What is the length of the missing leg? If necessary, round to the nearest tenth

The researcher can compare his sample results to the normal distribution (z-distribution) if certain conditions are met.  In order to compare sample results to the normal distribution using the z-distribution, certain conditions must be met.

The most important condition is that the population distribution should be approximately normal or at least follow a symmetric distribution. This condition is necessary because the z-distribution assumes a normal distribution. If the population distribution deviates significantly from normality, the use of the z-distribution may not be appropriate.

To determine whether the population distribution is normal, the researcher can conduct tests of normality, such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test, on the data collected. These tests can assess whether the data significantly deviate from a normal distribution. If the data is found to deviate from normality, alternative methods, such as non-parametric tests, may be more suitable for analyzing the results.

It is important for the researcher to carefully consider the assumptions and conditions necessary for using the z-distribution before proceeding with the comparison. If the population distribution is not normal or the assumptions are violated, alternative statistical approaches should be used to ensure accurate analysis and interpretation of the results.

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a) When Lily's age is 20, and Raphael's age is divided by 3 then the expression of Lily's age in terms of h is h < 10.

b) Ethan's age is half of Raphael's age therefore, Ethan's age is half Raphael's age.

a) If Raphael is twice as old as his sister Lily, we can represent their ages as 2h and h, respectively, where h is Lily's age. The sum of their ages is less than 30, so we can write the equation:

2h + h < 30

Combining like terms, we get:

3h < 30

Dividing both sides by 3, we get:

h < 10

This is an expression of Lily's age in terms of h.

b) If Ethan's age is 16, and Raphael's age is twice Ethan's age, we can represent Raphael's age as 2 × 16 = 32.

Ethan's age is 16, which is half of Raphael's age of 32. Therefore, Ethan's age is half of Raphael's age.

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The question is -

Raphael is twice as old as his sister. The sum of their ages is less than 30.

a) Lily's age is 20, and Raphael's age is divided by 3. Write an expression in terms of h for Lily's age.

b) An expression for Ethan's age 16. Write a sentence to describe how Ethan's age compares with Raphael's age.

Answer:

9 miles

Step-by-step explanation:

use Pythagoras theorem

15 squared - 12 squared = 81

square root of 81 is 9

Answer:

A. 9 mi.

Step-by-step explanation:

Here, use the Pythagorean Theorem, but leave "a" as it is.

a² + b² = c²

a² + 12² = 15²

a² + 144 = 225

a² = 225 - 144

a² = 81

a = √81

a = 9

The missing side is 9 miles long.

Answer:

(0.5,0) , (-3,0) ,and (0,-1.5)

Step-by-step explanation:

Just look where the points touch the x- and y-axis.

It touches twice on the x- and once on the y-axis.

Hope that helps!

The rectangle with dimensions 21 m by 21 m has the largest area among rectangles with a perimeter of 84 m.

To find the dimensions of a rectangle with a perimeter of 84 m that maximizes the area, we need to use the properties of rectangles.

Let's assume the length of the rectangle is l and the width is w.

The perimeter of a rectangle is given by the formula: 2l + 2w = P, where P is the perimeter.

In this case, the perimeter is given as 84 m, so we can write the equation as: 2l + 2w = 84.

To maximize the area, we need to find the dimensions that satisfy this equation and give the largest possible value for the area. The area of a rectangle is given by the formula: A = lw.

Now we can solve the perimeter equation for l: 2l = 84 - 2w, which simplifies to l = 42 - w.

Substituting this expression for l into the area equation, we get: A = (42 - w)w.

To maximize the area, we can find the critical points by taking the derivative of the area equation with respect to w and setting it equal to zero:

dA/dw = 42 - 2w = 0.

Solving this equation, we find w = 21.

Substituting this value of w back into the equation l = 42 - w, we get l = 42 - 21 = 21.

Therefore, the dimensions of the rectangle that maximize the area are l = 21 m and w = 21 m.

In summary, the dimensions of the rectangle are 21 m by 21 m, so the answer is A. 21, 21.

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Answer:

  (100√3)/3 square feet

Step-by-step explanation:

You want the area of the isosceles triangle that has a vertex angle of 120° and a base of 20 feet.

The altitude divides the triangle into two 30-60-90 right triangles with a long side of half the base, or 10 ft. That means the altitude is 10/√3 ft.

The area is ...

  A = 1/2bh

  A = 1/2(20 ft)(10/√3 ft) = 100/√3 ft²

We usually want the radical in the numerator, so that would be ...

  Area = (100√3)/3 ft²

Answer:

9

Step-by-step explanation:

there are 3 atoms in one co2 molecule. 3 x 3=9

Answer:

in three molecules of CO2 there are:

3 Carbon Atoms and 6 Oxygen Atoms

If your looking for the atoms in ONE molecule then there is:

One Carbon Atom and Two Oxygen Atoms

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A. Understand

The question is asking how much money is saved.

Given :

B. Plan

that is :

C. Solve

Hence, savings = Php 3544.55

The maximum money supply with a 5% reserve requirement and a $400 initial deposit is $8,000.

To calculate the maximum total amount of money that will be in the money supply, we need to consider the money multiplier effect based on the reserve requirement.

The money multiplier is given by the formula: MM = 1 / reserve requirement.

Given that the reserve requirement is 5% (rr = 0.05), the money multiplier is MM = 1 / 0.05 = 20.

The initial deposit is $400.

To calculate the maximum total amount of money in the money supply, we multiply the initial deposit by the money multiplier:

Maximum Money Supply = Initial Deposit * Money Multiplier

= $400 * 20

= $8,000.

Therefore, the maximum total amount of money that will be in the money supply is $8,000 when the reserve requirement is 5% and all currency is deposited in banks with no excess reserves.

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The standard equation of the plane is -5x - 23y - z + 18 = 0, and the general equation of the plane is x + (23/5)y + (1/5)z = 18.

The standard equation of a plane is:

Ax + By + Cz + D = 0

where A, B, C, and D are the coefficients of the plane and (x, y, z) is a point on the plane.

To find the standard equation of the plane, we can use the following steps:

Find a vector that is parallel to the plane.

Find the normal vector to the plane.

Substitute the values of the vector and the normal vector into the standard equation of the plane.

Step 1: Find a vector that is parallel to the plane.

We can find a vector that is parallel to the plane by subtracting any two points that lie on the plane. In this case, we can subtract the point ( (1,-1,2) ) from the point ( (-3,4,-1) ). This gives us the vector:

(-3 - 1, 4 - (-1), -1 - 2) = (-4, 5, -3)

Step 2: Find the normal vector to the plane.

The normal vector to the plane is perpendicular to the vector that is parallel to the plane. We can find the normal vector by taking the cross product of the vector that is parallel to the plane and any other vector that lies on the plane. In this case, we can take the cross product of the vector ( (-4, 5, -3) ) and the vector ( (3, -2, 5) ). This gives us the normal vector:

(-5, -23, -1)

Step 3: Substitute the values of the vector and the normal vector into the standard equation of the plane.

Now that we have the vector and the normal vector, we can substitute them into the standard equation of the plane. This gives us the following equation:

-5x - 23y - z + D = 0

We can substitute any point that lies on the plane into this equation to solve for D. In this case, we can substitute the point ( (1,-1,2) ). This gives us the following equation:

-5(1) - 23(-1) - 2 + D = 0

Solving for D, we get D = 18.

Therefore, the standard equation of the plane is:

-5x - 23y - z + 18 = 0

The general equation of the plane is:

(-5x - 23y - z) + 18 = 0

-5x - 23y - z = -18

x + (23/5)y + (1/5)z = 18

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Answer: D

Step-by-step explanation:

Use SOHCAHTOA

We are given the opposite of the angle and the hypotenuse. We can use the sine function to acquire the value of x°.

sin(x) = 7/13

Take the inverse sine on both sides by using a calculator to get:

x = 32.58°

Answer:

32.58° that the answer hope this helps

Answer:

25°

Step-by-step explanation:

25° because opposite angles are equal

the blue angle 25° is opposite the yellow angle x° making x=25°

Answer:

x = 25°

Step-by-step explanation:

We can see that the 25° and x° are vertical to each other and vertical angles are angles that are the same size and directly opposite each other thus they are equal!

The two sample means of 10 and 20 with variances of 20 and 25 will produce the largest value for an independent-measures t statistic.

An independent-measures t statistic is used to measure the differences between two independent groups. In this case, the two sample means are 10 and 20 with variances of 20 and 25. This will produce the largest value for an independent-measures t statistic because the larger the difference between the two sample means, the larger the t statistic will be. The larger the variance, the more spread out the data is which also results in a larger t statistic. Since the two sample means have a larger difference and the variances are also large, this will result in the largest value for an independent-measures t statistic.

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Using proportions, it is found that the value of x is of 5.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, since Figure A is a scale of Figure B, the side lengths are proportional, hence the following rule of three is established:

x/12.5 = 2/5

Applying cross multiplication:

5x = 25

x = 5.

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The angle x of the right angle triangle is 19 degrees.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The angles of a right angle triangle can be found using trigonometric ratios as follows:

Hence,

sin x = opposite / hypotenuse

Therefore,

sin x = 8 / 24

sin x = 1 / 3

x = sin⁻¹ 0.33333333333

x = 19.4712206325

Therefore,

x = 19 degrees.

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Answer: Division property of equality

Step-by-step explanation:

Answer:

associative property  of addition

Step-by-step explanation:

you always have to do what's in the Parenthesis first then move on to what's next in the PEMDAS.

Answer:

12

Step-by-step explanation:

If you solve the second equation and substiture to the first, you get y = 5, and x = -7.

5-(-7) = 5+7=12

Step-by-step explanation:

-3n + 3 > -11

-3n > -14

3n < 14

n < 14/3

14/3 = 4.66666666...

the only positive integers that are smaller than 4.666666... are

4, 3, 2, 1

their sum is

4+3+2+1 = 10

Answer:

it is 108

Step-by-step explanation:

you know that the 53 angle is also inside the triangle and that 180-125 gives you the second angle 55. you than calculate that the last inner angle is 72 and substract that from 180.

Answer:

108 degrees

Step-by-step explanation:

lets imagine that pqr are the angles of the triangle

<rpq=53°(opposite<)

for <prq 180°-125°(< on a straight line)=55°

<pqr= a+b+c

= 55°+53°+c= 180°(< in a ∆)

= 108°+c =180°

collect like terms

c= 108°-108°

c= 72°

Therefore<pqr= 72°

for the unknown angle which is x

55+53=108( the two sides are facing the exterior <)

Answer:

7 days

Step-by-step explanation:

What you have to do is divide 12(1)/(3) by 1(3)/(4)... the best way to do that is first turn them into exact form.

12(1)/(3) --> 12*3 plus 1= 37/3 (the denominator stays the same)

1(3)/(4) --> 1*4 plus 3= 7/4

Then you have (37/3) over (7/4), from this point you switch the numerator and the denominator on the second fraction so that you can multiply both equations. (7/4) --> (4/7)

(37/3) * (4/7) = (148/21)

When simplified... 7(1)/(21)... and since you want to know full days, you only take 7

a. The inequality that represents the additional number of passengers, p, that can board the plane will be D. 15+p≤44 15 plus p is less than or equal to 44

b. The option that represents the people who can board the plane is A. 30 more passengers cannot board the plane. Only 29 more passengers can board the plane.

From the information, the small airplane can hold 44 passengers. Fifteen passengers board the plane.

Let P = those that can board the plane.

P + 15 ≤ 44

Collect like terms

P ≤ 44 - 15

P ≤ 29

The highest number of passengers that can enter the plane is 29.

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As no diagrams attached provided the formulas which can helps you to solve by yourself

The expression to represent the perimeter of Melissa’s garden in terms of x is P = 8x + 14

The formula for calculating the perimeter of a rectangle is given as

P = 2(x+ y)

where;

x = 3x + 2

y = x + 5

Substitute

P = 2(3x + 2 + x + 5)

P = 2(4x + 7)
P = 8x + 14

Hence the expression to represent the perimeter of Melissa’s garden in terms of x is P = 8x + 14

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Answer:

  tan(α) = 1/tan(90°-α)

Step-by-step explanation:

The tangent of one is the reciprocal of the tangent of the other.

__

In a right triangle, ...

  tan = opposite/adjacent

For the two complementary acute angles in such a triangle, opposite and adjacent are swapped. That is the tangent of one is the inverse of the tangent of the other. (That inverse is also known as the cotangent.)

  tan(α) = cot(90°-α) = 1/tan(90°-α)

Reflect each point from the line y = -3

J = (0,-2) which reflected from y = -3 is (0,-4)

K = (1,-5) which reflected from y = -3 is (1,-1)

L = (4,-1) which reflected from y = -3 is (4,-5)

Answer:

the eero is on date in answer 'c' because the date of kangaroo is in an arrangement form

Answer:

14/3/2024 is on a Thursday, but it is the second Thursday, not the third.  

Step-by-step explanation:

If the first Thursday falls on March 1, the soonest the third Thursday could occur is 7+7+1 = March 15.

Answer:

sweet god yes it is unless she 12 feet tall then no

Step-by-step explanation:

Answer: No.

Step-by-step explanation: No, because 3.5 converted is 350 and you need 370. Might be to late but hopefully this can help someone else!

The corresponding equation is 4q + 3p = 22.

What is the slope of a line ?

The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's b in mathematics.

Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate. Locate two locations along the chosen line and find their coordinates.

Find the y-coordinate difference between these two places (rise). Find the difference between the x-coordinates of these two points (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).

The slope is defined as the relationship between the rise, or vertical change, between two points and the change, or horizontal change, between the same two points and can be represented as an equation.

Given that, coordinates are (p, 1/2) and (-8, q), slope is 3/4.

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

34 = (q - 1/2)/-8 - p

-24 - 3p = 4q - 2

4q + 3p = 22

The corresponding equation is 4q + 3p = 22.

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