3/ax - 4 = 20 What is x?



x =

The greatest common divisor of two given numbers is 15.

Given that, the least common multiple of A and B is 1575 and A: B=3: 7.

We need to find what is their greatest common divisor.

The least common multiple is also known as LCM (or) the lowest common multiple in math. The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers.

We know that the product of the GCF and the LCM of two numbers is always the product of the two numbers.

Let the GCF of two numbers be x.

Then A×B=1575×x

Take A:B=3k:7k

Now, 3k×7k=1575×x

⇒21k²=1575x

⇒k²=75x

x must be expressed as a square divided by 75.

Now, 75=3×5×5

If we multiply 3 to the above product we get the perfect square number.

So, k²=225

⇒k=15

Now, 3k=45 and 7k=105

45=3×3×5 and 105=3×5×7

So, GCD=3×5=15

Therefore, the greatest common divisor of two given numbers is 15.

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Your question is incomplete, probably the complete question/missing part is:

If the least common multiple of A and B is 1575, and the ratio A of B to 3 is 7 , then what is their greatest common divisor?

Answer: 75

Step-by-step explanation:

Since the ratio of A to B is 3:7:

There is an integer k for which A=3k and B=7k.

Moveover, k is the greatest common divisor of A and B, since 3 and 7 are relatively prime.

Recalling the identity lcm(A,B)*gcd(A,B)=AB, we find that 1575k=(3k)(7k), which implies k=1575/21=75.

Answer:

Step-by-step explanation:

d. Square root of 9

you’re welcome :)

The irrational number is 0.2535455565.....

The correct option is D.

Given, that identify the irrational number.

Irrational number : Irrational numbers are non terminating and non repeating.

1) Square root of 9: √9

= 3

It is rational number.

2) Number : 0.123123123....

It is Non terminating but repeating thus it is not an irrational number.

3) Fraction : 5/9

5/9 = 0.555555..

It is a repeating number thus its is not an irrational number.

4) Number: 0.2535455565....

The number is non terminating as well as non repeating. Thus it is an irrational number.

Therefore option D is correct.

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Answer:

35ab = 48

Step-by-step explanation:

given

5a = 6 ( divide both sides by 5 )

a = [tex]\frac{6}{5}[/tex]

and

7b = 8 ( divide both sides by 7 )

b = [tex]\frac{8}{7}[/tex]

substitute these values for a and b into the expression and simplify

35ab

= 35 × [tex]\frac{6}{5}[/tex] × [tex]\frac{8}{7}[/tex] ( divide 35 and 5 by 5 )

= 7 × 6 × [tex]\frac{8}{7}[/tex]

= 42 × [tex]\frac{8}{7}[/tex] ( divide 42 and 7 by 7 )

= 6 × 8

= 48

We know that an arc is a part of the entire perimeter of a circle.

Radian is defined as a unit of plane angular measurement that is equal to the angle subtended by the circle at the center by an arc that is of the length equal to the radius

We also know that the circle as a whole contains 2π radians

Now first we are required to find the perimeter of the circle

Perimeter of the circle is given by the formula 2πr

Hence, perimeter of the circle = 2πr= 2π x 10 =20π=62.851cm

Hence value of arc in radians = 40/62.851 x 2π =0.636 x 2 π =1.272π

Radian can be converted to degree by multiplying the radian measure by 180/π

Therefore, angle subtended by arc in degrees =1.272 π x 180 /π =229.1 °

Hence the angle subtended by arc is 229.1°

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The scale that is being used on the image is 1:7

From the question, we are to determine the scale that is being used on the image.

From the given information,

The image of the book shown on the website is 1.5 inches wide and 3 inches tall

Also, we have that

The actual width of the book is 10.5 inches

The scale = Width of the book on the website / Actual width of the book

Thus,

Scale = 1.5 inches / 10.5 inches

Scale = 1/7

∴ Scale = 1 : 7

Hence, the scale that is being used on the image is 1:7

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The maximum number of meals the family can eat at the restaurant is 11

Amount saved by Dana for her upcoming vacation = 450

Average cost when Dana cooks lunch or dinner  = 10

Average cost when the family goes to a restaurant for lunch or dinner = 40

Maximum number of meals the family can have at the restaurant  = Amount saved by Dana/Average cost of a meal when the family goes to a restaurant

=450/40

= 11.25 or 11

So, the maximum number of meals the family can eat at the restaurant is 11 with a budget of 450.

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Answer: 164.53%

Step-by-step explanation:

105.3/64=1.6453125

1.6453125*100=164.53125

164.53125=164.53%

Notice the answer is greater than 100 percent. This is because 105.3 is greater than 64, meaning that 105.3 is greater than 100% of 64, so 105.3 will have a greater percent value.

10² = 100

28.007 × 100 / 2800.7

third option = 2,800.7

Answer: The answer is within the picture!

Step-by-step explanation:

Answer:

Step-by-step explanation:

The ratio of seasoning to flour is 4:6.

This can also b re-written as a fraction. The fraction would be 4/6.

If you want to find the amount of seasoning per cup of flour, you must divide.

4/6  Divide the denominator (bottom number) by 6 to get a 1 on the bottom. Now divide the numerator (top number) be the same amount. This gives you a 0.66 on the top. Now you have 0.66/1.

0.66 is equivalent to 2/3, so for every 1 cup of flour, there is 2/3 a tablespoon of seasoning.

Hope this helps!

Answer:

Step-by-step explanation:

bag of oranges = $6.40

each bag = 16 oranges

48 divided by 16 = 3 (bags)

$6.40 x 3=  $19.20

The cost of 48 oranges would be $19.20 when the each cost 6.4

Given:

- Cost of a bag of oranges = $6.40

- Number of oranges in each bag = 16

First, let's find the cost per orange:

Cost per orange = Cost of a bag / Number of oranges in the bag

Cost per orange = $6.40 / 16 = $0.40

Now, the cost per orange is $0.40.

To find the cost of 48 oranges, multiply the cost per orange by the number of oranges:

Cost of 48 oranges = $0.40 * 48 = $19.20

Therefore, the cost of 48 oranges would be $19.20.

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The volume of cube in cm is (4cm)

Volume of cube is =96 CM^2

Let's consider he as the edge of cube

Surface area of is =6

That is symbol cube as (e^2)

As per the given question the surface are of cube is given as 96 cm^2

As we know

96=6^2

e^2=96/6

e^=16

e=√16

e=4cm

The volume of cube in centimetre is 4cm

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Answer:

B

Step-by-step explanation:

Graph is positive and y intercept is on negative 2.

Answer:

D.

Step-by-step explanation:

First distribute:
2/3x + 4 -14/15x

2/3 = 10/15

10/15-14/15=

-4/15

-4/15 + 4

The probability of getting a 7-card poker hand that contains at least two 3-of-a-kind is 0.0013

For given question,

We need to find the probability of getting a 7-card poker hand that contains at least two 3-of-a-kind.

Total number of cards = 52

If a 7-card poker hand contains at least two 3-of-a-kind,

3-of-a-kind means the three cards of the same rank.

The expression for the probability is,

[tex]P=\frac{ ^7C_3}{ ^{52}C_4} +\frac{ ^7C_2}{ ^{52}C_5} +\frac{ ^7C_1}{ ^{52}C_6}\\\\P=0.0013[/tex]

So, the required probability is 0.0013

Therefore, the probability of getting a 7-card poker hand that contains at least two 3-of-a-kind is 0.0013

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Answer:

(4, -1)

Step-by-step explanation:

See attached image.

1) The standard deviation of the temperature readings in degrees Celsius is 1.66° C.

2) The mean and standard deviation of Ferguson tip distribution is 1.1 and 0.3 respectively.

1) Let, X be the temperature in Fahrenheit and Y be the temperature in Celsius.

Mean = 77° F

[tex]77^\circ \ F=\frac{5\times77}{9}-\frac{160}{9}[/tex]

[tex]= 25^{\circ}C[/tex]

Variance in Fahrenheit is [tex]3^2=9[/tex]

[tex]Var(aX+b)=a^2VarX[/tex]

Here, [tex]a=\frac{5}{9}[/tex] and [tex]b=-\frac{160}{9}[/tex]

[tex]Var(Y)=\frac{25}{81}\times9[/tex]

[tex]=2.77[/tex]

Standard deviation [tex]= \sqrt{Var(X)[/tex]

[tex]= \sqrt{2.77}[/tex]

[tex]= 1.66^{\circ}[/tex]

2) Let, X be the cost of them meal and Y be the tip he gives.

[tex]Y=2+0.1X[/tex]

[tex]E[X]=9, Var[X] = 9[/tex]

Therefore,

[tex]E[Y]=E[2+0.1X][/tex]

[tex]=0.1E[X]+2[/tex]

[tex]=0.1\times9+2[/tex]

[tex]=1.1[/tex]

[tex]Var[Y] = 0.12Var[X] = 0.01\times9=0.09[/tex]

Standard deviation of [tex]Y = \sqrt{Var[Y]}[/tex]

[tex]= \sqrt{0.09}[/tex]

[tex]= 0.3[/tex]

Therefore,

1) The standard deviation of the temperature readings in degrees Celsius is 1.66° C.

2) The mean and standard deviation of Ferguson tip distribution is 1.1 and 0.3 respectively.

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"Your question is incomplete, probably the complete question/missing part is:"

Coach Ferguson uses a thermometer to measure the temperature (in degrees Fahrenheit) at 20 different locations in the school swimming pool. An analysis of the data yields a mean of 77 degrees Fahrenheit and a standard deviation of 3 degrees Fahrenheit. Recall that [tex]C^{\circ}=\frac{5^{\circ}F}{9} -\frac{160}{9}[/tex]. What is the mean temperature reading in degrees Celsius? What is the standard deviation of the temperature readings in degrees Celsius? When Sam goes to a restaurant, he always tips the server $2 plus 10% of the cost of the meal. If Sam's distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of his tip distribution?

Answer:

1st box: 2000

2nd box: 1

3rd box: 22.99

4th box: 0.11

5th box: 23

Step-by-step explanation:

It's simply splitting up the 2000 and 1, and then diving them by 87 each.
After that you can divide them and round to the nearest 10th, and add them to get 23.

Answer:

the total charged for a car is f(x)=x+5

Step-by-step explanation:

because ther is only on car the value 5 could be constant. but because there could be a number of people in the car that is described by x and is multiplied by the cost which is 1

So, the least number of cards they could have altogether is any value of integer Z, that is ranging from (0→∞). If starting from n=1, then X=8 and Y=9.

What is an integer?

Let Joe has x no. of cards,

then,

Millie has (3/4)x cards.

In that case, Let millie has a total y no. of cards,

then, Joe has (2/3) y cards.

This means that,

(3X)/4 = (2Y)/3

The alternate form shall be:

X = (8 Y)/9

(3 X)/4 - (2 Y)/3 = 0

Real solution:

Y=(9X)/8

Integer Solution shall be:

X=8n, Y=9n, n∈Z, where Z is the set of integers.

So, the least number of cards they could have altogether is any value of integer Z, that is ranging from (0→∞). If starting from n=1, then X=8 and Y=9.

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Answer:

6.244 x 10^-1

Step-by-step explanation:

The weight of the green squash is 33.76 pounds.

A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 3/4. A decimal is a non-integer that is made up of integers and non-integers that are separated by a decimal point. An example of a decimal is 1.2.

The weight of the green squash can be determined by multiplying the fraction of the green quash by the total pounds of green and yellow squash.

Pounds of green squash  = fraction of green squash x total pounds of squash

Fraction of green squash = 1 - 1/5 = 4/5

Pounds of green squash  = 4/5 X 42.2 = 33.76 pounds

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The vertex of the parabola of the quadratic function that is increasing in the interval (-∞, 2), and decreasing in the interval (2, ∞), is the highest point on the parabola.

The given description of the quadratic function is presented as follows;

The interval the function is increasing = (-∞, 2)

The interval the function is decreasing = (2, ∞)

The graph of the function is therefore increasing from -∞ up to the point just before 2.

The graph of the function is decreasing from the point just after 2 to infinity.

The point 2 is therefore the highest point of the graph and also, the vertex of the quadratic function.

Therefore;

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The least possible average (arithmetic mean) of the 21 integers is 6.

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The sides of angle JBA is ray BJ and BA.

In the geometry, angle is defined as the geometry formed by the multiple rays. Or we can say that the angle is the figure formed by two rays which has same initial point. These rays are also known as the sides of an angle. A angle can have two rays.

Some common terms related to angle :

Endpoint  : It is the point where the rays met to each other.

Ray : Ray is the side or line segment on which angle is formed.

Curve : It is a line but not straight i.e. a bended line.

Tangent : A line which touches the surface of curve.

In the given question, as ∠JBA is made between two lines or rays i.e. ray BJ and ray BA . Therefore sides of this angle are BJ and BA.

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Answer:

Perimeter = 2(length) + 2(width)

Perimeter = 2(17.4x - 0.8) + 2(6X)

Perimeter = 34.8x - 1.6 + 12x

Perimeter = 46.8x - 1.6

Answer:

Converse: If the air temperature is 32°F or less, then freezing rain is falling.

Inverse: If freezing rain is not falling, then the air temperature is not 32°F or less.

Contrapositive: If the air temperature is not 32°F or less, then freezing rain is not falling.

Explanation:

Statement: If p, then q.

Converse: If q, then p.

Inverse: If not p, then not q.

Contrapositive: If not q, then not p.

A contains 21 elements

Let's assume set A contains X elements ,

so , according to set theory ,  A ∪ B = 23

or, A + B - ( A ∩ B ) = 23

or ,X + 15 - 13 = 23

or, X + 2 = 23

or , X =  23 - 2

or, X = 21

So , there are 21 elements are present in set A .

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Solving the problem according to the set theory, we get that set A contains 21 elements.

A set is a well-defined collection of objects, whose elements remain fixed and do not vary. It means that set doesn't change from person to person and is invariable.

Let's assume that set A contains X elements,

So, according to the set theory, A ∪ B = 23

or, A + B - ( A ∩ B ) = 23

or ,X + 15 - 13 = 23

or, X + 2 = 23

or , X = 23 - 2

or, X = 21

From the above explanation, we get that there are 21 elements are present in set A .

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