Answer:
larger angle = 63°
Step-by-step explanation:
complementary angles sum to 90°
let x be the smaller angle then larger angle is x + 36 , then
x + x + 36 = 90
2x + 36 = 90 ( subtract 36 from both sides )
2x = 54 ( divide both sides by 2 )
x = 27
Then
larger angle = x + 36 = 27 + 36 = 63°
what is the volume of the cube shown
[tex] {( \frac{9}{4} )}^{3} [/tex]
=
[tex] \frac{729}{64} [/tex]
Answer: 11 25/64
Step-by-step explanation: 2 1/4 x 2 1/4= 5 1/16 x 2 1/4 = 11 25/64
Which triangle could be drawn as it is described?
The triangle which can be drawn as per the condition described is only option 2. an isosceles triangle with measure 20° and 80°.
Triangle which can be drawn as per the measurements are,
An acute triangle with sides measuring 7, 4, 2.
In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides.
According to the Pythagorean theorem.
7²< 4² + 2²
49 < 16 + 4
49 < 20
This is a contradiction, since 49 cannot be less than 20.
It is not possible to draw triangle.
An isosceles triangle with measures of angle 20° and 80°.
Sum of interior angles of a triangle is 180°
Here, third angle = 180° - ( 20° + 80° )
⇒Third angle = 80°
Two angles are congruent ⇒ opposite sides to congruent angles are also congruent.
It forms a isosceles triangle.
An obtuse triangle with sides measuring 5, 10 and 15.
Side lengths 5, 10, and 15 do not form a triangle at all.
Since the sum of the two shorter sides is less than the longest side.
5 + 10 = 15
It is not possible to have an obtuse triangle with sides measuring 5, 10, and 15.
An scalene triangle with angle measuring 110° and 35°.
Sum of the interior angles is always 180°.
Measure of the third angle ,
180° - 110° - 35° = 35°
Three angles of the triangle measure 110°, 35°, and 35°.
It represents isosceles triangle.
Therefore, the possible triangle as per the given condition is only option 2. isosceles triangle with measure 20° and 80°.
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A car is driving on a road with a velocity of 20 − 10t miles per hour,
where t is the time in hours since the car started driving. What is the total distance
travelled by the car between times t = 0 and t = 3? Show work.
a. 5mi
b. 10mi
c. 15mi
d. 20mi
e. 25mi
The total distance traveled by the car between t = 0 and t = 3 is given as follows:
c. 15 mi.
How to obtain the total distance?The velocity function is given as follows:
v(t) = 20 - 10t.
The distance function is the integral of the velocity function, hence it is given as follows:
d(t) = 20t - 5t².
The distance at t = 0 is given as follows:
d(0) = 20(0) - 5(0)²
d(0) = 0.
The distance at t = 3 is given as follows:
d(3) = 20(3) - 5(3)²
d(3) = 15.
Hence the total distance is given as follows:
15 - 0 = 15 mi.
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1. Lana completed 22 of the puzzles in
her puzzle book. There are 10 puzzles
remaining. What percent of the puzzle
has she completed?
Answer:
Lana has completed 22 out of 32 puzzles in her book. To find the percentage of the puzzle she has completed, divide the number of puzzles she has completed by the total number of puzzles in the book and multiply by 100.
22/32 x 100 = 68.75%
Lana has completed 68.75% of the puzzles in her book.
Answer:
Lana has completed 68.75% of the puzzles in her puzzle book.
Step-by-step explanation:
Lana has completed a total of 22 puzzles and there are 10 puzzles remaining, so the total number of puzzles in the book is:22 + 10 = 32To find the percentage of puzzles Lana has completed, we can use the following formula:percentage = (completed puzzles / total puzzles) x 100%Substituting the values, we get:percentage = (22 / 32) x 100%
percentage = 0.6875 x 100%
percentage = 68.75%Therefore, Lana has completed 68.75% of the puzzles in her puzzle book.
jashon will spin this spinner 150 times how many times should he expect to land on a 3
Okay, let's break this down step-by-step:
* The spinner has 5 equal sections, numbered 1 through 5.
* Each section represents a 1 in 5 chance of landing on a particular number.
* The spinner has a 3 section.
* Jashon will spin the spinner 150 times.
So, to calculate the expected number of times a 3 will come up:
* There is 1 section for the number 3 out of the 5 total sections.
* So the probability of landing on the 3 section is 1/5 = 0.2
* In 150 spins, the probability of landing on 3 will be 0.2 multiplied by 150 spins.
* So 0.2 * 150 = 30
Therefore, if Jashon spins the spinner 150 times, he can expect the number 3 to come up approximately 30 times.
Let me know if you have any other questions!
Helpppp this is for geometry
The correct statements regarding the transformations are given as follows:
FG and F'G' have the same length.<G and <G' have the same measure.What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.For the transformation 1, we have a reflection, which keeps both the side lengths and the angle measure constant, just changing the orientation of the figure.
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Use the model to estimate f(x) when
x
=
5
.
f(x) =
Use the model to estimate f(x) when
x
=
10
.
f(x) =
Using the model to estimate f(x) when x = 5 and x = 10, the vaues are 18.33 and 17.78
Using the model to estimate f(x) when x = 5 and x = 10From the question, we have the following function that can be used in our computation:
f(x) = -0.11x + 18.88
Also, we have
x = 5 and x = 10
Substitute the known values in the above equation, so, we have the following representation
f(5) = -0.11 * 5 + 18.88 = 18.33
f(10) = -0.11 * 10 + 18.88 = 17.78
Hence, the values are 18.33 and 17.78
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Complete question
Question: A statistician calculated the following linear model to describe the data: f(x) = – 0.11x + 18.88 Use the model to estimate f(x) when x = 5
If (2x, x + 17, x + 21, ....) is an arithmetic sequence find the value of x ?
Answer:
Since (2x, x + 17, x + 21, ...) is an arithmetic sequence, we know that the common difference between consecutive terms is constant.
The common difference can be found by subtracting any two consecutive terms in the sequence. Let's subtract the second term (x + 17) from the first term (2x):
2x - (x + 17) = x - 17
Now let's subtract the third term (x + 21) from the second term (x + 17):
(x + 17) - (x + 21) = -4
Since the common difference is constant, we can set the two expressions for the common difference equal to each other:
x - 17 = -4
Solving for x, we get:
x = 13
Therefore, the value of x that makes the sequence (2x, x + 17, x + 21, ...) an arithmetic sequence is x = 13.
Determine that the value x=9 of the following expiration given x2+3x-5
Step-by-step explanation:
To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:
9^2 + 3(9) - 5 = 81 + 27 - 5 = 103
Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.
rate my answer, please.
what fractional part of 70 is 28
The fractional part of 70/28 is 35/14 i.e., 2.5
Percentage:
A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100
28 of 70 can be written as:
=> [tex]\frac{28}{70}[/tex]
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
[tex]\frac{28}{70}[/tex] × [tex]\frac{100}{100}[/tex]
=> (28 × 100) /70 ×[tex]\frac{1}{100}[/tex]
=> 40/100
Therefore, the answer is 40%
The fractional part of 70/28 is 35/14 i.e., 2.5
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x − 9 ≥ −6
solve the inequality
Answer: x ≥ 3
Step-by-step explanation:
Need help don’t get it
Answer:
[tex] \frac{210}{360} = \frac{7}{12} [/tex]
This figure represents 7/12 of the circle.
This is for the following two questions.
A couple plans to retire in 35 years. At that time, they would like to have enough money in an account so that they can receive a $6,000 every month end for the next 25 years. The account earns 8% APR compounded monthly and will continue to do so until there is a zero balance in the account.
To achieve this goal, how much money does the couple need to have in this account by the time they retire?
If they have not saved any money yet, how much does the couple need to deposit each month end until they retire?
The couple needs to deposit about $554.49 each month end until they retire to reach their goal.
How to solveTo find the monthly deposit needed, we'll use the future value of an ordinary annuity formula:
FV = PMT * [((1 + r)^n - 1) / r]
We already know the future value (FV) as $953,776.53, and we want to solve for PMT, the monthly deposit:
PMT = FV / [((1 + r)^n - 1) / r]
We'll use the same r (0.08/12) and a new n (35 * 12) for the 35 years until retirement:
PMT = 953776.53 / [((1 + 0.08/12)^(35*12) - 1) / (0.08/12)]
PMT ≈ 554.49
Thus, the couple needs to deposit about $554.49 each month end until they retire to reach their goal.
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In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student has a dog given that they have a cat?
The probability that a student has a dog given that they have a cat is 2/5.
To find the probability that a student has a dog given that they have a cat, we need to use conditional probability. We can use the formula:
P(Dog | Cat) = P(Dog and Cat) / P(Cat)
where P(Dog and Cat) is the probability that a student has both a dog and a cat, and P(Cat) is the probability that a student has a cat.
From the given data table, we can see that there are a total of 25 students in the class, and 15 of them have a cat. Of the 15 students with a cat, 6 also have a dog. Therefore, P(Dog and Cat) = 6/25 and P(Cat) = 15/25.
Substituting these values into the formula, we get:
P(Dog | Cat) = (6/25) / (15/25) = 6/15 = 2/5
Therefore, the probability that a student has a dog given that they have a cat is 2/5 or 0.4.
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in the diagram at the right, the length of a square is (3x+7) units. The dimensions of the cut-out rectangle are x by (2x+5) units. Which choice expresses the area of the shaded regions, in square units?
[tex] {(3x + 7)}^{2} - ((2x + 5) \times x) [/tex]
[tex] = 7 {x}^{2} - 5x + 49[/tex]
Is the figure line symmetric?
If yes, how many lines of symmetry does the figure have?
Snow flake
A.
No
B.
Yes; 3 lines of symmetry
C.
Yes; 6 lines of symmetry
D.
Yes; 12 lines of symmetry
The figure is indeed symmetric and the number of lines of symmetry the snowflake has is C. Yes; 6 lines of symmetry.
How many lines of symmetry does a snowflake have ?Generally a snowflake is hexagonal and has 6-way radial symmetry. Thus, one can rotate it 60 degrees (the sixth of full rotation) and it still appears the same.
So, overall, this means that a snowflake holds 6 lines of symmetry which divide it into two identical halves reflecting each other. Consequently, it can be rotated in 60-degree increments and still holds identicality. Akin to this final property, the snowflake artifact possesses six uniquely divided
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PLS HELP ME RNNNNNNNNN
i) There is no solution for x when y<0.
ii) When y>0, the solutions for x are x=4 and x=0.
iii) When y=0, the solutions for x are x=4 and x=0
To use a graph to find the value of x for the given values of y in the equation y=-|x-2|+2, we can follow these steps:
i) When y<0:
The graph of y=-|x-2|+2 is below the x-axis when y<0. Therefore, there is no solution for x when y<0, because there is no point on the graph that has a negative y-coordinate.
ii) When y>0:
The graph of y=-|x-2|+2 intersects the x-axis at two points when y>0. To find the x-coordinates of these points, we can set y=0 in the equation y=-|x-2|+2 and solve for x, as shown in the previous answer.
The x-intercepts are at (4,0) and (0,0), which means that the graph crosses the x-axis at x=4 and x=0 when y>0.
iii) When y=0:
To find the x-coordinate(s) of the point(s) where the graph intersects the x-axis (i.e., where y=0), we can look at the x-intercepts that we found in part ii) above. The x-coordinate(s) of the point(s) where the graph intersects the x-axis are x=4 and x=0, so the solutions for x when y=0 are x=4 and x=0.
Therefore, i) There is no solution for x when y<0.
ii) When y>0, the solutions for x are x=4 and x=0.
iii) When y=0, the solutions for x are x=4 and x=0 (the x-intercepts).
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after the school carnival there were 20 apples left over eight students shared these apples equally how many apples did each student receive
Answer:
They would have gotten 2 full apples each. There would be 4 left over. If they decided to split those 4 apples, they would have gotten 2 1/2 apples each.
Step-by-step explanation:
20 ÷ 8 = 16 R 4
16 ÷ 8 = 2 (the full apples they got each_)
4 x 2 = 8 (split the 4 apples in half to make 8)
Therefore, each student would have gotten 2 full apples and 1/2 of an apple.
In 2016 , a clinical study in a small town of New Hampshire found that about 13 % of its population had the flu . The study also showed that 19 % of the people who had the flu tested negitive while 8% of of the people who did not have the flu tested positive . based on the given information construct a realative frequency table.
The relative frequency of a person having the flu and testing positive for the flu is 0.1053/0.901 = 0.117, or approximately 11.7%. The relative frequency table is given below.
To get the relative frequencies, we divide each cell value by the total frequency of the table.
This is how we construct relative frequency table.
To construct a relative frequency table, we need to determine the different possible outcomes and their corresponding frequencies based on the given information.
Let's define the following events:
A: a person has the flu
B: a person tests positive for the flu
Then, using the information given in the problem, we can construct the following relative frequency table:
A (has the flu) not A (does not have the flu) Total
B 0.13*0.81 = 0.1053 0.08*0.87 = 0.0696 0.1749
not B 0.19*0.81 = 0.1540 0.63*0.87 = 0.5471 0.7011
To 0.2843 0.6171 0.901
In this table, the values in the cells represent the product of the probability of the row event and the probability of the column event. For example, the value 0.1053 in the top left cell represents the probability of a person having the flu (event A) and testing positive for the flu (event B), which is calculated as 0.13 x 0.81.
The total frequency for each row and column is calculated by summing the values in that row or column. The total frequency for the entire table is the sum of all the values, which is 0.901 in this case.
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Find a quadratic equation which has solutions x=7 and x=-9. Write the quadratic form in the simplest standard form x^2+bx+c=0
Answer: x^2+2x-63
Step-by-step explanation:
Quadratic Equation = x^2-(Sum of Solution)x+(Product of Solution)
=x^2-(7-9)+(7*(-9))
=x^2+2x-63
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Which one of these tables are proportional? Show your work.
Answer:
Table B is proportional since y = 1.5x:
4.5 ÷ 3 = 1.5
7.5 ÷ 5 = 1.5
10.5 ÷ 7 = 1.5
An automobile purchased for use by the manager of a firm at a price of $32,500 is to be depreciated by using the straight-line method over 5 years. What will be the book value of the automobile at the end of 3 years? (Assume that the scrap value is $0.) $
The book value of the automobile at the end of 3 years is $13,000.
What is the book value?The straight-line method is method of depreciation that allocates the same depreciation expense each year.
Straight line depreciation expense = (Cost of asset - Salvage value) / useful life
($32,500 - 0) / 5 = $6,500
Total depreciation in 3 years = $6,500 x 3 = $19,500
Book value = cost of the automobile - total depreciation
$32,500 - $19,500 = $13,000
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Fill the blank with either E or to make the statement true.
- 13 {8, 13, 22, 36}
***
fill in the answer box to complete your choice
We can see here that the statements that are true are:
B. The symbol should be used because (8, 13, 22, 36) is a set and none of the elements in - 13 is a set.
C. The ∉ symbol should be used because ∉ is not an element of the set.
F. The ∈ symbol should be used because ∉ is not an element of the set.
What is a set?A set in mathematics is a collection of unique objects, referred to as elements or members, that are paired off according to some shared quality.
Numbers, letters, words, forms, persons, and other mathematical things can all be included in a set.
We can see here that -13 ∉ (8, 13, 22, 36).
These statements are true because -13 is not actually an element of (8, 13, 22, 36). Thus, in the given set of data, -13 is not seen in the given set.
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There are 200 kids in the 7th grade at smith middle school. If 25% of them purchase a school t-shirt that costs $20, how much money did the 7th grade spend on t-shirts?
Answer:
$1,000.
Step-by-step explanation:
200 kids divided by 25% or 4 = 50 then 50 x 20 = 1,000.
The product of p is and -8 is less than 24
The statement The product of p is and -8 is less than 24 as an expression is -8p < 24
Writing the statement as an expression
From the question, we have the following parameters that can be used in our computation:
The statement represented as
The product of p is and -8 is less than 24
Less than is represented using the symbol <
So, we have
The product of p is and -8 is less than 24: The product of p is and -8 is < 24
Represent products as *
So, we have
The product of p is and -8 is less than 24: -8p < 24
Hence, the expression is -8p < 24
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A rectangular prism shaped display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall. What is the volume of the display case in cubic inches?
A. 73 1/4 in
B. 320 1/4 in
C. 10, 328 1/16 in
D. 28,372 5/8 in
Answer:
The volume of the display case in cubic inches is 10,328 1/16 in.
PLEASE HELP Polygon KLMN is drawn with vertices at K(0, 0), L(5, 2), M(5, −5), N(0, −3). Determine the image vertices of K′L′M′N′ if the preimage is rotated 270° clockwise.
K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)
K′(0, 0), L′(−2, −5), M′(−5, 5), N′(−3, 0)
K′(0, 0), L′(−5, −2), M′(5, −5), N′(3, 0)
K′(0, 0), L′(−5, −2), M′(−5, −5), N′(0, 3)
Answer:
K′(0, 0), L′(−2, 5), M′(5, 5), N′(−3, 0)
Step-by-step explanation:
To rotate a point $(x,y)$ by $270^{\circ}$ clockwise, we first swap the $x$ and $y$ coordinates and then negate the new $y$ coordinate.
Using this, we can find the image vertices of the given polygon as follows:
For vertex K(0, 0), we have $(0,0) \rightarrow (0,0)$. So K′ is at the origin.
For vertex L(5, 2), we have $(5,2) \rightarrow (2,-5)$. So L′ is at (-2, 5).
For vertex M(5, -5), we have $(5,-5) \rightarrow (5,5)$. So M′ is at (5, 5).
For vertex N(0, -3), we have $(0,-3) \rightarrow (-3,0)$. So N′ is at (-3, 0).
Therefore, the image vertices of the polygon KLMN after a $270^{\circ}$ clockwise rotation are K′(0, 0), L′(−2, 5), M′(5, 5), and N′(−3, 0).
Thus, the correct option is:
K′(0, 0), L′(−2, 5), M′(5, 5), N′(−3, 0)
What fraction does each part represent? Drag the tiles to make a fraction that represents each part of Alexi's circle. 1 2 5 6 8
Answer:
To represent each part of Alexi's circle as a fraction, we need to determine the total number of parts in the circle and the number of parts represented by each tile.
Adding up the number of tiles, we get:
1 + 2 + 5 + 6 + 8 = 22
So there are a total of 22 parts in Alexi's circle.
To find the fraction represented by each tile, we can divide the number of parts represented by the tile by the total number of parts in the circle.
Starting with the first tile, which represents 1 part, the fraction it represents is:
1/22
Moving to the second tile, which represents 2 parts, the fraction it represents is:
2/22 = 1/11
Continuing in the same way for the remaining tiles, we get:
The tile representing 5 parts represents the fraction 5/22The tile representing 6 parts represents the fraction 6/22, which simplifies to 3/11The tile representing 8 parts represents the fraction 8/22, which simplifies to 4/11So the fractions represented by each part of Alexi's circle are
1/221/115/223/114/112 Construct an x chart. Answer the questions associated with each given data set.
The overall mean of data set is 49.57. Option D
How do we find the over all mean of a data set?The overall mean is all the sums of the means divided by the total number of set in the table.
All the mean in the table are 42. 75 + 51. 75 + 50.00 + 49.50 + 51.25 + 47.25 + 50.75 + 47.75 + 56.50 + 47.50 + 38.75 + 49.25 + 57.00 + 48.75 + 54.75 = 743.5
We see that there are 15 data set.
mean = 743.5/ 15
Overall mean = 49.57
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The dimensions of a cylinder are shown in the diagram
Round to the nearest whole number , what is the total surface area of the cylinder in cubic centimeters
Answer:
S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3
