Mrs. Everett is shopping for school supplies with her children. Rose selected 3 one-inch binders and 1 two-inch binder, which cost a total of $23. Judy selected 5 one-inch binders and 3 two-inch binders, which cost a total of $49. How much does each size of binder cost?
Answers
We define the following variables:
• x = cost of one-inch blinders,
,• y = cost of two-inch blinders.
From the statement of the problem, we know that:
• Rose selected 3 one-inch blinders and 1 two-inch blinder, which cost a total of $23, so we have that:
[tex]3x+y=23,[/tex]• Judy selected 5 one-inch blinders and 3 two-inch blinders, which cost a total of $49, so we have that:
[tex]5x+3y=49.[/tex]We have the following system of equations:
[tex]\begin{gathered} 3x+y=23, \\ 5x+3y=49. \end{gathered}[/tex]We must solve the system of equations using the elimination method, where you either add or subtract the equations to get an equation in one variable.
1) We multiply the first equation by 3, and we have:
[tex]\begin{gathered} 9x+3y=69, \\ 5x+3y=49. \end{gathered}[/tex]2) Now, we subtract the second equation to the first equation:
[tex]\begin{gathered} (9x+3y)-(5x+3y)=69-49. \\ 4x=20, \\ x=\frac{20}{4}=5. \end{gathered}[/tex]3) Replacing the value x = 5 in the second equation, and solving for y we get:
[tex]\begin{gathered} 5\cdot5+3y=49, \\ 25+3y=49, \\ 3y=49-25, \\ 3y=24, \\ y=\frac{24}{3}=8. \end{gathered}[/tex]We have found that:
[tex]\begin{gathered} x=5, \\ y=8. \end{gathered}[/tex]Answer
A one-inch binder costs $5, and a two-inch binder costs $8.
Related Questions
A farmer is telling a rectangle field that is 63 yards long and 60 yards wide what is the distance between opposite corners of the farmers field?
Answers
87 yards
Explanations:
Given the following parameters:
• Length of the rectangle = 63 yards
,• Width of the rectangle = 60 yards
The distance between opposite corners of the farmer's field is the diagonal of the rectangle.
To determine the diagonal of the rectangle (d), we will use the Pythagoras theorem:
[tex]\begin{gathered} d^2=l^2+w^2 \\ d^2=63^2+60^2 \\ d^2=3969+3600 \\ d^2=7,569 \\ d=\sqrt[]{7,569} \\ d=87yards \end{gathered}[/tex]Hence the distance between opposite corners of the farmers' field is 87 yards
Suppose a Ballon rises 250 ft during the first minute.................
Answers
Since for each succeeding minute the balloon rises 70% as much as it did in the previous minute, and in the first minute the balloon rises 250 ft, then in the minute n the balloon rises
[tex]250*0.70^{n-1}ft.[/tex]Therefore the height of the balloon in the minute n is
[tex]\sum_{k\mathop{=}1}^n250*0.70^{k-1}ft.[/tex]Therefore the height of the balloon in the minute 8 is:
[tex]\begin{gathered} 250*0.70^0ft+250*0.70^1ft+250*0.70^2ft+250*0.70^3ft \\ +250*0.70^4ft+250*0.70^5ft+250*0.70^6ft+250*0.70^7ft \\ \approx785.30ft \end{gathered}[/tex]Answer: Option d.
Describe the end behavior for the polynomial function described below.
Answers
ANSWER
As x → ∞, f(x) → ∞
As x → -∞, f(x) → -∞
EXPLANATION
The degree of this polynomial is 5, which is odd. Therefore, the ends of the graph will point one up and the other down.
The coefficient is positive - the coefficient is the coefficient of the variable with the highest degree, in this case x⁵ - so the right end (when x → ∞) points up (to ∞) and the left end points down (to -∞).
i need the range for city A and city B, and the standard deviation for city A and city B
Answers
The range in a data set is the highest value minus the lowest value.
The standard deviation is a quantity expressing by how much the members of a group differ from the mean value for the group.
City A (data set)
[tex]1.00,1.00,1.25,1.50,1.50[/tex]City B (data set)
[tex]0.00,1.00,1.75,1.75,2.25[/tex]City A RangeThe range is 1.50 - 1.00 = 0.50
City B Range
The range is 2.25 - 0.00 = 2.25
Now,
The formula for sample standard deviation is
[tex]s=\sqrt[]{\frac{\sum(x-\bar{x})^2}{n-1}}[/tex]Where
s is the sample standard deviation
x bar - mean of the sample
n is the number of numbers in the data set
Using a standard deviation calculator, let's calculate the standard deviation of both data sets.
City A Standard DeviationThe standard deviation is
[tex]s=\sqrt[]{\frac{(1.00-1.25)^2+\cdots(1.50-1.25)^2}{5-1}}=0.25[/tex]City B Standard DeviationThe standard deviation is
[tex]s=\sqrt[]{\frac{(0.00-1.35)^2+\cdots(2.25-1.35)^2}{5-1}}=0.8768[/tex]From the data calculations, we can see that City B
Consider the polynomial function p given by p(x) = 728 – 2x2 + 32 + 10. Evaluate the functionat x = -3
Answers
Answer:
-206
Step-by-step explanation:
We are given the following function:
p(x) = 7x³ - 2x² + 3x + 10
To evaluate it at x = -3, we replace x by -3. So
p(-3) = 7x³ - 2x² + 3x + 10 = 7*(-3)³ - 2*(-3)² + 3*(-3) + 10 = 7*(-27) - 2*9 - 9 + 10 = -189 - 18 + 1 = -189 - 17 = -206
15. Write the equation of a horizontal line going through the point (5,4). Equation:
Answers
Given the point: (5, 4)
We know that the general equation of a horizontal line is y = k
Where k is constant.
From the point: (5, 4)
The only way for a line that is horizontal to satisfy (x, y) ==> (5, 4) is if y = 4.
To determine the equation of a horizontal line, the x-corrdinate is ignored because a horizontal line touches all possible values of x.
Therefore, the equation of the horizontal line is:
y = 4
ANSWER:
y = 4
Bradley is trying to find a missing factor a product of that factor has a three in ones digit is the missing factor even or odd explain
Answers
The factor when Bradley is trying to find a missing factor a product is odd.
How to illustrate the information?From the information given, the product of that factor has a ones digit = 3. From the information, we have to find whether the missing factor is even or odd.
We know that, the product of two odd numbers is odd. The product of two even numbers is even.
The product of one even and one odd number is even.
If one digit of a number is odd then the number must be odd.
It means factors of odd numbers are odd.
If the product of that factor has 3 in the ones digit then, the missing factor will be odd.
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For the data in the table, does y very direction with x? If it does, write an equation for direct variation. Show your work. (2 points)
Hint: y=kx is the formula for direct variation. Find k, then substitute it back in to the formula.
Answers
In the given table, the values of y vary directly with the value of x. The equation for direct variation is y = 2.5x
Does y vary directly with x?Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases.
The equation that is used to represent direct variation is y = kx
Where:
y = dependent variable k = constant of variation x = independent variableIf y and x have a direct variation, the constant of variation for all the values of x and y would be equal.
k = y / x
5 / 2 = 2.5
15 / 6 = 2.5
25 / 10 = 2.5
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the decreasing number of wolves in the northern section of the southern the function p(t) = 80(0.956)t. In the function p(t) explain what 80 and 0.956 represent
Answers
The general form of the population or exponential decay is:
[tex]p(t)=p_0(1-i)^t[/tex]where p(t) is the population of wolve in time, p0 is the initial population and (1-i) is the rate of decay.
so 80 means the initial population of wolves
and 0.956 is the rate of decay
John got all 20 questions on math test all were right plus an additional bonus question correctly. Bonus was worth same as other questions. What was the test score in percent?
Answers
The question on the math test is
[tex]=20[/tex]The bonus question is
[tex]=1[/tex]The total questions scored correctly
[tex]\begin{gathered} =20+1 \\ =21 \end{gathered}[/tex]To calculate the test score in percent, we will use the formula below
Since she got all the questions plus the bonus question correctly( note: all questions worth the same points), then we will have
[tex]\text{test score(percent)=}\frac{\text{Total questions scored correctly}}{\text{Total questions on the math test}}\times100\text{ \%}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{test score(percent)=}\frac{\text{Total questions scored correctly}}{\text{Total questions on the math test}}\times100\text{ \%} \\ \text{test score(percent)}=\frac{21}{20}\times100 \\ \text{test score(percent)}=\frac{2100}{20} \\ \text{test score(percent)}=105\text{ \%} \end{gathered}[/tex]Hence,
The test score in percent = 105%
ABC=DEF. What sequence of transformations will move ABC into DEF?
Answers
Rotation 180 degrees
scale factor 2
Answer: D. A dilation by a scale factor of 2 centered at the origin , followed by 180 degree clockwise rotation about the origin.
Regular pentagon HIJKL is shown below. What is the measure of ANGLE HIK? (image attached)A. 36 degreesB. 54 degreesC. 72 degreesD. 108 degreesthank you ! :)
Answers
Given a regular pentagon HIJKL.
We are asked to find the measure of Angle HIK
To find the measure of a central angle of a regular pentagon, we make a circle in the middle of the pentagon. We know that a circle is 360 degrees around.
Now, we will divide the 360 by the five angles. Now, the measure of each central angle is equal to:
360/5
So,
Angle HIK = 360/5
Angle HIK = 72˚
Therefore, the correct option is C, which is 72˚.
show 1.25 and -1.25 as points on the number line. what is the distance between the two points explain
Answers
The distance between 1.25 and -1.25 is computed as follows:
1.25 - (-1.25) = 1.25 + 1.25 = 2.5
The sum of two numbers is 16. Their diference is 20. Find the numbers
Answers
Step 1
Let the numbers be x and y and let us assume x is the bigger number
The equations then are;
[tex]\begin{gathered} x+y=16----(1) \\ x-y=20--(2) \end{gathered}[/tex]Step 2
Add equations 1 and 2
Hence,
[tex]\begin{gathered} 2x=36 \\ \frac{2x}{2}=\frac{36}{2} \\ x=18 \end{gathered}[/tex]Step 3
Find the value of y from equation 2
[tex]undefined[/tex]The figure shows the results of a construction of the bisector of ∠P. Order the following steps for this construction using the numbers 1-4 (Ex. the first step is 1, second step is 2 and so on)
-Name the intersection of the two arcs X.
-Using a straightedge, draw the line through P and X.
-Draw two intersecting arcs with the same radius, one centered at Y and one centered at A, on the interior of ∠P
-Draw an arc centered at P, to create points Y and A.
Answers
Draw an arc that connects the sides of point A by positioning the compass's point there. The intersection's points x and y should be given names.
How to draw two intersecting arcs?Draw an arc that connects the sides of point A by positioning the compass's point there. The intersection's points x and y should be given names.A line should be drawn inside the angle by positioning the compass's point on point y.Placing the compass's point on point y and drawing another arc inside the angle are both possible without altering the compass's openness.Location y should be used to denote the point where the arcs intersect inside the angle p.Ay should be drawn with a straightedge.The radical line is created by the intersection of two circles. If three circles mutually overlap in one place, their point of intersection—also referred to as the radical center—is where their pairwise radical lines converge.
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Complete the table for each function. Then answer the questions that follow.X Y=4x Y=4x^2 Y=4^x0 0 0 11 4 a b2 c 16 d3 e f ga=? b=?c=?d=?e=?f=?g=?
Answers
Let's evaluate each function for the integers from 0 to 3:
[tex]undefined[/tex]F.28. 21 and 22 are vertical angles. If mZ1 =(6x + 11) and mZ2 = (10x - 9), find mZ1.mZ1 =
Answers
It is given that angle 1 and angle 2 are vertical angles.
It is known that the vertical angles are congruent.
Therefore it follows:
[tex]\begin{gathered} m\angle1=m\angle2 \\ 6x+11=10x-9 \\ 11+9=10x-6x \\ 20=4x \\ x=5 \end{gathered}[/tex]So the value of angle 1 is given by:
[tex]\begin{gathered} \angle1=6x+11 \\ =6\times5+11 \\ =41 \end{gathered}[/tex]Hence the angle is 41 degrees.
This list gives information about a classroom.Study the list carefully. Then, use the drop-down menu to complete the statementbelow about the listWidth in Feet:Length in FeetDesks:Computers:Total:35302114100CLEARCHECKItmake sense to add the items on the list because these quantities| be expressed using the same unit.The number 100have meaning for the classroom
Answers
the answer is
It does not make sense to add item on the list because these quantities to be expressed in the same units and the number 100 does not have meaning for the classroom.
Answer:
Step-by-step explanation:
describe your so how to find the following product using both an algorithm in the diagram 3 * 3/4
Answers
To multiply the given numbers, we can use 0.75 instead of 3/4.
Then, we multiply using the standard algorithm.
Notice that the result must have 4 decimal numbers since that's the number of decimals both numbers have at the beginning.
Now, we can use the areas model to show a diagram about the multiplication.
Notice that we've got 3 wholes with 3/4 each, that gives us 2.25 because it's the sum 0.75 + 0.75 + 0.75 = 2.25.
What interest rate would be necessary to obtain $6,500 in 8 years if $5,000 is the amount of the original investment and the interest is compounded yearly?
Answers
The formular is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]6500=5000(1+\frac{r}{1})^{1\times8}[/tex][tex]\frac{6500}{5000}=(1+r)^8[/tex][tex]1.3=(1+r)^8[/tex][tex]1.3^{\frac{1}{8}}=(1+r)^{8\times\frac{1}{8}}[/tex][tex]1.3^{0.125}=1+r[/tex][tex]1.0333=\text{ 1+r}[/tex]subtract 1 from bothside
[tex]r\text{ = 0.0333}[/tex]R = 0.0333 x 100% = 3.33%
What is the mean of the data?Number of Letters inOur First Name3 XX4 XX5 XXXX6 X7 X8 X I keep getting 3 but it was marked wrong with the correct answer of 5. Where am I going wrong?
Answers
Answer
Mean = 5
Explanation
The mean is the average of the distribution. It is obtained mathematically as the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
Since the number of X in front of each number denotes how many times that number occurs,
Σx = 3 + 3 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 7 + 8 = 55
N = Total number of X = 11
Mean = (Σx)/N
Mean = (55/11) = 5
Hope this Helps!!!
using the pythagorean theorem and finding distances
Answers
Scalene
Explanation
we have a triangle with 3 differents lengths and angles, so it is a Scalene triangle
A triangle is scalene if all of its three sides are different.
I hope this helps you
Question 10 (1 point)Givenm
Answers
The measure of angle ∠AOB is 139 degrees, that is the value of m∠AOB is 139.
We are given;
m∠AOC is a straight line = linear pair
m∠AOB = 8x + 51 degree
m∠BOC = 6x - 25 degree
We know that sum of the angles of linear pair is 180 degrees.
So,
∠AOB + ∠BOC = 180 degrees
8x + 51 degree + 6x - 25 degree = 180 degrees
14x = 180 - 26 degrees
x = 154/14 degrees
x = 11 degrees
Therefore,
m∠AOB = 8x + 51 degree = 8 * 11 + 51 degrees = 139 degrees.
m∠BOC = 6x - 25 degree = 6 * 11 - 25 degrees = 41 degrees.
Thus, the measure of angle ∠AOB is 139 degrees, that is the value of m∠AOB is 139.
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Which expression is not equivalent to 2rº + 10x + 12? (1) (2x + 4)(x + 3) (3) (2x + 3)(x + 4) (2) (2x + 6)(x + 2) (4) 2(x + 3)(x + 2)
Answers
(2x + 3)(x + 4) = 2x² + 8x + 3x + 12 = 2x² + 11x + 12 ≠ 2x² + 10x + 12
So, the expression (2x + 3)(x + 4) is not equivalent to 2x² + 10x + 12
The number of people filling up the Hard Rock Stadium for the Super Bowl was modeled withthe following equation where y represented the number of people and t represented the timein seconds. How many people were in the stadium in 30 seconds?* y = 9t 92718270
Answers
Given the equation:
y = 9t
to find how many people were in the stadium in 30 seconds, we have to replace t = 30, as follows:
y = 9(30)
y = 270
There were 270 people in the stadium in 30 seconds
Chris had a new refrigerator delivered to his home for $950. He gave the delivery
person a $20 tip. What percent tip did he give the delivery person?
2.1%
21%
0.021%
0.21%
Answers
He give the delivery person a tip of 2.1%
What is delivery ?
Transporting items from a source point to a predetermined destination is known as delivery. Roads, railroads, shipping lanes, and airline networks all play major roles in the delivery of cargo (physical products). Specialized networks, such as pipelines for liquid products, power grids for electrical power, computer networks like the Internet, or broadcast networks for electronic information, may be used to distribute specific sorts of goods. [1] A specific subcategory is car transport, and an associated variation is autorack, which involves shipping cars through railroad.
Delivery, which comprises both transportation and distribution, is a crucial aspect of trade and commerce.Distribution is the overall process of providing things, while logistics is the study of efficient delivery and disposition procedures for both persons and materials. Distributors are companies that specialize in moving commercial items from their site of manufacture or storage to their point of sale, whereas delivery services are companies that focus on moving goods to consumers. Deliveries of goods for both commercial and private purposes are also made by postal, courier, and moving services.
According to the question
The new refrigerator delivered to his home for $950
tip he gave to the delivery person = $20
let tip he gave to the person in percentage be x
$20= [tex]\frac{x}{100}(950)[/tex]
x =[tex]\frac{20(100)}{950}[/tex]
x=2.1%
Thus the tip is 2.1%
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darnell and donovan are both trying to calculate the area of an obuste trangle examine their calculations below who is correct and why
Answers
The area of triangle is
[tex]undefined[/tex]An apple is launched directly upward at 70 feet per second from a platform 100
feet high. The equation for this apple's height h at time t seconds after launch
is - 16t+70t+100. What is the height of the apple after 5 seconds?
Height of apple:
Answers
Answer:
530
Step-by-step explanation:
(16x5)+(70x5)+100=?
80+350+100=530
Given the function g(x) = 8x-2, compare and contrast g(-2) and gl4). Choose the statement that is true concerning these two values. O The value of g(-2) is larger than the value of g(4) OThe value of g(-2) is the same as the value of g(4). OThe value of g(-2) is smaller than the value of g(4) OThe values of g(-2) and g(4) cannot be compared.
Answers
Given: g(x) = 8x - 2
So, the value of g(-2) = 8 * -2 - 2 = -18
And g(4) = 8 * 4 - 2 = 30
We will check the given statements according to the values of g(-2) and g(4):
1) The value of g(-2) is larger than the value of g(4) [Wrong]
Because the value of g(-2) is smaller then the value of g(4)
2) The value of g(-2) is the same as the value of g(4) [Wrong]
3) The value of g(-2) is smaller than the value of g(4) [True]
4) The values of g(-2) and g(4) cannot be compared. [wrong]
So, the true statement is The value of g(-2) is smaller than the value of g(4)
1A shipment of sugar fills 4 1/5containers. If each container holds 2 1/3 tons of sugar, what is the amount of sugar in the entire shipment? Write your answer as a mixed number in simplest form
Answers
Answer:
9 4/5 tons of sugar.
Explanation:
The number of containers in a shipment of sugar = 4 1/5 containers
Amount of sugar in each container = 2 1/3 tons
Therefore, the amount of sugar in the entire shipment is:
[tex]\begin{gathered} =4\frac{1}{5}\times2\frac{1}{3} \\ =\frac{21}{5}\times\frac{7}{3} \\ =\frac{7\times7}{5} \\ =\frac{49}{5} \\ =9\frac{4}{5}\text{ tons} \end{gathered}[/tex]There are 9 4/5 tons of sugar in the entire shipment.