MATHEMATICS COLLEGE

Give the values of A, B, and C needed to write the equation's general form.(5 + x)(5 - x) = 7

1. A = 1; B = 0; C = -18
2. A= -1; B = 0; C = 25
3. A = 25; B = 0; C = -1

Answers

Answer 1
Answer:

Given:

The equation is:

(5+x)(5-x)=7

To find:

The value of A, B and C for the equation's general form.

Solution:

We have,

(5+x)(5-x)=7

Using distribution property, we get

(5)(5)+(5)(-x)+(x)(5)+(x)(-x)=7

25-5x+5x-x^2=7

25-x^2=7

Taking all terms on one side, we get

25-x^2-7=0

-x^2+18=0

-(x^2-18)=0

x^2-18=0

On comparing this equation with the general form of a quadratic equation Ax^2+Bx+C=0, we get

A=1

B=0

C=-18

Therefore, the correct option is 1.

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Ruben bought 666 comic books for \$21$21dollar sign, 21. Each comic book was the same price. What was the cost for 111 comic books?

A field is 53 1/3 yards wide. What is the width of the field in feet?

Answers

Answer: The  width of the field = 160 feet

Step-by-step explanation:

We are given that , A field is 53(1)/(3) yards wide.

That means , The width of the field = 53(1)/(3) yards

Since , the fraction is in mixed for , so first we convert this into improper fraction.

53(1)/(3)=(3(53)+1)/(3)=(160)/(3)

Therefore , the width of the field = (160)/(3) yards

Since 1 yard = 3 feet.

⇒ the width of the field = (160)/(3)*3 feet

Therefore , the width of the field = 160 feet

Consider an unreliable communication channel that can successfully send a message with probability 1/2, or otherwise, the message is lost with probability 1/2. How many times do we need to transmit the message over this unreliable channel so that with probability 63/64 the message is received at least once? Explain your answer. Hint: treat this as a Bernoulli process with a probability of success 1/2. The question is equivalent to: how many times do you have to try until you get at least one success?

Answers

Answer:

6 times we need to transmit the message over this unreliable channel so that with probability 63/64.

Step-by-step explanation:

Consider the provided information.

Let x is the number of times massage received.

It is given that the probability of successfully is 1/2.

Thus p = 1/2 and q = 1/2

We want the number of times do we need to transmit the message over this unreliable channel so that with probability 63/64 the message is received at least once.

According to the binomial distribution:

P(X=x)=(n!)/(r!(n-r)!)p^rq^(n-r)

We want message is received at least once. This can be written as:

P(X\geq 1)=1-P(x=0)

The probability of at least once is given as 63/64 we need to find the number of times we need to send the massage.

(63)/(64)=1-(n!)/(0!(n-0)!)(1)/(2)^0(1)/(2)^(n-0)

(63)/(64)=1-(n!)/(n!)(1)/(2)^(n)

(63)/(64)=1-(1)/(2)^(n)

(1)/(2)^(n)=1-(63)/(64)

(1)/(2)^(n)=(1)/(64)

By comparing the value number we find that the value of n should be 6.

Hence, 6 times we need to transmit the message over this unreliable channel so that with probability 63/64.

A police officer claims that the proportion of accidents that occur in the daytime (versus nighttime) at a certain intersection is 35%. To test this claim, a random sample of 500 accidents at this intersection was examined from police records it is determined that 156 accidents occurred in the daytime. The following is the setup for this hypothesis test: {H0:p=0.35Ha:p≠0.35 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. Provide your answer below:

Answers

Answer: -1.78

Step-by-step explanation:

As per given description, we have

Population proportion : p=0.35

Sample size : n= 500

Sample proportion : \hat{p}=(156)/(500)=0.312

Test statistic for population proportion :-

z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\n\n\n=\frac{0.312-0.35}{\sqrt{(0.35(1-0.35))/(500)}}\n\n=-1.78146747757\ \ \text{(Simplified)}\n\n\approx-1.78

Hence, the test statistic for this hypothesis test for a proportion= -1.78

A university was interested in examining the overall effectiveness of its online statistics course, along with the effectiveness of particular aspects of the course. First, the university wanted to see whether the online course was better than a standard course. Second, the university wanted to know whether students learned best using Excel, using RStudio, or using no statistical package at all. The university randomly selected a group of 30 students and administered one of the different variants of the course (i.e., traditional or online, coupled with one of the software options) to each student. The success of each variant was measured by the students' average improvement between a pre-test and a post-test. How many treatment groups are there in this study? a. 3
b. 4
c. 5
d. 6
e. 7

Answers

Answer:

A university was interested in examining the overall effectiveness of its online statistics course, along with the effectiveness of particular aspects of the course. First, the university wanted to see whether the online course was better than a standard course. Second, the university wanted to know whether students learned best using Excel, using RStudio, or using no statistical package at all. The university randomly selected a group of 30 students and administered one of the different variants of the course (i.e., traditional or online, coupled with one of the software options) to each student. The success of each variant was measured by the students' average improvement between a pre-test and a post-test. How many treatment groups are there in this study?

Option D is correct - There are 6 treatment groups in this study.

Step-by-step explanation:

The number of treatment groups is equal to the number of possible combinations of the values of the factors.

In the question given, we have two factors: type of instruction (traditional/online) and software (Excel/Minitab/none).

Since there are 2 values for 'type of instruction' and 3 values for 'software'. Hence the number of treatment groups = 2*3 = 6.

Answer:

The answer is D: 5

Step-by-step explanation:

-Online course,

-Program to use,

- Number of students,

-Administered variant,

-Measurement of the average student.

7h + 10 = 9h + 4

A. h=3

B. h=4

C. h=5

D. h=6

Answers

Answer:

A. h=3

Step-by-step explanation:

Step-by-step explanation:

soln

7h + 10 = 9h + 4

then you correct like terms together

9h - 7h = 10 - 4

2h = 6

2 2

h = 3

the is A

Find the quotient: –10/19÷(−5/7)

Answers

Answer:

14/19

Step-by-step explanation:

Note that there are two " - " signs here.  Thus, the end result will be " + "

We move from left to right, obtaining first 10/19 divided by (5/7):

10

----- ÷ (5/7)

19

To divide by (5/7), invert (5/7) and then multiply.  We get:

10      7      2(7)

----- * ----- = ------- = 14/19

19       5       19
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