I REALLY need help asap !

Answer:

Step-by-step explanation:

Answer:

a) The initial height of the rock is of 48 feet.

b) It takes 1 seconds for the rock to reach maximum height.

c) The rock's maximum height is 50 feet.

d) It takes 6 seconds for the rock to land on the ground.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

\(f(x) = ax^{2} + bx + c\)

It's vertex is the point \((x_{v}, f(x_{v})\)

In which

\(x_{v} = -\frac{b}{2a}\)

If a<0, the vertex is a maximum point, that is, the maximum value happens at \(x_{v}\), and it's value is \(f(x_{v})\)

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}\)

\(\bigtriangleup = b^{2} - 4ac\)

In this question:

The height of the ball after t seconds, in feet, is given by:

\(h(t) = -2t^2 + 4t + 48\)

Which is a quadratic equation with \(a = -2, b = 4, c = 48\)

a) What is the initial height?

This is \(h(0) = 48\). So the initial height of the rock is of 48 feet.

b) How many seconds does it take to reach the maximum height?

This is the value of t at the vertex. So

\(t_{v} = -\frac{b}{2a} = -\frac{4}{2(-2)} = 1\)

It takes 1 seconds for the rock to reach maximum height.

c) What is the rock's maximum height?

This is the height of the ball after 1 second. So

\(h(1) = -2(1)^2 + 4(1) + 48 = 50\)

The rock's maximum height is 50 feet.

d) How many seconds does it take to for the rock to land on the ground?

This is t for which \(h(t) = 0\), so we solve the quadratic equation.

\(\bigtriangleup = (4)^2-4(-2)(48) = 400\)

\(t_{1} = \frac{-4 + \sqrt{400}}{2*(-2)} = -4\)

\(t_{2} = \frac{-4 - \sqrt{400}}{2*(-2)} = 6\)

Time is a positive measures, so it takes 6 seconds for the rock to land on the ground.

Step-by-step explanation:

I am not sure about the units in 11. to 14.

is it also m (meter) ? the please add this to the result numbers.

11.

Pythagoras at the core :

x² + y² = (22×sqrt(3))² = 22²×3 = 484×3 = 1452

then we can use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with the sides being opposite of the related angles.

so,

22×sqrt(3)/sin(90) = y/sin(60)

22×sqrt(3)/1 = y/sin(60)

y = 22×sqrt(3)×sin(60) = 33

and now in the original Pythagoras equation :

x² + 33² = 1452

x² = 1452 - 33² = 1452 - 1089 = 363

x = sqrt(363) = 19.05255888... ≈ 19.1

12.

the same basic approach :

x² + sqrt(6)² = y²

x² + 6 = y²

then the law of sine :

y/sin(90) = y/1 = sqrt(6)/sin(30) = sqrt(6)/0.5

y = sqrt(6)/ 1/2 = sqrt(6)×2/1 =

= 2×sqrt(6) = 4.898979486... ≈ 4.9

back to the original Pythagoras :

x² + 6 = 4.9²

x² = 24 - 6 = 18

x = sqrt(18) = 4.242640687... ≈ 4.2

13.

the same basic approach again :

y² = x² + (4×sqrt(21))² = x² + 16×21 = x² + 336

the law of sine :

y/sin(90) = y/1 = 4×sqrt(21)/sin(60)

y = 21.16601049... ≈ 21.2

21.2² = x² + 336

448 - 336 = x² = 112

x = sqrt(112) = 10.58300524... ≈ 10.6

14.

there is a line shared by both triangles.

let's call it "a".

y² = z² + a²

a/sin(90) = a/1 = 17/sin(30) = 17/0.5 = 2×17 = 34

a² = 17² + x²

34² = 17² + x²

1156 = 289 + x²

x² = 1156 - 289 = 867

x = sqrt(867) = 29.44486373... ≈ 29.4

y/sin(90) = y/1 = a/sin(45) = 34/sin(45)

y = 48.08326112... ≈ 48.1

48.1² = z² + 34²

2312 = z² + 1156

z² = 2312 - 1156 = 1156

z = 34

15.

equilateral means all sides are equally long.

since the base is 8 m, it means that also both roof sides are 8 m.

the height in such a triangle creates a right-angled triangle with one roof side as Hypotenuse and half the base as second leg.

8² = height² + (8/2)² = height² + 4²

64 = height² + 16

height² = 64 - 16 = 48

height = sqrt(48) = 6.92820323... ≈ 6.9 m

16.

the same as in 15. just with side lengths 10 cm.

10² = height² + 5²

100 = height² + 25

height² = 100 - 25 = 75

height = sqrt(75) = 8.660254038... ≈ 8.7 cm

17.

the diagonal of a rectangle is the Hypotenuse of a right-angled triangle with one length and one width of the rectangle as legs.

diagonal² = 48² + 14² = 2304 + 196 = 2500

diagonal = 50 ft

so, the rope must be at least 50 ft long.

18.

remember, the sum of all angles in a triangle is always 180°.

the standing person and his shadow enclose a 90° angle.

the sun rays make an 60° angle with the ground, so the angle at the head of the standing person is

180 - 90 - 60 = 30°

and now remember the law of sine as above.

the standing person is opposite of the 60° angle, the shadow in the ground is posit of the 30° angle at the head.

so,

180/sin(60) = shadow/sin(30) = shadow/0.5 = 2×shadow

shadow = 180 / (2×sin(60)) = 90/sin(60) =

= 103.9230485... ≈ 104 cm

Answer:

9/10

Step-by-step explanation:

3/5 = 6/10 = 9/10 = 9/10

I'm not 100% sure of this answer someone please correct me if I'm incorrect.

The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.

To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.

In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:

tan(52) = 600 / d1

Rearranging the equation to solve for d1:

d1 = 600 / tan(52)

Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:

tan(46) = 600 / d2

Rearranging the equation to solve for d2:

d2 = 600 / tan(46)

Using a calculator, we can compute:

d1 ≈ 504.61 feet

d2 ≈ 681.95 feet

The distance between the two cars is the difference between d2 and d1:

Distance = d2 - d1

Plugging in the values, we have:

Distance ≈ 681.95 - 504.61

Distance ≈ 177.34 feet

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Answer:

Step-by-step explanation:

JK = 2x, I J = 5x, and I K = x + 6,

|<-------------- x + 6 ------------------->|

I____________J___________K

          5x                        2x

x + 6 = 5x + 2x

6 = 7x - x

6 = 6x

x = 6 / 6

x = 1

substitute x=1 to JK

JK = 2x

    = 2(1)

     = 2

Answer -

JK = 2x, I J = 5x, and I K = x + 6,

--------------------------------------------

x + 6 = 5x + 2x

6 = 6x

x = 6 / 6

x = 1

-------------------------------------------

make the x=1 to JK

JK = 2x

   = 2(1)

    = 2

A 15-lb mixture, she should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts.

Based on the given information, we can set up the following system of equations:
Equation 1: x + y = 15 (since the total weight of the mixture is 15 pounds)
Equation 2: (5.90 * x) + (14.75 * y) = 9.44 * 15 (since the total cost of the mixture is the cost per pound multiplied by the weight of each component)
Now, let's convert this system of equations into matrix form:
| 1  1 |   | x |   | 15 |
| 5.90  14.75 |   | y | = | 9.44 * 15 |
To solve for x and y, we can use matrix algebra. We can multiply the inverse of the coefficient matrix by the right-hand side matrix to get the solution matrix:
| x |   | 1  1 |^-1   | 15 |
| y | = | 5.90  14.75 |      | 9.44 * 15 |
Using matrix calculations, we find that the inverse of the coefficient matrix is:
| 0.0877  -0.0576 |
| -0.0059   0.0678 |
Now, multiplying the inverse matrix by the right-hand side matrix gives us:
| x |   | 0.0877  -0.0576 |   | 15 |
| y | = | -0.0059   0.0678 | * | 9.44 * 15 |
Simplifying the multiplication gives us:
x = 1.256
y = 13.744
Therefore, the saleswoman should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts to get a 15-pound mixture.

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Answer:

B

Step-by-step explanation:

Because 3/20 is 15%, 20%, 25%, 33%

All my work and answer is provided in the attached screenshot!

Have a great day!

The number of coupon codes that can be generated is given as follows:

247,808 coupon codes.

The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.

This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

The codes are composed as follows:

Thus the total number of codes is obtained as follows:

N = 22² x 8³

N = 247,808 coupon codes.

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Answer:

We conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.

We conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.

Step-by-step explanation:

We are given a random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen;

1.10, 5.09, 0.97, 1.59, 4.60, 0.32, 0.55, 1.45, 0.14, 4.47, 1.20, 3.50, 5.02, 4.67, 5.22, 2.69, 3.98, 3.17, 3.03, 2.21, 0.69, 4.47, 3.31, 1.17, 0.76, 1.17, 1.57, 2.62, 1.66, 2.05.

Let \(\mu\) = true average percentage of organic matter

So, Null Hypothesis, \(H_0\) : \(\mu\) = 3%      {means that the true average percentage of organic matter in such soil is 3%}

Alternate Hypothesis, \(H_A\) : \(\mu \neq\) 3%      {means that the true average percentage of organic matter in such soil is something other than 3%}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                         T.S.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean percentage of organic matter = 2.481%

             s = sample standard deviation = 1.616%

            n = sample of soil specimens = 30

So, the test statistics =  \(\frac{2.481-3}{\frac{1.616}{\sqrt{30} } }\)  ~ \(t_2_9\)

                                     =  -1.76

The value of t-test statistics is -1.76.

(a) Now, at 10% level of significance the t table gives a critical value of -1.699 and 1.699 at 29 degrees of freedom for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.

(b) Now, at 5% level of significance the t table gives a critical value of -2.045 and 2.045 at 29 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.

Answer:

heres the graph i don't rly understand this all but mabe it will help

Hope This Helps!!!

The relative frequency of an event is the quotient of the division between the event and the total number of the sample

From the given table

Add the numbers of males to find their total

Then add the numbers of females and males to find the total of the sample

Now, divide the number of males by the total to find the relative frequency

Round it to 2 decimal places, then

The relative frequency of the male students = 0.49

The tires can be arranged in 24 ways. Computed using permutation.

The permutation is a way of selecting a smaller set from a larger set when the order of selection is not of concern.

For selecting r number of items, from n number of items, with the order of selection not being a concern, we can calculate the number of ways using permutation:

nPr = n!/(n - r)!.

In the question, we are asked the number of ways in which the four tires can be arranged on a car.

As we need to select 4 tires, from 4 tires, with any order, we will use permutation.

Thus, the number of ways can be calculated as 4P4, which can be calculated using the formula, nPr = n!/(n - r)!.

Thus, 4P4 = 4!/(4 - 4)! = 4!/0! = 24/1 = 24.

Thus, the tires can be arranged in 24 ways. Computed using permutation.

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The slope of the equation is -7. Then the slope of the perpendicular line will be 1/7.

Let the equation of the line be y = mx + c. Then the equation of the perpendicular line that is perpendicular to the line y = mx + c is given as y = -(1/m) + d. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given as,

y = - 7x

The slope of the equation is -7. Then the slope of the perpendicular line will be

⇒ -(1/(-7))

⇒ 1/7

The slope of the equation is -7. Then the slope of the perpendicular line will be 1/7.

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Answer:

1,2,3,4,5,6

Step-by-step explanation:

You can roll a 1,2,3,4,5 or 6 on the dice

Hope it helps!

please mark brainliest

The used values are;

p = $10,000

r = 3.3%

n = 9 years

And, The amount after 9 years will be $14,593.

What is Simple interest?

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

A bank features a savings account that has an annual percentage rate of r = 3.3% with interest compounded quarterly.

And, Maia deposits $10,000 into the account.

Now,

Since, The interest rate is for compounded quarterly.

So, The used formula is,

⇒ \(A = P (1 + \frac{r}{4} )^n^t\)

Here, P = $10,000

r = 3.3% = 0.033

n = 4

t = 9

Substitute all the values, we get the amount after 9 years,

⇒ \(A = P (1 + \frac{r}{4} )^n^t\)

⇒ A = $10,000 (1 + 0.033/4)³⁶

⇒ A = $10,000 (1 + 0.008)³⁶

⇒ A= 10,000 × (1.008)³⁶

⇒ A = 10,000 x 1.45

⇒ A = $14,593

Thus, The amount after 9 years will be $14,593.

Therefore, The used values are;

p = $10,000

r = 3.3%

n = 9 years

And, The amount after 9 years will be $14,593.

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Answer: ∠16 and ∠11

Step-by-step explanation:

      All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.

The correct corresponding angles are ∠16 and ∠11.

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Hi there!

Convert 36 into 35 and 4/4 since if it is just a number, it can’t be multiply by 3/4.

\(36= 35 \frac{4}{4}\)

Multiply both fractions now but also turn 35 4/4 into a mixed number:

\(36=\frac{144}{4}\)

\(\frac{3}{4} x \frac{144}{4}= \frac{27}{1} = 27\)

Final Result: 27

We cannot make any conclusions about the statistical significance of this difference without conducting a formal statistical test.

A statistical test is a procedure used to make an inference or decision about a population based on a sample of data.

The mean values of each group, we can make the observation that the second group of cars has a higher fuel efficiency than the first group. Specifically, the mean fuel efficiency of the second group (49 mpg) is higher than the mean fuel efficiency of the first group (34 mpg).

Mathematically, we can represent the mean fuel efficiency of the first group as μ1 = 34 and the mean fuel efficiency of the second group as μ2 = 49. From this, we can see that the difference in means between the two groups is Δμ = μ2 - μ1 = 15 mpg, indicating that the second group has a higher fuel efficiency than the first group. However, we cannot make any conclusions about the statistical significance of this difference without conducting a formal statistical test.

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Answer:

E. 108 in.²

Step-by-step explanation:

The piece of wood has the shape of a triangular prism.

SA = lateral area + area of the bases

SA = perimeter × height + 2 × bh/2

SA = (5 + 3 + 4) in. × 8 in. + 3 in. × 4 in.

SA = 108 in.²

The expression |-4| has a value of 4 when evaluated

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

|-4|

The above expression is an absolute expression

So, the solution is the positive value of the expression in bracket

Evaluate the expressions in the brackets

So, we have the following representation

|-4| = 4

Hence, the expression has a value of 4

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Answer:

-5

Step-by-step explanation:

Answer:

−5a+6

Step-by-step explanation:

hope this is right

Hello!

x = the intersection

5x + 3 = 2x + 15

5x - 2x = 15 - 3

3x = 12

x = 12/3

x = 4

Answer: X=4

Step-by-step explanation: 5x + 3 and 2x + 15 are congruent. sub tract 3 from each side, 5x and 2x + 12 are equal. Subtract 2x from each side, 3x and 12 are equal. Divide each side by 3 and get X=4

Answer:

ones. duh.

Step-by-step explanation:

divide 8,164 by 78.5

it is 104. 4 is in the ones place.

Answer:

its a

Step-by-step explanation:

Answer:

26%

Step-by-step explanation:

Original price of the emerald ring

= $3000

Price after the sale

= $2220

Decrease in amount

= $(3000 - 2220)

= $780

Percentage decrease

\( \\ = (\: \frac{decrease \: in \: amount}{original \: amount} \times 100)\%\)

\( \\ = ( \frac{780}{3000} \times 100)\%\)

\( \\ = (26)\%\)

\( \\ = 26\%\)

Hence, by 26% has the price of the ring gone down.