(x²+3x+2)(x²+7x+12)=24
Answers
Answer:
x=0, 5 (-5±√15)/2
Step-by-step explanation:
see images for solution
Related Questions
Gail averages 153 points per bowling game with a standard deviation of 14.5 points. Suppose Gail's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X ∼ N ( 153 , 14.5 ) . z-score when x = 108 is _____. The mean is 153 . The z-score tell you that x = 108 is _____ standard deviations to the left of the mean.
Answers
x = 108 is 3.10 standard deviations to the left of the mean.
What is standard deviation?The standard deviation (SD, also written as the Greek symbol sigma or the Latin letter s) is a statistic that is used to express how much a group of data values vary from one another.
The z-score when x = 108 is:
z = (108 - 153) / 14.5
z = -3.10
This tells us that x = 108 is 3.10 standard deviations to the left of the mean.
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ASAP PLEASE!
1.
Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 3.8, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 2.4, 2.1
Determine the scale factor used.
one half
2
one fourth
3
2.
Question 4(Multiple Choice Worth 2 points)
(Dilations MC)
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−9, −9), B(9, 9), C(0, 9). Determine the scale factor used.
6
one sixth
3
one third
Answers
The first option, "one half," corresponds to the scale factor of 0.5.
How to find the scale factor?Scale factor = Dimensions of the new shape Dimensions of the original shape is the fundamental formula used to calculate it. The formula is expressed as Scale factor = Larger image dimensions Smaller figure dimensions in the event that the original figure is enlarged.
We can contrast the side lengths of triangles D and D′ to determine the scaling factor.
Let's contrast the side lengths for the two triangles.
Triangle D has sides that are 4.2 in length, and triangle D′ has sides that are 2.1 in length.
Scale factor = (Side length of triangle D′) / (Side length of triangle D)
Scale factor = 2.1 / 4.2
Scale factor = 0.5
The first option, "one half," corresponds to the scale factor of 0.5.
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Question is in the screenshot (matrices)
Answers
Value of matrix X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]
Define matricesMatrices are a type of mathematical object that consists of a rectangular array of numbers or other mathematical objects, such as variables, functions, or even other matrices. Matrices are widely used in mathematics, science, engineering, computer graphics, and other fields to represent and manipulate data, perform transformations, and solve systems of equations.
A matrix can be represented using a set of ordered pairs, where each pair represents a specific element of the matrix, and the position of the element is determined by its row and column indices. For example, a 3x3 matrix can be represented as:
| a11 a12 a13 |
| a21 a22 a23 |
| a31 a32 a33 |
Given matrix;
A=[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]
B=[tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]
C=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]
Solving the equation
(A-4B)X=C
[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]- 4 [tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}23&-22 \\-6&6 \\ \end{array}\right][/tex] X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]
Taking the inverse and multiplying it with RHS, we get
X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]
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Use the following data to answer questions 1-2.
1. Find the median, mean, and range of the elephant ages.
a) Median:.
b) Mean:,
Ages of 10 elephants (in years) living in zoos:
28, 14, 19, 20, 21, 28, 33, 36, 41
c) Range:.
years
years
years
Answers
b) mean-26.6
c) range-27
Answer:
median - 28
mean - 26.6 (6 repeating)
range - 27
Step-by-step explanation:
The elephant ages would go in the order of 14, 19, 20, 21, 28, 28, 33, 36, 41. To find the median, you need to look for the center of the numbers, which would be 28, since 28 is the middle number. To find the mean, you add all the numbers up and divide them by however many numbers there are, in this case, they add up to 240, and there is 9 numbers, so you would do 240 divided by 9 = 26.66 (repeating so a line over the 6's after the decimal) and to find the range you subtract the highest number and the lowest, which is 41 and 14 and that would give you 27.
I'M SO SORRY IF THIS DIDN'T MAKE SENSE!
the median home cost in the us in 1975 was $40,000. in 1990, an equivalent home cost $140,000. the trend continued into 2005 when the median home cost in the us was approximately $240,000. assuming that this data's relationship is steady in the future, what is a reasonable estimate of the median home cost in the us in 2025?
Answers
The reasonable estimate of the median home cost in the US in 2025 is $340,000
To assess the middle domestic taking a toll within the US in 2025, ready to utilize the verifiable drift and expect that the relationship between the middle domestic fetched and time (measured in a long time since 1975) is straight.
Let`s begin with calculating the rate of increment in median domestic fetched per year utilizing the information from 1975 to 2005. Ready to utilize the equation for the slant of a direct relapse line:
slant(slope) = (y2 - y1) / (x2 - x1)
where
y1 and y2 are the middle domestic costs in 1975 and 2005,
separately, and x1 and x2 are comparing a long time (0 and 30).
incline = ($240,000 - $40,000) / (30 - 0) = $6,000
This implies that the middle domestic taken a toll expanded by a normal of $6,000 per year amid this period.
Presently, ready to utilize this rate of increment to appraise the middle domestic taken a toll in 2025, which is 50 long times after 1975.
The year 2025 will be 50 a long time after 1975, so the number of a long time since 1975 will be x = 50. Utilizing the incline we fair calculated, able to assess the middle domestic fetched in 2025 as takes after
y = y1 + slant(slope) * x = $40,000 + $6,000 * 50 = $340,000
Therefore, a sensible assessment of the middle domestic taking a toll within the US in 2025, based on the presumption that the slant watched from 1975 to 2005 proceeds, is $340,000.
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find fy , the y-component of force that the wall exerts on the beam ( f ), using the axis shown. remember to pay attention to the direction that the wall exerts the force.
Answers
The y-component of the force that the wall exerts on the beam (f) is -400.5 N.
The y-component of the force that the wall exerts on the beam (f) can be found using the following steps:
Step 1: Calculate the magnitude of the force (f):
f = √[f_x² + f_y²]
f = √[(-500 N)² + (-300 N)²]
f = 600 N
Step 2: Calculate the angle of the force relative to the y-axis:
θ = tan-1(-300 N/500 N)
θ = -53.13°
Step 3: Calculate the y-component of the force (fy):
fy = f × sin(θ)
fy = 600 N × sin(-53.13°)
fy = -400.5 N
Therefore, the y-component of the force that the wall exerts on the beam (f) is -400.5 N.
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2. Given: MNOP is a rectangle.
Show: The diagonals bisect each other, and the diagonals are congruent.
M
-5
N
Answers
The answer of the given question based on the rectangle is , The MNOP congruence is shown by Side-Angle-Side (SAS) and the steps are given below.
What is Diagonal?In geometry, a diagonal is a straight line that connects two non-adjacent vertices of a polygon or a polyhedron. In other words, a diagonal is a line segment that joins two corners or vertices of a shape that are not next to each other. For example, in a rectangle, the diagonals are the line segments that connect opposite corners of the rectangle.
To show that the diagonals of a rectangle bisect each other and are congruent, we can use the following steps:
Draw the diagonal MO and the diagonal NP.Since MNOP is a rectangle, we know that angles M and N, as well as angles O and P, are right angles. Therefore, we have four right triangles: triangle MNO, triangle NOP, triangle OPM, and triangle PMN.Since each of these triangles shares side OP, we can use the Side-Angle-Side (SAS) congruence criterion to show that triangles MNO and OPM are congruent, and triangles NOP and PMN are congruent.Since these triangles are congruent, we know that their corresponding sides are congruent. In particular, we know that segment MP is congruent to segment NO.Since MO and NP intersect at point Q, we know that Q is the midpoint of both segments MO and NP. Therefore, the diagonals of rectangle MNOP bisect each other.Therefore, we have shown that the diagonals of a rectangle bisect each other and are congruent.
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Can someone show me step by step correctly for a better grade
There are approximately 7.48 liquid gallons in a cubic foot. If a cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet, what is the approximate height of the water tank? Approximate using π = 3.14 and round to the nearest tenth.
4.6 feet
14.4 feet
46.0 feet
147.1 feet
Answers
The height of the cylindrical water tank is 4.6 feet. Therefore, the answer is A.
How to find the height of the water tank?The cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet.
Therefore, the height of the tank can be calculated as follows:
7.48 liquid gallons = 1 ft³
1100 liquid gallons = ?
cross multiply
volume of the tank = 1100 / 7.48 = 147.058823529 ft³
Therefore, let's find the volume of the cylindrical tank.
volume of the cylindrical tank = πr²h
where
r = radiush = heightTherefore,
r = 3.2 feet
h = ?
The volume of the cylindrical tank in feet cube is 147.058823529 ft³
Let's find the height, h
volume of the cylindrical tank = 3.14 × 3.2² × h
147.058823529 = 3.14 × 10.24 × h
32.1536h = 147.058823529
divide both sides by 32.1536
h = 147.058823529 / 32.1536
h = 4.57363405653
Therefore,
height of the water tank = 4.6 feet
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Surface area of rectangular pyramid 2(½ ×w×h)+2(½×l×h)+(l×w)
Answers
The first term represents area of the two triangular faces having base of pyramid, second term represents area of two triangular faces having length of the rectangle, third term represents area of rectangular base.
A rectangular pyramid is a solid figure with a rectangular base and four triangular faces that meet at a single point, known as the apex. To find the surface area of a rectangular pyramid, we need to calculate the area of each face and add them together.
The formula for the surface area of a rectangular pyramid is:
Surface area = 2(1/2 x base x height) + 2(1/2 x length x height) + (length x base)
The first term, 2(1/2 x base x height), represents the area of the two triangular faces that share the base of the pyramid. The second term, 2(1/2 x length x height), represents the area of the two triangular faces that share the length of the rectangle. The third term, (length x base), represents the area of the rectangular base.
By multiplying each term by its appropriate values and adding them together, we can find the total surface area of the rectangular pyramid.
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Complete question is:
Surface area = 2(1/2 x base x height) + 2(1/2 x length x height) + (length x base). Explain what each term represents?
only a handful of birdseed is left in a birdfeeder. each time a bird lands on the feeder, one seed randomly falls from the feeder. if the feeder has only 40 sunflower seeds, 65 millet seeds, 60 rye seeds, and 35 corn seeds left, what is the probability that a millet seed will fall next?
Answers
Answer: The probability that a millet seed will fall next can be found by dividing the number of millet seeds by the total number of remaining seeds.
Total number of remaining seeds = 40 + 65 + 60 + 35 = 200
Probability that a millet seed will fall next = Number of millet seeds / Total number of remaining seeds
= 65 / 200
= 0.325 or 32.5% (rounded to one decimal place)
Therefore, the probability that a millet seed will fall next is 0.325 or 32.5%.
Step-by-step explanation:
Determine the point ths of the way from point A: (-3,-2) to point B. (4, -3) shown on the coordinate plane below.
Answers
Answer:
Step-by-step explanation:
To find the point that is a certain fraction of the way between two given points, we can use the midpoint formula and the scalar multiplication of vectors.
Let's first find the vector that points from point A to point B:
�
�
⃗
=
(
4
−
3
)
−
(
−
3
−
2
)
=
(
7
−
1
)
AB
=(
4
−3
)−(
−3
−2
)=(
7
−1
)
The scalar multiplication of a vector with a scalar value scales the length of the vector. To find the point that is 3/4 of the way from point A to point B, we can multiply the vector $\vec{AB}$ by 3/4:
3
4
�
�
⃗
=
3
4
(
7
−
1
)
=
(
21
4
−
3
4
)
4
3
AB
=
4
3
(
7
−1
)=(
4
21
−
4
3
)
Finally, we can add this vector to point A to get the point that is 3/4 of the way from point A to point B:
(
−
3
−
2
)
+
(
21
4
−
3
4
)
=
(
3
4
,
−
11
4
)
(
−3
−2
)+(
4
21
−
4
3
)=
(
4
3
,−
4
11
)
Estimate the measure of this
angle within 15°
Answers
Within 15° angle {15°,30°45°,60°75°,90°,105°,120°}
Should be 120°
Determine the value of y-intercept of a line with the given slope -3 that is a tangent
line to the curve y = -x² - 5x -5.
a. 0
b. -1
c. -3
d. -4
Answers
The y-intercept of the tangent line is b. -1
What is the y intercept of a line?The y-intercept of a line is the value of y at which the line crosses the y axis
To determine the value of y-intercept of a line with the given slope -3 that is a tangent line to the curve y = -x² - 5x -5.
We proceed as follows
First we differentiate the equation of the curve.
So, y = -x² - 5x -5.
dy/dx = d(-x² - 5x -5)/dx
= d-x²/dx - d5x/dx - d5/dx
= -2x - 5 - 0
= -2x - 5
Since the derivative of the curve equals the value of the tangent at the point, we have that
dy/dx = -3
-3 = -2x - 5
-3 + 5 = -2x
2 = -2x
x = 2/-2
x = -1
So, substituting x = -1 into the equation for y to find the y intercept, we have that
y = -x² - 5x -5.
y = -(-1)² - 5(-1) -5
= -1 + 5 - 5
= -1 + 0
= -1
So, the y-intercept is b. -1
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Triangulation
Here are two-five pointed stars. Both figures A and B are polygons.They are both composed of line segments and are
two dimensional. Neither have curves. Do you agree with the statement?
Answers
A plane is an infinite two-dimensional figure.
We have,
When two planes intersect, they form a line.
The vector equation for the line of intersection is given by
r = r₀ + tₓ
where r₀ is a point on the line
tₓ is the cross product of the normal vectors of the two planes.
The parametric equations for the line of intersection are given by
x = a , y = b and z = c
where a, b and c are the coefficients from the vector equation
r = a (i) + b (j) + c (k)
The line of intersection will be perpendicular to the normal of both the planes
The line of intersection lies on both the planes
Therefore , a line is observed at the intersection of two planes
Given data ,
A line is one-dimensional, a segment is a part of a line and is also one-dimensional, and a point is zero-dimensional.
A plane, on the other hand, is a flat, two-dimensional surface that extends infinitely in all directions.
It has length and width, but no thickness, and can be thought of as an infinitely large sheet of paper.
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complete question:
Which of the following is an infinite two-dimensional figure?
A. A line
B. A plane
C. A segment
D. A point
Please could you help its due tommorow
Answers
Answer:
x = 52.5
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360.
2x+100 +95+60 = 360
Combine like terms.
2x+255=360
Subtract 255 from each side
2x+255-255= 360-255
2x = 105
Divide each side by 2
2x/2 = 105/2
x = 52.5
Answer:
x = 52.5
Step-by-step explanation:
The sum of the interior angles of a quadrilateral is 360°.
Accordingly, let us find the value of x.
2x + 100 + 95 + 60 = 360
2x + 255 = 360
Subtract 255 from both sides.
2x = 360 - 255
2x = 105
Divide both sides by 2.
x = 52.5
Classify each number below as an integer or not.
Whoever answers it first ill give u brainliest
And if you dont figure the question ill report you so please help me
Answers
Answer:-91 is an integer
1/2 is not an integer
51 is an integer
-6/2 is not an integer
-99.34 is an integer
Step-by-step explanation: An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Answer:
-91 - yes
1/2 - no
51 - yes
-6/2 - yes
-99.34 - no
The tables represent the points earned in each game for a season by two football teams.
Panthers
14 10 10
10 17 3
28 13 17
32 16 10
14 7 21
Saints
21 12 3
3 10 10
14 3 12
28 40 10
17 20 7
Which team had the best overall record for the season? Determine the best measure of center to compare and explain your answer.
Saints; they have a larger mean value of about 14 points
Panthers; they have a larger mean value of about 14.8 points
Saints; they have a larger median value of 12 points
Panthers; they have a larger median value of 14 points
Answers
The team that had the best overall record for the season is Panthers. Therefore the best way to explain the answer B. Panthers; they have a larger mean value of about 14.8 points.
What are the mean values of the score of both team?For panthers, we calculate their mean values by totaling all their scores.
14+10+10+10+17+3+28+13+17+32+16+10+14+7+21 = 222
222/15 scores = 14.8
For Saints, 21+12+3+3+10+10+14+3+12+28+40+10+17+20+7 = 210
210/15 score = 14
This shows that Panthers have a larger mean value. Also, Panthers have a larger median value than saints. We find the median by arranging the scores from small to large and picking the number in between.
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The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. (b) What is the probability that the arrival time between vehicles is 12 seconds or less? (Round your answer to four decimal places.) (c) What is the probability that the arrival time between vehicles is 4 seconds or less? (Round your answer to four decimal places.) (d) What is the probability of 30 or more seconds between vehicle arrivals? (Round your answer to four decimal places.)
Answers
The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.6321.
Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1.
The exponential probability distribution with a mean of 12 seconds is given by
f(x) = (1/12) × e^(-x/12)
where x represents the time between arrivals of vehicles.
To find the probability that the arrival time between vehicles is 12 seconds or less, we need to integrate the probability density function from 0 to 12
P(X ≤ 12) = [tex]\int\limits^{12}_0[/tex] f(x)dx
= [tex]\int\limits^{12}_0[/tex] (1/12) × e^(-x/12) dx
= [(-e^(-x/12))]_[0,12]
= (-e^(-12/12)) - (-e^(0/12))
= 1 - e^(-1)
≈ 0.6321
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The given question is incomplete, the complete question is:
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. What is the probability that the arrival time between vehicles is 12 seconds or less?
Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce
Answers
After Derek drinks 1/4 ounce of water, he is left with 95/3 ounces of water in his glass.
Derek initially had 10 2/3 ounces of water in his glass. To find out how much water is left after he drinks 1/4 ounce of water, we need to subtract 1/4 from 10 2/3. To do that, we need to convert the mixed number (10 2/3) into an improper fraction.
To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and then add the numerator. In this case, we have:
10 x 3 + 2 = 32/3
Therefore, Derek initially had 32/3 ounces of water in his glass.
To subtract 1/4 from 32/3, we need to make sure the denominators are the same. We can convert 1/4 into twelfths by multiplying both the numerator and denominator by 3. This gives us:
1/4 x 3/3 = 3/12
Now that we have a common denominator of 12, we can subtract:
32/3 - 3/12 = 383/12 - 3/12 = 380/12
To simplify, we can divide both the numerator and denominator by 4:
380/12 ÷ 4/4 = 95/3
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Complete question is:
Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce of the water from his glass how much water is left in Derek's glass?
Express as a trinomial.
(
2
�
−
3
)
(
3
�
−
4
)
(2x−3)(3x−4)
Answers
Answer: 6x^2 - 17x + 12.
Step-by-step explanation:
To multiply these two binomials, we can use the FOIL method, which stands for First, Outer, Inner, Last. This gives us:
(2x - 3)(3x - 4) = (2x)(3x) + (2x)(-4) + (-3)(3x) + (-3)(-4)
Simplifying each term, we get:
(6x^2) + (-8x) + (-9x) + 12
Combining like terms, we can simplify this to:
6x^2 - 17x + 12
Therefore, (2x-3)(3x-4) can be expressed as the trinomial 6x^2 - 17x + 12.
Please help me I can also offer a commission too
Answers
The average rate of change of each function on the interval 2 ≤ x ≤ 6 is given as follows:
f(x): -1.25.g(x): -0.715.How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
For the function f(x), we have that:
When x = 2, y = 7.When x = 6, y = 2.Hence the rate is given as follows:
r = (2 - 7)/(6 - 2)
r = -5/4
r = -1.25.
For the function g(x), we have that:
When x = 2, y = 2(-5/7) - 6 = -7.43.When x = 6, y = 6(-5/7) - 6 = -10.29.Hence the rate is given as follows:
r = (-10.29 - (-7.43))/(6 - 2)
r = -0.715
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Question 90
The quality of milk reaching the ultimate consumer is largely determined
a. at the plant, where processing and handling occurs
b. at the farm, where the milk is processed
c. by the USDA through stringent testing and laboratory analysis
d. by the FDA in accordance with Federal regulations
Answers
The quality of milk reaching the ultimate consumer is largely determined at the plant, where processing and handling occurs. a
Once milk is collected from the farm, it is transported to processing plants where it undergoes a series of treatments to ensure that it is safe for consumption.
This includes pasteurization, homogenization, and standardization.
The pasteurization process involves heating the milk to a specific temperature for a certain amount of time to kill harmful bacteria.
Homogenization helps to evenly distribute the milk's fat content, while standardization ensures that the milk meets certain regulatory requirements for fat content and nutritional value.
The plant, milk undergoes rigorous quality control testing to ensure that it meets certain standards.
This includes testing for bacterial count, somatic cell count, and antibiotic residue.
Any milk that fails to meet these standards is discarded.
The USDA and FDA also play a role in ensuring that milk reaching consumers is of high quality.
The USDA sets standards for milk production, while the FDA regulates the use of antibiotics and other drugs in milk production.
The primary responsibility for ensuring milk quality rests with the processing plant.
The USDA and FDA do play a role in ensuring the quality of milk reaching consumers, the majority of the responsibility lies with the processing plant.
It is at the plant where the milk undergoes treatments to ensure that it is safe for consumption and undergoes rigorous quality control testing to meet certain standards.
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Sandy used a virtual coin toss app to show the results of flipping a coin 100 times, 500 times, and 1,000 times. Explain what most likely happened in
Sandy's experiment.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 500 flips.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
And please give me the answer
Answers
Answer: option C - Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips, is the most likely scenario.
Step-by-step explanation:
Based on the Law of Huge Numbers, the more times a coin is flipped, the closer the test likelihood will be to the hypothetical likelihood of 0.5 for heads and 0.5 for tails. In this manner, Sandy's exploratory likelihood is most likely to be closest to the hypothetical likelihood within the test with 1,000 flips.
In spite of the fact that it is conceivable that Sandy's exploratory likelihood might be near to the hypothetical likelihood within the explore with 100 flips or 500 flips, it is more likely that the bigger test measure of 1,000 flips will result in a more precise representation of the hypothetical likelihood.
Raj writes a polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5.
Answers
One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:
$4a^5 - 3a^4 + 2a^3 - 7a^2$
Polynomials expression explained.
A polynomial expression is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. The term "polynomial" comes from the fact that the expression can be thought of as a sum of many terms, each of which is a product of one or more variables raised to a non-negative integer power.
For example, the expression 3x^2 + 4x - 1 is a polynomial in one variable, x, with three terms. The first term is 3x^2, the second term is 4x, and the third term is -1. The highest power of the variable in this expression is 2, which makes it a polynomial of degree 2.
Polynomial expressions can be written in standard form, where the terms are arranged in descending order of degree and the coefficients are written with the highest power of the variable first. For example, the expression above could be written in standard form as 3x^2 + 4x - 1.
One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:
$4a^5 - 3a^4 + 2a^3 - 7a^2$
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Deondra is going to invest $64,000 and leave it in an account for 5 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest hundredth of a percent, would be required in order for Deondra to end up with $82,000?
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Answer:
To the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.
Step-by-step explanation:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the final amount (in this case, $82,000)
P = the principal (the initial investment, in this case, $64,000)
r = the interest rate (what we're trying to find)
n = the number of times the interest is compounded per year (in this case, 4, since it's compounded quarterly)
t = the number of years (in this case, 5)
Plugging in the values we know and solving for r, we get:
$82,000 = $64,000(1 + r/4)^(4*5)
$82,000/$64,000 = (1 + r/4)^20
1.28125 = (1 + r/4)^20
Taking the 20th root of both sides, we get:
(1.28125)^(1/20) = 1 + r/4
0.0167 = r/4
r = 0.0668 (rounded to four decimal places)
Therefore, to the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.
To landscape his 70 ft by 60 ft backyard, Austin is planning first to put down a 4 inch layer of topsoil. He can buy bags of topsoil at $2.50 per 3-ft3 bag, with free delivery. Or he
can buy bulk topsoil for $22.00/yd, plus a $20 delivery fee. Which option is less expensive?
I need volume of soil, cost of bags and cost of bulk
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Answer:
To calculate the volume of soil needed, we first convert the dimensions of the backyard to feet:
Length = 70 ft
Width = 60 ft
Depth = 4 in = 4/12 ft = 1/3 ft
Volume = Length x Width x Depth
Volume = 70 ft x 60 ft x (1/3) ft
Volume = 1400 ft³
Option 1: Bags of topsoil
Each bag of topsoil contains 3 ft³ of soil, so the number of bags needed is:
Number of bags = Volume / Bag size
Number of bags = 1400 ft³ / 3 ft³ per bag
Number of bags = 467 bags
The total cost of bags of topsoil is:
Cost = Number of bags x Cost per bag
Cost = 467 bags x $2.50 per bag
Cost = $1167.50
Option 2: Bulk topsoil
The volume of topsoil needed is 1400 ft³, which is equivalent to:
Volume = 1400 ft³ / 27 ft³ per yd³
Volume = 51.85 yd³ (rounded to two decimal places)
The cost of bulk topsoil is:
Cost = Volume x Cost per yd³ + Delivery fee
Cost = 51.85 yd³ x $22.00 per yd³ + $20.00 delivery fee
Cost = $1153.70
Therefore, buying bulk topsoil is less expensive than buying bags of topsoil. The cost of bulk topsoil is $1153.70, while the cost of bags of topsoil is $1167.50
Answer:
Bulk is less expensive
Step-by-step explanation:
First convert inches to feet: 4 in x 1 ft/12 in =0.333 ft
Volume of topsoil needed = 70 x 60 x 0.333 = 1400 ft³
Bagged topsoil: 1400 ft³ x $2.50/3 ft³ = $1166.67
Bulk: 1400 ft³ x 1 yd³/27 ft³ x $22.00/yd³ + $20 = $1160.74
Bulk is just a little cheaper
Convert 4.5 x 104 to decimal format.A) 45,000 B) 4,500 C) 0.00045 D) 0.0045 E) 0.000450
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After converting [tex]4.5 * 10^4[/tex] to decimal format, one gets 45,000 as an answer. Thus, option (A) is the correct answer.
To convert numbers multiplied by 10 with having an exponent number to decimal format, one first needs to check the sign on the exponent.
If the sign is positive, we must shift the decimal to the right with each power of 10. The exponent indicates the number of zeros added after the number in case no decimal is used.
And if the sign is negative, we have to shift the decimal to the left with each power of 10. One has to divide the number by the number one gets after multiplying 10 by itself as many times as the exponent.
Therefore, to convert [tex]4.5 * 10^4[/tex] to decimal format, we shift the decimal by 4 places and we get 45,000 as the answer.
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what is the correct alternative hypothesis for the wilcoxon rank sum test? group of answer choices ha: the two samples come from the same distribution. ha: the population slope coefficient is not equal to zero. ha: one distribution is shifted in location higher or lower than the other. ha: the population means are equal.
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The correct alternative hypothesis for the Wilcoxon rank sum test is: ha: one distribution is shifted in a location higher or lower than the other. Option C is the answer.
This means that the test is designed to determine if there is a significant difference between the medians of two independent groups, rather than testing for a difference in means.
The null hypothesis for the test is that there is no significant difference between the two groups, while the alternative hypothesis states that there is a significant difference.
The Wilcoxon rank sum test is a nonparametric test and is used when the assumptions of the t-test are not met, such as non-normality or unequal variances.
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6(4x - 3) > 30
need help pls?
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Answer:
[tex]6(4x - 3) > 30 \\ divide \: both \: sides \: of \: the \: \\ inequality \: by \: 6 \\ = 4x - 3 > 5 \\ = 4x > 5 + 3 \\ = 4x > 8 \\ = x > \frac{8}{4} \\ = x > 2[/tex]
hope it helps
how is this answer wrong?
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Answer:
its taking the immage on the right and moving it ounter clockwise 90°