write a linear equation with a slope of -7

the probability that there are at most 2 defective components in the box is approximately 0.9044 and the probability of having at most 3 defective components out of 250 boxes is very close to zero.

a) Let X be the number of defective components in a box of 10 components. Then X follows a binomial distribution with n=10 and p=0.01, since the probability of a component being defective is 0.01. We want to find the probability that there are at most 2 defective components in the box, i.e., P(X ≤ 2).

Using the binomial probability formula, we get:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= (10 choose 0) × 0.01⁰ × 0.99¹⁰ + (10 choose 1) × 0.01¹ × 0.99⁹ + (10 choose 2) × 0.01² × 0.99⁸

= 0.90438222

Therefore, the probability that there are at most 2 defective components in the box is approximately 0.9044 (rounded to four decimal places).

b) We want to find the probability of having at most 3 defective components out of 250 boxes, each containing 10 components. Since np = 100.01 = 0.1 < 5 and n × (1-p)=10 × 0.99=9.9 > 5, we can use the normal approximation to the binomial distribution, with mean μ = np = 2.5 and standard deviation σ = √np(1-p) = 1.577.

Let X be the number of boxes with at most 3 defective components. Then X follows an approximate normal distribution with mean μ' = np=2.5250 = 625 and standard deviation σ' = √np(1-p)) = 12.5 × 1.577 = 19.712.

We want to find P(X ≤ 250), which can be written as P(X < 251) since X is a discrete variable. Using the continuity correction, we can approximate this probability as P(X < 251.5). Then we standardize the variable:

z = (251.5 - μ')/σ' = (251.5 - 625)/19.712 = -18.919

Using a standard normal table or calculator, we find that P(Z < -18.919) is a very small number, practically zero. Therefore, the probability of having at most 3 defective components out of 250 boxes is very close to zero.

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Complete Question

factory produces components of which 1% are defective. The components are packed in boxes of 10. A box is selected by random a) Find the probability that there are at most 2 defective components in the box b) Use a suitable approximation to find the probability of having at most 3 defective (inclusive 3 cases) components out of 250.

Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading.

We will take a random sample of 20 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is a binomial distribution.

A binomial distribution is a statistical distribution that represents the likelihood of one of two outcomes in a sequence of independent trials. Binomial distributions can be used to model a variety of phenomena, including flipping coins, rolling dice, and performing multiple independent experiments.

The probability of getting k successes in n trials in a binomial distribution with probability of success p and probability of failure q is given by the following formula:P (k) = nCk * p^k * q^(n-k)Where nCk is the binomial coefficient, which represents the number of ways to select k items from a set of n items without regard to order.

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For x = -2, g(-2) = 2(-2)^3 - 5(-2)^2 + 4(-2) - 1 = 0, so there is a value of x such that g(x) = 0 for -3 ≤ x ≤ 2.

The absolute minimum value of g on the interval -7 ≤ x ≤ 9 is -765, and the absolute maximum value of g on the interval is 1720.

a. To determine if there is a value of x such that g(x) = 0 for -3 ≤ x ≤ 2, we can plug in each value of x in the interval into the equation and see if we get 0.

g(x) = 2x^3 - 5x^2 + 4x - 1

For x = -3, g(-3) = 2(-3)^3 - 5(-3)^2 + 4(-3) - 1 = -55, which is not 0.

For x = -2, g(-2) = 2(-2)^3 - 5(-2)^2 + 4(-2) - 1 = 0, so there is a value of x such that g(x) = 0 for -3 ≤ x ≤ 2.

b. To find the absolute minimum and maximum values of g on the interval -7 ≤ x ≤ 9, we can use the Extreme Value Theorem, which states that a continuous function on a closed interval will have both an absolute minimum and maximum value on that interval.

To find these values, we can take the derivative of g(x) and set it equal to 0 to find critical points, and then evaluate g(x) at those critical points as well as at the endpoints of the interval.

g(x) = 2x^3 - 5x^2 + 4x - 1

g'(x) = 6x^2 - 10x + 4 = 2(3x-2)(x-1)

Setting g'(x) = 0, we get critical points x = 2/3 and x = 1.

g(-7) = -765, g(2/3) = -23/27, g(1) = 0, and g(9) = 1720.

Therefore, the absolute minimum value of g on the interval -7 ≤ x ≤ 9 is -765, and the absolute maximum value of g on the interval is 1720.

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Answer:

15 Full orbits per day

Step-by-step explanation:

To work out the number of full orbits the ISS does in 1 day, we need to know how long it takes for the ISS to complete one orbit around the Earth.

We can use the information given to us to calculate the time it takes for the ISS to complete one orbit:

Distance traveled in one orbit = 42,600 kilometers

Speed of the ISS = 27,576 kilometers per hour

To calculate the time taken for one orbit:

Time taken = Distance traveled / Speed

Time taken = 42,600 kilometers / 27,576 kilometers per hour

Time taken = 1.54 hours (rounded to 2 decimal places)

So, the ISS takes approximately 1.54 hours to complete one orbit around the Earth.

Now, we can calculate the number of orbits the ISS does in one day:

Number of orbits per day = 24 hours / Time taken for one orbit

Number of orbits per day = 24 hours / 1.54 hours

Number of orbits per day = 15.58 (rounded to 2 decimal places)

Therefore, the ISS completes approximately 15 full orbits around the Earth in one day.

To begin, we know that the median of the original collection of five positive integers is 4, which means that the middle number is 4. We also know that the unique mode is 3, which means that there is only one number in the collection that occurs more frequently than any other number.

Let's call the five positive integers in the original collection a, b, c, d, and e.

Since the mean of the original collection is 4.4, we can set up the equation:

(a+b+c+d+e)/5 = 4.4

Multiplying both sides by 5 gives:

a+b+c+d+e = 22

We also know that the mode is 3, which means that one of the numbers in the collection must be 3. Let's assume that a = 3, then we have:

3+b+c+d+e = 22

b+c+d+e = 19

Since the median is 4 and 3 is the unique mode, we can conclude that b, c, d, and e must be either 4 or 5. However, since there is only one unique mode, we know that there is only one number in the collection that is equal to 3. Therefore, we can conclude that the collection of five positive integers must be: 3, 4, 4, 4, 5.

If we add 8 to this collection, the new collection becomes: 3, 4, 4, 4, 5, 8. The new collection has six numbers, so the median is now the average of the two middle numbers. Since the middle two numbers are 4 and 5, the median is (4+5)/2 = 4.5.

Therefore, the new median is 4.5, expressed as a decimal to the nearest tenth.

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Answer:

  5240 kg/m³

Step-by-step explanation:

You want the average density of a planet with radius 6052 km and mass 4.87×10^27 g.

The mass is given in grams, and the corresponding unit in the desired answer is kilograms. There are 1000 g in 1 kg, so 4.87×10^27 g = 4.87×10^24 kg.

The radius is given in km, and the corresponding unit in the desired answer is meters. There are 1000 meters in 1 km, so 6052 km = 6052×10^3 m. (We could adjust the decimal point, but we choose to let the calculator do that.)

The units of density tell you it is computed by dividing the mass by the volume:

  ρ = mass/volume

The volume of the sphere is found using the given formula, so the density is ...

  ρ = (4.87×10^24 kg)/(4/3π(6052×10^3 m)^3)

  ρ ≈ 5240 kg/m³

The average density of the planet is about 5240 kg/m³.

__

Additional comment

This is comparable to the average density of Earth, which is about 5520 kg/m³.

If you know 63 people have swim suits on and 43 have sunglasses, 32 people have swim suits on but not sunglasses.

To find out how many people have swim suits on but not sunglasses, we can use the principle of inclusion-exclusion.

We know that there are 75 people in the park, and 63 of them have swim suits on. We also know that 43 people have sunglasses. However, some people have both swim suits and sunglasses. Let's denote the number of people who have both by x. Then we can use the formula:

total = swim suits + sunglasses - both

Substituting in the given values, we get:

75 = 63 + 43 - x

Simplifying, we get:

x = 31

Therefore, 31 people have both swim suits and sunglasses, and the number of people who have swim suits on but not sunglasses is:

63 - 31 = 32

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The conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. Generally, insurance companies use the number of traffic violations and/or the number of claims a driver has had within a certain time period as indicators of their riskiness.

As Eric has had no accidents or traffic violations, the probability that he is a high-risk driver is very low. However, this does not mean that the probability is zero. There are many other factors which can contribute to a driver's risk, such as age, gender, experience, and location.

If Eric is an experienced driver, who has been driving for many years with no traffic accidents, then the probability of him being a high-risk driver will be lower than the average driver. On the other hand, if Eric is a new driver, or is located in an area with a high rate of traffic accidents, then the probability of him being a high-risk driver may be higher than the average driver.

Overall, the conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. However, this probability can change depending on other factors, such as his age, experience, and location.

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There is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.

This indicates a normal distribution, which is a type of continuous probability distribution. It is characterized by a bell-shaped curve that is symmetric about the mean, with a specific formula given by f(x) = [tex]1/(σ√2π)e^(-(x-μ)^2/2σ^2)[/tex]where μ is the mean, σ is the standard deviation, and x is the random variable.

In terms of calculation, we can use the formula to calculate the probability of a certain event occurring. For example, if we know the mean and standard deviation of a normal distribution, we can calculate the probability of a value between two given points. For example, if the mean is 5 and the standard deviation is 2, then the probability of a value between 3 and 7 is given by the integral of f(x) from 3 to 7, which is equal to 0.6826. This means that there is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.

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There are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.

The total number of ways to form the delegation from five pairs of dance partners can be calculated using the combination formula. The combination formula is used to calculate the number of different combinations of n objects taken r at a time without repetition.

In this question, n is the total number of dance partners (5) and r is the number of people on the delegation (4).

Therefore, the calculation is as follows:

total number of ways = nCr

                    = 5C4

                    = 5! / 4!(5-4)!

                    = 5! / 4!1!

                    = 5 x 4 x 3 x 2 x 1 / 4 x 1 x 1

                    = 5 x 4 x 3 x 2

                    = 120

Hence, there are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.

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Increasing the sample size leads to a more accurate estimation of the population mean.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number outcomes.

As the sample size, n, increases, the center of the sampling distribution of sample means becomes more precise and closer to the true population mean. This is known as the central limit theorem, which states that as the sample size increases, the distribution of sample means becomes approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In other words, as we take larger and larger samples, we are more likely to obtain sample means that are closer to the true population mean. This is because larger samples are less affected by random fluctuations and more likely to provide a representative picture of the population as a whole.

Therefore, increasing the sample size leads to a more accurate estimation of the population mean.

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One advantage of best-guess experiments is that they are often faster and more cost-effective than factorial or design experiments.

Best-guess (trial and error) experiments involve making a hypothesis and testing it through a series of trials until a satisfactory result is achieved. On the other hand, factorial or design experiments involve manipulating multiple variables simultaneously to determine their individual and interactive effects on a response variable.

Both approaches have their advantages and disadvantages depending on the specific research question and goals. They may also be useful in situations where there is limited knowledge about the variables of interest or when the system is too complex to be modeled accurately.

However, best-guess experiments may suffer from issues such as biased or subjective interpretation of results, a lack of control over extraneous variables, and a potential for false positives or negatives.

In contrast, factorial or design experiments provide a more systematic approach to testing hypotheses and offer greater control over variables, leading to more reliable and generalizable results. They may, however, be more time-consuming and expensive to conduct.

Ultimately, the choice between best-guess and factorial or design experiments depends on the research question, available resources, and desired level of precision and control.

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The value of p from the given equation is 4.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign [tex]=\\[/tex].

The given equation is [tex]0.5p-3.45=-1.2[/tex]

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The equation can be solved as follows

[tex]0.5p-3.45=-1.2[/tex]

[tex]0.5p= -1.2+3.45[/tex]

[tex]0.5p= 2.25[/tex]

[tex]p= 2.25\div0.5[/tex]

[tex]p= 4.5[/tex]

Therefore, the value of p is 4.5.

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Answer:

16 represents the hours available to sew gloves.

2 represents the cost of producing gloves for a small pair.

Step-by-step explanation:

As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

Three straight lines that cross at three different locations create the two-dimensional geometric outline of a triangle. A triangle's vertices, which are the three places at which those three lines intersect, are referred to as the triangle's sides. The dimensions of a triangle's edges and angles can be used to classify it. For instance, an isosceles triangle has two equal sides and two equal angles while an equilateral triangle has three equal sides and three equal angles of 60 degrees. An angle or side of a scalene triangle cannot be equivalent.

given

The right-angled triangle XYZ in the provided illustration has a side length of 6 units and an angle opposite to it that is labelled as 30°. The extent of the side YZ, denoted as x, must be determined.

To find x, we can use the trigonometric sine relation. The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. The hypotenuse in this instance is designated as 2x.

As a result, we have:

sin 30° = (6/2x)

Adding two times to both sides:

2x * sin 30° = 6

Using sin 30°, which has a value of 0.5:

x = (6/(2 * 0.5)) = 6/1 = 6

Consequently, the side YZ is 6 units long.

As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.

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The following factors work to reduce conflict and promote positive interaction between grieving couples who have lost a child by death is open and honest communication, expressing emotions in each other's company, and the ability of partners to reframe each other's behavior in a positive way. The correct option is B. 1, 2, and 4

When grieving couples lose a child due to death, it can lead to tension in their relationship, leading to conflicts between the couple. However, some factors work to reduce conflicts and promote positive interaction between grieving couples who have lost a child by death.

These factors include the following:

:Open and honest communication: Open communication is essential when it comes to expressing emotions, needs, and expectations from one another. It helps to build understanding, trust, and positive interaction between the couples. Honest communication provides room for clarification and better comprehension of each other's feelings and needs

Reframing each other's behavior in a positive way helps to build a healthy relationship and reduce conflicts.Crying separately to minimize the open grief and pain: Crying separately does not help reduce conflicts between the couple as it promotes distance and an unhealthy way of dealing with grief. It is important to grieve together and find support from each other to heal and move forward.

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Answer:

[tex]26 > n + 15[/tex]

[tex]11 > n[/tex]

[tex]n < 11[/tex]

Answer:

[tex]y-3=-\frac{3}{2}(x-2)[/tex]

Step-by-step explanation:

In order to find an equation that is parallel, it must have the same slope. This means the y intercept could literally be anything.

By equation of the line, we can write it in point slope form

[tex]y-y1=m(x-x1)[/tex]

where y1 and x1 are points on the coordinate plane and m is the slope.

We are already given the slope, so we just plug in the numbers.

[tex]y-3=-\frac{3}{2}(x-2)[/tex]

Answer: 1.26 × 10 to the 10th power

Step-by-step explanation:

The quadratic function that only has one root at 3 and passes through the point (0,4) is: f(x) = (4/9)(x - 3)^2

A quadratic equation is a polynomial equation of degree 2, meaning that the highest exponent of the variable is 2. It has the general form:

ax^2 + bx + c = 0

If a quadratic function has only one root at 3, then it must be of the form:

f(x) = a(x - 3)^2

where a is a constant. This is because a quadratic function with only one root must have a double root, meaning that the parabola only touches the x-axis at that point and does not cross it. And a quadratic function with vertex at (3,0) and opening upwards satisfies this condition.

To determine the value of a, we can use any additional information that may be provided, such as the value of the function at another point. For example, if we know that f(0) = 4, then we can substitute these values into the equation to get:

4 = a(0 - 3)^2

4 = 9a

a = 4/9

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The quadratic function that has only one root at 3 and passes through (0,4) is: [tex]f(x)=(\frac{4}{9} )(x-3)^{2}[/tex]

A quadratic equation is a second-degree algebraic problem in x. In its standard form, the quadratic equation is [tex]ax^2+bx+c=0[/tex], where an as well as b are the coefficients, x is the variable, and c is the value of the constant component. The essential requirement for a formula to be a quadratic equation is that the coefficient of [tex]x^2[/tex] is not zero (a 0). When writing an equation with quadratic equations in conventional format, the [tex]x^2[/tex] term comes first, then the x term, and lastly the constant term.

A quadratic equation is a polynomial expression of degree 2, which means that the variable's greatest exponent is 2. It takes the following basic form:

[tex]ax^2+bx+c=0[/tex]

If the quadratic function has only one root at 3, it must have the following form:

[tex]f(x)=a(x-3)^2[/tex]

This requirement is satisfied by a quadratic function with a vertex at (3,0) and an opening upwards.

We know that f(0) = 4, so we can plug these numbers into the equation to get:

[tex]4=a(0-3)^2[/tex]

simplify the above equation

4 = 9a

The value is,

a = 4/9

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Answer:

x = ±9

Step-by-step explanation:

If x² = k, then x = ±√k.

x² - 81 = 0

x² = 81

x = ±√81

x = ±9

Answer:772

Step-by-step explanation:

SA=PH+2b

SA=(10+8+10+8)(17)+2(8x10)

SA=772

Answer:

Step-by-step explanatin

multiply all of them

Answer:

Eighty biscuits.

Step-by-step explanation:

We need to find the limiting factor. We can do that by comparing ratio of mass of ingredient given to mass of ingredient needed for 20 biscuits

[tex]Butter:\\800:150\\=16:3\\=5.33\\Sugar:\\700:75=28:3\\=9.33\\Flour:\\1000:180\\=50:9\\=5.56\\Chocolate Chips:200:50\\=4:1\\=4\\[/tex]

We can clearly see that the choco. chips are the limiting factor since it has the lowest ratio, basically meaning we will run out of choco chips before anything else.

[tex]Biscuits=4*20=80[/tex]

Since we only have 4 times the choco chips needed to make 20 biscuits, we can only make 80 biscuits. Now you can see, we have other ingredients left, but choco chips have ran out which is why it was the limiting factor.

[tex]Flour:\\1000-4(180) = 280g[/tex]

After making 4 servings we still have 280g of flour left.

A minimum score of 88.95 is required to receive an "A" grade on the exam.

To determine the minimum score required to receive an "A" grade on an exam, we must first understand the meaning of standard deviation and mean. The mean is the average of a set of values, whereas the standard deviation is a measure of how far apart the values are from the mean. The minimum score required to receive an "A" grade is determined by calculating the z-score that corresponds to the top 12.3 percent of exam scores.

The formula for calculating the z-score is given as: z = (x - μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. Solving for z, we have: z = invNorm(1 - 0.123) = invNorm(0.877) ≈ 1.15. The inverse normal distribution function is used to determine the value of z that corresponds to the area to the right of the z-score. We can then use the formula for the z-score to solve for the raw score (x):
x = zσ + μ
Substituting the values we have, we get:
x = 1.15(17) + 68 ≈ 88.95
Therefore, a minimum score of 88.95 is required to receive an "A" grade in the exam.

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After dividing and simplifying we get (x-3)/(x+3)

One of the four fundamental operations of arithmetic, or how numbers are combined to create new numbers, is division. The additional operations are addition, subtraction, and multiplication.

At a fundamental level, counting the instances in which one number is contained within another is one interpretation of the division of two natural numbers. There is no requirement that this quantity be an integer. For instance, if there are 20 apples and they are divided equally among four people, each person will get 5 apples (see picture).

The integer quotient, which is the quantity of times the second number is entirely contained in the first number, and the remainder are both produced by the division with remainder or Euclidean division of two natural numbers.

1/(x+4) divide by  [tex](x-3)/(x^2 + 7x +12)[/tex]

Simplify : [tex]x^2 +7x +12[/tex]

[tex]x^2 + (3+4)x + 12[/tex]

[tex]x^2 + 3x +4x + 12[/tex]

[tex]x(x + 3) + 4(x + 3)[/tex]

[tex](x+3)(x+4)[/tex]

[tex]1/(x + 4) x (x-3)/(x+3)(x-4)[/tex]

After dividing and simplifying we get the following answer;

[tex]= (x-3)/(x+3)[/tex]

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The probability that 10 or more of 15 marketing personnel are extroverts is 0.719.

Since 80% of all marketing personnel are extroverts, the probability of any single marketing personnel being an extrovert is 0.8. The probability that 10 or more marketing personnel at the party of 15 are extroverts can be calculated using the Binomial Distribution formula:

P(X>=10) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]

P(X>=10) = 1 - [15C0*0.80*0.215 + 15C1*0.81*0.214 + 15C2*0.82*0.213 + 15C3*0.83*0.212 + 15C4*0.84*0.211 + 15C5*0.85*0.210 + 15C6*0.86*0.29 + 15C7*0.87*0.28 + 15C8*0.88*0.27 + 15C9*0.89*0.26]

P(X>=10) = 0.719

Therefore, 0.79 is the probability that 10 or more of the 15 marketing personnel at the party are extroverts.

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The transformation that would not result in a congruent figure when performed on triangle RST is A. A dilation by a scale factor of 2 with respect to point R.

The equation that has the same solution as the system of equations is C. 4x + 9y = 10

4x + 6y = 24.

Transformations that change the shape or size of a figure can change its congruency.  A dilation is a transformation that changes the size of a figure so this would mean that RST dilated would not result in a congruent figure.

When the system of equations, 4x + 9y = 10, 2x + 3y = 12 is solved, we find that x = 13 and y = - 14/ 3.

Options A,B, and D cannot have the same value because the numbers are the same and so they should have different values., Only option C can be the same and when the values are slotted in, this is proven.

Option C, 4x + 9y = 10 , 4x + 6y = 24 is therefore correct.

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In the following question, among the conditions given, There are 26^4 x 10^5 possible license plates that can be issued using this condition.

Hence, This is because the license plates consist of 4 letters and 5 digits. There are 26 possible letters that can be used in the first four places, so the total possible combinations of 4 letters is 26^4. There are 10 possible digits that can be used in the last five places, so the total possible combinations of 5 digits is 10^5. Multiplying these two together gives the total number of possible license plates: 26^4 x 10^5.

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There are a total of $26^4 × 10^5$ possibilities, which simplifies to 26,000,000,000 (twenty-six billion) possibilities. Therefore, with this condition, twenty-six billion license plates can be issued.

A state's license plates consist of 4 letters followed by 5 digits.

How many possible license plates can be issued using this condition?

When designing a license plate, the condition provided in the question suggests that a license plate should consist of 4 letters followed by 5 digits.

Therefore, we can count the total number of license plates in two phases.

The number of choices for each segment must be taken into account separately for the letters and the numbers.

When considering the letter possibilities, there are 26 options for each position since there are 26 letters in the alphabet.

For the first 4 positions, there are a total of $26^4$ = 456,976 possibilities.

Similarly, for the last 5 positions,

there are 10 options for each position since there are 10 digits.

There are $10^5$ = 100,000 possibilities for the last 5 positions.

The entire plate's total number of combinations is obtained by multiplying these numbers.

There are a total of $26^4 × 10^5$ possibilities

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The other diagonal of the rhombus is 4 cm.

The other diagonal of the rhombus can be found using the formula for the area of a rhombus, which is A = (d₁ × d₂)/2, where d₁ and d₂ are the lengths of the diagonals.

We're given that the area of the rhombus is 20 cm² and that one diagonal (d1) is 10 cm. Plugging these values into the formula, we get:

20 = (10 × d₂)/2

Simplifying, we get:

20 = 5 d₂

Dividing both sides by 5, we get:

d₂ = 4

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