solve for x. 4=6x/a +5

Answer:

Step-by-step explanation:

the equation for right cylinder surface area: 2πrh+2πr^2

Answer:

33π cm²

Step-by-step explanation:

To find surface area you add the area of every face.

Area of the 2 circle faces:

The formula for the area of circle is πr². If the diameter is 6 you divide that by 2 to get a radius of 3. The area of the circle is 9π. Sense the top and bottom are both circles you multiply the area by 2 to get 18π.

Area of side face:

To find the area of the side, it is the same as a rectangle (length [circumference] multiplied by height [2.5]). The forumla for the circumference of a circle is πd. The circumference is 6π so multiply that by the height of 2.5 to get the area of the side of 15π.

Total surface area:

Now add the 18π (area of 2 circle faces) with the 15π (area of side face) to get 33π cm² surface area.

The   total area that maritza will decorate is 656 cm².

Given: Maritza wants to decorate the top and bottom of the shoebox  which is a cuboid

As the cuboid has six rectangular faces, the total surface area of the cuboid is calculated as follows:

Assume that, l, w, h be the length, width, and height of the cuboid respectively.

Thus,

The front face area of cuboid = l x h

The back face area of the cuboid = l x h

The top face area of the cuboid = l x w

The bottom face area of the cuboid = l x w

The left face area of the cuboid = h x w

The right face area of cuboid = h x w

Hence, the total surface area is the sum of all the faces of a cuboid, then the TSA of a cuboid is:

Total Surface Area of Cuboid = lh + lh + lw+ lw+ hw+ hw

Total Surface Area of Cuboid  = 2 lh + 2 lw + 2 hw

Total Surface Area of Cuboid  = 2 (lh + lw+ hw)

h = 8 cm

w = 6 cm

l = 20 cm

Using the formula: TSA = 2 (lw + wh + hl)

2( (20×6) + (6×8) + (8×20))

= 2(120 + 48 + 160)

= 2(328)

= 656

So, the total surface area of this cuboid is 656 cm².

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3,523 gallons

Fractions can be defined as the representation of a part of a whole. A fractions consists of the numerator and the denominator.

let f(x) = \(\frac{p}{q}\)

then 'p' represents the numerator; while 'q' represents the denominator;

where p and q belong to integers for simple fractions, while when p and q belong to other sets they can from complex fractions.

To convert a fraction into an integer we need to multiply the fraction with the the denominator so that it cancels out leaving only the numerator behind.

For fractions present in equations to get rid of all the fractions we new to multiply the equation by the LCM of the denominator of all the fractions.

Where LCM is the least common multiple.

To give an example:

let y = \(\frac{3}{4}\)X + \(\frac{9}{5}\)

Then the LCM for 4 and 5 will be 20;

as factor of 4 are 1,2 and that of 5 are 1,5

then to eliminate the fractions from the equation

Multiplying both sides by 20

y x 20= \(\frac{3}{4}\)X x 20 + \(\frac{9}{5}\) x 20

20y= 3 x 5X + 9 x 4

20y = 15X + 36

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Answer:

(x-4)^2 + (y-5)^2 = 20

Step-by-step explanation:

Rearrange the line equation of 5x - 2y + 6 = 0

So y = 5/2x +3

The y-intercept of the line equation is 3 as when x=0, y=3.

We know the Circle has the formula \((x-4)^2 + (y-5)^2 = ?^2\) from the question but with the intercept, we can find the entire equation as the y-intercept is (0,3) so we can substitute it into the equation to find the full equations so:

\((0-4)^2 + (3-5)^2 = ?^2\)

This simplifies to:

\((-4)^2 +(-2)^2\) = \(?^2\)

16 + 4 = 20 = \(?^2\)

The answer is 20 so the equation of the circle is \((x-4)^2 + (y-5)^2 = 20\)

Answer:

x=3 and y= -1

Step-by-step explanation:

2x-7y=13

3x+y=8

Isolate y to get your third equation

y=8-3x

Sub third equation into first

2x-7(8-3x)=13

2x-56+21x= 13

23x= 13+56

x= 69/23

x=3

Sub x into third equation to get y value

y=8-3(3)

y= -1

Answer: 288

Step-by-step explanation: the number of songs downloaded this year will be x

x/12=30-6

= x/12=24

12*24= 288

x=288

Answer:

540

Step-by-step explanation:

1. We assume, that the number 900 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 900 is 100%, so we can write it down as 900=100%.

4. We know, that x is 3.5% of the output value, so we can write it down as x=3.5%.

5. Now we have two simple equations:

1) 900=100%

2) x=3.5%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

900/x=100%/3.5%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 3.5% of 900

900/x=100/3.5

(900/x)*x=(100/3.5)*x       - we multiply both sides of the equation by x

900=28.571428571429*x       - we divide both sides of the equation by (28.571428571429) to get x

900/28.571428571429=x

31.5=x

x=31.5

now we have:

3.5% of 900=31.5

Answer:

answer is sus.

Step-by-step explanation:

sus is the correct answer to your problrm. hope this helps!

Answer:

20 units squared

Step-by-step explanation:

Area = base times height

Area = 5 x 4 = 20

Answer:

The answer to this question is D.

Step-by-step explanation:

Congruent angles are the same

5x-24=9x-17

-4x=-41

x=10.25

The lights which were on was 48%.

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that there were 72 lights on, and 78 lights turned off.

We need to find the percent of the lights turned on.

So, percentage of something =

= number of thing / total number of the thing x 100%

Here, the number of thing = light on = 72

Total = 72 + 78 = 150

So, the percent of light on = 72 / 150 x 100% = 0.48 x 100%

= 48%

Hence the lights which were on was 48%.

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On solving the provided question we can say that the equations are \(250x + 1000\) and  (20%1000 + 1000)*\(x\)

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Marvin has $1,000 in his savings account.

Plan A, he will increase his account balance by $250 per year.

Plan B, he will increase his account balance by 20% each yea

for plan A,

\(250x + 1000\)

where x is months,

so 250*12+1000 = $4000

For plan B,

(20%1000 + 1000)*\(x\) = (200 + 1000)*12 = $14400

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Side b of right triangle ABC is approximately 40.33 ft.

A right triangle ABC with the right angle at C. Let's label the sides of the triangle according to the given information

Side a = 25.52 ft (opposite angle A)

Side c = 47.74 ft (hypotenuse)

Using the Pythagorean theorem, we know that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):

c² = a² + b²

Substituting the given values

(47.74 ft)² = (25.52 ft)² + b²

2278.7076 ft² = 652.5504 ft² + b²

1626.1572 ft² = b²

b = √(1626.1572 ft²)

b ≈ 40.33 ft

Therefore, side b is approximately 40.33 ft.

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The probability that the number of lost-time accidents occurring over a period of 7 days will be exactly 3 is 0.7295

Binomial Distribution

The binomial distribution is the sum of a series of multiple independent and identically distributed Bernoulli trials. In a Bernoulli trial, the experiment is said to be random and can only have two possible outcomes- success or failure.

In a binomial distribution the probability of getting success must remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is ½ or 0.5 for every trial we conduct, since there are only two possible outcomes.

Mean rate of lost time accident = 0.3 per day

probability that the number of lost-time accidents occurring over a period of 7 days will be no more than 3.

n = 7

Using binomial distribution formula :

P(x ≤3)

Probability of success (p) = 0.3

1 - p = 1- 0.3 = 0.7

nCx * p^x * (1 - p)^(n-x)

Using the binomial probability distribution calculator to save computation time :

P(x ≤3) = P(x = 0) + p(x = 1) + p(x = 2) + p(x = 3)

P(x ≤3) = 0.0403 + 0.1556 + 0.2668 + 0.2668

P(x ≤3) = 0.7295

0.7295

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The UCL (Upper Control Limit) using sigma = 3 for this process would be 30. The UCL utilizing sigma=3 for this process would be 28.036.

In statistical process control, the upper control limit (UCL) is utilized as a device to identify when to stop a process due to a high variation.

A process that exceeds its UCL will result in defective or inconsistent items, which should be avoided.

Marble Inc. produces high-end countertops from a variety of materials. The company employs the process of randomly selecting one countertop to count the number of blemishes as a means of monitoring the quality of its production processes.

The formula for calculating UCL is as follows: UCL = average of blemishes + 3 × standard deviation For ten samples with a different number of blemishes in each sample, the UCL is determined.

Using the given formula for UCL using sigma= 3: UCL = (2+3+4+5+6+7+8+9+10+17)/10 + 3 × √[(2-9.1)² + (3-9.1)² + (4-9.1)² + (5-9.1)² + (6-9.1)² + (7-9.1)² + (8-9.1)² + (9-9.1)² + (10-9.1)² + (17-9.1)²]/10UCL = 28.036

From the above calculations, the UCL utilizing sigma=3 for this process would be 28.036.

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The radius of the cone is approximately 0.99917 inches when the volume of the cone is 527.52 cubic inches.To find the radius of the cone, we need to use the formula for the volume of a cone, which is:

V = (1/3)πr^2h

where V is the volume, π is the mathematical constant pi (approximately 3.14), r is the radius, and h is the height of the cone. We are given that the volume of the cone is 527.52 cubic inches, so we can substitute that value into the formula:

527.52 = (1/3)πr^2h

We don't know the height of the cone, but we can simplify the formula by multiplying both sides by 3:

1582.56 = πr^2h

Now we can solve for r. We know that π is approximately 3.14, so we can substitute that value:

1582.56 = 3.14r^2h

We still don't know h, but we can eliminate it by dividing both sides by r^2:

1582.56/r^2 = 3.14h

Now we can solve for h:

h = 1582.56/(3.14r^2)

We can substitute this value for h back into the original formula:

527.52 = (1/3)πr^2h

527.52 = (1/3)πr^2(1582.56/(3.14r^2))

Simplifying this equation, we get:

527.52 = 1582.56/3

Multiplying both sides by 3, we get:

1582.56 = 1582.56

This is true, so we know that our calculation is correct. Now we just need to solve for r:

527.52 = (1/3)πr^2h
527.52 = (1/3)πr^2(1582.56/(3.14r^2))
527.52 = 526.9468r^2
r^2 = 0.998344
r = 0.99917 (rounded to the nearest hundredth)

Therefore, the radius of the cone is approximately 0.99917 inches when the volume of the cone is 527.52 cubic inches.

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Answer:

8 cups

Step-by-step explanation:

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Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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The required expression of the proportionality is given as y = 1.8x.

Given,

The data

x =    3,      7,  12

y = 5.4, 12.6,  21.6

We have to write an equation for the direct variation.

What is proportionality?

The relationship between two or more sets of values—whether they are directly proportional or inversely proportional to one another—is referred to as proportionality.

Here,

If y is proportional to x,

y ∝ x

y = k x

k = y/x

Then,

k = 5.4/3 = 12.6/7 = 21.6/12 = 1.8

So put k in the proportionality equation,

y = 1.8k

Thus, the required expression of the proportionality is given as y = 1.8x.

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The probability that the person will be cured of back pain is 2/7.

The probability that a person will be cured of back pain after being given a sugar pill can be determined by using the given information in the question. According to the question, for every 2 patients cured by the sugar pill, 5 patients were not cured by the sugar pill. This means that out of a total of 2 + 5 = 7 patients given the sugar pill, only 2 were cured. Therefore, the probability of a patient being cured of back pain after being given a sugar pill is 2/7.

To calculate the probability, we can use the formula:

P(cured) = number of patients cured / total number of patients

Plugging in the given values, we get:

P(cured) = 2 / 7

Therefore, the probability that a patient will be cured of back pain after being given a sugar pill is 2/7.

In conclusion, according to the results of the study, if a patient is given a sugar pill, the probability that the person will be cured of back pain is 2/7.

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Answer:

Step-by-step explanation:

As we see on the graph, the range is:

The proportion of children having an index of at least 115 is 0.2660

The proportion of children having an index of at least 72  is 0.9804

The 94th percentile index score is 129.88

6% of the population have an index score below 80.12

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

Mean = 105

Standard deviation = 16

So, the z-score is

z = (115 - 105)/16

Evaluate

z = 0.625

The probability is then represented as

P = P(z ≥  0.625)

Evaluate

P = 0.2660

Here, we have

z = (72- 105)/16

Evaluate

z = -2.0625

The probability is then represented as

P = P(z ≥  -2.0625)

Evaluate

P = 0.9804

The z score at 94th percentile is

z = 1.555

So, we have

Index = 1.555 * 16 + 105

Evaluate

Index = 129.88

The 94th percentile index score is 129.88

Here, we have

z = -1.555

So, we have

Index = -1.555 * 16 + 105

Evaluate

Index = 80.12

6% of the population have an index score below 80.12

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Answer:

  C) The difference between the 75th and 25th percentiles is 12 inches.

Step-by-step explanation:

The interquartile range is the length of the "box" in a "box and whisker" plot. One end is the 25th percentile, and the other end is the 75th percentile. It is the difference between the maximum and minimum of the middle 50% of the data.

For the baker's loaf-length data set, the interquartile range being 12 inches means the loaves in the 75th percentile are 12 inches longer than the loaves in the 25th percentile. This could be described by choice C.

Answer: The discounted price is $948. The value of the discount itself is $632.

Step-by-step explanation:

Answer:

Please check the question.  As written, the value is 1, which is not amoung the answers

Step-by-step explanation:

(-3 + 3) + (-2 + 3)

(-3 + 3) = 0

(-2 + 3) = 1

0 + 1 = 1