7.RP.
A supermarket is having a sale on canned foods. The sale includes 10 cans to beans for
$12.50. What is the unit price per can of beans?

The mass of the original sample of phosphorus-32 was approximately 717.7 grams.

To solve this problem, we can use the radioactive decay formula:

A = Ao * 2^(-t/h)

Where:

A = resulting amount after time t

Ao = initial amount (at t=0)

t = time

h = half-life of the substance

In this case, we are given that the half-life of phosphorus-32 is 14.28 days. We want to find the initial mass, represented by Ao.

After approximately 57 days, 55 g of phosphorus-32 remain unchanged. Let's plug these values into the equation:

55 = Ao * 2^(-57/14.28)

To solve for Ao, we can isolate it by dividing both sides of the equation by 2^(-57/14.28):

55 / 2^(-57/14.28) = Ao

Using a calculator to evaluate 2^(-57/14.28), we find that it is approximately 0.07666.

Therefore, the initial mass, Ao, is:

Ao = 55 / 0.07666 ≈ 717.7 g

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Answer:

z = 5

Step-by-step explanation:

-0.25z = -1.25

-1.25 ÷ -0.25 = 5

z = 5

The probabilities of the events are

From the question, we have the following parameters that can be used in our computation:

Poisson distribution

The probability is represented as

\(P(x) = \frac{\lambda^x}{x!}e^{-\lambda}\)

So, we have

a) P(z = 6) when μ = 2.5

\(P(x = 6) = \frac{2.5^6}{6!}e^{-2.5}\)

Evaluate

P(x = 6) = 0.0278

(b) P(x ≤ 4) when μ = 1.5

\(P(x \le 4) = (\frac{1.5^4}{4!}+ \frac{1.5^3}{3!}+ \frac{1.5^2}{2!}+ \frac{1.5^1}{1!}+ \frac{1.5^0}{0!}) *e^{-1.5}\)

Evaluate

P(x ≤ 4) = 0.9814

P(x > 9) when μ = 6

This is calculated as

P(x > 9) = 1 - P(x ≤ 9)

Using a graphing tool, we have

P(x > 9) = 1 - 0.9161

So, we have

P(x > 9) = 0.0839

(d) P(x<7) when μ = 5.5

This is calculated as

P(x < 7) = P(0) + ..... + P(6)

Using a graphing tool, we have

P(x < 7) = 0.68604

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Answer:

13.5

Step-by-step explanation:

because 18 times 75 equals 1350 then you divide 1350 by 100 and you get 13.5

Answer:2/3 i believe

Step-by-step explanation:

In a rhombus the parallel sides have the same slope so BC should have the same slope as AD.

Answer:

_31. I think

Step-by-step explanation:

PLEASE check

A six-sided number cube is rolled twice the expression 1/6 x 1/6 can be used to find P(5, then3). The correct option is D.

Probability is a measure of how likely an event is to occur. Many events are impossible to predict with absolute certainty.

The probability of rolling a 5 and then a 3 is independent, so we can find the probability by multiplying the probability of rolling a 5 on the first roll by the probability of rolling a 3 on the second roll.

The probability of rolling a 5 on the first roll is 1/6, and the probability of rolling a 3 on the second roll is also 1/6.

Therefore, the expression that can be used to find P(5, then 3) is: B. 1/6 * 1/6

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Your question seems incomplete, the probable complete question is:

A six-sided number cube is rolled twice, which expression can be used to find P(5, then 3).

A. 1/5*1/3

B. 1/6*1/5

C. 5/6*3/6

D. 1/6*1/6

A. The equation that represents the balance is, 2x + 3 = 15.

B. Each box contains, x = 6 apples.

Given the problem above, to write an equation that would represent the balance, we would assume both sides of the balance are separated by the equal sign, "=".

Therefore, let the unknown number of apples in each box be be represented as x.

A. Apples in the two boxes would be 2x, the total apples on the left of the balance would be expressed as:

2x + 3

On the right, we have 15 apples, therefore, the equation that represents the balance is: 2x + 3 = 15

B. Solve to find x, the number of apples in each box:

2x + 3 = 15

2x + 3 - 3 = 15 - 3

2x = 12

x = 12/2

x = 6

This means that there were 6 apples in each box.

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The 99% confidence interval for the true mean length of the manufactured bolt is (2.9177, 3.0823)

Here, we need to construct a 99% confidence interval for population mean (μ) is given by

μ = x + Zα/2 * σ/√n   or    μ = x - Zα/2 * σ/√n

where, μ = population mean

x = sample mean

  = 3 inches

σ = population standard deviation

  = 0.3 inches

Zα/2= z score for a two tailed test at level of significance α = 2.576( for a 99% confidence level)

So, the upper limit would be,

μ = 3 + 1.645 * (0.3/√36)

μ = 3 + 1.646 * (0.3/6)

μ = 3.0823

And the lower limit would be,

μ = 3 - 1.645 * (0.3/√36)

μ = 3 - 1.646 * (0.3/6)

μ = 2.9177

Hence, the 99% confidence interval is (2.9177, 3.0823)

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Answer:

0

Step-by-step explanation:

If you replace y with 0 (which you do since you are given y = 0 and you are trying to find x from the (_,0) point), you get \(2x = 5x\). The only way for x to satisfy this is x = 0.

(a) To find the rate of change of the potential at point P(4, 4, 6) in the direction of the vector v = i + j - k, we need to compute the dot product between the gradient of the potential and the direction vector. The gradient of V is given by:

∇V = (∂V/∂x)i + (∂V/∂y)j + (∂V/∂z)k

Taking the partial derivatives of V with respect to x, y, and z, we have:

∂V/∂x = 10x - 4y + yz

∂V/∂y = -4x + xz

∂V/∂z = xy

Substituting the values x = 4, y = 4, and z = 6 into these expressions, we obtain:

∂V/∂x = 10(4) - 4(4) + (4)(6) = 48

∂V/∂y = -4(4) + (4)(6) = 8

∂V/∂z = (4)(4) = 16

The rate of change of the potential at point P in the direction of the vector v is given by:

∇V · v = (∂V/∂x)i + (∂V/∂y)j + (∂V/∂z)k · (i + j - k) = 48 + 8 - 16 = 40.

Therefore, the rate of change of the potential at point P in the direction of the vector v = i + j - k is 40.

(b) The direction in which V changes most rapidly at point P is given by the direction of the gradient vector ∇V. The gradient vector points in the direction of the steepest ascent of the potential function. In this case, the gradient vector is:

∇V = (∂V/∂x)i + (∂V/∂y)j + (∂V/∂z)k = 48i + 8j + 16k.

So, the direction of the steepest ascent is (48, 8, 16).

(c) The maximum rate of change of the potential at point P corresponds to the magnitude of the gradient vector, which is given by:

|∇V| = √((∂V/∂x)^2 + (∂V/∂y)^2 + (∂V/∂z)^2) = √(48^2 + 8^2 + 16^2) = √(2304 + 64 + 256) = √2624.

Therefore, the maximum rate of change of the potential at point P is √2624.

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A) The point with y-coordinate 0.7 in Quadrant II, is approximately 134.47 degrees.

B) The point with y-coordinate -0.9 in Quadrant III, is approximately 216.87 degrees.

C) The point with y-coordinate -0.1 in Quadrant IV, is approximately 332.39 degrees.

To find the measure of the angle between 0 and 360 degrees counter-clockwise from the 3 o'clock position on the unit circle, we need to locate the point of intersection between the terminal ray and the unit circle based on the given y-coordinate and quadrant.

A) In Quadrant II, with a y-coordinate of 0.7, the terminal ray intersects the unit circle at an angle of approximately 134.47 degrees.

B) In Quadrant III, with a y-coordinate of -0.9, the terminal ray intersects the unit circle at an angle of approximately 216.87 degrees.

C) In Quadrant IV, with a y-coordinate of -0.1, the terminal ray intersects the unit circle at an angle of approximately 332.39 degrees.

To compute these angles, we use inverse trigonometric functions such as arccosine (for Quadrant II) and arcsine (for Quadrant III and IV), and convert the results from radians to degrees. These angles represent the counter-clockwise rotation from the positive x-axis on the unit circle to the terminal ray, providing the measure of the angle in the specified range of 0 to 360 degrees.

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The probability that the digit that is received (after having been transmitted across the 4 channels) is 0.3645

In communication systems, it is common to face the challenge of transmitting information accurately over a noisy channel. In this scenario, errors can occur during transmission, and it is essential to quantify the probability of receiving the correct information at the end of the channel.

In this problem, we are asked to calculate the probability that the digit received after transmitting a 0 across four channels is also a 0. We know that each channel can either transmit the digit correctly with probability 0.9 or incorrectly with probability 0.1. Therefore, we can use the concept of conditional probability to solve this problem.

Using Bayes' theorem, we can rewrite this as:

P(CCCC | 0 received) x P(0 received) / P(CCCC)

Here, P(CCCC | 0 received) represents the probability that all four channels transmitted the 0 correctly, given that a 0 was received. This probability can be calculated as:

P(CCCC | 0 received) = P(C) x P(C | C) x P(C | C | C) x P(C | C | C | C)

Substituting the given probabilities, we get:

P(CCCC | 0 received) = 0.9 * 0.9 * 0.9 * 0.9 = 0.6561

Similarly, we can calculate the probability of receiving a 0 in general as:

P(0 received) = P(CCCC | 0 received) x P(0) + P(IIII | 0 received) x P(1)

where P(IIII | 0 received) represents the probability that all four channels transmitted the digit incorrectly, given that a 0 was received. This probability can be calculated similarly as:

P(IIII | 0 received) = P(I) * P(I | I) x P(I | I | I) x P(I | I | I | I) = 0.1 x 0.1 x 0.1 x 0.1 = 0.0001

Substituting the given probabilities, we get:

P(0 received) = 0.6561 x 0.5 + 0.0001 x 0.5 = 0.3281

Finally, we can calculate the denominator P(CCCC) as:

P(CCCC) = P(CCCC | 0 received) x P(0) + P(CCCC | 1 received) x P(1)

where P(CCCC | 1 received) represents the probability that all four channels transmitted the digit correctly, given that a 1 was received. This probability can be calculated similarly as:

P(CCCC | 1 received) = P(I) x P(I | C) x P(I | C | C) x P(I | C | C | C) = 0.1 x 0.9 x 0.9 x 0.9 = 0.0729

Substituting the given probabilities, we get:

P(CCCC) = 0.6561 * 0.5 + 0.0729 * 0.5 = 0.3645

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Answer:

x=3

Step-by-step explanation:

From the given numbers nickels and quarters ,total value of given coins is less than $2.50 then maximum number of quarters to meet the given condition is equal to 3.

As given in the question,

Let x represents the number of nickels

And y represents the number of quarters

Total number of nickels and quarters are 35

Total value of given coins = $2.50

Required equation for the given condition is:

x + y = 35   ___(1)

1 nickel = 0.05 dollars

1 quarter = 0.25 dollars

0.05x + 0.25y <2.50 ___(2)

Substitute x = 35 - y in (2) we get,

0.05 ( 35 - y ) + 0.25y < 2.50

⇒1.75 - 0.05y + 0.25y < 2.50

⇒ 0.2y < 2.50 - 1.75

⇒ 0.2y < 0.75

⇒ y < 3.75

Maximum number of quarters for the given condition is equal to 3.

Therefore, for the given numbers nickels and quarters ,total value of given coins is less than $2.50 then maximum number of quarters to meet the given condition is equal to 3.

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A car with a weight of 300 N was moved by 3 students to a distance of 10m. Calculate the work done by the 3 students and explain the energy transfer involved.

Work done by the 3 studentsWork is defined as force acting over a distance. In this scenario, the force is applied by the three students in pushing the car. Therefore, the work done can be calculated as follows:Force, F = 300 N (weight of the car)Distance, s = 10mWork done, W = FsW = 300 x 10W = 3000 JTherefore, the work done by the three students in pushing the car through 10m is 3000 J.Energy transfer involvedThe energy transfer involved in this scenario is mechanical energy transfer. Mechanical energy is the energy possessed by an object due to its motion or position. In this scenario, the car was initially at rest and the students applied a force to move it.

This force caused the car to move and therefore, it possessed kinetic energy due to its motion. The kinetic energy transferred to the car by the students can be calculated as follows:Kinetic energy, K.E = 1/2mv²Where m = mass of the car and v = velocity of the carThe velocity of the car can be calculated using the formula:Velocity, v = s/tWhere s = 10m (distance covered by the car) and t = time taken to cover the distanceWe are not given the time taken by the car to cover the distance, therefore, we cannot calculate its velocity. However, we can say that the work done by the students was transferred to the car as kinetic energy.

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a. It is possible to have a certain number of statistically significant results even when there is no true effect present.

b. The specific impact on the correlation coefficient would depend on the data and the relationship between cognitive ability and age at first speak.

a) In hypothesis testing, the significance level of 0.05 means that we expect, on average, 5 out of 100 tests to result in a statistically significant finding purely by chance, even when there is no actual effect. This is because the significance level represents the probability of obtaining a statistically significant result when the null hypothesis is true. Therefore, it is possible to have a certain number of statistically significant results even when there is no true effect present.

b) Excluding a child who took 42 months to start talking from the analysis would affect the correlation coefficient between cognitive ability (Y) and age at first speak (X). The correlation coefficient measures the strength and direction of the linear relationship between two variables. By excluding the child with a longer delay in starting to talk, the correlation coefficient may shift towards a value closer to zero or become weaker. This is because the excluded child's data point, which might have contributed to a stronger negative or positive correlation, is no longer considered in the analysis. The specific impact on the correlation coefficient would depend on the data and the relationship between cognitive ability and age at first speak.

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Step-by-step explanation:

i) answer =1

ii) 2 -3m + 6n -2 x 3 3-m

Answer:

( i ) \(\boxed{1}\)

( ii ) \(\boxed{2^{6n - 3m - 2}\times 3^{3 - m}}\)

.

Step-by-step explanation:

( Part i )

\(\left(\frac{1}{x^{a - b}} \right)^{a + b}\left(\frac{1}{x^{b + a}} \right)^{b - a}\)

\(= \left(\frac{1}{x^{(a - b)(a + b)}} \right)\left(\frac{1}{x^{(b + a)(b - a)}} \right)\)

\(= \left(\frac{1}{x^{a^2 - b^2}} \right)\left(\frac{1}{x^{b^2-a^2}} \right)\)

\(= \frac{1}{x^{a^2 - b^2 + (b^2 - a^2)}}\)

\(= \frac{1}{x^0}\)

\(= \frac{1}{1}\)

\(= \boxed{1}\)

.

( Part ii )

\(\frac{2^{m + n}\times 3^{2m + 3} \times 4^{2n -1}}{6^{2m + n}\times 12^{m - n}}\)

\(=\frac{2^{m + n}\times 3^{2m + 3} \times 2^{2(2n -1)}}{(2\times3)^{2m + n}\times (3\times 2^2)^{m - n}}\)

\(=\frac{2^{m + n}\times 3^{2m + 3} \times 2^{4n -2}}{2^{2m + n}\times3^{2m + n}\times 3^{m - n}\times 2^{2(m - n)}}\)

\(=\frac{2^{m + n + 4n - 2}\times 3^{2m + 3}}{2^{2m + n + 2m - 2n}\times3^{2m + n + m - n}}\)

\(=\frac{2^{m + 5n - 2}\times 3^{2m + 3}}{2^{4m - n}\times3^{3m}}\)

\(= 2^{m + 5n - 2 - (4m - n)}\times3^{2m + 3 - 3m}\)

\(= \boxed{2^{6n - 3m - 2}\times 3^{3 - m}}\)

.

Happy to help :)

Answer:

2 (teal)

Step-by-step explanation:

this definition would be surface area not volume. volume is what could fit inside.

We may claim that the connection is equal as both sides of both the equation were equal.

A formula that explains how two expressions on either side of a sign are connected. It typically has an equal sign and one variable. akin to this 2. 2x - 4 = 2. The instance before has the integer x.

As every word with just an equals sign is an equation, your example is one as well. Equations are frequently utilized in mathematical equations because mathematicians love equal signs.

Before deciding if the ratios are proportional, we must first determine if they are equal.

\(1/2 = 0.5\)

\(1.5/3 = 0.5\)

Cross-multiplying is another way we can verify.

\(1/2 = 1.5/3\)

\(3 * 1/2 = 1.5\)

\(1.5 = 1.5\)

We may claim that the connection appears proportionate when both sides of a problem are equal.

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Answer:

x = 78

Step-by-step explanation:

(x-8) + 20 = 90

x - 8 = 90 - 20

x - 8 = 70

x = 70 + 8

x = 78

Check:

(78-8) + 20 = 90

70 + 20 = 90

Answer:Explanation: The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.

Step-by-step explanation:

The circle equation has a center located at (2, 5) and passes through the point (10, 3) is (x - 2)² + (y - 5)² = 68

An equation is an expression that shows the relationship between two or more variables and numbers.

The circle has a center located at (2, 5) and passes through the point (10, 3), hence:

\(Radius=\sqrt{(3-5)^2+(10-2)^2}=8.25\)

The equation of the circle is:

(x-2)² + (y-5)² = 8.25²

(x - 2)² + (y - 5)² = 68

The circle equation has a center located at (2, 5) and passes through the point (10, 3) is (x - 2)² + (y - 5)² = 68

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Answer:

im pretty sure its the second one

Answer:

9/10

Step-by-step explanation:

There are 10 possible choices for the 2nd digit : 0, 1, 2, 3, 4, 5, 6, 7, 8 , and 9.

Whatever the first digit is, there are 9 ways to make the 2nd digit different.

Answer:

0.069

Step-by-step explanation:

0.3*0.23=0.069

Answer:show ur homework page I have the same one I think

Step-by-step explanation:

Step-by-step explanation:

The cube have 6 sides.

The 2 sides are base surface and the other 4 are lateral surface.

A=4L

4A=4❨4L)

4A=16L

4A=16(2 3/4)

4A=16(11/4)

4A=4(11)

4A=44

so the lateral surface is 44

Answer:

D.

Step-by-step explanation: