2. Kira has three dogs, Luna, Cooper, and Daisy.
Cooper weighs 25 pounds less than Daisy. Luna
weighs 20 pounds less than three times Cooper.
If their combined weight is 175 pounds, how
much does Luna weigh?

A. 59 pounds
B. 74 pounds
C. 78 pounds
D. 82 pounds

The interest eared from the given amount, rate of interest and time period is $426.883.

Given that, amount = $700, rate of interest = 4% and time period = 2 years.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest is [tex]Amount=Principal(1+\frac{r}{100})^{nt}[/tex]

Let the money deposited be x.

So, [tex]700=x(1+\frac{4}{100} )^{2\times12}[/tex]

⇒ [tex]700=x(1+0.04)^{24}[/tex]

⇒ [tex]700=x(1.04)^{24}[/tex]

⇒ 700 = 2.563x

⇒ x=700/2.563

⇒ x=$273.117

So, interest = 700-273.117

= $426.883

Therefore, the interest eared from the given amount, rate of interest and time period is $426.883.

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Step-by-step explanation:

first order them from least to greatest

13,14,18,21,22,26,32,39,39,42

then just look for the term in the middle

sunset there are 2 numbers in the middle you will add them both and subtract them by 2

42+39 then / 2 =40.5

Answer:

5 = 1

or

5 = 25

Step-by-step explanation:

I've seen two answers to this.

1. Since we are told 1 = 5, then 5 = 1.

One answer is 1 = 5

2. Since each number on the right is 5 times the number on the left, then 25 corresponds to 5, and 5 = 25.

Answer: 5=1 (The correct answer) 5=25 (The answer that makes sense but is not correct).

Step-by-step explanation:

Explanation for answer 1: It say's that 1 = 5.

Explanation for answer 2: If we follow the pattern of adding 5 each time we go up a number then 5 would equal 25.

Answer:

Box A: -2x

Box B: 2/9

Step-by-step explanation:

Multiply 1/3 by each of the expressions above the rectangle.

Box A: 1/3 × (-6x) = -2x

Box B: 1/3 × 2/3 = 2/9

The statement that is correct regarding their solutions is A. Salina combined the x squared y terms correctly but then left the Plus x squared y term in her answer.

From the information, Salina and Nessa combined like terms using the same expression.

The expression given is illustrated as.

6x²y - 3 + x²y + 2xy² + 2xy - 6

It should be noted that the like terms are:

6x²y and x²y as well as -3 and -6.

Combine the like terms

6x²y + x²y = 7x²y

Also, -3 + (-6) = -9

Therefore, the value will be 7x²y + 2xy² + 2xy - 9

The correct option is A as it illustrated the mistake Salina made.

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Answer:

A is the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x(x + 7)(x²+49) = 0

(apply the zero product)

x=0 or x+7 =0 or x² + 49 = 0

x+7 =0

x=-7

x² + 49 = 0

no real solution for this i think

Answer = x=0 or x=-7

The linear equation that passes through the two given points is:

y = (-1/4)*x - 2/4

A general linear equation is written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:

m = (y₂ - y₁)/(x₂ - x₁)

Here we know that the line passes through (-1, -1/4) and (1, -3/4)

Then the slope is:

m = (-3/4 + 1/4)/(1 + 1)

m = (-2/4)/2 = -2/8 = -1/4

the line is:

y = (-1/4)*x + b

To find the value of v we can replace the point  (1, -3/4) so we get:

-3/4 = (-1/4)*1 + b

-3/4 + 1/4 = b

-2/4 = b

The linear equation is:

y = (-1/4)*x - 2/4

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Answer: (4,-3)

Step-by-step explanation:

4x+5y=1       (1)

3x-2y=18     (2)

Multiply both parts of equation (1) by 2 and both parts of equation (2) by 5:

8x+10y=2

15x-10y=90

Sum these equations:

23x=92

Divide both parts of the equation by 23:

x=4

Substitute the value of x=4 into equation (1):

4(4)+5y=1

16+5y=1

16+5y-16=1-16

5y=-15

Divide both parts of the equation by 5:

y=-3

Thus, (4,-3)

The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.

Given,

The cost for one calendar = $8

The cost for one coffee mug = $12

Dominique must sell at least $800 of merchandise and it should include at least 60 coffee mugs.

Here,

x be the number of calendars and y be the number of coffee mugs;

We have to find an inequality which represents the given situation;

So,

The inequality be;

8x + 12y ≥ 800 and x ≥ 60

That is,

The inequality that represents the given situation is option A 8x + 12y ≥ 800 and x ≥ 60.

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Answer:

P(les than/equal to 3): ½

Answer:

18

Step-by-step explanation:

x = 4

4x

= 4 * 4

= 16

y = 2

4x + y

= 16 + 2

= 18

Answer:

49

Step-by-step explanation:

35+14=49

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The probability that the Yankees will win when they score fewer than 5 runs is; 0.567

We are given;

Event A which is when Yankees win has a probability of; P(A) = -.45

Thus, Event that the Yankees don't win which is when they lose is;

P(A') = 1 - 0.45 = 0.55

Event B which is the event that the Yankees score 5 or more runs has a probability of; P(B) = 0.6

Event that the Yankees score 4 or less run is given by the probability;

P(B') = 1 - 0.6 = 0.4

The probability that the Yankees win and score 5 or more runs is;

P(A' ∩ B') = 0.34

Thus, the probability that the Yankees will win when they score fewer than 5 runs wanted is given by the chain rule in conditional probability of the formula;

P(A' | B') = P(A' ∩ B')/P(B') = 0.34/0.6

P(A' | B') = 0.567

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Using the substitution method, the solution to the system of equations is: x = -4 and y = 12.

To solve a system of equations using the substitution method, find the value of one of the variables in one equation, then substitute it in the second equation and solve to find the value of the second variable.

Given the equations:

x + y = 8 --> eqn. 1

y = -3x --> eqn. 2

Substitute -3x for y into equation 1:

x + (-3x) = 8

x - 3x = 8

-2x = 8

-2x/-2 = 8/-2

x = -4

Substitute x = -4 into equation 2:

y = -3(-4)

y = 12

The solution is, x = -4 and y = 12.

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Quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.

Graph is attached.

As given in the question,

Quadratic equation passes through the points (-4,2) and (1,2)

(x₁, y₁) =(-4,2)

(x₂ ,y₂) = (1,2)

(y-y₁)/ (x-x₁) = (y₂ -y₁)/(x₂ -x₁)

⇒(y-2)/(x +4) =(2-2)/)1+4)

⇒ (y-2)/(x+4) =0

⇒y -2 =0

⇒y =2

Quadratic equation formed from the given points (-4,2) and (1,2) is y =2.

which represents the horizontal line and does not have any vertex.

Graph of the quadratic equation y =2 is attached.

Therefore, quadratic equation that passes through the points (-4,2) and (1,2) and a form a graph of horizontal line y =2.

Graph is attached.

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Answer:

[tex]3x - 10 = 25 + x + 15[/tex]

according to theorem

[tex]3x - x = 40 + 10 \\ 2x = 50 \\ x = 25[/tex]

Hopefully this will help u

Answer:

C

Step-by-step explanation:

Even though quotient means divide I instead used the minus symbol since they both mean something negative or taking away. Then, the 7 goes before everything adding onto what was left from the second part.

The acceleration of the car three seconds before it comes to a stop is  -2.76 m/s² (Letter B).

Derivative indicates the rate of change of a function with respect to a variable. Thus, when you derivate the position function, you find the velocity function. And, when you derivate the velocity function, you find the acceleration function.

In other words, the velocity function represents the first derivative of the position, meanwhile, the acceleration function represents the second derivative of the position.

For derivating an equation, you should apply the rule: [tex](\frac{d}{dx} ) (x^n ) = nx^{n-1}[/tex]. Example: x²= 2x

The car stops when the velocity is equal to zero. Thus, v(t) = -3t² + 18t + 9 =0. Therefore, you  should solve this quadratic function:

Δ=b²-4ac=[tex]18^2-4\left(-3\right)\cdot \:9=324+12*9=324+108=432[/tex]

[tex]t_{1,\:2}=\frac{-18\pm \sqrt{432}}{2\left(-3\right)}\\ \\ t_{1,\:2}=\frac{-18\pm \sqrt{432}}{-6}[/tex]

[tex]t_1=\frac{-18+12\sqrt{3}}{-6}=3-2\sqrt{3}[/tex]

[tex]t_2=\frac{-18-12\sqrt{3}}{-6}=3+2\sqrt{3}[/tex]

Like t is a positive number, you should use [tex]t_2[/tex]. Thus, the value of t that you should apply to find the acceleration of the car three seconds before it comes to a stop is [tex]2\sqrt{3}[/tex].

The acceleration can be found from the derivative of the velocity function. See below.

a(t)= -6t+18 , for t=[tex]2\sqrt{3}[/tex]

a(t)= -6*[tex]2\sqrt{3}[/tex]t+18

a(t)= [tex]-12\sqrt{3}[/tex]t+18

a(t)=-2.76

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Step-by-step explanation:

this creates a right-angled triangle, with the length of the slide being the Hypotenuse (the side opposite of the 90° angle), and height and base are the legs.

so, we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse, a and b being the legs.

length² = 9² + 12² = 81 + 144 = 225

length = sqrt(225) = 15 ft

Step-by-step explanation:

Where's the calculator

Answer:

p=p=10/3

Explanation:

9-6p =-11=p=10/3

Using polar coordinates, volume of the given solid is, 32√3π.

What is volume of solid?

An object's space requirement is expressed in terms of its volume. The amount of unit cubes required to completely fill the solid is how much it weighs. We have a total of 30 unit cubes in the solid, so the volume is as follows: 2 units 3 units 1 unit Equals 30 cubic units

We have to find the volume of the solid Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4 using polar coordinates.

So, the volume is

[tex]2\int\limits\int\limits_D {\sqrt{16-x^2-y^2} } \, dA[/tex]

[tex]2\int\limits^2^\pi _0 {\int\limits^4_2 {\sqrt{16-r^2} } rdrdtheta[/tex]

[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(16-r^2)_2^4 } \, dtheta[/tex]

[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(-2\sqrt{3}) } \, dtheta[/tex]

[tex]\int\limits^2^\pi _0 {16\sqrt{3} } \, dtheta[/tex]

[tex]32\sqrt{3}\pi[/tex]

Hence, the volume of the given solid using polar coordinates is, [tex]32\sqrt{3}\pi[/tex].

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Answer:18.43

Step-by-step explanation:

A) The data modelling is an exponential function.

B) The explicit funciton that will be used to represent the data is;

f(n) = 2(2)^(n - 1)

C) The average rate of change here is; 7

A) We are given the coordinates as;

(1, 2), (2, 4), (3, 8), (4, 16)

From the given coordinates, we can observe a pattern which is that when x increases by 1, then y is multiplied by 2.

Thus, we can see that as the quotient between consecutive terms is the same, the data is a geometric sequence which is an exponential function.

B) The explicit formula that will be used for a geometric sequence with common ratio r and first term a is given by:

f(n) = ar^(n - 1)

Since first term ; a = 2

and common ratio r = 2, then we can say that;

f(n) = 2(2)^(n - 1)

C) The formula for average rate of change here is;

dy/dx = (y₂ - y₁)/(x₂ - x₁)

The coordinates of the 2nd and 4th day are;

(2, 4) and (4, 16)

Thus;

dy/dx = (16 - 4)/(4 - 2)

dy/dx = 14/2 = 7

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Answer:

------------------------------

Answer:

Step-by-step explanation:

i think the answer is 10 or 5

The total amount he will pay after 25 years is $18,97,500.

His monthly payment will be $6,325.

Given, the cost of mortgage is $720,000, and the owner of the house makes a down payment of $60,000, with 7.5% interest rate and 25 years repayment plan.

Now, the total amount of the loan be,

720000 - 60000 = 660,000

monthly rate = 7.5/12 = 0.625%

Number of payment periods = 25

Total amount he has to pay after 25 years,

660000 + (660000×7.5×25)/100

= $18,97,500

His monthly payment will be

1897500/25×12

= $6,325

Hence, the total amount he will pay after 25 years is $18,97,500

also, his monthly payment will be $6,325.

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