2. Generate two ordered pairs by substituting
zero for x and y. Then, find the rate of change.
4x-8y = -32

The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer:

This equation is never true since 1/2 = -1/2 is false.

Answer: (1) C. 65 + 28H < 250

(2) 6

Step-by-step explanation:

Here is the correct question:

Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $65 along with an

hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford.

Let H represent the whole number of hours that the plumber works.

1) Which inequality describes this scenario?

Choose 1 answer:

A. 28 + 65H < 250

B. 28 + 65H > 250

C. 65 + 28H < 250

D. 65 +28H > 250

2) What is the largest whole number of hours that Anand can afford?​

Since the initial fee charged by the plumber is $65 and an hourly rate of $28, and Anand would like to spend no more than $250. This means that the addition of the initial fee plus the hourly fee based on number of hours worked will have to be less than $250. This can be mathematically expressed as:

= 65 + 28H < 250

That means option C is the correct answer.

Option B and D are incorrect because the greater sign was used but Anand doesn't want to spend more than $250 but the options denoted that he spent more than $250 which isn't correct.

2)'The largest whole number of hours that Anand can afford goes thus:

65 + 28H < 250

28H < 250 - 65

28H < 185

H < 185/28

H < 6.6

Therefore, the largest whole number of hours that Anand can afford is 6.

Answer: The Answer is 65+28H < 250 and the largest amount of hours is 6

Step-by-step explanation:

Answer:

b) The average speed at which he travelled for the whole journey

Step-by-step explanation:

If he had travel 200- km/h and had broke down by which was at 10:30 a.m  you would have to subtract 200 km/h to 10:30  your answer would be 189.7 when they back on the road also the speed slowed down a bit about 50 km/h so you would add 50 km/h to 20 mins you would get 70km/h they were traveling by, then you add all of the numbers up by 100 you would get 640 so your answer would be 640

Answer:

The scale factor is 1 to 1.3

Step-by-step explanation:

Here, we want to get the scale factor

To get the scale factor, we divide corresponding sides by each other

That, we have that

9/7 = 1.3

the equation of the line passing through (-4,5) and (2,-13) is y=-3x-7.

To find the equation in terms of x of the line passing through the points (-4,5) and (2,-13), we will use the point-slope form.

In point-slope form, we use one point and the slope of the line to get its equation in terms of x.

Given two points: (-4,5) and (2,-13)The slope of the line that passes through the two points is found by the formula

\(\[m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]\)

Substituting the values of the points

\(\[\frac{-13-5}{2-(-4)}=\frac{-18}{6}=-3\]\)

So the slope of the line is -3.

Using the point-slope formula for a line, we can write

\(\[y-y_{1}=m(x-x_{1})\]\)

where m is the slope of the line and (x₁,y₁) is any point on the line.

Using the point (-4,5), we can rewrite the above equation as

\(\[y-5=-3(x-(-4))\]\)

Now we simplify and write in terms of\(x[y-5=-3(x+4)\]\y-5\\=-3x-12\]y=-3x-7\]\)So, the main answer is the equation of the line passing through (-4,5) and (2,-13) is y=-3x-7. Therefore, the correct answer is option B.

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The launching angle of the plane which has reached a height of 35000 ft is 15°

Let the distance travelled by the airplane horizontally be AB

The height reached by the airplane be BC

Thus AB = 130000 ft

        BC = 35000 ft

The launching angle of the airplane can be found using the formula

                                   tanθ = opposite / adjacent

                                                    (or)

                                           tanθ  = BC / AB

Let us substitute the known values in the above equation, we get

                                          tanθ  = 35000/130000

                                          tanθ  = 0.2692

                                               θ  = tan⁻¹ (0.2692)

                                               θ  = 15.067°

                                               θ  ≅ 15°

Therefore , the launching angle of the airplane is 15°

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The table that shows a proportional relationship is Table D.

Please find attached the graph of Table D created with MS Excel

The variables x and y in a set of ordered pair (x, y), are proportionally related, when the ratios of the x and y values for of all data points in the set are equivalent, such that a proportional relationship can be expressed in the form; y = k·x

Where;

k = The constant of proportionality

Therefore; k = y/x

The ratio of the y-values to the corresponding x-values in the table that shows a proportional relationship is therefore a constant.

Analyzing the Table C, we get;

The points are; (2, 1), (4, 3), (6, 5), (8, 7)
x/y for each data point is therefore;

1/2 ≠ 3/4 ≠ 5/6 ≠ 7/8

Table C does not show a proportional relationship

The coordinate points in Table D are; (2, 1), (6, 3), (8, 4), (10, 5)

The ratio, x/y at each point in the table are therefore;

1/2 = 3/6 = 4/8 = 5/10 = 1/2

The ratio, x/y at each point in the table is constant, therefore, Table D ahows a proportional relationship.

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This is not a probability model because at least one probability is less than 0

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

Color      Probability

Red          0.3

Green      -0.2

Blue         0.2

Brown      0.4

Yellow      0.2

Orange     0.1

The general rule is that

The smallest value of a probability is 0, and the maximum is 1

In the above, we have

P(Green) = -0.2

Hence, it is not a probability model

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Question

Color      Probability

Red          0.3

Green      -0.2

Blue         0.2

Brown      0.4

Yellow      0.2

Orange     0.1

determine why it is not a probability model. choose the correct answer below.

a. this is not a probability model because the sum of the probabilities is not 1.

b. this is not a probability model because at least one probability is greater than 0.

c. this is not a probability model because at least one probability is less than 0.

d. this is not a probability model because at least one probability is greater than 1.

Answer:

0.5

Step-by-step explanation:

The value of the trigonometry identity is tan(2x) = 4/7[√2]

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

cos(x) = 2√5/5 and 3π/2 < x < 2π

Start by calculating the sine function sin(x) using

sin(x) = √[1 - cos²(x)]

So, we have

sin(x) = √[1 - (2√5/5)²]

This gives

sin(x) = 1/10[√10]

The tangent is then calculated as

tan(2x) = (2sin(x)cos(x))/(cos²(x) - sin²(x))

This gives

tan(2x) = (2 * 1/10[√10] * (2√5/5))/(((2√5/5))² - (1/10[√10])²)

Evaluate

tan(2x) = 4/7[√2]

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Answer Las raíces de la ecuación x2 − 6x + 7 = 0 son α y β. Encuentra la ecuación con raíces α + 1 β y β + 1 α. Deduzco que α + β = − b a = 6 1 = 6 y que αβ = c a = 7 1 = 7.

Step-by-step explanation:

Step-by-step explanation: First, you have to multiply the numerators, for example, 1/2 x 1/4. 1x1=1. Then the denominator. 2x4=8. So, 1/2x1/4=1/8

Applying the definition of congruent triangles:

1. QS = 57 units; TV = 57 units

2. m∠B = 3°; m∠Q = 3°

The triangles that are congruent to each other have corresponding parts that are congruent, that is their corresponding sides and angles are equal to each other.

1. Given that triangles QRS and TUV are congruent triangles, therefore:

QS = TV [corresponding congruent sides]

QS = 4v + 5

TV = 5v - 8

Therefore:

4v + 5 = 5v - 8

4v - 5v = -5 - 8

-v = -13

v = 13

QS = 4v + 5 = 4(13) + 5 = 57 units

TV = 5v - 8 = 5(13) - 8 = 57 units

2. Given that triangles ABC and PQR are congruent, therefore:

m∠B = m∠Q

m∠B = 2v + 1

m∠Q = 8v - 5

Therefore:

2v + 1 = 8v - 5

2v - 8v = -1 - 5

-6v = -6

v = -6/-6

v = 1

m∠B = 2v + 1 = 2(1) + 1 = 3°

m∠Q = 8v - 5 = 8(1) - 5 = 3°

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Answer:

36

Step-by-step explanation:

12 x 3 =36

hope this helped :)

It can be concluded that the system manager's belief is supported by the data collected from the sample.

The hypothesis test is conducted to determine whether the percentage of spam emails at the corporation is greater than 69%. The null hypothesis is that the percentage of spam emails at the corporation is equal to or less than 69%, while the alternative hypothesis is that the percentage is greater than 69%.

A random sample of 500 emails is selected, and 365 of them are found to be spam. The significance level is set to 0.01 and 0.05, and the -value method is used with the table to determine if there is sufficient evidence to reject the null hypothesis.

The -value for the hypothesis test is calculated to be 0.0005. At the a=0.01 level of significance, the -value is less than the critical value of 2.33. Therefore, there is sufficient evidence to reject the null hypothesis and conclude that the percentage of spam emails at the corporation is greater than 69%.

At the a=0.05 level of significance, the -value is still less than the critical value of 1.645. Hence, there is also enough evidence to reject the null hypothesis at this level and conclude that the percentage of spam emails at the corporation is greater than 69%.

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Answer:

one

Step-by-step explanation:

The perpendicular distance from the point P(9, 8, 5) ft to the plane defined by A(3,9, 2) ft, B( – 2, – 7, 6) ft, and C(2, 3, -1) ft is 2 ft.

We should track down the opposite separation from the point P(13, 6, 5) m to the plane characterized by the three focuses A(1,8, 4) m, B( − 4, — 6, 6) m and C ( - 4, 2, 3) m. The equation for the opposite distance is given by the distance of the point P (x1, y1, z1) from the plane Hatchet + By + Cz + D = 0 is given by the formula:|Ax1

= By1 + Cz1 + D|/√(A²+B²+ C²) So we initially decide the condition of plane ABC utilizing any two focuses, for example, An and B. Utilizing two focuses the condition of the line through An and B is : Simplifying, 6y - 8x + 10z - 40 = 0 or 3y - 4x 5z - 20 = 0 means that A = 3, B = -4, C = 5, and D = -20. y - 8 / 6y - 8 = (z - 4) / (4 - 8) x - 1 / (-4 - 1) = (y - 8) / (6 - 8)

The vertical distance formula is given by the distance of the point P (x1, y1), z1) from the plane Ax By Cz D = 0 is given by the formula:|Ax1 By1 Cz1 D| / (A2 + B2 +C2)So we first determine the equation of the plane ABC using any two points such as A and B. Using the two-point form, we get the equation of the line through A and B from the equation: Simplifying, 7y - 4x - 3z15 = 0So, A = 7, B = -4, C = -3, and D = -15. y - 9) / (9 - 2) = (z - 2) / (2 - 3)x - 3 / (3 - 2) = (y - 9) / (9 - 2)

The following results are obtained by entering these numbers into the preceding formula:|7 (9) - 4 (8) - 3 (5) - 15| / (72+ (-4)2 + (-3)2) = 274 / 74 = 2. Accordingly, the perpendicular distance that separates P(9, 8, 5) feet from A(3, 9), 2) feet, B (– 2, – 7, 6) feet, and C(2, 3, -1) feet is 2

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Answer: 1/2

Step-by-step explanation: u go up one and then go to the right two times

The measure of angle ∠S in triangle RST is approximately 103.1 degrees.

To find the measure of angle ∠S in triangle RST, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and opposite angles A, B, and C respectively, the following equation holds true:

\(c^2 = a^2 + b^2 - 2abcos(C)\)

In our case, we know the side lengths r = 23 cm, s = 99 cm, and t = 94 cm. We want to find the measure of angle ∠S. Let's substitute the known values into the Law of Cosines equation:

s^2 = r^2 + t^2 - 2rtcos(S)

99^2 = 23^2 + 94^2 - 2(23)(94)cos(S)

9801 = 529 + 8836 - 4348cos(S)

9801 = 9365 - 4348cos(S)

4348cos(S) = 9365 - 9801

4348cos(S) = -436cos(S) = -436 / 4348

cos(S) ≈ -0.1

To find the measure of angle S, we can take the inverse cosine (cos^-1) of -0.1:

S ≈ cos^-1(-0.1)

Using a calculator, we find that S ≈ 103.13 degrees (rounded to the nearest 10th of a degree). Therefore, the measure of angle ∠S in triangle RST is approximately 103.1 degrees.

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Still 5 seconds.

(Assuming the Earth around that building is flat.

Answer:

x=-8

Step-by-step explanation:

pls give me brainliest

Answer:

-2x+ 8 = 10.

Simplified answer: 8.

I tried my best.

Step-by-step explanation:

The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey

The perimeter of one of the semi-circles is 43.3 cm.

To find the perimeter of one of the semi-circles, we first need to find the radius of the original circle. The circumference of a circle is equal to 2pir, where r is the radius of the circle and pi is a constant approximately equal to 3.14.

We can use this formula to solve for the radius:

r = circumference / (2pi)

= 86 cm / (23.14)

= 13.68 cm

Now that we know the radius, we can find the perimeter of one of the semi-circles. The perimeter of a semi-circle is equal to pi*r, so the perimeter of one of the semi-circles is:

perimeter = pi*r

= 3.14 * 13.68 cm

= 43.32 cm

Rounded to the nearest 1/10 cm, the perimeter of one of the semi-circles is 43.3 cm.

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Answer:

A′(−2.5, 3.75), B′(−1.25, 1.25), C′(2.5, −1.25), D′(2.5, 2.5)

Step-by-step explanation:

in the described situation you only need to multiply the coordinates by the scale factor (in our case the given 5/8)

A (-4, 6) turns into

A' (-4×5/8, 6×5/8) = A' (-2.4, 3.75)

and therefore we know already here that all the other answer options are wrong.

Answer: D. height when first thrown

Step-by-step explanation:

         The constant term, 5, in this equation represents the height of the ball when it was first thrown. This means that our answer is option D.

         This constant term (5) is also the y-intercept. When we graph this equation, the line starts at (0, 5) if you ignore the negative values since we cannot have a negative time for this scenario. This is a visual representation of the ball being thrown.

In the expansion of (2a+4b)⁸ the possible variable terms are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expansion is given by the following formula: \(\left(a + b\right)^{n} = \sum_{k=0}^{n} {\binom{n}{k}} a^{n - k} b^{k}\), where \({\binom{n}{k}} = \frac{n!}{\left(n - k\right)! k!}\)

As given to us, a = 2a, b = 4 b, and n = 8.

Therefore, \(\left(2 a + 4 b\right)^{8} = \sum_{k=0}^{8} {\binom{8}{k}} \left(2 a\right)^{8 - k} \left(4 b\right)^{k}(2a+4b)\).

Thus, \(\left(2 a + 4 b\right)^{8} = 256 a^{8} + 4096 a^{7} b + 28672 a^{6} b^{2} + 114688 a^{5} b^{3} + 286720 a^{4} b^{4} + 458752 a^{3} b^{5} + 458752 a^{2} b^{6} + 262144 a b^{7} + 65536 b^{8}.\)

Hence, In the expansion of (2a+4b)⁸ the possible variable terms are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.

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f(x) and g(x) are inverse functions as they intersect at y = x.

Given,  f(x) = x³, g(x) = 3√x(a) Algebraically f(g(x)) = f(3√x) ⇒ f(g(x)) = (3√x)³= 27x¹/²g(f(x)) = g(x³) ⇒ g(f(x)) = 3√(x³)⇒ g(f(x)) = 3x^(3/2)

Verify graphically:

We have to show that the composition of these two functions is the identity function: f(g(x)) = x and g(f(x)) = x

We can use the graph of f and g to verify graphically.

Given, f(x) = x³, g(x) = 3√xThe graph of f(x) and g(x) are as follows:

Graph of f(x)Graph of g(x)

To verify graphically, we need to make sure that the two curves intersect at y = x.

Since we are given the function that defines each curve, we can set them equal to each other to see where they intersect:

f(x) = g(x)⇒ x³ = 3√x^3⇒ x³ = 3x^(3/2)⇒ x^(1/2) = 3⇒ x = 9  (x cannot be negative since g(x) only takes positive values)

Therefore, the intersection of the two curves occurs at the point (9, 9).

Thus, f(x) and g(x) are inverse functions as they intersect at y = x.

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Answer:

Its B

Step-by-step explanation:

The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 is given by: Option B: 0.284 approx.

Suppose two dimensions are there, viz X and Y. Some values of X are there as \(X_1, X_2, ... , X_n\) and some values of Y are there as \(Y_1, Y_2, ... , Y_n\)

List them in title of the rows and left to the columns. There will be \(n \times k\) table of values will be formed(excluding titles and totals), such that:

Value(ith row, jth column) = Frequency for intersection of  \(X_i\)  and \(Y_j\)  (assuming X values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

\(\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}\)

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

\(P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}\)

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

The missing frequency table is attached below. If we name events as:

Then, the needed probability is P(B|A) (as it is already specified that the person would be older than 35 years.)

Using the table, we get:

\(P(A) = \dfrac{\text{Total person who are older than 35 years age}}{\text{Total person in survey}}\\\\P(A) = \dfrac{162}{429} \approx 0.3776\)

Using the table, we get the value on the place where A and B both occur(when person selected is older than 35 years and have hemoglobin between 9 and 11 ) as:

\(n(A \cap B) = 162 - 40 - 76 = 46\)

Thus, we get:

\(\\\\P(A\cap B) = \dfrac{\text{Total person older than 35 years age and have hemoglobin level between 9 and 11}}{\text{Total person in survey}}\\\\P(A \cap B) = \dfrac{46}{429} \approx 0.1072\)

Using the chain rule, we get:

\(P(B|A)P(A) = P(A\cap B)\\\\P(B|A) = \dfrac{P(A \cap B)}{P(A)} = \dfrac{0.1072}{0.3776} \approx 0.284\)

Thus, the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 is given by: Option B: 0.284 approx.

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