For the following data set, write a system of equations to determine the coefficients of the natural cubic splines passing through the given points. DO NOTE solve the system. x = 2 4 8 y = 2 8 12

The missing measures in △STU could be 28 degree.

WE have been Given △PQR ~ △STU,

WE need to find the missing measures in △STU.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

\(\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}\)

Remember that we took

\(\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}\)

\(\dfrac{sin\angle Q}{21} = \dfrac{sin\angle T}{6}\)

\(\dfrac{sin\angle 64}{21} = \dfrac{sin\angle T}{6} \\\\\dfrac{0.920}{21} = \dfrac{sin\angle T}{6} \\\\{sin\angle T} = \dfrac{0.920 \times 6}{21}\)

Sin angle T = 0.2628

△STU = 28 degree.

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Answer:

C. \(38.445\leq x\leq 38.555\)

Step-by-step explanation:

The measured length varies from the ideal length by 0.055 cm at most, so to find the range of possible lengths, we subtract 0.055 from the ideal, 38.5.

\(38.5-0.055=38.445\\38.5+0.055=38.555\)

The measured length can be between 38.445 and 38.555 inclusive. This can be written in an equation using greater-than-or-equal-to signs:

\(38.445\leq x\leq 38.555\)

38.445 is less than or equal to X, which is less than or equal to 38.555.

So the answer to your question is C.

Answer:

6/2 = 3

Step-by-step explanation:

there are 2 people, when you divide the 6 trout by the 2 people, they will each get 3 fishes

Answer:

(-1 , 0)

Step-by-step explanation:

I think this is it but I didn't know if it was 6 times 2 or 6 x 2

Answer:

144 in^2

Step-by-step explanation:

Using the A = s^2 and the text says that s= 12in

 the answer is 12 in * 12 in = 144 in^2

The two numbers are 21 and 57.

Let's call the two numbers x and y, where x is the smaller number and y is the larger number.

From the problem, we know that:

x + y = 78   --------- (1)   (the sum of two numbers is 78)

and

y - 2x = 15   --------- (2)   (twice the smaller number is subtracted from the larger number, the result is 15)

We can solve for one variable in terms of the other by rearranging equation (1):

x = 78 - y

Substituting this value for x into equation (2), we get:

y - 2(78 - y) = 15

Simplifying the equation, we get:

y - 156 + 2y = 15

Combining like terms, we get:

3y - 156 = 15

Adding 156 to both sides, we get:

3y = 171

Dividing both sides by 3, we get:

y = 57

Now that we have the value of y, we can use equation (1) to solve for x:

x + 57 = 78

x = 21

Therefore, the two numbers are 21 and 57.

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The hypotenuse of a right triangle is 3 less than twice the length of the shorter leg. The length of the hypotenuse is 15 centimeters.

Let's denote the shorter leg of the right triangle as 'x' and the hypotenuse as 'h'. We're given that the longer leg is 12 centimeters, so we can set up the following equations based on the given information:

h = 2x - 3 (Equation 1)

12^2 + x^2 = h^2 (Pythagorean theorem)

Substituting the value of 'h' from Equation 1 into the Pythagorean theorem equation, we get:

12^2 + x^2 = (2x - 3)^2

Expanding the equation, we have:

144 + x^2 = 4x^2 - 12x + 9

Rearranging the terms and simplifying, we get:

0 = 3x^2 - 12x - 135

Dividing the entire equation by 3, we have:

0 = x^2 - 4x - 45

Now, we can factorize the quadratic equation:

0 = (x - 9)(x + 5)

Setting each factor to zero and solving for 'x', we get two possible values:

x - 9 = 0 -> x = 9

x + 5 = 0 -> x = -5

Since the length of a side cannot be negative, we discard the value x = -5. Therefore, the length of the shorter leg is x = 9 centimeters.

To find the length of the hypotenuse, we can substitute this value back into Equation 1:

h = 2(9) - 3

h = 18 - 3

h = 15

Therefore, the length of the hypotenuse is 15 centimeters.

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The probability that the sample contains 2 female voters is 0.31104

Binomial distribution uses two values; n and p. n represent the counts of sample that are being collected. On the other hand, p represents the chances of being successful on any trial. Using the two values, the probabilities are computed for binomial distribution.

Probability that a random voter is female is 0.40(p).

Sampled voters are 6(n).

Let X be the number of females in the sampled voters.

Then,

X∼ Bin (n, p)

∼Bin (6,0.4)

Probability that the sample contains exactly 2 female voters is,

P (X =2) = 6C2 (0.4)2 (1−0.4)6−2

=0.31104

Therefore, the probability that the sample contains exactly 2 female voters is 0.31104

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The distribution of X is a binomial distribution with n = 80 and p = 0.36. Using the distribution of X, the probability that Mark has between 27 and 32 (including 27 and 32) hits is 0.1919. The distribution of p is a normal distribution with mean μ = 0.36 and standard deviation σ = 0.05367. Using the distribution of p, the probability that Mark has between 27 and 32 hits is 0.4344.

a. The distribution of X is a binomial distribution with n = 80 and p = 0.36.

Since we are dealing with a large number of trials (80 at-bats) and a binary outcome (hit or no hit), we can model X using a binomial distribution. The distribution of X is B(n=80, p=0.36), where n is the number of trials, and p is the probability of success (getting a hit).

b. Using the binomial distribution, the probability that Mark has between 27 and 32 (including 27 and 32) hits is:
P(27 ≤ X ≤ 32) = \(\sum_{k=27}^{k=32} P(X=k)\)

= \(\sum_{k=27}^{k=32}(80 choose k) \times 0.36^k \times (1-0.36)^{(80-k)}\)

= 0.1919 (rounded to 4 decimal places)

c. The distribution of p is a normal distribution with mean μ = p = 0.36 and standard deviation

\(\sigma = \sqrt{((p\times(1-p))/n)}\)

\(= \sqrt{((0.36(1-0.36))/80)}\)

= 0.05367.

d. Using the normal distribution, we can standardize the range of 27 to 32 hits to the corresponding range of sample proportions using the formula:

z = (x - μ) / σ
where x is the number of hits, μ is the mean proportion (0.36), and σ is the standard deviation of the proportion (0.05367).

So, for 27 hits:
z = (27/80 - 0.36) / 0.05367 = -0.4192

For 32 hits:
z = (32/80 - 0.36) / 0.05367 = 0.7453

Then, we can use the standard normal distribution table or calculator to find the probability that z is between -0.4192 and 0.7453:
P(-0.4192 ≤ z ≤ 0.7453) = 0.4344

Therefore, the probability that Mark has between 27 and 32 hits is approximately 0.4344.

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Answer:

164.6

Step-by-step explanation:   i'm a human calculator

Answer:

164.6

Step-by-step explanation:

Divide 987.6 by 6 = 987.6/6= 164.6

Answer:

I don't get it like you messed up on it

Step-by-step explanation:

Answer:

he needs to work at least 5 days

Step-by-step explanation:

Answer:

Azda's price is better

Step-by-step explanation:

Tisco

3 for £1.29

12 for £1.29*4= £5.16

Azda

4 for £1.68

12 for £1.68*3= £5.04

Azda offers better price for 12 items

Answer:

Tisco gets £5.16 per 12 items but Azda gets £5.04 per 12 items.

Step-by-step explanation:

Tisco has the best value

To find the number of times Shawn came to bat, we can set up a proportion based on the given information. The proportion states that 1 home run is hit every 12 times he comes to bat. Therefore, Shawn came to bat approximately 564 times in order to hit 47 home runs.

Let's denote the number of times Shawn came to bat as "x". The proportion that can be used to solve this problem is:

1 home run / 12 times = 47 home runs / x times

By cross-multiplying the proportions, we have:

1 * x times = 12 * 47 home runs

Simplifying the equation, we find:

x = 12 * 47

Evaluating the expression on the right side, we get:

x = 564

Therefore, Shawn came to bat approximately 564 times in order to hit 47 home runs.

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On solving the provided question we can say that - area of the given triangle will be A = 60 cm sq.

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

here,

B = 8cm

H = 15 cm

A = 1/2 BH = 1/2 X 8 X 15 = 60cm sq.

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Answer:

A) 25° C

Step-by-step explanation:

hope this helps :)

Answer:

Step-by-step explanation:

Use the given formula and substitute F with 77:

Answer:

The answer is B

Answer:

the numbers are 10 and 8

Answer:

Part A: 16x^2 -56x+49

I'm not quite sure on Part B and C though, sorry :/.

Step-by-step explanation:

To find the expression we need to solve (4x-7)•(4x-7)

4x•4x = 16x^2

4x•-7= -28x

-7•4x= -28x

-7•-7=49

Combine alike terms

16x^2-56x+49

Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!

The value of t when the ball hits the ground is 5 seconds. When the ball hits the ground, its velocity is 80 ft/sec. What is the time (value of t) at which the ball hits the ground? To determine the time (value of t) at which the ball hits the ground, the quadratic equation should be set to zero since the height of the ball when it strikes the ground is zero.s(t) = 0 ==> 160 + 48t - 16t^2 = 0.

A quadratic equation in standard form is: ax² + bx + c = 0where a = -16, b = 48, and c = 160Therefore, the quadratic equation is: -16t² + 48t + 160 = 0Divide each term by -16 to obtain the quadratic equation in the form: t² - 3t - 10 = 0Then solve the quadratic equation, using the quadratic formula:$$t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$Substitute the values of a, b and c in the quadratic formula.$$t = \frac{-48 \pm \sqrt{48^2 - 4(-16)(160)}}{2(-16)}$$Simplify the expression.$$t = \frac{-48 \pm \sqrt{2304 + 10240}}{-32}$$.$$t = \frac{-48 \pm \sqrt{12544}}{-32}$$.$$t = \frac{-48 \pm 112}{-32}$$t = -2 or t = 5The time when the ball hits the ground is t = 5 sec.

What is the velocity of the ball at the moment it hit the ground? To determine the velocity of the ball when it hits the ground, differentiate the height function s(t) with respect to time. It is given that s(t) = 160 + 48t - 16t²ds/dt = 48 - 32tWhen the ball hits the ground, the value of t is 5 seconds, and its velocity is given by:v = ds/dt at t = 5s.v = ds/dt at t = 5 = 48 - 32(5) = -32 ft/secTherefore, the velocity of the ball when it hits the ground is 80 ft/sec (downward direction).

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When y = (t2 + 5t + 3)(2t2 + 4), we may apply the product rule of differentiation to determine (frac)dydt.

Let's define each term independently.

((t2 + 5t + 3)), the first term, can be expanded to (t2 + 5t + 3).

The second term, "(2t2 + 4," is differentiated with regard to "(t") to provide "(4t").

When we use the product rule, we get:

Fracdydt = (t2 + 5 + 3) (2t2 + 4) + (2t2 + 4) cdot frac ddt "cdot frac" ((t2 + 5 t + 3)"

Condensing the phrase:

Fracdydt = (t2 + 5 + 3) cdot (2t + 5)) = (4t) + (2t2 + 4)

Expansion and fusion of comparable terms:

Fracdydt is defined as (4t3 + 20t2 + 12t + 4t3 + 10t2 + 8t + 10t2 + 20t + 15).

Simplifying even more

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Answer: it’s C

Step-by-step explanation: ^

Answer:

the domain of f(x) is x > 0

Step-by-step explanation:

mark brainliest

The solution to the initial-value problem y' = (1/2)y2, y(0) = 0.5y(1) is y = -2/x + 4.

a. Differential equations are used to model change. They represent the change in a variable y with respect to the change in another variable x. By looking at the differential equation of the form y' = ky, where k is a constant, you can say that the solution of the equation y is decreasing (or equal to 0) on any interval on which it is defined.

b. The given family of solutions y = 2/(x + C) is of the form y = k/(x + C), where k = 2 is a constant and C is the arbitrary constant of integration. The derivative of y with respect to x is y' = -k/(x + C)

2. Substituting this into the given differential equation y' = ky, we have:-k/(x + C)2 = k/k(x + C)y, which simplifies to y = 2/(x + C).

Therefore, all members of the family y = 2/(x + C) are solutions of the given differential equation.

c. To find a solution of the initial-value problem y' = (1/2)y2, y(0) = 0.5y(1), we need to solve the differential equation and use the initial condition y(0) = 0.5y(1).

Separating the variables and integrating both sides, we get:

dy/y2 = (1/2)dx.

Integrating both sides, we get:-1/y = (1/2)x + C, where C is the constant of integration.

Solving for y, we get:

y = -1/(1/2)x - C = -2/x - C.

We know that y(0) = 0.5y(1), so substituting x = 0 and x = 1 in the solution above, we get:-2/C = 0.5y(1), and y(1) = -2 - C.

Substituting C = -4, we have y = -2/x + 4. Therefore, the solution to the initial-value problem y' = (1/2)y2, y(0) = 0.5y(1) is y = -2/x + 4.

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(a) Given differential equation is `(1/2) y²`. For a solution of differential equation `y = f(x)`, the function `y = f(x)` must satisfy the differential equation.  

By looking at the differential equation, we can say that the function Y must be decreasing (or equal to 0) on any interval on which it is defined. Thus, the correct option is (A).

The differential equation is `(1/2) y²`. Let `y = f(x)`, then `(1/2) y²` can be written as,`dy/dx = y dy/dx`Dividing by `y²`, we get,`dy/y² = dx/2`Integrating both sides, we get,`-1/y = (x/2) + C`

Where C is the constant of integration. Rearranging the terms, we get,`y = -2/(x + C)`

This is the general solution of the differential equation. Now, we need to verify that all members of the family `y = 2/(x + C)` are solutions of the equation in part (a).(b) Let `y = 2/(x + C)`, then `y' = -2/(x + C)²`.

Substituting these values in the differential equation, we get,`(1/2) [2/(x + C)]² (-2/(x + C)²) = -1/(x + C)²`Simplifying, we get,`-1/(x + C)² = -1/(x + C)²`This is true for all values of x.

Hence, all members of the family `y = 2/(x + C)` are solutions of the equation in part (a).(c) We need to find a solution of the initial-value problem: `y' = y²/2, y(0) = 0.5 y(1)`.

We know that `y = 2/(x + C)` is the general solution of the differential equation. To find the particular solution that satisfies the initial condition, we substitute `x = 0` and `y = 0.5 y(1)` in the general solution, we get,`0.5 y(1) = 2/(0 + C)`or, `C = 4/y(1)`

Substituting this value of C in the general solution, we get,`y = 2/(x + 4/y(1))`

Hence, the solution of the initial-value problem is `y = 2/(x + 4/y(1))`.

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Answer:

See Explanation

Step-by-step explanation:

Given

(1) CALL and (2) BARK

Required

Why is the number of arrangement of (1) less than (2)

The reason is that in (1), letter L occurred twice. When there is a repetition of letters, the number of ways of arrangement reduces

For (1)

There are 4 letters and L is repeated twice.

\(Arrangement = \frac{4!}{2!}\)

\(Arrangement = \frac{24}{2}\)

\(Arrangement = 12\)

For (2)

There are 4 letters and no repetition

\(Arrangement = 4!\)

\(Arrangement = 24\)

The reason why the number of ways of CALL is less than the number of ways of arranging the letters of BARK should be explained below.

The reason should be that in (1), letter L occurred twice. At the time When there is a repetition of letters, the number of ways of arrangement decreases.

So here arrangement be like

When there is 4 letters and L is repeated twice.

=4!/2!

= 24/2

= 12

And,

When there is 4 letters and no repetition

= 4!

= 24

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Answer:

1. B) 71.2 m

2. D) 58.8 mi

3. C) 45.2 km

Answer: You can make more bracelets than necklaces. ✅

Step-by-step explanation:

You have 2.88 meters of copper wire and 5.85 meters of aluminum wire.

With 2.88 meters of copper wire, you can make 12 bracelets because each bracelet needs 0.24 meters of copper wire.

With 5.85 meters of aluminum wire, you can make 9 necklaces because each necklace needs 0.65 meters of aluminum wire.

So you can make 12 bracelets and 9 necklaces.

Therefore you can make more bracelets than necklaces.

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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Answer:

900,000

Explanation:

1 million is 10*100,000, so subtracting 100,000 from it is just like subtracting 1 from 10-- just much much larger numbers.

Answer:

99,900,000

Step-by-step explanation:

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{4 {x}^{3} + 6 {y}^{2} }}}}}\)

Step-by-step explanation:

\( \sf{5 {y }^{2} + 5 - 4 - 4 {y}^{2} + 5 {y}^{2} - 4 {x}^{3} - 1}\)

Collect like terms

⇒\(\sf{ 4 {x}^{3} + 5 {y}^{2} - 4 {y}^{2} + 5 {y}^{2} + 5 - 4 - 1}\)

⇒\( \sf{4 {x}^{3} + {y}^{2} + 5 {y}^{2} + 5 - 4 - 1}\)

⇒\( \sf{4 {x}^{3} + 6 {y}^{2} + 5 - 4 - 1}\)

Calculate

⇒\( \sf{4 {x}^{3} + 6 {y}^{2} + 1 - 1}\)

⇒\( \sf{4 {x}^{3} + 6 {y}^{2} }\)

Hope I helped!

Best regards! :D