Evaluate one and seven tenths raised to the sixth power divided by one and seven tenths raised to the fifth power, all raised to the second power.

1
1.7
2.89
3.4

Answer:

y= -5x-8

Step-by-step explanation:

Slope-intercept form equation: y=mx+b

b is where the line meets the y line. So it meets it at the number "-8". Then with the mx in the equation, you find that by doing rise over run. I got 5/-1, which goes to just plain old -5.

I hope this helps!!!

If the length of the garden is one digit whole number and the width is 5 meter, then the lease possible area is 5 meters

The shape of the region is rectangular

The length of the garden is one digit whole number

One digit whole numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

The width of the rectangular region = 5 meters

We know the area of the rectangle = Length × Width

Here we have to find the least possible area

So the width is given but the length of the garden is unknown but it is a one digit whole number

To get least possible area, the length should be least number, because the area is the product of length and width

The length of the garden = 1

The least possible area = 1 × 5

= 5 meter square

Therefore, the least possible area is 5 meter square

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The time taken by the horizon to develop is calculated with the half-life which is 675 years.

Organic matter particles have more negatively charged particles, which hold on the positively charged particles.

The organic matter in the soil affects the water holding capacity of the soil. Thus is if there are more organic matter, this means that the organic matter is more. Thus the farmer has to add more organic matter.

In order to reduce the the acidity, the farmers add Calcium oxide, Calsium hydroxide and so on.

The horizon s formed after years of sediment formation. Thus the process can take years.

This is the half-life of the soil and with the formula of half-life we get 225 * 3 = 675 years.

Therefore, the time taken by the horizon to develop is 675 years.

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The Distance from bottom of lamppost is 57.142 ft.

Triangles with the same shape but different sizes are called similar triangles. Examples of similar objects include squares with any side length and all equilateral triangles. To put it another way, if two triangles are similar, their angles are the same and their sides are the same size. The "~" symbol indicates the triangular resemblance here.

Given the height of lamp post is 20 ft

height of man is 6 ft

man walking away with speed of 5 ft per sec

distance covered 8 sec is 8 x 5 = 40 ft

let us consider a triangle ΔABC and consider the triangle with man ΔDEC

which is inside ΔABC as shown in figure,

AB = 20 ft, DE = 5 ft and AD = 40 ft

consider   ΔABC and ΔDEC

∠BAC = ∠EDC = 90⁰

∠BCA = ∠ECD = common angle

so    ΔABC ~ ΔDEC by (AA property)

according to similar triangles

AB/DE = AC/DC

let DC be x and AC is 40 + x

substitute the values

20/6 = (40 + x)/x

20x = (40 + x)6

20x = 240 + 6x

14x = 240

x = 17.142ft

AC = AD + DC = 40 + 17.142 = 57.142 ft

Hence the Distance from bottom of lamp post to the end of shadow is 57.142 ft.

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lower control threshold for the data is LCL = -0.007

The lower control limit on a control chart is the value below which any particular data point would be deemed to be out of statistical control owing to specific cause variation. It is represented by a line below the centerline.

The lower control limit formula: LCL = Pbar - [tex]3 \sqrt{p bar (1- p bar)/n}[/tex]

To date,

Size of sample = n

Sample size is 12 samples.

Televisions with defects = X

We have a sample defect = p

p chart week with n = 200

x = 4, 7, 5, 6, 8, 3, 12, 4, 4, 5, 6, 2.

P = x/n

p = 4/200 = 0.02

p = 7/200 = 0.035

p = 5/200 = 0.025

p = 6/200 = 0.03

p = 8/200 = 0.04

p = 3/200 = 0.015

p = 12/200 = 0.06

p = 4/200 = 0.02

p = 4/200 = 0.02

p = 5/200 = 0.025

p = 6/200 = 0.03

p = 2/200 = 0.01

total will be 0.33

p bar = 0.33/12

p bar = 0.0275

The lower control limit formula: LCL = Pbar - [tex]3 \sqrt{p bar (1- p bar)/n}[/tex]

LCL =  0.0275 - 3[tex]\sqrt{ 0.0275 (1- 0.0275/200}[/tex]

LCL = -0.007

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The perimeter of the rectangle is 44cm

Given:

Area: [tex]Area = 105cm^{2}[/tex]

width: [tex]w= 7 cm[/tex]

To find the perimeter first we need to find the length of the rectangle.

We find it with the formula for the area of a rectangle:

[tex]Area = width*length[/tex]

so clearing for length:

[tex]length = \frac{area}{width}[/tex]

substituting known values:

[tex]length = \frac{105}{7} \\length = 15 cm[/tex]

And now we can calculate the perimeter:

[tex]perimeter = 2(width + length)\\\\perimeter = 2(7cm + 15cm)\\\\perimeter = 44cm[/tex]

Hence , the perimeter of the rectangle is 44cm

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The system of equations y = (1/3)x + 7 and y = -2x³ + 5x² + x - 2 will have 1 solution thus option (B) is correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In other words, the equation must be constrained with some constraints.

As per the given equations,

y = (-1/3)x + 7 and y = -2x³ + 5x² + x - 2

The graph of both equations has been plotted below,

The number of points where both curves cut each other = 1

Thus, the number of solutions = 1

Hence "The system of equations y = (1/3)x + 7 and y = -2x³ + 5x² + x - 2 will have 1 solution".

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Answer:

1 solution

Step-by-step explanation:

Plato/Edmentum

Without using the triangle sum theorem, the proof that shows that m∠G + m∠K + m∠GHK = 180° is proved below.

Based on the triangle angle sum theorem, all the interior angles in a triangle will add up to the sum of 180 degrees.

The complete proof that shows that m∠G + m∠K + m∠GHK = 180 degrees is explained below.

Statement                                    Reason                                          

1. GK║HJ                                     1. Given

2. ∠G ≅ ∠IHJ                              2. Corresponding angles theorem

3. ∠K ≅ ∠JHK                             3. Alternate interior ∠s theorem

4. m∠IHK = m∠IHJ + m∠JHK     4. Additive property of angle measure

5. m∠IHK = m∠G + m∠K            5. Substitution

6. m∠IHK + m∠GHK = 180°        6. Angles forming a linear pair sum of 180°

7. m∠G + m∠K + m∠GHK = 180° 7. Substitution

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Answer:1/2

Step-by-step explanation:

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

3/4-1/2+1/4

1-1/2=1/2

The solution for the inequality |r| - 3 > 2 is r < -5 or r > 5.

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

|r| - 3 > 2.

Simplify the inequality,

|r| > 5,

Implies that,

r < -5 or r > 5

Interval notation (-∞, -5) ∪ (5, ∞).

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The component form of two vectors 2u - v is (10, 0), no magnitude in the second direction.

A vector is a quantity that has both magnitude and direction.

Given are two vectors u = (4, - 1) and v = (-2, - 2).

∴ The value of 2u - v in component form is 2(4, - 1) - (-2, - 2).

2u - v = (8, - 2) - (-2, - 2).

2u - v = (8+2, - 2+2).

2u - v = 10

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The population standard deviation sd would be 0.543 .

Given :

a survey is carried out at uiuc to estimate the proportion of students who like to wear costumes on halloween. 1000 students participated in the survey. if you were to create a confidence interval with 98% confidence and a 4% margin of error .

we know that

margin of error = z * s / [tex]\sqrt{n}[/tex]

Z score at 98% = 2.326

0.04 = 2.326 * s / [tex]\sqrt{1000}[/tex]

0.04 * [tex]\sqrt{1000}[/tex] = 2.326 * s

1.264 = 2.326 * s

s = 1.264 / 2.326

s = 0.543

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Answer:

3/48

Step-by-step explanation:

Answer: decimal form 20.5

Step-by-step explanation:

The value of b is 20.

What is Pythagorean theorem?

The Pythagoras theorem is a mathematical law that states that the sum of squares of the lengths of the two short sides of the right triangle is equal to the square of the length of the hypotenuse.

According to the given question:

∠S and ∠Q are right angles in RSTQ quadrilateral.

RTS and RTQ are right angled triangles.

Applying Pythagorean theorem on both the triangles

sin 35° = b + 60 / RT ⇒ RT = b + 60 / sin 35°

sin 35° = 4b / RT ⇒ RT = 4b / sin 35°

Since RT is common in both equations

b + 60 / sin 35° = 4b / sin 35°

b + 60 = 4b

3b = 60

b = 20

Hence the value of b is 20

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Answer:

3

Step-by-step explanation:

h(2) we find by looking at what y equals when x is 2

when x is 2 y or h(2) is about 3

hopes this helps please mark brainliest

Mr. Henderson paid a total of $98.40 for phone service and $79.20 for garbage pickup last year. To find his average cost per month for these two services, we need to divide the total amount he paid by the number of months in a year.

Since there are 12 months in a year, we can divide the total amount Mr. Henderson paid for phone service and garbage pickup by 12 to find his average cost per month. This is calculated as follows:

Average cost per month = (98.40 + 79.20) / 12

Average cost per month = 177.60 / 12

Average cost per month = $14.80

Therefore, Mr. Henderson's average cost per month for phone service and garbage pickup last year was $14.80. This means that, on average, he paid about $14.80 per month for these two services.

The rental cost for each movie is  $3.75

The rental cost for each video game is  $5.75

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

let the cost of renting movies be m and let the cost of video game rental be v

One month Ivan rented 9 movies and 7 video game $74

9m + 7v = $74

3 movies and 5 video games for a total of $40

3m + 5v = $40

The simultaneous equation

9m + 7v = $74

3m + 5v = $40

solving the equation gives

m = $3.75

v = $5.75

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By solving the given equation  20 + 0.44x = 19 + 1.69x we get x=0.8.

When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. For instance, an equation in French is described as having one or more variables, whereas in English, an equation is any properly written formula that consists of two expressions linked by the equals sign.

Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved.

Given,

20 + 0.44x = 19 + 1.69x

20-19=1.69x-0.44x

1=1.25x

x=0.8

Therefore, by solving the given equation  20 + 0.44x = 19 + 1.69x we get x=0.8.

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Step-by-step explanation:

The answer is in the image above

Answer:        

Step-by-step explanation:

Apply  distributive property.

5i(3+2i)

5i⋅3+5i(2i)

Multiply

3 by 5.15i+5i(2i)

Multiply

5i(2i) .

15i + 10i2

Simplify each term.

Rewrite

i2 as −1.15i+10⋅−1

Multiply

10 by −1.15i−10

Reorder

15i and −10.−10+15i

hope it helps :)

Finding line J's slope is the first step.The simplest approach to achieve this is to change the equation's format to y=mx+b, where m represents the slope.

9x-y=10

Take 9x off of both sides.

9x-y-9x=10-9x

Simpllify -y=-9x+10

Divide both sides by (-9x+10)-1, or -1 -y/-1.

Simplify y=9x-10

m=-1/9.

The notation (x1,y1) y-y1=m(x-x1) y-1=-1/9(x- -8) which reduces to y-1=-1/9(x+8)

y-1=-1/9x-8/9

then multiply both sides by 1.

y-1+1=-1/9x-8/9+9/9

(Using 9/9 as 1 makes it easier to use the common denominator to simplify the fractions.)

As the penultimate step, simplify.

y-1/9x+1/9

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Answer:

35,875

Step-by-step explanation:

35000x(1+2.5%)

35000x1.025%

35,875

(sorry if it's wrong I'm assuming it is the answer because i saw a similar equation and i used the same format..)

Answer:

Step-by-step explanation:

12x^2+17x = 5

12x^2+17x-5 = 0

(4x - 1)(3x+5) = 0

Solve (4x-1) and (3x +5)

4x - 1 = 0

4x = 1

x = 1/4

3x + 5 = 0

3x = -5

x = -5/3

x = { 1/4, -5/3 }

Therefore the solution to this question of proportion,  78% of what number is 42 is 53.84.

In general, the word "proportion" is used to describe a part, share, or amount that is compared to an entire. Two ratios are in proportion, according to the definition of proportion, when they are equal. Two ratios or fractions being equal is expressed by an equation or a statement.

Here,

If 78% of x (any number) equals 42, then we need to set this up as an equation in order to figure it out.

1) Writing down 78% as a fraction. Taking into account that we refer to a product when we say 78% of some amount (x).

78%=78/100 \s=>78x/100=42

2) Afterward, we can continue: 

100*78x/100=42*100

78x=4200

x=4200/78

x=53.84

Therefore the solution of 78% of what number is 42 is 53.84.

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Answer:

14.56 

Step-by-step explanation:

An experiment can be assumed to have internal validity if random assignment and experimental control is employed. So the option c is correct.

The degree to which a study reliably establishes a cause-and-effect link is a sign of its internal validity. The procedures used in the study and the level of care done have a significant impact on this type of validity.

Internal validity is essential because, if proven, it enables alternate explanations for a discovery to be disregarded.

An experiment can be assumed to have internal validity if  random assignment and experimental control is employed. So the option c is correct.

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The right question is:

An experiment can be assumed to have internal validity if:

A. the dependent variable is valid.

B. there is a strong manipulation of the independent variable.

C. random assignment and experimental control is employed.

D. confounding variables are present.

The value for n is n = the quantity 7 times c minus 25 all over negative p.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

−np − 3 = 7(c − 4)

Now, solving for n

-np - 3 = 7c - 28

-np = 7c - 28 + 3

-np = 7c -25

-n = 1/p( 7c- 25)

n= 1/ (-p) (7c- 25)

So, the value for n is n = the quantity 7 times c minus 25 all over negative p.

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Answer: 9x = 288, 32 hours

Step-by-step explanation:

x can be the variable and it represents the hours he worked. 9 is the amount made each hour, so it is multiplied by x. 288 is the total made, so 9x=288.

9x = 288 Divide by 9 on both sides to isolate x
x = 32 hours. Kevin worked 32 hours this week

Answer:32

Step-by-step explanation: 32x9=288