The maximum and minimum measurements are 5 and -3 respectively.
f ( x ) = -x^3 +3x^2+ 45 x + 10
f' l x ) = 0
0 = - 3x^2 +6x +45
x = 5,- 3.
f ( 4 ) = - ( 4 )^3+ 3( 4 )^ 2 + 45 ( 4 ) + 10 = 174
f ( - 4 ) = - ( - 4 )^3 + 3( - 4 )^2 + 45(- 4) + 10 = - 58
f ( - 3 ) = -(- 3 )^3 + 3 ( - 3)^2 + 45 (- 3) + 10 = - 7 1
+ ( 5 ) = -(5)^3 + 3(5 )^2 +45(5)+ 10 = 185
Absolute maximum = maxis{ f(4 ),f(5),f(-4),f( - 3 )}
= 185 at x=5
Absolute mininum=minis{f(4 ),f(5),f(-4),f( - 3 )}
= - 71 at x= -3
In light of this, the maximum and minimum values are 5 and -3, respectively.
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Which capital letters in the word TRANSFORMATION produce the same letter after being rotated 180°?
The capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter are I, N, O and S.
Define the term rotation?Geometry can be used to determine the meaning of rotation in mathematics. As a result, it is described as the movement of an object round the center or an axis.The point of rotation is the point where the object is rotated.An angle of rotation is the degree of rotation calculated in degrees.It is possible to rotate clockwise or counterclockwise. If an item needs to be rotated, there are several methods for doing so:
90 degrees counterclockwise90° counterclockwise180 degrees counterclockwiseanticlockwise 180 degreesWhen the capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter: I, N, O and S.
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Please Help! What is the ratio of a:b?
a+3b/5 = a-2b/2
The ratio of a : b in the given expression is 16:3 .
In the question ,
it is given that
the algebraic expression is (a+3b)/5 = (a-2b)/2
we have to find the ratio of a:b ,
in order to find the ratio,
we cross multiplying ,
On cross multiplying , we get
2 * (a+3b) = 5 * (a-2b)
2a + 6b = 5a - 10b
5a - 2a = 10b + 6b
3a = 16b
dividing both sides by b ,
a/b = 16/3
a:b = 16:3
Therefore , The ratio of a : b in the given expression is 16:3 .
The given question is incomplete , the complete question is
What is the ratio of a:b in the expression (a+3b)/5 = (a-2b)/2 ?
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Mr. solo invested in the certificate of deposit that pays 8% interest investment was $325 how much interest will she receive in one year
Using the simple interest formula, Mr. Solo received $26 interest.
In the given question we have to find how much interest Mr. Solo received.
The investment(P) = $325.
Interest rate(R) = 8%
Time(T) = 1 year
Finding the interest using the simple interest formula.
I = PRT/100
where I = interest
P = Principal Amount
T = Time
R = Interest Rate
Putting the value
I = 325*8*1/100
I = 26
Hence, Mr. Solo received $26 interest.
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If you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually? Is there anything you could change in the problem that would make you change your answer?
a. I would rather compound annually at 5 % interest
b. I would increase the simple interest rate if i were to change my answer
a. How to determine which option to choose?Since you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually, we need to determine the amount of each type of interest after 10 years.
Since you have $200 to invest for 10 years at 7% simple interest, using the simple interest formula for the amount, we have
A = P(1 + rt) where
P = principal amount = $ 200, r = rate = 7% = 0.07 and t = time = 10 yearsSubstituting the values of the variables into the equation, we have
A = P(1 + rt)
A = 200(1 + 0.07 × 10)
A = 200(1 + 0.7)
A = 200(1.7)
A = 340
Also, since you have $200 to invest for 10 years at 5% interest compounded annually, using the compound interest formula for the amount, we have
A' = P(1 + r)ⁿ where
P = principal amount = $ 200, r = rate = 7% = 0.07 and n = time = 10 yearsSubstituting the values of the variables into the equation, we have
A' = P(1 + r)ⁿ
A' = 200(1 + 0.07)¹⁰
A' = 200(1.07)¹⁰
A' = 200(1.9672)
A' = 393.43
Since A' = $393.43 > A = $340, i would rather compound annually at 5 % interest
b. Is there anything you could change in the problem that would make you change your answer?To change my answer, I would increase the simple interest rate if i were to change my answer
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Consider the line y=-3/4x-9.
Find the equation of the line that is perpendicular to this line and passes through the point (-4, 2).
Find the equation of the line that is parallel to this line and passes through the point (-4, 2).
Equation of perpendicular line:
Equation of parallel line:
Answer:
Equation of Perpendicular Line: 4x-3y=22
Equation of parallel line:3x+4y+4=
e-8/find-the-slope-from-two-points
On two poinICS ZAC
he line that passes through (10, 7) and (3, 1).
wer and write it as a proper fraction, improper fraction, or r
The slop m is ( 2-3).The slope formula, or the ratio of the change in the y values to the change in the x values, is m is equal to subtraction of y2 and y1 and divide by subtraction of x2 and x1 The initial point's coordinates are x1 and y1, respectively.
How to find slop?The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1). The initial point's coordinates are x1 and y1, respectively.
(10, 7) and (3, 1).
m=(y2-y1)/(x2-x1).
3-1 / 7-10= 2/-3
The slop m is ( 2-3)
When determining the slope of a straight line without its equation, there are three steps. The first point's coordinates are x1 and y1. Step one is to locate the line's first two points. Step 2: Decide which will be (x1, y1) and which will be (x2, y2). Step 3: Determine the slope using the slope equation.
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pls help with this question
Answer:99
Step-by-step explanation:
1/2 x18x11
99
time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 2 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (round your answer to four decimal places.)
We utilize the z statistic to find the probability percentage. Calculating the z value and then looking up the p value using the common probability tables is the process to follow. The z score formula is:
Z = (x - )/ ( / sqrt(n)
where,
x=11, sample score.10 is the sample mean.Standard deviation equals 2
sample size, n With n = 5, calculating the z and p values:
z =(11 - 10) / (2 / sqrt(5))z = 1.12The tables show that p(5) = 0.8686.
For n = 6, calculate the z and p values as follows:
z =(11 - 10) / (2 / sqrt(6))z = 1.22The tables show that p(6) = 0.8888.
If both days to occur, the probability that each day will last no more than 11 minutes is as follows:
p total = p(5) * p(6)p total = 0.8686 * 0.8888p total = 0.772learn more about probability click here:
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I don’t know the answer to this can you please help me
Answer:
The answer is 24 I think
Step-by-step explanation:
just multipy the numbers
Solve for y
q• (a + y) = 67y + 93
Answer: y = 160/q -a
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Write each trigonometrie ratio as a fraction and as a decimal rounded to the nearest hundredth.
Answer: length C to A is .001 and c to b is 0.03 and b to a is 0.04
Step-by-step explanation:
A youth group is planning a trip to a local amusement park. They are taking a van which holds 10 people. It will cost $25 for parking and tickets to enter the park are $18 per person. Create a table to represent the situation, showing the possible total costs for the various numbers of people who could go?
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located
1,-1), and Monique's desk is located at (-4, 5). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
O√7 feet
O√14 feet
√85 feet
O√61 feet
√14 feet, A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
What is coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
Coordinates are a pair of numbers that identify a specific point on a coordinate plane, which is a grid of integers. A point in a plane has specific coordinates, as we are aware. Any point's location on a plane can be described by an ordered pair of numbers, or coordinates, which are written as ((x,y)).
A coordinate can be expressed in one of three ways. a coordinate with an integer for degrees, a real number for minutes, and an integer for seconds (DMS). a coordinate that contains minutes (a real number) and degrees (an integer) (MinDec). a coordinate that merely contains degrees (real number).
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What is the end behavior for the liner function?
Lines do not end, so there can not be an end behavior.
What is straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The equation of the right sideline is y+8 = [tex]\frac{4+8}{2-0}[/tex] (x-0)
y+8 = 6(x -0)
y =6x - 8
Now the endpoint of the line is given so it will not extend indefinitely.
Hence the Lines do not end so there can not be an end behavior.
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find the quotient of 67.98÷28 round your answer to the hundredths place
Answer:
2.43
Step-by-step explanation:
The quotient is the answer to a division problem.
67.98/28 = ~2.42785714286
To round to the nearest hundredth, leave 2 decimal digits remaining. If the thousandth place (3rd decimal digit) is greater they or equal to 5, add 1 to the hundredths digits.
7 [tex]\geq[/tex] 5
2.42+0.01
2.43
Find the value of x and 3x
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
now let's consider the white, "cut-out" triangle on the left side.
the purple one angles at the top and bottom corner are 45°.
the withe outer angles at the same corners (they are the inner angles for the white triangle) are complementary angles (together they have 90°) to the purple ones, because due to the equal angles at the top and bottom we know the connection between the 2 45° angles (the white baseline) is at a 90° angle to the 45° to 135° sides.
so the 2 baseline angles of the left white triangle are also 45° (45+45 = 90).
and that means that the third white angle is
180 - 45 - 45 = 90°.
and because a full circle around the 3x° point must have 360° (as any full circle), we know that both angles (90° and 3x°) together are 360°.
360 = 90 + 3x
270 = 3x
x = 90°
3x = 270°
Toss one dime.
The probability of getting heads
is 1. Predict how many times
you would get heads if you
flipped the dime 200 times.
[?] times
We can get heads for 200 times if we flipped the dime for 200 times.
What do you mean by Probability?
Probability is a mathematical measurement to measure the possibility of happening a particular incident or event mathematically.
Also, from the definition of probability, Probability is the ratio of the Number of Favorable event points to the number of total event points with respect to a particular event or incident.
[tex]Probability=\frac{Number of Favorable event Points}{Number of Total event Points}[/tex]
According to the given problem,
The probability of getting heads is 1.
Total number of flip of dime is 200
so, we can get heads from 200 flips [tex]=200*1=200 Times[/tex]
Hence, we get 200 heads from 200 flips of dime.
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A point has the coordinates (0, k).
Which reflection of the point will produce an image at the same coordinates, (0, k)?
The reflection of point produce an image at the same coordinates, (0, k) is a reflection of the point across the y-axis.
What is Reflection?A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting a figure in a line or a point.
Every point of a figure is translated to an image across a fixed line via a reflection. The fixed line is referred to as the reflection line.
Given:
A point has the coordinates (0, k).
The rule for a reflection of a point across the x-axis is:
(x, y) ----> (x, -y)
and, the reflection is (0 , -k)
The rule for a reflection of a point across the y-axis is:
(x, y) ----> (-x, y)
and, the reflection is (-0 , k) or (0, k).
The rule for a reflection of a point across the line y = x is:
(x, y) ----> (y, x)
and, the reflection is (k, 0).
and, The rule for a reflection of a point across the line y = -x is:
(x, y) ----> (-y, x)
and, the reflection is (-k, 0)
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when the repeating decimal $0.\overline{12}$ is expressed as a common fraction in lowest terms, what is the sum of its numerator and denominator?
The sum of the numerator and denominator of the decimal is found as 111.
Define the term common fraction?A fraction with an integer for both the numerator and denominator is referred to as a common fraction or vulgar fraction.A fraction with an integer for both the numerator and denominator is described to as a common fraction or vulgar fraction.A ratio can be named with a common fraction.Boys outnumber females in a class 4:3, or 4/3. 4/3 is a popular proportion.As for the given question;
The decimal number is given as;
0.12 bar
Decimal to fraction conversion
100(0.12 bar) = 12(0.12 bar)
99.(0.12bar) = 100(0.12bar) - (0.12 bar)
99.(0.12bar) = 12 × 0.12bar - 0.12bar
99.(0.12bar) = 12
0.12 bar = 12/99 (lowest fraction)
Thus, in the result the numerator is found as 12 and the denominator is found as 99.
Add = 12 + 99
Add = 111
Thus, the sum of the numerator and denominator of the decimal is found as 111.
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Julio is running in a 13.1 mile race. There are water stops every 2.75 miles along the route from the beginning of the race. What is the distance between the last water stop and the end of the race?
There is 2.1 miles distance between the last water stop and the end of the race.
Total miles Julio will run = 13.1 miles
Distance at which water stops are location = 2.75
Total number of water stops in full race of 13.1 miles = 13.1 / 2.75
=4.764
so , there are 4 stops in the runs for drinking water every 2.75 miles
Distance from starting point of race and last water stops = 4 × 2.75 = 11 miles
Distance between the last water stop and the end of the race = 13.1 - 11
= 2.1 miles
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a student cycles for x hours at 12km/h and y hours at 16km/h.altogether, tge student cycles 66km in 5 hours. find x and y
Answer:
x = 3.5 hours
y = 1.5 hours
Step-by-step explanation:
There are two unknowns, x and y, both in umits of hours. We need at least two equations before we start trying to solve this with substitution. Looking at the information, this should be possible.
First, we know that Speed x Time = Distance.
The distance covered by the cyclyst would be the sum of (12km/h)*x and (16km/h)*y, where x is the time, in hours, for the slower speed and y for the faster. Together, the student travels 66 km.
The total distance of 66 km would be comprised of the two distances 12x and 16y:
12x + 16y = 66 km
For the second equation, we know that the total time is 5 hours. That would be the sum of x and y:
x + y = 5 hours
We now have 2 equations, so we stand a good chance of finding the answer. Pick one of the equations and isolate one of the variables to one side. Let's choose x + y = 5 hours, since that is easy to rearrange:
x = 5-y
Now take the first equation and substitute the definition of x from above (5-y):
12x + 16y = 66
12(5-y) + 16y = 66
60-12y + 16y = 66
4y = 66-60
4y = 6
y = (6/4) or 1.5 h
The time spent at 16 km/h was 1.5 hours.
Use this value of y in either equation to find x. Let's use x+y=5, since that will be easier:
x+y = 5 for y = 1.5
x+1.5 = 5
x = 3.5h
The time spent at 12 km/h was 3.5 hours
sam rolls 3 standard fair dice. that probability that the three numbers rolled on the dice are the sides of a triangle is , where are relatively prime positive integers. what is the value of ?
The required probability for three numbers rolled on the dice are the sides of a triangle is 31/36.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability.
Here,
When three dice are rolled, there are 63=216 possible outcomes, or triplets (x, y, z).
Once more, in a triangle, any two sides added together are larger than the third side, or (x+y)>z.
As a result, 186 outcomes or triplets are possible and satisfy this property.
Hence, the required probability is 186/216=31/36.
The required probability is 31/36 for three dice rolls to produce triangle sides.
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one serving of wheat square cereal has 11 grams of fiber, which is 32% of the recommended daily amount. what is the total recommended daily amount of fiber? round your answer to the nearest tenth if necessary.
Using the principle of proportional relationship, the total recommended daily amount of fiber is 34.4 grams
Let x be the recommended daily amount ( in grams ) of the fiber,
So, 32% of x = [tex]\frac{32}{100}x[/tex] = 0.32x
According to the question,
11 grams is 32% of the recommended daily amount of fiber,
That is, 0.32x = 11
x = 11/0.32 = 34.4 grams
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Which statement is true?
O
The letter has rotation symmetry only.
0
The letter has both reflection and rotation symmetry.
The letter has neither reflection nor rotation symmetry,
The letter has reflection symmetry only.
The letter has reflection symmetry only. When one half of an object or form reflects the other half, this is known as reflection symmetry. The line where you cut is referred to as the line of symmetry, generating the two equal portions, and the two halves are reflections of one another.
What is reflection symmetry?Mirror symmetry, line symmetry, reflection symmetry, and mirror-image symmetry are all terms used in mathematics to describe symmetry with respect to a reflection. To put it another way, a figure with reflectional symmetry is unaffected by reflection. There is a symmetry line or axis in 2D and a symmetry plane in 3D.
A sort of symmetry that pertains to reflections is called reflection symmetry. Line symmetry and mirror symmetry are other names for reflection symmetry. If a figure has at least one line dividing it into two halves, one half is said to be the mirror image of the other half.
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help me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
the flight path of a rocket or a thrown object is a parabola as described by the function.
h(t) = -16t² + 40t + 7
the negative sign of the prime coefficient (-16) tells us that the parabola opens downwards, and that the vertex as the extreme point of the parabola is a maximum.
we get the extreme point of a curve by finding the zero solution of the first derivative of the function.
and the extreme value itself by using that value in the original equation and calculate the result.
h'(t) = -32t + 40
0 = -32t + 40
32t = 40
t = 40/32 = 5/4 = 1.25 seconds
h(5/4) = -16×(5/4)² + 40×5/4 + 7 =
= -16×25/16 + 10×5 + 7 =
= -25 + 50 + 7 = 32 ft
the rocket will reach its maximum height of 32 ft after 1.25 seconds.
The legs of an isosceles triangle are 0.3 foot less than twice the base. The perimeter of the triangle is 4.9 feet.
What is the length of one of the triangle’s legs?
A. 1.1 feet
B. 1.4 feet
C. 1.9 feet
D. 2.2 feet
The length of the given isosceles triangle legs is 1.9 feet.
What is a Linear equation?A linear equation is a equation that has degree as one.
To find the solution of n unknown quantities n number of equations with n number of variables are required.
Given that,
The perimeter of an isosceles triangle is 4.9 feet.
And, legs of the triangle are 0.3 foot less than twice the base.
Suppose the base of the triangle be x.
Then, its legs are 2x - 0.3.
As per the question the expression for the perimeter of the triangle is,
2x - 0.3 + 2x - 0.3 + x = 4.9
=> 5x - 0.6 = 4.9
=> 5x = 5.5
=> x = 1.1
Thus, the legs can be found by substituting x = 1.1 in 2x - 0.3 as below,
2 × 1.1 - 0.3
= 1.9
Hence, the length of one of the triangle’s legs is 1.9 feet.
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Y-4=2/3(×+2) look like on line graph
The graph of the linear equation:
y - 4 = (2/3)*(x + 2)
Can be seen on the image at the end.
How to graph the linear equation?
Here we have the following linear equation:
y - 4 = (2/3)*(x + 2)
Isolating y, we get:
y = (2/3)*(x + 2) + 4
To graph the line, we just need to evaluate it in two different values of x so we get two points, once we get the points, we can graph them on a coordinate axis and then connect them with a line.
If we use x = 1 we get:
y = (2/3)*(1 + 2) + 4
y = (2/3)*3 + 4
y = 2 + 4 = 6
y = 6
Then we have the point (1, 6)
if x = 4 then:
y = (2/3)*(4 + 2) + 4
y = (2/3)*6 + 4
y = 4 + 4 = 8
So we have the point (4, 8)
Then the graph of the linear equation is the one you can see below:
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A large company releases summary statistics about the annual salaries for its employees. Mean standard deviation minimum Q1 median Q3 maximum $63,429 $38,439 $18,000 $50,000 $58,000 $68,000 $350,000 Based on this information, are there any outliers in the data? Explain your reasoning
Pieces of data such as $18,000 and $350,000 represent outliers in this chart in standard deviation .
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high. The standard deviation calculates how much the data vary from the mean value. It is helpful for contrasting data sets that might have the same mean but a different range.In this chart, there are outliers. The main outliers are $18,000 and $350,000. This is because we know the mean or average is $63,423, and therefore values that are too different from this average are considered outliers.
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2. Identify the proportional relationship.
7x-2=y y + 1 = 3x y = 5x y=2x +4
Describe the sampling distribution of p. Assume the size of the population is 30,000. n 700, p 0.388 Describe the shape of the sampling distribution of p. Choose the correct answer below. O A. The shape of the sampling distribution of p is not normal because n s0.05N and np(1-p)210. O B. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1-p) <10. C. The shape of the sampling distribution of pis not normal because n s05N and np(1-p)<10 O D. The shape of the samplingdistrbution of p is approximately normal because n s0.05N and np(1 -p)210 Determine the mean of the sampling distribution of p. Round to three decimal places as needed.) Determine the standard deviation of the sampling distribution of p. Round to three decimal places as needed.)
The correct option regarding the sampling distribution of p, considering the Central Limit Theorem, is given as follows:
D. The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.
The mean of the sampling distribution of p is of:
0.388.
The standard deviation of the sampling distribution of p is of:
0.0184.
What is defined by the Central Limit Theorem?The Central Limit Theorem defines the distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n, in which:
The mean is [tex]\mu = p[/tex].The standard deviation is [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]The shape is approximately normal.As long as these two conditions are respected:
[tex]n \leq 0.05N[/tex][tex]np(1 - p) > 10[/tex]The values of the parameters in this context are given as follows:
N = 30000, n = 700, p = 0.388.
Hence the conditions are:
n/N = 700/30000 = 0.0233 < 0.05.np(1 - p) = 700 x 0.388 x 0.612 = 166 > 10.Then the shape is approximately normal and option D is correct.
The mean of the distribution is of:
[tex]\mu = p = 0.388[/tex]
The standard error of the distribution is of:
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.388(0.612)}{700}} = 0.0184[/tex]
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