Answer:
Since f is increasing over its domain, we know that if a > b, then f(a) > f(b). Therefore, we have:
2x + 3 > 3x - 2
Solving for x, we get:
x < 5
So the solution set is:
Df = [3, infinity) intersect (-infinity, 5) = [3, 5)
Therefore, the inequality is true for all x in the interval [3, 5).
Since f is increasing over its domain, we know that if a > b, then f(a) > f(b). Therefore, we have:
x^2 - 2 < y^2 - 2
Simplifying, we get:
x^2 < y^2
Taking the square root of both sides, we get:
|x| < |y|
So the solution set is:
Df = [3, infinity)
|x| < |y| means that either x < y or -x < y. Therefore, the solution set can be divided into two parts:
Part 1: x^2 - 2 < 0, i.e., x is in the interval (-sqrt(2), sqrt(2)). For this part, we have:
Df intersect (-sqrt(2), sqrt(2)) = empty set
Part 2: x^2 - 2 >= 0, i.e., x is outside the interval (-sqrt(2), sqrt(2)). For this part, we have:
Df intersect (-infinity, -sqrt(2)] union [sqrt(2), infinity) = [3, infinity)
Therefore, the inequality is true for all x in the interval [3, infinity) except for the interval (-sqrt(2), sqrt(2)).
Step-by-step explanation:
For the polynomial 11x4 + 8x2 + x which represents how much Patrick won from Michael, find the degree of each term. Then find the degree of the polynomial.
The degree of the polynomial 11x⁴ + 8x² + x is 4, which is the highest degree among its terms. The degrees of the terms are 4, 2, and 1 for the first, second, and third terms, respectively.
The degree of a term in a polynomial is the exponent of its variable.
In the polynomial 11x⁴ + 8x² + x, the degree of the first term 11x⁴ is 4, the degree of the second term 8x² is 2, and the degree of the third term x is 1.
The degree of the polynomial is the highest degree among its terms. In this case, the highest degree is 4, which is the degree of the first term. Therefore, the degree of the polynomial is 4.
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100 POINTS!!! PLS ANSWER ASAP
The number of toys owned by eight classmates is shown below:
4, 3, 4, 5, 6, 6, 8, 4
Part A: What is the mean of the data? Show your work. (4 points)
Part B: Use your answer from Part A to calculate the mean absolute deviation for the data. Show your work. (6 points)
Answer:
the answer for part A is. 5
the absolute deviation is. 1
Step-by-step explanation:
to find the answer for part A add all numbers and divide it by 8
4+3+4+5+6+6+8+5/840/85 is the answersFor part B
4-5= |-1|= 1
3-5= |-2|= 2
4-5= |-1| =1
5-5= |0| =0
6-5= |1 | =1
6-5= |1 | =1
8-5= |3| =3
5-5= |0| =0
Then add all the number and divided them by 8
1+2+1+0+1+1+3+0/89/89/8 is the answerMAY I GET BRAINLIEST
The admission fee at an amusement park is $2.25 for children and $5.60 for adults. On a certain day, 269 people entered the park, and the admission fees collected totaled 1091 dollars. How many children and how many adults were admitted?
find the least common denominator
Sum of vectors a+b pick one of answer choices
Answer:
< - 1, 5 >
Step-by-step explanation:
a = < - 5, 2 >
b = < 4, 3 >
a + b
= < - 5, 2 > + < 4, 3 >
add corresponding elements
= < - 5 + 4, 2 + 3 >
= < - 1, 5 >
Determine each lengths in right triangle ABC.
BD———>
AB———>
The missing parts of the triangle are
BD = 8
AD = 8 sqrt(2)
How to find the missing partsThe missing part BD of the figure is solved using similar triangles
The expression is as follows
h / 8 = 8 / h
h^2 = 8 x 8
h^2 = 64
h sqrt = (64)
h = 8
Solving for AB we use Pythagoras theorem
AB^2 = h^2 + 8^2
AB^2 = 8^2 + 8^2
AB = sqrt(64 + 64)
AB = sqrt (128)
AB = 8 sqrt (2)
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what is the volume of a hemisphere with a diameter of 8ft (rounded to the nearest tenth of a cubic foot)
well, if the hemisphere has a diameter of 8, that means its radius is half that or 4, hmm let's find the volume of a Sphere with such a radius, then let's halve it.
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3} \\\\\\ \stackrel{\textit{now let's get half of that for the hemisphere}}{V=\cfrac{1}{2}\cdot \cfrac{4\pi (4)^3}{3}\implies V=\cfrac{128\pi }{3}}\implies \boxed{V\approx 134.0}[/tex]
The boxplot displays the total cost of attendance for all US public and private universities.
Use this graphic to complete the statements.
Both distributions of the total cost of attendance are
. The average cost of attendance is higher for
universities. The costs of more than
% of the public institutions were within the costs of the lowest 25% of private institutions. Both the range and IQR was higher for
universities. Both distributions have
outliers.
Both distributions of the total cost of attendance are skewed right
The average cost of attendance is higher for private universities.
The costs of more than 75 % of the public institutions were within the costs of the lowest 25% of private institutions.
Both the range and IQR was higher for private universities
Both distributions have outliers.
What is a box plot?A boxplot is a standardized way of displaying the distribution of data based on a five number summary (“minimum”, first quartile [Q1], median, third quartile [Q3] and “maximum”).
It can tell you about your outliers and what their values are
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Answer:
skewed right private 75 private do have outliers
Step-by-step explanation:
Right triangle XYZ, has vertex angles at the coordinates, X(0, 0), Y(-3, 0) and Z(-3, 4). Its Image, triangle X'Y'Z' has ve
angles at the coordinates, X(3, -5), Y(0, -5), and Z'(0, -1). Describe the horizontal and vertical translations that map
triangle XYZ onto its image, triangle X'Y'Z'.
Oright 5; down 3
Oright 3; up 5
Oright 3; down 5
O left 5; up 3
NEXT QUESTION
ASK FOR HELP
TURN
The horizontal and vertical translations that map triangle XYZ onto its image, triangle X'Y'Z' include the following: C. right 3; down 5.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.In order to map the two triangles, we would have to apply a vertical translation to f(x) by 5 units down and a horizontal translation by 3 units right.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Shane is 61 feet high on a ride at an amusement park. The angle of depression to the park entrance is 42°, and the angle of depression to his friends standing below is 80°. How far from the entrance are his
friends standing? Round to the nearest foot.
A circular table measures 2.5 feet across the diameter of its top. What is the approximate area of the table top. Use 3.14 for TT.
O 9.42 ft²
O 19.63 ft²
O 4.91 ft²
O 7.85 ft²
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations to solve the length of the room is
a) y² - 5y = 750
b) 750 - y ( y - 5 ) = 0
c) ( y + 25 ) ( y - 30 ) = 0
Given data ,
Let the area of a rectangular room is 750 square feet.
Let the width of the room is 5 feet less than the length of the room
So , on simplifying , we get
w = l - 5
Area of rectangle = length x width
And , A = l x w
A = l ( l - 5 )
750 = y ( y - 5 )
Therefore , the equation is
a) y² - 5y = 750
b) 750 - y ( y - 5 ) = 0
On simplifying the quadratic equation , we get
c) ( y + 25 ) ( y - 30 ) = 0
Hence , the length of the rectangular room is solved
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The complete question is attached below :
Which equations can be used to solve for y, the length of the room? Select three options.
a) y(y + 5) = 750
b) y² – 5y = 750
c) 750 – y(y – 5) = 0
d) y(y – 5) + 750 = 0
e) (y + 25)(y – 30) = 0
How to solve for X and Y
The values of x and y are 4 and 2√2
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Sin(tetha) = opp/hyp
tan(tetha) = opp/adj
cos(tetha) = adj/hyp
In the triangle;
y is the opposite to angle 45 and x is the hypotenuse
cos 45° = 2√2/x
1/√2 = 2√2/x
x = 2√2 ×√2
x = 2 × 2 = 4
since the triangle is isosceles,
y = 2√2
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1) Consider the quadratic function: f (x) = (x + 3)2 – 2 and a function, g(x), which is created by translating
f (x) three units to the right, two units up, and reflected vertically over the x-axis. Complete the following tasks:
a) 15 points: Graph f (x) on the axes below and label it. Graph g(x) on the axes below and label it.
10 points: Write the vertex form equation for g(x) below.
A graph of f(x) is shown in the image below.
A graph of f(x) is shown in the image below.
The vertex form equation for g(x) is g(x) = -x²
What is a translation?In Mathematics and Geometry, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
Since the parent function is f(x)= (x + 3)² - 2, g(x) would be created by translating f(x) three units to the right, two units up, and reflected vertically over the x-axis as follows;
f(x) = (x + 3)² - 2
g(x) = -[(x + 3 - 3)² - 2 + 2]
g(x) = -x²
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An hourglass is 6ft wide and 4 ft tall on top. On bottom the hourglass is 6ft wide and 2 feet tall. It can hold 2000 pounds. if the water takes exactly one year to pass through the hourglass, how much water pass through to the bottom each day? What is the linear function of the water passing through the hourglass?
The linear equation outlining the entire volume of water (y) which has coursed through the hourglass following x days. is
y = 5.48xThe volume of water passed each which is the slope is
5.48How to find the amount of water passing through the glass each dayTo ascertain the amount of water that is passing through the hourglass daily:
where:
Total water capacity: 2000 pounds
Time: 365 days
Water transpiring every day = Total water capacity / Time
Water pervading each day ≈ 200 / 365
Water pervading each day ≈ 5.48 pounds/day
the linear function of the water traveling through the hourglass.
Making x the number of days and y being the total quantity of water which has crossed through the hourglass after x days--as the fluid fluxes at a constant velocity--thus a linear relationship between x and y can be determined.
Every single day (x), the hourglass moves 5.48 pounds of water. This reveals the linear representation of:
y = 5.48x
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Last year, the rates of return on the investments in a large portfolio had an approximately mound-shaped distribution, with a mean of 20% and a standard deviation of 10%. What proportion of the investments had a return of between 10% and 30%? What proportion of the investments had a return of between -10% and 50%? b. What proportion of the investments had a return that was either less than 10% or more than 30%? What proportion of the investments had a positive return? (Hint: A mound-shaped distribution is symmetrical.)
a) The proportion of the investments had a return of between 10% and 30% is given as follows: 0.68 = 68%.
b) The proportion of the investments had a return of between -10% and 50% is given as follows: 0.997 = 99.7%.
c) The proportion of the investments had a return either less than 10% or more than 30% is given as follows: 0.32 = 32%.
d) The proportion of the investments had a positive return is given as follows: 0.9985 = 99.85%.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.Hence the percentages for this problem are given as follows:
Item a -> 68% -> within one standard deviation of the mean.Item b -> 99.7% -> within three standard deviation of the mean.Item c -> 32% -> More than one standard deviation of the mean.Item d -> all above the mean, 99.7% of the 50% below the mean -> 0.997 x 0.5 + 0.5 = 0.9985 = 99.85%.More can be learned about the Empirical Rule at https://brainly.com/question/10093236
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Simplify √ x + 3√ 3x − 5√ x.
Answer: -4rootx+3root3x
Step-by-step explanation:
think of the expression under the radicals as like terms, you can only add those that are the exact same 1-5=-4(rootx) can't do anything with the middle
1. On July 15, Piper Company sold $17,000 of merchandise (costing $8,500) for cash. The sales tax rate is 5%. On August 1, Piper sent the sales tax collected from the sale to the government.
2. On November 3, the Milwaukee Bucks sold a six-game pack of advance tickets for $510 cash. On November 20, the Bucks played the first game of the six-game pack (this represented one-sixth of the advance ticket sales).
1. Record entries for the July 15 and August 1 transactions.
2. Record the entries for the November 3 and November 20 transactions.
The table is attached.
A journal entry is used to record financial transactions of the business operations in a company's accounting records.
The journal entries of Piper Co. is recorded below:
The table for the journal entries is attached below for a clear understanding of the narration.
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Abdoulaye is planning to drive from City X to City Y. The scale drawing below shows the distance between the two cities with a scale of 1 inch = 5 miles. City X and City Y are 11/2 between
City X ---------- 11/2 ------------- City Y
What is the actual distance between the two cities?
The actual distance between the two cities is [tex]7\frac{1}{2}[/tex] miles .
What is the actual distance?A scale drawing is the reduced version of a larger image. The scale drawing is reduced at a constant proportion to the original image using a scale. An example of a scale drawing is a map of the city.
Actual distance between the cities can be determined by multiplying the distance in the scale drawing by the scale.
Actual distance = 1[tex]\frac{1}{2}[/tex] x 5
= [tex]\frac{3}{2}[/tex] x 5 = [tex]\frac{15}{2}[/tex] = [tex]7\frac{1}{2}[/tex] miles
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Nicholas and his father went fishing.
Nicholas caught a fish that weighed
14 1/2 pounds. His father caught a fish
that weighed half as much as the fish
Nicholas caught. What was the total
weight of the fish Nicholas and his
father caught, in pounds? Enter the
weight as an improper fraction.
The value of total weight of the fish Nicholas and his father caught, in pounds is,
⇒ 87/4 pounds
We have to given that;
Nicholas caught a fish that weighed 14 1/2 pounds.
And, His father caught a fish that weighed half as much as the fish Nicholas caught.
Hence, The weight of fish caught by his father is,
⇒ 14 1/2 ÷ 2
⇒ 29/2 × 1/2
⇒ 29/4
Thus, The value of total weight of the fish Nicholas and his father caught, in pounds is,
⇒ 14 1/2 + 29/4
⇒ 29/2 + 29/4
⇒ 58/4 + 29/4
⇒ 87/4 pounds
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You invest $1500 in an account at interest rate r, compounded continuously.Find the time required for the amount to double and triple.(Round your answer to two decimal places). r=0.0355
The time required for the amount to double and triple are 19.53 and 30.95 respectively.
How to find the time required for the amount to double and triple?In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):
[tex]f(t) = P_{0}e^{rt}[/tex]
Where:
f(t) represents the future value.P₀ represents the principal.r represents the interest rate.t represents the time measured in years.Based on the information provided above, we can reasonably infer and logically deduce that a function for the time required for the amount to double is given by;
[tex]2(1500) = 1500e^{0.0355t}\\\\3000= 1500e^{0.0355t}\\\\2=e^{0.0355t}[/tex]
Taking the natural log (ln) of both sides of the equation, we have:
0.0355t = ln(2)
Time, t = 19.53
Similarly, a function for the time required for the amount to triple is given by;
[tex]3(1500) = 1500e^{0.0355t}\\\\4500= 1500e^{0.0355t}\\\\3=e^{0.0355t}[/tex]
Time, t = 30.95
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20 pts
Need help asap!
The probability that the student is a sophomore, given that they are in work, is given as follows:
P(sophomore|work) = 30%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes for this problem are given as follows:
Total outcomes: 3 + 2 + 5 = 10 people at work.Desired outcomes: 3 sophomores at work.Hence the probability is obtained as follows:
P(sophomore|work) = 3/10 = 0.3 = 30%.
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What is the equation of the line in slope-intercept form?
Answer:
The answer is the second choice.
Step-by-step explanation:
The slope is rise over run, which is 3/-1, which is -3, which goes before the x. The line hits the y axis at -1, so it is -3x–1
What percentage do you have invested in bonds if your portfolio consists of $45,000 invested in U.S. Treasuries, $32,000 in high-grade corporate
bonds, and $74,000 in growth stocks?
51%
45%
50%
52%
To find the percentage invested in bonds, we need to add the amounts invested in U.S. Treasuries and high-grade corporate bonds, and then divide by the total value of the portfolio:
Total amount invested in bonds = $45,000 + $32,000 = $77,000
Total portfolio value = $45,000 + $32,000 + $74,000 = $151,000
Percentage invested in bonds = (Total amount invested in bonds / Total portfolio value) x 100%
= ($77,000 / $151,000) x 100%
= 51.0%
Therefore, the answer is 51%.
I hope this helps you!
Income 26-28 28-30 30-32 32-34 34-36
Frequency 2 11 8 5 4
The class that contains the 80th percentile is. a) 26-28 b) 28-30 c) 30-32 d) 32-34 e) 34-36
The class that contains the 80 th percentile is d) 32-34.
How to find the class ?First, find the total frequency of the income :
Total frequency = 2 + 11 + 8 + 5 + 4 = 30
The position of the number at the 80 th percentile would then be :
= 30 x 80 %
= 24 th position
The cumulative frequency of :
26 - 28 = 2
28 - 30 : 2 + 11 = 13
30 - 32 : 13 + 8 = 21
This then means that the 24 th position is in the next interval of 32 - 34.
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Question 1(Multiple Choice Worth 2 points) (Theoretical Probability MC) When rolling a 6-sided die twice, determine P(sum of 4). 1. 3/36 2. 5/36 3 8/36 4. 2/6
Answer:
5/36
Step-by-step explanation:
hope this helps
PLEASE HELP (WILL GIVE BRAINLIEST)
Answer:
[tex] \sqrt{ {13.5}^{2} - {8.6}^{2} } = \sqrt{108.29} = 7 \sqrt{2.21} = \frac{7}{10} \sqrt{221} [/tex]
V = (1/2)(8.6)(.7√221)(22.4) = 1,002.33 square meters
The closest answer is 1,001.73 square meters.
A student argues that y=x/9 does not represent a proportional relationship between x and y because we need to multiply one variable by the same constant to get the other one and not divide it by a constant. Do you agree or disagree with this student? Explain why.
The student's argument that y=x/9 does not represent a proportional relationship between x and y is false because there is constant factor which shows the proportional relationship.
A proportional relationship exists between two variables if they are related by a constant factor, meaning that multiplying one variable by a constant results in the other variable. However, this constant can also be obtained by dividing one variable by the other, as in the case of y=x/9.
To see why, we can rearrange the equation to x=9y, which shows that x is proportional to y with a constant factor of 9. Multiplying y by 9 results in x, just as dividing x by 9 results in y. Therefore, the relationship between x and y is still proportional, regardless of whether we multiply or divide to obtain the constant factor.
In general, we can say that a relationship between two variables is proportional if it can be written in the form y=kx, where k is a constant. It does not matter whether we use multiplication or division to express this constant, as long as it is the same for all values of x and y.
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an octagonal prism has a surface area of 50mm^2 and a volume of 88 mm^3 Another octagonal prism has a surface area of 450mm^2 and a volume of 792mm^3. Are these two shapes similar ? Explain your answer
The two octagonal prisms are similar because their corresponding sides are proportional.
How do we determine the octagonal prisms are similar?We can find out if two octagonal prisms are similar by checking if they have the same shape but may be different sizes. Two shapes are similar if their corresponding sides are proportional, and their corresponding angles are congruent.
Let's represent the dimensions of octagonal prism1:
Base edge length = a
Height = h
The octagonal prism2 dimensions:
Base edge length = b
Height = k
From the surface area and volume equations of an octagonal prism, we have the following system of equations:
50 = 2a² + 8ah
88 = 2a²h
450 = 2b² + 8bk
792 = 2b²k
We can simplify these equations by dividing the second equation by the first, and the fourth equation by the third, to eliminate h and k:
88/50 = 2a²h / (2a² + 8ah) => 44/25 = h / (a + 2h)
792/450 = 2b²k / (2b² + 8bk) => 44/25 = k / (b + 2k)
Then, we rearrange the equations to obtain expressions for h and k in terms of a and b, respectively:
h = (44/25) * (a + 2h)
k = (44/25) * (b + 2k)
Multiplying both sides of each equation by 25/19, we obtain:
h = (44/19) * a
k = (44/19) * b
We can now check if the corresponding sides are proportional:
Base edge length = a:b = 1:3
Height = h:k = 1:3
Since the corresponding sides are proportional, the two octagonal prisms are similar.
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Combine like terms to simplify the expression: 8y + 4 - 3y + 12?
Answer: image below
Step-by-step explanation:
