The table shows the cumulative number of minutes Alice practices clarinet for the first part of the school year:The table shows the cumulative number of minutes Alice practices clarinet for the first part of the school year:

Answer:

see explanation

Step-by-step explanation:

(a)

given y is inversely proportional to x³ then the equation relating them is

y = [tex]\frac{k}{x^3}[/tex] ← k is the constant of proportion

to find k use any of the ordered pairs from the table

using (1, 8 ) , then

8 = [tex]\frac{k}{1^3}[/tex] = [tex]\frac{k}{1}[/tex] ⇒ k = 8

y = [tex]\frac{8}{x^3}[/tex] ← equation of proportion

(b)

when y = 64 , then

64 = [tex]\frac{8}{x^3}[/tex] ( multiply both sides by x³ )

64x³ = 8 ( divide both sides by 64 )

x³ = [tex]\frac{8}{64}[/tex] = [tex]\frac{1}{8}[/tex] ( take cube root of both sides )

x = [tex]\sqrt[3]{\frac{1}{8} }[/tex] = [tex]\frac{1}{2}[/tex]

Answer: The answer is no solution because the x cancels out

Answer:

ƒ(−1) = −3

Explanation:

From the graph, we have the point (-1, -3).

This means that:

• When x=-1

• The value of f(x)=-3.

Therefore, the value of f(-1) is -3.

The constant of proportionality between x and y in the given graph above is determined as: 2.

The constant of proportionality of a proportional relationship between two variables, x and y, can be defined as the ratio of y to x, which is expressed as, k = y/x, where x and y are the coordinates of one point one the line that represents the proportional relationship.

Using the coordinates of a point on the graph, (2, 4), find the constant of proportionality, k:

Constant of proportionality (k) = y/x = 4/2

Constant of proportionality (k) = 2

Therefore, the constant of proportionality that represents the proportional relationship between the variables, x and y, is calculated as, 2.

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An airship propelled by some mechanical device travels five miles in ten minutes in the direction of the wind, but requires one hour to go back again to the starting point against the same wind. How long would it have taken to go the whole ten miles in a calm day without any wind? Hint: You don't have to use equations to solve this problem.

we have that

5 miles -------> 10 minutes (direction of the wind)

5 miles ------> 1 hour (against the same wind)

therefore

10 miles ------> ? (without any wind)

so

Let

x -----> speed of the wind

y -----> speed of the airship

direction of the wind

speed=d/t ------> 5/10=0.5 miles per min

against the same wind

speed=5/60=1/12 miles per min

so

x+y=0.5 ------> x=0.5-y -----> equation 1

y-x=1/12 -----> equation 2

solve the system

substitute equation 1 in equation 2

y-(0.5-y)=1/12

2y=(1/12)+1/2

2y=7/12

y=7/24=0.2917 miles per min

Find the value of x

x=(1/2)-7/24

x=5/24=0.2083 miles per min

therefore

10 miles without any wind

speed=d/t ------> t=d/speed

t=10/(7/24)

The sub-atomic particles located in the nucleus of an He^4 atom are 2 protons and 2 neutrons.

Helium belongs to double-electronic species, unlike alpha-particles which are devoid of electrons. The two electrons of Helium are accommodated in the 1s orbital, outside the nucleus.

Nucleons are always present in the nucleus of various elements. Nucleons collectively refer to protons and neutrons. In this case, 2 protons and 2 neutrons reside in the nucleus.

The number of protons is always equal to the atomic number of the element. The number of neutrons is always equal to the difference between the mass number and the atomic number of the element.

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Answer:

Explanation:

Here, we want to determine the type of correlation relationship

From science, we understand that engaging in exercise helps internal organs to function better. These are the sources of endurance

Exercising for a couple of more times, all things being equal means there will be more endurance. We can largely say that, for most people, it is expected that the higher the number of time spent exercising, the higher the endurance being built

Thus, we can conclude there is a positive correlation between the two

The arithmetic says we should subtract find the difference between 86.89 and 56.389.

Notice we have to put a place holder of 0 at the ending of 86.89 to do the subtraction. Then we have to borrow 1 from the hundredth term(9) of 86.890 to make 0 ten . so ten minus 9 should be 1. Then the difference of the hundreth term(8 - 8) is 0. 8 minus 3 is 5. 6 minus 6 is zero and finally 8 minus 5 is 3.

The answers are B and D

Answer: [tex]m=\frac{y2-y1}{x2-x1}[/tex]

Step-by-step explanation:

Choose two points and insert them for x and y.

(3,0) and (0,-4) will work

If you need extra help ask me, I'd be glad to help but i encourage you to try to solve it yourself

Answer:

Solve with the Quadratic Formula

Let's solve your equation step-by-step.

(3x)2+4x+1=0

Step 1: Simplify both sides of the equation.

9x2+4x+1=0

For this equation: a=9, b=4, c=1

9x2+4x+1=0

Step 2: Use quadratic formula with a=9, b=4, c=1.

x=

−b±√b2−4ac

2a

x=

−(4)±√(4)2−4(9)(1)

2(9)

x=

−4±√−20

18

Answer:

No real solutions.

Step-by-step explanation:

I did my best

Answer:

In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

You're very welcome my sir or ma'am

A triangle has all three angles summing up to 180. If two of the sides measure 40 degrees and 50 degrees, then the third side measures as follows;

The third angle, which is labelled as angle A measures 90 degrees, and that means the triangle is a "right angled triangle."

Step 1: Represent a with an unknown

Let a number be x

Step 2: Represent the given information with an equation

From the first statement, the sum of a number and seven is tripled can be represented with the equation below:

The second statement reflects that the result of the first statement is eight times a number. Eight times a number is

The result of the first statement and the second statement is

Step 3: Solve for the unknown

The solution of the unknown is as shown below:

Hence, the number is 4 1/5

Answer:

560 pounds

Step-by-step explanation:

175 pounds divided by 5 minutes.

= 35 pounds per minute

35 pounds per minute multiplied by 16 minutes

= 560 pounds

Answer:

[tex]\frac{11}{20}[/tex]

Step-by-step explanation:

2[tex]\frac{3}{4}[/tex] ÷ 5

Convert mixed number fraction to improper fraction

[tex]\frac{11}{4}[/tex] ÷ 5

To divide fractions we turn the second fraction (the one you want to divide by) upside down (this is now called a reciprocal) and we multiply

[tex]\frac{11}{4}[/tex] × [tex]\frac{1}{5}[/tex] = [tex]\frac{11}{20}[/tex]

We know that the probability of getting a head in a single coin is:

Now, we can calculate the probability of X out of N coins landing heads up with the binomal distribution:

With p = 0.5 and N = 4, we get:

Subtituting X = 1 ("getting one head"), we get that:

Answer:

0, 150, 100, 50 |    T=200-50x

Step-by-step explanation:

     So you start with 200 miles to go and you are going 50 miles per hour. In the first hour, 50 miles would have been completed meaning that you subtract 50 miles from the remaining distance. Same with the other hours.

     To put that in an equation, You would start with 200 and for every hour(x)you would subtract 50.

Answer:

-1, 0, 1, 2

Step-by-step explanation:

[tex]\sqrt{5-5} -1\\\sqrt{0} -1\\0-1\\-1[/tex]

[tex]\sqrt{6-5} -1\\\sqrt{1} -1\\1-1\\0[/tex]

[tex]\sqrt{9-5} -1\\\sqrt{4} -1\\2-1\\1[/tex]

[tex]\sqrt{14-5} -1\\\sqrt{9} -1\\3-1\\2[/tex]

1) an integer and a rational number

Explanation:

1) -√64 = -4

This is an integer.

Integers include natural numbers, the opposites of this numbers and zero.

-4 is a negative number and the opposite of the natural number 4

Hence -4 is an integer.

-4 can be written as a fraction:

-4 = -4/1

Hence, it is also a rational number

Answer:

B C and D

Step-by-step explanation:

Answer:

2π=6.2831853071795864769252867

Step 1: Let the remaining number of words be X.

The inequality equation becomes:

Hence, the number of words Petra has to write to have more than 1000 words should be greater than 316 words.

The fraction, 13 / 20 when converted to percentage is 65%.

A fraction is a non-whole number that has a numerator and a denominator. An example of a fraction is 13 / 20. 13 is the numerator and 20 is the denominator.

A percentage is when a fraction is converted to a number out of 100. In order to convert a fraction to a percentage, multiply the fraction by 100. The sign that represents percentage is %. Percentage is used to measure the frequency of a dataset.

In order to rewrite the fraction as a percentage, multiply the fraction by 100.

Percentage of times he hit the target = ( number of times he hit the target / number of hits) x 100

(13 / 20) x 100 = 65%

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It will take 28.5 seconds to Makayla to be twice as deep as Jonah.

What is an equation?

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15.

Given,

Jonah is at a depth of -20ft.

Makayla is at a depth of -12.5ft.

at the rate of descending is 0.5.

Given equation is

2(-20+0.25s) = -12.5-0.5s

-40 + 0.5 s = -12.5 -0.5s

0.5s + 0.5s = -12.5+40

1s = 28.5

Hence, the solution of the equation is 1s = 28.5.

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The speed is calculated as distance over time, so:

Replacing distance by 60 m and time by 3 seconds, we get:

The speed of the vehicle is 20 m/second

The table of values for the given equation is presented below:

x       y

-3    17

-2   2

-1    -7

0   -10

1    -7

2    2

3    17

The Standard form for a quadratic equation is  ax²+ bx + c=0, where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

To solve a quadratic function, you should find the discriminant: D=b²-4ac and then use this variable in the formula: [tex]x=\frac{-b \±\sqrt{\Delta} }{2a}[/tex].

The given equation is a quadratic function because have a degree equal to 2. Then, when you plot the graph, you obtain a parabola.

First, you should replace the given values for x in the equation y=3x²-10

x        y

-3   y=3*(-3)²-10= 3*9-10=27-10=17

-2   y=3*(-2)²-10= 3*4-10=12-10=2

-1    y=3*(-1)²-10= 3*1-10=3-10= -7

0    y=3*(0)²-10= 3*0-10=-10= -10

1     y=3*(1)²-10= 3*1-10=3-10= -7

2    y=3*(2)²-10= 3*4-10=12-10= 2

3    y=3*(3)²-10= 3*3-10=27-10= 17

Now, you have the points to draw the graph, show the attached image.

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The lower cost will occur at the extreme point, that is if the number of videos rented daily is 8 pieces and the cost will be $550.

The cost function is given by:

C(x) = 2x² - 32x + 678

The lowest cost happens at the extreme point. In this point the derivative of C(x) is equal to zero.

Take the derivative:

C'(x) = 4x - 32 = 0

4x = 32

x = 32/4 = 8

Hence, the lowest cost will occur if the number of video rented daily is 8 pcs.

Substitute x = 8 into the cost function:

C(8) = 2(8)² - 32.(8) + 678 =  550

Complete question:

The owner of a video store has determined that the cost c, C(x) = 2x² - 32x + 678 in dollars, of operating the store is approximately given by where x is the number of videos rented daily. find the lowest cost to the nearest dollar

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Answer:  70

Step-by-step explanation:

easy addition

The sampling distribution of the sample mean approaches a Normal Distribution when the sample size becomes larger.

According to the central limit theorem for samples, if we keep drawing larger .And larger samples and calculating their means, then the sample forms its . Own normal distribution (the sampling distribution). The mean of normal distribution has the same the original distribution and a variance that is equal to the original variance divided by the sample size. The variable p is the number of values whose average is taken together ,and not the number of times we do the experiments.

Thus, for a large random sample, the sample does not resemble the regular curve but for a large random sample it will closely resemble the normal curve.

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