In Tara's math class, each student made up a number pattern for classmates to identify. These are the numbers that Tara wrote. Find the pattern and identify the first and seventh numbers in the table.


a. first number:

b. seventh number:


Tara's Pattern


1st


2nd


3rd


4th


5th


6th


7th


3/8


5/16


9/32


17/64


33/128

Thus, 715,000 =  7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.

The number of times that decimal point must be moved to obtain a number between 1 and 10 is the exponent in scientific notation. The decimal point is shifted to the left in order to represent this number in scientific notation.

The main goal of scientific notation is to simplify computations using numbers that are abnormally large or small. With scientific notation, every digit counts because zeros are just no longer used to denote the decimal point.

Given expression:

715,000 __ 7.15 x 10⁵

LHS = 715,000

Take the RHS value :

= 7.15 x 10⁵

This, can be simplifies as:

= 7.15 x 100,000

Now multiply the two values,

= 715,000 (RHS values)

as, LHS  = RHS

LHS = 715,000

715,000 (RHS values)

Thus, 715,000 =  7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.

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Answer:

66

Step-by-step explanation:

the first answer is correct

Answer:

87

Step-by-step explanation:

just trust!

Answer:

-15

Step-by-step explanation:

When functions are "nested" like this (nested is not a math word; the mathy word is composed or composition) you need to start all the way on the inside.

f(g(-3))

means find g(-3) first, then put that answer into f.

g(x) = x - 7

g(-3) = -3 - 7

g(-3) = -10

We found g(-3) is -10, so now put -10 into f.

f(x) = 2x + 5

f(-10) = 2(-10) + 5

= -20 + 5

= -15

Answer:

13.4

Step-by-step explanation:

You multiple all of numbers and divide it by 4

Answer:

The probability of pulling out a green skittle in decimal form is 0.5

Step-by-step explanation:

Hope that helps

Step-by-step explanation:

To determine whether a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's denote the three sides of the given triangle as a = 23, b = 30, and c = 19. We can check if these side lengths satisfy the Pythagorean theorem as follows:

c^2 = a^2 + b^2

19^2 = 23^2 + 30^2

361 = 529 + 900

Since 361 is not equal to 529 + 900, we can see that the given triangle is not a right triangle.

Answer:

-24

Step-by-step explanation:

\(\frac{4^{2} }{2}\) + 4(-2) ³

I hope this helps!

Answer:

9. m(YZ) = 102°

10. m(JKL) = 192°

11. m<GHF = 75°

Step-by-step explanation:

9. First, find the value of x

4x + 3 = 3x + 15 (inscribed angle that are subtended by the same arc are equal based on the inscribed angle theorem)

Collect like terms

4x - 3x = -3 + 15

x = 12

4x + 3 = ½(m(YZ)) (inscribed angle of a circle = ½ the measure of the intercepted arc)

Plug in the value of x

4(12) + 3 = ½(m(YZ))

48 + 3 = ½(m(YZ))

51 = ½(m(YZ))

Multiply both sides by 2

51*2 = m(YZ)

102 = m(YZ)

m(YZ) = 102°

10. First, find the value of x.

7x + 5 + 6x + 6 = 180° (opposite angles in an inscribed quadrilateral are supplementary)

Add like terms

13x + 11 = 180

13x = 180 - 11

13x = 169

x = 169/13

x = 13

7x + 5 = ½(m(JKL)) (inscribed angle of a circle = ½ the measure of the intercepted arc)

Plug in the value of x

7(13) + 5 = ½(m(JKL))

96 = ½(m(JKL))

Multiply both sides by 2

2*96 = m(JKL)

m(JKL) = 192°

11. First, find x.

5x + 15 = ½(11x + 18) (inscribed angle of a circle = ½ the measure of the intercepted arc)

Multiply both sides by 2

2(5x + 15) = 11x + 18

10x + 30 = 11x + 18

Collect like terms

10x - 11x = -30 + 18

-x = -12

Divide both sides by -1

x = 12

m<GHF = 5x + 15

Plug in the value of x

m<GHF = 5(12) + 15

m<GHF = 60 + 15

m<GHF = 75°

Answer:

57

Step-by-step explanation:

Given that :

Standard deviation (σ) = 5 minutes = (5 *60) = 300 seconds

Margin of Error, E = 78

Assume a confidence interval of 95%;

Using the relation :

((Zα/2 * σ) / E)²

(1 - α)/2 = (1 - 0.95)/2 = 0.05 /2 = 0.025

Z0.025 = 1.96

Sample size = ((1.96 * 300) / 78)²

Sample size = (588 / 78)^2

Sample size = 7.5384615^2

Sample size = 56.828

= 57 samples

Answer:

Step-by-step explanation:

f(2) - g(2)

2^2 + 1 - 2(2) + 5

4 + 1 - 4 + 5

5 - 4 + 5

1 + 5 = 6

Answer:

6

Step-by-step explanation:

|-6| = 6

|6| = 6

- -6 = +6

so, we have

6 - 6 + 6 = 6

Answer:

$3.38

Step-by-step explanation:

75% of 13.50=

0.75×13.50=

13.50-10.125=

3.375 = $3.38..(If we rounded to the nearest cent will be 3.38)

Answer:

60 = a

Step-by-step explanation:

I attached a pic of how I got 60 = a

Answer:

.49 if you're dividing them.

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

20+12-E=2

32-E=2

-E=-30

E=30

Answer:

Step-by-step explanation:

option (d) 4hrs 40mins

Answer:

Solution,

\(b = 6 \: ft \\ h = \sqrt{ {5}^{2} - {3}^{2} } \\ \: \: \: \: \: = \sqrt{25 - 9} \\ \: \: \: \: \: = \sqrt{16} \\ \: \: = \sqrt{ {4}^{2} } \\ \: \: \: \: = 4\)

Now,

\(volume = \frac{1}{3} bh \\ \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times {6}^{2} \times 4 \\ \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times 36 \times 4 \\ \: \: \: \: \: \: \: \: \: \: \: = 48 \: {ft}^{3} \)

hope this helps...

Good luck on your assignment..

Answer:

Volume = 48 ft³

Step-by-step explanation:

Finding h first by Pythagorean Theorem:

=> \(c^2= a^2+b^2\)

=> \(5^2= 3^2 + h^2\)

=> \(h^2 = 25-9\\h^2 = 16\)

Taking sqrt on both sides

=> h = 4 ft

Now, The volume:

=> Volume = \(a^2\frac{h}{3}\)

=> Volume = \((6)^2\frac{4}{3}\)

=> Volume = \(36 \frac{4}{3}\)

=> Volume = 12 * 4

=> Volume = 48 ft³

Step-by-step explanation:

solution.

if variable d increases then w reduces

w=k.u ×1/d

=ku/d

therefore w=k.u/d

Answer:

Volume ≈ 60 in³

Step-by-step explanation:

Given the diagram of a cylinder with a radius of 2 inches, and a height of 5 inches. The prompt also tells us to use 3 for the value of π.

We can use the given formula for finding the volume of a cylinder:

Volume (V) = πr²h

Substitute the given values into the formula:

V = 3 × (2)²× 5

V = 3 × 4 × 5  

V = 60 in³

Therefore, the approximate volume of the given cylinder is 60 in³.

We've been provided with a cylinder who is having a radius of 2 inches and a height of 5 inches. We've been also given to take 3 for the value of π i.e (π = 3)

Here we have,

And we've been given to find out what is the volume (v) of given cylinder?

As we have been provided with the standard formula for calculating volume of a cylinder which is given by,

\(:\implies\tt{v = \pi {r}^{2} h}\)

\(:\implies\tt{v = 3 \times {2}^{2} \times 5}\)

\(:\implies\tt{v = 3 \times 4 \times 5}\)

\(:\implies\tt{v = 12 \times 5}\)

\(:\implies\tt{v = 60 {in}^{3} }\)

To find the unpaid balance after 13 months, we need to calculate how much of the loan principal has been paid off by the monthly payments. We can use an amortization table to help with this calculation.

Month Payment Interest Principal Balance

0 - - - 85,000.00

1 498.74 410.83 87.91 84,912.09

2 498.74 409.63 89.11 84,823.98

3 498.74 408.42 90.32 84,733.67

...

12 498.74 398.29 100.45 83,810.25

13 498.74 397.06 101.68 83,708.57

So after 13 months, the unpaid balance on the loan is $83,708.57.

To calculate how much interest the executive paid during this time period, we can subtract the amount of principal paid from the total amount of payments made and then round to two decimal places:

Total payments made in 13 months = $498.74/month x 13 months = $6,482.62

Interest paid = Total payments made - Principal paid = $6,482.62 - $1,307.50 = $5,175.12

Therefore, the executive paid $5,175.12 in interest during the first 13 months of the loan.

Answer:

  n = 27

  m = 36

Step-by-step explanation:

The isosceles triangle with n° as its base angle will have a sum of angles that is 180°.

  2n° +126° = 180°

  n +63 = 90 . . . . . . divide by 2°

  n = 27 . . . . . . . . . subtract 63

__

The external angle 126° is the sum of the remote interior angles m° and 90°.

  m° +90° = 126°

  m = 36 . . . . . . . . . . divide by °, subtract 90

Answer:

7 hours

Step-by-step explanation:

here,

270/18=105/x

x=(105*18)/270

x=7

Chau made $270 for 18 hours of work. At the same rate,  Therefore Chau would have to work 7 hours at the same rate to make $105.

To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:

Let x be the number of hours Chau needs to work to make $105.

We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:

Rate = Total earnings / Number of hours

Rate = $270 / 18 hours

Rate = $15 per hour

Now, we can set up the proportion:

$15 per hour = $105 / x hours

To find x, we can cross-multiply:

$15 × x = $105

Now, solve for x:

x = $105 / $15

x = 7 hours

So, Chau would have to work 7 hours at the same rate to make $105.

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The equation for the regression line from the data is y = -0.98x + 56.8

Given data ,

To find the equation of the regression line, we will use the method of least squares. The regression line is represented by the equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

We need to calculate the values of m and b. Let's begin by finding the mean values of x and y:

Mean of x (x₁) = (6 + 13 + 14 + 10 + 13) / 5 = 12.2

Mean of y (y₁) = (25 + 44 + 46 + 52 + 57) / 5 = 44.8

Next, we calculate the deviations from the mean for both x and y:

Deviation from the mean of x (Δx) = x - x₁

Deviation from the mean of y (Δy) = y - y₁

Now, we calculate the sum of the products of the deviations from the mean:

Σ(Δx * Δy) = (6 - 12.2) * (25 - 44.8) + (13 - 12.2) * (44 - 44.8) + (14 - 12.2) * (46 - 44.8) + (10 - 12.2) * (52 - 44.8) + (13 - 12.2) * (57 - 44.8)

Σ(Δx * Δy) ≈ -51.6

Next, we calculate the sum of the squared deviations from the mean of x:

Σ(Δx²) = (6 - 12.2)² + (13 - 12.2)² + (14 - 12.2)² + (10 - 12.2)² + (13 - 12.2)²

Σ(Δx²) ≈ 52.8

Now, we can calculate the slope (m) using the formula:

m = Σ(Δx * Δy) / Σ(Δx²)

m ≈ -51.6 / 52.8 ≈ -0.98

Finally, we can calculate the y-intercept (b) using the formula:

b = y₁ - m * x₁

b ≈ 44.8 - (-0.98) * 12.2 ≈ 56.8

Hence , the equation of the regression line for the given data is:

y = -0.98x + 56.8

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Answer: 25

9(3)-2

9(3)=27

27-2=25

Answer:

x = 12, x = -4.

Step-by-step explanation:

x² - 8x - 48 = 0.

This factors to (x - 12)(x + 4) = 0.

Proof:

(x - 12)(x + 4) = 0

first: x * x

outer: 4 * x

inner: -12 * x

last: -48.

first: x²

outer: 4x

inner: -12x

last: -48

x² + 4x - 12x - 48

x² - 8x - 48.

To find the zeros, take the individual pairs and find the values that make the equation 0.

x - 12 = 0

Add 12 to both sides.

x = 12.

x + 4 = 0

Subtract 4 from both sides.

x = -4.

Answer:

x= 4 + 2√5, x = 4 - 2√5

Step-by-step explanation:

So this is quadratics so you can solve it by completing the square and using the quadratic formula. The quadratic formula is x = (-b±√(b²-4ac)) / (2a).

Answer:

do you have an image for that?

Step-by-step explanation:

Answer: 62

Step-by-step explanation:

Tyler has 31%

31% of 200= (31/100) x 200= 62 votes

(Just answered and gotten it right)

Answer:

62

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].

To determine the number of minutes you would have to exercise each day to have a resting heart rate of 60 beats per minute, we need to consider the relationship between exercise and heart rate.

Regular exercise can help lower resting heart rate as it strengthens the cardiovascular system. The American Heart Association recommends engaging in moderate-intensity aerobic exercise for at least 150 minutes per week to maintain cardiovascular health.

If we assume that you exercise evenly throughout the week, we can calculate the daily exercise time as follows:

150 minutes per week ÷ 7 days = approximately 21.43 minutes per day.

Therefore, if you exercise for approximately 21.43 minutes per day, it can contribute to maintaining a healthy resting heart rate. It's important to note that individual results may vary, and consulting with a healthcare professional is always recommended before starting or modifying an exercise routine.

However, it's crucial to understand that exercise alone may not be the sole factor affecting resting heart rate. Other factors, such as genetics, overall health, stress levels, and lifestyle choices, can also influence heart rate. Additionally, achieving a resting heart rate of 60 beats per minute may not be feasible or suitable for everyone, as the ideal range can vary based on individual circumstances.

Therefore, while regular exercise can be beneficial for cardiovascular health, it's essential to consider personalized factors and consult with a healthcare professional for tailored advice on achieving and maintaining a healthy resting heart rate.

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The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

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