In 2016, the mean score on the ap statistics exam was 2.80, with a standard deviation of 1.35. the mean score on the ap calculus exam was a 2.86, with a standard deviation of 1.55. what is the combined mean and standard deviation for these exams?

mean, 2.83; standard deviation, 0.2

mean, 5.66; standard deviation, 2.9

mean, 5.66; standard deviation, 2.055

mean, 2.83; standard deviation, 2.9

mean, 5.66; standard deviation, 4.225

Answer:

80°

Step-by-step explanation:

Because the triangle are congruent, the 3rd angle of both triangle needs to bring the sum of the triangle to 180°, so the last angle must be 80

Therefore, the value of s that is RT is approximately 7.97 units.

A triangle is a two-dimensional geometric shape that is formed when three non-collinear points are connected with straight line segments. It has three sides, three angles, and three vertices. The sum of the angles of a triangle is always 180 degrees. Triangles can be classified based on their sides and angles, such as equilateral, isosceles, scalene, acute, obtuse, and right triangles. Triangles are commonly used in geometry, trigonometry, and other branches of mathematics.

Here,

To find the value of RT, we can use the law of cosines, which states that:

c² = a² + b² - 2ab cos(C)

where c is the side opposite angle C, and a and b are the other two sides.

In this case, we want to find RT, which is opposite angle S. So we can write:

RT² = RS² + TS²- 2(RS)(TS)cos(S)

Substituting in the values we know, we get:

RT² = 13² + 7² - 2(13)(7)cos(32)

RT² = 169 + 49 - 182cos(32)

RT² = 218 - 182cos(32)

Taking the square root of both sides, we get:

RT = √(218 - 182cos(32))

Using a calculator, we find:

RT ≈ 7.97 units

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The average root mean square velocity of the gas molecules of ozone (O3) at 100K is approximately 341 m/s, and at 3000K it is approximately 1925 m/s.

The root means square velocity (v rms) of a gas molecule is given by the formula:

v rms = √(3kT/m)

where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of a single molecule. The mass of a single ozone molecule (O3) is approximately 48 g/mol or 4.8x10^-26 kg.

At 100K, the root mean square velocity is calculated as:

v rms = √(3kT/m) = √(3 x 1.38x10^-23 J/K x 100K / 4.8x10^-26 kg) = 341 m/s

At 3000K, the root mean square velocity is calculated as:

v rms = √(3kT/m) = √(3 x 1.38x10^-23 J/K x 3000K / 4.8x10^-26 kg) = 1925 m/s

Therefore, the average root mean square velocity of the gas molecules of ozone (O3) at 100K is approximately 341 m/s, and at 3000K it is approximately 1925 m/s.

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(a) The economic loading of unit 4 and B are 11.54 MW and 138.46 MW, respectively.

To find the economic loading of the two units when the total load to be supplied by the power station is 150 MW, we need to minimize the total fuel cost. Let x be the power generated by unit 4 and y be the power generated by unit B. Then, we have:

x + y = 150 (total load)

The total fuel cost C is given by:

C = F4(x) + Fb(y)

where F4(x) and Fb(y) are the fuel costs for units 4 and B, respectively. Using the given relations, we have:

F4(x) = 0.06x^2 + 11.4x

Fb(y) = 0.07y^2 + 10y

Substituting x = 150 - y, we get:

C(y) = 0.06(150-y)^2 + 11.4(150-y) + 0.07y^2 + 10y

Expanding and simplifying, we get:

C(y) = 0.013y^2 - 3.6y + 1710

To minimize C(y), we take its derivative with respect to y and set it equal to zero:

dC/dy = 0.026y - 3.6 = 0

y = 138.46 MW

Substituting y back into x = 150 - y, we get:

x = 11.54 MW

(b) The negative value that is  -1297.5 indicates that there is a net decrease in fuel cost per hour if the load is equally shared by the two units.

To find the net increase in fuel cost per hour if the load is equally shared by the two units, we need to calculate the fuel cost for each unit when they generate half of the total load (i.e., 75 MW). Using the given relations, we have:

F4(75) = 0.06(75)^2 + 11.4(75) = 1282.5

Fb(75) = 0.07(75)^2 + 10(75) = 1312.5

Therefore, the total fuel cost is:

C = F4(75) + Fb(75) = 2595

If the load is equally shared by the two units, each unit generates 75/2 = 37.5 MW. The fuel cost for each unit is:

F4(37.5) = 0.06(37.5)^2 + 11.4(37.5) = 641.25

Fb(37.5) = 0.07(37.5)^2 + 10(37.5) = 656.25

Therefore, the total fuel cost is:

C' = F4(37.5) + Fb(37.5) = 1297.5

The net increase in fuel cost per hour is:

ΔC = C' - C = 1297.5 - 2595 = -1297.5

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The correlation coefficient must necessarily be equal to -0.70. The coefficient of determination (R-squared) is equal to the square of the correlation coefficient (r).

Therefore, taking the square root of 0.49 gives us a correlation coefficient of -0.70 or 0.70. Since the linear regression equation indicates an inverse relationship between X and Y (as the slope is negative), we know that the correlation coefficient must be negative.

When the standard error of the estimate Se is equal to zero, this means that the linear regression model explains all of the variation in the sample data, and the coefficient of determination is equal to one. However, in practice, a standard error of zero is not attainable as it would require a perfect fit between the data points and the regression line. Therefore, this scenario is unlikely to occur in real-world applications.

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By graphing both functions, we will see that there are two intersections at (-1.41, -2.12) and (3.28, 7.27).

Here we must solve:

\(2^x - 2.5 = 2x + 0.7\)

To do it, we can graph the functions:

\(y = 2^x - 2.5\\\\y = 2x + 0.7\)

And see where do the curves intersect.

The graph can be seen below, in there we can see two intersections.

One at (-1.41, -2.12) and (3.28, 7.27).

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Answer:

Step-by-step explanation:answer is $6 per candy bar/ c=6

Answer:

Everytime it is adding  506 to it

Step-by-step explanation:

so 253+506 is 759 and it keeps going

Let the unit digit be x

and the tens digit be x-2

The Sum of digits is x + x - 2  

                              = 2x - 2

Now,

   ⇒ 10(x - 2) + x

    ⇒ 10x + 20 + x

    ⇒ 11x - 20

Now, According to Question

    ⇒ 11x - 20 - 27

    ⇒ 11x - 2x = -2 + 47

    ⇒ 9x = 45

    ⇒ x = 5

Now,

The tens digit ⇒  x - 2

putting the value of x in equation

   ⇒ 5 - 2 = 3

So, the product of the digits is  3 × 5

Answer:

Step-by-step explanation:

Let's assume the initial number of men at the exhibition is 10x, and the initial number of women is 3x.

After 110 men left, the number of men remaining is 10x - 110.

The total number of people remaining is (10x - 110) + (3x) = 13x - 110.

According to the given information, the number of men remaining (10x - 110) is 5/12 of the total number of people remaining (13x - 110). We can write this as an equation:

10x - 110 = (5/12)(13x - 110)

To solve this equation, we can start by simplifying both sides:

10x - 110 = (65/12)x - (55/6)

To get rid of the fractions, we can multiply both sides of the equation by 12:

12(10x - 110) = 65x - 110(2)

120x - 1320 = 65x - 220

Next, we can bring the x terms to one side and the constant terms to the other side:

120x - 65x = 1320 - 220

55x = 1100

Dividing both sides by 55, we find:

x = 20

Now, we can substitute the value of x back into the initial expressions to find the number of men and women:

Number of men = 10x = 10(20) = 200

Number of women = 3x = 3(20) = 60

Therefore, there were 60 women at the exhibition

Hope this answer your question

Please rate the answer and

mark me ask Brainliest it helps a lot

a. The Red Sea trough refers to a dip in the upper-level height originating over the eastern Mediterranean moving southeastward, and deepening over the Red Sea.

b. This weather phenomenon manifests itself as it causes a sudden drop in temperatures, thunderstorms, and dust storms.

c. The Red Sea trough presents a challenge to weather forecasting as it is hard to predict when the trough will develop.

d. The Red Sea trough presents several hazards as causes heavy rainfall, strong winds, and a sudden drop in temperatures.

The Red Sea trough is one of the familiar weather patterns in Jordan. It is seen both in spring and fall.

a. The Red Sea trough is a dip in the upper-level height that originates over the eastern Mediterranean, advances southeastward, and deepens over the Red Sea. During the fall and spring seasons, this trough becomes more profound and generates a shallow low-pressure system over the Levant region, resulting in a northwesterly to northeasterly wind.

b. This weather phenomenon manifests itself in terms of weather in several ways. They are as follows:

c. The Red Sea trough presents a significant challenge to weather forecasting. It is difficult to predict when the trough will develop and the magnitude of its impacts on weather. The weather forecasters struggle to estimate the movement of the trough, its depth, and intensity, and the amount of rain and wind it will produce. As a result, the meteorological department often issues warnings and alerts, but the severity and impact of the weather are not always accurately forecasted.

d. The Red Sea trough presents several hazards. They are as follows:

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b. Estimate the volume by reading from the top of the meniscus.

When using a graduated cylinder to measure the volume of a liquid, it is important to estimate the volume by reading from the top of the meniscus.

The meniscus is the curved surface formed by the liquid inside the cylinder. It is not a flat surface, and its shape can vary depending on factors such as surface tension and the nature of the liquid.

To get an accurate measurement, you should position yourself at eye level with the graduated cylinder and read the volume at the bottom of the meniscus. However, reading from the bottom of the meniscus can introduce parallax errors, as the angle at which you view the meniscus can affect the perceived volume.

To minimize errors, it is recommended to read the volume from the top of the meniscus. The top of the meniscus represents the most accurate approximation of the liquid's volume, as it is less affected by parallax or other viewing angle discrepancies.

By estimating the volume from the top of the meniscus, you can obtain a more precise measurement when using a graduated cylinder.

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Answer:

the solution is c. perpendicular lines

Step-by-step explanation:

the slopes: 1/4 and -4 are perpendicular and intersecting

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Weak variation of curves refers to curves with bounded variation, while strong variation of weak variation curves adds the additional requirement of fixed initial and end points,

(1) Weak Variation of Curves (r):

In mathematics, a weak variation of curves refers to a concept related to the smoothness or regularity of a curve. A curve is said to have weak variation if it has bounded variation over a given interval.

Bounded variation means that the total amount of change or "variation" in the curve is limited or finite. It implies that the curve does not exhibit large and erratic oscillations or abrupt jumps. Instead, it may have small fluctuations or gradual changes within a certain range.

Formally, a curve f(x) defined on the interval [a, b] is said to have weak variation if there exists a constant M such that for any partition P of [a, b] into subintervals [x_i, x_{i+1}], the sum of absolute differences between consecutive points of the curve is bounded:

V[f, P] = Σ |f(x_{i+1}) - f(x_i)| ≤ M

This means that no matter how the interval [a, b] is divided, the sum of absolute differences between consecutive points will not exceed the constant M. It indicates that the curve has limited fluctuation and is relatively smooth in terms of changes between adjacent points.

(2) Strong Variation of (1) with Fixed Initial and End Points:

A strong variation of weak variation curves refers to a more restrictive condition, where not only is the curve required to have bounded variation, but it is also required to have fixed initial and end points.

In other words, if we consider a curve f(x) with weak variation over the interval [a, b], a strong variation of this curve would additionally require that the curve has fixed values at the endpoints a and b.

Formally, for a curve f(x) with weak variation over [a, b], it has a strong variation if and only if f(a) and f(b) are fixed and equal to certain specified values.

This condition ensures that the curve has a well-defined behavior and specific values at the endpoints, which can be useful in various mathematical and physical applications where fixed initial and end conditions are desired or necessary.

To summarize, weak variation of curves refers to curves with bounded variation, while strong variation of weak variation curves adds the additional requirement of fixed initial and end points, providing more constraints and determinacy to the behavior of the curve.

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Answer:

You didnt leave a picture

The value of the a and b will be 6 and 9 feet. Every 2 inches on the scale drawing represents 1.5 feet of the original house.

The process of converting the unit form is known as the unit conversion. For example, in the SI unit system, mass is in kg. While in CGS, it is represented in grams.

The given conversion is ;

\(\rm 2 \ inch = 1.5 \ feet \\\\ 1 inch = \frac{1.5}{2} \ feet\)

For 8, 12 inches, the values in feet is;

\(\rm 8 \times \frac{1.5}{2} = 6 \ feet\)

\(\rm 12 \times \frac{1.5}{2} = 9 \ feet\)

Hence, the value of the a and b will be 6 and 9 feet.

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The value a= 6 and b=9.

The process of converting the unit form is known as the unit conversion.

For example, in the SI unit system, distance is in meter while in CGS, it is represented in cm.

Given that:

2 inch = 1.5 feet

1 inch = \(\frac{1.5}{2}\)

then, 8 inches =\(\frac{1.5}{2} *8\)

                        = 1.5*4

                        = 6 feet

again, 12 inches= \(\frac{1.5}{2} *12\)

                          = 1.5*6

                         = 9 feet

and, 16 inches =\(\frac{1.5}{2} *16\)

                          = 1.5*8

                          = 12 feet

The value of a & b is 6 and 9 respectively.

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The shaded region is between the two horizontal lines, but does not include the lines themselves. Here's a graph of the solution:

  |

8__|_________________

  |                 |

  |                 |

3__|_________________|

  |

  |_________________

     <--- --->

      x-axis

An inequality is a mathematical statement that compares two values, expressing that one value is greater than, less than, or equal to the other. Inequalities use inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to) to indicate the relationship between the two values. Inequalities are commonly used in algebra and are used to describe ranges of values that satisfy a given condition or set of conditions.

Here,

The solution for the given linear inequality system includes all the points that satisfy the two inequalities y < 8 and y > 3. To graph the solution, we need to shade the region that satisfies both inequalities.

The inequality y < 8 represents all the points below the horizontal line passing through y = 8, but not including the line itself.

The inequality y > 3 represents all the points above the horizontal line passing through y = 3, but not including the line itself.

Therefore, the solution for the given system is the shaded region between the two horizontal lines, excluding the lines themselves.

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Answer:

Step-by-step explanation:

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

So,

\(17^2 +15^2 = ?\)

Well,

\(17^2 =289\)

and

\(15^2=225\)

So,

\(289+225=514\)

Now, we have to find the square root of 514.

\(\sqrt{514} =22.671568097509267786240958185847\) OR \(22.7\)

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

The best answer to submit for (515 x 0.0025) + 24.57 is 25.8575.

A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. Decimal notation is the name for the method used to represent numbers in the decimal system. The Hindu-Arabic numeral system has been expanded to include non-integer values.

To find the answer to the expression (515 x 0.0025) +24.57, we can simplify it by performing the multiplication and addition in the correct order:

(515 x 0.0025) + 24.57 = 1.2875 + 24.57 = 25.8575

Therefore, the best answer to report is C. 25.8575.

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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The exponent x²/₃/y⁻³/₄ in equivalent form is = (³√x²) . (⁴√y³)

Exponents are the power to which a variable is raised

Given the exponential expressions \(\frac{x^{\frac{2}{3} } }{y^{\frac{-3}{4} } }\), we want to find the expression it is equivalent to. We proceed as follows

Using the reciprocal law of exponents which states that x⁻¹ = 1/x on the denominator, we have that

\(\frac{x^{\frac{2}{3} } }{y^{\frac{-3}{4} } } = \frac{x^{\frac{2}{3} } }{\frac{1}{ y^{\frac{3}{4} }} } = x^{\frac{2}{3} } \times y^{\frac{3}{4} }\)

Now, using the power law of exponents which is \(x^{\frac{a}{b} } =\sqrt[b]{x^{a} }\), we have that

\(x^{\frac{2}{3} } \times y^{\frac{3}{4} } =\sqrt[3]{x^{2} } \times \sqrt[4]{y^{3} }\)

So,

 \(\frac{x^{\frac{2}{3} } }{y^{\frac{-3}{4} } } =\sqrt[3]{x^{2} } \times \sqrt[4]{y^{3} }\)

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Answer:

what equation.?

Step-by-step explanation:

The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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Answer:

Step-by-step explanation:

\(\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=13\\ \theta =115 \end{cases}\implies \begin{array}{llll} s=\cfrac{(115)\pi (13)}{180}\implies s=\cfrac{299\pi }{36} \\\\\\ s\approx 26.09~in \end{array}\)

Answer:

t > -7/4

Step-by-step explanation:

Step 1: Write out inequality

14 - (9t - 2) < -t + 30

Step 2: Distribute

14 - 9t + 2 < -t + 30

Step 3: Combine like terms

-9t + 16 < -t + 30

Step 4: Add 9t to both sides

16 < 8t + 30

Step 5: Subtract 30 on both sides

-14 < 8t

Step 6: Divide both sides by 8

-7/4 < t

Step 7: Rewrite

t > -7/4

Answer:

I think that there is indefinite.

Step-by-step explanation:

The reason why is because x and y could be any number

Answer:

thenk you for the points give me brainlist pleasee

Answer:

love you valentines

Step-by-step explanation:

The integer that matches the situation I go for a hike in Colorado. The top of the mountain is feet above sea level is 14000.

A number system is defined as a system of writing to express numbers.

Given,

I go for a hike in Colorado. The top of the mountain is ___ feet above sea level.

We need to find the suitable integer in the blank.

The top of a mountain would be a high number above sea level, 144 is around ground level above sea level therefore the top of the mountain would be 14,000 feet above sea level

Hence, the integer that matches the situation I go for a hike in Colorado. The top of the mountain is feet above sea level is 14000.

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