Given the following definitions: U = {1, 2, 3, 4, 5, 6, 7} A = {1, 2, 4, 5} B = {1, 3, 5, 7} How many elements are in A' ∪ B ?

The ratio of losses to wins for Kyle's team is 3 to 2. If the team had played the same number of games, but had won twice as man

Fiesta28 [93]

Answer: The new ratio will be 1/4

Explanation: The initial ratio of losses to wins is 3 to 2. If we sum the numer of losses and wins 3 + 2 = 5 games, that means they loss 3 out of 5 games , and they win 2 out of 5 games.

So if they had won twice as many of the games, that is 2*2=4. And since the number of games is the same ( 5 ), then they would have won 4 games and loss only 1.

So the new ratio of losses to wins will be 1 to 4, or expressed in a fraction: 1/4

4 0

1 year ago

Read 2 more answers

A group of 5 friends decides to share the cost of a party together. If the party costs $1,100, how much does each friend pay?

seraphim [82]

Answer:

1,100 dollars divided by 5 friends is 220 dollars so each friend would have to pay 220 dollars

Step-by-step explanation:

7 0

1 year ago

ANSWER ALL 5 PARTS.

N76 [4]

A function $f$ from a set A to a set B is defined as a relation that assings to each element $x$ in the set A exactly one element $y$ in the set B. The set A is called the domain of the function while the set B is the range. So we have five statements and need to find some functions. Melissa decides to reserve a patch in her vegetable garden for growing bell peppers. If each side of the tomato patch is $x$ feet, then we have a square patch as shown in the Figure below.

1.a) Write the function Wa(x) representing the width of the bell pepper patch.

We know that she wants its width to be half the width of the tomato patch. Let $x$ be the width of the tomato patch, then the function that matches this statement is:

$\boxed{Wa(x)=\frac{x}{2}}$

1.b) Write the function La(x) representing the length of the bell pepper patch.

In this case Melissa wants its length to exceed the length of the tomato patch by 2 feet. To do this we enlarge the length of the tomato patch 2 feet. Therefore the function is the following:

 $\boxed{La(x)=x+2}$

2. Area of the bell pepper patch in terms of x.

Given that the bell pepper patch is a rectangle, then the area of a rectangle is the product of the length and width. So:

 $A=(\frac{x}{2})(x+2) \\ \\ \therefore \boxed{A=\frac{x(x+2)}{2}}$

3. Combined area of the tomato patch and the bell pepper patch.

This function is the sum of both the area of the tomato patch and the bell pepper patch. So:

 $Aar(x)=x^{2}+\frac{x(x+2)}{2} \rightarrow Aar(x)=x^{2}+ \frac{x^{2}}{2}+x \rightarrow Aar(x)=\frac{3x^{2}}{2}+x \\ \\ \therefore \boxed{Aar(x)=\frac{x(3x+2)}{2}}$

4. Write the function Aa(x) for the remaining planting area in the garden.

The remaining planting area in the garden are the rectangles in red. So we need to subtract the width of the bell pepper patch from the width of the tomato patch and multiply it by 2. In mathematical language this is given by:

 $Aa(x)=2(x-\frac{x}{2}) \rightarrow Aa(x)=x$

5. Find the area of the remaining space in the garden after planting tomatoes and bell peppers.

Given that Melissa wants the area of the bell pepper patch to be 31.5 square feet, then it is true that:

 $31.5=\frac{x(x+2)}{2} \rightarrow x^{2}+2x-64=0 \\ \\ solving \ for \ x: \\ x=7.06$

Therefore the area of the remaining space is:

 $\boxed{Aa(7.06)=7.06ft^{2}}$

6 0

2 years ago

A list has 10 numbers. Each number is a 1, 2, or 3. The average is 2 and the SD is 0. What is the list?

OLga [1]

Answer:

1, 1, 1, 2, 2, 2, 2, 3, 3, 3

Step-by-step explanation:

Since the standard deviation = 0

And the mean of the number = 2

If X is the sum of all the numbers, then

X/10 = 2

Cross multiply and make X the subject of formula

X = 2 × 10 = 20

The sum of the numbers will be 20

The number will be

1, 1, 1, 2, 2, 2, 2, 3, 3, 3

The sum of the above numbers is equal to 20 and the average value of the numbers is equal to 2.

7 0

1 year ago

The following table shows the number of hours some teachers in two schools expect students to spend on homework each week: Schoo

Lerok [7]

Answer:

For school A: Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17, IQR=9.5

For school B: Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19, IQR=7.5

No, the box plots are not symmetric.

Step-by-step explanation:

Part A

The given data sets are

School A : 9,14,15,17,17,7,15,6,6

School B : 12,8,13,11,19,15,16,5,8

Arrange the data in ascending order.

School A : 6,6,7,9,14,15,15,17,17

School B : 5,8,8,11,12,13,15,16,19

Divide each data set in four equal parts.

School A : (6,6),(7,9),14,(15,15),(17,17)

School B : (5,8),(8,11),12,(13,15),(16,19)

For school A:

Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17

Interquartile range of the data is

$IQR=Q_3-Q_1=16-6.5=9.5$

For school B:

Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19

Interquartile range of the data is

$IQR=Q_3-Q_1=15.5-8=7.5$

Part B:

The box plots are not symmetric because the data values are different. Five number summary and IQR of both the data set are different.

4 0

2 years ago