A 7-kg bag of apples for $10

Answer:

x=2

Step-by-step explanation:

Since the are the same equation they are already equal

Answer:

x=2

Step-by-step explanation:

The solution to lim h→0 (9 + h)−1 − 9−1 h is -1/9.

To find the solution to lim h→0 (9 + h)−1 − 9−1 h, we can simplify the expression first.

Starting with (9 + h)−1, we can use the formula for the difference of squares to get:

\((9 + h)-1 = (9 + h - 9) / ((9 + h)(9 - 9)) = h / (9h + h^2)\)
Substituting this back into the original expression gives:

\((9 + h)-1 -9-1 h = h / (9h + h^2) - 1 / 9h\)

We can combine the two fractions by finding a common denominator of 9h(9 + h), giving:

(9h - (9 + h)) / (9h(9 + h)) = -1 / (9 + h)

Now we can take the limit as h approaches 0:

lim h→0 (9 + h)−1 − 9−1 h = lim h→0 -1 / (9 + h) = -1 / 9

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To prove that the group g is cyclic, we analyze the possible values of the order |g|. We consider the cases for each possible value and demonstrate that in all cases, g is either cyclic or leads to a contradiction.

For |g| = 1, 2, 3, 5, or 7, the groups of these orders are always cyclic.

If |g| = 4, 6, 8, 9, 10, 12, or 15, we show that g cannot have the required subgroups. Assuming g is not cyclic, we find an element x of order 2 and additional elements y, z, w, etc., also of order 2. This contradicts the given conditions since g would be isomorphic to Z₂ × Z₂ or have more than one subgroup of order 3 or 5.

For composite orders |g| = pq, where p and q are prime, we generalize the analysis. By Cauchy's theorem, g has elements of order p and q, and since there is only one subgroup of each order, they are cyclic. We show that the intersection of these subgroups cannot have an order of pq, leading to a contradiction. Hence, g is cyclic.

Therefore, in all cases, g is proved to be cyclic. QED.

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Answer:16

Step-by-step explanation:

The Laplace domain equation X(s) is found to be X(s) = (s + 2)/(s^2 + 5s + 6). The time domain equation x(t) can be obtained by applying the inverse Laplace transform to X(s), resulting in x(t) = e^(-t) - e^(-2t).

Given the Laplace domain equation X(s), we need to substitute the given parameters and find its expression in terms of s. The equation provided is X(s) = (s + 2)/(s^2 + 5s + 6).

To obtain the time domain equation x(t), we need to apply the inverse Laplace transform to X(s). The inverse Laplace transform of X(s) will give us x(t) in terms of t.

Applying the inverse Laplace transform to X(s) involves finding the inverse transform of each term separately. The inverse Laplace transform of (s + 2) is simply 1, representing the unit step function. The inverse Laplace transform of (s^2 + 5s + 6) is e^(-t) - e^(-2t), which can be obtained through partial fraction decomposition.

Therefore, the time domain equation x(t) is given by x(t) = e^(-t) - e^(-2t), where t represents time.

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The sampling distribution model for figuring out how many people in this group might not pay on time is:

E. mean = 8%; standard deviation = 1.1%.

The steps to determine the mean and standard deviation of the sampling distribution of the proportion of clients who may not make timely payments would be:

Start with the idea that 8% of the loans will have payments that are late. So the percentage of people who pay late is p = 0.08.

Calculate the sample size, which is given as n = 600.

Determine the mean of the sampling distribution. The mean of the sampling distribution of the proportion of late payments is equal to the population proportion, which is 0.08.

Find the standard deviation of the distribution of the samples. The standard deviation is discovered by taking the square root of the commodity of the sample size and the percentage of late payments in the whole population (1 - percentage of late payments in the whole population) and dividing it by the sample size:

σ = √( (p * (1-p)) / n )

σ = √( (0.08 * 0.92) / 600 ) ≈ 0.011

So, the answer will be option E. mean = 8%; standard deviation = 1.1%.

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The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).

To find the positive solution, to the nearest tenth, of f(x)=g(x) using Cora's process, the steps are as follows:

Input the initial value of x, for example x=0.

Calculate f(x) and g(x):

If f(x) is less than g(x), then x should be increased and vice versa.

Increase or decrease x accordingly and calculate the new values of f(x) and g(x).

Keep repeating steps 3 and 4 until the difference between the values of f(x) and g(x) is less than 0.1.

The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).

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The probability level used by researchers to indicate the cutoff probability level (highest value) that will allow them to reject the null hypothesis is called the alpha level.

Alpha level refers to a threshold value which is used to determine if a test statistic is statistically significant.  In a statistical test, it demonstrates an acceptable probability of a Type I error. As alpha corresponds to a probability, it lies in the range of 0 to 1. The alpha level denoted as alpha or α refers to the probability of rejecting the null hypothesis when it is true. For example, a alpha level of 0.05 demonstrate a 5% risk of concluding that a difference exists when there is no actual difference.

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Step-by-step explanation:

Diameter of base of cone = 30 cm .

Hence its radius = 30/2 cm = 15 cm

So , here the figure consists of a hemisphere and a cylinder . Now , here radius of the hemisphere is 15 cm . So , height of the Cylinder = ( 85 - 15 ) cm = 70 cm

→Volume of Cylinder :-

\(\large\boxed{\red{ Volume_{cylinder}=\pi r^2 h }}\)

→ Volume = π r²h

→ Volume = 22/7 * ( 15 cm)² * 70 cm

→ Volume = 49,500 cm³ .

Volume of hemisphere :-

\(\large\boxed{\green{Volume_{hemisphere}=\dfrac{2}{3}\pi r^3}}\)

→ Volume = ⅔ π r³

→ Volume = ⅔ * 22/7 * (15 cm)³

→ Volume = 10,607.14 cm³ ≈ 10 , 607 cm³ .

Hence Volume = ( 10 , 607 cm³ + 49,500 ) cm³ = 60,107 cm³

Answer: A good way to get a small standard error is to use a large sample.

Step-by-step explanation:

In order to find the small standard error, there is always need of a complete set which is called the large sample.

If tried to do a small or repeating sample, you will most likely not get an error and you could get a repetition. If you do a population sample, you wont get accurate results at all.

Therefore, a good way to get a small standard error is to use a large sample. Hope this helps!

-From a 5th Grade Honors Student

\(180^{\circ} = (2x + 45)^{\circ} + x^{\circ}\\180^{\circ} = 2x^{\circ} + 45^{\circ} + x^{\circ}\\180^{\circ} - 45^{\circ} = 2x^{\circ} + x^{\circ}\\135^{\circ} = 3x^{\circ}\\x^{\circ} = 45^{\circ}\)

Answer:

x = 45

Step-by-step explanation:

The angle measurement of the line is 180 degrees because it is a straight line. Therefore, the shown two angle measurements must add up to 180 as well. So:

(2x+45) + x = 180

Combine like terms to simplify

3x + 45 = 180

-45           -45

Subtract 45 on both sides to isolate the variable

3x = 135

Divide 3 on both sides to isolate the variable as well

x = 45

*Hope this helped! : )*

Check the picture below.

\(sin(35^o)=\cfrac{\stackrel{opposite}{12}}{\underset{hypotenuse}{BD}}\implies BD=\cfrac{12}{sin(35^o)} \\\\[-0.35em] ~\dotfill\\\\ \textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\)

\(\cfrac{sin(52^o)}{BD}=\cfrac{sin(102^o)}{CD}\implies CD=\cfrac{BD\cdot sin(102^o)}{sin(52^o)} \\\\\\ CD=\cfrac{\frac{12}{sin(35^o)}\cdot sin(102^o)}{sin(52^o)}\implies CD=\cfrac{12\cdot sin(102^o)}{sin(35^o)\cdot sin(52^o)}\implies CD\approx 26.0\)

The given statement, f1 + f3 + ... + f2n-1 = f2n, asserts that the sum of every other Fibonacci number up to the (2n-1)th term is equal to the (2n)th Fibonacci number. This can be proven by induction.

5We will assume that the statement holds true for some arbitrary positive integer k and show that it holds for k+1 as well. By using the recursive definition of Fibonacci numbers and substituting the induction hypothesis, we can establish the equality for k+1. Since we have shown that the statement holds true for k=1, the induction step demonstrates that the statement is valid for all positive integers n.

To prove the statement f1 + f3 + ... + f2n-1 = f2n, we will use mathematical induction. We begin by establishing the base case, which is n=1. Plugging in n=1, we get f1 = f2, which is true according to the definition of Fibonacci numbers.

Next, we assume that the statement holds true for some arbitrary positive integer k, which means that f1 + f3 + ... + f2k-1 = f2k.

Now we need to show that the statement holds for k+1 as well. We start by adding f2k+1 to both sides of the equation:

f1 + f3 + ... + f2k-1 + f2k+1 = f2k + f2k+1

By the recursive definition of Fibonacci numbers, we can rewrite the right side of the equation as f2k-1 + f2k = f2k+1:

f1 + f3 + ... + f2k-1 + f2k+1 = f2k+1

Therefore, we have shown that if the statement holds true for k, it also holds true for k+1. Since we have established the base case (n=1) and shown the induction step, we can conclude that the statement f1 + f3 + ... + f2n-1 = f2n holds for all strictly positive integers n.

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Answer:

its easy...are u in 5th

Step-by-step explanation:

The missing side (the adjacent side) is approximately 13.257 units long.

To find the missing side, we can use the cosine function which relates the cosine of an angle to the adjacent side and the hypotenuse of a right triangle.

cos(28°) = adjacent side / hypotenuse

We are given the measure of the angle and the length of one side, so we can plug in those values and solve for the missing side.

cos(28°) = adjacent side / 15

adjacent side = 15 cos(28°)

Using a calculator to evaluate cos(28°) to four decimal places:

cos(28°) ≈ 0.8838

Substituting into the equation:

adjacent side ≈ 15 × 0.8838

adjacent side ≈ 13.257

Therefore, the missing side (the adjacent side) is approximately 13.257 units long.

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To determine which outcome is more likely, we need to consider the probability of each outcome occurring.

(i) The sequence (2 2 2 2 2 2 2 2 2 2 2 2) consists only of the number 2. Since each roll of the fair die has 6 possible outcomes (numbers 1 to 6), the probability of getting a sequence consisting only of 2s is (1/6)^12, which is extremely low but not absolutely impossible.

(ii) The sequence (1 1 2 2 3 3 4 4 5 5 6 6) consists of two of each number from 1 to 6. There are 12!/(2!2!2!2!2!2!) possible arrangements of these numbers, which is much larger than the probability of getting sequence (i).

(iii) The sequence (4 6 2 1 3 5 2 6 4 3 1 5) is a random arrangement of the numbers 1 to 6. Similarly to (ii), there are 12!/(2!2!2!2!2!2!) possible arrangements.

Based on these considerations, we can conclude that (ii) and (iii) are both more likely to occur than (i). Therefore, the correct answer is option E: Both (B) and (C) are true.

Answer:

1/2x+7

Step-by-step explanation:

Answer: 11

Step-by-step explanation:

First use a step by step process called BODMAS which stands for brackets of(x) division multiplication additon and subtraction

Answer:

10

Step-by-step explanation:

We solve using Pythagoras Theorem. Pythagoras Theorem is used to solve for the missing side of a right angled triangle.

The formula for Pythagoras Theorem =

c² = a² + b²

c = √a² + b²

Where c is the longest side

From the above diagram, we are looking for c

c = ?

a = 6

b = 8

Hence,

c = √6² + 8²

c = √36 + 64

c = √100

c = 10

Therefore, side c = 10

The experimental probability is greater than the theoretical probability because the experimental probability is 20% while the theoretical probability is 12.5%.

To determine which is greater, the theoretical or experimental probability of spinning a 4, we need to calculate both probabilities.

The theoretical probability is the likelihood of spinning a 4 based on the total number of possible outcomes. Assuming the spinner has an equal number of sections (let's say there are 8 sections, each labelled with a number from 1 to 8), the theoretical probability can be calculated as follows:

The theoretical probability of spinning a 4 = Number of favourable outcomes (spinning a 4) / Total number of outcomes (8 sections)
Theoretical probability = 1/8 = 0.125 or 12.5%

The experimental probability is the actual outcome of spinning a 4 based on a series of trials (spins). Let's say you conducted 40 trials and spun a 4 eight times. The experimental probability can be calculated as follows:

Experimental probability of spinning a 4 = Number of successful trials (spinning a 4) / Total number of trials (40 spins)
Experimental probability = 8/40 = 0.2 or 20%

In this case, the experimental probability (20%) is greater than the theoretical probability (12.5%). This difference could be due to chance, as the experimental probability may get closer to the theoretical probability as the number of trials increases.

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Answer:

so...  18 / 2/3 =

I honestly think it's c.

The required original price of the coat is given as £95.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
let the original price of the coat be x,
According to the question
x - 17% of x = 78.85
x - 0.17x = 78.85
0.83x = 78.85
x = 78.85 / 0.83
x = £95

Hence, the cost of the coat before the sale is £95.

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Answer:

Step-by-step explanation:

All are true except for the second.  Only the second is false.

(pi)(d) is the circumference (not the area) of a circle.

The incorrect statement is \(A = \pi d\).

The correct option is 2.

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well. The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a form with a curved base and surface is equal to the sum of the two areas.

As per the given data:

We have to find out the incorrect statements out of the given options about the area of a circle.

\(A = \pi r^2\)

This statement is correct, as the area of a circle is pi times square of the radius.

\(A = \pi d\)

This statement is incorrect, as the area of a circle is given by:

\(A = \pi r^2 =\frac{ \pi d^2}{4}\)

The area of a circle determines how much space is covered by the circle.

This statement is correct.

The area of a circle describes the number of square units that fit inside the circle.

This statement is correct.

Hence, the incorrect statement is \(A = \pi d\).

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CM is the perpendicular bisector of AB at M, it means that CM is perpendicular to AB, and AM=BM. Therefore, we have two right triangles, triangle AMC and triangle BMC, with a shared side CM, and AM=BM.

By the Pythagorean theorem, we know that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Applying this to triangles AMC and BMC, we have:

AC² = AM² + CM²

BC² = BM² + CM²

Since AM=BM, we can substitute AM for BM in the second equation, giving:

BC² = AM² + CM²

Since the left-hand sides of these two equations are equal (by the given that CM is the perpendicular bisector of AB), we can set their right-hand sides equal to each other and simplify:

AC² = BC²

Taking the square root of both sides gives us:

AC = BC

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Answer:

I think it's either 10√3 or 10

Answer:

I believe the answer is about 34

Step-by-step explanation:

In the posttest control group design shown above, selection bias is eliminated by randomization.

Randomization is the best way to eliminate the effects of selection bias. The posttest control group design is an experimental design that entails the random selection of study participants into two groups: a control group that is not subjected to the intervention and a treatment group that receives the intervention. Following that, measurements are taken from the two groups. One of the benefits of the posttest control group design is that it eliminates the possibility of selection bias and assures the internal validity of the study.The aim of randomization is to ensure that study participants are chosen entirely at random and that the researcher does not have any impact on the selection process. As a result, this technique is used to guarantee that the two groups are equivalent at the beginning of the study in terms of variables that could affect the outcome. This technique eliminates the effect of selection bias on the study results.Therefore, in the posttest control group design shown above, selection bias is eliminated by randomization.

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Answer:

There are 18 pigs and 12 chickens.

Step-by-step explanation:

p = # of pigs

c = # of chickens

I'm assuming each animal has one head and all the pigs have 4 legs and all the chickens have 2 legs, therefore:

p+c = 30

4p+2c = 84

Elimination:

-2(p+c = 30)        -2p -2c = -60

4p +2c = 84         4p +2c = 84

                            2p    =     24

                               p    =    12

Now substitute p for 12:

12 + c = 30

c      =    18

Check:

4(12) + 2(18) = 84

48     + 36    = 84

84 = 84

There are 18 chickens and 12 pigs.

Answer:

The sum of a number and its additive inverse is equal to 0.

Step-by-step explanation: