Calculate the mean of the given frequency distribution Frequency A 11.43 B 12.38 Measurement 110-114 115-119 C 12.41 13 D 12.70 6 12.0-12.4 27 12.5-12.9 14 13.0-13.4 15 13.5-13.9 3 14.0-144 Total 80 1

Multiply 1 & 2 from 3 and 4 respectively and add to get product.

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Answer:

\(408\)

Step-by-step explanation:

Hey there,

\(34 \\ \times 12 \\ ................. \\ \: \: \: \: \: \: \: 6 8 \\ + 34 0 \\ ............. ... \\ = 40 8\)

Hope this helps you.

Let me know if you have any other questions:-):-)

Answer:

360\12=16.36

Step-by-step explanation:

formula=22/7*6*6*10=16.36

The two mathematical expressions 5(3t - 6) and 15t - 30 are equivalent.

Mathematical expressions are equivalent or equal when they have the same value.

Equivalent expressions work the same way despite their different looks.

We determine that two or more mathematical expressions are equivalent when simplified or yield the same value after substituting the variables.

Equivalent mathematical expressions are usually indicated using the equation symbol (=).

5(3t - 6) = 15t - 30

If t = 3

5(3t - 6) = 15

15t - 30 = 15

Thus, if two algebraic expressions are equivalent, then the two expressions have the same value.

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Answer:

2

Step-by-step explanation:

128divided by 7 = 126

The critical value for the 0.05 level of significance is k = 21.

To find the critical value, we can use the binomial distribution. The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success. In this case, the number of successes is the number of dog owners who say Woof Chow is their regular brand, and the number of trials is n = 100. The null hypothesis is that the true market share of Woof Chow is 25%, and the alternative hypothesis is that it is not 25%.

We can use the binomial cumulative distribution function (CDF) to find the critical value. The CDF gives the probability of getting k or fewer successes in n trials, given a probability of success p. The critical value is the smallest value of k such that the CDF at k is greater than or equal to 1 - alpha, where alpha is the level of significance. In this case, alpha = 0.05.

So, we want to find the smallest k such that:

P(X <= k) >= 1 - 0.05

where X is a random variable representing the number of dog owners who say Woof Chow is their regular brand. We can use a binomial calculator or a software package to calculate the binomial CDF, or we can use a table of critical values for the binomial distribution.

The critical value for the 0.05 level of significance is k = 21. This means that if the true market share of Woof Chow is 25%, then the probability of getting 23 or more dog owners who say Woof Chow is their regular brand is less than 0.05. Since the observed number of dog owners who say Woof Chow is their regular brand is 23, which is greater than 21, we can reject the null hypothesis that the true market share is 25%.

This means that based on the survey results, we cannot conclude that Woof Chow has a market share of 25%. The survey results suggest that Woof Chow may have a market share that is greater than 25%.

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Answer:

see explanation

Step-by-step explanation:

3

(f + g)(x)

= f(x) + g(x)

= 2x² - 4x - 5 + 3x - 13 ← collect like terms

= 2x² - x - 18

4

(f - g)(x)

= f(x) - g(x)

= 2x² - 4x - 5 - (3x - 13) ← distribute parenthesis by - 1

= 2x² - 4x - 5 - 3x + 13 ← collect like terms

= 2x² - 7x + 8

Supervisor can choose 6435 different such 8 people committees from 15 call center agents.

We know that we can choose ' r ' number elements or persons from ' n ' number of elements or persons respectively in C(n, r) ways if we do not replace once chosen elements.

Here the total number of staff of call center agent is = 15

So n = 15.

And supervisor of the call center has to choose 8 agents from that group of 15 agents.

So, here r = 8.

Here as supervisor chooses a person he or she cannot be selected as two people.

So the event is without replacement.

Thus by the combination formula, the number of different such committees can be chosen by supervisor is = C(15, 8) = 6435.

Hence, supervisor can choose 6435 different such 8 people committees from 15 call center agents.

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To find \(\(X\)\) such that \(\(AX = B\)\), where \(\(A\) and \(B\)\) are given matrices, we can use the formula \(\(X = A^{-1}B\), where \(A^{-1}\)\) represents the inverse of matrix \(\(A\)\).

To find \(\(X\)\), we need to multiply matrix \(\(A\) with \(X\)\) such that the result is matrix \(\(B\)\). In other words, we are looking for a matrix \(\(X\)\) that satisfies the equation \(\(AX = B\)\).

To solve this equation, we can multiply both sides by the inverse of matrix \(\(A\)\). The inverse of a matrix \(\(A\)\) is denoted as \(\(A^{-1}\)\) and has the property that \(\(A^{-1}A = I\)\), where \(\(I\)\) is the identity matrix.

By multiplying both sides of the equation \(\(AX = B\) by \(A^{-1}\)\)0

\(\(A^{-1}(AX) = A^{-1}B\)\)

Since \(\(A^{-1}A = I\)\), the left side simplifies to:

\(\(I(X) = A^{-1}B\)\)

Therefore, we have:

\(\(X = A^{-1}B\)\)

By evaluating the matrices \(\(A\) and \(B\)\) and finding the inverse of matrix \(\(A\)\), we can perform the matrix multiplication to find the value of \(\(X\)\) that satisfies the equation \(\(AX = B\)\).

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Answer:

10cm 5cm and 9cm

Step-by-step explanation:

just try this

take any two measurements and add them together if they are larger than the 3rd measurement it will work and all you have to do is do that to each measurement

10+5 is greater than 9

9+5 is greater than 10

9+10 is greater than 5

The following values are as follows: a) Mean = 0.6, b) standard deviation = 0.073 and c) Probability is 0.0855

a) As the number of samples is large enough which is up to 30 then the mean of the average number of moths in 30 traps is given as 0.6, given from the central limit theorem.

b) The population deviation divided by the square root of the sample size gives the standard deviation value.

standard derivation = σ/ \(\sqrt{n}\) = 0.4 / \(\sqrt{30}\) = 0.4/ 5.477 = 0.073

c) The probability that an approximately normally distributed data with the standard deviation, σ, with a sample size of n is greater than a number, x, and a mean, μ, is given by

1 - P (X < x)= P (X > x)

= 1 - P(z< x- µ/ σ/\(\sqrt{n}\))

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that the average number of moths in 30 traps is greater than 0.7 is given by:

1 -P (X - 0.7) = P (X > 0.7)

= 1 - P(z < \(\frac{0.7-0.6}{0.073}\)) = 1 - P(z < 1.369)

= 1 - 0.91455 = 0.0855

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Using an equation, the number of cutting boards sold is:

An equation is a mathematical statement of the equality or equivalence of two or more mathematical expressions.

The above statement shows that equations are formed by using the equal symbol (=) and algebraic expressions.

The selling price per large cutting boards = $18

The selling price per small cutting boards = $14

Let the number of large cutting boards sold at the fall festival = x

Let the number of small cutting boards sold at the festival = 3x

The total revenue generated from the fall festival = $420

18x + 14(3x) = 420

18x + 42x = 420

60x = 420

x = 7

The number of large cutting boards sold = 7

The number of small cutting boards sold = 21 (3 x 7)

The total number of cutting boards sold = 28 (7 + 21)

Thus, based on an equation, the total number of cutting baords sold is 28.

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\( \frac{2}{3} (x - 4) = 2x \\ \frac{2}{3} x - \frac{8}{3} = 2x \\ \frac{2}{3} x - 2x = \frac{8}{3} \\ \frac{2}{3} x - \frac{6}{3} x = \frac{8}{3} \\ \frac{ - 4}{3} x = \frac{8}{3} \\ - 12x = 24 \\ x = \frac{24}{ - 12} \\ x = - 2\)

The products obtained from the reactions of (E)- and (Z)-hex-3-ene with D2 in the presence of a platinum catalyst are related as enantiomers.

Hence, the correct option is E.

Enantiomers are stereoisomers that are non-superimposable mirror images of each other. In this case, the (E)- and (Z)-isomers have different spatial arrangements around the C=C double bond. When they react with D2 in the presence of a platinum catalyst, the deuterium atoms add to the double bond, resulting in two new chiral centers.

Since the two isomers have different spatial arrangements around the double bond, the addition of deuterium atoms will produce enantiomeric products. Therefore, the products obtained from the reactions of (E)- and (Z)-hex-3-ene with D2 are related as enantiomers.

Hence, the correct option is E.

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Savings account: $4 / $200 = 0.02 x 100 = 2%

Bond: $85 / $1000 = 0.085 x 100 = 8.5%

Real Estate: $6,400 / $40,000 = 0.16 x 100 = 16%

Answer:

∠ L = 109°

Step-by-step explanation:

Since the triangles are congruent, then corresponding angles are congruent.

Thus ∠ J = ∠ G , substitute values

3x + 12 = 2x + 19 ( subtract 2x from both sides )

x + 12 = 19 ( subtract 12 from both sides )

x = 7

Then

∠ G = 2x + 19 = 2(7) + 19 = 14 + 19 = 33°

∠ H = 4x + 10 = 4(7) + 10 = 28 + 10 = 38°

By the sum of angles in a triangle = 180°, then

∠ F = 180° - (33 + 38)° = 180° - 71° = 109°

∠ F and ∠ L correspond , thus

∠ L = ∠ F = 109°

Step-by-step explanation:

If the bottle contains 500ml of water and the water fills half of the bottle, then the total capacity of the bottle must be 1000ml (since half of 1000ml is 500ml).

To convert this to liters, we can divide by 1000, since there are 1000 milliliters in one liter.

1000ml / 1000 = 1 liter

Therefore, the bottle holds 1 liter of water.

We can conclude that the function f(t) is increasing at a varying rate over the interval [3, 3.1], and the average rate of change of 17.9 is a representation of this changing rate over the interval.

We are given the function f(t) = 4t^2 - 5 and the interval [3, 3.1]. We can find the average rate of change of f(t) over this interval using the formula:

average rate of change = [f(3.1) - f(3)] / [3.1 - 3]

First, we calculate f(3) and f(3.1):

f(3) = 4(3)^2 - 5 = 31

f(3.1) = 4(3.1)^2 - 5 = 36.59

Substituting these values into the formula, we get:

average rate of change = [36.59 - 31] / [3.1 - 3] = 17.9

So the average rate of change of f(t) over the interval [3, 3.1] is 17.9.

To compare this average rate of change with the instantaneous rates of change at the endpoints of the interval, we can calculate the derivatives of f(t) at t = 3 and t = 3.1:

f'(t) = 8t

f'(3) = 8(3) = 24

f'(3.1) = 8(3.1) = 24.8

The instantaneous rate of change of f(t) at t = 3 is 24, which is less than the average rate of change over the interval. This means that the function is increasing at a slower rate at t = 3 than it is over the interval [3, 3.1].

The instantaneous rate of change of f(t) at t = 3.1 is 24.8, which is greater than the average rate of change over the interval. This means that the function is increasing at a faster rate at t = 3.1 than it is over the interval [3, 3.1].

Therefore, we can conclude that the function f(t) is increasing at a varying rate over the interval [3, 3.1], and the average rate of change of 17.9 is a representation of this changing rate over the interval.

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Answer:

7/20

Step-by-step explanation:

5/5 same as 1 is the overall mixture

so 5/5 - 2/5 of the cherry = 3/5

3/5 is left and she puts 1/4 lime

3/5 - 1/4 = 7/20

7/20 is the fraction left and it goes to grape

Step-by-step explanation:

If the price of a price is p dollars, then the price of 2 bags is equal to (p × 2) dollars

Answer:

Step-by-step explanation:

56.1,12.1,23.6

Answer:

\(2\sqrt{2} \text{ mi}\)

Step-by-step explanation:

See the attached image for a picture of the situation.  The angle of depression lets you find the angle next to it but inside the triangle.  It, too, must measure 45 degrees.

That means the triangle is an isosceles triangle (two legs of equal length).

Apply the Pythagorean Theorem.

\(x^2+x^2=4^2\\2x^2=16\\x^2=18\\x=\sqrt{8}=2\sqrt{2}\approx 2.83\text{ mi}\)

Diana's average speed for the entire race was approximately 0.583 meters per second.

We can start by using the formula

average speed = total distance / total time

We know that Diana ran a total distance of 700 meters, and we can find the total time by adding the time for the first lap and the time for the second lap. Let's call the distance of each lap "x"

total distance = 700 meters

distance for each lap = x meters

So, the total time is

total time = time for first lap + time for second lap

To find the time for each lap, we can use the formula

time = distance / speed

For the first lap, we have

time for first lap = x / 7

For the second lap, we have

time for second lap = x / 5

So, the total time is

total time = (x / 7) + (x / 5)

We can simplify this by finding a common denominator

total time = (5x + 7x) / (35)

total time = (12x) / 35

Now, we can substitute the values we have into the formula for average speed

average speed = total distance / total time

average speed = 700 / [(12x) / 35]

average speed = (700 × 35) / (12x)

average speed = 204.166... / x

To find the average speed for the entire race, we need to find the value of "x" that makes this expression true. We know that the two laps are equal in distance, so we can set

x + x = 700

2x = 700

x = 350

Substituting this value of "x" into the expression for average speed, we get

average speed = 204.166... / 350

average speed ≈ 0.583 meters per second

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a) The GCF of 63 and 36 is 9

b)

a) To find the GCF of 63 and 36, we do the following:

Write 63 and 36 as follows:

The common factors are:

Therefore, the Greatest Common Factor (GCF) is 9

b) To find the factor 63 - 36

Answer:

81, 64, 47, 30, 13, -4

Answer:

The next two numbers are 13 and -4.

Step-by-step explanation:

We are subtracting 17 each time.

30 - 17 = 13

13 - 17 = -4

Answer:

f. 85

Step-by-step explanation:

All triangles add up to 180 degrees

BCE=25

then you need to find DBC, you can do that since ABD is isocilies that means all sides are equal in length and angle so 180 divided by 3 (number of side) is 60

isoceles triangle have 2 sides that are equiangular, cince we know BCA is 25 we also know BAC is 25, leaving angle ABC to be 130 (180-50=130)

we subtract angle ABD from angle ABC to get angle DBC, leaving angle DBC to equal 70 degrees

since 70 (angle DBC) + 25 (Angel BCA)= 95

we just subtrract 95 from 180 to get the answer 85 (:

Answer:

85 degrees

Step-by-step explanation:

if Δ ABD is equilateral  then the 3 sides and three angles are equal

sum of angles of Δ=180

180/3=60 degrees (∠A,∠B,∠D)

ΔBCA is isosceles then the two angles A and C are equal = 25

∠B=180-50=130

∠B in Δ BEC=130-60=70

∠E+∠B+∠C in Δ BEC=180

∠E= 180-70-25=85 degrees

Answer:

Rounded up percentages:

Corn: 15.65%

Green Beans: 16.52%

Tomatoes: 6.96%

Carrots: 13.04%

For exact percentages divide this with a calculator:

Corn: 360/2300

Green Beans: 380/2300

Tomatoes: 160/2300

Carrots: 300/2300

Answer:

A

Step-by-step explanation:

Simplify and subtract.

Answer:

Step-by-step explanation:

4(0.5x+2.5y-0.7x-1.3y+4)

2x+10y-2.8x-5.2y+16

-0.8x+4.8y+16

Answer:

27 liters

Step-by-step explanation:

18-4=14

14-2=12

12+12=24

24+3=27