Multiply: (√2x³ +√12x)(2√10x³ + √6x²
2√10x +2√3x³ +4√15x³ +6√2x
2x²√5 +2x√3x + 2x³√30 +3x√2x
4x √√5+2x²√√3x + 4x³√30+ 6x√√2x
x√20+x²√√6x + x³√120 + x√12x

Answer:

x = -11

Step-by-step explanation:

2x + 23 + 9 = x + 21

Combine common factors

2x + 32 = x + 21

Subtract x from both sides

x + 32 = 21

Subtract 32 from both sides

x = -11

The answer is 23/40

To simplify this expression, we need to find a common denominator for each pair of fractions that are being added or subtracted.

 
The common denominator for 1/4 and 1/5 is 20, so we can rewrite 1/4 as 5/20 and 1/5 as 4/20. Then, we can subtract these fractions to get 1/20.

 
The common denominator for -3/4 and 1/8 is 8, so we can rewrite -3/4 as -6/8. Then, we can add these fractions to get -5/8.

 
Now, we can combine the two simplified fractions by finding a common denominator of 40. We can do this by multiplying 20 and 8, which gives us 160.

Then, we can rewrite 1/20 as 2/40 and -5/8 as -25/40. Adding these fractions together gives us:

2/40 - 25/40 = -23/40.

The absolute value of any number is always positive so it becomes 23/40.

The simplified version of (1/4 - 1/5) + (-3/4 + 1/8) is 23/40.

Answer and Step-by-step explanation:

1a. The work is NOT correct.

1b. The mistake was keeping the 2 with the \(\frac{12}{15}\), in which this number was found by multiplying the denominator 5 by the whole number 2, then adding it to the numerator 2, resulting in \(\frac{12}{15}\).

1c. Multiply the denominator 5 by the whole number 2, then add it to the numerator 2, which results in \(\frac{12}{15}\). When you add \(\frac{1}{15}\), you get the answer to be \(\frac{13}{15}\).

Have a good day!

(a) The range is 19.

(b) The interquartile range is 9.

(c) The sample variance is 31.

(d) The sample standard deviation is 6.

(e) The range is 32.

The ranges for the box plots are the same, but their interquartile ranges are different

The standard deviation of the sampling distribution of the sample proportion is commonly used when you're sampling from a large population and the sampling is done with replacement.

It represents the variability of sample proportions you would expect to obtain if you repeated the sampling process many times.

Standard Deviation of Sampling Distribution of Sample Proportion = \(\sqrt{(p * (1 - p)) / n)}\)

Where,

p is the true proportion of the characteristic you're interested in within the population.

n is the sample size.

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Answer:

10)

11x-1+20x-3=151 (the exterior angle of an triangle is equal to the sum of two opposite interior angles)

31x-4=151

31x=151+4

31x=155

x=155/31

x=5°

11)

14x-13=4x+13+6x+2

14x-4x-6x=13+13+2

4x=28

x=28÷4

x=7°

The ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x.

The correct option is A: (-2, 2).

To determine which ordered pairs satisfy both inequalities y < -x + 1 and y > x, we need to check each pair's coordinates in both inequalities.

Let's test each ordered pair:

A: (-2, 2)

For y < -x + 1: 2 < -(-2) + 1 → 2 < 3 (True)

For y > x: 2 > -2 → 2 > -2 (True)

B: (1, 1)

For y < -x + 1: 1 < -(1) + 1 → 1 < 0 (False)

For y > x: 1 > 1 → 1 > 1 (False)

C: (0, 0)

For y < -x + 1: 0 < -(0) + 1 → 0 < 1 (True)

For y > x: 0 > 0 → 0 > 0 (False)

D: (-1, -1)

For y < -x + 1: -1 < -(-1) + 1 → -1 < 2 (True)

For y > x: -1 > -1 → -1 > -1 (False)

From the above calculations, we can see that only the ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x. Therefore, the correct answer is option A: (-2, 2).

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The complete question:

Which ordered pairs make both inequalities y < -x + 1 and y > x true?

A: (2, 2)

B: (1, 1)

C: (0,0)

D: (-1, -1)

The value of x when using addition property of equality to solve the given problem is; -44

The addition property of equality is a property of equality that states that when the same quantity is added to both sides of an equation, it will produce an equivalent equation. For example, 4 = 2 + 2 is an equation due to the fact that both the right and the left-hand sides of the equal sign represent the number 4.

The equation to solve is;

-60 = x - 16

By the use of addition property of equality, we will add 16 to both sides to get;

-60 + 16 = x - 16 + 16

x = -44

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The minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval is 791.

The standard deviation is given as (σ) = 1.69.

The mean number of dresses given (μ) = 7.6.

Margin of error given (M.E.) = 0.14.

Confidence level given = 98%.

Z-Score corresponding to 98% confidence interval (Z) = 2.33.

We are asked to find the minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval.

We assume the size of the sample to be n.

By the formula of Margin of Error:

M.E. = Z*(σ/√n).

Substituting the values, we get:

0.14 = 2.33*(1.69/√n),

or, √n = 2.33*1.69/0.14 = 28.126429,

or, n = 791.096 ≈ 791 (As sample size needs to be a whole number).

Thus, the minimum size of the sample required to ensure that the estimate has an error of at most 0.14 at the 98% level of the confidence interval is 791.

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To translate the given English statements into logical expressions using the provided predicates, here are the translations:

1. Everyone who was well went to work yesterday.

  - ∀x [(W(x) ∧ ¬P(x)) → W(x)]

2. Someone who was sick yesterday did not go to work yesterday.

  - ∃x (P(x) ∧ ¬W(x))

3. Someone who missed work was neither sick nor on vacation.

  - ∃x (¬(P(x) ∨ Q(x)) ∧ ¬W(x))

4. Joshua was on vacation yesterday and he did not go to work.

  - Q(Joshua) ∧ ¬W(Joshua)

5. Everyone was well and went to work yesterday.

  - ∀x (W(x) → W(x) ∧ ¬P(x))

Please note that these translations assume that the domain consists of all employees of the company, including Joshua. Also, the logical expressions are based on the provided predicates and their interpretations.

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Answer:a: 29.5774648%

B:29.8701299%

Step-by-step explanation:

a: First turn 21/71 into a decimal: 0.295774648 to change a decimal into a percentage, Multiply by 100. 21/71 as a percentage is 29.5774648%

B: 46/154 as a decimal: 0.298701299 multiplied by 100, 29.8701299%

No, T cannot map R^n onto R^n if it has the property that T(u) = T(v) for some pair of distinct vectors u and v in R^n. This is because since T(u) = T(v), then the same vector in R^n will be mapped to two different vectors in R^n, which is not a valid mapping.

1. Suppose a linear transformation T: R^n → R^n has the property that T(u) = T(v) for some pair of distinct vectors u and v in R^n.

2. This means that the same vector in R^n will be mapped to two different vectors in R^n.

3. This is not a valid mapping and therefore T cannot map R^n onto R^n.

No, T cannot map R^n onto R^n if it has the property that T(u) = T(v) for some pair of distinct vectors u and v in R^n. This is because since T(u) = T(v), then the same vector in R^n will be mapped to two different vectors in R^n, which is not a valid mapping.

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It is guaranteed that there will be at least two cards of the same denomination among the randomly selected 13 cards from a standard 52-card deck.

Yes, if 13 cards are randomly selected from a standard 52-card deck, at least two cards must be of the same denomination. This is known as the Pigeonhole Principle or the principle of the Dirichlet drawer.In a standard deck of 52 cards, there are 13 denominations (2, 3, 4, ..., J, Q, K, A), each with four cards of different suits (spades, hearts, diamonds, clubs). When selecting 13 cards, we can think of each denomination as a pigeonhole and the selected cards as pigeons. Since there are more pigeons (13) than pigeonholes (denominations), by the Pigeonhole Principle, at least two pigeons (cards) must occupy the same pigeonhole (denomination).Therefore, it is guaranteed that there will be at least two cards of the same denomination among the randomly selected 13 cards from a standard 52-card deck.

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Step-by-step explanation:

Because vertical angles have equal measure, angle CPB = 90 degrees. By extension, angle CPQ + angle QPB = 90 degrees

So 2x+4x+12=90

6x+12=90

6x=78

x=13

Answer:

41.67 kg

72 books

Step-by-step explanation:

mass of 150 books = 150/108 × 30 kg

= 41.67 kg

number of books = 20/30 × 108 books

= 72 books

Answer:

1.x,y is the answer to first question

2.y=2x+5

First, we need to convert the given weight to mass. Since we know that gravitational acceleration is 32 ft/s² and the weight is 1 pound, we can calculate the mass.

Weight = Mass × Gravitational acceleration
1 lb = Mass × 32 ft/s²
Mass = 1 lb / 32 ft/s² = 1/32 slugs
Now, we need to find the angular frequency (ω) using the formula ω = sqrt(k/m):
ω = sqrt(100 lb/ft / (1/32 slugs)) = sqrt(3200) = 40 rad/s
The equation of motion will be:
y(t) = A * cos(ωt)

Since the spring is stretched an additional 1 inch (1/12 ft), that will be the amplitude (A): Amplitude = 1/12 ft

Now we can write the complete equation of motion:
y(t) = (1/12) * cos(40t)

In conclusion: Amplitude: 1 inch (1/12 ft)
Period: π/20 seconds

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Answer:

uahabsihsb

Step-by-step explanation:

The probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi is 43.25%.

Given that,

The tensile strength of a synthetic fiber used to make carpet is regularly distributed, with a mean of 75.5 psi and a standard deviation of 3.5 psi. We have to determine probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi.

We know that,

The Z score is used to determine how far the raw score deviates from the mean, either above or below.

z = (score - mean) / (standard deviation ÷ √sample)

Mean 75.5 psi and standard deviation 3.5 psi. n = 6.

For > 75.75:

z = (75.75 - 75.5) / (3.5 ÷√6) = 0.17

P(z>0.17) = 1-P(z<0.17)

= 1-0.5675

= 43.25%

Therefore, The probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi is 43.25%.

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The expression that represents the value of Nandy's investment after 8 years is A = 1000 (1 + 3.5(8)).

So, the expression that can represent the above situation is:

The total money Nadya deposited is $1000.

Interest is 3.15%.

Total years are 8.

Simple interest formula: A = P (1 + rt)

Where a is the final amount, p is the principal amount, r is the interest return and t is the time in years.

Then, we have:

A = 1000 (1 + 3.5(8))

A = 1000(29)

A = 29,000

Therefore, the expression that represents the value of Nandy's investment after 8 years is A = 1000 (1 + 3.5(8)).

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Answer:

0.65

Step-by-step explanation: the first thing you got to do is 3.9 divided by 6 and then solve it

"Champagne" is a word that is likely from French based on the grapheme representing /sh/.

Based on the grapheme representing /sh/, the word that is likely from French is "champagne."

The /sh/ sound is commonly represented by the grapheme "ch" in English, as in words like "shop" and "sheep." However, in French, the same sound is often represented by the grapheme "ch" as well.

The word "champagne" is a well-known French term used to refer to a type of sparkling wine produced in the Champagne region of France. It contains the "ch" grapheme that represents the /sh/ sound in French.

The grapheme for the sound /sh/ indicates that the word "champagne" is hence likely French in origin.

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The grapheme /sh/ is commonly found in French words. An example from French is 'chaussure' where 'ch' represents the /sh/ sound. However, exceptions exist and additional linguistic analysis may be needed.

The grapheme representing the /sh/ sound is a common characteristic in French words. Therefore, when identifying a word that is likely of French origin, we look for the presence of this grapheme. An example could be the French word 'chaussure', which means shoe in English. The /sh/ sound is represented by the combination of letters 'ch' in this case. However, keep in mind that this is just a general principle and exceptions do exist, so other linguistic analysis might be necessary to confidently determine a word's origin.

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Answer:

25

Step-by-step explanation:

So find the number that is a perfect square and 2 times the square root = 10

The number is 25.

Check:

\((x+5)^2=x^2+10x+25\)

Answer:

The answer is 25.

Step-by-step explanation:

25 is a perfect square of 5. When x are added together, they form 10x.

\( {(x + 5)}^{2} \)

\( {x}^{2} + 2(x)(5) + {5}^{2} \)

\( {x}^{2} + 10x + 25\)

Answer:

the snail was going 0.005m/second

Step-by-step explanation:

15m/3000

False. In a static method of a class, you cannot use the "this" keyword to reference instance variables or instance methods of the same class.

A static method belongs to the class itself, not to any particular instance of the class, so it cannot access instance-specific information. Instead, you would need to use the class name followed by the variable name to access any static or instance variables within a static method of that same class. For example, if the class had an instance variable called "f" and a static method called "myStaticMethod", you could reference the instance variable from within the static method using "ClassName.f". It is important to note that if you attempt to reference an instance variable using "this.f" within a static method, you will receive a compilation error.

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Using the ratio between the length and width, the television has a width of 45 inches

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related. This can be said as the ratio of a quantity is a fraction of another quantity

In this problem, the ratio of length to width is 4 : 3.

If the length = 60 inches, we can calculate the width by;

60 : x = 4: 3

60 / x = 4 / 3

x = 60 * 3 / 4

x = 45

The width of the television is 45 inches

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Main answer: The majority of respondents who favored the legalization of marijuana identified as liberal or very liberal.

Supporting explanation: The table shows that out of the 486 respondents who favored the legalization of marijuana, 296 identified as liberal and 120 identified as very liberal. This means that 616 out of the 826 respondents who answered both questions identified as liberal or very liberal. On the other hand, only 60 respondents who favored the legalization of marijuana identified as conservative or very conservative. This suggests that there is a correlation between political leaning and views on the legalization of marijuana, with those on the left end of the political spectrum more likely to support it.

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Answer:

no

Step-by-step explanation:

one ratio is 2/3 and the other is 3/4

The ratio of yellow to red is not 3/4. Then the different colors will form.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

A specific shade of orange paint calls for 2 parts yellow and 3 parts red.

For the orange paint, the ratio of the yellow part and red part will be

⇒ 2: 3

Catie uses 3 cups of yellow paint and 4 cups of red paint to make orange paint. Then the ratio will be

⇒ 3: 4

The ratio of yellow to red is not 3/4. Then the different colors will form.

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Answer:

Step-by-step explanation:

∠QRT is supplementary to ∠SRT - meaning the sum of their angles equals 180°.

If ∠SRT = 110°, you can subtract 110 from 180 and find

that the measure of ∠QRT = 70°.

180 - 110 = 70°

The interior angles of a triangle add up to 180.

Add the two angles you have - ∠TQR and ∠QRT

74 +  70 = 144

Subtract from 180 - 144 = 36°

so ∠QTR = 36°

I did the first question as reference. Pretty simple once you get it!

Answer:

91.42 crates

Step-by-step explanation:

Let

Greatest Number of 140kg crates = x

weight of crate = 140-kilogram

Weight of other shipment = 13200 kilograms

greatest weight of container = 26000 kilograms

Weight of other shipment + (weight of crate * number of crates) ≤ greatest weight of container

13,200 + 140x ≤ 26,000

140x ≤ 26,000 - 13,200

140x ≤ 12,800

x ≤ 12,800/140

x ≤ 91.42 kilograms

Greatest Number of 140kg crates = 91.42 crates