Find the length of the diagonal of
rectangle whose length
is 12ft and whose
width 5 ft

Answer:

$6.41

Step-by-step explanation:

47.92 - 3.05 = 44.87

44.87/7 = $6.41

Answer:

Option B

Step-by-step explanation:

→ Find 2 coordinates through which the line passes through

( -2 , -5 ) and ( 0 , -1 )

→ Work out the gradient

[tex]\frac{-1--5}{0--2} =2[/tex]

→ Write into y = mx + c

y = 2x + c

→ Substitute in the coordinates ( 0 , -1 )

-1 = 0 + c so c = -1

→ Write equation

y = 2x - 1

→ Expand out all the equations and simply to see which gives y = 2x - 1

Option B

Answer:

8

Step-by-step explanation:

Step-by-step explanation:

Let's find the difference between 7508 and the other numbers.

A. 5706 - 7508 = -1802

B. 6993 - 7508 = -515

C. 8108 - 7508 = 600

D. 8522 - 7508 = 1014

E. 1050 - 7508 = -6458

If we do not take +ve / -ve into account,

the closest number to 7508 = the smallest difference

which in this case, is B, 6993.

Answer:

B. 6993

Step-by-step explanation:

hope this helps :)

Answer:

-4

Step-by-step explanation:

First you add together 75 + 65 to get 140 then you subtract that from 180 because 180° is the total of a triangle. Then you add -4 to 44 to get 40

Answer:

-4

Step-by-step explanation:

75 + 65 = 140

triangle angels equal 180°

then x +44 = 180-140

x +44 = 40

x = 40-44

x = -4

According to the question You have two coins, a blue and a red one. You choose one of the coins at random, each being chosen with probability are as follows :

(a) To compute P(H1), we need to consider the probability of getting heads on the first toss. There are two scenarios: either we picked the blue coin and got heads, or we picked the red coin and got heads.

[tex]\(P(H1) = P(H1 \cap B) + P(H1 \cap \bar{B}) = P(H1 | B)P(B) + P(H1 | \bar{B})P(\bar{B}) = 0.8 \times \frac{1}{2} + 0.2 \times \frac{1}{2} = 0.4 + 0.1 = 0.5\)[/tex]

(b) To compute P(H2), we can use the same reasoning as in part (a), considering the probability of getting heads on the second toss.

[tex]\(P(H2) = P(H2 \cap B) + P(H2 \cap \bar{B}) = P(H2 | B)P(B) + P(H2 | \bar{B})P(\bar{B}) = 0.8 \times \frac{1}{2} + 0.2 \times \frac{1}{2} = 0.4 + 0.1 = 0.5\)[/tex]

(c) To compute P(H1 ∩ B), we consider the probability of getting heads on the first toss given that we picked the blue coin.

[tex]\(P(H1 \cap B) = 0.8 \times \frac{1}{2} = 0.4\)[/tex]

(d) To compute P(H1 ∩ H2), we need to consider the probability of getting heads on both the first and second toss.

[tex]\(P(H1 \cap H2) = P(H1)P(H2 | H1)\)[/tex]

(e) The independence of events H1 and H2 can be determined by comparing [tex]\(P(H2 | H1)\)[/tex]  and [tex]\(P(H2)\)[/tex] .

(f) To compute P(H2 | H1), we use the formula for conditional probability:

[tex]\(P(H2 | H1) = \frac{P(H1 \cap H2)}{P(H1)} = \frac{0.4}{0.5} = 0.8\)[/tex]

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Answer:

12 cm difference

Step-by-step explanation:

√64 cm² = 8 cm

8 cm x 4 = 32 cm perimeter

√121 cm² = 11 cm

11 cm x 4 = 44 cm perimeter

44 cm - 32 cm = 12 cm difference

Answer:

your answer is 1/2 hope this helped have a good day :3

Step-by-step explanation:

Answer:

1/2 or 0.5

Step-by-step explanation:

5/3 + (- 7/6)​ = 5/3 - 7/6

Answer:

Step-by-step explanation:

Answer:

I don't see an "x" or an equation-

If Sº f(a)dz f(x)dx = 35 35 and o [*p12 g(x)dx = 12, find [3f(x) + 59(2)]da. The value of indefinite integral [3f(x) + 59(2)]da If Sº f(a)dz f(x)dx = 35 35 and o [*p12 g(x)dx = 12 is 223.

We are given the following conditions:

Sº f(a)dz f(x)dx = 35

35o [*p12 g(x)dx = 12

First, we need to evaluate the indefinite integral.

Hence, integrating (x² + x + 17)34c + x² with respect to x, we get,

x³/3 + 17x² + 34cx + x³/3 + C= (2/3) x³ + 17x² + 34cx + C

To find [3f(x) + 59(2)]da,

we need to integrate the same with respect to a.

[3f(x) + 59(2)]da= 3Sº

f(x)da + 59(2)a= 3Sº f(a)dz f(x)dx + 118

Therefore,[3f(x) + 59(2)]da= 3 × 35 + 118= 223

Therefore, [3f(x) + 59(2)]da= 223.

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The system has infinitely many solutions.

The given augmented matrix represents a system of linear equations. To find the reduced row-echelon form, we perform row operations to transform the matrix into a triangular form with leading entries (1s) and zeros below each leading entry. Let's denote the variables as x, y, and z.

After performing the necessary row operations, we arrive at the reduced row-echelon form:

From the reduced row-echelon form, we can deduce the following equations:

These equations reveal that the system contains infinitely many solutions. By assigning a parameter, such as z = t, where t represents any real number, we can express the solutions in terms of the parameter. Thus, the coordinates of the solution are given by:

In this case, there is an infinite number of possible solutions, and each solution is represented by a unique value of t. Therefore, the main answer is that the system has infinitely many solutions.

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Answer:

(a)

Step-by-step explanation:

Given

See attachment for sets A and B

Required

The true statement about both sets

First, we calculate the typical values (mean) of set A and set B.

This is calculated as:

[tex]Mean = \frac{\sum fx}{\sum f}[/tex]

For A:

[tex]A= \frac{0*1+2*1+5*1+6*1+7*1}{1+1+1+1+1}[/tex]

[tex]A= \frac{20}{5}[/tex]

[tex]A =4[/tex]

For B:

[tex]B = \frac{7 * 1 + 8 *1 + 9 * 2 + 10 * 1}{1+1+2+1}[/tex]

[tex]B = \frac{43}{5}[/tex]

[tex]B = 8.6[/tex]

Here, we can conclude that B has a larger typical value

Next calculate the spread (range) of sets A and B

This is calculated as:

[tex]Range = Highest -Least[/tex]

For A:

[tex]A = 7 - 0[/tex]

[tex]A = 7[/tex]

For B

[tex]B=10 - 7[/tex]

[tex]B = 3[/tex]

Here, we can conclude that A has a larger spread.

Hence, (a) is true

Answer:

804 cm3

Step-by-step explanation:

multiply the lenght and the width then multiply by 3.14 which is pi.

Answer:

234

Step-by-step explanation:

Answer:

234

Step-by-step explanation:

AREA FOR TRIANGLE: bh/2

b = base

h = height

-

30 x 15.6 = 468

468/2 = 234

-

hope this helped ! :D

18. Option B is correct, the outcomes of the first five spins tell us nothing about what will happen on the next five spins.

19. Option D is correct,  the overall sample is a simple random sample, biased due to imbalance and stratified sample, option d is correct.

18. Given that a  North American roulette wheel has 38 slots, of which 18 are red, 18 are black, and 2 are green.

Each spin of the roulette wheel is an independent event, and the outcomes of previous spins do not influence the outcomes of future spins.

The wheel has no memory of previous results, so the probability of getting a red outcome on the sixth spin is the same as any other spin – 18 out of 38.

So, the outcomes of the first five spins tell us nothing about what will happen on the next five spins.

19. At a large university, a simple random sample of five female professors is selected, and a simple random sample of 10 male professors is selected.

The overall sample of 15 professors is a combination of two simple random samples, one from the female professors and the other from the male professors.

This makes it a stratified sample because it involves dividing the population (professors) into distinct groups (male and female) and then randomly sampling from each group.

Additionally, the overall sample can also be considered a simple random sample because it was obtained by randomly selecting individuals from the population without any bias

Hence, the overall sample is a simple random sample, biased due to imbalance and stratified sample, option d is correct.

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Answer:

scale factor = 20%

Step-by-step explanation:

A scale factor is a multiplier which can be used to determine the rate between two or more dimensions.

In the given figure, the sides of the original triangle is 5 times greater than that of the copy. Thus,

the scale factor = [tex]\frac{copy length}{original length}[/tex] x 100%

                          = [tex]\frac{1}{5}[/tex] x 100%

                          = 20%

The scale factor of the original triangle to its copy is 20%. This implies that the dimensions of the original triangle are multiplied by 20% to determine that of the corresponding copy triangle. Thus, we scale down the dimensions of the original triangle by 20%.

Based on the information given, it should be noted that the critical value is +2.33.

We are given that the sample size is 42, the sample proportion is 0.247, and the significance level is 0.05. We want to test the claim that the population proportion is 0.325.

The critical value is the z-score that separates the rejection region from the non-rejection region. The rejection region is the area under the standard normal curve where we would reject the null hypothesis. The non-rejection region is the area under the standard normal curve where we would fail to reject the null hypothesis.

The z-table shows that the critical value for a two-tailed test with a significance level of 0.05 is +2.33. This means that if the z-score is greater than or equal to +2.33, we would reject the null hypothesis.

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Answer:

16ft by 16 ft: NO

10ft by 15ft: YES

15ft by 20ft: NO

12ft by 16ft: YES

Step-by-step explanation:

First, we know that the scale used is:

1 in = (1 + 1/2) ft.

This means that each inch on the drawing is equivalent to (1 + 1/2) ft.

We know that Michael uses a paper that has the measures:

width = (8 + 1/2) in

length = 11in

Then the maximum dimensions that can be represented with this paper are:

WIDTH = (8 + 1/2)*(1 + 1/2) ft. = (8 + 8/2 + 1/2 + 1/4) ft

            = (8 + 4 + 2/4 + 1/4) ft

            = (12 + 3/4) ft

LENGTH = 11*(1 + 1/2) ft = (11 + 11/2)ft = (11 + 10/2 + 1/2)ft

               = (11 + 5 + 1/2)ft = (16 + 1/2) ft.

Now let's analyze the options, we can only draw the rooms in the paper if the measures are equal or smaller than the ones we found above:

Where the measures are written as: "width by length".

a) 16ft by 16 ft.

width = 16ft

length = 16ft

We can not draw this, because the maximum width that we can draw is (12 + 3/4) ft, which is smaller than 16ft.

b) 10 ft by 15 ft

width = 10ft

length = 15ft

Both are smaller than the maximum measures we found, then yes, we can draw this room.

c) 15 ft by 20 ft

width = 15ft

length = 20ft

Both are larger than the maximum measures, so no, we can not draw this.

d) 12ft by 16ft

width = 12ft < (12 + 3/4) ft = maximum width

lenth = 16ft < (16 + 1/2) ft = maximum length.

Both measures are smaller than the maximum ones, then we can draw this one

Answer:

Step-by-step explanation:

An absolute value of |x| {modulus of x} is the value of a real number x. The given equation is not true.

An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number, for example, |-5| will give 5, and also, |5| will give 5 as well.

A hypothesis is a speculative conclusion or assertion that is made without proof. Now, to prove that the given equation is not true substitute the value of both the variables as -1. Therefore,

x = y = -1

Substitute the value on the left side of the equation,

|x - y|

= |-1 - (-1)|

= |-1 + 1|

= |0|

= 0

Substitute the value on the right side of the equation,

|x| - |y|

= |-1| - |-1|

= 1 + 1  

= 2

Since the left and the right side of the equation is not satisfied, therefore, it can be concluded that the given equation is not true.

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a. The function in graph q is classified as an odd function, as f(-x) = -f(x).

b. The function in graph q is classified as an even function, as f(-x) = f(x).

c. The function [tex]y = 3^x - 4[/tex] is classified as neither an odd function nor an even function.

For the third function, [tex]y = 3^x - 4[/tex], we have that:

No relation between f(1) and f(-1), hence the function is neither even nor odd.

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To find the area using the limit of a sum (a Riemann sum) of the region between the graph of y = f(x) and the x-axis from x = a to x = b, the formula is given by: Area = lim n → ∞ ∑ i = 1 n f(x* i )Δx, where f(x* i ) is the height of the ith rectangle and Δx is the width of the ith rectangle.

To find the area between the graph of y = f(x) and the x-axis from x = a to x = b using the limit of a sum, we need to first divide the interval [a, b] into n equal subintervals of length Δx = (b - a)/n. Then, we can choose any point x* i in the ith subinterval [x i-1 , x i ] and use it to determine the height of the ith rectangle f(x* i ).

Finally, we can take the limit as n approaches infinity to obtain the exact area of the region between the graph of y = f(x) and the x-axis from x = a to x = b.

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To sketch an approximate solution curve passing through specific points, integrate the differential equation numerically Euler's method, Runge-Kutta methods, or solve the equation analytically if possible

To generate a direction field for a given differential equation using computer software, you can use mathematical software packages such as MATLAB, Python with libraries like NumPy and Matplotlib, or dedicated software like Wolfram Mathematica. Here, I will explain the general procedure using Python and Matplotlib.

Define the differential equation: Write down the differential equation you want to work with. For example, let's say we have a first-order ordinary differential equation dy/dx = x - y.

Import the necessary libraries: In Python, you'll need to import the required libraries, such as NumPy and Matplotlib. You can do this with the following code:

python

Copy code

import numpy as np

import matplotlib.pyplot as plt

Define the direction field function: Create a Python function that calculates the slope at each point (x, y) based on the given differential equation. For our example equation dy/dx = x - y, the function can be defined as follows:

python

Copy code

def direction_field(x, y):

   return x - y

Generate a grid of points: Define the range of x and y values over which you want to generate the direction field. Create a mesh grid using NumPy's meshgrid function to generate a grid of points (x, y). For example:

python

Copy code

x = np.linspace(-5, 5, 20)

y = np.linspace(-5, 5, 20)

X, Y = np.meshgrid(x, y)

Calculate the slopes: Use the direction_field function to calculate the slopes (dy/dx) at each point in the grid. Store the result in a variable, such as dy_dx:

python

Copy code

dy_dx = direction_field(X, Y)

Plot the direction field: Use Matplotlib's quiver function to plot the direction field. This function creates arrows at each point (x, y) in the grid, indicating the direction of the slope (dy/dx). Here's an example:

python

Copy code

plt.figure(figsize=(8, 8))

plt.quiver(X, Y, np.ones_like(dy_dx), dy_dx)

plt.xlabel('x')

plt.ylabel('y')

plt.title('Direction Field')

plt.grid(True)

plt.show()

This code will display the direction field for the given differential equation.

To sketch an approximate solution curve passing through specific points, you can integrate the differential equation numerically using numerical integration methods such as Euler's method, Runge-Kutta methods, or solve the equation analytically if possible. Once you have the solution, you can plot it on top of the direction field using Matplotlib to compare it with the given points.

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Answer:

Try 8 if it's wrong sorry

Step-by-step explanation:

The 90% confidence level means that we are 90% confident that the true median household income for Arizona falls within the given interval.

In statistical analysis, a confidence interval provides a range of values within which the true population parameter is likely to lie. In this case, the 90% confidence interval for the 2015 median household income in Arizona is stated as $51,492 ± $431.

Interpreting this confidence interval, we can say that we are 90% confident that the true median household income for Arizona in 2015 falls between $51,061 ($51,492 - $431) and $51,923 ($51,492 + $431). This means that if we were to take multiple samples and calculate their respective confidence intervals, approximately 90% of these intervals would contain the true median household income.

The confidence level represents the degree of certainty associated with the interval. In this case, a confidence level of 90% means that there is a 90% probability that the true median household income lies within the given range. It indicates a high level of confidence but allows for a 10% chance of the true value falling outside the interval.

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a) The derivative of a constant times a constant is zero, so the derivative of da ([8] c*) with respect to c* is zero. b) there is no value of k that satisfies this equation. c) k = 2/e

a. The derivative of a constant times a constant is zero, so the derivative of da ([8] c*) with respect to c* is zero.

b. To find a value of k such that ekt is a solution to a = -4, we substitute ekt into the equation:

a = -4

ekt = -4

Since ekt is always positive, there is no value of k that satisfies this equation.

c. To find a value of k such that ekt is a solution to ' = 2, we substitute ekt into the equation:

' = 2

d(ekt)/dt = 2

Differentiating ekt with respect to t, we get:

kekt = 2

Dividing both sides by ek, we have:

k = 2/e

d. The general solution for the system of differential equations in the form x₁(t) = ? and x₂(t) = ? can be obtained by solving the system using the initial conditions and finding the values of the arbitrary constants A and B.

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Answer:

bit.[tex]^{}[/tex]ly/3a8Nt8n

Step-by-step explanation:

Answer: It would be "290 in.2"

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

its 3, -6,-1... got 100%

Step-by-step explanation: