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3 years ago

(40 points)

Mathematics

2 answers:

garik1379 [7]3 years ago

8 0

Answer:

${ \sec}^{2} x - { \tan}^{2} x = 1 \\ \\ { \sin}^{2} x + { \cos }^{2} x = 1$

Nady [450]3 years ago

4 0

Answer:

sec²x - tan²x = 1

sin²x + cos²x = 1

These two among the following are correct trigonometric identities.

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The ratio of children to adults at the football game was 23. If there were 140 children at the football game,

inessss [21]

Answer:

Therefore, the number of adults at the football game was 6.

Step-by-step explanation:

Let A represents the number of adults and C represents the number of children.

Therefore, the ratio of children to adults is given as follows:

23:1 = C:A ....................... (1)

Since C = 140, this is substituted into equation (1) as follows:

23:1 = = 140:A ....................... (2)

Transforming equation (2) and solve for A, we have:

23 / (23 + 1) = 140 / (140 + A)

23 / 24 = 140 / (140 + A)

0.958333333333333 = 140 / (140 + A)

0.958333333333333 (140 + A) = 140

(0.958333333333333 * 140) + 0.958333333333333A = 140

134.166666666667 + 0.958333333333333A = 140

0.958333333333333A = 140 -134.166666666667

0.958333333333333A = 5.833333333333

A = 5.833333333333 / 0.958333333333333

A = 6.08695652173878

Rounding to a whole number, we have:

A = 6

Therefore, the number of adults at the football game was 6.

5 0

3 years ago

The number 64 has the property that it is divisible by its units digit. How many whole numbers between 10 and 50 have this prope

sineoko [7]

Answer:

$\large \boxed{17}$

Step-by-step explanation:

Let's call the numbers "tu", where t is the tens digit and u is the units digit.

We can solve this by the "brute force" method — examining each number to see if it satisfies the conditions.

$\begin{array}{cccl}\mathbf{u}&\mathbf{tu}& \textbf{Divisible by u} & \\0 &20, 30, 40 & 0 & \text{Division by zero is impossible}\\1 & 11, 21, 31, 41 & 4& \text{All numbers are divisible by one}\\2 & 12, 22, 32, 42 & 4 & \text{All even numbers are divisible by two}\\3 & 13, 23, 33, 43 & 1 &\text{Only 33 is divisible by three}\\4 & 14, 24, 34, 44 & 2 & \text{Only 24 and 44 are divisible by four}\\5 & 15, 25, 35, 45 & 4 & \text{Numbers ending in 5 are divisible by five}\\\end{array}$

$\begin{array}{cccl}6 & 16, 26, 36, 46 & 1 & \text{Only 36 is divisible by six}\\7 & 17, 27, 37, 47 & 0 & \text{None of the numbers is divisible by seven}\\8 & 18, 28, 38, 48 & 1 & \text{Only 48 is divisible by eight}\\9 & 19, 29, 39, 49 & 0 & \text{None of the numbers is divisible by nine}\\& \textbf{TOTAL =} &\mathbf{17}& \\\end{array}\\\text{$\large \boxed{\mathbf{17}}$ numbers between 10 and 50 are divisible by their units digit}$

5 0

3 years ago

What does the histogram suggest about the length of 3/4 of an inch wood screws as printed on the box of 50 screws

svet-max [94.6K]

Answer:

The answer is "About half of the screws are written in the box within 0.01 cm in length".

Step-by-step explanation:

In this question some information is missing that is attachment of the image, which is attached.

In this question, there are several of the screws are in between 0.74 to 0.76 and its number is 28, that's why it is correct.

7 0

3 years ago

Find the amount of social security deducted from the check: $835 biweekly.

Inga [223]

Normally 8% is deducted as social security tax.

So,
8% of 835 = 8/100 x 835
= $56.36 (approx.)

4 0

3 years ago

Ben has two boxes. The red box has a volume of 46 cubic feet. The blue box has a height of 3 feet, a length of 7 feet, and a wid

Juliette [100K]

Answer:

The blue box is 38 cubic feet grater than the red box.

Step-by-step explanation:

Cuboid:

It is a three dimensional shape.
It has 6 faces.
The surface area of a cuboid is = 2(lb+bh+lh), where l = length, b= width, h= height.
The volume of a cuboid is = l×b×h

Given that,

Ben has two boxes.

The volume of the red box is 46 cubic feet.

The dimensions of the blue box is 7 feet by 4 feet by 3 feet.

The volume of the blue box is = length ×width × height

=(7×4×3) cubic feet

= 84 cubic feet

The blue box is (84-46) cubic feet =38 cubic feet grater than the red box.

8 0

3 years ago