A water pump is transferring water from a water tank to an empty container at a rate of 7 gallons per minute if the water tank contains 35 gallons of water how many minutes will it take for the amount of water in the water tank and the container to be equal

Answer:

change 290 grams to pounds= 0.639 pounds

change 87 grams to ounces= 3.069 ounces

change 1,038 mph to feet per second= 1522.4 feet per second

change 65 miles per hour to kilometers per hour

= 104.607 kilometers per hour

Hope this helps.

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

The cos(θ) term cancels out and we are left with -1. Therefore, the equivalent expression is -1.

We can start by using the trigonometric identities:

cos(-θ) = cos(θ)

tan(-θ) = -tan(θ)

csc(θ) = 1/sin(θ)

Substituting these identities into the original expression, we get:

cos(θ) * (-tan(θ)) * (1/sin(θ))

Simplifying this expression, we can cancel out the cos(θ) and the sin(θ) terms:

-1 * cos(θ) * (1/(cos(θ))) The cos(θ) term cancels out and we are left with -1. Therefore, the equivalent expression is -1.

In other words, the original expression simplifies to -1 for all values of θ where it is defined (i.e. θ ≠ (2n + 1)π/2, where n is an integer). This means that as θ varies, the value of the expression will always be -1 when it is defined. Trigonometric identities are mathematical equations that involve trigonometric functions and are true for every possible value of the variables involved. There are various types of trigonometric identities, including:

Pythagorean Identities:

\(sin^2a + cos^2a= 1\\tan^2a + 1 = sec^2a\\1 + cot^2a = csc^2a\)

Angle Sum and Difference Identities:

sin(α±β) = sin α cos β ± cos α sin β

cos(α±β) = cos α cos β ∓ sin α sin β

tan(α±β) = (tan α ± tan β) / (1 ∓ tan α tan β)

Double Angle Identities:

sin 2θ = 2 sin θ cos θ

cos 2θ =\(cos^2\)θ - \(sin^2\)θ = 2 \(cos^2\)θ - 1 = 1 - 2\(sin^2\)θ

tan 2θ = (2 tan θ) / (1 - \(tan^2\)θ)

Half Angle Identities:

sin (θ/2) = ± √[(1 - cos θ) / 2]

cos (θ/2) = ± √[(1 + cos θ) / 2]

tan (θ/2) = ± √[(1 - cos θ) / (1 + cos θ)]

Product-to-Sum Identities:

sin α sin β = (1/2) [cos (α-β) - cos (α+β)]

cos α cos β = (1/2) [cos (α-β) + cos (α+β)]

sin α cos β = (1/2) [sin (α+β) + sin (α-β)]

Sum-to-Product Identities:

sin α + sin β = 2 sin [(α+β)/2] cos [(α-β)/2]

sin α - sin β = 2 cos [(α+β)/2] sin [(α-β)/2]

cos α + cos β = 2 cos [(α+β)/2] cos [(α-β)/2]

cos α - cos β = -2 sin [(α+β)/2] sin [(α-β)/2]

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Answer:

18.457

Step-by-step explanation:

Answer:

The answer is 1 ⅓

Step-by-step explanation:

Anything in an absolute value whether negative or positive will always end up being a positive

Answer:

2 2/3

Step-by-step explanation:

1) First, find the absolute value of -2 2/3. The absolute value is 2 2/3.

2) Next, convert 2 2/3 to an improper fraction because we want to find the simplest form. The improper fraction is 8/3.

3) Finally, 8/3 cannot be reduced any further, so the answer is 2 2/3.

Hope this helps!

The absolute value is denoted by |x|.

Any negative value put in absolute becomes positive.

The absolute value of \(-2\frac{2}{3}\) as a mixed number in its simplest form is \(2\frac{2}{3}\).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

\(-2\frac{2}{3}\)

We have to write its absolute value.

The absolute value is denoted by |x|.

Any negative value put in absolute becomes positive.

Example:

|-1| = 1

|1| = 1

|-2| = 2

Now,

| \(-2\frac{2}{3}\) | = \(2\frac{2}{3}\)

This is in its simplest form.

Thus,

The absolute value of \(-2\frac{2}{3}\) as a mixed number in its simplest form is \(2\frac{2}{3}\).

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For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer:

w=1

Step-by-step explanation:

6(1-4w)=-18

(6*1)-(6*4w)=-18

6-24w=-18

-24w=-24

w=1

Will u mark me brainliest plz!!!!???!!!

w=1

Step-by-step explanation:

Let x be the original price of the object.

After the 40% discount, the price of the object now becomes;

x-0.4x=0.6x

0.6x is our new price after the first discount.

Now if we want to find the price after the second discount, (5%)

That would come off to be;

0.6x-0.6(0.05)x=0.6x-0.03x=0.57x

Our last price is 0.57x

If you notice, there was a 43% discount in total, as it goes to 57% of its original price.

This is very non intuitive for some people, as they may think there will be a 45% discount.

Answer:

-4x -10

Step-by-step explanation:

remove paranthese: 2x−4−6x−6

collect like terms: (2x−6x)+(−4−6)

−4x−10

The simplified Algebraic Expression of (2x-4) - (6x +6) is -4x - 10.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

(2x-4) - (6x +6)

Now, solving the above expression

= (2x-4) - (6x +6)

= 2x - 4 - 6x - 6

Combining the like terms

= (2x- 6x) + (-4-6)

= -4x - 10

Hence, the simplified expression is -4x-10.

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Answer:

5/6

Step-by-step explanation:

x > 1

x = 2,3,4,5,6

( quantity of 2,3,4,5,6)/(total)

5/6

Answer:

A. Paul can bowl 4 games.

B. Brandon can bowl 3 games.

C. Yes, Paul can have a pizza and a soda. Paul, with his bowling shoes, can afford exactly four games. When playing three games, Paul has a remained of $3.75

Step-by-step explanation:

No, the LaTeX that the app uses starts and ends with the [ tex ] and [/ tex ] tags (without the spaces). In (1), simply remove the \latex tag and the integral will appear in embedded form:

\( \int_a^b f(x)\, dx\)

This is meant to maintain the line spacing. If you want show the full size of the integral (or in display mode), add the \displaystyle tag after the [ tex ] like this

[ tex ]\displaystyle \int_a^b f(x)\, dx[/ tex ]

and the integral will look like this

\(\displaystyle \int_a^b f(x)\, dx\)

after removing the spaces in the \( tag. This works also for sums and product of a series and limits.

Answer:

Option (2)

Step-by-step explanation:

In an arithmetic progression,

\(a_1,a_2,a_3.........a_{n-1},a_n\)

First term of the progression,

a = \(a_1\)

Common difference 'd' = \((a_2-a_1)\)

Recursive formula for the sequence,

a = \(a_1\)

\(a_n=a_{n-1}+d\)

By applying these rules in the recursive formula,

\(a_1=\frac{4}{5}\)

\(a_n=a_{n-1}+\frac{3}{2}\)

Common difference 'd' = \(\frac{3}{2}\)

Therefore, Option (2) will be the answer.

The amount of money that it will cost to enclose the property with the fence would be = $118,125

To calculate the cost that it will take to enclose the fence is to determine the actual area of the rectangular fence.

The area of a rectangule = length×width.

Length = 5×15 = 75ft ( scale of 1in to 15ft)

Width = 7× 15 = 105 ft

Area = 105×75 = 7875 ft²

The cost of 1 feet = $15

7875 = X

make X the subject of formula;

X = 7875×15 = $118,125.

Therefore the amount available won't be enough for the fencing of the rectangular piece of property.

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Rational Function: any function that is found by a rational fraction.

Its form: \(\frac{1}{x}\)

Finding Zeros of  a Rational Function:

\(f(x)=\frac{(x-3)(x+2)}{(x-5)(x-3)}\)

   2. Find restrictions by equating the denominator to 0

\(x-5=0\)                \(x-3=0\)      when x=-5 and 3, the function is undefined

\(x=-5\)                   \(x=3\)

  3. Set the numerator equal to zero

\(x-3=0\)              \(x+2=0\)  

\(x=3\)                    \(x=-2\)

Be careful - since we have x-3 on both the numerator and denominator the graph will not intersect the x-axis at that point. This is what is called a removable discontinuity.

Therefore, the only zero occurs at (-2,0)

Answer:

A) 28

Step-by-step explanation:

x + 97 = 125

x = 28

The lengths of line segments AB and BC are AB = 10; BC = 28

Parallelograms are shapes with parallel and equal opposite sides

The given parameters are:

AB = 3y - 2

BC = x + 12

DC = y + 6

AD = 2x - 4

The above means that:

AB = DC

BC = AD

So, we have:

AB = DC

3y -2 = y + 6

Collect like terms

3y - y = 2 + 6

2y = 8

Divide by 2

y = 4

Also, we have:

BC = AD

x + 12 = 2x - 4

Collect like terms

2x - x = 4 + 12

x = 16

The lengths AB and BC are given as:

AB = 3y - 2

BC = x + 12

So, we have:

AB = 3*4 - 2

AB = 10

BC = x + 12

BC =16 + 12

BC = 28

Hence, the lengths of line segments AB and BC are AB = 10; BC = 28

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Answer:

D

Step-by-step explanation:

Answer:

The value of y is 216

(and the value of x is 12)

Step-by-step explanation:

The general formula for a geometric sequence is,

\(a_n = a_1(r)^{n-1}\)

Where n represents the nth term, a_1 is the first term and r is the common ratio,

we see that,

r = 6,

the first term is,

a_1 = (x-6)

the 2nd term is,

a_2 = 3x,

the 3rd term is,

a_3 = y, finding y,

first we find x, using the above given formula we have,

\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)

x = 12,

Now, for y we can use the relation between a_3 and a_2,

\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)

y = 216

the answer is B because u are adding the 15 to 3x and if u minus 15 from 90 u get 75 so now that u separated the skirts price u have the 3 sweaters price in total so all u have to do is divide 75 to 3 and get 25

To calculate the ratio as a decimal, we divide the number of owners by the total population for each city.

For Indianapolis: Ratio = 6,245 / 0.9 million = 0.006938

For New York: Ratio = 911,216 / 18.6 million = 0.049019

For Cairo: Ratio = 10,598 / 19.1 million = 0.000554

For Beijing: Ratio = 959,611 / 21.2 million = 0.045270

For Tokyo: Ratio = 1,700,510 / 26.5 million = 0.064234

To calculate the owners per 100, we multiply the ratio by 100.

For Indianapolis: Owners per 100 = 0.006938 * 100 = 0.7 (rounded to one decimal place)

For New York: Owners per 100 = 0.049019 * 100 = 4.9 (rounded to one decimal place)

For Cairo: Owners per 100 = 0.000554 * 100 = 0.1 (rounded to one decimal place)

For Beijing: Owners per 100 = 0.045270 * 100 = 4.5 (rounded to one decimal place)

For Tokyo: Owners per 100 = 0.064234 * 100 = 6.4 (rounded to one decimal place)

Therefore, the ratio as a decimal and the owners per 100 for each city are as follows:

Indianapolis: Ratio = 0.006938, Owners per 100 = 0.7

New York: Ratio = 0.049019, Owners per 100 = 4.9

Cairo: Ratio = 0.000554, Owners per 100 = 0.1

Beijing: Ratio = 0.045270, Owners per 100 = 4.5

Tokyo: Ratio = 0.064234, Owners per 100 = 6.4

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Answer:

-1 6/10

is greater than

- 5/3

Step-by-step explanation:

Answer:

x1 =  

⇒ 28.6

x2 =  

⇒ 64.3

x3 =  

⇒ 7.1

Step-by-step explanation:

edge 2020

The mode of the data lies at the end of the histogram, one can find that more values are concentrated at the ending of histogram, so the data is skewed data. Hence option 2: 32.0–32.1 ounces is the more appropriate.

As per the question statement, a brand of frozen green beans lists a weight of 32 ounces on its bag but because of variability in the manufacturing process, the bags often contain slightly more, or less, than 32 ounces of green beans then an inspector takes a random sample of 25 bags of green beans and records their weights and weights and their relative frequencies are summarized and an histogram was plotted.

A histogram titled Green Beans has been defined by actual weight (ounces) on the x-axis, and the relative frequency on the y-axis.

31.8 to 31.9, 0.04; 31.9 to 32.0, 0.04; 32 to 32.1, 0.12; 32.1 to 32.2, 0.2; 32.2 to 32.3, 0.36; 32.3 to 32.4, 0.23.

So, the  mode of the data lies at the end of the histogram, one can find that more values are concentrated at the ending of histogram, so the data is skewed data. Hence option 2: 32.0–32.1 ounces is the more appropriate.

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Answer:

40 students

Step-by-step explanation:

In this problem, one is given the ratio ( 8 : 3 ), since a ratio is another way of writing a fraction one can rewrite it as; \(\frac{8}{3}\) (8) represent the number of students who want to learn about magnets, and (3) represents the number of students who want to learn about magic tricks.

In the problem, it is also given that 25 more students wanted to learn about magnets compared to magic tricks. If one uses the parameter (x) to represent the factor by which the fraction \(\frac{8}{3}\) is reduced, then one can get the equation;

8x = 3x + 25

Use inverse operations to solve,

8x = 3x + 25

-3x

5x = 25

/5

x = 5

Substitute back in to find out how many students want to learn about magnets,

8x

= 8(5)

= 40

Answer:

Step-by-step explanation:

0.033

Answer:

Step-by-step explanation:

Answer:

we need to see the model

Step-by-step explanation:

model please