Answer:
[tex]\boxed{\sf x = 1, \ x = -5}[/tex]
Explanation:
[tex]\rightarrow \sf 4x^2 + 16x - 20 = 0[/tex]
[tex]\rightarrow \sf 4(x^2 + 4x - 5) = 0[/tex]
[tex]\rightarrow \sf x^2 + 4x - 5 = 0[/tex]
[tex]\rightarrow \sf x^2 + 5x -x- 5 = 0[/tex]
[tex]\rightarrow \sf x(x + 5) -1(x+ 5) = 0[/tex]
[tex]\rightarrow \sf (x-1)(x+ 5) = 0[/tex]
[tex]\rightarrow \sf x = 1, \ x = -5[/tex]
Because the two distributions displayed below have similar shapes, they have
the same standard deviation.
A. True
B. False
Answer:
False, distributions having the same mean and standard deviation can have very different shape of distribution.
GIVING 100 POINTS: The graph shown here displays the distance, in miles. traveled by a jet in a certain number of hours. Based on the graph, which of the following equations indicates the correct variables, and in how many hours does the jet travel 12,000 miles if it travels at the same speed?
Graph titled Motion of a Jet shows Time in hours on x axis and Distance in miles on y axis. A straight line joins the ordered pairs 0, 0 and 2, 1200 and 4, 2400 and 6, 3600.
y = 600x, the jet travels 12,000 miles in 20 hours
x = 600y, the jet travels 12,000 miles in 20 hours
y = 600x, the jet travels 12,000 miles in 22 hours
x = 600y, the jet travels 12,000 miles in 22 hours
Answer:
A. y = 600x, the jet travels 12,000 miles in 20 hours
Explanation:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Take two points: (2, 1200), (4, 2400)
[tex]\sf slope : \dfrac{2400-1200}{4-2 } = 600[/tex]
Equation:
y - 1200 = 600(x - 2)
y - 1200 = 600x - 1200
y = 600x
Miles the Jet travels at 20 hours:
y = 600(20) = 12000 milesMiles the Jet travels at 22 hours:
y = 600(22) = 13200 milesAnswer:
y = 600x, the jet travels 12,000 miles in 20 hours
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y = mx + b[/tex]
where:
m = slopeb = y-interceptTo find the slope, define two points on the line and use the slope formula to find the slope:
[tex]\textsf{let}\:(x_1,y_1)=(0,0)[/tex][tex]\textsf{let}\:(x_2,y_2)=(2, 1200)[/tex][tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1200-0}{2-0}=600[/tex]
From inspection of the graph, the y-intercept (where the line crosses the y-axis) is at (0, 0). Therefore, the equation of the line is:
y = 600x
y is defined as the distance (in miles). Therefore, to find the number of hours it takes for the jet to travel 12,000 miles, substitute y = 12000 into the found equation and solve for x:
[tex]\sf \implies 600x=12000[/tex]
[tex]\sf \implies x=\dfrac{12000}{600}[/tex]
[tex]\sf \implies x=\dfrac{120}{6}[/tex]
[tex]\implies \sf x=20[/tex]
Therefore, it takes the jet 20 hours to travel 12,000 miles.
Bacteria colonies can increase by 73%
every 2 days. If you start with 55 bacteria
microorganisms, how large would the
colony be after 10 days?
Future Amount = [?] microorganisms
←time
Hint: Future Amount = 1(1+r) periods
↑
initial growth
amount rate
Round to the nearest whole number.
The size of the colony after 10 days is 852.
What is the size of the colony after 10 days?The growth rate of the colony can be represented with an exponential equation with the form:
FV = P(1 + r)^n
Where:
p = present population r = rate of growth n = growth factor = 10 days / 2 days = 555(1.73)^5 = 852
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The figure shows a parallelogram PQRS of area 35cm². If T is a point on QR such that QT = 4 cm, TR = 3 cm, find the area of triangle PQT.
Answer:
area of a parallelogram equals to 1/2 x base x perpendicular height and area of a triangle equals to 1/2 base times height so you ought to search for the base in order to get the area of the triangle needed that's how I got the answer bye.
Write an equation for the polynomial graphed below
The expression for the polynomial graphed will be y(x) = (x + 3)(x - 1 )(x - 4 ).
How to factor the polynomial?From the graph, the zeros of the polynomial of given graph are:
x = -3
x = 1
x = 4
Equate the above equations to zero
x + 3 = 0
x - 1 = 0
x - 4 = 0
Multiply the equations
(x + 3)(x - 1 )(x - 4 ) = 0
Express as a function gives;
y = (x + 3)(x - 1 )(x - 4 )
Hence, the factored form of the polynomial will be y = (x + 3)(x - 1 )(x - 4 ) .
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Janelle and Jacob are considering a $130,000 mortgage for 30 years at 4.8%. With this information, their monthly payment
would be $682.06.
If they make only the minimum payment each month, what is the total payback of this loan?
How much of this total payback is interest?
Find equation in slope intercept form of the line passing through the points with given coordinates (-3,-4), (0,-3)
Answer:
Step-by-step explanation:
→ Find the gradient
( -3 --4 ) ÷ ( 0 --3) = 1/3
→ Write into format
y = 1/3x + c
→ Substitute in a coordinate pair
-3 = 0 + c
→ Solve for c
c = -3
→ Write into format
y = 1/3x - 3
I need this rnnn pls helpop
Answer:
200 sqin.
Step-by-step explanation:
10 x 10 + 10 x 10 = 100 + 100
= 200
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
At West Painting, they get about three calls a day asking for an estimate of the cost for having the interior of a house painted. To write up an estimate for the cost of a job, they need to know how much paint a job will take. If they average painting of a room with of a gallon of paint, then they can paint, on average,
rooms per gallon.
Answer:
Using the ratio and proportion method, we find that on an average 1.875 rooms can be painted per gallon.
Step-by-step explanation:
Concept: Use the method of ratio and proportion.
In this method, if a relationship is given between two values, then using that relationship we can find another relationship with respect to another variable.
Given that for 2/5 gallons of paint, we can paint 3/4 of rooms. So, for one gallon of paint, divide 2/5 by 3/4.
2/5 gallons of paint = 3/4 rooms
1 gallon of paint = [tex]\frac{\frac{3}{4} }{\frac{2}{5} } = \frac{15}{8} =1.875[/tex] rooms
So, on an average they can paint 1.875 rooms per gallon.
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Jacob spends 13/4 dollars to paint 9/3 square feet. Find the cost to paint a
square feet per dollar.
The cost to paint a is 12/13 square feet per dollar.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Jacob spends 13/4 dollars to paint 9/3 square feet.
[tex]\dfrac{\dfrac{9}{3}}{ \dfrac{ 13}{4}} = \dfrac{9}{3} \times \dfrac{ 4}{13}\\\\= \dfrac{ 36}{39}\\\\= \dfrac{ 12}{13}[/tex]
Hence, the cost to paint a is 12/13 square feet per dollar.
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What’s the vertex of this graph??
Answer:
(4, -3)
Step-by-step explanation:
A vertex is just a point where 2 lines going in different directions meet. so the answer is (4, -3)
Somebody help please!!
A football teams offense T is found by adding the total passing yardage P to the total rushing yardage R; that is, T=P+R. During the 2012 regular football season, the teams total offense was 4559 yards. The teams passing yardage was 3069 yards. How many yards did the team gain by rushing during the season?
The team gain 1490 yards by rushing during the season.
What is football yardage?Football yardage is the number of yards that a team or player manages to move the ball forward toward their opponent's end zone.
According to the question,
A football teams offense T is found by adding the total passing yardage P to the total rushing yardage R,
i.e. T=P+R
In 2012,
The teams total offense was 4559 yards.
The teams passing yardage was 3069 yards.
By using the formula
T=P+R
T = 4559 yards , P = 3069 yards
Put the values in the above equation;
4559 = 3069 - R
4559 - 3069 = R
R = 1490 yards
Therefore , 1490 yards the team gain rushing during the season.
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a teacher promised a movie day to the class that did better, on average, on their test. The box plot shows the results of the test
The question is incomplete. The complete question is
A teacher promised a movie day to the class that did better, on average, on their test. The box plot shown in the below-mentioned figure shows the results of the test.
Which class should get the reward, and why?
- The 2nd-period class should get the reward. They have the highest score, a perfect 100.
- The 2nd-period class should get the reward. They have a higher median.
- The 4th-period class should get the reward. Though the medians are the same, the first and third quartiles are higher, so the students did better on average than in the 2nd-period class.
- The 4th-period class should get the reward. Their lowest score is an outlier and should be thrown out.
The box plot shown in the question provides the information that
In 2nd period the minimum of the data is 77, first quartile is 78, median of the data is 89, third quartile is 92 and the maximum of the data is 100.
Hence, the mean of the results of 2nd period is
[tex]\frac{77+78+89+92+100}{5}=87.2[/tex]
In 2nd period the minimum of the data is 72, first quartile is 83, median of the data is 89, third quartile is 96 and the maximum of the data is 98.
Hence, the mean of the results of the 4th period is
[tex]\frac{72+83+89+96+98}{5}=87.6[/tex]
Hence, obviously, the 4th period is having more mean.
Moreover, we can observe that if more of the marks are on the higher side the average will automatically be more. Hence, as the first and the third quartiles are more on the 4th-period, so the average marks for the 4th period must be better.
So, just by observing the box plot, we can give the statement that "The 4th-period class should get the reward. Though the medians are the same, the first and third quartiles are higher, so the students did better on average than in the 2nd-period class. "
Therefore, the 4th-period class should get the reward. Though the medians are the same, the first and third quartiles are higher, so the students did better on average than in the 2nd-period class.
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Please help meeeeeeeeee
Answer:
a, b, d
Step-by-step explanation:
its one of those
Answer:
A, the first one
Please help !!! I will give 20 points to the correct answer!!
The function f(x) = 40(0.9)x represents the deer population in a forest x years after it was first studied. What was the deer population when it was first studied?
a. 44
b.40
c. 36
d.49
Answer:
36
Step-by-step explanation:
40*.9
Describe a scenario where the function value exists at x=c, but the limit does not exist.
The scenario can be described using a piecewise function like:
f(x) = 1/x if x < c.
f(x) = x if x = c
f(x) = 1/(x + 73) if x > c.
When the value exists but the limit does not?
Remember that the limit only exists if the limit from left and the limit from the right give the same value.
Then, we can just define a piecewise function of the form:
f(x) = 1/x if x < c.
f(x) = x if x = c
f(x) = 1/(x + 73) if x > c.
Clearly, this is not a continuous function.
Notice that:
[tex]f(c) = c.\\\\ \lim_{x \to c^{-}} f(x) = 1/c\\\\ \lim_{x \to c^{+}} f(x) = 1/(c + 73)[/tex]
So the limits from left and right are different, then:
[tex]\lim_{x \to c^{}} f(x)[/tex]
Does not exist.
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A table lamp emits light in the shape of a hyperbola. If the hyperbola is modeled by the equation 25x2 – 144y2 + 3,600 = 0, which of the following equations represents the boundaries of the light?
y equals five twelfths x and y equals negative five twelfths x
y equals twelve fifths x and y equals negative twelve fifths x
y equals five thirteenths x and y equals negative five thirteenths x
y equals thirteen fifths times x and y equals negative thirteen fifths times x
Answer:
(a) y = 5/12x and y = -5/12x
Step-by-step explanation:
Given the equation of a hyperbola 25x² – 144y² + 3,600 = 0, you want the equations of the asymptotes.
Standard formDividing by 3600 and doing a little rearrangement, we have ...
(y/5)² -(x/12)² = 1 . . . . . standard form equation of a hyperbola
AsymptotesThe equation of the asymptotes is ...
(y/5)² -(x/12)² = 0
Solving for y gives ...
(y/5)² = (x/12)²
y/5 = ±x/12 . . . . . . take the square root
y = ±5/12·x . . . . . . . matches the first choice
__
Additional comment
The equation of a hyperbola with vertices on the y-axis is often written as ...
y²/a² -x²/b² = 1
We have written it in the above form to better show the scale factors applied to x and y.
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Determine the rate of change equation by implicitly differentiating with respect to
time t.
x^4+ y^4 = 4y
By the power and chain rules, taking derivatives on both sides with respect to [tex]t[/tex] gives
[tex]4x^3 \dfrac{dx}{dt} + 4y^3 \dfrac{dy}{dt} = 4\dfrac{dy}{dt}[/tex]
or
[tex]4x^3 \dfrac{dx}{dt} + (4y^3-4) \dfrac{dy}{dt} = 0[/tex]
The mean amount of time it takes a kidney stone to pass is 12 days and the standard deviation is 4 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N
b. Find the probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it.
c. Find the minimum number for the upper quarter of the time to pass a kidney stone.
days.
The probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it is 0.15866 , the minimum number for the upper quarter of the time to pass a kidney stone days is 14.4 .
What is Probability ?Probability is the measure of likeliness of an event to happen
Let X denote the time to pass the kidney stone.
The random variable X follows normal Distribution
mean = 12 days days
standard deviation = 4 days
The distribution of X is X - N ( 12 , 4)
The probability that a randomly selected person with a kidney stone will take longer than 16 days to pass it is
P ( X > 16) = 1 - P( X ≤ 16)
= 1 - P( Z ≤ (16-12)/4)
= 1 - P ( Z ≤ 1 )
= 1 - 0.84134
= 0.15866
P( X < x₀) = 0.75
[tex]\rm P ( \dfrac{x - \mu }{\sigma} < \dfrac{x_0 -13}{6}) = 0.75[/tex]
[tex]\rm \phi (\dfrac { x_o - 12}{4}) = 0.75[/tex]
Using the excel function the z score for the area 0.75 is
z - score = 0.6745
[tex]\rm \dfrac {x_o - 12}{4} = 0.6745[/tex]
x₀ = 0.6 * 4 + 12
x₀ = 14.4
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What is the area of this triangle?
Answer:
sum of all sides
Step-by-step explanation:
x1y2 + x3y3 + x1y1
A piecewise function g(x) is represented by the graph.
Which functions represent a piece of the function? Select three options.
g(x) = −2x, −2 < x < 0
g(x) = −2, x < −2
g(x) = x − 2, −2 < x < 1
g(x) = −2x + 6, x ≥ 1
g(x) = + 1, –2 ≤ x < 1
For different function different results are shown below.
What is Function?A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.
We have been given a graph of piecewise function. Using that we have to select the function from given choices which is represented by graph.
g(x) = −2x, −2 < x < 0
Answer:
NO. Because g(x) = −2x has negative slope so that means it goes downward also there is no y-intercept in g(x) = −2x but the only graph that has y-intercept in given graph goes upward so that can't be answer.
g(x) = −2, x < −2
Answer:
YES. Because g(x) = −2 is a horizontal line which is only on the left side of x=-2. Graph of this part is present in given graph. So yes it is answer.
g(x) = x − 2, −2 < x < 1
Answer:
NO. Because g(x) = x−2 has y-intercept at y=-2 and slope 1 so that means graph of g(x)= x-2 must be going upward and crossing at y=-2 but there is no such graph. Hence this can't be answer.
g(x) = −2x + 6, x ≥ 1
Answer:
YES. Because g(x) = −2x+6 satisfies the graph which is going downward.
g(x) = x/2+ 1, –2 ≤ x < 1
Answer:
YES. Because g(x) = x/2+ 1 satisfies the graph which is going downward.
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Answer: i think this is the answer sorry if i am wrong.
g(x) = −2, x < −2,
g(x) = −2x + 6, x ≥ 1,
g(x) = x/2 + 1, –2 ≤ x < 1
Step-by-step explanation:
Here is the graph
There are two colored marbles and one white marble in a box. Julie mixes the marbles and then Sam draws two marbles at random without replacement. If the two marbles match, Sam wins; otherwise, Julie wins. Does each player have an equal chance of winning? Will adding another white marble give each player an equal chance of winning? What if a game with the same rules was played using three colored marbles and one white marble?
I will give Brainliest
Which is a discrete random variable?
W = "exact time it takes for a computer to update its software"
Z = "results of flipping two coins"
X = "weight of the microprocessor inside your computer"
Y = "height of an emperor penguin on Antarctica"
Answer:
I believe that it should be Y; Height of an emperor penguin on Antarctica
Answer:
Z = "results of flipping two coins"
Step-by-step explanation:
A discrete variable is one which can take only certain values and usually represents values that are counted. The result of flipping two coins can only take a certain number of values of heads or tails (1 head and 1 tail, two heads, or two tails); therefore it is a discrete variable.
A continuous variable is one which can take any value, and usually represents values that are measured. The rest of the options provided (W, X, and Y) are all measurements, and are therefore continuous, not discrete.
Also, among the options presented, option Z is the only one which is "random".
find the measure of angle ACB
Answer:
angle ACB=45º
Step-by-step explanation:
angle 135º lies on a straight line
a straight line = 180º
thus, angle ACB= 180-135=45º
definition of Identity property, Association property and communicative property please answer!
Answer:
09
Step-by-step explanation:
07
Using the distance formula calculate the distance show me example
Answer:
[tex]4\sqrt{26}[/tex]
Step-by-step explanation:
The distance formula is [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
Thus we can plug the numbers in:
[tex]\sqrt{(-2-(-6))^2+(10-(-10))^2}[/tex]
[tex]\sqrt{(4)^2+(20)^2}[/tex]
[tex]\sqrt{16+400}[/tex]
[tex]\sqrt{416}[/tex]
[tex]4\sqrt{26}[/tex]
16x^2+?x+36 perfect square trinomial
Answer:
16x² +48x +36
Step-by-step explanation:
A perfect square trinomial is of the form ...
(a +b)² = a² +2ab +b²
We want to match this form.
__
comparing termsComparing the known terms, we see ...
16x² = a² ⇒ a = 4x
36 = b² ⇒ b = 6
filling in the missing termThe missing term is the linear term:
2ab = 2(4x)(6) = 48x
? = 48
Flying against the jetstream, a jet travels 1710 miles in 3 hours. Flying with the jetstream, the same jet travels 5820 miles in 6 hours. What is the rate of the jet in still air and what is the rate of the jetstream
The rate of the jet against jetstream will be 570 miles per hour and the rate of the jet in still air will be 970 miles per hour.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
Given that:-
Flying against the jetstream, a jet travels 1710 miles in 3 hours. Flying with the jetstream, the same jet travels 5820 miles in 6 hours.The rate of the jet against the jetstream will be calculated as:-
V = [tex]\dfrac{1710}{3}[/tex] = 570 miles per hour
The rate of the jet in still air will be calculated as:-
V = [tex]\dfrac{5820}{6}[/tex] = 970 miles per hour.
Therefore the rate of the jet against jetstream will be 570 miles per hour and the rate of the jet in still air will be 970 miles per hour.
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