please help with this i’ll give brainliest

a) The distance of the stone above ground level at time t :

d(t)= -4.9t² + 950

b) It takes 13.92 seconds the stone to reach the ground

c)  With 136.42 m/s velocity the stone strikes the ground.

d) If the stone is thrown downward with a speed of 8 m/s, it will take 13.13 seconds to reach the ground

Here, a  stone is dropped from the upper observation deck of a tower, 950 m above the ground.

(a)  the distance of the stone above ground level at time t would be,

d(t)  = 0.5 (-9.8) t² + v(0) t + d(0)

      = (-4.9)t² + 0t + 950

      = -4.9t² + 950

(b) Now we find the time the stone takes to reach the ground.

i.e., the value of 't' when d = 0

Substituting d(t) = 0 in the above equation.

-4.9t² + 950 = 0

t² = (-950) / (-4.9)

t² = 193.88

t = 13.92 seconds

(c) We need to find the velocity the stone takes to strike the ground

i.e., the velocity when t  = 13.92 seconds

v(t) = v(0) + gt      

v(13.92) = 0 + (9.8)(13.92)

v = 136.42 m/s

(d) here, v(0) = -8 m/s  

Velocity is negative because stone is being thrown downward.

d(t) = 0

(-4.9)t² + v(0) t + d(0) = 0

(-4.9)t² -8t + 950 = 0

Using the quadratic formula we solve above equation for,

t = -14.76, 13.13

We can disregard the negative solution

So, we get t = 13.13 seconds.

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The amount you have after 18 months is $ 1143.96 .

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

\(A=P {(1 +\frac{r}{n})^{nt} }\)

Given:

P = 1000 , r in decimal  = 0.09 ,

n = 12 ,  t = 1.5 ( 18 months = one and a half years).

Substituting the values into the formula:

A = 1000 ( 1 + 0.09/ 12 ) ^[12 ( 1.5 )]          

  ≈ 1000 ( 1.143960 )          

  = 1143.960

Rounding to the nearest cent, we get $ 1143.96 .

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Answer:

3zx-15z+12x-60

Step-by-step explanation:

first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20

then distribute the 3 to get the answer

Answer

Step-by-step explanation:

Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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Answer:

Step-by-step explanation:

Using proportions, considering the relation between the height and the shadow, it is found that the cell phone tower is 50 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When the shadow is of 8 feet, the height is of 10 feet. What is the height when the shadow is of 40 feet? The rule of three is:

8 feet - 10 feet

40 feet - h feet

Applying cross multiplication:

8h = 10 x 40

Simplifying by 8:

h = 10 x 5 = 50 feet.

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Answer:

A. 1/x to the 4 y

Answer:

X = 10/(y-4)

Step-by-step explanation:

4X(y-4) = 40

X(y-4) = 10

X = 10/(y-4)

The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.

In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:

x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]

x = 284.372 mi

The distance x is equal to 284.372 miles.

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Answer:

Step-by-step explanation:

TU/26=(TU+24)/(26+39)

TU/26=(TU+24)/65

65TU=26TU+624

39TU=624

TU=16

Answer:

\(y = 32 - \frac{1}{2}x\)

Step-by-step explanation:

Given

\(Cups = 32\) ---- not 52

\(Students = x\)

\(Remainder = y\)

\(Each = \frac{1}{2}\) --- not z

Required

The equation for y

The remainder y is calculated as:

\(y = Cups - Students * Each\\\)

\(y = 32 - \frac{1}{2}x\)

Answer:

The solution to this question is 104.25cm²

Step-by-step explanation:

u

Answer:

hi

Step-by-step explanation:

i think so

A=

\( = \pi \times {r}^{2} \)

=3,14×5,76²=104,177

hope it helps

have a nice day

Answer:

(x, y) = (4,-3)

Step-by-step explanation:

...............

.

.

.

.

The missing number in Sequence 2 is 780.

To find the missing number in Sequence 2, let's analyze the pattern:

In Sequence 1, the numbers increase by 1 each time: 126, 127, 128, 129, ...

In Sequence 2, the numbers seem to follow a pattern where each number is obtained by multiplying the corresponding number in Sequence 1 by a certain factor:

2 x 126 = 252

3 x 127 = 381

4 x 128 = 512

5 x 129 = 645

...

Looking at this pattern, we can see that the missing number in Sequence 2 should be:

6 x 130 = 780

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Answer:

2.3 hours

Step-by-step explanation:

From 3:12 pm to 4:12 pm, one hour passes.

From 4:12 pm to 5:12 pm, another hour passes.

From 5:12 pm to 5:30 pm, there are 18 minutes that pass.

Therefore, the total time elapsed is 2 hours and 18 minutes out of 60 minutes in an hour.

To convert this to a fraction, we can write:

2 hours + 18 minutes = 2 + 18/60 hours = 2.3 hours

So, 2.3/1 hour passes from 3:12 pm to 5:30 pm.

Answer:

Hence, the data provides convincing evidence that a linear relationship exists between hours of sleep observed and academic performance as measured by GPA.

Step-by-step explanation:

Given the data:

Sleep (hrs) 9 8.5 9 7 7.56 7 5.5 6 8.5 6.5 8

GPA 3.8 3.3 3.5 3.6 3.4 3.3 3.2 3.2 3.2 3.4 3.6 3.1 3.4 3.7

The scatter plot shows a positive linear trend. With the correlation Coefficient depicting a R value of 0.56. The residual plot also depicts a a randomly scattered values of the residual values. Similarly, a plot of the normal values of  residuals

The data provided has a linear correlation between the hours of sleep observed and academic performance as measured by GPA.  

It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.

We have given data of the 14 seniors shown in the table.

To solve this question we will calculate the correlation coefficient 'r'

The formula for correlation coefficient :

\(\rm r =\frac{n\sum xy-\sum x \sum y}{\sqrt{[n\sum x^2-(\sum x)^2]}[n\sum y^2-(\sum y)^2]} }\)

From the table the value of n = 14

\(\rm \sum x = 104.5\) , \(\rm \sum y =47.7\) , \(\rm \sum xy =357.8\) , \(\rm \sum x^2 =797.25\) , \(\rm \sum y^2 =163.09\)

Put all the values in the above formula we get:

\(\rm r =\frac{14\times357.8-104.5 \times47.7}{\sqrt{[14\times 797.25-104.5^2][14\times163.09-47.7^2]} }\)

\(\rm r = \frac{5009.2-4984.65}{\sqrt{(241.25)(7.97)} }\)

\(\rm r = \frac{24.55}{43.849}\)

r = 0.559 ≈ 0.56

The value of the correlation coefficient is 0.56 which is between the values 0.5 to 0.7 shows that the variables are moderately correlated.

Thus, the data provided has a linear correlation between the hours of sleep observed and academic performance as measured by GPA.  

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As we know that formula of area of circle is πr²

So let's apply formula

π×8.6×8.6

=232.2

=200 is the nearest hundredth.

You have to do rest of all through this method.

Answer:

angleABC=isosceles triangle

angleB=(180-50)÷2=65

angle B=angleX(alternative angle)

angleB=65degree

The computed mean expenses of the XYZ Corporation based on the given information are 9,911.22.

The mean refers to the average value.

The mean is computed as the quotient that results from dividing the total value of the data set by the number of items in the set.

Name                      Total Sales      Total Expenses

Quezon City            14,950.00             4,933.50

Caloocan City         18,290.00             6,035.70

Marikina City          37,200.00           12,276.00

Cebu City                18,900.00            6,237.00

Davao City             45,000.00          14,850.00

Mandaluyong City 23,000.00           7,590.00

Cavite                     22,000.00          7,260.00

Laguna                    21,000.00          6,930.00

Manila                    66,000.00         21,780.00

Iloilo                       34,000.00          11,220.00

Total                                                  99,112.20

Mean Expenses = 9,911.22 (99,112.20 ÷ 10)

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\(\huge \bf༆ Answer ༄\)

Let's solve ~

If the numbers with same same base are multiplied them, their exponents add up ~

And we can also separate the base (when multiplied) to different bases with having same exponent as the original one.

======== \(\huge{\bf{Answer :}}\) ========

\( \bold{ \underline{Given : -}}\)

\( \: \)

\( \bold{ \underline{To \: Find : - }}\)

\( \: \)

\( \bold{ \underline{Solution : - }}\)

Did you know that there are exponential properties of matter such as the following :

Soo :

\( \sf \longmapsto (ab {)}^{37} \times {(ab)}^{42} \times {(ab)}^{51} \)

\( \sf \longmapsto {(ab)}^{37 + 42} \times {(ab)}^{51} \)

\( \sf\longmapsto (ab {)}^{79} \times {(ab)}^{51} \)

\( \sf \longmapsto {(ab)}^{79 + 51} \)

\( \sf \longmapsto \boxed { \bold{ \red{ {(ab)}^{130}}}} \)

\( \: \)

\( \bold{ \underline{ \: Conclusion : -}}\)

\( \: \)

I hope this helps!

I'll do the first 6 rows to get you started.

===========================================

In row 1, we have the number \(2^3\) which is the same as writing 2^3

The base is 2 and the exponent is 3. Think of "base" as in "basement" to remember that the base is under the exponent. The exponent tells us how many copies of the base to multiply out. In this case, we have three copies of the base "2" multiplied to get 2*2*2 = 8

============================================

In row 2, we have the number 3^2. The base is 3 and the exponent is 2.

We can say 3^2 = 3*3 = 9. We have two copies of the base multiplied. Think of a 3 inch by 3 inch square that has area of 9 square inches.

============================================

Row 3:

The number 5^4 means 5^4 = 5*5*5*5 = (5*5)*(5*5) = 25*25 = 625

The base is 5 and the exponent 4 tells us how many copies of the base to multiply.

============================================

Row 4:

We aren't given the number like in the earlier rows. But we can see that the base is 6 and the exponent is 2. So the number to fill in that first blank is 6^2

The expanded notation would be 6*6 because the exponent tells us how many copies of the base to multiply out.

The standard notation is 36 because 6*6 = 36.

============================================

Row 5:

This time we don't have an exponent, but we have the base and we have the expanded notation.

The expanded notation of 8*8*8 means the base is 8 and the exponent is 3

So 8^3 = 8*8*8 = 512

We'll have 8^3 to fill in the first blank of row five, 3 fill in the next blank, and finally 512 fill in the last blank.

============================================

Row 6:

We have six copies of '9' multiplied together

This tells us we have the number 9^6. The base is 9 and the exponent is 6

Use your calculator to determine that 9^6 = 9*9*9*9*9*9 = 531441

============================================

I'll let you do the rest of the remaining rows.

Answer:

c = 4.2h

Step-by-step explanation:

the rate is 16.80 /4

4.20 per hour

earn = hours * rate

c = 4.20h

Answer:

\(c=4.20h\)

Step-by-step explanation:

Given information:

Given variables:

To find Jasmine's hourly rate, divide the amount she earns by the number of hours worked:

\(\implies \dfrac{25.20}{6}=4.2\)

\(\implies \dfrac{16.80}{4}=4.2\)

Therefore, Jasmine earns $4.20 per hour.

The function that shows this information is:

\(\large\boxed{c=4.20h}\)

The solution to the trigonometry equation 2cos²(w) - 3cos(w) - 2 = 0 is 120

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

2cos²(w) - 3cos(w) - 2 = 0

Let x = cos(w)

So, we have the following representation

2x² - 3x - 2 = 0

Expand the equation

This gives

2x² + x - 4x - 2 = 0

Factorize the equation

So, we have

x(2x + 1) - 2(2x + 1) = 0

So, we have

(x - 2)(2x + 1) = 0

Solving for x, we have

x = 2 and x = -1/2

Recall that

x = cos(w)

So, we have

cos(w) = 2 and cos(w) = -1/2

Take the arc cos of both sides

w = cos⁻¹(2) and w = cos⁻¹(-1/2)

When evaluated, we have

w = undefined and w = 120

Hence, the trigonometry equation has a solution of w = 120

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Answer:

7, -5, 2/3, 5.79

Step-by-step explanation:

rational numbers are numbers you can put in fraction form. \(\sqrt{13}\) is not a perfect square, therefore you cannot put it in fraction form. \(\sqrt{-4}\) is an imaginary number. Rational numbers are in the Real Numbers category, so it is not a rational number.

Answer:

71*10⁻³

Step-by-step explanation:

7.1 x 10-^2 = 7.1*10⁻² = 71*10⁻³

Answer:

5 x 5 x 5 x 5 x 5

Step-by-step explanation: