The probability density function of X, the lifetime of a certain type of device (measured in months) is given by f(x) = 0 if x < 2121/x^2 if x > 21 f(x) Find the following: P(X > 48) = The cumulative distribution function of X: f(x)= if x < 21if x > 21 The probability that at least one out of 7 devices of this type will function for at least 44 months:

77 is the value of Q in linear equation.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                   Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

P ∝ 1/Q

PQ = K

AT P= 11

Q = 28

11 * 28 = K

K = 308

AT P = 4

4Q = 308

Q = 77

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Answer:

-12 is the y intercept while your slope is -4

Step-by-step explanation:

Distance from the base of tower to the airplane = 706ft.

The term "angle of depression" called   angle created when an observer looks down at an item and the horizontal line intersects with the line of sight. It determines how our field of vision shifts as we glance down. Say you are standing in your kitchen and gazing straight, and suddenly you spy an insect crawling on the floor.

Given, Angle of Depression=12°

Height of tower=150ft

For AB parallel to CD

∠ACD=∠cAB=12°

Tan12°=BC/AB

AB=BC/Tan12°

AB=706ft

Hence, Distance from the base of tower to the airplane = 706ft.

Diagram is attached below;

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Answer:

(a) To find the linear function, we need to determine the slope and y-intercept of the line that passes through the two given points: (50000, 7000) and (70000, 7800).

Slope = (change in y)/(change in x) = (7800 - 7000)/(70000 - 50000) = 800/20000 = 0.04

Y-intercept = 7000 - slope * 50000 = 5000

So the linear function that gives the account executive's compensation y for a given amount of monthly sales x is:

y = 0.04x + 5000

(b) To find the account executive's compensation for $75,000 in monthly sales, we can plug x = 75000 into the linear function we found in part (a):

y = 0.04(75000) + 5000 = 8000

So the account executive's compensation for $75,000 in monthly sales is $8,000.

Answer:

9

Step-by-step explanation:

-5 + (-18) +32

-23 + 32

32 -23

Since the volume of the sphere V = 36π cm³is greater than that of the cone, V' = 21π cm³ the ice cream will overflow.

The volume of a sphere is given by V = 4πr³/3 where r = radius of sphere

Now if the ice cream above is going to melt when it does, will it fit in the cone or will it overflow? Since the ice cream is a sphere, the ice cream will not overflow if the volume of the ice cream equals the volume of the cone. If is greater than the volume of the cone, it will overflow.

Now, since the ice cream is a sphere, its volume is given by V = 4πr³/3 where r = radius of sphere = 3 cm

So, substituting this into the equation, we have that

V = 4πr³/3

V = 4π(3 cm)³/3

V = 4π × 27 cm³/3  

= 4π × 9 cm³

= 36π cm³

Also, since the volume of the cone is given by V' = 1/3πr²h where r = radius of cone = 3 cm and h = height of cone = 7 cm

So, substituting the value of the variables into the equation, we have that

V' = 1/3πr²h

V' = 1/3π(3 cm)² × 7 cm

= 1/3π × 9 cm² × 7 cm

= 3π cm² × 7 cm

= 21π cm³

We see that V = 36π cm³ > V' = 21π cm³

Since the volume of the sphere is greater than that of the cone, the ice cream will overflow.

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Answer:

16/(8×2)=

16/8×2=

16-8/2=

8/2=

4

Step-by-step explanation:

first we subtract 8 from 16 and divide the result by 2.

Answer:

Solve the problems. a) The number a is 4/5 of the number b. What part of number a is number b?

Step-by-step explanation:

a) If a is 4/5 of b, then b is 5/4 of a.

To find what part of a is b, we divide b by a:

b/a = 5/4

This means that b is 5/4 times larger than a, or b is 125% of a.

To find what part of a is b, we subtract 1 from this fraction:

b/a - 1 = 5/4 - 1

b/a - 1 = 1/4

So, b is 1/4 of a, or b is 25% of a.

Answer:

<1= 61

<2= 61

<3= 119

Step-by-step explanation:

The option that is NOT an augmented functional dependency is: Q --> P, because it removes the attribute from the left-hand side of the existing functional dependency, which is not allowed in an augmented dependency.

Functional dependency: It is a concept in database management systems that describes the relationship between two attributes or sets of attributes in a table. In a functional dependency A → B, A is the determinant or the attribute(s) that uniquely determines the value of B.

Augmented functional dependency : It is formed by adding one or more attributes to the determinant side of an existing functional dependency.

From the given options, the only one that is not an augmented functional dependency is "Q → P". This is because it does not involve adding any attributes to the determinant side of an existing functional dependency.

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Sampling distribution of sample means with size 10, drawn randomly from a population with unknown mean and standard deviation, is approximately normal. It has a mean of 32 and a standard deviation of 6.32 (standard error of the mean). Option D is correct.

The sampling distribution of the mean of a large enough sample size follows a normal distribution, even if the underlying population is skewed.

The formula for the standard deviation of the sampling distribution of the mean is( σ / [tex](\sqrt(n))[/tex] ) ,

where sigma is the standard deviation of the population and n is the sample size.

Substituting the values, we get:

standard deviation of sampling distribution =[tex]20/(\sqrt(10))[/tex]= 6.32

Therefore, the sampling distribution of all possible samples of size 10 is approximately normal with a mean of 32 and a standard deviation of 6.32.

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The number which, when subtracted from 80, results in -30 is equal to 110.

To solve this problem, we can use algebraic equations to represent the given information. Let x be the number that we want to find.

According to the problem, when we subtract x from 80, we get -30:

80 - x = -30

To solve for x, we can isolate it on one side of the equation by adding x to both sides, and then simplify:

80 - x + x = -30 + x

80 = -30 + x

Next, we can isolate x by subtracting -30 from both sides:

80 - (-30) = x

Simplifying the right-hand side:

80 + 30 = x

110 = x

Therefore, the number that was subtracted from 80 and gave -30 as the result is 110.

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Answer:

22

Step-by-step explanation:

2-4i and i=6

2-4(6)

=22

Answer:

The other is 75/7.

Step-by-step explanation:

Let the other rational number be x, then:

(-7/15) * x =  -5

x = -5 * -15/7

  = 75/7

If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).

The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27.

Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).

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The length of the side on the prism is 5cm. The area of the shaded region is 72 cm².

Area is the total amount of area occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the region that its boundary encloses. The quantity of unit squares that span a closed figure's surface is its area. Square units like cm² and m² are used to quantify area. A shape's area is a two-dimensional measurement.

The region inside the perimeter or boundary of a closed shape is referred to as the "area". Such a shape has at least three sides that can be joined together to create a boundary. The "area" formula is used in mathematics to describe this type of space symbolically.

In this figure,

The 5cm flap will be adjacent to the side x. Therefore,

Length of the side x= 5cm

Area of the shaded region= l×b

because the shaded region is a rectangle.

area= 9*x

       =9*5= 45 cm²

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The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².

Quotient:

The quotient is the answer we get when we divide one number by another. For example, if we divide the number 6 by 3, we get 2, the quotient. The quotient can be integer or decimal. For an exact division like 10 ÷ 5 = 2, we have a whole number as the quotient, and for a division like 12 ÷ 5 = 2.4, the quotient is a decimal number. The quotient can be greater than the divisor, but always less than the dividend.

Based on the given conditions, Formulate:

6.208× 10⁹ /9.7×10⁴

Simply using exponent rule with same base:

[tex]a^n. a^m = a^(n+m)[/tex]

= 6.208 × 1/9.7

Now,

the sum or difference = [tex]6.208*\frac{1}{9.7}[/tex] × 10¹³

Now solving, we get:

6.208/9.7 × 10¹³

Converting fraction into decimal, we get:

  0.64× 10¹³

⇒ 6.4 × 10¹²

Therefore,

The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².

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The percentage of the original sample left after 85 days is approximately 30.73%.

The rate of decay of a radioactive substance is proportional to the amount of substance present. The radioactive decay law states that the amount of a radioactive substance left after t days is given by the formula N(t) = N₀ e^(-kt). Here, N₀ is the initial amount of the substance, and k is the decay constant.

We know that the half-life of the substance is 50 days. This means that N(t) = N₀/2 when t = 50. Therefore, we can use this information to find the decay constant k as follows:

N(50) = N₀ e^(-50k)

N₀/2 = N₀ e^(-50k)

1/2 = e^(-50k)

ln(1/2) = -50kln(e)

ln(1/2) = -50k

0.693 = 50k

k = -0.01386 (approx.)

Therefore, the formula for the amount of substance left after t days is given by N(t) = N₀ e^(-0.01386t). Now, we can use this formula to find the percentage of the original sample left after 85 days as follows:

N(85) = N₀ e^(-0.01386 * 85)

N(85) = N₀ e^(-1.1771)

N(85)/N₀ = e^(-1.1771)

N(85)/N₀ = 0.3073 (approx.)

Therefore, the percentage of the original sample left after 85 days is 30.73% (approx.). The answer is 30.73%.

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The two numbers that are in both sequences and between 10 and 30 are 14 and 26.

An ordered set of numbers that adhere to a pattern or rule is referred to as a sequence in mathematics. Sequences can be defined in a variety of ways, such as a formula or a recursive definition, and they can be finite or infinite. Several branches of mathematics, including calculus, algebra, and number theory, employ sequences to explore and answer problems related to the behaviour of functions. For instance, sequences may be used to create fractals and other geometric patterns, predict the rise of populations or the spread of illnesses, and examine the distribution of prime numbers.

The given sequence is 4n - 5, and the nth term is 3n + 2.

For numbers between 10 and 30 in the sequence we have:

4n - 5 ≥ 10

4n ≥ 15

n ≥ 3.75

And,

4n - 5 ≤ 30

4n ≤ 35

n ≤ 8.75

Now, we calculate the sequence for n from 4 to 8:

When n = 4, 3n + 2 = 14

When n = 5, 3n + 2 = 17

When n = 6, 3n + 2 = 20

When n = 7, 3n + 2 = 23

When n = 8, 3n + 2 = 26

Hence, the two numbers that are in both sequences and between 10 and 30 are 14 and 26.

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Answer:

AB ≈ 4.73

Step-by-step explanation:

using the sine ratio in the right triangle

sin25° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{2}{AB}[/tex] ( multiply both sides by AB )

AB × sin25° = 2 ( divide both sides by sin25° )

AB = [tex]\frac{2}{sin25}[/tex] ≈ 4.73 ( to the nearest hundredth )

Answer:

One way is to realize that since the total area is 1, the area below z = 1 is equal to 1 minus the area above z= 1 which we know from before is 0.1587. So the area below 1 is 1 - 0.1587 = 0.8413.

The result of each trigonometric functions are:

a) sin X = 7√149 / 149

b) sin Z = 10√149 / 149

c) cos X = 10√149 / 149

d) cos Z = 7√149 / 149

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this trigonometric functions, we can calculate sin X, sin Z, cos X, and cos Z as follows

sin X = YZ / XZ = 7 / √149

cos X = XY / XZ = 10 / √149

sin Z = XY / XZ = 10 / √149

cos Z = YZ / XZ = 7 / √149

To simplify these fractions, we can rationalize the denominator by multiplying the numerator and denominator by √149:

sin X = 7√149 / 149

cos X = 10√149 / 149

sin Z = 10√149 / 149

cos Z = 7√149 / 149

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The given question is incomplete, the complete question is:

Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.

Answer:

0.33

Step-by-step explanation:

To solve this, you first write the problem as an algebra equation as follows: 3x + 4 = 5

Then you solve the equation by subtracting 4 from both sides, and then divide both sides by 3. Here is the math to illustrate better:

3x + 4 = 5

3x + 4 - 4 = 5 - 4

3x = 1

3x/3 = 1/3

x = 0.33

Answer = 0.33

The best point estimate for the average number of school books per semester for all students at the local college is 5.2.

The average number of school books per semester for all students at the local college is 5.2. A sample of 39 students was taken, i.e., n = 39. To find, The best point estimate for the average number of school books per semester for all students at the local college.

The best point estimate for the average number of school books per semester for all students at the local college is the sample mean which can be calculated.

Therefore, the best point estimate for the average number of school books per semester for all students at the local college is 5.2.

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The probability that fewer than 3 of them use their smartphones in meetings or classes is 0.0366.

The binomial probability distribution is a discrete probability law with two parameters: trial number (n) and success probability (p) (p). When there are two mutually exclusive outcomes of finite trials, the binomial distribution is utilised.

The probability that a specific 3 people all use their smartphones in meetings or class is 0.53³.

Probability that remaining 7 people do not use their phone is 0.47⁷

¹⁰C₃ = 10*9*8/(3*2*1) = 120.

Thus, the probability of exactly 3 people using their smartphones in meetings or in class is 10C3*0.533*0.477, or 0.0905.

So, adding up the 3 possibilities (that 0 of them, 1 of them, or 2 of them use their smartphones in meetings or class) we get

¹⁰C₀*0.530*0.4710 + ¹⁰C₁*0.531*0.479 + ¹⁰C₂*0.532*0.478 = 0.0366.

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Complete question:

Assume that when adults with smartphones are randomly​ selected, 53​% use them in meetings or classes. If 10 adult smartphone users are randomly​ selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.

A function [tex]P(t) = 170.(1.30)^t[/tex]  that gives the deer population P(t) on the reservation t years from now

We were told there were 170 stags on reservation. The number of deer is increasing at a rate of 30% per year.

We could see the deer population grow exponentially since each year there will be 30% more than last year.

Since we know that an exponential growth function is in form:

[tex]f(x) = a*(1+r)^x[/tex]

where a= initial value, r= growth rate in decimal form.

It is given that a= 170 and r= 30%.    

Let us convert our given growth rate in decimal form.

[tex]30 percent = \frac{30}{100} = 0.30[/tex]

Upon substituting our given values in exponential function form we will get,

    [tex]P(t) = 170.(1+0.30)^t[/tex]

⇒ [tex]P(t)= 170.(1.30)^t[/tex]

Therefore, the function [tex]P(t) = 170.(1.30)^t[/tex] will give the deer population P(t) on the reservation t years from now.

Complete Question:

There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.

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The correct definition for the lines drawn to circle with centre C are:

A circle is a spherical shape without boundaries or edges.

Thus, on the basis of propertied of circle, the correct definition for the lines drawn to circle with centre C are:

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It will take 16 seconds to get to your class.

[tex]\bold{Distance}=\bold{Speed }\times \bold{Time}[/tex]

[tex]200m = 1.5m\div s \times t[/tex]

[tex]24=1.5\times t[/tex] (We want to get t by itself, so lets get rid of the [tex]\times1.5[/tex] by dividing both sides by 1.5)

[tex]t = 16 \ \text{seconds}[/tex]

Therefore, it will take 16 seconds to get to your class.