kristine has a $20 apps cash card and wants to buy some games and songs.Each game costs $2 and each song cost 1.25.Kristine wants to buy at least 12 items.Solve the system of inequalities by graphing to determine the possible number of games and songs that kristine can buy

Answer: Positive Integer factors of 610 = 2, 5, 10, 61, 610 divided by 2, 5, 61, gives no remainder. They are integers and prime numbers of 610, they are also called composite number.

Step-by-step explanation: In the answer hope it helps

Answer:

3⃣(1⃣2⃣5⃣-6⃣4⃣)

A sixth wind turbine will be placed near the intersections of the bisector. To find the location of the sixth wind turbine near the intersections of the bisector.

Start by identifying the bisector of the given intersections. The bisector is a line that divides the angle formed by the two intersections into two equal angles.Locate the midpoint of the bisector. This point will be equidistant from the two intersections.

From the midpoint, measure the desired distance to place the sixth wind turbine. This distance should be consistent with the placement of the other wind turbines. Mark the location of the sixth wind turbine at the measured distance from the midpoint along the bisector. This will ensure that it is equidistant from the two intersections.

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The question pertains to the placement of a wind turbine near the intersection of the bisectors, setting a scenario of using principles of geometry and the application of translation and rotation in real life for maximum utilization of wind energy.

The placement of a wind turbine near the intersection of the bisectors involves understanding the principles of geometry. In order to understand this, one needs to understand bisectors, which are a line, ray, or segment that divides an angle or segment into two equal parts.

In the case of wind turbines, these might be placed near the intersections of the bisectors based on the consideration of maximum distribution of wind energy. The bisectors could be representing the ideal locations to capture the wind from all directions equally. This concept combines both principles of translation and rotation. The turbines rotate to generate power (rotational motion), and they may be laid out in a grid (translational symmetry) to efficiently capture wind energy.

It's a great example of how rotational motion and principles of geometry may be applied in real life, especially in the field of renewable energy resources. Therefore, this is a blend of geometry and physical science, with a practical application in engineering and environmental science.

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According to the question we have  approximately 99.74 percent of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

To answer this question, we will use the normal distribution formula and z-score.

First, we need to find the z-score for the lower limit of $1.20:

z = (1.20 - 1.50) / 0.10 = -3

Next, we need to find the z-score for the upper limit of $1.80:

z = (1.80 - 1.50) / 0.10 = 3

Now, we can use a z-table to find the area under the curve between these two z-scores.

The area to the left of z = -3 is 0.0013, and the area to the left of z = 3 is 0.9987.

To find the area between these two z-scores, we subtract the area to the left of z = -3 from the area to the left of z = 3:

0.9987 - 0.0013 = 0.9974

Therefore, approximately 99.74% of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

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When dividing the period from 1993-2015 into three distinct periods based on the rate of growth of average student debt, one possible approach could be:

1. 1993-2003: Slow and steady growth
During this period, the rate of growth of average student debt was relatively stable and moderate. The increase in student debt was gradual, and the overall burden on students was not as pronounced as in later periods. For example, the average student debt may have increased by a few thousand dollars over these ten years.

2. 2003-2008: Accelerated growth
In this period, the rate of growth of average student debt started to accelerate. The increase in student debt became more significant, potentially due to factors such as rising tuition costs, increased borrowing, and changes in financial aid policies. For example, the average student debt may have doubled or tripled during this five-year period.

3. 2008-2015: Rapid and substantial growth
The period from 2008 to 2015 witnessed a sharp and substantial increase in the rate of growth of average student debt. This period corresponds with the aftermath of the 2008 financial crisis and its impact on the cost of education. The economic recession led to reduced financial support for higher education, resulting in higher borrowing rates for students. For example, the average student debt may have increased by tens of thousands of dollars or even more during this seven-year period.

It's important to note that the division of periods may vary based on the specific data and factors considered. The examples provided are meant to illustrate potential trends rather than represent precise figures. Additionally, it's crucial to consult reliable sources and data on average student debt to obtain accurate information for a comprehensive analysis of the topic.

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If the possibility of becoming ill be 50% then the probability that exactly one of the people becomes ill be 0.375.

Given that the possibility of becoming ill of a person is 50-50.

We are required to find the probability that exactly one of the people becomes ill.

Probability is basically the likeliness of happening an event that are possible. It cannot be negative. It lies between 0 and 1.

Probability=Number of items/Total of items.

We can find the probability that exactly one of the people becomes ill through binomial probability distribution.

Probability that the person will ill=0.5

Probability that the person will not ill=1-0.5=0.5.

Probability that exactly one of the people becomes ill can be =

=3\(C_{1}\)\((0.5)^{1} (0.5)^{2}\)

=3*0.5*0.25

=0.375

Hence if the possibility of becoming ill be 50% then the probability that exactly one of the people becomes ill be 0.375.

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The probability of catching a defect is approximately 99.9768%.

To calculate the probability of catching a defect, we need to consider the complement of the event, which is the probability of not catching a defect in any of the four inspections.

The probability of not catching a defect in inspection 1 is 1 - 0.9 = 0.1 (since the complement of catching a defect is not catching a defect). Similarly, the probabilities of not catching a defect in inspections 2, 3, and 4 are 1 - 0.8 = 0.2, 1 - 0.12 = 0.88, and 1 - 0.95 = 0.05, respectively.

Since the inspections are independent events, we can multiply these probabilities together to find the probability of not catching a defect in all four inspections: 0.1 × 0.2 × 0.88 × 0.05 = 0.0088.

Therefore, the probability of catching a defect is 1 - 0.0088 = 0.9912, or approximately 99.9768%.

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Answer:

135°+97°+x=180°. 232°+x=180°. x=232-180=102°

:x=102°

The result of the original integral is:

∫15sin3(x)cos2(x)dx = (15/2)(cos(3x + 2x) + cos(3x - 2x)) + 2C

What is the integration?

In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.

The integral of the product of sine and cosine functions can be evaluated using the identity:

sin(a)cos(b) = (1/2)(sin(a + b) + sin(a - b))

Therefore, we can rewrite the integrand as:

15sin3(x)cos2(x) = (15/2)sin(3x + 2x) + (15/2)sin(3x - 2x)

Now, we can integrate each of the two terms separately:

∫(15/2)sin(3x + 2x)dx = (15/2)cos(3x + 2x) + C

∫(15/2)sin(3x - 2x)dx = (15/2)cos(3x - 2x) + C

Therefore, the result of the original integral is:

∫15sin3(x)cos2(x)dx = (15/2)(cos(3x + 2x) + cos(3x - 2x)) + 2C

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The ship is 394.73 fr far from the base of the lighthouse.

According to the given question.

Angle of depression from the top of the light house is 21 degrees.

Let ∠ABC represents the angle of depression. And BC be the distance of ship from the base of light house.

Now in triangle ABC we have

tan 21 = AC/BC

⇒ 0.38 = 150/BC

⇒BC = 150/0.38

⇒ BC = 394.73ft

Hence, the ship is 394.73 fr far from the base of the lighthouse.

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A distribution of scores on a driver's license test forms is normally shaped. This is an example of a symmetrical distribution is TRUE.

A symmetrical distribution is a distribution where there is an equal number of data points on both sides of the center point, in which the mean, mode, and median of a data set are all similar.

A normal distribution is a bell-shaped distribution that is symmetrical, with most of the data falling near the mean and progressively less toward the tails. When data are symmetrical, the mean and median values are similar, and the standard deviation can be used to compute the proportions of data within a range of values surrounding the mean.

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Answer:

Step-by-step explanation:

x/3 = 14

x = 42

Either option is valid and correctly written in point-slope form using the point (−5,−2) as (x1,y1).

The point-slope form of an equation of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line

m is the slope of the line.

We can use the given point (−5,−2) as (x1,y1)

Choose any value for the slope m to write the equation of the line in point-slope form.

For example:

Option 1:

Let's choose the slope m to be 2.

Then the equation of the line becomes:

y - (-2) = 2(x - (-5))

Simplifying the equation:

y + 2 = 2(x + 5)

Option 2:

Let's choose the slope m to be -3.

Then the equation of the line becomes:

y - (-2) = -3(x - (-5))

Simplifying the equation:

y + 2 = -3(x + 5)

Either option is valid and correctly written in point-slope form using the point (−5,−2) as (x1,y1).

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Answer:

i had a breathing problem when i was 3 years old and i almost died, but i got surgery  and i got my breathing back to normal

Step-by-step explanation:

Answer:

x=-18

Step-by-step explanation:

Answer:

The answer is -18

Step-by-step explanation:

STEP 1:

\(3 \times \frac{2}{3} (x + 6) = 3( - 8)\)

2(x+6) = -24

______________________________________

STEP 2:

Divide both sides by 2:

\( \frac{2(x + 6)}{2} = \frac{ - 24}{2} \)

________________________________

STEP 3:

Simplify:

\(x + 6 = - 12\)

Subtract 6 from both sides:

\(x + 6 - 6 = - 12 - 6\)

________________________________

STEP 4:

\(x = - 18\)

Therefore, your answer is -18.

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Answer:

644

Step-by-step explanation:

SA=[2×(5×20 + 5×6 + 20×6)] +

[2×(4×12 + 4×6 + 12×6)] -

[ 2× 12×6]

= [2×(250)]+[2×(144)] - [144]

= 500+288-144

= 644 cm²

Answer:

17

Step-by-step explanation:

what's the value of y when x = -5?" Since x cannot = -5, then the answer is "null" or "does not exist". It's like saying "I have 4 US coins whose total value is 6 cents.

The estimator hat mu1 is unbiased and efficient, while hat mu2 is biased and less efficient.

In the first step, let's examine the bias of the estimators. To determine whether an estimator is unbiased, we compare its expected value to the true parameter value. For hat mu1, we have:

E(hat mu1) = E((n - 1)/n * hat Y)

Since the expected value is a linear operator, we can rewrite this as:

E(hat mu1) = (n - 1)/n * E(hat Y)

Now, since each Y_i is drawn from a normal distribution with mean mu, we have E(hat Y) = mu. Substituting this in, we get:

E(hat mu1) = (n - 1)/n * mu

This shows that hat mu1 is an unbiased estimator, as its expected value is equal to the true parameter mu. On the other hand, for hat mu2, we have:

E(hat mu2) = E(hat Y + 2/n)

Again, using linearity of expectation, we can split this into two terms:

E(hat mu2) = E(hat Y) + E(2/n)

Since E(hat Y) = mu, we can simplify further:

E(hat mu2) = mu + 2/n

This indicates that hat mu2 is biased, as its expected value is mu + 2/n, which is different from the true parameter mu.

Moving on to efficiency, we compare the variances of the estimators. The efficiency of an estimator is determined by its variance, with a more efficient estimator having a smaller variance. For hat mu1, the variance is:

Var(hat mu1) = Var((n - 1)/n * hat Y)

Since the observations are independent and identically distributed (iid) from a normal distribution, we can use the properties of variance to simplify this expression:

Var(hat mu1) = \(((n - 1)/n)^2 * Var(hat Y) = ((n - 1)/n)^2 * (sigma^2/n)\)

On the other hand, for hat mu2, the variance is:

Var(hat mu2) = Var(hat Y + 2/n)

Again, using the properties of variance, we get:

Var(hat mu2) = Var(hat Y) + Var(2/n) = Var(hat Y) + 0 = Var(hat Y)

Comparing the two variances, we find that Var(hat mu1) < Var(hat mu2), indicating that hat mu1 is more efficient than hat mu2.

In summary, hat mu1 is an unbiased and efficient estimator, while hat mu2 is biased and less efficient.

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Answer:

A. 0

Step-by-step explanation:

Slope tells you steepness or flatness of your line.

If you know two points on a line find slope by subtracting the y's and put that on top of a fraction. And subtract the x's and put that on the bottom of the fraction.

Subtract y's: 3 - 3

Put it on top: 0/...

Subtract x's: 5 - -4

same as 5+4

Put that on the bottom: 0/9

slope, usually called m, is 0/9, which is 0.

Notice if you graph these two points its a hOrizOntal line. HOrizOntal lines have zerO slope.

Yes, The matrix does indeed have an inverse.

A rectangular or square array of figures, characters, or expressions arranged in rows and columns is known as a matrix. In many different disciplines, including computer science, engineering, physics, and mathematics, matrices are frequently employed and Matrix representations of physical phenomena, such as the wave functions in quantum mechanics, are common in physics. To represent and simulate complicated systems, like circuits and control systems, engineers employ matrices. Matrix-based techniques are utilised in a variety of computer science applications, including image processing, computer graphics, and machine learning.

The elements of a matrix, which are often written with a rectangular bracket, can be used to symbolise it.

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Yes, the inverse of a matrix exists if the determinant of the matrix is -13.

What is a matrix?

Linear equations are expressed using matrices, which are ordered rectangular arrays of numbers. Columns and rows make up a matrix. Mathematical operations like addition, subtraction, and matrix multiplication can also be done on matrices. If there are m rows and n columns, the matrix is represented as m × n matrix. The inverse of a matrix is available only for square matrices.

Now the determinant is a value that is associated with a square matrix.

The product of all the elements in any row or column and their corresponding co-factors is the determinant of a matrix.

For an inverse matrix to exist, the determinant of the matrix should not be zero. This is because the determinant of the inverse matrix is the inverse of the determinant of the original matrix.

If the determinant is zero, then the determinant of the inverse matrix will be 1/0, which is undefined.

So, as long as the determinant is not equal to zero, the inverse matrix exists.

Therefore the inverse of a matrix exists if the determinant of the matrix is -13.

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When a plane intersects both nappes of a double-napped cone but does not go through the vertex of the cone, it forms a hyperbola.

A double-napped cone is a three-dimensional object with two identical nappes, or curved surfaces, that meet at a single vertex. The nappes extend infinitely in both directions away from the vertex.

When a plane intersects the double-napped cone, it cuts through both nappes, resulting in a curve that consists of two separate branches. These branches are symmetrical about the plane that contains the axis of the cone.

The resulting curve, known as a hyperbola, has two distinct arms or branches that open up in opposite directions. The hyperbola is characterized by its center, vertices, asymptotes, and foci. The plane intersects the cone at an angle, which determines the shape and orientation of the hyperbola.

Therefore, when a plane intersects both nappes of a double-napped cone but does not go through the vertex, it forms a hyperbola.

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Answer:

7

Step-by-step explanation:

The middle 2 numbers are 6 and 8. Add them both up and divide them by 2. Gets you 7.

The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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The difficulty of range as a measure of variability that is overcome by interquartile range is option b that is The range is influenced too much by extreme values.

The variance is the mean squared difference between each data point and the mean-centered distribution. A statistical assessment of the dispersion of values in a data collection is referred to as variance. Variance explicitly assesses how distant each number in the set is from the mean (average), and consequently from every other number in the set. Variance is a measure of how data points differ from the mean, whereas standard deviation is a measure of statistical data distribution. The primary distinction between the two is that standard deviation is expressed in the same units as the mean of the data, whereas variance is expressed in squared units.

Here,

The interquartile range overcomes the problem of range as a measure of variability. Extreme values have an undue impact on the range.

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Answer:1/7

Step-by-step explanation: You take the amount that are springer spaniels and you put them with the whole of the dogs in the park 14 so you would have 2/14. You can reduce this fraction to 1/7 by dividing both the top and bottom of the fraction by 2.

(1+i) ^18 ≈ 4.766×10^6 - 1.632×10^7i. a. To solve (e^-4-2i) ^2, we first need to simplify e^-4-2i. Using Euler's formula, we can rewrite e^-4-2i as e^-4 * e^-2i, which is equivalent to e^-4(cos (-2) +i*sin (-2)). Simplifying further, we get e^-4(cos(2)-i*sin(2)).

Now, we can square this expression to get (e^-4(cos (2)-i*sin (2))) ^2. Using the formula (a+bi)^2 = a^2 - b^2 + 2abi, we get:

(e^-4*cos(2))^2 - (e^-4*sin(2))^2 + 2*e^-4*cos(2)*i*sin(2)

Simplifying, we get:

e^-8 - e^-8*sin^2(2) + 2*e^-4*cos(2)*i*sin(2)

This is the form a+bi, so our final answer is:

a = e^-8 - e^-8*sin^2(2) ≈ 0.0153
b = 2*e^-4*cos(2)*sin(2) ≈ -0.0565

Therefore, (e^-4-2i)^2 ≈ 0.0153 - 0.0565i.

b. To solve (1+i)^18, we can use the binomial theorem, which states that (a+b)^n = Σ(n choose k)a^(n-k)*b^k, where Σ is the sum from k=0 to n. Applying this to (1+i)^18, we get:

(18 choose 0)1^18*i^0 + (18 choose 1)1^17*i^1 + (18 choose 2)1^16*i^2 + ... + (18 choose 18)1^0*i^18

Simplifying the coefficients using the formula (n choose k) = n!/((n-k)!k!), we get:

1 + 18i - 1530 - 3060i + 18564 + 145152i - 437580 - 947736i + 1352078 + 1081664i - 587863.5 - 575784i + 203887.5 + 405528i - 88749 + 35064i - 5400 + 304i

Adding up the real and imaginary parts separately, we get:

a = 4766436 ≈ 4.766×10^6
b = -16318512 ≈ -1.632×10^7

Therefore, (1+i)^18 ≈ 4.766×10^6 - 1.632×10^7i.

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