The table represents the function f (x) = 5x – 8. Find f (–4): f (–4) = 5(–4) – 8 f (–4) = –28 A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 3, 7. Column 2 is labeled f (x) with entries negative 28, a, b, c. Use the drop-downs to choose the value for the variables in the table. a = b = c =

The length of line segment RT is 8 units

The given triangles are similar triangles

So, we have the following similarity ratio

RS : RT = QC : QY

Substitute the known values in the above equation

4 : RT = 3 : 6

Express as fractions

RT/4 = 6/3

Multiply through by 4

RT = 4 * 6/3

Evaluate

RT = 8

Hence, the length of RT is 8 units

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Answer:

Graph in attachment

let's say x=cherries and y=grapes. (desmos only does x and y :( ).

the equation would be 9=4x+1.50y

Step-by-step explanation:

Answer:

it is 50 :)

Step-by-step explanation:

im taking the review on edg and i got it right

Answer:

The answer is 50. Edge 2022

Step-by-step explanation:

If you trace the way the points move you can find out it is 50.

The probability that Player A wins the game is 2/3, in which two players alternate tossing a fair coin until there is a head followed by a tail (HT), will be determined.

Let's consider the possible outcomes for the first two tosses: HH and HT. If the first two tosses result in HH, the game continues and it becomes Player B's turn. If the first two tosses result in HT, Player A wins the game. Thus, the probability of Player A winning on the second toss is 1/2.

For Player A to win on the third toss, the sequence of tosses must be HHT. The probability of this occurring is (1/2) * (1/2) * (1/2) = 1/8.

Similarly, the probability of Player A winning on the fourth toss is \((1/2)^{6}\) = 1/16, and so on.

Since each toss is independent and has a 1/2 probability of resulting in heads or tails, the probability of Player A winning the game can be represented as the infinite geometric series: P(A wins) = (1/2) + \((1/2)^{3}\) + \((1/2)^{5}\) + ...

This is a geometric series with a common ratio of (1/2)^2 = 1/4 and a first term of 1/2. Using the formula for the sum of an infinite geometric series, we find: P(A wins) = (1/2) / (1 - 1/4) = 2/3

Therefore, the probability that Player A wins the game is 2/3.

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The value of x from quadratic equation 8x²+15x=7x-4 is x=-1/2+i/2 and x=-1/2 - i/2

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given equation is 8x²+15x=7x-4

Let us convert it to a quadratic equation.

8x²+15x-7x+4=0

Add the like terms

8x²+8x+4=0

x=-8±√8²-4.8.4/2.8

x=-8±√64-128/16

x=-1/2+i/2 and x=-1/2 - i/2

Hence, the value of x from quadratic equation  8x²+15x=7x-4 is x=-1/2+i/2 and x=-1/2 - i/2

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The metric unit that would be best to measure the capacity of a cereal bowl is milliliters (ml).

Capacity is a measure of the amount of fluid that a container can hold. Cereal bowls are typically used to hold liquids such as milk or yogurt along with cereal. Milliliters are a commonly used metric unit of volume that would be appropriate for measuring the capacity of a cereal bowl. Other metric units of volume such as liters or cubic centimeters could also be used, but milliliters would provide a more precise measurement for a smaller container such as a cereal bowl. To measure the capacity of a cereal bowl in milliliters, one would simply pour a known amount of water into the bowl and measure the volume of the water using a measuring cup or a graduated cylinder.

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Answer:

the answer is 3

Step-by-step explanation:

Answer:

its 3

Step-by-step explanation:

The length and the width of the rectangle are 22 inches and 16 inches respectively

The given parameters are:

Length = 6 inches + width

Perimeter = 76 inches

The perimeter is calculated as:

Perimeter = 2 * (Length + Width)

This gives

76 inches = 2 * (6 inches + Width + Width)

Divide through by 2

38 inches = 6 inches + Width + Width

Evaluate the like terms

2 * Width = 32 inches

Divide both sides by 2

Width = 16 inches

Substitute Width = 16 inches in Length = 6 inches + width

Length = 6 inches + 16 inches

Evaluate

Length = 22 inches

Hence, the length and the width of the rectangle are 22 inches and 16 inches respectively

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Answer:

35 ok

Step-by-step explanation:

35 Men ok byeee3eeeeeeeeeeeeewwww

Answer:

The value of y is 46.715

Step-by-step explanation:

4y-10+3.14 = 180

4y = 180 + 10 - 3.14

4y = 186.86

4y ÷ 4 = 186.86 ÷ 4

y = 46.715

Answer:

maybe c sorry if wrong

Step-by-step explanation:

For Exercises 5-8:

To have an orthogonal set, we need the dot product of any two vectors to be zero. So, we can start by setting up dot product equations:

u · u2 = 0
u · u3 = 0
u2 · u3 = 0

Substituting in the given vectors:

(a,b,c) · (-4,1,2) = -4a + b + 2c = 0
(a,b,c) · (1,1,-1) = a + b - c = 0
(-4,1,2) · (1,1,-1) = -4 + 1 - 2 = -5

We can solve the first two equations for b and c in terms of a:

b = 4a
c = -a

Substituting back into the first equation:

-4a + 4a - 2a = 0
a = 0

Therefore, the only solution is a = b = c = 0, which means the vectors are not linearly independent and do not form an orthogonal set.

For Exercises 9-12:

We can use the formula for the projection of a vector v onto a unit vector u:

proj_u v = (v · u)u

To express v in terms of the basis B = {u1, u2, u3}, we can use the projections:

v = proj_u1 v + proj_u2 v + proj_u3 v

Substituting in the given vectors:

u1 = (1,0,1)
u2 = (1,1,0)
u3 = (-1,2,1)

To find the projections, we need to normalize the basis vectors:

|u1| = sqrt(2)
|u2| = sqrt(2)
|u3| = sqrt(6)

u1' = u1 / |u1| = (1/sqrt(2), 0, 1/sqrt(2))
u2' = u2 / |u2| = (1/sqrt(2), 1/sqrt(2), 0)
u3' = u3 / |u3| = (-1/sqrt(6), 2/sqrt(6), 1/sqrt(6))

Now we can calculate the projections:

proj_u1 v = (v · u1')u1' = (1*1/sqrt(2) + 0*0 + 1*1/sqrt(2))(1/sqrt(2), 0, 1/sqrt(2)) = (1/sqrt(2), 0, 1/sqrt(2))
proj_u2 v = (v · u2')u2' = (1*1/sqrt(2) + 1*1/sqrt(2) + 0*0)(1/sqrt(2), 1/sqrt(2), 0) = (1/sqrt(2), 1/sqrt(2), 0)
proj_u3 v = (v · u3')u3' = (-1*1/sqrt(6) + 2*2/sqrt(6) + 1*1/sqrt(6))(-1/sqrt(6), 2/sqrt(6), 1/sqrt(6)) = (0, 1, 0)

Therefore, v = (1/sqrt(2), 0, 1/sqrt(2)) + (1/sqrt(2), 1/sqrt(2), 0) + (0, 1, 0) = (1/sqrt(2), 1/sqrt(2), 1/sqrt(2)).
To find values a, b, and c such that {u, U2, U3} is an orthogonal set, we need to ensure that the dot product of any two of these vectors is zero. Given the vector u = [4, 7], let's represent U2 as [b, a] and U3 as [c, -E]. We will calculate the dot products and set them equal to zero.

1. u · U2 = (4 * b) + (7 * a) = 0
2. u · U3 = (4 * c) - (7 * E) = 0
3. U2 · U3 = (b * c) - (a * E) = 0

Now we have a system of three equations with three unknowns (a, b, and c). Unfortunately, since E is not specified, we cannot provide a unique solution for a, b, and c. If you can provide the value for E, we can then solve for a, b, and c.

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Answer:

\( \sqrt{30} \)

Answer:

4x and 3z are the only 2 terms in this esxpression.

The values of trigonometric functions sin(x/2) is \(\sqrt{\frac{7+4\sqrt{3}}{14}}\), cos(x/2) is \(\frac{1}{\sqrt{14(7+4\sqrt{3})}}\) and tan(x/2) is 7+4√3.

Given that the value of trigonometric function csc(x)=7 for 90°<x<180°.

We are given:

csc(x)=7 Where: 90° < x < 180°

This interval indicates that the angle x in the second quadrant and we know that at that quadrant sin(x) and CSC(x) functions are positive and all other trigonometric functions sign are negative.

Now:

sin(x)=1/csc(x)

sin(x)=1/7

Using the trigonometric identity sin²x+cos²x=1, we get

cosx=±√(1-sin²x)

cosx=±√(1-(1/7)²)

cosx=±√((49-1)/49)

cosx=±(4√3)/7

As x is in second quadrant.

Therefore, cosx=-(4√3)/7

consider the inequality, 90°<x<180°

Divide by 2, we get

45°<x/2<90°

This is the angle x/2 in the first quadrant and in that quadrant all functions sign are positive.

Substitute the value of cosx in half angle formula for sine function,

\(\begin{aligned}\cos x&=1-2\sin^2\left(\frac{x}{2}\right)\\ -\frac{4\sqrt{3}}{7}&=1-2\sin^2\left(\frac{x}{2}\right)\\ 2\sin^2 \frac{x}{2}&=1+\frac{4\sqrt{3}}{7}\\\sin \frac{x}{2}&=\pm\sqrt{\frac{7+4\sqrt{3}}{14}}\end\)

As x/2 lies in first quadrant then \(\sin \frac{x}{2}=\sqrt{\frac{7+4\sqrt{3}}{14}}\)

Again, Substitute the value of cosx in half angle formula for sine function,\(\begin{aligned}\sin x&=2\sin\left(\frac{x}{2}\right)\cos\frac{x}{2}\\ \frac{1}{7}&=2\sqrt{\frac{7+4\sqrt{3}}{14}}\cos\left(\frac{x}{2}\right)\\ \cos \frac{x}{2}&=\frac{1}{14\times\frac{\sqrt{7+4\sqrt{3}}}{\sqrt{14}}}\\\cos \frac{x}{2}&=\frac{1}{\sqrt{14(7+4\sqrt{3})}}\end\)

Now find tan(x/2) as shown below, we get

\(\begin{aligned}\tan\frac{x}{2}&=\frac{\sin\frac{x}{2}}{\cos \frac{x}{2}}\\&=\frac{\sqrt{7+4\sqrt{3}}}{\sqrt{14}}\times \frac{\sqrt{14}\sqrt{7+4\sqrt{3}}}{1}\\&=7+4\sqrt{3}\end\)

Hence, when trigonometric function csc(x)=7 for 90°<x<180° then sin(x/2) is \(\sqrt{\frac{7+4\sqrt{3}}{14}}\), cos(x/2) is \(\frac{1}{\sqrt{14(7+4\sqrt{3})}}\) and tan(x/2) is 7+4√3.

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T-test is commonly used to examine whether two groups are significantly different from each other or not.

A t-test is an inferential statistic used to determine if there is a significant difference between the means of two groups and how they are related. T-tests are used when the data sets follow a normal distribution and have unknown variances, like the data set recorded from flipping a coin 100 times.

It is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another.

T-test is used to determine whether two groups are different or not.

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The T-test is commonly used to examine whether two groups are significantly different from each other or not.

A T-test is used to determine if two groups are different.

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The mean of the given data is 25.396, rounded to three decimal places. The median is 25.400, also rounded to three decimal places. The standard deviation is 0.018, rounded to three decimal places.

The minimum value in the data is 25.37, rounded to two decimal places, and the maximum value is 25.42, also rounded to two decimal places.

The mean is calculated by summing up all the data points and dividing by the number of data points. In this case, the data points were not provided, so we cannot calculate the exact mean.

The median is the middle value in a sorted list of data. It is calculated by arranging the data in ascending order and finding the value that falls exactly in the middle. If there is an even number of data points, the median is the average of the two middle values.

The standard deviation measures the spread or dispersion of the data. It quantifies how much the individual data points deviate from the mean. A smaller standard deviation indicates that the data points are closely clustered around the mean.

The minimum and maximum values simply represent the smallest and largest values in the given data set.

These statistical measures provide useful information about the central tendency, spread, and range of the data, allowing for a better understanding of the dataset's characteristics.

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Answer:

The function is not continuous on the interval, so the extreme value theorem does not apply

Step-by-step explanation:

Recall that the Extreme Value Theorem states that if a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the interval. Given that the function is discontinuous at x=0 which gives off a vertical asymptote, this does not meet the requirements of the theorem.

Answer:

I think it's C.

Step-by-step explanation:

A. and D. don't make any sense so I assume they're incorrect. B. just seems wrong also by a small margin.

The area A of the region bounded by the functions f(x) = 2x\(x^{2}\)2/3 - x - 4 and g(x) = x\(x^{2}\)2 - 2x/3 - 6 can be calculated using the integral: A = int_[−2, 4] f(x) - g(x) dx. The integral evaluates to A = 65/3 units.

To evaluate the integral, we will first use u-substitution with u = x\(x^{2}\)2/3 and du = 2x/3dx. This substitution simplifies the integral to A = int_[−2\(x^{2}\)3, 4\(x^{2}\)3] (2u/3 - u - 4) du.

Next, we use integration by parts with u = 2u/3 - u - 4 and dv = du. This gives us A = (2u/3 - u - 4)v - int_[−2\(x^{2}\)3, 4\(x^{2}\)3] vdu.

We can now find the integral for v by integrating du, giving us v = u + C. Since v must equal zero when u = −2\(x^{2}\)3, we can set C = -2\(x^{2}\)3 and simplify the integral to A = (2u/3 - u - 4)(u + -2\(x^{2}\)3) - int_[−2\(x^{2}\)3, 4\(x^{2}\)3] (u + -2\(x^{2}\)3)du.

Finally, we can find the integral for u + -2\(x^{2}\)3 by integrating du again, giving us (u + -2\(x^{2}\)3) = 3u\(x^{2}\)2/2 + 2\(x^{2}\)3u + C. We can set C = 0 since u + -2^3 must equal zero when u = −2\(x^{2}\)3, and simplify the integral to A = (2u/3 - u - 4)(u + -2\(x^{2}\)3) - int_[−2\(x^{2}\)3, 4\(x^{2}\)3] (3u\(x^{2}\)2/2 + 2\(x^{2}\)3u) du.

Evaluating this integral gives us A = (2u/3 - u - 4)(u + -2\(x^{2}\)3) - 3(4\(x^{2}\)5/2 + 8\(x^{2}\)4)/2 + 2\(x^{2}\)3(4\(x^{2}\)3 + 8\(x^{2}\)2)/2. Substituting in u = 4\(x^{2}\)3 and u = -2\(x^{2}\)3 gives us A = 65/3 units.

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The SI units of the proportionality constant G is Newton \(Kg^{-2} m^2\)

Gravitational force is given by Newton's law of gravitation which states that every particle of matter in the cosmos is drawn to every other particle by a force of attraction that varies directly with the product of their masses and is inversely proportional to the square of the distance or degree of separation from each other.

F = G \($ \frac{m_1 m_2}{r^2}\)

Upon rearranging the terms we get,

G = \($\frac{F r^2}{m_1 m_2}\)

Where F is the gravitational force, \(m_{1}\) and \(m_{2}\) are masses, and r is the length.

Force has the SI units kg · m/s2

The SI units of the proportionality constant G

SI Unit of G = \($\frac{(\text { Newton })\left(\mathrm{m}^2\right)}{\mathrm{kg} ^2}\)

= Newton \(Kg^{-2} m^2\)

Therefore the units are Newton \(Kg^{-2} m^2\)

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Newton's law of universal gravitation is represented by F = G \($ \frac{m_1 m_2}{r^2}\) where F is the gravitational force, \(m_{1}\) and \(m_{2}\) are masses, and r is a length. force has the SI units kg· m/s2. what are the SI units of the proportionality constant G?

The value of sin(u+v) given tan u = 15/8 is -9/221

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the their angles.

A right-angled triangle has 3 sides, hypotenuse, opposite and adjacent. The following should be noted:

Sin = Opposite / Hypothenuse

Tan = Opposite / Adjacent

Cos = Adjacent / Hypothenuse

When tan u = 15/8

Opposite = 15

Adjacent = 8

Hypothenuse will be:

= ✓(15² + 8²)

= ✓(225 + 64)

= ✓289

= 17

Therefore sin u = 15/17

When cos v = -5/13, it should be noted that sin v will be -12/13.

Therefore, sin(u + v) will be:

= 15/17 + (-12/13)

= 15/17 - 12/13

= 195/221 - 204/221

= -9/221

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Answer:

Step-by-step explanation:

B

Answer:

29

Step-by-step explanation:

you could just plug in all you have done into a calculator unless step by step would be:

PEMDAS

-16(1.5)^2 + 10(1.5) + 50

-16(2.25) + 10(1.5)+50

-36 + 15 + 50

-36 + 65

29

Answer:

$1.50  per hour more then at the pool

Step-by-step explanation:

7.75 per hour at the pool

9.25 per hour at the beach

9.25 - 7.75 = $1.5

Answer:

Step-by-step explanation:

This is the correct answer

Answer:

The missing value of the table is 1,800 .

The probabilities for the hypergeometric distribution with the given parameters are:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

To determine the probabilities for the hypergeometric distribution with the given parameters, we can use the following formula:

P(X = k) = (choose(K, k) * choose(N-K, n-k)) / choose(N, n)

where "choose(a, b)" represents the binomial coefficient, calculated as a! / (b! * (a - b)!)

Let's calculate the probabilities:

a. P(X = 1):

P(X = 1) = (choose(20, 1) * choose(100-20, 4-1)) / choose(100, 4)

        = (20 * 80) / 3921225

        ≈ 0.000407

b. P(X = 6):

P(X = 6) = (choose(20, 6) * choose(100-20, 4-6)) / choose(100, 4)

        = (38760 * 0) / 3921225

        = 0

c. P(X = 4):

P(X = 4) = (choose(20, 4) * choose(100-20, 4-4)) / choose(100, 4)

        = (4845 * 80) / 3921225

        ≈ 0.098117

d. P(X = 0):

P(X = 0) = (choose(20, 0) * choose(100-20, 4-0)) / choose(100, 4)

        = (1 * 77) / 3921225

        ≈ 1.97e-05

Therefore:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

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The complete question is:

Suppose that X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: a. P(X = 1) b. P(X = 6) c. P(X = 4) d. P(X = 0).