An illinois study examined the effect of day care on behavior in toddlers. randomly selected parents who had a toddler in full-time day care were asked if their child had behavioral problems. the researchers found that among 987 parents surveyed, 212 said their child had behavioral problems. among 349 randomly selected parents with a toddler at home, 17 reported that their child had behavioral problems.

Answer:

its called a calculator division and multiplication

Step-by-step explanation:

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I think It must be 1,728.

So :

\( \sqrt[3]{1728} = 12\)

Thus each of its sides has a length of 12 inch.

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Answer:

step 2

Step-by-step explanation:

Erin's mistake is in step 2 it should be 8*2 first and 16* 5 which equals to 86

16.25 quarts

Note that:

1 cup = 0.25 quarts

Therefore:

65 cups = 65 x 0.25 quarts

65 cups = 16.25 quarts

Answer:

x=10

Step-by-step explanation:

First square root 36 cm^2

Then you square both 8 and 6

Then you square root the sum of the two numbers.

This is called Pythagorean Theorem, which can be shown as a^2 + b^2 = c^2

Answer:

Cupcake

Step-by-step explanation:

Because the sale price is bigger

Answer:

-------------------

Heron's formula states that the area of a triangle with side lengths a, b, and c is:

We have a triangle with side lengths:

We can first find the semi-perimeter:

Then we can plug this into Heron's formula to find the area:

So the area of the triangle is approximately 82.41 square units.

Answer:

B (HI/GI)

Step-by-step explanation:

Remember Soh Cah Toa.

Toa is the trick for tan, meaning the tan function is opposite divided by adjacent. The side opposite of angle G is HI, and the side adjacent to it is GI.

We must solve for n the following equation:

1) First, we assume n ≠ 0 and multiply both sides by √n, we get:

2) Now, we divide both sides by E:

3) Finally, taking the square on both sides, we get:

Hey there!

\(Answer:\boxed{0<x<3}\)

\(Explanation:\)

Graph below!

Hope this helps!

\(\text{-TestedHyperr}\)

Answer:I'm going to illustrate by converting 4325 to base 8. I an going to do it in two steps. First convert 4325 to base 10 and then convert this base 10 number to base 8.

Converting 4325 to base 10 just requires remembering what base 5 means.

4325 = 4 × 52 + 3 × 5 + 2 = 4 × 25 + 15 + 2 = 117.

To put 117 into base 8 imagine you have 117 CDs. Put them is stacks of 8 disks each. You get 14 stacks of 8 disks with 5 remaining (that is 117 ÷ 8 = 14 with a remainder of 5). Now take the 14 stacks and put them in groups of 8. You get 1 group of 8 stacks and 6 stacks remaining ((that is 14 ÷ 8 = 1 with a remainder of 6). Thus you have

1 group of 8 stacks (1 × 8 × 8 disks)

6 stacks (6 × 8 disks) and

5 individual disks.

Hence 117 = 1 × 82 + 6 × 81 + 5 = 1658

Here, more compactly is what I did

117 ÷ 8 = 14, remainder of 5

14 ÷ 8 = 1, remainder 6

1 ÷ 8 = 0, remainder 1

Read the remainders from bottom to top, 1658

Step-by-step explanation:

Fig. 2.6 alone does not provide sufficient information to calculate the percent elongation of materials. Percent elongation is a measure of the increase in length of a material after it has been subjected to a tensile load, and is calculated by dividing the increase in length by the original length and multiplying by 100.

Fig. 2.6 shows stress-strain curves for different materials, which provide information about the relationship between stress and strain for those materials. While the curve shape can provide some insight into the behavior of the material under load, it does not provide information about the original length or the change in length of the material, which are necessary to calculate percent elongation.

In order to calculate percent elongation, additional information about the material's original length and the change in length after a tensile load is required. This information can be obtained through laboratory testing or from material specifications provided by the manufacturer.

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Answer: 56

Step-by-step explanation:

Howard is incorrect the right answer is 56.

1.8 turns must an ideal solenoid should have if it is to generate a magnetic field of 1.5 mT when a current of 1.0 A passes through it

To calculate the number of turns required for an ideal solenoid, we can use the formula for the magnetic field inside a solenoid: B = μ₀ * n * I, where B is the magnetic field, μ₀ is the permeability of free space (constant), n is the number of turns per unit length, and I is the current.

Rearranging the formula, we have n = B / (μ₀ * I).

Given B = 1.5 mT (or 1.5 x 10⁻³ T) and I = 1.0 A, and knowing that μ₀ is a constant, we can substitute these values into the formula to find n.

n = (1.5 x 10⁻³) / (4π x 10⁻⁷ * 1.0) ≈ 1.19 x 10⁴ turns/m.

Since the solenoid is 10 cm (0.1 m) long, we can multiply n by the length to find the total number of turns:

Total turns = (1.19 x 10⁴ turns/m) * 0.1 m ≈ 1.19 x 10³ turns.

Rounding to the nearest whole number, the closest option is (b) 1.8.

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1.The machine will have no value after 48 months. 2.The graph of the machine's value over time will be a straight line. 3.The slope of the graph represents the rate of depreciation per month. 4.The intercepts of the graph indicate the initial value and zero value. 5.The expression V = -750x + 28,000 represents the value of the machine. 6.The machine has no value when x = 37 according to the expression. 7.The answer obtained using the expression differs from the answer in 8.question 1 due to possible rounding errors or calculation variations.

To determine when the machine has no value, we observe the pattern of depreciation. Based on the given data, the machine depreciates by $3,500 every 6 months. Therefore, it will take 48 months (8 cycles of 6 months) for the machine to have no value.

The table shows a consistent decrease in value over time with equal intervals of 6 months. This indicates a linear relationship between the number of months and the value. A linear relationship is represented by a straight line on a graph.

The slope of the graph can be determined by calculating the change in value divided by the change in time. In this case, the slope is (-750), meaning the value decreases by $750 per month. It represents the rate of depreciation per month.

The intercepts of the graph are obtained by determining the value of the machine at the start (initial value intercept) and when it reaches zero (zero value intercept). The initial value intercept is $28,000, which represents the starting value of the machine. The zero value intercept occurs when the machine has no value.

The expression V = -750x + 28,000 represents the value of the machine. The coefficient of x (-750) represents the rate of depreciation per month, while the constant term (28,000) represents the initial value.

Using the expression, when x = 37, the machine has no value. This differs from the answer in question 1 (48 months). The discrepancy could be due to rounding errors or variations in the method used to calculate the exact point at which the value reaches zero.

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The solution is,

1.   a, 99%       b71%

2. 64%, 44%

3. Number of particles   0, 1, 2, 3, 4,  5, 6, 7,  8, 9, 10, 11, 12, 13, 14

frequencies:                 1, 2, 3, 12, 11, 15, 18, 10,  12, 4, 5, 3, 1, 2, 1

Relative frequencies  0.01, 0.02,0.03,0.12,0.11,0.15, 0.18,0.1, 0.12,0.04,                        0.05,0.03,0.01,0.02,0.01

A histogram is an approximate representation of the distribution of numerical data.

here, we have,

Number of particles: 0, 1, 2, 3, 4, , 5, 6, 7

Frequency: 1, 2, 3, 12, 11, 15, 18, 10

Number of particles: 8, 9, 10, 11, 12, 13, 14

Frequency: 12, 4, 5, 3, 1, 2, 1

we solve by saying that  . one of th smaples wafer is with  any particles. we get the proportion by subtracting 1 from the total  divided by 100

100-1/100

.99

at least five particles , then we can subtract the number of those with particles less than five from 100 , divided by 100

100-(11+12+3+2+1)=71/100

0.71 or 71%

b. those particles within 5 and 10 inclusive

15+18+10+12+4+5=64/100

0.64

0r 64%

five and 10 exclusively will be

18+10+12+4=44/100

0.44

44%

c. Draw an histogram. first we have frequency table first

Number of particles    0, 1, 2, 3, 4,  5, 6, 7,  8, 9, 10, 11, 12, 13, 14

frequencies:                 1, 2, 3, 12, 11, 15, 18, 10,  12, 4, 5, 3, 1, 2, 1

Relative frequencies  0.01, 0.02,0.03,0.12,0.11,0.15, 0.18,0.1, 0.12,0.04,                        0.05,0.03,0.01,0.02,0.01

Relative frequencies is derived by dividing each frequencies over the total frequencies

we can say that it is unimodal or say that it is slightly positively skewed

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The space allοwed between the rοugh header and windοw head jamb shοuld be 1/4" tο 1/2"

When installing a windοw intο a rοugh οpening in a wall, it is impοrtant tο allοw fοr settling οr mοvement that may οccur in the building's structure οver time.

Settling can cause the windοw frame tο shift slightly, which can lead tο gaps οr misalignment between the windοw and the surrοunding wall. Tο prevent this frοm happening, a small gap is typically left between the rοugh header and the windοw head jamb.

This gap prοvides enοugh clearance fοr any settling οr mοvement that may οccur withοut affecting the perfοrmance οf the windοw οr causing any damage tο the surrοunding structure.

The recοmmended space allοwed between the rοugh header and windοw head jamb tο allοw fοr settling is typically 1/4" tο 1/2".

Therefοre,

The space allοwed between the rοugh header and windοw head jamb shοuld be 1/4" tο 1/2"

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After solving the word problem,  the change in the number of shares of stock he owns, is x-96.

In the given question we have to find  the change in the number of shares of stock he owns.

As given that Eric owns shares of a certain stock. If he sells off 8 shares each month for a year.

Let Eric owns x shares of a certain stock.

If he sells off 8 shares each months for a year.

So as we know that in a year have 12 months.

In 1 month = 8 shares sells

12 months = 12×8 shares sells

12 months = 96 shares sells

So in a year Eric sells 96 shares and he have total x shares.

So the remaining shares are x-96.

Hence, the change in the number of shares of stock he owns, is x-96.

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Step-by-step explanation:

The two lines intersect at one point so the system has exact same solution (one solution )

The sample space consists of 100 elements, since there are 10 possible outcomes when rolling the die, and 2 possible outcomes when flipping the coin (head or tail). The probability of getting a tail and rolling a 5 is 1/20, or 0.05. There are 190 ways to select two items from 20 if order does not matter, and 400 ways to select two items from 20 if order matters. The probability of event C is 0.55, the probability of their union is 0.6, and the probability of their intersection is 0.1. Events A and C are not mutually exclusive, and the probability of event B is 0.25.

Answer 1: The sample space consists of 100 elements, since there are 10 possible outcomes when rolling the die, and 2 possible outcomes when flipping the coin (head or tail).

Answer 2: The probability of getting a tail and rolling a 5 is 1/20, or 0.05. This is calculated by finding the probability of getting a tail (which is 1/2) and multiplying it by the probability of rolling a 5 (which is 1/10).

Answer 3: There are 190 ways to select two items from 20 if order does not matter. This can be calculated using the combination formula, nCr, where n is the total number of items (20) and r is the number of items chosen (2). Thus, there are 20C2 = 20!/(2!(20-2)!) = 190 ways to select two items.

Answer 4: There are 400 ways to select two items from 20 if order matters. This can be calculated using the permutation formula, nPr, where n is the total number of items (20) and r is the number of items chosen (2). Thus, there are 20P2 = 20!/(20-2)! = 400 ways to select two items.

Answer 5: P(C) = 0.55. This can be calculated by adding up all the individual probabilities for each sample point in event C. Thus, P(C) = 0.2 + 0.2 + 0.25 + 0.15 = 0.55.

Answer 6: P(AUB) = 0.6. This can be calculated by adding up all the individual probabilities for each sample point in events A and B. Thus, P(AUB) = 0.05 + 0.2 + 0.2 + 0.25 + 0.15 + 0.1 = 0.6.

Answer 7: P(A?B) = 0.1. This can be calculated by subtracting the probability of events A and B from the probability of their union. Thus, P(A?B) = P(AUB) – P(A) – P(B) = 0.6 – 0.05 – 0.25 = 0.1.

Answer 8: No, events A and C are not mutually exclusive because they share a common sample point, E?.

Answer 9: P(B) = 0.25. This is the probability of event B, as given in the question.

The sample space consists of 100 elements, since there are 10 possible outcomes when rolling the die, and 2 possible outcomes when flipping the coin (head or tail). The probability of getting a tail and rolling a 5 is 1/20, or 0.05. There are 190 ways to select two items from 20 if order does not matter, and 400 ways to select two items from 20 if order matters. The probability of event C is 0.55, the probability of their union is 0.6, and the probability of their intersection is 0.1. Events A and C are not mutually exclusive, and the probability of event B is 0.25.

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a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.

b) Nyoko cannot find a value of b so that the equation has no solutions.

The equation 1 is given as follows:

6x - 5 + 2x = 4(2x - 1) - 1.

Combining the like terms and applying the distributive property, the simplified equations are given as follows:

8x - 5 = 8x - 4 - 1

8x - 5 = 8x - 5.

As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.

The equation 2 is given as follows:

3x + 7 = bx + 7.

A system of linear equations will have zero solutions when:

As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.

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Answer:

Below.

Step-by-step explanation:

1.  Vertex is  (1, -9)

2. Axis of symmetry is x = 1.

3.  x-intercepts are at (-2,0) and (4,0).

4.  y-intercept is at (0, -8).

5. That is (3, -5).

Answer:

Vertex: In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero. This is typically a local maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extreme point of curvature.

The axis of symmetry of a parabola is a line about which the parabola is symmetrical. When the parabola is vertical, the line of symmetry is vertical. When a quadratic function is graphed in the coordinate plane, the resulting parabola and corresponding axis of symmetry are vertical.

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Y-intercept: In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

A^3 - B^3

a-b

5

Step-by-step explanation:

Hope this helps

Answer:

Li Ting's father:  40 years

Li Ting:                10  years

Step-by-step explanation:

Let F stand for Li Ting's father's current age, and L for Li Ting's current age.

We are told that "In five years' time, Li Ting's father will be three times as old as Li Ting"  We can write that as:

(F+5) = 3*(L+5)

We are also told that "Four years ago, her father was six times as old as her."  We can write that as:

(F-4) = 6(L-4)

---

We have two equations and two unknowns.  Find a way to eliminate one of the two variables (F or L) and solve for the remaining one.

(F+5) = 3*(L+5)

(F-4) = 6(L-4)

I'll choose the second equation and rearrange it to isolate F:

F = 6(L-4) + 4

F = 6L - 20

Now use this definition of F in the first equation:

(F+5) = 3*(L+5)

[6L-20]+5 = 3*(L+5)

6L - 20 + 5 = 3L + 15

3L = 15 +20 -5

3L = 30

L = 10 years old

Use this to solve either equation for F:

F = 6L - 20

F = 6*(10) - 20

F = 40 years old

=====

In five years:

F = 45, and L = 15   [Li Ting's father will be three times as old as Li Ting]

Four years ago:

F = 36 and L = 6  [Four years ago, her father was six times as old as her]

Answer:

Just do,

Step-by-step explanation:

(X x Z) = Y

(X/Z) = Y

The translations performed are

From the question, we have the following function that can be used in our computation:

f(x) = ln(x)

g(x) = -ln(x + 1) - 3

First, we have the transformation to be:

From f(x) = ln(x) to f(x) = -ln(x)

This means a reflection across the x-axis

Next, we have

From f(x) = -ln(x) to f(x) = -ln(x + 3)

This means the function is translated left by 3 units

Next, we have:

From f(x) = -ln(x + 3) to f(x) = -ln(x + 3) - 3

This means the function is translated down by 3 units

Hence, the translation is 3 units left and 3 units down

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(a) When n=2, the probability that Pat will pass the exam is: 1/8

(b) When n=10, the probability that Pat will pass the exam is approximately: 0.0258

(c) When n=100, the probability that Pat will pass the exam is extremely close to 0.

(a) When n = 2, Pat has four possible ways to answer the first question, and four possible ways to answer the second question. The total number of possible ways to answer the two questions is thus 4 * 4 = 16.

Since there is only one correct answer for each question, the probability of guessing the correct answer for a question is 1/4.

Thus, the probability of guessing the correct answer for both questions is (1/4) * (1/4) = 1/16. Pat will pass the exam if the grade is greater than 50%, which means if he gets at least one question right.

Since there are two questions, there are two possible ways in which Pat can pass the exam: by answering the first question correctly and answering the second question incorrectly, or by answering the second question correctly and answering the first question incorrectly.

The probability of Pat passing the exam is therefore 2 * 1/16 = 1/8.

(b) When n = 10, Pat has four possible ways to answer each of the 10 questions, so the total number of possible ways to answer the 10 questions is 4^10.

The probability of guessing the correct answer for a question is still 1/4, so the probability of guessing the correct answer for all 10 questions is (1/4)^10.

Pat will pass the exam if he gets at least 6 questions right. There are many ways in which Pat can get at least 6 questions right, so we will calculate the probability of Pat getting 5 or fewer questions right, and then subtract that from 1 to get the probability of Pat passing the exam.

The probability of Pat getting 5 or fewer questions right is the sum of the probabilities of Pat getting 0, 1, 2, 3, 4, or 5 questions right. Using the binomial probability formula, we can calculate these probabilities as follows:

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

where X is the number of questions Pat gets right.

P(X = k) = (10 choose k) * (1/4)^k * (3/4)^(10-k)

for k = 0, 1, 2, 3, 4, 5

Using a calculator or computer, we can calculate these probabilities as follows:

P(X = 0) ≈ 0.0563

P(X = 1) ≈ 0.1876

P(X = 2) ≈ 0.2814

P(X = 3) ≈ 0.2503

P(X = 4) ≈ 0.1452

P(X = 5) ≈ 0.0533

Therefore, P(X ≤ 5) ≈ 0.9742 and the probability of Pat passing the exam is1 - P(X ≤ 5) ≈ 0.0258

(c) When n = 100, the total number of possible ways to answer the 100 questions is 4^100.

The probability of guessing the correct answer for a question is still 1/4, so the probability of guessing the correct answer for all 100 questions is (1/4)^100. Pat will pass the exam if he gets at least 51 questions right.

There are many ways in which Pat can get at least 51 questions right, so we will calculate the probability of Pat getting 50 or fewer questions right, and then subtract that from 1 to get the probability of Pat passing the exam.

The probability of Pat getting 50 or fewer questions right is the sum of the probabilities of Pat getting 0, 1, 2, ..., 50 questions right.

Using the binomial probability formula, we can calculate these probabilities as follows:

P(X ≤ 50) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 50)

where X is the number of questions Pat gets right.

P(X = k) = (100 choose k) * (1/4)^k * (3/4)^(100-k)

for k = 0, 1, 2, ..., 50

Unfortunately, there is no way to calculate this sum directly, since there are too many terms to add up. However, we can use a normal approximation to estimate the probability. The binomial distribution is approximately normal when n is large and p is not too close to 0 or 1.

In this case, n = 100 and p = 1/4, so we can use a normal distribution to approximate the binomial distribution with mean µ = np = 25 and standard deviation σ = sqrt(np(1-p)) = 3.807. We can then use a standard normal distribution to estimate the probability as follows:

P(X ≤ 50) ≈ P(Z ≤ (50.5 - 25)/3.807)where Z is a standard normal variable.

Using a table or a calculator, we can find that P(Z ≤ 6.53) ≈ 1. Therefore, the probability of Pat passing the exam is approximately 1 - P(X ≤ 50) ≈ 0.

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Answer:

809

Step-by-step explanation:

787 susifx