The temperature of one furnace is 1400°C and cools at a rate of 2.5°C per minute. The temperature of another furnace is 1200°C and is heated at a rate of 1.5°C per minute. Write an equation that models when the temperature of the two furnaces will be equal.

Answer:

Step-by-step explanation:

a) The steering committee of 5 can be chosen from 15 members in 15 nCr 5 ways. Once the committee is chosen, the chair can be selected in 5 ways and the secretary can be selected in 4 ways (since the chair cannot also be the secretary). Therefore, the total number of different sets of committees (including officer selection) is:

15 nCr 5 * 5 * 4 = 3,003,600

b) Each of the 6 raffle prizes can be awarded to any of the 100 people, so there are 100 choices for the first prize, 99 choices for the second prize, and so on, down to 95 choices for the sixth prize. However, since the three $25 prizes are equivalent, we need to divide by 3! to account for the ways in which the $25 prizes can be arranged. Therefore, the total number of different raffle ticket winner selections is:

(100 * 99 * 98 * 97 * 96 * 95) / (3!) = 903,450,240,000

c) Since repeats are allowed and the code cannot begin with 0, there are 9 choices for the first digit and 10 choices for each of the remaining digits. Therefore, the total number of six-digit PIN codes that can be made is:

9 * 10^5 = 9,000,000

Answer:

a = 8

Step-by-step explanation:

4 x 2 = 8

8 x 2 = 16

Helping in the name of Jesus.

The initial investment was approximately $2,603.88, which is option (b).

Probability is a measure of the likelihood of an event occurring.

We can use the formula for compound interest:

A = [tex]P(1+r/n)^{nt}[/tex]

where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period in years.

In this case, we know that the final amount A is $3,820, the annual interest rate r is 5.5% (or 0.055 as a decimal), the interest is compounded 6 times a year (n = 6), and the time period is 7 years.

So we can rearrange the formula to solve for P:

P = A/[tex]P(1+r/n)^{nt}[/tex]

Plugging in the values, we get:

P = 3820 / [tex](1+0.055/6)^{6*7}[/tex]

P ≈ $2,603.88

Therefore, the initial investment was approximately $2,603.88, which is option (b).

To learn more about compound interest from the given link:

https://brainly.com/question/14295570

#SPJ1

Answer:

The file is attached below.

I disagree with Meghan.

Step-by-step explanation:

Hello!

The line plot is attached below.

I disagree with Meghan as the least amount of time someone recited the alphabet is 4 seconds and the greatest is 7.5 seconds.

The difference between these two numbers would be 3.5 seconds, which is not the same as 4 seconds.

If the equation is changed from y = x^2 to y = (1/4)x^2, the parabola will become wider.

The equation of the line is 3y-5x=3 and the graph is attached.

Geometrically speaking, a line is a one-dimensional figure because it has length but no width. A group of points can be extended endlessly in opposing directions to form a line. Two points in a two-dimensional plane determine it. There are, however, additional ways to formulate the equation of a line in a two-dimensional coordinate system. The three most popular methods are the point-slope form, slope-intercept form, and general or standard form of the equation of a line. As its name suggests, the point-slope form combines a line point and a straight-line slope. The equations of infinite lines with a particular slope can be expressed, however when we specify that the line passes through a particular point, we get a singularity.

the equation of a line is

y-y'=m(x-x')

[tex]y+4=\frac{5}{3}(x+3)\\\\3y+12=5x+15\\3y-5x=3[/tex]

learn more about straight lines.

https://brainly.com/question/29223887

#SPJ1

The total surface area must be calculated by adding the areas of all five faces, the four triangular faces, and the square base.

The term "square pyramid" refers to a three-dimensional geometric form with a square base and four triangular faces or sides that meet at a single point (known as a vertex). Because it has five faces, it is referred to as a pentahedron.

Given :

Let s represent the square base's side length and h represent the slant height of each triangle face. The area of a single triangle is then determined by:

A = (1/2) * s * h

The areas of all five face the four triangular faces and the square base must be added up in order to determine the overall surface area of the pyramid.

The overall surface area is: since the square base has a simple area of s2.

When we replace A with the expression, we obtain:

We require further details regarding the pyramid in order to determine the values of s and h.

To know more about the square pyramid visit:

https://brainly.com/question/27350043

#SPJ9

The function f(x) = 2x³-3x² - 12x + 1 does not have any local maximum or minimum values over the interval [2, 3].

To find the local maximum and minimum of a function over a given interval, we need to find the critical points of the function within that interval and then apply the second derivative test to classify those critical points as local maximum or minimum.

To find the critical points, we first take the derivative of the given function:

f'(x) = 6x² - 6x - 12 = 6(x² - x - 2)

x = -1 or x = 2

Both of these critical points fall outside the given interval [2, 3]. Therefore, there are no critical points of the function within the interval [2, 3], and so there are no local maximum or minimum values of the function over this interval.

In other words, the function f(x) = 2x³-3x² - 12x + 1 does not have any local maximum or minimum values over the interval [2, 3].

To know more about Maxima and Minima, click here,

https://brainly.com/question/29562544

#SPJ1

Answer:

Step-by-step explanation:

For the 90°/right angle part, we can subtract 35° from 90° to get the degree of that area.

90° - 35° = 55°

We can check off the "55°" box

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

Now, for the other half of the straight angle including the right angle, we can subtract 90° from 180°.

Getting 90°

We can check off the "90°" box

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

To find the degree of the "(7x + 5°)" -- assuming that that angle is vertical to the "other" -- we can make an equation of

⇒ 7x + 5° = 90° + 55°

Solve:

Add together 90 and 55 which is 145°

New equation:

7x + 5° = 145°

Subtract 5° from both sides, getting the equation

7x = 140°

Isolate x by dividing both sides by 7

x = 20°

Substitute what we have for x into the equation "7x + 5°"

7(20°) + 5

= 145°

We can check off the "145°" box

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

All the boxes checked off:

Hopefully this helps! -- mark me brainliest if you want ofc

To translate a shape, all of its vertices must be moved in the same direction and by the same amount. The responses to the five sections of the question are as follows:

Coordinates are used to identify the position of an object on a two-dimensional grid or in three-dimensional space. They are usually written as pairs of numbers, separated by a comma.

1. We must deduct 2 from all of the y-coordinates of the vertices of the parallelogram ABCD in order to translate it two units down. Let's assume that the vertices' initial coordinates are A(a,b), B(c,d), C(e,f), and D. (g,h). The vertices will then have the new coordinates A'(a,b-2), B'(c,d-2), C'(e,f-2), and D' (g,h-2). To obtain the translated parallelogram, plot these new vertex points.

2. To move the rhombus EFGH 2 units to the left and 4 units down, we must deduct 2 from all of its vertices' x-coordinates and 4 from all of its y-coordinates. Let's assume that the vertices' initial coordinates are E(a,b), F(c,d), G(e,f), and H. (g,h). The vertices will then have the new coordinates E'(a-2,b-4), F'(c-2,d-4), G'(e-2,f-4), and H' (g-2,h-4). To obtain the translated rhombus, plot these additional vertices.

3. If we want to translate a square with coordinates L(-5,5), M(-5,5), N(5,5), and O(5,5) 3 units to the right and 2 units up, we must add 3 to all of its x-coordinates and subtract 2 from all of its y-coordinates. The vertices' new coordinates are L'(-2,-7), M'(-2,3), N'(8,3), and O' (8,-7). To obtain the translated square, plot these new vertex points.

4. The new coordinates of triangle XYZ after translating 4 units down will be X' (2,-3), Y' (4,1) and Z' (5,-2). This is happening because when a triangle is translated 4 units down, the y-coordinate of each vertex is decreased by 4 units, while the x-coordinate remains the same.

5. I (4,-2) P (-4,-2) G (5,2) Q (6,-4) R (-2,2)

S (6,4) J (1,-1) U (-5,0) H (3,-1) K (-6,-5)

For more questions related to coordinates

https://brainly.com/question/27481419

#SPJ1

The function has the maximum revenue of $348,480 with the increasing rate of $33.

The highest and smallest values of a function, respectively, can either be found inside a specific range or distributed throughout the entire domain. They are also sometimes referred to collectively as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, accordingly.

Given data:

The overall revenue is thus:

y = (36 - 0.50x)(9600 + 160x)

Differentiate with respect to x.

y ' = (-0.50)(9600 + 160x) + 160(36 - 0.50x)

y' = -4800 - 80x + 5760 - 80x

y' = 960 - 160x

To find x, put y' = 0

960 - 160x = 0

x = 960/160 = 6 (critical point)

Function is decreasing in interval - [6, +∞)

Increasing Function in interval - (-∞, 6]

Thus, the function has the maximum value at x = 6.

maximum revenue f(6):

f(6) = (36 - 0.50x)(9600 + 160x)

f(6) = (36 - 0.50(6))(9600 + 160(6))

f(6) = $348,480

Rate : 36 - 0.50(6) = $33

The function has the maximum revenue of $348,480 with the increasing rate of $33.

Know more about the maxima of function

https://brainly.com/question/6787214

#SPJ1

Step-by-step explanation:

a) Since the temperature of the oven is decreasing by a percentage of its current temperature each minute, the function that best represents this situation is an exponential function.

b) Let T be the temperature of the oven in degrees Fahrenheit at time x minutes after it was turned off. The initial temperature of the oven was 450° F, and the temperature decreases by 10% each minute. This can be expressed as:

T = 450(0.9)^x

Therefore, the function that models the situation is:

f(x) = 450(0.9)^x

where f(x) is the temperature of the oven in degrees Fahrenheit x minutes after it was turned off.

As 80 percentage of 25 classmates is equal to 20. Krysti should have ordered 20 small t-shirts for her 25 classmates

Error is when a mistake is made while solving a mathematical problem.

Krysti's error in finding the number of small t-shirts is that she forgot to multiply the percentage by the total number of classmates.

If Krysti wanted to find the number of small t-shirts she should have ordered, she should have multiplied

80% * 25.

=0.8 * 25

= 20.

To explain it in another way, Krysti could have also 100/25 and then 80 divided by the answer that is 4. This would also give the same result of 20.

Krysti's error was that she did not correctly use percentages to find the number of small t-shirts she should have ordered.

For more questions related to Error

https://brainly.com/question/11472659

#SPJ9

Answer: Let's call the scale factor between the two containers "k". Then, we know that the ratio of their surface areas is equal to the square of the scale factor:

(surface area of B) / (surface area of A) = k^2

We also know that the ratio of their volumes is equal to the cube of the scale factor:

(volume of B) / (volume of A) = k^3

We can rearrange the first equation to solve for k:

k^2 = (surface area of B) / (surface area of A) = 10478 mm^2 / 1550 mm^2 = 6.75

Taking the square root of both sides, we get:

k = sqrt(6.75) = 2.6 (rounded to one decimal place)

Now we can use the second equation to find the volume of container A:

(volume of B) - (volume of A) = 62160 mm^3

(k^3)(volume of A) - (volume of A) = 62160 mm^3

Simplifying and solving for the volume of A, we get:

volume of A = 62160 mm^3 / (k^3 - 1) = 62160 mm^3 / (2.6^3 - 1) ≈ 4477 mm^3

Therefore, the volume of container A is approximately 4477 mm^3.

Step-by-step explanation:

Answer: 363+368=731

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that the right angle is made up of two angles viz 8z° and (3z+2)° .

As we know that the measure of a right angle is 90° , so the sum of the two angles would also be 90° . Hence here ,

→ 8z + 3z + 2 = 90

→ 11z + 2 = 90

→ 11z = 90-2

→ 11z = 88

→ z = 88/11

→ z = 8

Hence the value of z is 8 .

Answer:

x = 20

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{10\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

x × [tex]\sqrt{2}[/tex] = 20[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )

x = 20

Answer:

I think its 75 degrees and brainliest would be greatly appreciated

Answer:

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

Supplementary angles add up to 180°:

Substitute and solve for x:

Find the measure of ∠B:

The function is decreasing for x < -6, or over the interval (–∞, –6).

What is a graph?

In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines). Graphs are often used to represent relationships between objects or to model complex systems.

The derivative of the function y = |x + 6| is equal to -1 for x < -6 and 1 for x > -6. At x = -6, the derivative is undefined, but the function is not decreasing there, so we don't need to consider that point.

Thus, the function is decreasing for x < -6, or over the interval (–∞, –6). Therefore, the answer is A. (–∞, –6).

To learn more about graph from the given link:

brainly.com/question/17267403

#SPJ1

Answer:

Step-by-step explanation:

To express the difference in mean weights as a multiple of the MAD for both dog breeds, we can use the formula:

(difference in means) / (mean absolute deviation)

Let's plug in the values given in the problem:

(difference in means) = 13 - 11.5 = 1.5

(mean absolute deviation) = 2 + 1.8 / 2 = 1.9 (taking the average of the two MADs)

Now we can calculate:

(difference in means) / (mean absolute deviation) = 1.5 / 1.9 ≈ 0.7895

Therefore, the difference in mean weights between the two breeds is approximately 0.7895 times the average MAD for both breeds.

Answer:

x=1/3

          ≈ 0.333333333

x=4

Step-by-step explanation:

To win the game, your team needs to score more than   [tex]35[/tex] points, which means: 3f + 7t > 35 three possible game-winning combinations are:

[tex]t = 5, f = 11: 3(11) + 7(5) = 63[/tex]

[tex]t = 6, f = 8: 3(8) + 7(6) = 62[/tex]

[tex]t = 7, f = 5: 3(5) + 7(7) = 56[/tex]

Each of these combinations would result in your team scoring more than 35 points and winning the game.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=).

For example, the argument [tex]"2x + 3 = 9"[/tex]  asserts that the phrase [tex]"2x + 3"[/tex]  equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that allows the equation to be true.

Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation. [tex]"x2 + 2x - 3 = 0."[/tex]    Lines are utilised in many different areas of mathematics, such as  algebra, calculus, and geometry.

Let's let f be the number of field goals scored by your team and t be the number of touchdowns scored by your team.

a) To win the game, your team needs to score more than 35 points, which means:

3f + 7t > 35

We can simplify this inequality by dividing both sides by 1:

3f + 7t/1 > 35/1

3f + 7t > 35

b) Now, we need to find possible values for f and t that make this inequality true. Since we are looking for positive integer values for f and t, we can start by testing different values for t and solving for f:

If t = 5, then 3f + 7(5) > 35, so 3f > 0 and f > 0. Possible solutions are f = 1, f = 2, f = 3, and so on.

If t = 6, then 3f + 7(6) > 35, so 3f > 7 and f > 2. Possible solutions are f = 3, f = 4, f = 5, and so on.

If t = 7, then 3f + 7(7) > 35, so 3f > 14 and f > 4. Possible solutions are f = 5, f = 6, f = 7, and so on.

c) So, three possible game-winning combinations are:

[tex]t = 5, f = 11: 3(11) + 7(5) = 63[/tex]

[tex]t = 6, f = 8: 3(8) + 7(6) = 62[/tex]

[tex]t = 7, f = 5: 3(5) + 7(7) = 56[/tex]

Each of these combinations would result in your team scoring more than 35 points and winning the game.

Learn more about equation here:

brainly.com/question/649785

#SPJ1

The best height he can jump is 2.5 meters. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

It is believed that the four fundamental operations, often known as "arithmetic operations," adequately explain all real numbers. Division, multiplication, addition, and subtraction are the mathematical operations that come before quotient, product, sum, and difference.

We are given that Ivan Ukhov  jumps 2.4 metres which is 4% lower than the best height he can jump.

Let the best height be 'x'.

So, from the above information, we get

⇒ x - 0.04x = 2.4

⇒ 0.96x = 2.4                     (Using subtraction)

⇒ x = 2.5                             (Using division)  

Hence, the best height he can jump is 2.5 meters.

Learn more about arithmetic operations from the given link

brainly.com/question/30283549

#SPJ9

Rounding to the same number of significant digits as the measurement with the least number of significant digits (which is "350 ppm"), the expected CO₂ level by the end of 2030 would be 430 ppm.

Significant digits, also known as significant figures or sig figs, are the digits in a number that are considered to be accurate or meaningful. They represent the precision or reliability of a measurement or calculation.

In a number, all digits except for leading zeros are considered to be significant. For example, in the number 0.00456, there are three significant digits (4, 5, and 6), while the zeros before the 4 are not significant.

The rules for determining the number of significant digits in a number are:

All non-zero digits are significant.

Zeros between non-zero digits are significant.

Leading zeros are not significant.

To find the expected CO₂ level in the atmosphere by the end of 2030, we need to calculate the total increase in CO₂ levels from 2012 to 2030 and then add it to the 2012 CO₂ level of 396 ppm.

To calculate the total increase in CO₂ levels, we can use the following formula:

Total increase in CO₂ levels = rate of increase × time

where the rate of increase is 2.10 ppm per year and the time is the number of years from 2012 to 2030, which is 18 years.

Total increase in CO₂ levels = 2.10 ppm/year × 18 years = 37.8 ppm

Therefore, the expected CO₂ level in the atmosphere by the end of 2030 would be:

Expected CO₂ level = 2012 CO₂ level + total increase in CO₂ levels

Expected CO₂ level = 396 ppm + 37.8 ppm

Expected CO₂ level = 433.8 ppm

Rounding to the same number of significant digits as the measurement with the least number of significant digits (which is "350 ppm"), the expected CO₂ level by the end of 2030 would be 430 ppm.

To know more about rate visit:

https://brainly.com/question/31103012

#SPJ1

Answer:

It will take Jaime 36 days to run 96 miles.

Step-by-step explanation:

The formula for rate is:

[tex]\boxed{\sf Rate=\dfrac{Distance}{Time}}[/tex]

Therefore, Jaime's run rate is:

[tex]\implies \sf Rate=\dfrac{8\;miles}{3\;days}=\dfrac{8}{3} \;miles\;per\;day[/tex]

Rearrange the rate formula to isolate time:

[tex]\implies \sf Time=\dfrac{Distance}{Rate}[/tex]

To find how long it will take for Jaime to run 96 miles, substitute the distance and rate into the formula and solve for time:

[tex]\implies \sf Time=\dfrac{96\;miles}{\frac{8 \;miles}{3\;days}}[/tex]

[tex]\implies \sf Time=96\;miles \times \dfrac{3\;days}{8\;miles}[/tex]

[tex]\implies \sf Time= \dfrac{288}{8}\;days[/tex]

[tex]\implies \sf Time= 36\;days[/tex]

Therefore, it will take Jaime 36 days to run 96 miles.

The population will exceed 2627 after approximately 6.08 units of time.

A lοgarithm is a mathematical functiοn that tells us what expοnent is needed tο prοduce a given number, when that number is expressed as a pοwer οf a fixed base. In οther wοrds, lοgarithms tell us hοw many times we need tο multiply the base by itself tο get the desired number.

To solve for t when the population exceeds 2627, we can set the equation equal to 2627 and solve for t:

p(t) = 1000[tex]e^{(0.21t)}[/tex] = 2627

Dividing both sides by 1000, we get:

[tex]e^{(0.21t)}[/tex] = 2.627

Taking the natural logarithm of both sides, we get:

0.21t = ln(2.627)

Solving for t, we get: t = ln(2.627)/0.21 ≈ 6.08

Therefore, the population will exceed 2627 after approximately 6.08 units of time.

Learn more about exponential growth on:

brainly.com/question/12490064

#SPJ1

Each product of the fractions are

Part1. =17.33

Part2.= 0.73

Part3.=45.93

Multiplication is a mathematical operation that involves combining two or more numbers to obtain a product or result. Multiplication is a fundamental arithmetic operation that is used in a wide range of mathematical applications, from simple calculations such as calculating the area of a rectangle, to more complex problems in algebra, geometry, and calculus.

⅔×26

Multiplying 2 and 26, we get

52/3

Now, dividing it with3, we get

17.33

⅞×5/6

Multiplying 7 and 5 and 8 and 6, we get

35/48

Now, dividing 35 and 48, we get

.73

5 ⅕× 8 ×⅚

Solving the improper fractions;

26/5×53/6

Multiplying 26 and 53 and 5  and 6, we get

1378/30

Now, dividing 35 and 48, we get

45.93.

To know more about fractions, visit:

https://brainly.com/question/10708469

#SPJ1

Answer:

4/64

Step-by-step explanation:

The spinner is independent (the total won't be effected)

we know there is 2 whites with 8 coloured option.

we want the probability of getting two whites.

2/8 x 2/8 = 4/64

there is 3 ways to work out probability, fraction, decimal and percentage (i'd personally say fraction is the most easiest)