Which of the following inequalities are correct?
Some of the numbers involved are shown on the number line below.

Option D is the right option. The maximum height of the ball was 2.5 seconds after it was thrown.

Let b and h be the zeros of the function f(x). If this statement is true, then f(x)= k(x-a)(x-b) would be our equation. Let k be our coefficient.

From the given table,

At t = 0

h(0)= 0

At t = 5

h(5) = 0

So, 0 and 5 are the zeros of the function h(t).

h(t)=k(t-0)(t-5)

h(t)=k(t)(t-5)

Now substitute any point from the table i.e, (2, 96) in [1] to find k.

96=k(2)(2-5)

96=k(2)(-3)

Now, we simplify!

96=-6k

k=-16

Now, we have the equation for h(t)

h(t)=-16(t-5)

h(1)=-16t^2+80t

Initial height of the ball: h(0) = 0   To find the maximum height of the ball, we will use the quadratic equation  y=ax^2+bx+c.....[2], the the axis of symmetry is given by: x=-b/2a

Now that we know b= -16 and h= 80 we can perform this equation to find out for t:

t=-80/2(-16)=80/32=2.5 seconds

We can now come to the conclusion that the statement "The maximum height of the ball was reached 2.5 seconds after it was thrown." is the one true statement.

I hope this helps!!  o(〃＾▽＾〃)o

Answer: 81

Step-by-step explanation:

To estimate the mean per capita income for a major city in California with an error of at most $0.56 at the 85% confidence level, the economist needs to determine the required sample size.

To calculate the required sample size, we can use the formula: \(n = \left(\frac{{Z \cdot \sigma}}{{E}}\right)^2\), where \(n\) is the sample size, \(Z\) is the Z-score corresponding to the desired confidence level (in this case, for 85% confidence level, \(Z \approx 1.44\)), \(\sigma\) is the known standard deviation (\$6.6), and \(E\) is the desired margin of error (\$0.56). Plugging in the values, we have \(n = \left(\frac{{1.44 \cdot 6.6}}{{0.56}}\right)^2 \approx 52\). Therefore, a sample size of approximately 52 would be required to estimate the mean per capita income with an error of at most $0.56 at the 85% confidence level.

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Answer:

\(x = \dfrac{\sqrt{22}}{2}\)

Step by step explanation:

\(\text{This is an isosceles right triangle}~ \left(45^{\circ} - 45^{\circ} - 90^{\circ}\right).\\\\\text{Apply Pythagorean theorem,}\\\\~~~~~~\left(\sqrt{11}\right)^2 =x^2 +x^2 \\\\\implies 11 = 2x^2 \\\\\implies x^2 = \dfrac{11}2\\\\\implies x = \sqrt{\dfrac{11}{2}}\\\\\implies x = \dfrac{\sqrt{11}}{\sqrt 2}\\\\\implies x = \dfrac{\sqrt{11}\sqrt 2}{2}\\\\\implies x = \dfrac{\sqrt{22}}{2}\)

Step-by-step explanation:

im pretty sure it's 146

The answer is , the conditional probability that an even-numbered card is picked given that the 2 is picked is 1/2 or 0.5.

The conditional probability that an even-numbered card is picked given that the 2 is picked can be calculated using the formula for conditional probability.

Let's assume there are 52 cards in the deck, with half of them being even-numbered (26 cards) and 4 of them being twos (2 of which are even-numbered).

To find the conditional probability, we need to divide the number of favorable outcomes (even-numbered cards that are twos) by the total number of possible outcomes (all twos).

Therefore, the conditional probability can be calculated as:

Conditional Probability = Number of favorable outcomes / Number of possible outcomes

Conditional Probability = 2 / 4

Simplifying the fraction, we get:

Conditional Probability = 1/2

So, the conditional probability that an even-numbered card is picked given that the 2 is picked is 1/2 or 0.5.

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The magnitude of the resultant force can be found using the law of cosines, and it is approximately 692 pounds.

The direction of the resultant force can be found using the law of sines, and it is approximately 14.6° with respect to the positive x-axis

To find the magnitude of the resultant force, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of their magnitudes and the cosine of the included angle.

In this case, the two sides are the magnitudes of the given forces (300 pounds and 500 pounds), and the included angle is the angle between the forces.

Applying the law of cosines, we have: Resultant force^2 = 300^2 + 500^2 - 2 * 300 * 500 * cos(60° - (-45°))

Calculating this equation, we find that the resultant force^2 is approximately equal to 479,200 pounds^2. Taking the square root of this value, we get the magnitude of the resultant force, which is approximately 692 pounds.

To find the direction of the resultant force, we can use the law of sines. The law of sines states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, the sides are the magnitudes of the forces, and the opposite angles are the angles between the forces and the positive x-axis.

Applying the law of sines, we have: (sin θ) / 500 = (sin 60°) / Resultant force

Solving for θ, we find that sin θ is equal to (sin 60°) / (Resultant force / 500). Calculating this equation, we get sin θ is approximately 0.250.

Taking the inverse sine of this value, we find that θ is approximately 14.6°. Therefore, the direction of the resultant force is approximately 14.6° with respect to the positive x-axis.

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(a) The general solution of the homogeneous equation is \(yh(t) = e^{(-2t)}(Acos(t) + Bsin(t)).\)

(b) The particular solution of the forced equation is yp(t) = (-9/5)t + 47/5.

(c) The solution of the forced equation subject to the initial conditions is \(y(t) = e^{(-2t)}(sin(t))(9/5) - (9/5)t + 47/5.\)

(d) The overall behavior of the solution y(t) approaches (-9/5)t as t goes to infinity.

(a) The characteristic equation of the homogeneous equation y" + 4y' + 5y = 0 is given by r² + 4r + 5 = 0. Solving for r, we get r = -2 ± i. Therefore, the general solution of the homogeneous equation is \(yh(t) = e^{(-2t)}(Acos(t) + Bsin(t)).\)

(b) (1). To find a particular solution of the forced equation, we assume a solution of the form yp(t) = At + B.

Taking the derivatives of yp(t), we get yp'(t) = A and yp''(t) = 0. Substituting these into the original equation, we get:

0 + 4A + 5(At + B) = \(1 - e^{(-2t)}\)

Solving for A and B, we get A = -9/5 and B = 47/5. Therefore, a particular solution of the forced equation is yp(t) = (-9/5)t + 47/5.

(c) The general solution of the forced equation is \(y(t) = yh(t) + yp(t) = e^{(-2t)}(Acos(t) + Bsin(t)) - (9/5)t + 47/5.\) Using the initial conditions y(0) = 0 and y'(0) = 0, we get:

y(0) = A = 0, therefore A = 0

y'(0) = -2A + B - (9/5) = 0, therefore B = (9/5)

Thus, the solution of the forced equation subject to the initial conditions is \(y(t) = e^{(-2t)}(sin(t))(9/5) - (9/5)t + 47/5.\)

(d) The forcing function \(F(t) = 1 - e^{(-2t)}\) approaches 1 as t goes to infinity. As t approaches infinity, the exponential term \(e^{(-2t)}\) approaches zero, and the particular solution yp(t) approaches (-9/5)t.

Therefore, the overall behavior of the solution y(t) approaches (-9/5)t as t goes to infinity.

The function \(g(t) = e^{(-2t)}(sin(t))(9/5)\) approaches zero as t goes to infinity, so it does not have a significant impact on the long-term behavior of the solution.

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Answer:

The indicated z-score is 1.77

Step-by-step explanation:

procedure  finding the z-value is listed below:

1.From the table of the standard normal distribution, locate the probability value as 0.9616.

2.Move left until the first column is reached. Note as 1.7.

3.Move upward until the top row is reached. Note as 0.07.

4.Locate the probability value, by the intersection of the row and column values, gives the area to the left of z = 1.77

SEE THE FORMULA BELOW.

Answer:

True

Step-by-step explanation:

The population always grows by 5%, even though more bacteria are added with each hour. Each hour, due to exponential growth, the population size rises by 5%.

Answer: Your mom?

Step-by-step explanation: Your mom?

Answer:

x= 5/9 or 0.5556

Step-by-step explanation:

|2x-5| = -3x+4

|5x-5|=4

|5x|=9

|x|=5/9 or 0.5556

x= 5/9 or 0.5556

Answer:

B

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

If a radius of a circle and a tangent to a circle intersect at the point of tangency, then the radius and the tangent are perpendicular.

Answer: B.

Answer:

x = number of hours = 8 hours

Step-by-step explanation:

Let

x = number of hours

There are 3 people who rented bicycle from each shop

Ace bicycle shop:

Total cost = 3(4 + x)

= 12 + 3x

Best bicycle shop:

Total cost = 3(8 + 0.50x)

= 24 + 1.5x

Equate both equations and solve

12 + 3x = 24 + 1.5x

12 - 24 = 1.5x - 3x

-12 = -1.5x

x = -12/-1.5

x = 8 hours

x = number of hours = 8 hours

The coordinates of point P on the directed line segment AB, which divides AB in the ratio 1:3, are (5, 6.5).

To find the coordinates of the point P on the directed line segment AB that partitions AB in the ratio 1:3, we can use the concept of section formula.

Let's assume the coordinates of point P are (x, y). According to the section formula, the coordinates of P can be calculated as follows:

x = (3x2 + 1x1) / (3+1) = (37 + 1(-1)) / 4 = (21 - 1) / 4 = 20/4 = 5

y = (3y2 + 1y1) / (3+1) = (38 + 12) / 4 = (24 + 2) / 4 = 26/4 = 13/2 = 6.5

Therefore, the coordinates of point P on the directed line segment AB, which divides AB in the ratio 1:3, are (5, 6.5).

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The option that represents the first step is x² + 4x = -3

The equation is given as:

x² + 4x + 3 = 0

The first step is to isolate the constant.

So, we have:

x² + 4x = -3

Hence, the option that represents the first step is x² + 4x = -3

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Given number in factored form 7.7.7.7.7.7  can be represented in the following way :

Exponential form : 7⁶

Standard form. : 11.7649 × 10⁴

As given in the question,

Given number in factored form is equal to 7.7.7.7.7.7

Represent the given factored form number into exponential form and standard form is written as :

Exponential form is given by :

7.7.7.7.7.7

= 7¹⁺¹⁺¹⁺¹⁺¹⁺¹

= 7⁶

Standard form is given by :

7.7.7.7.7.7

= 117649

= 11.7649 × 10⁴

Therefore, given number in factored form 7.7.7.7.7.7  can be represented in the following way :

Exponential form : 7⁶

Standard form. : 11.7649 × 10⁴

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Answer:

12

Step-by-step explanation:

Create a ratio

AB : DE

5 : 4

BC : EF

15: x

5/4 = 15/x

5x = 15*4

5x = 60

x = 12

EF = 12

The value of the expression, in simplest form is 11/18.

The given expression is:

2 3/4 ÷ 4 1/2

We have to determine the value of the expression, in simplest form.

To solve the expression we first convert the mixed fraction in the form of improper fraction.

To convert 2 3/4 in the form of improper fraction multiply 2 by 4 then add the result of multiplication of 2 and 4 with 3.

So the improper form of 2 3/4 = 11/4

To convert 4 1/2 in the form of improper fraction multiply 4 by 2 then add the result of multiplication of 4 and 2 with 1.

So the improper form of 4 1/2 = 9/2

Now the simplest form of the expression is:

= 11/4 ÷ 9/2

We can write the expression as

= 11/4 × 2/9

After simplifying

= 11/2 × 1/9

= 11/18

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Answer:

Step-by-step explanation:

Use the table to find the slope and y-intercept

Find the slope:

Find b using the pair (1, 4):

The line is:

The y-intercept is 3

Answer:

b = 3

Step-by-step explanation:

Answer:

$21,240

Step-by-step explanation:

8 percent *9000 =

(8:100)*9000 =

(8*9000):100 =

72000:100 = $720 per years of interest

720* 17

= 12,240

12,240+9,000

= 21,240

Answer: 25 inches

Step-by-step explanation:

cos60 = adjacent over hypotenuse

cos60 = a/50

50cos60 = 25

Therefore, the justification for step 2 is "Addition Property of Equality" and the justification for step 3 is "Multiplication Property of Equality".

An equation is a mathematical statement that shows the equality of two expressions, usually separated by an equal sign. It means that the expressions on both sides of the equal sign represent the same value or quantity. Equations can involve one or more variables and may have different degrees of complexity. They are commonly used to model various real-world situations and to solve problems in mathematics, science, engineering, and other fields.

Here,

2. To isolate the variable term, add 9 to both sides. This yields:

x/2 - 9 + 9 = -4 + 9

Simplifying the left side, we get:

x/2 = 5

3. To solve for x, multiply both sides by 2. This yields:

x/2 * 2 = 5 * 2

Simplifying both sides, we get:

x = -10

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Answer:

C. LM ≅ JH

Step-by-step explanation:

The criteria that needs to be satisfied before two right triangles can be said to be congruent to each other is by the Hypotenuse-Leg Theorem are:

1. Both must have a corresponding leg that are congruent to each other.

In the diagram given above, NM is congruent to KH. They are corresponding legs that are congruent.

2. The hypotenuse of one triangle must be equal to that of the other.

We are not given if the hypotenuse of one, LM is congruent to the hypotenuse of the other, JH.

Therefore, the additional information required would be:

LM ≅ JH

After calculating the distance, Ranjan has driven 358.55 miles so far.

To solve this problem, we need to use the formula:

distance = fuel efficiency x fuel consumed

Let's start by calculating the total fuel consumed. At the first stop, Ranjan adds 6.7 gallons of gas, which means he consumed 6.7 gallons of gas since his tank was full at the beginning of the trip. At the second stop, he adds 3.4 gallons of gas, which means he consumed 3.4 gallons of gas between the first and second stops. Therefore, the total fuel consumed is:

6.7 + 3.4 = 10.1 gallons

Now we can calculate the distance driven using the fuel efficiency of 35.5 miles per gallon:

distance = 35.5 miles/gallon x 10.1 gallons = 358.55 miles

Therefore, Ranjan has driven 358.55 miles so far.

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Answer:

Can you add a screenshot of the equations? It's hard to figure it out in this format and I don't want to give you the wrong answer.

Step-by-step explanation:

Equation 1: x + y = $38

Equation 2: x = y + $6

Replace x in the first equation with the second equation :

y + 6 + y = 38

Simplify:

2y + 6 = 38

Subtract 6 from both sides:

2y = 32

Divide both sides by 2:

Y = 16

Now you know y, the cost of the jacket is $16

The shoes were $6 more so 15 + 6 = $22

Jacket cost $16

Shoes cost $22

Shoes: $22

Jacket: $16

Divide 38 by 2, which is 19

take away half of 6, which is 3.

Take 3 from 19, resulting in 16 which is your jacket

Add 3 to 19, resulting in 22 which are your shoes

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

The smallest angles of the triangle is angle A

In triangle ABC

The length of the side AB = 6.2 units

The length of the side AC = 9.5 units

The length of the side BC = 5.1 units

The opposite angle of AB is angle C, the opposite angle of AC is angle B and the opposite angle of BC is angle A

We know length of the line is BC which is 5.1 units which is the smallest side of the triangle. Then the opposite angle of BC will be the smallest angle in the triangle ABC

The opposite angle of the side BC is angle A, which is the smallest angle in the triangle

Hence, the smallest angles of the triangle is angle A

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