Function 1: Alan starts with $30 this week. He spends $5.30 per week. Let y be the amount remaining as a function of the number of weeks, X. 0 30 1 24.70 2 19.40 3 14.1
Answers
Answer:
y = 30 - 5.30x
Step-by-step explanation:
y-intercept: 30
slope: 5.30x
Just plug in the amount of weeks on x, and then subtract from 30.
Related Questions
find the total cost a) The radius of a circular field is 63 m. Find the perimeter of the field. Also, find the length of wire required to fence it with 5 rounds. =
Answers
The perimeter of the circle is 395.64 m, and the length of wire needed to fence it with 5 rounds is 1,978m
How to find the perimeter?We kow that for a circle, the perimeter is equal to its circumference, and the circumference of a circle of radius R is:
C = 2*pi*R
Where pi = 3.14
Then the perimeter of a circle of radius of 63m is:
Perimeter = 2*3.14*63m = 395.64 m
And the length of wire needed to fence it with 5 rounds is 5 times that, so we will get:
total length = 5*395.64 m = 1,978m
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an emergency room nurse believes the number of upper respiratory infections is on the rise. the emergency room nurse would like to test the claim that the average number of cases of upper respiratory infections per day at the hospital is over 21 cases. using the computed test statistic of 2.50 and the critical value of 2.33, is there enough evidence for the emergency room nurse to reject the null hypothesis?
Answers
To determine whether there is enough evidence to reject the null hypothesis, we need to compare the computed test statistic to the critical value.
In this case, the computed test statistic is 2.50 and the critical value is 2.33. If the computed test statistic falls in the rejection region beyond the critical value, we can reject the null hypothesis. Conversely, if the computed test statistic falls within the non-rejection region, we fail to reject the null hypothesis.In this scenario, since the computed test statistic (2.50) is greater than the critical value (2.33), it falls in the rejection region. This means that the observed data is unlikely to occur if the null hypothesis were true.
Therefore, based on the given information, there is enough evidence for the emergency room nurse to reject the null hypothesis. This suggests that there is sufficient evidence to support the claim that the average number of cases of upper respiratory infections per day at the hospital is over 21 cases.
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There is enough evidence to reject the null hypothesis in this case because the computed test statistic (2.50) is higher than the critical value (2.33). This suggests the average number of daily respiratory infections exceeds 21, providing substantial evidence against the null hypothesis.
Explanation:Yes, there is enough evidence for the emergency room nurse to reject the null hypothesis. The null hypothesis is typically a claim of no difference or no effect. In this case, the null hypothesis would be an average of 21 upper respiratory infections per day. The test statistic computed (2.50) exceeds the critical value (2.33). This suggests that the average daily cases indeed exceed 21, hence providing enough evidence to reject the null hypothesis.
It's crucial to understand that when the test statistic is larger than the critical value, we reject the null hypothesis because the observed sample is inconsistent with the null hypothesis. The statistical test indicated a significant difference, upheld by the test statistic value of 2.50. The significance level (alpha) of 0.05 is a commonly used threshold for significance in scientific studies. In this context, the finding suggests that the increase in respiratory infection cases is statistically significant, and the null hypothesis can be rejected.
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True or False
15. (True or False) Any 3 distinct points are always coplanar.
16. (True or False) Any 2 distinct circles are always coplanar.
17. (True or False) If 2 lines intersect once then the lines are coplanar.
18. (True or False) Two lines that are skew can sometimes intersect.
19. (True or False) An angle and a circle can have more than 3 intersections
20. (True or False) Two distinct circles can have more than 2 intersections.
21. (True or False) Any given line and point are always coplanar.
Answers
Answer:
15. True
16. False
17. True
18. False
19. True
20. False
21. True
Step-by-step explanation:
15. The three points can be taken as being two points on a line adjacent to a point which always forms a plain when the ends of the line are connected to the point
16. The two circles can be on different planes
17. With one line fixed, the other line can be rotated until both lines are in the flat plane
18. The definition of skew lines are lines in different planes that are not parallel and that do not intersect
19. Whereby the angle crosses the circumference of the circle twice, the number of intersections = 4
20. Two distinct circles can only intersect twice
21. A plane can always be drawn with any three points
3. Newton wins a $50 gift card to a craft
store. He uses the card to buy a
scrapbook for $19.99 and a set of
markers for $10.75. How much money
is left on his gift card?
Answers
Answer:
$19.26
Step-by-step explanation:
Newton wins a $50 gift card to a craft store. He uses the card to buy a scrapbook for $19.99 and a set of markers for $10.75. How much money is left on his gift card?
beginning = $50
so:
50 - 19.99 - 10.75 = $19.26
* This answer assumes no sales tax.
For which of the following is the shape of the sampling distribution of the sample mean approximately normal? a random sample of size 5 from a population that is approximately normal a random sample of size 10 from a population that is strongly skewed to the right a random sample of size 60 from a population that is strongly skewed to the left.
Answers
Answer:
a random sample of size 5 from a population that is approximately normal
a random sample of size 60 from a population that is strongly skewed to the left.
Step-by-step explanation:
They are both correct
Answer:
D. Approximately Normal
If a =2 , b=-3 , c =-4 prove that a MULTIPLY (b+c) =(a multiply b) + (a multiply c)
Answers
Answer:
Step-by-step explanation:
a(b+c) = (ab)+(ac)
by property of distribution
a(b+c) = ab + ac
Which one and don’t lie!!!!!!!!!!!!
Answers
Answer:
Im pretty sure the one with the negative slope, so A.(edited im wrong)
Step-by-step explanation:
Since its descending, its impossible for it to start at zero, making it non proportional
hopefully i helped
Answer:
The answer is the graph will not pass through (0,0)
Step-by-step explanation:
Triangle CDE has vertices C(2, -1), D(7,-4), and E(4, -6) with the translation rule: (x,y)-(x-3, y+8). C' would be (
Answers
C' would be (-1,7), Triangle Illustrations Triangles are three-sided polygons with three vertices.
What is meant by Triangle?A triangle is a 2-dimensional closed shape with three sides, three angles, and three vertices. A triangle is a type of polygon. The figure above depicts an ABC triangle. Triangle Illustrations Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The sum of the triangle's three angles equals 180 degrees. A triangle is a polygon with three sides. It has three sides as well as three vertices that form three angles. Any triangle with vertices is denoted as A B C and is illustrated below: Triangle shapes include: Triangle of Scalene: All of the sides are unequal in length.Therefore,
'a' unit up = (x,y) ⇒(x, y + a)
'a' unit down = (x,y) ⇒(x, y - a)
'a' unit left = (x,y) ⇒(x - a, y)
'a' unit right = (x,y) ⇒(x + a, y)
Given,
(x,y) ⇒(x-3),(y+8)
Simplifying,
C(2,-1)⇒C'(2-3, -1+8)
= C'(-1,7)
D(7,-4) ⇒ D'(7-3, -4+8)
= D'(4,4)
E(4,-6) ⇒ E'(4-4, -6+8)
= E'(0,2)
Hence, C'= (-1,7)
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What is the volume of this sphere rounded to the nearest hundredth?
Answers
Answer:
2144.7
Step-by-step explanation:
Volume of a sphere is V= \(\frac{4}{3} \pi r^{3}\)
V= \(\frac{4}{3} \pi 8^{3}\)
V=(4 /3)·π·8^3≈2144.66058 --> 2144.7
the tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,00 miles and a standard deviation of 2700 miles. what warranty should the company use if they want 96% of the tires to outlast the warranty?
Answers
According to the standard deviation, the company should offer a warranty period that covers at least 65,895 miles to ensure that 96% of the tires sold will outlast the warranty.
To do this, we use a z-score table, which gives the probability of getting a z-score less than or equal to a given value. The z-score is a measure of how many standard deviations a data point is from the mean.
To find the z-score for the top 4% of the tires, we first subtract 96% from 100% to get 4%. Then we divide this by 2 to get 2%, as we are interested in the area under the normal distribution curve in the right tail. Using the z-score table, we find that the z-score corresponding to a 2% area under the curve is approximately 2.05.
Next, we use the formula for converting a z-score to a data value:
z = (x - μ) / σ
where z is the z-score, x is the data value, μ is the mean, and σ is the standard deviation. Solving for x, we get:
x = z x σ + μ
Plugging in the values, we get:
x = 2.05 x 2700 + 60000
x ≈ 65,895
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Let d0, d1, d2, … be a sequence defined by the formula dn = 3n − 2n for every integer n ≥ 0. Fill in the blanks to show that d0, d1, d2, … satisfies the following recurrence relation. dk = 5dk − 1 − 6dk − 2 for every integer k ≥ 2. By definition of d0, d1, d2, …, for each integer k with k ≥ 2, in terms of k, dk = (*) dk − 1 = (**) and dk − 2 = (***). It follows that for each integer k ≥ 2, in terms of k, 5dk − 1 − 6dk − 2 = 5 − 6 by substitution from (**) and = · 3k − 1 − · 2k − 1 − 2 · 3 · 3k − + 2 · 3 · 2k − = · 3k − 1 − · 2k − 1 − 2 · 3k − + 3 · 2k − = · 3k − 1 − · 2k − 1 = 3k − 2k = dk by substitution from
Answers
On simplifying the above equation, 5dk - 1 - 6dk - 2 = -3k + 7 = 3k - 2k = dk. Thus, we have proved that the sequence satisfies the recurrence relation for every integer k ≥ 2.
Given that the sequence is defined as dn = 3n − 2n for every integer n ≥ 0. We need to fill in the blanks to show that d0, d1, d2, …
satisfies the following recurrence relation dk = 5dk − 1 − 6dk − 2 for every integer k ≥ 2.
By definition of d0, d1, d2, …, for each integer k with k ≥ 2, in terms of k,dk = 3k - 2kdk - 1 = 3(k-1) - 2(k-1)dk-2 = 3(k-2) - 2(k-2)
For k ≥ 2, let's substitute (*) dk - 1 as 3(k-1) - 2(k-1), (**) dk - 2 as 3(k-2) - 2(k-2),
which means, dk = 5dk - 1 - 6dk - 2= 5(3(k-1) - 2(k-1)) - 6(3(k-2) - 2(k-2))= 5(3k - 3 - 2k + 2) - 6(3k - 6 - 2k + 4)= 15k - 15 - 10 + 10 - 18k + 36 + 12k - 24= -3k + 7
On simplifying the above equation, 5dk - 1 - 6dk - 2 = -3k + 7 = 3k - 2k = dk
Thus, we have proved that the sequence satisfies the recurrence relation for every integer k ≥ 2.
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Someone text me on sc queenalyssa_05 :)
Answers
Answer:
No
Step-by-step explanation:
Answer:
Why... Um... ok
Step-by-step explanation:
Your favorite shoes were on sale for 35% off. The shoes have a regular price of $160. Sales tax was 4%. What is the total price paid for the shoes including the discount and tax?
Answers
Answer:
108.16
Step-by-step explanation:
n which of the following pairs do both numbers contain the same number of significant figures? (2.2 □ ) a. 3.44×10 −3
g and 0.0344 g b. 0.0098 s and 9.8×10 4
s c. 6.8×10 3
m and 68000 m d. 258.000 g and 2.58×10 −2
g
Answers
Answer:
ok, here is your answer
Step-by-step explanation:
The answer is (d) 258.000 g and 2.58×10^-2g.Both numbers have the same number of significant figures, which is six.The first number, 258.000 g, has three significant figures after the decimal point, and three before the decimal point. The zeros after the decimal point are significant because they are part of a measured quantity.The second number, 2.58×10^-2g, is written in scientific notation. It also has six significant figures because the number 2.58 has three significant figures, and the exponent -2 has two significant figures.-
mark me as brainliestPlease help me with my algebra homework?
What is the sum of the geometric sequence 1,-6,36,.... if there are 7 terms?(1 point)
Answers
Answer:
Step-by-step explanation:
a=1
r=-6/1=-6
\(S_{7}=a\frac{1-r^n}{1-r} =1\frac{1-(-6)^7}{1-(-6)} \\=\frac{1+6^7}{1+6} \\=\frac{1+279936}{7} \\=\frac{279937}{7} \\=39991\)
Complete the statement below.
The expression________
illustrates the commutative property of multiplication.
Answers
The expression that completes the blank is A. 11 * w * 3 = 11 * 3 * w
The commutative property is a mathematical concept that states that the order in which we multiply the factors does not affect the product.
According to the above, the example of commutative property is:
11 * w * 3 = 11 * 3 * wThis expression is the one with the commutative property because it has the same factors on both sides of the equal in different order and that does not affect the result.
This question is incomplete because you are missing the options, here are the options:
A. 11 * w * 3 = 11 * 3 * w
B. 11 * w * 3 = 11 * w * 3
C. (11 * w) * 3 = 11 * (w * 3)
D. 11 * (w * 3) = (11 * w) + (11 * 3)
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2. how many license plates can by made using either three uppercase english letters followed by three digits or four uppercase english letters followed by two digits?
Answers
There would be 63,273,600 and 43,524,000 license plates, if repetition is allowed, and not, respectively that can be made using either three uppercase English letters followed by three digits or four uppercase English letters followed by two digits.
Based on the given information, a license plate may either be:
1. three uppercase English letters followed by three digits
26 ways to fill in the first, second, and third letter and
10 ways to fill in the first, second, and third digit
2. four uppercase English letters followed by two digits
26 ways to fill in the first, second, third, and fourth letter and
10 ways to fill in the first and second digit
Thus, by Fundamental Principle of Counting, there are 63,273,600 possible license plates, if repetition is allowed, and 43,524,000 possible license plates, if repetition is not allowed.
(with repetition)
1. 26 x 26 x 26 x 10 x 10 x 10 = 17,576,000
2. 26 x 26 x 26 x 26 x 10 x 10 = 45,697,600
17,576,000 + 45,697,600 = 63,273,600
(without repetition)
1. 26 x 25 x 24 x 10 x 9 x 8 = 11,232,000
2. 26 x 25 x 24 x 23 x 10 x 9 = 32,292,000
11,232,000 + 32,292,000 = 43,524,000
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Identify the sampling technique used in each study. Explain your reasoning. (a) A journalist goes to a campground to ask people how they feel about air pollution (b) For quality assurance, every tenth machine part is selected from an assembly line and measured for accuracy. (c) A study on attitudes about smoking is conducted at a college. The students are divided by class (freshman, sophomore, junior, and senior). Then a random sample is selected from each class and interviewed.
Answers
The sampling technique used in each study is as follows: (a) convenience sampling, (b) systematic sampling, and (c) stratified random sampling.
(a) In the first study, where a journalist goes to a campground to ask people about their feelings regarding air pollution, the sampling technique used is convenience sampling. This is evident because the journalist approaches individuals who are readily available and easily accessible at the campground. However, convenience sampling may introduce bias as it does not ensure a representative sample of the population.
(b) In the second study, where every tenth machine part is selected from an assembly line for measurement, the sampling technique used is systematic sampling. Systematic sampling involves selecting every nth element from a population after establishing a sampling interval. In this case, every tenth machine part is selected to ensure a systematic and unbiased approach to quality assurance.
(c) In the third study, where attitudes about smoking are studied at a college and students are divided by class and then randomly sampled from each class for interviews, the sampling technique used is stratified random sampling. Stratified random sampling involves dividing the population into homogeneous subgroups (strata) and then randomly selecting samples from each subgroup. By dividing the students into different class strata and randomly selecting samples from each class, this study aims to ensure representation from each class in the final sample.
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1. sec x-tanx sinx = 1/sec x2. 1+cosx/sinx = csc x Cot x
Answers
Both of the given equations have no solution.
1. sec x-tanx sinx = 1/sec x
The left-hand side of the equation can be simplified by using the identity that sec(x) = 1/cos(x) and tan(x) = sin(x)/cos(x). So,
sec x - tan x sin x = 1/cos x - sin x/cos x sin x = 1/cos x - sin^2 x/cos x = 1/cos x - (1-cos^2 x)/cos x = 1/cos x - (1/cos x) = 1/cos x - 1/cos x = 0.
On the right-hand side, sec x = 1/cos x, so 1/sec x = cos x. Hence,
0 = cos x
This equation has no solution, which means that the original equation sec x - tan x sin x = 1/sec x has no solution.
2. 1 +cosx/sinx = csc x Cot x
We can simplify the left-hand side of the equation by using the identity that csc(x) = 1/sin(x) and cot(x) = cos(x)/sin(x). So,
1 + cos x/sin x = 1/sin x * cos x/sin x = cot x.
Hence,
1 + cot x = cot x
This equation has no solution, which means that the original equation 1 +cosx/sinx = csc x Cot x has no solution.
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Can yall help me with this. -4(2x-7)<10-2x Write the solution in the form x ? A, where ? Represents the correct inequality symbol and a represents the value of the solution.
Answers
Answer: x > 3
Step-by-step explanation:
We have the inequality:
-4*(2*x - 7) < 10 - 2*x
We want to find the possible values for x.
first, we expand the left side.
-8x + 28 < 10 - 2x
now we want to have all the terms with x in one side and the terms without x in the other side.
-8x + 2x < 10 - 28
-6x < -18
now we divide both sides by -6, as we divide by a negative number, the direction of the inequality changes:
x > 18/6 = 3
x > 3
This means that x must be larger than 3.
please help i will mark brainliest
Answers
Answer:
So I'm not sure if the shapes have to do anything for it but I solved for x
5. x = 1
AGAIN SORRY IF THIS IS WRONG I HAVENT DONE THIS KIND OF MATH IN 5 YEARS.
researchers wanted to see which species of lizard (a, b, or c) is most likely to survive a bacterial infection. so they infected a total of 38 lizards and recorded how many survived after 48 hours. of the 15 species b lizards, 40% survived. for those that were species c, one more survived than died. and of the 24 lizards that died, one-third of them were species a. a. create a contingency table to display this data. (3pt) b. what proportion of the lizards in this study were either species b or c? (1pt) c. what is the probability that a species b lizard in this study did not survive? (1pt) d. are survival and being species c independent events for these lizards? justify your answer. (3pt)
Answers
a. The contingency table for the given data is attached file below.
b. The proportion of lizards that were either species A or B is 0.605.
c. The probability that a species C lizard in this study did not survive is 0.4667.
a.
The contingency table for the given data is attached file below.
b.
The proportion of lizards that were either species A or B can be calculated as:
P(A or B) = (15+8)/(15+8+6+9+4)
P(A or B) = 23/38
P(A or B) = 0.605
c.
The probability that a species C lizard in this study did not survive can be calculated as:
P(Not survive| C) = 7/15
= 0.4667
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The table shows the distance Allison drove on one day of her vacation. Is the relationship between the distance and the time a proportional relationship? Did she drive at a constant speed? Complete the explanation.
Time (h) 1 2 3 4 5
Distance (mi) 55 100 165 280 250
Answers
Answer:
we conclude that the relationship between distance and time is NOT proportional.
Hence, she did not drive at a constant speed.
Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get the equation
y ∝ x
y = kx
k = y/x
where 'k' is called the constant of proportionality.
In our case, the table shows the distance Allison drove on one day of her vacation.
Time (h) 1 2 3 4 5
Distance (mi) 55 100 165 280 250
using the equation
k = y/x
susbtitute y = 55, x = 1
k = 55/1 = 55
substitute y = 100, x = 2
k = y/x
k = 100 / 2 = 50
substitute y = 165, x = 3
k = y/x
k = 165 / 3 = 55
substitute y = 280, x = 4
k = y/x
k = 280 / 4 = 70
substitute y = 250, x = 5
k = y/x
k = 250 / 5 = 50
It is clear that the value of 'k' does not remain constant.
Therefore, we conclude that the relationship between distance and time is NOT proportional.
Hence, she did not drive at a constant speed.
If (6 ki)² = 27-36i, the value of k is
Answers
Answer: k = √27-i
Step-by-step explanation:
i just need the final answer. thanks! :)
Answers
What is the length of the each side?
please someone help
Answers
Answer:
each side 5
Step-by-step explanation:
with 2 equal internal base angles, we know this is an isosceles triangle
this being isosceles also tells us that the 2 opposite sides are also equal
Therefore: x + 2 = 3x - 4
solving for x
x - 3x = -4 -2
-2x = -6
x = -6 ÷ -2
× = 3
substituting x:
x +2 = 3 + 2 = 5
3x-4 = 9 - 4 = 5
based on a random sample of 1505 us adults, we built a confidence interval for the proportion of us adults that say the country's best days are still ahead The 95% confidence interval is from 0.588 to 0.612. Select the statement below that correctly interprets this confidence interval. We are 95% confident that the sample proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612 We are 95% confident that the population proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612. 95% of the population proportions of US adults that believe owning a house is very important to their quality of life will fall within this interval. The probability that the population proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612 is 0.95.
Answers
The correct interpretation of the given confidence interval is: We are 95% confident that the population proportion of US adults that say the country's best days are still ahead is between 0.588 and 0.612.
This means that if we were to take many random samples of the same size from the population and construct 95% confidence intervals for each sample, about 95% of these intervals would contain the true population proportion of US adults that say the country's best days are still ahead. It does not say anything about the proportion of US adults who believe owning a house is very important to their quality of life or the probability of the population proportion falling within the interval.
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\(\sqrt{24n^3}\) (simplify radical) please show work
Answers
Answer:
The answer is
\(2n \sqrt{6n} \)Step-by-step explanation:
\( \sqrt{24 {n}^{3} } \)First of all factor out the perfect square out.
In this question the perfect squares are 4 and x²
So we have
\( \sqrt{4 \times {n}^{2} \times 6n} \)Separate the radicals
That's
\( \sqrt{4} \times \sqrt{ {n}^{2} } \times \sqrt{6n} \)Simplify
\( \sqrt{4} = 2 \\ \sqrt{ {n}^{2} } = n\)So we have
\(2 \times n \times \sqrt{6n} \)We have the final answer as
\(2n \sqrt{6n} \)Hope this helps
Answer:
\(2n \sqrt{6n} \)
Step-by-step explanation:
\( \sqrt{24n {}^{3} } \)
Factor out the perfect square ⬜\( \sqrt{2 {}^{2} } \times 6 {n}^{3} \)
\( \sqrt{ {2}^{2} } \times 6n {}^{2} \times n\)
Please the square root is for the entire formula ⬆️⬆️⬆️the root of the product is equals to the root of each Factor\( \sqrt{2 {}^{2} } \sqrt{n {}^{2} } \sqrt{6n} \)
reduce the index of the radical and exponent with 2\(2 \sqrt{n {}^{2} } \sqrt{6n} \)
\(2n \sqrt{6n} \)
Solution2n square root 6n
\(2n \sqrt{6n} \)
Hope this helps.....
Examine the following function f(x).
A “U” shape graph with a flattened vertex, opening up. It passes through points (negative 1, negative 6), (0, negative 7) and (1, negative 6).
© 2018 StrongMind. Created using GeoGebra.
Which statements are correct about the function f(x)?
Select all that apply.
f(x) is an even function.
f of x, is an even function.
f(−1)=f(1)f of negative 1 is equal to f of 1
f(x) is an odd function.
f of x, is an odd function.
f(−1)=−f(1)f of negative 1 is equal to negative f times 1
f(x) has rotational symmetry.
Answers
The two statements that are true about the given function are:
"f(x) is an even function" "f(1) = f(-1)"Which statements are true about the given function?
Remember that an even function is a function with the property:
f(x) = f(-x).
This means that the y-axis is an axis of symmetry.
In the image we can see that this is true, the y-axis (the horizontal axis) divides the graph in two equal halves.
Then the first statement:
"f(x) is an even function" is true.
From the definition of even functions, we conclude also that f(1) = f(-1), so the second statement is also true.
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What is the 13th term of the geometric sequence
4, 12, 36, 108, ...?
Answers
Answer: 2,125,764
Step-by-step explanation:
You can use the equation y=ar^n-1 to find the 13th term where a is the starting term, r is the common ratio, and n is the nth term
The next number is 12/4=3 times greater than the first. So if this sequence is a geometric one, then the next term must be 12*3=36. This is true, and the next term must be 36*3=108, which is also true. Therefore this sequence is a geometric one and its common ratio is 3. Therefore the equation is:
y=4*3^(n-1)
Substitute 13 for n:
y=4*3^(13-1)
y=4*3^12
y=2125764
Therefore, the 13th term of this geometric sequence is 2,125,764