any answers or suggestions

The linear function which represents a slope of -3 as required in the task content is; A two column table with five rows. The first column, x, has the entries, negative 5, negative 1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8.

It follows that the task requires that a linear function whose slope, i.e rate of change is -2 is to be determined.

Since slope is the rate of change in y with respect to x;

The required linear function is; A two column table with five rows. The first column, x, has the entries, -5, -1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8 so that we have;

Slope = (24 - 32) / (-1 -(-5)) = -8 / 4 = -2.

Remarks: The complete question is such that the required slope is -2.

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Answer: the second option

Step-by-step explanation:

i took the assignment

Answer: A = 37°

c = 8.31

b = 6.63

Step-by-step explanation:

I suppose that the triangle is something like the one below.

Then we know the measure of an angle and the length of the adjacent cathetus.

a = 5

B = 53°

Now we can use the relationships:

Tan(B) = (opposite cathetus)/(Adjacent cathetus) = b/a

Cos(B) = (adjacent cathetus)/(hypotenuse) = a/c

Sin(B) = (opposite cathetus)/(hypotenuse) = b/c

Then we have:

Tan(53°) = b/5

Tan(53°)*5 = b = 6.63

So we found the length of b.

Now we can use the second relationship to find the length of c:

cos(53°) = 5/c

c = 5/cos(53°) = 8.31

Now, to find the angle A we can use the fact that the sum of all interior angles of a triangle must be equal to 180°

We know that is a triangle rectangle, so we have an angle equal to 90°, this one is C = 90°, and we also know that B = 53°

Then:

A + B + C = 180°

A + 53° + 90° = 180°

A + 53° = 180° - 90° = 90°

A = 90° - 53° = 37°

Then:

A = 37°

c = 8.31

b = 6.63

Answer:

(b) Reserves with the bank of Ghana

The linear and exponential equations for the amount of money in the banks indicates;

TCF Bank Equation

y = 100·x + 1000

Well Fargo Bank Equation

y = (1.06)ˣ

The number of years it will take for both accounts to have the same amount of money is about 17 years

An exponential equation is an equation of the form; y = a·bˣ, where the input variable, x is an exponent.

The equation for calculating the amount in each bank, based on the details are;

TCF Bank;

Amount invested = $1,000

Amount added each year = 100·x

Well Fargo Bank Equation

The percentage of the amount earned as interest each year = 6% = 0.06

The exponential equation for compound interest amount is; y = 1000·(1 + 0.06)ˣ

Therefore; y = 1000·(1.06)ˣ

When the amount in the two accounts have the same amount of money, we get;

1000·(1.06)ˣ = 100·x + 1000

Therefore; (1.06)ˣ = (100·x + 1000)/1000 = 0.1·x + 1

(1.06)ˣ = 0.1·x + 1

Solving the above equation using the substitution method and graphing indicates that we get;

x = 0, and x ≈ 17.125732

Therefore, it takes about 17 years for the two accounts to have the same amount of money

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The amount of time he spent on bicycle is 4.5 hours.

Given Jim began a 145 mile bicycle trip.

The whole trip took 7 hours.

Jim walks at a rate of 4 miles per hour  and rides at 30 miles per hour.

speed = distance / time

time = distance / speed

ride:

d = distance ridden

t = d/30 (given from the problem)

walk:

t = (145 - d)/4 (given from problem)

total trip time:

7 = d/30 + (145 - d)/4.

7 = 4d/120 + 30(145 - d)/120

7×120 = 4d + 30(145 - d)

840= 4d +4350-30d

840 ₋ 4350 = ₋30d ₊ 4d

₋3510 = ₋26d

d = 3510/26

d = 135

d=135 then from here using the formula t = d / s we can solve

t=135/30 = 4.5 hours

hence the amount of time Jim spent on the bicycle is 4.5 hours.

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Answer: This game of darts involves the player calling the target they aim to hit and the winner is determined by hitting the section they called. The player starts by attempting to hit "low" (sectors 1-10), followed by "high" (sectors 11-20), then "bullseye", and this pattern continues until the player successfully hits the section they called.

Step-by-step explanation:

A subgroup of index p must contain all elements of g, hence it is normal. Therefore, every group of order p2 has a normal subgroup of order p.

Let p be a prime and g be a group of order p a for some a ∈ Z.

First, we prove that every subgroup of index p is normal in g.

Since the order of g is p a , and the index of a subgroup of g is p, the subgroup must contain all elements of g. Thus, the subgroup is normal in g.

We can now deduce that every group of order p2 has a normal subgroup of order p.

Since the order of a group of order p2 is p2, we can divide it into two subgroups: one of order p, and one of order p. Since the subgroup of order p has an index of p, it must be normal in the group of order p2. Therefore, every group of order p2 has a normal subgroup of order p. Every group of order p2 has a normal subgroup of order p due to the fact that a subgroup of index p must contain all elements of g.

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The required interval of domain for the composite function is  [-2, 3].

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

The domain of fog(x) is the set of all values of x for which the composition function fog(x) is defined.

fog(x) means that we plug g(x) into f(x), so we have:

fog(x) = f(g(x)) = f(x^2 - x) = √(6 - (x^2 - x))

= √(6 - x^2 + x)6

For the expression under the square root to be defined, we must have 6 - x^2 + x ≥ 0. This is a quadratic inequality that can be factored as:

-(x - 3)(x + 2) ≤ 0

The solutions of this inequality are -2 ≤ x ≤ 3.

However, we also need to check that the expression under the square root is non-negative, so we need to exclude the values of x that make 6 - x^2 + x < 0. This inequality holds for x < -2 or x > 3.

Therefore, the domain of fog(x) is [-2, 3].

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we have to do alot for this

so first we gotta change 12.3 into a mixed fraction

n = 5 so 5 ÷ 12.3

The expression/equation as written in the question is ∠A ≈ ∠C

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

∠A ≈ ∠C

The above expression means that

The angles A and C are congruent

From the question, we understand that

The question is not to be solved; we only need to write out the expression

Hence, the expression/equation as written is ∠A ≈ ∠C

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\(\cfrac{3}{5}\div\cfrac{3}{7}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5}\cdot \cfrac{7}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{7}{5}\implies 1\frac{2}{5}\)

Answer:

7.y-side by side

8.n-lines don't cross, not vertical

9.n-don't equal 90 degrees

10.n-don't equal 180 degrees

11.AOB

12.COE

13.EOD

14.DOC

15.DOC, BOA

Step-by-step explanation:

Answer:

it will 54

Step-by-step explanation:

1. If t= 45 then t+s it you put the t into the equation. So it will be

45 + s

2. And put s=9 into the equation. It will be

45 + 9

3. Just add them together

45 + 9 = 54

Answer: 54

Answer:

54

Step-by-step explanation:

We know t = 45 and s = 9, so all we have to do is substitute these values to each corresponding variable in the expression t + s.

t + s =

45 + 9 =

54

So, t + s is equal to 54

Hope this helps!

Answer:

It cannot be used to assess individual renal function or degree of obstruction. Sulfadiazine stones are also difficult to visualize on CT because of relatively low attenuation. It is relatively expensive.

Answer:

\(\boxed{v=300}\)

Step-by-step explanation:

Hey there!

To find v we’ll set up the following,

v ÷ 5 = 60

To get v by itself we’ll do

5*60 = 300

v = 300

Hope this helps :)

Step-by-step explanation:

a probability is always desired cases over total possible cases.

so, we have actually 8 systems (5 + 3) we can pick from.

therefore, the total possible cases are 8.

the desired case is in this question to pick one of the 3 Wii consoles.

the probability to pick a Wii is therefore

3/8 = 0.375

Answer:

3/8, or 37.5%

Step-by-step explanation:

There are 8 different playing devices there.

There are only 3 Nintendo Wii consoles.

So, the probability is 3/8

Answer:

5.196152423

Step-by-step explanation:

Answer for this problem: 6.33012701

The length of the unknown side length, |AB|, is 6.97

From the question, we are to determine the value of the unknown side length

The unknown side length is the hypotenuse

Using SOH CAH TOA

We can write that

sin 35° = 4/|AB|

∴ |AB| = 4 /sin35°

|AB| = 4 /sin35°

|AB| = 6.97

Hence, the length of the unknown side length, |AB|, is 6.97

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A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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Answer:

30.5

Step-by-step explanation:

Let L = the larger number

Let S = the smaller number

L + S = 144

L - S = 73

L = S + 73

S + S + 73 = 144

2S = 71

S = 30.5

1 cup for each of the 20 students.

1 x 20= 20

20 cups

4 cups =1 quart.

20/4 = 5

Answer: 5 quarts

Answer:

0.2637

Step-by-step explanation:

Population size is top 15 ranking restaurants.

Number of draws = 3

Number of observed successes = 5

Probability formula :  [r . x } { n -r] [n - x]

solving the equation we get 24 / 91 which is approximately 0.2637

The answer is:

minimum value = √121/11 = 2/11

maximum value = √17/11

Here's how to solve it:

The given function is c(z) = √z, and the domain interval is 121 ≤ z ≤ 17.

The minimum value of the function occurs at the endpoint of the domain interval where the function takes the smallest value. In this case, the smallest value of the function occurs at z = 17, so the minimum value of the function is:

c(17) = √17

The maximum value of the function occurs at the endpoint of the domain interval where the function takes the largest value. In this case, the largest value of the function occurs at z = 121, so the maximum value of the function is:

c(121) = √121 = 11

Therefore, the minimum value of the function is √17 and the maximum value of the function is 11/√121, which simplifies to 1/11.

If the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

If the triangle on the left had the same area as the circle on the right, it would mean that the triangle would have to be larger than its current size. This is because the area of a circle is determined by the formula A=πr^2, where r is the radius of the circle.

Therefore, if the area of the circle is equal to the area of the triangle, the radius of the circle would have to be equal to the height of the triangle, and the base of the triangle would need to be wider.

This would result in a larger triangle with a greater surface area than the current triangle. The larger triangle would also have a longer perimeter, which would make it more difficult to enclose and would require more material to construct.

Additionally, the larger triangle would have a higher center of gravity, which could make it more difficult to balance and more prone to tipping over.

Overall, if the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

It is important to consider both the area and the shape of an object when determining its practicality and effectiveness in a given situation.

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The length of the guy wire to the nearest foot would be = 10 ft.

The relationship between the tower, guy wire and pole forms the shape of a right angle triangle.

The distance from the stake to the pole (opposite) =a = 5 ft

The distance from the pole to the tower (adjacent) =b= 9ft

The length of the guy wire= c = X

Using the Pythagorean formula:

c² = a² + b²

c² = 5² + 9²

c² = 25+81

c² = 106

C = √106

C= 10 ft ( to the nearest foot)

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Complete question:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophie places a 7 ft tall pole to support the guy wire. After placing the pole, Sophie measures the distance from the stake to the pole to be 5 ft. She then measures the distance from the pole to the tower to be 9 ft. Find the length of the guy wire, to the nearest foot.

a. The decision rule for this hypothesis test is: Reject H0 if the test statistic z is less than -1.645 or greater than 1.645. b. The test statistic for this hypothesis test is:  -2.05.

In statistics, a hypothesis is an assumption or claim about a population parameter that can be tested by collecting and analyzing sample data.

According to given information:

a. The decision rule for this hypothesis test is:

Reject H0 if the test statistic z is less than -1.645 or greater than 1.645.

b. The sample proportion of customers who prefer black teas is:

= 0.41

The population proportion under the null hypothesis is:

p = 0.51

The sample size is:

n = 158

The test statistic for this hypothesis test is:

\(z = ( - p) / \sqrt(p * (1 - p) / n)\)

\(= (0.41 - 0.51) / \sqrt(0.51 * 0.49 / 158)\)

\(= -2.05\)

c. The test statistic z of -2.05 is less than the critical value of -1.645, so we can reject the null hypothesis H0. At the 0.10 significance level, there is enough evidence to suggest that the proportion of customers who prefer black teas is not 0.51, and the manager of Tea for Us should consider adjusting their stock orders accordingly.

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Answer:

(C) The area of the cylinder's base is \(\dfrac{1}{4} \pi x^2\) square units.

(E)The height of the cylinder is 4x units.

Step-by-step explanation:

If the Base Diameter = x

Therefore: Base radius = x/2

Area of the Base

\(=\pi (x/2)^2\\=\dfrac{ \pi x^2}{4} $ square units\)

Next, we know that:

The volume of a cylinder = Base Area X Height

\(\pi x^3=\dfrac{ \pi x^2}{4} \times Height\\Height =\pi x^3 \div \dfrac{ \pi x^2}{4}\\=\pi x^3 \times \dfrac{ 4}{\pi x^2}\\\\Height=4x$ units\)

Therefore, the correct options are: C and E.

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