Math is the only place where is not questionable as to why someone has 83.

The required exponent form is obtained as 2 x 2 x 2 x 2 = 2⁴.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

The given expression is 2 x 2 x 2 x 2.

It can be written in exponent form as,

2 x 2 x 2 x 2

The number 2 is multiplied to itself by four times,.

Thus, the exponent form is given as 2⁴.

Hence, the exponent form of the given expression is 2⁴.

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Answer:

x+y=5

Step-by-step explanation:

y=-x+5

add x to both sides

x+y=5

Answer:

x + y = 5

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = - x + 5 ( add x to both sides )

x + y = 5 ← in standard form

The value of x in the triangle is -5

The sum of angles in a triangle is 180 degrees.

So, we have:

x + 35 + 60 + 90 = 180

Evaluate the sum

x + 185 = 180

Subtract 185 from both sides

x = -5

Hence, the value of x in the triangle is -5

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Step-by-step explanation:

As in another equation to equal 3x + 5?

6/2x + 2.5 × 2 = 3x + 5

4 1/2 ⋅ 4 1/2=(4 x 4)^1/2

Answer:

Many northerners were opposed to the Mexican-American War. Many southerners supported this conflict. A big reason for the different viewpoints regarding our involvement in this war was the issue of slavery. ... The northerners were concerned that many new states would be created from the lands we would receive from Mexico

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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The probability that the random sample of 100 adults will have a sample proportion of less than 0.25, using the normal distribution, is of:

0.8944 = 89.44%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The proportion and the sample size are given as follows:

p = 0.2, n = 100.

Hence the mean and the standard error are given by:

The probability that the proportion is less than 0.25 is the p-value of Z when X = 0.25, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.25 - 0.2}{0.04}\)

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

The population proportion is of p = 0.2.

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Answer:

He can buy 3 DVD's

Step-by-step explanation:

To find the cost of each DVD take the total cost and divide by 4

56/4 =14

Take the amount of money he has and divide by 14

42/14 =3

He can buy 3 DVD's

Answer:

1430

Step-by-step explanation:

have a great day!

The equation cos(3x)=1/2 has two solutions between 0 and 120 degrees. The smaller solution is 20 degrees and the larger solution is 100 degrees.

The equation cos(3x) = 1/2 has two solutions between 0 and 120 degrees. To solve for x, we need to take the inverse cosine of both sides of the equation.

The inverse cosine of 1/2 is 60 degrees. Therefore, one solution is 3x = 60 degrees or x = 20 degrees. To find the other solution, we need to add the period of the cosine function, which is 360 degrees divided by the coefficient of x. In this case, the coefficient is 3, so the period is 120 degrees. Adding 120 degrees to 20 degrees, we get 140 degrees. Therefore, the smaller solution is 20 degrees and the larger solution is 140 degrees.
The equation cos(3x) = 1/2 has two solutions between 0 and 120 degrees. To find the solutions, we first need to find the angles for which cosine is 1/2. We know that cos(60°) = 1/2 and cos(300°) = 1/2.

Now, we need to divide these angles by 3, since the equation involves cos(3x). So, we have:

3x = 60° => x = 20°
3x = 300° => x = 100°

Thus, the smaller solution is 20 degrees and the larger solution is 100 degrees.

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The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

==================================================

Explanation using mental math:

He uses 11.5 cherries for his pie, which is half the amount left (after eating those 7 cherries).

This means 2*11.5 = 23 cherries were left over after he ate those seven. In other words, half of 23 is 11.5

If we reverse time, then we get those 7 cherries back to get 7+23 = 30 cherries total. Divide those up equally between the two bags and we get 30/2 = 15 cherries per bag.

Going forward in time we have 15 cherries per bag, so 2*15 = 30 total. He eats 7 to be left with 30-7 = 23 cherries. That cuts in half to 23/2 = 11.5 cherries for his pie.

---------------

Explanation using algebra

c = number of cherries in each bag.

10 < c < 30 based on the second sentence

2c = number of cherries total from both bags combined

2c-7 = the amount left after Chris eats those 7 cherries

(2c-7)/2 = he uses half of the remaining cherries for the pie

Set that equal to the 11.5 number stated and solve for c.

(2c-7)/2 = 11.5

2c-7 = 11.5*2

2c-7 = 23

2c = 23+7

2c = 30

c = 30/2

c = 15

We effectively follow similar steps as when we did the mental math route.

Notice how c = 15 makes 10 < c < 30 true.

The magnitude or length of AB, represented as ||AB||, is calculated using the distance formula resulting in √101.

To sketch AB, plot the initial point A(8, -4) and the terminal point B(-2, -3) on a coordinate plane. Then, draw a line segment connecting these two points. The line segment AB represents the vector AB.

To write AB in component form, subtract the x-coordinates of B from the x-coordinate of A and the y-coordinates of B from the y-coordinate of A. This gives us the vector (-2 - 8, -3 - (-4)), which simplifies to (-10, 1). Therefore, AB can be represented as the vector (-10, 1).

To find the magnitude or length of AB, we can use the distance formula. The distance formula calculates the distance between two points in a coordinate plane. Applying the distance formula to AB, we have √((-2 - 8)² + (-3 - (-4))²). Simplifying the equation inside the square root, we get √(100 + 1), which further simplifies to √101. Thus, the magnitude or length of AB, denoted as ||AB||, is √101.

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Answer:

n = 4.5

Step-by-step explanation:

5.8n + 3.7 = 29.8 ( subtract 3.7 from both sides )

5.8n = 26.1 ( divide both sides by 5.8 )

n = 4.5

Answer:

so the answer to this is n= 4.5

Step-by-step explanation:

so first because you can't subtract the one with the variable you subtract 3.7 from 3.7 and 29.8 - 3.7 that cancels the 3.7 so it looks like this

5.8n + 3.7=29.8

         -3.7   -3.7

5.8n = 26.1

____   ____  n= 4.5    the lines means divide

5.8        5.8

Answer:

If you put 9 in the equation instead of x the equation won’t be true

Step-by-step explanation:

Answer:

score a high  grade in another subject

Step-by-step explanation:

Answer:

AAA

Step-by-step explanation:

start filling out math and putting unnecary notes

The area and the circumference of the circle with a radius 3 m are 28.26 m² and 18.84 m respectively.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given is a circle with a radius of 3 m, we need to find the area and the circumference of the circle,

Area = π×radius²

= 3.14×3²

= 28.26 m²

Circumference = 2π×radius

= 2×3.14×3

= 18.84 m

Hence, the area and the circumference of the circle with a radius 3 m are 28.26 m² and 18.84 m respectively.

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We can write A = PAP where 1 P= and A= where P is an invertible matrix that maps the null space of A to itself.  

To find the matrix P, we need to solve the following system of linear equations:

λ_1 1 = 1

λ_2 (-4) 1 = 1

λ_3 (-1) 1 = 1

The eigenvalues are real and non-negative, so they can be written as λ = λ_1, λ_2, λ_3 = λ_1, -4, -1 respectively.

Using Cramer's rule, we have:

\(λ_1 * 1^T = 1 * 1^T = 1\)

\(λ_2 * (-4)^T = -4 * 1^T = -4\)

\(λ_3 * (-1)^T = (-1) * 1^T = -1\)

Multiplying the first and third equations, we get:

\(-λ_1 * λ_3 = -4 * (-1) = 4\)

Multiplying the second and third equations, we get:

\(-λ_2 * λ_3 = -4 * (-1) = 4\)

Subtracting the second equation from the first, we get:

\(λ_1^2 - λ_2^2 = 1^2 - (-4)^2 = 5\)

Multiplying the first and third equations, we get:

\(-λ_1 * λ_2 = -4 * (-1) = 4\)

Dividing the third equation by the second equation, we get:

\(-1/λ_2 = -1/λ_3\)

Taking the reciprocal of both sides, we get:λ_2 = λ_3

Substituting this into the second equation, we get:

-\(λ_1 * λ_3 = -4 * (-1) * λ_3 = -4\)

Simplifying, we get:

-4 = -4

This equation has no solution, so the matrix A cannot be written in the form A = PAP where 1 P= and A= Thus, the answer is no.  

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Full Question: the matrix, A, has eigenvectors and whose eigenvalues are 1, –4 and – 1 respectively. Then, using the same order, A can be written in the form A = PAP where 1 P= and A=

The greatest common factor of 6q3, 2q3, 20q4, 20q is 30q4.

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

The factors of the numbers are:

6q3 = 2 * 3 * q3

2q3 = 2 * q3

20q4 = 2 * 2 * 5 * q4

20q = 2 * 2 * 5*q

From the common factors, the highest powers are 2, 3, 5 , q4

Therefore, the GCF of the four expressions is 2*3 * 5  * q4= 30q4.

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(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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The point (-1, -2, 3) is not visible from the point (1, 2, 0) if there is an opaque ball of radius 1 centered at the origin.

To determine if the point (-1, -2, 3) is visible from the point (1, 2, 0) with an opaque ball of radius 1 centered at the origin, we need to check if the line segment connecting the two points intersects or lies entirely within the ball.

The distance between the two points can be calculated using the distance formula:

d = sqrt((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

For the given points, the distance is:

d = sqrt((1 - (-1))² + (2 - (-2))² + (0 - 3)²)

= sqrt(4² + 4² + 3²)

= sqrt(16 + 16 + 9)

= sqrt(41)

Since the distance between the two points is greater than the radius of the ball (sqrt(41) > 1), the line segment connecting the two points does not intersect or lie within the opaque ball. Therefore, the point (-1, -2, 3) is not visible from the point (1, 2, 0) with the given opaque ball.

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Estimated  large sample size need to be selected for the 90%  of confidence level with standard deviation of $900 is equal to 24.

Standard deviation = $900

Confidence level = 90%

Estimate the required sample size,

Use the formula for the margin of error,

Margin of Error = Z × (standard deviation / √(sample size))

where Z is the z-score corresponding to the desired level of confidence.

Using attached z-score table,

For 90% confidence level, Z = 1.645.

Rearrange the formula to solve for the sample size,

Sample size = (Z × standard deviation / margin of error) ^ 2

Substituting the given values, we get,

⇒ Sample size = (1.645 × 900 / 300) ^ 2

⇒ Sample size = 24.35

Round up to the nearest whole number = 24

Therefore, need a sample size of at least 28 to ensure that it is large enough to achieve the desired level of confidence level.

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Step-by-step explanation:

h o g   =   6 ( x^2 + x - 2)   + 1

             = 6x^2 + 6x -12 + 1

             = 6x^2 + 6x -11              put in -7 for 'x'

                  6 (-7^2) + 6 (-7) - 11

               = 241

* * * edited * * *

Answer:

\(x=-3\)

Step-by-step explanation:

'x = -3', when graphed, passes through the point (-3,7) and (-3,0).

Since the line passes (-3,0), the x-intercept is -3.

(-3, 7) lies on the equation.

I have attached a picture of the graphed equation.

'x = -3' should be the correct answer.

Write the equation of the line that has an x-intercept of -3 and passes through the point (-3, 7).

Answer:

x = -3

In the given research hypothesis that proposes that consuming low carbohydrate diets results in increased weight loss, the dependent variable will be the average number of pounds lost per person.

What is the dependent variable?The dependent variable is defined as the variable that is affected by the independent variable or experimental conditions. In other words, it is the variable whose changes are observed and measured based on the changes in the independent variable. In this given research hypothesis, the independent variable is the carbohydrate content of the diet, i.e. low-carb diet and high-carb diet.The dependent variable will be the average number of pounds lost per person, which is being compared between the two groups of people following low-carb and high-carb diets.

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Answer:

Ken’s error was showing a decrease in temperature by moving 2 units left on the number line. He should have moved 2 units right to represent an increase in temperature of 2°CStep-by-step explanation:

16 is 25% of what number?

\( = > \frac{16}{25} \times 100\)

\( = > 16 \times 4\)

\( = > 64\)

Answer:

160 days

Step-by-step explanation:

800 divided by 5 equal 160

Answer:

your answer is 160 days

Step-by-step explanation:

800÷5=160 days

I hope this helps

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