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2 years ago

A5 inch x 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger

Mathematics

1 answer:

My name is Ann [436]2 years ago

8 0

Answer:

8x+24

dimensions of the photograph

length - 7 inch

width - 5 inch

dimensions of the photo frame is 2x larger than both width and length

length - 7 + 2x

width - 5 + 2x

the perimeter is sum of all 4 sides

Perimeter = 2(7 + 2x) + 2(5 + 2x)

= 14 + 4x + 10 +4x

= 24 + 8x

correct answer is 8x+24

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45 children attend preschool the number of two-year-olds is 1/2 the number of three-year-olds the number for your old is the sam

Mkey [24]

There are 9 two-year-olds and 18 each of 3 and 4 year olds.

To solve this we could write and solve the equation below, letting x be the number of 3 and 4 year olds.

x/2 + x + x = 45
x + 2x + 2x = 90
5x = 90
x = 18

From here, we just divide 18 by 2 to get the number of 2 year olds.

6 0

3 years ago

The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.80. It is also known that P(A1 ∩ A2) = 0. Suppose P(

Umnica [9.8K]

Answer:

(a) $A_1$ and $A_2$ are indeed mutually-exclusive.

(b) $\displaystyle P(A_1\; \cap \; B) = \frac{1}{20}$ , whereas $\displaystyle P(A_2\; \cap \; B) = \frac{1}{25}$ .

(d) $\displaystyle P(A_1 \; |\; B) \approx \frac{5}{9}$ , whereas $P(A_1 \; |\; B) = \displaystyle \frac{4}{9}$

Step-by-step explanation:

$P(A_1 \; \cap \; A_2) = 0$ means that it is impossible for events $A_1$ and $A_2$ to happen at the same time. Therefore, event $A_1$ and $A_2$ are mutually-exclusive.

By the definition of conditional probability:

$\displaystyle P(B \; | \; A_1) = \frac{P(B \; \cap \; A_1)}{P(B)} = \frac{P(A_1 \; \cap \; B)}{P(B)}$ .

Rearrange to obtain:

$\displaystyle P(A_1 \; \cap \; B) = P(B \; |\; A_1) \cdot P(A_1) = 0.25 \times 0.20 = \frac{1}{20}$ .

Similarly:

$\displaystyle P(A_2 \; \cap \; B) = P(B \; |\; A_2) \cdot P(A_2) = 0.80 \times 0.05 = \frac{1}{25}$ .

Note that:

$\begin{aligned}P(A_1 \; \cup \; A_2) &= P(A_1) + P(A_2) - P(A_1 \; \cap \; A_2) = 0.20 + 0.80 = 1\end{aligned}$ .

In other words, $A_1$ and $A_2$ are collectively-exhaustive. Since $A_1$ and $A_2$ are collectively-exhaustive and mutually-exclusive at the same time:

$\displaystyle P(B) = P(B \; \cap \; A_1) + P(B \; \cap \; A_2) = \frac{1}{20} + \frac{1}{25} = \frac{9}{100}$ .

By Bayes' Theorem:

$\begin{aligned} P(A_1 \; |\; B) &= \frac{P(B \; | \; A_1) \cdot P(A_1)}{P(B)} \\ &= \frac{0.25 \times 0.20}{9/100} = \frac{0.05 \times 100}{9} = \frac{5}{9}\end{aligned}$ .

Similarly:

$\begin{aligned} P(A_2 \; |\; B) &= \frac{P(B \; | \; A_2) \cdot P(A_2)}{P(B)} \\ &= \frac{0.05 \times 0.80}{9/100} = \frac{0.04 \times 100}{9} = \frac{4}{9}\end{aligned}$ .

6 0

2 years ago

Kylie is comparing the cost of two housekeeping companies, DoItRight and CleanIt. The table describes the costs for DoItRight.

abruzzese [7]

Answer:

<u>First, find the cost function of DoItRight Housekeeping:</u>

Slope(m) = cost per hour = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{44-26}{3-1.5}=\frac{18}{1.5}=12$

<em>The y-intercept(b), representing the initial cost, can be calculated by substituting in values to the function:</em>

$f(x)=12x+b\\26=12(1.5)+b\\b=26-18=8$

<u>Therefore, the function for two companies are:</u>

The function for DoItRight is $f(x)=12x+8$
The function for CleanIt is $g(x)=10x+16$

When comparing the two functions, it's shown how CleanIt has a greater y-intercept than DoltRight, meaning that CleanIt has a greater initial cost than DotRight. The y-intercept is when the graph intercepts the y-axis, therefore, the coordinates there would be (0, y-value), which, in this case for CleanIt company, will be (0, 16). While CleanIt has a greater y-intercept(initial cost), DoItRight has a greater slope, meaning they cost more per hour.

7 0

2 years ago

How many minutes are in m hours? Which expression represents this?

sveta [45]

60m there's 60 minutes in an hour.

7 0

3 years ago

Read 2 more answers

А О 130<br> The answer to 15 divide 375 what is the answer

Amanda [17]

Answer:

the answer would be