Last year Liz bought a book for $10. This year the same book is on sale for $5. What was the percent of change?

In the given equation which is 3 + 2n = 7, the value of n = 2.

For, further explanation to find the value of the variable in the given equation, we can solve the given equation by transferring the non-variable digits to one side either to L.H.S or R.H.S.

Given equation = 2n + 3 =7

In the above equation, the variable is 'n' and the non-variable digits are '3' and '7'. To find the value of 'n', we can transfer the non-variable digits to the R.H.S (Right Hand Side) as shown below:

2n + 3 = 7

2n = 7 - 3

2n = 4

n = [tex]\frac{4}{2}[/tex]

n = 2.

So, from the above solution the value of 'n' is 2.

Given question is incomplete/incorrect, I assume the given question was to "obtain the value of n from the linear equation 3 + 2n = 7"

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Answer:

42 degrees

Step-by-step explanation:

So, first to find <QUT, which is a vertical angle, we have to figure out either QUR or TUS.  So:

9x+3=11x-27

solve for x:

x=15

Then, plug it into one of the equations.  Let's use 9x+3.

9(15)+3=138

So, we know that QUR is 138 degrees.

That means that TUS is ALSO 138.

138x2=276

Now we know that QUT and RUS have to equal whatever 360-276 is:

360-276=84

QUT and RUS have to equal 84 degrees, so we DIVIDE by 2.

84/2=42

So, QUT=42 degrees

Answer:

42 Degrees

Step-by-step explanation

Becuase (11x-27) and (9x+3) are vertical angles that means they are equal to each other

(11x - 27) = (9x + 3)

First you will add 27 to both sides

11x -27 = 9x +3

     +27         +27

Making it to:

11x = 9x + 30

Now you need to subtract 9x from both sides

11x = 9x +30

-9x   -9x

Turning it into this

2x= 30

Now Lastly, divide both sides by 2

2x = 30

2x     2x

And the answer is...... X=15

Now that you have the x value, we go back to the 11x-27 and replace the X with 15

11(15) -27 = 138 degress

Now because angle QUT and 138 degrees make a straight line that means together they will be 180 degress so you will subtract 180 by 138

Giving you the final answer of

42 Degrees

Answer: $0.85

:)

hope this hellps

Answer:

$3.40 per pint

Step-by-step explanation:

4 cups is equal to 2 pints, as there are 4 cups in 2 pints.

So let's set up an equation:

6.80/2

3.40

If your friend in college decides to purchase textbooks using his credit card. The number of  year his credit card balance be $1360 is 8 years.

We can use the continuous compounding formula to solve this problem:

A = Pe^(rt)

where A is the ending balance, P is the initial balance, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.

In this case, we want to solve for t when P = 500 and A = 1360. The interest rate is given as 12.5% compounded continuously, which means r = 0.125. Substituting these values into the formula, we get:

1360 = 500e^(0.125t)

Dividing both sides by 500, we get:

e^(0.125t) = 2.72

Taking the natural logarithm of both sides, we get:

0.125t = ln(2.72)

Solving for t, we get:

t = ln(2.72)/0.125 ≈ 8

Rounding to the nearest year, we get that it will take 8 years for the credit card balance to reach $1360 without making any payments.

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Explanation: We subtract the given value from 1

1-0.31 = 0.69

The complement of an event is the complete opposite.

Example: heads vs tails

To find the population of the city, we need to find the total number of people living in the city. We know that there are 1350 people per square mile, so we can find the total number of people by multiplying the number of square miles in the city by the number of people per square mile.

The area of the city is the length times the width, so:

Area = Length x Width

Area = 12 miles x 8 miles

Area = 96 square miles

Now, we can find the population by multiplying the area by the number of people per square mile:

Population = Area x People per square mile

Population = 96 square miles x 1350 people per square mile

Population = 129,600 people

Therefore, the population of the city is 129,600 people.

Hope this helps!

Answer:

  8%

Step-by-step explanation:

You want to know what percentage of milkshakes had whipped cream if 2 had whipped cream and 23 didn't.

The fraction of the total number that had whipped cream is ...

  2/(2+23) = 2/25

The percentage is found by multiplying the fraction by 100%:

  2/25 × 100% = 8%

8% of the milkshakes had whipped cream.

We can say with 95% certainty that the genuine rate of all patients at this clinic who have high blood pressure is between 24% and 42%. 

To develop a 95% certainty interim for the rate of all patients at this clinic that have tall blood weight, we will utilize the equation:

CI = p ± z*(p*(1-p)/n))

where p is the sampling extent, z is the z-score related to the required certainty level (in this case, 1.96 for 95% certainty), and n is the test measure.

We are given that out of a test of 100 patients, 33 have high blood weight. In this manner, the test extent is:

p = 33/100 = 0.33

Utilizing the equation over, we will calculate the edge of the mistake:

Arduino

ME = z*(p*(1-p)/n)) = 1.96*(0.33*(1-0.33)/100)) ≈ 0.09

At that point, we are able to develop the 95% certainty interim:

CI = p ± ME = 0.33 ± 0.09 = (0.24, 0.42)

Hence, able to say with 95% certainty that the genuine rate of all patients at this clinic who have high blood weight is between 24% and 42%. 

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Answer:5

Step-by-step explanation:

it would be 5 because

The value of k is approximately 0.034. The projected Hispanic resident population in 2015 is approximately 73.9 million. The Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.

To find k, we can use the fact that A = 35.3 million when t = 0 (i.e., in 2000), and A = 50.5 million when t = 10 (i.e., in 2010). Substituting these values into the exponential growth function, we get

35.3 = 35.3e^0k

50.5 = 35.3e^(10k)

Dividing the second equation by the first equation, we get

50.5/35.3 = e^(10k)

Taking the natural logarithm of both sides, we get

ln(50.5/35.3) = 10k

Solving for k, we get

k ≈ 0.034

Therefore, the exponential growth function is A = 35.3e^(0.034t).

To project the Hispanic resident population in 2015, we need to find A when t = 15 (i.e., 15 years after 2000). Substituting t = 15 into the exponential growth function, we get

A = 35.3e^(0.034*15) ≈ 73.9 million

Therefore, the projected Hispanic resident population in 2015 is approximately 73.9 million.

To find the year in which the Hispanic resident population reaches 70 million, we need to solve the exponential growth function for t when A = 70. Substituting A = 70 into the exponential growth function, we get

70 = 35.3e^(0.034t)

Dividing both sides by 35.3, we get

e^(0.034t) = 70/35.3

Taking the natural logarithm of both sides, we get

0.034t = ln(70/35.3)

Solving for t, we get

t ≈ 24.7

Therefore, the Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.

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Answer: It will cost $2.88 to frame Jayla's math certificate with the fancy frame.

Step-by-step explanation: To calculate the cost of framing Jayla's math certificate, we need to determine the perimeter of the certificate, which is the sum of the lengths of all four sides.

Perimeter = 2 × (height + width)

Perimeter = 2 × (19 + 29)

Perimeter = 2 × 48

Perimeter = 96 centimeters

So the perimeter of the certificate is 96 centimeters.

To find the cost of framing, we need to multiply the perimeter by the cost per centimeter of the fancy frame:

Cost = perimeter × cost per centimeter

Cost = 96 × $0.03

Cost = $2.88

Therefore, it will cost $2.88 to frame Jayla's math certificate with the fancy frame.

If a taxi company charges ​f(x)=2. 20+0. 6[4x] dollars, the cost of a 2.7-mile trip is $8.68.

To find the cost of a 2.7-mile trip using the given function f(x) = 2.20 + 0.6[4x], we substitute x = 2.7 in the function.

f(2.7) = 2.20 + 0.6[4(2.7)]

f(2.7) = 2.20 + 0.6[10.8]

f(2.7) = 2.20 + 6.48

f(2.7) = 8.68

The function f(x) = 2.20 + 0.6[4x] represents the cost of a taxi ride based on the distance traveled. The first term 2.20 represents the base fare, which is added to the cost regardless of the distance.

The second term 0.6[4x] represents the variable cost, which is calculated by multiplying the distance traveled by 4 and then by 0.6. This function helps the customers to calculate their fare in advance and plan their expenses accordingly.

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The sum of the NPV and false omission rate for any test will always be 100%.

The NPV (Negative Predictive Value) is the proportion of people who test negative for a condition and actually do not have it, while the false omission rate is the proportion of people who have the condition but test negative for it.

When we add together the NPV and the false omission rate for any test, we are essentially considering all the cases where the test result is negative.

The NPV represents the proportion of people who truly do not have the condition and test negative for it, while the false omission rate represents the proportion of people who actually have the condition but test negative for it.

Together, these two values cover all possible cases where the test result is negative, which means that they represent the entirety of the negative results for the test.

Since the sum of all probabilities for an event must always equal 100%, the sum of the NPV and false omission rate must also equal 100%.

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The area of the given circle is 616 sq.cm.

The volume of rectangular prism is 416 mm³

A circle is a particular type of ellipse when the eccentricity is zero and both foci are present. The locus of points drawn equally apart from the centre is also referred to as a circle. The radius of a circle is the separation between its centre and its periphery. The circle's diameter, which is equal to twice its radius, is the line that splits the circle into two equal pieces.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle. The unit of area is the square unit, such as m², cm², etc.

Area of Circle = πr² or πd²/4, square units

where π = 22/7 or 3.14

according to question,

Area = pi times the radius squared

A = pi * r²

A = 22/7 * 14²

A = 22/7 * 196

A = 4,312 / 7

A = 616 sq. cm.

V = l*w*h

To determine the volume, multiply all three dimensions together.

For Connexus users Rectangular prisms and volume quiz part 2:

l * w * h = 8 * 5 * 10.4 = 416

the volume of rectangular prism is 416 mm³

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From the graph of the parabola, line, and the given values we found out that the parabola will intersect the line at coordinates ([tex]2\sqrt{14}[/tex],7).

As the parabola is originating from the origin and opens at the y-axis, hence:

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Answer: We can use the properties of the normal distribution to solve both parts of this problem.

a) The number of months with sales greater than 100 is a binomial random variable with parameters n = the number of months and p = the probability of a single month having sales greater than 100. Since each month is an independent normal random variable, we can use the standard normal distribution to find this probability. Let X be the number of months with sales greater than 100. Then:

X ~ Binomial(n, p)

where n is the number of months and p is given by:

p = P(X_i > 100) = P(Z > (100 - a) / a)

where Z is a standard normal random variable.

Using the binomial probability formula, the probability of exactly k months having sales greater than 100 is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

So the probability of exactly 3 months having sales greater than 100 is:

P(X = 3) = (n choose 3) * p^3 * (1 - p)^(n - 3)

= (12 choose 3) * P(Z > (100 - a) / a)^3 * [1 - P(Z > (100 - a) / a)]^(12 - 3)

b) The total sales in the next 12 months is a normal random variable with mean 12a and standard deviation sqrt(12)a. Let Y be the total sales in the next 12 months. Then:

Y ~ Normal(12a, sqrt(12)a)

The probability of the total sales being greater than some value x can be found by standardizing Y and using the standard normal distribution:

P(Y > x) = P((Y - 12a) / (sqrt(12)a) > (x - 12a) / (sqrt(12)a))

= P(Z > (x - 12a) / (sqrt(12)a))

where Z is a standard normal random variable. So the probability of the total sales in the next 12 months being greater than 1500 is:

P(Y > 1500) = P(Z > (1500 - 12a) / (sqrt(12)a))

Step-by-step explanation:

Answer: We can use the halfangle formula for the tangent to answer this question. Using this formula we get that [tex]$\tan\left(\frac{11\pi}{12}\right) = \sqrt{3} - 2[/tex].

Step by Step Explanation:  The half angle formula for tangent is [tex]$\tan\left(\frac{A}{2}\right) = \frac{\sin(A)}{1+\cos(A)}[/tex]  . So

[tex]$\tan\left(\frac{11\pi}{12}\right)[/tex]

[tex]$= \frac{\sin(\frac{11\pi}{6})}{1+\cos(\frac{11\pi}{6})}[/tex]

[tex]$= \frac{\sin(2\pi - \frac{\pi}{6})}{1+\cos(2\pi - \frac{\pi}{6})}[/tex]

[tex]$ = \frac{-\sin(\frac{\pi}{6})}{1+\cos(\frac{\pi}{6})}[/tex]

[tex]$= \frac{-1/2}{1 + \sqrt{3}/2}[/tex]

[tex]$= -\frac{1}{2+\sqrt{3}}[/tex]

 [tex]$= - \frac{2-\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}[/tex]

[tex]= - \frac{2 -\sqrt{3}}{4-3}}[/tex]

[tex]= \sqrt{3} -2[/tex]

These are some of the common halfangle identities:

[tex]\cos(A/2) = \sqrt{\frac{1+\cos(A)}{2}[/tex]

[tex]\sin(A/2) = \sqrt{\frac{1-\cos(A)}{2}[/tex]

[tex]\tan(A/2) = \frac{\sin(A)}{1+\cos(A)} = \frac{1 - \cos(A)}{\sin(A)}[/tex]

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The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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The coordinates of point P are (6.4, 18, -12).

A coordinate of a point refers to a set of values that specify the position of that point in a particular reference system or coordinate system. Coordinates are used to uniquely identify the location of a point in a geometric space, such as a plane or a three-dimensional space.

According to the given information:

To find the coordinates of point P, we can use the concept of vector comparison. We are given that the ratio of vector AB to vector AP is 6:4.

Let's denote the coordinates of point P as (x, y, z).

Given:

AB vector = (10, 2, -6)

B coordinates = (4, 6, -8)

AB:AP = 6:4

We can calculate the coordinates of point P as follows:

Since AB:AP = 6:4, we can express this as a vector equation:

(10, 2, -6) / (x - 4, y - 6, z + 8) = 6/4

Now we can cross-multiply to get:

10 / (x - 4) = 6/4

2 / (y - 6) = 6/4

-6 / (z + 8) = 6/4

Simplifying further, we have:

10(x - 4) = 6 * 4

2(y - 6) = 6 * 4

-6(z + 8) = 6 * 4

Expanding the equations, we get:

10x - 40 = 24

2y - 12 = 24

-6z - 48 = 24

Solving these equations, we get:

10x = 64

2y = 36

-6z = 72

Dividing by the respective coefficients, we get:

x = 6.4

y = 18

z = -12

So, the coordinates of point P are (6.4, 18, -12).

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The polar form of the rectangular coordinates (-3√3, 0) is r = 3√3 and θ = 0

To convert the rectangular coordinates (-3√3, 0) into polar form, we can use the following equations:

r = √(x² + y²)

θ = tan⁻¹(y/x)

In this case, x = -3√3 and y = 0, so we have:

r = √((-3√3)² + 0²) = 3√3

θ = tan⁻¹(0/(-3√3)) = tan⁻¹(0) = 0

Since the angle is given in radians over the interval 0 ≤ θ < 2π (which is equivalent to 0 ≤ θ < 6.28318), we need to add 2π to θ if it is negative, to ensure that θ is in the specified interval.

However, in this case, θ is already equal to 0, which is within the specified interval.

Therefore, the polar form of the rectangular coordinates (-3√3, 0) is:

r = 3√3

θ = 0 (in radians, over the interval 0 ≤ θ < 2π)

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The length of curve DE is equal to 26.25 units.

In Mathematics and Geometry, Pythagorean's theorem is modeled by the following mathematical expression:

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

In order to determine the length of the hypotenuse in this right-angled triangle, we would have to apply Pythagorean's theorem as follows;

AC² + BC² = AB²

20² + 15² = AB²

AB² = 400 + 225

AB = √625

AB = 25 units.

For the length of curve DE, we have:

DE = 105% of AB

DE = 1.05 × 25

DE = 26.25 units.

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The prism's surface area is 138 [tex]cm^{2}[/tex]. As a result, option (a) is correct.

A three-dimensional object's surface area is the sum of all its faces.

The formula for the surface area of a right rectangular prism is:

surface area = 2lw + 2lh + 2wh

where l, w, and h are the prism's length, breadth, and height, respectively.

When we substitute the provided values, we get:

Surface Area = 2(4.5)(6) + 2(4.5)(4) + 2(6)(4)

Surface Area = 54 + 36 + 48

surface area = 138 [tex]cm^{2}[/tex]

As a result, the prism's surface area is 138 [tex]cm^{2}[/tex]. As a result, option (a) is correct.

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Answer:  Construct the perpendicular bisector of segment XY

Step-by-step explanation:

Construct the perpendicular bisector of segment XYI am pretty sure this is the answer. I assume you r taking flvs just like me. this is the answer because to construct a circumscribed circle u will need to draw a perpendicular bisector to the sides of the polygon. Which o think is the first step.

Answer:

16286.01632

Step-by-step explanation:

V=πr2h=π·122·36≈16286.01632

John will be able to fill 8 glasses with iced tea.

To convert quarts to cups, we need to multiply the number of quarts by 4, since 1 quart is equal to 4 cups. So, 3 quarts of iced tea is equivalent to 3 x 4 = 12 cups of iced tea.

Since each glass holds 1½ cups of iced tea, John will need to divide the total cups of iced tea by the capacity of each glass: 12 cups / 1.5 cups/glass = 8 glasses.

Therefore, John will fill 8 glasses with iced tea.

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Applying the Angles of Intersecting Chords Theorem, the value of x in the circle is: x = 69 degrees.

The Angles of Intersecting Chords Theorem if two chords intersect inside a circle, then the size of the angle formed by the intersection is equal to half the sum of the sizes of the intercepted arcs, along with the size of its vertical angle.

Apply the theorem to find the value of x by creating the equation below:

x = 1/2 * (86 + 52)

x = 1/2 * (138)

x = 69 degrees.

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If the price of the packet of chips decreases by 12%, the new price will be:

New price = $9.99 - (12/100) x $9.99

New price = $9.99 - $1.199

New price = $8.791

Therefore, the new price of the packet of chips will be $8.791.