In the context of the question, the Y-intercept represents the cost of the tablet that Mio purchased before counting the ongoing costs per month for internet service.
Explanation:In the context of this problem, the Y-intercept in the graph represents the cost of buying the tablet. Using the algebraic equation for a line, which is y = b + mx, the 'b' term is the Y-intercept. When x (in this case, the number of months) equals zero, y is the initial cost, which serves as our Y-intercept. This is the starting point on the Y-axis, and in the context of Mio's spending, this would be her initial expenditure which is the cost of the tablet itself.
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Marcelo played a carnival games six times he spent three tokens to play each game and he won seven tokens each time write two different expressions that can be used to find the total profit and tokens that Marcello made
Answer:
24
Step-by-step explanation:
let W represent the number of wins and let P represent the number of plays let T represent profit from each play. from the question, Marcelo played 3 times, this means 3P can represent the first equation He won 7 times, 7W can represent the second equation
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Certainly! Marcelo played the carnival games six times, spending three tokens for each game and winning seven tokens from each. To find the total profit in tokens that Marcello made, we can create two different expressions:
1. The first method involves directly calculating the net tokens won over all the games:
- We calculate the total tokens won by multiplying the number of tokens won per game (7) by the number of games played (6).
- Then we calculate the total tokens spent by multiplying the number of tokens spent per game (3) by the number of games played (6).
- Finally, we determine the total profit by subtracting the total tokens spent from the total tokens won.
Using this method, the first expression to calculate the total profit (P_1) is:
\[
P_1 = (\text{Tokens won per game} \times \text{Games played}) - (\text{Tokens spent per game} \times \text{Games played})
\]
\[
P_1 = (7 \times 6) - (3 \times 6)
\]
\[
P_1 = 42 - 18
\]
\[
P_1 = 24
\]
So, using this expression, Marcello's total profit is 24 tokens.
2. The second method is to calculate Marcello’s profit per game and then multiply that by the number of games played:
- First, we find the profit per game by subtracting the number of tokens spent per game (3) from the number of tokens won per game (7).
- Then we multiply the profit per game by the total number of games played (6) to find the total profit.
Using this method, the second expression to calculate the total profit (P_2) is:
\[
P_2 = (\text{Profit per game}) \times \text{Games played}
\]
\[
P_2 = (\text{Tokens won per game} - \text{Tokens spent per game}) \times \text{Games played}
\]
\[
P_2 = (7 - 3) \times 6
\]
\[
P_2 = 4 \times 6
\]
\[
P_2 = 24
\]
So, using the second expression, Marcello's total profit is also 24 tokens.
In both scenarios, the profit that Marcello makes from playing the six games is 24 tokens. The first expression gives us a direct calculation of the total, while the second expression calculates the profit on a per-game basis and then accumulates it.
What is the next number in this pattern? 1,7,8,15,23,38,61
Answer:
72
Step-by-step explanation:
1 then 7+1=8 8+7=15 15+8=23 23+15=38 38+23=61
Ta Da I have taught you the pattern now you can show your work just in case you have one of those teachers hope this helped
The next number in the pattern 1,7,8,15,23,38,61 is 99. The pattern can be understood by calculating the differences between consecutive numbers, and observing a pattern in these differences.
Explanation:Let's take a look at the pattern 1,7,8,15,23,38,61 closely. At every step, we're adding an increasing number to get to the next term in the sequence. From 1 to 7, we add 6. From 7 to 8, we add 1. From 8 to 15, we add 7, from 15 to 23, we add 8, from 23 to 38, we add 15 and from 38 to 61, we add 23.
The difference between these numbers (6, 1, 7, 8, 15, 23) reads as follows: 5, 6, 1, 7 and 8. So, the next difference could be 15 (continuing the pattern in the differences). So, the next term would be obtained by adding 15 to previous term's difference (23) and then adding that result to 61.
Finally, we calculate 61 + (23 + 15) = 61 + 38 = 99. So, the next number in this pattern should be 99.
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Which two operations are needed to write the expression that represents "eight more than the product of a number and twa
multiplication and subtraction
division and subtraction
multiplication and addition
division and addition
Answer:
multip[laction and addition
Step-by-step explanation:
Joe bought 5.8 pounds of
grapes to have as a snack with
his 10 friends. If he shares his
grapes evenly, how many
pounds of grapes will each of
his friends get?
Answer:6.8
Step-by-step explanation:
Answer:
0.58 pounds per friend
Step-by-step explanation:
divide 5.8 into the 10 friends.
Could these triangles be congruent?
Answer:
no, because the hypotenuses must have different lengths.
Step-by-step explanation:
Vivian does this work to find the decimal equivalent of 42/99 What does her work tell you
about the decimal equivalent?
Answer:
It is 0.42 repeated, with a line on top of the 4 and the 2.
Step-by-step explanation:
The decimal repeats when she divides into the same number twice.
Jeremy didn't pay his previous month's credit card bill in full. This month's bill shows a finance charge of $85.50. Jeremy calculates the average daily balance in the new bill to be $5,343.75 What is the monthly Pentage rate on the card?
A 1.6%
B. 1.92%
C 16%
D. 19.2%
Answer:
The monthly percentage rate would be 1.6%
Step-by-step explanation:
Given,
Finance charge = $ 85.50,
Amount of bill in this month = $ 5,343.75,
Hence, the monthly rate of percentage
[tex]=\frac{\text{Finance charge}}{\text{Amount of bill}}\times 100[/tex]
[tex]=\frac{85.5}{5343.75}\times 100[/tex]
[tex]=\frac{8550}{5343.75}[/tex]
[tex]=\frac{855000}{534375}[/tex]
= 1.6 %
i.e. OPTION A would be correct.
The monthly percentage rate on Jeremy's credit card is [tex]\[ {1.6\%} \][/tex]. So option (a) is correct.
To determine the monthly percentage rate on Jeremy's credit card, follow these steps:
Step 1: Identify the Given Values
Finance charge: $85.50
Average daily balance: $5,343.75
Step 2: Understand the Formula
The following formula is used to determine the finance charge:
[tex]\[ \text{Finance Charge} = \text{Average Daily Balance} \times \text{Monthly Percentage Rate} \][/tex]
Step 3: Set Up the Equation
Let ( r ) represent the monthly percentage rate (in decimal form).
[tex]\[ 85.50 = 5343.75 \times r \][/tex]
Step 4: Solve for the Monthly Percentage Rate
The equation should be rearranged to find ( r ):
[tex]\[ r = \frac{85.50}{5343.75} \][/tex]
Step 5: Perform the Calculation
[tex]\[ r = \frac{85.50}{5343.75} \approx 0.016 \][/tex]
Step 6: Convert the Decimal to a Percentage
[tex]\[ \text{Monthly Percentage Rate} = 0.016 \times 100 = 1.6\% \][/tex]
Therefore, the monthly percentage rate on Jeremy's credit card is:
[tex]\[ {1.6\%} \][/tex].
Factor −13 out of −13x−8.
−13x−8=
Answer:
- 13(x + [tex]\frac{8}{13}[/tex])
Step-by-step explanation:
Given
- 13x - 8 ← factor out - 13 from each term
= - 13(x + [tex]\frac{8}{13}[/tex])
The question asked to factor out -13 from the expression -13x - 8. The steps include dividing each term by -13. Therefore, the expression factored out by -13 is -13(x + 8/13).
Explanation:In this mathematical problem, we are asked to factor out -13 from the expression -13x - 8. Factoring out in algebra means to divide each term in the expression by that common factor, which in this case is -13. So, we proceed as follows:
Divide -13x by -13 to get x.Divide -8 by -13 to get 8/13.Therefore, the expression -13x - 8 factored out by -13 is -13(x + 8/13).
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Latoya's cow gives 1 1/2gallons milk each day. How much is this in quarts?
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
6 quarts
Step-by-step explanation:
1 gallon = 4 quarts
1 1/2 gallon * (4 quarts / 1 gallon) = (1 + 1/2) * 4 = 1*4 + 1/2*4 = 4 +2 = 6 quarts
Divide 2x4- 4x3 - 11x2 + 3x - 6 by x + 2
The answer would be 32/3 or 10.67
Ok, so the formula would be set up like this...
[tex]\frac{(2*4)-(4*3)-(11*2)+(3x-6)}{x+2}[/tex]
then, you can simplify the numerator into
[tex]\frac{8-12-22+3x-6}{x+2}[/tex]
srry but i am just going to assume that you are trying to find what x equals.
if you are, then read on!
so this means that [tex]\frac{8-12-22+3x-6}{x+2}=0[/tex]
now multiply (x+2) on both sides, geting [tex]8-12-22+3x-6=0[/tex]
simplify this, and you got [tex]3x-32=0[/tex] and then [tex]3x=32[/tex]
divide both sides and u got [tex]x=\frac{32}{3}=10.67[/tex]
if the stuff doesn't load, reload the screen hope this helps!
Darius wrote the number 84,273. Then he wrote a different number in which the digit 2 has 10 times the value it has in the number 84,273. Which could be the other number Jackson wrote? A 78,325 B 62,541 C 34,482 D 25,847
Answer:
option B) 62541
Step-by-step explanation:
The given number is 84273.
The number can be written as 80000+4000+200+70+3=84273.
Here in the given number, the digit 2 has value 200.
Given that, value of two in new number is ten times means, 200 x 10=2000.
thus, 2 should be at thousandth's place, which is only in 62541 in given options.
62541=60000+2000+500+40+1
while others are,
78325=70000+8000+300+20+5
34482=30000+4000+400+80+2
25874=20000+5000+800+70+4 ,
none of which has 2 at thousandth's place.
It takes Linda 40 minutes to read 10 2/3 pages of a book. What is her average reading rate in pages per minute?
Answer:
4/15 pages per minute
Step-by-step explanation:
10 2/3=32/3
(32/3)/40
(32/3)(1/40)=32/120
simplify
4/15
Answer:
4/15 pages per minute
Step-by-step explanation:
This unit rate is found as follows:
10 2/3 pages 32/3 pages
----------------------- = ----------------------
40 minutes 40/1 minutes
To divide 32/3 by 40/1, invert 40/1 and multiply instead:
32 1
------- * -------
3 40
Dividing both 32 and 40 by 8, to reduce the fractions, we get:
4 1
------- * ------- = 4/15 pages per minute
3 5
A cell phone company mistakenly advertises that their data plan costs "0.02 cents" for every kilobyte of data
The cell phone company made a error in the conversion of cents to dollars in their advertisement. They advertised the cost as 0.02 cents/kilobyte, but they probably meant $0.02/kilobyte.
Explanation:The cell phone company is advertising their data plan costs at 0.02 cents per kilobyte but it seems like they may have meant $0.02/kilobyte which is different. Understanding the difference requires Mathematics concepts such as understanding of decimals and units conversion. If we take the advertised rate of 0.02 cents/kilobyte, it means for every 1 kilobyte of data, we will only be charged 0.0002 dollars. This is very cheap compared to charging $0.02/kilobyte. The error occurred because the company did not convert cents to dollars correctly, as $1 is equal to 100 cents, not 1 cent.
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Jaquez completed 1/8 of his test in 3/5 hour. If Jaquez's rate stayed the same, how much of his test was finished in one hour. Show Work!
(A) 3/40
(B) 1/24
(C) 1/12
(D) 5/24
Answer:[tex]\dfrac{5}{24}[/tex]
Step-by-step explanation:
Let [tex]r[/tex] be the rate at which Jaquez completes his test.
Let [tex]x[/tex] part of test be completed by Jaquez in [tex]t[/tex] hours.
Then,
[tex]x=rt[/tex]
Given that Jaquez completed 1/8 of his test in 3/5 hour.
So,[tex]\frac{1}{8}=r\times \frac{3}{5}[/tex]
[tex]r=\frac{5}{24}[/tex]
To know how much he completes in one hour,substitute [tex]1[/tex] in the above equation.
So,[tex]x=r\times 1=\frac{5}{24}[/tex]
Jaquez completes [tex]\frac{5}{24}[/tex] of his test in [tex]1[/tex] hour
Answer:
Option (d)
5/24
Explanation:
Hour taken to complete 1/8 of his test=3/5 hour
Suppose r is the rate at which Jackuez completes his test
For completing the test in t hours
The equation is
y= r t
where y is the part of test which will be completed in t hour
with the information given
substituting the values
[tex]\frac{1}{8}=r \frac{3}{5}[/tex]
[tex]r=\frac{5}{24}[/tex]
now when t=1 hour
substituting the value
[tex]\mathrm{x}=\frac{5}{24} \times 1[/tex]
[tex]\mathrm{x}=\frac{5}{24}[/tex]
hence at 1 hour his test was completed [tex]\frac{5}{24}[/tex]
11 X +11 Y equals -5
Answer:
Step-by-step explanation:
11x+11y=-5
Marsha serves the Volleyball to Rhonda with an upward velocity of 14.5 ft./s. The bar is 4 feet above the ground when she strikes it. How long does Rhonda have to react, before the Volleyball hits the ground? Round your answer to two decimal places.
Answer:
The taken by Rhonda to react before volleyball hits ground is 2.39 seconds
Step-by-step explanation:
Given as :
The upward velocity of the volleyball = 14.5 ft/s
The height of the ball above ground = 4 feet
Consider value of acceleration due to gravity = 9.8 m/s
Let the time for Rhonda to react before ball hits ground = t sec
Now,
S = u t + [tex]\frac{1}{2}[/tex] a t²
where s = height
u = initial velocity , a = acceleration due to gravity , t = time in sec
So, 4 = 14.5× t + [tex]\frac{1}{2}[/tex] × 9.8 × t²
or, 4 = 14.5 t + 4.9 t²
or, 4.9 t² + 14 .5 t - 4 = 0
Now, solve for t
t = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
or, t = [tex]\frac{-14.5\pm \sqrt{14.5^{2}-4\times 4.9\times (4)}}{2\times 4.9}[/tex]
Or, t = [tex]\frac{-14.5\pm \sqrt{80.5025}}{9.8}[/tex]
Or, t = - 2.39 , - 2.76
Hence The taken by Rhonda to react before volleyball hits ground is 2.39 seconds . Answer
HELPPPPPPPPPPPPPPP RATE 5 STARSS
Answer:
13. c,
14. a.
Step-by-step explanation:
13. The length of a side PQ with coordinates of
P as (x,y) and Q as (w,z)
is: [tex]\sqrt{(x-w)^{2} +(y-z)^{2} }[/tex]
so, the length of the side AB =[tex]\sqrt{(5-5)^{2}+(-2+7)^{2} } =\sqrt{0^{2}+5^{2} } =5[/tex]
the length of side BC =[tex]\sqrt{(5-1)^{2}+(-7+2)^{2} } =\sqrt{(4)^{2}+(-5)^{2} } =\sqrt{4^{2}+5^{2} }[/tex]
the length of side AC=[tex]\sqrt{(5-1)^{2} +(-2+2)^{2} } =\sqrt{4^{2} } =4[/tex]
now, the easiest one will be when the vertices are on the coordinate axes.
so, option c will be the most appropriate one.14. If u see the figure clearly, the lines l and FH are parallel.
the parallel postulate, i.e, the alternate interior angles will always be congruent.
here, the alternate interior angles are angle1 and angle4.therefore to prove this step, he used parallel postulate as a reason.so, the correct option is "a"Which of the following is the correct factorization of the polynomial below?
x3 -12
O A. (x+3)(x-4)
O B. (x-3)(x + 4)
O C. (x+3)(x2 - 4x + 4)
O D. The polynomial is irreducible.
Answer: The polynomial is irreducible
Step-by-step explanation:
There is nothing we can subtract between x3-12
For example: you are trying to find the polynomial of x4-6
Options:
A. (x+4)(x-6)
B. (x+1+3)(x-6)
C. None the polynomial is irreducible.
You would chose C because there is no subtraction sign in between the parentheses. If you would choose a right answer, you would rewrite it as:
(x+4)-(6)
The range of which function is (2, infinity)? y = 2x y = 2(5x) y = 5x +2 y = 5x + 2
Answer:
I think your functions are [tex]y=2^{x}[/tex] ,[tex]y=2*5^{x}[/tex] and [tex]y=2+5^{x}[/tex]
If yes then then the third function which is [tex]y=2+5^{x}[/tex].
Step-by-step explanation:
The function [tex]c^{x}[/tex] where c is a constant has
Domain : [tex]c\geq 0[/tex]
Range : ( 0 , ∞ )
The above range is irrespective of the value of c.
I have attached the graph of each of the function, you can look at it for visualization.
[tex]y=2^{x}[/tex] ⇒ This function is same as [tex]c^{x}[/tex] so its range is ( 0 , ∞ ).[tex]y=2*5^{x}[/tex] ⇒ If we double each value of the function [tex]y=5^{x}[/tex], which has range ( 0 , ∞ ), but still the value of extremes won't change as 0*2=0 and ∞*2=∞. Therefore the range remains as ( 0 , ∞ ).[tex]y=2+5^{x}[/tex] ⇒ If we add 2 to each value of the function [tex]y=5^{x}[/tex], which has range ( 0 , ∞ ), the lower limit will change as 0+2=2 but the upper limit will be same as ∞. Therefore the range will become as ( 2 , ∞ ).Answer:
y = 5∧× + 2
Step-by-step explanation:
A cylindrical can is to hold 20[tex]\pi[/tex] cubic meters. the material for the top and bottom costs $10 per square meter, and material for the side costs $8 per square meter. fond the radius r and the height h of the most economical can i.e. such that the cost is minimal
Answer:
The cost of the can is minimal when r=2 m and h=5 m
Step-by-step explanation:
This is an optimization problem which will be solved by the use of derivatives
We must find an expression for the total cost of the cylindrical can and then find its dimensions to make the cost minimal
Let's picture a cylinder of radius r and height h. Its volume is computed as
[tex]V=\pi r^2h[/tex]
To make the lids we need two circle-shaped pieces of a material which costs $10 per square meter
The area of each lid is
[tex]A_l=\pi r^2[/tex]
The cost of both lids will be
[tex]C_l=(2)(10)(\pi r^2)=20\pi r^2[/tex]
The lateral side of the cylinder can be constructed with a rectangle of material which costs $8 per square meter
The rectangle has a height of h and a width equal to the length of the circumference
[tex]A_s=2\pi rh[/tex]
The cost of the side of the cylinder will be
[tex]C_s=16\pi rh[/tex]
The total cost of the can is
[tex]C=20\pi r^2+16\pi rh[/tex]
We know the volume of the can is [tex]20\pi[/tex] cubic meters
[tex]V=\pi r^2h=20\pi[/tex]
Isolating h we have
[tex]h=\frac{20}{r^2}[/tex]
Using this value into the total cost
[tex]C=20\pi r^2+16\pi r(\frac{20}{r^2})[/tex]
[tex]C=20\pi r^2+\frac{320\pi}{r}[/tex]
Differentiating with respect to r
[tex]C'=40\pi r-\frac{320\pi}{r^2}[/tex]
To find the critical point, we must set C'=0
[tex]40\pi r-\frac{320\pi}{r^2}=0[/tex]
Operating
[tex]40\pi r^3-320\pi=0[/tex]
Solving for r
[tex]r=\sqrt[3]{\frac{320\pi}{40\pi}}=\sqrt[3]{8}[/tex]
r=2
And since
[tex]h=\frac{20}{r^2}=\frac{20}{2^2}[/tex]
h=5
Differentiating again we find
[tex]C''=40\pi +\frac{640\pi}{r^3}[/tex]
Which is always positive for r positive. It makes the critical point found a minimum
The cost of the can is minimal when r=2 m and h=5 m
Rome was able to gain its empire in large part by extending some form of citizenship to many of the people it conquered. Military expansion drove economic development, bringing enslaved people and loot back to Rome, which in turn transformed the city of Rome and Roman culture.
Answer:
is this a question or a passage
Answer:
very confused, are you trying to inform us?
Step-by-step explanation:
A metalworker has a metal alloy that is 30% copper and another alloy that is 55% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 50% copper alloy? The metal worker should use (blank) kilograms of the metal alloy that is 30% copper and (blank) kilograms of the metal alloy that is 55% copper. (show your work)
Answer:
20kg
Step-by-step explanation:
eanyone know??? get it correct u get 50 points
Answer:
J would be the answer, my friend.
log2 (24/3) = log5 (x)
log(8)/log(2) = log(x)/log(5)
log(x) = [log(5)][3]
log(x) = log(5^3)
x = 5^3 = 125
Step-by-step explanation:
Answer:
x = 125
Step-by-step explanation:
[tex] \log_2 24 - \log_2 3 = \log_5 x [/tex]
Use the rule of subtracting logs:
[tex] \log_b x - \log_b y = \log_b \dfrac{x}{y} [/tex]
[tex] \log_2 \dfrac{24}{3} = \log_5 x [/tex]
[tex] \log_2 8 = \log_5 x [/tex]
[tex] 3 = \log_5 x [/tex]
Use the definition of log:
[tex] \log_b x = y ~~\Longleftrightarrow ~~ b^y = x [/tex]
[tex] x = 5^3 [/tex]
[tex] x = 125 [/tex]
What fraction of an hour is 2 minutes
Answer:
Step-by-step explanation:
hour 60 min 2
min of a hour is 60/2
Answer:
[tex]\frac{1}{30}[/tex]
Step-by-step explanation:
There are 60 minutes in 1 hour thus as a fraction
= [tex]\frac{2}{60}[/tex] ← divide numerator/ denominator by 2
= [tex]\frac{1}{30}[/tex]
What is the value of x if e3x+6=8
To solve the equation e3x+6 = 8 for 'x', first take the natural logarithm of both sides (3x + 6 = ln(8)) to isolate 'x', resulting in x = (ln(8) - 6) / 3. If calculated, the approximate answer is x ≈ -0.307.
Explanation:This question pertains to solving for unknown variable 'x' in an exponential equation. The equation provided is e3x+6 = 8. In solving for 'x', you must first rearrange the equation by taking the natural logarithm (ln) of both sides. This is because the inverse operation for the base of natural logarithm 'e' is natural logarithm 'ln'. Thus, you get 3x + 6 = ln(8). Afterwards, you subtract 6 from both sides and divide by 3 to get x = (ln(8) - 6) / 3. The numerical solution for this can be calculated with a scientific calculator, which yields x as roughly -0.307.
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Which equation has infinitely many solutions?
A. 12 + 4x = 6x + 10 – 2x
B. 5x + 14 – 4x = 23 + x – 9
C. x + 9 – 0.8x = 5.2x + 17 – 8
D. 4x – 2x = 20
An equation has infinitely many solutions if it can be manipulated all the way to an identity (i.e. an equality where the right and left hand side are the same). We have:
A) [tex]12+4x=6x+10-2x \iff 12+4x=10+4x \iff 12=10[/tex]
which is impossible
B) [tex]5x+14-4x=23+x-9 \iff x+14 = x+14[/tex]
which is an equality
C) [tex]x+9-0.8x=5.2x+17-8\iff 0.2x+9=5.2x+9 \iff 0.2x=5.2x\iff x=0[/tex]
which has a unique solution
D) [tex]4x-2x=20 \iff 2x=20 \iff x=10[/tex]
which has a unique solution
From 10 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many different committees are possible?
Answer:
Number of committees that are possible =210
Step-by-step explanation:
Total names in ballot = 10
Total members to be elected for the committee = 4
So, we need the number of different ways in which 4 names out of 10 can be elected for the committee.
To find the number of ways in which the committee can be elected, we use the combinations which is given as
[tex]aCb=\frac{a!}{(a-b)!b!}[/tex]
where [tex]a[/tex] represents total number of members and [tex]b[/tex] represents total number of members to be elected.
So, [tex]10C4=\frac{10!}{(10-4)!4!}[/tex]
[tex]10C4=\frac{10!}{6!4!}[/tex]
[tex]10C4=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{6\times5\times4\times3\times2\times1\times4\times3\times2\times1}[/tex]
[tex]10C4=\frac{10\times9\times8\times7}{4\times3\times2\times1}[/tex] [Canceling the common numbers]
[tex]10C4=210[/tex]
∴ Number of committees that are possible =210
Using the combinations formula, we will see that 210 different committees are possible.
How many different committees are possible?
Here we need to use the combinations function. It says that for a set of N elements, the number of different subsets of K elements (such that K is equal or smaller than N) that we can make is:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
In this case, we have N = 10 and K = 4, replacing that we will get:
[tex]N(10, 4) = \frac{10!}{(10 - 4)!*4!} = \frac{10!}{6!*4!} = \frac{10*9*8*7}{4*3*2} = 210[/tex]
This means that from 10 names, there are 210 different committees of 4 members that can be made.
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Apply the distributive property to create an equivalent expression.
(m−3+4n)⋅(−8)
Answer:
-8m + 24 - 32nStep-by-step explanation:
The distributive property:
[tex]a(b+c)=ab+ac[/tex]
[tex](m-3+4n)(-8)=(m)(-8)+(-3)(-8)+(4n)(-8)\\\\=-8m+24-32n[/tex]
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Answer:
Point S
ST
Step-by-step explanation:
Answer:
[tex]\boxed{\sf point \ S}[/tex]
Step-by-step explanation:
Line QS and ST intersect at one point, the intersection is point S.
A television and DVD player cost a total of $1192 . The cost of the television is three times the cost of the DVD player. Find the cost of each item.
The cost of the television is $894, and the cost of the DVD player is $298.
Let's denote the cost of the DVD player as x dollars.
Since the cost of the television is three times the cost of the DVD player, we can express the cost of the television as 3x dollars.
According to the given information, the total cost of both items is $1192. Therefore, we can set up the following equation:
[tex]\[ x + 3x = 1192 \]Now, let's solve for \(x\):\[ 4x = 1192 \]\[ x = \frac{1192}{4} \]\[ x = 298 \][/tex]
Now that we have found the cost of the DVD player [tex](\(x = 298\) dollars)[/tex], we can find the cost of the television, which is three times the cost of the DVD player:
[tex]\[ \text{Cost of television} = 3 \times 298 = 894 \][/tex]