In linear equation, No of Adults = 2,179, No of Children = 3,221 .
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.Let Number of Adult admission be x
Number of children's admission be y
Total tickets were sold = 5400
so x+y= 5400 ....... eq 1
One adult ticket costs $5.50 ,so total Adult ticket costs = 5.50x
One Child ticket costs $ 3.50, so total Children tickets cost= 3.50 y
receipt totaled = $23,258
so 5.50x+3.50y= $23,258....... eq 2
multiply 5.50 to the eq 1, we get,
5.50x +5.50y = 29,700...... eq 3
subtract eq 2 from eq 3, we get,
5.50y-3.50y = 29,700- 23,258
2y= 6,442
divide by 2 both sides ,we get, y= 3,221
substitute the value of y in eq 1, we get,
x+ 3,221 =5400
x= 5400- 3221
x= 2,179
No of Adults = 2,179, No of Children = 3,221
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A box contains different-colored marbles. If P(blue) = P(green) = and P(blue and green) = whic
statement is true?
O The events are independent because P(blue) P(green) = P(blue and green).
Answer:
p(blue and green)
Step-by-step explanation:
the events are independent because p(blue) p(green)=p(blue and green).
Which inequality is equivalent to this one?y-85-2y-8+82-2+ 8y-8+8 <-2+8y-8+25-2+8y-8+25-2+2
Explanation
[tex]y+8=2[/tex]solve for y :
The subtraction property of equality tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same
hence,
subtract 8 in both sides
[tex]\begin{gathered} y+8=2 \\ y+8-8=2-8 \\ y=-6 \end{gathered}[/tex]so, the answer is
y=-6
I hope this helps you
Please Answer the following 2 questions asked in the image provided, Asap.
1 Fristly you do M1=M2 as it is parallel
You get M2 then use it to find equation
note that y= -1.5
2 for second question you find coefficient of X and y you get M1 then find equation of given line easily.
#note equaction of straight line passing through two points is y-y1=m(x-x1)
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:
Step-by-step explanation:
h = number of hours
s = number of shirts made
28h+2s=144
4h=s
h=4, s=16
(Didn't I already answer this? i think i might have.. lol)
Find the average rate of change of f(x)=x²-4x+1 from x=3 to x=7.
Simplify your answer as much as possible.
( explain pls )
At x=3 to x=7, the average rate of change of the given function
f(x) = x2- 4x + 1 is 6.
Solution:Given function,
f(x) = x² - 4x + 1
given x=3 and x=7
To find the average rate of change of a function, find its slope(m),
To find m ,
m= (y2 - y1) / (x2 - x1)
here y1 and y2 not given.
then substitute the given values of x into f. (x)
when x=3 ,
y1 = (3² - 4×3 +1)
= (9 - 12 +1)
= -2
so (x1,y1) = (3,-2)
similarly to find y2,
substitute x = 7 to f(x)
y2 = (7² - 4×7 + 1)
= (49 - 28 +1)
= 22
so (x2,y2) = (7,22)
To find m, substitute the values.
m= (y2 - y1) / (x2 - x1)
= (22 -( - 2)) / (7 - 3)
= 24/4
= 6
As a result, the average rate of change of the function x2-4x + 1 is 6.
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3. How many tens are there between 9,312 and 9,522? Explain your thinking
The number of tens between the given numbers are 1883.
The number of tens between two numbers can be calculated by the concept of proportions. A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem. Now, to find the number of tens we divide the number by 10. So, the number of tens in the given numbers are
9312/10 = 931 (approximately)
9522/10 = 952 (approximately).
Now, the numbers of tens between the two given numbers can be calculated by adding the number of tens in them that is,
952 + 931 = 1883 tens between the two numbers.
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i only need help with 12 & 13 only and show work please. note the picture is sideways
Answer:
12. 65:6 = 65/6 = 65 to 6
13: 21:4 = 21/4 = 21 to 4
Step-by-step explanation:
You want the numerical values of the given ratios of blood donors written three ways.
In each case, replace the blood type with the corresponding number of donors. Ratios can be written using a colon, a division bar, or the word "to".
12. A+ and B+ to AB+Using the numbers, this is ...
(45 +20) : 6 = 65 : 6 = 65/6 = 65 to 6
13. A- and B- to AB-Using the numbers, this is ...
(21 +0) : 4 = 21 : 4 = 21/4 = 21 to 4
(a) Give a secant line.(b) Give a chord.(c) Give a tangent line.
Solution
Secant is a line that touches a circle at two distinct points
See figure below
Chord is a straight line that touches two points on the the circumference of the circle
A
HELP ASAP 100 POINTS!!!!!!!!!
The points (6,2) and (10,4) fall on a particular line. What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
[tex]y-2=\dfrac{1}{2}(x-6)[/tex]
Step-by-step explanation:
To find the equation of a line that passes through two given points, first find its slope by substituting the given points into the slope formula.
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Define the points:
(x₁, y₁) = (6, 2)(x₂, y₂) = (10, 4)Substitute the points into the slope formula:
[tex]\implies m=\dfrac{4-2}{10-6}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Therefore, the slope of the line is ¹/₂.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
To find the equation in point-slope form, substitute the found slope and one of the given points into the point-slope formula:
[tex]\implies y-2=\dfrac{1}{2}(x-6)[/tex]
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
55.17
Step-by-step explanation:
[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]
I have a question for quantitative reasoning. Alcohol use by high school seniors in a certain state decreased from 50.3% in 2000 to 32.7% in 2015. Describe this change as an absolute change in terms of percentage points and as a relative change in terms of a percentage.
The of senior high school students who reported consuming alcohol is mathematically given as
33.99% of
This is further explained below.
What percentage of senior high school students report consuming?Absolute change is the straightforward difference between the indicator's two time periods.
Absolute change = final value - initial value
Absolute change =(33 *1-50.3)% points
=-17.2% points
Decrease absolute change $=17.2% point
- ve hours decreased
+ve shows increased
The percentage of high school seniors using alcohol decreased by 17.2%. point
Relative change expresses absolute change as the ax of the value in the initial period
[tex]$=\frac{\text { absolute change }}{\text { intial value }} \times 100$$=\frac{33.1-50.3}{50.3} \times 100$[/tex]
=-33.99 %
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What is a rule for the nth term of Geometric sequence -3,-6,-12,-24,-48
The sequence is given as,
[tex]-3,\text{ -6, -12, -24, -48.......}[/tex]For the given sequence,
[tex]\begin{gathered} First\text{ term\lparen a\rparen = -3} \\ Common\text{ ratio\lparen r\rparen = }\frac{-6}{-3}=\text{ 2} \end{gathered}[/tex]nth term of a geometric progression is given as,
[tex]a_n\text{ = ar}^{n-1}[/tex]Where,
a = First term
r = common ratio
Therefore the nth term is calculated as,
[tex]a_n=\text{ -3\lparen2\rparen}^{n-1}[/tex]Thus the required answer is,
[tex]a_n=\text{ -3\lparen2\rparen}^{n-1}[/tex]1 5/6+1 3/6 pls help
Answer:
10/3
Step-by-step explanation:
[tex]1\frac{5}{6} = \frac{11}{6}\\ \\\ 1\frac{3}{6} = \frac{9}{6}[/tex]
11/6 + 9/6 = 10/3 =3.333333333
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
Your grandmother was in the hospital and was put on a liquid diet. After examining her chart, a mistake was found stating that her weight was 500 kg. The dietician decided my grandma weighed too much and put her on a liquid diet. How much did they believe that she weighed in pounds? (Show all work using dimension analysis, round to nearest whole pound)
Your grandmother was in the hospital and was put on a liquid diet. The approximate weight of grama in pounds is 1100 pounds
This is further explained below.
What is the conversion?Generally, Simply rephrasing the query as "what is the equivalent of 500 kg in Pounds" will accomplish the same thing.
In order to do this, we need to know how many kilograms are in one pound: It weighs something about 2.2 pounds.
Therefore, one hundred and ten kilograms is equal to five hundred and two point two pounds (and a little more since one kg is a little more than 2.2 pounds).
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Royal Furniture bought a sofa for $820. The sofa had a $1,420 list price. What was the trade discount rate Royal received? (Round your answer to the nearest hundredth percent.)
The received trade discount amount is $600 and percentage is 42.25%.
The trade discount in amount is = Original price - New price
Keep the values in formula to find the trade discount
The trade discount in amount is = 1420 - 820
Performing subtraction on Right Hand Side of the equation
The trade discount amount is = $600
Finding the trade discount in percentage
Trade discount in percentage = discount ÷ original price × 100
Keep the values in formula to find the trade discount in percentage
Trade discount in percentage = (600/1420)× 100
Performing multiplication and division
Trade discount in percentage = 42.25%
The trade discount is $600 and 42.25%.
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Which situation yields data with variability?The distance covered by different vehicles traveling at a constant rate of 60 mph for 45 minutes The length of different professional American football fieldsThe weight of 6th grade studentsThe moon cycle duration in a year
Answer:
The weight of 6th-grade students
Explanation:
We have variability if each value in the data is different.
When a vehicle travels at a constant rate for the same amount of time, the distance covered will be always the same. So, this situation doesn't yield data with variability.
In the same way, the length of a professional American football field and the moon cycle duration in a year are standard, they always have the same value so these situations don't yield data with variability.
Finally, each student of 6th grade has a different weight, so this is the situation that yields data with variability.
Therefore, the answer is:
The weight of 6th-grade students
A machine at the candy factory dispensed different numbers of lemon-flavored candies into various bags. Number of lemon-flavored candies Number of bags 29 1 69 4 108 5 4 118 5 162 4 167 2 186 X is the number of lemon-flavored candies that a randomly chosen bag had. What is the expected va of X? Write your answer as a decimal.
In order to calculate the expected value of x, we just need to divide the total number of lemon-flavored candies by the total number of bags, so we have:
[tex]\begin{gathered} E(x)=\frac{29\cdot1+69\cdot4+108\cdot5+118\cdot4+162\cdot5+167\cdot4+186\cdot2}{1+4+5+4+5+4+2} \\ E(x)=\frac{3167}{25} \\ E(x)=126.68 \end{gathered}[/tex]So the expected value of x is 126.68.
The variable cost for a product is $1.00 and the total fixed costs are $88,000. The company sells the products for $3.00 each. How many products will the company have to sell to break even?
The breakevenpoint is the point at which costs and sales are equal to each other and therefore, the profit is zero.
The breakeven point in terms of number of units sold can be determined as follows;
[tex]\begin{gathered} Breakeven\text{ units=}\frac{Fixed\text{ costs}}{\text{ Selling price per unit-}Variable\text{ cost per unit}} \\ \text{Breakeven units=}\frac{88000}{3-1} \\ \text{Breakeven units=}\frac{88000}{2} \\ \text{Breakeven units=44000} \end{gathered}[/tex]In order to breakeven, the company will have to sell 44,000 units
Helppppp please !!!
Consider the parabola given by the equation:
f
(
x
)
=
−
2
x
2
−
12
x
−
9
Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two
x
intercepts of the parabola and write them as a list of points of form (x, y) separated by commas:
It is OK to round your value(s) to to two decimal places.
The features of the given parabola are as follows:
a) Vertex: (3,9).
b) Vertical intercept: y = -9.
c) x-intercepts: (-5.12, 0) and (-0.88, 0).
Features of the quadratic functionThe equation of the parabola is given by:
f(x) = -2x² - 12x - 9.
Hence the coefficients are:
a = -2, b = -12, c = -9.
The formula for the coordinates of the vertex, considering the coefficients of a quadratic equation, is given as follows:
x = -b/2a.y = -(b² - 4ac)/(4a).The coordinates of the vertex are given as follows:
[tex]x_v = -\frac{-12}{2(-4)} = -3[/tex]
[tex]y_v = -\frac{(-12)^2 - 4(-2)(-9)}{4(-2)} = 9[/tex]
Hence (3,9).
The vertical intercept is given as follows:
f(0) = -2(0)² - 12(0) - 9 = -9.
The roots are given as follows:
[tex]x_{1} = \frac{-b + \sqrt{b^2 - 4ac}}{2a} = \frac{12 + \sqrt{(-12)^2 - 4(-2)(-9)}}{2(-2)} = -5.12[/tex][tex]x_{2} = \frac{-b - \sqrt{b^2 - 4ac}}{2a} = \frac{12 - \sqrt{(-12)^2 - 4(-2)(-9)}}{2(-2)} = -0.88[/tex]Hence the points are:
(-5.12, 0) and (-0.88, 0).
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1) Movie Checkout for the week Days 2 3 4 A. 10 How many movies were checked out on Day 1? Number of Movies 30 45 60 C. 20 B. 15 D. 25
Condense the left-hand side into a single logarithm.log(4) + log(2) + log(y) = log(____)
Condensation of left-hand side of the given expression into a single logarithm is :log(4) + log(2) + log(y) = log(8y)
How to condense log?To evaluate logarithmic expressions, methods for condensing logarithms in order to rewrite multiple logarithmic terms into one can be used. it is a useful tool for the simplification of logarithmic terms. To condense logarithms we use the rules of logarithms: the product rule, the quotient rule and the power rule.
According to the product laws of logarithm,
log x+log y = log (xy)
For the given expression,
log(4) + log(2) + log(y) = log(____)
So, after applying the product rule:
log(4) + log(2) + log(y) = log(4×2×y)
log(4) + log(2) + log(y) = log(8y)
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In the figure above, if k II I, what is the value of y?
B. 45
C. 50
A. 40
D. 60
The values of measure of angle y is found as 65 degrees.
What is defined as the linear pair?Once two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair has always been 180°. These angles are also referred to as supplementary angles. A adjacent angles are those that share a vertex. As a result, the linear angles get a common vertex here as well.For the given question;
Line k || Line l
(x + 5) + (3x + 15) = 180 (linear pair)
Solving;
4x + 20 = 180
4x = 160
x = 40
Put the value of x in angles (2x + 30)
2x + 30 = 2×40 + 30 = 110
Now,
2x + 30 = y + (x + 5) (alternate interior angles)
Solving;
110 = y + 40 + 5
y = 110 - 45
y = 65 degrees.
Thus, the values of measure of angle y is found as 65 degrees.
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Find the intercepts (if an answer does not exist enter DNE) be sure to graph the line as well
Question:
Solution:
x-intercept:
the x-intercept is when y= 0. Thus replacing this value into the given equation we get:
[tex]15x+10(0)\text{ = 30}[/tex]this is equivalent to:
[tex]15x+0\text{= 30}[/tex]this is equivalent to:
[tex]15x\text{ = 30}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{30}{15}\text{ = 2}[/tex]so the point of x-interception is :
[tex](x,y)\text{ = (2,0)}[/tex]y-intercept:
the y-intercept is when x= 0. Thus replacing this value into the given equation we get:
[tex]15(0)+10y=30[/tex]this is equivalent to:
[tex]0\text{ + 10y = 30}[/tex]this is equivalent to:
[tex]10y\text{ = 30}[/tex]solving for y, we get:
[tex]y\text{ = }\frac{30}{10}=\text{ 3}[/tex]so the point of y-interception is :
[tex](x,y)\text{ = (0,3)}[/tex]We can conclude that the correct answer is:
x-intercept :
[tex](x,y)\text{ = (2,0)}[/tex]y-intercept is :
[tex](x,y)\text{ = (0,3)}[/tex]Gretchen runs backwards at a speed of -4m/s. Mika continues running at a speed of 3 m/a. If Gretchen dropped her baton-48 meters from her current position how far ahead will Mika be?
The distance by which Mika will be ahead is equal to 36 m from present location.
According to the question Gretchen and Mika are at the same point when Gretchen runs backward at the speed of 4 m/s in opposite direction to pick her baton and Mika runs in the direction of the race at the speed of 3 m/s. We need to find the distance covered by Mika form the current location in the time when Gretchen picks her baton up. Let us assume that the time taken by Gretchen to pick up her baton be equal to t. It is given that 48 meters from her current location she dropped her baton. Since she is running at the speed of 4 m/s then the time will be equal to t = 48/4 = 12 seconds. Now, Gretchen will be able to pick up the baton in 12 seconds. Thus, the distance covered by Mika in 12 seconds will be equal to 3×12 = 36m.
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Complete Question:
Gretchen and Mika are involved in a relay race. Both runners are at the same point on the course when Gretchen realizes that she dropped her baton and has to turn around to retrieve it. Gretchen runs backwards at a speed of −4 m/s, relative to the direction of the race. Mika continues running at a speed of 3 m/s. If Gretchen dropped her baton −48 meters from her current location, relative to the direction of the race, how far ahead will Mika be when Gretchen picks her baton up?
For each relation, decide whether or not it is a function.
Relation 1: No, the inputs of desk and leaf each correspond to two different outputs.
Relation 2: No, the input of 7 corresponds to three different outputs.
Relation 3: Yes, each input corresponds to only one output.
Relation 4: No, the input of -7 corresponds to two different outputs: a and h.
The Pederson family needed to cut expenses on their cell and landline phone service, cable television service, and Internet service. The best prices they found for basicservice, using different service providers, are listed below. They found a company with a package deal with all 4 services for $143.66. What is the percentage decrease bypurchasing the package deal? Cell Phone Service: $34.15 per month Landline Phone Service: $31.36 per month Cable TV Service: $56.25 per month Internet Service:$41.48 per month9.7%10.9%11.4%12.0%None of these choices are correct.
From the information given, the original costs per month were
Cell phone service $34.15
Landline phone service = $31.36
Cable TV service = $56.25
Internet service = 41.48
The total cost per month would be
34.15 + 31.36 + 56.25 + 41.48 = 163.24
For the new company that they found, the total cost is $1431
The rent in an urban neighborhood is normally distributed. The mean is $650 per month with a standarddeviation of $50. Estimate the percent of apartment residents who pay from $600 to $750 per month.Show Your Work
Solution
The z-score, also referred to as standard score, z-value, and normal score, among other things, is a dimensionless quantity that is used to indicate the signed, fractional, number of standard deviations by which an event is above the mean value being measured. Values above the mean have positive z-scores, while values below the mean have negative z-scores.
Mean is $650
Standard deviation = $50
[tex]\begin{gathered} \mu=650 \\ \sigma=50 \end{gathered}[/tex][tex]Z=\frac{x-\mu}{\sigma}=\frac{600-650}{50}=-\frac{50}{50}=-1[/tex][tex]Z=\frac{x-\mu}{\sigma}=\frac{750-650}{50}=\frac{100}{50}=2[/tex][tex]P(-1Therefore the estimated percent of apartment residents = 81.86%
Suppose you want to have $700,000 for retirement in 30 years. Your account earns 5% interest. How much would you need to deposit in the account each month?$_________________
The formula for a final amount A by depositing a regular amount R each month for n years with a interest rate r is given by:
[tex]A=R\frac{\lbrack(1+\frac{r}{12})^{^{12n}}-1\rbrack}{\frac{r}{12}}[/tex]For A = $700,000, r = 0.05, n = 30, we have:
[tex]\begin{gathered} 700000=R\cdot\frac{\lbrack(1+\frac{0.05}{12})^{12\cdot30}-1\rbrack}{\frac{0.05}{12}} \\ 700000=832.26R \\ R=\text{ \$841.08} \end{gathered}[/tex]