The temperature in Austin is 33.5◦F and rising at a rate of 2.5◦F per hour. The temperature in San Antonio is 37.5◦F and rising at a rate of 1.5◦F per hour. Write an inequality that shows how long the temperature in Austin will remain colder than that in San Antonio.

The quadratic equation will be written as F(x) = -2x² - 4x + 1.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

The point from which the quadratic equation passes are,

(0,1), (-1,3), and (-2,1).

The quadratic equation will be written as,

y =ax²+ bx +c

For point (0,1)

1 = 0 + 0 + c

c = 1

For points (-1,3),

3 = a - b + c

3 = a - b + 1

a - b = 2

For point (-2,1),

1 = 4a - 2b + c

1 = 4a - 2b + 1

4a = 2b

b = 2a

calculate the values of a and b,

a - b = 2

a  - 2a = 2

-a = 2

a = -2

b = 2a = 2 x -2 = -4

The quadratic equation will be written as,

F(x) = -2x² - 4x + 1

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The amount borrowed is $66,000, the annual interest rate is 4 %, the number of payments per year is 12, the loan term is 20 years, and the payment amount is $10668.39.

Compound interest is applicable when there will be a change in the principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

The total amount paid is,

A = 4800[1 + 0.04/12]^(12 x 20)

A = $10668.39

Hence "The amount borrowed is $66,000, the annual interest rate is 4 %, the number of payments per year is 12, the loan term is 20 years, and the payment amount is $10668.39".

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To find the coordinates of a point on a circle with radius 10 corresponding to an angle of 325 degrees, you can use the following formula:

(x, y) = (r * cos(θ), r * sin(θ))

where (x, y) are the coordinates of the point, r is the radius of the circle, and θ is the angle in radians.

To convert the angle from degrees to radians, you can use the following formula:

θ (radians) = θ (degrees) * (π / 180)

Substituting the values into the formula and converting the angle to radians, you get:

(x, y) = (10 * cos(325 * (π / 180)), 10 * sin(325 * (π / 180)))

= (-5.5, 9.5)

Therefore, the coordinates of the point on the circle with radius 10 corresponding to an angle of 325 degrees are (-5.5, 9.5).

What are the coordinates point?

The coordinates of a point in a coordinate system are a set of numerical values that specify the position of the point in relation to an origin. In a two-dimensional coordinate system, such as the Cartesian coordinate system, a point is represented by an ordered pair (x, y), where x and y are the coordinates of the point. The x-coordinate represents the point's position along the horizontal axis, and the y-coordinate represents the point's position along the vertical axis.

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Area of composite figure is 48 square feet.

What do you mean by composite figure?

A compound shape or figure is a two-dimensional figure made up of basic two-dimensional shapes such as triangles, rectangles, circles, and semicircles.

To find the perimeter of a compound 2D shape, add the lengths of the sides. Find individual regions for each part of the compound shape. The area of ​​a composite shape is the sum of its individual areas.

Let the given composite figure be divided into four rectangles A,B,C and D having dimension 3 and 4

Area of rectangle A = 3 × 4 = 12

Area of rectangle A = area of rectangle B = area of rectangle C = area of rectangle D = 12 square feet.

Total area = Area of rectangle A + area of rectangle B + area of rectangle C + area of rectangle D = 12 + 12 + 12 + 12 =48 square feet

Therefore, area of composite figure is 48 square feet.

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Answer:

The answer is 4

Step-by-step explanation:

The group candidate is 8

with a division between the number of candidates and the number of selection will the result.

8 candidates ÷ 2 candidates = 4

The way in which 2 candidates can be selected from the pool of 8 candidates to be a city commissioner is 4.

The required values of a and b for the given case are 10000 and 15.08 respectively.

An exponentially decaying function has a general form f(x) = (1 -r)ˣ, where r is called the decay rate. it can be found by having any two values of x for which f(x) is known.

The given problem can be solved as follows,

The function is f(x) = abˣ

And, the given points on the function are (0, 10000) and (3, 3430).

Substitute x = 0 and f(x) = 10000 in the f(x) to obtain,

f(0) = ab⁰

=> 10000 = a

Again, substitute x = 3 and f(x) = 3430 in the f(x) to obtain,

f(3) = ab³

=> 3430 = 10000 × b³

=> b = ∛0.3430

=> b = 15.08

Hence, the values of a and b for the given exponential function are 10000 and 15.08 respectively.

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Answer:

  x = y = 60

Step-by-step explanation:

You want the values of angles marked x° and y° in the given figure involving equilateral triangles and parallel lines.

All of the triangles in the figure are congruent equilateral triangles. Each of their internal angle measures is 60°.

  x° = y° = 60°

__

Additional comment

The (inside) base angles of the outside two triangles are alternate interior angles with respect to the top two angles of the center triangle. Hence they are congruent. The center triangle is marked as equilateral, so its angles are all 60°. That means all of the acute angles in the figure are 60°.

The cost of each apple and each orange will be $2.5 and $1.75, respectively. The cost of 1 apple and 1 orange will be $4.25.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

9 apples and 6 oranges cost $33 and 18 apples and 20 oranges cost $80.

Let 'x' be the cost of each apple and 'y' be the cost of each orange. Then the equations are given as,

9x + 6y = 33               ...1

18x + 20y = 80          ...2

Multiply equation 1 by negative 2, then we have

-18x - 12y = - 66          ...3

Add equations 2 and 3, then we have

20y - 12y = 80 - 66

8y = 14

y = $1.75

Then the cost of each apple is calculated as,

9x + 6(1.75) = 33

9x = 33 - 7.5

9x = 22.5

x = $2.5

The cost of each apple and each orange will be $2.5 and $1.75, respectively.

The cost of 1 apple and 1 orange will be given as,

⇒ $2.5 + $1.75

⇒ $4.25

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The required value of dosage in mg/min is given as 8 mg/min.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

Given that,

The dose administered per hour is 60 mL/hr.

And, the infusion is given as 4g for 500 mL.

In order to calculate the dosage in mg/min, ratio and proportion method can be used as follows,

The 500 mL is for 4g.

Then for 1 mL, there is 4/500 g.

Thus, for 60 mL, there is 4/500 × 60 g.

Since 1 g = 1000 mg.

The above expression can be written as,

4/500 × 60 × 1000 mg = 480 mg

Now, the dosage can be calculated as,

480 mg/hr

= 480/60 mg/min

= 8 mg/min

Hence, the dosage in milligram per minutes is given as 8 mg/min.

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The graph of the given function f(x)=|x−6|−4 is shown where the line is parallel to the x-axis.

A graph is a structure that resembles a set of items in discrete mathematics, more specifically in graph theory, in which some pairs of objects are conceptually "connected."

The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Write the equation in the form y = MX + b to determine the slope m and the y-intercept.

This will allow you to graph the equation using the slope and y-intercept (0, b).

So, the given function is: f(x)=|x−6|−4

Take f(x) as 0 which means:

f(x)=|x−6|−4 = 0

Now, graph the function as follows:
(Refer to the graph attached below)

The line is parallel to the x-axis.

Therefore, the graph of the given function f(x)=|x−6|−4 is shown where the line is parallel to the x-axis.

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Answer:

[tex]\huge\boxed{\sf Option \ 2}[/tex]

Step-by-step explanation:

Given that,

8 + (n - 4)

According to Associative Property:

Using Associative property for the given expression.

We get:

[tex]\rule[225]{225}{2}[/tex]

The answer to this question is = 12 + n is the expression not equivalent to 8 + (n - 4)

Let us consider any random value of n for example let us take the value of n = 5

As per the original equation given in question 8 + (n - 4) if we substitute the value of n = 5

= 8+ (5 - 4)

= 8+1

= 9

Now we will be substituting the value of n in all the answer options-

Option 1- (8 - 4) + n

= (8 - 4) + 5

= 4 + 5

= 9

Therefore, this answer matches the original equation so this is not the correct option

Option 2- (8 + 4) - n

= (8 + 4) - 5

= 13 - 5

= 9

Therefore, this answer matches the original equation so this is not the correct option

Option 3- n+4

= 5 + 4

= 9

Therefore, this answer matches the original equation so this is not the correct option

Option 4- 12 + n

= 12 + 5

= 17

Therefore, this answer does not match the original equation so the correct option is = 12 + n

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Answer:

0.009

Step-by-step explanation:

0.00892

first significant figure will be

0.00900

or = 0.009

i hope this helps

Answer:

0.009

Step-by-step explanation:

0.00892(a significant figure is a number greater than zero)

so the first number after zero is 8

the next number is 9, so round 9 up and it becomes 1.

Add 1 to 8 to give you 9

=0.00900 or 0.009

Hope it helped you

The rectangular coordinates are (-3.825,-1.169).

In a rectangular coordinate system, we were plotting points based on an ordered pair of (x, y). In the polar coordinate system, the ordered pair will now be (r, θ). The ordered pair specifies a point’s location based on the value of r and the angle, θ, from the polar axis.

The value of r can be positive, negative, or zero. The sign of r is very important in locating the exact position of the point. The absolute value of r, |r|, is the distance between the point and the pole.

1. If r is positive (r > 0) then the point lies on the terminal side of θ

2. If r is negative (r < 0) then the point lies on the ray opposite of the terminal side of θ

3. If r is zero (r = 0) then the point lies at the pole regardless of θ

Given,

P= (4,197)

Finding rectangular coordinates (x,y)

x = r cosθ

x = 4 cos 197

x = 4* (-0.956)

x = -3.825

y = r sinθ

y = 4 sin 197

y = 4*(-0.292)

y = -1.169

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Answer:

gg

Step-by-step explanation:

Answer:

Total interest paid:$112.65

Total payments:$632.65

Step-by-step explanation:

Answer: You would have to know the number of yards separate from his neighbors yard to get the answer.

Step-by-step explanation:

For example if his yard was 50 yards from his neighbors than you would add that to the width. Length plus width to get your answer.

Let (r,q) represent P's polar coordinates, with r being positive and 0 equaling q being pi/2. If so, r = 3m. And A = 0.20136

All points in a plane that are at a specific distance from a specific point, the center, form a circle.
Formula for the first circle: x²+ y² = 9

Formula for the second circle:

center is (0, 7.5) and the radius is 15/2, so

x² + (y - 7.5)² = (7.5)²

Combining these yields:

9 - y² + (y - 7.5)² = (7.5)²

9 - y² + y² - 15y + (7.5)² = 7.5²

9 - 15y = 0

y = 9/15 = 3/5

∴ y = 0.6

x² + y² = 9 = x² + (3/5)²

x² = 9 - (9/25)

x² = [(225 - 9)/25] = 216/25

∴ x = 2.9394

r = √(x² + y²) =

r = √[( 216/25) + (9/25)]

r = √(225/25) = 15/5
∴ r = 3

The x and y values appear to be accurate because this must be the same as the radius of the circle cantered at the origin.

sin(A) = y/r

sin(A) = (3/5)/3 = 1/5

Sin(A) = 0.2

∴ A = 0.20136

COMPLETE QUESTION:

A circle C has center at the origin and radius 4. Another circle K has a diameter with one end at the origin and the other end at the point (0,14). The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,q) be the polar coordinates of P, chosen so that r is positive and 0 = q =pi/2. Find r and q.

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The total years taken to double the money according to Compounding will be 12.5  years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $900

Total amount = $1800

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/1200)^12t

T = A[tex](1+r/1200)^{12t[/tex]

1800 = 900 (1+6/1200)^12t

2 = (1+1/200)^12t

2 = 1.005^12t

taking log on both sides

log 2 = 12t *log 1.005

0.3/0.002 = 12t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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The amount A in an account to the nearest cent, the amount A in the account after 10 years is $30,441.65.

Generally, To find the amount A in the account after 10 years, we can use the formula for continuous compound interest:

A(t) = A(0) * e^(rt)

where A(t) is the amount in the account after t years, A(0) is the initial amount in the account, r is the interest rate, and t is the number of years.

In this case, we know that A(0) = $15,000, A(8) = $22,377.37, and t = 10 years. We can rearrange the formula to solve for r:

r = (1/t) * ln(A(t)/A(0))

Substituting the known values, we get:

r = (1/10) * ln(22377.37/15000)

Solving this equation, we get r = 0.0658082.

Now that we have the value of r, we can use the formula for continuous compound interest to find the amount A in the account after 10 years:

A(10) = 15000 * e^(0.0658082 * 10)

Solving this equation, we get A(10) = $30,441.65.

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Answer:

Step-by-step explanation:

a. The music stalls collected Ks 3000.

b. The game stalls collected Ks 4800, which is a fraction of the total amount of money collected. To find the fraction, we can divide the amount collected by the game stalls by the total amount collected by all the stalls:

$\frac{Ks 4800}{Ks 3000 + Ks 4800 + Ks 3000} = \frac{Ks 4800}{Ks 10800} = \frac{2}{9}$

Therefore, the game stalls collected $\frac{2}{9}$ of the total amount of money.

c. The food stalls collected Ks 4800, which is a percentage of the total amount of money collected. To find the percentage, we can divide the amount collected by the food stalls by the total amount collected by all the stalls and multiply by 100%:

$\frac{Ks 4800}{Ks 3000 + Ks 4800 + Ks 3000} \times 100% = \frac{Ks 4800}{Ks 10800} \times 100% = 44.44%$

Therefore, the food stalls collected 44.44% of the total amount of money.

d. The handicraft stalls collected Ks 3000, and the music stalls collected Ks 3000. The ratio of the money collected by the handicraft stalls to the money collected by the music stalls is therefore 1:1. We can write this ratio as $\frac{1}{1} = 1$, or simply as 1.

0.933 is approximate probability that x is less than 6.3 (round off to third decimal place).

What is Probability?

Calculating or estimating how likely or "possible" something is to occur is the subject of probability.

                     Words like "certain," "impossible," or "probable" can be used to express the likelihood of an event occurring.

                      Probabilities in mathematics are always represented as fractions, decimals, or percentages with values ranging from 0 to 1.

Given X₁,X₂, ............X₃₀₀ are IID random samples from Xi ~ Gamma ( shape = 3 scale = 2 ) . The mean and variance are

     E(Xi) = 3 * 2 = 6

      Var (Xi) = 3 * 2² = 12

According to CLT,

                 X =  X₁ + X₂ +  ............+ X₃₀₀/300

has approximately normal distribution X ~ N( 6,12/300) So the probability,

       P( X < 6.3 ) = P( Z < 6.3 - 6/√12/300

    P ( X < 6.3 ) = P( Z < 1.5 )

    P (X < 6.3 ) = Ф (1.5 )

     P (X < 6.3 ) = 0.933

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A function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function is f(t) = 2900 × (1.0624)^t and APY is 6.24%.

Compound interest in simple words is the interest earning for your savings with the interest which those savings earn.

The formula for calculating the amount in Compound Interest is,

A = P( 1 + [tex]\frac{r}{n}[/tex] )ⁿᵇ

where A is the amount, P is the principal, r is the rate of interest, n is the number of times interest compounded in a year and b is the number of years.

Here, P = $2900, r = 6.1% = 0.061, n = 4 (quarterly) and b = t years

A = 2900 (1 + [tex]\frac{0.061}{4}[/tex])^4t

A = 2900 (1.0153)^4t

A = 2900 × (1.0624)^t

So A can be said as a function of t.

f(t) = 2900 × (1.0624)^t

Percentage of growth per year (APY) = ( 1 + [tex]\frac{r}{n}[/tex] )ⁿ - 1

                                                              = (1 + [tex]\frac{0.061}{4}[/tex])⁴ - 1

                                                              = 1.0624 - 1

                                                              = 0.0624 = 6.24%

Hence the function of the value of the account after t years is f(t) = 2900 × (1.0624)^t, where the value 1.0624 is a constant.

Percentage of growth per year is 6.24%.

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Answer: none of these

Step-by-step explanation:

okay, your answers b and c are the same so maybe you typed or copied them in wrong

but if the function is g(x)=1/(x+3)-5 than the answer would be…

translate it 3 right and up 5

I hope this helps!

Answer: 120

Step-by-step explanation:

We can put it in an equation like this:

6 = 5%x

Then, we solve:

6 = 1/20 x

x = 20/1 *6

x=120

Therefore, 5% of 120 is 6.

Answer:

120

Step-by-step explanation:

5/100=6/x

Cross multiply

5x=100(6)

5x=600

/5. /5

x=120

Hopes this helps please mark brainliest

Answer:

n = 45

m = 135

Step-by-step explanation:

The sum of the interior angles of a triangle is 180

180 - 55 - 80 = 45

m = the sum of 55 + 80

n= 45°;

m= 135.

The sum of all interior angles of a triangle must equa 360°. Hence, the value of n is given by the following expression:

[tex]n+55+80=180\\ \\n=180-55-80\\\\ n=45[/tex]

Since "m" and "n" are opposites angles and, since there's a straight line adjacent to them, the sum of m and n should equal 180 (check the attached image). Find m with the following expression:

[tex]45+m=180\\ \\m=180-45\\ \\m=135.[/tex]

The answers to all the parts are given below.

We have a function h = -16t² + 1800, that gives the height of the person at time [t] seconds.

[A] -

For [x] = 1000ft, we can write -

1000 = -16t² + 1800

16t² = 800

t² = (800/16)

t² = 50

t = 7.07 seconds

[B] -

For [x] = 950ft, we can write -

950 = -16t² + 1800

16t² = 850

t² = 53.125

t² = √(53.125)

t = 7.29 seconds

[C] -

The domain of the function will be -

0 ≤ x ≤ 10

[D] -

The range of the function will be -

0 ≤ h ≤ 1800

Therefore, the answers to all the parts are given above.

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Seven more than the quotient of a number b and 45 is greater than 5 then the inequality is b > -90.

What is inequality?

7 more than the quotient of a number b and 45 is greater than 5.

interpretation

7 + b/45 > 5

collect the like terms

b/45>5-7

b/45>-2

cross multiply

∴ b>-2×45

b > -90

Hence, Seven more than the quotient of a number b and 45 is greater than 5 then the inequality is b > -90.

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