Answer:
2
Step-by-step explanation:
y² = 4²= 16 (in substitution way)
16÷8= 2
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Answer:
2
Step-by-step explanation:
y^2/8
4^2/8
16/8
2
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Given that f(x) = x² + 4x, evaluate f(-2). -12 -8 -4
Answer:
-4
Step-by-step explanation:
(-2)^2 + 4(-2) =
= 4 - 8 =
= -4
the reaction time of a driver to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.005 seconds. what is the probability that a reaction requires more than 0.5 seconds?
Answer:0.02275
Normal distribution:
Which is symmetrical about mean.
Mean:
It is the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Complement rule:
When two disjoint sets are meant to occur then the sets are said to be complementary.
Given:
Mean= 0.4 seconds
Standard deviation= 0.005 seconds
Let, X be the reaction time for the driver to view stimulus.
So, distribution of X is given by:
X~ N( 0.4, 0.005)
Where σ= 0.05 and µ= 0.4
Solving this ques by using normal standard deviation and z score given as:
z=\frac{x-µ}{σ}
Applying formula:
P(X>0.5)= P{(x-µ/σ) > (0.5-µ/σ)} P {Z > (0.5-0.4/0.05)}
=P(Z > 2)
By using complement rule we get,
P(Z>2) = 1- P(Z<2)
Using normal standard table we have,
P(Z>2)=1- P(Z<2)
= 1- 0.97725
= 0.02275
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The probability that a reaction requires more than 0.5 seconds is 0.0227
Z-score standardization:
The amount of standard deviations the data point deviates from the mean is shown by the standardized z-score.
• If the z-score increases when it is higher than the mean (0).
• If the z-score is below the mean and takes a negative value (0).
Given that,
Mean = μ =0.4
Standard deviation = σ =0.005
The probability that a reaction requires more than 0.5 seconds is obtained by;
Let X denotes the reaction time of a driver which follows a normal distribution with a mean of 0.4 seconds and a standard deviation of 0.005 seconds.
P(X > 0.5) = 1 - P(X < 0.5)
= 1 - P(0.4 < X < 0.5) (0.5 - 0.4/0.005)
= 1 - P(25.06)
= 1 - P(252)
From the “standard normal table”, the area to the left of is 0.9773.
P(X > 0.5) = 1 - P(252)
= 1 - 0.9773
= 0.0227
Hence, the probability that a reaction requires more than 0.5 seconds is 0.0227
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Dakota found a vintage skateboard from the 1980s in her parents' garage. The owner of the local skate shop told her the skateboard is currently worth $380 and will increase in value by about 7% each year. Write an exponential equation in the form y=a(b)x that can model the skateboard's value, y, in x years. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = To the nearest dollar, how much will the skateboard be worth in 7 years?
1. An exponential equation modeling the skateboard's value, y, in x years is y = 380 x 1.07ˣ.
2. The value of the skateboard will be worth $610.28 in seven years.
What is an exponential equation?An exponential equation is a mathematical function that depicts an equation with variable exponents.
The exponential function is always written in the form of y = abˣ.
Where a = the constant or initial value, b = the continuous growth rate, and x or t = the time variable.
Y represents the value that we are looking for after the growth rate has been applied for several (t) years.
The current worth of the skateboard = $380
Annual increase = 7% = 0.07
Number of years = 7 years
Y = 380 x 1.07⁷
= 380 x 1.606
= 610.28
= $610.28
Thus, in seven years, using the exponential equation, the skateboard will be worth $610.28.
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How do i graph this? 4x - 2y > 12
Step-by-step explanation:
X-intercept is where the line crosses the x-axis or where y = 0
So, put y = 0 in the given equation
4x + 2(0) = 12
4x = 12
x = 12/4
x = 3
Please help ASAP!! Screenshot below. 10 points
Answer:
The answer to this equation is (-1,1)
For every 1/3 cups of flour, there are
7/8 cups of pumkin. How much flour (in
cups) should I use for 1 cup of
pumpkin?
Answer: 0.4176 cups of flour
Step-by-step explanation: First you'll need to convert both amounts to the same denominator, using their LCM, which is 24. 1/3 x 8 = 8/24, 7/8 x 3 = 21/24. Then calculate what you need to multiply 21/24 with to get 24/24, 21/24 = 0.875 1.000- 0.875 = 0.125. Finally, multiply 1/3 by 0.125 which is 0.416... / 0.4167, so you'll need 0.4167 cups of flour, or 4,167/10,000 of a cup os flour.
on saturday leon biked an average speed of 14.5 miles per hour for 1.5 hours. then on sunday he biked an average speed of 15 miles per hour for 2.75. what was the total distance leon biked in miles that weekend
The total distance leon biked in miles that weekend is 19.5 miles.
The answer provided below has been developed in a clear step by step manner.
On Saturday, Leon biked 1.5 hours at a speed of 14.5 miles per hour that means distance = 14.5 * 1.5 = 21.75 miles
On Sunday, he biked 2.75 hours at a speed of 15 miles per hour that means distance =15 * 2.75 =41.25 miles
Distance = speed*time use this formula
He farther did in sunday = 41.25 - 21.75 miles = 19.5 miles
Therefore, that weekend Leon rode his bike a total of 19.5 miles.
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23. Amy says, "To find 50 x 20, I multiply 5 x 2 and then place the total number of zeros in both factors at the end." Do you agree? Explain.
That is one way to find out the answer
Can anyone write the equation of the graph?
The equation of the graph represented by the figure is f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we have the following graph that can be used in our computation:
The graph is an absolute value graph
As a general rule, an absolute value is expressed as
y = |x - h| + k
In this case, the vertex is
Vertex = (h, k)
As a general rule, the vertex of a function is the minimum point on the graph
On the given graph, the minimum point is (3, 5)
This means that
(h, k) = (3, 5)
Substitute the values (h, k) = (3, 5) in the equation y = |x - h| + k
So, we have the following representation
y = |x - 3| + 5
Rewrite the equation as a function
f(x) = |x - 3| + 5
Hence, the equation is f(x) = |x - 3| + 5
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Write the equation for the absolute value function graphed
Thank you!
The equation for the absolute value function is y = -2lx-4l + 2
An absolute value function is what?
A function that surrounds an algebraic expression in absolute value symbols is called as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value. The definition of the absolute value parent function is given as follows: f(x)=x if x>00 if x=0 if x0.
Y=a| x+h |+k is the form of the equation for an absolute value function. Also:
The graph's vertex is (h,k).
The range of the graph is y≥k for a>0 and its domain is a set of all real numbers.
The range of the graph is y≤k when a0, and its domain is a set of all real numbers.
X=h is the symmetry axis.
If a>0, it opens up; if a0, it opens down.
The graph of y=a| xh |+k can be created by translating the line graph y=| x | by h units horizontally and k units vertically.
If | a | 1 and if | a | >1, the graph of y=a| x | is wider than the graph of y=| x | and narrower.
So here (h,k)=(4,2)
range of y≤2
and its narrower so a≥1
hence the equation is y = -2 l x-4 l +2
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Answer:
Answer:table B represents the linear equation which is:[tex]y=-3x+11[/tex]The graph of the linear function is also attached below.Step-by-step explanation:Given the table B values x
On May 1st, the temperatures at midnight in five European cities were
measured and the results were as follows.
Glasgow 2°C,
Nice 6°C,
Berlin 0°C,
London 4°C, Oslo -3°C
List the cities in order of the temperature at midnight, starting with the lowest.
Tell whether x and y show a positive, negative, or no relationship.
The coordinates of x and y on the graph can not form a function.
x and y do not show any relationships.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates from the graph.
(2, 0)
(2, 1)
(-1, 2)
(1, 3)
(0, -1)
(2, -3)
(-1, -1)
(3, -2)
We can say that,
A function can not have one to many.
We have,
(2, 0), (2, 1), and (2, -3).
This means,
For x = 2, y = 0, 1, -3.
This is not possible.
Thus,
The coordinates of x and y on the graph can not form a function.
x and y do not show any relationships.
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81% of the tickets sold at an amusement park were discount tickets. If the park sold 800 tickets in all, how many discount tickets did it sell?
Answer:
40% = 0.40800 / 0.40 = 2000 total tickets were sold
Step-by-step explanation:
Answer:
648
Step-by-step explanation:
ans: 81/100 x800
=648
In ΔTUV, m∠T = 58° and m∠U = 97°. Which list has the sides of ΔTUV in order from longest to shortest?
The angle ∠U is the largest in triangle ΔTUV. Then the largest side will be TV.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In ΔTUV, m∠T = 58° and m∠U = 97°.
Then the third angle of the triangle will be given as,
∠T + ∠U + ∠V = 180°
58° + 97° + ∠V = 180°
155° + ∠V = 180°
∠V = 180° - 155°
∠V = 25°
In a triangle, the opposite angle of the largest side will be the largest one.
The angle ∠U is the largest in triangle ΔTUV. Then the largest side will be TV.
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What is the generator for the sequence: 1, 3, 9, 27, 81, ... *
O 2
O 4/3
O 8/3
O 3
Answer:
3
Step-by-step explanation:
what it means by generator is the continuance of the multiplication process so 1x3=3 and then 3x3=9 and so on.
Which of these is not the net of a cube?
a)
b)
B
C
D
Only 1 attempt allowed
Answer: b)
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11. A carpenter needs to be sure that a frame he has built is rectangular. He knows that the opposite
sides of his frame are congruent. Give one additional fact that would be sufficient to guarantee that the
frame is rectangular.
PLEASE HELP
Write the equation of a line that is perpendicular to y = 5 and that passes through the point
(-7, --5).
The equation of the line that is perpendicular to y = 5 and that passes through the point (-7, -5) is x = -7.
We have to find the equation of a line that is perpendicular to y = 5 and that passes through the point (-7, -5).
y = 5 is a line that is parallel to the x-axis hence, the line perpendicular to it will be parallel to the y-axis.
Also, the line touches (-7,-5) hence, it will touch the line y = 5 at (-7,5).
Hence, the line perpendicular to y = 5 and that passes through the point (-7, -5) is x = -7.
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A line passes through point (-2, 8) and has a slope of -5. Write an equation in Ax + By =C form for this line. Use integers for A, B, and C.
25 points
The equation of line with a slope of -5 and which passes through point (-2, 8) is 5x + y = -2.
What is the equation of line with the given point and slope?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point (-2,8)
x = -2y = 8Slope m = -5First, we determine the y-intercept 'b'. Plug the coordinates and slope into the equation of line formula and solve for b.
y = mx + b
8 = (-5)(-2) + b
8 = 10 + b
b = 8 - 10
b = -2
Now, plug values of slope m and y-intercept b into y = mx + b to determine the equation of the line.
y = mx + b
y = (-5)x + (-2)
y = -5x - 2
Convert to standard form; Ax + Bx = C
y = -5x - 2
Reorder the equation
5x + y = - 2
Therefore, the equation of the line is 5x + y = - 2.
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Kelly works at her own nail salon. Today, she did 11 manicures and received $55.00 in overall tips. If x represents the cost of each manicure, which of the following equations can be used to find the total amount of money she earned, including tips, for her nail salon today?
Answer:
5
Step-by-step explanation:
Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
Answer:
The answer is –3 < 1
Step-by-step explanation:
-3 is below zero. 1 is above zero. therefore, -3 less than 1
reggiethenerd10 what is (8.7 + 3.3) x (1/2) 2 to the second power
Answer:
3
Step-by-step explanation:
The value of the operation is 3.
The first step is to solve for the terms in the brackets.
The decimals would be added first 8.7 + 3.3 = 12
The second step is to determine the square of one-half² = x = 1/4
The third step is to multiply, 1/4 by 12 1/4 x 12 = 3
31.24 to 1 deecimal place
Round 31.24 to 1 decimal place:
31.2
Answer:31.2
Step-by-step explanation:
you remove the 4 because it is less than 5.
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Frances owns a landscaping business. She has 425 plants and is placing an equal number of plants into 47 yards. After planting, how many plants will she have left to take home and plant in her own yard?
A. 0 plants
B. 1 plant
C. 2 plants
D. 3 plants
Complete the two column proof.
The two-column table to prove ∠ABC ≅ ∠DBE using the angle addition postulate is presented as follows;
Statements [tex]{}[/tex] Reasons
1. ∠ABD is a right angle [tex]{}[/tex] 1. Given
∠CBE is a right angle
2. ∠ABD are complementary [tex]{}[/tex] 2. Definition of complementary angles
3. ∠CBE are complementary [tex]{}[/tex] 3. Definition of complementary angles
4. ∠ABC ≅ ∠DBE [tex]{}[/tex] 4. Congruent complements theorem
What is the angle addition postulate?The angle addition postulate states that the when two angles are placed side by side such that they share a common ray, the measure of the angle formed by the two angles is the sum of the measure of the individual angles.
∠ABD = ∠ABC + ∠CBD (angle addition postulate)
∠ABD = 90° (definition of right angle)
∠ABC + ∠CBD = 90° (substitution property of equality)
∠ABC and ∠CBD are complementary (definition of complementary)
Similarly
∠CBE = ∠CBD + ∠DBE (angle addition postulate)
∠CBE = 90° (definition of right angle)
∠CBD + ∠DBE = 90° (substitution property of equality)
∠CBD and ∠DBE are complementary (definition of complementary)
∠ABC is a complementary angle to ∠CBD and ∠DBE is a complementary angle to ∠CBD
Therefore;
∠ABC is congruent to ∠DBE (congruent complements theorem)
∠ABC ≅ ∠DBEThe congruent complement theorem states if an angle ∠A is a complement to an angle ∠C and if an angle ∠B is also a complement of angle ∠C then ∠A is congruent to ∠B.
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Write an equation for each line using slope intercept form
Answer:
y = -5/3 - 3
Step-by-step explanation:
Since it's given a graph, we can use rise over run to figure it out
We pick 2 points that are integers on the graph , which means two points on the graph that the line goes through
Example- I picked (-3, 2) and (0, -3), you can indicate them so you don't forget or anything
We now draw a triangle formed by those two points (a line that goes from (-3, 2) to (-3, -3) and a line from (0, -3) to (-3, -3)
Rise (Which is the height of the triangle you just drew) is 5 units, but it's going down, so -5
The base (Run) is 3 units. Using rise/run, the slope is -5/3
The y-intercept, which is at the point where the graph crosses the y-axis, is -3.
The slope intercept form is y=mx+b, where m = slope and b = y-intercept, so the equation of the graph is y = -5/3x -3
1/2 : 2/3 = X:1
[1 mark]
The value of X for the given equation is X = 3/4.
What are the ratio and proportion?A percentage is the equality of two ratios, while a ratio is the divisional comparison of two numbers. As well as being written as x: y or x/y, ratios are sometimes expressed as x is to y.
A proportional equation declares that two ratios are similar on a comparative basis. A ratio means that x is to y as z is to w and is represented as x: y: z: w. Since w and y are not equal in this situation, x/y = z/w.
The given equation is
1/2 : 2/3 = X:1
We can rewrite it as
(1/2)/ (2/3) = X
X = 1/2 × 3/2
X= 3/4
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0.1 times n equal's89.5