Answer:
The answer you chose is correct
Step-by-step explanation:
A lumber supplier sells 96-inch pieces of oak. Each piece must be within ¼ of an inch of 96 inches. Write and solve an inequality to show acceptable lengths.
Answer:
[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]
Step-by-step explanation:
Given that a lumber supplier sells 96 inch Pieces of oak which must be within 1/4 of an inch.
This situation can be represented by the following absolute value inequality:
[tex]|x \: - 96| \: \leqslant \: \frac{1}{4} [/tex].
The absolute value can be thought of as the size of something because length cannot be negative. The length must be no more than 1/4 away from 96.
To simplify this, pretend this is a standard equality, |x-96| = 1/4. 1/4 is the range of acceptable length, 96 is the median of the range, and x is the size of the wood.
First apply the rule |x| = y → x = [tex]\pm[/tex]y
|x-96| = 1/4
x - 96 = [tex]\pm[/tex]1/4
x = [tex]96 \pm 1/4[/tex]
(These are just the minimum, and maximum sizes)
Now with a less than or equal to, the solutions are now everything included between these two values.
Therefore:
[tex]96 - 1/4 \: \leqslant x [/tex] [tex]\leqslant \: 96 + 1/4 [/tex]
With less than inequalities, you must have the lower value on the left, and the higher value on the right.
If x represents the size of the pieces, then the acceptable lengths are represented by this following inequality:
[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]
This is interpreted as x (being the size of the oak) is greater than or equal to 95 3/4, and less than or equal to 96 1/4 in inches.
Pls answer fast Y=Mx+b for x
Answer:
y=mx+b
y=mx+b-b
y-b=mx
y-b/m = mx/m
y-b/m = x
Answer:
x = (y - b)/M.
Step-by-step explanation:
y = Mx + b
Mx = y - b
x = (y - b)/M.
Question 1 (2 points)
Bentley is trying to get better at skateboarding. He has a goal of skateboarding 5 miles total this week with two short runs and one longer run. His two short runs total 2.25 miles. How long will his long skateboard run need to be in order to hit his goal?
To find the length of Bentley’s long run, you would use:
5 – 2.25
Question 1 options:
True
False
Answer:
True
Step-by-step explanation:
If he is doing 2 short runs and one long run, and his 2 short runs equal 2.25 miles, you'd need to subtract them from the total to find out the long run.
A dog-washing salon is filling up the tub to was a dog. When the employee got to the tub,
there were already 2 gallons of water in the tub. She will fill the tub at a rate of 3 gallons a
minute.
Answer:
If there was 2 gallons in the tub at the moment, it must mean that it has been 2/3 of a minute or 40 seconds.
The two rates would be 3:60 and 2:40 and so on 1:20
Step-by-step explanation:
Good luck! Hope this helps! <3
Graph the line y-3=-1/3(x+2)
Slope: 1/2
y-intercept(s): (0, 7/3)
x: 0, 7
y: 7/3, 0
Step-by-step explanation:
y=-3 -1/3(1+2)=2/3.3=1.3=3
y=3
What is 837 divided by 27
Answer: 31
Step-by-step explanation: long division
function rule y=3x-3
Answer:
-15, -9, -3, 3
Step-by-step explanation:
First One:
y =3(-4)-3 is -15
Second:
y= 3(-2)-3 is -9
Third:
y= 3(0)-3 is -3
Last One:
y= 3(2)-3 is 3
if you subtract 19 from my number and multiply the difference by -2, the result is -8
Answer:cool
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
let the number be 'a'
-2(a - 19)= -8
open the brackets
-2a + 38 = -8
collect like terms
38 + 8 = 2a
46 = 2a
a = 23
Please help!!
x^2-2x+1-9y^2
Answer:
[tex]\left(x-1+3y\right)\left(x-1-3y\right)[/tex]
Step-by-step explanation:
[tex]x^2-2x+1-9y^2\\\\factor(skip for time)\\\\\left(x-1\right)^2-9y^2\\\\[/tex]
A little algebra process later...
you got the answer
Hoped this helped ya
<3
RedAnswer:
(x-1-3y) x (x-1+3y)
Step-by-step explanation:
x^2-2x+1-9y^2
Using a^2 - 2ab + b^2 = (a-b)^2 (factor the expression) = (x-1)^2 - 9y^2
(x-1)^2 - 9y^2 = (x-1-3y) x (x-1+3y) should be the answer :)
Rectangle A’B’C’D’ is the image of rectangle ABCD after which of the following rotations?
Answer:
You're right!
Step-by-step explanation:
Answer:
Were you right?
Step-by-step explanation:
3. How many solutions are there to the
equation 2x^2 - 3x +12=0? Tell how
you know.
Answer:
If you're talking about solutions in general (real and imaginary solutions), there is 2, because the fundamental theorem of algebra says that the number of roots of any polynomial is the degree if it's highest power, which is 2.
If you're talking about only real solutions, there is 0. To show that, we can take the discriminant (b^2-4ac) part of the quadratic equation, and plug in the know values. We then get:
(-3)^2-4*2*12
=9-96
=-87
Remember, the discriminant will be taken the square root. Since this is negative, the answer will be imaginary. Therefore, there is no real solution.
Tickets for a drumline competition cost $5 at the gate and $3 in advance. One hundred more tickets were sold in advance than at the gate. The total revenue from ticket sales was $1990. How many tickets were sold in advance?
Answer:
The number of tickets sold at the gate is [tex] G = 211.25[/tex]
The number of tickets sold in advance is [tex] A = 311.25 [/tex]
Step-by-step explanation:
From the question we are told that
The cost of a tickets at the gate is [tex]a = \$ 5[/tex]
The cost of a ticket in advance is [tex]b = \$ 3[/tex]
Let the number of ticket sold in the gate be G
Let the number of ticket sold in advance be A
From the question we are told that
One hundred more tickets were sold in advance than at the gate and this can be mathematically represented as
[tex]G + 100 = A[/tex]
From the question we are told that
The total revenue from ticket sales was $1990 and this can be mathematically represented as
[tex]5 G + 3A = 1990[/tex]
substituting for A in the equation above
[tex]5 G + 3[G + 100]= 1990[/tex]
[tex]5 G + 3G + 300= 1990[/tex]
[tex] 8G + 300= 1990[/tex]
[tex] 8G = 1690[/tex]
=> [tex] G = 211.25[/tex]
Substituting this for G in the above equation
[tex]5 [211.25] + 3A = 1990[/tex]
=> [tex] 3A = 1990 - 1056.25[/tex]
=> [tex] A = 311.25 [/tex]
3g+h=18 2g+3h=26 what is h and what is g
Answer:
g=4 h=6
Step-by-step explanation:
3g +h = 18 (Equation 1)
2g+3h=26 (Equation 2)
From equation 1
3g+ h =18
h= 18-3g (equation 3)
substitute equation 3 into equation 2
2g+3h= 26
2g+ 3(18-3g)= 26
2g+3×18+3(-3g)=26
2g+54-9g=26
9g-2g= 54-26
7g=28
7g÷7 = 28÷7
g= 4
substitute g into equation 1
3g+h=18
3(4)+ h= 18
12+h= 18
h=18-12
h= 6
Answer:
g = 4; h = g
Step-by-step explanation:
When solving an equation with two variables, the goal is to isolate at least one of the variables so that you can plug it in to the equation to get the other. There are multiple ways to solve this so I'll just be giving one.
3g + h = 18
2g + 3h = 26
In these two equations, I notice that if I multiply the first equation by 3, the two equations will have the same values of h, so I'd be able to isolate g:
9g + 3h = 54
2g + 3h = 26
Now, subtract the second equation from the first to isolate g:
9g + 3h = 54
-2g + 3h = 26
= 7g = 28
= g = 4
Now that we have solved for g, we can plug it into either of the equations and solve for h:
2(4) + 3h = 26
= 8 + 3h = 26
= 3h = 18
= h = 6
And in conclusion, g = 4 and h = 6.
What is the absolute value of 5,234?
Answer:
Step-by-step explanation:
5.234
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-10x^2+600x-3588
y=−10x
2
+600x−3588
Answer:
Step-by-step explanation:
The maximum profit will be found in the vertex of the parabola, which is what your equation is. You could do this by completing the square, but it is way easier to just solve for h and k using the following formulas:
[tex]h=\frac{-b}{2a}[/tex] for the x coordinate of the vertex, and
[tex]k=c-\frac{b^2}{4a}[/tex] for the y coordinate of the vertex.
x will be the selling price of each widget and y will be the profit. Usually, x is the number of the items sold, but I'm going off your info here for what the vertex means in the context of this problem.
Our variables for the quadratic are as follows:
a = -10
b = 600
c = -3588. Therefore,
[tex]h=\frac{-600}{2(-10)}=30[/tex] so the cost of each widget is $30. Now for the profit:
[tex]k=-3588-(\frac{(600)^2}{4(-10)})[/tex] This one is worth the simplification step by step:
[tex]k=-3588-(\frac{360000}{-40})[/tex] and
k = -3588 - (-9000) and
k = -3588 + 9000 so
k = 5412
That means that the profit made by selling the widgets at $30 apiece is $5412.
Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].
What is the maximum profit?
Maximum profit, or profit maximisation, is the process of finding the right price for your products or services to produce the best profit.
Here given that,
A company sells widgets. The amount of profit, [tex]y[/tex], made by the company, is related to the selling price of each widget, [tex]x[/tex], by the given equation.
As the maximum profit found in the vertex of the parabola,
Here, [tex]x[/tex] will be the selling price of each widget and [tex]y[/tex] will be the profit.
The number of items sold is [tex]x[/tex].
So, the quadratic equation is:-
[tex]a = -10b = 600c = -3588.[/tex]
Therefore, so the cost of each widget is $[tex]30[/tex].
For the profit:-
[tex]k = -3588 - (-9000) andk = -3588 + 9000 sok = 5412[/tex]
Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].
To know more about the maximum profit
https://brainly.com/question/16755335
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What formula is used to
determine the expected value for a variable?
Try it
Solve the system of equations.
2x + 3y = 1
5x + 2 = 8
What is the solution?
Answer:
x=6/5 ,y= -7/15
Step-by-step explanation:
we are going to solve this simultaneously.
2x+3y=1.......(i)
and
5x+2=8
5x=6
x= 6/5 .......(ii)
Now let's put value of x into equation number (i)
2x+3y=1
2(6/5) +3y=1
12/5 +3y =1
3y= 1-(12/5)
3y = -7/5
y = (-7/5) ÷3
y= -7/15
How many years will it take for Steven to make a total of $21,200?
(7 points)
12
8
6
10
Need help got until 12:10
If you roll a die once, what is the probability of rolling a 3?
Answer:
1/6
Step-by-step explanation:
there are 6 sides, and 3 is one of the 6 sides. thus, the answer is 1/6
Answer:
1/6
Step-by-step explanation: there are 6 incomes and 1 number 3 in a die
Write the equation of the line:
(0,3); slope -2
Answer:
y=-2x+3
Step-by-step explanation:
the y-intercept is (0,3) and the slope is -2, just plug that in to the slope intercept form, y=mx+b
Pls mark as brainliest thank u.
what is the pattern 2 10 40 120
Answer:
2 plus 3
Step-by-step explanation:
HELP ASAP IT'S AN EMERGENCY
PLEASE HELP
ILL GIVE BRAINLIEST
Answer:
f(7x−1)=63x−16
Step-by-step explanation:
Answer:
x=3
Step-by-step explanation:
since f(x) and g(x) are equal, we can make the equation, 9x-7 = 7x - 1
9x = 7x + 6, 2x = 6, x = 3
The table below shows the weekly change in the price of one gram of gold for four weeks.
ONE GRAM OF GOLD
Week
Weekly Change in the Price (dollars)
1
+ 1.
2
-3.
3
+ 2.
4
+3.
By how much did the price of one gram of gold change from the beginning of week 1 to the end of week 4? Did the price increase or decrease? explain
At the end of week 4, the price per gram of gold was $39. What was the price per gram of gold at the beginning of week 1?
Show your work in the box below.
Answer _____________ price per gram of gold
Answer:
THEY DIDN'T IT WAS BECAUSE THEY MADE UP A FAKE RUMER AND HAD TO MAKE IT LOOK REAL
Step-by-step explanation:
PLEASE HELP Please i don’t understand
Answer:
answer is 5
Step-by-step explanation:
f(5)= -5×5^2+26×5
= -125+130
= 5
From a circular sheet of paper with a radius 20 cm, four circles
of radius 5 cm each are cut out. What is the ratio of the uncut to
the cut portion?
Answer:
3 : 1
Step-by-step explanation:
The biggest circle has a radius of 20 cm
So that means, its area will be,
Area = [tex]\pi r^{2}[/tex]
Area = [tex]\pi * 20^{2}[/tex]
A = [tex]\pi * 400[/tex]
=> A = 400[tex]\pi[/tex]
We do not need to solve this because it is nit required
Then, one small circle has an area of,
Area = [tex]\pi r^{2}[/tex]
Area = [tex]\pi *5^{2}[/tex]
Area = [tex]\pi *25[/tex]
=> Area = 25[tex]\pi[/tex]
As there are 4 circles in, we get that the area covered by the small squares,
=> [tex]25\pi * 4[/tex]
=> [tex]100\pi[/tex]
So, the amount shaded = 100/400 (We can omit the [tex]\pi[/tex] at this stage because we are finding out a ratio)
=> 1/4
So, there is 1 cut region and the remaining is the uncut region,
As we need to find uncut to cut, the ratio will be,
=> remaining : 1
=> 3 : 1
If my answer helped, kindly mark me as the brainliest!!
Thanks!!
________ and ________ are two ways that substances pass through a cell membrane out of the cell. A Photosynthesis, diffusion B Diffusion, active transport C Active transport, mitosis D Photosynthesis, mitosis
Answer:
b. diffusion and active transport
Step-by-step explanation:
these are two ways that substances, like nutrients, pass through cell membranes.
Answer:
b
Step-by-step explanation:
Suppose that Elsa and Frank determine confidence intervals based on the same sample proportion and sample size. Elsa uses a larger confidence level than Frank. How will midpoint and width of confidence intervals compare
Answer:
elsa's interval width will be greater than that of frank
Step-by-step explanation:
first of all we are told that both Elsa and Frank have the same sample proportion so their midpoint is also going to be the same.
now as the confidence level goes higher, so also would the margin of error increase. then the width of the confidence interval would rise so it can be more confident.
from this question elsa has a larger confidence level therefore her intervals width will be greater than franks own.
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.18 F and a standard deviation of 0.65 F. Using the empirical rule, find each approximate percentage below.
a.
What is the approximate percentage of healthy adults with body temperatures within 3 standard deviation of the mean, or between 96.23 F and100.3 F?
Answer:
99.7%
Step-by-step explanation:
Empirical rule formula states that:
• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
From the question, we have mean of 98.18 F and a standard deviation of 0.65 F
The approximate percentage of healthy adults with body temperatures between 96.23 F and100.13 F is
μ - 3σ
= 98.18 - 3(0.65)
= 98.18 - 1.95
= 96.23 F
μ + 3σ.
98.18 + 3(0.65)
= 98.18 + 1.95
= 100.13 F
Therefore, the approximate percentage of healthy adults with body temperatures between 96.23 F and 100.13 F which is within 3 standard deviations of the mean is 99.7%