Without using a calculator, convert the fraction to a decimal.
4
5
=
5
4
​
=start fraction, 4, divided by, 5, end fraction, equals

A chi-square test of independence is indeed a one-tailed test. The reason for this is that we are testing whether the observed frequencies of two categorical variables are significantly different from the expected frequencies.

We square the deviations between the observed and expected frequencies, and since deviations can only be positive, the test statistic always lies at or above zero. Hypothesis tests are one-tailed when dealing with sample data because we have a specific direction for our research question. In the case of a chi-square test of independence, we are interested in whether one variable is dependent on the other variable, so we have a directional hypothesis. Furthermore, the chi-square distribution is positively skewed, meaning that the majority of the distribution is on the right-hand side. This is important to consider when interpreting the results of a chi-square test.

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Answer:

D

Step-by-step explanation:

Answer:

The third option

Step-by-step explanation:

The domain is saying x is greater than or equal to 2, so the third option fits that description.

Hopefully this helps!

Brainliest please?

The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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Randi earn $24,300 next year.

Here,

Given that;

Two years ago Randi earned $18,400. last year she earned $19,700.

And, she earns $21,600 this year.

The average of four year is $21,000

We have to find, the amount she earn in next year.

What is Average?

A number that is calculated by adding quantities together and dividing the total by the number of quantities.

Now,

Let she earn $ x in next year.

The average of four year is $21,000.

Hence, Average of money for four year is;

\(\frac{18,400+19,700+21,600+x}{4} = 21,000\)

\(59,700 + x = 84,000\)

\(x = 24,300\)

So, She earn $24,300 in next year.

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Answer:

A. 190 lb

Step-by-step explanation:

Hope this helps

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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Answer:

\(\boxed {y = -\frac{1}{2}x + 3}\)

Step-by-step explanation:

Convert the equation from Standard Form to Slope-Intercept Form:

\(Ax + By = C\)  ⇒  \(y = mx + b\)

-The following equation:

\(x - 2y = 6\)

-Solve:

\(x - 2y = 6\)

\(x - x - 2y = 6 - x\)

\(2y = -x + 6\)

\(\frac{2y}{2} = \frac{-x}{2} + \frac{6}{2}\)

\(\boxed {y = -\frac{1}{2}x + 3}\)

So, the equation in Slope-Intercept Form is \(y = -\frac{1}{2}x + 3\).

In 139.4 \(\pi\) \(ft^2\)sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.

What is area of circle?

 For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much fabric is required to completely cover a circular table, for example. We can determine the boundary length, or the circle's circumference, using the area formula.

Here area of circle

=> A= π\(r^2\)--------> 1

Differentiating 1 with respect to to time then

=> \(\frac{dA}{dt}= 2\pi r\frac{dr}{dt}\)

If the radius is  increasing at a constant rate 3.3ft/sec then after 6.4 seconds, radius is

=> 6.4*3.3=21.12 ft.

We know \(\frac{dr}{dt}= \frac{3.3ft}{sec}\) and so ,

=> \(\frac{dA}{dt}\) = 2*\(\pi\)*21.12*3.3=139.4 \(\pi\) \(ft^2\)sec.

Hence In 139.4 \(\pi\) \(ft^2\)sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.

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Answer:

(-4,-1) is the answer to this.

Answer:

11.92418

Step-by-step explanation:

I hope it's right sorry if it's not.

The equation of the circles is:

\((x-2)^2 + (y-8)^2 = 9\\(x-5)^2 + (y+13)^2 = 121\\(x+9)^2 + (y+7)^2 = 1156\\(x+8)^2 + y^2 = 25\\x^2 + (y+16)^2 = 15\\(x-12)^2 + (y+1)^2 = 209\\\)

We have,

The equation of a circle with center (a, b) and radius r is:

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

Now,

Center = (2, 8) and radius = 3

Substituting the given values in the equation of a circle, we get:

(x - 2)² + (y - 8)² = 3²

Simplifying, we get:

(x - 2)² + (y - 8)² = 9

Centre = (5, -13) and radius = 11

Substituting the given values in the equation of a circle, we get:

(x - 5)² + (y + 13)² = 11²

Simplifying, we get:

(x - 5)² + (y + 13)² = 121

Centre = (-9, -7) and radius = 34

Substituting the given values in the equation of a circle, we get:

(x + 9)² + (y + 7)² = 34²

Simplifying, we get:

(x + 9)² + (y + 7)² = 1156

Centre = (-8, 0) and radius = 5

Substituting the given values in the equation of a circle, we get:

(x + 8)² + y² = 5²

Simplifying, we get:

(x + 8)² + y² = 25

Centre = (0, -16) and radius = √15

Substituting the given values in the equation of a circle, we get:

x² + (y + 16)² = (√15)²

Simplifying, we get:

x² + (y + 16)² = 15

Centre = (12, -1) and radius = √209

Substituting the given values in the equation of a circle, we get:

(x - 12)² + (y + 1)² = (√209)²

Simplifying, we get:

(x - 12)² + (y + 1)² = 209

Thus,

The equation of the circles is:

\((x-2)^2 + (y-8)^2 = 9\\(x-5)^2 + (y+13)^2 = 121\\(x+9)^2 + (y+7)^2 = 1156\\(x+8)^2 + y^2 = 25\\x^2 + (y+16)^2 = 15\\(x-12)^2 + (y+1)^2 = 209\\\)

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The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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The penny will fall from distance of 232 feet during the 8th second only, as it falls 960 feet in the first 8 seconds, but 728 feet in the first 8 seconds.

The distance the penny falls each second is increasing by 32 feet (16 feet + 32 feet = 48 feet, 48 feet + 32 feet = 80 feet, and so on). Therefore, during the 8th second, the distance it will fall is:

16 + 48 + 80 + ... + (8 - 1) * 32 feet

Using the formula for the sum of an arithmetic sequence, we get:

(8 / 2) * (16 + (8 - 1) * 32) feet

= 4 * (16 + 7 * 32) feet

= 4 * 240 feet

= 960 feet

So the penny will fall 960 feet during the first 8 seconds. However, we need to subtract the distance it fell during the first 7 seconds to find the distance it fell during the 8th second only. The total distance it fell during the first 7 seconds is:

16 + 48 + 80 + ... + (7 - 1) * 32 feet

= (7 / 2) * (16 + (7 - 1) * 32) feet

= 3.5 * (16 + 6 * 32) feet

= 3.5 * 208 feet

= 728 feet

Therefore, the penny will fall 960 - 728 = 232 feet during the 8th second only.

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According to the solving the area of the square is 68.0625.

As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.

The box formed after cutting the square from each corner will have the dimensions as,

length = 104 - 2x, width = 39 - 2x, height = x.

∴ volume of the box = length × width × height

∴ v = (104 - 2x)(39 - 2x)(x) -----(i)

∴ v = (104 - 2x) (39x - 2\(x^{2}\))

∴ v = 104(39x - 2\(x^{2}\)) -2x(39x - 2\(x^{2}\))

∴ v = 4056x - 208\(x^{2}\) - 78\(x^{2}\) + 4\(x^{3}\)

∴ v = 4\(x^{3}\) - 286\(x^{2}\)  + 4056x

let f(x) =  4\(x^{3}\) - 286\(x^{2}\)  + 4056x  -----(ii)

To, find x for which f(x) is maximum,

⇒we should apply second derivative test ,

According to this test, first we should find critical points at which f'(x) = 0.

then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.

∴ let us consider, f'(x) = 0.

now, f(x) =  4\(x^{3}\) - 286\(x^{2}\)  + 4056x

⇒ f'(x) = 12\(x^{2}\) - 572x + 4056.  -----(iii)

⇒ f'(x) = 4(3\(x^{2}\) - 143x + 1014)

⇒ f'(x) = 0.

⇒  f'(x) = 4(3\(x^{2}\) - 143x + 1014) = 0

⇒ x = (-b ± \(\sqrt{b^{2} - 4ac }\))/2a    ; where a = 3, b = -143, c = 1014.

∴ x = (-(-143) ± \(\sqrt{(-143)^{2} -4(3)(1014)}\))/2×3

∴ x = (143 ± \(\sqrt{8281}\))/6.

∴ x = \(\frac{143 + 91}{6}\)  , x = \(\frac{143 - 91}{6}\)

⇒ x = 39, 8.25

the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.

Area of the square is = \(x^{2}\) = \(8.25^{2}\)

∴ Area = 68.0625

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Answer:

-7,3

Step-by-step explanation:

Answer:

-3x3x-3x-3

Get yourself some braincells in the future, please.

The quadrilateral WXYZ is not a square using the distance formula

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

W(-1,1),X(3,4),Y(6,0) and Z(2,3)

The lengths of the sides can be calculated using the following distance formula

Length = √[Change in x² + Change in y²]

Using the above as a guide, we have the following:

WX = √[(-1 - 3)² + (1 - 4)²] = 5

XY = √[(3 - 6)² + (4 - 0)²] = 5

YZ = √[(6 - 2)² + (0 - 3)²] = 5

ZW = √[(2 + 1)² + (3 - 1)²] = 13

The sides that are congruent are WX, XY and YZ

This means that WXYZ is not a square

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Answer:

73 dollars and 50 cents

Step-by-step explanation:

Initial Deposit:

70

Years to Save:

1

Estimated Rate of Return

5

Compound Frequency:

Annually

Earned Interest

$3.50

Total Balance

$73.50

Hope this helps!

Answer:

73.50

Step-by-step explanation:

math

Answer:  -7.5

Step-by-step explanation:  Simplify. turn the 1/2 into a decimal and it will make it much easier

Answer: A)72.8067226km/hr (final asnwer)
b) volume of a cube= a^3 (sides^3) =4.5^3= 91.125 cm^3 (final asnwer)

c) 1 day cost= $(35.9 +11.55 + 35) =$82.45
therefore for 5 days= $82.45 * (multiplied) by 5 = $412.25 (final asnwer)

Step-by-step explanation:

Answer:

(a)≈72.8 kilometer per hour

(b)91.125 cm^3

(c)272.25$

Step-by-step explanation:

(a)speed=mile/hour

=371mile/8.2hours

=371×1.609kilometers/8.2hours

≈72.8 kilometer per hour

(b)the vol: of cube= a^3 (a=side)

=(4.5)^3

=91.125cm^3

(c) for 5 days, (35.9×5)+(11.55×5)+35 ($35 is ofor one-off charge so there is no need to multiply with 5)

=272.25$

Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

The side lengths of the right triangle are: shorter leg = 7 cm, longer leg = 24 cm, and hypotenuse = 25 cm.

Let's denote the length of the shorter leg as x.

According to the information:

The length of the longer leg is 3 cm more than three times the length of the shorter leg, which can be expressed as 3x + 3.

The length of the hypotenuse is 4 cm more than three times the length of the shorter leg, which can be expressed as 3x + 4.

In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Using this, we can set up the equation:

(x)²+ (3x + 3)² = (3x + 4)²

Expanding and simplifying the equation:

x² + (9x² + 18x + 9) = (9x² + 24x + 16)

Combining like terms:

10x² + 18x + 9 = 9x² + 24x + 16

Moving all terms to one side of the equation:

10x² + 18x + 9 - 9x² - 24x - 16 = 0

Simplifying:

x² - 6x - 7 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. Factoring, we have:

(x - 7)(x + 1) = 0

Setting each factor to zero:

x - 7 = 0   or   x + 1 = 0

Solving for x:

x = 7   or   x = -1

Since lengths cannot be negative, we discard the solution x = -1.

Therefore, the length of the shorter leg is x = 7 cm.

Using this value, we can find the length of the longer leg and the hypotenuse:

Length of the longer leg = 3x + 3 = 3(7) + 3 = 21 + 3 = 24 cm

Length of the hypotenuse = 3x + 4 = 3(7) + 4 = 21 + 4 = 25 cm

So, the side lengths of the triangle are:

Shorter leg = 7 cm

Longer leg = 24 cm

Hypotenuse = 25 cm

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Answer:

Adults = 61

Students = 92

Children = 122

Step-by-step explanation:

a adults

x students

c children

a + c + x = 275

c / a = 2

5c + 7x + 12a = 1986

Simplify and solve the system.

a + 2a + x = 275

3a +x = 275

x = 275 - 3a. and c= 2a

The revenue equation can be written in terms of just one variable, a.

5(2a) + 7(275-3a) + 12a = 1986

Solve for a

a = 61

use it to find x and c.

c = 2a = 2 x 61 = 122

x = 275-a-c

x = 275 - 61-122

x = 92

Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:

3x + 2 >= 0

Step-by-step explanation:

Since this is a 4th root, not a cubic root, the radical can only contain 0 or positive numbers. Therefore there is 3x + 2 >= 0.

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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