Drag the tiles to the boxes to form correct pairs
Match the identities to their values, taking these conditions into consideration: sin X = pi2/2 cos y = -1/2 angle x is in the first quadrant, and angle
y is in the second quadrant.
What is the value of sin(x + y)?
- (2 + √3)
√3-2
-(√6 + √2)/4
What is the value of tan(x - y)?
What is the value of cos(x + y)?
(√6-√2)/4
What is the value of tan(x + y)?

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

Answer:

second quadrant

Step-by-step explanation:

quadrant II

Answer:

9.2

Step-by-step explanation:

8×1.15 = 9.2

I think..

Question:

Ahmed multiplies 8 by 1.15. Which number is he trying to find?

______________________________________________

Solution:

On multiplying 8 by 1.15, we get,

= 8 * 1.15

= 1¹ . 1⁴ 5

* 8

9 . 2 0

To the power 1 and 4 show that 1 and 4 carried over.

Hence the number he is trying to find is 9.20 or 9.2.

Answer:

=

Step-by-step explanation:

0.01 is = to 0.01

The measure of the hypotenuse of the right-angle triangle is 53.21 feet.

Given that:

Perpendicular, P = 50 feet

Angle, Ф = 70°

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The measure of the hypotenuse of the right-angle triangle is calculated as,

sinФ = P/H

sin 70° = 50 / x

x = 53.21 feet

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The correct diagram and the equation to find the interior angles of the hexagon is option (C)

The given figure is the regular hexagon

Consider the number of side of the polygon is n

The number of sides of the hexagon = 6

We know interior angle of a regular hexagon = 120 degrees

The interior angle of the hexagon d = 180(n-2) / n

Substitute the value of n = 6 in the equation

The interior angle of the hexagon = 180(6-2) / 6

= 180×4 /6

= 720 / 6

Divide the terms

= 120 degrees

Hence, the correct diagram and the equation to find the interior angles of the hexagon is option (C)

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all work should be in the picture, lmk if theres anything confusing

Answer:

1/2

Step-by-step explanation:

-6-4 / 3-(-2) = -2

-2(m2) = -1

m2= 1/2

Answer:

We conclude that not more than 500 gallons of wastewater per hour, on average, is discharged into a neighboring lake.

Step-by-step explanation:

We are given that an industrial plant can discharge not more than 500 gallons of wastewater per hour, on average, into a neighboring lake.

Four one-hour periods are selected randomly over a period of one week. The following are observed:

1384, 683, 1534, 405

Let \(\mu\) = population average gallons of wastewater discharged per hour

So, Null Hypothesis, \(H_0\) : \(\mu \leq\) 500 gallons      {means that not more than 500 gallons of wastewater per hour, on the average, is discharged into a neighboring lake}

Alternate Hypothesis, \(H_A\) : \(\mu\) > 500 gallons     {means that more than 500 gallons of wastewater per hour, on the average, is discharged into a neighboring lake}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                                T.S.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean = \(\frac{\sum X}{n}\) = 1001.5 gallons

             s = sample standard deviation = \(\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }\) = 543.79

             n = sample of periods = 4

So, the test statistics =  \(\frac{1001.5-500}{\frac{543.79}{\sqrt{4} } }\)  ~ \(t_3\)

                                    =  1.844

The value of t-test statistics is 1.844.

Since in the question we are not given with the level of significance so we assume it to be 5%. Now, at 0.05 level of significance, the t table gives a critical value of 2.353 at 3 degrees of freedom for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.844 < 2.353, so we have insufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that not more than 500 gallons of wastewater per hour, on average, is discharged into a neighboring lake.

Answer:

150 minutes

Step-by-step explanation:

Total plants are 16 and only 5 can be placed in one go. so total number of rounds for the plants will be: 16/5 = 3.2 rounds

As there are 3.2 rounds to go in 8 hours, so the time for 1 round will be: 8/3.2= 2 hours and 30 minutes

Answer:

150 minutes

Step-by-step explanation:

16/5 = 3.2  turns

8 hours /3.2 turns  = 2.5 hours (150 minutes)

Answer: 41

is what I got as an answer

Answer:

35.71%

Step-by-step explanation:

So, let's determine the number of jobs the industry will have in 2030.

So, in 2020, the industry has 123,200 jobs.

Each year, the industry loses 4,400 jobs.

Thus, by 10 years in (2030), the industry would have lost (4,400)(10) or 44,000 jobs.

This means that in 2030, there will only be 123,200-79200 jobs left.

Now, percentage change is given by:

\(PC=\frac{New-Old}{Old}\cdot100\%\)

The new value is 79200 and the old value is 123,200. Substitute them:

\(PC=\frac{(79200)-(123200)}{123200}\cdot100\%\\\)

Use a calculator. Simplify:

\(PC=\frac{-44000}{123200}\cdot100\%\\ PC\approx-0.3571\cdot100\%\\PC\approx-35.71\%\)

If the result is negative, then it's a decrease. Therefore, the percentage change from 2020 to 2030 is approximately 35.71%

Answer:

The answer is 35.71%

Step by step explanation

In 2020 the industry has 123,200 jobs.

Each year, the industry loses 4,400 jobs.

Thus, by 10 years in (2030), the industry would have lost (4,400)(10) or 44,000 jobs.

This means that in 2030, there will only be 123,200-79200 jobs left.

Now, percentage change is given by:

New−Old

⋅100%

The new value is 79200 and the old value is 123,200. Substitute

123200

(79200)−(123200)

⋅100%

Simplify:

PC≈−0.3571⋅100%

PC≈−35.71%

the percentage change from 2020 to 2030 is 35.71%

Answer:

76%

Step-by-step explanation:

57/75

(57 X 100)/ 75

5700/75

1900/25

76/1

76

Answer:

sorry dont know

Step-by-step explanation:

Answer:

47 degree

Step-by-step explanation:

23x - 5 + 37x +5 = 360

x = 6

The measure of the arc = 5x + 17 = 5 *6 +17 = 47 degree

The range is greater for the girls and the mean is greater for the girls. So, correct option is B.

A) The statement "The range is greater for the girls" is true. The range is the difference between the highest and the lowest values in a data set.

Looking at the line plots, the highest value for the boys is 10, and the lowest is 3, giving a range of 7 hours. The highest value for the girls is 9, and the lowest is 5, giving a range of 4 hours. Therefore, the range is greater for the boys.

B) The mean is the sum of all values divided by the total number of values. To calculate the mean for the boys, we add up all the hours and divide by 10, which gives us:

(3 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 10) / 10 = 7.4 hours

To calculate the mean for the girls, we add up all the hours and divide by 10, which gives us:

(5 + 6 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 9) / 10 = 7.1 hours

Therefore, the mean for the boys is 7.4 hours and the mean for the girls is 7.1 hours, so the statement "The mean is greater for the girls".

So, correct option is B.

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For binomial probability mass function formula and compound interest formula, These both involve the use of exponents, they are not otherwise related to each other in any significant way.

What is Compound interest?

Compound interest is the interest that is earned not only on the initial principal amount of an investment, but also on any interest that has accumulated over time. In other words, it is interest that is "compounded" or added to the principal amount at specific intervals, such as daily, monthly, quarterly, or annually.

Now,

The binomial probability mass function formula and the compound interest formula are not directly related to each other, as they are used to model different types of phenomena.

The binomial probability mass function is used to calculate the probability of obtaining a certain number of successes in a fixed number of independent trials, where each trial has two possible outcomes (success or failure) and the probability is same. The binomial probability mass function is

P(x) = pˣ (1-p)ⁿ⁻ˣ

where X is the number of successes, k is the specific number of successes we are interested in, n is the total number of trials, p is the probability of success on each trial, and represents the binomial coefficient.

The compound interest formula, on the other hand, is used to calculate the value of an investment over time, assuming a fixed interest rate and compounding periods. The future value is

FV = PV x (1 + r/n)ⁿˣ

where FV is the future value of the investment, PV is the present value of the investment, r is the interest rate (expressed as a decimal), n = number of times interest is compounded per year, and x = number of years.

While both formulas involve the use of exponents, they are not otherwise related to each other in any significant way.

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The binomial probability mass function formula and the compound interest formula are not directly related to each other.

The binomial probability mass function formula is used to calculate the probability of observing a certain number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant across all trials. The formula is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where X is the random variable representing the number of successes, k is the number of successes we want to observe, n is the total number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

On the other hand, the compound interest formula is used to calculate the value of an investment that earns a fixed interest rate over a certain period of time, assuming that the interest is compounded at regular intervals. The formula is:

A = P * (1 + r/n)^(nt)

where A is the final amount of the investment, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, t is the number of years, and (1 + r/n)^(nt) represents the growth factor of the investment.

While both formulas involve exponents and use the terms (1 - p) and (1 + r/n), they are fundamentally different in their purpose and application.

Answers:

B ' (6, 4)

C ' (2, 3)

D ' (3, -1)

E ' (7, 0)

=================================================

Explanation:

The y-axis reflection rule is:

\((\text{x},\text{y})\to (-\text{x},\text{y})\)

The x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same.

So for example, the point B(-6,4) moves to B ' (6, 4).

You can use a graphing tool like GeoGebra to confirm the answers are correct.

As per the given scatter plot, if the outlier were removed, r would get closer to 1.

The term scatter plot in math is used to plot data points on a horizontal and a vertical axis in the attempt to show how much one variable is affected by another

Here we have given that a local ice cream shop kept track of the number of cans of cold soda it sold each day and the temperature that day, for two months during the summer by using the scatter plot.

Here we have also know that X-axis is temperature measured in degrees Fahrenheit with a range from about 55 to 100 degrees and the value of Y-axis is the number of cans of soda sold with a range from about 165 to 195 cans.

While we take into consideration that a reasonable value of the correlation coefficient r for these data is 1.2.

Where as if the temperature were measured in degrees Celsius (C = 5/9 * (F - 32)), then the value of r would change accordingly.

Thus makes that the correlation coefficient would increase and be closer to 1.

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Answer:

\((x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}\)

\((x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

The points that are a distance of 5 units from P(-8, 4) will be all the points on the circumference of a circle with center (-8, 4) and radius 5.

Substitute the center and radius into the formula to create an equation of the circle:

\(\implies (x+8)^2+(y-4)^2=25\)

The y-value of any point on the x-axis is zero.

Therefore, to find the points on the x-axis that are 5 units from point P, substitute y = 0 into the equation of the circle and solve for x:

\(\implies (x+8)^2+(0-4)^2=25\)

\(\implies (x+8)^2+(-4)^2=25\)

\(\implies (x+8)^2+16=25\)

\(\implies (x+8)^2+16-16=25-16\)

\(\implies (x+8)^2=9\)

\(\implies \sqrt{(x+8)^2}=\sqrt{9}\)

\(\implies x+8=\pm3\)

\(\implies x+8-8=\pm3-8\)

\(\implies x=-8\pm3\)

\(\implies x=-11, x=-5\)

Therefore:

\((x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}\)

\((x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}\)

Answer: 76kg

Step-by-step explanation:

If the mass of sugar in one jar is 19kg, then the mass of 4 such jars of sugar can be found by multiplying the mass of one jar by 4:

Therefore, the total mass of 4 jars of sugar is 76kg.

__________________________________________________________

The mass of sugar is 19 kg. What is the total mass of 4 such jar of a sugar?

The total mass of four jars of sugar is 76 kg.

The total mass of four jars of sugar can be found by multiplying the mass of one jar by 4:

\(\large\rm{Total\: mass = 19\: kg \times 4 = \boxed{\rm{\:76\: kg\:}}}\)

\(\therefore\) The total mass of four jars of sugar is 76 kg.

- Mass is a measure of the amount of matter an object contains. It is a fundamental property of an object and is typically measured in units such as kilograms or grams. Mass is different from weight, which is the force of gravity acting on an object's mass. Mass is an intrinsic property of an object and remains constant regardless of its location, while weight can vary depending on the gravitational field it is in. Essentially, mass determines an object's resistance to acceleration or change in motion.

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Answer:

C

Step-by-step explanation:

So you can use the 30, 60, 90 degree triangle ratio of x: 2x: x√3

The 3 is the x, and the hypotenuse is the 2x, so it's 6

Answer:

C. 6

Step-by-step explanation:

I just finished the test and I got 100 percent

Answer:

7p, 7*p

Step-by-step explanation:

The length of ST is 24.

In geometry, a tangent is a line that touches a curve at a single point, without crossing over the curve at that point. This point of contact is called the point of tangency.

For example, in a circle, a tangent is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at the point of tangency.

Tangents are important in geometry because they allow us to find the slope of a curve at a specific point. The slope of the tangent line at a point on a curve is equal to the derivative of the function representing the curve at that point.

To find the length of ST, we need to find the length of SR and add it to the length of RT.

Using the tangent-tangent theorem, we know that RP is perpendicular to RT at point R. Therefore, angle RPT is a right angle.

We can use the Pythagorean theorem to find the length of RT. Let's call the length of RP "a" and the length of PT "b". Then, we have:

a² = (x+6)² + b² (from right triangle PQR)

a² = (2x-9)² + (b+3)² (from right triangle PSR)

Setting these two equations equal to each other, we have:

(x+6)² + b² = (2x-9)² + (b+3)²

Expanding and simplifying, we get:

x² - 24x + 90 = 0

Solving for x using the quadratic formula, we get:

x = (24 ± √(24² - 4190)) / (2*1) = 15 or 6

Since x cannot be negative, we take x = 15.

Now we can use the Pythagorean theorem to find the length of SR:

a² = (2x-9)² + (b+3)²

a² = (2*15-9)² + (b+3)²

a² = 276 + (b+3)²

We also know that SR = 3, so:

3² = (b+3)²

9 = b² + 6b + 9

b² + 6b - 0 = 0

Solving for b using the quadratic formula, we get:

b = (-6 ± √(6² - 410)) / (2*1) = -3 or 0

Since b cannot be negative, we take b = 0.

Therefore, we have:

a² = (x+6)² + b²

a² = (15+6)² + 0²

a² = 441

So, RT = a = √(441) = 21.

Finally, we have:

ST = SR + RT = 3 + 21 = 24.

Therefore, the length of ST is 24.

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Answer:

x₁=1; x₂=-1; x₃=-0.5; x₄=-2.

Step-by-step explanation:

\(2x^4+5x^3-5x-2=0; \ < = > \ 2(x^4-1)+5x(x^2-1)=0; \ < = > \ 2(x^2+1)(x^2-1)+5x(x^2-1)=0; \ < = >\)

\((x^2-1)(2x^2+2+5x)=0; \ < = > \ (x^2-1)(2x^2+5x+2)=0; \ = >\)

\(= > \ \left[\begin{array}{ccc}x=1\\x=-1\\x=-\frac{1}{2} \\x=-2\end{array}\)

Answer:

2 -7  6   7

1 3    -4  5

1 6  -15  -6

Step-by-step explanation:

An augmented matrix is the coefficients of the variables and then the solution in rows

Rewriting the equations

2x -7y +6x = 7

x +3y -4z = 5

x +6y -15z = -6

The matrix is

2 -7  6   7

1 3    -4  5

1 6  -15  -6

Answer:

this is the final answer

thankyou

Step-by-step explanation:

V=lwh

3