Increase £150 by 33%

Number of sociology textbooks = 67

And, Number of physics textbooks = 201

We have to given that,

Total number of physics and sociology textbooks sold in a week is, 268

And, The number of physics textbooks sold was three times the number of sociology textbooks sold.

Let us assume that,

Number of sociology textbooks = x

So, Number of physics textbooks = 3x

Then,

x + 3x = 268

Solve for x,

4x = 268

Divide by 4,

x = 268/4

x = 67

Therefore, Number of sociology textbooks = 67

So, Number of physics textbooks = 3 x 67 = 201

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Answer: A.Spreads: The weights of the tigers are more spread out.

B.Centers:The leopards have a lower median weight than the tigers

Step-by-step explanation:

On analyzing the dot plots, we find that the weight of Leopards are more spread out and the weight of Leopards has a lower median than Tiger.

Median is a statistical measure that determines the middle value of a dataset listed in ascending order. The measure divides the lower half from the higher half of the dataset.

Median of Weight of Leopard = 50 kg

Median of Weight of Tiger = 125 kg

This implies that the Leopards have a lower median weight than Tigers.

What is spread of data?

Spread describes the variation of the data. One of the measures of spread is range.

Range of weight of Leopards= 40 kg

Range of weight of Tigers = 90 kg

This implies that the weight of Tigers are more spread out.

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Answer:

HI = 34

Step-by-step explanation:

KL  is a mid segment of the triangle and is half the length of HI , that is HI is twice KL , so

HI = 2 × KL

8x - 14 = 2(- 25 + 7x)

 8x - 14  = - 50 + 14x ( subtract 14x from both sides )

- 6x - 14 = - 50 ( add 14 to both sides )

- 6x = - 36 ( divide both sides by - 6 )

x = 6

Then

HI = 8x - 14 = 8(6) - 14 = 48 - 14 = 34

The coordinates of the specified vertex after the given transformations is  R'(3,3).

From the figure:

Finding the coordinates:

Q(1,3)

R(3,-3)

S(0,-2)

T(-2,1)

The coordinates is transformed 90 degrees about the origin:

The rule for transforming coordinates(x,y) 90 about the origin is (-y,x).

we need to find R':

R(3,-3) → R'(-(-3),3)

R(3,-3) → R'(3,3)

Therefore the coordinates of the specified vertex after the given transformations is  R'(3,3).

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Answer:

Step-by-step explanation:

18/32 is the same as 9/16 or 0.5625

To calculate the probability of getting 5 or more questions correct, we can use the binomial distribution formula:

P(X ≥ 5) = 1 - P(X < 5)

where X is the number of correct answers and P(X < 5) is the probability of getting less than 5 correct answers.

The probability of getting exactly k correct answers out of 11 questions is:

P(X = k) = (11 choose k) * (1/5)^k * (4/5)^(11-k)

Using this formula, we can calculate the probability of getting less than 5 correct answers:

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

P(X < 5) = (11 choose 0) * (1/5)^0 * (4/5)^11 + (11 choose 1) * (1/5)^1 * (4/5)^10 + (11 choose 2) * (1/5)^2 * (4/5)^9 + (11 choose 3) * (1/5)^3 * (4/5)^8 + (11 choose 4) * (1/5)^4 * (4/5)^7

P(X < 5) ≈ 0.948

Therefore, the probability of getting 5 or more questions correct is:

P(X ≥ 5) ≈ 1 - 0.948 ≈ 0.052

So, the answer is (B) 0.0504.

To find the expected number of correct answers, we can again use the binomial distribution formula:

E(X) = n * p

where n is the number of trials (11 questions in this case) and p is the probability of getting a correct answer (1/5 in this case).

E(X) = 11 * 1/5

E(X) = 2.2

Therefore, the answer is (A) 2.2.

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Answer:

\(h=16inches\)

Step-by-step explanation:

From the question we are told that:

Base of  flag \(l_b=8inch\)

Area of flag \(A=64 inch^2\)

Generally the equation for a triangle is mathematically given by

 \(Area=\frac{1}{2}l_b*h\)

Therefore

 \(h=\frac{2A}{l_b}\\h=\frac{2*64}{8}\)

 \(h=16inches\)

Therefore the hieght of the ship is  mathematically given as

 \(h=16inches\)

I hope this helps you

Answer:

C

Step-by-step explanation:

(f + g)(x) = f(x) + g(x), then

f(x) + g(x)

= \(4^{x}\) - 8 + 5x + 6 ← collect like terms

= \(4^{x}\) + 5x - 2 → C

To compute a heaviest Longest Increasing Subsequence (LIS) in a given sequence efficiently with a time complexity of O(n), we can use the concept of dynamic programming.

The algorithm follows these steps: 1. Initialize two arrays, "lis" and "sum," both of size n, where n is the length of the sequence. The "lis" array will store the length of the LIS ending at each element, and the "sum" array will store the maximum sum of the LIS ending at each element.

2. Initialize the "lis" and "sum" arrays with values of 1 and the corresponding element values of the sequence, respectively.

3. Traverse the sequence from left to right. For each element, compare it with all previous elements. If the current element is greater than the previous element and the sum of the LIS ending at the previous element plus the current element is greater than the sum at the current element, update the "lis" and "sum" arrays accordingly.

4. Finally, find the element in the "sum" array with the maximum value and trace back the LIS by following the indices stored in the "lis" array.

By following these steps, we can compute a heaviest LIS in linear time, O(n), where n is the length of the input sequence. The dynamic programming approach allows us to efficiently update and store the necessary information for calculating the maximum sum.

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Answer:

I think the answer is

the second one

In Analysis of variance,  X (bar) is not affected by whether or not the population means are equal.

Analysis of variance  is a statistical method for examining differences in means. It consists of a number of statistical models and the accompanying estimating techniques (such as the "variation" within and between groups). Ronald Fisher, a statistician, created Analysis of variance. The rule of total variance, on which the Analysis of variance is based, divides the observed variance in a given variable into components owing to various causes of variation.

ANOVA generalizes the t-test beyond two means by offering a statistical test to determine if two or more population means are equal. In other words, the Analysis of variance is employed to determine whether two or more means differ from one another.

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The answer to Math.round(3.6) is D. 4.0. The Math.round() method is used to round a number to the nearest integer.

When we apply Math.round(3.6), it rounds off 3.6 to the nearest integer which is 4.

This method uses the following rules to round the given number:

1. If the fractional part of the number is less than 0.5, the number is rounded down to the nearest integer.

2. If the fractional part of the number is greater than or equal to 0.5, the number is rounded up to the nearest integer.

In the given question, the number 3.6 has a fractional part of 0.6 which is greater than or equal to 0.5, so it is rounded up to the nearest integer which is 4. Therefore, the correct answer to Math.round(3.6) is D. 4.0.

It is important to note that the Math.round() method only rounds off to the nearest integer and not to a specific number of decimal places.

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The store should have 445 picks remaining, not 450 as estimated by the manager. To determine if the store manager's estimate is reasonable, let's analyze the situation.

The store initially has 500 guitar picks. They order 15 boxes, and each box contains 9 picks. So the total number of picks they receive from the order is:

15 boxes * 9 picks/box = 135 picks

Next, the store sells 19 boxes, with each box containing 10 picks. Therefore, the total number of picks sold is:

19 boxes * 10 picks/box = 190 picks

To find the remaining number of picks, we can subtract the sold picks from the received picks:

Total remaining picks = Initial picks + Received picks - Sold picks

Total remaining picks = 500 + 135 - 190 = 445 picks

According to the calculations, the store should have 445 picks remaining, not 450 as estimated by the manager.

However, it's important to note that we are working with whole numbers, so there might be some rounding involved in the manager's estimate. It's possible that the manager rounded up to 450 for simplicity or other reasons.

Given the small discrepancy of 5 picks between the calculated value and the manager's estimate, it is reasonable to conclude that the manager's estimate is close enough to the actual number of picks. The discrepancy could be due to rounding or a small counting error. It's unlikely to have a significant impact on the store's operations or inventory management.

In summary, while the manager's estimate of 450 guitar picks may not be exactly accurate, it is reasonably close to the actual remaining number of picks based on the given information.

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Answer:

  identity element property

Step-by-step explanation:

June's value did not change, so the value she added was the additive identity element: 0.

She made use of the identity element property of addition, which says that adding the identity element does not change the value.

Answer:

1. 14

2. 8

Step-by-step explanation:

you are finding the greatest common factor so list all the numbers that can go in to 154 without going over or under for both of them 14 is the only answer for the two 14 x 10 = 140and 14 x 11=154

Answer:

Step-by-step explanation:

To find the greatest number, you need to find the GCF of both numbers

1) 154 = 7 * 2 * 11

140 =  7 * 2 * 2 * 5

GCF = 7*2 = 14

She can  place 14 cards in each row.

2) 16 = 2 * 2 * 2 * 2

   40 = 2 * 2 * 2 * 5

GCF = 2*2*2 = 8

There are approximately 47,129,751,002,866,480 ways for the lead researchers to pick 20 students from the 50 eager candidates.

To solve this problem, we can use the concept of combinations.

Combinations allow you to find the number of ways to choose a certain number of items from a larger set without considering the order of the items.
In this case, the lead researchers need to pick 20 students from the 50 eager candidates.

This can be calculated using the combination formula:
C(n, k) = n! / (k! * (n-k)!)
where "n" represents the total number of items (50 students), "k" represents the number of items to choose (20 students), and "!" denotes a factorial, which is the product of all positive integers up to that number.
Applying the formula to this problem:
C(50, 20) = 50! / (20! * (50-20)!)
C(50, 20) = 50! / (20! * 30!)
Now, calculate the factorials and divide:
C(50, 20) ≈ 47,129,751,002,866,480.

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The function \(h(x) = (x + 7)²\) can be expressed in the form f(g(x)), where\(f(x) = x²\), and \(g(x) = x + 7.\)

Given function: \(h(x) = (x + 7)²\)

To express the given function h(x) in the form of\(f(g(x))\), we need to find an intermediate function g(x) such that \(h(x) = f(g(x)).\)

Let's find the intermediate function \(g(x):g(x) = x + 7\)

Therefore, we can express h(x) as:

\(h(x) = (x + 7)²\\= [g(x)]²\\= [x + 7]²\)

Now, let's define \(f(x) = x²\)

So, we can express h(x) in the form of f(g(x)) as:

\(f(g(x)) = [g(x)]²\\= [x + 7]²\\= h(x)\)

Therefore, the function \(h(x) = (x + 7)²\) can be expressed in the form f(g(x)), where\(f(x) = x²\), and \(g(x) = x + 7.\)

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The amount of fiber asked by the doctor to be consumed is 30 grams .

Method to calculate percentages :

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100 .

Let the amount of fiber asked by the doctor to be consumed be x .

According to question ,

40 % of x = 12

Solving the equation ,

( 40 / 100 ) * x = 12

x = 1200 / 40

x = 30

Hence ,  the amount of fiber asked by the doctor to be consumed is 30 grams .

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Answer:

30

Step-by-step explanation:

Answer:

Remember that £ has a greater value compared to $ and vice versa.

Answer:

18.4 if it is in square root

Step-by-step explanation:

it may help you to understand.

Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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Answer:

\(y=1,\:y=-1\)

Step-by-step explanation:

\(y^2+14=3y^2\cdot \:5\\\y^2+14-14=3y^2\cdot \:5-14\\y^2=15y^2-14\\y^2-15y^2=15y^2-14-15y^2\\-14y^2=-14\\\frac{-14y^2}{-14}=\frac{-14}{-14}\\y^2=1\\\\y=\sqrt{1},\:y=-\sqrt{1}\\y=1,\:y=-1\)

Answer:

y = ± 1

Step-by-step explanation:

Given

y² + 14 = 3y² × 5, that is

y² + 14 = 15y² ( subtract y² from both sides )

14 = 14y² ( divide both sides by 14 )

1 = y² ( take the square root of both sides )

± \(\sqrt{1}\) = y , that is

y = ± 1

Thus y = - 1 or y = 1

The complex conjugate of 2 + 7i is 2 - 7i.

The complex conjugate of a complex number a + bi is obtained by changing the sign of the imaginary part. In this case, the given complex number is 2 + 7i. To find its complex conjugate, we simply change the sign of the imaginary part, resulting in 2 - 7i.

2 + 7i is a complex number with a real part of 2 and an imaginary part of 7i. The complex conjugate, 2 - 7i, has the same real part but a negated imaginary part.

The complex conjugate is useful in various mathematical operations, such as finding the modulus or magnitude of a complex number, simplifying complex expressions, and dividing complex numbers.

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Answer and Step-by-step explanation:

The answer to this expression is 0.

This is because 0 times any number is 0.

#teamtrees #PAW (Plant And Water)

Answer:

0 because anything times 0 equals 0

Step-by-step explanation:

The commutative, associative, and distributive property are the properties of addition and multiplication.

Commutative Property - The Commutative Property is derived from the word commute, which means to move. It states that the product or sum of two numbers do not change even if the places of numbers are changed or if the numbers move from one place to another. The commutative property of addition states that a + b = b + a and the commutative property of multiplication states that a × b = b ×  a.

Associative Property - It is related with the grouping of numbers. It states that the product or sum of three numbers do not change even if the grouping of numbers are changed. The associative property of addition states that (a + b) + c = a + (b + c) and the associative property of multiplication states that: (a × b) × c = a × (b ×  c).

Distributive Property - It is related with the distribution of numbers. It states that the product of three numbers do not change even if the distribution of numbers are changed. The distributive property of multiplication states that: a × (b + c) = (a × b) + (a ×  c).

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Answer:

3x−y=2

Step-by-step explanation:

Answer:6. -6 is the answer

Step-by-step explanation:add 10 to -10 and -40 and bring down 5x since -10 and 10 cancel out you have to cross it out and have -30 from -40 +10 and now 5x=-30 you have to divide 5 on each side and that would give you -6

Answer:

787,210

Step-by-step explanation: