The weekly salary of a security guard, $S, is based on the formula, S=B+8H where B is the basic wage in dollars, and H is the number of hours he is on duty per week.

(a) Given that the security guard received $710 for a total of 45 hours of work in a particular week, find the basic wage.

(b)
(i) Calculate the salary he received after working for 42 hours in one week.
(ii) At the end of another week, the security guard earned $662. Find the number of hours worked that week.​

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ty! ~

Answer:

0.32

Step-by-step explanation:

3/10=0.3

2/5=0.4

0.32 is between these two numbers.

Hope this Helps

Answer:

24

Step-by-step explanation:

6/2 = x/8

x=24

24 oil changes

The area inside one leaf of the rose: r=6sin(6θ) is 3π/2 after evaluating the integral over the limit 0 to  π/6

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have:

r=6sin(6θ)

First we have to find the limits:

r = 0

6sin(6θ) = 0

θ = nπ/6

n = 0 to n = 1

θ = 0 to  θ = π/6

[tex]\rm Area = \int\limits^{\dfrac{\pi}{6}}_0 {6sin6\theta} \, d\theta[/tex]

After calculating the above definite integral, we will get:

Area = 3π/2

Thus, the area inside one leaf of the rose: r=6sin(6θ) is 3π/2 after evaluating the integral over the limit 0 to  π/6

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The region outside the circle r = 3 and inside the circle r = - 6cos θ is given below.

[tex]\rm Area = \dfrac{12\pi - 9\sqrt3 }{2}[/tex]

When the two curves intersect then they bound the region is known as the area bounded by the curve.

The region outside the circle r = 3 and inside the circle r = - 6cos θ

Then the value of the θ will be

[tex]\begin{aligned} -6\cos \theta &= 3\\\\\cos \theta &= -\dfrac{1}{2}\\\\\theta &= -\dfrac{2\pi}{3}, \dfrac{2\pi}{3} \end{aligned}[/tex]

Then the area will be given as

[tex]\rm Area = \dfrac{1}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [-6 \cos \theta)^2 - 3^2 ] d \theta \\\\\\Area = \dfrac{1}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [18 (2\cos ^2 \theta ) - 9]d \theta \\\\\\Area = \dfrac{9}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [2(1 + \cos 2\theta ) - 1] d \theta \\\\\\Area = \dfrac{9}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [2 \cos 2\theta ) + 1] d \theta \\\\[/tex]

[tex]\rm Area = \dfrac{9}{2} [ \sin 2\theta + \theta ] _{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} \\\\\\ Area = \dfrac{9}{2} [ \sin 2( \frac{2\pi}{3}) +\frac{2\pi}{3} - \sin 2 (\frac{2\pi}{3}) - \frac{2\pi}{3}] \\\\\\[/tex]

On simplifying, we have

[tex]\rm Area = \dfrac{12\pi - 9\sqrt3 }{2}[/tex]

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Answer:

30.96

Step-by-step explanation:

First you must find the diameter of the circle which is 12

Then you must use the formula A=πr²

So it should be = to A = 3.14 ×144 which is 30.96

[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]

[tex] \large\underline{ \boxed{ \sf{✰\:Notes }}}[/tex]

[tex] \rule{70mm}{2.9pt}[/tex]

[tex] \large\underline{ \boxed{ \sf{✰\: formule\: used\:✰ }}}[/tex]

[tex]{ \boxed{✟\underline{ \boxed{ \sf{\: Area \: of \: circle = \pi {r}^{2} \: }}}✟}}[/tex]

[tex]{ \boxed{✟\underline{ \boxed{ \sf{\: Area \: of \: square = side \times side \: or \: ( {s}^{2}) \: }}}✟}}[/tex]

[tex] \rule{70mm}{2.9pt}[/tex]

✛ 1st taking out the the area of circle✛

[tex] \qquad \rm{➛ \: radius(r) = \frac{12}{2} } \\ \\ \qquad \rm{➛ \: radius(r) = \frac{ \cancel{12}}{ \cancel2} } \\ \\ \qquad \rm{➛ \: radius(r) =6m}[/tex]

[tex] \\ \qquad \rm{➛Area \: of \: circle = 3.14 \times {6}^{2} \:} \\ \\ \qquad \rm{➛Area \: of \: circle = \:3.14 \times 36} \\ \\ \qquad \rm{➛Area \: of \: circle = \:113.04 {m}^{2} }[/tex]

[tex] \rule{70mm}{2.9pt}[/tex]

✛ now finding the area of square✛

[tex]\\ \qquad \rm{➛Area \: of \:square = 12×12} \\ \\ \\ \qquad \rm{➛Area \: of \:square = 144 {m}^{2} }[/tex]

[tex]\\ \rm{➛Area \: of \:shaded \: part = \: area \: of \: circle - area \: of \: squre} \\ [/tex]

★ Let's substitute value ★

[tex]\\ \rm{➛Area \: of \:shaded \: part =113.04-144} \\ \\ \qquad \rm{➛Area \: of \:shaded \: part =30.96 {m}^{2} }[/tex]

[tex] \rule{70mm}{2.9pt}[/tex]

★ Hence area of shaded part =

[tex]{ \boxed{✜\underline{ \boxed{ \sf{ \: 30.96 {m}^{2} \green✓\: }}}✜}}[/tex]

★ note here we neglect minus (-)

[tex] \rule{70mm}{2.9pt}[/tex]

Hope it helps !

The number of tops on the 6th day based on the exponential model is 64, and the number of tops on the 6th day based on the linear model is 17.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where a is a constant and a>1

First day class collected = 2 tops

Third day class collected = 8 tops

The exponential function can be modelled:

[tex]\rm D(N) = 2^N[/tex]

D(1) = 2  (first day)

D(3) = 8  (third day)

D(6) = 64 (sixth day)

The linear function can be modeled:

D(N) = 3N -1

D(1) = 2  (first day)

D(3) = 8 (third day)

D(6) = 17 (sixth day)

Thus, the number of tops on 6th day based on exponential model is 64, and the number of tops on the 6th day based on the linear model is 17.

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Answer: 113 ( 34x3+11

Step-by-step explanation:

34x 3 on top + 7 + 24/6

34 x 3 on top + 7 = 4

34 x 3 on top + 7 + 4

34 x 3 on top + 11

34 x 3 on top + 11

Answer:

Step-by-step explanation:

(1 + 11)/(-2+5)= 12/3=4

y + 11 = 4(x + 5)

y + 11 = 4x + 20

y = 4x + 9

The Solution of -x +y = 84, x + 3y = 12, x - 7y + z = 15 be [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

The correct option is (C)

The inverse of matrix is another matrix, which on multiplying with the given matrix gives the multiplicative identity.

Given equation are:

-x +y = 8

4x + 3y = 12

x - 7y + z = 15

So,

[tex]\left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right] \;*\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

then,

[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \; \left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right]^{-1} \; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

Now, Calculating the inverse of Matrix we have,

[tex]\left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right]^{-1} \;[/tex] =      [tex]\left[\begin{array}{ccc}-3/7&1/7&0\\4/7&1/7&0\\31/7&6/7&1\end{array}\right][/tex]

so, [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; = \;\left[\begin{array}{ccc}-3/7&1/7&0\\4/7&1/7&0\\31/7&6/7&1\end{array}\right]\; \left[\begin{array}{ccc}8\\12\\15\end{array}\right][/tex]

[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-12/7\\44/7\\425/7\end{array}\right][/tex]

 [tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

Hence ,[tex]\; \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \; =\left[\begin{array}{ccc}-1.76\\6.24\\60.76\end{array}\right][/tex]

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The positive integer for which g(x) first exceeds f(x) is 178 according to the number line.

The function f of (x) is used to denote a linear algebra that can be represented on the graph.

Given that:

We are to determine a positive integer for which g(x) first exceeds f(x). Using the following option;

Therefore, we can conclude that the positive integer for which g(x) first exceeds f(x) is 178 according to the number line.

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Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

1. Convert both mixed numbers into improper fractions:

[tex]\frac{15}{4} x = \frac{5}{4}[/tex]

2. Multiply both sides by 4:

4 · [tex]\frac{15}{4} x=\frac{5}{4}[/tex] · 4

15x = 5

3. Isolate x:

x = 1/3

hope this helps!

Step-by-step explanation:

cubic root(56) + cubic root(189) =

= cubic root(7×8) + cubic root(27×7) =

= 2×cubic root(7) + 3×cubic root(7) = 5×cubic root(7) =

= 9.564655914...

Answer:

[tex]P(X=3)\approx27\%[/tex]

Step-by-step explanation:

Use the binomial distribution

[tex]\displaystyle P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}\\\\P(X=3)=\binom{4}{3}(0.52)^3(1-0.52)^{4-3}\\\\P(X=3)=\frac{4!}{3!(4-3)!}(0.52)^3(0.48)^1\\ \\P(X=3)=0.26996736\\\\P(X=3)\approx0.27\\\\P(X=3)\approx27\%[/tex]

Therefore, the probability that exactly 3 students out of 4 randomly chosen students have brown hair is about 27%

Answer:

here

Step-by-step explanation:

find the circumference of the lid (this is like a side length of a rectangle)

2*pi*2= 12.566in

Then multiply by 3 (the other side length)

12.566*3= 37.7in squared :)

Answer:

B is the correct answer from my understanding

Step-by-step explanation:

The movement of the particle on the circle is its displacement.

The value of dy/dt at this time is -9/2.

Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.

A particle moves on the circle x^2 + y^2=25 in the XY-plane for time t≥0. At the time when the particle is at the point (3,4), dxdt=6.

The equation of the circle is given as:

[tex]\rm x^2 + y^2=25[/tex]

Differentiate with respect to time

[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0[/tex]

Substitute all the values in the equation

[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0\\\\2(3) \times 6+2(4)\times \dfrac{dy}{dt}=0\\\\ 6 \times 6+8 \times \dfrac{dy}{dt}=0\\\\ 36+8\times \dfrac{dy}{dt}=0\\\\ 8\times \dfrac{dy}{dt}=-36\\\\ \dfrac{dy}{dt}= \dfrac{-36}{8}\\\\ \dfrac{dy}{dt}= \dfrac{-9}{2}[/tex]

Hence, the value of dy/dt at this time is -9/2.

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Answer:

45.5 m²

Step-by-step explanation:

Area (Shaded) = Area (Rectangle) - Area (Trapezoid)

Area of trapezoid:-

Area of triangle:-

Which part is shaded not said so both shaded regions area calculated

Answer:

its 3

Step-by-step explanation:

id ont know the formula but im certain im a very smart 6th grader!

Answer:

6

Step-by-step explanation:To find the median, first order your data. Then calculate the middle position based on n, the number of values in your data set. If n is an odd number, the median lies at the position (n + 1) / 2. If n is an even number, the median is the mean of the values at positions n / 2 and (n / 2) + 1.

Answer:

6

Step-by-step explanation:

Answer:

10 times

Step-by-step explanation:

4 in 547 is equal to 40

4 in 84 is equal to 4

When you separate that number into smaller parts

Ex: 547 = 500 + 40 + 7

The completed code to generate and save a number in the program which allow a user to guess a number from (1,10) is input.

Program or programming is the combination of codes. These codes are used to generate the program such that a machine can understand the inputs given to it.

The program is written to allow a user to guess a number. This number should be between the number 0 to 10.

Here, the input is needed to a machine or computer, for which it's process the number and show if the guessed number is correct or not.

Hence, the completed code to generate and save a number in the program which allow a user to guess a number from (1,10) is input.

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Answer:

[tex]\csc \left(x\right)=\frac{\csc \left(x\right)+\sec \left(x\right)}{1+\tan \left(x\right)}[/tex]

[tex]=\frac{1}{\sin \left(x\right)}[/tex] (expressed with sine and cosine)

[tex]\frac{1}{\sin \left(x\right)}=\csc \left(x\right)[/tex]

[tex]=\csc \left(x\right)[/tex]

Therefore, the identity has been proven true.

Answer:

[tex]\textsf{Area of a triangle}=\dfrac{1}{2} ab \sin C[/tex]

(where [tex]a[/tex] and [tex]b[/tex] are the sides, and [tex]C[/tex] is the included angle)

[tex]\textsf{Area of a sector}= \dfrac{\theta}{360} \pi r^2[/tex]

(where [tex]\theta[/tex] is the angle in degrees and [tex]r[/tex] is the radius)

Therefore, using the above formulas:

[tex]\begin{aligned}\textsf{Area of segment } \rm (A) & = \textsf{area of sector}- \textsf{area of triangle}\\& = \dfrac{\theta}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin \theta\\\end{aligned}[/tex]

Given:

Substitute the given values into the formula and solve for r:

[tex]\begin{aligned}\implies 20 & = \dfrac{90}{360} \pi r^2 - \dfrac{1}{2}r^2 \sin 90\\\\20 & = \dfrac{1}{4} \pi r^2 - \dfrac{1}{2}r^2 (1)\\\\20 & = \left(\dfrac{1}{4} \pi -\dfrac{1}{2}\right)r^2\\\\20 & = \left(\dfrac{\pi -2}{4}\right)r^2\\\\r^2 & = 20\left(\dfrac{4}{\pi -2}\right)\\\\r^2 & =\dfrac{80}{\pi-2}\\\\r & =\sqrt{\dfrac{80}{\pi-2}}\\\\r & = 8.37\: \sf (2\:dp)\end{aligned}[/tex]

Answer:

-13f

The length of the hypotenuse will be equal to H=122.25 when value of x=14.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal the square of the sum of the other two sides.

It is given that:

Value of x=14

The perpendicular is  =6x+5=6x14+5=89

The base is  =6x=84

So by using the Pythagorean theorem:-

[tex]H^2=P^2+B^2\\\\\\H^2=89^2+84^2\\\\\\H=\sqrt{89^2+84^2}\\\\\[/tex]

Hence the value of hypotenuse will be H=122.25

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The value of the expressions (-0.3)⁴ equal to 0.0081.

A mathematical expression is the representation of numbers in the form of powers or mathematical signs.

Here we have the (-0.3)⁴

Now by evaluating the expression we will get:

(-0.3)⁴=(-0.3x-0.3x-0.3x-0.3)

Hence the value of the given expression will be 0.0081

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Answer:

Step-by-step explanation

the figure is composed of a square with an isosceles right triangle inside, we find the area of ​​the square and we take away the area of ​​the triangle.

Triangle area = lxl, right-angled triangle area side by side divided by two.

8 * 8 = 64cm²

6 * 6 : 2 = 18 cm²

Area of the shaded region

64 - 18 = 46 cm²

Answer:

25 to 3 power ÷ 3 = 69

Answer:

X intercepts are (-4,0) and (2,0)

Step-by-step explanation:

use the desmos graphing calculator for a simple answer