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2 years ago

10

caroline and sarah win some money and share it in the ratio of 6:1 caroline gets £70 more than her how much did they get altoget

her

1 answer:

svetlana [45]2 years ago

4 0

Answer: £84

Explanation:
84-70=14
14*6=84
6:1
84:14

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Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per we

Maru [420]

A) System of inequalities

Income from babysitting: 6x
Income from tutoring: 10y

Goal for this week: at least $ 75 => 6x + 10y ≥ 75
Number of hours: maximum $20 => x + y ≤ 20

x and y have to be zero or positvie => x≥0 and y ≥ 0

Answer of part A.

6x + 10y ≥ 75
x+y ≤ 20
x ≥ 0
y ≥ 0

Part B. Graph

The solution is a region closed by 4 lines and you can find it in the file attached.

In that graph:

1) the line x + y = 20 is the upper limit
2) the line 6x + 10 y = 75 is the lower incclined line
3) y = 0 is the botton horizontal line it is the x-axis
4) x = 0 is the left vertical line, in is the y-axis

Part C.

Use, for example the point (7,10).

It is in the region of the graph limited by the above equations.

It implies:

Number of hours worked = 7 + 10 = 17 which is less than 20.

Income: 6(7) + 10(10) = 42 + 100 = 142, which is greater than 75

Of course, both are greater than 0.

In this way we proved that the point (7,10) is a true solution for the model.

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2 years ago

URGENT!! <br> Find the average rate of change of f(x)=x−2√x on the interval [1,9].

loris [4]

Please let me know if you have any questions!

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2 years ago

If this particular arithmetic sequence, a7=34 and a15=74. What is the value of a21

Ilya [14]

This is an arithmetic sequence, meaning, to get the next term, you simply add some value to the current one, namely the "common difference" "d".

now, we know the 17th term is 34, let's go to the 15term then

34 + d
34 + d + d
34 + d + d + d
34 + d + d + d + d
34 + d + d + d + d + d
34 + d + d + d + d + d + d
34 + d + d + d + d + d + d + d
34 + d + d + d + d + d + d + d + d

now, notice, we got to the 15th term, which is 34 + d + d + d + d + d + d + d + d, or namely 34 + 8d, it just so happen we know is 74, therefore,

$\bf 34+8d=74\implies 8d=40\implies d=\cfrac{40}{8}\implies \boxed{d=5}$

ok, now that we know what the common difference is, let's find the first term in the sequence using the 7th term of 34,

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=7\\
d=5\\
a_7=34
\end{cases}
\\\\\\
a_7=a_1+(7-1)5\implies 34=a_1+(7-1)5
\\\\\\
34=a_1+30\implies \boxed{4=a_1}$

and now let's use those 2 found folks, to get the 21st term,

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=4\\
d=5\\
n=21
\end{cases}
\\\\\\
a_{21}=4+(21-1)5\implies a_{21}=4+100\implies a_{21}=104$

3 0

2 years ago

15) Bob has 12 black pen, 14 red pen, 15 green pens, 24 blue pens and 3 boxes of

cricket20 [7]

Answer:

13, 16, 18

Step-by-step explanation:

Sabemos que podemos calcular el total de plumas amarillos, por medio de la media.

16 = (12 + 14 + 15 + 24 + x + y + z) / 7

16 * 7 = 12 + 14 + 15 + 24 + x + y + z

112 = 65 + x + y + z

x + y + z = 112-65

x + y + z = 47

sabemos que la mediana es el valor medio, y que ese 46 debe dividirse entre 3 valores porque son 3 cajas, entonces debemos buscar los números adecuados para el valor 15 esté en la mitad, es decir de cuarto.

Sin meter los valores nuevos, el ranking sería así:

12

14

15

24

el 15 esta de tercero, para que quede de cuarto, debe tener dos valores por debajo y un por arriba, así:

X

12

14

15

y

z

24

Por lo tanto, valores mayores a 15 serían por ejemplo y = 16 y z = 18:

16 + 18 = 34

x = 47-34 = 13

quedaría:

12

13

14

15

dieciséis

18 años

24

Si recalculamos la media:

m = (12 + 14 + 15 + 24 + 13 + 16 + 18) / 7 = 16

8 0

2 years ago

Given that Annie chooses a red shirt at random, what is the probability that the shirt will be large? Use the formula P(A | B)=

lesya692 [45]

Im also doing this question lemme see...

probability of red and large
______________
probabiltiy of large shirt

0.05
____

0.35

answer 0.1428
answer after rounding 0.1

6 0

2 years ago