Consider the inequality 5≤x+12 5 ≤ x + 12
And can you please solve the inequality.

Answer:

3.8

Step-by-step explanation:

1. Use sine rule

d/sin(D) = f/sin(F) (d=EF, f=DE=3)

2. cross multiply

d=f(sin(D)/sin(F)) = 3(sin(75)/sin(50))=3.783

Answer:

  (b)  3.8

Step-by-step explanation:

Often, simple relations will help you solve geometry problems. Here, you only need to know that larger angles are opposite longer sides.

__

The angle opposite side EF is angle D, which is 75°. That angle is larger than angle F, which is opposite the side marked as having length 3.

This means EF > 3.

There is only one answer choice greater than 3. Choice B is 3.8.

  EF ≈ 3.8

______

The only "work" is remembering that larger angles are opposite longer sides.

x1 and x2 are uncorrelated random variables.

Given that y1 and y2 are independent random variables with mean 0 and variance σ^2, and x1 and x2 are related to y1 and y2 as follows:

x1 = y1 and x2 = ρy1√(1-ρ^2)y2

We can find the mean and variance of x1 and x2 as follows:

Mean of x1:

E(x1) = E(y1) = 0 (since y1 has mean 0)

Variance of x1:

Var(x1) = Var(y1) = σ^2 (since y1 has variance σ^2)

Mean of x2:

E(x2) = ρE(y1)√(1-ρ^2)E(y2) = 0 (since both y1 and y2 have mean 0)

Variance of x2:

Var(x2) = ρ^2Var(y1)(1-ρ^2)Var(y2) = ρ^2(1-ρ^2)σ^2 (since y1 and y2 are independent)

Now, let's find the covariance between x1 and x2:

Cov(x1, x2) = E(x1x2) - E(x1)E(x2)

= E(y1ρy1√(1-ρ^2)y2) - 0

= ρσ^2√(1-ρ^2)E(y1y2)

= 0 (since y1 and y2 are independent and have mean 0)

Therefore, x1 and x2 are uncorrelated random variables.

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Answer:

n=63°

Step-by-step explanation:

the angle around the point needs to add up to 360°

360°-297°=63°

Answer:

63

Step-by-step explanation:

When you have questions like this you get 360 and subtract 297 and get 63. 360-297=63

a) The margin of error for an 80% confidence interval in Arkansas is 0.1041

b) if we want to get an 80% confidence interval with a small margin of error, say only 7%. then the sample size must be 53,599,359

The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.

n = 3600

standard deviation = 399.876

Confidence Interval = 80%

a) α = 0.20

The margin of error = Zα/2 (σ / √n)

Zα/2 = 1.4395 --- (From the tabular value)

The margin of Error = 1.4395 + 399.876 / √3600

Therefore, the Margin of Error = 8.1041

b) Margin of Error = 0.07 = 7%

α = 0.20

Critical Value = 1.2816

Sample Size = (Zc²σ² / ME²) = (Zcσ / ME)²

n = [(1.2816 * 399.876) / 0.07]²

n = 53599358.98

Therefore, Sample size, n = 53599359

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The distance traveled in the first 2 seconds is 48 units, given the units of the velocity function.

To calculate the distance traveled during the time interval [0, 2] seconds, we need to integrate the velocity function over that interval. From part (d), we have the velocity function: v(t) = -16t + 40. To find the distance traveled, we integrate the absolute value of the velocity function over the interval [0, 2]: Distance = ∫[0, 2] |v(t)| dt. Using the given velocity function, we have: Distance = ∫[0, 2] |-16t + 40| dt.

To evaluate this integral, we need to split it into two parts based on the different intervals of the absolute value function: Distance = ∫[0, 2] (16t - 40) dt for 0 ≤ t ≤ 2. Integrating this expression, we get: Distance = [8t^2 - 40t] evaluated from 0 to 2. Plugging in the limits of integration, we have: Distance = [8(2)^2 - 40(2)] - [8(0)^2 - 40(0)]. Simplifying, we find: Distance = [32 - 80] - [0 - 0];Distance = -48. Therefore, the distance traveled in the first 2 seconds is 48 units, given the units of the velocity function.

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Question:

A shop is having a sales all items are reduced by 25%. Work out the sale price of an item normally priced at £60?

Answer:

The new price is £45

Step-by-step explanation:

Given

\(Sales\ price = \pounds 60\)

\(Rate = 25\%\)

First, calculate the reduction

\(Reduction = Rate * Sales\ price\)

\(Reduction = 25\% * \pounds 60\)

\(Reduction = \pounds 15\)

The new price is:

\(New = Sales\ price - Reduction\)

\(New = \pounds 60 - \pounds 15\)

\(New = \pounds 45\)

They are related as u^T transposes of each other. v and v^T u are scalar values that represent the dot product of u and v. uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.

If u and v are vectors in R^n, then:

u^T v and v^T u are related as transposes of each other. Specifically, if

u = [u_1, u_2, ..., u_n]^T

and v = [v_1, v_2, ..., v_n]^T

then:

u^T v = v^T u

= u_1 * v_1 + u_2 * v_2 + ... + u_n * v_n

So, u^T v and v^T u are scalar values that represent the dot product of u and v.

uv^T and vu^T are related as transposes of each other. Specifically, if u = [u_1, u_2, ..., u_n]^T and v = [v_1, v_2, ..., v_n]^T

then:

uv^T = [u_1 * v_1, u_1 * v_2, ..., u_1 * v_n;

u_2 * v_1, u_2 * v_2, ..., u_2 * v_n;

...;

u_n * v_1, u_n * v_2, ..., u_n * v_n]

vu^T = [v_1 * u_1, v_2 * u_1, ..., v_n * u_1;

v_1 * u_2, v_2 * u_2, ..., v_n * u_2;

...;

v_1 * u_n, v_2 * u_n, ..., v_n * u_n]

So, uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.

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The volume of the rectangular prism with the given height, width and length is 576 cubic centimeters.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

Given that;

V = w × h × l

V = 16cm × 9cm × 4cm

V = 576cm³

Therefore, the volume of the rectangular prism with the given height, width and length is 576 cubic centimeters.

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From the given function f(x) the value of expression f(f(81)) is equal to 3.

Let's see how to find the answer to the question:

Find (f0f)(81)

In the given question, we need to find the value of (f0f)(81). This notation means (f◦f)(81).

Given that f(x)= sqrt(x) and g(x) =\((x - 7)^2\).

We know that to find (f◦f)(x), we need to evaluate f(f(x)).

This means we need to first evaluate f(x), and then evaluate f(f(x)).

To find (f◦f)(81), we need to find f(f(81)).

Using the function f(x), we find f(81):

f(81) = sqrt(81) = 9

Now, we use the function f(x) again to find f(f(81)):

f(f(81)) = f(9)

= sqrt(9)

= 3

Thus, we have found that

(f◦f)(81) = f(f(81))

= 3

Hence, the value of (f0f)(81) is 3.

Therefore, the value of (f0f)(81) is 3.

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Answer:The result obtained by differentiating the result of an integral.

The derivative of an integral is given by the fundamental theorem of calculus. More specifically, if f(x) is a continuous function on the interval [a, b], then the derivative of the integral of f(x) from a to x is given by f(x).

In other words, if F(x) is an antiderivative of f(x), then the derivative of the integral of f(x) from a to x is F'(x) = f(x).

Symbolically, we can write:

d/dx ∫[a,x] f(t) dt = f(x)

where the integral sign ∫ represents the integral operation and d/dx represents the derivative operation.

This result is very useful in calculus, as it allows us to easily compute derivatives of functions that are defined as integrals.

In comparison to 1/3 to 3/9, both numbers are located at the same point on a number line.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

It is given that:

In comparison 1/3 to where would 3/9 be located on a number line

As we know, a number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

1/3 = 0.333

3/9 = 1/3 = 0.333

If we plot the above fractions on a number line we will see these two fractions are on the same point.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

Thus, in comparison to 1/3 to 3/9, both numbers are located at the same point on a number line.

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-2 - √3i is a known root not a possible root, option 4 will be the correct answer.

What are real and imaginary roots ?

A real root to an equation is a real number. A complex root to an equation is an imaginary root represented as complex numbers.

In other words real roots can be represented in a number line where as imaginary roots can not.

Here, the given root is -2 + √3i :

It is known that the complex roots comes in pairs that is in form a ±ib, where, a is real part of imaginary root and b is imaginary part.

Therefore, the other root will be -2 - √3i.

So, -2 - √3i is a known root not a possible root, option 4 will be the correct answer.

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Answer:

5305.1647 times

Step-by-step explanation:

The Circumference of a circle : πd

d = diameter of circle = 30 cm

Circumference of wheel = π * 30cm = 94.247779 cm

1km to cm

1km = 100000cm

5 km = 500000 cm

Hence, number of times wheel rotate on a 5km journey :

500000 cm / 94.247779 cm

= 5305.1647 times

9514 1404 393

Answer:

  (c) Supplementary angles

Step-by-step explanation:

The angles of a linear pair are supplementary. Angles 'a' and 'b' form a linear pair. That is, ...

  ∠EAB + ∠BAC = ∠EAC, a straight line

Consequently, angles 'a' and 'b' are supplementary.

Answer:

The expected values from the product of 2 marbles are 1,2,3,4,5,6,8,10,12,15,20

Step-by-step explanation:

THe expected values are 1,2,3,4,5,6,8,10,12,15,20

It reaches a high of 51.8 degrees Fahrenheit. There is a 59.4 degree F range. 12.6 degrees Fahrenheit is the standard deviation. The average temperature is 33.8°F. The median temperature is 35.6 °F. IQR is 60.8 degrees Fahrenheit.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. The study of gathering, analyzing, interpreting, presenting, and organizing data in a particular way is the focus of the mathematic branch known as statistics. The process of gathering data, classifying it, presenting it in a way that makes it understandable, and then conducting additional analyses of the data is known as statistics.

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Answer:

Step-by-step explanation:

the independent variable is money.

sodas are the dependent.

the amount of sodas you buy are dependent on the amount of money you have.

Answer:

2.30139104 US dollar

i think

Step-by-step explanation:

Answer:

\(x {}^{2} - 4x - 12 = 0 \\ (x - 6)(x + 2) = 0 \\ x = 6 \: \: x = - 2\)

The points will  meet x when it is folded are C or E

A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.

Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.

Given that,

A green colored Net,

After folding x point will  meet the points = ?

When we start folding,

First step,

Side ABCD and DEFG will be folded,

C and E will meet with each other

Second Step,

Side ABCD and AGHI will be folded,

B and I will meet with each other

Third step,

Side DEFG and AGHI will be folded,

F and H will meet each other

Fourth step,

Upper portion AHI will cover the upper portion BCF of the box

X will at position of C or E

Hence, the X will meet C or E

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Answer:

849

Step-by-step explanation:

Change: 11.18 $

Formula:

Change = Bill - Cost

Cost = (qty * price) * tax amount

Solution:

Cost = (3.5 * 2.40) * 1.05 = 8.4 * 1.05 = 8.82$

Change = 20 - 8.82 = 11.18 $

NB:

3(1/2) = 3.5 yds

5% Tax increase = amount + (amount *0.05) = amount * 1.05

Simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.

As given in the question,

Simple Interest:

The simple interest is an amount that is paid for loan or borrowed money over a certain period at a fixed percentage of borrowed money.

Principal amount:

Principal amount is the money that is taken as loan or borrowed.

Formula of Simple Interest:

Simple interest = Principal amount × Rate × Time

Since,

Principal amount = $10,000

Rate = 4% per year

Time = 5 years

Then,

Simple interest = 10,000 × 4 × 5

Simple interest = $ 12000

Total value after 5 years = $ 12000

Principal amount = $ 10000

Interest Earned = (Total value) - (Principal amount)

Interest Earned = $ 12000 - $ 10000

Interest Earned = $ 2000

Therefore, simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.

The complete question is:

Fabian is taking out a loan in the amount of $10,000. His choices for the loan are a 5-year loan at 4% rate of interest .What is the amount of simple interest and interest earned Fabian would have to pay?

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Answer:

$48

Step-by-step explanation:

1 t-shirt will be $6 (18/3)

So for 8 shirts you have to multiply $6 (cost of one shirt) with 8 and you get $48.

Hope that helps :)

Answer:

Search on mathaway

Step-by-step explanation:

The mode is the value that appears most frequently in a dataset. In this case, the mode is 4, as it has the highest frequency of occurrence.

The median is the middle value when the data is arranged in ascending or descending order. Since there are an odd number of families (21 in total), the median will be the value of the 11th observation when the data is sorted. Arranging the data in ascending order, we find that the median is also 4, as it is the middle value.

The mean is the average value and is calculated by summing up all the values and dividing by the total number of observations. In this case, we can calculate the mean by multiplying each number of pets by its corresponding frequency, summing up these products, and dividing by the total number of families (21). Using this approach, the mean can be calculated as:

Mean = (0*2 + 1*1 + 2*8 + 3*1 + 4*9 + 5*0) / 21 ≈ 2.76

Therefore, based on the provided data, the mode, median, and mean number of pets owned by the families are all approximately 4.

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Answer:

147

Step-by-step explanation:

x = 7,

3x² = 3 × 7²

= 3 × 49

= 147