the sum of all positive rational numbers that are less than 10 and that have a denominator 30 is 400.
What is Rational Number?
Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.
So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that the numerator or denominator doesn't have commonly divisible.
As a small addition, you get 4+12+20+…+76, which is an arithmetic sequence. There are ten terms, so you can use
So the sum will be 10(4+76)/2 = 400
Hence the sum of all positive rational numbers that are less than 10 and that have a denominator 30 is 400.
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I need help please. I’m struggling.
option 3
The mean is the same as the average.
9.4 / 16.92
Am too lazy to do this so yea, my bro wants me to do his homework but no.
c(1) = -20
c(n) = c(n − 1) + 10
Find the 2nd term in the sequence.
Answer:
-10
Step-by-step explanation:
So we are going to find c(2)
c(2)=c(1)+10
c(2)=-20+10
c(2)=-10
How do you dilate an image with a scale factor?
To dilate an image with a scale factor, multiply the scale factor with the dimensions of the image
The dilation is the process of changing the size of the given shape or figure ,the shape of the figure will be always same. Therefore dilation is one form transformation of shapes
The scale factor is the ratio of the measurement of the new shape to the measurement of the original shape.
We can use the scale factor for the dilation
To get the dilate and image with scale factor, we have to multiply the scale factor with the measurement of the original shape
The equation will be
The dimension after dilation = scale factor × original dimensions
Therefore, to dilate an image, multiply the scale factor and the original dimensions
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Use the information to answer the following question.
Carolyn was asked to solve the following system of equations.
Her work is shown.
Step 1: 3x – 2y = 7
Step 2: 3x – 2(x + 2) = 7
Step 3: 3x – 2x + 4 = 7
Step 4: x + 4 = 7
Step 5: x = 3
Step 6: y = x + 2
Step 7: y = 3 + 2
Step 8: y = 5
Solution: (3, 5)
Did Carolyn make an error in her work?
Yes, Carolyn did not correctly combine like terms in Step 2.
Yes, Carolyn should have substituted the x-value into the first equation in Step 6.
No, Carolyn solved the system of equations correctly.
Yes, Carolyn did not correctly distribute the negative in Step 3.
Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.
System of EquationsA system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.
3x – 2y = 7
3x – 2(x + 2) = 7
3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).
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What is the measure of one of the central angles in the regular Pentagon What is the measure of one of the congruent base angles in triangle ABC?
The measure of one of the central angles of a regular pentagon is 72° .
In the question ,
a regular pentagon is given ,
we have to find the measure of one of central angle ,
we know that a pentagon has 5 equal sides .
and the sum of the central angles is 360° .
it is given that the pentagon is regular , So , all the central angles are equal in measure .
The central angle can be calculated using the formula ,
central angle = 360°/n , where n is number of sides .
substituting the value of number of sides as = 5 ,
we get ,
central angle = 360°/5 = 72° .
Therefore , the central angle is = 72° .
The given question is incomplete , the complete question is
What is the measure of one of the central angles in the regular Pentagon ?
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1) x-2y=15
2) x-3=4y
A) rearrange equation (2) to make x the ubject
B) uing your anwer to part a) olve the imultaneou equation uing ubtitution
x= -9 and y= -3
What is equation?
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
A) rearranging equation (2) to make x the subject
[tex]x-3=4y\\x-4y=3[/tex]
Also,
[tex]4y=x-3\\y=(x-3)/4[/tex]
by subtitution method
putting this value of y in equation 1)
[tex]x-2((x-3)/4)=15\\\\x-2x+6=15\\x=-9\\y=(-9-3)/4\\y=-3[/tex]
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Maya uses 14 blue tiles and 10 white tiles to design section of an outdoor patio. Which ratio compares the number of blue tiles to the total number of tiles in the section
Answer:9 : 20
Step-by-step explanation:
mr. smith has two children. at least one of them is a boy. what is the probability that both children are boys?
The probability that both children are boys is 1/2.
What is probability?
The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty).
Given in the question,
Mr. Smith has two children, one of them is boy.
So, the possible combinations are,
(Boy, Boy) and (Boy, Girl)
It means number of total outcomes is 2,
we have to find probability of (Boy, Boy)
It means number of favorable outcomes is 1,
The formula for the calculation of probability is:
Probability = number of favorable outcomes/ number of total outcomes,
So,
Probability = 1/2
Therefore, The probability that both children are boys is 1/2.
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Select all the correct answers.
A pharmaceutical company claims that regular consumption of its new children's vitamin Increases the average number of hours that a
child sleeps each night. To test this claim, a researcher decided to conduct an experiment. The researcher randomly selected
500 children, grouped by age. Over the course of a year, half of the children received the children's vitamin and half of the children
received a placebo. At the end of the year, the researcher compared the average number of hours that the children in each group slept
each night.
Which statements about this study are true?
This study uses random sampling.
This study uses blinding.
This study uses blocking.
This study uses a repeated measures design.
This study uses a control group.
The statements that are true concerning the study that was carried out by the pharmaceutical company include the following: This study uses random sampling, This study uses blinding and This study uses a control group. That is option A, B and E.
What is a pharmaceutical company?A pharmaceutical company is defined as the company that has been certified to manufacture and distribute drugs such as the children's vitamin.
While selecting sample for the study, it was stated that 500 children grouped by age was randomly selected.
Out of the total samples, 250 was given the vitamin while the remaining half was given a placebo ( a blind) which would serve as concealment of the group allocation from them as they are serving as the control.
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Answer:
A,B,C,
Step-by-step explanation:
PLATO
the coefficient of determination resulting from a particular regression analysis was 0.85. what was the correlation coefficient, assuming a positive linear relationship? group of answer choices -0.5 0.922 0.5 there is insufficient information to answer the question.
The coefficient of determination resulting from a particular regression analysis was 0.85. Then, the correlation coefficient, assuming a positive linear relationship is 0.922.
The coefficient of determination, denoted R2 or r2 and pronounced "R-squared," is the proportion of predictable variation in the dependent variable from the independent variables.
R2 has several definitions, sometimes the same. One class of such cases involves simple linear regression where r2 is used instead of R2. If only one bin is included, r2 is simply the square of the sample correlation coefficient (that is, r) between the observed outcome and the observed prediction. If additional regressors are included, R2 is the square of the multiple correlation coefficient. In both cases, the coefficient of determination is usually between 0 and 1.
Regression analysis consists of a dependent variable (often called the "outcome" or "response" variable, or "label" in machine learning parlance) and one or more independent variables (often called "predictors"). ). ', 'covariate', 'explanatory variable' or 'feature'). The most common form of regression analysis is linear regression, which finds the best fit line (or more complex linear combination) to the data according to mathematical criteria. For example, the ordinary least-squares method computes a unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). For certain mathematical reasons (see linear regression), researchers can estimate the conditional expected value (or population mean) of the dependent variable given that the independent variable takes on a particular set of values . Less common forms of regression use slightly different techniques to estimate alternative site parameters (such as quantile regression and requirement analysis, or conditional expectations on a broader collection of nonlinear models. estimating values (such as nonparametric regression). Regression analysis is primarily used for two conceptually distinct purposes.
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I need help understanding number 3, please help!
Answer:
Step-by-step explanation:
It's asking you to find the measures for all the angles.
For example, angle 1 would be 59° because it is equal to the angle across from it.
Angle 2 would equal 31° because it's a supplement angle to 59° and so on
Idenify the slope and y-intercept
Answer:
The slope is -2 and the y-intercept is (0,1)
a combination lock requires three selections of numbers, each from 1 through 35. suppose the lock is constructed in such a way that no number may be used twice in a row, but the same number may occur both first and third. for example, 20 13 20 would be acceptable, but 20 20 13 would not. how many different combinations are possible? to answer this question, note that some combinations will consist of three different numbers, whereas in others the first and third numbers can be the same. the total number of combinations is
Answer:
Below
Step-by-step explanation:
35 choices for first number
34 choices for second number (because it cannot be same as first)
34 choices for third number ( because it cannot be same a second)
35 x 34 x 34 = 40 460 combos
(c) To reduce the percentage of defective chips, the company contracts with a new supplier for some
important components. In the next month, the sample of 200 chips has only 8 defective ones. Can the
company conclude that the new components have reduced the rate of defective chips produced?
Explain.
Mean: 12
Standard Deviation: 3.3586
This is binomial distribution.
There is enough evidence to conclude that the new components have reduced the rate of defective chips produced.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the amount has decreased, that it still is of 12, hence:
[tex]H_0: \mu = 12[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the amount has decreased, that is, it is less than 12, hence:
[tex]H_1: \mu < 12[/tex]
We have a left-tailed test, with a significance level of 0.05, hence the test statistic needed for there to be enough evidence is less than -1.645, which is the critical value.
What is the test statistic?The equation that determines the test statistic is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters in this problem are of:
[tex]\overline{x} = 8, \mu = 12, \sigma = 3.3586, n = 12[/tex]
Hence the test statistic is of:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{8 - 12}{\frac{3.3586}{\sqrt{12}}}[/tex]
z = -4.13.
Less than the critical value, hence there is enough evidence that the amount has decreased.
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What is 5-kilometers / 400 meters
Answer: 12.5 meters!
Step-by-step explanation:
1km = 1000 meters
So 5km = 5000 meters
So take 5000 divided by 400 = 12.5 meters
Answer:
12.5 is the answer for this question
does this graph represent a function?why or why not x 2 2 3 4 5 y 1 4 4 2 5
The correct statement regarding whether the graph represents a function is given as follows:
B. No, because it fails the vertical line test.
When does a graph represent a function?A graph is a relation, and it represents a function if each value of the input is mapped to only one output, that is, if the graph does not contain vertically aligned points.
From the graph given by the image at the end of the answer, the inputs for x > 2 are mapped to multiple outputs, meaning that a vertical line at any of these points would cross the function twice, meaning that the graph has vertically aligned points.
Since the graph has vertically aligned points, it fails the vertical line test, and hence the graph does not represent a function, and option B is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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PLS HELP AND PLS PUT THE WORK!!!!****, PLS ASAP
In a game, the probability of winning is 20%. If i play 48 times, how many times should I expect to win?
Answer:
Step-by-step explanation:
I will try to get the answer for you just give me a minute.!
What is the equation of the line that passes through the points − 1/3 and 1 11?
the equation of the line that passes through the points − 1/3 and 1 11 is
y = 3x + 8 with slope 12 1/3.
1. Find the slope of the line.
m = (11 - -1/3) / (1 - -1/3)
m = 12 1/3
2. Using the point-slope equation, substitute the slope and one point from the line
y - y1 = m(x - x1)
y - -1/3 = 12 1/3 (x - (-1/3))
3. Solve for y
y = 12 1/3x + 8
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Rewrite the function by completeing the square x^2-x-20
By algebra properties, the quadratic function x² - x - 20 = 0 is equivalent to the quadratic function (x + 1 / 2)² - 81 / 4 = 0.
How to complete the quadratic function
In this problem we have a quadratic function whose form does not correspond with a perfect square trinomial, that is, a polynomial of the form (x + a)² = x² + 2 · a · x + a². Herein we can modify part of the function by means of completing the square, an application of algebra properties.
First, write the quadratic function described in the statement:
x² - x - 20 = 0
Second, use algebra properties until the square is complete:
x² - x - 20 = 0
x² - x = 20
x² - x + 1 / 4 = 20 + 1 / 4
(x + 1 / 2)² = 81 / 4
(x + 1 / 2)² - 81 / 4 = 0
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Solve for ttt:
-18 = -3t−18=−3t
Answer: 4z
Step-by-step explanation:
1. In the figure below, segments LJ and A F are perpendicular. What is the value of x+y?
2. In the figure below, LJ is perpendicular-bisector of A F. What is the value of m + n?
1) The value of the expression x + y is; 30
2) The value of the expression m + n is; 16
How to solve Algebraic Expressions?1) We are told that segments LJ and A F are perpendicular. This means that; 4x + 50 = 90 and 7y - 50 = 90
Let us solve for x and y;
4x + 50 = 90
4x = 90 - 50
4x = 40
x = 10
Similarly;
7y - 50 = 90
7y = 90 + 50
7y = 140
y = 140/7
y = 20
Thus;
x + y = 10 + 20
x + y = 30
2) We are told that LJ is a perpendicular-bisector of A F. Thus;
AJ = FJ and AL = FL
Thus;
FL = AL gives;
3m = 42
m = 42/3
m = 14
Similarly;
2m + 3n = 34
2(14) + 3n = 34
28 + 3n = 34
3n = 6
n = 2
m + n = 14 + 2 = 16
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What is the mode when mean is 15 and median is 10?
The mode in this situation is not defined because there is only one value for each of the mean and median.
Mean (15) and median (10) are two different measures of central tendency. The mean is the average of all values, while the median is the middle value when all the values are arranged in order. The mode is the most frequent value in a set of data, and there can be more than one mode. Since there is only one value for both the mean and median, there is no mode in this situation.
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What is the slope of the line whose equation is 2y=3x +4
solve for y
y = 1.5x + 2
notice this is in form y = mx + b
m is slope, b is y intercept
m = 1.5
slope is 1.5
hope this helps :)
jeron
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 7.
The area of the surface is 5/3 [tex]\sqrt{14}[/tex][tex]\pi[/tex]
Consider that the part of the plane x+2y +3z=1 that lies inside the cylinder [tex]x^{2}[/tex] + [tex]y^{2}[/tex] =5
The surface area of an equation z= g(x,y) is given by the following formula:
[tex]\int\limits^d_d \sqrt {\alpha z/\alpha x]^{2} . [\alpha z/\alpha y]^{2} +1da[/tex]
where the D is the domain of integration.
Since the plane lies inside the cylinder[tex]x^{2}[/tex] + [tex]y^{2}[/tex] = 5, we have the domain of
D= ( (r,0) |0 [tex]\leq[/tex]r [tex]\leq[/tex][tex]\sqrt{5}[/tex],0[tex]\leq[/tex]θ[tex]\leq[/tex]2[tex]\pi[/tex])
The partial derivatives of z = 1/3 ( 1 - x - 2y) are
[tex]\alpha z/ \alpha x[/tex] = 1/3, [tex]\alpha z / \alpha y[/tex] = - 2/3
[tex]\int\limits^d_d \sqrt {[-1/3]^{2} . [-2/3]^{2} +1da[/tex]
= [tex]\int\limits^d_d \sqrt{14} / 9 da[/tex]
= [tex]\sqrt{14}/3 \int\limits^0_ {2^{\pi }[/tex] [tex]\int\limits^\sqrt{5[/tex]r dr dθ
Evaluating the integral we have
[tex]\sqrt{14}/3 \int\limits^0_ {2^{\pi }[/tex][tex]\int\limits^\sqrt{5[/tex]rdrdθ = [tex]\sqrt{14} /3[/tex] 2 [tex]\pi[/tex] [ 5/2]
= 5/3 [tex]\sqrt{14}[/tex][tex]\pi[/tex]
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How do you figure the area of a rectangle?
Answer: the area of a rectangle is l x w length x width
Step-by-step explanation:
Answer: Formula of an area of a rectangle: Length x Width
Step-by-step explanation:
There are about 2.54 centimeters in 1 inch. if a segment is 2.7 centimeters long, how many inches is it, rounded to the nearest hundredth?
The number of inches of a segment is 1.06 inches if a segment is 2.7 centimeters long.
What is meant by line segment?In geometry, a line segment is a portion of a straight line that is bounded by two distinct end points and includes all of the points on the line that fall inside those endpoints. A line segment's length is determined by the Euclidean distance between its endpoints.
In geometry, a line segment is a portion of a straight line that is bounded by two distinct end points and includes all of the points on the line that fall inside those endpoints. A line segment's length is determined by the Euclidean distance between its endpoints.
Given,
In 1 inch there are about 2.54centimeters
And the segment is 2.7 centimeters long
The number of inches=?
2.7/2.54=1.0629
When it is rounded to the nearest 100, we get
1.06 inches.
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An altitude is drawn from the vertex of an isosceles triangle, forming a right angle
and two congruent triangles. As a result, the altitude cuts the base into two equal
segments. The length of the altitude is 15 inches, and the length of the base is 11
inches. Find the triangle's perimeter. Round to the nearest tenth of an inch.
The perimeter of the triangle is 50.96 inches.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
An isosceles triangle.
This means,
Two sides are equal.
Now,
The length of the altitude = 15 inches.
The length of the base = 11 inches.
Now,
The right triangle:
Base = 11/2 = 5.5 inches.
Height = 15 inches.
The other side = x
Applying the Pythagorean theorem.
x² = 5.5² + 15²
x² = 30.25 + 225
x² = 255.25
x = √255.25
x = 19.98 inches.
Now,
The perimeter of the triangle.
= 2x + 11
= 2 x 19.98 + 11
= 50.96 inches.
Thus,
The triangle's perimeter is 50.96 inches.
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Ashley buys 6 bottles of orange juice at the corner store for a total cost of $2.40. If each bottle costs the same amount, how much is each bottle of juice?
How long is the shortest route from Asheboro to Fort Jennings using the roads shown?
If necessary, round your answer to the nearest tenth.
miles
The shorted distance from Asheboro to Fort Jennings is, 20.4 miles.
What is Pythagorean theorem?
The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.
In this problem we have to find the shortest route from Asheboro to Fort Jennings using the roads shown.
From the given route the shorted distance from Asheboro to Fort Jennings is,
= 3 mi + 8 mi + (distance from North lean to Fort Jennings)
Let distance from North lean to Fort Jennings is x.
To find the value of x using Pythagorean theorem.
x^2 = 8^2 + 5^2
x^2 = 64 + 25
x^2 = 89
x = 9.433
x = 9.4
So, the total distance is, 3 mi + 8 mi + 9.4 mi =20.4 miles.
Hence, the shorted distance from Asheboro to Fort Jennings is, 20.4 miles.
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Complete question:
Complete question is attached below.