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2 years ago

5

The amount of rhubarb in the original recipe is 3 1/2 cups. Using what you know of whole numbers and what you know of fractions,

explain, how you could triple that mixed number.

1 answer:

Alexxx [7]2 years ago

8 0

The easiest way, I think, is to convert the mixed number into an improper fraction, then multiply by 3.
3 1/2 = 7/2
7/2 · 3 = 21/2
now just change the improper fraction back to a mixed number by dividing and putting the remainder into fraction form
21/2 = 10 1/2

You could also multiply the whole number by 3 and the fraction by 3, ending up with 9 3/2, but then have to convert the improper fraction into a mixed number
3/2 = 1 1/2
then add the numbers together
9 + 1 1/2 = 10 1/2
either way works, whatever is easiest for you.

You might be interested in

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assig

Keith_Richards [23]

Answer:

1. Null hypothesis: $\mu_{A}=\mu_{B}=\mu_{C}$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=A,B,C$

2. D. 36

3. C. 34

4. B. 1.059

5. B. 8.02

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Part 1

The hypothesis for this case are:

Null hypothesis: $\mu_{A}=\mu_{B}=\mu_{C}$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=A,B,C$

Part 2

In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.

If we assume that we have $p$ groups and on each group from $j=1,\dots,p$ we have $n_j$ individuals on each group we can define the following formulas of variation:

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

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

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

And we have this property

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

We need to find the mean for each group first and the grand mean.

$\bar X =\frac{\sum_{i=1}^n x_i}{n}$

If we apply the before formula we can find the mean for each group

$\bar X_A = 27$ , $\bar X_B = 24$ , $\bar X_C = 30$ . And the grand mean $\bar X = 27$

Now we can find the sum of squares between:

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

Each group have a sample size of 4 so then $n_j =4$

$SS_{between}=SS_{model}=4(27-27)^2 +4(24-27)^2 +4(30-27)^2=72$

The degrees of freedom for the variation Between is given by $df_{between}=k-1=3-1=2$ , Where k the number of groups k=3.

Now we can find the mean square between treatments (MSTR) we just need to use this formula:

$MSTR=\frac{SS_{between}}{k-1}=\frac{72}{2}=36$

D. 36

Part 3

For the mean square within treatments value first we need to find the sum of squares within and the degrees of freedom.

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

$SS_{error}=(20-27)^2 +(30-27)^2 +(25-27)^2 +(33-27)^2 +(22-24)^2 +(26-24)^2 +(20-24)^2 +(28-24)^2 +(40-30)^2 +(30-30)^2 +(28-30)^2 +(22-30)^2 =306$

And the degrees of freedom are given by:

$df_{within}=N-k =3*4 -3 = 12-3=9$ . N represent the total number of individuals we have 3 groups each one with a size of 4 individuals. And k the number of groups k=3.

And now we can find the mean square within treatments:

$MSE=\frac{SS_{within}}{N-k}=\frac{306}{9}=34$

C. 34

Part 4

The test statistic F is given by this formula:

$F=\frac{MSTR}{MSE}=\frac{36}{34}=1.059$

B. 1.059

Part 5

The critical value is from a F distribution with degrees of freedom in the numerator of 2 and on the denominator of 9 such that we have 0.01 of the area in the distribution on the right.

And we can use excel to find this critical value with this function:

"=F.INV(1-0.01,2,9)"

And we will see that the critical value is $F_{crit}=8.02$

B. 8.02

5 0

2 years ago

House price y is estimated as a function of the square footage of a house x and a dummy variable d that equals 1 if the house ha

tresset_1 [31]

Answer:

a-1. The predicted price of a house with ocean views and square footage of 2,000 is $411,500.00.

a-2. The predicted price of a house with ocean views and square footage of 3,000 is $531,500.00.

b-1. The predicted price (in $1,000s) of a house without ocean views and square footage of 2,000 is $358,900.

b-2. The predicted price of a house without ocean views and square footage of 3,000 is $478,900.00.

c. The correct option is An ocean view increases the value of a house by approximately $52,600.

Step-by-step explanation:

Given:

yˆ = 118.90 + 0.12x + 52.60d ………………. (1)

a-1. Compute the predicted price (in $1,000s) of a house with ocean views and square footage of 2,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.)

This implies that we have:

x = 2,000

d = 1

Substituting the values into equation (1), we have:

yˆ = 118.90 + (0.12 * 2000) + (52.60 * 1) = 411.50

Since the predicted price is in $1,000s, we have:

yˆ = 411.50 * $1000

yˆ = $411,500.00

Therefore, the predicted price of a house with ocean views and square footage of 2,000 is $411,500.00.

a-2. Compute the predicted price (in $1,000s) of a house with ocean views and square footage of 3,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.)

This implies that we have:

x = 3,000

d = 1

Substituting the values into equation (1), we have:

yˆ = 118.90 + (0.12 * 3,000) + (52.60 * 1) = 531.50

Since the predicted price is in $1,000s, we have:

yˆ = 531.50 * $1000

yˆ = $531,500.00

Therefore, the predicted price of a house with ocean views and square footage of 3,000 is $531,500.00.

b-1. Compute the predicted price (in $1,000s) of a house without ocean views and square footage of 2,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.)

This implies that we have:

x = 2,000

d = 0

Substituting the values into equation (1), we have:

yˆ = 118.90 + (0.12 * 2000) + (52.60 * 0) = 358.90

Since the predicted price is in $1,000s, we have:

yˆ = 358.90 * $1000

yˆ = $358,900.00

Therefore, the predicted price of a house without ocean views and square footage of 2,000 is $358,900.00.

b-2. Compute the predicted price (in $1,000s) of a house without ocean views and square footage of 3,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.)

This implies that we have:

x = 3,000

d = 0

Substituting the values into equation (1), we have:

yˆ = 118.90 + (0.12 * 3,000) + (52.60 * 0) = 478.90

Since the predicted price is in $1,000s, we have:

yˆ = 478.90 * $1000

yˆ = $478,900.00

Therefore, the predicted price of a house without ocean views and square footage of 3,000 is $478,900.00.

c. Discuss the impact of ocean views on the house price.

Since the coefficient of d in equation (1) is 52.60 and positive, and the predicted price is in $1,000s; the correct option is An ocean view increases the value of a house by approximately $52,600.

3 0

2 years ago

A composite figure is comprised of a square, trapezoid, and a rectangle. The square has side lengths of 10 centimeters. The trap

Evgesh-ka [11]

The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.

Step-by-step explanation:

The given is,

Dimensions of square has length of 10 cm

Trapezoid has base lengths of 8 cm and 14 cm

The length of the trapezoid is 4 cm

Rectangle has side length of 20 cm and 6 cm

Step:1

Area of composite figure = Area of square + Area of Trapezoid

+ Area of rectangle.......................(1)

Step:2

Formula for area of square,

$A_{square} = a^{2}$

where, a - side of length = 10 cm

$=10^{2}$

$=100$

Area of square, $A_{square}$ = 100 Square centimeter

Step:3

Formula for area of Trapezoid,

$A_{Trapezoid}$ = $\frac{a+b}{2} h$ .......................................(2)

Where, a - 8 cm

b - 14 cm

h - 4 cm

From equation (2)

= $\frac{8+14}{2} 4$

= $(11)(4)$

= 44

Area of Trapezoid, $A_{Trapezoid}$ = 44 square centimeters

Step:4

Formula for area of rectangle,

$A_{Rectangle} =lb$ ......................................(3)

Where, l = 20 cm

b = 6 cm

Equation (3) becomes,

$= (20)(6)$

= 120

Area of rectangle, $A_{Rectangle}$ = 120 square centimeters

Step:5

From Equation (1),

$A_{Composite}$ = 100 + 44 + 120

= 264 square centimeters

Result:

The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.

4 0

2 years ago

Read 2 more answers

The diagram shows a pentagon. It has one line of symmetry.

Nina [5.8K]

Answer:

A) 10x + 8 = 21

B) x = 1.3

Step-by-step explanation:

2(2x + 3) + 2(x + 1) + 4x = 21

4x + 6 + 2x + 2 + 4x = 21

10x + 8 = 21

10x = 13

x = 1.3 cm

7 0

2 years ago

A community hall is in the shape of a cuboid the hall is 40m long 15m high and 3m wide. 10 litre paint covers 25m squared costs

krek1111 [17]

Answer:

Total cost for tiles and paints is $924.

Step-by-step explanation:

We have been given that a community hall is in the shape of a cuboid. The hall is 40m long 15m high and 3m wide.

The paint will be required for 4 walls and ceiling.

Let us find area of walls and ceiling.

$\text{Area of walls and ceiling}=(2*40*15)+(2*3*15)+(40*3)$

$\text{Area of walls and ceiling}=1200+90+120$

$\text{Area of walls and ceiling}=1410$

Therefore, the area of walls and ceiling is 1410 square meters.

Given: Cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter. Therefore,

$\text{ The total painting cost}=10*(\frac{1410}{25})$

$\text{ The total painting cost}=10*56.4=564$

Therefore, the total painting cost is $564.

Tiles will be required for floor. Let us find the area of floor.

$\text{Area of floor} = 40*3\text{ square meters}$

$\text{Area of floor} =120\text{ square meters}$

Given: 1m squared floor tiles costs $3. So,

$\text{Total cost for tiles} = 3*120 = 360$

Therefore, the total cost for tiles is $360.

Now let us find combined total cost of tiles and paint.

$\text{Combined total cost}= 564+360 = 924$

Therefore, the combined total cost of tiles and paint is $924.

5 0

2 years ago