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1 year ago

01 L1 - Perimeter Word Problems

Mathematics

1 answer:

stich3 [128]1 year ago

5 0

Answer: x*(x-5)

Step-by-step explanation:

Plexiglass is a cuboid

which means that the area would be l*w

in the question it states that the width is 5 cm shorter than the length

since we dont know the values

we represent them as x

so using l*w

we write x*(x-5)

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A stone is dropped into a barrel of water and sinks to the bottom. The ball is completely covered by water. By how much does the

Rom4ik [11]

Answer:

Answer: 5/12 or approx. 0.42

Step-by-step explanation:

The ball will displace as much water as its volume.

Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.

Volume of a sphere:

$V_s=\frac{4}{3} \pi r^3$

The radius is half the diameter. The diameter of the sphere is 10, thus:

$r = d/2 = 10/2 = 5$

5^3 = 5*5*5 = 25*5 = 125

$V_s=\frac{4}{3} \pi * 5^3=\frac{4}{3} \pi * 125$

The volume of a cylinder, which will be the shape of the increase in water, is the following:

$V_c=\pi r^2 h$

We know the radius r, as we know the diameter.

$r=d/2=40/2=20$

$V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400$

We are looking for the height of the cylinder, h, as that will be the height of the water rise.

Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:

$V_s = V_c$

$\frac{4}{3} * 125 * \pi = 400 * h * \pi$

We can get rid of pi by dividing both sides by pi:

$\frac{4}{3} * 125 = 400 * h$

And now divide both sides by 400:

$\frac{4}{3} * \frac{125}{400}= h$

Just reversing it and putting h to the left:

$h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}$

I see that I can divide both the numerator and the denominator by 4:

$h =\frac{125}{3 * 100}= \frac{125}{300}$

I'll now divide both the numerator and the denominator by 25 to simplify the expression:

$h=\frac{125}{300} =\frac{125 / 25}{300 / 25} = \frac{5}{12}$

Answer: The water rises by 5/12 (five twelfths).

If I want an approximate decimal answer, I can simply run this expression in a calculator:

$\frac{5}{12}$ ≈ $0.416666667$ ≈ $0.42$

7 0

1 year ago

The course length of the Boston Marathon is about 4.2×104 meters. The course length of the Iditarod Trail Invitational ultra-mar

GREYUIT [131]

Answer:

The ultra-marathon Idita Rod Trail is about 38 times longer than the Boston Marathon.

Step-by-step explanation:

Let

x -----> the length of the Boston Marathon in meters

y -----> the length of the Idita rod Trail Invitational ultra-marathon in meters

we have

$x=4.2*10^4\ m$

$y=1.6*10^6\ m$

we know that

To find out how many times as long is the course of the Idita rod Trail ultra-marathon as that of the Boston Marathon, divide the length of the Idita rod Trail Invitational ultra-marathon by the length of the Boston Marathon

$\frac{y}{x}$

$\frac{x}{y}=\frac{1.6*10^6}{4.2*10^4}$

Remember that

To divide two numbers in scientific notation, divide their coefficients and subtract their exponents

$\frac{1.6*10^6}{4.2*10^4}=\frac{1.6}{4.2}*(10^{6-4})=0.381*(10^{2})=38.1$

therefore

The ultra-marathon Idita Rod Trail is about 38 times longer than the Boston Marathon.

5 0

2 years ago

Isosceles triangle LMN is graphed with vertices L(0, 1), M(3, 5), and N(6,1). What is the slope of side LN? Negative StartFracti

Mekhanik [1.2K]

Answer:

the answer is 0

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

You work two jobs. You earn $11.90 per hour as a salesperson and $10.50 per hour stocking shelves. Your combined earnings this m

Delicious77 [7]

178.50 = 11.90y + 10.50x ⇒ equation in standard form.

4 0

2 years ago

Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of

nikitadnepr [17]

Answer:

a) Reject H₀

b) [0.31; 3.35]

Step-by-step explanation:

Hello!

a) The objective of this example is to compare if the population means of the production rate of the assembly lines A, B and C. To do so the data of the production of each line were recorded and an ANOVA was run using it.

The study variable is:

Y: Production rate of an assembly line.

Assuming that the study variable has a normal distribution for each population, the observations are independent and the population variances are equal, you can apply a parametric ANOVA with the hypothesis:

H₀ μ₁= μ₂= μ₃

H₁: At least one of the population means is different from the others

Where:

Population 1: line A

Population 2: line B

Population 3: line C

α: 0.01

This test is always one-tailed to the right. The statistic is the Snedecor's F, constructed as the MSTr divided by the MSEr if the value of the statistic is big, this means that there is a greater variance due to the treatments than to the error, this means that the population means are different. If the value of F is small, it means that the differences between populations are not significant ( may differ due to error and not treatment).

The critical region is:

$F_{k-1;n-k; 1-\alpha } = F_{2;15; 0.99} = 6.36$

If F ≥ 3.36, the decision is to reject the null hypothesis.

Looking at the given data:

$F= \frac{MSTr}{MSEr}$ = 11.32653

With this value the decision is to reject the null hypothesis.

Using the p-value method:

p-value: 0.001005

α: 0.01

The p-value is less than the significance level, the decision is to reject the null hypothesis.

At a level of 5%, there is significant evidence to say that at least one of the population means of the production ratio of the assembly lines A, B and C is different than the others.

b) In this item, you have to stop paying attention to the production ratio of the assembly line A to compare the population means of the production ratio of lines B and C.

(I'll use the same subscripts to be congruent with part a.)

The parameter to estimate is μ₂ - μ₃

The populations are the same as before, so you can still assume that the study variables have a normal distribution and their population variances are unknown but equal. The statistic to use under these conditions, since the sample sizes are 6 for both assembly lines, is a pooled-t for two independent variables with unknown but equal population variances.

t= (X[bar]₂ - X[bar]₃) - ( μ₂ - μ₃) ~t $_{n_2+n_3-2}$