Ann-Marie can order 5 fewer pounds of cheese
so that her order of 75 pounds of cheese and
50 boxes of crackers will make exactly 25 gift
baskets.

2x − y = 0

The standard form of a linear equation is:

Ax + By= C

where, if at all possible, A, B, and C are integers, A is non-negative, and, A, B, and C have no common factors other than 1.

The equation in the problem can be converted into standard form by the following method:

−2x + y= −2x + 2x

−2x + y = 0

−1(−2x+y) = −1 × 0

2x − y = 0

2x − 1y = 0

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The amount of money he must put in the account is $16666.66

A portion of the total loan amount that the borrower is required to pay the lender as interest over a predetermined timeframe.

This year, the Bank of Canada quickly increased its policy rate, taking it from 0.25% in March 2022 to 4.25% in December 2022, and in the process, driving up mortgage and prime rates. An interest rate is the portion of a loan, deposit, or borrowing that must be paid in interest each period. The total amount of interest charged depends on the amount lent or borrowed, the interest rate, the frequency of compounding, and the length of time it was lent, deposited, or borrowed.

Given,

r=4%

T=5 years

Total amount=SI+P

=20000

SI+P=20000

SI=20000-P

SI=PTR/100

20000-P=(P×5×4)/100

2000000-100P=20P

120P=2000000

P=16666.66

Therefore, The amount of money he must put in the account is $16666.66.

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Two foci of the ellipse are ( 2 - √3) and moves clockwise three fourth is ( 2 + √3).

As given in the question,

Given equations are :

x = 1 + sin(t)

⇒ sin(t) = (x - 1)

y = 6 + 2cos(t)

⇒cos(t) = (y - 6)/2

We know that,

sin²t + cos²t = 1

Substitute the value of sin(t) and cos(t) we get,

(x - 1)²/ 1² + (y - 6)²/ 2² = 1

Standard Equation of the ellipse  is:

( x -h)²/b² + (y - k)²/a² = 1

Center of the ellipse = (h , k)

(h , k) = (1, 6)

here b = 1 and a = 2

'c' is the distance from focus to the center

c = √a² - b²

  = √4 -1

  = √3

Therefore , two foci for the given ellipse are ( 2 - √3) and moves clockwise three fourth is ( 2 + √3).

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Answer:

h/g is 3

Step-by-step explanation:

h=12 and g=4 12/4 is 3 so its h/g

Answer:

H/g

Step-by-step explanation:

12/4 = 3

The amount that Lucy pays for the shoes is $61.56.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this situation, Lucy buys a $68 pair of shoes. she receives a 15% employee discount and the sales tax is 6 1/4. The amount paid will be:

= $68 - (15% × $68)

= $57.80

Addition of the sale tax will be:

= $57.80 + (6.5% × $57.80)

= $57.80 + $3.76

= $61.56.

The price is $61.56.

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The correct option is b) ii only

From the given data we can construct confidence interval. So, the statement that we are 95% confident that the average rent for students at the university is between $ 564 and $664 is true.

What is meant by distribution?

The methodical effort to account for how the owners of the labor, capital, and land inputs divide the country's income. Rent, wages, and profit margins have historically been the focus of economists' research into how these expenses and margins are set.

What are the 3 types of distribution?

The Three Types of Distribution

What are the 5 factors of distribution?

Market, Product, Company, Channel, and Environment Related Factors are 5 Important Factors Affecting Distribution Channel Selection. The distribution of goods can be done through a variety of routes.

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Answer:

x = 3

Step-by-step explanation:

8x + 2 = 26

8x = 26 - 2

8x = 24

x = 24/8

x = 3

Check:

8*3 + 2 = 26

24 + 2 = 26

Manuel's argument is correct on why the volume of cone W and  square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.

A thick or empty device with an approximately round or elliptical base that tapers to a notch is known as a cone.

on the other hand ,

A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.

Cone W has a radius of 6 cm and a height of 5 cm.

The base area of the cone will be

A = πr²

A = π (6)²

A = 113.04 square cm

Then the volume of the cone will be

V = (1/3) x base area x height

V = (1/3) x 113.04 x 5

V = 188.4 cubic cm

Square pyramid X has the same base area and height as cone W.

Then the volume of the square pyramid will be

V = (1/3) x base area x height

V = (1/3) x 113.04 x 5

V = 188.4 cubic cm.

Manuel's argument is correct on why the volume of cone W and  square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.

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Inequality for each part be

a) x + 12 ≤ -8

b)  x - 8 > 12

c) x + 8 < 12

What do you mean by inequality?

In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size.

The notation a < b means that a is less than b.

The notation a > b means that a is greater than b.

Let the number be x

According to the question:

a) The sum of a number and 12 is at most -8.

inequality become:

x + 12 ≤ -8

b) A number increased by -8 is greater than 12

inequality become:

x + (-8) > 12

⇒ x - 8 > 12

c)  -8 less than a number is no more than 12

x - (-8) < 12

⇒ x + 8 < 12

Therefore, inequality for each part be

a) x + 12 ≤ -8

b)  x - 8 > 12

c) x + 8 < 12

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The solution is written in Python

The given problem can be solved by using the rand() function that generates a random number over the range [0, RAND_MAX] and with the help of the value returned by this function, any number in any range [L, R] can be generated as (rand() % (R – L + 1)) + L. Follow the steps below to solve the problem:

Initialize an empty string, say S.

Iterate over the range [0, N – 1] and perform the following steps:

Store a random number in the range [0, 1] using rand() function.

Append the randomly generated 0 or 1 to the end of the string S.

After completing the above steps, print the string S as the resulting binary string.

This binary is to hold the binary string.

Next, we declare variable decimal, quotient and remainder (Line 2-4). We assign a test value 13 to decimal variable and then get the first quotient by dividing decimal with 2 (Line 3). Then we get the remainder by using modulus operator, % (Line 4). The first remainder will be the first digit joined with the binary string (Line 5).  

We need to repeat the process from Line 3-5 to get the following binary digits. Therefore create a while loop (Line 7) and set a condition that if quotient is bigger than 0 we keep dividing decimal by 2 and calculate the quotient and remainder and use the remainder as a binary digit and join it with binary string from the front (Line 9-11).

At last, we print the binary to terminal (Line 13).

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The solution is Option D.

The ratio of smoothie size to mangoes used for Kim is the same as the ratio of smoothie size to mangoes used for Angela

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the equation be represented as A

Now , the value of A is

The number of mangoes used by Bri = 1 mango

The amount of smoothie size of Bri = 7 oz

The number of mangoes used by Kim = 3 mangoes

The amount of smoothie size of Kim = 21 oz

The number of mangoes used by Angela = 4 mangoes

The amount of smoothie size of Angela = 28 oz

Now , the proportion is given by

The ratio of smoothie size to mangoes used by Kim = amount of smoothie size of Kim / number of mangoes used by Kim

Substituting the values in the equation , we get

The ratio of smoothie size to mangoes used by Kim = 21 / 3

The ratio of smoothie size to mangoes used by Kim = 7 : 1

Now , the proportion is

The ratio of smoothie size to mangoes used by Angela = amount of smoothie size of Angela / number of mangoes used by Angela

Substituting the values in the equation , we get

The ratio of smoothie size to mangoes used by Angela = 28 / 4

The ratio of smoothie size to mangoes used by Angela = 7 : 1

So , The ratio of smoothie size to mangoes used by Kim = The ratio of smoothie size to mangoes used by Angela = 7 : 1

Hence , ratio of smoothie size to mangoes used by Kim is equal to ratio of smoothie size to mangoes used by Angela

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Answer:

d

Step-by-step explanation:

i took the test and its right :)

Answer:

58

Step-by-step explanation:

There are 5 lines between 50 and 60

60 - 50 = 10

10 / 5 = 2

This means that each increment is 2.

We see the end of the box plot is above the fourth increment above 50.

4 x 2 = 8

50 + 8 = 58

Since the function f(x) = 9.25x + 3 represents the amount of money that Radda earns dog walking for x hours, Radda's earnings would increase by $12.25 each hour.

In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being earned by Radda for dog walking;

T = mx + b

Where:

Therefore, the required linear function that represents the total amount of money that is being earned by Radda for dog walking per hour is given by this mathematical expression;

f(x) = T = 9.25x + 3

When the number of hours Radda spend dog walking is equal to 1 (x = 1), the rate of change(slope) can be calculated as follows;

f(1) = T = 9.25(1) + 3

f(1) = T = 9.25 + 3

f(1) = T = $12.25.

In this context, we can reasonably infer and logically conclude that Radda's earnings increases each hour by $12.25.

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Complete Question:

The function f(x) = 9.25x + 3 represents the amount Radda earns dog walking for x hours. How much does Radda's earnings increase each hour?

Answer:

Part A: 38.1% of the members are seniors that play the trumpet

Part B:  22.9% of the members who are seniors play trumpet

Step-by-step explanation:

Part A:

8 of the 21 members play trumpet that are seniors

8/21 = .381 or %38.1 of the members

Part B:

8 of the 35 seniors in the marching band play trumpet

8/35 = .229 or %22.9 of the members

The inequality that represents the possible number of boxes of chips (x) and boxes of candy bars (y) Maria could buy is 13.80x + 6.60y ≤ 100.

Maria is selling chips and candy bars. each box of chips has 20 bags for $13.80 and the candy bars is $6.60 for a box of 12 bars.

Maria has only 100 dollars to spend. The inequality that represent the possible number of boxes of chips (x) and boxes of candy bars (y) Maria could buy can be calculated as follows:

Therefore,

Hence each box of chips is 13.80 dollars and each candy bars is 6.60 dollars.

Therefore, the inequality is 13.80x + 6.60y ≤ 100.

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The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.

The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]

Given that,

Length of the ladder is, [tex]l=9ft[/tex]

Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.

Now, from triangle ABC,

[tex]AB^{2} +BC^{2} =AC^{2}[/tex]

[tex]h^{2} +b^{2} =l^{2}[/tex]

[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]

[tex]h^{2} +b^{2}[/tex] = 81               (Equation-1)

Differentiating the above equation with respect to time, 't'.

So,

We can write,

[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)

[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0

[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0

[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0                (Equation-2)

In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.

Let us assume,

h = 3 ft and db/dt = 3 ft/s

We can substitute values in equation-1,

[tex]3^{2} +b^{2}[/tex] = 81

9 + [tex]b^{2}[/tex] = 81

[tex]b^{2}[/tex] = 81-9

[tex]b^{2}[/tex] = 72

b = [tex]\sqrt{72}[/tex]

b = 8.48 ft

Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]

3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0

3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0

3*[tex]\frac{dh}{dt}[/tex] = - 25.44

[tex]\frac{dh}{dt}[/tex] = -25.44/3

[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s

Therefore,

The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.

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Answer: B & A

Step-by-step explanation: I think?

Answer:

a. Let Q be the total number of quarters you take with you when you go shopping. The total number of quarters you have is 20, and you find 40% more quarters in your room, which is an additional 0.4 * 20 = <<0.420=8>>8 quarters. Therefore, the total number of quarters you have after finding more quarters in your room is 20 + 8 = <<20+8=28>>28 quarters. When you go shopping, you spend 50% of the total number of quarters, which is 0.5 * 28 = <<0.528=14>>14 quarters. Therefore, the total number of quarters you take with you when you go shopping is 28 - 14 = <<28-14=14>>14 quarters. This can be represented by the expression Q = 28 - 0.5 * 28.

b. If you have 14 quarters with you when you go shopping, and you spend 50% of the total number of quarters, then you have 0.5 * 14 = <<0.514=7>>7 quarters left. Since each quarter is worth $0.25, you have 7 * 0.25 = $<<70.25=1.75>>1.75 left. Answer: \boxed{1.75}.

Answer:

2

Step-by-step explanation:

The value of the c in the function c = 19m - 15 when m=10 is 175.

A relationship between a number of inputs and outputs is termed a function. In a function, which is an association of inputs, each input is associated to exactly one output. Each function has a domain, range, and co-domain.

Given the function;

c = 19m - 15,

where m represents the number of months and c represents the total number of car sent to New York.

To find the value of c:

when m = 10,

Substitute the value of m to the function;

c = 19 (10) - 15

c = 190 - 15

c = 175.

Therefore, the value of c is 175.

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Answer:

7.51

Step-by-step explanation:

16.72 - 9.21

The critical value that corresponds to a confidence interval of 95.9% is 1.99.

The distribution of the sample mean will be roughly normally distributed, according to the Central Limit Theorem, if we have an unknown population with a mean and standard deviation and adequately small random samples (n < 30) are chosen from the population with replacement.

Then, the mean of the sample means is given by,

μ(x) = μ

And the standard deviation of the sample means is given by,

σ = σ / [tex]\sqrt{n}[/tex]

In this case the sample selected is of size, n = 7.

As the sample size n = 7 < 30, the sampling distribution of sample mean will be approximately normal.

So, a z-interval will be used to estimate the population mean.

The confidence level is, 95.9%.

The value of α is:

∝ = 1 - confidence level

∝ = 1 - 0.959

∝ = 0.041

The critical value is:

[tex]z_{\frac{∝ }{2} }[/tex] =  [tex]z_{\frac{0.041}{2} }[/tex]

[tex]z_{\frac{∝ }{2} }[/tex] = [tex]z_{0.0205}[/tex]

[tex]z_{\frac{∝ }{2} }[/tex] = -1.99

[tex]z_{1-∝/2}[/tex] = 1.99

Use a z-table.

Therefore,

The critical value that corresponds to a confidence interval of 95.9% is 1.99.

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Answer:

B

Step-by-step explanation:

The vertical dashed line is x = -3. Since the shading is to the right, that is x > -3.

The solid line has slope -4/5 and y-intercept -2. It's shaded above, so it is y ≥ -x - 2.

Answer: B

The rational zeros of the function can be found using the Rational Zero Theorem. The possible rational zeros of the function are ±1, ±5, ±1/7, ±5/7.

Zeros:

x=-5, -1/7, 0, 1, 5

The Rational Zero Theorem states that if a polynomial function of degree n has integer coefficients, then the possible rational zeros of the function will be of the form ±p/q, where q is a factor of the leading coefficient and p is a factor of the constant term.

In this case, the degree of the polynomial is 4, which means that the leading coefficient is 7 and the constant term is 5. Thus, the possible rational zeros of the function will be of the form ±p/q, where p is a factor of 5 and q is a factor of 7. The factors of 5 are ±1 and ±5, and the factors of 7 are ±1 and ±7. This means that the possible rational zeros of the function are ±1, ±5, ±1/7, and ±5/7.

To find the zeros of the function, we can use the rational zeros we found and plug them into the original equation. We can then solve for the zeros and find that the zeros of the function are x=-5, -1/7, 0, 1, 5.

x=-5: 7(-5)^4 +27(-5)^3 -40(-5)^2 +(-5) +5= 0

x=-1/7: 7(-1/7)^4 +27(-1/7)^3 -40(-1/7)^2 +(-1/7) +5= 0

x=0: 7(0)^4 +27(0)^3 -40(0)^2 +(0) +5= 0

x=1: 7(1)^4 +27(1)^3 -40(1)^2 +(1) +5= 0

x=5: 7(5)^4 +27(5)^3 -40(5)^2 +(5) +5= 0

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Interest is the price you pay to borrow money or the cost you charge to lend money.

To find the difference of 310 and 285, subtract 310 from 285. This will give you the added interest cost.

310-285 = 25

So, Polly will pay $25 in interest.

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Answer:

[tex]133^{\circ}[/tex]

Step-by-step explanation:

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]x+13+10x+13+2x-2=180 \\ \\ 13x+24=180 \\ \\ 13x=156 \\ \\ x=12 \\ \\ m\angle Q=10(12)+13=133^{\circ}[/tex]