Mathswatch Question:


Liam is a tyre fitter.


It takes him 124 minutes to fit 4 tyres to a lorry.


a) How long would it take him to fit 6 tyres to a lorry. ?


b) If he works for 93 minutes, how many tyres can he fit?


Working out for question a:


a) 124×6÷4=186(minutes)


Correct answer for question a is 186.


Correct answer for question b is 3

Answer:

2 8c+3

Step-by-step explanation:

Answer:

8c+3

Step-by-step explanation:

for #2

The value of cos(8) is 0.992.

Given the equation, tan e = 35/2 and 8 is an angle in quadrant I. To find the value of cos(8), we can use the Pythagorean identity of sin²θ + cos²θ = 1.

1. Draw a right triangle in quadrant I with an angle of 8 and a hypotenuse of 150 (which is obtained by dividing the opposite and adjacent sides of the tan(e) equation by sin(e) to obtain the hypotenuse).

2. To find the adjacent side (which is equal to cos(8)), use the Pythagorean identity:

cos²8 + sin²8 = 1cos²8 + (35/150)² = 1cos²8 + 0.025 = 11.0091 - 0.025 = cos²8cos8 = ±√(0.9841)cos8 = ±0.992 (rounded to 3 decimal places)

But since angle 8 is in quadrant I, where cos is positive, the value of cos(8) is:

cos(8) = 0.992 (rounded to 3 decimal places)

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Answer:

 C. Pages Read in an Hour: 10, 14, 16, 16, 18, 19, 21, 25

Step-by-step explanation: Got it on my study island question.

Regression equations are used to represent the relationship between the x and y variables.

To determine the quadratic regression equation, we make use of a graphic calculator

Using a graphing calculator, we have the quadratic regression equation to be \(\mathbf{y =-6.407 X^2 +216.721 X -975.561}\)

When the selling price is $14.25, it means that:

\(\mathbf{x = 14.25}\)

So, we have:

\(\mathbf{y =-6.407 \times 14.25^2 +216.721 \times 14.25 -975.561}\)

Evaluate the exponents

\(\mathbf{y =-6.407 \times 203.0625+216.721 \times 14.25 -975.561}\)

Evaluate the products

\(\mathbf{y =-1301.0214375+3088.27425 -975.561}\)

Evaluate like terms

\(\mathbf{y =811.6918125}\)

Approximate to the nearest dollar

\(\mathbf{y =812}\)

Hence, the profit for a selling price of $14.25 is $812

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Answer (assuming that the equation can be written in point-slope form):

\(y-8 = -5(x+\frac{1}{2} )\)

Step-by-step explanation:

Use the point-slope formula, \(y-y_1 = m (x-x_1)\) , to write the equation of the line in point-slope form. Substitute values for the \(m\), \(x_1\), and \(y_1\) in the formula.

Since \(m\) represents the slope, substitute -5 in its place. Since \(x_1\) and \(y_1\) represent the x and y values of one point the line intersects, substitute the x and y values of (-0.5, 8) into the formula as well. Remember that we can convert -0.5 to a fraction: \(-\frac{1}{2}\). So, substitute \(-\frac{1}{2}\) for \(x_1\) and 8 for \(y_1\). This gives the following answer and equation:

\(y-8 = -5(x+\frac{1}{2} )\)    

The internal energy of the system is given by U = -2ε/kT exp(-ε/kT) + (1/kT) exp(-2ε/kT), where ε is the energy difference between the first and second energy levels, T is the temperature, and k is Boltzmann's constant.

The internal energy U of the system can be calculated using the canonical ensemble partition function:

Z = Σi \(g_i\) exp(-\(E_i\)/kT)

where \(g_i\) is the degeneracy of the \(i_{th}\) energy level and Ei is the energy of the \(i_{th}\) level. The internal energy is then given by:

U = - (∂lnZ/∂β)|V,N

where β = 1/(kT) is the inverse temperature.

Substituting the energy levels and degeneracies, we have:

Z = 1 + 2 exp(-ε/kT) + exp(-2ε/kT)

Taking the natural logarithm of both sides, we get:

lnZ = ln[1 + 2 exp(-ε/kT) + exp(-2ε/kT)]

Using the Taylor series expansion of ln(1+x), we can approximate lnZ as:

lnZ ≈ 2 exp(-ε/kT) - (1/2) exp(-2ε/kT)

Differentiating lnZ with respect to β, we obtain:

(∂lnZ/∂β)|V,N = -kT^(-2) (∂lnZ/∂T)|V,N

= kT^(-2) [2ε/kT^2 exp(-ε/kT) - ε/kT^2 exp(-2ε/kT)]

Substituting this expression into the formula for the internal energy, we get:

U = -kT^(-2) [2ε/kT^2 exp(-ε/kT) - ε/kT^2 exp(-2ε/kT)]

Simplifying, we get:

U = -2ε/kT exp(-ε/kT) + (1/kT) exp(-2ε/kT)

Therefore, the internal energy of the system is given by U = -2ε/kT exp(-ε/kT) + (1/kT) exp(-2ε/kT), where ε is the energy difference between the first and second energy levels, T is the temperature, and k is Boltzmann's constant.

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Step-by-step explanation:

ANGLE ,x=60

B=C(isoscles)

A=B.As sides are equal.

To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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Answer:

C

Step-by-step explanation:

Answer:

b = y - mx

Step-by-step explanation:

Given

y = mx + b ( subtract mx from both sides )

y - mx = b

Answer:

No Clarice could not verify her answer since she was supposed to get 7 1/2 as a result in her multiplication. Clarice did the multiplication wrong since she should've multiplied 5 by 1 giving her 5 then 5 by 1/2 giving her 2 1/2 and add them giving her 7 1/2.

Step-by-step explanation:

(7 1/2)/1 1/2=5

5*1 1/2=5 1/2

Answer:

No. Clarice’s answer does not equal the dividend. She did not change the mixed number into an improper fraction before multiplying.

This is the sample response for Edge 2020 -2021

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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The linear function that describe the situation is; 3730 = 900 + 370x.

If a variable is taking its values independently of any visible direct cause, then that variable is called independent variable.

The variables who take their values based on some other variables' values are called dependent variables.

Given; The cost of leasing a car is $900 for the down payment and processing fee plus $370 per month.

We need to find For how many months can you lease the car with $3730.

Let x be the months.

The equation for the linear function;

3730 = 900 + 370x

Therefore, the linear function that describe the situation is; 3730 = 900 + 370x.

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Answer:

they are reciprecants of eachother

The common endpoint of the rays, indicated by M, is called the Vertex.

Step-by-step explanation:

Step-by-step explanation:

always remember (for your life) : the sum of all angles in a triangle is always 180°.

and the sum of all angles around a single point on one side of a line is also always 180°.

so,

180 = 65 + 51 + angle PSR

angle PSR = 180 - 65 - 51 = 64°

angle PST is the supplementary angle to angle PSR (that means together they have 180°), because of the principle of all angles around a single point (S) on one side of a line (TSR).

so,

180 = angle PST + angle PSR = angle PST + 64

angle PST = 180 - 64 = 116°

Answer:114

Step-by-step explanation:

The area of the shape is 260 ft².

The formula for the area of a triangle standing on a rectangular base is:

A = ¹/₂bh  + LW

where;

The area of the shape is calculated as follows;

A = ¹/₂ x 20 ft  x 10 ft  +   8ft x 20ft

A = 260 ft²

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Answer:

1

Step-by-step explanation:

GCF of 343 and 477 is 1, because no number can multiply and get both of them.

The greatest common factor of 343 and 477 is 1, indicating that the two numbers have no common factors other than 1.

To find the greatest common factor (GCF) of 343 and 477, we can determine the common factors of both numbers and identify the largest one.

First, let's list the factors of each number:

The factors of 343 are: 1, 7, 49, 343.

The factors of 477 are: 1, 3, 9, 53, 159, 477.

Now, we identify the common factors from both lists: 1.

Therefore, the greatest common factor of 343 and 477 is 1.

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The width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

Let's represent the width of the pool as x. Then, the length of the pool would be x + 6.

The total area of the pool and walk is given by:

Total area = (length + 2(4)) × (width + 2(4))

Total area = (x + 6 + 8) × (x + 4)

Total area = (x + 14) × (x + 4)

The area of the pool itself is given by:

Pool area = length × width

Pool area = x(x + 6)

Pool area = x² + 6x

We're told that the total area is 272 more than the area of the pool:

Total area = Pool area + 272

(x + 14) × (x + 4) = x² + 6x + 272

Expanding the left side of the equation:

x² + 18x + 56 = x² + 6x + 272

Simplifying the equation:

12x = 216

Solving for x:

x = 18

So the width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

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Full Question: A rectangular pool is surrounded by a walk 4 feet wide. The pool is six feet longer than its wide. If the total area is 272 ft² more than the area of the pool,what are the dimension of the pool?

(a) The gradient of f is Vf(x, y) = 4y^3j.

(b) The gradient at point P(1, 2) is Vf(1, 2) = 32j.

(c) The rate of change of f at point P(1, 2) in the direction of the vector u is D_u f(1, 2) = 160 / √29.

To find the gradient of the function f(x, y) = y^4, we need to compute its partial derivatives with respect to x and y.

Gradient of f:

Vf(x, y) = (∂f/∂x) i + (∂f/∂y) j

Taking the partial derivatives:

∂f/∂x = 0 (since there is no x term in the function)

∂f/∂y = 4y^3

Therefore, the gradient of f is:

Vf(x, y) = 0 i + 4y^3 j

          = 4y^3 j

Evaluating the gradient at point P(1, 2):

Vf(1, 2) = 4(2)^3 j

         = 4(8) j

         = 32 j

So, Vf(1, 2) = 32 j.

To find the rate of change of f at point P in the direction of the vector u, we need to take the dot product of the gradient with the unit vector in the direction of u.

Given u = (2i + 5j) / √(2^2 + 5^2),

the unit vector in the direction of u is:

u = (2i + 5j) / √29

The rate of change of f at P in the direction of u is:

D_u f(1, 2) = Vf(1, 2) ·

Taking the dot product:

D_u f(1, 2) = (32 j) · ((2i + 5j) / √29)

           = (0i + 32j) · (2i + 5j) / √29

           = 0(2) + 32(5) / √29

           = 160 / √29

So, the rate of change of f at P in the direction of the vector u is 160 / √29.

***V = nabla.

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Answer:63

Step-by-step explanation:

A. The extent to which the same results would be obtained if another random sample were drawn from the same population

Precision is a measure of how accurately a set of data can represent a population. It is typically defined as the extent to which the same results would be obtained if another random sample were drawn from the same population.

Precision is a measure of the reliability of a data set and its ability to accurately represent a population. In order to determine precision, statisticians take a sample from a population and compare its results to the results of another random sample from the same population. If the two samples yield similar results, the data set is considered to be precise. If the results of the two samples vary greatly, the data set is considered to be imprecise.

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a) P(x ≥ 2) = 60%

b) P(x > 2) = 21%

c) P(at least one alcoholic drink) = 92%

d) Mean = 1.76 drinks

e) Standard Deviation ≈ 0.692 drinks

To solve this problem, let's analyze the given data:

a) P(x ≥ 2): This represents the probability that a randomly selected customer orders two or more alcoholic drinks.

From the given data, we know that:

39% of customers order 2 alcoholic drinks.

18% of customers order 3 alcoholic drinks.

3% of customers order 4 alcoholic drinks.

To find the probability of ordering two or more alcoholic drinks, we sum up the probabilities of ordering 2, 3, and 4 alcoholic drinks:

P(x ≥ 2) = P(x = 2) + P(x = 3) + P(x = 4)

= 39% + 18% + 3%

= 60%

Therefore, the probability that a randomly selected customer orders two or more alcoholic drinks is 60%.

b) P(x > 2): This represents the probability that a randomly selected customer orders more than two alcoholic drinks.

To find this probability, we sum up the probabilities of ordering 3 and 4 alcoholic drinks:

P(x > 2) = P(x = 3) + P(x = 4)

= 18% + 3%

= 21%

Therefore, the probability that a randomly selected customer orders more than two alcoholic drinks is 21%.

c) To find the probability that a randomly selected customer orders at least one alcoholic drink, we need to find the complement of the probability of ordering zero alcoholic drinks:

P(at least one alcoholic drink) = 1 - P(x = 0)

= 1 - 8%

= 92%

Therefore, the probability that a randomly selected customer orders at least one alcoholic drink is 92%.

d) The mean (or average) number of alcoholic drinks ordered by customers at this bar can be found by multiplying the number of drinks ordered by their respective probabilities and summing them up:

Mean = (0 × 8%) + (1 × 32%) + (2 × 39%) + (3 × 18%) + (4 × 3%)

= 0 + 0.32 + 0.78 + 0.54 + 0.12

= 1.76

Therefore, the mean number of alcoholic drinks ordered by customers at this bar is 1.76.

e) The standard deviation for the number of alcoholic drinks ordered can be calculated using the following formula:

Standard Deviation = sqrt([Σ(x - μ)² × P(x)], where Σ denotes summation, x represents the number of drinks, μ is the mean, and P(x) is the probability of x.

Using the above formula, we can calculate the standard deviation as follows:

Standard Deviation = sqrt([(0 - 1.76)² × 0.08] + [(1 - 1.76)² × 0.32] + [(2 - 1.76)² × 0.39] + [(3 - 1.76)² × 0.18] + [(4 - 1.76)² × 0.03])

= sqrt([3.8912 × 0.08] + [0.1312 × 0.32] + [0.016 × 0.39] + [0.2744 × 0.18] + [2.3072 × 0.03])

= sqrt(0.312896 + 0.0420224 + 0.00624 + 0.049392 + 0.069216)

= sqrt(0.4797664)

≈ 0.692

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Answer:

not positive but i would say 48

Step-by-step explanation:

Answer:

here is your correct answer dude

Answer:

I Think B.

Step-by-step explanation:

Im Not But CARRY ON LEARNING

Answer:

1. Percent

2. Rate

3. Proportion

4. Ratio

5. 29% and/or 7.25/25

6. 7/20 and/or 0.35

7. 0.4 and/or 40%

8. 1,461 days

9. 6.3 miles

Answer:

152 miles

Step-by-step explanation:

Ratios:

\(\frac{40}{2} =\frac{x}{7.6} \\\\2x=304\\x=152\)

The probability that the auto dealer will need to order more new transmissions is the sum of the probabilities of having 3, 4, 5, 6, or 7 defective transmissions among the seven trucks sold.

To calculate the probability that the auto dealer will need to order more new transmissions, we can use the binomial probability formula.

Given that the probability of a defective transmission is \(20\%\) (or 0.2), and the dealer has sold seven trucks with two new transmissions in stock, we want to find the probability of having more than two defective transmissions among the seven sold.

Let's denote X as the number of defective transmissions among the seven sold. We need to calculate \(\(P(X > 2)\).\)

Using the binomial probability formula, we can calculate the probability of X using the following formula:

\(\[P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k}\]\)

Where:

\(- \(\binom{n}{k}\)\) is the number of combinations of choosing \(\(k\)\) items from a set of n items.

- p is the probability of success (defective transmission).

- n is the total number of trials (number of trucks sold).

To calculate \(\(P(X > 2)\),\) we need to sum the probabilities of having 3, 4, 5, 6, or 7 defective transmissions.

\(\[P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)\]\)

Now let's calculate each term and sum them:

\(\[P(X = 3) = \binom{7}{3} \cdot (0.2)^3 \cdot (0.8)^{7 - 3}\]\[P(X = 4) = \binom{7}{4} \cdot (0.2)^4 \cdot (0.8)^{7 - 4}\]\[P(X = 5) = \binom{7}{5} \cdot (0.2)^5 \cdot (0.8)^{7 - 5}\]\[P(X = 6) = \binom{7}{6} \cdot (0.2)^6 \cdot (0.8)^{7 - 6}\]\[P(X = 7) = \binom{7}{7} \cdot (0.2)^7 \cdot (0.8)^{7 - 7}\]\)

Finally, we sum these probabilities to get the desired result:

\(\[P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)\]\)

Calculating these probabilities will yield the probability that the auto dealer will need to order more new transmissions.

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