Answer:
y=2x-1
Step-by-step explanation:
use slope formula
the substitute into slope intercept form
An ice cube is melting, and the lengths of its sides are decreasing at a rate of 0.8 millimeters per minute At what rate is the volume of the ice cube decreasing when the lengths of the sides of the cube are equal to 18 millimeters? Give your answer correct to the nearest cubic millimeter per minute. Rate of decrease: millimeters3 per minute.
Answer:
The rate of decrease is: [tex]43.2mm^3/min[/tex]
Step-by-step explanation:
Given
[tex]l = 18mm[/tex]
[tex]\frac{dl}{dt} = -0.8mm/min[/tex] ---- We used minus because the rate is decreasing
Required
Rate of decrease when: [tex]l = 18mm[/tex]
The volume of the cube is:
[tex]V = l^3[/tex]
Differentiate
[tex]\frac{dV}{dl} = 3l^2[/tex]
Make dV the subject
[tex]dV = 3l^2 \cdot dl[/tex]
Divide both sides by dt
[tex]\frac{dV}{dt} = 3l^2 \cdot \frac{dl}{dt}[/tex]
Given that: [tex]l = 18mm[/tex] and [tex]\frac{dl}{dt} = -0.8mm/min[/tex]
[tex]\frac{dV}{dt} = 3 * (18mm)^2 * (-0.8mm/min)[/tex]
[tex]\frac{dV}{dt} = 3 * 18 *-0.8mm^3/min[/tex]
[tex]\frac{dV}{dt} = -43.2mm^3/min[/tex]
Hence, the rate of decrease is: 43.2mm^3/min
Based on data from the U.S. Census Bureau, a Pew Research study showed that the percentage of employed individuals ages 25-29 who are college educated is at an all-time high. The study showed that the percentage of employed individuals aged 25-29 with at least a bachelor's degree in 2016 was 40%. In the year 2000, this percentage was 32%, in 1985 it was 25%, and in 1964 it was only 16%.+
What is the population being studied in each of the four years?
a. college educated individuals
b. college educated individuals aged 25-29
c. individuals aged 25-29
d. employed individuals aged 25-29
e. employed individuals
Answer:
d. employed individuals aged 25-29
Step-by-step explanation:
"Population" in a research study is the comprehensive group that the experimenter or the researcher is interested in.
It is given that US Census Bureau, showed that percentage of the employed individual who are of age group 25 years to 29 years are college educated and is at all time high.
The research study focuses on the specific age group of individuals those who graduated form college or at least have a bachelor degree.
Thus the population of the research study those who studied in each of the four years are the employed individuals aged from 25-29.
12 ducks fly overhead. Each of 6 hunters picks one duck at random to aim at and kills it with probability 0.6. What's the expected number of hunters who hit the duck they aim at?
Answer:
The expected number of hunters who hit the duck they aim at is 3.6
Step-by-step explanation:
Given;
number of hunters, n = 6
the probability of killing a duck, p = 0.6
The expected number of hunters who hit the duck they aim at?
In binomial distribution, the expected value is equal to the product of the number of trials and the probability of success.
The expected number of hunters who hit the duck they aim at is calculated as follows;
E = np
E = 0.6 x 6
E = 3.6
Therefore, the expected number of hunters who hit the duck they aim at is 3.6
What is the value of x?
O 20
(x + 40)
(3x)
R
O 35
w
O 60
S
070
Answer:
Hello! answer: 20
Step-by-step explanation:
These are vertical angles meaning they will have the same measure so... 20 + 40 = 60 20 × 3 = 60 therefore x = 20 hope that helps!
In the given scenario, the value of x is 20. The correct option is A.
What is parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. This means that opposite sides of a parallelogram are parallel and congruent, and opposite angles are congruent as well.
To find the value of x in the given diagram, we need to use the fact that the opposite sides of a parallelogram are equal in length.
Therefore, we can set the expressions for the opposite sides equal to each other and solve for x:
x + 40 = 3x
Simplifying the equation, we get:
40 = 2x
Dividing both sides by 2, we get:
x = 20
Therefore, the value of x is 20.
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A ball thrown in the air has a height of y = - 16x² + 50x + 3 feet after x seconds. a) What are the units of measurement for the rate of change of y? b) Find the rate of change of y between x = 0 and x = 2?
(a) ft/s
(b) 1ft/s
Step-by-step explanation:Given equation;
y = (- 16x² + 50x + 3)ft -------------(i)
Where;
y is measured in feet(ft)
x is measured in seconds(s).
(a) The rate of change of y with respect to x is found by dividing the total change in y by the total change in x. i.e
Δy / Δx
Where;
Δy = y₂ - y₁
Δx = x₂ - x₁
∴ Δy / Δx = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] --------------(ii)
Since y is measured in feet, Δy will also be measured in feet.
Also, since x is measured in seconds, Δx will also be measured in seconds.
Therefore, the rate of change of y with respect to x (Δy / Δx) will be measured in feet per second (ft/s)
(b) The rate of change of y between x = 0 and x = 2 can be found by using equation (ii)
Where;
y₂ is the value of y at x = 2 found by substituting x = 2 into equation (i)
y₁ is the value of y at x = 0 found by substituting x = 0 into equation (i)
=> y₂ = - 16(2)² + 50(2) + 3 = 39
=> y₁ = - 16(1)² + 50(1) + 3 = 37
Now, substitute the values of y₂, y₁, x₂ and x₁ into equation (ii)
Δy / Δx = [tex]\frac{39 - 37}{2 - 0}[/tex]
Δy / Δx = [tex]\frac{2}{2}[/tex]
Δy / Δx = 1
Therefore, the rate of change of y is 1 ft/s
A survey of 2392 adults ages 18 and over asked what type of food they would be most likely to choose at a restaurant. The results are shown in the figure.
A circle graph titled Survey Results is divided into 6 regions showing different types of restaurants. Starting from the top right, the regions are labeled, American 670, Italian 526, Mexican 407, Chinese 383, Japanese 167, Other 239.
What is the probability that an adult chosen at random prefers Italian food? Round your answer to the nearest whole percent.
Answer:
22%
Step-by-step explanation:
their is a total of 2392 adults, the number of people, who would be most likely to chose Italian food is 526.
p= 526/ 2392=22%
The probability of choosing Italian food is 21.9%.
What is probability?"Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one".
For the given situation,
Total number of adults = 2392
American food = 670
Italian food = 526
Mexican food = 407
Chinese food = 383
Japanese food = 167
Others = 239
The event is the probability of choosing Italian food.
[tex]P(e)=\frac{526}{2392}[/tex]
⇒[tex]P(e)=0.219[/tex]
Rounded to nearest whole percent = [tex]0.219[/tex] × [tex]100[/tex]
⇒[tex]21.9\%[/tex]
Hence we can conclude that the probability of choosing Italian food is 21.9%.
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Which statement correctly identifies the line of reflection?
The triangles are reflected across the x-axis.
The triangles are reflected across the y-axis.
The triangles are reflected across the line y = x.
The triangles are reflected across the line y = –x.
what is
3⋅f(−4)−3⋅g(−2)=
Answer:
[tex]3 * f(-8) - 3 * g(-2) = 6[/tex]
Step-by-step explanation:
Given
This question has a missing graph (See online)
Required
[tex]3 * f(-8) - 3 * g(-2)[/tex]
From the graph:
[tex]f(-8) = -2[/tex]
and
[tex]g(-2) = -4[/tex]
So, we have:
[tex]3 * f(-8) - 3 * g(-2) = 3 * -2 -3 * -4[/tex]
[tex]3 * f(-8) - 3 * g(-2) = 6[/tex]
help please quick please
Answer:
the answer is 3.5
Step-by-step explanation:
I need help, please answer A and B.
Answer:
a. 81 square inches
b. 108 inches
Step-by-step explanation:
The area of all 5 squares combined is 405 square inches. This is 5 times the area of 1 square. 405/5 = 81. The area of 1 square is 81 square inches.
Since this is a square, the sides are equal. Thankfully the area of 1 square is a perfect square so the length of one side of the square is a full number, which is 9. All of the squares are congruent as shown in the diagram so we simply add every length together (there are 12 sides, each side is 9 inches).
12*9 = 108 and that is the perimeter.
Answer:
area
Step-by-step explanation:
a = 405/5 = 81
a =81 square inches
perimeter
p = √81
= 9
=4×9×5
=180 inches
find the median of the data in the dot plot below. Mass of each rock in Nija's collection
Answer:
40
Step-by-step explanation:
The median is the middle number
There are 10 numbers
The middle is between 5th and 6th number
Take the 5th and 6th numbers and average them
(39+41)/2 = 80/2 = 40
The median is 40
Mass of each rock in Nija's collection is 40.
Answer:
The median is the middle number
n=10 numbers
The middle is between 5th and 6th number
Taking the 5th and 6th numbers:
average(39+41)/2 = 80/2 = 40
Find the angle(s) of intersection between the equations f (x) = x^2 + 2x + 1 and g(x) = 1.
There could be more that one answer
18.4
26.6
71.6
63.4 (already know that this is definitely one of the options)
Answer:
seems to be the same as the other angle
Step-by-step explanation:
i use desmos for these graphs btw
What is the value of x?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
x =___m
Answer:
<W=180 - (30+81)
<W=69°
Using Sine rule to evaluate x
x/sin30 = 19/sin69
x= 19sin30/sin69
x= 10.2m ( Nearest tenth)
Which of the following is most likely the next step in the series?
Answer:
B
Step-by-step explanation:
Hi there!
TL;DR: Observe the vertices of the shapes inside the circles and their relationship with the circle.
For the first figure, the rectangle has 4 vertices and there are 4 dots on the perimeter of the circle.
For the second figure, the triangle has 3 vertices and there are 3 dots on the perimeter of the circle.
For the third figure, the line has 2 points and there are 2 dots on the perimeter of the circle.
For the fourth figure, there would most likely be only one dot on the perimeter of the circle (4, 3, 2, 1). The only option that shows this is B.
I hope this helps!
What is the probability that you roll a dice and get 3, then get an ace from a deck, then (without replacing the other card) draw a black 2?
I Really need help!
=============================================================
Explanation:
1/6 is the probability of rolling a '3' since there is one side we want out of 6 total.
The probability of getting an ace is 4/52 because there are 4 aces out of 52 cards total.
If that card isn't put back, then we have 52-1 = 51 cards left. That means the probability of drawing a black 2 is 2/51. The numerator 2 has nothing to do with the card value of '2'. It has to do with the fact we have 2 black cards (2 of spades, 2 of clubs) out of 51 left over.
We multiply the fractions to get the final answer
(1/6)*(4/52)*(2/51)
(1*4*2)/(6*52*51)
8/15912
1/1989
When using a calculator, we can see that,
1/1989 = 0.0005 = 0.05%
There is a very small chance of all three events happening at the same time.
The hours of daylight, y, in Utica in days x from January 1, 2013 can be modeled by the equation y = 2.89sin(0.0145x-1.40) + 10.99. How many hours of daylight, to the nearest tenth, does this model predict for February 21, 2013?
Answer:
9.3 hours
Step-by-step explanation:
Given
[tex]y = 2.89\sin(0.0145x-1.40) + 10.99.[/tex]
Required
Hours of sunlight on Feb 21, 2013
First, calculate the number of days from Jan 1, 2013 to Feb 21, 2013
[tex]days = 52[/tex]
So:
[tex]x = 52[/tex]
So, we have:
[tex]y = 2.89\sin(0.0145x-1.40) + 10.99.[/tex]
[tex]y = 2.89\sin(0.0145*52-1.40) + 10.99.[/tex]
[tex]y = 2.89\sin(0.754-1.40) + 10.99.[/tex]
[tex]y = 2.89\sin(-0.646) + 10.99.[/tex]
[tex]y = 2.89*-0.6020 + 10.99.[/tex]
[tex]y = -1.740 + 10.99.[/tex]
[tex]y = 9.25[/tex]
[tex]y = 9.3[/tex] --- approximated
Solve the homogeneous linear system corresponding to the given coefficient matrix.
[1 0 0 1]
[0 0 1 0]
[0 0 0 0]
(x1, x2, x3, x4) =________
This question is incomplete, the complete question is;
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)
[1 0 0 1]
[0 0 1 0]
[0 0 0 0]
(x1, x2, x3, x4) =________
Answer:
the solution for the given system is; ( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )
Step-by-step explanation:
Given the data in the question;
coefficient matrix
[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right][/tex]
Now, from linear system;
[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right] \left[\begin{array}{ccc}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{ccc}0\\0\\0\\0\end{array}\right][/tex]
So, with the matrix, the associated equation is;
x₁ + x₄ = 0, x₃ = 0
Number of variables is 4 and ranked of the matrix is 2,
Hence, there are infinite solutions,
There are also two free variables;
from the question,
Let x₄ = t and x₂ = s be the free variables
so
x₁ + x₄ = 0
x₁ + t = 0
x₁ = -t
Therefore, the solution for the given system is;
( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )
Consider the function f(x) = 2^x
and function g
g(x) = f(x) + 6
How will the graph of function g differ from the graph of function ?
Answer:
The graph of function g is the graph of function f shifted 6 units up
Step-by-step explanation:
If you plug in the values, [tex]g(x) = 2^{x} + 6[/tex]. If the 6 was added or subtracted from the x in the exponent, it would shift horizontally (left and right), but adding 6 to f(x) separately moves the graph vertically (up and down). Hope this helps.
please help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
the correct answer is marked
Step-by-step explanation:
The circle with center (h, k) and radius r has equation ...
(x -h)² +(y-k)² = r²
For the given center, that is ...
(x -1)² +(y +1)² = r²
The value of r² can be found by using the given point for x and y, and seeing what value of r² makes the equation true.
(5 -1)² +(7 +1)² = 4² +8² = 16 +64 = 80
So, r² = 80 makes the equation true, and that equation is ...
(x -1)² +(y +1)² = 80
How do I do this ahh!?
Find the final total value of a 5-year investment of $2600 at a simple annual rate of
3.53%
Answer:
A = $3,101.09
A = P + I where
P (principal) = $2,600.00
I (interest) = $501.09
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.53/100
r = 0.0353 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 2,600.00(1 + 0.0353/12)(12)(5)
A = 2,600.00(1 + 0.002941667)(60)
A = $3,101.09
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $2,600.00 at a rate of 3.53% per year compounded 12 times per year over 5 years is $3,101.09.
uppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5 and a standard deviation of 0.37. Using the empirical rule, what percentage of the students have grade point averages that are no more than 3.24
Answer:
[tex]P(x \le 3.24) = 0.97725[/tex]
Step-by-step explanation:
Given
[tex]\bar x = 2.5[/tex]
[tex]\sigma = 0.37[/tex]
Required
Percentage that is not more than 3.24
The above implies that:
[tex]x = 3.24[/tex]
Calculate z score
[tex]z = \frac{x - \bar x}{\sigma}[/tex]
[tex]z = \frac{3.24 - 2.5}{0.37}[/tex]
[tex]z = \frac{0.74}{0.37}[/tex]
[tex]z = 2[/tex]
So, the probability is represented s:
[tex]P(x \le 3.24) = P(z \le 2)[/tex]
From z probability
[tex]P(z \le 2) = 0.97725[/tex]
Hence:
[tex]P(x \le 3.24) = 0.97725[/tex]
Find the amount of interest for a 18-year investment of $4300 at a simple annual rate
of 4.07%
PLEASE ANSWE QUICK
Complete the factored form of the linear expression.
15x + 12y = ( )( + )
Answer:
3(5x + 4y)
Step-by-step explanation:
Given
15x + 12y ← factor out 3 from each term
= 3(5x + 4y) ← in factored form
Simplify: -8x +7-5-5x + 5x
A
- 8x + 2
B
-18x+12
-x-5
D
-X+12
Answer:
A) -8x+2
Step-by-step explanation:
-8x + 7 - 5 - 5x + 5x
-8x -5x + 5x + 7 - 5
- 8x+2
A video game that usually costs $30.65 is marked down 60%. Kelvin determined that the new price of the game would be $18.39. Look at Kelvin's work and find his error. ($30.65)(0.60) = $18.39
*Please give an explanation longer than 1 sentence :,)
Answer:
Kelvin’s error is that when he got the final result, that was the amount that was marked down. He still needed to find the price after the original price was marked down by that number wich in this case is $18.39. So using one of his steps, 30.65(0.6)=18.39. We can subtract 30.65 (original price) and 18.39 (mark down price). You’d get 11.26 dollars as the final price.
Suppose annual salaries for sales associates from Geoff's Computer Shack have a mean of $32,500 and a standard deviation of $2,500.
a. Calculate and interpret the z-score for a sales associate who makes $36,000.
b. Suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. Use the empirical rule to calculate the percentage of sales associates with salaries between $27,500 and $37,500.
c. Use the empirical rule to determine the percentage of sales associates with salaries less than $27,500.
d. Still suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. A sales associate makes $42,000. Should this salary be considered an outlier? Explain.
Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) = $32500, standard deviation (σ) = $2500.
a) The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
For x < 36000:
[tex]z=\frac{36000-32500}{2500}=1.4[/tex]
From the normal distribution table, P(x < 36000) = P(z < 1.4) = 0.9192 = 91.92%
b) One standard deviation of mean = μ ± σ = (32500 ± 2500) = (30000, 35000)
Two standard deviation of mean = μ ± 2σ = (32500 ± 2*2500) = (27500, 37500)
Empirical rule states that 68% of data falls within one standard deviation from the mean, 95% falls within two standard deviation from the mean and 99.7% falls within one standard deviation from the mean.
Hence 95% of salaries is between $27,500 and $37,500.
c) 95% of salaries is between $27,500 and $37,500.
P(x < 27500) = (100% - 95%) / 2 = 2.5%
d) If the z score is less than -3 or greater than 3, it is considered an outlier.
For x < 42000:
[tex]z=\frac{42000-32500}{2500}=3.8[/tex]
Hence $42000 is an outlier
which point lies on the line described by the equation below?
( I am pulling an all nighter for high school and this question is really important)
Answer:
F (5,-8)
Step-by-step explanation:
By rearranging,
y= 4x-28
Substitute each of the x values of the answers, eventually you will get to F and discover that when x = 5, y= -8
y= 4(5) - 28
y= -8
So, when x= 5, y= -8,
Point F is (5,-8)
Right answers only pls I am gonna fail rn pls help
Answer:
y = 5x – ¼
Step-by-step explanation:
The equation for the slope intercept form is given by:
y = mx + c
Where m and c are the slope and intercept on the y-axis respectively.
From the equation i.e y = mx + c, we can see that y is the subject of the equation.
Now, comparing the equation of the slope intercept form (i.e y = mx + c) with those given in the question above, we can see that only the equation:
y = 5x – ¼
has y as the subject of the equation.
Therefore, y = 5x – ¼ gives the correct answer to the question.
1)Light travels at the speed of 3,00,000 km in one second ,if it has
already travelled 1,05,342 km, how much more distance is left for the
ray of light to travel?
Answer:
1,94,658km
Step-by-step explanation:
If you are talking about how much distance it has to travel in 1 second then you can simply subtract 1,05,342 from 3,00,000. This process gives total of 1,94,658km remaining for it to travel.
Goodluck