Simplify the expression, but leave it in exponential form. Two to the fourth divided by two to the seventh
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1 point
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Two cubed

One divided by two cubed

One eighth

Using the normal distribution, it is found that the z-score of the height of a women 5.5 feet tall is 0.51.

The problem asks for the z-score of the height of a women 5.5 feet tall.

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]

Considering that each feet has 12 inches, the parameters are given as follows:

[tex]X = 5.5 \times 12 = 66, \mu = 64.1, \sigma = 3.7[/tex]

Hence the z-score is:

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

Z = (66 - 64.1)/3.7

Z = 0.51.

The z-score of the height of a women 5.5 feet tall is 0.51.

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Answer: [tex]\pm3[/tex]

Step-by-step explanation:

[tex][(4(x^{2} -5)-7)/3]+6=9[/tex]

[tex]((4x^{2} -20)-7)/3=9-6[/tex]

[tex]4x^{2} -27=3*3[/tex]

[tex]4x^{2} =9+27[/tex]

[tex]x^{2}=36/4=9[/tex]

[tex]x=\sqrt{9} =\pm3[/tex]

[tex]x = 3[/tex]

Answer:

14/25

Step-by-step explanation:

Answer

Estimate each product 13.92*2.7

37.584

We can actually deduce here that considering the conditional statement and scenario, the conditional statement is false.

Conditional statement is actually known to be an if-then statement. It is usually used to show and emphasizes the relationship that exists between two ideas. This means that one idea comes as a result of the other.

Conditional statements actually helps one to make proper deductions in a clear and rigorous way.

We see here that considering the scenario that "the power went out and reset all the clocks in the house", even if alarm was set, it wouldn't ring out because all the clocks in the house were reset when the power out.

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Answer: Depth d = 767 feet.

Step-by-step explanation:

In certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth of D feet below the surface, is given by the following equation:

                               P= 13+ 5d/13

If a scientific team uses special equipment to measures the pressure under water and finds it to be 308 pounds per square foot, at what depth is the team making their measurements?

Given data,

The relationship between the pressure, p of sea water in certain deep parts of oceans is and the distance, d below the surface is given by the following equation,

                                 P= 13+ 5d/13

Where,

p is in pounds per square foot.

d is in feet

The pressure of seawater is 308 pounds per square foot at a depth

                             308 = 13+ 5d/13           (eq-1)

                             308 - 13 = 5d/13

Cross multiplying, it becomes                            

                             295 = 5d/13

                             295 * 13 = 5d

                              3,835 = 5d

                               3,835/5 = d

                                d = 767 feet

At a depth of 308 feet below the surface of the water, the pressure of seawater is,

Substitute d value in equation 1,

So, we can write,

                              P= 13+ 5d/13

                              P = 13+ 5 (767) /13

                              P = 13 + 3835/13

                              P = 13 + 295

                              P = 308 pounds per square foot.

Therefore,

                        Depth d = 767 feet.

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Answer:

x = 0, x = 5

Step-by-step explanation:

2x² = 10x ( subtract 10x from both sides )

2x² - 10x = 0 ← factor out 2x from each term on the left side

2x(x - 5) = 0

equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

x - 5 = 0 ⇒ x = 5

a) the average velocity during each time period.

(b) 0.08 cm/s is the instantaneous velocity of the particle when t = 1.

Step-by-step explanation:

Given that

                s = 5 sin(t) + 5 cos(t),

To find

                (1)[1,2]? cm/s

                (2)[1,1.1]? cm/s

                (3)[1,.101]? cm/s

                (4)[1,1.001]? cm/s

So, according to the question

a) The average velocity during each time period.

                (1)[1,2]? cm/s

                (2)[1,1.1]? cm/s

                (3)[1,.101]? cm/s

                (4)[1,1.001]? cm/s

We have the displacement equation at time t :

                s = 5 sin(t) + 5 cos(t)

Now differentiate it by t to get velocity.

               v(t) =  ds/dt

                     [tex]= \frac{d}{dt} (5sint+5cost)\\= 5(\frac{d}{dt} sint+\frac{d}{dt}cost)\\\\[/tex]

              v(t)  [tex]= 5( cost - sint)[/tex]    

velocity at t = 1,

               v(1) = 5 { cos(1)- sin(1) }    = 5( 0.99-0.017) = 5 x 0.982 = 4.91 cm/s        

velocity at t = 2,

               v(2) = 5 { cos(2)- sin(2) }    = 5( 0.999 - 0.0348)  = 4.82 cm/s  

velocity at t = 1.1,

               v(1.1) = 5 { cos(1.1)- sin(1.1) }    = 5( 0.999 - 0.0191)  = 4.90 cm/s  

velocity at t = 0.101,

          v(0.101) = 5 { cos(0.101)- sin(0.101) } = 5( 0.999 - 0.0176)  = 4.99 cm/s

velocity at t = 1.001,

         v(1.001) = 5 { cos(1.001)- sin(1.001) } = 5( 0.999 - 0.0174)  = 4.911 cm/s    

Now,

The average velocity at [1,2]

          = (4.91+4.82)/2 = 4.87 cm/s

The average velocity at [1,1.1]

          = (4.91+4.90)/2 = 4.90 cm/s

The average velocity at [1,0.101]

          = (4.91+4.99)/2 = 4.95 cm/s

The average velocity at [1,1.001]

          = (4.91+4.911)/2 = 4.91 cm/s

b) instantaneous velocity at 1s.

        instantaneous velocity[tex]= \frac{instantaneous\; displacement }{instantaneous\; time}[/tex]

                                   v(1) = [tex]\frac{s(1)-s(0)}{1-0}[/tex]

  s(1) = 5 {sin(1) + cos(1)} = 5 (0.017 + 0.999) = 5.08 cm

  s(0) = 5 {sin(0) + cos(0)} = 5 (0 + 1) = 5.0 cm

Now, putting the all values

                v(1) = (5.08 - 5.0)/1 = 0.08 cm/s

Answer:

   a) the average velocity during each time period.

  (b) 0.08 cm/s is the instantaneous velocity of the particle when t = 1.

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She must have a score greater than the average of 75 on her final exam.

Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.

Let the required score be x

Mean = 79 + 69 + 61 + 91 + x/5

⇒ 79 + 69 + 61 + 91 + x/5 > 75

⇒ 300 + x/5 > 75

⇒ 300 + x > 375

⇒ x > 375 - 300

⇒ x > 75

This implies that she needed a score on her final exams that were higher than the average of 75.

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The required transformation of graphs are represented and attached below.

Given:

(a) function f(x) = |x| transformed to g(x) = 3 |x ₋ 1 | ₊ 3

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Parent Function : f(x) = |x|

Horizontal Shift: Right 1 Units

Vertical Shift: Up 3 Units

Reflection about the x-axis: None

Vertical Stretch: Stretched

(b) If there is a horizontal or vertical shift, reflection around the x-axis or y-axis, or vertical stretch, the function has undergone transformation. To identify the transformation, compare the function to the parent function.

Parent Function : f(x) = |x|

Horizontal Shift: Right 1 Units

Vertical Shift: Up 6 Units

Reflection about the x-axis: None

Vertical Stretch: Stretched

Hence the required graphs are plotted.

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Step-by-step explanation:

MAR ME AS A BRAINLIST

THANKS

Answer:

  (c)  39 mm²

Step-by-step explanation:

You want to know an estimate of the area of the irregular figure.

The areas of irregular figures are often easily computed by decomposing the figure into shapes whose areas have formulas. Here, we can draw a vertical line from the upper left vertex to divide the figure into a triangle on the left and a trapezoid on the right.

The triangle has a base of 3 squares and a height of 6 squares, so an area of ...

  A = 1/2bh = 1/2(3)(6) = 9 . . . . square mm

The trapezoid has vertical parallel bases of 6 and 7 squares, and a width of 5 squares. Its area is ...

  A = 1/2(b1 +b2)h = 1/2(6 +7)(5) = 65/2 = 32 1/2 . . . . square mm

Then the total area of the figure shown is ...

  area = triangle area + trapezoid area

  area = 9 mm² +32.5 mm² = 41.5 mm²

The closest estimate of those offered is 39 square mm.

Answer:

$178571.43

Step-by-step explanation:

14% of a number is 25000

multiply 25000 by 100 and divide the product by 14

you will get 178571.428571

round up the 100ths place and it's 178571.43

Answer:

24 is the answer to the Equation

The length of the KL by additive property is 5 units.

The additive property of equality in an equation asserts that the sides stay equal whether we add or subtract the same amount from both sides of the equation. For entire numbers as well, this property is valid.

An example of the additive property is :

If A=B then A+n=B+n where n∈R.

Now the given line segment is KM is x+10

And KL=5x and LM=6

Now using additive property we can say that

KL+LM=KM

Substituting the values in the equations we get:

5x+6=x+10

or, 4x=4

or, x=1

Now using this value of x we can find the length of KL.

Therefore KL=5x=5×1=5

Hence the length of the KL by additive property is 5 units.

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Perpendicular lines from angles that measure (90) degrees

Answer:

  x + 9

------------

  x + 1

Step-by-step explanation:

2x + 4          -x + 5           x + 9

------------  +  ------------  =  -----------

  x + 1             x + 1           x + 1

I hope this helps!

Answer:

x=0, x=-7/3, x=-3

Step-by-step explanation:

The rounded numbers are   1200 and 1100

The two numbers that we have been given are 1183 and 1145.

We have been asked to round of each number to the nearest hundred.

Note that when we are rounding of number to the nearest hundred then we have to check the tens place.

If it is greater than or equal to 5 then we will increase the hundred place number by 1

And if it is less than 5 then we will not change anything in the hundreds place.

And after the required changes in the hundred place number, the numbers after that will convert into zero.

Therefore,  

1183 is rounded of to = 1200 as 8 which is in the tens place is greater than 5, we will add 1 to 1 in the hundreds place

1145 is rounded of to = 1100 as 4 is less than 5, 1 will not change

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The percentage of fraction 3/7 is 42.8571%.

Percentage, a relative value indicating hundredth parts of any quantity. One percent  is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

Given fraction:

3/7

To convert the fraction into percentage we have multiply 100

3/7*100

=300/7

= 42.8571%

Hence, the percentage of fraction 3/7 is 42.8571%.

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Answer: 9/13 ==> A

Step-by-step explanation:

sin is between 0 and 1 if 0° < theta < 180° ==> sin is positive when y is positive

sin is between -1 and 0 is 180° < theta < 360° ==> sin is negative when y is negative

sin theta * csc theta = 1

sin theta * 13/9=1

sin theta * 13/9 * 9/13 = 1 * 9/13

sin theta = 9/13 ==> A

Answer:

The length of the parking lot is 89metres

Step-by-step explanation:

Area of a rectangle = Lenght × Breadth

[tex]7031 {m}^{2} = x \times 79m \\ divide \: both \: sides \: by \: 79 \\ x = \frac{7031}{79} \\ x = 89m[/tex]

to get the slope of any straight line, we simply need two points off of it, let's use those two points on the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{2}}} \implies \cfrac{-3 -4}{2 -2}\implies \cfrac{-7}{0}\implies und efined[/tex]

Answer:

LCM=18 and GCF = 3

Step-by-step explanation:

Multiples of 9: 9, 18, 27

Multiples of 6: 6, 12, 18

LCM = 18

Factors of 9: 1, 3, 9

Factors of 6: 1, 2, 3, 6

GCF = 3

Answer:

im not to sure but i think its this

Step-by-step explanation:

The expected duration of participant participation

The value of x is 81 since similar triangles have equal ratios of corresponding sides.

Given:

PQ ǁ MN

OQP=  N

QPO=  M

ΔOQP=ΔONM

OP/OM=OQ/ON  

45/X=40/72

X= (72×45)/40

X=81

If two figures have the same shape, they are said to be comparable. In more formal terms, two figures are said to be comparable if their respective angles are congruent and their corresponding side length ratios are identical. The scale factor is the name of this usual ratio.

Therefore, the value of X is calculated as 81.

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Answer: 60 years

Step-by-step explanation:

ur answer is 60 because it's the same as 3+3 its 6 but it's

kind of the opposite way

The equation of slope-intercept form of the line is y = 14/3x + 8.

What is in slope-intercept form?

Given,

        m = 14/3

the point = ( 0,8 )

A line with a slope of 14/3 passes through the point (0,8).

y - y₁ = m ( x- x₁)

y - 8 = 14/3 ( x - 0 )

3(y - 8 )  = 14x

3y - 24  = 14x

3y = 14x + 24

y = 14/3x + 8

Finally, the equation of the line is

y = 14/3x + 8

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Answer:

a) 41 customers purchased only mysteries.

b) 19 customers purchased mysteries and science fiction, but not romance novels.

c) 19 customers purchased mysteries and science fiction.

d) 19 customers purchased mysteries and science fiction, but not romance novels.

e) 15 and 10 customer purchased mysteries

Answer:

x = 14

Step-by-step explanation:

m<DBC = m<DBE + m<EBC

105 = 4x + 5x - 21

105 = 9x - 21

126 = 9x

9x = 126

x = 126/9

x = 14