The cost c in dollars of renting a paddle board for h hours is given by c = 25 + 7h. After how many hours is the cost $81?
When using the formula zx = x − μ σ for the z-score for the 11.7 data point:
1. x= 11.7 μ = 7
2. z11.7= 1.3
3. Is 11.7 within a z-score of 3?
a. Yes because z11.7 < 3.
4. Which statement is true of z11.7?
b. z11.7 is between 1 and 2 standard deviations of the mean.
The value of the z-score is 1.33.
What is a z-score?The z-score is defined as the mean (average) values, measured in terms of standard deviations from the mean.
The formula is used to calculate z-score is;
Z-score = X-μ / σ
= 11.7-7 / 3.52
= 4.7/3.52
= 1.33
Hence, the value of the z-score is 1.33.
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Identify the fraction as proper, improper, or mixed . (If the fraction is equivalent to 1, choose "one" in the blank.)
find the slope of the line that contain the following points A(5,6),B(10,8)
Find the sum of (x+5) and (2x+3)
Subtract 8 1/5-4 2/5. Simplify the answer and write as a mixed number.
Answer: 4 1/5
Step-by-step explanation:
Subtract 8 1/5 - 4 2/5
Simplify answer
Write as mixed number
8-4 = 4
1/5 - 2/5 = 4 1/5
Simplify: (27)^1/3•(27)^2/3
Answer:
3
Step-by-step explanation:
Because i said so
Which choice represents the simplified form of the expression below and the values of x for which it is defined?
√3x^3 ÷ √x
A x √3 when x > 1
B x√ 3 when x < 0
C x √2x when x >0
D x√3 when x>0
An art store offers prints in two sizes. The store earns $15 on each small print sold and $25 on each large print sold. The owner needs to make a daily profit of at least $700 in order to cover costs. Due to equipment limitations, the number of small prints made must be more than three times the number of large prints. Given that x represents the number of small prints sold and y represents the number of large prints sold, determine which inequalities represent the constraints for this situation. x + y ≤ 60 15x + 25y < 700 x > 3y 15x + 25y ≥ 700 y > 3x x + 3y ≥ 60 Which combinations of small prints and large prints satisfy this system? (45,10) (35,15) (30,10) (40,5)
The constraints for this problem are represented by the inequalities x > 3y and 15x + 25y ≥ 700. The combinations that satisfy the constraints is (45,10) as it meets both conditions.
Explanation:The constraints for the art store situation are represented by the inequalities x > 3y and 15x + 25y ≥ 700. The first inequality, x > 3y, represents the condition that the number of small prints made must be more than three times the number of large prints sold. The second inequality, 15x + 25y ≥ 700, characterizes the fact the store needs to make a daily profit of at least $700 in order to cover costs.
With these inequalities, we can determine which pairs of small print and large print quantities satisfy this system of constraints. Checking each pair, we find that the combination (45,10) satisfies both inequalities as 45 is more than three times 10, and 15*45 + 25*10 = $775, which is greater than $700. Thus, selling 45 small prints and 10 large prints will satisfy the constraints.
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What is the value of k?
How to write 0.0000000000372 in scientific notation?
YO!! I'm in need of assistance
Last year, the average math SAT score for students at one school was 475. The headmaster introduced new teaching methods hoping to improve scores. This year, the mean math SAT score for a sample of students was 481. If the teaching method had no effect, there would be roughly a 3 in 10 chance of seeing such an increase. Does the result have practical significance? Why or why not?
Answer and step-by-step explanation:
Yes, it does have practical significance.
If the method was ineffective, the chance of an increase this large was 3/10, or 30%. This means with an ineffective teaching method, there was a 100-30 = 70% chance of not seeing a score increase this large.
Since we did see a result this large, and 30% is not a very large chance, we can say that the method was most likely effective.
The difference in SAT scores is statistically significant because there's only a 3/10 chance of observing such an increase by chance. However, it might lack practical significance because a 6-point increase, although positive, is relatively small and may not have a meaningful impact in real-world terms.
Explanation:The question you're asking relates to the concept of statistical significance and practical significance in Mathematics. Statistical significance means that the difference in results (in this case, the increase in SAT scores from 475 to 481) isn't likely due to chance. You've mentioned that there's a 3 in 10 chance of observing such an increase, so statistically, the new teaching method seems to have a significant effect.
However, practical significance refers to whether the difference is meaningful in real-world terms. This depends on context and judgement. In this case, a 6-point increase in the SAT score is a positive change, but it's relatively small and might not make a substantial difference to university admissions or student's mathematical competence. Therefore, one could argue that while the result is statistically significant, it may lack practical significance.
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whats 22 less than a number n
Eight times a number is not less than the sum of the number and fifty
If 3,200 cars were sold all year, how many cars were sold in the jan/feb period?
12 months per year
3200/12 = 266.66 per month
jan/feb = 2 months
266.666 x 2 = 533.33 round off to 533 cars sold
If 3,200 cars were sold all year, then approximately 533 cars were sold in the Jan/Feb period.
We need to calculate the proportion of the year that these two months represent and then apply that proportion to the total number of cars sold in the year.
Since there are 12 months in a year, the Jan/Feb period represents [tex]\(\frac{2}{12}\)[/tex] of the year. We can simplify this fraction to [tex]\(\frac{1}{6}\)[/tex] by dividing both the numerator and the denominator by 2.
To find the number of cars sold in the Jan/Feb period, we multiply the total number of cars sold in the year by the fraction representing Jan/Feb:
[tex]\[ \text{Number of cars sold in Jan/Feb} = \text{Total cars sold} \times \frac{2}{12} \][/tex]
Substituting the given total number of cars sold:
[tex]\[ \text{Number of cars sold in Jan/Feb} = 3,200 \times \frac{2}{12} \][/tex]
[tex]\[ \text{Number of cars sold in Jan/Feb} = 3,200 \times \frac{1}{6} \][/tex]
[tex]\[ \text{Number of cars sold in Jan/Feb} = \frac{3,200}{6} \][/tex]
Performing the division:
[tex]\[ \text{Number of cars sold in Jan/Feb} = 533.\overline{3} \][/tex]
[tex]\[ \text{Number of cars sold in Jan/Feb} \approx 533[/tex]
2,438,783 divided 893
Answer:
quotient=2,731
Remainder=0
Step-by-step explanation:
893) 2,438,783 (2,731
- 1 786
---------
6527
- 6251
---------
2768
- 2679
-----------
893
- 893
---------
0
12 foot by 15 foot swimming pool has a 3 ft wide no slip surface around it what is the outer perimeter of the no slip surface
the pool is 12 x 15
add 6ft to each dimension ( 3 feet on each side)
12+6 = 18
15+6 = 21
21 *2 = 42
18*2 = 36
42 +36 = 78 feet perimeter
Ball bearings are shipped in boxes. Each bearing has a diameter of 0.96 cm each box can hold 8000 cm of ball bearings. How many ball bearings can one box hold.
By calculating the volume of each ball bearing and considering the box's capacity, we determine that a box can theoretically hold 17,276 ball bearings. However, accounting for random packing efficiency, a box can actually hold approximately 11,059 ball bearings.
To determine how many ball bearings can fit in a box, we need to calculate the volume each ball bearing occupies and then see how many of these volumes can fit into the box's total capacity.
The diameter of each ball bearing is 0.96 cm. The radius (r) is half of the diameter: 0.96 cm / 2 = 0.48 cm.Next, we use the formula for the volume of a sphere, V = (4/3)πr³. Plugging in the radius:Additionally, taking into account the closest random packing efficiency of approximately 0.64 for loose ball bearings:
Effective volume available for ball bearings = 0.64 × 8000 cm³ = 5120 cm³.Therefore, the actual number of ball bearings that one box can hold = 5120 cm³ / 0.463 cm³ ≈ 11059.18, which rounds down to 11,059 ball bearings.Which ordered pair is on the inverse of f(x)?
Find three consecutive odd integers whose sum is between 27 and 51
Final answer:
To find the three consecutive odd integers whose sum is between 27 and 51, set up an inequality with n representing the smallest integer. Solve the inequality to find the possible values for n, which are then used to derive the consecutive integers.
Explanation:
To find three consecutive odd integers whose sum lies between 27 and 51, we need to establish variables for the integers and then solve for them. Let's call the smallest integer n, the next integer will then be n+2 (since odd numbers are two units apart), and the largest integer will be n+4. The equation will be n + (n+2) + (n+4), which simplifies to 3n + 6.
Since their sum must be between 27 and 51, our inequalities are:
27 < 3n + 6 < 51
Subtract 6 from all parts of the inequality:
21 < 3n < 45
Now, divide everything by 3:
7 < n < 15
Since n must be an odd integer, we have the options 9, 11, or 13 for n. Therefore, our sets of three consecutive odd integers could be:
(9, 11, 13), (11, 13, 15), or (13, 15, 17).
y varies inversely as x, and y = 50 when x = 10. What is the value of y when x = 20? 100
25
10
Answer:
[tex]y=25[/tex]
Step-by-step explanation:
We have been given that y varies inversely as x and [tex]y=50[/tex], when [tex]x=10[/tex].
We know that when y varies inversely with x, then the equation is: [tex]y=\frac{k}{x}[/tex], where, k represents constant of variation.
First of all, we will find constant of variation using point [tex]y=50[/tex], and [tex]x=10[/tex] as shown below:
[tex]50=\frac{k}{10}[/tex]
[tex]50*10=\frac{k}{10}*10[/tex]
[tex]500=k[/tex]
Upon substituting [tex]k=500[/tex] in inversely proportion we will get:
[tex]y=\frac{500}{x}[/tex]
To find the value of y, we will substitute [tex]x=20[/tex] in above equation as:
[tex]y=\frac{500}{20}[/tex]
[tex]y=\frac{50}{2}[/tex]
[tex]y=25[/tex]
Therefore, the value of y is 25.
0.66 repeating as a fraction
What is 0.26 repeating as a fraction
Answer:
0.26 repeating as a fraction is [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
Given : Expression 0.26 repeating.
To find : What is expression as a fraction?
Solution :
Let [tex]x=0.26666[/tex] ....(1)
Multiply both side by 10,
[tex]10x=2.666...[/tex] .....(2)
Subtract (1) and (2),
[tex]10x-x=(2.666...)-(0.2666...)[/tex]
[tex]9x=2.4[/tex]
[tex]x=\frac{2.4}{9}[/tex]
[tex]x=\frac{24}{90}[/tex]
[tex]x=\frac{4}{15}[/tex]
Therefore, 0.26 repeating as a fraction is [tex]\frac{4}{15}[/tex]
Solve for x. x - 3/8 = - 5/8
x = 1/4
x = - 1/4
x = -1
x = 1
Answer:
-1/4 should be the answer
Step-by-step explanation:
What is 3,920,000,000,000 in scientific notation? A. B. C. D.
How do you find the measures of the angles in a rhombus with the given angle 54 degrees?
Identify the transformation that maps the figure onto itself.
A) Reflect across the line y = -3
B) Reflect across the line x = 3
C) Rotate 180° about the point (3, -3)
D) Rotate 180° about the point (5, -5)
I believe it's B because transformation is moving it in a straight line, rotating is moving in a circle, therefore, it can't be C or D.
Answer:
The correct option is A.
Step-by-step explanation:
The given is a isosceles trapezium because the length of two non-parallel sides are equal.
An isosceles trapezium has a axis of symmetry which divides the trapezium in two equal and symmetric parts.
The axis of symmetry intersecting the parallel line at their midpoint.
From the below figure we can say that the sides AB and CD are parallel and y=-3 is the axis of symmetry.
So, when we respect the figure across y= -3, then we get the same figure.
Rotation 108 degree across any point will never maps the figure onto itself.
Therefore the reflection across the line y = -3 maps the figure onto itself and option A is correct.
In the right triangle ABC, CH (H is plotted on AB) is the altitude to the hypotenuse. Find the ratio of AH:HB, if the measure of BAC=30 degrees
Pls include full proof tysm!! <3
58 people answered a survey saying they like cheese. There was a total of 74 people surveyed. What is the percentage of people who liked cheese? Round to the nearest tenth.