5. Find the area of the composite figure. The two
triangles have the same dimensions.
2.5 cm
7.5 cm
-13 cm-
8 cm
1
1

The equation that expresses the law of refraction is known as Snell’s law or the law of refraction.

The law of refraction is used to determine the direction in which light bends when it enters a new medium.

What is the law of refraction?

The law of refraction (also known as Snell's law) is a principle of optics used to explain how light behaves at the boundary between two media with different refractive indexes.

The law of refraction states that when light passes from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.

The equation for the law of refraction is as follows:

$$\frac{\sin \theta_1}{\sin \theta_2}= \frac{v_1}{v_2}=\frac{\lambda_1}{\lambda_2}=\frac{n_2}{n_1}$$

Where:θ1 = Angle of incidence

           θ2 = Angle of refraction

           v1 = Velocity of light in medium 1

           v2 = Velocity of light in medium 2

           λ1 = Wavelength of light in medium 1

           λ2 = Wavelength of light in medium 2

           n1 = Refractive index of medium 1

           n2 = Refractive index of medium 2

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As a result, the radian measure of the relevant center angle is around 3.07 radians.

An arc is any smooth curve that connects two locations. The length of an arc is referred to as its arc length. A graph arc is an ordered pair of neighboring vertices in a graph. An arc is defined as any segment (other than the complete curve) of a circle's circumference.

Here,

The formula for the length of an arc in a circle is given by:

Arc Length = (Central Angle / 2π) * Circumference

We know the Arc Length and the Radius of the circle, so we can find the Central Angle as follows:

Arc Length = (Central Angle / 2π) * 2π * Radius

66/5 * π = (Central Angle / 2π) * 2π * 22

66/5 * π = Central Angle * 22

Central Angle = (66/5 * π) / 22

The radian measure of an angle is equal to the ratio of the length of the arc that it intercepts to the radius of the circle. Hence, the radian measure of the central angle is given by:

Central Angle (in radians) = Arc Length / Radius

= (66/5 * π) / 22

So, the radian measure of the corresponding central angle is approximately 3.07 radians.

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Answer:

qcrit ≈ 3.04.

Step-by-step explanation:

The tukey hsd test, if there are 16 df associated with mswithin, and α = .05 and the number of groups = 3, qcrit = 3.842.

To determine the value of qc rit for the Tukey HSD (Honestly Significant Difference) test, we need to use the Studentized range distribution with the appropriate degrees of freedom and significance level.

In this case, the number of groups is 3, which means we have 3 - 1 = 2 degrees of freedom associated with the numerator of the F-ratio.

The denominator degrees of freedom for mswithin is 16, which will be the denominator degrees of freedom for the F-distribution.

To find the value of qcrit, we can use a statistical table or a statistical software. For α = 0.05, with 2 and 16 degrees of freedom, the value of qcrit is approximately 3.842.

Therefore, qcrit = 3.842.

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Answer:

4

Step-by-step explanation:

your slope-intercept will be 4

Answer:

y = 4x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x - 3 ← is in slope- intercept form

with slope m = 4

Parallel lines have equal slopes

Thus parallel line has m = 4 and c = 5

y = 4x + 5 ← equation of parallel line

Answer:

the total amount is £ 756.

hope it helps..

Answer:

m  = 2 /5

Step-by-step explanation:

Answer:

k

Step-by-step explanation:

6 is the slope im pretty sure. i followed the slope formula rise over run

( y2-y1 / x2-x1 ) and got 6

Answer:

it is makeing me do it

Step-by-step explanation:

A perpendicular bisector of a line segment will never be a line of reflection for the line segment so option (A) will be correct.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

Reflection of an line segment is mirror image of an axis.

If we reflect any line about perpendicular then it will not be formed because the mirror doesn't exist for a perpendicular view.

Therefore a perpendicular to the line segment can never be a line of reflection of that line.

Hence "A perpendicular bisector of a line segment will never be a line of reflection for the line segment".

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Answer:

The acceleration is 965 kg•ms^-2

Step-by-step explanation:

Mathematically;

Force = mass * acceleration

From the question;

Force = 1930 N (kg• ms^-2)

mass = 2kg

Acceleration = Force/mass = 1930/2 = 965 ms^-2

To get the box's volume, apply the following equation:

14 . 8 . 5 = V

Volume of the shoebox = 560 in³

The volume of a cuboid is a measure of how much space it takes up. A three-dimensional shape with length, breadth, and height is the cuboid. If we start with a rectangular sheet and keep stacking them, we will eventually have a shape with a certain length, breadth, and height.

The base area and height are multiplied to determine the cuboid's volume.

The base area of the cuboid is l b.

The formula for a cuboid's volume is V = l b h = lbh.

Now in the question,

Length of the shoebox, l = 14 inches

Breadth of the shoebox, b = 8 inches

Height of the shoebox, h = 5 inches

Volume of the shoebox, V = l × b × h

⇒ V= 14 × 8 × 5

⇒ V =560 in³

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Step-by-step explanation:

Examples of like terms in math are x, 4x, -2x, and 7x. These are like terms because they all contain the same variable, x. The terms 8y2, y2, and -2y2 are like terms as well. These all contain the same variable, y, raised to the second power.

The given circle having two external tangents, according to circle

theorem, have the following values;

r² + 1.6² = (0.4 + r)²

(0.4 + r)² - (r² + 1.6²) = 0

0.8·r - 2.4 = 0

0.8·r = 2.4

r = 2.4 ÷ 0.8 = 3

y = 49°

From the two tangent angle theorem, we have;

m∠1 = ((82 + 98 + 82) - (360 - ((82 + 98 + 82)))) ÷ 2 = 82

According to circle theorems, angle at the center is twice angle

subtended at the circumference.

m∠2 = (360 - (82 + 98 + 82)) ÷ 2 = 49°

The length of the chord subtended by the arc x is equal to the length of

the chord subtended by 89°, which gives;

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Answer: 56

Step-by-step explanation:

You add 4 from 24 with 2 from 32 and you get 6 for the right side

you add 2 from 24 and 3 from 32 to get 5 on the left side

= 56

To use the simplify square roots calculator, you need to enter the value whose square root you want to simplify and click on the "Simplify" or "Calculate" button to get the simplified form of the square root.

A simplify square roots calculator is a tool that simplifies square roots of numbers to their simplest form. To use this calculator, you simply need to enter the value whose square root you want to simplify. Here are the steps to use a simplify square roots calculator:

The simplify square roots calculator can be helpful in solving problems in algebra and calculus, as well as in everyday life, such as when working with measurements that involve square roots.

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The effective interest rate on the operating lease is 12.45%

Under the straight-line method of depreciation, the annual depreciation for the computers can be determined as follows:

Depreciation expense = (Cost - Residual value) / Useful life

Depreciation expense = ($120,000 - $0) / 6 years = $20,000 per year

Hence, semi-annual depreciation is $10,000 ($20,000 / 2) per payment.

The operating lease payments are $15,000 per semi-annual payment. The total amount of the lease payments for the 2-year term is $60,000 ($15,000 x 4).

Thus, the present value of the operating lease payments can be computed as follows:PV of lease payments = ($10,000 / 0.0609) x [1 - (1 / 1.0609^8)]PV of lease payments = $47,907.29

The implicit interest rate on the lease is 0.0609 or 6.09% (computed by dividing the lease interest by the present value of the lease payments).

The effective interest rate is 12.45% (computed by doubling the implicit interest rate).

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When testing partial correlation, the impact of a third variable is removed.

Partial correlation is a statistical technique used to measure the relationship between two variables while controlling for the effect of one or more additional variables, known as "covariates" or "control variables." By removing the effect of the covariates, the partial correlation measures the direct relationship between the two variables of interest. This technique is useful when we want to examine the relationship between two variables after accounting for the effect of one or more confounding variables.

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Answer:

C

Step-by-step explanation:

a number is only divisible by 4, if the number formed by the last 2 digits is divisible by 4.

The solution to the inequality "Twice w is at least -18" is w ≥ -9.

We have,

The inequality "Twice w is at least -18" can be expressed mathematically as:

2w ≥ -18

To solve for w, we can divide both sides of the inequality by 2.

However, when dividing by a negative number, the inequality sign must be flipped. In this case, since we are dividing by 2 (a positive number), the inequality sign remains the same.

w ≥ -18 / 2

w ≥ -9

Therefore,

The solution to the inequality "Twice w is at least -18" is w ≥ -9.

This means that w must be greater than or equal to -9 for the inequality to hold true.

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Answer:

Step-by-step explanation:

lbs kiwi+lbs cherries 3+1.5 3+1.5 4.5 pounds4.5​ poundsTotal pounds, xx pounds of kiwi and yy pounds of cherries:lbs kiwi+lbs cherries lbs kiwi+lbs cherries x+yx+y​

4.5 pounds of fruit does she buy if she buys 3 pounds of kiwi and 1.5 pounds of cherries and the pounds of fruit does she buy if she buys x pounds of kiwi and y pounds of cherries will be x+y.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, Kiwi cost $2.25 per pound and cherries cost $4.25 per pound and she buys 3 pounds of kiwi and 1.5 pounds of cherries.

The pounds of fruit does she buy if she buys 3 pounds of kiwi and 1.5 pounds of cherries is,

=3+1.5

=4.5 pound

The pounds of fruit does she buy if she buys x pounds of kiwi and y pounds of cherries,

= x+y

Thus, 4.5 pounds of fruit does she buy if she buys 3 pounds of kiwi and 1.5 pounds of cherries and the pounds of fruit does she buy if she buys x pounds of kiwi and y pounds of cherries will be x+y.

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Answer:

Expression D has the least value

pr(z < 2.3) is =NORMSDIST(2.3) which equals 0.9893 or a probability of 0.9893 that a standard normal random variable is less than 2.3.

The probability that a standard normal random variable is less than 2.3 can be calculated using the cumulative distribution function (CDF) of the standard normal distribution. This function gives us the probability that a standard normal random variable is less than or equal to a given value.

In Excel, you can use the NORMSDIST function to calculate the CDF of the standard normal distribution. The syntax for this function is:

=NORMSDIST(x)

where x is the value for which you want to calculate the CDF.

In this case, to calculate the probability that a standard normal random variable is less than 2.3, we would use the following formula in Excel:

=NORMSDIST(2.3)

This gives us the result of 0.9893 or a probability of 0.9893 that a standard normal random variable is less than 2.3.

Note: The cumulative distribution function can also be approximated using tables or calculators that have the function built in. The result obtained using these methods may have some slight differences compared to the result obtained using Excel.

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Answer:

c

Step-by-step explanation:

if I understand this right, then the expression is

2×sqrt(28) - 5×sqrt(63)

let's look for squared factors in the numbers under the square roots.

28 = 4×7 (4 is a squared number)

63 = 9×7 (9 is a squared number)

so,

2×sqrt(4×7) - 5×sqrt(9×7) =

= 2×2×sqrt(7) - 5×3×sqrt(7) = 4×sqrt(7) - 15×sqrt(7) =

= (4 - 15)×sqrt(7) = -11×sqrt(7)

Answer:

\(\frac{5}{9}\)

Step-by-step explanation:

Using the rules of exponents/ radicals

\(a^{\frac{m}{n} }\) ⇔ \(\sqrt[n]{a^{m} }\) , \(a^{0}\) = 1

\(a^{-m}\) = \(\frac{1}{a^{m} }\)

Given

\(27^{-\frac{2}{3} }\) × \(25^{\frac{1}{2} }\) × \(5^{0}\)

= \(\frac{1}{27^{\frac{2}{3} } }\) × \(\sqrt{25}\) × 1

= \(\frac{1}{9}\) × 5 × 1

=\(\frac{5}{9}\)

Answer:h

Step-by-step explanation:

If given vectors are v = -6i + 3j and w = -1 - 3j, the result of 2v - 9w is -12i + 33j + 9.

To find 2v - 9w, we need to multiply each component of v and w by their respective scalars and then subtract the corresponding components.

Given that v = -6i + 3j and w = -1 - 3j, we can calculate 2v and 9w as follows:

2v = 2(-6i + 3j) = -12i + 6j

9w = 9(-1 - 3j) = -9 - 27j

Now, we subtract the corresponding components:

2v - 9w = (-12i + 6j) - (-9 - 27j)

= -12i + 6j + 9 + 27j

= -12i + 33j + 9

This means that the x-component of the result is -12, the y-component is 33, and there is a constant term of 9. The vector 2v - 9w represents a combination of a movement of -12 units in the x-direction, 33 units in the y-direction, and a constant shift of 9.

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The unit that is most appropriate for the time at which the number of weeks is 120 is given as follows:

Week.

The general format for an exponential function is given as follows:

\(y = a(b)^{\frac{x}{n}}\)

The parameters for the exponential function are defined as follows:

The number of weeds in my yard doubles every 3 weeks, and the initial number of weeks is of 80, hence the values of the parameters are given as follows:

a = 80, b = 2, n = 3.

As n = 3, we have that the unit of the output variable is of weeks, hence weeks is the appropriate measure in this problem.

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Answer:

Nitrogen is needed for plant growth the energy to grow, and produce fruit or vegetables. Nitrogen is part of the chlorophyll molecule, which gives plants their green color and is involved in creating food for the plant.

With too much nitrogen, plants produce excess biomass, or organic matter, such as stalks and leaves, but not enough root structure.

Plants take nitrogen from the soil by absorption through their roots as amino acids, nitrate ions, nitrite ions, or ammonium ions. Plants do not get their nitrogen directly from the air.From here, various microorganisms convert ammonia to other nitrogen compounds that are easier for plants to use.

Step-by-step explanation:

The number of people who waited at least 6 minutes is given as follows:

50 people.

The height of each bin of the histogram represents the number of observations of the data-set in the desired interval.

The desired outcomes for this problem are given as follows:

Hence the number of people who waited at least 6 minutes is given as follows:

20 + 15 + 10 + 5 = 50 people.

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