Part A
There were 600 water samples taken for an experiment using pH and iron levels. The results are shown in the table.
What are the probabilities for the listed events? Write your answers as decimals rounded to the thousandths place.
Answers
Answer:
The answer to your problem is, 0.275 0.273 0.400 and 0.300
Step-by-step explanation:
My calculation ( May not be correct )
P ( low iron or LI ) [tex]\frac{165}{600}[/tex] = 0.275
P ( low pH | LI ) = [tex]\frac{45}{165}[/tex] = 0.273
P ( low pH ) = [tex]\frac{150}{600}[/tex] = 0.400
P ( LI | Low pH ) = [tex]\frac{45}{150}[/tex] = 0.300
Thus by making these calculations the answer to your problem is, 0.275 0.273 0.400 and 0.300
Related Questions
If the adult dosage of a drug is 257mL , how much should a 2-year old child receive? Round your answer to the nearest hundredth.
Answers
In this particular case, a 2-year old child should receive a dosage of approximately 16.15mL of the drug. This figure is calculated by using the following formula: (adult dosage/150) x (child's weight in kg).
What is dosage?Dosage is a term used to describe the amount of medicine or drug prescribed for a particular individual to take at a given time. It is usually prescribed by a doctor or healthcare provider based on the patient's age, weight, and medical condition. Dosage may vary from person to person depending on their health condition and other factors.
The appropriate dosage of a drug for a 2-year old child is calculated by taking into account the weight, age and health status of the child. Before administering any medications, it is important to consult with a doctor or a pharmacist to ensure that the appropriate dosage is used.
The adult dosage of 257mL is divided by 150 to obtain the base dosage of 1.71mL. This is then multiplied by the child's weight in kilograms (which is usually around 9 kg) to obtain the final dosage of 16.15mL.
It is important to note that the dosage should be rounded to the nearest hundredth. Therefore, the recommended dosage for the 2-year old child in this case would be 16.2mL. It is important to ensure that the dosage is not rounded up, as this could lead to an overdose of the drug, which could have serious consequences.
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10.3 Surface Area of Triangular Prisms.
Please help with these 6 answers in photo
Answers
The letter of the 3D figure which matches the statement of the student with regards to the surface areas of the figures are;
The net of this triangular prism covers the smallest total surface area; B
The lateral surface area is 96.6 unit²; C
The total surface area is 111.6 units²; C
The lateral surface area is 85.56 unit²; A
The total surface area is 103.96 unit²; A
The net of this triangular prism covers the largest lateral surface area; C
What is the surface area of a 3D figure?
The surface area of a three dimensional, (3D), figure is the area of the boundary surface that surrounds the space occupied by the figure.
The surface areas and the lateral surface areas of the nets and the prisms are presented as follows;
Figure A;
Surface area = 2×(1/2)×4.6×4 + 3×6.2×4.6 = 103.96
The lateral surface area = 3×6.2×4.6 = 85.56
Figure B;
Surface area = 2×(1/2)×4×3.8 + 2×4.3×6 + 4×6 = 90.8
The lateral surface area = 2×4.3×6 + 4×6 = 75.6
Figure C;
Surface area = 2×(1/2)×5×3 + 5×7 + 3×7 + 5.8×7 = 111.6
The lateral surface area = 5×7 + 3×7 + 5.8×7 = 96.6
Therefore;
The net of the triangular prism in Figure B covers the smallest surface areaFigure C has a lateral surface area of 96.6The total surface area of Figure C is 111.6 unit²The lateral surface area of Figure A is 85.56 unit²The total surface area of Figure A is 103.96 unit²The triangular prism with the largest surface area is Figure C with a surface area of 111.6 unit²Learn more on the surface area of a prism here: https://brainly.com/question/16421693
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solve this proof? flow chart proof
Answers
Since HM = NK and ∠FGH = ∠KGH = 45°, we have FG = KH by the hypοtenuse-leg (HL) cοngruence theοrem.
What is Triangles?A triangle is geοmetric shape that is fοrmed by the three straight line segments that cοnnect tο fοrm the three sides. These sides enclοse regiοn in plane, and three pοints where line segments intersect are called vertices.
We are given that HF GK, and ZF and ZK are right angles.
Tο prοve: FG KH
We will use the fοllοwing steps tο prοve the statement:
Draw perpendiculars frοm F and G tο HK, and label the pοints οf intersectiοn as M and N, respectively.
Since ZF is a right angle, we have ∠FMH = 90°.
Similarly, since ZK is a right angle, we have ∠GNK = 90°.
We are alsο given that HF GK, sο triangle HFG is cοngruent tο triangle KFG by the hypοtenuse-leg (HL) cοngruence theοrem.
Therefοre, FH = GK and ∠HFG = ∠KFG.
Since ∠FMH = 90° and FH = GK, we have HM = NK.
Alsο, since ∠HFG = ∠KFG, we have ∠FGH = ∠KGH.
Using angle additiοn pοstulate, we have ∠FGH + ∠KGH = ∠FGK = 90°.
Thus, ∠FGH = ∠KGH = 45°.
Finally, since HM = NK and ∠FGH = ∠KGH = 45°, we have FG = KH by the hypοtenuse-leg (HL) cοngruence theοrem.
Therefοre, FG KH, which cοmpletes the prοοf.
Hence, we have prοved that FG KH.
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Oak Creek Company is preparing its master budget for 2020. Relevant data pertaining to its sales, production, and direct materials budget are as follows.
Sales: Sales for the year are expected to total 1 million units. Quarterly sales are 20%, 25%, 25% and 30% respectively. The price is expected to be at $40 per unit for the first three quarters and $45 per unit beginning in the fourth quarter. Sales in the first quarter of 2021 are expected to be at 10% higher than the budgeted sales for the first quarter of 2020.
Production: Management desires to maintain the ending finishing goods inventories at 20% of the next quarter’s budgeted sales volume.
Direct materials: Each unit requires 2kg of raw materials at a cost of $10 per kilogram, Management desires to maintain raw materials inventories at 10% of the next quarter’s production requirement for the first quarter of 2020 are 500,000kg.
Prepare the sales, production, and direct materials budgets by quarters for 2020.
Answers
Q1:
Sales = 1,000,000 x 20% = 200,000 units
Revenue = 200,000 x $40 = $8,000,000
Q2:
Sales = 1,000,000 x 25% = 250,000 units
Revenue = 250,000 x $40 = $10,000,000
Q3:
Sales = 1,000,000 x 25% = 250,000 units
Revenue = 250,000 x $40 = $10,000,000
Q4:
Sales = 1,000,000 x 30% = 300,000 units
Revenue = (250,000 x $40) + (50,000 x $45) = $10,750,000
Total Revenue = $38,750,000
Production Budget:
Q1:
Production = 200,000 / (1 - 0.2) = 250,000 units
Raw Materials Required = 250,000 x 2 kg = 500,000 kg
Q2:
Production = 250,000 / (1 - 0.2) = 312,500 units
Raw Materials Required = 312,500 x 2 kg = 625,000 kg
Q3:
Production = 250,000 / (1 - 0.2) = 312,500 units
Raw Materials Required = 312,500 x 2 kg = 625,000 kg
Q4:
Production = 300,000 / (1 - 0.2) = 375,000 units
Raw Materials Required = 375,000 x 2 kg = 750,000 kg
Raw Materials Budget:
Q1:
Raw Materials Required = 500,000 kg
Add: Desired ending inventory = 10% x 625,000 kg = 62,500 kg
Total Raw Materials Required = 562,500 kg
Less: Beginning inventory = 10% x 500,000 kg = 50,000 kg
Raw Materials to be Purchased = 512,500 kg x $10/kg = $5,125,000
Q2:
Raw Materials Required = 625,000 kg
Add: Desired ending inventory = 10% x 625,000 kg = 62,500 kg
Total Raw Materials Required = 687,500 kg
Less: Beginning inventory = 10% x 562,500 kg = 56,250 kg
Raw Materials to be Purchased = 631,250 kg x $10/kg = $6,312,500
Q3:
Raw Materials Required = 625,000 kg
Add: Desired ending inventory = 10% x 625,000 kg = 62,500 kg
Total Raw Materials Required = 687,500 kg
Less: Beginning inventory = 10% x 687,500 kg = 68,750 kg
Raw Materials to be Purchased = 618,750 kg x $10/kg = $6,187,500
Q4:
Raw Materials Required = 750,000 kg
Add: Desired ending inventory = 10% x 750,000 kg = 75,000 kg
Total Raw Materials Required = 825,000 kg
Less: Beginning inventory = 10% x 687,500 kg = 68,750 kg
Raw Materials to be Purchased = 756,250 kg x $10/kg = $7,562,500
Therefore, the sales, production, and direct materials budgets by quarters for 2020 are as follows:
Sales Budget:
Q1: $8,000,000
Q2: $10,000,000
Q3: $10,000,000
Q4: $10,750,000
Production Budget:
Q1: 250,000 units
Q2: 312,500 units
Q3: 312,500 units
Q4: 375,000 units
Raw Materials Budget:
Q1: $5,125,000
Q2: $6,312,500
Q3: $6,187,500
Q4: $7,562,500
The graph below is on a semi-log scale, as indicated.
Find an equation for the graph shown
Answers
The equation of the graph is y = 0, which means that the graph is a horizontal line at y=0.
Describe Equation?An equation is a mathematical statement that asserts that two expressions are equal. It is typically written with an equals sign (=) separating the two expressions. For example, the equation "2x + 1 = 7" asserts that the expression "2x + 1" is equal to the expression "7". Equations can contain variables, which are symbols that represent unknown values. In the example equation, "x" is the variable that we want to solve for. Equations can be used to solve problems and find solutions to unknown values. There are various techniques and methods to solve equations depending on their complexity and nature.
Since the graph is on a semi-log scale, we know that the vertical axis is a logarithmic scale and the horizontal axis is a linear scale. Therefore, the equation of the graph is of the form:
y = a * bˣ
where a and b are constants to be determined.
We are given two points on the graph: (1,0) and (0.5,0). Let's use these points to find the values of a and b.
Using the point (1,0):
0 = a * b¹
0 = a * b
Using the point (0.5,0):
0 = a * b^0.5
0 = √(a)
Therefore, we have:
a = 0
b can be any non-zero number
So the equation of the graph is:
y = 0 * bˣ
which simplifies to:
y = 0
So the equation of the graph is y = 0, which means that the graph is a horizontal line at y=0.
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Consider the system of equations and the partial solution below.
6x+3y=9
5x+4y=10
Multiply the first equation by -4.
Multiply the second equation by 3.
Add the resulting system of equations.
Which terms will cancel when you add the resulting system of equations?
-36 and 36
-24x and 24x
O-15x and 15x
-12y and 12y
Answers
-15x and 15x is the answer
Answer:
-12y and 12y
Step-by-step explanation:
lets do the multiplication to each equation
[tex]\left \{ {{(6x+3y)(-4)=9(-4)} \atop {(5x+4y)3=10(3)}} \right.[/tex]
this is
[tex]\left \{ {{-24x-12y=-36} \atop {15x+12y=30}} \right.[/tex]
if we add the systems notice the values that do cancel are -12y and 12y
and the results of the adition is
[tex]-9x=-6[/tex]
from this
[tex]x=\frac{-6}{-9} =\frac{2}{3}[/tex]
and you can find y from any of the first equation.
[tex]y=3-2x=3-\frac{4}{3} =\frac{5}3}[/tex]
The population of a country has been decreasing for several decades. In 1990, the population was about 122 million people. In 2010, the population was about 113million people. Determine the percent decrease in the country's population during this time period.
Answers
Answer:
About a 7.3 percent Decrease
Step-by-step explanation:
First, calculate the diffrence between the two numbers:
122-113=9
Then, divide this number by the original number, it being 122, and then multiply that number by 100.
the simplified version of this number to the tenths place is 7.38%
I need help!!!!!!!!!!!!!!!!!!!
Answers
Answer:
B. 0.25x² + 0.8x - 8 = 0
C. 5x² + 7x = 15
Step-by-step explanation:
Let's try by solving all equations;
(x + 3)² = 36
x² + 3² = 36
x² + 9 = 36
x² = 36 - 9
x² = 27
x = √27
x ≈ 5.2
No quadratic
What about others
0.25x² + 0.8x - 8 = 0
Hmm.... that can only be solved by quadratic
[tex] \sf { \fbox{0.25x² + 0.8x - 8 = 0} \: can \: only \: be \: solved \: by \: quadratic}[/tex]
Also, 5x² + 7x = 15
[tex] \sf { \fbox{5x² + 7x = 15} \: can \: only \: be \: solved \: by \: quadratic}[/tex]
(x + 8)(x + 9) = 0
x² + 9x + 8x + 72 = 0
x² + 17x + 72 = 0
(x + 8)(x + 9) = 0
Not truly quadratic but can be solved with quadratic.
That leaves us with only B and C as the answer
The Director of Nursing (DON) in a long-term care facility receives a gross yearly salary of $67,000. The DON is married with three dependents and has enrolled in the company's insurance family plan. The long-term care facility employees receive paychecks every other week. a. Calculate the gross salary per pay period. b. Compute the net salary per pay period.
Answers
a. To calculate the gross salary per pay period, we need to divide the yearly salary by the number of pay periods in a year:
Gross salary per pay period = Yearly salary / Number of pay periods per year
Since there are 26 pay periods in a year (bi-weekly paychecks), we have:
Gross salary per pay period = $67,000 / 26 = $2,576.92
Therefore, the DON's gross salary per pay period is $2,576.92.
b. To compute the net salary per pay period, we need to take into account federal and state taxes, Social Security, and Medicare deductions, as well as any other pre-tax or post-tax deductions, such as health insurance premiums or retirement contributions.
Assuming a standard tax withholding rate of 20%, Social Security and Medicare deductions of 7.65%, and health insurance premiums of $200 per pay period, we can calculate the net salary per pay period as follows:
Net salary per pay period = Gross salary per pay period - Taxes - Social Security and Medicare - Health insurance
Net salary per pay period = $2,576.92 - ($2,576.92 x 0.20) - ($2,576.92 x 0.0765) - $200
Net salary per pay period = $2,576.92 - $515.38 - $197.02 - $200
Net salary per pay period = $1,664.52
Therefore, the DON's net salary per pay period is $1,664.52.
Question
The average daily balance of a credit card for the month of December was $5600, and the unpaid balance at the end of the
month was $6900. If the monthly interest rate is 2.5% of the average daily balance, what is the total balance on the next
billing date January 1? Round your answer to the nearest cent. Do not use commas to separate numbers or dollar signs. For
example, $5, 678.00 should be entered as 5678.00.
Answers
Answer:
The first step is to determine the amount of interest charged for the month of December based on the average daily balance:
Average Daily Balance = $5600
Monthly Interest Rate = 2.5%
Interest Charged for December = Average Daily Balance * Monthly Interest Rate * Number of Days in December
Number of days in December is 31.
Interest Charged for December = $5600 * 0.025 * 31 = $4340.00
The total balance on the credit card on January 1 will be the sum of the unpaid balance at the end of December and the interest charged for December:
Total Balance on January 1 = Unpaid Balance at End of December + Interest Charged for December
Total Balance on January 1 = $6900 + $4340.00
Total Balance on January 1 = $11240.00
Rounded to the nearest cent, the total balance on the next billing date January 1 is $11,240.00.
The nearest cent, the total balance on the next billing date, January 1, is $12640.00.
To calculate the total balance on the next billing date, we need to consider the average daily balance for December, the unpaid balance at the end of December, and the monthly interest rate.
The monthly interest rate is 2.5% of the average daily balance. Let's calculate the interest charged for the month of December:
Interest charged = (2.5/100) * Average daily balance
= (2.5/100) * $5600
= $140
Next, let's calculate the total balance on the next billing date, January 1:
Total balance = Average daily balance + Interest charged + Unpaid balance
= $5600 + $140 + $6900
= $12640
Rounded to the nearest cent, the total balance on the next billing date, January 1, is $12640.00.
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How many times more powerful were the seismic waves of the Belair earthquake than standard seismic waves?
Answers
The seismic waves from the earthquake in Caracas were 12589.25 times stronger than typical seismic waves.
How do seismic waves work?Seismic waves are acoustic energy waves that passes through the Earth. It can be brought on by massive landslides, volcanic eruptions, magma movement, earthquakes, and artificial explosions that discharge a lot of low-frequency acoustic energy.
By using formula for, M= log(w/w_0), we can find:
10^M= w/w_0, it means 10^M.w_0, = w
but M=4.1, so 10^4.1 = 12589.25
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find the exact value of x.
Answers
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{6}{x}=\cfrac{x}{8}\implies 48=x^2\implies \sqrt{48}=x\implies \sqrt{4^2\cdot 3}=x\implies 4\sqrt{3}=x[/tex]
Answer this question please
Answers
Shape P could have been transformed using a translation, rotation, reflection or a combination of these transformations.
What is tranformations?Transformation in maths is a way of changing the position, size or shape of a given object. It involves moving the object from one position to another. This can be done using a combination of translation, rotation, reflection and enlargement.
A translation is when a shape is moved in a straight line and all points are moved the same distance in the same direction. A rotation is when a shape is rotated around a fixed point and all points are moved the same angle. A reflection is when a shape is flipped over a line and all points are reversed on the other side of the line.
In the case of Shape P, since one point was invariant, the transformation must have been either a translation, rotation or a combination of both. A translation would have been impossible as all points are moved the same amount and direction, hence, the invariant point would have been moved. A rotation is possible as all points are moved the same angle, and the angle of rotation could be adjusted to keep the invariant point in the same place. A combination of both of these transformations could also have been used to keep one point invariant.
Overall, Shape P could have been transformed using a translation, rotation, reflection or a combination of these transformations. In this case, the transformation must have been either rotation or a combination of both translation and rotation. The angle of rotation or the combination of translation and rotation would have been adjusted to keep the invariant point in the same place.
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Complete the ratio table.
8
40
48
56
3
15
18
36
Answers
Answer:
52 : 39 56 : 42 60 : 45
64 : 48 68 : 51
Step-by-step explanation:
The list below shows the scores for each of Sarah’s homework assignments.
100, 95, 47, 83, 87, 89, 89
If the score 47 is removed from the list, which of the following statements is true
Answers
The correct statement regarding the mean of the data-set when the score of 47 is removed is given as follows:
The mean increased by about 6.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
The observations for this problem are given as follows:
100, 95, 47, 83, 87, 89, 89.
There are 7 observations, and their sum is given as follows:
100 + 95 + 47 + 83 + 87 + 89 + 89 = 590.
Hence the mean is of:
590/7 = 84.29.
Removing the observation of 47, there will be 6 observations, with a sum of 590 - 47 = 543, hence the mean is of:
543/6 = 90.5.
Meaning that the mean increases by about 6.
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Alisha has some number cards that each have a whole number on them. If she chooses a card at random, the probability that the number on it is even is. Work out the ratio of even cards to odd cards that Alisha has. Give your answer in its simplest form.
Answers
The ratio is [tex]\frac{3}{2}[/tex] in its simplest form.
EquationIf the probability of choosing an even card is [tex]\frac{3}{5}[/tex] , then the probability of choosing an odd card is 1- [tex]\frac{3}{5}[/tex] = [tex]\frac{3}{2}[/tex].
Let e be the number of even cards Alisha has, and let o be the number of odd cards. Then, we have:
[tex]\frac{e}{e+0}[/tex]
which simplifies to:
5e=3(e+o)
Expanding the right side gives:
5e=3e+3o
Simplifying further gives:
2e=3o
Dividing both sides by 2 gives:
e= [tex]\frac{3}{2}[/tex]o
[tex]\frac{3}{2}[/tex]
What is probablity?Probability is a branch of mathematics that deals with the study of random events or experiments. It involves the analysis of the likelihood or chance of an event occurring, usually expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event is certain to occur.
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I NEED HELP QUICK FILE ATTACHED
Answers
After answering the presented question, we can conclude that equation Therefore, the solution to the given system of equations is (x, y) = (2, 2).
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by the equal symbol '='. 2x - 5 Equals 13, for example. Expressions include 2x-5 and 13. The character '=' joins the two expressions. A mathematical formula with two algebraic expressions on either side of an equal sign (=) is known as an equation. It demonstrates the relationship of equivalence between the left and right formulas. In every formula, LHS = RHS (left side = right side).
[tex]4x + y = 10 ...(1)\\y = 2x - 2 ...(2)\\y = 2x - 2 ...(2)\\y + 2 = 2x ...(2)\\x = (y+2)/2 ...(3)\\4x + y = 10 ...(1)\\4[(y+2)/2] + y = 10 \\[/tex]
[tex]2(y+2) + y = 10 \\3y + 4 = 10\\3y = 6\\y = 2 \\y = 2x - 2 ...(2)\\2 = 2x - 2 \\4 = 2x \\x = 2 \\[/tex]
Therefore, the solution to the given system of equations is (x, y) = (2, 2).
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[tex]|x| - 5 |x + 6 = 0[/tex]
Where [x] the greatest integer function then the solution for X is
Answers
The greatest integer value for x is -8
How to determine the greatest integer value for xFrom the question, we have the following parameters that can be used in our computation:
|x| - 5|x + 6 = 0
Express properly
So, we have
|x| - 5|x + 6| = 0
This gives
|x| = 5|x + 6|
When both sides of the equation are compared, we have
x = 5x + 30
So, we have
4x = -30
Divide by 4
x = -7.5
Approximate to an integer
x = -8
Hence, the value of x is -8
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A student is trying to solve the system of two equations given below:
Equation P: y + z = 6
Equation Q: 5y + 9z = 1
Which of the following is a possible step used in eliminating the y-term?
Please help
Answers
Answer:
Leaving equation Q the same, multiply both sides of equation P by -5.
(y + z = 6) × -5
What is the missing measure of the missing angle 59 86?
Answers
The missing measure of the angle on the triangle will be 45°.
How to calculate the angleAn angle is the measure of the space between two intersecting lines or planes. It is usually measured in degrees or radians. A degree is a unit of measurement for angles, where a full circle is 360 degrees, while a radian is a unit of measurement for angles defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (more than 90 degrees and less than 180 degrees), or straight (exactly 180 degrees).
The missing angle will be:
= 180° - (76° + 59°)
= 180° - 145°
= 35°
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need help with This Math
Answers
The number of intersection points is (a) 1 point or 2 points.
How to determine the number of intersection pointsGiven that
Line AB and circle P lie on the same plane.
And, we have
AP = 6 mm
BP = 8 mm
The intersection points can be 0, 1, or 2.
Since the radius of circle P is 6mm, any intersection point must also be 6mm away from P.
Next, we have the following test cases
If line AB intersects circle P at one point, then that point must be on the circle centered at P and have a radius of 6mm. If line AB intersects circle P at two points, then both points must be on the same circle centered at P with a radius of 6mm.Hence, the answer is (A) 1 point or 2 points.
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solve the system of equations graphed on the coordinate axes below
Answers
Answer (0,0)
Step-by-step explanation:
Method 1)
look at the graph to see where the two lines intersect, which is at (0,0).
Method 2)
[tex]\frac{4}{3} x[/tex] = -2x ............................set the 2 equations equal
[tex]\frac{10}{3} x[/tex] = 0.................................set the equation to 0 (by adding 2x to both sides)
x = 0.....................................solve for x (by dividing both sides by [tex]\frac{10}{3}[/tex]
Note: you can use y = [tex]\frac{4}{3} x[/tex] OR y = -2x
y= -2x
y = -2(0)...............................plug in the x
y = 0.....................................solve
(x,y)
(0,0)......................................plug in x and y value
Brainliest!! Pls help!! Find the equation of a line parallel to y = -x+6 that passes through the point (-5,-9).
Answers
Question 3 of Ariel sings a song in 5.92 minutes. Carlos sings the same song in 7.73 minutes. How much longer does it take Carlos to sing the song? Estimate by rounding to the nearest whole number. If the answer is not a whole number, enter it as a decimal. Do not include units in your answer.
Answers
It takes Carlos 2 minutes longer than Ariel to sing the song.
Estimating the difference in the time takenTo find out how much longer it takes Carlos to sing the song, we need to find the difference between the time it takes Ariel and Carlos to sing the song.
Time taken by Ariel = 5.92 minutes
Time taken by Carlos = 7.73 minutes
So, we have
Difference = 7.73 - 5.92 = 1.81 minutes
Rounding to the nearest whole number, we get:
Difference = 2 minutes (rounded to the nearest whole number)
Therefore, the time taken is approximately 2 minutes longer
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Can you help me solve this
Answers
We can see that linear function B has a greater rate of change than function A.
Which function has the greater rate of change?The general linear function is written as:
y = a*x +b
Where a is the rate of change.
If we know two points on the linear function, (x₁,y₁) and (x₂, y₂), then the rate of change is given by:
a = (y₂ -y₁)/(x₂ - x₁)
For function A we use the first two on the table (1, 5) and (2, 7)
a = (7 - 5)/(2 - 1) = 2
For the function B we willuse (1, 1) and (2, 4), then:
a = (4 - 1)/(2 - 1) = 3
Function B has a greater rate of change.
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A car is traveling at a steady speed. It travels 1 1/2 miles in 2 1/4 minutes. How far will it travel in 34 minutes ? In 1 hour ?
Answers
let's firstly convert the mixed fractions to improper fractions.
[tex]\stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}}~\hfill \stackrel{mixed}{2\frac{1}{4}} \implies \cfrac{2\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{ccll} miles&minutes\\ \cline{1-2} \frac{3}{2}&\frac{9}{4}\\[1em] x&34 \end{array}\implies \cfrac{~~ \frac{3 }{2 } ~~}{x}~~ = ~~\cfrac{~~ \frac{9}{ 4} ~~}{34}\implies \cfrac{3}{2x}=\cfrac{9}{(4)(34)}\implies \cfrac{3}{2x}=\cfrac{9}{136} \\\\\\ (3)(136)=18x\implies \cfrac{(3)(136)}{18}=x\implies \cfrac{68}{3}\implies \stackrel{ miles }{x=22\frac{2}{3}}[/tex]
Step-by-step explanation:
11/2 is equivalent to 21/4 is
equivalent to 9/4
The unit rate will be:
3/2 miles= x
9/4 min 1 min
Now use this unit to find how far the car will travel in 26 minutes
2/3 mile •26 min= 52/3 miles or 17 and 1/3
miles
1 min
Since 1 hour is equal to 60 minutes, we can
multiply the unit rate by 60 to find the distance traveled in 1 hour.
2/3 mile• 60 min = 120/3 = 40 miles
traveled in 1 hour
1 min
helppp pls show work
Answers
4) Where the hypotenuse is 100 and the adjacent side is x and α = 45°, the x = 70.71
5) Where the opposite side is 100, and α = 45°, the hypotenuse is 141.42
6) Where the hypotenuse is 88 and β = 45°, x (the opposite side) is 62.23
7) Therefore, the length of each leg of the 45°-45°-90° triangle with a hypotenuse length of 26 is approximately 18.33 units.
8) Therefore, the approximate length of the hypotenuse of the 45°-45°-90° triangle with a leg length of 50 centimeters is 70.71cm.
9) Where the Base is 11 and α = 30°, Hypothenus (x) = 22 and Opposite (y) = 19.05
10) Where the hypotenuse is 8√3, and β = 45°, opposite (x) = 11.99 and adjacent (y) = 6.93
11) Where the adjacent is 5√3 and α = 30°, opposite (x) = 14.99 and Hypothenus (y) = 17.32
12) where hypotenuse = 30, and the β = 60°, the adjacent (x) = 15 and the opposite (y) = 25.98
13) where opposite is 36.372 and the β = 60°, the hypothenus (x) = 41.99 and the adjacent (y) = 20.99
14) where the hypotenuse is 90.316 and β = 60°, the opposite (x) = 78.22 and the adjacent (y) is 45.16
15) An equilateral triangle has an altitude length of 27 feet, and the length of a side is 15.588 feet.
16) the length of a side of the equilateral triangle is 22 feet.
What is the explanation for the above results?The basic rule applied here (from 4-14) is the principle of SOHCAHTOA.
The principle of SOHCAHTOA is a mnemonic device used to remember the three basic trigonometric ratios in a right triangle:
Sine (sin) = opposite/hypotenuse
Cosine (cos) = adjacent/hypotenuse
Tangent (tan) = opposite/adjacent
In SOHCAHTOA, each letter represents one of the ratios:
"S" stands for sine, which relates the opposite side to the hypotenuse.
"O" stands for opposite, which is the side opposite to the angle of interest in the right triangle.
"H" stands for the hypotenuse, which is the longest side of the right triangle and is opposite to the right angle.
"C" stands for cosine, which relates the adjacent side to the hypotenuse.
"A" stands for adjacent, which is the side adjacent to the angle of interest in the right triangle.
"T" stands for the tangent, which relates the opposite side to the adjacent side.
By using SOHCAHTOA, we can quickly and easily find any of the three basic trigonometric ratios, given two sides of a right triangle and an angle.
In 4) This is an example of a right triangle, where one of the angles is 90 degrees. In a right triangle, the side opposite the 90-degree angle is called the hypotenuse, while the other two sides are called the adjacent and opposite sides.
In this case, the hypotenuse is given as 100 units, and the angle between the hypotenuse and adjacent side (x) is given as 45 degrees. To find the length of the adjacent side, we can use the trigonometric function cosine, which relates the adjacent side to the hypotenuse and the angle between them:
cos(α) = adjacent/hypotenuse
Substituting the given values, we get:
cos(45°) = x/100
Simplifying, we get:
x = 100 * cos(45°)
Using the identity cos(45°) = √2/2, we get:
x = 100 * √2/2
Simplifying further, we get:
x = 50√2
To find the approximate value of x in decimal form, we can use a calculator or approximate the value of √2 as 1.414. Then, we get:
x ≈ 50 * 1.414 = 70.71
Therefore, x is approximately equal to 70.71 units.
In 8) Where we needed to find the length of the hypotenuse of a 45°-45°-90° triangle with a leg length of 50 centimeters.
In a 45°-45°-90° triangle, the two legs are congruent, and the length of the hypotenuse is √2 times the length of each leg.
Therefore, if one leg of the triangle has a length of 50 centimeters, then the other leg also has a length of 50 centimeters, and the hypotenuse has a length of:
hypotenuse length = leg length x √2
hypotenuse length = 50 cm x √2
To simplify the expression, we can multiply the numerator and denominator of the fraction by √2:
hypotenuse length = 50 cm x √2 x √2 ÷ √2
hypotenuse length = 50 cm x 2 ÷ √2
hypotenuse length = 100 cm ÷ √2
To rationalize the denominator, we can multiply the numerator and denominator of the fraction by √2:
hypotenuse length = 100 cm ÷ √2 x √2 ÷ √2
hypotenuse length = 100√2 ÷ 2
hypotenuse length = 50√2
Therefore, the length of the hypotenuse of the 45°-45°-90° triangle with a leg length of 50 centimeters is 50√2 centimeters or 70.71cm.
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Bruce won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Bruce a bucket of fish to divide evenly among 5 dolphins. Each dolphin gets 4 fish
Answers
The equation which can be use to find the number of fish f in the bucket before Brooke feeds the dolphins is [tex]4 * 3 = f[/tex].
Which equation can you use to find the number of fish?An equation refers to a mathematical statement that is made up of two expressions connected by an equal sign.
Let f be the number of fish in the bucket before Brooke feeds the dolphins. The equation that can be used to find the value of f is: [tex]4 * 3 = f[/tex]
This equation represents the fact that there are 4 dolphins and each dolphin receives 3 fish, so the total number of fish in the bucket must be equal to 4 times 3. Solving this equation, we get:
f = 12
Therefore, there were 12 fish in the bucket before Brooke fed the dolphins.
Full question "Brooke won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Brooke a bucket of fish to divide evenly among 4 dolphins. Each dolphin gets 3 fish. Which equation can you use to find the number of fish f in the bucket before Brooke feeds the dolphins"
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The volume of a cube is 64 cubic meters. Find the length of an edge.
FIND THE LENGTH IN METERS!!!!
Answers
Answer:
Below
Step-by-step explanation:
Volume = L X W X H For a CUBE, all of the dimesions L, W, and H are the same ...so this becomes volume =L x L x L = L^3
Volume = L^3
64 = L^3 take the cube root of both sides of the equation:
L = 4 meters
Which of the following would most likely reduce the monthly premium a policyholder pays for automobile insurance?
1. Buying a minivan
II. Maintaining an accident-free driving record over time
III. Paying a speeding ticket
IV. Taking a job with a longer commute by car
O I, II
O III, IV
O II, III
OI, IV
Answers
The factors that would most likely reduce the monthly premium a policyholder who pays for automobile insurance is -
Option A: I, II
What is insurance?
Insurance is a legal agreement, evidenced by a policy, under which a policyholder receives financial security or compensation from an insurance provider against losses. In order to make payments to the insured more manageable, the company pools the risks of its clients.
The factors that can affect the monthly premium a policyholder pays for automobile insurance include the type of vehicle, driving record, and other personal factors.
Out of the options given, buying a minivan and maintaining an accident-free driving record over time would most likely reduce the monthly premium a policyholder pays for automobile insurance.
Minivans are generally considered safer and less expensive to repair than other types of vehicles, and having an accident-free driving record indicates that the policyholder is a lower risk for filing a claim in the future.
Paying a speeding ticket and taking a job with a longer commute by car are unlikely to reduce the monthly premium a policyholder pays for automobile insurance.
Paying a speeding ticket indicates a violation of traffic laws and a higher risk for accidents, and a longer commute by car increases the risk of accidents and damages.
Therefore, the answer is buying a minivan and maintaining an accident-free driving record over time.
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Answer: option a (I, II)
Step-by-step explanation: Person above is correct!