As a result, the total distance traveled by Mary in her round trip is 3/2 mile + 3/2 mile = 6/2 mile = 3 mile
How to calculate total distance?We can calculate the total distance traveled by a body with position function s (t) if it moves along a coordinate line without changing direction from t = a to t = b. If the body changes direction during the journey, we must integrate the body's speed |v (t)| to find the total distance traveled.
Therefore,
We know Mary spent only a third of the time coming from school as she did going because she traveled three times as fast coming from school as she did going to school (6 miles per hour versus 2 miles per hour). If x represents the time it took her to get to school, then x/3 represents the time it took her to return.
Knowing that the total trip took 1 hour, we have:
x + x/3 = 1
3x/3 + 1x/3 = 1
4x/3 = 1
x = 3/4
So we know it took Mary 3/4 of an hour to get to school (and 1/4 of an hour to get home).
Remembering that distance = rate × time, Mary's commute to school was (2 miles per hour) × (3/4 of an hour) = 3/2 mile. Furthermore, because she returned via the same route, she must have traveled 3/2 of a mile.
As a result, the total distance traveled by Mary in her round trip is 3/2 mile + 3/2 mile = 6/2 mile = 3 mile.
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question allistair throws a biased six-sided dice. the probability of getting a 6 with this dice is 0.4. the other numbers are equally probable. if he throws the dice 3 times, what is the probability that he gets 5, 3, and 2 in this order?
The probability that he gets 5, 3, and 2 in this order is 0.92, 0.52, and 0.32 respectively.
The possibility of rolling a 6 with these dice is 0.4, according to the question. The possibility of rolling a 1 through 5 on the dice is also the probability of not obtaining a 6.
a) Chance of receiving 5:
P(6) + Q(6) = 5
Q(6) = 5 - P(6)
Q(6) = 5 - 0.4
Q(6) = 4.6
The probability of obtaining 5 to 5 is 4.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 4.6
The first five numbers have an equally likely probability.
P(1) = 4.6 ÷ 5
P(1) = 0.92
b) Probability of getting 3:
P(6) + Q(6) = 3
Q(6) = 3 - P(6)
Q(6) = 3 - 0.4
Q(6) = 2.6
The probability of obtaining 3 to 5 is 2.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 2.6
The first five numbers have an equally likely probability.
P(1) = 2.6 ÷ 5
P(1) = 0.52
c) Probability of getting 2:
P(6) + Q(6) = 2
Q(6) = 2 - P(6)
Q(6) = 2 - 0.4
Q(6) = 1.6
The probability of obtaining 2 to 5 is 1.6 overall.
The probability of receiving one is,
P(1) + P(2) + P(3) + P(4) + P(5) = 1.6
The first five numbers have an equally likely probability.
P(1) = 1.6 ÷ 5
P(1) = 0.32
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3/4 - (-1/2) as a fraction
Answer:1/4
Step-by-step explanation:
Triangle EFG is dilated by a scale factor of 2 centered at (0, 2) to create triangle E′F′G′. Which statement is true about the dilation?
Answer:Triangle EFG is dilated by a scale factor of 2 centered at (0, 2) to create triangle E'F'G'. Which statement is true about the dilation? segment EG ≅ segment E prime G prime. The slope of segment EF is the same as the slope of segment E prime H prime.
Step-by-step explanation:
is the ordered pair (-8 1) a solution to the equation y=1/2x-3
Answer: No.
Step-by-step explanation:
To test this ordered pair, we plug it back into the equation given as (x, y), and then simplify to solve. If we end up with an equal equation, the answer is yes. If not, the answer is no.
y = 1/2x - 3
(1) = 1/2(-8) - 3
1 = -4 - 3
1 ≠ -7
This ordered pair is not a solution.
explain how you got it please
The simplest form of the expression as we have it is; (-4x^4z^2)(2xy^3z^2)
What does it mean to simplify?When we are asked to simplify, what we are asked to do is to write the expression that we have in a form that is simplest. That is, we should put the expression in a form that there would not be any simpler presentation of the expression.
We have;
(-2x^2z)^2(2xy^3z^2)
Then we now have to deal with the exponent outside the bracket;
(-4x^4z^2)(2xy^3z^2)
Thus, we now have the expression in the simplest form that it can take and it can not be further broken down.
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enter 2 Expressions that represent the retail price of the clothes you see for your variable and exclusive clothing boutiques quadruples the price of the items it purchases for resale.
Explanation
Step 1
Let
c represent the original price
if the boutiques quadruples the price of the items it purchases for resale.then
[tex]\begin{gathered} \text{new price=4}\cdot c \\ percentage \\ 4=4\cdot\frac{100}{100} \\ 4=\frac{400}{100} \\ 4=400\text{ per cent} \end{gathered}[/tex]400 percent
Step 2
expressions
[tex]\begin{gathered} \text{new price=4}\cdot c \\ \text{new price= 400 percent of C} \end{gathered}[/tex]4c and 400%c
I hope this helps you
Please help!
4|x+7| < 8
3
so this is a
You also will not know precisely how many sentences will appear in the random paragraph. But some piano roll artists made a name with pieces that could not possibly be played by an precise individual. Most of his research deal with difficult meters and polyrhythms. Many include distinct voices enjoying the identical line at different tempos, usually in odd ratios. On top of this, most of the traces themselves tend to be highly dissonant and exhausting to actually play. Someday we might come nose to nose with pure house, that could presumably be a nothingness waiting to be filled.
Robert finds some nickels and pennies in his change purse. How many
coins does he have if he has 110 nickels and 130 pennies? How many
coins does he have if he has n nickels and p pennies?
Total coins, 110 nickels and 130
pennies:
Total coins, n nickels and p pennies:
Pls answer fast
Answer:
Step-by-step explanation:
If coins 110 plus 130 will give you 240 coins
If actual money 110 times 5 will give you 550 plus 130 will give you 680 or 6 dollars and 80 cents.
N times 5 plus p will be your equation
[x-6] +4 =10 solve for X
Answer:
x=12
Step-by-step explanation:
(x-6)=6
x=12
which of the following best describes XWO A. Angle bisectorB. MedianC. AltitudeD. Perpendicular bisector15W15Z
INFORMATION:
We have the next triangle
And we must select the answer that best describes XW segment
STEP BY STEP EXPLANATION:
We can see that XW segment divides the YZ side into two equal parts, which measure 15 units. And we can also see that the XW segment starts in one of the vertex of the triangles and goes to the opposite side.
Then, we can analyze the definition for the median of a triangle
Finally, if we compare, we can see that the definition of median describes the XW segment.
ANSWER:
B. Median.
Determine the intercepts
Y - 3 = 5(x-2)
Answer: x-intercept(s): (7/5, 0)
Y intercept(s): (0,−7)
Which compound inequality is equivalent to the absolute value inequality lbl >6?
hand
Answer:
b > 6, b < -6
Step-by-step explanation:
Hello!
Using absolute value rules:
|b| > 6; b > 6, b < -6The compound inequality is as follows: b > 6, b < -6
This makes sense because all values turn positive in the asbolute value. So a number that is negative and less than -6 (say -7), would turn positive to be 7, which is greater than 6.
And any number already greater than 6 will always be greater than 6.
The demand for a certain product is given by p+3q=315, and the supply for this
product is given by p-7q = 65, where p is the price and q is the number of
products. Complete parts (a) and (b) below.
a. Find the price at which the quantity demanded equals the quantity supplied.
$
b. Find the equilibrium quantity.
In linear equation, The price at which the quantity demanded equals the quantity supplied is $ 260." option (b) is answer.
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.a. The demand for a product is given by p+3q= 315 or, q = (315 - p)/3 and the supply for this product is given by p-7q = 65 or, q = (p- 65)/7
The price at which the quantity demanded equals the quantity supplied is given by
315 - p/3 = p - 65/7
7( 315 - p ) = 3( p - 65 )
2405 - 7p = 3p - 195
2405 + 195 = 3p + 7p
2600 = 10p
p = 2600/10 = 260
Thus, the required price is $ 260.
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PLEASE HELP ME ASAP.
An engineer is designing the parking lot shown below for a local grocery store. The parking spaces are marked with lines where XD←→∥TZ←→∥YF←→∥LP←→ and WC←→− is a transversal. m∠CNL=(6x−17.6)°, m∠FBH=(12y−22)°, and m∠THR=(3x+29.2)°
Answer:
Step-by-step explanation:
If the mean weight of 3 outfielders on the baseball team is 192 lb and the mean weight of the 6 other players is 228 lb, what is the mean weight of the 9-person team?
Answer:
Step-by-step explanation:
If the mean weight of 3 outfielders on the baseball team is 194 lb and the mean weight of the 6 other players is 229 lb, what is the mean weight of the 9
ickets to the zoo cost $15 for adults and $10 for children. The school has a budget of $300 for the field
trip. An equation representing the budget for the trip is 15x+10y = 300.
a. With a budget of $300, determine if 21 students and 6 adults can go to the zoo. Explain how you
know.
b. If there are four adults who need tickets, what is the maximum number of students who can go to
the zoo while staying within the school budget? Show or explain your reasoning.
c. Solve the equation15x+10y = 300 for y.
Answers: lol sorry very long answer
part a answer: Yes, because if we substitute the variables, the equation will be 15(6) + 10(21) = 300. Simplifying this will be 90 + 210 = 300. And since 90 + 210 does equal 300, 21 students and 6 adults can go to the zoo
part b answer: 24 students. Using the equation 15x + 10y = 300, we can find out the maximum number of students who can go to the zoo. First we can substitute x for 4 because that's how many adults who need the tickets. The equation will now be 15(4) + 10y = 300. Simplifying this will be 60 + 10y = 300. Now we can subtract 60 on both sides to isolate the y term. The equation will be 10y = 240. Divide each side by 10 to find out what y is and we get y = 24. So if 4 adults go the zoo, up to 24 students can go.
part c answer: y = 30 - 1.5x. To solve 15x + 10y =300, we first need to move 15x to one side of the equation. To do this we will subtract it on both sides. The equation is now 10y = 300 -15x. Then you will divide 10 on both sides to find out what y is. y = 30 - 1.5x.
The perimeter of a rectangular garden is 72 meters. The length is 6 meters longer than
twice the width. Find the dimensions of the garden.
P = 2L + 2W
P = 72
L = 12W (that's an odd way to put it -- 6x 2x)
P = 2(12W) + 2W
P = 24W + 2W
72 = 26W
W = 2.769
I just want the answer :)
The diagonals of a rectangle are congruent, so RT = SU, that is
3x + 8 = 6x - 4 (subtract 4x from both sides)
3x + 8 = 6x - 4
Subtract 8 from both sides 3x + 8 - 8 = 6x - 4 - 8
Simplifying the above equation, we get
3x = 6x-12
Subtract 6x from both sides 3x - 6x = 6x - 12 - 6x
Simplifying the above equation, we get
-3x = -12
Divide both sides by -3
[tex]$\frac{-3 x}{-3}=\frac{-12}{-3}[/tex]
x = 4
Then, R T= 3x + 8 = 3(4) + 8 = 20
The diagonals bisect each other, then
RV = 0.5 × 20 = 10
∠ RVU = ∠ SVT = 54° ( vertical angles)
RV = UV ( diagonals are congruent and bisect each other)
Then Δ RVU is isosceles with base angles congruent, then
∠ VUR =[tex]$\frac{180-48}{2}[/tex] = 66°.
In the rectangle, RV = 3x+8, SV = 6x-4, and ∠ VRS = 54° then the value of x is 4 and ∠ VUR is 66°.
How to estimate the value of x?The diagonals of a rectangle are congruent, so RT = SU, that is
3x + 8 = 6x - 4 (subtract 4x from both sides)
3x + 8 = 6x - 4
Subtract 8 from both sides 3x + 8 - 8 = 6x - 4 - 8
Simplifying the above equation, we get
3x = 6x-12
Subtract 6x from both sides 3x - 6x = 6x - 12 - 6x
Simplifying the above equation, we get
-3x = -12
Divide both sides by -3
[tex]$\frac{-3 x}{-3}=\frac{-12}{-3}[/tex]
x = 4
Then, R T= 3x + 8 = 3(4) + 8 = 20
The diagonals bisect each other, then
RV = 0.5 × 20 = 10
∠ RVU = ∠ SVT = 54° ( vertical angles)
RV = UV ( diagonals are congruent and bisect each other)
Then Δ RVU is isosceles with base angles congruent, then
∠ VUR =[tex]$\frac{180-48}{2}[/tex] = 66°.
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You begin with $25 in a saving account and $50 in a checking account. Each week you deposit $5 into saving and $10 into checking. After how many weeks is the amount in checking twice the amount in saving?
Answer:
1 week
Step-by-step explanation:
After 1 week
Saving account: $25 + $5 = $30
Checking amount: $50 + $10 = $60
30 x 2 = 60
So it's 1 week
Perimeter and area polynomials
The combined perimeter of
2b (14y - 12)
2c (18y + 4)
2d (14y - 16), is
[tex]P=14y-12+18y+4+14y-16[/tex]Add the like terms
[tex]\begin{gathered} P=(14y+18y+14y)+(-12+4-16) \\ \\ P=46y+(-24) \\ \\ P=46y-24 \end{gathered}[/tex]The combined perimeter is (46y - 24)
The combined area of
1b (10y^2 - 27y +5)
1c (20y^2 + 11y - 3)
1d (12y^2 -24y), is
[tex]A=10y^2-27y+5+20y^2+11y-3+12y^2-24y[/tex]Add the like terms
[tex]\begin{gathered} A=(10y^2+20y^2+12y^2)+(-27y+11y-24y)+(5-3) \\ \\ A=42y^2+(-40y)+2 \\ \\ A=42y^2-40y+2 \end{gathered}[/tex]The combined area is (42y^2 - 40y + 2)
Write an integer that lies between-7.73 & -6.41, what is the answer?
Which sequence shows the numbers in order from least to greatest?
A. |-8.23| < 8 1/5 < 8.3
B. 8 1/5 > 8.3 > |-8.23|
C. 8 1/5 < |-8.23| < 8.3
D. 8.3 < |-8.23| < 8 1/5
The sequence that shows the numbers in order from least to greatest is A. |-8.23| < 8 1/5 < 8.3
How to illustrate the information?It's important to note that arranging numbers from the least to the greatest simply means ascending order.
In this case, it's vital to note that the negative value is the smallest. Then 8 1/5 is 8.2. This conea after. The greatest number is 8.3 since it's the biggest.
In conclusion, the correct option is A.
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The quotient of 2 and a number.
Answer:
it should be the variable divided by 1. For example, x/2.
A hen was given $10, a spider was given $40, a bee was given $30. How much would be given to a dog?
Answer:
Umm 20 dollars?
Step-by-step explanation:
please dont use any big words & give an essay explanation
We want to create a real-life reasonable problem in which we can apply the laws of exponents.
Using a compound interest example;
Word Problem:
Calculate the final value of a $2,000 investment in an account with a 5% interest compounded Quarterly for 5 years.
Solving the word problem;
We have the following parameters;
[tex]\begin{gathered} \text{ Principal P = \$2,000} \\ \text{Rate r = 5\%} \\ \text{Time t = 5 years} \\ \text{ Number of times compounded n = 4} \end{gathered}[/tex]Recall that the formula for compound interest is;
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]Substituting the given values;
[tex]\begin{gathered} F=2000(1+\frac{0.05}{4})^{4(5)} \\ F=2000(1+0.0125)^{20} \\ F=2000(1.0125)^{20} \\ F=2000\times(1.0125)^{20} \\ F=\text{ \$2,564.07} \end{gathered}[/tex]Therefore, the solution to the problem is;
The final
Xavier has a bag of 20 marbles. 8 are blue, 7 are red, and 5 are green. Xavier pulls out a marble, records what color it is, and puts it back. He then selects another marble and records its color What is the probability of pulling out a blue marble and then a green marble?
Answer:
0.1
Step-by-step explanation:
chance of pulling out a blue marble can be described as 8 equally probable outcomes (blue marbles) out of 20 equally probable outcomes (all marbles).
Similarly, the chance of pulling out a green marble is 5 out of 20.
In total, we have 8*5 (combinations of blue then green) outcomes out of 20*20 (any two marbles):
8*5 / (20*20) = 40 / 400 = 1/10 = 0.1
Karen made costumes for the annual school play. She used a total length of928.8 in of blue fabric. The fabric came in 2 rolls that each had the samelength. How much fabric was in each roll? Write your answer in yards.Use the table of conversion facts as necessary, and do not round your answer.=Conversion facts for length12 inches (in) = 1 foot (ft)3 feet (ft) = 1 yard (yd)36 inches (in) = 1 yard (yd)5280 feet (ft) = 1 mile (mi)1760 yards (yd) = 1 mile (mi)ydX 5 ?
what is the type of angle are <1 and <14??????????
1° and 14° are acute angles.
An acute angle is one that is less than 90°, or one that is between 0° and 90°.
The opposite of an acute angle is an obtuse angle. In other terms, an obtuse angle is one that is larger than 90° and less than 180°. It is the angle that is between 90° and 180°.
90° is the standard for a right angle. Any angle that is less than 90° is called acute, and any angle that is larger than 90° is called obtuse.
∠1 and ∠14 are less than 90° therefore, they are acute angles.
Correct question :
What type of angle are 1° and 14°?
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t - 2 < 21 solve the inequality for t simplify your answer as much as possible
Answer:
t < 23
Step-by-step explanation:
t - 2 < 21
Step 1 : Add 2 on both sides.
t - 2 + 2 < 21 + 2
t < 23