-) Ms. Cohen is buying supplies for her kindergarten classroom. She can spend at most $30.
She wants to buy boxes of crayons that cost $2 per box. She also buys a poster for $5.
Ms. Cohen wants to know how many boxes of crayons she can buy.
1) Let b be the number of boxes of crayons Ms. Cohen buys.
Write an inequality that represents the situation.
+
30
5
2
b.

Yes I give brainless!!

Answer:

Step-by-step explanation:

The dimension of the basis is {[1 0 0 2], [-1 1 0 0]}.

To find a basis for the subspace S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]}, we can use the same method as in the example. First, we put the vectors in a matrix and row-reduce it:

[1 -1 0 2]
[3 -5 4 8]
[0 1 -2 -1]

R2 - 3R1 -> R2
R3 -> R3 + 2R1

[1 -1 0 2]
[0 -2 4 2]
[0 1 -2 -1]

-1/2R2 -> R2

[1 -1 0 2]
[0 1 -2 -1]
[0 1 -2 -1]

R3 - R2 -> R3

[1 -1 0 2]
[0 1 -2 -1]
[0 0 0 0]

We can see that the last row is all zeros, so we have only two pivots and one free variable. This means that the dimension of the subspace S is 2. To find a basis, we can write the pivots as linear combinations of the original vectors:

[1 -1 0 2] = [1 0 0 2] + [-1 1 0 0]
[0 1 -2 -1] = [0 1 -2 -1]

Therefore, a basis for S is {[1 0 0 2], [-1 1 0 0]}.

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Answer:

C

Step-by-step explanation:

If u need an explanation I already did in the comment section before haha brainly is finally letting me answer

Image of triangle is missing, so i have attached it.

Answer:

x = 18

Step-by-step explanation:

From the diagram attached, we can see that the 3 given sides have dimensions of x, 16 and 30.

Also, we see the angle opposite the dimension of x is 30°

Thus,we can use law of cosine to fjnd the value of x. Thus:

x² = 16² + 30² - 2(16 × 30)cos 30

x² = 256 + 900 - (960 × 0.866)

x² = 324.64

x = √324.64

x = 18.02

Approximating to the nearest tenth gives; x = 18

Answer:

-5 -= -3; 0= 2; 3=5

Step-by-step explanation:

True; In MATLAB, array indices must be positive integers or logical values.

In MATLAB, array indices must indeed be positive integers or logical values. This means that when accessing elements within an array, the index values should be integers greater than zero or logical values (true or false). It is not permissible to use negative integers or non-integer values as array indices in MATLAB.

For example, consider an array called "myArray" with five elements. To access the first element of the array, you would use the index 1. Similarly, to access the fifth element, you would use the index 5. Attempting to use a negative index or a non-integer index will result in an error.

Using valid indices is crucial for proper array manipulation and accessing the correct elements. MATLAB arrays are 1-based, meaning the index counting starts from 1, unlike some programming languages that use 0-based indexing.

In MATLAB, array indices must be positive integers or logical values. This ensures proper referencing and manipulation of array elements. By adhering to this rule, you can effectively work with arrays in MATLAB and avoid errors related to invalid indices.

To know more about

In MATLAB, array indices start from 1. They are used to access specific elements within an array.

In MATLAB, array indices are used to access or refer to specific elements within an array. The index of an element represents its position within the array. It is important to note that array indices in MATLAB start from 1, unlike some other programming languages that start indexing from 0.

For example, consider an array A with 5 elements: A = [10, 20, 30, 40, 50]. To access the first element of the array, we use the index 1: A(1). This will return the value 10.

Similarly, to access the third element of the array, we use the index 3: A(3). This will return the value 30.

Array indices can also be logical values, which are either true or false. Logical indices are used to select specific elements from an array based on certain conditions. For example, if we have an array B = [1, 2, 3, 4, 5], we can use logical indexing to select all the elements greater than 3: B(B > 3). This will return the values 4 and 5.

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Answer:

A line of best fit is drawn through a scatterplot to find the direction of an association between two variables. This line of best fit can then be used to make predictions. To draw a line of best fit, balance the number of points above the line with the number of points below the line.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Using the changing base formula, log base 2 raised to 7 can be written as log7/log2

The correct answer is D. log(7) / log(2).

To find the equivalent of log2(7), you can use the change of base formula for logarithms.

The change of base formula states that log base a of b is equal to log base c of b divided by log base c of a.

In this case, we want to find the equivalent of log2(7), so we can use the change of base formula with base 10 as follows:

log2(7) = log(7) / log(2)

Therefore, the correct answer is D. log(7) / log(2).

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Answer: 78

Step-by-step explanation:

Area=b x h
13 x 6 =78

Answer:

78 m

Step-by-step explanation:

The formula to find the area of a rectangle or square = length * Height

A = L * H

In this scenario, the length is 6 and the height is 13

So the area (A) = 6 * 13 = 78

And don't forget your units ;)

Answer:

Yes

Step-by-step explanation:

Answer:

$699.52

Step-by-step explanation:

Theres two ways to solve this.

(1) You can either find 7 percent of 653.76 and then add it on

or

(2) You can just multiply the tax with the 653.76

Option (1)

You find 7 percent of 653.76. Now percent means out of a hundred so 7 percent is really 7/100 or 0.07

Now you multiply 653.76 by 0.07 which is 45.76 (rounded to nearest cent)

Now add it up to the total.

653.76+45.76= $699.52

Option (2)

This is the easier method in my opinion. SInce you want to find the total of the product including tax. The tax is technically multiplying the total. The total of course is 653.76 and total means everything. Everything means 100%. So you can add 100% to the tax cause technically thats what your doing becuase you grinding 7percent of the total which is 100 percent. So in this case your price is increasing by 107 percent.

(Example)

So If you want to find 100 percent of a product it would be the same exact result. Like 100 percent of 653.76 is 654.76… So using that we can just add the amount of tax to the 100%. 100+7=107%

Proof that this works is this

usually when you want to find a percentage of something, you turn the percentage into a decimal then multiply. So 100 percent of 653.76 is 653.76*1.00 which is 653.76. So the 100 percent is a place holder to prevent you from doing more steps. Now just add 7 percent since your increasing the total by 7 percent (tax). Now its 653.76*1.07 which when solved you would get $699.52. The same exact result. Less steps same result.

Final answer: $699.52

Answer:

108 cm²

Step-by-step explanation:

A = πr²

A = 3 * 6²

A = 3 * 36

A = 108

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Step-by-step explanation:

please mark me as brainlest

Answer: the answer is B which is x < -1

Step-by-step explanation: trust me bro and happy holidays :)

Answer:

\(\huge\boxed{B)\ x<-1}\)

Step-by-step explanation:

Solve this inequality the same way you would solve an equation: by isolating x.

Simply subtract 6 from both sides to get -4x > 4.   Then merely divide both sides by -4 to get x < -1.  (Notice that when dividing by a negative number, you must flip the sign of the inequality.)

Hope it helps :)

Answer: -45/4 = -11 1/4

Answer:

99 in³

Step-by-step explanation:

Let the radius and height of each be r and h in. respectively.

Write an equation for the volume of cone.

Volume of cone= ⅓πr²h

⅓πr²h= 33

Multiply both sides by 3:

πr²h= 99

Volume of cylinder= πr²h

We have found the value of πr²h previously, which is 99.

Thus, the volume of the cylinder is 99 in³.

3×3×3×3×3 in exponential form is 3⁵.

When we represent a number in the exponential form then we can say that its power has been raised by an exponent. The exponential form is an easier way of representing repeated multiplication involving base and exponents.

For example, If we have to write the exponential form of a×a×a×a×a, we can write it as a base and the number of a's as the power that is

a×a×a×a×a = a⁵

Where

a is the base

5 is the power of a

We can simply write 3×3×3×3×3 in exponential form by raising the power to the base 3,

3×3×3×3×3 = 3⁵

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The height of the flag pole which is described as in the task content is; 8.2m.

The horizontal distance between the 6m house and the flagpole in discuss can be evaluated by means of the angle of depression and trigonometric identity, tan as follows;

tan 22° = 6/x

x = 6/tan 22 = 14.9m.

Consequently, the horizontal distance from the top of the house to the top of the flagpole is therefore;

tan 9° = y/14.9

y = 14.9 tan 9° = 2.2m

Ultimately, the height of the flagpole is; 6+2.2 = 8.2m.

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The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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Answer:

TUNNEL:

f(x) = -2/4.9  \(x^{2}\)  + 9.8

TRUCK:

Width (m) < 9.8

Height (m) <  -2/4.9 ( \(Width^{2}\) /4 - \(4.9^{2}\) )

Step-by-step explanation:

Please see attachment

If the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.

Any function of the form\(\rm f(x) =ax^2+bx+c\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

It is given that, If the maximum height of the tunnel is the same as its maximum width, 9.8 meters.

We have to determine a quadratic model to represent the tunnel.

The quadratic function is formed as,

f(x) =K(x-x₁)(x-x₂)

x₁=width/2

x₁=9.8/2 = 4.9

x₂= -x₁ = -4.9

Substitute the obtained value as,

f(x) = K(x-4.9)(x-(-4.9))

f(x) =K(x²-4.9²)

f(0)=9.8

The value of K is obtained as a result,

K=-2×4.9/(4.9)²

K= -2/4.9

Substitute the value of K as,

f(x) = -2/4.9(x²-4.9²)

f(x) = (-2/4.9)x²+2×4.9

f(x)= (-2/4.9)x²+9.8

Thus, if the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.

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Answer:

The formula for the area of a circle is:

A = πr^2

where A is the area and r is the radius.

In this case, we are given that the area is 4π cm². Solving for the radius, we get:

4π = πr^2

r^2 = 4

r = 2

So the radius of the circle is 2 cm.

The formula for the circumference of a circle is:

C = 2πr

Plugging in the value for the radius, we get:

C = 2π(2) = 4π

Therefore, the circumference of the circle is 4π cm.

The code creates a new data frame that filters for chocolate bars that contain at least 80% cocoa and have a rating of at least 3.75 points.

filter(cocoa.percent >= 80, rating >= 3.75)

1. Start by creating a new data frame called best_trimmed_flavors_df that uses the trimmed_flavors_df data frame

2. Use the %>% operator to pipe the trimmed_flavors_df data frame into the new data frame

3. Use the filter() function to filter the new data frame for chocolate bars with at least 80% cocoa and a rating of at least 3.75 points

The code creates a new data frame that filters for chocolate bars that contain at least 80% cocoa and have a rating of at least 3.75 points.

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Answer:

x = 7

Step-by-step explanation:

These are alternate interior angles. The rule for this type of angles is that they are equal to each other. Hence, you would do the following:

2x+5 = 3x-2 (Add 2 to each side)

2x+7 = 3x (Subtract 2x from each side)

7 = x ; x = 7

I hope this helps :D

The number of times scientific books were sold compared to mystery books is 1000 times or one thousand times.

The numbers provided to represent the number of copies that were sold from each book are given in scientific notation. In this type of notation, the exponent represents the number of zeros. Based on this principle, the number of books sold from each type is:

To find out this, simply divide the number of science fiction book copies into the number of mystery book copies:

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Answer:

Step-by-step explanation:

1. 6x + 12 = 3x - 27

   3x + 12 = -27

   3x = -39

    x = -13

2. 2p - 3 = 3p + 2

    -p - 3 = 2

     -p = 5

      p = -5

3. 6x - 2 - 35x -28 = 18x - 27

   -29x - 30 = 18x - 27

   -47x - 30 = -27

    -47x = 3

    x = -3/47

Let's use the formula provided:

We have shown that there are elements m, n ∈ S with m - n divisible by 16.

Answer:Let's consider the remainders of elements of S when divided by 16. These remainders can only be integers between 0 and 15, so there are only 16 possible remainders. However, we have 17 elements in S, so by the Pigeonhole Principle, at least two of these elements must have the same remainder when divided by 16. Let's call these elements m and n. Since they have the same remainder when divided by 16, their difference must be divisible by 16. In other words, m - n is divisible by 16. Therefore, we have shown that there are elements m, n ∈ S with m - n divisible by 16.

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Answer:

Green line

Step-by-step explanation:

This is the only line that has coordinates (1,2) and the slope is positive.

Answer: You've probably already seen the basic method for graphing straight lines; namely, make a T-chart, plot some points, put your ruler against them, and draw the line. But the "nice" form of a straight line's equation (being the slope-intercept form, y = mx + b) can make graphing even simpler and faster.

Step-by-step explanation: hope this helps.

The radius of the cone whose volume is 3π is approximately 2.121 as per the concept of cone.

To find the radius of a cone whose volume is 3π, we can equate the given volume to the volume formula of a cone and solve for the radius.

The volume formula of a cone is given as:

\(V = \frac{1}{3} \pi}r^{2}h\)

Given:

V = 3π

h = 2

Substituting these values into the volume formula, we have:

\(3\pi = \frac{1}{3} \pi}r^2(2)\)

Simplifying the equation, we get:

\(3 = \frac{1}{3} r^2(2)\)

Multiplying both sides by 3 to eliminate the fraction, we have:

\(9 = 2r^2\)

Dividing both sides by 2, we get:

\(4.5 = r^2\)

Taking the square root of both sides, we have:

r = √4.5

Using a calculator to evaluate the square root of 4.5, we find:

r ≈ 2.121

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The complete question:

The volume of a cone of height 2 and radius r is \(V = \frac{3}{2} \pi}r^{2}h\). What is the radius of such a cone whose volume is 3π ? r= help (numbers)

To prove that a strictly increasing function from R to itself is one-to-one, we need to show that for any two distinct inputs in the domain, the function produces two distinct outputs in the range.

Let f be a strictly increasing function from R to itself, and let x, y be two distinct inputs in the domain of f, with x < y. Then, since f is strictly increasing, we know that f(x) < f(y), since x < y. This means that the outputs f(x) and f(y) are distinct, and therefore f is one-to-one.

To see why this is the case, suppose that f(x) = f(y) for some inputs x and y in the domain of f. Then, since f is strictly increasing, we know that x < y if f(x) < f(y), and x > y if f(x) > f(y). But if f(x) = f(y), then neither of these inequalities can hold, since they both require f(x) and f(y) to be distinct. Therefore, we have a contradiction, and it must be the case that f is one-to-one.

In summary, a strictly increasing function from R to itself is one-to-one because it produces distinct outputs for any two distinct inputs in the domain. This follows from the fact that if f(x) = f(y) for some x, y in the domain of f, then this would contradict the strict monotonicity of f.

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The mathematical relationship between simple and compound interest lies in the compounding effect of interest over time. Simple interest is calculated only on the initial principal amount, while compound interest takes into account both the principal and accumulated interest.

Let's consider an example to illustrate this relationship. Suppose we have an investment of $10,000 with an annual interest rate of 5%. If we calculate simple interest for a period of one year, the interest earned would be $500 (10,000 * 0.05). In this case, the interest remains constant throughout the investment period.

However, if we calculate compound interest, the interest is added to the principal at regular intervals, typically compounded annually, semi-annually, quarterly, or monthly.

Let's assume the interest is compounded annually. After one year, the investment would grow to $10,500 (10,000 + 500). In the second year, the interest would be calculated on the new principal of $10,500, resulting in $525 (10,500 * 0.05). This process continues for subsequent years.

The key difference is that compound interest allows for the growth of interest over time, resulting in higher returns compared to simple interest. As the interest is reinvested and compounded, it accumulates on the previously earned interest as well, leading to exponential growth. In contrast, simple interest remains constant and does not benefit from compounding, resulting in lower returns over time.

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