3(m-5) + m

I need to simplify

Answer:

1.7

Step-by-step explanation:

( 5x + 2y = 7 ) 2

( - 2x + 6y = 9 ) 5

10x + 4y = 14

-10x + 30y = 45

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

34y = 59

y = 1.7

The y-coordinate of the solution to the system of equations 5x + 2y = 7 and -2x + 6y = 9 is 1.8 when rounded to the nearest tenth.

To solve the system of equations 5x + 2y = 7 and -2x + 6y = 9, we'll use the method of substitution or elimination. I will demonstrate the elimination method:

This is the y-coordinate of the solution for the given system of equations.

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Let [tex]x[/tex] be the amount of the 30% alloy and [tex]y[/tex] the amount of the 60% alloy the metalworker will use. However much is used, the final alloy will have a mass of

[tex]x+y=100[/tex]

kilograms. For each kg of the 30% alloy used, 0.3 kg is copper; similary, each kg of the 60% alloy contributes 0.6 kg, so that

[tex]0.3x+0.6y=0.54(x+y)=54[/tex]

Now,

[tex]x+y=100\implies y=100-x[/tex]

[tex]\implies0.3x+0.6(100-x)=54[/tex]

[tex]\implies60-0.3x=54[/tex]

[tex]\implies0.3x=6[/tex]

[tex]\implies x=20[/tex]

[tex]\implies y=100-20=80[/tex]

Answer:

Step-by-step explanation:

Problem One

Blue =   5

Black  =2

Red    = 3

First of all there are 10 marbles, 2 of which are black.

That means that 8 others are not black

You can draw any one of the 8.

P(not black) = 8/10 = 4/5

Problem Two

There are 10 marbles in all

3 of them are red.

P(Red) = 3/10  

Answer:

See image

Step-by-step explanation:

Palto

Answer:

x = 1.36

Step-by-step explanation:

We are given the following equation;

7^x = 14

we are required to determine the value of x;

the first step is to introduce natural logs on both sides of the equation;

[tex]ln(7^{x})=ln(14)\\\\xln(7)=ln(14)\\\\x=\frac{ln(14)}{ln(7)}\\\\x=1.3562[/tex]

A ratio is the part divided by the whole. Johnny took 3 pieces of pizza when the whole pizza had 8. Johnny has 3/8 (3 out of 8) pieces of pizza, or .375 parts. To find that number, literally divide your part from your whole to get the decimal form.

Answer:

17 4/5

Step-by-step explanation:

Fist, add the whole numbers.

5 + 6 + 5 = 16

Now add the fractions.

2/3 and 1/3 have the same denominator so you can add easily.

2/3 + 1/3 = 3/3 = 1

Now 16 + 1 = 17

Then what's left is Mr. Caswall's 4/5 and then we add that to 17.

So it's 17 4/5

Hope this helps!

Answer:

17 4/5 miles.

Step-by-step explanation:

First add the integer parts of the mixed numbers:

5 + 5 + 6 = 16 miles.

Now add the fractions:

2/3 + 1/3 + 4/5

LCD of 3 and 5 is 15 so we have:

10/15 + 5/15 + 12/15

= 27/15

= 9/5

= 1 4/5 miles.

So our answer is 16 + 1 4/5

= 17 4/5 miles.

Answer:

y = 2x + 3

Step-by-step explanation:

The y-intercept is clearly marked:  it's b = 3 (or 0, 3).

Going from the point (-3, -3) to the point (0, 3),

x increases by 3 and y increases by 6.  Thus, the slope of the line through these two points is m = rise / run = 6 / 3, or m = 2.

Starting with the slope-intercept form of the equation of a straight line:

y = mx + b, we substitute 2 for m and 3 for b, obtaining:

y = 2x + 3

Answer:

y = 2x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 3) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3+3}{0+3}[/tex] = [tex]\frac{6}{3}[/tex] = 2

note the line crosses the y- axis at (0, 3) ⇒ c = 3

y = 2x + 3 ← equation of line

40; base it off of the y-intercept [C]. What is the unit of measurement?

Answer:

The maxima is the point where it is the highest it can possibly get. I promise this isn't a scam but I have a picture that shows what I mean

Step-by-step explanation:

So this graph shows that (1.75, 89) is the maximum height

I hope this helps:)

Answer:

The value of the missing side is [tex]x=2\ units[/tex]

Step-by-step explanation:

In this problem i assume that the length side x is tangent to the circle

so

the length side x is perpendicular to the radius

Applying the Pythagoras Theorem in the right triangle

we have that

[tex](1.5+1)^{2}=1.5^{2}+x^{2}[/tex]

Solve for x

[tex](2.5)^{2}=1.5^{2}+x^{2}[/tex]

[tex]x^{2}=2.5^{2}-1.5^{2}[/tex]

[tex]x^{2}=4[/tex]

[tex]x=2\ units[/tex]

Answer:

x=2

Step-by-step explanation:

The area for one side is S^2 where S is the length of one side.

The area for one side = 1/2^2 = 1/4 square foot.

A cube has 6 sides. Total surface are = 1/4 x 6 = 1 1/2 square feet.

Volume of a cube is S^3

1/4^3 = 1/64 cubic foot.

For this case we have that by definition, the density is given by:

ρ =[tex]\frac {M} {V}[/tex]

Where:

M: It's the mass

V: It's the volume

The volume of a solid cone is given by:

[tex]V = \frac {1} {3} \pi * r ^ 2 * h[/tex]

Where:

A: It's the radio

h: It's the height

Substituting the data we have:

 [tex]V = \frac {1} {3} \pi * (4) ^ 2 * 21\\V = \frac {1} {3} \pi * 16 * 21\\V = 401.92 \ cm ^ 3[/tex]

On the other hand, we have that by definition, the density of the platini is given by:

[tex]21.45 \frac {g} {cm ^ 3}[/tex]

Substituting in the initial formula, we look for the mass:

[tex]M = 401.92 \ cm ^ 3 * 21.45 \frac {g} {cm ^ 3}\\M = 8621.184 \ g[/tex]

ANswer:

The mass of the platinum cone is 8621.2 grams.

To find the mass of a solid platinum cone with a height of 21 cm and a diameter of 8 cm, calculate the volume using the formula for a cone (⅓πr²h) and then multiply by platinum's density (21,450 kg/m³) to get approximately 30.342 kg.

Calculate the Mass of a Platinum Cone

To determine the mass of a solid cone made of platinum with a given height and diameter, we must first calculate its volume and then use the density of platinum to find its mass. The density of platinum is approximately 21,450 kg/m³. The volume of a cone is given by the formula ⅓πr²h, where r is the radius and h is the height. For our cone with a height (h) of 21 cm and a diameter of 8 cm, the radius (r) would be half of the diameter, so r = 4 cm = 0.04 m. Plugging the values into the formula, we get:

Volume (V) = ⅓π(0.04 m)²×21 cm = ⅓π(0.0016 m²)× 0.21 m = 0.0014136 m³.

To find the mass (m), we multiply the volume by the density of platinum (ρ):

Mass (m) = Density (ρ) × Volume (V) = 21,450 kg/m³ × 0.0014136 m³ = 30.342 kg.

Therefore, the mass of the solid platinum cone is approximately 30.342 kilograms.

Answer:

3544

Step-by-step explanation:

This is a problem of compound growth. The formula is

[tex]F=P(1+r)^t[/tex]

Where F is the value in the future (in this case, the population after 13 years)

P is the intial amount (here, the initial population of 2000, so P = 2000)

r is the rate of growth (here, it is 4.5%, in decimal, 0.045)

t is the time frame (here, it is 13 years, so t = 13)

we can plug the numbers into the formula and solve for F:

[tex]F=P(1+r)^t\\F=2000(1+0.045)^{13}\\F=2000(1.045)^{13}\\F=3544.4[/tex]

rounded to the nearest whole number, the population after 13 years would be 3544

Answer:

The  population after 13 years = 3544

Step-by-step explanation:

Points to remember

Compound interest

A = P[1 +R/n]^nt

Where A - amount

P - principle amount

R = rate of interest

t -   number of years

n - number of times compounded yearly

Here we have to consider compounded growth.

To find the population

Here P = 2000 , R = 4.5% = 0.045% and n = 13 years

A =  P[1 +R/n]^nt

 = 2000[1 + 0.045/1]^(1 * 13)

 = 2000 * 1.77

 = 3544

Therefore the  population after 13 years = 3544

Answer:

a segment cd only

Step-by-step explanation:

segment cd is the only line that passes through segment ab at a right angle

Answer:

a.  [tex]\frac{1}{6}[/tex]

b.  [tex]\frac{67}{450}[/tex]

Step-by-step explanation:

Theoretical probability is what we expect to happen and experimental probability is what actually happens.

a. In theoretical probability, it doesn't matter what happened in the past. So basically we want to know the probability of rolling a 3 when a number cube is rolled.

There are 6 faces (from 1 to 6) in a number cube. And there is 1 "3". So the probabilty of rolling a 3 is:

1/6

b. In experimental probability, we need to know what happened before. When the cube was rolled 450 times, it came up "3", 67 times.

Hence the experimental probabilty of rolling a "3" is:

67/450

Answer: false

Step-by-step explanation:

Final answer:

The probability of any number from 0 to 4 appearing in a randomly generated list is 1/5, not 1/4. The false notion might come from misinterpreting randomness or falling prey to the gambler's fallacy.

Explanation:

Your question pertains to the concept of probability in a random distribution of numbers. Specifically, you are asking whether the probability of each number occurring in a randomly generated list of numbers from 0 to 4 is 1/4. This statement is false. Since there are five possible outcomes (0, 1, 2, 3, and 4), and assuming that each number has an equal chance of being selected, the correct probability of each number occurring would be 1/5, not 1/4.

The misconception that the probability is 1/4 likely arises from a misunderstanding of randomness and probability. People often have a preconceived notion of what randomness looks like, influenced by incidents of the gambler's fallacy, where they believe past events affect the likelihood of future events. Which is not mathematically accurate. For example, the gambler's fallacy is when someone thinks that after flipping a coin and getting heads multiple times, tails is 'due' to occur. However, each flip is independent, and the probability remains at 50% for heads or tails, regardless of past flips.

Understanding true randomness means recognizing that each outcome in a set of distinct outcomes has an equal chance of occurring, and that chance is determined by dividing 1 by the total number of possible outcomes. In the scenario with the list of numbers from 0 to 4, since there are 5 possible outcomes, the correct probability should be calculated as 1/5.

Tessellation is possible only for equilateral triangles, squares and regular hexagons. Therefore, there are only three regular polygons that tessellate.

Tessellation is possible, if each interior angle of a polygon is a factor of 360 degrees.

Now, in the given image, pentagon and octagon cannot tessellate.

And the triangle does not seem to be an equilateral triangle. But in general we can say that triangle tessellates.

So, the answer might be triangle (if its equilateral)

4 + 4= 8/2= 4

the median number is 4

The answer is 24.

Hope this helps!

Answer: OPTION C

Step-by-step explanation:

Given the quadratic equation [tex]x^2 - 7x + 10[/tex] and the value of the variable "x" [tex]x = -2[/tex], you need to substitute the given value of the variable. Then:

[tex]=(-2)^2 - 7(-2) + 10[/tex]

And finally, you need to evaluate.

Remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Therefore, you get the following result:

[tex]=4+14 + 10[/tex]

[tex]=28[/tex]

This matches with the option C.

4y-7=2y-1

Subtract 2y from both sides

2y-7=-1

Add 7 to both sides

2y=6

Y=3

Answer:

6 ft^2 and 2ft^2

Step-by-step explanation:

Multiply the height and length of each hole to get the answers. Not sure if you wanted both or not.

Answer:

im on the same question but i think u just have to multiply length times width for all of them then u subtract. hope it helps

Step-by-step explanation:

Answer:

7. C

8. D

Step-by-step explanation:

7. The interest rate is 8% or .08. You find that by solving I=Prt (interest=original amount*rate*time in years)

8. The discounted price would be $48 (80*(1-.40)) Then you multiply that 48 by .08 and add that amount to the $48.

Answer:

They intersect but not perpendicular.

She bought 2 fancy shirts and 5 plain shirts.

2 x 28=$56, and 5x15=$75. 75 plus 56 is 131

[tex]

3x-4y=16 \\

5x+2y=44 \\ \\

3x-4y=16 \\

10x+4y=88 \\ \\

13x=104 \\

x=\boxed{104\div13=8}\\ \\

3\times8-4y=16 \\

24-4y=16 \\

-4y=-8 \\

y=\boxed{2}

[/tex]

The value of the integral ∫ ln(x)/x dx is  ln²(x)/2 + c

From the question, we have the following parameters that can be used in our computation:

S lnx/x dx

Express properly

So, we have

∫ ln(x)/x dx

The above expression can be integrated using substitution method

Let u = ln(x)

So, we have

du/dx = 1/x

Make dx the subject

du = dx/x

So, we have

∫ u du

Apply the power rule to integrate

∫ u du = u²/2

Substitute u = ln(x)

When integrated, we have

∫ ln(x)/x dx = ln²(x)/2 + c

Where c is a constant

Hence, the value of the integral is ln²(x)/2 + c

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Answer:

The correct options are 1 and 3.

Step-by-step explanation:

From the given box plot it is clear that

[tex]\text{Minimum values}=34[/tex]

[tex]Q_1=42[/tex]

Q₁ is 25% of a data.

[tex]Median=46[/tex]

Median is 50% of a data.

[tex]Q_3=70[/tex]

Q₃ is 75% of a data.

[tex]\text{Maximum values}=76[/tex]

34 is minimum value of the data and 46 is median it means 50% of the data values lies between 34 and 46. Therefore option 1 is correct.

42 is first quartile and and 70 is third quartile. it means 50% of the data values lies between 42 and 70. Therefore option 2 is incorrect.

The difference between Minimum value and first quartile, Maximum value and third quartile is less than 1.5×(IQR), therefore it is unlikely to have any outliers in the data.

Hence option 3 is correct.

The interquartile range of the data is

[tex]IQR=Q_3-Q_1[/tex]

[tex]IQR=70-42=28[/tex]

The interquartile range is 28. Therefore option 4 is incorrect.

Range of the data is

[tex]Range=Maximum-Minimum[/tex]

[tex]Range=76-34=42[/tex]

The range is 42. Therefore option 5 is incorrect.

Answer:

A,C

Step-by-step explanation:

got it right on edge 2021

    have a wonderful day

Answer:

11.76%

Step-by-step explanation:

use % error formula:[tex]\frac{|approx-exact|}{exact}[/tex]

where approx is 60

and exact is 68

so

[tex]\frac{|60-68|}{68}[/tex]

[tex]\frac{|-8|}{68}[/tex] =0.1176

0.1176=11.76%

hope this helps!

Answer:

7

Step-by-step explanation:

Given:

Simulation of randomly checking 25 vans, with over 100,000 miles=

                                                96408 03766 36932 41651 08410

Here  the digits 1, 2, and 3 represent a van with check engine light that turn on.

Approximately how many vans will have check engine lights come on?

From the above given data the digits 1, 2 and 3 that represented the particular model of van having check engine lights on are repeated 7 times in the simulation of randomly checking 25 vans, with over 100,000 miles

Hence 7 vans will have check engine lights come on!

In a simulation using the provided set of digits, we find that out of 25 vans, approximately 6 have check engine lights that turn on.

To solve this problem, we'd first identify all the digits that are either 1, 2, or 3 within the provided sequence of randomly generated digits. These digits, according to your problem, represent vans with check engine lights that turn on. The string you provided is 96408, 03766, 36932, 41651, and 08410.

Upon counting, the following digits in the string are 1, 2, or 3: '3', '2', '3', '1', '1', and '1'. This gives us a total of 6 occurrences.

Therefore, based on this simulation, if we were to randomly check 25 vans with over 100,000 miles, approximately 6 of them would have check engine lights that come on.

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Answer:

the answer is D (4,3)

Step-by-step explanation:

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

2 divided by 6 is [tex]\frac{1}{3}[/tex]

To confirm it,

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