Give reasons for the following statements.

i) V cannot be subtracted from any number in Roman Numerals
ii) Closest Estimation is nearest to the actual value
as it is estimated to the nearest place value

TRIGONOMETRY CAN BE USED TO FIND AN UNKNOWN SIDE LENGTH OF A RIGHT ANGLE TRIANGLE

Answer:

Step-by-step explanation:

Since the triangle is a right angled triangle we can use the Pythagoras theorem to find the missing side

Using the Pythagoras theorem

That's

\( {a}^{2} = {b}^{2} + {c}^{2} \)

From the question

x is the hypotenuse or the longest side of the triangle

Substituting the values into the above formula we have

\( {x}^{2} = {9}^{2} + {7}^{2} \)

\( {x}^{2} = 81 + 49\)

\( {x}^{2} = 130\)

Find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

To add scientific notation with different exponents, you need to adjust the exponents so that they are equal. Once the exponents are aligned, you can add or subtract the corresponding coefficients.

First, identify the numbers in scientific notation that you want to add. Let's say you have two numbers, A and B, expressed in scientific notation as A x 10^n and B x 10^m, where n and m are the exponents.

To add these numbers, you need to adjust one of them so that the exponents are the same.

Choose the number with the smaller exponent and multiply both its coefficient and exponent by the appropriate power of 10 to match the exponent of the other number.

For example, if n < m, you would multiply number A by \(10^{m-n}\), which means multiplying the coefficient of A by \(10^{m-n}\) and keeping the exponent of 10 as n.

Once the exponents are aligned, you can add or subtract the coefficients of the adjusted numbers.

This will give you the final result in scientific notation.

It's important to note that if the exponents are significantly different, adjusting the exponents may involve multiplying or dividing by large powers of 10, which can affect the precision of the final result.

Therefore, it's advisable to retain the appropriate number of significant figures in your calculations.

In summary, to add scientific notation with different exponents, you adjust one of the numbers by multiplying its coefficient and exponent by an appropriate power of 10 to match the exponent of the other number.

Then, you can add or subtract the coefficients and express the result in scientific notation.

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Answer: 2x + 4 = 10 is your answer :)

Step-by-step explanation:

Answer:

x = 3 is your answer :3

Step-by-step explanation:

Answer:

Solving for x : x = 3y/5 - 6/5.              Solving for y : y= 5x/3 +2

Step-by-step explanation:

Solving for x: Solve for x  by simplifying both sides of the equation, then isolating the variable.

Solving for y: Combine 5/3 and x.

You didn't say which one to solve for so I put out both for you.

Hoped this helped!

Brainly, Please?

Answer:

7..

Step-by-step explanation:

5+2=7

Answer:

Step-by-step explanation:

x = 12

Step-by-step explanation:

The slope-intercept form formula, , can be used to write an equation for the line.

Where,

m = slope =  

b = y-intercept, which is the point at which the line intercepts the y-axis. At this point, x = 0.

Let's find the slope (m) using the coordinates of the two points given, (0, 30), (3, 60).

Let,

y-intercept of the line, b = 30

Equation for the line would be:

Using the equation, find x when y = 150.

Simply substitute the value for y in the equation to find x.

Subtract 30 from both sides

Divide both sides by 10

x = 12

To construct a 98% confidence interval for B₁, we can use the t-distribution since the sample size is small (n = 12).

Given the sample mean (B₁ = 46), sample standard deviation (s = 5.7), and sum of squares (SSzz = 57), we can calculate the confidence interval.

The formula for a confidence interval is:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

For a 98% confidence level and n = 12, the critical value is approximately 2.681 (obtained from a t-distribution table).

The standard error is calculated as the sample standard deviation divided by the square root of the sample size (s / √n).

Plugging in the values:

Standard Error = 5.7 / √12 ≈ 1.647

Confidence Interval = 46 ± (2.681 * 1.647)

Therefore, the 98% confidence interval for B₁ is approximately (42.21, 49.79).

In conclusion, we can be 98% confident that the true value of B₁ falls within the range of 42.21 to 49.79 based on the given sample data.

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Answer:

1.478 kg

Step-by-step explanation:

Considering density=mass/volume, when we rearrange, we get mass=density*volume. Therefore, as we are given the density, we just need to find the volume to know the mass. The volume of a cylinder is πhr^2, and our radius is 28/2=14, so the volume of the cylinder is π*3*14^2=588π. Then, 588π*0.8=470.4π which is about 1477.8052 g. Then, to convert to kg, we can divide this by 1000 and get about 1.478 kg.

a) Anaiah currently spending $150 on these goods

b) His behavior is irrational because,

option (1) He is not spending his entire income, option (2) He is spending too much on kiwis and option (3) He is not balancing his spending on each good to achieve maximum total utility.

Based on the given information, Anaiah is currently spending $150 on these goods, which is calculated by adding the total cost of eggplants and kiwis as follows:

Cost of 20 eggplants = 20 x $3 = $60

Cost of 30 kiwis = 30 x $3 = $90

Total cost = $60 + $90 = $150

Anaiah is behaving irrationally because he is not spending his entire income of $180, which means he is not maximizing his utility. Additionally, he is spending too much on kiwis, as indicated by the higher marginal utility per dollar spent on the 30th kiwi compared to the 20th eggplant.

This suggests that he would derive more satisfaction from spending more on eggplants and less on kiwis. Lastly, his marginal utility per dollar spent is not the same for both goods, which implies that he is not balancing his spending on each good to achieve the maximum total utility. Therefore, Anaiah could improve his spending behavior by adjusting his purchases to reflect a better balance of marginal utility per dollar spent on each good.

Therefore, the correct options are  option (1) He is not spending his entire income, option (2) He is spending too much on kiwis and option (3) He is not balancing his spending on each good to achieve maximum total utility.

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First, we should remember the criteria for congruence of triangles: SSS (side-side-side), ASA (angle-side-angle), AAS (angle-angle-side) and SAS (side-angle-side).

First Angle

In the figure above, we know that the angles

It means, that are congruent.

Second Angle

Also, the angles shown with a small square are right, and are congruent:

A side

At last, we know that the side AC belongs to both triangles, and it is congruent with itself (it means, its size is the same as the same segment).

We have then two angles and a side. As the side is between the to angles, we have the criteria SAS, and the triangles ABC and ADC are congruent.

Answer:

Lesser x = -14

Greater x = 0

Step-by-step explanation:

Given equation:

\(\sf (x+7)^2-49=0\)

Add 49 to both sides:

\(\implies \sf (x+7)^2-49+49=0+49\)

\(\implies \sf (x+7)^2=49\)

Square root both sides:

\(\implies \sf \sqrt{(x+7)^2}=\sqrt{49}\)

\(\implies \sf x+7=\pm7\)

Solve for x:

\(\implies \sf x+7=7 \implies x=0\)

\(\implies \sf x+7=-7 \implies x=-14\)

As -14 < 0

According to the given information, Cpl = 0.9 and Cpu = 1.9. The correct option is 6- B, D, AND F.

Based on this information, the correct option is 6- B, D, AND F.

Here is an explanation: Process capability indices (Cp, Cpk, Cpl, Cpu) are statistical tools for analyzing process performance and identifying process control problems.

The lower the Cp, the more variation there is in the process. The higher the Cp, the more consistent the process is. If Cpl is lower than 1.0, the process will not meet the lower specification limit, and if Cpu is lower than 1.0, the process will not meet the upper specification limit.

A process is considered out of control if it is not in statistical control, which means that the variation is beyond the upper and lower control limits. If Cpl or Cpu is less than 1, the process is not capable of meeting the corresponding specification limit, indicating that the process is not centered and out of control.

Based on the above information, the process is not centered, out of control, and incapable of meeting the specifications.

Therefore, the correct option is 6- B, D, AND F.

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Step-by-step explanation:

|-x+2|≤-7

-x+2≤-7 or -(-x+2)≤-7

-x≤-9 x-2≥-7

x≥9 x≥-7+2

x≥-5

....

Answer:

C+7d

5+7(8)

5+56=61

Step-by-step explanation:

Answer: 61

Step-by-step explanation:

This is an algebraic equation. You need to replace the variables with their values.

Step 1: Given c=5 and d=8.

5 + 7*8

Step 2: Solve the equation. Following the rules of PEMDAS, first multiply the 7 times the 8. Then, add 5 to that.

7 * 8 = 56

5 + 56 = 61

Here, we use the property of multiplication of exponential expression which states when we multiply two exponential expressions with the same base, we keep the base and add the exponents.

Therefore,

\(x^(3+5) = x^8\)

Now,

\(x^(3+5) = x^8\)

is of the form:

\(x^b = x^p\)

When we have two equal expressions on either side of the equation, the power of the base remains the same. Therefore,

p = 8

There we have it. The value of p is 8. The full solution is shown below:

\(x^3 × x^5 \\= x^px^8\\ = x^p\)

We can see that the base of the exponential expression on either side is equal.

Therefore, the power of the base must be equal as well. In other words

,p = 8.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3860\\ r=rate\to 3.08\%\to \frac{3.08}{100}\dotfill &0.0308\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-monthly, thus 24} \end{array}\dotfill &24\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 3860\left(1+\frac{0.0308}{24}\right)^{24\cdot 2} \implies A = 4105.09\)

The fact that black youths are tried as adults more frequently than other races is a statistic. However, without further information such as sample size and significance level, it is difficult to determine the contribution to the test statistic and the p-value.

A larger sample size could potentially increase the test statistic and decrease the p-value, indicating a stronger relationship between race and being tried as an adult. On the other hand, a smaller sample size could result in a weaker relationship and a higher p-value. It is important to consider all relevant factors when interpreting statistics and making conclusions.
This result contributes to the test statistic, which is a numerical value that helps determine if there is a significant difference between the compared groups.

In this case, the test statistic would be larger, indicating a greater difference between the rates of black youths tried as adults and those of other races. A larger test statistic typically leads to a smaller p-value, which is a measure of the probability of observing such a difference by chance alone. A smaller p-value (usually less than 0.05) suggests that the observed difference is not due to chance and is statistically significant, indicating a possible disparity in the treatment of black youths within the justice system.

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The measure of the missing angles are d= 77° , e= 31° ,and f = 72°.

As given in the question,

Angle e is vertically opposite to the given angle 31°

⇒Measure of angle e = 31°

Angle d is vertically opposite to the given angle 77°

⇒Measure of angle d = 77°

Angle e , Angle f and angle d are linear pairs

⇒∠e +∠f +∠d =180°

⇒31° +∠f + 77°=180°

⇒ ∠f =180° -108°

⇒ ∠f =72°

Therefore, the measure of the missing angles are d = 77° , e = 31° and

f = 72°.

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Answer:

Option B 240m^3

Step-by-step explanation:

just use the formula BxH

Answer:

It's D. Because 12 x 6 = 96. 96 x 20 = 1920.

Lynn used \(47.826\) gallons fuel in each month.

Average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Gallon is the unit for measuring liquids (fuel).

Mile is a unit of large distance.

Given,

Lynn drive her car for work an average of \(1100\) miles

Car get \(23\) miles per gallon.

It's mean car covers \(23\) miles distance in \(1\) gallon of fuel.

She used fuel in each month

\(=\frac{Total miles}{miles per gallon} \\=\frac{1100}{23}\\ =47.8260 gallon\)

Lynn used \(47.826\) gallons fuel in each month.

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When the sum of their squares is as largest as possible the numbers are 0 and 20, when the sum of their squares is as small as possible, the numbers are 10 and 10

Sum of the two numbers = 20

First we have to find the sum of their squares is as large as possible

Consider the first number as x and second number as y

To get the largest values the value of x or the value of y should be zero

Then the two numbers are 0 and 20

To get the small as possible

x^2 + (20-x)^2 = x^2 + x^2 - 20x +400

= 2x^2 -20x + 400

= 2(x^2 - 10x + 100)

The one number will be 10 and the other number will be 10

Therefore, to get the largest value the numbers will be 0 and 20 and to get the smallest value the numbers will be 10 and 10

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Answer:

A. $22.10

Step-by-step explanation:

52 x 0.4 = 20.8

20.8 x 1.0625 = 22.1

Answer:

see explanation

Step-by-step explanation:

given a tangent and a secant drawn from an external point to the circle, then the square of the measure of the tangent is equal to the product of the secant's external part and the entire secant , that is

ST × RT = TU²

given RT = 13 and ST = 4 , then

TU² = 4 × 13 = 52 ( take square root of both sides )

TU = \(\sqrt{52}\) = 2\(\sqrt{13}\) ≈ 7.21 ( to 2 decimal places )

Step-by-step explanation:

intersecting secants theorem :

let's assume the second line would not be a tangent but a true secant with a second circle intersection point V, then

ST × RT = TU × TV

in other words : the product of the lengths of the short (external) segment and the full secant is the same for every secant line originating from the same point.

now we have the extreme case that U = V due to the tangent situation.

but the same principle applies. just TU = TV, and therefore

ST × RT = TU²

RT = TU²/ST

for the same reason and with the same approach, yes, we can calculate TU out of a given set of RT and ST :

TU² = ST × RT

TU = sqrt(ST × RT) = sqrt(4 × 13) = sqrt(52) = 2×sqrt(13) =

= 7.211102551...

Answer:

Step-by-step explanation:

4c + 18 = 74​         {subtract 18 from both sides}

4c = 56               {divide both sides by number by x (4)}

 c = 14

Answer:

44%

Step-by-step explanation:

5 ½=5.5

12½=12.5

5.5/12.5=0.44

0.44×100=44%

Answer:

Answer:

44%

Step-by-step explanation:

5 ½=5.5

12½=12.5

5.5/12.5=0.44

0.44×100=44%

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(b)

Given

x² - 8x + 20 = (x - 4)² + 4

(x - 4)² will be positive for all real values of x , except x = 4, where it will be zero.

Then (x - 4)² > 0, so

(x - 4)² + 4 > 0 , that is always positive