Shanti wrote the predicted values for a data set using the line of best fit y = 2.55x – 3.15. She computed two of the residual values.

What are the values of a and b?
a = 0.4 and b = –0.15
a = –0.4 and b = 0.15
a = 8.6 and b = 14.25
a = –8.6 and b = –14.25

Answer:

c

Step-by-step explanation:

The correct option is Option B: is an A.P., because d = 10

An arithmetic progression, also known as an arithmetic sequence, is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is called the common difference and is denoted by 'd'.

The given sequence is:

-5, 5, 15, 25, ....

In every Arithmetic Progression (A.P.)

The common difference d

d= 2nd term - 1st term = 3rd term - 2nd term

d = 5-(-5) = 15 - 5

d = 10

Hence the common difference is 10,

Therefore  the sequence is an A.P., because d = 10

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The correct question

The sequence: -5, 5, 15, 25, ...

A. is not an A.  P.

B. is an A.P., because d = 10

C. is an A.P because d = 5

D is an A. P., because d = -10

Answer:

1.circle

2.triangle

3.trapezoid

4.parallelogram

Step-by-step explanation:

Step-by-step explanation:

Tn = n + 7

The first three terms of the sequence is

T1 = 1 + 7 = 8

T2 = 2 +7 = 9

T3 = 3 + 7 = 10

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

The first three terms of the sequence is 8 , 9 and 10

Now

The tenth term of the sequence is

T10 = 10 + 7 = 17

Hope it will help you. :)

a) The first three terms of the sequence is given by 8 , 9 , 10 respectively

b) The tenth term of the sequence is a₁₀ = 17

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the arithmetic progression be represented as A

Now , the equation will be

A = n + 7   be equation (1)

a)

when n = 1

Substitute the value of n = 1 in the equation , we get

The value of a₁ = 1 + 7 = 8

when n = 2

Substitute the value of n = 2 in the equation , we get

The value of a₂ = 2 + 7 = 9

when n = 3

Substitute the value of n = 3 in the equation , we get

The value of a₃ = 3 + 7 = 10

b)

The tenth term of the arithmetic sequence is when n = 10

Substitute the value of n = 10 in the equation , we get

The value of a₁₀ = 10 + 7 = 17

Hence , the tenth term of the AP is  a₁₀ = 17

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Answer:

88.2 squared

Step-by-step explanation:

The formula to find the area of a circle is a = pi * r ^2

Let's replace the values that we know.

a = 3.14 x 5.3 ^2

First, we should do 5.3 ^2, which is 28.09.

a = 3.14 x 28.09

Now we are able to do 3.14 x 28.09 which is 88.2026

But that isn't it! We need to round to the nearest tenth, which is this digit:

88.2026

Since next to the 2 there is a 0, you take out all the numbers after that 2. Which leaves you with:

88.2

Final answer:

The area of the round mirror with a radius of 5.3 inches, when calculated using the formula A = πr^2 and rounded to the nearest tenth, is 88.2 square inches.

To find the area of the round mirror with a radius of 5.3 inches, we will use the formula for the area of a circle, which is A = πr^2, where A is the area, π is approximately 3.14, and r is the radius of the circle.

Given that the radius of the mirror is 5.3 inches, we can substitute this value into the formula to find the area:

A = π(5.3)^2 ≈ 88.2 square inches.

Let's plug in the radius:

When rounded to the nearest tenth, the area of the mirror is 88.2 square inches.

Answer:9

Step-by-step explanation:

12-9=3 12-3=9 3+9=12

So C=9

Hey there!

[tex]\large\boxed{c=9}[/tex]

12 - 9 + c = 12

Combine like terms.

3 + c = 12

Subtract 3 from each side of the equation.

3 - 3 + c = 12 - 3

c = 9

Check:

12 - 9 + c = 12

12 - 9 + 9 = 12

3 + 9 = 12

12 = 12

Hope this helps!

Answer: The functions are v1(t)=10000*(1.04)^5  and v2(t)=8000(1.06)^5

v1(5)=12166$

v2(5)=10705 $

Step-by-step explanation:

Given:

Investment cost for 1st=10,000$  ,at 4%rate.

Investment cost for 2nd=8000$ ,at 6% rate.

To Find:

Exponential growth functions ,

that could be used to find v1(t) and v2(t),

the value of each investment after 5 years

And difference between their values.

Solution:

Consider for 1st investment function be v1(t) and for 2nd be v2(t)

and t be time period

Exponential growth is given by, as time function,

v(t)=initial cost*(1+rate)^time period.

for 1st investment its cost is 10000$  at 4 % rate.

[tex]v1(t)=10000(1+0.04)^t[/tex]

[tex]v1(t)=10000(1.04)^t[/tex]

for 2nd investment its cost is 8000$  at 6% rate.

[tex]v2(t)=8000(1+0.06)^t[/tex]

[tex]v2(t)=8000(1.06)^t[/tex]

For t=5 calculating for both investment,

[tex]v1(5)=10000(1.04)^5[/tex]

[tex]=10000*1.2166[/tex]

v1(5)=12166 $

For 2nd investment,

[tex]v2(5)=8000(1.06)^5[/tex]

[tex]=8000*1.3382[/tex]

v2(t)=10705.8 $

Now after 5 years the difference is =v1(t)-v2(t)

Which is about 1460 $ only.

This because of the both functions depends upon time,initial investment and rate of interest .

Here time period being same.But the rate of interest are different and initial values are different.

Answer:

I THINK all but C apply for the second one. Just suggesting, but I hope it helps.

Answer:

Option B is the right choice.

Step-by-step explanation:

Given:

An are CE and an inscribed angle CBE.

Measure of inscribed angle CBE = 25 °

We have to find the measure of the arc CE.

Concept:

To find the measure of arc CE.

⇒ [tex]\angle CBE = \frac{1}{2} \times m\ (arc\ CE)[/tex]

⇒ [tex]2\times \angle CBE = m\ (arc\ CE)[/tex]

⇒ [tex]2\times 25 = m\ (arc\ CE)[/tex]

⇒ [tex]50 = m\ (arc\ CE)[/tex]

Measure of intercepted arc CE = 50 degrees.

The measure of arc CE = 50° so, option B is the right choice.

Answer:

Step-by-step explanation:

Looking at the information given, the population mean and population standard deviation are known. We would apply the formula

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

From the information given,

µ = 70

σ = 10

1) x = 60

The probability that the heart rate if an individual is less than 60 is expressed as

P(x < 60)

z = (60 - 70)/10 = - 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.16

The percentage rates of heart rates less than 60 is 0.16 × 100 = 16%

2) x = 80

The probability that the heart rate if an individual is less than 80 is expressed as

P(x < 80)

z = (80 - 70)/10 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

The percentage rates of heart rates less than 80 is 0.84 × 100 = 84%

3) x = 50

The probability that the heart rate if an individual is greater than 50 is expressed as

P(x > 50) = 1 - P(x ≤ 50)

z = (50 - 70)/10 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.23

P(x > 50) = 1 - 0.23 = 0.77

The percentage rates of heart rates greater than 50 is 0.77 × 100 = 77%

the answers are:

Caspian Sea

Fedchenko Glacier

and Tian Shan Mountains

Step-by-step explanation:

i got it right in my quiz

Answer: 14

Step-by-step explanation:

the question is just asking you to replace the x and y with the corresponding numbers.

x = 4

y = -3

Since x is 4 squared it would be 16.

-4 times -3 equals positive 12.

That would make the equation

(16 + 12) divided by 2

16 + 12 = 28 divide that by 2 and you’ll get 14.

Answer: 14

Step-by-step explanation:

First plug 4 in for x.

4^2 is equal to 16 because 4 x 4 is 16.

Next, plug in -3 for y.

-4 x -3

4 times 3 is 12 and they are both negative, therefore it turns out as a positive 12.

Then add the numbers on the top of your equation.

16+12=28.

Finally divide the sum by 2.

28 divided by 2= 14

Your answer is 14.

Hope this helps!

Answer:

(assuming the height is 13 and the width is 10 or vice versa) 65

Step-by-step explanation:

a = 1/2 base × height

1/2 13 × 10 or 10×13

130 ÷ 2

65

Area of isosceles triangle = [tex]\( \frac{13\sqrt{231}}{4} \)[/tex] square centimeters, approximately 43.03 square centimeters.

To find the area of an isosceles triangle, you can use the formula:

[tex]\[ Area = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Since it's an isosceles triangle, the height divides the triangle into two right-angled triangles of equal size.

Given:

Base = 13 cm

Height = ?

To find the height, we can use the Pythagorean theorem.

Let's denote the height as  [tex]\( h \),[/tex] and half of the base (since the triangle is isosceles, and the height splits the base into two equal parts) as  [tex]\( \frac{13}{2} \).[/tex]

Then, using the Pythagorean theorem:

[tex]\[ (\text{height})^2 + \left(\frac{13}{2}\right)^2 = 10^2 \]\[ (\text{height})^2 + \left(\frac{13}{2}\right)^2 = 100 \]\[ (\text{height})^2 + \frac{13^2}{2^2} = 100 \]\[ (\text{height})^2 + \frac{169}{4} = 100 \]\[ (\text{height})^2 = 100 - \frac{169}{4} \]\[ (\text{height})^2 = \frac{400}{4} - \frac{169}{4} \]\[ (\text{height})^2 = \frac{231}{4} \][/tex]

Now, let's solve for the height:

[tex]\[ \text{height} = \sqrt{\frac{231}{4}} \]\[ \text{height} = \frac{\sqrt{231}}{\sqrt{4}} \]\[ \text{height} = \frac{\sqrt{231}}{2} \][/tex]

Now that we have the height, we can calculate the area using the formula:

[tex]\[ Area = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Substituting the values:

[tex]\[ Area = \frac{1}{2} \times 13 \times \frac{\sqrt{231}}{2} \]\[ Area = \frac{13 \sqrt{231}}{4} \][/tex]

So, the area of the isosceles triangle is  [tex]\( \frac{13 \sqrt{231}}{4} \)[/tex]  square centimeters.

The complete question is here.

Find the area of the isosceles triangle with a base of 13 cm and a height of 10 cm.

a) The function that represent this situation is y = 90 + 8x.

b)  His weight be after 8 weeks is 154 lbs.

Step-by-step explanation:

It is given that,

a) Write a function to represent this situation. Use x and y as your variables.

Hence the equation can be framed as,

Total weight = starting weight + weight gained in x weeks.

We know that, each week he gains 8 lbs. Therefore, for 8 weeks he gained 8x lbs of weight.

⇒ y = 90 + 8x.

∴ The function that represent this situation is y = 90 + 8x.

b) What would his weight be after 8 weeks?

To find his week after 8 weeks, substitute x=8 in the function y = 90 + 8x.

⇒ 90 + 8(8)

⇒ 90 + 64

⇒ 154 lbs.

∴ His weight be after 8 weeks is 154 lbs.

Answer:

(0,1)

Step-by-step explanation:

The limit of the given infinite series is undefined.

The given series is:

∑n=1∞(3n5/6n6+1)

To find the limit, we can simplify the series by dividing the numerator and denominator by the highest power of n:

∑n=1∞(3/n-1/6n-1+n-6)

As n approaches infinity, the terms containing n-1 and n-6 approach 0, so we are left with:

∑n=1∞(3/n)

This is a harmonic series with the form 1+1/2+1/3+1/4+... which is known to diverge. Therefore, the limit of the given infinite series is undefined.

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Answer:

2.18

Step-by-step explanation:

tan 70°=x/6

by cross multiplication

xtan70°=6

divide both sides by tan70°

x=6/tan70°

x=6/2.7475

x=2.18

Answer:

Sum a + b is irrational

Step-by-step explanation:

Any irrational number plus a rational number is always irrational.

Answer:

4 meters

Step-by-step explanation:

7-3=4 m

Answer: Lulu has 4 meters of tape left.

Hope this helps!!

Answer:

The measurements of all the right angles and the lengths of the two sides and the measurement of the included angle.

Step-by-step explanation:

the measurements of two angles

the measurements of two angles and the length of the included side

the lengths of two sides and the measurement of the included angle

Answer:

1. >

2. <

Step-by-step explanation:

When a > 0, the graph opens upwards, or positively, because the way the line curves is determined by a.

When a < 0, the graph opens downwards, or negatively, for the same reason.

Final answer:

The graph of a quadratic function opens upwards when the coefficient of the squared term is positive (a > 0), and opens downwards when this coefficient is negative (a < 0).

Explanation:

The graph of a quadratic function opens up or down based on the sign of the coefficient of the squared term (usually represented as 'a' in the quadratic equation ax2 + bx + c). When this coefficient a is positive (a > 0), the parabola opens upwards. Conversely, if the coefficient a is negative (a < 0), the parabola opens downwards. The orientation of the parabola reflects whether the quadratic function has a minimum value (opening upwards) or a maximum value (opening downwards).

Calculate the value of z and its probability, since with this we can know how likely it is that this will happen.

We have that the mean (m) is equal to 8.3, the standard deviation (sd) 1.2 and the sample size (n) = 15

They ask us for P (x =7.2)

For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / (sd / (n ^ 1/2))

We have all these values, replacing we have:

z = (7.2 - 8.3) / (1.2 / (15 ^ (1/2))

z = -3.55

With the normal distribution table (attached), we have that at that value the approximate probability is:

P (z = -3.55) = 0.0001

The probability is 0.01 %

This affirms that the students do not sleep what the study says because the probability of this happening according to the survey is almost nil.

Answer:

rdgvvsssddas

Step-by-step explanation:

42423412

Answer:  

1: -2.33 or -7/3

2: - 2.16 or -13/6

3: 3.49 x 10^4

4: 4.28*10-7

5: 0.81 or 9/11

6. 3

7: 8

8: 9 or up

9: 5 or up

10: 0-36

I hope any of this helps.... :D

Answer:  The answer is 0.3

Step-by-step explanation:

Lily should expect to buy 1.5 boxes to get all four prizes.

This question belongs to the field of probability in Mathematics. The problem is asking how many boxes Lily should expect to buy in order to get all four prizes. This is a geometric problem because each box has a probability of 1/4 of containing a prize, and each trial is independent with the same probability of success. To solve this problem, we can use the concept of expected value.

The expected value is the average number of boxes Lily needs to buy to get all four prizes. The expected value can be calculated by multiplying the probability of each outcome by the number of boxes it takes to achieve that outcome, and then summing up these products:

Expected value = (1/4) * 1 + (1/4) * 2 + (1/4) * 3 + (1/4) * 4 = 1.5

Therefore, Lily should expect to buy approximately 1.5 boxes to get all four prizes.

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Answer:

8

Step-by-step explanation:

Step-by-step explanation: -3x - 2

-3 x 3 = -9

-9 -2 = -11

-11 is the answer.

Hope it helps I alrady solved it

Answer:

n = 3

Step-by-step explanation:

Ratio from Triangle A to Triangle B is 2:1.

n+2 = 5

n = 3