Question 27: Find side x

Inequality shows a relationship between two numbers or two expressions.

The solution for the inequality is x ≤ -2.

The graph is given below.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

Example:

2x > 4

We have,

x + 7 ≤ 5

Subtract 7 on both sides we get,

x + 7 - 7 ≤ 5 - 7

x ≤ -2

This inequality can be graphed as given below:

x is equal and less than -2.

Thus,

The solution for the inequality is x ≤ -2.

The graph is given below.

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Answer:

x^5+5x^4−x^3

Step-by-step explanation:

Expand by distributing terms

x^3x^2+x^3*5x-x^3

Use the product rule x^a+x^b=x^a+b

x^3+2 +x^3*5x-x^3

Simplify 3+2 to 5

x^5+x^3*5x-x^3

Regroup

x^5+5x^33-3^3

Use product rule x^a+x^b=x^a+b

x^5+5x^3+1   -x^3

Simplify 3+1 to 4

x^5+5x^4−x^3

The results tell us that jersey numbers on a football team vary much more than expected, as evidenced by the large range and standard deviation. The sample variance is also relatively high, indicating that there is a fair amount of variability among the jersey numbers in the sample. These statistics are meaningful and can provide insight into the distribution of jersey numbers on the team.

To find the range, we need to subtract the smallest number from the largest number in the sample. So, the range is:

94 - 15 = 79

To find the sample variance and standard deviation, we first need to find the mean of the sample. We can do this by adding up all the numbers and dividing by the total number of players:

(33 + 74 + 70 + 65 + 56 + 47 + 39 + 72 + 57 + 94 + 15) / 11 = 54.18

Next, we need to find the difference between each number and the mean, square them, and add them up. This gives us the sum of squares:

[(33 - 54.18)^2 + (74 - 54.18)^2 + (70 - 54.18)^2 + (65 - 54.18)^2 + (56 - 54.18)^2 + (47 - 54.18)^2 + (39 - 54.18)^2 + (72 - 54.18)^2 + (57 - 54.18)^2 + (94 - 54.18)^2 + (15 - 54.18)^2] = 15864.4

The sample variance is then calculated by dividing the sum of squares by the total number of players minus one:

15864.4 / 10 = 1586.44

Finally, we can calculate the sample standard deviation by taking the square root of the variance:

√1586.44 ≈ 39.83

The results tell us that jersey numbers on a football team vary much more than expected, as evidenced by the large range and standard deviation. The sample variance is also relatively high, indicating that there is a fair amount of variability among the jersey numbers in the sample. These statistics are meaningful and can provide insight into the distribution of jersey numbers on the team.

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The number of teachers is 4 and number of students is 10 on the trips if the tickets were $22.00 each for teachers and $8.50 each for students.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

In Maths museum tickets were $22.00 each for teachers and $8.50 each for students, and the group paid $173.00 in total.

Let's suppose the number of teachers is x and number of students is y

22x + 8.5y = 173 ...(1)

5.5x + 2y = 42  ...(2)

After solving the above equation by substitution method we get;

From equation (1):

Multiply by 2 with equation (1)

\(\rm x=\dfrac{346-17y}{44}\)

\(\rm 5.5\cdot \dfrac{346-17y}{44}+2y=42\)

y = 10

\(\rm x=\dfrac{346-17\cdot \:10}{44}\)

x = 4

Thus, the number of teachers is 4 and number of students is 10 on the trips if the tickets were $22.00 each for teachers and $8.50 each for students.

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The median number of 1 2 3 4 is 2.5

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

The number given is 1 2 3 4

We have to determine the median of the above number.

If the number of words is even, we must add two middle terms and divide the result by two. The median is what we obtain as a mean.

Substitute the value in above equation we get,

=(2+3)/2

Adding the two number we get,

=5/2

Now dividing 5 by 2 we get,

2.5

Median=2.5

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Answer:

a) 9.3

b) 13

Step-by-step explanation:

a) 5+3+9+11+4+28+0+30+0+23/10 = 9.3

b) 5+3+9+11+4+28+0+30+0+23+30/11 = 13

The calculated value of the expression x² + y² + 8 is 12 - 2xy

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

x + y + 2 = 0

This can be expressed as

x + y = -2

Using the sum of two squares, we have

x² + y² = (x + y)² - 2xy

So, we have

x² + y² = (-2)² - 2xy

Evaluate

x² + y² = 4 - 2xy

Add 8 to both sides

x² + y² + 8 = 12 - 2xy

Hence, the value of the expression x² + y² + 8 is 12 - 2xy

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Answer:

3.75 hours

Step-by-step explanation:

Given data

DIstance driven from Gary, Indiana to Indianapolis= 160 mile

Time taken= 2 1/2 hours or 2.5 hours

Speed= distance/time

Speed= 160/2.5

Speed= 64 miles per hours

We want to find the time it will take to drive 240 miles at the same speed

Time= distance/speed

Time= 240/64

Time= 3.75 hours

Using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.

The square of a side of a plane triangle is equal to the sum of the squares of the other sides minus twice the product of those sides and the cosine of the angle between them, according to a trigonometry rule.

So, it is a given that the distance between the home plate and the pitcher's mound on a softball field is 43 feet.

27° east of the pitcher's mound is the angle at which a ball is struck.

Before an outfielder catches the ball, it travels 162 feet.

Using the law of cosines, we may now:

a² = b² + c² - 2bcosA

When b=43, c=162, and A=27° are entered, we get:

a² = 43² + 162² - 2(43)(162)cos27°

a² = 1849 + 26244 - 12413.4

a² = 15679.6

a = 125.21

a = 125ft

Therefore, using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.

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Complete question;
On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines: a2 = b2 + c2 – 2bccos(A) Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.

a. To find the height of the enlarged photo, we can use the concept of proportional scaling. Since the width of the enlarged photo is 48 inches, we can set up the following proportion:

\(\(\frac{{\text{{Height of enlarged photo}}}}{{\text{{Width of enlarged photo}}}} = \frac{{\text{{Height of original photo}}}}{{\text{{Width of original photo}}}}\)\)

Plugging in the given values, we have:

\(\(\frac{{\text{{Height of enlarged photo}}}}{{48}} = \frac{{4}}{{6}}\)\)

Cross-multiplying, we get:

\(\(\text{{Height of enlarged photo}} = \frac{{4}}{{6}} \times 48\)\)

Simplifying, we find:

\(\(\text{{Height of enlarged photo}} = 32\) inches\)

Therefore, the enlarged photo will be 32 inches tall.

b. To find the width of the wallet-sized photo, we can use the same concept of proportional scaling. Since the height of the wallet-sized photo is 1.5 inches, we can set up the following proportion:

\(\(\frac{{\text{{Width of wallet-sized photo}}}}{{\text{{Height of wallet-sized photo}}}} = \frac{{\text{{Width of original photo}}}}{{\text{{Height of original photo}}}}\)\)

Plugging in the given values, we have:

\(\(\frac{{\text{{Width of wallet-sized photo}}}}{{1.5}} = \frac{{6}}{{4}}\)\)

Cross-multiplying, we get:

\(\(\text{{Width of wallet-sized photo}} = \frac{{6}}{{4}} \times 1.5\)\)

Simplifying, we find:

\(\(\text{{Width of wallet-sized photo}} = 2.25\) inches\)

Therefore, the wallet-sized photo will be 2.25 inches wide.

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Answer: 10 I think

Step-by-step explanation: Jill sold half and you dont know how much it is you know that now she has 36, but before she bought 16 so 36 - 16 = 20 but she sold half

Answer:10 magazines

Step-by-step explanation:

36-16/2=m

20/2=m

10=m. m=magazine

Answer:

(a) Because the confidence interval does not include includes 0​, it appears that there is not a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.

(b) The correct option is (A).

(c) The correct option is (C).

Step-by-step explanation:

The 95% confidence interval for the difference between the two population​ mean hemoglobin level is:

CI = (-1.76 < μ₁ - μ₂ < -1.62)

(a)

The hypothesis to test the equality of the mean hemoglobin level in women and the mean hemoglobin level in​ men is:

H₀: The two population means are equal, i.e. μ₁ = μ₂.

Hₐ: The two population means are not equal, i.e. μ₁ ≠ μ₂.

The (1 - α)% confidence interval can be used to draw conclusion about the hypothesis test.

Decision rule:

If the (1 - α)% confidence interval does not consist of the null value then the null hypothesis will be rejected and vice-versa.

The 95% confidence interval for the difference between the two population​ means is:

CI = (-1.76, -1.62)

The 95% confidence interval does not consist of the null value, i.e. 0.

Thus, the null hypothesis will be rejected.

"Because the confidence interval does not include includes 0​, it appears that there is not a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men."

(b)

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

So, the 95% confidence interval (-1.76, -1.62) implies that there is a 95% confidence that the above interval actually contains the value of the difference between the two population means, (μ₁ - μ₂).

The correct option is (A).

(c)

Now it is provided that the measures from men is denoted as population  1 and measures from women is denoted as population  2.

The confidence interval for the difference between two mean is:

\(CI=(\bar x_{1}-\bar x_{2})\pm MOE\)

According to the information:

\(\bar x_{1}=\bar x_{2}\\\\\bar x_{2}=\bar x_{1}\)

So, the new confidence interval will be:

\(CI=-(\bar x_{2}-\bar x_{1})\pm MOE\)

Then the confidence interval with measures from men being population

1 and measures from women being population  2 is:

\(CI=(1.62<\mu_{1}-\mu_{2}<1.76)\)

The correct option is (C).

This is the square root of 6 over 3. The 3 is not inside the square root.

========================================================

Explanation:

sqrt = square root

We have sqrt(6) in the denominator. Your teacher wants you to rationalize the denominator, which means to take out the square root and instead have an integer here.

To achieve this, we multiply top and bottom of the fraction by sqrt(6) like so

\(\frac{2}{\sqrt{6}}\\\\\frac{2*\sqrt{6}}{\sqrt{6}*\sqrt{6}}\\\\\frac{2\sqrt{6}}{\sqrt{6*6}}\\\\\frac{2\sqrt{6}}{\sqrt{36}}\\\\\frac{2\sqrt{6}}{6}\\\\\frac{2\sqrt{6}}{2*3}\\\\\frac{\sqrt{6}}{3}\\\\\)

Therefore,

\(\frac{2}{\sqrt{6}}=\frac{\sqrt{6}}{3}\\\\\)

Let x = 1.4888... .

Then 10x = 14.888... and 100x = 148.888..., so that

100x - 10x = 148.888... - 14.888...

90x = 147

x = 147/90 = 49/30

Since the distance from the origin to point (5, 5) is equal to the radius of the circle then point (5, 5) is on the circle.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape. A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

It is clear that a circle is not a function. Because, a function is defined by each value in the domain is exactly associated with one point in the codomain, but a line that passes through the circle, intersects the line at two points on the surface. The mathematical way to describe the circle is an equation.

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Coordinates of equation 3x + 2y = 18 are (0.9) and (6,0).

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y). Coordinates are a collection of numbers that aid in displaying a point's precise location on the coordinate plane. Meaning of a Coordinate Plane. A coordinate plane is a 2D plane that is created by the junction of the x-axis and y-axis, two perpendicular lines.

Given

Equation

3x + 2y = 18

For coordinates,

When x is 0

3(0) + 2y =18

2y = 18

y = 9

Points (0,9)

When y is 0.

3x + 2(0) = 18

3x = 18

x = 6

Points (6,0)

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The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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The correct answer is (E) The possible p-values are 0.22 and 0.88.

If the experimenter conducted a one-tailed hypothesis test on the same set of data, the possible p-value(s) that they could have obtained would depend on the direction of the test.

In a one-tailed test, the hypothesis is directional and the experimenter is only interested in one side of the distribution (either the upper or lower tail). Therefore, the p-value would only be calculated for that one side.

If the original two-tailed test had a p-value of 0.44, it means that the null hypothesis was not rejected at the significance level of 0.05 (assuming a common level of significance).

If the experimenter conducted a one-tailed test with a directional hypothesis that was consistent with the direction of the higher tail of the original two-tailed test, then the possible p-value would be 0.22 (half of the original p-value). If the directional hypothesis was consistent with the lower tail of the original two-tailed test, then the possible p-value would be 0.88 (one minus half of the original p-value).

Therefore, the correct answer is (E) The possible p-values are 0.22 and 0.88.

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Answer:

you have given no information.

Step-by-step explanation:

You just say one large pizza and some soft drinks..

Answer:

No, because a triangle will have to add up to 180 degrees. And if the two angles are already set for both triangles, there is only one answer that will make these triangles equal 180 degrees. So no there is no way possible.

Step-by-step explanation:

Greetings from Brasil...

In a triangle the sum of the internal angles is 180 °.... Thus,

Ô = 180 - 30

Ô = 60

The desired area is the area of the rectangle triangle, minus the area of the circular sector whose angle 60

A1 = area of the rectangle triangle

TG B = OA/AB

AB = OA / TG B

AB = 6 / TG 30

AB = 6√3

A1 = (AB . OA)/2

A1 = (6√3 . 6)/2

A2 = area of the circular sector

(rule of 3)

 º                       area

360    ------------   πR²

60     ------------    X

X = 60πR²/360

X = 6π

So,

Then the area shaded is:

A = A1 - A2

Answer:

Step-by-step explanation:

∠3 = 180 - ∠1      {linear pair}

     = 180 - 105

      = 75°

∠2 = ∠3    {Corresponding angles"

∠2 = 75

Answer:

The height of the garden will be 3 ft.

Step-by-step explanation:

Given;

area of trapezoid, A = 1/2(B+b)h

Where;

A is the area

h is the height

B is the big base

b is the small base

If; A = 27 ft²

B = 10 ft

b = 8 ft

h = ?

\(A= \frac{1}{2} (B+b)h\\\\27= \frac{1}{2} (10+8)h\\\\27*2 = 18h\\\\54 = 18h\\\\h = \frac{54}{18}\\\\ h = 3 \ ft\)

Therefore, the height of the garden will be 3 ft.