what is the solution for

2x + y = 4

3x + 3y =9

It will take the golf ball 12 seconds to hit the ground using the kinematic equation for vertical motion.

To determine the time it takes for the golf ball to hit the ground, we can use the kinematic equation for vertical motion:

\(h = ut + (1/2)gt^2\)

Where:

h is the height (0 feet, as the ball is on the ground)

u is the initial velocity (192 feet per second)

g is the acceleration due to gravity (-32 feet per second squared, considering downward direction)

t is the time we want to find

Plugging in the given values, we get:

\(0 = (192)t + (1/2)(-32)t^2\)

Simplifying the equation, we have:

\(-16t^2 + 192t = 0\)

Factoring out t, we get:

t(-16t + 192) = 0

Setting each factor equal to zero, we have:

t = 0 (not applicable in this case)

-16t + 192 = 0

Solving for t, we get:

-16t = -192

t = 12

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The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

The time it takes for the golf ball to hit the ground can be determined using the equation of motion. We can use the formula:

h0 = 0

v0 = 192

g = 32.2

a = 16.1

b = 192

t1 = 0

t2 = -b / a

t(-16t + 192) = 0

Setting each factor equal to zero, we have:

t = 0 (not applicable in this case)

-16t + 192 = 0

Solving for t, we get:

-16t = -192

t = 12

t2 >= 0:

   time_to_hit_ground = t2

   time_to_hit_ground = t1

The time it takes for the golf ball to hit the ground is approximately", round(time_to_hit_ground, 2 seconds.

The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

Since time cannot be negative in this context, we discard the negative solution. Therefore, the time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

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A speculative statement about the relationship between two or more variables is known as a b - hypothesis.

Variables:

A variable is a measurable trait or characteristic that is subject to change under different conditions.

Given,

Here we need to find what is meant by a speculative statement about the relationship between two or more variables.

The definition of Hypothesis is,

It is basically a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

So, a speculative statement about the relationship between two or more variables is known as a b - hypothesis.

So, the option (b) - Hypothesis is correct.

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Therefore, the probability of selecting a number greater than 6 and less than 12 from the given sample space is 5/9 or approximately 0.556 (rounded to three decimal places).

To find the probability of selecting a number greater than 6 and less than 12 from the sample space {5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

The numbers greater than 6 and less than 12 in the given sample space are 7, 8, 9, 10, and 11. Therefore, we have 5 favorable outcomes.

The total number of possible outcomes in the sample space is 9 (since we are excluding 5, 12, 13, and 14).

To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:

P(greater than 6 and less than 12) = favorable outcomes / total outcomes
                                = 5 / 9

Therefore, the probability of selecting a number greater than 6 and less than 12 from the given sample space is 5/9 or approximately 0.556 (rounded to three decimal places).

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Answer: 2√14

Step-by-step explanation: First you have to

The proportion of students who can roll their tongues will be estimated and the margin of error for a 95 percent confidence interval for the true proportion of tongue rollers among students will be determined. There were 317 tongue rollers out of a sample of 400 students.

      As a result, the sample proportion is 317/400 = 0.7925.

      We'll compute the margin of error next. The margin of error (E) for a 95 percent confidence interval is:

                E = zα/2 * sqrt[p(1 - p) / n]

                              where zα/2 is the z-score that corresponds to the level of confidence α/2, p is the sample proportion, and n is the sample size.

               E = 1.96 * sqrt[0.7925 * (1 - 0.7925) / 400]E

                  = 1.96 * sqrt[0.7925 * 0.2075 / 400]E

                  = 1.96 * sqrt(0.00040875)E

                  = 1.96 * 0.0202E

                  = 0.0395

    The margin of error is approximately 0.04 or 4 percent. Hence, the correct option is 0.04.

The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to 0.04

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Answer:

f the value of x increases then the value of the expression decreases. Therefore, if the value of x increases then the value of the expression decreases.

Step-by-step explanation:

Answer:

6x divived by 5 times 4

Step-by-step explanation:

Answer:

\(\frac{4}{15}\) kilograms

Step-by-step explanation:

  We will take the total amount of beads and divide it by 3, since there are 3 friends.

\(\frac{4}{5}\) kg / 3

\(\frac{4}{5}\) kg * \(\frac{1}{3}\)

\(\frac{4*1}{5*3}\)

\(\frac{4}{15}\) kg

Each friend recieves \(\frac{4}{15}\) kilograms of the beads.

The general expression for the slope of a line tangent to the curve of the function y = 2x^2 + 2x at the point P(x, y) is mtan = 4x + 2. The slope for x = -2 is -6, and the slope for x = 0.5 is 4. We can sketch the curve and the tangent lines to visualize their relationship.

To find the slope of the tangent line to the curve at any point P(x, y), we take the derivative of the function y = 2x^2 + 2x with respect to x. The derivative gives us the rate of change of y with respect to x, which represents the slope of the tangent line.

Taking the derivative of y = 2x^2 + 2x, we get dy/dx = 4x + 2. This is the general expression for the slope of the tangent line.

To find the slopes for specific values of x, we substitute those values into the derivative expression. For x = -2, we have mtan = 4(-2) + 2 = -6. For x = 0.5, we have mtan = 4(0.5) + 2 = 4.

To sketch the curve and the tangent lines, we plot the graph of y = 2x^2 + 2x and draw the tangent lines at the corresponding x-values. The slope of each tangent line represents the steepness or inclination of the curve at that particular point.

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The reason for the last step in the given proof is option E; For parallel lines cut by a transversal, corresponding angles are congruent.

Angles that are of the same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of the same measure, then

\(m\angle A = m\angle B\)

is the notation to say that they are of the same measurement, where the small m shows that it's the measurement of the angles they're preceding.

We write the congruency between them as;

\(\angle A \cong \angle B\)

The last step is as folows

∠JIK ≅∠IJL

For parallel lines cut by a transversal, corresponding angles are congruent.

Since the two angles are corresponding angles and the two parallel lines are cut by a transversal.

The reason for the last step in the given proof is option E; For parallel lines cut by a transversal, corresponding angles are congruent.

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Answer:

Step-by-step explanation:

E

Answer:

1. 24w+8

2. 4s+28t

3. 150-75b

Answer:

  4 pairs

Step-by-step explanation:

You want the number of pairs of integers (m, n) such that m > n and m² -n² = 96.

The difference of squares is factored as ...

  m² -n² = (m -n)(m +n)

In order for the difference to be 96, these factors must be factors of 96.

The prime factorization of 96 is ...

  96 = 2^5 · 3

The number of divisors of 96 is the product of the exponents of these factors, each increased by 1:

  (5+1)(1+1) = 12

That is, there are 12/2 = 6 factor pairs ab such that a<b. They are ...

   96 = 1·96 = 2·48 = 3·32 = 4·24 = 6·16 = 8·12

The values of m and n relate to the values of 'a' and 'b' by ...

  m = (a+b)/2

  n = (b-a)/2

In order for m and n to be integers, the values of 'a' and 'b' must both have the same parity. That is, they must both be even, or both be odd. This eliminates the factor pairs 1·96 and 3·32, leaving 4 (a, b) pairs, hence 4 (m, n) pairs. Possible ordered pairs are ...

  (m, n) ∈ {(25, 23), (14, 10), (11, 5), (10, 2)} . . . . . 4 pairs

the probability P(z > 1.39) is approximately 0.0823 when rounded to four decimal places.

To find P(z > 1.39), we need to locate the value 1.39 in the standard normal probability table. The table provides the area under the standard normal curve up to a certain z-score. Since we need the probability for z > 1.39, we subtract the value in the table from 1 to find the remaining area.

By looking at the standard normal probability table, we find that the value corresponding to 1.3 in the left column and 0.09 in the top row is 0.9177. Therefore, P(z > 1.39) = 1 - 0.9177 = 0.0823.

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Two corresponding sides of the triangles are congruent by congruence postulate, meaning DE ≅ AB and EF ≅ BC. The included angle between the congruent sides is also congruent, meaning ∠DEF ≅ ∠ABC.

To prove that ΔDEF and ΔABC are congruent by SAS (Side-Angle-Side), we need to have the following additional information:
1. The length of two sides of each triangle must be equal.
2. The included angle between these two sides must be equal.
3. The length of the third side of each triangle must be equal.
If we have this information, we can use the SAS congruence postulate to prove that ΔDEF and ΔABC are congruent.

To prove that ΔDEF and ΔABC are congruent by the Side-Angle-Side (SAS) Congruence Postulate, you'll need the following additional information:
Once you have this information, you can apply the SAS Congruence Postulate to conclude that ΔDEF and ΔABC are congruent.

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Answer: mp • (3m3 + 8m2p - 2p2)

Step-by-step explanation:

3m4p + 8m3p2 - 2mp3  =   mp • (3m3 + 8m2p - 2p2)

8.2  Factoring    3m3 + 8m2p - 2p2

To answer this question, we need to use the concept of unit rate. In this case, to find the payment per hour of Job number 1, we can proceed as follows:

Therefore, Job number one pays $7.50 per hour (to the nearest cent).

(We divided the total amount of money by the total amount of time to find the number of dollars per hour.)

Answer:

11am- 2pm

Step-by-step explanation:

the flat line shows where time is constant

Answer:

19.5 kilometers

Step-by-step explanation:

to find how much he ran we can multiply the two numbers

26 * 0.75 is 19.5

he only ran 19.5 kilometers

Answer:

2

Step-by-step explanation:

as x increases by 2, y increases by 4, slope= rise/run, so the slope= 4/2=2

The correct answer is option d. Soto buys a similar oven from another dealer for $6,500. Soto measure of damages is $1,500, plus any additional expense to obtain the oven.

The purpose of a contracts' damages clause is to place the non-breaching party in the same situation that he or she would have been in if the agreement had been upheld.

In this instance, Soto had originally agreed to pay $5,000 to Restaurant Appliances Inc. for the purchase of an oven, but the seller did not fulfil the agreement. Soto was then compelled to pay $6,500 to another dealer for a comparable oven.

The difference between the $5,000 initial contract price and the $6,500 cost of the oven that Soto bought from the other dealer is one of the damages that Soto may claim from Restaurant Appliances Inc. This results in a $1,500 difference.

Soto is also entitled to reimbursement for any additional costs he may have expended in order to get the oven, such as shipping or installation charges. Soto's estimate of damages is therefore $1,500 plus any further costs incurred in obtaining the oven.

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The minterms for the Boolean expressions are: F = Σ(0, 1, 2, 3, 11, 12, 14, 15), A = Σ(0, 1, 2, 3, 11, 12, 14, 15), B = Σ(2, 3, 11, 12, 14, 15), C = Σ(0, 1, 2, 3, 11, 12), and D = Σ(0, 1, 11, 12, 14, 15).

To find the minterms of the given Boolean expressions, we first plot each function on a Karnaugh map. The minterms for each function are then determined by examining the values represented by the marked cells on the map.

Given the Boolean expressions F(w, x, y, z) = wxyz - wyzwx' + wxz, A = Σ(0, 1, 2, 3, 11, 12, 14, 15), B = Σ(2, 3, 11, 12, 14, 15), C = Σ(0, 1, 2, 3, 11, 12), and D = Σ(0, 1, 11, 12, 14, 15), we plot each function on a Karnaugh map. By marking the cells corresponding to the "1" values for each function, we identify the minterms. For function F, the minterms are OAF = Σ(0, 1, 2, 3, 11, 12, 14, 15).

For function B, the minterms are ORF = Σ(2, 3, 11, 12, 14, 15). For function C, the minterms are OcFu = Σ(0, 1, 2, 3, 11, 12). And for function D, the minterms are ODFE = Σ(0, 1, 11, 12, 14, 15).

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T test is used to compute the confidence interval, when the mean and standard deviation is given.

What is Standard Deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be very close to the set mean. The lower case Greek letter (sigma), again for population standard deviation, or even the Latin letter s, again for sample standard deviation, are most frequently used in mathematical texts and equations to represent standard deviation. Standard deviation may be abbreviated as SD. A random variable, specimen, statistical population, data set, as well as probability distribution's standard deviation is equal to the square root of its variance. When the number in a sample, sample mean and sample standard deviation is given, the test statistic that should be used when computing a confidence interval is t test

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\( \to \sf6x - 3(2x - 1)\)

\( \\ \\ \)

\( \to \sf6x - 6x + 3\)

\( \\ \\ \)

\( \to \sf0 + 3\)

\( \\ \\ \)

\( \to \sf 3\)

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

Answer:

The number of days it take to reach half its height is 99 days

Step-by-step explanation:

The given parameters are;

The height to which the beans stalk grew daily = Twice the initial height

The time duration for the bean stalk to reach maximum height = 100 days

Therefore, the growth of the bean stock is in the form of a geometric progression with a common ratio, r = 2

The formula for a  geometric progression = a×r⁽ⁿ⁻¹⁾

Therefore, the height of the bean is given by the formula a×r⁽ⁿ⁻¹⁾

Where;

The first term = a  = 1 (for analysis)

The number of terms (days) = n = 100 for 100 days

Therefore, we have;

After 100 days, the height of the bean = 1×2⁽¹⁰⁰⁻¹⁾ = 2⁹⁹ = 6.34 × 10²⁹

Half the height = 6.34 × 10²⁹/2 = 3.1291265 × 10²⁹

Which gives;

1×2⁽ⁿ⁻¹⁾ = 3.1291265 × 10²⁹

n - 1 = ㏒(3.1291265 × 10²⁹)/㏒(2) = 98

Which gives;

n - 1 = 98

n = 98 + 1 = 99 days.