Using a system of equations, it is found that Allison bought 2 bottles of juice and 9 bottles of soda.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are:
Variable x: bottles of juice purchased.Variable y: bottles of soda purchased.Allison purchased a total of 11 bottles of juice, hence:
x + y = 11 -> x = 11 - y.
These 11 bottles contain 445 grams of sugar, hence, considering the amounts of each bottle, we have that:
20x + 45y = 445
Since x = 11 - y:
20(11 - y) + 45y = 445
25y = 225
y = 225/25
y = 9.
x = 11 - y = 11 - 9 = 2.
She bought 2 bottles of juice and 9 bottles of soda.
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30% of 70 is what percent of 2000?
Answer:
1.05
Step-by-step explanation:
Because 30% of 70 is [tex]30\% \times 70 = \frac{30}{100} \times 70 = 0.3 \times 70 = 21[/tex], so the question becomes "21 is what percent of 2000?"
To answer this, we can solve for [tex]x[/tex] in the equation [tex]21 = x\% \times 2000[/tex], which is:
[tex]21 = x\% \times 2000\\21 = \frac{x}{100} \times 2000\\21 = 20x\\x=\frac{21}{20}=1.05[/tex]
So the answer is 1.05 percent.
If 55 people enrolled in a psychology course but only 25 completed it, what percent of the students completed the course? (Round to the nearest tenth of a percent.)
Answer:
45%
Step-by-step explanation:
Simply, 25/55 which gives you 0.454545.
Convert that to a percentage and you get 45%
the confidence interval for the population variance is
(730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15. This can be obtained by using formula for confidence interval and using statistical table for values.
Find the confidence interval for population variance:The formula for finding the confidence interval for population variance is:
[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]
where n is the size of the sample, (n - 1) is the degrees of freedom, s is the standard deviation, α is the significance level.
Here it is given that,
confidence level = 1 - α = 0.98 significance level = α = 0.02standard deviation = 39 sample size n = 15degrees of freedom (n - 1) = 15 - 1 = 14α/2 = 0.02/2 = 0.01
1 - α/2 = 1 - 0.01 = 0.99
For (n - 1) degrees of freedom,
[tex]\chi^{2}_{\frac{\alpha}{2} }[/tex] = 29.141 , and [tex]\chi^{2}_{1-\frac{\alpha}{2} }[/tex] = 4.660 (Using statistical table)
Using the formula we get,
[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]
[tex]\frac{(14)39^{2} }{29.141} < \sigma^{2} < \frac{(14)39^{2} }{4.660}[/tex]
[tex]730.72 < \sigma^{2} < 4569.53[/tex]
The confidence interval for the population variance is (730.72, 4569.53)
Hence (730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15.
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Knowing the first day Anna and Tamara stop for sightseeing and lost 2 hours of travel time and the second day, they gain 1 hour because they did not stop for lunch, write an algebraic expression that represents how many hours Anna and Tamara traveled the first two days. Let x be the number of hours driven.
The algebraic expression that represents the number of hours Anna and Tamara traveled the first two days is (2x - 1) hours.
How to write Algebraic Word Problems?
We are told that;
On the first day, Anna and Tamara stop for sightseeing and lost 2 hours of travel time.
On the second day, they did not stop for lunch and gained 1 hour.
Now, we are told that x is the number of hours driven per day. Thus, for two days, number of hours driven is expressed as 2x.
Now, since they lost 2 hours on the first day, then total hours travelled is;
2x - 2 hours
On the second day, they gained 1 hour. Thus;
Final total number of hours traveled = 2x - 2 + 1
Final total number of hours traveled = (2x - 1) hours
Thus, we can conclude that the algebraic expression that represents how many hours Anna and Tamara traveled the first two days is (2x - 1) hours.
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50% prefferd fruit cake 1/5 preferred spong and the remainder preferred cheesecake
What percent like cheesecake?
The percentage of people who preferred cheesecake if 50% prefferd fruit cake 1/5 preferred sponge is 40%.
PercentageTotal percentage = 100%Fruit cake = 50%Percentage remaining = 100% - 50%
= 50%
Sponge cake = 1/5
Percentage of sponge cake = 1/5 × 50%
= 1/5 × 0.5
= 10%
Percent that likes cheesecake = Total - (fruits cake + sponge cake)
= 100% - (50% + 10%)
= 100% - (60%)
= 40%
Therefore, the percentage of people who preferred cheesecake if 50% prefferd fruit cake 1/5 preferred sponge is 40%.
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Use the coordinate grid to determine the coordinates of point A:
Coordinate grid shown from negative 2 to positive 2 on x axis and negative 2 to positive 2 on y axis. There are increments of 1 over 4 for each grid line on each of the two axes. Only the whole numbers are labeled on either side of the axis. A point A is shown at the intersection of 5 grid lines to the left of the y-axis and 3 grid lines above the x-axis.
What are the coordinates of point A?
( fraction negative 1 and 1 over 4, fraction 3 over 4)
( fraction 1 and 1 over 4, fraction negative 3 over 4)
( fraction negative 3 over 4, fraction 1 and 1 over 4)
( fraction 3 over 4, fraction negative 1 and 1 over 4)
Based on the given coordinate grid, and the increment for each grid line, the coordinates of point A is ( fraction negative 1 and 1 over 4, fraction 3 over 4) or (-1¹/₄, ³/₄).
What are point A's coordinates?
The x-value of point A is said to be 5 grid lines to the left of y-axis. This means that the x value will be negative.
The increments are 1/4 so the x-value is:
= -1/4 x 5
= -1¹/₄
The y-value is given by the 3 grid lines above the x-axis which means that this value is positive:
= 1/4 x 3
= 3 /4
The coordinates of A are:
(-1¹/₄, ³/₄)
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At the beginning of this year, you went out and purchased $300 worth of gold coins. Every 3 months for the next 8 years, you purchase an additional $300 worth of coins. At the end of the first 3 years, the price of gold starts to come back down, and when you decide to cash out, your coins are only worth what you paid for them. What is the value of your account now?
Answer:
9900
Step-by-step explanation:
You start with 300, and add 300 32 times (once for every 3 months in 8 years).
[tex]300+9600=9900[/tex]
12. The base of a triangle with an area of 36 squared inches is 4.2 inches. What is the area of a similar
triangle whose base measures 5.6 inches?
The 4.2 inches base length and 36 in.² area of the given triangle and the 5.6 inches base length of the similar triangle gives the area of the similar triangle as 64 square inches
Which method can be used to find the area of the similar triangle given the dimensions?Area of a triangle = (Base length × Height)/2
Area of the given triangle = 36 in.²
Base length of the given triangle = 4.2 inches
Base length of the similar triangle = 5.6 inches
Therefore;
Area of the given triangle = (Base length × Height)/2
Which gives;
36 = (4.2 × h)/2
Where;
h = Height of the given triangle
36 × 2 = 4.2 × h
[tex]h = \mathbf{\frac{36 \times 2}{4.2}} = 17 \frac{1}{7} [/tex]
Height of the given triangle, h = 17+ 1/7
The ratio of corresponding sides of similar triangles are the same, which gives;
[tex] \frac{5.6}{4.2} = \frac{h'}{17 \frac{1}{7}} [/tex]
Where;
h' = The height of the similar triangle
Which gives;
[tex] h' = \frac{5.6}{4.2} \times 17 \frac{1}{7} = 22 \frac{6}{7} [/tex]
The area, A', of the similar triangle is therefore;
[tex] A' = \frac{1}{2} \times 5.6 \times 22 \frac{6}{7} = 64 [/tex]
The area of the similar triangle A' = 64 in.²The area can also be obtained using the scale factor of area as follows;
(4.2/5.6)² = 36/A'Which gives;
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In the figure below, the segment is parallel to one side of the triangle. Find the value of x.
x+7
18²/3
0 24
025²/
16
22
Step-by-step explanation:
answer=18^2/3
according to the congruent triangles are present there.
so divide corresponding sides
ASAP help me with this question <3 number 12
Answer:
False
Step-by-step explanation:
Consider an isoscles trapezoid with angles 75° and 105°.
George paid a total of $985 to rent a storage unit.
He initially paid $290 plus an extra amount for
each month that he rented the storage unit. Write
an equation to find the extra amount George paid
each month if he had the storage unit for 5 months.
[?] + 5m= [ ]
Answer:
290 + 5m = 985
Step-by-step explanation:
Given information:
Initial payment = $290Total payment = $985Extra amount each month = mLength of rental = 5 monthsFrom the given information, we can create the following equation:
Initial payment plus extra amount each month for 5 months equals total payment.
⇒ 290 + 5m = 985
To solve the equation:
Subtract 290 from both sides:
⇒ 290 + 5m - 290 = 985 - 290
⇒ 5m = 695
Divide both sides by 5:
⇒ 5m ÷ 5 = 695 ÷ 5
⇒ m = 139
Therefore, the extra amount George paid each month was $139.
Answer: [tex]\Large\boxed{290+5m=985}[/tex]
Step-by-step explanation:
Given information
Initial cost = $290
Total cost = $985
Number of months = 5 months
Cost each month = ?
Set variable
Let [ m ] be the cost each month
The equation in verble sense
Initial paid + Extra each month = Total cost
Convert verbal equation to mathematical sense
$290 + 5m = $290
Therefore, to find the extra amount paid each month, the equation is [tex]\Large\boxed{290+5m=985}[/tex]
---------------------------------------------------------------------------------------------------------
EXTRA The following will be solving the derived equation, please ignore this part if it is useless for you.
Given equation
290 + 5m = 985
Subtract 290 on both sides
290 + 5m - 290 = 985 - 290
5m = 695
Divide 5 on both sides
5m / 5 = 695 / 5
m = $139
Hope this helps!! :)
Please let me know if you have any questions
If a translation maps point A(-3,1) to point A′(5,5), the translation is:
A. (x+2,y+4)
B. (x+8,y+6)
C. (x+2,y+6)
D. (x+8,y+4)
Answer:
D is the correct answer -3+8=5 ,1+4=5
What is the length of S?
Answer:
c
Step-by-step explanation:
By the Pythagorean theorem,
[tex]28^2 + 15^2 = s^2 \\ \\ s^2 = 1009 \\ \\ s = \sqrt{1009}[/tex]
write the equations after translating the graph of y=|x+2| one unit to the right
write the equations after translating the graph of y=|x+2| one unit to the left
I need help with the problem
Answer:
you better give me brainliest
Step-by-step explanation:
The answer is the first two
K
An employment agency specializing in temporary construction help pays heavy equipment operators $124 per day and general laborers $82 per day If thirty-seven people were hired
and the payroll was $3916, how many heavy equipment operators were employed? How many laborers?
The number of heavy equipment operators hired was?
The number of general laborers hired was?
Step-by-step explanation:
x = number of heavy equipment operators
y = number of general laborers
x + y = 37 (37 people were hired)
out if this we get e.g.
x = 37 - y
124x + 82y = 3916 (daily rate for each role, in total 3916)
now we use the first equation in the second :
124(37 - y) + 82y = 3916
4588 - 124y + 82y = 3916
672 - 42y = 0
672 = 42y
y = 16
x = 37 - y = 37 - 16 = 21
21 heavy equipment operators were hired.
16 general laborers were hired.
A car is traveling at a speed of 60 miles per hour. What's the dependent variable in this situation? Question 5 options: A) The speed at which the car travels B) The distance the car has traveled C) The age of the car D) The number of hours the car has traveled
The dependent variable in this situation is; the speed at which the car travels.
Distance and speedSpeed of the car = 60 miles per hourSpeed = Distance / Time
The dependent variable in this situation is; the speed at which the car travels.
The independent variable; The distance the car has traveled.
What is dependent variable?This is the variable whose value depends on one or more variables in the equation.
Independent variable
This is the variable whose value is not dependent on any other in the equation.
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Which of the following describes the transformations of g (x) = negative (2) Superscript x + 4 Baseline minus 2 from the parent function f (x) = 2 Superscript x?
Using translation concepts, the transformations are described as follows:
Reflection over the x-axis.Shifted up 4 units.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the parent function is:
[tex]f(x) = 2^x[/tex]
The transformed function is:
[tex]g(x) = -2^x + 4[/tex]
We have that the transformations in this problem can be described as follows:
f(x) was multiplied by -1, hence it was reflected over the x-axis.4 was added to the function, hence it was shifted up 4 units.More can be learned about translation concepts at https://brainly.com/question/28098112
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Find the experimental probability that only 2
of 4 children in a family are boys.
The problem has been simulated by tossing 4
coins (one to represent each child). Let "heads"
represent a boy and "tails" represent a girl. A
sample of 20 coin tosses is shown.
HTHH HTTH TTTT THTT HTHT
HHTT HHHT THHT
TTHH
HTTT HTHT TTHH THTH HTHH
TTHT HTTT HTHT HHHT HHHH
HTTH
Experimental Probability = [?]%
The experimental probability that only 2 of 4 children in a family are boys is 50%.
What is experimental probability?Experimental probability refers to the chance of an expected success being achieved in a series of experiments conducted.
Experimental probability is the number of times that the expected success occurs as a fraction of the total number of times the experiment was conducted.
Like all probabilities, the experimental probability is based on the likelihood that what the experimenter expects is achieved.
Expected number of boys = 2
The number of children in the family = 4
Experimental probability = 50% (2/4 x 100)
Thus, we can conclude, based on the experimental probability, that 50% (or 2) of the 4 children in the family are boys.
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Answer:
15%
Step-by-step explanation:
Step 1: Count samples with one H
Why; Only 1 of 4 children in families are boys. The problem is simulated with samples.
Step 2: Count samples with only one H.
Why; The H represents the one boy in the family.
Step 3: Add the samples you counted with one H.
Answer: Your answer should be 3/20 after you change it into a percentage your final answer is 15%
Which is a factor of 144 - 49x²?
O 12-7x²
O 72-7x²
O 12-7x
O 72 + 7x
Answer: C: 12-7x
Step-by-step explanation:
This expression is a good example of the difference of two squares, as 144 is the square of 12, while 49x² is the square of 7x.
Any difference of two squares [tex]a^2-b^2[/tex] can be factored into the sum of their square roots times the difference of their square roots [tex](a+b)(a-b)[/tex].
Let's factor our expression.
[tex]144-49x^2=(12+7x)(12-7x)[/tex]
Out of all the options given, only [tex]12-7x[/tex] is a factor. Hence, option C is correct.
Between which two integers is the value of √11?
9 and 10
5 and 6
7 and 8
O3 and 4
1 and 2
Find the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3.
The remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
How to determine the remainder?The function is given as:
f(x)=−2x3+x2−4x+1 is divided by x+3.
Set the divisor to 0
x + 3 = 0
Solve for x
x = -3
Calculate f(-3)
f(-3)=−2(-3)^3+(-3)^2 − 4(-3) + 1
Evaluate the expression
f(-3)= 76
Hence, the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
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Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measure.
m∠1=(50x−50)∘, m∠2=(20x+70)∘
Alt. Ext. ∠s Thm.
m∠1 = 130°, m∠2 = 130°
Same-Side Int. ∠s Thm.
m∠1 = 130°, m∠2 = 130°
Alt. Int. ∠s Thm.
m∠1 = 150°, m∠2 = 150°
Corr. ∠s Post.
m∠1 = 150°, m∠2 = 150°
The theorem used and the angle measures are:
D. corresponding angles postulate
m∠1 = 150°, m∠2 = 150°
What is the Corresponding Angles Postulate?According to the corresponding angles postulate, if two angles lie on same relative corner along a transversal that cuts two parallel lines (corresponding angles), then their measures are equal.
Thus, ∠1 and ∠2 are corresponding angles, therefore:
m∠1 = m∠2 [corresponding angles postulate]
Given the following:
m∠1 = (50x − 50)∘,
m∠2 = (20x + 70)∘
Therefore, we would have:
50x − 50 = 20x + 70
Subtract 20x from both sides
50x − 50 - 20x = 20x + 70 - 20x
30x − 50 = 70
Add 50 to both sides of the equation
30x − 50 + 50 = 70 + 50
30x = 120
Divide both sides by 30
30x/30 = 120/30
x = 4
Plug in the value of x
m∠1 = (50x − 50) = 50(4) − 50 = 150°
m∠2 = (20x + 70)∘ = 20(4) + 70 = 150°
Thus, the answer is: D. corresponding angles postulate
m∠1 = 150°, m∠2 = 150°
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In the following activity, match each pair of equivalent expressions(will give 50 points)
A bookstore carries 48 magazines. 75% of the magazines are women's magazines. How many women's magazines does the bookstore carry?
Answer:
36
Step-by-step explanation:
75/100
75/100=0.75
0.75*48 =36
Anna does sit-ups to get ready for her first triathlon. When she starts, she does a sit-up every 2 seconds. But, as she gets tired, each sit-up takes longer to do. Is the number of sit-ups Anna does proportional to the time she spends doing them?
Answer: No
Step-by-step explanation: proportional means corresponding in size or amount to something. However, the number of her sit-ups isn't consistent, so it isn't proportional to the time she spends doing them.
solve the system of equations using substitution
The solution to the given simultaneous equation; x + 2y = -4, 2x + 5y = 1 using substitution method is x = -22 and y = 9
Simultaneous equationx + 2y = -4
2x + 5y = 1
Using Substitution method
From equation (1)
x = -4 - 2y
Substitute x = -4 - 2y into equation (2)
2x + 5y = 1
2(-4 - 2y) + 5y = 1
-8 - 4y + 5y = 1
- 4y + 5y = 1 + 8
y = 9
Substitute y = 9 into
x + 2y = -4
x + 2(9) = -4
x + 18 = -4
x = -4 - 18
x = - 22
Therefore, the solution to the given simultaneous equation; x + 2y = -4, 2x + 5y = 1 using substitution method is x = -22 and y = 9
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Given angle YMC = 170 degrees, find the measure of angle AMC.
Answer:
i think 10 because in triangle there is 180 and 180-170 = 10
Answer:
Step-by-step explanation:
hjhj
PLS HELP ME ASAP I NEED THE ANSWER NOW BEFORE 5 mins PLS Help ME I WILL MARK BRAINLIST IF YOUR ANSWER IS CORRECT AND WAS ANSWERED 4 MIN AGO HELP ME PLSSS
The table below shows that 1 day equals 24 hours. Notice that 12 hours is one-half of that. Use the table to help you determine how many days are equal to 42 hours.
1 day
24 hours
12 hours 12 hours
1 and 1 over 4. days (wrong)
1 and 1 over 2. days
1 and 3 over 4. days
2 days
Answer:
42 - 24 = 18
18/24 = 3/4
the answer would be 1 and 3/4 days
Answer:
1 and 3 over 4 days
Step-by-step explanation:
Since 24 hours is 1 day all we have to do is divide 42 into 24 and see what the resulting fraction is
42/24 = 7/4 (reducing to lowest fraction)
7/4 = 1 3/4 days (7 ÷ 4 gives quotient 1 and remainder is 3)
Answer:
1 and 3 over 4 days
Four seniors and six juniors are competing for four places on a quiz bowl team.
What is the approximate probability that all four seniors will be chosen at random?
what’s the % ?
Answer:
.00476
Step-by-step explanation: