How do I Factor 42p⁴+9p³q²-18p²q²​

Answer: 2

Step-by-step explanation:

Answer:

\(y - 3 = - 4(x + 2)\)

Answer:

Step-by-step explanation:

Could you show two points need to be calculated? A and D are the same in this case

Therefore , the solution of the given problem of fraction comes out to be paint the entire area10/3 cans of paint will be required.

To symbolise a whole, any number of equal parts or fractions may be used. The amount of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. In mathematics, the ratio to denominator ratio is used to symbolise numbers.

Here,

To solve the issue, we can commence by using a proportion. Assume that x cans are required to paint the entire area.

We can establish the proportion if 1 1/3 cans, which are equivalent to 4/3 cans, can paint 2/5 of the space.

x cans / 1 full room Equals 4/3 cans / 2/5 room.

We can cross-multiply and reduce to find x's value:

1 full room times 4/3 cans equals 2/5 room times x cans.

4/3 = 2/5 x

x = (4/3) / (2/5)

x = (4/3) * (5/2)

x = 10/3

To paint the entire area, 10/3 cans of paint will be required. This is the same as 3.33 cans, or 3 1/3 cans (rounded to two decimal places).

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The probability that you will get at least one "6" when you roll a fair six-sided die, with faces numbered "1" through "6," ten times is approximately 83.8%.

The probability that you will get at least one "6" when you roll a fair six-sided die, with faces numbered "1" through "6," ten times is given as  97.2% (rounded to the nearest tenth of a percentage).Explanation:To find the probability of getting at least one 6 in ten rolls, we can use the complement rule. We can calculate the probability of rolling a non-6 on each roll (which is 5/6) and then take the complement of the probability that none of the rolls are 6. The probability of getting at least one 6 is then:

1 - (5/6)⁽¹⁰⁾= 1 - 0.1615 (rounded to four decimal places)= 0.8385 (rounded to four decimal places)≈ 83.85% (rounded to the nearest hundredth of a percentage)

Option B is correct answer.

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Answer:

(Altitude)^2+(Base)^2=(Hypotenuse)^2

Answer:

43 p

Step-by-step explanation:

total cost = 10 - 4.84 = 10.00 - 4.84 = £5.16

b + t = 5.16

t = 11b

b + 11b = 5.16

12b = 5.16

12 / 12 b = 5.16/12

b = £0.43

Answer:

94 pence

Step-by-step explanation:

128=20

divide both by 128, so

1 = 0.15625

now times both by 6

6 = 0.9375

£0.94 (rounded)

Answer:

50

Step-by-step explanation:50 is the right answer!!

Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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Answer:

72.73% is the answer.

Hope this helps!

(i) To calculate the probability that the time between buses will be at least 20 minutes,

we need to find the area under the exponential distribution curve for values greater than or equal to 20.

Using the formula for the exponential distribution, we have: P(X ≥ 20) = 1 - P(X < 20) = 1 - e^(-20/20) = 1 - e^(-1) ≈ 0.632, Therefore, the probability that the time between buses will be at least 20 minutes is approximately 0.632.

(ii) To calculate the probability that the time between buses will exceed 20 minutes but will be less than 30 minutes,

we need to find the area under the exponential distribution curve between 20 and 30. Using the formula for the exponential distribution, we have:

P(20 < X < 30) = ∫[from 20 to 30] λe^(-λx) dx
               = [-e^(-λx)] from 20 to 30
               = [-e^(-30/20) + e^(-20/20)]
               ≈ 0.117

Here, T represents the inter-arrival time, λ is the rate parameter (1/mean), and t is the time we want to calculate the probability for. In this case, λ = 1/20 and t = 20 minutes.

P(T >= 20) = e^(-1/20 * 20) = e^(-1) ≈ 0.368

We want to find P(20 < T < 30), which can be calculated as P(T <= 30) - P(T <= 20).

P(T <= 30) = 1 - e^(-1/20 * 30) ≈ 0.776
P(T <= 20) = 1 - e^(-1/20 * 20) ≈ 0.632

P(20 < T < 30) = 0.776 - 0.632 ≈ 0.144

So, the probability that the time between buses will exceed 20 minutes but be less than 30 minutes is approximately 0.144 or 14.4%.

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Answer: The slope is 5

Step-by-step explanation:

The slope of an equation in slope intercept form is always the coefficient of the x variable, or the number that comes before x. And the coefficient of x is 5.

The correct answer is D) m = -√3/2. To find the slope of the given curve at the point (x, y), we need to take the derivative of the curve with respect to x and evaluate it at the given point.

The equation of the curve is x = cos(y), and we want to find the slope at the point (x, y) = (-π/3). Taking the derivative of x = cos(y) with respect to x, we get: dx/dy = -sin(y) * dy/dx. To find the slope at the point (-π/3), we substitute y = -π/3 into the derivative expression: dx/dy = -sin(-π/3) * dy/dx = -(-√3/2) * dy/dx = √3/2 * dy/dx.

Therefore, the slope of the curve at the point (-π/3) is √3/2. Hence, the correct answer is D) m = -√3/2.

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Answer:

Hold on let me seee!!!!!!!

Step-by-step explanation:   6  22  22  51

one orange box is 10  the other box looks like 15

the scale factor is 15/10  or 1.5

the smaller triangle blue box is a 4

multiply 4 by the scale factor  1.5

  4 × 1.5  = 6

To implement the given function using one 8x1 multiplexer, we first need to identify the inputs and outputs. The inputs are A, B, C, and D, and the output is F.

We can use the 8x1 multiplexer as a logic function generator by using the select inputs to choose which input is passed to the output.

To implement the given function, we can use the following steps:

1. Connect A and D to the select inputs of the multiplexer.
2. Connect B and C to the remaining two inputs of the multiplexer.
3. Set the outputs of the multiplexer as follows:
- Connect output 0 to VCC.
- Connect output 1 to B.
- Connect output 2 to A.
- Connect output 3 to BC'.
- Connect output 4 to AB.
- Connect output 5 to AC.
- Connect output 6 to B'CD.
- Connect output 7 to ABCD'.

4. Connect the multiplexer outputs to a logical OR gate to generate the final output F.

By setting the select inputs appropriately, the multiplexer will output the required terms of the function, which are then combined using the OR gate to produce the final output F.
Hi! To implement the given function F(A, B, C, D) = A'C'B + AB'C' + B'C'D + ABCD' using one 8x1 multiplexer, follow these steps:

1. Identify the input and control lines: Since it is an 8x1 multiplexer, we need three control lines. Choose A, B, and C as the control lines. The input lines will be connected based on the function.

2. Map the function to the input lines: For an 8x1 multiplexer, the inputs are connected as follows:
 - I0 = A'B'C'D'
 - I1 = A'B'C'D
 - I2 = A'B'CD'
 - I3 = A'B'CD
 - I4 = AB'C'D'
 - I5 = AB'C'D
 - I6 = ABCD'
 - I7 = ABCD

3. Connect the corresponding function terms to the input lines:
 - I0 = 0 (A'B'C'D' does not appear in the function)
 - I1 = A'C'B (A'B'C'D matches the first term)
 - I2 = 0 (A'B'CD' does not appear in the function)
 - I3 = B'C'D (A'B'CD matches the third term)
 - I4 = AB'C' (AB'C'D' matches the second term)
 - I5 = 0 (AB'C'D does not appear in the function)
 - I6 = ABCD' (ABCD' matches the fourth term)
 - I7 = 0 (ABCD does not appear in the function)

By connecting the input lines according to the function terms and using A, B, and C as the control lines, you can implement the given function F(A, B, C, D) using one 8x1 multiplexer.

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Let the price of the hot dogs be x and drink be y.

It is given that you can get 6 hotdogsand 2 drinks for $18.00 so it follows:

Simplify to get:

It is also given that you can get 7 hotdogs and 8 drinks for $46.50 so it follows:

Multiply (i) by 8 to get:

Subtract (ii) from (iii) to get:

Substitute x=1.5 in (i) to get:

Hence the cost are:

1.5$ per hotdog.

4.5$ per drink.

The general solution of the differential equation y′′(t)+k²y(t)=0 is given by y(t) = c1sin(kt) + c2cos(kt) for arbitrary k>0.

Consider the differential equation y′′(t)+k²y(t)=0,

where k is a positive real number.

We need to verify the given conditions:(a) Verify by substitution that when k=1, the general solution of the equation is

y(t)=C1sint+C2cost

General solution:

Let's consider the differential equation y′′(t)+k²y(t)=0,

where k = 1. So, y′′(t)+y(t) = 0

We need to find the general solution of the above differential equation.

So, let us assume the solution to be of the form:

y(t) = Ae^{rt}

Here, A and r are constants.

y'(t) = rAe^{rt} and y''(t) = r^2Ae^{rt}

Putting the values of y(t), y'(t) and y''(t) in the differential equation:

y′′(t)+y(t) = r^2Ae^{rt}+ Ae^{rt}= 0⇒ (r^2+1)Ae^{rt}= 0⇒ (r^2+1) = 0⇒ r = ±i

The general solution of the given differential equation will be:

y(t) = c1sin(t) + c2cos(t)

where c1 and c2 are arbitrary constants.

To verify the given solution, let's differentiate y(t)twice and substitute in the given differential equation. The result is obtained as:

y′′(t)+y(t) = (-c1sin(t) + c2cos(t))+ c1sin(t) + c2cos(t) = 0

Verify by substitution that when k=2, the general solution of the equation is y(t)= C1 sin2t+C2 cos2t

General solution:

Let's consider the differential equation y′′(t)+k²y(t)=0, where k = 2.So, y′′(t)+4y(t) = 0

We need to find the general solution of the above differential equation.

So, let us assume the solution to be of the form:

y(t) = Ae^{rt}

Here, A and r are constants. y'(t) = rAe^{rt} and y''(t) = r^2Ae^{rt}

Putting the values of y(t), y'(t) and y''(t) in the differential equation:

y′′(t)+4y(t) = r^2Ae^{rt}+ 4Ae^{rt}= 0⇒ (r^2+4)Ae^{rt}= 0⇒ (r^2+4) = 0⇒ r = ±2i

The general solution of the given differential equation will be:

y(t) = c1sin(2t) + c2cos(2t) where c1 and c2 are arbitrary constants.

To verify the given solution, let's differentiate y(t) twice and substitute in the given differential equation.

The result is obtained as: y′′(t)+4y(t) = -4c1sin(2t) + 4c2cos(2t)+ 4c1sin(2t) + 4c2cos(2t) = 0(c)

Give the general solution of the equation for arbitrary k>0 and verify your conjecture.

General solution:

Let's consider the differential equation y′′(t)+k²y(t)=0.

We need to find the general solution of the above differential equation.

So, let us assume the solution to be of the form:y(t) = Ae^{rt}

Here, A and r are constants. y'(t) = rAe^{rt} and y''(t) = r^2Ae^{rt}

Putting the values of y(t), y'(t) and y''(t) in the differential equation:

y′′(t)+k²y(t) = r^2Ae^{rt}+ k²Ae^{rt}= 0⇒ (r^2+k²)Ae^{rt}= 0⇒ (r^2+k²) = 0⇒ r = ±ki

The general solution of the given differential equation will be:

y(t) = c1sin(kt) + c2cos(kt)

where c1 and c2 are arbitrary constants.

To verify the given solution, let's differentiate y(t) twice and substitute in the given differential equation. The result is obtained as:

y′′(t)+k²y(t) = -k²c1sin(kt) + k²c2cos(kt)+ k²c1sin(kt) + k²c2cos(kt) = 0

Thus, the general solution of the differential equation y′′(t)+k²y(t)=0 is given by y(t) = c1sin(kt) + c2cos(kt) for arbitrary k>0.

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Answer:

yes

Step-by-step explanation:

6/ 16 both divided by 2

Answer:

Yes

Step-by-step explanation:

3/8 and 6/16 are equivalent fractions

Step-by-step explanation:

Given parameters:

Amount of discount on goods= 20%

Original price of the good  = 700

Unknown:

Total amount he saved  = ?

Solution:

The total amount he saved will be the value of the discount charged on the original price.

 Amount of discount  = Percentage discount x original price of goods

 Amount of discount = \(\frac{20}{100}\) x 700

 Amount of discount  = 140

The amount saved is 140

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Since the directrix is y=-4, use the equation of a parabola that opens up or down.

where vertex is at (h,k) and focus is at (h,k+p)

The vertex is halfway between the directrix and focus. Find the y-coordinate of the vertex using the following

Find the distance from the focus to the vertex.

The distance from the focus to the vertex and from the vertex to the directrix is |p|. Subtract the y-coordinate of the vertex from the y-coordinate of the focus to find p.

Substitute in the known values for the variables into the equation

Simplify

in y=ax^2+bx+c form:

The type of error that could have been committed in this scenario is a Type I error.

In hypothesis testing, a Type I error occurs when the null hypothesis is rejected, even though it is true. It means that the researcher incorrectly concludes that there is a significant result or effect when there is actually no real effect present in the population. In this case, if the researcher rejects the null hypothesis that the dropout rate is 45% and concludes that it is different, she might be committing a Type I error if the null hypothesis is actually true.

A Type II error, on the other hand, occurs when the null hypothesis is not rejected, even though it is false. It means that the researcher fails to detect a significant result or effect when there is actually a real effect present in the population. The question states that the null hypothesis is rejected, so a Type II error is not relevant in this situation.

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In the Fixed deposit account, you will not be able to withdraw your money before time without a penalty fee from the bank and you will receive a fixed amount of interest on your original deposit.

In a Fixed-Term Deposit account, an account is opened with a bank wherein, the bank pays a guaranteed interest rate on the sums deposited for a fixed period or tenure.

This type of account allows you to earn higher returns (interest) on funds lying idle in your Savings Account.

Banks are free to charge their own penalty fee in the case of premature withdrawal of Fixed Deposit.

At the end of the stipulated period, the deposit will automatically be renewed unless you update your maturity instructions.

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The solution to the inequality expression is x > 11

Given the inequality expression

-12(-12+x)<12

Expand

144 - 12x < 12

Subtract 144 from both sides

-12x < 12 - 144

-12x < -132

Divide both sides by -12

-12x/-12 > -132/-12

x > 11

Hence the solution to the inequality expression is x > 11

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When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13  degrees

The distance between point a to point b = 5.3 feet

The length of the top side = 3 feet

Therefore, it will form a right triangle

Here we have to use trigonometric function

Here adjacent side and the hypotenuse of the triangle is given

The trigonometric function that suitable for the given conditions is

cos θ = Adjacent side / Hypotenuse

Substitute the values in the equation

cos θ = 3 / 5

θ = cos^-1(3 / 5)

θ = cos^-1(0.6)

θ = 53.13 degrees

Therefore, the value of θ is 53.13  degrees

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To determine the sequence of transformation matrices that map the shape on the left to the shape on the right, we need to analyze the changes in the shape's position, size, and orientation.

One possible sequence of transformation matrices is:

1. Translation matrix to move the shape to the right position.
2. Scaling matrix to adjust the size of the shape.
3. Rotation matrix to rotate the shape to the desired orientation.

The specific values of each transformation matrix will depend on the precise changes between the two shapes. For example, the translation matrix will have different values depending on how far the shape needs to be moved and in which direction. Similarly, the scaling matrix will depend on the degree of change in size required, while the rotation matrix will depend on the angle of rotation needed.

By applying these three transformation matrices in the correct order, we can map the shape on the left to the shape on the right.

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Answer:

6

Step-by-step explanation:

id say the answer is 6 or 9 :)