Solve:
9 + 2 - 10x = 1 - 10x

Answer:

Step-by-step explanation:

p=  a/3  -  1/3

The probability that the sample proportion is between 0.70 and 0.80 is 0.7498.

Assuming that we have a simple random sample of size n from a population with proportion p, the sample proportion is defined as:

p1 = x/n

where x is the number of individuals in the sample with the characteristic of interest.

The standard error of the sample proportion is given by:

SE(p) = sqrt((p1 * (1 - p)) / n)

To standardize the sample proportion, we can use the following formula:

z = (p1 - p) / SE(p1)

where p is the population proportion.

Once we have calculated the z-score, we can use a standard normal distribution table or calculator to find the probability that the sample proportion is between 0.70 and 0.80.

Here's an example:

Suppose we have a sample of 100 individuals, and we know that the population proportion is 0.75. We can calculate the standard error of the sample proportion as:

SE(p1) = sqrt((0.75 * (1 - 0.75)) / 100) = 0.0433

To find the z-score for a sample proportion of 0.70, we can use the formula:

z = (0.70 - 0.75) / 0.0433 = -1.15

Similarly, to find the z-score for a sample proportion of 0.80, we can use the formula:

z = (0.80 - 0.75) / 0.0433 = 1.15

We can use a standard normal distribution table or calculator to find the probabilities associated with these z-scores. From the table, we find that:

P(z < -1.15) = 0.1251

P(z < 1.15) = 0.8749

To find the probability that the sample proportion is between 0.70 and 0.80, we can subtract these probabilities:

P(-1.15 < z < 1.15) = P(z < 1.15) - P(z < -1.15) = 0.7498.

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A word which has reflectional symmetry across a horizontal line is CHECKBOOKS

Therefore, the correct answer is an option (B)

We know tha a reflection symmetry is nothing but if there exists at least one line that divides a figure into two halves such that one half is the mirror image of the other half.

In case of reflectional symmetry across a horizontal line, if we divide a figure by horizontal line into two halves, then where upper-half of the figure reflects the lower half of the figure.

Consider a word CHECKBOOKS

If we draw a horizontal line through this word such that a line divides the word into two halves.

We can observe that, the letters B, C, H, E, K, O, and S are symmetrical across a horizontal line.

Therefore, the correct answer is an option (B)

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Answer: Juan

Step-by-step explanation: Because if you divide 27 by 30 that makes 0.9 which if you multiply by a hundred you have 90 which means that Kim scored 80% and Juan scored 90%.

Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.

Herein we must make use of trigonometric expressions and properties of trigonometric functions to find the right value. According to trigonometry, both cosine and sine are negative in the third quadrant. Thus, by using the fundamental trigonometric expression (sin² α + cos² α = 1) and substituting all known terms we find that:

\(\sin \theta = -\sqrt{1 - \cos^{2}\theta}\)

\(\sin \theta = - \sqrt{1 - \left(-\frac{13}{30} \right)^{2}}\)

sin θ ≈ - √731 / 30

Based on the knowledge of trigonometric expressions and properties of trigonometric functions, the value of the sine function is equal to - √731 / 30.

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The velocity vector of the path is (-2sin(2t), -4, 0).

To determine the velocity vector of the path (cos(2t), 7-4t, -7), we need to take the derivative of each component with respect to time:

dx/dt = -2sin(2t)
dy/dt = -4
dz/dt = 0

So the velocity vector is (dx/dt, dy/dt, dz/dt) = (-2sin(2t), -4, 0). However, since we are not given a specific value of t, we cannot simplify this any further. Therefore, the velocity vector of the path is (-2sin(2t), -4, 0).

The velocity vector gives us information about the direction and magnitude of the movement of an object along a path. In this case, the object moves with a changing horizontal component and a constant vertical component.

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Betty's children have greater age dispersion than Ryan's children. Their ages range from 10 to 17, while Ryan's children range from 2 to 17.

Betty's children have the greatest dispersion. Dispersion refers to the extent to which the values in a set of data are spread out. The difference between the youngest and oldest child in Betty's family is 7 years, while the difference in Ryan's family is 15 years. The greater difference indicates a higher level of dispersion, meaning Betty's children have a greater range of ages and are spread out over a larger range of values than Ryan's children.

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Answer:

9/40

Step-by-step explanation:

3/5 - 3/8

24/40 - 15/40

= 9/40

( I hope this was helpful) >;D

Answer:

1,3 and 4

it is what it be

The two fractions with denominators of 2 and 6 that add up to 19/3 are 3/6 and 29/3, respectively.

First, let's break down what that mixed number means in terms of fractions. 6 1/3 is the same as 19/3.

Now, we need to find two fractions with different denominators that add up to 19/3. One way to do this is to use a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of the two denominators.

Let's say we want to find two fractions that add up to 19/3, with denominators of 2 and 6. The LCM of 2 and 6 is 6. So, we can rewrite the fractions with a denominator of 6:

1/2 = 3/6

x/6

Now we need to find the value of x that makes the sum of the fractions equal to 19/3:

3/6 + x/6 = 19/3

To solve for x, we can multiply both sides by 6:

3 + x = 38/3

Then, we can subtract 3 from both sides:

x = 29/3

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\(S_1 = 2+4+6+8+...+26 \\\\~~~~=2(1+2+3+4+...+13)\\\\~~~~=2 \cdot \dfrac{13(13+1)}2~~~~~~~~;\left[\text{Sum of consecutive positive integers }= \dfrac{n(n+1)}2 \right] \\\\~~~~=13 \cdot 14\\\\~~~~=182\\\\S_2 = 1+3+5+7+...+25\\\\\text{It is an arithmetic series wihere}\\\\\text{First term, a =1, ~Common difference, d = 2,~ number of terms = n} \\\\~~~~\text{Nth term} = a+(n-1)d\\\\\implies 25 = 1+(n-1)2\\\\\implies 2n-2 = 24\\\\\implies 2n = 24+2\\\\\implies 2n= 26\\\\\)

\(\implies n = \dfrac{26}2 \\\\\implies n= 13\\\\\text{S} _2= \dfrac{\text{n(First term+ Last term)}}{2}\\\\~~~~~~=\dfrac{13(1+25)}2\\\\~~~~~~=\dfrac{13 \times 26}2\\\\~~~~~~=13 \times 13\\\\~~~~~~=169\\\\\text{Hence,}~~ S_1 - S_2 =182 - 169 =13\)

Answer:

13

Step-by-step explanation:

2 + 4 + 6 + 8 + ...... + 26

n = 13

Sum of first 'n' even numbers = n( n +1)

                                                 = 13 * 14

                                                  = 182

1 + 3 + 5 + 7 + .....+25

n = 13

Sum of first 'n' odd numbers = n²

                                               = 13 * 13

                                               = 169

2 + 4 + 6 + 8 + ... + 26 - (1 + 3 + 5 + 7 + ......+25) = 182 - 169

                                                                            = 13

Answer: 4

Step-by-step explanation:

In triangle OCB,

OB2  =  OC2 + BC2

52  =  32 + BC2

BC2  =  25 - 9

BC2  =  16

BC  =  4

Solution

Question 1:

Question 2:

Final Answer

Question 1:

The exponential function to model the scenario is

Question 2:

The number of rabbits that will hop out of the hat on the 13th Day is 12,288 rabbits

A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one. Option A is the correct answer.

The standard normal distribution, often known as the z-distribution, is a special sort of ordinary distribution with a mean of zero and a standard deviation of one. Option A is the correct answer.

Any normal distribution can be standardized through transforming its values into z scores. The Z scores indicate how many standard deviations a certain result is from the mean. All normal distributions are unimodal, symmetrically distributed, and have a bell-shaped curve. One such distribution is the common normal distribution. On the other hand, a normal distribution's mean and standard deviation can be any value. In the typical normal distribution, the mean and standard deviation remain constant.

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A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.

A standard normal distribution, also known as the Z-distribution, is a specific type of normal distribution. It has a mean of zero and a standard deviation of one. The Z-distribution is often used in statistics to standardize data and calculate probabilities.

The standard normal distribution is represented by a bell-shaped curve that is symmetric around the mean of zero. The area under the curve represents the probability of a random variable falling within a certain range.

The Z-score, which measures the number of standard deviations a data point is from the mean, is commonly used in hypothesis testing and confidence interval calculations.

The standard normal distribution is widely used in various fields, including finance, psychology, and quality control.

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There are three conditions for inference, which are:The sample is representative of the population.The sample size is sufficiently large.The sampling distribution is normal since the sample size is large enough.Below are the necessary steps to determine if the conditions for inference are met.

Step 1: Identifying the Population and Parameter Let p be the proportion of puppies that are house-trained by the time they are 6 months old. Since the objective is to determine if there is sufficient evidence to claim that p > 0.75, this implies that the hypothesis of interest is the alternative hypothesis which is:H1: p > 0.75 The null hypothesis, which is the complement of the alternative hypothesis, is:H0: p ≤ 0.75 Step 2: Checking the Randomization Condition The randomization condition is met if we assume that the 50 puppies are randomly selected from the population of all puppies.

The randomization condition is met.Step 3: Checking the Sample Size Condition A sample size of 50 puppies is not a small sample size, and this condition is met.Step 4: Checking the Independence Assumption It is assumed that the 50 puppies are independent. tribution to calculate the p-value or use the z-test for proportion to carry out the hypothesis test for the claim that more than 75% of puppies are house-trained by the time they are 6 months old.

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The answer is C aka answer 3

Representing m greater than or equal to 1 as in inequality will be m ≥ 1.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this situation, representing m greater than or equal to 1 as in inequality will be m ≥ 1.

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Complete question

Represent m greater than equal to 1 as in inequality

Answer:

-2

Step-by-step explanation:

Answer:

-2 the other person is also definitely right.

Answer:

D

Step-by-step explanation:

The graph of the function y = x²+ 6x + 7 is given in the attachment.

To graph the quadratic function y = x²+ 6x + 7:

Find the vertex using the formula -b/(2a), where a is the coefficient of x²and b is the coefficient of x.

The vertex will be at (-3, -2).

Plot the vertex (-3, -2) on the graph.

Choose additional x-values and calculate the corresponding y-values by substituting them into the equation.

Plot these points on the graph.

Connect the plotted points smoothly to form a U-shaped curve, which represents the parabola.

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QR has a length of 2√3. According to the given question

HOW TO CALCULATE THE SIDE OF THE SQUARE ?

In order to solve for QR, we need to use the information given to us in the problem and apply some basic geometry concepts.

First, we know that the diagonals of a square are perpendicular bisectors of each other, meaning they intersect at a 90-degree angle and divide each other in half. This tells us that the length of the diagonal is equal to the square root of two times the length of one of the sides of the square, or d = s√2.

Next, we are given that the midpoint of one of the diagonals is point U, and that US has a length of 3. Because U is the midpoint of the diagonal, we know that SU and UR are equal in length. Let's call this length x.

Now we can use the Pythagorean theorem to solve for x:

(US)²+ (UR)² = (SR)²

3²+  x= (s√2)²

9 + x² = 2s²

We also know that SU and UR are each equal to x, so:

2x² = s²

We can substitute 2x² for s² in the previous equation:

9 + x² = 2(2x²)

9 + x²= 4x²

3x² = 9

x² = 3

x = √3

Now we can use x to solve for the length of QR:

QR = 2x = 2√3

Therefore, QR has a length of 2√3.

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The volume of water in the trough when it is 7 inches deep is 12 x (1/12 x 7) = 7 ft3.The rate of increase in water level is equal to the rate of water flow divided by the volume of water in the trough.Rate of increase in water level = 13 ft3/min / 7 ft3 = 1.86 ft/min

The trough is 12 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1 ft. We need to calculate how fast the water level is rising when the water is 7 inches deep. First, we need to calculate the volume of water in the trough when it is 7 inches deep. The volume of water in the trough is 12 x (1/12 x 7) = 7 ft3.Now, we can calculate the rate of increase in water level. The rate of increase in water level is equal to the rate of water flow divided by the volume of water in the trough.

(12 ft)(7 in/12 ft)(1 ft)

= 7/12 ft3

(13 ft3/min) / (7/12 ft3)

= (13/7) (12/1) ft/min

The rate of water level rising when the water is 7 inches deep is (13/7) (12/1) ft/min.

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Answer: 7%

(Hope this is right.)

Step-by-step explanation:

Let's solve this using the information we have and an equation.

Shane: $32,000 - (Given)

Theresa: 18,000+14x, if x=1,160 - (Given)

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

Step two: (Theresa) 14(1,160) =16,240 (Algebra)

Step three: (Theresa) 18,000+16,240=34,240 (Algebra, given.) - cost of Theresa's car.

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

Finally,

They're asking for how much more she paid for her car as a percentage of what Shane paid.

34,240-32,000=2,240 and

2,240/32,000=0.07

0.07x100=7

Answer 7% more than what Shane paid.

The given unity feedback system is the type-1 system, which can be observed from the given open-loop transfer function G(s).

Steady state error is the difference between the input and the output as time approaches infinity. It is also the difference between the desired value and the actual output at steady-state.

The steady-state error is calculated using the error coefficient, which depends on the type of the system.Find the steady-state error if the input is 80u(t):The transfer function of the given system can be written as follows;G(s) = 80(8²)/(s+4)(8+6)(8+17)The type of the given system is the type-1 system.

As the input to the system is u(t), the error coefficient is given as,Kp = lims→0sG(s) = 80/4(6)(17) = 5/153The steady-state error can be found out by the following formula;

ess = 1/Kp = 153/5.

Therefore, the steady-state error of the given system if the input is 80u(t) is 153/5.Find the steady-state error if the input is 80tu(t):As the input to the system is tu(t), the error coefficient is given as,Kv = lims→0s²G(s) = 0The steady-state error can be found out by the following formula;ess = 1/Kv = ∞.

Therefore, the steady-state error of the given system if the input is 80tu(t) is infinity.Find the steady-state error if the input is 80t²u(t):As the input to the system is t²u(t), the error coefficient is given as,Ka = lims→0s³G(s) = ∞The steady-state error can be found out by the following formula;

ess = 1/Ka = ∞.

Therefore, the steady-state error of the given system if the input is 80t²u(t) is infinity.

By using the error coefficient formula, we have found that the steady-state error of the given system if the input is 80u(t) is 153/5, steady-state error of the given system if the input is 80tu(t) is infinity and steady-state error of the given system if the input is 80t²u(t) is infinity.

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75% of the bacteria to live for approximately 130.11 minutes

To answer your question, we'll be using the concept of standard deviation and the normal distribution.

Given that the average lifespan of bacteria in a culture is 2 hours (120 minutes) with a standard deviation of 15 minutes, we can expect at least 75% of the bacteria to live for a certain amount of time. Using the normal distribution, we can determine the corresponding z-score for the 75th percentile, which is approximately 0.674.

Now, we can apply the z-score formula:
z = (X - mean) / standard deviation

Rearrange the formula to solve for X (the time at which 75% of the bacteria will live):
X = mean + (z * standard deviation)

Plugging in the given values:
X = 120 + (0.674 * 15) ≈ 130.11 minutes

So, we can expect at least 75% of the bacteria to live for approximately 130.11 minutes.

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Answer:

-130

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

Order of operations, multiplication first, then subtraction and addition

Answer:

1

Step-by-step explanation:

1) First, place the given equation in slope-intercept form (\(y = mx +b\) format) to find its slope easier. Isolate the y:

\(2x + 2y = 28\\2y = -2x + 28\\y = -x+14\)

So, the equation of the line in slope-intercept form is \(y = -x + 14\). When an equation is in slope-intercept form, the \(m\), or the coefficient of the x-term, represents the slope. Thus, the slope for the given line would be -1.

2) Lines that are perpendicular have slopes that are opposite reciprocals of each other. We need to find the opposite reciprocal of -1, then.

To find the opposite reciprocal of a number, write the given number as a fraction first -- making -1 be written as   \(-\frac{1}{1}\) -- then switch the sign and flip the numerator and denominator. So, the opposite reciprocal of -1 is 1, and 1 is the slope of the perpendicular line.

The angle theta lies in quadrant I or III.

Hence, option (C) is the correct choice.

The coordinate system's two axes, the x-axis and the y-axis, constitute an area called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes.

Cosθ=(1/Sinθ)

And, Secθ = (1/Cosθ)

As we know,

In the first Quadrant.

The value of Sinθ is positive, so the corresponding value of Cosθ will be also Positive.

As, In the second case the value of Secθ should be less than 0,

We know the value of Cosθ is negative in the third Quadrant.

So, the value of the Secθ will be less than 0 in the third quadrant.

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The expression "raise b to the 2nd power" means to multiply b by itself, which can be written as \(b^2\). The expression \((b^2)/8\) represents this quotient.

When we say "raise b to the 2nd power", it means we are squaring b, which is equivalent to multiplying b by itself. So, \(b^2\) represents the result of multiplying b by itself.

Next, the phrase "find the quotient of the result and 8" means we need to divide \(b^2\) by 8. Dividing \(b^2\) by 8 gives us the expression \((b^2)/8\), which represents the quotient we are looking for. We do not simplify the expression any further, because the instructions say to "not simplify any part of the expression."

So, \((b^2)/8\) is the final answer. This expression is still in fraction form, and it can be useful to keep it in this form if we are using it to solve a larger problem or if we want to keep the answer as precise as possible. If we want to convert it to decimal form, we can use a calculator to divide \(b^2\) by 8.

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