x = number of appointments
y = total amount earned in dollars
The total earnings equation is y = 2x+40
The 2x is from her earning $2 per appointment. If she makes x of them, then she earns 2x dollars. This is on top of the $40 from working the full day.
She wants to earn at least $75. This means she wants to earn $75 or more.
This means,
[tex]y \ge 75\\\\2x+40 \ge 75\\\\2x \ge 75-40\\\\2x \ge 35\\\\x \ge \frac{35}{2}\\\\x \ge 17.5[/tex]
Since x is the number of appointments, and we can't have a fractional number of appointments, we must round up to x = 18. This is the lowest number of appointments she can do and earn $75 or larger.
If x = 17, then
y = 2x+40 = 2*17+40 = 34+40 = 74
which is not 75 or larger
But if x = 18, then
y = 2x+40 = 2*18+40 = 36+40 = 76
which is larger than 75, so we've cleared the hurdle.
We can say the solution set is [tex]x \ge 18[/tex] where x is a whole number. So she could book x = 18, x = 19, x = 20, x = 21, etc as the number of appointments to reach her goal.
In summary, she must schedule at least 18 appointments to earn $75 or more.
Since she makes $2 for every appointment she makes we would need to use 40+2n so she would get $2 per appointment no matter how many appointments she makes. Also, we wouldn't use an equal sign because they didn't say she needed to earn exactly $75. They said she needed to earn "at least" $75. At least means equal to or greater than ≥. So the inequality would be 2n+40≥75. PRO TIP: Any time it asks you to write an inequality you will use either <, >, ≤, or ≥ not an =.An equation uses =, an inequality uses the other symbols
Evaluate the expression x + 3y - 4(z - 3) when x = 4, y = 6 and z = 5
Hello!!!!! Could someone please explain to me in a simple manner what the slope intercept form is as well as what the point slope form is? Are they the same thing? What does form mean? Thank you soooo much in advance!!!
Answer:
Step-by-step explanation:
They're both ways of expressing the equation of a line. Depending on the information you're given, it's easier to use one or the other. Like if you're given the slope and y intercept, it might be easier to use slope intercept equation. If you're given 2 points on a line, it might be easier to calculate the slope between them and then use the pointslope equation using one of the two points given to find the euqation of the line. Let me know if there's more I need to clarify
PLS IT'S DUE!!
The longer leg of a 30⁰-60⁰-90⁰ triangle is 5√3 . Find the length of the hypotenuse.
explain how you got it.
Answer:
The answer is 10
Step-by-step explanation:
The longer leg of this triangle is √3 times longer than the shorter leg. Since the longer leg is 5√3, then the shorter leg will be 5. The hypotenuse is twice the size of the shorter leg, so 5*2 is 10.
How did the temp. change if at first it increased by 25% and then decreased by 40%?
Answer:
The temperature would have dropped 15 degrees so it would have been colder
Step-by-step explanation:
what is the difference b/w matrix and vector
Answer:
Matrix is array of number while vector is a list of numbers
Answer:
a vector is a form of a matrix having one row or one column or just say a "vector" is a list of values, a "matrix" is a table (or list of lists.................
Step-by-step explanation:
A nutritionist wants to study the effects of storage time
(6, 12, & 18 months) on the amount of vitamin C present
in freeze dried fruit. Vitamin C is measured in milligrams
per 100 milligrams of fruit. Six fruit packs were randomly
assigned to each of the three storage times.
The treatment is ?
The values are missing in the question. They are : 16.3,12.8,13,32.2,28.1,34.4,46.4,53,15.4,18.2
Step-by-step explanation:16.3,12.8,13,32.2,28.1,34.4,46.4,53,15.4,18.2
We calculate sample mean and std deviation from given data.
Sample Mean, =269.8/10=26.98
Sample Variance, =1859.496/9=206.610667
Sample std dev,s==√206.610667≈14.373958
We want to test two tailed hypothesis:
: σ=12
: σ≠12
Given: s=14.373958⇒ =206.610667,n=10
Significance level, a=0.1 Degrees of freedom, df=n-1=9
Since this is two tailed test, we need area of α=0.1 on either side of critical value. This means area of 0.05 on right of positive critical value.
Critical values are given by with 9 degrees of freedom.
We can use chi-square table or following excel commands:
CHISQ. INV(0.95,9)=3.32511284307
CHISQ. INV (0.05,9)=16.9189776046
Critical Values, =3.325 and =16.919
Since this is two tailed test, the decision rule or rejection criteria is:
Reject null hypothesis if test statistic is less than or equal to left critical value OR more than or equal to right critical value, i.e,
Reject if ≤3.325 OR ≥16.919
Test statistic is given by =((9)*206.610667)/144=12.913167
Test statistic, =12.913
since test statistic is between two critical values, we (do not reject ) (i.e, we fail to reject .
Conclusion: There is (not sufficient) evidence to conclude that standard deviation is not equal to 12 .
Alternatively, we can use p-value approach. The decision rule or rejection criteria is: reject null hypothesis if p-value is less than or equal to significance level (α), i.e, reject if p-value ≤0.1
P-value is twice the (smaller) tail area of test statistic because this is two tailed test. We can use excel function to find this. 2*M IN (CHISQ.DIST (12.913167,9, TRUE ) 1-CHISQ.DIST 12.913167,9, TRUE ) =0.333149809868
P-value =0.3331
since p-value is greater than significance level (α),we (do not reject ) (i.e, we fail to reject ).
Conclusion: There is (not sufficient) evidence to conclude that standard deviation is different from 12 .
A recipe requires 7/8 stick of butter for each 1 1/4 cups of flour. Find the unit rate of sticks of butter to cups of flour.
Let R = unit rate
R = (7/8) ÷ 1_1/4
R = (7/8) ÷ (5/4)
R = (7/8) • (4/5)
R = (7/2) • (1/5)
R = 7/10
Negative one plus negative four
Answer:
-5
Step-by-step explanation:
-4+(-1) A negative number added by another negative number will stay negative.( like a positive number by a positive will be positive.)
Idk wby it sets it up so weird in word form so imma just put this here
Answer:
141/2, 279/4
Step-by-step explanation:
Answer: wow ur right like ummm
Step-by-step explanation: wby lol
Kayla works in a shoe store and is paid a 12% commission on her sales. In January, her sales total was $3,740. About how much did Kayla earn in commission for January?
Answer:
Kayla had $3,740 x .12 = 448.80 by January.
Step-by-step explanation:
f(t) = t² – 2t; Find f(-7)
Answer:
f(-7) = 63
General Formulas and Concepts:
Order of Operations: BPEMDAS
Substituting and EvaluatingStep-by-step explanation:
Step 1: Define
f(t) = t² - 2t
f(-7) is t = -7
Step 2: Solve
Substitute: f(-7) = (-7)² - 2(-7)Exponents: f(-7) = 49 - 2(-7)Multiply: f(-7) = 49 + 14Add: f(-7) = 63CAN SOMEONE HELP ME ! Please and thank you.
A car dealership likes to have 4 blue cars on the lot for every 3 white cars. At this rate, how many white cars will be on the lot when there are 16 blue cars?
Answer:
12 white cars
Step-by-step explanation:
Our ratio is 4:3
16:?
We can determine white cars by dividing 16/4 to find how many more cars we have than our original ratio.
16/4 = 4
3 x 4 = 12
16:12 = 4:3
Answer:
Step-by-step explanation:
15
Shalah mowed 12 lawns in 3 hours. What is her RATE? *
help me plz
Answer: I think the answer is 4 because usually when you find the rate of something it means you divided the two numbers or however many numbers you have... So, 12 divided by 3 is 4... So, 4 hours for each lawn she mows... or something like that... So, 4 lawns per hour...
Final answer is 4 lawns per hour... If this isn't the correct answer i am very sorry... Stay safe and have a great weekend!!! :D
Answer:
4 lawns per hour
Step-by-step explanation:
4 lawns per hour or 1 lawn per 15 mins.
12/3 is the unit rate so 4/1.
Hope this helps plz hit the crown :D
X-2
——=5
3
I am supposed to solve for x but I have no clue how
Answer:
4
Step-by-step explanation:
Answer:
x = 17
Step-by-step explanation:
Nice set up. It's very clear.
Multiply both sides by 3
3(x-2)
===== = 5 *3
3
Cancel the 3 on the left. Combine the right.
x - 2 = 15
Add 2
x - 2 + 2 = 15 + 2
x = 17
==============
(17 - 2) / 3
15/3
5
The right hand side is also 5
someone knows what number multiplied twice by the same can give me results 1109 helpppp! Plis
Answer: Hey! no need to fret ok so your trying to find what multiplied by itself would get 1109. Make an algebra equation and solve for x:
x • x = 1109
x ≈ 33.302
Step-by-step explanation:Hoped I helped! Have a great day and put this on brainliest please. Thank you!
write an inequality to represent the product of x and 7 is at least 15
Answer:
[tex]7x\geq 15[/tex]
Step-by-step explanation:
This problem lays out pretty clearly what needs to be done.
First, we know that we are writing an inequality.
Then, it tells us that we need 'the product of x and 7'. A product is the result of multiplication, so we can multiply 7 and x together to get 7x.
Next, it tells us that the product (7x) is at least 15. At least means that the product has to greater than or equal to 15. That clue tells us which inequality symbol will be used.
Put it all together and:
[tex]7x\geq 15[/tex]
Hope this helped!
Graph the line.
y=-2x-3
please please hurry! 15 points
Answer:
you want to put your first pint at negative 3 on the Y axis. and then you want to go down 2 and right 1 to crest your slope.
√5+√3 /√5-√3 + root 5 + root 3 upon root 5 minus root 3 + root 5 minus root 3 upon root 5 + root 3
Answer:
√5+√3 /√5-√3 + root 5 + root 3 upon root 5 minus root 3 + root 5 minus root 3 upon root 5 + root 3
Step-by-step explanation:
√5+√3 /√5-√3 + root 5 + root 3 upon root 5 minus root 3 + root 5 minus root 3 upon root 5 + root 3
Find the 74 thterm of -19, -14, -9, -4, ..
-0.9 -0.4. Make sense at all???
im so counfused right now please help
For the equation 6 - m = 3, how many solutions are there for m?
0
1
infinite
2
Answer:
1.
Step-by-step explanation:
The only way to get 3 as an answer to (6-m) is if m were to equal 3. Think about how many numbers can you replace m with to make the statement true. For example, try putting 1 as your m and see if it works. 6-1=3 -> 5=3. as you can see, this statement isnt true. The only solution that would work to make this statement true is one number, 3. Hope this helps.
Can somebody help me with this math question plz
Step-by-step explanation:
hope this helps, happy learning!!!
Select the sequences that are geometric.
18, 36, 54, 72,...
4.1, 8.2, 16.4, 32.8,...
answer:
Both sequences are geometric
Step-by-step explanation:
because both have common differences of 2 times
Answer:
4.1, 8.2, 16.4, 32.8,... is a geometric sequence.
Step-by-step explanation:
Given the first sequence
18, 36, 54, 72,...
we know that the geometric sequence is the sequence that has the same common ratio 'r' (constant ratio).
Computing the ratios of all the adjacent terms:
[tex]\frac{36}{18}=2,\:\quad \frac{54}{36}=1.5,\:\quad \frac{72}{54}=1.33333\dots[/tex]
As the ratio is not constant.
Hence, 18, 36, 54, 72,... is NOT the geometric sequence.
Given the second sequence
4.1, 8.2, 16.4, 32.8,...
we know that the geometric sequence is the sequence that has the same common ratio 'r' (constant ratio).
Computing the ratios of all the adjacent terms:
[tex]\frac{8.2}{4.1}=2,\:\quad \frac{16.4}{8.2}=2,\:\quad \frac{32.8}{16.4}=2[/tex]
As the ratio of all the adjacent terms is the same (constant ratio).
Hence, 4.1, 8.2, 16.4, 32.8,... is a geometric sequence.
Therefore, 4.1, 8.2, 16.4, 32.8,... is a geometric sequence.
Ex plane how knowing 50 x 4 = 200 helps you find 500 x 400
Help with Geometry ,please
Answer:look at the angle bro and you got the angle just look at it good enough
Step-by-step explanation:
Which expression is equivalent to 350−−√⋅22−−√?
1522−−√
1511−−√
3022−−√
3011−−√
Answer:
it looks like d to me
Step-by-step explanation:
Answer:
The answer is D. [tex]30\sqrt{11}[/tex]
good luck!
7) A different stock loses half of its value every 2 months. If the original price was $128,
how much is it worth after 14 months.
What is the constant of proportionality?
Answer:
To find the constant of proportionality we use the formula k= y/x so we have k=20/500 =0.04
Step-by-step explanation:
Mrs. Barnes gave her class 30 minutes of
recess after lunch. Rachel and Diamond
spent 4 minutes on the monkey bars, 7
minutes jumping rope, and 5 minutes
playing tag. How much longer do they
have for recess?
Answer:
14
because 4plus 7 plus5 equealas 16 and 30 minuse 16 equals 14
can u help me thank you
Answer:
I believe the answer choice you already selected is correct.
Answer:
The slope is 2.
Step-by-step explanation:
(0,-5),(20,35)
m=y²-y¹/x²-x¹
m=35-(-5)/20-0
m=40/20
m=2
Pick an dinner for every single day?
Answer:
The last one please.