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2 years ago

Solve the proportion: 3/2 = 4/p + 9

Mathematics

1 answer:

AlladinOne [14]2 years ago

8 0

The answer is p = -8/15

Proportion can simply be defined as equating two ratios

The proportion of 3/2 = 4/p +9 can be calculated as follows

3/2 - 9/1 = 4/p

-15/2 = 4/p

cross multiply both sides together to find the value of p

-15×p= 4×2

-15p= 8

p= -8/15

Hence the answer is p= -8/15

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4x – 3y=8<br> 2. 5x – 2y = -11

AlladinOne [14]

Answer:

$x = -7$

$y = - 12$

Step-by-step explanation:

The given system is:

4x-3y=8

5x-2y=-11

We make x the subject in the top equation to get:

$x = \frac{3}{4}y + 2$

Plug this expression for x in the bottom equation to get

$5( \frac{3}{4}y + 2) - 2y= - 11$

We expand to obtain

$\frac{15}{4} y + 10 - 2y = - 11$

Multiply through by 4

$15y + 40 - 8y = - 44$

Group similar terms

$15y - 8y = - 44 - 40$

$7y = - 84$

$y = - \frac{84}{7} =-12$

This means

$x = -12\times \frac{3}{4} + 2$

$x = - 7$

6 0

4 years ago

A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the

forsale [732]

<h3>The probability of student passing the quiz with at least 50% of the questions correct is 0.05457.</h3>

Step-by-step explanation:

Here, the total number of T/F question = 10

The minimum answers needed correctly answered = 8

So, student needs to answer at least 8 questions correctly.

Here, the possibility of answering a question correctly = $(\frac{1}{2})$ = p = 0.5

Also, the possibility of answering a question wrong = $(\frac{1}{2})$ = q = 0.5

Now, to pass he needs to answer 8 or more ( 8 , 9 or 10) answers correctly.

P(answering 8 correct answer) = $^{10}C_8(p)^8(q)^2 = ^{10}C_8(0.5)^8(0.5)^2 = 0.0439$

P(answering 9 correct answer) = $^{10}C_9(p)^9(q)^1 = ^{10}C_9(0.5)^9(0.5)^1 = 0.0097$

P(answering 10 correct answer) = $^{10}C_{10}(p)^{10}(q)^0 = ^{10}C_{10}(0.5)^{10}(0.5)^0 = 0.00097$

So, the total Probability = P(8) + P(9) + P(10)

= (0.0439) + (0.0097) + (0.00097)

= 0.05457

Hence, the probability that the student passes the quiz with at least 8 of the questions correct is 0.05457.

6 0

4 years ago

5x + 2x + 2 = 9x + 4

bija089 [108]

Step-by-step explanation:

Given

5x + 2x + 2 = 9x + 4

9x - 5x - 2x = 2 - 4

9x - 7x = - 2

2x = - 2

x = - 2 / 2

Therefore x = -1.

5 0

3 years ago

Read 2 more answers

F(9) if f (x)=5x-16, what is the answer to the math problem

Anastasy [175]

F(9)
sub 9 forx
f(9)=5(9)-16
f(9)=45-16
f(9)=29

f(9)=29

3 0

3 years ago

Laura, David, and Carlos served a total of 115 orders Monday at the school cafeteria. David served 3 times as many orders as Car

Korvikt [17]

Answer:

Step-by-step explanation: ts 6 11 19 56

Laura, David, and Carlos served a total of 115 orders

David served 3 times as many orders as Carlos. David = 3x

Laura served 10 more orders than Carlos. let Carlos = x

How many orders did they each serve? Laura = x + 10

Carlos + David + Laura = 115

x + 3x + x+10 = 115

5x + 10 = 115

5x = 115 - 10

5x = 105

x = 21 Carlos

63 Davide

31 Laura

add then up 115 Total

4 0

3 years ago