Graph this line y+4=1/4(x+10)

Step-by-step explanation:

based on the geometric mean theorem

h² = pq

h = height of the main right-angled triangle.

p and q are the segments of the baseline of the main right-angled triangle.

12² = 36x

144 = 36x

x = 144/36 = 4

so, DC is 4 units long.

For the given surface ;

(a) the equation of the tangent is x + y + z = 11    ,

(b) equation of normal is (x - 3) [tex]=[/tex] (y - 3) = (z - 5)   .

In the question ,

it is given that ,

the equation of the surface is 2(x-2)² + (y-1)² + (z-3)² = 10 ,

we have to find the equation of the tangent at (3,3,5) .

the partial derivative fₓ = 4(x -2)

[tex]f_{y}[/tex] = 2(y-1)   and   [tex]f_{z}[/tex] = 2(z-3) .

the partial derivatives at (3,3,5)  will be fₓ = 4(3 -2) = 4

[tex]f_{y}[/tex] = 2(3-1)  = 4   and   [tex]f_{z}[/tex] = 2(5-3) = 4  .

Part(a)  

the equation of tangent at the point (3,3,5) is

fₓ(x - x₁) + [tex]f_{y}[/tex](y - y₁) +  [tex]f_{z}[/tex](z - z₁) = 0 ,

Substituting the values form above ,

we get ,

4(x-3) + 4(y-3) + 4(z-5) = 0

4x - 12 + 4y - 12 + 4z - 20 = 0

after simplifying , we have  4x + 4y + 4z = 44 .

dividing both sides by 4 ,

we get ,

x [tex]+[/tex] y [tex]+[/tex] z [tex]=[/tex] 11  .

Part(b) ,

the equation of Normal is ;

(x-x₁)/fₓ  = (y-y₁)/ [tex]f_{y}[/tex] = (z-z₁)/ [tex]f_{z}[/tex]

(x - 3)/4 = (y - 3)/4 = (z - 5)/4

(x - 3) [tex]=[/tex] (y - 3) [tex]=[/tex] (z - 5)

Therefore , the equation of tangent is x + y + z = 11  , and equation of normal is (x - 3) = (y - 3) = (z - 5)   .

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The total years taken to double the money according to Compounding will be 13.75 years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 2%

amount = $1700

Total amount = $2200

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/400)^4t

T = A[tex](1+r/400)^{4t[/tex]

2200 = 1700(1 +2/400)^4t

22/17 = (1 +1/200)^4t

22/17 = (1.005)^4t

1.29 = (1.005)^4t

taking log on both sides

0.11/0.002 = 4t

t = 13.75 years.

Hence the time taken to double the money is 13.75 years.

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Answer: False

Step-by-step explanation:

Answer: 20/48

(simplified) 5/12

Step-by-step explanation:

We will use 6/8 - 2/6 for our example

6/8 - 2/6

Multiply the denominator on the right side by the denominator on the left side: 6x8 = 48

Make 48 the denominators on both sides: /48,  /48

Now multiply the denominator on the left side with the numerator on the  left side: 6x6 = 36

Make the first fraction's numerator 36: 36/48

Now multiply the denominator on the left side by the numerator on the right side: 8x2 = 16

Now make 16 the numerator of the second fraction: 16/48

Now that the denominators are the same, we can subtract!

36/48-16/48 = 20/48

Now to simplify:

divide 20/48 by 4 = 5/12

So the answer is 20/48 and when it is simplified it comes out to 5/12

This is how you subtract fractions with different denominators.

You can use the same method when adding, the only difference is that instead of adding in the last step, you add instead!

a) The Test statistic of the hypothesis is; 0.23

b) The p-value from the test statistic is; 0.409

c) The final conclusion is there is not sufficient evidence to determine whether the antidepressant drug had an effect on changing working habits after one year.

Test statistic is defined as a number, calculated from a statistical test, used to find if your data could have occurred under the null hypothesis. In this case, we are dealing with proportions and as such the test statistic has the formula;

z = (p1 - p2)/standard error

p1 = 14/167 = 0.084; s1 = √(0.084 * 0.916/167) = 1.285

p2 = 316/833 = 0.38; s2 = √(0.38 * 0.62/833) = 0.0168

Hence, for the distribution of differences, the mean and the standard error are given as follows:

Mean: p = 0.38 - 0.084 = 0.296

Standard error: s = √(1.285² + 0.0168²) = 1.2854

a) Test statistic = p/s = 0.296/1.2854

Test statistic = 0.23

b) From p-value from z-score calculator, we get that;

p-value = 0.409

c) The p-value is greater than the significance value of 0.04, we fail to reject the null hypothesis and conclude that there is not sufficient evidence to determine whether the antidepressant drug had an effect on changing working habits after one year.

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Answer:

-2.5

Step-by-step explanation:

For a quadratic equation [tex]ax^2 + bx+c=0[/tex], the sum of the roots is [tex]-b/a[/tex].

Here, [tex]b=5[/tex] and [tex]a=2[/tex], so the sum is [tex]-2.5[/tex].

Answer:

$4,140.00

Step-by-step explanation:

Interest = principle x rate x time

I = 3600 x .03 x 5

I = 540

Add the interest to what is already in the account

540 + 3600

4140

The speed (in km/hr) of the ships changing at 4.00pm is 20.62km/hr

The given parameters are;

The distance between A and B = 170km=m

The distance between B and C is 30km=m

Time is 12.00 noon to 4.00 pm = 4 hours

From the given parameters,

m=170-35*4 = 170-140=30

The Distance (D)=√(30²+120²

D=30*√(1²+4²)

Simplifying to get

30√17

From the Pythagoras theorem,

D²=m²+n²

Applying differential calculus,

⇒2m(dm/dt)+2n(dn/dt)=2D(dD/dt)

Applying the figures from the question we have

2*30*(-35)+2*120*30=2*30√17*dD/dt

Simplify to get

120-35=√17dD/dt

This implies that dD/dt=85/√17

⇒5√17=20.6155281km/h

Therefore, the speed between the ships is ≅20.62km/hr

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Answer:

Below

Step-by-step explanation:

a)  All possible rolls  ( 36 of them)

1   1 , 2 , 3 , 4 , 5 , 6

2   1, 2, 3, 4, 5 , 6

3    1 , 2 , 3 , 4,5,6

4  1,2,3,4,5,6

5  1,2,3,4,5,6

6  1,2,3,4,5,6

b) underlined above    21 out of 36    or 7/12

c )   3 out of 36    1/12

d )  11/36

Answer:

(5,-3), (10,-6)

Step-by-step explanation:

The number of cows are 9 and the number of chickens are 13.

Given that, a farm has 22 cows and chicken altogether.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let the x be the number of cows and y be the number of chicken.

Now, x+y=22 -------(I)

The farmer counted 62 legs total.

So, 4x+2y=62 -------(II)

Multiply equation (I) by 2, we get

2x+2y=44 -------(III)

Subtract equation (III) from equation (II), we get

4x+2y-(2x+2y)=62-44

⇒ 2x=18

⇒ x=9

Substitute x=9 in equation (I), we get

9+y=22

⇒ y=13

Hence, the number of cows are 9 and the number of chickens are 13.

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Step-by-step explanation:

since it's -14 then it will be√-14

√-14=√-2 multiplied is by √7

so that will be √-2√7

the whole distance containing all three points will be AC, and we know that AC = 72 km, now point B is between splitting the AC segment into AB and BC to a 4 : 5 ratio.

well, hell for that let's simply grab the total amount of 72 and split it up by dividing it by (4 + 5) and distribute accordingly.

[tex]A\stackrel{\text{\LARGE 4}}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\text{\LARGE 5}}{\rule[0.35em]{14em}{0.25pt}} C \\\\\\ \stackrel{AB}{4}~~ : ~~\stackrel{BC}{5} ~~ \implies ~~ \stackrel{AB}{4\cdot \frac{72}{4+5}}~~ : ~~\stackrel{BC}{5\cdot \frac{72}{4+5}} \\\\\\ \stackrel{AB}{4\cdot 8}~~ : ~~\stackrel{BC}{5\cdot 8} ~~ \implies ~~ \stackrel{AB}{\text{\LARGE 32}}~~ : ~~\stackrel{BC}{40}[/tex]

The coefficient of correlation is -0.90

The percentage of the dependent variable's variance that is predicted from the independent variable is known as the coefficient of determination or R squared method. It shows how much variety there is in the given data collection.

The range of the coefficient of determination, which is the square of the correlation(r), is 0 to 1.

The square of the correlation between the x and y variables is used to calculate the coefficient of determination in linear regression.

The dependent variable cannot be predicted from the independent variable if R2 is equal to 0.

The dependent variable can be accurately predicted from the independent variable if R2 is equal to 1.

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7.14 unit² is the area of the rectangle shown on the coordinate plane

The length and breadth of the rectangle multiplied together provide the area of the rectangle. To determine the area occupied by a rectangle within its perimeter, we compute the area of the rectangle.

Consider rectangle with vertices A(-1,-2), B(-3,-4), C(-6,-1) and D(-4,1). The area of the rectangle is:

Area = length × width

Now, find the length and the width:

Length (BC) = [tex]\sqrt{[-3-(-6)]^2 + [(-4)-(-1)]^2}[/tex]

or, BC = [tex]\sqrt{(3)^2 +(-3)^2}[/tex]

or, BC = [tex]\sqrt{18}[/tex] unit

Width (AB) = [tex]\sqrt{[(-1) -(-3)]^2 + [(-2)-(-4)]^2}[/tex]

or, AB = [tex]\sqrt{(2)^2 +(2)^2}[/tex]

or, AB = [tex]\sqrt{8}[/tex] unit

Then the area of the rectangle ABCD is

Area(ABCD) = length (BC) × width (AB)

or, Area(ABCD) = [tex]\sqrt{18} *\sqrt{8}[/tex]

or, Area(ABCD) = 7.14 unit²

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Answer:

15 cents

Step-by-step explanation:

[tex]\frac{11}{33} =\frac{5}{y}[/tex]

Cross Multiply.

11 · y = 5 · 33

11y = 165

11y ÷ 11 = 165 ÷ 11

y = 15

Answer:

the average contribution to the political campaign was $0.12.

Step-by-step explanation:

To find the average contribution to the political campaign, we first need to convert the total amount of money contributed and the number of people who contributed to scientific notation.

The total amount of money contributed to the political campaign was $9.48 million, which can be written in scientific notation as $9.48 * 10^6.

The number of people who contributed to the campaign was 79 thousand, which can be written in scientific notation as 79 * 10^3.

To find the average contribution, we need to divide the total amount of money contributed by the number of people who contributed. Therefore, we can substitute the values in scientific notation into the formula to find the average contribution:

Average contribution = Total amount / Number of people

                   = 9.48 * 10^6 / 79 * 10^3

                   = 9.48 / 79

                   = 0.12

Therefore, the average contribution to the political campaign was $0.12.

By using the properties of parallel lines, it can be inferred that -

Corrosponding angle goes in the place of first question mark and substitution property of equality goes in the place of second question mark.

What are parallel lines?

Two lines are said to be parallel if on extending them indefinitely, they will never intersect

Transversal is a line that intersects two or more parallel lines

For the first question mark

[tex]\angle ASR \cong \angle AVU[/tex] [Corrosponding angle]

For the second question mark

[tex]m\angle AVU = 90^{\circ}[/tex] [Substitution property of equality]

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By using simultaneous linear equation, it can be concluded that-

They should sell only scratching post during the last two weeks of the fundraiser

Third option is correct

What is simultaneous linear equation?

At first, it is important to know about linear equation.

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here, a system of simultaneous linear equation needs to be solved

Let the cost of one collar be $x and the cost of one scratching post be $y

The first week they sold seven collars and 10 scratching posts and donated $299.83.

7x  + 10y = 299.83 ..... (1)

The second week they sold nine collars and 18 scratching posts and donated $482.85.

9x + 18y = 482.85 .... (2)

Multiplying (1) by 9 and (2) by 5

63x + 90y = 2698.47 ..... (3)

45x + 90y = 2414.25 ... (4)

Subraction (4) from (3)

18x = 284.22

x = [tex]\frac{284.22}{18}[/tex]

x = $15.79

Putting the value of x in (1)

7 [tex]\times[/tex] 15.79 + 10y = 299.83
110.53 + 10y = 299.83

10y = 299.83 - 110.53

10y = 189.3

y = [tex]\frac{189.3}{10}[/tex]

y = $18.93

Since the cost of one scratching post is more than cost of one collars, they should sold scratching post  during the last two weeks of the fundrasiser

Third option is correct

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Complete Question

The complete Question has been attached

Answer:

4.67 (nearest hundredth)

Step-by-step explanation:

In 3 weeks, Landscape Elementary uses 14 reams of paper.

In 1 week, Landscape Elementary uses 14/3 reams of paper. = 4.66666...

The digit at thousandth place is 6 and it is more than 5. Thus add 1 with hundredth digit.

4.66666... = 4.67 (nearest hundredth)

Solving proportional relationship and options given we have value of x in second row as 5 and in third row as 8, value of y in third row as 2.4

What is proportional constant ?

The ratio between two proportional quantities' constant values is known as the constant of proportionality.

When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship.

The Direct Variation and Inverse Variation types of proportions between the two provided quantities determine the proportionality constant's value.

To show proportional relationship we need to have  [tex]\frac{y}{x}[/tex] as a constant value k.

From first set of data, we can have our constant k as

[tex]k=\frac{.6}{2} =0.3[/tex]

Now to fill 2nd row of table we have value of y given and as discussed above  [tex]\frac{y}{x}[/tex]  will remain constant. So, solving we get

 [tex]x = \frac{1.5}{0.3} = 5[/tex]

So, value of x in second row will be 5

For third row we can substitute as value of x as 8 and value of y as 2.4 that will give us proportional constant as calculate in above cases.

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Cr Cash 4,900 which is Interest paid annually on December 31.

Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.

Pretzelmania, Inc., issues 7%, 10-year bonds with a face amount of $70,000 $70,000 on January 1, 2015. The market interest rate for bonds of similar risk and maturity is 7%. Interest is paid annually on December 31.

January 1, 2015, bonds issued at par value

Dr Cash 70,000

   Cr Bonds payable 70,000

June 30, 2015, first coupon payment

Dr Interest expense of 4,900

   Cr Cash 4,900

Thus, Cr Cash 4,900 which is Interest paid annually on December 31.

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Answer:

h≈1.15cm is the correct answer

Answer: h is about 1.15 cm

Step-by-step explanation:

Answer:

= about 1436.75504

Step-by-step explanation:

V = 4/3 π r³

The correctly labels the population of employees is, 001 - 250.

What is population?

The term "population" refers to all citizens who are either permanently residing in a nation or are only temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.

Given:

The CEO of a company wants to determine if taking the employees to a company retreat would boost their morale.

He decides to use a random number table to survey a simple random sample of 50 of the 250 employees.

As the population consist of 250 employees and simple random sample of size 50, to use a random number table to survey a sample random sample of 50 of the 250 employees, the population of employees should be labeled as 001-250.

Hence, the correctly labels the population of employees is, 001 - 250.

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Applying the properties of a rhombus, the value of each angle listed are:

m∠JKL = 72°

m∠MLK = 108°

m∠JMK = 36°

m∠MJL = 54°

m∠KNL = 90°

A rhombus is a quadrilateral with the following properties:

Given, m∠JKM = 36°, apply the properties of a rhombus to solve the missing values.

m∠JKL = 2(36)

m∠JKL = 72°

m∠MLK = 180 - 72 [adjacent angles are supplementary in a rhombus]

m∠MLK = 108°

m∠JMK = 36°

m∠MJL = 1/2(m∠MLK)

m∠MJL = 1/2(108)

m∠MJL = 54°

m∠KNL = 90° [bisection of the diagonals of a rhombus at right angles).

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12 bottles of soda cost  $15.84  next week

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Price of  5 bottles = $6

Price of  1 bottle = 6/5 = $1.2

10% of 1.2 = (10/100)*1.2 = 0.12

new price of 1 bottle = 1.2+ 0.12 = $1.32

Price of  12 bottles = 12*1.32 = $15.84

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the height of 4.6 units when the trapezoid's area is 70 units and its first and second bases are

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. A shape's "space enclosed within the perimeter or the boundary" is referred to as its area. Math formulas are used to determine the area of various forms.

given

area of the trapezoid is 70 units

and the 1st base = 20 units and 2nd base = 10 units

length CE ?

area of trapezoid = 1/2( b1 + b2)*h

70= 1/2 (20 + 10 )*h

70 = 1/2(30)*h

h = 4.6 units

the height of 4.6 units when the trapezoid's area is 70 units and its first and second bases are

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