Tammy installs bathroom tiles. Her current job requires tiles that are equilateral triangles and all the tiles have to be congruent to each other. She has a big sack of tiles all in the shape of equilateral triangles. Although she knows that all the tiles are equilateral, she is not sure they are all the same size. What must she measure on each tile to be sure they are congruent? Explain.

The time taken, to the nearest minute, by the element to decay until only 30 grams of it are left is 14 minutes.

An element with an initial mass of 200 gram, decays by 12.6% per minute. We need to find out, to the nearest minute, how long it took for the element to decay until only 30 grams were left.

In exponential decay, a quantity diminishes slowly at first and then rapidly. The exponential decay formula is used to calculate population decay (depreciation), and it may also be used to calculate half-life (the amount of time for the population to become half its size).

Let the initial mass, remaining mass, decay rate, and time taken be represented by the variables M, m, d, and t, respectively. We can form the equation given below.

m = M(1 - d)^t

30 = 200(1 - 0.126)^t

3/20 = (0.874)^t

Take the logarithm on both sides of the equation.

log(3/20) = t × log(0.874)

t = log(3/20)/log(0.874)

t = 14.087

t ≈ 14

Hence, the time taken, to the nearest minute, by the element to decay until only 30 grams of it are left is 14 minutes.

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The factor most likely results in the loss of genetic variation from a small population is called genetic drift.

Small populations tend to lose genetic variation at a faster rate than large populations due to genetic drift (stochastic sampling error). Genetic drift refers to the change in an existing gene variant frequency in the population due to random chance. Genetic drift may result in the disappearance of gene variants completely and thus decreases genetic variation. Furthermore, it could initially cause rare alleles to become much more frequent, and even fixed. The loss of some versions of a gene due to random chance is more likely to happen when populations are small.

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Answer:

2 : 12 and 3 : 24 are the two equivalent ratios

Answer:

Hi !!!

Step-by-step explanation:

6.2×(-2.7)

=-16.74

= -1.674×10¹

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The number ester,sarai and kurry chose are 0.009,0.09 and 0.9 respectively

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. For example 3+3+3+3+3 can be written as 3× 5 .

to find the ester's number= 1/10 of sarai's number

= 1/10× 0.09

= 0.009

to find kurry^s number = 10 × sarai's number

= 10× 0.09

= 0.9

Therefore ester , sarai and kurry chose 0.009, 0.09,0.9 respectively.

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Answer:

25/0 aka infinity

Step-by-step explanation:

Equation used:

(y2-y1)/(x2-x1)

1. Plug in the values to get (27-2)/(9-9)

2. Simplify to get 25/0

3. This results in an infinity

Answer:

13

Step-by-step explanation:

To evaluate meant to find its Value at the givens

At a = 1 , b = -3 , c = - 1

[tex]b^{2}-4ac=(-3)^{2} -4*1*-1=9+4=13[/tex]

Glad to Help

Answer:

Step-by-step explanation:

Let y be the distance the car travels, in miles.  Let t be the time traveled, in hours.  The speed is 45 m/h.  We know that the distance the car travels is given by the equation:

Distance = (speed)*(time)

Using the assigned variables, we can rewrite this as:

   d(t)  = (45 m/h)(t hours)

We want an equation that will tell us the position of the car, y, at any time, t, including t = 0, the start.  

d(t) = ?

At time = 0, the starting point of the car is P.  We can write:

d(0) = P

For x[tex]\geq[/tex]0, we would find the car at:

     d(t) = P + (45)*t

The 45 is in units of miles/hour,  t is in hours and d is in miles.  Let's assume an intital position, P, for this car to be 10 miles.  P = 10 miles.

The function is:  d(t) = 10 + (45)*t

If we leave the units in, it can be written as:  d(t) = (10 miles) + (45 miles/hr)*t(in hr)

We can see that the term "(45 miles/hr)*t(in hr)" will eventually reduce to just miles one we enter the time in hours, since the hours cancel out.

The graph of this function is attached.   The line crosses the y axis at 10 (miles) when time, t, is 0 : the car has not started.  

The slope of the graph can be determined by calculating the Rise/Run of the line.  Pick any two points.  I'll choose:  (2,100) and (4,190).

 Rise (change in y) is (190-100) = 90

 Run (change in x) is (4 - 2) = 2

Slope = Rise/Run = (90/2) or 45.

The slope has the same value as the speed, as it should.  The slope is telling us the rate of change, which for this graph, is the speed of the car.  The y-intersect is (0, 10).  The car is at 10 miles at the start (t=0).

To create a scenario where could have a negative value requires some imagination.  There is really no such thing as negative time, except in time travel movies.  But we can define t, perhaps, as the start of a race.  (High noon, for example).  If the cars were allowed to start moving before noon as long as they started back (negative direction) from the starting point of the race.  If t is defined as "hours after 12:00 noon" then a value of t = -1  means 11:00 AM.  If the car were approaching the staring line at 45 miles/hour, ahread of the official start time, the graph would make sense.  Not the race, so much, but the graph would be accurate.

The a-values of the business are classified as follows:

The a-value of a business depends on the behavior of the earning function for these business, as follows:

From the table given by the image at the end of the answer, for the lawn care business, a concave down parabola represents the situation, as the earnings start increasing but then during the 3rd month they start to decrease. Hence, the a-value of the business is negative.

For the dog walking and for the house-sitting business, the values are always increasing over the time interval of the table, hence the a-value of these two businesses is positive.

The table is given by the image at the end of the answer.

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Michael will be spending the cost of $ 15.652 on the Furry Fabric.

Given, that Michael is dressing up as Maggie,

He is making his costume and he needs 8.6 yards of furry fabric

The fabric costs $1.82 per yard.

So, as he needs 8.6 yards of fabric and each yard of that fabric costs him $1.82.

1 yard of Furry Fabric = $1.82

8.6 yards of Furry Fabric = $1.82 × 8.6

8.6 yards of Furry Fabric = $ 15.652

Hence, Michael will be spending the cost of $ 15.652 on the fabric.

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Answer:

80

Step-by-step explanation:

16x5=80

The coordinates of the point that is one-half the distance between A(-1,-2) and B(6,12) is (2.5,5)

What is the midpoint?

The mid-point lies midway between the two ends. Its x value lies in the middle of the other two x values. Its y value lies in the middle of the other two y values.

Given, [tex]A(6,12) = (x_{1}, y_{1} )[/tex]

           [tex]B(6,12) = (x_{2}, y_{2} )[/tex]

Let M is a midpoint of AB, then

[tex]M(x,y)=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2}}{2} )= (\frac{-1+6}{2} ,\frac{-2+12}{2} )=(2.5,5)[/tex]

The midpoint of point AB is M(2.5,5)

Therefore, the coordinates of the point which is one-half the distance between A(-1,-2) and B(6,12) is M(2.5,5).

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8 percentage of her total monthly budget does she plan for savings.

The proportion of value in relation to the original value is measured using the percentage concept. In business, percentages are frequently employed to calculate a company's profit or loss percentage. Additionally, it is used in schools and colleges to show the grades that pupils have earned. A percentage formula can be used to assess the pupils' grades. In general, the definition of a percentage is any ratio of a value to the total value multiplied by 100. The percentage is denoted by the sign %.

Given,

Melissa's monthly budget is shown in the table,

Melissa' s saving = $250

Total amount = 3125

Percentage = Value/ Total × 100

Percentage = 250/3125 × 100

Percentage = 0.08 × 100

Percentage = 8%

8 percentage of her total monthly budget does she plan for savings.

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0.01 is the results of the two-sided significance test  in confidence interval,

What is alpha in statistics?

confidence level = 1 - alpha

so alpha = 1 - confidence level = 1 - 0.99 = 0.01

In statistics, alpha is the number that evaluates the test statistic to see if it is significant or not. In other words, alpha is the allowable type 1 error margin. The significance level, or alpha, is the antithesis of the confidence level. Confusion level + significance level = 1.

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Answer: Diverge Reasoning I took the test

The probability of the randomly selected bank being a) guilty of fraud is 0.1 and b) guilty of fraud, it is given it is a private bank is 0.15

Here

let A be the event of the Bank being a fraud

Let B be the event of the bank being private

Here we see that 100 banks have been sampled.

a)

Probability = no. of favorable outcomes/total no. of outcomes

Here we see that under the row of Bank Fraud and Yes section there are

6 + 4

= 10 banks.

Hence,

n(A) = 10

n = 100

Therefore,

P(A) = 10/100

= 0.1

b)

The conditional Probability

P(X|Y) = P(X ∩ Y) / P(Y)

Here,

we need to find the bank is a fraud given that it is a private bank. Hence we need to find,

P(A|B)

= P(A ∩ B) / P(B)

Here we see that the private banks that are fraud are given to be 6.

Hence,

n(A ∩ B) = 6

Therefore,

P(A ∩ B) = 6/100

n(B) = 6 + 34 = 40

P(B) = 40/100

Hence P(A|B) = (6/100) / (40/100

= 6/40

= 3/20

= 0.15

Complete Question

(Information attached as an image)

if an audit company picks a bank at random for audit what is the probability that a bank

(a) is guilty of fraud?

(b) is guilty of fraud given it is a private bank?

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If they are competing for 1st, 2nd, and 3rd place ribbons. The number of different ways can the winners be chosen is:  B. 60.

Given data:

Number of people =5

Number of places = 1st, 2nd, and 3rd

Hence,

Different combinations =5 ×4×3

Different combinations = 60 ways

Therefore the winners will be chosen by  60 different possible ways ,

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Answer: Your question is too long for me to answer

Step-by-step explanation:

The newly translated function of  f(x) = 7x + 1 is; g(x) = 7(x - 1) + 1

In transformation of functions, there are different operations such as translation, reflection, dilation, rotation.

Now, we are told that the function is given as;

f ( x ) = 7x + 1

We are told that it is translated by 5 units to the right.

It is pertinent to note that when talking about translation, it is as good as saying moving from one point to the other without changing the dimensions or shape.

Now, when we shift a function f(x) = x - 1 by a units to the left, it means the translated function is; f'(x) = (x + 1) - 1

However, when we shift a function f(x) = x - 1 by a units to the right, it means the translated function is; f'(x) = (x - 1) - 1

Now, applying that translation rule to our given function gives;

g(x) = 7(x - 1) + 1

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The temperature of the hottest day in Oklahoma in Celsius to the nearest tenth of a degree is 48.89 degrees.

The process of converting a temperature value from one unit to another is known as temperature conversion. On scales like Kelvin, Celsius, Fahrenheit, etc., we measure temperature. The freezing point and boiling point of water, respectively, are 273.15K and 373.15K on the Kelvin scale. The freezing point and boiling point of water, respectively, are 32°F and 212°F on the Fahrenheit scale. The freezing point and boiling point of water, respectively, are 0°C and 100°C on the Celsius scale.

Given, The hottest day recorded in Oklahoma was 120° Fahrenheit

F=(9/5)C+32

120=(9/5)C+32

(9/5)C=88

C=48.89

Therefore, the temperature of the hottest day in Oklahoma in Celsius to the nearest tenth of a degree is 48.89 degrees.

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Answer:

1) t = -2

2) t = 8

3) t = -2
4) t = 1

5)t = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

1)-22t+6 = 11t + 72

 -33t = 66

      t = -2

2) 3t + 4t - 20 = t + 28

 6t = 48

   t = 8

3) -8 -10t - 6t = 3t + 30

   -19t = 38

       t = -2

4) 12t - 6t + 24 = 12t + 12 +6

   -6t = -6

       t = 1

5) -12-21t-3t=48t-36

    -24t - 48t = 12 - 36

    -72t = -24

     t = [tex]\frac{1}{3}[/tex]

The equivalent expression of the expression 54x + 18 will be 18(3x + 1). Then the correct option is E.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 54x + 18

Simplify the expression, then we have

⇒ 54x + 18

⇒ 18(3x + 1)

The equivalent expression of the expression 54x + 18 will be 18(3x + 1). Then the correct option is E.

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The complete question is given below.

Drag each expression to show whether it is equivalent to 54x + 18, 18(3x – 1), or (6 • 9x) + (6 • 1).

expressions: A-54x B-(6 • 9x) + (6 • 3) C-54x + 6 D-3(18x+2) E-18(3x+1) F-(9*6x)-(9*2)

The value of the expression 3(3+5g) is 9 + 15g.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, we want to simplify 3(3 + 5g)

It's important to open the parentheses. This will be:

=3(3 + 5g)

= 9 + 15g

Therefore, the value is 9 + 15g.

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Answer:

let the width be x

perimeter= 2(l+b)

78= 2(7 +x)

78-14= 2x

32= x

this must be the ans

The statements which are as a result of corresponding parts of congruent triangles being congruent are:

1) EFGH is a rectangle.

The above statements is not true in general. EFGH is a quadrilateral with opposites sides are equal, it may be rectangle in some cases but it is not always be a rectangle.

2). EFGH has 4 congruent sides.

The above statement is also false. EFGH has two opposite sides are congruent.

3). Diagonal FH bisect angles EFG and EHG.

The above statement is true. Triangle EFH and FGH both are isosceles triangles and hence they both have equal angles for the equal sides. Thus, it is true in all cases.

4). Diagonal FH is perpendicular to side Fe.

The above case is not true in general.

5). Angle FEH is congruent to angle FGH.

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Answer:

Step-by-step explanation:

And here is how to use it:

Example: simplify √12

12 is 4 times 3:

√12 = √(4 × 3)

Use the rule:

√(4 × 3) = √4 × √3

And the square root of 4 is 2:

√4 × √3 = 2√3

So √12 is simpler as 2√3

Another example:

Example: simplify √8

√8 = √(4×2) = √4 × √2 = 2√2

(Because the square root of 4 is 2)

And another:

Example: simplify √18

√18 = √(9 × 2) = √9 × √2 = 3√2

It often helps to factor the numbers (into prime numbers is best):

Example: simplify √6 × √15

First we can combine the two numbers:

√6 × √15 = √(6 × 15)

Then we factor them:

√(6 × 15) = √(2 × 3 × 3 × 5)

Then we see two 3s, and decide to "pull them out":

√(2 × 3 × 3 × 5) = √(3 × 3) × √(2 × 5) = 3√10

Fractions

There is a similar rule for fractions:

root a / root b  = root (a / b)

Example: simplify √30 / √10

First we can combine the two numbers:

√30 / √10 = √(30 / 10)

Then simplify:

√(30 / 10) = √3

Some Harder Examples

Example: simplify  

√20 × √5

√2

See if you can follow the steps:

√20 × √5

√2

√(2 × 2 × 5) × √5

√2

√2 × √2 × √5 × √5

√2

√2 × √5 × √5

√2 × 5

5√2

Example: simplify 2√12 + 9√3

First simplify 2√12:

2√12 = 2 × 2√3 = 4√3

Now both terms have √3, we can add them:

4√3 + 9√3 = (4+9)√3 = 13√3

The value of the cards in Bentley's original hand given the value of the cards currently, is 25.

The value of the cards that are currently in Bentley's hands are worth $75. This amount is triple the value in this original hands.

Given that the value of cards now is triple the value in Bentley's original hands, the value in Bentley's original hands can be found by performing a division of 3 on the current hand:

= Current value / 3

= 75 / 3

= $25

In conclusion, the value of the cards in the original hand was $25.

Full question is:

The cards in Bentley's hand have a value of $75 after the value of the cards in his original hand tripled. What was the value of the cards in his original hand?

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Answer:

X = 1

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

To solve for x we should try to isolate the x by itself so :

Let's add 3 to both sides :

2x-3 + 3 = 1 + 3

-3+3 = 0

2x(+0) = 4

2x = 4

Divide both sides by 2 so we have just x on its own :

2x÷2 = 4÷2

x = 2

Let's check by putting this x value in the question :

2(2)-3 = 1

2(2) = 2×2 = 4

4 - 3 = 1

1 = 1

✅

So x = 2

Hope this helped and have a good day