Solve for j.
12≥53–j

The measure of angle x from the given diagram is 130 degrees

Find the diagram attached

<b and 100⁰ are supplementary i.e they sum up to 180 degrees as shown:

<b + 100 = 180

<b = 180 - 80

<b = 80 degrees

Get the measure of angle "x"

x = <a + <b

x = 50 + 80

x = 130 degrees

Hence the measure of angle x from the given diagram is 130 degrees

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Answer:

I believe it says the vertex at Y is moved to T:

the angle of each side changes by 360 / 8 = 45 at each vertex

If 3 vertices separate Y and T the the total rotation would be

3 * 45 = 135 deg

The octagon rotated 135 degree.

An octagon is a polygon with eight sides.

The total angle at the center is 360 degree and for a regular octagon, the angle made by each side is equal to 360/8 = 45 degree.

The octagon STUVWXYZ is rotated clockwise such that, the vertex Y moves to T.

Movement of Y to T is moving 3 steps clockwise

= 45* 3

= 135 degree

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Answer:

x = 1

Step-by-step explanation:

First you distribute so you get

2x + 10 - 4x + 8 = 16

Then you add the stuff together that you can add and get

-2x + 18 = 16

Then you subtract 18 on the left side to get it to 0 and you have to do the some to the other side so it becomes

-2x = -2

Then you divide each side by -2 giving you

x = 1

I attached the filled out table.

We can immediately fill out the girl/winter slot and boy/summer spot.

Knowing that there are 17 total summer lovers and 7 boy/summer, we know 10 girls love summer.

Twice as many girls picked summer than spring, so 10/2 is 5 girls picking spring.

The last clue reads weird, but says that if you pick a spring lover, there is an 18.75% chance of it being a boy, so x/(x+5)=0.1875 x=1.

38% of interviewed students preferred summer, so: 17/x = 0.38 Total students= 45

Now the annoying part:

We know that for every 8 guys, there are 11 girls.

So if we fiddle around with scaling that ratio to find the combination the adds up to 45, we get a scale of 2.35.

2.35*8=19 and 2.35*11=26

So the total number of girls is 26, meaning the number of girl/autumn is 26-5-4-10=7

Three more boys chose autumn than the girls, so 10 boy/autumn.

Total boys is 19, 1 spring, 7 summer, and 10 autumn leaves 1 to pick winter.

Good lord that took me too long to do.

Answer:

36 pizzas

no sauce left over

Step-by-step explanation:

Take the total amount and divide by 4

144/4 =36

The cook can make 36 pizzas

Ther is no sauce left over

Answer:

Vertex of the parabola is (2,3)

Step-by-step explanation:

The parabola is a negative, it opens down and the maximum place it can reach is 3 (y).

Among a group of six students, at least two received the same grade on the final exam.

This problem is a classic example of the Pigeonhole Principle, which states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. In this case, the pigeons are the grades assigned to the six students, and the pigeonholes are the possible grades they could have received (A, B, C, D, or F).

Since there are five possible grades and six students, at least one grade must have been assigned to two or more students. This is because if each student received a different grade, there would be five grades in total, which is one less than the number of students, so at least one grade must be repeated.

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Answer:

1

Step-by-step explanation:

because if he invites 2 then he will have to spend 24 and if he invites 6 he'll have to spend 72 because 12×6 is 72

On a circle with center O, points P and A are marked such that the arc PA is a 46º arc. This implies that angle POA is half the measure of the intercepted arc PA, which is 23º. When segment PO is extended to meet the circle again at point T, the size of angle PTA is also 23º

In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. Since arc PA is a 46º arc, angle POA, which intercepts arc PA, will have half that measure, which is 23º.

When segment PO is extended to meet the circle again at point T, we can observe that angle PTA is an inscribed angle. As a result, angle PTA will also have the same measure as its intercepted arc PT. Since point P lies on arc PT, which has a measure of 46º, angle PTA will also measure 46º.

This relationship between the intercepted arc and the inscribed angle is a fundamental property of circles. It allows us to determine the measure of an inscribed angle if we know the measure of its intercepted arc, and vice versa. In this case, the measures of both angle POA and angle PTA are determined by the 46º arc PA.

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Answer:

B. 7 1/2

Step-by-step explanation:

8x=12

x = 1.5

2y+10=22

2y = 12

y = 6

1.5 + 6 = 7.5

So, the sum of the solutions of the two equations is

B. 7 1/2

Answer:

Step-by-step explanation:

firstly we solve 8x=12 we divide both sides by 8 since 8 is the coefficient of x so we are trying to find x that is 8x divided by 8 which is x =12 divided by 8 which is 1.5 which means x=1.5 then we solve the second one 2y+10=22 we collect like terms which means 2y=22-10 as you should know the 10 changes to negative when crossed over to the other side so then 2y=12 is the answer then we divide both sides by the coefficient of y which is 2 so 2y divided by 2 =y 12 divided by 2 = 6 so y=6 then we add both of them together x=1.5+(y=6) so add 1.5 and 6 together answer is 7.5 or 7  1/2

Answer:

sq55 < 7.6 repeating

Step-by-step explanation:

The square root of 55 is 7.4161984, which is less than 7.66666

Answer:

im pretty sure its sq55 < 7.6 repeating

Step-by-step explanation:

Answer: The best I could come up with is √65, −√65 or, 1, you pick!

(Decimal: 8.06225774…, −8.06225774…)

Step-by-step explanation:

Rewrite the equation as

x^2 = 8^2 + 1^2.

One to any power is one.

x^2 = 8^2 + 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

x = ± √8^2 + 1

x = ± √64 + 1

Add 64 and 1.

x = ± √65

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

x = √65

Next, use the negative value of the ± to find the second solution.

x = −√65

The complete solution is the result of both the positive and negative portions of the solution.

x = √65, −√65

The result can be shown in multiple forms.

Exact Form:

x = √65, −√65

Decimal Form:

x = 8.06225774..., −8.06225774…

Answer:

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

Given a right triangle with the missing hypotenuse.

Use Pythagorean to find the missing side:

By applying the Intermediate Value Theorem to the function f(x) = x^4 + x - 3 on the interval [1, 2], we can conclude that there exists a root of the equation x^4 + x - 3 = 0 in the interval (1, 2).

The Intermediate Value Theorem states that if a function f(x) is continuous on a closed interval [a, b], and if f(a) and f(b) have opposite signs, then there exists at least one number c in the interval (a, b) such that f(c) = 0.

In this case, we have the function f(x) = x^4 + x - 3, which is a polynomial and thus continuous for all real numbers. We are interested in finding a root of the equation f(x) = 0 on the interval [1, 2].

Evaluating the function at the endpoints, we find that f(1) = 1^4 + 1 - 3 = -1 and f(2) = 2^4 + 2 - 3 = 13. Since f(1) is negative and f(2) is positive, f(a) and f(b) have opposite signs.

Therefore, by the Intermediate Value Theorem, we can conclude that there exists a number c in the interval (1, 2) such that f(c) = 0, indicating the presence of a root of the equation x^4 + x - 3 = 0 in the specified interval.

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Answer:

x = 2, y = -1

Step-by-step explanation:

Now change the equation,

→ x + y = 1

→ y = 1 - x

Then the value of x will be,

→ 2x + y = 3

→ 2x + 1 - x = 3

→ x = 3 - 1

→ [ x = 2 ]

Therefore, the value of x is 2.

Now value of y will be,

→ y = 1 - x

→ y = 1 - 2

→ [ y = -1 ]

Hence, the value of y is -1.

Answer:

(2, -1)

-------

x = 2

y = -1

Step-by-step explanation:

1st equation:

rewrite

2nd equation:

rewrite

Solve simultaneously:

When x = 2, y = 1 - x

                    y =  1 - 2

                    y = -1

Answer: C

Step-by-step explanation:

area of rectangle = (5--2) × (2--2) = 7 × 4 = 28

area of triangle = ((12-5) × (6--6)) ÷ 2 = (7 × 12) ÷ 2 = 84 ÷ 2 = 42

total area = 28 + 42 = 70

ii) the probability of a woman having a cholesterol level between 5.2 and 6.2 mmol/l is 0.3643.

To calculate the z-scores and probabilities for the given cholesterol levels, we'll use the formula for z-score:

z = (x - μ) / σ

where x is the cholesterol level, μ is the mean, and σ is the standard deviation.

i) Above 6.2 mmol/l:

x = 6.2 mmol/l

μ = 5.1 mmol/l

σ = 1.0 mmol/l

z = (6.2 - 5.1) / 1.0 = 1.1

To find the probability of a cholesterol level above 6.2 mmol/l, we need to find the area under the normal distribution curve to the right of the z-score.

Using a standard normal distribution table or calculator, we can find the probability:

Prob = 1 - P(Z ≤ 1.1)

Using the standard normal distribution table, we find that P(Z ≤ 1.1) ≈ 0.8643.

Prob = 1 - 0.8643 = 0.1357

Therefore, the probability of a woman having a cholesterol level above 6.2 mmol/l is approximately 0.1357.

ii) Below 5.2 mmol/l:

x = 5.2 mmol/l

μ = 5.1 mmol/l

σ = 1.0 mmol/l

z = (5.2 - 5.1) / 1.0 = 0.1

To find the probability of a cholesterol level below 5.2 mmol/l, we need to find the area under the normal distribution curve to the left of the z-score.

Prob = P(Z ≤ 0.1)

Using the standard normal distribution table, we find that P(Z ≤ 0.1) ≈ 0.5398.

Prob = 0.5398

Therefore, the probability of a woman having a cholesterol level below 5.2 mmol/l is 0.5398.

iii) Between 5.2 and 6.2 mmol/l:

For this case, we need to find the probability of a cholesterol level between 5.2 and 6.2 mmol/l.

Using the z-scores calculated earlier:

For x = 5.2 mmol/l, z = (5.2 - 5.1) / 1.0 = 0.1

For x = 6.2 mmol/l, z = (6.2 - 5.1) / 1.0 = 1.1

To find the probability, we subtract the area under the normal distribution curve to the left of the lower z-score from the area to the left of the higher z-score.

Prob = P(0.1 ≤ Z ≤ 1.1)

Using the standard normal distribution table, we find that P(0.1 ≤ Z ≤ 1.1) ≈ 0.3643.

Prob = 0.3643

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The vertex form of the new function is \(\rm (x+7)^2 -47\).

The function \(\rm f(x) = x^2 + 22x + 58\)  is translated 4 units to the right and 16 units up.

The vertex of a parabola is the point at which the parabola passes through its axis of symmetry.

The standard equation which represents the vertex form of the function is;

\(\rm f(x) = (x - h)^2 + k\)

Where h and k are vertexes of the given parabola.

The new function after translating 4 units to the right and 16 units up is;

\(\rm f(x) = x^2+22x+58\\\\f(x) = x^2 + 22x + 58 +(11)^2 -(11)^2\\\\\f(x) = x^2+22x+(11)^2 +58-(11)^2\\\\ f(x) = (x+11)^2+58-121\\\\f(x)=(x+11)^2-63\)

On comparing with the standard equation of vertex of parabola;

h = -11 and k = -63

Then,

The vertex form of the new function is after translated 4 units to the right and 16 units up.

h = -11 + 4 and k = -63+16 = -47

Therefore,

The vertex form of the new function is;

\(\rm =(x+7)^2 -47\)

Hence, the vertex form of the new function is \(\rm (x+7)^2 -47\).

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Answer:

C

Step-by-step explanation:

Answer:

bro what is the diagonal of second square.

The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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Step-by-step explanation:

1. secx / cscx

2. sinx /cosx

Answer:

Step-by-step explanation:

4x - 5y = -17

-4x - 24y = -244

-29y = -261

y = 9

x + 54 = 61

x = 7

(9,7) Option B

Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

The student's conclusion is not appropriate or no, because there were not enough measurements to use standard deviation.

Given:

suppose a student repeats a measurement two times and then calculates the standard deviation. because the standard deviation is small, the student reports that their experiment was extremely precise.

standard deviation:

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.

To find standard deviation :

σ =  x - μ / z

But here sample mean and proportion , z score not given so there are not enough measurements to use standard deviation.

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he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer:

the answer is A. 0.48 $

Step-by-step explanation:

the price of ounce of the watermelon is :

\( \frac{5.76}{12} = 0.48 \: \)

Answer:

c

Step-by-step explanation:

Answer:

O. 10+y=4

y=4-10

y=-6

D -10 + y = 3

y=3+10

y=13

C. -11+ x = -5

x=-5+11

x=6

K -13 + a = -60

a=-60+13

a=-47

a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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The rule of inference used to arrive at the statements s(y) and c(y) from the statement s(y) ∧ c(y) is called Simplification. Simplification allows us to extract individual components of a conjunction by asserting each component separately.

The rule of inference used in this scenario is Simplification. Simplification states that if we have a conjunction (an "and" statement), we can extract each individual component by asserting them separately. In this case, the conjunction s(y) ∧ c(y) represents the statement "y is a movie produced by Sayles and y is a movie about coal miners."

By applying Simplification, we can separate the conjunction into its individual components: s(y) (y is a movie produced by Sayles) and c(y) (y is a movie about coal miners). This allows us to conclude that there is a movie produced by Sayles (s(y)) and there is a movie about coal miners (c(y)).

Using the Simplification rule of inference enables us to break down complex statements and work with their individual components. It allows us to extract information from conjunctions, making it a useful tool in logical reasoning and deduction.

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