Mary and Julie are trying to raise $1000,mary raises $12 every 4 days, Julie raises $19 every six days.who reaches the goal first?explane

Answer:

5+5x-(3x-9)

5+5x-3x+9

2x+14

2(x+7)

Step-by-step explanation:

Answer:

2x+14

explanation:

5+5x-(3x)--9

5+5x-3x+9

add 5 and 9 to get 14

then subtract 3x from 5x to get 2x

2x+14

4/9 is not an Extraneous solution of the equation

Given Equation is √x+ 2√x=2.

On Squaring both the side of the equation, we get

(√x+ 2√x)² = 2²

Using the identity (a + b)² = a² + b² + 2ab on the left hand side of the equation

(√x)² + (2√x)² + 2(✓x)(2✓x) = 4

x + 4x + 4x = 4

9x = 4

x = 4/9

Check for Extraneous Solutions

Putting the value of x = 4/9 in the original equation √x+ 2√x=2, we get

✓(4/9) + 2(✓4/9) = 2

2/3 + 2(2/3) = 2

2/3 + 4/3 = 2

6/3 = 2

2 = 2

LHS = RHS

∴ 4/9 is not an Extraneous solution of the equation.

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when multiplying fractions , multiply across the numerator and denominator

you dont need common denominators

example

\(\frac{1}{2}*\frac{4}{5}=\frac{1*4}{2*5}\)

Hope this helps : -)

- Jeron

Answer:

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Step-by-step explanation:

A. Yes. She solved the problem correctly.

B. No. She multiplied the dividend by the divisor instead of finding the reciprocal.

C. No. She multiplied the denominators instead of finding a common denominator.

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Her workings

7 ÷ 2/ 5

=1/ 7 × 2/ 5

= 2/35

Dividend=7

Divisor=2/5

The correct working

7 ÷ 2/ 5

=7 × 5/2

=35/2

Answer:

D

Step-by-step explanation:

I got an 100% on the quiz I took with this question :)

Hope I could help good luck on passing!!

To determine if the vectors are normal, we need to check if they are orthogonal, i.e., if their dot product is zero.

Let's calculate the dot product of the given vectors:

(-2, 6) ⋅ (-9, -18) = (-2)(-9) + (6)(-18) = 18 + (-108) = -90

Since the dot product is not equal to zero (-90 ≠ 0), the vectors (-2, 6) and (-9, -18) are not orthogonal, and therefore, they are not normal vectors.

In general, for two vectors to be normal, their dot product must be zero, indicating that they are perpendicular or orthogonal to each other. However, in this case, the dot product is non-zero, indicating that the vectors are not orthogonal and, therefore, not normal.

Hence, the given vectors (-2, 6) and (-9, -18) are not normal.

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The kitchen is 30 meters long.

Because 16+16+30+30 = 92

It's more so trial and error if anything

The value of the triple integral ∭\(e^{x^{2} y^{2} }\) dv in cylindrical coordinates is ∞ * (16 - 4(\(r^{2}\))) * 2π.

To evaluate the triple integral ∭\(e^{x^{2} y^{2} }\)dv in cylindrical coordinates, we need to express the differential volume element dv in terms of cylindrical coordinates.

In cylindrical coordinates, we have:

x = r * cos(θ)

y = r * sin(θ)

z = z

The differential volume element in Cartesian coordinates (dx * dy * dz) can be expressed in cylindrical coordinates as:

dv = r * dr * d(θ) * dz

Now, let's convert the integral limits and the integrand into cylindrical coordinates.

The solid e is bounded by the circular paraboloid z = 16 - 4(\(x^{2}\) + \(y^{2}\)) and the xy-plane. In cylindrical coordinates, the equation of the paraboloid becomes:

z = 16 - 4(\(r^{2}\))

The integral limits for cylindrical coordinates are:

r: 0 to ∞

(θ): 0 to 2π

z: 0 to 16 - 4(\(r^{2}\))

The integrand is: \(e^{x^{2} y^{2} }\)

Substituting the expressions in cylindrical coordinates, the triple integral becomes:

∭\(e^{x^{2} y^{2} }\) dv = ∫∫∫r * \(e^{r^{2} }\)* \(cos^{2}\)(θ) * \(sin^{2}\)(θ)) * r * dr * d(θ) * dz

Simplifying:

∭\(e^{x^{2} y^{2} }\) dv = ∫∫∫\(e^{2}\) * \(e^{r^{2} }\) * \(cos^{2}\)(θ) * \(sin^{2}\)(θ)) * dr * d(θ) * dz

Now, let's evaluate the triple integral using the provided limits.

∫∫∫\(r^{2}\) * \(e^{r^{2} }\) * \(cos^{2}\)(θ) * \(sin^{2}\)(θ)) * dr * d(θ) * dz

The innermost integral with respect to r:

∫\(r^{2}\) * \(e^{r^{2} }\) *\(cos^{2}\)(θ) * \(sin^{2}\)(θ)) dr = (1/2) * \(e^{r^{2} }\) * \(cos^{2}\)(θ) *\(sin^{2}\)(θ))

Integrating the above expression with respect to r from 0 to ∞, we get:

(1/2) * ∞ - (1/2) * 0 = ∞

Now, the remaining integral is:

∫∫∫∞ * d(θ) * dz

Integrating the above expression with respect to theta from 0 to 2π and z from 0 to 16 - 4(\(r^{2}\)), we get:

∫(0 to 2π) ∫(0 to 16 - 4(\(r^{2}\))) ∞ * d(theta) * dz = ∞ * (16 - 4(\(r^{2}\))) * 2π

Therefore, the value of the triple integral ∭\(e^{x^{2} y^{2} }\) dv in cylindrical coordinates, where e is the solid bounded by the circular paraboloid z = 16 - 4(\(x^{2}\) + \(y^{2}\)) and the xy-plane, is ∞ * (16 - 4(\(r^{2}\))) * 2π.

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Answer:

2 distance

Step-by-step explanation:

you solve it and see it's easy know first try I will do it

The equation in point slope form will be -

y - 2 = 2(x - 3).

The general equation of a straight line is -

Other possible equations of lines are -

We have some equations of line as given in the question.

The point slope form is -

(y - y₁) = m(x - x₁)  

The points are -

(3, 2) and (5, 6)

So -

m = (6 - 2)/(5 - 3)

m = 4/2

m = 2

Equation will be -

y - 2 = 2(x - 3)

Therefore, the equation in point slope form will be -

y - 2 = 2(x - 3)

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The curl of vector field F is -i - j and the divergence of the vector field F is 0.

We have to follow the below steps:

Step 1: Find curl.

Step 2: Find divergence.

Curl :

Curl is the vector operator that defines the cross product of two vectors. It is applied to a vector field to generate another vector field.

Step 1:

Find the curl of vector field

Curl of the vector field F is defined as ,F = (P, Q, R)

Curl F = (Ry - Qz)i + (Pz - Rx)j + (Qx - Py)k

Where, Ry denotes the partial derivative of R with respect to y. Qz denotes the partial derivative of Q with respect to z, Pz denotes the partial derivative of P with respect to z .Rx denotes the partial derivative of R with respect to x, Qx denotes the partial derivative of Q with respect to x. Py denotes the partial derivative of P with respect to y.

Here,P = -x, Q = y, and R = -2.Then

Ry = 0, Qz = 0, Pz = 0, Rx = 0, Qx = 0, and Py = 0

Therefore, the curl of F = (Ry - Qz)i + (Pz - Rx)j + (Qx - Py)k= -i - j + 0k= -i - j

Then, the curl of vector field F is -i - j.

Divergence:

Divergence is a vector operator that operates on a vector field to produce a scalar value. It measures the magnitude of the outward flux of the vector field from an infinitesimal region around a particular point. Divergence is given by,

Divergence of the vector field F = (P, Q, R)div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z

Here, P = -x, Q = y, and R = -2.Then, ∂P/∂x = -1, ∂Q/∂y = 1, and ∂R/∂z = 0

Therefore, the divergence of the vector field F is

div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z= -1 + 1 + 0= 0

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(a) The probability that the entire system works is  0.3136

(b) The probability that the component a is not working is 0.3

Probability is a scale between 0 and 1 that represents the possibility of an event happening. An event with probability 1 is guaranteed to happen, while an event with probability 0 is impossible. The number of favorable outcomes divided by the total number of potential outcomes in the sample space yields the probability of an event A, commonly denoted as P(A). The sample space, for a fair six-sided die, is the set of all potential outcomes, such as 1, 2, 3, 4, 5, and 6. The probability of rolling a 4 is 1/6. Numerous disciplines employ probability to make predictions, deduce conclusions, and make judgments in the face of uncertainty.

(a) To find the probability that the entire system works, we need to find the product of the probabilities of the individual components working.

For the components connected in series, A and B, the probability that both work is equal to the product of their individual probabilities:

P(A and B) = P(A) * P(B) = 0.7 * 0.8 = 0.56

For the components connected in series-parallel, C, D, and E, the probability that all three work is equal to the product of their individual probabilities:

P(C and D and E) = P(C) * P(D) * P(E) = 0.8 * 0.8 * 0.9 = 0.576

To find the probability of the entire system working, we need to find the product of the probability of A and B working and the probability of C, D, and E working:

P(system works) = P(A and B) * P(C and D and E) = 0.56 * 0.576 = 0.3136

(b) Given that the system works, the probability that component A is not working would be equal to 1 minus the probability that component A is working:

P(A not working | system works) = 1 - P(A working | system works) = 1 - 0.7 = 0.3

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The complete question is

Answer:

y = (-4)

Step-by-step explanation:

Given equation is,

-2y = 4y + 24

By subtracting 4y from both the sides of the equation,

-2y - 4y = (4y + 24) - 4y

-6y = 24

By dividing the equation by (-6),

\(\frac{-6y}{-6}=\frac{24}{-6}\)

y = (-4)

c. a sample

A sample acts as a representative of the population. In statistics, a sample is a subset of individuals or observations taken from a larger group, known as the population.

By studying the characteristics of a sample, statisticians can make inferences or draw conclusions about the population as a whole.

The goal is to ensure that the sample is selected in a way that is representative of the population, so that the findings can be generalized.

By carefully selecting a sample, researchers aim to minimize bias and ensure that the characteristics of the sample closely reflect those of the population. This process is known as sampling. There are various sampling techniques, such as simple random sampling, stratified sampling, and cluster sampling, which help ensure that the sample is representative.

Once a representative sample is obtained, researchers can make statistical inferences about the population based on the characteristics and behaviors observed within the sample. This process is the foundation of inferential statistics.

In summary, a sample acts as a representative of the population by providing valuable information about the larger population, allowing researchers to draw meaningful inferences and make accurate generalizations.

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Answer:

Y=5

Step-by-step explanation:

Total distance travelled by lisa before falling off is 56.52 m

The circumference of a circle is the straight-line distance around it. In other words, if you open a circle and draw a straight line, the length of that line will be the perimeter. The perimeter is the total distance around the circle. Then find the perimeter using the formula C = 2πr.

Given,

Unicycle wheel diameter = 0.6 m

Unicycle wheel radius = 0.3 m

Number of revolutions before falling = 32

Circumference (C) = 2 x Pi x Radius

= 2 × π × r

= 2 × 3.14 × 0.3

= 1.884 m

Distance travelled by lisa = 30 × 1.884

= 56.52 m

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Electrical energy consumption is measured at kilowatt-hour (KWh). Thus the cost of energy consumed for the month is $28.512

What does kilowatt-hour mean?

The rate of consumption of energy is measured in kilowatt-hour.

In the given question

11 cent is paid per kilowatt-hour.

60 watts of light for 1 hour = 0.06 KWh

3 light bulbs of 60 Watts each for 1 hour = 3 x  0.06

                                          = 0.18 KWh

But,

30 days = 30 x 24 hours

                       = 1440 hours

The total energy consumed for the month = 1440 x 0.18

                                     =  259.20 KWH

The total cost for the month = 0.11 x 259.20

                                              = $28.512

Thus, the total cost for the month is $28.512

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The values of t for which g(x) ≤ 2 - t are:

-7 ≤ t ≤ 3

To solve for the values of t, we need to set up the inequality:

g(x) ≤ 2 - t

Substituting the given function g(x) in the inequality, we get:

3x^2 - 5 ≤ 2 - t

Adding 5 to both sides, we get:

3x^2 ≤ t + 7

Dividing both sides by 3, we get:

x^2 ≤ (t + 7)/3

Taking the square root of both sides, we get:

x ≤ ±√((t + 7)/3)

Therefore, the values of t for which g(x) ≤ 2 - t are:

-7 ≤ t ≤ 3

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Answer:

3/4 or 0.75

Step-by-step explanation:

M=y2-y1/x2-x1

Answer:

4/3

Step-by-step explanation:

Use the formula

x2-x1 over y2-y1

since it goes by (x,y) label the given points

(6,7) and (10,10)​

6 is your first x (x1)

7 is you first y (y1)

onto the next point...(10,10)

10 would be your second x (x2)

and your second y would also be 10 (y2)

Now plug into formula x2-x1 over y2-y1

10-6 over 10-7= 4/3

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

You could also use a online graphing calculator!

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

So, Tracy paid $12.50 for the encyclopedia and $45.50 for the math book.

In mathematics, an equation is a statement that shows the equality between two expressions. The expressions can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. An equation usually has an equals sign (=) between the two expressions. The equals sign indicates that the two expressions have the same value.

Here,

Let's use variables to represent the prices of the math book and the encyclopedia.

Let x be the price of the encyclopedia.

According to the problem, the price of the math book is 8 dollars more than 3 times the price of the encyclopedia. So, the price of the math book can be represented as:

=3x + 8

The total cost of the two books is given as 58 dollars. Therefore, we can write the equation:

x + (3x + 8) = 58

Simplifying and solving for x, we get:

4x + 8 = 58

4x = 50

x = 12.50

So, the price of the encyclopedia is $12.50.

To find the price of the math book, we can substitute x = 12.50 into the expression we derived earlier:

=3x + 8

= 3(12.50) + 8

= 37.50 + 8

= 45.50

Therefore, the price of the math book is $45.50.

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Answer:

1046.1 ft³

Step-by-step explanation:

V = πr²h

A:  V = π(14/2)²(18) = 2770.9 ft³

B:  V = π(18/2)²(15) = 3817.0 ft³

Empty portion of container B = B - A = 3817.0 - 2770.9 = 1046.1 ft³

The singular solution of the given equation, where p = ∂z/∂x and q = ∂z/∂y, can be found by solving the equation and expressing it in terms of p and q.

To find the singular solution, we follow these steps:

Step 1: Start with the given equation:

z = px + qy + p^2 + q^2 + pq

Step 2: Express the partial derivatives of z with respect to x and y:

∂z/∂x = p

∂z/∂y = q

Step 3: Substitute the partial derivatives back into the equation:

z = x(p) + y(q) + p^2 + q^2 + pq

Step 4: Simplify the equation:

z = px + qy + p^2 + q^2 + pq

Step 5: Rearrange the terms to obtain a quadratic expression in terms of p and q:

z = p^2 + q^2 + pq + px + qy

Step 6: Group the terms involving p and q:

z = (p^2 + pq + px) + (q^2 + qy)

Step 7: Factor out p and q:

z = p(p + q + x) + q(q + y)

Step 8: Set the expression in parentheses equal to zero to find the singular solution:

p + q + x = 0

q + y = 0

Step 9: Solve the system of equations for p, q, x, and y:

From the first equation, we have p = -q - x.

Substituting this into the second equation, we get -q - x + y = 0.

Rearranging, we have y = q + x.

Therefore, the singular solution is given by the equations p = -q - x and y = q + x.

In summary, the singular solution of the given equation is p = -q - x and y = q + x, where p = ∂z/∂x and q = ∂z/∂y.

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The zeros of the polynomial will be 2, -4 and -3

Given the polynomial function expressed as \( x^3 + 5x^2 - 2x - 24 \). IF x - 2 is a factor, this shows that 2 is a zero of the polynomial.

Find the quotient of \( x^3 + 5x^2 - 2x - 24 \) and \(x-2\) as shown:
\(\frac{x^3+5x^2-2x-24}{x-2} =x^2+7x+!2\)

Factorize the quotient as shown:

\(x^2+7x+12\\ =x^2+3x+4x+12\\ =x(x+3)+4(x+3)\\ =(x+4)(x+3)\\ \)

The zeros of the polynomial will be 2, -4 and -3

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Answer:

780

Step-by-step explanation:

Estimate: 200 x 4 = 800

Answer:

780

Step-by-step explanation:

The product of 195×4

=780.

The answer is 780.

Answer:

its 2 1/2 its width

Step-by-step explanation:

Answer

Step-by-step explanation:

rise over run so it'd be 3/3 positive or y= 3x-3