When x is divided by 3 the quotient is more than 7

Answer:

Option A) EF = 15 units.  

Step-by-step explanation:

We are given the following information in the question:

ΔABC ≅ ΔDEF

AB = 12, BC = 15, and AC = 17

If two triangles are congruent then they have the following properties:

AB = DE

BC = EF

AC = DF

[tex]\angle A = \angle D \\\angle B = \angle E \\\angle C = \angle F[/tex]

Hence, by congruency:

BC = EF

EF = 15 units.

Thus, option A is the correct answer.

The Interest is $12.595 while the value of the Proceeds is $307.405

The amount of loan; A = $320

The discount rate = 16%=0.16

Time = 90 days = 90/365 year = 0.246 year

The formula of interest is;

Interest = Amount × Discount rate × Time

Thus;

Interest = 320 × 0.16 × 0.246

Interest = $12.595

Proceed = Amount - Interest

Proceed = $320 - $12.595

Proceeds = $307.405

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Answer:

12.80

307.20

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

:D

The value of the x is 20.

We have given that,

[tex]81^5 = 3^x[/tex]

We have to determine the value of x.

3^4 = 81

Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b, and the exponent or power n, and pronounced as b raised to the power of n.

exponent 4 x 5 = 20

so, 3^20 = 81^5

Therefore the value of the x is 20.

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To find the number Wilma is thinking of, we create an equation and solve for x.

To solve this problem, we need to create an equation based on the information given. Let's suppose the number Wilma is thinking of is x. According to the problem, if we add 4 to x and then multiply that result by 3, we get 30. We can write this as the equation 3(x + 4) = 30. To find the value of x, we need to isolate it. First, distribute the 3 to both terms inside the parentheses: 3x + 12 = 30. Next, isolate x by subtracting 12 from both sides of the equation: 3x = 18. Finally, solve for x by dividing both sides of the equation by 3: x = 6. Therefore, Wilma is thinking of the number 6.

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The area of the front cover of the square notebook is A = 400 cm²

A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.

A square is a 4 sided polygon where all the sides are of equal length.

The area of the square is the square of any one of its side

Let a be the side of the square

Area of the square = a²

Given data ,

Let the area of the square be represented as A

Now , the side length of the notebook a = 20 cm

And , the area of the front cover of the notebook = area of square

On simplifying , we get

The area of front cover A = a²

The area of the front cover of the notebook A = 20 x 20

The area of the front cover of the notebook A = 400 cm²

Hence , the area of the square notebook is 400 cm²

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The formula for the distance Lorrae swims at a constant speed for 2 hours is d = 2s, where d is distance and s is her speed.

The question is asking for a formula to calculate the distance that Lorrae swims. Since distance (d) is equal to speed (s) multiplied by time (t), and we know that Lorrae swims at a constant speed, s, for 2 hours, a formula for her distance would be d = s * t.

In this case, the time, t, is 2 hours. So, we can substitute t with 2 in our formula. Hence, the formula for the distance Lorrae swims is d = s * 2 or d = 2s. This is the equation you can use to compute the distance Lorrae swims for any given speed at a constant period of 2 hours.

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Answer:

The statement is false.

Step-by-step explanation:

To begin an indirect proof, you assume the converse of what you intend to prove is true. This is false.

Rather the correct answer is that to begin an indirect proof, you assume the inverse of what you intend to prove is true.

The converse can be either true or false, depending on what the original statement is, so assuming the converse is pointless.

The scale factor of the two rectangular prisms is 3/2 of the given problem the volumes of two similar rectangular prisms are 40 mm and 135 mm

To find the scale factor between two similar rectangular prisms, we can compare their volumes. The scale factor is the ratio of the cube root of the volumes.

Let's denote the volume of the first rectangular prism as V1 and the volume of the second rectangular prism as V2.

[tex]V1 = 40 mm^3\\V2 = 135 mm^3[/tex]

The scale factor (SF) can be calculated as follows:

[tex]SF = (V2)^{(1/3)} / (V1)^{(1/3)[/tex]

Plugging in the given values:

[tex]SF = (135)^{(1/3)} / (40)^{(1/3)[/tex]

To simplify the calculation, we can rewrite the values as prime factorization:

[tex]135 = 3^3 * 5\\40 = 2^3 * 5[/tex]

Now, let's calculate the cube roots:

[tex]SF = (3^3 * 5)^{(1/3) }/ (2^3 * 5)^{(1/3)}[/tex]

Using the property of exponents [tex](a^{(m/n) }= (a^m}^{(1/n)})[/tex]:

[tex]SF = (3^{(3/3)} * 5^{(1/3)}) / (2^{(3/3)} * 5^{(1/3)})[/tex]

Simplifying the fractions:

[tex]SF = 3 * 5^{(1/3)} / 2 * 5^{(1/3)[/tex]

The [tex]5^{(1/3)}[/tex] terms cancel out:

SF = 3/2

Therefore, the scale factor of the two rectangular prisms is 3/2 of the given problem the volumes of two similar rectangular prisms are 40 mm and 135 mm.

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Answer: Each face would have an area of 22 * 22 = 484 square inches.

Since a cube has 6 faces, then the total area = 6 * 484 = 2,904 square inches.

Step-by-step explanation:

Answer:

CPCTC; JP≅MI; SAS

Step-by-step explanation:

For the first question, we use the congruence statement.  When we are using the congruence statement to match corresponding pieces, the justification is that Congruent Parts of Congruent Triangles are Congruent, or CPCTC.

For the second question, we again use CPCTC and the congruence statement.  P matches T and B matches I, so PB = TI and B = I.  J matches M also, so BJP = IMT.  However, P does not match I, so JP does not equal MI.

For the third question, we have two sides (AM matching ZD and BD matching itself) and an included angle (AMD and ZDM).   This is Side-Angle-Side, or SAS.

In modified boxplots, a data value is a potential outlier if it is outside the range of Q3 + (1.5)(IQR) or Q1 - (1.5)(IQR). The IQR is the spread of the middle 50% of the data, calculated as Q3 - Q1.

In modified​ boxplots, a data value is​ a potential outlier if it is above Q3 + (1.5)(IQR) or below Q1 - (1.5)(IQR). The interquartile range (IQR) is crucial in this determination, representing the spread of the middle 50 percent of the data. It is found by subtracting the first quartile (Q1) from the third quartile (Q3). For example, if Q1 is 2 and Q3 is 9, the IQR is 7. Any data value greater than 9 + (1.5)(7) or less than 2 - (1.5)(7) would be considered a potential outlier.

Constructing a box plot involves identifying these five key values: minimum value, first quartile, median, third quartile, and maximum value. The box plot visually represents the data's spread, with whiskers extending to the most extreme values within the acceptable range, and separate marks for potential outliers.

the answer is A x=15 and y =12

The rate of change of length of the Clupea harengus (Atlantic herring) at t = 7 years is approximately 2.8 cm per year.

To determine how fast the length of Clupea harengus (Atlantic herring) is changing at age t = 7 years, you need to calculate the derivative of the given function, l(t) = 32(1 − e−0.37t), with respect to time. The derivative measures the rate of change of a function, which in this case corresponds to the speed of growth of the herring.

The derivative of l(t) with respect to t is given by: l'(t) = 32 * 0.37e^(-0.37t).

Substitute t = 7 into this derivative function to get: l'(7) = 32 * 0.37e^(-0.37*7) ≈ 2.8 cm/year.

So, the length of the Atlantic herring is increasing at approximately 2.8 cm per year when the herring is 7 years old.

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To find the rate at which the length of the Atlantic herring is changing at age t = 7 years, we need to take the derivative of the length function and evaluate it at t = 7.

To find the rate at which the length of the Atlantic herring is changing at age t = 7 years, we need to find the derivative of the length function with respect to time. The function l(t) = 32(1 − e−0.37t) represents the average length of the herring at age t. Taking the derivative of this function gives us:

l'(t) = 32 * (-0.37) * e−0.37t

Now, we can substitute t = 7 into the derivative to find the rate of change at that age:

l'(7) = 32 * (-0.37) * e−0.37(7)

This expression can be simplified further to find the exact value of the rate of change.

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In 24 ways the first, second, third, and fourth place be assigned

A permutation is an arrangement of objects in a definite order. .

Given that, for a spelling contest awards four prizes Tim, Sam, Jen, and Kate all made it to the final round.

We need to find in how many ways can first, second, third, and fourth place be assigned.

This can be arranged in 4! ways.

4!=4×3×2×1

4!=24

Hence in 24 ways the first, second, third, and fourth place be assigned.

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Answer: "Use the straightedge to draw a line through points X and Y." is the right answer.

Step-by-step explanation:

To perpendicular bisector of line segment AB. There are following steps:

1) Draw arcs from points A and B on the both sides of AB.

2) Name the intersection points as X and Y.

3) Use the straightedge to draw a line through points X and Y.

4) Name the point as O

hence we have construct perpendicular bisector XY of AB which bisects at O.

Answer: A(11x=55)

Step-by-step explanation:

in the equation 2x + 3y = 55, subsitute 3y for 3x, because y = 3x. this will result in the equation 2x + 3(3x) which equals 11x. so 11x=55

Answer: 5/9 will be the fraction of the space will be for storage and baking.

Step-by-step explanation:

Since area of bakery will be used as our storefront, where customers come to visit= 100/225

Thus, the total area of bakery = 225  

And, the area will be used our storefront, where customers come to visit= 100

So, the remaining area which is used for storage and baking = 225 - 100 =125

So the part of area which is used for storage and baking= the remaining area which is used for storage and baking/ total area

=125/225= 5/9

which is the simplest form.