A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute. Let w = quarts of water left in the tub and t = time in minutes.

Final answer:

To find the total hours worked in a year, multiply the number of hours worked per week by the number of weeks in a year.

Explanation:

To calculate the total hours worked in a year:

Hours worked per week = 40 hours

Weeks worked per year = 52 weeks

Total hours worked in a year = 40 hours/week x 52 weeks = 2080 hours

Answer:

B) 918 miles

Step-by-step explanation:

Here with I have attached the figure of the story.

Here we need to find side c, which represents distance from the second destination back to Dallas.

We have to use the cosine formula to find the missing side.

If we are given two sides and one included angle, we can use the cosine formula and find the missing side.

a = 720, b = 290 and ∠C =125°

[tex]c^2 = a^2 + b^2 - 2ab cos C[/tex]

Now plug in the given values and simplify.

[tex]c^2 = {720}^2 + 290^2 - 2*720*290 cos 125[/tex]

[tex]c^2 = 518400 + 84100 - 417600 cos125[/tex]

[tex]c^2 = 602500 - (-239,525.5)\\c^2 = 602500 + 239,525.5\\c^2 = 842025.5[/tex]

Taking the square root on both sides, we get

c = 917.6

Which is equivalent to 918 miles (rounded off to the nearest whole number)

Answer:

4^2 + 5^2 = X^2

16 + 25 = X^2

41 = x^2

X = sqrt(41)

x = 6.40

hypotenuse = 6.40

Step-by-step explanation:

x = −10 ± 5√2

Solve. x²+ 20x + 100 = 50

Subtracting 50 from both sides

[tex] x^{2} +20x+100-50=50-50 [/tex]

[tex] x^{2} +20x+50=0 [/tex]

To solve the quadratic equation, let us use quadratic formula

For, [tex] ax^{2} +bx+c=0 [/tex] , [tex] x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a} [/tex]

So, a=1, b=20, c=50

So, we get,

x=[tex] \frac{-20+-\sqrt{20^{2}-4*1*50}}{2*1} [/tex]

[tex] x=\frac{-20+-\sqrt{400-200}}{2} [/tex]

[tex] x=\frac{-20+-\sqrt{200}}{2} [/tex]

[tex] x=\frac{-20+-10\sqrt{2}}{2} [/tex]

[tex] x=\frac{-10+-5\sqrt{2}}{1} [/tex]

[tex] x=-10+-5\sqrt{2} [/tex]

Option(a) Answer

So, x=-10+5[tex] \sqrt{2} [/tex]

or, x=-10-5[tex] \sqrt{2} [/tex]

Answer: 16

Step-by-step explanation:

Final answer:

The pitch of the roof, which rises vertically 7 ft through a horizontal run of 42 ft, is 2. This means the roof rises 2 inches for every 12 inches of horizontal run.

Explanation:

The question asks about calculating the pitch of a roof with a vertical rise of 7 ft and a horizontal run of 42 ft. The pitch of a roof is generally expressed as the amount of vertical rise per 12 inches of horizontal run. To find the pitch, we first need to calculate the rise per 12 inches of horizontal run.

Given:

Rise = 7 ft

Run = 42 ft

To find how much the roof rises for every 12 inches of run, we use the formula:

Pitch = (Rise / Run) × 12

Plugging in the given values:

Pitch = (7 / 42) × 12 = 2

Thus, the pitch of the roof is 2, meaning the roof rises 2 inches for every foot (12 inches) of horizontal run.

The product of Zx (x-4) is:

Zx2 - 4Zx

Explanation and Solution:

Multiply Zx to each term of the expression inside the parenthesis

Zx multiplied by x is equal to Zx2     

Zx multiplied by -4 is equal to -4Zx,

Combining all the product, we have Zx2 - 4Zx as the answer.

PS. The x2 there is X squared

Answer:

total number of arrangements the florist sold during the first 9 months = 7665 arragements

Explanation:

Florist start a business.

In his 1st month Florist sold 15 arrangement.

He grow his business, he sold twice arrangements as compare to the previous month.

First month = 15

Second month = 2*15 = 30

Third month = 2*30 = 60

15, 30, 60 .....

we need to find the total number of arrangements in first nine months

This sequence is geometric series.

A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term, i.e.,

r = [tex] \frac{30}{15} = \frac{60}{30} = 2 [/tex]

Sum of Terms in a Geometric Progression ([tex] S_{n} [/tex])= [tex] \frac{a_{1} (r^{n} -1)}{r-1} [/tex]

where [tex] a_{1} [/tex] is first term = 15

n is the number of terms = 9

r is common ratio = 2

[tex] S_{9} =\frac{15(2^{9}-1)}{2-1} [/tex]

[tex] S_{9} =\frac{15*(512-1)}{1} [/tex]

[tex] S_{9} = 7665 [/tex]

total number of arrangements the florist sold during the first 9 months = 7665.

Answer:7665

Step-by-step explanation:

To solve this problem, set up a system of equations representing the number of student and adult tickets sold. Solve the system using substitution to find the numbers of each type of ticket sold.

To solve this problem, we can set up a system of equations to represent the number of student tickets and adult tickets sold.

Let x be the number of student tickets sold and y be the number of adult tickets sold.

We know that the total number of tickets sold is 150, so we have the equation:

x + y = 150

We also know that the total amount collected is $1000, so we have the equation:

3x + 8y = 1000

We can solve this system of equations using substitution.

From the first equation, we can solve for x in terms of y as:

x = 150 - y

Substituting this into the second equation, we have:

3(150 - y) + 8y = 1000

Simplifying, we get:

450 - 3y + 8y = 1000

Combining like terms, we get:

5y = 550

Dividing both sides by 5, we get:

y = 110

Substituting this value back into the first equation, we have:

x + 110 = 150

Simplifying, we get:

x = 40

Therefore, 40 student tickets and 110 adult tickets were sold.

The image of point B is B'(1.5,6).and this can be determined by finding the dilation factor and then multiplying point B by the dilation factor.

Given :

In order to determine the image of point B, first, determine the dilation factor. let 'x' be the dilation factor, then:

[tex]-4\times x = -6[/tex]

[tex]x = \dfrac{3}{2}[/tex]

Now, after dilation the point B becomes:

[tex]\rm B(1,4)\to B'(1\times \dfrac{3}{2},4\times \dfrac{3}{2})[/tex]

Simplify the above expression.

[tex]\rm B'\left(\dfrac{3}{2},6\right) = B'(1.5,6)[/tex]

The image of point B is B'(1.5,6).

For more information, refer to the link given below:

https://brainly.com/question/19347268

Answer:

1.25

Step-by-step explanation:

Answer:

The value of x in the given figure is, [tex]34^{\circ}[/tex]

Step-by-step explanation:

Complementary angle states that the two angles sum up to 90 degree.

From the given figure

[tex]x^{\circ}[/tex] and [tex]56^{\circ}[/tex] are complementary angles.

by definition of complementary angles;

[tex]x^{\circ} +56^{\circ} = 90^{\circ}[/tex]

Subtract  [tex]56^{\circ}[/tex]  from both sides we get;

[tex]x^{\circ} = 90^{\circ} -56^{\circ}[/tex]

Simplify:

[tex]x = 34^{\circ}[/tex]

therefore, the value of x in the given figure is, [tex]34^{\circ}[/tex]

Answer:

-a^2 + 2 ab + b^2

Step-by-step explanation:

To solve this, you need to distribute the letters into the parenthesis.

Then, you sum equal things, and you get the result.

[tex]b(a+b)-a(a-b)=\\ba + b^{2} -a^{2}  + ab=\\ b^{2} + 2ab -a^{2}[/tex]

So, the rigth answer is number three: -a^2 + 2 ab + b^2

Answer: C.  0.215

Step-by-step explanation:

Given: A circle with a diameter of 124 m is inscribed in a square .

Thus side of square =124 m

Now, area of square=[tex](side)^2=(124)^2=15,376\ m^2[/tex]

Radius of circle=[tex]\frac{d}{2}=\frac{124}{2}=62\ m[/tex]

Area of circle=[tex]\pi\ r^2=3.14\times(62)^2=3.14\times3.14=12,070.16\ m^2[/tex]

Now, Area of shaded region= Area of square-Area of circle

Area of shaded region=[tex]15,376-12,070.16=3,305.84\ m^2[/tex]

Probability that a point picked at random in the square is in the shaded region

[tex]=\frac{\text{area of shaded region}}{\text{area of square}}=\frac{3305.84}{15376}=0.215[/tex]

Answer:

Opposite angles are congruent

Step-by-step explanation:

The parallelogram has parallel opposite sides and also the opposite sides are congruent. Few other properties of parallelogram are -

So, the answer is D.) opposite angles are congruent.

Answer:

D. Opposite angles are congruent.

Step-by-step explanation:

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