if seven less than three times a number is negative one. What is the number?

Step-by-step explanation:

we know :

sin(2t) = 2×sin(t)×cos(t)

cos(2t) = cos²(t) – sin²(t) = 2×cos²(t) – 1 = 1 – 2×sin²(t)

tan(t) = sin(t)/cos(t)

tan(2t) = sin(2t)/cos(2t) = (2×tan(t))/(1 – tan²(t))

sin²(t) + cos²(t) = 1

as t is in quadrant I, 2t must be in either quadrant I or II.

sin(t) = 7/9

sin²(t) = (7/9)² = 49/81

cos²(t) = 1 - sin²(t) = 1 - 49/81 = 81/81 - 49/81 = 32/81

cos(t) = sqrt(32)/9

sin(2t) = 2×sin(t)×cos(t) = 2×7/9 × sqrt(32)/9 =

= 14×sqrt(32)/81 ≈ 0.98

cos(2t) = cos²(t) - sin²(t) = 32/81 - 49/81 = -17/81 ≈

≈ -0.21

tan(2t) = sin(2t)/cos(2t) =

= 14×sqrt(32)/81 / -17/81 =

= 14×sqrt(32)/81 × -81/17 =

= -14×sqrt(32)/17 ≈ -4.66

Answer:

285.76 kilograms       1.1 cubic yard

Step-by-step explanation:

Answer:

1.11121 cubic yards.

Step-by-step explanation:

First, let's convert the weight of 1 bag of garden soil from pounds to kilograms:

1 lb = 0.45359237 kg

42 lbs = 42 * 0.45359237 kg = 19.05 kg

So, the weight of 1 bag of garden soil is 19.05 kilograms.

Next, let's find the weight of 15 bags of garden soil:

15 bags * 19.05 kg/bag = 285.75 kg

So, 15 bags of garden soil weigh 285.75 kilograms.

Next, let's find the volume of 15 bags of garden soil in cubic yards:

1 cubic foot = 0.037037 cubic yards

2 cubic feet * 15 bags = 30 cubic feet

30 cubic feet = 30 * 0.037037 cubic yards = 1.11121 cubic yards

So, 15 bags of garden soil have a volume of 1.11121 cubic yards.

Answer:

The answer is provided in the image below.

Answer:

Below

Step-by-step explanation:

It has two sides that are parallel  ( the 'bases' )  and different lengths ( making the other two sides NOT parallel)

Answer:

Step-by-step explanation:

A trapezoid is a quadrilateral with at least one pair of parallel sides. In other words, a trapezoid has two opposite sides that are parallel, called the bases, and the other two sides are called the legs or lateral sides.

So, to conclude that a quadrilateral is a trapezoid, you must determine that:

1)Two of its sides are parallel.

2)The other two sides are not parallel.

If these two conditions are met, then the quadrilateral is a trapezoid.

(If a trapezoid has two pairs of parallel sides, then it is known as a parallelogram, which is a special type of trapezoid.)

Part A:

Look at photo

Part B:

After 5 minutes, the altitude of the airplane is 20,500 feet. This means that the airplane has been descending for 5 minutes and has lost an altitude of 10,250 feet.

After 30 minutes, the altitude of the airplane is -29,250 feet. This means that the airplane has been descending for 30 minutes and has lost an altitude of 60,000 feet. The negative value of the altitude indicates that the airplane has landed or is close to landing.

At both 5 minutes and 30 minutes, the airplane is descending. The rate of descent is constant, as represented by the slope of the equation, and is equal to -1025 feet per minute. At 5 minutes, the airplane is still at a high altitude, while at 30 minutes the airplane has landed or is close to landing, as indicated by the negative value of the altitude.

Answer:

Step-by-step explanation:

Part A:

x  |  y  |  Equation

0  | 30,750 | y = -1025*0 + 30,750

5  | 27,250 | y = -1025*5 + 30,750

8  | 23,750 | y = -1025*8 + 30,750

10 | 20,250 | y = -1025*10 + 30,750

30 | -20,250 | y = -1025*30 + 30,750

Part B:

After 5 minutes, the altitude is 27,250 feet. This means that the airplane has been descending steadily for 5 minutes and is now at a lower altitude than when it started.

After 30 minutes, the altitude is -20,250 feet. This means that the airplane has been descending steadily for 30 minutes and is now much lower than when it started. The airplane is close to the ground and about to land.

The combined volume of a 4-foot cube and a 6-foot cube is not equal to the volume of a 10-foot cube.

The volume of a cube is calculated by cubing the length of its side.

here,

Let's denote the length of the sides of the 4-foot and 6-foot cubes as "a" and "b", respectively. Then the length of the side of the 10-foot cube is "c", and we know that:

a³ + b³ = c³

We want to confirm if the combined volume of a 4-foot cube and a 6-foot cube is equal to the volume of a 10-foot cube. We can calculate the volumes of the cubes as follows:

Volume of 4-foot cube: a³ = 4³ = 64 cubic feet

Volume of 6-foot cube: b³ = 6³ = 216 cubic feet

Volume of 10-foot cube: c³ = 10³ = 1000 cubic feet

The sum of the volumes of the 4-foot and 6-foot cubes is:

64 + 216 = 280

Therefore, the combined volume of a 4-foot cube and a 6-foot cube is not equal to the volume of a 10-foot cube.

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Unfortunately, a lot of software apps tend to use up battery life even if you aren't currently using the phone. This leads to the phone feeling more sluggish over time. To help combat this, it's helpful to clear out any unused apps and clear up the cache.

Even if software was perfectly written the most efficiently, and apps weren't intrusive, the physical nature of the battery itself has limitations. The capacity of the battery will slowly decay each time you charge or use your phone. Even just sitting idle it slowly loses capacity. This loss is very small that it's hard to detect. But add it up over time and the losses will get more noticeable. This is why you cannot simply charge a battery an infinite number of times. As with all things in life, there's a limit.

Summary: Yes the capacity will go down but ever so slightly. It depends how often the updates are done and what software is being updated. Ideally the updated software should be more efficient with the battery life. However, life isn't perfect and there will likely be flaws.

The percent tax you paid when you bought the bike is approximately 8.493%.

What is percentage ?

Percentage can be defined as the product of ratio of given value, total value and hundred.

given ,

You paid $29.75 in tax when you bought a $350 bike

To find the percent tax, we can divide the amount of tax by the total cost (including tax) and multiply by 100 to express the result as a percentage.

tax = 29.75

total = 350

percent tax = (tax / total) * 100

So the percent tax would be

percent tax = (29.75 / 350) * 100

= 8.493%

Therefore, The percent tax you paid when you bought the bike is approximately 8.493%.

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The equation (p+1)x² + (2p+3)x+ (p+2)=0 has real roots for all real values of p at x = -1, -2

A polynomial equation is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.

Given that:

(p+1)x² + (2p+3)x + (p+2) = 0

Open brackets;

px² + x² + 2px + 3x + p + 2 = 0

Move all terms not containing p to the right side of the equation.

px² +  2px + p = −x² − 3x − 2

Factor p out of px² + 2px + p.

p(x² + 2x + 1) = −x² − 3x − 2

Factor using the perfect square rule.

p(x+1)² = −x² − 3x − 2

Divide each term in p( x + 1 )² = −x² − 3x − 2 by (x + 1)² and simplify.

[tex]p= - \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}[/tex]

Set [tex]p= - \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}[/tex] to be equal to zero;

[tex]- \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}=0[/tex]

Solve for x;

-x² - 3x - 2 = 0

Factor the left side of the equation.

-(x + 1) (x + 2) = 0

x = -1

x = -2

The final solution is all the values that make -(x + 1) (x + 2) = 0 true

x = -1, - 2

Exclude the solutions that do not make  [tex]- \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}=0[/tex] true.

Therefore, x  = -2

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-17, -15 and -13 are the three consecutive odd integers.

Linear equation are equation that has a leading degree of 1

Let the smallest integer is '2x - 1'

The next two integers are 2x + 1 and 2x + 3

If the sum of three consecutive odd integers is 19 less than twice the smallest of the three integers, hence;

2x  - 1 + 2x + 1 + 2x + 3 = 2(2x-1) - 19

6x + 3 = 4x - 21

6x - 4x = -21 -3

3x = -24

x = -8

First number = 2(-8) - 1 = -17

Second number = 2(-8) + 1 = -15

Third number = 2(-8) + 3 = -13

Hence the 3 consecutive odd integers are -17, -15 and -13.

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Complete question

The sum of 3 consecutive odd integers is 19 less than twice the smallest of integers , what are the integers?

The solution is 0.3486 or 34.86%, chance that exactly one other guest has the same birthday as you.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

For each guest, the probability that they share a birthday with you is 1 in 365. Aside from you, there are 499 guests.

Therefore, this problem can be modeled by a binomial probability model with probability of success 1/365.

The probability of exactly 1 success in 499 trials is given by:

P(x=1) = 0.3486

There is a 0.3486 or 34.86% chance that exactly one other guest has the same birthday as you.

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Answer:

Prepaid expenses are payments made in advance for goods or services that will be received or used in the future. These expenses are considered assets on a company's balance sheet because they provide future economic benefits. Examples of prepaid expenses include rent payments made in advance, insurance premiums, and prepaid service contracts. They are recorded as an asset on the company's balance sheet until the expense is incurred, at which point it is recognized as an expense on the income statement.

Step-by-step explanation:

Answer: Balu originally had 40 sweets.

Step-by-step explanation:

Let x be the number of sweets Balu originally had.

After Amal gives one third of his sweets to Balu, Balu's number of sweets becomes x + (1/3)x = (4/3)x.

After Balu gives one third of his sweets to Chandran, Chandran's number of sweets becomes 40 + (1/3)(4/3)x = 40 + (1/3)x.

After Chandran gives one third of his sweets to Amal, Amal's number of sweets becomes (2/3)x + (1/3)(40 +(1/3)x) = (2/3)x + (1/3)x + 40/3 = (5/3)x + 40/3.

Since all three of them now have the same number of sweets, we can set the number of sweets each of them has equal:

(4/3)x = (5/3)x + 40/3.

Now, we will isolate x by rearranging the equation. Subtracting (5/3)x from both sides, we get:

(4/3)x - (5/3)x = 40/3

Simplifying the left side:

-x/3 = 40/3

Dividing both sides by -1/3:

x = 40

Thus, Balu originally had 40 sweets.

The probability both get a 3 is 1/60

From the question, we have the following parameters that can be used in our computation:

Jim = 1 to 10

Lyn = 1 to 6

Using the above as a guide, we have the following:

P(Jim = 3) = 1/10

P(Lyn= 3) = 1/6

Using the above as a guide, we have the following:

Required probability = 1/10 * 1/6

Evaluate the product

Required probability = 1/60

Hence, the probabilty is 1/60

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There are 16% of the Green were Planes.

The percentage is defined as a ratio expressed as a fraction of 100.

Total number of green planes = 250

The total number of all planes = 1550

The percent of green planes = (number of green planes/number of total planes ) x 100

The percent of green planes = (250/1550) x 100

The percent of green planes = 0.1612 x 100

The percent of green planes = 16.129

Round to the nearest percent, and we get

The percent of green planes = 16%

Thus, 16% of the Green were Planes.

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Answer:

151.37

Step-by-step explanation:

Answer:

151.372868 but rounded is 151.37

Step-by-step explanation:

1863.4/12.31=151.372868 rounded is 151.37

Answer:

f(2) = 18

Step-by-step explanation:

If f(x) = 3 * (x + 4)

Than f(2) = 3 * (2 + 4) (coz x is an argument)

f(2) = 3 * (2 + 4)

f(2) = 3 * 6

f(2) = 18

A reasonable exponent is one that is fractional. For instance, 412 4 1 2 can be used to represent the number 4.

Given,

[tex]$\left(\frac{4 y^2}{5}\right)^2[/tex]

Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]

[tex]$=\frac{\left(4 y^2\right)^2}{5^2}[/tex]

Simplify [tex]$\left(4 y^2\right)^2: 16 y^4$[/tex]

[tex]$=\frac{16 y^4}{5^2}[/tex]

The we get,

[tex]$& =\frac{16 y^4}{25}[/tex]

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Answer: $31.20

Step-by-step explanation:

0.6% = 0.006

.: fee = 0.006 x 5200 = $31.20

A circle graph titled social media usage, with four sections labeled vidtok 17 percent, headbook 48 percent, picturegram 25 percent, and tweeter 10 percent.

What is the division?

Division is an arithmetic operation that is the inverse of multiplication. It involves splitting a quantity into equal parts or determining how many times one quantity is contained within another.

If you add all of the numbers together you get 500, but you need to make it 100 percent so you divide the total number by five. to know what percent out of 100 you need to divide all of the variables by 5.

85 ÷ 5 = 17

240 ÷ 5 = 48

125 ÷ 5 = 25

50 ÷ 5 = 10

Hence, A circle graph titled social media usage, with four sections labeled vidtok 17 percent, headbook 48 percent, picturegram 25 percent, and tweeter 10 percent.

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Answer:

BBBBBBBBB

Step-by-step explanation:

Answer:

Step-by-step explanation:

Evaluate the expression 10 - 2x for the x-values given below.

a. x = 2 \quad b. x = \frac {1}{2}\quad c. x = -2

a.x=2b.x=

2

1

​

a.x=-2

300.5 ml of antihistamine is needed for a 100​-pound person to take in a​ week

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

1 day = 24 hours

1 week = 7 days = 24 hours per day * 7 days = 168 hours

A typical dose for a 100​-pound person is 22 mg every six hours. Hence for one week:

Dosage in one week = (22 mg per 6 hours) * 168 hours = 616 mg

Antihistamine also comes in a liquid form with a concentration of 12.3 ​mg/ 6 mL. For 616 mg:

Amount of antihistamine = 616 mg / (12.3 ​mg/ 6 mL) = 300.5 ml

300.5 ml of antihistamine is needed

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Answer:

Below

Step-by-step explanation:

Put '9' where  'n' is and compute

(9)^2 + 6(9) ÷ 3 =

81  +    54 ÷3  =

81  + 18 =   99

The minimum length of the box to hold the smaller mirror is 10 inches for largest mirror fits in a box that is 18 inches wide by 20 inches long her smaller mirror.

What is proportion ?

In mathematics, proportion refers to the equality of two ratios. Two ratios are said to be proportional if they have the same relative size, meaning they represent the same relationship between quantities.

For example, if we have two ratios, such as 2/3 and 4/6, they are proportional because they represent the same relationship between two quantities. We can say that 2 is to 3 as 4 is to 6, and we can simplify both ratios by dividing the numerator and denominator of each by their greatest common factor, which in this case is 2.

Since the smaller mirror is similar in proportion to the larger mirror, the ratio of their corresponding sides is the same. Therefore, the width of the smaller box is half of the width of the larger box (9 inches is half of 18 inches).

To find the minimum length of the smaller box, we need to use the same ratio of sides. The length of the larger box is 20 inches, so the length of the smaller box should be half of 20 inches, which is 10 inches.

Therefore, the minimum length of the box to hold the smaller mirror is 10 inches.

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The angles x and 3x - 12 are two vertical angles and the measure of the vertical angle x is equal to 48°.

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

We shall evaluate for the measure of x as follows:

x + x + 3x - 12 + 3x - 12 = 360° {sum of angles at a point}

2x + 6x - 24 = 360°

8x - 24 = 360°

8x = 360° + 24 {add 24 to both sides}

8x = 384°

x = 384°/8 {divide through by 8}

x = 48°

Therefore, since the angles x and 3x - 12 are two vertical angles we have derived the measure of the vertical angle x to be equal to 48°.

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Answer:

x = 42°

Step-by-step explanation:

Please here it is.

If Erin were to lay the index cards in one long row, the row would be 35 inches long.

What is Multiplication?

Multiplication is an arithmetic operation that is used to find the result of combining equal groups of a given quantity. It involves repetitive addition of equal groups, where one factor represents the number of groups, and the other factor represents the number of items in each group.

Solution:

If Erin has 10 index cards, and each index card is 3 ½ inches long, then the total length of the row would be:

10 cards x 3 ½ inches per card = 35 inches

Therefore, if Erin were to lay the index cards in one long row, the row would be 35 inches long.

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To find the projected average rate of change of the world population between 2020 and 2026, we can take the difference in population between 2020 and 2026 and divide it by the number of years (6). This gives us 0.556 million people per year.

(a) The yearly percent rate of growth of the world population is 1.0103%.

(b) The world population in 2020 was 7.68 billion people. The model predicts that the world population in 2026 will be 8.336 billion people.

(c) The projected average rate of change of the world population between 2020 and 2026 is 0.556 million people per year.

(a) The yearly percent rate of growth of the world population can be found by taking the exponential rate of change of the equation. The rate of change is 1.0103%.

(b) To find the world population in 2020, we can plug in t=0 into the equation. This gives us P=7.68 billion people. To find the world population in 2026, we can plug in t=6 into the equation. This gives us P=8.336 billion people.

(c) To find the projected average rate of change of the world population between 2020 and 2026, we can take the difference in population between 2020 and 2026 and divide it by the number of years (6). This gives us 0.556 million people per year.

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If I am equivalent to 3/2, and sum of my numerator and my denominator is 30. Then, i am a fraction is equals to the 18/12.

I am equivalent to 3/2. Let us assume i am a fraction x/y. That is my denominator of fraction = y

My numerator of fraction = x

Now, according to problem, sum of my numerator and my denominator is 30.

=> x + y = 30 --(1)

Also, difference between my denominator and my numerator is 6.

=> y - x = 6 or -y + x = 6 --(2)

Add eqution(1) and (2)

=> x + y + y - x = 30 + 6 or x + y +x - y = 30 + 6

=> 2y = 36 or 2x = 36

=> y = 36/2 or x = 36/2

=> y = 18 or x = 18

Now, when y = 18 => x = 30 - 18 = 12

similarly, x = 18 , => y = 12

so, possible fraction are 12/18 = 2/3 or 18/12 = 3/2, but my fraction is equivalent to 3/2 not 2/3. Therefore, the required fraction is 18/12

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Complete question :

I am equivalent to 3/2 . The sum of my numerator an my denominator is 30 . The difference between my denominator and my numerator is 6 . What fraction am I?

Answer:

the solution is done in the given picture..

thank you