Given the following triangle, which Trig function would you use to solve for the missing side length? *


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Sine
Cosine
Tangent

The velocity of the particle at time t is given by v(t) = (2t² + 1)i + (3t² - 1)j + (tk + 1)k, where t is the time. It represents the motion of the particle in three-dimensional space.

To find the velocity of the particle at time t, we need to integrate the acceleration vector with respect to time.

To find the velocity vector v(t), we integrate each component of the acceleration vector:

∫a(t) dt = ∫(4ti + 6tj + k) dt

Integrating each component separately:

∫(4ti) dt = 2t²i + C₁

∫(6tj) dt = 3t²j + C₁

∫k dt = tk + C₃

where C₁, C₂, and C₃ are constants of integration.

Combining the integrals, we have:

v(t) = (2t² + C₁)i + (3t² + C₂)j + (tk + C₃)k

Given that v(0) = i - j + k, we can substitute t = 0 into the velocity equation:

v(0) = (2(0)² + C1)i + (3(0)² + C₂)j + (0k + C₃)k

i - j + k = C₁i + C₂j + C₃k

Comparing the coefficients, we get:

C₁ = 1

C₂ = -1

C₃ = 1

Substituting these values back into the velocity equation:

v(t) = (2t² + 1)i + (3t² - 1)j + (tk + 1)k

Therefore, the velocity of the particle at time t is given by:

v(t) = (2t² + 1)i + (3t² - 1)j + (tk + 1)k

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Answer:

\( ( \sqrt{x + 10 - 1} ) {}^{2} = x { }^{2} \\ \\ x + 10 - 1 = x { }^{2} \\ x + 10 = x {}^{2} + 1\)

If 2 layers will fill the entire truck then the volume of the truck is 16 cubic meters.

Since the floor of the truck can be completely covered with a layer of 8 boxes, we know that the area of the truck's floor is equal to the total area of 8 boxes.

The volume of each box is one cubic meter, which means each box has a height, length, and width of 1 meter. Therefore, the area of the truck's floor is 8 square meters (8 boxes x 1 square meter per box).

If two layers of boxes will fill the entire truck, we need to multiply the area of the truck's floor by the height of two layers. Since each box has a height of 1 meter, the height of two layers will be 2 meters.

The volume of the truck = Area of the floor x Height

Volume of the truck = 8 square meters x 2 meters

Volume of the truck = 16 cubic meters

Therefore, the volume of the truck is 16 cubic meters.

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Given

Find

Express as a single term

Explanation

now,

Final Answer

Therefore, the single expression is

The solution to the equation is p = -72.

The equation, we need to isolate the variable 'p' on one side of the equation. Let's go through the steps:

-p/12 = 6

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

12 * (-p/12) = 12 * 6

This simplifies to:

-p = 72

To isolate 'p,' we can multiply both sides of the equation by -1:

(-1) * (-p) = (-1) * 72

This gives us:

p = -72

Therefore, the solution to the equation is p = -72.

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Answer:

They are parallel because they have the same slope.

Step-by-step explanation:

Both equations have a slope of 3.

The function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.

From the complete information, it should be noted that the function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.

Also, f(x) = x³ and g(x) = |x|³ are not equal. This is because both functions are not equal for x < 0. This can be illustrated when x = -1. In this case, f(x) = -1 and g(x) = 1.

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The function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.

Two functions are equal if they have the same domain and codomain and their values are the same for all elements of the domain.

The function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.

Also, f(x) = x³ and g(x) = |x|³ are not equal.

This is because both functions are not equal for x < 0.

This can be illustrated when x = -1. In this case, f(x) = -1 and g(x) = 1.

Hence, the function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.

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Answer:

o

Step-by-step explanation:

Yes, 2/5 times x  always represent 40 percent of that number.

A percentage is a way of expressing a portion or fraction of a whole as a quantity out of 100. It is represented by the symbol "%". For example, 25% is equivalent to 25 out of 100, or 0.25 as a decimal

To convert a fraction to a percentage, you need to multiply it by 100. So, 2/5 times x can be written as:

(2/5) x 100% = 40% of x

So, when x represents a number, then 2/5 times x will represent exactly 40% of that number.

 For example, if x=7, then 2/5 times x is (2/5) x 7 = 2.8, which is exactly 40% of 7 (which is 2.8/7 = 40/100 = 0.4 or 40%).

So, in general, 2/5 times x will represent 40% of x .

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Answer:

\( \frac{1}{20} \)

Step-by-step explanation:

\(1. \: \frac{3}{4} \times \frac{1}{15} \\ 2. \: \frac{3 \times 1}{4 \times 15} \\ 3. \: \frac{3}{4 \times 15} \\ 4. \: \frac{3}{60} \\ 5. \: \frac{1}{20} = 0.05\)

Answer:

56 degrees

Step-by-step explanation:

the total sum of the angles in a triangle is 180

90+34+b=180

b=180-124

=56

Answer:

56°

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°.

The triangle shown in the image is a right triangle so one of the angle measure is 90°.

Given, the other angle is 34°, we can find the value of missing angle with the following equation:

x + 90° + 34° = 180°

x + 124° = 180°

x = 56°

Answer:

In order - Not statistical, statistical, statistical, statistical, statistical, statistical

Step-by-step explanation:

A statistical question is one which has answers based on the gathering of data (possibly multiple answers).

A non statistical question is one which requires no data gathering, and has only one answer.

The null hypothesis get rejected comparing the 95% confidence interval to the proportion of the given central valley residents and bay area residents .

As given in the question,

Total number of voters in California = 7525

x₁ = Number of voters of central valley residents approved California legislature

   = 68

n₁ = Total number of voters of central valley residents

   = 200

x₂ = Number of voters of bay area residents approved California legislature

   = 156

n₂= Total number of voters of bay area residents

   = 300

p₁ = proportion of voters of central valley

p₂= proportion of voters of bay area

p₁ = x₁/ n₁

   = 68/200

   = 0.34

p₂ = x₂/n₂

    = 156/300

    = 0.52

Standard error = √p₁(1 -p₁) / n₁ + p₂( 1- p₂)/n₂

                        = √0.34(1-0.34) / 200 + 0.52(1-0.52)/ 300

                        = √0.001122 + 0.000832

                        = 0.044

\(p_{w}\) = (68 + 156 )/ (200 + 300)

   = 0.448

\(q_{w} = 1- p_{w}\)

    = 1 - 0.448

    = 0.552

null hypothesis p₁ - p₂ = 0

z = ( 0.52 - 0.34 ) - 0/ √(0.448)(0.552)( 1/200 + 1/300)

  = 4

Tabular value for confidence interval 95% = 1.96

4 > 1.96

We reject the null hypothesis.

Therefore, the difference of proportion of central valley residents and the bay area residents rejection of null hypothesis as per given 95% confidence interval.

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Step-by-step explanation:

x1, y1 = (-5,-2)

slope,m = -6/5

general equation, y= MX + C

(y-y1)/(x-x1)=m

(y+2)/(x+5)=-6/5

5y+10=-6x-30

5y=-6x-40

y=-(6x/5) - 8

Answer:

20% increase good luckkkkk

Answer:

11.4

Step-by-step explanation:

Answer:

11.4

Step-by-step explanation:

The rate of change in the given graph is 21/4.

The rate of change defines the speed of a variable changes over another variable. On the given graph, we can calculate the rate of change using the formula:

Rate of change = Δy / Δx

To calculate the rate of change of the given graph, we need to identify 2 points first. We take:

(0, 0)

(4, 21)

Rate of change = Δy / Δx

Rate of change = y₂ - y₁

                             x₂ - x₁

Rate of change = 21 - 0

                               4 - 0

Rate of change = 21/4

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The correct statement regarding the congruence of the triangles in this problem is given as follows:

Yes, they are congruent by either ASA or AAS.

The Angle-Side-Angle (ASA) congruence theorem states that if any of the two angles on a triangle are the same, along with the side between them, then the two triangles are congruent.

The sum of the internal angles of a triangle is of 180º, hence the missing angle measure on the triangle to the right is given as follows:

180 - (85 + 42) = 53º.

Hence we have a congruent side between angles of 53º and 42º on each triangle, thus the ASA congruence theorem can be used for this problem.

As the three angle measures are equal for both triangles, and there is a congruent side, the AAS congruence theorem can also be used.

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Answer:

\(x=18\)

Step-by-step explanation:

By rearranging and multiplying by 6 at the end:

\(\frac{1}{2}x - 7 = \frac{1}{3}(x-12)\\\frac{1}{2}-7 = \frac{1}{3}x - 4\\\frac{1}{2}x - \frac{1}{3}x = -4 + 7\\(\frac{3}{6} - \frac{2}{6})x = 3\\\frac{1}{6}x = 3\\x = 3 \cdot 6 = 18\)

Answer:

5 / 56 or 0.089

Step-by-step explanation:

We are given 5 / 14 x 4

5 / 56

This cannot be further simplified, so 5 / 56 will be the answer, if you need the answer in a decimal form it will be 0.089

Answer:

Hence he will be 4 large containers and 4 small containers

Step-by-step explanation:

Given data

Let the number of small containers be x

and the number of large containers be y

x+y= 8---------1

also

2x+4y= 24-----2

the system of equation to solve the problem is

x+y= 8

2x+4y= 24

from 1

x=8-y

put this in 2

2(8-y)+4y= 24

16-2y+4y= 24

2y= 24-16

2y= 8

y= 8/2

y= 4

put y= 4 in 1

x+4=8

x= 8-4

x= 4

Hence he will be 4 large containers and 4 small containers

The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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(a) The probability that the proportion of successes in the sample will be between 0.27 and 0.34 (b) The probability that the proportion of successes in the sample will be between 0.27 and 0.34.

To solve this problem, we will use the normal approximation to the binomial distribution, since the sample size is large (n = 500 for part a and n = 200 for part b) and the conditions for the normal approximation are met.

The conditions for using the normal approximation to the binomial distribution are:

1. The sample is a simple random sample.

2. The sample size is sufficiently large (np ≥ 10 and n(1 - p) ≥ 10).

Given:

p = 0.30 (probability of success)

q = 1 - p = 0.70 (probability of failure)

n = 500 (sample size for part a)

n = 200 (sample size for part b)

(a) To calculate the probability that the proportion of successes in the sample will be between 0.27 and 0.34 when the sample size is 500, we need to calculate the z-scores corresponding to these proportions and use the standard normal distribution table.

First, we calculate the mean and standard deviation of the sampling distribution of the sample proportion:

mean (μ) = p = 0.30

standard deviation (σ) = sqrt((p * q) / n) = sqrt((0.30 * 0.70) / 500) ≈ 0.0203

Next, we calculate the z-scores for the lower and upper limits:

z1 = (0.27 - μ) / σ = (0.27 - 0.30) / 0.0203 ≈ -1.4764

z2 = (0.34 - μ) / σ = (0.34 - 0.30) / 0.0203 ≈ 1.9724

Using the standard normal distribution table or a calculator, we find the corresponding probabilities:

P(z1 ≤ Z ≤ z2) ≈ P(-1.4764 ≤ Z ≤ 1.9724) ≈ 0.9329 (rounded to four decimal places)

Therefore, the probability that the proportion of successes in the sample will be between 0.27 and 0.34 when the sample size is 500 is approximately 0.9329.

(b) To calculate the probability that the proportion of successes in the sample will be between 0.27 and 0.34 when the sample size is 200, we follow the same steps as in part (a), but with the updated sample size.

mean (μ) = p = 0.30

standard deviation (σ) = sqrt((p * q) / n) = sqrt((0.30 * 0.70) / 200) ≈ 0.0316

z1 = (0.27 - μ) / σ = (0.27 - 0.30) / 0.0316 ≈ -0.9487

z2 = (0.34 - μ) / σ = (0.34 - 0.30) / 0.0316 ≈ 1.2658

P(z1 ≤ Z ≤ z2) ≈ P(-0.9487 ≤ Z ≤ 1.2658) ≈ 0.8800 (rounded to four decimal places)

Therefore, the probability that the proportion of successes in the sample will be between 0.27 and 0.34 when the sample size is 200 is approximately 0.8800.

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Answer: 29

Step-by-step explanation:

From the question, we are informed that one serving of oatmeal has 9 grams of fiber, which is 31 % of the recommended daily amount.

Let the total recommended amount of fiber be represented by x. Therefore, 31% of x = 9

31/100 × x = 9

0.31 × x = 9

0.31x = 9

x = 9/0.31

x = 29

The recommended amount of river is 29gram

The perimeter of the resulting hexagon is 60 meters.

In this problem we find the perimeter of a regular hexagon, which is dilated around its center. Regular hexagons are polygons with six sides of equal length. Dilations are rigid operations of the form:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

The perimeter is the sum of the side lengths of the hexagon and by dilation we find the following relationship between original and resulting perimeters (p, p'):

p' = k · p

If we know that p = 45 and k = 4 / 3, then the resulting perimeter is:

p' = (4 / 3) · (45)

p' = 60

The resulting hexagon has a perimeter of 60 meters.

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Answer:

The simplified expression is sec^2a

Step-by-step explanation:

We can start by using the trigonometric identities:

cot^2 a + 1 = csc^2 a

tan^2 a + 1 = sec^2 a

Using these identities, we can rewrite the expression as:

(cos^2 a - cot^2 a)/(sin^2 a - tan^2 a)

= (cos^2 a - (csc^2 a - 1))/(sin^2 a - (sec^2 a - 1))

= (cos^2 a - csc^2 a + 1)/(sin^2 a - sec^2 a + 1)

Now we can use the identity:

sin^2 a + cos^2 a = 1

to rewrite the expression further:

= (1/sin^2 a - 1/sin^2 a cos^2 a)/(1/cos^2 a - 1/cos^2 a sin^2 a)

= (1 - cos^2 a)/(sin^2 a - sin^2 a cos^2 a)

= sin^2 a / sin^2 a (1 - cos^2 a)

= 1 / (1 - cos^2 a)

= sec^2 a

Therefore, the simplified expression is sec^2 a.

Answer:

1 and 3 so 3

Step-by-step explanation:

6:1,2,3,6

3:1,3

If you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.

A statement that upholds the equality of two mathematical expressions is known as an equation. An identity is a statement that is true regardless of the value of each variable. A conditional equation is one that only holds true for certain values of one or more variables.

On the other hand, an inequality is a claim that indicates that one quantity has a greater or lesser value than another using the symbols > for greater than or for lesser than. An inequality has values for every variable, much like an identity. It concentrates on two-variable inequalities with a single exponent.

If both sides of an inequality are multiplied or divided by a negative value, the inequality sign must be reversed. This is due to the fact that adding or subtracting a negative integer causes the numbers on the number line to appear in reverse order.

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