How do you write 2.74 x 10 to the negative 3rd power in standard notation?

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 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:

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.

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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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:

$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

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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Answer:

5/8 of pizza left

Step-by-step explanation:

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]

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

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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Based on the information given, it can be deduced that the chart that is being described is the OHLC chart.

A statistical graph or chart is defined as the pictorial representation of statistical data in graphical form. The statistical graphs are used to represent a set of data to make it easier to understand and interpret statistical information.

It should be noted that an open-high-low-close chart (OHLC) chart simply means a type of chart that's used to illustrate the movements in the price of a financial instrument for a particular period of time.

The vertical line on the chart illustrates the price range over a unit of time. It's useful in assessing volatility as it shows the full price range of the period.

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Answer:

Step-by-step explanation:

[tex]\displaystyle\\ x^8-\frac{1}{81} \\\\x^8-\frac{1}{3^4} =\\\\x^8-(\frac{1}{3})^4 =\\\\x^{4*2}-(\frac{1}{3})^{2*2}= \\\\(x^4)^2-((\frac{1}{3} )^2)^2=\\\\(x^4-(\frac{1}{3})^2)(x^4+(\frac{1}{3} ) ^2)=\\\\(x^{2*2}-(\frac{1}{3})^2)(x^4+\frac{1^2}{3^2} )=\\\\((x^2)^2-(\frac{1}{3})^2)(x^4+\frac{1}{9})=\\\\(x^2-\frac{1}{3} )(x^2+\frac{1}{3})(x^4+\frac{1}{9})[/tex]

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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Answer:

the answer would be x=8

Step-by-step explanation:

6×4=24

24/3=8

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 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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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]

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:

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

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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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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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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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 domain of the function is all the real numbers and the range is from -2 to 2.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

In the image, we can see that the value of the function varies from -2 to 2 at all the possible values of the real numbers.

Therefore, the domain of the function is all the real numbers and the range is from -2 to 2.

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