Step-by-step explanation:
Let the price of CD, tshirt and jeans be x,y and z respectively.
given:
x+2y+2z=133......(i)
y=x+13.......(ii)
2z=y+30....(iii)
in eqn (iii) ,
2z=y+30
or, 2z=x+13+30
or, z=(x+43)/2....(iv)
now in eqn (i),
x+2y+2z=133
or, x+2(x+13)+2((x+43)/2) =133
or, x+2x+26+x+43=133
or, 4x=133-69
or, x= 64/4
•°• x=$16
6. The area of a rectangular sheet of paper is 300 cm squared. The length is 5 cm more than the width
a) If the width of the rectangle is x cm, state an expression for the length of the rectangle.
b) Write and algebraically solve a quadratic equation to determine the length and
width of the rectangle.
Answer:
Step-by-step explanation:
width = x
length= x + 5
a) x + 5
b) x * (x+5) = 300
x^2 + 5x = 300
x^2 + 5x - 300 = 0
Δ = 25 + 1200 = 1225
width = (-5 + 35)/2 = 15 cm
lenght = 15 + 5 = 20 cm
Answer:
a) length = x + 5
b) [tex]x^{2}[/tex] + 5x - 300 = 0
Step-by-step explanation:
x = width
x + 5 = length
(x)(x + 5) = 300
[tex]x^{2}[/tex] + 5x = 300
[tex]x^{2}[/tex] + 5x - 300 = 0
(x+20)(x-15)
x = -20 or x = 15 ( disregard the -20. measurements can't be negative)
width = 15
length = x+ 5 = 15+5 = 20
The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage? b) Assume that a recent survey suggests that about 87% of adults have heard of the brand.
Answer:
He must survey 123 adults.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Assume that a recent survey suggests that about 87% of adults have heard of the brand.
This means that [tex]\pi = 0.87[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
How many adults must he survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage?
This is n for which M = 0.05. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.645\sqrt{\frac{0.87*0.13}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.645\sqrt{0.87*0.13}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.87*0.13}}{0.05}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645\sqrt{0.87*0.13}}{0.05})^2[/tex]
[tex]n = 122.4[/tex]
Rounding up:
He must survey 123 adults.
Given C(4, 3) and D(-4, -3) are two points on a circle, centered at the origin. Given
that CD is a diameter of the circle,
a) Find the radius of the circle.
b) State the equation of the circle
Answer:000
Step-by-step explanation:000
Y= 2x - 3; Y = (1/2)x - 4
Answer:
(-2/3, -13/3)
Step-by-step explanation:
Given the expressions;
[tex]y= 2x - 3\\y = (\frac{1}{2} )x - 4[/tex]
Equating both expressions;
[tex]y=y\\2x-3=\frac{1}{2}x-4\\[/tex]
Collect the like terms:
[tex]2x-\frac{1}{2}x=-4+3\\\frac{3x}{2}=-1\\3x=-2\\x=\frac{-2}{3}[/tex]
Substitute [tex]x=\frac{-2}{3}[/tex] into any of the expressions to get 'y'
[tex]Recall\ y= 2x-3\\y=2(\frac{-2}{3} )-3\\y=\frac{-4}{3}-3\\y=\frac{-4-9}{3} \\y=\frac{-13}{3}[/tex]
Hence the solution to the equation is (-2/3, -13/3)
The value of the expression 23 +32–3x4–52-5+(7x4) is
Answer:
24
Explanation:
(23+32)-(3×4)-(52-5)+(7×4)
(55)-(12)-(47)+(28)
55-12=43-47+28= -1943-19=24what is the sum of the angles of a triangle?
I need two examples of a decimal number to the tenths place minus a decimal number to the hundredths place. Show all work
Answer:
ok
Step-by-step explanation:
.1 - .01 = .99
.1 - .99 = .1
.4 -.03 =37
The firm has bonds with par value of 10,000,000 VND, coupon rate of 11%, annual interest payment, and the remaining maturity period is 07 years. If the bond's interest rate and current risk level have a return rate of 12%, what price should company C sell the bond in the present?
a.
10,000,000
b.
14,152,000
c.
12,053,000
d.
11,150,000
Use the distributive property to remove the parentheses.
-5(6u - 4w-2)
Answer:
-30u+20w+10
Step-by-step explanation:
multiple each term inside the parenthesis by -5. remember negative times negative = positive
Find the mass of wire that lies along the curve , ()=(2−1)+2, 0≤≤ 1, h = (3)
Step-by-step explanation:
sorry bestie but it hard to find
Evaluate −a2+c2 when c=−4.
Answer:
[tex]a = 4, -4[/tex]
Step-by-step explanation:
Step 1: Plug in -4 for c
[tex]-a^{2} + c^{2}[/tex]
[tex]-a^{2} + (-4)^{2}[/tex]
[tex]-a^{2} + 16[/tex]
Step 2: Solve for a
[tex]-a^{2}+16-16=0-16[/tex]
[tex]-a^{2}/-1 = -16/-1[/tex]
[tex]a^{2} = 16[/tex]
[tex]\sqrt{a^{2}} = \sqrt{16}[/tex]
[tex]a = 4, -4[/tex]
Answer: [tex]a = 4, -4[/tex]
Help what is this question
Answer:
0
Step-by-step explanation:
find the length of y, assume the triangles are similar
Answer:
y = 3.6
Step-by-step explanation:
Since the triangles are similar, we can write the following proportion:
[tex]\frac{y}{6.3} = \frac{2.4}{4.2} = \frac{2.8}{x}[/tex]
We don't need the fraction on the left because it is not necessary to solve for y. Instead, we can simplify the rest:
[tex]\frac{y}{6.3} = \frac{2.4}{4.2}[/tex]
[tex]\frac{y}{6.3} = \frac{0.4}{0.7}[/tex]
Now, we can cross-multiply:
[tex]0.7y = 6.3 * 0.4[/tex]
[tex]0.7y = 2.52[/tex]
[tex]y = 3.6[/tex]
Given:
The length of both triangle are in the same ratio,
2.4:2.8:y = 4.2:x:6.3
To find:
The value of 'y'
Steps:
Since 2.4 : y = 4.2 : 6.3, we can find the value of 'y'
2.4/y = 4.2/6.3
2.4 * 6.3 = 4.2 * y
15.12 = 4.2y
15.12/4.2 = y
3.6 = y
y = 3.6
Therefore, the value of y is 3.6
Happy to help :)
If you want help, feel free to ask
1
Select the correct answer.
Simplify the following expression.
우
O A.
OB. 12
Oc. 1
OD.
64
Reset
Next
Answer:
1/64
Step-by-step explanation:
4^ (-11/3) ÷ 4 ^ (-2/3)
We know a^b ÷a^c = a^(b-c)
4 ^(-11/3 - - 2/3)
4^(-11/3 +2/3)
4^(-9/3)
4^ -3
We know a^-b = 1/a^b
1/4^3
1/64
How do u determine the equation of the line through each pair of points in slope-intercept form (y=mx+b). (3,0) and (2,4) (-6,3) and (2,-2)
Answer:
Y =-4X +12
Y =-0.625X -0.75
Step-by-step explanation:
(3,0) and (2,4)....
x1 y1 x2 y2
3 0 2 4
(Y2-Y1) (4)-(0)= 4 ΔY 4
(X2-X1) (2)-(3)= -1 ΔX -1
slope= -4
B= 12
Y =-4X +12
~~~~~~~~~~~~~~~~~
(-6,3) and (2,-2)
x1 y1 x2 y2
-6 3 2 -2
(Y2-Y1) (-2)-(3)= -5 ΔY -5
(X2-X1) (2)-(-6)= 8 ΔX 8
slope= - 5/8
B= - 3/4
Y =-0.625X -0.75
MIN-
Bill is measuring a piece of material for some curtains.
It is 215 cm wide, how many mm is this?
There are 10 mm in 1 cm.
mm
Answer:
2,150 mm
Step-by-step explanation:
If every cm is 10 mm you multiply 215 by 10. I hope this helped!
7/18 - 1/3 , 1/2 - 1/5 - 1/10 and 3 1/2 - 2 5/9 please help thank you
Answer:
Step-by-step explanation:
7/18=7/18
it cant be divided agian
1/3=1/3
it cant be divded agian
1/5=1/5
it cant be divded agian
1/10=1/10
it cant be divded agian
3 1/2=3/2
2 5/9 =10/9
i am not sure if this is what you wanted ...
Real life problem for (-10+-2)=12
Hello!
[tex]\bf [ (-10) + (-2) ] = 12 [/tex]
[tex]\bf [ (-10) - 2 ] = 12 [/tex]
[tex]\bf -10 - 2 = 12 [/tex]
[tex]\bf -12 ≠ 12 [/tex]
Answer: Wrong
Good luck! :)
I need two examples of Solve a proportion with a mixed number in one of its numerators. SHOW ALL WORK!!!!!!!!!!!!
Answer:
A proportion equation is something like:
[tex]\frac{A}{B} = \frac{x}{C}[/tex]
Where A, B, and C are known numbers, and we want to find the value of x.
Now we want two cases where in one of the numerators we have a mixed number, where a mixed number is something like:
1 and 1/3
which actually should be written as:
1 + 1/3
1) a random problem can be:
[tex]\frac{1 + 1/3}{4} = \frac{x}{5}[/tex]
We can see that the numerator on the left is a mixed number.
First, let's rewrite the numerator then:
1 + 1/3
we need to have the same denominator in both numbers, so we can multiply and divide by 3 the number 1:
(3/3)*1 + 1/3
3/3 + 1/3 = 4/3
now we can rewrite our equation as:
[tex]\frac{4/3}{4} = \frac{x}{5}[/tex]
now we can solve this:
[tex]\frac{4/3}{4} = \frac{4}{3*4} = \frac{x}{5} \\\\\frac{1}{3} = \frac{x}{5}[/tex]
now we can multiply both sides by 5 to get:
[tex]\frac{5}{3} = x[/tex]
Now let's look at another example, this time we will have the variable x in the denominator:
[tex]\frac{7}{12} = \frac{3 + 4/7}{x}[/tex]
We can see that we have a mixed number in one numerator.
Let's rewrite that number as a fraction:
3 + 4/7
let's multiply and divide the 3 by 7.
(7/7)*3 + 4/7
21/7 + 4/7
25/7
Then we can rewrite our equation as
[tex]\frac{7}{12} = \frac{25/7}{x}[/tex]
Now we can multiply both sides by x to get:
[tex]\frac{7}{12}*x = \frac{25}{7}[/tex]
Now we need to multiply both sides by (12/7) to get:
[tex]x = \frac{25}{7}*\frac{12}{7} = 300/49[/tex]
plot the following points in the number line, -1/4, 1 1/2, 0.75 (PLS ANSWER ASAP)
Answer:
-1/4 is the least, 0.75 is second, and 1 1/2 is the greatest
Step-by-step explanation:
-1/4 is the least already because it is negative.
1 1/2 is really 1.5 so now compare 0.75 and 1.5.
1.5 is bigger therefore the order is :
-1/4, 0.75, 1 1/2
answer this question
Answer:
(-2, 13) (-1,8) (0, 5) (1, 4) (2, 5) (3, 8)
(2.4 , 6) or (-0.4, 6)
Step-by-step explanation:
Graph y = 6 on top of y = [tex]x^{2}[/tex] -2x + 5 and use the points where the two lines meet.
i spend 3 hours a day out of a 8 hour shift, what percentage is that
Answer:
0.375 = 38%
Step-by-step explanation:
Just divide 3 from 8 and that will give you 0.375
Then you round that to the nearest one which is 38 and
that will get your percentage
Answer: 37.5%
Step-by-step explanation: I just divided 3 by 8 then once I got my answer I moved the decimal point over to the right by 2.
Calculus 3 Problem
7. Determine if the field F(x, y, z) = ye^z i + xe^z j + xy e^z k is conservative. If it is, find a potential function.
Step-by-step explanation:
Given:
[tex]\vec{\textbf{F}}(x, y, z) = ye^z\hat{\textbf{i}} + xe^z\hat{\textbf{j}} + xye^z\hat{\textbf{k}}[/tex]
A vector field is conservative if
[tex]\vec{\nabla}\textbf{×}\vec{\text{F}} = 0[/tex]
Looking at the components,
[tex]\left(\vec{\nabla}\textbf{×}\vec{\text{F}}\right)_x = \left(\dfrac{\partial F_z}{\partial y} - \dfrac{\partial F_y}{\partial z}\right)_x[/tex]
[tex]= xe^z - ye^z \neq 0[/tex]
Since the x- component is not equal to zero, then the field is not conservative so there is no scalar potential [tex]\phi[/tex].
Consumer products are required by law to contain at least as much as the amount printed on the package. For example, a bag of potato chips that is labeled as 10 ounces should contain at least 10 ounces.Assume that the standard deviation of the packaging equipment yields a bag weight standard deviation of 0.2 ounces. Assume the bag weight distribution is bell-shaped. Determine what average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag.
Answer:
The average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag=9.802
Step-by-step explanation:
We are given that
Standard deviation, [tex]\sigma=0.2[/tex]ounces
We have to find the average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag.
[tex]P(x\geq 10)=0.99[/tex]
Assume the bag weight distribution is bell-shaped
Therefore,
[tex]P(\frac{x-\mu}{\sigma}\geq 10)=0.99[/tex]
We know that
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the value of z
Now,
[tex]\frac{10-\mu}{0.2}=0.99[/tex]
[tex]10-\mu=0.99\times 0.2[/tex]
[tex]\mu=10-0.99\times 0.2[/tex]
[tex]\mu=9.802[/tex]
Hence, the average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag=9.802
A road crew must repave a road that is 2/3 miles long. They can repave 1/12 miles each hour. How long will it take the crew to repave the road?
Write your answer in simplest form.
Select the correct answer. This table represents a quadratic function. x y 0 -3 1 -3.75 2 -4 3 -3.75 4 -3 5 -1.75
I really need one fast
I give all my points
Answer:
1/4
Step-by-step explanation:
that is the answer
I found the constant which was -3
a = 1/4
b=-1
Answer:
the value of a in the function's equation is 1/4
Step-by-step explanation:
Plato answer
Write the sentence as an inequality. The cost of a ticket t will be no more than $52.
Answer:
t is less than or equal to $52, or t <= $52
Step-by-step explanation:
If you can't have more than $52, then use less than symbol (<). The sentence doesn't state that a ticket shouldn't cost $52, so it's safe to assume that you can have exactly $52.
José corrió 3/10 Kilómetros y Juan 1/2 kilometro
¿Cuántos kilómetros corrieron entre los dos?
Answer:
3/10 + 5/10 = 8/10
8/10 kilometers
Step-by-step explanation:
Answer:
3/10+1/2=3/10+5/10
=8/10km
Find the missing side lengths leave your answer as a racials simplest form
Answer:
u = 26
v = 13√3
it's 30-60-90 triangle
consumer product manufacturers, link with customer satisfaction surveys and product warranty cars that are sent back to the company. And Outdoors company redesign the popular camping tent, and it wants to know what does the customers like the newer version rather than older one. So they include in the warranty registration of car to serve it as two questions first one of the customer on the older version of the tent and the second newest version better what variable was measured by this experiment
Answer:
sorry
Step-by-step explanation:
