Can write the equation of the graph?

The function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function

The function is  

f(x) =[tex]2(\frac{1}{2})^x[/tex]

The function is defined as the expression that represents the relationship between one variable and another variable.

The function is in the form of

f(x) = a × [tex]b^x[/tex]

Such functions are called exponential function

Here  

The value of a = 2

The value of b = 1/2

If the value of b > 1, the function is called exponential growth function.

If the value of b < 1, the function is called exponential decay function.

Here b < 1

Therefore it is exponential decay function

Hence, the function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function

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You started with a total of 28 muffins

From the question, the given parameters are:

Proportion carried away = 16 of the total muffins

Proportion carried away = 4/7 of the total muffins

The above parameters implies that

4/7 of the total muffins = 16

Represent the amount you started with x

So, we have the following representation

4/7 of x = 16

Express as products

4/7x = 16

Make x the subject

x = 7 * 16/4

Evaluate

x = 28

Hence, the total number of muffins is 28

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For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years.

As given in the question,

The formula given to us is A = P[tex]e^{rt}[/tex] where

A = accumulation value

P = principal money

t = time period

r = interest rate compounded

P = 9500

A = 2*9500

r = 0.12

By applying it in the given formula we get

19000 = 9500 * [tex]e^{0.12t}[/tex]

2 =    [tex]e^{0.12t}[/tex]

Take natural log on both sides

㏑(2) = 0.12t

0.6931 = 0.12t

t = 5.775

Therefore , For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years after rounding it off to one place after decimal.

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The equation of the line that passes through the point (-8,-3) and has a slope of -3/4 is y = -3/4x - 9

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

Slope, m = -3/4

Points, (x₁, y₁) = (-8, -3)

A linear equation can be represented as

y = slope * x + y-intercept i.e. y = m(x - x₁) + y₁

Substitute the known values in the above equation

So, we have the following equation

y = -3/4(x + 8) - 3

Open the brackets

So, we have the following equation

y = -3/4x - 6 - 3

Evaluate the like terms in the above equation

So, we have the following representation

y = -3/4x - 9

The above equation cannot be further simplified

Hence. the linear equation is y = -3/4x - 9

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Answer:

Her piggy bank can hold 720 pennies.

Step-by-step explanation:

1/2= 3/6, and 2/3=4/6, meaning the difference of 1/6=120 pennies. 120x6=720.

The probability that it has a hairline crack is 19/27.

Given that;

In a shipment of 54 vials, only 16 do not have hairline cracks.

Let shipment of 54 Vials;

x(s) = 54

Let,' A ' be the event that selects 16

x(A) = 16

P(A) = x(A) / x(s)

       = 16/54

But only 16 don't have hairline Crakes;

To solve a given case;

The probability that it has a hairline crack is:

P(A') = 1 - P(A)

       = 1- 16/54

P(A') = 19/27

Hence, the probability that it has a hairline crack is 19/27.

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the best question is that if they can examine a sample of tires used for 60,000 miles and determine the proportion that is worn out, then how likely is that proportion to be 3.6% or less?

we are given the information that an A tire manufacturer has a 60,000-mile warranty and the manufacturer considers the overall tire quality to be accepted if less than 5% are worn out at 60,000 miles, also the manufacturer tested 250 tires that have been used for 60,000 miles. they find that 3.6% of them are worn out. So here the Hypotheses can be that:

1) The proportion of tires that are worn out after 60,000 miles is equal to 0.05 and

2) The proportion of tires that are worn out after 60,000 miles is less than 0.05.

We need to deny the first hypothesis with an alternative one. You cannot demonstrate that the average is 3.6%, but if you by one means or another decide that the probability the average is greater than 3.6% is lower than 100% minus your confidence level, at that point you'll be able to deny the first hypothesis and acknowledge the second one as new average.

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0.3814 is the probability that the sample contains two white balls and two red ones .

What is probability in math?

Total number of balls = 8 + 12 = 20

Total number of elementary cases

           = ( 20 4 )

Total number of favourable cases

           = ( 8 2 ) * ( 12 2 )

Required probability

   = ( 8 2 )  *  ( 12 2 )/( 20  4 )

 = 0.3814

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Answer: 25 cents i am sorry if this is wrong

Step-by-step explanation: 3 dimes are 30 cents plus 50 is 80 plus 35 is $1.15 so then when she removers 3 nickles she is getting rid of 15 cents which would leave $1.00 finally when you remove 75 cents you have 25 cents

The the locus of the equation y = x is a straight line. The slope of the linear function → y = x is [m] = 1 and the [y] intercept is at [c] = 0.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is the function -

x = y

We have the function -

y = x

Now, we can define locus as -

A curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions.

This equation -

y = x

is a straight line.

Refer to the graph attached.

The slope of the line is [m] = 1

The [y] intercept is at [c] = 0

Therefore, the the locus of the equation y = x is a straight line. The slope of the linear function → y = x is [m] = 1 and the [y] intercept is at [c] = 0.

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The dimensions that maximize the area are 150ft × 300ft.

So, let y be the length of the side parallel to the river and x be the length of each of the two sides perpendicular to it.

The following provides the total fencing length:

The rectangular pen's surface area is:

We may determine the value of x required to maximize the area by determining the value of x for which the derivative of the area function is zero:

The value of y is: for x=150

Therefore, the dimensions that maximize the area are 150ft × 300ft.

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Answer:

x + 3 = 18

Step-by-step explanation:

original number of kids: x

additional kids: 3

new total number of kids: x + 3

actual total number of kids: 18

Equation: x + 3 = 18

The enclosure can be as large as 606 m2 in total.

Given that,

Let x be length of y be width of enclosure

fencing material cost $ 30 / m

Partition material cost $25/m

Total cost = (x+x+y+y)x 30+(y + y) x 25

c= 60(x+y) + 50y = 60 x + 110 y

4000 = 60 x + 110y

y = ( 400 - 6x / 11)

Now,Area of enclosure = x*y

A = x*(400 - 6x / 11)

A'(x)= 400-12x/11

for maximum area A'(x) = 0

400 - 12x/11 = 0,12x = 400,x = 100/3

A " ( x) = - 12/11 < 0  i.e., maximum

y = 400 - 6( 400/12 ) = 200/11 m

Maximum area = xy = 100/3 * 200/11 = 20000/33

                                                            =606.0606

A max = 606m²

Hence, the maximum area you can achieve for the enclosure is 606m²

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The terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.

It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.

Let's check all the options. Then we have

a) √6, 2.5, 8/3, convert the numbers into a decimal form. Then we have

⇒ 2.449, 2.5, 2.667, order is in ascending form.

b) √8, 11/4, 2.9, convert the numbers into a decimal form. Then we have

⇒ 2.828, 2.75, 2.667, order is not in ascending form.

c) 9/5, 1.9, √5, convert the numbers into a decimal form. Then we have

⇒ 1.8, 1.9, 2.236, order is in ascending form.

d) 13/5, 2.8, √7, convert the numbers into a decimal form. Then we have

⇒ 2.6, 2.8, 2.645, order is not in ascending form.

e) 1.8, 7/4, √3, convert the numbers into a decimal form. Then we have

⇒ 1.8, 1.75, 1.732, order is not in ascending form.

The terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.

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Assuming it is a standard deck of 52 cards and a standard dice of 6 faces.

There are 13 heart cards in a standard deck, therefore the odd of getting a heart is 13 : 52 = 1/4.

There is only 1 six in a standard dice, therefore the odd of getting a six is 1/6.

For these events to happen simultaneously, we multiply the chances.

Therefore, the chance of getting a heart in a deck of cards and a six on a dice is 1/4 x 1/6 = 1/24.

Answer:

heart from a deck of cards= 13/52 = 1/4

getting a six on a dice= 1/6 = 1/6

Step-by-step explanation:

heart from a deck of cards :

In the context of ordinary maths questions the answer is so obvious as to almost not be worth mentioning. There are 52 cards in an ordinary deck and 13 of them have heart pips, so 13/52 = 1/4.

six from a dice :

There is a 1/6 chance of rolling a 6. There are only 6 sides on a die, and only 1 of them is 6, so there is a 1/6 chance of rolling a 6.

at the same time is:

13/15 + 1/6 = 31/30 = 1/30

Answer:

The answer should be -5/2

Step-by-step explanation:

To find the slope take two plots from the table:

(-2,6) and (0,1)

M= y2-y1 / x2-x1

M= 1-6 / 0--2=-5/2

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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Answer:

  Barlow School has 178 more boys

Step-by-step explanation:

At Barlow School, 4/9 of 873 students are boys. At Willow School, 2/3 of 630 students are girls. You want to know which school has more boys, and by how many.

The number of boys is ...

  4/9 × 873 = 388

The 1/3 of students that are not girls are presumed to be boys. That number is ...

  1/3 × 630 = 210

The difference in the number of boys is ...

  388 -210 = 178

Barlow School has 178 more boys.

The equation that has x = -11 as the solution is given by -

y = x + 11

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the following equation that has a variable on both sides and x = -11 as a solution.

An equation of a straight line can be used to depict the problem given. We can write the equation as -

y = x + 11

Therefore, the equation that has x = -11 as the solution is given by -

y = x + 11

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We can put 8 distinguishable balls into 3 distinguishable boxes such that each box has at least one ball in 21 ways.

Given, that there are 3 boxes and we have to put 8 balls in them such that no box is empty.

Let, a + b + c = 8, where a , b , c represent three different boxes.

The equation be reduced by allotting 1 ball to each box so that no box remains empty.

Hence, a + b + c = 5

Now, using the formula of "no. of ways in which 'n' objects can be grouped into 'r' groups" i.e. C(n+r-1 , r-1)

So, the required number of ways = C(5+3-1 , 3-1) = C(7 , 2)

Calculating, C(7 , 2) = (7×6)/2 = 21

Hence, we can put 8 distinguishable balls into 3 distinguishable boxes such that each box has at least one ball in 21 ways.

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Answer:

Triangular prism

Step-by-step explanation:

If you were to fold all the creases and glue it together you would get a tent shape which is a triangular prism

Answer: m (slope) = 3

Step-by-step explanation: Slope Solution

m=rise run=ΔyΔx

m=y2−y1x2−x1

m=8−53−2

m=31

m = 3

Point Slope Form

y−y1=m(x−x1)

y−5=3(x−2)

Slope Intercept Form

Find the Equation of the Line:

y=mx+b

by solving for y using the Point Slope Equation.

y−y1=m(x−x1)

y−5=3(x−2)

y−5=3x−(3×2)

y−5=3x−6

y=3x−6+5

y=3x−1

m=3

b=−1

Hope this helps :)

The values of x after applying congruency to solve the complete shape is 3.5.

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. The symbol to represent two congruent shapes is ≅.

To calculate the values of x in the diagram, we need to first join point Q to point H and point G to form ΔQHG also, we join point Q to point E and point F to form ΔQFE.

Comparing ΔQHG and  ΔQFE, we can deduce that

Therefore,

Hence, the values of x in is 3.5.

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Answer:

67.5 (rounded down to 67, usually)

45/2 is 22.5 so that is for one hour

22.5 x 3 = 67.5

Answer:

add me on brainliest please

Step-by-step explanation:

65 is the answer

The number -58 is a real number and it cannot be represented as a complex number

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

Expression = -58

The given expression above is a number

And also, it is a negative number

Negative numbers of this form are real numbers

This means that the such numbers cannot be represented as a complex number

Hence, the number -58 does not have a complex equivalent

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The current price of the clarinet and the various discounts and markups illustrate that the amount the store paid was $90.

First find out the selling price of the clarinet:

= Discounted price / ( 1 - discount rate)

= 93.60 / ( 1 - 20%)

= $117

This selling price is 30% more than what the store paid so the price the store paid was:

= Selling price / ( 1 + rate of increase)

= 117 / ( 1 + 30%)

= $90

In conclusion, the amount the store paid was $90.

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Complete question

A music store buys instruments and then sells them for 30% more than they paid. During a 20% off sale, the store offers a clarinet for $93.60.

How much did the store pay for the clarinet?

The congruency can be proved using SAS rule.

What are congruent triangles?

Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles is slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of harmoniousness is’ ≅’.

Main Body:

In ΔPQR and ΔRST

PR = RT           ---(1)

as both the sides are congruent , the third sides of triangles is also equal.

QR = RS          ----(2)

∠PRQ = ∠SRT   ----(3)

Hence by side- angle -side

ΔPQR and ΔRST are congruent.

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The altitude of the original pyramid is about 75.11 units

Given that,

Let h stand in for the original pyramid's height. The cut-off top then stands at a height of (h -22). The square of the scale factor for height is the scale factor for area, therefore we get :

Altitude of Pyramid means The slant height of a regular pyramid is its lateral face's height. Slant height in a non-rectangular pyramid is not specified. When determining the height (or altitude) of a regular, right pyramid, the vertex (the top) is used as the point perpendicular to the base. The base will intersect at this position.

(Height ratio)^2 = 1/2

((h -22)/h) ^ 2 = 1/2

(h-22) / h = 1/[tex]\sqrt{2}[/tex]

h-22 = h /[tex]\sqrt{2}[/tex]

h = 75.11 units

Consequently, the original pyramid's altitude is around 75.11 units.

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