Answer:
To solve this problem we can construct an linear algebraic expression for each person, principally denoted as:
where
y :is our dependent variable (which is a function of )
x :is our independent variable
a :is the slope
c :is the y-intercept constant value (if any present)
Part A: Write a system of equations to represent the situation. Let x = hours and y = widgets.
Tamara
Has already made 20 widgets and produces at a rate of 8 widgets per hour thus here c=20 and a=8 , so Tamara's equation reads: yT=8x+20
Jason
Has not produced any widgets yet and produces at a rate of 12 widgets per hour thus here c=0 and a=12 , so Jason's equation reads:yj=12x
So the system of equations will be
yT=8x+20
yj=12x
Part B: How much time does it take for Tamara and Jason to produce the same number of widgets?
Since we want to find the amount of time (i.e. the value of x ) it takes for both of them to produce the same number of widgets we can just equate the two equations ans solve for x as follow:
yT=yj
8x+20=12x
8x-12x=-20
-4x=-20
x=5
So it takes them 5 hours to produce the same amount of widgets
Part C: How many widgets will Tamara and Jason have produced?
Now we can simply plug in the value of x=5 in any of the two equations (i.e. either for Tamara or Jason) to find the number of widgets produced.
yT=8(5)+20=40+20=60
So in a time-space of 5 hours Each will have produced 60 widgets and in total will be 60+60 = 120 widgets.
Step-by-step explanation:
mrk me brainliest i worked really hard on this plzzzzzzzzzzzzzzz
How do you solve complex fraction equations?
To solve complex fractions there are two methods -
1 - Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator and then simplify further if necessary.
2 - Multiply the numerator and denominator of the overall complex fractions and then simplify further if necessary.
What is a complex fraction?
A rational expression with a fraction in the numerator, denominator, or both is referred to as a complex fraction.
There are two ways to solve a complex fraction -
Method 1 : Take an example - (1/3-1/4)/(1/8+1/2)
Step 1 - If necessary, combine the denominator and numerator into a single fraction.
Add the numerator -
=1/3-1/4
=(4-3)/12
=1/12
Add the denominator -
=1/8+1/2
=(1+4)/8
=5/8
Combine back to form a complex fraction -
=(1/12)/(5/8)
Step 2: Multiply the numerator by the denominator's reciprocal, then divide the result by the denominator.
Step 3: Simplify the rational expression if necessary.
=(1/12)×(8/5)
=8/60
=2/15
Method 2: Take an example - [(2x+1)/(x^2-25)]/[(4x^2-1)/(x-5)]
Step 1 - Divide the LCD of the smaller fractions by the numerator and denominator of the total complex fractions.
(x^2-25)=(x+5)(x-5)
The denominator of the denominator’s fraction has the following factor -
(x-5)
Using the highest exponent and combining all the other factors, we arrive at the LCD shown below for all the little fractions -
(x+5)(x-5)
By multiplying the LCD by the numerator and denominator -
=[{(2x+1)/(x+5)(x-5)}×(x+5)(x-5)]/[{(2x+1)(2x-1)/(x-5)}×(x+5)(x-5)]
=(2x+1)/(2x+1)(2x-1)(x+5)
Step 2 - Simplify the rational expression if necessary.
=(2x+1)/(2x+1)(2x-1)(x+5)
=1/(2x-1)(x+5)
Therefore, there are two methods to solve complex fractions.
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Please help I don’t understand this
9514 1404 393
Answer:
WV = 6
Step-by-step explanation:
The hash marks indicate the corresponding lines are the same length. That is, W is the midpoint of YZ, because YW ≅ WZ. Similarly, V is the midpoint of XY, because XV ≅ VY.
Using this information, it can be shown that ∆YWV ~ ∆YZX. This means corresponding sides have the same ratio.
Because YW is half of YZ, WV is half of ZX.
YW/YZ = 1/2 = WV/ZX = WV/12
Multiplying by 12 gives the value of WV:
WV = 12(1/2)
WV = 6
_____
This is a long way to say that the midsegment (WV) is half the length of the base (ZX) of a triangle.
if 0°<0<90° and sin0=12/13, find cos0 using trigonometric identities.
• 12/5
• 5/12
• 12/13
• 5/13
here's the solution,
we know :
[tex] \sin( \theta) = \dfrac{perpendicular}{hypotenuse} [/tex]
So,
[tex] \dfrac{p}{h} = \dfrac{12}{13} [/tex]
so.. let the perpendicular be 12x and hypotenuse be 13x
now,
by applying pythagoras theorem,
[tex]b {}^{2} = h {}^{2} - p {}^{2} [/tex]where,
b = base h = hypotenuse p = perpendicularSo,
[tex]b {}^{2} = ({13x})^{2} - ({12x})^{2} [/tex][tex] b {}^{2} = 169x {}^{2} - 144x {}^{2} [/tex][tex] {b}^{2} = 25x {}^{2} [/tex][tex]b = 5x[/tex]so,
[tex] \cos( \theta) = \dfrac{b}{h} [/tex][tex] \cos( \theta) = \dfrac{5x}{13x} [/tex][tex] \cos( \theta) = \dfrac{5}{13} [/tex]hope it helps !!
What is an equation of the line that passes through the points (-3, -5) and (-3, -8)?
This is an undefined problem
Answer:
x = -3
Step-by-step explanation:
Hi there!
Typically, linear equations would be organized in slope-intercept form: y=mx+b where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis).
However, notice how the two x-coordinates of the given points are the same. They're both -3. This means that this is a vertical line, and vertical lines are organized in this equation: x=d where d is the x-intercept (the value of x when the line crosses the x-axis).
We know that the x-intercept is -3, since all the x-coordinates of the points that a vertical line passes through are the same. Therefore, the equation of this line is x=-3.
I hope this helps!
A circular mirror is surrounded by a square metal frame. The radius of the mirror is 3x. The side length of the metal frame is 15x. What is the area of the metal frame? (Type your answer in factored form. Type an exact answer in terms of pi.
The area of the frame is __ square units
The area of the frame is 196.73 x²
What is area ?
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2. The area of a form is computed by dividing its length by its breadth.
(15x)^2 = 225x^2
Area of the frame
= π (3x)²
= 28.27 x²
Metal area surrounding the frame
225 x² - 28.27 x²
= 196.73 x²
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A granola recipe calls for 3 cups of oats, 1 cup of almends. 1 cup of pecans, and 1 cup of dried fruit. What is the ratio of fruit to eats? Yolanda says that for every 2 cups of nuts, there are 2 cups of fruit. Explain why her answer is incorrect and give the correct ratio of nuts to fruit. Explain your answer.
The ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a granola recipe calls for 3 cups of oats, 1 cup of almonds. 1 cup of pecans, and 1 cup of dried fruit
The ratio of nuts to fruits is -
r = (3 oat cups + 1 almond cup + 1 pecan cup)/(1 dried fruit cup)
r = 5/1
5 : 1
For every 5 cups of nuts, there is 1 cup of dried fruit cup.
Therefore, the ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.
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Find the value of c in the triangle shown below.
9
8
Choose 1 answer:
Help me please and thank you!
Answer:
-4/3
Step-by-step explanation:
-2 - 1 is -3
6-2 is 4
There is a mixed group of 100 students and/or teachers; 45 are boys, 55 are girls, and 23 are female teachers. People are selected at random. What is the probability that the person chosen is either a boy or a teacher?
Answer:
68%
Step-by-step explanation:
what is 5 2/3 x 3/4 equal?
Answer: 4 1/4
Step-by-step explanation: Decimal= 4.25
Answer:
Exact form: 17/4
Decimal Form: 4.25
Mixed number form: 4 1/4
Bob bought 40 gumballs from a quarter machine. The number of each flavor he got is shown in the table.
- grape amount 4
- cherry amount 12
- Cola amount 16
- Orange amount 8
If there are 140 gumballs left in the machine, what is a good prediction for the number of cola flavored gumballs left?
Answer:
56 Cola-flavored gumballs remaining.
Step-by-step explanation:
There are 180 gumballs. Bob purchased 40 gumballs, which leaves 140 gumballs remaining.
There are four flavors. This is the chance (shown as a percentage) of each flavor Bob recieved:
║GR: 4 ⇒ 10%
║CH: 12 ⇒ 30%
║CO: 16 ⇒ 40%
║OR: 8 ⇒ 20%
So, how can we predict the number of Cola flavored gumballs remaining?
[There is a 40% chance of getting a Cola-flavored gumball from the machine. If we find 40% of 140, we can predict that is close to the number of Cola gumballs left in the machine]
║0.40 ⋅ 140 = 56
40% of 140 is 56, so we can predict there are 56 Cola-flavored gumballs remaining.
The area of the base of the cone is 9π^2 in and a height of 6 in. What is the volume of the cone, in terms of π? Need answer ASAP!
Answer: 18pi^2
Step-by-step explanation:
Volume of cone formula = 1/3 x base area x height
so 1/3 x 9pi^2 x 6
= 18pi^2
Solve for the value of x.
Answer:
x = 3
Step-by-step explanation:
x + x + x could also be written as 3x, and count the number of "1's" given on both sides:
3x + 4 = 13
=> subtract 4 on both sides of "="
3x = 9
=> Divide by 3 on both sides of "="
x = 3
Hope this helps!
Answer:
x=3
Step-by-step explanation:
I believe the answer would be x is equal to 3.
If you first create the equation you get 3x*4= 13
There are 3 green 'x' so that is 3x. The four orange boxes can be represented as 4, and the 13 orange boxes can be represented as 13.
Then, you solve the equation.
3x * 4 =13
Subtract 4 from both sides.
3x= 9
And simplify.
x=3.
I hope this helps! (:
what is the volume of cylinder when the radius is 3 and height is 13.33
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=13.33 \end{cases}\implies V=\pi (3)^2(13.33)\implies V\approx 376.90[/tex]
you do not have to exsplain
Answer:
V=87.92
Step-by-step explanation:
v=bh,V=3.14*2*2*7
Jeri had 1 ¾ pounds of gummi worms, which she shared equally with her best friend. How many pounds of gummi worms did they each get? PLZ HELP
They have 0.875 pounds of gummy each
Just divide by 2
Describe the likehood of the event given its probability . you make a free throw 70 percent of the time
Answer:
Yes. 70% is a good percentile, most people understand the workings of a free throw (where you stand on the line, how to place your feet, how to shoot) and standing still gives you an advantage. For the people who don’t understand the workings, they are apart of that 30%.
Write answer in scientific notation
Answer:
5 x 10^7
Step-by-step explanation:
(5 x 10^4)·(1 x 10³) = 5 x 10^7 = 50 million
Aliyah had $28 to spend on six pencils.After buying them she had $10. How much did each pencil cost?
Answer:
$3
Step-by-step explanation:
28-10=18
18/6=3
When 10 is substacted from the square of a number the result is 3 times the number find the positive solution
Answer: So the positive solution is:
ANSWER: X = 5
(x = 5 ), (x = - 2 )
Step-by-step explanation:
when 10 is subtracted from the square of a number the result is 3 times the number.
Find the positive solution.
Let: x = number
Let x^2 = square of a number.
x^2 - 10x = 3x transpose
x^2 - 3x - 10 = 0
Apply Factoring: Fractions of 10 are 5 and 2
( - 5)(2) = - 10
- 5 + 2 = - 3
( x - 5 )(x + 2) = 0
x - 5 = 0 x + 2 = 0
x = 5 x = - 2
So the positive solution is:
ANSWER: X = 5
I hope that helps!!!!
The casino game of chuck-a-luck seems quite simple and that it would be a pretty good bet. In this game, three dice are rolled (usually inside a wire cage). You can bet a set amount, let's say $5, on a specific number 1-6. You win the amount of your bet for each appearance of your number on the dice. If the number does not appear, you lose your bet. For example, let's say you bet $5 on the number 3. If it appears on exactly one die, you win $5 (and keep your bet) with probability 75/216. If it appears on exactly two dice, you win $10 (and keep your bet) with probability 15/216. If it appears on all three dice, you win $15 (and keep your bet) with probability 1/216. If it appears on none of the dice, you lose your original $5 bet. Construct the probability distribution for chuck-a-luck and determine your expected winnings on a $5 bet.
The expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.
Therefore, the game is not a good bet, as you are expected to lose money in the long run.
What is the probability distribution?
A probability distribution is a mathematical function that describes the probability of different possible values of a variable.
The probability of winning on a $5 bet on a specific number in chuck-a-luck is determined by the number of ways that the number can appear on the three dice and the total number of possible outcomes.
If the number appears on exactly one die, there are 3 ways that this can happen out of a total of 6^3 = 216 possible outcomes, giving a probability of 3/216 or 1/72.
If the number appears on exactly two dice, there are 3 ways to choose the two dice on which it appears, and 3 ways to choose the third die, giving a total of 33 = 9 ways out of 216 possible outcomes, giving a probability of 9/216 or 1/24.
If the number appears on all three dice, there is only 1 way this can happen out of 216 possible outcomes, giving a probability of 1/216.
If it appears on none of the dice, there are (543) ways this can happen, giving a probability of (54*3)/216 = 20/216.
We can use this information to construct the probability distribution for chuck-a-luck:
x P(x)
-5 (losing the bet) 20/216
5 (winning the bet for one appearance) 1/72
10 (winning the bet for two appearances) 1/24
15 (winning the bet for three appearances) 1/216
To find the expected winnings on a $5 bet, we can multiply the value of each outcome by its corresponding probability, and sum the results:
E(X) = (-5)(20/216) + (5)(1/72) + (10)(1/24) + (15)(1/216)
E(X) = -5/43.2 + 5/72 + 5/12 + 15/216
E(X) = -0.1157
Hence, the expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.
Therefore, the game is not a good bet, as you are expected to lose money in the long run.
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i need help with number seven with a full explanation please
The value of x would be 32.
What are a congruent quadrilaterals?
In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.
In the given figure PQRS ~ WXYZ
x = YZ
x = 32.
Hence, the value of x would be 32.
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By analyzing the figure, The value of x would be 32.
What are a congruent quadrilaterals?In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.
In the given figure PQRS ~ WXYZ
x = YZ
x = 32.
Hence, the value of x would be 32.
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Karen drew a triangle The longest side of Karen's triangle measures 8 inches What must be true about the lengths in inches a and b of the two shorter sides of Karen'sHow many triangles can be drawn with side lengths 3, 5, and 9
The 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.
What is hypotenuse in a Triangle?n a triangle, the longest side (the hypotenuse) is opposite the largest angle, and the other two sides are opposite the smaller angles. According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the length of the third side. So, if the longest side of Karen's triangle measures 8 inches, it means that the sum of a and b (the two shorter sides) must be greater than 8 inches. Therefore [tex]a+b > 8 inches[/tex].
For the second part of your question, only one triangle can be drawn with side lengths 3, 5, and 9. The three numbers 3, 5, and 9 form a Pythagorean triple, meaning they can be used as the lengths of the sides of a right triangle. Since the longest side (the hypotenuse) must be greater than the other two sides, the 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.
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Which of the following will cause a logical error if you are attempting to compare x to 5?
Answers:
a. if (x >= 5)
b. if (x = 5)
c. if (x == 5)
d. if (x <= 5)
Logical Error: In computer programming language, a logic error is a bug or in a program or code that causes it to operate incorrectly, but not to terminate abnormally (or crash).
A logic error developed unintended or undesired output or other behavior, although it may not immediately be recognized as such.
For example, assigning a value to the wrong variable may cause a many of unexpected program errors.
These errors can be programmer mistakes or sometimes machine less memory to load the code.
if(x>=5) {
// program
}
else if(x==5) {
//program
}
else(x<=5) {
//program
}
they all do not give any error.
x=5 gave an error because it is value assigning to 5.
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Solve the equation for all values of x by completing the square,
x^2 + 2x = 35
Answer:
x = 5
Because, if you substitute 5 for x you will get 35.
5^2 + 2*5= 25+10, or 35
Step-by-step explanation:
I need your help! I'm struggling and need help solving. If you can include an explanation that would be great!
Answer:
Answer choice A
Step-by-step explanation:
It's nice to know which way the equation is going, so graphing it helps (if you can, use Desmos!)
Since the equation is facing up (BOTH SIDES UP) as x approaches infinity & negative infinity, f(x) is always going to be increasing so it is always going towards infinity.
ORIGINAL ANSWERS PLEASE
A student's course grade is related to class attendance. The grade can be modeled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. For a student who was in attendance for 75 days and has a grade of 82%, find and interpret the residual.
The residual of the given situation is 0.8
What is residual of a function?The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y.
Given that, The grade can be modelled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. We are asked to find residual if student who was in attendance for 75 days and has a grade of 82%,
Finding the actual value,
y = 0.66 × 75 + 33.3
y = 82.8
The predicted value = 82
Residual = actual y value − predicted y value
Therefore,
Residual = 82.8-82 = 0.8
Therefore, y = 0.8
Hence, the residual of the given situation is 0.8
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Triangle ABC is similar to triangle DFE. What scale factor is required to dilate triangle DFE so that its image, D′F′E′, is congruent to triangle ABC?
Answer:
1/4
Step-by-step explanation:
Solve the system.
6x - y = -15
x+2y = 17
Enter your answer as a coordinate pair in the blank.
The coordinate pair of the given system is (-1,9)
What are coordinate pairs?An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Multiply the first equation by 2 and add the equation 2(6x - y) = 2(-15)
Add the new equation 12x - 2y = -30 to the second equation
12x - 2y = -30, x+2y = 17, add the two equations to eliminate y
13x = -13
x = -1
Substitute -1 back into the equation x+2y = 17.
-1 + 2y = 17
2y = 18
y = 9
So the solution of the system is x = -1, y = 9
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HELPPPPPPPPPPPPPPPPP
Answer:
1/2 + 1/3 = 3/6 + 2/6 = 5/6
5/6 roughly equals to 0.8
The answer is C
Which of the following best estmates the sum: 1/2 + 1/3
Answer: C) 0.8