If the odds in favor of an event E are a : b, then the probability of event E is?

Using z-scores, it is found that due to the higher z-score, Luna did better on the exam.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

From the two bullet points, it is found that the student who did "better" is the one whose grade has the higher z-score.

For Hazel, the parameters are given as follows:

[tex]X = 93, \mu = 80, \sigma = 8[/tex]

Hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (93 - 80)/8

Z = 1.625.

For Luna, the parameters are given as follows:

[tex]\mu = 68, X = 40, \sigma = 15[/tex]

Hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (68 - 40)/15

Z = 1.87.

Due to the higher z-score, Luna did better on the exam.

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Based on the packaging of the cookies, the number of ways you can buy 36 cookies is 12 ways.

The ways you can buy the cookies include:

In conclusion, there are 12 ways to buy the cookies.

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The yield on the corporate bond of a face value of $1000 is 7.77%.

What is the percentage discount?

The percentage discount is the discount given on a product as compared to the given discount on 100 rupees.

Given, the face value of the bond is $1000.

Discounted price of the bond is $900.

Therefore, the fixed interest on the bond for that period will be

= $1000 × 7/100 = $70.

Now, the yield on that corporate  bond = 70 × 100/900 % = 7.77% .

Hence, the yield on the corporate bond of a face value of $1000 is 7.77%.

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The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be $715.7.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

We know that the compound interest is given as

[tex]\rm A = P \left ( 1 + \dfrac{r}{n} \right ) ^{nt}[/tex]

Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.

For interest compounded monthly, the value of n is 12.

The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be

[tex]\rm A = 500 \left ( 1 + \dfrac{0.09}{12} \right ) ^{12 \times 4}[/tex]

Simplify the equation, then we have

A = 500 (1.0075)⁴⁸

A = 500 x 1.4314

A = $715.70

The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be $715.7.

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The dimensions of the rectangle are; length 63 inches and width is 20 inches.

Let 'L' be the length of the rectangle.

Let 'W' be the breadth of the rectangle.

As, the length of a rectangle is three more than triple the width.

Thus,

L = 3 + 3W

The formula for the perimeter is;

Perimeter = 2 (L+W)  

The value of perimeter is 166 inches.

Thus,

166 = 2(3 + 3W +W)

166 = 2(3 + 4W)

166 = 6 + 8W

166 - 6 = 8W

W = 20

W = width = 20 inches

L = 3 + 3W

L = 3 + 3(20)

L = 3 + 60

L = 63 inches.

Thus, the dimensions of the rectangle are; length 63 inches and width is 20 inches.

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Answer:

Step-by-step explanation:

-6+2y=10

2y=10+6

2y=16

2y/2=16/2

y=8

so the final answer of first question is y=8

The next one is

6x-2y=-10

as we got from the first question y=8 so

6x-2(8)=-10

6x-16=-10

6x=-10+16

6x/6=6/6

so the final answer is 1

Clare will have traveled 9 miles in 45 minutes.

So, Clare is riding her bike at a speed of 12 miles per hour.

Distance traveled in 45 minutes or 45/60 hours at the same speed will be = Speed Time

Therefore, Clare will have traveled 9 miles in 45 minutes.

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Answer:

x = 0

Step-by-step explanation:

Let's solve the problem,

→ (x/9) + 8 = 8

→ x/9 = 8 - 8

→ x = 0 × 9

→ [ x = 0 ]

Thus, the value of x is 0.

Step-by-step explanation:

no calculator at hand ?

f(-3.5) means that we have to replace every x in the function expression by -3.5 and then calculate.

f(-3.5) = (-3.5)² - 5(-3.5) + 6 = 12.25 + 17.5 + 6 = 35.75

Answer: 105 degrees

Step-by-step explanation:

two sides of a trapezoid add up to 180 degrees

180 - 75 = 105

The value of y' according to the given equation in the task content is; 1.

According to the task content, it follows that the equation given is; 2x³y - 3x² = 4y'.

On this note, the value of y' can be determined by substituting the given values of x and y as follows;

2(2)³×1 - 3(2)² = 4y'

16 - 12 = 4y'

y' = 4/4

y' = 1.

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the slope is represented by m

the x coordinate of the ordered pair is x1

the y coordinate of the preferred pair is y1

y-y1=m(x-x1)

The width of the rectangle = 15 yd

The length of the rectangle = 60 yd.

Perimeter of a rectangle = 2(length + width).

Given the following:

Width of the rectangle = w

Length of the rectangle = 4w

Perimeter of the rectangle = 150 yd.

Therefore:

2(4w + w) = 150

2(5w) = 150

10w = 150

10w/10 = 150/10

w = 15

Width of the rectangle = w = 15 yd

Length of the rectangle = 4w = 4(15) = 60 yd.

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Answer:

$600

Step-by-step explanation:

450 = 3/4 (because 75%=3/4)

450/3=150. 150 = 1/4, or 25%. Now it's just as simple as multiplying 150 4 times to get 100%, or the original cost, 150 times 4 equals 600. Therefore the notebooks original price is $600

Answer:

3.7517%

Step-by-step explanation:

take 3.7 and divide it by 4 to get 0.925

then apply 0.925% to x 4 times to find out the compounded rate

The distance between the school and the hospital on the map  is 8 cm

Here, we want to find the distance between the school and the hospital on the map

The scale is that 4cm to 5km

So ;

if 4 cm = 5km

Then x cm = 10km

x * 5 = 4 * 10

5x = 40

x = 40/5

x = 8 cm

Therefore the distance between the school and the hospital on the map  is 8 cm

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There are 11 scores, (N)  in the population.

The given parameters are:

Variance, s^2 = 5

Sum of squares, SS = 50

The variance of the population is calculated using

s^2 = SS/[N - 1]

So, we have

5 = 50/[N - 1}

Cross multiply

So, we have

5(N - 1) = 50

This gives

N - 1 = 10

Add 1 to both sides

N = 11

Hence, there are 11 scores, (N)  in the population.

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1. 1/2

2. 3/10

3. 2 and 3/5

4. 1 and 7/12

5. 1 and 1/3

[tex]f(x)=3x^2+3\hspace{5em}\displaystyle \lim_{h\to 0}~\cfrac{f(2+h)~~ - ~~f(2)}{h} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{f(2+h)~~ - ~~f(2)}{h}\implies \cfrac{[3(2+h)^2+3]~~ - ~~[3(2)^2+3]}{h} \\\\\\ \cfrac{[3(4+4h+h^2)+3]~~ - ~~[3(4)+3]}{h}\implies \cfrac{[(12+12h+3h^2)+3]~~ - ~~[15]}{h} \\\\\\ \cfrac{[12h+3h^2+15]~ - ~~[15]}{h}\implies \cfrac{12h+3h^2}{h}\implies \cfrac{h(12+3h)}{h}\implies 12+3h \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{h\to 0}~\cfrac{f(2+h)~~ - ~~f(2)}{h}\implies \lim_{h\to 0}~12 + 3h\implies 12+3(0)\implies \text{\LARGE 12}[/tex]

Answer:

5/8 of pizza left

Step-by-step explanation:

The value of x in the equation x = [a^2 + a^2]/[ab + 1] is [2a^2]/[ab + 1]

Equations are mathematical expressions that are represented by the equal to or equality sign i.e =

Examples of equations are:

a + b = c

y = mx + c

Ax + By = C

y = ax^2 + bx + c

y =  x

The equation is given as

x = [a^2 + a^2]/[ab + 1]

To start with, we evaluate the like terms i.e. we add a^2 and a^2

This is represented as

a^2 + a^2 = 2a^2

Substitute 2a^2 for a^2 + a^2 in the given equation

So, we have

x = [2a^2]/[ab + 1]

The above equation cannot be further simplified

Hence, the value of x in the equation x = [a^2 + a^2]/[ab + 1] is [2a^2]/[ab + 1]

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The value of integral ₀∫¹ ( eˣ - 2 )² dx is 8 + ( e² - 1) / 2 - 4e.

When infinitesimal data are combined, notions such as displacement, area, and volume can be created. An integral assigns numbers to functions in a way that describes these concepts. Integration is the action of locating integrals.

Consider the integral expression,

₀∫¹ ( eˣ - 2 )² dx

Using ( a + b )² = a² + b² + 2ab

[tex]\int_0^{1}( e^{x} - 2 )^{2} dx = \int_0^{1}(e^{2x}+4-2e^{x})dx[/tex]

[tex]\int_0^{1}( e^{x} - 2 )^{2} dx = \int^0_{1}e^{2x} dx +\int_0^{1}4 dx - \int_0^{1}4e^{x} dx[/tex]

Now, integration of eˣ is eˣ + c where c is constant.

Therefore,

[tex]\int_{0}^{1} ( e^{x} - 2 )^{2} dx = [ \frac{e^{2x}}{2} ]_0^{1} + [ 4x ]_0^{1} - [ 4e^{x}]_0^{1}[/tex]

₀∫¹ ( eˣ - 2 )² dx = ( e² / 2 - e⁰/2 ) + ( 4 - 0 ) - ( 4e¹ - 4e⁰ )

₀∫¹ ( eˣ - 2 )² dx =  e² / 2 - 1/2 + 4 - 4e + 4

₀∫¹ ( eˣ - 2 )² dx = e² / 2 - 4e + 8 - 1/2

₀∫¹ ( eˣ - 2 )² dx =  = 8 + ( e² - 1) / 2 - 4e

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Answer:

97

Step-by-step explanation:

To find x² + y², use the identity (x - y)² = x² + y² - 2xy.

(x - y)² = x² + y² - 2xy

Substitute xy = 36 and x - y = 5 in the above formula,

   5²    =  x² + y² - 2*36

 25     = x² + y² - 72

Add 72 to both sides,

25 + 72 = x² + y²

x² + y² = 97

Answer: 2x²-4x-16

Step-by-step explanation:

[tex](2x+4)(x-4)=\\2x(x)+2x(-4)+4(x)+4(-4)=\\2x^2-8x+4x-16=\\2x^2-4x-16[/tex]

Answer:

the answer would be x=8

Step-by-step explanation:

6×4=24

24/3=8

The domain and range of the function is -3 ≤ x < 7 and -7 ≤ x < 6 respectively.

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

For domain :-

Since, the domain is the set of all allowed x inputs of a function.

The smallest x can get is x = -3 as shown by the left-most point.

The largest x can get is x = 7, though we can't actually reach this value due to the open hole at the right-most point.

The interval of all possible x values is -3 ≤ x < 7  which converts to the interval notation [-3, 7)

We use a square bracket to include the endpoint and a parenthesis to exclude the endpoint.

We can say "x is any number between -3 and 2, including -3 but excluding 2".

For range :-

Since, the range is the set of all allowed y inputs of a function.

The smallest x can get is x = -7 as shown by the left-most point.

The largest x can get is x = 6, though we can't actually reach this value due to the open hole at the right-most point.

The interval of all possible x values is -7 ≤ x < 6  which converts to the interval notation [-7, 6)

We use a square bracket to include the endpoint and a parenthesis to exclude the endpoint.

Hence, the domain and range of the function is -3 ≤ x < 7 and -7 ≤ x < 6 respectively.

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The condition that will create a biased estimator of a population parameter is D. The expected value of the estimator is not equal to the population parameter.

It should be noted that a parameter is a descriptive measure applied to a whole population. There are numerous population parameters exist. For instance, the population size (N) is one parameter.

For T(x) to be an unbiased estimator of population parameter, it is necessary that the expected value of the estimator is equal to population parameter.

Therefore, the condition that will create a biased estimator of a population parameter is that the expected value of the estimator is not equal to the population parameter.

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