For the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.
As given in the question,
Geometric mean GM = 30
Let us assume the first number is x
and second number i.e. 9 times of the first number is 9x
By the formula GM = [tex]\sqrt{x.y}[/tex]
Now putting the value
30 = [tex]\sqrt{x.9x}[/tex]
30 = [tex]\sqrt{9x^{2} }[/tex]
30 = 3x (∴ square root of 9 is 3 and sq root of x² is x)
10 = x (by dividing both the side by 3)
Therefore, for the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.
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what is the value of m and n?
The value of m is 36 degrees and the value of n is 27 degrees
Consider the triangle on right side
Two sides of the triangle is equal, therefore it is an isosceles triangle.
One angle of the triangle = 126 degrees
Other two angles of the triangle is equal
The sum of interior angles of the triangle is 180 degrees
Then, the equation will be
126 + n + n = 180
2n + 126 = 180
2n = 180 - 126
2n = 54
n = 54/2
n = 27 degrees
Consider the full triangle
The equation will be
(m +27) + 90 +27 = 180
m + 27 + 90 + 27 = 180
m + 144 = 180
m = 180 - 144
m = 36 degrees
Hence, the value of m is 36 degrees and the value of n is 27 degrees
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The scatter graph shows the maximum temperature and the numbers of hours of sunshine in 13 British towns in one day.
A line of best fit has also been drawn.
One of the points in an outliner.
a) Write down the coordinates of this point. (1)
b) For all the other points write down the type of correlation in just one word. (1)
On the same day, in another British town, the maximum temperature was 17.4C.
c) Estimate the number of hours of sunshine in this town on this day. (2)
You must use the drawing tool to show how the line of best fit has been used to get your answer.
A weatherman says that temperatures are lower on days when there is less sunshine.
d) Does the scatter graph support this? (1)
A yes B no C can't say
Total marks: 5
Answer:
See attached worksheet.
Step-by-step explanation:
The worksheet summarizes the steps for analyzing the data on the graph. Note that a "line of best fit" was drawn to help illustrate the linear behavior of the data, and to better the question concerning hours of sunshine in another British town. There are techniques for ensuring a line such as this fits the actual data as closely as possible. These techniques draw a line that has the least overall deviation from the actual data. For our purposes, a hand-drawn line appears to match the data reasonably well, so we are able to concule that the relationship is liner: There is a proportional change in y for every set change in x. That change is known as the slope. The slope of this liner would represent the direct relationship between hours of sun and maximum temperature.
The table of ordered pairs (x, y) gives an exponential function.
Write an equation for the function.
X
-1
0
1
2
y
1
3
2
12
72
The equation for the function of the ordered pair is y =10x+2.
What is equation for the function?
An equation that has one solution for y for each value of x is referred to be a function. For each input of a particular type, a function assigns precisely one output. The names f(x) or g(x) are frequently used in place of y when naming functions. If our function's value is f(2), then we should calculate its value when x=2. Each functional equation contains some information about a function or several functions. An illustration of a functional equation is f (x) f (y) = x y, f(x) f(y) = x y.
Here in given order pair , let us take any two points,
[tex](x_1,y_1)=(0,2)\\(x_2,y_2)=(1,12)[/tex]
Now using slope formula,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m =10/1 = 10
Now using equation formula,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y-2 =10(x-0)
=> y-2 = 10x
=> y=10x+2.
Therefore equation of the following order pair is y = 10x+2.
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a physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. he has the following probability distribution. x p (x) 1 0.35 2 0.2 3 0.15 4 ? 5 0.10 6 0.05 (a) on average, how many years would you expect a physics major to spend doing post-graduate research?
It can take 3 years that a physics major to spend doing post-graduate research
Given that,
A physics professor is curious about the proportion of physics majors who will pursue post-graduate study during the coming years. He has the probability distribution shown below. x P(x) x*P (x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05
To find P(X<=3)
P(X<=3)=P(X=0,1,2,3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)
= 0.35+0.20+0.15
= 0.7
P(X<=3)=0.7
Hence, A physics major may need to spend three years conducting post-graduate research. and the probability that a physics major will spend no more than three years conducting post-graduate research is 70% or 0.7
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Multiply 12. 462 by 13.
Answer:
162.006
Step-by-step explanation:
Find g(x), where g(x) is the translation 2
units left of f(x)= -5x + 5.
Answer:
g(x)=(-5x+2)+5
Step-by-step explanation:
Charis invested 140. She earned a simple interest of 3% per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charis received at the end of two years?
The amount received by Charis on Simple interest in 2 years will be $8.4
What is Simple Interest?
The process of figuring out how much interest will accrue on a given principal sum of money is known as simple interest (S.I.).
It's formula is given by S.I. = PRT/100 where P = principle amount
R= rate and T = time.
Main Body:
P= $140
R= 3%
T= 2 years
so S.I. = 140*2*3/100
S.I. = $ 8.4
Hence total amount received by Charis at the end of 2 years will be $8.4
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I need this by tonight would be appreciated. :) I know this is basic stuff I'm in Middle School but when I signed up for this there wasn't a middle school option.
The area of the floor of the convenience store would be = 212.5 ft²
What is the area of an object?The area of an object is defined as the total space that is being occupied by that object.
To calculate the area of the convenience store is to find the area of the shaded part which would be = area of square - area of the triangle.
Area of square = l ×w = 15 × 15 = 225ft²
Area of triangle= 1/2 base ×height
= 1/2 × 5 × 5
(Note: 15 - 10 = 5 ft from the diagram used as base and height)
= 25/2
= 12.5 ft²
The area of the convenience store;
= 225 - 12.5
= 212.5 ft².
Therefore, the area that is covered by the convenience store should be = 212.5ft².
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Eva says
3
4
is equivalent to
15
20
. Check her work by completing the table of equivalent ratios.
The equivalent ratio table is:
3 4
6 8
9 12
12 16
15 20
What is a Ratio?A ratio indicates the number of times one number contains another.
To find the equivalent ratio of 3/4 write the table of 3 in one column of the table and write the table of 4 in another column of the table.
The equivalent ratio table is:
3 4
6 8
9 12
12 16
15 20
The above table indicates that 3/4 = 6/8 = 9/12 = 12/16 = 15/20.
Therefore, from the table, 3/4 is equivalent to 15/20.
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Examine the equation below used for determining the balance on a bank account. Look through this chapter and your notes to help you write a problem that could be modeled by the equation.
The balance on the bank account at the end of the third quarter of the year is 2,630.80
How to find the compound interest?
Compound interest is defined as the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest is found using the formula
A=P(1+r/n)ⁿˣ where:
A= Amountr= interest raten= number of interest applied per period and x= number of time periodTherefore, the amount (A)=2630.80
The P=2500
interest rate is 0.17%
Number of interest applied per period is 365 periods and
number of time period is 3.
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Example of a slope intercept form equation with a negative slope and y-intercept of 0
Answer:
An example would be y = -x.
Step-by-step explanation:
Since the y-intercept is 0, we don't have to write it out. The slope has to be negative, so I chose -1 as the slope. We don't have to write 1 when we use it as a coefficient, so that is why I wrote it as -x. Now to put it all together in slope intercept form, we get y = -x.
Hope this helps.
Give brainliest please
Hey, I haven't been able to get any of these right, I wasn't a there the day we learned this and i'm needing help getting the rest of it done before 3:00. Could any of you please help me out on this, it'd mean a lot!
The correct graph for each of the equations are respectively;
5) Graph C
6) Graph A
7) Graph B
How to Interpret Linear Equation Graphs?The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
5) We are given the linear equation as;
-9x + 3y = 0
3y = 9x + 0
y = 3x + 0
The slope is 3 and y-intercept is zero. Thus, the correct graph for this function is; Graph C
6) We are given the linear equation as;
4x - 6y = 12
Rearranging we have;
6y = 4x - 12
y = ⁴/₆x - 2
y = ²/₃x - 2
Thus, slope is 2/3 and y-intercept is -2. The correct graph is graph A
7) The correct graph of the function 25x - 10y = -50 is the graph B.
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It take an ant farm 2 day to conume 1/2 of an apple. At that rate, in how many day will the ant farm conume 2 apple?
the ant will take 8 days to consume 2 apples.
Given, an ant takes 2 days to consume 1/2 of an apple.
We have to find the number of days ant will take to consume 2 apples.
So, ant takes 2 days = consumption of 1/2 apple
ant takes 4 days = consumption of 1 apple
Consumption of 1 apple = ant takes 4 days
Consumption of 2 apples = ant takes 4×2 days
Consumption of 2 apples = ant takes 8 days
Hence, the ant will take 8 days to consume 2 apples.
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PLEASE HELP!!!Which is an equation in point-slope form for the line that passes through the points (−1,4) and (3,−4)?
100 POINTS!!!!!
Answer:
y - 4 = - 2(x + 1)-------------------------
GivenPoints (-1, 4) and (3, - 4)Find the slopem = (- 4 - 4)/(3 - (-1)) = - 8/4 = - 2Use one of the points and the point-slope formy - y₁ = m(x - x₁)y - 4 = - 2(x - (-1)) ⇒ y - 4 = - 2(x + 1)A class of 25 children shares 600 beads.
On a day when 1 child is absent, what is the ratio of the number of children present to the number of beads?
Answer:
Step-by-step explanation:
The answer would be 24:600. One student is absent so there are 24 students present. The number of beads is still 600, so the ratio is 24:600 which simplifies to 1:25.
how many ways are there to seat four of a group of ten people around a circular table where two seatings are considered the same when everyone has the same immediate left and immediate right neighbor?
The number of ways which are there to seat four of a group of ten people around a circular table is 1260.
To choose 4 people from a group of ten we need to count such people, which can be found using 10! / 4! × (10-4)! , after solving this we need to multiply 3! by this to get the desired answer. This is done because for that 4 people to sit in a circle, the possibilities for n people to sit around a circle is (n-1)! , and since n here is 4 the possibilities will also be (4-1)! which is 3! here.
Hence the final answer: 3! × 10! / 4! × (10-4)! = 1260
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Pls help/ A function (x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x)=
The function rule in slope-intercept form is y = -4x - 2
How to calculate the slope-intercept form of this function?Mathematically, the slope-intercept form of a straight line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.From the graph of this line, we have the following data points:
Point (x, y) = (-1, 2)
Point (x, y) = (0, -2)
In Mathematics, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-2 - 2)/(1 - 0)
Slope, m = -4/-1
Slope, m = -4
Note: The y-intercept occurs at the point where the x-value is equal to zero (0).
Now, we can write the function rule for this line in slope-intercept form as follows:
y = mx + c
y = -4x - 2
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The red figure is congruent to the blue figure. Which choice describes a sequence of transformations in which the blue figure is the image of the red figure?
1. Rotate the triangle 90º counterclockwise about the origin and then translate it 7 units left and 1 unit up.
2. Rotate the triangle 90º clockwise about the origin and then translate it 7 units left and 1 unit up.
3. Rotate the triangle 90º counterclockwise about the origin and then translate it 1 unit left and 7 units down.
4. Rotate the triangle 90º clockwise about the origin and then translate it 1 unit left and 7 units down.
The choice which describes a sequence of transformations in which the blue figure is the image of the red figure is: 4. Rotate the triangle 90º clockwise about the origin and then translate it 1 unit left and 7 units down.
What is a rotation?In Mathematics, the rotation of a geometric figure 90° about the origin in a clockwise or counterclockwise direction would produce a geometric figure that has these coordinates (y, -x).
From the information provided in the graph about the transformation applied to the red triangle to create the blue triangle, we have the following ordered pairs that represents a rotation of 90º clockwise:
(x, y) → (y, -x)
Ordered pair A = (-5, 2) Ordered pair A' = (2, 5)
Ordered pair B = (-5, 6) Ordered pair B' = (6, 5)
Ordered pair C = (-1, 2) Ordered pair C' = (2, 1)
After a translation of 1 unit left and 7 units down, we have:
Ordered pair A' = (2, 5) → Ordered pair A' = (2 - 1, 5 - 7) = (-1, -2)
Ordered pair B' = (6, 5) → Ordered pair B' = (6 - 1, 5 - 7) = (.5, -2)
Ordered pair C' = (2, 1) → Ordered pair C' = (2 - 1, 1 - 7) = (-1, -6)
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answer please will give 20 points
Answer:plot the point (2,5)
Step-by-step explanation:
1. Why is identifying
the domain and range important when
defining a function?
Identifying the domain and range is important when defining a function because domain gives all the input values and range gives all the output values a function can take. It is very essential to know domain and range of a function.
Domain are represented by independent variable and are graphed on x coordinate of the axis.
Range are dependent values and are graphed on y axis of the graph.
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3b(2x-z^3)=2h-7gx change the subject to x
Answer:
Step-by-step explanation:
3b(2x - z^3) = 2h - 7gx Distribute 3b
6bx - 3bz^3 = 2h - 7gx Add 3bz^3 to both sides
6bx = 3bz^3 + 2h - 7gx Add 7gx to both sides
6bx + 7gx = 3bz^3 + 2h Factor left side, factor out a gcf of x
x(6b + 7g) = 3bz^3 + 2h Divide both sides by (6b + 7g) to isolate x
x = (3bz^3 + 2h)/ (6b + 7g)
List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
The reduced fraction is 6/7 using GCF method.
What is GCF method?
The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)
Given,
the fraction = 24/28.
the factors of 24 = 2×2×2×3
The factors of 28 = 2×2×7
The gcf is 2 × 2 = 4
divide the denominator and numerator by 4
24 ÷ 4 = 6
28÷ 4 = 7
We get,
the fraction = 6/7.
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What is the inverse of [tex]f(x) = \sqrt{3x - 2}[/tex] for [tex]x \geq \frac{2}{3}[/tex]
Answer:
[tex]f^{-1}(x)=\cfrac{x^2+2}{3}[/tex]============
Given function[tex]f(x)=\sqrt{3x-2}[/tex]Find its inverse, substitute x with y and f(x) with x[tex]x=\sqrt{3y-2}[/tex][tex]x^2=3y-2[/tex][tex]3y=x^2+2[/tex][tex]y=\cfrac{x^2+2}{3}[/tex]The inverse of f(x) is[tex]f^{-1}(x)=\cfrac{x^2+2}{3}[/tex]helppp PLSSSSSSSSSSSSS I NEEED HELPPPPPPPPPPPPPPPPP
Answer:
15c + 19d
Step-by-step explanation:
Here to simplify we have to add like-terms
3c + 14d + c + 11c + 5d = ( 3c + c + 11c) + ( 14d + 5d) = 15c + 19d
Glad to Help
Write equivalent fractions for 8/9 and 5/8 using the least common denominator.
Type the fractions, using a slash ( / ) to separate the numerator and denominator.
8/9 =
5/8 =
The equivalent fractions for 8/9 and 5/8 using the least common denominator are 8/9 = 64/72 and 5/8 = 45/72.
What is the Least Common Denominator?
The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator (LCD). The smallest number that may be used as the denominator to produce a group of comparable fractions that all have the same denominator is known as the lowest common denominator.
The given fractions are 8/9 and 5/8.
The denominators of these fractions are 8 and 9.
so Least Common Divisor(LCD) of 8 and 9 will be = 8 × 9
= 72.
so the equivalent fraction can be calculated as
for 8/9 = [tex]\frac{8*8}{9*8}[/tex]
= 64/72
and for 5/8 = [tex]\frac{5*9}{8*9}[/tex]
= 45/72
Hence, the equivalent fractions are 64/72 and 45/72.
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37, 38, 39, and 40 show that the series is convergent. how many terms of the series do we need to add in order to find the sum to the indicated accuracy?
In order to find the sum to the indicated accuracy we need to add
5 terms as the series is said to be convergent.
Given Series is Σ(-1/3)^n / n where error is less than 0.0005
= Σ (-1)^n / n3^n
For this series, we will use ratio test
if [tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = L < 1 then series in convergent,
Let an = (-1)^n / n3^n , an+1 = (-1)^n+1 / (n+1)3^n+1
[tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = [tex]\lim_{n \to \infty} | ((-1)^n+1 / (n+1)3^n+1)(n3^n/(-1)^n) |[/tex]
By solving we get,
[tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = 1/3 < 1
Then given series is convergent.
By alternating series estimation theorem we have,
|Rn|=|S-Sn| <= an+1
an+1 <= 0.0005
1 / (n+1)3^n+1 <= 0.0005
(n+1)3^n+1 >= 2000
2 * [tex]3^{2}[/tex] >[tex]\neq[/tex] 2000 (n=1)
4 * [tex]3^{4}[/tex] >[tex]\neq[/tex] 2000 (n=3)
6 * [tex]3^{6}[/tex] >= 200 (n=5)
So required terms is n=5
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In ΔSTU, TU = 11, US = 17, and ST = 18. Which statement about the angles of ΔSTU must be true?
For the given triangle STU all the angles of ΔSTU are not equal to each other is the true statement .
As given in the question,
In the given triangle STU,
TU = 11
US = 17
ST = 18
we can see that
TU < US < ST
⇒ 11 < 17 < 18
⇒ 11 + 17 = 28
⇒ 28 > 18
All the sides of the triangle are not equal to each other.
This implies that all the angles opposite to the unequal sides are also not equal to other.
Therefore, for the given triangle STU all the angles of ΔSTU are not equal to each other is the true statement .
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In a two-digit number, the unit digit is 5 more than the tens digit. The number itself is three times the sum of the digits. What is the number?
Answer:
27
Step-by-step explanation:
You want a 2-digit number that is 3 times the sum of its digits, where the units digit is 5 more than the tens digit.
SetupLet t represent the tens digit. Then the units digit is (t+5) and the sum of digits is ...
t +(t +5) = 2t+5
The value of the number is ...
10t +(t+5) = 11t +5
The value is 3 times the sum of digits, so we have ...
11t +5 = 3(2t +5)
Solution11t +5 = 6t +15
5t = 10 . . . . . . . . . . subtract (6t+5)
t = 2
(t+5) = 7
The number is 27.
consider performing a partial f test to test for the inclusion of pctrush in the model. either in words or formula, what are the null and alternative hypotheses for this test?
The null and alternative hypothesis of the pctrush are explained below.
Given that;
By performing a partial F-test;
In hypothesis testing, the F test is a statistical test that is used to determine whether or not the variances of two populations or two samples are equal. The data in a f test follows a f distribution. In this test, two variances are divided and compared using the f statistic. Depending on the problem's characteristics, a f test can be either one- or two-tailed.
The one-way ANOVA (analysis of variance) test is run using the f value discovered after running the f test. More information on a f test, the f statistic, its critical value, formula, and how to perform a f test for hypothesis testing will be provided in this article.
The f test statistic is used in a test called the f test to determine if the variances of two samples (or populations) are equal. An f test needs a f distribution in the population and independent events for the samples in order to be valid. The null hypothesis can be rejected after conducting the hypothesis test if the f test results are statistically significant; otherwise, it cannot be rejected.
Null hypothesis:
The idea that there is no influence on the population is known as the null hypothesis.
We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no effect in the population (p). If not, we are unable to rule out the null hypothesis.
Although it may sound odd, statisticians only accept the phrase "fail to reject." Avoid using words like "prove" or "accept" when referring to the null hypothesis.
Alternative hypothesis:
The alternate response to your research question is the alternative hypothesis (Ha). It asserts that the populace is affected.
Your research hypothesis and your alternate hypothesis are frequently identical. It is, in other words, the assertion that you anticipate, or hope will be accurate.
The complement of the null hypothesis is the alternative hypothesis. The exhaustive nature of null and alternative hypotheses ensures that they account for all potential outcomes. Additionally, they are mutually exclusive, so only one of them can be true at once.
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y=½x+4 solve this slope
Answer:
Slope: [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The slope-intercept form is y = m x + b , where m is the slope and b is the y-intercept.
The expression given is already in slope intercept form. In this case [tex]m=\frac{1}{2}[/tex]
Therefore the slope is [tex]\frac{1}{2}[/tex]
Answer:
slope = [tex]\frac{1}{2}[/tex]
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 )
y = [tex]\frac{1}{2}[/tex] x + 4 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
