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hjlf
3 years ago
13

A vendor sells ice cream from a cart on the boardwalk. He offers vanilla, chocolate, strawberry, blueberry, and pistachio ice cr

eam, served on either a waffle, sugar, or plain cone. How many different single-scoop ice-cream cones can you buy from this vendor?
Mathematics
1 answer:
Agata [3.3K]3 years ago
7 0

Answer:

The different single-scoop ice-cream cones can you buy from this vendor=12

Step-by-step explanation:

Given that a  vendor sells ice cream from a cart on the boardwalk. He offers vanilla, chocolate, strawberry, blueberry, and pistachio ice cream, served on either a waffle, sugar, or plain cone.

Different types of icecreams are 4

Types of cones are 3

For each ice cream say we can have either waffle, sugar or plain cone.

i.e. for each type of ice cream, we have 3 different cones.

Hence for 4 types of ice creams we have 3*4=12 different single scoop ice creamcones.

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An auto company claims that the fuel efficiency of its sedan has been substantially improved. A consumer advocate organization w
zzz [600]

Answer:

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021

df=n-1=12-1=11

p_v =P(t_{(11)}>2.021) =0.0342

If we compare the the p value with the significance level provided \alpha=0.1, we see that p_v < \alpha, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.  

Let put some notation :

x=test value 2017 , y = test value 2019

x: 28.7 32.1 29.6 30.5 31.9 30.9 32.3 33.1 29.6 30.8 31.1 31.6

y: 31.1 32.4 31.3 33.5 31.7 32.0 31.8 29.9 31.0 32.8 32.7 33.8

Solution to the problem

The system of hypothesis for this case are:

Null hypothesis: \mu_y- \mu_x \leq 0

Alternative hypothesis: \mu_y -\mu_x >0

Because if we have an improvement we expect that the values for 2019 would be higher compared with the values for 2017

The first step is calculate the difference d_i=y_i-x_i and we obtain this:

d: 2.4, 0.3, 1.7,3,-0.2, 1.1, -0.5, -3.2, 1.4, 2, 1.6, 2.2

The second step is calculate the mean difference  

\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{11.8}{12}=0.983

The third step would be calculate the standard deviation for the differences, and we got:

s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =1.685

We assume that the true difference follows a normal distribution. The 4th step is calculate the statistic given by :

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021

The next step is calculate the degrees of freedom given by:

df=n-1=12-1=11

Now we can calculate the p value, since we have a right tailed test the p value is given by:

p_v =P(t_{(11)}>2.021) =0.0342

If we compare the the p value with the significance level provided \alpha=0.1, we see that p_v < \alpha, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

4 0
2 years ago
In triangle A B D , the measure of angle A is 10 degree less than the measure of angle B . The measure of angle D is 20 degree m
elixir [45]

Answer:

<u><em>Measure of angle A is 27 7/9 degrees.</em></u>

Step-by-step explanation:

Lets call measure of angle A is <em><u>X-10</u></em>

Lets call measure of angle B is X

Lets call measure of angle D is 2.5X+20

We know that the sum of triangles add up to 180 degrees

X+X-10+2.5X+20=180

X=37 7/9

So measure of angle A is 27 7/9 degrees.

I hope this is right. :)

8 0
2 years ago
In a lab experiment, 1900 bacteria are placed in a petri dish. The conditions are such
GREYUIT [131]

Answer:

393 bacteria

Step-by-step explanation:

First find how much it would increase per hours :

1900 / 29 = 65.5172414

Then take this and multiply it by 6 to get :

393.103448

Round it to the nearest whole number to get:

393 bacteria

3 0
2 years ago
Find the quotient of these Complex Numbers. <br><br><br> (5-i) / (3+2i)
JulsSmile [24]

Let the given complex number

z = x + ix = \dfrac{5-i}{3+2i}

We have to find the standard form of complex number.

Solution:

∴ x + iy = \dfrac{5-i}{3+2i}

Rationalising numerator part of complex number, we get

x + iy = \dfrac{5-i}{3+2i}\times \dfrac{3-2i}{3-2i}

⇒ x + iy = \dfrac{(5-i)(3-2i)}{3^2-(2i)^2}

Using the algebraic identity:

(a + b)(a - b) = a^{2} - b^{2}

⇒ x + iy = \dfrac{15-10i-3i+2i^2}{9-4i^2}

⇒ x + iy = \dfrac{15-13i+2(-1)}{9-4(-1)} [ ∵ i^{2} =-1]

⇒ x + iy = \dfrac{15-2-13i}{9+4}

⇒ x + iy = \dfrac{13-13i}{13}

⇒ x + iy = \dfrac{13(1-i)}{13}

⇒ x + iy = 1 - i

Thus, the given complex number in standard form as "1 - i".

5 0
3 years ago
What is the value of the 5 in the number 2.005?<br> 0.05<br> 0.5<br> 0.005<br> 5
Bogdan [553]

Answer:

0.005

Step-by-step explanation:

4 0
3 years ago
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