Ann is 4 years older than julie. 4 years ago ann was twice as old as julie find their present ages

The remainder would be 12 as per the remainder theorem if the function P is defined by P(x) = x³ +7x² - 26x - 72.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

Let   P(x) = x³ +7x² - 26x - 72  ...(i)

Divisor = (x+9)

Apply remainder theorem,

x + 9 = 0

x = -9

Substitute the value of x = -9 in equation (i),

⇒ P(-9) = (-9)³ +7(-9)² - 26(-9) - 72

⇒ P(-9) = (-729) +7(81) - 234 - 72

⇒ P(-9) = -729 + 567 - 234 - 72

⇒ P(-9) = -468

Therefore, the remainder would be -468.

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Option a) The similar triangles are ⇒ ΔADE ≅ ΔABC

Option b) ∠ADE = ∠ABC

According to the figure given in the question,

We can observe that there are two right-angled triangles present and we have to derive the similarities between them

Let one triangle be = ΔADE

Another triangle be = ΔABC

Let us consider the angle arc at point A,

We can conclude that ⇒ ∠BAC = ∠DAE ( according to the property of similar angles )

⇒ ∠ADE = ∠ABC ( by the similar 90° angles )

and both angles are making a total of 180°

So, from the above expressions, we can say that,

⇒ ∠AED = 180° - ∠A - ∠ABC

⇒ ∠ACB = 180° - ∠A - ∠ABC

Hence, ∠AED = ACB ⇒ ΔADE ≅ ΔABC

Therefore,

Option a) The similar triangles are ⇒ ΔADE ≅ ΔABC

Option b) ∠ADE = ∠ABC

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"The analysts at the casino try to choose the spread so that there is a 50% chance that the outcome will be below that amount, and a 50% chance that the outcome will be above that amount" is TRUE.

The analysts at the casino do not try to choose the spread so that there is a 50% chance of the outcome being below or above that amount. The spread is chosen based on factors such as the teams playing, their past performances, and other relevant statistics.

The goal of the casino is to balance the amount of money bet on each side, not to ensure a 50/50 chance of winning for either side. The spread is simply a tool used to even out the betting and ensure a profit for the casino.
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The given sequence is 9, 16, 24, 33. To find the next number, let's look for a pattern in the differences between the terms.

The difference between 16 and 9 is 7, between 24 and 16 is 8, and between 33 and 24 is 9.

The pattern in the differences is that they are increasing by 1 each time. So, the next difference would be 10.

To find the next number, we add the next difference to the last term in the sequence. Adding 10 to 33 gives us 43.

Therefore, the next number in the sequence is 43.

To find the next number in the given sequence, we looked for a pattern in the differences between the terms. We observed that the differences were increasing by 1 each time. Using this pattern, we added the next difference to the last term in the sequence to find the next number.

The next number in the sequence 9, 16, 24, 33 is 43.

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The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.

a) The probability that in any given hour zero new visitors will arrive at the website is given by;P(X = 0) = (e^-λ λ^0)/0!Where λ = 2.3Thus;P(X = 0) = (e^-2.3 2.3^0)/0!P(X = 0) = (0.1003)/1P(X = 0) = 0.1003b) The probability that in any given hour exactly one new visitor will arrive at the website is given by;P(X = 1) = (e^-λ λ^1)/1!Where λ = 2.3Thus;P(X = 1) = (e^-2.3 2.3^1)/1!P(X = 1) = (0.2303)/1P(X = 1) = 0.2303c) The probability that in any given hour two or more new visitors will arrive at the website is given by;P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)Thus;P(X ≥ 2) = 1 - 0.1003 - 0.2303P(X ≥ 2) = 0.6694d) The probability that in any given hour fewer than three new visitors will arrive at the website is given by;P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)Thus;P(X < 3) = 0.1003 + 0.2303 + 0.2642P(X < 3) = 0.5948Therefore,The probability that in any given hour zero new visitors will arrive at the website is 0.1003.The probability that in any given hour exactly one new visitor will arrive at the website is 0.2303.The probability that in any given hour two or more new visitors will arrive at the website is 0.6694.The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.

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The second solution to the differential equation is y2(x) = x3 + 3x4.

The method of reduction of order can be used to find a second linearly independent solution to a differential equation when one solution is already known. This method works by substituting the known solution y1 into the differential equation, and then solving the resulting equation for a second solution y2.

For example, in problem 38, we are given the differential equation \(x2y" + xy' – 9y = 0 (x > 0)\), and the solution y1(x) = x3. To find the second solution, y2, we substitute y1(x) = x3 into the differential equation:

\(x2(3x2) + x(3x) – 9x3 = 0\)

Simplifying this equation yields\(9x5 – 9x3 = 0\), which is satisfied when x = 0.

Now, we can use the method of reduction of order to find y2(x):

\(y2(x) = y1(x) + ∫f(x, y1(x), y1'(x))dx\)

Substituting in our values yields \(y2(x) = x3 + ∫[0 – 9x3]dx = x3 + 3x4.\)

Therefore, the second solution to the differential equation is \(y2(x) = x3 + 3x4.\)

The same process can be applied to problems 39 through 42 to find the second solution for each differential equation.

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The probability that the sample mean of the waiting times is less than 1.5 minutes is approximately 0.0057, or 0.57%.

To calculate the probability that the sample mean of the waiting times is less than 1.5 minutes, we can use the Central Limit Theorem (CLT) since we have a large enough sample size (n = 35) and the waiting times are uniformly distributed.

According to the CLT, the sample mean of a sufficiently large sample size will follow an approximately normal distribution, regardless of the underlying distribution. In this case, the population mean is E(X) = 2 (the midpoint of the uniform distribution between 0 and 4), and the population standard deviation is σ(X) = √(4²/12) = √(16/12) = √(4/3) ≈ 1.155.

The standard deviation of the sample mean (also known as the standard error) is given by σ(X)/√(n), which in this case is approximately 1.155/sqrt(35) ≈ 0.196.

To calculate the probability that the sample mean is less than 1.5 minutes, we can standardize the value using the z-score formula:

z = (sample mean - population mean) / standard error

z = (1.5 - 2) / 0.196 ≈ -2.551

Next, we can look up the probability corresponding to this z-score in the standard normal distribution table.

From the table, we find that the probability of obtaining a z-score less than -2.551 is approximately 0.0057.

Therefore, the probability that the sample mean of the waiting times is less than 1.5 minutes is approximately 0.0057, or 0.57%.

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Given that a rectangle ABCD, where AB = 4, side BC that AP 3 and P lies on diagonal AC such 3/2. We have to find the distance PB.Solution:In the given rectangle ABCD,AB = 4Therefore,

AD = BC = 4 [because opposite sides of a rectangle are equal]P lies on diagonal AC and AP = 3We have to find PBWe will use the Pythagorean theorem and properties of similar triangles to find the distance PB.From triangle APD,

Using Pythagorean theorem,PD2 = AD2 + AP2 = 42 + 32 = 16 + 9 = 25PD = √25 = 5From triangle ABC,Using Pythagorean theorem,AC2 = AB2 + BC2 = 42 + BC2BC2 = AC2 - AB2= (3/2)2 - 42= 9/4 - 16= - 55/4 [As, the value inside the square root can't be negative, Therefore PB can't exist, and we can say that PB is imaginary or it doesn't exist]Hence, the distance PB is imaginary or it doesn't exist.

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Answer:

2)

3)

4)

5)

6)

Step-by-step explanation:

Answer:

.75

Step-by-step explanation:

Because three divided by four is .75

Answer:

Question 22: 0.75 or 75%

Question 23:   5:2

Step-by-step explanation:

Question 22: 3 divided by 4 equals 0.75

Question 23:  

2.5  = 2.5/1

2.5 × 10/10 equals 25/10

25/10 divided by 5 equals 5/2

5/2= 5:2

Answer:

Product of

Step-by-step explanation:

Product  = X

Answer:

C. the product of

Step-by-step explanation:

A. "shared equally among" indicates division (ex. 16 apples are shared equally among 4 people ⇒ 16÷4)

B. "increased by" indicates addition (ex. the number of apples, 16, increased by 2 ⇒ 16+2)

C. "the product of" indicates multiplication (ex. the product of 5 and 6 ⇒ 5×6)

D. "the quotient of" indicates division (ex. the quotient of 40 and 10 ⇒ 40÷10)

I hope this helps!

Answer:

Step-by-step explanation:

Arc length = θ/360 × 2πr

= 150/360 ×2π×12

= 31.4 ft

The missing number of the series is 21.

The given sequence appears to follow the pattern of the Fibonacci sequence, where each number is the sum of the two preceding numbers. The Fibonacci sequence starts with 0 and 1, and each subsequent number is obtained by adding the two previous numbers.

Using this pattern, we can determine the missing number in the sequence.

0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55

Looking at the pattern, we can see that the missing number is obtained by adding 8 and 13, which gives us 21.

Therefore, the completed sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.

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The missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55 is 21.

To find the missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55, we can observe that each number is the sum of the two preceding numbers. This pattern is known as the Fibonacci sequence.

The Fibonacci sequence starts with 0 and 1. To generate the next number, we add the two preceding numbers: 0 + 1 = 1. Continuing this pattern, we get:

Therefore, the missing number in the sequence is 21.

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Answer:

9 x 12

Step-by-step explanation:

We can set 4/30 equal to 1.2/x

We cross multiply to get 4x = 36, so her width equals 9

We then set 6/45 equal to 1.6/x

Cross multiply to get 6x = 72, so her length equals 12

Hope this helps

The solution to the initial value problem is y = x^3 + 3x^2 + 4.

To solve the initial value problem y'' = 6x + 6 with y'(1) = 9 and y(0) = 4, we'll first solve the given second-order differential equation and then apply the initial conditions to find the constants.

1. Solve the differential equation y'' = 6x + 6:
Integrate once: y' = 3x^2 + 6x + C1
Integrate again: y = x^3 + 3x^2 + C1x + C2

2. Apply the initial conditions:
y(0) = 4 => 4 = 0^3 + 3(0)^2 + C1(0) + C2 => C2 = 4

y'(1) = 9 => 9 = 3(1)^2 + 6(1) + C1 => C1 = 0

Now, substitute the constants back into the general solution:
y = x^3 + 3x^2 + 0x + 4

So, the solution to the initial value problem is y = x^3 + 3x^2 + 4.

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The correct answer is D) 4.

In a two-way analysis of variance, we are examining the effects of two independent variables (or factors) on a dependent variable. We must calculate four F-ratios to test the significance of these effects: two for the main effects of each factor, and two for the interaction effect between the two factors.

The F-ratio is a statistical test that compares the amount of variability between groups to the amount of variability within groups. By calculating F-ratios for each effect, we can determine whether the differences between groups are statistically significant and whether the independent variables have a significant impact on the dependent variable.

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Answer:

1/2 hour

Step-by-step explanation:

he ran 1.25 miles in 7.5 mins

so

1.25x=37.5

x=30 MINS

30 mins =.5 hours or 1/2 hours

Answer:

c

Step-by-step explanation:

y = \(\frac{5}{2}\) x + 2 → (1)

2y = 5x + 4 ( divide through by 2 )

y = \(\frac{5}{2}\) x + 2 → (2)

the 2 equations are the same and will have infinitely many solutions

Answer:

D Over the interval [4, 7], the local minimum is -7.

Step-by-step explanation:

To complete the right or left matrix of rotation about the point (0, 0) for 2D graphics in the homogeneous system (z = 1), we use the following formulas:$$\textbf{Left Matrix of Rotation: } \begin{bmatrix} \cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$$$$\textbf{Right Matrix of Rotation: } \begin{bmatrix} \cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$$where $\theta$ is the angle of rotation.

The given matrix, we have $2p$ in the first row and $\cos a$ in the second row. Therefore, we can conclude that it represents a horizontal line segment of length $2p$ at a height of $\cos a$ above the $x$-axis. Now, we need to find the appropriate matrix for rotating this line segment about the point $(0, 0)$ by an angle of $\theta$.Since we want to know the matrix for the rotation of the line segment, we need to consider the effect of the rotation on the endpoints of the line segment.

The endpoints of the line segment can be represented in the homogeneous system as $(p, \cos a, 1)$ and $(-p, \cos a, 1)$.Left Matrix of Rotation:For the left matrix of rotation, we have:$$\begin{aligned}\begin{bmatrix} \cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} p \\ \cos a \\ 1 \end{bmatrix} &= \begin{bmatrix} p\cos \theta + \sin \theta \cos a \\ -p \sin \theta + \cos \theta \cos a \\ 1 \end{bmatrix} \\ \begin{bmatrix} \cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} -p \\ \cos a \\ 1 \end{bmatrix} &= \begin{bmatrix} -p\cos \theta + \sin \theta \cos a \\ p \sin \theta + \cos \theta \cos a \\ 1 \end{bmatrix}\end{aligned}$$Therefore, the left matrix of rotation is:$$\boxed{\begin{bmatrix} \cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}}$$Right Matrix of Rotation.

For the right matrix of rotation, we have:$$\begin{aligned}\begin{bmatrix} \cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} p \\ \cos a \\ 1 \end{bmatrix} &= \begin{bmatrix} p\cos \theta - \sin \theta \cos a \\ p \sin \theta + \cos \theta \cos a \\ 1 \end{bmatrix} \\ \begin{bmatrix} \cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} -p \\ \cos a \\ 1 \end{bmatrix} &= \begin{bmatrix} -p\cos \theta - \sin \theta \cos a \\ -p \sin \theta + \cos \theta \cos a \\ 1 \end{bmatrix}\end{aligned}$$Therefore, the right matrix of rotation is:$$\boxed{\begin{bmatrix} \cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}}$$Therefore, the left matrix of rotation is represented by the letter $\boxed{L}$ and the right matrix of rotation is represented by the letter $\boxed{R}$.

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Answer:

x=67

y=113

z=50

Step-by-step explanation:

x=180-28-85=67

y=180-67=113

z=17+113=50

Answer:

The answer to this should be D on ed2020

Step-by-step explanation:

There's another post for this question where Cheerchar13 had answered.

Answer:

the answer is d. edge 2021

Step-by-step explanation:

Answer: 0.6841

Step-by-step explanation:

Given: Probability of all SMES would file for bank loans next year = 3.5% = 0.035

Sample size : n = 100

Binomial probability distribution formula :

\(P(X=x)=^nC_xp^x(1-p)^{n-x}\)

The probability that at least 3 will file bank loans next year :

\(P(x\geq3)=1-P(x<3)\\\\=1-(P(x=0)+P(x=1)+P(x=2))\\\\=1-(^{100}C_0(0.035)^0(1-0.035)^{100}+\ ^{100}C_1(0.035)^1(1-0.035)^{99}+^{100}C_2(0.035)^2(1-0.035)^{98})\\\\=1-(0.3159)\\\\=0.6841\)

Hence, the required probability= 0.6841

3/5 is the probability that he will win, you must find a fraction which adds to make 100%.

2/5 would be the fraction for his probability to lose.

0.4 or 40%.

The number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.

To calculate the number of kilowatt-hours (kW-hrs) consumed by the air conditioner in a week, we need to consider the power rating of the air conditioner (850 Watts) and the duration it is left on each day.

Power of the air conditioner = 850 Watts

Duration of usage per day = 24 hours (left on all day)

Number of days in a week = 7 days

To calculate the energy consumption, we can use the formula:

Energy (kW-hrs) = Power (kW) * Time (hours)

First, let's convert the power from Watts to kilowatts by dividing it by 1000:

Power (kW) = 850 Watts / 1000 = 0.85 kW

Now we can calculate the energy consumption in a week:

Energy (kW-hrs) = Power (kW) * Time (hours)

Energy (kW-hrs) = 0.85 kW * 24 hours/day * 7 days

Energy (kW-hrs) = 14.28 kW-hrs

Therefore, the number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.

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Answer:

Please add a picture!

Step-by-step explanation:

Answer:

x= 60.4

Step-by-step explanation:

y = 60.4

z= 29.6

x= 60.4

By complementary angle rule

Answer:

Step-by-step explanation:

Answer: 67/9 or 7 4/9

Step-by-step explanation: