Math expression work

Answer: To calculate the % confidence interval for the proportion of US adults who spend less than three hours watching TV on an average day, we can use the following formula:

p +/- z*(sqrt(p(1-p)/n))

Where:

p = proportion of US adults who spend less than three hours watching TV on an average day (0.42)

z = standard normal score for a given level of confidence (e.g. for a 95% confidence level, z = 1.96)

n = sample size (1031)

Plugging in the given values, we get:

0.42 +/- 1.96*(sqrt(0.42*(1-0.42)/1031))

Simplifying, we get:

0.42 +/- 0.0156

So the 95% confidence interval for the proportion of US adults who spend less than three hours watching TV on an average day is approximately (0.40,0.44)

So the answer is (0.40,0.44)

Step-by-step explanation:

Answer: The unit cost for a pound of sugar is $0.75. This means that for every pound of sugar, it costs $0.75.

Step-by-step explanation:

To find the unit cost for a pound of sugar, we need to divide the total cost of the 4 lb bag of sugar by the weight of the bag.

Unit cost = Total cost / Weight

Total cost = $2.99

Weight = 4 lbs

Unit cost = $2.99 / 4 lbs = $0.75 per pound

So, the unit cost for a pound of sugar is $0.75. This means that for every pound of sugar, it costs $0.75.

It's worth noting that this calculation gives us the unit price of the sugar, which is the price per pound of sugar, and not the unit cost which is the total cost of production divided by the total number of units produced.

It's also worth noting that some sellers may use different units of measurement, and you should always check that you are comparing the same units when comparing prices.

Answer:

The unit cost for a pound of sugar would be $0.75.

To find the unit cost, divide the total cost by the number of pounds: $2.99 / 4 lbs = $0.75/lb.

Step-by-step explanation:

Answer:

b.

Step-by-step explanation:

the result is created :

first result row first result element =

= first A row × first B column

first result row second result element =

= first A row × second B column

...

third result row second result element =

= third A row × second B column

third result row third result element =

= third A row × third B column

the multiplication of a row and a column is done by :

left row element × top column element +

middle row element × middle column element +

right row element × bottom column element

AB =

-4×3 + -3×-5 + 5×-1 -4×-4 + -3×-5 + 5×-3 -4×-1 + -3×1 + 5×2

-5×3 + -4×-5 + -2×-1 -5×-4 + -4×-5 + -2×-3 -5×-1 + -4×1 + -2×2

-1×3 + -2×-5 + -4×-1 -1×-4 + -2×-5 + -4×-3 -1×-1 + -2×1 + -4×2

=

-2 16 11

7 46 -3

11 26 -9

so, b is correct.

Hope it helps. If you have any query, feel free to ask.

A quadratic equation, or second-order polynomial equation with a single variable, has the form ax^2 + bx + c = 0. The solution to the given equation is v = 7, -5 and 3

The form ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given the quadratic expression below:

(v-7)(v+5)(v-3)=0

Required

The solution to the system of equation

Equate each expression to zero calculate the value of 'v' as shown:

v - 7 = 0

v = 0 + 7

v = 7

Also, v + 5 = 0

v = 0 - 5

v = -5

Similarly, v - 3 = 0

v = 0 + 3

v = 3

Hence the solution to the given equation is v = 7, -5 and 3

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Answer:

11 days

Step-by-step explanation:

It will last: 10/1 : 9/10 = 10/1 x 10/9 = 100/9 = 11,111... days

Answer: 11.1 days

Step-by-step explanation:

Everyday, Sandy uses 9/10 of a bag of cups.

Use unitary method.

9/10 bag - 1 day

10 bag - 10/(9/10) = 100/9 ≈ 11.1 days

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The equation for Khloe's distance from her car in miles, y, as a function of the time in hours, x, is y = -3x + 11.

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables but does not have exponents to the variables or the exponent of the variable is 1.

We have the two points of x and y.

After 1 hour, Khloe is 8 miles from her car.

When x = 1, y = 8

After 3 hours, Khloe is 2 miles from the car.

When x = 3, y = 2

Points of the linear function are (1, 8) and (3, 2)

Slope of the line = (2 - 8) / (3 - 1) = -6/2 = -3

Take a point (1, 8).

Equation of the linear function in point slope form can be written as,

y - 8 = -3(x - 1)

y - 8 = -3x + 3

y = -3x + 3 + 8

y = -3x + 11

Hence the linear function representing the situation is y = -3x + 11.

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Answer: (6,2) (0,-2) (-3,-4)

Step-by-step explanation:

If you find the other coordinate pair groups on the graph, there is at least one that doesn't land on the line on the graph.

In the top left, (-6,-5) is not on the graph. If it had been (-6,-6) then it would've been correct, but it isn't.

In the bottom left, (0,-3) isn't on the graph. Instead, (0,-2) is.

In the bottom right, (3,-4) isn't on the graph, but (-3,-4) is.

Answer: To find the length of the diagonal cut, we can use the Pythagorean theorem.

The diagonal cut is the hypotenuse of a right triangle, with legs of length 9 and 12.

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs. So, the length of the diagonal cut is the square root of (9^2 + 12^2)

So, the length of the diagonal cut is √(9^2 + 12^2) = √(81 + 144) = √225 = 15cm

Therefore, the diagonal cut that Danny made is 15 centimeters long.

Step-by-step explanation:

The derivation of the function y = (4x+9x^2)(3x-7x^4) by the means of direct formulas is y = 12x^2 + 27x^3 - 28x^5 - 63x^6.

The direct formula method is a way to multiply two or more algebraic expressions together by applying the distributive property and combining like terms. It is also known as the "FOIL" method for multiplying binomials.

The direct formula method involves breaking down each expression into its individual terms and then using the distributive property to multiply each term in the first expression by each term in the second expression. After that, the resulting terms are combined according to the addition and subtraction rules of like terms.

To derive the function y = (4x+9x^2)(3x-7x^4) using the direct formulas method, we need to multiply the two expressions inside the parentheses:

y = (4x+9x^2)(3x-7x^4)

y = 4x3x + 4x-7x^4 + 9x^23x + 9x^2-7x^4

Using the distributive property, we can simplify the expression by combining like terms:

y = 12x^2 - 28x^5 + 27x^3 - 63x^6

y = (12x^2 + 27x^3) - (28x^5 + 63x^6)

So the final expression is y = 12x^2 + 27x^3 - 28x^5 - 63x^6

The direct formulas method uses the distributive property and the combination of like terms to derive the final expression of the function.

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The amount of discount in dollars is 28.17

To find the amount of the discount, we need to multiply the original price by the percentage that was discounted.

Discount = Original Price x (Discount Percentage/100)

Discount = 46.95 x (60/100) = 28.17

So, the amount of discount in dollars is 28.17

Answer:

The change in gravitational potential energy from point A to point B can be calculated using the formula:

ΔU = mgh

Where:

m = mass of the pendulum = 1.5 kg

g = acceleration due to gravity = 9.8 m/s^2

h = change in height = yB - yA = 0.12 m - 0.04 m = 0.08 m

So, the change in gravitational potential energy from A to B is:

ΔU = (1.5 kg)(9.8 m/s^2)(0.08 m) = 1.176 J

So, the change in gravitational potential energy from A to B is 1.176 Joules.

The area of the rectangle with a length of (x + 5) cm and width of (x + 2) cm is (x² + 7x + 10) cm²

An equation is an expression that shows the relationship between two or more numbers and variables.

A rectangle is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel. The area of a rectangle is the amount of space that it occupies. The area is calculated using:

Area = length * width

The rectangle shown has a length of (x + 5) cm and width of (x + 2) cm. Hence:

Area = length * width

Substituting:

Area = (x + 5)(x + 2)

Area = x² + 2x + 5x + 10

Area = (x² + 7x + 10) cm²

The area of the rectangle is (x² + 7x + 10) cm²

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Answer:

The circumference of a tire can be found by using the formula C = πd, where C is the circumference, and d is the diameter.

For the old bicycle with 12 inch diameter tires, the circumference is:

C = π * 12 = 12 * π inches

For the new bicycle with 16 inch diameter tires, the circumference is:

C = π * 16 = 16 * π inches

To find the difference in the circumference of the tires, we subtract the circumference of the old tire from the circumference of the new tire:

16π - 12π = 4π inches

So the difference in the circumference of the two tires is 4π inches.

It's around 12.56 inches.

An equation in general form that describes the locations within the receiving distance of the tower is (x - 25)² + (y - 32)² = (45)².

And  Squirrel Hills is within the receiving distance of the signal.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

Given:

A radio station has a tower that is 25 miles east and 32 miles north of downtown Squirrel Hills.

The tower emits a signal that reaches receivers that are within 45 miles of its location.

From the attached image,

(25, 32) is the location of the tower.

And (0, 0) is the location of Hill.

So, equation,

(x - 25)² + (y - 32)² = (45)²

To determine if Squirrel Hills is within the receiving distance of the signal:

That means,

when (x, y) = (0, 0),

(0 - 25)² + (0 - 32)² = (45)²

1649 < 2025

That means, the Squirrel Hills is within the receiving distance of the signal.

Therefore, the Squirrel Hills is within the receiving distance of the signal.

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The given relation {(-1, 1), (1, 1), (-2, 4), (2, 4)} is a function because: A. yes each input has exactly one output.

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two (2) or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).

In this context, we can reasonably infer and logically deduce that given relation is a function because each input variable (domain) has exactly an output variable (range) as illustrated below;

x      F(x)

-1       1

1        1

-2      2

2       4

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The relationship between the trigonometric ratios of the non-right angles in a triangle and the measures of the angles are;

1.) c.) They are reciprocals

2.) a.) They are equal

3. b.) They are complementary

The non-right angles in a right triangle are he two acute angles in the right triangle.

1) Complementary angles are angles that have a sum of 90°

Let A and B be two complementary angles, we get;

m∠A + m∠B = 90°

Let a and b represent the lengths of the opposite sides to the complementary angles ∠A and ∠B

Let side a represent the side opposite to the angle ∠A and let side b  represent the side opposite to the angle ∠B, we get

tan(A) = a/b tan B = b/a

Therefore, tan(B) is the reciprocal of tan(A)

The correct option is c,) They are reciprocals

2) Let r represent the length of the hypotenuse of the right triangle, we get;

sin(A) = a/r

cos(A) = b/r

sin(B) = b/r

cos(B) = a/r

The values, sin(A) = cos(B), and sin(B) = cos(A), therefore;

3) The sum of angles in the right triangle is 180°, therefore;

m∠A + m∠B + 90° = 180°

m∠A + m∠B = 180° - 90° = 90°

m∠A + m∠B = 90°

The sum of the two non-right angles in a triangle is 90°,  therefore, the two non-right angles re complementary.

The correct option is therefore; b.) They are complementary

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The interest paid at the term end will be $5400.

What is interest and its types(Simple and compound interest)?

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.

​The formula for these are

Simple Interest= P×r×n

where:

P=Principal amount

r=Annual interest rate

n=Term of loan, in years

Compound Interest=P×(1+r)^t−P

where:

P=Principal amount

r=Annual interest rate

t=Number of years interest is applied

Here,

Interest rate will be risk percentage + LIBOR

i.e.4.8%

Hence,  the interest can be found by using formula for simple interest

Therefore,

SI=P*r*t

=$450000*0.048*0.25               (Time is 3 month or  0.25 years.)

SI (Interest paid)=$5400

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The total interest paid for the period of three months will be $5225 on the loan amount of $450000.

What is interest?

The interest is the charges levied on the amount which we borrow from any bank for a particular period of time.

Here in the question given data is

P= $450000

R=2.2%+2.8%=5%

T=1/4 years or three months

So from the simple interest formula

SI= PNR/100

SI=15000×5×1/`100×4

SI=$5625

Hence the total interest paid for the period of three months will be $5225 on the loan amount of $450000.

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The gigabytes of music  downloaded in one hour is 19.8 gb per hour

From the question, we have the following parameters that can be used in our computation:

Size =  75.24 gigabytes

Time = 3.8 hours

The rate is then calculated as

Rate = Size/Time

Substitute the known values in the above equation, so, we have the following representation

Rate = 75.24/3.8

Evaluate

Rate = 19.8

Hence, the rate is 19.8 gb per hour

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Answer: -2

Step-by-step explanation:

Given, aₙ = aₙ - ₁ - 3

so,

a₂ = a₁ - 3 = 7 - 3 = 4

a₃ = a₂ - 3 = 4 - 3 = 1

a₄ = 1 - 3 = -2

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Answer:

y = 2x -2

Step-by-step explanation:

y = mx + b

We need the slope (m) and the y-intercept (b) to write the eqation.

The slope is the change in y over the change in x.  We can see from the table that the y is changing by 2 as the x changes by 1

So the slope is 2/1 which is the same as 2

The slope (m) is 2.

The y-intercept is the place where the line crosses the y axis.  It is at the point (0,b).  When x is zero, what is y?  If we follow the patter and move to the number before x is 1, we get x = 0.  That means that we have to move back 2 units of the y's.  That would be -2.  So the y-intercept is the point (0,-2).

The y-intercept (b) is -2

y = 2x - 2

The distance from Earth to the Sun is 396 times larger than the distance from the Earth to the moon.

Scientific notation.

This is a mode of expressing large numbers of great power. Its helps in the simple expression of numbers so that some arithmetic operations can be performed as required.

In the given question, we have;

distance from Earth to the Sun = 1.47 X 10^11 meters

and

distance from Earth to moon = 3.71 X 10^8 meters

Thus,

to determine by how much is the distance between the Earth and Sun greater than that between the Earth and moon;

n = distance from Earth to the Sun/ distance from the Earth to the moon

  = 1.47 X 10^11/ 3.71 X 10^8

  = 3.962 x 10^2

n = 396

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Answer: C

Step-by-step explanation: If you solve each of them (1 x 4=4, 2x4=8, 3x4=12, 6x4=24), You can see that the are rational.

Answer:

a₄ = 25

Step-by-step explanation:

using the recursive formula [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] and a₁ = 4 , then

a₂ = 2a₁ - 1 = 2(4) - 1 = 8 - 1 = 7

a₃ = 2a₂ - 1 = 2(7) - 1 = 14 - 1 = 13

a₄ = 2a₃ - 1 = 2(13) - 1 = 26 - 1 = 25

A model rocket is launched from the roof of a building. It's flight path is modeled by -5t^2 + 30t + 10 and the Distance from ground = 10 + height after 3 sec

Where h is the height of the rocket above the ground in meters and t is the time after the launch in seconds.

Ans as h = -5t2+30t+10

at t=0, H = 10, which is height of the building from the ground

at t= 2 sec

h= -5.4+30.2+10

= -20+60 +10 = 50 m

For max height dh/dt = 0

-10t+30 = 0

t=3 sec

Therefore, the Distance from ground = 10 + height after 3 sec

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If D and R are independent, then P(D or R) = 0.8412

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)

P(D) = 0.26 and P( R) = 0.26 , if D and R are independent, then,

P(D or R) = P(D) + P(R) - P(DnR)

then P(DnR) = P(D) × P(R) = 0.26×0.38 = 0.0988

P(D or R) = 0.26+0.38-0.0988

= 0.8412

Therefore the probability of P(D or R) if D and R are independent is 0.8412

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On solving the provided question we can say that 1,000,000 nanometers =  1 millimeter; 1e-6 millimeter = nanometers

A nanometer, often known as a nanometer, is a unit of measurement that is one billionth of a metre and one thousandth of a picometre in the International System of Units. In scientific notation, a nanometer is represented by the numbers 1 109 m and 1/1000000000 metres. The prefix "nano" refers to one billionth, or 10-9, in the International System of Units. An nanometer is therefore one billionth of a metre. The metric unit of length known as a nanometer is one billionth of a metre (0.000000001 m). It is a small length unit, abbreviated as nm. One billionth of a metre or one billionth of a micrometre is what is known as a nanometer (nm), which is 109 metres. Atoms and the molecules they make up are measured using this scale.

1,000,000 nanometers =  1 millimeter

1e-6 millimeter = nanometers

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The simultaneous equation 5x + 2y = 9 and x + y = -3 is solved by elimination method as follows

There are various methods of solving simultaneous equation however for this problem we solve with elimination method

The equation is 5x + 2y = 9 and x + y = -3

multiply x + y = -3 by 2

2x + 2y = -6

subtract 2x + 2y = - 6 from 5x + 2y = 9

5x + 2y = 9

2x + 2y = - 6

this will result to 3x = -15

solve for x by dividing by 3

x = -5

substitute x = -5 to x + y = -3

-5 + y = -3

y = -3 + 5

y = 2

hence x = -5 and y = 2

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The debts to assets ratio is 0.63

The formula for calculating debts to assets ratio is

total liabilities/total assets

The total liabilities is $3,228

The total assets is $5,091

Therefore the debts to assets ratio is

3228/5091

= 0.63

Hence the debts to assets ratio is 0.63

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