The required hours will they have ran the same number of miles is 3.
What is distance and speed?Speed distance time is the equation used to make sense of the connection between speed, distance and time. That is speed = distance ÷ time. Or on the other hand to put it one more way distance isolated by speed will give you the time. Given you know two of the sources of info you can resolve the third.
According to question:Eric has already ran 5 miles and is continuing to run at a pace of 1 mile per hour.Erick distance:: 5 + 1x
Similarly for jess,
Jess distance:: 2 + 2x
To cover same number of miles, above two equations will be equate;
5 + x = 2 + 2x
x = 3 hrs
Thus, requierd number of hours is 3.
To know more about Distance visit:
https://brainly.com/question/18246609
#SPJ4
Correct question:
Eric has already ran 5 miles and is continuing to run at a pace of 1 mile per hour. Jess has only run 2 miles and is continuing to run at a pace of 2 miles per hour. In how many hours will they have ran the same number of miles?
The product of four consecutive positive integers is 1 less than $461^2$. What is the least of these four numbers?.
Therefore, 20 is the lowest of the four numbers.
What is integers ?An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.
Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers that consists of the following:
Positive, negative, and zero are all examples of integers.
The Latin word "integer" signifies "whole" or "intact." Thus, fractions and decimals are not included in integers.
According to our question-
4 numbers added together yields the product 4612 - 1.
The least of the four integers is the required information. Let N-2, N-1, N, and N + 1 be the numbers.
According to our calculations
, (N - 2)(N)(N + 1)(N - 1) = 4612 - 1 (N - 2)(N)(N + 1)(N - 1)- (4612 - 1) = 0
This results in N4 - 2N3 - N2 + 2N - 212520 = 0.:
(N + 21)(N - 22)(N2 - N + 460) = 0. N = 22 or -21 are hence potential solutions. However, the necessity for positive integers results in
N = 22 as a potential solution.
Because of this, where the four numbers are N-2, N-1, N, and N + 1, we get the following numbers:
22 -2, 22 -1, 22 + 1, which equals
20, 21, 22, and 23.
Therefore, 20 is the lowest of the four numbers.
learn more about integers click here:
https://brainly.com/question/929808
#SPJ4
Use the following function rule to find f(5). f(x) = –4 |x| − 3 f(5) = \
A function is a relationship between inputs where each input is related to exactly one output.
The value of f(x) at x = 5 is -23.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = -4 |x| - 3
The value of f(x) at x = 5.
f(5) = -4 |5| - 3
f(5) = -4 x 5 - 3
f(5) = -20 - 3
f(5) = -23
Thus,
The value of f(x) at x = 5 is -23.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
Kiran is going to invest $6,600 and leave it in an account for 8 years. Assuming the
interest is compounded daily, what interest rate, to the nearest hundredth of a
percent, would be required in order for Kiran to end up with $9,500?
Answer:
Step-by-step explanation:1.08%
Interest rate required in order for Kiran to end up with $9,500 is 4.55%.
What is Compound Interest?Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.
Given,
Principal amount = $6,600
Time in years = 8 years
Final amount = $9,500
The final amount is calculated in compound interest by the formula,
A = P (1 + [tex]\frac{r}{n}[/tex]) ^ (n t)
Here, P is the principal amount, r is the rate of interest, n is the number of years.
Substituting in the formula,
9500 = 6600 (1 + [tex]\frac{r}{365}[/tex]) ^(365 × 8)
9500 / 6600 = (1 + [tex]\frac{r}{365}[/tex])²⁹²⁰
1.4394 = (1 + [tex]\frac{r}{365}[/tex])²⁹²⁰
1.000125 = 1 + [tex]\frac{r}{365}[/tex]
[tex]\frac{r}{365}[/tex] = 0.00125
r = 0.045531
r = 4.5531% ≈ 4.55%
Hence the interest rate to the nearest hundredth of a percent is 4.55%.
Learn more about Compound Interest here :
https://brainly.com/question/29335425
#SPJ2
Determine if each function is linear or nonlinear. Drag each function into a box to correctly classify it.
y= x/2 -3 , y+3x = 12 and y = x are determined as linear equations , while y=6/x -2 and y= 3x^3 +5 are non-linear equations.
What do you mean by linear equations?A linear equation is a mathematical equation that forms a constant straight line on a graph.
What exactly is a nonlinear equation?Non-linear equations are functional equations that form different types of curves or other non-linear shapes on a graph.
According to the slope-intercept formula of the straight line : y=mx+b
1. y=6/x - 2 ,is not satisfying the above formula of straight line , having x in the denominator, hence it is a non-linear equation.
2. y=x/2-3 , here slope(m)=1/2 and intercept(b)=-3 which are real numbers and satisfy the straight line formula , hence it is a linear equation.
3. y=-3x+12, here slope(m)=-3 and intercept(b)=12 as real numbers and satisfy the straight line graph formula , hence it is a linear equation.
4. y = 3x^3+5, here slope(m)=3x^2 which is not a real number, hence not satisfying the given formula it is a non-linear equation.
5. y = x , here slope(m)=1 and intercept(b) =0 which are real numbers and satisfy the straight line graph formula ,hence it is a linear equation.
To learn more about linear and non-linear equations visit to the given link
https://brainly.com/question/20054300
#SPJ1
~Describe the transformation, by giving the coordinate rule.
7.) (x,y) --> (______,_______)
Answer:
(-x,y)
Step-by-step explanation:
a and b are vectors that are not parallel.
FG = 2a − 3b
-
Choose all of the vectors below which are parallel to
FG.
a-b10a-15
3a-2b-4a+6b 2a + 3b
2a-3b-4a 2a-12b +4a + 3b
Answer:
[tex]\boxed{\textbf{a}-\dfrac{3}{2}\textbf{b}}[/tex]
[tex]\boxed{10 \textbf{a}-15\textbf{b}}[/tex]
[tex]\boxed{-4 \textbf{a}+6\textbf{b}}[/tex]
[tex]\boxed{2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}}[/tex]
Step-by-step explanation:
Given vector:
[tex]\overrightarrow{\rm FG}=2 \textbf{a}-3\textbf{b}[/tex]
Two vectors are parallel if one can be written as a scalar multiple of the other.
Therefore, the following vectors are parallel to FG:
[tex]\textbf{a}-\dfrac{3}{2}\textbf{b}=\dfrac{1}{2}(2 \textbf{a}-3\textbf{b})[/tex]
[tex]10 \textbf{a}-15\textbf{b}=5(2 \textbf{a}-3\textbf{b})[/tex]
[tex]-4 \textbf{a}+6\textbf{b}=-2(2 \textbf{a}-3\textbf{b})[/tex]
[tex]2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}=6\textbf{a}-9\textbf{b}=3(2 \textbf{a}-3\textbf{b})[/tex]
Can somebody help me with 2 and 3 please
(2) The statements and reasons in the two-column method are presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{BD}[/tex] bisects ∠ABC [tex]{}[/tex] 1. Given
2. ∠BAD ≅ ∠BCD [tex]{}[/tex] 2. Given
3. ∠ABD ≅ ∠CBD [tex]{}[/tex] 3. Definition of angle bisector
4. [tex]\overline{BD}[/tex] ≅ [tex]\overline{DB}[/tex] [tex]{}[/tex] 4. Reflexive property
5. ΔABD ≅ ΔCBD [tex]{}[/tex] 5. AAS congruency postulate
(3) The two-column method used to prove the congruency of triangles ΔQRS and ΔSTU, is presented as follows;
Statement [tex]{}[/tex] Reason
1. S is the midpoint of [tex]\overline{QU}[/tex] [tex]{}[/tex] 1. Given
2. [tex]\overline{QR}[/tex] ≅ [tex]\overline{ST}[/tex] [tex]{}[/tex] 2. Given
3. [tex]\overline{RS}[/tex] ≅ [tex]\overline{TU}[/tex] [tex]{}[/tex] 3. Given
4. [tex]\overline{QS}[/tex] ≅ [tex]\overline{SU}[/tex] [tex]{}[/tex] 4. Definition of midpoint of [tex]\overline{QU}[/tex]
5. ΔQRS ≅ ΔSTV [tex]{}[/tex] 5. SSS congruency postulate
What is the two-column method used to prove geometric statements?The two column method consists of statements and the associated reasons arranged sequentially side by side in a two-column tabula format.
The reasons used to prove the above statements are as follows;
Angle bisector
An angle bisector is a segment that divides an angle into two angles of the same measure.
Reflexive property
The reflexive property of equality states that the value of an object or the measure of a dimension is equal to itself
AAS congruency postulate
AAS which is the acronym for Angle-Angle-Side congruency, states that if two angles and a non included side of one triangle are congruent to two angles and the non included side of another triangle, then the two triangles are congruent
Midpoint of a line
The midpoint of a line is a point that divides the line into two segments of the same measure.
SSS congruency postulate
The Side-Side-Side congruency postulate states that two triangles are congruent if three sides are congruent to three sides of the other triangle
Learn more about congruent of triangles here:
https://brainly.com/question/2938476
#SPJ1
9. If one-sixth is one-half of three-fourths of a certain number, what is that number?
A. [tex] \frac{3}{16} [/tex]
B. [tex] \frac{4}{9} [/tex]
C. [tex] \frac{5}{4} [/tex]
D. [tex] \frac{3}{2} [/tex]
E. [tex] \frac{9}{4} [/tex]
Answer:
B) 4/9---------------------------
Convert the statement into equation, considering the number as x, and solve:
1/6 = 1/2×3/4×x Equation 1/6 = 3/8×x Simplify the RHSx = 1/6 ÷ 3/8 Divide both sides by 3/8x = 1/6 × 8/3 Change division to multiplication x = 4/9 AnswerCorrect choice is B.
A recipe for banana bread uses 4 cups of bananas for every 8 cups of flour. How many cups of bananas are needed when 2 cups of flour are used?.
Answer:
1 cup of banana for 2 cups of flour
Step-by-step explanation:
Divide 4 cups of banana by 4 and 8 cups of flour by 4
Then you will get 1 cup of banana for 2 cups of flour
the population of bulford was 16,200 in 2010 and 13,824 in 2016. find the rate of change
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{x}{year}&\stackrel{y}{population}\\ \cline{1-2} 2010&16200\\ 2016&13824\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{2010}~,~\stackrel{y_1}{16200})\qquad (\stackrel{x_2}{2016}~,~\stackrel{y_2}{13824}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{13824}-\stackrel{y1}{16200}}}{\underset{run} {\underset{x_2}{2016}-\underset{x_1}{2010}}} \implies \cfrac{ -2376 }{ 6 } \implies \text{\LARGE -396} ~~ \textit{per year}[/tex]
A deli is trying out new labels for their cylindrical-shaped wheels of cheese. The label covers the entire wheel except the circular top and bottom.
If the wheel has a radius of 30 centimeters and a height of 20 centimeters, how many square centimeters of the wheel does the label cover? (Approximate using pi equals 22 over 7)
A: 792,000 over 7 square centimeters
B: 66,000 over 7 square centimeters
C: 26,400 over 7 square centimeters
D: 2,640 over 7 square centimeters
The cylindrical wheels covers about 9428.7 squared centimeter
Area of CylinderThis is the total area covering the entire body of the cylinder.
The formula of surface area of a cylinder is given as;
A = 2πrh + 2πr²
A = Area of cylinderh = height of cylinderr = radius of cylinderA = 2(22/7) × 30 × 20 + 2(22/7)×30²
A = 9428.57 cm²
The area of the wheel is 9428.7cm²
Learn more on area of a cylinder here;
https://brainly.com/question/76387
#SPJ1
Answer:
Step-by-step explanation:
During a walkathon, Team A walks total 6x+12 miles and Team B walks a total of 4x-7 miles. What is the difference in miles walked between the two teams?
Difference in miles walked between 2 teams is 2x+12.
Team A walks total of 6*x+12 miles.
let's suppose Team A walks y1 miles
y1 = 6*x+12.
Team B walks total of 4x-7 miles
let's suppose Team B walks y2 miles
y2 = 4*x-7
Let's understand what means by difference?
One of the most crucial mathematical operations, which is obtained by removing two numbers, produces difference in mathematics. It reveals how much one number deviates from another. To determine how many numbers are between the two given numbers is the goal of finding the difference in math.
Difference in miles walked between 2 teams
= y1-y2.
= 6x+12-(4x-7)
= 6x+12-4x+7
=2x+12
So the difference in miles walked between 2 teams is 2x+12.
To know more about difference here
https://brainly.com/question/20393062
#SPJ4
what is the solution of -4(8-3x)>or=6x-8?
Answer: x > or = to 4 (Inequality Form), [4, infinity) (Interval Notation)
Step-by-step explanation:
Isolate the equation.
Divide each side by the factors that do not contain x.
Solve for x.
Antonio bought 3 medium and 2 large submarine sandwiches for a total of $29.95 Sophie spend $28.45 on her purchase of 4 and 1 large submarine sandwiches. find the cost of each medium sandwich and each large sandwich.
price of a medium submarine sandwich $
price of a large submarine sandwich $
Answer:
medium is 5 dollars and 39 cents
large is 6 dollars and 89 cents
Step-by-step explanation:
3m + 2l = 29.95
4m + l = 28.45
3m + 2l = 29.95
8m + 2l = 56.9
-5m = -26.95
5m = 26.95
m = 5.39
3(5.39) + 2l = 29.95
16.17 + 2l = 29.95
2l = 13.78
l = 6.89
Mariel and Sam Trent's savings account had a balance of $9,544 on May 1. The account earns interest at a rate of 5.25% compounded
vide. More than f U.S. banking
monthly until the end of August.
Answer: its around 25,000 during the end of august
Step-by-step explanation:
13. Find the slope and a point on the line for the lines with the following equations
a. y - 9=-3/4(x - 4)
b. y = 3 - 2/3 (x +4)
The slopes and points are:
a) (-3/4) and the point is (4, 9)
b) (-2/3), and the point is (-4, 3)
How to identify the slope and point on these lines?
A line with a slope a and a known point (h, k) can be written as:
y - k = a*(x - h)
So that is the slope-point form of the linear equation.
a) The first linear equation is:
y - 9 = (-3/4)*(x - 4)
Comparing this with the general line above, we can see that the slope is (-3/4) and the point is (4, 9)
b) y = 3 - 2/3 (x +4)
We can rewrite this as:
y - 3 = -(2/3)*(x + 4)
Then in this case the slope is (-2/3), and the point is (-4, 3)
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Solve for X using Trigonometry Will give thanks and five stars
Answer:
x= 19.5
Step-by-step explanation
sin58 = x/23
x = 23×sin58
x = 19.5
Colette ha 5/6 of a pitcher of water. She ue 3/5 of the water to water her plant. How much water doe he ue (in term of pitcher)? b) How much water i left (in term of pitcher)?
[tex]\frac{7}{30}[/tex] of water is left in the pitcher
What is Least common multiple ?Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
According to the given information
Total water in container = [tex]\frac{5}{6}[/tex]
Total water used to water the plants = [tex]\frac{3}{5}[/tex]
Water left in pitcher = [tex]\frac{5}{6} - \frac{3}{5}[/tex]
Taking LCM we will get
= [tex]\frac{25-18}{30}[/tex]
= [tex]\frac{7}{30}[/tex]
[tex]\frac{7}{30}[/tex] of water is left in the pitcher
To know more about Least common multiple
https://brainly.com/question/28932085
#SPJ4
with the correct sampling method, you expect to obtain a sample mean exactly the same as the population mean. t or f
False. While using the right sampling technique can increase the probability of getting sample mean values that are close to population mean values.
What is the mean of population?A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics.
What is population mean and sample mean?The sample mean is the mathematical average of values selected at random from the population. The population mean is a representation of the population's real mean.
It is impossible to ensure that the sample mean and population mean will be a perfect match. This is because sampling has intrinsic variability and randomness, which can cause discrepancies between the sample and the population even in studies that are carefully planned. Additionally, there could still be some variability or error in the estimates even if the sample mean is quite near to the population mean, which might have an impact on the accuracy of the findings.
to learn more about population mean visits:
https://brainly.com/question/15020296
#SPJ4
A pebble is tossed into the air from the top of a cliff. The height of the pebble over time is modeled by the equation y = -16x2 + 32x + 80. What is the maximum height, in feet, reached by the pebble?
In linear equation, x = 1 is the maximum height, in feet, reached by the pebble.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The height of the pebble over time is modeled by the equation
y = -16x2 + 32x + 80
At the maximum height, the final velocity of the pebble is zero.
The velocity of the pebble will be obtained by taking the derivative of the given equation.
That is
y' = dy/dx
= d/dx (-16x2 + 32x + 80 )
= -32x + 32
At the maximum height, y' = 0 .
So,
-32x + 32 = 0
32x = 32
x = 32/32
x = 1
Learn more about linear equation
brainly.com/question/11897796
#SPJ4
Shane and abha earned a team badge that required their team to collect no less than 2000 20002000 cans for recycling. Abha collected 178 178178 more cans than shane did. Write an inequality to determine the number of cans, s ss, that shane could have collected.
Inequality is 2x+178 >=2000. and Solution set is x>=911 i.e., the no: of cans that Shane should have collected
What is inequality explain?The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has different meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are shared.
What are the 3 types of inequality?Lifetime Inequality (the distribution of incomes across households or individuals over a person's lifetime), Inequality of Wealth (the distribution of wealth across households or individuals at a particular point in time), and Inequality of Opportunity (the impact on income of factors that people cannot control) are all related concepts.
Let the number of cans collected by Shane = x and the number of cans collected by Abha = y.
It is given that, Abha collected 178 cans more than Shane.
So, we have, .
Since, they both have to collect cans no less than 2000 i.e. greater than or equal to 2000.
So, the equation representing the situation is,
Shane + Abha ≥ 2000
i.e. y + x ≥ 2000
Thus, by substitution we have,
Inequality for the number of cans Shane collected is .2x+178 >=2000.
Solution set of the inequality is x>=911.
To learn more about inequality click the following link:-
https://brainly.com/question/24372553
#SPJ4
Greg evaluated his spending and found that he was spending about $50 more per month on utilities than he has budgeted. He can transfer money from other categories to increase his utilities budget to $125 per month. If his total monthly income is $2,400, to the nearest percent, what percent of his monthly income will be budgeted for utilities?.
The percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.
According to the question,
We have the following information:
Greg evaluated his spending and found that he was spending about $50 more per month on utilities than he has budgeted. He can transfer money from other categories to increase his utilities budget to $125 per month. If his total monthly income is $2,400.
Now, let's take the percent to be x.
We have the following expression:
2400*x/100 = 125
24x = 125
x = 125/24
x = 5.21%
Hence, the percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.
To know more about percent here
https://brainly.com/question/28063156
#SPJ4
u/5 = 17/11 Solve the following proportion for u. Round your answer to the nearest tenth.
On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.
What do you think about proportionality?We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
What is proportionality?When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.
Here,
[tex]\frac{U}{5} = \frac{17}{11} \\\\[/tex]
[tex]U = \frac{17}{11} X 5\\[/tex]
[tex]U = \frac{85}{11}\\ U = 7.72[/tex]
To know more about proportionality visit:
https://brainly.com/question/8598338
#SPJ1
There is such a positive integer: if it is divided by 5, the remainder is 3; if it is divided by 6, the remainder is 4; if it is divided by 7, the remainder is 1. Find the least possible value of such number.
Answer:
The least possible number is 148---------------------------------------------------
Let the number be N.
If N is divided by 5 the remainder is 3:
N = 5k + 3,Similarly:
N = 6p + 4,N = 7q + 1.We can observe N + 2 is divisible by both 5 and 6, then it can be represented as:
N + 2 = 30m,so
30m = 7q + 1 + 2 or30m - 3 = 7qThe left side is divisible by 3, then q = 3t:
30m - 3 = 7*3t10m - 1 = 7tThe least m and t would be m = 5 and t = 7.
Then:
N + 2 = 30*5 = 150 ⇒ N = 148 is the least possible number.Proof:
148/5 = 29 (rem 3)148/6 = 24 (rem 4)148/7 = 21 (rem 1)in an examination, the following was found 40% passed in mathematics 45% passed in science 55% passed in health. how many candidates passed in all three subjects?
5% of the students either passed all 3, or none of the tests.
What is amount ?
Mass nouns are referred to by the word amount. Count nouns are referred to as numbers.
To illustrate the process of thinking, tets assume there are no people who passed all subjects.
40% (Maths) - 10%(+sceince) - 15% (+english) = 15% only maths
45% - 10% - 20% = 15% only science
55% - 20% - 15% = 20% only english.
That gives
15+15+20 = 50% of the students passing only one course
10+20+15 = 45% of students passing only 2 courses
… that’s 95% together …
… but we need to get to 100%; obviously.
If we assume there are X% students that passed in all 3 courses, then from the first line, we substracted this person twice: (once for +science, and once for +english). Considering we only need to substract ’m once, that’s the same as substracting twice and adding once. we get:
40% (Maths) - 10%(+sceince) - 15% (+english) + X% = 15+X % only maths
and likewise
45% - 10% - 20% + X= 15 +X % only science
55% - 20% - 15% +x X= 20 +X % only english.
Now, for the students who passed exactly 2 classes, that’s
10 - X % only maths and science
20 - X %
15 - X%
And of course, the amount of students who passed all three exams: X.
This gives us
(15+X) + (15+X) + (20+X) + (10-X) + (20 - X) + (15 - X) + X = 100
95 + X = 100
X = 5
Or, 5% of students passed all 3 tests.
edit: this answer assumes all students pass at least one test. The actual summation should be: As pointed out with the first line, if that answer is
0%, the amount of students mentioned is 95%.
The actual answer is
5% of the students either passed all 3, or none of the tests.
To learn more about amount visit:https://brainly.com/question/13024617
#SPJ4
how do i find the maximum value of the function
Answer:
The maximum value of a function can be found at its highest point, or vertex, on a graph
Step-by-step explanation:
I need help, what does y equal?
In the provided figure, the value of y is 5.5 units.
What is trigonometric ratios?Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilized in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more. The values of all trigonometric functions depending on the ratio of sides of a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.
Here,
cos 30°=b/15
b=15*cos 30°
b=13 units
since this is square so all sides are equal.
sin 30°=p/15
p=15*sin 30°
p=7.5 units
required difference=13-7.5
=5.5 units
The value of y in the given figure is 5.5 units.
To know more about trigonometric ratios,
https://brainly.com/question/25122832
#SPJ1
Which box-and-whisker plot represents this data: 6, 9, 13, 13, 18, 20, 22, 25, 26, 28, 30, 30 ?
The box and whisker plot that represents the data given is option D (see attachment below).
How to Determine the Box and Whisker Plot that Represents a Data Set?The box and whisker plot that represents a data set will display the five-number summary of the data, which include minimum and maximum values, upper quartiles and lower quartiles, and the median of the data.
Given the data set, 6, 9, 13, 13, 18, 20, 22, 25, 26, 28, 30, 30, the five-number summary that would be displayed on the box and whisker plot include:
Minimum: 6 (at the beginning of the whisker to the left)
First Quartile: 13 (at the beginning of the edge of the box)
Median: 21 (at the middle line on the box)
Third Quartile: 27 (at the end of the edge of the box)
Maximum: 30 (at the end of the whisker to the right)
Therefor, the box and whisker plot would be the option D (see image below).
Learn more about the box and whisker plot on:
https://brainly.com/question/12343132
#SPJ1
Find the midpoint of AC is at -2 and C is at 3 on a number line
The midpoint of AC is 0.5 where A is at -2 and C is at 3 on the number line.
What is number line?A number line is a line on which numbers are pointed at some intervals, it is used to show numerical operations.
Given that,
A and C are two points on number line.
A is at -2 and C is at 3
The midpoint of AC can be given by finding average of both the points,
Midpoint of AC = (-2 + 3) / 2
= 1 /2
= 0.5
The required midpoint of AC where A is at -2 and C is at 3 is 0.5.
To know more about Number line on:
https://brainly.com/question/27114736
#SPJ1
Water is being from a pool. The volume of water in the pool t minutes after begin draining is given by the function V(t)=4522(0.94)^t. Which of the following is the closest to the percent volume that has drained out of the pool after 10 minutes
The closest percentage volume that has drained out is 46%
How to determine the percentage volume?From the question, we have the following parameters that can be used in our computation:
V(t) = 4522(0.94)^t
The initial volume is calculated when t = 0
So, we have
V(0) = 4522(0.94)^0
Evaluate
V(0) = 4522
The new volume is calculated when t = 10
So, we have
V(10) = 4522(0.94)^10
Evaluate
V(10) = 2435.62
The percentage is then calculated as
Percentage = (V(10) - V(0))/(V(0))
So, we have
Percentage = (2435.62 - 4522)/4522
Evaluate
Percentage = -46%
Hence, the percentage is 46%
Read more about exponential functions at
https://brainly.com/question/11464095
#SPJ1