All categories

3 years ago

Examples of a TRUE biconditional statement, please.

Mathematics

1 answer:

andrey2020 [161]3 years ago

7 0

Answer: two angles have the same measure if only and only if they are congruent

explanation:

A true biconditional statement is true both "forward" and backward". All definitions can be written as true biconditional statements.

You might be interested in

A school debate team has 4 girls and 6 boys. A total of 3 of the team members will be chosen to participate in the district deba

mariarad [96]

There are 4+6=10 people in the team.
First calculate in how many ways you can choose 3 people from a group of 10 people, using combination:
$(^{10} _3)=\frac{10!}{3!(10-3)!}=\frac{10!}{3! \times 7!}=\frac{7! \times 8 \times 9 \times 10}{6 \times 7!}=\frac{8 \times 9 \times 10}{6}=\frac{720}{6}=120$
You can choose 3 people in 120 ways.

You can select 1 girl from a group of 4 girls in 4 ways.
Calculate in how many ways you can choose 2 boys from a group of 6 boys:
$(^6 _2)=\frac{6!}{2! (6-2)!}=\frac{6!}{2! \times 4!}=\frac{4! \times 5 \times 6}{2 \times 4!}=\frac{5 \times 6}{2}=\frac{30}{2}=15$
You can choose 2 boys in 15 ways.
Using the rule of product, you can calculate that you can choose 1 girl and 2 boys in 4×15=60 ways.

The probability of choosing 1 girl and 2 boys is the number of ways you can choose 1 girl and 2 boys divided by the number of ways you can choose 3 people from the group.
$P=\frac{60}{120}=\frac{1}{2}=50\%$

The probability is 1/2, or 50%.

4 0

3 years ago

Simplify 8^-7 x 8^5 please show work

Pie

When you are multiplying exponents with the same base, you can add the exponents. This is represented as:

$x^a \cdot x^b = x^{(a +b)}$

In our case we are multiplying exponents with the same base 8 and exponents -7 and 5. The sum of -7 and 5 is -2, so our answer is $\boxed{8^{-2}}$ .

7 0

3 years ago

Evaluate to one decimal place

ANTONII [103]

Answer:

<u>The correct answer is C. 1.6</u>

Step-by-step explanation:

Let's recall that e or Euler's number is a mathematical constant that is the base of the natural logarithm, in other words, the unique number whose natural logarithm is equal to one. The value of e is approximately 2.71828.

Now, replacing e, we have:

2.71828∧(1/2) = √2.71828 = 1.6 (Rounding to one decimal place)

<u>The correct answer is C. 1.6</u>

3 0

3 years ago

Which of the following equations best represents the regression line for the data given in the

True [87]

The regression equation for the data given is y= -8.57 -2.31x

Step-by-step explanation:

The first step is to form a table as shown below;

x y xy x² y²

1 4 4 1 16

2 1 2 4 1

3 5 15 9 25

4 10 40 16 100

5 16 80 25 256

6 19 114 36 361

7 15 105 49 225

28 60 360 140 984 ------sum

A linear regression equation is in the form of y=A+Bx

where ;

x=independent variable

y=dependent variable

n=sample size/number of data points

A and B are constants that describe the y-intercept and the slope of the line

Calculating the constants;

A=(∑y)(∑x²) - (∑x)(∑xy) / n(∑x²) - (∑x)²

A=(60)(140) - (28)(360) / 7(140)-(28)²

A=8400 - 10080 /980-784

A= -1680/196

A= - 8.57

B= n(∑xy) - (∑x) (∑y) / n(∑x²) - (∑x)²

B= 7(360)-(28)(60) / 7(60) - (28)²

B=2520 - 1680 /420-784

B=840/-364

B= -2.31

y=A+Bx

y= -8.57 -2.31x

Learn More

Regression equation :brainly.com/question/12280902

Keywords : equations, regression line, data

#LearnwithBrainly

7 0

3 years ago

Each week Charlene uses 3/4 of a bag of cat food to feed her cats. She has 112 bags of cat food in stock. How long will her stoc

inessss [21]

The stock of cat food will last for 149 weeks.

Step-by-step explanation:

Given,

Bags of cat food in stock = 112

Bags used each week = $\frac{3}{4}\ of\ one\ bag$

Let,

x be the number of weeks.

Therefore,

$\frac{3}{4}x=112$

Multiplying both sides by 4/3

$\frac{4}{3}*\frac{3}{4}x=112*\frac{4}{3}\\x=\frac{448}{3}\\x=149.33$

Rounding off to nearest whole number;

x=149

The stock of cat food will last for 149 weeks.

Keywords: fraction, multiplication

Learn more about fractions at:

#LearnwithBrainly

4 0

3 years ago