if sally gets scores 73, 85, 93, the 4th score is 20 points less than 5th score which is 2/3 of the average of the first three. what must she score on the 6th and 7th test to average an 85

Answer:

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Answer:

i) The order of matrix is 2 ×3

ii)The order of matrix is 3×3

f(n)=5^n

f(4)=?

soln...

just put the value n=4

f(4)=5^4

=625.......

The child can make 120 different bracelets using one of each charm. To solve this problem, we need to use a combinatorial approach.

The number of different bracelets that the child can make depends on the number of charms that can be used for each bracelet & the order in which they are arranged. Since each charm can be used only once, we have to choose five charms out of the total of five available charms, which can be done in 5C5 ways.

We can think of this problem as a permutation problem. There are five distinct charms, and we need to choose five of them to make a bracelet. The order in which we choose the charms matters, as each order gives us a different bracelet. Therefore, we need to use the formula for permutations.

The formula for permutations is given by:

nPr = n! / (n-r)!

where n is the total number of objects, and r is the number of objects we want to choose.

For this problem, n = 5 (since there are five distinct charms), and r = 5 (since we want to choose all five charms).

Plugging these values into the formula, we get:

5P5 = 5! / (5-5)! = 5! / 0! = 5 x 4 x 3 x 2 x 1 / 1 = 120

Therefore, the child can make 120 different bracelets.

Alternatively, we can also think of this problem as a multiplication principle problem. There are five distinct charms, & we need to choose one charm out of five for the first position, one charm out of four for the second position, one charm out of three for the third position, one charm out of two for the fourth position, & one charm out of one for the fifth position.

Using the multiplication principle, we can multiply these numbers together to get the total number of different bracelets:

5 x 4 x 3 x 2 x 1 = 120

Therefore, the child can make 120 different bracelets using one of each charm.

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Step-by-step explanation:

54, 54, 72

\(180 - 2 \times 54 = \\ = 180 - 108 = \\ = 72\)

Answer:

(f + g)(x) = -x + 6

Step-by-step explanation:

Step 1: Define

f(x) = -3x + 6

g(x) = 2x

Step 2: Find (f + g)(x)

(f + g)(x) = -3x + 6 + 2x

(f + g)(x) = -x + 6

Answer:

-x +6

Step-by-step explanation:

f(x) = -3x + 6

g(x) = 2x

(f + g)(x)= Add the two functions

            = -3x + 6 + 2x

Combine like terms

            = -x +6

Answer:

\(-\dfrac{4}{5}\)

Step-by-step explanation:

We have the following expression

\(3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x\)

and asked to evaluate this expression at  \(\[x = {2\over\displaystyle 5\]\)

First convert \(3 \; \dfrac{1}{2}\)   and  \(5 \; \dfrac{1}{2}\)  to mixed fractions

\(3 \; \dfrac{1}{2} = \dfrac{3 \times 2 + 1}{2} = \dfrac{7}{2}\\\)

\(5 \; \dfrac{1}{2} = \dfrac{5 \times 2 + 1}{2} = \dfrac{11}{2}\)

Therefore
\(3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x\\\\= \dfrac{7}{2}x - \dfrac{11}{2}x\\\\= \dfrac{7 - 11}{2} x\\\\= -\dfrac{4}{2}x \\\\= -2x\\\\\)

\(\mathrm{For \;x =\dfrac{2}{5}},\\\\= -2x \\= - 2 \times \dfrac{2}{5}\\\\= -\dfrac{4}{5}\)

When we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

To subtract 3 from 22, we can perform the subtraction operation as follows:

22

3

19

We align the numbers vertically and subtract each corresponding place value from right to left. In this case, subtracting 3 from 2 requires borrowing or regrouping. However, since 2 is greater than 3, we can directly subtract 3 from 2 and write the difference, which is 1, in the one's place.

Therefore, the simplified answer is 19.

The subtraction process involves taking away or removing a certain quantity from another. In this case, we subtracted 3 from 22, resulting in a difference of 19. The process of simplifying the answer is simply expressing the result in its most concise and reduced form.

By subtracting 3 from 22, we removed 3 units from the original value of 22, leaving us with 19. This can be visualized as taking away three objects from a group of 22 objects, resulting in a remaining count of 19.

In summary, when we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

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Given point and line are Po(-4, 5, -1) and x = -4 - t, y = 5 + 3t, z = -5t, -[infinity]o respectively. To find the equation for the plane through Po(-4,5,-1) perpendicular to the line, we will use the following steps  First, we will calculate the direction vector for the given line.

We know that the direction ratios of the line are (-1, 3, -5)Therefore, the direction vector of the line is given as V1 = (-1, 3, -5) We know that the given plane is perpendicular to the given line and passes through the given point, therefore the normal vector of the plane is equal to the direction vector of the given line.Let the normal vector of the plane be V2 = (a, b, c) = V1 = (-1, 3, -5) Therefore, a = -1, b = 3, and c = -5.

Now, we will use the equation of the plane in the normal form that is (a, b, c) . (x - x1, y - y1, z - z1) = 0Here, (x1, y1, z1) = (-4, 5, -1)Therefore, the equation of the plane is (-1, 3, -5) . (x + 4, y - 5, z + 1) = 0 Simplifying the above equation, we get the following equation:: The equation of the plane through Po(-4,5,-1) perpendicular to the given line is x + 3y - 5z + 32 = 0.:Given point and line are Po(-4, 5, -1) and x = -4 - t, y = 5 + 3t, z = -5t, -[infinity]o respectively. To find the equation for the plane through Po(-4,5,-1) perpendicular to the line, we will use the following steps.Step 1: First, we will calculate the direction vector for the given line.

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It has been proved that if the bisectors of ∠B and ∠C intersect each other at O, then; ∠BOC = 90°+  ¹/₂∠A

A △ ABC such that the bisectors of ∠ ABC and ∠ ACB meet at a point O.

To prove :

∠BOC = 90° + ¹/₂∠A

Proof :

In △BOC, we have

∠1 + ∠2 + ∠BOC = 180°

In △ ABC, we have, ∠A + ∠B + ∠C = 180°

∠A + 2(∠1) + 2(∠2) = 180°

¹/₂∠A + ∠1 + ∠2 = 90°

∠1 + ∠2 = 90° -  ¹/₂∠A

Therefore, in equation 1,

90° -  ¹/₂∠A + ∠BOC = 180°

∠BOC = 90°+  ¹/₂∠A

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Problem 3

Explanation: The angles opposite the congruent sides, are congruent angles. We consider these the base angles. This triangle is isosceles.

==================================================

Problem 4

Explanation:

Refer to the diagram below. Note how I've added in the variable y and marked another angle as 53 degrees which is one of the base angles of the left triangle. The base angles of the triangle on the right are y degrees each. Also, note the vertical angles both are y.

For the left triangle, the three angles add up to 180 which means we can solve for y to go from 53+53+y = 180 to y = 74

Then the interior angles of the triangle on the right has the three angles (y,y,x) add to 180 as well. So we have y+y+x = 180 which turns into 74+74+x = 180. That solves to x = 32

==================================================

Problem 5

Explanation:

Refer to the diagram below. I've added another base angle x, and the angle 90-x is complementary to this. This is because the two pieces must add to 90.

For the triangle on the bottom, the two base angles 74 and 74, add to the third angle 90-x and we would get 180. So we solve 74+74+(90-x) = 180 to get x = 58

Answer:

3. x = 47

4. x = 32

5. x = 58

Step-by-step explanation:

Answer:

2 is the equivalent to the expression

After computing the composition of f(g(x)) and g(f(x)), it is clear that f(x) and g(x) are not inverse functions of each other.

To determine whether f(x) and g(x) are inverse functions of each other, we need to check whether the composition of the two functions f(g(x)) and g(f(x)) result in the identity function, which is equal to x.

First, let's find f(g(x)):

f(g(x)) = f(5x - 5/4) (substituting g(x) into f(x))

f(g(x)) = 4/5(5x - 5/4) + 1 (substituting the expression for f(x))

f(g(x)) = 4x - 1 + 1

f(g(x)) = 4x

Now let's find g(f(x)):

g(f(x)) = g(4/5x + 1) (substituting f(x) into g(x))

g(f(x)) = 5(4/5x + 1) - 5/4 (substituting the expression for g(x))

g(f(x)) = 4x + 5 - 5/4

g(f(x)) = 4x + 20/4 - 5/4

g(f(x)) = 4x + 15/4

Since f(g(x)) = 4x and g(f(x)) = 4x + 15/4, we can see that the two compositions are not equal to x, which means that f(x) and g(x) are not inverse functions of each other.

Therefore, we can conclude that f(x) and g(x) are not inverse functions of each other.

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Answer:

x=6

Step-by-step explanation:

x = 6x = 6

x = 6x = 6

thanks

Please mark it as brainliast

Answer:

D

Step-by-step explanation:

The probability shows that when one name is drawn from the jar, the country that has the best chance of having a name drawn is Great Britain.

It should be noted that Great Britain has won 6 golds in the 1500 meters Olympics and the next placed country is Kenya. In this case, the country that has the best chance of having a name drawn is Great Britain.

Note that New Zealand has 3 gold medals while Australia has 2 gold medals. Also, the Olympics has taken place 29 times.

The probability that the winners will be from either New Zealand or Australia will be:

= 3/29 + 2/29

= 5/29

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Answer

A. Great Britain

B. 3/29+2/29=5/29

please give me the brainliest.

The statement that the blue radius is perpendicular to the green cord is false

From the complete question,

The blue radius does not bisect the green chord

This means that the blue radius and the green chord do not meet at 90 degrees

Since both lines do not meet at 90 degrees, then they are not perpendicular

Hence, the statement that the blue radius is perpendicular to the green cord is false

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To evaluate the line integral using Green's Theorem, we need to find the curl of the vector field and then calculate the double integral over the region enclosed by the curve. Answer :  the critical points of the function z = (x^2 - 4x)(y^2 - 5y) are (x, y) = (0, 0) and (x, y) = (0, 4)

Given the vector field F = (xy^2, x^5), we can find its curl as follows:

∇ × F = (∂Q/∂x - ∂P/∂y)

where P is the x-component of F (xy^2) and Q is the y-component of F (x^5).

∂Q/∂x = ∂/∂x (x^5) = 5x^4

∂P/∂y = ∂/∂y (xy^2) = 2xy

Therefore, the curl of F is:

∇ × F = (2xy - 5x^4)

Now, we can apply Green's Theorem:

∮C P dx + Q dy = ∬D (∇ × F) dA

where D is the region enclosed by the curve C.

In this case, C is the rectangle with vertices (0,0), (3,0), (3,5), and (0,5), and D is the region enclosed by this rectangle.

The line integral becomes:

∮C xy^2 dx + x^5 dy = ∬D (2xy - 5x^4) dA

To evaluate the double integral, we integrate with respect to x first and then with respect to y:

∬D (2xy - 5x^4) dA = ∫[0,5] ∫[0,3] (2xy - 5x^4) dx dy

Now, we can calculate the integral using these limits of integration and the given expression.

As for the second part of your question, to find the critical points of the function z = (x^2 - 4x)(y^2 - 5y), we need to find the points where the partial derivatives with respect to x and y are both zero.

Let's calculate these partial derivatives:

∂z/∂x = 2x(y^2 - 5y) - 4(y^2 - 5y)

      = 2xy^2 - 10xy - 4y^2 + 20y

∂z/∂y = (x^2 - 4x)(2y - 5) - 5(x^2 - 4x)

      = 2xy^2 - 10xy - 4y^2 + 20y

Setting both partial derivatives equal to zero:

2xy^2 - 10xy - 4y^2 + 20y = 0

Simplifying:

2y(xy - 5x - 2y + 10) = 0

This equation gives us two cases:

1) 2y = 0, which implies y = 0.

2) xy - 5x - 2y + 10 = 0

From the second equation, we can solve for x in terms of y:

x = (2y - 10)/(y - 1)

Now, substitute this expression for x back into the first equation:

2y(2y - 10)/(y - 1) - 10(2y - 10)/(y - 1) - 4y^2 + 20y = 0

Simplifying and combining like terms:

4y^3 - 32y^2 + 64y = 0

Factoring out 4y:

4y(y^2 - 8y +

16) = 0

Simplifying:

4y(y - 4)^2 = 0

This equation gives us two cases:

1) 4y = 0, which implies y = 0.

2) (y - 4)^2 = 0, which implies y = 4.

So, the critical points of the function z = (x^2 - 4x)(y^2 - 5y) are (x, y) = (0, 0) and (x, y) = (0, 4).

To classify these critical points, we can use the second partial derivative test or examine the behavior of the function in the vicinity of these points.

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According to the question The local sidereal time (LST) at noon on March 21st is approximately 12:00 (option c).

To determine the LST, we need to consider the rotation of the Earth and its relation to the stars. LST is based on the apparent motion of the vernal equinox, which completes a full cycle in approximately 24 hours.

Since noon is halfway through the day, we can estimate that the LST at noon would be approximately half of 24 hours, which is 12:00. This assumes that we are considering a location where the local time is synchronized with the standard time zone and there are no factors like daylight saving time or variations in the location's longitude that can affect the LST calculation.

Therefore, the correct answer is option c) 12:00 local sidereal time.

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Answer:

false

Step-by-step explanation:

Answer:

34.

Step-by-step explanation:

The three integers would be 34,35,36 because the sum of the three numbers is 105.

The probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

Let's use the following notation:

P(TB) represents the probability that an adult has tuberculosis, which is given as 0.05.

P(POS|TB) represents the probability that the test is positive given that an adult has tuberculosis, which is given as 0.746.

P(NEG|TB) represents the probability that the test is negative given that an adult has tuberculosis, which is 1 - P(POS|TB) = 0.254.

We are asked to find the probability of an adult getting a NEG result and truly having tuberculosis, which can be calculated using Bayes' theorem as follows:

P(TB|NEG) = P(NEG|TB) * P(TB) / P(NEG)

We can calculate P(NEG) using the law of total probability, which considers the two possible cases for an adult: having tuberculosis (TB) or not having tuberculosis (TB').

P(NEG) = P(NEG|TB) * P(TB) + P(NEG|TB') * P(TB')

= 0.254 * 0.05 + 0.7653 * 0.95

= 0.7352

Now we can substitute the values into Bayes' theorem:

P(TB|NEG) = 0.254 * 0.05 / 0.7352

= 0.01725

Therefore, the probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

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Answer:

-5

Step-by-step explanation:

Answer:

vegetarians= 28

chickens= 44

Step-by-step explanation:

let the number of vegetarians be x

and chickens be y

So

x+2.7y=119.6----------1

x+y=72--------------2

from 2, x= 72-y

put x= 72-y in 1

72-y+2.7y=119.6

-y+2.7y=119.6-72

1.7y=47.6

divide both sides by 1.7

y=47.6/1.7

y=28

put y=28 in 1

x+28=72

y= 72-28

y=44

Player 1 has a greater batting average than Player 2 since their batting average is calculated as 42/90, which is greater than 38/80.

batting average, we need to calculate the batting averages for both Player 1 and Player 2 based on the given information.

Batting average is calculated by dividing the number of hits by the number of times at bat.

For Player 1, we have 42 hits and 90 at-bats. So, the batting average for Player 1 can be calculated as:

Batting Average = Number of Hits / Number of At-Bats

= 42 / 90

= 0.4667

For Player 2, we have 38 hits and 80 at-bats.

Thus, the batting average for Player 2 is:

Batting Average = Number of Hits / Number of At-Bats

= 38 / 80

= 0.475

Comparing the two batting averages, we can see that Player 2 has a higher batting average of 0.475, whereas Player 1 has a batting average of 0.4667.

Therefore, Player 2 has the greater batting average between the two players.

It's worth noting that batting average is typically represented as a decimal rounded to three decimal places.

In this case, Player 2 has a higher batting average of 0.475, indicating a greater success rate in getting hits relative to at-bats compared to Player 1's batting average of 0.4667.

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The results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

Performing the calculation:

(10.52)(0.6721) = 7.0671992

Rounding to the correct number of significant figures, we have:

(10.52)(0.6721) ≈ 7.07

Next, let's calculate (19.09 - 15.347):

(19.09 - 15.347) = 3.743

Rounding to the correct number of significant figures, we have:

(19.09 - 15.347) ≈ 3.74

Therefore, the results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

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phase shift is 0

General equation

c is phase shift

Midline is D

A is amplitude

B is period

So

Final equation

Not mandatory from now

For some special cases 2π/T=omega

So Equation yields

Answer:

\(f(x)=2 \cos (2x)+5\)

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function:

f(x) = A cos(B(x + C)) + D

Given:

Inputting the given values into the standard form:

\(\implies f(x)=2 \cos (2x)+5\)

These steps are often referred to as the principle of mathematical induction or PMI.

The steps for mathematical induction are:

Base Case: Show that the statement holds for some particular value of n, usually n = 1 or n = 0.

Inductive Hypothesis: Assume that the statement holds for some arbitrary value of n = k, where k is a positive integer.

Inductive Step: Using the inductive hypothesis, show that the statement also holds for n = k + 1.

Conclusion: By the principle of mathematical induction, the statement is true for all positive integers n.

These steps are often referred to as the principle of mathematical induction or PMI. They are used to prove statements that involve an infinite set of integers by showing that the statement holds for a base case, assuming that it holds for an arbitrary value, and then showing that it holds for the next integer in the set.

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