Manuel's heart beats 9 times per 10 seconds while he is resting. How many times would Manuel's heart beat during 3 minutes of rest?

Answer:

  7 m/s²

Step-by-step explanation:

Since force and acceleration are proportional, multiplying the force by a factor of 14/6 = 7/3 will multiply the acceleration by that same factor:

  acceleration = (3 m/s²)(7/3) = 7 m/s²

The correlation coefficient is -7.44, which shows a strong negative correlation.

To calculate the correlation coefficient, you can use the following formula:

r = (n Σ(xy) - Σ(x) Σ(y)) / √((n Σ(x²) - (Σ(x))²) (n Σ(y²) - (Σ(y))²))

Where n is the number of data points, x is the variable on the x-axis, y is the variable on the y-axis, Σ(xy) is the sum of the products of x and y, Σ(x) is the sum of x, Σ(y) is the sum of y, Σ(x²) is the sum of the squares of x, and Σ(y²) is the sum of the squares of y.

Plugging in the values from the data, we get:

r = (5 x 198 - 39 x 91) / √((5 x 114 - 39²) x (5 x 187 - 91²))

Simplifying this equation gives us:

r = (-179) / √((-97) x (-6))

r = (-179) / √(582)

r = (-179) / 24.07

r = -7.44

The correlation coefficient is -7.44, which indicates a strong negative correlation. This means that as the value of x increases, the value of y decreases. Conversely, as the value of x decreases, the value of y increases.

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Answer:

Using points ( 2 , - 4) and ( 0 , 2)

Slope = 2+4/0-2 = 6/-2 = - 3

Since the lines are parallel their slope will be the same

So the slope of the line parallel to the one in the picture is - 3

That's option A.

Hope this helps.

Answer:

i believe its:     -1/3

Step-by-step explanation:

if the line is parallel to the original line, the slope should be the same, and the slope of the original line is - 1/3. the slope is negative because the line is heading downwards, or in a negative direction. hope this helped!!

A solution of \(y" + 2y' + 2y = 3f1(t) + f2(t)\) using the superposition principle is given by: \(y = ((3-f2(t))/8) y1 + ((1+3f1(t))/8) y2\)

It be found by taking a linear combination of the two given solutions y1 and y2. Let c1 and c2 be constants, then the solution y can be expressed as y = c1y1 + c2y2.  To find c1 and c2, we differentiate y twice and substitute it into the given differential equation:

\(y' = c1(2cos(3t) - 6tsin(3t)) + c2(-6e^-{t sin(6t)} - e^{-t cos(6t)})\)

\(y" = c1(-18sin(3t) - 36tcos(3t)) + c2(-36e^{-t sin(6t)} + 12e^{-t cos(6t)})\)

Substituting these expressions for y and its derivatives into the differential equation and simplifying, we get: \((3c1 + c2) f1(t) + (c1 + 3c2) f2(t) = 0\)

Since this must hold for all t, we can equate the coefficients of f1(t) and f2(t) to zero to get the system of equations: \(3c1 + c2 = 3, c1 + 3c2 = 1\)

Solving for c1 and c2, we get \(c1 = (3-f2(t))/8\) and \(c2 = (1+3f1(t))/8.\)

Note that this solution is valid only if f1(t) and f2(t) are continuous and differentiable.

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The total length of the fencing is the perimeter of the rectangular yard which is P = 260 feet

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

Let the perimeter of the rectangular yard be = P

Now , the equation will be

The width of the rectangular yard W = 55 feet

The length of the rectangular yard L = 75 feet

And , the required fencing = Perimeter of rectangular yard

Perimeter of rectangular yard P = 2 ( L + W )

Substituting the values in the equation , we get

Perimeter of rectangular yard P = 2 ( 55 + 75 )

Perimeter of rectangular yard P = 2 ( 130 )

Perimeter of rectangular yard P = 260 feet

Therefore , the value of P is 260 feet

Hence , the perimeter of yard is 260 feet

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Answer:

\( \sf \: 6 + 3b + 8 = 32\)

Step-by-step explanation:

Given expression,

→ 6 + 3b + 8

Now we have to use,

→ b = 6

Let's solve the expression,

→ 6 + 3b + 8

→ 6 + 3(6) + 8

→ 6 + 18 + 8

→ 24 + 8

→ 32 => final value

Hence, the answer is 32.

Z-score of given data comes to be -5.30.

It is given that

Population mean μ= 310

Standard deviation σ= 20

Mean of sample data X= 295

Sample size n= 50

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

For a hypothesis test

Z-score = (X-μ)/(σ/√n)

Where, X = observed value

μ= mean

σ = standard deviation

n =sample size

Z-score of above data = (295-310)/(20/√50)

Z-score = -5.30

Therefore, the Z-score of the given data comes to be -5.30.

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This equation is always true, which means that it is an identity. In other words, any value of x will satisfy the equation. Therefore, the equation has infinitely many solutions.

In mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equals sign ("="). The expressions on either side of the equals sign are called the left-hand side and the right-hand side of the equation, respectively. The purpose of an equation is to describe a relationship between two or more variables or quantities, such as x + 3 = 7 or y = 2x - 5. Equations can be used to solve problems and answer questions in various fields of study, such as algebra, geometry, physics, chemistry, and engineering. Solving an equation typically involves finding the value or values of the variable(s) that make the equation true. Some equations may have a unique solution, while others may have multiple solutions or no solutions at all. The study of equations and their properties is a fundamental topic in mathematics.

Here,

To solve the equation 8x + 6 = 14 - 4(2 - 2x), we can first simplify the right-hand side:

8x + 6 = 14 - 8 + 8x

Simplifying further, we get:

8x + 6 = 6 + 8x

Subtracting 8x from both sides, we get:

6 = 6

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Answer:

(B). F(X)=2x^2+2x-4

Step-by-step explanation:

-4 means it passes through -4 at the y axis

B and D have -4

graph passes thru x axis at -2 and 1

if you enter x = -2 or 1 in the formula

(B). F(X)=2x^2+2x-4

you get 0

it's not D because when you enter -2 or 1 for x

you don't get 0

you get 8 and -4

Answer: (B). F(x) = 2x² + 2x - 4

Step-by-step explanation:

      Let us think about the parent function F(x) = x² to pick our answer.

      Options A and C have only shifted 2 units down (showed by the "-2" at the end) and the function graphed is shifted four units down.

      Between options B and D, one is shifted 2 units to the right, and one is shifted 2 units to the left. We need the one shifted 2 units to the left. This is shown by the "+2x" in option B meaning it is our answer.

Answer:

182.88

Step-by-step explanation:

I hope this helped

Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.

One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.

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Answer:

A=l×w×h

Step-by-step explanation:

5×5×6×7

1050. or if we add 4 in the solution part 2400

Answer:

The slope is 1/4.

Step-by-step explanation:

M = Y2 - Y1

X2 - X1

M = 6 - 2

9 - (-7)

M = 4

16

M = 1

4

Answer:

120°

Step-by-step explanation:

From the question,

The expression for the dot product of two vector is given as

a.b = abcosθ................... Equation 1

make θ the subject of the equation

θ =cos⁻¹ (a.b/ab)......................... Equation 2

Where θ = angle between the vector.

Given: a.b = -27, a = 6, b = 9

Substitute these values into equation 2

θ = cos⁻¹[-27/(6×9)]

θ = cos⁻¹(-27/54)

θ = cos⁻¹(-0.5)

θ = 120°.

Hence the angle between the vector is 120°

Answer:

B

Step-by-step explanation:

Edge 2021

a trough has ends shaped like isosceles triangles, with width 2 m and height 5 m, and the trough is 10 m long. then the height of the water change when the water is 4 m deep is 1/8 m/min

The depth of the water is 4/5 of the depth of the trough, so the width of the surface will be 4/5 of the width of the trough:

 4/5 × 2 m = 8/5 m

Then the surface area of the water is ...

 Area = LW = (10 m)(8/5 m) = 16 m²

The rate of change of height multiplied by the area gives the rate of change of volume:

 2 m³/min = (16 m²)(h')

 h' = (2 m³/min)/(16m²) = 1/8 m/min

Hence , the height of the water change when the water is 4 m deep is 1/8 m/min

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Answer:

CA=6x-24 and BD = 2x+8

Find CE

CA=BD => 6x-24=2x+8 => x=8

CE=1/2(CA) or 1/2(BD) => 1/2(6x-24)=12

CE=12

CA=24

BD=24

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

The equation that can be used as statement 5 to prove that if segment ST is parallel to segment RQ, is:
"28:40 = x:(x+15) that is (Option D)

A mathematical statement is a sentence that is either true or false but is depicted in a mathematical format using mathematical operators.

Note that although mathematical statements are either true or false, they cannot be both.

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The mean and variance of the lengths are 590. 50  and 0. 075 respectively

Given that the lengths are;

590.1,  590. 2, 590. 3, 590. 4, 590. 5, 590. 6, 590. 7 , 590. 8, 590. 9

Mean = sum of terms/ number of terms

Mean = 590.1 +  590. 2 + 590. 3 + 590. 4 + 590. 5 + 590. 6 + 590. 7 + 590. 8 + 590. 9/ 9

Find the sum of the numerator

Mean = 5314. 5/ 9

Mean = 590. 500

Variance = sum of the distances from the mean/ total number - 1

Variance = (590. 1 - 590. 5)² + (590. 2 - 590. 5)² +  (590. 3 - 590. 5)² +  (590. 4 - 590. 5)² +  (590. 5 - 590. 5)² +  (590. 6 - 590. 5)² +  (590. 7 - 590. 5)² +  (590. 8 - 590. 5)² +  (590. 9 - 590. 5)² ÷ 9 - 1

Variance = 0. 16 + 0. 09 + 0. 04 + 0. 01 + 0 + 0. 01 + 0. 04 + 0. 09 + 0. 016 ÷8

Variance = 0. 6/ 8

Variance = 0. 075

Thus, the mean and variance of the lengths are 590. 50  and 0. 075 respectively

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Answer:

The perimeter is =36 (unit = 1 square)

If the unit is 5 squares then the perimeter is 7.2

Step-by-step explanation:

Just apply Pitagora's theorem

The exact x-coordinate of the point  is frac{1163}{291}6

The curve is given by {x = t² + 1, y = t² - t}.

Let's find dy/dx in terms of t as follows:

frac{dy}{dx} = frac{dy/dt}{dx/dt} = frac{(2t - 1)}{(2t)} = 1 - frac{1}{2t}

Therefore, when dy/dx = 27, we have:

1 - frac{1}{2t} = 27

Rightarrow 2t - 1 = frac{2}{27}

Rightarrow t = frac{29}{54}

The x-coordinate is given by x = t² + 1, therefore, we have:

x = left(frac{29}{54}right)^2 + 1

= frac{1163}{2916}

Hence, the exact x-coordinate of the point on the curve where the tangent line has slope 27 is frac{1163}{291}6

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Answer:

Band A:y=700

Band B:y=550+1.50x

Step-by-step explanation:

Band A: since they are a fixed rate no matter how many students the equation  would be y=700 . There is no need for x since there is no extra price for students

Band B: Since this band charges 550 plus 1.50 per student we will need a x in our equation

y=550+1.50x

The difference between the two equations is that in Band B we need to add the price per student.

The simplified form of the expression is

2m²p² ⁴√m (2 - p³)

Here, we have,

To simplify the radical expression, we can simplify the terms separately and then combine them.

at, first, we have,

1) Simplify the term 4 ⁴√m⁹p⁶  :

The index of the radical is 4, so we can rewrite the expression as:

4 ⁴√m⁹p⁶ = 4 ⁴√m⁸ * m * p⁴ * p²

Taking the fourth root of each factor inside the radical, we have:

Simplifying further:

4m²p² ⁴√m

2) Simplify the term 2m²p⁴√mp² :

The square root of mp² can be expressed as : √m * √p²

so, we get,

2m²p⁴√m p

Now we can combine the simplified terms:

4m²p² ⁴√m - 2m²p⁴√m p

Simplifying further, we can factor out the common terms:

2m²p² ⁴√m (2 - p³)

Therefore, the simplified form of the expression is

2m²p² ⁴√m (2 - p³).

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Answer:

C = 2 \pi r

Step-by-step explanation:

The statement is true. Simple random sampling is a method of selecting a sample from a larger population in which every member of the population has an equal chance of being selected for the sample.

This method is associated with a high degree of generalizability because it ensures that the sample is representative of the population. When a sample is representative of the population, the findings from the sample can be generalized to the entire population with a high level of confidence.

Simple random sampling is considered to be one of the most reliable and unbiased methods of sampling, making it a popular choice in many research studies.

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Answer:

B) \(\$8395.80\)

Step-by-step explanation:

\(A=P(1+rt)\\A=7996(1+0.06\cdot\frac{10}{12})\\A=7996(1+0.05)\\A=7996(1.05)\\A=\$8395.80\)

This is all assuming that r=6% is an annual rate, making t=10/12 years

6 is not a significantly high number of girls in 8 births. The answer is B. No, since the appropriate probability is greater than 0.05, it is not a significantly high number.

a. To find the probability of getting exactly 6 girls in 8 births, we need to refer to the probability distribution table. From the table, we can see that the probability of getting exactly 6 girls is 0.21875.
b. To find the probability of getting 6 or more girls in 8 births, we need to sum up the probabilities of getting 6, 7, and 8 girls. From the table, we can see that the probabilities for getting 6, 7, and 8 girls are 0.21875, 0.10938, and 0.02734 respectively. Adding these probabilities, we get 0.35547.

c. The probability that is relevant for determining whether 6 is a significantly high number of girls in 8 births is the result from part b, since it represents the probability of getting the given or more extreme result.
d. To determine if 6 is a significantly high number of girls in 8 births, we compare the appropriate probability to the threshold of 0.05. In this case, the appropriate probability is 0.35547, which is greater than 0.05. Therefore, 6 is not a significantly high number of girls in 8 births. The answer is B. No, since the appropriate probability is greater than 0.05, it is not a significantly high number.

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Answer:

-19 and 3

Step-by-step explanation:

-19 x 3 = -57

-19 + 3 = -16

Answer:

Step-by-step explanation: To find the answer to "What two numbers have a product of 57 and a sum of 16?" we first state what we know. We are looking for x and y and we know that x • y = 57 and x + y = 16.

Before we keep going, it is important to know that x • y is the same as y • x and x + y is the same as y + x. The two variables are interchangeable. Which This means that when we create one equation to solve the problem, we will have two answers.

To solve the problem, we take x + y = 16 and solve it for y to get y = 16 - x. Then, we replace y in x • y = 57 with 16 - x to get this:

x • (16 - x) = 57

Like we said above, the x and y are interchangeable, therefore the x in the equation above could also be y. The bottom line is that when we solved the equation we got two answers which are the two numbers that have a product of 57 and a sum of 16. The numbers are:

5.35425

10.64575

That's it! The two numbers that have a product of 57 and a sum of 16 are 5.35425 and 10.64575 as proven below:

5.35425 • 10.64575 = 57

5.35425 + 10.64575 = 16

HOPE THAT HELP YOU PLS MARK ME BRANLITS PLSSSS

Answer:

y=3x-10

Step-by-step explanation:

Slope: (y2-y1)/(x2-x1)

(2-8)/(4-6)

slope= -6/-2 = 3

Point: (6,8)

Slope-intercept: y-y1=m(x-x1)

y-8=3(x-6)

y-8=3x-18

y=3x-10

Diogo's optimal bundle is q1 ≈ 12.77 units of chocolate candy and q2 ≈ 74.46 units of slices of pie.

To find Diogo's optimal bundle, we need to maximize his utility function subject to his budget constraint. The budget constraint is given by:

p1q1 + p2q2 = Y

Substituting the given values:

2q1 + 1q2 = 100

We can rewrite this as:

q2 = (100 - 2q1) / 1

Now, let's maximize Diogo's utility function:

U(q1, q2) = q1^0.2 * q2^0.8

Substituting the expression for q2:

U(q1) = q1^0.2 * [(100 - 2q1) / 1]^0.8

To find the optimal bundle, we need to find the value of q1 that maximizes U(q1). We can do this by taking the derivative of U(q1) with respect to q1 and setting it equal to zero:

dU(q1) / dq1 = 0.2q1^(-0.8) * [(100 - 2q1) / 1]^0.8 - 0.8q1^0.2 * [(100 - 2q1) / 1]^(-0.2) * (-2 / 1) = 0

Simplifying the equation:

0.2[(100 - 2q1) / q1]^0.8 = 0.8

[(100 - 2q1) / q1]^0.8 = 4

Taking both sides to the power of 1/0.8:

(100 - 2q1) / q1 = 4^(1/0.8)

Solving for q1:

100 - 2q1 = 4^(1/0.8) * q1

100 = (4^(1/0.8) + 2) * q1

q1 = 100 / (4^(1/0.8) + 2)

Calculating the value of q1:

q1 ≈ 12.77

Now we can substitute this value back into the budget constraint to find q2:

2q1 + q2 = 100

2(12.77) + q2 = 100

25.54 + q2 = 100

q2 = 100 - 25.54

q2 ≈ 74.46

Therefore, Diogo's optimal bundle is q1 ≈ 12.77 units of chocolate candy and q2 ≈ 74.46 units of slices of pie.

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