Answer:
$38,640.00
Step-by-step explanation:
We know that Catrina earns $19.32 an hour. We also know she works 40 hours a week. So first, let's multiply 19.32 by 40 to see how much she makes a week.
19.32 × 40 = 772.80
Because of this, we now know that Catrina makes $772.80 a week. There are 52 weeks in a year. However, since she takes 2 weeks of vacation, we need to take off 2 weeks in the year. This leaves us with 50.
Finally, we multiply 772.80 and 50 to find her annual earnings:
772.80 × 50 = 38640
Therefore, her annual earnings will be $38,640.00.
how to right equivalent ratios
Answer
A ratio is a comparison of two quantities by division. Ratios describe a part-to-part comparison or a part-to-whole comparison. Ratios are written three ways: as a fraction, with a colon, and with the word “to.” The ratio for quantity a to quantity b is : a to b, a over b, and a:b
2. The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of ten batteries is subjected to an accelerated life test by running them continuously at an elevated temperature until failure, and the follow ing lifetimes (in hours) are obtained: 25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7. a. The manufacturer wants to be certain that the mean battery life exceeds 25 h. What conclusions can be drawn from these data (use a= 0.05)? b. Construct a 90% two-sided confidence interval on mean life in the accelerated test.
Answer:
Kindly check explanation
Step-by-step explanation:
Assuming a normal distribution :
Sample (x) :25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, 25.7
Null hypothesis : μ = 25
Alternative hypothesis : μ > 25
α = 0.05
Decision region :
Reject Null if :
t0 > t
t can be obtained from the t distribution table at : df = (n - 1) = 10 - 1 = 9 ; α = 0.05
Hence, t(0.05, 9) = 1.833
From the sample given ; t0
t0 = (m - μ) / (s /√n)
n = sample size = 10
s = sample standard deviation
m = sample mean
Using calculator :
25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, 25.7
Sample mean(m) = 26
Sample standard deviation (s) = 1.624
t0 = (26 - 25) / (1.624 /√10) = 1.947
1.947 > 1.833
Hence, reject Null
B)
Confidence interval at 90% ; α = 0.1
m ± t(0.1/2 ; 9) * s/√n
m - t * s/√n ≤ μ ≤ m + t * s/√n
26 - 1.833 * (1.624/√10) ≤ μ ≤ 26 + 1.833 * (1.624/√10)
25.059 ≤ μ ≤ 26.941
Determine the intercepts of the line.
y- intercept (_,_)
x- intercept (_,_)
Answer:
Therefore, the y-intercept is (0,2.5) and x-intercept is (3.5,0) .
Step-by-step explanation:
Intercept means the line touching the axis. As you look at the graph, y-intercept (line touching y-axis) is (0,2.5) and the x-intercept is (3.5,0) .
Take note :
When finding y-intercept, x-coordinate must be 0.
When finding x-intercept, y-coordinate must be 0.
Use square roots to solve the equation X^2= -64 over the complex numbers
Answer:
+/- 8i
Step-by-step explanation:
x^2 = -64
square root (x^2) = square root of (-64)
x = +/- 8* the square root of (-1)
x = plus or minus 8i
The solution for the given quadratic equation are 8i and -8i.
The given quadratic equation is x²=-64.
What is the complex number?A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.
Here, square root on both the sides of an equation
That is, x=√(-64)
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
= ±8i
Therefore, the solution for the given quadratic equation are 8i and -8i.
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Hello Please Answer Quickly:
Answer:
17 1/30
Step-by-step explanation:
Answer:
The answer is 1/6.
53/6 is the largest and -26/3 is the smallest.
LISTEN
Cal jogs from 10:28 AM until 11:15 AM. For about how long does Cal jog?
Answer:
47 minutes
Step-by-step explanation:
In elapsed time, it's better to make your problem more readable so it's easier to solve. Add 2 minutes into 10:28 so it turns into 10:30. Then add 30 minutes so it turns into 11:00 AM. Finally, add 15 minutes so it turns into the 11:15 you were looking for. When you combine the minutes allotted (2, 30, and 15) you get 47 minutes.
Consider this right triangle.
A
15
17
B
8
Which of the following ratios represents cos(B)?
Your friend says the absolute value equation |3x+8|-9=-5 has no solution because the constant on the right side of the equation is negative. Is your friend correct?
Make sure to show the work and solution the problem, as well as the explanation.
Answer:
No, ur friend is not correct
| 3x + 8 | - 9 = -5 You have to get the absolute value (and everything in it) on one side of the equal sign, and everything else on the other side. So we have to get that -9 across the equal sign by adding 9 to both sides.
| 3x + 8 } = -5 + 9
| 3x + 8 | = 4 So that number is not negative anymore.
now u can set up ur 2 equations and solve for x, your 2 equations would be:
3x + 8 = 4 and 3x + 8 = -4
** If that -9 would not have been there, then ur friend would have been correct.
Hope this helps!!
Step-by-step explanation:
In order to know that a graph shows a proportional relationship WITHOUT finding any y/x ratios or doing division, two conditions must be met. Name ONE of the two ways you know a graph is proportional JUST BY LOOKING AT IT. (You will come across another question that asks you to name the other condition, if you haven't already.) (10 points) please help
Answer:
I wish I've known, but try using Symbo-Lab or Math-Way. They help a lot.
Step-by-step explanation:
Graph y= -2x + 5. Help please.
Answer:
Step-by-step explanation:
What is the slope of a line perpendicular to the line whose equation is
15x + 12y = -144. Fully reduce your answer.
Step-by-step explanation:
Hey there!
Let the unknown slope be M2.
The given equation is;
15x + 12y = -144
From equation;
[tex]slope( m) = \frac{ - coeff. \: of \: x}{coeff. \: of \: y} [/tex]
[tex]m = \frac{ - 15}{12} [/tex]
[tex]m = \frac{ - 5}{4} [/tex]
For the condition of perpendicular lines;
[tex]m \times m2 = - 1[/tex]
[tex] \frac{ - 5}{4} \times m2 = - 1[/tex]
[tex] - 5m2 = - 4[/tex]
[tex]m2 = \frac{ - 4}{ - 5} [/tex]
Therefore, the slope is 4/5.
Hope it helps....
At pizza express it takes 6 cups of cheese to make 15 pizzas. At perfect pizza it takes 4 cups of cheese to make 6 pizzas. If the number of pizzas,y,is proportional to the cups of cheese,x, which pizza place has a larger constant of proportionality?
Pizza Express has a larger constant of proportionality than Perfect Pizzas because 1.6 > 1.5
15/6 6/4
Simplify
5/3 > 3/2
PE: 5/3 or 1.6
PP: 3/2 or 1.5
I had this on my math test
Describe the parametric equations which traces the unit circle starting (-1,0) in a clockwise direction.
Step-by-step explanation:
There are several ways we can do this.
x = cos t, y = sin t, t ≥ 0 traces the unit circle in a counterclockwise direction starting at (1, 0).
To change the direction, we can multiply one of these by -1. Then choose an initial value of t so that the starting point is (-1, 0).
x = -cos t, y = sin t, t ≥ 0
x = cos t, y = -sin t, t ≥ π
Or, we can change the direction by switching the equations.
x = sin t, y = cos t, t ≥ 3π/2
We can also multiply both by -1:
x = -sin t, y = -cos t, t ≥ π/2
Of these four examples, I would say the first is the simplest and most straightforward, but all of them achieve the same result.
3. After 6 weeks, who earned more money? How much more money?
Step-by-step explanation:
David earns $8 per hour. He works 40 hours each week. How much does he earn in 6 weeks? . After 6 weeks, who earned more money? How much more money?
he would earn 1,680 because if he works 40 hours per week when you divide by 7 cuz there a 7 days in a week he works 5 hours each day. then we multiply 5 with 8 and it's 40 so he earns 40 dollars per day then if week multiply 40 with 7 we get 280 and that's what he earns per week. then I came and tried to figure out how many days are in 6 weeks and I got 42 so then i came and multiplied the hours(5) which then gave me 210 then I multiped that (210) and 8 together and got 1,680
1.Michael earns $9 per hour. He works 28 hours each week. How much does he earn in 6 weeks?
so what i did was divide 28 by 7 the 7 was for the days and the 28 was for the hours so per day he works 4 hours and he earns 36 dollars per day .and then i came to know what the final answer was I came a figured out how many days are in 6 weeks and it's 42 so then I came and multiped the hours with the days which gave me 168 then I multiped that by the amount of money he earns per hour and it gave me 1,512 per 6 weeks
Factor the trinomial and solve
x²-10x+21
Answer:
(x-3)(x-7)
Step-by-step explanation:
Paula knits hats. The number of hats h she can knit varies directly with the amount of yarn (y) in yards she has. What does the constant of proportionality, 42, represent in this situation? The constant of proportionality is 42.
Answer:
y=42h or h=y/42
Step-by-step explanation:
The constant would be the number of yards of yarn required for each hat .
Explain why the triangles are similar. Then find the missing length, x. 5 m 8 m 4 m 10 m X 6 m Choose the reason that the triangles are similar A. Both triangles contain right angles and a corresponding angle of equal measure. Thus, two angles of the large triangle are equal in measure to two angles of the small triangle B. All right triangles are similar. C. Both triangles are right and scalene. OD The Pythagorean theorem states that a + b = c2. Thus, the corresponding sides are proportional. Find the missing length 2 X= m
Answer:
A. Both triangles contain right angles and a corresponding angle of equal measure. Thus, two angles of the large triangle are equal in measure to two angles of the small triangle
x = 3 m
Step-by-step explanation:
The figure given shows two right angles triangles having corresponding angles that are congruent and of the same measure.
If we find the ratios of their given corresponding side lengths, their ratios would be the same.
Thus: ratio of the side of the smaller ∆ to the larger ∆ = 4:8 = 5:10 = 4/8 = 5/10 = ½
½ is the scale factor. Therefore, both triangles are similar.
To find x, multiply the corresponding side length of the other triangle by the scale factor.
x corresponds to side length that is 6 m in the other triangle.
Therefore,
x = 6*½ = 3 m
The value of 'x' in the smaller triangle is 2 and both the triangles are similar because triangles contain right angles and a corresponding angle of equal measure. Therefore, two angles of the large triangle are equal in measure to two angles of the small triangle.
Given :
Two triangles are given in the figure.
The Pythagorean theorem can be used in order to determine the value of 'x' in the smaller triangle.
[tex]5^2=4^2+x^2[/tex]
[tex]x^2= 25-16[/tex]
x = 3
According to the given figure of the triangles, both triangles contain right angles and a corresponding angle of equal measure. Therefore, two angles of the large triangle are equal in measure to two angles of the small triangle. Hence both the triangles are similar.
Therefore, the correct option is A).
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Which of the following equations is equivalent to 2(a + 6) – 3(a – 5) = 18?
A: 5a + 27 = 18
B: 5a - 3 = 18
C: -a + 27 = 18
D: -a + - 3 = 18
Answer:
c
Step-by-step explanation:
what is the solution to the equation 1/4 x + 2 = -5/8 x - 5
Answer:
x = -8
Step-by-step explanation:
Original Equation:
1/4x + 2 = -5/8x - 5
Add 5 to both sides.
1/4x + 7 = -5/8x
Subtract 1/4x from both sides.
7 = -7/8x
Divide both sides by -7/8
Your answer is -8
Hope I helped :)
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Which list of numbers is in order from least to greatest value?
A. l-5l, l-2l, l3l, l4l
B. l-5l, l3l, -1l , l0l
C. l6l, l7l, l-5l, l-8l
D. l0l, l-4l, l5l, l-7l
What are the next three numbers in this pattern
11,22,12,23
Answer:
2,1,and 3????
Step-by-step explanation:
i really dunno if i am right always happy to help <3 have a nice day
HELP.!!!!
The area of a rectangular yard is given by the trinomial 2x^2 + x - 36. What are the possible dimensions of the yard?
A
(2x + 9) and (x-4)
B
(-2x + 9) and (-x + 4)
С
(2x - 2) and (x-4)
D
(2x - 4) and (x + 4)
Answer:
A . (2x + 9) and (x-4)
Explanation:
Given parameters:
Given trinomial;
2x² + x - 36
Possible dimensions of the yard = ?
Solution:
To solve this apply the quadratic factorization;
2x² + x - 36 = 0
2x² -8x + 9x - 36 = 0
2x(x - 4) + 9(x -4) = 0
(2x + 9) (x -4) = 0
The possible dimensions of the rectangular yard is (2x + 9) and (x -4)
What is the ratio 15 to 35 written as a fraction in lowest terms? 1/3 3/7 3/5 5/7
Answer:
3/7
Step-by-step explanation:
15 divided by 5 = 3
35 divided by 5 = 7
hope this helps
One number is 4 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 280, find the numbers. The three numbers are:
Answer: The first number is 30.
The second number is 120.
The third number is 130
Step-by-step explanation:
x + 4x + x+ 100 = 280
6x = 280-100
6x= 180
x = 30
A computer is normally $600. It is discounted and now it is only $450. What percent of the original price do you now pay?
Answer:
Hi there
Your answer is
We pay 75% of the original price.
Step-by-step explanation:
600$=100%
/600
1$ = 1/6%
*450
450$ = 75%
what is the answer? pls help
Answer:
There is no constant slope. I hope this helps!
Answer:
-3
Step-by-step explanation:
You can use the slop formula--
22-1 divided by 8-1 = 21/7 = 3
You can check by using any other two points and see if you get the same answer.
Hope this helps!
the table shows the gallons filled in a pool over time (ASAP)
Answer:
125, 250, 500, 625
Step-by-step explanation:
As you can see, half of the pool is 500. 2 halves would make a whole, concluding the pool is 1000. Then for the 1/8, do 1000/8. Getting 125. 1000/4 would make it 250. And then taking the 125 from the earlier division of 8 and multiplying by 5 will get you 625. Hope this helps <3
Which theorem or postulate justifies this statement? WILL GIVE BRAINLIEST THANK YOU
∠1≅∠11
vertical angles theorem
linear pair postulate
alternate interior angles theorem
alternate exterior angles theorem
corresponding angles postulate
Answer:
Correct answer is: Alternate Exterior Angles Theorem
Step-by-step explanation:
See attached picture.
The angles ∠1≅∠11 are equal by alternate exterior angles theorem and corresponding angles postulate. The correct options are A and D.
What is an alternate exterior angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
According to the alternate outside angle theorem, alternate exterior angles are regarded as congruent angles or angles of equal measure when two parallel lines are intersected by a transversal.
In the given image there are two parallel lines and one line is intersecting the two parallel lines at some angle.
Angle 1 and angle 11 will be equal to each other because of the two properties of angles that are alternate exterior angles theorem and corresponding angles postulate.
Therefore, the angles ∠1≅∠11 are equal by alternate exterior angles theorem and corresponding angles postulate. The correct options are A and D.
The image of the complete question is attached with the answer below.
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Dora saved $35. She earned $9.50 per hour at her job. How many hours must she work to have a total of $358 in her savings?
Answer:
34 Hours
Step-by-step explanation:
358-35= 323
323÷9.50= 34
Functionally important traits in animals tend to vary little from one individual to the next within populations, possibly because individuals who deviate too much from the mean have lower fitness. If this is the case, does variance in a trait rise after it becomes less functionally important? Billet et al. (2012) investigated this question with the semicircular canals (SC) of the three-toed sloth (Bradypus variegatus). The authors proposed that since sloths don't move their heads much, the functional importance of SC is reduced, and may vary more than it does in more active animals. They obtained the following measurements of the ratio of the length to width of the anterior SC in 6 sloths. Assume this represents a random sample. In other, more active animals, the standard deviation of this ratio is 0.09.
Answer:
The 95% confidence interval for the standard deviation is (0.14, 0.54).
Step-by-step explanation:
The complete data and question is:
Sloth CW Ratios ; {1.5 , 1.09 , 0.98 , 1.42 , 1.49 , 1.25}
The 95% confidence interval for the standard deviation of this data is < σ < (two decimals - include the leading zero) .
Solution:
Compute the sample standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum x=\frac{1}{6}\times 7.73=1.2883\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{6-1}\times 0.2387}=0.2185[/tex]
The (1 - α)% confidence interval for the variance is:
[tex]CI=\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2}}<\sigma^{2}<\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2}}[/tex]
Confidence level = 95%
⇒ α = 0.05
The degrees of freedom is,
df = n - 1 = 6 - 1 = 5
Compute the critical values of Chi-square:
[tex]\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.025,5}=12.833\\\\\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{0.975,5}=0.831[/tex]
*Use a Chi-square table.
Compute the 95% confidence interval for the variance as follows:
[tex]CI=\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2}}<\sigma^{2}<\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2}}[/tex]
[tex]=\frac{5\times (0.2185)^{2}}{12.833}<\sigma^{2}<\frac{5\times (0.2185)^{2}}{0.831}\\\\=0.0186<\sigma^{2}<0.2873\\\\=\sqrt{0.0186}<\sigma<\sqrt{0.2873}\\\\=0.1364<\sigma<0.5360\\\\\approx 0.14<\sigma<0.54[/tex]
Thus, the 95% confidence interval for the standard deviation is (0.14, 0.54).