Is 285mg more or less than 34.4 mg? My problem is not knowing for sure because of the decimal

Answer:

The dimension of the TV = 11.2 inches × 8.4 inches

Step-by-step explanation:

Let x be the length of the TV

Let y be the width of the TV

x : y = 4:3

\(\frac{x}{y} = \frac{4}{3} \\cross-multiplying\\3x = 4y \\x = \frac{4}{3} y- - - - - (1)\)

From the figure attached:

using Pythagoras theorem

x² + y² = 42²

where:

\(x = \frac{4}{3} y\\(\frac{4}{3}y)^2 + y^2 = 42^2\\\frac{16}{9}y^2 + y^2 = 1764\\ \frac{16y^2}{9} + \frac{y^2}{1} = 1764\\\frac{16y^2 +9y^2}{9}= 1764\\ cross-multiplying\\16y^2 + 9y^2 = 1764\\25y^2 = 1764\\y^2 = \frac{1764}{24}\\y^2 = 70.56\\y = \sqrt{70.56} \\y = 8.4\ inches\\Finding\ x:\\x = \frac{4}{3} y\\x = \frac{4}{3} \times 8.4\\ x = 1.33 \times 8.4\\x = 11.2\ inches\\\therefore\ the\ dimensions\ are\ 11.2\ inches \times 8.4\ inches\)

The matrix is 3 × 3 square matrix . Its values are:

\(a_{11} = 50 \\ a_{12} = 44 \\a_{13} = -43 \\a_{21} = 31 \\a_{22} = 16 \\a_{23} = 7 \\a_{31} = 37 \\a_{32} = 119 \\a_{33} = 94\)

Given,

Matrix A and Matrix B

Now,

According to matrix multiplication rule first row of one matrix will be multiplied with first column of second matrix if the columns in first matrix is equal to the rows of second matrix.

So,

Apply multiplication rule,

\(a_{11} = 30 + 14 + 6 = 50 \\ a_{12} = 55 + 7 - 18 = 44 \\a_{13} = -20 -35 + 12 = -43 \\a_{21} = 24 - 2 + 9 = 31 \\a_{22} = 44 -1 -27 = 16 \\a_{23} = -16 + 5 + 18 = 7 \\a_{31} = 36 + 16 - 15 = 37 \\a_{32} = 66 + 8 + 45 = 119 \\a_{33} = -24 -40 -30 = -94\)

Thus the values of the matrix can be calculated.

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Answer:

The set of vectors A and C are linearly independent.

Step-by-step explanation:

A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:

\(p_{1}(t) = 1\), \(p_{2}(t)= t^{2}\) and \(p_{3}(t) = 3 + 3\cdot t\):

\(\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0\)

\(\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0\)

\((\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0\)

The following system of linear equations is obtained:

\(\alpha_{1} + 3\cdot \alpha_{3} = 0\)

\(\alpha_{2} = 0\)

\(\alpha_{3} = 0\)

Whose solution is \(\alpha_{1} = \alpha_{2} = \alpha_{3} = 0\), which means that the set of vectors is linearly independent.

\(p_{1}(t) = t\), \(p_{2}(t) = t^{2}\) and \(p_{3}(t) = 2\cdot t + 3\cdot t^{2}\)

\(\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0\)

\(\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0\)

\((\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0\)

The following system of linear equations is obtained:

\(\alpha_{1}+2\cdot \alpha_{3} = 0\)

\(\alpha_{2}+3\cdot \alpha_{3} = 0\)

Since the number of variables is greater than the number of equations, let suppose that \(\alpha_{3} = k\), where \(k\in\mathbb{R}\). Then, the following relationships are consequently found:

\(\alpha_{1} = -2\cdot \alpha_{3}\)

\(\alpha_{1} = -2\cdot k\)

\(\alpha_{2}= -2\cdot \alpha_{3}\)

\(\alpha_{2} = -3\cdot k\)

It is evident that \(\alpha_{1}\) and \(\alpha_{2}\) are multiples of \(\alpha_{3}\), which means that the set of vector are linearly dependent.

\(p_{1}(t) = 1\), \(p_{2}(t)=t^{2}\) and \(p_{3}(t) = 3+3\cdot t +t^{2}\)

\(\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0\)

\(\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2}+ \alpha_{3}\cdot (3+3\cdot t+t^{2}) = 0\)

\((\alpha_{1}+3\cdot \alpha_{3})\cdot 1+(\alpha_{2}+\alpha_{3})\cdot t^{2}+3\cdot \alpha_{3}\cdot t = 0\)

The following system of linear equations is obtained:

\(\alpha_{1}+3\cdot \alpha_{3} = 0\)

\(\alpha_{2} + \alpha_{3} = 0\)

\(3\cdot \alpha_{3} = 0\)

Whose solution is \(\alpha_{1} = \alpha_{2} = \alpha_{3} = 0\), which means that the set of vectors is linearly independent.

The set of vectors A and C are linearly independent.

Answer:

p = - 5

Step-by-step explanation:

–2.5p – 20 = 9p + 37.5

combine like terms:

- 2.5p - 9p = 37.5 + 20

simplify:

- 11.5p = 57.5

p = 57.5 / -11.5

p = - 5

Answer:

The answer is p = -5

Step-by-step explanation:

-2.5p - 20 = 9p + 37.5

(move constants to one side by adding 20 to both sides)

-2.5p = 9p + 57.5

(move all terms with the "p" variable to one side by subtracting 9 from both sides)

-11.5p = 57.5

(divide both sides by -11.5 to isolate the variable)

p = -5

Answer:

I don't know if you still need an answer but- here ya go :)

a. -22 + 5 = -17

b. -22 - (-5) = -22 + 5 = -17

c. (-22)(-5) = 110

d. (-22) / 5 = -4.4

Answer:

Line AB and the last AB

Step-by-step explanation:

\( \huge \pink{ \underline \mathfrak{ \green{Answer}}} \: \\ \\ \: \: \rightarrow \fbox{ a). \blue{ \: 54 \: }}\)

Step-by-step explanation:

\( \bf{Given} \: \colon 4w² + w-6, when \: \: w = -4 \\ \\ \tt \underline \red{Solution} \colon \\ \\ \rightarrow \: 4w {}^{2} + w \: - 6 \\ \\ \: put \: \: value \: \: of \: \: w \: \: in \: \: given \: \: equation \\ \\ \rightarrow \: 4( - 4) {}^{2} + \: (- 4 )\: - 6 \\ \\ \rightarrow \: 4(16) \: - 4 \: - 6 \\ \\ \rightarrow \: 64 \: - 10 \\ \\ \bf \rightarrow54\)

Answer:

1/6 as a decimal is 1.66 or 1.6 repeating.

The x-values at which the function f(x) is differentiable are all real numbers, excluding those values where the derivative is undefined. This can be expressed using interval notation as (-∞, -4) ∪ (-4, 0) ∪ (0, 4) ∪ (4, ∞).

The function mentioned is a continuous function on the interval 4 < x < 5, h(x), which is described in the table provided. This function has a vertical asymptote at 4 and 5, meaning that its values approach positive or negative infinity at these points.

The function's domain is 4 < x < 5, meaning that it is defined and can take a value for any x within this interval. The function's range is not specified, so it can take any value for an x within the given interval. Additionally, the function is differentiable for all values of x within the given interval, meaning that its rate of change can be calculated using derivatives.

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Answer:

15 weeks

Step-by-step explanation:

I just answered this one not too long ago

It will take 15 weeks for Emanuel to lose at most 251 pounds.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given that, Emanuel is trying to lose weight, he starts 2017 weighing 296 pounds.

If he plans to burn enough calories to lose 3 pounds per week,

We need to find that how many weeks will pass before Emanuel is at most 251 pounds,

So, let the number of weeks be x,

We will use here the concept of equations solving,

So, establishing the equations,

296 - 3x = 251

296 - 251 = 3x

45 = 3x

x = 15

Hence, it will take 15 weeks for Emanuel to lose at most 251 pounds.

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Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

The statements that are true are B and D.

Given are some statements we need to check which is true.

Let's analyze each statement:

A. 4 is a perfect cube.

False. 4 is not a perfect cube because there is no integer that can be cubed to give 4.

B. 16 is a perfect square.

True. 16 is a perfect square because it can be expressed as 4^2, where 4 is an integer.

C. 2,197 is both a perfect square and a perfect cube.

False. 2,197 is not a perfect square because there is no integer that can be squared to give 2,197.

However, it is a perfect cube because 13³ equals 2,197.

D. 8 is a perfect cube.

True. 8 is a perfect cube because it can be expressed as 2³, where 2 is an integer.

E. 18 is neither a perfect square nor a perfect cube.

True. 18 is neither a perfect square nor a perfect cube because there is no integer that can be squared or cubed to give 18.

Therefore, the statements that are true are B and D.

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Answer:

-4x-31

Step-by-step explanation:

1.6(5x-10)-(12x+15)

8x-16-12x-15

-4x-31

The simplified expression is -4x - 31.

We know,

In mathematics, an expression refers to a combination of numbers, variables, operations, and mathematical symbols that represents a mathematical statement or computation. It can involve arithmetic operations (addition, subtraction, multiplication, division).

We have Equation,

1.6(5x - 10) - (12x + 15)

Now simplifying the equation

1.6(5x - 10) - (12x + 15)

= 8x - 16 - 12x - 15

= -4x - 31

Thus, the simplified expression is -4x - 31.

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Answer:

a^(1+2+3) so a^6

Step-by-step explanation:

Answer:

  22.4 psi

Step-by-step explanation:

The inversely proportional relationship means the pressure will be multiplied by the inverse of the ratio of the volumes:

  new pressure = (28 psi)(120 in³)/(150 in³) = 22.4 psi

The pressure at 150 cubic inches is 22.4 psi.

We can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

To determine the interval within which 95 percent of the sample means will fall, we need to calculate the margin of error using the standard deviation and the desired level of confidence.

The formula to calculate the margin of error is given by:

Margin of Error = Z * (Standard Deviation / √n)

Where:

Z is the critical value corresponding to the desired level of confidence

Standard Deviation is the standard deviation of the population

n is the sample size

Since the sample size is 41 and we want to find the interval at a 95 percent confidence level, we need to find the critical value corresponding to a 95 percent confidence level.

The critical value can be found using a standard normal distribution table or a calculator. For a 95 percent confidence level, the critical value is approximately 1.96.

Now we can calculate the margin of error:

Margin of Error = 1.96 * (0.0050 / √41)

Calculating this, we find:

Margin of Error ≈ 0.001624

To find the interval within which 95 percent of the sample means will fall, we need to subtract and add the margin of error to the true mean:

Interval = True Mean ± Margin of Error

Interval = 0.9550 ± 0.001624

Calculating this, we find:

Interval ≈ (0.9534, 0.9566)

Therefore, we can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

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Answer:

(a) 9.18% of people have an intraocular pressure lower than 12 mm Hg.

(b) 80% of adults in the general population have an intraocular pressure that is greater than 13.47 mm Hg.

Step-by-step explanation:

We are given that the distribution of intraocular pressure in the general population is approximately normal with mean 16 mm Hg and standard deviation 3 mm Hg.

Let X = intraocular pressure in the general population

So, X ~ Normal(\(\mu=16,\sigma^{2} = 3^{2}\))

The z score probability distribution for normal distribution is given by;

                             Z  =  \(\frac{ X-\mu}{\sigma } }\)  ~ N(0,1)

where, \(\mu\) = population mean = 16 mm Hg

           \(\sigma\) = standard deviation = 3 mm Hg

(a) Percentage of people have an intraocular pressure lower than 12 mm Hg is given by = P(X < 12 mm Hg)

       P(X < 12) = P( \(\frac{ X-\mu}{\sigma } }\) < \(\frac{ 12-16}{3 } }\) ) = P(Z < -1.33) = 1 - P(Z \(\leq\) 1.33)

                                                   = 1 - 0.9082 = 0.0918 or 9.18%

The above probability is calculated by looking at the value of x = 1.33 in the z table which has an area of 0.9082.

(b) We have to find that 80% of adults in the general population have an intraocular pressure that is greater than how many mm Hg, that means;

        P(X > x) = 0.80      {where x is the required intraocular pressure}

        P( \(\frac{ X-\mu}{\sigma } }\) > \(\frac{ x-16}{3 } }\) ) = 0.80

        P(Z > \(\frac{ x-16}{3 } }\) ) = 0.80

Now, in the z table the critical value of z which represents the top 80% of the area is given as -0.842, that is;

                           \(\frac{ x-16}{3 } } = -0.842\)

                           \(x -16 = -0.842 \times 3\)

                           x = 16 - 2.53 = 13.47 mm Hg

Therefore, 80% of adults in the general population have an intraocular pressure that is greater than 13.47 mm Hg.

Answer:

translate?

Step-by-step explanation

translate it and i can help

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

The volume of aggregate that she needs to build the patio is 13.18 ft^3

We know that the backyard is 14ft long, 6 feet wide and 4 inches deep.

Rememeber that:

1ft = 12 in

Then:

4 in = (4/12) ft = (1/3) ft

Then the volume of the backyard is:

V = (14ft)*(6ft)*(1/3 ft) = 28ft^3

Now we know that we have a mix of 4 parts aggregate to 4.5 parts loose cement that need to fill these 28 cubic feet.

Note that:

4 + 4.5 = 8.5

How many times we have 8.5 in 28?

28/8.5 = 3.294

Now for each of these we have 4 parts of aggregate, then the volume of aggregate that we need is:

4*3.294 ft^3 = 13.18 ft^3

The volume of aggregate that she needs to build the patio is 13.18 ft^3

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ANSWER

EXPLANATION

We want to solve the trigonometric equation given:

First, subtract 9 from both sides of the equation:

Then, divide both sides by 8:

Now, apply the trigonometric inverse property i.e. find the sine inverse of both sides of the equation:

where n = 0, 1, 2, 3. . .

Finally, divide both sides by 8:

That is the answer.

Answer:

x = 13

Step-by-step explanation:

Add 3x and 4x - 1 together to get 7x-1.  Since the angle on the bottom right is 90 degrees, we can safely assume that the remaining angles add up to 90 degrees.  Add 1 on both sides to get 7x = 91.  Divide 7 on both sides to get 13 as your x value.

To plug in the x value, plug 13 in.  The one on the bottom left should equal to 39 degrees and the one on the top right should equal to 51 degrees.

Answer:

I believe the answer is J: 40 times

Step-by-step explanation:

Answer:

Hello! answer: 40 times

Step-by-step explanation:

9/27 × 120 = 40 times therefore 40 is the answer

Answer:

Checking your credit history and credit scores can help you better understand your current credit position. Regularly checking your credit reports can help you be more aware of what lenders may see. Checking your credit reports can also help you detect any inaccurate or incomplete information.

Step-by-step explanation:

hope this helps if not let me know have a blessed day

Answer:

Less

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

5.904 is greater because the 9 is closer to the decimal than the 9 of 5.094

Answer:

1/12

Step-by-step explanation: