At the beginning of the year, Harper had $30 in savings and saved an additional $10 each week thereafter. Stella started the year with $45 and saved $7 every week. Let H represent the amount of money Harper has saved t weeks after the beginning of the year and let S represent the amount of money Stella has saved t weeks after the beginning of the year. Write an equation for each situation, in terms of t, and determine the number of weeks after the beginning of the year until Harper and Stella have the same amount of money saved.

S=__

H=___

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:

(-10) - (-16) = 6

Step-by-step explanation:

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:

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.

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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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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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 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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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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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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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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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]

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]

Answer:

h≈1.15cm is the correct answer

Answer: h is about 1.15 cm

Step-by-step explanation:

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:

-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].

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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Answer: False

Step-by-step explanation:

Answer:

0.95-1.05 (please give brainliest)

Step-by-step explanation

1x.95=.95

1x1.05=1.05

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

Answer:

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

Step-by-step explanation:

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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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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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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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

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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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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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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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