The City Zoo has different admission prices for adults and children. When three adults and two children went to the zoo, the bill was $77.50. If two adults and three children got in for $70.00 then what is the price of an adult's ticket and what is the price of a child's ticket?

Answer:

$508.41

Step-by-step explanation:

Compound interest is calculated with the formula:

[tex]CI = P(1 + R)^T - P[/tex]

where P = Principal/ Initial amount = $850

R = Rate = 4.8% = 0.048

T = Time elapsed = 10 years

Hence, the compound interest is:

[tex]CI = 850(1 +0.048)^{10} - 850\\\\\\CI = 850(1.048)^{10} - 850\\\\\\CI = (850 * 1.598) - 850\\\\\\CI = 1358.41 - 850\\\\\\[/tex]

CI = $508.41

The interest after the first 10 years is $508.41

The first account with an initial deposit of $850 at a 4.8% interest rate compounded annually will earn approximately $510.87 in interest over 10 years.

The student asked how much interest the first account, which is a college savings account with an initial deposit of $850 at a 4.8% interest rate compounded annually, will earn in 10 years. To calculate this, we can use the formula for compound interest:

A = P(1 + r/n)^nt

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for, in years.

In this case, P = $850, r = 4.8/100 = 0.048, n = 1 (since the interest is compounded annually), and t = 10 years. So, the calculation is:

A = 850(1 + 0.048/1)1*10

A = 850(1 + 0.048)10

A = 850(1.048)10
A ≈ 850(1.60103)
The total amount in the account after 10 years will be approximately $1,360.87.

To find the interest earned, we subtract the original principal from the total amount:

Interest Earned = Total Amount - Original Principal
Interest Earned ≈ $1,360.87 - $850
Interest Earned ≈ $510.87
Therefore, the interest earned in the first account after 10 years is approximately $510.87.

Answer:

A  y = 3x

Step-by-step explanation:

We can check each line to see if the point is on it

A  y = 3x  6 = 2*3  6=6  this is true so the point is one the line

B  y = 4-x   6 = 2-4  6 = -2  false

C  y = -3x   6 = -3(2)  6=-6  false

D  y =-x+4   6 = -2+4   6 = 2  false

Answer: a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

i got it correct on edg

have a good day :D

Answer:

The amplitude is 4 and the period is 2

Step-by-step explanation:

In the equation y = A sin (B x)  

∵ The equation is y = 4 sin(πФ)

- Compare it with form above

∴ A = 4 and B = π

∵ A is the amplitude

∴ The amplitude is 4

∵ Period = [tex]\frac{2\pi }{B}[/tex]

∴ Period = [tex]\frac{2\pi }{\pi }[/tex]

∴ Period = 2

∴ The period is 2

Answer:

The probability of winning the last prize is  [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

Total Number of guests = 22

Total Number of prizes = 14

We have to find the probability of winning the last prize. When its turn to announce the last prize, the previous all prizes would have been already distributed. This means, 13 of the prizes would have been already distributed. Since multiple winning is not allowed, the last prize would be distributed in the remaining guests.

After distributing 13 prizes, the number of guests who can win the last prize will be = 22 - 13 = 9

We have only 1 last prize and 9 people among which only 1 will win the prize. Probability is defined as the ratio of favorable outcomes to total number of outcomes.

In this case the favorable outcome is the person with numbered ticket who is going to win a prize. This means favorable outcome is only 1. Total number of outcomes is total number of people remaining, which is 9.

Therefore, the probability of winning the last prize is 1 in 9 i.e. [tex]\frac{1}{9}[/tex]

Answer:

a)  P (  1100 < X < 1400 ) = 0.755

b) P (  X < 1000 ) = 0.755

c) proportion ( X > 1200 ) = 65.66%

d) 5.87% percentile

Step-by-step explanation:

Solution:-

- Denote a random variable X: The number of chocolate chip in an 18-ounce bag of chocolate chip cookies.

- The RV is normally distributed with the parameters mean ( u ) and standard deviation ( s ) given:

                               u = 1252

                               s = 129

- The RV ( X ) follows normal distribution:

                       X ~ Norm ( 1252 , 129^2 )  

a) what is the probability that a randomly selected bag contains between 1100 and 1400 chocolate​ chips?

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( x1 < X < x2 ) = P ( [ x1 - u ] / s < Z <  [ x2 - u ] / s )

- Taking the limits x1 = 1100 and x2 = 1400. The standard normal values are:

     P (  1100 < X < 1400 ) = P ( [ 1100 - 1252 ] / 129 < Z <  [ 1400 - 1252 ] / 129 )

                                        = P ( - 1.1783 < Z < 1.14728 )

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( -1.1783 < Z < 1.14728 ) = 0.755

Hence,

      P (  1100 < X < 1400 ) = 0.755   ... Answer

b) what is the probability that a randomly selected bag contains fewer than 1000 chocolate​ chips?

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( X < x2 ) = P ( Z <  [ x2 - u ] / s )

- Taking the limit x2 = 1000. The standard normal values are:

     P (  X < 1000 ) = P ( Z <  [ 1000 - 1252 ] / 129 )

                                        = P ( Z < -1.9535 )

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( Z < -1.9535 ) = 0.0254

Hence,

       P (  X < 1000 ) = 0.755   ... Answer

​(c) what proportion of bags contains more than 1200 chocolate​ chips?

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( X > x1 ) = P ( Z >  [ x1 - u ] / s )

- Taking the limit x1 = 1200. The standard normal values are:

     P (  X > 1200 ) = P ( Z >  [ 1200 - 1252 ] / 129 )

                                        = P ( Z > 0.4031 )

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( Z > 0.4031 ) = 0.6566

Hence,

      proportion of X > 1200 = P (  X > 1200 )*100 = 65.66%   ... Answer

d) what is the percentile rank of a bag that contains 1050 chocolate​ chips?

- The percentile rank is defined by the proportion of chocolate less than the desired value.

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( X < x2 ) = P ( Z <  [ x2 - u ] / s )

- Taking the limit x2 = 1050. The standard normal values are:

     P (  X < 1050 ) = P ( Z <  [ 1050 - 1252 ] / 129 )

                                        = P ( Z < 1.5659 )

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( Z < 1.5659 ) = 0.0587

Hence,

       Rank = proportion of X < 1050 = P (  X < 1050 )*100

                 = 0.0587*100 %  

                 = 5.87 % ... Answer

The cost of filling the planter with soil is $6.24. option C

What is the cost of filling the planter with soil?

Length = 2 ft

Width = 2 ft

Height = 6 ft

Volume of the square based pyramid = ⅓ × length × Width × height

= ⅓ × 2 × 2 × 6

= ⅓ × 24

= 8 cubic feet

Cost of soil per cubic foot = $0.78

Therefore,

Cost of filling the planter with soil = Volume of the square based pyramid × Cost of soil per cubic foot

= 8 × $0.78

= $6.24

Complete question:

A planter in the shape of a square pyramid with dimensions 2 ft by 2 ft by 6 ft is being filled with soil. Soil cost $0.78 per cubit cubic foot What is the cost of filling the planter with soil?

a $24.00

b $8.00

c. $6 24

d. $18.72

Answer:

y = x^2 - 4x - 5

y = (x + 1)(x - 5)

Answer:

[tex] Standard \: form :\:y= {x}^{2} - 4x - 5\\

Factored\: from:\:y = (x + 1) (x - 5)[/tex]

Step-by-step explanation:

[tex]y = (x - 2)^{2} - 9 \\ y= {x}^{2} - 4x + 4 - 9 \\ \red{ \boxed{ \bold{y= {x}^{2} - 4x - 5}}} \\ is \: in \: standard \: form \\ \\ y = (x - 2)^{2} - 9 \\ y = (x - 2)^{2} - {3}^{2} \\ y = \{(x - 2) + 3\} \{(x - 2) - 3 \} \\ y = \{x - 2 + 3\} \{x - 2- 3 \} \\ \purple{ \boxed{ \bold{y = (x + 1) (x - 5)}}} \\ is \: in \: factored \: form[/tex]

Answer:

D) 240 000 cm³​

Step-by-step explanation:

V = 100cm×80cm×(80-50)cm

= 8000cm²×30cm

=  240 000 cm³

Answer:

[tex]17\dfrac{4}{7} \:hours[/tex]

Step-by-step explanation:

A concert lasts [tex]5\dfrac{6}{7}[/tex] hours.

The band performs three concerts on the weekend.

Total length of time performed by the band is given as:

Hour Per Concert X Number of Concerts

[tex]5\dfrac{6}{7} X 3\\=\dfrac{41}{7} X 3\\=\dfrac{123}{7}\\=17\dfrac{4}{7} hours[/tex]

The band performs a total of [tex]17\dfrac{4}{7} hours[/tex].

Answer:

[tex]b^6z^612a^5[/tex]

Step-by-step explanation:

The first step is to combine like terms, and multiply them together first. Since multiplication is commutative, it doesn't matter in what order you do it. Therefore, this can be rewritten as [tex](2a^2\cdot 6a^3)\cdot(b^4\cdot b^2)\cdot(z\cdot z^5)=(12a^5)\cdot(b^6)\cdot(z^6)=b^6z^612a^5[/tex]. Hope this helps!

Answer:

Step-by-step explanation:

(2a²b⁴z)(6a³b²z⁵ = 2*6*a²⁺³ b⁴⁺² z¹⁺⁵

= 12a⁵b⁶z⁶

Answer:

-0.9231

Step-by-step explanation:

Given cos theta = 0.3846 within the range 3π/2<theta<2π

Costheta = 0.3846

Theta = arccos(0.3846)

Theta = 67.38°

Since 67.38° didn't fall within the range of theta, we will locate our theta using the quadrant.

Since cos is positive in the 4th quadrant,

Theta = 360-67.38°

Theta = 292.62°

Sin(theta) = sin(292.62°)

= -0.9231

Answer:

This may be incorrect but $4

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Answer:

C (I'm not 100% sure that this is correct)

Step-by-step explanation:

I don't think that an act of genocide in the regions of Africa occurred recently.

Answer:

I think you might get a better answer if you put this question under the social studies category instead of math.

Answer:

12 boys

Step-by-step explanation:

boys : girls

4      : 5

Add a total column

boys : girls: total

4      : 5     : 4+5 =9

To get to a total of 27 we multiply each term by 3

boys : girls: total

4*3      : 5*3  : 9*3

12        :15     :27

There are 12 boys

Final answer:

There are 12 boys in the class of 27 students.

Explanation:

The ratio of boys to girls in the class is 4:5, which means for every 4 boys, there are 5 girls. To find out how many boys there are, if there are 27 students in total, we need to work with this ratio.

Step-by-step Solution:

Therefore, there are 12 boys in the class of 27 students.

Answer:

The answer should be 6 miles..

3(6)x2=20

Step-by-step explanation:

Answer:

i think:

A number times four minus nine is one

Equivalent expression are expressions that have equal values, when expanded. The equivalent expression of ln(2x)^4  is 4ln(2) + 4ln(x))

The expression is given as:

[tex]\ln(2x)^4[/tex]

Apply the following logarithmic rule to the above equation

[tex]\ln(a)^b = b\ln(a)[/tex]

So, we have:

ln(2x)^4  = 4ln(2x)

Next, apply the following product rule of logarithm to the above equation

ln(ab) = ln(a) + ln(b)

So, we have:

ln(2x)^4  = 4 * [ln(2) + ln(x)]

Expand the bracket

ln(2x)^4  = 4ln(2) + 4ln(x))

Hence, the equivalent expression of ln(2x)^4  is 4ln(2) + 4ln(x))

Read more about equivalent expressions at:

https://brainly.com/question/2972832

Answer:

ln (2x)4

✅ 4 ln 2 + 4 ln x

❎ 4 ln 2 + ln x

❎ 8 ln x

ln

4y5

x2

❎ ln 4 - 2 ln x - 5 ln y

✅ ln 4 - 2 ln x + 5 ln y

❎ -8 ln x + 5 ln y

Answer:

The probability is 1/8

Step-by-step explanation:

In this question, we are tasked with calculating that if a coin is flipped three times, we have the outcome in the question; THH

Now before we go on to calculate this probability, we need to understand some technicalities. Flipping a coin can only result into two outcomes as there are only two sides of a coin. These are the head and the tail. What this means is that if a coin is flipped, we should only expect landing on the head and on the tail.

Now these opposite sides have equal probability. This means the probability of landing on the head = probability of landing on the tail. These probabilities are equal as they are the only two options we have. Hence, the probabilities are 1/2 each

Hence, P(H) = P(T) = 1/2

Now, we proceed to calculating the probability of HTT

this mathematically means P(H) * P(T) * P(T) = 1/2 * 1/2 * 1/2 = 1/8

Answer:

1/8

Step-by-step explanation:

Answer:

You start the shelf 4 ft. 9 in. from the wall

Step-by-step explanation:

The game plan is to take the length of the shelf away from the length of the wall, and then divide the remaining part into two equal pieces.  

13 ft.

-  3 ft. 6 in.  

12 ft  12 in,

- 3ft    6 in

9 ft   6 in.  

9 ft. 6 inches divided by 2 equals 4.5 ft, 3 in.

.5 ft * 12 inches = 6 inches

Answer:

56 inches.              

Step-by-step explanation:

Answer:

Number of green counters is 144

Step-by-step explanation:

Please refer to the attached image for explanations

Calculate the total number of parts in the ratio. Determine the total number of green and red counters, which are 4 parts out of a total of 11. Multiply this fraction by the total number of counters (444) to get the total number of green and red counters. The number of green counters is 3 parts out of this total, so a similar multiplication gives the number of green counters.

The problem involves the concept of ratios and arithmetic. We need to solve the question in two stages:

https://brainly.com/question/32531170

#SPJ12

Answer: x= y /5z+3

Step-by-step explanation:

Final answer:

To solve for x in the given equation y = 3x + 5xz, rearrange the equation to isolate x by dividing (y - 5xz) by 3.

Explanation:

Solve for x: y = 3x + 5xz

Given the equation y = 3x + 5xz, we need to isolate x. To do this, we can rearrange the equation:

x = (y - 5xz) / 3

44 boots were sold all together. To figure this out first you need to find how many of the other boots there were. 8 rugby boots and 12 hiking boots. 8 + 12 + 24 = 44.

Answer:

350042 chairs

Step-by-step explanation:

Given: Number of chairs produced by a furniture company each month = [tex]5000600[/tex]

Percentage increase in chairs = [tex]7\%[/tex]

To find: an increase in the new number of chairs produce each month

Solution:

As 5000600 chairs are produced by a furniture company each month percentage increase in chairs is [tex]7\%[/tex]

So, increase in the new number of chairs produce each month = [tex]7\% \,\, of \,\, 5000600=\frac{7}{100} (5000600)=350042[/tex]

Answer:

6x-14

Step-by-step explanation:

its f of g of x so insert the g function when x appears in the f function

3(2x-4) -2

6x - 12 -2

6x-14

Answer:

C

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 ) = (4, - 2) and (x₂, y₂ ) = (- 4, - 4)

m = [tex]\frac{-4+2}{-4-4}[/tex] = [tex]\frac{-2}{-8}[/tex] = [tex]\frac{1}{4}[/tex] , thus

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation.

Using (- 4, - 4), then

- 4 = - 1 + c ⇒ c = - 4 + 1 = - 3

y = [tex]\frac{1}{4}[/tex] x - 3 → C