The sets of number to which - 2/5 belongs is a rational number.
What is a rational number?If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so forth. A rational number is any number that can be expressed as a ratio (or fraction) of two integers.
P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers.
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Carlos sold half of his comic books then bought 14 more. He now has 33 comics books. How many did he start with?
Answer: Carlos started with 38 comic books.
Step-by-step explanation:
33 - 14 = 19
19 x 2 = 38
find the indicated sum in each sequence 7,10,17,27,44,71,115...,a10
The sequence of numbers, 7, 10, 17, 27, 44, 71, 115... in which each new term is given by the sum of the previous two terms, gives the sum of the first 10 terms as 1,265
What is a sequence of numbers?A number sequence consists of a listing of numbers that are connected to each other by a rule.
The given sequence is presented as follows;
7, 10, 17, 27, 44, 71, 115..., [tex] a_{10}[/tex]
From the given sequence, we have;
a_n = a_{(n-1)} + a_{(n-2)}
The first 10 terms of the sequence is therefore;
7, 10, 17, 27, 44, 71, 115, (71+115), (115+(71+115)), ((71+115)+(115+(71+115)))
Which gives;
7, 10, 17, 27, 44, 71, 115, 186, 301, 487
The sum of the first 10 terms of the sequence is therefore;
7 + 10 + 17 + 27 + 44 + 71 + 115 + 186 + 301 + 487 = 1265
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What is the equation of the graph?
The required equation of the graph is y = x - 1.
How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)
What is the y-intercept for a given line?
When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0.
What is the general equation of a line?
The equation for a standard line is y = mx + c, where m is the slope and c is the y-intercept.
Given, the line passes through the points (-1, 0) and (0, 1).
Also, the y-intercept for the line = c = -1
Now, using the formula established in the literature, we get:
slope = m = (y₂ - y₁)/(x₂ - x₁) = (1 - 0)/(0 - (-1)) = 1/1 = 1
y-intercept = c = -1
Therefore, equation of the standard line is y = mx + c, thus y = (1*x) + (-1)
Thus, the required equation of the graph is y = x - 1.
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Two parallel lines are cut by a transversal. Suppose <1 and <2 are alternate interior angles and that m<1=4(x+2) and m<2=2x+24. What is the m<2?
The value of m∠2 will be equal to 40°.
Transversal may be defined as a line which cuts two different lines which lie on the same plane at two different points. Alternate interior angles may be defined as the angles which are formed when a transversal cut the two different lines. These angles lie on the interior of the parallel lines, but they are on the opposite side of the transversal. If two parallel lines are cut by a transversal, then their alternate interior angles are equal. Thus, m∠1 = m∠2
4(x + 2) = 2x + 24
4x + 8 = 2x + 24
2x = 16
=> x = 16/2
=> x = 8
Now, m∠2 = 2x + 24
m∠2 = 2×8 + 24
m∠2 = 40° which is the required answer.
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Evaluate. Write your answer as a whole number or as a simplified fraction.
Answer:
1000
Step-by-step explanation:
Hello!
Use the Quotient Property of Exponents to evaluate the expression:
[tex]\frac{a^b}{a^c} = a^{b-c[/tex]
In this case, a is 10, b is 5, and c is 2.
Evaluate:[tex]\frac{10^5}{10^2}[/tex][tex]10^{5-2}[/tex][tex]10^3[/tex]If we simplify 10³, we should get 1000.
I have no idea what I’m doing And could use help! Anyone who takes time out of their day to help I appreciate you!!
Answer: It is impossible for two obtuse angles to be a straight angle
Step-by-step explanation:
Definition of a straight angle: An angle that is exactly 180 degrees
Definition of obtuse angle: An angle that is more than 90 degrees
1) X = obtuse angle
x > 90
Set minimum to test:
x = 91
2) Set up the question
(<= less than or equal to)
2x <= 180
3) Sub the first equation
2(91) <= 180
182 <= 180
4) Answer the question
It is impossible for two obtuse angles to be a straight angle
Help pls
Explain how to simplify ((a^3)^4)^-2 using the properties of exponents.
Answer: a^24
Hope this helps you!
Look at this set of ordered pairs:
(7, -17)
(5,3)
(7,3)
Is this relation a function?
yes
no
The given relation is not a function.
What is function?
A function is a relationship between inputs where each input is related to exactly one output.
Given that, (7, -17) , (5. 3) , (7, 3)
Here 7 is connected with two elements i.e. -17 and 3 but the condition of a function is that one element must be related to only one element of another set.
Hence, the given relation is not a function.
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the temperature outside must be between 32 degrees Fahrenheit is 95 degrees Fahrenheit and inclusively for students for students to be allowed to play outside during recess at an elementary school.write the compound inequality to show the temperature that are within the given range
The compound inequality which correctly shows the temperatures that are within the given range is; 32°F ≤ T ≤ 95.
What is the compound inequality which shows the temperatures that are within the given range?It follows from the task content that the temperature outside is said to be between 32 degrees Fahrenheit and 95 degrees Fahrenheit and inclusively.
On this note, it follows from the statement above that the upper limit of the temperature is; 95°F while the lower limit is; 32°F.
Therefore, the required compound inequality is;
32°F ≤ T ≤ 95.
Ultimately, the required compound inequality which shows the temperature that are within the given range is; 32°F ≤ T ≤ 95.
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According to the Empirical Rule, what percent of values in a normal distribution will fall between 1 standard deviations above the mean and 3 standard deviations above the mean?
According to the Empirical Rule, 99.7% percent of values in a normal distribution will fall between 1 standard deviations above the mean and 3 standard deviations above the mean.
What is the Empirical Rule?The Empirical Rule is also referred to as the 68-95-99.7 rule and it can be defined as a statistical rule which states that:
The middle 68% of a normal distribution would be within one (1) standard deviation of its mean.The middle 95% of a normal distribution would be within two (2) standard deviations of its mean.The middle 99.7% of a normal distribution would be within three (3) standard deviations of its mean.In this context, we can reasonably infer and logically deduce that 99.7% of a normal distribution would fall within three (3) standard deviations of its mean in accordance with the Empirical Rule.
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the group u(49) is cyclic. using only the sage commands described previously, use sage to find a generator for this group. now using only theorems about the structure of cyclic groups, describe each of the subgroups of u(49) by specifying its order and by giving an explicit generator. do not repeat any of the subgroups — in other words, present each subgroup exactly once
then the generator is the element which can generate whole set
therefore U(49) has 12 generator
What is meant by cyclic group?
A cyclic group is a group that can be generated by a single element. (the group generator). Cyclic groups are Abelian.
the group u(49) is cyclic. using only the sage commands described previously, use sage to find a generator for this group.
elements of U(49) are {1,2,3,5,,7,11,,13,17,19,23,29,31,37,39,,41,47}
then the generator is the element which can generate whole set
therefore U(49) has 12 generator
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Match the financial activities to their relevant management type within the wealth management phase. (Cash management or Credit and debt management)
keeping an emergency
fund
reducing credit use
spending plans
stop credit misuse
debt reduction
cash reserve
recording income and
spending
paying off credit cards
Each financial activities should be matched to their relevant management type within the wealth management phase as follows:
Cash management:
Keeping an emergency fund.Spending plans.Cash reserve.Recording income and spending.Credit and debt management:
Reducing credit use.Stop credit misuseDebt reduction.Paying of credit cards.What is wealth management?Wealth management can be defined as an investment advisory service that is designed and developed to provide advices and solutions to meet the needs of a wide array of affluent clients, especially by combining other financial services.
The phases of financial activities.Generally speaking, there are three (3) distinct phases of a person's financial activities and these include the following:
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Answer:
Cash management:
- keeping an emergency fund
- spending plans
- cash reserve
- recording income and spending
Credit and debt management:
- paying off credit cards
- stop credit misuse
- reducing credit use
- debt reduction
Step-by-step explanation:
correct on plato
graph this function f(x) = -7x - 64
The graph of the function f(x) = -7x - 64 will be a straight line.
A function may be defined as an expression in which for every input variable x there is only one output variable y. The input variable is called independent variable and output variable is called dependent variable. The function f(x) = -7x - 64 is in the form of linear equation in one variable as it is expressed in the form of f(x) = ax + b where a, b are coefficients and x are the independent variable. When we plot this function, we compare it from the slope intercept form of line that is y = mx + c where m is slope and c is y intercept. It will be a straight line having a negative slope which is equal to -7 and the y intercept will be equal to -64 as compared from slope intercept form. The graph of the function plotted is attached below. For x intercept we put f(x) = 0, so we get x intercept equal to -64/7. Coordinates of x intercept is (-64/7, 0) and that of y intercept is (0, -64).
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What is the y-intercept of the equation 4x + 5y = 20?
(0, 4)
(0, 5)
(4, 0)
(5, 0)
Answer:
(0,5)
Step-by-step explanation:
Answer:
(0, 4 )
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4x + 5y = 20 ( subtract 4x from both sides )
5y = - 4x + 20 ( divide through by 5 )
y = - [tex]\frac{4}{5}[/tex] x + 4 ← in slope- intercept form
with y- intercept c = 4 or in coordinate form (0, 4 )
One card is drawn from a standard deck of 52 cards. Find the probability of drawing the following. an eight or a diamond
The probability of a simple event to occur is this:
[tex]P(x)=\frac{\text{total number of favorable outcomes}}{\text{total }number\text{ of possible outcomes}}[/tex]In the question given, the favorable outcomes are either 8 or diamond.
In a deck of cards, there are 13 diamond cards and 4 eights however one of the diamond cards is also 8. Therefore, total favorable outcome is 13 + 4 - 1 = 16.
Of course, the total number of possible outcomes is 52. So, the probability of getting an eight or a diamond is:
[tex]p(x)=\frac{16}{52}=\frac{4}{13}\approx0.3077[/tex]The probability, in fraction, is 4/13.
In decimal form, it is 0.3077.
In percentage form, it is 30.77%
Write the word sentence as an inequality.
A number b multiplied by -5 is at most -30
The word sentence as an inequality phrase is -5[tex]\leq[/tex]30.
What is the inequality phrase?
An algebraic statement that uses the symbols less than (), less than or equal to (), larger than (>), or greater than or equal to () in place of the equal sign (=) is known as an inequality equation. How do you work out mathematical inequalities? Similar to how equations are solved, inequalities may be resolved by separating the variable and combining like terms.
Different types of inequalities
Equations that are linear
When the variables' highest exponent is power 1, inequality is said to be linear.
Triangle inequalities
A quadratic inequality is one in which the largest exponent is power 2, which is present in the inequality.
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HELP PLEASE!!!!!!!
A rectangle is 32ft by 8ft. Ross dilated the rectangle and the dimensions of the image were 80ft by 20ft. What was the scale factor used?
The scale factor of the dilation = 2.5
The original dimensions of the rectangle:
Length = 32 ft
Width = 8 ft
The dimensions of the rectangle after dilation:
Length = 80 ft
Width = 20 ft
Dilation is a transformation where the dimensions of the figure is enlarged by multiplying with a number. This number multiplied with all dimensions of the original figure is called its scale factor.
So the new dimension of the figure will be scale factor times the original dimensions of the figure.
Thus the scale factor can be defined as the ratio of larger dimension to the smaller dimension of a figure.
Hence the scale factor used here is the ratio of new length to the original length or the ratio of new width to the original width of the rectangle.
That is, scale factor = 80/32 = 20/8 = 2.5
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PLEASE HELP ME IT WOULD MAKE MY MONTH!!! ILYSM
How many pounds of apples will he get if he goes to David’s orchard?
Answer:
David's orchid: 20 +x
Pam's orchid: 25 + 0.75x
Step-by-step explanation:
Framing linear equations:
David's apple orchid:Cost of first 10 pounds = 10 * 2 = $ 20
Let the weight of additional apples picked = x pounds
Cost of 'x' pounds = 1 * x = $ x
Total cost = cost of first 10 pounds + cost of additional 'x' pounds
= 20 + x
Pam's orchid:Entry fee = $ 10
Cost of first 10 pounds = 10 * 1.50 = $ 15
Cost of 'x' pounds = 0.75*x = 0.75x
Total cost = Entry fee + cost of first 10 pounds + cost of additional 'x' pounds
= 10 + 15 + 0.75x
= 25 + 0.75x
Question 9
The preimage of M(-3,-5) under a translation is M'(6, -1).
Using the same translation, find the image of B', if B is (3,-2).
B'
By using the same translation applied to point M, the image of point B' is equal to (12, 2).
What is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.
Since the x-coordinate moved from a negative to a positive sign, we know that point M was translated to the right and then shifted down because it moved from a negative to a negative sign on the y-coordinate.
Next, we would determine the translation rule that was applied to point M:
(x, y) → (x + n, y - z)
-3 + n = 6
n = 6 + 3
n = 9.
-5 - z = -1
z = -5 + 1
z = -4
Now, we can determine the image of B':
(x, y) → (x + n, y - z)
Point B (3, -2) → Point B' (3 + 9, -2 - (-4)) = (12, 2).
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What common factor of 10 and 14 can you use to write in simpler form?
Answer:
1 and 2
and the greatest common divisor is 2
Measure of angle 1 = 110 degrees. You only need to type 110.
The unknown angles are as follows:
∠1 = 110°∠2 = 70°∠3 = 110°∠4 = 70°∠5 = 110°∠6 = 70°∠7 = 110°∠8 = 70°How to find angles?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, linear angles, alternate angles etc.
Therefore,
∠1 = 110 degrees(given)
∠2 = 180 - 110 (sum of angles on a straight line)
∠2 = 70°
∠3 = ∠1 (vertically opposite angles)
Vertically opposite angles are congruent.
Therefore,
∠3 = 110°
∠2 = ∠4 (vertically opposite angles)
∠4 = 70°
∠1 = ∠5 (corresponding angles)
Corresponding angles are congruent
∠5 = 110°
∠6 = ∠4(alternate angles)
Alternate angles are congruent.
∠6 = 70°
∠1 = ∠7 (alternate exterior angles)
∠7 = 110°
∠2 = ∠8(alternate exterior angles)
∠8 = 70°
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What point is located at (4, 1)?
Answer:
Step-by-step explanation:
I think it might be C
but I'm sorry if I'm wrong
PLS HELP!!!
Zane deposited $3,000 in an account earning 11% interest compound annually. To the nearest cent, how much will he have in 4 years?
Answer:4554.21
Step-by-step explanation:
Please answer if blurry let me know
Answer:
[tex]P'(-6,4)[/tex]
Step-by-step explanation:
P(x,y) -> rotate 90 degrees -> P'(-y,x)
P'(-6,4)
:]
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A simple random sample of size n is obtained from a population that is skewed left with and. Does the population need to be normally distributed for the sampling distribution of to be approximately normally distributed? why? what is the sampling distribution of ?.
Normal distributions are frequently employed in the natural and social sciences to describe real-valued regressors with uncertain distributions, normal distributions are essential to statistics.
The central limit theorem is one reason they are significant.
This claim argues that, in some circumstances, the average of many samples (observations) of a random variable with finite variance and mean is itself a random variable, whose distribution tends to become normal with an increase in sample size. Because of this, distributions of physical quantities that are meant to be the culmination of multiple separate processes, such as error margins, frequently resemble normal distributions.Only the normal distribution has additional cumulants after the first two that are zero. It is also the continuous distribution with the highest level of entropy for a given mean and variance. Assuming that the mean and variance are finite, Geary has shown that the normal distribution is the only distribution in which the mean and variance calculated from a collection of independent drawings are independent of one another.The normal distribution is a form of elliptical distribution. The normal distribution is symmetric about its mean and non-zero over the whole real line. Consequently, it could not be an appropriate model for variables that are inherently positive or highly skewed, such as a person's weight or the value of a share.To learn more about normal distribution visit:
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Jeremy Charges his neighbors $15.00 to wash their car. Howmany cars must he wash next summer if his goal is to earn at least $2000?
Answer: 134 cars
Since Jeremy charges $15.00 per car and he plans to earn at least $2000, if we let 'x' be the number of cars, we will have:
[tex]15x=2000[/tex]Solving for x:
[tex]\begin{gathered} 15x=2000 \\ x=\frac{2000}{15} \\ x=133.33 \end{gathered}[/tex]Since cars can only be counted as whole numbers, Jeremy would need to wash 134 cars to earn at least $2000
on a bike trip across the united states rodney notes that he covers about 190 miles every 4 if he continues at this rate use a ratio table to determine about how man miles he could bike in 6 days
In 6 days 285 miles can be travelled.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
190 miles cover in 4 days.
let x miles travelled in 6 days
So, using proportion
190/4 = x/6
190 x 6 = 4x
4x= 1440
x= 285 miles.
Hence, in 6 days 285 miles can be travelled.
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Boris's art class is 8 hours long. How long is his class in minutes?
Answer:
480 minutes
Step-by-step explanation:
that's your answer
Answer:
480 minutes.
Step-by-step explanation:
8×60=480.
the head of institutional research at a university believed that the mean age of full-time students was declining. in 1995, the mean age of a full-time student was known to be 27.4 years. after looking at the enrollment records of all 4934 full-time students in the current semester, he found that the mean age was 27.1 years, with a standard deviation of 7.3 years. he conducted a hypothesis of : 27.4 years versus : 27.4 years and obtained a p-value of 0.0020. he concluded that the mean age of full-time students did decline. is there anything wrong with his research?
No, there is nothing wrong in the research that is done by the head of the institution. He said correct that the mean age of the full time students has declined.
Given above that a university's director of institutional research thought that the average age of full-time students was lowering. The average age of a full-time student in 1995 was 27.4 years old.
He registered all 4934 pupils for this and the average age was 27.1 years.
The fact that the inquiry concerns the average age of a full-time student makes this situation ideal. This is a trustworthy approach when the mean is calculated after accounting for all full-time students at the university.
Given that this is a left-tailed test, the hypothesis is also correct.
He rejected the null hypothesis because p = 0.0020.05.
The average age did decrease, in conclusion. The situation is ideal.
Therefore his hypothesis is absolutely correct. There is nothing wrong with it.
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we have a dataset of household income, with mean 80,000 and median 50,000 and standard deviation 40,000.we standardize this dataset by calculating the z-scores (the standard scores). a datapoint is mapped to number 2.5 in the standardized dataset. how much was the income of this household?
The income of the household having mean 80,000 and standard deviation 40,000 is 1,80,000
The mean of the Household income = 80,000
The median of the Household income = 50,000
Standard deviation of the household income = 40,000
Z- score of these household income = 2.5
Thus , the income of the household can be calculated by using the normal distribution formula
Z = (X - μ) /σ
where X is the income of the household
μ is the mean of the household income
σ is the standard deviation of the household income.
So, we can re-write this equation as
X = Zσ + μ
Now, let us substitute the known values in the above equation , we get
X = 2.5(40,000) + 80,000
X = 1,00,000 + 80,000
X = 1,80,000
Therefore, the income of the household is 1,80,000 .
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