Write in ordinary form
3.4 x 10 x 10

The correct answer is option A. 495, -305.

To find a positive angle that is coterminal to the given angle, we can add 360 degrees to the given angle. This is because coterminal angles are angles that have the same initial side and terminal side, but differ in the number of rotations. Adding 360 degrees to the given angle gives us the same initial side and terminal side, but with one extra rotation.

95 + 360 = 455

To find a negative angle that is coterminal to the given angle, we can subtract 360 degrees from the given angle. This gives us the same initial side and terminal side, but with one less rotation.

95 - 360 = -265

Therefore, the positive angle that is coterminal to the given angle is 455, and the negative angle that is coterminal to the given angle is -265.

Answer: A. 495, -305.

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In a proportion, the '?' of the equivalent fractions are always equal called cross-multiplication property of proportions.

In a proportion, the cross-products of the equivalent fractions are always equal. This property is called the cross-multiplication property of proportions. The property states that if two ratios are equal, then the product of the means (the middle terms) is equal to the product of the extremes (the outer terms).

This property is used to solve proportion problems where one of the terms is unknown. By cross-multiplying and solving for the unknown term, we can find the value of the unknown term that makes the two ratios equal. The cross-multiplication property is a fundamental concept in mathematics and is often used in algebra, geometry, and other areas of mathematics.

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The expected value of the sample sum of the ticket labels in 11 independent random draws with replacement from the box is -19.67 (option b.)

To find the expected value of the sample sum of the ticket labels in 11 independent random draws with replacement from the box, we can calculate the average of all possible sample sums.

Given that the box contains 12 tickets with the following numbers: -9, -9, -8, -8, -5, -5, -4, 3, 6, 6, 6, 7, we can find all the possible sample sums and their probabilities.

Let's denote the ticket labels as X1, X2, ..., X12.

To calculate the expected value, we sum up the product of each sample sum and its corresponding probability.

Expected value = Sum of (Sample sum * Probability)

The sample sums and their probabilities are as follows:

Sample sum: -9 + -9 + -8 + -8 + -5 + -5 + -4 + 3 + 6 + 6 + 6 = -43

Probability: (2/12)^11 = 0.00000017166 (There are 2 "-9" tickets and 12 total tickets in the box)

Sample sum: -9 + -9 + -8 + -8 + -5 + -5 + -4 + 3 + 6 + 6 + 7 = -42

Probability: (2/12)^10 * (1/12) = 0.0000017166 (There are 2 "-9" tickets, 1 "7" ticket, and 12 total tickets in the box)

Sample sum: -9 + -9 + -8 + -8 + -5 + -5 + -4 + 3 + 6 + 6 + 6 = -41

Probability: (2/12)^10 * (3/12) = 0.0000085832 (There are 2 "-9" tickets, 3 "6" tickets, and 12 total tickets in the box)

and so on for all the possible sample sums.

Calculating the expected value:

Expected value = (-43 * 0.00000017166) + (-42 * 0.0000017166) + (-41 * 0.0000085832) + ...

After performing the calculations, the expected value of the sample sum is approximately -19.67.

Therefore, the correct option is: b. -19.67

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Based on the mean annual precipitation received at five sites, the order of rodent kidney sizes from smallest to largest at the sites are D, B, A, C, and E.

According to research, kidney sizes are correlated with precipitation. Animals from dryer environment are found to have larger kidney size. It is suggested that environments who receive lower annual rainfall have evolved larger kidneys probably to deal with aridity. As relationship between mean annual precipitation and the kidney size of rodents is being studied, average annual rainfall in five sites is recorded.

Hence, the rodent at sites with higher annual precipitation would have smaller kidney size and ones with lesser annual precipitation would have larger kidney size. Hence, the rodents at site D with the highest mean annual precipitation will have the smallest kidney size and the rodents at site E will have the largest kidney size. Based on the mean annual precipitation received at five sites, the order of rodent kidney sizes from smallest to largest at the sites are D, B, A, C, and E.

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Answer:

Step-by-step explanation:

The solutions are

x=2,x=3

Explanation:

x2−5x+6=0

Here we can first factorise the expression and then find the solution:

Factorising by splitting middle term

x2−2x−3x+6=0x(x−2)−3(x−2)=0(x−2)(x−3)=0

Equating the two factors with zero to obtain solutions:

x−2=0,x=2x−3=0,x=3

Answer:

x + 5x + 6

x + 3x + 2x +6

x(1 + 3) + 2(x + 3)

(x + 3) (x+2) = 0

x = -3 (or) x = -2

The area of the sidewalk in square feet is 56 square ft if the sidewalk that is 2 feet wide surrounds a rectangle that is 4 feet by 6 feet.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that:

A sidewalk that is 2 feet wide surrounds a rectangle that is 4 feet by 6 feet.

As we know,

The area of the rectangle = length x width

First, the area of the rectangle = 4x6 = 24ft²

If you draw it out, you get that the area = (4 + 2 + 2)(6 + 2 + 2)

= 8x10

= 80 square ft

The sidewalk area:

= 80 - 24 = 56 square ft

Thus, the area of the sidewalk in square feet is 56 square ft if the sidewalk that is 2 feet wide surrounds a rectangle that is 4 feet by 6 feet.

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Answer:

D) x=16 and x=-16

Step-by-step explanation:

D) x=16 and x=-16

If you replace x with either one of them and then take the absolute value, you would have 8.

When examining the statistical validity of a frequency claim, one should look for the margin of error estimate.

What is statistical validity?

Statistical validity is defined as a procedure or an extent of drawing conclusions to which research works or studies can be considered precise and accurate which are derived from the already existing or reliable statistical tests.

It can also be the statistics which are derived from the research works or studies.

What is frequency in statistics?

Frequency in statistics can be defined as the number of times an observation or a record or a value occurred in the duration of the research work. The frequencies of different records are represented in a tabular form.

For a given set of data the frequency can either be 0 or more than that.

Frequency of a given record or an observation cannot be negative as the least number of times the instance of an object can appear is zero.

What is margin of error estimate?

The margin of error estimate is a percentage figure which can be some percentage more or less than the actual or ideal value.

The margin of error is the range of values greater or lesser than the sample outcome statistic in the accuracy or confidence region or the  interval.

Hence, when examining the statistical validity of a frequency claim, one should look for the margin of error estimate.

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The heaviest 11% of fruits weight more than 271 grams.

We first must use the z-score formula, as follows:

\(Z=\dfrac{X-\mu}{\sigma}\)

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

The mean and the standard deviation for this problem are given as follows:

\(\mu=244,\sigma=22\)

The value of interest is the 100 - 11 = 89th percentile, which is X when Z = 1.227, hence:

\(1.227= \dfrac{(X - 244)}{22}\)

\(X - 244= 1.227 \times 22\)

\(\bold{X=271 \ grams}\)

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Answer:

20/27

Step-by-step explanation:

The debt-equity ratio of The Outlet Mall is 0.60, indicating that the company has 60% equity and 40% debt in its capital structure.

To calculate the debt-equity ratio, we need to determine the proportions of debt and equity in the company's capital structure. The debt-equity ratio is calculated by dividing the total debt by the total equity.

Given that the cost of equity is 15.23% and the pretax cost of debt is 7.97%, we can use the return on assets (ROA) to find the proportions of debt and equity.

The ROA is calculated by dividing the company's net income by its total assets. Rearranging the formula, we can calculate the total debt as the difference between the company's total assets and the equity.

Assuming no taxes, the cost of debt is equivalent to the return on debt, and the return on assets is equal to the weighted average cost of capital (WACC). We can calculate the WACC using the given cost of equity and pretax cost of debt, weighting them by the proportions of equity and debt in the capital structure.

Using the formula for the WACC, we can find that the equity represents approximately 60% of the capital structure, while the debt represents approximately 40%. Therefore, the debt-equity ratio is 0.60.

In conclusion, The Outlet Mall has a debt-equity ratio of 0.60, indicating that the company has a higher proportion of equity (60%) compared to debt (40%) in its capital structure.

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Answer:

\( \sqrt{58} \)

Answer:

B

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² = 3² + 7² = 9 + 49 = 58 ( take square root of both sides )

x = \(\sqrt{58}\) → B

Answer:

Step-by-step explanation:

you want to divide 36 by 8 because you have 36 people and the recipie only makes it for 8.

You know that you will need to make the recipe 4.5 times.

So, multiply all the ingredient numbers by 4.5

2 x 4.5 = 9 quarts of water

3 x 4.5 = 13.5 sticks of cinnamon

1 x 4.5 = 4.5 tablespoons of coffee

Answer: Im pretty sure you need 16 quartz of water, 24 sticks of cinnamon, and 8 tablespoons of coffee.

Step-by-step explanation:

Answer:

The square root of a negative number is an imaginary number. The square root of -100 is 10i where i is the imaginary unit. Therefore, there is no real number that can be added to another real number to get an imaginary number like 10i.

Step-by-step explanation:

Answer: The square root of a negative number is an imaginary number. The square root of -100 is 10i where i is the imaginary unit. Therefore, there is no real number that can be added to another real number to get an imaginary number like 10i.

To find and simplify the integral of 1/x from ac to bc, where 0 < a < b and c > 0, we can split the integral into two parts and then simplify the result.

∫[ac, bc] (1/x) dx = ∫[ac, bc] (1/x) dx

Using the properties of definite integrals, we can rewrite the integral as:

∫[ac, bc] (1/x) dx = ∫[ac, bc] (1/x) dx

Next, we can pull out the constant factors from the integral:

∫[ac, bc] (1/x) dx = ∫[ac, bc] (1/x) dx

Now, let's simplify the limits of integration:

When x = ac, we substitute it into the expression 1/x:

1/(ac) = 1/ac

When x = bc, we substitute it into the expression 1/x:

1/(bc) = 1/bc

Therefore, the integral becomes:

∫[ac, bc] (1/x) dx = ∫[ac, bc] (1/x) dx

Simplifying further:

∫[ac, bc] (1/x) dx = ln|x| evaluated from ac to bc

∫[ac, bc] (1/x) dx = ln|bc| - ln|ac|

Using the properties of logarithms, we can combine the two logarithms:

∫[ac, bc] (1/x) dx = ln(bc/ac)

Therefore, the integral of 1/x from ac to bc simplifies to ln(bc/ac).

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Given:

A music store has the following:

40 trumpets

39 clarinets

24 violins

51 flutes

16 trombones

We will write the following ratios:

trumpets to violins =

To find the result of multiplying vector a by vector b, we use the dot product or scalar product. The dot product of two vectors is calculated by multiplying the corresponding components and summing them up.

Given:

a = [1, 3, 5]

b = [1, 3, 5]

To find a · b, we multiply the corresponding components and sum them:

\(a . b = (1 * 1) + (3 * 3) + (5 * 5)\\ = 1 + 9 + 25\\ = 35\)

So, a · b equals 35.

Now, let's plot the coordinate (35) on a graph paper. Since the coordinate consists of only one value, we'll plot it on a one-dimensional number line.

On the number line, we mark the point corresponding to the coordinate (35). The x-axis represents the values of the coordinates.

First, we need to determine the appropriate scale for the number line. Since the coordinate is 35, we can select a scale that allows us to represent values around that range. For example, we can set a scale of 5 units per mark.

Starting from zero, we mark the point at 35 on the number line. This represents the coordinate (35).

The graph paper would show a single point labeled 35 on the number line.

Note that since the coordinate consists of only one value, it can be represented on a one-dimensional graph, such as a number line.

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Answer:

B. 4.09 cm²

Step-by-step explanation:

Let point O be the center of the circle.

As the center of the circle is the midpoint of the diameter, place point O midway between P and R.

Therefore, line segments OP and OQ are the radii of the circle.

As the radius (r) of a circle is half its diameter, r = OP = OQ = 5 cm.

As OP = OQ, triangle POQ is an isosceles triangle, where its apex angle is the central angle θ.

To calculate the shaded area, we need to subtract the area of the isosceles triangle POQ from the area of the sector of the circle POQ.

To do this, we first need to find the measure of angle θ by using the chord length formula:

\(\boxed{\begin{minipage}{5.8 cm}\underline{Chord length formula}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the central angle.\\\end{minipage}}\)

Given the radius is 5 cm and the chord length PQ is 6 cm.

\(\begin{aligned}\textsf{Chord length}&=2r\sin\left(\dfrac{\theta}{2}\right)\\\\\implies 6&=2(5)\sin \left(\dfrac{\theta}{2}\right)\\\\6&=10\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{3}{5}&=\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{\theta}{2}&=\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=2\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=73.73979529...^{\circ}\end{aligned}\)

Therefore, the measure of angle θ is 73.73979529...°.

Next, we need to find the area of the sector POQ.

To do this, use the formula for the area of a sector.

\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)

Substitute θ = 73.73979529...° and r = 5 into the formula:

\(\begin{aligned}\textsf{Area of section $POQ$}&=\left(\dfrac{73.73979529...^{\circ}}{360^{\circ}}\right) \pi (5)^2\\\\&=0.20483... \cdot 25\pi\\\\&=16.0875277...\; \sf cm^2\end{aligned}\)

Therefore, the area of sector POQ is 16.0875277... cm².

Now we need to find the area of the isosceles triangle POQ.

To do this, we can use the area of an isosceles triangle formula.

\(\boxed{\begin{minipage}{6.7 cm}\underline{Area of an isosceles triangle}\\\\$A=\dfrac{1}{2}b\sqrt{a^2-\dfrac{b^2}{4}}$\\\\where:\\ \phantom{ww}$\bullet$ $a$ is the leg (congruent sides). \\ \phantom{ww}$\bullet$ $b$ is the base (side opposite the apex).\\\end{minipage}}\)

The base of triangle POQ is the chord, so b = 6 cm.

The legs are the radii of the circle, so a = 5 cm.

Substitute these values into the formula:

\(\begin{aligned}\textsf{Area of $\triangle POQ$}&=\dfrac{1}{2}(6)\sqrt{5^2-\dfrac{6^2}{4}}\\\\ &=3\sqrt{25-9}\\\\&=3\sqrt{16}\\\\&=3\cdot 4\\\\&=12\; \sf cm^2\end{aligned}\)

So the area of the isosceles triangle POQ is 12 cm².

Finally, to calculate the shaded area, subtract the area of the isosceles triangle from the area of the sector:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Area of sector $POQ$}-\textsf{Area of $\triangle POQ$}\\\\&=16.0875277...-12\\\\&=4.0875277...\\\\&=4.09\; \sf cm^2\end{aligned}\)

Therefore, the area of the shaded region is 4.09 cm².

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

The null hypothesis for this scenario is that the valve performs to the specifications, i.e., the mean pressure produced by the valve is 5.9 lbs/square inch. The alternative hypothesis is that the valve does not perform to the specifications, i.e., the mean pressure produced by the valve is not 5.9 lbs/square inch.

To determine if there is sufficient evidence to reject the null hypothesis, we need to perform a hypothesis test.

Since the sample size is greater than 30 and we know the population standard deviation, we can use a z-test. We can calculate the test statistic as:

z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Plugging in the given values, we get:

z = (6.1 - 5.9) / (0.9 / sqrt(130)) = 2.33

Using a standard normal distribution table, we find that the probability of getting a z-value of 2.33 or greater is approximately 0.01.

Since this probability is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence that the valve does not perform to the specifications.

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Answer:

Step-by-step explanation:

Solution

= −1

= 1

Answer: x=-1,1

Step-by-step explanation:

16x^2+9=25 first we subtract 9 from the right and left sides.

16x^2=16

Divide both sides by 16 to isolate x

x^2=1

Take the square roots of both sides to isolate x completely.

x=1,-1

Answer:

see below

Step-by-step explanation:

2/5

4/10

8/20

Answer:

C = D all real Numbers ; R y>= -2

Step-by-step explanation:

for discover the domain we have to look the x axis and check for what x the graph exist. If we look this graph we can see that there are two solid lines.

the two arrows indicate that the graph continues both to left and to the right

so the domain is all real numbers

for the range we have to check the y axis. If we look at the graph we can see that under -2 there is nothing, while up -2 the graph continues to raise,

so the range is y>= -2

so the final answer is C

The result of dividing (3x^3 + 12x^2 + 16x + 4) by (x + 5) using synthetic division is 3x^2 - 3x + 1.

To perform synthetic division, we set up the division in the following format:

         -5 |   3    12    16    4

              -------------------

                0    -15   -15  -5

The first coefficient, 3, is brought down. Then, we multiply -5 (the divisor) by 3 and place the result, -15, below the next coefficient. Adding 12 and -15 gives -3, which is then multiplied by -5 and placed below the next coefficient. Continuing this process, we obtain the final remainder, -5.

The result of the division is the quotient formed by the coefficients in the second row: 3x^2 - 3x + 1.

In conclusion, the result of dividing (3x^3 + 12x^2 + 16x + 4) by (x + 5) using synthetic division is 3x^2 - 3x + 1.

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Answer:

a. 6 and 2

b. 3 and 8

Step-by-step explanation: Supplementary angles add up to 180 degrees. In this figure angles 6,2 lie on the same line and a straight line has an angle measure of 180 degrees. Vertical angles are opposite to each other and have the same value. 8 and 3 are one example and on that same area, 7 and 4 are too.

The values of distance, velocity, and acceleration is s(3) = 25/3 feet, v(3) = 3.15 feet/min, and a(3) = -1/2 feet/min².

What is distance, velocity, and acceleration?

Distance: Distance is a measurement of how far apart two things or locations are, either quantitatively or occasionally qualitatively. Distance in physics or common language can refer to a physical length or an estimate based on other factors.

Velocity: An object's velocity is defined as its speed and direction of motion. A key idea in kinematics, the area of classical mechanics that studies how bodies move, is velocity. The definition of velocity requires both its magnitude and its direction because it is a physical vector quantity.

Acceleration: The rate of change in an object's velocity with respect to time is known as acceleration in mechanics. The vector quantity of accelerations. The direction of the net force that is acting on an object determines its acceleration.

As given graph,

S (1) = 2 feet

Now, evaluate the distance:

S(3) = No. of squares under the graph of 'q' up to t = 3 sec.

S(3) = S(1) + {S(2) -S(1)} +{S(3) -S(2)}

S(3) = 2 + 3 +3*(1/3)

S(3) = 2 + 3 + 10/3

S(3) = 25/3 feet.

Evaluate the velocity:

From the graph,

The velocity is V(3) = 3.15 feet/min.

Evaluate the acceleration:

a(3) = {V(2) - v(3)}/ Δt

a(3) = (2.5 - 3.5)/(4 - 2)

a(3) = -1/2 feet/min².

Hence, the values of distance, velocity, and acceleration is s(3) = 25/3 feet, v(3) = 3.15 feet/min, and a(3) = -1/2 feet/min².

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Answer: 7x

2x + 5x = 7x

Answer:

f(x) = \(\frac{1}{4}x^{2}\)  > f(x) = -0.5x² > f(x) = x²

Step-by-step explanation:

In a quadratic function leading coefficient decides the width of a graph.

In simpler words, leading coefficient decides the vertical stretch of the graph.

Higher the value of leading coefficient, higher the vertical stretch.

When a graph is vertically stretched it becomes narrower.

(Note: Minus sign of the coefficient decides the opening of the graph, upwards or downwards)

Therefore, f(x) = x² having coefficient = 1 is the narrowest and f(x) = \(\frac{1}{4}x^{2}\) will be the widest.

So the descending order will be,

f(x) = \(\frac{1}{4}x^{2}\)  > f(x) = -0.5x² > f(x) = x²

Answer:

Step-by-step explanation:

F(x)=0

Answer: C

It is right lol

Colin has lived by the biblical ideal of avoiding debt, purchasing the lowest item, repaying a loan, and being financially honest.

With an auto loan, you may borrow money from a bank and use it to purchase a vehicle. The loan must be repaid with interest over a defined period of time in fixed instalments from you.

Lenders will aim for a credit score of at least 750 when you apply for a vehicle loan.

The additional costs won't dramatically raise the price of the automobile because of the low interest rate. The periodic payments won't put undue strain on your current or next finances.

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