Answer:
They can buy up to 240 drinks.
Step-by-step explanation:
Let x = number of drinks
The price of 1 drink is 75¢ = $0.75
The price of x drinks is 0.75x
The store gives a discount of $100.
The rice of x drinks is
0.75x - 100
The total price of the drinks must be less than or equal to $80.
0.75x - 100 ≤ 80
Add 100 to both sides.
0.75x ≤ 180
Divide both sides by 0.75
x ≤ 240
Answer: They can buy up to 240 drinks.
Find the product of the given polynomials. (5 x +8 -6x) (4+ 2x 87)
a. -2x2+19x -24
b-2x2 -24x +19
c- 2x2 +19x +24
d- 2x2 +13x -24
Answer:
[tex]- 2x^2 +19x -24[/tex]
Step-by-step explanation:
Given
[tex](5x + 8 - 6x)(4 + 2x - 7)[/tex]
Required
Evaluate
We have:
[tex](5x + 8 - 6x)(4 + 2x - 7)[/tex]
Collect like terms
[tex](5x - 6x+ 8 )(4 - 7+ 2x )[/tex]
[tex](- x+ 8 )(- 3+ 2x )[/tex]
Expand
[tex]3x - 2x^2 -24 + 16x[/tex]
Rewrite as:
[tex]- 2x^2 + 3x+ 16x -24[/tex]
[tex]- 2x^2 +19x -24[/tex]
The total sound power, in decibels, from x objects each producing 50 decibels of sound power is given by the function f(x) = 50 + 10 log x. Suppose each of the x objects increases its sound power by 10 decibels, so that the new total sound power, in decibels, is given by the function g(x) = f(x) + 10. Which shows the graphs of f(x) and g(x)? On a coordinate plane y = g (x) starts at (0, 60) and curves up through (10, 70). Y = f (x) starts at (0, 50) and curves up through (10, 60). On a coordinate plane y = f (x) starts at (0, 50) and curves up through (10, 60). y = g (x) starts at (0, 40) and curves up through (10, 50). On a coordinate plane, y = f (x) starts at (0, 50) and curves up through (10, 60). Y = g (x) starts at (10, 50) and curves up through (20, 60). On a coordinate plane, y = g (x) starts at (negative 10, 50) and curves up through (0, 60). Y = f (x) starts at (0, 50) and curves up through (10, 60). Mark this and return
Answer:
Graph A
Step-by-step explanation:
correct answer on edge :)
The statement that represents the graphs of the functions f(x) and g(x) : On a coordinate plane y = g (x) starts at (0, 60) and curves up through (10, 70). Y = f (x) starts at (0, 50) and curves up through (10, 60).
What is a function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."For given question,
The total sound power, in decibels, from x objects each producing 50 decibels of sound power is given by the function f(x) = 50 + 10 log x.
If each of the x objects increases its sound power by 10 decibels, then the new total sound power, in decibels, is given by the function
g(x) = f(x) + 10.
The graph of the function f(x) would starts at (0, 50)
For x = 10 the value of the function f(x) would be,
f(10) = 50 + 10 log (10)
f(10) = 50 + 10 (1)
f(10) = 60
This means, the graph of the function f(x) passes though point (10, 60)
Also, the graph of the function g(x) would starts at (0, 60)
For x = 10 the value of the function g(x) would be,
g(10) = f(10) + 10
g(10) = 60 + 10
g(10) = 70
This means, the graph of the function g(x) passes though point (10, 70)
Therefore, on a coordinate plane y = g (x) starts at (0, 60) and curves up through (10, 70). Y = f (x) starts at (0, 50) and curves up through (10, 60).
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1) What is the opposite of adding 5?
2) What is the opposite of subtracting 20?
3) What is the opposite of multiplying by 1/2?
4) What is the opposite of dividing by 10?
Answer:
1) subtracting 5
2) adding 20
3) dividing by 2 (multiplying by 1/2)
4) multiplying by 1/10 (dividing by 10)
Step-by-step explanation:
There are four main operations in math: adding, subtracting, multiplying, and dividing. Each of the operations has an opposite. Adding and subtracting are opposites and multiplying and dividing are opposites. This means that subtracting can undo adding and vice versa; additionally, dividing can undo multiplying or vice versa. So, to find the opposite of something switch the operation to the opposite and keep the number. However, it is important to note that with multiplying and dividing you can also find the opposite by keeping the operation while changing the number to the reciprocal.
If gasoline costs $ 4.01 per gallon when you pay with a credit card, but $ 0.05 per gallon less if you pay with cash, how much do you save by filling up a 13 -gallon tank and paying for it with cash?
Answer:
$0.65
Step-by-step explanation:
You can just do 0.05 * 13 to find the difference between the two prices.
I believe the answer is 7% but it says round to the nearest tenth of a percent so I am not sure if it is a decimal answer or not. Can someone help me out please?
Answer: 6.1% decrease
Note: It appears that your teacher doesn't want you to type in the percent sign, as that's already covered for you.
=========================================================
Explanation:
The salary decreased by 51500-48355 = 3145
Divide this over the initial salary to get 3145/51500 = 0.0611 which is approximate.
This converts to the percentage 6.11% and that rounds to 6.1%
----------------
As an alternative, you can use the formula method below
A = old value = 51500
B = new value = 48355
C = percent change when going from A to B
C = [ (B-A)/A ] * 100%
C = [ (48355-51500)/51500 ] * 100%
C = (-3145/51500)*100%
C = -0.0611*100%
C = -6.11%
C = -6.1%
The negative C value indicates a percent decrease.
Which table represents the graph below?
On a coordinate plane, points are at (0, negative 3), (1, negative 1), (2, 1), (3, 3), (4, 5), and (5, 7).
Answer:
0,-3
Step-by-step explanation:
it will help u
Answer:
A
Step-by-step explanation:
The length of a rectangle is six times it’s width. If the area of the rectangle is 486 cm^2, find the perimeter.
Answer:
54 cm is the perimeter I think
Write the slope intercept form of the equation of each line.
1) The line through the point (4,2) and parallel to y+ -3/4x-5
Answer:
[tex]y = -\frac{3}{4}x + 5[/tex]
Step-by-step explanation:
Given equation y = -3/4x - 5
Step 1 : Find slope.
Since the lines are parallel to each other, the slopes are same.
[tex]therefore, m = \frac{-3}{4}[/tex]
Step 2 : Find the equation of the line.
[tex]( y - y_1) = m ( x - x_ 1) \ \ \ where \ x_ 1 = 4 \ and \ y_ 1 = 2[/tex]
[tex]( y - 2 ) = -\frac{3}{4}( x - 4)\\\\y - 2 = -\frac{3}{4}x + 3\\\\y = -\frac{3}{4}x + 3 + 2\\\\y = -\frac{3}{4}x + 5[/tex]
Find the equation of the line passing through the points (2, 4) and (3, 2).
Someone please help me
Answer:
[tex]x < 4368 \frac{8}{19} [/tex]
Step-by-step explanation:
[tex]28x < 83000 + 9x[/tex]
[tex]28x - 9x < 83000[/tex]
[tex]19x < 83000[/tex]
[tex]x < 4368 \frac{8}{19} [/tex]
Look at the graph shown below:
which equation best represents the line?
A: y=3x+3
B: y=1/2x-3
C: y= 1/2x+3
D: y=3x+ 1/2
Answer:
the answer is C
the y intercept is +3
if you do rise over run, the slope will be 1/2
The following data includes the year, make, model, mileage (in thousands of miles) and asking price (in US dollars) for each of 13 used Honda Odyssey minivans. The data was collected from the Web site.
year make model mileage price
2004 Honda Odyssey EXL 20 26900
2004 Honda Odyssey EX 21 23000
2002 Honda Odyssey 33 17500
2002 Honda Odyssey 41 18999
2001 Honda Odyssey EX 43 17200
2001 Honda Odyssey EX 67 18995
2000 Honda Odyssey LX 46 13900
Required:
Compute the correlation between age (in years) and price for these minivans.
Find complete data below :
Answer:
R = - 0.94
Step-by-step explanation:
Since data was collected in 2005 ; we subtract the data collection year from the make year to obtain the age :
Age (x) :
1,1, 3,3,4,4,5,5,5,5,6,7,10
Price (y) :
26900,23000,17500,18999,17200,18995,13900,15250,13200,11000,13900,8350,5800
Using technology, the correlation Coefficient between age of car and price is : - 0.94
With a correlation Coefficient of - 0.94, we can conclude that there exists a strong negative correlation between age and price of the Odyssey mini vans. This could be interpreted to mean that ; As the age of cars in increases, the price decreases
Suppose Z has a normal distribution with a mean of 10.0 and a standard deviation of 5.0 what is the P(2.0
Answer:
.0548
Step-by-step explanation:
(2-10)/5= -1.6
go to a ztable and get .0548
In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home. Give the value of the standard error for the point estimate.
Answer:
The value of the standard error for the point estimate is of 0.0392.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home.
This means that [tex]n = 100, p = \frac{81}{100} = 0.81[/tex]
Give the value of the standard error for the point estimate.
This is s. So
[tex]s = \sqrt{\frac{0.81*0.19}{100}} = 0.0392[/tex]
The value of the standard error for the point estimate is of 0.0392.
Type the standard form of "three thousand four hundred eight."
The solution is
Answer:
the standard form of "three thousand four hundred eight is
3408hope it is helpful to you ☺️
In standard form we can write 3408 as 3.408 x [tex]10^{3}[/tex].
We have the following statement - three thousand four hundred eight
We have to write it in standard form.
What do you understand by Standard form of a Number ?A number when expressed as a decimal number, between 1 and 10, multiplied by a power of 10, is said to be in standard form.
According to the question, we have -
three thousand four hundred eight.
In the digit form, we can write it as - 3408.
In Standard form, we can write it as -
3408 = 3.408 x [tex]10^{3}[/tex]
Hence, in standard form we can write 3408 as 3.408 x [tex]10^{3}[/tex].
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Last week at the business where you work, you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items?
Answer:
240
Step-by-step explanation:
minus how much u sold them and how much it cost to make
3-1=2
times 2 and 120
2(120)
240
01:55:07
The point-slope form of the equation of the line that passes through (-9, -2) and (1, 3) is y – 3 = {(x - 1). What is the
slope-intercept form of the equation for this line?
O y = 3x+2
O y= 2x-4
O y=+*+
O y = 3x - 2
Answer
y = 3x - 2
Step-by-step explanation
The slope-intercept form of the equation for this line is,
⇒ y = x + 2
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point-slope form of the equation of the line that passes through points (-9, -2) and (1, 3) is,
⇒ y - 3 = (x - 1)
Now, We can simplify as;
⇒ y - 3 = (x - 1)
⇒ y - 3 + 3 = (x - 1) + 3
⇒ y = x + 2
Thus, The slope-intercept form of the equation for this line is,
⇒ y = x + 2
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Four brands of lightbulbs are being considered for use in the final assembly area of the Ford F-150 truck plant in Dearborn, Michigan. The director of purchasing asked for samples of 200 from each manufacturer. The numbers of acceptable and unacceptable bulbs from each manufacturer are shown below. At the 0.10 significance level, is there a difference in the quality of the bulbs?
Manufacturer
A B C D
Unacceptable 29 17 9 22
Acceptable 171 183 191 178
Total 200 200 200 200
H0: There is no relationship between quality and manufacturer.
H1: There is a relationship.
1) State the decision rule using 0.10 significance level. (Round your answer to 3 decimal places.)
Reject H0 if chi-square >
2) Compute the value of chi-square. (Round your answer to 3 decimal places.)
Chi-square value
Answer:
Decison region :
Reject H0 : if χ² > 6.251
12.229
Step-by-step explanation:
Given :
Manufacturer A B C D
Unacceptable 29 17 9 22
Acceptable 171 183 191 178
Total 200 200 200 200
H0: There is no relationship between quality and manufacturer.
H1: There is a relationship.
Testing using the goodness of fit :
Chisquare = (observed - Expected)² / Expected
Expected Values:
19.25 19.25 19.25 19.25
180.75 180.75 180.75 180.75
Chi-Squared Values:
4.93831 0.262987 5.45779 0.392857
0.525934 0.0280083 0.581259 0.0418396
χ² = 4.93831 + 0.262987 + 5.45779 + 0.392857
+ 0.525934 + 0.0280083 + 0.581259 + 0.0418396 = 12.229
Degree of freedom, df = (4-1)(2-1) = 3*1= 3
The critical value,
χ² at 0.10, 3 = 6.251
Decison region :
Reject H0 : if χ² > 6.251
Reject H0 : 12.229 > 6.251
A sphere has radius 7cm then find its volume
Answer:
1437.3 cm^3 is the volume of sphere whose radius is 7cm
Please kindly help
According to a newspaper article 15% more home remodeling was done in 1985 than in 1984. Professionals performed 75% of all remodeling. If $80.4 billion was spent on residential remodeling in 1985 what was the value of the work done by professionals in 1985?
(1) $ 8.4 billion
(2) $12.06 billion
(3) $20.1 billion
(4) $60 billion
(5) $60.3 billion
Answer:
(3) $20.1 billion
Step-by-step explanation:
hope it help
Answer:
(5) $60.3 billion
Step-by-step explanation:
What is the minimum of y=1/3 x^2 + 2x + 5
Answer:
min at x = -3
Step-by-step explanation:
steps are in the pic above.
The U.S. average for state and local taxes for a family of four is $4172. A random sample of 20 families in a northeastern state indicates that they paid an annual amount of $4560 with a standard deviation of $1590. At α = 0.05, is there sufficient evidence to conclude that they pay more than the national average of $4172?
Answer:
Calculating p-value from excel
p-value = 0.144458 (From excel =T.DIST.RT(1.091,19))
p-value = 0.144458 > 0.05
So, we failed to reject the null hypothesis. There is sufficient evidence to conclude that they pay not more than the national average of $4172.
Step-by-step explanation:
Here the given de4tails are,
Hypothesized mean = 4172
Sample Standard deviation = 1590
Sample mean = 4560
Sample size n = 20
Formulation of hypothesis
Can anyone help please?
Answer:
h(t) = -16t(t-6)
h(2) = 128
Step-by-step explanation:
h(t) = -16t² + 96t
h(t) = -16t(t-6)
t = 3
h(2) = -16(2)(2 - 6)
h(2) = 128
Which pair of functions are inverses of each other?
O A. f(x) = f and g(x) = 8x?
O B. f(x) = 4 + 9 and g(x) = 4x - 9
O C. Ax) = 5x – 9 and g(x) = 149
O D. f(x) = 3 - 7 and g(x) = 247
10=−4x+3x^2 solve
please help!
Answer:
-1.28 AND 2.61
Step-by-step explanation:
[tex]10= -4x+3x^2\\ 3x^2 -4x - 10 = 0\\\\[/tex]
use quadratic formula
x = [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] x = [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]
Solution/X-Intercepts: -1.28 AND 2.61
A single, six-sided die is rolled. Find the probability of rolling an even number or a number less than 6 .
Answer:
P=1
Step-by-step explanation:
P(even or less than 6) = P(even)+P(less than 6) -P(even ∩ less than 6)
P(even)=3/6 (numbers 2,4, and 6)
P(less than 6) =5/6 (numbers 1,2,3,4, and 5)
P(even ∩ less than 6)=2/6 (numbers 2 and 4)
(3/6)+(5/6) -(2/6) = (3+5-2)/6 = 6/6=1
what is the equation of the directx for the following parabola -8(x-5)=(y+1)^2
Answer:
x=7
Step-by-step explanation:
The directrix of a parabola is the vertical line found by subtracting
p from the x-coordinate h
of the vertex if the parabola opens left or right.
x=h-p
Substitute the known values of
p and h
into the formula and simplify.
x=7
For which pair of functions is the vertex of k(x) 6 units below the vertex of
f(x)?
A. Ax) = x2 and k(x) = x2 + 6
B. f(x) = x2 and k(x) = (x+6)2
C. Ax) = x and k(x) = (x – 6)2
D. f(x) = x2 and k(x) = x2 - 6
Using translation concepts, the vertex of k(x) is 6 units below the vertex of f(x) = x² for:
D. f(x) = x² and k(x) = x² - 6.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
We want to shift the vertex 6 units down, hence the transformation is y -> y - 6, so the correct pair is:
D. f(x) = x² and k(x) = x² - 6.
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please answer me as soon as posible
Answer:
yes your answer is right
Answer:
Yes it's Perfectly correct
solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!
Answer:
[0.25, 2]
Step-by-step explanation:
We have
4t² ≤ 9t-2
subtract 9t-2 from both sides to make this a quadratic
4t²-9t+2 ≤ 0
To solve this, we can solve for 4t²-9t+2=0 and do some guess and check to find which values result in the function being less than 0.
4t²-9t+2=0
We can see that -8 and -1 add up to -9, the coefficient of t, and 4 (the coefficient of t²) and 2 multiply to 8, which is also equal to -8 * -1. Therefore, we can write this as
4t²-8t-t+2=0
4t(t-2)-1(t-2)=0
(4t-1)(t-2)=0
Our zeros are thus t=2 and t = 1/4. Using these zeros, we can set up three zones: t < 1/4, 1/4<t<2, and t>2. We can take one random value from each of these zones and see if it fits the criteria of
4t²-9t+2 ≤ 0
For t<1/4, we can plug in 0. 4(0)²-9(0) + 2 = 2 >0 , so this is not correct
For 1/4<t<2, we can plug 1 in. 4(1)²-9(1) +2 = -3 <0, so this is correct
For t > 2, we can plug 5 in. 4(5)²-9(5) + 2 = 57 > 0, so this is not correct.
Therefore, for 4t^2 ≤ 9t-2 , which can also be written as 4t²-9t+2 ≤ 0, when t is between 1/4 and 2, the inequality is correct. Furthermore, as the sides are equal when t= 1/4 and t=2, this can be written as [0.25, 2]