Write the equation of the line through (1, 1) that is perpendicular to 6x + y = −10.

The percent error in Abigail 's calculation for the height of the cake to the nearest tenth is 3.64 %.

When compared to the real number and expressed in percent format, percentage error seems to be the variance between the projected amount and the actual number.

By deducting the actual value from the estimated value, you may get the percentage error. Then, divide the real number's absolute value by the absolute value of the error. You will receive the error in decimal form as a result. The percentage error can then be calculated by multiplying the result by 100%.

Given data:

Required height of cake =  78.25 inches

Actual height = 75.5 inches.

Thus,

percent error = (Required height - Actual height)/actual height *100%

percent error = (78.25 - 75.5)/75.5 * 100

percent error = 3.64 %

Thus, the percent error in Abigail 's calculation for the height of the cake to the nearest tenth is 3.64 %.

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Answer:

The answer to your problem is, A. 536,866,822

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

If a fair coin is tossed 29 times, the total number of outcomes will be expressed as: [tex]2^{29} = 536,870,476[/tex]

If at least 2 tails occur, the expected outcome will be 29 times

Pr(at least 2 tails occur) = [tex]2^{29} - 29 - 1[/tex]

Pr(at least 2 tails occur) = [tex]536,870,912 - 30 = 536,866,822[/tex]

Thus the answer to your problem is, A. 536,866,822

The perimeter of the circle formed by bending the rectangular wire will be equal to the length of the wire.

Perimeter of the circle = Length of the wire

2πr = 2(l+b) where r is the radius of the circle, l is the length of the wire, and b is the breadth of the wire.

Substituting the given values, we get:

2 x 3.14 x r = 2(32 + 12)

6.28r = 88

r = 14 cm

Therefore, the radius of the circle is 14 cm.

Answer:

14.01 cm

Step-by-step explanation:

The length of the wire is equal to the perimeter of the rectangle. So, the length of the wire is:

When this wire is bent into a circle, its length becomes equal to the circumference of the circle. The formula for the circumference of a circle is:

(let r = radius)

So, we can write:

Solving for r, we get:

So, the exact value of the radius of the circle formed by bending this rectangular wire is 14.01 cm.

Answer: -2.5

Step-by-step explanation: The absolute value of 0.5 is "0.5".

Therefore; if you subtract the value "3" from "0.5", you will end up with -2.5 as an answer.

Therefore, the potential likelihood of selecting a blue stone is roughly 0.1333 or 13.33%.

Mathematics' study of chance events is known as probability, and there are four major kinds of probability: axiomatic, classical, observational, and subjective.

To find the theoretical probability of choosing a blue marble, we need to divide the number of blue marbles by the total number of marbles in the bag.

Total number of marbles = 3 green + 2 blue + 5 red + 5 yellow = 15

Number of blue marbles = 2

Therefore, the theoretical probability of choosing a blue marble is:

P(Blue) = Number of blue marbles / Total number of marbles = 2 / 15

= 0.1333 (rounded to 4 decimal places)

So, the theoretical probability of choosing a blue marble is approximately 0.1333 or 13.33%.

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Answer : B. 36 Square Centimetres

Explanation : 9 × 8 = 72        72 ÷ 2 = 36

Answer:36 b

Step-by-step explanation:

Pythagoras - Has a theorem named after him

Thales - Contributed to the five basic theorems of geometry

Pythagoras was a Greek philosopher, mathematician, and founder of the Pythagorean school of philosophy. He lived in the 6th century BCE on the Greek island of Samos and is known for his contributions to mathematics, geometry, music, and philosophy.

Pythagoras is most famous for the theorem that bears his name, the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem is fundamental to the study of geometry and has applications in many fields, from architecture to physics.

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Answer:

-13

Step-by-step explanation:

The term in the polynomial which doesn't have any variables is called constant.

So, (-13) is the constant.

Answer:

a)168.725

b)168.735

168.725≤x<168.735

Step-by-step explanation:

a)168.73 - 0.005

168.725

b) 168.73 + 0.005

168.735

Here's what you need to do:

We know that Ryan can install 144 square feet of flooring in 3 hours.

So, if we take 144 square feet, and divide by 3 hours, 144 / 3, we end up with 48, meaning Ryan can install 48 square feet of flooring every hour.

Then, simply multiply 48 by 18, 48 x 18, and you end up with 864.

Meaning, in 18 hours, Ryan can install 864 square feet of flooring.

Answer: 864 square feet.

Answer:   76.67%

Step-by-step explanation:

Answer:

f(x) = - [tex]\frac{1}{2}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 0 ) , x- intercept and (x₂. y₂ ) = (0, - 4) , y- intercept

m = [tex]\frac{-4-0}{0-2}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (- 4, 7 ) into the partial equation

7 = - [tex]\frac{1}{2}[/tex] (- 4) + c = 2 + c ( subtract 2 from both sides )

5 = c

y = f(x) = - [tex]\frac{1}{2}[/tex] x + 5 ← equation of function

The first term of the geometric sequence is 1/2 and the common ratio is 2.

What is the geometric sequence?

A geometric sequence is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed number called the common ratio. The general form of a geometric sequence is:

a, ar, ar², ar³, ar⁴, ...

where 'a' is the first term, 'r' is the common ratio, and the subscripts represent the position of the term in the sequence.

Let's denote the first term of the geometric sequence by "a" and the common ratio by "r".

We know that the third term of the sequence is 2, which means that:

a * r² = 2 (1)

We also know that the sixth term of the sequence is 16, which means that:

a * r⁵ = 16 (2)

Now we can solve for "a" and "r" by dividing equation (2) by equation (1):

(a * r⁵)/(a * r²) = 16/2

Simplifying, we get:

r³ = 8

Taking the cube root of both sides, we get:

r = 2

Now we can use equation (1) to solve for "a":

a * 2² = 2

Simplifying, we get:

4a = 2

a = 1/2

Therefore, the first term of the geometric sequence is 1/2 and the common ratio is 2.

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Answer:

(f•g)(x)=16x²+1

(g•f)(x)=4x²+4

Step-by-step explanation:

f(x)=x²+1, g(x)=4x

(f•g)(x)=f(g(x))

=f(4x)

=(4x)²+1

=16x²+1

(g•f)(x)=g(f(x))

=g(x²+1)

=4(x²+1)

= 4x²+4

Option D. The approximate surface area of the drum is 2744 1/7 in². The surface area of a cylinder can be calculated using the formula:

A = 2πr² + 2πrh

where r is the radius of the base, h is the height of the cylinder, and π is the mathematical constant pi, which we can approximate as 3.14.

Plugging in the given values, we get:

A = 2 x 3.14 x 13² + 2 x 3.14 x 13 x 20.5

= 1060.04 + 1684.06

≈ 2744.1

Rounding this to the nearest 1/7, we get:

2744 1/7 in²

Therefore, the approximate surface area of the drum is 2744 1/7 in². However, none of the given answer choices match this result exactly.

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A cylindrical chemical drum with a radius of 13 inches and a height of 20 1/2 inches needs painting. net of a cylinder What is the approximate surface area of this drum? Use 22,7 for pi.

A. 1062 2/7 in²

B. 1675 1/7 in²

C. 2737 3/7 in²

D. None of the above

Answer:c

Step-by-step explanation:

Answer:

a) 76

b) 26

I could only do the first two.

The amount (Present Value) that Crystal Nelson can invest today so that she can withdraw $46,500 at the end of each year for 20 years when she retires in 5 years' time is $454,047.76.

Firstly, the present value of the periodic withdrawals for 20 years is determined and used as the future value for determining the present value in 5 years.

The present value is the future value discounted to the current period, removing the effect of compound interest.

N (# of periods) = 20 years

I/Y (Interest per year) = 5%

PMT (Periodic Withdrawals) = $-46500

FV (Future Value) = $0

Results:

Present Value (PV) = $579,492.78

Sum of all periodic payments = $-930,000.00

Total Interest = $350,507.22

N (# of periods) = 5 years

I/Y (Interest per year) = 5%

PMT (Periodic Payment) = $0

FV (Future Value) = $579,492.78

Results:

Present Value (PV) = $454,047.76

Total Interest = $ 125,445.02

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The function f(x) = 81 − x2 is increasing on the interval (−∞, 9) and decreasing on the interval (9, ∞).

Parabola is a type of curve which is defined by the quadratic equation. It has a distinct "U" shape, with the vertex of the curve being the highest or lowest point.

The point x = 9 is the vertex of the parabola, which marks the point at which the function changes from increasing to decreasing.

Since the function is a parabola, it is also a polynomial of degree 2, and it is always decreasing for points greater than the vertex, and increasing for points less than the vertex.

This means that the function is increasing on the interval (−∞, 9) and decreasing on the interval (9, ∞).

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Using the appropriate statistical relation, the confidence interval estimate for the net worth of the wealthiest celebrities is (150.35; 204.77).

Given the samples :

X = 256,196,190,166,163,162,148,148,143.

Using a calculator, we could obtain the sample mean and sample standard deviation is-

Mean, μ = [tex]\sum\frac{x}{n}[/tex] = 174.55

Standard deviation, σ = 38.8

The confidence interval can be defined thus :

Mean ± standard error

Standard Error = Tcritical × σ/√n

Tcrit ; 95% ; df = n - 1 = 9 - 1 = 8; T-critical = 2.26

Standard Error = (2.26 × 38.06/√10) = 27.20

Lower confidence boundary = 177.55 - 27.20 = 150.35

Upper confidence boundary = 177.55 + 27.20 = 204.77

Therefore, the confidence interval is (150.35; 204.77)

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Suppose that there is a random variable y, denotes the number of cars observed at car entering an intersection time.

a) Possible values of y are present in above table figure.

b) Five different outcomes and their associated y-values are also present in above figure 2.

Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead (S). The experiment terminates as soon as a car is observed to go straight. Suppose that the random variable y denotes the number of cars observed. List five different outcomes and their associated y-values. In this experiment, each car entering an intersection is observed to see whether it turns left or right or goes straight. Let y denote the number of cars observed.

a) The experiment will terminate as soon as a car is observed to go straight. For this experiment, the possible outcomes are as shown above figure.

b) Also, from the above outcome, the five different outcomes are given below:

Outcome Value of y

RRRS 4

LLRLLS 6

RRS 3

LRRRLS 6

S 1

Hence,

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Complete question :

Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead

(S). The experiment terminates as soon as a car is observed to go straight. Suppose that the random variable y denotes the number of cars observed.

a) what is the possible value of y?

(b)List five different outcomes and their associated y-values.

Outcome Value of y

RRRS

LLRLLS

RRS

LRRRLS

S

Therefore, the expression that represents the balance after two months is: 1500 * (1 + 0.01) * (1 + 0.01) = 1530.15.

Percent, denoted by the symbol "%", is a way of expressing a number as a fraction of 100. For example, 50% is equivalent to the fraction 50/100, which can be simplified to 1/2. Percentages are commonly used to express ratios, proportions, or rates in various contexts such as finance, statistics, and everyday life. For instance, an interest rate of 3% means that for every $100 borrowed, the borrower will be charged $3 per year. Similarly, a score of 80% on an exam means that the student has answered 80 out of 100 questions correctly.

by the question.

To calculate the balance after two months, we first need to calculate the balance after the first month, including the interest earned:

Balance after 1 month = 1500 + (1% of 1500) = 1500 + 15 = 1515

Then, we can calculate the balance after two months, including the interest earned in the second month:

Balance after 2 months = 1515 + (1% of 1515) = 1515 + 15.15 = 1530.15

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Answer:

$0.75 per pound

Step-by-step explanation:

On the graph, the x is the number of pounds of tomato, and the y is the price.

We see when the x is 1 pound of tomato; the y is $0.75. So the unit rate is $0.75 per pound.

Answer:

A

Step-by-step explanation:

B: would lead to g being in the same spot

C: would still be missing the rotation

D:It would be the flipped version of H

Answer:

Any number greater than 10;   11, 12, 15, 20, 100...etc

Step-by-step explanation:

Order the data from least to greatest and strikethrough numbers on each side until you reach the middle 1 or 2 numbers. In this case there are 9 numbers, so the middle number is our median.

8, 8, 8, 8, 10, v, 18, 18, 18

the variable v can be many numbers, but in order for the median to be 10, v must be a number greater than 10. If v = 11, the median is 10. Likewise, if v = 100000, the median is still 10 because it is the middle of the set.

The sum of 8 3/4 + 2 and 1/2 is 11 1/4 ( optionB)

A sum is the result of an addition. For example the sum of 10,15,4,6,12 is obtained by adding all the numbers together.

= 10+15+4+6+12 = 47

Similarly, the sum of 8 3/4 + 2 and 1/2 is obtained by,

35/4 +2 +1/2

The LCM of 4,2 and 1 is 4 and 8 can also be used.

= (70+16+4)/8

= 90/8

= 11 2/8

simplifying the fraction

= 11 1/4.

therefore the the sum of 8 3/4 + 2 and 1/2 is 11 1/4

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According to the solving $310 money you have in savings after 26 weeks, we can use either the recursive or explicit formula:

The explicit equations for L-functions are Riemann's relations between sums over an L-function's complex number zeroes and sums over prime powers for the Riemann zeta function.

a) Recursive formula:

Let S(n) be the amount of money in savings after n weeks. Then:

S(0) = 50 (initial amount)

S(n) = S(n-1) + 10 (deposit of $10 per week)

b) Explicit formula:

The explicit formula for this sequence is:

S(n) = 50 + 10n, where n is the number of weeks.

c) To find how much money you have in savings after 26 weeks, we can use either the recursive or explicit formula:

Using the recursive formula:

S(0) = 50 (initial amount)

S(1) = S(0) + 10 = 50 + 10 = 60

S(2) = S(1) + 10 = 60 + 10 = 70

S(3) = S(2) + 10 = 70 + 10 = 80

and so on, until:

S(26) = S(25) + 10 = 310

Therefore, after 26 weeks, you have $310 in savings.

Using the explicit formula:

S(26) = 50 + 10(26) = 50 + 260 = 310

after 26 weeks, you have $310 in savings.

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To start, denote x as the number of lbs utilized per each coffee type (type A and type B). Further, let ax be the quantity of lbs for type A coffee and bx be the quantity of lbs for type B coffee. So, ax and bx are in units of quantity*lbs.

The cost of type A and type B coffee can be equated as follows:

Cost (A) = 5.95/lb and Cost (B) = 4.65/lb

The key information given ("This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $796.00") can be represented algebraically as follows:

Cost (Blend) = Cost(A)*ax + Cost(B)*bx = $796.00. Since the quantity of type B coffee is 3 times the quantity of type A coffee, it follows that a = 1 and b = 3.

Therefore, 5.95/lb*(x) + 4.65/lb*(3x) = 796--> 5.95/lb*(x) + 13.95/lb*(x) = 796 or (5.95+13.95)(x) = 796.

Therefore, quantity (lbs) = 796/(13.95+5.95) = 796/(19.9) = 40.

Using the previous relation, we know that 3x + x = 40 or 4x = 40. So, the number of lbs for type A coffee utilized in the blend equates to the following:

x = 10 lbs.