Please help with the problem in the picture ^ I’ll give brainliest if you give me a small explanation! :)

Let's do

#a

\(\\ \rm\Rrightarrow 3^{-3}\times 3^{-2}\)

\(\\ \rm\Rrightarrow 3^{-3-2}\)

\(\\ \rm\Rrightarrow 3^{-5}\)

\(\\ \rm\Rrightarrow \dfrac{1}{3^5}\)

\(\\ \rm\Rrightarrow \dfrac{1}{243}\)

#b

\(\\ \rm\Rrightarrow \dfrac{-3}{(-3)^2}\)

\(\\ \rm\Rrightarrow \dfrac{-3}{9}\)

\(\\ \rm\Rrightarrow \dfrac{-1}{3}\)

\(\mathbb{PROBLEM:}\)

Evaluate:

a. 3 to the -3 power x 3 to the -2 power

b. -3/(-3) to the 2 power

\(\mathbb{SOLUTION:}\)

a. 3 to the -3 power x 3 to the -2 power

\( \tt \: {3}^{ - 3} \times {3}^{ - 2} \)

\( \tt \: {3}^{ - 3 - 2} \)

\( \tt {3}^{ - 5} \)

\( \tt \frac{1}{3.5} \)

\(\underline \bold\green{ \frac{1}{243} }\)

b. -3/(-3) to the 2 power

\( \tt \: \frac{ \: \: - 3}{ \: ( - 3) {}^{2} } \)

\( \tt \: \frac{ \: \: - 3}{ 9} \)

\( \underline \bold \green{ \frac{ \: - 1}{3 \: } }\)

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The equation of each line that satisfies the given conditions are:

1. y - 2 = 5/2(x - 3)

2. y - 4 = m(x + 3)

3. y = -3x + 5

1. Given the points, (3, 2) and (5, 7), find the slope (m):

Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)

m = 5/2

Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):

y - 2 = 5/2(x - 3)

2. Given:

A point = (-3, 4)

Slope (m) = 2

Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):

y - 4 = m(x + 3) [equation of the line]

3. Given:

Slope (m) = -3

Y-intercept (b) = 5

Substitute m = -3 and b = 5 into the equation y = mx + b:

y = -3x + 5

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The total points scored in the game is 44.

We have,

Let's assume that the total number of points scored in the game is 'x'.

As per the problem,

75% of the points were scored by 2 players, which means 25% of the points were scored by the remaining players.

So,

The points scored by the remaining players.

= 25% of x

= 25/100 of x

= 0.25x

Now, it is given that the 2 players scored 33 points.

So, the points scored by the remaining players will be:

x - 33

Also, it is given that the points scored by the remaining players are 25% of x.

So,

0.25x = x - 33

Solving this equation, we get:

0.75x = 33

x = 44

Therefore,

The total points scored in the game is 44.

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\(4(x + 1) = 5(x - 3) \\ 4x + 4 = 5x - 15 \\ 5x - 4x = 4 + 15 \\ x = 19\)

Answer:

50% of 30 is 15.

30% of 10 is 3

Answer:

The exact value of the other leg is 10.

Step-by-step explanation:

Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.

Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.

Substituting known values, we get:

(10√2)^2 = 10^2 + b^2

200 = 100 + b^2

b^2 = 100

b = 10

Therefore, the exact value of the other leg is 10.

\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)

Its dividing by -2

................................

A number repeated as a term three times can be expressed as a sequence or as a repeated multiplication.

A number repeated as a term three times means that the same number is used three times in a row. It can be expressed as a sequence or as a repeated multiplication.

For example, if the number is 5, the expression "5, 5, 5" represents the number 5 repeated three times in a sequence. It indicates that the number 5 is repeated consecutively as three separate terms.

Alternatively, the repeated multiplication of the number can also represent the concept. In this case, "5 x 5 x 5" would be equal to 125, which means that the number 5 is multiplied by itself three times.

In both cases, the idea is that the number is used three times in succession, either as a sequence or through multiplication, resulting in a repeated representation of the number.

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Answer:

  (c)  y = 3^x

Step-by-step explanation:

A function is described as exponential if the independent variable is found in the exponent.

  y = x^(1/2) . . . a square root function, not exponential

  y = 2x^3 . . . . a cubic (polynomial) function, not exponential

  y = 3^x . . . . . an exponential function

In the figure, the length of any line segment in the image is longer the length of the corresponding line segment in the preimage. The scale factor of the dilation is 2

The scale factor of dilation is defined as the change in size of a figure. Thus, a scale factor that is greater than 1 is referred to as an enlargement while a scale factor that is greater than 0 but less than 1 is referred to as a reduction.

Now, we are told that ΔABC has been dilated from center D to form ΔRST, This means that the lengths in ΔRST are longer than the lengths in ΔABC.

Secondly, by close inspection we can see that it was dilated by a scale factor of 2.

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a. The store should charge $90

b. The first revenue model results in a greater maximum monthly revenue.

a. We have

R(n) = (120 - 6n)(80 + 8n)

using product ruile

δr/δn = (120 - 6n)(8) + (80 + 8n)(-6)

δr/δn = 960 - 48n - 480 - 48n

δr/δn = -96n + 480

Now, we set the derivative to zero and solve for n:

0 = -96n + 480

96n = 480

n = 5

we put n as 5 in the equation

120 - 6x 5

= 120 - 30

= 90

To maximize the revenue then $90 is charged.

b. For the 4 dollar decrease in price R'(n) = (120 - 4n)(80 + 5n)

Using the product rule, we have:

dR'/dn = (120 - 4n)(5) + (80 + 5n)(-4)

this is = 600 - 20n - 320 - 20n

= -40n + 280

equate to 0

-40n + 280 = 0

n = 7

The new price would then be

120 - 4 * 7

= 120 - 28

= 92 dollars

(120 - 65)(80 + 85)

= 90(120)

= $10,800

(120 - 47)(80 + 57)

= 92(115)

= $10,580

The first revenue model results in a greater maximum monthly revenue.

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The value of k(3) in the function given is 37

Given the function :

To find k(3) ; substitute t = 3 into the equation

k(3) = 13(3) - 2

k(3) = 39 - 2

k(3) = 37

Therefore, the value of k(3) would be 37.

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Answer:

21 and 10.5 respectively

Step-by-step explanation:

Remember circumference of a circle is given as;

C= 2×π×r; r is raduis

r = C / 2×π

=65.98/(2×3.142)= 10.50

D= 2× r = 2× 10.50= 21.0( D represent diameter)

Note π = 3.142 a known constant

Answer:

Step-by-step explanation:

Point-slope equation for line of slope m that passes through (x₀, y₀):

y-y₀ = m(x-x₀)

apply your data

y-2 = 4(x-6)

Answer:

y−2= −2(x−7)

Step-by-step explanation:

khan academy says its right

Answer:

f(1) = 7

f(2) = 18

f(3) = 31

f(4) = 46

f(5) = 63

f(6) = 82

f(7) = 103

f(8) = 126

f(9) = 151

f(10) = 178

Step-by-step explanation:

f(1) = (-1)^2+8(1)-2 = 7

Continue plugging in values...

Answer:

0.0668 = 6.68% probability that the height of a randomly selected tree is as tall as mine or shorter.

0.0228 = 2.28% probability that the full height of a randomly selected tree is at least as tall as hers.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 137.1, \sigma = 3.2\)

A tree of this type grows in my backyard, and it stands 132.3 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.

This is the pvalue of Z when X = 132.3. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{132.3 - 137.1}{3.2}\)

\(Z = -1.5\)

\(Z = -1.5\) has a pvalue of 0.0668

0.0668 = 6.68% probability that the height of a randomly selected tree is as tall as mine or shorter.

My neighbor also has a tree of this type growing in her backyard, but hers stands 143.5 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers.

This is 1 subtracted by the pvalue of Z when X = 143.5. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{143.5 - 137.1}{3.2}\)

\(Z = 2\)

\(Z = 2\) has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the full height of a randomly selected tree is at least as tall as hers.

The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.

We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.

(1/2) * Base * Height = Area

We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.

Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters

Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).

Using these values as a substitute in the formula, we obtain:

Area =\((1/2) * 54 * 56 = 1512\) square centimeters

centimetres square

It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.

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Answer:

1)1920 in2  (2)120 in3

Step-by-step explanation:

The height of the cylinder with the same base and volume as the cone is 12 cm.

The volume of a cone and a cylinder of the same base and height can be found using the formula V = πr2h. The radius (r) is half the diameter which, in this case, is 5 cm. Therefore, the equation for the cone is V = \(π(5^2)12\)and the equation for the cylinder is V = π(5^2)h. To find the height of the cylinder, both equations must be set equal to each other, V =\(π(5^2)12\) = \(π(5^2)h\), and h can be isolated by dividing both sides by \(π(5^2)\). This yields h = 12 cm. Thus, the height of the cylinder with the same base and volume as the cone is 12 cm.

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If Tina is training for a biathlon. She runs the downhill portion of the course at 10 miles per hour.

(s-5) = speed on level ground

Time = distance /speed

Level time + downhill time = 1 hr

Hence,

3/(s-5) + 4/s =1

multiply by s(s-5), resulting in

3s + 4(s-5) = s(s-5)

3s + 4s - 20 = s^2 - 5s

Arrange as a quadratic equation on the right

0 = s^2 - 5s - 7s + 20

s^2 - 12s + 20 = 0

factors to

(s-2)(s-10) = 0

s = 10 mph

Therefore the speed is 10mph.

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Answer: ~ 2.27 points per question

Step-by-step explanation:

Want points/question.

So, we do 100 points / 44 questions

~ 2.27 points per question

Answer:

-22 ft.

Step-by-step explanation:

So we know that the diver descends (goes deeper) at a rate of 2 feet per second.

We also know that he/she is already at an elevation of -8 feet.

The first we need to do to solve this question is to find out the number of feet the diver descends in 7 seconds:

We do this by multiplying the amount of time by the number of feet (7 x 2)

as we all know 7 x 2 = 14 feet

So the diver dove deeper by 14 feet.

Now we have to add 14 and 8 to find the divers new elevation:

14 + 8 = -22 ft.

The divers' elevation after descending for 7 seconds is -22 ft.

plz mark me brainliest if correct :)

The diver's elevation after she descends for 7 seconds will be -22 ft.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

So we know that the diver descends (goes deeper) at a rate of 2 feet per second.

We also know that he/she is already at an elevation of -8 feet. The first we need to do to solve this question is to find out the number of feet the diver descends in 7 seconds:

We do this by multiplying the amount of time by the number of feet (7 x 2)

As we all know 7 x 2 = 14 feet. So the diver dove deeper by 14 feet. Now we have to add 14 and 8 to find the diver's new elevation:

14 + 8 = -22 ft.

Therefore, the diver's elevation after she descends for 7 seconds will be -22 ft.

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Answer:

\(P(X\leq 1) = 0.331\)

Step-by-step explanation:

Given

Poisson Distribution;

Average rent in a week = 2.3

Required

Determine the probability of renting no more than 1 apartment

A Poisson distribution is given as;

\(P(X = x) = \frac{y^xe^{-y}}{x!}\)

Where y represents λ (average)

y = 2.3

Probability of renting no more than 1 apartment = Probability of renting no apartment + Probability of renting 1 apartment

Using probability notations;

\(P(X\leq 1) = P(X=0) + P(X =1)\)

Solving for P(X = 0) [substitute 0 for x and 2.3 for y]

\(P(X = 0) = \frac{2.3^0 * e^{-2.3}}{0!}\)

\(P(X = 0) = \frac{1 * e^{-2.3}}{1}\)

\(P(X = 0) = e^{-2.3}\)

\(P(X = 0) = 0.10025884372\)

Solving for P(X = 1) [substitute 1 for x and 2.3 for y]

\(P(X = 1) = \frac{2.3^1 * e^{-2.3}}{1!}\)

\(P(X = 1) = \frac{2.3 * e^{-2.3}}{1}\)

\(P(X = 1) =2.3 * e^{-2.3}\)

\(P(X = 1) = 2.3 * 0.10025884372\)

\(P(X = 1) = 0.23059534055\)

\(P(X\leq 1) = P(X=0) + P(X =1)\)

\(P(X\leq 1) = 0.10025884372 + 0.23059534055\)

\(P(X\leq 1) = 0.33085418427\)

\(P(X\leq 1) = 0.331\)

Hence, the required probability is 0.331

7/12 of the people who visited the West branch of the store indicated that they had not purchased the product.

Out of the 168 people who visited the West branch of the store,

98 indicated that they had not purchased the product.

Therefore, the fraction of people who visited the West branch and had not purchased the product is:

98/168

Simplifying this fraction by dividing the numerator and denominator by 14, we get:

7/12

Hence, 7/12 of the people who visited the West branch of the store indicated that they had not purchased the product.

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Answer:

The digit 5 is equal to is 5,000 :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

The thousandth digit!

Step-by-step explanation:

Answer:

a) P(rolling a number less than 4 on Die 1 and rolling a 5 on Die 2) = \(\frac{1}{9}\)

b) P( the sum of both dice adding up to 4) = \(\frac{5}{54}\)

Step-by-step explanation:

Given - You roll two six-sided dice. Die 1 is fair. Die 2 is unfair such that the probability of rolling an odd number is \(\frac{2}{3}\) and the probability of rolling an even number is \(\frac{1}{3}\) , though the probability rolling of each odd number is the same, and the probability of rolling each even number is the same.

To find - What is the probability of:

              a) rolling a number less than 4 on Die 1 and rolling a 5 on Die 2.

              b) the sum of both dice adding up to 4.

Proof -

The sample space , S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

                                          (2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

                                          (3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

                                          (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

                                          (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

                                          (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

Now,

Given that , Dice 1 is fair

⇒P₁(1) = P₁(2) = P₁(3) = P₁(4) = P₁(5) = P₁(6) = \(\frac{1}{6}\)

Also, Given Dice 2 is unfair

⇒P₂(1) = P₂(3) = P₂(5) = \(\frac{2}{3}.\frac{1}{3} = \frac{2}{9}\)

   P₂(2) = P₂(4) = P₂(6) = \(\frac{1}{3}.\frac{1}{3} = \frac{1}{9}\)

Now,

a)

P(rolling a number less than 4 on Die 1 and rolling a 5 on Die 2) = P₁(1)P₂(5) + P₁(2)P₂(5) + P₁(3)P₂(5)

= P₂(5) [ P₁(1) + P₁(2) + P₁(3) ]

= \(\frac{2}{9}\) [ \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) ] = \(\frac{2}{9}[ \frac{3}{6}]\\\) = \(\frac{1}{9}\)

⇒P(rolling a number less than 4 on Die 1 and rolling a 5 on Die 2) = \(\frac{1}{9}\)

b)

P( the sum of both dice adding up to 4) = P₁(1)P₂(3) + P₁(2)P₂(2) + P₁(3)P₂(1)

                                                                  = \(\frac{1}{6}\) × \(\frac{2}{9}\)  + \(\frac{1}{6}\) × \(\frac{1}{9}\) + \(\frac{1}{6}\) ×\(\frac{2}{9}\)   = \(\frac{5}{54}\)

⇒P( the sum of both dice adding up to 4) = \(\frac{5}{54}\)

9514 1404 393

Answer:

  A:  (b) 320 is what percent of 400

  B:  80%

Step-by-step explanation:

Part A:

This is a reading comprehension question. You are told that ...

  $320 is the amount needed

  $400 is the amount earned

and you are asked to find ...

  what percent of the amount earned is the amount needed?

The question can be rephrased as ...

  the amount needed is what percent of the amount earned?

Filling in the amounts you are told, the rephrased question becomes ...

  $320 is what percent of $400 . . . . . matches choice (b)

__

Part B:

If we let x represent "what percent", then we can write the above question as ...

  320 = x · 400

Dividing by 400 gives ...

  320/400 = x = 0.80 = 80%

That is, 320 is 80% of 400.