Marta recorded the temperature at 8 p.m. as 56°F and the temperature at 8 a.m. the next morning as 36°F. Marta assumed the temperature changed at a constant rate. She wrote an equation to find the number of degrees the temperature dropped each hour, h, of the night. Which equation did Marta write?

To solve this problem, we can use the formula for probability:

P(event) = number of favorable outcomes / total number of outcomes

First, let's find the total number of outcomes. We are selecting 4 balls from 11 without replacement, so the total number of outcomes is:

11C4 = (11!)/(4!(11-4)!) = 330

where nCr is the number of combinations of n things taken r at a time.

Now let's find the number of favorable outcomes for each part of the problem.

Part 1: Exactly two white balls and two red balls

To find the number of favorable outcomes for this part, we need to select 2 white balls out of 6 and 2 red balls out of 5. The number of ways to do this is:

6C2 * 5C2 = (6!)/(2!(6-2)!) * (5!)/(2!(5-2)!) = 15 * 10 = 150

So the probability of selecting exactly two white balls and two red balls is:

P(2W2R) = 150/330 = 0.45 (rounded to two decimal places)

Part 2: At least two white balls

To find the number of favorable outcomes for this part, we need to consider two cases: selecting 2 white balls and 2 red balls, or selecting 3 white balls and 1 red ball.

The number of ways to select 2 white balls and 2 red balls is the same as the number of favorable outcomes for Part 1, which is 150.

To find the number of ways to select 3 white balls and 1 red ball, we need to select 3 white balls out of 6 and 1 red ball out of 5. The number of ways to do this is:

6C3 * 5C1 = (6!)/(3!(6-3)!) * (5!)/(1!(5-1)!) = 20 * 5 = 100

So the total number of favorable outcomes for selecting at least two white balls is:

150 + 100 = 250

And the probability of selecting at least two white balls is:

P(at least 2W) = 250/330 = 0.76 (rounded to two decimal places)

Answer:

29.575

Step-by-step explanation:

6.5(6.24-1.69)= 6.5(4.55) = 29.575

Answer:

\(6.5(6.24 - 1.69) \\ = 6.5 \times 4.55 \\ = 29.575\)

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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Answer:

Step-by-step explanation:

25%

80%

60%

100%

25%

Answer:

r≤-11+20

r≤9

r≤9 is the answer

triangle UTV similar with triangle YZX

Step-by-step explanation:

that mean UT/YZ = TV/ZX = UV/YX is the answer

Answer:

the parabola opens down

Step-by-step explanation:

The quadratic equation is

ax^2 + bx + c

When a < 0 the parabola opens down

          a > 0 it opens up

since a  = -2 the parabola opens down

Answer:

Only when any equation you find among those numbers can be simplified into one of the four main equations, which means you only have four different true statements and lots of equivalences. 20 = 40 - 20. As the two addends are the same, so there would be only four different equations for a set of math mountain numbe

Step-by-step explanation:

The probability that the randomly selected person attending the concert is an adult or has purchased the ticket in advance is 188/250.

We have,

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given a table which shows when the tickets for a concert are sold and the types of tickets that are sold.

The probability of A or B can be calculated as,

P(A or B) = P(A) + P(B) - P(A and B)

Let A denote the people is an adult.

Let B denote the people who has purchased the ticket in advance.

P(A) = 148/250

P(B) = 140/250

P(A and B) = 100/250

Probability that a randomly selected person attending the concert is an adult or has purchased the ticket in advance is,

P(A or B) = 148/250 + 140/250 - 100/250

              = 288/250 - 100/250

              = 188/250

Hence the required probability is 188/250.

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Answer:

n= 2x-5

Step-by-step explanation:

The Expression for the statement is x= 2y -5.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

A number is five less than twice another number.

let the number be x and the another be y.

So, the mathematical Expression is

five less than twice another number.

= 2y -5

So, the expression is

x= 2y -5.

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We have the points R(1,3) and S(-2,6).

We have to calculate the mid point.

The mid point will have coordinates that are the average of each point's coordinate.

In this case, being M the mid point, the coordinate X will be:

The Y coordinate will be:

The midpoint between R and S is M=(-1/2, 9/2).

Answer:

1,5,25,125,

all can be added or multiplied to equal 125

Answer:

\(s \ne \±2\)

\(x_1 = \frac{3s - 2}{3(s^2 -4)}\)

\(x_2 = \frac{2(s- 6)}{5(s^2 - 4)}\)

Step-by-step explanation:

Given

\(3sx_1 +5x_2 = 3\)

\(12x_1 + 5sx_2 =2\)

Required

Determine the value of s

Express the equations as a matrix

\(A =\left[\begin{array}{cc}3s&5\\12&5s\end{array}\right]\)

Calculate the determinant

\(|A|= (3s*5s -5 *12)\)

\(|A|= (15s^2 -60)\)

Factorize

\(|A|= 15(s^2 -4)\)

Apply difference of two squares

\(|A|= 15(s -2)(s + 2)\)

For the system to have a unique solution;

\(|A| =0\)

So, we have:

\(15(s -2)(s+2) = 0\)

Divide both sides by 15

\((s -2)(s+2) = 0\)

Solve for s

\(s -2 = 0\ or\ s +2 = 0\)

\(s = 2\ or\ s = -2\)

The result can be combined as:

\(s =\±2\)

Hence, the system has a unique solution when \(s \ne \±2\)

Next, we solve for s using Cramer's rule.

We have:

\(mat\ x_1 = \left[\begin{array}{cc}3&5\\2&5s\end{array}\right]\)

Calculate the determinant

\(|x_1| = (3 * 5s - 5 *2)\)

\(|x_1| = 15s - 10\)

So:

\(x_1 =\frac{|x_1|}{|A|}\)

\(x_1 = \frac{15s - 10}{15(s -2)(s+2)}\)

Factorize

\(x_1 = \frac{5(3s - 2)}{15(s -2)(s+2)}\)

Divide by 5

\(x_1 = \frac{3s - 2}{3(s -2)(s+2)}\)

\(x_1 = \frac{3s - 2}{3(s^2 -4)}\)

Similarly:

\(mat\ x_2 =\left[\begin{array}{cc}3s&3\\12&2\end{array}\right]\)

Calculate the determinant

\(|x_2| = 3s * 2 - 3 * 12\)

\(|x_2| = 6s- 36\)

So:

\(x_2 =\frac{|x_2|}{|A|}\)

\(x_2 = \frac{6s- 36}{15(s -2)(s+2)}\)

Factorize

\(x_2 = \frac{6(s- 6)}{15(s -2)(s+2)}\)

Divide by 3

\(x_2 = \frac{2(s- 6)}{5(s -2)(s+2)}\)

\(x_2 = \frac{2(s- 6)}{5(s^2 - 4)}\)

If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:

637 = π(3²)h

Simplifying:

637 = 9πh

h = 637 / (9π)

h ≈ 7.06

Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.

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Answer: To find the derivative of the function h(x), we can use the quotient rule, which states that if f(x) = u(x) / v(x), then f'(x) = [v(x)u'(x) - u(x)v'(x)] / [v(x)]^2.

Using this rule, we can find the derivative of h(x) as follows:

h(x) = (x + 2) / (x - 2)

h'(x) = [(x - 2)(1) - (x + 2)(1)] / (x - 2)^2 // apply the quotient rule and differentiate numerator and denominator

h'(x) = (-2 - 2x) / (x - 2)^2

Therefore, the derivative of h(x) is h'(x) = (-2 - 2x) / (x - 2)^2.

Step-by-step explanation:

First, let's figure out the pattern that this series follows. We can see that the first number is increased by 1/2 to get to 2 1/2. Then, the second number is decreased by 1 to get to 1 1/2. Finally, the pattern repeats.

So, let's apply this pattern to find the next number in this series.

2, 2 1/2, 1 1/2, 2, 1

The next number in this series is 1.

Hope this helps!! :)

Step-by-step explanation:

you have to substitute the function g(x) where there's x in the function f(x)

gf(x)=2(x213)-4

if that's x two thirteen then you can multiply the 2 outside the brackets by it

giving you a final answer of

gf(x)=426x-4

hope it helps and sorry if am wrong

i) The profit/loss when no cars are produced is a loss of 6600 Rupees.

II) The break even point is at 20 cars

III) The profit/loss if 400 cars are produced is;  a loss of 13400Rupees.

(i) When no cars are produced, x = 0.

Thus, plugging this value into the function p(x) = -x² + 350x - 6600, we have;

p(0) = -0² + 350(0) - 6600 = -6600.

Therefore, the profit/loss when no cars are produced is a loss of 6600 thousand Rupees.

(ii) The break-even point is the point at which the profit is zero, i.e., p(x) = 0. Setting p(x) = 0 and solving for x, we find that;

-x² + 350x - 6600 = 0

x = 20

Therefore, the break-even point is x = 20 cars. T

(iii) If 400 cars are produced, the profit can be found by plugging this value into the function p(x) = -x² + 350x - 6600.

We find that p(400) = -400² + 350(400) - 6600

= -160000 + 140000 + 6600 = -13400. Therefore, the profit/loss if 400 cars are produced is a loss of 13400 Rupees.

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Answer:

7/6

Step-by-step explanation:

Since 3 + 1/2 - (2 + 1/3) will give a final result of 7/6. (1.1666667)

Answer:

\(1 \frac{1}{6} = \frac{7}{6} \)

Step-by-step explanation:

3 ½ - 2 ⅓

(3 - 2) + (½ - ⅓)

1 + ⅙

= 1 ⅙ = ⁷/6

Answer:

(8,-43)

(4,-22)

Step-by-step explanation:

In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.

For example:

(4,-22)

x=4 ; y=-22

Plug y into the inequality

y≤0

-22≤0

Since the statement is true, I know that (4,-22) must be a solution to the inequality.

Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

Answer:

Step-by-step explanation:

To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.

Let's check each ordered pair:

(8, -43):

The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(4, -22):

The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(-3, 25):

The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

(-7, 45):

The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

So, the solutions to the inequality y ≤ 0 are:

(8, -43) and (4, -22).

The highest value you would still hold the stock is $23.97

From the question, the given parameters about the distribution are

Mean value of the set of data = $26.94

Standard deviation value of the set of data = $3.54

Proportion = Highest 20%

This means that the p value is

p = 20%

Express as decimal

p = 0.2

At a p value of 0.2, the z-score is

z = -0.84

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

-0.84 = (x - 26.94)/3.54

Cross multiply in the above equation

So, we have

x - 26.94 = -0.84 * 3.54

Evaluate the products

x - 26.94 = -2.97

Add 26.94 to both sides of the equation

So, we have the following representation

x = 26.94 -2.97

Evaluate the difference

x = 23.97

Hence, the highest value is 23.97

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When point is rotated 90 degrees counterclockwise about the origin, point (x,y) becomes (-y,x).

We're given

Make the y-coordinate negative:

(4,0)

Switch around the coordinates:

(0,4)

(0,4)

Answer:

180

Step-by-step explanation:

The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180. If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°.

Hope it helped :)

Answer:

4.28%

Step-by-step explanation:

We Know

Last year you earned $72,400

This year you earned $75,500

What was the rate of change in your earnings since last year?

We Take

(75,500 ÷ 72,400) x 100 ≈ 104.28%

Then We Take

104.28 - 100 = 4.28%

So, the earning increased by about 4.28%.

Answer:

30

Step-by-step explanation:

150/5 = 30

Answer: 30

Step-by-step explanation:

If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:

Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).

Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).

Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).

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To find arcsin, we need to use the identity:

sin(arcsin(x)) = x

Since arcsin is negative, sin(arcsin) is also negative. Therefore, we can say:

sin(arcsin) = -sqrt(1 - (cos)^2)

where (cos)^2 = 8/17

Substituting, we get:

sin(arcsin) = -sqrt(1 - (8/17))

Simplifying, we get:

sin(arcsin) = -sqrt(17/17 - 8/17)

Simplifying further, we get:

sin(arcsin) = -sqrt(9/17)

Therefore, arcsin = -sqrt(9/17)

To find arctan, we need to use the identity:

tan(arctan(x)) = x

Substituting, we get:

tan(arctan) = -8/17

Therefore, arctan = -8/17

So, arcsin is -sqrt(9/17) and arctan is -8/17.

The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.

The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.

From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).

The x-values of these points are 0, 1, and 4.

Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.

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