The prism below is made of cubes which measure of a centimeter on one side.
Which of the following represents the volume of the prism?

Answer:

Yes

Step-by-step explanation:

Isosceles triangle with base of 3 units and sides of 5 units

Answer:

yes

Step-by-step explanation:

use a+b > c, a+c > b, and b+c > a if two sides are bigger than one side for every combination then you can form a triangle

9=-5b-23

9+23=-5b

32=-5b

32/-5=b. ..(here 32/-5= 32 upon -5)

-6.4=b

The required simplified value of b for the given expression is b = -2.8.

GIven that,
To determine the simplified value of b for the expression 9 = - 5b - 23.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
the given expression,

9 = - 5b - 23
Simplifying,
-5b = 23 - 9
-5b = 14
b = -14 / 5
b = -2.8

Thus, the required simplified value of b for the given expression is b = -2.8.

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The sample distribution is a collection of the parameters of all possible samples of a particular size taken from a particular population. The correct answer is option E.

A sampling distribution refers to a probability distribution of a statistic which comes from selecting random samples of a given population. Also known as a finite-sample distribution, it represents the distribution of frequencies on how spread apart various outcomes will be for a specific population.

As sample sizes increase, the sampling distributions approach a normal distribution. With infinite numbers of successive random samples, the mean of the sampling distribution is equal to the population mean (µ). The mean of the sampling distribution of a sample proportion is np, the sample size times the probability of success for each trial (or observation).

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Answers:

===================================================

Explanation:

When given this template 2x2 matrix

\(\begin{bmatrix}a&b\\c&d\end{bmatrix}\)

The determinant is a*d-b*c

We multiply the diagonal entries, then subtract the products. This applies to 2x2 matrices only.

In this case we have:

So this particular determinant is:

a*d - b*c = 13*4 - 3*16 = 52 - 48 = 4

The determinant is 4

The nonzero determinant tells us that the matrix inverse does exist.

If the determinant was zero, then the matrix inverse would not exist. This is because the inverse involves the factor \(\frac{1}{\text{determinant}}\). Recall that dividing by zero is not allowed.

Answer:

  y = 2x

Step-by-step explanation:

The graph is of a straight line through the origin. Its slope can be determined from the grid points it passes through. That slope will be the constant of proportionality for the proportion represented.

__

When the graph is a line through the origin, it is a representation of a proportion that can have the equation ...

  y = kx

where k is the constant of proportionality, also the slope of the line.

The value of k will be the y-value when x=1. Reading from the graph, we find the line goes through point (1, 2), so y = 2 when x = 1. That means k = 2 and the equation of the line is ...

  y = 2x

Answer:

it increased 20 percent

Step-by-step explanation

Answer:

volume of sphere =4/3πr^3=4/3*22/7*6*6*6=905.14m^3

The scalar product P.Q = 33, P.S = -25, and Q.S = -2. The scalar product P-Q, P-S, and Q-S are not defined.

The scalar product, also known as the dot product, is a mathematical operation that takes two vectors and returns a scalar quantity. To compute the scalar product of two vectors, we multiply their corresponding components and sum the results.

For the given vectors, P = (11)i + (10)j + (11)k, Q = (3)i + (4)j - (5)k, and S = -4i + j - 2k.

To find P.Q, we multiply the corresponding components of P and Q and sum the results: P.Q = (11)(3) + (10)(4) + (11)(-5) = 33.

Similarly, P.S = (11)(-4) + (10)(1) + (11)(-2) = -25, and Q.S = (3)(-4) + (4)(1) + (-5)(-2) = -2.

However, the scalar product P-Q, P-S, and Q-S are not defined since these operations involve subtracting vectors, and the scalar product is not defined for vector subtraction.

Therefore, the scalar products P.Q = 33, P.S = -25, and Q.S = -2, while the scalar products P-Q, P-S, and Q-S are not defined.

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Answer:

9

Step-by-step explanation:

Scott has 45 * 1/5 football cards

45 / 5 can be simplified to 9

Answer:

Scott has 9 football cards.

Step-by-step explanation:

If Scott has 1/5 as many football cards as Fred, then the number of football cards Fred has times 1/5 would result in the number of football cards Scott has;

Fred * 1/5 = Scott

45 * 1/5 = 9

We can use the formula for gravitational potential energy (GPE) to find the height at which Jessie is off the ground:

GPE = mgh

where m is the mass of the object (in kg), g is the acceleration due to gravity (9.8 m/s² on Earth), h is the height (in meters) above some reference point where the GPE is defined.

In this case, we know that Jessie has a mass of 50 kg and 4,900 joules of GPE. Plugging these values into the formula, we get:

4900 = (50 kg)(9.8 m/s²)(h)

Solving for h, we get:

h = 4900 J / (50 kg x 9.8 m/s²)

h = 10 meters

Therefore, Jessie is 10 meters off the ground at the point where she has 4,900 joules of GPE.

Answer:

10 meters

Step-by-step explanation:

P.E = mgh

4900 = 50 × 9.8 × h

4900 = 490 × h

h = 10 m

The diagonal matrix A' for T relative to the basis \(\(B'\)\) is:

\(\[A' = \left[ \begin{array}{ccc} 3 & -4 & 0 \\ -2 & -1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

To find the diagonal matrix A' for the linear transformation T relative to the basis B', we need to perform a change of basis using the given matrix A and basis B'.

Let's denote the standard basis as \(\(B = \{(1, 0, 0), (0, 1, 0), (0, 0, 1)\}\).\)

To perform the change of basis, we need to find the matrix P such that P[B'] = B.

We can write the vectors in B' as column vectors:

\(\[B' = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

To find \(P\), we solve the equation P[B'] = B for P:

\(\[P \cdot B' = B\]\\\\\P = B \cdot (B')^{-1}\]\)

Calculating the inverse of \(\(B'\)\):

\(\[B'^{-1} = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]^{-1} = \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Now we can calculate \(\(P\)\):

\(\[P = B \cdot B'^{-1} = \left[ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right] = \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Now, the diagonal matrix A' for T relative to the basis B' can be calculated as:

\(\[A' = P^{-1} \cdot A \cdot P\]\)

Calculating\(\(P^{-1}\):\)

\(\[P^{-1} = \left[ \begin{array}{ccc} -1 & 1 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right]^{-1} = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Substituting the values into the equation for \(\(A'\)\):

\(\[A' = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]^{-1} \cdot \left[ \begin{array}{ccc} -1 & -2 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Performing the matrix multiplication:

\(\[A' = \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & -2 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right] \cdot \left[ \begin{array}{ccc} -1 & 2 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Calculating the matrix multiplication, we get:

\(\[A' = \left[ \begin{array}{ccc} 3 & -4 & 0 \\ -2 & -1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

Therefore, the diagonal matrix A' for T relative to the basis B' is:

\(\[A' = \left[ \begin{array}{ccc} 3 & -4 & 0 \\ -2 & -1 & 0 \\ 0 & 0 & 1 \end{array} \right]\]\)

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Answer:

The additive inverse of -61 is 61. For additive inverse just reverse the sign.

After considering the given data we conclude that 1.50 moles of barium hydroxide will produce 3.00 moles of ammonium hydroxide.

To describe the number of moles of ammonium hydroxide produced when 1.50 moles of barium hydroxide are reacted, we have to balance the chemical equation and use the stoichiometric ratios.
The balanced chemical equation for the reaction is:
\(Ba(OH_{2} ) + (NH_4) _2 SO_4 -- > 2NH_4OH + BaSO_4\)
From the balanced equation, we can see that 1 mole of barium hydroxide reacts with 2 moles of ammonium hydroxide. Therefore, the stoichiometric ratio is 1:2.
Given that we have 1.50 moles of barium hydroxide, we can evaluate the moles of ammonium hydroxide produced using the stoichiometric ratio:
1.50 moles  \(Ba(OH)_2\) × (2 moles \(NH_4OH\) / 1 mole \(Ba(OH) _2\)= 3.00 moles \(NH_4OH\)
Therefore, 1.50 moles of barium hydroxide will produce 3.00 moles of ammonium hydroxide.

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Answer:

1,950 cubic units

Step-by-step explanation:

The computation of the volume of the prism is shown below:

Area of the rectangle = length × breadth

= 10 units × 13 units

=  130 units^2

Now the volume of the prism is

= Base × height

= 130 units × √(17^2 - 8^2)

= 130 units × 15 units

= 1,950 cubic units

Answer:

1,950 Cubic Units

Step-by-step explanation:

Because I said so.

Answer:

A≈28.27mi²

Step-by-step explanation:

\(A=\pi r^2\)

\(\pi \times 3^2\)

≈ 28.27433mi²

A≈28.27mi²

I think its (x,y-(-x,-y)

The composite figure that has an area of 40 square yards would be composed of a rectangle and a triangle.

It is not true that when two composite figures have the same area, they must also have the same perimeter.

The composite figure is composed of a rectangle and a triangle placed side by side. The rectangle has a width of 5 yards and a length of 6 yards. The triangle is a right triangle with a base of 4 yards and a height of 5 yards.

Area Calculation:

The area of the rectangle is length × width = 5 yards × 6 yards = 30 square yards.

The area of the triangle is (1/2) × base × height = (1/2) × 4 yards × 5 yards = 10 square yards.

The total area of the composite figure is the sum of the rectangle's area and the triangle's area: 30 square yards + 10 square yards = 40 square yards.

I disagree with your friend's statement that when two composite figures have the same area, they must also have the same perimeter. It is possible for two composite figures to have the same area but different perimeters.

Example:

Consider a square with a side length of 4 units. Its area is 16 square units, and its perimeter is 16 units.

Now, consider a rectangle with a length of 8 units and a width of 2 units. Its area is also 16 square units (8 x 2), but its perimeter is 20 units (8 + 8 + 2 + 2).

Both the square and the rectangle have the same area (16 square units) but different perimeters (16 units and 20 units, respectively).

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The given information states that a sample of 40 shortbread cookies was taken for research purposes. The average weight of these 40 cookies was found to be 6400 mg, with a standard deviation of 312 mg.

The average weight of 6400 mg represents the mean weight of the 40 shortbread cookies in the sample. This indicates that, on average, each cookie weighs approximately 6400 mg. The standard deviation of 312 mg reflects the variability or spread of the weights within the sample of 40 shortbread cookies.

A higher standard deviation indicates greater variation in the weights, suggesting that the weights of the cookies in the sample may vary from the mean weight of 6400 mg by approximately 312 mg. These statistics provide valuable insights into the weight distribution of the sampled shortbread cookies and are useful for understanding the characteristics of the cookies in the given research context.

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Answer:

Part A)

The height of the water level in the rectangular vessel is 2 centimeters.

Part B)

4000 cubic centimeters or 4 liters of water.

Step-by-step explanation:

We are given a cubical vessel that has side lengths of 10cm. The vessel is completely filled with water.

Therefore, the total volume of water in the cubical vessel is:

\(V_{C}=(10)^3=1000\text{ cm}^3\)

This volume is poured into a rectangular vessel that has a length of 25cm, breadth of 20cm, and a height of 10cm.

Therefore, if the water level is h centimeters, then the volume of the rectangular vessel is:

\(V_R=h(25)(20)=500h\text{ cm}^3\)

Since the cubical vessel has 1000 cubic centimeters of water, this means that when we pour the water from the cubical vessel into the rectangular vessel, the volume of the rectangular vessel will also be 1000 cubic centimeters. Hence:

\(500h=1000\)

Therefore:

\(h=2\)

So, the height of the water level in the rectangular vessel is 2 centimeters.

To find how how much more water is needed to completely fill the rectangular vessel, we can find the maximum volume of the rectangular vessel and then subtract the volume already in there (1000 cubic centimeters) from the maximum volume.

The maximum value of the rectangular vessel is given by :

\(A_{R_M}=20(25)(10)=5000 \text{ cm}^3\)

Since we already have 1000 cubic centimeters of water in the vessel, this means that in order to fill the rectangular vessel, we will need an additional:

\((5000-1000)\text{ cm}^3=4000\text{ cm}^3\)

Sincer 1000 cubic centimeters is 1 liter, this means that we will need four more liters of water in order to fill the rectangular vessel.

The required values of k for which given matrix is diagonalizable is 0.

A matrix is symmetric if and provided that it is equivalent to its translate. All sections over the primary inclining of a symmetric grid are reflected into equivalent passages beneath the slanting. ■ A lattice is slant symmetric if and provided that it is something contrary to its render.

We have,

A = \(\left[\begin{array}{cc}4&k&0&4\\\end{array}\right]\)

Keep in mind, each symmetric matrix with genuine coefficients is diagonalizable. Note that the coefficients of An are reals. In this way, on the off chance that we take with the end goal that An is symmetric.

For A is symmetric matrix,

k = \(a_{12}=a_{21}\) = 0

Thus, required value of k for given matrix is 0.

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The cost of petrol the car used in October is;

Amount spent on fuel in October = £79.76

Distance sally drove in October = 560 miles

She used 1 gallon of petrol for every 34.5 miles she drove.

Thus, number of gallons of petrol she used for the month of October on the car = 560/34.5 gallons

Now, we are told that;

1 gallon = 4.55 litres

Thus; 560/34.5 gallons = (560/34.5) × 4.55/1

Quantity of petrol she used for the month in liters = 73.855 litres

Petrol costs £1.08 per liter.

Thus;

Amount spent on fuel in October = 1.08 × 73.855

Amount spent on fuel in October = £79.7634 ≈ £79.76

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The amount of money in Lucia's account after 5 years will be $1,105.5.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. Then the amount of money after 5 years will be given as,

A = $600 × (1 + 0.13)⁵

A = $600 × (1.13)⁵

A = $600 × 1.84

A = $1,105.5

The amount of money in Lucia's account after 5 years will be $1,105.5.

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Answer:

348 of them are not postgraduates

Step-by-step explanation:

Answer:

348

Step-by-step explanation:

Out of 725 employees, 52% are postgraduates.

First find the percentage who are not postgraduates, or the "remaining."

100% - 52% = 48%

48% of 725 employees = how many employees?

48/100 × x/725

Cross multiply

48 × 725 = 100 × x

34800 = 100x

Divide both sides by 100

34800 ÷ 100 = 100x ÷ 100

348 = 1x

348 employees are not postgraduates

Answer:

Value of x = 97 degrees

Step-by-step explanation:

In the given quadrilateral

One angle = 83

2 other angles = 90 degrees each

Sum of all the four angles in a quadrilateral = 360 (Angle Sum Property of     quadrilaterals)

=>90+90+x+83= 360

=>180+83+x = 360

=> 263+x= 360

=>x= 360-263

=>x=97

Answer:

centroid

EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Yes, it is possible to find a whole number less than 100 that when divided by 10 has a remainder of 4 and when divided by 47 has a remainder of 17.

To find this number, follow these steps:
Write down the two congruences based on the given information:
  a) x ≡ 4 (mod 10)
  b) x ≡ 17 (mod 47)
Now, solve the congruences to find the smallest positive integer solution for x. In this case, you can use trial and error to find the smallest positive integer that satisfies both congruences. Start by testing the first congruence:
  a) x = 10n + 4, where n is an integer.
Substitute this expression into the second congruence and solve for n:
  b) 10n + 4 ≡ 17 (mod 47)
  c) 10n ≡ 13 (mod 47)
Find the smallest positive integer for n that satisfies this congruence.

In this case, n = 5 is the smallest positive integer,

since 10(5) ≡ 13 (mod 47).
Substitute the value of n back into the expression for x:
  x = 10(5) + 4 = 54
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Assumption that \( a \) is not even (odd) must be incorrect.Therefore, we can conclude that if \( a^2 \) is even, then \( a \) must be even.This completes the proof by contradiction.

To prove by contradiction that if \( a^2 \) is even, then \( a \) is even, we assume the opposite, i.e., that \( a \) is not even.

Assumption: \( a \) is not even (odd).

Since \( a \) is odd, we can write it as \( a = 2k + 1 \), where \( k \) is an integer.

Now, let's square both sides:

\( a^2 = (2k + 1)^2 = 4k^2 + 4k + 1 = 2(2k^2 + 2k) + 1 \)

We can see that \( a^2 \) can be expressed in the form \( 2m + 1 \), where \( m = 2k^2 + 2k \), which means \( a^2 \) is odd.

However, this contradicts our initial assumption that \( a^2 \) is even.

Hence, our assumption that \( a \) is not even (odd) must be incorrect.

Therefore, we can conclude that if \( a^2 \) is even, then \( a \) must be even.

This completes the proof by contradiction.

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Answer:

m = -3

Step-by-step explanation:

The slope formula is y2 - y1 / x2 - x1

7 - -5 = 7 + 5 = 12

-4 - 0 = -4

12 / -4 = -3

I hope this helps :))