A large bank vault has several automatic burglar alarms. The probability is 0.55 that a single alarm will detect a burglar.(a) How many such alarms should be used to be 99% certain that a burglar trying to enter is detected by at least one alarm? (Enter the smallest number of alarms needed to be at least 99% certain.) ___alarms(b) Suppose the bank installs eight alarms. What is the expected number of alarms that will detect a burglar?___ alarms

The derivative of f(x) + g(x) is cosx+2cos2x

Derivative : In mathematical calculus, the derivative is the rate of change of a function at a instant point.

Derivative of a function is denoted by dy/dx, where derivative of y is happening with respect to x.

We have to add f(x) and g(x), then differentiate the whole addition with respect to x.

Given that, f(x) = sin(x) & g(x) = sin(2x)

So, f(x) + g(x) = sin(x) + sin(2x)

Now, differentiating with respect to x we get,

(f(x)+g(x))' = d/dx(sinx) + d/dx(sin 2x)

               = cosx+2cos2x

Derivative of  f(x) + g(x) = cosx+2cos2x

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The solution to the system of equations is ( 1 , -1 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

y = -6x + 5   be equation (1)

Let the second equation be represented as B

Now , the value of B is

y = x - 2   be equation (2)

On simplifying the equations , we get

Substitute the value of y from equation (2) in equation (1) , we get

x - 2 = -6x + 5

Adding 6x on both sides of the equation , we get

7x - 2 = 5

Adding 2 on both sides of the equation , we get

7x = 7

Divide by 7 on both sides of the equation , we get

x = 1

Substitute the value of x in equation (2) , we get

y = 1 - 2

y = -1

Hence , the value of x and y is 1 and -1 respectively

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Answer:

(137.75 - 15.25)/24.5=x

122.5/24/5=x

5=x

x= number of friends who can go to the amusement park

Step-by-step explanation:

137.75 is the total amount of money.

First, we need to subtract 15.25 because this money is going to be spent on parking.

Once we have our total after subtracting 15.25, all we need to do is divide that number by 24.5 to see the number of people who can go to the amusement park.

Hope this helped!

By solving a linear equation we will see that 5 people can go to the amusement park.

We know that the friends have $137.75, and the parking costs $15.25, so after paying the parking they have:

$137.75 - $15.25 = $122.50

Now we know that each ticket costs $24.50, so if the friends pay for x tickets they will have y money left, given by the linear equation:

y = $122.50 - $24.50*x

To see the number of people that can go to the amusement park we need to solve the above equation for y = $0 (the case where they use all the money).

$0 = $122.50 - $24.50*x

$24.50*x = $122.50

x = $122.50/$24.50 = 5

So with that amount of money, 5 people can go to the amusement park.

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Answer:

1unit scale on map is equal to 100.16 km in real life

Step-by-step explanation:

since in map 12.cm =1262km in real life

1cm=(1262/12.6) km

therefore it gives us 100.158km which is approximately 100.16 km .

Answer:

multiply 6:8 by 2

12:16

If m = -5 or m = 3, the system of linear equations has no solution.

To determine the values of m for which the system of linear equations has no solution, we need to check the determinant of the coefficient matrix, which is:

| 3 m |

| m+2 5 |

The determinant is

=  (3 x 5) - (m x (m+2))

= 15 - m^2 - 2m

= -(m^2 + 2m - 15)

= -(m+5)(m-3)

So, for the system to have no solution, the determinant must be zero, so we have:

-(m+5)(m-3) = 0

This gives us two values of m: m = -5 and m = 3.

Thus, if m = -5 or m = 3, the system of linear equations has no solution.

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The Answers for the four parts are

a)  5-9+7-6=-3

b) -8 + 12-9-2=-7

c) 10-3-5 + 11 =13

d)  −2+2+7+8= 15

Integers come in three types:

Given:

a)  5-9+7-6

= -4 +7-6

= 3-6

=-3

So, the value of 5-9+7-6 is (-3).

b) -8 + 12-9-2

= 4-9-2

= -5-2

=-7

So, the value of -8 + 12-9-2 is (-7).

c) 10-3-5 + 11

= 7-5+11

= 2+11

=13

So, the value of  10-3-5 + 11 is (13).

d)  −2+2+7+8

= 0+7+8

= 7+8

= 15

So, the value of −2+2+7+8 is (15).

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The Translation of the Attached Question:

Solve as in the example

The answer is net three

Answer:

It is 3

Step-by-step explanation:

THE ANSWER IS NET 3

Answer: 42 pieces of gum

Step-by-step explanation: 2x+4=88

The operation that will result in a trinomial for the given expression is subtraction operator ( - ).

A trinomial is an algebraic expression that has three terms. It is also a polynomial consisting of three terms or monomials.

The given polynomial expression;

( 4x⁵ - 8x ) ?  (3x² - 8x + 9 )

To simplify the given polynomial expression into trinomial, we will use the following operation.

The chosen operation will be such that, we will have only three terms left after simplification.

So we will choose subtraction operator "-"

( 4x⁵ - 8x ) -  (3x² - 8x + 9 )

= 4x⁵ - 8x  - 3x² + 8x - 9

simplify further; (-8x and +8x will cancel out)

= 4x⁵ - 3x² - 9

Finally, we have our desired trinomial as 4x⁵ - 3x² - 9.

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Answer:

$49.72

Step-by-step explanation:

First, you need to apply the 10% discount:

65 x 0.1 = 6.5

65 - 6.5 = 58.5

Then, apply the 15% discount to the new price:

58.5 x 0.15 = 8.775

58.5 - 8.775 = 49.72

To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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Answer:

Step-by-step explanation:

H=2/3

Answer:

one real solution

Step-by-step explanation:

:)

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         \(\boxed{b= 1}\)

    Equation of line in slope-intercept form:

                  \(\boxed{\bf y = x + 1}\)      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

\(\sf{y-y_1=m(x-x_1)}\)

Slope is 1 so

\(\sf{y-y_1=1(x-x_1)}\)

Simplify

\(\sf{y-y_1=x-x_1}\)

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

\(\sf{y-(-2)=x-(-3)}\)

Simplify

\(\sf{y+2=x+3}\)

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

\(\sf{y=x+1}\)

Answer:

Step-by-step explanation:

Sample space is 36C4

Now, we want to know all of the combinations that have 1 digit in it.

So, we can have one here:

1XXX

X1XX

XX1X

XXX1

But we have 10 different digits to choose from. So, we need to introduce the combination term, nCr, where n is a list of all digits and r is how many we want.

Since we only want one, we will need 10C1 for the number of digits. But we need to choose three lowercases, so it becomes 10C1 × 26C3

Since it's a probability question, we need to divide that by our sample space, 36C4, and our percentage becomes 44%

Answer:

28%

Step-by-step explanation:

It is not 44%. I put that and it was wrong.

Answer:

b = 25 degrees

c = 81 degrees

d = 64 degrees

Answer:

D. If two planes intersect, their intersection is a point.

Step-by-step explanation:

Let's verify the answer choices:

A. Given any two distinct points, there is exactly one line that contains them.

B. Every plane contains at least three points that do not lie on the same line.

C. If two points lie in a plane, the line containing these points also lies in the plane.

D. If two planes intersect, their intersection is a point.

Answer: geometry Euclidean

Step-by-step explanation:

Mary Lou Mason's total taxes on her purchase would be $1.37.

Taxes are mandatory payments to the government that are used to fund public services such as infrastructure, education, and health care. Taxes can be direct, such as income taxes, or indirect, such as sales taxes.

Mary Lou Mason's total purchase was $19.14.

To calculate the total taxes for her purchase, we can use the following formula:

Tax = (State Sales Tax %) x (Total Purchase) + (County Tax %) x (Total Purchase)

Therefore, the total taxes for Mary Lou Mason's purchase would be:

Tax = (6.5%) x ($19.14) + (1.5%) x ($19.14)

Tax = (0.065 x 19.14) + (0.015 x 19.14)

Tax = 1.24 + 0.13

Tax = $1.37

Mary Lou Mason's total taxes on her purchase would be $1.37.

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Answer:

(A) x= -4

Step-by-step explanation:

The question requires you to find the equation of the line parallel to x=7

Line x=7 is a vertical line crossing the x-axis at x=7

A vertical line has undefined slope, no slope

However, parallel lines are those that do not meet and has the same slope. This means you should expect that the equation required should also have an undefined slope, slope of zero.

The line will pass through point (-4,1) and be a vertical line.

The equation of the line will be: x= -4

the inital equation is:

so we can simplify it so:

Answer:6/6

Step-by-step explanation:

1/6 divide 6

Keep

Flip

Change

your gonna keep 1/6 as a fraction

then flip the second fraction so 6 would’ve been 6/1 but it’s gonna flip so it should look like this 1/6

after you will change the  sign so the division will become multipliaction so it should look like 1/6 x 6/1 which will equal to 6/6

The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

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Answer: y = 5x-2

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

c.  8√(2^4 )

given 2^(4/8)  can be written as 2^(4×1/8)  

eg: 2^(1/2) is √2 hence same rule we can apply here and since 2^(1/8) we can write as 8√2 and given 2^4

further knowledge: so if asked to expand more we can write it as 8√16 simplifying this further we get 2^(1/2) which is actually √2

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