for a 5 oz. medium cup of frozen yogurt Phil charges $3.00. toppings cost $0.50 each.
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Write an equation in slope-intercept form for the situation shown in the image
The slope-intercept form of a line is:
y = mx + b
On Phill's Frozen Yogurt Shop, Phill charges $3.00 for a medium cup of frozen yogurt and $0.50 for each topping.
Let's call x=number of toppings selected for the yogurt.
Since each topping costs $0.50, the x toppings cost 0.50x. The total cost (y) is calculated as:
y = 0.50x + 3
For Frank's Pizzeria, the cost (y) of a medium pizza is
y = 10 + 1.75x
Where x is the number of toppings.
To write this equation in slope-intercept form, we only need to rearrange it as follows:
y = 1.75x + 10
Related Questions
1. Alexis needs to save at least $1,100 to buy a new laptop. So far she has saved $400. She makes $12 an hour babysitting.inequality_____________
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Let:
x = number of hours babysitting
So far she has saved $400, and she needs to save at least $1100
Therefore, the inequality which represents this situation is:
[tex]400+12x\ge1100[/tex]In case you need to solve for x:
[tex]\begin{gathered} \text{Subtract 400 from both sides:} \\ 12x\ge1100-400 \\ 12x\ge700 \\ \text{Divide both sides by 12:} \\ x\ge\frac{700}{12}=58.33 \\ x\ge58.33 \end{gathered}[/tex]Therefore, Alexis needs to work at least 58.33 hours in order to buy her new laptop
Simplify the expression to a polynomial in standard form:(x-1)(2x^2-3x-8)(x−1)(2x 2 −3x−8)
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Given:-
[tex](x-1)(2x^2-3x-8)[/tex]To find the simplified form.
So now we multiply and find the simplified form. so we get,
[tex](x-1)(2x^2-3x-8)=2x^3-3x^2-8x-2x^2+3x+8=2x^3-6x^2-5x+8[/tex]So the simplified form is,
[tex]\begin{equation*} 2x^3-6x^2-5x+8 \end{equation*}[/tex]If the mean of a given dataset is85 and the standard deviation is12, where will a majority of thedata lie?A. 55 to 85B. 73 to 97C. 85 to 100
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Given:
mean = 85
Standard deviation = 12
Assuming that the data is normally distributed, about 68% of the data would lie one standard deviation from the mean.
Using the z-score formula:
[tex]\begin{gathered} z\text{ = }\frac{x-\varphi}{\sigma} \\ \text{where:} \\ \psi\text{ is the mean} \\ \text{and } \\ \sigma\text{ is the standard deviation} \end{gathered}[/tex]set z= 1:
[tex]\begin{gathered} 1\text{ = }\frac{x_2-\text{ 85}}{12} \\ x_2-\text{ 85 = 12} \\ x_2=\text{ 12 + 85} \\ x_2=\text{ 97} \end{gathered}[/tex]set z = -1:
[tex]\begin{gathered} -1\text{ = }\frac{x_1-85}{12} \\ x_1-85\text{ = -12} \\ x_1=\text{ 85-12} \\ x_1=\text{ 73} \end{gathered}[/tex]Hence, the majority of the data would lie between 73 to 97
Answer:
73 to 97 (Option B)
State the postulate of the theorem that justifies the answer
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From the given information, we can note that angle1 and angle2 are corresponding angles with respect to line u. Angle2 and angle9 are alternate exterior angles with respect to the right vertical line and angle5 and angle7 are alternate interior angles with respect to line v.
Therefore, the theorems which justify the answer are, respectively: Corresponding angles theorem, Alternater exterior angles theorem and Alternate Interior angles theorem.
30) Each year the local country club sponsors a tennis tournament. Play starts with 128participants. During each round, half of the players are eliminated, y = 128(.50)* represents thenumber of players left after x rounds. How many players will be left by the 5th round?
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Given:
[tex]y=128(0.50)^x[/tex]y represents the number of players left after x rounds.
Required:
We need to find the number of players who will be left after5 rounds.
Explanation:
Substitute x =5 in the equation to find the number of players who will be left after5 rounds.
[tex]y=128(0.50)^5[/tex][tex]y=4[/tex]Final answer:
4 players will be left after the 5th round.
Kaitlin purchased a prepaid phone card for $15. Long distance calls cost 16 cents a minute using this card. Kaitlin used her card only once to make a longdistance call. If the remaining credit on her card is $9.88, how many minutes did her call last?
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where x is the minutes
we can solve x
[tex]\begin{gathered} -0.16x=9.88-15 \\ -0.16x=-5.12 \\ 0.16x=5.12 \\ x=\frac{5.12}{0.16} \\ x=32 \end{gathered}[/tex]so your call lasted 32 minutes
Help in the Accompanying diagram of the circle O chord CD ….
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Answer:
The length of ED is;
[tex]ED=8[/tex]Explanation:
Given the figure in the attached image.
Chord CD bisects chord AB at E.
So;
[tex]AE=EB=\frac{AB}{2}[/tex]Also applying the Bisecting chord formula;
[tex]AE\cdot EB=CE\cdot ED[/tex]Given;
[tex]\begin{gathered} CE=2 \\ AB=8 \\ AE=EB=\frac{AB}{2}=\frac{8}{2}=4 \\ AE=4 \\ EB=4 \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} AE\cdot EB=CE\cdot ED \\ 4\cdot4=2\cdot ED \\ 16=2\cdot ED \\ ED=\frac{16}{2} \\ ED=8 \end{gathered}[/tex]Therefore, the length of ED is;
[tex]ED=8[/tex]433Plot and connect the points A (3,-3), B (-3, -2), C (-5, 1), D (-5, 4), E (-4,6), F (-2, 6), G (3, 2), and find the length of EF.OA 5 unitsOB.2 unitsO C. 3 unitsOD. 4 unitsResetSubmit
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To find the length of EF we will use the formula for finding the distance between two points.
[tex]E(-4,\text{ 6) and F(-2, 6)}[/tex]From the points E and F:
[tex]undefined[/tex]The function f(x) = 260 – 55x represents the distance, in miles, remaining on atrip x hours into the trip. What is the value of f(3)?
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f(3)=95
Given: Mis the midpoint of TV. Solye for k 9k + 4 M i Response
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Solving for k:
[tex]\begin{gathered} 24k=18k+8 \\ 6k=8 \\ k=\frac{8}{6} \\ k=\frac{4}{3} \end{gathered}[/tex]a car travels for 7 hours at 55 miles per hour use the formula D equals R times T where D equals distance R equals right in SQL time to find a distance the car traveled
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We have the next information
d=r*t
where
t=time=7 hours
r=rate=55 miles/hr
we substitute the values
[tex]undefined[/tex]A student researches the average cost of electricity, in cents per kilowatt-hour, in the United States since 2000 and creates the scatter plot below.
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Given: A scatter plot as shown in the image
To Determine: The image that best represent the model function fitted for the given
Solution
The 'line of best fit' is a line that goes roughly through the middle of all the scatter points on a graph.
Let us examine each of the options
From the above the best model function fitted for the given data is
A city currently has 130 streetlights. As part of a urban renewal program, the city council has decided to install 2 additional streetlights at the end of each week for the next 52 weeks.How many streetlights will the city have at the end of 40 weeks?
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Since the increment of number of lights is constant we can model the number of lights with a linear equation; we know that the line with slope (or rate of change) m and y-intercept b is given by:
[tex]y=mx+b[/tex]In this case, the slope of the line will be 2 and the y-intercept is 130; hence the number of lights in any week is given by:
[tex]y=2x+130[/tex]Now that we have an expression we can plug the week we want to know to determine the number of lights, since we want to know the number of lights at the end of week 40 we have that x=40; then:
[tex]\begin{gathered} y=2(40)+130 \\ y=80+130 \\ y=210 \end{gathered}[/tex]Therefore, at the end of week forty there will be 210 lights.
Use the equation to identify the center and radius of the circle (X+3)^2+(y-7^2=11
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To find the radius od the circle using (X+3)²+(y-7)²=11
(x-a)²+(y-b)²=r² is the equation for a circle in a Cartesian plane
the center is given by c= (a,b) so the center would be (-3,7)
and to find the r use
11 =r²
√11 = r
3.31 = r
For a standard normal distribution, find Find P(z
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It is given that,
[tex]P(zHere 'z' is the standard normal variate.CASE-1 Assuming that 'c' lies on right side of z=0 line.
Simplify the expression as,
[tex]P(z<0)+P(0We know that the probability of z being less than zero, is 0.5,[tex]0.5+P(0Observe that the probability comes out to be negative, which is not possible.CASE-2 Assuming that 'c' lies on the left side of z=0 line.
Then,
[tex]\begin{gathered} P(zFrom the Standard Normal Distribution Table, we see that the probability 0.1316 corresponds to the score close to 0.34 i.e.[tex]\varnothing(0.34)=0.1331[/tex]Thus, the value of the variable 'c' is 0.34 approximately.
In 2020, there were about 282 million gas powered cars on the road. This number isexpected to decrease at a rate of 3.1% per year. In 10 years, if this information iscorrect then what is the best prediction of the number of people driving gas powered cars? Round answer to a whole number.
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The amount of cars in 10 years will be 205,819,671
If x is a binomial random variable, compute p(x) for each of the cases below.a. n = 4,-1, p=0.6b.n=6,x=3,q=0,3d.n=4, X = 2, p=0.7e.n=6, x3, 0.7c. n 3, x0, p=0.8fin= 3,1.-0,9a. p(x) = (Round to four decimal places as needed.)27Enter your answer in the answer box and then click Check Answer,Help Me Solve ThieView anyamanlaGot Mora Hain
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SOLUTION:
Step 1 :
If x is a binomial random variable, compute p( x ) for the following:
a) n = 4, x = 1 , p = 0.6
Step 2:
[tex]\begin{gathered} U\sin g\text{ the binomial random variable, we have that:} \\ p^{}(x)=^nC_{x_{}}(p)^x(q)^{n\text{ - x}} \\ p\text{ + q = 1} \\ 0.6\text{ + q = 1} \\ \text{q = 1 - 0. 6} \\ q\text{ = 0. 4} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} p^{}(1)=^4C_1(0.6)^1(0.4)^{4-\text{ 1}}_{^{}^{}} \\ =4X0.6X(0.4)^3 \\ =\text{ 4 X }0.6\text{ X 0. 0064} \\ p(\text{ 1 ) = 0.1536 ( 4 decimal places)} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]p\text{ ( 1 ) = 0. 1536 ( 4 decimal places)}[/tex]cooper finds show me drawings and quarters and his change purse . how much money (in dollars) does he have if he has 4 dimes and 7 quarters ?how much money (in dollars) dose he have if he has x dimes and y quarters?
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Note that 10 dimes make a dollar, and
4 quarters make a dollar
If Cooper has 4 dimes and 7 quarters, then his total amount of money is;
[tex]\begin{gathered} \text{Total}=4(0.1)+7(0.25) \\ \text{Total}=0.4+1.75 \\ \text{Total}=2.15 \\ \text{The total money he has is \$2.15} \end{gathered}[/tex](b) if he has x dimes and y quarters, then his total money would be;
[tex]\begin{gathered} \text{Total}=x(0.1)+y(0.25) \\ \text{Total}=0.1x+0.25y \end{gathered}[/tex]Solve the system of equations by elimination. 3x − y − z = 2 x + y + 2z = 4 2x − y + 3z = 9
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Given:
The system of equations is,
[tex]\begin{gathered} 3x-y-z=2.\text{ . .. . . .(1)} \\ x+y+2z=4\text{ . . . .. . (2)} \\ 2x-y+3z=9\text{ . . . . . . .(3)} \end{gathered}[/tex]The objective is to solve the equations using the elimination method.
Explanation:
Consider the equations (1) and (2).
[tex]\begin{gathered} 3x-y-z=2 \\ \frac{x+y+2z=4}{4x+z=6} \\ \ldots\ldots\ldots.(4)\text{ } \end{gathered}[/tex]Now, consider the equations (2) and (3).
[tex]\begin{gathered} x+y+2z=4 \\ \frac{2x-y+3z=9}{3x+5z=13} \\ \ldots\ldots\text{ . . . .. (5)} \end{gathered}[/tex]On multiplying the equation (4) with (-5),
[tex]\begin{gathered} -5\lbrack4x+z=6\rbrack \\ -20x-5z=-30\text{ . . . . . .(6)} \end{gathered}[/tex]To find x :
On solving the equations (5) and (6),
[tex]\begin{gathered} 3x+5z=13 \\ \frac{-20x-5z=-30}{-17x=-17} \\ x=\frac{-17}{-17} \\ x=1 \end{gathered}[/tex]To find z :
Substitute the value of x in equation (6),
[tex]\begin{gathered} -20(1)-5z=-30 \\ -5z=-30+20 \\ -5z=-10 \\ z=\frac{-10}{-5} \\ z=2 \end{gathered}[/tex]To find y :
Now, substitute the values of x and z in equation (2).
[tex]\begin{gathered} x+y+2z=4 \\ 1+y+2(2)=4 \\ y=4-1-4 \\ y=-1 \end{gathered}[/tex]Hence, the value of x is 1, y is -1 and z is 2.
Make a table of values and then graph the function:Where is there an asymptote?
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f(x) = (1.5)^x
Table
x y
-2 0.4
-1 0.6
0 0.1
1 1.5
2 2.25
Exponential functions have a horizontal asymptote. The equation of the asymptote is y = 0
Horizontal Asymptotes: y = 0
3. A store has two square rugs on sale. Thearea of the smaller rug is 52 square feet. Thesides of the larger rug are 1.5 times the length ofthe sides of the smaller rug. Which of thefollowing is closest to the area of the larger rug?A. 65 sqftB. 78 sqftC. 117 sqft
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Answer:
C. 117 sqft
Step-by-step explanation:
Square:
A square has side s.
It's are is given by:
A = s²
In this question:
A = s² = 52.
Larger rug:
Sides 1.5 times the smaller rug.
So
A = (1.5s)² = (1.5)²*s² = 2.25s²
Since s² = 52.
A = 2.25s² = 2.25*52 = 117
The answer is C. 117 sqft
Find the distance between the coordinates (-3,5) and (4.-9) WRITE YOURANSWER ROUNDED TO THE NEAREST HUNDREDTH PLACE
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Answer:
The distance between these two points is of 15.65 units.
Step-by-step explanation:
Distance between two points:
Suppose we have two points, (x1,y1) and (x2,y2).
The distance between them is given by:
[tex]D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]In this question:
Points (-3,5) and (4,-9)
The distance is:
[tex]D=\sqrt[]{(4-(-3))^2+(-9-5)^2}=\sqrt[]{7^2+(-14)^2}=\sqrt[]{245}=15.65[/tex]The distance between these two points is of 15.65 units.
Construct the matrix A=(ij) of type 5x5,
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Solution:
The matrix of the type 5x5 is a matrix with 5 rows and 5 columns.
Then, the matrix is:
The matrix above is of type 5x5.
How do I solve? So far no one could be of help. It’s asking for the area of this regular polygon.
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We can notice the triangle on the square, hypotenuse is 8m and the base is half of the lengt of the square we will name it x
then
we can use pythagoras to solve
[tex]a^2+b^2=h^2[/tex]where a and b aer sides of the triangle and h the hypotenuse
replacing
[tex]\begin{gathered} x^2+x^2=8^2 \\ 2x^2=64 \\ x^2=\frac{64}{2} \\ \\ x=\sqrt[]{32}=4\sqrt[]{2} \end{gathered}[/tex]the length of x is half of the side of the square then the side of the square is
[tex]4\sqrt[]{2}\times2=8\sqrt[]{2}[/tex]each side of the square is 8v2 meters
Area
we use formula of the area
[tex]\begin{gathered} A=l\times l \\ A=8\sqrt[]{2}\times8\sqrt[]{2} \\ \\ A=128 \end{gathered}[/tex]area of the square is 128 square meters
Perimeter
we use formula of the perimeter
[tex]\begin{gathered} P=4l \\ P=4\times8\sqrt[]{2} \\ P=32\sqrt[]{2} \end{gathered}[/tex]perimeter of the square is 32v2 meters
what is the sum of rocks between Pablo and Javier?
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Answer:
4r-5
Explanation:
Maria collected r rocks.
Javier collected twice as many rocks as Maria = 2r
Pablo collected 5 less than Javier = 2r - 5
Therefore, the sum of rocks between Pablo and Javier
[tex]\begin{gathered} =2r+2r-5 \\ =4r-5 \end{gathered}[/tex]For reference:
the slope, m, of the line is the same as the coefficient of the x variable when the equation is in the form y equals MX plus b. what is the slope of the line whose equation is 2x + y equals 10
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Slope m of 2x + y = 10
Then slope m = 2
How many different committees can be formed from 11 teachers and 46 students if the committee consists of 2 teachers and 4 students?The committee of 6 members can be selected in different ways.Help me solve thisView an example Get more help.D
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Solution
Number teachers = 11
Number of students = 46
Then we want to form a committee of 2 teachers and 4 students
[tex]^{11}C_2\times^{46}C_4=55\times163185=8975175[/tex]22.) In the figure, point P is the circumcenter of triangle JKL.Which of the following statements must be true?I. PX = PYII. PJ = PKIII. PK = PLF I onlyG II onlyH III onlyJ II and III only
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It's important to knwo taht
PX=PY statements must be true, So statement I is correct.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
In the figure, point P is the circumcenter of triangle JKL
The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect.
The circumcenter is formed by drawing the perpendicular bisectors of all the sides of the triangle using a compass. Extending all the perpendicular bisectors to meet at a point.
The intersection point is the circumcenter.
As the angles are same at X and Y are ninety degrees and has line through the circumcenter.
The lines PX and PY are equal.
Hence PX=PY statements must be true, So statement I is correct.
To learn more on Triangles click:
https://brainly.com/question/2773823
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I need to know where to graph the system of linear equations. -1/2y = 1/2x + 5 and y=2x + 2 The solution to the system is( , )
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the given expression is
-1/2y = 1/2x +5
multiply the above equation by -2
-2(-1/2y) = -2(1/2x +5)
y = - x - 10 .....(1)
and the other equation is y = 2x + 2 .......(2)
in equation (1) we will put x = 0 , 1 , 2 and find the value of y
when x = 0 then y = -0 - 10 = -10 so point is (0,-10)
x =1 , y = -1 - 10 = -11 so point is (1, -11)
x = 2 , y = -2 - 10 = -12 , so point is (2, -12)
now you will draw the point graph and draw the line by joining them.
in equation (2) put x = 0 , 1 , 2
when x = 0 , y = 2(0) + 2 = 0 + 2 = 2 so point is (0, 2)
x = 1, y = 2(1) + 2 = 4, so the point is (1, 4)
x =2 , y = 2(2) +2 = 6 so the point is (2, 6)
now you will draw the point graph and draw the line by joining them.
Now you will get two lines
after drawing of these lines you will get the intersection point of these lines.
and the intersection point will be (-4, - 6)
Ramona has a new job as à chef. She earns the sameamount per hour as she did in her old job, plus she got a$100 sign-on bonus. Line p represents Ramona's earnings inher old job. Line q represents her earnings in her new job.Write an equation for line p. What does the slope mean?How can you use the equation for line p to write anequation for line q?Amount
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Using the graph of line p, we select two points in order to find the slope through the equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]if we select points (0,0) and (4,40),
[tex]\begin{gathered} m=\frac{40-0}{4-0} \\ m=\frac{40}{4} \\ m=10 \end{gathered}[/tex]then, since the line passes through the point (0,0) the equation for line p is
[tex]y=10x[/tex]The meaning of the slope is the amount she earns per hour she works.
Since she earns the same on both jobs per hour worked, it means the slope of the line is the same in both cases, however, she hets a $100 bonus, which means that the resulting equation for q is:
[tex]y=10x+100[/tex]Answer:
- The equation of line p is: y=10x
- The slope means she earns $10 for every hour she works
- Both lines have the same slope, but line q has the bonus, meaning the equation is: y=10x+100