francesca bought 27 keychains of two different kinds to make goodie bags for her birthday party. leather keychains were three dollars and beaded keychains for two dollars. she spent $73. how many keychains of each kind did she buy

Here, y can be expressed as a linear combination of a1, a2, and a3 is y = (-1/8) a1 + (9/4) a2 - (5/2) a3.

We can express y as a linear combination of a1, a2, and a3 if and only if y is a linear combination of the column vectors of the matrix A whose columns are a1, a2, and a3. We can write this as:

y = c1 a1 + c2 a2 + c3 a3

where c1, c2, and c3 are constants to be determined. We can solve for these constants by writing the system of equations in matrix form:

A [c1; c2; c3] = y

where [c1; c2; c3] is a column vector of the constants c1, c2, and c3. We can solve for [c1; c2; c3] by multiplying both sides by the inverse of A (assuming it exists):

[c1; c2; c3] = A^(-1) y

If A^(-1) exists, then y can be expressed as a linear combination of a1, a2, and a3. Otherwise, y cannot be expressed as a linear combination of a1, a2, and a3.

For y = [1 2 4 0], we have:

A = [-1 3 0 1; 3 1 2 0; 1 1 1 1]

We can compute the inverse of A using row reduction:

[A | I] = [-1 3 0 1 | 1 0 0;

3 1 2 0 | 0 1 0;

1 1 1 1 | 0 0 1]

[R2 - 3R1, R3 - R1] = [-1 3 0 1 | 1 0 0;

0 -8 2 -3 | -3 1 0;

0 -2 1 0 | -1 0 1]

[R2 / (-8), R3 + 2R2] = [1/8 -3/8 0 3/8 | 3/8 -1/8 0;

0 1 0 -1/4 | 3/4 -1/4 0;

0 0 1 -1/2 | 1/2 -1/2 1]

Therefore, A^(-1) = [1/8 -3/8 0 3/8;

0 1 0 -1/4;

0 0 1 -1/2;

0 0 0 0]

We can now compute [c1; c2; c3]:

[c1; c2; c3] = A^(-1) y = [1/8 -3/8 0 3/8;

0 1 0 -1/4;

0 0 1 -1/2;

0 0 0 0] [1; 2; 4; 0] = [-1/8; 9/4; -5/2; 0]

Therefore, y as a linear combination of a1, a2, and a3:

y = (-1/8) a1 + (9/4) a2 - (5/2) a3

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_____The given question is incomplete, the complete question is given below:

Exercise 1.3.4 in each case, either express y as a linear combination of a1 = [-1 3 0 1], a2 = [3 1 2 0], and a3= [1 1 1 1], or show that it is not such a linear combination. here: y = [1 2 4 0]

The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.

The given equation is [tex](e - 2\sqrt{3} )^2[/tex] = f - 20√3.

Expanding the left side of the equation we have:

[tex](e - 2\sqrt{3} )^2[/tex] = (e - 2√3)(e - 2√3)

= [tex]e^2[/tex] - 2e√3 - 2e√3 + 12

= [tex]e^2[/tex] - 4e√3 + 12

Substituting back in the function

[tex]e^2[/tex] - 4e√3 + 12 = f - 20√3

[tex]e^2[/tex] - 4e√3 - f + 20√3 - 12 = 0

Using the quadratic formula:

e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2

e = [4√3 ± √(4f - 64√3)] / 2

e = 2√3 ± √(f - 16√3)

Now for,

(e - 2√3)² = f - 20√3

(2√3 + √(f - 16√3) - 2√3)² = f - 20√3

f - 20√3 = f - 16√3

f = 4√3

Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

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Answer:

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

Area of rectangle formula:

Given:

Find the missing side length:

Answer:

7.2cm

Step-by-step explanation:

We are here given that, the area of a rectangle is 33.12cm² and one of the side is 4.6cm .

We are interested in finding the length of the other side,

As we know that the area of rectangle is calculated using the formula,

Area = l * b

where l is the length and b is the breadth.

Now substitute the respective values,

33.12cm² = l * 4.6cm

l = 33.12cm²/4.6cm

l = 7.2 cm

Hence the value of second side is 7.2cm

Answer:

Let's call the number we are looking for "x". We are told that the digit 8 appears ten times as often in "x" as it does in 18.

The digit 8 appears once in the number 18, so it must appear 10 times in "x".

Let's count the number of 8's in "x" in terms of the number of digits of "x".

If "x" has 1 digit, then it cannot have 10 8's, so we can rule out this case.

If "x" has 2 digits, then the maximum number of 8's it can have is 9 (e.g., 88). This is still not enough, so we can rule out this case as well.

If "x" has 3 digits, then the maximum number of 8's it can have is 27 (e.g., 888), which is enough.

Therefore, the number we are looking for is a 3-digit number that contains 10 8's. We can write such a number as:

x = 888x8x8x8

where "x" can be any digit other than 8.

Note that there are other 3-digit numbers that contain 10 8's, but this is one possible solution.

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Solved  equation x=80 and z=2, y=40

An element, feature, οr factοr that is liable tο vary οr change

If y varies directly as x and inversely as the square οf z, we can write the fοllοwing prοpοrtiοnality:

y ∝ x/z²

where ∝ denοtes prοpοrtiοnality cοnstant.

Tο find the value οf ∝, we can use the given values οf y, x, and z:

y = ∝ x/z²

28 = ∝ (63)/(3)²

∝ = 28 * (3)² / (63)

∝ = 4/3

Nοw we can use this value οf ∝ tο find y when x=80 and z=2:

y = ∝ x/z²

y = (4/3) * (80)/(2)²

y = 40

Therefοre, when x=80 and z=2, y=40.

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Inside the sphere, the potential is given by [tex]$V(r)=\frac{Q}{4\pi\epsilon_0r}$[/tex], where Q is the total charge enclosed within the sphere. Since the sphere shell has no charge inside, Q=0, and thus V(r)=0 inside the sphere.

Outside the sphere, the potential is given by

[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{Q'}{4\pi\epsilon_0r'}$[/tex]

where Q is the total charge of the sphere shell, Q'= σ4πR²is the charge on an imaginary sphere of radius r'>R enclosing the sphere shell, and r is the distance from the center of the sphere. Using the result from Ex. 3.9, the potential outside the sphere becomes

[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{\sigma_0 R^2}{2\epsilon_0 r}$[/tex]

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Answer:

The probability that a single college student has not taken a mathematics course is 1 - 0.8 = 0.2.

The probability that all ten selected college students have taken a mathematics course is (0.8)^10 = 0.1074 (rounded to four decimal places).

Therefore, the probability that at least one of the ten selected college students has not taken a mathematics course is:

1 - 0.1074 = 0.8926 (rounded to four decimal places).

So the answer is 0.8926, which is closest to option C (0.7927).

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Answer:

y=9/x  => proportional

y = x - 12 ==> non-proportional

h = 3d ==> proportional

f = 1/3 e = proportional

Step-by-step explanation:

A proportional equation is of the general form

y = kx (directly proportional) or

y = k/x  (inversely proportional)

k is known as the constant of proportionality

y = 9/x ==> k = 9  proportional
y = x - 12  cannot be expressed as y = kx or y = k/x

h = 3d ==> k = 3  proportional

f = 1/3 e ==> k = 1/3   proportional

Answer:

There is no value of x that solves the proportion (x^2-x-12)/(x+5) = x-6.

The proportion for this problem is defined by the equation presented as follows:

(x^2-x-12)/(x+5) = x-6.

As the measures are proportional, we can apply cross multiplication, hence:

x² - x - 12 = (x + 5)(x - 6)

x² - x - 12 = x² - x - 30

-12 = -30.

-12 = -30 is a false statement, hence there is no value of x which can solve the proportion (x^2-x-12)/(x+5)=x-6 presented in this problem.

The problem asks for the value of x that solves the proportion (x^2-x-12)/(x+5) = x-6.

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A set in R⁵ must be linearly independent because of the dimensionality of the space.

A Set of vectors in R⁵, the five-dimensional Euclidean space, must be linearly independent because of the dimensionality of the space.

The maximum number of linearly independent vectors in any set in R⁵ is 5 since any set with more than 5 vectors would necessarily contain a linearly dependent subset.

This is because any vector in R⁵ can be expressed as a linear combination of at most 5 linearly independent vectors, as the dimension of R⁵ is 5.

Therefore, any set with more than 5 vectors would have at least one vector that could be written as a linear combination of the other vectors in the set, making the set linearly dependent.

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The given question is incomplete, the complete question is

Explain why a set in R⁵ must be linearly independent.

Answer:

Here is a diagram and transition matrix for this case:

Diagram:

        +---(0.65)---> State 1 (work)

        |

Start ---+

        |

        +---(0.35)---> State 2 (procrastinate)

                  |

                  +---(0.15)---> State 1 (work)

                  |

                  +---(0.85)---> State 2 (procrastinate)

Transition matrix:

         |  State 1  |  State 2  |

----------+-----------+-----------+

State 1   |   1.00    |   0.00    |

----------+-----------+-----------+

State 2   |   0.15    |   0.85    |

----------+-----------+-----------+

In the transition matrix, the rows represent the starting state and the columns represent the ending state. The entries in the matrix represent the probabilities of transitioning from the starting state to the ending state. For example, the entry in row 1 and column 2 (0.00) represents the probability of transitioning from State 1 to State 2, which is 0.00.

Answer:

Step-by-step explanation:

To find the adoption rate as a percentage, we need to divide the number of dogs adopted by the total number of dogs in the shelter, then multiply by 100.

adoption rate = (dogs adopted / total dogs) * 100%

adoption rate = (6 / 80) * 100%

adoption rate = 0.075 * 100%

adoption rate = 7.5%

Therefore, the adoption rate as a percent is 7.5%.

Answer:

2%

Step-by-step explanation:

Given,P = $73000

A = $104000

T = 18 years, Compounded annually.

To find: r%

Soln: By formula, A = 73000*(1+r/100)^18

=> (104/73)^1/18 = (100+r)/100

=> 1.0198 = 100+r/100

=> 101.98 -100 = r

=> 1.98 = r

To the nearest percent, 2 = r

Hence, Rate of interest = 2%

Answer: Somewhere around 40%, write 0.4.

Step-by-step explanation:

I took all of the outcomes from the games got the. probabilities of winners and got 40%.

Answer:

center: (0, -2)

radius: 6

Step-by-step explanation:

You have to "complete the square" this allows you to fold up the expressions and put the equation in a standard kinda of format where you can pick the center and radius right out of the equation.

see image.

Answer:

2.5

Step-by-step explanation:

diameter is 5 and the radius is half of the diameter so it is 2.5

hope this helps :)

Answer:

Noah would need to work 30 hours to equal Mason's earning for 40 hours

Step-by-step explanation:

Mason;

8.10 x 40 = 324

324 ÷ 10.80 = 30 hours.

Helping in the name of Jesus.

Answer:

30 hours

Step-by-step explanation:

40 times 8.10 is 324 and 324 divided by 10.8 is 30 hours

The calculated coordinates of U if STUV is a kite is (10, 18)

From the question, we have the following parameters that can be used in our computation:

The figute of a kite

Also, we have

S = (0, 18)

And the distance SU to be

SU = 10

If the quadrilateral STUV is a kite, then the coordinates S and U are on the same horizontal level (according to the figure)

So, we have

U = (0 + 10, 18)

Evaluate

U = (10, 18)

Hence, the coordinates of U if STUV is a kite is (10, 18)

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The correlation coefficient is close to zero, we can conclude that the two judges do not appear to agree in their standards.

Nevertheless, a correlation between two variables does not always imply that a change in one variable is the reason for a change in the values of the other.

There is a causal link between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.

For the given ranks for two judges the difference between their ranks is:

d: 0.0 4.0 -2.0 1.0 -0.5 1.5 -1.0 -1.0 0.5 2.0

Squaring the given distance we have:

d²: 0.0 16.0 4.0 1.0 0.25 2.25 1.0 1.0 0.25 4.0

Σd² = 29.75

The Spearman's rank correlation coefficient is given as:

ρ = 1 - (6Σd²)/(n(n²-1))

ρ = 1 - (629.75)/(10(10²-1))

ρ ≈ 0.03

Since the correlation coefficient is close to zero, we can conclude that the two judges do not appear to agree in their standards.

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The complete question is:

Answer:

True.

Step-by-step explanation:

CPCTC is commonly used at or near the end of a proof, which asks the student to show that two angles or two sides are congruent. It means that once two triangles are proven to be congruent, then the three pairs of sides that correspond must be congruent and the three pairs of angles that correspond must be congruent.

(a) By using the exponential density function, the probability that a customer warts less than a second for credit card approval is 0.334

(b) The probability that a customer waits more than 3 seconds is 0.154

(c) The minimum approval time for the slowest 5% of transactions is 4.013 seconds

(a) To find the probability that a customer waits less than a second for credit card approval, we need to use the exponential density function:

f(x) = [tex]\lambda e^{-\lambda x}[/tex]

Where λ is the rate parameter, which in this case is the reciprocal of the mean approval time. So, λ = 1/1.6 = 0.625.

The probability that a customer waits less than a second can be calculated by integrating the density function from 0 to 1:

P(X < 1) = ∫[tex]0^1 \lambda e^{-\lambda x}[/tex] dx

P(X < 1) = [tex][-e^{-\lambda x}]0^1[/tex]

P(X < 1) = [tex]-e^{(-0.625)}[/tex] + 1

P(X < 1) = 0.334

Therefore, the probability that a customer waits less than a second for credit card approval is 0.334.

(b) To find the probability that a customer waits more than 3 seconds for credit card approval, we can use the same exponential density function and integrate from 3 to infinity:

P(X > 3) = ∫[tex]3^{\infty} \lambda e^{-\lambda x}[/tex] dx

P(X > 3) = [[tex]-e^{-\lambda x}[/tex])][tex]3^{\infty}[/tex]

P(X > 3) = [tex]e^{-1.875}[/tex]

P(X > 3) = 0.154

Therefore, the probability that a customer waits more than 3 seconds for credit card approval is 0.154.

(c) We can use the exponential distribution's inverse function to find this value:

P(X > x) = 0.05

[tex]e^{-\lambda x}[/tex] = 0.05

-xλ = ln(0.05)

x = ln(0.05)/(-λ)

x = ln(0.05)/(-0.625)

x = 4.013 seconds

Therefore, the minimum approval time for the slowest 5% of transactions is 4.013 seconds.

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the weight that corresponds to each of the events are:

a) The weight is less than 380 grams: [tex]$P(X < 380)=0.266$[/tex].

b) The weight is between 375 and 395 grams: [tex]$P(375 < X < 395)=0.7887$[/tex].

c) The weight is greater than 400 grams: [tex]$P(X > 400)=0.0304$[/tex].

Let X be the weight of a small Starbucks coffee. We are given that X is normally distributed with mean [tex]$\mu=385$[/tex] grams and standard deviation [tex]$\sigma=8$[/tex].

We want to find the weight that corresponds to each of the following events:

a) The weight is less than 380 grams.

b) The weight is between 375 and 395 grams.

c) The weight is greater than 400 grams.

To solve these problems, we first standardize the distribution by finding the corresponding z-scores using the formula:

[tex]$z=\frac{X-\mu}{\sigma}$$[/tex]

a) The weight is less than 380 grams.

We want to find P(X<380). We can find the z-score for X=380 as follows:

[tex]$z=\frac{380-385}{8}=-0.625$$[/tex]

Using a standard normal table or calculator, we find that the probability P(Z<-0.625)=0.266. Therefore,

[tex]$P(X < 380)=P\left(Z < -\frac{0.625}{1}\right)=0.266$$[/tex]

b) The weight is between 375 and 395 grams.

We want to find [tex]$P(375 < X < 395)$[/tex]. We can find the z-scores for X=375 and X=395 as follows:

[tex]$z_1=\frac{375-385}{8}=-1.25,\quad z_2=\frac{395-385}{8}=1.25$$[/tex]

Using a standard normal table or calculator, we find that the probability P(-1.25<Z<1.25)=0.7887. Therefore,

[tex]$P(375 < X < 395)=P\left(-1.25 < Z < 1.25\right)=0.7887$$[/tex]

c) The weight is greater than 400 grams.

We want to find P(X>400). We can find the z-score for X=400 as follows:

[tex]$z=\frac{400-385}{8}=1.875$$[/tex]

Using a standard normal table or calculator, we find that the probability P(Z>1.875)=0.0304. Therefore,

[tex]$P(X > 400)=P\left(Z > \frac{1.875}{1}\right)=0.0304$$[/tex]

Therefore, the weight that corresponds to each of the events are:

a) The weight is less than 380 grams: [tex]$P(X < 380)=0.266$[/tex].

b) The weight is between 375 and 395 grams: [tex]$P(375 < X < 395)=0.7887$[/tex].

c) The weight is greater than 400 grams: [tex]$P(X > 400)=0.0304$[/tex].

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When space is spanned by the two functions of linear transformation from into itself with respect to the basis we need to apply T to each basis vector vi to get the column vectors T(vi) = [T(vi)]B.

where [T(vi)]B is the coordinate vector of T(vi) with respect to the basis B. Arrange the column vectors [T(v1)]B, [T(v2)]B, ..., [T(vn)]B into a matrix. This matrix is the matrix of T with respect to the basis B.

In this case, you have two functions that span a vector space, so you need to specify the basis B. Once you have chosen the basis, you can apply the above steps to find the matrix of the linear transformation.

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Hence, throughout March and April, the cafeteria served 1020 quarts of milk.

The unitary method is a mathematical approach where issues are solved by determining a single unit rate. To relate various quantities to one another, proportions must be used. This approach is frequently employed in issues involving direct and inverse proportionality. In inverse proportionality, the product of the two quantities is constant, whereas in direct proportionality, the two numbers fluctuate in the same ratio.

given

We must first determine the total number of cups of milk served in both March and April in order to calculate the total number of quarts of milk served in both months.

4080 cups of milk totaled from 2420 + 1660 cups.

We can convert the total number of cups to quarts by dividing by 4 because 1 quart equals 4 cups:

4080 cups of milk divided by 4 equals 1020 quarts total.

Hence, throughout March and April, the cafeteria served 1020 quarts of milk.

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The correct research hypothesis and distribution is directional, t-test for independent means.

The research hypothesis that "people can hear better when they have just eaten a large meal" is a directional hypothesis because it predicts the direction of the effect (i.e., hearing ability will improve after a large meal).

The appropriate statistical test to use would be a t-test for independent means, which compares the means of two independent groups to determine if there is a statistically significant difference between them.

Therefore, the correct answer is B. Directional; t-test for independent means.

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Step-by-step explanation:

For RIGHT triangles  :  sin ( angle) = opposite LEG / Hypotenuse

   so   sin B = 32 / 68 =  8 / 17

8.The method that resulted in Garcia winning might not be fair to the other nominees because it does not account for their individual achievements or skill sets.

Nominees are individuals or organizations that have been selected or chosen from a given group to represent them in a certain process or event. Nominees are usually chosen for their proficiency, expertise, or reputation in a certain field or area. For example, in some elections, political parties nominate individuals to represent them in the election and these nominees are then voted upon by the public. Similarly, some organizations nominate a particular individual or group of individuals to represent them in awards or recognition ceremonies for their excellence and achievements.

It simply rewards the nominee with the most votes, regardless of their ability or accomplishments. This could lead to someone who is less qualified or experienced receiving the award, while the more deserving candidates are overlooked.

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Answer:

p < -4

Step-by-step explanation:

-6(4p+5) > 34 - 8p

-24p - 30 > 34 - 8p

-16p - 30 > 34

-16p > 64

p < -4