Whats 2x2 i will give you 14 points

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer:

P(A n B) = 0

Step-by-step explanation:

Given

\(A \to\) Traces of TNT detected

\(B \to\) No traces of TNT

Required

Probability of false positive

From the question, we understand that A and B must occur to get a positive and the result is 0.

The probability of A and B is represented as: P(A n B)

Include the result (0), we get:

P(A n B) = 0

Answer:

Meter

Step-by-step explanation:

The standard unit of length based on the metric system is a meter (m). According to the length that needs to be measured, we can convert a meter into various units like millimeters (mm), centimeter (cm), and kilometer (km).

Let

the original price = a

60% of the original price can be expressed as follows

The original cost of the dress is $40. The equation can be represented as follows

0.6a = 24

The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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Answer:

See edit

A 20 km / hour

Step-by-step explanation:

The exact answer is 30 km / 172 which is less than 1 km / hr. Since that answer isn't offered, I suspect there is something wrong with the question. If there is a decimal after the 1 in 172 you would get 17.44 km / hr. That's roughly A.

If the decimal is not there, I think you should either resubmit the question or answer A.

Edit

The note said (below) that the ship went 30 km in 1 1/2 hours.

Rate = distance / time

distance = 30 km

time = 1 1/2 hours = 1.5 hours

rate = 30 / 1.5 = 20 km / hr

Answer:

a. A hen needs 9,125 grasshoppers per year

b. 3,330,625 grasshoppers are needed for a year's supply of hens for the farmer each year

c. The total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year 3330.625 kg

d. 99918.750 kg of soybeans are needed to feed all the grasshoppers for one year.

Step-by-step explanation:

a. To calculate the number of grasshoppers a hen needs per year.

There are 365 days days in a year.

From the question,  1 hen eats 25 grasshoppers/day

If 1 hen eats 25 grasshoppers per day, then

1 hen will eat 25 × 365 grasshoppers per year

25 × 365 = 9125

Hence, a hen needs 9,125 grasshoppers per year.

b. To determine how many grasshoppers are needed for a year's supply of hens for the farmer each year

From the question, The farmer lives on 1 hen/day for a year.

That is, for a year, the farmer lives on 365 × 1 hen = 365 hens

Now, we will determine how many grasshoppers 365 hens will need for a year.

Since, a hen needs 9,125 grasshoppers per year

Then, 365 hens will need 365 × 9125 grasshoppers per year

365 × 9125 = 3330625 grasshoppers

Hence, 3,330,625 grasshoppers are needed for a year's supply of hens for the farmer each year.

c. To determine the total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year

From the question, 1,000 grasshoppers have a mass of 1 kg.

That is, 1,000 grasshoppers have a mass of 1000 g

(NOTE: 1000g = 1kg)

If 1,000 grasshoppers have a mass of 1000 g

Then, 1 grasshopper will have a mass of (1 × 1000) /1000 = 1 g

From b., the total number of grasshoppers needed to feed all the hens for one year is 3,330,625 grasshoppers.

Now, we will determine the mass of 3,330,625 grasshoppers

1 grasshopper have a mass of 1 g

∴ 3,330,625 grasshoppers will have a mass of (3,330,625 × 1) / 1 = 3,330,625 g

Now, we will convert this to kilograms (kg)

If 1000 g = 1 kg

Then, 3,330,625 g = (3,330,625 × 1) / 1000 = 3330.625 kg

Hence, the total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year 3330.625 kg.

d. To determine how many kilograms of soybeans are needed to feed all the grasshoppers for one year

From the question, 1 grasshopper requires about 30 g of soy/yr

From b., 3,330,625 grasshoppers are needed for a year's supply of hens for the farmer each year

If 1 grasshopper requires about 30 g

Then, 3,330,625 grasshoppers will require (3,330,625 × 30) / 1 = 99918750 g of soy/yr

Now, we will convert this to kilograms

If 1000 g = 1 kg

Then, 99918750g = (99918750 × 1) / 1000 = 99918.750 kg

Hence, 99918.750 kg of soybeans are needed to feed all the grasshoppers for one year.

Answer: 5(3n+4r)

Step-by-step explanation:You need to find the gcf/factor .So the gcf of 15 and 20 is 5.So know that you know the gcf ,you divide 15n by 5 which gives you 3n and divide 20r by5 which gives you 4r.Now the last thing you do is,take the GCF which is 5 and place a Parentheses and take 3n and 4r and add them together.

So you get 5(3n+4r) as your expression that  is equivalent to  15n + 20r .

Hope it helps . :)

Answer:

y - 5 = -2(x + 3)

Step-by-step explanation:

When you write an equation in point-slope form, you only need two things: a point and a slope.

Given:

point: (-3, 5)

slope (m): -2

The standard point-slope equation is

y - y₁ = m(x - x₁)

Plug in what you know.

y - (5) = -2(x - (-3))

Simplify.

y - 5 = -2(x + 3)

This is your equation.

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y√y i.e Option (B) is  equivalent to the expression below when y> 0.

Equivalent means that two things have the same value, meaning, or measure. For example, 2 + 2 and 4 + 0 are equivalent equations because both equal 4. Another example is 1/2 and 0.5, which are equivalent because they are both equal to one-half.Equivalent in mathematics refers to two expressions that have the same value or the same outcome when evaluated.

Equivalent means having the same value, measure, or effect as something else. For example, two dollars is equivalent to two euros.

Let's start with the expression:

√\(y^{3}\)+√\(16y^{3}\)-\(4y\)√\(y\)

where y > 0. (this allow us to have y inside a square root, so we don't mess with complex numbers).

We want to find the equivalent expression to this one.

Here, we can do the next two simplifications:

√\(16y^{3}\) = √\(16\) √\(y^{3}\) = \(4\)√\(y^{3}\)

And

\(y\)√\(y\) = √\((y^{2}. y)\)= √\(y^{3}\)

If we apply these two to our initial expression, we can rewrite it as:

√\(y^{3}\)+√\(16y^{3}\)-\(4y\)√\(y\)

√\(y^{3}\) + \(4\)√\(y^{3}\)-\(4\)√\(y^{3}\) = √\(y^{3}\)=\(y\)√\(y\)

Therefore, Option (B) is correct.

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Answer:

Reasoning:

You multiply x by 9 and 2 by 9 and it expands out from 9(x+2) to 9x+18

I hope this helps and good luck!

Answer:

9x + 18

Step-by-step explanation:

9 times x = 9x

9 x 2 = 18

Answer:

Step-by-step explanation:

Given the dataset 147, 154, 156, 161, 162,

Mean is the sum of the dataset divided by the total number of dataset.

a) Mean = \(\sum Xi/N\)

\(\overline x = \dfrac{147+154+156+161+162}{5}\\ \\\overline x = \dfrac{780}{5}\\ \\\overline x= 156\)

b) The formula for calculating the deviation from the mean for each value is expressed as \(Xi - \overline X\) where;

Xi is value of each item

xbar is the mean = 156

Mean deviation of 147 = 147-156 = -9

Mean deviation of 154 = 154-156 = -2

Mean deviation of 156 = 156-156 = 0

Mean deviation of 161 = 161-156 = 5

Mean deviation of 162 = 162-156 = 6

c) Sum of the deviations \(\sum Xi - \overline X\) = (-9-2+0+5+6)

\(\sum Xi - \overline X\) = -11+11

\(\sum Xi - \overline X\) = 0

Hence the sum of deviation from the mean is 0

Answer:

195.5 m²

Step-by-step explanation:

A = bh/2

A = (23)(17)/2

A = 391/2

A ≈ 195.5 m²

Answer:

14

Step-by-step explanation:

Answer:

57 seconds

Step-by-step explanation:

55.7 + 1.3 = 57 seconds

Answer:

a direct proof

Step-by-step explanation:

Answer:

direct proof

Step-by-step explanation:

any kind of chart wouldnt be helpful, and an indirect proof wouldnt either.

Answer:

x = 10°

Step-by-step explanation:

Because <A and <B are vertical angles, they are equal.

4x+8 = 2x+28

Subtract 2x and 8 on both sides,

4x - 2x = 28 - 8

2x = 20

Divide by 2,

x = 10°

Answer:

Hope this helps

Step-by-step explanation:

As vertical angles are always equal,

Angle A = angle B

That is,

4x + 8 = 2x + 28

4x - 2x = 28 - 8

2x = 20

X = 20/2

X = 10

The expansion of \((2a + 5b)^4\) using Pascal's triangle is

\((2a+5b)^4=16a^4+160a^3b+600a^2b^2+1000ab^3+ 625b^4\)

What is Pascal's triangle?

Blaise Pascal's triangle, often known as the Pascal's triangle, is a unique triangle in which the number 1 is placed at the top, followed by 1s on each side of the triangle to the end.

Each of the middle numbers is the sum of the two numbers just above it.

(n + 1) elements make up the nth row, which has that many components.

Refer to the attachment for Pascal's triangle.

We can infer from Pascal's triangle that

\((x+y)^4=x^4+4x^3y+6x^2y^2+4xy^3+y^4\)

According to the given question:

Substituting x = 2a and y = 5b in the above equation to get

\((2a+5b)^4=(2a)^4+4(2a)^3(5b)+6(2a)^2(5b)^2+4(2a)(5b)^3+(5b)^4\)

On solving the left hand side further we get

\((2a+5b)^4=16a^4+160a^3b+600a^2b^2+1000ab^3+ 625b^4\)

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Therefore , the solution to the given problem of composite number comes out to be Since Morgan's claim regarding Composite Numbers is true, we can infer that he is right.

Prime numbers can really be expressed as the sum of two different numbers. The sum of two or more numbers is what is referred to as a composite number. Examples of prime numbers include 2,3,5,71,11 since they only have two factors, one and itself. Examples of composite numbers include 4,6,8,10,12 since they contain more than two contributing variables.

Here,

we can see Morgan's claim that any numbers with a 2 in the place of a one are composite numbers.

We can conclude that Morgan is correct given the prior description of composite numbers by stating that all numbers with a 2 in the place of a one are composite numbers.

In actuality, any even integer—aside from 2—is a composite number.

Therefore , the solution to the given problem of composite number comes out to be Since Morgan's claim regarding Composite Numbers is true, we can infer that he is right.

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11.5, 10.5, 6.1 --> Yes, can form a triangle. 9.5, 3.5, 4.5 --> Yes, can form a triangle. 8, 6.7, 1 --> No, cannot form a triangle. 8, 6.7, 9.8 --> Yes, can form a triangle. 5, 6, 8 --> Yes, can form a triangle. 9.5, 7.5, 8.5 --> Yes, can form a triangle.

A triangle is a polygon with three sides and three angles. It is a two-dimensional figure with three straight sides that connect three vertices or corners. The sum of the interior angles of a triangle is always 180 degrees, and the exterior angles add up to 360 degrees. Triangles are classified based on the length of their sides and the measure of their angles, and they can be equilateral, isosceles, scalene, acute, obtuse, or right-angled. Triangles have many important properties and are used extensively in geometry and trigonometry.

Here,

Set 1: 11.5, 10.5, 6.1

To determine if these segments can form a triangle, we need to check if the sum of the two smaller sides is greater than the longest side:

10.5 + 6.1 = 16.6 > 11.5, so yes, this set of segments can form a triangle.

Set 2: 9.5, 3.5, 4.5

Again, we check if the sum of the two smaller sides is greater than the longest side:

3.5 + 4.5 = 8 < 9.5, so no, this set of segments cannot form a triangle.

Set 3: 8, 6.7, 1

Checking:

6.7 + 1 = 7.7 < 8, so no, this set of segments cannot form a triangle.

Set 4: 8, 6.7, 9.8

Checking:

6.7 + 9.8 = 16.5 > 8, so yes, this set of segments can form a triangle.

Set 5: 5, 6, 8

Checking:

5 + 6 = 11 < 8, so no, this set of segments cannot form a triangle.

Set 6: 9.5, 7.5, 8.5

Checking:

7.5 + 8.5 = 16 > 9.5, so yes, this set of segments can form a triangle.

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The cost to buy enough lemons to make three 9-inch lemon pies, each is $9.48.

Money is a means of payment and used for making transactions.

The three 9-inch lemon pies has each requiring half a cup of lemon juice. The cups of juice needed will be:

= 3 × 1/2 cup of juice

= 3/2 cups of juice.

It's important to note that 1 cup = 16 tablespoon

3/2 cups will be:

= 3/2 × 16

= 24 tablespoon

Since each lemon yields about 2 tablespoons of juice, the number of lemons required will be:

= 24 / 2

= 12 lemons.

The store is selling lemons at $0.79 each, the total cost will be:

= Cost × Number of juice

= $0.79 × 12

= $9.48

The cost is $9.48.

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The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

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Answer:

Step-by-step explanation:

h(x)=ax^2

Given h=30 when x=150 we get

a(150)^2=30

a=30/22500=1/750 so

h(x)=x^2/750

The equation  \(\rm h(x)= \frac{1}{750} x^2\)   represents the height of the cable at a distance x feet from the center.

It is given that the cable for a certain suspension bridge is modeled by a parabola with vertex (0,0).

It is required to derive the equation that represents the height of cable at a distance x feet from the center.

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have the bridge is modeled by a parabola with vertex (0,0)

We know the general equation of parabola:

\(\rm y= a(x-h)^2+k\)  with vertex (h,k)

Here the value of h = 0 and k = 0

\(\rm h(x)= ax^2\)    ( ∵ y = h(x) represented the function in terms of height)

We have h = 30 at x = 150 (From the question)

Putting the value of h and x in the parabola equation, we get:

\(\rm 30 = a(150)^2\)

\(\rm a = \frac{1}{750}\)

Putting the value of 'a' in the parabola equation, we get:

\(\rm h(x)= \frac{1}{750} x^2\)

Thus, the equation  \(\rm h(x)= \frac{1}{750} x^2\)   represents the height of the cable at a distance x feet from the center.

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Answer:

Step-by-step explanation:

This equation represents the relationship between the exponential functions y = e^x and y = (10^(x-1)). These two functions are equal to each other for all values of x. This can be shown by taking the natural logarithm of both sides of the equation, which gives us:

ln(e^x) = x-1

In this equation, ln(e^x) is equal to x, since the natural logarithm of an exponential expression with a base of e is the exponent. Therefore, we can simplify the equation by taking the natural logarithm of both sides:

ln(10^(x-1)) = x-1

e^(x-1) = 10^x

The two functions e^x and 10^(x-1) are the same function with different bases, so they follow the same pattern. The fact that these two functions are equal to each other for all values of x can also be shown by graphing the two functions and seeing that they overlap perfectly.

come on now

\(\underset{\textit{like-bases with exponents}}{5^{11}\cdot 5^3\cdot 5^{17}}\implies \stackrel{\textit{add the exponents}}{\underset{\textit{keep the base}}{5^{11+3+17}}}\implies 5^{31}\)

With a significance level of 0.05, the. option that shows the correct test statistic, P- value, and conclusion is A. Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

In statistics, the significance level (denoted by α) is the probability of making a Type I error, which is rejecting a true null hypothesis. In other words, it is the maximum allowable probability of observing a result as extreme as or more extreme than the one observed, assuming the null hypothesis is true.

The significance level is typically set by the researcher before conducting a hypothesis test and is usually set to 0.05 (5%) or 0.01 (1%). If the p-value of the test is less than or equal to the significance level, the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the significance level, the null hypothesis is not rejected.

The correct option is A.

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With a significance level of 0.05, which of the following shows the correct test statistic, P- value, and conclusion?

Test statistic, -1.952; P-value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

Test statistic, = 0.3619; P-value, 0.6392. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

Test statistic, -1.952; P-value, 0.0509. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.

Test statistic, t=0.3651; P-value, 0.6425. There is insufficient evidence to reject the null hypothesis of

no difference between the triglyceride test levels.

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

We have,

To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.

The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).

Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.

Substituting these into the expression,

We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).

Now, let's evaluate the limit term by term:

lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).

lim(x approaches 0) (x (1/(sin(x))³))

= 0 (1/(sin(0))³)

= 0 x 1/0 (which is also undefined).

Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.

Therefore,

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

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