Which number produces a rational number when multiplied by 7/8

Answer:

8/27. Though the question is a bit confusing. If your asking which term describes it, its this a multiple choice question?

Step-by-step explanation:

8 /27

is already in the simplest form. It can be written as 0.296296 in decimal form (rounded to 6 decimal places).

Steps to simplifying fractions :

Find the GCD (or HCF) of numerator and denominator

GCD of 8 and 27 is 1

Divide both the numerator and denominator by the GCD

8 ÷ 1

27 ÷ 1

Reduced fraction:  

8 /27

Therefore, 8/27 simplified to lowest terms is 8/27.

Answer:

-8/27

Step-by-step explanation:

Answer: 1075 sq. ft

Step-by-step explanation:

A = length times width

First split the shape into two rectangles

Area of rec 1 = 25 times 8 = 200

Area of rec 2 = 35 times 25 = 875

200+875 = 1075 sq. ft

Answer:

2.2 % per minute

35 minutes

Step-by-step explanation:

(0,23%) and (30, 89%)

We can find the slope

m = ( y2-y1)/(x2-x1)

    = (89-23)/(30-0)

   66/30

   =2.2 % per minute

To get to full change we need 100-23 = 77 %

77% * 1 minute/ 2.2 % =35 minutes

Inequality represents number of months (m) it will take Gabriela to save at least $5,600 is m ≥ 6.

As given in the question,

Amount Gabriela plans to save to buy a car = at least $5,600

Amount she already has = $2500

Amount she needs to save at least = $(5600 -2500)

                                                          =$3100

Plans to save each month =$500

Inequality to represents the number of months to save at least $5600

m ≥ 3100/500

⇒ m ≥ 6

Therefore, inequality represents number of months (m) it will take Gabriela to save at least $5,600 is m ≥ 6.

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The value of f(-0.01) is approximately 0.99005.

To evaluate f(-0.01), we substitute -0.01 into the function f(x) = (1+x)^(1/x). Thus, we have f(-0.01) = (1+(-0.01))^(1/(-0.01)).

Using a calculator, we simplify this expression to f(-0.01) = 0.99005. Therefore, the value of f(-0.01) rounded to five decimal places is approximately 0.99005.

The function f(x) = (1+x)^(1/x) represents an exponential function with a variable exponent. In this case, we are evaluating the function at x = -0.01.

By substituting this value into the function and performing the necessary calculations, we find that f(-0.01) is approximately 0.99005. This means that when x is equal to -0.01, the function value is approximately 0.99005.

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The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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7 is not included and hence it is depicted on the number line using an open dot. Hence, solution to the inequality is option B.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The given inequality is:

x + 8 > 15

Subtracting 8 on both sides of the equation:

x + 8 - 8 > 15 - 8

x > 7

Here, 7 is not included and hence it is depicted using an open dot.

Hence, option B is the correct answer.

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The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:

A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.

A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.

A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.

A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.

B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.

B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.

Finally, performing the remaining operations:

(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.

(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.

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The subgroup of S4 that is isomorphic to Z2 is {e, (1 2)(3 4)}.

Answer:

Step-by-step explanation:

Letter B is the correct answer

Initial population is 200, tripled every hour

200 x 3 = 600

First hour 200

Second hour = 600 + 200 = 800

Third hour 800x3 = 2400 + 800 = 3200

and so on.

Answer:

C.

Step-by-step explanation:

Choose two points on the line and find the slope. For example, let's use coordinates (0,2) and (5,4).

Use the slope formula to find the slope between these points.

y2-y1/x2-x1

4-2/5-0 = 2/5

Slope of the new line is 2/5.

With the slope, compare the two fractions. Set them up side by side and cross multiply. Whichever one gives you the larger number is the larger fraction. Larger slopes are going to be steeper. So, C is right.

Refer to my picture to see what I mean by cross multiplying.

Answer:

a=7, b=3

Step-by-step explanation:

Subtracting, we get the area of QRXY is 63 cm².

Using the area formula of a rectangle, we get 9a=63, and thus a=7.

Using the area formula again on triangle PXYS, 7b=21, and thus b=3.

The value of side 'a' is 7cm and side b is 3 cm.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

It is given that the area of PQRS is 84 square cm and the area of PSYX is 21 square cm.

The area of QRXY is calculated as,

Area QRXY = 84 - 21

Area QRXY = 63 square cm

The side a will be calculated as,

a x 9 = 63

a = 63 / 9

a = 7 cm

The side of b will be,
b x 7 = 21

b = 21 / 7

b = 3 cm

Therefore, the value of side 'a' is 7cm and side b is 3 cm.

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Answer:

The highest altitude that the object reaches is 576 feet.

Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be \(h(t) = -16\cdot t^{2} + 128\cdot t + 320\), the first and second derivatives are, respectively:

First Derivative

\(h'(t) = -32\cdot t +128\)

Second Derivative

\(h''(t) = -32\)

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

\(-32\cdot t +128 = 0\)

\(t = \frac{128}{32}\,s\)

\(t = 4\,s\) (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

\(h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320\)

\(h(4\,s) = 576\,ft\)

The highest altitude that the object reaches is 576 feet.

There must be 46 chairs in each row and total number of chairs are 1058

To meet the given conditions, we need to find a number that has the following properties:

It should be divisible by 2, as there are an even number of chairs in each row.

It should be divisible by 23, as there are 23 rows of chairs.

It should be the same number in each row.

The smallest number that satisfies these conditions is 46, which is the least common multiple of 2 and 23.

So, we need to set up 46 chairs in each row.

The total number of chairs required will be:

Total number of chairs = 23 rows x 46 chairs per row = 1058 chairs

Hence, the total number of chairs are 1058

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Answer:

D

Step-by-step explanation:

Set D is not a functions. Functions are defined as each x having only 1 y value associated with it. 2 in the x column has two values associated with it: 1 and 2

D is not a function.

We have the following figure:

First let's find the perimeter of the figure:

since one linear foot costs $1.19 of the trim, then the total cost would be:

therefore, it will cost $64.26 for the trim.

Answer:

★ Mercantilism - loosely related policies developed by Britain so that the colonies could be used as a source of raw materials.

★ Import - when items are brought in from other countries.

★ Export - when items are sold from one country to another.

★ Enumerated Article - certain crops and items, such as sugar, tobacco, cotton, ginger, and some dyes, that could not be shipped, carried, conveyed, or transported under the Navigation Act of 1660.

★ Legislature - a group of people coming together to legitimize decisions.

★ Indentured Servant - colonists who received free passage to North America in exchange for working without pay for a certain number of years.

★ Navigation Acts - band of laws that restriced the use of foreign shipping for trade only between england and its colonies.

★ Dominion of New England - an english governing organization that united the New England colonies into a single administrative unit from 1686 to 1689.

★ English Bill Of Rights - act passed by parliament, that ensured the superiority of parliament over the monarchy.

Step-by-step explanation:

Hope you have a great day ;-)

Answer :

⠀

Explanation :

⠀

Solution :

where,

⠀

We know that,

\( {\longrightarrow \bf \qquad (AC) {}^{2} = (AB) {}^{2} +( BC) {}^{2} }

\)

⠀

Now, we will substitute the given values in the formula :

\( {\longrightarrow \sf \qquad (AC) {}^{2} = (8) {}^{2} +( 6) {}^{2} }\)

⠀

We know that, (8)² = 64 and (6)² = 36. So,

\( {\longrightarrow \sf \qquad (AC) {}^{2} = 64 + 36 }\)

⠀

Now, adding 64 and 36 we get :

\( {\longrightarrow \sf \qquad (AC) {}^{2} = 100 }\)

⠀

Now, we'll take the square root of both sides to remove the square from AC :

\( {\longrightarrow \sf \qquad \sqrt{(AC) {}^{2}} = \sqrt{100} }\)

⠀

\( {\longrightarrow \sf \qquad AC = \sqrt{100} }\)

⠀

We know that, square root of 100 is 10 .

\( {\longrightarrow \bf \qquad AC = 10 }\)

⠀

So,

Answer:

m∠a = 110°

m∠b = 110°

m∠c = 70°

m∠d = 70°

m∠i = 110°

m∠h = 110°

m∠j = 70°

m∠g = 110°

m∠f = 70°

m∠e = 70°

m∠k = 57°

m∠m = 70°

m∠l = 167°

Step-by-step explanation:

Let the measure of the yellow angle = 110°

Therefore;

m∠a = 110°  by vertically opposite angles

m∠b = m∠a = 110° by opposite interior angles of a parallelogram

m∠c = 180° - 110° = 70° by same side interior angles

m∠d = m∠c = 70° by opposite interior angles of a parallelogram

m∠i and m∠c are supplementary angles, therefore, m∠i = 110°

m∠h = m∠i = 110° by vertically opposite angles

m∠j = m∠c = 70° by vertically opposite angles

m∠g and m∠d are supplementary angles, therefore, m∠g = 110°

m∠f = m∠d = 70° by alternate interior angles

m∠f = m∠e = 70° by vertically opposite angles

m∠k = 180° - (m∠h + 13°) = 180° - (110° + 13°) = 57°

m∠b and m∠m are supplementary angles, therefore, m∠m = 70°

m∠l and 13° are supplementary angles, therefore, m∠l = 167°

Answer:

12

Step-by-step explanation:

Since we can infer that those lines are the same length...

5x-15 = 3x+9

2x -15 = 9

2x = 24

x = 12

Answer:

y = 6x + 26. perpendicular = -1/6

Step-by-step explanation:

multiply out the equation:

y - 2 = 6x + 24

move the 2 over and add it:

y = 6x + 24 + 2 = 6x + 26.

y = 6x + 26.

gradient = 6

if gradient is m, perpendicular is given by -1/m

= -1/6

Answer:

It’s 16.09

Step-by-step explanation:

Answer:

16.09

I just added it all together

To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.

We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.

The z-score formula is:

z = (x - μ) / σ

Where:

x = value (62 seconds)

μ = mean (61 seconds)

σ = standard deviation (1.5 seconds)

Calculating the z-score:

z = (62 - 61) / 1.5

z ≈ 0.6667

Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.

Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.

To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:

Number of trials = Proportion * Total number of trials

Number of trials = 0.7461 * 39

Number of trials ≈ 29.08

Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.

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Answer:

5

Step-by-step explanation:

Answer:

x2 + 5 x − 6  using the AC method.  ( x − 1 ) ( x + 6 )

If it is wrong I am sorry!

In linear equation, 16 is represent The speed at which Serena is cycling from the dance class to her home

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

6x + y = 16

6x = 16 - y

x = 8/3 - y/6

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A normal distribution has a mean of 50 and a standard deviation of 3 , the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241  option a) 0.025.

In probability theory, normal distribution is also known as Gaussian distribution. It is a probability distribution that is symmetrical, bell-shaped, and a continuous probability distribution. It's also a part of continuous probability distribution that describes real-valued random variables whose probability density function is affected by two parameters: the mean μ and the variance σ².

Let us consider the problem. Suppose a normal distribution has a mean of 50 and a standard deviation of 3. Firstly, we need to standardize the random variable X that is to convert it to the standard normal distribution. We use the following formula for this Z = (X - μ) / σwhere X is the random variable and μ is the mean, σ is the standard deviation of the population.

So in this case, we can write this as Z = (44 - 50) / 3 = -2

We have now obtained the standard score or standard deviation for the random variable X.

Now we need to calculate the probability P(X ≤ 44) = P(Z ≤ -2).

The probability of Z being less than -2 is denoted by the area under the standard normal curve to the left of Z = -2.

Using the standard normal table we look for the probability that corresponds to -2 and the closest we find is 0.0228.

This probability represents the area under the standard normal distribution to the left of Z = -2.

To calculate the area to the left of Z = -2, we add the area to the left of the next integer, which is -3, which we find from the standard normal table as 0.0013, 0.0228 + 0.0013 = 0.0241.

Therefore, the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241 or 0.025 (rounded to three decimal places)Therefore, the answer is option A. 0.025.

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