Solve the equation for x.


x2 = 9

Answer:

42

Step-by-step explanation:

The product of the prime factors of 1764 is

1764 = 2² × 3² × 7² , thus

\(\sqrt{1764}\)

= \(\sqrt{2^{2}(3^{2} )(7^{2} ) }\)

= \(\sqrt{2^{2} }\) × \(\sqrt{3^{2} }\) × \(\sqrt{7^{2} }\)

= 2 × 3 × 7

= 42

Answer:

2 bus

Step-by-step explanation:

The expected value of y is larger than the expected value of x. This is because y takes into account the number of students on all 4 buses, while x only takes into account the students on the bus with the randomly selected student.

The expected value of a random variable represents the average value of that variable over multiple trials. In this case, x is a random variable representing the number of students on the bus carrying the randomly selected student, and y is a random variable representing the number of students on the randomly selected bus.

The expected value of x can be calculated as follows:

E[x] = (10/100)×10 + (20/100)×20 + (30/100)×30 + (40/100)×40

= 16 + 12 + 9 + 16

= 53/4

= 13.25

This means that, on average, the bus carrying the randomly selected student would have 13.25 students.

The expected value of y can be calculated as follows:

E[y] = (1/4)×10 + (1/4)×20 + (1/4)×30 + (1/4)×40

= 25

This means that, on average, the randomly selected bus would have 25 students.

As expected, the expected value of y is larger than the expected value of x. This is because y takes into account the number of students on all 4 buses, while x only takes into account the students on the bus with the randomly selected student. Since the number of students on the other 3 buses can vary widely, y has a higher expected value than x.

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Answer:

It should be -7/10

Answer:  The answer is -7/10 :)

Step-by-step explanation:

-1/2-1/5=-7/10

Answer:

a = 40π

Step-by-step explanation:

a = (∅/360) * πr²

a = (144/360) * π(10)²

a = 40π

Seventeen-year-old Simon went through a period of conflict over issues relating to his identity, but now he feels comfortable with the choices and commitment he has made. Thomas has achieved what Erik Erikson would call: integrated identity

Thomas has achieved what Erik Erikson would call "identity achievement." Erikson's theory of psychosocial development proposes that during adolescence, individuals go through a stage called identity versus role confusion.

This stage is marked by a period of conflict and exploration in which adolescents seek to establish a sense of identity and make meaningful life choices.

Identity achievement refers to the successful resolution of this conflict, where individuals have gone through a process of exploration, self-reflection, and decision-making, ultimately arriving at a clear and coherent sense of self. They have made commitments to particular values, beliefs, relationships, and life goals, and feel a sense of comfort and confidence in their choices.

In the case of seventeen-year-old Simon, who has experienced conflict but now feels comfortable with his choices and commitments, he has likely reached the stage of identity achievement according to Erikson's theory. He has successfully navigated the complexities of adolescence and emerged with a clear and solid sense of his own identity.

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Complete Question:

Seventeen-year-old Simon has gone through a period of conflict over issues relating to his identity, but now he feels comfortable with the choices and commitment he has made. Thomas has achieved what Erikson would call a(n): ___________.

Answer:

\( - 3 \leqslant x \leqslant 5\)

Answer:

a) tan x = 1

b) tany = 4 + tanx /2tanx - 3

Step-by-step explanation:

a) Given the equation

2(sinx + 2cosx) = sinx +5cosx

Open the bracket

2sinx + 4cosx =  sinx +5cosx

Collect like terms

2sinx - sinx = 5cosx - 4cosx

sinx = cos x

Divide both sides by cos x

sinx/cosx = cosx/cosx

tanx = 1

Hence the value of tan x is 1

b) Given the expression

sinxcosy + 3cosxsiny = 2sinxsiny - 4cosxcosy

We are to express tany in terms of tan x

Divide through by cosx cosy

sinxcosy/cosx cosy + 3cosxsiny/cosx cosy = 2sinxsiny/cosx cosy - 4cosxcosy/cosx cosy

sinx/cosx + 3siny/cosy = 2tanxtany - 4

tanx +3tany =  2tanxtany - 4

Collect like terms

tanx - 2tanxtany = -4 - 3tany

- 2tanxtany+3tany = -4 - tanx

tany (-2tanx+3) = -4 - tanx

tan y = -4 - tanx/-2tanx+3

tan y = -(4+tanx)/-(2tanx-3)

tany = 4 + tanx /2tanx - 3

Hence the function of tany in term of tan x is tany = 4 + tanx /2tanx - 3

The scale factor of the the larger triangle to the smaller triangle is: 3.25.

When a figure is dilated, the figure is enlarged or reduced. The scale factor is calculated as: dimension of the new figure / corresponding dimension of the old figure.

Find the scale factor of the larger triangle to the smaller triangle:

One dimension of the larger triangle = 13

Corresponding dimension of the smaller triangle = 4

Scale factor of the dilation = 13/4

Scale factor of the dilation = 3.25

Therefore, the scale factor of the the larger triangle to the smaller triangle is: 3.25.

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9514 1404 393

Answer:

  (c)  1

Step-by-step explanation:

To find f(-2), locate -2 in the x column. Then find the corresponding f(x) value.

 -2 is in the second row, opposite f(x) = 1, so f(-2) = 1.

Answer: c

Step-by-step explanation:

Answer:

12 grams of fibre

Step-by-step explanation:

4 {times} 3

The sine of the other acute angle is 15/17 if the cosine of one acute angle of a right triangle is 8/17.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have a cosine of one acute angle of a right triangle is 8/17.

Let's suppose the angle is α

\(\rm Cos\alpha = \frac{8}{17}\)

As we know the cos is the ratio of adjacent to hypotenuse and Sin is the ratio of the opposite to hypotenuse.

Let's suppose the length of the hypotenuse is x units

From the Pythagoras theorem:

\(\rm 17^2=x^2+8^2\)

x = 15 units

Now the Sin ratio:

\(\rm Sin\alpha = \frac{15}{17}\)

Thus, the sine of the other acute angle is 15/17 if the cosine of one acute angle of a right triangle is 8/17.

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The area of the rhombus is 832 square m if the length of the diagonals are 104 m and 16 m.

A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.

We have given a rhombus with diagonals.

The length of the long diagonal p = 2×52 = 104 m

The length of the short diagonal q = 2×8 = 16 m

Area = pq/2 = (104×16)/2 = 832 square m

Thus, the area of the rhombus is 832 square m if the length of the diagonals are 104 m and 16 m.

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The root of the function \(\(f(x) = 5\cos(x) - \sqrt{x^2 + 1} + 2^{x-1}\)\) lies within the interval \(\([-1, 0]\)\).

To find the interval where the root of the given function lies, we need to analyze the behavior of the function within certain intervals. Let's consider the interval  \(\([-1, 0]\)\).. For \(\(x = -1\)\), we have \(\(f(-1) = 5\cos(-1) - \sqrt{(-1)^2 + 1} + 2^{-2}\)\). Since \(\(\cos(-1)\)\) is positive and the other terms are also positive, the value of \(\(f(-1)\)\) is positive.

Now, for \(\(x = 0\)\), we have \(\(f(0) = 5\cos(0) - \sqrt{0^2 + 1} + 2^{-1}\)\). Since \(\(\cos(0)\)\) is positive and the other terms are positive, the value of \(\(f(0)\)\) is positive.

As the function is continuous, and it changes sign from positive to negative within the interval  \(\([-1, 0]\)\) (as \(\(f(-1)\)\) and \(\(f(0)\)\) have different signs), by the Intermediate Value Theorem, there exists at least one root of the function within this interval. Therefore, we can conclude that the root of \(\(f(x)\)\) lies within the interval  \(\([-1, 0]\)\).

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The radius of the semicircle that will make the rectangular region a maximum is 40 feet.

The physical fitness room consists of a rectangular region with a semicircle at each end, and the perimeter of the room is a 200ft running track. To maximize the rectangular region, you need to find the radius of the semicircle.

Let the radius of the semicircle be r and the length and width of the rectangle be L and W, respectively. Since there are two semicircles, the total length of their circumferences is equal to the full circle with radius r. Therefore, the perimeter of the room can be expressed as:

Perimeter = L + 2W + πr = 200

To maximize the rectangular area (A = L * W), we should express either L or W in terms of r and use calculus to find the maximum. Let's express W in terms of r:

W = (200 - L - πr) / 2

Now, we can find the area:

A = L * W = L * (200 - L - πr) / 2

To find the maximum area, take the derivative of A with respect to L and set it to zero:

dA/dL = (200 - 2L - πr) / 2 = 0

Solve for L:

L = (200 - πr) / 2

Since L is the length of the rectangle, it must equal the diameter of the semicircles (2r):

2r = (200 - πr) / 2

Solve for r:

4r = 200 - πr
5r = 200
r = 40 ft

Thus, the radius of the semicircle that will make the rectangular region a maximum is 40 feet.

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Answer: La Conferencia de las Naciones Unidas sobre el Desarrollo Sostenible (Río+20) representa una gran oportunidad para que el mundo reconozca y aproveche los vínculos inextricables que existen entre la salud humana y el desarrollo sostenible.

Step-by-step explanation:

A histogram is a column chart that displays the frequency of occurrence on the vertical axis.

In a histogram, the horizontal axis represents the range or categories of data, and the vertical axis represents the frequency or count of data falling within each range or category. The height of each column in the histogram corresponds to the frequency or count of data in that particular range or category.

Histograms are commonly used to visualize the distribution of numerical data and provide insights into the shape, center, and spread of the data. They are particularly useful in identifying patterns, outliers, and understanding the overall distributional characteristics of a dataset.

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The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.

Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:

x² + (LV/2)² = DV²/4

y² + (OE/2)² = LE²/4

Simplifying each equation and substituting the given values, we get:

x² + (LV/2)² = 81/4

y² + (OE/2)² = 225/4

We also know that the diagonals bisect each other, so we can set up another equation:

LV/2 + OE/2 = LO = VE

Substituting the given value for LE, we get:

LV/2 + OE/2 = 15

Solving this equation for one of the variables, we get:

LV = 30 - OE

Substituting this expression into the first equation above, we get:

x² + ((30 - OE)/2)² = 81/4

Simplifying and rearranging, we get:

OE² - 60OE + 675 = 0

Using the quadratic formula, we get:

OE = (60 ± √(3600 - 2700)) / 2

OE = 15 or 45

If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:

x² + 7.5² = 81/4

y² + 7.5² = 225/4

Solving these equations, we get:

x = 3√7

y = 9/√7

If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:

LV = OE = 15

x = 3√7

y = 9/√7

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Complete question:

LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.

Answer:

16000=140x

It will take 90 minutes to hit 12,600 ft above ground.

Step-by-step explanation:

Just swap out 16000 for 12600. Then solve from there.

Hope it helped!

if H is the midpoint of IJ, and IH = 0.75, then the length HJ is 0.75 units.

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

We are given that;

Midpoint of Line  IJ is point H. This means that the line is divided equally into

This means that IH must be equal to HJ.

Now, we are given that the length of IH is equal to 0.75. Thus, from deductions above we can say that;

IH = HJ = 0.75 Units

Thus, we conclude that if H is the midpoint of IJ, and IH = 0.75, then the length HJ is 0.75 units.

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Divide the number of micrometers by 10,000 to get the equivalent number of centimeters.

To convert micrometers to centimeters, you need to use the conversion factor between the two units. There are 10,000 micrometers in a centimeter.

Here are the steps to convert micrometers to centimeters:

1. Start with the number of micrometers you want to convert.
2. Divide the number of micrometers by 10,000 to get the equivalent number of centimeters.
3. The result is the number of centimeters equivalent to the given number of micrometers.

For example, if you want to convert 50,000 micrometers to centimeters, you would divide 50,000 by 10,000 to get 5 centimeters.

So, the conversion formula is:

centimeters = micrometers ÷ 10,000

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Answer:

The gradient of the line segment between the two points is -1

Step-by-step explanation:

The gradient of the line segment between two points is also known as the slope,

We  can find this by using the formula; y₂ - y₁ /  x₂ - x₁

The points given to us are;(-1,2) and (-2,3).

This implies x₁ = -1  ,     y₁=2         x₂ =  -2        y₂= 3

We can now proceed to insert our values into the formula;

Gradient = y₂ - y₁ /  x₂ - x₁

               = 3 - 2  /  -2-(-1)

                = 1  /  -2 + 1

                 =1/-1

Gradient = -1

Therefore the gradient of the line segment between the two points is -1

Heyy I'm the person who helped you with the test. Anyway I disagree with the person who answered on top. The correct answer is -5/2!

The value of the z-score in a hypothesis test is influenced by the size of the treatment effect, the population standard deviation, and the number of scores in the sample.

Increasing the size of the treatment effect will increase the z-score. A larger treatment effect means a larger difference between the sample mean and the hypothesized population mean, resulting in a larger z-score. This indicates stronger evidence against the null hypothesis.

Increasing the population standard deviation will increase the variability in the data, leading to a larger standard error and a larger z-score. A larger standard deviation means the data points are more spread out from the mean, making it easier to detect significant differences.

Increasing the number of scores in the sample will decrease the standard error and the z-score. With a larger sample size, the estimate of the population mean becomes more precise, reducing the variability and resulting in a smaller standard error. Consequently, the z-score decreases, indicating a smaller deviation from the hypothesized mean.

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Answer:

A) the fraction of the week that Jamaar spent in this garden.

The interpretation would be: "Based on the given sample data, we are 95% confident that the true proportion of defectives in the circuits lies between the lower bound and the upper bound of the confidence interval."

To test the hypothesis H0: p = 0.05 versus H1: p ≠ 0.05, where p represents the proportion of defectives in the circuits, we can use the binomial distribution and perform a two-tailed test. Here's how you can calculate the P-value and answer part (a):

(a) Calculating the P-value:

Define the null hypothesis (H0): p = 0.05.

Calculate the sample proportion of defectives: P = x/n, where x is the number of defectives (13) and n is the sample size (300). In this case, P = 13/300 = 0.0433.

Calculate the test statistic (z-score) using the formula:

z = (P - p0) / sqrt[(p0 * (1 - p0)) / n]

where p0 is the hypothesized proportion under the null hypothesis. In this case, p0 = 0.05 and n = 300.

z = (0.0433 - 0.05) / sqrt[(0.05 * (1 - 0.05)) / 300] ≈ -0.6147

Determine the P-value by comparing the absolute value of the test statistic to the standard normal distribution (z-distribution) at the desired significance level (α = 0.05).

Since this is a two-tailed test, we need to find the area in both tails.

P-value = 2 * P(Z < -0.6147), where Z is the standard normal random variable.

Using a statistical table or calculator, you can find the P-value to be approximately 0.5397.

Therefore, the P-value for the test is approximately 0.5397.

(b) Using a confidence interval:

Alternatively, you can answer the question using a confidence interval. A confidence interval provides a range of plausible values for the true proportion of defectives.

To construct a confidence interval for the proportion, you can use the following formula:

CI = P ± z * sqrt((P * (1 - P / n),

where CI represents the confidence interval, P is the sample proportion of defectives, z is the critical value corresponding to the desired level of confidence, and n is the sample size.

For example, to construct a 95% confidence interval (α = 0.05), the critical value z is approximately 1.96.

CI = 0.0433 ± 1.96 * sqrt((0.0433 * (1 - 0.0433)) / 300)

By calculating this, you can find the lower and upper bounds of the confidence interval.

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Answer:

the length— 6

width— is 9

Step-by-step explanation:

you said One side— 3m MORE

so we will consider the length Number as X

we will consider width As three plus X

- You want to know the Perimeter. So we have to

add.

— so the expression is 3+3+x+x+x+x = 30

it is then simplified to 6+4x= 30

then we should be able to find out the X  which is 6

when we substitute the values with dimensions, you will get

your final Answer

I hope This Helped!

Answer:

i believe the answer is 2 and 3

Step-by-step explanation:

Hope that helps!

Answer:

D. 2 and 3

Step-by-step explanation:

vertical angles are opposite angles made by two intersecting lines

The correct option for this question is option D. 2 more than the exponent.

An exponent is a number that indicates how many times a base number should be multiplied by itself.

For example, in the expression "x^3", the exponent is 3, and it means that the base number "x" should be multiplied by itself 3 times.

In other words, "x^3" is equivalent to "xxx". The base number is usually written in the base of the expression, and the exponent is written as a superscript.

The number of zeros in the product of 20 and 105 is 2 more than the exponent. This is because 20 has two zeros at the end and 105 has one zero at the end, for a total of 3 zeros. The exponent, in this case, is 1, because there is only one factor of 10 in the product (10 is being multiplied by itself once).

Therefore, the number of zeros in the product is 2 more than the exponent.

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