Use the formula A=(1+r/n)^nt to solve the compound interest problem.
Find how long it takes for 900$ to double if it is invested at 6% interest compounded monthly.
The money will double in value in approximately ? years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)

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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Answer:

(-10) - (-16) = 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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Answer: Come up with questions that make sence. That are good solvablequestions. Make sure that you are able to take data off of it to see how people result in it.

Step-by-step explanation:

Refer to the attachment for graph.

What are vector equations ?

Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.

Given  vector equation:

r(t) = < t², t, 2 >

When t= -2,

r(-2) = < (-2)², -2, 2 >

      =  < 4, -2, 2 >

This means. when t= -2, the curve touches the point   ( 4, -2, 2 )

Similarly, when t= -1, the curve touches the point   ( 1, -1, 2 )

Table is attached.

graph is attached.

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A 95% two-sided confidence interval is 0.46 < a <0.31 .

The formula for confidence interval for population standard deviation is,

[tex]s\sqrt{\frac{n-1}{X^{2} _{1-a/2,n-1} } }[/tex]  < a < [tex]s\sqrt{\frac{n-1}{X^{2} _{a/2,n-1} } }[/tex]

Given in question,

Significance level, a = 1 - 0.95

                                 = 0.05

Sample size, n = 51

Sample standard deviation, s = 0.37

By using chi-square distribution table, we get

[tex]X^{2} _{1-a/2,n-1}[/tex] = [tex]X^{2} _{0.975,50}[/tex]

                  = 32.36

[tex]X^{2} _{a/2,n-1}[/tex] = [tex]X^{2} _{0.025,50}[/tex]

              = 71.42

Confidence interval for population standard deviation is :

[tex]0.37\sqrt{\frac{50}{32.36} }[/tex]  < a  < [tex]0.37\sqrt{\frac{50}{71.42} }[/tex]

0.45992018426 < a < 0.30958278534

Hence, a 95% two-sided confidence interval is 0.46 < a <0.31 .

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Answer:

a=-2400

Step-by-step explanation:

We have -x*y*z = 150. We want to find the value of -2x*2y*-4z. Let's set this to a variable, a. We have now that [tex]2x*2y*4z = a[/tex] (because the negatives combine to a positive), where we want to solve for a. This is equal to [tex]16xyz = a[/tex], and dividing by 16 on both sides results in [tex]xyz = a/16[/tex]. Recall that we know [tex]-xyz = 150.[/tex] Negating each side gives us [tex]xyz = -150.[/tex]

Now we have two equations that are equal to the same thing(xyz), so we can set them equal to each other. This gives us [tex]-150 = a/16[/tex]. To solve for a, we multiply both sides by 16, giving us a = -2400. This is our answer!

Hope this helps!

From the expression, when simplified, (1)   16a+b  (2) 17b+11a (3) 17b.

An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

The given algebraic terms are

3a+b+13a

Collect the like terms

3a+13a+b

Add the like terms

16a+b

Therefore, 3a+b+13a matches 16a+b

20b+11a-3b

Collect like terms

20b-3b+11a

=17b+11a

Therefore, 20b+11a-3b matches 17b+11a

20b-5b+2b

All the terms are alike, therefore do the arithmetic operation

15b+2b

=17b

Therefore, 20b-5b+2b matches 17b

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Answer: a=33

Step-by-step explanation:

Answer:

a=33

Step-by-step explanation:

1. Multiply both sides of the equation by 11

231=6a+33

2. Move 6a to the left side by subtracting

231-6a=33

3. Move 231 to the right side by subtracting

-6a=33-231

4. Find the difference

-6a=-198

5. Divide -6 on both sides to get "a" by itself

a=33

The first six terms of the given sequence are given as  3, -7, -17, -27, -37 and -47.

An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.

This difference is known as the common difference of the sequence.

The given problem can be solved as follows,

The first term of the sequence is a₁ = 3

And, the common difference is d = -10.

Now, the first six terms can be written as,

a₁ = 3

a₂ = 3 - 10

   = -7

a₃ = -7 - 10

    = -17

a₄ = -17 - 10

    = -27

a₅ = -27 - 10

    = -37

a₆ = -37 - 10

    = -47

They can be graphed on the number line as follows,

Hence, the first six terms are given as 3, -7, -17, -27, -37 and -47.

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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:

h≈1.15cm is the correct answer

Answer: h is about 1.15 cm

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

x(XY) = 6(WX)

x(x + 11) = 6(6 + 15)

x² + 11x = 126

x² + 11x - 126 = 0

126 = 7 × 18

(x + 18)(x - 7) = 0

x + 18 = 0   or   x - 7 = 0

x = -18   or   x = 7

We discard the negative answer.

x = 7

The number of cans of soup purchased and the number of frozen dinners purchased are 8 and 3 respectively.

A system having more than two equations is known as a system of equations.

Given that, the can of soup contains 350 mg of sodium and the frozen dinner contain 650 mg of sodium.

Let the numbers of cans of soups and frozen dinners purchased be s and f, then,

s + f = 11

s = 11-f       (1)

The total sodium in all 11 cans is 4750 mg which can be expressed as:
350s + 650f = 4750

Substitute s = (11-f) into the above equation:

350(11 - f) + 650f = 4750

3850 - 350f + 650f = 4750

300f = 4750 -3850

300f = 900

f = 3

Substitute f = 3 into equation (1):

s = 11-3

s = 8

Hence, the number of cans of soup purchased and the number of frozen dinners purchased are 8 and 3 respectively.

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For an average intake of 2200 calories per day, the number of acres of land is approximately 2.

A function having the formula f(x) = ax' + b is said to be linear.

It appears to be a standard linear equation, except the linear function symbol is f rather than y. (x).

You would be given the value of f(x) and asked to locate x when solving a linear function.

C(x) is a variable that tells the number of calories consumed daily by a person

x is the number of acres that person own.

C(x) = 270ln(x+1)+1900

In the given question number of acres ask a person have who consumed 2200 calories in a day.

Therefore,

C(x)=2200

2200=270ln(x+1)+1900

2200-1900=270ln(x+1)

300=270ln(x+1)

300/270 = ㏑(x+1)

10/9 = ㏑(x+1)

x+1 = e^(10/9)

x+1 = 3.037

x= 3.037-1

x=2.037

x=2(round off)

Therefore, 2 acres of land a person can consume 2200 calories in a day.

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The probablity that the two balls are orange and blue is 1/8

Describe Probability:

This is the chance or likelihood that an event will take place.

One orange ball, one yellow ball, and two blue balls are there in a bag.

The total number of sample space  or outcome can be given as

Total outcome = 1 + 1 + 2=4

Probablity of occouring an orange ball  can be given as, 1/4

Probablity of occouring a blue ball  can be given as, 2/4

Probablity of an orange ball and a blue ball = 1/4 * 2/4

Probablity of an orange ball and a blue ball = 1/8

Consequently, there is a 1/8 chance that the two chosen balls are orange and blue

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a. The table for the given data is as follows :

Year                  2014       2015        2016       2017

Value (in $) 254000 293000 338000 372000

b. Domain and Range for the given relation is:

Domain : {2014, 2015, 2016, 2017}

Range : {254000, 293000, 338000, 372000}

c. From the table we observe that for each year it is having a unique value so it is related to the function.

What is Domain?

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

What is Range?

The range of a function is the set of values that the function assumes.

What is Relation?

A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the items x and y come from different sets, then the objects are said to be connected

a. The table for the given data is as follows :

Year                  2014       2015        2016       2017

Value (in $) 254000 293000 338000 372000

b. Domain and Range for the given relation is:

Domain : {2014, 2015, 2016, 2017}

Range : {254000, 293000, 338000, 372000}

c. From the table we observe that for each year it is having a unique value so it is related to the function.

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To keep the obtuse isosceles triangle design, the railing that he should order a duplicate of to create his dining area is of:

12 meters.

A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.

The measurements in this triangle are given as follows:

If he orders a duplicate of the largest measurement, the smallest measurement would be the base of the isosceles triangle, meaning that it would be an acute isosceles triangle.

Then he should order a duplicate of the smallest measurement, of 12 meters, as then they would be the sides between the obtuse angle of the isosceles triangle.

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Answer:

Step-by-step explanation:

To keep the obtuse isosceles triangle design, the railing that he should order a duplicate of to create his dining area is of:

12 meters.

When does a set of three measurements can represent a triangle?

A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.

The measurements in this triangle are given as follows:

Smallest: 12 meters.

Largest: 22.8 meters.

If he orders a duplicate of the largest measurement, the smallest measurement would be the base of the isosceles triangle, meaning that it would be an acute isosceles triangle.

Then he should order a duplicate of the smallest measurement, of 12 meters, as then they would be the sides between the obtuse angle of the isosceles triangle.

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:12

Step-by-step explanation:

Answer:

Option C

The first two hours cost $4. Between two hours and six hours cost $2 per hour, and all hours after that cost $1.

Step-by-step explanation:

From the first part of the graph we can see that there is a flat rate of $4 for the first two hours. So the first two hours cost $4.

We can eliminate options A and B leaving C and D as only possible options.

Look at the second part of the graph

Between 2 hours and 6 hours(difference of 4 hours), the cost increases from $4 to $8 or an increase of $8

So rate per hour is $8/4 = $ 2 per hour between 2 hours and 6 hours

This information alone is enough to eliminate D but let's go to the rate beyond 6 hours just to make sure. This is the third part of the graph

Between 6 and 7 hours (1 hour) we can see the cost goes from $12 to $13 or a difference of $1. This means for every hour after 6 hours, the rate is $1 per hour.

So option C is the correct choice

The system of linear inequalities is graphed is  x < -2; y ≤ -x+2. Hence option c is the correct.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The graph consists of two inequalities.

Since the one graph line is solid, thus the inequality sign either "less than or equal" or "greater than or equal". The other one is dotted, thus it will be less than or greater than

First find the equation of line.

One line passes through the points (-2,0) and (0,-2).

The equation of line that passes through the point (a,0) and (0,b) is

x/a + y/b = 1

The equation of the line is x/(-2) + y/(-2) =1

x + y = -2

y = -x - 2

The equation of the inequality will be either y ≤ -x - 2 or y ≥  -x - 2.

Putting x =0  and y = 0 in y ≤ -x - 2

0  ≤ - 0 -2

0≤ -2 (false)

In the graph (0,0) does not include in the shaded region. Therefore the inequality is   y ≤ -x - 2.

The second line is parallel to y-axis.

The equation of line will be x = a

The line passes through the point (-2,0)

Putting x = -2 and y =0  in x = a

-2 = a

Therefore the equation of the dotted line will be x = -2

The equation of the inequality will be either x > -2 and  x < -2:

Putting x =0  and y = 0 in x < -2

0 < -2

0 < -2 (false)

In the graph (0,0) does not include in the shaded region. Therefore the inequality is  x < -2.

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Answer: B. ( - ∞ , 1 ) U ( 1, 2]

Step-by-step explanation:

The equation of H(x) is [tex]\frac{\sqrt{2-x} }{x-1}[/tex]

For the bottom denominator, x-1 cannot equal zero

x-1=0

x=1

For the numerator, 2-x square root has to be greater or equal to zero.

[tex]2-x\geq 0[/tex]

[tex]x\leq 2[/tex]

so the domain is

( - ∞ , 1 ) U ( 1, 2]

Different arrangements of the display are possible is 2520.

Given:

the artist r. locklen jones selects 5 paintings from a collection of 7 to display in a row.

Permutation :

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order.

= [tex]7_P_5[/tex]

we know that,

[tex]n_P_r[/tex] = n! / ( n - r ) !

[tex]7_P_5[/tex] = 7! / ( 7 - 5 ) !

= 7! / ( 2 ) !

= 7! / 2!

= 7 * 6 * 5 * 4 * 3 * 2! / 2!

= 42 * 20 * 3

= 840 * 3

= 2520

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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 amount of flour he get in per dollar will be;

⇒ 1.625 dollars

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Pablo bought 13 pounds of flour for $8.

Now,

Since, Pablo bought 13 pounds of flour for $8

Hence, The amount of flour he get in per dollar = 13/8

                                                                          = 1.625 pounds

Thus, The amount of flour he get in per dollar will be;

⇒ 1.625 dollars

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The disparity -9x/11 - 7 < -5 is x > -22/9

The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.

Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality.

-9x/11 < 2 (add 7 to both sides) (add 7 to both sides)

-9x < 22 (multiply both sides by 11) (multiply both sides by 11)

x > 22/-9 Because you are dividing by a negative integer, change the sign.

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Answer: x > [tex]\frac{-22}{9}[/tex]

Step-by-step explanation:

     To solve this inequality, we will isolate the variable, x, with inverse operations.

   Given:

[tex]\frac{-9x}{11}[/tex]- 7 < -5

   Add 7 to both sides of the inequality:

[tex]\frac{-9x}{11}[/tex] < 2

   Multiply both sides of the inequality by 11:

-9x < 22

   Divide both sides of the inequality by -9:

* note, we must "flip" the sign since we are dividing by a negative integer

x > [tex]\frac{-22}{9}[/tex]

Answer:

0.95-1.05 (please give brainliest)

Step-by-step explanation

1x.95=.95

1x1.05=1.05

Answer:

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

Step-by-step explanation: