In ΔQRS, q = 960 cm, r = 420 cm and ∠S=31°. Find the area of ΔQRS, to the nearest square centimeter.

The value of cos θ is equal to 1/3 when sec θ= √6/2.

Since we are given the value of secant of theta, we can use the relationship between secant and cosine to find the value of cosine of theta.

Let's start by recalling the definitions of secant and cosine functions. The secant of an angle is defined as the reciprocal of the cosine of that angle.

In other words, secθ = 1/cosθ

Conversely, the cosine of an angle is defined as the reciprocal of the secant of that angle.

cosθ = 1/secθ

We are given that secθ= √6/2

We can use this value to find cosθ= 1/secθ

cosθ = 1 / (√6/2)

To simplify this expression, we can multiply both the numerator and denominator by 2/sqrt(6).

cosθ = ((2/√6) / (√6/2) * (2/√6))

cosθ = (2/√6) / 1

cosθ = (2/√6 * √6/√6)

cosθ = 2/6 = 1/3

Therefore, the value of cosθ is equal to 1/3 when secθ = sqrt(6)/2.

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Hence, the number of miles traveled by car, when it has gasoline of 15 gallons is 420 miles

Answer:

impossible

Step-by-step explanation:

a denominator can’t be equal to 0. So:

d ≠ 0 ; d ≠ 2

(10 + 4d - 8)/d(d-2) = 5d/ d(d-2)

4d + 2 = 5d

d = 2

But we have said that d can’t be equal to 2, so the equation is impossible.

Answer:

your picture is blank if you can fix it i will be glad to help you

Step-by-step explanation:

Answer:

First option

Step-by-step explanation:

The line corresponds to the f(x).

Hope this helps

Answer:

15 markers in all

Step-by-step explanation:

5 + 2 + 3 + 5 =

5 + 5 = 10

+

2 + 3 = 5

=

10 + 5 = 15

Brainliest Please!!

The length of the longest metal rod that can be sent in a 7-inch cube box is 12 inches.

To determine the length of the longest metal rod that can be sent in a 7-inch cube box, we need to consider the diagonal of the cube as the maximum length of the rod.

In a cube, the diagonal can be calculated using the Pythagorean theorem. The formula for the diagonal of a cube is:

diagonal = √(side^2 + side^2 + side^2)

Since we know that the cube has sides of 7 inches, we can substitute this value into the formula:

diagonal = √(7^2 + 7^2 + 7^2)

diagonal = √(49 + 49 + 49)

diagonal = √147

diagonal ≈ 12.124 inches

Therefore, the correct answer is:

12 inches

This means that the metal rod should not exceed 12 inches in length in order to fit inside the 7-inch cube box for shipping. Any rod longer than 12 inches would not be able to fit diagonally within the box.

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15,386 ft² an area of helicopter pad covers .

What does a circle's area mean?

The area a circle occupies in a two-dimensional plane is known as the area of the circle. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius.

                          Area is measured in square units, such as m2, cm2, etc. Where = 22/7 or 3.14, the area of a circle is equal to r2 or d2/4, in square units.

D = 140

r = 140/2 = 70

area of helicopter = πr²

                              = 3.14 ×70 × 70

                              = 15,386 ft²

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Answer:

$0.27875 or $0.28 1 cup = 2 ounces Number of cups in 1 jar = 4 ounce

Step-by-step explanation:

123,772.8.

Why do you need these answers so bad?

Answer:

Hope this helps :) 123,772.8.

Step-by-step explanation:

The given ratio of 0.42 to 1 means that for every 1 active subscription, there are 0.42 expired subscriptions.

What is a ratio?

The ratio is a comparison of two quantities that is expressed as a fraction. It is used to compare two values in mathematics. It is possible to write the ratio between a and b as:

a : b or a/b.

What does a ratio of 0.42 to 1 mean? The ratio of 0.42 to 1 means that there are 0.42 expired subscriptions for every 1 active subscription. It is worth noting that the ratio is less than 1, indicating that there are fewer expired subscriptions than active subscriptions.

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Answer:

the slope is 2

Step-by-step explanation:

y2-y1

divided by

x2-x1

equals

4-0

divided by

0- (-2)

equals

4/2 which is 2

150 ÷ 20 = 7.5 minutes per 1 mile

7.5 x 6 = 45 minutes

7.5 + 7.5 = 15 minutes or 2 miles in 15

60 ÷ 7.5 = 8 mph

mpm = 7.5

90 ÷ 5 = $18 per hour

18 x 8 = $144

18 x 3 = 54 (close to $60)

Step-by-step explanation:

hope this helps

Answer: (a) Sarah     (b) 45 minutes     (c) 2 miles     (d) 8 miles per hour  

              (e) 7.5 minutes per mile          (f)  $144         (g) 3 1/3 hours

Step-by-step explanation:

\(\text{Joey:}\quad \dfrac{\$11}{3\ hours}\\\\\\\text{Sarah:}\quad \dfrac{\$2}{\frac{1}{2}\ hour}\times \dfrac{6}{6}=\dfrac{\$12}{3\ hours}\)

When comparing the same number of hours, Sarah earns $12, Joey earns $11.

***************************************************************************************************

                            \(\dfrac{20\ miles}{150\ minutes}=\dfrac{6\ miles}{x}\)

Cross Multiply:     20(x) = 150(6)

Divide by 20:             x = 900/20

Simplify:                     x = 45 minutes

***************************************************************************************************

                             \(\dfrac{20\ miles}{150\ minutes}=\dfrac{x}{15\ minutes}\)

Cross Multiply:      20(15) = 150(x)

Divide by 150:       300/150 = x

Simplify:                 2 miles = x

***************************************************************************************************

Use conversion: 60 minutes = 1 hour

\(\dfrac{20\ miles}{150\ minutes}\times \dfrac{60\ minutes}{1\ hour}=\quad \dfrac{1200\ miles}{150\ hour}\quad =\large\boxed{\dfrac{8\ miles}{1\ hour}}\)

***************************************************************************************************

\(\dfrac{150\ minutes}{20\ miles}\div \dfrac{20}{20}=\quad \large\boxed{\dfrac{7.5\ minutes}{1\ mile}}\)

***************************************************************************************************

                           \(\dfrac{\$90}{5\ hours}=\dfrac{x}{8\ hours}\)

Cross Multiply:     5(x) = 90(8)

Divide by 5:             x = 720/5

Simplify:                   x = $144

***************************************************************************************************

                            \(\dfrac{\$90}{5\ hours}=\dfrac{\$60}{x}\)

Cross Multiply:     5(60) = 90(x)

Divide by 90:        300/90 = x

Simplify:               3 1/3 hours = x

Answer:

Use photo math, it will explain all the steps

Step-by-step explanation:

One leg is x, the second leg is 2x and the hypotenuse is:

Perimeter is:

The sides are:

The number 459 in the citation 319 N.W. 2d 459 represents the page number where the case or legal opinion can be found in the North Western Reporter, Second Series. The North Western Reporter is a series of case reporters that includes court decisions from various states in the northwestern region of the United States.

In legal citations, the number before the "N.W." indicates the volume number of the reporter. So in this case, "319" refers to the specific volume where the case is located. The abbreviation "N.W." stands for North Western Reporter, which is the name of the reporter series. The number "2d" after "N.W." indicates that this is the second series of the North Western Reporter.

To locate the case within the volume, the number "459" refers to the page number where the case begins. This allows readers, such as lawyers, judges, or researchers, to easily find and reference the specific case within the reporter.

In summary, the number "459" in the citation 319 N.W. 2d 459 represents the page number where the case can be found in the North Western Reporter, Second Series.

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Answer:

k = 24

Step-by-step explanation:

\(\frac{8(3+k)}{k}=9\\\\k[\frac{8(3+k)}{k}]=k[9]\\\\8(3+k)=9k\\\\8(3)+8(k)=9k\\\\24+8k=9k\\\\24+8k-8k=9k-8k\\\\24=k\)

In hypothesis testing, data miners develop a model prior to the analysis and apply statistical techniques to data to estimate the parameters of the model.

In hypothesis testing, data miners formulate a hypothesis or a model about a population parameter based on prior knowledge or assumptions. This model specifies the relationship between variables and the expected values of the parameters. The next step is to collect data and analyze it using statistical techniques to estimate the parameters of the model.

The estimation of parameters involves using the available data to make inferences about the unknown population parameters. This can be done using various statistical methods such as maximum likelihood estimation, least squares estimation, or Bayesian estimation. These techniques aim to find the best estimates of the parameters that are consistent with the observed data and the assumptions of the model.

Once the parameters are estimated, data miners can then evaluate the goodness of fit of the model and draw conclusions about the population based on the estimated parameters. This process allows for hypothesis testing and making inferences about the population based on the sample data and the estimated parameters of the model.

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The total cost of the camera with sales tax included is $811.47.

The total cost refers to the summation of all the cost involved from the manufacturing to sales, it majorly involves the fix cost and variable cost.

To find the total cost we need to derive a formula

total cost = listed price + ( listed price x sales tax rate)

now by placing the values given in the question we can calculate the the total cost

listed price = $761. 98

sales tax rate = 6. 5%

then,

total cost = 761.98 + (761.98 x 0.065)

total cost = 761.98 + 49.49

total cost = $811.47

The total cost of the camera with sales tax included is $811.47.

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Adjacent angles are angles that share a common vertex and a common side. They are side by side and do not overlap. The sum of adjacent angles is always 180 degrees


An angle or angle pair that satisfies the condition of being adjacent is called adjacent angles. Adjacent angles are two angles that share a common vertex and a common side. They are also known as linear pairs.

Here's a step-by-step explanation:

1. Adjacent angles have the same vertex: The vertex is the common point where the two angles meet.

2. Adjacent angles have a common side: The common side is the side that is shared by both angles.

3. Adjacent angles do not overlap: This means that the angles are not on top of each other or intersecting. They are side by side.

4. Adjacent angles add up to 180 degrees: If you measure the two adjacent angles, their sum will always be 180 degrees. This is because adjacent angles form a straight line.

For example, let's consider a line segment AB. If we place two points C and D on the same side of the line, we can create two adjacent angles, ∠ABC and ∠CBD.

These angles share the common vertex B and the common side BC. Since they form a straight line, their sum is always 180 degrees.

In summary, adjacent angles are angles that share a common vertex and a common side. They are side by side and do not overlap. The sum of adjacent angles is always 180 degrees.

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Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Answer:

see explanation

Step-by-step explanation:

using the property of exponents

• \(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

given

3x²\(y^{5}\) × 4x³\(y^{7}\) ( separate like parts in the product )

= 3 × 4 × x² × x³ × \(y^{5}\) × \(y^{7}\)

= 12 × \(x^{(2+3)}\) × \(y^{(5+7)}\)

= 12\(x^{5}\)\(y^{12}\)

a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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The game is not fair as 6 times the expected sum is less than the cost, $43.

In the question, we are asked if the game is fair.

For the game to be fair, 6 times the expected sum for the pair from the game has to be greater than or equal to $43, that is,

6E(X) ≥ 43.

The expected sum for the pair, E(X) can be calculated using the formula,

E(X) = ∑x.p(x),

or, E(X) = 1/18 + 1/6 + 1/3 + 5/9 + 1/6 + 7/9 + 10/9 + 1 + 5/6 + 11/18 + 1/3,

or, E(X) = 107/18.

Now, 6E(X) = 6*(107/18) = 107/3 = 35.67.

Since, the total return from the game is $35.67, which is less than the cost of $43, the game is not fair.

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Answer:

shifted 5 up and 4 to the left

Step-by-step explanation:

The angles that cannot be an interior angle in a regular polygon are 40 72° 108° 148°

A polygon is a closed polygonal chain made up of a limited number of straight line segments and is a type of planar figure in geometry. A polygon is an area that is bordered by a bounding circuit, a bounding plane, or both. A polygonal circuit's segments are referred to as its edges or sides.

A regular polygon has equal internal angles all around. A polygon's interior angle is calculated using the following formula: interior angle of a polygon = sum of interior angles number of sides. The total of a polygon's outer angles is 360°.

Given the different angles in degree.

We have to find angle which can't be interior angle in a regular polygon

We apply the formula for each angle = (n - 2) 180 / n to determine the size of each interior angle of a regular polygon.

Let the interior angle be  108 degree

(n - 2) 180 / n = 108

n = 0.5 not possible

Let the interior angle be  148 degree and 179 degree

(n - 2) 180 / n = 148

n = 1.125 not possible

(n - 2) 180 / n = 179

n = 36 possible

Let the interior angle be  40 degree and 72 degree

(n - 2) 180 / n = 40

n = 0.9 not possible

(n - 2) 180 / n = 72

n = 0.33 not possible

Hence angles that cannot be an interior angle in a regular polygon are 40 72° 108° 148°

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The angles that cannot be an interior angle

in a regular polygon are 40 72° 108° 148°

A polygon is a planar figure in which closed polygonal chain made up of a limited number of straight line. A polygon is an area that is bounded by a bounding circuit or a bounding plane or both.

A regular polygon is a polygon which has equal internal angles all around it.

In a polygon, the interior angle = sum of interior angles number of sides.

Total outer angle of a polygon is 360°.

Here we have to find the angle which can't be an interior angle of a regular polygon.

The size of each interior angle of a regular polygon = [(n-2)×180°] /n

1. 108 degree

[(n-2)×180°] /n = 108

180n - 360 = 108n

72n=360

n = 0.2 This is not possible since n is a natural number

2. 148 degree

[(n-2)×180°] /n = 148

180n - 360 = 148n

72n=360

n = 0.2 This is not possible since n is a natural number

Let the interior angle be 148 degree and 179 degree

(n-2) 180 / n = 148

n = 1.125 not possible

(n-2) 180 / n = 179

n = 36 possible

Let the interior angle be 40 degree and 72 degree

(n-2) 180 / n = 40

n = 0.9 not possible (n-2) 180 / n = 72

n = 0.33 not possible

Hence angles that cannot be an interior angle in a regular polygon are 40 72° 108° 148°

Given : 2.31/0.790 =?, (2.08 x 10³) x (3.11 x 10²) = 10⁵We know that division is the arithmetic operation used to separate the objects into equal groups. Also, the division is the inverse operation of multiplication.

Therefore,To solve the problem 2.31/0.790 = Step 1: First, write the given values. Step 2: Divide 2.31/0.790=2.924050633 Step 3: Finally, the value of the given problem is 2.924050633. Hence 2.31/0.790=2.924050633To solve the problem (2.08 x 10³) x (3.11 x 10²) = 10⁵Step 1: First, write the given values.

Step 2: Multiply 2.08 x 10³ and 3.11 x 10²=6.4608 x 10⁵Step 3: Finally, the value of the given problem is\(6.4608 x 10⁵. Hence (2.08 x 10³) x (3.11 x 10²) = 6.4608 x 10⁵Therefore, 2.31/0.790 = 2.924050633, (2.08 x 10³) x (3.11 x 10²) = 6.4608 x 10⁵.

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We have:

Image of book on website

Wide = 1.5 inches

Tall = 3 inches

Actual book

Wide = 9 inches

Tall = ?

a) Scale used for the image:

Answer: scale = 6 inches

b) Tall actual book

Answer: tall = 18 inches

It is proved that <QST + <TSV = 180° becasue of the linear pair.

Here we know that vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

The sum of linear pair is equal to 180 degree

<QSVX= 180°

<TSR= 180°

Therefore, <QST= 90°

<TSV= 90°

Thus, <QST + <TSV = 180°

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