Answer: The equation has 2 positive integer solutions:
x1 = 0 y1 = 2
x2 = 1 y2 = 0
Step-by-step explanation:
The value of x = -4.334 and y = 10.667.
What is linear equations in two variables?When written as ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e., a and b, respectively, are not zero, an equation is said to be a linear equation in two variables.
For this kind of equation, the solution is a pair of values, one for x and one for y, which also make the two sides equal.
Given Equations 12x + 6y = 12...….(1)
y = x + 15
y - x = 15...….(2)
divide eq. (1) by 6
(12x + 6y)/6 = 12/6
2x + y = 2
subtract from eq. (2)
y - x - (2x + y) = 15 - 2
-3x = 13
x = -13/3 = -4.334
substitute value of x in eq. (2)
y - (-4.334) = 15
y = 15 - 4.334
y = 10.667
Hence the solution of equations gives x = -4.334 and y = 10.667.
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Could I get help with this? Thank you
Answer:
Equation: [tex]y=-\frac{5}{4} x[/tex]
Slope: [tex]-\frac{5}{4}[/tex]
Point: [tex](-4,5)[/tex]
Step-by-step explanation:
To find the slope, you need two points [tex](-4,5)[/tex] and [tex](0,0)[/tex].
Then use the Slope Formula to Identify the slope.
M = Slope
M = [tex]\frac{y2-y1}{x2-x1}[/tex] Second y being subtracted by the first y / the second x being subtracted by the first x.
M = [tex]\frac{0-5}{0--4}[/tex] Plot the x and y values (In order) Then subtract
M = [tex]\frac{-5}{4}[/tex] Move the negative sign
M = [tex]-\frac{5}{4}[/tex]
Slope = [tex]-\frac{5}{4}[/tex]
Then the Equation has to be written in Slope-Intercept Form (y=mx+b)
y = [tex]-\frac{5}{4} x[/tex]
A worker is exposed to 98 dB for five hours and 82 dB for three hours, giving an eight-hour working day. On average, what noise level is this worker exposed to?
Answer:
92 dB
Step-by-step explanation:
Use the mean formula, mean = sum of elements / number of elements.
Since it is a 8 hour work day, there are 8 elements.
mean = sum of elements / number of elements
mean = (98 + 98 + 98 + 98 + 98 + 82 + 82 + 82) / 8
mean = 736 / 8
mean = 92
So, the average noise level is 92 dB
Question 2 (Essay Worth 10 points)
(02.03, 02.05 MC)
The linear function f(x) = 0.5x + 80 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents the average
test score in your science class, where x is the number of the test taken.
x g(x)
1 81
2 83
3 85
Part A: Determine the test average for your math class after completing test 2. (2 points)
Part B: Determine the test average for your science class after the completing test 2. (2 points)
Part C: Which class had a higher average after completing test 4? Show work to support your answer. (6 points)
Answer:
(a) [tex]f(2) = 81[/tex]
(b) [tex]g(2) = 83[/tex]
(c) Test average for maths class after test 2 is greater
Step-by-step explanation:
Given
[tex]f(x) = 0.5x + 80[/tex]
[tex]x \to g(x)[/tex]
[tex]1 \to 81[/tex]
[tex]2 \to 83[/tex]
[tex]3 \to 85[/tex]
Solving (a): f(2)
We have:
[tex]f(x) = 0.5x + 80[/tex]
[tex]f(2) = 0.5*2+80[/tex]
[tex]f(2) = 1 + 80[/tex]
[tex]f(2) = 81[/tex]
Solving (b): g(2)
From the table:
[tex]g(x) = 83[/tex] when [tex]x = 2[/tex]
So:
[tex]g(2) = 83[/tex]
Solving (c): Which is greater f(2) or g(2)
In (a) and (b),
[tex]f(2) = 81[/tex]
[tex]g(2) = 83[/tex]
Hence, test average for maths class is greater
The Camden street Debate team is planning a trip to Florida. The trip cost $17,250
for 15 students to attend. How much is the cost per student? Write a equation to
help you solve the model.
Answer:
Step-by-step explanation:
divide the cost to the students.
use x
x+15= 17250
move 15 other side. which becomes negative
Answer: it is 1,150 per student
Step-by-step explanation: simple 17,250 divided by 15 = 1,150 now double check by 1,150 times 15 =17,250 so I am correct it is 1,150 per student
A stamp gets more expensive each year. It increases in value by 60 % each year. Wha
is the growth FACTOR?
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Answer:
1.60
Step-by-step explanation:
The growth factor is 1 more than the growth rate:
1 + 60% = 1 + 0.60 = 1.60 = growth factor
tank contains 250 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
Solution :
Given data :
[tex]c_{in}[/tex] = 1 g/L
[tex]r_{in}[/tex] = 5 L/min
[tex]r_{out}[/tex] = 5 L/min
[tex]$v_0$[/tex] = 250 L
[tex]A_0[/tex] = 20 g
∴ [tex]r_{net} = r_{in}- r_{out}[/tex]
= 5 - 5
= 0
[tex]c_{out} = \frac{A}{250} \ g/L[/tex]
Now, [tex]\frac{dA}{dt}=(r_{in} \times c_{in}) - (r_{out} \times c_{out})[/tex]
[tex]$\frac{dA}{dt} = 5-5\left(\frac{A}{250}\right)$[/tex]
[tex]\frac{dA}{dt}+5 \left(\frac{A}{250}\right) = 5[/tex]
[tex]\frac{dA}{dt}+5 \left(\frac{A}{250}\right) = 5 \text{ with} \ A_0 = 20[/tex]
Integrating factor = exp(5 t/250)
Therefore,
[tex]A \times \exp (5t \ /250) = \text{integral of}\ 5 \times \exp (5t / 250) + C[/tex]
Put [tex]A_0=250+C[/tex]
C = -230
[tex]A \times \exp(5t/250) = 250 \exp(5t/250) + (-230)[/tex]
[tex]A(t) = 250-230 \exp(-5t/250)[/tex]
[tex]A(t) = 250-230e^{\left(\frac{-t}{50}\right)} \ g[/tex]
In the figure below, which term best describes point A?
S
A
R
A. Incenter
B. Orthocenter
C. Centroid
D. Circumcenter
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 247 feet and a standard deviation of 41 feet. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent. a) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 216 feet
Answer:
77.5% probability that this ball traveled fewer than 216 feet.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 247 feet and a standard deviation of 41 feet.
This means that [tex]\mu = 247, \sigma = 41[/tex]
What is the probability that this ball traveled fewer than 216 feet?
The probability as a decimal is the p-value of Z when X = 216. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{216 - 247}{41}[/tex]
[tex]Z = 0.756[/tex]
[tex]Z = 0.756[/tex] has a p-value of 0.775
0.775*100% = 77.5%
77.5% probability that this ball traveled fewer than 216 feet.
A plumber and his assistant work together to replace the pipes in an old house. The plumber charges $30 an hour for his own labor and $20 an hour for his assistant's labor. The plumber works twice as long as his assistant on this job, and the labor charge on the final bill is $2000. How long did the plumber and his assistant work on this job
Answer:
The plumber worked 50 hours, and his assistant worked 25 hours.
Step-by-step explanation:
Since a plumber and his assistant work together to replace the pipes in an old house, and the plumber charges $ 30 an hour for his own labor and $ 20 an hour for his assistant's labor, and the plumber works twice as long as his assistant on this job, and the labor charge on the final bill is $ 2000, to determine how long did the plumber and his assistant work on this job the following calculation must be performed:
40 x 30 + 20 x 20 = 1200 + 400 = 1600
50 x 30 + 25 x 20 = 1500 + 500 = 2000
Therefore, the plumber worked 50 hours, and his assistant worked 25 hours.
What is the vertex and equation of the axis of symmetry of the graph of y=x^2-6x-7
Answer:
Vertex: (3,16)
Axis of symmetry: x = 3
Step-by-step explanation:
The vertex is the minimum or maximum of the graph.
The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
Write the solution of one-half of two-thirds of three out of four-fifths of 200
Answer:
53 1/3
Step-by-step explanation:
200×4/5=160
160×2/3=106 2/3
106 2/3×1/2=53 1/3
Step-by-step explanation:
200×1/2=100
100×2/3=66.6666666667
so, the question is wrong
Choose the best selection for the
quadrilateral with vertices at the
following points:
(-5,0), (0,4), (5,0), (0,-4)
Hint: Start by graphing the points.
Distance Formula: d= (x2 – x1)2 + (72 - yı)2
A. Rectangle
B. Square
C. Rhombus
D. Trapezoid
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Answer:
C. Rhombus
Step-by-step explanation:
The symmetry of the coordinates tells you the figure has equal-length sides, but the angles are not right angles. Such a figure is a rhombus.
Help with both please
Answer:
Step-by-step explanation:
12. To find the carpet needed. Find the area :
The figure is combination of semi circle and a rectangle.
So Area = Area of semi circle + Area of rectangle
[tex]Area \ of \ semi \ circle = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi \times 25 = 39.25 \ ft^2 \\\\Area \ of \ rectangle = Length \times Breadth = 15 \times 10 =150 \ ft^2[/tex]
Area = 150 + 39.25 = 189.25 sq ft
13. Cost per square feet = $$9.95
Therefore cost for 189.25 square feet = 9.95 x 189.25 = $1883.04
An actuary was analyzing the loss experienced by flooding on houses and concluded that it was uniformly distributed on [0, 1000]. After taking another look at the data, he realized the loss amounts used were in real dollars. He then determined that the inflation rate was at 6.5%. Assume that the rest of his analysis still holds true. Calculate the probability that the loss in nominal dollars is less than 1000, given that the loss in nominal dollars is greater than 200.
Answer:
100% probability that the loss in nominal dollars is less than 1000, given that the loss in nominal dollars is greater than 200.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Uniformly distributed on [0, 1000].
This means that [tex]a = 0, b = 1000[/tex]
Given that the loss in nominal dollars is greater than 200.
This means that [tex]a = 200[/tex]
Calculate the probability that the loss in nominal dollars is less than 1000
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
[tex]P(X < 1000) = \frac{1000 - 200}{1000 - 200} = 1[/tex]
100% probability that the loss in nominal dollars is less than 1000, given that the loss in nominal dollars is greater than 200.
Zara and John are hiking on a trail that 2 miles long .there are signs to mark each eighth of a mile along the trail
Evaluate the expression.
4!
Answer:
4! = 24
Step-by-step explanation:
4! = 4 * 3 * 2 * 1
4! = 24
Each side of a square is (7 + 3x) units. Which is the perimeter of the square?
I’m not sure what it’s asking?
b and c will be reduced
Step-by-step explanation:
exterior angle= sum of other two angles
in the pic the sum is 152 so the exterior angle should've been 152 but it has been decreased so b and c will also decrease........
PLEASE HELP!!!!!!!!!!!!!!!!!!
What are the coordinates of Point P?
Answer:
(-1.5, 0.5)
Step-by-step explanation:
x = -1.5
y = 0.5
(-1.5, 0.5)
2x + y = 3
x - 2y = -1
If equation two is multiplied by -2 and then the equations are added, the result is
3y = 5
5y = 5
-3y = 3
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Answer:
5y = 5
Step-by-step explanation:
-2(x -2y) +(2x +y) = -2(-1) +(3) . . . . -2 times [eq2] + [eq1]
-2x +4y +2x +y = 2 +3 . . . . eliminate parentheses
5y = 5 . . . . . . . . collect terms
And then next time we will come back and
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 16 feet and a height of 19 feet. Container B has a diameter of 20 feet and a height of 15 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?
18.9% is the answer
Step-by-step explanation:
volume of a cylinder = πd²/4 x h
where d is diameter and h is height of cylinder.
thus
vol of A is
[tex]vol \: of \: a \: = \pi \times \frac{ {d}^{2} }{4} \times h \\ = \pi \times \frac{ {16}^{2} }{4} \times 19 \\ = \pi \times 4 \times 16 \times 19 \\ = 3818.24[/tex]
and
[tex]vol \: of \: b = \pi \times \frac{ {20}^{2} }{4} \times 15 \\ = \pi \times 5 \times 20 \times 15 \\ = 4710[/tex]
difference in vol of a and b is
[tex]diff \: = vol \: of \: b \: - vol \: of \: a \\ = 4710 - 3818.24 \\ = 891.76[/tex]
this volume will remain empty after container A is pumped into container B.
this volume as a percentage of total volume of B is
[tex]\% = \frac{diff \: vol}{total \: vol} \times 100 \\ = \frac{891.76}{4710} \times 100 \\ = 18.9\%[/tex]
3 Alex is the manager of a hospital canteen.
He reviews the meals the patients choose.
On Monday there were 240 patients in total.
1/3 of these patients chose pasta.
3/8 of these patients chose beef stew. The other patients chose chicken.
How many patients chose chicken on Monday?
The number of patients chose chicken on Monday is 90.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Given that, there were 240 patients in total.
1/3 of these patients chose pasta.
Number of patients chose pasta
= 1/3 ×240
= 60
3/8 of these patients chose beef stew.
Number of patients chose beef stew
= 3/8 ×240
= 90
Number of patients chose chicken
= 240-(60+90)
= 240-150
= 90
Therefore, the number of patients chose chicken on Monday is 90.
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which undefined term can contain parallel lines?
The difference between the measures of two complementary angles is 56 determine the measures of the two angles. The larger angle has a measure of? And the smaller angle has a measure of?
Answer:
Larger angle= 73, smaller angle= 17
Step-by-step explanation:
I wrote an equation, and x is the measure of one of the angles
90=2x-56
90+56=2x-56+56
146=2x
73=x
One of the angles is 73, so subtract 53 from 73 to find the second angle. 73+56=17
You can make sure it adds up to a complementary angle by seeing if 17+73=90
In circle R, What is the name of line segment BE and AD?
a diameter is a line that starts from the circumference to the other part of the circumference
find the area for brainlest
Answer:
A = 30 units²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 12 and h = 5 , then
A = [tex]\frac{1}{2}[/tex] × 12 × 5 = 6 × 5 = 30 units²
will mark brainliest
Answer:
equation 1or 2 divide
3x+y=7
2x+5y=22
or, equation 1 multiple 5
15x+5y=35
2x+5y=22
or,13x=13
therefore x=1 again
value of x put the y in equation 2
2.1 + 5y=22
5y=11
therefore y=11/5
The dean of a major university claims that the mean number of hours students study at her University (per day) is at most 4.9 hours. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis
Answer:
If the null hypothesis is rejected, the interpreatation is that there is significant evidence at the desired significance level to conclude that the mean time the students study at her university is of more than 4.9 hours.
Step-by-step explanation:
The dean of a major university claims that the mean number of hours students study at her University (per day) is at most 4.9 hours.
At the null hypothesis, we test if the mean is of at most 4.9 hours, that is:
[tex]H_0: \mu \leq 4.9[/tex]
At the alternative hypothesis, we test if the mean is more than 4.9 hours, that is:
[tex]H_1: \mu > 4.9[/tex]
Accepting the null hypothesis:
If the null hypothesis is accepted, the interpretation is that there is not significant evidence to conclude that the mean time the students study at her university is of more than 4.9 hours.
Rejecting the null hypothesis:
As is the case in this question, if the null hypothesis is rejected, the interpreatation is that there is significant evidence at the desired significance level to conclude that the mean time the students study at her university is of more than 4.9 hours.