Hot tea is brought to a boil at 212F and must be cooled to a temperature of 160°F The room temperature is 68°F
Newtons law of cooling can be used to find how long it takes a liquid to be cooled. The formula T= (To-Tr)e^-rt +Tr where Tr is the air temperature, To is initial temperature, T is the expected temperature, and r is rate of cooling and t is time in minutes. How long does it take for tea to cool if the rate of cooling is 0.05?

A. 3.9
B. 9.0
C. 12.9
D. 37.9

If she picks 45 oranges in 5 minutes then in 1 minute

= 45/5

= 9 oranges

It means that Malik picked 9 oranges in 1 minute

Answer:

opposite angles are equal

Step-by-step explanation:

The reason is that opposite angles are equal. I don't know if it says it but if you need 3 reason, if P is the midpoint, nP = P to the end of that line and mP = P to the end of that line giving you 3 reasons

Step-by-step explanation:

I don't know what you can do regarding predefined options.

but yes, the proof goes

angle 2 + angle 3 = 180°

angle 3 + angle 4 = 180°

therefore,

angle 2 + angle 3 = angle 3 + angle 4 | ‐ angle 3

angle 2 = angle 4

that's it.

you were totally close. just this one last little step was missing.

again, I don't know. what options you have to express this.

The length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

By Pythagoras rule we can evaluate for b as follows:

x = √(7.5² - 2.5²)

x = √50

x = x = 7.0711

f = √[(√78)² - 7²]

f = √(78 - 49)

f = √29

f = 5.3852

d = 2 × √(11² × 8²)

d = 2 × √53

d = 15.0996

Therefore, the length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

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The statistics that seem to be fair estimators of the population parameter are statistics A, according to the information provided.

The collection, description, analysis, and inference of conclusions from quantitative data are all part of the field of statistics, which is applied mathematics. Calculus of differential and integrals, linear algebra, and probability theory are key mathematical concepts in statistics.

Statistics is a technique used in mathematics for deciphering, analyzing, and summing up data. The following characteristics are used to categorize the different types of statistics: Inferential and descriptive statistics. We analyze and interpret the data based on the way it is presented, such as in tables, bar graphs, or pie charts.

The unbiased estimator of the population parameter is statistic A, it should be noted. This is due to the fact that it is centered around the population parameter of 75.

The population parameter would be more accurately estimated by statistic A. This is so because the population mean of 75 is the same as the sample mean of 75.

Given that statistic D is equal to the population means, it would serve as a more accurate estimator of the population parameter.

Last but not least, it is important to remember that statistic C has no distribution shape.

The complete question is:

Four different statistics have been proposed as estimators of a population parameter. To investigate The behavior of these estimators, 500 random samples are selected from a known population and it statistic is calculated for each sample. The true value of the population parameter is 75. the graphs below show the distribution of values for each statistic.

A. Which of the statistics appear to be unbiased estimators of the population parameter? How can you tell?

B. Which of the statistics a or B would be better estimate or of the population parameter? Explain your choice.

C. Which of the statistics of your day would be better estimator of the population parameter? Explain your choice.

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Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Given the equations a × b = 5742 × 6368, a × c = 5748 × 6362, and c × b = 5738 × 6372, we need to determine the relationship between the three variables a, b, and c.

By comparing the given equations, we notice that the numbers on the right-hand side of each equation are very close to each other, differing only by small amounts. This suggests that a, b, and c are approximately equal.Since a × b, a × c, and c × b involve the same numbers with slight variations, we can conclude that a, b, and c are all very close in value.

Therefore, the inequality we can infer from this information is a ≈ b ≈ c, indicating that a, b, and c are approximately equal.

In simple terms, based on the given equations, it suggests that the values of a, b, and c are very similar or approximately equal to each other.

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The equation of each line that satisfies the given conditions are:

1. y - 2 = 5/2(x - 3)

2. y - 4 = m(x + 3)

3. y = -3x + 5

1. Given the points, (3, 2) and (5, 7), find the slope (m):

Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)

m = 5/2

Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):

y - 2 = 5/2(x - 3)

2. Given:

A point = (-3, 4)

Slope (m) = 2

Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):

y - 4 = m(x + 3) [equation of the line]

3. Given:

Slope (m) = -3

Y-intercept (b) = 5

Substitute m = -3 and b = 5 into the equation y = mx + b:

y = -3x + 5

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Answer:

six and a half litres

Step-by-step explanation:

if 3g = 900

what about 1950

you cross multiply

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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Answer:

(x) ∠CAB

Step-by-step explanation:

In ΔCOD and ΔBOA

\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)

Also,

∠COD = ∠BOA (vertically opposite angles)

⇒ ΔCOD and ΔBOA are similar

⇒ ∠CDO = ∠BAO

⇒ ∠CDB = ∠BAC

⇒ ∠CDB = ∠CAB

Answer:

4y

Step-by-step explanation:

y - -3y

Subtracting a negative is like adding

y+3y

Combine like terms

4y

Answer:

\(4y\)

Step-by-step explanation:

\(y - ( - 3y) \\ y + 3y \\ = 4y\)

hope this helps

brainliest appreciated

good luck! have a nice day!

The evaluation of logarithmic expressions is given.

The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

Given, log₅2 = r and  log₅3 = 8

Properties of Logarithms

1. logₐ (uv) = logₐ u + logₐ v

2. logₐ (u / v) = logₐ u - logₐ v

3. logₐ un = n logₐ u.

(1) To find log₅6:

Rearranging,

log₅6 =  log₅(2x3)

From the first property,

log₅6 =  log₅(2x3) = log₅2 + log₅3

 log₅6 = r+8

(2) To find log₅18:

log₅18 = log₅(6x3)

          = log₅6 + log₅3

          = r+8+8

log₅18  = r+16

(3) To find log₅15:

log₅18 = log₅(3x5)

          = log₅3 + log₅5

          = 8+ 1

log₅18 = 9

(4) To find log₅20:

log₅20 = log₅(2²x 5)

           = 2log₅2 + log₅5

log₅20 = 2r+1

(5) To find log₅(3/5)

log₅(3/5) = log₅3 - log₅5

              = 8-1

log₅(3/5) = 7

Therefore, the evaluation log₅6 = r+8,  log₅18  = r+16, log₅18 = 9, log₅20 = 2r+1 and log₅(3/5) = 7.

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Two-tailed test with α = .05, t = ± 2.447

One-tailed test with α = .05, t = 2.015

Two-tailed test with α = .01, t = ± 4.032

A one-tailed test is a statistical procedure in which the critical region of a distribution is one-sided, meaning that it may only be either higher than or less than a specific number. The alternative hypothesis will be adopted in place of the null hypothesis if the sample being tested falls inside the one-sided critical region.

To determine if the sample mean differs substantially from and from the population mean, a two-tailed hypothesis test is used. Testing the region beneath both tails (sides) of a normal distribution gives rise to the two-tailed test's name.

N = 6 of 5

Two-tailed test with α = .05, t = ± 2.447

One-tailed test with α = .05, t = 2.015

Two-tailed test with α = .01, t = ± 4.032

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Step-by-step explanation:

1.)you find

f(g(x))

2)set up the composition function and evaluate

f(2x+4) = -12x - 19

The median of the given data set is 26.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

Given the data set, we need to find the median.

So, let's arrange the numbers from smallest to largest in order to find the median.

\(\sf 15,20,22,26,28,35,36.\)

\(\text{Median}=\sf 26\)

Therefore, the median of the data set is 26.

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The surface area of the sphere is 1810 cm²

A sphere is a three-dimensional object that is round in shape. Examples of object with spherical shape is a ball, an egg e.t.c.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of sphere is expressed as;

A = 4πr². where r is the radius.

A = 4 × 3.14 × 12²

A = 1809.7 cm²

approximately to the nearest whole number

A = 1810 cm²

Therefore the surface area of the sphere to the nearest whole number is 1810 cm².

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Answer:

B. $104.95

Step-by-step explanation:

$160.45-$55.50=$104.95

Answer:

C & D

Step-by-step explanation:

In both these pairs, the x-coordinates are not changed while the y-coordinates are having a difference of 8 between them so they are really much corresponding

9-1=8

-3-(-11)=-3+11=8

Answer:

= (-3)/2

Step-by-step explanation:

Compute the slope of the line through the following points:

p_1 = (-2, 6) and p_2 = (-4, 9)

The slope of the line through (x_1, y_1) and (x_2, y_2) is:

(y_2 - y_1)/(x_2 - x_1)

Substitute (x_1, y_1) = (-2, 6) and (x_2, y_2) = (-4, 9):

= (9 - 6)/(-4 - -2)

9 - 6 = 3:

= 3/(-4 - -2)

-(-2) = 2:

= 3/(-4 + 2)

-4 + 2 = -2:

= 3/(-2)

Multiply numerator and denominator of 3/(-2) by -1:

Answer:  = (-3)/2

Answer:

P(X < 3) = 0.9375

Step-by-step explanation:

If the coins tossed by the 3 people all turn up the same, it means that we will have either; HHH or TTT

H is head and T is tail.

Thus; the probability of failure in each trial is;

q = P(HHH) + P(TTT)

P(H) = ½ and P(T) = ½.

Hence;

q = P(HHH) + P(TTT) = (½ × ½ × ½) + (½ × ½ × ½) = ⅛ + ⅛ = ¼ = 0.25

In binomial probability, p = 1 - q

Thus; p = 1 - 0.25 = 0.75

Now to find the probability that fewer than 3 tosses are needed is given by the expression;

P(X < 3) = P(1) + P(2)

Now, because the toss trials are independent, it means that x = 1.

Since x = 1,we can make use of geometric distribution formula which is given by;

P(X = x) = p^(x) • q^(n - x)

Thus;

P(1) = 0.75^(1) × 0.25^(1 - 1)

P(1) = 0.75 × 1

P(1) = 0.75

P(2) = 0.75^(1) × 0.25^(2 - 1)

P(2) = 0.75 × 0.25

P(2) = 0. 75 × 0.25

P(2) = 0.1875

Thus;

P(X < 3) = 0.75 + 0.1875

P(X < 3) = 0.9375

Step-by-step explanation:

Flip f(x) about the x-axis by multiplying it by -1

  - f(x)

  the squish it skinnier by multiplying it by 4

g(x) = - 4 f(x)   = -4 x^2

Answer:

t= 12.9 years

Step-by-step explanation:

Applying the triangle proportionality theorem, the length of Jk in the diagram given is: 16 units.

The triangle proportionality theorem states that when a side of a triangle is parallel to a line that intersects the other two sides of the triangle, then it divides the two sides of the triangle, proportionately.

Using the triangle proportionality theorem, we have the ratio if JK is x:

x/(36 - x) = (63 - 35)/35

x/(36 - x) = 28/35

35x = 28(36 - x)

35x = 1,008 - 28x

35x + 28x = 1,008

63x = 1,008

x = 16

JK is: 16 units.

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Triangle Midpoint Theorem-

The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

As given in the question,

QV = SV, so V is the mid point of QS,

SU = RU, so R is the mid point of RS.

Hence, UV is the line joining the midpoints of QS and RS.

Applying Triangle Midpoint Theorem,

Therefore, the side length of QR is 12 units.

Answer: D

Step-by-step explanation:

To determine which ordered pair is a solution to the inequality, we can substitute the values of x and y into the inequality and check if it is true.

Let's start with ordered pair A (80, 6):

1/4x ≤ 7/3y + 2

1/4(80) ≤ 7/3(6) + 2

20 ≤ 14 + 2

20 ≤ 16

This is not true, so ordered pair A is not a solution to the inequality.

Now let's try ordered pair B (48, 9):

1/4x ≤ 7/3y + 2

1/4(48) ≤ 7/3(9) + 2

12 ≤ 21 + 2

12 ≤ 23

This is also not true, so ordered pair B is not a solution to the inequality.

Next, let's try ordered pair C (40, 3):

1/4x ≤ 7/3y + 2

1/4(40) ≤ 7/3(3) + 2

10 ≤ 7 + 2

10 ≤ 9

This is false, so option C is not a solution to the inequality.

Finally, we have option D: (2, -6)

1/4(2) ≤ 7/3(-6) + 2

1/2 ≤ -14 + 2

1/2 ≤ -12

This is true, so option D is a solution to the inequality.

Therefore, the answer is D: (2, -6).

With all questions???

Answer:

Step-by-step explanation:

-12 = -9+ P/3 what is p​?

-12 + 9 = P/3

-3 = P/3

P = -9

------------------------

check

-12 = -9 + (-9/3)

-12 = -9 - 3

-12 = -12

the answer is good

The equation to find the number of leaves which Aidan has now, n is given by 8 × 12 - 7 = n.

In Mathematics, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

Next, we would write the equation that gives n, the number of leaves Aidan would have after collecting leaves for an art project as follows:

The number of leaves that Aidan collected from 8 different trees is equal to 8 leaves. Additionally, Aidan picks 12 leaves from each tree to have a total of 96;

n = 8 × 12 = 96.

Lastly, Aidan lost 7 leaves on his way home. Therefore, we would subtract 7 leaves from the total number of leaves that Aidan collected from 8 different trees;

n = 96 - 7 = 89 leaves.

In conclusion, the complete equation is represented by 8 × 12 - 7 = n.

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