Graph the system of linear inequalities.
y < −x + 3
y ≥ 2x − 1
Give two ordered pairs that are solutions and two that are not solutions.

Usando el interés compuesto, se encuentra que el interes obtenido es de 1609.

\(I(t) = P\left[\left(1 + \frac{r}{n}\right)^{nt} - 1\right]\)

En que:

En este problema, los parámetros son:

\(P = 9500, t = \frac{900}{365} = 2.4658, r = 0.065, n = 1\)

Por eso:

\(I(t) = P\left[\left(1 + \frac{r}{n}\right)^{nt} - 1\right]\)

\(I(2.4658) = 9500\left[\left(1 + \frac{0.065}{1}\right)^{2.4658} - 1\right]\)

\(I(2.4658) = 1609\)

El interes obtenido es de 1609.

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The interest earned on the amount is 1,595.05.

The formula for calculating the compound interest is expressed as:

A = P(1+r)^t

A = 9500(1+0.065)^2.4658

A = 9500(1.065)^2.4658

A = 11,095.05

Interest = Amount - Principal

Interest = 11,095.05 - 9500

Interest = 1,595.05

Hence the interest earned is 1,595.05.

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Answer:

see explanation

Step-by-step explanation:

The angle at the circumference b , is half the angle subtended at the centre by the arc XZ, that is

b = 0.5 × 72 = 36

OZ and OX are congruent ( both radii of the circle )

Thus Δ OXZ is isosceles with base angles congruent, thus

a = \(\frac{180-72}{2}\) = \(\frac{108}{2}\) = 54

∠ XZY = 90° ( angle in a semicircle is right )

The upper and lower limits for the sample mean control chart are:

UCL = 6.66

LCL = 3.36

To calculate the upper and lower limits for the sample mean control chart, we need to use the given data and formulas.

Sample size (n) = 15

Sample mean values: 13.30, 3.16, 3.21, 3.30, 3.27, 3.20

Range values: 0.49, 1.41, 2, 3, 0.47, 14, 5, 6, 0.49, 0.46, 0.54

First, we calculate the average range (R-bar) using the range values:

R-bar = (Sum of ranges) / (Number of samples)

R-bar = (0.49 + 1.41 + 2 + 3 + 0.47 + 14 + 5 + 6 + 0.49 + 0.46 + 0.54) / 11

R-bar ≈ 2.86 (rounded to 2 decimal places)

Next, we use the average range (R-bar) to calculate the control limits for the sample mean chart:

Upper Control Limit (UCL) = X-double bar + A2 * R-bar

Lower Control Limit (LCL) = X-double bar - A2 * R-bar

Where X-double bar is the average of sample means and A2 is a constant based on the sample size (n). For n = 15, A2 is 0.577.

Calculating the average of sample means (X-double bar):

X-double bar = (Sum of sample means) / (Number of samples)

X-double bar = (13.30 + 3.16 + 3.21 + 3.30 + 3.27 + 3.20) / 6

X-double bar ≈ 5.01 (rounded to 2 decimal places)

Calculating the control limits:

UCL = 5.01 + 0.577 * 2.86 ≈ 5.01 + 1.65 ≈ 6.66 (rounded to 2 decimal places)

LCL = 5.01 - 0.577 * 2.86 ≈ 5.01 - 1.65 ≈ 3.36 (rounded to 2 decimal places)

Therefore, the upper and lower limits for the sample mean control chart are:

UCL = 6.66

LCL = 3.36

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Answer:

7 + 11i

Step-by-step explanation:

Simplify: (2 +8i)-(-5 - 3i) = 2 + 8i + 5 + 3i  

Add real numbers to real numbers and imaginary to imaginary: 2 + 8i + 5 + 3i = 7 + 11i

A complex number can be shown as a pair of integers (a, b). The difference of the complex number (2 +8i)-(-5 - 3i) is 7+11i.

A complex number can be shown as a pair of integers (a, b) forming a vector on an Argand diagram, which represents the complex plane.

The difference of the complex number can be done as following,

(2+8i)-(-5-3i)

= 2 + 8i + 5 + 3i

= 5+2 + 8i+3i

= 7 + 11i

Hence, the difference of the complex number (2 +8i)-(-5 - 3i) is 7+11i.

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The correct options according given identity of tangent are;

1) Write tan(x + y) as sin(x + y) over cos(x + y)

2) Use the sum identity for sine to rewrite the numerator

3) Use the sum identity for cosine to rewrite the denominator

4) Divide both the numerator and denominator by cos(x)·cos(y)

5) Simplify fractions by dividing out common factors or using the tangent quotient identity

According to the statement

we have given that the a identity and we have to use in the given conditions.

So, For this purpose, we know that the

Given that the required identity of Tangent is Tangent (x + y) = (tangent (x) + tangent (y))/(1 - tangent(x) × tangent (y)),

we have:

tan(x + y) = sin(x + y)/(cos(x + y))

sin(x + y)/(cos(x + y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y))

(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y))

(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y)) = (tan(x) + tan(y))(1 - tan(x)·tan(y)

∴ tan(x + y) = (tan(x) + tan(y))(1 - tan(x)·tan(y)

After solving this identity according to the statement it is clear that all the options are correct.

So, The correct options according given identity of tangent are;

1) Write tan(x + y) as sin(x + y) over cos(x + y)

2) Use the sum identity for sine to rewrite the numerator

3) Use the sum identity for cosine to rewrite the denominator

4) Divide both the numerator and denominator by cos(x)·cos(y)

5) Simplify fractions by dividing out common factors or using the tangent quotient identity

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Examine the following steps. Which do you think you might use to prove the identity Tangent (x) = StartFraction tangent (x) + tangent (y) Over 1 minus tangent (x) tangent (y) EndFraction question mark

Check all that apply.

-Write tan(x + y) as sin (x + y) over cos(x +y).

-Use the sum identity for sine to rewrite the numerator.

-Use the sum identity for cosine to rewrite the denominator.

-Divide both numerator and denominator by cos(x)cos(y).

-Simplify fractions by dividing out common factors or using the tangent quotient identity.

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Surveying 200 likely voters from each group of libertarians, independents, Democrats, and Republicans is an example of stratified sampling.

The survey conducted, which involves sampling 200 likely voters from each group of libertarians, independents, Democrats, and Republicans, exemplifies stratified sampling. Stratified sampling is a sampling technique where the population is divided into distinct subgroups or strata based on certain characteristics, and then samples are selected from each subgroup in proportion to their representation in the population.

In this case, the four political groups serve as the strata, and by selecting an equal number of likely voters from each group, the survey aims to ensure that each group is adequately represented in the sample. Stratified sampling allows for more accurate analysis and conclusions by considering the characteristics of each subgroup separately, enhancing the overall validity and reliability of the survey results.

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The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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Dr. Raynor is 95% confident that the true population proportion of students with concerning behaviors that impact their performance in the classroom is between 10.2% and 14.6%.

The 12.4% calculation made by Dr. Raynor is referred to as a confidence interval. A confidence interval is a range of numbers that is likely to contain a population parameter. In this case, the population parameter is the percentage of students in the school with concerning behaviors that impact their performance in the classroom. To calculate the confidence interval, Dr. Raynor first determined the sample proportion, which is 12.4%. Then, she used the following formula to calculate the confidence interval:

Confidence Interval = (Sample Proportion ± Margin of Error)

In this case, the margin of error was 2.2%, which is calculated by multiplying the sample proportion by 1.96 (1.96 being the critical value for a 95% confidence interval). Thus, the confidence interval of 10.2% to 14.6% was determined. This confidence interval means that Dr. Raynor is 95% confident that the true population proportion of students with concerning behaviors that impact their performance in the classroom is between 10.2% and 14.6%.

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Answer:

11 cows and 22 Chickens

Step-by-step explanation:

Cows have four legs so they take majority of the feet.

44 ÷ 4 = 11

Chickens only have two legs.

44 ÷ 2 = 22

I think this is correct but if not my apologies- fairly new at this.

Answer:

x-cows

y-chickens

x+y=16/*(-2)    -2x-2y=-32    2x=12  x=6

4x+2y=44       4x+2y=44      y=16-6=10

x=6 number of cows

y=10number of chicken

Step-by-step explanation:

The measures of angles of the kite are ∠JHL = 91°

Given data ,

Let the kite be represented as KLHJ

where the measure of angle ∠HLK = 128°

And , the measure of ∠JKL = 50°

Now , kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles

So , the angles are

128° + 50° + 2x = 360°

On simplifying , we get

2x = 360° - 178°

2x = 182°

Divide by 2 on both sides , we get

x = 91°

Hence , the angle of kite is 91°

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Answer:

2 miles

Step-by-step explanation:

Answer:

610m²

Step-by-step explanation:

183/5 × 50/3

= 61×10

= 610m²

Multiplying every score in a sample by 3 will change the value of the standard deviation, making the statement "multiplying every score in a sample by 3 will not change the value of the standard deviation" false.

The standard deviation is a measure of the amount of variation or dispersion in a set of data points. It is calculated as the square root of the variance, which is the average of the squared differences between each data point and the mean.

When every score in a sample is multiplied by 3, it effectively changes the scale of the data. The original values are now three times larger, resulting in a larger spread of values around the mean. As a result, the variance and standard deviation will also be three times larger, since they are based on the squared differences between the data points and the mean.

Therefore, multiplying every score in a sample by 3 will change the value of the standard deviation, making the statement "multiplying every score in a sample by 3 will not change the value of the standard deviation" false.

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Answer:

m =40

Step-by-step explanation:

m/4 -3 = 7

Add 3 to each side

m/4 -3+3 = 7+3

m/4 = 10

Multiply each side by 4

m/4 *4 = 10*4

m = 40

The limit of lim (x − 9)/ (x² − 81)  using the l'Hospital's Rule is 1/18.

                  x→9

We can directly substitute the value 9 in the given limit expression.

We get,

lim (x − 9)/ (x² − 81) = (9 - 9)/(9^2 - 81)

= 0/0

The given limit is in indeterminate form. We can apply L'Hospital's rule here.

Differentiating both the numerator and the denominator with respect to x, we get,

lim (x − 9)/ (x² − 81) = lim (1)/(2x)

Now we can directly substitute the value of x in the above expression.

lim (x − 9)/ (x² − 81) = lim (1)/(2x) = 1/18

Therefore, the limit of the given expression is 1/18.

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Answer:

Where is that question you're talking about please

Answer:

\(\frac{7^2}{7^6}\)

If you have a negative exponent you must place it in the opposite part of the fraction.

Step-by-step explanation:

1/(7^6)*1/1/(7^2)

1/(7^6)*(7^2)/1

(7^2)/(7^6)

7^(2-6)

7^(-4)

1/7^4

Answer: same distance but different side

Step-by-step explanation:

Answer:C

Step-by-step explanation:

Answer:

It is C. Yes, Paul used stratified random sampling.

Step-by-step explanation:

Answer:

Jeremy ran about 1.2 miles and jimmy ran 2 miles so jimmy ran more miles

Explanation:

If Jeremy ran 10 laps on a 1/8 mile long track, he ran about 1.25 miles in total

(10*1/8)

If Jimmy ran 8 laps on a 1/4 mile long track, he ran 2 miles in total.

(8*1/4)

Answer:

The hexagon is one whole

Step-by-step explanation:

This is because one whole shape = one whole so it is One whole of the  hexagon

Answer:

A hexagon is one whole because it has 2 halves

Step-by-step explanation:

Answer:

i hope that was helpful

ANSWER

EXPLANATION

A coterminal angle to an angle is one that terminates in the same position or on the same side as the angle considered.

Since we are looking for a coterminal angle between 0 and 360, we have to keep subtracting a full revolution (360 degrees) from the given angle until we get an angle that satisfies the condition.

Therefore, we have:

Since 410 is not less than 360, subtract 360 degrees again:

That is the measure of the angle, a, that is coterminal with the given angle.

Answer:

Step-by-step explanation:

37

Answer: 37

Step-by-step explanation:

To find the mode, or modal value, it is best to put the numbers in order. Then count how many of each number. A number that appears most often is the mode. All you have to do is look for the number that occurs in any of those the lists the most and that number is the mode.

Answer:

67%

Step-by-step explanation:

If you take the 365 days in a year and divide that by the 246 sunny days, you should get the number 0.67397260274, rounded to 67%.e

Answer:

an equation is a mathematical expression that contains an equals sign. It tells us that two expressions represent the same number. For example, y = 12x is an equation. An inequality is a mathematical expression that contains inequality signs.

Step-by-step explanation:

The difference in volume between the two pyramids is 12,371,740 cubic feet.

To find the volume of a square pyramid, you use the formula :

V = (1/3)Bh, where B is the area of the base and h is the height.

Using the dimensions given in the table, we can calculate the volumes of the two pyramids:

- Volume of Bent Pyramid = (1/3)(619 feet * 619 feet)(332 feet) = 26,384,053.33 cubic feet
- Volume of Red Pyramid = (1/3)(722 feet * 722 feet)(341 feet) = 38,755,793.33 cubic feet

To find the difference in volume between the two pyramids, we subtract the smaller volume from the larger volume:

38,755,793.33 - 26,384,053.33 = 12,371,740 cubic feet.

Rounding to the nearest cubic foot, the difference in volume between the two pyramids is 12,371,740 cubic feet.

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We are asked to find out whether the given lengths correspond to a right-angled triangle.

Recall that a right-angled triangle must satisfy the Pythagorean theorem.

Let us substitute the given values into the above formula

As you can see, the Pythagorean theorem is satisfied.

Therefore, the given lengths form a right triangle.