The common difference of an arithmetic sequence is -5. If a12 is 22, what is a1?

Answer:

x = \(\frac{1}{3}\)

Step-by-step explanation:

using the rule of exponents

\((a^m)^{n}\) = \(a^{mn}\) , then

\(8^{x}\) = 2

\(2^3)^{x}\) = 2 , that is

\(2^{3x}\) = \(2^{1}\)

since the bases on both sides are equal, both 2, then equate the exponents

3x = 1 ( divide both sides by 3 )

x = \(\frac{1}{3}\)

Answer:

hey we can talk here

Step-by-step explanation:

Answer:

733 1/3 feet

\((733.\bar{3} \: ft) \)

Step-by-step explanation:

There are 60 seconds in a minute and 60 minutes in an hour.

S = d/t →

S × t = d/t × t →

St = d →

D = st.

Because the speed is in mph, the time is relative to hours.

This means that t = 1 at one hour.

To find the distance, we need to know how many seconds are in an hour.

Knowing that 60 seconds are in a minute and 60 minutes are in an hour.

60 × 60 = 3600.

3600 seconds / hour.

Given the speed is 100 miles / hour,

and that the time traveled is 5 seconds.

D = s × t = D = (miles per hour) × (seconds / 3600) =

100 × 5 / 3600 = 500 / 3600 =

10 / 72 miles.

There are 5280 feet in a mile, so

5280 × 10 / 72 = 52800 / 72 =

26400 / 36 = 13200 / 18 =

6600 / 9 = 2200 / 3 = 733 1/3

The correct answer is Option C. A researcher might choose purposive sampling over systematic sampling for several reasons. One key reason is that purposive sampling allows the researcher to study a particular type of participant.

This means that the researcher can select individuals who possess specific characteristics or traits that are relevant to their study.

By handpicking participants, the researcher can ensure that the sample represents the specific population they are interested in studying, which is particularly useful when investigating rare or hard-to-reach populations.

On the other hand, systematic sampling involves selecting participants at regular intervals from a larger population.

This method may not provide the same level of control in selecting participants based on specific characteristics.

While systematic sampling can be more efficient in terms of time and cost, it may not be suitable for certain research objectives that require a targeted approach.

It is important to note that neither method is inherently cheaper or more expensive than the other, and the choice between them depends on the research objectives and the specific population under investigation.

Therefore, option A is incorrect.

Option B is also incorrect because external validity is still important in research regardless of the sampling method chosen.

Option D is also incorrect since researchers using purposive sampling must still specify their population of interest.

Thus, the correct answer is option C.

For more questions on researcher

https://brainly.com/question/32544768

#SPJ8

The original price of the desk before discount was $900.

A discount is the reduction in the marked price of items, discounts are generally given to customers to attract them towards some items or on sale.

Given that a desk is at sell today, the shop is offering 33% discount on it, which will give a selling price of $603.

We need to find the desk's yesterday price,

So, let the yesterday price be x,

Therefore,

100 - 33 = 67

Therefore,

67% of x = 603

x = 603 × 100 / 67

x = 900

Hence the original price of the desk before discount was $900.

Learn more about discount click;

https://brainly.com/question/31430480

#SPJ2

The pair adjacent angles are CAD and DAE

The pair of complimentary angles are BAC and CAD.

The pair of supplementary angles are BAD and DAE

The pair of vertical angles are BAC and FAE.

Adjacent angles are two angles which have common side and a common vertex.

Complementary angles are when two angles add up to 90 degrees.

Supplementary angles are when two angles add up to 180 degrees.

Therefore,

Adjacent angles are CAD and DAE

Complimentary angles are BAC and CAD.

Supplementary angles are BAD and DAE

Vertical angles are BAC and FAE.

Read more on complimentary angles:

https://brainly.com/question/16281260

#SPJ1

Answer:

8v+4

This correct because basically what you are doing is multiplying the 2 so if 4v multiply it by 2 and you would get 8v

The antiderivative of the function f(x) = e^(-x) - e^(4x) is given by -e^(-x) - (1/4)e^(4x)/4 + C, where C is the constant of integration. This represents the general solution to the indefinite integral of the function.

In simpler terms, the antiderivative of e^(-x) is -e^(-x), and the antiderivative of e^(4x) is (1/4)e^(4x)/4. By subtracting the antiderivative of e^(4x) from the antiderivative of e^(-x), we obtain the antiderivative of the given function.

To evaluate a definite integral of this function over a specific interval, we need to know the limits of integration. The indefinite integral provides a general formula for finding the antiderivative, but it does not give a specific numerical result without the limits of integration.

To compute the antiderivative of the function f(x) = e^(-x) - e^(4x), we can use basic integration formulas.

∫(e^(-x) - e^(4x))dx

Using the power rule of integration, the antiderivative of e^(-x) with respect to x is -e^(-x). For e^(4x), the antiderivative is (1/4)e^(4x) divided by the derivative of 4x, which is 4.

So, we have:

∫(e^(-x) - e^(4x))dx = -e^(-x) - (1/4)e^(4x) / 4 + C

where C is the constant of integration.

This gives us the indefinite integral of the function f(x) = e^(-x) - e^(4x).

If we want to compute the definite integral of f(x) over a specific interval, we need the limits of integration. Without the limits, we can only find the indefinite integral as shown above.

Learn more about indefinite integral here:

brainly.com/question/28036871

#SPJ11

(a) P(0) = 117218, P(10) = 195468, P(15) = 229593, P(20) = 263718, P(25) = 297843. The population is growing.

(b) dp/dt = 787.5.

(c) P'(0) = 787.5, P'(10) = 668.75, P'(15) = 543.75, P'(20) = 412.5, P'(25) = 275. The rate of growth is decreasing

(a) To evaluate P for t = 0, 10, 15, 20, and 25, we substitute the given values of t into the population model:

P(0) = -14.77 + 117.218 = 102.448 thousand people

P(10) = -14.77 + 787.5(10) + 117.218 = 875.718 thousand people

P(15) = -14.77 + 787.5(15) + 117.218 = 1,321.968 thousand people

P(20) = -14.77 + 787.5(20) + 117.218 = 1,768.218 thousand people

P(25) = -14.77 + 787.5(25) + 117.218 = 2,214.468 thousand people

These values represent the estimated population of the country (in thousands) at the given points in time. As we can see, the population is growing over time.

(b) To determine the population growth rate, we take the derivative of the population model with respect to time:

dP/dt = 787.5

This means that the population is growing at a rate of 787.5 thousand people per year.

(c) To evaluate dP/dt for the same values as in part (a), we substitute the values of t into the expression for dP/dt:

P'(0) = 787.5 thousand people per year

P'(10) = 787.5 thousand people per year

P'(15) = 787.5 thousand people per year

P'(20) = 787.5 thousand people per year

P'(25) = 787.5 thousand people per year

These values are all the same, indicating that the population growth rate is constant over time. However, since the population is growing exponentially, the rate of growth (in percentage terms) is actually decreasing over time.

Learn more about  rate of growth

https://brainly.com/question/13870574

#SPJ4

Answer:

The height of the tower is 310.6 ft

The height of the tower 310.6 ft if the angle of depression and elevation is given.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that  tower is located 327 feet from a building

A person from the second story measures an angle of elevation to the top of the tower as 32° and an angle of depression to the bottom of the tower as 18°.

We have to find the height of the tower.

By using angle of elevation we find the height.

327/sin 72 = x / sin18

343.8 = x/ sin 18

x=sin 18(343.8)

x= 106.25

Now 327/sin 58 = y/sin 32

385.59 = y/sin32

y=204.33

Height is 106.25+204.33 which is 310.6 ft.

Hence,  the height of the tower to the nearest tenth of a foot is 310.6 ft.

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ2

Answer:

17/18

Step-by-step explanation:

okay this one is a bit different

you have to take the total number that are batwing-shaped (12) and the total number that are made of cotton (12) and then subtract the ones that are both batwing-shaped and made of cotton.

so 12+12-7 which is 17

then you put that over the total (18)

17/18 doesn't simplify

Minimax Regret Approach takes place when the decision chosen is the one corresponding to the minimum of the maximum regrets.

In the Minimax Regret Approach, decisions are evaluated based on their maximum possible regret. It aims to minimize the potential regret associated with a decision by selecting the option that corresponds to the minimum of the maximum regrets.

In decision-making scenarios, individuals often face uncertainty about the outcomes and have to choose from various alternatives. The Minimax Regret Approach provides a systematic method for evaluating these alternatives by considering the regrets associated with each decision.

To apply this approach, the decision-maker identifies the potential outcomes for each decision and determines the corresponding payoffs or losses. The regrets are then calculated by subtracting each payoff from the maximum payoff across all decisions for a particular outcome. The decision with the smallest maximum regret is chosen as it minimizes the potential loss or regret.

Learn more about Minimax Regret Approach

brainly.com/question/32228433

#SPJ11

No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

For more such question on fraction

https://brainly.com/question/17220365

#SPJ8

Answer:

B

Step-by-step explanation:

i hope this helps a bit.

The probability that the second card is a jack given that the first card was a 2 is 52/51.

To calculate the probability that the second card is a jack given that the first card was a 2, we need to consider the remaining cards in the deck after the first card is drawn.

When the first card is drawn and it is a 2, there are 51 cards remaining in the deck, out of which there are 4 jacks.

The probability of drawing a jack as the second card, given that the first card was a 2, can be calculated using conditional probability:

P(Second card is a jack | First card is a 2) = P(Second card is a jack and First card is a 2) / P(First card is a 2)

Since the first card is already known to be a 2, the probability of the second card being a jack and the first card being a 2 is simply the probability of drawing a jack from the remaining 51 cards, which is 4/51.

The probability of the first card being a 2 is simply the probability of drawing a 2 from the initial deck, which is 4/52.

P(Second card is a jack | First card is a 2) = (4/51) / (4/52)

Simplifying the expression:

P(Second card is a jack | First card is a 2) = (4/51) * (52/4)

P(Second card is a jack | First card is a 2) = 52/51

To learn more about probability click here:

brainly.com/question/30736116

#SPJ11

Answer:

4.7

Step-by-step explanation:

Substitute value

6,5 - 1.8

=4.7

Answer:

D. \( y = \frac{ {x}^{2} - w }{2z} \)

Step-by-step explanation:

\(w = {x}^{2} - 2yz \\ \\ 2yz = {x}^{2} - w \\ \\ \huge \red{ y = \frac{ {x}^{2} - w }{2z} }\)

The value of the integral ∫√(2) dx from 0 to 49 using the substitution x = 7tanθ is (7π√(2))/4.

To evaluate the integral ∫√(2) dx from 0 to 49, the substitution x = 7tanθ will be the most helpful.

Let's substitute x = 7tanθ, then find dx in terms of dθ:

\(x = 7tanθ\)

Differentiating both sides with respect to θ using the chain rule:

\(dx = 7sec^2θ dθ\)

Now, we rewrite the integral using the substitution\(x = 7tanθ and dx = 7sec^2θ dθ:\)

\(∫√(2) dx = ∫√(2) (7sec^2θ) dθ\)

Next, we need to find the limits of integration when x goes from 0 to 49. Substituting these limits using the substitution x = 7tanθ:

When x = 0, 0 = 7tanθ

θ = 0

When x = 49, 49 = 7tanθ

tanθ = 7/7 = 1

θ = π/4

Now, we can rewrite the integral using the substitution and limits of integration:

\(∫√(2) dx = ∫√(2) (7sec^2θ) dθ= 7∫√(2) sec^2θ dθ\)

\(= 7∫√(2) dθ (since sec^2θ = 1/cos^2θ = 1/(1 - sin^2θ) = 1/(1 - (tan^2θ/1 + tan^2θ)) = 1/(1 + tan^2θ))\)

The integral of √(2) dθ is simply √(2)θ, so we have:

\(7∫√(2) dθ = 7√(2)θ\)

Evaluating the integral from θ = 0 to θ = π/4:

\(7√(2)θ evaluated from 0 to π/4= 7√(2)(π/4) - 7√(2)(0)= (7π√(2))/4\)

Learn more about the integral here:

https://brainly.com/question/17015884

#SPJ11

Answer:

x = 6

Step-by-step explanation:

Given

\(\frac{4}{3}\) = \(\frac{8}{x}\) ( cross- multiply )

4x = 24 ( divide both sides by 4 )

x = 6

Answer:

-2 or -2/1

Step-by-step explanation:

Since the equation is in y = mx + b form with m equaling the slope, we can see that -2 is in m's place, so -2 is the slope.

Answer:

So, his normal weight is 80 kg

Step-by-step explanation:

Let his normal weight be x

If the normal weight               increasing percent         now weighs

       100                                               10                                 110

         x                                                  10                                88

Now we can get a equation as,

\(100 = 110\\x = 88\)

We can write this as a fraction

\(\frac{100}{x} = \frac{110}{88}\)

You can use cross multiplication to solve this

\(88*100=110x\\8800=110x\\\frac{8800}{110} =\frac{110x}{110} \\80kg = x\)

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

An equivalent ratio in simplest term is: 3 : 5

Answer:

um

Step-by-step explanation:

um

Answer:

y-5=6*(x+2)

Step-by-step explanation:

Answer:

y-5=6(x--2)

The formula for point slope form is: y-y1=m(x-x1)

Answer:

a,c,d

Step-by-step explanation:

I did the quiz

Answer:

acd edge 2023

Step-by-step explanation:

Option D correctly describes the expression as multiplying p by 0.25 (to calculate the discount) and subtracting that amount from p to obtain the sale price

The best description for Marcia's expression 0.75p, which represents the sale price of a television regularly costing p dollars with a 25% discount, is option D. She multiplied p by 0.25 then subtracted that from p.

When a store offers a discount, it means the price is reduced from the original price. In this case, the discount is 25%, which can be written as 0.25 or 25/100. To calculate the sale price, Marcia needs to subtract this discount from the original price.

To do so, she multiplies the original price p by 0.25, which represents 25% of p. Multiplying p by 0.25 gives the amount of the discount itself. By subtracting this discount amount from the original price p, Marcia arrives at the sale price.

The expression 0.75p indicates that 0.25p (25% of p) is subtracted from p. The remaining 0.75p represents 75% of the original price, which is the sale price after the discount. Thus, the expression accurately represents the sale price.

for similar questions on Discount

https://brainly.com/question/23865811

#SPJ8

Answer:

100.571429.

Step-by-step explanation:

2*22/7*(4)^2

=44/7*16

=100.571429

Answer to the question is (a) longest path. The critical path is determined by identifying all the possible paths and calculating their durations, and the one with the longest duration is identified as the critical path.

The number of paths can vary depending on the specific situation or system being analyzed.

The critical path is the longest path in terms of duration or time required to complete all its activities. It is the sequence of tasks or activities that must be completed in order to complete the project within the minimum possible time.

The critical path determines the total duration of the project, and any delay in the critical path activities will cause a delay in the project's completion time.

Therefore, the answer to the question is (a) longest path. The critical path is determined by identifying all the possible paths and calculating their durations, and the one with the longest duration is identified as the critical path.

The critical path method (CPM) is a popular technique used in project management to identify and manage the critical path.

Learn more about critical path.

brainly.com/question/16519233

#SPJ11

a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

Learn more about homeostasis at: https://brainly.com/question/3888340

#SPJ4