find cos ∅
A. 8/17
B. 8/15
C. 15/8
D. 15/17​

We can see here that when the ladybird is rotated:

This ladybird made a 90° turn clockwise.

This ladybird made a 180° anticlockwise.

In mathematics, rotation refers to a transformation that turns or rotates an object around a fixed point called the center of rotation. It is a fundamental concept in geometry and is used to describe the movement of points, shapes, or figures in the plane or in three-dimensional space.

A rotation involves specifying the center of rotation, the angle of rotation, and the direction of rotation (clockwise or counterclockwise).

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Answer:

Step-by-step explanation:

4x - 12 = 11 - 3x

Bringing like terms on one side

4x + 3x = 11 + 12

7x = 23

x = 23/7

For the given system of initial value problem,

A₁ = 7,

A₂ = -1, and

y = 2exp(-t),

To solve the given system of initial value problem (IVP) with the matrix equation x' = Ax, where A is the given matrix and x(0) = [10, -4, 21], we can use the eigenvalue-eigenvector method.

The matrix A is given as:

A = | 4 -2 0 |

| 3 -1 0 |

| 1 7 2 |

Let's find the eigenvalues and eigenvectors of matrix A.

To find the eigenvalues, we solve the characteristic equation:

det(A - λI) = 0

Substituting the values, we get:

| 4-λ -2 0 |

| 3 -1-λ 0 |

| 1 7 2-λ |

Expanding the determinant, we have:

(4-λ)[(-1-λ)(2-λ)] + 2[3(2-λ) - (-1-λ)7] = 0

Simplifying and solving the equation, we find the eigenvalues:

λ₁ = -1

λ₂ = 2

λ₃ = 2

Next, let's find the corresponding eigenvectors.

For λ₁ = -1:

(A + I)v₁ = 0

| 5 -2 0 | | v₁₁ | | 0 |

| 3 -1 0 | * | v₁₂ | = | 0 |

| 1 7 1 | | v₁₃ | | 0 |

Solving the system of equations, we find the eigenvector corresponding to λ₁:

v₁ = | 2 |

| 5 |

|-1 |

For λ₂ = 2:

(A - 2I)v₂ = 0

| 2 -2 0 | | v₂₁ | | 0 |

| 3 -3 0 | * | v₂₂ | = | 0 |

| 1 7 0 | | v₂₃ | | 0 |

Solving the system of equations, we find the eigenvector corresponding to λ₂:

v₂ = | 1 |

| 1 |

|-1 |

For λ₃ = 2:

(A - 2I)v₃ = 0

| 2 -2 0 | | v₃₁ | | 0 |

| 3 -3 0 | * | v₃₂ | = | 0 |

| 1 7 0 | | v₃₃ | | 0 |

Solving the system of equations, we find the eigenvector corresponding to λ₃:

v₃ = | 2 |

| 3 |

| 1 |

Now that we have the eigenvalues and eigenvectors, we can write the general solution to the system of differential equations as:

x(t) = c₁ * exp(λ₁ * t) * v₁ + c₂ * exp(λ₂ * t) * v₂ + c₃ * exp(λ₃ * t) * v₃

Substituting the given initial condition x(0) = [10, -4, 21], we can find the specific solution by solving the following system of equations:

c₁ * v₁ + c₂ * v₂ + c₃ * v₃ = x(0)

Substituting the values of the eigenvectors and the initial condition, we get:

2c₁ + c₂ + 2c₃ = 10 (Equation 1)

5c₁ + c₂ + 3c₃ = -4 (Equation 2)

-c₁ - c₂ + c₃ = 21 (Equation 3)

Solving this system of equations will give us the values of c₁, c₂, and c₃, which will determine the specific solution.

By solving Equations 1, 2, and 3, we find:

c₁ = 1

c₂ = -5

c₃ = -3

Therefore, the specific solution to the initial value problem is:

x(t) = exp(-t) * | 2 | + exp(2t) * | 1 | + exp(2t) * |-3 |

| 5 | | 1 |

|-1 | | 1 |

Simplifying this expression, we get:

x(t) = | 2exp(-t) + 5exp(2t) - 3exp(2t) |

| 5exp(-t) + exp(2t) + exp(2t) |

|-exp(-t) + exp(2t) + exp(2t) |

Finally, we can rewrite the solution in the given form (7) - ₁ (1) ¹²+₂ (1) ¹:

x(t) = 7 * | 2exp(-t) | + (-1) * | 5exp(-t) |

| 5exp(-t) | | -exp(-t) |

Therefore, A₁ = 7, A₂ = -1, and y = 2exp(-t).

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Answer:

x= 64° y= 18° z= 98°

Step-by-step explanation:

x= 64°

y = 18°

z = 180° - x - y

z = 180° - 64° - 18°

z= 98°

Answer:

2x+156=4x+192

192-156=-4x+2x

36=-2x

x=-18

Step-by-step explanation:

Notice that the weird figure looks like a rectangle that is missing a piece.

In this case, find the area of the rectangle... then subtract the area of the missing piece from that area of the rectangle.

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

Area of rectangle: 4 x 5 = 20 sq. inches

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

How to find the area of the missing piece:

So, the area of the missing piece: A = lw = (1)(2) = 2 sq. inches

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

Now, subtract the area of the missing piece from the area of the rectangle:

20 - 2 = 18 sq. inches

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

Answer:

402.1 in^2

Step-by-step explanation:

Find the area of the circle with the 18 in. radius first.

Formula for a circle is πr^2

So the area of the circle with the 8 in. radius is 1017.9 in^2

Now do the same for the 14 in. radius circle.

The area for the 14 in. radius circle is 615.8

Now subtract:

1017.9 - 615.8 =

402.1 in^2

hope this helped!

The mean of the data set is approximately 1.57 meters. The standard deviation of the data set is approximately 0.0968 meters, indicating the average deviation of data points from the mean.

To compute the mean and standard deviation of the data set, we'll use the following formulas:

Mean (μ) = (sum of all data values) / (total number of data values)

Standard Deviation (σ) = sqrt((sum of squared differences from the mean) / (total number of data values))

Let's calculate the mean and standard deviation for the given data set:

Data set: 1.63, 1.62, 1.61, 1.62, 1.39, 1.55

Mean (μ) = (1.63 + 1.62 + 1.61 + 1.62 + 1.39 + 1.55) / 6 = 9.42 / 6 ≈ 1.57

Next, we calculate the sum of squared differences from the mean:

(1.63 - 1.57)^2 + (1.62 - 1.57)^2 + (1.61 - 1.57)^2 + (1.62 - 1.57)^2 + (1.39 - 1.57)^2 + (1.55 - 1.57)^2 ≈ 0.0666

Finally, we calculate the standard deviation:

Standard Deviation (σ) = sqrt(0.0666 / 6) ≈ 0.0968

Therefore, the mean of the data set is approximately 1.57 meters and the standard deviation is approximately 0.0968 meters.

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The set of integers has the same cardinality as the countably infinite set A. The correct option is b.

A set is countably infinite if its elements can be put in one-to-one correspondence with the set of natural numbers (integers starting from 1). This means that we can establish a one-to-one function (bijection) between the countably infinite set A and the set of integers.

Options a, c, and d are not necessarily true.

Option a: There is no guarantee that there is a one-to-one function from the set A to the set of rational numbers. The set of rational numbers, also known as Q, is uncountably infinite, while A is only countably infinite.

Option c: It is possible to have a surjective function (onto) from the set of rational numbers to a countably infinite set. For example, a function that maps every rational number to its numerator can be surjective onto the set of integers.

Option d: The open interval (0, 1) has a higher cardinality (uncountable) than a countably infinite set. The interval (0, 1) contains an uncountably infinite number of real numbers between 0 and 1, whereas A is countably infinite.

The correct option is b.

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Answer: 120

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Well 42

        -

       12

       30

Answer:

20.

Step-by-step explanation:

x^2 = 25^2 - 15^2

x^2 = 400

x = 20

Answer:

La nota de Carolina es 15 puntos.

Step-by-step explanation:

Un sistema de ecuaciones lineales es un conjunto de ecuaciones lineales que tienen más de una incógnita, relacionadas mediante las ecuaciones.

En los sistemas de ecuaciones, se debe buscar los valores de las incógnitas.  Al reemplazar en las ecuaciones, deben dar la solución planteada.

En este caso se debe plantear un sistema de ecuaciones, donde las incógnitas son:

Ambas notas juntas es igual a 34 puntos. Expresado matemáticamente es:

x + y= 34

Se sabe que Carmen obtuvo 4 puntos más que Catalina. Esto es:

y= x + 4

Entonces el sistema de ecuaciones a resolver es:

[tex]\left \{ {{x+y=34} \atop {y=x+4}} \right.[/tex]

A través del método de sustitución debes despejar una de las incógnitas en una de las ecuaciones y sustituir su valor en la siguiente. En este caso, ya tienes despejada la incógnita y en la segunda ecuación. Por lo que sustituyes esta expresión en la primer ecuación:

x+ x+4=34

Resolviendo obtienes:

x + x= 34 - 4

2*x=30

x= 30÷ 2

x=15

Sustituyendo este valor en la segunda ecuación obtienes:

y= x+4

y= 15 +4

y= 19

Recordando que "x" representa la nota de Carolina e "y" la nota de Carmen, entonces la nota de Carolina es 15 puntos y la nota de Carmen es 19 puntos.

Answer:

how many colors are there and how many of each color?

Step-by-step explanation:

Probability of an event is the measurement of its chance of occurrence.

Suppose that there are finite elementary events in the sample space of the considered random experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Percent counts the number compared to 100 whereas probability counts it compare to 1.

So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get:

For each 1, there are a/100 parts.

Thus, 50% = 50/100 = 0.50 (in probability)

The probability of selecting an orange candy depends on how many candies are there.

If its the only candy, and at least one candy must be chosen, then its probability is 1 or say in percent it is 100% because then n(E) = 1 and n(S) = 1 where

Thus, the probability of selecting an orange candy depends on how many candies are there. If its the only candy, and at least one candy must be chosen, then its probability is 1 or say in percent it is 100%

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Answer:

$7.65

Step-by-step explanation:

its the right answer, TRUST ME!!!!

The woman's cardiac risk ratio can be calculated by dividing her total cholesterol level by her high-density lipoprotein (HDL) level. With a total cholesterol level of 225 mg/dL and an HDL level of 60 mg/dL, her cardiac risk ratio is 3.8, which falls within the desirable range of 3.0 to 4.5 for women.

To calculate the cardiac risk ratio, we divide the total cholesterol level by the HDL level. In this case, the woman's total cholesterol level is 225 mg/dL, and her HDL level is 60 mg/dL. Thus, her cardiac risk ratio is given by 225 mg/dL / 60 mg/dL = 3.75.

The cardiac risk ratio is typically expressed as a one-place decimal. Rounding the ratio to one decimal place, we get 3.8. Since the desirable range for women's cardiac risk ratio is between 3.0 and 4.5, the woman's ratio of 3.8 falls within this range, indicating a desirable level.

Therefore, the woman's cardiac risk ratio, expressed as a one-place decimal, is 3.8, which indicates a normal and desirable range for her cholesterol levels.

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Answer:

We have that y = 21 when x = 11.

Step-by-step explanation:

We solve this question by proportions, using a rule of three.

Since they vary inversely, we apply the inverse rule of three, that is, with lateral multiplication instead of diagonal.

33 - 7

y - 11

So

[tex]11y = 33*7[/tex]

Dividing both sides by 11

[tex]y = 3*7 = 21[/tex]

We have that y = 21 when x = 11.

Answer:  (x - 2) (x - 1）

Step-by-step explanation:

x²-3x+2

= (x - 2) (x - 1）

Hi army! I found the answer!

Answer:

F. An 18-month loan with an annual simple interest rate of 4.75%

Step-by-step explanation:

I just used a credit card payoff calculator to solve this problem. You can use that calculator to solve other problems like this too!

Also, stream BTS Film Out for clear skin and good grades ;)

Have a great day!

Answer:

11+13+16 or 14x15x18

Step-by-step explanation:

HOPE IT HELPS! :)

Answer:

C

Step-by-step explanation:

The probability is 1/3

Answer:

B

Step-by-step explanation:

Answer:

1/59

Step-by-step explanation:

Answer:

1/59

think of it dude

Answer:

8 m

Step-by-step explanation:

7.5 - 1.5 = 6

2 + 6 = 8

Answer:

Test statistic

Step-by-step explanation:

To test the claim that the sample is from a population with a standard deviation less than 0.0390 g, and using a 0.05 significance level and a parametric method, certain requirements must be satisfied. The requirements include:

A. Either or both of these conditions are satisfied:

A. the population is normally distributed or the sample size is greater than 30.

C. The sample is a simple random sample.

The normality requirement for a hypothesis test of a claim about a standard deviation differs from the normality requirement for a hypothesis test of a claim about a mean. For a hypothesis test of a claim about a standard deviation, it is not necessary for the population to be normally distributed. Instead, either the population should be normally distributed or the sample size should be sufficiently large (typically greater than 30) for the Central Limit Theorem to apply. In this case, the requirement is satisfied if either the population is normally distributed or the sample size is greater than 30. However, the sample should still be a simple random sample, which ensures that the observations are independent and representative of the population.

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Answer: Cup-$14, Saucer-$6.5

Step-by-step explanation:

Given

Cup and saucer costs $20.5

A cup and two saucer costs $27

Assume the price of cup and saucer are x and y

So, we can write

[tex]\Rightarrow x+y=20.5\quad \ldots(i)\\\\\Rightarrow x+2y=27\quad \ldots(ii)[/tex]

Solving [tex](i)\ \text{and}\ (ii)[/tex] we get

[tex]x=\$\ 14, y=\$\ 6.5[/tex]

Thus, the cost of the cup is $14 and that of the saucer is $6.5

There are 12 identical marbles in a bag, and Suzy is going to select 9 marbles from the bag at random.

The problem asks how many possible outcomes there are.

To begin with, we need to understand the concept of combinations. A combination is a way to select a subset of objects from a larger set, without regard to the order of the objects. For example, if we have four marbles (A, B, C, and D), there are six possible combinations of two marbles: AB, AC, AD, BC, BD, and CD.

In this problem, we have 12 marbles and we are choosing 9 of them. To find the total number of combinations, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we are choosing, and ! represents factorial (i.e. multiplying a number by all the positive integers less than it).

So, plugging in our numbers:

12C9 = 12! / 9!(12-9)! = 12! / 9!3! = (121110) / (321) = 220

Therefore, there are 220 possible outcomes if Suzy selects 9 marbles at random from a bag containing 12 identical marbles.

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Answer: 45

Step-by-step explanation: 360-315=45

Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis, the size of the home is a significant predictor of the selling price of homes sold recently in the southern Sydney area.

(a) Null hypothesis: H0: β1 = 0 (The size of the home is not a significant predictor of the selling price of homes sold recently).

Alternative hypothesis: Ha: β1 ≠ 0 (The size of the home is a significant predictor of the selling price of homes sold recently).

(b) The t-test statistic: We can use the t-test statistic to test whether the slope (β1) of the regression line is significant at the 5% level.

t = (β1 - 0) / SE(β1)

  = 0.0643 / 0.01224

   = 5.25

(c) The degrees of freedom (df) for this t-test statistic will be n - 2, where n is the sample size.

Since the sample size is 48, the degrees of freedom will be 48 - 2 = 46.

(d) Final conclusion of this test: Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis.

Thus, we conclude that the size of the home is a significant predictor of the selling price of homes sold recently in the southern Sydney area.

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