Let's define the following variables first.
A = number of tickets sold for adults
C = number of tickets sold for children
From the question, we can say that or form the following equations:
1. A + C = 790 tickets
2. $7A + $4C = $4, 390
The first equation can also be written as A = 790 - C. We can use this equation and replace "A" in the second equation.
[tex]7(790-C)+4c=4,390[/tex]From that, we can solve "C" by solving the equation formed above.
[tex]\begin{gathered} \text{Distribute 7 to the terms inside the parenthesis.} \\ 7(790)-7(C)+4C=4,390 \\ 5,530-7C+4C=4,390 \\ \text{Subtract 5,530 on both sides of the equation.} \\ -7C+4C=-1140 \\ -3C=-1140 \\ \text{Divide -3 on both sides.} \\ C=380 \end{gathered}[/tex]Therefore, 380 tickets for children were sold.
Since there are 790 tickets in total that are sold and 380 tickets for children were sold, we can say that 410 tickets for adult was sold.
[tex]\begin{gathered} A=790-C \\ A=790-380 \\ A=410 \end{gathered}[/tex]Richard and teo have a combine age of 38 Richard is 11 years okder than twice teo age how old are Richard and teo?
Answer: Richard is 29 and Teo is 9.
Step-by-step explanation: Use Substitution
what is 16 divided by 3,482
Answer:217.625
Step-by-step explanation:
9. Determine where the graph represents a function explain your answer.
The vertical line test is a visual test to determine if a graph represents a function; since a function can only have one output for every input if a vertical line intersects a curve in more that one point the it is not the graph of a function.
In this case we any vertical line will only intersect one point then we conclude that:
The graph represents a function. Using the vertical line test, the graph intersects any vertical line at only one point.
What are the vertex and range of y = |x + 3| + 2?
a (−3, 2); 2 ≤ y < ∞
b (−3, 2); −∞ < y < ∞
c (0, 5); 2 ≤ y < ∞
d (0, 5); −∞ < y < ∞
The vertex of the equation is (-3, 2). And the range will be the set of all real numbers equal to or larger than 2, written as:
y ≥ 2.
What is the vertex and range of the absolute value function?
For an absolute value function of the form:
y = |x - a| + b
The vertex is a the point (a, b).
And the range (the set of the possible values of y that we can get with the function) will be the set of all real values equal or larger than b.
In this case, the absolute value function is:
y = |x + 3| + 2
Comparing it with the general one, we can see that the vertex is (-3, 2)
And then the range is y ≥ 2.
Learn more about absolute value equations:
https://brainly.com/question/1782403
#SPJ1
Consider x = 10-y.
a. Complete the table for the equation.
y
X
0
1
2
Answer: 0-10
1-9
2-8
Step-by-step explanation:
Which function is shown in the graph?
Answer:
1st option
Step-by-step explanation:
Factor 24cd − 36c^2d.
Answer:
12cd(2-3c)
Step-by-step explanation:
check:
12cd( 2 - 3c)
12cd(2) - 12cd(3c)
24cd - 36[tex]c^{2}[/tex]d
Please answer the following questions. What is the slope of the line? How much does the distance increase for each hour since Alan crossed the bridge?
SOLUTION
The slope of the line can be gotten using the formula
[tex]\begin{gathered} \text{Slope =}\frac{change\text{ in distance}}{\text{change in time }}\text{ = }\frac{d2-d1}{t2-t1} \\ \text{Taking two points on along the line we have } \\ \text{Slope = }\frac{350-100}{7-2} \\ \\ \text{Slope =}\frac{250}{50} \\ \\ \text{Slope = 50} \end{gathered}[/tex]The slope is 50. This means the distance increased by 50 miles for every hour.
Which statement about this function is correct?
A.The y-intercept is (71, 0), and the 71 represents the number of hours until the temperature reaches 71°F.
B.The y-intercept is (71, 0), and the 71 represents the number of hours until the temperature reaches 0°F.
C.The y-intercept is (0, 71), and the 71 represents the starting temperature.
D.The y-intercept is (0, 71), and the 71 represents the temperature after 1 hour
Answer:
C
Step-by-step explanation:
1 we need you to provide the function for people to better understand how to answer.
2 Option c was the only one that made sense.
pls mark brainliest
Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculatorlog5 (15x + 20y)
The given expression is
[tex]\log _5(15x+20y)[/tex]Factor out the greatest common factor between 15x and 20y.
[tex]\log _5(5(3x+4y))[/tex]Then, use the product property to expand the logarithm.
[tex]\log _55+\log _5(3x+4y)[/tex]At last, simplify the first logarithm because its base is equal to its argument.
[tex]1+\log _5(3x+4y)[/tex]Therefore, the simplest form of the logarithm is
[tex]1+\log _5(3x+4y)[/tex]Determine whether the given pair of lines is parallel, perpendicular, or neither. 3x + 4y = 5 and 6x + 7y= 8 Choose the correct answer below. A. The lines are neither parallel nor perpendicular. B. The lines are perpendicular. C. The lines are parallel.
If two lines are parallel, then they have the same slope.
If two lines are perpendicular, then the slope of one line is the negative reciprocal of the other line.
The equation of a given line is expressed as
y = mx + b
Where
m represents slope
c represents y intercept
Considering the first equa
write in 1/3×1/4 lowest terms1/62/71/71/12
A box has a width of 12 cm and a length of 9 cm. the volume of the box is decreasing at a rate of 541 cubic cm per second, with the width and length being held constant. what is the rate of change of the height, in cm per second, when the height is 6 cm?
With the width and length being held constant, the height of the box decreases at rate 5 cm/s
Let:
l = length
w = wide
h = height
Then, the volume of the box is given by:
V = l . w. h
The length and the width are assumed to be constant. Hence, the derivative with respect to time is:
dV/dt = l . w dh/dt
Parameters given:
dV/dt = - 541 cm³/dt
l = 9 cm
w = 12 cm
Plug these parameters into the formula:
-541 = 12 . 9 . dh/dt
dh/dt = 5 cm/s
Learn more about derivative here:
https://brainly.com/question/22716418
#SPJ4
PLEASE HELP
50 POINTS
Answer:
9. [tex]256u^8 v^{16}[/tex]
10. [tex]-32x^{10} y^{35}[/tex]
11. [tex]-x^{12}y^{20}[/tex]
12. 1
13. [tex]\frac{2}{3xy^3}[/tex]
14. [tex]\frac{h^8}{3j^6k^6}[/tex]
15. [tex]\frac{1}{4z}[/tex]
Answer:
9. 256u^8 v^16
10. -32x^10 y^35
11. x^12 y^21
12. 1
Step-by-step explanation:
If you can, please give me a Brainliest; thank you! I put a lot fo times to solve it !
Is it possible for polygon ABCDE to be dilated to figure VWXYZ? Explain yourreasoning.
In the given figures, ratio of all corresponding sides are
[tex]\frac{1}{2}[/tex]Except the ratio of AE and VZ
[tex]\begin{gathered} \frac{AE}{VZ}=\frac{10}{12} \\ =\frac{5}{6} \\ \ne\frac{1}{2} \end{gathered}[/tex]Hence, the polygon ABCDE can't be dilated to VWXYZ because ratio of corresponding sides are not equal.
So, the correct answer is (C)
Data were collected on the distance a baseball will travel when hit by a baseball bat at a certain speed. The speed, s, is measured in miles per hour, and distance, y, is measured in yards. The line of fit is given by ŷ = 3.98 + 53.59s. If the ball travels for a duration of 5 seconds, what is the predicted distance of the ball?
The predicted distance of the ball would be 27.1.93 yards when the ball travels for a duration of 5 seconds.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
The distance, y, is measured in yards and the speed, s, is measured in miles per hour.
The regression line is defined as ŷ = 3.98 + 53.59s ... (i)
The slope and y-intercept of the regression line must be determined.
The general equation for a linear regression line is y = a + bx...(ii), where x is a variable. The variable is indicated by s in the above equation.
When I and (ii) are compared, we obtain a = 3.98 and b = 53.59.
It indicates that the slope is 53.59 and the y-intercept is 3.98.
The slope, b = 53.59, implies that for every mile per hour of speed, the distance rises by 53.59 yards.
The ball travels for a duration of 5 seconds
Substitute the value of s = 5 in equation (i) to get
ŷ = 3.98 + 53.59(5)
ŷ = 271.93
Thus, the predicted distance of the ball would be 27.1.93 yards.
Learn more about Velocity here:
https://brainly.com/question/12904979
#SPJ1
Answer:
271.93
Step-by-step explanation:
Use play so value to solve. Derek measured an insect wing that was 0.1 meter long. Leslie measured a different wing that was 1/10 as long as that wing that Derek measured how long is the wing that Leslie measured
Please help I’m desperate thank you
Two or more expressions with an Equal sign is called as Equation. Derek measured 0.01 metres is the wing that Leslie measured.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that
Derrick measured wing length was 0.1 m
The wing that Leslie measured was (1/10) as long as the wing that derrick measured.
We need to measure how long is the wing that Leslie measured.
Multiply 0.1 by (1/10)
0.1×1/10
=0.01 metres.
Hence Derek measured 0.01 metres is the wing that Leslie measured.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 centimeters and the lengths of the prisms vary. It costs $0.04 per square centimeter to fabricate the prisms and the factory owner has set a limit of $11 per prism. What is the maximum length of each prism?
The maximum length of each prism is equal to 7.99 centimeter.
How to calculate the maximum length of each prism?First of all, we would determine the maximum surface area of this regular hexagonal prism by using this mathematical expression:
Maximum surface area (quantity) = Cost/unit price
Maximum surface area (quantity) = $11/$0.04
Maximum surface area (quantity) = 275 square centimeter (cm²).
Mathematically, the surface area of a regular hexagonal prism can be calculated by using this formula:
A = 6al + 3√3a²
Where:
A represents the surface area of a regular hexagonal prism.a represents the edge length (apothem) of a regular hexagonal prism.l represents the length of a regular hexagonal prism.Substituting the given parameters into the formula, we have;
275 = 6 × 4l + (3√3 × 4²)
275 = 24l + 48√3
24l = 275 - 48√3
24l = 191.8616
l = 191.8616/24
Length, l = 7.99 centimeter.
Read more on hexagonal prism here: https://brainly.com/question/27216897
#SPJ1
For Problems 3–6, find the opposite of the number.4.5
ANSWER
-4.5
EXPLANATION
We want to find the opposite of the number 4.5
The opposite of a number is the number that is the same distance from 0 on the number line but on the other side.
So, if the number is on the right hand side, its opposite is on the left hand side.
In simpler terms, the opposite of a number is the negative of a number.
So, the opposite of 4.5 is -4.5.
4. Round the number 5,997 to the nearest hundred.
Answer:
6,000
Step-by-step explanation:
Please help 50 points!!!
Given: △ABC≅△BAD.
Prove: △AED≅△BEC.
Say what each proof was for each statement.
The proof of △AED is congruent to △BEC
What is congruency?
Two figures or objects are congruent in geometry if they have the same shape and size, or if one has the same shape and size as its mirror counterpart. In more technical terms, two sets of points are said to be congruent if and only if one of them can be changed into the other by an isometry, which is a combination of rigid movements such as translation, rotation, and reflection. This implies that one item may be relocated and reflected (but not scaled) to perfectly align with the other. So two separate plane figures on a piece of paper are congruent if they can be cut out and then entirely matched up. It is OK to flip the paper over.
Given, △ABC is congruent to △BAD.
and △AEB is common in both, so
△AED is congruent to △BEC (proved)
To know more about congruency, click on the link
https://brainly.com/question/17239461
#SPJ13
what is 3 divided by 706
3/706 is 0.00424929178, but if you mean 706/3, then the answer is 235 and 1/3. Hope this helps! :)
52 points helppp composite functions give most simplified answer
Answer:
[tex](f \circ g)(24)=-36[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=-9x+9\\g(x)=\sqrt{x+1}\end{cases}[/tex]
Function Composition is applying one function to the results of another.
The composite function (f o g)(x) means to substitute the function g(x) in place of the x in function f(x).
Therefore (f o g)(24) means to substitute the result of g(24) in place of the x in the function f(x).
Calculate g(24) by substituting x = 24 into function g(x):
[tex]\begin{aligned}\implies g(24)&=\sqrt{24+1}\\&=\sqrt{25}\\&=5 \end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\implies (f \circ g)(24) & = f[g(24)]\\& = f(5)\\& = -9(5)+9\\&=-45+9\\&=-36\end{aligned}[/tex]
Answer:
(f∘g)(24) = -36
Step-by-step explanation:
Pre-SolvingGivenWe are given f(x) = -9x + 9 and [tex]g(x)= \sqrt{x+1}[/tex].
We want to find (f∘g)(24).
This means that we first want to find g(24), then substitute the value of that into f(x).
SolvingStart by substituting 24 for x in g(x).
[tex]g(24)= \sqrt{24+1}[/tex]
Add 24 and 1 together.
[tex]g(24)= \sqrt{25}[/tex]
Take the square root of 25.
g(24) = 5
Now, substitute 5 as x in f(x) = -9x + 9.
f(5) = -9(5) + 9
Multiply.
f(5) = -45 + 9
Add the numbers together.
f(5) = -36
f(5) in this case has the same value as (f∘g)(24)
This means that (f∘g)(24) = -36
suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 15 days and a standard deviation of 5 days. let x be the number of days for a randomly selected trial. round all answers to 4 decimal places where possible. a. what is the distribution of x? x ~ n( , ) b. if one of the trials is randomly chosen, find the probability that it lasted at least 12 days. c. if one of the trials is randomly chosen, find the probability that it lasted between 17 and 22 days. d. 72% of all of these types of trials are completed within how many days? (please enter a whole number)
a. the distribution of X ~ N(15,5)
b. the probability that it lasted at least 12 days = 0·72575
c. the probability that it lasted between 17 and 22 days = 0.30567
d. 72% of all of these types of trials are completed within 13 days
(a)
The x follow normal distribution with mean standard deviation
X ~ N(15,5)
(b)
probability at least 12 days.
P(X≥12) = 1 - P(X ≤12)
= 1 - P((X - μ)/б ≤ (12-15)/5 ]]
= 1 - P[Z < -0.6]
= 1 - 0·27425
= 0·72575
(c)
Probability at least between 16 & 21 days
P(16 < x < 21) = p( (16-15)/5 < (X - μ)/б - (21-15)/5]
= p (0.2 < Z < 1.2 )
= p[Z < 1.2] - P[Z < 0.2]
= 0.8849 - 0.5792
= 0.30567
(d)
standard normal table z is 0.65
p (Z < 0.65) = 0.74215
using Z score formula
X = Z x б + μ
X = 0.65 x 5 + 15
X = 13
Explain probability ?This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.
To learn more about probability, visit;
https://brainly.com/question/13932428
#SPJ4
for f(x)=3/8x-7, find f(-16)
The given function is
[tex]f(x)=\frac{3}{8}x-7[/tex]The expression f(-16) means we have to evaluate the function when x = -16.
[tex]\begin{gathered} f(-16)=\frac{3}{8}(-16)-7 \\ f(-16)=-3\cdot2-7=-6-7=-13 \end{gathered}[/tex]Therefore, f(-16) is equal to -13.The line passing through the points (-2: 1) and (1: 4) has the same angular coefficient as the line passing through the points (1-2) and (3: p) Find the value of p
Answer:
Explanation:
The angular coefficient is also referred to as the slope of the line.
Given that the slope of the lining joining these pair of points are the same:
• (-2, 1) and (1, 4)
,• (1, -2) and (3, p)
Then:
[tex]\frac{4-1}{1-(-2)}=\frac{p-(-2)}{3-1}[/tex]We solve the equation for p:
[tex]undefined[/tex]Which expression is equivalent and show work if you can pls help thanks if u do
The expression is equal to 0.00333333333.
A = 0.00333333333
B = 0.00426666666
C = 0.03125
D = 33.3333333333
Therefore, the answer is A. Hope this helps! :)
Round off each to the nearest thousand
1565
3408
5671
7364
9761
8975
Answer:
1. 1600
2. 3,000
3. 6,000
4. 7,000
5. 10,000
6. 9,000
Step-by-step explanation:
A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.
C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
In this case, Rule A applies and 1565 rounded to the nearest hundred is:
1600
NOBODY IS ANSWERING!! I WILL GIVE BRAINLIEST!! PLS HELP!!
i need help with questions a b c d e and f
its actualy geometry
Answer:
a: 120 = 2x + 40
80 = 2x
x = 40
b: (3x + 10) + (x-30) = 180
4x - 20 = 180
4x = 200
x = 50
c: 105 = 2x - 11
116 = 2x
58 = x
d: 8y + 36 = 14y - 24
-6y = -60
y = 10
64 = 48 + x
16 = x
y = 10, x = 16
e: 75 + (2x - 5) = 180
70 + 2x = 180
2x = 110
x = 55
2(55) - 5 =y
y = 105
f: (2x + 8) + (3x + 17) = 180
5x + 25 = 180
x = 31
3(31) + 17 = 5y + 15
110 = 5y + 15
95 = 5y
y = 19, x = 31