Answer:
The solved given equation
[tex](\frac{x+2}{5})+(\frac{x+1}{3})=(\frac{x-3}{10})-2[/tex] is x=-7
Step-by-step explanation:
Given equation is [tex](\frac{x+2}{5})+(\frac{x+1}{3})=(\frac{x-3}{10})-2[/tex]
To solve the given equation as below :
[tex](\frac{x+2}{5})+(\frac{x+1}{3})=(\frac{x-3}{10})-2[/tex] ( by using the distributive property )
[tex]\frac{3x+6+5x+5}{15}=\frac{x-3-20}{10}[/tex] ( adding the like terms )
[tex]\frac{8x+11}{15}=\frac{x-23}{10}[/tex]
Multiply into (10(15) on both sides we get
[tex]\frac{8x+11}{15}\times (10)(15)=\frac{x-23}{10}\times (10)(15)[/tex]
[tex](8x+11)\times (10)=(x-23)\times (15)[/tex] ( by using the distributive property )
[tex]80x+110-15x+345=0[/tex] ( adding the like terms )
[tex]65x+455=0[/tex]
[tex]65x=-455[/tex]
[tex]x=-\frac{455}{65}[/tex]
Therefore x=-7
Therefore the solved given equation is x=-7
Jane has rolled a fair die 7 times and each time has gotten a 3. She says that the probability that she will get a 3 on the next roll is high (close to 1). Is she correct?
A) No, the probability of getting a 3 on a fair die does not change. It will always be 1/6
no matter what she got on the previous roll.
B) Yes, since she has gotten a 3 on the last 7 rolls, the probability of getting a 3 is higher on the next roll.
C) No, the probability of getting a 3 will be slightly higher than any other number but not close to 1.
D) There is no way to tell until she rolls the die. You cannot accurately predict what she will get.
A) No, the probability of getting a 3 on a fair die does not change. It will always be 1/6 no matter what she got on the previous roll.
Step-by-step explanation:
Lets define probability first
"Probability is the likeliness of occurrence of an event"
When we call a die fair, that means that each number on the die has an equal chance of occurrence when rolled.
If on 7 rolls, the outcomes were 7 each time, this doesn't mean that the chances of rolling a specific number on a fair die is changed. On the next roll, 3 will have the same probability as before that is 1/6
So,
The correct answer is:
A) No, the probability of getting a 3 on a fair die does not change. It will always be 1/6 no matter what she got on the previous roll.
Keywords: Probability, die roll
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Multiply.
35⋅34
A. 920
B.410
C. 45
D. 54
Answer: 1190
None of these answer choices are correct I showed my work on paper.
Answer:
it seems that you meant to use fractions. as a K12 student the answer is 9/20. Hope that helps!
8. (5 + 4 - 2) * (-2) = ?
A. -14
B.-22
O c. 14
D. 22
Answer: A. -14
Step-by-step explanation:
Answer: A. -14
Step-by-step explanation: Use PEMDAS
(5+4-2) x (-2)
= (9-2) x (-2)
= 7 x (-2)
= -14
What is the point slope equation of line that passes through the point (2,-3) and has the same y intercept as y =5×+2
Answer:
y + 3 = (-5/2)(x - 2)
Step-by-step explanation:
First look at y =5x + 2. It's immediately apparent that the y-intercept is 2, or (0, 2). (0, 2) must then be a point on the new line, and we are told that (2, -3) is also on this new line.
The general point-slope equation is y - k = m(x - h).
We need to determine the slope of the new line.
Let h = 2, k = -3, x = 0 and y = 2. Then:
2 + 3 = m(0 - 2). Therefore, -2m = 5, and m = -5/2.
Then the equation of the new line, in point-slope form, is
y + 3 = (-5/2)(x - 2)
Let's check this result. Do the coordinates of the y-intercept, (0, 2) satisfy this equation?
Is 2 + 3 = (-5/2)(0 - 2) true?
Is 5 = (-5/2)(-2) true? YES
The equation of line is 2y = -5x+ 4.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. The slope of the line is the ratio of the rise to the run, or the rise divided by the run, therefore the change in y coordinate with regard to the change in x coordinate may be expressed as follows
m = Δy/Δx
where, m is the slope
In the coordinate plane, it describes the slope of the line.
Given:
passes through the point (2,-3) and has the same y intercept as y =5×+2
The, the intercept for the required line is 2.
Now, using y= mx+b
-3 = m(2) + 2
2m = -5
m= -5/2
Now, the equation of line passes through (2, -3)
y - y1 = m(x- x1)
y + 3= -5/2( x-2)
2y + 6= -5x+ 10
2y = -5x+ 4
Hence, the equation of line is 2y = -5x+ 4.
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What are the coordinates of point A?
Answer:
by definition
The coordinates of point A are:
(cosθ , sinθ)
Which answer best describes the system of
equations shown in the graph?
6x + 4y = 2
3x + 2y = 1
consistent and independent
inconsistent
consistent and dependent
not enough information
Answer:
Step-by-step explanation:
6x + 4y = 2 3x + 2y = 1
4y = -6x + 2 2y = -3x + 1
y = - 3/2x + 1/2 y = -3/2x + 1/2
same line, infinite solutions.....Consistent and dependent
Answer:
Consistent and dependent
Step-by-step explanation:
Allie measured a house and its lot and made a scale drawing. She used the scale 9 inches = 5 feet. What scale factor does the drawing use
Answer:
Therefore the scale used is 1 inch : 6.667 inches
Step-by-step explanation:
i) Scale used is 9 inches = 5 feet
ii) Scale used 9 inches = 5 [tex]\times[/tex] 12 inches = 60 inches
iii) Scale used is 1 inch [tex]= \dfrac{60}{9}\hspace{0.2cm} = \hspace{0.2cm}\dfrac{20}{3} \hspace{0.2cm} = 6.667\hspace{0.2cm} inches[/tex]
iv) Therefore the scale used is 1 inch : 6.667 inches
There are 6 red marbles, 8 blue marbles, and 11 green marbles in a bag. What is the probability that you
will randomly draw either a red or a blue marble?
24%
56%
O 32%
o
10%
NEXT QUESTION
ASK FOR HELP
TURN IT IN
TERMS OF USE
Answer:
14/25
Step-by-step explanation:
p(red or blue)=6/(6+8+11) +8/(6+8+11)=6/25+8/25=14/25
Answer:
56% yall
Step-by-step explanation:
A dog weighs 40 pounds and the veterinarian thinks it needs to lose 9 pounds Mikala wrote the equation x + 9 = 40 to represent this situation Kirk wrote the equation 40-x=9 which equation is correct? Enter another equation that represents the situation
Answer:
Both equations are correct because the veterinarian recommended that the weight the dog should have is 31 pounds. Another equation that represent the situation is:
31 = x
Step-by-step explanation:
Let's analyze the equation written by Mikala:
x + 9 = 40
x = 40 - 9
x = 31
Now, let's solve for x the equation written by Kirk:
40 - x = 9
- x = 9 - 40
- x = -31
x = 31
Both equations are correct because the veterinarian recommended that the weight the dog should have is 31 pounds. Another equation that represent the situation is:
40 - 9 = x
31 = x
A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first the tax and the first city was 6% and the tax and the second city was 10% total hotel tax paid for two cities with $670 how much was the hotel charge in each city before tax
Answer:
The hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.
Step-by-step explanation:
Given:
A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.
The tax of the first city was 6% and the tax of the second city was 10%.
Total hotel tax paid for two cities with $670.
Now, to find the hotel charge in each city before tax.
Let the hotel charge in first city before tax be [tex]x.[/tex]
And the hotel charge in second city before tax be [tex]y.[/tex]
So, as the hotel charge of the second city was 1500 higher than the first.
Thus,
[tex]y=x-1500[/tex] ........(1)
And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.
6% of [tex]x[/tex] + 10% of [tex]y[/tex] = $670.
[tex]\frac{6x}{100} +\frac{10y}{100} =670[/tex]
[tex]0.06x+0.10y=670[/tex]
Substituting the value of [tex]y[/tex] from equation (1) we get:
[tex]0.06x+0.10(x-1500)=670[/tex]
[tex]0.06x+0.10x-150=670[/tex]
[tex]0.16x-150=670[/tex]
Adding both sides by 150 we get:
[tex]0.16x=820[/tex]
Dividing both sides by 0.16 we get:
[tex]x=5125.[/tex]
The hotel charge in first city before tax = $5125.
Now, substituting the value of [tex]x[/tex] in equation (1) we get:
[tex]y=x-1500[/tex]
[tex]y=5125-1500[/tex]
[tex]y=3625.[/tex]
The hotel charge in second city before tax = $3625.
Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.
Order 3/50 4/52 7/99 11/120 17/333 least you greatest
Answer:
Step-by-step explanation:
17/333 11/120 7/99 4/52 3/50
Simplify -5/1 the slope
Answer:
Step-by-step explanation:
The only possible simplification of the slope -5/1 is -5.
Given a grid with 15 sections, determine how many sections in the grid need to be shaded so the probability of a point chosen at random in the shaded area is exactly 0.8. Explain your reasoning
Answer:
12
Step-by-step explanation:
0.8 is equal to 80%
you need to figure out 80% of 15
100% = 15
10% = 1.5
(x8)
80% = 12
you would need to shade 12 out of 15 boxes which gives 0.8 chance of picking a shaded one
Answer:
Sample answer: The number of squares that are shaded divided by 15 must equal 0.8, so the number of squares must be 0.8(15), which equals 12. The fraction 12/15 reduces to 4/5 which is equal to 8/10.
Step-by-step explanation:
The sample answer on edge
x - 3(2x - 7) = 76
Help!
Answer:
To solve this equation your goal is to get x by itself
First we need to distribute the 3 through the (2x-7)
x-6x+21=76 (-3*2x=-6x, -7*-3=21)
Your next step is to combine like terms
-5x+21=76 (x-6x=-5x)
Next subtract 21 from both sides
-5x=55 (21-21=0, 76-21=55)
Last you need to divide both sides by -5
x=-11 (-5/-5=1, 55/-5=-11)
x=-11
Hope this helps ;)
The solution to the given equation x - 3(2x - 7) = 76 is x = -11.
The equation is given as follows:
x - 3(2x - 7) = 76
First, distribute the 3 to the terms inside the parentheses:
x - 6x + 21 = 76
Combine like terms:
-5x + 21 = 76
Subtract 21 from both sides:
-5x = 76 - 21
-5x = 55
Divide both sides by -5 to solve for x:
x = 55 / -5
x = -11
Therefore, the solution to the given equation x - 3(2x - 7) = 76 is x = -11.
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The complete question is as follows:
Solve the below equation.
x - 3(2x - 7) = 76
Halfway through a cross-country meet, a runner’s speed is 4 m/s. In the
last stretch, she increases her speed to 7 m/s. What is her change in
speed?
Answer:
The change in her speed is 7 m/s - 4 m/s = 3 m/s.
Step-by-step explanation:
Speed is defined as the rate of change of distance with time.
i) Let the total distance of the cross country be x meters.
ii) The change in her speed is 7 m/s - 4 m/s = 3 m/s.
Karyn cuts a length of ribbon into 4 equal pieces each 1 1/4 feet long. How long is the ribbon
Answer:
5 feet long
Plz give brainliest
The graphed line shown below is y = 5x-10.
Which equation, when graphed with the given equation, will form a system that has no solution?
y = -5x+10
y = 5 (x + 2)
y = 5 (x-2)
y = -5x - 10
Answer:
y = 5x - 10 and y = 5(x + 2) are the system of equations that has no solution.
Step-by-step explanation:
The slope-intercept form of a straight line equation is given by, y = mx + c, where m is the slope and c is the y-intercept.
Now, only a system of parallel straight lines has no solution.
And the parallel straight lines have an equal slope and different y-intercept.
Hence, the given equation, y = 5x - 10 has slope equals to 5 and y-intercept - 10.
And the lines given in the options, only the second line i.e. y = 5(x + 2) has the same slope i.e. 5 and different y-intercept i.e. 10 ≠ - 10.
So, y = 5x - 10 and y = 5(x + 2) are the system of equations that has no solution. (Answer)
Answer:
B: y=5(x+2)
Step-by-step explanation:
Consider circle c with angle 3/4 radians. If minor arc AB measures 9n inches, what is the length of
the radius of circle C? If necessary, round your answer to
the nearest inch.
6 inches
12 inches
18 inches
24 inches
The radius of circle is 12 inches
Solution:
Given that,
Consider circle c with angle [tex]\frac{3 \pi }{4} \text{ radians }[/tex]
Minor arc AB measures [tex]9 \pi[/tex] inches
Therefore, we can say,
[tex]Central\ angle\ in\ radians = \frac{3 \pi }{4}\\\\Arc\ length = 9 \pi[/tex]
To find: Radius of circle
The length of arc when angle given in radians is:
[tex]s = r \times \theta[/tex]
Where,
"s" is the arc length and "r" is the radius and [tex]\theta[/tex] is the central angle in radians
[tex]9 \pi = r \times \frac{3 \pi }{4}\\\\r = 9 \times \frac{4}{3}\\\\r = 12[/tex]
Thus the radius of circle is 12 inches
Answer:
B.) 12 inches
Step-by-step explanation:
Whats the value of 3x+4y-10 when x=3 and y=2
First person to answer will get the brainliest
Answer:
7
Explanation:
(3)(3)+(4)(2) − 10
(3)(3)
= 9
(4)(2)
= 8
9 + 8 = 17
17 - 10 = 7
Answer:
7
Step-by-step explanation:
3(3)+4(2)-10
9+8-10
17-10
7
An account was overdrawn. The status of his account was -$248. He did not realize the problem and wrote another check for $73. The bank charged him $15. What was the new status of the account?
Answer:
-$336.00
Step-by-step explanation:
-$248.00+-$73.00+-$15.00=-$336.00
Wanda started walking along a path 27 seconds before Dave. Wanda walked at a constant rate of 3 feet per second. Face walked along the same path at a constant rate of 4.5 feet per second. Graph the system of linear equations. How long after Dave starts walking will he catch up with Wanda
Answer:
54
Step-by-step explanation:
4.5x=3(x+27)
4.5x=3x+81
1.5x=81
x=54
What does 23/2 reduce down to in its simplest form?
To simplify this improper fraction we can turn it into a mixed number. The fact that the denominator is 2 and the numerator isn't divisible by 2 shows that it can't simplified any further as a improper fraction.
23/2 = 11 1/2
Best of Luck!
Write the slope -intercept form of an equation of the line that passes through the given point and is parallel to the graph of the equation.
5,-5,3x+y=-2
A. y=10x+3
B. y=-3x+10
C. y=1/3x-10
D. y=-3x-10
Answer:
The equation of the required line in the slope-intercept form is
y = -3x + 10
Step-by-step explanation:
i) the required line passes through the point (5, -5)
ii) the required line is also parallel to the line 3x + y = -2 ⇒ y = -3x - 2
Therefore the slope of the given line is -3.
Therefore the slope of the required line is also -3
The equation of the required line in the slope-intercept form is
y - (-5) = -3(x - 5) ⇒ y + 5 = -3x + 15 ⇒ y = -3x + 10 ∴ 3x + y = 10.
help quick pls 20 points
Answer:
your answer is 70
Step-by-step explanation:
Show me how you got Christmas paper that was 8 feet long and 8 ft wide and the perimeter is 32 how
Answer:
The Proof is below.
Therefore the Perimeter of Christmas paper is 32 feet ..Proved
Step-by-step explanation:
Let the Christmas Paper have Dimensions as
Length = 8 feet
Width = 8 feet
To Show:
Perimeter of Christmas Paper = 32
Solution:
Christmas Paper is in Rectangle Shape,
Therefore Perimeter of a Rectangle is given as
[tex]Perimeter\ of\ Rectangle=2(Length+Width)[/tex]
Substituting the values we get
[tex]Perimeter=2(8+8)=2\times 16=32\ feet[/tex]
Therefore the Perimeter of Christmas paper is 32 feet ..Proved
The perimeter of a square is calculated by adding the lengths of all four sides. An 8 ft by 8 ft square has a perimeter of 32 ft, because 8 ft multiplied by 4 (the number of sides in a square) equals 32 ft.
Explanation:This question involves understanding the concept of perimeter in the context of a square. If you have a piece of Christmas paper that is 8 feet long and 8 feet wide, you actually have a square because all sides are of equal length. To calculate the perimeter of a square, you simply add up the lengths of all four sides.
Since each side is 8 feet, the perimeter P is given by:
P = side + side + side + side
P = 8 ft + 8 ft + 8 ft + 8 ft
P = 32 ft
So, the perimeter of the Christmas paper, if shaped like a square, is 32 feet, which is simply four times the length of one side.
If
f
(
x
)
=
x
6
+
3
x
−
1
f(x)=x
6
+3x−1, then what is the remainder when
f
(
x
)
f(x) is divided by
x
+
1
x+1?
One light-year equals 5.9 x 1012 miles. How many light-years are in 6.79
1016 miles?
O
O
A. 8,689 light-years
B. 11,508 light-years
O
C. 1,151 light-years
O
D. 1.15 light-years
Option B
The number of light years in [tex]6.79 \times 10^{16}[/tex] miles is 11508 light years
Solution:
Given that,
One light-year equals 5.9 x 10^12 miles
Therefore,
[tex]1 \text{ light year } = 5.9 \times 10^{12} \text{ miles }[/tex]
To find: Number of light years in [tex]6.79 \times 10^{16}[/tex] miles
Let "x" be the number of light years in [tex]6.79 \times 10^{16}[/tex] miles
Then number of light years in [tex]6.79 \times 10^{16}[/tex] miles can be found by dividing [tex]6.79 \times 10^{16}[/tex] miles by miles in 1 light year
[tex]\text{Number of light years in } 6.79 \times 10^{16} miles = \frac{6.79 \times 10^{16}}{5.9 \times 10^{12}}\\\\\text{Use the law of exponent }\\\\\frac{a^m}{a^n} = a^{m-n}\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = \frac{6.79}{5.9} \times 10^{16-12}\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = 1.1508 \times 10^4\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = 11508[/tex]
Thus number of light years in [tex]6.79 \times 10^{16}[/tex] miles is 11508 light years
apply the distributive property to Factor out the greatest common factor of 75+20
Final answer:
The greatest common factor of 75 and 20 is 5, and by applying the distributive property, the expression 75+20 can be factored as 5(19).
Explanation:
The greatest common factor (GCD) of 75 and 20 is 5. Applying the distributive property to factor out 5, we get:
75 + 20 = 5 × (15 + 4)
Here's the breakdown:
Find the GCD: The largest factor that divides both 75 and 20 is 5.
Divide each term by the GCD: Divide 75 by 5 to get 15 and divide 20 by 5 to get 4.
Rewrite with the GCD factored out: Combine the results from step 2 and multiply by the GCD: 5 × (15 + 4).
Therefore, the factored expression using the distributive property is 5 × (15 + 4).
Thus, the factored form of the expression 75+20 is 5(19).
The following chart shows a store's records of sales of stuffed toys over two months.
September
October
Teddy Bears
Teddy Bears
346
Rabbits
que
Cats
Cats
245
Horses
Other
199
Other
If the trend shown in these graphs stays constant, what percent of the market will teddy bears occupy in November? (Round
your answer to the nearest tenth.)
a. 24.8%
b. 23.4%
C. 22.5%
d. 20.7%
The percent of the market will teddy bears occupy in November is 28.47%.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Form a table as shown
Months Teddy Bears Rabbits Cats Horses Others Totals toys
September 225 275 245 260 199 1204
October 346 308 186 297 285 1422
November 467 341 127 334 371 1640
So, the percent of the market will teddy bears occupy in November
= 467 / 1640 x 100
= 0.2847 x 100
= 28.47%
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An investment advisor invested &14,000 in tow accounts. One investment earned 8% annual simple interest. And the other 6.5% annual simple interest. The amount of interest earned for 1 year was $1,027 how much was invested
Answer:
Investor invested $7,800 at 8% and $6,200 at 6.5%
Step-by-step explanation:
Use formula
[tex]I=P\cdot r\cdot t,[/tex]
where
I = interest
P = principal
r = rate (as decimal)
t = time
First investment:
[tex]P_1=x\\ \\r_1=0.08\\ \\t_1=1[/tex]
then
[tex]I_1=x\cdot 0.08\cdot 1\\ \\I_1=0.08x[/tex]
Second investment:
[tex]P_2=14,000-x\\ \\r_2=0.065\\ \\t_2=1[/tex]
then
[tex]I_2=(14,000-x)\cdot 0.065\cdot 1\\ \\I_2=0.065(14,000-x)[/tex]
The amount of interest earned for 1 year was $1,027, then
[tex]I_1+I_2=1,027\\ \\0.08x+0.065(14,000-x)=1,027\\ \\0.08x+910-0.065x=1,027\\ \\0.08x-0.065x=1,027-910\\ \\0.015x=117\\ \\x=7,800\\ \\14,000-x=6,200[/tex]
Investor invested $7,800 at 8% and $6,200 at 6.5%