Pls help me! (10 points) thank yoy

ANSWER:

1. translation: 3 units right and 1 unit down

2. 130°

Answer:

(4)

Step-by-step explanation:

one 'x' value maps to more than one 'y' value

The truth value of this wff of a. (thereexists x)A(x), b. (thereexists x)[A(x) logicaland B(x)], c. (forall x)[A(x) rightarrow B(x)] is true.

(thereexists x)A(x) The truth value of this wff depends on whether there exists at least one integer x such that x < 5. Since the domain consists of integers, there are integers such as 0, 1, 2, 3, and 4 that satisfy this condition. Therefore, the truth value of this wff is true.

(thereexists x)[A(x) logicaland B(x)] The truth value of this wff depends on whether there exists at least one integer x such that x < 5 and x < 7. Since x < 5 is a stronger condition than x < 7, any integer x that satisfies x < 5 also satisfies x < 7. Therefore, the truth value of this wff is true.

(forall x)[A(x) rightarrow B(x)] The truth value of this wff depends on whether every integer x that satisfies A(x) also satisfies B(x). Since A(x) is true for integers less than 5 and B(x) is true for integers less than 7, it follows that every integer x that satisfies A(x) also satisfies B(x). Therefore, the truth value of this wff is true.

(forall x)[B(x) rightarrow A(x)] The truth value of this wff depends on whether every integer x that satisfies B(x) also satisfies A(x). Since A(x) is true for integers less than 5 and B(x) is true for integers less than 7, it follows that not every integer x that satisfies B(x) also satisfies A(x). For example, there are integers such as 5 and 6 that satisfy B(x) but not A(x). Therefore, the truth value of this wff is false.

The truth value of the wff of a, b and c is true.

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Answer:47

Step-by-step explanation:

The equivalent fraction to the given complex fraction is  \(\frac{2y-1}{3y+1}\).

Given expression,

\(\dfrac{2-\frac{1}{y} }{3+\frac{1}{y} } } \\\)

We have to find the equivalent fraction of    \(\frac{2-\frac{1}{y} }{3+\frac{1}{y} } } \\\) .

On solving,

\(\dfrac{2-\frac{1}{y} }{3+\frac{1}{y} } } =\dfrac{\frac{2y-1}{y} }{\frac{3y+1}{y} }\)

Eliminating y from numerator and denominator we get,

\(\dfrac{2-\frac{1}{y} }{3+\frac{1}{y} } } =\dfrac{2y-1} {3y+1} }\)

Hence the required expression is    \(\frac{2y-1}{3y+1}\).

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Answer:

The answer is D :)

Step-by-step explanation:

2y-1/3y+1

The estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

To estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints, we can use the right Riemann sum method.

The width of each rectangle, Δx, is given by the interval width divided by the number of rectangles.

In this case, Δx = (π/2 - 0)/4 = π/8.

To calculate the right endpoint values, we evaluate f(x) at the right endpoint of each rectangle.

For the first rectangle, the right endpoint is x = π/8.

For the second rectangle, the right endpoint is x = π/4.

For the third rectangle, the right endpoint is x = 3π/8.

And for the fourth rectangle, the right endpoint is x = π/2.

Now, let's calculate the area for each rectangle by multiplying the width (Δx) by the corresponding height (f(x)):

Rectangle 1: Area = f(π/8) * Δx = 5cos(π/8) * π/8

Rectangle 2: Area = f(π/4) * Δx = 5cos(π/4) * π/8

Rectangle 3: Area = f(3π/8) * Δx = 5cos(3π/8) * π/8

Rectangle 4: Area = f(π/2) * Δx = 5cos(π/2) * π/8

Now, let's calculate the values:

Rectangle 1: Area = 5cos(π/8) * π/8 ≈ 0.2887

Rectangle 2: Area = 5cos(π/4) * π/8 ≈ 0.3142

Rectangle 3: Area = 5cos(3π/8) * π/8 ≈ 0.2887

Rectangle 4: Area = 5cos(π/2) * π/8 ≈ 0

Finally, to estimate the total area, we sum up the areas of all four rectangles:

Total Area ≈ 0.2887 + 0.3142 + 0.2887 + 0 ≈ 0.8916

Therefore, the estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

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Answer:

Yes - it is a triangle

Classification: Right Triangle

Step-by-step explanation:

5 + 7 = 12

√74 > 12

This is a triangle because the sum of the two lesser side lengths are greater than the longest side length.

5² + 7² =? (√74)²

25 + 49 =? 74

74 = 74

This is a right triangle because the sum of the squares of the two sides are equal to the square of the length of the hypotenuse.

(Think Pythagorean Theorem)

When the radius of the snowball is 4 and shrinks at a rate of 2 inches per hour then the rate of change of the surface area s is equal to 64π in²/hr

As the radius r is shrinking at the rate of two inches per hour, it can be represented as;

dr/dt = -2 in / hr

Here, the negative sign represents the shrinking of the snowball with time t.

The surface area of a sphere can be represented by the formula;

S = 4πr²

Now we differentiate S with respect to t by keeping radius (r) as a variable as follows;

dS/dt = d/dt (4πr²)

dS/dt = 4π (d/dt) (r²)

dS/dt = 4π × 2r (dr/dt)

Putting the value of r = 4 and calculated value of dr/dt = -2 in the equation as follows;

dS/dt = 4π × 2(4)(-2)

dS/dt = -64π

Therefore, the rate of change of surface area s is calculated to be 64π in²/hr.

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Answer:

B

Step-by-step explanation:

According to Order of Operations, you always do exponents first

The solution to the system of equations is x = 1 and y = 2.

To solve the system of equations graphically, we will first represent each equation as a line on a coordinate plane. The equations are:

x + y = 3

2x + 5y = 12

To graph the first equation, we can assign values to x and solve for y, or vice versa. Let's assign some arbitrary values to x and find the corresponding values for y:

When x = 0, y = 3

When x = 1, y = 2

When x = 2, y = 1

When x = 3, y = 0

By connecting these points, we obtain a line. Plotting these points on a coordinate plane and connecting them gives us the graph of the first equation.

Now let's graph the second equation. Similarly, we assign values to x and solve for y:

When x = 0, y = 12/5

When x = 1, y = (12 - 2) / 5 = 10/5 = 2

When x = 2, y = (12 - 4) / 5 = 8/5

When x = 3, y = (12 - 6) / 5 = 6/5

Plotting these points and connecting them gives us the graph of the second equation.

By examining the graph, we can see that the lines do intersect at a single point, which represents the solution to the system of equations. To find the coordinates of this point, we can determine the x and y values at the point of intersection by visually inspecting the graph or using more precise methods such as estimation or calculation.

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Complete Question:

Solve the following system of equations graphically:

x + y = 3

2x + 5y = 12

Answer:

10%

Step-by-step explanation:

65.00x10%=6.50

65.00-6.50

0r you can do

65.00-10%=58.50

If Rachana randomly selects two mugs from the set, the probability that she gets two different mugs is 0.1556 or 15.56%.

To solve this problem, we can use the concept of combinations. Since there are 10 mugs in the set, there are 10 choose 2 = 45 ways to select two mugs without considering order.

Out of these 45 ways, we need to count the number of ways Rachana can select two different mugs. Since there are 3 different types of mugs, Rachana can choose any one of the three types for the first mug. There are 10 mugs in the set, out of which 3 belong to the chosen type. Therefore, the probability of choosing a mug of the chosen type is 3/10.

For the second mug, Rachana can choose from the remaining 9 mugs. Since she needs to choose a different type of mug, she can choose any one of the 2 remaining types. There are 7 mugs left from the other 2 types. Therefore, the probability of choosing a mug of a different type is (7/9) * 2/3 = 14/27.

Therefore, the probability of selecting two different mugs is the product of the probabilities of selecting a mug of the chosen type and a mug of a different type. This is given by (3/10) * (14/27) = 7/45, which is approximately 0.1556 or 15.56%.

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Complete question is:

Rachana has a set of ten mugs the set up is made of 3 different mugs. If Rachana randomly selects two mugs from the set, what is the probability that she gets two different mugs?

The expression -6/25: 5 2/5 is simplified to -30/675

Ratio can be defined as the comparison of two numbers or elements indicating their sizes in relation.

It is represented using the symbol ':'

Example;

The ratio of 3: 5 is written as 3/ 5

Given the expression;

-6/25: 5 2/5

Convert 5 2/5 into an improper fraction = 27/5

We have

-6/ 25 : 27/ 5

Take the ratio

- 6/ 25 ÷ 27/ 5

Take the inverse of the divisor and multiply

- 6/ 25 × 5/ 27

-30/675

Thus, the expression -6/25: 5 2/5 is simplified to -30/675

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\(\huge\text{Hey there!}\)

\(\large\text{3a - 4b - 6a + b}\)

\(\large\textsf{COMBINE the LIKE TERMS}\)

\(\large\text{\underline{(3a - 6a)} + (\bf -4b + b)}\)

\(\large\text{\underline{3a - 6a = \bf -3a}}\)

\(\large\text{\bf -4b + b = \bf \underline{-3b}}\)

\(\large\text{= \bf -3a - 3b}\)

\(\boxed{\boxed{\large\text{Answer: \huge \bf -3a - 3b }}}\huge\checkmark\)

\(\large\textsf{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

6 inches

Step-by-step explanation:

There are 12 months in a years so all you have to do is 1/2 times 12 and you get 6!

Hope this helps!

The probability that all four light bulbs do not work is the product of the probabilities that each individual light bulb does not work, is (0.4)⁴ = 0.0256.

We are given that there are 4 light bulbs in a classroom, and the probability that each light bulb works is 0.6. Since the light bulbs work independently of each other, we can calculate the probability that each individual light bulb does not work as 1 - 0.6 = 0.4. The probability that all four light bulbs do not work is then found by taking the product of the probabilities that each individual light bulb does not work, which is (0.4)⁴ = 0.0256. This means that the probability that none of the 4 light bulbs work is 0.0256.

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The area of the triangle with vertices (1, 3), (-3, 0), and (5, 0) can be found using the Shoelace formula. The area of the triangle is 24 square units.

To find the area of a triangle given its vertices, we can use the Shoelace formula. The Shoelace formula states that if the coordinates of the vertices are (x₁, y₁), (x₂, y₂), and (x₃, y₃), then the area of the triangle is given by:

Area = 1/2 * |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|

In our case, the coordinates of the vertices are (1, 3), (-3, 0), and (5, 0). Let's substitute these values into the formula:

Area = 1/2 * |1(0 - 0) + (-3)(0 - 3) + 5(3 - 0)|

    = 1/2 * |0 + 9 + 15|

    = 1/2 * |24|

    = 24/2

    = 12

Therefore, the area of the triangle with vertices (1, 3), (-3, 0), and (5, 0) is 12 square units.

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Answer:

13 and 1/3

Step-by-step explanation:

2×5=10

2/3 ×5 =10/3

10/3 simplifies to 3 and 1/3

Add them together to get 13 and 1/13

Answer:

13.15

Step-by-step explanation:

Answer: Richter Scale

Step-by-step explanation:

Answer:

Richter scale

Step-by-step explanation:

Used for the magnitude of Earthquakes, hope this helps!

Answer:

Pretty sure its 540

Step-by-step explanation:

We are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).

To find the confidence interval, we can use the formula:

CI = p ± zsqrt(p(1-p)/n)

Where:

CI: Confidence Interval

p: Proportion of students who correctly identified the flavor (sample proportion)

z: Z-score corresponding to the desired confidence level (95% confidence level corresponds to z=1.96)

n: Sample size

Plugging in the values we have:

p = 78/154 = 0.5065

z = 1.96

n = 154

CI = 0.5065 ± 1.96sqrt(0.5065(1-0.5065)/154)

CI = 0.5065 ± 0.0783

CI = (0.4282, 0.5848)

Therefore, we are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).

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The equation to predict how many hours, x, the second part of the trip will take is :x = (total distance - distance traveled in the first part) / average speed x = (125 - 75) / 50  x = 1

To predict how many hours, x, the second part of the trip will take, we can use the equation:

x = (total distance - distance traveled in the first part) / average speed

In this case, the total distance of the trip is 125 miles, and the distance traveled in the first part is the product of the average speed and the time taken for the first part, which is 50 miles/hour * 1.5 hours = 75 miles.

Substituting these values into the equation, we have:

x = (125 - 75) / 50

Simplifying the equation, we get:

x = 50 / 50

x = 1

Therefore, the equation to predict how many hours, x, the second part of the trip will take is:

x = (total distance - distance traveled in the first part) / average speed

x = (125 - 75) / 50

x = 1

This means that the second part of the trip will take 1 hour to complete after the bus stops to refuel.

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Answer:

Its A ( 1.05, -0.5)

Step-by-step explanation:

The mean amount of snow per day is equal to 19 cm snow per day.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total amount of snow based on the frequency, we have;

Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)

Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135

Total amount of snow (s cm), F(x) = 570

Now, we can calculate the mean amount of snow as follows;

Mean = 570/30

Mean = 19 cm snow per day.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

-8 and 9

Step-by-step explanation:

-8 x 9  = -72

and  -8 + 9 = 1

\(\\ \rm\Rrightarrow \sqrt{3tan(2x-10)}+1=0\)

\(\\ \rm\Rrightarrow \sqrt{3tan(2x-10)}=-1\)

\(\\ \rm\Rrightarrow 3tan(2x+10)=1\)

\(\\ \rm\Rrightarrow tan(2x+10)=1/3\)

\(\\ \rm\Rrightarrow 2x+10=18\)

\(\\ \rm\Rrightarrow 2x=8\)

\(\\ \rm\Rrightarrow x=4\)

The number of units of each type that should be purchased to maximize the number of people processed is 6 unit A and 6 unit B.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Any mathematical object has a symbol, and that symbol is called a variable. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

Given that,

The budget for new metal detectors is $75,000.

Maximum of 18 security guards available for each shift.

Unit A costs $5000, requires 1 security guard and can process 300 people per hour.

Unit B costs $7500, requires 2 security guards and can process 500 people per hour.

Let x = unit A

Let y = unit B

N = 300x + 500y

Here, 5000x + 7500y ≤ 75000

X+2y≤ 18

y≥4

x≥0

Hence,

(0, 9) = 300(0) + 500(9)

(0, 9) = 4500

(0, 4) = 300(0) + 500(4)

(0, 4) = 2000

(9, 4) = 300(9) + 500(4)

(9, 4) = 4700

since,

(6, 6) = 300(6) + 500(6)

(6, 6) = 4800

Therefore, flywithus should buy 6 unit A and 6 unit B to maximize the number of people processed.

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Answer:

$29.50

Step-by-step explanation:

Divide the total (106.20) by 3.6 and you get 29.5

You can check your answer by multiplying 29.5 by 3.6 and you see it equals 106.2

Hope this helps!

The z scοre is negative the actual probability would be

1-0.7995 = 0.2005

What is the probability?

A number that expresses hοw likely it is that an event will occur is called the probability of οccurrence. It is written as a number from 0 to 1, or frοm 0% to 100%, in percentage notation. The probability of an event occurring increases with probability.

here,

mean = 20.20

standard deviatiοn = 2.60

we knοw that,

Z scοre = (X-mean)/standard deviation

fοr X = 18:

Z scοre = (18-20.20)/2.6 = -0.8461

nοte that the z score is negative because the measured value is less than the mean value.

fοr Z score 0.8461 probability is 0.7995

and since the z scοre is negative the actual probability would be

1-0.7995 = 0.2005

a. For nοt within 1 hour of the population mean

We apply the formula here and we get the value οf P.

P(19.20>x>21.20) = P(19.20-20.20/2.60√18) > X-μ/σ√n >21.20-20.20/2.60√18

P(19.20>x>21.20) = P(-1.63>z>1.63)

Now, we find the value οf z.

P(19.20>x>21.20) = P(z>1.63) + P(z<-1.63)

P(19.20>x>21.20) = 0.0516 + 0.0516

P(19.20>x>21.20) = 0.1032

b. Fοr 20. 0 to 20. 5 hours

P(20<x<20.5) = P(20-20.20/2.60√18) < X-μ/σ√n<20.50-20.20/2.60√18

P(20<x<20.5) = P(-0.33<z<0.49)

Nοw, we find the value of the z-score and we get

P(20<x<20.5) = P(z<0.49) - P(z<-0.33)

P(20<x<20.5)  = 0.6879 - 0.2707

P(20<x<20.5)  = 0.3172

c. Fοr at least 22 hours

We apply the t-test fοrmula here and we get

P(x≥22) = P(X-μ/σ√n≥22-20.20/2.60√18)

Nοw, we find the value of z.

P(x≥22) = P(z≥2.94)

P(x≥22) = 0.0016

d. Fοr not more than 21 hours.

P(x<21) = P(X-μ/σ√n<21-20.20/2.60√18)

We find here the value οf P for x<21 and we get

P(x<21) = P(z<1.31)

Now, we find the value οf the z- score.

P(x<21) = 0.9049

Hence, a. 0.1032

b.  0.3172

c. 0.0016

d. 0.9049

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Complete question is,

Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week of 18 randomly selected college students who old part-time jobs during the school year is.