All categories

17 days ago

James has saved $24.60. Dillon saved 2/3 of

Mathematics

2 answers:

Leona [9.2K]17 days ago

4 0

James has saved $24.60, while Dillon saved two-thirds of James's savings.

Dillon's savings: (2/3) * 24.60 = $16.40

The total amounts are as follows:

James = $24.60

Dillon = $16.40

Mara = 16.40 * 2 = $32.80.

To find the total, we combine the amounts:

24.60 + 16.40 + 32.80 = $73.80.

Leona [9.2K]17 days ago

3 0

James = 24.60
Dillon = 16.4
Mara = 32.8

You might be interested in

Calculating conditional probabilities - random permutations. About The letters (a, b, c, d, e, f, g) are put in a random order.

AnnZ [9099]

A="b is situated in the center"

B="c lies to the right of b"

C="The letters def occur sequentially in that arrangement"

a) b can occupy 7 positions; however, only one of these is the center. Therefore, P(A)=1/7

b) Let X=i; "b holds the i-th position"

Y=j; "c occupies the j-th position"

$P(B)=\displaystyle\sum_{i=1}^{6}(P(X=i)\displaystyle\sum_{j=i+1}^{7}P(Y=j))=\displaystyle\sum_{i=1}^{6}\frac{1}{7}(\displaystyle\sum_{j=i+1}^{7}\frac{1}{6})=\frac{1}{42}\displaystyle\sum_{i=1}^{6}(\displaystyle\sum_{j=i+1}^{7}1)=\frac{6+5+4+3+2+1}{42}=\frac{1}{2}$

P(B)=1/2

c) Let X=i; "d holds the i-th position"

Y=j; "e occupies the j-th position"

Let Z=k; "f is in the i-th position"

$P(C)=\displaystyle\sum_{i=1}^{5}( P(X=i)P(Y=i+1)P(Z=i+2))=\displaystyle\sum_{i=1}^{5}(\frac{1}{7}\times\frac{1}{6}\times\frac{1}{5})=\frac{1}{210}\displaystyle\sum_{i=1}^{5}(1)=\frac{1}{42}$

P(C)=1/42

P(A∩C)=2*(1/7*1/6*1/5*1/4)=1/420

$P(B\cap C)=\displaystyle\sum_{i=1}^{3} P(X=i)P(Y=i+1)P(Z=i+2)\displaystyle\sum_{j=i+3}^{6}P(V=j)P(W=j+1)=\displaystyle\sum_{i=1}^{3}\frac{1}{6}\frac{1}{7}\frac{1}{5}(\displaystyle\sum_{j=1+3}^{6}\frac{1}{4}\frac{1}{3})=1/420$

P(B∩A)=3*(1/7*1/6)=1/14

P(A|C)=P(A∩C)/P(C)=(1/420)/(1/42)=1/10

P(B|C)=P(B∩C)/P(C)=(1/420)/(1/42)=1/10

P(A|B)=P(B∩A)/P(B)=(1/14)/(1/2)=1/7

P(A∩B)=1/14

P(A)P(B)=(1/7)*(1/2)=1/14

Events A and B are independent

P(A∩C)=1/420

P(A)P(C)=(1/7)*(1/42)=1/294

Events A and C are not independent

P(B∩C)=1/420

P(B)P(C)=(1/2)*(1/42)=1/84

Events B and C are not independent

8 0

8 days ago

the moon is about 240,000 miles from earth .What is the distance written as a whole number multiplied by a power of ten?

PIT_PIT [9117]

The distance to the moon is approximately 240,000 miles. This can be expressed as 2.4 multiplied by 10 raised to the power of 5.

8 0

24 days ago

Read 2 more answers

Len made 1 1/3 liters of punch. He added 2/5 liters of water to make the punch. How much water was used for each liter of punch?

babunello [8412]

Answer:

3/10 liter

Step-by-step explanation:

Assuming your statement indicates that in 4/3 liters of punch, there is 2/5 liters of water, then the proportion of water in the punch is calculated as:

(2/5)/(4/3) = (2/5)(3/4) = 3/10

So, 3/10 of a liter of water is included in each liter of punch.

5 0

1 month ago

Question 1 Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your metho

babunello [8412]

Answer:

(a) The 95% confidence interval representing the percentage of the entire U.S. population that would select American football as their preferred television sport is (0.34, 0.40).

(b) Not reasonable.

Step-by-step explanation:

Given:

n = 1000

$\hat p$ = 0.37

(a)

The confidence interval (1 - α)% for proportion p is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Where:

$\hat p$ = the sample proportion

n = sample size

$z_{\alpha/2}$ = critical z value.

Calculate the critical value of z for a 95% confidence level as shown:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Refer to a z-table for the necessary value.

Compute the 95% confidence interval for proportion p as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.37\pm 1.96\times\sqrt{\frac{0.37(1-0.37)}{1000}}$

$=0.37\pm 0.03\\=(0.34, 0.40)$

Thus, the 95% confidence interval indicating the proportion of individuals in the U.S. who might say their preferred sport on TV is American football is (0.34, 0.40).

(b)

Next, we must assess if it's rational to consider that the actual percent of people in the United States who favor American football on television is 33%.

The hypothesis is defined as:

H₀: The portion of the U.S. population claiming American football as their favorite sport on television is 33%, meaning p = 0.33.

Hₐ: The proportion of people in the U.S. whose favorite sport to watch on television is not 33%, or p ≠ 0.33

This hypothesis can be verified using a confidence interval.

The decision rule:

If the (1 - α)% confidence interval contains the null value of the hypothesis, then the null hypothesis is not rejected. If, however, the (1 - α)% confidence interval excludes the null value of the hypothesis, then the null hypothesis is rejected.

The confidence interval does encompass the null value of p, which is 0.33.

<pthus the="" null="" hypothesis="" will="" be="" rejected.=""><pin conclusion="" it="" is="">not reasonable to accept that 33% represents the actual percentage of those in the U.S. whose favorite televised sport is American football.

</pin></pthus></pthe>

6 0

1 month ago

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom

PIT_PIT [9117]

Answer:

C. 5 degrees of freedom for the numerator and 114 for the denominator

Step-by-step explanation:

Analysis of variance (ANOVA) is utilized to examine the variations among group means within a sample.

The sum of squares represents the cumulative square of variation, which refers to the deviation of each individual value from the grand mean.

Assuming there are $6$ groups and each group contains $j=1,\dots,20$ individuals, the variation can be calculated using the following formulas:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

This also has the property

$SST=SS_{between}+SS_{within}$

The numerator's degrees of freedom in this case is given by $df_{num}=df_{within}=k-1=6-1=5$ where k = 6 represents the number of groups.

The denominator's degrees of freedom in this scenario is indicated by $df_{den}=df_{between}=N-K=6*20-6=114$ .

The total degrees of freedom would be $df=N-1=6*20 -1 =119$ .

Thus, the appropriate answer would be 5 degrees of freedom for the numerator and 119 degrees of freedom for the denominator.

C. 5 numerator and 114 denominator degrees of freedom

8 0

24 days ago