Weekly paycheck of Catherine is $573.5 and her annual income is $29,904.01.
What is Unit Rate?Unit rate is defined as the number of one quantity needed for a single other quantity.
In other words, if we know the unit rate, we can calculate any amount of one quantity corresponding to any amount of the other quantity by multiplying the unit rate with the number of other quantity.
Here unit rate of Catherine's pay = $15.50 per hour
Given that Catherine works 37 hours per week.
Weekly paycheck of Catherine = unit rate × number of hours per week
= 15.50 × 37
= $573.5
Annual Income of Catherine = Unit rate × number of hours per year
There are 52.143 weeks in a year.
Catherine works 37 hours per week.
Number of hours Catherine working in an year = 52.143 × 37 = 1929.291
Annual Income of Catherine = 15.50 × 1929.291
= $29,904.01
Hence, calculation of student is wrong since the weekly paycheck is $573.5 and her annual income is $29,904.01.
To learn more about Unit Rate, click:
https://brainly.com/question/29781084
#SPJ1
What are the polar coordinates of the rectangular coordinates (2, -2√3)?
A. (4, 11π/6)
B. (4, 5π/3)
C. (2, 5π/3)
D. (2, 11π/6)
9514 1404 393
Answer:
B. (4, 5π/3)
Step-by-step explanation:
If you sketch the location of the point, you find the coordinates correspond to the side lengths of a 30°-60°-90° "special" triangle. The reference angle is 60°, or π/3 radians, and the magnitude of the vector is twice the short dimension, so is 2×2 = 4.
The polar coordinates are (4, 5π/3).
h(t)=3t-5
g(t)=t-2
Find (h·g)(t)
Answer:
[tex](3x - 5)(x - 2) = 3 {x}^{2} - 6x - 5x + 10 \\ = 3 {x}^{2} - 11x + 10[/tex]
What's the area of the following triangle? 8 ft 16 ft
Answer:
128 :)
Step-by-step explanation:
The area of the given triangle in the figure is 64 ft.².
A triangle is one of the most elementary geometric figures with 3 edges, 3 angles, and 3 vertices. The sum of the three angles of a triangle is 360°. The area of a triangle can be found using many methods but the most basic method is to half the product of height and length of the base of the triangle.
Given that
The height of the given triangle is 16 ft. and the length of the base is 16 ft.
As it is known that the area of a triangle is defined as
[tex]Area\ of\ a\ triangle = \frac{1}{2}\times height\times base[/tex]
So,
[tex]Area\ of\ a\ triangle = \frac{1}{2}\times 8\times 16\\Area\ of\ the\ triangle = 64 ft.^2[/tex]
Thus, the area of the given triangle is 64 ft.².
Learn more about Triangles here:
https://brainly.com/question/2773823
#SPJ6
A bi-monthly sports magazine has 48,000 subscribers when it charges $20 for a one year subscription. For every $1 increase in the yearly subscription price, the magazine assumes that it will lose 2,000 subscribers resulting in the equation below. Using the equation below, how much should the magazine sell for in order to maximize revenues? f (x) = (48,000 – 2,000x) (20 + x)
Answer:
To maximize the profits of the company, the subscription price should be raised to $ 22.
Step-by-step explanation:
Given that a bi-monthly sports magazine has 48,000 subscribers when it charges $ 20 for a one year subscription, and for every $ 1 increase in the yearly subscription price, the magazine assumes that it will lose 2,000 subscribers resulting in the equation below, to determine, Using the equation below, how much should the magazine sell for in order to maximize revenues, the following calculations should be performed:
f (x) = (48,000 - 2,000x) (20 + x)
X = 48,000 x 20 = 960,000
X = (48,000 - 2,000x1) x (20 + 1)
X = 46,000 x 21
X = 966,000
X = (48,000 - 2,000x2) x (20 + 2)
X = 44,000 x 22
X = 968,000
X = (48,000 - 2,000x4) x (20 + 4)
X = 40,000 x 24
X = 960,000
Therefore, to maximize the profits of the company, the subscription price should be raised to $ 22.
PLEASE HELP ME!! First correct answer gets branliest!!!
At the end of the football season a team analysis a number of goals they conceded each game the table shows that information.
Conceded goals: 0, 1, 2, 3, 4. Frequency 2, 8, 4, 10,6, 8.
A) Find out the median of the number of goals conceded.
B) Work out the mean number of goals conceded.
Answer:
median is 2
mean is 6.333
Step-by-step explanation:
arranging values in ascending or descending order you pick the middle for odd numbers which is 2. mean is sum of the total data divided by the number of items in the set which is 2+8+4+10+6+8 divide by 6 which is 6.333
i need help with this!
Answer:
1.4
Step-by-step explanation:
Please help!!!! I’m about to fail and I don’t want to
Answer:
But, you didn't ask any question.
Step-by-step explanation:
Remember to post your question next time.
A person's level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean and standard deviation of What is the probability that, for an adult after a 12-hour fast, x is less than 104
Answer:
The pvalue of Z when X = 104.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
What is the probability that, for an adult after a 12-hour fast, x is less than 104?
This is the pvalue of Z when X = 104.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{104 - \mu}{\sigma}[/tex]
[tex]\mu[/tex] and [tex]\sigma[/tex] are the values of the mean and of the standard deviation, respectively.
Find the surface area of the rectangular prism.
2 cm
6 cm
3 cm
3 cm
Answer:
72. If the second 3cm has some relevance, leave a note and I'll come back and modify my answer.
Step-by-step explanation:
Givens
L = 6 cm
W = 3 cm
H = 2 cm
I don't know what the extra 3 cm is for.
Formula
SA = 2*L*W + 2*L*H + 2*H*W
SA = 2*6*3 + 2*6*2 + 2*2*3
SA = 36 + 24 + 12
SA = 72
Answer:
Step-by-step explanation:
Please help me I will give you brainliest
ok here you go its B
ADDITION Mrs Kelly, please help him ga + 3 31 + 3 = + 3 5 + 3 6 + 3 4+ + LESTER GREEN, NIGHT SCHOOL
Answer:
2+3=5
3+3=6
4+3=7
5+3=8
6+3=9
Step-by-step explanation:
What is the unit digit of 3^(25) + 325 ? (Please show work and I will mark brainlist)
A. 1
B. 3
C. 5
D. 6
E. 8
Unit digit of [tex]3^{25} + 325[/tex] is 8.
Thus option E is correct .
Given , expression [tex]3^{25} + 325[/tex]
To identify the unit digit firstly the cyclicity of 3 ,
Cyclicity of 3 :
[tex]3^1 = 3\\\\3^2 = 9\\\\3^3 = 27\\\\3^4 = 81\\\\3^5 = 243\\\\3^6 = 729\\\\3^7 = 2187[/tex]
[tex]3^8 = 6561[/tex]
Here the cyclicity of 3 is 4 that is the unit digit of exponent of 3 will be repeating after every fourth power.
Here, the exponent of 3 is 25.
Divide 25 by the cyclicity of 3.
25/4
Remainder = 1
Hence the unit digit of [tex]3^{25[/tex] will be 3.
Unit digit of 325 is 5.
Add 5 + 3
= 8
Hence the unit digit will be 8.
Option E is correct .
Know more about exponents,
https://brainly.com/question/5497425
#SPJ4
7p≤42 help me in this thank it is 12 i have school tomorrow
In an effort to reduce boarding time, an airline tries a new method of boarding its planes. Historically, only 32% of passengers were satisfied with the boarding process random sample of 32 passengers using the new boarding process found 44% who said they were satisfied with the boarding process, yielding a test statistic of _______.
(a) What is the p-value of the hypothesis test to determine if this new boarding process resulted in improved passenger satisfaction?______ (4 decimals)
(b) What is the meaning of a Type 11 error in this context? The airline concludes a greater proportion of passengers were satisfied, when in reality, the same proportion of passengers were satisfied.
(c) Which significance level would minimize the likelihood of making a Type II error?
a = 0.01
a = 0.10
Answer:
Test statistics of 1.455
P-value = 0.0728
Step-by-step explanation:
From the given information:
The test statistics can be computed as:
[tex]Z = \dfrac{\hat p - p }{\sqrt{\dfrac{p(1-p)}{n} }} \\ \\ \\ Z = \dfrac{0.44 -0.32}{\sqrt{\dfrac{0.32(1-0.32)}{32} }}[/tex]
Z = 1.455
We want to test if the customer satisfaction increased significantly(one-tailed test)
Null hypothesis:
[tex]H_o : p= 0.32[/tex]
Alternative hypothesis:
[tex]H_a: p>0.32[/tex]
P-value = P(Z>1.455)
= 0.0728
b) Type II error implies the error of accepting [tex]H_o \ (i.e\ \text{ the null \ hypothesis)}[/tex]when [tex]H_a \ (i.e\ \text{ the alternative \ hypothesis)}[/tex] is true.
This implies inferring that there is no huge improvement in passenger's satisfaction when there is.
c) Type 1 and Type II errors are inversely proportional. In this situation, as one increases, the other definitely decreases.
∴ A Smaller value of Type II error will be achieved by a higher type I error.
⇒ 0.10
A 2003 study of dreaming found that out of a random sample of 111 people, 93 reported dreaming in color. However, the rate of reported dreaming in color that was established in the 1940s as 0.24. Check to see whether the conditions for using a one-proportion z-test are met assuming the researcher wanted to test to see if the proportion dreaming in color had changed since the 1940s. Are the conditions met?
A. No, the observations are not independent.
B. Yes, all the conditions are met.
C. No, the sample size is not large enough to produce at least 10 successes and 10 failures.
D. No, the population is not more than 10 times bigger than the sample size.
Answer:
B. Yes, all the conditions are met.
Step-by-step explanation:
According to the question
There is a random sample of 111 people also these people are independent
The population size is also not given so we assume that it should be on infinity i.e. it should be more than 10 times higher as compared with the sample size
And, the number of success in the sample is 93
So, the number of failure would be
= 111 - 93
= 18
So, the 93 and 18 would be higher than 10
Therefore, the option b is correct
what property is 8 • 1 and 8
PLEASE HELP ASAPPP!!!!
Answer: The answer is C. x = 3.46 cm i believe. sorry if im wrong
Step-by-step explanation:
Answer:
2.4 cm
Step-by-step explanation:
Since that they are similar, what you can do is:
3.0/1.2 = 2.5
1.2 * 2.5 = 3.0
0.96 * 2.5 = 2.4 cm
In the following diagram,
ℓ
∥
m
.
Solve for each of the variables w, x, y, and z. For each solution, explain, in complete sentences which special angles allowed you to create an equation in order to find a solution.
Answer:
x + 75 = 180, as these two angles form a straight angle.x = 180° - 75° = 105°y and x are supplementary angles as p is transversal of l and m:
y + x = 180°y = 180° - x = 180° - 105° = 75°z is same as 86° as vertical angles:
z = 86°w and z are supplementary angles as g is transversal of l and m:
w + z = 180°w = 180° - z = 180° - 86° = 94°
PLEASE HELP !! ILL GIVE BRAINLIEST !! 100 POINTS
Answer:
124
Step-by-step explanation:
Elm St. and Oak St. are parallel lines.
Cedar St. is a transversal to the other two streets.
When parallel lines are cut by a transversal, corresponding angles are congruent.
The angles with measures 9x + 61 and 3x + 103 are corresponding angles, so they are congruent and have the same measure.
9x + 61 = 3x + 103
Subtract 3x from both sides.
6x + 61 = 103
Subtract 61 from both sides.
6x = 42
Divide both sides by 6.
x = 7
9x + 61 = 9(7) + 61 = 63 + 61 = 124
3x + 103 = 3(7) + 103 = 21 + 103 = 124
a right rectangular prism has a length of 10 centimeters, a width of 2.5 centimeters and a height of 0.9 centimeters. what is the volume of the rectangular prism?
Answer:
22.5 cm
Step-by-step explanation:
length times width times height
Sophie’s Clues:
Sophie made up some clues about the rectangles. She only thought of numbers between 1 through 30.
Rectangle #1 Clue:
Width = N. Length = 2 N
Draw a picture for a rectangle that fits the information. Label each dimension.
What is the value of N in this case? Why does it make sense?
Answer:
322223
Step-by-step explanation:
Does anyone know the answer to this?
explain how to draw a line segments that measures 2 7/16 inches
if a picture please type the words for me
9514 1404 393
Answer:
draw the line using a ruler on which you have identified points 2 7/16 inches apart
Step-by-step explanation:
On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.
Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches long.
Find the value(s) of the variable(s). If necessary, round decimal answers to the nearest tenth.
Answer:
x = 16.2
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 54°
Hypothenus = 20
Opposite = x =?
The value of x can be obtained by using the sine ratio as illustrated below:
Sine θ = Opposite / Hypothenus
Sine 54° = x / 20
Cross multiply
x = 20 × Sine 54
x = 20 × 0.8090
x = 16.2
Thus, the value of x is 16.2
In ΔEFG, the measure of ∠G=90°, the measure of ∠E=78°, and GE = 33 feet. Find the length of FG to the nearest tenth of a foot.
Answer:
I just did this on Delta Math lol:
Answer: 155.3 ft
Step-by-step explanation:
What is the area of the kite?
Answer:
Step-by-step explanation:
area of kite=product of diagonals ÷2=(30×4)÷2=120/2=60 ft²
anyone caring to help me?? please and thank you it would be very much appreciated <3
Answer:
75
90
15, i think ??
165
hope this helps !!!! :D
Step-by-step explanation:
Solution:
Here,
In triangle LKM,
6x+5x+x=180
12x=180
x=180/12
x=15
Now,
1.75
2.90
3.15
4.165
What is four x equals twelve
Answer:
x= 3
Step-by-step explanation:
12 ÷ 4 +3
The algebraic expression 4x = 12 represents "four x equals twelve" and the solution of the expression 4x = 12 is the value of variable x is 3.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The given statement is "four x equals twelve"
According to the given question, translate the phrase into an algebraic expression:
⇒ 4x = 12
Thus, the algebraic expression is 4x = 12 represents "four x equals twelve"
Now the above expression solves for variable x,
⇒ 4x = 12
Divided by 4 into both sides of the above equation,
⇒ 4x / 4 = 12 / 4
⇒ x = 3
Therefore, the solution of the expression 4x = 12 is the value of variable x is 3.
To learn more about the Algebra link is given below.
brainly.com/question/953809
#SPJ2
Jack and Carl share a 30-ounce bucket of clay. By the end of the week, Jack has used 1/10 of the bucket, and Carl has used 2/5 of the bucket of clay. How many ounces are left in the bucket?
Answer:
15
Step-by-step explanation:
Since we're working with fractions, and the thirty ounce bucket is equivalent to 30/30. In order to make this easier, let's use the denominator of 30 for all of the fractions. Now that we've made them all equal, turning 1/10 to 3/30, and 2/5 to 12/30, let's add. 12 + 3 is 15, and 15/30 is half of 30/30. There was 15 ounces, or 1/2 of the tub, left.
A researcher is 95% confident that the interval from 19.8 to 31.5 captures y = the true mean number of unbroken
crackers in a certain-sized bag.
Is it plausible that the true mean number of unbroken crackers for all bags of this size may be 302
ОООО
No, this is not a plausible value for the population mean, because 30 is within the 95% confidence interval.
No, this is not a plausible value for the population mean, because 30 is not within the 95% confidence interval.
Yes, this is a plausible value for the population mean, because 30 is within the 95% confidence interval.
Yes, this is a plausible value for the population mean, because 30 is not within the 95% confidence interval.
No, this is not a plausible value for the population mean, because 30 is not within the 95% confidence interval.
What is confidence interval?Based on a sample from a population, a confidence interval is a range of values that is likely to include the true value of that population parameter. In statistics, samples are frequently used to calculate population characteristics like the mean or percentage. The estimate could not be precisely equal to the real value of the population parameter, though, as the sample is only a portion of the population.
According to the statement in the issue, there should be between 19.8 and 31.5 unbroken crackers in a bag of a specific size with 95% confidence.
Hence, no, this is not a plausible value for the population mean, because 30 is not within the 95% confidence interval.
Learn more about confidence interval here:
https://brainly.com/question/29680703
#SPJ1