A concert was recently held at the civic auditorium. All 5000 tickets were sold. a. 25% of the tickets were reserved seats that sold for $45 each. What was the total amount in sales for the $45 tickets?

Answer:

Step-by-step explanation:

a) area of rhombus = 1/2 × d1 × d2 = 90cm^2

here d1 and d2 are the diagonals

d1 = 18 cm

1/2 × 18 × d2 = 90

9 × d2 = 90

d2 = 90/9

d2 = 10 cm

∴The length of other diagonal is 10 cm

b) d1 = 28 cm

d2 = 24 cm

area = 1/2 × d1 × d2

= 1/2 × 28 × 24

= 336 cm^2

∴ The are of the rhombus = 336 cm^2

Hope this helps

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Answer:

a. A(0) is $2500 and A(10) is $3700.61

b. The beginning value and the value after ten years

c. 17.673 years

d. That after roughly 17 and a half years, his investment will be doubled.

The probability density function (PDF) of X is: fx(x) = 0.4 for -3 < x < 5 and fx(x) = 0.2 for 5 < x < 7.

The probability that X is equal to 5 is zero since X is a continuous random variable.

The probability that X is between -2 and 4 is: P(-2 < X < 4) = Fx(4) - Fx(-2) = 0.8 - 0.4 = 0.4.

The probability that X is greater than or equal to 3 is: P(X >= 3) = 1 - Fx(3) = 1 - 0.4 = 0.6.

The expected value of X is: E[X] = ∫(-3 to 5) xfx(x) dx + ∫(5 to 7) xfx(x) dx = -0.2 + 0.4 + 0.4 = 0.6.

The variance of X is: Var[X] = E[X\(^2\)] - (E[X]\()^2\) = ∫(-3 to 5) x\(^2\)fx(x) dx + ∫(5 to 7) x\(^2\)fx(x) dx - (0.6\()^2\) = 4.44 - 0.36 = 4.08.

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Step-by-step explanation:

First find the total weight of the male students

5/3 = x / 870     cross multiply

4350 = 3x

x = total boys' weight = 1450 kg

    if the mean is GREATER THAN 80 then    

               1450 / n > 80     where n is the number of boys

                   1450/80 > n

                              n< 18.125         max number would be 18 boys

Answer: -37/38

Step-by-step explanation:

A confidence interval for the mean is said to be symmetrical around the population mean. Symmetry means that the central tendency measures are equally positioned about the middle of the interval.

When constructing a confidence interval, the interval width on either side of the point estimate is equal (assuming a symmetric distribution). The critical values, the margin of error, and the point estimate are all equidistant from the midpoint of the interval.

This is why a confidence interval for the mean is said to be symmetrical around the population mean. Therefore, a confidence interval for the mean is symmetrical around the population mean as long as the population is normally distributed.

Also, it is worth noting that a confidence interval can only be symmetrical if the sample size is large enough. In the case of a smaller sample size, the distribution of the confidence interval may not be entirely symmetrical and may skew to the left or right. The larger the sample size, the more symmetrical the distribution will be.

A confidence interval is typically expressed in a specific range, such as 95 percent, which means that the population mean is expected to fall within that range 95 percent of the time. In conclusion, the symmetry of a confidence interval around the population mean is important for statistical inference because it ensures that the confidence level is maintained.

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Answer

she will need to invest 77 dllors

Step-by-step explanation:

Answer:

The volume of a cylinder is πr²h, where r is the radius, and h is the height. The radius of the candle is 2 inches, and the height is 8 inches. The candle loses 6 cubic inches of volume per hour.

After 2 hours, the candle will have lost 12 cubic inches of volume. The remaining volume of the candle is πr²h - 12 cubic inches.

Plugging in the values for r and h, we get the following equation:

The height of the candle after 2 hours is 36 cubic inches / π(2²) = 36 / 12.5663706144 = 2.87 inches.

Therefore, the height of the candle after 2 hours is 2.87 inches.

hope this helps :))

Answer:the answer is 60 m x 10 m

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 500

Answer:

0

3

Step-by-step explanation:

Answer:

b = 73

c = 34

Step-by-step explanation:

<T and <R are equal because they are opposite equal sides.

So b = 73°

Every triangle has 180 degrees

b + c + 73 = 180

73 + c + 73 = 180

146 + c = 180

c = 180 - 146

c = 34

the limit of the sequence {(1 + 14/n)ⁿ} as n approaches infinity is 14.

To find the limit of the sequence {(1 + 14/n)ⁿ} as n approaches infinity, we can use the limit properties.

Let's rewrite the sequence as:

a_n = (1 + 14/n)ⁿ

As n approaches infinity, we have an indeterminate form of the type (\(1^\infty\)). To evaluate this limit, we can rewrite it using exponential and logarithmic properties.

Take the natural logarithm (ln) of both sides:

ln(a_n) = ln[(1 + 14/n)ⁿ]

Using the logarithmic property ln(\(x^y\)) = y * ln(x), we have:

ln(a_n) = n * ln(1 + 14/n)

Now, let's evaluate the limit as n approaches infinity:

lim(n->∞) [n * ln(1 + 14/n)]

We can see that this limit is of the form (∞ * 0), which is an indeterminate form. To evaluate it further, we can apply L'Hôpital's rule.

Taking the derivative of the numerator and denominator separately:

lim(n->∞) [ln(1 + 14/n) / (1/n)]

Applying L'Hôpital's rule, we differentiate the numerator and denominator:

lim(n->∞) [(1 / (1 + 14/n)) * (d/dn)[1 + 14/n] / (d/dn)[1/n]]

Differentiating, we get:

lim(n->∞) [(1 / (1 + 14/n)) * (-14/n²) / (-1/n²)]

Simplifying further:

lim(n->∞) [14 / (1 + 14/n)]

As n approaches infinity, 14/n approaches zero, so we have:

lim(n->∞) [14 / (1 + 0)]

The limit is equal to 14.

Therefore, the limit of the sequence {(1 + 14/n)ⁿ} as n approaches infinity is 14.

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Answer: she drove 3 miles per gallon

Step-by-step explanation:

21 / 7 = 3 i hope this helps

Given dimensions of rectangular design:

Width = w1 = 5 in

Length = l1 = 8 in

As mentioned, Katie uses a copy machine to enlarge her rectangular design. Therefore,

new width = w2 = 10 in

new length = l2 = x in

Katie creates a large copy of the original design. Therefore, the ratio of length to width must remain the same (as the original design). So, we can write as:

Now, let's put all the values in the equation

or

x = 16

Therefore, the new length would be 16.

Answer:

z = 110°

Step-by-step explanation:

Since the figures are similar then corresponding angles are congruent, thus

∠ H = ∠ D = 110°, that is

z = 110°

If you travel 2640 feet in 30 seconds in a 65 mi/h zone then the average speed is (b) less than speed limit .

The Distance travelled in 30 seconds is = 2640 feet ,

Average Speed can be calculated by formula; Speed = Distance / Time ,

So , the speed of the person in feet per second will be = 2640/30 ft/sec .

we know the conversion rate that 1 mile = 5280 feet and 1 hr = 3600 sec ,

So , On converting the speed to mi/hr ,

it can be written as = (2640 × 3600)/(5280 × 30)

= 60 mi/hr .

The Speed Limit is given as 65 mi/hr .

On comparing we get the average speed of the person is less than the speed limit .

Therefore , The Average Speed is Less than the Limit .

The given question is incomplete , the complete question is

You travel 2640 feet in thirty seconds while in a 65 mi/h zone. (There are 5280 ft in one mi). Your average speed is:

(a) exactly the speed limit.

(b) less than the speed limit.

(c) larger than the speed limit.

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Your average speed is 98.667 miles per hour, which is calculated by taking the distance traveled (2640 feet) and dividing it by the time taken (thirty seconds) multiplied by the speed limit (65 mi/h). This is based on the fact that there are 5280 feet in one mile.

Step 1: Convert 2640 feet to miles.

1 mile = 5280 feet

2640 feet / 5280 feet = 0.5 miles

Step 2: Calculate speed.

Speed = Distance / Time

Speed = 0.5 miles / (30 seconds/60 seconds)

Speed = 0.5 miles / 0.5 minutes

Speed = 1 mile / 0.5 minutes

Speed = 2 miles/minute

Speed = 2 miles/minute * 60 minutes/hour

Speed = 120 miles/hour

Speed = 120 miles/hour * 65 mi/h

Speed = 78 miles/hour

Speed = 98.667 miles/hour

The average speed is calculated by dividing the distance traveled (2640 feet) by the time taken (thirty seconds) and then multiplying it by the speed limit (65 mi/h). This is based on the fact that there are 5280 feet in one mile. First, the distance (2640 feet) was converted to miles (0.5 miles). Then, the speed (0.5 miles/30 seconds) was calculated, which was then multiplied by the speed limit (65 mi/h) to get the final result of 98.667 miles/hour.

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Answer:

I think 20,000 sheets of paper

Step-by-step explanation:

800 x 25 is 20,000

Answer:

The school has 20,000 sheets of paper.

Step-by-step explanation:

800 sheets in one pound

800X25=20,000

When proving that the diagonals of a rectangle are congruent, certain elements are necessary.

To prove that the diagonals of a rectangle are congruent, we need to establish the properties and characteristics of a rectangle. The necessary elements for the proof include the definition of a rectangle, which states that it is a quadrilateral with four right angles.

Additionally, we need to consider the properties of diagonals in a rectangle, such as the fact that diagonals bisect each other and form congruent triangles. These properties are crucial in proving that the diagonals of a rectangle are congruent.

Furthermore, we may need to employ other geometric principles and theorems to support the proof. These may include the properties of parallel lines, perpendicular lines, and the congruence of corresponding angles and sides in triangles. By utilizing these principles and theorems, we can establish the necessary conditions to prove that the diagonals of a rectangle are congruent.

In conclusion, when proving that the diagonals of a rectangle are congruent, it is essential to consider the definition and properties of rectangles, as well as employ relevant geometric principles and theorems to support the proof.

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Answer:

Simple random sampling

Step-by-step explanation:

The type of sampling used here is simple random sampling(SRS) because SRS is defined as the sampling technique where a group of subjects known as sample are selected for study from a larger group known as population. Thereafter, each individual will be entirely chosen by chance and then each member of the population will have an equal opportunity of being included in the sample.

Thus question given corresponds to this definition.

Answer:

31 years

Step-by-step explanation:

65000*(1.07) ^31 is around $529000

however, 65000*(1.07) ^30 is around $491000

so you would need 31 years to gain more than $500,000.

It will take approximately 30 years to reach $500,000 in savings with an investment that earns an average of 7% per year.

To determine the number of years it will take to reach $500,000 in savings with an investment that earns an average of 7% per year, we can use the given investment model equation: y = 65000(1.07)ˣ.

We need to find the value of x, which represents the number of years.

Setting y = $500,000, we can solve for x:

500,000 = 65,000(1.07)ˣ

500,000/65,000 = (1.07)ˣ

100/13 = (1.07)ˣ

To solve for x, we take the logarithm of both sides:

ln 100/13 = ln (1.07)ˣ

ln 100/13 = x ln (1.07)

x = (ln 100/13)/(ln (1.07))

x = 30

Therefore, it will take approximately 30 years to reach $500,000 in savings with an investment that earns an average of 7% per year.

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Answer:

y= 1/2x -7

Step-by-step explanation:

Find the y-intercept. It is where the line crosses "y" which is -7

Next find the rise and the run for "x"

Rise - 1

Run - 2

Then put them in slope intercept form

y=1/2x -7

\(\bold{\boxed{\huge{\blue{\underline{Answer }}}}}\)

\(\bold{\underline{Given :- }}\)

\(\sf{The \: perimeter\:of\:the\:rectangle = 88}\)

\(\sf{The \: length \: is\: 5 \:more \:than \: 2 × width }\)

\(\bold{\underline{To \: Find :- }}\)

\(\bold{\underline{Let's \:Begin :- }}\)

\(\sf{ Let\: the\: breath \:be \: x }\)

\(\sf{\underline{ We\: know\: that, }}\)

\(\sf{\red{ Perimeter\: of \: rectangle = 2( L + W)}}\)

\(\sf{\underline{ According\: to\: the \:question }}\)

\(\sf{The \: length \: is \: 5 \:more \:than \: 2 × width }\)

\(\sf{\underline{That \:is }}\)

\(\sf{ Length = 2x + 5 }\)

\(\sf{\underline{Subsitute the \:required \:values }}\)

\(\sf{ Perimeter \:of\: rectangle = 2( L + W) }\)

\(\sf{ 88 = 2( 2x + 5 + x) }\)

\(\sf{ 88 = 4x + 10 + 2x }\)

\(\sf{ 88 = 6x + 10 }\)

\(\sf{ 88 - 10 = 6x }\)

\(\sf{ 78 = 6x }\)

\(\sf{ x = 78/6 }\)

\(\sf{ x = 13 }\)

\(\sf{ Thus,\: the \:width \:is \:13\: feet }\)

\(\bold{\underline{ Now }}\)

\(\sf{ Length = 2x + 5 }\)

\(\sf{ Length = 2(13) + 5 }\)

\(\sf{ Length = 26 + 5 }\)

\(\sf{ Length = 31 }\)

\(\sf{\pink{ Hence, \: Length\: and \:breath \:are\: 13 \:and\: 31 \: feet}}\)

Correct Question:-

The length is 5more than twice the width.

Solution:-

ATQ

\(\\ \tt\hookrightarrow 2(L+B)=88\)

\(\\ \tt\hookrightarrow 2(x+2x+5)=88\)

\(\\ \tt\hookrightarrow 2(3x+5)=88\)

\(\\ \tt\hookrightarrow 6x+10=88\)

\(\\ \tt\hookrightarrow 6x=78\)

\(\\ \tt\hookrightarrow x=13\)

Question:

What is the measure of an interior angle of a 21-gon?

Concept:

Define a 21-gon

A 21-gon is a 21 sided polygon also know as An icosikaihenagon

In the case of this polygon, the value of n is

We will then calculate the sum of interior angles of a 21-gon and then divide the sum by the number of sides n...

Therefore,

The formula we will use to calculate the measure of an interior angle of a 21-gon is given below as

The formula for the sum of interior angles is given below as

Hence,

We will have

Step 2:

Substitute the value of n=21 in the formula above, we will have

Hence,

The final answer = 162.86°

Answer:

\((-2,-5)\)

Step-by-step explanation:

\(\begin{bmatrix}y=-4x-3\\ y=-2x+1\end{bmatrix}\)

\(\mathrm{Substitute\:}y=-2x+1\)

\(\begin{bmatrix}-2x+1=-4x-3\end{bmatrix}\)

Isolate x for -2+1=-4x-3: x=-2

\(\mathrm{For\:}y=-2x+1\)

\(\mathrm{Substitute\:}x=-2\)

\(y=-2\left(-2\right)+1\)

\(-2(-2)+1=5\)\(4+1=5\)

\(y=5\)

Answer:

a)

x=4, y=-2

b)

x=2, y=2

c)

x=0, y=0

d)

x=1, y=1

e)

x=3, y=3

f)

x=4, y=4

Step-by-step explanation:

a) (x,-2) = (4,y)

x=4

y=-2

b) (3x, 4) = (6, 2y)

3x=6 => x=2

2y=4 => y=2

c) (2x-1, y + 2) = (-1,2)

2x-1 =-1 => x=0

y+2 = 2 => y=0

d) (2x + 4, y + 5) = (3x + 3,6)

2x+4 = 3x+3 => x=1

y+5 = 6 => y=1

e) (x + y,y + 3) = (6, 2y)

x+y = 6 => x+3 = 6 => x=3

y+3 = 2y => y=3

f) (x + y, x - y) - (8,0)​

x+y = 8 => 2x=8 => x=4

x-y = 0 => x=y => y=4

A.

when you graph it that's the correct one.