You invested $11,000 in two accounts paying 3% and 7% annual interest, respectively. If the total interest earned for the year was $730, how much was invested at each rate? The amount invested at 3% is $​

The solid - I'll call it R - is best described in spherical coordinates:

[tex]R = \left\{(\rho,\theta,\varphi) \mid \sqrt{a}\le\rho\le\sqrt{b}, 0\le\theta\le2\pi, 0\le\varphi\le\dfrac\pi4\right\}[/tex]

Then the volume of R is

[tex]\displaystyle\iiint_R\mathrm dV = \int_0^{\frac\pi4}\int_0^{2\pi}\int_{\sqrt a}^{\sqrt b}\rho^2\sin(\varphi)\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi \\\\\\ \displaystyle = \boxed{\frac{2\pi}3\left(b^{\frac32}-a^{\frac32}\right)\left(1-\dfrac1{\sqrt2}\right)}[/tex]

Answer:

Step-by-step explanation:

x+15+x+115+90=380 degree(sum of interior angles of four angles is 360 degree)

2x+220=360

2x=360-220

x=140/2

x=70 degree

Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

We can find the slope by using two points

( -1,0) and (0,1)

m = (y2-y1)/(x2-x1)

   = (1-0)/(0- -1)

    = ( 1-0)/(0+1)

    1/1

Solution :

The probability of winning when you choose n is =  [tex]$^nC_2\left(\frac{1}{2}\right)^n$[/tex]

[tex]$n\left(\frac{n-1}{2}\right)\times \left(\frac{1}{2}\right)^n = n(n-1)\left(\frac{1}{2}\right)^{n+1}$[/tex]

Apply log on both the sides,

[tex]$f(n) = \log\left((n)(n-1)\left(\frac{1}{2}\right)^{n-1}\right) = \log n +\log (n-1)+(n+1) \ \log\left(\frac{1}{2}\right)$[/tex]

Differentiation, f(x) is [tex]$f'=\frac{1}{x}+\frac{1}{(x-1)}+\log\left(\frac{1}{2}\right)$[/tex]

Let us find x for which f' is positive and x for which f' is negative.

[tex]$\frac{1}{x}+\frac{1}{(x-1)} > 0.693$[/tex]       , since [tex]$\log(1/2) = 0.693147$[/tex]

For x ≤ 3, f' > 0 for [tex]$\frac{1}{x}+\frac{1}{x-1}+\log\left(\frac{1}{2}\right)>0$[/tex]

[tex]$\frac{1}{x}+\frac{1}{x-1}-0.6931470$[/tex]

That means f(x) is increasing function for n ≤ 3

[tex]$\frac{1}{x}+\frac{1}{x-1}< 0.693147 $[/tex] for x > 4

f' < 0 for n ≥ 4, that means f(n) is decreasing function for n ≥ 4.

Probability of winning when you chose n = 3 is [tex]$3(3-1)\left(\frac{1}{2}\right)^{3+1}=0.375$[/tex]

Probability of winning when you chose n = 4 is [tex]$4(4-1)\left(\frac{1}{2}\right)^{4+1}=0.375$[/tex]

Therefore, we should chose either 3 or 4 to maximize chances of winning.

The probability of winning with an optimal choice is n = 0.375

Answer:

1 miles= 1.609km

so, 25x1.609 = 40.225km

Answer:

x-intercepts= (-3,0) , (1,0) and y-intercepts= (0,-3)

For the graph part it would be graphed and shaped like a U.

Step-by-step explanation:

Hope this helps :)

Answer:

a1 = 1, a2 = 2Step-by-step explanation:

Answer:

1. Negative

2. No correlation

3. Positive

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

(B) The number of labor hours was 20.

Step-by-step explanation:

(1000-240)/38=x

760/38=x

20=x

Answer:

the work done in propelling the satellite is 919.2 mile-tons

Step-by-step explanation:

Given the data in the question;

we know that, the weight of a body varies inversely as the square of its distance from center of of earth;

⇒ F(x) = c / x²

given that F(x) = four-metric-ton = 4 × 1.102 = 4.408 tons

radius of earth = 4000 miles

we substitute

⇒ 4.408 = c / ( 4000 )²

c = 4.408 × ( 4000 )² = 70528000

so increment of work will be;

ΔW = ( 70528000 / x² ) Δx

Now work done in propelling to a height of 220 miles above Earth;

W = ₄₀₀₀∫⁴²²⁰  ( 70528000 / x² ) dx

W = 70528000[ - 1/x ]⁴²²⁰₄₀₀₀

W = 70528000[ - 1/4220 + 1/4000 ]

W = 70528000[ 1.3033175 × 10⁻⁵ ]

W = 919.2 mile-tons

Therefore, the work done in propelling the satellite is 919.2 mile-tons

Answer:

23 years

Step-by-step explanation:

Step 1: Calculate the rate constant (k) for the radioactive decay

A radioactive substance with initial concentration [A]₀ decays to 97% of its initial amount, that is, [A] = 0.97 [A]₀, after t = 1 year. Considering first-order kinetics, we can calculate the rate constant using the following expression.

ln [A]/[A]₀  = - k.t

k = ln [A]/[A]₀ / -t

k = ln 0.97 [A]₀/[A]₀ / -1 year

k = 0.03 year⁻¹

Step 2: Calculate the half-life of the substance

We will use the following expression.

[tex]t_{1/2}[/tex] = ln2/ k = ln 2 / 0.03 year⁻¹ = 23 years

Answer:

Answer:

36.8 i think

Step-by-step explanation:

Answer:

[tex]\frac{\sin(x)}{46}=\frac{\sin(45^{\circ})}{34}[/tex]

Step-by-step explanation:

In any triangle, the Law of Sines holds true:

[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]

(the ratio of any angle and its opposite side will be maintained)

Therefore, we have:

[tex]\boxed{\frac{\sin(x)}{46}=\frac{\sin(45^{\circ})}{34}}[/tex]

Answer:

19.2m

Step-by-step explanation:

"Slice" the rectangle into two right triangles (slice along the diagonal). Now you can use the Pythagorean theorem to calculate the length of the diagonal:

[tex]a^{2} +b^{2} =c^{2} \\12^{2}+15^{2} =c^{2} \\144+225=c^{2} \\\sqrt{369} =\sqrt{c^{2} }\\19.2m =c[/tex]

3800 mm

Hope it helps you...

Thank you!!

Answer:

i) 18 = 7 + 11

ii) 26 = 7 + 19

iii) 30 = 7 + 23

Step-by-step explanation:

Answer:

the probability is a fraction or a percentage, some times even a decimal

Answer:

x=49 or B)49

Step-by-step explanation:

its is a linear pair so that means it is equal to 180 degrees

you equation will be

x-18+149=180 simplify

x+131=180 subtract 131 from both sides

x=49

Answer:

6381.4 cm²

Step-by-step explanation:

Applying,

A = n/2(a×h)................ Equation 1

Where A = Area of the regular polygon, n = number of sides of the polygon, a = length of one side of the polygon, h = length of the apothem

But,

a = 2htan∅.............. Equation 2

Where ∅ = angle substands at the center by the regular polygon.

∅ = 360/n.................... Equation 3

Substitute equation 3 into equation 2

a = 2htan(360/n)........... Equation 4

Substitute equation 4 into equation 1

A = n/2[2htan(360/n)×h).............. Equation 5

From the question,

Given: n = 6 side, h = 24.78 cm

Substitute these values into equation 5

A = 6/2[24.78×24.78×2×tan(360/6)]

A = 3[24.78×(24.78×2×tan60°)]

A = 6381.4 cm²

Step-by-step explanation:

hi, this looks complicated, however, let's deal with it.

using sine rule,

we have,

a/sin A= c/sin C

4.83/sin 46= 5.5/sin C

cross multiply

4.83sin C=5.5sin 46

sin C= (5.5sin46)/4.83

sin C= 0.8191

C=sin inverse of 0.8191

C=54.99 approximately 55

since we have C, we can now find B to get b or rather AC

A+B+C=180. (sum of angles in a triangle)

46°+ B + 54.99°=180°

B+ 100.99°=180°

B°=180°-100.99°

B=79°

since we have B, we can find b or rather AC

using cosine rule,

b²=c²+a²-2 x c x a x cos B

b²= 5.5² + 4.83² - 2 x 5.5 x 4.83 x cos 79°

b²=30.25+23.33-53.13cos79

b²=53.58-10.14

b²=43.44

b=6.59 approximately 6.6

Answer:

77 boxes

Step-by-step explanation:

Take the total number of boxes and divide by the number of girls

1000 boxes / 13 girls

76.92307692

Round up

77 boxes

Check

77*13 = 1001 boxes

Answer:

77 boxes

Step-by-step explanation

Hello there! Let's solve this problem together:

First, we will review our numbers.

13 girls have to sell 1,000 boxes.

Now, we will do the math.

We will solve this problem by dividing.

We will keep multiply by one until we reach 1000 or more.

They have to each sell at least 77 boxes.

As shown in the picture, I sent two pictures.

Answer:

2x+1

Step-by-step explanation:

f(g(x))= (2x)+1

(2)x+1

Answer:

61.92

Step-by-step explanation: