If a is an inversely proportional to b and a =1.5 when b =30,what is a when b =5

An exponential function would best fit the data because as x increases, the y values change multiplicatively. The rate of change of the function is of approximately 0.8275.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant, which is the rate of change of the exponential function.

The rate of change for this problem is approximated as follows:

Hence the rate can be rounded to 0.8275.

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Answer:

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Answer:

[tex]y = 0.0625(2) {}^{x} [/tex]

Step by step

[tex]y = a(b^{x} )[/tex]

X = 1 y = 0.125

[tex]0.125 = ab^{1} \\ a = \frac{0.125}{b} [/tex]

X = 4 y = 1

[tex]1 = a( {b}^{4} ) \\ ab^{4} = 1 \\ replace \: a = \frac{0.125}{b} \: in \: ab^{4} = 1 \\ \frac{0.125}{b} \times b^{4} = 1 \\ {b}^{3} = \frac{1}{0.125} \\ b = \sqrt[3]{ \frac{1}{0.125} } \\ b = 2[/tex]

[tex]replace \: b = 2 \: in \: a = \frac{0.125}{b} \\ a = \frac{0.125}{2} \\ a = 0.0625[/tex]

[tex]therefore \: \\ y = 0.0625( {2})^{x} [/tex]

Answer:

$839.20

Step-by-step explanation:

To find the finance charge, we need to first calculate the total amount financed, which is the price of the snow thrower minus the down payment.

The down payment is 20% of $1,501, which is:

0.20 x $1,501 = $300.20

So the total amount financed is:

$1,501 - $300.20 = $1,200.80

The total amount of the 12 monthly payments is:

12 x $170 = $2,040

The finance charge is the difference between the total amount of the payments and the amount financed:

$2,040 - $1,200.80 = $839.20

Therefore, the finance charge is $839.20.

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The operating charges, including parcel  expenditure and payroll costs( including sales commissions, amounted to$ 7,242. thus, the net profit before  levies for the month of February was$ 11,758.          

Donation  periphery income statement for Naomi's Quilt Shoppe for the month of February  Deals  profit  95 bedspreads  vended

x$ 490 per spread = $ 46,550  Cost of goods  vended  95 bedspreads  vended x$ 290 cost per spread = $ 27,550  

Gross profit  Deals  profit- cost of goods  

vended = $ 46,550-$ 27,550 = $ 19,000  

Operating charges  Lease  expenditure = $ 1,300  

Payroll charges( including deals commissions)$ 1,800 8 of$ 46,550 = $ 5,942

Total operating charges$ 1,300$ 5,942 = $ 7,242.

Net profit before  levies  Gross profit- operating charges = $ 19,000-$ 7,242 = $ 11,758  .

Naomi's Quilt Shoppe's  donation  periphery income statement shows that the shop earned$ 19,000 in gross profit from dealing  95 Amish bedspreads, after paying the cost of goods  vended.

The operating charges, including parcel  expenditure and payroll costs( including deals commissions), amounted to$ 7,242. thus, the net profit before  levies for the month of February was$ 11,758.

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The linear function giving the volume of the balloon after t seconds is given as follows:

V(t) = 4 + 0.5t.

The time that it takes to fill the balloon is given as follows:

24 seconds.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

The slope and the intercept for this problem are given as follows:

Hence the linear function giving the volume of the balloon after t seconds is given as follows:

V(t) = 4 + 0.5t.

The total capacity is of 16 ft³, hence the time needed to fill the balloon is obtained as follows:

16 = 4 + 0.5t

0.5t = 12

t = 12/0.5

t = 24 seconds.

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Answer: 7.635 square meters

Step-by-step explanation:

Both triangles have the diameter as one of their sides and they both have a vertex on the circumference of the circle. Thus, the two triangles are right triangles, and the hypotenuse of the triangles is the diameter.

Use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

Square root both sides to isolate c (hypotenuse/diameter): [tex]c=\sqrt{a^2+b^2}[/tex]

Plug in the values of a and b to calculate c: [tex]c=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

The diameter of the circle is 5 meters, so the radius of the circle is 2.5 meters.

Plug in the radius into the equation for the area of a circle: Area = [tex]\pi r^2=\pi *2.5^2=6.25\pi[/tex] square meters.

The equation for the area of a triangle is [tex]\frac{1}{2}bh[/tex], where b is the base of the triangle and h is the height of the triangle.

Since we have two congruent triangles, the total area of the two triangles combined is simply b*h.

Plug in the values of b and h to get b*h = 3*4 = 12 square meters.

Subtract the total area of the two triangles combined from the area of the circle to get the area of the shaded region: [tex]6.25\pi - 12=7.635[/tex] square meters.

Answer:

Each bundle of wood weighs approximately 56.3 pounds.

Explanation:

To determine the weight of one bundle, we divide the total weight of all the bundles by the number of bundles. Thus, the weight of one bundle is equal to 3,941 pounds divided by 70 bundles, which is approximately 56.3 pounds. Therefore, each bundle of wood weighs approximately 56.3 pounds.

Find the sum of the first six terms of the geometric sequence for which a2 = 0.7 and a3 = 0.49.

Let the common ratio of the geometric sequence be r. Then we have:

a2 = ar = 0.7

a3 = ar^2 = 0.49

Dividing the second equation by the first, we get:

r = a3/a2 = 0.49/0.7 = 7/10

So the first six terms of the sequence are:

a1 = a2/r = 0.7/(7/10) = 1

a2 = 0.7

a3 = 0.49

a4 = ar^2 = 0.343

a5 = ar^3 = 0.2401

a6 = ar^4 = 0.16807

The sum of the first six terms is:

S6 = a1 + a2 + a3 + a4 + a5 + a6

S6 = 1 + 0.7 + 0.49 + 0.343 + 0.2401 + 0.16807

S6 = 2.94017

Therefore, the sum of the first six terms of the geometric sequence is approximately 2.94017.

Rewrite using radicals.

The expression (x^3/4)^2 can be rewritten as:

(x^3/4)^2 = x^3/4 * x^3/4

(x^3/4)^2 = (x^3)^2 / 4^2

(x^3/4)^2 = x^6 / 16

So (x^3/4)^2 is equivalent to (x^6/16) using radicals.

Rewrite using rational exponents.

The expression √(a^3b^2) can be rewritten using rational exponents as:

√(a^3b^2) = (a^3b^2)^(1/2)

√(a^3b^2) = a^(3/2)b^(1)

So √(a^3b^2) is equivalent to a^(3/2)b^(1) using rational exponents.

Answer:

The answer is located inside the file sent below

Step-by-step explanation:

Continuous compounding formula   e^(rt)

  2 = e^(.13 * t)                   '2' is 'double    r = .13 which is 13% in decimal

LN   both sides

   ln(2) = .13 t

   ln (2) / .13 = t = 5.33 yrs

a) According to Chebyshev's Theorem, at least 89% of the lifetimes are between 655 hours and 1201 hours.

b) According to Chebyshev's theorem, at least 75% of the lifetimes lie between 746 hours and 1110 hours.

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

The lifetimes within 2 standard deviations of the mean are given as follows:

The lifetimes within 3 standard deviations of the mean are given as follows:

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The Trigonometric functions sine (s) and cosine (c) c(5) ≈ -0.2837.

The trigonometric functions sine (s) and cosine (c). To determine s(5), we need to know the value of sine of 5 radians.

We can use a scientific calculator or a trigonometric table to find this value.

Using a calculator, we can simply enter "sin(5)" and get the answer. On most calculators, the answer will be displayed as a decimal.

Using a trigonometric table, we can look up the value of sine for 5 radians. The table will list the sine of angles in degrees, so we need to convert 5 radians to degrees first. One radian is equal to 180/π degrees, so

5 radians = (5 × 180)/π degrees ≈ 286.48 degrees

Looking up the sine of 286.48 degrees in the table, we get:

sin(286.48°) ≈ -0.9589

Therefore, s(5) ≈ -0.9589.

To determine c(5), we need to know the value of cosine of 5 radians.

We can again use a calculator or a trigonometric table to find this value.

Using a calculator, we can enter "cos(5)" to get the answer.

Using a trigonometric table, we can look up the cosine of 5 radians. Since we have already converted 5 radians to degrees, we can simply look up the cosine of 286.48 degrees in the table. We get:

cos(286.48°) ≈ -0.2837

Therefore, c(5) ≈ -0.2837.

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The measure of x is 25.2 degree

Given that,

Total number of votes = 3200

Bowerman's share = 224

Now the percentage of  Bowerman's  share = (224/3200)x100

                                                                         = 7%

Now we know that.

The complete angle of circle is 360 degree.

Therefore the value of x shown in the figure is,

x = 7% 360

  = (7 x 360)/100

  = 25.2 degree

Therefore,

⇒ x  = 25.2 degree

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The Standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.

To write an expression in standard form, we need to arrange the terms in descending order of degree and combine like terms.

The given expression is:

48 + 24x3 - x + 10x4 - 5x2

First, we arrange the terms in descending order of degree:

10x4 + 24x3 - 5x2 - x + 48

Next, we combine the like terms:

10x4 + 24x3 - 5x2 - x + 48 = 10x^4 + 24x^3 - 5x^2 - x + 48

Therefore, the standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.

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The y-intercept of the graph of 3x + y = 6 is (0,

A graph of 3x + y = 6 is shown in the image below.

A graph of x + y = 4 is shown on the same grid in the image below.

A solution to the simultaneous equations is (1, 3).

In Mathematics, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear equation or function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the information provided about the equation, the y-intercept can be calculated as follows:

3x + y = 6

y = -3x + 6

f(0) = -3(0) + 6

f(0) = 0 + 6

f(0) = 6.

Based on the graph shown (see attachment), we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph, which is given by the ordered pair (1, 3).

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The surface area of the Triangular pyramid is approximately 331.3 square millimeters.

The surface area of a triangular pyramid, we need to calculate the area of its base and the area of each triangular face, then add them together. The formula for the surface area of a triangular pyramid is:

SA = (1/2)P*l + B

where SA is the surface area, P is the perimeter of the base, l is the slant height of each triangular face, and B is the area of the base.

In this case, the base of the triangular pyramid is an equilateral triangle with legs of 13 millimeters and a height of 11.3 millimeters. To find the area of the base, we can use the formula for the area of an equilateral triangle:

B = (sqrt(3)/4)*a^2

where a is the length of a side of the equilateral triangle.

Substituting a = 13 into the formula, we get:

B = (sqrt(3)/4)*13^2

B = (sqrt(3)/4)*169

B = 43.7 square millimeters (rounded to one decimal place)

Next, we can find the perimeter of the base:

P = 3a

P = 3*13

P = 39 millimeters

Now we can use the formula for the surface area of a triangular pyramid:

SA = (1/2)P*l + B

Substituting P = 39, l = 17, and B = 43.7, we get:

SA = (1/2)*39*17 + 43.7

SA = 331.3 square millimeters (rounded to one decimal place)

Therefore, the surface area of the triangular pyramid is approximately 331.3 square millimeters.

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The monthly payments you can withdraw from the retirement account is $1,583.4.

The monthly payments you can withdraw from the retirement account, is calculated as;

PV = Px [(1 - (1 + r)⁻ⁿ) / r]

where;

The total number of periods = 25 years x 12 months/year = 300 months

PV = P x [(1 - (1 + r)⁻ⁿ) / r]

$300,000 = P x [(1 - (1 + 0.04/12)⁻³⁰⁰) / (0.04/12)]

$300,000 = P x 189.47

P = $300,000 / 189.47

P= $1,583.4

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The exponential function for the data in the table is given as follows:

[tex]y = 0.0625(2)^x[/tex]

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

When the input x increases by one, the output y is doubled, hence the parameter b has the value given as follows:

b = 2.

The parameter a is the value of y when x = 0. When x = 1, the output is double when x = 0, as b = 2, hence:

2a = 0.125

a = 0.0625.

Thus the function is:

[tex]y = 0.0625(2)^x[/tex]

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The net force on the knot is 42.7 N. Therefore, option D is the correct answer.

The force of 301 N to the North can be broken into components of 301 N in the x-direction and 0 N in the y-direction.

The force of 280 N at 10.0° South of East can be broken into components of 250.5 N in the x-direction and -247.8 N in the y-direction.

The force of 313 N to the Southwest can be broken into components of -208.1 N in the x-direction and -278.9 N in the y-direction.

The net force is then the sum of the components in both the x- and y-directions.

The net force in the x-direction is 301 N + 250.5 N - 208.1 N = 343.4 N and the net force in the y-direction is 0 N - 247.8 N - 278.9 N = -526.7 N.

The net force is then the hypotenuse of a right triangle with the x- and y-components as the legs.

The net force is thus equal to √(343.4 N² + (-526.7 N)²) = 42.7 N.

Therefore, option D is the correct answer.

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The x intercepts of the parabola are -1 + i√(2) and -1 - i√(2)

Using the equation:

y = a(x - h)²+ k

where (h, k) is the vertex of the parabola

y = a(x  + 1)²+ 2

solving for a at the y intercept

y = a(x  + 1)²+ 2

3 = a(0  + 1)²+ 2

a = 1

To find the x intercepts we need to set y = 0 and solve for x:

0 = (x  + 1)²+ 2

x + 1 = ±√(-2)

x + 1 = ±i√(2)

x = -1 ± i√(2)

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The linear equation that gives the graph expression is: d = 2h

The general formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

We are given the equation as: d = rh

where:

d is dollars

r is rate

h is hours,

From the graph, we can find the rate by finding the slope of the graph.

(1, 4) and (2, 8)

Thus:

Slope = (8 - 4)/(2 - 1)

Slope = 2

Thus, r = 2

Then d = 2h

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The speed of the plane in calm air is 372 km/h

Given that a plane is travelling from Winnipeg to Calgary against a 50 km/hr headwind.

This flight takes half an hour longer than it would in calm air.

The distance between Winnipeg and Calgary is 1200 km.

Since we know that,

Speed may be defined as the distance travelled by an item in relation to the time it takes to travel that distance.

In other words, it measures how rapidly an item travels but does not provide direction. The term "velocity" refers to the combination of direction and speed.

The speed is defined by the rate of distance.

We must determine the plane's speed in calm air.

xy=1200

(x-50)(y+1/2) =1200

x² - 50 x-12000=0

By using quadratic formula.

x=372 as x>0

Hence, 372 km/h is the speed of the plane in calm air

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The number 1 is a solution to the equation 2x = 2.

We have the Equation

2x = 2

Now, dividing both side by 2 we get

2x/2 = 2/2

x = 1

So, the number 1 is a solution to the equation 2x = 2.

When x is 1, the left side of the equation becomes 2(1) = 2, which is equal to the right side of the equation.

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Step-by-step explanation:

Starting with the equation E = mgh, we can solve for h in terms of E, m, and g as follows:

E = mgh

Divide both sides by mg:

E/mg = h

Therefore, h = E/mg.

So the solution for h in terms of E, m, and g is h = E/mg.

Answer:

5(x + 3)

Step-by-step explanation:

the sum of x and 3 is x + 3, then multiply by 5 to obtain

5(x + 3)

Answer:

A translation of (x+6, y-3)

Step-by-step explanation:

X goes left or right, while Y goes up or down. So, to move the triangle 6 units to the right, we take our current x coordinate, and add 6 to it.

The figure shows a graph of the function fx in the coordinate plane. f2 is greater than g2.

As the graph of function f(x) is a parabola, so that the equation of function f(x) is:

f(x) = [tex]ax^2+bx+c[/tex]

As it can be seen in thee figure, the graph of function f(x) cross points (0;8) ;(-2; 0) and (4;0)

=> f(0) = 8; f(-2) = 0; f(4) = 0

We have:

f(x=0) = a x 0 + b x 0 + c = 8  => c = 8

We have:

+) 4a -2b + 8 = 0 => 2 x (4a -2b + 8) = 8a - 4b + 16 = 0 (1)

+) 16a + 4b + 8 = 0 (2)

We take (2) minus (1)

=> (16a + 4b + 8) - (8a - 4b + 16) = 0

=> 8a - 8 = 0 => a = 1

Replace a = 1 into (1)

=> 8 x 1 - 4b + 16 = 0 => b = 6

f (2) = 2^2 + 6 x 2 + 8 = 24

g (2) = 3 -2 + 2 = 3

Thus, f(2) is greater than g(2).

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If a rectangular container is 25cm by 37cm by 21cm, then it will overflow after reaching the volume of 19425 cm³.

To know the volume after which the container will overflow, first we have to calculate the volume it can contain.

As, Volume of cuboid= length × breadth × height

So, Volume of rectangular container = 25 × 37 × 21 cm³

Volume = 19425 cm³

So, volume of rectangular container whose dimensions are  25cm by 37cm by 21cm is 19425 cm³ and it will overflow after reaching this volume.

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