How many degrees would a trapezoid need to be rotated to carry it onto itself? A) 45° B) 90° C) 180° D) 360°

Answer:

Cos² x

Step-by-step explanation:

    \(\sf Cos^2 \ x *Csc^2 \ x-Cos^2 \ x *Cot^2 \ x = Cos^2 \ x (Csc^2 \ x - Cot^2 \ x)\)

                                                        \(\sf = Cos^2 \ x \left(\dfrac{1}{Sin^2 \ x} - \dfrac{Cos^2 \ x}{Sin^2 \ x}\right)\\\\= Cos^2 \ x \left(\dfrac{1-Cos^2 \ x}{Sin^2 \ x}\right)\\\\\boxed{\bf Indentity: \ 1 - Cos^2 \ x = Sin^2 \ x}\\\\\\= Cos^2 \ x \left(\dfrac{Sin^2 \ x}{Sin^2 \ x}\right)\\\\= Cos^2 \ x\)

Answer:

47

Step-by-step explanation:

they are corresponding

According to the question At least 16 days must pass before the class must repeat a seating arrangement.

To determine the number of days that must pass before the class must repeat a seating arrangement, we can consider the concept of permutations.

In the given scenario, there are 8 students and 8 desks, and we want to find out how many different seating arrangements are possible.

The first student can choose any of the 8 desks, the second student can choose any of the remaining 7 desks, the third student can choose any of the remaining 6 desks, and so on.

Therefore, the total number of seating arrangements is given by the product of the numbers from 8 down to 1, which can be calculated as 8 factorial (8!). Mathematically, it can be represented as:

\(\(8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40,320\)\)

So, there are 40,320 different seating arrangements possible.

Now, to find the number of days that must pass before the class must repeat a seating arrangement, we can use the concept of the pigeonhole principle. According to this principle, if we have more items (seating arrangements) than the number of containers (days), at least two items must occupy the same container.

Since there are 40,320 seating arrangements and we want to find the minimum number of days, we can use the formula for finding the minimum number of containers required for a given number of items:

\(\( \text{Minimum number of containers} = \lceil \log_2 (\text{number of items}) \rceil \)\)

Using this formula, we can calculate the minimum number of days required:

\(\( \text{Minimum number of days} = \lceil \log_2 (40,320) \rceil = 16 \)\)

Therefore, at least 16 days must pass before the class must repeat a seating arrangement.

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Answer:

. g bdhdjejbzjehshsuhrbxhhdhsgusuedhhdhdbdhejdbxbrjnxc

Answer:

Step-by-step explanation:

Let's solve your equation step-by-step.

−6(x+1)=2(1−3x)−7

Step 1: Simplify both sides of the equation.

−6(x+1)=2(1−3x)−7

(−6)(x)+(−6)(1)=(2)(1)+(2)(−3x)+−7(Distribute)

−6x+−6=2+−6x+−7

−6x−6=(−6x)+(2+−7)(Combine Like Terms)

−6x−6=−6x+−5

−6x−6=−6x−5

Step 2: Add 6x to both sides.

−6x−6+6x=−6x−5+6x

−6=−5

Step 3: Add 6 to both sides.

−6+6=−5+6

0=1

Answer:

There are no solutions.

Answer:

0x = +1

Step-by-step explanation:

–6(x + 1) = 2(1 – 3x) – 7

–6x –6 = 2 – 6x – 7

– 6x –6 = –6x + 2 – 7

–6x – 6 = – 6x – 5

–6x + 6x = – 5 + 6

0 = +1

This means that there is no solution for x

Answer: 14085 m^3.

Step-by-step explanation: To find the volume of a right rectangular prism, you need to multiply the length, width, and height.  The equation is below:

l x w x h = V where l is the length, w is the width, h is the height, and V is the volume of the right rectangular prism.

The length of this recycling bin is 9 meters, the width is 5 meters, and the height is 313 meters.  Now that we know the length, width, and height, we can substitute the variables with the information we've gathered.

9 x 5 x 313 = 14085.

Therefore, 14085 m^3 is your answer.

Have a great day! :)

Answer:

Y'(-5, 5)

Step-by-step explanation:

To find the coordinates of Y' after the translation, we apply the given rule to the coordinates of point Y(-3, 4).

Using the translation rule (x, y) → (x - 2, y + 1), we can substitute the coordinates of Y(-3, 4) into the rule:

x' = x - 2 = -3 - 2 = -5

y' = y + 1 = 4 + 1 = 5

Therefore, the coordinates of Y' are (-5, 5).

The probability of selecting exactly 2 refurbished computers out of the 6 chosen computers ≈ 0.00004714.

To compute the probability that among the chosen computers, two are refurbished, we can use the concept of combinations and the probability formula.

Total number of computers in the store: 30

Number of brand new computers: 22

Number of refurbished computers: 8

We need to select 6 computers randomly, and we want to find the probability of selecting exactly 2 refurbished computers.

The probability of selecting 2 refurbished computers out of 6 can be calculated as follows:

Probability = (Number of ways to select 2 refurbished computers) / (Total number of ways to select 6 computers)

To calculate the number of ways to select 2 refurbished computers, we can use combinations:

Number of ways to select 2 refurbished computers = C(8, 2)

= 8! / (2! * (8-2)!) = 28

To calculate the total number of ways to select 6 computers from the store, we can use combinations again:

Total number of ways to select 6 computers = C(30, 6)

= 30! / (6! * (30-6)!) = 593775

Substituting these values into the probability formula:

Probability = 28 / 593775 ≈ 0.00004714

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Answer:

-15°

Step-by-step explanation:

We know that at 7 pm it started at -6°, and that every 2 hours until 2 am, it dropped by 2 degrees.

From that we can form this expression:

-6-2x, with x being the number of hours it dropped.

From 7 pm to 2 am is 7 hours, therefore -6-2(7) = -20°

From 2 am until 7 am, it began raising 1 degree per hour.

We can write that as:

-20 + x, with x being the number of hours it went up.

From 2 am to 7 am is 5 hours:

-20 + 5 = -15°

Therefore, the temperature at 7 am is -15°.

If we have the triangle ABC and we want to obtain the triangle DEF, we need to multiply every side of the triangle ABC by 3 as:

5 * 3 = 15

4 * 3 = 12

3 * 3 = 9

So, the scale factor of triangle ABC to triangle DEF is 3

Answer: 3

To calculate the probability that no letters are repeated when 7 letters are typed, we need to consider the number of possible arrangements without repetition and divide it by the total number of possible arrangements with repetition. The probability can be determined by calculating the ratio of these two quantities.

When 7 letters are typed without repetition, the first letter can be chosen from all 26 alphabets, the second letter from the remaining 25, the third from 24, and so on. This can be calculated as 26 x 25 x 24 x 23 x 22 x 21 x 20 = 17,748,480.

On the other hand, if 7 letters are typed with repetition allowed, each letter can be chosen from the 26 alphabets independently, resulting in 26 x 26 x 26 x 26 x 26 x 26 x 26 = 26^7 = 8,031,810,176.

Therefore, the probability that no letters are repeated is given by 17,748,480 / 8,031,810,176 ≈ 0.002213 (rounded to the nearest thousandth).

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

total bricks = 5500

# bricks per horizontal layer = 321

Step 02:

long division:

we must analyze the division to find the solution.

total horizontal layers of bricks = 17

total remaining bricks = 43

The answer is:

total horizontal layers of bricks = 17

total remaining bricks = 43

Answer:

8 boxes

Step-by-step explanation:

The amount of blueberry muffins doesn't matter. You only need 96 muffins, and 12 muffins in each box.

For the answer, you will have to divide m, muffins, by b, boxes.

m/b = 96/12

96/12 = 8

↝ Quadratic Function has the domain of all real numbers. (Even not given the specific domain.)

↝ The equation \(y=-3(x-5)+8\) is a parabola with (5,8) as a vertex. We call the equation \(y=a(x-h)^2+k\) as vertex equation.

The domain of -3(x-5)+8 is all set of real numbers.

↝ Interval Notation ↝

Since the domain of the equation is set of all real numbers.

Therefore, the domain is x ∈ R or (-∞,∞) or -∞<x<∞

There of them work. Recall that the domain of quadratic function is all set of real numbers.

Answer:

Step-by-step explanation:

F

                 ______________              _______. F f f f f.  F

Answer:a

Step-by-step explanation:

no me aparec e nada lo siento

Answer: x = \(\sqrt{y^2 -1}\)

Step-by-step explanation:

When interpreting the expression as \((tanx)^{(sinx)\), the limit using L'Hospital's Rule is -∞ as x approaches 0+. However, when interpreting the expression as\(tan(x^{sinx})\), the limit is not well-defined due to the indeterminate form of 0^0.

To calculate the limit using L'Hospital's Rule, let's consider both interpretations of the expression and find the limits for each case:

Case 1: lim\((tanx)^{(sinx)\) as x approaches 0+

Taking the natural logarithm of the expression, we have:

\(ln[(tanx)^{(sinx)}] = sinx * ln(tanx)\)

Now, we can rewrite the expression as:

\(lim [sinx * ln(tanx)]\)as x approaches 0+

Applying L'Hospital's Rule, we differentiate the numerator and denominator:

\(lim [(cosx * ln(tanx)) + (sinx * sec^{2}(x))] / (1 / tanx)\) as x approaches 0+

Simplifying the expression:

\(lim [cosx * ln(tanx) + sinx * sec^{2}(x)] * tanx\) as x approaches 0+

\(lim [cosx * ln(tanx) + sinx * sec^{2}(x)] * (sinx / cosx)\) as x approaches 0+

\(lim [(cosx * ln(tanx) + sinx * sec^{2}(x)) / cosx] * sinx\) as x approaches 0+

\(lim [ln(tanx) + (sinx / cosx) * sec^{2}(x)] * sinx\) as x approaches 0+

\(lim [ln(tanx) + tanx * sec^{2}(x)] * sinx\) as x approaches 0+

Since lim ln(tanx) as x approaches 0+ = -∞ and\(lim (tanx * sec^{2}(x))\) as x approaches 0+ = 0, we have:

\(lim [ln(tanx) + tanx * sec^{2}(x)] * sinx\) as x approaches 0+ = -∞

Therefore, the limit of \((tanx)^{(sinx)\) as x approaches 0+ using L'Hospital's Rule is -∞.

Case 2: lim\(tan(x^{sinx})\)as x approaches 0+

We can rewrite the expression as:

lim\(tan(x^{(sinx)})\) as x approaches 0+

This expression does not have an indeterminate form of \(0^0\), so we do not need to use L'Hospital's Rule. Instead, we can substitute x = 0 directly into the expression:

lim \(tan(0^{(sin0)})\) as x approaches 0+

lim\(tan(0^0)\)as x approaches 0+

The value of \(0^0\) is considered an indeterminate form, so we cannot determine its value directly. The limit in this case is not well-defined.

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Answer:

Equation: 2x+1 = 53 (x is 26)

Integers: 26, 27

Step-by-step explanation:

53 is the sum of 2 consecutive integers. That means one of the integers is one larger than the other. This means that twice one integer plus one equals 53, so the equation becomes x + (x + 1) = 53.

x + (x+1) = 53

Combine x and x to get 2x.

2x + 1 = 53

Subtract 1 from both sides to cancel the +1.

2x = 52

Divide both sides by 2 to undo the multiplication by 2.

x = 26

With this we know the first integer is 26. The second is one more than that, so that's 27. So the two integers here are 26 and 27.

The cross-sectional area of a sphere that passes through its center is a circle with a diameter equal to the diameter of the sphere. In this case, the diameter of the sphere is 6.69 meters * 2 = 13.38 meters.

The formula for the area of a circle is: A = π * r^2, where r is the radius.

Therefore, the cross-sectional area of the sphere that passes through its center is: A = π * (13.38/2)^2 = π * (6.69)^2 = 136.57 square meters.

A sphere is a three-dimensional shape that has a uniform, rounded surface that is symmetrical in all directions. When you cut a sphere through its center, you get a cross-sectional area that is a circle.

This is because a sphere can be thought of as a set of circular cross-sections that are concentric with each other and with the center of the sphere.

The cross-sectional area of the sphere that passes through its center is called the central cross-section of the sphere. It has the same diameter as the sphere itself and its area can be calculated using the formula for the area of a circle: A = π * r^2, where r is the radius of the circle.

In this case, the sphere has a radius of 6.69 meters, which means that its diameter is 6.69 * 2 = 13.38 meters.

The radius of the central cross-section of the sphere is half of the diameter, which is 6.69 meters. Therefore, the area of the central cross-section of the sphere is: A = π * (6.69)^2 = 136.57 square meters.

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The mean of the new distribution will be 33 after the addition of 3 points to each score.

Here, correct option will be:- b. 33

The mean of a population is a measure of central tendency that provides an average of the data within a data set. In this question, we are given the mean of a population as 30 and are asked to determine the mean of the new distribution after 3 points have been added to each score.

To answer this question, we must recognize that adding 3 points to each score in the population will increase the mean of the population by 3 points.

Therefore, the new mean of the distribution will be 33 i.e option b. This is because the addition of 3 points to each score will increase the total sum of all the scores, which will in turn increase the mean of the population.

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Answer:

(0, 4.5)

Step-by-step explanation:

*The equation can be put into Desmos, to find the point, but the work to prove it is here*

f(x)=c/1+Ae^-Bx

Y=C

C=18      A=3      -B=-0.1

*Replace x with 0 in the equation, so you know 0 is the x value, and it leads you to the y value*

f(0)=18/1+3e^-o.1(0)

= 18/1+3e^0

=18/1+3(1)

=18/1+3

=18/4

=4.5

x=0    y=4.5

Maximum growth rate = (x,y) --> (0, 4.5)

Hope this helps:))!!

The actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

The margin of error in the report stating that a 10-year-old American child spends an average of 20.02 to 25.36 minutes playing outdoors per day can be calculated by subtracting the lower value from the higher value and dividing by 2. In this case, the margin of error is :

To find the margin of error, we need to calculate the halfway point between these two values.
(25.36 - 20.02) / 2 = 2.67

Therefore, the margin of error is approximately 2.67 minutes. This means that the actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

Thus, the actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

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The given homogeneous system of equations can be represented as a matrix equation Ax = 0, where A is the coefficient matrix and x is the vector of variables.

To find the solution set in parametric vector form, we can perform row operations on the augmented matrix [A|0] and express the variables in terms of free parameters.

The augmented matrix for the given system is:

[3 3 6 | 0]

[-9 -9 -18 | 0]

[0 -7 -7 | 0]

Using row operations, we can transform this matrix to row-echelon form:

[3 3 6 | 0]

[0 -6 -12 | 0]

[0 0 -7 | 0]

Now, we can express the variables in terms of free parameters. Let x2 = t and x3 = s, where t and s are arbitrary parameters. Solving for x1 in the first row, we get x1 = -2t - 2s.

Therefore, the solution set in parametric vector form is:

x = [-2t - 2s, t, s], where t and s are arbitrary parameters.

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a brick staircase has a total of number of 12 steps. the bottom step requires 100 bricks.A total of 246 bricks are required to build the staircase.

The total number of steps in the brick staircase is 12. The bottom step requires 100 bricks. Each successive step requires 4 less bricks than the prior one. Therefore, the number of bricks required to build the staircase can be calculated as follows:

The first step requires 100 bricks.

The second step requires 96 bricks (100 - 4 = 96).

The third step requires 92 bricks (96 - 4 = 92).

This pattern continues until all 12 steps are accounted for.

Adding the number of bricks required for each step gives a total of 246 bricks required to build the entire staircase.

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Answer:

The value of x is 4%

Transformation of a function is shifting the function from its original place in the graph.

The functions have a maximum and are transformed to the left and down of the parent function are,

\(q(x) = -5(x +10)^2 -1\)

\(t(x) = -2x^2 - 4x - 3\)

Thus the option B and E is correct.

Transformation of a function is shifting the function from its original place in the graph.

Types of transformation-

Given information-

The given function in the problem is,

\(f(x)=x^2\)

The functions have a maximum and are transformed to the left and down of the parent function.

In the option B the function is shifted 10 units left and 1 units down as,

\(q(x) = -5(x +10)^2 -1\)

Thus the option B is the correct option.

In the option E the function is shifted 1 units left and 2 units down as,

\(t(x) = -2x^2 - 4x - 3\\t(x)=-2x^2 - 4x - 1-2\\t(x)=-2(x+1)^2-2\)

Thus the option E is the correct option.

Hence, the functions have a maximum and are transformed to the left and down of the parent function are,

\(q(x) = -5(x +10)^2 -1\)

\(t(x) = -2x^2 - 4x - 3\)

Thus the option B and E is correct.

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Answer:

Option (2).

Step-by-step explanation:

In the figure attached,

PB is a tangent and m(arc VU)= 80°, m(arc ST) = 40°

By theorem of angle between intersecting secants,

"If two secants have been drawn to a circle from a point outside the circle, then the angle between the secants will measure the half of the difference of the intercepted arcs."

\((m\angle 1)=\frac{1}{2}(m\widehat{VU}-m\widehat{ST})\)

          \(=\frac{1}{2}(80-40)\)

          = 20°

Therefore, Option (2) will be the answer.

The value for t is -1.19, indicating a negative difference between the means of the two conditions. This suggests that, on average, individuals remembered fewer words in the drug condition compared to the placebo condition.

To calculate the value of t, we need to perform a paired samples t-test. This test compares the means of two related groups, in this case, the scores of individuals in the drug condition versus the placebo condition. The formula for calculating t in a paired samples t-test is t = (mean difference) / (standard deviation of the differences / √(sample size)).

First, we need to calculate the mean difference between the two conditions. Taking the difference between the scores of each individual in the drug and placebo conditions, we get the following differences:

2, 2, 2, 1, and -1. The mean difference is (2 + 2 + 2 + 1 - 1) / 5 = 2/5 = 0.4.

Next, we calculate the standard deviation of the differences. To do this, we first calculate the squared differences:

4, 4, 4, 1, and 1. Taking the average of these squared differences, we get (4 + 4 + 4 + 1 + 1) / 5 = 14 / 5 = 2.8. Finally, we take the square root of 2.8, which is approximately 1.67.

Now, we can calculate t using the formula mentioned earlier. t = 0.4 / (1.67 / √5) = -1.19.

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