Answer:
x = 16°, tan x = 0.3
Step-by-step explanation:
[tex]sin \: 2x = cos \: (3x + 10) \\ cos(90 - 2x) = cos \: (3x + 10) \\ 90 - 2x = 3x + 10 \\ 90 - 10 = 3x + 2x \\ 80 = 5x \\ x = \frac{80}{5} \\ \huge \red{ \boxed{x = 16 \degree }}\\ \\ tan \: x = tan \: 16 \degree \\ = 0.2867453858 \\ = 0.3[/tex]
According to a survey, 2323% of residents of a country 25 years old or older had earned at least a bachelor's degree. You are performing a study and would like at least 1010 people in the study to have earned at least a bachelor's degree. (a) How many residents of the country 25 years old or older do you expect to randomly select? (b) How many residents of the country 25 years old or older do you have to randomly select to have a probability 0.9450.945 that the sample contains at least 1010 who have earned at least a bachelor's degree? (a) The number of randomly selected residents is 4444. (Round up to the nearest integer.) (b) The number of randomly selected residents, with a probability 0.9450.945 containing at least 1010 who have earned at least a bachelor's degree, is 2828. (Round up to the nearest integer.)
Answer:
a) 44
b) 64
Step-by-step explanation:
Applying the central limit theorem, the proportion of the random sample of 25 years old or older that have earned at least a bachelor's degree will be equal to the population proportion of 23%.
Mean = np
Mean = 10
p = 0.23
n = ?
10 = n×0.23
N
n = (10/0.23) = 43.5 = 44 to the nearest whole number.
b) This is a binomial distribution problem with the probability known and the number of trials unknown.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = ?
x = Number of successes required = 10
p = probability of success = 0.23
q = probability of failure = 1 - 0.23 = 0.77
P(X ≥ 10) = 0.945
P(X ≥ 10) = 1 - P(X < 10) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]
0.945 = 1 - [Σ P(X=x)] (with the summation of x from 0 to 9)
Using the trial and error method on the binomial distribution formula calculator, n is obtained to be 64.
Hope this Helps!!!
Final answer:
To have a high likelihood of sampling at least 10 people with a bachelor's degree, using the survey information that 23% of the population holds such a degree, you would want to sample about 44 individuals. For a probability of 0.945 of having at least 10 degree-holders in your sample, you would need to sample approximately 28 individuals.
Explanation:
Considering the survey indicating that 23% of residents 25 years old or older have earned at least a bachelor's degree, to ensure at least 10 people in a study have a bachelor's degree, you would ideally use the proportion of the population with this degree to determine the size of the sample needed.
Expected Sample Size
If you are selecting individuals at random and want to calculate the expected number of people you need to sample to find 10 people with a bachelor's degree, you divide the number of people needed by the probability of an individual having a bachelor's degree. In mathematical terms, you are expected to sample 10 / 0.23 ≈ 43.48, which we round up to the next whole number, giving us 44 people.
Sample Size for Desired Probability
To achieve a probability of 0.945 that your sample contains at least 10 people with a bachelor's degree, you would utilize statistical methods or software that applies the binomial or hypergeometric distribution formulas. This question seems to indicate that the answer is 28 individuals, which suggests that a calculation has already been made to determine this number.
A scientist claims that a smaller proportion of members of the National Academy of Sciences are women when compared to the proportion of women nationwide. Let p1 represent the proportion of women in the National Academy of Sciences and p2 represent the proportion of women nationwide. Which is the correct alternative hypotheses that corresponds to this claim?
A.Ha: p1 - p2 < 0
B.Ha: p1 - p2 > 0
C.Ha: p1 - p2 ? 0
Answer:
Correct option: (A) p₁ - p₂ < 0.
Step-by-step explanation:
The claim made by the scientist is that the proportion of female members of the National Academy of Sciences is less than the proportion of female members nationwide.
To test this claim we can difference between two proportions z-test.
It is assumed that p₁ is the proportion of women in the National Academy of Sciences and p₂ is the proportion of women nationwide.
Then we nee to test whether p₁ - p₂ < 0 or not.
The hypothesis can be defined as:
H₀: The proportion of women in the National Academy of Sciences is not less than the proportion nationwide, i.e. p₁ - p₂ ≥ 0.
H₀: The proportion of women in the National Academy of Sciences is less than the proportion nationwide, i.e. p₁ - p₂ < 0.
Thus, the correct option is (A).
A company needs 150,000 items per year. It costs the company $640 to prepare a production run of these items and $7 to produce each item. If it also costs the company $0.75 per year for each item stored, find the number of items that should be produced in each run so that total costs of production and storage are minimized.
The requried x represents the number of items produced in each run, we should produce approximately 127 items in each run to minimize the total costs of production and storage.
To find the number of items that should be produced in each run to minimize the total costs of production and storage, we can use the following steps:
Let x be the number of items produced in each run. The total cost of production and storage (C) can be expressed as:
C(x) = (640/150,000) + (7x) + (0.75 * 150,000 / x)
The first term (640/150,000) represents the cost of preparing a production run, the second term (7x) represents the cost of producing each item, and the third term (0.75 * 150,000 / x) represents the cost of storing each item.
To minimize the total cost, we need to find the value of x that minimizes the function C(x). We can do this by taking the derivative of C(x) with respect to x and setting it equal to zero:
C'(x) = 0
Now, let's find the derivative of C(x):
C'(x) = d/dx [(640/150,000) + (7x) + (0.75 * 150,000 / x)]
C'(x) = 0 + 7 - (0.75 * 150,000 / x²)
Now, set C'(x) equal to zero and solve for x:
7 - (0.75 * 150,000 / x²) = 0
0.75 * 150,000 / x² = 7
150,000 / x² = 7 / 0.75
150,000 / x² = 9.333...
Now, solve for x:
x² = 150,000 / 9.333...
x² ≈ 16,071.43
x ≈ sqrt(16,071.43)
x ≈ 126.77
Since x represents the number of items produced in each run, we should produce approximately 127 items in each run to minimize the total costs of production and storage.
Learn more about minimizing the total costs of production here:
https://brainly.com/question/24107867
#SPJ4
A model of a soccer ball is made up of regular pentagons and hexagons.
A soccer ball is made up of regular pentagons and hexagons.
The side length of one of the pentagons measures 2 inches and the apothem measures about 1.38 inches. What is the area of one of the pentagons? State your answer to the nearest tenth.
square inches
The side length of one of the hexagons measures 2 inches and the apothem measures about 1.73 inches. What is the area of one of the hexagons? State your answer to the nearest tenth.
square inches
Answer:
- pentagon area= 6.9
-hexagon area=10.4
Answer:
Pentagons: 6.9 square inches
Hexagons: 10.4 square inches
Step-by-step explanation: i got it right on edge
Please help!!
Which expression is equivalent to 10 - 8?
Choose 1 answer:
Answer:
Option A is the right answer choice.
Step-by-step explanation:
10 plus a negative number is the same as subtracting it as a positive
John has 1/3 as much money as grant. Grant gives John 9$. Now grant has 6$ more than John. How much money do grant and John have in all
Answer:
48 dollars
Step-by-step explanation:
grant originally had 36 and john had 12
decrease grant by 9 and increase john by 9
grant has 27, and john has 21
difference is 6 so the sum is 48.
Answer:
48 dollars
Step-by-step explanation:
Total money of Grant : 36
Total money of John : 12
Grant gave 9 dollars to John : 36 - 9 = 27
Now John has 21 dollars ( 12 + 9 = 21 )
So , 21 + 27 = 48
Thus , John and Grant have 48 dollars in total
The regression equation Credits = 17.9 − 0.09 Work was estimated from a sample of 21 statistics students. Credits is the number of college credits taken and Work is the number of hours worked per week at an outside job. (Round your answers to 1 decimal place.) (a) Choose the correct statement. An increase in the number of hours worked per week increases the expected number of credits. A decrease in the number of hours worked per week decreases the expected number of credits. An increase in the number of hours worked per week decreases the expected number of credits. (b) Choose the right option. The intercept is not meaningful as a student who works outside may not earn any credits. The intercept is meaningful as a student may not have a job outside of school. (c) If Work = 0, then Credits = . If Work = 60, then Credits = .
Answer:
Step-by-step explanation:
Hello!
Given the regression equation
Credit= 17.9 - 0.09 Work
That was estimated from a sample of n= 21 statistic students.
Y: number of college credits taken
X: number of hours worked per week at an outside job
a)
The estimation for the slope is -0.09
As you see the estimated slope is negative, this means that the association between the two variables is indirect or inverse. Meaning, when the number of Work increases, the number of Credit decreases. (negative regression)
The correct option is: "An increase in the number of hours worked per week decreases the expected number of credits."
b)
The estimation for the intercept is 17.9
In general, the intercept is the estimated average of Y when X=0. You can interpret the intercept of this equation as "the value of Credits earned by a student that does not work outside of school"
The correct option is: " The intercept is meaningful as a student may not have a job outside of school. "
c)
If Work=0, then Credit= 17.9 (As explained in item b)
By replacing the value in the equation: Credit= 17.9 - 0.09 * 0= 17.9
If Work=60, you replace it in the equation and:
Credit= 17.9 - 0.09 Work= 17.9-0.09*60= 12.5
If the student works 60 hs outside of school it is expected that he takes 12.5 college credits.
I hope this helps!
The correct answers are that an increase in work hours decreases the number of expected credits, the intercept is meaningful as it represents the credits for a student not working, and credits equal to 17.9 when work hours are zero and 12.5 when work hours are 60.
The regression equation given is Credits = 17.9 - 0.09 Work, where Credits is the number of college credits taken and Work is the number of hours worked per week at an outside job.
(a) From this equation, we can see that for an increase in the number of hours worked (Work), the number of expected credits (Credits) decreases because the coefficient of Work is negative (-0.09). So, the correct statement is: An increase in the number of hours worked per week decreases the expected number of credits.
(b) Regarding the intercept, it is meaningful since it represents the expected number of credits a student would take if they did not work at all (Work = 0). Therefore, the correct option is: The intercept is meaningful as a student may not have a job outside of school.
(c) If Work = 0, then Credits = 17.9. If Work = 60, then Credits = 17.9 - 0.09(60) = 17.9 - 5.4 = 12.5.
The table shows information about the numbers of hours 30 children spent on their tablets one evening. a) find the class interval that contains the median. B)work out an estimate for the mean number of hours
(a) The class interval that contains the median is [tex]\( 1 < h \leq 2 \).[/tex] (b)The estimated mean number of hours is 1.8 hours.
To analyze the data and answer the questions about the time 30 children spent on their tablets one evening, let's break it down step by step.
(a) The median is the value that separates the higher half from the lower half of the data. For 30 children, the median position will be the average of the 15th and 16th values in the ordered data set.
Given the frequencies:
- [tex]\( 0 < h \leq 1 \): 6[/tex] children
- [tex]\( 1 < h \leq 2 \):[/tex] 13 children
- [tex]\( 2 < h \leq 3 \):[/tex] 7 children
- [tex]\( 3 < h \leq 4 \): 4[/tex] children
To find the median class interval, we need to determine where the 15th and 16th values fall.
Cumulative frequency:
[tex]- \( 0 < h \leq 1 \): 6\\ - \( 1 < h \leq 2 \): 6 + 13 = 19\\ - \( 2 < h \leq 3 \): 19 + 7 = 26\\ - \( 3 < h \leq 4 \): 26 + 4 = 30[/tex]
From the cumulative frequency:
The 15th and 16th values fall within the second class interval [tex]\( 1 < h \leq 2 \),[/tex] because the cumulative frequency reaches 19 in this interval.
The class interval that contains the median is [tex]\( 1 < h \leq 2 \).[/tex]
(b) To estimate the mean, we'll use the midpoint of each class interval and multiply by the frequency of that interval, then divide by the total number of children.
Determine the midpoints of each class interval:
[tex]- \( 0 < h \leq 1 \): midpoint = \( \frac{0 + 1}{2} = 0.5 \)\\ - \( 1 < h \leq 2 \): midpoint = \( \frac{1 + 2}{2} = 1.5 \)\\ - \( 2 < h \leq 3 \): midpoint = \( \frac{2 + 3}{2} = 2.5 \)\\ - \( 3 < h \leq 4 \): midpoint = \( \frac{3 + 4}{2} = 3.5 \)[/tex]
Multiply each midpoint by its respective frequency:
[tex]- \( 0.5 \times 6 = 3 \)\\ - \( 1.5 \times 13 = 19.5 \)\\ - \( 2.5 \times 7 = 17.5 \)\\ - \( 3.5 \times 4 = 14 \)\\[/tex]
Sum these products:
[tex]\[ 3 + 19.5 + 17.5 + 14 = 54 \][/tex]
Divide by the total number of children to find the mean:
[tex]\[ \text{Mean} = \frac{54}{30} = 1.8 \][/tex]
The estimated mean number of hours is 1.8 hours.
The complete question is:
The table shows information about the numbers of hours 30 children spent on their tablets one evening.
Number of hours (m) Frequency
D<h<1 6
1<h<2 13
2<h<3 7
3<h<4 4
a) Find the class interval that contains the median.
b) Work out an estimate for the mean number of hours.
Individuals filing federal income tax returns prior to March 31 had an average refund of $1102. Consider the population of "last-minute" filers who mail their returns during the last five days of the income tax period (typically April 10 to April 15).
a. A researcher suggests that one of the reasons that individuals wait until the last five days to file their returns is that on average those individuals have a lower refund than early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s contention.
b. For a sample of 600 individuals who filed a return between April 10 and April 15, the sample mean refund was $1050 and the standard deviation was $500. Compute the p-value.
c. Using α =.05, what is your conclusion?
d. Test the hypotheses using the critical value approach (α = 0.025).
Answer:
a) The null hypothesis states that the last-minute filers average refund is equal to the early filers refund. The alternative hypothesis states that the last-minute filers average refund is less than the early filers refund.
[tex]H_0: \mu=1102\\\\H_a:\mu < 1102[/tex]
b) P-value = 0.0055
c) The null hypothesis is rejected.
There is enough statistical evidence to support the claim that that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund.
d) Critical value tc=-1.96.
As t=-2.55, the null hypothesis is rejected.
Step-by-step explanation:
We have to perform a hypothesis test on the mean.
The claim is that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund ($1102).
a) The null hypothesis states that the last-minute filers average refund is equal to the early filers refund. The alternative hypothesis states that the last-minute filers average refund is less than the early filers refund.
[tex]H_0: \mu=1102\\\\H_a:\mu < 1102[/tex]
b) The sample has a size n=600, with a sample refund of $1050 and a standard deviation of $500.
We can calculate the z-statistic as:
[tex]t=\dfrac{\bar x-\mu}{s/\sqrt{n}}=\dfrac{1050-1102}{500/\sqrt{600}}=\dfrac{-52}{20.41}=-2.55[/tex]
The degrees of freedom are df=599
[tex]df=n-1=600-1=599[/tex]
The P-value for this test statistic is:
[tex]P-value=P(t<-2.55)=0.0055[/tex]
c) Using a significance level α=0.05, the P-value is lower than the significance level, so the effect is significant. The null hypothesis is rejected.
There is enough statistical evidence to support the claim that that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund.
d) If the significance level is α=0.025, the critical value for the test statistic is t=-1.96. If the test statistic is below t=-1.96, then the null hypothesis should be rejected.
This is the case, as the test statistic is t=-2.55 and falls in the rejection region.
a four sectioned spinner is numbered 1-4. What is the probability you spin a 2, and then a 4?
Answer:
1/4 25%
Step-by-step explanation:
The spinner has 4 sides so the denomination is 4 and you are trying to get one of the 4 sides each so it would be a 1/4 chance for both answers so 25%
Is a triangle whose side measure 12 ft, 16 ft and 20 ft a right triangle?
Answer:
This is a Right Triangle
Step-by-step explanation:
12=a 16=b 20=c
Now lets solve
a^2+b^2=c^2
144+b^2=c^2
144+256=c^2
144+256=400
c^2=400
The square root of 400 is 20..
This IS a Right Triangle
Yes, a triangle with sides of lengths 12ft, 16ft and 20ft is a right triangle. This is proven by using the Pythagorean theorem, which these side lengths satisfy.
Explanation:To verify if a triangle is a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
In the triangle you provided with sides of lengths 12 ft (a), 16 ft (b), and 20 ft (c, as the hypotenuse is usually the longest side), you would plug those values into the equation: 12² + 16² = 20²?
144 + 256 = 400?
400 = 400
Because the equation is true, this proves that the triangle is indeed a right triangle.
Learn more about Pythagorean theorem here:https://brainly.com/question/28361847
#SPJ2
Evaluate the following expression. Round your answer to two decimal places.
Answer: 2.18
Step-by-step explanation:
log(11)/log(3)=2.18
Answer:
2.18
Step-by-step explanation:
I just did it and got it right
5.Richard Miyashiro purchased a condominium and obtained a 30-year loan of $196,000 at an annual interest rate of 8.20%. (Round your answers to the nearest cent.)
(a) What is the mortgage payment?
$
(b) What is the total of the payments over the life of the loan?
$
(c) Find the amount of interest paid on the mortgage loan over the 30 years.
$
6.
Marcel Thiessen purchased a home for $205,700 and obtained a 15-year, fixed-rate mortgage at 7% after paying a down payment of 10%. Of the first month's mortgage payment, how much is interest and how much is applied to the principal? (Round your answer to the nearest cent.)
interest $
applied to the principal $
Answer:
5 a) PMT=$1,465.60
b) Total Payments=$527,616
c) Total Interest=$331,616
6a) Interest=$1,079.93
b) Principal=$584.07
Step-by-step explanation:
a. Given the loan amount is $196,000, annual rate is 8.2% and the loan term is 30 years.
-The monthly mortgage payment can be calculated as follows:
[tex]PMT=A(\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}})[/tex]
Where:
PMT is the monthly mortgage paymentr is the annual interest raten,t is the number of annual payments and time in years respectively-We substitute to solve for PMT:
[tex]PMT=A(\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}})\\\\=196000[\frac{(0.082/12)}{1-(1+\frac{0.082}{12})^{-12\times30}}]\\\\=\$1,465.60[/tex]
Hence, the monthly mortgage payment is $1,465.60
b. The total number of payments is obtained by multiplying the total number of payments by the amount of each payment:
[tex]\sum(payments)=PMT\times nt\\\\=1465.60\times 12\times 30\\\\=\$527,616.00[/tex]
Hence, the total amount of payments is $527,616
c. The amount of interest paid over the loan's term is obtained by subtracting the principal loan amount from the total payments made:
[tex]Interest=Payments-Principal\\\\=527,616.00-196,000.00\\\\=\$331,616[/tex]
Hence, an interest amount of $331,616 is paid over the loan's term.
6 a) We first obtain the effective loan amount by subtracting the down-payment:
[tex]Loan \ Amount= Regular \ Price -Downpayment\\\\=205700-0.1(205700)\\\\=\$185,130[/tex]
The interest paid on the first mortgage payment is calculated as below:
[tex]I=\frac{r}{n}\times P\\\\I=Interest\\r=interest \ rate\\n=Payments \ per \ year\\P=Outstanding \ loan \ balance\\\\\therefore I=\frac{0.07}{12}\times 185130\\\\=\$1,079.93[/tex]
Hence, the amount of interest in the first payment is $1,079.93
b. The amount of principal repaid is obtained by subtracting the interest amount from the monthly mortgage payments;
[tex]Principal \ Paid=PMT-Interest\\\\PMT=A[\frac{(r/n)}{1-(1+\frac{r}{n})^{-nt}}]\\\\=185130[\frac{(0.07/12)}{1-(1+\frac{0.07}{12})^{-180}}\\\\=1664.00\\\\\\Principal \ Paid=1664.00-1079.93\\\\=\$584.07[/tex]
Hence, the amount of principal applied is $584.07
Height of rectangular prism if the volume is 334.8 meters
Only the volume is given, so you can already assume the rectangular prism is a cube, which in that case you can divide by 3 to get the answer.
Calculations the mean of 13, 8, 12, 10, 27
Answer:
14
Step-by-step explanation:
M = (13+8+12+10+27)/5
= 70/5
= 70 : 5
= 14
Amy can run the 150 meter dash in 50 seconds. John can run 120 meters in 400 seconds. Who runs faster per second?
Answer:
Amy
Step-by-step explanation:
amy completed a longer distance in a shorter amount of time
rather than john completed a shorter distance in a longer time
pls mark me brainliest
Amy runs faster than John.
What is speed?Speed is defined as the ratio of distance of an object to the time taken to complete the distance.
Speed of any object can be calculated by the equation,
Speed = Distance / Time
Here, Speed of Amy = 150/50 = 3
Speed of John = 120/400 = 0.3
Amy runs at a speed of 3 meters per seconds and John runs at a speed of 0.3 meters per second.
Hence Amy runs faster than John.
To learn more on speed, click:
https://brainly.com/question/7359669
#SPJ3
c - 12 > 30, if c = 13
Answer:
False
Step-by-step explanation:
Substitute 13 in for c
c - 12 > 30
13 - 12 > 30
1 > 30
This is false, because 1 is not greater than 30
The solution:
c - 12 > 30
Add 12 to both sides
c > 42
Find the product.
-1(5) =
Answer:
-5
Step-by-step explanation:
when you multiply a number by -1 it becomes its opposite
A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If this is to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network receives 827 responses, of which 438 indicate that they would like to see the new show in the lineup.
a. The test statistic for this hypothesis would be:_______
b. Calculate the critical value at α = 0.10.
c. What should the television network do?
1. Do not reject H0, the television network should keep its current lineup.
2. Reject H0, the television network should not keep its current lineup.
d. Select the hypotheses to test if the television network should give its newest television show a spot during prime viewing time at night.
H0: p = 0.50; HA: p < 0.50
H0: p > 0.50; HA: p < 0.50
H0: p < 0.50; HA: p > 0.50
Final answer:
The test statistic for this hypothesis is the Z-score. The television network should reject H0 and the correct hypotheses to test are H0: p = 0.50 and HA: p > 0.50.
Explanation:
a. The test statistic for this hypothesis would be Z-score.
b. To calculate the critical value at α = 0.10, you can use a Z-table. Look up the value corresponding to an alpha of 0.10 in the one-tailed column. The critical value would be the corresponding Z-score.
c. The television network should reject H0, as the p-value is less than the significance level of 0.10. This means there is enough evidence to suggest that viewers prefer the new show over the current lineup.
d. The correct hypotheses to test would be H0: p = 0.50 and HA: p > 0.50, as the network wants to determine if the proportion of viewers who prefer the new show is greater than 0.50.
Which of the following is equivalent to 5/13^3
Answer:
.00227 or 5/2197
Step-by-step explanation:
following the basic rules of PEMDAS, we know that we have to solve for the exponent first.
so.... 5/2197
as a decimal, this is .00227...
can you guys pls help ( MARKING BRAINLIST ) :)!!
Answer:
(36/4)-(36/9)=5
(8x3)-12=12
Step-by-step explanation:
36/4=9, 36/9=4, and 9-4=5
8x3=24 and 24-12=12
i need to know number 7
Answer:
it would be A. -25
Step-by-step explanation:
`for example if she sold 0 dollars worth of necklaces and she spent 25 dollars on supplies she would have lost 25 dollars so it would be -25.
Answer:A,-$25
Step-by-step explanation:
She bought the necklace. When she sold it, she sold it for $25 less than what she bought it for. Therefore, she lost $25, the same as -$25.
Aiden needs to find the percent of shaded squares in the bar diagram. Which model should he use? plz help
Answer: C
Step-by-step explanation:
Answer:
It might be C
Step-by-step explanation:
I am so sorry if it is the wrong answer. I didn't have a test about this.... :(
Find the slope of the line that passes through the two points below (-4,9) and (8,7)
Answer:
-1/6
Step-by-step explanation:
The slope of the line can be found by
m = (y2-y1)/(x2-x1)
= (7-9)/(8 - -4)
-2 /(8+4)
-2/(12)
-1/6
at a breakfast diner a cup of coffee costs $2.75 and a muffin is $3.25. What is the sales tax on the two items if the rate was is 7.5%
Answer:$0.45
Step-by-step explanation:
Multiply 2.75 by .075 then multiply 3.25 by .075 and add them together
The sales tax amount of the breakfast is A = $ 0.45
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
To find the sales tax on the coffee and muffin, we first need to find the total cost of the items before tax:
Total cost = Cost of coffee + Cost of muffin
= $2.75 + $3.25
= $6.00
Next, we can calculate the sales tax by multiplying the total cost by the tax rate:
Sales tax = Total cost x Tax rate
On simplifying the equation , we get
A = $6.00 x 0.075
A = $0.45
Hence , the sales tax on the coffee and muffin is $0.45
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ3
a student says the prime factors of 17 are 1 and 17. Is the student correct? explain.
Answer:
Correct
Step-by-step explanation:
1. Factors
Are whole numbers that can divide the number completely.
2. Prime number
Number of factors that can be express in form of prime factorisation.
Prime factorisation of a number can be done by repeated division by prime numbers (number is written as the product of its prime factors)
For example, 17
List of factors, 1 and 17
Prime number, 17
Prime factorisation, 1×17=17
So why prime numbers cannot be express in form of prime factorisation?
Because, a prime number can only be divided by 1 or itself, so it cannot be factored any further. Not like the other number.
Brainliest would be appreciated :)
Final answer:
The student is incorrect; 17 is a prime number, and the only prime factor of 17 is 17 itself. The number 1 is not considered a prime factor as it is not a prime number.
Explanation:
No, the student is not correct in stating that the prime factors of 17 are 1 and 17. Prime factors are numbers that are both prime and divide the original number without leaving a remainder. The definition of a prime number is a number greater than 1 that has no positive divisors other than 1 and itself. In the case of 17, it is indeed a prime number, so it cannot have any prime factors other than itself. Therefore, the only prime factor of 17 is 17.
The number 1 is not considered a prime factor, as it is not a prime number because it does not meet the basic criterion of having exactly two distinct natural number divisors: 1 and itself. Examples of prime factors can be seen in other numbers, such as 15, whose prime factors are 3 and 5, both of which are prime numbers that divide 15 without leaving a remainder. In contrast, 17 can only be divided evenly by 1 and 17, and since 1 is not a prime number, 17 is the sole prime factor of 17.
Two tanks of brine are connected via two tubes. Tank 1 contains x(t) pounds of salt in 500 gallons of brine, and tank 2 contains y(t) pounds of salt in 500 gallons of brine. Brine is pumped from tank 1 to tank 2 at a rate of 50 gallons/min and brine is pumped from tank 2 to tank 1 at the same rate of 50 gallons/min, ensuring that the total volume of brine in the tanks remains constant over time.
a) Show that x(t) and y(t) satisfy the differential equations x'= − (1/10)x + (1/10)y ; y' = (1/10)x − (1/10)y.
b) If initially tank 1 contains no salt, and tank 2 contains 10 pounds of salt, use the method of elimination to find x(t) and y(t).
a. Salt flows into tank A at a rate of
(y(t)/500 lb/gal) * (50 gal/min) = y(t)/10 lb/gal
and out at a rate of
(x(t)/500 lb/gal) * (50 gal/min) = x(t)/10 lb/gal
so the net rate of change of the amount of salt in tank A is
[tex]x'(t)=\dfrac{y(t)}{10}-\dfrac{x(t)}{10}[/tex]
Similarly, you would find
[tex]y'(t)=\dfrac{x(t)}{10}-\dfrac{y(t)}{10}[/tex]
b. We have
[tex]x'=-\dfrac x{10}+\dfrac y{10}\implies x''=-\dfrac{x'}{10}+\dfrac{y'}{10}[/tex]
Notice that x' = -y', so
[tex]x''=-{2x'}{10}\implies 5x''+x'=0[/tex]
Solve for x: the characteristic equation
[tex]5r^2+r=r(5r+1)=0[/tex]
has roots [tex]r=0[/tex] and [tex]r=-\frac15[/tex], so
[tex]x(t)=C_1+C_2e^{-t/5}[/tex]
Again using the fact that y' = -x', we then find
[tex]x'(t)=-\dfrac{C_2}5e^{-t/5}\implies y'(t)=\dfrac{C_2}5e^{-t/5}\implies y(t)=C_1-C_2e^{-t/5}[/tex]
Given that x(0) = 0 and y(0) = 10, we find
[tex]\begin{cases}0=C_1+C_2\\10=C_1-C_2\end{cases}\implies C_1=5,C_2=-5[/tex]
how do the identity and associative property work?
Answer:
Step-by-step explanation:
The associative property is helpful while adding or multiplying multiple numbers. By grouping, we can create smaller components to solve. It makes the calculations of addition or multiplication of multiple numbers easier and faster. Here, adding 17 and 3 gives 20.
the identity property of 1 says that any number multiplied by 1 keeps its identity. In other words, any number multiplied by 1 stays the same. The reason the number stays the same is because multiplying by 1 means we have 1 copy of the number.
The weights of six animals at the zoom are shown in the table below
5
24
38
52
66
85
What is the mean absolute deviation? Round to the nearest tenth
Answer:
22.7
Step-by-step explanation:
To find the mean absolute deviation (MAD), first find the mean (or average).
μ = (5 + 24 + 38 + 52 + 66 + 85) / 6
μ = 45
Next, subtract the mean from each value and take the absolute value.
|5 − 45| = 40
|24 − 45| = 21
|38 − 45| = 7
|52 − 45| = 7
|66 − 45| = 21
|85 − 45| = 40
Sum the results and divide by the number of animals.
MAD = (40 + 21 + 7 + 7 + 21 + 40) / 6
MAD ≈ 22.7
what is the exact circumference of the circle?
Answer:
40
Step-by-step explanation: