Find the value of the expression (4x – 12)+(1/3xy – 5) when x = 6 and y=2

Answer:

I. k = -8

II. y = -96

Step-by-step explanation:

Given the mathematical expression and data;

y = 24

x = -3

y = kx (y varies directly as x).

To find the constant of proportionality k;

y = kx

Substituting the values into the expression, we have;

24 = k(-3)

24 = -3k

k = -24/3

k = -8

Next, to find the value of y when x = 12

y = kx

Substituting the values, we have;

y = -8 * 12

y = -96

Answer:

[tex] \displaystyle d) 36 \: {in}^{2} [/tex]

Step-by-step explanation:

the polygon can be separated in two parts

let's figure out the area of the rectangle

recall that,

given that,

thus substitute:

simplify multiplication:

let's figure out the area of the triangle

remember that,

[tex] \displaystyle A_{ \rm triangle} = \frac{1}{2} \times b\times h[/tex]

substitute the value of b and h:

[tex] \displaystyle A_{ \rm triangle} = \frac{1}{2} \times 9\times 2[/tex]

reduce fraction:

[tex] \displaystyle A_{ \rm triangle} = 9[/tex]

now the area of the polygon would be the total area of the rectangle and triangle thus

[tex] \displaystyle A_{ \rm polygon} = 27 + 9[/tex]

simplify addition:

[tex] \displaystyle A_{ \rm polygon} = 36[/tex]

hence our answer is D)

Answer:

2

Step-by-step explanation:

14·[tex]\frac{1}{7}[/tex]=2

Answer:

2

Step-by-step explanation: 1/7th's of 14 is 2.

1/7 x 14 = 2.

Answers:

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Explanations:

Problem 7)

There are 2 red aces (hearts, diamonds) out of 52 cards total, so 2/52 = 1/26 is the probability of picking a red ace.

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Problem 8)

There are 4 kings out of 52 cards total, so 4/52 = 1/13 are the odds of picking a king.

This is the same as say focusing on one suit (eg: clubs) and finding the probability of pulling out a king.

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Problem 9)

There are 3 face cards per suit (Jack, Queen, King) so 3*4 = 12 face cards in all. The odds of picking a face card are 12/52 = 3/13. That makes 10/13 the odds of not picking a face card, since 3/13+10/13 = 1.

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

Problem 10)

The answer is 1/2 because half of the cards are red.

You could say 26/52 = 1/2 since there are 26 red cards out of 52 cards total.

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Problem 11)

There are 4 copies of '2' and 4 copies of '3', so there are 4+4 = 8 cards we want to avoid. The probability of picking either of them is 8/52 = 2/13. The odds of not picking any of these cards is 11/13  (refer to problem 9).

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Problem 12)

We have 4 copies each of '7', '8' and '9'

That gives 4*3 = 12 cards total we want to pick.

So 12/52 = 3/13 is the answer.

Answer:

x=in5

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Required

Equation of line

passes through [tex](6,2)[/tex]

In an equation of the form [tex]y =mx + b[/tex]; the slope is [tex]m[/tex]

So, by comparison;

The slope of [tex]y = 3x + 1[/tex] is: [tex]m =3[/tex]

From the question, we understand that the required equation is perpendicular to [tex]y = 3x + 1[/tex]

This means that its slope is:

[tex]m_2 =-\frac{1}{m}[/tex]

So, we have:

[tex]m_2 =-\frac{1}{3}[/tex]

The line equation is:

[tex]y = m_2(x - x_1) + y_1[/tex]

Where:

[tex](x_1,y_1) = (6,2)[/tex]

So, we have:

[tex]y = -\frac{1}{3}(x - 6) + 2[/tex]

[tex]y = -\frac{1}{3}x + 2 + 2[/tex]

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

Answer:

approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million

Step-by-step explanation:

For normal distribution conditions

1) Sample size is greater than 30

2) Population standard deviation is known

3) population is normal distributed

Above any condition given problem if satisfied than it's distribution will approximately normal.

n = 40 > 30

Sample size(n) greater than 30 and population standard deviation is known.

So the distribution will approximately be normal

Hope this helps!

The shape  of the distribution of the sample mean for all possible random samples of size 40 from this population is approximately Normal

The following any or all conditions should be there for normal distribution:

Now  

n = 40 > 30

Here  

Sample size(n) more than 30 and population standard deviation is known.

Learn more: brainly.com/question/17429689

Answer:

1)x=−3/5y+17/5  

2)x=−3/8y+−9/8

Step-by-step explanation:

Let's solve for x.

5x+3y=17

Step 1: Add -3y to both sides.

5x+3y+−3y=17+−3y

5x=−3y+17

Step 2: Divide both sides by 5.

5x/5=−3y+17/5

x=−3/5y+17/5

Answer:

x=−3/5y+17/5  

Let's solve for x.

−8x−3y=9

Step 1: Add 3y to both sides.

−8x−3y+3y=9+3y

−8x=3y+9

Step 2: Divide both sides by -8.

−8x/−8=3y+9/−8

x=−3/8y+−9/8

Answer:

x=−3/8y+−9/8

I HOPE THIS IS CORRECT IF NOT TELL ME AND ILL FIX IT.

Answer:

0.7888 = 78.88% probability that the first machine produces an acceptable cork.

0.9772 = 97.72% probability that the second machine produces an acceptable cork.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

First machine:

Mean 3 cm and standard deviation 0.08 cm, which means that [tex]\mu = 3, \sigma = 0.08[/tex]

What is the probability that the first machine produces an acceptable cork?

This is the p-value of Z when X = 3.1 subtracted by the p-value of Z when X = 2.9. So

X = 3.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3.1 - 3}{0.08}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a p-value of 0.8944

X = 2.9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.9 - 3}{0.08}[/tex]

[tex]Z = -1.25[/tex]

[tex]Z = -1.25[/tex] has a p-value of 0.1056

0.8944 - 0.1056 = 0.7888

0.7888 = 78.88% probability that the first machine produces an acceptable cork.

What is the probability that the second machine produces an acceptable cork?

For the second machine, [tex]\mu = 3.04, \sigma = 0.03[/tex]. Now to find the probability, same procedure.

X = 3.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3.1 - 3.04}{0.03}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

X = 2.9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.9 - 3.04}{0.03}[/tex]

[tex]Z = -4.67[/tex]

[tex]Z = -4.67[/tex] has a p-value of 0

0.9772 - 0 = 0.9772

0.9772 = 97.72% probability that the second machine produces an acceptable cork.

Answer:

The smaller number is 4√2 and the larger number is (4√2 + 1).

Step-by-step explanation:

Let the two numbers be x and y, where y is the larger of the two numbers.

Since y is the larger number, it is one more than the smaller number. So:

[tex]y=x+1[/tex]

When negative two times the smaller is added to the square of the larger, the result is 33. In other words:

[tex]-2x+y^2=33[/tex]

Substitute:

[tex]-2x+(x+1)^2=33[/tex]

Solve for x. Square:

[tex]-2x+(x^2+2x+1)=33[/tex]

Simplify:

[tex]x^2+1=33[/tex]

Subtract one from both sides:

[tex]x^2=32[/tex]

And take the square root of both sides:

[tex]x=\pm\sqrt{32}=\pm 4\sqrt{2}[/tex]

Since y is positive, we can ignore the negative case. So, the smaller number is:

[tex]x=4\sqrt{2}\approx5.66[/tex]

And the larger number is:

[tex]y = 4\sqrt{2} + 1 \approx6.66[/tex]

Answer:

Actual growth of population - Birth - Death + In migration - Out Migration. ...

Answer:

at first put the value of X

after that do the equation.

Step-by-step explanation:

hope it will help you

Answer:

a = 2

Step-by-step explanation:

substitute x with the number 5.

5+8a=25+5a-7a

subtract 5a from both sides

5+3a=25-7a

add 7a to both sides

5+10a = 25

subtract 5 from both sides

10a=20

divide both sides by 10

a = 2

Answer:

B

Step-by-step explanation:

Base area = side^2 = 3^2 = 9 m^2

Base perimeter = side x 4 = 3 x 4 = 12 m

LA = (base perimeter x slant height)/2 = (12 x 5)/2 = 30 m

SA = base area + LA = 9 + 30 = 39 m^2

Answer:

[tex]a_5 = 120[/tex]

Step-by-step explanation:

Given

[tex]a_1 = 1[/tex]

[tex]a_n = n(a_{n-1})[/tex]

Required

[tex]a_5[/tex]

This is calculated as:

[tex]a_5 = 5(a_{5-1})[/tex]

[tex]a_5 = 5*a_4[/tex]

Calculate [tex]a_4[/tex]

[tex]a_4 =4(a_{4-1})[/tex]

[tex]a_4 =4*a_3[/tex]

Calculate [tex]a_3[/tex]

[tex]a_3 =3*a_2[/tex]

Calculate [tex]a_2[/tex]

[tex]a_2 = 2 * a_1[/tex]

[tex]a_2 = 2 * 1[/tex]

[tex]a_2 = 2[/tex]

So:

[tex]a_3 =3*a_2[/tex]

[tex]a_3 = 3 * 2 = 6[/tex]

So:

[tex]a_4 =4*a_3[/tex]

[tex]a_4 = 4 * 6 =24[/tex]

Lastly;

[tex]a_5 = 5*a_4[/tex]

[tex]a_5 = 5 * 24[/tex]

[tex]a_5 = 120[/tex]

Answer:

(0.5b+20b)*3b=c

Step-by-step explanation:

The requried equation that shows the amount Beverly charges per bracelet is C = 21.5b

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

The amount Beverly charges, C, per bracelet, b, is given by:

C = 20 + 3(0.5)

C = 20 + 1.5

C = 21.5

So the equation that shows the amount Beverly charges per bracelet is:

C = 21.5b

Learn more about models here:
https://brainly.com/question/22591166
#SPJ3

Answer:

dh/dt =  0.4 m/min

Step-by-step explanation:

The volume of the cone is:

V(c) = (1/3)*r² *h              if always  h = 3r    then    r = h/3

The volume of the cone as a function of h will be:

V(h)  =  (1/3)* (h/3)²*h

V(h) =  (1/27)*h³

The increasing rate of the volume is equal to the rate of sand added the:

D(V)/dt   = (1/27)*3*h²*dh/dt

D(v) / dt  =  10 m³/min

h =  15 m      and   dh/dt is the rate of increasing of the height

By substitution

10 m³/min  = ( 1/9)* 225 * dh/dt  (m²)

dh/dt =  90 / 225   m/min

dh/dt =  0.4 m/min

Answer:

because i decided that

Step-by-step explanation:

Answer:

[tex] \orange{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]

Step-by-step explanation:

[tex]y = x \sqrt[3]{1 + {x}^{2} } \\ assuming \: log \: both \: sides \\log y = log(x \sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + log(\sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + \frac{1}{3} log({1 + {x}^{2} } ) \\ differentiating \: both \: sides \: w.r.t.x \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{1}{3} . \frac{1}{(1 + {x}^{2}) } (0 + 2x) \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{2x}{3(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3(1 + {x}^{2}) + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 3{x}^{2} + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 5{x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{dy}{dx} =\frac{y(3 + 5{x}^{2} )}{3x(1 + {x}^{2}) } \\ \\ \frac{dy}{dx} =\frac{x \sqrt[3]{1 + {x}^{2} } (3 + 5{x}^{2} )}{3x(1 + {x}^{2}) }\\ \\ \frac{dy}{dx} =\frac{(3 + 5{x}^{2} )\sqrt[3]{1 + {x}^{2} } }{3(1 + {x}^{2}) }\\ \\ \purple{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]

Answer:

4/5 is ur answer

Step-by-step explanation:

ok just like the last one but this one is COS

ok so we know that COS is A/H

A= adjacent and ofc H= hypotenuse

so lets see its the COS of a which means it will be A/H

A= 4 and the H=5

Answer:

17

Step-by-step explanation:

12+5

Let's start by writing the equation of a circle.

The center of the circle is (h, k), and the radius, r, is 4 so

we can simply plug these values into the formula.

So we have [(x) - (2)]² + [(y) - (-4)]² =  (7)².

Notice that I changed the parenthses that were in the original formula

to brackets so that we wouldn't have too many sets of parenthses

when plugging our values into the formula.

Finally, we simplify inside the brackets.

So we have (x - 2)² + (y + 4)² = 49.

Now, I changed the brackets back to parenthses in the final answer.

Answer:

Solution given:

B: 9x - 4/x^2 - 4

Step-by-step explanation:

.k

Answer:

as we know Sara need 8 tube in 3 experiment

she will use 2 tube in 1 experiment

now she have 6 tube in other experiments

so the question said to find how many tube were used in both experiment equally so 3,3 test tube were needed for each of the other two experiment

Step-by-step explanation:

total tube=8 (3 experiment)

used =2tube (1 experiment)

remaining=8-2=6

now ,

dividing 6 into 2 equal part

so,=6/2=3

so 3 tube were used in 2nd experiment and 3in 3rd experiment

Answer: 7290

Step-by-step explanation:

Three times is asking you to multiply the points before them by three. Level one, as we know is 10. Then, to get level two's points, you would multiply 10 by 3, to get 30, & so on.

Level One:10

Level Two: 10x3=30

Level Three: 30x3=90

Level Four: 90x3=270

Level Five: 270x3=810

Level Six: 810x3=2430

Level Seven: 2430x3= 7290

*** If you are still confused, comment on this question, & I will be happy to walk you through the whole question. ***

Answer:

7290 :)

Step-by-step explanation:

Took the quiz.

Answer:

The 1st graph is the answer and matches

-x/2 + 2   -2  ≤ x < 2 because it is equal to -2

The 4th graph is incorrect slightly at = 2x - 3   x  ≥ 2

as  the graph is descending and shows x = -1/2 as the gradient 4/-2 = -1/2

m = -1/2 would be the equation.

Therefore 2 (-1/2) = -1 and  -1 - 3 = -4 and 4 is not  greater than 2 so is wrong/.

Step-by-step explanation:

Answer:

2 is the same as 4

Step-by-step explanation: