what is the slope of (2,3) (10,15)

The speed of the boat in still water is 16 miles per hour. So, the given speed of 0.5 is incorrect.

Let, v = the speed of the boat in still water.

The current of a river is 4 miles per hour.

On going upstream, the boat travels  v−4  miles per hour.

On going downstream, the boat travels  v+4  miles per hour.

So we can write,

( 30 miles × 1 hour ) / (v − 4 miles) = 30 / ( v − 4 ) hours

( 30 miles × 1 hour ) / ( v + 4 ) miles= 30 / ( v + 4 )hours

a boat travels to a point 30 miles upstream and back in 4 hours. So, on adding equation 1 and equation two we will get 4. Mathematically,

{30 / ( v − 4 )}  + {30 / ( v + 4 )} = 4

30 ( v + 4 ) + 30 ( v - 4 ) = 4 ( v - 4 ) ( v + 4 )

60v =  4 ( \(v^{2} - 16\) )

4 \(v^{2}\) - 60 v - 64 = 0

\(v^{2}\) - 15v - 16 = 0

( v - 16 ) (v + 1 ) = 0

v = -1 , 16

speed in still water cannot be negative. So, we can neglect -1 .  the speed of the boat in still water is 16  miles per hour.

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Answer: The solutions to the equation 3(x-5)(2x+3) = 0 are x = 5 and x = -3/2.

Step-by-step explanation: So, we have:

3(x-5)(2x+3) = 0

Using the zero product property, we can set each factor equal to zero:

x - 5 = 0 or 2x + 3 = 0

Solving for x in each equation, we get:

x = 5 or x = -3/2

Therefore, the solutions to the equation 3(x-5)(2x+3) = 0 are x = 5 and x = -3/2.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools.

To determine if there is sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools, we can use a two-sample z-test for the difference in proportions.

The null hypothesis is that there is no difference between the proportions of students with ear infections at the two schools, while the alternative hypothesis is that there is a difference.

Let p1 be the proportion of students with ear infections at the first school and p2 be the proportion at the second school. The test statistic is given by:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat is the pooled proportion, n1 and n2 are the sample sizes from the first and second schools, respectively.

The pooled proportion is given by:

p_hat = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of students with ear infections in each school.

Using the given data, we have:

n1 = 40, n2 = 30

x1 = 11, x2 = 12

p1 = x1/n1 = 11/40 = 0.275

p2 = x2/n2 = 12/30 = 0.4

p_hat = (x1 + x2) / (n1 + n2) = (11 + 12) / (40 + 30) = 0.355

The test statistic is:

z = (0.275 - 0.4) / sqrt(0.355 * 0.645 * (1/40 + 1/30)) = -1.197

Using a standard normal table or calculator, the p-value for a two-tailed test with a test statistic of -1.197 is approximately 0.231.

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Answer:

hey its 8

Step-by-step explanation:

Hold on, our servers are swamped. Wait for your answer to fully load.

The required minimum sample size is 2875

Given that,

A government organization wanted to determine how many drivers between the ages of 16 and 24 had recently engaged in an accident. The agency wanted to make the estimate with a 90% confidence level and within one percentage point.

From the standard normal table, the z-critical value at 90% confidence is 1.65.

The information represent E = 0.01, p = 0.12 and z. =1.65 for finding sample size.

n = (Zc / E )² x P(1-P)

  = (1.65 2x0.12(1 - 0.12)0.01

  = 2874.96 ~ 2875

Hence, 2875 is the necessary number of samples, minimum.

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The inverse Laplace transform of G(s) is \(g(t) = 10e^{-t} - 10e^{-3t}\).

To find the inverse Laplace transform of the given function G(s), we can use partial fraction decomposition and known Laplace transforms. The partial fraction decomposition of G(s) is:

\(G(s) = 10s^2e^{-s} / (s+1)(s+3)\)

To perform the partial fraction decomposition, let's write G(s) in the following form:

G(s) = A/(s+1) + B/(s+3)

To find the values of A and B, we need to find a common denominator for the two fractions on the right-hand side:

\(10s^2e^{-s} = A(s+3) + B(s+1)\)

Expanding the right-hand side:

\(10s^2e^{-s} = As + 3A + Bs + B\)

Now, equating the coefficients of \(s^2\), s, and the constant term:

Coefficient of \(s^2\):

10 = A

Coefficient of s:

0 = A + B

Constant term:

0 = 3A + B

From the first equation, A = 10. Substituting this value in the second and third equations:

0 = 10 + B

0 = 3(10) + B

From the second equation, B = -10. Substituting B = -10 into the third equation:

0 = 3(10) - 10

0 = 30 - 10

0 = 20

Now that we have the values of A and B, we can rewrite G(s) as:

G(s) = 10/(s+1) - 10/(s+3)

To find the inverse Laplace transform of G(s), we can use the known Laplace transform pairs. The inverse Laplace transform of 10/(s+1) is 10e^(-t), and the inverse Laplace transform of \(-10/(s+3) is -10e^{-3t}\). Therefore, the inverse Laplace transform of G(s) is:

\(g(t) = 10e^{-t} - 10e^{-3t}\)

So, the inverse Laplace transform of G(s) is \(g(t) = 10e^{-t} - 10e^{-3t}\).

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D: "\(c_{1} = 10\) and \(c_{2} = 2\)" are programmer-defined constants for quadratic probing that cannot be used in a quadratic probing equation. Option D is correct answer.

The quadratic probing equation is defined as:

h (k, i) = (h′(k) + \(c_{1}\) * i + \(c_{2}\) * i^2) mod m,

where h′(k) is the hash value of key

k and m is the size of the hash table.

The constants \(c_{1}\) and \(c_{2}\) are programmer-defined constants that are used to compute the new hash index when a collision occurs in the hash table.

The given hash function is h(k) = k % 10.

Therefore, the hash value of any key will be between `0` and `9`.Now, let's check which of the given programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation:

Option A: `c1 = 1 and c2 = 0`This option can be used in the quadratic probing equation. It means that linear probing is being used.

Option B: \(c_1 = 5\) and \(c_2 = 1\) This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 5i + i^2) mod m`.

Option C: \(c_1 = 1\) and \(c_2 = 5\) This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + i + 5i^2) mod m`.

Option D: \(c_1 = 10\) and \(c_2 = 2\) This option cannot be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 10i + 2i^2) mod m`.

Since \(c_{1}\) is greater than or equal to `m`, this equation will always result in a hash index that is greater than or equal to `m`. Therefore, it is not possible to use `\(c_{1}\)= 10` in the quadratic probing equation. Hence, the correct option is D.

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The present value is $1, the growth rate is 12.0% (or 0.12 as a decimal), and the number of years is 75. So, the future value is approximately $4,913.06. The correct answer is \(\( \$ 4,913.06 \).\)

To calculate the future value of an amount growing at a given rate over a certain period of time, we can use the formula for compound interest:

Future Value = Present Value * (1 + Growth Rate)^Number of Years

In this case, the present value is $1, the growth rate is 12.0% (or 0.12 as a decimal), and the number of years is 75. Plugging in these values, we can calculate the future value:

\(Future Value = $1 * (1 + 0.12)^75\)

Calculating this, the future value is approximately $4,913.06.

Therefore, the correct answer is \(\( \$ 4,913.06 \).\)

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Answer:

yes

Step-by-step explanation:

lol

The rule for the translation is (-3, -4).

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

JKL is the original figure.

J'K'L' is the transformed figure after applying cetain rule.

We obtain J'K'L' by translating the original image left 3 units and down by 4 units.

The rule should be (-3, -4)

Hence,  the rule for the translation is (-3, -4).

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Answer:

Step-by-step explanation:

here you go mate

step 1

(x^3)4  equation

step 2

(x^3)4  simplify

answer

4x^3

can i get brainliest if you dont mind

The solution to the following system using substitution is (2,1).

What is system of equations ?
Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

\($$\left[\begin{array}{c}y=-4 x+9 \\y=3 x-5\end{array}\right]$$\)

Substitute y=3 x-5

[3 x-5=-4 x+9]

Isolate x for 3 x-5=-4 x+9: x=2

For y=3 x-5

Substitute x=2

\(y=3 \cdot 2-5\)

Simplify

y=1

The solutions to the system of equations are:

y=1, x=2

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We need to find the inverse of the function gof (x). First we need to find the composite function gof (x) which is given by:

\(g(f(x)) = g(3x - 6)\)

= \((1/3)(3x - 6) + 1\)

= x - 1 + 1

= x

Thus,

gof (x) = x.

Now we need to find the inverse of the function gof (x) to obtain

\((gof)^-1 (x).\)

We have gof (x) = x

which implies\((gof)^-1 (x)\)

= gof (x)^-1

= x^-1

= 1/x,

x ≠ 0

Therefore,

\((gof)^-1 (x) = 1/x\)

which is option (3) (x+1) since 1/x can be written as 1/(x+1-1), where (x+1-1) is the denominator of 1/x.

Hence, the correct option is (3).

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To find (g(f))^-1 (x), substitute the expression for f(x) into g(x) and simplify. The composition of g(f) is x and its inverse is also x. Therefore, (g(f))^-1 (x) equals x.

To find (g(f))^-1 (x), we need to first find the composition of g(f) and then find its inverse. Start by substituting the expression for f(x) into g(x): g(f(x)) = g(3x-6) = \frac{1}{3}(3x-6) + 1 = x - 1 + 1 = x. So, g(f(x)) = x. Now, to find the inverse of g(f), we switch the x and y variables and solve for y: y = x. Therefore, (g(f))^-1 (x) = x.

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Temperature less than 0° C is -9° C.

To subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less.

Given a temperature 9 less than 0,

0° C - 9 = -9° C

Hence, Temperature less than 0° C is -9° C.

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Answer:

r = 0.84

Step-by-step explanation:

The mean reading time obtained with the stopwatch measurements was 4.34 ± 0.57 seconds (196.21 ± 21.79 wpm), versus 4.44 ± 0.59 seconds (192.24 ± 22.20 wpm) by computer measurement (r = 0.84).

Answer:

y=-4/3x-3

Step-by-step explanation:

The equation of the line that passes through the given point will be equal to (-4/3)x - 3.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the given information in the question,

The given equation is,

4x + 3y = 15

And the point is (-3, 1)

3y = 15 - 4x

y = (-4/3)x + 15

The line has a slope, of -4/3.

Then, use the equation,

B = y - mx

B = 1 - (-4/3 × 3)

B = -3

So,

y = (-4/3)x - 3

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Answer:

Two intersecting chords is the correct answer

thank you

Answer:

intersecting chords theorem

Answer:

2 1/3

Step-by-step explanation:

multiply like terms

Answer:

$25

Step-by-step explanation:

Answer:

\(\mathrm{A.\: 39.3}\)

Step-by-step explanation:

Let \(h\) represent the height of the two smaller triangles in this figure. Because all three triangles are similar, we can set up the following proportion:

\(\frac{33}{h}=\frac{h}{y}\), for \(y=x-33\).

We can solve for \(h\) using the Pythagorean theorem on the second largest triangle:

\(33^2+h^2=36^2,\\h=\sqrt{36^2-33^2},\\h=\sqrt{207}\).

Now plugging in \(h=\sqrt{207}\) into our proportion \(\frac{33}{h}=\frac{h}{y}\), we can solve for y:\(\frac{33}{\sqrt{207}}=\frac{\sqrt{207}}{y}\).

Cross-multiply to get:

\(33y=207,\\y=\frac{207}{33},\\y\approx 6.3\).

Since we \(y=x-33, y+33=x\).

Therefore, our answer is:

\(x=33+y=33+6.3=\fbox{$\mathrm{A.\: 39.3}$}\).

Answer:

16

Step-by-step explanation:

If x = 3, then all we must do is substitute.

y=7(3)-5

y= 21 -5

y= 16

---

Hope I helped :)

Answer:

a) 0.09

b) 2 ways

Step-by-step explanation:

a) Probability Pedro's shot will score will be given as) :

P(score) = 0.30

The probability he will score in 2 consecutive shots will be calculated as:

P(score) * P(score)

= 0.30 * 0.30

= 0.09

Therefore, probability he will score in 2 consecutive shots is 0.09

b) Jillian has 3 bracelets: X, Y, & Z as a gift. If bracelet Y is chosen first, the number of ways Jillian can give out the bracelets since bracelet Y is chosen first, she will have 2 bracelets remaining. So, number of ways to distribute these 2 bracelets are :

= 2!

= 2 * 1

= 2

Which could be in this order:

YXZ or YZX

Therefore, the number of ways if Y is chosen first is = 2 ways

Answer: A. 0.09

Just took test.

The median number of siblings for the ten students is: (2 + 3) / 2 = 2.5

To find the median, we first need to arrange the data in order from smallest to largest:

1, 1, 2, 2, 2, 3, 3, 3, 4, 6

The middle value of the data set is 2, since there are five values on either side. Thus, the median number of siblings for the ten students is 2.

Since there are an even number of values, the median is the average of the two middle values, which are 2 and 3. Therefore, the median number of siblings for the ten students is:

(2 + 3) / 2 = 2.5

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The length of the trout that represents the 45th percentile is 32 centimeters.

The trout with a length of 34 centimeters is at the 70th percentile.

From the data:

26, 28, 28, 29, 30, 31, 31, 31, 32, 33, 33, 33, 33, 34, 36, 36, 37, 38, 38, 40

Using this formula, we can calculate the index of the observation that represents the 45th percentile:

= (45/100) × 20 = 9

For the second part,

= [(14/20) × 100] = 70

This means that the trout with a length of 34 centimeters is at the 70th percentile.

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answer: 16 plates

I apologize if this is an incorrect answer,however, I believe that the fraction was added to throw you off. so if you divide the number of bowls you get 2 and then you multiply 8 by 2

If you spend all your money just on plates. Then the number of plates that you can buy will be 20.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Wendy spends 3/5 of her money on 3 bowls and 8 plates. With the rest of your money, you can buy another 6 bowls.

Let 'x' be the cost of each bowl, 'y' be the cost of each plate, and 'T' be the total amount of money. Then the equations are given as,

3x + 8y = (3/5) T          ...1

6x = (2/5) T

x = (1/15) T                 ...2

From equations 1 and 2, then the cost of each plate is calculated as,

3(1/15)T + 8y = (3/5)T

8y = 2/5

y = (1/20)T

If you spend all your money just on plates. Then the number of plates that you can buy will be given as,

⇒ T / (T / 20)

⇒ 20

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The integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.

To determine the values of p for which the integral ∫10x^p * ln(x) dx converges, we need to consider the convergence of the integrand for different values of p. The integral will converge if the integrand is well-behaved and does not exhibit any divergence.

Let's analyze the integrand in two separate cases:

Case 1: p ≠ -1

When p ≠ -1, the integrand is well-defined for all x > 0. We can proceed with evaluating the integral.

∫10x^p * ln(x) dx = [x^(p+1) * ln(x)] / (p+1) + C

To calculate the value of the integral for a specific value of p, we can substitute the limits of integration into the antiderivative expression and evaluate the resulting expression.

Case 2: p = -1

When p = -1, the integrand becomes 10x^(-1) * ln(x), which poses a potential issue at x = 0. To determine if the integral converges for this case, we need to examine the behavior of the integrand near x = 0.

As x approaches 0, the expression ln(x) approaches negative infinity, which would cause the integrand to diverge. Therefore, for p = -1, the integral does not converge.

In summary, the integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.

Please note that when evaluating the definite integral for specific limits of integration, you should substitute the limits into the antiderivative expression and then calculate the difference of the resulting expressions evaluated at the upper and lower limits.

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Answer:

The correct answer is 5.

Step-by-step explanation:

For the first circle,

When we add 6,18,12,

we get 6+18+12 = 36

Now

when we divide 36 with 6 we get 6.

again,

for second circle,

When we add 10,53,18

we get 10 + 53 + 18 = 81

when we divide 81 with 9 we get 9.

Now

let the unknown number be x.

so,

Pattern : When we add all of the number in the circle excluding the smallest number and dividing it by the smallest number we get the same number.

following the pattern,

Here in the options x>=5 (smallest number in the circle 3)

so, we can take smallest number as 5.

As the pattern,

(x+10+10)/5 = x

or, (x+20)/5 = x

or, x+20 = 5x

or, 5x-x = 20

or, 4x = 20

so, x = 5

Answer:

√3/10 = 0.1732

Step-by-step explanation:

√15 / 5√20 = (√5 x √3) / 5(√5 x √4) = √3 / (5 x√4) = √3 / 10