Answer:
10.35 miles/hour
Step-by-step explanation:
Hence, Sam ran at the rate of 10.35 miles/hour .
4x - 8y = -4
-2x + 8y = -2
Solve by elimination
Answer:
X=1 Y=0
Step-by-step explanation:
Multiply the second equation (-2x + 8y = -2) by 2 in order to get -4x+16y=-4.
Using this equation, you can eliminate the x
4x - 8y = -4
-4x+16y=-4.
=
8y=0
y = 0
Now, knowing that y=0, plug y into the second equation:
-2x+8(0)=-2
simplify
-2x=-2
lastly, divide both sides by -2
x=1
What % of 780 shirts is 46
Answer:
i think the answer will be 6%
Answer:
below
Step-by-step explanation:
46 / 780 * 100% = 5.9 %
Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)
Vertex: (2, 3); point: (0, 2)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=2\\ k=3 \end{cases}\implies y=a(x-2)^2 +3\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ 2=a(0-2)^2 + 3\implies -1=a(-2)^2\implies -1=4a\implies \cfrac{-1}{4}=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-\cfrac{1}{4}(x-2)^2 + 3 \end{array}} ~\hfill[/tex]
please help me plsssssssss
An initial balance of $4,000 grows at a rate of 12.3% compounded quarterly. What is the balance after 5 years?
Answer:
7330.36
Step-by-step explanation:
A = P (1+i)^n
n = 4×5 = 20
i = 0.03075
12.3% / 4 = 3.075 × 1/100
= 0.03075
A = 4000 ( 1+ 0.03075 ) ^20
= 7330.36
Find the equation of the line with slope 5 that passes through (2, 8). Write the
equation in slope-intercept form.
Answer:
y = 5x - 2
Step-by-step explanation:
y-8 = 5(x-2)
y-8 = 5x - 10
y = 5x - 10 + 8
y = 5x -2
Yosef drove 11,190 miles last year. His truck's fuel efficiency averages 19 mpg, and the average cost of gas last year was $2.15 per gallon. Determine Yosef's average weekly fuel cost.
$32.12
$24.35
$28.55
$30.05
Yosef's average weekly fuel cost is $24.35.
How to find the the average weekly fuel cost?Yosef drove 11,190 miles last year. His truck's fuel efficiency averages 19 mpg, and the average cost of gas last year was $2.15 per gallon.
Yosef average weekly fuel cost can be computed as follows:
Yosef used 11190 / 19 = 588.95 gallons to drive 11190 miles.
Therefore, the average cost of gas last year was 2.15 dollars per gallon.
Therefore, Yosef's average weekly fuel cost would be as follows:
Yosef's average weekly fuel cost = 2.15 x 588.95 ÷ 52 = $1266.23684211 ÷ 52
Yosef's average weekly fuel cost = 24.350708502
Yosef's average weekly fuel cost = $24.35
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Create a slope intercept equation with given information (3,1) m =0
Answer:
y = x - 2
Step-by-step explanation:
Since m = 0, what we have so far is y=x+b
We have a point, which is (3,1)
Substitute the x and y with the x and y values in the coordinate point to solve for b (y-intercept).
1=3+b
1-3=3+b-3 undo the 3 by subtracting
-2 = b
y = x + -2 simplify
y = x - 2
Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.L1: x = 5-12t, y = 3+9t, z = 1-3tL2: x = 3+8s, y = -6s, z = 7+2s
The given lines L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t and L2 ⇒ x = 3+8s, y = -6s, z = 7+2s are parallel lines .
In the question ,
it is given that ,
the two lines are :
L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t
L2 ⇒ x = 3+8s, y = -6s, z = 7+2s
If the lines are intersecting then :
5 - 12t = 3 + 8s
8s + 12t = 2
4s + 6t = 1 ; .....equation(1)
and 3 + 9t = -6s
3t + 2s + 1 = 0
multiplying both sides by 2 ,
we get ,
6t + 4s + 2 = 0 ....equation(2)
Solving equation(1) and equation(2) , we get
3 ≠ 0 .
So , the lines are not intersecting .
For lines to be parallel , the cross product of their directions must be 0 .
So , [tex]\left|\begin{array}{ccc}i&j&k\\-12&9&-3\\8&-6&2\end{array}\right|[/tex]
On simplifying further ,
we get ,
⇒ 0i - 0j + 0k
= 0
So , the cross product is 0 , lines will be parallel .
Therefore , the lines L1 and L2 are parallel .
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The height / (in feet) of a badminton birdie t seconds after it is hit can be modeled by the function h = -16^2t+32t+ 4.
a. Find the maximum height of the birdie.
The maximum height of the birdie is ___ feet.
b. How long does it take for the birdie to hit the ground?
About ___seconds
The ball may rise up to a height of 20 feet. and it will strike the ground in 1 second.
Describe height.Height is the vertical measurement from an object's top to its base. On sometimes, it has the designation "altitude."
The vertex at point (h,k) of a parabola, y = ax2 + bx + c, is first determined using the equation h = -b / 2a, and then that point is entered into the equation to determine k.
Let's now solve for h in this issue. We know that a = -16, b = 32, and c = 4 in the equation y = -16t2 + 32t + 4.
h = -b/2a
h = -(32) / 2(-16) (-16)
1 second is equal to h = -32/-32.
This means the the ball will reach it's maximum height after 1 seconds. But the problem is asking is for what that height is. So for our final step, let's plug in t=1 to our equation:
y = -16t^2 + 32t + 4
y = -16*(1)^2 + 32*(1)+ 4
y = -16 + 36
y = 20 feet
which means that the final answer is that the maximum height of the ball is 20 feet. and it will take 1sec to hit the ground.
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W 5. Suppose that 40% of the cars in a certain town are white A person stands at an intersection waiting white car. Let X= the number of cars that must drive by until a white one drives by. What is the exp value of X?
The no. of cars that must drive by until a white one drives by is 40.
What is a binomial distribution in probability?In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment). The binomial probability is
[tex]^nC_xp^Xq^{n-x}[/tex].
We know the expected value of a binomial distribution E(x) = np.
Given, Suppose that 40% of the cars in a certain town are white.
Therefore 50% of cars in the town are not which.
Let, The no. of cards in the town be 'n'.
So, p = 40/n and q = 60/n
Therefore from the formula E(x) = np we get,
E(x) = n×40/n
E(x) = 40.
So, The expected value of X is 40.
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Answer: We expect 2.5 cars to
The expected value of X is 2.5.
Step-by-step explanation:
In this case, it is a geometric distribution because we do not have a fixed number of trials.
We use the formula of a geometric distribution to find the mean (the expected value) such that mu_x = 1/p.
In this case:
mu_x=1/0.4 = 2.5
In this case, we do not round up or down even if we cannot have half a car because we want the expected value (mean).
Let F be any nonconstant vector field of the form F = f (x) i + g (y) j + h (z) k and let G be any nonconservative vector field of the form G = f (y, z) i + g (x, z)j + h (x, y) k. Indicate whether the following statements are true or false by placing ''T'' or ''F'' to the left of the statement. 1. G is incompressible 2. F is irrotational 3. G is irrotational 4. F is incompressible
1. G is incompressible- True
2. F is irrotational- True
3. G is irrotational- False
4. F is incompressible- False
Divergence and Curl In Mathematics, divergence is a differential operator, which is applied to the 3D vector-valued function. Similarly, the curl is a vector operator which defines the infinitesimal circulation of a vector field in the 3D Euclidean space .
So if we calculate for F:
F has a divergence potentially
divF = df/dx + dg/fy + dh/dz
But curl(F )= 0(all cross derivatives df/dy df/dz, dg/dx etc = 0)
For G
G has zero divergence.
divG = df/dx + dg/fy + dh/dz = 0 + 0 + 0 = 0
But it may have a curl.
curl(G) = df/dy may be non-zero
df/dz, dg/dx etc may all be non-zero
Now, we also know that if the divergence is zero, the vector field is incompressible and if the curl is zero, the vector field is irrotational, that is,
div = 0 = incompressible and
curl = 0= irrotational
Thus,
1. G is incompressible- True
2. F is irrotational- True
3. G is irrotational- False
4. F is incompressible- False
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Write the statement "the sum of a number and 10.7 is at most −3.2" as an inequality.
100 PTS HURRY
−3.2 + b > 10.7
−3.2 + b < 10.7
b + 10.7 ≥ −3.2
b + 10.7 ≤ −3.2
The given statement can be written in terms of inequality as b + 10.7 ≤ 3.2. The correct option is (d).
What is linear inequality?Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.
Unlike a linear equation it can have a range of values inside an interval.
The given statement can be written in terms of inequality as follows,
The statement is, "the sum of a number and 10.7 is at most −3.2".
Suppose the number be b.
The following expression can be written,
b + 10.7 ≤ 3.2
Hence, the required inequality expression for the given problem is b + 10.7 ≤ 3.2.
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7. Solve the proportion.
2/3=a/15
8. Solve the proportion.
4/7=44/m
Answer:
a=10
m=28
Step-by-step explanation:
2/3= 0.666666666666666
a/15=??????
try all numbers divided by 15 untill you found 0.666666666666666 which is =10/15
4/7=0.571428571428571
44/m=???????
do the same as the first one
it will be 44/28=0.571428571428571
I lowkey need help like immediately
The answers to all the parts are given below.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have a function h = -16t² + 1800, that gives the height of the person at time [t] seconds.
[A] -
For [x] = 1000ft, we can write -
1000 = -16t² + 1800
16t² = 800
t² = (800/16)
t² = 50
t = 7.07 seconds
[B] -
For [x] = 950ft, we can write -
950 = -16t² + 1800
16t² = 850
t² = 53.125
t² = √(53.125)
t = 7.29 seconds
[C] -
The domain of the function will be -
0 ≤ x ≤ 10
[D] -
The range of the function will be -
0 ≤ h ≤ 1800
Therefore, the answers to all the parts are given above.
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Solve for x: −8 < x − 1 < 5
−7 < x < 6
7 < x < 6
−7 > x > 6
7 > x > 6
Answer:
- 7 < x < 6
Step-by-step explanation:
- 8 < x - 1 < 5 ( add 1 to each interval )
- 7 < x < 6
A water tank initially contained 57 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many minutes have passed m when the tank contains 35 liters? Round go the nearest tenth
Answer:
8.8 minutes
Step-by-step explanation:
first we figure out how many liters are being lost
57 - 35 = 22
then divide that by 2.5
22 / 2.5 = 8.8
8.8 minutes
Which of the following is true?
Triangle B C D. The exterior angle at B is labeled 1 and the interior angle is labeled 2. Angle C has measure 70 degrees. The exterior angle at D has measure 130 degrees.
A. m∠BCD − m∠DBC = 10°
B. m∠BCD − m∠DBC = 20°
C. m∠BCD − m∠DBC = 60°
D. m∠BCD − m∠DBC = 80°
Answer:
answer :J LOOK THE DIAGRAM CAREFULLY AND UNDERSTAND
Answer:
A <c - <b = 10
Step-by-step explanation:
What is the equation of the line of best fit for the following data? Round the slope and y-intercept of the line to three decimal places. x y 2 2 5 9 7 20 12 19 16 30
y = -1.893x + 31.901
Detailed explanation:
We are given the following values in a table:
x y
2 30
5 19
7 20
12 9
16 2
It is now abundantly evident from the set of values that when x increases, the y-value decreases, indicating a negative connection.
Therefore, the line of best fit will have a negative slope.
Consequently, a scatter plot is used to display the data values.
As can be seen, the line of best fit equation
y = -1.893x + 31.901T
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Maria is making an apple pie. She needs 1/4 cup of sugar for each pie Maria has 2 1/2 cups of sugar how many pies can she make
The number of cups she can make is 2 cups
How to determine the number of cups she can makeFrom the question, we have the following parameters that can be used in our computation:
Cups of sugar needed = 1/4
Cups of sugar available = 1/2
Assume there exist a proportional relationship between the cups
The number of cups she needs can be calculated using the following equation
number of cups = (1/2)/(1/4)
Evaluate the quotient
number of cups = 2
Hence, the cups is 2 cups
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A water tank initially contained 65 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many liters of water are in the tank after 109 seconds? Round answers to the nearest whole liter.
(p-124) / 9 min many liters of water are in the tank after 109 seconds.
for 4 min = 65 + (6.5x4) = 91 lit
for 109 sec = 65 + (9x 109/60) = 81.35 lit
for m min = 65 + (9m) lit
how long time
for 151 lit = (151 - 124)/9 = 3 min
for 191.5 lit = (191.5-124) /9 = 67.5/9 = 7.5 min means 7 min 30 sec
for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 means 16 min 15 sec
for p lit = (p-124) / 9 min
What is liters ?
The water must be measured and expressed in the same unit for all of the containers. The litre is the name of that common unit for measuring liquid. Liquids are measured in litres, millilitres, centilitres, kiloliters, etc., including water, milk, gasoline, and oil.
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It takes a bus 1 hour and 30 minutes to travel 42 miles.
Calculate the average speed of the bus in mph.
If your answer is a decimal, give it to 1 d.p.
28 mph is the average speed of the bus in mph.
What is speed?
The speed of a change in an object's location in any direction. The distance traveled relative to the time it took to travel that distance is how fast something is moving.
Meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) are the most popular speed units (mph). The distance an object covers in a given amount of time is its speed. Speed = distance x time is the speed formula. The meter per second, also known as the m/s or ms-1, is the SI unit of velocity.
time = (1+ 1/2)hr = 3/2 hr = 1.5 hr
distance = 42 miles
average speed = total distance/total time
42/1.5 = 28 mph
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determine the equation of the line of the line of best fit from the data in the table on the right. x 4 5 6 7 10 y = 14 14 17 19 26
The equation for the line of best fit from the given data, will be y = 2.12 x + 4.42.
How to find the line of best fit ?The line of best fit would be the line that has an equal number of points above it, as the number of points beneath it.
Going by this definition, two points that would be on the line are (6, 17) and ( 7, 19 ).
The slope of this line would be:
= ( Y2 - Y1 ) / ( X 2 - X1)
= ( 19 - 17 ) / (7 - 6 )
= 2.12
The y intercept would be:
y = mx + c
19 = 2.12 (7 ) + c
c = 4.42
The equation of the line of best fit is then :
y = 2.12 x + 4.42
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Elvia has a bag of snack mix that contains 5 cereal pieces, 4 peanuts, 5 pretzels, and 1 bagel chip. Suppose that she is equally likely to pick any individual object from the bag. What is the probability that Elvia will randomly pull a pretzel from the bag?
Answer: 33%
Step-by-step explanation: a third of the items in the bag are pretzels.
What is the total surface area of the rectangular prism?
Answer:
256 feet.
Step-by-step explanation:
The equation for the surface area of a rectangular prism is lw x lh x hw. That means it would be 12x4, 12x5, and 4x5. In total that is 256.
What expression is an equivalent expression of 12x+10+4y
The expression that is an equivalent expression of 12x+10+4y is D 2(6x + 5 + 2y).
How to illustrate the expression?In Mathematics, expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case, the expression that is an equivalent expression of 12x+10+4y is 2(6x + 5 + 2y). The correct option is D.
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Which expression is an equivalent expression of 12x + 10 + 4y?
A.) 2(6x + 2y + 6)
B.) 3(4x + y + 10)
C.) 2(6x + 4y + 8)
D.) 2(6x + 5 + 2y)
One of the legs of a right triangle measures 2 cm and the other leg measures 7 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
Hypotenuse = 7.3 cm
Step-by-step explanation:
We can find the hypotenuse using the Pythagorean Theorem, which is:
[tex]a^2+b^2=c^2[/tex], where a and b are the legs of the right triangle and c is the hypotenuse.
By plugging in 2 and 7 for a and b, we have:
[tex]2^2+7^2=c^2\\4+49=c^2\\53=c^2\\7.2801=7.3=c[/tex]
The top-selling Red and Voss tire is rated 60000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 70000 miles and a standard deviation of 7000 miles.
A) The probability that the tyre wears out before 60000 miles is 0.4221
B) The probability that the tyre lasts more than 83000 miles is 0.49534
The distance the tyres can run until wear-out is a normally distributed, the formula for normal distribution is expressed as
z = (x - u)/s
Where
x = the distance the tyres can run until wear-out
u = mean distance
s = standard deviation
From the information given,
u = 70000 miles
s = 7000 miles
A) We want to find the Probability that the tyre wears out before 60000 miles. It is expressed as
P(x lesser than 60000)
For x = 60000,
z = (60000 - 70000)/7000 = - 1.42
Looking at the normal distribution table, the corresponding z score is 0.4221
B)We want to find the probability that the tyre lasts more than 83000 miles. It is expressed as
P(x greater than 83000) = 1 - P(x lesser than or equal to 83000)
For x = 83000,
z = (83000 - 70000)/5000 = 2.6
Looking at the normal distribution table, the corresponding z score is 0.49534
P(x greater than 83000)
= 1 - 0.49534 = 0.50466
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Two Truths & One Lie: Which of the 3 statements below is a lie? Explain how you made your decision.
x=2 y=5 z=7
Answer:
The 3rd statement is a lie and other two are truth.
Step-by-step explanation:
when two same numbers with power are divided their respective powers are subtracted.
1.
[tex] {b}^{a } \div {b}^{c} = {b}^{a - c} [/tex]
Using this formula for
[tex] {b}^{9} \div {b}^{y} = {b}^{4} [/tex]
[tex] {b}^{9 - 5} = {b}^{4} [/tex]
Here RHS =LHS
so the equation is true
2.
[tex] {b}^{z} \div {b}^{x} = {b}^{5} [/tex]
[tex] {b}^{7 - 2} = {b}^{2} [/tex]
Here RHS=LHS,
so the equation is true
3.[tex] {b}^{8} \div {b}^{x} = {b}^{8} [/tex]
[tex] {b}^{8 - 2} = {b}^{8}[/tex]
Here RHS is not equal to LHS
so the equation is false
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Write the equation x^2 - 10x + 17 = 0 in the form (x+p)^2 = q (50 points!)
Answer: (x-5)²=8
Step-by-step explanation:
x²-10x+17=0
x²-2(x)(5)+5²-5²+17=0
(x²-2(x)(5)+5²)-25+17=0
(x-5)²-8=0
(x-5)²-8+8=0+8
(x-5)²=8
Answer:
(x - 5)² = 8
--------------------------
Given
Expression x² - 10x +17.
Convert this to vertex form by completing the square.
Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:
x² - 10x + 17 =
x² - 2*5*x + 5² - 5² + 17 =
(x - 5)² - 25 + 17 = (x - 5)² - 8
(x - 5)² = 8