The system of inequalities that models the situation is given as follows:
x + y ≥ 85.20(x + y) ≥ 1000.x ≥ 0.y ≥ 0.Which system of inequalities models the situation?Before we build the inequalities, we have to consider that the variables of the system are given as follows:
Variable x: Number of hours worked by Jeremy.Variable y: Number of hours worked by his dad.Jeremy and his dad worked at least 85 combined hours last week, hence the first inequality is:
x + y ≥ 85.
They collected a total of more than $1000 by charging $20 per hour, hence the second inequality is:
20x + 20y ≥ 1000.
20(x + y) ≥ 1000.
The minimum number of hours that each can work is of 0, that is, they cannot work a negative number of hours, hence the constraints are:
x ≥ 0.y ≥ 0.What is the missing information?The problem is incomplete, and it asks for the system of inequalities that models the situation.
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one out of every 9 light bulbs is defective. What constant of proportionality relates defective bulbs to total bulbs?
the constant of proportionality that relates defective bulbs to total bulbs is 1 / 9.
We are given that 1 bulb out of every 9 bulbs is defective.
So, this means that if there is a total of 9 bulbs, then 1 bulb in it will be defective.
Let us assume:
Total bulbs = 9
So, this implies that:
Defective bulbs = 1
Constant of proportionality = Defective bulbs / Total bulbs.
Substituting the values in this, we get that:
Constant of proportionality = 1 / 9
Therefore, we get that, the constant of proportionality that relates defective bulbs to total bulbs is 1 / 9.
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HELP PLEASE!! I’ll give
The square root x^4= x^2
In Exercises 3 and 4, plot the points in a coordinate plane. Then determine whether
AB and CD are congruent.
3. A(-7, 1), B(-4, 1), C(3, -5), D(3, -2)
4. A(1, -1), B(1, 1), C(3, -4), D(5,-4)
AB is congruent to CD as an angle in front of them is congruent so, the sides are also congruent.
What is congruency?If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence. In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.So, all coordinates are shown on the graph as follows:
(Refer to the image attached below)
Now, we can see that in the 4th quadrant, two triangles are formed that are ABE and CDE.
We can see that:Then, we can conclude that:
AB ≅ CD (Angle in front of them is similar so, the sides are also similar)Therefore, AB is congruent to CD as an angle in front of them is congruent so, the sides are also congruent.
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David, Eva and Farooq share a sum of money.
1/6
David gets
- of the money and Eva gets -
1
4
- of the money.
Farooq gets the rest of the money.
David gets £2.50
Work out how much money Farooq gets.
Answer:
Farooq gets £8.75
Step-by-step explanation:
Let's represent the amounts obtained by David, Eva and Farooq as D, E and F to make things simpler. Let M be the total amount of money shared
D = 2.50 and represents 1/6 of the total amount of money(M)
So
M/6 = 2.50
Multiply both sides by 6 => M = 2.50 x 6 = £15
Eva gets 1/4th of this so E = 15 x 1/4 = £3.75
David gets £2.50
Together they get £2.50 + £3.75 = £6.25
The balance goes to Farook so F = 15 - 6.25 = £8.75
Given that [tex]\alpha , \beta[/tex], roots of [tex]4x^{2} - x + 1 = 0[/tex], without finding the value of [tex]\alpha , \beta[/tex] ; evaluate
a. [tex]\beta x^{2} +\alpha x^{2} -\alpha \beta[/tex]
b. [tex]\frac{\alpha }{\beta } + \frac{\beta }{\alpha }[/tex]
Considering the product and the sum of the roots of the quadratic function, the numeric value of the expressions are given as follows:
1. [tex]\beta x^2 + \alpha x^2 - \alpha\beta = \frac{1}{4}(x^2 - 1)[/tex]
2. [tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{7}{4}[/tex]
What are the product and the sum of the roots of the quadratic function?A quadratic function is defined according to the following rule:
y = ax² + bx + c.
In which a and b are the coefficients of the equation.
Supposing that the equation has roots [tex]\alpha[/tex] and [tex]\beta[/tex], the product and the sum of the roots of the quadratic function are given as follows:
[tex]\alpha\beta = \frac{c}{a}[/tex][tex]\alpha + \beta = -\frac{b}{a}[/tex]In this problem, the equation is:
4x² - x + 1.
Hence the coefficients are:
a = 4, b = -1, c = 1.
Then the product and the sum of the roots of the quadratic function are given as follows:
[tex]\alpha\beta = \frac{1}{4}[/tex][tex]\alpha + \beta = \frac{1}{4}[/tex]Then the numeric values for the expressions can be found as follows:
[tex]\beta x^2 + \alpha x^2 - \alpha\beta = x^2(\alpha + \beta) - \alpha\beta = \frac{1}{4}x^2 - \frac{1}{4} = \frac{1}{4}(x^2 - 1)[/tex]
For the second expression:
[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{\alpha^2 + \beta^2}{\alpha\beta} = 4(\alpha^2 + \beta^2)[/tex]
The sum of the squares of the roots is:
[tex]\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta[/tex]
Hence:
[tex]\alpha^2 + \beta^2 = \frac{1}{16} - \frac{1}{2} = -\frac{7}{16}[/tex]
Then:
[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{28}{16} = -\frac{7}{4}[/tex]
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Which choice is the value of three over five raised to the second power?
three over twenty-five
three over ten
nine over twenty-five
six over seven
The value of three over five raised to the second power is nine over twenty-five.
How can the operation be performed?From the question , we were given that three over five raised to the second power which can be interpreted as (3/5)^2 then we can find the square of the given value so that we can arise at the answer.
In this case , (3/5)^2 = 9/25 which implies that the value of the (3/5)^2 is been found and to calculate the value of (3/5)^2, we will need to find the square of 3 which is the numerator as well as the square of 5 which is the denominator.
Therefore, the third option is correct.
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A football team lost 14 yards on their first play then lost another 7 yards on the next play. What integer represents the total change in yards for the two plays?
Answer:
- 21
Step-by-step explanation:
They lost 14 yards, then lost and additional 7 more. You would simply add and make it a negative number due to the key word " lost ".
The equation would look like this: -14 + ( -7 ).
Another way to solve this equation is to multiply. ( + ) x ( - ) = -.
Your equation will the look this this: -14 - 7.
Now you just solve.
Thus, your answer should be - 21.
Hopes the helps!
Have a great day.
Answer: -21
Step-by-step explanation:
.A football team will lose an additional 7 yards if they lost 14 on their first play.
. Since the first play resulted in a loss of 14 yards, the integers that reflect the overall change in yards for the two plays are negative.
.In the second play, we score 14 points but lose 7 yards, which is a loss of 7 points.
.Negative 14 + Negative 7 = Negative 21, which is the overall change in yards.
. Hence, the answer would be -21 yards.
. -21 would be the correct integer that will represent the the total change in yards for the two plays.
The area of the compound shape below is 92 cm². Find the value of x.
Answer:
Step-by-step explanation:
Find the sum of AP 35+29+23+....... as far as the 15th term
Answer: The answer is y=6x.
If 2y+ 5x = 5 and 4y - x = 21, then what is the value of x + y ?
The value of equation (x + y) will be 1.
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The equation are;
2y + 5x = 5 ... (i)
4y - x = 21 ... (ii)
Now, Solve both the equation and find the value of x and y as;
Multiply by 2 in equation (i) we get;
4y + 10x = 10
Subtract above equation by (ii);
4y + 10x - (4y - x) = 21 - 11
11x = 11
x = 1
And, 2y + 5x = 5
Substitute x = 1;
2y + 5x = 5
2y + 5 = 5
2y = 0
y = 0
So, x + y = 1 + 0 = 1
Thus, The value of (x + y) will be 1.
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Hey, could someone help me out on this?
All of the following represent three multiplied by six except:
03x6
03-6
O3(6)
3:6
Help please
Answer:
Except the last one 3:6 because its not multiplied by six but divided. Therefore the correct answer is the last one
Step-by-step explanation:
hope it helps
< A and < B are supplementary angles. If m m < B= (2x+30), then find the measure of < A.
Answer:
m<A = 50°
Step-by-step explanation:
supplementary angles add up to 180°
m<B = 2x + 30
we don't know m<A, so we'll say the value of it is x
2x + 30 + x = 180°
3x + 30 = 180
3x = 150
x = 50
plug this value back in for x
m<B = 2(50) + 30 = 130
m<B = 130°
m<A = x = 50
m<A = 50°
to prove these are supplementary angles, 130 + 50 = 180
The sum of an integer and 2 times the next consecutive integer is -13. Find the value of the greater integer.
Answer:x+x+1=13
2x+1=13
2x=13−1
2x=12
x=
2
12
x=6
x+1=6+1=7
Step-by-step explanation:yes
2. we want to estimate the mean of a population. a random sample of subjects is selected and the sample mean is computed. what is the probability that the sample mean is within 3 units of the true mean if the standard error is 1.8?
Given,
Sample mean = ±3 of true mean
Standard error = 1.8
Therefore,
Required probability of sample mean being within 3 units of the true mean is,
P ( sample mean - 3 < mean < sample mean + 3 )
= P [( sample mean - 3 ) - mean / 1.8 ] < mean - sample mean / 1.8 < [ ( sample mean + 3 ) - mean / 1.8 ]
= P ( - 1.67 < ∉ < 1.67)
= P (∉ < 1.67) - P( ∉ < 1.67)
= 0.952 - 0.047
= 0.905
Hence, the probability that the sample mean is within 3 units of the true mean if the standard error is 1.8 is 0.905.
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suppose that a large mixing tank initially holds 400 gallons of water in which 80 pounds of salt have been dissolved. pure water is pumped into the tank at a rate of 4 gal/min, and when the solution is well stirred, it is then pumped out at the same rate. determine a differential equation for the amount of salt a(t) in the tank at time
The differential equation for the amount of salt A(t) in the tank at the time (dA / dT) / (A / 100) = 0, A(0) = 30
It is Given that a large tank holds 400 gallons of water, in which 80 ponds of salt have been dissolved, given that pure water is pumped into the tank at a rate of 8 gallons/min. here we have to find the differential equation for the amount of salt in the tank at the time when the solution is well stirred. we have to multiply both 400 gallons of water and pumped water at the rate of 8 gallons/min.
dA / dT = Rin - Rout
Rin = 0
Rout = A(t) / 400 * 8
= A / 50
So,
dA / dt = Rin - Rout
dA / dt = 0 - A /50
After solving the differential equation we get
A(0) = 30
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Given mn, find the value of x.
(8x-7)°
(9x-28)°
Answer: top: x= -15 bottom: x= -37
Step-by-step explanation: First you need to get x by itself so for example on the top one you would do 8-8 to get x alone and then you would also do -7- 8 because whatever you do to one side you have to do to the other.
Hope this helped!!!
Solve for x. 1/4+1/2+x=−3/4 Enter your answer as a fraction in simplest form in the box.
Answer:
yes!! finally a question i can solve:
so,
Step-by-step explanation:
Exact Form:
x = − 3/2
Decimal Form:
x = −1.5
Mixed Number Form:
x = -1 1/2
help past due!
Multiply the polynomials (5a² + 2a − 7) and (3a² − a + 1). Simplify
the answer.
Answer:
C
Step-by-step explanation:
Use the distributive property to solve.
(5a²+2a-7)(3a²-a+1)
=15a⁴-5a³+5a²+6a³-2a²+2a-21a²+7a-7
=15a⁴+a³-18a²+9a-7
What is the value of |−13|?
Answer:
+ 13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
when you see the absolute value and the number is negative or positive it is just the whole number inside
In the equation
2H₂ + 102 →→ 2H₂O
if you change the 2H₂ to 3H2 molecules and balance the equation, which statement is correct?
If you change the 2H₂ to 3H₂ molecules and balance the equation the equation will produce three molecules of water.
The provided chemical equation is,
2H₂ + O₂ → 2H₂O.
Changing 2H₂ with 3H₂
The chemical equation becomes,
3H₂ + O₂ → 2H₂O.
By doing this, the equation has become completely imbalanced,
So first we will balance it,
3H₂ +3/2O₂ → 3H₂O
Now, there will be 3 molecules of water formed.
As we observe the reaction more closely, we can see that the number of atoms of all the elements are equal on both the sides of the reaction.
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Write the slope-intercept form of the equation of each line given the slope and y-intercept. Slope = 3/5, y-intercept = 0
Answer:y=3/5x
Step-by-step explanation:
just plug 3/5 in and you don’t need to add the 0
6. Find the equation for a parabola with vertex (5,-8) containing the point (1,1).
Answer:
[tex]y=\frac{9}{16}(x-5)^2-8[/tex]
Step-by-step explanation:
The equation in vertex form is [tex]y=a(x-5)^2-8[/tex].
Substituting in the coordinates [tex](1,1)[/tex] to solve for [tex]a[/tex],
[tex]1=a(1-5)^2-8 \\ \\ 1=16a-8 \\ \\ 9=16a \\ \\ a=9/16[/tex]
So, the equation is [tex]y=\frac{9}{16}(x-5)^2-8[/tex].
when playing roulette at a casino, a gambler is trying to decide whether to bet $ on the number or to bet $ that the outcome is any one of the possibilities . the gambler knows that the expected value of the $ bet for a single number is . for the $ bet that the outcome is , there is a probability of of making a net profit of $ and a probability of losing $. a. find the expected value for the $ bet that the outcome is . b. which bet is better: a $ bet on the number or a $ bet that the outcome is any one of the numbers ? why?
The answers to both the subparts with the help of probability are:
(A) The $15 wager's expected value is a loss of $3.16.(B) Since the bet on a single number has a higher expected value, it is better.What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is equal to the variety of possible outcomes: the total number of outcomes that could occur. For instance, there is only one way to get a head and there are a total of two possible outcomes, so the probability of flipping a coin and getting heads is 1 in 2 (a head or tail).So, Item A:
The probability of earning $75 is 5/38.The likelihood of losing $15 is 33/38.The expected value is the total of each result times the associated probability, so:
[tex]E(X)=75 \frac{5}{38}-15 \frac{33}{38}=\frac{75(5)-15(33)}{38}=-3.16[/tex]The $15 wager should have a value of -3.16 dollars.
Item B:
The wager on a single number has an expected value of $-0.79 (or -$0.79).The best wager is a bet on a single number because it is higher than the expected value of the bet on multiple numbers.Therefore, the answers to both the subparts with the help of probability are:
(A) The $15 wager's expected value is a loss of $3.16.(B) Since the bet on a single number has a higher expected value, it is better.Know more about probability here:
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The complete question is given below:
When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 34 or to bet $15 that the outcome is any one of the five possibilities 00 comma 0 comma 1 comma 2 comma or 3. The gambler knows that the expected value of the $15 bet for a single number is negative 0.79 cents. For the $15 bet that the outcome is 00 comma 0 comma 1 comma 2 comma or 3, there is a probability of StartFraction 5 Over 38 EndFraction of making a net profit of $75 and a StartFraction 33 Over 38 EndFraction probability of losing $15. a. Find the expected value for the $15 bet that the outcome is 00 comma 0 comma 1 comma 2 comma or 3. b. Which bet is better: a $15 bet on the number 34 or a $15 bet that the outcome is any one of the numbers 00 comma 0 comma 1 comma 2 comma or 3? Why?
ind the radius of a circle that has a circumference of 16.
r = 4
r = 8
r = 12
r = 16
8 units is the radius of the circle with a circumference of 16π.
What is the radius of the given circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The circumference of a circle is expressed mathematically as;
C = 2 × π × r
Where r is radius and π is constant pi ( π = 3.14 )
Given the data in the question;
Circumference C = 16πRadius r = ?To find the radius of the circle, plug the given value into the circumference formula and solve for r.
C = 2 × π × r
16π = 2π × r
r = 16π / 2π
r = 16/2
Radius r = 8
Therefore, the radius of the circle is 8.
Option B is the correct answer.
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PLEASE HELP ! :)
1. G(X)=1/4x+1
what is g(-16)?
g(-16)=
In many cases, when we evaluate functions, we just have to replace x with a given value and simplify the expression.
Solving the Question[tex]g(x)=\dfrac{1}{4}x+1[/tex]
⇒ To solve for g(-16), plug in -16 as x:
[tex]g(x)=\dfrac{1}{4}(-16)+1\\\\g(x)=-4+1\\\\g(x)=-3[/tex]
Answerg(-16) = -3
Is the relationship between the number of tickets sold and the number of hours proportional? If so, how many tickets were sold in 8 hours?
hours.
1) 3
2) 5
3) 9
Tickets sold
1) 240
2) 400
3) 720
r(x) = 8/9x - 17; r(x) = 15
Answer: 0.049382716
Step-by-step explanation: SOLVE FOR R, X
x=
4
1215
=303
4
3
=303.75
r=
81
4
≈0.049382716
Picture attached below, and it's not a rectangle. It's a pentagonsolve a and b
a)
The perimeter is given by
[tex]2x+3+4x+5+3x+15+40[/tex]b)
Then we simplify by summing similar terms we obtain that the expression of the perimeter is
[tex](2x+4x+3x)+(3+5+15+40)[/tex][tex]9x+63[/tex]Ling painted a picture of a local historic landmark for her history project. First, she painted a statue using a mix of black and white paint. Then, she painted a stone building using double the amount of black paint and double the amount of white paint. Which structure was a darker shade of gray?
Answer: Neither They were the same shade of Grey.
Step-by-step explanation:
it’s the right answer trust me
Color would be the same for both statue and stone buildings.
Let's, consider paint black as = x
and paint white as = y
If both the paints are mixed then paint z which is grey is formed.
Represented as,
x(black) + y(white) = z(grey)
Whereas, for the stone building double the amount of black and white colors are being used,
2x + 2y = 2z, coating of grey color would be also double.
Canceling 2 from both sides,
x + y = z
x(black) + y(white) = z(grey)
Therefore color would be the same for both statue and stone buildings.
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