The unit price of one can of juice, when a 6-pack costs $3.48, is $0.58 per can.
The question asks us to calculate the unit price of a juice can when a pack of 6 cans costs $3.48.
To find the unit price, we divide the total cost of the pack by the number of cans in a pack.
In this case, we divide $3.48 by 6, which gives us $0.58.
$3.48 / 6 = $0.58
Therefore, the unit price per can is $0.58.
Check all of the values that have three significant figures
a) 1.04
b) 44.65
c) 0.0760
d) 1089 ...?
One estimate of the population of the world on January 1, 2005, is 6,486,915,022. The population is estimated to be increasing at the rate of 1.4 percent per year. At this rate, what will the population of the world be on January 1, 2024? Round your answer to the nearest whole number. ...?
David invests £5000 in a savings account.
The account pays 3.2% compound interest per year.
Works out the value of his investment after 3 years.
Give your answer to the nearest penny.
Frankos pizza is selling pizza for 35% cheaper than usual. if a pizza normally costs 12.00 how much is it now
Bradley and Kelly are out flying kites at a park one afternoon. A model of Bradley and Kelly's kites are shown below on the coordinate plane as kites BRAD and KELY, respectively:
Which statement is correct about the two kites?
They are similar because Segment BR to segment DB is 1:2 and Segment KE to segment YK 1:2.
They are not similar because Segment BR to segment DB is 1:5 and Segment KE to segment YK is 1:2.
They are not similar because Segment BR to segment DB is 1:2 and Segment KE to segment YK is 1:5.
They are similar because Segment BR to segment DB is 1:5 and Segment KE to segment YK is 1:5.
1. The vertices B, D and R have coordinates (9,9), (1,5) and (11,5), respectively. Then
[tex] BR=\sqrt{(11-9)^2+(5-9)^2}=\sqrt{4+16} = 2\sqrt{5} ,\\BD=\sqrt{(1-9)^2+(5-9)^2}=\sqrt{64+16} = 4\sqrt{5}. [/tex]
The ratio
[tex] \dfrac{BR}{BD}= \dfrac{2\sqrt{5}}{4\sqrt{5}} =\dfrac{1}{2}. [/tex]
2. The vertices K, E and Y have coordinates (13,9), (14,10) and (14,2), respectively. Then
[tex] KE=\sqrt{(13-14)^2+(9-10)^2}=\sqrt{1+1} = \sqrt{2} ,\\KY=\sqrt{(13-14)^2+(9-2)^2}=\sqrt{1+49} = 5\sqrt{2}. [/tex]
The ratio
[tex] \dfrac{KE}{KY}= \dfrac{\sqrt{2}}{5\sqrt{2}} =\dfrac{1}{5}. [/tex]
Answer: correct answer is C (they are not similar because segment BR to segment DB is 1:2 and segment KE to segment YK is 1:5.)
Merle Fonda opened a new savings account. She deposited $40,000 at 10 percent compounded semiannually. At the start of the fourth year, Merle deposits an additional $20,000 that is also compounded semiannually at 10 percent. At the end of 6 years, the balance in Merle's account is:
Answer:
$98,636.72
Step-by-step explanation:
if cos2X=1/3 and 0<=2X<=pi, find cosX ...?
When cos2X=1/3 and 0<=2X<=pi, you can use the double angle formula for cosine to solve for cosX. The result is sqrt(6)/3.
Explanation:To solve for cosX given that cos2X=1/3 and 0<=2X<=pi, you need to use the double angle formula for cosine, which is:
cos2X = 2cos²X - 1
Plugging in 1/3 for cos2X, we get:
1/3 = 2cos²X - 1
Solving this equation for cos²X gives us :
cos²X = 2/3
The square root of this is ±sqrt(2/3), or ±sqrt(2)/sqrt(3). However, since X falls in the range 0<=X<=pi/2 (because 0<=2X<=pi), cosX is positive. Therefore:
cosX = sqrt(2)/sqrt(3) = sqrt(6)/3
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A regular box of cereal holds 14 ounces. If an economy box is made by doubling all the dimensions of the regular-sized box, how many ounces will the economy box hold? ...?
Answer: The economy box will hold 112 ounces.
Step-by-step explanation:
Since we have given that
A regular box of cereal holds = 14 ounces
Let the dimesion of regular box be x .
so, Volume of regular box is given by
[tex]x\times x\times x =x^3= 14[/tex]
According to question, if the box is made by doubling all the dimensions of the regular sized box.
So, volume becomes
[tex]2x\times 2x\times 2x\\\\=2^3\times x^3\\\\=8\times x^3\\\\=8\times 14\\\\=112\ ounces[/tex]
Hence, The economy box will hold 112 ounces.
What statement makes the open sentence 3x + 20 = 5x + 6 true? x = 13 x = 2 x = 4 x = 7
Describe the roots of the equation shown below.
3x^2-10x-5=0
A. There are two real, irrational roots.
B. There is one real, double root.
C. There are two real, rational roots.
D. There are two complex roots.
...?
Steve is buying a home worth $275000. His closing costs will amount to 6%, & his down payment is 15%. How much is each fee.
A. The closing cost are $16,500, & the down payment is $41,250.
B. The closing cost are $16,500, and the down payment is $42,000
C. The closing cost are $42,500, & the down payment is $165,000
Answer: For Plato users
A. The closing costs are $16,500 ,and the down payment is $41,250
Step-by-step explanation:
Just took the test
The closing costs are $16,500, & the down payment is $41,250.Option A is correct.
What is percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol. The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages.
It is given that, Steve is buying a home worth $275000. His closing costs will amount to 6%, & his down payment is 15%
Closing cost = 6 % of $275000
Closing cost = 6/100 × $275000
Closing cost = $16500
Down payment = 15% of $275000
Down payment = 15/100 × $275000
Down payment = $41,250.
Thus closing costs are $16,500, & the down payment is $41,250.Option A is correct.
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The gray area is the sidewalk. the area of the sidewalk is ___________ square units.
Answer:
72
Step-by-step explanation:
Hailey has a summer job at the water slide park. She earns $9.50 an hour as a lifeguard, but never works more than 25 hours in a week. She determines that her salary is modeled by the function s = 9.5h. What is the domain of this function in this situation? A) s ≤ 237.50 B) all real numbers C) {0 ≤ h ≤ 25} D) {0 ≥ h ≥ 25}
Answer: C) {0 ≤ h ≤ 25}
Step-by-step explanation:
The domain of a function is the set of all values for independent variable for which the function must be defined.Given: The amount earned by Hailey for one hour work =$9.50
She determines that her salary is modeled by the function [tex]s = 9.5h[/tex].
Here h is the independent variable such that 's' is dependent on 'h'.
Since she never works more than 25 hours in a week.
Therefore, the maximum hours she will work = 25
Hence, the domain of this function in this situation is {0 ≤ h ≤ 25}, where h is number of hours she works.
HELP PLEASE?!
Multiply: 3x4(4x4 − x5 + 2)
A.) 7x8 − 3x9 + 6x4
B.) 12x8 − 3x9 + 6x4
C.) 12x4 − x9 + 6x4
D.) 12x16 − 3x20 + 6x4
Answer:
[tex]12x^8-3x^9+6x^4[/tex]
B is the correct option.
Step-by-step explanation:
We have to multiply the expression
[tex]3x^4(4x^4-x^5+2)
Using the distributive property a(b+c)=ab+ac
[tex]3x^4\times4x^4+3x^4\times(-x^5)+3x^4\times2[/tex]
Now, using the exponent rule [tex]x^a\times x^b=x^{a+b}[/tex]
[tex]12x^{4+4}-3x^{4+5}+6x^4[/tex]
On simplifying, we get
[tex]12x^8-3x^9+6x^4[/tex]
B is the correct option.
1. What is the apparent solution to the system of equations graphed above?
(0,-1)
(0,3)
(1,2)
(2,1)
Answer:
the answer is (,2)
Step-by-step explanation:
the system of solutions is the point that two equations/line cross
the two lines cross at (1,2)
Mr hower can buy a computer with a down payment of 510$ and 8 monthly payments of 35.75 if he pays cash for the computer the cost is 699.99$ how much will he save if he pays cash the computer instead of paying for it in monthly payments
Which statement is true about 109?
a. it is a prime number.
b. it is a composite number.
c. it is a whole number that is neither prime nor composite.
d. it is not a whole number.
Answer:
its a
Step-by-step explanation:
What is the difference between 90p and £3.25?
The difference between 90 pence and 3 pounds 25 pence is 235 pence, or 2 pounds 35 pence.
Explanation:The question is asking for the difference between two amounts of money, 90 pence (90p) and 3 pounds 25 pence (£3.25). To find the difference, you would subtract the smaller amount from the larger amount. In this scenario, since both amounts are in British currency, it is a straightforward subtraction.
£3.25 is equal to 325 pence (since there are 100 pence in a pound). Now, subtract:
325p - 90p = 235p
Therefore, the difference between 90p and £3.25 is 235 pence, which can also be expressed as £2.35.
8% of rides in the park are water rides. If there are 4 water rides, how many rides are there in total
Answer:
50
Step-by-step explanation:
So 8 percent equals to 4 so just multiply the reciprocal of 8/100 and you get 50
A light bulb consumes 2400 watt-hours per day. How long does it take to consume 11400 watt-hours?
Answer: 4 days and 18 hours
Step-by-step explanation:
Each student wrote a two step equation. peter wrote the equation 4x - 2 =10, and andres wrote the equation 16x - 8 = 40. the teacher looked at their equations and asked them to compare them. describe one way in which the equations are similar
Both equations are two-step equations involving a variable term multiplied by a constant and then subtracting another constant. Peter's is 4x - 2 = 10 and Andres's is 16x - 8 = 40.
One way in which Peter's equation 4x - 2 = 10 and Andres's equation 16x - 8 = 40 are similar is that they both involve a variable term multiplied by a constant and then subtracting another constant.
In Peter's equation, 4x represents four times a variable x, and then subtracting 2 from the result.
Similarly, in Andres's equation, 16x represents sixteen times a variable x, and then subtracting 8 from the result.
This common structure of multiplying a variable term by a constant and then subtracting another constant makes both equations two-step equations, even though the specific values and constants differ.
1. The Spokesman-Review wants to know the public opinion on the construction of a new library downtown. It is decided that 48 people will be surveyed using a simple random sample. Which of the following will produce a simple random sample?
Number the residents using the latest census data, then use a random number generator to pick 48 people.
Record the opinion of the first 48 people who visit the newspaper's website.
Survey every fourth person who enters the current library until 48 have responded.
Randomly select 48 people from the phone book.
Randomly select 12 people each from the downtown, south hill, northwest, and hillyard parts of the city.
2. The Morning News radio station is interested in predicting the proportion of registered voters who support an increase in the state sales tax. Listeners were asked to go to the station's website and indicate whether they favored an increase in the tax in order to support the State Park system. 1744 listeners logged on and 922 were against the increase. The population of interest is:
All people who listen to the station
The 1744 listeners who logged in and indicated their preference
The 922 listeners who were against the issue
All registered voters
Only the portion of the 1744 listeners who voted that are actually registered to vote
Answer:
(a) Number the residents using the latest census data, then use a random number generator to pick 48 people.
(b) The 1744 listeners who logged in and indicated their preference
Step-by-step explanation:
(a) Sampling method is said to be Simple Random Sampling if unit from the population are drawn randomly without any criteria, such that each unit as same chance of selection.
Since, In only first option each unit has same chance of selection. Thus, method of selection is Simple Random Sample.
(b) Since, population of interest is asked and 1744 listeners logged on in the support of State Park.
Thus, first option is correct.
At what value(s) of x does f(x)=x^4-18x^2 have a critical point where the graph changes from decreasing to increasing?
The values of x at which f(x) = x^4 - 18x^2 has a critical point and changes from decreasing to increasing are x = 3 and x = -3.
Explanation:To determine at what values of x the function f(x) = x^4 - 18x^2 has critical points where the graph changes from decreasing to increasing, we must find the first derivative of f(x), set it to zero, and solve for x. The first derivative of f(x) is f'(x) = 4x^3 - 36x. Setting the derivative to zero gives us 4x^3 - 36x = 0, which can be factored as 4x(x^2 - 9) = 0. The solutions to this are x = 0, x = 3, and x = -3.
Next, to determine if these points are minima (where the graph changes from decreasing to increasing), we must examine the second derivative, or use the first derivative test. The second derivative f''(x) is 12x^2 - 36. Entering our critical points into this equation, we find that for x = ±3, the second derivative is positive, indicating a minima, whereas for x = 0, the second derivative is negative, which indicates a maxima.
Thus, the values of x at which f(x) has a critical point and the graph changes from decreasing to increasing are at x = 3 and x = -3.
The critical points of the function [tex]f(x) = x^4 - 18x^2[/tex], we need to find the derivative f'(x) and set it equal to zero. The critical points are x = 0, -3, and 3. At x = -3, the graph changes from decreasing to increasing.
The critical points of the function[tex]f(x) = x^4 - 18x^2,[/tex] we need to find the derivative f'(x) and set it equal to zero. Let's find the derivative:
[tex]f(x) = x^4 - 18x^2[/tex]
[tex]f'(x) = 4x^3 - 36x[/tex]
Now, set f'(x) equal to zero and solve for x:
[tex]4x^3 - 36x = 0[/tex]
Factor out 4x:
[tex]4x(x^2 - 9) = 0[/tex]
Now, set each factor equal to zero:
4x = 0 → x = 0[tex]x^2 - 9 = 0[/tex] x = ±3So, the critical points are x = 0, -3, and 3.
To determine whether each critical point corresponds to a minimum, maximum, or an inflection point, we can use the second derivative test. The second derivative is:
[tex]f''(x) = 12x^2 - 36[/tex]
Evaluate f''(x) at each critical point:
At x = 0, f''(0) = -36 (negative), so x = 0 corresponds to a local maximum.At x = -3, f''(-3) = 72 - 36 = 36 (positive), so x = -3 corresponds to a local minimum.At x = 3, f''(3) = 108 - 36 = 72 (positive), so x = 3 corresponds to a local minimum.Therefore, at x = -3, the graph changes from decreasing to increasing.
what is equivalent to 625/1000
Two triangles with the same corresponding side lengths will be congruent.
True
False
Two triangles with the same corresponding side lengths will be congruent - False
False. Two triangles with the same corresponding side lengths are not guaranteed to be congruent. They may still be similar triangles with equal corresponding angles but different sizes.
the following equation can be used to predict the average height of boys anywhere b/w birth and 15 years old: y=2.79x+25.64, where x is the age(in yrs) and y is the height (in inches). what does the slope represent? interpret the slope in the cintext of the problem. What does the y-intercept represent in this problem? intercept the y-intercept in the context of the problem. ...?
slope = growth during 1 year y-intercept = their original height i.e. the height when they were born
The standard linear equation is given by :-
[tex]y=mx+c[/tex], where m is the slope and c is the y-intercept.
Given equation to predict the average height of boys anywhere b/w birth and 15 years old:
[tex]y=2.79x+25.64[/tex], where x is the age(in yrs) and y is the height (in inches).
By comparing this equation to the standard linear equation, we have
Slope = 2.79 and y-intercept = 25.64
The slope tells that the rate of change of average height of boys with respect to age is 2.79 .
The y-intercept tells that the initial average height of boys =25.64 inches
If f(x) = √x + 12 and g(x) = 2√x, what is the value of (f-g)(144)?
-84
–60
0
48
we have
[tex]f(x)=\sqrt{x}+12[/tex]
[tex]g(x)=2\sqrt{x}[/tex]
we know that
[tex](f-g)(144)=f(144)-g(144)[/tex] -------> equation A
Step 1
Find the value of [tex]f(144)[/tex]
For [tex]x=144[/tex]
substitute in f(x)
[tex]f(144)=\sqrt{144}+12[/tex]
[tex]f(144)=12+12[/tex]
[tex]f(144)=24[/tex]
Step 2
Find the value of [tex]g(144)[/tex]
For [tex]x=144[/tex]
substitute in g(x)
[tex]g(144)=2\sqrt{144}[/tex]
[tex]g(144)=2(12)[/tex]
[tex]g(144)=24[/tex]
Step 3
Find [tex](f-g)(144)[/tex]
Substitute the values in the equation A
[tex]24-24=0[/tex]
therefore
the answer is the option
[tex]0[/tex]
*Need Help??!!
Which table is a probability distribution table?
Photo is attached.
Answer: Hi!
in a probability table, the x represents a given event, and p is the probability of such event.
There are two rules if you have n events; then p₁ + p₂ + ... + pₙ = 1, this is because the probability is normalized.
whit this info you can discard the third option, because there is a probability bigger than 1, and then the addition of al the probabilities is bigger than 1.
The second rule is that there do not exist negative probabilities (because they don't have sense) then you can also discard the second option.
Now we need to check the first and the fourth options, we need to add the 4 probabilites in each and see if the result is 1.
for the first options we have :
0.2 + 0.35 + 0.15 + 0.25 = 0.95
this is not normalized, this is not a probability distribution table.
for the fourth option we have:
0.4 + 0.15 + 0.25 + 0.2 = 1
this is normalized, then this is a probability distribution table.
Then the only right answer is option 4.
If cosx=4/5,cscx<0, then sin2x=
cos2x=
tan2x= ...?
Given cosx = 4/5 and cscx < 0, we can find sin2x = -24/25, cos2x = 7/25, and tan2x = -3/8 using trigonometric identities.
Explanation:To find sin2x, cos2x, and tan2x given cosx = 4/5 and cscx < 0, we can use trigonometric identities. First, let's find sinx using the Pythagorean identity: sinx = sqrt(1 - cos^2x) = sqrt(1 - (4/5)^2) = sqrt(1 - 16/25) = sqrt(9/25) = 3/5. Since cscx < 0, we know that sinx is negative. Therefore, we have sinx = -3/5.
Next, we can use the double angle identities to find sin2x, cos2x, and tan2x. The double angle identities state that sin2x = 2sinxcosx, cos2x = cos^2x - sin^2x, and tan2x = 2tanx / (1 - tan^2x).
Using the values we found earlier, we can calculate:
sin2x = 2(-3/5)(4/5) = -24/25
cos2x = (4/5)^2 - (-3/5)^2 = 16/25 - 9/25 = 7/25
tan2x = 2(-3/5) / (1 - (-3/5)^2) = -6/5 / (1 - 9/25) = -6/5 / (16/25) = -6/16 = -3/8
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The correct values for sin2x, cos2x, and tan2x given that cosx = 4/5 and cscx < 0 are as follows:
sin2x = -24/25
cos2x = 7/25
tan2x = -24/7
To find these values, we will use trigonometric identities and the given information.
First, since cosx = 4/5 and cosx is positive, we know that x must be in the first or fourth quadrant. However, because cscx < 0 (which means sinx is negative), x must be in the fourth quadrant since cscx is the reciprocal of sinx.
In the fourth quadrant, sinx is negative, so we can find sinx using the Pythagorean identity:
sin^2x + cos^2x = 1
sin^2x = 1 - cos^2x
sin^2x = 1 - (4/5)^2
sin^2x = 1 - 16/25
sin^2x = 25/25 - 16/25
sin^2x = 9/25
Since sinx is negative in the fourth quadrant, sinx = -3/5.
Now, we can use the double-angle identities to find sin2x, cos2x, and tan2x:
sin2x = 2sinxcosx
sin2x = 2 * (-3/5) * (4/5)
sin2x = -24/25
cos2x = cos^2x - sin^2x
cos2x = (4/5)^2 - (-3/5)^2
cos2x = 16/25 - 9/25
cos2x = 7/25
tan2x = sin2x/cos2x
tan2x = (-24/25) / (7/25)
tan2x = -24/7
Jose bought 750 bags of peanuts for $375.00. He intends to sell each bag for $0.15 more than he paid. How much should he charge for each bag?