2(-6x-4)+3 = 3(3x-3)+4

Answer:

20

Step-by-step explanation:

so we need to see that

3/4 x ? = 15

so we say

3 x ? = 15x4

? =60/3

?= 20

Solution a needed 70 ounces and solution b needed 50 ounces

What does "1 ounce" mean?

One ounce weighs 437.5 grains or 28.349 grams and is a sixteenth of a pound (avoirdupois) of weight.

One ounce, abbreviated "oz," equals 480 grains, or 31.103 grams, and is one-twelfth of a Troy or Apothecaries' pound in weight. abbreviation for fluid ounce. a tiny amount or percentage.

So, let x=the of ounces of the 50% acid solution. The total volume after both are mixed is 100 ounces so the amount of the 20% solution will be 120-X. The equation will therefore be:

50% * x + 20% * (100-x) = 41% * 100

Dropping the ‘%’ we get

50x + 2000 - 20x = 4100

30x = 2100

x = 2100/30 = 70

Hence 70 ounces will be needed

Solution a = 70 ounces

Solution b = 50 ounces

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Answer:

x=-3,1

Step-by-step explanation:

The roots (zeros) are the  

x

values where the graph intersects the x-axis. To find the roots (zeros), replace  

y

with  

0

and solve for  

x

.

The number of positive integers from 1 to 2000 that are multiples of 20 or 25 is 180.

To count the number of positive integers from 1 to 2000 that are multiples of 20 or 25 using the inclusion-exclusion principle, we need to consider the individual counts of multiples of 20 and multiples of 25 and then subtract the count of multiples of both 20 and 25 to avoid double-counting.

Multiples of 20:

The largest multiple of 20 less than or equal to 2000 is 2000.

The count of multiples of 20 from 1 to 2000 is given by 2000 / 20 = 100.

Multiples of 25:

The largest multiple of 25 less than or equal to 2000 is 2000.

The count of multiples of 25 from 1 to 2000 is given by 2000 / 25 = 80.

Multiples of both 20 and 25 (common multiples):

To determine the count of multiples of both 20 and 25, we need to find the least common multiple (LCM) of 20 and 25, which is 100.

The count of multiples of 100 from 1 to 2000 is given by 2000 / 100 = 20.

Now, using the inclusion-exclusion principle, we can calculate the total count:

Total count = Count of multiples of 20 + Count of multiples of 25 - Count of multiples of both 20 and 25

= 100 + 80 - 20

= 180.

Therefore, the number of positive integers from 1 to 2000 that are multiples of 20 or 25 is 180.

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Answer:

AB=13

Step-by-step explanation:

1/2AC^2+1/2BD^2=AB^2

AB=13

The second fundamental theorem of calculus states that if f is continuous on [a,b] and F is an antiderivative of f on the same interval, then:

             \(\int\limits^b_a\)f(x) dx = F(b) - F(a)

The second fundamental theorem of calculus states that if f is continuous on [a,b] and F is an antiderivative of f on the same interval, then:

             \(\int\limits^b_a\)f(x) dx = F(b) - F(a)

It uses the mean value theorem of integration and the limit of an infinite Riemann summation. But I tried coming up with a proof and it was barely two lines. Here it goes:

Since F is an antiderivative of f, we have dFdx=f(x). Multiplying both sides by dx, we obtain dF=f(x)dx. Now, dF is just the small change in F and f(x)dx represents the infinitesimal area bounded by the curve and the x axis. So integrating both sides, we arrive at the required result.

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A student says that the function represented by the rule \(y = x^{2} -1\) is ,

Then the x = 0 and y = -1 represented by rule \(y = x^{2} -1\) is correct the error.

Then the x = 1 and y = 1 represented by rule \(y = x^{2} -1\) is incorrect the error.

Then the x = 3 and y = 5 represented by rule \(y = x^{2} -1\) is incorrect the error.

Then the x = 3 and y = 5 represented by rule \(y = x^{2} -1\) is incorrect the error.

Then the x = 4 and y = 7 represented by rule \(y = x^{2} -1\) is incorrect the error.

Consider function,

\(y = x^{2} -1\)

For x = 0 and y = -1

\(y = x^{2} -1\)

We can substitute x = 0 and y = -1 values,

-1 = \(0^{2}\) - 1

-1 = 0-1

-1 = -1

Then the x = 0 and y = -1 represented by rule \(y = x^{2} -1\) is correct the error.

For x = 1 and y = 1

\(y = x^{2} -1\)

We can substitute x = 1 and y = 1 values,

\(y = x^{2} -1\)

1 = \(1^{2}\) -1

1 = 1-1

1  ≠ 0

Then the x = 1 and y = 1 represented by rule \(y = x^{2} -1\) is incorrect the error.

For x = 2 and y = 3

\(y = x^{2} -1\)

We can substitute x = 2 and y = 3 values,

\(y = x^{2} -1\)

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

3 = 4 -1

3 = 3

Then the x = 2 and y = 3 represented by rule \(y = x^{2} -1\) is correct .

For x = 3 and y = 5

\(y = x^{2} -1\)

We can substitute x = 3 and y = 5 values,

\(y = x^{2} -1\)

5 = \(3^{2}\) - 1

5 = 9 - 1

5 ≠ 8

Then the x = 3 and y = 5 represented by rule \(y = x^{2} -1\) is incorrect the error.

For x = 4 and y = 7

\(y = x^{2} -1\)

We can substitute x = 4 and y = 7 values,

\(y = x^{2} -1\)

7 = \(4^{2}\) - 1

7 = 16 - 1

7 ≠ 15

Then the x = 4 and y = 7 represented by rule \(y = x^{2} -1\) is incorrect the error.

Therefore,

The function represented by the rule \(y = x^{2} -1\) is ,

x = 0 and y = -1 represented by rule \(y = x^{2} -1\) is correct the error.

x = 1 and y = 1 represented by rule \(y = x^{2} -1\) is incorrect the error.

x = 3 and y = 5 represented by rule \(y = x^{2} -1\) is incorrect the error.

x = 3 and y = 5 represented by rule \(y = x^{2} -1\) is incorrect the error.

x = 4 and y = 7 represented by rule \(y = x^{2} -1\) is incorrect the error.

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Answer:

False

Step-by-step explanation:

12+9<20

21≮20

False

The tool in which a normal or bell-shaped curve would be expected if no special conditions are occurring is a histogram.

A histogram is a graphical representation of data that displays the distribution of a set of continuous data. It is a bar chart that shows the frequency of data within specific intervals or bins. When data is normally distributed, or follows a bell-shaped curve, it is expected that the majority of the data will fall within the middle bins of the histogram, with fewer data points at the extremes.

A flow chart is a tool used to diagram a process and is not typically associated with statistical data analysis. A cause and effect diagram, also known as a fishbone diagram or Ishikawa diagram, is used to identify and analyze the potential causes of a problem, but it does not involve the representation of data in the form of a histogram. A check sheet is a simple tool used to collect data and record occurrences of specific events or activities, but it does not provide a graphical representation of the data. In contrast, a histogram is a tool that is commonly used in statistical analysis to represent the distribution of data. It can be used to identify the shape of the distribution, such as whether it is symmetric or skewed, and to identify any outliers or unusual data points. A normal or bell-shaped curve is expected in a histogram when the data is normally distributed, meaning that the data follows a specific pattern around the mean value.

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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Answer:

the answer is A

Step-by-step explanation:

have a nice day!!

Answer:

A

Step-by-step explanation:

\(2n^2 + 11n + 9 = 0\\2n^2 + 9n + 2n + 9 = 0\\n(2n + 9) + 1(2n + 9) = 0\\(2n + 9)(n + 1) = 0\\when, 2n + 9 = 0\\2n = -9\\n = \frac{-9}{2}\\\\when, n + 1 = 0\\n = -1\\\\\thus n = -1, \frac{-9}{2}\)

Considering the definition of probability, the probability that the smoke will be detected by either a or b or both is 99%.

Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

The union of events AUB is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs.

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

where the intersection of events A∩B is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.

In first place, let's define the following events:

Then you know:

Considering the definition of union of eventes, the probability that the smoke will be detected by either a or b or both is calculated as:

P(A∪B)= P(A) + P(B) -P(A∩B)

P(A∪B)= 0.95 + 0.98 -0.94

P(A∪B)= 0.99= 99%

Finally, the probability that the smoke will be detected by either a or b or both is 99%.

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the data provide convincing evidence of a difference in the proportions of teens and young adults who own an iPod or MP3

To determine if there is convincing evidence of a difference in the proportions of all teens and young adults who own an iPod or MP3 player, we can perform a hypothesis test.

Let's define the following parameters:

- p₁: Proportion of all teens who own an iPod or MP3 player.

- p₂: Proportion of all young adults who own an iPod or MP3 player.

The null hypothesis (H₀) assumes that there is no difference between the proportions:

H₀: p₁ = p₂

The alternative hypothesis (H₁) assumes that there is a difference between the proportions:

H₁: p₁ ≠ p₂

To test this hypothesis, we can use a two-proportion z-test. We calculate the test statistic using the formula:

z = ((p₁ - p₂) - 0) / √((\(\hat{p}_1\) * (1 - \(\hat{p}_1\)) / n₁) + (\(\hat{p}_2\) * (1 - \(\hat{p}_2\)) / n₂))

Where:

- \(\hat{p}_1\): Sample proportion of teens who own an iPod or MP3 player (79% or 0.79)

- \(\hat{p}_2\): Sample proportion of young adults who own an iPod or MP3 player (67% or 0.67)

- n₁: Sample size of teens (800)

- n₂: Sample size of young adults (400)

Using the given values, we can calculate the test statistic:

z = ((0.79 - 0.67) - 0) / √((0.79 * (1 - 0.79) / 800) + (0.67 * (1 - 0.67) / 400))

Calculating this yields the test statistic z = 5.525.

Next, we can determine the critical value or p-value associated with this test statistic using a significance level (α). Assuming a significance level of 0.05, for a two-tailed test, the critical values are approximately -1.96 and 1.96.

Since the calculated test statistic (5.525) is beyond the critical values of -1.96 and 1.96, we can reject the null hypothesis. There is convincing evidence to suggest that there is a difference in the proportions of all teens and young adults who own an iPod or MP3 player.

In conclusion, the data provide convincing evidence of a difference in the proportions of teens and young adults who own an iPod or MP3 player.

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The appropriate hypotheses for testing the difference in proportions of all teens and young adults who own an iPod or MP3 player are:

Null Hypothesis (H0): The proportion of teens who own an iPod or MP3 player is equal to the proportion of young adults who own an iPod or MP3 player.

Alternative Hypothesis (Ha): The proportion of teens who own an iPod or MP3 player is not equal to the proportion of young adults who own an iPod or MP3 player.

To test if there is a significant difference in the proportions of all teens and young adults who own an iPod or MP3 player, we need to set up appropriate hypotheses. Let's denote the proportion of teens who own an iPod or MP3 player as p1 and the proportion of young adults who own an iPod or MP3 player as p2.

The null hypothesis (H0) assumes that there is no difference between the proportions, so we can state it as:

H0: p1 = p2

The alternative hypothesis (Ha) assumes that there is a difference between the proportions, so we can state it as:

Ha: p1 ≠ p2

Here, p1 represents the true proportion of teens who own an iPod or MP3 player, and p2 represents the true proportion of young adults who own an iPod or MP3 player.

To test these hypotheses, we can use a significance level (α) of 0.05, which is a common choice in hypothesis testing. If the p-value (the probability of observing a test statistic as extreme as the one calculated) is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in the proportions.

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Answer:

\(\displaystyle x^{-1}=\frac{1}{25}\)

Step-by-step explanation:

We are given the value of x:

\(x= (4/5)^{-2}\) divided by \((1/4)^2\)

We need to find the reciprocal of x or:

\(\displaystyle x^{-1}=\frac{1}{x}=\frac{\frac{1}{4}^2}{\frac{4}{5}^{-2}}\)

Operating:

\(\displaystyle x^{-1}=\frac{1}{4}^2*\frac{5}{4}^{-2}\)

\(\displaystyle x^{-1}=\frac{1}{16}*\frac{16}{25}\)

\(\mathbf{\displaystyle x^{-1}=\frac{1}{25}}\)

Answer:

41.16 m³

Step-by-step explanation:

Volume = area triangle x height

1/2(2.8x4.2) = 1/2( 11.76) = 5.88

5.88 x 7 = 41.16

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

1. 2/5

2. 2/3

3. 455/48

4. -48/7

5. -22/13

6. 77/30

7. 65/27

8. -2/1

9. -98/25

10. -6/1

You may need to simplify some, depending on what your instructor tells you. Glad I could help! :)

Since a + b + c are vertically opposite angles, e = 130.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question-

d=70, opposite vertical angle

180 - 70 - 40 = 2 using angles on a straight line.

We now possess the two angles, and since they are perpendicular to one another, a and c = 35.

Because of the vertically opposed angles, b = 40.

4. Because 90-70, a=30.

Because an is 30, divide 90 by 30 to obtain b, 70.

vertically opposite angles, d=70

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The function y in the differential equation y‴−13y″+40y′=56eˣ, y(0)=20, y′(0)=19, y″(0)=10 as a function of x is: y(x) = -18 + e⁵ˣ + (9/32)e⁸ˣ + 2eˣ.

To solve this problem, we need to find the general solution to the differential equation y‴−13y″+40y′=56eˣ and then use the initial conditions to find the particular solution.

First, we find the characteristic equation:

r³ - 13r² + 40r = 0

Factorizing it, we get:

r(r² - 13r + 40) = 0

Solving for the roots, we get:

r = 0, 5, 8

So the general solution is:

y_h(x) = c1 + c2e⁵ˣ + c3e⁸ˣ

To find the particular solution, we can use the method of undetermined coefficients. Since the right-hand side of the differential equation is of the form keˣ, where k = 56, we assume a particular solution of the form:

y_p(x) = Aeˣ

Taking the first three derivatives:

y′_p(x) = Aeˣ

y″_p(x) = Aeˣ

y‴_p(x) = Aeˣ

Substituting these into the differential equation, we get:

Aeˣ - 13Aeˣ + 40Aeˣ = 56eˣ

Simplifying, we get:

28Aeˣ = 56eˣ

So A = 2. Substituting this value back into y_p(x), we get:

y_p(x) = 2eˣ

Therefore, the general solution is:

y(x) = y_h(x) + y_p(x)

= c1 + c2e⁵ˣ + c3e⁸ˣ + 2eˣ

Finding the values of the constants c1, c2, and c3:

y(0) = c1 + c2 + c3 + 2 = 20

y′(0) = 5c2 + 8c3 + 2 = 19

y″(0) = 25c2 + 64c3 = 10

Solving these equations simultaneously, we get:

c1 = -18

c2 = 1

c3 = 9/32

Therefore, the particular solution is:

y(x) = -18 + e⁵ˣ + (9/32)e⁸ˣ + 2eˣ

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The point labeled D is to the right of the intersection of the two linear functions. This means that its x-coordinate is greater than the x-coordinate of the point of intersection.

We can find the point of intersection by setting the two functions equal to each other:

3x + 4 = (-1/2)x - 5

Solving for x, we get:

(7/2)x = -9

x = -18/7

So the point of intersection is (-18/7, -29/7).

Since the x-coordinate of point D is greater than -18/7, we can eliminate options A and C.

Now we need to check whether option B or option D includes point D as a solution. To do this, we can simply plug in the coordinates of D into the two inequalities and see which one holds true.

Option B:

f(x) ≥ 3x + 4

2 ≥ 3(D) + 4

2 ≥ 3D + 4

-2 ≥ 3D

D ≤ -2/3

g(x) ≤ (-1/2)x - 5

2 ≤ (-1/2)(D) - 5

7 ≤ -D

D ≥ -7

Since -2/3 is less than -7, option B does not include point D as a solution.

Option D:

f(x) ≥ 3x + 4

2 ≥ 3(D) + 42 ≥ 3D + 4

-2 ≥ 3D

D ≤ -2/3

g(x) ≥ (-1/2)x - 5

2 ≥ (-1/2)(D) - 5

7 ≥ -D

D ≤ -7

Since -2/3 is less than -7, option D does not include point D as a solution either.

Therefore, neither option B nor option D includes point D as a solution. The correct answer is that neither system of inequalities has point D as a solution.

The motion of a physical pendulum can be described using the nonlinear pendulum problem. The simple pendulum in a vertical plane is described by the mass of the rod which is negligible and no external damping or driving forces acting on the system.

The arc s of a circle of radius l is related to the central angle θ by the formula s = lθ. The angular acceleration a is a = d²s/dt² = I d²θ/dt². By Newton's second law, we have

F = mgsinθ = ma, thus we can obtain the second-order ODE: I d²θ/dt² + gsinθ = 0.The IVP problem setup with θ(0) = ϕ₁ and θ′(0) = ϕ₂ can be solved using the following method:

First, we need to find the first derivative of θ, which is given by:dθ/dt = ϕ₂

Next, we need to find the second derivative of θ, which is given by:

d²θ/dt² = -g sin(θ)/l

Using the initial conditions, θ(0) =

ϕ₁ and θ′(0) = ϕ₂,

we can find the constants of integration as follows:ϕ₁ = θ(0)

= C₁ϕ₂ = θ′(0)

= -g sin(ϕ₁)/l + C₂

Thus, we have the following equation:

C₂ = ϕ₂ + g sin(ϕ₁)/l C₁

= ϕ₁

Then, the solution to the IVP problem is given by:θ(t)

= ϕ₁ + ϕ₂t - (g/l)sin(ϕ₁)t²/2

Therefore, the complete modelling problem we left up in class under IVP problem setup with θ(0)

= ϕ₁ and θ′(0) = ϕ₂, and there is no linearization, directly solving the IVP problem is given by the above formula.

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Answer:

True is the most reasonable than False.

Step-by-step explanation:

If we go by "logic", we know that radius and anything that tells you how long, how far, how tall, etc; the value must always be positive.

The area of circle is expressed as:

\( \displaystyle \large{A = \pi {r}^{2} }\)

Where r = radius

Since we know that radius cannot be negative going with logic and real basic geometry, the only radius that satisfies A = 9π is r = 3.

\( \displaystyle \large{A = \pi {3}^{2} } \\ \displaystyle \large{A = 9\pi }\)

Now if we do not go by logic of real basic geometry, such as length being negative and all.

Since A = 9π, substitute A = 9π in.

\( \displaystyle \large{9\pi = \pi {r}^{2} }\)

Divide both sides by π.

\( \displaystyle \large{ \frac{9\pi}{\pi} = \frac{\pi {r}^{2} }{\pi} } \\ \displaystyle \large{ 9 = {r}^{2} }\)

Square both sides, adding plus-minus, apply QE.

\( \displaystyle \large{ \pm \sqrt{9} = \sqrt{ {r}^{2} } } \\ \displaystyle \large{ \pm 3 = r}\)

So r = ±3 or radius = +3 and -3

So r can be both 3 or -3 if we do not follow logic itself.

However, the answer should be true instead of false as radius being only positive sounds more logical and reasonable rather than radius being negative.

Answer:

Step-by-step explanation:

Permutations and combinations are mathematical concepts that deal with counting the number of different arrangements or selections of objects from a set.

Permutations:

A permutation is an arrangement of objects in a specific order. For example, consider a set of three letters: A, B, and C. There are 3! = 6 possible permutations of these letters, which are ABC, ACB, BAC, BCA, CAB, and CBA. The notation "3!" is the factorial notation, which means 3 × 2 × 1.

Combinations:

A combination is a selection of objects, where the order does not matter. For example, consider a set of three letters: A, B, and C. There are 3 C 2 = 3 possible combinations of two letters from this set, which are AB, AC, and BC. The notation "3 C 2" is the combination notation, which means the number of ways to choose k objects from a set of n objects.

In summary, permutations deal with the arrangement of objects in a specific order, while combinations deal with the selection of objects without regard to the order.

Answer:

D

Step-by-step explanation:

Somehting bknbye3uehnfhnjun Español uno, como sulfhídrica

Answer:

False. The union of two events A and B has outcomes from event A or event B or both A and B.

At least 75% of healthy adults have body temperatures within 2 standard deviations: 98.26 °F. Minimum possible body temperature within this range:97.14 °F,maximum possible body temperature:99.38 °F.

Using Chebyshev's theorem, we can determine a lower bound on the percentage of healthy adults with body temperatures within 2 standard deviations of the mean. We can also calculate the minimum and maximum possible body temperatures within this range based on the given mean and standard deviation.

Step 1: Apply Chebyshev's theorem, which states that for any data set, regardless of its shape, at least (1 - 1/k^2) of the data falls within k standard deviations of the mean. In this case, k = 2.

The percentage of healthy adults with body temperatures within 2 standard deviations of the mean is at least (1 - 1/2^2) = (1 - 1/4) = 75%.

Step 2: Calculate the minimum and maximum possible body temperatures within 2 standard deviations of the mean.

Minimum temperature = mean - (2 * standard deviation)

Maximum temperature = mean + (2 * standard deviation)

Substitute the given values: minimum temperature = 98.26 - (2 * 0.56) = 97.14 °F and maximum temperature = 98.26 + (2 * 0.56) = 99.38 °F.

Therefore, at least 75% of healthy adults have body temperatures within 2 standard deviations of 98.26 °F. The minimum possible body temperature within this range is 97.14 °F, and the maximum possible body temperature is 99.38 °F.

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Answer:

whojhuokk

tuhhjhkk

Step-by-step explanation:

kjufig(hgggjkooujjlkhy

Answer:

She will actually do it on the 35th day of gym