The flow of water can fill a 4-gallon container in 28 seconds.
Given:
Number of gallons = 4
Time = 28 seconds
Hence, the ratio of gallons to seconds will be 4 : 28
[tex]\begin{gathered} As\text{ a rate in gallons per second = }\frac{\text{number of gallons}}{time\text{ taken}} \\ As\text{ a rate in gallons per second = }\frac{4}{28}=\frac{1}{7} \\ As\text{ a reduced fraction, the rate in gallons per second is }\frac{1}{7}\text{gallons per second} \end{gathered}[/tex]Therefore, the faucet fills the container at the rate of 1/7 gallon per second
how many seconds does it take until the ball hits the ground ?
Given:
The quadratic model of the ball is given as:
[tex]h(t)=-16t^2+104t+56[/tex]Required:
Find the time when it takes to hit the ground.
Explanation:
When the ball hits the ground then h(t)=0.
[tex]\begin{gathered} -16t^2+104t+56=0 \\ -8(2t^2-13t-7)=0 \\ 2t^2-13t-7=0 \end{gathered}[/tex]Solve the quadratic equation by using the middle term splitting method.
[tex]\begin{gathered} 2t^2-14t+t-7=0 \\ 2t(t-7)+1(t-7)=0 \\ (t-7)(2t+1)=0 \\ t=7,-\frac{1}{2} \end{gathered}[/tex]Since time can not be negative.
So t = 7 sec
Final Answer:
The ball will take 7 sec to hits the ground.
Two ships left a port at the same time. Onetravelled due north and the other due eastat average speeds of 25.5 km/h and 20.8 km/h,respectively. Find their distance apart
Given:
Two ships left a port at the same time.
One travelled due north at an average speed of 25.5 km/h
And the other ship was due east at average speeds of 20.8 km/h
We will find their distance apart using the Pythagorean theorem.
The distance = Speed * Time
Let the time = t
So, the distance of the first ship = 25.5t
And the distance of the second ship = 20.8t
So, the distance between the ships (d) will be as follows:
[tex]\begin{gathered} d^2=(25.5t)^2+(20.8t)^2 \\ d^2=1082.89t^2 \\ \\ d=\sqrt{1082.89t^2} \\ d=32.907t \end{gathered}[/tex]So, the answer will be:
The distance in terms of time = 32.907t
We will find the distance when t = hours
So, distance = 164.54 km
what is the answer to 850x+40(x)
ANSWER
854x
EXPLANATION
We have that:
850x + 40(x)
First, expand the bracket:
850x + 40x
Because the two terms are of the same kind (terms of x) we can add them up:
850x + 4x = 854x
That is the answer.
How do I find the linear equation for this? (y=mx+b)
Okay, here we have this:
Considering the provided table, we are going to find the corresponding linear equation, so we obtain the following:
To do this we will start using the information in the slope formula, then we have:
m=(y2-y1)/(x2-x1)
m=(190-(-30))/(19-9)
m=220/10
m=22
Now, let's find the y-intercept (b) using the point (9, -30):
y=mx+b
-30=(22)9+b
-30=198+b
b=-30-198
b=-228
Finally we obtain that the linear equation is y=22x-228
Answer:
Step-by-step explanation:
These are the two methods to finding the equation of a line when given a point and the slope: Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Use the m given in the problem, and the b that was just solved for, to create the equation y = mx + b.
1. Which expression is equivalent to 2 x (5 x 4)?a. 2+ (5 x 4)b. (2 x 5) x 4c. (2 x 5) x 4d. (5 x 4) x (2 X4)
We are given the following expression
[tex]2\times(5\times4)[/tex]Recall the associative property of multiplication
[tex]a\times(b\times c)=(a\times b)\times c[/tex]The associative property of multiplication says that when you multiply numbers, you can group the numbers in any order and still you will get the same result.
So, if we apply this property to the given expression then it becomes
[tex]2\times(5\times4)=(2\times5)\times4[/tex]Therefore, the following expression is equivalent to the given expression.
[tex](2\times5)\times4[/tex]16. Solve for "x".
a. 6
b. 100
c. 36
Answer:
A. 6
Step-by-step explanation:
Using the Pythagorean theorem which states that: Hypotenus² = Opposite² + Adjacent²
Where: hypotenus = 10, opposite = x, adjacent = 8
So:
[tex] {10}^{2} = {x}^{2} + {8}^{2} [/tex]
Solving for x
[tex]100 = {x}^{2} + 64[/tex]
Collect like terms to make x the subject of formula
[tex]100 - 64 = {x}^{2} →36 = {x}^{2} [/tex]
[tex]36 = {x}^{2} ⟹ {x}^{2} = 36[/tex]
square root both sides of the equation to find the value of x
[tex] \sqrt{ {x}^{2} } = \sqrt{36} →x = 6[/tex]
Therefore: Option A is correct
the table below shows the height of trees in a park. how many trees are more than 8m tall but not more than 16m tall?
Write the number 0.2 in the form a over b using integers to show that it is a rational number
Hello! Let's solve this exercise:
We have some ways to show it, look:
[tex]\begin{gathered} \frac{a}{b}=0.2 \\ \\ \frac{1}{5}=0.2 \\ \\ \frac{2}{10}=0.2 \end{gathered}[/tex]So, as it can be written as a fraction, is a rational number.
From the given information. Write the recursive and explicit functions for each geometric sequence. Please use these terms. recursive f(1) = first term, f(n) = pattern*f(n-1). what is the 1st term and pattern? explicit is y = pattern^x * 0 term. work backwards to find 0 term
We know that a geometric sequence is given by:
[tex]f(n)=f(1)r^{n-1}[/tex]where r is the common ratio of the sequence.
For this sequence we have that the common ratio is r=2, this comes from the fact that in the first day we have 6 dots, for the second day we have twelve and for the third day we have 24. We also notice that the first term is:
[tex]f(1)=8[/tex]Therefore the sequence is given by:
[tex]f(n)=8(2)^{n-1}[/tex]Now, to find the zeoth term we plug n=0 in the sequence above, therefore the zeroth term is:
[tex]\begin{gathered} f(0)=8(2)^{0-1} \\ f(0)=8(2)^{-1} \\ f(0)=4 \end{gathered}[/tex]Manny opened a savings account 7 years ago the account earns 9%interest compounded monthly if the current balance is 400.00 how much did he deposit initially
We have the following:
The formula for compound interest is as follows
[tex]\begin{gathered} A=P(1+r)^t \\ \end{gathered}[/tex]A is amount (current balance 400), P is the principal ( deposit initially), r is the rate (0.07) and is the time ( 7 years)
replacing:
[tex]\begin{gathered} 400=P(1+0.07)^{7^{}} \\ P=\frac{400}{(1.07)^7} \\ P=249.09 \end{gathered}[/tex]Which means that the initial deposit was $ 249.09
The graph shows the function f(x) = |x – h| + k. What is the value of h?
h = –3.5
h = –1.5
h = 1.5
h = 3.5
While munching on some skittles, Bobby the Vampire lost a tooth that just so happened to be one of his fangs. He measured it to be 27 centimeters long. How long was his tooth in inches?
Answer: 10.6299
Step-by-step explanation:
There are 0.3937 inches in a cm., So, the length of the tooth in inches is [tex]27(0.3937)=10.6299 \text{ in }[/tex]
Use inductive reasoning to find a pattern then make a reasonable conjecture for the next three items in the pattern p g q h r I
Consider the first, third, and fifth terms of the sequence: p,q,r; these are consecutive letters starting with p.
Similarly, as for the second, fourth, and sixth terms: g,h, i; these are consecutive letters starting with g.
Thus, the seventh term has to be the letter that follows r; this is, s.
Analogously, the eighth and ninth terms are
[tex]\begin{gathered} \text{ eighth}\to\text{letter that follows i}\to j \\ \text{ ninth}\to\text{ letter that follows s}\to t \end{gathered}[/tex]Thus, the missing terms are: s, j, and t.
Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the Equation.
Answer: y=80+2x
Step-by-step explanation:
In y=mx+b format the answer is y=80+2x
I think I’m off to a good start but I’m still confused
The radius is given 3.5 ft and height is given 14 ft.
ExplanationTo find the surface area of cylinder,
Use the formula.
[tex]S=2\pi rh+2\pi r^2[/tex]Substitute the values.
[tex]\begin{gathered} S=2\pi r(h+r) \\ S=2\times3.14\times3.5(14+3.5) \\ S=384.65ft^2 \end{gathered}[/tex]The volume of cylinder is determined as
[tex]V=\pi r^2h[/tex]Substitute the values
[tex]\begin{gathered} V=3.14\times3.5^2\times14 \\ V=538.51ft^3 \end{gathered}[/tex]AnswerThe surface area of cylinder is 384.65 sq.ft.
The volume of cylinder is 538.51 cubic feet.
What is the slope between (2,-1 ) and ( 5,4 )
the slope will be 5/3 because:
[tex]\frac{4-(-1)}{5-2}=\frac{5}{3}[/tex]7. Julie has $250 to plan a party. There is a one-time fee of $175 to reserve a room. It also cost $1.25 perperson for food and drinks. What is the maximum number of people that can come to the dance?
Julie has $250 to plan the party.
The room costs $175 to reserve plus $1.25 per person for food and drinks.
Let "x" represent the number of people she can invite, you can express the total cost for the party as follows:
[tex]175+1.25x\leq250[/tex]From this expression, we can determine the number of people she can invite, without exceeding the $250 budget.
The first step is to pass 175 to the right side of the expression by applying the opposite operation "-175" to both sides of it:
[tex]\begin{gathered} 175-175+1.25x\leq250-175 \\ 1.25x\leq75 \end{gathered}[/tex]Next, divide both sides of the equation by 1.25 to reach the value of x:
[tex]\begin{gathered} \frac{1.25x}{1.25}\leq\frac{75}{1.25} \\ x\leq60 \end{gathered}[/tex]She can invite up to 60 people to the party
Could I please get help with finding the correct statements and reasonings. I think I messed up line number four because it keeps saying the line is incorrect and that I can not validate it l but
Answer:
Step-by-step explanation:
[tex]undefined[/tex]In the circle below, if the measure of arc ACB = 260 °, find the measure of < B.
Given:
There is a figure given in the question as below
Required:
If
[tex]arcACB=260\degree[/tex]than find the value of angle B
Explanation:
Value of arcADB is
[tex]arcADB=360\degree-arcACB=360\degree-260\degree=100\degree[/tex]Now to find the angle B
[tex]\angle B=\frac{1}{2}arcADB=\frac{1}{2}*100=50\degree[/tex]Final answer:
a
What is the area of the composite figure?o 52.5 cm^2o 60 cm^2o 40 cm^265 cm^2
we have that
The area of the composite figure is equal to the area of a rectangle plus the area of a right triangle
so
step 1
Find out the area of the rectangle
A=L*W
A=8*5
A=40 cm2
step 2
Find out the area of the right triangle
A=(1/2)(b)(h)
where
b=8-(2+1)=8-3=5 cm
h=5 cm
A=(1/2)(5)(5)
A=12.5 cm2
therefore
the total area is
A=40+12.5=52.5 cm2
52.5 cm2polynomials - diving polynomialssimplify the following expression with divisionbare minimum of steps
3 4. Diego estimates that there will need to be 3 pizzas for every 7 kids at his party. Select all the statements that express this ratio. (Lesson 2-1) (A.) The ratio of kids to pizzas is 7 : 3. B.) The ratio of pizzas to kids is 3 to 7. The ratio of kids to pizzas is 3: 7. (D. The ratio of pizzas to kids is 7 to 3. E. For every 7 kids, there need to be 3 pizzas.
The statements in (A), (B), (E) are correct and satisfy the conditions in question.
What is ratio and proportion?
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. Because b is not equal to 0, the ratio establishes the link between two quantities such as a:b.
Given, for every 7 kids, pizzas needed = 3 --(iii)
Therefore, for every 1 kid, pizza needed = (3/7)
Thus, for every x kids, pizza needed = (3/7)x
Again, ratio of pizzas to kids is = 3:7 --(i)
Also, the ratio of kids to pizza is = 7:3 --(ii)
From (A), using (ii), the statement in (A) is correct.
From (B), using (ii), the statement in (B) is correct.
From (C), using (i), the statement in (C) is incorrect.
From (D), using (i), the statement in (D) is incorrect.
From (E), using (iii), the statement in (E) is correct.
Thus, the statements in (A), (B), (E) are correct and satisfy the conditions in question.
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sorry you have to zoom in to see better. its a ritten response.
A: height is increasing from 0-2 interval.
B: Height remains the same on 2-4
C: 4-6 the height is decreasing the fastest, because the slope is the steepest on that interval.
D: Baloon would be on the ground at 16 seconds, and will not fall down further. that is the way it is in real-world (constraint).
Use the trapezoidal approximation to estimate he distance the turtle traveled from 0 to 10 seconds.
we have that
The trapezoidal approximation is equal to
[tex]A=\frac{1}{2}\cdot\lbrack f(a)+f(b)\lbrack\cdot(b-a)[/tex]where
a=0
b=10
f(a)=f(0)=0.05
f(b)=f(10)=0.043
substitute given values
[tex]\begin{gathered} A=\frac{1}{2}\cdot\lbrack0.05+0.043\lbrack\cdot(10-0) \\ A=0.465\text{ m} \end{gathered}[/tex]therefore
the answer is 0.465 metersHelp with number one a and b is both parts of number one
Solving the operation_
We are given two figures that represent a garden. We are asked to determine its areas.
The shape of figure A is a rectangle of 9 ft by 12 ft. The area of a rectangle is the product of its dimensions therefore, we have:
[tex]A_A=\left(9ft\right)\left(12ft\right)[/tex]Solving the operations:
[tex]A_A=108ft^2[/tex]The shape of figure B is a circle of radius 5ft. The area of a circle is:
[tex]A_B=\pi r^2[/tex]Where "r" is the radius. Substituting we get:
[tex]A_B=\pi\left(5ft\right)^2[/tex][tex]A_B=25\pi ft^2[/tex]In decimal notation, the area is:
[tex]A_B=78.54ft^2[/tex]In a survey of 200 college students it is found that:61 like cooking32 like reading73 like video games19 like both cooking and reading23 like cooking and video games92 like reading or video games6 like all 3 hobbiesa. How many do not like any of these hobbiesb how many like reading onlyc how many like reading and video gamesd how many do not like cooking or video games
Given:
The number of total students = 200
The number of students like cooking = 61
The number of students who like reading = 32
The number of students who like both cooking and reading= 19
The number of students who like video games = 73
The number of students who like cooking and video games= 23
The number of students who like reading and video games = 92
The number of students who like all 3 hobbies = 6
Required:
(a)
solve the equation x 1.)132.)13/33.) 104.) none of these choices
Answer:
2. 13/3
Step-by-step explanation:
x will be equal to 13/3.
Given,
5^(2x - 1) = 5^(5x - 14)
We can see that base is the same for both the exponents on each side of the equation.
Now, on using the Logarithm on both sides with base 5, we can see that the base on both sides of the equation cancels out with the log (base 5) function.
And new equation becomes:
(2x - 1) = (5x - 14)
This derives us to another conclusion that if the base of an exponent is equal then,
the powers must be equal too.
(2x - 1) = (5x - 14)
=> 5x - 2x = -1 + 14
=> 3x = 13
which gives us,
=> x = 13/3.
Therefore x = 13/3.
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(f o g)(x) = x(g o f)(x) = xwrite both domains in interval notation
the fact that both functions are polynomial of degree 1 we get that the domain and range of both functions are the real numbers. In intervalo notation this is:
[tex]\begin{gathered} \text{domain:}(-\infty,\infty) \\ \text{range:}(-\infty,\infty) \end{gathered}[/tex]12345678912345678900[tex]11447 \times \frac{333}{999} \times {141}^{2} - x \times y = \sqrt[255]{33} [/tex]Jardin De Ronda. updtCHECK EQUATION in QUESTION ! UPDT 2 :) `!!!z
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The average American man consumes 9.6 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible. a. What is the distribution of X? X - NO b. Find the probability that this American man consumes between 9.7 and 10.6 grams of sodium per day. C. The middle 10% of American men consume between what two weights of sodium? Low: High:
The variable of interest is
X: sodium consumption of an American male.
a) This variable is known to be normally distributed and has a mean value of μ=9.6grams with a standard deviation of δ=0.8gr
Any normal distribution has a mean = μ and the variance is δ², symbolically:
X~N(μ ,δ²)
For this distribution, we have established that the mean is μ=9.6grams and the variance is the square of the standard deviation so that: δ² =(0.8gr)²=0.64gr²
Then the distribution for this variable can be symbolized as:
X~N(9.6,0.64)
b. You have to find the probability that one American man chosen at random consumes between 9.7 and 10.6gr of sodium per day, symbolically:
[tex]P(9.7\leq X\leq10.6)[/tex]The probabilities under the normal distribution are accumulated probabilities. To determine the probability inside this interval you have to subtract the accumulated probability until X≤9.7 from the probability accumulated probability until X≤10.6:
[tex]P(X\leq10.6)-P(x\leq9.7)[/tex]Now to determine these probabilities, we have to work under the standard normal distribution. This distribution is derived from the normal distribution. If you consider a random variable X with normal distribution, mean μ and variance δ², and you calculate the difference between the variable and ist means and divide the result by the standard deviation, the variable Z =(X-μ)/δ ~N(0;1) is determined.
The standard normal distribution is tabulated. Any value of any random variable X with normal distribution can be "converted" by subtracting the variable from its mean and dividing it by its standard deviation.
So to calculate each of the asked probabilities, you have to first, "transform" the value of the variable to a value of the standard normal distribution Z, then you use the standard normal tables to reach the corresponding probability.
[tex]P(X\leq10.6)=P(Z\leq\frac{10.6-9.6}{0.8})=P(Z\leq1.25)[/tex][tex]P(X\leq9.7)=P(Z\leq\frac{9.7-9.6}{0.8})P(Z\leq0.125)[/tex]So we have to find the probability between the Z-values 1.25 and 0.125
[tex]P(Z\leq1.25)-P(Z\leq0.125)[/tex]Using the table of the standard normal tables, or Z-tables, you can determine the accumulated probabilities:
[tex]P(Z\leq1.25)=0.894[/tex][tex]P(Z\leq0.125)=0.550[/tex]And calculate their difference as follows:
[tex]0.894-0.550=0.344[/tex]The probability that an American man selected at random consumes between 10.6 and 9.7 grams of sodium per day is 0.344
c. You have to determine the two sodium intake values between which the middle 10% of American men fall. If "a" and "b" represent the values we have to determine, between them you will find 10% of the distribution. The fact that is the middle 10% indicates that the distance between both values to the center of the distribution is equal, so 10% of the distribution will be between both values and the rest 90% will be equally distributed in two tails "outside" the interval [a;b]
Under the standard normal distribution, the probability accumulated until the first value "a" is 0.45, so that:
[tex]P(Z\leq a)=0.45[/tex]And the accumulated probability until "b" is 0.45+0.10=0.55, symbolically:
[tex]P(Z\leq b)=0.55[/tex]The next step is to determine the values under the standard normal distribution that accumulate 0.45 and 0.55 of probability. You have to use the Z-tables to determine both values:
The value that accumulates 0.45 of probability is Z=-0.126
To translate this value to its corresponding value of the variable of interest you have to use the standard normal formula:
[tex]a=\frac{X-\mu}{\sigma}[/tex]You have to write this expression for X
[tex]\begin{gathered} a\cdot\sigma=X-\mu \\ (a\cdot\sigma)+\mu=X \end{gathered}[/tex]Replace the expression with a=-0.126, μ=9.6gr, and δ=0.8gr
[tex]\begin{gathered} X=(a\cdot\sigma)+\mu \\ X=(-0.126\cdot0.8)+9.6 \\ X=-0.1008+9.6 \\ X=9.499 \\ X\approx9.5gr \end{gathered}[/tex]The value of Z that accumulates 0.55 of probability is 0.126, as before, you have to translate this Z-value into a value of the variable of interest, to do so you have to use the formula of the standard normal distribution and "reverse" the standardization to reach the corresponding value of x:
[tex]\begin{gathered} b=\frac{X-\mu}{\sigma} \\ b\cdot\sigma=X-\mu \\ (b\cdot\sigma)+\mu=X \end{gathered}[/tex]Replace the expression with b=0.126, μ=9.6gr, and δ=0.8gr and calculate the value of X:
[tex]\begin{gathered} X=(b\cdot\sigma)+\mu \\ X=(0.126\cdot0.8)+9.6 \\ X=0.1008+9.6 \\ X=9.7008 \\ X\approx9.7gr \end{gathered}[/tex]The values of sodium intake between which the middle 10% of American men fall are 9.5 and 9.7gr.