The sum of the digits in a two-digit number is 14. If you reverse and double the original number, the sum is 222. Find the original number.

Answer: 5/12

Step-by-step explanation:

- For the ease of the problem, turn them into improper fractions, so it would be:

13/3 divided by 14/5 divided by 26/7

- Next, let's turn the equation from division to multiplication. This can be done by flipping the fractions of everything being divided, so:

13/3 times 5/14 times 7/26

- We can cross out some parts of the fraction, like 13 and 26, 14 and 7, which simplifies our equation to:

1/3 times 5/2 times 1/2 = 5/12

Answer:

[tex]\dfrac{5}{12}[/tex]

Step-by-step explanation:

Given equation:

[tex]4 \frac{1}{3} \div 2 \frac{4}{5} \div 3 \frac{5}{7}[/tex]

Convert the mixed numbers into improper fractions:

[tex]\dfrac{4 \times 3+1}{3} \div \dfrac{2 \times 5+4}{5} \div \dfrac{3 \times 7+5}{7}[/tex]

[tex]\dfrac{13}{3} \div \dfrac{14}{5} \div \dfrac{26}{7}[/tex]

[tex]\textsf{Apply the fraction rule:} \quad \dfrac{a}{c}\div\dfrac{b}{d}=\dfrac{a}{c}\times \dfrac{d}{b}[/tex]

[tex]\dfrac{13}{3} \times \dfrac{5}{14} \times \dfrac{7}{26}[/tex]

Multiply the fractions:

[tex]\dfrac{13\times5\times7}{3 \times14 \times 26}[/tex]

[tex]\dfrac{455}{1092}[/tex]

The greatest common factor of 455 and 1092 is 91.

Therefore, divide the numerator and denominator by the GCF:

[tex]\dfrac{455 \div 91}{1092\div 91}=\dfrac{5}{12}[/tex]

Answer:

654

Step-by-step explanation:

An increase of 9% would mean 1.09 times 600 which equals 654

Daniella and her friends collected a total of 44 shells.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

Given ,

Daniella and her 10 friends are collecting shells on the beach to make crafts.

After they have collected the shells and put them in a pile, they split them evenly among the group. Each person gets 4 shells.

The correct equation for this problem is:

s = 11 x 4

where s is the total number of shells collected.

Simplifying this equation, we have:

s = 44

Therefore, they collected a total of 44 shells.

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To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element. All elements in the set have a multiplicative inverse except for 0.

To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element (usually 1).

For example, in the set {1, 2, 3, 4, 5} under multiplication modulo 6, we have:

The multiplicative inverse of 1 is 1 (1 x 1 = 1 mod 6).

The multiplicative inverse of 2 is 4 (2 x 4 = 8 = 1 mod 6).

The multiplicative inverse of 3 is 5 (3 x 5 = 15 = 3 x 1 = 1 mod 6).

The multiplicative inverse of 4 is 2 (4 x 2 = 8 = 2 x 4 = 1 mod 6).

The multiplicative inverse of 5 is 3 (5 x 3 = 15 = 3 x 5 = 1 mod 6).

Note that every element in the set has a multiplicative inverse except for 0. This is because any number multiplied by 0 is 0, not 1.

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The probability that the department store will get at most 3 calls in a 55 minute period is 0.066

The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within “x” period of time.

It is given that a department store gets an average of 16 calls in a 2 hour or 161055 = 223 calls per minute

Find the probability by Poisson distribution with parameter

λ = 223

P(X = x) = λˣе - λx!

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

   = (223)⁰е - 223(0!) +(223)¹е - 223(1!) +(223)²е - 223(2!) +(223)³е - 223(3!)

  = 0.0006 + 0.004 + 0.018 + 0.043

P(X ≤ 3) ≈ 0.066

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In part (a), we used the Central Limit Theorem (CLT) to approximate the sampling distribution of the sample mean. The CLT states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.

The conditions for the CLT are:

The sample is randomly drawn from the population.

The sample size is large (usually, n >= 30 is considered large enough).

The samples are independent.

In this case, we assume that the sample was randomly drawn from the population of diameters, and the sample size of 25 is large enough to satisfy the second condition. The samples are assumed to be independent, as we are sampling without replacement from a large population.

Therefore, we can apply the CLT and use the normal distribution to approximate the sampling distribution of the sample mean.

For a sample of size 2, the sample mean will still have a sampling distribution, but the CLT may not be applicable. If the population distribution is highly skewed or has heavy tails, a sample size of 2 may not be sufficient to smooth out the sampling distribution, and it may not be normal.

In this case, a normal approximation may not be appropriate, and other methods, such as bootstrapping or permutation tests, may be more appropriate for inference.

In summary, the normal approximation based on the CLT is valid for large sample sizes, regardless of the population distribution. For small sample sizes, other methods may be more appropriate, and the normal approximation may not be valid if the population distribution is highly skewed or has heavy tails.

Question: The basal diameter of a sea anemone is an indicator of its age. The density curve shown here represents the distribution of diameters in a certain large population of anemones; the population mean diameter is 4.2cm, and the standard deviation is 1.4cm.

Let Y dash represent the mean diameter of 25 anemones randomly chosen from the population.

(a) Find the approximate value of Pr{4 ≤ Ydash ≤ 5}.

(b) Why is your answer to part (a) approximately correct even though the population distribution of diameters is clearly not normal? Would the same approach be equally valid for a sample of size 2 rather than 25?Why or why not?

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The statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.

To determine which statement about 4 √2x + 4 √x + 3 = 0 is true, we need to solve the equation.

However, it is not possible to solve the equation exactly because it contains square roots. We can simplify the equation by multiplying both sides by the conjugates of the square roots, which eliminates the square roots.

Multiplying both sides by (2x + x + 3) / (2x + x + 3), we get:

(4 √2x + 4 √x + 3) * (2x + x + 3) / (2x + x + 3) = 0 * (2x + x + 3) / (2x + x + 3)

Expanding the left-hand side, we get:

12x + 6 = 0

Solving for x, we get:

x = -1/2

So, the statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.

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Answer:

y – 7 = 3(x – 5)

Step-by-step explanation:

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 3}(x-\stackrel{x_1}{5}) \\\\\\ y-7=3x-15\implies {\Large \begin{array}{llll} y=3x-8 \end{array}}[/tex]

A polygon with a sum of interior angles of 3960 has 22 sides.

The sum of the interior angles of a polygon can be calculated using the formula:

(n-2) * 180

where n is the number of sides of the polygon. This formula is derived from the fact that the total degree measure of a polygon is equal to the sum of the degree measures of its interior angles. In a polygon with n sides, there are n angles, each measuring 180 degrees. So the total degree measure of a polygon with n sides is n * 180.

Now, if we subtract the degree measures of two angles, we are left with the sum of the degree measures of the remaining n-2 angles. This is why the formula for the sum of the interior angles of a polygon is given as (n-2) * 180.

To find the number of sides of a polygon given its sum of interior angles, we can rearrange the formula as follows:

n = (Sum of interior angles / 180) + 2

So, if the sum of the interior angles is given as 3960, we can plug that into the formula:

n = (3960 / 180) + 2

n = 22

Therefore, a polygon with a sum of interior angles of 3960 has 22 sides.

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How many sides does a polygon have if the sum of the interior angles is 3960?

Answer: x=8

Step-by-step explanation: since we know 2 sides of both quadrilaterals and they are similar,

just put 32/40 = 24/3x+6 ,

cross multiply ( 32 x 3x+6   and 40 x 24),

they become 96x +192 = 960.

move 192 to the other side and divide both sides by 96

The measure of the length of the shortest side will be 15 units.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. How frequently one value contains or is contained within another is shown by the numerical connection between the two values.

Given that the perimeter of the triangle is 100 and the ratio of the sides of the triangle is 3:5:12.

The length of the shortest side will be calculated as:-

3x + 5x + 12x = 100

20x = 100

x = 20

Length = 3x

Length = 3 x 5 = 15 units

Hence, the shortest side will be 15 units.

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(a) Potential on the opposite sides of the positive and negative plates is 8475 V and -8475 V, respectively. (b). 772 m/s is the speed at which the positive plate will be struck.

A more technical or sophisticated phrase, velocity, is occasionally used interchangeably with speed to refer to extremely high rates of linear or circular speed, such as the velocity of a bullet.

a). Positivplate should be on the right and negativeplate should be on the left.

Potential equals zero at the center of the plates.

Electric field between it plates: 30e⁻⁶/8.85e⁻¹² (338 V/m) = sigma/e0

Potential is equal to 3389830x, where x is the distance in meters from the center of the plates.

Where x is the distance in meters from the center of the plates, the potential to the left of either the middle point equals -3389830x.

Potential outside of the positive plate is equal to 3389830*0.005/2, or 8475 V.

The potential is -8475 V on the contrary side of the negative plate.

Potential between it plates is equal to -8474 + 3389830x, where x is the distance in meters from the negative plates.

b). Electron energy at the positive plate is equal to [8475 - -8475]. eV = 2*8475*1.6e⁻¹⁹ = 2.712*10⁻¹⁵ J

Speed = sqrt(2E/m) = sqrt(2*2.712e-15/9.1e⁻³¹) = 772 meters per second.

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The value of z   is -1.09.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data collection.

Given: P(Z<z)=0.14

To find the value of z such that 0.14 of the area lies to the left of z.

We will use z-score table to get the value of z here.

IN z-score table, we have

For P(Z<-1.09)=0.14

Hence, the value of z is -1.09.

Its approximate value is -1.09

So the final answer is z=-1.09.

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An article appearing in a certain journal included the following acrylamide content for five brands of biscuits. 344 , 294, 333, 276, 248. The mean acrylamide level (in nanograms/gram) is 299.

In statistics, the mean is a measure of central tendency that represents the sum of all values in a dataset divided by the total number of values. It is commonly referred to as the average.

To calculate the mean, all the data values are added together, and then this sum is divided by the number of data points in the dataset. The formula for calculating the mean is:

mean = (sum of values) / (number of values)

To calculate the mean acrylamide level, we need to add up all the acrylamide levels for the five brands of biscuits and divide the sum by the total number of brands.

Sum of acrylamide levels = 344 + 294 + 333 + 276 + 248 = 1495

Total number of brands = 5

Mean acrylamide level = (Sum of acrylamide levels) / (Total number of brands) = 1495 / 5 = 299

Therefore, the mean acrylamide level is 299 nanograms/gram.

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Answer:

Step-by-step explanation:

He is now 14 years old because if you minus 21 and 7, it will be 14

Answer:

If your friend says that he will be 21 years old in seven years, then he is currently 21 - 7 = 14 years old.

Step-by-step explanation:

The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.

An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."

In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.

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Using the distributive property, we can write (z-5)(z+3) is equal to  [tex]z^2[/tex] - 2z - 15.

Let us expand the expression (z-5)(z+3).

We will distribute the terms in the first set of parentheses (z-5) to the terms in the second set of parentheses (z+3) as follows -

(z-5)(z+3) = z(z+3) - 5(z+3)

Now, we will simplify the expression by distributing z to both terms inside the first set of parentheses, and then distributing -5 to both terms inside the second set of parentheses as follows -

z(z+3) - 5(z+3) = [tex]z^2[/tex] + 3z - 5z - 15

Combining the like terms, we get,

(z-5) (z+3) = [tex]z^2[/tex] - 2z - 15

Therefore, (z-5)(z+3) is equal to  [tex]z^2[/tex] - 2z - 15.

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Answer:

b.  53.1°

c.  126.9⁰

Step-by-step explanation:

These are SSA triangles;  use Law of Sines to find the unknown angle:

b)  sin30/15 = sinA/24

sinA(15) = sin30(24)

sinA = sin30(24)/15 = 0.80

m∠A = sin⁻1(0.80) = 53.1°

c)  m∠A = 180 - 53.1 = 126.9⁰

Answer:

∠ BAC = 53.13° , ∠ BAC = 126.87°

Step-by-step explanation:

using the Sine rule in Δ ABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]

where a is the side opposite ∠ A and c is the side opposite ∠ C

here a = BC = 24 and c = AB = 15 , then

[tex]\frac{24}{sinA}[/tex] = [tex]\frac{15}{sin30}[/tex] ( cross- multiply )

15 sinA = 24 sin30° ( divide both sides by 15 )

sin A = [tex]\frac{24sin30}{15}[/tex] , then

A = [tex]sin^{-1}[/tex] ( [tex]\frac{24sin30}{15}[/tex] ) = 53.13°

(b)

acute angle BAC = 53.13°

(c)

the sine of an angle is positive in both the first and second quadrant , so

obtuse angle BAC = 180° - 53.13° = 126.87°

If 18% of middle school student voted in a school election and number of students who voted is 213 , then the total students in the middle school is approximately 1184 students .

Let "x" be = total number of middle school students.

We know that 18 percent  of the students voted = 0.18x, and is equal to 213  ;

that means , ⇒ 0.18x = 213 ;

Now we need to solve for x,

We divide both sides by 0.18 ;

⇒ x = 213/0.18  ;

Simplifying, we get:

⇒ x = 1183.33

Since the number of students cannot be in decimal ,

So ,  the actual number of students must be greater than or equal to 1183.33.

Therefore, the middle school has approximately 1184 students.

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Answer:

8 < f

8 must be strictly lesser than f, not greater than or equals to.

Answer:

The length of one lap around the path is 2π x 350 m, which is equal to 2200 m.

Jimmy jogs 2200 m x 3 laps x 5 days, which is equal to 33000 m or 33 km.

Step-by-step explanation:

The height of the cylinder is 18 cm and its volume is 450π cubic centimeters, given that the radius of its base is 5 cm and its total surface area is 165πcm².

A right circular cylinder is a three-dimensional geometric shape with a circular base and a curved surface that extends upward in a cylindrical fashion.

Let's begin by identifying the formula for the total surface area of a cylinder. It is given by:

Total surface area = 2πr(h + r)

Where r is the radius of the base, h is the height, and π is a mathematical constant (approximately 3.14). We are given that the total surface area of the cylinder is 165πcm², and the radius of its base is 5 cm. Substituting these values in the formula, we get:

165π = 2π(5 + h)5 + 2π(5)²

Simplifying this equation, we get:

165π = 10πh + 150π

Dividing both sides by 10π, we get:

h + 15 = 33

Therefore, the height of the cylinder is 18 cm (33 - 15).

Now, let's find the volume of the cylinder. The volume of a cylinder is given by:

Volume = πr²h

Substituting the values of r and h, we get:

Volume = π(5)²(18)

Simplifying this equation, we get:

Volume = 450π

Therefore, the volume of the cylinder is 450π cubic centimeters.

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Complete Question:

The total surface area of a right circular cylinder is 165πcm². If the radius of its base is 5 cm; find its height and volume.

If $4400 is placed in account at 8.25% for 22 years , then the final amount received after 22 years will be $26480.08  .  

We use the formula for compound interest to find the final amount  :

that is ⇒  A = P(1 + r)ˣ  ;

where:  A = the amount of money in the account after "x years"  ;

P(initial amount) = $4400 ;   r (interest rate) = 0.0825  ;

⇒ x(time) = 22 years

we get ;

⇒ A = 4400×(1 + 0.0825)²²  ;

⇒ A =  4400×(1.0825)²²  ;

⇒ A =  4400×6.018028  ;

⇒ A = 26480.08  ;

Therefore , the amount in the account after 22 years is $26480.08  .

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Answer: .75 + .25x ≤ 7

Step-by-step explanation: The x equals the amount that you can buy for each item.

Answer:

Rs 3520 is divided in the ratio 11:12:17 as rs 968, rs 1056, and rs 1469

Step-by-step explanation:

According to the question, we have to divide rs 3520 in the ratio 11:12:17

let the common ratio be x

so, total share= (11+12+17)x = 40 x

for the first person, share would be (11x/40x)*(Rs 3520)

=Rs 968

for the second person, share would be (12x/40x)*(Rs 3520)

=Rs 1056

for the third person, share would be (17x/40x)*(Rs 3520)

=Rs 1496

The shares are Rs 968, Rs 1056, and Rs 1469

hope this helps :)

The number of gifts ason can wrap  with the ribbon he has is 12.

A quantity that is multiplied or divided between one set of units and another is termed as a conversion factor. If a conversion is required, it must be carried out with the right conversion factor to generate a value that is identical.

To change a value or expression from one form to another.

Now in the given question,

ason wraps a gift using one third of a foot of ribbon.

he has total ribbon of 4 feet.

so, we have the equation,

[tex]\frac{1}{3} x=4\\\\x=12[/tex].

hence, 12 gifts can be wrapped with the ribbon ason has.

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Answer: approx 13.54 (full decimal : 13.416666667)

Step-by-step explanation:

Area = Base Area x Height   OR    Length x Width x Height

5/3 x 13/4 x 5/2

5 x 13 x 5 = 325

3 x 4 x 2 = 24

325/24 = approx 13.54

3 minutes is the cost of the call that is same for both plans

Two or more expressions with an Equal sign is called as Equation.

Let's assume the call duration in minutes is represented by x.

For David, the cost of the call can be represented by the equation: C(d) = 4 + x

For Alec, the cost of the call can be represented by the equation: C(a) = 1 + 2x

Since the cost of the call is the same for both plans, we can set the two equations equal to each other and solve for x:

4 + x = 1 + 2x

Solve for x.

3 = x

Hence, the call duration that costs the same on both plans is 3 minutes.

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An estimated Rs. 1863.40 will be needed to cement the route.

Diameter of park [tex]$=7 \mathrm{~m}$[/tex]

so, radius of park [tex]$=\mathrm{r}_1=3.5 \mathrm{~m}$[/tex]

Width of park [tex]$=0.7 \mathrm{~m}$[/tex]

Bigger radius of park [tex]$=\mathrm{r}_2=0.7+3.4=4.2 \mathrm{~m}$[/tex]

Now, Area of path = area of bigger circle -area of smaller circle

[tex]$=\pi r_2^2-\pi r_1^2=$ $\pi\left(r_2^2-\mathrm{r}_1^2\right)=\frac{22}{7}\left(4.2^2-3.5^2\right)=\frac{22}{7}(17.64-12.25)=16.94 \mathrm{~m}^2$[/tex]

Also, Cost of expenditure = rate [tex]$\times$[/tex] area [tex]$=110 \times 16.94=1863.40$[/tex]

Cost of Expenditure of cementing the path is Rs. 1863.40.

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