10√1/5 find the mixed surd..
​

The value of q is 0.35.

The value of p is 0.16.

The value of r is 0.27.

The value of P(A given NOT B) is approximately 0.4211.

To calculate the values of p, q, and r, we can use the information provided in the Venn diagram and the probabilities of events A and B.

Given:

P(A) = 0.43

P(B) = 0.62

P(A∩B) = 0.27

Calculating the value of p:

The value of p represents the probability of event A occurring without event B. In the Venn diagram, p corresponds to the region inside A but outside B.

We can calculate p by subtracting the probability of the intersection of A and B from the probability of A:

p = P(A) - P(A∩B)

= 0.43 - 0.27

= 0.16

Therefore, the value of p is 0.16.

Calculating the value of q:

The value of q represents the probability of event B occurring without event A. In the Venn diagram, q corresponds to the region inside B but outside A.

We can calculate q by subtracting the probability of the intersection of A and B from the probability of B:

q = P(B) - P(A∩B)

= 0.62 - 0.27

= 0.35

Therefore, the value of q is 0.35.

Calculating the value of r:

The value of r represents the probability of both event A and event B occurring. In the Venn diagram, r corresponds to the intersection of A and B.

We are given that P(A∩B) = 0.27, so the value of r is 0.27.

Therefore, the value of r is 0.27.

Finding the value of P(A given NOT B):

P(A given NOT B) represents the probability of event A occurring given that event B does not occur. In other words, it represents the probability of A happening when B is not happening.

To calculate this, we need to find the probability of A without B and divide it by the probability of NOT B.

P(A given NOT B) = P(A∩(NOT B)) / P(NOT B)

We can calculate the value of P(A given NOT B) using the provided probabilities:

P(A given NOT B) = P(A) - P(A∩B) / (1 - P(B))

= 0.43 - 0.27 / (1 - 0.62)

= 0.16 / 0.38

≈ 0.4211

Therefore, the value of P(A given NOT B) is approximately 0.4211.

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Given the Trigonometric Functions:

Using your calculator you get:

By definition, Secant is negative in Quadrant III.

Finds its Reference Angle as follows:

Because:

Then, you get:

Notice that:

Then, you can conclude that it is in Quadrant II.

Therefore its Reference Angle is:

So you can set up:

By definition:

Therefore, you can rewrite it in this form:

Hence, the answer is:

The resulting graph is a circle with center at (-3,-1) and radius 3.

The graph of the equation (x+3)²+(y+1)²=9

is a circle with center at (-3,-1) and radius 3. The equation of a circle with center (a,b) and radius r is given by the equation (x-a)² + (y-b)² = r². By comparing the given equation with the standard equation of a circle, we can easily see that the center of the circle is (-3,-1) and the radius is 3. To graph a circle, we need to first plot the center of the circle, which is (-3,-1) in this case. Next, we need to mark the radius of the circle, which is 3 units. We can do this by measuring 3 units from the center in any direction and marking the point. Since the radius of the circle is the same in all directions, we can repeat this process for other directions to get points on the circumference of the circle. We can use a compass to make this process easier. After plotting a sufficient number of points, we can draw a smooth curve passing through all the points to obtain the graph of the circle.

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Answer: 3/4 mile

Step-by-step explanation:

To find the answer, you divide 1/2 by 2/3. You do KCC so it turns into 1/2 x 3/2. The final answer is 3/4.

So we know that Robin ran 1/2 of a mile and he finish 2/3 of the race.

To find the answer, you divide 1/2 by 2/3.

You do keep change change, so it turns into 1/2 x 3/2 which is 3/4.

Final result: 3/4

It would take 10 men approximately 7.2 hours to dig the hole if they work at the same rate.

To find out how long it would take 10 men to dig the same hole if they work at the same rate, we can use the concept of man-hours.

We are given that 8 men can dig the hole in 9 hours.

This means that the total man-hours required to complete the task is 8 men \(\times\) 9 hours = 72 man-hours.

Since the number of men has increased to 10, we need to determine the new time it would take for them to complete the task at the same rate.

If we assume that the work rate remains constant, the total man-hours required to dig the hole would still be the same, which is 72 man-hours.

To find the new time, we divide the total man-hours by the number of men:

72 man-hours / 10 men = 7.2 hours.

Therefore, it would take 10 men approximately 7.2 hours to dig the hole if they work at the same rate.

Note: It's important to keep in mind that this calculation assumes a linear relationship between the number of men and the time taken.

In practice, other factors such as coordination and efficiency may come into play, potentially affecting the actual time required.

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The average rate of change for the interval from x =  7 to x =  8 is 35.  

To calculate the average rate of change for the interval from x =  7 to x =  8, we need to find the difference in y- values and divide it by the difference inx-values within that interval.

Let's calculate it step by step using the given table  

For the interval from x =  7 to x =  8  x1 =  7, y1 = -37  x2 =  8, y2 = -2   Difference in y- values Δy =  y2- y1 = -2-(- 37) =  35  

Difference inx-values Δx =  x2- x1 =  8- 7 =  1  

Average rate of change =  Δy/ Δx =  35/ 1 =  35  

Thus, the average rate of change for the interval from x =  7 to x =  8 is 35.   Note: It's important to mention that the values calculated then are grounded solely on the given data. Please  insure you  corroborate the  delicacy of the  handed data and  environment before using the answer in any important or critical  operations.

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Answer:

2%

Step-by-step explanation:

Probability of rain, P(R) = 0.2

Probability of leak Given that it rains, P(L|R) = 0.1

Probability of leak Given that it does not rain, P(L|R') = 0

According to Baye's Rule:

P(L) = [P(L|R) * P(R)] + [P(L|R') * P(R')]

P(R') = 1 - P(R) = 1 - 0.2 = 0.8

P(L) = [0.1 * 0.2] + [0 * 0.8]

P(L) = 0.02 + 0

P(L) = 0.02

Hence, probability of a roof leak on Thursday is 0.02 = (0.02 * 100%) = 2%

Answer:

A=46 degrees, B=33.4 degrees, C=100.6 degrees

a=34, b=27, c=48.2

Step-by-step explanation:

(a/sin(A)) = (b/sin(B)) = (c/sin(C))

we are given

(34/sin(46)) = (27/sin(B))

34sin(B) = 26sin(46)

34sin(B) = 18.702834809

sin(B) = 0.550083377

note use inverse sin function to find angle B

B = 33.372733167 approx 33.4 degrees then

C = 180 - (46 + 33.4) = 100.6

Then, (b/sin(B)) = (c/sin(C))

27/0.550083377 = c/0.982935349

0.550083377 * c = 27 * 0.982935349

0.550083377 * c = 26.539254427

c = 48.245876056 approx 48.2 .

Lastly, you get: A=46 degrees, B=33.4 degrees, C=100.6 degrees

a=34, b=27, c=48.2

Answer:

43.6 has 3 significant figures.

A reflection over a line l  moves every point P  of the plane to the point P ′  on the perpendicular from  P to the line l and on the same distance from l .

If the line is the  x  -axis, a point P  =  ( p 1   p 2 )  moves to the point  P ′  =  ( p 1 , − p 2 ) .

The image of the triangle A B C  is the triangle  A ′ B ′ C ′ with  B ′  =  ( 9 , − 5 )

Answer: 30(x-5)

Explanation:

$30 per overtime hours,

30*(x-5)

The probability of a defect is 5.7330 x \(10^{-5}\) and the number of defects is 5.73.

To calculate the probability of a defect, we need to find the area under the standard normal curve that lies outside of the process control limits of 9.75 ounces and 10.25 ounces. We can use the standard normal distribution table to find this area.

First, we need to standardize the weight limits as follows -

\(Z_{lower}\) = (9.75 - 10) / 0.25 = -4

\(Z_{upper}\) = (10.25 - 10) / 0.25 = 4

Next, we will find the area under the standard normal curve that lies outside of these limits as follows -

P(Defect) = P(Z < -4) + P(Z > 4)

Using a standard normal distribution table, we can find that P(Z < -4) = 2.8665 x   \(10^{-5}\)  and P(Z > 4) = 2.8665 x  \(10^{-5}\) .

So, the total probability of a defect is -

P(Defect) = 2.8665 x  \(10^{-5}\)  + 2.8665 x  \(10^{-5}\)  = 5.7330 x  \(10^{-5}\)

Finally, we will find the number of defects for a 1,000-unit production run as follows -

The number of defects = 1000 * 5.7330 x  \(10^{-5}\)  = 5.73 (rounded to the nearest whole number).

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Answer:

10

Step-by-step explanation:

The common ratio of the geometric sequence 10,60, 360,... is 6.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, A geometric sequence 10,60, 360,...

We know the common ratio r in a geometric sequence is

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Therefore,

The common ratio in this geometric sequence  10,60, 360,... is,

= 60/10 = 360/60 = 6.

So, The common ratio is 6.

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Using matrices the simultaneous equation is solved to get x = 3 and y = 5

This method required finding determinants in three occasions then dividing

The given equation

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right]= \left[\begin{array}{c}19\\8\\\end{array}\right]\)

the determinant is

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right]\)

3 * 1 - 2 * 1 = 3 - 2 = 1

Solving for x

determinant while replacing x values

\(\left[\begin{array}{cc}19&2&\\8&1\\\end{array}\right]\)

19 * 1 - 2 * 8 = 19 - 16 = 3

solving for x = 3/1 = 3

Solving for y

determinant while replacing y values

\(\left[\begin{array}{cc}3&19&\\1&8\\\end{array}\right]\)

3 * 8 - 19 * 1 = 24 - 19 = 5

solving for y = 5/1 = 5

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Answer:

Option A: $44746

Step-by-step explanation:

Step 1:

6.95% of $51000 = 3544.5

Federal & state Tax = $2250 + $460 = $2710

Total tax deducted = 3544.5 + 2710 = $6254.5

So,

$51000 - $6254.5 = $44,746.

After solving the Algebraic Expression 2(x + 8)= 2x + 8, we will get x∈∅. Variable x is dissolved in itself, making it impossible to find its value.

Before moving to solve the equation , let's learn how to solve any algebraic expression:

Step 1: Determine whether the Distributive is necessary.

Property. If so, spread the word!

Step #2: Group similar terms together on either side of the equals symbol.

(meaning: combine all of the similar factors AND

Add up each and every integer (number).

Step #3: Align the variables so that they are all to one side of the equals symbol.

utilizing the inverse process. REMEMBER: No matter what you do

You MUST do to the other side of the equals sign what you did to the one side.

equals (symbol).

Fourth Step: When all of your variables are situated on the same side of the

You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:

fourth Step: When all of your variables are situated on the same side of the

You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:

You MUST do anything you do to one side of the equals sign.

the reverse of the equals symbol).

Step #5: Using the variable's ALONE state, isolate it

the opposite process. DO NOT FORGET: No matter what you do to one

You MUST change the other side of the equals symbol to the equals symbol

Given:

2(x + 8)= 2x + 8

2 × x + 2 × 8= 2x + 8

2x+16= 2x+ 8

16= 8

So, x∈∅.

In this equation , the value of x could not be find because variable x is dissolved in itself.

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Answer:

4i ,2i√6

Step-by-step explanation:

√-16

so we know that negatives can be square rooted....

However imaginary numbers exist

and i which is imaginary numbers symbol is equal to

i^2=-1

i= √-1

You can show the number in two parts (imaginary number and real part)

so the 16 is the real part and the -1 is imaginary

so now we can simplfiy the two radicals

√16 x √-1

4 x i

4i

Again

√24 √-1

√4 x √6 x √-1

√4 x √6 x √-1

2 x √6 x i

2i√6

Answer:

Step-by-step explanation:

8) a) In a parallelogram, opposite sides are equal and parallel.

               BC = AD

         12x - 1 = x  + 21

         12x      = x + 21  + 1

              12x = x + 22

         12x - x = 22

                11x = 22

                  x = 22 ÷ 11

                 x = 2

AD = x + 21

     = 2 + 21

AD = 23

In a parallelogram, adjacent angles are supplementary.

   ∠A + ∠D = 180°

\(\sf y - 9 + \dfrac{y}{2}=180\\\\ \dfrac{2y}{2}+\dfrac{y}{2}=180+9\\\\\)

        \(\dfrac{3y}{2}=189\\\\y =189*\dfrac{2}{3}\\\\y=63*2\\\\y = 126\)

∠D = 126 ÷2

     = 63

In parallelogram, opposite angles are congruent.

 ∠B = ∠D

   ∠B = 63°

Answer:

Scale factor of dilation is \(\frac{1}{3}\)

Step-by-step explanation:

\(\\\frac{QR}{Q'R'} = \frac{6}{2} \frac{QR}{Q'R'} = 3\)

Cross multiplication gets:

QR = 3 * Q'R'

Q'R' = 1/3 * QR

So it's 1/3

The value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

To perform the calculation and express the answer in standard form, follow these steps:

Multiply 0.045 by 2.05:

0.045 × 2.05 = 0.09225

Divide the result by 0.0025:

0.09225 / 0.0025

= 36.9

Convert the answer to standard form by writing it as a decimal multiplied by a power of 10:

36.9 = 3.69 × 10

Therefore, the value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

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Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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the answer to this question would be 3g-2 because you need to use functions and function notation

Answer:

Problematic is that - only one factor should be analysed at a time. However she has considered both.

Step-by-step explanation:

Groups for any experimental study should be selected on the basis of one variable, other factor(s) remaining constant.

In this case, here are two variables - lights on or off, music playing or not playing - effecting relax level during exams.

She selects 10 students for exam with lights off , 10 for exam without music. This is problematic, as at once only lights or only music factor should be considered.

If one group is with light on , other should be with light off. If one group is with music, other should be without music. This mix up of one light off aspect & one music without music is inapt.

Your analysis is correct. Here's a summary:

If it is sunny, then it is 80° Fahrenheit. (Original statement)

Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)

If it is not sunny, then it is not 80° Fahrenheit. (Original statement)

Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)

Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)

Counterexample: A day that is 80° Fahrenheit and cloudy.

In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").

Answer:

F. 4d + h + 2f

Step-by-step explanation:

have a good day!

Answer:

F. 4d + h + 2f

Step-by-step explanation:

There are 4 drinks (4d)

2 Fries (2f)

And 1 Hamburger (h)

Answer:

Step 2 is wrong. It's 16n-14. Not -16n+14.

Step-by-step explanation:

Do -16n+14, then add both sides.

16n=-14+18

16n+14n= -14n+18+14n

30n=18

30n/30 18/30

n=3/5

Based on an equation, the amount that Isabel spent on bread was $2.42.

To solve the equation for the amount spent on bread, we determined the total amount Isabel spent by subtracting the change from the total bills she had.

An equation is a mathematical statement of the equality or equivalence of two or more mathematical expressions.

The amount Isabel spent on vegetables = $15.91

The amount she spent on fruits = $11.22

Let the amount she spent on bread = x

The total amount she went with = $30 (3 x $10)

The change she got after giving the cashier $30 = $0.45

The total amount Isabel spent for vegetables, fruits, and bread = $29.55 ($30.00 - $0.45)

x = $2.42 ($29.55 - $15.91 - $11.22)

Check:

Vegetables = $15.91

Fruits = $11.22

Bread = $2.42

Total expenses = $29.55

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Answer: 80%

Step-by-step explanation:

divide 120 by 150 and you get .8 then you move the decimal over 2

The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

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