The side of the base of a square prism is decreasing at a rate of 7 kilometers per minute and the height of the prism is increasing at a rate of 10 kilometers per minute. At a certain instant, the base's side is 4 kilometers and the height is 9 kilometers.

Answer:

27.5 in (69.85 cm)

Step-by-step explanation:

The normal growth rate for an infant after birth is 1 in per month.

After six month, the infant will be 27.5 in which is equivalent to 69.85 cm.

Answer: In total Katy earned $190

Katy earn  $190 in all on Friday, Saturday, and Sunday.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS is; Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given that Katy earns $10 per hour. She worked 4 hours on Friday, 9 hours on Saturday, and 6 hours on Sunday. ​

Therefore, total time = 4+9+6=19

Then 19 x 10 = 190

so, she made $190

Hence, Katy earn  $190 in all on Friday, Saturday, and Sunday.

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Final answer:

The estimated tuition at this college in 2020 is $51,137.

Explanation:

To find the equation to determine the tuition y for x years after 2000, we need to use the given information: the annual tuition in 2000 was $20,500 and it increased to $45,120 in 2018.

Let's calculate the rate of increase per year:

The change in tuition over the number of years is:

(Tuition in 2018 - Tuition in 2000) / (Year in 2018 - Year in 2000) = (45,120 - 20,500) / (2018 - 2000)

Now, we can use this rate of increase to find the tuition in any given year x:

Tuition in a specific year = Tuition in 2000 + (Rate of increase per year) * x

To estimate the tuition in 2020, we substitute x = 20 into the equation:

Tuition in 2020 = 20,500 + ((45,120 - 20,500) / (2018 - 2000)) * 20 = $51,137

Answer:

Interval level of measurement

Step-by-step explanation:

Interval level of measurement:

Thus,

Interval level of measurement is the level of measurement where outcomes are based on some underlying continuum where it is possible to speak about how much more a higher performance is than a lower one:

Answer:

biases

Step-by-step explanation

i toke the test

Bias is the systematic tendency to use information about others.

The propensity to give facts that can be quickly recalled from memory as much weight as possible while making a decision.

You may reap the rewards of group judgments while avoiding frequent challenges to effective judgment in groups by managing group judgment processes well. Fundamental judgment ideas may be learned, but like with other abilities, practice is required. A professional judgment framework is a useful example of a sound decision-making procedure and enables you to identify potential areas for error. A shared framework enables the use of a common language and understanding. It normally pays off to put in some work up front, especially in the initial few stages of the judging process.

Therefore, A few properties of systematic bias are Heuristics are quite effective; typically speaking, benefits outweigh costs; yet, they may lead to biased judgment.

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Answer:

[tex] k = - \frac{40 W/m^2}{\frac{20-40 C}{0.05 m}}= 0.1 \frac{W}{m C}[/tex]

Step-by-step explanation:

Previous concepts

The Fourier's law, states that the "rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows".

And we have the following formula given:

[tex] q_x = -k A \frac{dT}{dx}[/tex]

For this case we have the following data given:

[tex] L= 50 mm * \frac{1m}{1000 mm}=0.05m[/tex]

[tex] T_i = 40 C[/tex] represent the inner surface temperature

[tex] T_o = 20 C[/tex] represent the outer surface temperature

[tex] \frac{q_x}{A} = 40 W/m^2 [/tex] represent the heat flux

So then we are interested on the value of k.

Solution to the problem

if we solve for the value of k from the formula:

[tex] q_x = -k A \frac{dT}{dx}[/tex]

We got:

[tex] k = - \frac{q_x}{A \frac{dT}{dx}}[/tex]

We can rewrite this expression like this:

[tex] k = - \frac{q_x}{A \frac{T_o -T_i}{L}}[/tex]

And if we replace the values given we got:

[tex] k = - \frac{40 W/m^2}{\frac{20-40 C}{0.05 m}}= 0.1 \frac{W}{m C}[/tex]

Using Fourier's law of heat conduction, the thermal conductivity of the wood slab is calculated to be 0.1 W/m·K given a heat flux of 40 W/m², a temperature difference of 20°C, and a thickness of 50 mm.

The student is asking about the thermal conductivity of a wood slab, given its thickness, the temperature difference across it, and the heat flux. To find the thermal conductivity (k), we can use Fourier's law of heat conduction which states:

Q/t = k × A × (T2 − T1) / d

where:

Rearranging the formula to solve for k gives:

k = Q/t × d / (T2 − T1)

Plugging in the values:

k = 40 W/m² × 0.05 m / 20°C

k = 0.1 W/m·K

So, the thermal conductivity of the wood is 0.1 W/m·K.

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Answer:

[tex]CD = 7.8[/tex]

Step-by-step explanation:

Given:

Δ DBC is a right angled triangle.

[tex]\angle B = 90\°\\\\\angle C = 59\°[/tex]

BC = 4

We need to find the value of CD

Solution:

Now we know that:

[tex]cos\ \theta = \frac{adjacent \ side}{hypotenuse}[/tex]

So we can say that;

[tex]Cos \angle C =\frac{BC}{CD}[/tex]

Substituting the given values we get;

[tex]Cos\ 59 = \frac{4}{CD}\\\\\\CD = \frac{4}{Cos\ 59} = 7.766[/tex]

Rounding to nearest tenth we get;

[tex]CD = 7.8[/tex]

Hence the Value of CD is 7.8.

Answer:

Variability expected among these Proportions is given by Standard deviation = 0.125

Step-by-step explanation:

The probability of tossing heads is the same for a fair coin as the probability of tossing tails.

The probability of tossing heads is then 1 chance out of 2

P = 1/2 = 0.5

The standard deviation of the sample distribution of the sample proportion = √Pq/n

Standard deviation = √p(1-p)/n

= √0.5(1-0.5)/16

Standard deviation = 0.125

The variability among the proportions of heads obtained in the coin tosses is due to the random nature of the experiment. The law of large numbers explains that as the number of tosses increases, the observed relative frequencies of heads will approach the theoretical probability of 0.5.

The amount of variability that can be expected among the proportions of heads obtained by the students tossing a coin 16 times can be determined by understanding the concept of probability.

In a single coin toss, the probability of getting a head is 0.5. However, when the coin is tossed more times, the observed proportions of heads will vary from the theoretical probability of 0.5.  

The variability among these proportions is attributed to the random nature of the coin tosses and is due to the fact that the short-term results of an experiment do not necessarily match the theoretical probability. The law of large numbers states that as the number of repetitions of an experiment is increased, the observed relative frequencies of heads will tend to become closer to the theoretical probability of 0.5.

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Answer:

Length of bases of the trapezoid are 5 inch and 15 inch.

Step-by-step explanation:

Let the length of the second base be 'x'.

Given:

one base of a trapezoid is 3 times the length of the second base.

So we can say that;

Length of the first base = [tex]3x[/tex]

Also Given:

the height of the trapezoid is 2 in smaller than the second base

So we can say that;

Height of the trapezoid = [tex]x-2[/tex]

Area of the trapezoid = 30

We need to find the length of both the bases.

Solution:

Now we know that;

Area of trapezoid is equal to half of the sum of the length of two bases multiplied by height of the trapezoid.

framing in equation form we get;

[tex]\frac{x+3x}{2}\times(x-2)=30\\\\\frac{4x}{2}\times (x-2)=30\\\\2x(x-2)=30[/tex]

Now Dividing both side by 2 we get;

[tex]\frac{2x}{2}(x-2)=\frac{30}{2}\\\\x(x-2)=15\\\\x^2-2x-15=0[/tex]

Now we will find the roots by factorizing the equation we get;

[tex]x^2-5x+3x-15=0\\\\x(x-5)+3(x-5)=0\\\\(x+3)(x-5)=0[/tex]

Now we find the values of x by solving separately we get;

[tex]x+3=0 \ \ \ \ Or \ \ \ \ \ \ x-5=0\\\\x=-3 \ \ \ \ \ \ \ Or \ \ \ \ \ \ x=5[/tex]

Now we have got 2 values of 'x' one positive and one negative.

Now we know that length of the base of trapezoid cannot be negative hence we will discard it and consider the positive value of 'x'.

Length of second base = 5 in

Length of first base = [tex]3x=3\times5 =15\ in[/tex]

Hence Length of base of the trapezoid are 5 inch and 15 inch.

Answer:

The answer to your question is the last choice

Step-by-step explanation:

                               [tex](4z^{8})^{-3}[/tex]

Process

1.- Use the exponent law "Power"

                               [tex]4^{-3} z^{(8)(-3)}[/tex]

2.- Simplify

                               [tex]4^{-3} z^{-24}[/tex]

3.- Use the exponent law "Negative exponent"

                               [tex]\frac{1}{4^{3} z^{24}}[/tex]

                               [tex]\frac{1}{64z^{24}}[/tex]

4.- Conclusion    

He should have applied the exponent -3 to 4 to get   [tex]\frac{1}{64z^{24}}[/tex]            

Answer:

d

Step-by-step explanation:

Answer:

The total area of the rectangle is found by counting the total number of 1 cm squares inside the rectangle.

Note: This question is missing some details.

A more complete question is this: Use a ruler to measure the side lengths of the rectangle in centimeters. Mark each centimeter with a point and connect the points to show the square units. Then, count the squares you drew to find the total area.

Step-by-step explanation:

This method is used to determine area of a rectangle by counting the square unit inside the given rectangle.

For example, if the measurement of the sides of the rectangle is 8 cm and 5 cm respectively. To find the area;

Step 1: Mark out 1 cm points on each side of the rectangle.

Step 2: Connect each of the points.

Step 3: Count the number  1 cm squares within the triangle. The total number of squares gives the area of the triangle.

In this example, the number of 1 cm squares will be found to be 40. So the area of the rectangle is 40 cm squares or 40 cm².

9514 1404 393

Answer:

  CD = 8 ft.

  BD = 8 ft.

Step-by-step explanation:

To make use of the SAS postulate, Anna needs to identify two sides on either side of congruent angles.

The only marked angle is the right angle. We know that AD is congruent to itself, so Anna also needs to use the segments CD and BD, which are on the other side of the right angle in the right triangles.

The two choices in which BD and CD have the same length are

Answer:

(4,0,-5)

Step-by-step explanation:

Since we move 4 points along +ve x-axis so,  x coordinate is 4

We did not move any point along y-axis so  y coordinate is 0

we moved 5 points along -ve z-axis so z coordinate is -5

so our position is (x,y,z) = (4,0,-5)

Answer: [tex]H'(4,-3)[/tex]

Step-by-step explanation:

For this exercise you must remember that the original figure (before a transformation) is called "Pre-Image" and the one obtained after the transformation is called "Image".

 A Translation is defined as a transformation in which the figure is moved a  fixed distance in a fixed direction. In this kind of transformatiosn the size and shape do not change and the figure is not flipped.

In this case you know that the Pre-Image is the Triangle FGH.

You can identify in the picture that its vertex H has these coordinates:

[tex]H(1,-2)[/tex]

Where:

[tex]x=1\\y=-2[/tex]

Since the rule is:

[tex](x,y)[/tex] → [tex](x+3,y-1)[/tex]

You can substitute the coordinates of H into the given rule in order to find the coordinates of H'. This is:

[tex]H'=(1+3,-2-1)=(4,-3)[/tex]

The coordinates of H after translation using the rule (x,y) > (x+3,y-1) are obtained by adding 3 to the x-coordinate and subtracting 1 from the y-coordinate of H's original position.

To determine the coordinates of H after applying the translation rule (x,y) > (x+3,y-1), you have to add 3 to the x-coordinate and subtract 1 from the y-coordinate of point H's original position.

For example, if H originally has coordinates (a,b), then after the translation, the new coordinates of H will be (a+3, b-1).

The given translation rule does not change regardless of the element being translated, be it point or vector, as the rule is applied to each coordinate independently.

Therefore, if you know the original coordinates of point H, you just apply the rule directly to find the translated coordinates.

Answer:

The container can hold 24 gallons of water.

Step-by-step explanation:

Let the Amount of water in gallons container can hold be 'x'.

Now given:

the container that holds the water for the football team is  1/4 full.

therefore Amount of water in container = [tex]\frac14x[/tex]

We need to find the Amount of water in gallons container can hold.

Solution:

Now given:

after pouring in 10 gallons of water, it is 2/3 full.

So equation can be framed as;

[tex]\frac14x+10=\frac23x[/tex]

Now Combining the like terms we get;

[tex]10=\frac23x-\frac14x[/tex]

Now We will use LCM to make the denominator common we get;

[tex]10=\frac{2x\times4}{3\times4}-\frac{1x\times3}{4\times3}\\\\10=\frac{8x}{12}-\frac{3x}{12}[/tex]

Now the denominators are common so we will solve the numerator we get;

[tex]10=\frac{8x-3x}{12}\\\\10=\frac{5x}{12}[/tex]

Now Multiplying both side by [tex]\frac{8}{12}[/tex] we get;

[tex]10\times\frac{12}{5}=\frac{5x}{12}\times \frac{12}{5}\\\\x=24 \ gallons[/tex]

Hence The container can hold 24 gallons of water.

Answer:

i) amplitude is 4/2 =2

ii) period of the graph  = 3.14 ( radians), (or 180°)

iii) the frequency of the given function is f  = 2Hz ( hertz).

iv) The midline for the function is y = -3.

v) The maximum value of the problem of the function is -1.

vi) the minimum value of the function is -5.

Step-by-step explanation:

i) the Peak to Peak is = -1 - (-5) = 4

  therefore amplitude is 4/2 =2

ii) The period of the graph  = 3.14

iii) one cycle is over 2π radians

    one cycle of the given function is over π radians. Therefore the given    

     function will have 2 cycles over 2π radians. Therefore the frequency of the given function is f  = 2 hertz.

iv) The midline for the function is y = -3.

v) The maximum value of the problem of the function is -1

vi) the minimum value of the function is -5.

Answer:

Step-by-step explanation:Original price is $1200.and he paid $700 to start with meaning he has $500 more to pay

$1200-$700=$500

If he now pays $50 every months then he has 10months to pay up

$500/$50=10./

Answer: the maximum length of the sandbox is 42 feet.

the maximum width of the sandbox is 16 feet.

Step-by-step explanation:

Let L represent the length of the sandbox.

Let W represent the width of the sandbox.

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

The perimeter of the sandbox must be less than or equal to 116 feet. This means that

2(L + W) ≤ 116

Dividing through by 2, it becomes

L + W ≤ 116/2

L + W ≤ 58 - - - - - - - - -1

The length of the sandbox will be 6 less than 3 times the width. This means that

L = 3W - 6

Substituting L = 3W - 6 into equation 1, it becomes

3W - 6 + W ≤ 58

4W ≤ 58 + 6

4W ≤ 64

W ≤ 64/4

W ≤ 16

L = 3W - 6 = 3 × 16 - 6

L ≤ 42

Answer:

What am I suppose to do?

Step-by-step explanation:

Answer:

From the plot and from inspection of the equation the following are true

a.) The domain is the set of all real numbers greater than 2

b.) The x-intercept = (10,0) and there is no y-intercept

c.) A vertical asymptote is at x = 2

f.) The graph of g(x) is symmetric to its inverse exponential function over the line y = x

Step-by-step explanation:

The plot of the graph is attached.

From the plot and from inspection of the equation the following are true

a.) The domain is the set of all real numbers greater than 2

b.) The x-intercept = (10,0) and there is no y-intercept

c.) A vertical asymptote is at x = 2

f.) The graph of g(x) is symmetric to its inverse exponential function over the line y = x

Answer:Jason is 5 years old.

John is 4 years old.

Jackson is 12 years old.

Step-by-step explanation:

Let x represent the age of Jason.

Let y represent the age of John.

Let z represent the age of Jackson.

The ages of three siblings Jason John and Jackson totals 21 years. It means that

x + y + z = 21 - - - - - - - - - - -1

Jason is one year older than John. It means that

x = y + 1

Jackson is three times as old as John. It means that

z = 3y

Substituting x = y + 1 and z = 3y into equation 1, it becomes

y + 1 + y + 3y = 21

5y = 21 - 1 = 20

y = 20/5 = 4

x = y + 1 = 4 + 1

x = 5

z = 3y = 3 × 4

z = 12

Answer:

a.

For all non zero fraction 1(1/x), 1/x is a fraction

For all 1/(1/x), if 1/(1/x) is non zero, 1/x is a fraction

b.

For all polynomial function f(x) = x³ + x² + x - 1, the derivative (dy/dx) is a polynomial function

For all f(x) x³ + x² + x - 1, if f(x) is polynomial, f'(x) is a polynomial function

c.

For all angles x,y,z of a triangle, the sum, x + y + z = 180

For all x,y,z, if x,y and z are the angles of a triangle, x+y+z = 180

d.

For all irrational numbers x, -x is irrational

For all x, if x is irrational then -x irrational.

e.

For two integers, x and y, the sum x+y is an integer

For x,y if x and y are integers, then x + y is an integer

f.

For two fractions, x/y and a/b the product ax/by is a fraction

For x/y and a/b, if x/y and a/b are fractions then ax/by is a fraction

Final answer:

The statements have been rewritten in both universal quantification and conditional forms to describe relationships in mathematics, such as the property of being a fraction, polynomial function, or summing up to 180 degrees for triangles.

Explanation:

To rephrase the given statements in mathematical terms:

The total water needed to fill the pool is 75π cubic feet.

Given: The pool is 10 feet in diameter and 3 feet tall. To find: The total water needed to fill the pool using V = πr²h formula.

Calculations: Radius (r) = 5 feet, Height (h) = 3 feet. Substitute values into formula: V = π(5)^2(3) = 75π cubic feet.

Answer: The total water needed to fill the pool is 75π cubic feet.

Answer:

Mike estimated the difference to be 72.

The actual difference is 72.74.

Step-by-step explanation:

Mike estimated 79 as 79.44 and 7 as 6.7, therefore Mike estimated the difference, this way:

79 - 7 = 72

Actual difference of the numbers is:

79.44 - 6.7 = 72.74

Mike estimated the difference to be 72.

The actual difference is 72.74.

Andre can complete 1.5 facts in one second.

Step-by-step explanation:

Given,

Number of multiplication facts completed in 90 seconds = 135

Therefore;

90 seconds = 135 facts

Dividing both sides by 90 to fins the facts per second

[tex]\frac{90}{90}\ seconds=\frac{135}{90}\ facts\\\\1\ second = 1.5\ facts[/tex]

Andre can complete 1.5 facts in one second.

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Andre can answer 1.5 multiplication facts per second by dividing the total number of facts he completed (135) by the time it took (90 seconds).

Andre has been answering multiplication facts at a consistent pace. To find out how many facts he can answer per second, we need to divide the total number of facts he answered by the total number of seconds it took him to answer them.

Andre answered 135 multiplication facts in 90 seconds.

To calculate the rate per second, the formula is:

Therefore, Andre can answer 1.5 facts per second.

Answer:

Step-by-step explanation:

(2x+y)(3x²+y)=2x(3x²+y)+y(3x²+y)=6x³+2xy+3x²y+y²=6x³+3x²y+2xy+y²

Answer:

.

Step-by-step explanation:

a.) 72 ÷ 8 × 9 = 81 (we divide 72 by 8 first then multiply the result with 9)

b.) -72 ÷ 8 × 9 = -81 (it's same with a only differ by negative sign)

c.) 72 ÷ (-8) × 9 = -81 (dividing 72 by -8 will give us -9 and multiplying -9 by -9 will give the result of -81)

d.) 72 ÷ 8 × (-9) = -81 (divide 72 by 8 and it will be 9, mutliply it by -9 and again it will give -81)

e.) -72 ÷ 8 × (-9) = 81 (divide -72 by 8 and it will be -9 multiplying it by -9 will give a positive 81 since two negative signed numbers multiplied or divided gives positive result)

Answer:

A)81

B)-81

C)-81

D)-81

E)81

Step-by-step explanation:

Answer:D

Step-by-step explanation:

The solution is: : $117,783.05 will be her balloon payment at the end of 7 years if she chooses this mortgage.

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

here, we have,

Step 1

Calculate the number of monthly payments for 7 years.

The formula we would be using is given as:

Monthly payment = [Loan amount × (rate/number of year)] ÷ [1 - (1 +r/n)^nt)]

Loan amount =$146,000

Rate = 4.75% = 0.0475

n = number of payments = 12

t= number of years = 23

Monthly payment = [ 146,000× (0.0475/12)] ÷ [1 - (1 +0.0475/12)^-276)]

Monthly payment = $870.49

Step 2

Calculate the amount left after 7 years using the formula

Ballon payment after 7 years = Loan amount ( 1 + r)ⁿ - P[(1 +r)ⁿ - 1 /r]

r = 4.75% for 12 years

= 146,000( 1 + 0.0475/12)^84 - 870.49[((1 + 0.0475/12)^84 - 1)/0.0475/12]

= $117,783.05

Hence, The solution is: : $117,783.05 will be her balloon payment at the end of 7 years if she chooses this mortgage.

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complete question:

Yvette is considering a 7/23 balloon mortgage with an interest rate of 4.75%

to purchase a house for $146,000. What will be her balloon payment at the end of

7 years if she chooses this mortgage?

Step-by-step explanation:

To find the solution, Tanisha can graph each side of the equation as its own function:

y₁ = log₃(5x)

y₂ = log₅(2x + 8)

The solution is where the two curves cross.  From the graph, that happens at x ≈ 0.957.

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