Answer:
110.00
Step-by-step explanation:
The admission fee at a local zoo is $1.50 for children and $3.00 for adults. On a certain day, 2400 people enter the zoo and $4,800.00 is collected. How many children and how many adults?
Answer:
Step-by-step explanation:
c = children
a = adults
2200 people enter the zoo mean :
c + a = 2200
$4,550.00 is collected mean :
1.5 c + 4 a = 4550
Now you must solve system:
c + a = 2200
1.5 c + 4 a = 4550
c + a = 2200 Subtract c to both sides
c + a - c = 2200 - c
a = 2200 - c
1.5 c + 4 a = 4550
1.5 c + 4 ( 2200 - c ) = 4550
1.5 * c + 4 * 2200 - 4 c = 4550
1.5 * c + 8800 - 4 c = 4550
- 2.5 c + 8800 = 4550 Subtract 8800 to both sides
- 2.5 c + 8800 - 8800 = 4550 - 8800
- 2.5 c = - 4250 Divide both sides by - 2.5
c = - 4250 / - 2.5
c = 1700
a = 2200 - c = 2200 - 1700 = 500
1700 children and 500 adults
Proof :
c + a = 1700 = 2200
$ 1.5 * c + $ 4 * a =
$ 1.5 * 1700 + $ 4 * 500 =
$ 2550 + $ 2000 = $ 4550
The number of children and the number of adults are 1600 and 800, respectively.
What is the solution to the equation?The allocation of weights to the relevant variables that produce the calculation's optimum is referred to as a direct consequence.
A nearby zoo charges $1.50 for kids and $3.00 for adults to enter. 2400 persons visit the zoo on a certain day, and $4,800.00 is gathered.
Let x be the number of children and y be the number of adults. Then the equation is written as,
x + y = 2400 ...1
1.5x + 3y = 4800
x + 2y = 3200 ...2
Subtract equation 1 from equation 1, then
2y - y = 3200 - 2400
y = 800
Then the value of x is calculated as,
x + 800 = 2400
x = 2400 - 800
x = 1600
The number of children and the number of adults are 1600 and 800, respectively.
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simplify
21m^2−122m+112/9m^2−196
Answer:
3m-8/7m+14
Step-by-step explanation:
Suppose that the price p (in dollars) and the demand x (in thousand of units) of a commodity satisfy the demand equation 6p+x+xp=94
How fast is demand changing when the price is set at $9 and the price is rising at the rate of $2 per week?
dx/dt
=
The demand is decreasing at the rate of _________units per week.
The demand is decreasing at the rate of 2units per week.
Given the price p (in dollars) and the demand x (in thousands of units) of a commodity satisfy the demand equation 6p+x+xp=94
Differentiating the function with respect to time will result in;
[tex]6\frac{dp}{dt}+\frac{dx}{dt} + x \frac{dp}{dt} + p\frac{dx}{dt} = 0[/tex]
Given the following paramters
p = $6
dp/dt = $2/wk
Substitute the given parameters into the formula to have:
[tex]6(2)+\frac{dx}{dt} + 2x + 9\frac{dx}{dt} = 0[/tex]
To get the demand x, we will simply substitute p = 9 into the expression to have:
6(9)+x+9x=94
10x+54 = 94
10x = 94 - 54
10x = 40
x = 4
Substitute x = 4 into the derivative to have:
[tex]6(2)+\frac{dx}{dt} + 2x + 9\frac{dx}{dt} = 0\\6(2)+\frac{dx}{dt} + 2(4) + 9\frac{dx}{dt} = 0\\6(2)+\frac{dx}{dt} + 8 + 9\frac{dx}{dt} = 0\\20 + 10\frac{dx}{dt} =0\\10\frac{dx}{dt} =-20\\\frac{dx}{dt} =\frac{-20}{10}\\\frac{dx}{dt} =-\$2/wk[/tex]
Hence the demand is decreasing at the rate of 2units per week.
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evaluate -x^3 - 3x^2 + 4 when x = -2
Answer:
32
Step-by-step explanation:
x = -2
-x^3 - 3x^2 + 4
-(-2)^3+6^2+4
8+36+4=48
Hope this helps :)
M<1=m<5 true or false
Answer:
True
Step-by-step explanation:
Since m<1 and m<7 is equal to m<3 and m<5, therefore m<1 is also equal to m<5
4. In a simple random sample of 120 women and 150 men from
a population of 150,000, 25% of the women and 37% of the men
are smokers. Suppose you are interested in comparing the
proportion of smokers by sex, compute the Z statistic.
The z-test compares the two sample to determine the existence of a
difference in the two proportion.
The Z-statistic or test of the difference in proportion is approximately -2.106.Reasons:
The given parameter are;
Number of women, n₁ = 120 women
Number of men, n₂ = 150 men
The population size = 150,000
Percentage of women that are smokers in population, [tex]\hat p_1[/tex] = 25%
Percentage of men that are smokers in population, [tex]\hat p_2[/tex] = 37%
The Z statistic is given as follows;
[tex]\displaystyle Z= \mathbf{\frac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})\left (\frac{1}{n_{1}}+\frac{1}{n_{2}} \right )}}}[/tex]
Number of men = 0.37 × 150 = 55.5
Number of women = 0.25 × 120 = 30
[tex]\displaystyle \hat p = \frac{55.5 + 30}{150 + 120} = \frac{19}{60}[/tex]
Which gives;
[tex]\displaystyle Z=\frac{0.25-0.37}{\sqrt{\frac{19}{60} (1-\frac{19}{60} )\left (\frac{1}{120}+\frac{1}{150} \right )}} \approx -2.106[/tex]
The Z-statistic is approximately -2.106
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If an object's position over time is given by the function d(t)=(t^2 +3)e^-1/2 for greater than 0 , on what interval is the object's position increasing and concave down ?
Answer:
Step-by-step explanation:
[tex]d(t)=(t^2+3)e^\frac{-1}{2} \\d'(t)=2t e^{-\frac{1}{2} }\\it~ is~ increasing ~if~d'(t)>0\\e^{-\frac{1}{2} } =\frac{1}{e^\frac{1}{2} } >0\\so~t>0\\and~decreasing~if~t<0\\[/tex]
so it is concave upward at t=0
Please helpppp me step my step all the wayyy
Carla and Diane Bought identical suit cases at a different stores. Carla’s suitcase originally cost $75 and was discounted 15% Daniels suitcase originally cost 85$ and was on sale for 20% off the original price which suitcase was a the better deal? What do we know ? List important facts ? What do we want to find out ?? Solve ??? Show ur work? Explain starts ur Asnwer and give details ? And justify your steps ?
SOMEONE PLEASE HELPPPPPP MEEEEE
THIS IS DUEEEE RIGHT NOWWW
WITH ALL THE WORK I TRIED ALL NIGHT PLEASEEEEEEE
Answer:
carlas had the better deal
Step-by-step explanation:
if you buy an suitcase at $85 with 20% discount, you will pay 85 - 17 = 68 dollars.
if you buy an suitcase at $75 with 15% discount, you will pay 75 - 11.25 = 63.75
divide 20% by a 100 =0.2 than times 0.2 by $85 which will equal 17 subtract 17 from $85
do the same for the second one.
Find the equation of the line.
Answer:
y= 4/1x +1
Step-by-step explanation:
the number on the y axis is the b and you do rise over run to find m you rise (so you go up or down) 4 times and run( go to the sides) once.
rise 4
-------- = -----
run 1
Answer:
y = 3x + 1
Step-by-step explanation:
Slope: As it rises 3, it runs 1
Slope = Change in y/change in x
Slope = 3/1
y - intercept = 1 ,the point of intersection
Equation : y = mx + b
m = slope
b = y-intercept
Equation : y = 3x + 1
-Chetan K
A vehicle purchased for $25000 depreciates at a constant rate of 5% per year. Determine the approximate value of the vehicle 12 years after purchase. Round to the nearest whole number.
Answer:
$13,509.
Step-by-step explanation:
After each year the vehicle is worth 95% of the previous value.
95% = 0.95.
So after 12 years the approximate value
= 25000 * 0.95^12
= $13,509.
Does each function describe exponential growth or decay?
Drag and drop the equations into the boxes to correctly complete the table.
Growth
Decay
y = 250(1 + 0.004)^t
y = 426(0.98)^t
y = 12,000(1/2) ^t
9514 1404 393
Answer:
growthdecaydecayStep-by-step explanation:
An exponential function will describe growth if the base of the (positive) exponent is greater than 1. It will describe decay of the base is less than 1.
y = 250(1 + 0.004)^t . . . . . 1.004 > 1 ⇒ growth
y = 426(0.98)^t . . . . . . . . . 0.98 < 1 ⇒ decay
y = 12,000(1/2) ^t . . . . . . . 1/2 < 1 ⇒ decay
fkjlfljkfleruhgowjfgwklgnerql;ng;
Answer:
THX for points XD
Step-by-step explanation:
find the formula for a function of the form y=ae^(-x)+bx with global minimum at (1,10).
The formula for a function of the form [tex]y = a\cdot e^{-x} + b\cdot x[/tex] with global minimum at [tex](1, 10)[/tex] is [tex]y = 5\cdot e^{1-x}+5\cdot x[/tex].
We can use first and second derivative tests to determine all coefficients of the function described in statement so that the point given is an absolute minimum. The expressions for such tests are introduced below:
FDT
[tex]-a\cdot e^{-x}+b = 0[/tex] (1)
[tex]b = a\cdot e^{-x}[/tex]
SDT
[tex]y''=a\cdot e^{-x}[/tex] (2)
Where [tex]y'' > 0[/tex].
If we know that [tex](x, y) = (1, 10)[/tex], then we have the following system:
[tex]10 = a\cdot e^{-1}+b[/tex] (3)
[tex]b = a\cdot e^{-1}[/tex] (4)
[tex]y'' = a\cdot e^{-1}[/tex] (5)
By (4) in (3):
[tex]10 = 2\cdot a\cdot e^{-1}[/tex]
[tex]a = \frac{10}{2\cdot e^{-1}}[/tex]
[tex]a = 5\cdot e[/tex]
By (5) we prove that [tex]y'' > 0[/tex], and we get the value of [tex]b[/tex] by (4):
[tex]b = 5[/tex]
Thus, the formula for a function of the form [tex]y = a\cdot e^{-x} + b\cdot x[/tex] with global minimum at [tex](1, 10)[/tex] is [tex]y = 5\cdot e^{1-x}+5\cdot x[/tex].
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distance from the point to 0, so it can never be
negative.
a. Coordinate plane
b. Opposite
c. Absolute value
d. Quadrant
distance from the point to O, so it can never be negative so answer is
b.oppsite
a meal came to $16.41 without tax. calculate the 6% sales tax, and then calculate the 15% tip based on the sum of the meal and the tax. what is the total cost of the meal?
Answer:
$20
Step-by-step explanation:
correct me if im wrong(┬┬﹏┬┬)
7. Karen opened a savings account with $500. The money earns 0.2% interest per month. If she does not make any withdraws or any more deposits, approximately how much money will Karen have in the account after two years?
(North Carolina Math 2)
A. $502 B. $512 C. $515 D. $525
Answer:
The answer is A
Step-by-step explanation:
0.2% of 500 is 1 so in two year she would have 502$
See attachment picture please
Answer:
How can we answer it without question?
what is the probability of a 200 year flood this year
Answer:
0.5 chance
Step-by-step explanation:
Likewise, the term "100-year storm" is used to define a rainfall event that statistically has this same 1-percent chance of occurring.
Answer:
0.5
Step-by-step explanation:
The possibility are very very very low, but never a no
If 12 cats can kill 12 mice in 12 hours, how many hours will it take for 2021 cats to kill 2021 mice
Step-by-step explanation:
168 hours I guess
have a food day
There are 15 pieces of fruit in a bowl and 6 of them are apples. What percentage of the pieces of fruit in the bowl are apples?
40%
6/15 is 0.4. Multiplied by 100, that makes 40%.
The height of a parallelogram is 6[tex]a^{2}[/tex][tex]b^{5}[/tex] and the base of a parallelogram is 4[tex]a^{3}[/tex][tex]b^{4}[/tex] Find the area of the parallelogram using the formula A = bh
[tex]\text{Area of parallelogram} = \text{Base}~ \times~\text{Height} = (4a^3b^4)(6a^2 b^5)=24a^5 b^9[/tex]
Jamie Lee needs to save a total of $9,000 in order to get started in her cupcake café venture. She is presently depositing $1,800 a year in a regular savings account. Calculate the future value of these deposits.
Answer: 16,200,000
Step-by-step explanation: divide both numbers
The future value of her deposit would be in 5 years.
The total amount needed to start a cupcake cafe venture
= $9,000
Deposit per year = $1,800
Therefore, if $1,800 = 1 year
$9,000 = X
[tex]x = \frac{9000}{1800} [/tex]
[tex]x = 5[/tex]
Therefore in 5 years, Jamie Lee would be able to start her cupcake café venture.
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Explain the differences and similarities of the steps for dividing whole numbers and decimals.
Answer: Comparing a whole numbers and a decimals:
First let’s talk about the similarities of comparing whole numbers and decimals:
=> their place value always matters.
Now, let’s proceed to their differences
=> in comparing whole numbers, we don’t care about the value to the nearest decimal points or the value of ones. We always look at the highest value, not unless the highest values are all the same.
=> In comparing decimals, the value to the nearest decimal points or the tenths place value always matters.
Step-by-step explanation:
can somebody help me with my language arts please???
Answer:
yes!
Step-by-step explanation:
The letters A, B, and C can be arranged in six ways. Five ways are listed below.
Find the sixth way.
АВС ACB BAC ВСА САВ
Answer:
CBA would be the sixth
Step-by-step explanation:
Nicole drinks 0.25 L of milk every day. How much milk does she drink on 13 days?
Answer:
3.25 L
Step-by-step explanation:
0.25*13=3.25
When bisecting segments and angles, which step is the same?
A nutrition company is marketing a low-calorie snack brownie. A serving size of the snack is 3 brownies and has a total of 50 calories. Determine how many calories 14 brownies would have. Round to the nearest calorie
The number of calories in 14 brownies is 233 calories.
The first step is to determine the average calorie in 1 brownie.
Average calorie = 50 calories / 3 = 16.667 calories
In order to determine the number of calories in 14 brownies, multiply the average calorie by 14 brownies.
Total calories = 16.67 x 14 = 233 calories
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The perimeter of the triangle is
equal to the area of the rectangle.
What is the value of x?
Answer:
x=-21
Step-by-step explanation:
make the equation
2x+9x-1+40=6(x-11)
simplify
11x+39=6x-66
solve
5x=-105
x=-21
The function f(x) = mx + 5 is its own inverse. Find the value of m?
mx + 5 = (x - 5) / m
mx + 5 = x/m - 5/mAnswer:
Step-by-step explanation:
first find the inverse equation
y = mx + 5
y - 5 = mx
(y - 5) / m = x
(x - 5) / m = f⁻ˣ(x)
The original function is a line with slope m and y intercept of 5
The inverse function is a line with a slope 1/m and x intercept of 5
so the common line is where m = 1/m
m = 1/m
m² = 1
m = ± 1
The only line with a common slope between these two options is when
m = -1 and y intercept is 5