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2 years ago

Please help need answers fast questions is in the picture

Mathematics

1 answer:

Liono4ka [1.6K]2 years ago

4 0

Answers are

a. 32 m
(2x6 + 2x10)

b. 45.2 cm
(4 x 11.3)

c. 23 in.
(6 + 7 + 10)

d. 34.6 cm
(2x 5.3 + 2 x 12)

e. 8 cm
(4 x 2)

f. 29 ft
(4 + 13 + 12)

Perimeter of each of these figures is found by adding the total of the sides.

You might be interested in

Find the area of the figure

VLD [36.1K]

Answer:

132 cm²

Step-by-step explanation:

Consider the shape as a trapezoid with a rectangle added on top.

The area of the trapezoid is (7+19)/2 × 8 =104

The area of the rectangle is 7×4 = 28

Add the two areas: 104+28= 132

OR consider the shape as a tall rectangle with the two triangles added to the sides.

The area of the rectangle is 7(4+8) = 84

The area of the triangles is 8(19-7)/2= 48

[Each triangle is 24 cm²]

Add those areas

84+48=132

Same result: 132 cm²

4 0

3 years ago

3. Problem 2: Suppose a radio manufacturer has the total cost function C (x) = 43x + $ 1850 and the revenue function R (x) = $ 8

OLEGan [10]

Given that,

Total cost function, C (x) = 43x + $1850

The revenue function R (x) = $80x

To find,

The number of units that must be produced and sold to break even.

Solution,

At break even, cost = revenue

43x + $1850 = $80x

Subtract 80x from both sides.

43x + 1850 -80x = $80x -80x

1850 = 80x-43x

37x = 1850

x = 50

So, the required number of units are 50.

8 0

3 years ago

In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 3.0 m/s up a 22.0° inclined track

Aloiza [94]

Answer:

Approximately $0.31\; \rm m$ , assuming that $g = 9.81\; \rm N \cdot kg^{-1}$ .

Step-by-step explanation:

Initial kinetic energy of the sled and its passenger:

$\begin{aligned}\text{KE} &= \frac{1}{2}\, m \cdot v^{2} \\ &= \frac{1}{2} \times 14\; \rm kg \times (3.0\; \rm m\cdot s^{-1})^{2} \\ &= 63\; \rm J\end{aligned}$ .

Weight of the slide:

$\begin{aligned}W &= m \cdot g \\ &= 14\; \rm kg \times 9.81\; \rm N \cdot kg^{-1} \\ &\approx 137\; \rm N\end{aligned}$ .

Normal force between the sled and the slope:

$\begin{aligned}F_{\rm N} &= W\cdot \cos(22^{\circ}) \\ &\approx 137\; \rm N \times \cos(22^{\circ}) \\ &\approx 127\; \rm N\end{aligned}$ .

Calculate the kinetic friction between the sled and the slope:

$\begin{aligned} f &= \mu_{k} \cdot F_{\rm N} \\ &\approx 0.20\times 127\; \rm N \\ &\approx 25.5\; \rm N\end{aligned}$ .

Assume that the sled and its passenger has reached a height of $h$ meters relative to the base of the slope.

Gain in gravitational potential energy:

$\begin{aligned}\text{GPE} &= m \cdot g \cdot (h\; {\rm m}) \\ &\approx 14\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times h\; {\rm m} \\ & \approx (137\, h)\; {\rm J} \end{aligned}$ .

Distance travelled along the slope:

$\begin{aligned}x &= \frac{h}{\sin(22^{\circ})} \\ &\approx \frac{h\; \rm m}{0.375}\end{aligned}$ .

The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:

$\begin{aligned} & - (-x)\, f \\ = \; & x \cdot f \\ \approx \; & \frac{h\; {\rm m}}{0.375}\times 25.5\; {\rm N} \\ \approx\; & (68.1\, h)\; {\rm J}\end{aligned}$ .

In other words, the sled and its passenger would have lost (approximately) $((137 + 68.1)\, h)\; {\rm J}$ of energy when it is at a height of $h\; {\rm m}$ .

The initial amount of energy that the sled and its passenger possessed was $\text{KE} = 63\; {\rm J}$ . All that much energy would have been converted when the sled is at its maximum height. Therefore, when $h\; {\rm m}$ is the maximum height of the sled, the following equation would hold.

$((137 + 68.1)\, h)\; {\rm J} = 63\; {\rm J}$ .

Solve for $h$ :

$(137 + 68.1)\, h = 63$ .

$\begin{aligned} h &= \frac{63}{137 + 68.1} \approx 0.31\; \rm m\end{aligned}$ .

Therefore, the maximum height that this sled would reach would be approximately $0.31\; \rm m$ .

7 0

3 years ago

Customers arrivals at a checkout counter in a department store per hour have a Poisson distribution with parameter λ = 7. Calcul

IgorLugansk [536]

Answer:

(1)14.9% (2) 2.96% (3) 97.04%

Step-by-step explanation:

Formula for Poisson distribution: $P(k) = \frac{\lambda^ke^{-k}}{k!}$ where k is a number of guests coming in at a particular hour period.

(1) We can substitute k = 7 and $\lambda = 7$ into the formula:

$P(k=7) = \frac{7^7e^{-7}}{7!}$

$P(k=7) = \frac{823543*0.000911882}{5040} = 0.149 = 14.9\%$

(2)To calculate the probability of maximum 2 customers, we can add up the probability of 0, 1, and 2 customers coming in at a random hours

$P(k\leq2) = P(k=0)+P(k=1)+P(k=2)$

$P(k\leq2) = \frac{7^0e^{-7}}{0!} + \frac{7^1e^{-7}}{1!} + \frac{7^2e^{-7}}{2!}$

$P(k \leq 2) = \frac{0.000911882}{1} + \frac{7*0.000911882}{1} + \frac{49*0.000911882}{2}$

$P(k\leq2) = 0.000911882+0.006383174+0.022341108 \approx 0.0296=2.96\%$

(3) The probability of having at least 3 customers arriving at a random hour would be the probability of having more than 2 customers, which is the invert of probability of having no more than 2 customers. Therefore:

$P(k\geq 3) = P(k>2) = 1 - P(k\leq2) = 1 - 0.0296 = 0.9704 = 97.04\%$

4 0

3 years ago

The perimeter of a rectangular garden is 44 meters. The length of the rectangle is 5 less than twice the width. Find the length

defon

9514 1404 393

Answer:

width: 9 m
length: 13 m

Step-by-step explanation:

Let w represent the width. Then the length is 2w-5, and the perimeter is ...

P = 2(L+W)

44 = 2((2w-5) +w)

44 = 6w -10

54 = 6w

9 = w

2(9) -5 = 13 = length

The length of the rectangle is 13 meters; the width is 9 meters.

6 0

3 years ago