Problem of the Week Problem C Ice Box A metal box in the form of a rectangular prism has an 18 cm by 22 cm base and a height of 77 cm. The box is to be filled with water, which will then be frozen. When water freezes it expands by approximately 10%. Determine the maximum depth to which the box can be filled with water so that when the water freezes, the ice does not go above the top of the container.​

The required appropriate properties to fit the black space is given as,
(a) Congruent angles
(b) Addition of angles
(c) straight angles
(d) Subtraction of angles.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

It is given that m ∠ AOB = 42 ∘ and m ∠ EOF = 66 ∘ . By the definition of congruent angles, ∠ EOF ≅ ∠ BOC. Therefore, m ∠ BOC = 66 ∘ . In the addition, m ∠ AOC = 108 ∘ , and by definition of the straight angle, m ∠ AOC + m ∠ COD = 180 ∘ . After application of the subtraction of the angle, m ∠ COD = 72 ∘ .

Thus, the required appropriate properties to fit the black space is given as,
(a) Congruent angles
(b) Addition of angles
(c) straight angles
(d) Subtraction of angles.

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Answer:

It is given that m∠AOB = 42º and m∠EOF = 66º. By the vertical angles theorem, ∠EOF ≅ ∠BOC. By the angle addition postulate, m∠AOC = 108º, and by the linear pair theorem, m∠AOC + m∠COD = 108º. After the application of the subtraction property of equality, m∠ COD = 72º.

Step - by - step

first box: vertical angles theorem

second box: angle addition postulate

third box:  linear pair theorem

fourth box: subtraction property of equality

Answer:

[tex]\frac{7d}{15}[/tex]

Step-by-step explanation:

The correct static test is [tex]$z=\frac{0.30-0.25}{\sqrt{\frac{0.30(0.70)}{80}}}$[/tex]

Number of residents in a certain area with wingspan measurements larger than 10 inches = =30% = 0.30

[tex]$=p_o=30 \%=0.30$[/tex]

20 of the 80 bats in a n=80 random sample from outside the area have wingspan measurements larger than 10 inches to ascertain whether there is any variation in the proportion of bats with a wing span more than 10 inches that live outside the region and those that do.

In response to the query;

an investigation using a one-sample z-test,

The following definition applies to the hypothesis:

[tex]$p=\frac{x}{n}$[/tex]

[tex]$p=\frac{20}{80}$[/tex]

H0: The fraction of bats with a wingspan larger than 10 inches that reside outside of the region and those that do so are equal.

= p - p₀ = 0.

Ha! There is a discrepancy between the percentage of bats with a wingspan larger than 10 inches that reside outside of the region and those that do.

= p - p₀ ≠ 0.

n = 80 , X = 20 , p₀ = 0.30

The analysis will be conducted using the z-test for a single proportion.

Following is a sample of the percentage of bats residing outside the area whose wingspan is larger than 10 inches:

The test statistic is,

[tex]& z=\frac{p-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}} \\[/tex]

[tex]& z=\frac{0.25-0.30}{\sqrt{\frac{0.30(1-0.30)}{80}}}[/tex]

The correct test statistic is

[tex]$=\frac{0.30-0.25}{\sqrt{\frac{0.30 \times 0.70)}{80}}}$[/tex]

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Answer:

y = [tex]-\frac{3}{4}[/tex] x

Step-by-step explanation:

y = mx + b , where "m" is a slope and "b" is an y-intercept.

If a║b ⇒ [tex]m_{a}[/tex] = [tex]m_{b}[/tex] and [tex]b_{a}[/tex] ≠ [tex]b_{b}[/tex]

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~

y = [tex]-\frac{3}{4}[/tex] x + 1

( 8 , - 6 )

y - ( - 6 ) = [tex]-\frac{3}{4}[/tex] ( x - 8 )

y + 6 = [tex]-\frac{3}{4}[/tex] x + 6

y = [tex]-\frac{3}{4}[/tex] x

Answer:

Step-by-step explanation:

Answer:

244.5

Step-by-step explanation:

Use A Budgeting Calc This Anwser Is Correct

Answer:

see below

Step-by-step explanation:

3²-5 = -5x-3

9-5 =- 5x-3

-5x = 7

so x= -7/5

According to the given data, the firm in question must be a price-taker, which is a perfectly competitive firm.

A price-taker is basically an individual or a particular company that must accept prices that are prevailing in a market and lacks the market share to be able to influence the market price on its own. All the economic participants can be considered to be price-takers in a market consisting of perfect competition.

In the given data set, the marginal revenue is constant which is very typical for competitive firms. This happens because the market decides the optimal price level and companies do not have much say over the price. This is a way by which they can maximize profits.

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When a test is two-sided and one-sided: We will reject the null hypothesis at the = X 0.01 0.050. 10 significance level if the value of interest falls outside a 95% confidence interval. If the value of interest falls outside a 99% confidence interval, the null hypothesis will be rejected at the = 0.010.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used. The confidence interval is the range of values within which you expect your estimate to fall a certain percentage of the time if you repeat your experiment or re-sample the population in the same manner.

Here,

When a test is two-sided and one-sided: If the value of interest falls outside a 95% confidence interval, we will reject the null hypothesis at the = X 0.01 0.050. 10 significance level. The null hypothesis will be rejected at = 0.010 if the value of interest falls outside a 99% confidence interval.

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Answer:

two sided.

.05

.01

Step-by-step explanation:

This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.

What is equal angles ?

Equal angles can be defined as the angles which are equal .

Given ,

The picture shows two ladders propped against facing walls. The end of the first ladder is 5m above the base of the second wall. The second

ladder is 5m above the base of the first wall.

the angles ∠BAD and ∠ADC are alternate angles, and therefore equal. Likewise, angles ∠ABC and BCD are also alternate and therefore equal.

∠BEA and ∠CED are opposite, which means that they are equal. You can see these equal angles in the diagram on the right.

This means that the triangles ABE and DCE have the same angles as each other, and are therefore similar.

so,

This means:

AE/ED=AB/DC=5m/10m=1/2

Therefore AE=1/3 AD.

This means E is 1/3 of the way up from the floor to D, so is at a height of

This means E is 13 of the way up from the floor to D, so is at a height of 10m/ 3=3 1/3m

If instead B is a metres above the floor, then:

AE/ED=AB/DC=a/10

Therefore AE=a/10+a AD.

This means E is the same fraction of the 10m above the floor, so is 10a/10+a metres above the floor.

If instead D is b metres above the floor, then:

AE/ED=AB/DC=a/b

Therefore AE=a/a+b AD.

This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.

Therefore, This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.

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If Jennifer wants to use the money to buy a new bicycle in 2 years, she can spend (future value) $388.54 on the bike as the account earns 13% interest, compounded monthly.

Compound interest is a system of interest computation where interest accumulates on the principal and previously accumulated interests.

Compounding the present value means adding interest to the principal amount when calculating subsequent interests.

N (# of periods) = 24 months (2 years x 12)

I/Y (Interest per year) = 13%

PV (Present Value) = $300

PMT (Periodic Payment) = $0

Results:

Future Value (F) = $388.54

Total Interest = $88.54

Thus, with a deposit of $300, Jennifer can spend $388.54 after earning 13% monthly compounded interest.

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Selecting elements from an ordered sampling frame is a statistical approach used in survey methodology known as systematic sampling and in the given situation (D) systematic sampling would be the best.

Systematic sampling is a statistical technique used in survey methodology that involves choosing components from an ordered sampling frame.

An equiprobability approach is the most typical type of systematic sampling.

This method treats the list's evolution in a cyclical manner, returning to the top after it has been completed.

The sampling process begins with the random selection of one element from the list, followed by the selection of every kth element in the frame, where k is the sampling interval, also known as the skip, and is equal to:
k = N/n.

Therefore, in the given situation (D) systematic sampling would be the best.

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Answer: 5

Step-by-step explanation:

The area of the square with side length [tex]5x[/tex] is [tex]25x^2[/tex].

The area of the square with side length [tex]2x[/tex] is [tex]4x^2[/tex].

The area of the triangle is [tex]\frac{1}{2}(2x)(5x)=5x^2[/tex].

It follows that [tex]25x^2 +4x^2 +5x^2=850 \implies x=5[/tex]. Note that we reject [tex]x=-5[/tex] since the length cannot be negative.

The sampling distribution of the sample mean based on samples of size 2 for a population can be approximated by a normal distribution.

The histogram of the sampling distribution would therefore look like a bell-shaped curve. The mean of the sampling distribution is equal to the population mean, and the standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size (in this case, 2).

Therefore, the formula for the sampling distribution of the sample mean for a population of size 2 is:

Mean = Population Mean

Standard Deviation = Population Standard Deviation / √2

The histogram of the sampling distribution would look like a bell-shaped curve with the mean and standard deviation determined by the formula above.

Therefore, the histogram most likely representing the sampling distribution of the sample mean based on samples of size 2 for the population is a bell-shaped curve with the mean and standard deviation determined by the formula above.

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Answer:

12x^4y^7

Step-by-step explanation:

base(b)=8x^3y^5

height(h) =3xy^2

Area= (b x h)/2 =12x^4y^7

Answer:

[tex]A = 12x^4y^7[/tex]

Step-by-step explanation:

The formula for the area of a triangle is:

[tex]A = \dfrac{1}{2}bh[/tex]

where [tex]b[/tex] is the length of the triangle's base and [tex]h[/tex] is the length of the triangle's height.

In this problem, we are given the length of the base of the triangle as [tex]8x^3y^5[/tex] and the length of the height of the triangle as [tex]3xy^2[/tex].

Thus, the area of the given triangle is:

[tex]A = \dfrac{1}{2} \cdot 8x^3y^5 \cdot 3xy^2[/tex]

We can simplify this by combining like terms and using the exponent addition rule ([tex]x^a \cdot x^b = x^{a+b}[/tex]).

[tex]A =\left(\dfrac{1}{2} \cdot 8 \cdot 3 \right)(x^3 \cdot x)(y^5 \cdot y^2)[/tex]

[tex]A = (4 \cdot 3)(x^{3 + 1})(y^{5+2})[/tex]

[tex]A = 12x^4y^7[/tex]

The missing length is given as follows:

LN = 44.

The theorem used to solve this problem is given as follows:

A line parallel to one side of a triangle divides the other two proportionately.

The parallel lines for this triangle are given as follows:

VU and LM.

Hence the proportional relationship regarding the remaining side lengths is given as follows:

x/24 = 11/8

Applying cross multiplication, we have that:

8x = 24 x 11

x = 3 x 11

x = 33.

Hence the missing length is given as follows:

LN = 33 + 11

LN = 44.

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The x-intercept of the line is (-1, 0). And the y-intercept of the line is not there.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, the line is parallel to the y-axis, then the equation of the line parallel to the y-axis will be given as,

x = c

From the equation, the line is passing through (-1, 0), then we have

- 1 = c

c = - 1

Then the equation of the line is x = -1. Then the x-intercept of the line is (-1, 0). And the y-intercept of the line is not there.

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The limit of f(x) as x approaches 0 is 1.

The limit of f of x as x approaches 0 can be calculated using limit theorems. First, we rewrite the function as:

f(x) = (x + 1) / (1 / (x - 1))

Then, we can simplify this by multiplying both the numerator and denominator by (x - 1):

f(x) = (x + 1)(x - 1) / 1

Next, we can apply the limit theorem that states the limit of a product is the product of the limits. Thus, we can calculate the limit as:

lim f(x) = lim (x + 1)(x - 1) / 1

= lim (x + 1) * lim (x - 1) / 1

= 0 + 1 * 0 - 1 / 1

= 1 / 1

= 1

Therefore, the limit of f(x) as x approaches 0 is 1.

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The plot inverse function g^-1(x) is attached below.

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

X           3    4    6   10   18

g^-1(x)    0   1/2   1    3/2   2

In the given table x and g^-1(x) is shown.

Hence, THe plot inverse function g^-1(x) is attached below.

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The account balance after 5 years will be $3935.53.

Compound interest is interest that is paid on both principal and interest at regular intervals. The first year of compound interest is similar to the first year of simple interest, but the difference begins in the second year.

Continuously compounded interest means that an account balance is constantly earning interest and reinvesting that interest so that it, too, earns interest.

Given that Jessica invests $3,065 in a savings account with an annual interest rate of 5% compounded continuously.

The account balance after 5 years will be calculated as:-

[tex]P(t) = P_oe^{rt}\\P(t) = 3065\times e^{0.05\times 5}\\P(t) = \$3935.53[/tex]

Therefore, the balance in the account after 5 years will be $3935.53.

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The two cuts that are being roasted for each time-temperature combination are an example of replication.

Option (c) is correct.

What is temperature?

Temperature is a measure of the average thermal energy of the particles in a substance. It is a scalar quantity, meaning it has only a magnitude and not a direction. The most commonly used unit of temperature measurement is the degree Celsius (°C) or the degree Fahrenheit (°F), but it can also be measured in Kelvin (K) in scientific and engineering applications.

Given options are:

(a) The two cuts that are being roasted for each time-temperature combination are an example of conduction

(b) The two cuts that are being roasted for each time-temperature combination are an example of convection

(c) The two cuts that are being roasted for each time-temperature combination are an example of replication

(d) None of the above

(c) The two cuts that are being roasted for each time-temperature combination are an example of replication.

In the question it is given that  From 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. Here it is an act of copying the exact sahpe size of the lamb in all cuts, which is nothing but replication. Moreover, this replication can help in proper comparision.

Hence, The two cuts that are being roasted for each time-temperature combination are an example of replication.

Option (c) is correct.

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Answer:

Step-by-step explanation:

d = 6 would not be a solution to the inequality below because it would make the inequality untrue! Plugging in, we get:

13 < d + 3

13 < 6 + 3
13 < 9
We know that 9 is not a solution to the inequality!

To solve, we isolate the d, and from there we can find all values that are a solution to the inequality to the solution!

[tex]13 < d + 3\\\\13 - 3 < d\\\\10 < d[/tex]

Thus, one can say that the solutions to the inequality are: [R, d > 10]!

if b is the span of the given vectors, so we can express b as the linear combination of the other given two vector.

given that,

[tex]a_{1} =\left[\begin{array}{ccc}-1&\\3&\\-1\end{array}\right] , a_{2} =\left[\begin{array}{ccc}-2\\-3\\6\end{array}\right] , b=\left[\begin{array}{ccc}-6\\9\\2\end{array}\right] \\\\\\\\\\\\\\\\\\\\\\\\[/tex]

We have determined that b is span of given vector a1 and a2.

we can write.   [tex]a_{1} =(-1,-3,-1) ,a_{2}=(-2,-3,6) , b=(-6,9,2)[/tex] .

A vector is a quantity that has magnitude and direction.

if x,y,z...., v are vectors and a,b,c....k are scalars then the linear combination is ax+by+cz+......+kv  

The set of linear combinations is called span for set of vectors.

So, b is span of given vector.

[tex]b=(c)a_{1} +(d)a_{2}[/tex]   ...... equation (A)

where c and d are scalars.

Now,

[tex](-6,9,2)=c(-1,3,-1)+d(-2,-3,6)\\(-6,9,2)=(-c,3c,-c)+(-2d,-3d,6d)\\(-6,9,2)=(-c-2d,3c-3d,-c+6d)\\[/tex]

equating the equations,

[tex]-c-2d=-6\\3c-3d=9\\-c+6d=2\\[/tex]

now we shall solve the above linear equations.[tex]subtract \\-c-2d-(-c+6d) = -6-2\\-8d=-8\\d=1\\now, \-c=-6+2d\\c=6-2=4\\c=4[/tex]

So, value of scalars c, d satisfied equation A,

thus, b is span of given vector a1 and a2.

The complete question is.

Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors. a1=[-1 3 -1], a2=[-2 -3 6]= [-6 9 2]

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Using the equation

Since Pat is the CEO of Pat's Pickle-Packing Plant, but can still pack 18 jars of pickles per hour. Kim, a rising star in the industry, packs 24 jars per hour. Kim arrived at work at 9:00 am one day to find that Pat had been packing pickles since

7:30 am. Later that day, Kim had packed exactly the same number of jars as Pat.To find the time and number of jars picked, we solve an equation.

An equation is a mathematical expression that shows the relationship between two variables.

Let

Since Pat picks at a rate of 18 jars of pickles per hour, the number of jars Pat picks is n = 18t

Also, Kim picks at a rate of 24 jars per hour, 1.5 hours later the number of jars Kim picks is n' = 24(t + 1.5)

Since n = n', we have that

18t = 24(t - 1.5)

18t = 24t - 36

18t - 24t = -36

-6t = -36

t = -36/-6

t = 6 hours

Since Kim's time is t - 1.5 = 6 - 1.5 = 4.5 hours

To find the number of jars each picked, substitute t = 6 into n. so, we have that

n = 18t

= 18(6)

= 108 jars

So,

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According to the solving the exponential form of the given number is as follows:

= 6² × 7⁴

= (-104)³

Bases and powers are employed in the exponential form to write numbers. It informs us of the amount of times we must actually multiply a number in order to obtain the answer. When we write the number 125 as 53, for instance, we can see that it is the third power of 5, or the number 125, which looks to be a typical three-digit number when observed.

When a single integer is multiplied by itself a certain number of times, x, the equation y takes on the base component b to the power of x, which is the quantity being multiplied, and is known as the exponential form.

The exponential form of the given number is :

= 6х6х7х7x7x7

= 6² × 7⁴

The exponential form of the given number is :

= -104 x -104 x -104

= (-104)³

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The translated function g(x) can be written as:

g(x) = (x + 2)^2

First, remember that an horizontal shift of N units applied to a function f(x) is:

g(x) = f(x + N)

if N > 0, the shift is to the right.

if N < 0, the shift is to the left.

Here we want a shift of 2 units to the left is:

g(x) = f(x + 2)

Where f(x) = x^3

Then the formula for the function g(x) is:

g(x) = (x + 2)^2

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If the sum of the squares on its other two sides equals the square of its greatest side.

Given:

AB = 9 cm CB = 40 cm AC = 41 cm

The Pythagorean Theorem states that

If the largest side's square is equal to the sum of the squares on the other two sides, the triangle will have a right angle.

AB = 9 cm CB = 40 cm AC = 41 cm

The Pythagorean Theorem states that

AC 2 =BC² +AB ²

41²=40²+9²

41 ²=40 ² +9 ²

1681 = 1600 + 81

1681 = 1681

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The question is incomplete

Show that the triangle ABC is a right-angled triangle; if:

AB = 9 cm, BC = 40 cm, and AC = 41 cm.

Answer:Use a graphing utility to graph the function and approximate (to two decimal places) any relative minima or maxima. (If an answer does not exist, enter DNE.)

f

(

x

)

=

x

3

−

3

x

2

−

x

+

3

relative minimum

(

x

,

y

)

=

c

Step-by-step explanation:

Answer:

The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology). 2nd Option B

Step-by-step explanation: I saw it in another one so id like to help

Answer: The commutative property is applied when finding the GCF by  taking the factor that has more than 1 factor other than itself(composite) and multiply them until you can no longer multiply. You then take the factors that are in common and multiply them.

Step-by-step explanation: my teacher made me use this way.