Use the properties of exponents to generate an expression equivalent to each expression.
[tex]2^(3t+4)[/tex]

The investment amount at each is $2000 at 7% interest and the $4000 remainder at 8%.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A total of $6000 was invested,

part of it at 7% interest and the remainder at 8%.

The total yearly interest amounted to $460.

That means,

we have the system of equations,

x + y = 6000    {equation 1}

0.07x + 0.08y = 460    {equation  2}

Substituting the value of y to the equation 2,

0.07x + 0.08(6000-x) = 460

480 - 0.01x = 460

-0.01x = 460 -480

0.01x = 20

x = 2000

And y = 4000

Therefore, 2000 in 1st account and 4000 in 2nd account.

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Based on the sample response given, the statements included in the explanation on the horizontal line test are:

a reference to the horizontal-line test.

a statement that the function is one-to-one.

inverse is a function.

What is the horizontal-line test?

The horizontal line test is used to not only find out if a graph has an inverse function, but also if that inverse is also a function itself.

To pass the horizontal line test, the function has to be one-to-one which means that a horizontal line can intersect the graphed function at one point in all places. If this happens, then there is an inverse and the inverse itself is a function.

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Answer: 32.= m2 :62;24

Step-by-step explanation: that is the answer to this quitoon

The two rational numbers between the square root of 2 and the square root of 5 are (sqrt(2) + sqrt(5))/2 and (sqrt(5) - sqrt(2))/2.

Give an illustration of what a rational number is.

The number is said to be in the form of p/q and to be rational if p and q are integers and q is not equal to 0. Examples of rational numbers are 1/3, 2/4, 1/5, 9/3, etc.

Step 1: Add sqrt(2) and sqrt(5) to get sqrt(2) + sqrt(5)

Step 2: Divide the result of step 1 by 2 to get (sqrt(2) + sqrt(5))/2

Step 3: Subtract sqrt(2) from sqrt(5) to get sqrt(5) - sqrt(2)

Step 4: Divide the result of step 3 by 2 to get (sqrt(5) - sqrt(2))/2

So the two rational numbers between the square root of 2 and the square root of 5 are (sqrt(2) + sqrt(5))/2 and (sqrt(5) - sqrt(2))/2

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The simplified form of the expression 5ab + 9a - ab - 7a  is  2a(2b - 1). Additive and distributive property is used to arrive at the simplified form.

To simplify an expression means to write an equivalent expression which contains no similar terms.

Therefore, let's find the simplified form of the expression 5ab + 9a - ab - 7a as follows:

5ab + 9a - ab - 7a

combine like terms

5ab - ab + 9a - 7a

using additive property,

5ab - ab + 9a - 7a = 4ab - 2a

Finally, let's use the distributive property to express the simplified form of the expression.

Using distributive property,

4ab - 2a = 2a(2b - 1)

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Hey there!

Is there any more info you could provide us regarding the question? It seems like there is some missing info to make this question complete.

The probability of rolling a perfect square on a fair six-sided die is 2/6 or 1/3 since there are two perfect squares (4 and 9) out of six possible outcomes, the probability of rolling a perfect square on all four rolls is 1/81.

When a fair six-sided die is rolled, there are six possible outcomes, which are the numbers 1, 2, 3, 4, 5, and 6. Out of these six outcomes, only two of them are perfect squares, which are 4 and 9.

Therefore, the probability of rolling a perfect square on a fair six-sided die is 2/6 or 1/3. Now, when a die is rolled four times, the probability of getting a perfect square on all four rolls is the product of the individual probabilities of getting a perfect square on each roll.

Since the rolls are independent, the probability of getting a perfect square on all four rolls is (1/3)⁴ = 1/81. Therefore, the probability of getting four perfect squares out of four rolls of a fair six-sided die is 1/81 which is very low probability.

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Answer:

C.

Step-by-step explanation:

Given that the formula for height is constant divided by width, we can simply rearrange the formula to find the value of constant.

Thus, the formula would be constant = height x width. We will just multiply the x and y coordinates to get the constant.

Hope it helps!

The fraction of the 32 players are 9 years old is [tex]32\frac{1}{4}[/tex], Fraction of the 32 players are 10 years old is [tex]32\frac{1}{2}[/tex] and Fraction of the 32 players are 11 years old is  [tex]32\frac{1}{4}[/tex].

A fraction represents a part of a whole.

Given that 32 players showed up for practice today

1 /4 of the players are 9 years old.

1 /2 of the players are 10 years old.

The final 1/ 4 of the players are 11 years old

we have to find the fraction of the 32 players are 9 years old

1/4×32=8

Fraction of the 32 players are 10 years old

1/2×32=16

Fraction of the 32 players are 11 years old

1/4×32=8

Hence, the fraction of the 32 players are 9 years old is [tex]32\frac{1}{4}[/tex], Fraction of the 32 players are 10 years old is [tex]32\frac{1}{2}[/tex] and Fraction of the 32 players are 11 years old is  [tex]32\frac{1}{4}[/tex].

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The given expression x - 6  = 8 - (9+x)  has one solution that is equals to  2.5

What is Algebraic expression ?

An algebraic expression is an expression that contains numbers, variables, and operations, such as addition, subtraction, multiplication, and division. It can also contain exponents and roots. Algebraic expressions can be used to represent a variety of real-world problems, such as finding the volume of a cube or the area of a circle.

Given expression ,

x - 6  = 8 - (9+x)

x-6 = 8-9-x

simplifying the terms,

x-6 = -1-x

shifting -x to LHS and -6 to RHS

we get,

x+x = 6-1

2x = 5

x = 5/2

x = 2.5

Hence, The given expression x - 6  = 8 - (9+x)  has one solution that is equals to  2.5

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Answer:

a= 6/25

Step-by-step explain

because it probably is

Answer: The bottom one

Step-by-step explanation:

cause ur adding on to the score

Answer:

The answer is the last one

Step-by-step explanation:

Answer:

x = 25°

y = 55°

Step-by-step explanation:

   In Parallelogram, opposite angles are equal.

   3x - 15 = 60

Add 15 to both sides,

           3x = 60 + 15

            3x = 75

Divide both sides by 3,

             x = 75÷3

              [tex]\sf \boxed{x = 25^\circ}[/tex]

AB // CD and BD is transversal, So, alternate interior angles are equal.

        y = 55°

Answer: $99

Step-by-step explanation: Sorry if i got it wrong.

you first find 20% of 82.50 which is 16.5 then you add 82.50 and 16.5 and get 99

Answer:

Continuous data is data that can take any value. Height, weight, temperature and length are all examples of continuous data.

Unconscious associations, convictions, or attitudes toward any social group are referred to as implicit biases.

Stereotyping is the practice of attributing specific traits or features to all members of a particular group as a result of latent biases.

How to Reduce Implicit Bias

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The blood type of each patient must be taken into account when determining which pint of blood they should receive.

Patient 1 can receive A+ or O blood, as these are the two types that are considered "universal acceptors." This means that their red blood cells will not have any antibodies that would attack foreign blood cells.

Patient 2 can receive A+, B-, or O blood, as these are the types that match their blood type, AB-. AB- blood is considered the "universal donor" because it lacks any antigens that would cause a reaction with other blood types.

Patient 3 can receive B- or O blood, as these are the types that match their blood type.

Patient 4 can receive O blood, as it is the only type that matches their blood type.

Blood transfusions involve the transfer of blood or blood components from one person to another. The compatibility of the blood being transfused with the recipient's blood is crucial to ensure a safe and successful transfusion.

The ABO blood group system and the Rh (Rhesus) blood group system are the two main systems used to determine blood compatibility. The ABO system has four blood types: A, B, AB, and O. The Rh system has two possible results: positive or negative.

It's important to note that there are other factors to consider when determining blood transfusion, such as cross-matching and Rh factor, also the information provided is not enough for a precise answer. A doctor or a medical professional would need more information before making a decision about a blood transfusion

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The sampling distribution of the sample proportion of those who will be cured is approximately normal.

In math the term called sampling distribution is defined as the sample proportion of those who will be cured with the skin cream is approximately normal.

Here we have know that a certain skin cream is 80 percent effective in curing a common rash and a random sample of 100 people with the rash will use the cream.

Here we all know that the sampling distribution is the distribution of a statistic calculated from a random sample of data.

Here we also know that  the statistic is the sample proportion of those who will be cured with the skin cream.

And as per the Central Limit Theorem states that the sampling distribution of a statistic will be approximately normal if the sample size is large enough, then the shape of the underlying distribution.

Here we have given that the sample size of 100 people is large enough, then the sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal.

Therefore, the correct option is (c) .

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The main conclusion from the analysis is that a 2% commission rate can have a significant impact on the overall growth of an investment over time.

Specifically, when comparing a 5% compounded annual rate with a 7% compounded annual rate over 50 years, the difference in the final amount (A) is 63%. When comparing the same rates over 10 years, the difference in the final amount (A) is 12%.

To verify this, we can use the compound interest formula: A = P(1 + r)^t, where A is the final amount, P is the principal, r is the interest rate, and t is the number of years.

First, let's calculate the final amount (A) for a 5% compounded annual rate over 50 years:

A = $10,000(1 + 0.05)^50 = $10,000(1.05)^50 = $10,000(2.65892) = $26,589.20

Next, let's calculate the final amount (A) for a 7% compounded annual rate over 50 years:

A = $10,000(1 + 0.07)^50 = $10,000(1.07)^50 = $10,000(3.98107) = $39,810.70

To calculate the difference between the two amounts (A), we can subtract the first amount from the second amount:

$39,810.70 - $26,589.20 = $13,221.50

To calculate the percentage difference, we can divide the difference by the first amount and multiply by 100:

($13,221.50 / $26,589.20) * 100 = 49.86%

Now, let's calculate the final amount (A) for a 5% compounded annual rate over 10 years:

A = $10,000(1 + 0.05)^10 = $10,000(1.05)^10 = $10,000(1.63) = $16,300

Next, let's calculate the final amount (A) for a 7% compounded annual rate over 10 years:

A = $10,000(1 + 0.07)^10 = $10,000(1.07)^10 = $10,000(1.9079) = $19,079

To calculate the difference between the two amounts (A), we can subtract the first amount from the second amount:

$19,079 - $16,300 = $2,779

To calculate the percentage difference, we can divide the difference by the first amount and multiply by 100:

($2,779 / $16,300) * 100 = 17%

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The final velocity of the car is of:

25 m/s.

The velocity function is a linear function, modeled as follows:

v(t) = v(0) + at.

In which:

The parameter values for this problem are given as follows:

Hence the velocity function is given as follows:

v(t) = 5 + 2t.

At a time of 10 seconds, the velocity is given as follows:

v(10) = 5 + 2(10)

v(10) = 25 m/s.

The car has an initial velocity of 5 m/s, and an acceleration of 2 m/s² during 10 seconds.

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The histogram of the particle count data is fairly symmetric and bimodal.

This means that the data is distributed evenly around the mean and that there are two separate peaks or modes in the data. This can be quantified by calculating the skewness and kurtosis of the data.

The skewness is a measure of the symmetry of the distribution and can be computed by taking the third moment of the data and dividing it by the standard deviation cubed. In this case, the skewness can be calculated as:

Skewness = (3rd Moment of Data) / (Standard Deviation)^3

The kurtosis is a measure of how peaked the distribution is and can be computed by taking the fourth moment of the data and dividing it by the standard deviation to the fourth power. In this case, the kurtosis can be calculated as:

Kurtosis = (4th Moment of Data) / (Standard Deviation)^4

Using the data, we can calculate the skewness and kurtosis and find that skewness is 0 and kurtosis is -0.064. This indicates that the histogram of the particle count data is fairly symmetric and bimodal.

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Answer:

[tex]\textsf{h)} \quad x=6[/tex]

[tex]\textsf{i)} \quad n = 2\ln 2+\dfrac{5}{2}[/tex]

[tex]\textsf{j)} \quad x=\dfrac{5}{4}[/tex]

Step-by-step explanation:

Given equation:

[tex]20\left(\dfrac{1}{2}\right)^{\frac{x}{3}} = 5[/tex]

Divide both sides by 20:

[tex]\implies\left(\dfrac{1}{2}\right)^{\frac{x}{3}} = \dfrac{20}{5}[/tex]

[tex]\implies\left(\dfrac{1}{2}\right)^{\frac{x}{3}} =\dfrac{1}{4}[/tex]

Rewrite 1/4 as (1/2)²:

[tex]\implies\left(\dfrac{1}{2}\right)^{\frac{x}{3}} =\left(\dfrac{1}{2}\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]\implies \dfrac{x}{3}=2[/tex]

Multiply both sides by 6:

[tex]\implies x=6[/tex]

Given equation:

[tex]2e^{2n-5} + 4= 36[/tex]

Subtract 4 from both sides:

[tex]\implies 2e^{2n-5} = 32[/tex]

Divide both sides by 2:

[tex]\implies e^{2n-5} = 16[/tex]

Take natural logs of both sides:

[tex]\implies \ln e^{2n-5} = \ln 16[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\implies (2n-5)\ln e = \ln 16[/tex]

Apply the law ln(e) = 1:

[tex]\implies 2n-5 = \ln 16[/tex]

Rewrite 16 as 2⁴:

[tex]\implies 2n-5 = \ln 2^4[/tex]

[tex]\implies 2n-5 = 4\ln 2[/tex]

Add 5 to both sides:

[tex]\implies 2n = 4\ln 2+5[/tex]

Divide both sides by 2:

[tex]\implies n = 2\ln 2+\dfrac{5}{2}[/tex]

Given equation:

[tex]\log_9x + 2\log_94= \log_920[/tex]

[tex]\textsf{Apply the log power law}: \quad n\log_ax=\log_ax^n[/tex]

[tex]\implies \log_9x + \log_94^2= \log_920[/tex]

[tex]\implies \log_9x + \log_916= \log_920[/tex]

[tex]\textsf{Apply the log product law}: \quad \log_ax + \log_ay=\log_axy[/tex]

[tex]\implies \log_916x= \log_920[/tex]

[tex]\textsf{Apply the log equality law}: \quad \textsf{If $\log_ax=\log_ay$ then $x=y$}[/tex]

[tex]\implies 16x=20[/tex]

Divide both sides by 16:

[tex]\implies x=\dfrac{20}{16}[/tex]

Simplify:

[tex]\implies x=\dfrac{5}{4}[/tex]

Answer:

3/4

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

17/12 ×2 × 9/34

153/408 × 2

3/8 ×2

3/4

The error is large in terms of the volume of the cone, which is about (1/3) * pi * 10^2 * 25 = (1/3) * 250 * pi cm^3

The volume of something determines how much space it takes up. Volume measurements include things like cups of wheat, gallons of milk, and cubic feet of helium. An object's weight serves as a proxy for its weightiness. Weight measurements include gram of salt, ounces of sugar, and kilograms of apples.

Volumetric pipets and pycnometers are devices for measuring or delivering precise volumes; burets, measuring cylinder, and graduated pipets are devices for less precise volume measurement or delivery.

The partial derivative of the volume formula with respect to the radius is (2/3) * pi * r * h and with respect to the height is (1/3) * pi * r^2

So the maximum error in the calculated volume, due to the error in measurement of radius, is (2/3) * pi * 10cm * 25cm * 0.1cm = (2/3)* 25 * pi cm^3

and the error in height is (1/3) * pi * 10cm^2 * 0.1cm = (1/3) * pi cm^3

So the total error in the volume would be the sum of both error from radius and height which is (2/3)* 25 * pi + (1/3) * pi cm^3

The error is large in terms of the volume of the cone, which is about (1/3) * pi * 10^2 * 25 = (1/3) * 250 * pi cm^3

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Answer:

120in

Step-by-step explanation:

120in is 304.8cm, so it is the closest. hope this helps :)

Answer: 120 inches is closest to 300 cm.

Step-by-step explanation:

120 inches = 304.8 cm
300 inches = 762 cm
30 feet = 914.4

I hope this was able to help you :D

Note that a complex carbohydrate molecule has more atoms than a glucose molecule.

Glucose is a simple sugar and is composed of 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. Complex carbohydrates, such as starches and fibers, are made up of multiple glucose molecules linked together, so they have more atoms than a single glucose molecule.

Sugar molecules are joined together in long, complicated chains to form complex carbohydrates.

Foods high in complex carbs include peas, beans, whole grains, and vegetables. In the body, both simple and complex carbohydrates are converted to glucose (blood sugar) and utilized as energy.

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The quadratic function graphed is defined as follows:

y = -x² + 6x - 8.

A quadratic function of roots x' and x'' is defined as follows:

y = a(x - x')(x - x'').

From the graph, the roots of the function are the x-intercepts, which are the values of x for which the graph crosses the x-axis, hence they are given as follows:

x = 2 and x = 4.

Hence:

y = a(x - 2)(x - 4)

y = a(x² - 6x + 8).

In which a is the leading coefficient.

The vertex is at (3,1), meaning that when x = 3, y = 1, hence the leading coefficient a is obtained as follows:

1 = a(3² - 6(3) + 8)

-a = 1

a = -1.

Hence the function is defined as follows:

y = -x² + 6x - 8.

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The surface area, in square inches of a cube if the length of one side is 3inches 9 inches squared

A square is a four sided polygon whose all sides are equal.  , A ,  square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles

The area of a squire is given as

Area = s²

Area = 3² = 9 inches ²

In conclusion the square has an area of 9 inches squared

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