Pls help
a. Do you know how to find equivalent fractions, without context, like ½ = 3/6?


b. Do you know how to set up equivalent ratios, that means if it is “a per b” then a/b?


c. What method do you use to find equivalent ratios or fractions?


d. What help do you need to confidently set up and find equivalent fractions and ratios?

The 8th term οf the sequence is -4096.

The given sequence is: 1/4, -1, 4, -16, ...

Tο find the 8th term οf the sequence, we can use the fοrmula fοr a geοmetric sequence:

[tex]an = a1 * r^(n-1)[/tex]

where:

an = the nth term οf the sequence

a1 = the first term οf the sequence

r = the cοmmοn ratiο οf the sequence

n = the number οf the term we want tο find

We can see that the cοmmοn ratiο οf this sequence is -4, since:

-1 / 1/4 = -4

4 / -1 = -4

-16 / 4 = -4

Therefοre, the fοrmula fοr the nth term οf the sequence is:

[tex]an = a1 * (-4)^{(n-1)[/tex]

Substituting the given values, we have:

a1 = 1/4

n = 8

[tex]an = (1/4) * (-4)^{(8-1)[/tex]

[tex]an = (1/4) * (-4)^7[/tex]

an = (1/4) * (-16384)

an = -4096

Therefοre, the 8th term οf the sequence is -4096.

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Check the picture below.

The correct matchings for the given question according to the diagram are 1. c, 2. a and 3. b.

According to the diagram,

1. Skew - c. DE and CF

Skew lines are those lines in three-dimensional space that are not parallel and never intersect, according to the definition of skew lines.

2. Intersecting - a. AD and AC

Intersecting lines are two or more lines that have exactly one point in common. The point of junction is this central location that connects all of these lines.

3. Parallel - b. BE and CF

Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel.

Therefore from the diagram 1. c, 2. a and 3. b are the correct matchings,

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The number 3 107/125 is greater than  3.151.

A number that is stated as bοth a whοle number and a fractiοn, such 3 1/2, is referred tο as a mixed number. A fractiοn, such as 7/2, that has the numeratοr higher than οr equal tο the denοminatοr is referred tο as an imprοper fractiοn. Yοu must multiply the whοle number by the denοminatοr, add the numeratοr, and then place it οver the οriginal   denοminatοr in οrder tο cοnvert a  mixed number tο an imprοper fractiοn.

Divide the numeratοr by the denοminatοr and then write the residue as a fractiοn with the same denοminatοr tο turn an imprοper fractiοn intο a mixed number.

The given numbers are: 3.515 οr 3 107/125.

Cοnvert 3 107/125 tο a decimal.

3 107/125 = (3 * 125 + 107)/125 = 482/125 = 3.856

Cοmparing the twο 3.515 and 3.856 we οbserve that 3.856 is greater than 3.515.

Hence, the number 3 107/125 is greater than 3.151.

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Suppose sin t = 5/7 and cos t < 0. The exact value :
cos t = -√(1 - (5/7²)
tan t =  -(5√6)/12
csc t =7/5
sec t =  -(7√6)/12
cot t =  -12/(5√6)

Since sin t = 5/7 and cos t < 0, we can use the Pythagorean identity cos² t + sin² t = 1 to find cos t:

cos² t + (5/7)²= 1

cos² t = 1 - (5/7)²

cos t = -√(1 - (5/7)²) (since cos t < 0)

Next, we can use the definitions of the trigonometric functions to find the remaining values:

tan t = sin t / cos t = (5/7) / (-√(1 - (5/7)^2)) = -5/√24 = -(5√6)/12

csc t = 1/sin t = 7/5

sec t = 1/cos t = -1/√(1 - (5/7)²) = -7/√24 = -(7√6)/12

cot t = 1/tan t = -12/(5√6)

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Answer:

X-intercept: (2/3,0)

Y-intercept: (0,1)

Step-by-step explanation:

To find the x-intercept, we put in 0 for y. To find the y-intercept, we put in 0 for x.

Find x-intercept

3x + 2(0) = 2

3x = 2

x = 2/3

So, the x-intercept is (2/3,0)

Find y-intercept

3(0) + 2y = 2

2y = 2

y = 1

So, the y-intercept is (0,1)

Answer:

Below

Step-by-step explanation:

x - y = 11

2x+y = 19       <====add the two equations together....this will eliminate 'y'

3x = 30

x =10    <====use this value of 'x' in one of the equations to calculate 'y'

x-y =11

10 - y = 11

y = -1

Answer:

x = 10 and y = -1

Step-by-step explanation:

Let's solve your system by elimination.

x−y=11;2x+y=19

x−y=11

2x+y=19

Add these equations to eliminate y:

3x=30

Then solve 3x=30 for x:

3x=30

x = 10

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

x−y=11

Substitute 10 for x in x−y=11:

10−y=11

−y+10=11  (Simplify both sides of the equation)

−y+10+−10=11+−10  (Add -10 to both sides)

−y=1

y = -1

The volume of the solid generated by revolving the region bounded by x=6y, x=−7y, and y=2 about the x-axis is 208π/3 cubic units.

To find the volume of the solid generated by revolving the region bounded by x=6y, x=−7y, and y=2 about the x-axis, we can use the method of cylindrical shells.

First, we need to find the limits of integration. The region is bounded by the lines x=6y and x=−7y, so we can set up the integral as follows:

V = ∫[y=0 to y=2] 2πy(x_max - x_min) dy

where;

To find x_max and x_min, we can solve for x in each of the given equations:

x=6y => y = x/6

x=-7y => y = -x/7

At a given y, the maximum x-value will be given by x_max = 6y and the minimum x-value will be given by x_min = -7y.

Now, we can substitute these expressions into our integral and simplify:

V = ∫[y=0 to y=2] 2πy[(6y) - (-7y)] dy

V = ∫[y=0 to y=2] 2πy(13y) dy

V = 26π ∫[y=0 to y=2] y² dy

V = 26π [(2³)/3]

V = 208π/3

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If ∠ABC = 74° and x = 4 cm, then the length of AC is 4.8 cm.

We know that : AB = BC and ∠ABC = 74°,

So, ∠BCA = ∠BAC = (180° - ∠ABC)/2 = 53°.

Now, By using law of sines to find the length of AC.

The "Law-Of-Sines" states that in any triangle-ABC having sides a, b, and c and the opposite angles A, B, and C:

⇒ a/sin(A) = b/sin(B) = c/sin(C)

In this case, the side AC, is opposite angle C.

and we know that AB = x = 4 cm and ∠BAC = 53°,

So, We can write,

⇒ x/sin(53°) = AC/sin(74°)

⇒ AC = (x/sin(53°)) × sin(74°)

⇒ AC = (4/sin(53°)) × sin(74°)

⇒ AC ≈ 4.8 cm

Therefore, the length of AC is approximately 4.8 cm.

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The given question is incomplete, the complete question is

In the triangle ABC, ∠ABC = 74° and AB = x = 4 cm, and side AB = BC. Find the length of AC. Give your answer rounded to 1 DP.

The required number of moles of hydrogen fluoride (HF) produced by chemist in an experiment is equal to 0.245 moles.

Mass of hydrogen fluoride (HF) produced by chemist  is equals to 4.9 grams

The number of moles of hydrogen fluoride produced,

Use the formula of moles we have,

moles = mass / molar mass

The molar mass of hydrogen fluoride (HF) is approximately equals to  20 g/mol.

Thus,

Calculate the number of moles of hydrogen fluoride produced by substituting the values as follows,

⇒ moles = 4.9 g / 20 g/mol

⇒ moles = 0.245 mol

Therefore, the chemist produced 0.245 moles of hydrogen fluoride during the experiment.

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the 88% confidence interval for the proportion of college professors who wear eyeglasses is (0.487, 0.625).

To generate an 88% confidence interval for the proportion of college professors who wear eyeglasses, we can use the normal approximation to the binomial distribution. The formula for the confidence interval is:

p ± z*√(p(1-p)/n)

where p is the sample proportion, z is the z-score corresponding to the desired level of confidence (88% in this case), and n is the sample size.

First, we need to calculate the sample proportion:

p = 139/250 = 0.556

Next, we need to find the z-score corresponding to the 88% confidence level. We can use a standard normal distribution table or calculator to find this value. For an 88% confidence level, the z-score is approximately 1.553.

Now, we can substitute these values into the formula to calculate the confidence interval:

0.556 ± 1.553*√(0.556(1-0.556)/250)

Simplifying the expression gives us:

0.556 ± 0.069

the 88% confidence interval for the proportion of college professors who wear eyeglasses is (0.487, 0.625).  

This means that we are 88% confident that the true proportion of college professors who wear eyeglasses is between 0.487 and 0.625. In other words, if we were to repeat this study multiple times, we would expect the true proportion to fall within this interval in 88% of the cases.

It is important to note that confidence intervals are a range of plausible values for the population parameter (in this case, the proportion of college professors who wear eyeglasses), and do not provide definitive answers. Therefore, it is necessary to interpret the interval in the context of the study and the research question.

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Answer:

trust me on this it's 1 1/2

Step-by-step explanation:

The best function that models this set of data is option B. C(x) = 745000 * [tex](1.04)^2[/tex]

Exponential refers to a mathematical operation or function involving a constant called the base, raised to a power that is a variable, which is usually represented by the letter x.

The best function that models this set of data is option B.

C(x) = 745000 [tex]* (1.04) ^ x[/tex]

This is an exponential function that models the growth of the number of homes with computers over time. The base of the exponential function is 1.04, which indicates that the number of homes with computers is growing at a rate of 4% per year.

We can verify this by checking the values in the table.

When x = 1,

C(1) = 745000 * [tex](1.04) ^ 1[/tex]

C(1) = 774800

When x = 2,

C(2) = 745000 * [tex](1.04) ^ 2[/tex]

C(2) = 805792

We can see that the function closely matches the given data points. Therefore, option B is the best function that models this set of data.

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Answer:

74

Step-by-step explanation:

37 divided by 50 then multiply by 100% will give us the answer 74%

Using Pythagoras theorem, we can find the value of as follows:

a = √48.

b = √96.

h = √32.

The three sides of a right-angled triangle are related, according to the Pythagorean theorem, which is often referred to as the Pythagorean relation.

According to the Pythagorean theorem, a triangle's hypotenuse square is equal to the sum of its other two sides squares.

Here in the right-angled triangle,

The equations that we can derive are as follows:

a² + b² = 12²

a² = 4² + h²

b² = 8² + h²

Now we have 3 equations.

Using the 2nd & 3rd equations in the 1st we get,

4² + h² + 8² + h² = 12²

⇒ 2h² + 16 + 64 = 144

⇒ 2h² = 144 - 80

⇒ h² = 32

⇒ h = √32.

Now putting the value of h in equation 2 and 3 we can get the values of a and b as follows:

a² = 4² + h²

⇒ a² = 16 + 32

⇒ a² = 48

⇒ a =√48.

b² = 8² + h²

⇒ b² = 64 + 32

⇒ b = √96.

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Answer: i don’t know

Step-by-step explanation:

As per the given standard deviation, the target inventory level for maintaining a service level of 95% is 416.6 bottles of water.

To calculate the target inventory level, we need to take into account the delivery lead-time of 4 days. This means that we need to order enough inventory to cover the demand for the next 4 days, plus a safety stock to cover any unexpected variations in demand during that time. The safety stock is the extra inventory that we keep on hand to avoid stockouts.

To determine the target inventory level, we can use the following formula

u = d x L + z x σ x √(L)

where:

u = target inventory level

d = average daily demand (mean)

L = delivery lead-time (in days)

z = z-score corresponding to the desired service level (in this case, z = 1.65 for a service level of 95%)

σ = standard deviation of daily demand

Substituting the given values, we get:

u = 100 x 4 + 1.65 x 10 x √(4)

u = 400 + 16.6

u = 416.6

This means that we need to order enough inventory to cover the demand for the next 4 days, plus an extra 416.6 bottles to ensure that we don't run out of stock. The cost of carrying this inventory will be $0.91 per bottle per year.

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sin D is 4/5 or 0.8, sin E is 3/5 or 0.6, and cos D is 3/5 or 0.6.

Just dividing the numerator by the denominator is all that is required to convert a fraction to a decimal. Nothing else needs to be said!

Divide the opposite side by the hypotenuse to find sin D and sin E; similarly, divide the adjacent side by the hypotenuse to find cos D.

opposite/hypotenuse = 4/5 = 0.8 sin D (rounded to 4 decimal places)

opposite/hypotenuse = 3/5 = 0.6 sin E (rounded to 4 decimal places)

adjacent/hypotenuse = 3/5 = 0.6 cos D (rounded to 4 decimal places)

The resulting values for sin D, sin E, and cos D are 4/5, 0.8, 3/5, and 0.6 respectively.

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Answer:

4(x-1)(x)(x-7)

Step-by-step explanation:

4x³-24x²-28x

=4(x+1)(x)(x-7)

The average rate of change of the function f(x)=−2x^2+5 between x=-1 and x=3 is -16.

The average rate of change of the function f(x)=−2x^2+5 between x=-1 and x=3 is -16.What is the average rate of change?The average rate of change of a function is the ratio of the change in the y value of the function over the change in the x value of the function within a certain interval.For a function f(x),

the average rate of change from x=a to x=b is given by the formula below;Average rate of change = (f(b) − f(a)) / (b − a)Substituting the values in the formula we get,Average rate of change= [-2(3)^2+5-{-2(-1)^2+5}]/ (3-(-1))= [-2(9)+5-{-2(1)+5}] / (3+1)= (-18+5+2-5)/4 =-16 Therefore, the average rate of change of the function f(x)=−2x^2+5 between x=-1 and x=3 is -16.

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a) Equivalence relations are those which satisfy three properties: symmetric, reflexive, and transitive. If these three conditions are met, then a relation is an equivalence relation.

If the relation satisfies these three conditions, we can say it is an equivalence relation. This relation has no equivalence class as there is only one element. For every x belongs to X, (x,x) belongs to R. Thus, R is a reflexive relation.

For every x, y belongs to X, if (x,y) belongs to R then (y,x) belongs to R. Thus, R is a symmetric relation. For every x, y, and z belongs to X, if (x,y) belongs to R and (y,z) belongs to R then (x,z) belongs to R. Thus, R is a transitive relation.

b) If we consider S as the relation of persons who are spouses of each other, then it is an equivalence relation as it satisfies the three properties that an equivalence relation must satisfy.

Therefore, the spouses in the domain would be partitioned into equivalence classes, where each equivalence class contains a couple that are spouses of each other.

c) We know that an integer z is even if z=2k for some integer k. Thus, xEy if x+y=2k. It is an equivalence relation, as it satisfies the three conditions of an equivalence relation. In this relation, there are two equivalence classes: {2k,2k}, {2k+1,2k-1}.

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The real part of f(x) is [tex]1/sqrt(1+x^2)[/tex], the imaginary part of f(x) is [tex]x/sqrt(1+x^2),[/tex] and the magnitude of f(x) is [tex]1/sqrt(1+x^2).[/tex] Where [tex]X[/tex] is real.

The function f(x) = 1/(1-ix) can be rewritten as function [tex]f(x) = (1+ix)/(1+x^2)[/tex]by multiplying the numerator and denominator by the complex conjugate of the denominator, which is [tex](1+ix).[/tex]

The real part of f(x) can be found by taking the real part of the numerator and dividing by the magnitude of the denominator. The real part of the numerator is 1, and the magnitude of the denominator is [tex]sqrt(1+x^2)[/tex], so the real part of f(x) is [tex]1/sqrt(1+x^2).[/tex]

The imaginary part of f(x) can be found by taking the imaginary part of the numerator and dividing by the magnitude of the denominator. The imaginary part of the numerator is x, and the magnitude of the denominator is [tex]sqrt(1+x^2),[/tex] so the imaginary part of [tex]f(x) is x/sqrt(1+x^2).[/tex]

The magnitude of f(x) can be found by taking the square root of the sum of the squares of the real and imaginary parts. The magnitude of f(x) is [tex]sqrt((1/sqrt(1+x^2))^2 + (x/sqrt(1+x^2))^2) = sqrt(1/(1+x^2) + x^2/(1+x^2)) = sqrt(1+x^2)/(1+x^2) = 1/sqrt(1+x^2).[/tex]

Therefore, the real part of f(x) is 1/sqrt(1+x^2), the imaginary part of f(x) is [tex]x/sqrt(1+x^2)[/tex], and the magnitude of f(x) is [tex]1/sqrt(1+x^2).[/tex]

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Answer:

the result of the square root os -100 is 0 + 10i

Step-by-step explanation:

Answer:

X

-5

-1

0

2

4

/(×)

12

0

-3

-9

-15

The equivalent logarithmic equation for e^-7.5 = h is ln(h) = -7.5.

The logarithmic function is the inverse of the exponential function. So, to rewrite the equation e^(-7.5) = h as a logarithmic equation, we need to determine the base of the exponential function.

In this case, since there is no specified base, we can assume that the base is e. Then, we can write the equation as:

log_e(h) = -7.5

This equation states that the logarithm of h with base e is equal to -7.5. Alternatively, we could also write this as:

ln(h) = -7.5

since ln is the natural logarithm function with base e. Both of these equations are equivalent to e^(-7.5) = h.


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Answer:

All four types of transformations - translation, rotation, reflection and dilation - involve a change in the position and/or size of a figure. However, the major difference between dilation and the other three types of transformations is that dilation affects the size of the figure, whereas the other three transformations do not. Translation moves an object without changing its size or orientation, rotation moves an object in a circular motion and reflection flips an object across an axis.

We can convert the amount of oil in the barrel from quarts to cups to make the calculation easier. Since 1 quart is equal to 4 cups, the barrel holds 21 x 4 = 84 cups of oil.

from the question;

Trina drains the barrel at a rate of 6 cups per minute. To find the time it takes for her to empty the barrel, we can divide the amount of oil in the barrel by the rate at which she drains it:

time = amount of oil ÷ rate

time = 84 cups ÷ 6 cups per minute

time = 14 minutes

Therefore, it takes Trina 14 minutes to empty the barrel at a rate of 6 cups per minute.

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Answer: 1619.15

Step-by-step explanation:

cp = 1378

sp = cp + profit % of cp

= 1378 + 17.5/ 100 * 1378

= 1378 + 241.15

= 1619.15

The measure of center shows that the Allstars typically have the tallest players.

Mean is the average of all the values in the dataset, while median is the middle value in a sorted list of values. Mean is affected by outliers, while median is not.

Calculating the means:

Allstars: (73+62+60+63+72+65+69+68+71+66+70+67+60+70+71)/15 = 1005/15 = about 67.1 inches

Champs: (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)/15 = 996/15 = about 66.4 inches

Calculating the medians:

Allstars: 68 inches (arrange the values in ascending order: 60, 60, 62, 63, 65, 66, 67, 68, 69, 70, 70, 71, 71, 72, 73; the middle value is 68)

Champs: 67 inches (arrange the values in ascending order: 58, 60, 60, 62, 65, 66, 67, 67, 68, 69, 70, 70, 69, 75, 70; the middle value is 67)

Comparing the means and medians, we can see that the Allstars have a slightly higher mean and median than the Champs. Therefore, based on the measure of center, the Allstars typically have the tallest players.

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Answer: the answer should be A or the first option

The Allstars, with a mean of about 67.1

Step-by-step explanation:

Allstars: 73+62+60+63+72+65+69+68+71+66+70+67+60+70+71=1007

Champs: 62+69+65+68+60+70+70+58+67+66+75+70+69+67+60=996

1007 divided by 15 = 67.1

996 divided by 15 = 66.4

the mean of the allstars is 67.1

the mean of the champs is 66.4

The given distribution is not a probability distribution for a discrete random variable, x. This is because the sum of the probabilities is not equal to 1.
In a probability distribution for a discrete random variable, the sum of the probabilities for all possible values of x must be equal to 1. In the given distribution, the probabilities for x = 3, x = 6, x = 9, x = 12, and x = 15 are not given. Therefore, it is not possible to determine if the sum of the probabilities is equal to 1.
Additionally, the given distribution is not complete as it does not include the probabilities for each possible value of x. A probability distribution for a discrete random variable must include the probabilities for all possible values of x.
Therefore, the given distribution is not a probability distribution for a discrete random variable, x.

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