During a drought, the water level in a reservoir dropped 3 in. each week for 5 straight weeks. Express the overall change in water level as a signed number.​

So, making x subject of the formula, x = [m - 2pt³ ±√(m²  - 4pt²m)]/{2t⁵}

Since p = √(mx/t) - t²x

So, p + t²x = √(mx/t)

Squaring both sides, we have

(p + t²x)² = [√(mx/t)]²

p² + 2pt²x + t⁴x² = mx/t

Multiplying through by t,we have

(p² + 2pt²x + t⁴x²)t = mx/t × t

p²t + 2pt³x + t⁵x² = mx

p²t + 2pt³x + t⁵x² - mx = 0

t⁵x² + 2pt³x - mx + p²t = 0

t⁵x² + (2pt³ - m)x + p²t = 0

Using the quadratic formula, we find x.

[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex]

where

Substituting the values of the variables into the equation, we have

[tex]x = \frac{-(2pt^{3} - m) +/-\sqrt{(2pt^{3} - m)^{2} - 4(t^{5})(p^{2}t) } }{2t^{5} }\\= \frac{-(2pt^{3} - m) +/-\sqrt{4p^{2} t^{6} - 4pt^{2}m + m^{2} - 4p^{2}t^{6} } }{2t^{5}}\\= \frac{-(2pt^{3} - m) +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}\\= \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]

So, making x subject of the formula,  [tex]x = \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]

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The volume of the oblate spheroid is approximately equal to 75.398 cubic feet.

In this problem we have the shape of an ellipse centered at origin, whose vertex form is shown below:

x² / a² + y² / b² = 1        (1)

Where a, b are the lengths of the semiaxes, in feet.

An oblate spheroid is generated by revolving half of the ellipse about the y-axis. Oblate spheroids are a kind of ellipse:

x² / a² + y² / b² + z² / a² = 1       (2)

Where a, b, c are the lengths of the semiaxes, in feet.

And the volume of the oblate spheroid is:

V = (4 / 3) · π · a² · b      (3)

If we know that a = 3 ft, b = 2 ft, then the volume of the oblate spheroid is:

V = (4 / 3) · π · (3 ft)² · (2 ft)

V ≈ 75.398 ft³

The volume of the oblate spheroid is approximately equal to 75.398 cubic feet.

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The magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.

Sum of vectors in x direction, ∑X = 5 - 1 = 4

Sum of the vectors in y direction, ∑Y = 6 + 14 = 20

Resultant vector = √(∑X² + ∑Y²)

Resultant vector = √(4² + 20²) = 20.4 units

θ = arc tan (ΣY/ΣX)

θ = arc tan (20/4)

θ = arc tan (5)

θ = 78.7⁰

θ ≈ 79⁰

Thus, the magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.

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Answer:

16 packages

Step-by-step explanation:

5 2/5 + 2 1/4  Use the common denominator of 20

5 8/20 + 2 5/20  

7  13/20

I know that I will need 14 packages for the 7 pounds.  For the fraction part, 10/20 would be half, so I would need to buy a half pound for that, but I need 13/20 which would be more than a half pound, so I will need to buy 2 more pounds for the fraction part.

14 + 2 = 16

Using simple interest, it is found that:

Simple interest is used when there is a single compounding per time period.

The amount of money after t units of time in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

For this problem, the parameters are given as follows:

A(0) = 875, r = 0.0004273, t = 32.

Hence the amount paid is given by:

A(32) = 875 x (1 + 0.0004273 x 32) = $887.

The amount of interest is given by:

I = 887 - 875 = $12.

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The inequalities that represents the third side of the triangle is  c ≥ 4 or c ≤ 20

The triangle inequality theorem states that that the sum of any two sides of a triangle is greater than or equal to the third side.

Therefore, the two sides of the triangle are 12 cm and 8 cm.

A triangle with sides a, b and c follows the principle below;

a + b ≥ c.

Therefore,

let

c = third sides

12 + 8 ≥ c

20 ≥ c

c + 8 ≥ 12

c ≥ 4

c + 12 ≥ 8

Therefore, the third third should be greater than or equals to 4 or less than or equals to 20

c ≥ 4 or c ≤ 20

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The average of the five consecutive numbers ending with b in discuss when expressed in terms of a is; Choice D; a+3.

First, since it was given in the task content that the average of six positive consecutive odd integers starting with a is equal to b, it therefore follows that;

(a+a+2+a+4+a+6+a+8+a+10)/6 = b

6b=6a+30

b=a+5

Also, let the average of the consecutive intergers ending with b be denoted by; x.

(b+b-1+b-2+b-3+b-4)/5 = x

=(5b-10)/5

=b–2

The average, x=b – 2 (where b = a-5)

Ultimately, the value of the required average is; = a+5-2 = a+3.

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Answer:

Q1: Third Choice. 15√3

Q2: Fourth Choice. 15√3

Q3: First Choice. 12√10

Step-by-step explanation:

Given expression

8√3 + 7√3

Simplify by addition

Remember that terms with the same radical part can add together directly

= (8 + 7) √3

[tex]\Large\boxed{=15\sqrt{3} }[/tex]

Given expression

√15 × √45

Factorize each radical

= √(3 × 5) × √(9 × 5)

= √3 × √5 × √9 × √5

Simplify necessary radicals

= √3 × √5 × 3 × √5

= 3 × √3 × √5 × √5

Simplify by multiplication

When radicals multiply, combine them under one radical sign

= 3√3 × √(5 × 5)

= 3√3 × 5

[tex]\Large\boxed{=15\sqrt{3} }[/tex]

Given expression

15√10 - 3√10

Simplify by subtraction

Remember that terms with the same radical part can subtract each other directly

= (15 - 3) √10

[tex]\Large\boxed{=12\sqrt{10} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The factors of polynomial [tex]3x^{2} +25x-18[/tex] is (3x-2)(x+9) that's why the correct option is (3x-2) which is option c.

Given a polynomial [tex]3x^{2} +25x-18[/tex].

We are required to find the factors of polynomial given as [tex]3x^{2} +25x-18[/tex].

Polynomial is a combination of algebraic terms which is formed by using algebraic operations.

Factors are those numbers which when divided gives the number whose factors they are.

[tex]3x^{2} +25x-18[/tex]

To find the factors we need to break the middle term of the polynomial so that the broken parts when multiplied gives the product of both the first term and last term.

[tex]3x^{2}[/tex]+27x-2x-18

3x(x+9)-2(x+9)

(3x-2)(x+9)

Hence the factors of polynomial [tex]3x^{2} +25x-18[/tex] is (3x-2)(x+9) that's why the correct option is (3x-2) which is option c.

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The slope of another line is changed to 20 degree to keep the segments parallel.

According to the statement

We have given that the If ac is parallel to bd and m <5 is decreased by 20 degrees And we have to find that the how must m <2 be changed to keep the lines parallel.

So, For this purpose,

We know that the Slope or gradient of a line is a number that describes both the direction and the steepness of the line.

And here

The slopes of two lines will only same when these lines are parallel.

In other words, Only parallel lines have a same slope.

So, if slope of one line is decreased by 20 degree then we have to kept these line parallel. Then we have to decrease the slope of other line by 30 degree also.

So, The slope of another line is changed to 20 degree to keep the segments parallel.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

If ac is parallel to bd and m <5 is decreased by 20 degrees how must m <2 be changed to keep the lines parallel?

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Answer:

SAS and SSA

Kindly award branliest

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Congruency refers to the criteria of making two identical shapes that can hide each other properly when overlapped.

The criterias that guarantee congruence are :

[tex] \qquad \large \sf {Conclusion} : [/tex]

We should combining 8 ounces of the 50/50 nuts with 8 ounces of the 80% chocolate-covered nuts, to create the 60% mixture required for each bag.

You are offering to assist with the Valentine's Day fundraiser for the soccer team, according to the query. At least 60% of the 16-ounce bags of nuts that the team sold had to be coated in chocolate.

However, they supplied two sizable containers of mixed nuts instead of a shipment that was divided into plain and chocolate nuts. First, it claims to be equally split between plain and chocolate-covered. The second one has almonds that are 80 percent chocolate-covered.

In order to create the 60% mixture required for each bag, we should combine 8 ounces of the 50/50 nuts with 8 ounces of the 80% chocolate-covered nuts.

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To make the 60 percent mixture needed for each bag, we should combine 8 ounces of the 50/50 nuts with 8 ounces of the 80 percent chocolate-covered nuts.

According to the question, you are willing to help with the Valentine's Day fundraiser for the soccer team. The team had to cover at least 60% of the 16-ounce bags of nuts they sold in chocolate.

Instead of a cargo that was split into plain and chocolate nuts, they instead provided two substantial containers of mixed nuts. First, it asserts that the basic and chocolate-covered portions are split equally. The second one has almonds that have been wrapped in 80 percent chocolate.

We need to combine 8 ounces of the 50/50 nuts with 8 ounces of the 80% chocolate-covered nuts.to make the 60 percent combination needed for each bag.

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By definition of surface area and the area formulae for squares and rectangles, the surface area of the composite figure is equal to 166 square centimeters.

According to the image, we have a composite figure formed by two right prisms. The surface area of this figure is the sum of the areas of its faces, represented by squares and rectangles:

A = 2 · (4 cm) · (5 cm) + 2 · (2 cm) · (4 cm) + (2 cm) · (5 cm) + (3 cm) · (5 cm) + (5 cm)² + 4 · (3 cm) · (5 cm)

A = 166 cm²

By definition of surface area and the area formulae for squares and rectangles, the surface area of the composite figure is equal to 166 square centimeters.

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When the acceleration is 7 m/s², it means that the force will be 70 N.

From newton's first law of motion, we know that;

F = ma

where;

m is mass

a is acceleration

We are given;

F = 60 N

a = 6 m/s²

Thus;

m = F/a = 60/6

m = 10 kg

When acceleration is 7 m/s², we have;

F = 10 * 7

m = 70 N

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Answer: 9 and 2/3 cases  

Step-by-step explanation:

6 goes into 58 9 times to make 54 so makes 4 left over 4/6 simplified makes 2/3.

To ship 58 items with 6 items per case, you will need 9 complete cases and 1 additional case with the remaining 4 items, making a total of 10 cases.

We have,

To find the number of cases required to ship 58 items when there are 6 items per case, we can use division.

Number of cases = Total items / Items per case

Number of cases = 58 items / 6 items per case

Number of cases = 9 with a remainder of 4

When we divide 58 items by 6 items per case, we get 9 with a remainder of 4.

This means that 9 cases can be fully filled with 6 items each, and there will be 4 items left that won't fit in a complete case.

Therefore,

To ship 58 items with 6 items per case, you will need 9 complete cases and 1 additional case with the remaining 4 items, making a total of 10 cases.

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The complete question:

How many cases are required to ship 58 items if there are 6 items per case?

Answer:

a company powder large group of people to assess the company's reputation in the surrounding

The preparation of the Cost of Goods Sold Budget for MingWare Ceramics Inc. in September is as follows:

Beginning inventory of finished goods $11,850

Cost of goods manufactured                485,310

Ending inventory of finished goods      (12,670)

Cost of Goods Sold                          $484,490

The cost of goods sold budget sums the costs of the beginning inventory of finished goods with the cost of goods manufactured and subtracts the ending inventory of finished goods.

The cost of goods sold budget is based on the cost of goods manufactured budget.

Direct materials:                            Enamel        Paint     Porcelain      Total    

Total direct materials purchases

budgeted for September            $35,870    $7,530    $139,890  $183,290

Estimated inventory, September 1   1,730        4,150          6,920      12,800 Desired inventory, September 30 (2,980)      (2,710)         (7,150)    (12,840)

Materials used in production                                                          $183,250

Direct labor cost:           Kiln Department    Decorating Department   Total

Total direct labor cost

 budgeted for September    $51,550                   $149,500        $201,050

Finished goods inventories:             Dish       Bowl     Figurine             Total

Estimated inventory, September 1  $5,810   $3,310     $2,730        $11,850

Desired inventory, September 30    3,720    4,590       4,360         12,670

Work in process inventories:

 Estimated inventory, September 1      $3,540

Direct materials used in production $183,250

Direct labor costs                              $201,050

Total factory overhead costs             $99,450

 Desired inventory, September 30       (1,980)

Cost of goods manufactured           $485,310

Indirect factory wages $80,400

Depreciation of plant and equipment 10,550

Power and light 5,110

Indirect materials 3,390

Total 99,450

Thus, to prepare the cost of goods sold, as above, MingWare Ceramics, requires to determine the cost of goods manufactured for September.

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Answer:

C

Step-by-step explanation:

Area of a 1/4 sector of a circle = 1/4 * pi r^2

Givens

100 of these quarter sectors

pi = 3.14

r = 12

Solution

You are using area because you are going to paint each one of the sectors. You must cover every cm^2 with paint.

Area = 1/4 * 3.14 * r * r

Area = 1/4 * 3.14 * 12 * 12

Area = 113.25

But there are 100 of them. so the area is

100 * Area = 11325 cm^2

Rounded to the nearest 100 hundreds = 11300 cm^2

Answer:

The answer is 11,300 cm²

Step-by-step explanation:

I got it right on edmentum jope this helps your question.

Converting the portions to decimal, the grade that has the greatest portion of students is: 3rd grade.

The bigger the digit that is close to the decimal point, the bigger the number given.

Also, percentage can be converted to decimal by dividing the given percent by 100. Percent means over 100.

Fractions can also be converted to decimals by simply dividing the numerator by the denominator.

To compare the portion of students interested in playing an instrument in each grade, let all the portions be in decimals.

Converting 25/36 to decimal, we have: 0.694 (3rd grade)

Converting 61.24% to decimal, we have: 61.24/100 = 0.6124 (4th grade)

From the rest of the portions given, 0.694 is greater than the others.

Therefore, the grade that has the greatest portion of students is: 3rd grade.

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Answer:

(3+3) x (3+1)

Step-by-step explanation:

free

We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.

» (1 + 3) × (3 + 3)

» (4) × (6)

» 24

Here's our answer..!!

It should be noted that Group A is a cluster of points with similar property or relationship and Point B is an outlier. This is the point outside of the common relationship in the scatterplot

It should be noted that scatter plots are the graphs that present the relationship between two variables in a data-set. It represents data points on a two-dimensional plane or on a Cartesian system.

In this case, the independent variable or attribute is plotted on the X-axis, while the dependent variable is plotted on the Y-axis.

The association between students' test scores and the number of hours they exercise is that there is a negative tendency. As number of hours spent on computer games increase, the test scores decrease.

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===========================================================

Explanation:

Let's use the distance formula to find the distance from D to E

[tex]D = (x_1,y_1) = (-7,2) \text{ and } E = (x_2, y_2) = (3,4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-7-3)^2 + (2-4)^2}\\\\d = \sqrt{(-10)^2 + (-2)^2}\\\\d = \sqrt{100 + 4}\\\\d = \sqrt{104}\\\\d = \sqrt{4*26}\\\\d = \sqrt{4}*\sqrt{26}\\\\d = 2\sqrt{26}\\\\d \approx 10.198\\\\[/tex]

Note: uppercase D refers to the point, while lowercase d is the distance from D to E.

The length of segment DE is roughly 10.198 units long.

----------------

Repeat for the distance from E to F.

[tex]E = (x_1,y_1) = (3,4) \text{ and } F = (x_2, y_2) = (5,-7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-5)^2 + (4-(-7))^2}\\\\d = \sqrt{(3-5)^2 + (4+7)^2}\\\\d = \sqrt{(-2)^2 + (11)^2}\\\\d = \sqrt{4 + 121}\\\\d = \sqrt{125}\\\\d = \sqrt{25*5}\\\\d = \sqrt{25}*\sqrt{5}\\\\d = 5\sqrt{5}\\\\d \approx 11.1803\\\\[/tex]

Segment EF is roughly 11.1803 units long.

----------------

Repeat for the distance from F to D.

[tex]F = (x_1,y_1) = (5,-7) \text{ and } D = (x_2, y_2) = (-7,2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(5-(-7))^2 + (-7-2)^2}\\\\d = \sqrt{(5+7)^2 + (-7-2)^2}\\\\d = \sqrt{(12)^2 + (-9)^2}\\\\d = \sqrt{144 + 81}\\\\d = \sqrt{225}\\\\d = 15\\\\[/tex]

Unlike the others, this result is exact.

----------------

Add up the three segment lengths to get the perimeter

DE + EF + FD

10.198 +  11.1803 + 15

36.3783

The perimeter is approximately 36.3783 units which rounds to 36.4

The answer has been confirmed with GeoGebra.

The measures of the remaining angles of the parallelogram are m ∠ B = 138°, m ∠ C = 42° and m ∠ D = 138°

In this problem we know the measure of an angle and we should find the values of the three remaining angles. According to Euclidean geometry, the sum of internal angles in a parallelogram equals 360° and there exists the following property between each pair of angles:

Then, the measures of the missing angles are, respectively:

m ∠ B = 180° - m ∠ A

m ∠ B = 180° - 42°

m ∠ B = 138°

m ∠ D = 138°

m ∠ C = 42°

The statement is poorly formatted, presents typing mistakes and image is missing, correct form is shown below:

On parallelogram ABCD, m ∠ A = 42, m ∠ B = ____, m ∠ C = _____, m ∠ D = _____

A representation of the parallelogram is shown in the image attached below.

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One way to capture the domain of integration is with the set

[tex]D = \left\{(x,y) \mid 0 \le x \le 1 \text{ and } -x \le y \le 0\right\}[/tex]

Then we can write the double integral as the iterated integral

[tex]\displaystyle \iint_D \cos(y+x) \, dA = \int_0^1 \int_{-x}^0 \cos(y+x) \, dy \, dx[/tex]

Compute the integral with respect to [tex]y[/tex].

[tex]\displaystyle \int_{-x}^0 \cos(y+x) \, dy = \sin(y+x)\bigg|_{y=-x}^{y=0} = \sin(0+x) - \sin(-x+x) = \sin(x)[/tex]

Compute the remaining integral.

[tex]\displaystyle \int_0^1 \sin(x) \, dx = -\cos(x) \bigg|_{x=0}^{x=1} = -\cos(1) + \cos(0) = \boxed{1 - \cos(1)}[/tex]

We could also swap the order of integration variables by writing

[tex]D = \left\{(x,y) \mid -1 \le y \le 0 \text{ and } -y \le x \le 1\right\}[/tex]

and

[tex]\displaystyle \iint_D \cos(y+x) \, dA = \int_{-1}^0 \int_{-y}^1 \cos(y+x) \, dx\, dy[/tex]

and this would have led to the same result.

[tex]\displaystyle \int_{-y}^1 \cos(y+x) \, dx = \sin(y+x)\bigg|_{x=-y}^{x=1} = \sin(y+1) - \sin(y-y) = \sin(y+1)[/tex]

[tex]\displaystyle \int_{-1}^0 \sin(y+1) \, dy = -\cos(y+1)\bigg|_{y=-1}^{y=0} = -\cos(0+1) + \cos(-1+1) = 1 - \cos(1)[/tex]

well, we're assuming all along that Merina owes Bradford $2000, because in the 1st scenario, she was going to pay twice $1000.

on the 2nd scenario, she'll be paying the same $2000 but split 7 months from now and then 7 months later, same 2000 bucks, at which point Bradford applied 8.5% interest.

using those assumptions, since the wording is not quite clear, we can say that Merina is simply paying 2000 bucks plus the 8.5%

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.5\% of 2000}}{\left( \cfrac{8.5}{100} \right)2000}\implies 170 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\stackrel{principal}{2000}~~ + ~~\stackrel{interest}{170}}{2}\implies \stackrel{\textit{two equal payments of}}{1085}[/tex]

Answer:

1/2 - 4, 1/2 2, 2 1/4,

Step-by-step explanation:

1/2, - 4 1/2 2,2,1/4

The table when completed looks like this:

x   -2   -1   0   1   2

f(x) 4   2   1    2   4.

We plot these points on the graph: (-2, 4), (-1, 2), (0, 1), (1, 2), (2, 4).

A function exists as a relation between a dependent variable (f(x)) and an expression of an independent variable (x), utilized to define the value of a dependent variable from a provided value of an independent variable.

We have been given a function,

[tex]$f(x)=\left \{ {{(1/2)^{x},x\leq 0 } \atop {2^x > 0}} \right.[/tex]

We have to estimate the value of f(x) when x = {-2, -1, 0, 1, 2}

If the values of x ≤ 0, take f(x) = (1/2)ˣ then

f(-2) = (1/2)⁻² = 2² = 4

f(-1) = (1/2)⁻¹ = 2¹ = 2

f(0) = (1/2)⁰ = 1

If the values of x > 0,  take f(x) = 2ˣ then

f(1) = 2¹ = 2

f(2) = 2² = 4

The table exists as follows

x   -2   -1   0   1   2

f(x) 4   2   1    2   4.

We plot these points on the graph: (-2, 4), (-1, 2), (0, 1), (1, 2), (2, 4).

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Answer: Option (2)

Step-by-step explanation:

When x=10,

13.2 is closer to 14 than 16.6, so the least-squares regression line is a better prediction.

Answer:

Step-by-step explanation:

Comment

I can't be sure what you mean by 2001/2. I will interpret it the way it is written.

1 hour produces 2001/2

8 hours produces x

What you have is a proportion.

Solution

1/8 = 2001/2 // x                       Cross multiply

1*x = 2001/2 *  8                       Combine

x = 8004

Answer

The printer will produce 8004 printed pages.

Answer:

fully factored form = 3(x-4)(x+8)

Step-by-step explanation:

first you factor 3 out

3(x^2+4x-32)

then factor it

3(x-4)(x+8)

Answer:

3(x-4)(x+8) This is the answer :)

Step-by-step explanation:

3x^2+12x - 96

3(x^2+4x-32)

3(x^2+4x--32)

3(x^2+8x-4x-32)

3(x^2+8x-4x-32)

3(x(x+8)-4(x+8))

3(x(x+8)-4(x+8))

3(x-4)(x+8)

3(x=4)(x+8)