The * must be replaced by a digit of 1, hence the solution to the equation is given as follows:
x = 143.
What is the rule for divisibility by 10?A number is divisible by 10 if and only if its last digit is 0. This is because 10 is a multiple of 5 and 2, which are the prime factors of 10. Therefore, a number is divisible by 10 if it can be divided evenly by both 5 and 2.
For this problem, the equation is given as follows:
10x + 11 = 144*
Hence, when * = 1, we have that:
10x + 11 = 1441
10x = 1430.
Then the solution for the equation is obtained as follows:
x = 1430/10
x = 143.
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which events are independent? check all that apply.each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. sarah picks a number less than 5, keeps it, and then picks an odd number.
The events that are independent are,
1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.
2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.
3) Olivia choosing an ace and the dart hitting the bull's-eye
The events that are independent are:1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.
2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.
3) Olivia choosing an ace and the dart hitting the bull's-eye.
The other events are dependent because the outcome of the first event affects the outcome of the second event. Specifically
1) Sarah picking a number less than 5 and then picking an odd number. The second event depends on the outcome of the first event.
2) A number cube being rolled and a spinner being spun. The two events are independent of each other, but the outcomes of each event are not independent.
3) Two cards being randomly chosen from a standard deck, and Eliza choosing a jack, replacing it, and then choosing a black card. The outcome of the second event depends on the outcome of the first event, and the outcome of the first event affects the composition of the deck for the second event.
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The given question is incomplete, the complete question is:
Which events are independent? Check all that apply. Each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. Sarah picks a number less than 5, keeps it, and then picks an odd number. A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner. Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card. Two pairs of socks are randomly chosen from a drawer. Hayden chooses a black pair of socks, puts them on, and then chooses another black pair. A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull’s-eye.
What is the quotient of 3.013 × 10^(8) and 6.55 × 10^(5) expressed in scientific notation?
The quotient of 3.013 × [tex]10^{8}[/tex] and 6.55 × [tex]10^{5}[/tex] expressed in scientific notation is equal to 0.46 × [tex]10^{3}[/tex].
What is a quotient?In Mathematics, a quotient is a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).
Generally speaking, any numerical data (number) can be written in scientific notation as shown below:
a × [tex]b^n[/tex]
Where
a represent a real number.b represent an integer.Next, we would rewrite the given numerical data (number) in scientific notation by dividing by 6.55 × [tex]10^{5}[/tex] as follows:
Scientific notation = 3.013 × [tex]10^{8}[/tex]/(6.55 × [tex]10^{5}[/tex])
Scientific notation = 0.46 × [tex]10^{8-5}[/tex]
Scientific notation = 0.46 × [tex]10^{3}[/tex].
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What is the value of angle h?
How do you know (what type of angle pairs are they)?
The value of h is 34.
What is the angle formed when two lines intersect?
Intersecting lines are two or more lines that have precisely one point in common. The point of junction is this central location that connects all of these lines. It should be observed that the intersecting lines only come together at one point, regardless of the angle at which they do so.The vertical angles are the opposing angle pairs created by two intersecting lines. Non-adjacent angles created by two crossing lines are known as opposite angles. Angles at opposite sides are equal. (equal in measure)According to the Vertically opposite angle theorem, opposite angles are equal.
So, h = 34.
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Proportional or not proportional?
Step-by-step explanation:
A is not proportional
Use the graph to record the value of y axis when x is 1, 2, 3, 4, 5, 6
And record the values of x when y is 1, 2, 3, 4, 5, 6 till the end
Using the graph Value of y
(1, 0.9) (2,1.5) (3,2.2) (4,2.5) (5, 3) (6,4) (7, 5) (10,6)
Using the graph, find the value of x when y is 1 - 10)
1.2, 2.5, 5,.....
The slope of the graph also shows that it is not proportional
B is proportional
X is 0 and y is 0
When x is 5, y is 10
Ratio x: y = 5:10 = 1:2
When x is 10, y is 20
Ratio x:y is 10: 20 = 1:2 same as above
C is not proportional
When Moyra is 32, daughter is 8
When her daughter is 22, Moyra will also be 4years older, which is 36
32: 8 = 4:1
36: 12 =3:1
The Saad family is setting up for their annual New Year's party. There will be 143 adults and 62 children coming in the evening. Each table holds 15 people. How many tables will they need for all guests?
Answer:
There are a total of 143 + 62 = 205 people coming to the party.
To calculate the number of tables needed, we divide the total number of people by the number of people per table:
205 ÷ 15 = 13 with a remainder of 10
Since we can't have a fraction of a table, we need to round up to the nearest whole number, which means the Saad family will need 14 tables for all guests.
reading to children fifty-eight percent of american children (ages 3 to 5 ) are read to every day by someone at home. suppose 5 children are randomly selected. what is the probability that at least 1 is read to every day by someone at home?
To calculate the probability that at least 1 of 5 randomly selected American children (ages 3 to 5) is read to every day by someone at home.
To find the probability that none of the 5 children are read to, we can use the fact that the probability that a single child is not read to every day is 1 - 0.58 = 0.42. We can then use the multiplication rule to find the probability that none of the 5 children are read to, which is (0.42)⁵ = 0.0075. Finally, we can use the complement rule to find the probability that at least 1 child is read to every day, which is 1 - 0.0075 = 0.9925. Therefore, the probability that at least 1 of 5 randomly selected American children (ages 3 to 5) is read to every day by someone at home is 0.9925.
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If a regular polygon had 360 side, what would each exterior angle measure? What would each interior angle measure?
Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.
what is angle ?In mathematics, an angle is a figure made up of two rays that share a shared endpoint and are referred to as the sides of the angle and the vertex of the angle, respectively. Angles are typically measured in degrees, radians, or other angle measurement units. Angles can be categorized based on how wide they are. An acute angle is one that is less than 90 degrees, an obtuse angle is one that is higher than 90 degrees but less than 180 degrees, and a right angle is one that is 90 degrees. A reflex angle is greater than 180 degrees but less than 360 degrees, and a straight angle is precisely 180 degrees.
given
Since a polygon with that many sides would have sides that are extremely tiny in relation to the radius, if a regular polygon has 360 sides, it is a circle. Since every group of points in a regular polygon has an equal exterior angle and the sum of all exterior angles in a circle is 360 degrees, each exterior angle in a regular polygon would be measured as follows:
360 edges / 360 degrees = one degree.
Each interior angle of a regular polygon with n sides can be determined using the following formula:
Inner angle is equal to (n-2) x 180 / n.
When we enter n = 360 into this algorithm, we obtain:
(360-2) x 180 degrees / 360 = 178 degrees is the interior angle.
Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.
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according to a recent survey, 67% of cell-phone owners find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating. suppose we randomly select 5 cell-phone owners.
According to the question, "Suppose we randomly select 5 cell-phone owners. What is the probability that all 5 of them find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating?"The formula for finding the probability of an event is:P(E) = number of favorable outcomes/number of total possible outcomes.The given data in the question states that 67% of cell-phone owners find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating.
Therefore, the probability of any cell-phone owner checking their phone when it is not ringing or vibrating is:P(E) = 67/100 = 0.67To find the probability of 5 cell-phone owners checking their phones when they are not ringing or vibrating, we have to use the multiplication rule of probability. [tex]P(E₁∩E₂∩E₃∩E₄∩E₅) = P(E₁) × P(E₂) × P(E₃) × P(E₄) × P(E₅)P(E₁∩E₂∩E₃∩E₄∩E₅) = 0.67 × 0.67 × 0.67 × 0.67 × 0.67P(E₁∩E₂∩E₃∩E₄∩E₅) = 0.2197[/tex]
Therefore, the probability that all 5 of them find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating is approximately 0.2197 or 22%.
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you have been tracking how long you spend on each course subject during your homework sessions. you want to see what percentage each subject represents. which type of chart would be best for this purpose?
a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
For visualizing the percentage distribution of different course subjects, a pie chart would be the most suitable type of chart. Pie charts are ideal for displaying the relative proportions of different categories or groups as slices of a circular pie. Each slice of the pie represents a proportion of the whole, which in this case would be the total time spent on all course subjects during homework sessions. The size of each slice will correspond to the percentage of time spent on each course subject. Therefore, a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
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vital capacity is a measure of the amount of air that someone can exhales after taking a deep breath. what is the probability that we see our sample average difference or higher given there is no difference? g
a. The exit pressure is 19.76 lbf/in².
b. The ratio of the inlet area to the exit area is 3.125.
C. The exit area ratio (0.32) is less than the critical area ratio (1.89), the nozzle is converging-diverging in cross section.
To solve this problem, we need to apply the conservation equations for mass, momentum, and energy along with the isentropic relations.
a. To determine the exit pressure, we can use the isentropic relation for pressure ratio across a nozzle:
[tex]P_2/P_1 = (T_2/T_1)^{\frac{\gamma}{\gamma -1}}[/tex]
where [tex]P_1[/tex] and [tex]T_1[/tex] are the inlet pressure and temperature,
[tex]P_2[/tex] and [tex]T_2[/tex] are the exit pressure and temperature, and
γ is the specific heat ratio of air.
Using Table A-22E, we find that γ = 1.4 for air at 800°R.
Substituting the given values and solving for P2, we get:
[tex]P_2[/tex] = [tex]P_1 \times (T_2/T_1)^\frac{\gamma}{\gamma -1}[/tex] = [tex]45 \times (1500/480)^{(1.4/0.4)}[/tex]= 19.76 lbf/in²
b. To determine the ratio of the exit area to the inlet area, we can use the continuity equation:
[tex]A_1V_1 = A_2V_2[/tex]
where [tex]A_1[/tex] and [tex]A_2[/tex] are the inlet and exit areas, and
[tex]V_1[/tex] and [tex]V_2[/tex] are the inlet and exit velocities.
Substituting the given values, we get:
[tex]A_2/A_1 = V_1/V_2[/tex] = 480/1500 = 0.32
The ratio of the exit area to the inlet area is 0.32, or equivalently, the ratio of the inlet area to the exit area is 1/0.32 = 3.125.
c. To determine whether the nozzle is diverging only, converging only, or converging-diverging in cross section, we can compare the exit area ratio to the critical area ratio.
The critical area is the minimum area that allows the flow to reach sonic conditions, and it depends on the pressure and temperature of the flow.
For a converging-diverging nozzle, the exit area ratio is less than the critical area ratio, which is given by:
A* / [tex]A_1[/tex] = [tex](2/(\gamma+1))^{(\gamma+1)}/(2(\gamma-1)/(\gamma+1))^{(\gamma+1)/(\gamma-1)}[/tex]
where A* is the critical area,
[tex]A_1[/tex] is the inlet area, and
γ is the specific heat ratio.
Using the given values and γ = 1.4, we find that:
A* / [tex]A_1[/tex] = 1.89
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Question:-
Air enters a nozzle operating at steady state at 45 lbf/in.2, 800°R, with a velocity of 480 f/s, and expands isentropically to an exit velocity of 1500 ft/s. Using data from Table A-22E as needed, determine
a. the exit pressure, in lbf/in². 19.76
b. the ratio of the exit area to the inlet area. 0.577
c. whether the nozzle is diverging only, converging only, or converging-diverging in cross section. conv-div
factor the expression 6x^3 + 5x
Answer:
x(6x^2 + 5)
Step-by-step explanation:
To factor the expression 6x^3 + 5x, we can first factor out the greatest common factor of the two terms, which is x. This gives:
x(6x^2 + 5)
We can see that 6x^2 + 5 cannot be factored any further using integer coefficients, so the final factored form of the expression is:
x(6x^2 + 5)
during normal breathing, about 12% of the air in the lungs is replaced after one breath. write an exponential decay model for the amount of the original air left in the lungs if the initial amount of air in the lungs is 500 ml. approximately how much original air is left in the lungs after 5 breaths?
If the initial amount of air in the lungs is 500 ml. approximately then original air is left in the lungs after 5 breaths is 263.86 ml.
During normal breathing, about 12% of the air in the lungs is replaced after one breath,
initial amount of air in the lungs is 500 mL.
After 1 breath original air in lung = 500 - (12/100)500
= 500*(88/100)
= 500 (0.88)
After 2 breath original air in lung = 500 (0.88) - (12/100)500 (0.88)
= 500 (0.88) (1 - 12/100)
= 500 (0.88) (0.88)
= 500(0.88)²
After n breaths original air in lung = 500(0.88)ⁿ
original air is present after 5 breaths = 500(0.88)⁵
= 263.86 ml
Therefore, original air is left in the lungs after 5 breaths is 263.86 ml.
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i do not understand please help asap
Step-by-step explanation:
Lets assume this is a right triangle.
If you use pythagorean theorem, lets assume the tower is the longest line on the triangle.
If this is true, lets say that 9^2 (distance from end of slide to base of tower) + x^2 (length of slide) = 23^2 (height of tower)
we get the length of the slide is 21.2 meters.
the perimeter of a rectangle is 24 inches. if the width of the rectangle is 7 inches, what is the length?
The length of the rectangle with a perimeter of 24 inches and a width of 7 inches is 5 inches.
The perimeter of a rectangle is given by the formula: P = 2l + 2w where P is the perimeter, l is the length, and w is the width. We know that the perimeter of the rectangle is 24 inches and the width is 7 inches.
Substituting the given values in the formula for the perimeter of the rectangle, we have:
24 = 2l + 2 × 7
Simplifying, 24 = 2l + 14
Subtracting 14 from both sides, we get:
10 = 2l
Dividing both sides by 2, we get: l = 5
Therefore, the length of the rectangle is 5 inches.
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What is the area of a circle with the radius of 11.5 meters? Use 3.14 for pi or put pi in your answer for an exact answer.
Answer:
Area = [tex]415.265 m^2[/tex]
Step-by-step explanation:
Area of a circle = [tex]\pi r^2[/tex]
[tex]A = (3.14)(11.5^2)=(3.14)(132.25)=415.265[/tex]
11. Find m
H= 5x+8
J= 7x-16
Answer:
let angle GJK be x
GJK=GHK (Base angle of isosceles triangle)
Step-by-step explanation:
x=5x+8
5x-x=8
4x=8
x=8/4
x=2 ans.
Hence,
5x+8
5*2+8
10+8
18.ans
the empirical rule says that 95% of the population is within 2 standard deviations of the mean, but when i find the z-scores that mark off the middle 95% of the standard normal distribution i calculate -1.96 and 1.96. is this a contradiction? why or why not? in other words why are the normal distribution calculators not agreeing with the empirical rule?
The empirical rule states that approximately 95% of the population lies within 2 standard deviations of the mean for a normal distribution, but you found that the z-scores that mark off the middle 95% of the standard normal distribution are -1.96 and 1.96. This does not represent a contradiction, and I will explain why is it so ?
The empirical rule, also known as the 68-95-99.7 rule, is a useful guideline to help us understand the proportions of data in a normal distribution. According to this rule, about 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. However, it is essential to note that the empirical rule is a simplified approximation.
On the other hand, the z-scores that you calculated, -1.96 and 1.96, are more precise values based on the actual standard normal distribution. These values come from a more accurate calculation using the cumulative distribution function (CDF) of the normal distribution, which gives the exact probability for any given range of z-scores.
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a centrifuge in a medical laboratory rotates at an angular speed of 3450 rev/min in the positive direction. when switched off, it rotates through 45.8 revolutions before coming to rest. Find the constant angular acceleration of the centrifuge.
The constant angular acceleration of the centrifuge is approximately [tex]-331283[/tex] rad/min² in the negative direction.
To find the constant angular acceleration of the centrifuge, we can use the following kinematic equation:
ω² = ω₀² + 2αθ
Here, ω is the final angular velocity (0 rad/min, since it comes to rest), ω₀ is the initial angular velocity (3450 rev/min), α is the constant angular acceleration we want to find, and θ is the angular displacement (45.8 revolutions).
First, we need to convert the given angular values to radians. We know that 1 revolution equals 2π radians.
Initial angular velocity, ω₀ = 3450 rev/min × 2π rad/rev = 6900π rad/min
Angular displacement, θ = 45.8 rev × 2π rad/rev = 91.6π rad
Now, substitute the values into the kinematic equation:
[tex]0 = (6900π)² + 2α(91.6π)[/tex]
[tex]α = - (6900π)² / (2 × 91.6π)[/tex]
[tex]α ≈ -331283 rad/min²[/tex]
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when a group is thought to be related to a certain behavior or attitude when an individual has little experience with that group:
Answer:
When an individual has little experience with a group, and the group is believed to be related to a particular behavior or attitude, this is known as stereotyping.
Step-by-step explanation:
Stereotyping refers to a systematic method of categorizing individuals on the basis of a single characteristic, such as age, gender, or race, and then using that classification to make broad assumptions about them. It is a broad generalization that is made about a particular category or group of people. Stereotyping is an unfortunate part of our society, but it is not something that can be prevented entirely.
The most obvious effect of stereotyping is that it causes people to be unfairly labeled and judged. This can lead to discrimination, as well as negative behavior and attitudes towards certain groups of people. Stereotyping can also limit people's opportunities, both personally and professionally. When people are stereotyped, they are often overlooked for jobs, promotions, and other opportunities that they might otherwise be qualified for.
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please help i will give brainliest along with 20 pnts. ONLY ANSWER IF YOU KNOW IT
Giovanna deposited $1600 into two accounts, half in First Oak and half in West United.
Interest earned in First Oak account after 5 years at 6% simple interest:
= 0.06 x $800 x 5
= $240
Interest earned in West United account after 5 years at 5% compounded annually:
= $800 x (1 + 0.05)^5 - $800
= $800 x 1.27628 - $800
= $221.02
Total interest earned in both accounts:
= $240 + $221.02
= $461.02
Therefore, Giovanna will have earned $461.02 in interest from both accounts at the end of 5 years.
GUYS PLEASE HELP
* I’LL GIVE YOU BRAINLIEST
Compare the maximum values and the end behavior of the functions of f and g.
Therefore , the solution of the given problem of function comes out to be even though the two functions' maximum numbers are different, their final behavior is the same.
What is function?On the midterm exam, there will be inquiries about design, mathematics, each topic, and both actual and hypothetical locations. a summary of the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input. Each post also has a particular location, that could be the enclave, an area, or even something completely different.
Here,
When x = 2, the maximum value of function f is 6, and
when x = -2, the highest value of function g is 3.
Both functions result in the same action in the end.
Both functions move closer to positive infinity as x gets closer to positive or negative infinity.
This is due to the positive quadratic component that dominates the behavior of the leading term in both functions as x increases in magnitude.
As a result, even though the two functions' maximum numbers are different, their final behavior is the same.
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if the path around the edge of a circular lawn is 132 feet, what is the approximate area inside the circular path? complete the answer sentence. solve on paper. then, enter your answer on zearn. you may consider writing your answer to the hundredths place and using the calculator to help you solve.
As a result, the circumference of the circular walkway is approximately 367.06 square feet.
what is circle ?A circle is a geometric shape made up of all points that are equally spaced apart from the center. It is a flat, two-dimensional object whose radius or diameter serves as its sole defining characteristic. A circle's circumference is the distance around it, while the area of the circle is the amount of space inside it.
given
We must deduct the area of the smaller circle from the size of the larger circle in order to determine the area inside the circular path. Let's use the abbreviations "r" for the smaller circle's radius and "R" for the larger circle's radius. We are aware that the circumference of the smaller circle, which is 132 feet, is equal to the distance around the circular path.
The wider circle's circumference is 132 feet.
2πR = 132
R = 21
The breadth of the circular path, which is equal to the difference between the radii of the two circles, can now be used to calculate the radius of the smaller circle:
R - r = diameter of the circle
21 - r = diameter of the circle
r = 18
The smaller circle therefore has a radius of 18 feet.
Inside the arc of the path, there is:
R2 - r2 equals (21 - 18) = (44 - 324) = (117) 367.06 square feet.
As a result, the circumference of the circular walkway is approximately 367.06 square feet.
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how many ways are there to seat six people around a cir- cular table where two seatings are considered the same when everyone has the same two neighbors without re- gard to whether they are right or left neighbors?
the number of distinct seating arrangements when two seatings are considered the same when everyone has the same two without neighbors regard to whether they are right or left neighbors is:5!6⋅2=10.6⋅25! = 10
There are $(6-1)! = 5! = 120$ ways to seat six people around a circular table if the seatings are considered distinct. However, we must divide this number by $6$ to account for the fact that rotations of the same seating arrangement are considered the same. We also must divide by $2$ to account for the fact that reflections (i.e., reversing the order of people) of the same seating arrangement are also considered the same.
Therefore, the number of distinct seating arrangements when two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors is:
5!6⋅2=10.6⋅25! = 10
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Find the circumference of each circle.Use your calculators value of pi.Round your answer to the nearest tenth.
Answer:
5) 59.7 in
6) 39.0 mi
7)
8) 50.3 mi
Step-by-step explanation:
5) C = [tex]\pi (19)[/tex]
C = 59.7 in
6) C = [tex]2\pi (6.2)[/tex]
C = 39.0 mi
7) RADIUS IS CUT OFF
use C = [tex]2\pi r[/tex]
8) C = [tex]2\pi (8)[/tex]
C = 50.3 mi
If the measur of BEC is (2x3) and x is 30 which expression could represent the measure of AED
The expression that equals ∠BEC is 3x - 27, and the answer is B.
First, we find the measure of ∠BEC using the given information and the value of x. We get
2x + 3 = 63, which simplifies to x = 30.Then, we use the fact that ∠AED is vertically opposite to ∠BEC, so ∠AED = ∠BEC = 63 degrees.
Finally, we need to find the expression among the given choices that equals 63 when x = 30.
Option A is too large, option C is too large, and option D is too small. Option B gives us
3x - 27 = 3(30) - 27 = 63which matches the measure of ∠BEC. Therefore, the answer is B.
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Complete Question:
If the measure of BEC is (2x+3) and x=30, which expression could represent the measure of AED?
How can the area of this triangle be determined by forming a rectangle?
Select from the drop-down menus to correctly complete the statements.
The length of the rectangle is what units.
The width of the rectangle is what units.
The area of the rectangle is what square units.
The area of the triangle is half the area of the rectangle, so the area of the triangle is
what square units.
Answer:
the area ot the triangle is half the area of the rectangle, so the area of the triangle is what sqauare units
Answer: It's much easier to form a rectangle and multiply the width and the length and then divide it by 2
Jared's average daily balance for the last month was $560. The finance charge was $8. 12. What was the monthly percentage rate? What was the APR?
The monthly percentage rate is 1.45%, and the APR is 17.4%.
To calculate the monthly percentage rate, we can divide the finance charge by the average daily balance, then multiply by 100 to convert to a percentage
Monthly percentage rate = (finance charge / average daily balance) x 100
Monthly percentage rate = ($8.12 / $560) x 100
Monthly percentage rate = 0.0145 x 100
Monthly percentage rate = 1.45%
To calculate the APR (annual percentage rate), we need to multiply the monthly percentage rate by the number of months in a year:
APR = Monthly percentage rate x 12
APR = 1.45% x 12
APR = 17.4%
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Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem.
A cube-shaped box has an edge length of 45 meter.
What is the volume of the container?
Enter your answer, as a fraction in simplest form, in the box.
The volume of the container is 91125 cubic meters.
What is volume?
A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.
A sphere is the most basic and typical form of a three-dimensional shape. A sphere's radius is the simplest parameter to measure. The radius of the sphere is used to determine its volume.
Given the edge of a cube is 45 meters.
The formula of volume is V = s³.
The volume of the container is
45³
= 91125 cubic meter.
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Two ballons, Balloon A and Balloon B, have a total volume of 3/5 gallon. Balloon A has a greater volume than Balloon B. The difference of their volumes is 1/5 gallon. Write and solve a system of equations using elimination to find the volume of each balloon.
PLEASE HELP
The volume of balloon A is [tex]\frac{2}{5}[/tex] gallon and the volume of balloon B is [tex]\frac{1}{5}[/tex] gallon.
What is volume?
Any three-dimensional solid's volume is simply the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids.
We are given that two balloons have a total volume of [tex]\frac{3}{5}[/tex] gallon.
Let the volume of balloon A be x and the volume of balloon B be y.
So, we get
x + y = [tex]\frac{3}{5}[/tex]
Also, it is given that the difference of their volumes is [tex]\frac{1}{5}[/tex] gallon and Balloon A has a greater volume than Balloon B.
So, we get another equation as
x - y = [tex]\frac{1}{5}[/tex]
Now, on adding both the equations, we get
⇒ 2x = [tex]\frac{4}{5}[/tex]
Now, on solving we get
⇒ x = [tex]\frac{2}{5}[/tex]
Now, on substituting the value of x in the equation, we get
⇒ [tex]\frac{2}{5}[/tex] + y = [tex]\frac{3}{5}[/tex]
⇒ y = [tex]\frac{1}{5}[/tex]
Hence, the volume of balloon A is [tex]\frac{2}{5}[/tex] gallon and the volume of balloon B is [tex]\frac{1}{5}[/tex] gallon.
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is it possible to have a c2 strictly convex function on a compact domain that is not also strongly convex?
Yes, it is possible to have a c2 strictly convex function on a compact domain that is not also strongly convex.
Let's have a look at the following details of it.
Definition of a Strictly Convex Function:A strictly convex function is a function whose Hessian matrix is positive-definite for all arguments. As a result, if f is differentiable and convex, it is strictly convex if and only if its Hessian matrix is positive-definite for all arguments.
The Definition of Strong Convexity: A function is said to be strongly convex if it meets the following criteria:
Let C be a convex subset of a Hilbert space H, and let f:C→ℝ be a continuously differentiable function. There is a positive constant μ such that, for all x,y∈C: f(y)≥f(x)+⟨∇f(x),y−x⟩+μ/2‖y−x‖2
Thus, it is clear from the above-mentioned definitions that it is possible to have a c2 strictly convex function on a compact domain that is not also strongly convex.
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