Consider the equation.

10−2(−2x+1)=5(x+2)−2x

What is the value of x in the equation?


−2

-1/2

1/2

2

The width of the new rectangle cut out by Maryam is 12 inches

Perimeter of a rectangle = 2l + 2w

where

Therefore,

30 = 2(9) + 2w

30 - 18 = 2w

w = 12 / 2

w = 6 inches

Therefore, the width of the new rectangle is as follows:

width of the new rectangle = 6(2) = 12 inches

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Answer:

if the diameter if the basketball is 18 inches then the circumference is about

56.5487 or 57

Step-by-step explanation:

An estimate for the total volume of food and water you've ingested in the last day is 3000-5000 milliliters. On average, the heart pumps about 5 liters of blood per minute. 10-20% or more error I'm expecting. Calculating heart blood volume compared to food and drink consumption is crucial for understanding circulation and liver function.

D.1 Estimating the amount of food and water consumed in a day can be difficult without specific measurements, but a rough estimate can be made based on typical intake amounts. On average, a person may consume 2-3 liters of water and 1000-2000 calories per day, resulting in an estimated total volume of 3000-5000 milliliters.

D.2 The amount of blood pumped by the heart varies from person to person and depends on factors such as heart rate and overall health. On average, the heart pumps about 5 liters of blood per minute, which is much larger than the estimated volume of food and water intake.

D.3 Estimating food and water intake and blood flow is prone to error due to variability and uncertainties in personal measurements. Individuals' habits, health, and physical activity levels can affect these estimates, potentially resulting in a significant error of 10-20% or more.

D.4 The calculation of the heart's blood volume compared to food and drink consumption is crucial for understanding the circulation system and liver role.

The liver processes nutrients, detoxifies, and produces blood components, while the heart is responsible for circulating blood throughout the body. The vast difference in volume between the two is emphasized, emphasizing the heart's crucial role in maintaining circulation.

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Answer:

We need at least 100 terms of the series to approximate the sum with an error of less than 0.05.

The 4 terms are required to approximate the sum of the series with an error of less than 0.05.

To determine the number of terms required to approximate the sum of the series with an error of less than 0.05, we need to use the formula for the error of an alternating series:

Error = |a_n+1|

where a_n+1 is the next term in the series.

Since the series is -1^n/2n!, the next term in the series is -1^(n+1)/2(n+1)!.

We need to find the smallest value of n that satisfies the inequality:

|a_n+1| < 0.05

|-1^(n+1)/2(n+1)!| < 0.05

1/2(n+1)! < 0.05

2(n+1)! > 1/0.05

2(n+1)! > 20

Now we can try different values of n to find the smallest one that satisfies the inequality:

n = 1: 2(1+1)! = 2(2)! = 2(2)(1) = 4 (not greater than 20)

n = 2: 2(2+1)! = 2(3)! = 2(3)(2)(1) = 12 (not greater than 20)

n = 3: 2(3+1)! = 2(4)! = 2(4)(3)(2)(1) = 48 (greater than 20)

Therefore, the smallest value of n that satisfies the inequality is n = 3.

So, the number of terms required to approximate the sum of the series with an error of less than 0.05 is n+1 = 3+1 = 4.

4 terms are required to approximate the sum of the series with an error of less than 0.05.

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Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

To determine whether Alicia's estimate of the surface area of the rectangular prism is reasonable, we first need to check if her calculation of the volume of the rectangular prism is correct.

The formula for calculating the volume of a rectangular prism is:

Volume = length x width x height

Substituting the given values in the formula, we get:

Volume = 11 meters x 5.6 meters x 7.2 meters

Volume = 449.28 cubic meters

As we can see, Alicia's estimate of 334 cubic meters is significantly lower than the actual volume of the rectangular prism, which is 449.28 cubic meters. Therefore, her estimate of the surface area is likely to be incorrect as well.

It is also important to note that the problem statement asks about the estimate of the surface area, not the volume. However, since the formula for calculating the surface area of a rectangular prism also involves the dimensions of length, width, and height, it is highly likely that Alicia's estimate of the surface area would also be incorrect given her miscalculation of the volume.

In conclusion, Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

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0•47 as an ordinary number

Answer:

c. 4x + 20 = 140

Step-by-step explanation:

Perimeter = 140 feet

Width = L + 10

P = 2w + 2L

P = 2(L + 10) + 2L

P = 2L + 20 + 2L

P = 4L + 20

We are given the expression:

We, simply replace the values of solution given and then determine in which it is not a solution, but we can see that when we replace x = 0, we will get:

So, this proves that the function is not an identity.

Using trigonometric identities, If sinA + sin² A = 1, then the value of the expression (cos²A + cos⁴A) is; 1

We are told that sinA + sin² A = 1.

Now, we want to find (cos²A + cos⁴A).

From trigonometric identities, we know that;

cos²A = 1 -  sin² A

Thus;

cos²A + cos⁴A = 1 -  sin² A + cos⁴A

Similarly, using trig identities on the given expression;

From sinA + sin² A = 1, we can say that;

sinA = 1 - sin² A

Since cos²A = 1 -  sin² A, then we can say that;

sinA = cos²A

Thus;

sin²A = cos⁴A

Thus;

cos²A + cos⁴A = 1 -  sin² A +  sin²A

= sinA +  sin²A= 1

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Correct question is;

If sinA + sin² A = 1, then the value of the expression (cos²A + cos⁴A) is

Answer:

3/5 of a foot

Step-by-step explanation:

1/5+2/5=3/5

Answer:(x + 6) + (y + 2)^2 = 13

Step-by-step explanation:

The centre of the circle is halfway along the diameter = (-6, -2)

r^2 = (-4 - -6)^2 + ( 1 - -2)^2 = 2^2 + 3^2 = 13

So circle equation is (x - -6)^2 + (y - -2)^2 = 13

99.85% of adults in the city have a systolic blood pressure of less than 110 mmHg.

Using 68-95-99.7 rule, we know that

99.7% of values lie between the interval (mean - 3 × standard deviation, mean + 3 × standard deviation)

(100 - 99.7) = 0.3% values lie outside the interval (mean - 3 × standard deviation, mean + 3 × standard deviation).

Since the normal distribution is bell-curved and symmetrical,

we can say

0.3/2 = 0.15% values are less than the mean - 3 × standard deviation

and 0.3/2 = 0.15% values are greater than mean + 3 × standard deviation.

Here,

Mean + 3 × standard deviation.

= 110 + 3 × 10 = 140

So, 0.15% of values  are greater than 140

So, (100 - 0.15) = 99.85% values are less than 140.

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The value of x is 3.

Given that,

If  \(5 + 20 \times 2^{2-3x}\),

And Baseline = \(10 \times 2^{-2x}+5\)

We have to find,

The value of x?

According to the question,

To determine the value of x in the equation following all the steps given below.

Equation; \(\rm 5 + 20 \times 2^{2-3x} = 10 \times 2^{-2x}+5\)

                   \(\rm5- 5 + 20 \times 2^{2-3x} = 10 \times 2^{-2x}+5-5\\\\\rm 20 \times 2^{2-3x} = 10 \times 2^{-2x}\)

                    \(\rm 20 \times 2^{2-3x} = 10 \times 2^{-2x}\\\\\dfrac{ 20 \times 2^{2-3x} }{10}= \dfrac{10 \times 2^{-2x}}{10}\\\\\rm 2 \times 2^{2-3x} = 2^{-2x}\)

                   \(\rm 2 \times 2^{2-3x} = 2^{-2x}\\\\2^1 \times 2^{2-3x} = 2^{-2x}\\\\2^{2-3x+1} = 2^{-2x}\\\\\)

                    \(\rm 2-3x+1 = -2x\\\\-3x+2x = -1-2\\\\-x = -3\\\\x=3\)

Hence, The required value of x is 3.

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Answer:

Step-by-step explanation:

This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!

The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.

If:

\(s(t)=-16t^2+112t+360\), then the velocity function, the first derivative is:

v(t) = -32t + 112 and solve for t:

-112 = -32t so

t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.

Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:

\(s(3.5)=-16(3.5)^2+112(3.5)+360\) and

s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.

Step-by-step explanation:

Step one:

given data

let the shirts be x

and the  pants be y

Required

the number of shirts and pants

the systems of the equation for the situation is

2x+6y=11-------------1

5x+8y=18.75-------2

2x+6y=11-------------1X 5

5x+8y=18.75-------2 X2

10x+30y=55-------------1

-10x+16y=37.5-------2

0x+14y=-17.5

divide both sides by 14

y=17.5/14

y=1.25

pants= $1.25

put y=2.32 in eqn 1 2x+6y=11

2x+6(1.25)=11

2x+7.5=11

2x=11-7.5

2x=3.5

x=3.5/2

x=$1.75

Shirts = $1.75

The population of the town in 5 years will be approximately 28,982.

A data pattern known as exponential growth exhibits faster expansion over time. Compounding generates exponential profits in finance. Exponential growth is possible in savings accounts with a compounding interest rate. Compound returns in finance lead to exponential development. One of the most potent forces in finance is the power of compounding. With the help of this idea, investors may generate sizable sums with little start-up money. Compound interest savings accounts are typical instances of exponential development.

Given that, population of a town increases by 3% each year.

The population after 5 years is calculated by:

Population in 5 years = Initial population x (1 + rate) raised to time.

That is,

Population in 5 years = 25,000 x (1 + 0.03)⁵

Population in 5 years = 25,000 x 1.159274

Population in 5 years = 28,981.85

Hence, the population of the town in 5 years will be approximately 28,982.

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Answer:

B is the answer

Step-by-step explanation:

We are given an equation that models the distance an object has fallen after t seconds.

\(\Rightarrow d=13x^2\)

And are asked to find the objects average speed over the interval,\(a\leq x\leq a+h\).  

Take the derivative of the "d" function, which is a function of position, to get a function for velocity.        

\(\Longrightarrow d=13x^2 \Longrightarrow d'=26x \Longrightarrow \boxed{v=26x}\)

\(average \ speed = \boxed{ \bar v=\frac{d'(a)+d'(a+h)}{2}}\)

\(\Longrightarrow \bar v = \frac{26a+26(a+h)}{2} \Longrightarrow \bar v = \frac{26a+26a+26h}{2} \Longrightarrow \bar v = \frac{52a+26h}{2} \Longrightarrow \bar v = \frac{52a}{2}+\frac{26h}{2}\)

\(\Longrightarrow \boxed{ \bar v=26a+13h} \therefore Sol.\)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Alternative way (without derivatives):

\(average \ speed = \bar v=\frac{d(a+h)-d(a)}{a+h-a} = \boxed{\frac{d(a+h)-d(a)}{h} }\)

\(\Longrightarrow v = \frac{d(a+h)-d(a)}{h} \Longrightarrow \frac{13(a+h)^2-13a^2}{h}\Longrightarrow \frac{13(a^2+h^2+2ah)-13a^2}{h}\)

\(\Longrightarrow \frac{13a^2+13h^2+26ah-13a^2}{h} \Longrightarrow \frac{13h^2+26ah}{h} \Longrightarrow \frac{13h^2}{h}+\frac{26ah}{h}\)

\(\Longrightarrow \boxed{\bar v = 13h+26a} \therefore Sol.\)

Answer:

25

Step-by-step explanation:

For box plot, the box contains 50percent and the line is the 50percent for the whole plot

25% of the data values are between 50 and 75.

Important information:

We need to find, what percentage of the data values are between 50 and 75.

From the given box plot it is clear that 50 is the median and 75 is the third quartile.

We know that 25% of data values are between the median and the third quartile.

Thus, 25% of the data values are between 50 and 75.

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Jorge is incorrect since he is estimating the required number of cars using the incorrect methodology. Divide 22 by 4, and the outcome is not 5 with a remnant of 2, but rather 5 with a remainder of 2.

An individual or distinct unit is referred to as "unitary." The goal of this method is to establish values in terms of a single unit as a consequence. The unitary technique, for instance, can be used to calculate how many kilometers a car will travel on one litre of fuel if it currently goes 44 on two.

The following approach can be used to determine how many automobiles are required to carry the remaining passengers:

To determine the necessary number of full cars, divide the number of passengers still on board by each car's capacity: 22 passengers divided by four automobiles results in 5.5 autos.

Find the total required number of cars by rounding up to the next whole number: 6 cars.

Therefore, the answer is six cars will be required by the group to transport the remaining passengers.

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Answer:

y-y1=m(x-x1)

y-1/3=3/4(x-4)

y=3/4x-8/3

Answer:

I dont think you gave the entire question but
bridget is saying x > 3
dana is saying x < 3

A biased sample is created when a sample is collected with some members not as likely to be chosen as others .

When a sample is collected with some members not as likely to be chosen as others, the resulting sample is biased. Bias in sampling occurs when the sample is not representative of the population being studied, leading to incorrect or misleading conclusions.

For example, if a survey on the popularity of a new product is conducted by asking only a select group of individuals who are already known to be fans of the product, the results may be biased and not accurately reflect the true popularity of the product among the general population.

Bias can occur for many reasons, such as non-random sampling techniques, self-selection bias, or researcher bias. It is important to avoid bias in sampling to ensure the accuracy and validity of research findings.

This can be achieved by using random sampling techniques, increasing sample size, and ensuring that all members of the population have an equal chance of being selected for the sample.

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Answer:

1- it is irrational

2- it is rational