Given parameters:
First term of the sequence = x
Second term = x + 2
Third term = x + 4
Sum of the first three terms = 72
Unknown:
First term of the sequence = ?
Solution:
The sum of the first three terms is unknown;
(x) + (x + 2) + (x + 4) = 72
Solve for x;
x + x + 2 + x + 4 = 72
3x + 6 = 72
3x = 72 - 6
3x = 66
x = [tex]\frac{66}{3}[/tex] = 22
The first term of the sequence is 22
Study the solutions of the three equations on the right. Then, complete the statements below. There are two real solutions if the radicand is There is one real solution if the radicand is There are no real solutions if the radicand is 1. y = negative 16 x squared + 32 x minus 10. x = StartFraction negative 32 plus-or-minus StartRoot 384 EndRoot Over negative 32 EndFraction. 2. y = 4 x squared + 12 x + 9. x = StartFraction negative 12 plus-or-minus StartRoot 0 EndRoot Over 8 EndFraction. 3. y = 3x squared minus 5 x + 4. x = StartFraction 5 plus-or-minus StartRoot negative 23 EndRoot Over 6 EndFraction.
Answer:
There are two real solutions if the radicand is
✔ positive.
There is one real solution if the radicand is
✔ zero.
There are no real solutions if the radicand is
✔ negative.
Step-by-step explanation:
ON MY DOG KIDS DIS RIGHT
Answer:
1.Postieve
2.Zero
3.Negative.
Step-by-step explanation
i did it on ed and got it right.
Find the values of x and y.
Consider this right triangle.
A
15
17
B
8
Which of the following ratios represents cos(B)?
what’s 2x+y=4 in slope intercept form
g In 2013, the Pew Research Foundation reported that 43% of U.S. adults report that they live with one or more chronic conditions. However, this value was based on a sample, so it may not be a perfect estimate for the population parameter of interest on its own. The study reported a standard error of about 1.7%, and a normal model may reasonably be used in this setting. Create a 95% confidence interval for the proportion of U.S. adults who live with one or more chronic conditions. Report your answer as a percentage rounded to 3 decimal places. We are 95% confident that the true proportion of U.S. adults who live with one or more chronic conditions is between % and % Submit All Parts Question 6
Answer:
We are 95% confident that the true proportion of U.S. adults who live with one or more chronic conditions is between 39.7% and 46.33%
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 43\% = 0.43[/tex]
The standard error is [tex]SE = 0.017[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100-95)\%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * SE[/tex]
=> [tex]E = 1.96 * 0.017[/tex]
=> [tex]E = 0.03332 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
=> [tex]0.43 -0.03332 < p < 0.43 + 0.03332[/tex]
=> [tex] 0.39668 < p < 0.46332[/tex]
Converting to percentage
[tex] (0.39668 * 100)< p < (0.46332*100)[/tex]
[tex] 39.7\% < p < 46.33 \%[/tex]
Simplify this expression:
2x? - 5xy - 6+ 4x2 – 3xy +1-xły
O 6x? - 9xy - 5
O 5x2 – 8xy-5-y
O 6x2 - 8xy-5-xy
O 6x² + 2xy-by-xy
Answer:
3xy⋅(4x
2
+2x−3y)
Step-by-step explanation:
Answer:
its c
Step-by-step explanation:
1. Maya's ice cream machine makes 10 cups of ice cream from 0.5 cup of sugar. How many cups of ice cream can be made with 5 cups of sugar?
Answer:
100
Step-by-step explanation:
Since ten cups of ice cream is made from .5 cups of sugar, lets first find out how many cups of ice cream can be made form one cup of sugar
.5*2=1
10*2=20
Since the ratio of sugar to ice scream is .5/10 if you do anything to the top you need to do it to the bottom
so now you have 1/20
for every one cup of sugar there are 20 cups of icecream
now you need to multiply both top and bottom by five
1*5=5
20*5=100
5/100
You can make 100 cups of ice cream
*don't forget to label your answer with cups of ice cream*
100 cups of ice cream can be made with 5 cups of sugar.
What are comparing quantities?
Comparing quantities is the qualitative relation between two quantities which reflects the relative size of both the quantities.
It is given that,
10 cups of ice cream requires = 0.5 cup of sugar
⇒ 1 cup of sugar = 10/0.5 cups of ice cream
⇒ 1 cup of sugar = 20 cups of ice cream
Hence we see that Maya's ice cream machine makes 20 cups of ice cream from 1 cup of sugar.
Similarly, 5 cups of sugar = 5 x 20 cups of ice cream
⇒ 5 cups of sugar = 100 cups of ice cream
Therefore,100 cups of ice cream can be made with 5 cups of sugar.
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What is the slope of this line that contains these points: (-4, -6) and (2,6)?
Answer:
The slope is 2
Step-by-step explanation:
y1-y2 . 6--6
--------- ------ =2
x1-x2 . 2--4
Percentages
Your favorite store is having a sale. You run across a shirt that originally sold for $47, but
is on a -40% Off" rack. A pair of jeans that originally
sold for $60 is advertised for "30%
Off". Your eye is attracted to a pair of designer shoes on sale for $35. You decide to
purchase the shirt, jeans, and shoes.
1) What is the sale price of the shirt?
What is the sale price of
the jeans?
2) What is the subtotal of the shirt, jeans, and the shoes?
3) You discover a coupon for 25% off the purchase price and give it to the cashier. With
the 25% off coupon what is the pre-tax cost of your purchase?
4) If the sales tax on your purchase is 5%, what is the total amount you are charged?
5) Your credit card has a monthly interest rate of 2% and a minimum payment of $10. You
make the minimum payment every month. Fill in the chart below until you pay off your
purchase.
Payment
Balance
$10.00
New Balance
Interest
Remaining
Balance
Month
1
2
3
4
5
6
7
8
9
10
Answer:
1) Shirt = $28.20 Jeans = $42
2) subtotal = $105.20
3) with the discount from the coupon, the pre-tax cost is $83.90
4) about $ 88.10 (actual answer was $88.095)
5) i have no clue bro, im sorry
Step-by-step explanation:
The sale price of the shirt is [tex]\$28.20[/tex] The sale price of the jeans [tex]\$42.00[/tex] Subtotal is [tex]\$[/tex]105.20 Pre-tax cost [tex]\$78.90[/tex] The total amount charged with 5% sales tax is [tex]\$42.00[/tex]
The sale price of the shirt:
Given -The original price of the shirt is $47, and it is on a "40% Off" sale. To find the sale price, we can calculate [tex]40\% of \$47[/tex]and subtract it from the original price:
The sale price of the shirt = [tex]\$47 - (40\% \times\$47)[/tex]
The sale price of the shirt =[tex]\$47 - (\$18.80)[/tex]
The sale price of the shirt =[tex]\$28.20[/tex]
The sale price of the jeans:
Given =The original price of the jeans is $60, and it is advertised as "30% Off." Similar to the shirt, we can calculate the sale price of the jeans:
The sale price of the jeans =[tex]\$60 - (30\% \times\$60)[/tex]
The sale price of the jeans =[tex]\$60 - (\$18.00)[/tex]
The sale price of the jeans = [tex]\$42.00[/tex]
Subtotal of the shirt, jeans, and shoes:
Subtotal = Sale price of the shirt + Sale price of the jeans + Sale price of the shoes
Subtotal = [tex]\$[/tex]28.20 + [tex]\$[/tex]42.00 +[tex]\$[/tex]35.00
Subtotal =[tex]\$[/tex]105.20
The pre-tax cost of your purchase with the[tex]25\%[/tex] off coupon:
The 25% off coupon is applied to the subtotal. We calculate 25% of the subtotal and subtract it from the subtotal to find the pre-tax cost:
Pre-tax cost = Subtotal -[tex](25\% \times Subtotal)[/tex]
Pre-tax cost = [tex]\$105.20 - (25\% \times \$105.20)\\[/tex]
Pre-tax cost =[tex]\$105.20 - (\$26.30)[/tex]
Pre-tax cost = [tex]\$78.90[/tex]
The total amount charged with 5% sales tax:
To calculate the total amount charged, we need to add the sales tax to the pre-tax cost:
Sales tax = [tex]5\% \times Pre-tax cost[/tex]
The Total amount charged = Pre-tax cost + Sales tax
The Total amount charged =[tex]\$78.90 + (5\% \times \$78.90)[/tex]
The total amount charged = [tex]\$78.90 + \$3.94[/tex]
The total amount charged =[tex]\$82.84[/tex]
The credit card payments for months are;
Payment | Balance | New Balance | Interest | Remaining Balance
Month 1 | $10.00 | $72.84 | $1.46 | $71.46
Month 2 | $10.00 | $61.46 | $1.23 | $60.69
Month 3 | $10.00 | $50.69 | $1.01 | $49.70
Month 4 | $10.00 | $39.70 | $0.79 | $38.49
Month 5 | $10.00 | $28.49 | $0.57 | $27.06
Month 6 | $10.00 | $17.06 | $0.34 | $16.40
Month 7 | $10.00 | $6.40 | $0.13 | $6.53
Month 8 | $6.53 | $0.00 | $0.00 | $0.00
The remaining balance is paid off in full by the 8th month, and the interest is calculated based on the remaining balance each month.
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a person can read 24 pages of a book in 1/3 of an hour what is the persons reading rate in pages per hour
Answer:
72.73 pages in one hour
or 72.73/hr
True or false and why?
====================================================
Explanation:
Utility is another way of saying happiness more or less. Marginal utility is getting that extra bit of satisfaction from buying/consuming one additional item. Saying the marginal utility is diminishing but not negative, means we have an increasing utility curve that has its rate of increase slow down. An example would be a log curve.
Inflation can be thought of as an expense. For example, if it costs $1 to get a loaf of bread one year, and then next year that cost jumps to $1.50 for that same loaf of bread, then the worker has effectively lost 50 cents on their paycheck. Zero inflation means there isn't any such expense. So in a way, this is like getting a raise.
Being paid more due to higher labor costs means that the worker gets even more money on top of the bonus money saved from zero inflation. These two aspects would provide a lot of incentive for the person to work more hours. Of course, there would be a point in which the marginal utility is far too small. In other words, the amount of additional money earned isn't worth the additional time spent working. This is likely when the worker would take time off, seek out a raise, or find some other job.
х
0
1
у
—125
-121
-93
-17
131
2
3
4
Answer:
12
Step-by-step explanation:
FIRST ONE TO AWNSER CORRECTLY GETS BRAINLEIST-1.8 + (2.1) Show your work
Answer:
0.3
Step-by-step explanation:
2.1
-1.8
---------
0.3
Plz help this is my last time to turn in everything and plz get the answer right!!
Its letter: H
Answer:
$37.05
Step-by-step explanation:
please help :,(( it's due in 30 minutes
Answer:
brain went bye bye
Step-by-step explanation:
area of a 18cm wide rectangle is 342 cm squared. what is the length?
6x+2 -1 -48-3-2x+2
Helpppppppp
x=12
This the answer hope this helps
If you need the steps please feel free to contact me in the comments
Quadrilateral ARMY is rotated 90° about the origin.
Answer:
what's the question??
Find the midpoint of the segment having the given endpoints.
(8,4) and (-5,-9)
Answer:
-5.6
Step-by-step explanation:
What is the slope of the line that passes through the points
(4, -3) and (8, -2)?
Step-by-step explanation:
Hey there!
The points are;(4,-3) and (8,-2).
Use slope formula.
[tex]slope(m) = \frac{y2 - y1}{x2 - x1} [/tex]
Put all values.
[tex]m = \frac{ - 2 + 3}{8 - 4} [/tex]
[tex]m = \frac{1}{4} [/tex]
Therefore, the slope is 1/2.
Hope it helps...
Teresa started a game at 6:25 PM and finished it at 7:41 PM.
How long did it take her? Give your answer in minutes.
Answer:
It took 1 hour and 16 minutes
Step-by-step explanation:
Evaluate f(x) = 1/4x for x = -5.
A. 20
B. -1/20
C. -1 1/4
D. -4/5
Answer: C
Step-by-step explanation:
1/4th of -5 is -1.25 so in fractions that is -1 1/4 (ANSWER IS C)
the answer is C
Two part-time instructors are hired by the Department of Statistics and each is assigned at random to teach a single course in probability, inference, or statistical computing. Assume that more than one section of each course is offered. List the outcomes in the sample space [Hint: each element consists of a pair of assignments]. Find the probability that they will teach different courses. Note: carefully define your notation (e.g. any events) in words before solving the problem.
Answer:
The probability that they will teach different courses is [tex]\frac{2}{3}[/tex].
Step-by-step explanation:
Sample space is a set of all possible outcomes of an experiment.
In this case we will write the sample space in the form (x, y).
Here x represents the course taught by the first part-time instructor and y represents the course taught by the second part-time instructor.
Denote every course by their first letter.
The sample space is as follows:
S = {(P, P), (P, I), (P, S), (I, P), (I, I), (I, S), (S, P), (S, I) and (S, S)}
The outcomes where the the instructors will teach different courses are:
s = {(P, I), (P, S), (I, P),(I, S), (S, P) and (S, I)}
The probability of an events E is the ratio of the number of favorable outcomes to the total number of outcomes.
[tex]P(E)=\frac{n(E)}{N}[/tex]
Compute the probability that they will teach different courses as follows:
[tex]P(\text{Different courses})=\frac{n(s)}{n(S)}=\frac{6}{9}=\frac{2}{3}[/tex]
Thus, the probability that they will teach different courses is [tex]\frac{2}{3}[/tex].
The ___________________ of a right triangle are the two sides that make up the right angle.
Answer:
a and b are the "legs" of the triangle, which are the two sides that make up the 90 degree angle. c is the "hypotenuse" of the triangle, and is the side of the triangle that is opposite the right angle (another way to say a 90º angle is "right angle"). The hypotenuse is also the longest side of the right triangle.
One day in July, the temperature at ground level at the airport was 90°. A pilot reported
the temperature at 10,000 feet was 50°. How much did the temperature drop per 1000
feet?
Answer:
it droped 40 degres
Step-by-step explanation:
Answer:
The temperature dropped 4 degrees per 1000 feet.
Step-by-step explanation:
90 - 50)/(10,000:1,000) = 40/10 = 4 degrees per 1000 ft
3. Find the slope of the graph.
101
a.
WIN
8
3
b.
2
-2
2
3
-10 -3 -6 -4 -2
24
6
8 10
2
3
d.
2
=6
-8
-10
Answer:
It's is 3/2
Step-by-step explanation:
since the line is going up, the rise/run is going to be positive
Classify the following triangle. Check all that apply.
Answer: A.) obtuse & F.) isosceles
Explanation:
Obtuse because the large angle is greater than 90°
isosceles because two of the sides are equal length
If the value of two integers differs by 3, and the product of the two integers is 108, what is the sum of the two integers?
A.21
B.19
C.25 D.23
Answer:
A
Step-by-step explanation:
Let the smallest number be n.
If the next integer differs by 3 then:
n + 3 is our second integer.
If the product is 108 then we would multiply them together.
n * (n + 3) = 108 Now solve for n.
(n*n) + (n*3) = 108
[tex]n^{2} +3n = 108[/tex] Now we move 108 to the other side by subtracting so we can factor.
[tex]n^{2} + 3n - 108 = 0[/tex]
(n )(n ) = 0
Find all the multiples of 108
1 x 108
2 x 54
3 x 36
4 x 27
6 x 18
9 x 12
Which one can we add or subtract together to get 3?
9 x 12 because 12 - 9 = 3
[tex]n^{2} + 3n - 108 = 0[/tex]
(n 12)(n 9) = 0 Now we figure out the signs. Since we have -108 one must be negative, and the 3 in the 2nd term (3n) is positive so:
(n + 12)(n - 9) = 0 Is our factored equation.
Our smallest number is 9, so n = 9
Our second number is n + 3 and 9 + 3 = 12
So our 2 integers are 9, 12, there sum would be 9 + 12 = 21
Option A.
Help asap
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Answer:
no
Step-by-step explanation:
two points cant be on the same line in a vertical pattern
A teacher can spend as much as
$125.00 to take students to a movie.
A movie theater charges a
$10.00 group fee and
$5.50 per ticket.
Which of the following inequalities represents the problem and could be solved to find the maximum number of students,
x, who could attend the movie?
The maximum number of students, x, who could attend the movie are,
⇒ x ≈ 21
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
A teacher can spend as much as $125.00 to take students to a movie.
And, A movie theater charges a $10.00 group fee and $5.50 per ticket.
Let maximum number of students, x, who could attend the movie = x
Hence, We can formulate;
5.50x + 10 ≤ 125
Solve for x;
5.50x ≤ 125 - 10
5.50x ≤ 115
x ≤ 115 / 5.50
x ≤ 20.90
x ≈ 21
Thus, The maximum number of students, x, who could attend the movie are,
⇒ x ≈ 21
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