Help me with the questions 1-4, thank you! :)

Answer:

-1

Step-by-step explanation:

Answer:

x=-10

Step-by-step explanation:

3=-(4x+7)+3x

move all terms to the left:

3-(-(4x+7)+3x)=0

calculate terms in parentheses: -(-(4x+7)+3x), so:

-(4x+7)+3x

add all the numbers together, and all the variables

3x-(4x+7)

get rid of parentheses

3x-4x-7

add all the numbers together, and all the variables

-1x-7

Back to the equation:

-(-1x-7)

get rid of parentheses

1x+7+3=0

add all the numbers together, and all the variables

x+10=0

move all terms containing x to the left, all other terms to the right

x=-10

The relationship between a statistic and a parameter is the same as the relationship between , Option(A) a sample and a population

The Population is defied as an entire group of individuals that we are interested in studying, while a sample is a subset of that population that we actually observe and collect data from.

A Parameter is defined as a numerical characteristic of a population, such as its mean or variance, whereas a statistic is a numerical characteristic of a sample, such as its sample mean or sample standard deviation.

The relationship between a sample and a population is similar to the relationship between a statistic and a parameter because a sample is used to estimate  information about the population, and a statistic is used to estimate  information about a parameter.

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Answer:

Meters, miles, feet, centimeters

Step-by-step explanation:

A minimum sample size of 1069 is required to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle such that the margin of error is no more than 0.03 for a 95 percent confidence interval.

In order to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle, a researcher in campaign finance law wants to determine the minimum sample size such that the margin of error is no more than 0.03 for a 95 percent confidence interval.

Assuming that the researcher wants to establish a 95% confidence interval, the level of significance (α) is 1 - 0.95 = 0.05. Furthermore, we can assume that there is no prior knowledge of the population proportion, which is the proportion of elementary, middle, and high school teachers who contributed to a candidate during the election cycle. The standard deviation of a proportion is calculated using the following formula:

\(σ_p=√(p(1−p)/n)\)

Here, n is the sample size and p is the proportion of elementary, middle, and high school teachers who contributed to a candidate during the election cycle. Because there is no prior knowledge of p, it is assumed that the sample proportion, p-hat, is equal to 0.5.

Using these values, we can calculate the minimum sample size required for a margin of error of 0.03 for a 95 percent confidence interval.

α/2=0.025 can be determined by dividing the level of significance (α) by two. This will allow us to calculate the appropriate critical value. To calculate the critical value, we can look up the value of 0.025 in a standard normal distribution table.

Z_α/2=1.96 is the corresponding z-value for a 95% confidence interval.With the critical value, we can now calculate the minimum sample size using the formula below:

\(n = (Z^2) (p) (1 - p) / (E^2)\)

where, Z = critical valueα = level of significance (0.05)

E = margin of error (0.03)

p-hat = 0.5

The minimum sample size for a 95% confidence interval with a margin of error of 0.03 and no prior knowledge of the population proportion is as follows:

\(n = (1.96)^2 (0.5) (0.5) / (0.03)^2n = 1068.44444 ≈ 1069\)

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Answer:

-2/25

Step-by-step explanation:

Use the slope formula: rise/run to find the slope

Answer:

slope = - \(\frac{2}{25}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 20, 18) and (x₂, y₂ ) = (30, 14)

m = \(\frac{14-18}{30-(-20)}\) = \(\frac{-4}{30+20}\) = \(\frac{-4}{50}\) = - \(\frac{2}{25}\)

Among the given statements, statement A is correct, which states that for any term x^a * y^b in the expansion of (x + y)^n, the sum of the exponents a and b is equal to n. The other statements, B, C, and D, are incorrect.

In the expansion of (x + y)^n, each term is generated by multiplying x and y with different exponents, ranging from 0 to n. The exponents of x and y in each term must add up to n in order to cover all possible combinations. This is represented by statement A, which correctly states that a + b = n.

Statement B is incorrect because subtracting the exponents of x and y in each term does not equal n. Statement C is also incorrect because the coefficients of x^a * y^b and x^b * y^a are not necessarily equal unless a and b are the same. Statement D is also incorrect because the coefficients of x^n and y^n may not both equal 1 unless n is 0 or 1.

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In solving the given question, we can say that ∠ZEFI and ∠ZJIK are equal parallel lines  by  co-exterior angles property.

Geometry parallel lines are coplanar infinite lines that do not intersect anywhere. In a given three-dimensional space, parallel faces are faces that never intersect. Curves with a constant minimum distance between them and no tangents or intersections are said to be parallel. Two lines that lie in the same plane, are equally spaced, and never intersect are called parallel lines in geometry. Can be applied horizontally or vertically. Parallel lines are found in everyday objects such as railroad tracks, rows of books, and crosswalks.  

∠ZHIK and ∠ZEFI are equal by alternative angles property.

∠ZGFD and ∠ZEFD are equal by co-interior angles property.

∠ZGFD and ∠ZEFI are equal by interior alt. angles property.

∠ZEFI and ∠ZJIK are equal by  co-exterior angles property.

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Two equal-size vectors at right angles to each other have a resultant that is equal to \(\sqrt{2}\) times the magnitude of each individual vector.

The magnitude of the resultant vector of two equal-size vectors at right angles to each other can be determined using the Pythagorean theorem.

Let's assume the magnitude of each vector is represented by "a".

According to the Pythagorean theorem, the magnitude of the resultant vector, denoted as "R", can be calculated as:

R =\(\sqrt{a^2 + a^2}\)

R = (\(\sqrt{2a^{2} )}\)

R = \(\sqrt{2}\) a

Therefore, the magnitude of the resultant vector is equal to \(\sqrt{2}\) times the magnitude of each individual vector.

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Equation y'' + y = 0 have confirmed by differentiation that y = 4cos(t) + 3sin(t) is a solution to the given equation.

To check that y=4cost+3sint is a solution to y''+y=0, we need to differentiate y twice.
y = 4cos(t) + 3sin(t)
y' = -4sin(t) + 3cos(t)  (differentiating each term with respect to t)
y'' = -4cos(t) - 3sin(t)  (differentiating each term with respect to t again)
Now, we can substitute y and y'' into the equation y''+y=0 and simplify:
y'' + y = (-4cos(t) - 3sin(t)) + (4cos(t) + 3sin(t))
y'' + y = 0
Therefore, since y''+y=0, we have shown that y=4cost+3sint is indeed a solution to this differential equation.
First, let's find the first derivative, y':
y' = -4sin(t) + 3cos(t)
Now, let's find the second derivative, y'':
y'' = -4cos(t) - 3sin(t)
Now, we have:
y = 4cos(t) + 3sin(t)
y'' = -4cos(t) - 3sin(t)
Let's check if y'' + y = 0:
(-4cos(t) - 3sin(t)) + (4cos(t) + 3sin(t)) = 0
After combining like terms, we get:
0 = 0
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If the data is symmetrical, then the mean is the best measure of central tendency to use, and the standard deviation is the best spread to use.

If the data is asymmetrical, the median is the best measure of central tendency to use, and the inter-quarterly range is the best spread to use.

A histogram for symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of the central tendency to use is the mean. The standard deviation shows how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency in this case, the standard deviation should be used as the spread.

A histogram for a an asymmetric data set will give an asymmetric shape, and the mean is not always equal to the median. Therefore, the best measure of central tendency to use is the median. The inter-quarterly range shows the range of the middle 50% of a certain data, which is considered from the median value. Since the median is used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.

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(a) The equation 5x^2 - 6xy^2z^2 = 7 in cylindrical coordinates can be expressed as:

ρ^2 cos^2(θ) - 6ρ^2 sin^2(θ)z^2 = 7,

where ρ represents the radial distance from the origin, θ denotes the azimuthal angle, and z represents the height coordinate.

(b) The equation z = 2x^2 - 2y^2 in cylindrical coordinates can be written as:

z = 2(ρ cos(θ))^2 - 2(ρ sin(θ))^2,

where ρ represents the radial distance from the origin, θ denotes the azimuthal angle, and z represents the height coordinate.

Cylindrical coordinates provide an alternative way to express points in three-dimensional space. In this system, a point is specified by its radial distance (ρ), azimuthal angle (θ), and height coordinate (z). These coordinates are related to the familiar Cartesian coordinates (x, y, z) through the following equations:

x = ρ cos(θ),

y = ρ sin(θ),

z = z.

The first equation relates the radial distance ρ and the azimuthal angle θ to the x-coordinate. The second equation relates them to the y-coordinate, and the third equation simply states that the z-coordinate remains the same. By substituting these equations into a given Cartesian equation, we can express it in cylindrical coordinates.

The transformation between Cartesian and cylindrical coordinates is widely used in various fields of science and engineering, particularly in problems involving rotational symmetry or cylindrical symmetry. Understanding these coordinate systems allows for more intuitive interpretations and simplifications of equations in different contexts.

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Step-by-step explanation:

\(3 {}^{2} (189 \div 9) - 30 \\ 9 \times 189 \div 9 - 30 \\ 189 \div 1 - 30 \div 1 \\ 189 - 30 \div 1 \\ = 159\)

according to bodmas

Answer:

159

Step-by-step explanation:

Using BODMAS - Bracket Of Division Multiplication Addition Subtraction

Step 1: Bracket

189/9=21

Hence [3^2 x (21)]-30

Step 2:

3^2= 9

Step 3: Calculate within parentheses [9* 21] :    189

9*21=189

Step 4: Open bracket

[189]-30=159

Answer:

a) It is not possible to find the mean because these are words, not numbers.

b) If we put these words in alphabetical order, we have:

blue, blue, green, purple, purple, purple, red, red

The median word here is purple.

c) It is possible to find the mode, which in this case is the word that appears the most times in this list. That word is purple, which appears three times.

Answer:

8 for $2.99.

Step-by-step explanation:

Compare the unit prices:

5 for 1.99:

Unit price = 1.99 / 5 = $0.398.

8 for 2.99:

Unit price = 2.99 / 8 = $0.374.

Answer:

65

Step-by-step explanation:

The sum of the first 16 terms of an arithmetic progression (A.P) is 240

The sum of the next 4 terms is 220

The sum of n terms in an A.P is given by;

\(s_{n}\) = n/2(2a + (n - 1)d)

240 = 8(2a + 15d) ... (i)

460 = 10(2a + 19d) .... (ii)

Simplifying this gives;

2a + 15d = 30 ... (i)

2a + 19d = 46 ... (ii)

Subtracting (i) from (ii) we get;

4d = 16

d (common difference) = 4

and a (first term) = (30 - 60)/ 2 = -15

The sequence upto 21 terms is here:

-15, -11, -7, -3, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 51, 55, 59, 61, 65

So the next term (21^st term) is 65.

Answer:  a₂₁ = 65

Step-by-step explanation:

The Sum of an Arithmetic Progression is the sum of the first term plus the sum of the last term divided by 2 and multiplied by the number of terms.

\(a_1\ \text{is the first term}\\a_n=a_1+d(n-1)\quad \text{is the value of the nth term}\\\\\)

Let's find the 16th term (n = 16)

\(a_{16}=a_1+d(16-1)\\\\.\quad =a_1+15d\)

Now let's find the sum of the first 16 terms. This will be Equation 1:

\(S_{16}=\dfrac{(a_1)+(a_1+15d)}{2}\times 16=240\\\\\\.\qquad 8(2a_1+15d)=240\\\\\\.\qquad 2a_1+15d=30\qquad \leftarrow \text{Equation 1}\)

************************************************************************************

Repeat what we did above for the next 4 terms (n = 17 to n = 20). This will be Equation 2:

\(a_{17}=a_1+d(17-1)\\\\.\quad =a_1+16d\\\\\\a_{20}=a_1+d(20-1)\\\\.\quad =a_1+19d\)

\(S_{17-20}=\dfrac{(a_1+16d)+(a_1+19d)}{2}\times 4=220\\\\\\.\qquad 2(2a_1+35d)=220\\\\\\.\qquad 2a_1+35d=110\qquad \leftarrow \text{Equation 2}\)

*********************************************************************************************

Now we have a system of equations. Solve using the Elimination Method:

2a₁ + 15d = 30   → -1(2a₁ + 15d = 30)     →    -2a₁ - 15d = -30    

2a₁ + 35d = 110  →  1(2a₁ + 35d = 110)    →     2a₁ + 35d = 110  

                                                                             20d = 80

                                                                                  d = 4

Input d = 4 into one the equations to solve for a₁:

Equation 1: 2a₁ + 15d = 30

                  2a₁ + 15(4) = 30

                    2a₁ + 60 = 30

                             2a₁ = -30

                               a₁ = -15

Given a₁ = -15 and d = 4, we can find the next term (n = 21)

\(a_n=a_1+d(n-1)\\\\a_{21}=-15+4(21-1)\\\\.\quad =-15+4(20)\\\\.\quad = -15+80\\\\.\quad = 65\)

There are 595 boys at the school.

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)

The concept is used in this proportion, multiplication and subtraction.

1. First calculate how many students at the school are girls multiplying the total number of students at the school by the proportion of girls:

1309 × \(\frac{6}{11}\)

= 714 girls.

2. Then to find out how many students at the school are boys, subtract the number of girls from the total number of students at the school, that is:

1309 - 714

= 595 boys

Therefore, there are 595 boys at the school.

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The total number of boys in school are calculated by ratios in which total of 1309 students are 595 boys.

The number of boys in the school are found by using ratios and proportions. If two ratios are set equal to each other then they are in proportion. Like for an example if there are 2 girls and 5 boys we could write it as the ratio 2:5 (like for every 2 girls, there are 5 boys)

The concept used here is subtraction and multiplication.

i . Given the number of girls in the school are 6/11 of total number of students in the school , so we can find the number of girls by multiplying the proportion of girls with the total number of students.

6/11 * 1309 = 714 girls.

ii . Then to find the total number of boys in the school, we subtract the number of girls from the total number of students. so, by subtracting the number of girls from total number of students we get number of boys as,

1309-714 = 595 boys

Thus , there are total of 595 boys present in the school

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Answer:

x=33

Step-by-step explanation:

A triangle is 180 degrees.

So, 3x-49+x-2+3x=180

Group the like terms and combine them:

7x-51=180

Add 51 to both sides to eliminate -51:

7x=231

Divide by 7 on both sides

x=33

Answer:

x = 33°

Explanation:

First you add all the angles together and on the other side of the equal sign put 180. The angles added up equals 180°

(x - 2) + (3x) + (3x - 49) = 180

Then, you add them all up the numbers with 180 and the x's together, and make sure they are on separate sides.

x - 2 + 3x + 3x - 49 = 180

x + 3x + 3x -2 -49 = 180

x + 3x + 3x = 180 + 2 + 49

Lastly, divide each side by 7.

7x = 231

x = 33°

Hope this helped :)

Answer:

2/5  or 0.4 pound for 1 can

Step-by-step explanation:

Divide the number of pound by the number of cans to know how much pound per can  2/5 = 0.4

       OR  

5 cans ------------2 pounds

1 can------------------x

Cross multiplication

5x = 2

x= 2/5

The true statements about the inequality are

n > -24.

The circle is open.

The arrow points right.

To solve for n in the inequality -2/3n < 16, we need to isolate the variable n on one side of the inequality.

First, we can multiply both sides by -3/2 to get rid of the fraction:

(-3/2) * (-2/3n) > (-3/2) * 16

n > -24

Therefore, the solution for n in the inequality -2/3n < 16 is n > -24.

The circle is open means that the inequality sign is either less than or greater than

Having greater that means it points to the right

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Answer: Cynthia will receive $5,400, Moses will receive $8,100, John will receive $13,500

Step-by-step explanation:

       First, we will see how many "portions" the money is broken up into.

2:3:5 can become 2 + 3 + 5 = 10

       Next, we will see how much money each "portion" is worth using division.

$27,000 / 10 = 2,700

       Finally, we will multiply to see how much each person will receive.

2:3:5

2 * $2,700 = $5,400 [Cynthia]

3 * $2,700 = $8,100 [Moses]

5 * $2,700 = $13,500 [John]

Answer:

Cynthia's money = $5,400

Moses' money = $8,100

John's money = $13,500

Step-by-step explanation:

The full ratii of the money will be 2+3+5 = 10

Cynthia's ratio = 2 × $27,000

10

= 2 × 2,700

= $5400

Moses' ratio = 3 × $27,000

10

= 3 × 2,700

= $8100

John's ratio = 5 × $27,000

10

= 5 × 2,700

= $13,500

SOLUTION

We want to find which of the following values make the inequality

x ≤ 16.3 to be true.

This inequality means that x is equal to 16.3 or less than 16.3. So the numbers that fall under this are numbers smaller than 16.3 and also 16.3.

The numbers that fall under here are 8, 1/4, -3 and 16.3

Hence the answer b, c, e and f

Answer:

Exact: 9.42

Approx: 9

Step-by-step explanation:

The area of a circle is pi*radius^2 (pi=3.14 r=radius ^2= power of 2/squared)

The diameter is two times the radius. So, we need to divide the diameter by two for the first step of solving this.

6/2=3

Now, we know the radius is 3.

Let's square it:

3^2= 3*3

3*3=9

Now, the last step is to multiply it by pi (3.14)
3.14*3=9.42

There we go! The area is 9.42 feet!

For the given scenarios, Considering the conditions for the binomial distribution, The answer is YES.

A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that various possible outcomes of an experiment will occur. In terms of its sample space and event probability, it is a mathematical description of a random phenomena.

In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.

From the given conditions, Yes the conditions are met for the binomial distribution.

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Step-by-step explanation:

the correct answer is option a 6a-7

None of the options A, B, C, or D are the necessary step to verify InB + 2 = -2t as a solution to dB/dt = -2B.

what is differential equations?

Differential equations are mathematical equations that describe the relationship between an unknown function and its derivatives (or differentials).

To verify that InB + 2 = -2t is a solution to dB/dt = -2B, we can substitute InB + 2 for B in the differential equation and check if it satisfies the equation.

So, let's first differentiate InB + 2 with respect to t:

d/dt (InB + 2) = 1/B * dB/dt

Using the given differential equation, we can substitute dB/dt with -2B:

d/dt (InB + 2) = 1/B * (-2B)

Simplifying this expression, we get:

d/dt (InB + 2) = -2

Now, substituting InB + 2 for B in the original differential equation, we get:

dB/dt = -2(InB + 2)

We can differentiate this expression with respect to B to get:

d/dB (dB/dt) = d/dB (-2(InB + 2))

d²B/dt² = -2/B

Since we have already established that d/dt (InB + 2) = -2, we can differentiate this expression with respect to t to get:

d²B/dt² = d/dt (-2) = 0

Therefore, d²B/dt² = -2/B if and only if d/dt (InB + 2) = -2.

Now, let's check if the given solution satisfies this condition. Substituting InB + 2 = -2t in d/dt (InB + 2), we get:

d/dt (InB + 2) = d/dt (In(-2t) + 2) = -2/t

Since -2/t is not equal to -2, the given solution does not satisfy the differential equation dB/dt = -2B, and hence, we cannot verify it as a solution.

Therefore, none of the options A, B, C, or D are the necessary step to verify InB + 2 = -2t as a solution to dB/dt = -2B.

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Answer: I think it is the first one

Step-by-step explanation:

Answer:

I'm pretty sure it's x^2 - 4x

Step-by-step explanation:

Answer:

2-2 times

4-5 times

6-2 times

4 is the mod

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The choices are 2, 4, or 6, and the mode is the number that appears most frequently. The number of each is as follows:

2-2

4-5

6-2

4 appeared most often, so it is the answer.

A compound event is any event combining two or more simple events.

From the question, we have the following parameters that can be used in our computation:

combining two or more simple events.

As a general rule

When two or more simple events are combined, the result is a compound event

An example is selecting 1 in a die and head in a coin

This means that the statement that completes the blank is compound event

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