1. My brother is 6 feet tall, and I was thinking approximately how many yards was his height?
a. 4 yards
b. 3 yards
c. 2yards
d. 1 yard​

The critical value value needs to be lower than the calculated or obtained value (test statistic) to reject the null hypothesis

What is Null Hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Reason:

Critical value < calculated or obtained value (test statistic) to reject the null hypothesis

We are unable to reject the null hypothesis if the statistic is less than or equal to the crucial threshold (e.g. no effect). If not, it is turned down. This interpretation can be summed up as follows: Critical Value = Test Statistic fail to invalidate the statistical test's null hypothesis.

If the test statistic is less than the crucial value in a lower-tailed test, the decision rule requires that the investigators reject H0. If the test statistic in a two-tailed test is extreme—either bigger than an upper critical value or smaller than a lower critical value—investigators are required by the decision rule to reject H0.

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Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm.

Step 1: State the hypotheses.

- Null Hypothesis (H₀): The mean length of the bolts is 4.00 cm (μ = 4.00).

- Alternative Hypothesis (H₁): The mean length of the bolts is not equal to 4.00 cm (μ ≠ 4.00).

Step 2: Compute the value of the test statistic.

To compute the test statistic, we will use the z-test since the population standard deviation (σ) is known, and the sample size (n) is large (n = 121).

The formula for the z-test statistic is:

z = (X- μ) / (σ / √n)

Where:

X is the sample mean (4.21 cm),

μ is the population mean (4.00 cm),

σ is the population standard deviation (0.83 cm), and

n is the sample size (121).

Plugging in the values, we get:

z = (4.21 - 4.00) / (0.83 / √121)

z = 0.21 / (0.83 / 11)

z = 0.21 / 0.0753

z ≈ 2.79 (rounded to two decimal places)

Step 3: Determine the critical value and make a decision.

With a level of significance of 0.02, we perform a two-tailed test. Since we want to determine if the mean length of the bolts is different from 4.00 cm, we will reject the null hypothesis if the test statistic falls in either tail beyond the critical values.

For a significance level of 0.02, the critical value is approximately ±2.58 (obtained from the z-table).

Since the calculated test statistic (2.79) is greater than the critical value (2.58), we reject the null hypothesis.

Conclusion:

Based on the computed test statistic, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines. The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm, indicating that the machine's output is not meeting the desired length. The manufacturer should take action to recalibrate the machines to ensure the bolts meet the required length of 4.00 cm.

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Answer:

-19/5

Step-by-step explanation:

2x+3x+19=0

5x=-19

x=-19/5

The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.

In this problem we know the three vertices of a triangle on a Cartesian plane and we must determine the coordinates of its image by applying rigid transformations. According to the statement, the vertices of the image are obtained by applying a translation formula:

P'(x, y) = P(x, y) + T(x, y)        (1)

Where:

If we know that P(x, y) = (2, - 4), Q(x, y) = (4, - 5), R(x, y) = (7, - 2) and T(x, y) = (- 6, 3), then the coordinates of the vertices of the image are:

P'(x, y) = (2, - 4) + (- 6, 3)

P'(x, y) = (- 4, - 1)

Q'(x, y) = (4, - 5) + (- 6, 3)

Q'(x, y) = (- 2, - 2)

R'(x, y) = (7, - 2) + (- 6, 3)

R'(x, y) = (1, 1)

The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.

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Find the centre first by reoriganisation it into the form (x - cx)^2 + (y -cy)^2 = r^2

x^2 + y^2 + 6x -6y +5 = 0

(x + 3)^2 - 9 + (y - 3)^2 - 9 + 5 = 0

(x + 3)^2 + (y - 3)^2 = 13

The radius does not matter the centre is ( -3, +3)

The diameter must pass through the center so substituting into the equation for the line

2x-y+a = 0

-6 -3 + a = 0 so a = 9

The value of 'a' in the equation (2x - y + a = 0) is 0 and this can be determined by using the generalized equation of a circle.

Given :

Circle Equation  --  \(x^2-2x+y^2-4y-4\)

Line equation -- 2x - y + a = 0

First, convert the given equation of a circle in the generalized equation of a circle which is given by:

\((x-a)^2+(y-b)^2=r^2\)

where (a,b) represents the center of the circle and 'r' is the radius of the circle.

The generalized form of the given equation of a circle is:

\((x-1)^2-1+(y-2)^2-4-4=0\)

\((x-1)^2+(y-2)^2=3^2\)

So, the center of the circle is (1,2) and the radius is 3.

The center of the circle satisfy the line passing through it, that is:

2(1) - (2) + a = 0

a = 0

So, the value of a in the equation (2x - y + a = 0) is 0.

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The lowest common denominator of 3/8 and 3/5 is 40.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

3/8 and 3/5

LCD means the lowest common denominator.

So,

8 x 5 = 40

5 x 8 = 40

Thus,

The lowest common denominator of 3/8 and 3/5 is 40.

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By applying the exponential and logarithmic functions, we have

\(x^{\sin(x)} = \exp \left(\ln \left(x^{\sin(x)}\right)\right)\)

Then in the limit,

\(\displaystyle \lim_{x\to0} x^{\sin(x)} = \lim_{x\to0} \exp \left(\ln \left(x^{\sin(x)}\right)\right)\)

\(\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \ln \left(x^{\sin(x)}\right)\right)\)

\(\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \sin(x) \ln(x) \right)\)

\(\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \frac{\ln(x)}{\csc(x)} \right)\)

As x approaches 0 (from the right), both ln(x) and csc(x) approach infinity (ignoring sign). Applying L'Hopitâl's rule gives

\(\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \frac{\frac1x}{-\csc(x)\cot(x)} \right) = \exp \left( -\lim_{x\to0} \frac{\sin^2(x)}{x\cos(x)} \right)\)

Recall that

\(\displaystyle \lim_{x\to0} \frac{\sin(x)}{x} = 1\)

Then

\(\displaystyle \lim_{x\to0} \frac{\sin^2(x)}{x\cos(x)} = \lim_{x\to0} \frac{\sin(x)}{\cos(x)} = \lim_{x\to0} \tan(x) = 0\)

So, our limit is

\(\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp(0) = \boxed{1}\)

The cost of each sandwich, given the number that was sold and the profit made was  $15.

Let S be the price of a sandwich and A be the price of a salad.

From the lunch sale, we know:

14 S + 14 A = $280

From the evening sale, we know:

42S + 154 A = $ 1400

Simplify the first equation by dividing through by 14:

S + A = $20

Solving this equation for S gives:

S = $20 - A

Substitute this equation into the second equation:

42 ( $20 - A ) + 154 A = $1400

$ 840 - 42 A + 154 A = $1400

112A = $560

A = $5

Substitute A = $5 into the first equation:

S + $5 = $20

S = $15

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Answer: I think 70 percent

Step-by-step explanation:

Answer:

5683200

Step-by-step explanation:

Move the decimal 4 places to the right because \(10^4\) has 4 zeros.

Answer:

Please check attachment for graph

Step-by-step explanation:

B. With hawaii airline = -0.300

Without hawaii airline = 0.197

With hawaii airline

EX = 475.3

EY = 157.17

XY = 8042.11

X² = 26883.55

Y² = 3159.375

The correlation coefficient

= 72378.99-74702.9/7737.421

= -2323.91/7737.421

= -0.300

Without hawaii airline

EX = 396.9

EY = 152.11

EXY = 7645.406

X² = 20736.99

Y² = 3133.772

= 790.789/4021.161

= 0.197

Answer:

See explanation

Step-by-step explanation:

It appears that the second graph is better since it seems to be rather consistent. The graph of the first one seems out of place. Therefore it seems to be confusing and could be misleading.

The equation of the perpendicular bisector of the line segment with endpoints (-7, 2) and (-1, -6) is y = (3/4)x + 1.

To find the equation of the perpendicular bisector of a line segment, we need to determine the midpoint of the line segment and the slope of the line segment. The perpendicular bisector will have a negative reciprocal slope compared to the line segment and will pass through the midpoint.

Given the endpoints (-7, 2) and (-1, -6), we can find the midpoint using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((-7 + (-1))/2, (2 + (-6))/2)

= (-8/2, -4/2)

= (-4, -2)

The midpoint of the line segment is (-4, -2).

Next, we need to find the slope of the line segment using the slope formula:

Slope = (y2 - y1)/(x2 - x1)

Slope = (-6 - 2)/(-1 - (-7))

= (-6 - 2)/(-1 + 7)

= (-8)/(6)

= -4/3

The slope of the line segment is -4/3.

Since the perpendicular bisector has a negative reciprocal slope, the slope of the perpendicular bisector will be 3/4.

Now, we can use the midpoint (-4, -2) and the slope 3/4 in the point-slope form of a line to find the equation of the perpendicular bisector:

y - y1 = m(x - x1)

y - (-2) = (3/4)(x - (-4))

y + 2 = (3/4)(x + 4)

y + 2 = (3/4)x + 3

y = (3/4)x + 1.

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Answer:

\(P(G_1) = \frac{5}{13}\)

\(P(G_2) = \frac{1}{3}\)

\(P(X \ge 1) = \frac{25}{39}\)

Step-by-step explanation:

Given

\(G = 5\)

\(R = 4\)

\(B = 4\)

\(n = 13\)

Solving (a): \(P(G_1)\)

This is calculated as:

\(P(G_1) = \frac{G}{n}\)

\(P(G_1) = \frac{5}{13}\)

Solving (b): \(P(G_2)\)

This is calculated as:

\(P(G_2) = \frac{G - 1}{n - 1}\) -- this is so because the selection is without replacement

\(P(G_2) = \frac{5 - 1}{13 - 1}\)

\(P(G_2) = \frac{4}{12}\)

\(P(G_2) = \frac{1}{3}\)

Solving (c): \(P(X \ge 1)\)

Using the complement rule, we have:

\(P(X \ge 1) = 1 - P(X = 0)\)

To calculate \(P(X = 0)\), we have:

\(G = 5\) --- Green

\(G' = 8\) ---- Not green

The probability that both selections are not green is:

\(P(X = 0) = P(G'_1) * P(G'_2)\)

So, we have:

\(P(X = 0) = \frac{G'}{n} * \frac{G'-1}{n-1}\)

\(P(X = 0) = \frac{8}{13} * \frac{8-1}{13-1}\)

\(P(X = 0) = \frac{8}{13} * \frac{7}{12}\)

Simplify

\(P(X = 0) = \frac{2}{13} * \frac{7}{3}\)

\(P(X = 0) = \frac{14}{39}\)

Recall that:

\(P(X \ge 1) = 1 - P(X = 0)\)

\(P(X \ge 1) = 1 - \frac{14}{39}\)

Take LCM

\(P(X \ge 1) = \frac{39 -14}{39}\)

\(P(X \ge 1) = \frac{25}{39}\)

r = 5.8 cm r = 7.1 cm

d = 11.6 cm d = 14.2 cm

C = 36.44 cm C = 44.611 cm

A = 105.68 cm2 A = 158.37 cm2

( I can't find where square is )

Answer:

21.4

Step-by-step explanation:

took the quiz

Answer:

72 7th graders

Step-by-step explanation:

7th Grade:

18(Yearbook) + 20(Student Council) + 2(Jump Rope) = 40 students total in 7th grade

If staying true to the ratio when there is 200 7th graders then the amount of 7th graders involved in the year book will be this:

40 current students: Required 200.

200/40 = 5

Multiply all current club values by 5:

18x5 = 90 7th graders in year book

20x5 = 100 7th graders in student council

2x5 = 10 7th graders in jump rope.

= 200 total students.

How many more 7th graders are in the year book?

90 students - 18 students = 72 7th graders in year book

\(f(x)=2(3)^{x+1} \\\\[-0.35em] ~\dotfill\\\\ f(2)=2(3)^{(2)+1}\implies f(2)=2(3)^3\implies f(2)=2(3^3) \\\\\\ f(2)=2(27)\implies f(2)=54\)

Approximately 273 cubes with a side length of 1/2 inch will be needed to fill the prism.

To determine the number of cubes with a side length of 1/2 inch needed to fill the prism, we need to calculate the volume of the prism and divide it by the volume of a single cube.

The given dimensions of the pencil box are:

Length: 6 1/2 inches

Width: 3 1/2 inches

Height: 1 1/2 inches

To find the volume of the prism, we multiply the length, width, and height:

Volume of the prism = Length \(\times\) Width \(\times\) Height

\(= (6 1/2) \times (3 1/2) \times (1 1/2)\)

First, we convert the mixed numbers to improper fractions:

\(6 1/2 = (2 \times 6 + 1) / 2 = 13/2\)

\(3 1/2 = (2 \times 3 + 1) / 2 = 7/2\)

\(1 1/2 = (2 \times 1 + 1) / 2 = 3/2\)

Now we substitute the values into the formula:

Volume of the prism \(= (13/2) \times (7/2) \times (3/2)\)

\(= (13 \times 7 \times 3) / (2 \times 2 \times 2)\)

= 273 / 8

≈ 34.125 cubic inches.

Next, we calculate the volume of a single cube with a side length of 1/2 inch:

Volume of a cube = Side length \(\times\) Side length \(\times\) Side length

\(= (1/2) \times (1/2) \times (1/2)\)

= 1/8

To find the number of cubes needed to fill the prism, we divide the volume of the prism by the volume of a single cube:

Number of cubes = Volume of the prism / Volume of a single cube

= (273 / 8) / (1/8)

= 273

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Answer:

6x-3=15

Step-by-step explanation:

Answer:

$60

Step-by-step explanation:

In a set of data, the median is the value that is placed in the middle. to find the median, we must order the numbers from least to greatest, like so:

20, 40, 40, 50, 60, 60, 60, 60, 70, 70

Using this representation, we find that there are two numbers in the middle: 60 and 60 (since the amount of data is an even number, there will be two numbers in the center).

When something like this occurs, find the average of the two numbers in the middle (and the values and divide by the number of values). We have:

60 + 60 = 120;

\(\frac{120}{2} = 60\)

Therefore, the median is $60.

The sides of the right triangle are:

a) AC

b) CB

c)  AB

We have the diagram of a right triangle, and we want to identify the side that is opposite to angle B.

That would be the side that does not intercept the vertex B, so it is AC.

Then we want to get the adjacent side to B that is not the hypotenuse.

That would be the side that intercepts vertex B and intercepts the vertex with the small red square, it is CB.

Finally, the vertex is the side opposite to the small red square (90° angle) so it is AB.

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Answer:

Third one

Step-by-step explanation:

;b

Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.

When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).

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Answer:

20%

Step-by-step explanation:

The total number of students is: 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30 (students)

The probability is: 6/30 = 1/5 = 0.2 = 20%

The probability that the student is a male given that he's a sophomore is approximately 60%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The probability that the student is a male given that it's a sophomore can be calculated using the formula:

P(male | sophomore) = P(male and sophomore) / P(sophomore)

The number of male sophomores is 6, and the total number of sophomores is 6+4=10.

So, the probability of selecting a sophomore is:

P(sophomore)

= (number of sophomores) / (total number of students)

= 10 / 23

The number of male sophomores is 6.

So,

The probability of selecting a male sophomore is:

P(male and sophomore) = 6 / 23

Therefore,

The probability that the student is a male given that it's a sophomore is:

P(male | sophomore)

= (6 / 23) / (10 / 23)

= 6 / 10

= 3 / 5

Rounding to the nearest whole percent, we get:

P(male | sophomore) ≈ 60%

Thus,

The probability that the student is a male given that he's a sophomore is approximately 60%.

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Check the picture below.

so hmm we have a 6x6 square atop and a triangle with base of 6 and a height of "h", let's get "h".

\(\sin( 42^o )=\cfrac{\stackrel{opposite}{h}}{\underset{hypotenuse}{2}} \implies 2\sin(42^o)=h \implies 1.34\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{6})(\underset{h}{1.34})}~~ + ~~\stackrel{ square }{(6)(6)}} ~~ \approx ~~ 4.02+36~~ \approx ~~ \text{\LARGE 40.0}\)

The side x of the triangular base prism is 0.4 centimetres.

The diagram above is a triangular prism. The triangular base of the prism is a right triangle. Therefore, the unknown side x can be found using Pythagoras's theorem,

c²= a² + b²

where

Therefore,

x² = 0.5² - 0.3²

x² = 0.25 - 0.09

x = √0.16

x = 0.4 cm

Therefore,

x = 0.4 centimetres.

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Answer:7

Step-by-step explanation:

This question is on the ukmt junior maths challenge which I'm doing now, out of the options given I got 7, because 2+4+6+5+(5×20)+(7×7)= 166, (then dividing that by the number of numbers to get the mean) so 166÷31= 5.354.....

Also the 3 has a recurring symbol above it

The 7 is times seven so uh yeah<3

The smallest possible value of 'q' is 7 and this can be determined by using the hit and trial method and mean formula.

Given :

The following steps can be used in order to determine the smallest possible value of q:

Step 1 - The formula of the mean can be used in order to determine the smallest possible value of q.

Step 2 - The mean of all the numbers is given by:

\(\rm \dfrac{2+4+6+5+5p+7q}{6+p+q}=5.3\)

\(\rm \dfrac{21 + 5p + 7 q}{6+p+q} = 5.3\)

Step 3 - So, by the hit and trial method, the value of q can be determined.

Therefore, the value of 'q' is 7.

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