researchers asked students in michigan, what traits they viewed as important and compiled the two way table shown above from their results. what is the probability that a student is in 4th grade given that they did not choose popular as the most important trait?

Answer:

2,075 = 5 × 5 × 83

√2,075 = 5√83 = about 45.55

The value of x if number of men is equal to number of women, is,

⇒ x = 8

We have to given that;

Number of men voters = √(9+2x) - √2x

And, Number of women voters = 5/√9+2x

Now, We have number of men is equal to number of women. ​

Hence, We get;

⇒ √(9+2x) - √2x = 5/√9+2x

⇒ √(9+2x) - 5/√9+2x = √2x

⇒ [(9 + 2x) - 5] /√9+2x = √2x

⇒ (4 + 2x) / √9+2x = √2x

⇒ (4 + 2x) =  √9+2x × √2x

⇒ (4 + 2x)² = 2x (9 + 2x)

⇒ 4x² + 16 + 16x = 18x + 4x²

⇒ 16 = 2x

⇒ x = 16 / 2

⇒ x = 8

Thus, The value of x is,

⇒ x = 8

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Answer:

6

Step-by-step explanation:

\(-2x+6=30-6x\\\\4x+6=30\\\\4x=24\\\\x=6\)

1. add 6x to both sides

2. subtract 6 from both sides

3. divide both sides by 4

\(\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}\)

Replace x in the equation with 2.

-2(2) +4 = -4 + 4 = 0

The answer is 0

The value of the expression z + 3x4 using arithmetic operation where z = 15, is 27. The answer is A) 27.

The given expression is z + 3x4, where z = 15. To evaluate this expression, we substitute 15 for z and perform the multiplication. First, we multiply 3 and 4, which gives us 12. Then, we add 15 and 12 to get the final result of 27.

z + 3x4 = 15 + 3x4

= 15 + 12

= 27

Therefore, the value of the expression when z = 15, is 27. In other words, using arithmetic operation of multiplication and addition, which gives us the final answer of 27. So, the correct answer is option A).

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____The given question is incomplete , the complete question is given below:

Evaluate the expression, where z = 15

z + 3x4

A. 27

B. 32

C. 56

D. 1,304

Answer:

400

Step-by-step explanation:

okay so 400 because you find the height and the base sides and you get the answer, sorry if incorrect

The number 0.898998999899998999998... is rational. It can be expressed as the fraction 8099/9000, which means it is a ratio of two integers. The repeating pattern in the decimal representation of the number allows us to express it as a fraction, indicating its rationality.

To determine if the number 0.898998999899998999998... is rational or irrational, we need to examine its decimal representation. The repeating pattern in the decimal representation is "8989". This pattern repeats indefinitely.

To express the number as a fraction, we can assign a variable, say x, to the repeating part "8989". By multiplying x by 10000, we can shift the decimal point and obtain 10000x = 8989.8989...

Next, we subtract x from 10000x to eliminate the repeating part:

10000x - x = 8989.8989... - 0.8989...

9999x = 8989

x = 8989/9999

Simplifying the fraction, we get:

x = 8099/9000

Since the number can be expressed as the ratio of two integers, it is rational. Therefore, 0.898998999899998999998... is a rational number.

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Answer:

quadrant 2 you're welcome :-)

Answer:

Quadrant 2

Step-by-step explanation:

Since the x coordinate is negative, it must in quadrant 2 or 3

Since the y coordinate is positive, it must in quadrant 1 or 2

It must be in quadrant 2

Answer:

Amount of solution = 15 liter

Step-by-step explanation:

Given:

One third of solution is acid

Amount of acid = 5 Liter

Find:

Amount of solution

Computation:

Amount of solution = Amount of acid (1 / One third of solution is acid)

Amount of solution = Amount of acid (3)

Amount of solution = (5)(3)

Amount of solution = 15 liter

Tthe orthonormal basis for R³ using the Gram-Schmidt process on the given basis {(1, 1, 2), (1, 0, 3), (2, 3, 0)} is:{(1/√6, 1/√6, 2/√6), (-1/√15, -7/√15, 5/√15), (1/√245, -23/√245, 35/√245)}.

To find an orthonormal basis using the Gram-Schmidt process, follow these steps:

Step 1: Start with the given basis vectors.

v₁ = (1, 1, 2)

v₂ = (1, 0, 3)

v₃ = (2, 3, 0)

Step 2: Normalize the first vector, v₁.

u₁ = v₁ / ||v₁||

u₁ = (1, 1, 2) / √(1² + 1² + 2²)

u₁ = (1/√6, 1/√6, 2/√6)

Step 3: Compute the projection of v₂ onto u₁.

proj(v₂, u₁) = (v₂ · u₁) * u₁

where "·" denotes the dot product.

(v₂ · u₁) = (1, 0, 3) · (1/√6, 1/√6, 2/√6)

= (1/√6) + (0/√6) + (6/√6)

= 7/√6

proj(v₂, u₁) = (7/√6) * (1/√6, 1/√6, 2/√6)

= (7/6, 7/6, 14/6)

Step 4: Compute the orthogonal vector, v₂ - proj(v₂, u₁).

w₂ = v₂ - proj(v₂, u₁)

w₂ = (1, 0, 3) - (7/6, 7/6, 14/6)

w₂ = (1 - 7/6, 0 - 7/6, 3 - 14/6)

w₂ = (-1/6, -7/6, 5/6)

Step 5: Normalize the orthogonal vector, w₂.

u₂ = w₂ / ||w₂||

u₂ = (-1/6, -7/6, 5/6) / √((-1/6)² + (-7/6)² + (5/6)²)

u₂ = (-1/√15, -7/√15, 5/√15)

Step 6 : Compute the projection of v₃ onto u₁ and u₂.

proj(v₃, u₁) = (v₃ · u₁) * u₁

proj(v₃, u₂) = (v₃ · u₂) * u₂

(v₃ · u₁) = (2, 3, 0) · (1/√6, 1/√6, 2/√6)

= (2/√6) + (3/√6) + (0/√6)

= 5/√6

(v₃ · u₂) = (2, 3, 0) · (-1/√15, -7/√15, 5/√15)

= (-2/√15) + (-21/√15) + (0/√15)

= -23/√15

proj(v₃, u₁) = (5/√6) * (1/√6, 1/√6, 2/√6)

= (5/6, 5/6, 10/6)

proj(v₃, u₂) = (-23/√15) * (-1/√15, -7/√15, 5/√15)

= (23/15, 161/15, -115/15)

Step 7: Compute the orthogonal vector, v₃ - proj(v₃, u₁) - proj(v₃, u₂).

w₃ = v₃ - proj(v₃, u₁) - proj(v₃, u₂)

w₃ = (2, 3, 0) - (5/6, 5/6, 10/6) - (23/15, 161/15, -115/15)

w₃ = (2 - 5/6 - 23/15, 3 - 5/6 - 161/15, 0 - 10/6 + 115/15)

w₃ = (1/30, -23/30, 35/30)

Step 8: Normalize the orthogonal vector, w₃.

u₃ = w₃ / ||w₃||

u₃ = (1/30, -23/30, 35/30) / √((1/30)² + (-23/30)² + (35/30)²)

u₃ = (1/√245, -23/√245, 35/√245)

u₃ = (1/√245, -23/√245, 35/√245)

Therefore, the orthonormal basis for R³ using the Gram-Schmidt process on the given basis {(1, 1, 2), (1, 0, 3), (2, 3, 0)} is:

{(1/√6, 1/√6, 2/√6), (-1/√15, -7/√15, 5/√15), (1/√245, -23/√245, 35/√245)}.

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Step-by-step explanation:

To find a numerator, read the number on the top of the fraction.

To find a denominator, read the number on the bottom of the fraction.

To find a missing numerator, follow these steps given:

1. Find the amount that the first denominator is multiplied or divided by to get to the denominator that is missing its numerator.

2. Multiply or divide the known numerator by this same amount to find the unknown numerator.

To find a missing numerator, look at the denominators of the fractions.

One fraction has both a numerator and denominator. Find the number that this denominator is multiplied by to get to the denominator that is missing its numerator.

Multiply the known numerator by this number to find the unknown numerator.

To find a missing denominator, follow these steps given:

1. Find the amount that the first numerator is multiplied or divided by to get to the numerator that is missing its denominator.

2. Multiply or divide the known denominator by this same amount to find the unknown denominator.

To find the value that a numerator has been multiplied by in an equivalent fraction, divide the largest numerator by the smallest numerator.

To find the missing denominator, first look at the numerators of the fractions.

One fraction has both a numerator and denominator. Find the number that this numerator is multiplied by to get to the numerator that is missing its denominator.

Multiply the known denominator by this number to find the unknown denominator.

Answer:

Check the answer below.

Step-by-step explanation:

This is a very trivial but professional question. Note that all of millimetre, centimetre and metres are acceptable metric units but the millimetre is more preferable by builders and architects because:

1. It is easier to work with integer values on building and architectural plans, an advantage given by measuring and recording in millimetre.

2. working in millimetre allows for precision. The builder will record values that are very close to the true value

3. The measurement will be easily readable by anybody that sees it.

Answer:

102

Step-by-step explanation:

On quadrilateral ABCD it shows BC = 20 and CD = 30

20+30 = 50

on quadrilateral A'B'C'D'

it says B'A' = 22

and D'A' = 32

22+32 = 52

52+50 = 102

Answer:

55units

Step-by-step explanation:

The correct order of sentences to bisect the angle Q is (1) draw a line from Q to where the arc crosses (2) vertex: set the compass to any convenient width (3) from where the arc crosses lag, make an arc.. (4) place the compass point on the angle Q.

We should know that an angle is the intersection of two or more straight lines.

In construction of angles, using the compass, the first thing is to locate a point say Q.  The open the leg of the compass to a convinient radius, make an arc at another point say P.  From the point P, bisect the initial arc so made then joion to the starting point Q.

Second, from the point where the arcs met on the two lines, make another two arcs above the points, then join them to the starting point Q

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Answer:

5x = 30

x = 6

Step-by-step explanation:

3x+2(x-5)=20

to simplify the expression, open the bracket

3x + 2x - 10 = 20

combine like terms

3x + 2x = 20 + 10

add like terms together

5x = 30

to solve the equation, divide both sides of the equation by 5

x = 30 / 5

x = 6

Answer:

it would be 170 it its 5 or over round up

Step-by-step explanation:

The correct calculation to find the probability that x is less than 2 is:

d. P [z < (2 - 2.3 / (1.3/√40))]

We know that the distribution of monthly bonuses earned by all employees last year has mean 2.3 and standard deviation 1.3.

Since we have a sample of size 40, we can use the central limit theorem to approximate the distribution of the sample mean x with a normal distribution with mean 2.3 and standard deviation 1.3/√40.

To find the probability that x is less than 2, we need to find the z-score corresponding to x = 2, given the distribution of x. We can do this using the formula:

z = (x - μ) / σ

where μ is the mean of the distribution of x (which is 2.3) and σ is the standard deviation of the distribution of x (which is 1.3/√40).

Plugging in the values, we get:

z = (2 - 2.3) / (1.3/√40)

z = -1.63

So, the probability that x is less than 2 is equal to the probability that z is less than -1.63, which is given by the standard normal distribution table as:

P [z < -1.63]

Therefore, the correct calculation to find the probability that x is less than 2 is:

d. P [z < (2 - 2.3 / (1.3/√40))]

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Answer:

12.5

Step-by-step explanation:

5*5*0.5=12.5

Answer:  (a-b+c)²-(b-c+a)²​

=((a-b+c)) - ((b-c+a)) ((a-b+c)) - ((b-c+a))

= (a-b+c-b+c-a) ( a-b+c+b-c+a)

= (-2b + 2c ) (2a)

= (2( -2b/2+2c/2)) (2a)

=(2(-b+c)) (2a)

=2(-b+c) (2a)

Find copies per minute:

80 / 2.5 = 32 copies per minute.

Multiply copies per minute by total minutes:

32 x 0.25 = 8 copies

Answer:

460

Step-by-step explanation:

Answer:

2 3/4

Step-by-step explanation:

If x = 4, y = 5, z = 1/2 , then

(a) It will take 3 minutes  to secure door ,

(b) It will take 56 minutes to complete system check ,

(c) It will take 44 minutes to fill pantry with astronaut food .

The values of x , y and z are x = 4, y = 5, z = 1/2 ;  

Part(a) ;

The Number of minutes to secure door is calculated the by expression

⇒ 7x - 5y .

Substituting values as x = 4 and y = 5 ,

we get ;

⇒ 7(4) - 5(5) = 28 - 25 = 3 minutes .

Part(b) ;

The Number of minutes to fill pantry with astronaut food is calculated the by expression :

⇒ 12z + 2y² ,

Substituting values as z = 1/2 and y = 5 ,

we get ;

⇒ 12z + 2y² = 12(1/2) + 2(5)² = 6 + 2×25 = 6 + 50 = 56 minutes .

Part(c) ;

The Number of minutes to complete system check is calculated the by expression

⇒ 2xy + 8z ,

Substituting values as x = 4 , z = 1/2 and y = 5 ,

we get ;

⇒ 2xy + 8z = 2(4)(5) + 8(1/2) = 40 + 4 = 44 minutes .

The given question is incomplete , the complete question is

Evaluate the following expressions to help the astronauts prepare for take off. These numbers will help calculate the amount of time it will take to prepare for take off.

In this case x = 4, y = 5, z = 1/2 ;  

(a) Number of minutes to secure door is found by expression ⇒ 7x - 5y .

(b) Number of minutes to complete system check is found by expression ⇒ 12z + 2y² ,

(c) Number of minutes to fill pantry with astronaut food is found by expression ⇒ 2xy + 8z .

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The statement is true: If x and y are linearly independent, and if z is in Span {x, y}, then {x, y, z} is linearly dependent.

The statement is true.
Let's first understand the terms used:
Linearly independent:

A set of vectors is linearly independent if none of them can be expressed as a linear combination of the other vectors. In other words, no vector in the set can be written as a sum of scalar multiples of the other vectors.
Span:

The span of a set of vectors is the set of all linear combinations of those vectors.

In this case, Span\({x, y}\) is the set of all vectors that can be formed by adding scalar multiples of x and y.
Now, let's consider the given statement:
If x and y are linearly independent, it means that neither x nor y can be expressed as a linear combination of the other. However, it is given that z is in the Span\({x, y}.\)

This means that z can be expressed as a linear combination of x and y:
\(z = ax + by\), where a and b are scalar constants.
Let's analyze the set\({x, y, z}\). We know that z can be expressed as a linear combination of x and y, as shown above. This implies that the set \({x, y, z}\)is linearly dependent, because one vector (z) can be expressed as a linear combination of the others \((x and y)\).

Thus, the statement is true: If x and y are linearly independent, and if z is in Span\({x, y}\), then\({x, y, z}\) is linearly dependent.

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Based on both the p-value method and the critical value method, we fail to reject the null hypothesis and cannot infer that the two groups differ in the mean number of pictures printed.

To determine if the two groups (digital camera owners and standard camera owners) differ in the mean number of pictures printed, we can conduct a hypothesis test using both the p-value method and the critical value method.

Let's define our hypotheses:

Null Hypothesis (\(H_0\)): The mean number of pictures printed is the same for both groups.

Alternative Hypothesis (\(H_1\)): The mean number of pictures printed differs between the two groups.

We'll use a significance level of 0.05 (5%).

First, let's calculate the test statistic for the two-sample t-test using the provided summary statistics:

Digital:

Mean = 18.25

Standard Deviation = 6.5

Sample Size = 8

Standard:

Mean = 16.5

Standard Deviation = 19.2

Sample Size = 8

Using the formula for the two-sample t-test, the test statistic (t) is given by:

\(t = (mean_1 - mean_2) / \sqrt{(s_1^2/n_1) + (s_2^2/n_2)}\)

Substituting the values, we have:

\(t = (18.25 - 16.5) / \sqrt{(6.5^2/8) + (19.2^2/8)}\)

t ≈ 0.75

Now, let's perform the hypothesis test using both methods:

1) P-value Method:

Using the t-distribution with \((n_1 + n_2 - 2)\) degrees of freedom, we can calculate the p-value associated with the test statistic.

The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

Using a t-table or statistical software, we find that the p-value corresponding to t ≈ 0.75 is approximately 0.47.

Since the p-value (0.47) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean number of pictures printed differs between the two groups.

2) Critical Value Method:

Using the t-distribution with \((n_1 + n_2 - 2)\) degrees of freedom and a significance level of 0.05, we can find the critical value.

The critical value is the value beyond which we would reject the null hypothesis.

For a two-tailed test at a 5% significance level and 14 degrees of freedom (8 + 8 - 2), the critical value is approximately ±2.145.

Since the test statistic (0.75) does not exceed the critical value (±2.145), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean number of pictures printed differs between the two groups.

In conclusion, based on both the p-value method and the critical value method, we do not have sufficient evidence to infer that the two groups differ in the mean number of pictures printed.

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$$3,666.67 should be invested in the CD account by mother for her son's future education.

To calculate the amount of money invested in the CD account:

Let the amount invested in the CD account be x dollars.

Amount mother want to invest =  $11,000.00

The remainder, will be $11,000.00 - x dollars, which is to be invested in the savings bond.

Interest earned on Certificate of Deposit (CD) = 4%

The interest earned from the CD account will be x * 0.04 (4% expressed as a decimal),

Interest earned on savings bond = 7%

i.e (11,000.00 - x) * 0.07 (7% expressed as a decimal).

According to the given problem, the total interest earned after one year is $660.00. The equation we get,

x * 0.04 + (11,000.00 - x) * 0.07 = $660.00

Simplifying and solving this equation:

0.04x + 770.00 - 0.07x = $660.00

-0.03x = $660.00 - $770.00

-0.03x = -$110.00

x = -$110.00 / -0.03

x = $3,666.67

Therefore, $3,666.67 was invested in the CD account.

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Answer:

d = 4

Step-by-step explanation:

First, we take the equation 2d = 8

In order to find out what the value of 9 must be in order to make this equation true, we must isolate the variable. That can be done by doing the opposite operation. In this case, the opposite operation would be division since d is being multiplied by 2 to get 8.

So, we have to divide both sides of the equation by 2:

2d = 8

2      2

2d divided by 2 is equal to d.

And 8 divided by 2 is equal to 4.

Therefore, d is equal to 4.

Hope this helps!!

Answer:

d=4

.......................................                        

The set of expressions that is NOT an example of the associative property is B. (8 - 2) + 3 and 8 + (-2 + 3).

The associative property states that the way you group numbers when adding or multiplying does not change the result. For example, (8 + 2) + 3 is the same as 8 + (2 + 3). However, the associative property does not apply to subtraction or division. Therefore, (8 - 2) + 3 is not the same as 8 + (-2 + 3).

Besides associative property, there are 3 other mathematical properties that only works on adding and multiplying. They are:

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A polynomial is described as a mathematical expression that contains one or more algebraic in which a constant is multiplied by one or more variables that give rise to a non-negative integral power such as ax² + bx + c.

By considering a polynomial with two terms. Methods and polynomials can be used with these methods.

        2x³ - 5x² = x²(2x - 5)

         x³ - 27  then this be factored as

         x³ - 27 = (x - 3)(x² + 3x + 3²).

         x³ + 27 = (x + 3)(x² - 3x + 3²).

           x² - 16  =  (x + 4)(x - 4)

where perfect-square trinomial and factoring by grouping require more than two terms.

Therefore, the polynomial that has two terms in the factoring methods the Common Factor, the Difference of cubes, the sum of cubes, and the difference of squares can only be considered.

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Answer:

problem 2

Step-by-step explanation:

The feeding time constraint for cats can be written symbolically as:

12 minutes/day * number of cats <= 8 hours/day

The feeding time constraint for dogs can be written symbolically as:

20 minutes/day * number of dogs <= 8 hours/day

The pampering time constraint for cats can be written symbolically as:

16 minutes/day * number of cats <= 8 hours/day

The pampering time constraint for dogs can be written symbolically as:

20 minutes/day * number of dogs <= 8 hours/day