Answer:
Step-by-step explanation:
The roots are the values of x for which x² + 3x - 5 = 0.
Quadratic formula:
x = [-3±√(3²-4(1)(-5))]/(2·1) = [-3±√29]/2
A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds.
a) Conduct the appropriate hypothesis test using a 0.1 level of significance.
b) What is the test statistic? Give your answer to four decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) What is the appropriate conclusion?
i. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.1.
ii. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.1.
iii. Reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.1.
iv. Reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.1.
Answer:
Step-by-step explanation:
99% =2.58
xbar / Point Est. 50.67
µ 50
σ 3.9
n 36
Confidence Interval
50-> (48.9,52.44) -> Fail to Reject H0
Test Statistic 1.0308
P-Value 0.1549
Teddy wants to taste all of the flavors of ice cream at the mall, one by one. Tasting any one flavor will change the way the next flavor taste after it. The flavors are chocolate, vanilla, strawberry, birthday cake, Rocky Road, and butter pecan. In how many ways can he taste the ice cream.
A. 30
B.120
C. 360
D.720
Answer: (d)
Step-by-step explanation:
Given
There are six flavors of ice-cream that is chocolate, vanilla, strawberry, birthday cake, rocky road, and butter pecan
First ice-cream can be tasted in 6 different ways
Second can be in 5 ways
similarly, remaining in 4, 3, 2 and 1 ways
Total no of ways are [tex]6\times5\times 4\times 3\times 2\times 1=720\ \text{ways}[/tex]
Option (d) is correct.
Adam sleeps for nine hours each night, five nights a week, and 11 hours for two nights a week.
Which is closest to the percentage of the whole week that Adam spends sleeping?
A) 25%
B) 30%
C) 33%
D) 40%
E) 50%
Answer:
E
Step-by-step explanation:
The percentage of the whole week that Adam spends in sleeping is 33%.
What is percentage?
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
How to find percentage of a number?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
According to the give question.
Adams sleeps for nine hours each night, five nights a week.
⇒ Number of hours he sleep for five nights = 5 × 9 = 45 hours
Also, 11 hours for two nights a week.
So, the total number of hours Adam sleeps in a week = 45 + 11 = 56 hours
And, total number of hours in a week = 24 × 7 = 168
Therefore,
The percentage of the whole week that Adam spends in sleeping
= (total number of hours Adam sleep in a week/Total numbers of hour in a week) × 100
[tex]=\frac{56}{168}[/tex] × 100
= 33.33%
= 33%
Hence, the percentage of the whole week that Adam spends in sleeping is 33%.
Find out more information about percentage here:
https://brainly.com/question/24159063
#SPJ2
How do you Graph 3x+4y< -16 on the coordinate plane
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Take note of the inequality symbol. It is < (not ≤), so the "equal to" case is not included. That means the line 3x+4y=-16 is not part of the solution set. That boundary line is graphed as a dashed line.
Take note of where the variables are in relation to the inequality symbol. Both are on the "less than" side, so the shading of the graph will be where the values of x and y are less than those on the boundary line. The boundary line has a negative slope, so the values less than those on the boundary are to the left and below the line.
Plot the dashed boundary line 3x +4y = -16, or y = -3/4x -4, and shade the area below and to its left.
1 simplify 6x64 ÷ 16 +7-21
Answer:
10
Step-by-step explanation:
I really need help!!!
Answer:
the third option (a=1, h=0, k=6)
Step-by-step explanation:
if I understand correctly what your teacher wants from you, then you need find a (the factor of x² in the equation) and the vertex (turnaround point) of the parabola represented by such a quadratic equation.
the vertex point coordinates are called (h, k).
the general form of such an equation equation is
y = ax² + bx + c
so, we have a right away : a=1
now we can make this quickly by using common sense, or a bit more complex by going through mathematical formulas.
the fast, practical way is to know that y=x² is the very basic parabola with its vertex at (0, 0).
y = x² + 6 is simply the same parabola just lifted up (y direction) by 6 units, that makes the vertex (0, 6).
in pure theory, though, we need to find the transformation from the general y = ax² + bx + c form to
y = a(x - h)² + k
we see right away that k = f(h) = h² + 6
y = a(x² - 2xh + h²) + k
a=1
y = x² - 2xh + h² + k = x² - 2xh + h² + h² + 6 =
= x² - 2xh + 2h² + 6
comparing with y = x² + 6
we know that
-2×h = 0
as we have no term with just x.
=> h = 0
2h² + 6 = k
2×0² + 6 = 6 = k
What is the slope of the points (-2,7) and (2,-5)?
4
-3
-12
3
Answer:
The slope of a line that goes through both [tex](-2,\, 7)[/tex] and [tex](2,\, -5)[/tex] would be [tex](-3)[/tex].
Step-by-step explanation:
The slope of a line is the ratio between rise and run between these two points.
The rise between two points is the change to the corresponding [tex]y[/tex] coordinates. Between [tex](-2,\, 7)[/tex] and [tex](2,\, -5)[/tex], the rise would be [tex](-5) - 7 = (-12)[/tex] (subtract the first [tex]y\![/tex]-coordinate from the second.)
The run between two points is the change to the corresponding [tex]y[/tex] coordinates. Between [tex](-2,\, 7)[/tex] and [tex](2,\, -5)[/tex], the rise would be [tex]2 - (-2) = 4[/tex] (likewise, subtract the first [tex]x[/tex]-coordinate from the second.)
Hence, the slope of this line would be:
[tex]\begin{aligned} \frac{\text{rise}}{\text{run}} &= \frac{-12}{4} = -3\end{aligned}[/tex].
During a 1966 Tabiona High School track meet, Levere ran the 100 yard dash in
10.63 seconds. Ross took second with a time of 10.98 seconds.
a. Levere’s time was _______% shorter than Ross’.
b. Ross’ time was _______% longer than Levere’s.
c. Levere’s time was _______% of Ross’.
Answer:
a) 3.19
b) 3.29
c) 96.81
Step-by-step explanation:
Question a:
Levere's: 10.63s
Ross: 10.98s
10.98 - 10.63 = 0.35s shorter than 10.98s, so:
0.35*100%/10.98 = 3.19% shorter.
Question b:
35s longer than 10.63s, so:
0.35*100%/10.63 = 3.29% longer.
Question c:
3.19% shorter, so 100 - 3.19 = 96.81% of Ross.
Explain how you would solve the following system of equations using substitution. math step in your explanation, too!! This is the system that you should use: y= 4x -5 y = 3x -3
Answer:
[tex]x=2\\y=3[/tex]
Step-by-step explanation:
Solve by substitution method
[tex]y=4x-5\\y=3x-3[/tex]
First, solve [tex]y=4x-5[/tex] for [tex]y[/tex]:
Substitute [tex]4x-5[/tex] for [tex]y[/tex] in [tex]y=3x-3[/tex]
[tex]y=3x-3[/tex]
[tex]4x-5=3x-3[/tex]
[tex]4x-3x=5-3[/tex]
[tex]x=2[/tex]
Now that we have the value of x
substitute [tex]2[/tex] for [tex]x[/tex] in [tex]y=4x-5[/tex]
[tex]y=4x-5[/tex]
[tex]y=4(2)-5[/tex]
[tex]y=8-5[/tex]
[tex]y=3[/tex]
∴ The value of [tex]x[/tex] is [tex]2[/tex] and the value of [tex]y[/tex] is [tex]3[/tex]
Judy got 27 546 points and 34 668 points in the first two rounds of a
game. How many points did Judy get in all?
Answer:
62 214Step-by-step explanation:
Given,
Points got by Judy in 1st round = 27 546
Points got by Judy in 2nd round = 34 668
Therefore,
Total points Judy got in the first two rounds
= 27 546 + 34 668
= 62 214 (Ans)
find the solution of the general equation of the differential equation:
(1-cosx)y' - ysinx =0, x ≠ k2π
Notice that the condition x ≠ 2πk for (presumably) integer k means cos(x) ≠ ±1, and in particular cos(x) ≠ 1 so that we could divide both sides by (1 - cos(x)) safely. Doing so lets us separate the variables:
(1 - cos(x)) y' - y sin(x) = 0
==> (1 - cos(x)) y' = y sin(x)
==> y'/y = sin(x)/(1 - cos(x))
==> dy/y = sin(x)/(1 - cos(x)) dx
Integrate both sides and solve for y. On the right, substitute u = 1 - cos(x) and du = sin(x) dx.
∫ dy/y = ∫ sin(x)/(1 - cos(x)) dx
∫ dy/y = ∫ du/u
ln|y| = ln|u| + C
exp(ln|y|) = exp(ln|u| + C )
exp(ln|y|) = exp(ln|u|) exp(C )
y = Cu
y = C (1 - cos(x))
Write the following as an expression: How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol? The answer is an EXPRESSION, not an actual answer!! WILL MARK BRAINLIST!!!
Answer: [tex]\dfrac{11}{9}I[/tex]
Step-by-step explanation:
Given
There is [tex]l[/tex] liter of pure alcohol
Suppose [tex]x[/tex] liters of water is added
After addition of water, alcohol becomes 45% in concentration
[tex]\Rightarrow \dfrac{l}{x+l}=45\%\\\\\Rightarrow \dfrac{I}{0.45}=x+I\\\\\Rightarrow \dfrac{20}{9}I-I=x\\\\\Rightarrow x=\dfrac{11}{9}I[/tex]
Thus, [tex]\dfrac{11}{9}I[/tex] of water is added to the pure alcohol.
find the surface area of the triangular prism below.
Step-by-step explanation:
At first you need to take its lateral surface area by using the perimeter of base of the triangle and the height of prism.
Then after calculating it you need to find out its total surface area which is asked in the question and that is calculated by adding the area of both triangles of the prism in the lateral surface area.
Then that's your answer.
9514 1404 393
Answer:
544 square units
Step-by-step explanation:
The surface area is the sum of the area of the two triangular bases and the three rectangular faces. The relevant area formulas are ...
A = 1/2bh . . . . area of a triangle with base b and height h
A = LW . . . . . are of a rectangle of length L and width W
__
SA = 2(1/2)(12)(8) + (10 +10 +12)(14)
SA = 96 +448 = 544 . . . square units
You need to build a box from an 8 inchby 10 inch piece of cardboard. To do this, you cut out squares of length x from the four corners of the box in order to fold the sides up. Verify that the volume of the box is given by the equation:
V= 4x^3â36x^2+ 80x
Answer:
Step-by-step explanation:
From the attached image below, let assume we have a square of diameter x by x which is to be cut from each corner of the cardboard sheet.
Thus, from the diagram
the length = 8 - 2x the width = 10 - 2x and the height = x
So, the volume V = L*w*h
Volume (V) = (8 - 2x) (10 - 2x) x
V = (80 - 16x - 20x +4x²)x
V = 80x -36x² + 4x³
By rearrangement:
V = 4x³ - 36x² + 80x
Three jackets cost as much as five shirts. Each jacket costs $16 more
than each shiri. What is the cost of one shirt?
Answer:
$3.20
Step-by-step explanation:
Divide the number 16 (as in the cost per Jacket) by 5. (The amount of shirts you could buy with $16)
Then once you have divided 16 by 5, your answer should be 3.2, so the cost of one shirt is $3.20
Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?
7x + 2y = –1
7x + 2y = 1
14x + 4y = –1
14x + 4y = 1
9514 1404 393
Answer:
(b) 7x + 2y = 1
Step-by-step explanation:
You don't need to know how to find the equation. You just need to know how to determine if a point satisfies the equation. Try one of the points and see which equation fits. (The numbers are smaller for point K, so we prefer to use that one.)
7(1) +2(-3) = 1 ≠ -1 . . . . . tells you choice A doesn't work, and choice B does
The equation is ...
7x +2y = 1
__
Additional comment
The equations of choices C and D have coefficients with a common factor of 2. If the constant also had a factor of 2, we could say these equations are not in standard form, and we could reject them right away. Since the two points have integer values for x and y, we can reject these equations anyway: the sum of even numbers cannot be odd.
Answer:
b
Step-by-step explanation:
CAN SOMEBODY HELP WITH THIS QUESTION ASAP
Answer:
The rectangles are not similar
Step-by-step explanation:
In order to check whether they are similar, we need to take the ratio of their similar sides and ensure they are equal to a constant k.
Hence;
AB/PL = AD/LM = k
32/26 = 18/12 = k
16/13 = 9/6 = k
Since the scale factor is not the same, hence the rectangles are not the same.
A rectangle with the dimensions of 2 feet
by 8 feet is similar to a rectangle with the
dimensions of
А 4 feet by 16 feet
B. 6 feet by 12 feet
C 12 feet by 32 feet
D 22 feet by 28 feet
Given rectangle: 2 feet by 8 feet. Similar rectangle: Option A (4 feet by 16 feet).
Use the concept of the rectangle defined as:
Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.
Given that,
Rectangle dimensions: 2 feet by 8 feet
And here are the options provided:
A) 4 feet by 16 feet
B) 6 feet by 12 feet
C) 12 feet by 32 feet
D) 22 feet by 28 feet
To determine if two rectangles are similar,
Compare their corresponding side lengths.
In this case,
A rectangle with dimensions 2 feet by 8 feet.
After simplifying it we can write 1:4
Let's check each option to see if it matches the similarity:
A) 4 feet by 16 feet:
The ratio of the corresponding side lengths is 2:8, which simplifies to 1:4. However, the given rectangle has side lengths of 4:16,
Which simplifies to 1:4 as well.
So, option A is similar to the given rectangle.
B) 6 feet by 12 feet:
The given rectangle has side lengths of 6:12,
Which simplifies to 1:2.
So, option B is not similar to the given rectangle.
C) 12 feet by 32 feet:
The given rectangle has side lengths of 12:32,
Which simplifies to 3:8.
So, option C is not similar to the given rectangle.
D) 22 feet by 28 feet:
The given rectangle has side lengths of 22:28,
Which simplifies to 11:14.
So, option D is not similar to the given rectangle.
To learn more about rectangle visit:
https://brainly.com/question/15019502
#SPJ3
What's the dependent variable shown in the table?
A)
The amount of water given to the plant
B)
The color of the flowers
C)
The number of flowers on the plant
D)
The speed at which the plant grows
Answer:
The number of flowers on the plant
Step-by-step explanation:
Answer:
C: Number of flowers on the plant
Step-by-step explanation:
i got it right on my test
how far from "0 is the green rectangle
Option 4
3-1/2"
Must click thanks and mark brainliest
Answer:
3 1/2
Step-by-step explanation:
That’s the distance from 0 to the green rectangle
How many of each coin does he have?
_____nickels
_____quarters
Use the order of operations to simplify the following expression.
-2 3 + |7| - 4 · 2
-38
-23
-9
-10
Answer:
-9
Step-by-step explanation:
-2 3 + |7| - 4 · 2
I assume -2 3 means -2^3.
-2^3 + |7| - 4 · 2 =
= -8 + 7 - 8
= -1 - 8
= -9
Answer:
-9
Step-by-step explanation:
-2^ 3 + |7| - 4 · 2
Parentheses first and an absolute value is considered parentheses
-2 ^3 + 7 - 4 · 2
Then exponenets
Since the sign is outside of the exponent it is considered multiplication
-1 * (2^3)+ 7 - 4 · 2
-1 *8 + 7 - 4 · 2
Then multiply
-8 +7 -8
Then add and subtract from left to right
-1-8
-9
Find the measure of the missing angles.
Answer:
Step-by-step explanation:
Help with this Area question
Step 1: Find the area of the rectangle
A = base x height
A = 39 x 20
A = 780
Step 2: Find the area of the semi-circles
---Two semi-circles is the same as one whole circle, so I will be finding the area of one whole circle.
A = pi x r^2
A = pi x 10^2
A = 100pi = 314
Step 3: Find the area of the figure
Area = area of the rectangle - area of the semi-circles
A = 780 - 314
A = 466 cm^2
Hope this helps!
Answer:
466 cm^2
Step-by-step explanation:
This one is done basically the same as the other.
Rectangle = 20 x 39
Circle = (3.14) x 10^2
Rectangle = 780
Circle = 314
rectangle - circle
780 - 314 = 466
We have that 2a+1=1 and b-a=1. What is the value of b?
Answer:
b=1
Step-by-step explanation:
2a+1 =1
Subtract 1 from each side
2a+1-1 = 1-1
2a=0
a=0
Now find b from the second equation
b-a =1
b-0=1
b=1
Answer:
Equation: 2a+1=1
Subtract 1 from both sides: 2a=0
Divide by 2: a=0
Equation: b-a=1
Substitute: b-0=1
Combine: b=1
So, b=1.
Let me know if this helps.
∫[tex]\frac{x+2019}{x^{2}+9 }[/tex]
Split up the integral:
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx[/tex]
For the first integral, substitute y = x ² + 9 and dy = 2x dx. For the second integral, take x = 3 tan(z) and dx = 3 sec²(z) dz. Then you get
[tex]\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)[/tex]
and
[tex]\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C[/tex]
Then
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}[/tex]
Determine if f(x, y) = 10 − x^2 − y^2
is increasing or decreasing at (7, −3) if we
take y to be constant and let x vary. Also determine if f(x, y) is increasing at
(7, −3) if we take x to be constant and let y vary.
Answer:
Step-by-step explanation:
f(x,y)=10-x^2-y^2
To find derivative of z w.r.t. x is treat any other variable as a constant.
dz/dx=0-2x-0
dz/dx=-2x
Evaluating this at (7,-3) gives us dz/dx=-2(7)=-14.
Since this result is negative, it mrans as x increases z decreases.
f(x,y)=10-x^2-y^2
To find derivative of z w.r.t. y is treat any other variable as a constant.
dz/dx=0-0-2y
dz/dx=-2y
Evaluating this at (7,-3) gives us dz/dy=-2(-3)=6.
Since this result is positive it mrans as y increases z decreases.
What is the equation of a line that passes through the point (1,8) and is perpendicular to the line whose equation is y=x/2+3?
Answer:
m=1/2
y-8=1/2(x-1)
y-8=1/2x-1/2
multiply through by 2
2y-16=x-1
2y-16+1-x=0
2y-15-x=0
2y-x-15=0
Please help! Question and answers are in the pic
So far she worked 4 days at 5 1/2 hours a day for a total of 22 hours.
22 hours x $8.50 = $187
Subtract that from the cost of the computer:
899-187 = $712
She needs $712 more.
Amount she makes per shift: $8.50 x 5 1/2 hours = $46.75
Divide what she needs by amount per shift:
712 / 46.75 = 15.22 shifts
She needs to work 16 more shifts.
Find the missing side lengths.
Answer:
x is 18, and y is 9 √ 3
Step-by-step explanation:
Since this is a right triangle that contains a 30 degree angle, we know this is a special right triangle, and the missing angle is 60 degrees since a triangle is 180 degrees, and 180 - 90 - 30 = 60.
The relationship is listed below:
The side opposite of the 30 degrees can be represented as a variable, say "p", and the hypotenuse which is x in your question is twice this. The side opposite of the 60 degree angle is x + √3
So x is 18, and y is 9√3
