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1 year ago

5

Two steamers leave a port on a river at the same time, traveling in opposite directions. Each is traveling 22 miles per hour. Ho

w long will it take for them to be 110 miles apart

2 answers:

Xelga [282]1 year ago

5 0

Answer:

2.5 hours.

Step-by-step explanation:

Let x represent time taken by each steamer.

We have been given that two steamers leave a port on a river at the same time, traveling in opposite directions.

$\text{Distance}=\text{Speed}\times \text{Time}$

Since both steamers has same speed, so distance traveled by each steamer in x hours would be $22x$ .

We have been given that both steamers traveled a distance of 110 miles, so we can represent this information in an equation as:

$22x+22x=110$

Let us solve for x:

$44x=110$

$\frac{44x}{44}=\frac{110}{44}$

$x=\frac{10}{4}$

$x=2.5$

Therefore, it will take both steamers 2.5 hours to be 110 miles apart.

Alik [6]1 year ago

4 0

After 1 hour >> 44 miles apart
after 2 hour >> 88 miles apart
after 2 1/2 hour >> 110 miles apart

Two & half hours

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John's commute to work is 20kmhr while Sheri's commute is 500mmin. Who has the fastest commute to work in mihrif 1.61km=1mi? A S

Andreyy89

Answer:

A) Sheri has the faster commute by 6.2 miles/hr.

Step-by-step explanation:

Given

John's commute to work $=20\ km/hr$

Sheri's commute to work $=500\ m/min$

$1.61\ km = 1\ mile$

John's commute to work in miles per hour = $\frac{20\ km}{1 hr}\times \frac{1\ mile}{1.61\ km}= 12.42\ miles/hr$

Sheri's commute to work in miles per hour = $\frac{500\ m}{1\ min}\times \frac{1\ km}{1000\ m}\times \frac{1\ mile}{1.61\ km}\times \frac{60\ min}{1\ hr}= 18.63\ miles/ hr$

We can see that Sheri has a faster commute.

Difference between the rates = $18.63\ miles/ hr-12.42\ miles/hr=6.21\ miles/hr\approx 6.2\ miles/hr$

∴ Sheri has the faster commute by 6.2 miles/hr.

3 0

2 years ago

Pietro made 18 baskets during a basketball game.The number of 3 pointers are 3 more than half of the 2 point shots.how many type

blagie [28]

Total points is 23

<u>Explanation:</u>

Given:

Total number of baskets = 18

Let the number of 2 pointer shots be x

Let the number of 3 pointer shots be y

According to the question:

$y = \frac{x}{2} + 3$ -1

The equation can be formed as:

$\frac{x}{2} + 3 + x = 18$

On solving this equation further we get:

$\frac{x+6+2x}{2} = 18\\\\9x = 36\\\\x = 4$

Putting the value of x = 4 in equation 1

$y = \frac{x}{2}+3\\ \\y = \frac{4}{2} + 3\\\\y = 5$

Points for 2 pointer shots = 4 X 2

= 8

Points for 3 pointer shots = 5 X 3

= 15

Total points = 8 + 15

= 23

Therefore, total points is 23

5 0

2 years ago

On a coordinate plane, a triangle has points A prime (negative 2, 10), B prime (negative 6, 4), and (negative 10, 8). What is th

schepotkina [342]

Answer:

A(10,-2).

Step-by-step explanation:

It is given that, on a coordinate plane, a triangle has points A'(-2, 10), B'(-6, 4), and C'(-10, 8).

We need to find the pre-image of vertex A' if the image shown on the graph was created by a reflection across the line y = x.

If a figure reflected across the line y=x, then

$A(x,y)\rightarrow A'(y,x)$

It is given that A'(-2,10).

$A(y,x)=A'(-2,10)$

On comparing both sides, we get

$x=10,y=-2$

Therefore, the coordinates of preimage of A' are (10,-2).

8 0

1 year ago

A probability calculator is required on this problem; answer to six decimal places. Suppose we will spin the wheel pictured 400

KiRa [710]

Answer:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=400, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

We need to check the conditions in order to use the normal approximation.

$np=400*0.2=80 \geq 10$

$n(1-p)=400*(1-0.2)=320 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=400*0.2=80$

$\sigma=\sqrt{np(1-p)}=\sqrt{400*0.2(1-0.2)}=8$

So then we can approximate the random variable as $X \sim N(\mu = 80, \sigma = 8)$

And we want this probability:

$P(90< X< 110)$

We can use the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

And replacing we got:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

8 0

2 years ago

Emma's sister is nine years older than Emma. Their combined ages add up to 49.How old is Emma. write and equation and solve

Genrish500 [490]

E= Emma's age
emma's sister's age= e+9 (emma's age plus 9)

e+9=49
(isolate your variable)
e+9-9=49-9
e=40
Emma is 40 years old
To check: Emma's sister is 9 years older right? take emmas age 40 plus the nine more years and you still get the total of 49! hope that helps good luck

5 0

2 years ago

Read 2 more answers