the length of a rectangle is 6ft longer than it's width. if the perimeter of the rectangle is 32ft​

1. The velocity at time t , v(t) = (18t² + 3 ) m/s

2. The velocity at time t = 3 seconds = 165 m/s

3. The acceleration at time t, a(t) =( 36t )m/s²

4. The acceleration at time t = 3 seconds = 108 m/s²

The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity.

Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.

1. s(t) = 6t³ + 3t +9

to find the velocity at time t, we differentiate s(t)

= 18t² + 3

2. at t = 3s

= 18(3)² +3

= 165 m/s²

3. v(t) = 18t² + 3

to get the acceleration at time t, we differentiate v(t)

= 36t

4. when t = 3

a = 36 × 3

= 108 m/s²

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Answer:

17.637 ounces

Step-by-step explanation:

35.274 ounces is 1 kilogram so divide 35.274 by 2

The circular is around 305 cm in circumeference.

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle.

Substituting d = 97 cm and using the value of π to be 3.14159, we get:

C = πd

C = 3.14159 × 97 cm

C ≈ 304.731 cm

Rounding this to 3 significant figures, we get:

C ≈ 305 cm

Therefore, the circumference of the circle is approximately 305 cm.

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Answer:

i think is -1 because the value is -1

Answer:

D. -1

Step-by-step explanation:

ed2021

Answer:

\(P(Work | Senior) = 0.14\)

Step-by-step explanation:

Given

The attached table

Required

\(P(Work | Senior)\)

This is calculated using:

\(P(Work | Senior) = \frac{P(Work \ n\ Senior)}{P(Senior)}\)

This gives:

\(P(Work | Senior) = \frac{n(Work \ n\ Senior)}{n(Senior)}\)

From the table:

\(n(Work \ n\ Senior) = 5\)

\(n(Senior) = 25 + 5+ 5 = 35\)

So:

\(P(Work | Senior) = \frac{5}{35}\)

\(P(Work | Senior) = 0.14\)

Answer:

14%

Step-by-step explanation:

add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).

Answer:

I'm so sorry no answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that the radius of the circle is √91 units and its centre is (-3,2) .

We know that the standard equation of circle is,

\(\longrightarrow (x-h)^2+(y-k)^2=r^2 \\\)

where,

On substituting the respective values, we have;

\(\longrightarrow \{ x-3\}^2+\{ y-(-2)\}^2= (\sqrt91)^2 \\\)

Simplify,

\(\longrightarrow \red{ (x-3)^2+(y+2)^2=91} \\\)

This is the required equation of the circle.

Answer:

(x - 3)² + (y + 2)² = 91

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (3, - 2 ) and r = \(\sqrt{91}\) , then

(x - 3)² + (y - (- 2) )² = ( \(\sqrt{91}\) )² , that is

(x - 3)² + (y + 2)² = 91 ← equation of circle

Answer: y=1.25

Step-by-step explanation:

First things first you have to find what is in the bracket things (i don’t know what it’s called) So 3 - 7 is -4y but since it’s absolute it’s going to be 4y.

So now you’ve got 4y - 10 = -5. Your going to want to eliminate 10 so, subtract 10 to both sides giving you 4y = -5

Lastly to get y by itself you need to divide it by its self so, 4y divided by 4. Do it to both sides. This gives you…

Y = 1.25

Answer:

Adjacent Angles are 2 angles with common sides and a common vertex that don't overlap in any way.

Step-by-step explanation:

Leave a comment if you need any more help. Give Brainiest, please.

If the Federal Reserve sells $60,000 in Treasury bonds to a bank at 8% interest, the immediate effect on the money supply is B. It is decreased by $60,000.

One of the monetary factors that decreases the money supply in the economic is when the Federal Reserve raises the banks' reserve requirements.

Another factor that can decrease the money supply is the sale of treasury bonds to banks.

Raising the interest rates also decreases the money supply.

Thus, by selling $60,000 in Treasury bonds to a bank at 8% interest, it decreases the money supply.

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Answer:

\(\frac{10x^2+3}{y^2+4}\)

Step-by-step explanation:

When adding rational numbers, if the denominator is the same you simply keep the denominator (bottom of fraction) as it is and apply the operation given to the numerator ( top of fraction )

So we have \(\frac{6x^2+5}{y^2+4} +\frac{4x^2-2}{y^2+4} =\frac{(6x^2+5)+(4x^2-2)}{y^2+4}\)

==> remove parenthesis and apply signs

\(\frac{x^2+5+4x^2-2}{y^2+4}\)

==> simplify numerator by combining like terms

\(\frac{10x^2+3}{y^2+4}\)

and we are done!

Note:

like terms are terms with the same variable and exponent

An example of like terms are 6x^7 and 3x^7 as they have x as a variable and a power of 7

The like terms being combined here were (6x² and 4x²) and (5 and -2)

Answer:

\(\frac{10x^{2} +3}{y^{2}+4 }\)

Step-by-step explanation:

\(\frac{6x^{2} +5}{y^{2}+4 } +\frac{4x^{2} -2}{y^{2}+4 }\)

make the common denominator

\(\frac{6x^{2} +5+4x-2}{y^{2}+4 }\)

combone the like terms

\(\frac{10x^{2} +5-2}{y^{2}+4 }\)

subtract numbers

\(\frac{10x^{2} +3}{y^{2}+4 }\)

we have to do alot for this

so first we gotta change 12.3 into a mixed fraction

n = 5 so 5 ÷ 12.3

If the test's p-value is less to 0.05, we should reject the null hypothesis therefore decide that the diet plan is beneficial since we will adopt a significance level of a=0.05.

Under this situation, the appropriate null as well as alternative hypothesis would be:

H0: μbefore = μafter

H1: μbefore > μafter

As we are only concerned with whether the clients' weight has fallen as a result of the diet program, this constitutes a one-tailed test.

If the test's p-value is less to 0.05, we should reject the null hypothesis therefore decide that the diet plan is beneficial since we will adopt a significance level of a=0.05.

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The formula relating mass, density, and volume is:

Let's find density of both of them.

1. Helium

Mass = 12.99

Volume = 29 ml

So, Density is:

2.Carbon Dioxide

Mass = 17.2

Volume = 75 ml

So, Density is:

Of course, the denser gas would be helium.

Last Answer Choice is right, Helim with 0.44 g/ml

Answer:

no, it isnt

Step-by-step explanation:

Answer:

$20

Step-by-step explanation:

2=10

4=20

The equation that best describes the relation is y = -x+1 ( optionD)

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Taking x(0,1) and y ( 1,0)

therefore the slope of the line

= 0-1/1-0

= -1/1 = -1

the equation a line is given as

y-y1 = m(x-x1)

= y-1 = -1( x - 0)

= y-1 = -x

y = -x +1

therefore the equation that describe relation is y = 1-x or y = -x+1

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Answer:

45 degrees

Step-by-step explanation:

DBC: 180 - 135

DBC: 45 degrees

Hope that helps!

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Answer:Monthly payment is $682.06

Step-by-step explanation:

Answer:

The formula to calculate the final cost:

C = 130000 x (1  + (4.8/100)/12)^(30 x 12) = 547116.69

Minimum payment each month:

M = 547116.69/(30 x 12) = 1519.77

Interest they have to pay: 547116.69 - 130000 = 417116.69 dollar

Hope this helps!

:)

Answer: 50in²

Step-by-step explanation:

The area of the ice cream cone will be equal to 50.13 square inches.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the semicircle in a two-dimensional plane is called the area of the semicircle.

The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

Given that the diameter of the semicircle is 6 inches and the height of the triangle is 12 inches.

The area of the cone will be calculated as,

A = Area of semicircle + Area of triangle

A = (1/2)πr² + (1/2) x B x H

A = (1/2) π (3)² + (1/2) x 12 x 6

A = 14.137 + 36

A = 50.13 square inch

Therefore, the area of the ice cream cone will be equal to 50.13 square inches.

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The difference in overall gain between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price is $239.50.

To determine the difference in overall gain or loss between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price, we need to calculate the selling prices of the stocks.

Stock A:

High price = $105.19

Low price = $103.25

Close price = $103.38

Stock B:

High price = $145.18

Low price = $143.28

Close price = $144.05

The investor purchased 50 shares of stock A at $90 per share and 75 shares of stock B at $145 per share.

To calculate the selling prices, we need to multiply the number of shares by the respective selling price.

Selling price of stock A at the high price: 50 shares \(\times\) $105.19 = $5,259.50

Selling price of stock A at the low price: 50 shares \(\times\) $103.25 = $5,162.50

Selling price of stock B at the high price: 75 shares \(\times\) $145.18 = $10,888.50

Selling price of stock B at the low price: 75 shares \(\times\) $143.28 = $10,746.00

Now, let's calculate the difference in overall gain or loss:

Difference in overall gain = Selling price at the high price - Selling price at the low price

= ($5,259.50 + $10,888.50) - ($5,162.50 + $10,746.00)

= $16,148.00 - $15,908.50

= $239.50

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Answer:

Multiply 7 by 3.

Step-by-step explanation:

In PEMDAS, parenthesis, exponents, multiply, divide, addition, subtratcion, you start with parenthesis first. Then you look inside the parenthesis, and ythere is no division problems. So you do the multiplication inside the parenthesis.

Answer:

0.6

Step-by-step explanation:

Answer: 0.5

Step-by-step explanation:

Since the three portfolios are 20%, 30% and 50%, and the 20% and 30% are already there in the form of 0.2 and 0.3, then Z must be the 50%, or 0.5

Answer:

Four and twenty nine thousandths

Step-by-step explanation:

Answer:

117in

Step-by-step explanation: 9in x 13in=117in

So, Edward needs to use a round cast iron pan with a radius of 177 inches to have the same area as the rectangular pan. correct answer is (d).

To find the area of a circle, you need to know its radius (the distance from the center of the circle to any point on its perimeter). Once you know the radius, you can use the following formula:

\(Area = \pi * radius^2\)

where π (pi) is a mathematical constant approximately equal to 3.14159.

So, to find the area of a circle, follow these steps:

Measure the radius of the circle.

Square the radius (multiply it by itself).

Multiply the squared radius by π.

Round your answer to the desired number of decimal places (usually 1 or 2).

The area of a 9-in. by 13-in. rectangular pan is:

Area = length x width = 9 in. x 13 in. = 117 in.²

So, the area of the rectangular pan is 117 in.².

To use a round cast iron pan with the same area, Edward needs to find the radius of the circle with an area of 117 in.²:

Area of a circle = πr²

\(= \pi r^2\)

\(= 117 in.^2 /\)

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the complete question: Edward's grandmother used to make him Pannukakku when he was little. He wants to surprise.

her by making it himself. The recipe he found requires a 9-in. by 13-in. rectangular pan.

Edward would like to use a round cast iron pan like his grandmother does.

What is the area of a 9-in. by 13-in. pan?

\((a) 22in^{2} \\(b)44in^{2} \\(c)108in^{2} \\(d)117in^{2}\)

Answer:

\(A)58\)

Step-by-step explanation:

\([Kindly\ refer\ the\ attachment]\\We\ are\ given:\\GH\ is\ the\ diameter\ of\ the\ circle.\\ Also,\\ GM=3\ units\ and\ MH=7\ units\\From\ the\ figure,\\GH\ subtends\ an\ angle\ at\ two\ points\ specifically\ M\ and\ N\ on\ the\\ arc.\\Now,\\We\ know\ that,\\'The\ Angle\ subtended\ by\ the\ diameter\ anywhere\ over\ the\ arc\ of\ the\\ circle\ is\ always\ 90\ degrees'.\\Hence,\\\angle GMH\ = \angle GNH=90\\\)

\(Also,\\Pythagoras\ Theorem\ states\ that: 'In\ a\ right\ triangle,\ the\ sum\ of\ squares\\ \ of\ the\ legs\ is\ equal\ to\ the\ square\ of\ the\ hypotenuse'\\In\ \triangle GMH,\\Since\ \angle GMH=90,\\GM^2+MH^2=GH^2[Through\ Pythagoras\ Theorem]\\Hence,\\Substituting\ GM=3,\ MH=7:\\3^2+7^2=GH^2\\GH^2=9+49=58\)

\(Similarly,\\In\ \triangle GNH,\\Since\ \angle GNH=90,\\GN^2+NH^2=GH^2\\Hence,\\Substituting\ GN=x\ and\ NH=y:\\x^2+y^2=GH^2\\x^2+y^2=58\)