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3 years ago

The nine cat in a pet store were weighed. their weights (in pounds) are given 7,7,7,2,4,4,7,1,9

2 answers:

8 0

To easily find the mode, put the numbers in order from least to greatest

Which is, 1,2,4,4,7,7,7,7,9

Count how many times each number occurs. The number that occurs the most is the mode!

7 occurs the most! So the mode is 7.

Find the largest and smallest values in the set

They are 1 and 9.

Subtract the smallest value from the largest value to find the range

1 - 9 = 8

The range is 8.

bulgar [2K]3 years ago

3 0

The mode is the number in a set of numbers that you see the most...
The range is the difference between the highest and lowest number....
So for the numbers 7, 7, 7, 2, 4, 4, 7, 1, 9,
The mode would be 7 as it's the most common number
The range would be 8 because if you subtract the lowest number from the highest (9-1) you would get 8

Hope this helps! :)

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Complete the identity. 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

The expression $(a -b) (a+ 2 b)$ becomes

$(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

..............................................................................................................................

In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

..............................................................................................................................

Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

................................................................................................................................

In trigonometry

$secx = \frac{1}{cosx}$

$tanx = \frac{sinx}{cosx}$

Substitute the expressions for secx and tanx

................................................................................................................................

$(secx)^2+ 2 (tanx)^2$ becomes

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

Open bracket

$\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})$

$\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}$

Add Fraction

$\frac{1 + 2sin^2x}{cos^2x}$ ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

$sin^2x + cos^2x= 1$

Make $sin^2x$ the subject of formula

$sin^2x= 1 - cos^2x$

................................................................................................................................

Substitute the expressions for $1 - cos^2x$ for $sin^2x$

$\frac{1 + 2(1 - cos^2x)}{cos^2x}$

Open bracket

$\frac{1 + 2 - 2cos^2x}{cos^2x}$

$\frac{3 - 2cos^2x}{cos^2x}$ ---------------------- This is another equivalence

8 0

3 years ago

The area of a rectangular patio is 9 5/8 square meters. The width of the patio is 2 3/4 meters. What is the length? Enter your a

Oduvanchick [21]

Answer:

3 1/2 meters

Step-by-step explanation:

A = LW

9 5/8 = L x 2 3/4

L = 9 5/8 / 2 3/4 = 77/8 / 11/4 = 77 x 4 / 8 x 11 = 7/2 = 3 1/2

5 0

3 years ago

Read 2 more answers

I dont get this simple math 3 2/1÷ 4/3=

mel-nik [20]

uhm I can't help with that... sorry

7 0

3 years ago

Write a number sentence that will calculate a reasonable estimate for the quotient of 3325÷5

Doss [256]

Answer:

3325/5=665

Step-by-step explanation:

3 0

3 years ago

Lisa used the rule "Red, Yellow, Yellow, Yellow" to make a bracelet with a repeating pattern. She

konstantin123 [22]

Answer:

28 beads were used to make the bracelet. 7 beads were not yellow.

Step-by-step explanation:

3/4 beads used to make the bracelet are yellow

If 21 beads are 3/4 of the bracelet and yellow

1/3 of the 21 beads would be 1/4 of the bracelet

7 beads are 1/3 of 21 beads

7 × 4 = 28 beads

8 0

3 years ago