multiple comparisons procedure. A pairwise comparison involves comparing the means of two treatments only.The total number of pairwise comparisons is given by the combination formula:$$ \frac{k!}{2!(k-2)!} = \frac{k(k-1)}{2} $$Therefore, the total number of pairwise comparisons for k is (k*(k-1))/2.

Learn more about pairwise

brainly.com/question/30882986

#SPJ11

A 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5 gram tennis ball is dropped from the same 3 meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9, determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls. (Balls meet at 0.5073 m above ground, final height of tennis ball = 12.6 m above the ground)

Answers

Given that a 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5-gram tennis ball is dropped from the same 3-meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9,

    determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls.

The balls meet at a height of 0.5073 m above the ground. Hence the height that the tennis ball bounces above the ground is to be calculated.

Given that the coefficient of restitution between the ball and the ground is e = 0.87The coefficient of restitution between the tennis ball and the basketball is e = 0.9

The coefficient of restitution(e) is defined as the ratio of the relative velocity of separation and relative velocity of approach between two objects.

When a ball falls from height, it gains potential energy.

Potential energy (PE) = mghWhere, m = mass of the object, g = acceleration due to gravity, h = height

PE of Basketball = mgh= 0.625 kg * 9.81 m/s² * 3 m= 18.4 Joules

Initial kinetic energy (KE) = PE of Basketball

KE of Basketball = 18.4 J

Let the velocity of the basketball before collision be u1 and the velocity of the tennis ball before collision be u2. After the collision, let the velocity of the basketball be v1 and the velocity of the tennis ball be v2.

Using the coefficient of restitution (e) we can find the velocity of the balls after collision

   v1 - v2 = -e(u1 - u2)

Initial momentum (P) = Final momentum (P)

before the collision  P = m1u1 + m2u2

after collision  P = m1v1 + m2v2P = (0.625 kg * u1) + (0.0585 kg * u2)P

                           = (0.625 kg * v1) + (0.0585 kg * v2)

        Using the above two equations and the given coefficients of restitution, we can find the velocity of the balls after collisionv1 = (m1u1 + m2u2 + e * m2 * (u2 - u1)) / (m1 + m2)v2 = (m1u1 + m2u2 + e * m1 * (u1 - u2)) / (m1 + m2)

     Here, m1 = mass of basketball

                     = 0.625 kg,

                m2 = mass of tennis ball

                      = 0.0585 kg,

  u1 = 0, u2 = 0P = m1v1 + m2v2 => v1 + v2 = P / (m1 + m2)

Also given that the time taken by the balls to meet is 0.15 seconds

Let h be the height to which the tennis ball bounces after the collision.

When the tennis ball bounces to height h, it gains potential energy.

KE + PE = Total energy

             = Constant Using the principle of conservation of energy we can find the height to which the tennis ball bounces after collision(1/2) * m2 * v2² + (1/2) * m2 * g * h

              = (1/2) * m2 * u2² + (1/2) * m2 * g * 0(1/2) * m2 * v2²

              = (1/2) * m2 * u2² - (1/2) * m2 * g * h(1/2) * v2²

              = (1/2) * u2² - g * h

Substituting the values of u1, u2, m1, m2, e, t and g, we get:

v1 = (0 + 0.0585 kg * 9.81 m/s² + 0.9 * 0.0585 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v1

   = 1.96 m/sv2

    = (0.625 kg * 0 + 0 + 0.9 * 0.625 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v2

    = 5.5 m/s

Here, u1 = u2 = 0.

Using the above equation, we can find the height to which the tennis ball bounces after collision (1/2) * (0.0585 kg) * (5.5 m/s)² = (1/2) * (0.0585 kg) * (0 m/s)² - (0.0585 kg) * 9.81 m/s² * h12.83 J

                = -0.286 J - 0.572 h0.572 h

                = -12.83 J / 2h

                = -12.83 J / (2 * 0.572)

                = 11.2 m

Hence the height to which the tennis ball bounces above the ground after the collision is 11.2 m.

#SPJ11

Learn more about basketball is dropped and the coefficient of restitution at: https://brainly.com/question/19339515

Each of the following is not a vector space. For each of them, determine at least one part of the vector space definition that fails. (a) A={ax2+1:a∈R}with vector addition and scalar multiplication defined as forPn​. (b) B=R2 with scalar multiplication defined as usual for Rn but with vector addition defined as below: [\begin{array}{c}a1\\b1\end{array}\right] + [\begin{array}{c}a2\\b2\end{array}\right] = [\begin{array}{cc}a1-a1\\b1-b2\end{array}\right]

Answers

The definition of vector space that fails is part A and B  because it does not satisfy the any property of vector space.

The following statement can be determined if at-least one part of vector space definition that fails as:

(a) A is not a vector space because it does not contain the zero vector.

The zero vector is the unique vector that satisfies the property that when it is added to any other vector in the space, the result is the original vector.

However, in this case, the [a1, b1] + [a2, b2] = [a1 - a2, b1 - b2] is 0x² + 1, which is not an element of A. Therefore, A fails to satisfy the requirement of having a zero vector, and it is not a vector space.

(b) B is not a vector space because it does not satisfy the distributive property of scalar multiplication over vector addition.

In general, scalar multiplication must distribute over vector addition, meaning that for any scalar a and any vectors u and v in the space, a(u+v) = au + av.

However, in B, the scalar multiplication is defined as usual for R², but the vector addition is defined differently. In particular,[a1, b1] + [a2, b2] = [a1 - a2, b1 - b2].

The vector space definition fails because the vector addition is not associative, and it is also not commutative, which are the first two conditions for vector spaces. Therefore, the first and second conditions of the definition are not met.

To learn more about the vector space:

https://brainly.com/question/11383

#SPJ11

10) Find the vertex form of the parabola.

Answers

Step-by-step explanation:

4x + y^2 + 2y =  - 5

4x = - y^2 -2y - 5          

4x = - (y^2 + 2y)   - 5      'complete the square' for y

4x = - ( y +1)^2   + 1    - 5

 x = - 1/4 ( y+1)^2  - 1             vertex is at -1, -1

-14x+2y^2-8y -20 = 0

14x = 2y^2 -8y-20

14x = 2 ( y^2 - 4y) - 20     complete the square for y

14x = 2(y-2)^2  -8 - 20

x = 1/7 ( y-2)^2 - 2                Vertex is at   -2 , 2

Factorise fully - 4x² - 16x

Answers

Answer: 4x(x - 4)

Step-by-step explanation:

4x² - 16x = 4x(x - 4)

Now we can see that the expression inside the parentheses can also be factored:

x - 4 = (x - 4)

So the fully factorized expression is:

4x² - 16x = 4x(x - 4) = 4x(x - 4)

Answer:

- 4x( x + 4 )

Step-by-step explanation:

[tex]\large{\pmb{\sf{ - 4x^{2} - 16x}}}[/tex]

[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{4}} \: As \: Common:-}}}}[/tex]

[tex]\large{\pmb{\sf{\leadsto{- 4(x^{2} + 4x)}}}}[/tex]

[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{x}} \: As \: Common:-}}}}[/tex]

[tex]\large{\purple{\boxed{\pmb{\sf{\leadsto{- 4x(x + 4)}}}}}}[/tex]

━━━━━━━━━━━━━━━━━━━━━━

[tex]\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star[/tex]

[tex]\large{\dashrightarrow}[/tex] Two positive always makes positive sign when multiplied.

[tex]\large{\dashrightarrow}[/tex] Two negatives always makes positive sign when multiplied.

[tex]\large{\dashrightarrow}[/tex] A positive and a negative always makes negative sign when multiplied.

[tex]\large{\dashrightarrow}[/tex] The sum of two positives is always positive with a positive sign.

[tex]\large{\dashrightarrow}[/tex] The sum of two negatives is always positive with a negative sign.

[tex]\large{\dashrightarrow}[/tex] The sum of a positive and a negative is always negative with the sign of whose number is greater.

Please help it’s for tmr, I only have 18 minutes left
Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation

Answers

Leo might therefore have 36 or 48 toy soldiers, which is a choice between the two numbers.

What is the greatest number that is possible?

The attempt to demonstrate that your integer is larger than anyone else's integer has persisted through the ages, despite their being more numbers than there are atoms in the universe. The largest number that is frequently used is a googolplex (10googol), which equals 101¹⁰⁰.

We'll name Leo's collection of toy soldiers "x" the amount. We are aware of:

We can infer x to be one of the following figures from the first condition: 28, 32, 36, 40, 44, 48, or 52.

To find out which of these integers meets the other two requirements, we can try each one individually:

x + 6 = 34 and x + 3 = 31, neither of which is a multiple of five, if x = 28.

X + 6 = 38 and X + 3 = 35, none of which is a multiple of 5, follow if x = 32.

When x = 36, x + 6 = 42, a multiple of 7, and x + 3 = 39, a multiple of 5, follow. This might be the answer.

x + 6 = 46 and x + 3 = 43, neither of which is a multiple of five, if x = 40.

x + 6 = 50 and x + 3 = 47, neither of which is a multiple of five, if x = 44.

When x = 48, x + 6 = 54, a multiple of 7, and x + 3 = 51, a multiple of 5, follow.

x + 6 = 58 and x + 3 = 55, neither of which is a multiple of five, if x = 52.

To know more about two numbers visit:-

https://brainly.com/question/1814627

#SPJ1

The spinner above is used in a game. What is the theoretical probability of the given event with one spin?

P (5)

Answers

Answer:

B

Step-by-step explanation

so there is 8 numbers so when you spin you have a 1/8 chance of spinning the number

7) Roy buys pizza for his friends. A whole pizza costs P 190. 00 and P 40. 00 for every
additional topping. If he spent P 1070 for pizza with 3 sets of additional toppings, how
many whole pizzas did he buy?

Answers

Roy purchased whole pizzas for P 190.00 each. To determine the number of whole pizzas he bought, we can divide the total cost of the pizzas by the cost of each pizza. Therefore, the calculation P 950.00 / P 190.00 results in 5, indicating that Roy bought five whole pizzas.

Roy spent a total of P 1070 for pizza with 3 sets of additional toppings. Since each set of additional toppings costs P 40.00, then the total cost of the toppings is 3 x P 40.00 = P 120.00. Subtracting this from the total amount spent gives us P 950.00, which is the cost of the pizzas alone.

Since each whole pizza costs P 190.00, we can divide the cost of the pizzas by the cost of each pizza to find the number of whole pizzas Roy bought. Therefore, P 950.00 / P 190.00 = 5.

Thus, Roy bought 5 whole pizzas.

Learn more about arithmetic here: brainly.com/question/11559160

#SPJ4

Jenny wants to measure the height of a tree she sites the top of the tree using a mirror that is lying flat on the ground. The mirror is 20 feet from the tree, and Jenny is standing 8 feet from the mirror as shown in the figure, her eyes are 5 feet above the ground how tall is the tree?

Answers

The Height of tree is around 8.33 feet tall.

What is the connection among Height and distance?

In science, we work out the Height of an item utilizing distance and points. Distance is the even distance between the items, and point is the point over the level of the article's top, which gives the item's level.

We can utilize the rule of comparable triangles.

The hypotenuse of this triangle would be the line associating Jenny's eyes to the highest point of the tree (we should refer to this distance as "h").

We can set up the accompanying extent between the two triangles:

h / 20 = (h + 5) / 8

To solve for "h", we can cross-multiply and simplify:

8h = 20(h + 5)

8h = 20h + 100

12h = 100

h = 8.33 feet

To know more about Height visit:-

https://brainly.com/question/10726356

#SPJ1

The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 7 cm and the width is 5 cm, how fast is the area of the rectangle increasing (in cm²/s)?

Answers

Answer:

Step-by-step explanation: In the problem, they tell us that

dL / dt = 7 cm/s (the rate at which the length is changing) and

dw / dt = 8 cm/s (the rate at which the width is changing)

Want dA/dt (the rate at which the area is changing) when L = 7 cm and w = 5 cm

The equation for the area of a rectangle is:

A = L·w, so will need the product rule when taking the derivative.

dA/dt = L (dw/dt) + w (dL/dt)

Now just plug in all of the given numbers:

dA/dt = (7)(7) + (5)(8) = 49+40 = 89  cm²/s

find the long leg: b =

Answers

Answer:

b ≈ 12.1

Step-by-step explanation:

using the tangent ratio in the right triangle

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{7}[/tex] ( multiply both sides by 7 )

7 × tan60° = b , then

b ≈ 12.1 ( to the nearest tenth )

What is 25.71 rounded to 2 Decimal Place?

Answers

The rounded value of 25.71 to 2 decimal places is 25.71 itself.

How to find 25.71 rounded to 2 Decimal Place

To round 25.71 to 2 decimal places, we need to look at the third decimal place, which is 1.

If the third decimal place is 5 or greater, we round up the second decimal place. If the third decimal place is less than 5, we simply drop it and keep the second decimal place as is.

In this case, the third decimal place is 1, which is less than 5, so we simply drop it and keep the second decimal place as is. Therefore, 25.71 rounded to 2 decimal places is:

25.71 ≈ 25.71 (no rounding necessary)

So, the rounded value of 25.71 to 2 decimal places is 25.71 itself.

Learn more about decimal at https://brainly.com/question/703656

#SPJ1

The mayor of a town sees an article that claims the national unemployment rate is
8%. They suspect that the unemployment rate is lower in their town, so they plan to take a sample of 200 residents to test if the proportion of residents that are unemployed in the sample is significantly lower than the national rate. Let p represent the proportion of residents that are unemployed.
Which of the following is an appropriate set of hypotheses for the mayor's significance test?
Choose 1 answer:

Answers

The required correct answers are [tex]$$H_0: p = 0.08$$[/tex] , [tex]$$H_a: p < 0.08$$[/tex].

What is Hypothesis test?

Let p be the proportion of residents in the town who are unemployed. The null hypothesis [tex]$H_0$[/tex] is that the proportion of unemployed residents in the town is the same as the national unemployment rate of 8%. The alternative hypothesis [tex]$H_a$[/tex] is that the proportion of unemployed residents in the town is significantly lower than the national unemployment rate.

Using the appropriate notation, the hypotheses can be expressed as:

$H_0: p = 0.08$

$H_a: p < 0.08$

Therefore, the appropriate set of hypotheses for the mayor's significance test are:

[tex]$$H_0: p = 0.08$$[/tex]

[tex]$$H_a: p < 0.08$$[/tex]

Note that this is a one-tailed test since the alternative hypothesis is only considering the possibility of the proportion being lower than the national unemployment rate

To know more about Hypothesis test visit:

brainly.com/question/30588452

#SPJ1

if belongs to the interval , at which values of does the curve have a tangent line parallel to the line ?

Answers

Answer:

you need to show the numbers

Step-by-step explanation:

At a party to celebrate a successful school play, the drama club bought 999 large pizzas. Each pizza had sss slices. All together, there were 727272 slices of pizza for the club to share.
Write an equation to describe this situation.
How many slices does each pizza have?

Answers

Answer:

Step-by-step explanation:

Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:

999n = 727272

To solve for "n", we divide both sides by 999:

n = 727272/999

Using a calculator or long division, we get:

n ≈ 728.56

Therefore, each pizza has approximately 728 slices.

You ride your bike 1 3/4 miles to your friend's apartment and then another
1 3/10 miles to school. How many miles do you ride your bike in all?

Answers

Answer:3 1 /20

Step-by-step explanation:= 1+3/4+1+3/10

Helpppppppppp pleaseeee I really need itttttt

Answers

Answer: 96

Step-by-step explanation:

M = 180 - 84 = 96

m<k = 96

Determine whether the set StartSet left bracket Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 0 3rd Row 1st Column negative 3 EndMatrix right bracket comma left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 3 2nd Row 1st Column 1 3rd Row 1st Column 6 EndMatrix right bracket comma left bracket Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column negative 1 3rd Row 1st Column 0 EndMatrix right bracket EndSet 1 0 −3 , −3 1 6 , 1 −1 0 is a basis for set of real numbers R cubedℝ3. If the set is not a​ basis, determine whether the set is linearly independent and whether the set spans set of real numbers R cubedℝ3. Which of the following describe the​ set?

Answers

The set [1 0 −3 , −3 1 6 , 1 −1 0] is not a basis for set of real numbers R cubed(ℝ3).

The reason why it is not a basis is because it is not linearly independent. However, the set does span set of real numbers R cubed(ℝ3).To determine if the given set is a basis for set of real numbers R cubed(ℝ3), we need to test for linear independence and for span.Linear independence

The given set is said to be linearly independent if and only if the only solution to the equation a[1 0 −3] + b[−3 1 6] + c[1 −1 0] = [0 0 0] is the trivial solution where a, b and c are constants.If the given set is linearly independent then it is a basis for R3; if it is not linearly independent, it is not a basis for R3.

SpanThe given set is said to span R3 if every vector in R3 can be written as a linear combination of vectors in the given set.

If the given set spans R3, then it can be considered a basis for R3.For us to test if the given set is linearly independent, we can form a matrix by placing the three given vectors into the columns of a 3 x 3 matrix as follows:[1 0 1] [−3 1 −1] [−3 6 0]

By expanding the determinant of the matrix above, we get: det(A) = 0 - 0 - (-3) = 3

Since the determinant is non-zero, we can say that the given set is linearly independent. Since the given set is linearly independent, we can then use it to span R3. Hence the given set does not form a basis for R3 but it is linearly independent and spans R3.

To know more about linearly independent click on below link:

https://brainly.com/question/30720942#

#SPJ11

17. The sum of the interior angles of a pentagon is6x + 6y. Find y in term of x

Answers

Answer:

We know that, the sum of interior angles of an n-sided polygon is (n−2)×180⁰

For a pentagon, n=5

so,

[tex] \implies \rm \: 6x + 6y = (n - 2)180[/tex]

[tex] \implies \rm \: 6(x + y) = (5 - 2)180[/tex]

[tex] \implies \rm \: 6(x + y )= 3 \times 180[/tex]

[tex] \implies \rm \: (x + y) = \dfrac{3 \times 180}{6} [/tex]

[tex] \implies \rm \: (x + y) = \dfrac{ 3 \times \cancel{180} \: \:30}{ \cancel6} [/tex]

[tex] \rm \implies \: x + y = 90[/tex]

[tex] \underline{\boxed{\implies \rm \: y= 90 - x}}[/tex]

Pentagon Formulas

There are many formulas related to a pentagon. A few basic ones are given below.

Diagonals of a pentagon: = n × (n − 3) ÷ 2 = 5 × (5 − 3) ÷ 2 = 5Sum of interior angles of a pentagon: = 180° × (n − 2) = 180° × (5 − 2) = 540°Each exterior angle of a regular pentagon: = 360° ÷ n = 360° ÷ 5 = 72°Each interior angle of regular pentagon: = 540° ÷ n = 540° ÷ 5 = 108°Area of a regular Pentagon = 1/2 × Perimeter × ApothemPerimeter of Pentagon = (side 1 + side 2 +side 3 + side 4 + side 5)

when an automatic press is a manufacturing process is operaing properly, the lengths of the component it produces are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches. what is the probability thata randomly selected component is shorter than 7 inches long? (report your answer to 4 decimal places.)

Answers

The probability that a randomly selected component is shorter than 7 inches long is approximately 25.14%.

What is the probability of randomly selected component?

We are given that the lengths of components produced by the automatic press are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches.

We need to find the probability that a randomly selected component is shorter than 7 inches long.

We can use the standard normal distribution to find this probability. We first need to convert the length of 7 inches to a z-score:

z = (7 - 8) / 1.5 = -0.67

Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the probability that a randomly selected component is shorter than 7 inches long:

P(z < -0.67) = 0.2514

Learn more about probability here: https://brainly.com/question/24756209

#SPJ1

Six more than the quotient of a number and 8 is equal to 4

use the variable x for the unknown number

!!!TRANSLATE INTO A EQUATION!!!

Answers

Answer:

x/8 + 6 = 4

Step-by-step explanation:

x / 8 + 6 = 4

x/8 = -2

x = 8*-2 = -16.

which sampling approach was used in the following statement?kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in wisconsin to study their attitudes toward evidence-based practice.

Answers

The sampling approach that was used in the statement "Kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in Wisconsin to study their attitudes toward evidence-based practice" is Stratified random sampling.

What is Stratified random sampling?

Stratified random sampling is a method of sampling that is based on dividing the population into subgroups called strata. Stratified random sampling is a statistical sampling method that involves the division of the population into subgroups or strata, and a sample is then drawn from each stratum in proportion to the size of the stratum. It's a sampling method that ensures the representation of all population strata in the sample, making it more effective than simple random sampling.

Stratified random sampling is used when there are variations in the population that are likely to influence the outcome of the study. The stratified random sampling method is used to ensure that these differences are reflected in the sample. In this way, the results of the study are more representative of the entire population than they would be if a simple random sample were used.

Learn more about Stratified random sampling here: https://brainly.com/question/20544692.

#SPJ11

a confidence interval for a population mean was reported to be to . if , what sample size was used in this study? (round your answer up to the next whole number.)

Answers

The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.

What is deviation?

Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.

Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.

To learn more about deviation

https://brainly.com/question/12402189

#SPJ1

The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.

What is deviation?

Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.

Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.

To learn more about deviation
brainly.com/question/12402189
#SPJ1

Complete Question:
A 95% confidence interval for a population mean was reported to be 152 to 160. If s 15, what sample size was used in this study?

The accurate scale diagram shows a telephone mast and a box.
Find an estimate for the real height, in metres, of the telephone mast.
telephone mast
5.5
+2.5 m
box
+
Total marks: 2

Answers

Using proportions, the real height of the telephone mast is estimated to be 9 meters.

What exactly is a proportion?

A proportion is a fraction of a total amount, and equations are constructed using these fractions and estimates to find the desired measures in the problem using basic arithmetic operations like multiplication and division. Because the telephone box and the mast are similar figures in this problem, their side lengths are proportional.

The following proportional relationship is established as a result:

x / 1.5 cm = 10.8 cm / 1.8 cm.

The relationship's left side can be simplified as follows:

6 = x / 1.5 cm.

The estimate is then calculated using cross multiplication, as shown below:

6 x 1.5 cm = 9.5 cm².

To know more about fraction, visit:

https://brainly.com/question/10354322

#SPJ1

Other Questions
what are the roots of 2x^2+10x+9=2x Which religion dominated the German states? you are looking for signs as to whether a culture is low context. which of the following would be an obvious indicator of that fact? according to raiders of the lost ark, in what third intermediate period city was the lost ark located? Sophie invested $92,000 in an account paying an interest rate of 6 1/8% compoundedcontinuously. Damian invested $92,000 in an account paying an interest rate of 6 5/8%compounded monthly. After 14 years, how much more money would Damian have inhis account than Sophie, to the nearest dollar? ___________ involve bringing the suspect back to the scene of the crime or the location of the witness to see if the witness can identify the suspect as the perpetrator. ms. beal recognized a $42,400 net long-term capital gain and a $33,000 net short-term capital loss this year. what is her current net income tax cost from her capital transactions if her marginal rate on ordinary income is 37%? What do you enjoy most about learning english They don't deliver the letters themselves. They _____ a separate delivery service. ______ shows the actual performance of ads in terms of awareness, costs efficiency, or sales and those that don't do well may be dropped. according to the multiple nuclei model, an airport is likely to attract nearbyhotels and warehousesretail and wholesale shopsresidences and highwaysuniversities and colleges According to ________, various economic classes have different degrees of power when it comes to who can make and enforce laws in society.a. C. Wright Millsb. Karl Marxc. Robert Mertond. Emile Durkheim as a 4.4-kg object moves from (2 i 5 j) m to (6 i - 2 j) m, the constant resultant force acting on it is equal to (4 i - 3 j) n. if the speed of the object at the initial position is 4.9 m/s, what is the work done by the force, and what is its kinetic energy at its final position? as your answer in canvas, write the kinetic energy in joules.\ if having your license suspended for driving too fast makes you less likely to speed when you get it back, then the suspension is an example of Both Bond Bill and Bond Ted have 12.4 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 5 years to maturity, whereas Bond Ted has 22 years to maturity. Requirement 1: If interest rates suddenly rise by 3 percent, what is the percentage change in the price of these bonds? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).) Percentage change in priceBond Bill %Bond Ted %Requirement 2: If rates were to suddenly fall by 3 percent instead, what would be the percentage change in the price of these bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Percentage change in priceBond Bill %Bond Ted % this component of the male duct system carries sperm from outside the body into the abdominal cavity. fit for life foods reports the following income statement accounts for the year ended december 31 gain on sale of equipment 6320depreciation expense office copier 480office supplies expense760sales discounts15 700insurance expense1 370sales returns and allowances3 900sales217 000tv advertising expense2 200office salaries expense31 300interest revenue600rent expense selling space10 300cost of goods sold89 000sales salaries expense23 100sales commission expense13 000prepare a multiple step income statement imagine a scenario where a man is stranded on a desert island. he first finds a source of potable water and some fruits to eat. only after his thirst and hunger are satisfied does he set about building a shelter for the night. once the man has met his physiological and security needs, he will set about searching for other people on the island. which of the following needs of the man stranded on a desert island does this scenario illustrate? group of answer choices o prepotent needs ocreative behavior o self-actualizationo needs intrinsic o motivation FILL IN THE BLANK.an advantage of behavior checklists over interviews is that checklists allow a clinician to ___ while interview typically do not. Analyze the proportion below and complete the instructions that follow. Use a model to find the missing value in the proportion. A. 4 B. 5 C. 10 D. 22 Please select the best answer from the choices provided A B C D