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3 years ago

Anna and Bobie joined two different swimming classes at the same time.

Mathematics

2 answers:

Black_prince [1.1K]3 years ago

7 0

Answer: It would be 10 months for the price of $320.

Step-by-step explanation:

jeyben [28]3 years ago

6 0

Answer:

It would be 10 months for the price of $320.

Step-by-step explanation:

First we need to find how much Anna's swimming charge and Bobie's charge is.

PA=70+t The price of the month equals to the starting fee and monthly charge

120=70+2t The price of 2 months times the monthly charge

50=2t

25=t is Anna's monthly charge

PB=250+t is Bobies starting price and monthly charge

264=250+2t is the month charge for Bobie after 2 months

14=2t

7=t is Bobie's monthly charge

70+25x=250+7x We need to find x which is what month will satisfy both equations

25x=180+7x Subtract 70 from both sides

18x=180 Subtract 7x from both sides

x=10 divide 18 from both sides

Now we have the months that satisfy both equations we need to find the total price that matches with it. So we plug it back into both equations.

PA=70+25x PB=250+7x

PA=70+25(10) PB=250+7(10)

PA=70+250 PB=250+70

PA=320 PB=320

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A large sample of tires from cabs driven within a city have an average tire tread depth of 0.25cm at the end of the winter. If t

frutty [35]

Answer:

0% probability cab tires depths would be shallower than 0.25cm.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 2.2, \sigma = 0.33$

What is the probability cab tires depths would be shallower than 0.25cm.

This probability is the pvalue of Z when X = 0.25. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0.25 - 2.2}{0.33}$

$Z = -5.9$

$Z = -5.9$ has a pvalue of 0.

0% probability cab tires depths would be shallower than 0.25cm.

7 0

3 years ago

Two thirds of a number decreased by six is two. what is the number?

Kisachek [45]

Answer: The number is: " 12 ".

____________________________________
Let "x" represent "the unknown number" (for which we wish to solve.

The expression:

$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;
_______________________________________________
Method 1)

Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:

→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Multiply each side of the equation by " $\frac{3}{2}$ " ; to isolate "x" on one side of the equation ; and to solve for "x" ;
______________________________________________
→ $\frac{3}{2}$ * $\frac{2}{3}$ x = 8 * $\frac{3}{2}$ ;

→ x = 8 * $\frac{3}{2}$ ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;

= $\frac{8*3}{1*2}$ ;

= $\frac{24}{2}$ ;

= 12 .
______________________________________________
x = 12 .
______________________________________________
Method 2)
______________________________________________
$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;

Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:
→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Multiply each side of the equation by "3" ; to get rid of the "fraction" ;
 → 3 * $\frac{2}{3}$ x = 8 * 3 ;
→ $\frac{3}{1}$ * $\frac{2}{3}$ x = 8 * 3 ;
→ $\frac{3*2}{1*3}$ x = 8 * 3
→ $\frac{6}{3}$ x = 24 ;

→ 2x = 24 ;

→ Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" :

2x / 2 = 24 / 2 ;

x = 12 .
__________________________________________________
Method 3).
__________________________________________________
$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;
_______________________________________________
Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:

→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Now, divide each side of the equation by " $\frac{2}{3}$ " ;
to isolate "x" on one side of the equation; & to solve for "x" ;
___________________________________________________
{ $\frac{2}{3}$ x } / { $\frac{2}{3}$ } = 8 / { $\frac{2}{3}$ } ;

to get: x = 8 / { $\frac{2}{3}$ } ;

= 8 * ( $\frac{3}{2}$ ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;

= $\frac{8*3}{1*2}$ ;

= $\frac{24}{2}$ ;

= 12 ;
___________________________________________
x = 12 .
___________________________________________
NOTE: Variant: (in "Methods 2 & 3") :
___________________________________________
At the point where:
___________________________________________
= 8 * ( $\frac{3}{2}$ ) ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;
__________________________________________
We can cancel out the "2" to a "1" ; and we can cancel out the "8" to a "4" ;
__________________________________________
{since: "8÷2 = 4" ; and since: "2÷2 =1" } ;
__________________________________________
and we can rewrite the expression:
__________________________________________
$\frac{8}{1}$ * $\frac{3}{2}$ ;
__________________________________________
as: $\frac{4}{1}$ * $\frac{3}{1}$ ;
__________________________________________
which equals:
__________________________________________
→ $\frac{4*3}{1*1}$ ;

= $\frac{12}{1}$ ;

= 12 .
__________________________________________
x = 12 .
__________________________________________
Answer: The number is: " 12 ".
__________________________________________

8 0

4 years ago

Solve the exponential equation: 6x-3 = 216x-3

wariber [46]

Answer:X=-37

Step-by-step explanation:

5 0

4 years ago

Read 2 more answers

Three friends collected aluminum cans from the neighborhood to recycle in total they receive 300 cans many collected 90 Jim coll

spin [16.1K]

Given

Total cans = 300

Manny= 90

Jim =100

Bob=110

Now their percentage

Manny percentage

$\begin{gathered} manny=\frac{90}{300}\times100\text{ \%} \\ \\ Manny\text{ percentage=}\frac{90}{3}\text{ \%} \\ \\ Manny\text{ percentage =30 \%} \end{gathered}$

Jim Percentage

$\begin{gathered} Jim=\frac{100}{300}\times100\text{ \%} \\ Jim\text{ percentage=}\frac{1}{3}\times100\text{ \%} \\ Jim\text{ percentage=33.333\%} \end{gathered}$

Bob percentage

$undefined$

6 0

1 year ago

During the first part of a trip, a canoeist travels 18 miles at a certain speed. the canoeist travels 4 miles on the second par

storchak [24]

We can set it up like this, where s is the speed of the canoeist:

$\frac{18}{s} + \frac{4}{s-5} = 3$

To make a common denominator between the fractions, we can multiply the whole equation by s(s-5):

$s(s-5)[\frac{18}{s} + \frac{4}{s-5} = 3] \\ 18(s-5)+4s=3s(s-5) \\ 18s - 90+4s=3 s^{2} -15s$

If we rearrange this, we can turn it into a quadratic equation and factor:

$18s - 90+4s=3 s^{2} -15s \\ 22s-90=3 s^{2} -15s \\ 3 s^{2} -37s+90=0 \\ (3s-10)(s-9)=0 \\ s= \frac{10}{3} ,9$

Technically, either of these solutions would work when plugged into the original equation, but I would use the second solution because it's a little "neater." We have the speed for the first part of the trip (9 mph); now we just need to subtract 5mph to get the speed for the second part of the trip.

$9-5 = 4$

The canoeist's speed on the first part of the trip was 9mph, and their speed on the second part was 4mph.

5 0

4 years ago