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3 years ago

14

How do you solve the question? Ryan gave 7 of his cars to a friend. Then he bought 6 more cars. Now Ryan has 13 cars. How many c

ars did Ryan start with?

1 answer:

andrew-mc [135]3 years ago

8 0

Answer: 14 cars

Step-by-step explanation: x-7+6=13

X-1=13, x=14

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8^-8 in fraction form show work please and thank you

Strike441 [17]

If there is a negative exponent, bring the exponent and it’s base to the denominator:
1/8^8
Then, simplify
1/16777216
Hope this helps!

6 0

3 years ago

A linear sequence starts a+3b a+7b a+11b the 2nd term has value 19 the 5th term has value 67 work out the values of a and b

alekssr [168]

Answer:

$a = -9$

$b = 4$

Step-by-step explanation:

Given

Sequence: a+3b, a+7b, a+11b

2nd term = 19

5th term = 67

Required

Find a and b

First, the 5th term needs to be calculated;

Using formula for Arithmetic Progression (AP), the formula goes thus

$T_n = T_1 + (n - 1)d$

Where n = 5

T_1 = a + 3b ------------ FIrst term

$d = T_2 - T_1 or T_3 - T_2$ --- Difference between two successive terms

$d = a + 7b - (a + 3b)$

$d = a + 7b -a - 3b$

$d = a - a + 7b - 3b$

$d = 4b$

So, $T_n = T_1 + (n - 1)d$ becomes

$T_5 = a + 3b + (5 - 1)4b$

$T_5 = a + 3b + (4)4b$

$T_5 = a + 3b + 16b$

$T_5 = a + 19b$

Now that we have values for 2nd and 5th term;

From the second, T2 = 19 and T5 = 67

This gives

$a + 7b = 19$ --- Equation 1

$a + 19b = 67$ ---- Equation 2

Make a the subject of formula in (1)

$a = 19 - 7b$

Substitute these values in equation 1

$a + 19b = 67$ becomes

$19 - 7b + 19b = 67$

$19 + 12b = 67$

Collect like terms

$12b= 67 - 19$

$12b = 48$

Divide both sides by 12

$\frac{12b}{12} = \frac{48}{12}$

$b = 4$

Recall that b = 4

Substitute a = 19 - 7b and nothing will hire

$a = 19 - 7(4)$

$a = 19 - 28$

$a = -9$

Hence, the values of a and b are -9 and 4 respectively.

5 0

3 years ago

2 and 1/7 :(15a)= 5/14 :(0.8)

murzikaleks [220]

Answer:

<u>a = 0.32</u>

Explanation:

This question requires that you find the value of $a$ given that:

$2\frac{1}{7}:(15a)=(5/14)/(0.8)$

That is you have to solve the equation for a.

1. Rewrite the equation in form of fractions, convert the mixed number into an improper fraction, and convert the decimal number into fraction too.

$2\frac{1}{7}:(15a)=(5/14)/(0.8)\\ \\ \frac{2+\frac{1}{7} }{15a} =\frac{5/14}{8/10}\\ \\\frac{(14+1)/7}{15a} =\frac{5\times 10}{8\times 14}\\ \\ \frac{15}{7\times 15a} =\frac{50}{112}$

2. Cross multiply to leave a alone:

$a=15\times 112/(7\times 15\times 50)\\ \\a=1680/5250\\ \\a=0.32$

4 0

3 years ago

Emma reads at a constant rate. In 6 hours, Emma read a 130-page book and a 90-page book. If h represents the number of hours it

LenaWriter [7]

Answer:

D

Step-by-step explanation:

i'm doing the activity rn and got it right

8 0

2 years ago

Each sample of water has a 30% chance of containing a particular organic pollutant. Assume that the samples are independent with

Luba_88 [7]

Answer:

d) 0.383

Step-by-step explanation:

For each sample, there are only two possible outcomes. Either they contain the pollutant, or they do not. The probability of a sample containing the pollutant is independent of any other sample. Thus, the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

30% chance of containing a particular organic pollutant.

This means that $p = 0.3$

Next 10 samples

This means that $n = 10$

Probability that two or less contain the pollutant.

This is:

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.3)^{0}.(0.7)^{10} = 0.028$

$P(X = 1) = C_{10,1}.(0.3)^{1}.(0.7)^{9} = 0.121$

$P(X = 2) = C_{10,2}.(0.3)^{2}.(0.7)^{8} = 0.233$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.028 + 0.121 + 0.233 = 0.382$

A little rounding difference, but the correct answer is given by option d.

6 0

2 years ago