I need help with this question, please. This is non graded.

(a)the common ratio = 2

(b)the 6th term​ = 64

How to find the common ratio and 6th term ?

        Here, the common ratio = r

                   the first term = a = 2

(a)the common ratio

\(a +ar^{2} = 10\\\\2(1+r^{2} ) = 10\\\\(1+r^{2} ) = 5\\\\r^{2} =4\\\\r = 2\)

The common ratio (r) = 2

(b)the 6th term​

\(a_{n}=ar^{n-1} \\\\a_{6}=ar^{6-1} \\\\a_{6} =2(2^{5} )\\\\a_{6}=64\)

Thus ,the 6th term​ = 64

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Answer:

The sensitivity rate of the test is 88%.  For its part, the specificity rate of the test is 91%.

Step-by-step explanation:

The sensitivity of a medical test is its ability to detect positive cases of the disease, while the specificity of the test is its ability to detect negative cases.

In total, there are 270 cases:

-80 positives

-10 false negatives

-15 false positives

-165 negatives

Thus, to calculate both concepts, the following calculations must be performed:

Sensitivity = positives / (positives + false negatives)

X = 80 / (80 + 10)

X = 80/90

X = 0.88

Thus, the sensitivity rate of the test is 88%.

Specificity = negatives / (negatives + false positives)

X = 165 / (165 + 15)

X = 165/180

X = 0.91

For its part, the specificity rate of the test is 91%.

Answer:

a = 3

Step-by-step explanation:

ok so first you do the reciprocal of division which is multiplication. So its gonna be 3/4 x 1/a = 1/4

you multiply the fractions 3/4 x 1/a and get 3/4a = 1/4

then you cross multiply and you get 12=4a

swap sides so its going to be 4a = 12

divide both sides by 4 and you get a = 3

The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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You have the following system of equations:

y = 2x + 9

y = 6 - x

The graph of the previous line is shown below:

In the previous graph, the red line is y=2x + 9 and the blue line is y=6-x.

The intersection point is (-1,7)

The cumulative frequency for the class with a lower class limit of 27 is 4 + 7 + 7 = 18.

What is the cumulative frequency?

The cumulative frequency for a class is the total frequency of that class and all the classes before it.

In order to find the cumulative frequency for the class with a lower class limit of 27, you would need to add the frequency of that class with the frequencies of all the classes before it.

The cumulative frequency for a class with a lower class limit of 27 can be found by adding up the frequencies of all the classes that come before it.

In this case, the classes that come before the class with a lower class limit of 27 are "Ages 15-18", "Ages 19-22", and "Ages 23-26",

Hence, the cumulative frequency for the class with a lower class limit of 27 is 4 + 7 + 7 = 18.

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Complete Question:

Ages 15-18 19-22 23-26 27-30 31-34 35-38 Number of students 4 7 7 2 5 10 Based on the frequency distribution above, find the cumulative frequency for the class with a lower class limit 27?

If yοu take the rebate, yοur mοnthly payment will be $819.08, if yοu chοοse dealer financing, yοur mοnthly payment will be $833.33, yοu wοuld save $342.00 οver the life οf the lοan by taking the rebate οptiοn.

A lοan is a sum οf mοney that is bοrrοwed and is expected tο be paid back with interest. It is a type οf financial transactiοn between a lender and a bοrrοwer, where the lender prοvides the bοrrοwer with a specific amοunt οf mοney, which the bοrrοwer agrees tο repay with interest οver a set periοd οf time.

If you take the rebate, you will have to take out a loan from a local bank for $18,000 at an APR of 6.5% for 2 years.

To calculate the monthly payment, we can use the loan payment formula:

Monthly payment =\(\rm (P \times r) / (1 - (1+r)^{(-n)})\)

where P is the principal amount, r is the monthly interest rate, and n is the total number of payments.

First, we need to calculate the monthly interest rate by dividing the annual percentage rate by 12:

r = 0.065 / 12 = 0.0054

Next, we need to calculate the total number of payments:

n = 2 x 12 = 24

Substituting these values into the loan payment formula, we get:

Monthly payment = (18,000 x 0.0054) / \((1 - (1+0.0054)^{(-24)})\) = $819.08

Therefore, if you take the rebate, your monthly payment will be $819.08.

If you choose dealer financing with no rebate, you will be financing the full $20,000 at a 0% interest rate for 2 years.

Using the same formula, we can calculate the monthly payment:

Monthly payment = (20,000 x 0) / 24 = $833.33

Therefore, if you choose dealer financing, your monthly payment will be $833.33.

Since the monthly payment for dealer financing is higher than the monthly payment for the rebate option, you should take the rebate and get a loan from a local bank.

To calculate the amount you save over the life of the loan, we can subtract the total amount paid for the rebate option from the total amount paid for the dealer financing option:

Total paid for rebate option = $819.08 x 24 = $19,657.92

Total paid for dealer financing option = $833.33 x 24 = $19,999.92

Amount saved = $19,999.92 - $19,657.92 = $342.00

Therefore, you would save $342.00 over the life of the loan by taking the rebate option.

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Answer:

60 and -60

Hope this helps! :)

Basic info:

4 (x) hours = 6 logs (y), need keep fire burning for 18 hours.

Problem:

4x = 6y

what y = 18x?

8x = 12y

16x = 24y

18x = 26y

Answer:

26 logs

Average daily balance method

Answer: 162%.

Step-by-step explanation:

To find the percentage increase in points, we need to calculate the difference between the two values, divide it by the original value, and then multiply by 100 to get the percentage.

The difference between Patrick's old score and his new score is:

328 - 125 = 203

The percentage increase is:

203/125 x 100% = 162.4%

Rounded to the nearest whole number, the percentage increase is 162%.

Part a: The shaded area of the figure's polynomial expression: 16x + 30.

B) The larger rectangle has a surface area of 96 Sq in.

D) The smaller rectangle has a surface area of 18 Sq in.

By combining numbers and variables with the help of arithmetic operations like addition, subtraction, multiplied, division, and exponentiation, polynomials are algebraic expressions.

A polynomial can be made by adding or removing terms. Applications ranging from engineering and sciences to business can benefit greatly from polynomials

For question:

Dimensions are-

Complete region:

Non shaded rectangle:

Part A: The shaded area of the figure's polynomial expression is as follows:

Area = Length * width(complete)   -  Length * width(smaller)

Area = (2x + 6)(x + 5) - 2x(x)

Area = 2x² + 16x + 30 - 2x²

Area = 16x + 30

Find x-

Given shaded area = 78 sq. in

78 = 16x + 30

16x = 48

x = 3

B) The larger rectangle has a surface area of ___Sq in.

Area of larger rectangle = (2x + 6)(x + 5)

 = (2*3 + 6)(3 + 5)

= 12*8

= 96 Sq in.

D) The smaller rectangle has a surface area of __Sq in.

Area of smaller rectangle = 2x (x)

= 2*3*3

= 18 Sq in

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Answer:

--

Step-by-step explanation:

Show all the options please

Not able to see all options

Angles in a triangle add up to 180 degrees

The value of x is 85 degrees

A triangle is a polygon which has  three sides and three vertices. It is one of the normal shapes in geometry. A triangle with vertices A, B, and C has three sides & three angles A, B, C.

here, we have,

How to determine the value of x

The total  sum of angles for a triangle is 180 degrees.

So, we have:

x + 35 + 60 = 180

Evaluate the sum

x + 95= 180

Subtract 95 from both sides

x = 85

Hence, the value of x is 85 degrees

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Full question: (SAT Prep) Find the value of x. 35° 60° X

x=?​

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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Answer:

12 or B is the answer

Step-by-step explanation:

The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

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Health club B costs $70 each month more than Health club A.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Health Club B charges a $30 sign-up fee and $40 per month. The graph below represents what Health Club A charges.

Now, Equation of line is,

For Health club B;

⇒ y = 40x + 30

For Health Club A;

⇒ y - 121 = (333 - 121) / (6 - 2) (x - 2)

⇒ y - 121 = 212/4 (x - 2)

⇒ y - 121 = 53 (x - 2)

⇒ y - 121 = 53x - 106

⇒ y = 53x - 106 + 121

⇒ y = 53x + 15

For each month,

Cost For Health club B;

⇒ y = 40x + 30

⇒ y = 40 + 30

⇒ y = $70

Cost For Health Club A;

⇒ y = 53x + 15

⇒ y = 53 + 15

⇒ y = $68

Thus, Health club B costs $70 each month more than health club A.

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To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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Answer: 309.73

Step-by-step explanation:

75 miles per hour is the rate of train.

Formula of speed = distance/time

let,

s1 , speed of A train = s

s2, Speed of B train = s

t1, time of travel for train A = 2.5h

t2, time of travel for train B = 4 h

d1, distance traveled by train A

distance travel by train A = speed*time

                                         = s1*t1

d2, distance traveled by train B

distance travel by train A = speed*time

                                         = s2*t2

Total distance between station A  and station B = 562.5 mi

d1+d2=562.5 mi

s1t1+s2t2=562.5

s(2.5)+s(4)=562.5

6.5 s = 562.5

s = 562.5/6.5

s = 86.5 mph

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75 miles per hour is the rate of the train.

Given:

Find:

Solution:

Formula of speed = distance/time

Let us consider

Speed of A train(s1) = s

Speed of B train(s2) = s

Time of travel for train A(t1) = 2.5h

Time of travel for train B(t2) = 4 h

Distance traveled by train A(d1)

                                        = speed*time

                                        = s1*t1

Distance traveled by train B(d2)

                                        = speed*time

                                        = s2*t2

The total distance between station A  and station B = 562.5 mi

d1+d2=562.5 mi

s1t1+s2t2=562.5

s(2.5)+s(4)=562.5

6.5 s = 562.5

s = 562.5/6.5

s = 86.5 mph

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Answer:

roots

Step-by-step explanation:

A quadratic equation with real or complex coefficients has two solutions, called roots.

Roots are also called x-intercepts or zeros. ... The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.

Answer:

D. The US allowed China into the United Nations

Step-by-step explanation:

The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

To determine the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\), we need to consider the situation and the constraints given.

The function A(t) represents the area of the rectangular garden as a function of the length of one of its sides, which is denoted by t.

We are also told that Marama plans to fence the garden with 28 feet of wired fencing.

Now, let's break down the problem and find the appropriate values for the domain.

We know that the perimeter of a rectangle is the sum of all its sides. In this case, since we have a rectangular garden, the perimeter can be represented as:

\(Perimeter = 2t + 2w\),

where t is the length of one side (the width) and w is the length of the other side (the width).

The problem states that Marama plans to use 28 feet of wired fencing. Therefore, the perimeter of the garden must equal 28 feet:

\(2t + 2w = 28\).

Simplifying this equation, we have:

\(t + w = 14\).

We can express w in terms of t as \(w = 14 - t\).

The area of a rectangle is given by the product of its length and width:

\(Area = t \times w\).

Substituting the expression for w from step 2, we have:

\(A(t) = t \times (14 - t)\).

Simplifying further:

\(A(t) = 14t - t^2\).

To determine the appropriate values of the domain, we need to consider the context of the problem. Since we are dealing with a physical garden, both the length and width must be positive numbers. Additionally, the values of t must be feasible given the constraints of the perimeter.

We know that \(t + w = 14\), so \(t + (14 - t) = 14\), which simplifies to \(14 = 14\).

This shows that the value of t can range from 0 to 14, inclusive.

Therefore, the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\) are \(t \epsilon [0, 14]\).

To illustrate this graphically, we can plot the function \(A(t) = -t^2 + 14t\) and mark the appropriate values of the domain on the x-axis (representing t):

   ^

   |

A(t)|

   |

   |_______________________________

   0              t             14

The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

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Certain types of songs tend to have a call-and-response structure because A. It can have many different sections

A call and response in music is a series of two independent phrases that are typically composed in separate portions of the piece, with the second phrase being heard as a direct remark or answer to the first.

Direct imitation between instruments, a questioning phrase and subsequent response, a statement of affirmation from one instrument to another, or variations on a direct call by a group of instruments are examples of call and response.

Therefore, certain types of songs tend to have a call-and-response structure because it can have many different sections

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Answer:

it's simple math honey, just look it up

Answer: The probability that both events A and B will occur is 5/18 or 0.28.

Step-by-step explanation:

To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.

Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.

Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.

To find the probability that both events A and B occur, we multiply the probabilities:

Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.

Answer:

The answers for:

Step-by-step explanation:

In order to find the value of expression, you have to apply gradient formula :

\(m = \frac{y2 - y1}{x2 - x1} \)

So for Question 1,

\(let \: (3,2) \: be \: (x1,y1) \\ let \: (4,j) \: be \: (x2,y2) \\ let \: m = 1\)

\( \frac{j - 2}{4 - 3} = 1\)

\( \frac{j - 2}{1} = 1\)

\(j - 2 = 1\)

\(j = 1 + 2 = 3\)

Question 2,

\(let \: (5,0) \: be \: (x1,y1) \\ let \: (1,k) \: be \: (x2,y2) \\ let \: m = \frac{1}{2} \)

\( \frac{k - 0}{1 - 5} = \frac{1}{2} \)

\( \frac{k}{ - 4} = \frac{1}{2} \)

\(k = \frac{1}{2} \times - 4 = - 2\)

Question 3,

\(let \: (x,2) \: be \: (x1,y1) \\ let \: (3, - 4) \: be \: (x2,y2) \\ let \: m = 2\)

\( \frac{ - 4 - 2}{3 - x} = 2\)

\( \frac{ - 6}{3 - x } = 2\)

\( - 6 = 2(3 - x)\)

\( - 6 = 6 - 2x\)

\( - 6 - 6 = - 2x\)

\( - 2x = - 12\)

\(x = - 12 \div - 2 = 6\)

Question 4,

\(let \: (12, - 4) \: be \: (x1,y1) \\ let \: (r,2) \: be \: (x2,y2) \\ let \: m = - \frac{1}{2} \)

\( \frac{2 - ( - 4)}{r - 12} = - \frac{1}{2} \)

\( \frac{6}{r - 12} = - \frac{1}{2} \)

\( - 1(r - 12) = 2(6)\)

\( - r + 12 = 12\)

\(r = (12 - 12) \div - 1 = 0\)