The statement "Angle ∠AEC and ∠DEB are complementary angles" is false.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
Angle ∠AEC and ∠DEB are supplementary angles because the sum is 180 degrees.
Thus, the given statement is false.
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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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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:
What meaning of the statement this?
We can see here that the statement means that H is a subgroup of a group, and aЄ H is an element of that subgroup.
What is a mathematical statement?We can define a mathematical statement to be a claim that, depending on the circumstances, may be true or false. It frequently incorporates mathematical objects and their relationships or characteristics, such as integers, sets, functions, or geometric shapes.
We can see here that it shows that a is an element of the subgroup of H.
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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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Marcus surveys the students in his school about their favorite lunch.
Lunch
Grilled Cheese
Roast Beef
Chili
Frequency
80
40
50
20
60
Use the data to describe the favorite lunch of students at Marcus's school. Round to the nearest percent and the nearest 10 students.
% of students surveyed preferred grilled cheese, so in a group of 3500 students, about
Chicken & Rice
Other
students will prefer grilled cheese.
32% of the students surveyed preferred grilled cheese, so in a group of 3500 students, about 1120 students will prefer grilled cheese.
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 total number of people surveyed is given as follows:
80 + 40 + 50 + 20 + 60 = 250.
80 students preferred grilled cheese sandwich, hence the percentage is obtained as follows:
p = 80/250 x 100%
p = 32%.
Hence the expected amount of 3500 students is given as follows:
0.32 x 3500 = 1120 students.
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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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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
It usually it supposed to be in radical form, but I do not know why they give correct answer choices in the vector form.
Answer:
I think its 221
Step-by-step explanation:
The growth of an investment is given by the formula A = 1200 × 1.3 n , where A is the amount the investment is worth and n is the number of years. Estimate how many days it would take for the investment to be valued at £3,800.
The number of days it would take for the investment to be valued at £3,800 is 4.4 days
Estimate the number of days it would takeFrom the question, we have the following parameters that can be used in our computation:
A = 1200 × 1.3^n
For the investment to be valued at £3,800, the value of A would be
A = 3800
Substitute the known values in the above equation, so, we have the following representation
1200 × 1.3^n = 3800
Divide both sides by 1200
1.3^n = 3800/1200
So, we have
n = ln(3800/1200)/ln(1.3)
Evaluate the quotient
n = 4.4
Hence, it would take 4.4 days
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Which type of relationship is indicated by the residual plot? Non-linear relationship. Linear relationship Exponential relationship
The type of relationship that is indicated by the residual plot is given as follows:
Non-linear relationship.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
For this problem, we have an alternative pattern, where the function neither multiplied nor added/subtracted by a constant value when the input is increased by one, hence we merely classify the relationship as a non-linear relationship.
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8 cupcakes in 1 box = 16 cupcake in X boxes
Answer:
2 boxes
Step-by-step explanation:
8 cupcakes in 1 box = 16 cupcake in x box
We Take
16 ÷ 8 = 2 boxes
So, the answer is 2 boxes.
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.
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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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
Triangle ABC
A
B
C
and triangle DEF
D
E
F
are similar. What is the measure of side DF
D
F
?
Answer:
DF = 15 cm
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{DF}{AC}[/tex] = [tex]\frac{EF}{BC}[/tex] ( substitute values )
[tex]\frac{DF}{9}[/tex] = [tex]\frac{25}{15}[/tex] ( cross- multiply )
15 DF = 9 × 25 = 225 ( divide both sides by 15 )
DF = 15
Answer:
12
Step-by-step explanation:
1. Use the Pythagorean theorem for triangle ABC
a squared (one side of the triangle) + b squared (another side) = c squared (hypotenuse)
so
c squared - b squared = a squared
225 - 81 = 144 ( Find the square root )
which is 12
since Triangle ABC is the same with Triangle DEF then
DF = 12
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 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!
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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A box falls off a window ledge on a tall building. The height of the box above the ground can be found using the function h(t)=-16t^2+150, where r stands for the number of seconds since the box fell.
a). Find the height of the window ledge.
Answer:
The height of the window ledge is the height of the box when t = 0. So, we need to find h(0).
```
h(0) = -16(0)^2 + 150
h(0) = 150
```
Therefore, the height of the window ledge is 150 feet.
Step-by-step explanation:
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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X
-2
-1
01
2
3
-2
0
7
What is the rate of change for the interval between 0
and 2 for the quadratic equation as f(x)=2x²+x-3
represented in the table?
O
5
10
The rate of change for the interval between 0 and 2 for the quadratic equation is 10.
What is the change in interval of the quadratic equation?
A quadratic equation is a type of polynomial equation of the second degree, which means it has one or more terms that are raised to the power of two.
The general form is;
ax² + bx + c = 0
Where;
x is the variablea, b, and c are constantsThe rate of change for the interval between 0 and 2 for the quadratic equation is calculated as;
f(2) - f(0) = 7 - (-3)
= 7 + 3
= 10
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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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A person ordering a certain model of car can choose any of 4 colors, either manual or automatic transmission, and
any of 6 audio systems, How many ways are there to order this model of car?
A) 48 ways
B) 44 ways
C 58 ways
D) 56 ways
Answer:
Step-by-step explanation:
4*2*6=48a
Select all of the figures that show axis symmetry.
Answer: All of them
Step-by-step explanation:
All of them can be divided into two equal halves.
The figures that show axis symmetry are 1, 2, and 3.
What is the axis of symmetry?The axis of symmetry is a line, plane, or other axis that divides a geometric figure into two mirror-image halves that are congruent to each other.
A figure has axis symmetry if it looks the same after being rotated around an axis.
Out of the given figures, the ones that have axis symmetry are:
Sphere (has infinite axis symmetry)Cone (has rotational symmetry around its central axis)Cylinder (has rotational symmetry around its central axis)The figures that do not have axis symmetry are:
Cube (has only point symmetry)Rectangular cone (has no rotational symmetry)So, the figures that show axis symmetry are 1, 2, and 3.
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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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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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wo ships, the Queen Elizabeth and the Queen Mary, are parallel to the shore and 35 km apart. How far is each ship from a lighthouse if the Queen Elizabeth is at an angle of 68° and the Queen Mary is at an angle of 45° to the lighthouse
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.
Will give Brainliest and points!!!!
The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
The slope of the line and its meaning in terms of the real-world scenario is; C. The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
How to calculate or determine the rate of change or slope of a line?In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (0 - 24)/(6 - 0)
Slope (m) = -24/6
Slope (m) = -4.
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Please help !!!!!!!!!!!!!!!!!!!
a) Latonya is correct, as the scale factor of the dilation is of 12.8/4.8.
b) The scale factor was obtained dividing the side length on the dilated figure by the equivalent side length of the original figure.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The ratios for the scale factor are given as follows:
12.8/4.8 = 7.2/2.7 = 4.8/1.8 = 4/1.5 = 8/3.
8/3 as 4 x 2 = 8 and 1.5 x 2 = 3.
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