Answer:
y = -4x^2 - 40x - 103
Step-by-step explanation:
to get the standard form, you have to formulate the equation as
y = ax^2 + bx + c
we have to expand the (x+5)^2
y = -4((x+5)^2) - 3 = -4(x^2 + 10x + 25) - 3 = -4x^2 - 40x - 100 - 3 = -4x^2 - 40x - 103
skiing eight people compete in a downhill ski race. assuming that there are no ties, in how many different orders can the skiers finish?
Eight people skiing downhill in a race can finish in 40,320 different orders.
Calculating probabilities for a set of possibilities keeping in account the order they are in is called permutation ([tex]{n}_P_{r}[/tex]).
If we overlook the order, it becomes a problem of combination ([tex]{n}_C_{r}[/tex]).
Permutation plays an important role in probability problems where the order of the possible outcomes is concerned. It does not allow repetition of outcomes.
Mathematically, permutation can be represented as:
[tex]{n}_P_{r}=\frac{n!}{(n-r)!}[/tex]
where 'n' represents the total objects/values/instances and 'r' represents our selected number of objects/values/instances.
In this case, we have total 8 drivers (n=8) and 8 positions we are selecting i.e. the order skiing people finish in (r=8);
[tex]{n}_P_{r}=\frac{8!}{(8-8)!}=\frac{8!}{0!}=\frac{40320}{1}[/tex]
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Nasim is working two summer jobs, making $9 per hour walking dogs and $8 per hour clearing tables. Nasim must earn no less than $130 this week. Write an inequality that would represent the possible values for the number of hours walking dogs, dd, and the number of hours clearing tables, cc, that Nasim can work in a given week.
The inequality that would represent the possible values for the number of hours walking dogs is 9d + 8c ≥ 130
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Let number of hours walking dogs = d
Let number of hours clearing tables = c
The appropriate inequality is 9d + 8c ≥ 130.
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Ms.Salgado needs to have her car repaired but does not want to spend more than $375 for the repairs. The mechanic says that the part needed for the repair will cost $100 and the labor will cost an additional $40 per hour. Which inequality below represents the greatest number of hours mechanic can work without exceeding ms. Salgado’s budget?
Answer:
6 hours without exceeding
Step-by-step explanation:
7 hours goes over
100+40x7=380
6 hours is under
100+40x6=340
Solve the compound inequality. Graph the solution set and write it in interval notation
x< 1 and and x > -5
help asap! only the solution set
The interval notation of the compound inequality (x < 1) and [x > (-5)] is
[(-5) < x < 1], and the graph of it's solution set is a straight line lying on the x-axis from 1 to (-5).
As per the question statement, we are provided with a compound inequality (x < 1) and [x > (-5)],
And we are required to determine the interval notation of the above mentioned compound inequality, and graph it's solution set.
Now, the interval notation of a compound inequality is simply the combination of the separate inequalities, that is, the interval notation of the compound inequality (x < 1) and [x > (-5)] is [(-5) < x < 1].
And since "x" is less than 1, but greater than (-5), the values in the solution set of [(-5) < x < 1] are (0, -1, -2, -3, -4), and the graph of these values is a straight line lying on the x-axis from 1 to (-5).
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find the slope of the best least squares line through the three points (-2, 4), (0, 3), (2, 0). enter your answer rounded to five correct digits after the decimal point.
The slope of the best least squares line through the three points (-2, 4), (0, 3), (2, 0) is -1.
Given:
Three points (-2, 4), (0, 3), (2, 0).
x y x^2 xy
-2 4 4 -8
0 3 0 0
2 0 4 0
∑ 0 7 8 -8
[tex]SS_{xx}[/tex] = ∑[tex]x^{2}[/tex] - 1/n(∑x)^2
= 8 - 1/3(0)^2
= 8 - 1/3*0
= 8 - 0
= 8
[tex]SS_{xy}[/tex] = ∑xy - 1/n(∑x)(∑y)
= -8 - 1/3(0)(7)
= -8 - 1/3*0
= -8 - 0
= -8
slope m = [tex]SS_{xy} /SS_{xx}[/tex]
= -8/8
= -1
Therefore the slope of the best least squares line through the three points (-2, 4), (0, 3), (2, 0) is -1.
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Write an equation of the line in point-slope form that passes through the given points.
(4,-3/4) and (2,5/4)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-\frac{3}{4}})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{\frac{5}{4}}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{5}{4}}-\stackrel{y1}{\left( -\frac{3}{4} \right)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{4}}} \implies \cfrac{~~ \frac{5 }{4 }+\frac{3}{4} ~~}{-2} \\\\\\ \cfrac{~~ \frac{ 5+3}{ 4} ~~}{-2}\implies \cfrac{~~ \frac{8 }{4 } ~~}{-2}\implies \cfrac{2}{-2}\implies -1\qquad \impliedby m[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\left(-\frac{3}{4} \right)}=\stackrel{m}{-1}(x-\stackrel{x_1}{4})\implies {\large \begin{array}{llll} y+\cfrac{3}{4}=-(x-4) \end{array}}[/tex]
What is the answer to this question
Answer:
negative
Step-by-step explanation:
because the line falls from left to right, the line has a negative slope. =)
Answer: Negative
Step-by-step explanation:
This line is "going down the stairs," or starting from the upper lefthand side to the bottom righthand side. This means we have a negative slope.
If you need to find the slope;
We will use the "rise over run" method. Starting at (-2, 3) we will count 4 units down and three units right to (1, 1) for a slope of -4/3.
You can see this graph has also shown the change of -4 in the y and the change of 3 in the x.
in a rhombus, all the side lengths are $10,$ and one of the angles is equal to $120^\circ.$ find the area of the rhombus.
The area of the rhombus is 50[tex]\sqrt{3}[/tex] .
Given:
In a rhombus, all the side lengths are $10,$ and one of the angles is equal to $120^\circ.
If angle = 120 the its half is 60 which forms a right angled triangle.
sin 60 = Height / 10
[tex]\sqrt{3}[/tex]/2 *10 = height
height = 5[tex]\sqrt{3}[/tex].
Area of rhombus = base * height
= 10*5[tex]\sqrt{3}[/tex]
= 50[tex]\sqrt{3}[/tex] .
Therefore the area of the rhombus is 50[tex]\sqrt{3}[/tex] .
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) find the approximations t10 and m10 for 2 15 e1/x dx. 1 (round your answers to six decimal places.)
For integral 2 15 e1/x dx. 1, the approximate value of T10 = 27.05 and M10 = 30.29
In this question, we need to find the approximations T10 and M10 for 2 15 e1/x dx. 1
i.e., To find: Integral approximate using Trapezoid rule and midpoint rule
f(x) = 15e^(1/x)
a = 1, b = 2, bx = 1/10
T10 = bx/2 [f(1) + 2f(1.1) + 2f(1.2) + 2f(1.3) + . . . + f(2) ]
= 1/20[15e + 30e^(1/1.1) + 30e^(1/1.2) + . . . + 15e^(1/2)]
= 1/20 * 30 [(e/2) + e^(1/1.1) + e^(1/1.2) + . . . + (e^(1/2) / 2)]
= 1.5 * 18.0362
= 27.05
Now we find M10
M10 = Δx [f(1.05) + f(1.15) + . . . + f(1.95)]
= 1/10 [15e^(1/1.05) + 15e^(1/1.15) + . . . + 15e^(1/1.95)]
= 15/10 [e^(1/1.05) + e^(1/1.15) + . . . + e^(1/1.95)]
= 1.5 * 20.1909
= 30.29
Therefore, for integral 2 15 e1/x dx. 1, the approximate value of T10 = 27.05 and M10 = 30.29
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2/4= =
fraction present decimal
Answer:
0.5
Step-by-step explanation:
2/4
= 1/2
Multiply 5 to both numerator and denominator.
= 1/2 x 5/5
= ( 1 x 5 )/( 2 x 5 )
= 5/10
= 0.5
Graph the line that passes through the given point and has the given slope m. (2,8); m= -1/3
Step-by-step explanation:
Refer to the picture above
hi so were learning to do multi step equations i dont get it so could you tell how to do it and make really easy i am in the lower class
Answer:
Step-by-step explanation:
First, Multiply to clear any fractions or decimals, this is OPTIONAL THOUGH, IF YOU DO NOT MIND WORKING WITH THEM
Then, Simplify each side by clearing parentheses (e.g. (5x6) and combine the like terms (e.g. 5 and 2, -3 and -92)
Use the properties of equality to isolate the variable
Check the solution
7. Write each expression in exponential form. a) (5 x 5 x 5) x (5 x 5 x 5) x (5 x 5 x 5) x (5 × 5 ×,5)
b) [(-9) × (-9)] x [(-9) × (-9)] × [(-9) × (-9)] x [(-9) × (-9)] × [(-9) × (-9)]
Answer: A. (5³) x (5³) x (5³) x (5³)
B. (-9²) x (-9²) x (-9²) x (-9²) x (-9²)
Step-by-step explanation: 5x5x5=5³ we have four 5³
9x9=9² we have five 9²
Bill's bank charges $27.50 for overdraft fee and $3.50 for using an ATM out of network. Bill has $25 in his checking account at First Bank. Later that day he had a check clear his account for $50 and then added an ATM debit of $80. How much does Bill owe the bank. Explain your answer
Total sum that Bill owe the bank is $36
Given,
The overdraft fee charged by the bank = $27.50
The charge for using an ATM out of network = $3.50
The amount in the checking account = $25
The amount for check clearing = $50
ATM debit amount added = $80
We have to find the money Bill owe the bank;
Overdraft;-
A bank will grant a customer an overdraft when their account balance is 0 so they may pay their payments and other expenses.
Here,
Total sum in bank = 25 + 50 - 80
Total sum in bank = -5
Then,
Total Sum he owe = 5 + 27.5 + 3.5
Total sum he owe = $36
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What is SSS SAS ASA AAS?.
Answer:
SSS means Side-Side-Side. SAS means Side-Angle-Side. ASA means Angle-Side-Angle. AAS means Angle-Angle-Side.
Hopes this helps! :)
A line's slope is 9, and its y-intercept is 9. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
A survey by the national retail federation found that women spend on average r146.on a saturday lunch. assume the standard deviation is r29.44. find the percentage of women who spend less than r190.00 on a saturday lunch. assume the variable is normally distributed
The percentage of women who spend less than $190.00. Assume the variable is normally distributed is 0.0694 or 6.94%
Given that,
Women spend an average of $146 on a Saturday lunch, according to a national retail federation poll. Suppose $29.44 is the standard deviation.
To find : How many ladies or the percentage of ladies spend less than $190 on a Saturday lunch
P(X < 190) = P(x-μ/σ < 190 -146.21 /29.44)
= P(Z > 1.487)
= 0.0694
So, the proportion of female consumers who spend less than $190 and that the variable has a 0.0694 or 6.94% normal distribution.
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I would like to know what the equation would be.
I forgot how to do this stuff
A spinner has four sections A,B, C and D.
Pls solve this asap.
Answer:
0.35
Step-by-step explanation:
since there are only 4 sides the probability of all 4 should equal 1
0.2+0.3+0.15
0.5+0.15
0.65
1-0.65
0.35 is the probability of D
Hopes this helps please mark brainliest
systems of linear equations and inequalities
solve the system of equations.
x-y=4
2x+y=5
Answer:
∴ x = 1, y = -3
Step-by-step explanation:
x - y = 4 ------ equation (1)
2x + y = 5 ------ equation (2)
Add equations (1) and (2):
(2x + y) + (x - y) = 5 - 4
2x + y - x - y = 1
∴ x = 1
Substitute x = 1 into equation (1):
1 - y = 4
-y = 3
∴ y = -3
What are 2 congruent segments?.
Segments that are congruent are same in length. Collinear points are those that share a line. A mathematical claim that can be supported by evidence is called a theorem. A segment's midpoint is the point at which it is divided into two congruent segments.
What are congruent segments?
Segments that are congruent have the same length. Collinear points are those that share a line. A mathematical claim that can be supported by evidence is called a theorem. A point that separates a segment into two congruent segments is the segment's midpoint.What is an example of congruent segments?
Any line segment with equal measure is referred to as a congruent line segment. Congruent line segments, for instance, refer to the sides of an equilateral triangle since they all have the same length.Learn more about congruent segments
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how long does a ford raptor traveling at 75 mph take to travel 259 mi, in hours
A. 0.4
B. 10/3
C. 0.3
D. 175
Answer:
3.45 hours. The closest answer option to this value would be (10/3), which is technically 3.3333 hours, but it is the closest correct option, by far. 3.333 hours would suggest the distance was 250 miles, not 259 (250/75) = 3.33333)
Step-by-step explanation:
Distance, D, is found by multiplying the speed (75 mph) times the time, x (in hours. If distance is 259 miles, we can write:
259 miles = (75 miles/hr)*x
Rearrange to find x [divide both sides by (75 miles/hr):
x = (259 miles/(75 miles/hr)
Note the units: miles cancel and hours moves to the top, leaving only hours, which is what we want.
(259 hours)/75 = 3.45 hours
Find the value of x (and y) if you know L||m
Answer:
x=50 y=140
Step-by-step explanation:
Since l and m are parallel, all you have to do is add 40 and y.
Because a straight line has a 180-degree angle, you can subtract 40 from 180 you can find y.
180-40=140
Now we know that 3x-10=140 so we just have to solve.
First, add 10 to each side
3x=150
Then divide by 3
x=50
What is the image point of (-3,0) after the transformation T3,5 o D₂?
The image of the point (-3,0) after the given transformation is (0,5) and this can be determined by using the rules of transformation.
What are translations rules?An operation known as a transformation involves moving, flipping, or altering the preimage to produce a new shape (called the image). An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction.Although there are many different types of linear transformations, just a few are common. Here, we examine rotations, reflections, shears, dilations, and projection.The following steps can be used to determine the image of the point after transformation:
As per the given data translate the point (-3,0) by (3,5).
[tex]( x, y )[/tex] = [tex]( x + 3, y+ 5)[/tex] = (0, 5)
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A Car travelled from Suva to sigatoka at an average Speed of 50km/hr Covering distance of 125 km.
a.) Calculate the time taken for the Journey.
The time taken to cover Suva to Sigatoka is 2 Hours and 30 Minutes.
We know that, Time taken = (Distance Covered)/(Average Speed)
Given that the car travelled from Suva to Sigatoka and travelled 125 Km.
Average speed is = 50 km/hr
So the time taken to cover the distance = 125/50 = 5/2 hr = 2 hours and 30 minutes.
Hence the time taken to cover Suva to Sigatoka is 2 Hours and 30 Minutes.
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Solve the equation 6 1/9m+ 3 1/3m = 28 1/3 for m. HELPPPP SOMEBODY
The value of m on solving the equation 6 1/9m+ 3 1/3m = 28 1/3 is 3
We need to solve the equation
6 1/9m+ 3 1/3m = 28 1/3 for m
converting mixed fractions into improper fractions
55/9 m + 10/3 m = 85/3
Upon taking L.C.M.
55/9 m + 10x3/3x3 m = 85/3
(55 + 30)m/9 = 85/3
3 x 85m = 85 x 9
m = 3
Therefore, the value of m on solving the equation 6 1/9m+ 3 1/3m = 28 1/3 is 3
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a store sells coffee beans for $8 per bag. if a bag contains 5 lbs., find the cost of coffee beans per pound.
The cost of the coffee beans per pounds is 1.6 pounds.
Given that,
Coffee beans are available in stores for $8 per bag.
We have to find the price of coffee beans per pound if a bag weighs 5 pounds.
one lb is one pound.
To convert it from pounds to kilogram's, increase it by 1. (or just change the unit). This shows that the number of pounds is exactly the same.
Let us take the cost as x.
We get,
5x=8
x=8/5
x=1.6
Therefore, The cost of the coffee beans per pounds is 1.6 pounds.
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what function creates a scatterplot and then adds a small amount of random noise to each point in the plot to make the points easier to find?
The geom_jitter() function is the function creates a scatterplot and then adds a small amount of random noise to each point in the plot to make the points easier to find
Given that,
In order to make the points in the plot easier to find, function first creates a scatterplot and then adds a small amount of random noise to each point in the plot.
Generally, To make the points in the scatterplot easier to find, the geom jitter() method first builds a scatterplot and then adds a little amount of random noise to each point in the plot.
What is the purpose of the Geom jitter () function? Description. The geom point (position = "jitter") shortcut is the jitter geom. It is a practical method of managing overplotting brought on by discreteness in smaller datasets by adding a little degree of random variation to the location of each point.
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The geom_jitter() function is a funcreates a scatterplot and then adds a small amount of random noise to each point in the plot to make the points easier
Given that,
Function first makes a scatterplot, then adds a small amount of random noise to each point in the plot to make the points in the field easier to find.
The geom jitter() method often produces a scatterplot first, then adds a small amount of random noise to each point in the plot to make the points in the field easier to find.
What does the Geom jitter () function do? The jitter geom is the shortcut geom point with a position equal to "jitter". It is a helpful technique for controlling overplotting caused by discreteness in smaller datasets by giving each point's location a small amount of random variation.
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Please solve 6-11, giving brainliest
Equation:
a) 4 + 3x = 3x- 7 has no solution.
b) 5.4x + 12 = 2(2.7x - 9 ) has no solution
c) 6 + 2.5x = 0.5x - 8 has one solution.
Define equation.A formula that expresses the connection between two expressions on each side of a sign is called equation. Typically, it has a single variable and an equal sign. Like this: 2x - 4 = 2.
Given,
Equations:
a) 4 + 3x = 3x- 7
3x - 3x = -7 -4
0
4 + 3x = 3x- 7 has no solution.
b) 5.4x + 12 = 2(2.7x - 9 )
5.4x + 12 = 5.4x - 18
0
b) 5.4x + 12 = 2(2.7x - 9 ) has no solution
c) 6 + 2.5x = 0.5x - 8
2.5x - 0.5x = -8 -6
2x = -14
x = -7
c) 6 + 2.5x = 0.5x - 8 has one solution.
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a coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. if a sample of 9 cups is selected, find the probability that the mean of the sample will be greater than 12.1 ounces. find the probability if the sample is just 1 cup.
Answer:i don't know really im just another student and i'm just doing this for the points my guy so don't be mad if you get a bad response
Step-by-step explanation:
1. I have no idea
