if sec2a is 3 find the value of sina.​

a) The Probability density function of given uniform distribution example is

F(x) = 1/3.5 for 8.5 < x< 12

Uniform distribution in Statistics is a type of probability distribution in which all possible outcomes have equally likely chance to occur. It is generally represented by U(x,y) where

x ---> minimum value and y---> maximum value

Probability density function is a probability function which defines the density of continuous random variable lying between specified range

values. It is denoted by f( a<X<b)

Probability density function for uniform distribution is F(x) = 1/(b-a) for a<x<b where a and b are parameters of uniform distribution.

We have following informations,

weigh of mini iPad = 11 ounces or 50% lighter than standard iPad.

Assume that the battery of iPad is uniformly distributed between 8.5 hours to 12 hours.

this implies a = 8.5 , b = 12

F(x) = 1/(12 - 8.5) = 1/3.5 for 8.5<x<12

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#Complete Qestion :

In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal. Assume that the battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

a) What is the probability that the battery life for an iPad Mini will be 10 hours or less?

The probability that the sum of the numbers rolled on the dice is even =1/2.

For the given question,

A fair dice is rolled twice.

Six different results are available with a single roll of the dice (1,2,3,4,5,6)

Therefore, if two dice are rolled, there are a total of 36 possible results, or 6².

Sample space for the sum of even = [(1,1), (1,3), (1,5), (2,2), (2, 4),(2,6), (3, 1), (3,3),(3,5),(4,2),(4,4),(4,6), (5, 1), (5,3),(5,5),(6,2),(6,4),(6,6)]

Total sample space for sum of even = 18

For the probability that the sum of the numbers rolled is even is -

probability (sum is even) = 18 / 36 = 1/2

Thus, the probability that the sum of the numbers rolled is even is 1/2.

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Answer:

800

Step-by-step explanation:

we gotta go with the highest value to round since it’s only one sig fig

In order to round to 1 significance the remaining digit will marks as zero thus 837 to 1 significant figure will be 800.

To round up or down tens place then we need to look at the unit place if it is less than 5 then we need to keep it as it and if it is greater than 5 then we need to round up the tens digit.

In order to round to a hundred, we need to look at the tens digit if it is less than 5 then we keep as it is and if it is 5 or greater than 5 then we will round up.

In order to round to 1 significance the remaining digit will mark as zero

As per the given,

837 Here, 1 significant figure is 8.

The ramainging digit = 3 and 7

Put 0 instant of 3 and 7

837 → 800

Hence "In order to round to 1 significance the remaining digit will marks as zero thus 837 to 1 significant figure will be 800".

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Answer:

15-p

Step-by-step explanation:

15-p

Answer:

A and D

Step-by-step explanation:

8(6) means 8x6 so that's 48

and 12(4) is the same as 4(12) so that should be simple enough

297 children like at most one kind of ice cream.

Total number of children = 397

Let C and P be the number of children like chocolate and pistachio ice cream respectively.

n(C) = 175

n(P) = 225

The number of student do not like chocolate or pistachio ice cream is,

n(P' and C') = 97

n(P or C)' = 97, by De Moivre's theorem

n(P or C) = 397-97 = 300

n(P) + n(C) - n(P and C) = 300

175 + 225 - n(P and C) = 300

400 - n(P and C) = 300

n(P and C) = 100

So the required number of children like at most one kind of ice cream = 397-n(P and C) = 397-100 = 297

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Answer:

8^18

Step-by-step explanation:

8^15

8^−3

=

8^15

8−3

= 8^15− (−3)

= 8^18

The probability that the dart lands in centre is = √2-1.

acc to our question-,

hence,The probability that the dart lands in centre is = √2-1.

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Answer:

x = -1

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ -10 + x + 4 - 5 = 7x - 5

Then the value of x will be,

→ -10 + x + 4 - 5 = 7x - 5

→ -11 + x = 7x - 5

→ 7x - x = -11 + 5

→ 6x = -6

→ x = -6/6

→ [ x = -1 ]

Hence, the value of x is -1.

For the given triangle and the measures of the given angle the value of x is equal to -11° .

As given in the question,

For the given triangle,

Let us consider the triangle name ABC,

Where,  m ∠A = x + 51° ,

m ∠ABC = 80° ( vertically opposite angle of given 80° angle.)

m ∠ACB = 60° ( vertically opposite angle of given 60° angle.)

To get the value of x we have,

Sum of all the interior angles of a triangle is equal to 180°

m ∠A + m ∠B + m ∠C = 180°

⇒ x + 51° + 80° + 60° = 180°

⇒ x + 191° =  180°

⇒ x = 180° - 191°

⇒ x = - 11°

Therefore, for the given triangle and the measures of the given angle the value of x is equal to -11° .

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Andre takes 36 minutes to walk to the school.

Given, It take Jada 20 minutes to walks to school.

It takes Andre 80% a long to walk to school.

As, Andre takes 80% more to walk to school

So, the time Andre takes = 20×180/100

the time Andre takes = 2×18

the time Andre takes = 36 minutes

Hence, Andre takes 36 minutes to walk to the school.

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Dad's car's gas tank holds 14.8 gallons of the gas.

A mixed fraction is one generated by integrating a whole number as well as a fraction.

Changed the mixed fraction in decimal.

Total gas purchased = 37/2 = 18.5 gallons of gas.

Let x be the gallons of gas tank contains.

Then,

(1/2)x + (3/4)x = 18.5

Multiply both sides by 4,

2x + 3x = 74

5x = 74

x = 14.8 gallons

Thus, Dad's car's gas tank holds  14.8 gallons of the gas.

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Answer: 50%

Step-by-step explanation:

Answer:

D. 75%

Step-by-step explanation:

There are 20 marbles, so each 1 has a chance of 5% If you were to choose randomly 75% of the time you will get either red or black and 25% you will get green or white

Which is the order from least to greatest of the following

A. 4/3, 0.8, 1/5, 30%

1.33 , 0.8 , 0.2 , 0.3

B. 30%, 4/3, 0.8, 1/5

0.3 , 1.33 , 0.8 , 0.2

C. 1/5, 4/3, 30%, 0.8

0.2 , 1.33 , 0.3 , 0.8

D. 1/5, 30%, 0.8, 4/3

0.2 , 0.3 , 0.8 , 1.33 these are listed smallest to largest

Answer:

The distance between [tex](-5,-6),(-9,-4)[/tex] is [tex]6 units[/tex].

Step-by-step explanation:

Distance Formula :

[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]

Given,

The two points are

[tex](-5,-6),(-9,-4)[/tex]

To calculate the distance between two points, use the distance formula.

[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]

Substitute the actual values of the points into the distance formula.

Distance[tex]=\sqrt{((-9)^{2} -(-5)^{2}) +( (-4)^{2} -(-6)^{2})}[/tex]

[tex]=\sqrt{(81-25)+(16-36)}[/tex]

[tex]=\sqrt{36}[/tex]

[tex]=6[/tex]

Answer:

When you have the base of 10 and an exponential index of “n”, the powers of 10 says that the resulting number will be 1 followed by “n” number of zeros. So for example, 10 to the 7th represents the same thing as 1 followed by 7 zeros. The result is 10,000,000 (10 million). Multiplying whole numbers by a power of ten would mean that you ...

Pi([tex]\pi[/tex]) is the ratio of circumference to diameter for any circle.

Perimeter is the distance around a circle.

Circumference of circle [tex]C = \pi d[/tex].

Perimeter of circle [tex]= 2 \pi r[/tex]

What is circle ?

A circle is a spherical shape without boundaries or edges.

A circle is a closed, curved object with two dimensions in geometry.

Consider two small arcs AB and CD of two circles of radii x and y units, both of which make an angle of measure θ at the centers P and Q respectively.

For smaller values of θ, the arc length AB is almost equal to the length of the line segment [tex]\bar{AB}[/tex]. Similarly, arc CD ≅ [tex]\bar{CD}[/tex].

Using the SAS rule of triangle similarity, we can say that APB and CQD are similar triangles because their angles are the same and their ratios are AP: PB = CQ: QD = 1: 1. So, it stands to reason that AB: AP = CD: CQ.

Circumference = [tex]\pi \times[/tex] diameter or circumference = 2[tex]\pi \times[/tex] radius if this constant equals some value.

So it was proved.

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In a sequence of first term-10 and the 2nd term is 1. the 5th term of this sequence is -17

information given in the question

The 1st term of a certain sequence is -10

the 2nd term is 1

Each subsequent term is obtained by adding the 2 immediately preceding terms

the 5th term of this sequence = ?

Each subsequent term is obtained by adding the 2 immediately preceding terms. This statement means is applied as below

Therefore:

third term

3rd term

= first term + 2nd term

= -10 + 1

= -9

4th term

= 3rd term + 2nd term

= -9 + 1

= -8

5th term

= 4th term + 3rd term

= -9 + -8

= -9 - 8

= - 17

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m ∠5 and m ∠7 is  72 ° . All straight angles are 180 degrees, according to the straight angle theorem. A straight angle is formed when the angle's legs point precisely in the opposite directions. The symbol for a straight angle is 180 degrees, or  π (in radians).

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The names of basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle and full rotation. An angle is geometrical shape formed by joining two rays at their end-points. An angle is usually measured in degrees.

m ∠4 = 108°

m ∠5 = m ∠1

m ∠1 is in same line of m ∠4

So

m ∠1 = 180 - m ∠4

m ∠1 = 180 - 108

m ∠1 = 72 °

So m ∠5 = 72 °

m ∠7 is opposite to m ∠5 , opposite angles will be equal

Therefor m ∠7 = 72 °

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The little monsters solved 15 problems in March's Math meet

Given, that in November's math meet, the little monsters of beast academy solved 1/5 of the problems.

In March's math meet, they solved 2/3 of the problems.

In total, the little monsters solved 13 of 30 problems over both math meets.

Let, the number of problems in November be n,

and  the number of problems in March be m

According to the question,

n + m = 30 as, the total problems be 30

Now, (1/5)n + (2/3)m = 13 as, they solved total 13 problems

n + m = 30 ... (1)

n/5 + 2m/3 = 13 ... (2)

On simplifying Eq (2) becomes

3n + 10m = 195 ... (2)

On multiplying Eq (1) by 3, we get

3n + 3m = 90

3n + 10m = 195

On subtracting, we get

- 7m = - 105

m = 105/7

m = 15

So, the problems asked in March's Math meet be 15.

Hence, 15 problems were asked at March's Math meet.

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The required expression for the laundry service is y = 0.89x.

Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.

proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.

here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x

Thus, the required expression for the laundry service is y = 0.89x.

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Answer:

Step-by-step explanation:

The required expression for the laundry service is y = 0.89x.

Given that,

The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.

What is proportionality?

proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.

here

Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.

According to the question,

y ∝ x

y = kx

Put x = 25 and y = 22.25

22.25 = k 25

k = 0.89

Put back k in the proportional equation,

y = 0.89x

Thus, the required expression for the laundry service is y = 0.89x.

Answer:  [tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]

90 degree counter-clockwise rotation around the origin.

===================================================

Explanation:

Focus on A(-1,2) and A'(-2,-1)

The coordinates of point A have swapped to go from "-1,2" to "2,-1". Then we stick a negative in front of the new x coordinate to get "-2,-1"

In other words, we've gone from (x,y) to (y,x) to (-y,x)

Representing this with arrows looks like:

[tex]\left(\text{x}, \text{y}\right) \to \left(\text{y}, \text{x}\right) \to\left(-\text{y}, \text{x}\right)[/tex]

or in short

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]

which represents a 90 degree counter-clockwise rotation around the origin.

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

Let's see if this rule works with point B(2,5). We should rotate to B'(-5,2)

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(2,5\right) \to \left(-5, 2\right)[/tex]

Sure enough, it works for point B.

Lastly, let's check if it works for point C.

We should go from C(3,-4) to C'(4,3).

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(3,-4\right) \to \left(-(-4), 3\right)\\\\\left(3,-4\right) \to \left(4, 3\right)\\\\[/tex]

All points have been confirmed.

Thus, 72 is divided into 32 and 40 in a 4:5 ratio. A ratio expresses the number of times one number contains another.

Given:

The given ratio is 4:5.

To find: We have to divide 72 in this ratio.

To divide 72 in the 4:5 ratio, we must perform the following steps:

The ratio is 4:5.

We can write the number of the ratio as 4x and 5x by multiplying a constant x.

The total ratio is 4x+5x=9x.

So, 9x is equal to 72.

We can write-

9x=72

x=8.

So, putting the value of x we get-

4×8 and 5×8

So, the numbers are 32 and 40.

Thus 72 divides itself as 32 and 40 in 4:5 ratio.

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It a because i told the tese

The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.

By using the normal distribution method, a mean u and standard deviation σ,

The ratio of people who wants the Giants to eat patriots is p = 0.90,

The assumed sample size denoted by n is 100,

and their distribution's mean is u = 0.90,

by using the standard deviation formula is

σ = √(p(1 - p) ÷ n),

σ = √(0.90(1 - 0.90) ÷ 100),

σ = 0.03,

we get that the standard deviation is σ = 0.03

Here the probability that at least 15% of 100 Indianapolis residents encouraged the Patriots in the gaint match  Super Bowl XLVI is

P(X > 0.15) = 1 - P((X - u) ÷ σ) > (0.90 - 0.15) ÷ 0.03))

The significant value of X,

X - u ÷ σ = Z

we get,

P(X > 0.75) = (Z<5)-1

P(X < 0.75) = 1.293 - 1

P(X < 0.75) = 0.293

By solving we get, The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.

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