The highest calorie treat tested by the group was 1,270 total calories. People need roughly 2,200 to 2,500 calories per day. Using a daily average, how many additional calories should a person consume after eating the ice cream?

Answer: 104.1

Step-by-step explanation:

If \(P(t)\) represents the initial population in millions. \(t\) years after 1990, then \(P(t)=64e^{0.027t}\).

2008 is 18 years after 1990, so \(P(18)=64e^{0.027 \cdot 18} \approx 104.1\)

The exponential growth of population in 2008 is 95.4 million

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the population of the country in 1993 be = 64 million

The exponential growth rate r = 2.7 %

So , the population of the country in 2008 is calculated by

The time t in years = 2008 - 1993

                               = 15 years

So , the equation for exponential growth rate is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

And substituting the values in the equation , we get\

x ( 15 ) = 64 × ( 1 + 0.027 )¹⁵

x ( 15 ) = 64 × ( 1.027 )¹⁵

x ( 15 ) = 64 × 1.49127

x ( 15 ) = 95.4413

So , the value of x ( 15 ) = 95.4 million

Hence , The exponential growth of population in 2008 is 95.4 million

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The concentration of the drug after 8 hours is equal to 24 mg/L.

The interval over which the concentration increases is 0 < t < 2.

The interval over which the concentration decreases is 2 < t < ∞.

The drug is at its maximum concentration when t = 2 hours and the maximum concentration is 64 mg/L.

After the drug reaches its maximum concentration, the number of hours that are required for the concentration to decrease to 16 mg/L is 8 hours.

After 1 week and 1 month, we can predict that the concentration of the drug kept decreasing after reaching 20 hours.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of the given function, we can reasonably infer and logically deduce the following:

The function is increasing over the interval [0, 2] or 0 < t < 2.

The function is decreasing over the interval [2, ∞] or 2 < t < ∞.

In conclusion, the vertex (2, 64) of the graph represent the point where the drug is at its maximum concentration, which is time (t) = 2 hours and the maximum concentration is y = 64 mg/L.

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According to the given data the length of a \(90^{0}\) arc is \(\pi /2\) or approximately \(1.57\) feet.

In geometry, the length of an arc is the distance along the curved line that makes up the arc. It is a measure of the "length" of a portion of a circle's circumference, and it is usually expressed in the same units as the circle's radius.

According to the given information:

The length of a \(90^{0}\) arc in a circle with radius \(1\) foot can be calculated using the formula:

Length of arc = (angle/\(360\)) x \(2\pi r\)

where angle is the central angle of the arc in degrees, r is the radius of the circle, and \(\pi\) is a mathematical constant approximately equal to \(3.14159\).

Substituting the given values, we have:

Length of arc = (\(90/360\)) x \(2\pi(1 ft)\)

Length of arc = \((1/4)\) x \(2\pi ft\)

Length of arc = \(\pi /2 ft\)

Therefore, the length of the \(90^{0}\) arc is \(\pi /2 feet\) or approximately \(1.57 feet\)

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the length of the 90° arc is π/4 feet or approximately 0.785 feet

What is arc of circle?

In geometry, an arc of a circle is a portion of the circle's circumference. It is defined by two endpoints and all points along the circle between those endpoints. The measure of an arc is typically given in degrees or radians and can be used to calculate various properties of the circle, such as its length, area, and sector angles.

The formula for the length of an arc is:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle of the arc in degrees, and r is the radius of the circle.

In this case, θ = 90° and r = 1 ft, so we have:

L = (90/360) × 2π(1) = (1/4) × π = π/4

Therefore, the length of the 90° arc is π/4 feet or approximately 0.785 feet (rounded to 3 decimal places).

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The fraction of the original passengers remaining on the bus is 11/21.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A crowded bus makes several stops along a city street, with no passengers boarding the bus at any stop.

.At the 1st stop 1/3 of the passengers exit.

At the 2nd stop, 3/7 of the remaining passengers exit the bus.

Therefore, The fraction of the original passengers who remain on the bus is,

= [(1 - (1×1/3) - (1)×(1/3)×(3/7)].

= [ 1 - (1/3) - (3/21)].

= [ (2/3) - (3/21)].

= [(14 - 3)/21].

= 11/21.

So, 11/21 remains on the bus.

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Answer:

2 divided

Step-by-step explanation:

Answer:

x=9.5 and y=15.3

Step-by-step explanation:

to find x you do sine of 32 = x/18 because the sine is opposite/hypotenuse

you put in a calculator sine (32) x 18 and get 9.538546756

so x equals 9.538546756 but it says to round to the nearest tenth so x equals 9.5

to find y you do the cosine of 32 = y/18 because cosine is adjacent/hypotenuse

cosine of (32) x 18 = 15.26486573 so you equals 15.26486573 but since you have to round to the nearest tenth y = 15.3

The value of x is 9.54.

The value of y is 15.3.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

From the figure,

Sin 32 = x / 18

Cos 32 = y / 18

Now,

Sin 32 = 0.53

Cos 32 = 0.85

Now,

0.53 = x / 18

Multiply 18 on both sides.

x = 0.53 x 18

x = 9.54

0.85 = y / 18

Multiply 18 on both sides.

y = 0.85 x 18

y = 15.3

Thus,

The value of x is 9.54.

The value of y is 15.3.

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The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

He would drive 536 miles in 5 hours

Step-by-step explanation:

First set up your equation:

804 = 12x

Divide 804 by 12 and get 67 = x

Since per one hour you drive 67 miles, multiply 67 by 8 and get 536.

So, he drives 536 miles in 5 hours

Answer: I think 402

Step-by-step explanation: I divided 804 to 4 and I got 201 then I added 201+201= 402 and each 4 hours he went 201 miles so if you add 201 and 201 you get 402 miles. Hope it helped!! :)

Answer:

In y = 2x the value of y is twice the value of x, and in y = x + 2 the value of y is two more than the value of x.

Same for the y=4x and y=x+4, just plug the numbers into the sentence.

Step-by-step explanation:

Answer:

a.

y= 40x +4000

x= 100 --> y= 40(100)+4000= 4000+4000=8000

x=200 --> y= 40(200)+4000= 6000+4000= 10000

x=300 --> y= 40(300)+4000= 12000+4000= 16000

(in $)

b.

y= 40x+4000

6200= 40x+4000

6200-4000= 40x

2200= 40x

2200/40= x

55= x

(in unit)

Step-by-step explanation:

I hope this helps

if u have question let me know in comments ^_^

Answer/Step-by-step explanation:

✔️Find EC using Cosine Rule:

EC² = DC² + DE² - 2*DC*DE*cos(D)

EC² = 27² + 14² - 2*27*14*cos(32)

EC² = 925 - 756*cos(32)

EC² = 283.875639

EC = √283.875639

EC = 16.85 cm

✔️Find the area of ∆DCE:

Area = ½*14*27*sin(32)

Area of ∆DCE = 100.15 cm²

✔️Since ∆DCE and ∆ABE are congruent, therefore,

Area of ∆ABE = 100.15 cm²

✔️Find the area of the sector:

Area of sector = 105/360*π*16.85²

Area = 260.16 cm² (nearest tenth)

✔️Therefore,

Area of the logo = 100.15 + 100.15 + 260.16 = 460.46 ≈ 460 cm² (to 2 S.F)

Answer:

I believe its 42

Step-by-step explanation:

Here is the final answer. Let me know if it help!

Answer:

(x+4)^2  -25

Step-by-step explanation:

x²+8x-9 in the form  (x+k)² +h.

We need to complete the square.

x^2 +8x   -9

Take the coefficient of x.

8

Divide by 2.

8/2 =4

Square it.

4^2 = 16

Add this then subtract i.

x^2 +8x+16    -16   -9

The x^2 +8x+16 becomes  (x+4) ^2  and we can simplify the remaining terms.

(x+4)^2  -25

Iris should use an income value of approximately $3,137.50 when making her budget.

When making her budget as a freelancer, Iris should use an income value that reflects her average earnings over the past four months. By calculating the average income, Iris can have a more stable and reliable estimate for her budget planning.

To determine the average income, Iris needs to add up the total income earned over the four months and divide it by the number of months. Summing up the income values, we get:

$2700 + $4600 + $3550 + $1700 = $12,550

Next, dividing the total income by four (the number of months), we find:

$12,550 / 4 = $3,137.50

Therefore, Iris should use an income value of approximately $3,137.50 when making her budget. This average value allows her to account for fluctuations in her monthly income and provides a more accurate representation of her earning potential.

It is important for Iris to consider her expenses and financial goals when budgeting. By using the average income, she can create a budget that balances her income and expenses, allowing her to allocate funds appropriately for various needs such as bills, savings, investments, and personal expenses.

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The probable question may be:

Iris is a working freelancer and has been tracking her monthly income for the last four months, which are $2700, $4600, $3550, and $1700. What income value should she use when making her budget?

The probability that the second ball is red is 11/25 .

IN THE EVENT OF SELECTING THE FIRST BALL

- The probability of selecting white ball is P(W) = 2/5

- Probability of selecting red ball is P(R) = 3/5

IN THE EVENT OF SELECTING THE SECOND BALL

P(R|W) = 1/2

P(R|R) = 3/5

So the probability of selecting a red ball as the second is

P(R2) = P(R|W)P(W) + P(R|R)P(R)

= (1/2)(2/5) + (2/5)(3/5)

= 1/5 + 6/25

= 11/25

The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

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Answer:

Step-by-step explanation:

3x + 18 - 2x - 4 > 10

x - 14 > 10

x > 24

Answer:

35

Step-by-step explanation:

30+20=50

50-15=35

(Brainliest helps)

Answer:

Answer on imagine math ;)

Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.

The average balance of the account is $1126.37.

An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.

Consider the table that shows the balance (in dollars) of a bank account for three months.

Months            Account Balance

1                       $1285.12

2                       $961.36

3                       $1132.63

As we are aware, the following formula for the mean or average of any set of data:

Mean, \(\overline X=\frac{\sum X}{n}\)

where,  ∑X is the sum of all the observations in the data and n  is the number of observations in the data

Therefore, the average balance in the account is:

\(Average{~}balance=\frac{1285.12+961.36+1132.63}{3}\)

\(Average{~}balance=\frac{3379.11}{3}\)

Average balance = $ 1126.37

So, the account's average balance is $1126.37.

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The complete question is mentioned below:

The table shows the balance (in dollars) of a bank account each month for three months. What is the average balance of the account?

Table:

Month 1, account balance: $1285.12

Month 2, account balance: $961.36

Month 3, account balance: $1132.63

The average balance of the account is $1126.37

Average: An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.

Consider the table that shows the balance (in dollars) of a bank account for three months.

Months            Account Balance

1                       $1285.12

2                       $961.36

3                       $1132.63

As we are aware, the following formula for the mean or average of any

set of data,

Mean,

where,  ∑X is the sum of all the observations in the data and n  is the number of observations in the data

Therefore, the average balance in the account is,

Average balance of the account = $ 1126.37

So, the account's average balance is $1126.37

The complete question is mentioned below,

The table shows the balance (in dollars) of a bank account each month for three months.

Table:

Month 1, account balance: $1285.12

Month 2, account balance: $961.36

Month 3, account balance: $1132.63

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Answer:

2z-4

Step-by-step explanation:

By using distributive property, 2/3 * 3z =  2z and 2/3 * -6 = -4

This means the answer is 2z-4

\(Answer: \large\boxed{2z-4}\)

Step-by-step explanation:

To solve:

\(\frac{2}{3} (3z-6)\)

We must use the distributive property and distribute 2/3 to the 3z and -6

...

\(\frac{2}{3} (3z-6)\)

\(=\frac{2}{3} (3z) + \frac{2}{3} (-6)\)

\(=\frac{6z}{3} + -\frac{12}{3}\)

\(=2z-4\)

The equation that can be used to determine the points that Clare scored are c = 1.5t and c= (1+0.5)t (options A and E).

Percentage is the fraction of an amount expressed as a number out of hundred. Percentage is a measure of frequency. The sign that represents percentage is %.

The equation that can be used to represent the points scored by Clare is a linear equation.

The form of the equation is:

Points scored by Clare = points scored by Tyler x (100 + percentage )

c = t x (100 + 50%)

c = t x ( 1 + 0.5)

c = (1 + 0.5)t

c = 1.50t

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Answer:

1/3 foot longer

Step-by-step explanation:

2/3-1/3=1/3

There is no stationary point at x = 2. The nature of the curve at x = 2 cannot be determined since there is no stationary point.

To verify that the curve has a stationary point at x = 2, we need to find the derivative of the equation and set it equal to zero.

Given the equation:

y = 2x + 1/(x-1)²

Let's find the derivative dy/dx:

dy/dx = d/dx [2x + 1/(x-1)²]

To find the derivative, we can use the power rule and the chain rule. Let's differentiate each term separately:

For the first term, 2x, the derivative is 2.

For the second term, 1/(x-1)², we can rewrite it as (x-1)^(-2) to apply the power rule. The derivative is then:

d/dx [(x-1)^(-2)] = -2(x-1)^(-3) * d/dx (x-1)

Using the chain rule, d/dx (x-1) = 1, so the derivative becomes:

-2(x-1)^(-3) * 1 = -2/(x-1)^3

Now, let's set dy/dx equal to zero and solve for x:

-2/(x-1)^3 = 0

This equation is satisfied when the numerator is equal to zero:

-2 = 0

However, -2 is not equal to zero, which means there is no x value that makes dy/dx equal to zero.

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Answer:

24.93

Step-by-step explanation:

Rounding to two decimal places is the same as rounding to the nearest hundredth.

Locate the hundredth:

24.927

Check the number to the right of it:

24.927

If the number is greater than or equal to 5, then we round up. If the number is less than or equal to 4, we round down.

7 is greater than 5. So, we round up.

24.927 ≈ 24.93

2.94 is the answer.

The first digit after the decimal represents the tenth place. the subsequent digit after the decimal represents the hundredth area. The closing digits retain to fill within the vicinity values till there are no digits left.

Rounding a decimal quantity to two decimal locations is the same as rounding it to the hundredth place, that's the second area to the right of the decimal factor. as an instance, 2.83620364 may be spherical to two decimal locations as 2.94, and 0.7035 can be spherical to 2 decimal places as zero.70.

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The answer would be C - "Cheetah B has a higher ratio of miles per minute than Cheetah A because 17 over 8 is less than 56 over 20."

also "get it right please" ?! how rude

The set of side measurements that could be used to form a right triangle is

The problem is solved using the Pythagoras theorem is applicable to right triangle.  

the formula of the theorem is

hypotenuse² = opposite² + adjacent²

the set of sides that adheres to this theorem can form a right triangle

plugging the values as in the problem  6, 8, 10

say side 10 = x

x² = 6² + 8²

x² = 36 + 64

x² = 100

x = √100

x = 10

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