Answer:
$14
Step-by-step explanation:
if Gerald's coins have the same value as his brothers, then that means they have exactly the same amount
12) The school that Danielle goes to is selling tickets to a choral performance. On the first day of
ticket sales the school sold 5 senior citizen tickets and 9 student tickets for a total of $144. The
school took in $192 on the second day by selling 14 senior citizen tickets and 6 student tickets.
What is the price each of one senior citizen ticket and one student ticket?
Answer:
Senior citizen tickets = $9
Student tickets = $11
Step-by-step explanation:
We begin by converting these into simultaneous linear equation;
Senior citizen tickets = a
Student tickets = b
5a + 9b = 144
14a + 6b = 192
5a = 144 - 9b
a = 144/5 - 9b/5
a = 28.8 - 1.8b
We now substitute this into the first equation
14(28.8 - 1.8b) + 6b = 192
403.2 - 25.2b +6b = 192
-19.2b = 192 - 403.2
b = -211.2/-19.2
b = 11
Put the value of b into either equation
5a + 9b = 144
5a + 9(11) = 144
5a +99 = 144
5a = 144-99
5a = 45
a = 9
If f(x) = 3x + 2 and g(x) = x^2– X, find each value.
A. g(36)
B. f(2) + 1
A) g(36) = 1260
B) f(2) + 1 = 9
Solution:
Given that,
[tex]f(x) = 3x + 2\\\\g(x) = x^2-x[/tex]
Find each value
A) g(36)Substitute x = 36 in g(x)
[tex]g(36) = (36)^2 - 36\\\\g(36) = 1296-36\\\\g(36) = 1260[/tex]
B) f(2) + 1Substitute x = 2 in f(x)
[tex]f(2) + 1 = 3(2) + 2 + 1\\\\f(2) + 1 = 6 + 2 + 1\\\\f(2) + 1 = 9[/tex]
Thus the values are found
Final answer:
To solve the functions, substitute the given values into the relevant function. After performing calculations, g(36) is found to be 1260, and f(2) + 1 is calculated to be 9.
Explanation:
To find the values for given functions, we need to substitute the relevant inputs into each function and then perform the necessary calculations.
A. g(36)
Given g(x) = x² \\- x, we substitute x with 36:
g(36) = 36² \\- 36 = 1296 \\- 36 = 1260.
B. f(2) + 1
Given f(x) = 3x + 2, we first find f(2):
f(2) = 3(2) + 2 = 6 + 2 = 8.
Now, we add 1 to f(2):
f(2) + 1 = 8 + 1 = 9.
Which statements about the factors of the terms in the expression 12x+18xy-24y are true. Select three options
A:the factors common to 12x and 18xy are 1,2,3,6,x,y
B:the factors common to 12x and 18xy are 1,2,3,6,x
C:the factors common to 12x and 24y are 1,2,3,4,6,12
D:the GCF of the expression is 6xy
E: the GCF of the expression is 6
The factors common to 12x and 18xy are 1, 2, 3, 6, and x.
The factors common to 12x and 24y are 1, 2, 3, 4, 6, and 12.
The GCF of the expression is 6.
Answer: Options B, C and E.
Explanation:
Factors are numbers we can increase together to get another number. At the point when we discover the components of at least two numbers, and afterward discover a few variables are the equivalent ("normal"), at that point they are the "basic elements".
These are the factors which are common in the whole expression or are common in any two equations at the time of comparison. The common factor which is the biggest is known as the greatest common factor.
Answer:
B,C,E
Step-by-step explanation:
The round wading pool at the Greenville Community Center has a diameter of 8 feet. What is the pool's circumference? use 3.14 for pi
Answer:
25.12 feet
Step-by-step explanation:
To find the circumference of the round wading pool with an 8-foot diameter using 3.14 for pi, the formula C = πd is used, resulting in a circumference of 25.12 feet.
The question is asking to find the circumference of a round wading pool with a diameter of 8 feet using 3.14 for pi. The formula for the circumference of a circle is C = πd, where C represents the circumference, π (pi) is approximately 3.14, and d is the diameter of the circle. Given that the diameter (d) of the pool is 8 feet, we substitute the values into the formula to get:
C = 3.14 × 8 feet = 25.12 feet
Therefore, the circumference of the wading pool is 25.12 feet.
If the equation of a function is y = x2 - 5, what is the output when the input is -1?
Answer:
y = - 4
Step-by-step explanation:
The output is the value of y for a given input x
For an input of - 1, substitute x = - 1 into the equation.
y = (- 1)² - 5 = 1 - 5 = - 4 ← output
A line has a slope of -1/7 and passes through (4, -2) and (p, -1) what is the value of p
Answer:
Therefore the value of p is -3.
Step-by-step explanation:
Given a line has a slope of [tex]-\frac{1}{7}[/tex] and passes through (4,-2)and (p,-1)
The slope of a line which passes through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex]=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here [tex]x_1= 4,y_1=-2, x_2=p[/tex] and [tex]y_2= -1[/tex]
Therefore the slope of the line which passes through the given points is
[tex]=\frac{-1+2}{p-4}[/tex]
According to the problem,
[tex]\frac{-1+2}{p-4}= -\frac{1}{7}[/tex]
[tex]\Leftrightarrow \frac{1}{p-4} =-\frac{1}{7}[/tex]
[tex]\Leftrightarrow p-4=-7[/tex]
[tex]\Leftrightarrow p = -7+4[/tex]
[tex]\Leftrightarrow p = -3[/tex]
Therefore the value of p is -3.
Find the greatest common factor (GCF) of both terms 30 and 60
Answer:
30
Step-by-step explanation:
What is 199000/10000 as a decimal?
Answer:
19.9
Step-by-step explanation:
divide 199000 by 10000
=19.9
Answer:
19.9
Step-by-step explanation:
A scale diagram of a garden shows the length as 14.5 cm. If the scale is 1:150, what is the actual length? The garden is m in length
The actual length of the garden is 2175 cm.
Explanation:To find the actual length of the garden, we can use the scale. The scale indicates that 1 cm on the diagram represents 150 cm in real life. Since the length on the diagram is 14.5 cm, we can multiply this length by the scale factor to find the actual length.
Actual Length = Length on Diagram × Scale Factor = 14.5 cm × 150 = 2175 cm
Therefore, the actual length of the garden is 2175 cm.
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What is the volume of this figure? Show your calculations.
Answer:
The volume of the figure given is [tex]4000[/tex] cubic units
Step-by-step explanation:
The given figure is in the shape of a Right Square Pyramid.
The volume of a right square pyramid can be calculate by:
Volume of a right square pyramid =
[tex]a^3\frac{h}{3}[/tex]
where 'a' is the length of the base of the pyramid which is equal for all the four side of the base and 'h' is the height of the pyramid which is perpendicular to the base of it.
Given: [tex]a=10[/tex] units
[tex]h=12[/tex] units
Putting the values in the volume of the right square pyramid.
[tex]=10^3\frac{12}{3}\\\\ =10^3*4\\\\=4000[/tex]
The volume of the figure given is [tex]4000[/tex] cubic units
Which expression correctly represents "nine less than the quotient of a number and four, increased by three"?
Answer:9-x/4+3
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Be sure to explain your reasoning.
Sally makes a fruit drink using ⅔ of a cup of orange juice for every ¼ of a cup of pineapple juice. How many cups of orange juice will Sally need if she uses 2 cups of pineapple juice?
Answer:
Sally need [tex]5\frac{1}{3}[/tex] cups of orange juice.
Step-by-step explanation:
Given:
Sally makes a fruit drink using ⅔ of a cup of orange juice for every ¼ of a cup of pineapple juice.
If she uses 2 cups of pineapple juice.
Now, to find the cups of orange juice.
So, to solve by using unitary method:
As, ¼ of a cup of pineapple juice is needed for orange juice of = ⅔ cup.
So, 1 cup of pineapple juice is needed for orange juice of = [tex]\frac{2}{3}\div \frac{1}{4}[/tex]
[tex]=\frac{2}{3}\times \frac{4}{1}[/tex]
[tex]=\frac{8}{3}[/tex] cups.
Thus, 2 cups of pineapple juice is needed for orange juice of = [tex]\frac{8}{3} \times 2[/tex]
= [tex]\frac{16}{3}[/tex]
= [tex]5\frac{1}{3}[/tex] cups.
Therefore, Sally need [tex]5\frac{1}{3}[/tex] cups of orange juice.
please i need help
Answer:
P = (0,4) Q = (2,0)
Step-by-step explanation:
Add
(-1 - i) + (-10 + 3i)
Answer:
the sum of the 2 expressions is -11+2i.
Step-by-step explanation:
-1-10=-11
-i+3i=2i
-11+2i
Can you please help me just need the answer pls.please need help
Answer:
20
Step-by-step explanation:
Terry Wade's variable costs for his car
totaled $1,876.88 last year and his fixed
costs totaled $1,685. If he drove 10,846
miles last year, what was his cost per
mile? Round to the nearest cent.
A $0.45
B $0.33
C $0.64
D $0.35
To find Terry Wade's cost per mile, his variable and fixed costs are summed and then divided by the total miles driven, yielding a cost per mile of approximately $0.33.
Explanation:To calculate Terry Wade's cost per mile for using his car, we first need to add together his variable and fixed costs, and then divide this total by the number of miles he drove last year.
This gives us the cost per mile.
Step 1: Add variable and fixed costs.
Variable costs = $1,876.88
Fixed costs = $1,685
Total costs = Variable costs + Fixed costs = $1,876.88 + $1,685 = $3,561.88
Step 2: Divide the total costs by the number of miles driven.
Number of miles driven = 10,846 miles
Cost per mile = Total costs ÷ Number of miles driven = $3,561.88 ÷ 10,846 miles
Cost per mile ≈ $0.328 or rounded to the nearest cent, $0.33.
Therefore, the cost per mile for Terry Wade last year was $0.33, making the correct answer B $0.33.
13-9-x/11=3x/22+121/2
Answer:
x=-248 3/5
Step-by-step explanation:
13-9-x/11=3x/22+121/2
4-x/11=3x/22+121/2
4-121/2=3x/22+x/11
8/2-121/2=3x/22+2x/22
-113/2=5x/22
5x/22=-113/2
5x=(-113/2)*22
5x=-113*22/2
5x=-113*11
x=-1243/5
x=-248 3/5
11,647 rounded to the nearest hundred
Answer:
11,600
Step-by-step exp
the 4 in the tens place means the 6 stays the same
Answer:
11,600
Step-by-step explanation:
think of 100... that 1 is in the hundred place. when rounding you look to the number to the right of that place. if that number is less than 5 you dont round up. if the number is 5 or greater you round up. in this case 11,647 the number 6 is in the hundred place. look to the right of it. in this case it is 4. 4 is less than five so you don't round up. your number 11,647 rounded to the hundred place is 11,600.
A city has a population of 250,000 people. Suppose that each year the population grows by 6%. What will the population be after 12 years ?
Answer:
503,049
Step-by-step explanation:
250,000 × 1.06^12 is the formula.
You take the percentage which is 6% and you add 1 to it.
So, you get 1.06
Then you take the 1.06 and raise it to the number of years which is 12.
1.06^12
Then you multiply that number to the base number which is 250,000 and get 503,049.
Hope this helps!
Final answer:
To find the population after 12 years given a 6% annual growth, we apply the exponential growth formula. With an initial population of 250,000, the formula gives approximately 503,054 as the population after 12 years.
Explanation:
To calculate the population of a city after 12 years when it grows by an annual rate of 6%, we utilize the formula for exponential growth, P(t) = P0 * [tex](1 + r)^t[/tex], where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the number of years.
Given:
Initial population P0 = 250,000Growth rate r = 6% or 0.06Time t = 12 yearsThe population after 12 years can be calculated as follows:
P(12) = 250,000 * [tex](1 + 0.06)^{12}[/tex]
P(12) = 250,000 * [tex](1.06)^{12}[/tex]
P(12) ≈ 250,000 * 2.0122
P(12) ≈ 503,054
Therefore, the estimated population after 12 years is approximately 503,054.
John paid $34 for 2 books and 3 pencils. He paid $36 for 3 books and 2 pencils. How much was each?
Cost of each book is $ 8 and cost of each pencil is $ 6
Solution:
Let "a" be the cost of 1 book
Let "b" be the cost of 1 pencil
John paid $34 for 2 books and 3 pencils
Therefore,
2 books x cost of 1 book + 3 pencil x cost of 1 pencil = 34
[tex]2 \times a + 3 \times b = 34[/tex]
2a + 3b = 34 ----------- eqn 1
He paid $36 for 3 books and 2 pencils
3 books x cost of 1 book + 2 pencil x cost of 1 pencil = 36
[tex]3 \times a + 2 \times b = 36[/tex]
3a + 2b = 36 -------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 2
4a + 6b = 68 ---------- eqn 3
Multiply eqn 2 by 3
9a + 6b = 108 --------- eqn 4
Subtract eqn 3 from eqn 4
9a + 6b = 108
4a + 6b = 68
( - ) -------------
5a = 40
a = 8
Substitute a = 8 in eqn 1
2(8) + 3b = 34
16 + 3b = 34
3b = 34 - 16
3b = 18
b = 6
Thus cost of each book is $ 8 and cost of each pencil is $ 6
Western North Carolina Woods have a deer population density of 3.5 deer per acre. If there are a total of 435 deer, how many acres are in this parcel of woods?
There are about 124.29 acres in this parcel woods
Step-by-step explanation:
The given is:
Western North Carolina Woods have a deer population density of 3.5 deer per acreThere are a total of 435 deerWe need to find how many acres are in this parcel of woods
∵ The population density = 3.5 deer per acre
- That means 1 acre for every 3 dears
∵ There are a total of 435 deer
∴ [tex]\frac{3.5}{1}=\frac{435}{x}[/tex] , where x is the number of acres
- By using cross multiplication
∴ 3.5 × x = 1 × 435
∴ 3.5 x = 435
- Divide both sides by 3.5
∴ x = 124.29
There are about 124.29 acres in this parcel woods
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1 1/6 • 20 13/24 =? What is the answer to this?
Immediately after jumping out of a plane, a 65kg skydiver starts to fall towards the
Earth with an acceleration of 9 8ms? Calculate the downwards force on the
skydiver at the instant he leaves the plane (show working):
it's physics not maths don't know how to change it
Answer:637kgms-2
Step-by-step explanation:the force acting on him will be Made X acceleration due to gravity. Then since the mass is 65, multiply it with 9.8, then you will get the force which is 637kgms-2
On a map with a scale of 2 cm = 1 km, the
distance from Beau's house to the beach is
4.6 centimeters. What is the actual distance?
A 2.3 km
B 4.6 km
© 6.5 km
D 9.2 km
Answer:
A. 2.3km
Step-by-step explanation:
Since 2cm = 1km
4.6cm = xkm
xkm = 4.6 x 1 / 2
= 2.3km
Answer:
I would believe that the answer is A. 2.3 km
Step-by-step explanation:
If 2cm=1km
then 4cm=2km
not to mention the km is 1/2 or the cm
so i would believe that .6cm would be .3km
therefore the answer must be 2.3km
YOU WON'T ANSWER THIS!!!!
Using the exponential function 2x + 3, what is the average rate of change between the values 1 ≤ x ≤ 5?
explain answer step by step
Answer:
7.5
Step-by-step explanation:
The given exponential function is
[tex]f(x) = {2}^{x} + 3[/tex]
The average rate of change over a≤x≤b is given by;
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
This implies that the average rate of change between the values 1 ≤ x ≤ 5 is
[tex] \frac{f(5) - f(1)}{5 - 1} [/tex]
We evaluate to get:
[tex]\frac{ {2}^{5} + 3 - {2}^{1} - 3}{4} = \frac{30}{4} = \frac{15}{2} = 7.5[/tex]
A cube has side lengths of 4 in.
What is the volume of the cube?
Enter your answer in the box.
Answer:
This would equal 64
Step-by-step explanation:
To find the volume of a cube you multiply the length x width x height.
So in this case this would be 4 x 4 x 4 = 64
This is the easiest shape to find the volume.
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What is distance formula?
Answer:
d = distance
(x_1, y_1) = coordinates of the first point
(x_2, y_2) = coordinates of the second point
Step-by-step explanation:
Answer:
The distance formula itself is actually derived from the Pythagorean Theorem which is a 2 + b 2 = c 2 {a^2} + {b^2} = {c^2} a2+b2=c2
Step-by-step explanation:
What is the quotient? Negative StartFraction 4 over 5 EndFraction divided by 2 Negative 1 and three-fifths Negative two-fifths One-half 1 and three-fifths
Answer:
a
Step-by-step explanation:
The quotient of the given expression is -2/5.
What is quotient?The number we obtain when we divide one number by another is the quotient
Given is the expression as -
- (4/5) ÷ 2
The given expression is -
- (4/5) ÷ 2
- (4/5) x 1/2
- 2/5
Therefore, the quotient of the given expression is -2/5.
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If there is a 61% chance that carol gets accepted to Andover university, what is the chance, or probability, that carol does not get accepted
Answer: if I am correct it is 39%
Step-by-step explanation:
11. What must be true about p and q if the equation shows equivalent fractions
Answer:
p and q are both equal to 20.
Step-by-step explanation:
40 / 2 = p, so p = 20
100 / 5 = q, so q = 20