Solve the initial value problem for r as a vector function of t. Differential Equation: dr/dt = 9/2(t+ 1)^1/2 i + 6e^-t j+ 1/t+1k Initial condition: r(0) = k r(t) =

Answer:

C)  There is a positive linear association between the math and science scores, with one of the data points being an outlier.

Step-by-step explanation:

Correlation measures how closely two variables are linked.  

If two variables are correlated, you can draw a line of best fit on the scatter plot.

From inspection of the given scatter plot:

All data points (with the exception of one) are very close to being in a straight line with a positive slope.  This is called a positive linear correlation.

As the one data point is far from the general pattern of the other points, it is an outlier.

There is a positive linear association between the math and science scores, with one of the data points being an outlier.

The probability of event F given that event E has occurred is approximately 0.5850.

The conditional probability of an event F given that event E has occurred is the probability that both events E and F occur, divided by the probability that event E occurs. It is denoted as P(F|E).

In this problem, Here,  P(E) = 0.326, P(F) = 0.298, and P(E ∩ F) = 0.191. We want to calculate P(F|E).

Using the conditional probability formula, we have:

P(F|E) = P(E ∩ F) / P(E)

Substituting the given probabilities, we get:

P(F|E) = 0.191 / 0.326

Simplifying the expression, we get:

P(F|E) ≈ 0.5850

Therefore, the probability of event F given that event E has occurred is approximately 0.5850.

Learn more about probability here, https://brainly.com/question/31583169

#SPJ11

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer:

25

Step-by-step explanation:

let there be x questions on the test

80% of x = 20

80% * x = 20

80% = 0.8

0.8 * x = 20

divide both sides by 0.8 to isolate x

x = 20/0.8 = 25

Answer:

\(\text{log}_a(1.5^{-1})=\frac{-9}{5}\)

Step-by-step explanation:

Given;

\(\text{log}_a(2)=\frac{1}{2}\)

\(\text{log}_a(3)=5\)

By using logarithmic properties,

\(\text{log}_a(2)-\text{log}_a(3)=\frac{1}{2}-5\)

\(\text{log}_a(\frac{2}{3})=\frac{1}{2}-5\)

\(\text{log}_a(\frac{1}{\frac{3}{2}})=\frac{1}{2}-5\)

\(\text{log}_a(\frac{1}{1.5})=\frac{1}{2}-5\)

\(\text{log}_a(1.5^{-1})=\frac{1-10}{5}\)

\(\text{log}_a(1.5^{-1})=\frac{-9}{5}\)

The value of x is 16.

The value of y is 1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x - 2y = 14 ____(1)

x = 14 + 2y _____(2)

x + 3y = 9 _____(3)

Putting (2) in (3) we get,

14 + 2y + 3y = 9

14 + 5y = 19

5y = 19 - 14

5y = 5

y = 1

Now,

y = 1 in (2)

x = 14 + 2 x 1

x = 14 + 2

x = 16

Thus,

The value of x and y is 16 and 1.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Answer:

Median: 20

first quartile: 9.75

third quartile: 28.75

interquartile range: 19

Explanation:

First we arrange the data from least to greatest

Answer:

not a right triangle

Step-by-step explanation:

Including all relevant disciplines and considering various disciplinary perspectives are important aspects of integration, they do not directly address the completeness of the integration process itself.

The difference between partial integration and full integration is whether or not all insights have been integrated to form a single theory. Partial integration refers to the process of integrating some of the insights or components into a cohesive whole, but not necessarily incorporating all of them. On the other hand, full integration implies that all relevant insights or components have been brought together to create a comprehensive and unified theory or understanding.

The other two answer choices mentioned, whether all relevant disciplines are included as part of the investigation and whether all disciplinary perspectives have produced alternative integrations, are not the defining factors that differentiate partial integration from full integration. While including all relevant disciplines and considering various disciplinary perspectives are important aspects of integration, they do not directly address the completeness of the integration process itself.

Learn more about Partial integration here:

https://brainly.com/question/32116693

#SPJ11

Answer:

\(-\frac{6x^4y^3}{z^7}\)

Step-by-step explanation:

\(=-6x^4y^3\frac{1}{z^7}\) <- Apply the exponent rule.
\(=-\frac{6x^4y^3\cdot \:1}{z^7}\) <- Apply the fraction rule.

\(=-\frac{6x^4y^3}{z^7}\)

Brody would need an interest rate of 4.5% compounded daily.

How to calculate interest rate of investment?

We can use the compound interest formula to solve the problem:

\(A = P(1 + r/n)^(^n^t^)\)

where:

A = final amount of money ($790)

P = initial investment ($350)

r = interest rate (unknown)

n = number of times interest is compounded per year (365, since interest is compounded daily)

t = time in years (18)

So, we can plug in the given values and solve for r:

\(790 = $350(1 + r/365)^(^3^6^5^1^8^)\)

\(2.25714 = (1 + r/365)^(^3^6^5^1^8^)\)

\(ln(2.25714) = ln[(1 + r/365)^(^3^6^5^1^8^)]\)

\(ln(2.25714) = 18ln(1 + r/365)\)

\(ln(2.25714)/18 = ln(1 + r/365)\)

\(e^(^l^n^(^2^.^2^5^7^1^4^)^/^1^8^)^ =^ 1^ +^ r^/^3^6^5\)

\(1.0345 = 1 + r/365\)

\(r/365 = 0.0345\)

\(r = 12.5925\)

Therefore, Brody would need an interest rate of approximately 12.6% (rounded to the nearest tenth of a percent) in order to end up with $790 after 18 years with daily compounding.

Learn more about interest

brainly.com/question/30393144

#SPJ11

Work Shown:

y = 15.6 - 3.8x

y = 15.6 - 3.8*3

y = 4.2

Using the Well-Ordering Principle (WOP), it can be proven that in every tournament with n players (where n is a natural number), there is at least one top player, defined as someone who either beats every other player or beats someone who beats the other player.

We will prove this statement by contradiction. Assume that there exists a tournament with n players where there is no top player. This means that for each player, there exists either another player who beats them or a chain of players such that each player beats the next one. Now, consider the set S of all players in this tournament. Since S is a non-empty set of natural numbers, it has a least element, let's say k.

Now, player k either beats every other player in the tournament, making them a top player, or there exists a player, let's say player m, who beats player k. In the latter case, we have a chain of players: k, m, p_1, p_2, ..., p_t, where p_1 beats p_2, p_2 beats p_3, and so on until p_t.

However, this contradicts the assumption that there is no top player, as either player k beats every other player (if m does not exist), or player m beats someone who beats the other player (if m exists). Hence, by contradiction, we have shown that in every tournament with n players, there is at least one top player.

Learn more about non-empty set here:

https://brainly.com/question/1581607

#SPJ11

Answer:

Using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

What is the right rectangular prism?

The right rectangular prism has four rectangle-shaped side faces and two parallel end faces that are perpendicular to each of the bases.

Parallelograms make up the sides of an oblique prism, a non-right rectangular prism.

A cuboid is yet another name for a right rectangle prism.

So, the volume of the right rectangular prism:

V = wlh

Insert values:

V = wlh

V = 6*8*4.5

V = 216cm³

Now, the volume of the cube:

V = a³

V = 2³

V = 8cm³

Then, the number of cubes that can be fitted in the right rectangular prism:

216/8 = 27

Therefore, using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

Know more about the right rectangular prism? here:

brainly.com/question/3317747

#SPJ1

Correct question:

How many cubes, with side measures of 2 cm, will fit inside a right rectangular prism with dimensions of 6 cm by 8 cm by 4 1/2 cm?

Group of answer choices

a. 24

b. 27

c. 108

d. 54

The final answer is 27

To determine how many cubes will fit inside the right rectangular prism, we need to find the volume of the prism and the volume of the cubes, then divide the volume of the prism by the volume of the cubes.

Volume of a cube (V_cube) = side^3
V_cube = 2 cm * 2 cm * 2 cm = 8 cubic cm

Volume of the right rectangular prism (V_prism) = length * width * height
V_prism = 6 cm * 8 cm * 4.5 cm = 216 cubic cm

Now, divide the volume of the prism by the volume of the cubes:
Number of cubes = V_prism / V_cube = 216 cubic cm / 8 cubic cm = 27 cubes

Therefore, 27 cubes with side measures of 2 cm will fit inside the right rectangular prism.

To know more about cubes visit : https://brainly.com/question/28134860

#SPJ11

The formula for expected value is E(p) = Σ [p(x) * x] where x are the possible values of p and p(x) is the probability of x.

Without the probability distribution of p, it is impossible to determine the expected value of p.

The expected value (also known as the mathematical expectation or mean) of a random variable is a measure of the central tendency of the variable's possible values. The expected value of a discrete random variable p is the sum of the product of each possible value of the variable and its corresponding probability.

To find the expected value of p, you would need to know the probability distribution of the variable, which tells you the likelihood of each possible value of p. The probability distribution would typically be provided in a problem statement, or can be determined through experimentation or survey data.

To know for about random variable refer to:

brainly.com/question/16147308

#SPJ4

Answer: $755.9

Explanation:

The total cost of all repairs is the sum of the timing belt kit cost, the brake pads cost, and the labor cost.

Since they require 4.6 hours for the timing belt kit and 1.8 hours for the brake pads. the total labor cost is:

$95 * (4.6 hours + 1.8 hours )

$95 * (6.4 hours)

$608

Because the labor rate is $95/hour

Therefore, the total cost of repair is:

$89.95 + $57.95 + $608 = $755.9

So, the answer is $755.9

Applying the definition of congruent polygons, the side that is congruent to UP is: a. SM.

When we state that two polygons are congruent to each other, then it implies that they have the same shape and size, and this means that the corresponding sides are equal to each other, as well as all pairs of corresponding angles.

We are given that polygon PEOTU is congruent to polygon MCVNS, this means that all their pairs of corresponding angles will be equal.

Thus, the corresponding side to side Up is side SM. Therefore, UP is congruent to a. SM.

Learn more about congruent polygons on:

https://brainly.com/question/30449822

#SPJ1

The true statement about trend lines include the following: B. The distance from the points to the line should be as small as possible.

In Mathematics and Statistics, a trend line is sometimes referred to as a line of best fit and it can be defined as a statistical tool which is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any form of correlation (either positive or negative) between a given data.

Generally speaking, the line of best fit or trend line should be very close to the data points as much as possible. This ultimately implies that, a characteristics of a trend line is that the distance from each of the data points to the line must be as small as possible i.e closer to the line.

Read more on line of best fit here: brainly.com/question/12284501

#SPJ1

Answer:

15 stamps he collected that werent foreign

Step-by-step explanation:

When bound to CR1 (complement receptor 1), C3b is cleaved by Factor I, resulting in the generation of pathogen-associated B-cell co-receptor ligands.

The complement system is a part of the immune system that plays a crucial role in recognizing and eliminating pathogens. C3b is a component of the complement system that can opsonize pathogens, marking them for phagocytosis by immune cells. When C3b binds to CR1, which is present on B cells, the cleavage of C3b occurs. This cleavage is performed by an enzyme called Factor I, which is regulated by co-factors such as membrane cofactor protein (MCP). Factor I acts by proteolytically cleaving C3b into smaller fragments, resulting in the generation of pathogen-associated B-cell co-receptor ligands.

These pathogen-associated B-cell co-receptor ligands play a role in the activation of B cells, promoting their immune response against the pathogen. By cleaving C3b, Factor I helps regulate and fine-tune the complement system, ensuring an appropriate immune response while preventing excessive inflammation or damage to host tissues.

Learn more about Factor here:

https://brainly.com/question/14549998

#SPJ11

Answer:

x = 12

y = 9

z = 11

Step-by-step explanation:

so, let's just do all the calculations in there :

(3×5)⁴ = 3⁴×5⁴

(2×3)⁵ = 2⁵×3⁵

(2×5)⁷ = 2⁷×5⁷

multiplying all 3 terms is then

3⁴×5⁴×2⁵×3⁵×2⁷×5⁷

more let's "group" and combine these terms based on the bases of the power operations, as we need to get an expression showing 2, 3 and 5 with their powers.

so, for the base of 2 we have

2⁵×2⁷ = 2¹²

for the base of 3 we have

3⁴×3⁵ = 3⁹

fire the base of 5 we have

5⁴×5⁷ = 5¹¹

so we get

2¹² × 3⁹ × 5¹¹

=>

x=12

y=9

z=11

Answer:

true

Step-by-step explanation:

square root functions are just half of a parabola rotated 90° so depending on which half of the parabola (top has minimum and bottom has maximum) it is, it will have one, but it cannot have both since it is a continuous function after the max or min

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

'A rock was thrown from the top of a cliff such that its distance above sea level was given by s(t)=at²+bt+c, where t is the time in seconds after the rock was released. After 1 second the rock was 63 m above sea level, after 2 seconds 72 m, and after 7 seconds 27 m. a. Find a, b and c and hence an expression for s(t). b. Find the height of the cliff. c. Find the time taken for the rock to reach sea level.'

Given the equation of the distance modelled as s(t)=at²+bt+c

If after 1 second the rock was 63 m, then 63 = a+b+c

If after 2 seconds, the distance was 72 m then 72 = 4a+2b+c

Also if after 7 seconds, the distance is 27 m, then 27 = 49a+7b+c

i) Solving the 3 equations simultaneously to get a, b and c we have;

a+b+c = 63 ... 1

4a+2b+c = 72 ...2

49a+7b+c = 27 ...3

Subtracting 2 from 1 and 3 from 2 we will generate 2 new equations as shown;

eqn 2- eqn1: 3a + b = 9...4

eqn 3- eqn 2: 45a + 5b = -45

eqn 3- eqn 2: 9a+b = -9 ... 5

solving 4 and 5 simultaneously

3a + b = 9 ...4

9a+b = -9 ... 5  

Taking the difference of 4 and 5 we have

6a - -9-9

6a = -18

a = -3

substituting a = -3 into equation 4 to get b we have;

3(-3)+b = 9

-9 + b = 9

b = 9+9

b = 18

substituting a = -3 and b = 18 into equation 1 to get c we have;

-3+18+c = 63

15+c = 63

c = 48

a = -3, b= 18 and c = 48

The distance function will be s(t) = -3t²+18t+48

ii) If the height of the cliff is modelled by the equation  s(t)=at²+bt+c

The height of the cliff is at when t = 0

s(0) = -3(0)²+18(0)+48

s(0) = 48m

The height of the cliff is 48m

iii) At the sea level, the height of the rock will be 0m, substituting this into the modeled equation for the height to get the time we have;

s(t)=at²+bt+c

0 = -3t²+18t+48

3t²-18t-48 = 0

t² - 6t - 16 =0

t² - 8t+2t - 16 = 0

t(t-8)+2(t-8) = 0

(t+2)(t-8) = 0

t = -2 or 8

Taking the positive value of the time, t = 8secs

Time taken for the rock to reach sea level is 8secs

Answer:

The right choice is Esther's

Step-by-step explanation:

Present worth of GH¢ after 3 years is better as its present really worth may be very high than GH¢ a thousand of today. Here fee of interest is not given to compare however GH¢ 3000 after three years will be equivalent to present well worth GH¢ 1000 if charge of interest >44.5% which may be very very excessive. Thus charge of interest > 44.5% Then GH¢ 3000 payable after 3 years could be equivalent to GH¢ 1000 Hence vide has made the proper preference. If interest price >44.5%.

Then Esther's preference will he right. (thinking about time value of money).

Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

Answer:

C

Step-by-step explanation:

for the sum of interior angles of a polygon, multiply the number of triangles (!) in the polygon by 180°.

as the sum of all angles in a triangle is always 180°.

the number of triangles you get when you pick one vertex and connect it straight with every other vertex.

there you see that you create a triangle with every other vertex except for the 2 neighboring vertexes (where the connection are actual side lines of the polygon).

so, in general, the formula for the sum of interior angles is (n − 2)×180. "n" is the number of sides.

Answer:

\(m=\frac{-5}{3}\)

Step-by-step explanation:

We want to find the slope between the points (-2,5) and (1,0).

The slope (m) can be found using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are points.

We are already given the values of the points, but let's label their values to avoid any confusion and mistakes.

\(x_1=-2\\y_1=5\\x_2=1\\y_2=0\)

Now, substitute into the formula.

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{0-5}{1--2}\)

Simplify this to:

\(m=\frac{0-5}{1+2}\)

\(m=\frac{-5}{3}\)

The slope is -5/3.

Answer:

2/3 lemons to cup ratio

The critical values for a 2-tailed sign test for 13-coin flips (alpha of. 05) is: ± 1.96

For given question,

We need to find the critical values for a 2-tailed sign test for 13-coin flips.

We have been given an alpha level of 0.05 that is 5%

⇒ α = 0.05

We know that in hypothesis testing, a critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.

These are the points on the distribution which have the same probability as your test statistic, equal to the significance level α.

The critical values are assumed to be at least as extreme at those critical values.

Now we find 1 - α

⇒ 1 - α = 1 - 0.05

⇒ 1 - α = 0.95

Because it is a two-tailed test, we are going to divide 0.95 by 2.

⇒ 0.95/2 = 0.475

Now we look in the z-table to find out cutoff points.

For the area of 0.475, the critical values is ± 1.96 .

Therefore, the critical values for a 2-tailed sign test for 13-coin flips (alpha of. 05) is: ± 1.96

Learn more about the two-tailed test here:

https://brainly.com/question/16633647

#SPJ4