In a factory, a sample of 40 light bulbs was selected from a box of 1,000 light bulbs. In the sample, 2 light bulbs would not work. Based on this sample, how many non-working light bulbs would be expected in the group of 1,000 light bulbs?
The number of non-working light bulbs that would be expected in the group of 1,000 light bulbs is: 50 bulbs
How to find the probability of selection?In survey sampling, the term probability of selection is one that refers to the chance (i.e. the probability from 0 to 1) that a member (element) of a population can be chosen for a given survey.
We are told that a sample of 40 bulbs were picked from a box of 1000 bulbs and it was discovered that 2 of the bulbs were not working. Thus:
Fraction of bulbs not working = 2/40 = 0.05
Thus, number of bulbs not working in a sample of 1000 bulbs is:
0.05 * 1000 = 50 bulbs
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What is the volume? round to the nearest thousandth
The volume of the sphere is 5,575.28 ft³.
What is the sphere?The volume of the sphere is calculated by applying the following formula as shown below;
V = ⁴/₃ πr³
where;
r is the radius of the sphereThe radius of the sphere is calculated as follows;
r = d/2
where;
d is the diameterr = 22 ft / 2
r = 11 ft
The volume of the sphere is calculated as;
V = ⁴/₃ π(11)³
V = 5,575.28 ft³
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help fill in these answers please
This has to do with the solution the quadratic equation given as: y=x² - 5x -14.
What is the solution and related quantities?
To factorize the quadratic equation - y = x² - 5x -14, we need to find two numbers that multiply to -14 and add up to -5.
We can list out the factors of -14 as follows:
-1 and 14
1 and -14
-2 and 7
2 and -7
Out of these pairs, the numbers that add up to -5 are -2 and 7.
Therefore, we can factorize the equation as:
y = (x - 2)(x + 7)
To find the zeros or x-intercepts, we set each factor equal to 0 and solve for x:
x - 2 = 0, x + 7 = 0
x = 2, x = -7
So the solutions are (2, 0) and (-7, 0).
The axis of symetry is the average of the x-intercepts
This is (2 - 7)/2 = -2.5.
Substituting this value into the equation:
y = (-2.5 )² - 5 (-2.5 ) - 14 = - 20.25
So the vertex is ( -2.5, -20.25).
The domain of the function is all real numbers, since there are no restrictions on the input x.
The range of the function is y ≥ -20.25, since the vertex is the lowest point of the parabola and the graph extends upward from there. See the graph attached.
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Express each of the following as a function of 50°:
1. sin310°
Expressing the trig ratio as a function of 50°, we have sin310° = sin(360 - 50)°
Expressing each as a function in terms of 50 degreesFrom the question, we have the following trigonometry function that can be used in our computation:
sin310°
The above expression is a sine function of 310 degrees
By mathematical expression, we have
360 - 50 = 310 degrees
This means that we can replace 310 degrees with (360 - 50) degrees in sin310°
So; in terms of 50 degrees, we have
sin310° = sin(360 - 50)°
Hence, the expression sin310° in terms of 50 degrees is sin(360 - 50)°
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S = [10, 11, 13, 19, 21, 23, 29, 30]
A = The number is At least 21
B = the number is Between 12 and 25
O = number is Odd
L = number is a Less than 25
Find the P(A and L) = [____] Round to 2 d.p
The probability of A and L is 0.25, rounded to two decimal places
To find the probability of A and L, we need to find the number of elements in the intersection of A and L and divide by the total number of elements in the set S.
A = {x ∈ S | x ≥ 21}
= {21, 23, 29, 30}
L = {x ∈ S | x < 25}
= {10, 11, 13, 19, 21, 23}
A ∩ L = {x ∈ S | x ≥ 21 and x < 25}
= {21, 23}
Therefore, the probability of A and L is:
P(A and L) = |A ∩ L|/|S|
= 2/8
= 0.25
Therefore, the required probability of A and L is 0.25, rounded to two decimal places
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Ms. Garcia bought 3 packs of red notepads,
5 packs of yellow notepads, and 8 packs of
green notepads. There were 3 notepads in each
package. How many notepads did Ms. Garcia
buy in all?
Answer: red = 9, yellow = 15 green = 24, total = 48 notepads were bought.
Step-by-step explanation:
3 x 3 = 9, so 9 red. 3 x 5 = 15, so 15 yellow. 3 x 8 = 24, so 24 green. In total this is equal to 48 notepads. 9 + 15 + 24 = 48.
18 plus what equals 54
Answer:
Step-by-step explanation:
54 - 18 = 36
so...
18 + 36 = 54
A city official would like to know if there is public support for increasing funding for arts programs. To collect data, the city official stands outside a concert hall after a show and surveys every 25th person to exit and asks their opinion about raising funds for the arts. Which of the following describes the population in this scenario?
A. all residents of the city
B. the members of the city council
C. all city residents who support the arts
D. the people surveyed by the city official
All city residents who support the arts. Therefore, the option C is the correct answer.
As the city official would lie to know that if public support for increased funding of arts programs. By collecting data the officials show the survey after every 25 persons and ask for their opinion.
They also tend to raise a fund that states the population in the scenario of a city resident that supports the arts.
The population in this scenario is the people surveyed by the city official. The city official is conducting a survey outside a concert hall after a show, which means they are targeting people who have just attended a show. Since the city official is asking every 25th person to exit their opinion about raising funds for the arts, these are the people who are included in the population being surveyed.
Therefore, the option C is the correct answer.
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PLEASE HURRY
Let a = apple and c = cherry.
Mathland Bakery sells apple pies for $7.00 and cherry pies for $11.00.
The total number of pies sold in one day was 36. If the amount collected for all the pies that day was $304.00, how many of each type were sold?
Mathland Bakery sold 23 apple pies and 13 cherry pies on that day.
Simultaneous equation problemSince a represents apple and c represents cherry:
Total number of pies sold: a + c = 36 (1)Total amount collected from sales: 7a + 11c = 304 (2)We can now go ahead to solve for a and c using a simultaneous equation approach.
From equation (1)
a = 36 - c
Substituting this expression into equation (2), we get:
7(36 - c) + 11c = 304252 - 7c + 11c = 3044c = 52c = 13Therefore, 13 cherry pies were sold. To find the number of apple pies sold, we can substitute this value of c into equation 1:
a + 13 = 36a = 23Therefore, 23 apple pies were sold.
In other words, Mathland Bakery sold 23 apple pies and 13 cherry pies on that day.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The distributive property of multiplication can be used to calculate the sum of the difference between the multiples of the variables expression as follows;
[tex]\sum\limits_{i = 1}^{124} (29\cdot a_i - 13 \cdot b_i)[/tex] = -30
What is the distributive property?The distributive property states that multiplying the difference between addend by a value produces a result which is equivalent to the multiplication of each addend individually and finding the difference from the resulting values.
The distributive property of multiplication indicates that we get;
Where; [tex]\sum\limits_{i=1}^{124} a_i = -10[/tex], and [tex]\sum\limits_{i=1}^{124} b_i = -20[/tex]
[tex]\sum\limits_{i=1}^{124} (29\cdot a_i - 13\cdot b_i) = 29 \times \sum\limits_{i=1}^{124} a_i - 13 \times \sum\limits_{i=1}^{124} b_i = 29 \times (-20) - 13 \times (-10))[/tex]
29 × (-10) - 13 × (-20) = -30
Therefore;
[tex]\sum\limits_{i=1}^{124} (29\cdot a_i - 13\cdot b_i) =-30[/tex]
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HURRY ASAP!!! NEED THE ANSWER
The graph shows f(x). The absolute value function g(x) is described in the table.
The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 2, a point at negative 1 comma 3, and a point at 1 comma 3.
x g(x)
−1 5
0 4
1 3
2 2
3 3
If g(x) = f(x + k), what is the value of k?
k = −2
k is equal to negative one half
k is equal to one half
k = 2
Answer:
A
Step-by-step explanation:
Please solve piecewise
The numeric values of the piecewise function in this problem are given as follows:
f(-4) = -4.f(0) = 0.f(3) = 1.How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
A piecewise function is a function that has different definitions, based on the input x of the function.
For values of x that are of 1 or less, the function is defined as follows:
f(x) = x.
Hence the numeric values in this interval are given as follows:
f(-4) = -4.f(0) = 0.For values of x that are greater than 1, the function is defined as follows:
f(x) = -x + 4.
Hence, at x = 3, the numeric value of the function is given as follows:
f(3) = -3 + 4 = 1.
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Use the marks to identify the correct name for point T. The options are:
- Centroid
- Orthocenter
- Circumcenter
- Incenter
- None of the above
Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.
How to explain the triangleCircumcenter : The point of intersection of the three perpendicular bisectors.
Incenter : The point of intersection of the three angle bisectors.
Centroid : The point of intersection of the three medians.
Orthocenter : The point where all the three altitudes of the triangle meet or intersect each other.
In conclusion, based on the information, Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.
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What is the constant of proportionality in this table?
X
2
5
7.5
y
31
77.5
116.25
In this table, the constant of proportionality is 15.5.
What is the constant of proportionality?The constant of proportionality is the ratio that one value has compared to another.
In other words, the constant of proportionality is the quotient of the numerator and the denominator.
The constant of proportionality can also be referred to as the slope, gradient, or unit rate.
X y Constant of Proportionality
2 31 15.5 (31/5)
5 77.5 15.5 (77.5/5)
7.5 116.25 15.5 (116.25/7.5)
Thus, the constant of proportionality, which can also be computed as the slope or unit rate is 15.5.
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What is the solution to the inequaiity -3(x-3)>5-5x
x < -2 is the solution for the given inequality.
To solve the inequality:
-3(x - 3) > 5 - 5x
We can start by using the distributive property and simplifying both sides of the inequality:
-3x + 9 > 5 - 5x
Next, we can add 5x to both sides of the inequality to get the x terms on one side:
2x + 9 > 5
Then, we can subtract 9 from both sides of the inequality to isolate the variable:
2x > -4
Finally, we divide both sides by 2, remembering to reverse the inequality because we are dividing by a negative number (-3):
x < -2
Therefore, the solution to the inequality is x < -2.
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2 1/2 yards of fabric cost 7.00.. 3 rolls of ribbon cost 2.50 how much money is spent
The total amount spent is $9.50.
We have,
2 1/2 yards of fabric cost 7.00.
3 rolls of ribbon cost 2.50.
So, the total amount of money spend
= Cost of fabric + cost of ribbon
= 7 + 2.50
= $9.50
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Find the Independent and Dependent variables in the below Research Question.
Is there a difference in time finding a parking spot at SDSU than across other San Diego universities?
The independent variable in the research question is the location of the universities, with SDSU being the specific location of interest. The dependent variable is the time it takes to find a parking spot.
The research question is seeking to compare the time it takes to find a parking spot at SDSU to the time it takes at other San Diego universities, with the location being the independent variable that may affect the dependent variable, which is the time taken to find a parking spot.
By identifying the independent and dependent variables in the research question, researchers can design a study that will collect data on these variables, analyze the data, and
draw conclusions about whether there is a significant difference in the time it takes to find a parking spot at SDSU compared to other universities in San Diego.
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Perry and Darryl are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and bags of daffodil bulbs. Perry sold 1 bag of windflower bulbs and 1 bag of daffodil bulbs for a total of $20. Darryl sold 7 bags of windflower bulbs and 1 bag of daffodil bulbs for a total of $68. What is the cost for each bag of windflower bulbs and one bag of daffodil bulbs?
A bag of daffodil bulbs costs $12 and a bag of windflower bulbs $8.
Let's use the letters "w" for the price of a bag of windflower bulbs and "d" for the price of a bag of daffodil bulbs.
We may construct the following system of equations based on the above information:
Perry's sales:
w + d = 20 (equation 1)
Darryl's sales:
7w + d = 68 (equation 2)
To solve for w and d, we can use the elimination method. Multiplying equation 1 by -1, we get:
-w - d = -20
Adding this to equation 2, we eliminate d and get:
6w = 48
Dividing both sides by 6, we get:
w = 8
Substituting this value of w into equation 1, we can solve for d:
8 + d = 20
d = 12
Therefore, a bag of windflower bulbs costs $8 and a bag of daffodil bulbs costs $12.
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If ∠A is a complementary angle of ∠B and ∠C is a complementary angle of ∠B, then which of the following statements is true?
B) ∠A ≅ ∠C
C) ∠A ≅ ∠B
D) ∠B ≅ ∠C
If "∠A" is complementing angle "∠B" and "∠C" is complementing "∠B", then the true statement is (a) ∠A ≅ ∠C, because both the angles have the same measure.
The "Complementary-Angles" are two angles that add up to 90 degrees, which is also known as a right-angle. When two angles are complementary, they are said to complement each other.
Since the angles : ∠A and ∠C are both complementary to ∠B, we can write :
⇒ ∠A + ∠B = 90°,
⇒ ∠B + ∠C = 90°,
Next, We subtract "∠B" from both sides of each equation,
We get;
⇒ ∠A = 90° - ∠B,
⇒ ∠C = 90° - ∠B,
We see that the measure of the angle "A" and angle "C" is same.
Therefore, ∠A and ∠C have the same measure, option (a) is the correct answer.
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The given question is incomplete, the complete question is
If ∠A is a complementary angle of ∠B and ∠C is a complementary angle of ∠B, then which of the following statements is true?
(a) ∠A ≅ ∠C
(b) ∠A ≅ ∠B
(c) ∠A + ∠C ≅ ∠B
(d) ∠B ≅ ∠C
The ratio of the speeds of pulleys is inversely proportional to the ratio of their diameters. The speed reduction required on a pulley and belt drive is 4 to 1. If the drive is 4 inches in diameter, what size would be required for the driven pulley?
1 inch is the diameter of the driven pulley.
Let's use D to represent the driven pulley's diameter. The speed decrease needed, according to the issue description, is a 4 to 1 reduction.
This implies that the ratio of the diameters is also 4 to 1, as the speeds are inversely proportional to the diameters:
D/4 = 1/4
Multiplying both sides by 4 gives:
D = 1
Therefore, the diameter of the driven pulley should be 1 inch.
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Equivalent fractions are those that simplify to the same fraction.
Provide 3 equivalent fractions for the fraction 9/12.
Answer:
[tex]\frac{3}{4} = \frac{6}{8} = \frac{9}{12} = \frac{18}{24} [/tex]
Which table represents the function? Pls help me
A linear equation is an equation in which each term has at max one degree. The table that represents a linear function is Table 1. Thus, the correct option is A.
We have,
A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c
Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.
For the table to represent a linear function, the function must have a constant slope between any two points.
For the first table, the slope between the first two points is,
m = (7-3)/(2-1) = 4
The slope between the last two points is,
m = (15-11)/(4-3)
Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.
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I need the correct answer to this.
The addition of the outlier will affect the distribution in that b) The distribution will become skewed left.
Why is the skew left ?When a score of 12 is added as an outlier, it shifts the distribution of data towards the left-sided direction resulting in skewness. This can be deduced from observing that the median is closer to the lower end of the range of collected data.
Additionally, the introduction of the outlier has substantially decreased the mean value, indicating that the deviation value has pulled the mean downwards and altered the symmetry of the original distribution by making it asymmetrically distributed in a leftward manner.
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Select the correct answer.
A number is selected at random from the set (2, 3, 4,... 10). Which event, by definition, covers the entire sample space of this experiment?
O A.
O B.
O C.
OD.
The number is even or less than 12.
The number is not divisible by 5.
The number is neither prime nor composite.
The number is greater than 2.
Reset
Next
1. Daniel's yearly income is $90,000. He budgets
28% of his monthly income for his monthly rent
payment. What is the amount of monthly rent Daniel
has budgeted?
1,440
Answer:
1875
Step-by-step explanation:
Yearly income = $90000
Monthly income = 90000÷12 = $7500
Monthly rent = 25%×7500 = $1875
HELP ASAP ASAP PLS PLS I NEED DONE NOW AND BRAINLIEST
Mr. Harris graded papers at the end of the school day. The table below shows how many papers he graded in minutes.
Minutes Number of papers graded
6 4
12 8
24 16
45 30
At this rate, how many papers will Mr. Harris grade in 60 minutes?
34 papers
40 papers
44 papers
75 papers Mr. Harris graded papers at the end of the school day. The table below shows how many papers he graded in minutes.
Minutes Number of papers graded
6 4
12 8
24 16
45 30
At this rate, how many papers will Mr. Harris grade in 60 minutes?
34 papers
40 papers
44 papers
75 papers
Answer:
40
Step-by-step explanation:
6:4 = 1,5 which means he grades 1 paper per 1,5 minute. 60:1,5 = 40 papers
3 to the 8th power times 3
Answer:
19683
Step-by-step explanation:
3 to the power of 8 is 6561,
so just put 6561 multiplied by itself 3 times.
(6561 X 6561 X 6561).
Answer:
3⁸ × 3 = 19,683
The magnitude and direction of two forces acting on an object are 100 pounds, S80°E, and 90 pounds, N55°E,
respectively. Find the magnitude, to the nearest hundredth of a pound, and the direction angle, to the nearest tenth
of a degree, of the resultant force.
The magnitude is approximately ? pounds.
(Do not round until the final answer. Then round to the nearest hundredth as needed.)
The resultant force is gotten as 173.3780
What is a Resultant Force?A resultant force is described as the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition
we determine resultant force by following these steps:
Establish the magnitude and direction of each individual force acting on the object first.Next, we use Trigonometry to establish the x and y components for each one. For example, if a force comes at the object at 30 degrees from the x-axis with a strength of 10 N, then its x-component would be 8.66 N after calculating 10cos(30), while the y-component will be 5 N which is solved by applying 10sin(30).we then add all x components of the various forces together.See attached image for full working
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Which of the following should one consider when choosing a career?
a. the potential earnings
b. the work environment
C. the required education
all of the above
d.
Please select the best answer from the choices provided
O A
OB
OC
OD
The factor that one should consider when choosing a career is D. All of the above.
The factors in making a career choice:In choosing a career, a student should consider the required education and training involved, the work environment, and their potential earnings.
Other factors to consider include:
Job AvailabilityInterest and passionSoft SkillsTalent and strengthAttitude to work.Thus, all the listed factors should be considered when choosing a career.
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Karen's company makes solid metal balls for various industrial uses. A customer wants copper balls that have a diameter of 3 in. If Karen must make 90 of these balls, how much copper will she need?
Use 3.14 for n, and do not round your answer.