You will pay tax on a purchase of $27.89. The tax
rate is 6.5%. How much will your total be?

Answer:

64.428

Step-by-step explanation:

well to find the mean we add all of the numbers up and then divide it by the amount of numbers in the sequence

so if we add all of the numbers up it will give us

451

then if we divide that by the number of numbers in the sequence which is 7 then that will leave us with

around 65 or exactly it would be

64.428

a) The 99% confidence interval for n = 64 is (21.129, 45.671).

b) The 90% confidence interval for n = 256 is (29.331, 37.469).

c) A larger sample size leads to a smaller standard error, resulting in a narrower interval.

To find the confidence intervals, we'll use the formula:

a. For a 99% confidence interval with n = 64:

Mean (μ) = 33.4

Standard Deviation (σ) = 37

Sample Size (n) = 64

First, we need to find the critical value associated with a 99% confidence level. For a normal distribution, this corresponds to a z-score of 2.576.

Confidence interval = 33.4 ± (2.576)  (37 / √(64))

Confidence interval = 33.4 ± (2.576)  (4.625)

Calculating the upper and lower limits of the confidence interval:

Lower Limit = 33.4 - (2.576) (4.625) ≈ 21.129

Upper Limit = 33.4 + (2.576)  (4.625) ≈ 45.671

Therefore, the 99% confidence interval for n = 64 is (21.129, 45.671).

b. For a 90% confidence interval with n = 256:

Mean (μ) = 33.4

Standard Deviation (σ) = 37

Sample Size (n) = 256

The critical value associated with a 90% confidence level for a large sample size can be approximated using a z-score of 1.645.

Confidence interval = 33.4 ± (1.645)  (37 / √(256))

Confidence interval = 33.4 ± (1.645)  (2.3125)

Calculating the upper and lower limits of the confidence interval:

Lower Limit = 33.4 - (1.645) (0.3125) ≈ 29.331

Upper Limit = 33.4 + (1.645)  (2.3125) ≈ 37.469

Therefore, the 90% confidence interval for n = 256 is (29.331, 37.469).

c. The width of a confidence interval is given by the difference between the upper and lower limits.

Thus, for part a, the width is 45.671 - 21.129 ≈ 24.542,

and for part b, the width is 37.469 - 29.331 ≈ 8.138.

When quadrupling the sample size while holding the confidence coefficient fixed, the width of the confidence interval is expected to decrease. This is because a larger sample size leads to a smaller standard error, resulting in a narrower interval.

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If the function f(x) = x⁵ + (x + 3)² will be 3 then x = -1.

The graph is a function if any vertical line drawn through it can cross it at most one point. The graph is not a function if it has any locations where a vertical line can pass through the graph at two or more different places.

A mathematical function from a set X to a set Y assigns exactly one element of Y to each element of X. The function's domain and codomain, respectively, are the sets X and Y as a whole. Initially, functions represented the desired relationship between two fluctuating values.

A function is a relation that specifically links members of one set to those of another set. Formally speaking, a function from to is an object such that each is specifically connected with an object. Therefore, a function is a many-to-one (or occasionally, a one-to-one) relation.

Let the given function be f(x) = x⁵ + (x + 3)²

When x = -1 then f(-1) = (-1)⁵ + (-1+3)² = -1 + 4 = 3.

Therefore, the function f(x) = x⁵ + (x + 3)² will be 3 then x = -1.

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Answer:

= 7/2

Step-by-step explanation:

−

p = 3.5

Step-by-step explanation:

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

Answer:

Blue:  32.4 mpg

Red:  28 mpg

The Blue car will travel farther on a gallon of gasoline

Step-by-step explanation:

Blue: 40.5/1.25=32.4 mpg

Red: (22 2/5)/(4/5) =22.4/0.8=28 mpg

The value of BD will be 22 for the given line segment.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

Given the line segment BD with a between point C

Now,

BC = 3X = 15

X = 5

So,

CD = 4(5) - 13 = 7

So,

BD = BC + CD

BD = 15 + 7 = 22

Hence "The value of BD will be 22 for the given line segment".

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Answer:

whats the question for this?

Step-by-step explanation:

Answer:

17×6=102 because he gave 2 boxes to his brother so he have 6 boxes

Complete question :

Taylor earns $5 each time she walks her neighbor's dog. She has already earned $25. Write and solve an equation to find out how many more times Taylor needs to walk the dog to earn enough to buy a bike that costs $83.

Answer:

12

Step-by-step explanation:

Amount earned for walking dog = $5 per walk

Amount already earned = $25

How many more times dog needs to be walked to buy a bike which costs $83

Target amount = 83

(Target amount - already earned amount) / amount earned per Walk

(83 - 25) / 5

58 / 5

= 11.6

Hence, Taylor needs to walk her neighbor's dog 12 more times

Answer:

Yes

Step-by-step explanation:

A slanted straight line is one-to-one:  It passes the "horizontal ilne test."  This means that any line drawn horizontally through the given line intersects that line only once.  The significance of this is that the given line/function has an inverse.  y = x is one-to-one and has the inverse y = x.  y = 2x is one-to-one and has the inverse y = (1/2)x.

Answer:

y + 8 = 1/2(x + 3)

Step-by-step explanation:

Hope this helpss!!!

Answer:

i think its 5.0 or -11

Step-by-step explanation:

Answer:

x+12=12(opposite sides of parallelogram are equal)

x=0

The x-intercept of the function  is -3

One example of an intercept is the X-intercept, which is when a line crosses the x-axis.

Where a line crosses the y-axis is known as the y-intercept.

One play in numerous football formats is the interception.

Donald Hamilton's 1980 thriller The Mona Intercept

Nixon announced Operation Intercept as a drug-prevention initiative.

Telephone monitoring, often known as third-party eavesdropping on phone and online talks

Android smartphone Samsung Intercept (SPH-M910) Visual Intercept, a Microsoft Windows-based software defect monitoring tool

A measurement of the linearity of an electrical device is the intermodulation intercept point.

A telephone recording known as the intercept message informs the caller that the call cannot be finished.

The Intercept is an online news source run by Jeremy Scahill, Laura Poitras, and Glenn Greenwald.

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Answer:

To find the x-intercept of the function, we need to find the value of x where the function h(x) is equal to zero.

Setting h(x) = 0, we have:

0 = 3∛(x - 5) + 6

Subtracting 6 from both sides, we get:

-6 = 3∛(x - 5)

Dividing both sides by 3, we get:

-2 = ∛(x - 5)

Cubing both sides, we get:

-8 = x - 5

Adding 5 to both sides, we get:

x = -3

Therefore, the x-intercept of the function is -3.

The answer is: -3.

If we can notice the difference between 10- and 11-pound weight, we can  differentiate 110-pound weight from a 100-pound weight.

All things close to Earth are constantly subject to the force known as weight. All items are pulled downward toward the Earth's core by the gravity of the planet. On the other hand, weight is a measurement of how much gravity pulls an item downward. The mass of the thing has an impact on this force; the heavier the object, the stronger gravity's pull is. The force of gravity acting on a body is the most typical definition of weight given in introductory physics textbooks. This is sometimes formulated as W = mg, where W is the weight, m is the object's mass, and g is the acceleration due to gravity.

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The given information is:

- The area of the sector of the circle is 31.2 cm^2.

- The exterior of the sector angle is 256°.

The area of the sector is given by the formula:

Where theta is the sector angle and r is the radius of the circle.

The whole circle measures 360°, so the sector angle can be found as follows:

Now, replace theta and the area value in the formula to solve for r:

The radius of the circle is 5.9 cm.

The system of equations has no solution. Option A is the correct optio.

What is the system of equations?

Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.

Given system of equations is

3x - 9y =0 .....(i)

-x + 3y = -3 .....(ii)

Multiply -3 with equation (ii)

3x - 9y = 9 .....(iii)

Subtract equation (i) from (iii):

3x - 9y = 9

3x - 9y =0

________

        0 = 9

Which is a false statement.

Thus the system of equations has no solution.

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Answer:

the answer is A. 0

The ordered pairs for the system of equations f(x) = x^2 -2x + 3 and f(x) = -2x + 12 are (3, 6) and (-3, 18)

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0)

f(x) = x^2 -2x +3 and f(x) = -2x + 12

which means

x^2 -2x +3  = -2x + 12

x^2 -2x +3  + 2x - 12 = 0

x^2 -9 = 0

by factorizing we have

(x-3)(x+3) = 0

x = 3 or -3

when x = 3

f(x) = -2x + 12

f(3) = -2(3) + 12 which is 6

when x = -3

f(-3) = -2(-3) + 12 which is 18

ordered pairs are (3, 6) and (-3, 18)

In conclusion, (3, 6) and (-3, 18) are the ordered pairs

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Answer:

x = 9 ; y = 18

Step-by-step explanation:

This is a 30° 60° 90° triangle meaning the length of the big leg will be the value of the small leg times √3 and the hypotenuse will be double the length of the small leg.

Answer:

x = 9

y = 18

Step-by-step explanation:

tan(60) = 9 radical 3 / x

x = 9 radical 3 / tan(60)

x = 9

a² + b² = c²

9² + 9radical3² = c²

324 = c²

c = 18

y = 18

Answer:

slope: 4/5

y-intercept: (0,4)

slope intercept form: y = 4/5 x + 4

Step-by-step explanation:

to find the slope, you have to find the difference of the x coordinants and the difference of the y coordinants. since the two coordinants we have are 0,4 and 5,0 and we know that 0 - 5 is -5 and 0 - 4 is -4 we then have to divide the two. so now we get -4/-5. since a negative divided by a negative is a positive, the negative signs cancel out. since the fraction is in simplest form, that is our answer. also, since its rise over run, it means that everytime you go up or down 4 and over 5, you will reach a whole number on the graph.

okay, now the y-intercept is when the line crosses the y-axis/when x=0. the y-intercept for this example would be 4 or (0,4). i hope that makes sense. like i said ill get back to you on the slope thing in a minute just a second...

Answer: y - 6 = -(1/2)(x+1)

Step-by-step explanation:

1. First step is to remember point slope form (a common way of expressing the equation for a line).

y - y1 = m(x - x1)

2. Next fill in the data we are given.

y - 6 = m(x -(-1)) ----> y - 6 = m(x + 1)

3. Next step is to find the value of the slope (m) using slope formula.

m = (y2 - y1) / (x2 - x1)

4. Fill in the data

m = (5 - 6) / (1 +1) = - 1 /2

5. Add the calculated slope to the point slope form.

y - 6 = -(1/2)(x+1)

Answer:

draw another segment I think. __________

Step-by-step explanation:

The complete sentence is

Danielle’s drive is 10 times less than that of Nina’s drive

From the question, we are complete the given sentence

The given sentence is

Danielle’s drive is _____ than that of Nina’s drive.

That is,

We are to determine how many times less or greater Danielle’s drive is to Nina’s drive

From the given information,

Nina drives 0.9 of a mile to the grocery store

and

Danielle drives 0.09 of a mile to school

First, we will divide 0.9 by 0.09

0.9/0.09 = 10

This means 0.9 is 10 times greater than 0.09

OR

0.09 is 10 times lesser than 0.9

Thus,

Danielle’s drive is 10 times less than that of Nina’s drive

Hence, the complete sentence is

Danielle’s drive is 10 times less than that of Nina’s drive

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The probability that each of the final rolls is at least as large as the roll preceding it is \(1/6^6\) or 1/46656.

Given data,

A fair die is rolled n times. We have to find the probability that each of the final rolls is at least as large as the roll preceding it.The probability that each of the final rolls is at least as large as the roll preceding it means the probability of getting each number greater than the preceding one. So, there will be no duplicates.

First, find the total possible outcomes on a fair die. The total possible outcomes on a fair die are 6 because the numbers are 1,2,3,4,5,6. The number of possible outcomes for each roll of the die is 6. Then the total number of possible outcomes on the nth roll of a die is\(6^n\). There will be only one possible sequence in which each of the final rolls is at least as large as the roll preceding it. Let's check it from the following table.

Roller 1Roller 2Roller 3Roller 4Roller 5Roller 61-2-3-4-5-6

Here, we got only one sequence 1,2,3,4,5,6 to have each number greater than the preceding one. So, the probability of getting this sequence is \(1/6^6\).

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Answer:

cindy is 51

Step-by-step explanation:

70 divided by 2 is 45

45+ 6 is 51

The volume common to two spheres, each with radius r, if the distance between their centres is r/2 is V = (11/12)×π×r³.

The attached diagram shows 2 circumferences with radius r and separated centres by r/2.

Let´s call circumferences  1 and 2; by symmetry, rotating area A will produce a volume V₁ identical to a V₂, Obtained by rotating area B ( both around the x-axis), then the whole volume V will be:

V = 2× V₁

V₁ = ∫π×y²×dx         (1)

Now

( x - r/2)²  +  y² = r²       the equation of circumference 1

y² = r² - ( x - r/2)²

Plugging this value in equation (1)

V₁ = ∫π×[  r² - ( x - r/2)²]×dx        with integrations limits    0 ≤ x ≤ r/2

V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx

V₁ = π× [  r²×x - x³/3 + (r/2)²×x - (1/2) × r × x²]    evaluate between 0 and r/2

V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) × r × x²]

V₁ =  π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ -  (1/2) × r × (r/2)²]

V₁ =  π× [ (5/8)×r³ - r³/24 - r³/8]

V₁ =  π× (11/24)×r³

Then

V = 2× V₁

V = 2×π×11/24)×r³

V = (11/12)×π×r³

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Answer:

\(=\frac{49}{9}\)

Step-by-step explanation:

Given the following question:

\(5\frac{4}{9}\)

In order to convert a mixed number into an improper fraction, you have to multiply the denominator by the whole number (in this case; 9 and 5) and then add the numerator (in this case; 4) to receive your answer. Of course, keeping the denominator the same.

\(5\frac{4}{9}\)
\(5\frac{4}{9}=9\times5=45+4=49=\frac{49}{9}\)
\(=\frac{49}{9}\)

Hope this helps.

The improper fraction for the given mixed fraction is 49/9.

The given fraction is \(5\frac{4}{9}\).

These are just improper fractions written as a sum of whole number and a proper fraction. (improper fraction has the upper value(also called numerator) bigger or equal to denominator(the bottom value) and proper fraction has numerator value is less than that of the denominator)

They are written and can be converted to fraction as \(a\frac{b}{c}=\frac{(a\times c)+b}{c}\)

Now, \(5\frac{4}{9}=\frac{(5\times9)+4}{9}\)

= (45+4)/9

= 49/9

Therefore, the improper fraction for the given mixed fraction is 49/9.

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The sine rule is the ratio of perpendicular and hypotenuse. Then the length of the hypotenuse is 3 units.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Then the length of the hypotenuse is given by the sine rule.

\(\rm \sin \theta = \dfrac{Perpendicular}{Hypotenuse}\)

We have

θ = 45°

P = 3√2

Then we have

\(\rm H = 3\sqrt2 \sin 45^o\\\\H = 4.2426 \times 0.7071\\\\H = 2.9999 \approx 3\)

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The sample space for the experiment of spinning a four-part spinner is the set of all possible outcomes of the experiment.

In this case, the sample space would be: s = {q, r, s, t}

This means that the possible outcomes of the experiment are q, r, s, and t. Each of these outcomes is equally likely to occur when the spinner is spun.

Option s = {q, r, r, t} is incorrect because it includes two occurrences of the outcome r, which is not possible in this experiment.

Option s = {r, a, t} is incorrect because it includes the outcome a, which is not part of the sample space.

Option s = {s, q, q} is incorrect because it includes two occurrences of the outcome q, which is not possible in this experiment.

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Answer:

\(s=-9\pm8\sqrt{2}\)

Step-by-step explanation:

\(s^2+18s=47\\\\s^2+18s-47=0\\\\s=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\s=\frac{-18\pm\sqrt{(18)^2-4(1)(-47)}}{2(1)}\\ \\s=\frac{-18\pm\sqrt{324+188}}{2}\\\\s=\frac{-18\pm\sqrt{512}}{2}\\\\s=\frac{-18\pm16\sqrt{2}}{2}\\ \\s=-9\pm8\sqrt{2}\)

This is all assuming that your problem is a quadratic equation