5/12 x 5/12 x 5/12.

The written description of the given expression would be 14 less a number. That is option A.

Less than which is represented by the symbol such as < is used in arithmetics to show that a given value is less than the value of which it is being compared to.

The given expression = X - 14. Where X is the unknown number which is compared with 14.

Therefore, according to the expression, 14 less than a number is the same as X - 14.

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Since the angles in DBC and BDA are equal, we have:

DBC ≅ BDA

What is the Angle-Angle Similarity Theorem?

The Angle-Angle Similarity Theorem, also known as the AA Similarity Theorem, states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Given: AD // BC, AB // CD

To prove: DBC =~ BDA

From the given, we have AD // BC and AB // CD.

This means that AD is parallel to BC and AB is parallel to CD.

Since AB is parallel to CD, corresponding angles are equal.

Let the angle BCD = x.

Then, angle BAD = x.

Since AD // BC, corresponding angles are equal.

Let the angle DCB = y.

Then, angle DAC = y.

Now, we can see that angle BDA + angle DAC = y + x.

And angle DBC + angle DCB = y + x.

Since the sum of the angles in a triangle is 180 degrees,

angle BDA + angle DAC + angle DBC = 180.

So, y + x + y + x = 180.

Therefore, 2y + 2x = 180.

And, y + x = 90.

Since the angles in DBC and BDA are equal, we have:

DBC =~ BDA

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The equation of line m passing through the points (0, 0) and (1, 6) is y = 6x

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Line M goes through the points (0, 0) and (1, 6). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-0=\frac{6-0}{1-0} (x-0)\\\\y=6x[/tex]

The equation of line m is y = 6x

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Answer: 4a = D; 4b = B

Step-by-step explanation:

The inches of snow that fall at this rate is 8 inches

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

10 inches of snow fall for 1 1/4 hour

Ths means that the unit rate is

Unit rate = 10 inches/1 1/4 hour

Evaluate the quotint

Unit rate = 8 inches per hour

For one hour, we have

Snow = 8 * 1

Evaluate

Snow = 8

Hence, the amount is 8 inches

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Answer:

The answer is 3.2 x 10-21.

Step-by-step explanation:

To solve this problem, we need to use the rules of exponents. The first step is to calculate the exponents for each number.

For 9 × 104, the exponent is 3 (9 × 104 = 90000).

For 3,000,000, the exponent is 2 (3,000,000 = 3000000).

For 0.00243, the exponent is -3 (0.00243 = 0.00000243).

Now, we can calculate the answer by multiplying the exponents:

3 × 2 × (-3) = -6

Then, we need to multiply the numbers together to get the final answer:

(9 × 104)² × (3,000,000)² × (0.00243) = 9 x 10-6 x 9 x 10-12 x 0.00243 = 3.2 x 10-21.

Note that 11 > S or S < 11 is given in the in the Line Graph attached. The above simply means that 11 as a quantity is greater that the factore represented by "s".

A line graph is a graphical depiction of changing information over time. It is a diagram created by connecting points with line segments.

Line graphs may be used to demonstrate how something evolves over time.

Line graphs are useful for displaying data that has peaks (ups) and troughs (downs) or was gathered in a short period of time. The pages that follow discuss the various components of a line graph.

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Answer:

a ) $11.5

b.) 10 million gallons

Step-by-step explanation:

a.) Since it's asking for p if x = 20, we can plug 20 into the original equation

[tex]0.2(20) + 4p = 50[/tex]

0.2 times 20 is 4

4 + 4p = 50. Next we would subtract 4 from each side giving us

4p = 46. Lastly, divide each side by 4

p = 11.5

b.) If the p, also known as p increases by 50 cents, that means it goes from 11.5 to 12.

Now we plug in 12 to p and look for x, the opposite

[tex]0.2x + 4(12) = 50[/tex]

4 times 12 is 48, making it

0.2x + 48 = 50. This is where we subtract 48

0.2x = 2. and lastly, divide by 0.2, making...

x = 10

So demand decreased by 10 million because 20-10=10

The maximum value of the August electric bills of used by customers using the box and whisker plot is equal to $320 .

In box and whisker plot , Data is plotted in as it is divided into :

Five number summary set of data ,

Minimum value ,Maximum value, First Quartile, Third Quartile , Median.

Data of August electric bills ($)  as per given data is:

200  240  160   280  320

Minimum value = $160

Maximum value = $320

First quartile = $200

Third Quartile = $280

Median = $240

Therefore, the maximum value of the August electric bills shown as box and whisker plot is $320.

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_____The above question is incomplete ,the complete question is:

The local utility company released a report showing the August electric bills of their customers. ​ ​This box-and-whisker plot shows the results.

200  240  160 280  320  

August electric bills ($) What is the maximum value?

The value of a is given as follows:

a = 12.

We have two parallel lines that are cut by a transversal, and the two angles are between the parallel lines and on the same side of the transversal, meaning that they are consecutive interior angles.

Consecutive interior angles are supplementary, meaning that the sum of their measures is of 180º, hence the value of a can be found as follows:

10a + 2 + 5a - 2 = 180

15a = 180

a = 180/15

a = 12.

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Answer: a = 12.

Step-by-step explanation: did the same question got it right

The approximate surface area of this wheel of cheese is 437.6 square inches.

As per the given data, a wheel of cheese has a radius of 7 inches.

Radius r = 7 inches.

Also, a wheel of cheese has a height of 3 inches.

Height h = 3 inches

Also, given to consider the value of pi as 3.14.

π = 3.14

Here we have to determine the total surface area (TSA)of the wheel of cheese.

Since the cheese is a cylinder shaped thing.

The formula for the total surface area (TSA) of the wheel:

TSA = 2πr (r + h)

Substituting the values of the variables into the formula, we have

= 2 (3.14)(7)(7 + 3)

= 2 (21.88)(10)

= 2 (218.8)

= 437.6 square inches.

Therefore the total surface area is 437.6 square inches.

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The area and the perimeter of the room having rectangular shaped base are respectively,   121 feet² & 44 feet

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

Given that,

2 of the walls are 11 and 11,

The room is into rectangle shape,

Base area of room = length x width

                               =  11 x 11

                               =   121 feet²

Perimeter of base of the room = Sum of lengths and widths

                                                   = 11 + 11 + 11 + 11

                                                   =   44 feet

Hence, the area and perimeter are respectively 121 feet² & 44 feet

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There were 75 total number of persons present at the party

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The amount of people who ate lasagna was 12 less than 3/5 of the total number of people.

Let x represent the total number of people at the party.

The number of people that ate lasagna = (3/5)x - 12

The number of people who ate lasagna were 33. Hence:

The number of people that ate lasagna = 33

Therefore the equation is:

33 = (3/5)x - 12

(3/5)x = 45

x = 75

The total number of people is 75

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Based on the information provided, Derek will have made $480 more in buttered popcorn than in caramel popcorn.

To calculate his earnings with popcorn, let's use the expression given for each type of popcorn:

Buttered popcorn:

8w+9

8 x 12 + 9

96 + 9 =105

105 x 11 = $1155 (Total earnings for buttered popcorn)

Caramel popcorn:

6w-11

6 x 12 - 11

72 - 11 = 61

61 x 11 = $671 (Total earnings for caramel popcorn)

Now, let's calculate the difference:

$1155 - $671 =$480

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Answer:

1

Step-by-step explanation:

To find slope, m, we use the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

The top Y on the table is 7 and the bottom one is -1, so we'll plug those into the top.

The top X on the table is 6 and the bottom one is -2, so we'll plug those into the bottom

[tex]m = \frac{7 - ( - 1)}{6 - ( - 2)} [/tex]

[tex]m = \frac{8}{8} = 1[/tex]

Yes she is correct, because 810 km is approximately 500 miles

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

The distance between Cale and Johannesburg is 810 km.

1 mile is converted as 1.609km

There 1km = 1/1.609 miles

810 km = 1/1.609 × 810

= 503.4 miles

If this value is approximated to the nearest hundred,then it will be

500 miles

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Answer:

If x-y=9 is a true equation, we can substitute this equation into 5+x−y to find its value.

5 + x - y

= 5 + x - (x - 9) (since x - y = 9)

= 5 + x - x + 9

= 5 + 9

= 14

So, the value of 5 + x - y would be 14 if x-y=9 is a true equation.

From the given data points representing the number of new homes that built in each neighborhood. The median number of houses is 26.

The median is the middle value of a set of numerical data when the data is arranged in ascending or descending order. In a set of odd number of data points, the median is the middle value. In a set of even number of data points, the median is the average of the two middle values.

To find the median, you arrange the numbers in order from least to greatest and then pick the middle number(s).

5, 12, 13, 20, 26, 29, 30, 31

In this case, there are 8 numbers, so the median is the middle number, which is 26.

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Answer:

that means it's a short yam

The length of the yarn is n < 7.5 inches.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

The length of the yarn is less than 7.5 inches.

Let the length of the yarn is n inches.

To show the length of the yarn:

We will establish an inequality.

So,

n < 7.5 inches.

Therefore, n < 7.5 is the inequality.

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Answer:

Step-by-step explanation:

B. 64^(1/2) is greater than 64^(1/3).

Answer:

25% increase

Step-by-step explanation:

Percentage increase = [tex]\frac{100-80}{80} * 100=\frac{20}{80} * 100 = 25%[/tex]

Answer:

5 cm^2

Step-by-step explanation:

I just had this same question and I got it right.

hope this helps

This can be modeled as a Poisson distribution. The mean number of patients admitted per day is 2.5, so the Poisson parameter λ = 2.5. The probability that the hospital will not have enough beds on any given day is the probability that more than 1 patients will be admitted, which is given by:

P(X > 1) = 1 - P(X <= 1)

= 1 - (P(X = 0) + P(X = 1))

= 1 - (e^-2.5 * 0 + e^-2.5 / 1!)

= 1 - e^-2.5 * (1 + 2.5)

This is the probability that the hospital will not have enough beds to accommodate its newly admitted patients on any given day.

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The sum of the squares of the solutions of the mentioned equation is 161.38.

The solution of the given quadratic equations can be calculated through factorization. So, rewriting the equation to factorize it.

x² - 13x + 4 = 0

Based on Dharacharya formula, stated as -

x = - b ± ✓b² - 4ac/ 2a, we get the roots -

x = 12.7 and 0.3

Now, the next formula to solve will be -

x = 12.7² + 0.3²

Taking the square of each number

x = 161.29 + 0.09

Performing addition on Right Hand Side of the equation

x = 161.38

Thus, the required answer is161.38.

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Answer:

C. 6/48

Step-by-step explanation:

mutliply both numerator and denominator

The coordinates of triangle ABC after dilation are; (-6, -3), (0, 9) and (3, 3)

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Given that, a triangle ABC with coordinates, A (-2, -1) B (0, 3) C (1, 1)

This triangle is dilated by a scale factor of 3,

SInce, the scale factor is greater than 3, therefore, dilation shows an enlargement.

The rule of dilation is given by;

(x, y) → (kx, ky), where k is dilation factor.

Let triangle ABC is dilated to form triangle A'B'C'

Therefore, the coordinates of triangle A'B'C' are;

A' = 3(-2, -1) = (-6, -3)

B' = 3(0, 3) = (0, 9)

C' = 3(1, 1) = (3, 3)

The graph is attached.

Hence, the coordinates of triangle ABC after dilation are; (-6, -3), (0, 9) and (3, 3)

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The financial planner invested $4,737.50 in the mini-mall development plan and $1,012.50 in the savings account.

The amount invested in the savings account is equal to the total amount invested minus the amount invested in the mini-mall development plan. We can express this as an equation:

Total Investment - Investment in Mini-Mall Development Plan = Investment in Savings Account

Substituting the values given in the problem, we get:

$5,750 - Investment in Mini-Mall Development Plan = Investment in Savings Account

To solve for the Investment in Mini-Mall Development Plan, we need to use the combined interest earned for the first year. We can express this as an equation:

Interest Earned = (Investment in Savings Account x Interest Rate) + (Investment in Mini-Mall Development Plan x Interest Rate)

Substituting the values given in the problem, we get:

$475 = (Investment in Savings Account x 0.02) + (Investment in Mini-Mall Development Plan x 0.12)

Solving for Investment in Mini-Mall Development Plan, we get:

Investment in Mini-Mall Development Plan = ($475 - (Investment in Savings Account x 0.02))/0.12

Substituting the values given in the problem, we get:

Investment in Mini-Mall Development Plan = ($475 - ($5,750 - Investment in Mini-Mall Development Plan x 0.02))/0.12

Solving for Investment in Mini-Mall Development Plan, we get:

Investment in Mini-Mall Development Plan = $4,737.50

Therefore, the financial planner invested $4,737.50 in the mini-mall development plan and $1,012.50 in the savings account.

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The length of ED is,  3√10

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

In a figure,

⇒ PB = BC = 6

Now, By the figure,

⇒ ΔFPD and ΔEMD are congruent.

Hence, We can formulate;

⇒ FP / EM = PD / MD

Let the length of MD = x

⇒ FP / EM = PD / MD

⇒ 6 / 3 = (9 + x) / x

⇒ 2x = 9 + x

⇒ 2x - x = 9

⇒ x = 9

Hence, The length of MD = 9

Now, In  ΔEMD;

⇒ ED² = EM² + MD²

⇒ ED² = 3² + 9²

⇒ ED² = 9 + 81

⇒ ED² = 90

⇒ ED = √90

⇒ ED = 3√10

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