600 is writtena s 2^a x b x c^d
where a , b, c and d are all prime numbers
Find the value of a,b,c and d

the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. So  10.2% of gadgets were powered by batteries for fewer than 63 hours.

Given that,

Data have a mean of 74.6 hours and a standard deviation of 9.1 hours, and they are regularly distributed.

The standard deviation is defined as ?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

\(p(X\leq 63) = p(Z\leq 63-74.6/9.1)\)

From standard deviation,

         \(p(X\leq 63) = p(Z\leq -1.279)= 0.1061\)

a certain percentage of gadgets have battery life of less than 63 hours.

X= 63 hours

Percentage of devices ran on the batteries for fewer than 63 hours = 10.2%

Therefore, 10.2% of electronic devices had battery life of less than 63 hours

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Answer: $1125

Step-by-step explanation: 7500 x 3%=  225   Then multiply 225 by the 5 years. You will then get 1125.  Marsha earned $1,125 in interest.

I hoped this helped, have a great rest of your day!

Answer:

$1125

Step-by-step explanation:

plz crown

Answer:   7 is 6 feet by 21 feet

8 is 12 inches

Step-by-step explanation:

According to the above, the point s coincides with number -5, the point t coincides with number -8.24 and the point u coincides with number 6.28.

To identify the points that coincide with the expressions we must perform the mathematical operations shown. In this case, we must find the roots and multiply the 2 by the number pi as shown in the expressions column.

An important point is that we must do these operations in the positive form and then put the negative symbol because it is not possible to find the root of a negative number.

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Answer:

They are not located next to the other states.

Step-by-step explanation:

The reason Hawaii and Alaska are not considered part of the contiguous United States is that they are not located next to the other states. The contiguous United States refers to the 48 states that are located on the North American continent and are connected to each other, excluding Alaska and Hawaii. While Alaska is located on the North American continent, it is separated from the contiguous states by the Canadian province of British Columbia. Hawaii, on the other hand, is an archipelago located in the Pacific Ocean and is geographically separate from the continental United States.

Answer:

They are not located next to the other states.

Step-by-step explanation:

:D have a nice day!

Answer:

I don't see a data table, but I think it's venus??

Step-by-step explanation:

Answer:

its venus I remember it from the quiz lol

Step-by-step explanation:

Answer:

27 degrees

Step-by-step explanation:

90 - 63 = 27

Answer:

Step-by-step explanation:

Given the expression (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we are to take the product of all the complex values. We must note that i² = -1.

Rearranging the expression [(3 - i)(3 + i)] [(2 + i)(1 - i)](1 + 2i)

On expansion

(3 - i)(3 + i)

=  9+3i-3i-i²

= 9-(-1)

= 9+1

(3 - i)(3 + i) = 10

For the expression (2 + i)(1 - i), we have;

(2 + i)(1 - i)

= 2-2i+i-i²

= 2-i+1

= 3-i

Multiplying 3-i with the last expression (1 + 2i)

(2 + i)(1 - i)(1 + 2i)

= (3-i)(1+2i)

= 3+6i-i-2i²

= 3+5i-2(-1)

= 3+5i+2

= 5+5i

Finally,  [(3 - i)(3 + i)] [(2 + i)(1 - i)(1 + 2i)]

= 10(5+5i)

= 50+50i

Hence,  (3 - i)(3 + i)(2 + i)(1 - i)(1 + 2i) is equivalent to 50+50i

Answer:

It’s b

Step-by-step explanation:

The product is 30 - t when soloved

Answer:

1/4

Step-by-step explanation:

Possible outcomes from rolling the cube that satisfy the "greater than 3" criterion are {4, 5, 6}  out of a total of six possibilities {1, 2, 3, 4, 5, 6}.  Thus, the probability of rolling a number greater than 3 is 3/6, or 1/2.

Probability of flipping heads is 1/2.

These are entirely independent events.  Thus, the joint probability is (1/2)(1/2), or 1/4.

Answer. I think is A

Step-by-step explanation:

Answer:

Step-by-step explanation:

The recursive form is a(n + 1) = a(n) + 2, with a(1) = 8.

The next term is a(6) = a(5) + 2, which heere is a(6) = 16 + 2 = 18

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.

In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.

For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

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The increase in the amount of wages of Gabriela is $ 41,400

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount after increase in wages be = A

Now , the initial amount of Gabriela be = $ 36,000

And , the percentage increase in the wages = 15 %

So , the equation will be

Total amount after increase in wages A = initial amount + ( percentage increase x initial amount )

Total amount after increase in wages A = 36,000 + ( 15/100 x 36,000 )

Total amount after increase in wages A = 36000 + ( 15 x 360 )

Total amount after increase in wages A = 36000 + 5400

Total amount after increase in wages A = $ 41,400

Therefore , the value of A is $ 41,400

Hence , The increase in the amount of wages of Gabriela is $ 41,400

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Answer:

any other part of the question?

Step-by-step explanation:

It should be noted that the concept of chords and central angles are used in the design since the diameter and circumference of the angles are taken into consideration.

A ferris wheel simply means an amusement ride that contains a rotating uprights wheel that has multiple passenger-carrying components attached to a rim.

It should be noted that the consideration in designing a ferris wheel is that the circumference and the measurement of the central angle formed will be known.

Lastly, if a ferries wheel is not circular in design, it'll be a challenge for it to rotate.

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

Explanation:

We have a triangle with these side lengths

The order of 'a' and b doesn't matter, but we must have c as the largest value. Usually a,b,c are in ascending order.

Plug those values into the formula for the pythagorean theorem. If we get the same thing on both sides, then we have a right triangle.

\(a^2 + b^2 = c^2\\\\31^2 + 72^2 = 78^2\\\\961+5184 = 6084\\\\6145 = 6084\\\\\)

We have a false statement at the end, which means the original equation is false for those a,b,c values.

Therefore, we do not have a right triangle.

Instead, this triangle is acute since the \(a^2+b^2\) side is larger than the \(c^2\) side

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

Rules to have in your notebook or on a reference sheet:

\(\text{If }a^2 + b^2 = c^2 \text{ then it is a right triangle}\\\\\text{If }a^2 + b^2 > c^2 \text{ then the triangle is acute}\\\\\text{If }a^2 + b^2 < c^2 \text{ then the triangle is obtuse}\\\\\)

For more information, check out the converse of the pythagorean theorem.

The height of a man with a z-score of 0 is 69 inches.

The average height of adult men = 69.0 inches, Standard deviation of adult men = 2.8 inches to find the Z-score the following formula is used:

z = (x- μ)/σ where z is the z-score, x is the value to be standardized, μ is mean and σ is the standard deviation.

To find the height of a man with a z-score of Standardized value(z) = 0

z = (x - μ)/σ

0 = (x - 69)/2.8

x = 69 + 0 (2.8)

x = 69 inches.

Therefore, the height of a man with a z-score of 0 is 69 inches.

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The estimated standard deviation from the range rule is 145.5 cm3.As it is 29.8 cm3 smaller than the exact standard deviation, we consider that the estimation is not accurate enough.

Generally, brain volumes which are smaller than 921.1 cm3 can be considered significantly low and bigger than 1417.5 cm3 can be considered significantly high. Hence, brain volume of 1457.5 cm3 is bigger than the expected maximum, so it can be considered significantly high.

The calculation goes like this,

According to the range rule, the standard deviation and range, or the distance between the maximum and smallest value, are roughly inversely proportional:

\(s=R/4\)

If we have a sample of 50 brains volumes, and they range from 910 cm3 to 1492 cm3, we can estimate the standard deviation as:

\(s=max-min/4\)

s=1492-910/4=582/4=145.5

The exact standard deviation is 175.3 cm3.The difference is 175.3-145.5=29.8 cm3, so the estimation is not accurate enough.

The range rule of thumb states that we should anticipate a maximum value that is approximately two standard deviations above the mean and a lowest value that is approximately two standard deviations below the mean. The expected ranges are as follows given our mean volume of 1169.3 cm3 and standard deviation of 124.1 cm3:

Min= M-2s=1169.3-2*124.1=921.1

Max=M+2s=1169.3+2*124.1=1417.5

The brain capacity of 1457.5 cm3 can be regarded as significantly high because it is higher than the predicted maximum.

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Since 80 out of 100 free throws were successful, the standard deviation of the success rate would be 8, and the standard deviation of a binomial distribution is the square root of (p*q)/n, where p is the probability of success, q is the probability of failure (1-p), and n is the total number of trials.

Standard deviation is calculated as follows:

p*q/n = 0.8*0.2/100 = 0.0016 = 0.04 = 8

Since 80% of 100 equals 80 successful free throws, the standard deviation of the successes from 100 free throws would be 8. The dispersion in a set of data is measured by standard deviation. A binomial distribution's standard deviation is equal to the square root of (p*q)/n, where p is the success probability, q is the failure probability (1-p), and n is the number of trials. Since the success rate in this instance is 80%, p = 0.8, q = 0.2, and n = 100. The standard deviation is then equal to the square root of (p*q/n): (0.8*0.2/100) = (0.0016) = (0.04), which equals 8. Therefore, the standard deviation of the successes from 100 free throws for a basketball player who makes 80% of them would be 8.

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To bring the 2,000 kg wagon to rest, the buffer stop needs enough springs to absorb its kinetic energy. The number of springs and their stiffness can be calculated using given parameters and formulas.



To calculate the number of springs required in the buffer stop, we need to find the energy of motion that needs to be absorbed. The kinetic energy (KE) of the wagon is given by KE = (1/2)mv^2, where m is the mass (2,000 kg) and v is the velocity (0.69 m/s). The KE is 477.9 J.Next, we calculate the potential energy stored in the compressed springs. The compression distance is 15 cm, which is 0.15 m. The potential energy (PE) stored in each spring is given by PE = (1/2)kx^2, where k is the stiffness of the spring and x is the compression distance.

The total energy absorbed by all the springs is equal to the kinetic energy of the wagon. Therefore, the number of springs required is given by N = KE / PE, where N is the number of springs.To determine the stiffness of the spring, we use the formula k = (Gd^4) / (8nD^3), where G is the shear modulus (0.8 x 10^5 N/mm^2), d is the wire diameter (2 cm), n is the number of coils (15), and D is the mean diameter of the coils (20 cm).

By substituting the values into the equations, we can find the number of springs and the stiffness of each spring.

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The t times u is approximately equal to -139.7.

To find t times u, we use the formula for the dot product: t · u = |t||u|cosθ, where θ is the angle between the vectors. Since we are only given the vectors t and u, we need to find their magnitudes and the angle between them.

The magnitude of t is |t| = √(7^2 + (-3)^2) = √58, and the magnitude of u is |u| = √((-10)^2 + (-8)^2) = √164.

To find the angle between t and u, we use the formula cosθ = (t · u)/(|t||u|). Substituting the values we know, we get cosθ = ((7)(-10) + (-3)(-8))/((√58)(√164)) = -74/(2√1017). Using a calculator, we find that θ ≈ 131.5 degrees.

Now we can find t · u: t · u = |t||u|cosθ = (√58)(√164)(cos(131.5)) ≈ -139.7.

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1. 12a²b² + -7a²b² + 9a²b²

= 14a²b² (the terms a²b² are like terms so don't look at them, just add 12 + (-7) + 9.

= 14 (ab)² (you can write like this too because both a & b are squared).

2. y² - (-5y²)

= 6y² (subtract -5 from 1, y² is the like term).

The value of X is 0. This means that point P is exactly on side AB, which means that P is the centroid of the quadrilateral.  

In the given diagram, P is circumscribed about quadrilateral ABCD, which means that P is inside the quadrilateral and touches all of its sides. We can draw a circle with center at P and radius equal to the distance between P and the point where the circumcircle touches the opposite side to P.

Let O be the center of the circle and A, B, C, and D be the vertices of the quadrilateral. Then, we can see that the distance between O and A is the same as the distance between O and B, and the distance between O and C is the same as the distance between O and D.

The distance between P and the opposite side to P is equal to the distance between P and any one of the other three vertices. Without loss of generality, let's assume that P is closest to vertex A. Then, the distance between P and A is equal to the radius of the circle, which we can call r.

We know that the circumcircle touches opposite sides to P at points X and Y. Let's call the point where the circumcircle touches side BC point X and the point where it touches side CD point Y. We can draw a line from P through X, which is parallel to side BC, and another line from P through Y, which is parallel to side CD.

These lines divide the circle into two equal parts. Therefore, we can say that:

r = |XA + YB| / 2

here XA and YB are the lengths of the segments from point X to side BC and from point Y to side CD, respectively.

We also know that:

AB = AC

since the quadrilateral is a parallelogram. Therefore, we can say that:

\(r^2 = XA^2 + YB^2\\\)

Now, we can use the fact that P is the circumcenter of the quadrilateral to find the value of X. The distance between the circumcenter O and any point on side BC is equal to the length of side BC, while the distance between the circumcenter O and any point on side AD is equal to the length of side AD. Therefore, we can say that:

XA = r

and

YB = r

Substituting these values into the expression for r, we get X:

\(= r * (1 - (r^2 - r^2))\\= 0 * (1 - (r^2 - r^2))\\\)

X = 0

Therefore, the value of X is 0. This means that point P is exactly on side AB, which means that P is the centroid of the quadrilateral.  

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Correct Question:

In the diagram below, P is circumscribed about quadrilateral ABCD. What is the value of X?

Answer:

$1,126.37

Step-by-step Explanation:

Given:

Account balance for:

Month 1 = $1285.12

Month 2 = $961.36

Month 3 = $1132.63

Required:

Average balance of account

SOLUTION:

Average balance of account = sum of account balance for the 3 months ÷ 3

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

Average balance of account = \( \frac{3,379.11}{3} \)

Average balance of account = \( 1,126.37 \)

Answer:

$1,126.37

Step-by-step Explanation:

Given:

Account balance for:

Month 1 = $1285.12

Month 2 = $961.36

Month 3 = $1132.63

Required:

Average balance of account

SOLUTION:

Average balance of account = sum of account balance for the 3 months ÷ 3

Average balance of account =  

Average balance of account =  

Average balance of account =