Hey, the question is with the image. Pls help

Answer:

Margin of Error = ME =± 5.2592

Step-by-step explanation:

In the given question n= 20 < 30

Then according to the central limit theorem z test will be applied in which the standard error will be  σ/√n.

Sample Mean = μ = 64

Standard Deviation= S= σ = 12

Confidence Interval = 95 %

α= 0.05

Critical Value for two tailed test for ∝= 0.05 = ±1.96

Margin of Error = ME = Standard Error *Critical Value

ME = 12/√20( ±1.96)=

ME    = 2.6833*( ±1.96)= ± 5.2592

The standard error for this test is σ/√n

=12/√20

=2.6833

Answer:

the null hypothesis would be: p = 70%/0.7

The alternative hypothesis would be: p < 0.7

Step-by-step explanation:

The null hypothesis is most of the time always the default statement while the alternative hypothesis is tested against the null and is its opposite.

In this case study the null hypothesis would be: the proportion of men who own cats is 70%: p = 0.7

The alternative hypothesis would be: the proportion of men who own cats is smaller than 70% : p < 0.7

Answer:

D.$80

Step-by-step explanation:

$5.26 x 15.5= $81.53

The closest amount to $81.53 is D.$80

Answer:

Categorical independent variables are ___FACTORS__

The independent variables that are categorial should be factors.

In terms of mathematics, factor represents the no of algebraic expression where it split the other number that contains the zero remainder. As the factor of 12 should be 3 and 4. So based on this, the independent variables that are categorical should be considered as the factors.

Therefore, we can conclude that The independent variables that are categorial should be factors.

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Answer:

504 ways.

Step-by-step explanation:

In this case, order matters. If Amy were lead, Bob were record keeper, and Charles were researcher, that would be different than if Bob were lead, Charles were record keeper, and Amy were researcher. So, we will be using a permutation formula to compute.

The formula is n! / (n - k)!, where n is the total number of people (9), and k is the number you are selecting (3).

9! / (9 - 3)! = 9! / 6! = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (6 * 5 * 4 * 3 * 2 * 1) = 9 * 8 * 7 = 72 * 7 = 504 ways.

Hope this helps!

Answer:

Variance=134.8943 kg

Step-by-step explanation:

The relationship between standard deviation and variance is that standard deviation is the square root of the variance.

So given the value of standard deviation to be 11.6144kg, the variance will be the square of the number.

Standard deviation= √variance

Standard deviation ²=√variance²

Standard deviation ² = variance

11.6144²= variance

134.8943

Variance=134.8943 kg

Answer:

122.4409 kg

Step-by-step explanation:

Answer:

2.09 seconds.

Step-by-step explanation:

We are given...

y = 70 feet

v0 = 0 feet/second

a = 32 feet/second^2

We need to find t using the following equation...

y = v0 * t + (1/2) * a * t^2

70 = 0 * t + (1/2) * 32 * t^2

70 = (1/2) * 32 * t^2

70 = 16t^2

16t^2 = 70

t^2 = 4.375

t = sqrt(4.375)

t = 2.091650066

So, it will take the toy about 2.09 seconds to hit the ground.

Hope this helps!

Answer:

78 pork sliders

Step-by-step explanation:

The food concession owner sold 120 beef, vegetable and pork sliders.

20% were beef.

15% were vegetable.

The percentage of pork sliders sold is:

100 - (20 + 15) = 100 - 35 = 65%

The number of pork sliders sold is therefore:

65/100 * 120 = 78

78 pork sliders were sold.

Answer:

The point of interception of the graph and x axis are -2.366 and -0.634.

The only graph that satisfy this conditions is Graph A

Step-by-step explanation:

Given the equation;

[tex]y = 2x^2 + 6x + 3\\[/tex]

at y = 0

[tex]2x^2 + 6x + 3=0\\[/tex]

the roots of the quadratic equation (at y =0) can be calculated using the quadratic formula;

[tex]x = \frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]

Using the quadratic equation to solve for the roots;

[tex]x = \frac{-6\pm \sqrt{6^2 -4*2*3}}{2*2}\\x = \frac{-6\pm \sqrt{36 - 24}}{4}\\x = \frac{-6\pm \sqrt{12}}{4}\\so, we have \\x = -2.366\\or\\x = -0.634\\[/tex]

Therefore, the point of interception of the graph and x axis are -2.366 and -0.634.

The only graph that satisfy this conditions is Graph A

Answer:

I got x=3,-3

Step-by-step explanation:

Squares are the results of multiplying a value by itself. The value of x in the given equation 2x² - 5 = 13 is -3 and 3.

Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.

The value of x for the given equation 2x²-5=13, can be solved as shown below.

2x² - 5 = 13

Add 5 on both the sides of the equation,

2x² - 5 + 5 = 13 + 5

2x² = 18

Divide both the sides of the equation by 2,

2x² / 2 = 18 / 2

x² = 9

Taking the square root on both the sides of the equation,

√x² = √9

x = ±3

x = -3, 3

Hence, the value of x in the given equation 2x² - 5 = 13 is -3 and 3.

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A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is C, Incenter.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

In a triangle, the point at which all the angle bisectors of the triangle meet is known as the Incenter.

Since In ΔRST, all the angles are bisected by the angle bisector, and the point at which all the angle bisectors meet is represented by U. Thus, it can be concluded that the point U represents the incenter of the triangle.

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Answer:

C). 0.83193

Step-by-step explanation:

There are total of 90 passengers of which 27 are for business.

The probability of passengers for business = 27/90

The probability of passengers for business p = 0.3

The probability of passengers not for business q = 1-The probability of passengers for business

= 1-0.3

= 0.7

Random sample of 5 passenger, probability of at least one business passenger = 1 - probability of no business passenger

probability of no business passenger

= 5C0(0.3)^0 * (0.7)^5

= 1 *1*0.16807

= 0.16807

probability of at least one business passenger = 1 - probability of no business passenger

= 1-0.16807

=0.83193

Answer:

option B is the right option.

Step-by-step explanation:

[tex] \frac{bc}{ab} = \frac{ab}{bd} [/tex]

Plug the values:

[tex] \frac{20}{12} = \frac{12}{x} [/tex]

Apply cross product property

[tex]20 \times x = 12 \times 12[/tex]

Calculate the product

[tex]20x = 144[/tex]

divide both sides of the equation by 20

[tex] \frac{20x}{20} = \frac{144}{20} [/tex]

Calculate:

[tex]x = 7.2[/tex]

hope this helps..

Good luck...

this is another type of lazy.... : )

Step-by-step explanation:

Answer:

The standard error  S.E of the mean is 5

Step-by-step explanation:

From the given data;

Fifty students are enrolled in a Business Statistics class.

After he first examination, a random sample of 5 papers was selected.

Now; let consider a random sample of 5 papers was selected. with the following grades : 60, 75, 80, 70, and 90

The objective of this question is to determine the standard error of the mean

In order to achieve this ; we need to find the mean and the standard deviation from the given data.

TO start with the mean;

Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{n} \sum x_i[/tex]

Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{5} (60+75+80+70+90)[/tex]

Mean [tex]\overline X[/tex] = 0.2(375)

Mean [tex]\overline X[/tex] = 75

On the other hand; the standard deviation is :

[tex]s = \sqrt{\dfrac{1}{n-1}\sum(x_i - \overline X)^2}[/tex]

[tex]s = \sqrt{\dfrac{1}{5-1}((60-75)^2+(75-75)^2+(80-75)^2+(70-75)^2+(90-75)^2 )}[/tex]

[tex]s = \sqrt{\dfrac{1}{4}(225+0+25+25+225 )}[/tex]

[tex]s = \sqrt{\dfrac{1}{4}(500 )}[/tex]

[tex]s = \sqrt{125}[/tex]

s = 11.18

Finally; the standard error  S.E of the mean is:

[tex]S.E = \dfrac{s}{\sqrt{n}}[/tex]

[tex]S.E = \dfrac{11.18}{\sqrt{5}}[/tex]

[tex]S.E = \dfrac{11.18}{2.236}[/tex]

[tex]S.E = 5[/tex]

The standard error  S.E of the mean is 5

Answer:

No.

Step-by-step explanation:

Substitute 4 (as x) and 2 (as y) into the 2 equations to see if they fit.

y = x - 2

2 = 4 - 2

2 = 2

The first equation is true for (4,2).

Now try the 2nd one.

y = 3x + 4

2 = 3(4) + 4

2 ≠ 16

So the 2nd equation is not true for (4,2).

Either one not true makes the solution incorrect.

No, (4, 2) is not the solution for system of Equation.

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.

To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

Equations:

y= x-2 ............(1)

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

Put the value of y from equation 1 to equation (2), we get

x- 2 = 3x+ 4

x- 3x = 4+ 2

-2x = 6

x= -3

and, y= -3 -2 = -5

So, the solution to the system is (-3, -5)

and, (4, 2) can only satisfy the Equation y= x-2 but does not satisfy y= 3x+ 4.

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Answer:

Disks = $4 each and Notebooks = $7 each

Step-by-step explanation:

-4(2D + 3N = 29)

3(5D + 4N = 48)

-8D - 12N = -116

15D + 12N = 144

7D = 28

D = $4

2(4) + 3N = 29

8 + 3N = 29

3N = 21

N = $7

Answer:

Option C is the correct option

Step-by-step explanation:

[tex] \frac{x}{3x - 1} \div \frac{x - 2}{2x} [/tex]

To divide by a fraction, multiply by the reciprocal of that fraction

[tex] \frac{x}{3x - 1} \times \frac{2x}{x - 2} [/tex]

Multiply the fractions

[tex] \frac{2 {x}^{2} }{(3x - 1)(x - 2)} [/tex]

Multiply the parentheses

[tex] \frac{2 {x}^{2} }{3x(x - 2) - 1(x - 2)} [/tex]

[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 6x - x + 2 } [/tex]

Collect like terms

[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 7x + 2 } [/tex]

Hope this helps...

Best regards!!

Answer:

a) P(B'|A) = 0.042

b) P(B|A') = 0.625

Step-by-step explanation:

Given that:

80% of the light aircraft that disappear while in flight in a certain country are subsequently discovered

Of the aircraft that are discovered, 63% have an emergency locator,

whereas 89% of the aircraft not discovered do not have such a locator.

From the given information; it is suitable we define the events in order to calculate the probabilities.

So, Let :

A = Locator

B = Discovered

A' = No Locator

B' = No Discovered

So; P(B) = 0.8

P(B') = 1 - P(B)

P(B') = 1- 0.8

P(B') = 0.2

P(A|B) = 0.63

P(A'|B) = 1 - P(A|B)

P(A'|B) = 1- 0.63

P(A'|B) = 0.37

P(A'|B') = 0.89

P(A|B') = 1 - P(A'|B')

P(A|B') = 1 - 0.89

P(A|B') = 0.11

Also;

P(B ∩ A) = P(A|B) P(B)

P(B ∩ A) = 0.63 × 0.8

P(B ∩ A) = 0.504

P(B ∩ A') =  P(A'|B) P(B)

P(B ∩ A') = 0.37 × 0.8

P(B ∩ A') = 0.296

P(B' ∩ A) = P(A|B') P(B')

P(B' ∩ A) = 0.11 × 0.2

P(B' ∩ A) = 0.022

P(B' ∩ A') =  P(A'|B') P(B')

P(B' ∩ A') = 0.89 × 0.2

P(B' ∩ A') = 0.178

Similarly:

P(A) = P(B  ∩  A ) + P(B'  ∩  A)

P(A) = 0.504 + 0.022

P(A) = 0.526

P(A') = 1 - P(A)

P(A') = 1 - 0.526

P(A') =  0.474

The probability that it will not be discovered given that it has an emergency locator is,

P(B'|A) =  P(B' ∩ A)/P(A)

P(B'|A) = 0.022/0.526

P(B'|A) = 0.042

(b) If it does not have an emergency locator, what is the probability that it will be discovered?

The probability that it will be discovered given that it does not have an emergency locator is:

P(B|A') = P(B ∩ A')/P(A')

P(B|A') = 0.296/0.474

P(B|A') = 0.625

Answer:

   sqrt( 146)

Step-by-step explanation:

To find the distance, we use the following formula

d = sqrt( ( x2-x1) ^2 + ( y2-y1) ^2)

    sqrt( ( -9-2) ^2 + ( 0-5) ^2)

  sqrt( ( -11) ^2 + ( -5) ^2)

   sqrt( 121+25)

   sqrt( 146)

Answer:

 [tex]x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]

Step-by-step explanation:

According to the given situation, The computation of all x in a set of a real number is shown below:

First we have to determine the [tex]\bar x[/tex] so that [tex]A \bar x = 0[/tex]

[tex]\left[\begin{array}{cccc}1&-3&5&-5\\0&1&-3&5\\2&-4&4&-4\end{array}\right][/tex]

Now the augmented matrix is

[tex]\left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\2&-4&4&-4\ |\ 0\end{array}\right][/tex]

After this, we decrease this to reduce the formation of the row echelon

[tex]R_3 = R_3 -2R_1 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&2&-6&6\ |\ 0\end{array}\right][/tex]

[tex]R_3 = R_3 -2R_2 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]

[tex]R_2 = 4R_2 +5R_3 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&4&-12&0\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]

[tex]R_2 = \frac{R_2}{4}, R_3 = \frac{R_3}{-4} \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&1\ |\ 0\end{array}\right][/tex]

[tex]R_1 = R_1 +3 R_2 \rightarrow \left[\begin{array}{cccc}1&0&-4&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]

[tex]R_1 = R_1 +5 R_3 \rightarrow \left[\begin{array}{cccc}1&0&-4&0\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]

[tex]= x_1 - 4x_3 = 0\\\\x_1 = 4x_3\\\\x_2 - 3x_3 = 0\\\\ x_2 = 3x_3\\\\x_4 = 0[/tex]

[tex]x = \left[\begin{array}{c}4x_3&3x_3&x_3\\0\end{array}\right] \\\\ x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]

By applying the above matrix, we can easily reach an answer

Answer:

your third answer

Step-by-step explanation:

its easy just plug in each domain into your function and the result will be the range

Answer:

[tex]\Large \boxed{\sf \ \ 4\sqrt{a^2+b^2} \ \ }[/tex]

Step-by-step explanation:

Hello,

You can use Pythagoras in the 4 right triangles.

For one triangle it comes [tex]\sqrt{a^2+b^2}[/tex].

Then for the polygon it gives [tex]4\cdot \sqrt{a^2+b^2}[/tex].

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

H0: p=0.85;

Ha: p>0.85

Step-by-step explanation:

What was being tested is that:

the coach wanted to know if the proportion of basketball players who are over 72 inches is more than 85%.

The null hypothesis which we are testing against would be that the proportion of basketball players who are over 72 inches is 85%.

H0: p=0.85;

Ha: p>0.85

Answer:

[tex]\boxed{\frac{1}{8} }[/tex]

Step-by-step explanation:

[tex]\frac{5}{4} / 10[/tex]

Changing "division" into multiplication and inverting the term after it:

[tex]\frac{5}{4} * \frac{1}{10}[/tex]

=> [tex]\frac{1*1}{4*2}[/tex]

=> 1/8

Answer:

1/8

Step-by-step explanation:

Well to do 5/4 ÷ 10 let's set up the following.

[tex]\frac{5}{4} / \frac{10}{1}[/tex]

Then we use the keep, change, and flip rule.

So keep 5/4 change the / to a * and flip the 10/1 ro a 1/10.

[tex]\frac{5}{4} * \frac{1}{10}[/tex]

Now we multiply them to get,

5/40

simplified

1/8

Thus,

the answer is 1/8.

Hope this helps :)

Answer:

6.96x10^-3

Step-by-step explanation:

0.00696

We move the decimal point to between 6 and 9

since the number with the decimal point should be between 0 and 9.

Then we count the numbers.

6.96x10^-3.

Hope this helps. ❤❤❤

Answer: 6.96 * 10^(-3)

Step-by-step explanation:

In scientific notation, you multiply a number that has a value in the ones place and no value in the tens place by 10 raised to an exponent.

Hope it helps <3

Step-by-step explanation:

RD=BL

RE=BU

ED=UL

Please mark brainliest!!!

Answer:

8 units

Step-by-step explanation:

We need to rewrite an equation in the standard for  a circle form.

r is radius.

(x−h)²+(y−k)²= r²

x² + y² – 2x + 8y – 47= 0

x² - 2x + y² + 8y - 47 = 0

x² - 2*x *1+ 1 ²- 1² + y² + 2*4*y + 4² - 4² - 47 = 0

(x - 1)² + (y + 4)² - 1 - 16 -47 =0

(x - 1)² + (y + 4)² - 64=0

(x - 1)² + (y + 4)² = 8²

Radius is 8.

The radius of the circle is 8 units

The radius of a circle is a line drawn from the center to the circumference of the circle

The equation of the circle is given as;

[tex]x^2 + y^2 - 2x + 8y - 47 = 0[/tex]

Rewrite the equation as:

[tex]x^2 - 2x + y^2 + 8y = 47[/tex]

Next, we rewrite the equation in the standard form

So, we have:

x^2 - 2x + 1^2 - 1^2 + y^2 + 8y + 4^2 - 4^2 = 47

Evaluate the exponents

x^2 - 2x + 1 - 1 + y^2 + 8y + 16 - 16 = 47

Rewrite the equation as follows:

x^2 - 2x + 1 + y^2 + 8y + 16 = 47 + 1 + 16

Express as perfect squares

(x - 1)² + (y + 4)² = 64

(x - 1)² + (y + 4)² = 8^2

The radius of the circle is calculated as:

r^2 = 8^2

By comparison, we have:

r = 8

Hence, the radius of the circle is 8 units

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Answer:

(-1,-2)

Step-by-step explanation:

[tex]6x-y=-4\\y=6x+4\\y=6(-2)+4=-8\\y=6(-1)+4=-2\\y=6(0)+4=4[/tex]

so the only one is (-1,-2)

Answer:

Initial amount (a)= 620

Growth factor (b)= 7.8

Step-by-step explanation:

620 is the initial amount and is multiplied by 7.8 x which is the growth factor.