Please help. I’ll mark you as brainliest if correct!

Answer:

6

Step-by-step explanation:

We can establish 6 as an upper bound, since 1*2*3 = 6, and 6 is clearly the greatest number that is a divisor of itself.

We can show that the product of any three consecutive numbers is divisible by 6, because out of any three consecutive integers, at least one must be divisible by 3, and at least one must be divisible by 2. Since the product must have factors of 2 and 3, it must also have 6 as a factor.

The approximate volume only applies when pi = 3.14

Use either answer, but not both of course.

===============================================

Work Shown:

V = volume of cylinder

V = pi*r^2*h

V = pi*2^2*8

V = pi*32

V = 32pi .... exact volume in terms of pi

V = 32*3.14

V = 100.48 .... approximate volume when we use pi = 3.14

Answer:

Step-by-step explanation:

Substitute n = 1, n = 2, n = 3 and n = 4 to the equation f(n) = n² - 1:

f(1) = 1² - 1 = 1 - 1 = 0

f(2) = 2² - 1 = 4 - 1 = 3

f(3) = 3² - 1 = 9 - 1 = 8

f(4) = 4² - 1 = 16 - 1 = 15

Answer:

.006

:)

Step-by-step explanation:

8 servings can David make with the current amount of spice.

Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

The rice-to-spice ratio = 15:1

The 75 grams of rice in one serving will require

⇒75/15

⇒5 gram of spice.

David's inventory of 40 gram of spice is enough for

40 g/(5 g/serving) = 8 servings

Hence, 8 servings can David make with the current amount of spice.

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Answer:

3(sqrt42) ft

Step-by-step explanation:

If l is side length of square patio, then area of patio would be l^2.

l^2 = 378

l = sqrt378 = 3(sqrt42)

Answer and Step-by-step explanation: To find the B-coordinate vector of x:

[tex]b_{1} = \left[\begin{array}{ccc}1\\2\\-3\end{array}\right][/tex] , [tex]b_{2} = \left[\begin{array}{ccc}-4\\-7\\11\end{array}\right][/tex], x = [tex]\left[\begin{array}{ccc}-10\\-17\\27\end{array}\right][/tex]

The augmented matrix will be:

[tex]\left[\begin{array}{ccc}1&-4&-10\\2&-7&-17\\-3&11&27\end{array}\right][/tex]

Transforming into reduced row-echelon form:

= [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&-1&-3\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&0&0\end{array}\right][/tex]

= [tex]\left[\begin{array}{ccc}1&0&2\\0&1&3\\0&0&0\end{array}\right][/tex]

The values for the vector will be:

x = 2

y = 3

The B-coordinate vector is of the form:

V = [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]

The B-coordinate vector of x is V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]

Answer:

Ok, we have a system of equations:

6*x + 3*y = 6*x*y

2*x + 4*y = 5*x*y

First, we want to isolate one of the variables,

As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:

(6*x + 3*y)/(2*x + 4*y) = 6/5

now we isolate one off the variables:

6*x + 3*y = (6/5)*(2*x + 4*y) =  (12/5)*x + (24/5)*y

x*(6 - 12/5) = y*(24/5  - 3)

x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y

Now we can replace it in the first equation:

6*x + 3*y = 6*x*y

6*(0.5*y) + 3*y = 6*(0.5*y)*y

3*y + 3*y = 3*y^2

3*y^2 - 6*y = 0

Now we can find the solutions of that quadratic equation as:

[tex]y = \frac{6 +- \sqrt{(-6)^2 - 4*3*0} }{2*3} = \frac{6 +- 6}{6}[/tex]

So we have two solutions

y = 0

y = 2.

Suppose that we select the solution y = 0

Then, using one of the equations we can find the value of x:

2*x + 4*0 = 5*x*0

2*x = 0

x = 0

(0, 0) is a solution

if we select the other solution, y = 2.

2*x + 4*2 = 5*x*2

2*x + 8 = 10*x

8 = (10 - 2)*x = 8x

x = 1.

(1, 2) is other solution

Answer:

8w : 3.8974342 ≈ 3.9 or 4 (hope it help)

Step-by-step explanation:

1w : 2

2w : 2 + 10% = 2.2

3w : 2.2 + 10% = 2.42

4w : 2.42 + 10% = 2.662

5w : 2.662 + 10% = 2.9282

6w : 2.9282 + 10% = 3.22102

7w : 3.22102 + 10% = 3.543122

8w : 3.543122 + 10% = 3.8974342

3.8974342 ≈ 3.9 or 4

Answer:

Below

Step-by-step explanation:

The initial length of the road was 56. 56 is the y-intercept assuming that the graph of this function is a line.

so the equation is:

y= mx+56

m is the slope of the function wich is by how much the function grows.

By analogy, m is the distance added to the road each day.

● y= 3x+56

X is the number of days.

■■■■■■■■■■■■■■■■■■■■■■■■■■

To find the length of the road after 33 days, replace x by 33.

y= 3*33+56 = 155

So after 33 days the road is 155 miles.

Answer:

D. A discrete data set because there are a finite number of possible values.

Step-by-step explanation:

Assuming in a test of a method of gender selection, 725 couples used the XSORT method and 368 of them had baby girls. The value given is from a discrete data set because there are a finite number of possible values.

In Mathematics, a discrete data is a data set in which the number of possible values are either finite or countable.

On the other hand, a continuous data is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable.

Hence, if 725 couples used the XSORT method and 368 of them had baby girls; this is a discrete data because the values (725 and 368) are finite and can be counted.

Answer:

the value of the series;

[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]

C) 59

Step-by-step explanation:

Recall that;

[tex]\sum_{1}^{n}a_n = a_1+a_2+...+a_n\\[/tex]

Therefore, we can evaluate the series;

[tex]\sum_{k=1}^{6}(25-k^2)[/tex]

by summing the values of the series within that interval.

the values of the series are evaluated by substituting the corresponding values of k into the equation.

[tex]\sum_{k=1}^{6}(25-k^2) =(25-1^2)+(25-2^2)+(25-3^2)+(25-4^2)+(25-5^2)+(25-6^2)\\\sum_{k=1}^{6}(25-k^2) =(25-1)+(25-4)+(25-9)+(25-16)+(25-25)+(25-36)\\\sum_{k=1}^{6}(25-k^2) =24+21+16+9+0+(-11)\\\sum_{k=1}^{6}(25-k^2) = 59\\[/tex]

So, the value of the series;

[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]

Answer: Speed = 5.6 mph

              Oxygen consumption = 71.6 mL/lb/min

Step-by-step explanation: For the oxygen consumption to be the same, functions must be equal:

f(x) = g(x)

[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x+10=11x+10[/tex]

Resolving:

[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x - 11x =0[/tex]

[tex]\frac{5}{3}x^{2} + \frac{5}{3}x - \frac{33x}{3}=0[/tex]

[tex]\frac{5}{3}x^{2} - \frac{28x}{3}=0[/tex]

[tex]\frac{x}{3}(5x - 28)=0[/tex]

[tex]\frac{x}{3} = 0[/tex]

x=0

5x - 28 = 0

[tex]x = \frac{28}{5}[/tex]

x = 5.6

The speed when the oxygen consuption is the same is 5.6 mph.

For the level of oxygen consumption:

f(5.6) = g(5.6)

g(5.6) = 11*5.6 + 10

g(5.6) = 71.6

The level of oxygen consumption is 71.6 mL/lb/min

At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.

The level of oxygen consumption is 71.6 milliliter per pound per minute

The oxygen consumption for a person walking at x mph is given by,

             [tex]f(x)=\frac{5}{3} x^{2} +\frac{5}{3}x+10[/tex]

The oxygen consumption for a runner at x mph is approximated given by the function,

             [tex]g(x)=11x+10[/tex]

To be oxygen consumption same for both walker and runner, both function must be equal.

             [tex]f(x)=g(x)\\\\\frac{5}{3} x^{2} +\frac{5}{3}x+10=11x+10\\\\\frac{5}{3} x^{2} +\frac{5}{3}x-11x=0\\\\x(\frac{5}{3} x-\frac{28}{3} )=0\\\\x=0,x=28/5=5.6mph[/tex]

At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.

The level of oxygen consumption at that speed is,

             [tex]g(5.6)=11(5.6)+10=71.6[/tex]

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Answer:

12/13

Step-by-step explanation:

First we must calculate the hypotenus using the pythagoran theorem

Now let's calculate sin0

So the exact value is 12/13

Answer:

C.) 12/13

Step-by-step explanation:

In a right angle triangle MN = 12, ON = 5 and; angle N = 90°

Now,

For hypotenuse we will use Pythagorean Theorem

(MO)² = (MN)² + (ON)²

(MO)² = (12)² + (5)²

(MO)² = 144 + 25

(MO)² = 169

MO = √169

MO = 13

now,

Sin O = opp÷hyp = 12÷13

Answer:

8 colors

Step-by-step explanation:

There should be at least 8 different colors available for coloring the sections. The one color is used to color all the small triangles on the upper most and lower most lines, then there will be required another color so that the edges does not matches with the previous color. For the bigger hexagon shapes in the center we will require different colors for all of them because all of the hexagon shapes touches a line and an edge with each other.

Answer:

its 2 trust me

Step-by-step explanation:

its two cause if you think about it and color in the hexagons and triangles two different colors it works

Answer:

12

Step-by-step explanation:

The second diagram is most helpful for finding the surface area.

If you want further tutoring help in geometry or other subjects for FREE, check out growthinyouth.org.

Answer:

Step-by-step explanation:

Hello!

This is an example of a pared sample test, the experiment is based on two dependent variables:

X₁: centimeters on a pain scale before hypnosis

X₂: centimeters on a pain scale after hypnosis

Out of these two variables a new variable is determined Xd= X₁-X₂

If the variables have an approximate normal distribution then the variable resulting from their difference will also have an approximate normal distribution.

The claim is that "hypnosis reduced the pain" if so you'd expect the population mean of the difference to be less than zero, symbolically: μd<0

The statistic for this test is a paired sample t test:

[tex]t= \frac{\frac{}{X_d} - Mu_d}{Sd} ~t_{n-1}[/tex]

To calculate the sample mean and variance you have to calculate the difference between the pairs first.

[tex]\frac{}{Xd}[/tex]= ∑Dif/n

[tex]S_d^2= \frac{1}{n-1} [sumDif^2- \frac{(sumDif)^2}{n} ][/tex]

∑Dif= 6.4

∑Dif²= 12.64

[tex]\frac{}{Xd}[/tex]= 6.4/5= 1.28

[tex]S_d^2= \frac{1}{4} [12.64- \frac{(6.4)^2}{5} ]= 1.112[/tex]

Sd= 1.05

[tex]t_{H_0}= \frac{\frac{}{Xd}-Mu_d }{Sd} = \frac{1.28-0}{1.05} = 1.219= 1.22[/tex]

I hope this helps!

Answer:

101.98 yards.

Step-by-step explanation:

Please refer to the diagram that I drew (sorry for the messiness; I do not own a stylus and so I was using my mouse to try to draw it).

Since the triangle is a right triangle, you can use SOH CAH TOA. In this case, you are trying to figure out the opposite length, but you are given the adjacent. So, we will use tangent to solve this (TOA = Tangent, Opposite over Adjacent).

The angle is 22.6 degrees, and the tangent of the angle is equivalent to the opposite length, x, divided by the adjacent length, 245 yards.

tan(22.6) = x / 245

x / 245 = tan(22.6)

x = tan(22.6) * 245

x = 0.4162598242 * 245

x = 101.9836569

So, you are about 101.98 yards from the cabin.

Hope this helps!

Step-by-step explanation:

5 log₅ x − ¼ log₅ (8−x)

log₅ x⁵ − log₅ (8−x)^¼

log₅ x⁵ − log₅ ∜(8−x)

log₅ (x⁵ / ∜(8−x))

The expression 5 log₅ x - 1/4 log₅ (8 - x) can be condensed to [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , using the laws of logarithms and exponents.

A logarithmic expression x = logₐb, implies that aˣ = b.

Some properties used to solve logarithmic expressions are:

In the question, we are asked to condense the expression:

5 log₅ x - 1/4 log₅ (8 - x)

= [tex]log_{5}x^{5} - log_{5}(8 - x)^{1/4}[/tex], (using the power law: logₐ xⁿ = n.logₐ x)

= [tex]log_{5}x - log_{5}\sqrt[4]{8 - x}[/tex], (since, [tex]x^{1/a} = \sqrt[a]{x}[/tex])

= [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , (using the quotient law: logₓ a - logₓ b = logₓ a/b).

∴ The expression 5 log₅ x - 1/4 log₅ (8 - x) can be condensed to [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , using the laws of logarithms and exponents.

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Answer:

Step-by-step explanation:

Given,

a = 4

y = -6

Now,

[tex] - a + 3y[/tex]

Plug the values

[tex] = - 4 + 3 \times ( - 6)[/tex]

Multiply the numbers

[tex] = - 4 + ( - 18)[/tex]

When there is a (+) in front of an expression in parentheses, the expression remains the same.

[tex] = - 4 - 18[/tex]

Calculate

[tex] = - 22[/tex]

Hope this helps..

Best regards!!

Answer:

14

Step-by-step explanation:

-4 + 3(6)

-4+18

14

Answer:

Step-by-step explanation:

Part A

(m + n)x = 4x + 5 + 8x - 5

(m + n)x = 12x   The fives cancel

Part B

(m - n)x = 4x + 5 - 8x + 5

(m - n)x = -4x + 10

Part C

The trick here is to put n(x) into m(x) wherever m(x) has an x.

m[n(x)] = 5(n(x)) + 5

m[n(x)] = 5(8x - 5) + 5

m[n(x)] = 40x - 20 + 5

m[n(x)] = 40x - 15

S = sample space = set of all possible outcomes

S = set of whole numbers 1 through 6

S = {1,2,3,4,5,6}

E = event space = set of outcomes we want to happen

E = set of odd numbers between 1 through 6

E = {1,3,5}

We have 3 items in set E and 6 items in set S. So there are 3 ways to get what we want to happen out of 6 ways total. The probability is therefore 3/6 = 1/2

Answer:

Standard form: [tex]12x+3y-2=0[/tex]

A = 12, B = 3 and C = -2

Step-by-step explanation:

Given:

The equation:

[tex]y= -4x + \dfrac{2}3[/tex]

To find:

The standard form of given equation and find A, B and C.

Solution:

First of all, let us write the standard form of an equation.

Standard form of an equation is represented as:

[tex]Ax+By+C=0[/tex]

A is the coefficient of x and can be positive or negative.

B is the coefficient of y and can be positive or negative.

C can also be positive or negative.

Now, let us consider the given equation:

[tex]y= -4x + \dfrac{2}3[/tex]

Multiplying the whole equation with 3 first:

[tex]3 \times y= 3 \times -4x + 3 \times \dfrac{2}3\\\Rightarrow 3y=-12x+2[/tex]

Now, let us take all the terms on one side:

[tex]\Rightarrow 3y+12x-2=0\\\Rightarrow 12x+3y-2=0[/tex]

Now, let us compare with [tex]Ax+By+C=0[/tex].

So, A = 12, B = 3 and C = -2

Answer:

That is correct

Step-by-step explanation:

yes sir you are corret                            

Answer: m= 2

Step-by-step explanation: First Expand the brackets! 5-m+4=2m+3m-3

                                    Then Do the addition and subtraction in both sides!

                                     9-m=5m-3

                                 Then bring m to one side and the constants the other!

                                   6m=12

                                    Then solve for m where m=2

                                     If you want you can check your answer bu substituting m as 2. 5-(2-4)=7 and 2(2) + 3(2-1) which also = 7.

Answer:

D) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.

Step-by-step explanation:

We are given that the owner of a shoe store randomly selected 10 receipts and identified the total spent by each customer. The totals (rounded to the nearest dollar) are given below;

X: 125, 99, 219, 65, 109, 89, 79, 119, 95, 135.

Let [tex]\mu[/tex] = average customer bought worth of shoes.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] $100      {means that the mean is smaller than or equal to $100}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $100      {means that the mean is greater than $100}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                            T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = [tex]\frac{\sum X}{n}[/tex] = $113.4

             s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = $42.78

             n = sample of receipts = 10

So, the test statistics =  [tex]\frac{113.4-100}{\frac{42.78}{\sqrt{10} } }[/tex]  ~  [tex]t_9[/tex]

                                    =  0.991

The value of t-test statistics is 0.991.

Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.

Since the value of our test statistics is less than the critical value of t as 0.991 < 1.833, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean is smaller than or equal to $100.

Answer:

1/2 or 0.5

Step-by-step explanation:

To find out what 2/3 is out of 3/4, we just have to multiply them together to get our exact answer.

[tex]\frac{2}{3} *\frac{3}{4}=\frac{6}{12}=\frac{1}{2}[/tex]

Our final answer is 1/2 or 0.5.

Answer:

third option

Step-by-step explanation:

We just have to calculate 2x² - 4x - (x² + 6x). 2x² - x² = x² and -4x - 6x = -10x so the answer is x² - 10x.

Answer:

x^2-10x

Step-by-step explanation:

f(x)-g(x)

(2x^2-4x)-(x^2+6x)

carry through the negative

2x^2-4x-x^2-6x

x^2-10x

Answer:

0.1875

Step-by-step explanation:

σM=σ/√N

=8/√7500

=8/86.608

=0.092

Z=(x-μ)/σ/√N

=(25.5-36)/8/√7500

=-10.5/0.0092=-1141.304

Z score = -1.3125

=(27-36)/8/√7500 =

=9/0.0092=978.261

Z score= -1.125

-1.125-(-1.3125)=-1.125+1.3125)= 0.1875

The probability that the sample mean will be between 25.5 and 27 years

P(between 25.5 and 27) = 0.1875

see attachment a=400 rpm b and c = 200 rpm d = 40 rpm

Answer:

pulley B 200, pulley C 200, pulley D 160