Grace took one of her friends out to lunch. The lunches cost $100 and she paid 9% sales tax. If Grace left a 15% tip on the $100, how much in total did she pay?
Answer:
124
Step-by-step explanation:
100 x .09=9
100 x ,15=15
9 + 15=24
100+24=124
Which expression is equivalent to -8 + 7.25 – 6 + 0.5?
A. 7.25 +0.5 - (8 - 6)
B. -(8 + 6) + (7.25 +0.5)
C.-13 + 7.75
D. -14 - 7.25
If $700 is invested in an account that pays 3% compounded annually, the total amount, A(t), in the account after t years is Ant 700(1.03)^t.
Required:
a. Find the average rate of change per year of the total amount in the account for the first four years of the investment (from t= 0 to t= 4).
b. Find the average rate of change per year of the total amount in the account for the second four years of the investment (from t=4 to t=8)
c. Estimate the instantaneous rate of change for t =4.
d. The average rate of change per year of the total amount in the account for the first years of the investment â(from t= 0 to t=4â) is ___________â$
e. The average rate of change per year of the total amount in the account for the second years of the investment â(from t= 0 to t=4â) is_____________ â$
f. The instantaneous rate of change for t=4 is about â$_____________
Answer:
21.96 ; 24.72
Step-by-step explanation:
Given that :
Give the equation:
A(t) = 700(1.03)^t
A.)
Average rate of change over the first 4 years ;
(t=0 to t=4)
At t = 0
A(0) = 700(1.03)^0 = 700
A(1) = 700(1.03)^1 = 721
A(2) = 700(1.03)^2 = 742.63
A(3) = 700(1.03)^3 = 764. 9089
A(4) = 700(1.03)^4 = 787.856167
[(721 - 700) + (742.63 - 721) + (764.9089 - 742.63) + (787.856167 - 764.9089)] / 4
= 87.856167 / 4
= 21.96404175
= 21.96
Over the 2nd 4 years :
A(4) = 700(1.03)^4 = 787.856167
A(5) = 700(1.03)^5 = 811.49185201
A(6) = 700(1.03)^6 = 835.8366075703
A(7) = 700(1.03)^7 = 860.911705797409
A(8) = 700(1.03)^8 = 886.73905697133127
[(811.49185201 - 787.856167) + (835.8366075703 - 811.49185201) + (860.911705797409 - 835.8366075703) + (886.73905697133127 - 860.911705797409)] / 4
= 98.88288997133127 / 4
= 24.72
PLSSS HELP AND SHOW WORK PLEASE!
*Ms.Wilson ate 1/4 of a pizza in 12 minutes.*
1. If the pizza has 8 slices, how many slices will she eat in 18 minutes?
2. What fraction of the pizza will she eat in 30 minutes?
Problem 1
Answer: 3 slices-------------------------------------
Explanation:
1/4 = 0.25
She eats 25% of a pizza in 12 minutes
We can form the ratio 0.25/12
This ratio is then set equal to x/18. The value of x represents what proportion of the pizza is eaten after 18 minutes.
Solve for x
0.25/12 = x/18
0.25*18 = 12x ..... cross multiply
4.5 = 12x
12x = 4.5
x = 4.5/12
x = 0.375
x = 375/1000
x = (125*3)/(125*8)
x = 3/8
She ate 3/8 of the whole pizza in 18 minutes.
There are 8 slices in a full pizza, so (3/8)*8 = 3 means that she ate 3 slices.
Or you could say "eating 3 slices out of 8 total means she ate 3/8 of the full pizza".
===================================================
Problem 2
Answer: 5/8-------------------------------------
Explanation:
We'll use the same idea as before. Though now we're setting 0.25/12 equal to x/30
Solving for x leads to...
0.25/12 = x/30
0.25*30 = 12x
7.5 = 12x
12x = 7.5
x = 7.5/12
x = 0.625
x = 625/1000
x = (125*5)/(125*8)
x = 5/8
She will eat 5/8 of the pizza in 30 minutes.
Find the length of the third side of a triangle, given the legs are 12in. and 36 in
Answer:
37.94
Step-by-step explanation:
not sure if this is what you need but if you use Pythagoras therom you should get there
a^2 + b^2= c^2
12^2+36^2=c^2
12^2+36^2= 1440
the square root of 1440 is 37.9433192
5. Which of the following is a pair of alternate exterior angles?
Angles 1 and 4
Angles 2 and 8
Angles 1 and 7
Angles 4 and 7
Answer: angle 1 and 7
Step-by-step explanation: you just do it
Are 5x²y and 5y^2x LIKE TERMS or NOT LIKE TERMS?
1. A wagon wheel has a radius of 4.9 inches. Which of the following is closest to the distance the wagon
travels in two turns of the wheel?
A 31 inches
B 15 inches
C 62 inches
D 75 inches
Answer:
b.
Step-by-step explanation:
Simplify by dividing (-3/8) -5/9
Answer:
[tex]\frac{-27}{40}[/tex]
Step-by-step explanation:
[tex](\frac{-3}{8})[/tex]÷[tex]\frac{5}{9}[/tex]
[tex]\frac{-3}{8}[/tex]×[tex]\frac{9}{5}[/tex]
[tex]\frac{-27}{40}[/tex]
72/120 simplified help help help
Answer:
3/5
you get this by dividing 24 to both sides of 72/120
when multiplying or dividing by a negative coefficient, you must flip the sign.
•True
or
•False
Answer:
I think the answer is True!
Step-by-step explanation:
Hope this helps
Answer:
true
Step-by-step explanation:
a negative times a negative is a positive same with dividing a negative by a negative
a positive times a negative is also negative
Tourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Orlando Sentinel). Hotel occupancy data for February in two consecutive years are as follows.
Current Year Previous Year
Occupied Rooms 1,470 1,440
Total Rooms 1,750 1,800
Required:
a. Formulate the hypothesis test that can be used to determine if there has been an increase in the proportion of rooms occupied over the one-year period. (Let p1 = population proportion of rooms occupied for current year and p2 = population proportion of rooms occupied for previous year.)
b. What is the estimated proportion of hotel rooms occupied each year?
c. Calculate the test statistic.
Answer:
Step-by-step explanation:
The null hypothesis and alternative hypothesis can be formulated as:
[tex]\mathbf{H_o: P_1 - P_2 \le 0}[/tex]
[tex]\mathbf{H_1 : P_1 -P_2> 0}[/tex]
From the information given:
The sample proportion of rooms occupied for the current year.
[tex]P_1 = \dfrac{1470}{1750}[/tex]
[tex]P_1 = 0.84[/tex]
Sample size [tex]n_1[/tex] = 1750 (total number of rooms for the current year)
The sample proportion of rooms occupied for the previous year.
[tex]P_2 = \dfrac{1440}{1800}[/tex]
[tex]P_2 =0.8[/tex]
Sample size [tex]n_2[/tex] = 1800 (total number of rooms for the previous year)
Thus, the estimated proportion of the hotel rooms occupied each year are:
Current Previous
0.84 0.80
Since this is a one-sided right-tailed test;
The pooled proportion can be computed as:
[tex]\hat p= \dfrac{p_1 \times n_1 + p_2 \times n_2}{n_1 + n_2}[/tex]
[tex]\hat p= \dfrac{0.84 \times 1750 + 0.80 \times1800}{1750 +1800}[/tex]
[tex]\hat p=0.8197[/tex]
The standard error SE = [tex]\sqrt{\hat p ( 1- \hat p) ( \dfrac{1}{n_1} + \dfrac{1}{n_2} )}[/tex]
[tex]= \sqrt{0.8197 ( 1-0.8197) ( \dfrac{1}{1750} + \dfrac{1}{1800} )}[/tex]
[tex]= \sqrt{0.8197 ( 0.1803) (0.00112698 )}[/tex]
[tex]=0.0129[/tex]
Finally, the test statistics is calculated as:
[tex]Z_{calc} = \dfrac{(0.84 - 0.8)}{0.0129}[/tex]
[tex]Z_{calc} = 3.101[/tex]
Three machines turn out all the products in a factory, with the first machine producing 30% of the products, the second machine 20%, and the third machine 50%. The first machine produces defective products 13% of the time, the second machine 9% of the time and the third machine 9% of the time. What is the probability that a non-defective product came from the second machine
Answer:
0.2027 = 20.27% probability that a non-defective product came from the second machine
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Non-defective product.
Event B: From the second machine.
Probability of a non-defective product:
100-13 = 87% of 30%(first machine)
100-9 = 91% of 20%(second machine)
100-9 = 91% of 50%(third machine).
So
[tex]P(A) = 0.87*0.3 + 0.91*0.2 + 0.91*0.5 = 0.898[/tex]
Non-defective and from the second machine:
91% of 20%. So
[tex]P(A \cap B) = 0.91*0.2 = 0.182[/tex]
What is the probability that a non-defective product came from the second machine
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.182}{0.898} = 0.2027[/tex]
0.2027 = 20.27% probability that a non-defective product came from the second machine
What is the answer to 1014.16667 rounded to the nearest tenths
What is the answer to
-5 +2y = 9
y = 7x ?
Answer:
x = 1
y = 7
Step-by-step explanation:
Two equations, two unknowns. We know that y = 7x so we can substitute that into the first equation to get:
[tex]-5+2\left(7x\right)=9[/tex]
[tex]-5+14x=9[/tex]
[tex]14x=14[/tex]
This gives us x = 1.
Now plug this bag into either equation to find y, I will use the second since it's easier:
y = 7(1) = 7
Which number in the expression is the CONSTANT?
бу — 5
Two students, Alice and Bob, forgot to put their names on their exam papers. The professor knows that Alice does well with probability 0.8, and Bob does well with probability 0.4, independently of each other. What is the probability that exactly one of Alice and Bob does well on the exam
Answer:
[tex]Probability = 0.56[/tex]
Step-by-step explanation:
Represent the probability that Alice does well with P(A), the probability that Bob does well with P(B).
So, we have:
[tex]P(A) = 0.8[/tex]
[tex]P(B) = 0.4[/tex]
Required
Determine the probability that only one of them do well
This event is represented as: (A and B') or (B and A')
Where B' means Bob does not perform well and A' means Alice does not perform well.
And:
[tex]P(B') = 1 - P(B)[/tex]
[tex]P(A') = 1 - P(A)[/tex]
So, the probability becomes:
[tex]Probability = P(A\ and\ B')\ or\ P(B\ and\ A')[/tex]
[tex]Probability = P(A) * P(B')\ +\ P(B)*P(A')[/tex]
[tex]Probability = P(A) * (1-P(B)) +\ P(B)*(1-P(A))[/tex]
[tex]Probability = 0.8 * (1-0.4) +\ 0.4*(1-0.8)[/tex]
[tex]Probability = 0.8 * 0.6 +\ 0.4*0.2[/tex]
[tex]Probability = 0.48 + 0.08[/tex]
[tex]Probability = 0.56[/tex]
Hence, the required probability is 0.56
what are the 3 points
Answer:
(0,-2) (3,-4) (6,-6)
Step-by-step explanation:
I think you start at (0,-2) then go over 3 to the right and down 2 since it's negative each time
can anyone help me with this please
Answer:
n+6
Step-by-step explanation:
Chang is 6 inches taller then Nancy so you must add 6 inches to Nancy's height to figure out Chang's height.
Answer:
it's n+6
Step-by-step explanation:
nancys height is unknown so n is the variable and Chang is 6 inches taller so you add Nancy's height plus 6
I need help fast find the answer
Answer:
22
Step-by-step explanation:
need help plssssssssssssssssssssssssssssssss
Answer:
29
Step-by-step explanation:
PEMDAS
PARENTHESIS: [3-10]=7
EXPONENTS: 3^3= 27
MULTIPLICATION:8×7=56
DIVISION:NONE
ADDITION:NONE
SUBTRACTING: 56-27=29
ANSWER: 29
Help me out with this mathematic question please
Answer:
The answer is 95°!
Step-by-step explanation:
180°-60°-25°= 95°
Dan used 942 units of electricity from July to October.
The meter reading in July was 32,347 units
Work out the meter reading in October
Answer:
89n
Step-by-step explanation:)
Answer:
33289
Step-by-step explanation:
July reading + Useage
= 32347 + 942 = 33289
Aniyah has 10 1/3 feet of ribbon. She wants to cut the ribbon into 1 2/5 size pieces. How many full pieces of ribbon can she cut? helpppp
Answer:
7
Step-by-step explanation:
Because 10 1/3 divided by 1 2/5 would be 7 and something and the question is asking how many full pieces, so just 7
Suppose 88% of all batteries from a supplier have acceptable voltages. A certain type of flashlight requires two D batteries, and the flashlight will work only if both its batteries have acceptable voltages. Treat all batteries and flashlights as independent of one another. Suppose 20 randomly selected batteries are placed into 10 flashlights. What is the probability that at least 9 of the flashlights function properly
Answer:
0.3036 = 30.36% probability that at least 9 of the flashlights function properly.
Step-by-step explanation:
For each flashlight, there are only two possible outcomes. Either it works, or it does not. Flashlights are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Flashlight works correctly if both its batteries have acceptable voltages:
Each battery has an 88% = 0.88 probability of working correctly(having acceptable voltage), so the probability of the flashlight working correctly is given by:
[tex]p = (0.88)^2 = 0.7744[/tex]
10 flashlights.
This means that [tex]n = 10[/tex]
What is the probability that at least 9 of the flashlights function properly?
This is
[tex]P(X \geq 9) = P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{10,9}(0.7744)^{9}.(0.2256)^{1} = 0.2260[/tex]
[tex]P(X = 10) = C_{10,10}(0.7744)^{10}.(0.2256)^{0} = 0.0776[/tex]
[tex]P(X \geq 9) = P(X = 9) + P(X = 10) = 0.2260 + 0.0776 = 0.3036[/tex]
0.3036 = 30.36% probability that at least 9 of the flashlights function properly.
What is the ansar to 2+2 please I’m 3 and I hove preK hamewark
Answer:
4
Step-by-step explanation:
2+2=4
Which is true about ballistic stretching exercises?
Answer:
its too donk
Step-by-step explanation:
alright ill go open up the shades
2(x-5) + 3y + 12 - y
Answer:
2(x+y+11)
Step-by-step explanation:
2(x+5)+3y+12−y
Use the distributive property to multiply 2 by x+5.
2x+10+3y+12−y
Add 10 and 12 to get 22.
2x+22+3y−y
Combine 3y and −y to get 2y.
2x+22+2y
Answer:
2x+22 +2y
Step-by-step explanation:
Subtract -13xy from -5xy so
-5xy -(-13xy)=?
Answer:
8xy
Step-by-step explanation:
Subtract -13xy from -5xy
-5xy - (-13xy) =
-5xy + 13xy =
8xy
good luck, i hope this helps:)
A sample of 25 PCC studentsspent an average of $75 with a standard deviation of $17.50. Another sample of 20 ELAC studentsshowed that they spent an average of $89 with a standard deviation of $14.40. Assume that the amounts by all PCCand all ELAC students are normally distributed with equal but unknown population standard deviations.
Required:
Using 5% significance level and a formal hypothesis test can you conclude that the mean amount spent by all PCC students is less than the mean spent by all ELAC students?
Answer:
Step-by-step explanation:
Given that:
For PCC
The sample size [tex]n_1[/tex] = 25
sample mean [tex]\overline x_1[/tex] = 75
standard deviation [tex]s_1[/tex] = 17.50
For ELAC
The sample size [tex]n_2[/tex] = 20
Sample mean [tex]\overline x_2 = 89[/tex]
Standard deviation [tex]s_2[/tex] = 14.40
Significance level = 0.05
The null hypothesis:
[tex]H_o : \mu_1 =\mu_2[/tex]
The alternative hypothesis;
[tex]H_1 : \mu_1< \mu_2[/tex]
Since the population standard deviation are synonymous pooled standard deviation; Then:
[tex]sp = \sqrt {\dfrac {(n_1-1)s_1^2)+(n_2-1)s_2^2 }{n_1+n_2-2}[/tex]
[tex]sp = \sqrt {\dfrac {(25-1)17.50^2)+(20-1)14.40^2 }{25+20-2}[/tex]
[tex]sp = 16.20[/tex]
The test statistics can be computed as:
[tex]t = \dfrac{\overline x_1 -\overline x_2}{sp \times \sqrt{\dfrac{1}{n_1} + \dfrac{1}{n_2} }}[/tex]
[tex]t = \dfrac{75-89}{16.20 \times \sqrt{\dfrac{1}{25} + \dfrac{1}{20} }}[/tex]
[tex]t = -2.88[/tex]
The p-value [tex]= P(t_{n_1+n_2-1} <t)[/tex]
[tex]= P(t_{43} <-2.88)[/tex]
= 0.0031
Decision Rule: To reject the null hypothesis if the p-value is less than the significance level
Conclusion: There is sufficient evidence to conclude that the mean amount spent by all PCC students is less than the mean amount spent by all ELAC students.