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Lelu [443]
3 years ago
13

hilary wants to fill a mini cake pan with batter to make a mini cake for philip's party. the cake pan is 4.0 inches long, 9.0 in

ches wide, and 2.2 inches deep. what is the volume of the cake pan?
Mathematics
1 answer:
igomit [66]3 years ago
6 0
Simple,

4x9x2.2 = volume = 79.2 cubic centimeters

79.2/1000 = 0.0792 litres

not sure if you wanted it in cubic or litres FYI if it doesn't say put the answer in cubic :)
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What number must you add to complete the square? x2 + 14x = -5
denis-greek [22]
U take half of the x term and square it....then add to both sides

14/2 = 7.......7^2 = 49...so u add 49 to both sides
6 0
3 years ago
Read 2 more answers
In the figure on the right, Triangle EFG is congruent to Triangle LMN. Find the value of x. Then describe the Transformations th
Reptile [31]

Answer:

Step-by-step explanation:

ΔEFG ≅ΔLMN

Therefore,  MN = FG    { corresponding part of congruence triangle}

x + 3 = 13

x = 13 - 3

x = 10 cm

3 0
3 years ago
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3. The average age of online consumers a few years ago was 23.3 years with a standard deviation of 5.3 years. It is believed the
Slav-nsk [51]

Answer:

We cant say, with α =0.01, that the average age changed. The p-value is 0.014

Step-by-step explanation:

As a consecuence of the Central Limit Theorem, the mean sample has a distribution approximately normal, with unknown mean and standard deviation \sigma = 5.3/\sqrt{20} = 1.1851 (the standard deviation of one single sample divided by the  sqaure root of the sample lenght).

The null hypothesis H₀ is that the average age is still 23.3 (the mean is 23.3). The alternative hypothesis is that the mean is different. We want to see if we can refute H₀ with significance level α =0.01.

Lets call X the mean of a random sample of 20 online shoppers. As we discuse above, X is approximately normal with unknown mean and standard deviation equal to 1.1851 . If we take the hypothesis H₀ as True, then the mean will be 23.3, and if we standarize X, we have that the distribution

W = \frac{X - 23.3}{1.1851}

Will have a distribution approximately normal, with mean 0 and standard deviation 1.

The values of the cummulative ditribution of the normal function can be found in the attached file. Since we want a significance level of 0.01, then we need a value Z such that

P(-Z < W < Z) = 0.99

For the symmetry of the standard Normal distribution, we have that Φ(Z) = 1-Φ(-Z), where Φ is the cummulative distribution function of the standard Normal random variable. Therefore, we want Z such that

Φ(Z) = 0.995

If we look at the table, we will found that Z = 2.57, thus,

0.99 = P(-2.57 < W < 2.57) = P(-2.57 < \frac{X-23.3}{1.1851} < 2.57)\\ = P(-2.57*1.1851 + 23.3 < X < 2.57*1.1851 + 23.3) = P(20.254 < X < 26.345)

Thus, we will refute the hypothesis if the observed value of X lies outside the interval [20.254, 26.345].

Since the observed value is 26.2, then we dont refute H₀, So we dont accept that the number average age of online consumers has changed.

For us to refute the hypothesis we need Z such that, for the observed value, |W| > Z. Replacing X by 26.2, we have that [tex] W = \frac{26.2-23.3}{1.1851} = 2.4470. We can observe that Φ(2.447) = 0.993, substracting that amount from 1 and multiplying by 2 (because it can take low values too), we obtain that the p-value is 0.014.  

Download pdf
8 0
3 years ago
a garden pond is in the shape of a rectangle that measures 5 m by 3 m. a stone path is built all around the pond. this path is t
Inessa [10]

Answer:

<u>1.16 m (approximately)</u>

Step-by-step explanation:

Let x be the width of the path.

Total area  = (5+2x)(3+2x) = 39

Expand and simplify

4x²+ 16x+15-39 = 0

4x² + 16x - 24 = 0

Simplify

x² + 4x -6 = 0

Rational factoring does not work, so use quadratic formula

x = +/- sqrt(10) -2

= 1.16 or -5.16 (reject)

= <u>1.16 m (approximately)</u>

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3 years ago
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