Celia bought 40 lbs of clay for her art projects. She used 17.4 lbs to make a sculpture, and 1.01 lbs for each mug. How many mugs did Celia make if she had 7.45 lbs of clay left over?

[tex]-37 < -12v+1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ v=-11\hspace{5em}-37 < -12(-11)+1\implies -37 < 133 ~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-9\hspace{5em}-37 < -12(-9)+1\implies -37 < 109~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-5\hspace{5em}-37 < -12(-5)+1\implies -37 < 61~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=6\hspace{5em}-37 < -12(6)+1\implies -37 < -71 ~~ \bigotimes[/tex]

The number of malaria cases in 2017 is 2700.

Let the dependent variable, y is malaria cases in thousands and the independent variable, x is the year.

Here, x is the number of years starting in the year 2000.

The required model is obtained as [tex]y = 299e^{0.1295x}[/tex]

Now, the predicted number of malaria cases in the year 2017, that is, x = 17 years can be computed as,

[tex]y = 299e^{0.1295(17)}\\\\= 299(9.020\\\\= 2700[/tex]

Hence, the number of malaria cases in 2017 is 2700.

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Answer:

The function that is a translation one unit right of the function f(x) = log x is k(x) = log(x - 1).

When we shift a function f(x) one unit right, we replace x with (x - a) where "a" is the amount of the shift. In this case, "a" is equal to 1. Therefore, the function becomes:

f(x - 1) = log(x - 1)

This means that the function k(x) = log(x - 1) is obtained by shifting the function f(x) one unit to the right.

The students in 8th class who choose music are 16 in number,

The students in 7th class who choose music are 32 in number

The total who choose world language is 270

The totals who are in 7th grade be 194

The number of students who choose world language in 7th class are 162

Let x be the students in 8th class who choose music

x+108=124

x=124-108

x=16 students

Now  y be the students in 7th class who choose music

16+y=48

y=48-16

y=32

Let z be the total who choose world language

48+z=318

z=318-48

z=270

Now the totals who are in 7th grade be A

124+A=318

A=318-124

A=194

B be the number of students who choose world language in 7th class

Now 32+B=194

B=194-32

B=162

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Conversion models can be used to express numbers of different bases to base-2 and base-5. To convert a number from base-10 to base-2, we use division-by-2, and for base-5, we divide by 5. To convert between bases, we convert to base-10 first and then to the desired base. for example 25 in binary is 11001, 45 in base-5 is 104, 89 to base-2 is 1011001.

In computer science and mathematics, binary (base-2) and quinary (base-5) numbering systems are commonly used to represent numbers. However, it is often necessary to express numbers in other bases as well. This is where conversion models come into play.

To convert a number from base-10 to base-2, we can use the division-by-2 method.

The process involves repeatedly dividing the decimal number by 2 and keeping track of the remainders until the quotient becomes 0. We then write the remainders in reverse order to get the binary representation of the number.

For example, to convert the number 25 to binary

25 / 2 = 12 R1

12 / 2 = 6 R0

6 / 2 = 3 R0

3 / 2 = 1 R1

1 / 2 = 0 R1

Therefore, 25 in binary is 11001.

To convert a number from base-10 to base-5, we can use a similar method. Instead of dividing by 2, we divide by 5 and keep track of the remainders. For example, to convert the number 45 to base-5

45 / 5 = 9 R0

9 / 5 = 1 R4

1 / 5 = 0 R1

Therefore, 45 in base-5 is 104.

We can also convert a number from base-2 to base-5 or vice versa. To convert a number from base-2 to base-5, we can first convert it to base-10 and then to base-5. For example, to convert the binary number 101110 to base-5

1*2⁵ + 0*2⁴ + 1*2³ + 1*2² + 1*2¹ + 0*2⁰ = 46

46 to base-5 is 141

To convert a number from base-5 to base-2, we can first convert it to base-10 and then to base-2. For example, to convert the quinary number 324 to base-2

3*5² + 2*5¹ + 4*5⁰ = 89

89 to base-2 is 1011001

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Answer:

Step-by-step explanation:

your supposed to learn things in class pay attetion

The limit as a definite integral is  given as   lim (n → ∞) Σ(8i²)/n³ = 8/3n³

The area under the curve f(x) from x= a to x  = b is represented by the definite integral of f(x  )

There are 2 kinds of    integrals

To express the limit as a definite integral, we can use the following formul

lim(n → ∞  ) Σf(i)/n = ∫  a^bf(x)dx

where....

a and b are the lower and upper limts of the definite integral

f (x) is the function being integrated

In this case, we have

lim(n → ∞) Σ(8i²)/n³

Let f  (x) = x ²

So, f(i/n) = (i/n) ²

And, the sum can be written as

Σ(8i^2)/n³ = 8/n³ Σi²

= 8/n³ Σ(i/n)²

= 8/n³ Σ[f(i/n)]

= 8/n³ ∫0¹ f(x) dx (using the formula above)

Therefore, the limit can be   expressed as

lim(n → ∞) Σ(8i²)/n³ = 8/n³ ∫0¹ x² dx

Simplifying the integral, we get....

8/n³  ∫0¹ x₂ dx = 8/n^3 [x³/3] from 0 to 1

= 8/3n ³

Se we can say here that  the limit as a definite integral is lim(n → ∞) Σ(8i ₂)/n^3 = 8/3n ₃

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Answer:14

Step-by-step explanation:

2 pants can only go with the different shirts once. So it should be 14

well, if the hemisphere has a diameter of 8, that means its radius is half that or 4, hmm let's find the volume of a Sphere with such a radius, then let's halve it.

[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3} \\\\\\ \stackrel{\textit{now let's get half of that for the hemisphere}}{V=\cfrac{1}{2}\cdot \cfrac{4\pi (4)^3}{3}\implies V=\cfrac{128\pi }{3}}\implies \boxed{V\approx 134.0}[/tex]

Answer:

First, we need to calculate the volume of the rectangular fish tank. The volume of a rectangular solid is given by the formula:

volume = length x width x height

Plugging in the values we have, we get:

volume = 35 cm x 30 cm x 25 cm = 26,250 cubic cm

Next, we need to find the volume of water in the fish tank. The volume of water is equal to the volume of the space the water occupies, which is a rectangular solid with length 35 cm, width 30 cm, and height 20 cm. The volume of this rectangular solid is:

volume = length x width x height = 35 cm x 30 cm x 20 cm = 21,000 cubic cm

To convert cubic centimeters (cm^3) to liters (L), we need to divide by 1000:

volume = 21,000 cm^3 ÷ 1000 = 21 L

Therefore, the volume of water in the fish tank is 21 liters.

Step-by-step explanation:

The graph of the function f(x) = 4(2/3)^x is added as an attachment

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

f(x)=4⋅(

2

3

​)

x

Express the equation properly

So, we have

f(x) = 4(2/3)^x

The above expression is a an equation of a exponential function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the equation in a graphing tool and attach the display

See attachment for the graph of the function

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A symbolic representation of the contrapositive is

letter D

Answer:

b

Step-by-step explanation:

The volume of this rectangular prism include the following: 84.375 cubic meters.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular prism = 5 × 4 1/2 ×  3 3/4

Volume of rectangular prism = 5 × 4.5 ×  3.75

Volume of rectangular prism = 84.375 cubic meters.

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Rewriting the expression based on the information will be 72(1 + z/72).

In order to transform 72 + z into a product based on 72, we can apply the distributive property of multiplication over addition. Essentially, this property maintains that:

a x (b + c) = a x b + a x c

By extension, we can create the following equation:

72 + z = 72 + 1 x z

In order to produce an equivalent expression as a multiple of 72 and another factor, we would then need to use the distributive rule once again:

72 + 1 x z = 72 x 1 + 72 x z/72

Simplification leads us to arrive at:

72 + z = 72(1 + z/72)

Our end result is expressed as a synthesis between 72 and the expression (1 + z/72), namely:

72(1 + z/72).

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Answer:

B

Step-by-step explanation:

Answer:

I think It's b or a

Step-by-step explanation:

did this like 4 weeks ago.

Note that  in the line graph presented, 3/4 the distance from A to B is 12, thus, t = 12.

Given:

A (- 2 , 0) and B(14, 0)

Using distance formula,      we can determine the distance between coordinates given:

d    = √ ( (x2 - x1)² + ( y2 - y1) ²)

In this case,  x1 = -2  y1 = 0,

x2 = 14, and y2 =  0.

Substituting these     values into the formula, we get:

d = √(  (14 -   (-2 ) ) ² + (0 - 0) ²)

= √((16)² + (0)² )

= √(256)

= 16

The distanc between the points (-2,0) and (14,0) is 16   units.

Recall that we need to find the position of t which    is 3/4 the distance between A and B.

That is:

3/4 x 16

t = 12.


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Answer:

π(5^2)(8) + (1/2)(4/3)π(5^3)

= 200π + 250π/3 = 850π/3 cubic meters

= about 889.67 cubic meters

Beth could not join the club because the highest age which is allowed here is only 55 years

Since, A statistical expression obtained from a list of data that refers an abnormal gap from other values.

The statistical rules that instruct us to divides the data or observation values into four parts.

After analyzing the stem leaf diagram, we noticed the youngest age allowed to join the club is 10 years and the club allow highest 55 years old to join.

the plot also defines that the number of members is declined with the age. There is only person in the club who is 55 years. There are few members with the age over 40 years.

hence, Beth did not join the club because her age was above the highest age that allowed in this club.

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The probability that a person surveyed is 40 or older and gets the news by reading the paper is 60%. The Option C is correct.

We must find the probability of a person getting their news by reading the paper and are given with a condition that the person must be 40 or older.

Data

The survey is conducted among 80 people.

Number of people aged 40 or older = 40

No of people aged 40 or older and read paper = 24

The probability of a person aged 40 or older reads a paper will be:

= (No. of People aged 40 or older and read paper)/(No. of people aged 40 or older)

= 24/40

= 0.6

= 60%

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The monthly payments and total cost of interest depend on the interest rate and the length of the loan. Generally, a lower interest rate or a shorter loan term results in lower total interest costs.

To calculate the monthly payments, we can use the formula for the present value of an annuity:

[tex]PV = P * (1 - (1 + r)^{-n}) / r[/tex]

where PV is the present value of the loan, P is the principal (the amount borrowed), r is the monthly interest rate, and n is the number of monthly payments.

(a) 30 years, 5%:

PV = 0.9 * $90,000 = $81,000 (since she puts 10% down)

r = 0.05 / 12 = 0.0125(monthly interest rate)

n = 30 * 12 = 360 (number of monthly payments)

Using the formula, we get:

PV = $81,000

Monthly payment = $436.82

Total cost of interest = $57,255.85

(b) 30 years, 5.12%:

r = 0.0512 / 12 = 0.00427 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $439.88

Total cost of interest = $59,956.19

(c) 30 years, 6%:

r = 0.06 / 12 = 0.005 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $485.24

Total cost of interest = $95,687.34

(d) 15 years, 3.78%:

n = 15 * 12 = 180 (number of monthly payments)

r = 0.0378 / 12 = 0.00315 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $591.93

Total cost of interest = $34,147.07

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The exponential function represented in the table is given as follows:

y = 3^x.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

From the table, we have that when x=  0, y = 1, hence the parameter a is given as follows:

a = 1.

When x is increased by one, y is multiplied by three, hence the parameter b is given as follows:

b = 3.

Hence the function is:

y = 3^x.

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The opposite side of the right triangle is determined as 10.6 cm.

The value of x is calculated by applying trigonometry ratio as shown below;

we will use the short form; SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The hypotenuse side of the right triangle is given, and we are required to find the opposite side of the right triangle.

sin (62) = x/12

x = 12 sin (62)

x = 10.6 cm

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Answer:

The correct option that compares the end behavior of the functions f and g is D.

For function f, as x → ∞, f(x) → -∞, which means that the function approaches negative infinity as x approaches infinity. This is because the leading term of the function is -17x, which approaches negative infinity as x approaches infinity.

For function g, as x → ∞, g(x) → -∞, which means that the function also approaches negative infinity as x approaches infinity. This is because the leading term of the function is -78/87x, which approaches negative infinity as x approaches infinity.

Therefore, both functions have the same end behavior, which is approaching negative infinity as x approaches infinity.

If Mark  used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug then the number of mugs he can make is 57.

Mark bought 55 lbs of clay for his art projects

He used 12.4 lbs to make a sculpture

The left over clay is 55-12.4 = 42.6

We know that 0.75 lbs for each mug

We have to find the number of mugs he can make from left over clay

To find this we have to divide 42.6 by 0.75

Number of mugs = 42.6/0.75

=56.8

=57

Hence, if Mark  used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug then the number of mugs he can make is 57.

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The following equation denotes the correlation between the duration and output of an activity: A = kT

It should be noted that A represents the amount of production, T is the period of working on the task, and k consists of a constant ratio.

Therefore, it can be conclusively stated that the culminating yield is in direct correlation to the amount of effort contributed, as denoted by the factor of proportionality k, thus producing a linear relationship when displayed upon a graph.

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The exact volume of the soup can is 18.375 π cubic inches. So, correct option is C.

The volume of a cylinder can be found by multiplying the area of the base (circle) by the height of the cylinder. In this case, the diameter of the base is 3.5 inches, which means the radius is 1.75 inches (since radius = diameter/2).

So the area of the base can be calculated as:

π × (1.75 in)² = π × 3.0625 in²

The height of the cylinder is given as 6 inches.

Therefore, the exact volume of the soup can would be:

π × (1.75 in)² × 6 in = π × 3.0625 in² × 6 in = 18.375 π cubic inches (rounded to two decimal places)

So, correct option is C.

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