What is -5n+7<57 and 6n+2<8

Answer:

81

Step-by-step explanation:

double digit numbers begin at 10 and end at 99

10 → 19 has 10 double digits

20 → 29 has 10 double digits

and so on up to 90 → 99

that is there are 90 double digits from 10 → 99

double digits with same value are 11, 22, 33, 44, 55, 66, 77, 88, 99

that is 9 double digits with the same value

Then double digits with different values = 90 - 9 = 81

Answer:

81 double digits numbers.

Step-by-step explanation:

From 1 to 99, first 9 numbers are single digit numbers

Double digit numbers = 99 - 9 =90

In this 90 numbers, 11,22,33,44,55,66,77,88,99 have same digits.

90 - 9 = 81

The rank of matrix A can be determined based on the given information in the question is as follows.

The rank of a matrix refers to the maximum number of linearly independent columns (or rows) in the matrix. From the given information:

a. Since A has linearly independent columns, the rank is equal to n, where n is the number of columns.

b. If Null(A)={0}, it means that the only solution to the homogeneous equation Ax=0 is the trivial solution (where x=0). This implies that the columns of A are linearly independent. Since A is a 6-by-4 matrix, the rank is equal to the number of columns, which is 4.

c. The dimension of the null space (denoted as dim(Null(A))) is equal to the number of linearly independent solutions to the homogeneous equation Ax=0. In this case, dim(Null(A))=3, which means that there are 3 linearly independent solutions. Since A is a 5-by-6 matrix, the rank can be found by subtracting the dimension of the null space from the number of columns: rank(A) = 6 - dim(Null(A)) = 6 - 3 = 3.

d. The determinant of a square matrix measures its invertibility. If det(A) is non-zero, it means that A is invertible, and an invertible matrix has full rank. Therefore, the rank of A is equal to the number of columns, which is 3.

e. The dimension of the row space (denoted as dim(Row(A))) represents the number of linearly independent rows in A. Since dim(Row(A))=3, it means that there are 3 linearly independent rows. Thus, the rank of A is 3.

f. An invertible matrix is non-singular and has full rank. Therefore, if A is a 4-by-4 invertible matrix, its rank is equal to the number of columns, which is 4.

g. If the system Ax=b has either a unique solution or no solution, it means that the column space of A has dimension 3. Hence, the rank of A is 3.

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Based on the information in the graph, we can infer that the missing numbers are: 9, 4, 19, 30, 84, 16, 8, 22, and 40.

To complete the table correctly we must identify the columns or rows with more data. These will be the easiest to complete. First of all, we must fill in those that already have a number in the total box because we can add the available numbers and later subtract them from the total to identify the missing number.

We can also find the numbers in the total cells by adding all the numbers in a column or row to find this result. Finally, the boxes that are being completed serve as clues to complete the others.

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We have shown that T is bipartite with vertex set partitioned into two color classes, which completes answer of the proof.

To prove using reverse induction that every tree with n vertices is bipartite, we need to follow these steps: Firstly, we will establish the base case: If a tree has a single vertex, it is both a bipartite graph and a tree as well. This tree has n=1 vertices, and we can see that this satisfies the definition of a tree since it has a single vertex (as opposed to none or multiple) and it has no edges (since an edge would connect two vertices, but there is only one). As for bipartiteness, this graph has two color classes: an empty set, and a set consisting of its single vertex. Since each vertex is connected to 0 other vertices, it is trivially the case that all vertices in each color class are non-adjacent, and therefore it is bipartite. Hence, we can say that the statement is true for n=1. Now we need to prove the statement for all trees with n vertices, where n≥2.Now suppose that every tree with n vertices, where n≥2, is bipartite. Let us show that every tree with n+1 vertices is also bipartite. Take any tree T with n+1 vertices, and consider a vertex v of degree one. Since T is connected, it must be possible to reach v from any other vertex by following a path of edges. Now let u be the neighbor of v. Remove v and the edge (u, v) from T, leaving a tree T′ with n vertices. By the inductive hypothesis, we can say that T′ is bipartite, with its vertex set partitioned into two color classes A and B. Note that since v has degree one, it can only be adjacent to u in T. Thus, we must place v in the opposite color class of u. That is, if u is in A, then we place v in B, and vice versa. This is the only possibility for placing v since u and v must be in different color classes for the entire tree T to be bipartite.

Now, we need to show that T is bipartite with vertex set partitioned into two color classes. For that, we need to show that any two adjacent vertices of T lie in different color classes. Let x and y be any two vertices in T that are adjacent. If neither of them is v, then since T′ is bipartite, we know that they are colored differently in T′. Hence, they must be colored differently in T as well, which makes T bipartite. If one of them is v, then we can assume without loss of generality that x is v and y is u. As we mentioned above, we have placed u and v in different color classes, so x and y are colored differently as well. Therefore, we have shown that T is bipartite with vertex set partitioned into two color classes, which completes the answer of the proof.

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Answer:

Yes the triangles are similiar

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:

1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).

The area below z=1.04 is approximately 0.851, rounded to three decimal places.

(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:

1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.

The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.

(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:

1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

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Answer:

10

Step-by-step explanation:

How many times less is 50 than 500?

500/50 = 10

The interior volume of the tent where the cross sections are triangles is given is 120ft³.

There are two cross sectional triangles

The  one smaller triangle with the height and base of 2ft

The other bigger triangle has a base and height of 4 ft

And the total length of the Tent is given as 6 ft.

Therefore,

Area of smaller triangle = 2 x 2 = 4m²

Area of bigger triangle = 4 x 4 = 16 ft²

So the Volume of the tent is given by ,

Total length x (Area of smaller triangle + Area of bigger triangle)

= 6 x ( 4 + 16 )

=6 x ( 20 )

= 120 ft ³

A measurement of three-dimensional space is volume.  Numerous imperial or US customary units, as well as SI-derived units (such the cubic metre and litre), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The capacity of a container is typically regarded to be its volume.

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Answer:

y = 2x+1

Step-by-step explanation:

From the question,

Using the equation of a straight line

y = mx+c................. Equation 1

Where m = slope of the line, c = intercept on the y axis.

From the graph, The two point co-ordinate shown os

Point 1 = (-2,0)

Point 2 =(6,4)

s = (y₂-y₁)/(x₂-x₁).............. Equation 2

Where y₂ = 6, y₁ = -2, x₂ = 4, x₁ = 0

Substitute into equation 2

s = (6-(-2))/(4-0)

s = (6+2)/4

s = 8/4

s = 2.

Also from the graph,

c = 1

Substitute these values into equation 1

y = 2x+1

Hence the equation of the line is y = 2x+1

Answer:

Step-by-step explanation:

its the top left one heres proof

the (images)

Divide total miles driven by number of gallons of gas used.

243 miles / 9 gallons = 27 miles per gallon

324 miles / 12 gallons = 27 miles per gallon.

She can drive 27 miles on one gallon of gas.

Therefore, the derivative of the function

\(f(x) = 20x^_(1/5)\) is

d/dx(f(x)) = \(4 x^_(-4/5)\).

Hence, option (A) is the correct answer.

The given function is f(x) = \(20x^_(1/5)\).

We are supposed to find the derivative of the function f by using the rules of differentiation.To find the derivative of the function

f(x) =\(20x^_(1/5)\),

we will use the formula for derivative of x^n which is `\(d/dx(xⁿ) = nx^_(n-1)\)`

Using this formula, we can write the derivative of the given function as:

d/dx(f(x)) =\(d/dx(20x^_(1/5))\)\(d/dx(f(x))\)

= 20\(d/dx(x^_(1/5))\)

Now, using the formula for derivative of \(x^n\) where n = 1/5, we get:

\(d/dx(x^_(1/5))\)

= \((1/5) x^_(1/5 - 1)\)\(d/dx(x^_(1/5))\)

=\((1/5) x^_(-4/5)\)

Now, substituting this value in the previous equation, we get:

d/dx(f(x))

= 20 \(d/dx(x^_(1/5))\)\(d/dx(f(x))\)

= 20\((1/5) x^_(-4/5)\)\(d/dx(f(x))\)

= 4 \(x^_(-4/5)\)

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The statements with the correct relationships are:

A. ∠1 and ∠8 are alternate exterior angles.

B. ∠4 and ∠6 are same side interior angles.

E. ∠3 and ∠6 are alternate interior angles.

Alternate interior angles and alternate exterior angles are pairs of angles that are formed when a transversal intersects two parallel lines.

Alternate interior angles are a pair of nonadjacent interior angles that are on opposite sides of the transversal and are located between the two parallel lines. In other words, they are the interior angles that are not adjacent to the corresponding exterior angle on the same side of the transversal. Alternate interior angles are always congruent if the two parallel lines are cut by a transversal.

In the diagram above, angle 1 and angle 8 are alternate exterior angles while angle 3 and angle 6 are alternate interior angles.

Also, angles 4 and 6 form same side interior angles.

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Answer:

x=-3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

6x = 3(x-4) - x

6x = 3x - 12 -x

6x = 3x - x - 12

6x = 2x - 12

6x - 2x = 12

4x = 12

x = 3

Answer:

draw a line like this / through zero than draw another line like this \ through zero

Step-by-step explanation:

Answer:

(x + 2)(4x - 2).

Step-by-step explanation:

(x+2)(2x+1)+(x+2)(2x-3)

Note that  (x + 2) is common to 2 parts of the expression. So we have:

(x + 2)(2x + 1 + 2x - 3)

= Ix + 2)(4x - 2)

The correct answer is C. $11,250.

To calculate the interest on a 90-day, 9% note for $50,000, we can use the simple interest formula:

Interest = Principal × Rate × Time

Given:

Principal (P) = $50,000

Rate (R) = 9% = 0.09 (decimal)

Time (T) = 90 days

Since the interest is calculated based on a 360-day year, we need to convert the time in days to a fraction of a year:

Time (T) = 90 days / 360 days = 0.25 (fraction of a year)

Now we can calculate the interest:

Interest = $50,000 × 0.09 × 0.25

Interest = $11,250

Rounded to the nearest dollar, the interest on the 90-day, 9% note for $50,000 is $11,250.

Therefore, the correct answer is C. $11,250.

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Answer:

b

Step-by-step explanation:

The point in the feasible region is (3, 0)

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

Objective function:  C = 5x - 4y

Subject to: x ≥ 0

y ≥ 0

-x + 3 ≥ y

y ≤ 1/3x + 1

Next, we plot the graph of the constraints

The vertices of the feasible region are

(1.5, 1.5), (0, 1) and (3 , 0)

Substitute (1.5, 1.5), (0, 1) and (3 , 0) in C = 5x - 4y

So, we have

C(1.5, 1.5) = 5 x 1.5 - 4 x 1.5 = 1.5

C(0, 1) = 5 x 0 - 4 x 1 = -4

C(3, 0) = 5 x 3 - 4 x 0 = 15

The maximum value is 15, so the point is (3, 0)

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Answer:

I) 225

2) 225

3) 18000

Step-by-step explanation:

\(\sf{}\)

Answer: Joseph can prepare 4 vegetable plates with the given amount of cucumbers and carrots.

Step-by-step explanation:

To divide the cucumbers and carrots evenly with nothing left over, we need to find the greatest common factor (GCF) of 20 and 48.

One way to find the GCF is to list the factors of each number and find the largest factor they have in common. The factors of 20 are 1, 2, 4, 5, 10, and 20. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The largest factor they have in common is 4.

Therefore, we can divide both the cucumbers and carrots into groups of 4. Each group will have 5 cucumbers and 12 carrots.

To find the total number of vegetable plates Joseph can prepare, we need to divide the total number of cucumbers and carrots by the number of vegetables in each plate.

The number of plates = (total number of cucumbers + total number of carrots) / (number of cucumbers + number of carrots in each plate)

The total number of cucumbers is 20, and the total number of carrots is 48. The number of cucumbers and carrots in each plate is 5 + 12 = 17.

Number of plates = (20 + 48) / 17 = 4

Therefore, Joseph can prepare 4 vegetable plates with the given amount of cucumbers and carrots.

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Answer:

1/3

Step-by-step explanation:

perimeter = sum of all sides

= 4.3 + 7 + 4.3 + 7 + 4.3 + 7 + 2.7

= 36.6 cm

Answer:

36.6 cm

Step-by-step explanation:

Each side, starting with the one all the way to the left and going anticlockwise.

7 + 4.3 + 7 + 4.3 + 7 + (7 - 4.3 = 2.7) + 4.3 = 36.6

Step-by-step explanation:

the volume of a 3D object is always calculated in some way by multiplying the 3 dimensions with each other.

so, if every dimension is then changed by a factor f (4 in our case), then the volume changes by f×f×f = f³, as the factor has to be included in the calculation for each dimension. and as they are multiplied with each other, so are the scaling factors in each case.

in our case the prism is dilated by the factor 4.

that means that every side length, every height, ..., each dimension is increased by the factor 4.

and therefore, the volume increases by the factor 4³ = 64.

so, the volume of the new image is

244 × 64 = 15,616 cm³

Volume changes by f × f × f = f³

Volume increases by the factor of 4³ = 64

The volume of the new image exists 244 × 64 = 15616 cm³.

The volume of a 3D object exists always computed in some form by multiplying the 3 dimensions by each other.

The volume changes by f × f × f = f³, as the factor, contains to be included in the calculation for each dimension and as they exist multiplied with each other, so exist the scaling factors in each case.

Here, the prism exists dilated by factor 4 which indicates that every side length, every height and each dimension exists increased by factor 4.

Volume increases by the factor of 4³ = 64

The volume of the new image exists 244 × 64 = 15,616 cm³.

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Answer:

$29

Step-by-step explanation:

You divide 2.5 by 100 the you multiply that by 725 and sense its months it would be converted to 1.6 so you multiply 725 1.6 and the answer to 2.5 divide by 100