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2 years ago

How many odd numbers with 4 different digits, can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8? (No repetition is allowed)

Mathematics

1 answer:

olga55 [171]2 years ago

6 0

Answer:

840 ( D )

Step-by-step explanation:

GIVEN DIGITS : 1,2,3,4,5,6,7,8

Number of odd numbers = 4

Number of even numbers = 4

therefore the number of odd numbers with 4 different digits can be formed by the same way the number of even numbers ( without repetition )

Hence the number of ways odd numbers with 4 different digits = Total number of ways of forming 4 digit numbers / 2

8*7*6*5 = 1680 / 2 = 840 ways

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Alice and Bob are playing a game. Alice starts first. On Alice's turn, she flips a coin. If she gets a heads, she wins. If not,

trapecia [35]

Answer:

The probability that Alice wins the game= $\frac{1}{2}$

Step-by-step explanation:

We are given that Alice and Bob are playing a game .

We have to find the probability that Alice wins the game .

If Alice win when she gets head and lose when she gets tail.Bob wins when she gets tail and she lose when she gets head.

Total results in a coin=Head, tail=2

Number of head in a coin=1

Number of tail in a coin= 1

Probability is defined as the possibility of an event that occurred

$P(E)=\frac{Number\;of\;favourable\;cases}{total\;of\;cases}$

The probability that Alice wins the game= $\frac{Number\;of\;favourable\;cases}{Total\;number\;of\;cases}$

The probability that Alice wins the game= $\frac{number \;of \;heads}{Total\; results}$

The probability that Alice wins the game= $\frac{1}{2}$

8 0

2 years ago

What are the differences among an experiment, a study, and a survey? Complete the explanation of the differences by selecting th

artcher [175]

Answer:

The full question is

What are the differences among an experiment, a study, and a survey?

1. In an observational study, randomization of subjects ______

A. occurs

B. does not occur

We understand randomization as a random process of assigning experimental subjects to treatment groups. Through this process, we have more control about variables which are not related to the experiment.

In an observational study, the researcher doesn't change anything, he or she studies the events as they are, without using any randomization process.

Therefore, the right answer here is B. 

2. A survey _______

A. poses no interference on subjects

B. makes inferences about a population

A survey poses no interference on subjects, actually if it does, then that survey is not reliable. An important charactersitic of a survey is that it must be objective, that way it will be reliable enough to use it in the research.

Therefore, the right answer is A.

3. In an experiment, ___________ to discern differences in a response variable.

A. treatment is imposed

B. inferences are made

C. randomization does not occur

Experiments are characterized by having certain "stimulus" at least in one group of subjects, that way researches compare data sets to prove their hypothesis.

Therefore, the right answer here is A.

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2 years ago

There are 1800 gym members in total. 3 4 are aged 25 - 59 years, 1 5 are over 60 years and the remainder are under 25 years. How

fomenos

There are 1751 members under the age of 25.

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1 year ago

In a scale drawing of an apartment 1 centimeter represents 2 3/4 feet. if the length of the kitchens is 4 1/2 cm on the scale dr

rusak2 [61]

Given: 1 cm = 2 3/4 ft ; kitchen length = 4 1/2 cm
2 3/4 = 11/4; 4 1/2= 9/2

11/4 x 9/2 = 99/8 =12 3/8

OR You could use decimals

2 3/4 = 2.75 ; 4 1/2 = 4.5
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5 0

2 years 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