Answer with Step-by-step explanation:
Let x be the cost of 1 pen and y be the cost of 1 pencil
8 pens and 7 pencils cost $3.37 while 5 pens and 11 pencils cost $3.10
8x+7y= 3.37 -----------------(1)
and 5x+11y= 3.10 -----------------(2)
equation (1)×5-equation(2)×8
5(8x+7y)-8(5x+11y)=3.37×5-3.10×8
40x+35y-40x-88y= -7.95
-53y = -7.95
y= 0.15
Putting y=0.15 in equation (1), we get
8x+7×0.15=3.37
8x+1.05=3.37
8x=2.32
x=0.29
Hence, Cost of 1 pen=$ 0.29
Cost of 1 pencil= $ 0.15
A survey was taken of 100 potential voters, asking them which candidate they would vote for in a local election. The results are given in the table below.
CANDIDATE X Y Z
NUMBER OF SUPPORTERS 63 17 20
If 5000 people vote in the actual election, which is the best prediction for the number of votes for candidate X, based on the results of this poll?
630
850
1000
3150
Part b what is the value of the smallest bond angle in xef4?
Answer:
90 degrees
Step-by-step explanation:
Which is the image of Triangle ABC for a 180° counterclockwise rotation about P?
Answer:
Triangle GHI is rotating 180° counterclockwise .
Step-by-step explanation:
Given : Triangles.
To find : Which is the image of Triangle ABC for a 180° counterclockwise rotation about P.
Solution : We have triangle ABC .
If we Rotate GHI triangle in counterclockwise 180 degree we get triangle ABC.
We can prove it by rotating triangle ABC in clockwise direction 180° We get triangle GHI.
Therefore, Triangle GHI is rotating 180° counterclockwise .
The order of operations is not important to solving math problems.
True
or
False
Make a table of ordered pairs for the equation.
y=−1/3x+1
Answer:
The answer is the next table:
x y
0 1
3 0
6 -1
9 -2
Step-by-step explanation:
In order to determine the table with ordered pairs, we have to know about replacing values.
In a linear function, there are two variables, the dependent variable (y) and the independent variable (x). If we replace any value in the "x" variable, we get the "y" value. The process is called "replacing value".
To get the table, we choose some value to replace in the "x" variable:
[tex]x=0\\y=-\frac{1}{3}(0)+1=1\\[/tex]
[tex]x=3\\y=-\frac{1}{3}(3)+1=-1+1=0[/tex]
[tex]x=6\\y=-\frac{1}{3}(6)+1=-2+1=-1[/tex]
[tex]x=9\\y=-\frac{1}{3}(9)+1=-3+1=-2[/tex]
The table with some ordered pairs is:
x y
0 1
3 0
6 -1
9 -2
I have attached an image that shows a graph with the ordered pairs.
Which of the following is a like radical to 3x sqrt 5?
X(3sqrt 5)
Sqrt 5y
3(3sqrt 5x)
Y sqrt 5
The like radicals to 3x√5 from the given options is: D. y√5.
What are Like Radicals?Like radicals can be defined as radicals having the same root number (i.e. square) and also have the same radicand.
Given, 3x√5, the root here is a square, while the radicand is 5. Thus, like radicals to 3x√5 will have same root and radicand.
Therefore, the like radicals to 3x√5 from the given options is: D. y√5.
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The like radical to 3x sqrt 5 is y sqrt 5.
Explanation:Given the expression 3x sqrt 5, we can see that the square root is applied only to 5 and not to 3x. To find a like radical, we need to find an expression in which the square root is also applied only to the same number.
Looking at the options, the only expression that matches this criterion is y sqrt 5. The square root is applied only to 5, just like in the original expression. Therefore, y sqrt 5 is the like radical to 3x sqrt 5.
Write a real-life situation that can be modeled by the expression .
5 x 3/4
Answer:
On Zira's birthday Lizzy, Amy Wilson Amara, and Ria want only 3/4 inches of the cake how much cake do you need for all of them?
Solutions 5 x3/4 = 3.75 inches of cake
Step-by-step explanation:
S=la+2b solve for a?
The required simplification of function for the a is given as a = -2b / l + s / l.
Given that,
To simplify the expression S=la + 2b for a.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
s = la + 2b
Transposition of 2b on right side
s - 2b = la
dividing both sides by l
a = s / l - 2b / l
Thus, the required simplification of function for the a is given as a = -2b / l + s / l.
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you roll a number cube twice. what is the probability of rolling a 2 first and then rolling an odd number
The probability of rolling a 2 on a die and then rolling an odd number on a second roll is 1/12.
The probability of rolling a 2 on a die is 1/6 because there are six sides on a die, each with an equal chance of landing face up. When rolling the dice a second time, there are three odd numbers (1, 3, and 5), so the probability of rolling an odd number is 3/6, or 1/2. To find the combined probability of both events occurring in sequence (rolling a 2 first and then an odd number), we multiply the individual probabilities: (1/6) × (1/2) = 1/12.
At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?
At 4:00 PM, the distance between the ships is changing at a rate of 6160 km/h.
Explanation:To find the rate at which the distance between the ships is changing, we can use the concept of relative velocity. At 4:00 PM, ship A has been sailing east for 4 hours, covering a distance of 40 km/h * 4 h = 160 km. Ship B has been sailing north for 4 hours, covering a distance of 20 km/h * 4 h = 80 km.
To find the distance between the ships at 4:00 PM, we can use the Pythagorean theorem. The distance between the ships is the hypotenuse of a right triangle with legs of 170 km and 80 km. Using the theorem, we find that the distance between the ships is √(170^2 + 80^2) ≈ 186.45 km.
To find the rate at which the distance is changing, we can use the derivative of the distance formula. Let D be the distance between the ships. Then, D^2 = (170 + 40t)^2 + (80 + 20t)^2, where t is the time in hours. Taking the derivative of D^2 with respect to t and solving for dD/dt, we get: dD/dt = (170 + 40t)(40) + (80 + 20t)(20).
Substituting t = 4 into the expression, we find that dD/dt = (170 + 40(4))(40) + (80 + 20(4))(20) = 6160 km/h. Therefore, the distance between the ships is changing at a rate of 6160 km/h at 4:00 PM.
Esteban counted the number of steps it took him to walk to school.He counted 1,138 steps.How many steps does he take walking to and from school each day?
John must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70. Which inequality will tell him at least how many more points he needs to pass the class?
A. 72 + 78 + 70 + x ≤ 289 B. 72 + 78 + 70 + x > 289 C. 72 + 78 + 70 + x < 289 D. 72 + 78 + 70 + x ≥ 289
John needs to use the inequality 72 + 78 + 70 + x ≥ 289 to determine the minimum number of additional test points required to pass his math class.
Explanation:The student, John, needs to determine how many more test points he requires to pass his math class. Given his current test scores, the inequality to represent this scenario should account for the minimum points he needs to achieve the threshold.
Therefore, the inequality should include an 'at least' condition, meaning the total points must be greater than or equal to the pass mark of 289. Adding his current scores of 72, 78, and 70 gives a total of 220, so the inequality will include an unknown variable, x, which represents the additional points needed. The correct inequality is D. 72 + 78 + 70 + x ≥ 289.
Final answer:
John needs to use the inequality 72 + 78 + 70 + x ≥ 289, which simplifies to x ≥ 69, to determine he requires at least 69 more points to pass. Option D
Explanation:
John needs to determine how many more points he requires to pass his math class, with a target score of at least 289 points. He already has test scores of 72, 78, and 70. To find out the least number of additional points he needs, he should use an inequality that allows for the sum of his scores and an unknown quantity x (representing the points he needs) to be at least as great as 289. This is represented by the inequality 72 + 78 + 70 + x ≥ 289. This can be simplified to x ≥ 69, which means John needs at least 69 more points to pass the class.
WILL GIVE BRAINEST
Leo had $91, which is 7 times as much......
A plumber charges a flat fee of $79 to visit a home and examine a clogged drain. The plumber charges an additional $21 per hour spent fixing the drain. The total cost, c (in dollars), for fixing a drain that takes, h hours is given by the following function.
C(h)=79+21h
(a) What is the total cost for fixing a drain that takes 7 hours?
(b) If the plumber charges a total of $310, how many hours did he spend fixing the drain?
Final answer:
The total cost for fixing a drain that takes 7 hours is $226. If the plumber charges a total of $310, he spent 11 hours fixing the drain.
Explanation:
The cost function given by the plumber is C(h) = 79 + 21h, where C represents the total cost and h represents the number of hours spent fixing the drain.
To find the total cost of fixing a drain that takes 7 hours, we substitute h with 7 in the given equation: C(7) = 79 + 21(7). Calculating this, we get C(7) = 79 + 147, which equals $226. Therefore, the total cost for fixing a drain that takes 7 hours is $226.To find out how many hours the plumber spent fixing the drain when the total charge is $310, we set C(h) equal to 310 and solve for h: 310 = 79 + 21h. Subtracting 79 from both sides gives us 231 = 21h. Dividing both sides by 21 yields h = 11 hours. Thus, the plumber spent 11 hours fixing the drain.If the ratio of areas of two similar polygons is 25:49, what is the ratio of the corresponding side lengths
Answer: 5:7
Step-by-step explanation:
The person above is right
I just did the test
Based upon a smaller sample of only 170 st. paulites, what is the probability that the sample proportion will be within of the population proportion (to 4 decimals). probability
Final answer:
Explanation of sampling distributions and probabilities for different sample sizes in relation to the population proportion in St. Paulites.
Explanation:
In part a, when selecting a sample of 540 St. Paulites, the sampling distribution of p would have a mean of 0.32 and a standard error of 0.0201.
The probability that the sample proportion will be within 0.05 of the population proportion is 0.9871.
In part c, with a sample of 170 St. Paulites, the sampling distribution of p has a mean of 0.32 and a standard error of 0.03145.
The probability that the sample proportion will be within 0.05 of the population proportion is 0.9907.
The gain in precision by taking the larger sample is substantial, with the probability increasing from 0.9907 to 0.9871, reducing the error by a factor of 0.9999.
seven less than the product of 3 and a number is -16
Ron sees 3 dogs at the park. Hal sees twice as many dogs as Ron. How many dogs do they see in all?
Find derivative: [5sin(x)]/3 -2x
Olivia started her banking account with $100 and is increasing the account $20 per month. The independent variable
Answer:
Wee is the independent variable, and deposit is the dependent variable
Step-by-step explanation:
Given that Olivia started her banking account with $100 and is increasing the account $20 per month.
Here the variable which changes independently is the independent variable
Hence no of weeks elapsed would be the independent variable
The dependent variable would be the variable which changes whenever number of weeks changes.
Here dependent variable is the total balance in the account in a particular week
D=100+20n wbere n= no of weeks that eapsed
and D= depositisin in the bank
Calculate the perimetet of the quadrilateral
What is the word that means the answer to an addition problem i forgot
Evaluate 3f(2) = .
what does this equal
Answer:
The answer is 12
Step-by-step explanation:
Suppose a florist is creating a bouquet with 3 different types of flowers and 3 different types of greenery. If there are 7 types of flowers in the shop and 6 types of greenery to choose from, how many ways can the florist design the bouquet?
The florist can design the bouquet in 700 unique ways, using 3 different types of flowers and 3 different types of greenery chosen from 7 types of flowers and 6 types of greenery respectively.
Explanation:The subject of this question is within the realm of Mathematics, specifically combinatorics, which studies the various ways in which objects can be selected, arranged, and combined. To find the total number of ways the florist can design the bouquet given 7 types of flowers and 6 types of greenery, we can employ the combination (or 'choose') formula given by n choose r, where n is the total number of objects and r is the number of objects selected. Hence, the number of ways to choose 3 flowers out of 7 is '7 choose 3', and similarly for the greenery we have '6 choose 3'.
Using the formula for combinations, we have:
Combinations of flowers = 7 choose 3 = 7! / (3!(7-3)!) = 35
Combinations of greenery = 6 choose 3 = 6! / (3!(6-3)!) = 20
Since the flowers and the greenery are selected independently of each other, we multiply the two results to get the total number of combinations. Therefore, the number of unique ways in which the florist can design the bouquet is 35 * 20 = 700.
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How do you find the x intercepts of 3x^(5/3) - 4x^(7/3)
0.05 is 1/10 the value of?
Answer
0.5
Explanation
0.05 is 1/10 the value of?
In other words the question is asking, what must be multiplied by 1/10 to give 0.05.
let that value be X.
1/10 × X = 0.05
X/10 = 0.05
X = 0.05 × 10
= 0.5
The value that must be multiplied by 1/10 which gives 0.05 would be 0.5.
What is the fundamental principle of multiplication?If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We need to find the value that must be multiplied by 1/10 which gives 0.05.
Let that value be X.
1/10 × X = 0.05
X/10 = 0.05
X = 0.05 × 10
= 0.5
Thus, the value that must be multiplied by 1/10 which gives 0.05 would be 0.5.
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Dilate using a scale factor of 2
(2,3) (5,2) (3,-2)
Find the probability that the sample mean deviates from the population mean μ = 108 by no more than 2.
choose a method then find the product 16 * 60
Mel Company has a net income, before taxes, of $95,000. The treasurer of the company estimates 45% of net income will have to be paid for federal and state taxes. The tax for both federal and state is:
Answer:
The tax will be $42,750.
Step-by-step explanation:
Mel Company has a net income, before taxes, of $95,000.
The treasurer of the company estimates 45% of net income will have to be paid for federal and state taxes.
So, the tax for both federal and state is:
[tex]0.45\times95000=42750[/tex] dollars
Therefore, the tax will be $42,750.