All the numbers are rational numbers.
We have,
Rational numbers are those numbers that are terminating and recurring non-terminating.
Irrational numbers are those numbers that are non-terminating and non-recurring.
The numbers are:
1)
0.020202
This is non terminating recurring number.
It is a rational number.
2)
0.8
This is a terminating number.
It is a rational number.
3)
0.020202
This is non terminating recurring number.
It is a rational number.
Thus,
All the numbers are rational numbers.
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The function f(x) = 2-5* can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function? 0 2 05 10 • 32
The given function does not represent the curve passing through the given points. The multiplicative rate of change of the function is 5.
What is Curve Line ?A curve is a continuous, smooth line that gradually alters direction. Rather than being straight line that follows a curve may be referred to as a curve line. A curve line can be made by connecting a number of non-straight-line-lying sites. In mathematics, a curve is a geometrical object that can be described by equations, such as parametric or function equations.
The rate of change of a function is the ratio of the change in the output (y) to the change in the input (x). In this case, we can calculate the rate of change between the first two points:
Changing at what rate between (1, 10) and (2, 50)?
Y change = 50 – 10 = 40
Variation in x = 2 - 1 = 1
Rate of change equals change in y/change in x, or 40/1, or 40.
In a similar manner, we can determine how quickly the second and third points will change:
The change between (2, 50) and (3, 250) is as follows:
Changing y by 250 - 50 equals 200
Variation in x = 3 - 2 = 1
Rate of change equals change in y/change in x, which is 200/1, or 200.
Now that we have the second rate of change, we can compute the multiplicative rate of change by dividing it by the first:
Multiplicative rate of change is equal to 200/40, or 5.
The function's multiplicative rate of change is thus 5.
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The prism below is made of cubes which measure
1
4
of an inch on one side. What is the volume?
A 3D illustration view of a blank tabular with 5 rows and 2 columns.
Note: Figure is not drawn to scale.
A.
15
32
cubic in
B.
5
2
cubic in
C.
30
cubic in
D.
15
2
cubic in
The volume of the prism is B. 2.5 cubic inches.
How to calculate the volumeAccording to the question, the prism measures 1/4 of an inch on one side. Now we will assign values to the length, width, and height of this prism as follows:
Length = 2 × 1/4
Width = 5 × 1/4
Height = 3 × 1/4
= 2/4 + 5/4 + 3/4
= 2 2/4
= 2.5 cubic inches.
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Find a polynomial f(x) of degree 5 that has the following zeros.
0, 1 (multiplicity 2), -6, -3
Leave your answer in factored form.
This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.
How to solveA polynomial f(x) of degree 5 with the given zeros can be represented in factored form as:
f(x) = [tex]A(x - 0)(x - 1)^2(x + 6)(x + 3)[/tex]
Since the leading coefficient is not specified, we can leave A as a constant factor. Simplifying the expression, we have:
f(x) = [tex]A(x)(x - 1)^2(x + 6)(x + 3)[/tex]
This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.
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which of the following sample spaces would satisfy the definition of a continuous random variable?
x={odd integers between 5 and 15}
×=[0,500]
x=[0,1,2,3]
x=[the number of days in the week that have the letter "r"]
Answer:The sample space that satisfies the definition of a continuous random variable is: ×=[0,500]
Step-by-step explanation:
The sample space that satisfies the definition of a continuous random variable is: ×=[0,500]
A continuous random variable is a variable that can take on any value within a certain range of values, typically a continuous interval. This means that there are an infinite number of possible values that the variable can take on, and the probability of any particular value is zero.
In contrast, the other sample spaces listed are all discrete random variables, meaning that they can only take on a finite or countable number of values. For example, the first sample space x={odd integers between 5 and 15} can only take on 6 possible values (5, 7, 9, 11, 13, or 15), and the third sample space x=[0,1,2,3] can only take on 4 possible values.
The fourth sample space x=[the number of days in the week that have the letter "r"] is also a discrete random variable, as it can only take on values of 0, 1, 2, or 3 (depending on how many days of the week have the letter "r").
Therefore, the only sample space that satisfies the definition of a continuous random variable is ×=[0,500].
A total of 480 black and red jerseys were produced in a factory. Each black Don jersey was sold at $56. Each red jersey was sold at $75. After all the jerseys were sold, the amount of money collected from the sale of the black jerseys was $18315 less than that of the red jerseys. (a) How many black jerseys were sold? (b) How much money was collected from the sale of the red jerseys?
Answer:
Step-by-step explanation:
100 POINTS!!!!!! please answer will give brainliest If the length of each side of the right triangle shown on the grid is measured in cm; find the area of the triangle: 25 cm2 50 cm2 100 cm? 225 cm?'
Answer:
B) 50cm^2
Step-by-step explanation:
A movie theater considers upgrading to offer luxury seating. The manager randomly surveys 1,200 resident who live within 10 miles of the theater. What is the sample in the situation
Please it’s due in 2min
In this circumstance, the sample consists of 1,200 inhabitants living within a ten-mile radius of the movie theater that were selected for random deliberation by the overseer.
What is a sample?Samples are frequently utilized to gain information concerning a larger population through the study of a single set of individuals or objects. The aim of selecting a sample is to inspect the populace by delving into a representative, relatively small group.
Surveys, polls, and experiments often utilize samples to make evidence-based inferences regarding the target population. For exact and dependable results, an instance should be randomly chosen, accurately mirroring those present in the whole population so as to reduce prejudice and fully optimize the evaluation.
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On average, a front desk operator receives 2 calls per 30 seconds.
(1)Find the probability that at most 1 call is received in 10 seconds
The probability that at most 1 call is received in 10 seconds is given as follows:
0.8557 = 85.57%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are listed and explained as follows:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.On average, a front desk operator receives 2 calls per 30 seconds, hence the mean for 10 seconds, which is one third of the time, is given as follows:
[tex]\mu = \frac{2}{3}[/tex]
The probability of at most one call is given as follows:
P(X <= 1) = P(X = 0) + P(X = 1)
Hence:
[tex]P(X = 0) = \frac{e^{-\frac{2}{3}}\frac{2}{3}^{0}}{(0)!} = 0.5134[/tex][tex]P(X = 1) = \frac{e^{-\frac{2}{3}}\frac{2}{3}^{1}}{(1)!} = 0.3423[/tex]Hence:
P(X <= 1) = P(X = 0) + P(X = 1) = 0.5134 + 0.3423 = 0.8557 = 85.57%.
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on any day ,the probability that marcus will get a seat on the schoo bus is 0.93 . what is the probability that he does not get a seat on the school bus?
Marcus not getting a seat on the school bus is therefore 0.07 or 7% likely as 0.07 percent of people will not receive a seat .
what is probability ?The prospect of an event happening is assessed by probability. It is a number between zero and 1, where 0 denotes an improbable occurrence and 1 denotes a certain occurrence. For instance, if we flip a fair coin, the odds of obtaining heads are 0.5, or 50%, and the odds of receiving tails are also 0.5, or 50%. In each case, there are various ways to compute probability. In general, if an event has n equally possible results and k of them are favourable, the likelihood that the event will occur is: Event P = k/n . All possible outcomes are thought to be equally likely under what is referred to as the classical probability.
given
Simply put, the likelihood that Marcus won't obtain a seat on the school bus is the complement of the likelihood that he will.
By deducting the probability from 1, one can determine the complement of a probability. So:
Chance of not being seated equals one less than the likelihood of being seated.
The likelihood of not getting a seat is equal to 1 - 0.93.
0.07 percent of people will not receive a seat.
Marcus not getting a seat on the school bus is therefore 0.07 or 7% likely as 0.07 percent of people will not receive a seat .
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1. Ashenge Private Limited Company is about to start production of new products. Before the start of the new production, it cost the company $200,000 to construct the factory building. Once the construction is over, the cost per unit of production is estimated to be Birr 20. Upon selling, the company will incur a 20% commission expense. Moreover, the price per unit of products is decided to be Birr 50.
Required:
a) Construct the total cost equation in terms of quantity.
b) Determine the break-even quantity and break-even revenue.
The total cost equation is 200,000 + 40n and the break-even revenue is 20,000.
Given that a company is starting a new production, it cost the company $200,000 to construct the factory building.
The cost per unit of production is estimated to be Birr 20.
The company will incur a 20% commission expense.
The price per unit of products is decided to be Birr 50.
We need to find the total cost equation in terms of quantity and determine the break-even quantity.
a) The fixed cost of the company is $200,000, and 40 per unit sell,
Therefore for n units the total cost =
200,000 + 40n
b) BEQ = FC / P−VC
= 200,000 / 50-40
= 20,000
Hence the total cost equation is 200,000 + 40n and the break-even revenue is 20,000.
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Solve by using a system of equations.
A goldsmith has two gold alloys. The first alloy is 30% gold; the second alloy is 80% gold. How many grams of each should be mixed to produce 40 grams of an alloy that is 60% gold?
The amount of grams of each alloy that should be mixed to produce 40 grams of an alloy that is 60% gold are 16 grams and 24 grams respectively.
How to write a system of equations to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the quantity of first alloy (30% gold) and the quantity of second alloy (80% gold) respectively, and then translate the word problem into a linear equation as follows:
Let the variable y represent the quantity of first alloy (30% gold).Let the variable x represent the quantity of second alloy (80% gold).Therefore, a system of linear equations to describe this situation can be written as follows;
x + y = 40 .....equation 1.
0.3x + 0.8y = 0.6(40) .....equation 2.
From equation 2, we have the following:
0.3x + 0.8y = 24
0.3x + 0.8(x - 40) = 24
0.3x + 32 - 0.8x = 24
-0.5x = -8
x = -8/-0.5
x = 16 grams.
y = 40 - x
y = 40 - 16
y = 24 grams.
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Suppose that the function g is defined, for all real numbers, as follows. Find g(-5) ,g (-2), and g(-1)
If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.
A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :
g(x) = {-(1/2)x + 1, for x<-2
= {-(x+1)², for -2≤x≤1
= {4 for x>1
We have to find the value of g(-5) ,g (-2), and g(-1),
For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,
⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,
For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function
"-(x+1)²" will be used,
⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,
For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,
⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,
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Laquita has $3,500 a month in cash inflows and $3,240 a month in forecasted cash
outflows. How much can she contribute annually to her liquidity fund?
Answer: $3120
Step-by-step explanation:
3500-3240
=260
260*12=3120
Which of the following values are solutions to the inequality -8- 4x > 1?
4
I. - 10 II. - 1
O None
O II only
O I and II
O II and III
O I only
O III only
○ I and III
O I, II and III
III. 6
Submit Answer
Answer:
the answer is:l only
because -10 only states the true statement while -1 and 6 gave False Staments...
Please Help With Question Inside of the picture
The workers percentile score is given as follows:
69.15%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The z-score for this problem is given as follows:
z = 0.5.
Hence the percentile score is of 69.15%, as z = 0.5 has a p-value of 0.6915.
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18. Name a pair of complementary angles in this figure.
Answer:
Step-by-step explanation:
Angle KEF and JEK
Answer:
∠DEH and ∠HEJ or∠JEK and ∠KEF----------------------------
Complementary angles are the angles that together form a right angle.
In the picture we see two right angles:
∠DEJ and ∠JEFThe first one, ∠DEJ has a pair of complementary angles:
∠DEH and ∠HEJThe second one, ∠JEF has a pair of complementary angles:
∠JEK and ∠KEFSomeone help i really need help with this
The percentage increase in the number of water bottles from February to April is 19%.
How to find the percentage increase?A company manufactures water bottles. The list describes the amount of water bottles manufactured in three months.
Therefore,
February: 4100 water bottles
March: 7% more water bottles than in February
April: 500 more water bottles than in march
Therefore,
Number of water bottles in march = 4100 + 7% of 4100
Number of water bottles in march =4100 + 7 / 100 × 4100
Number of water bottles in march = 4100 + 287
Number of water bottles in march = 4387
Hence,
Number of water bottles manufactured in April = 4387 + 500 = 4887
Therefore,
percentage increase from February to April = 4887 - 4100 / 4100 × 100
percentage increase from February to April = 787 / 4100 × 100
percentage increase from February to April = 78700 / 4100
percentage increase from February to April = 19.1951219512
percentage increase from February to April = 19%
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Apply the United States rule to determine the balance at maturity and the total interest paid if the borrower makes two partial payments and the remainder of the loan is paid at maturity.
Principal $1450
Interest Rate % 15.0
Loan Length (Days) 280
Partial Payment
$5800.00
$4350.00
Payment on Day #
112
196
Answer: The United States rule is a method for calculating interest and balances on loans that have partial payments during their term. The rule assumes that each partial payment is applied to the interest first, then to the principal. Here's how to use the United States rule to calculate the balance and interest for this loan:
Calculate the daily interest rate by dividing the annual interest rate by 360 (the number of days in a standard year for most loans).
Daily Interest Rate = 15.0% / 360 = 0.04167%
Calculate the interest due for the first partial payment of $5800 made on day 112. Since this payment is larger than the remaining principal, it will pay off the loan entirely and no interest will accrue beyond this date.
Days between start of loan and first payment = 112 daysInterest due on first payment = (1450 x 0.04167% x 112) = $8.10Principal remaining after first payment = $0.00
Calculate the interest due for the second partial payment of $4350 made on day 196.
Days between first payment and second payment = 84 daysInterest due on second payment = (0 x 0.04167% x 84) = $0.00Principal remaining after second payment = $0.00
Calculate the interest due on the remaining principal at maturity (day 280).
Days between second payment and maturity = 84 daysInterest due at maturity = (0 x 0.04167% x 84) = $0.00
Add up the interest due from each period to get the total interest paid over the life of the loan.
Total interest paid = $8.10 + $0.00 + $0.00 = $8.10
Add up the principal amounts from each payment to get the total amount paid.
Total amount paid = $5800.00 + $4350.00 = $10,150.00
Subtract the total amount paid from the original principal to get the balance at maturity.
Balance at maturity = $1450.00 - $10,150.00 = -$8700.00 (which means the lender owes the borrower this amount)
Therefore, the balance at maturity is -$8700.00 (meaning the lender owes the borrower this amount) and the total interest paid over the life of the loan is $8.10.
Find F(7)…………………………………………
Based on the given function conditions of f(x) , the value of f(7) is equal to -6
To find f(7), we need to determine which function definition to use based on the value of x.
Since x = 7 is greater than 5, we know that we'll be using the third definition of the function: f(x) = -x + 1 for 2 < x ≤ 5.
Therefore, we can substitute x = 7 into the third definition of the function:
f(7) = -7 + 1 = -6
So, f(7) = -6.
In summary, to find f(7), we identified which function definition to use based on the value of x. Since x = 7 is greater than 5, we used the third definition of the function, f(x) = -x + 1 for 2 < x ≤ 5, and found that f(7) = -6.
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Fixed expenses are defined as those that do not very with changed in volume. Examples include:
A( direct staffing costs
B( lease costs and taxes
C( utilities and supplies utilized in production of service or product
D( utilities, rent, lease, depreciation
Answer:
B (lease costs and taxes) and D (utilities, rent, lease, depreciation) are examples of fixed expenses as they typically do not vary with changes in volume.
Direct staffing costs (A) and utilities and supplies utilized in the production of service or product (C) are generally considered variable expenses as they tend to vary based on the volume of production or sales. For example, if a business produces more goods or provides more services, it will typically need to hire more staff and use more supplies, leading to an increase in expenses.
Step-by-step explanation:
help pls im in a rush
The reason for the statements of the proof to show that ∠A ≅ ∠C are:
ABCD is a parallelogram: (Given)Draw BD: (Construction)AB || DC, AD || BC: Given∠1 ≅∠4, ∠2 ≅ ∠3: (Opposite angles of a parallelogram are congruent)DB ≅ DB: (Reflexive Property)ΔABD ≅ ΔCDB: (ASA congruence theorem)∠A ≅ ∠C: Corresponding parts of congruent triangles are congruent. What is a parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram.
In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The ASA congruence theorem states that two triangles are congruent if two angles and the side separating two angles of one triangle are congruent with the corresponding angles and side of another triangle.
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please help me
What degree of rotation about the origin will cause the triangle below to map
onto itself?
Please help me i dont get this. PLEASE I GIVE 20 points. And I give BRAINLIEST
Answer:
A B
Step-by-step explanation:
Is between A or B
Answer: A yes
Step-by-step explanation:
The answer is A because they divided both sides by 5
Not by variable and they didn't add/sub
This equations are equivalent
‼️‼️WILL MARK BRAINLIEST IF HELPFUL‼️‼️
Answer:
Step-by-step explanation:
(a) Given: r=4 h=3
Formula for cylinder: V=Bh = [tex]\pi r^{2} h[/tex]
Solution:
V= [tex]\pi r^{2} h[/tex]
V= [tex]\pi[/tex]4²(3) >square
V= [tex]\pi[/tex] (16)(3) >multiply numbers
V=48[tex]\pi[/tex] >leave as pi
(b) Given: 4 h=6
This volume will be greater because you are multiplying by 6 instead of 4
V=96[tex]\pi[/tex]
Factor out the Greatest Common Factor (GCF): 64d³ - 24d²
The factored form of 64d³ - 24d² is 8d²(8d³ - 3).
Define greatest common factorThe greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that divides evenly into two or more given numbers. For example, the GCF of 12 and 18 is 6, since 6 is the largest number that divides both 12 and 18 without leaving a remainder.
The greatest common factor (GCF) of the given terms is 8d². We can factor it out by dividing each term by 8d²:
64d³/8d² - 24d²/8d²
Simplifying the fractions:
8d³ - 3
Therefore, the factored form of 64d³ - 24d² is 8d²(8d³ - 3).
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The mayor of a town has proposed a plan for the construction of a new bridge. A political study took a sample of 800 voters in the town and found that 53% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 49%. Find the value of the test statistic. Round your answer to two decimal places.
the value of the test statistic is approximately 5.19.we can get the answer by using formula .
what is statistic ?
A statistic is a numerical value or measure that is calculated from a sample of data, and is used to describe or make inferences about a population. Statistics are used in various fields, including business, economics, social sciences, and natural sciences, to analyze data
In the given question,
To test the claim that the percentage of residents who favor construction is more than 49%, we can use a one-sample z-test. The test statistic can be calculated as:
z = (p - P) / √(P * (1 - P) / n)
where:
p = the sample proportion (0.53)
P = the hypothesized population proportion under the null hypothesis (0.49)
n = the sample size (800)
Substituting the given values into the formula, we get:
z = (0.53 - 0.49) / √(0.49 * 0.51 / 800) ≈ 5.19
Rounding the test statistic to two decimal places, we get:
z ≈ 5.19
Therefore, the value of the test statistic is approximately 5.19.
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hi I need help on questions 10-17 on this paper. if you are a expert (know what to do) of vertical angles and angle relationships in a triangle then please help me.
Answer:
10) 73
11) 107
12) 107
13) x = 23
14) 135
15) 45
16) 123, 28 29
17) 180 - 72 - 28 = 80
Angle K is 80
Step-by-step explanation:
10:
Vertical angels are congruent. The same measurement.
11:
Supplements angles add to 180
180 - 73 = 107
12:
Same as 11
13:
135
Vertical angles are congruent
5x + 20 = 3x + 66 Subtract 3x from both sides
2x + 20 = 66 Subtract 20 from both sides
2x = 46 Divide both sides by 2
x = 23
14:
5x + 20 Substitute 23 for x
5(23) + 20
115 + 20
135
15:
This angle is supplemental to ABC
180 - 135 = 45
16:
The sum of the interior angles of a triangle is 180
123 + x-2 + x -3 = 180 Combine like terms
118 +2x = 180 Subtract 118 from both sides
2x = 62 Divide both sides by 2
x = 31
x- 2
31 - 2 = 29
x - 3
31 - 3 = 28
Three angles 123, 29, 28
17:
The sum of the interior angles is 180
180 - 72 - 28 = 80
Helping in the name of Jesus.
8) If Bonnie can waterproof 450 square foot of decking with 2 gallons of sealant, she will need 6 gallons (10pts)
of sealant for 1200 square foot of decking.
True
O False
Answer:
FALSSOO
Step-by-step explanation:
lol srry I pretty sure its false I did teh math
Hope its right and it helps! c:
what is the probability that either event will occur
The probability that either event will occur is 7/25
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100% in percentage.
Probability = sample space /Total outcome
P(A or B) = P(A) +P(B) -P(A and B)
The total element = 25+5+15+5 = 50
therefore total outcome = 50
P(A) = 25/50
P(B) = 15/50
P(A and B) = 5/40
Therefore P(A and B) = 25/50+15/50 - 5/50
= 35/50 = 7/25
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Create a bar graph from the results of the following survey question: "On average, how much time do you spend using your cell phone each week?"
The bar graph from the results of the following survey question titled "Hours spent using your cell phone each week" is found in the attachment.
What is a bar graph?A bar chart, also called a bar graph, is a visual representation of categorical data that uses rectangular bars with heights or lengths that correspond to the measure of the values they represent.
The bars in a bar chart can be plotted either vertically or horizontally.
Vertical bars, horizontal bars, grouped bars, or stacked bars can all be used to make bar graphs.
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