my last try anone willing to help

My Last Try Anone Willing To Help

Answers

Answer 1

Logarithmic function log₍ₓ₊₂₎(4) = 3x can be written in exponential form as  4 = 3x ⁽ˣ⁺²⁾

Which property of log function is used?

The properties of log are nothing but the rules of logarithms and these are derived from the exponent rules.

These properties of logarithms are used to solve the logarithmic equations and to simplify logarithmic expressions.

A log function can be written in exponential form using

logₐ m = x ⇒ m = ax

According to the given question:

The given logarithmic function is

log₍ₓ₊₂₎(4) = 3x

On applying the property we get

4 = 3x ⁽ˣ⁺²⁾

Hence the required exponential form is 4 = 3x ⁽ˣ⁺²⁾

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Related Questions

Mr. Wright is investing $1 million. He has options with Bank of Munich, Coralbank, and Lone Star Credit Union.
Bank of Munich is willing to pay him an interest rate of 2% on up to $250,000 of his money, and 1.25% on everything beyond that point.
Coralbank is providing him an interest rate of 3% on the first $500,000 he invests with them and 1% on whatever else he invests beyond that point.
Lone Star Credit Union is offering an interest rate of 1.75% on all funds invested with them.
Mr. Wright plans to leave whatever funds he invests in the account for 15 years.
ROUND ALL ANSWERS TO THE NEAREST TEN THOUSAND AND DO NOT USE COMMAS IN YOUR RESPONSE.
How much money should Mr. Wright expect to have after 15 years if he invests all of his funds with Coralbank?
How much money would he have if he invests everything with Bank of Munich for the full 15 years?
If he plans carefully and invests his funds to gain the maximum amount of interest across all three institutions, how much money will he have in each bank
after 15 years?
Bank of Munich:
Coralbank
Lone Star Credit Union:

Answers

In Coralbank $ 1,359,468.19 and In Bank of Munich $ 1,240,088.97

What is Interest?

The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

Given:

Coralbank is providing him an interest rate of 3% on the first $500,000 he invests with them and 1% on whatever else he invests beyond that point.

So, After 15 years

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03 rate per year,

Then solve the equation for A

A = P[tex](1 + r/n)^{nt[/tex]

A = 500,000.00[tex](1 + 0.03/1)^{(1)(15)[/tex]

A = 500,000.00[tex](1 + 0.03)^{(15)[/tex]

A = $778,983.71

and, for Another $500,000

A = P[tex](1 + r/n)^{nt[/tex]

A = 500,000.00 [tex](1 + 0.00/1)^{(1)(15)[/tex]

A = 500,000.00 [tex](1 + 0.01/1)^{(1)(15)[/tex]

A = $580,484.48

Total he Invests= $ 1,359,468.19

and, Bank of Munich is willing to pay him an interest rate of 2% on up to $250,000 of his money, and 1.25% on everything beyond that point.

Then solve the equation for A

r = R/100

r = 2/100

r = 0.02 rate per year,

Then solve the equation for A

A = P[tex](1 + r/n)^{nt[/tex]

A = 250,000.00[tex](1 + 0.02/1)^{(1)(15)[/tex]

A = 250,000.00 [tex](1 + 0.02)^{(15)[/tex]

A = $336,467.08

and, for Another $750,000 .

A = P[tex](1 + r/n)^{nt[/tex]

A = 750,000.00[tex](1 + 0.0125/1)^{(1)(15)[/tex]

A = 750,000.00 [tex](1 + 0.0125)^{(15)[/tex]

A = $903,621.89

Total he Invests= $ 1,240,088.97

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jo adds up all the positive integers from 1 to 100. kate does a similar thing with the first 100 positive integers; however, she first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 100 values. what is the positive difference between jo's sum and kate's sum?

Answers

Jo's sum is easy   = (100)(101)/2  =  50 * 101   =  5050

Given,

In the question:

Jo adds up all the positive integers from 1 to 100. Kate does a similar thing with the first 100 positive integers.

She first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 100 values.

To find the what is the positive difference between jo's sum and Kate's sum?

Now, According to the question:

Kate  would first start with 5  [ since 1 - 4 ]  are rounded to 0

Starting with 5 thru 14  she will have ten 10s

15 - 24   she will have  ten 20s

25 - 34 she will have  ten 30s

.

.

.

.

.

85 - 94 she will have ten 90s

95 - 100   she will have six 100s

So.....her sum is

10  [10  + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90]  + 6 [100]

10  [ (10) (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) ] + 6[100]  

10 (10)  [  sum of the first nine positive integers ] + 6 [ 100]

100  [  (9)(10) / 2 ]  + 6[100]  

100 [ 45]  + 6[100]

100 [ 45 + 6 ]  

100 [ 51 ]

5100

Hence, The positive difference is 5100 - 5050  =  50

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how many ways are there for eight men and five women to stand in a line so that no tow women stand right next to each other

Answers

In 609638400 ways eight men and five women can stand in a line so that no two women stand next to each other.

What is meant by Permutation?

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are organized in a linear or sequential manner. The permutation of the set A=1,6 is 2, for instance, 1,6, and 6,1. There is no alternative way to organize the components of set A, as you can see.

In contrast to combination, where the order of the parts is irrelevant, permutation calls for a specific arrangement of the elements in many ways.

We genuinely wonder how the timetables of trains, buses, and airlines are set up in accordance with the convenience of the general population. Of course, the permutation is quite useful in planning the departure and arrival timetables for these.

How to solve?

For 8 men in a line: 8! = 40320  

In order to separate 2 women, we have to choose 5 out of 9

C(9,5) = 9! / 5!4! = 126

Random place 5 women in the 5 chosen places: 5! = 120

Total ways= 40320 * 126 * 120 = 609638400

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If I buy a new video game set that is originally $40, how much will I save if they are 40% off?

Answers

Answer: $16 dollars

Step-by-step explanation: 40% of 40 is 16 so you save $16. Game would now cost $24.

24$ you will have to pay

78. the probability that a marksman will hit a target each time he shoots is 0.89. if he fires 15 times, what is the probability that he hits the target at most 13 times?

Answers

The probability that the marksman will hit the target 13 times is 0.279.

Here, we are given that the probability that a marksman will hit a target each time he shoots is 0.89.

Thus, the probability that he will not hit the target = 1 - 0.89 = 0.11

Here, we can use the concept of binomial distribution to find the probability.

There are a total number of 15 trials, thus, n = 15

Success ⇒ marksman hits the target

Probability of success ⇒ p = 0.89

Failure ⇒ marksman fails to hit the target

Probability of failure ⇒ q = 0.11

Number of successful outcomes required ⇒ x = 13

Now, according to the formula for calculating binomial probability-

P(x) = [tex]nCx *p^{x} *q^{n-x}[/tex]

P(x) = [tex]15!/(13!*2!) *(0.89)^{13} *(0.11)^{2}[/tex]

P(x) = (15*14/2) (0.2198) (0.0121)

P(x) = 105* 0.0026

P(x) = 0.279

Thus, the probability that the marksman will hit the target 13 times is 0.279.

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if someone tossed a fair coin in the air three times and it came up heads all three times, what is the likelihood that it will come up heads on the fourth try?

Answers

The probability that the coin will come up heads on the fourth try is 1/2.

Given,

If a fair coin were tossed three times and each time it landed on its head.

We have to find the probability that it will come up heads on the fourth try;

Here,

Coming up short in the first three of four attempts.

The probability will not depend on the first three occurrences in the fourth try.

Consequently, the likelihood of winning the fourth time will be as follows:

Desired outputs as a percentage of overall output

=> 1 / 2

Hence,

The probability of the coming head in the fourth time is 1/2 because the coming head in the fourth time is independent of the coming head in the first three times.

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every fifth adult entering an airport is checked for extra security screening. what sampling technique is used?

Answers

It belongs to isometric sampling or systematic sampling in every fifth adult entering an airport is checked for extra security screening.

What is systematic sampling?

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval.

Security workers at an airport randomly choose one of the first 50 people to pass through a checkpoint for extra security screening.

After that person, they choose every 50th person who passes through for extra screening as well

By the topic

The sampling interval is 50, which is periodic.

It belongs to isometric sampling or systematic sampling.

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melissa makes bracelets at a constant rate. she spends 45 minutes making 25 bracelets. which equation describes the relationship between the time in minutes she spends making bracelets, t, and the total number of bracelets she makes, n?

Answers

Answer:09.8990

Step-by-step explanation: take one and add

Determine the factors of x2 + 4x - 12.

Answers

Answer:

(x+6)(x-)

Step-by-step explanation:

what was the major flaw in the stanford prison experiment? group of answer choices zimbardo did not use a control group. the respondents wanted to leave, but zimbardo would not let them. the students were not randomly assigned. the study went on too long.

Answers

The answer is (a) Zimbardo did not use a control group.

The stanford prison experiment was a two week simulation of a prison environment that examined the effect of situational variables on participants reactions and behaviors.

The Stanford prison experiment, one of the most famous and compelling psychological studies of all time.

The major flaw in the research design of the Stanford prison experiment was that the Zimbardo did not use a control group.

A control group is used to establish a cause-and-effect relationship by isolating the effect of an independent variable. A control group was necessary to study a particular variable in prison. He had no alternative group to compare to measure the results of the experiment.

A control group in an experiment does not receive the treatment. Instead, it serves as a comparison group for the treatments.

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the teacher orders tights for the dance class. She buys as many tights as there are students. What equation can solve the amount of tights needed.

Answers

The equation that can be solve to know the amount of tights needed is c = 20p.

What equation can solve the amount of tights needed?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the teacher orders 20 tights for the dance class and she buys as many as p tights as there are students.

The equation will be illustrated thus:

Let total amount be c

c = 20 × p

c = 20p

The equation is c = 20p.

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Complete question

A teacher orders 20 tights for the dance class. She buys as many as p tights as there are students. What equation can solve the amount of tights needed?

in preparation, you identify all possible outcomes and the probability of each outcome. which approach to negotiation are you using? game theory individual differences cognitive approach situational characteristics

Answers

By identifying all possible outcomes and the probability of each outcome the negotiation used here is Game theory.

The study of mathematical models of strategic interactions between rational beings is known as game theory and it has uses in computer science, logic, systems science, and all branches of social science.

The most well-known application of game theory is The Prisoner's Dilemma for instance take two offenders who were detained following an arrest as an example. The prosecution lacks concrete proof to prove their guilt. Officials, however, take the inmates out of their isolation cells and question each one separately in order to extract a confession.

The area of mathematics known as "game theory" is concerned with the analysis of such games. Classical game theory and combinatorial game theory are the two primary subfields of game theory. Traditional game theory examines games where participants can move, wager, or strategize all at once.

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convert 6 yards 5 feet to inches

(conversion factors) 12 inches = 1 foot; 3 feet + 1 yard

NEED HELP ASAP PLEASE

Answers

276 inches

1 yard-36 inches
5*12=60
6*36=216
60+216=276

Answer:

276 inches

Step-by-step explanation:

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does someone know this?

Answers

Multipluy the equations i think...

The regular price of a sweater is $32. For a sale, the price of the sweater is marked down 30%. What is the sale price of the sweater?​

Answers

Answer: $22.40

Step-by-step explanation:

30% of 32, or 0.3(32) is equal to 9.6. Then you have to subtract that amount, which is 32 - 9.6, which then gets us to 22.40.

Help solve the proportion

Answers

Answer: 9

Step-by-step explanation:

Solve for d -9a-12=12-d

Answers

Answer:

d= 24 + 9a

Step-by-step explanation:

– 9a – 12 = 12 – d

by collecting like terms

–9a +d = 12 +12

–9a +d = 24

d= 24 + 9a

Answer:

Step-by-step explanation:

-9a-12=12-d

d=9a+24

40 divided by 5 times (24-23)

Answers

It’s eight I think :)

What i the point-lope from the line with lope -1/4 that pae through the point (-2,9)

Answers

The equation of the line in point slope form is y = -1/4x + 17/2.

Define the term point slope form?A line's equation written using a single point mostly on line and the line's slope is referred to as the point-slope form. The slope is really the rise over distance, or the proportion of the change there in y values over change in the x values, and the point form is denoted as (x,y).

The slope of the equation of the line is given as;

slope m = -1/4

Passing point = (-2,9)

Equation of the line;

y - y1 = m(x - x1)

y - 9 = -1/4(x + 2)

y = -1/4x -1/2 + 9

y = -1/4x + 17/2

Thus, the equation of the line in point slope form is y = -1/4x + 17/2.

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find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 40. b) 48. c) 56. d) 64.

Answers

With any of the six correct integers, there is a 0.35 percent probability of not winning the lottery.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, considering that n is 40:

n = 40 as a positive integer

Probability of not choosing any of the six ideal numbers in a lottery:

C(34 , 6)/C(40 , 6)

The likelihood of choosing none of the six correct integers in a lottery:

1344904/3838380

Probability of not winning a lottery with any of the six correct integers:

0.35

Therefore, with any of the six correct integers, there is a 0.35 percent probability of not winning the lottery.

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Correct question:
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.)

a) 0.40

b) 0.48

c) 0.56

d) 0.64

e) 0.35

explain why the analysis of differences is important in the confirmation of accounts receivable, even if the misstatements in the sample are not material.

Answers

The purpose of accounts receivable confirmations is to obtain third-party verification of the account's balance and to determine how frequently misstatements take place.

Here,

Only a small portion of the entire population is often subject to accounts receivable confirmation. The confirmation's goals are to gain external confirmation of the account's balance and to get a sense of how frequently misstatements in the accounts occur.

The majority of errors revealed by discrepancies on the confirmation replies won't be significant; however, discrepancies must be examined individually and collectively to establish their impact on the total balance of accounts receivable.

Even while the discrepancies between individuals may not be significant, they could point to a significant issue with the internal controls over accounts receivable when applied to the entire population.

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Which graph matches the following system of equations?

Answers

The answer would be A

What is the circumference in terms of pi for a circle with a area 81?

Answers

Answer:

C≈31.9

Step-by-step explanation:

Solve each inequality. Use the number line provided to test intervals.

Thank you!! :)

Answers

Answer:

  [-2, 2/5] ∪ [2, ∞)

Step-by-step explanation:

You want the solution to the inequality 7x³ -20x +11 ≥ 2x³ +2x² +3.

Factors

The inequality can be rewritten to a comparison with zero by subtracting the right-side expression.

  7x³ -20x +11 -(2x³ +2x² +3) ≥ 0

  5x³ -2x² -20x +8 ≥ 0 . . . . . . . simplify

  x²(5x -2) -4(5x -2) ≥ 0 . . . . . . factor pairs of terms

  (x² -4)(5x -2) ≥ 0 . . . . . . . . . . remove common factor

  (x -2)(5x -2)(x +2) ≥ 0 . . . . . factor difference of squares

Intervals

The values of x that make this product equal to zero are

  x -2 = 0   ⇒   x = 2

  5x -2 = 0   ⇒   x = 2/5

  x +2 = 0   ⇒   x = -2

These x-intercepts divide the domain into 4 intervals where we need to check the sign.

From left to right:

(-∞, -2)

  Using x = -3, we find the product to be ...

  (-3 -2)(5(-3) -2)(-3 +2) = (-5)(-17)(-1) = -85, less than 0

[-2, 2/5]

  Using x = 0, we find the product to be ...

  (0 -2)(5·0 -2)(0 +2) = (-2)(-2)(2) = 8, part of the solution

(2/5, 2)

  Using x = 1, we find the product to be ...

  (1 -2)(5·1 -2)(1 +2) = (-1)(3)(3) = -9, less than 0

[2, ∞)

  Using x = 3, we find the product to be ...

  (3 -2)(5·3 -2)(3 +2) = (1)(13)(5) = 65, part of the solution

The solution to the inequality is [-2, 2/5] ∪ [2, ∞).

__

Additional comment

The function we're comparing to zero is a cubic with a positive leading coefficient. That means the general shape of its graph is /, negative on the left and positive on the right.

The graph changes sign at each of the zeros, so we already know the curve is positive between the left two x-intercepts, and to the right of the rightmost x-intercept. We just need to define the intervals so the zeros themselves are included in the solution set.

Multiply: (9x + 8) (3x² + x − 1)
O 27x³ + 9x² - 8
O 27x³ + 33x² + 17x + 8
O 3x² + 10x + 7
O 27x³ +33x² - x - 8​

Answers

Answer:

[tex]\textsf{D)} \quad 27x^3+33x^2-x -8[/tex]

Step-by-step explanation:

Given expression:

[tex](9x+8)(3x^2+x-1)[/tex]

Distribute the parentheses:

[tex]\implies 9x \cdot 3x^2+9x \cdot x+ 9x \cdot (-1) + 8 \cdot 3x^2 + 8 \cdot x +8 \cdot(-1)[/tex]

Simplify:

[tex]\implies 27x^3+9x^2-9x + 24x^2 + 8x -8[/tex]

Collect like terms:

[tex]\implies 27x^3+9x^2+ 24x^2-9x + 8x -8[/tex]

Combine like terms:

[tex]\implies 27x^3+33x^2-x -8[/tex]

Surface Area =
A. 52 in2
B. 78 in2
C. 45 in2

Answers

Answer:

78 in²   (Choice B)

Step-by-step explanation:

Since they have exploded the 3-D cuboid into 2-D, it is easier to compute

Looking at the 2-D version you can see 4 rectangles each 3" x 5"

At the bottom on each side are 2 squares each 3" x 3"

Area of a rectangle = l x w

In this case, area of each rectangle = 3 x 5 = 15

Since there are 4 rectangles, total area of these four = 4 x 15 = 60 in²

Each square is area 3" x 3" = 9"

Since there are 2 such squares, total area of these two = 9 x 2 = 18in²

Total area of the 2-D blowup which is the same as the Surface Area of the prism = 60 in² +  18in² = 78 in²

Describe and correct the error in solving the equation for x.

Answers

Answer:

[tex]\frac{10 +3b}{a} =x[/tex]

Step-by-step explanation:

By manipulating equations, we can solve for different variables.

Error

The error in the equation is in the factoring. In the second line, the x is factored out of the expression; however, this cannot be factored. Factoring is like dividing. When you factor x out you divide the terms by x. Since there is not an x in 3b, x cannot be factored out.

A correct version of factoring looks like:

ax - 3bx + 2cx = x (a - 3b + 2c)

Correction

Now, we can go back to the beginning and solve for x correctly using the properties of equality. First, rewrite the equation.

10 = ax - 3b

Then, add 3b to both sides.

10 + 3b = ax

Finally, divide by a.

[tex]\frac{10 +3b}{a} =x[/tex]

This is the final, correct equation solved for x.

Point O is the incenter of triangle A B C. Lines are drawn from the points of the triangle to point O. Lines are drawn from point O to the sides of the triangle to form right angles and line segments O Q, O R, and O S. Angle O B C is 15 degrees. Angle O C R is 30 degrees.
What is mAngleQOB?
a. 30°
b. 60°
c. 75°
d. 90°

Answers

The measure of angle QOB is  75°.

What is right angle?

90 degrees is the angle of a right.

The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol stands for a right angle.

Given:

Point O is the incenter of triangle ABC.

Lines are drawn from the points of the triangle to point O.

Lines are drawn from point O to the sides of the triangle to form right angles and line segments OQ, OR, and OS.

Angle OBC is 15 degrees. Angle OCR is 30 degrees.

OBC= 15

OCR =30

In OBQ

OBQ + QOB + OQB = 180

OBQ= OBC=15

OQB= 90

So,

QOB = 180- OBQ- OQB

= 180-15 -90

= 75

Hence, the measure of angle QOB is  75°.

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Multiply the following polynomials. Write the simplified answer in descending order. Use the ^ (shift + 6) to indicate exponents.

DO NOT add spaces between any numbers or characters. For example: (x+2)(x+3) = x^2+5x+6.

(3xy - 1)(4xy + 2)

Answers

Answer:

12x^2.y^2 + 2xy - 2

Step-by-step explanation:

I put the dot so you don't get confused thinking it is 2y. Tell me if I misinterpreted the question

Apply the ditributive property to factor out the greatet common factor. 60 − 40 y =

Answers

The factors by applying distributive property out the greatest common factor is 20(3 - 2y).

Define the term greatest common factor?The largest of these shared factors is the greatest common factor of the two integers.

For the stated equation;

= 60 − 40 y

Do the prime factorization of the both numbers-

60 = 2×2×3×5

40 = 2×2×2×5

Thus, the greatest common factor from both numbers is-

2×2×5 = 20

Taking 20 common from both terms in equation-

Using distribute property;

= 20(3 - 2y)

Thus, factors by applying distributive property out the greatest common factor is 20(3 - 2y).

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Solve the equation 4 2/5 + k = -3 2/11K=? If I drive at ......... miles per hour, my journey will take ......... hours.How long will my journey take if I drive at ......... miles per hour? An ideal gas contained in a piston-cylinder device undergoes an isothermal compression. Help me please answers:10 -1 the following program is supposed to compute only profits (positive earnings) for the first half of the year (6 months). what is logically wrong with the implementation? the brinton clothing company wants to create and build brand awareness. it would use advertising. multiple choice persuasive push reminder pull informative FILL IN THE BLANK. Fill in the blank: A technique is used to balance traffic by iterating a list of items one by one from is known as ____. multiple choice, shuffle1. Round Robin2. Recursion3. Authoritative lookup4. Multiplexing select the statement that best defines required reserves. the amount banks are required by law to hold on each mortgage. the amount of reserves a bank has below the required amount. the amount of reserves banks have on hand to satisfy the demands of other competitors. the amount of reserves a bank must keep on deposit at the fed or in their vault on a given deposit. abc industries has a cash balance of $50,000; accounts payable of $150,000; inventory of $190,000; accounts receivable of $250,000; notes payable of $210,000; and accrued wages and taxes of $40,000. how much net working capital does the firm need to fund? which legally required form divulges information about financial advisors? a. form dav b. form avd c. form adv d. form dva please select the best answer from the choices provided although goats and sheep appear similar and can be mated (gametes fuse), their offspring are rarely born alive. this is an example of . your team is getting ready to start coding a new digital product based on validated learning about a focal user and some key propositions. you've got a story map of focal user experiences with user stories. before jumping into development, you think the team should take a step that would help to keep user outcomes top of mind. what might you recommend that the team focus on next? What is the goal of staging? A. to make the player feel scared B. to visually set the mood or idea C. to communicate the rules of the game D. to show the player how to beat the game What happens to the gravitation force between two objects that are 15 m apart, when one of them moves 3 m closer? (1 point). Trade promotions and other short-term discounts offered by a manufacturer result in large orders during the promotion period followed by very small orders after that. True or False Fifteen minutes after receiving the antiemetic, Mr. Dunner has stopped vomiting, appears relaxed, and denies further nausea. He states that he is comfortable enough for the RN to being the admission assessment and asks the RN to call him Calvin.3. The RN begins the client interview, focusing on the gastrointestinal system. For the RN to learn about the client's bowel patterns, what information is most important to obtain from Mr. Dunner?-Any difficulty with defecation-Presence of abdominal distention-Recent onset of flatulence-Amount of fiber in the diet there has been a decrease in investment. as a result, real gdp will in the short run, and in the long run. group of answer choices decrease; increase to its initial level increase; increase further increase; decrease to its initial value decrease; decrease further PLS HELP MEALSO THE LAST ONE IS STATE THE TREND IN DESNITY SHOWN IN TABLE Two angles of a triangle have the same measure and the third one is 54 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle. how did the actions of slaves themselves, northern military strategy and the emancipation proclamation combine to end slavery?