It is given that there are
[tex]1\frac{1}{4}=\frac{5}{4}\text{miles}[/tex]run in 2 minutes.
So, we have to determine time required to run
[tex]1\frac{1}{2}=\frac{3}{2}\text{miles}[/tex]Apply the unitary method,
For 5/4 miles required 2 minutes.
So , for 1 miles, time required
[tex]\frac{2}{\frac{5}{4}}=\frac{2\times4}{5}=\frac{8}{5}\min [/tex]Therefore,for 3/2 miles , time required is
[tex]\frac{3}{2}\times\frac{8}{5}=\frac{12}{5}\text{min}=2.4\min [/tex]Hence the time required is 2.4 minutes.
Benjamin invested an amount of $12,000.00 in a mutual fund. After 4 years and 6 months the accumulated value of his investment was $13,407.58. What is the nominal interest rate of the investment if interest is compounded semi-annually?__________%Round to two decimal places
Given:
The accumulated value of investment is A = 13,407.58.
The invested amount is P = 12,000.00.
The time period is 4 years and 6 months.
Explanation:
The formula for the accumulated value at r rate of interest is compounded semi-annually.
[tex]A=P(1+\frac{r}{200})^{2\cdot t}[/tex]Substitute the values in the formula to determine the value of r.
[tex]\begin{gathered} 13407.58=12000(1+\frac{r}{200})^{2\cdot4.5} \\ \frac{13407.58}{12000}=(1+\frac{r}{200})^9 \\ 1+\frac{r}{200}=(\frac{13407.58}{12000})^{\frac{1}{9}} \\ \frac{r}{200}=1.01239-1 \\ r=0.01239\cdot200 \\ =2.478 \\ \approx2.48 \end{gathered}[/tex]So the rate of interest is 2.48%.
Find the equation of the line passing through point (3,5) and with a slope ⅓
hello
we are given 1 point with x and y co-ordinate and a slope, we can easily write down the equation of the line
standard equation of a straight line is
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}[/tex]to solve this problem, we need to find the intercept first
substitute the x and y co-ordinates in the equation
[tex]\begin{gathered} y=mx+c \\ m=\frac{1}{3} \\ y=5 \\ x=3 \\ 5=\frac{1}{3}(3)+c \\ 5=1+c \\ c=4 \end{gathered}[/tex]we know our intercept is equal to 4 and we can proceed to write out our equation
[tex]y=\frac{1}{3}x+4[/tex]we can leave it this way or multiply through by 3
[tex]3y=x+12[/tex]Text-to-Speech6.For the expression, combine like terms and write an equivalentexpression with fewer terms.4- 2x + 5xВ ІΣSave answer and go to next question
hello
the question given request we write an equivalent expression as the one given which is
[tex]4-2x+5x[/tex]an equivalent expression to the one above would be
[tex]4+3x[/tex]so, we can say
[tex]4-2x+5x=4+3x[/tex]Making an inference usingig a two-way frequency tableA group of 150 college students who took math fost term were interviewed. They were asked whether they passed their math course and whether they live oncampus. Their responses are summarized in the following tablePassed math Failed mathve on campus2466Live off campus392152(a) What percentage of the students passed moth? []%(b) What percentage of the students live off campus? []%(c) What percentage of the students who live off campus passed math? []%(d) Is there evidence that students who live off campus tend to pass math more often than average?Yes, because the percentage found in part (e) is much greater than the percentage found in part (0)Yes, because the percentage found in part() is much greater than the percentage found in part (b)No, because the percentage found in part(e) is about the same as the percentage found in part (a).No, because the percentage found in part (5) is about the same as the percentage found in part (b).
1) Considering that there are 150 students
A) Adding 24+39 we got 63 students
150------------100%
63 ----------- x
x=6300/150
x= 42% of the students passed Math.
B) Adding the number of those students who live off-campus 39 +21
150 ----------------100%
60------------------ y
y=6000/150
y=40%
C) 60 students live off-campus 39 succeded. So we can write
60 --------- 100%
39 --------- z
z= 3900/60
z=65% passed math (off-campus)
D) Comparing that 65% of students who live off-campus passed math and that among those who live on campus and that 58% of all students failed
Then we can state:
A)
what is the line that passes through points(-6,-10)(-2,-10)
The line passes through the points, (-6,-10) and (-2,-10)
We know equation of the line passing through points (x',y') and (x'',y'') is given by:
[tex]y-y^{\prime}=\frac{y^{\prime}^{\prime^{}}-y^{\prime}}{x^{\prime}^{\prime}-x^{\prime}}(x-x^{\prime})[/tex]So the equation of the line is:
[tex]\begin{gathered} y-(-10)=\frac{-10-(-10)}{-2-(-6)_{}}(x-(-6)) \\ \Rightarrow y+10=0 \\ \Rightarrow y=-10 \end{gathered}[/tex]The equation of the line is y=-10
i invest $250 in a simple account that earns 10% annually. After 6 years, how much money have i earned? Hint round to the nearest cent.
We have to use the simple interest formula
[tex]A=P(1+rt)[/tex]Where P = 250; r = 0.10 (10%); t = 6. Replacing these values, we have
[tex]A=250(1+0.10\cdot6)=250(1+0.6)=250(1.6)=400[/tex]Hence, after 6 years, you have $400.
If we subtract this amount from the investment, we get the profits.
[tex]400-250=150[/tex]Hence, the earnings are $150.Graph the solution set of the system. -2x-y ≥2 y ≥-2 x ≥-4
The graph of the given equations as;
-2x-y ≥2
The graph of the inequality y ≥-2
The graph of the inequality, x ≥-4
Now, the graph for the set of the system as;
...
Solve each equation for the given variable.-2x + 5y = 12 for ySolve each equation for y. Then find the value of y for each value if x.y + 2x = 5; x = -1, 0, 3
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
-2x + 5y = 12
y = ?
Step 02:
We must apply algebraic rules to find the solution.
-2x + 5y = 12
5y = 12 + 2x
y = 12 / 5 + 2x / 5
[tex]y\text{ =}\frac{12}{5}\text{ + }\frac{2x}{5}[/tex]The answer is:
y = 12 / 5 + 2x / 5
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a card with number from 2 to 9.
The probability that we do not dealt a card with number 2 to 9 is 5/13
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given,
A pack of card = 52 cards
The Cards having Hearts = 13
The Cards having Spade = 13
The Cards having Diamond = 13
The Cards having Clubs = 13
According to question
The cards numbered from 2 to 9 are 8 cards, specifically 2, 3, 4, 5, 6, 7, 8, and 9.
But there are four suits: diamonds, hearts, spades, and clubs.
Therefore you multiply 8 by 4 to get 32
The probability of getting dealt one of those cards would be:
32/52, or
8/13
But we have to find the probability of not getting such cards
Thus,
1 - 8/13 = 5/13
Hence, the probability that you are not dealt a card with number from 2 to 9 will be 5/13
To learn more about Probability click on the link
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Rearrange the formula 5w-3y +7=0 to make w the subject.
Hello I need help with this question as fast as possible please , I am on my last few questions and I have been studying all day for my final exam tomorrow. It is past my bed time and I am exhausted . Thank you so much for understanding:))
Solution:
Given the inequality below
[tex]2\left(4+2x\right)\ge \:5x+5[/tex]Solving the inequality to find the value of x
[tex]\begin{gathered} 2\left(4+2x\right)\ge \:5x+5 \\ Expand\text{ the brackets} \\ 8+4x\ge \:5x+5 \\ Collect\text{ like terms} \\ 4x-5x\ge5-8 \\ -x\ge\:-3 \\ x\le \:3 \end{gathered}[/tex]Hence, the answer is
[tex]x\le \:3[/tex]Question 23A company's logo was designed using circles of 3 different sizes. The diameters of two of the circles are shown6 cm12 cmWhich measurement is closest to the area of the largest circle in square centimeters?D2021 Illuminate Education Inc.
SOLUTION
A company's logo was designed using circles of 3 different sizes. The diameters of two of the circles are shown:
6 cm
12 cm
Which measurement is closest to the area of the largest circle in square centimeters?
The measurement is closest to the area of the largest circle in square centimeters is
12 cm since it has a radius of 6 cm with 36 pi square centimetres; unlike the diameter
of 6 cm which has 3 cm radius and 9 pi square centimetres.
The correct answer is 12 cm.
What is the slope of the line with points (3,7) and (3,-2)
Answer:
slope = 0
Given:
(3, 7)
(3, -2)
The formula for the slope is solved by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the given, we know that:
x₁ = 3
x₂ = 3
y₁ = 7
y₂ = -2
Substituting these values to the formula, we will get:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{-2-7}{3-3} \\ m=\frac{-9}{0} \\ m=0 \end{gathered}[/tex]Therefore, the slope would be 0.
Write a formula for the function in the image below.
The vertex form of a quadratic function is:
[tex]f(x)=a(x-h)^2+k[/tex]Where (h, k) is the vertex. Looking at the graph, the vertex is at (-1, 2), then:
[tex]\begin{gathered} h=-1 \\ k=2 \\ \Rightarrow f(x)=a(x+1)^2+2 \end{gathered}[/tex]Finally, to find "a" we use the fact that 1 is the y-intercept of the graph (where the function is evaluated at x = 0). Then:
[tex]\begin{gathered} f(0)=1\Rightarrow a(0+1)^2+2=1 \\ a=1-2 \\ \Rightarrow a=-1 \end{gathered}[/tex]The final form of the function is:
[tex]f(x)=-(x+1)^2+2[/tex]Use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. (If the first expression is not a factor of the second, enter DNE.)x − 2, 3x4 − 6x3 − 8x + 16(x − 2)=
Find out the division
3x^4-6x^3-8x+16 : (x-2)
3x^3-8
-3x^4+6x^3
-----------------------
-8x+16
8x-16
------------
0
The remainder is zero
that means
The expression (x-2) is a factor of the polynomial
so
3x^4-6x^3-8x+16=(x-2)(3x^3-8)
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is divisible by 6". Find P(A). Outcome Probability 1 0.394 - 2. 0.152 3 0.001 4 0.09 5 0.112 6 0.047 7 0.053 8 0.151
Problem-Solving in Probability.
Prob( A ) = Prob( Outcome divisible by 6 ):
only outcome 6 is divisible by 6, and it has a probability of 0.047
Hence,
[tex]\text{Prob(A) =Prob(outcome 6) = 0.047}[/tex]Hence, the correct answer is 0.047
(2-5). (6.0)Find the midpoint
Let:
(x1,y1)=(2,-5)
(x2,y2)=(6,0)
The midpoint is given by:
[tex]\begin{gathered} xm=\frac{x1+x2}{2} \\ xm=\frac{2+6}{2} \\ xm=\frac{8}{2}=4 \\ ym=\frac{-5+0}{2}=-\frac{5}{2}=-2.5 \end{gathered}[/tex]Therefore the midpoint is:
M = (4 , -5/2) or M = (4, -2.5)
(Combining Equation)What is the result of subtracting the second equation from the first ?-2x + y = 0 -7x + 3y = 2
We are given the following two equations
[tex]\begin{gathered} -2x+y=0\quad eq.1 \\ -7x+3y=2\quad eq.2 \end{gathered}[/tex]Let us subtract the second equation from the first equation.
Therefore, the result of subtracting the second equation from the first is
[tex]5x-2y=-2[/tex]Palge counted the number of items in other people's shopping carts while waiting in line at the grocery store. Palge counted the following items in seven carts: 13, 24, 17, 43, 38, 22, and 35. What is the median number of items in the shopping carts? items
ANSWER
24
EXPLANATION
The median of a data set is the middle number of the set - when they are arranged from least to greatest. If the amount of numbers in the data set is even, the median is the average of the two middle numbers.
In this case, there are 7 charts. To find the middle number we have to arrage the set from least to greatest: 13, 17, 22, 24, 35, 38, 43
The middle number is 24. This is the median.
What is the missing coefficient of the x-term of the product (−x−5)^2 after it has been simplified?−25−101025
Given:
The terms is
[tex](-x-5)^2[/tex]Required:
What is the missing coefficient of the x-term of the product after it has been simplified?
Explanation:
We have to find the missing coefficient of the x term of the given product
We know
[tex](a-b)^2=a^2-2ab+b^2[/tex]So,
[tex](-x-5)^2=x^2+10x+25[/tex]Therefore, the missing coefficient of the x-term is 10.
Answer:
Therefore, the missing coefficient of the x-term is 10.
A dwarf seahorse swims 3/4 inch in a minute. How many minutes would take the seahorse to swim 1/3 inch?
A. 1/3 divided by 3/4= 4/9
B. 1/3 times 3/4= 1/4
C. 3/4 divided by 1/3= 9/4
D. 3/4 + 1/3= 13/12
Answer:
A
Step-by-step explanation:
we have 3/4 in / minute.
so, we divide this by 3/4 to get the time for 1 inch.
and then we multiply by 1/3 to get the time for 1/3 inch.
that combination, dividing by 3/4 and multiplying by 1/3, can be done in any sequence (commutative property of multiplication).
therefore, this can be expressed as 1/3 divided by 3/4. and A is the correct answer.
Assume that a particular professional baseball team has 10 pitchers, 6 Infielders, and 9 other players. If 3 players' names are selected at random determine the probability that 2 are pitchers and 1 is an infielderWhat is the probability of selecting 2 pitchers and 1 infielder?Type an integer or a simplified fraction)
The probability of choosing 2 pitcher and one infielder out of the total number of player can be obtained as follows:
We need to slect two pitchers and one infielder out of 10 pitchers and 6 infielders, the number of ways we can do this is:
[tex](_{10}C_2)(_6C_1)=270[/tex]Out of the 25 players if we choose 3 we can do this in the following number of possibilities:
[tex]_{25}C_3=2300[/tex]Then the probability is:
[tex]P=\frac{270}{2300}=\frac{27}{230}[/tex]Therefore, the probability of choosing 2 pitchers and one infielder is 27/230.
A rectangular garden plot measure 3.1 meters by 5.6 meters as shown Find the area of the garden in square meters
Given:
Length(l) of the garden is 3.1 meters
Width(w) of the rectangular garden is 5.6 meters
[tex]\begin{gathered} \text{Area of the garden=}l\times w \\ =3.1\times5.6 \\ =17.36 \end{gathered}[/tex]Area of the garden is 17.36 square meters.
Cory has 20 crayons. He wants to give the same number of crayons to eachof his friends.Part A Write two different questions about Cory's crayons that can be answeredusing division.
He has 20 cranyons.
Part A Write two different questions about Cory's crayons that can be answered using division.
Question 1:
He divided the cranyons among 5 of his friends. How many cranions did each of them get?
Answer: 20/5 = 4
Question 2:
One of his friends got 8 cranyons. The remaining cranyons, he divided among 4 other friends. How many each of those got?
20 - 8 = 12
12/4 = 3
if x=2, then x^2=4, what is the inverse or give a counterexample
Step-by-step explanation:
if x = 2, then x^2 = 4, the inverse would thus be: if x^2 = 4, then x = 2.
This is partially true though since multiple values would satisfy the equation x^2 = 4, or rather 2 values. negative two and positive two. So x=2 is one solution, but just because x^2 = 4, that doesn't necessarily imply that x=2.
A bicycle wheel is 63 centimeters from top to bottom . When the wheel goes all the way around one time , the bicycle travels 198 centimeters . How can this information be used to estimate the value of pi
Given :
A bicycle wheel is 63 centimeters from top to bottom .
So, the diameter of the wheel = 63 cm
When the wheel goes all the way around one time , the bicycle travels 198 centimeters .
So, the circumference of the circle = 198 cm
The circumference of the circle of diameter = d will be :
[tex]\pi\cdot d[/tex]So,
[tex]\begin{gathered} \pi\cdot63=198 \\ \\ \pi=\frac{198}{63}=\frac{22}{7} \end{gathered}[/tex]Graph the inequality. Then write the solution set in interval notation.
Representing intervals as we are doing for your question means we will represent all the possible values of x. To do that we will colour in blue all possible values of x but there is a detail we must to consider. The limits of the interval. for that we have two symbols, [ that means "closed on the value" and ( that means "opened on the value". So if there is a [ on a number it means that number makes part of the interval, but if there is a ( it means that number is not in the interval.
Now, for our inequality we have
Once x can be equal or superior to 2 it means 2 is part of the interval because x can be this value, but x is inferior to 8 but it can not be 8 so 8 is not on the interval. Once we know that, know we can represent our interval as follows:
And that is our final answer.
For an interval notation we can write [2,8).
Convert the function p(x) = 2(x – 4)(x + 3)
Expanding the expression,
[tex]\begin{gathered} p(x)=2(x-4)(x+3) \\ \rightarrow p(x)=2(x^2+3x-4x-12) \\ \rightarrow p(x)=2(x^2-x-12) \\ \rightarrow p(x)=2x^2-2x-24 \end{gathered}[/tex]We get that:
[tex]p(x)=2x^2-2x-24[/tex]80.39 rounded to nearest whole number
Answer:
80
Step-by-step explanation:
It is 80 because .39 is not quite 4.
so in a instance like this you would round .39 to .4 and .4 cant be rounded up to .5 so it would go down because it is to the nearest whole number to instead of it being 81 ( if it could be rounded to 80.5 ), it goes to just 80.
One way to help with rounding is:
" 4 and below let it go
if its 5 and above give it a shove. " rugrat k aka rgr k
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Find the trigonometric ratio using the diagram. Write the fraction in itssimplest form.
Answer
KM = 30 units
Tan M = (8/15)
Explanation
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question,
a = KM = ?
b = KL = 16
hyp = LM = 34
a² + b² = (hyp)²
KM² + 16² = 34²
KM² + 256 = 1,156
KM² = 1,156 - 256
KM² = 900
Take the square root of both sides
√(KM²) = √(900)
KM = 30 units
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
Using M as the given non-right angle,
Hypotenuse = LM = 34
Opposite = KL = 16
Adjacent = KM = 30
Using trignometric identities, we know that TOA means
Tan M = (Opp/Adj)
Tan M = (16/30)
Divide numerator and denominator by 2
Tan M = (16/30) = (8/15)
Hope this Helps!!!
