Answer:
(49 - 29) + 1 =(50 - 29)
Step-by-step explanation:
The 20 comes from the subtraction of 29 in both sides of the previous step equality. In the following, I transcript the complete procedure and I add the step that you need to understand why 20 appears (in bold numbers):
29+20=49
49+1=50
(49 - 29) + 1 =(50 - 29)
20+1=21
50-29=21
hence, it was only nesseraty to subtract 29
The perimeter of a rectangular is 20 centimeters the length is 6 centimeters what is the area of the rectangular
Answer:
24 centimeters
Step-by-step explanation:
Since the longer side is 6 then multiply it by 2 which is 12, now subtract it by 20 since that is its perimeter. then u divide 8 by 2 since theres 2 sides. now do 6 times 4 which is 24
Professor Isaac Asimov was one of the most prolific writers of all time. Prior to his death, he wrote nearly 500 books during a 40-year career. In fact, as his career progressed, he became even more productive in terms of the number of books written within a given period of time. The data given in increments of 100:
Number of books, x: 100 200 300 400 500
Time in months, y: 237 350 419 465 507
a. Assume that the number of books x and the time in months y are linearly related. Find the least-squares line relating y to x.
b. Plot the time as a function of the number of books written using a scatterplot, and graph the least-squares line on the same paper. Does this seem to provide a good fit to the data points?
c. Construct the ANOVA table for the linear regression.
Answer:
Step-by-step explanation:
n = sample size = 5
a) Let us determine the sum
[tex]\sum x_i= 100+200+300+400+490=1490[/tex]
[tex]\sum x_i^2= 100^2+200^2+300^2+400^2+490^2=540100[/tex]
[tex]\sum y_i = 237+350+419+465+507=1978[/tex]
[tex]\sum y_i^2= 237^2+350^2+419^2+465^2+507^2=827504[/tex]
[tex]\sum x_i y_i=100 \times 237 + 200\times350+300 \times 419 + 400 \times 465 + 490 \times 507=653830[/tex]
Now we can determine [tex]S_x_x, S_x_y, S_y_y[/tex]
[tex]S_x_x = \sum x_i^2-\frac{(\sum x_1)^2}{n} \\= 540100 - \frac{1490^2}{5} \\= 96080[/tex]
[tex]S_x_y = \sum x_i y_i -\frac{(\sum x_i)(\sum y_i) }{n} \\\\[/tex]
[tex]653830 - \frac{1490 \times 1978 }{5} = 64386[/tex]
[tex]S_y_y = \sum y_i^2-\frac{(\sum y_i)^2 }{n} = 82750-\frac{1978^2}{5} \\\\= 45007.2[/tex]
The estimate b of the slope β is the ratio of [tex]S_x_y[/tex] and [tex]S_x_x[/tex]
[tex]b = \frac{S_x_y}{S_x_x}[/tex]
[tex]\frac{64386}{96080} = 0.67[/tex]
The mean is the sum of all value divide by number of values
[tex]\bar x= \frac{\sum x_i}{n} \\\\= \frac{100+200+300+400+490}{5} \\\\= \frac{1490}{5} = 298[/tex]
[tex]\bar y= \frac{\sum y_i}{n} \\\\= \frac{237+350+419+465+507}{5} \\\\= \frac{1978}{5} = 395.6[/tex]
The estimate a of the intercept is
[tex]a = \bar y - b \bar x[/tex]
[tex]= 395.6 - 0.69 \times 298\\= 195.9[/tex]
General least square equation;
[tex]\bar y = \alpha + \beta x[/tex]
replace alpha by a = 3 and beta by b = 0.67 in general least equation
y = a + bx
195.9 + 0.67x
b)
Scatter plot is shown in the attached file
x is on the horizontal axis
y is n the vertical axis
The degree of freedom of regression is 1
because we use one variable s predictor variable
[tex]d_f_R = 1[/tex]
The degree of freedom of error is the sample size n decrease by 2
[tex]d_f_E =n-2= 5 - 2=3[/tex]
Total df is equal to the sum of seperate degree of freedom dfR and dfE
total df = 1 +3 4
[tex]SSR = \frac{(S_x_y)^2}{S_x_x} = \frac{64386^2}{96080} \\\\= 43146.9296[/tex]
Total SS =Syy= 45007.2
SSE + Total SS = SSR
= 45007.2 - 43146.9296
= 1860.2705
Finding the work done in stretching or compressing a spring.
Hooke's Law for Springs.
According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x)=kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive.
In this problem we assume that the force applied doesn't distort the metal in the spring.
A 2 m spring requires 11 J to stretch to 2.4 m. Find the force function, F(x), for the spring described.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images below to see the step by step explanation to the question above.
graph x2 - y2 = 16 what are the lines of symetry
Answer:
it has 4 lines of symetery the x - axis,the y-axis,y=x,and y ''Cx every line through the center is a line of symetry
Step-by-step explanation:
I'll give you brainiest
Explain how to translate the statement into an equation. Use n for the variable.
Sixty-three is the product of nine and a number.
Answer:
9n= 63
n=7
Step-by-step explanation:
hope this helps, good luck. :)))
brainliest ?? :)))
Based on the statement sixty-three is the product of nine and a number, the equation will be 9n = 63.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between.
WE have been given that sixty-three is the product of nine and a number, Use n for the variable.
We need to find the statement into an equation.
The equation in this case will be as follows;
9n = 63
n = 63/9
n = 7
Therefore, the equation is 9n = 63 and the value of n is 7.
Learn more about equations here;
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A number increased by 11 is equal to twice the number decreased by 12
Answer: 10
Step-by-step explanation:
Find the lateral surface area below given prism:
Answer:
the answer should be 158 but I'm not a hundred percent sure
A girl and a puppy are 850 feet apart when they start running towards each other. The girl runs at a speed of 8 feet per second, and the puppy runs at a speed of 7 feet per second. How soon will they meet?
Answer:
The correct answer is 56.6666666667 second's
Answer:
56 2/3
Step-by-step explanation:
Giving brainliest for CORRECT awnser.
Answer:
x < 18 - 10
x < 8
Step-by-step explanation:
Answer:
8 > x
Step-by-step explanation:
-10 > x- 18
Isolate the variable, x. Note the inequality sign, treat it like an equal sign; what you do to one side, you do to the other. Add 18 to both sides:
-10 (+ 18) > x - 18 (+18)
-10 + 18 > x
Simplify. Combine like terms:
(-10 + 18) > x
18 - 10 > x
8 > x
8 > x is your answer.
~
Mark computer weighs 35.769 pounds rounde to the nearest hundreds
Answer:
35.800
Step-by-step explanation:
Describe a free market economy
Answer:
soviet russia
Step-by-step explanation:
just kidding
The free market is an economic system based on supply and demand with little or no government control. ... Based on its political and legal rules, a country's free market economy may range between very large or entirely black market
Countries that have a market economy are Mexico, United States, United Kingdom, Germany, and Canada . These countries have a market economy because the prices of goods and services are set by supply and demand
A line has the equation 3x–4y–12=0.
Is the point (2, −1) on the graph?
Answer:
The point (2, -1 ) is not on the graph of the line.
Step-by-step explanation:
3x–4y–12=0
3*2 - 4*(-1) - 12= 0
6 + 4 - 12 =0
10 - 12 = 0
- 2 = 0 , false, so the point (2, -1 ) is not on the graph of the line.
Find the 70th term of the arithmetic sequence -26, -19, -12
Answer:
457
Step-by-step explanation:
The general term of an arithmetic sequence is given by ...
an = a1 +d(n -1)
where a1 is the first term (-26), and d is the common difference (7).
The 70th term of your sequence can be found by putting the numbers into this formula:
a70 = -26 +7(70 -1) = -26 +483
a70 = 457
The 70th term of the sequence is 457.
What is the GCF of 45 and 72?
Answer:
The common factors of 45 and 72 are 9, 3, 1
Step-by-step explanation:
Answer:
The GCF of these two numbers is nine.
Step-by-step explanation:
They share three common factors: 1, 3 and 9. The greatest out of all of those is 9. Hope this helps!
Please help me with my work for math
Answer:
AAA
Stp-by-step explanation:
use the figure to help you explain the statement
The base(b) of a triangle is ----------inches
The height (h) of the triangle is--------inches
The area of a triangle is ------- Square inches
The area of the rectangle is ------ Square centimeters
help fassstttt
Step-by-step explanation:
base is 6 in
height is 4 in
to get the area of a triangle is 1/2base×height
being 1/2(6)(4)=12
to get the area of a rectangle is length×width being 9×8=72
By observing the given figure,
The base(b) of a triangle is 6 inches
The height(h) of a triangle is 4 inches
The area of the triangle is 12 square inches
The area of the rectangle is 72 square centimeter
What is Triangle?A triangle is a polygon with three edges and three vertices
What is Rectangle?A rectangle is a quadrilateral with four right angles
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface
From the given figure
The base(b) of a triangle is 6 inches
The height(h) of a triangle is 4 inches
The area of a triangle = [tex]\frac{1}{2}bh[/tex]
=[tex]\frac{1}{2}(6)(4)[/tex]
=12 square inches
Length of the rectangle = 8 centimeter
Width of the rectangle = 9 centimeter
Area of the rectangle = l × w = 9×8=72 square centimeter
Hence,
The base(b) of a triangle is 6 inches
The height(h) of a triangle is 4 inches
The area of the triangle is 12 square inches
The area of the rectangle is 72 square centimeter
Learn more about Triangle, Rectangle and Area here
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In one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is ok. Among 810 airport baggage scales, 102 are defective (based on data from the NY Department of Consumer Affairs). If four of the scales are randomly selected and tested, what is the probability that the entire bath will be accepted
Answer:
[tex]X \sim Hyp (N = 810, M=102, n=4)[/tex]
[tex] P(X=0) = \frac{(102C0)(810-102 C 4-0)}{810C4}[/tex]
And solving we got:
[tex] P(X=0)= \frac{(102C0) (708C4)}{810C4} = 0.583[/tex]
So then for the problem given the probability that the entire bath will be accepted (none is defective among the 4) is 0.583
Step-by-step explanation:
For this case we can model the variable of interest with the hypergeometric distribution. And with the info given we can do this:
[tex]X \sim Hyp (N = 810, M=102, n=4)[/tex]
[tex]P(X=k)= \frac{(MCk)(N-M C n-k)}{NCn}[/tex]
Where N is the population size, M is the number of success states in the population, n is the number of draws, k is the number of observed successes
And for this case we want to find the probability that none of the scales selected would be defective so we want to find this:
[tex] P(X=0)[/tex]
And using the probability mass function we got:
[tex] P(X=0) = \frac{(102C0)(810-102 C 4-0)}{810C4}[/tex]
And solving we got:
[tex] P(X=0)= \frac{(102C0) (708C4)}{810C4} = 0.583[/tex]
So then for the problem given the probability that the entire bath will be accepted (none is defective among the 4) is 0.583
If you flipped a fair coin 18 times about how many times would you expect heads to appear?
Answer:
9 times
Step-by-step explanation:
hope this helps
Answer:
9
Step-by-step explanation:
Mathematically, 9, although reality wise, you could flip the coin and get heads every time, or the opposite.
I think you mean mathematically though, so yes, it would be 9.
1.(1 0) You measure the distance, l, a projectile travels several times using the same apparatus and find the following values (cm): 5.11, 4.89, 5.04, 4.94, 4.93, 5.06 and 5.09. Assuming that the errors are random: a) What is the mean value forl? b) What is the standard deviation for this data set? c) What is the uncertainty associated with your best estimate forl? d) How should one report the result of this measurement along with the uncertainty at the 95 % confidence level? e) If you desire to reduce the statistical uncertainty associated with the reported result using the same apparatus to be only 0.01 cm, how many measurements must be made?
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Tate is paid $17.35 per hour with time and a half overtime. What will his gross pay period in which he worked 35 hours one week and 44 hours next week for a total 79 hours?
Answer:
The new rule has a higher salary level for exemption from overtime, at $684 a week. This means that lower-pay exempt employees may qualify for overtime.
Step-by-step explanation: this is your answer plz rate e the most brainlest
If a punnet of strawberries wrighs 100g, how many punnets would weigh 1 kg
Step-by-step explanation:
1kg = 1000g so
10 x 100 = 1000
So 100 punnets of strawberries weigh 1 kg
A company makes cones out of solid foam. Each cone has a height of 9 inches, and its base has a diameter of 5 inches. How much foam is needed to make 120 cones?
Answer: 2250 pi
Step to do:
where is the volume of the cone, is the radius of the base, and is the height of the cone.
In the given problem, we know that and . Using this, we can find the volume of a single cone:
Since the problem asks how much foam is needed to make 120 cones, we can multiply this result to get our answer:
6. A golfer is standing at the tee,
looking up to the green on a hill. If the
tee is 36 yards lower than the green
and the angle of elevation from the tee
to the hole is 12º, find the distance from
the tee to the hole.
Answer:
173.15 yards is the distance from tee to hole.
Step-by-step explanation:
Please refer to the image attached.
Let A is the position of tee and where the golfer is standing.
C is the position of hole.
CB is the vertical distance between greens and tee.
Angle of elevation, [tex]\angle BAC = 12^\circ[/tex]
To find: side AC.
Using trigonometric functions, we know that value of sine is:
[tex]sin\theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]
Here [tex]\theta = \angle BAC = 12^\circ[/tex]
Perpendicular is side CB.
Hypotenuse is side AC.
[tex]sin12^\circ = \dfrac{\text{CB}}{\text{AC}}\\\Rightarrow \text{CB} = \dfrac{36}{sin12^\circ}\\\Rightarrow \text{CB} = 173.15\ yards[/tex]
Hence, 173.15 yards is the distance from tee to hole.
6³=216. Using exponents, write three expressions whose value is 216.
Please help I don't understand.
9514 1404 393
Answer:
216 = 2³·3³ = 8·3³ = 27·2³
Step-by-step explanation:
6³ = 2·2·2·3·3·3
The string of factors can be grouped however you like, and any repeated factors in the group can be expressed using an exponent.
= 2·2²·3³
= 8·3³
= 6·2²·3²
= 6·6²
= 27·2³
In a comparison of the body fat percentage of four different ethnic groups, the body fat percentage was measured for 200 African-Americans, 160 Whites, 220 Hispanics, and 310 Others. Because a comparison of average body fat percentage between these groups is desired, an ANOVA test was conducted, which resulted in p-value of 0.11. What conclusion can you make if level of significance is 0.05?
Answer:
There is not enough evidence to support the claim that the fat percentage of at least one of the four ethnic groups is different.
Step-by-step explanation:
The Analysis of Variance (ANOVA) test is used to determine whether there is any significant difference between the mean of various independent groups.
In this case an ANOVA test is being performed to determine whether the fat percentage of four different ethnic groups are different or not.
The hypothesis can be defined as:
H₀: The fat percentage of four different ethnic groups are same, i.e. μ₁ = μ₂ = μ₃ = μ₄.
Hₐ: The fat percentage of at least one of the four ethnic groups is different, i.e. at least one μ[tex]_{i}[/tex] is different.
The significance level of the test is, α = 0.05.
The decision rule is:
If the p-value of the test is less than the significance level, then the null hypothesis will be rejected.And if the p-value of the test is not less than the significance level, then the null hypothesis will not be rejected.The p-value of the ANOVA test is computed as, p-value = 0.11.
p-value = 0.11 > α = 0.05.
The null hypothesis was failed to be rejected.
Hence, it can be concluded that there is not enough evidence to support the claim that the fat percentage of at least one of the four ethnic groups is different.
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
D
Step-by-step explanation:
Answer:C and D
Step-by-step explanation:
7x^2-42x=0
First find the highest common factor of 7x^2 and 42x
7x^2=7 x X x X
42x=2 x 3 x 7 x X
Highest common factor is 7x
7x(x-6)=0
7x=0. or x-6=0
x=0. or x=6
There is 500 mg of potassium in 1 cup (240 ml) of orange juice. Your renal patient must watch his potassium intake not to exceed 2 mg per kg of body weight per day from Orange juice alone. How much juice (in ml) can this patient have per day if the patient weighs 135 lb?
Answer:
58.79 mL of juice
Step-by-step explanation:
To do this, let's gather the data first:
In 1 cup of orange juice we have 500 mg of potassium. A patient weights 135 lb, and he needs to take care of it's potassium intake and not exceed 2 mg of K / kg per day.
So obviously he cannot drink a whole cup of orange juice. It has to be less. In order to know this, we need to know first the weight in kg. 1 lb equals 0.4536 kg so in 135 lb:
W = 135 lb * 0.4536 kg/lb = 61.24 kg
Now, we need to know with this weight, how much potassium it can takes:
Intake = 61.24 kg * 2 mg/kg = 122.48 mg of K
So, the maximum amount of potassium per day is 122.48 mg. This means that the quantity of orange juice this person can take is:
Juice = 122.48 mg * 240 mL / 500 mg
Juice = 58.79 mL of juice or simply 59 mL
Find the middle term of the expansion of (x+y)^8 a40x^2y^2 b70x^2y^2
Answer:
the middle term = 70x⁴y⁴
Step-by-step explanation:
Given;
(x+y)⁸
This expression can be expanded as follows, using Paschal triangle;
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
At level 8, the middle coefficient is 70
Also the power of x and y will be equal in the middle term = A(xⁿ yⁿ)
A = 70 ,
n +n = 8
n = 4
Thus, the middle term = 70x⁴y⁴
The roots of a quadratic equation are 6 and 3/4. If one of the two factors of the equation is x – 6, what is the second factor?
A. 3x - 4
B. 3x + 4
C. 4x - 3
D. 4x + 3
Answer:
C. 4x - 3
Step-by-step explanation:
The factor could be (x -3/4). Apparently, you're expected to show the factor as 4 times this, or ...
4x -3 . . . . . matches choice C
___
If r is a root, then (x -r) is a factor. As here, factors containing fractional roots can be multiplied by the denominator to make the coefficients be integers.
Need help ASAP! Simplify the expression so there is only one positive power for the base, -5. (The questions/answers are in the group chat.)
A.
B.
C.
D.
Answer: C
Step-by-step explanation:
-5^7 ➗ -5^2
(-5)^(7-2)
-5^5
