a sample of 400 observations will be taken from an infinite population. the population proportion equals 0.8. find the probability that the sample proportion will be greater than 0.78.

By using some exponent properties we will get:

2*(1/b)^15

Remember that the product of exponents can be written as:

(a^x)*(a^y) = a^(x*y)

In this case, we have the expression:

2*b^(-1.5)*b^10

Using the above property we can rewrite:

2*b^(-1.5)*b^10 = 2*b^(-1.5*10) = 2*b^(-15)

And a negative exponent means that we need to take the inverse of the base, then:

2*b^(-15) = 2*(1/b)^15

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Value of angle T is 60°, angle U is 60°, TS is 13 cm and SU is 22.49 cm.

Given in question,

Triangle STU,

TU = 13 cm

∠S = 60°

ST = TU

    = 13 cm

∠U = ∠S    (Their sides are equal)

     = 60°

∠S + ∠T + ∠U = 180°

60 + ∠T + 60 = 180

      ∠T + 120 = 180

                ∠T = 180 - 120

                      = 60

Hence, ∠T is 60°.

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The solution to the inequality expression is f >-3

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

-2f - 3.7 < 2.3

Add 3.7 to both sides of the expression

This gives

-2f < 6

Divide both sides of the expression by -2

So, we have the following representation

f >-3

Hence, the solution is f >-3

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506.433 minutes elapse before the minute hand next points in the same direction as the hour hand.

Conversion of hours to minute:

As we all know, an hour is made up of sixty minutes, therefore

1 hour=60minutes

Thus, all you need to do to convert time from hours to minutes is to multiply the time in hours by 60 to get the time in minutes.

If you want to convert minute to hours divide the given time in minutes by 60.

The hands line up 11 times every 12 hours, or roughly every 1:05.5 hours; the precise number is 1:05.4545 repeating.

The repetition time is 8:43.6363. When expressed in seconds, the result is 8:43:38.1818 repeating, or 8:43:38 and 2/11.

This is 261 and [tex]\frac{9}{11}[/tex] degrees, or 261.818 repeated.

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Joseph removes 5/8 gallon of white paint from a can.The amount of paint in the can  = - 2.8 gallons

Step-by-step explanation:

Let X be the starting amount of paint in the can, in gallons.

"Removes 5/8 gallon" can be written -(5/8)gal

"Adds 3/8 gallon" becomes +(3/8)gal

The result is :  X - (5/8)gal + (3/8)gal = Remaining Paint (gallons)

Consolidating:  Remaining (gallons) = X - (2/8)gal

If we want the overall increase/decrease, subtract the initial volume:

Initial - Remaining = Change in amount of paint in can

Change =  (X-(2/8)gal) - X = - (2/8) gallons

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Answer:

Step-by-step explanation:

so use the properties of powers, recall that powers like [tex]x^{2^{2} }[/tex] is the same as [tex]x^{2} *x^{2}[/tex] which can also be written as  [tex]x^{2*2}[/tex] = [tex]x^{4}[/tex].

I want to make this clearer.

[tex]x^{3^{3} }[/tex] = [tex]x^{3}[/tex]  * [tex]x^{3}[/tex] * [tex]x^{3}[/tex]  = [tex]x^{3*3*3}[/tex] =[tex]x^{27}[/tex]

I'm not sure if that's making it clearer or not.

so for your question  of  [tex](8x^{6}) ^{2/3}[/tex]  we can rewrite it to look like the above multiplication of powers

[tex]8x^{6*(2/3)}[/tex]

[tex]\frac{6}{1}[/tex] * [tex]\frac{2}{3}[/tex] = [tex]\frac{12}{3}[/tex]  = 4

[tex]8x^{4}[/tex]

The first step in simplifying is to apply that outer exponent of [tex]\frac{2}{3}[/tex] to each factor inside the parentheses.

      [tex]\left(8\cdot x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3}[/tex]

Now using the concept that [tex](a)^{m/n} = \sqrt[m]{a^n}[/tex] for positive real numbers a and integers m and n, we can evaluate the first part:

       [tex](8)^{2/3} = \sqrt[3]{8^2} = \sqrt[3]{64} =4[/tex]

For the second part, we use the power-to-a-power rule, that says [tex](a^m)^n = a^{m\cdot n}[/tex]:

    [tex]\left(x^6\right)^{2/3} = x^{6\cdot \frac{2}{3}} = x^4[/tex]

Putting that all together, we have

    [tex]\left(8 x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3} = 4x^4[/tex]

Answer:

[tex]y=-7x+6[/tex]

Step-by-step explanation:

1 ) Our given equation is [tex]Y\left(x\right)+8=-7\left(x-2\right)[/tex]

2 ) We can now graph this equation ( desmos is a good online graphing calculator ). The graph is shown in the attachment...

3 ) Now that the equation has been graphed we can see that the slope intercept form is [tex]y=-7x+6[/tex]

Hope this helps! :)

The values of m<1, m<2, m<3, m<4, m<5, m<7, m<8 are given by 49, 131, 49, 131, 49, 49, 131 respectively.

Given the measure of angle 6 is 131.

We can see that from the figure, angle 6 and angle 2 are corresponding angles and angle 6 and angle 4 are alternative angles.

So, angle 2 = angle 6 = 131

angle 4 = angle 6 = 131

Since angle 1 and angle 4; angle 2 and angle 3 are Linear pairs. So.

angle 3 = 180 - angle 2  = 180-131 = 49

angle 1 = 180 - angle 4 = 180-131 = 49

Since, angle 1 and angle 5; angle 4 and angle 8; angle 3 and angle 7 are corresponding angles to each other.

angle 5 = angle 1 = 49

angle 7 = angle 3 = 49

angle 8 = angle 4 = 131

Hence the values of m<1, m<2, m<3, m<4, m<5, m<7, m<8 are given by 49, 131, 49, 131, 49, 49, 131 respectively.

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The line of best fit for the data presented in the scatterplot is y = 0.5x. (Option B)

A line of best fit represents a straight line that is the best approximation of the given set of data used to examine the nature of the relation between two variables. It is an educated guess about where a linear equation might fall in a set of data plotted on a scatter plot. The slope-intercept form of a linear equation is given by y = mx + b where m is the slope of the line and b is the y intercept of the graph. For any two points (x1, y1) and (x2, y2), the slope is given by:

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

Choosing two points from the line say (180, 90) and (220,110),

m = (110 – 90)/(220 – 180) = 20/40 = 0.5

Hence, y = 0.5x + b

Substituting a point from the graph into the equation say (240, 120)

120 = 0.5(240) + b

120 = 120 + b

b = 0

Hence, the equation is y = 0.5x

Note: The question is missing the scatterplot (which is attached) and options which are A. y = -0.5x, B. y = 0.5x, C. y = -2x, D. y = 2x.

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The region which have strongest negative correlation is Midwest.

Given that,

From your data folder, import the states.csv dataset into rstudio. create a scatter plot with high (x-axis) and pctdemocrat (y-axis) data points that are colored according to region. Stat smooth is used

To find : Which region has the strongest negative correlation

What Is Negative Correlation?

A link between two variables known as "negative correlation" occurs when one variable rises as the other falls, and vice versa. In statistics, -1.0 denotes a perfect negative correlation, 0 denotes no connection, and +1.0 denotes a perfect positive correlation. The relationship between two variables is always absolutely opposite when there is a perfect negative correlation.

Therefore, the region which have strongest negative correlation is Midwest.

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Answer:127 degrees

Step-by-step explanation: 180-74 = 106 106+21 = 127 180-127 = 53 180-53 =127

Answer:

C

Step-by-step explanation:

(h - g)(2)

= h(2) - g(2)

= 2² + 1 - 2(2) = 4 + 1 - 4 = 1

Answer:

(2.3*10^2)(3*10^5)

in scientific notation 

Step-by-step explanation:

6.9 × 10^7

The amounts, using proportions, are given as follows:

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem from which the fraction was built.

The tip is of 20% of the total bill of $54.65, hence it's value is given as follows:

Tip = 0.2 x 54.65 = $10.93.

(because 0.2 is the decimal equivalent to the percentage of 20%, then it is multiplied by the total amount to find the desired amount).

The total cost of the meal is given by the sum of the bill of the meal plus the tip, hence:

Total Cost = 54.65 + 10.93 = $65.58.

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Answer:

ñ/3 and 3√25

Step-by-step explanation:

pi is irrational and the cube root of 25 is irrational :)

The can's minimum surface area should have a height of 8 cm and a radius of 4 cm.

Given:

The volume of closed right circular cylindrical cans = 128π cm³

As we know the volume of a cylinder = πr²h

By equating;

πr²h = 128π

h = 128/r²

To get the dimensions of a can with minimum surface area;

S = 2πrh + 2πr

Put h = 128/r²;

Therefore, S(r) = 256π/r + 2πr²

                 S'(r) =  -256π/r² + 4πr

                S''(r) = -(2*256π)/r³ + 4π

Now, for S(r) = 0;

               r = 4cm

         for S''(4) > 0 at r = 4 is minimum point.

Hence,

h = 128π/(π*4*4)

h = 8cm

Therefore, the minimum surface area of the can should have a radius of 4 cm and a height of 8 cm.

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The time that it will take Joe to catch up with Mary is; 8 hours

We are told that;

Time Mary leaves the house = 12 pm

Time that Joe leaves the house = 2 pm

Speed of Mary = 45 mi/hr

Speed of Joe = 60 mi/hr

This means that Mary had a 2 hour time lead over Joe.

Thus;

Distance is calculated from the formula;

Distance = Speed * time

Thus;

Distance covered by Mary in the 2 hours lead is;

Distance = 45 * 2 = 90 miles

Thus, time that it will take Joe to catch up with mary is;

t = 2 + (90/(60 - 45))

t = 2 + 6

t = 8 hours

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Step-by-step explanation:

look at where the dotted line is : it is vertical at x = -3.

that is automatically is equation : x = -3.

now, look at where the shaded side of that line is - to the left or to the right of the line ?

it is to the left of the line. and that message all values smaller than x = -3. but not equal indicated by the dotted line (that means the line itself is not included).

so, this is described by x < -3.

therefore, the first answer option is out.

now, look at the solid line.

what is the y-intercept (the y- value when x = 0) ?

when x = 0, the y-value is -1.

and everything to the left and below of the line is included (incl. the line itself, hence the solid line), so, the line inequality is then (just given by the available choices)

y <= -x - 1

and the 3rd answer option is therefore correct.

Answer:

[tex]\begin{cases}x < -3\\y \leq -x-1\end{cases}[/tex]

Step-by-step explanation:

When graphing inequalities:

From inspection of the given graph, there is a dashed line at x = -3 with shading under the line (to the left).

Therefore, the inequality that represents this is:  

The solid line has a negative slope.  For each decrease of 1 unit in the y-direction, the x-values increase by 1 unit.  Therefore, the slope of this line is -1.  

From inspection of the given graph, the y-intercept of the solid line is -1.

Therefore, the equation of this line is  y = -x - 1.  

As the shading is under the line, the inequality that represents this is:

Therefore, the system of linear inequalities that represents the graph is:

[tex]\begin{cases}x < -3\\y \leq -x-1\end{cases}[/tex]

Answer:

Step-by-step explanation:

Emma's age= x

Kate's age= x-12

sum of their ages=24

so Emma's age= 24-12

x=24-12

x=12

Emma's age=12

Answer:

40;100

step by step explanation:

Answer:

Step-by-step explanation:

Answer:

x = - 2 ± [tex]\sqrt{\frac{19}{3} }[/tex]

Step-by-step explanation:

3x² + 12x = 7 ← factor out 3 from each term on the left side

3(x² + 4x) = 7

to complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 4x

3(x² + 2(2)x + 4 - 4) = 7

3(x + 2)² - 12 = 7 ( add 12 to both sides )

3(x + 2)² = 19 ( divide both sides by 3 )

(x + 2)² = [tex]\frac{19}{3}[/tex] ( take square root of both sides )

x + 2 = ± [tex]\sqrt{\frac{19}{3} }[/tex] ( subtract 2 from  both sides )

x = - 2 ± [tex]\sqrt{\frac{19}{3} }[/tex]

The inequality is x ≤ 39.2. The actual number of items that can be bought is 39.

There is a set budget of $145 to buy some items. The price of each item is $3.70. We need to form an inequality for the given information and solve it.

Let the number of items be denoted by the variable "x". Then we can say that :

3.70*x ≤ 145

x ≤ 145/3.70

x ≤ 39.2

The actual number of items that can be bought must be a whole number. We will take the greatest integer less than or equal to the solution.

The actual number of items that can be bought is 39.

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Answer:

4

Step-by-step explanation:

The answer really just popped into my head.

4^2 + 4^2 = 32

4x4=16

The interest on the loan is $1200.

Given,

In the question:

You get a loan from the loan star bank to help pay for your home.

and, if you borrowed $12,000 at 10% for one year.

To find the interest on the loan.

Now, According to the question;

Based on the given conditions:
Formulate:

Borrowed= $12,000

At 10% for one year

12000 x 10%

Convert percentage into decimal

12000 x 0.1

calculate the product or quotient:

= 1200

Hence, The interest on the loan is $1200.

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Step-by-step explanation:

a) 100

b)45

trust me it will helps you

Answer:

  (-1, -8)

Step-by-step explanation:

You want the image of P(-8, 1) after rotation 90° counterclockwise about the origin.

The transformation for 90° CCW is ...

  (x, y) ⇒ (-y, x)

Then

  P(-8, 1) ⇒ P'(-1, -8)

__

Additional comment

We observe that this answer is not among the choices listed in this problem statement. We suspect a typo somewhere. The transformations represented by the given choices are ...

  A: reflection across the x-axis and rotation 90° CCW

  B: reflection across the x-axis

  C: reflection across the x-axis and rotation 90° CW

  D: reflection across the origin

These are shown in the second attachment.