In virginia, each automobile license plate consists of a single digit followed by three letters, followed by three digits. how many distinct license plates can be formed if there are no restrictions on the digits or letters?

Answer:

8/13 - 1/13i

Step-by-step explanation:

Final answer:

To convert the expression (1-2i)/(2-3i) to standard form, multiply by the complex conjugate of the denominator (2+3i). After simplification, the standard form of the complex number is 0.8 - 0.1i.

Explanation:

To write the expression (1-2i)/(2-3i) as a complex number in standard form, we need to eliminate the imaginary unit i from the denominator. This can be achieved by multiplying both the numerator and the denominator by the complex conjugate of the denominator. The complex conjugate of a complex number 2-3i is 2+3i.

Multiplying the expression by the complex conjugate, we get:

(1-2i)(2+3i) / (2-3i)(2+3i).

Now, we can expand both the numerator and denominator:

Numerator: (1 × 2) + (1 × 3i) - (2i × 2) - (2i × 3i) = 2 + 3i - 4i - 6(i²)

Denominator: (2 × 2) + (2 × 3i) - (3i × 2) - (3i × 3i) = 4 - 6(i²)

Recall that i² = -1, so we can simplify the expression further.

Numerator: 2 + 3i - 4i + 6 = 8 - i

Denominator: 4 + 6 = 10

Therefore, our complex number in the standard form is:

(8 - i) / 10 = 0.8 - 0.1i.

Answer:

You would shift this to the right 8 places

Step-by-step explanation:

Answer: The matrix would be

[tex]\left[\begin{array}{ccc}48&19\\\\44&21\end{array}\right][/tex]

Step-by-step explanation:

Since we have given that

Number of Styrofoam balls bought by Bradley in May = 48

Number of figurines sold by Bradley in June = 19

Number of Styrofoam balls bought by Lupe in May = 44

Number of figurines sold by Lupe in June = 21

So, it will be written as

                          Purchases      Sales

May                            48               19

June                          44               21

So, the matrix would be

[tex]\left[\begin{array}{ccc}48&19\\\\44&21\end{array}\right][/tex]

Answer:

A. Length of a bead necklace compared with the number of identical beads

Step-by-step explanation:

Using identical beads in a necklace means that the length of the necklace will depend on the total number of identical beads in the necklace.

For each bead added, the length of the necklace will increase a given, constant, amount.  This is a constant rate of change.

Answer: A. Length of a bead necklace compared with the number of identical beads

Step-by-step explanation:

A. Length of bead necklace increases simultaneously compared with the increases in number of identical beads . This is a proportional relationship .

So, There is constant rate of change which is equals to the length of each bead.

B. Distance a school bus travels compared with the number of stops .

There is no constant rate of change between the quantities .[The time when bus stops matter]

C.Number of trees in a park compared with the area of the park.

There can be free space ,so there is not proportional relationship .

D.Number of runs scored in a baseball game compared with the number of innings

Not proportional relationship.

The probability of getting heads then a number less than 4 is, 0.15

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

The formula of the probability of an event A is:

[tex]P(A)=\frac{n(A)}{n(S)}[/tex] , where [tex]n(A)[/tex] is the number of favorable outcomes and [tex]n(S)[/tex] is the total number of events in the sample space.

For given situation,

Let, event A: getting heads on a coin toss

and event B: choosing a number less than four from 1-10

For event A, [tex]n(A)=1[/tex] and [tex]n(S)=2[/tex] (either head or tail)

So, [tex]P(A)=\frac{1}{2}[/tex]

Similarly, for event B:

choosing a number less than four = {1, 2, 3}

So, [tex]n(B)=3[/tex] and [tex]n(S)=10[/tex]

⇒ [tex]P(B)=\frac{3}{10}[/tex]

The probability of getting heads and choosing a number less than 4 is:

⇒ [tex]\frac{1}{2}[/tex] × [tex]\frac{3}{10}[/tex]

[tex]=\frac{3}{20}[/tex]

[tex]=0.15[/tex]

Hence, the probability of getting heads then a number less than 4 is 0.15

Learn more about probability here,

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To find the ratio of corresponding sides for similar triangles, compare the lengths of the corresponding sides in both triangles. If the triangles are similar, these ratios will be equal. To simplify the ratio, divide each term by the greatest common factor.

In mathematics, to write the ratio of corresponding sides for similar triangles, you need to compare the lengths of the sides that have the same relative position. These corresponding sides are proportional in similar triangles. Let's consider a simple scenario where we have two similar triangles

A'B'C' and ABC.

If these two triangles are similar, the ratio of their corresponding sides will be equal. Hence our ratios will look like this:

a'/a = b'/b = c'/c.

This is the ratio of corresponding sides for the similar triangles. To reduce the ratio to the lowest term, you simply divide each term by the greatest common factor of all the terms.

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To find the ratio of corresponding sides of similar triangles, identify the corresponding sides and write a ratio comparing the lengths of these sides. For example, if side AB in triangle ABC corresponds to side DE in triangle DEF with lengths 3 and 6 respectively, the ratio is 3/6 or 1/2 when reduced.

To write the ratio of corresponding sides for similar triangles, we must first identify which sides correspond in the two triangles. Usually, triangles are labeled so that corresponding sides have the same label (like "a", "b", etc.). Once you've identified which sides correspond, simply write a ratio comparing the length of one side in the first triangle to the length of the corresponding side in the second triangle. This could look something like a1/a2.

For example, if triangle ABC is similar to triangle DEF and side AB corresponds to DE with lengths 3 and 6, respectively, then the ratio of the corresponding sides is 3/6 or 1/2 in reduced form.

Understanding the ratio of corresponding sides is key to understanding the properties of similar triangles and can be extremely helpful in solving problems involving these figures not just in geometry, but in other branches of mathematics as well.

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The answer to this question is A: 31

The area of the lawn that the sprinkler covers is approximately 708.25 square feet. This was calculated using the formula for the area of a sector of a circle, converting the rotation angle to radians, and then substituting the given values into the formula.

The area of the lawn that the water sprinkler covers can be calculated using the formula for the area of a sector of a circle. The formula is Area = 1/2 * r2 * θ, where r is the radius (which is the distance the sprinkler can spray, 25 feet in this case) and θ is the central angle in radians. First, we must convert the given angle from degrees to radians. We know that 180 degrees equals π radians. Therefore, to convert 130 degrees to radians, we multiply by π/180, getting approximately 2.26893 radians.

Substituting these values into the formula, we get: Area = 1/2 * 252 * 2.26893 = 708.25 square feet.

So,

the sprinkler covers an area of approximately 708.25 square feet

when rotating through an angle of 130 degrees.

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In hypothesis testing of two population means with a 5% significance level, we compare the difference between two sample means against a null hypothesis that states no difference, using t- or z-distributions depending on whether population standard deviations are known.

Hypothesis Testing of Two Population Means

In statistics, when we want to test the claim about the difference between two population means,
(μ1 and μ2), we use a procedure known as a hypothesis test. If we assume that the samples are random, independent, and drawn from normally distributed populations, we usually proceed with a formula involving the sample means, sample standard deviations, and sample sizes.

In a hypothesis test, the null hypothesis (H0) typically states that there is no difference between the two population means (H0: μ1 = μ2). The alternative hypothesis (Ha) suggests that there is a difference (Ha: μ1 ≠ μ2). To assess the validity of H0, we calculate a test statistic that follows a known distribution (typically a t-distribution if standard deviations are unknown and a z-distribution if they are known) under the assumption that H0 is true.

For a test at the 5 percent level of significance (α=0.05), we determine the critical value(s) from the statistical tables of the chosen distribution. If the calculated test statistic falls into the critical region determined by α, we reject the null hypothesis in favor of the alternative hypothesis. If not, we fail to reject the null hypothesis. This process is essentially a two-tailed test, given that we allow for the possibility of the sample mean being either larger or smaller than the hypothesized population mean.

The assumption of normality is critical when the sample sizes are small. For larger samples, according to the Central Limit Theorem, the sampling distribution of the mean will be approximately normal regardless of the underlying distribution of the population.

It is important to note that while we can never prove a hypothesis definitively, hypothesis testing allows us to make probabilistic statements about whether data is consistent with a given hypothesis.

Answer:

80%

Step-by-step explanation:

24/30=.80

.80=80%

Hope this helps :)

To solve what percent of 24 is 30, set up the equation 30/24 times 100 = p, which results in 125%. Therefore, 30 is 125% of 24.

To find what percent of 24 is 30, we need to set up a proportion where 30 is the part, 24 is the whole, and we are solving for the percentage (we'll call this p). The equation for percent is (part/whole) times 100 = percent. So in this case, the equation becomes (30/24) tmes 100 = p.

Next, we'll divide 30 by 24 to get a decimal, then multiply by 100 to convert it to a percent. The calculation looks like this: (30 / 24) times 100 which gives us 125%. This means that 30 is 125% of 24.

Always remember to round to the nearest hundredth if necessary, but in this case, 125% is already to the nearest whole percent.

Answer:

[tex]x_{1}=1.53\\x_{2}=-1.53[/tex]

Step-by-step explanation:

The given quadratic equation is

[tex]9x^{2}-21=0[/tex]

To solve this equation, we just have to isolate the variable, because the quadratic expression has only one variable, the linear term is not present. So

[tex]9x^{2} =21\\x^{2} =\frac{21}{9}[/tex]

Now, we apply a square root, to have the variable complete isolated

[tex]\sqrt{x^{2} }=\sqrt{\frac{21}{9} } \\x=\±1.53[/tex]

Remember that all square roots have two results, one positive and one negative.

Therefore, the solutions for this equation are

[tex]x_{1}=1.53\\x_{2}=-1.53[/tex]