The equation for total amount to be paid represented as y and pounds of potatoes represented as x will be y = 0.64x
What is linear equation?Ax + By + C = 0 can be used to express a linear equation in two variables, where x and y are the two variables, and each has a degree of one.
Ex. -2x+3y=8
Total weight of potatoes in pounds Dontrell bought= x
Let total amount Dontrell he pays= $ y
It is given 5.5 pounds are bought by paying $3.52
5.5 pounds = $3.52
1 pound = $ 3.52/5.5
1pound=$0.64(Using Unitary method)
Dontrell buy x pounds potatoes and he pays $y
Therefore,
y=0.64x
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Each morning Tess chooses either red ribbon or blue ribbon at random to wear in her hair what is the probability that Tess will choose a red ribbon on both Monday and Tuesday
The probability of choosing red ribbon on both Monday and Tuesday is 1/4.
What is the probability?
The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.
Given that each morning Tess chooses either red ribbon or blue ribbon at random to wear in her hair.
That means probability of choosing between blue or red is 1/2 in one morning.
Now the probability of choosing red ribbon on both Monday and Tuesday,
1/2 × 1/2
= 1/4
Therefore, the probability of choosing red ribbon on both Monday and Tuesday is 1/4.
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Cameron is deciding between two landscaping companies for his place of business.
Company A charges $25 per hour and a $300 equipment fee. Company B charges $55
per hour and a $150 equipment fee. Let A represent the amount Company A would
charge for t hours of landscaping, and let B represent the amount Company B would
charge for t hours of landscaping. Write an equation for each situation, in terms of t,
and determine the interval of hours, t, for which Company A is cheaper than
Company B.
Answer:
A = 25t + 300
B = 55t + 150
Less than 5 hours, company B would be cheaper. At 5 hours the cost is equal. After 5 hours, company A would be cheaper.
Step-by-step explanation:
Company B would be cheaper for lower hours.
The the two equation equal to each other and solve for to find out when the costs will be equal.
25t + 300 = 55t + 150 Subtract 25t from both sides
300 = 30t + 150 Subtract 150 from both sides
150 = 30t Divide both sides by 30
5 = t
At 5 hours the cost are the same, after 5 hours company A would be cheaper.
1.6y+y-4/15y+1 1/6y=2 1/3 pls help
The simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.
What is the domain of the function?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
We have,
1.6y+y-4/15y+7/6y=21/3
Move all terms to the left:
1.6y+y-4/15y+7/6y-(21/3)=0
Domain of the equation: 15y!=0
y!=0/15
y!=0
y∈R
Domain of the equation: 6y!=0
y!=0/6
y!=0
y∈R
Add all the numbers together, and all the variables
1.6y+y-4/15y+7/6y-7=0
Add all the numbers together, and all the variables
2.6y-4/15y+7/6y-7=0
calculate fractions
2.6y+(-24y)/90y²+105y/90y²-7=0
multiply all the terms by the denominator
(2.6y) * 90y² + (-24y) + 105y - 7 * 90y² = 0
Add all the numbers together, and all the variables
(2.6y) * 90y² + (-24y) + 105y - 7 * 90y² = 0
Add all the numbers together, and all the variables
105y+(+2.6y)*90y² + (-24y) - 7*90y² = 0
multiply elements
-630y+105y+(+2.6y)*90y² + (-24y) = 0
get rid of parentheses
-630y² + 105y + (+2.6y)*90y² - 24y = 0
Add all the numbers together, and all the variables
-630y² + 81y + (+2.6y) * 90y² = 0
Hence, the simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.
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please help in this grade 7 percentage question im desperate
Answer:
See below
Step-by-step explanation:
320 x .1 = 32
320 + 32 = 352
352 x .5 = 176
352 + 176 = 528
320 x .65 = 208
320 + 208 = 528
Use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) squareroot of (9 + 49^x2) dx
The indefinite integral of given integral ∫√(9+49x^2)dx is ∫√(9+49x^2)dx = [tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex].
In the given question we have to find the indefinite integral.
The given integral is
∫√(9+49x^2)dx
Now finding the indefinite integral using the C for the constant of integration.
An integral is regarded to be indefinite if it has no lower or upper bounds. In mathematics, the most generic antiderivative of f(x) is known as an indefinite integral and expressed by the expression f(x) dx = F(x) + C.
We can write it as:
[tex]\int\sqrt{(9+49x^2)}dx = \int\sqrt{[(3)^2+(7x)^2]}dx[/tex]
Taking common 7^2
[tex]\int\sqrt{(9+49x^2)}dx = 7\int\sqrt{[(3/7)^2+(x)^2]}dx[/tex]
Using the formula
[tex]\int\sqrt{(a^2+x^2)}dx = \frac{1}{2}\times\sqrt{a^2+x^2} + \frac{1}{2}\cdot a^2In|x+\sqrt{a^2+x^2}|+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{(3/7)^2+x^2}+\frac{1}{2}\cdot(\frac{3}{7})^2In|x+\sqrt{(3/7)^2+x^2}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{9/49+x^2}+1/2\cdot(9/49)In|x+\sqrt{(9/49)+x^2}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+1/2\cdot(9/49)In|x+\frac{\sqrt{9+49x^2}}{7}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+(9/98)In|\frac{7x+\sqrt{9+49x^2}}{7}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex]
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14. A zip wire is shown as the dashed line AC in the diagram.
The zip wire is supported by two vertical posts AB and CD standing on horizontal ground.
CD=2.6 BD=12
The zip wire makes an angle x with the horizontal, as shown in the diagram. The design of the zip wire requires the angle x to be at least 5⁰.
Work out the least possible height of the post $A B$ Give your answer correct to 3 significant figures.
The least possible height of AB is 3.650 m.
What is a word problem?
A word problem is described as a few phrases outlining a "real-life" situation where a problem needs to be solved using mathematics.
For everything from counting pennies to calculating a tip, we can employ the three primary sorts of word problems: part-part whole, separate and join, and multiply and divide.
Given, CD=2.6 m, BD=12 m
From the figure,
or, tan x = [tex]\frac{AB - 2.6}{12}[/tex]
or, tan 5 [tex]\leq \frac{AB - 2.6}{12}[/tex]
When AB be least, then
[tex]\frac{AB - 2.6}{12}[/tex] = tan 5
or, AB = (12*tan 5) + 2.6
or, AB = 3.650 m
Hence, the least possible height of the AB is 3.650 m.
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Complete the ratio 4:16 = 1:?
Answer:
1:4
Step-by-step explanation:
4:16 = 1:?
4/4 = 1
16/4 = 4
= 1:4
A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t3 + 8t2 + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million. According to the graph of the function, what other quantity of product would result in the same profit?
The required value of the production at which the company attained the same profit is 4 thousand skin care items.
Given that,
A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t³ + 8t² + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million.
Here,
Plotting the graph of the polynomial equation,
P(t) = –2t³ + 8t² + 2t,
From the graph at x = 4,
The polynomial gives the same value as it gave at x = 1,
Thus, the required value of the production at which the company attained the same profit is 4 thousand skin care items.
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A side of the triangle below has been extended to form an exterior angle of 156°. Find the value of x.
The value of x inside the triangle is 24°
How to calculate the value of x(angle)?
A straight line's total number of angles adds up to 180°. Supplementary angles are two angles whose sums equal 180 degrees. Angles are referred to as neighbouring if they have a similar vertex and side.A straight angle in mathematics is one with a degree value of 180. Because it resembles a straight line, it is called straight.Angles in a straight line are the total of all the angles that can be arranged in a straight line. Straight line angles add up to 180°.The angle of the straight line = 180°
156° + x = 180°
x = 180° - 156°
x = 24°
Hence, the value of x inside the triangle is 24°.
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Write an equation in slope-intercept form of the line that passes through (-2,-7) and (-1,6)
Which ordered pair satisfies the inequality? 6x + 5y < -15
The ordered pair of the inequality 6x + 5y < -15 are (2, 0) and (3, 2).
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Considering the provided inequality and the provided ordered pairs, we will check it by replacing one by one in the inequality; if the inequality is fulfilled, they are the solution; otherwise, they are not, so we obtain:
(2, 0):
6x + 5y > 2
6(2)+5(0)>2
12+0>2
12>0
Since the inequality holds, then the ordered pair is a solution.
(7, -8):
6x + 5y > 2
6(7)+5(-8) > 2
42-40>2
2>2
Since the inequality is not satisfied, then the ordered pair is not a solution.
(3, 2):
6x + 5y > 2
6(3)+5(2) >2
18+10>2
28>2
Since the inequality holds, then the ordered pair is a solution.
(-8, 6):
6x + 5y > 2
6(-8)+5(6) >2
-48 + 30 > 2
-18 > 2
Since the inequality is not satisfied, then the ordered pair is not a solution.
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PLEASE HELPPP!!!
The admission fee at the museum is 8.50 for children and 12.50 for adults on a certain day, a total of 240 people entered the museum and 2400$ was collected.
Use the variable c to represent children and the variable a to represent the adult
Answer:
Below
Step-by-step explanation:
a + c = 240 re-arrange to c = 240-a
revenue from child tix = 8.50 ( 240-a)
revenue from adult tix = 12.50 a summed, the revenues = 2400
8.5(240-a) + 12.5 a = 2400
2040 - 8.5 a + 12.5 a = 2400
4.5 a = 360
a = 80 tix then c = 240 - a = 160 tix
A dice game involves rolling 2 dice. If you roll a 2, 3, 4, 10, 11, or a 12 you win $5. If you roll a 5, 6, 7, 8, or 9 you lose $5. Find the expected value you win (or lose) per game.
The correct answer is option B which is -1.67 is the expected value.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
You have a higher probability of losing money than gaining it due to the distribution of probability.
There are more chances to lose than win.
As a result, you are expected to lose money.
Only -1.67 is the only negative option, which means that we don't even need to do real math since there's already only one choice.
Hence, the correct answer is option B which is -1.67 is the answer.
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Answer:
You will Gain 5 points.
Step-by-step explanation:
Got it right on the test!
The following are rules for repeating patterns. For which rule will the 12th shape be a circle?
A.
triangle, circle, square
B.
circle, square
C.
rectangle, circle
D.
circle, circle, triangle
Answer:
A Square
B Square
C Circle
D Triangle
Chandrani had a Rs 100 note she bought a geometry box for ₹ 37 . 75. Find the amount left with her
Answer:
The amount left with her si 62.25
which model can be used to find 4/5 divided by 1/10
Apply the fraction rule model can be used to find 4/5 divided by 1/10.
What is fraction rule?
For fractions to be added or subtracted, their denominators must match (the bottom value). the same denominators are used for addition and subtraction. It only requires adding or subtracting the numerators if the denominators are already equal.
[tex]$\frac{\frac{4}{5}}{\frac{1}{10}}$[/tex]
Apply the fraction rule: [tex]$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}$[/tex]
[tex]$=\frac{4 \cdot 10}{5 \cdot 1}$[/tex]
Cancel [tex]$\frac{4 \cdot 10}{5 \cdot 1}: 8$[/tex]
=8
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50 minus 2.5 x greater-than-or-equal-to 20. Negative 2.5 x greater-than-or-equal-to negative 30. x greater-than-or-equal-to 12.
Negative 2.5 x greater-than-or-equal-to negative 30 is the equivalent expression of 50 minus 2.5 x greater than or equal to 20
How to find an equivalent expression?Equivalent expressions can be defined as expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will give you the same value when you simplify
Given: 50 minus 2.5 x greater than or equal to 20
50 - 2.5x ≥ 20
Subtract 50 from both sides:
-2.5x ≥ 20-50
-2.5x ≥ -30
Therefore, the equivalent expression is "negative 2.5 x greater-than-or-equal-to negative 30"
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write an expression that is equivalent to 2/3 (4x + 9)
Hello,
I hope you and your family are doing well!
To write an expression that is equivalent to 2/3 (4x + 9), you can simply distribute the 2/3 over the parentheses:
2/3 (4x + 9) = (2/3 * 4x) + (2/3 * 9)
This simplifies to:
2/3 (4x + 9) = (8/3)x + (18/3)
Therefore, an expression that is equivalent to 2/3 (4x + 9) is (8/3)x + (18/3).
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Happy Holidays & New Year!
Answer: 2 2/3x + 6
Step-by-step explanation: 1 of 3 ways to find how to make the equivalent is to use the distributive property. So, that means we need to multiply or distribute 2/3 to both 4x and 9. So, 2/3 x 4 is roughly 2 2/3. Also, 2/3 x 9 = 6. So, I combined the like terms to get 2 2/3x + 6 as my equivalent expression. I hope this helps.
A bag contains five white balls and three black balls. Your goal is to draw two white balls.
(a) You simultaneously draw two balls at random. What is the probability that they are both white?
(b) You simultaneously draw two balls at random. Once you have drawn two balls, you put back any black balls, and redraw so that you again have two drawn balls. What is the probability that you now have two white balls? (Include the probability that you chose two white balls on the first draw.)
The probability is the first and the second case will be 0.625 and 0.3683, respectively.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
A pack contains five white balls and three torpedoes. You want to draw two white balls.
Total events = 5 + 3
Total events = 8
You all the while drawing two balls aimlessly. Then the probability that they are both white is given as,
P = 5 / 8
P = 0.625
You all the while drawing two balls aimlessly. Whenever you have drawn two balls, you set back any debases, and redraw with the goal that you again have two drawn balls. Then the probability is given as,
P = [(3/8) x (5/8)] + [(3/8) x (5/8) x (4/7)]
P = (15 / 64) + (60 / 448)
P = 0.3683
The probability is the first and the second case will be 0.625 and 0.3683, respectively.
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Prove that the roots of the equation mx² + (m − 2)x − (m + 1) = 0 are real for all values of m
Answer:
Below
Step-by-step explanation:
For REAL numbers, the discriminant of the Quadratic Formula has to be a positive value (or zero)
b^2 - 4ac >= 0 where a = m b = m-2 c = -m-1
(m-2)^2 - 4(m)(-m-1) >=0
5m^2 +4 >= 0
5 m^2 +4 <===== will always be >= 0 for any value of 'm'
so all roots will be real
PS bisects ∠QPR . Complete the proof that ∠PSR ≅ ∠PSQ .
The proof is shown in the image.
Reasons for statement
Any line that bisects an angle divides the angle into two equal parts The two lines are congruent by cpct as the triangles are congruent The angle subtended the bisector line divides equally into two angles. Also, the triangles are congruent so angle QPS = angle RPS by cpct The common line between congruent triangles is the same Triangles are congruent by side angle side rule Angles are equal by corresponding parts of the congruent triangle rule.To know more about congruent triangles,
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Identify the terms coefficients and constant 6m + 8+4+3m
Answer:
Below
Step-by-step explanation:
6m + 8+4+3m <==== 6 and 3 are coefficients 8 and 4 are constants
9m + 12 <===== 9 is a coefficient 12 is a constant
Answer:
The coefficients are 6 and 3
The constants are 8 and 4
Step-by-step explanation:
coefficients are the numbers before the letters.
Constants do not have letters.
a) Work out the minimum number of dogs that could have a mass of more than 24kg}
b) Work out the maximum number of dogs that could have a mass of more than 24kg
The minimum number of dogs 24kg is 6 and the maximum number of dogs is 18
Maximum and Minimum:The highest amount or value or number that may be obtained or reached or can be counted is the Maximum value
The least amount or value or number that may be admitted or reached or can be counted is the Minimum value
Here we have a table
Which represents the masses of various dogs
Mass (x) kg frequency
0 ≤ x < 10 2
10 ≤ x < 20 7
20 ≤ x < 30 12
30 ≤ x < 40 6
Here the mass of dogs is represented in class intervals
a) The minimum number of dogs with a mass of more than 24kg.
From the given table,
24 kg will lie in class intervals 20 ≤ x < 30, and 30 ≤ x < 40
In class interval 20 ≤ x < 30, there is a possibility that the mass of dag will be less than 24 kg since it started from 20 kg and is up to 30 kg
In class interval 30 ≤ x < 40, there is no possibility that the mass will be less than 24 kg since it started from 30 kg and is up to 40 kg
So The minimum number of dogs that have a mass of more than 24kg the frequency of class interval 30 ≤ x < 40
Therefore,
The minimum number of dogs with a mass of more than 24kg is 6
b) The maximum number of dogs that have a mass of more than 24kg.
To get the maximum number of dogs we need to take the class interval of 20 ≤ x < 30 as in this the mass could be more than 24 kg.
And in class 30 ≤ x < 40 the mass will be more than 24 kg.
Thus, the Maximum number of dogs with more than 24 kg = 12 + 6 = 18
Therefore,
The maximum number of dogs with a mass of than 24kg is 18
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6x + 3y = 3 3x - y = 4
Answer:
x = 1
y = -1
Step-by-step explanation:
Given equations:6x + 3y = 3 -------------(1)
3x - y = 4 ----------------(2)
Multiply Eq. (2) by 2
2(3x - y) = 4 × 2
6x - 2y = 8 -------------(3)
Subtract Eq. (3) from Eq. (1)
6x + 3y - (6x - 2y) = 3 - 8
6x + 3y - 6x + 2y = -5
3y + 2y = -5
5y = -5
Divide 5 to both sides
y = -5/5
y = -1Put y = -1 in Eq. (1)
6x + 3(-1) = 3
6x - 3 = 3
Add 3 to both sides
6x = 3 + 3
6x = 6
Divide 6 to both sides
x = 1[tex]\rule[225]{225}{2}[/tex]
Writing Equations of lines
Write the equation of each line with the given information
through: (-3, 4) and (-5, -1)
Answer:
y = 5/2x + 11.5
Step-by-step explanation:
(-3, 4) (-5, -1)
m = -1-4/ -5+3
m = -5 / -2
m = 5/2
y = 5/2x + b
-1 = 5/2(-5) + b
-1 = -12.5 + b
b = 11.5
y = 5/2x + 11.5
Answer:
y-y1=y2-y1/x2-x1(x-x1)
y-4= (-1-4/-5+3) (x+3)
y-4= -5/-2(x+3)
y=5/2x+15/2+4
y=5/2x+15+8/2
y=5/2x+23/2
help please very easy proportional relationship due hurry please than u!
1) h=1/5 k
(10/2 = 1/5, 20/4 = 1/5... etc)
2) k=5/4 h
(5/4 = 5/4, 10/8=5/4... etc)
3) h=5/1 k
(25/5 = 5/1, 30/6 = 5/1 ... etc)
Hope this helps!
:]
HELPME Mike has $25.00 to rent paddleboards for himself and a friend for 3 hours. Each paddleboard rental costs $3.75 per hour.
A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?
Write the following as an inequality.
−8 is less than or equal to w, and 3 is greater than or equal to w
Use w only once in your inequality.
Answer:
Step-by-step explanation:
If -8 is less than or equal to w, and 3 is greater than or equal to w, then we can combine these two inequalities into a single inequality by combining the left and right sides:
-8 ≤ w ≤ 3
This inequality can be read as "w is greater than or equal to -8 and less than or equal to 3." It represents all values of w that are greater than or equal to -8 and less than or equal to 3, including -8 and 3.
I hope this helps! Let me know if you have any questions.
Angle ABC is taken by a dilation with centerpoint, P and scale factor of four to angle A’B’C’ the measure of angle, BCA is 75° what is the measure of angle B’C’A’
Answer:
75°
Step-by-step explanation:
You want to know the measure of the image angle B'C'A' after angle A'B'C' is dilated by a factor of 4 about point P. Angle BCA is 75°.
DilationDilation does not affect angle measures, so angle B'C'A' has the same measure as angle BCA, 75°.
m∠B'C'A' = 75°