If h(x) = x – 7 and g(x) = x2, which expression is equivalent to (g circle h) (5)?

The given function is f(x) = 15(1.02)^x, where x is the number of years from the date at which money is initially deposited.

This means that $15 were initially deposited into the account, and the amount grows at an annual rate of 2% (which is represented by 1.02 being raised to the power of x).

Therefore, the correct answer is: $15 were initially deposited into the account, which grows at an annual rate of 2%.

Hope I helped you...

The expression is equivalent to 45m^-6p^2v^12/15m^-2p^8v^-4 is Option b 3v^16/m^4p^6 .

Given :

expression is equivalent to for all values of m , p , and v where the expression is defined

= ( 45m^-6 ) * p^2 * v^12 / 15m^-2 * p^8 * v^-4

= ( 45 / 15 ) ( m^-6 / m^-2 ) ( p^2 / p^8 ) ( v^12 / v^-4 )

= 3 ( m^-6 - ( -2 ) ( p^2 - 8 ) ( v^12 - ( - 4 )

= 3 ( m^-6 + 2 ) ( p^-6 ) ( v^12 + 4 )

= 3 ( m^-4 ) ( p^-6 ) ( v^16)

= 3 * v^16 / m^4 * p^6

= 3v^16 / m^4p^6

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b can be written as a linear combination of a1 and a2 with weights x1 = 3 and x2 = 3.
Thus, (b) x1 = 3, x2 = 3 is the right response.

To determine whether b can be written as a linear combination of a1 and a2, we need to find weights x1 and x2 such that x1a1 + x2a2 = b.

Here a1 = [2 6 -4], a2 = [-2 6 6], and b = [0 36 6], we have the following system of equations:

2x1 - 2x2 = 0
6x1 + 6x2 = 36
-4x1 + 6x2 = 6

Solving for x1 and x2, we have:

From the first equation, we can write x1 = x2.

Substituting x1 = x2 in the second equation, we get:
6x1 + 6x1 = 36
12x1 = 36
x1 = 3

Since x1 = x2, we have x2 = 3 as well.

Now, substituting the values of x1 and x2 in the third equation, we get:
-4(3) + 6(3) = 6
-12 + 18 = 6
6 = 6

Since the system is consistent, there is a solution. Therefore, b can be written as a linear combination of a1 and a2 with weights x1 = 3 and x2 = 3.

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Answer:

\(\large \boxed{\sf \ \ \dfrac{x^2}{x^4+1}=\dfrac{1}{7} \ \ }\)

Step-by-step explanation:

Hello,

We know that (let's assume that x is different from 0 as we cannot divide by 0)

   \(x+\dfrac{1}{x}=3\)

and we want to estimate

   \(\dfrac{x^2}{x^4+1}\)

Let's take the square.

\(9=3^2=(x+\dfrac{1}{x})^2=x^2+2\cdot x \cdot \dfrac{1}{x}+\dfrac{1}{x^2}=x^2+2+\dfrac{1}{x^2}=\dfrac{x^4+1}{x^2}+2\)

So, we can write

\(\dfrac{x^4+1}{x^2}=9-2=7 \\ \\\\\text{*** let's take the inverse ***} \\ \\\dfrac{x^2}{x^4+1}=\dfrac{1}{7}\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Step-by-step explanation:

if y = 9x - 4, then we can substitute y for equation 8x + 6y = 15. It's equal to :

y = 9x - 4

8x + 6y = 15

=> 8x + 6(9x - 4) = 15

Correct Option : D

Subject : Mathematics

Level : JHS

Chapter : Linear Equations

ANSWER

EXPLANATION

We want to round up 14326.7815723 to a whole number.

This means that we want to write it as an integer.

To do that, we check the number immediately after the decimal.

If the number is greater than or equal to 5, we round up to 1 and add to the number before the decimal but if it is lesser than 5, we round down to 0.

Since the number after the decimal is greater than 5, the number becomes:

We have rounded it up to whole number.

The statement, which shows the meaning of the taxi driver’s equation for the mileage and fee formula are statement B and E.

Linear equation or formula is the equation in which the highest power of the unknown variable is one.

Given information-

The formula equation for the mileage is,

\(3.00+0.50m=9.50\)

In the above formula the term m represents the number of miles traveled.

This formula written by the taxi driver shows the relation between the mileage and fee for his last customer. Using this expression the number of miles can be calculated as,

\(3.00+0.50m=9.50\)

Subtract with 3 both the sides,

\(0.50m=9.50-3.00\\0.50m=6.50\)

Divide by number 0.5 both the sides,

\(m=\dfrac{6.5}{0.5}\\m=13\)

Thus, his last costumer traveled 13 miles.

The 13 times 0.5 plus $3 is equal to the $9.50 which means nine dollars and fifty cents. Thus the option B is the correct option.

The number of miles traveled by customer is 13 miles. 13 miles of 50 cent  is equal to $6.5. If we add three dollars in it the result will be equal to the nine dollars and fifty cents. Thus the option E is correct.

Hence, the statement, which shows the meaning of the driver’s equation, are,

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Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

In this scenario, there are four people in a room. Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

The remaining person is a foreign agent who has chosen a pair randomly. Thus, if any two of the three people with the valid pairs collaborate, they can successfully uncover the secret, as per the properties of the Shamir secret sharing scheme.

The presence of the foreign agent does not affect the security of the scheme unless they collaborate with another person possessing a valid pair.

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Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

Answer:

area = 228 m^2

Step-by-step explanation:

here's your solution

=> length = 20 m. , width = 12 m

=> Area of rectangle = length*width

=> Area of rectangle = 12*20

=> Area of rectangle = 240 m^2

now we need to find area of traingle

=> base = 4 m. , height = 6 m

=> area of traingle = 1/2*base*height

=> area of traingle = 1/2*4*6

=> area of traingle = 12 m^2

=> now , area of figure = 240 m^2 - 12 m^2

=> 228 m^2

hope it helps

Answer:

p= 66.32 m

a= 228 m squared

Step-by-step explanation:

Answer:

The answer is 20 feet

Step-by-step explanation:

We know that her apartment sketch is 6 by 4 inches.

If the 6 inch side is actually 30 feet and 6 goes into 30 5 times, we should multiply 4 by 5 to get proportionate answers.

Therefore her apartment is 20*30 feet

Hope this helps

The maximum height of the stone is 45 meters. It would take 1 second to reach its maximum height

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

The height (h) of the stone after x seconds is given by:

h(x) = -5(x - 1)² + 45

h(x) = -5(x² - 2x + 1) + 45 = -5x² + 10x + 40

h(x) = -5x² + 10x + 40

The maximum height is at h'(x) = 0, hence:

h'(x) = -10x + 10

-10x + 10 = 0

10x = 10

x = 1

h(1) = -5(1 - 1)² + 45

h(1) = 45

The maximum height of the stone is 45 meters

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Answer:

The sum of 3 1/4 and 6 3/4 is 10.

Step-by-step explanation:

To add the mixed numbers 3 1/4 and 6 3/4, you can first convert them to improper fractions:

3 1/4 = 13/4

6 3/4 = 27/4

Now you can add the numerators and keep the same denominator:

13/4 + 27/4 = 40/4 = 10

So the sum of 3 1/4 and 6 3/4 is 10.

Answer: 3 1/4 + 6 3/4 = 1/10 and 10

it right have a good day

Step-by-step explanation:

The probability that the digit that is received (after having been transmitted across the 4 channels) is 0.3645

In communication systems, it is common to face the challenge of transmitting information accurately over a noisy channel. In this scenario, errors can occur during transmission, and it is essential to quantify the probability of receiving the correct information at the end of the channel.

In this problem, we are asked to calculate the probability that the digit received after transmitting a 0 across four channels is also a 0. We know that each channel can either transmit the digit correctly with probability 0.9 or incorrectly with probability 0.1. Therefore, we can use the concept of conditional probability to solve this problem.

Using Bayes' theorem, we can rewrite this as:

P(CCCC | 0 received) x P(0 received) / P(CCCC)

Here, P(CCCC | 0 received) represents the probability that all four channels transmitted the 0 correctly, given that a 0 was received. This probability can be calculated as:

P(CCCC | 0 received) = P(C) x P(C | C) x P(C | C | C) x P(C | C | C | C)

Substituting the given probabilities, we get:

P(CCCC | 0 received) = 0.9 * 0.9 * 0.9 * 0.9 = 0.6561

Similarly, we can calculate the probability of receiving a 0 in general as:

P(0 received) = P(CCCC | 0 received) x P(0) + P(IIII | 0 received) x P(1)

where P(IIII | 0 received) represents the probability that all four channels transmitted the digit incorrectly, given that a 0 was received. This probability can be calculated similarly as:

P(IIII | 0 received) = P(I) * P(I | I) x P(I | I | I) x P(I | I | I | I) = 0.1 x 0.1 x 0.1 x 0.1 = 0.0001

Substituting the given probabilities, we get:

P(0 received) = 0.6561 x 0.5 + 0.0001 x 0.5 = 0.3281

Finally, we can calculate the denominator P(CCCC) as:

P(CCCC) = P(CCCC | 0 received) x P(0) + P(CCCC | 1 received) x P(1)

where P(CCCC | 1 received) represents the probability that all four channels transmitted the digit correctly, given that a 1 was received. This probability can be calculated similarly as:

P(CCCC | 1 received) = P(I) x P(I | C) x P(I | C | C) x P(I | C | C | C) = 0.1 x 0.9 x 0.9 x 0.9 = 0.0729

Substituting the given probabilities, we get:

P(CCCC) = 0.6561 * 0.5 + 0.0729 * 0.5 = 0.3645

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(a) The probability that a randomly selected policyholder lives more than 80 years is approximately 0.3106.  (b) Given that a male policyholder just turned 80, the probability that he will live for at least three more years is approximately 0.6166.

(a) To find the probability that a randomly selected policyholder lives more than 80 years, we need to calculate the cumulative probability of survival beyond 80 for both males and females separately, and then weigh them based on the gender distribution.

For males: Using the normal distribution with mean 75 and standard deviation 8, we find the probability of survival beyond 80 is approximately 0.3446.

For females: Using the normal distribution with mean 78 and standard deviation 6, we find the probability of survival beyond 80 is approximately 0.2847.

The weighted probability for a randomly selected policyholder is (0.60 * 0.3446) + (0.40 * 0.2847) = 0.3106.

(b) Given that a male policyholder just turned 80 years old today, we can use conditional probability to calculate the likelihood of him living for at least three more years.

Using the normal distribution with mean 75 and standard deviation 8, the probability of survival beyond 83 (80 + 3) is approximately 0.8621.

Therefore, the probability that a male policyholder, who just turned 80, will live for at least three more years is 0.8621.

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Answer:

∠QST = 115°

Step-by-step explanation:

Because all angles on a straight line must add to 180 and so should the total angles in a triangle:

∠UST + 23x = 180

And:

∠UST + 12x + 55 = 180

So knowing this, ∠U + ∠T must add up to 23x because 180 - ∠UST is the same for both above equations:

55 + 12x = 23x

Subtract 12x from both sides to isolate the 55 and 23x:

55 + 12x - 12x = 23x - 12x

55 = 11x

Divide both sides by 11:

\(\frac{11x}{11} = \frac{55}{11}\)

x = 5

As ∠QST = 23x, we can substitute in the known x:

23x =

23(5) =

23 * 5 = 115

So ∠QST = 115°

Hope this helps!

Answer:

qst 115

Step-by-step explanation:

sum of a triangle add up 180

Subtract the given angle from 180° and the missing angle measurements is 42°.

What is meant by angle ?

A+B+C=180°

57°+81°+C°=180°

138°+C=180°

C=138°-180°

C=42°.

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Ndidi rides y km at 10 km/hr, then walks 0.5y km at 3 km/hr. She is away from. home less than 4hours.Range of the values of Y is =24/7

Let's call the total time spent riding and walking t hours. We know that t is less than 4 hours, so:

t = time spent riding + time spent walking < 4 hours

The time spent riding is given by y / 10 km/hr and the time spent walking is given by 0.5y / 3 km/hr. So, we can write the inequality as:

t = y / 10 + 0.5y / 3 < 4

Expanding and simplifying the expression on the left side gives:

7/6y < 4 * 6/7

Multiplying both sides by 6/7 gives:

y < 4 * 6/7 * 6/7 = 24/7

So, the range of values of y is 0 < y < 24/7 km. This means that Ndidi rode less than 24/7 km, but more than 0 km.

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The expression that can be express in the form  (ax + b)(ax - b), are x² - 9 and  9x² - 4.

The expression that can be written in the form (ax + b)(ax - b), where a and b are integers can be represented as follows:

Therefore,

The expression should be able to be express in the form as follows:

(ax + b)(ax - b)

x² - 9 = (x - 3)(x + 3)

Therefore,

(x - 3)(x + 3) = x² + 3x - 3x - 9

x² + 3x - 3x - 9  = x² - 9

Therefore,

(x - 3)(x + 3) = x² - 9

9x² - 4 = (3x + 2)(3x - 2)

(3x + 2)(3x - 2) = 9x² - 6x + 6x - 4

9x² - 6x + 6x - 4 = 9x² - 4

Therefore, the expression are x² - 9 and  9x² - 4

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The correct answer is (b) The average rate of change of temperature is 0 from 2 PM to 4 PM and also from 10 AM to 8 PM.

What is a temperature simple definition?

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The complete question is-

The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City.Time of Day10 AM12 Noon2 PM4 PM6 PM8 PM10 PMTemperature (F)30353636343028Over which period(s) of time is the average rate of change zero? What, if anything, can you conclude about the actual temperature fluctuation within this period?a.The average rate of change of temperature is 0 from 2 PM to 4 PM; Nothing can be concluded about the actual temperature fluctuation.b.The average rate of change of temperature is 0 from 2 PM to 4 PM and also from 10 AM to 8 PM; Nothing can be concluded about the actual temperature fluctuation.c.The average rate of change of temperature is 0 from 10 AM to 8 PM; Nothing can be concluded about the actual temperature fluctuation.d.The average rate of change of temperature is 0 from 2 PM to 4 PM and also from 10 AM to 8 PM; The conclusion that can be drawn is that the temperature will not change for that time period.

The value of polynomial for x = 2 that is f(2) will be 32.  

In many branches of mathematics and science, polynomials are used. For instance, they are used to define polynomial functions, which show up in settings ranging from basic chemistry and physics to economics and social science.

They are also used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to form these functions. Polynomial rings and algebraic varieties, two fundamental ideas in algebra and algebraic geometry, are constructed in advanced mathematics using polynomials.

We have given polynomial f(x)=3x²8x+4

We have to find the value of f(2

We have to find the value of polynomial for x = 2

So for finding this value we have to just put x = 2 in polynomial

So f(2) will be

So the value of polynomial for x = 2 will be 32

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Answer:

A. x= -12

B. y=4

Step-by-step explanation:

A. The first one is called,

Product of Powers, a^m * a^n = a^m+n

a=7, m=-9, and n=-3

7^-9+-3=7^-12

x=-12

B. The second one is called,

Quotient of Powers, a^m/a^n = a^m-n

a=11, m=-4, and n=-8

11^-4-(-8)=4

(A negative minus a negative equals a positive)

y=4

Hope this was helpful, have a good day.

Step-by-step explanation:

First take the sum angle of triangle ABC .

Then the angle of x execute ..i.e. 37°

so after that take triangle ADC Then find the value of Y .I e. 106°

Answer:

x+69+90=180

x+159=180

x=180-159

x=61

and

y=90

The concept of the unit circle is presented throughout it's answer.

The unit circle is a circle with a radius of 1 unit that is centered at the origin (0,0) of a coordinate plane. It is a fundamental concept in trigonometry and geometry, and it is used to define the trigonometric functions (sine, cosine, and tangent) of angles in the Cartesian plane.

The format of each coordinate on the unit circle is given as follows:

\((\cos{\theta}, \sin{\theta})\).

Hence we can calculate the trigonometric measures for any angle, as the tangent, the secant, the cossecant and the cotangent of an angle are all functions of the sine and the cosine obtained by the unit circle.

The problem is incomplete, hence the unit circle concept is presented in this answer.

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Answer:

I'm pretty sure the answer would be 3.

Step-by-step explanation:

I'm not super sure but that makes sense

Answer:

The diameter of the circle is 7/2.

Step-by-step explanation:

⭐What is the radius of a circle?

⭐What is the diameter of a circle?

Thus, the diameter of said circle is twice the radius of said circle.

diameter = 2(radius)

diameter = 2(7/4)                   . . . . substitute known values

diameter = 14/4                      . . . . multiply the numerator & denominator

diameter = 7/2                       . . . . simplify

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The required value of the lesser integer is -4 for the given statement.

The quadratic equation is defined as a function containing the highest power of a variable is two.

Let's represent the two consecutive negative even integers x and x+2. Then, the equation representing the statement is:

x × (x + 2) = 8

Expanding the right-hand side:

x² + 2x - 8 = 0

This is a quadratic equation that can be solved using the factor method:

x² + 2x - 8 = 0

x² + 4x - 2x - 8 = 0

(x - 2)(x + 4) = 0

(x - 2) = 0 and (x + 4) = 0

x = 2, and  x = -4

Hence, the value of the lesser integer is -4.

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Answer:

Y = a(x-h)^2 +k

Step-by-step explanation:

The first one, since the vertex form is in subtraction form. You need the a, the x, the h, and the k for the formula.

Answer:

y=a(x-h)^2+k

Step-by-step explanation:

This is the answer because numbers in the -h and k is the vertex point in this form.

e.g. y=2(x-4)^2+5

the vertex here is (4,5)

(btw, for h, when there's a negative sign in front of it, it's the opposite and when there's a plus sign in front of h, it's the opposite.)

The number of student like at least one kind of ice cream is given by (d) 275.

Let C be the student who like chocolate ice cream and P be the student who like Pistachio ice cream.

Now given that, n(C) = 145, n(P) = 150

Also given that, 123 students do not like neither chocolate or pistachio ice cream.

So, n(P' and C') = 123

The required number of student like at least one kind of ice cream is given by,

N = 398 - n(P' and C') = 398-123 = 275

Hence the correct option is (d).

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