7. Julie has $250 to plan a party. There is a one-time fee of $175 to reserve a room. It also cost $1.25 perperson for food and drinks. What is the maximum number of people that can come to the dance?
Answers
Julie has $250 to plan the party.
The room costs $175 to reserve plus $1.25 per person for food and drinks.
Let "x" represent the number of people she can invite, you can express the total cost for the party as follows:
[tex]175+1.25x\leq250[/tex]From this expression, we can determine the number of people she can invite, without exceeding the $250 budget.
The first step is to pass 175 to the right side of the expression by applying the opposite operation "-175" to both sides of it:
[tex]\begin{gathered} 175-175+1.25x\leq250-175 \\ 1.25x\leq75 \end{gathered}[/tex]Next, divide both sides of the equation by 1.25 to reach the value of x:
[tex]\begin{gathered} \frac{1.25x}{1.25}\leq\frac{75}{1.25} \\ x\leq60 \end{gathered}[/tex]She can invite up to 60 people to the party
Related Questions
Assuming a fixed hourly pay rate, how much would an employee earn for working 4 hours based on this wage table? Hourly Pay Table Hours Worked 2 Money Earned $12.00 $24.00 $36.00 ? A. $36.00 B. $45.00 C. $64.00 D. $48.00
Answers
We have the following table
hour pay
1 12
2 24
3 36
4 ?
It seems that for each hour we work, we end up earning $12. Then, we know that if we work 3 hours we earn 36. So, if we work one more hour (4) we should add 12 to what we earn for working 3 hours. That is
[tex]12+36\text{ = 48 }[/tex]So we aren 48 for working 4 hours.
Determine the x-intercept for 3x + 2y = 14.A) (7,0) B) (0,7) C) (14/3,0) D) (0,14/3)
Answers
By definition, when the line intersects the x-axis, the value of "y" is:
[tex]y=0[/tex]Knowing this, you can substitute that value of "y" into ithe equation given in the exercise:
[tex]\begin{gathered} 3x+2y=14 \\ 3x+2(0)=14 \end{gathered}[/tex]Now you must solve for the variable "x" in order to find the x-intercept. This is:
[tex]\begin{gathered} 3x+0=14 \\ 3x=14 \\ x=\frac{14}{3} \end{gathered}[/tex]Then, you get this point:
[tex](\frac{14}{3},0)[/tex]The answer is: Option C.
Given the equation y = x (x - 3)(2x + 7), find the rational roots. Complete theexplanation.The rational roots are x =, and. I found my answers bygraphing the equation, then finding where the equation crossed the (select) ▼4'
Answers
ANSWER
[tex]0,3,-\frac{7}{2}[/tex]EXPLANATION
The roots are the x values where the equation intercepts the x-axis.
which of the following are like terms3y^5, 2x^53y^5, 2y^56y^2, 2 z3y^4, 4x^3
Answers
In this case the answer is very simple.
3y^5, 2y^5 are like terms.
Because the variables and their exponents are the same.
3x - 7 = 3(x - 3) + 2
Answers
3x - 7 = 3x - 7
3x - 3x = -7 + 7
0 = 0
This is obviously always true!
Any value of x will satisfy the original equation.
The numerator of the sum 1+1/3+2 is (a) 1 (b) 2 (c) 5 (d) 6.
Answers
The expression is given as,
[tex]\frac{1}{2}+\frac{1}{3}[/tex]Note that the denominator of both the fractions are prime numbers. So their lowest common multiple, LCM(2,3) will be the product of the numbers,
[tex]undefined[/tex]Find the slope of the line that passes through (4,2) and (2,1) which set up in the formula is correct? Select all that apply.
Answers
The formula for calculating the slope of a line passing through the points (x1, y1) and (x2, y2) is expressed as:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}\text{ }or\text{ }\frac{y_1-y_2}{x_1-x_2}[/tex]Given the coordinate points (4,2) and (2,1), the possible set up formulas are:
[tex]\begin{gathered} x_1=4 \\ y_1=2 \\ x_2=2 \\ y_2=1 \end{gathered}[/tex][tex]\begin{gathered} slope=\frac{1-2}{2-4} \\ slope=\frac{2-1}{4-2} \end{gathered}[/tex]This are the slopes of the line formula
How long can you lease the car before the amount of the lease is more than the cost of the car
Answers
ANSWER:
48 months
STEP-BY-STEP EXPLANATION:
According to the statement we can propose the following equation, where the price of the car is more than or equal to the amount of the lease. Just like this:
Let x be the number of months
[tex]16920\ge600+340x[/tex]We solve for x, just like this:
[tex]\begin{gathered} 600+340x-600\le16920-600 \\ \frac{340x}{340}\le\frac{16320}{340} \\ x\le48 \end{gathered}[/tex]Therefore, for 48 months, the car rental will be lower
Solve pls. I neeeeeeeeed your help.
Answers
Answer:
70 over 39
Step-by-step explanation:
here's the solution first multiple the numbers with the fraction then calculate after that simply the fractions and the answer is
[tex] \frac{70}{39} [/tex]
y+2=−3(x−4)y, plus, 2, equals, minus, 3, left parenthesis, x, minus, 4, right parenthesis Complete the missing value in the solution to the equation.
Answers
The required equation is 11y = 3x + 2.
What is equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Given y+2=−3(x−4)y .....................(1)
Simplifying (1) and we get
y+2=−3x + 12y
=> 3x + y - 12y + 2 = 0
=> 3x -11y + 2 = 0
=> 3x - 11y = -2
=> 11y - 3x = 2
=> 11y = 3x + 2
Therefore, the required equation is 11y = 3x + 2.
To learn more about equation from the given link
https://brainly.com/question/25896797
#SPJ9
A trapezoid has a height of 16 miles. The lengths of the bases are 20 miles and 35miles. What is the area, in square miles, of the trapezoid?
Answers
Given:
A trapezoid has a height of 16 miles.
The lengths of the bases are 20 miles and 35 miles.
To find:
The area of the trapezoid.
Explanation:
Using the area formula of the trapezoid,
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]On substitution we get,
[tex]\begin{gathered} A=\frac{1}{2}(20+35)\times16 \\ =\frac{1}{2}\times55\times16 \\ =440\text{ square miles} \end{gathered}[/tex]Therefore the area of the trapezoid is 440 square miles.
Final answer:
The area of the trapezoid is 440 square miles.
Today, October 20, 2022, seven friends ate lunch together at Chipotle.
Friend #1 eats there every day - including weekends.
Friend #2 eats there every other day - including weekends
Friend #3 eats there every third day - including weekends
Friend #4 eats there every fourth day - including weekends
Friend #5 eats there every fifth day - including weekends
Friend #6 eats there every sixth day - including weekends
Friend #7 eats there every seventh day - including weekends
Assuming that none of them catch Covid or miss any days, what will be the date when the friends again all eat lunch together at Chipotle?
Answers
The most appropriate choice for LCM of two numbers will be given by -
All the friends together can eat lunch on 14th December 2023.
What is LCM?
LCM means Lowest Common Multiple. LCM of two numbers a and b is the least number that is divisible by both a and b.
Friend 1 eats lunch together at Chipotle everyday including weekends
Friend 2 eats lunch together at Chipotle every other day including weekends
Friend 3 eats lunch together at Chipotle every third day including weekends
Friend 4 eats lunch together at Chipotle every fourth day including weekends
Friend 5 eats lunch together at Chipotle every fifth day including weekends
Friend 6 eats lunch together at Chipotle every sixth day including weekends
Friend 7 eats lunch together at Chipotle every seventh day including weekends
Number of days after which all the friends together can eat lunch
= LCM of 1, 2, 3, 4, 5, 6, 7 = 420 days
All the friends together can eat lunch after 420 days
All the friends together can eat lunch on =
(31 - 20) + 30 + 31 + 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 +14 = 14th December 2023
To learn more about LCM of two numbers, refer to the link -
https://brainly.com/question/16054958
#SPJ9
The function f(x) = 5x+3 is one to one. Find an equation for f-1(x) the inverse function.
Answers
Given the function:
[tex]f\mleft(x\mright)=5x+3[/tex]To find the inverse function, we make x the subject of the equation.
[tex]\begin{gathered} 5x=f(x)-3 \\ x=\frac{f(x)-3}{5} \end{gathered}[/tex]Next, we replace x with f-1(x) and f(x) with x.
Therefore, the inverse function is:
[tex]f^{-1}(x)=\frac{x-3}{5}[/tex]List the elements in the set
{x 1 x is a negative multiple of 5}
Answers
S={-5,-10,-15,-20,-25......}; these are few negative multiples of 5 as stated in the set builder form of set theory {x :x is a negative multiple of 5}.
What is set?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things.
What is set builder form?Set builder notation is a type of mathematical notation used to describe sets by listing their components or highlighting the requirements that each member of the set must meet. We write sets in the form of in the set-builder notation.
{y | (properties of y)} OR {y : (properties of y)}
Here,
{x :x is a negative multiple of 5}
S={-5,-10,-15,-20,-25.....}
According to the set builder form of set theory, {x:x is a negative multiple of 5} S={-5,-10,-15,-20,-25...}; these are a few negative multiples of 5.
To know more about set,
https://brainly.com/question/28952278
#SPJ13
4x^{3}=3y+2x^{3}y^{3}
Answers
Answer: This would be the answer to your question!!
Step-by-step explanation:
Given points C(-3,-8) and D(-6.5,-4.5), find the coordinate of the point that is 2/3 of the way from C to D.
Answers
Answer:
(-16/3,-17/3)
Explanation:
Let the point which is 2/3 of the way from C to D = X
It means that point X divides the line segment CD internally in the ratio 2:1.
To determine the coordinate of point X, we use the section formula for internal division of a line segment:
[tex](x,y)=\left\{ \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right\} [/tex][tex]\begin{gathered} (x_{1,}y_1)=(-3,-8) \\ (x_2,y_2)=(-6.5,-4.5) \\ m\colon n=2\colon1 \end{gathered}[/tex]Substituting these values into the formula above, we have:
[tex]X(x,y)=\left\{ \frac{2(-6.5)+1(-3)}{2+1},\frac{2(-4.5)+1(-8)}{2+1}\right\} [/tex]We then simplify:
[tex]\begin{gathered} X(x,y)=\left\{ \frac{-13-3}{3},\frac{-9-8}{3}\right\} \\ =\left\{ \frac{-16}{3},\frac{-17}{3}\right\} \end{gathered}[/tex]Therefore, the exact coordinate of the point that is 2/3 of the way from C to D is (-16/3,-17/3).
Solve the system you any method. State the final answer as an ordered pair. DO NOT include spaces or dollar signs in your answer.
Answers
To solve the problem, we notice that both of the equations are written with the y solved then we can equate the expressions of x and solve the resulting equation of x:
[tex]\begin{gathered} x-12=-3x+12 \\ x+3x=12+12 \\ 4x=24 \\ x=\frac{24}{4} \\ x=6 \end{gathered}[/tex]Once we have the value of x we plug it on the first equation to find y:
[tex]\begin{gathered} y=6-12 \\ y=-6 \end{gathered}[/tex]Therefore, the solution of the system of equations is (6,-6)
For the data shown in the scatter plot, which is the best estimate of r?The answer choices are .94 .-45 .-94 .45
Answers
Pearson's correlation coefficient, r, measures the linear relationship between two variables. The correlation coefficient can take a range of values from +1 to -1.
• A value of 0 indicates that there is no association between the two variables.
,• A value ,greater than 0, indicates a ,positive association., That is, as the value of one variable increases, so does the value of the other.
,• A value ,less than 0, indicates a ,negative association,; that is, as the value of one variable increases, the value of the other decreases.
Graphically,
In this case, you can see that as the value of a variable x increases, the value of the variable y other decreases. Then, the correlation coefficient of these two variables is negative.
Also, you can see that the values of the variables do not completely fit a line but are very close to one.
Therefore, the best estimate of r is -.94.
(Score for Question 1: ___ of 5 points)1. Wendy wants to find the width, AB, of a river. She walks along the edge of the river 300 ft and markspoint C. Then she walks 80 ft further and marks point D. She turns 90° and walks until her location,point A, and point C are collinear. She marks point E at this location, as shown.AriverAD 80 ft300 ftBE(a) Can Wendy conclude that AABC and AEDC are similar? Why or why not?(b) Suppose DE = 50 ft Calculate the width of the river, AB. Show all your work.Answer
Answers
We know that two triangles are similar if two pairs of corresponding angles are equal.
In this case, we have:
• Angles EDC and ABC are right angles. Then, these angles are equal.
,• Angles DCE and ACB are ,vertical angles,. In other words, they are opposite angles made by two intersecting lines. Vertical angles are ,congruent,, then these angles are equal.
AnswerSince the above condition is fulfilled, triangles ABC and EDC are similar.
Part b)When two triangles are similar, their corresponding sides are in the same ratio.
[tex]\frac{a}{e}=\frac{b}{d}=\frac{c}{c^{\prime}}[/tex]Then, we can write and solve the following equation:
[tex]\begin{gathered} \frac{300ft}{80ft}=\frac{c}{50ft} \\ 3.75=\frac{c}{50ft} \\ \text{ Multiply by 50ft from both sides} \\ 3.75*50ft=\frac{c}{50ft}*50ft \\ 187.5ft=c \end{gathered}[/tex]AnswerThe width of the river is 187.5 feet.
what is the minimum surface area that such a box can have
Answers
Given a rectangular box with an open top and square base, the dimensions of the box are:
[tex]a\times a\times b[/tex]The volume can be calculated as:
[tex]V=a\cdot a\cdot b=a^2\cdot b[/tex]The area of the sides is:
[tex]A_L=a\cdot b[/tex]The area of the base:
[tex]A_B=a^2[/tex]There are 4 lateral sides and 1 base (the top is open), so the total surface area is:
[tex]A_{\text{total}}=4\cdot A_L+A_B=4\cdot a\cdot b+a^2[/tex]We have a fixed volume of 2048 in³, then:
[tex]\begin{gathered} a^2\cdot b=2048 \\ b=\frac{2048}{a^2} \end{gathered}[/tex]Using this result on A_total:
[tex]A_{\text{total}}=4\cdot a\cdot\frac{2048}{a^2}+a^2=\frac{8192}{a}+a^2[/tex]To find the minimum surface area, we take the derivative:
[tex]\begin{gathered} \frac{dA_{total}}{da}=-\frac{8192}{a^2}+2a=0 \\ a^3=4096 \\ a=16 \end{gathered}[/tex]Now, we calculate the minimum total area using a:
[tex]A_{\text{total}}=\frac{8192}{16}+16^2=768in^2[/tex]Need help with this review question. I need to know how to find the measurements from the cyclic quadrilateral
Answers
Given a quadrilateral ABCD
A cyclic quadrilateral has all its vertices on the circumference of the circle
Also cyclic quadrilateral
has the opposites angles add up to 180°
then
[tex]\angle a+\angle c=180[/tex][tex]\angle b+\angle d=180[/tex]then
Option A
A=90
B=90
C=90
D=90
since A+C= 180
and B+D = 180
measures from Option A could come from a cyclic quadrilateral
Option B
A=80
B=80
C=100
D=100
Since A+C = 80+100 = 180
and B+D = 80 + 100 = 180
measures from Option B could come from a cyclic quadrilateral
Option C
A=70
B=110
C=70
D=110
Since A+C=70+70 = 140
And B+D =110+110=220
measures from Option C could NOT come from a cyclic quadrilateral
Option D
A=60
B=50
C=120
D=130
A+C= 60+120 = 180
B+D= 50+130 = 180
measures from Option D could come from a cyclic quadrilateral
Option E
A=50
B=40
C=120
D=150
A+C=50+120= 170
B+D=40+150 = 190
measures from Option E could NOT come from a cyclic quadrilateral
Then correct options are
Options
A,B and D
Solve for the remaining angle and sides of the triangle described below. Round to the nearest hundredtheA = 50°. B = 45,a=3
Answers
Given:
The angels and sides of the triangle are
A = 50°. B = 45°, and a=3
Aim:
We need to find the angle C and sides c and b.
Explanation:
Use sine law.
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex][tex]\text{ Consider }\frac{\sin A}{a}=\frac{\sin B}{b}\text{ to find side b.}[/tex]Substitute A = 50°. B = 45°, and a=3 in the equation.
[tex]\frac{\sin 50^o}{3}=\frac{\sin 45^o}{b}[/tex][tex]b=\frac{\sin 45^o}{\sin 50^o}\times3[/tex][tex]b=2.77[/tex]Use the triangle sum property to find the angle C.
[tex]A+B+C=180^o[/tex]Substitute A = 50°. and B = 45° in the equation.
[tex]50^o+45^o+C=180^o[/tex][tex]95^o+C=180^o[/tex][tex]C=180^o-95^o[/tex][tex]C=85^o[/tex][tex]\text{ Consider }\frac{\sin A}{a}=\frac{\sin C}{c}\text{ to find side c.}[/tex]Substitute A = 50°. C= 85°, and a=3 in the equation.
[tex]\frac{\sin50^o}{3}=\frac{\sin 85^o}{c}[/tex][tex]c=\frac{\sin 85^o}{\sin 50^o}\times3[/tex][tex]c=3.90[/tex]Final answer:
[tex]C=85^o[/tex][tex]b=2.77[/tex][tex]c=3.90[/tex]This is matching:#1 If solving a problem with population growth compounding CONTINUOUSLY, which of the following formulas would you use?#2 If solving a problem with population growth compounding ANNUALLY, which of the following formulas would you use?#3 If solving a problem with population growth compounding QUARTERLY, which of the following formulas would you use?#4 If solving a problem with continuously compounding interest, which of the following formulas would you use?A: A(t)=P(1+r÷n)^ntB: A(t)=Pe^rtC: P(t)=P0(1+r)^tD: P(t)=P0^e^rt
Answers
#1
The formula for continuous compounding is:
[tex]A(t)=P_{}e^{r\cdot t}[/tex]#2
Since the population grows compounding annually, we have that:
[tex]P(t)=P_0(1+r)^t[/tex]#3
For a problem with population growth compounding quarterly, we have to divide the rate between n=4, therefore:
[tex]A(t)=P(1+\frac{r}{n})^{n\cdot t^{}}[/tex]#4
Finally, for continuously compounded interest we have the formula:
[tex]P(t)=P_0e^{r\cdot t}[/tex]Check off all of the equations that would give infinitely many solution
Answers
All of the equations that would give infinitely many solutions are given as follows:
[tex]\begin{gathered} 1)\text{ 3x + 12 = 3x + 12} \\ 2)\text{ 2\lparen3x - 4\rparen = 6x - 8} \end{gathered}[/tex]Thus the correct answer is option 3 and option 5.
is H less than 9?[tex]h \leqslant 9[/tex]
Answers
3) The given inequality is
[tex]h\text{ }\leq\text{ 9}[/tex]The inequality symbol is that of less than. Since it has an equal to sign attached, then, the meaning is h is less than or equal to 9. In words, h is at most 9, no more than 9.
12 is what percent of 18
Answers
We have that
[tex]12\cdot\text{ }\frac{100}{18}=\text{ }\frac{1200}{18}\text{ = 66.6666}[/tex]So the answer is: 66.6666 .
7. Explain It Draw a net for a triangular pyramid. Explain how you know your dagram is correct.
Answers
The definition of geometry net is the 2-dimensional shape that if folded, it will produce or yield to the 3-dimensional image
Since the triangular pyramid, has 4 sides (4 triangular faces), when we unfold it on the edges from one tip/corner, it will produce a 2-dimensional image of 3 triangles attached to the sides of one triangle
Use the Distributive Property to solve the equation 2/3 (9a + 6) = 23.8
Answers
Distributive property tell us how to solve expressions in the form a(b+c), it says:
a(b+c)=ab+ac
Then,
[tex]\begin{gathered} \frac{2}{3}(9a+6)=23.8 \\ \frac{18a}{3}+\frac{12}{3}=23.8 \\ 6a+4=23.8 \\ 6a=23.8-4 \\ a=\frac{19.8}{6}=3.3 \end{gathered}[/tex]Select the polynomial functions for which (x+3) is a factor. Select all that apply.
Answers
If x+3 is a factor, then the result of replacing x=-3 in each equation would be 0.
Replacing x=-3 in the polynomials, we have:
Option A
[tex]\begin{gathered} f(-3)=(-3)^4-12(-3)^3+54(-3)^2-108(-3)+81=1296\text{ } \\ \text{ We see that option A is incorrect.} \end{gathered}[/tex]Option B
[tex]\begin{gathered} f(-3)=(-3)^4-3(-3)^3-(-3)+3=168\text{ } \\ \text{We see that option B is incorrect.} \end{gathered}[/tex]Option C
[tex]\begin{gathered} f(-3)=(-3)^5+2(-3)^4-23(-3)^3-60(-3)^2=0\text{ } \\ \text{We see that option C is correct.} \end{gathered}[/tex]Option D
[tex]\begin{gathered} f(-3)=(-3)^5+5(-3)^4-3(-3)^3-29(-3)^2+2(-3)+24=0\text{ } \\ \text{We see that option D is correct.} \end{gathered}[/tex]The answers are options C and D.
Suppose that you earn $15
Answers
Answer: 800 hours
Step-by-step explanation:
