A can of soda is placed inside a cooler. As the soda cools, its temperature T(x) in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler.

T(x)=-5+27e^-0.03x

Find the initial temperature of the soda and its temperature after 20 minutes, Round your answers to the nearest degree as necessary.

initial temperature:
temperature after 20 minutes:

Answer:

3

Step-by-step explanation:

=4-1=3f(N)

Answer:

[tex]t=0[/tex]

Step-by-step explanation:

[tex]10=4+3(t+2)\\\mathrm{or,\ }10=4+3t+6\\\mathrm{or,\ }10=10+3t\\\mathrm{or,\ }3t=0\\\therefore t=0[/tex]

Answer: t = 0

Step-by-step explanation:

Given equation

10 = 4 + 3 × (t + 2)

Subtract 4 on both sides

10 - 4 = 4 + 3 × (t + 2) - 4

6 = 3 × (t + 2)

Divide 3 on both sides

6 ÷ 3 = 3 × (t + 2) ÷ 3

2 = t + 2

Subtract 2 on both sides

2 - 2 = t + 2 - 2

[tex]\huge\boxed{t=0}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

R and p is included through pair of angle

The side that is  included between the given pair of angles is:

P and Q

Looking at the given triangle PQR, we see that the longest side of the triangle PQR is PQ.

Now, from the given triangle, if any point will be projected to form an angle, it will be the two points on the longest side of the triangle.

From the above, we can see clearly that P and Q were projected to form the angle QR and as a result we can easily deduce that P and Q are the points between the given pair of angles.

The conclusion is that points P and Q are correct.

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Answer:

Step-by-step explanation:

The formula Length into Length i.e. LxL

Lets say you have a square with length 4.

Then your area will be 4x4=16

The answer to the following are below:

Total water area for Alabama and Florida = 2.9 × 10⁷

Total water area for Hawaii and Michigan = 8.5 × 10⁷

Difference of water area of Florida and Hawaii = 3.3 × {10}^{- 1}

Difference of water area of Michigan and Alabama = 2.3 × 10¹

Alabama = 1.7 × 10³

Florida = 1.2 × 10⁴

Hawaii = 4.5 × 10³

Michigan = 4.0 × 10⁴

Total water area for Alabama and Florida = (1.7 × 10³) + (1.2 × 10⁴)

= (1.7 + 1.2) × {10}^{3 + 4}

= 2.9 × 10⁷

Total water area for Hawaii and Michigan = (4.5 × 10³) + (4.0 × 10⁴)

= (4.5 + 4.0) × {10}^{3 + 4}

= 8.5 × 10⁷

Difference of water area of Florida and Hawaii = (4.5 × 10³) - (1.2 × 10⁴)

= (4.5 - 1.2) × {10}^{3 - 4}

= 3.3 × {10}^{- 1}

Difference of water area of Michigan and Alabama = (4.0 × 10⁴) - (1.7 × 10³)

= (4.0 - 1.7) × {10}^{4 - 3}

= 2.3 × 10¹

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This test cannot be considered as a highly reliable tool for measuring the fitness level.

Cronbach's alpha coefficient (α) is an assessment tool that measures the internal reliability of a psychometric test's multiple item data set. This measure's internal consistency indicates the degree to which items in a set are related to each other or to a latent (unobserved) variable called a construct. Alpha is a measure of the extent to which a set of items, when measured as a composite, generates scores that are both reliable and valid.This formula is used to calculate Cronbach's alpha coefficient, which ranges from 0 to 1, with higher values indicating greater internal consistency or reliability.
Cronbach's alpha (α) for the fitness measure is calculated by formula, given as:
[tex]α = N / (N - 1) * (1 - Σi=1k σi^2 / σx^2)[/tex]
where
N = number of items
[tex]σi^2[/tex] = variance of the ith item
[tex]σx^2[/tex] = variance of the test scores
k = number of items in the test
Here, the total number of valid data points N = 5.
Variance for trial 1, trial 2, trial 3 and total are given as 2.300, 2.000, 3.800, and 11.500 respectively.
We will now solve for Cronbach's alpha coefficient (α) using the above formula.
[tex]α = 5 / (5 - 1) * (1 - [(2.300 + 2.000 + 3.800) / 11.500])α = 5 / 4 * (1 - [8.1 / 11.5])α = 0.638[/tex]
Cronbach's alpha coefficient ac for this test is 0.638.
This coefficient is a measure of the extent to which the tests are reliable and consistent in measuring the same construct. Since Cronbach's alpha coefficient is in between 0.6 and 0.7, it indicates that the internal consistency of this test is moderate.

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Step-by-step explanation:

We have to solve :

[tex]2^4 + 2 (10 - 4) - 3 [/tex]

BODMAS will be used here,

B = Bracket

O = off

D = Division

M = Multiplication

A = addition

S = Subtraction

First let's solve

[tex]2^4[/tex]

[tex]2 \times 2 \times 2 \times 2[/tex]

[tex]16[/tex]

Now,

Bracket of ,

16 + 2 (6) - 3

16 + 12 - 3

28 - 3

25

Answer:

10.5

Step-by-step explanation:

Missing number, 9.8, 9.1

We see that each time it subtracts 0.7

We take

9.8 + 0.7 = 10.5

So, the missing number is 10.5

Answer:

AB = 28 , BC = 17.5 , X = 13.2

Step-by-step explanation:

since the figures are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{AB}{PQ}[/tex] = [tex]\frac{AD}{PS}[/tex] ( substitute values )

[tex]\frac{AB}{8}[/tex] = [tex]\frac{14}{4}[/tex] ( cross- multiply )

4 AB = 8 × 14 = 112 ( divide both sides by 4 )

AB = 28

and

[tex]\frac{BC}{QR}[/tex] = [tex]\frac{AD}{PS}[/tex] ( substitute values )

[tex]\frac{BC}{5}[/tex] = [tex]\frac{14}{4}[/tex] ( cross- multiply )

4 BC = 5 × 14 = 70 ( divide both sides by 4 )

BC = 17.5

similarly for the 2 similar figures

[tex]\frac{x}{6}[/tex] = [tex]\frac{11}{5}[/tex] ( cross- multiply )

5x = 6 × 11 = 66 ( divide both sides by 5 )

x = 13.2

Answer:

[tex]\overline{AB}=28[/tex]

[tex]\overline{BC}=17.5[/tex]

[tex]x=13.2[/tex]

Step-by-step explanation:

If quadrilateral PQRS is similar to quadrilateral ABCD, their corresponding sides are in the same ratio:

[tex]\overline{PQ} : \overline{AB} = \overline{QR} : \overline{BC} = \overline{RS} : \overline{CD} = \overline{SP}:\overline{DA}[/tex]

From inspection of the two quadrilaterals, the given side lengths are:

[tex]\overline{PQ} = 8[/tex]

[tex]\overline{QR} = 5[/tex]

[tex]\overline{RS} = 6[/tex]

[tex]\overline{SP} = 4[/tex]

[tex]\overline{DA} = 14[/tex]

Substitute these into the ratio equation:

[tex]8 : \overline{AB} = 5 : \overline{BC} = 6 : \overline{CD} = 4:14[/tex]

Solve for AB:

[tex]8 : \overline{AB} = 4:14[/tex]

   [tex]\dfrac{8}{\overline{AB}}= \dfrac{4}{14}[/tex]

 [tex]8 \cdot 14=4 \cdot{\overline{AB}}[/tex]

   [tex]\overline{AB}=\dfrac{8 \cdot 14}{4}[/tex]

  [tex]\boxed{\overline{AB}=28}[/tex]

Solve for BC:

[tex]5 : \overline{BC} = 4:14[/tex]

  [tex]5 \cdot 14=4 \cdot \overline{BC}[/tex]

    [tex]\overline{BC}=\dfrac{5 \cdot 14}{4}[/tex]

   [tex]\boxed{\overline{BC}=17.5}[/tex]

[tex]\hrulefill[/tex]

Assuming the two figures are similar, their corresponding sides are in the same ratio. Therefore:

[tex]x:6=11:5[/tex]

   [tex]\dfrac{x}{6}=\dfrac{11}{5}[/tex]

   [tex]x=\dfrac{11 \cdot 6}{5}[/tex]

   [tex]x=\dfrac{66}{5}[/tex]

  [tex]\boxed{x=13.2}[/tex]

If Mira had spent the same total amount of time but an equal amount of time on each problem, each problem would have taken around 2.36 minutes.

In the given plot, Mira spent varying amounts of time on each of the 55 math problems. To find out how many minutes each problem would have taken if Mira had spent an equal amount of time on each problem, we need to calculate the total time she spent and divide it by the number of problems.

Looking at the plot, we can estimate the total time Mira spent by counting the dots above each tick mark and multiplying them by the corresponding time interval. Let's break it down step by step:

The tick marks on the plot are at 7, 7.5, 8, 8.5, 9, 9.5, and 10 minutes per problem.

There are 2 dots above the unlabeled tick mark between 8 and 8.5 minutes per problem. We can assume it represents 8.25 minutes.

There are 3 dots above the 9.5 minutes per problem tick mark.

Now, let's calculate the total time Mira spent:

(7 * 2) + (7.5 * 2) + (8 * 2) + (8.25 * 2) + (9 * 2) + (9.5 * 3) + (10 * 2) = 129.5 minutes.

Since Mira spent a total of 129.5 minutes on 55 problems, each problem would have taken approximately 2.36 minutes (rounded to two decimal places) if she had spent an equal amount of time on each problem.

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In the given question, the statement "A plot of log(y) vs log(x) would be linear with a slope of 3" is true.

Given equation is:

y = 5x³

On taking logarithm both sides:

log(y) = log (5x³)

log (y) = log(5) + log(x³)      (∵log ab = log a + log b)

log(y) = log(5) + 3 log(x)      (∵log [tex]a^b[/tex]= a log b)

log(y) = 3log(x) + log(5)

On comparing with the general form of a straight line:

y = mx + C, where m is the slope of the line and C is the constant

m = 3

Since the slope of the line is 3, so, plot of log(y) vs log(x) would be linear with a slope of 3.

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Answer:

Por lo tanto, el área de un círculo con un diámetro de 9cm es de aproximadamente 63.62cm^2.

Step-by-step explanation:

Para calcular el área de un círculo con un diámetro de 9cm, debemos utilizar la fórmula:

Área = π x (radio)^2

Primero, debemos encontrar el radio. Sabemos que el diámetro es de 9cm, por lo que el radio es la mitad de esto:

Radio = diámetro / 2 = 9cm / 2 = 4.5cm

Ahora, podemos sustituir el valor del radio en la fórmula del área:

Área = π x (4.5cm)^2

Área = π x 20.25cm^2

Área = 63.62cm^2 (aproximadamente)

Step-by-step explanation:

in what form do we need the equation ?

slope-intercept ?

that would be

y = ax + b

with "a" being the slope and "b" being the y-intercept (the y-value when x = 0).

in any case, since we have the slope and a point, we can start with the point-slope form :

y - yp = a(x - xp)

"a" is again the slope, and (xp, yp) is the given point.

so,

y - 5 = 1×(x - 3) = x - 3

adding 5 to both sides gives us

y = x + 2

and that is our desired equation in slope-intercept form.

Step-by-step explanation:

Find his unit rate of miles per hour :

1/2 mi  /  1/10 hr   =  5 miles  per hour  

Derived quantities are physical quantities that are obtained by combining base quantities using mathematical operations.

Derived quantity is a physical quantity that is computed from two or more measurements of other physical quantities. It is a measure of an aspect of a physical system or experiment that cannot be directly measured, but is a function of one or more measured quantities, which are typically called base or fundamental quantities. Derived quantities are expressed in terms of base quantities, which are the fundamental quantities that are defined independently of other physical quantities.

Derived quantities, unlike base quantities, are determined by the mathematical relationships that describe the physical systems they represent.

They are derived from base quantities by mathematical operations such as multiplication, division, exponentiation, or taking the square root, for example. For instance, speed is a derived quantity obtained by dividing distance by time. Other examples of derived quantities include force, energy, power, acceleration, density, pressure, and torque. These quantities are all derived from base quantities such as length, mass, and time. The derived quantities are often represented using specific units of measurement that are derived from the base units of the SI system.

For example, the derived quantity of force is measured in newtons, while energy is measured in joules, power is measured in watts, and acceleration is measured in meters per second squared.

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Explanation:

Find the areas of three parts individually and sum the areas.

The probability that the sample mean is more than 47 is approximately 0.1841 or 18.41%.

To find the probability that the sample mean is more than 47, we can use the properties of the normal distribution and the Central Limit Theorem.

Given that the population distribution is normal with a mean of 45 and a standard deviation of 22, we know that the distribution of the sample means will also be normal, with the same mean but a smaller standard deviation.

The standard deviation of the sample means, also known as the standard error, can be calculated by dividing the population standard deviation by the square root of the sample size.

In this case, the standard error is 22 / √29.

To find the probability that the sample mean is more than 47, we need to calculate the z-score for the value 47, using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard error.

z = (47 - 45) / (22 / √29) = 2 / (22 / √29) = 0.908

Using a standard normal distribution table or a calculator, we can find the probability corresponding to the z-score of 0.908.

This probability represents the area under the curve to the right of the z-score.

P(Z > 0.908) ≈ 1 - 0.8159 ≈ 0.1841

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1. Trey will be able to claim a child tax credit of $4,000 for his daughters.

2. Trey will be able to claim a child tax credit of $3,000 for his daughters.

3. Trey will be able to claim a child tax credit of $2,995 for his daughters.

AGI: $100,000:

The child tax credit for each qualifying child under the age of 17 is $2,000. Since Trey has two qualifying children, the total child tax credit would be $2,000 * 2 = $4,000.

AGI: $420,000

The child tax credit begins to phase out for higher-income taxpayers. It is reduced by $50 for each $1,000 (or fraction thereof) of AGI exceeding the threshold amount. The threshold amount for taxpayers filing a joint return is $400,000.

AGI exceeding the threshold amount = $420,000 - $400,000 = $20,000

Reduction in child tax credit = ($20,000 / $1,000) * $50 = $1,000

Child tax credit before reduction = $2,000 * 2 = $4,000

Child tax credit after reduction = $4,000 - $1,000 = $3,000

AGI: $420,100 (daughters ages 10 and 12)

The child tax credit begins to phase out for higher-income taxpayers. It is reduced by $50 for each $1,000 (or fraction thereof) of AGI exceeding the threshold amount.

The threshold amount for taxpayers filing a joint return is $400,000.

AGI exceeding the threshold amount = $420,100 - $400,000 = $20,100

Reduction in child tax credit = ($20,100 / $1,000) * $50 = $1,005

Child tax credit before reduction = $2,000 * 2 = $4,000

Child tax credit after reduction = $4,000 - $1,005 = $2,995

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The equation that describes the graphed function is Option C: g(x) = -f(x) + 2.

The given function is f(x) = √x, which represents the square root function. To determine which equation describes the graphed function, we need to analyze the transformations applied to the original function.

Option A, g(x) = f(-x) + 2:

This equation represents reflecting the graph of f(x) across the y-axis (due to the negative sign in front of x) and then shifting it vertically upward by 2 units. However, this transformation does not match the graph of f(x) = √x.

Option B, g(x) = -f(x + 2):

This equation represents taking the negative of the original function f(x) and shifting it horizontally left by 2 units. This transformation does not match the graph of f(x) = √x.

Option C, g(x) = -f(x) + 2:

This equation represents taking the negative of the original function f(x) and shifting it vertically upward by 2 units. This transformation matches the graph of f(x) = √x.

Option D, g(x) = f(-x + 2)

This equation represents reflecting the graph of f(x) across the y-axis (due to the negative sign in front of x) and shifting it horizontally right by 2 units. This transformation does not match the graph of f(x) = √x.

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Answer:

Step-by-step explanation:

This is a 30-60-90 right triangle, with sides x, 2x, and x*square root of 3. I'm assuming that v3 means the square root of 3...

So: since your question is confusing,

Method 1: v3 means the square root of 3

If x=square root of 3, than x(square root of 3)=3

So the hypotenuse is 2*square root of 3

Method 2: v3 means 3

Since x=3, the hypotenuse is 6.

By the way, in a 30-60-90 triangle, the hypotenuse is twice of the shorter side.

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The figure that shows a translation is (c)

From the question, we have the following parameters that can be used in our computation:

The figures

In the figure (c), we have:

This means that the only transformation in figure (c) is translation

So, the figure that shows a translation is (c)

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1) The equation of the given line is: y = ¹/₃x

2) The equation of the given line is: y = -3x + 4

3) The triangles are similar

4) The triangles are not similar

The formula for the equation of a line between two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

1) The two coordinates we will use are:

(-3, -1) and (3, 1)

Thus:

(y + 1)/(x + 3) = (1 + 1)/(3 + 3)

(y + 1)/(x + 3) = 2/6

y + 1 = ¹/₃x + 1

y = ¹/₃x

2) The two coordinates we will use are: (1, 1) and (2, -2)

Thus:

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

(y - 1)/(x - 1) = -3/1

y - 1 = -3x + 3

y = -3x + 4

3) For two triangles to be similar, the ratio of their corresponding sides must be equal.

In this case, the ratio of corresponding sides are equal and as such they are similar.

4) The ratio of corresponding sides are not equal and as such they are not similar triangles.

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Answer:

Step-by-step explanation:

Formula for transformation for parent function f(x) = |x|  is

g(x) = a |x -h| + k                    

Where a is your stretch/compression

(h, k) is your vertex or shift (x, y) directions

If the function is shifted down 3 that's  -3 in y direction

g(x) = |x| - 3

Step-by-step explanation:

EACH week the cost is  ( 49 + 14 + 12 ) = 75 dollars

   he has FOUR of these weeks     4  x  $75 = $ 300.   for four weeks .

I believe this question requires you to set up a system of equations.

Let x = the total mass (in kg) of the 25% copper alloy

Let x = the total mass (in kg) of the 70% copper alloy

Thus, you can form two equations with the data provided:

0.7(y) + 0.25(x) = 0.61(50)

y + x = 50

Using "y+x=50"

x = 50 - y

Plus "x = 50-y" into the other equation. Note that 0.61(50) = 30.5

0.7y + 0.25(50-y) = 30.5

Distribute 0.25 over (50-y)

0.7y + 12.5 - 0.25y = 30.5

Subtract 12.5 from both sides and add 0.7y to -0.25y

0.45y = 18

Dividing 0.45 on each side leaves you with y = 40

Now, plug y = 40 in "x + y = 50" to solve for the total mass of the 25% copper alloy.

x + 40 = 50

x = 10

Thus, you need 10 kilograms of the 25% alloy combined with 40 kilograms of the 70% alloy to create a 50 kilogram alloy composed of 61% copper.

Hope this helps!

The equation of a line with slope of 1 / 2 and the points are (-2, -4) is  y = 1 / 2x - 3.

The equation of a line can represented as follows:

y = mx + b

where

Therefore, the equation of the line has a slope of 1 / 2 and it passes through the points (-2, -4).

Hence,

y = 1 / 2 x + b

Using (-2, -4),

-4 = 1 / 2(-2) + b

-4  = -1 + b

b = -4 + 1

b = - 3

Therefore, the equation is y = 1 / 2x - 3.

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Answer:

[tex]\huge\boxed{\sf 32.5}[/tex]

Step-by-step explanation:

= 25% of 130

Key: "%" means "out of 100" and "of" means "to multiply"

= 25/100 × 130

= 1 / 4 × 130

= 130 / 4

[tex]\rule[225]{225}{2}[/tex]

Answer:

32.5

Explanation:

First, divide 130 by 100:

[tex]\sf{130\div100=1.30}[/tex]

Multiply by 25:

[tex]\sf{1.30\times25=32.5}[/tex]

Hence, 25% of 130 is 32.5.

Without additional details, we cannot determine the number of two-dozen tulip arrangements the florist should expect to sell with the anticipated 4,600 more customers.

To determine the number of two-dozen tulip arrangements the florist should expect to sell if they anticipate 4,600 more customers, we need to examine the given results and make a reasonable assumption based on the available information.

Unfortunately, the given results or information regarding the number of tulip arrangements sold or the relationship between customers and sales are not provided. Without this data, it is not possible to accurately estimate the number of arrangements that will be sold with an additional 4,600 customers.

To make an accurate prediction, we would need more information such as the average number of tulip arrangements sold per customer or any patterns or trends observed in the sales data.

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Answer:

The number that was removed was 75

Look in explanation for working out how you get this

Step-by-step explanation:

mean1 = 25

if one is removed, we get mean2 = 15

now, mean1 is mean of 6 numbers, so,

[tex]mean1 = (n1+n2+n3+n4+n5+n6)/6[/tex]

so,

[tex](mean1)(6) = (n1+n2+n3+n4+n5+n6) \ \ \ (I)[/tex]

where "n" means number

now, we removed a number, let that number be n6,

so, after we remove it, we get the 2nd mean,

[tex]mean2 = (n1+n2+n3+n4+n5)/5\\\\and,\\(5)(mean2) = (n1+n2+n3+n4+n5)[/tex]

so, n1 + n2 +n3+n4+n5 = (5)(mean2)

putting the value of n1 + n2 +n3+n4+n5

in eq (I), we get,

[tex](mean1)(6) = (5)(mean2)+n6 \ \ \[/tex]

so, we know the values of mean1 =25 and mean2 = 15

we get,

[tex](6)(25)=(5)(15) = n6\\n6 = (25)(6)-(15)(5)\\n6=150-75\\n6=75[/tex]

Hence the number that was removed was 75

There are approximately 4,357,068 Mexicans living in Los Angeles.

To calculate the number of Mexicans living in Los Angeles, we need to multiply the Hispanic population by the Mexican population rate: Mexican population = Hispanic population * Mexican population rate

Substituting values:

Mexican population = 6,012,300 * 0.725

Mexican population = 4,357,067.5

Therefore, there are approximately 4,357,068 Mexicans living in Los Angeles.

Full question:

'In the city of Los Angeles, California, the Hispanic population is 6012300. If we consider that the Mexican population rate is 72.5%, how many Mexicans live in Los Angeles.

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