Answer:
2/5 or 0.4
Step-by-step explanation:
First we have to make equation into the gradient slope form :
y=mx+c m is gradient and c is y-intercept
15y-6x=8
First we add 6x to both sides :
15y = 6x+8
Now we divide both sides by 15 :
y = 6x+8 / 15
Split the fraction on the right :
y = 6x/15 + 8/15
6x/15 = 6/15x
Our gradient will be 6/15 = 2/5 or 0.4
Hope this helped and have a good day
Listed below are systolic blood pressure measurements (in mmHg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05.
The regression equation between the variables is y = 1.03x + 62.12 and the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg is 149.67
How to determine the regression equation?From the table of values, we make use of the following representations:
Represent the Right Arm on the x axisRepresent the Left Arm on the y axisUsing the above representations, we can now plot our data values on a graphing calculator
From the graphing calculator, we have the following summary:
Sum of X = 458Sum of Y = 782Mean X = 91.6Mean Y = 156.4Sum of squares (SSX) = 601.2Sum of products (SP) = 618.8The regression equation is
y = bx + a
Where
b = SP/SSX = 618.8/601.2 = 1.02927
a = MY - bMX = 156.4 - (1.03*91.6) = 62.11843
This gives
y = 1.03x + 62.12
Hence, the regression equation between the variables is y = 1.03x + 62.12
To predict the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg, we have
y = 1.03 * 85 + 62.12
Evaluate
y = 149.67
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Consider the steps to solve the equation. 2 5 ( 1 2 y + 20 ) − 4 5 = 9 20 (2y − 1)
Distribute: 1 5 y + 8 − 4 5 = 9 10 y − 9 20
What is the next step after using the distributive property?
*Use the multiplication property of equality to isolate the variable term on one side of the equation.
*Use the multiplication property of equality to isolate the constant on one side of the equation.
*Combine the like terms on the right side of the equation.
*Combine the like terms on the left side of the equation.
Answer:
D
Step-by-step explanation:
I did the assignment
hope this helps :)
A spaceship is traveling at a steady rate. The table shows the distance the spaceship travels in a given period of time. Find the distance the spaceship travels in 4 minutes.
Ty.
The distance of the spaceship in discuss as in the task content given can be evaluated as; 800miles.
What is the distance the spaceship travels in 4 minutes?The distance travelled by the spaceship in discuss can be evaluated by means of the slope of the linear relationship as follows;
Hence it follows from ratios that by observation, the linear relationship has a slope of 200mi/min.
Consequently, we can evaluate the distance travelled after 4 minutes as;
Distance = 200 × 4 = 800mi.
Ultimately, the distance travelled per minute by the spaceship is; 800mi.
Remarks:
600 miles
520 miles
800 miles
1,080 miles
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Find the value of z
A. 50
B. 110
C. 65
D. 130
Find the missing segment in the image below.
Answer:
105.
Step-by-step explanation:
x/120 = 56/64 where x is the length of missing segment
64x = 120*56
x = (120*56)/64
= 105.
Solve the system to answer the questions.
How many premium car washes were ordered?
premium car washes
How many quick car washes were ordered?
quick car washes
The number of quick car and premium car washes ordered are 75 and 50 respectively.
How to find the number of premium and quick car washes ordered?The system of equation models the situation
x + y = 125
5x + 8y = 775
Therefore,
5x + 5y = 625
5x + 8y = 775
3y = 150
divide both sides 3
3y / 3 = 150 / 3
y = 50
Therefore,
x + y = 125
x + 50 = 125
x = 125 - 50
x = 75
Therefore, the number of quick car and premium car washes ordered are 75 and 50 respectively.
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Answer:
50 and 75
Step-by-step explanation:
Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
According to the developed scale, a radiant day is 16 times brighter than a dim day.
We assume the brightness of a dim day to be x.
According to the developed scale, the brightness of an illuminated day will be 4 times that of a dim day.
Thus, the brightness of an illuminated day = 4*the brightness of a dim day = 4x.
According to the developed scale, the brightness of a radiant day will be 4 times that of an illuminated day.
Thus, the brightness of a radiant day = 4*the brightness of an illuminated day = 4*4x = 16x.
Now, the ratio of the brightness of a radiant day to the brightness of a dim day = 16x:x = 16x/x = 16:1.
Thus, according to the developed scale, a radiant day is 16 times brighter than a dim day.
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The question provided is incomplete. The complete question is:
"Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
Dim=2
Illuminated=3
Radiant=4
Dazzling=5"
2 Question is down below.
The height of the flagpole is 12.4 meters and the altitude of the balloon is 29.1 meters
How tall is the flagpole?See attachment for the diagram, when redrawn
Start by calculating the length AB using the following tangent function
tan(22) = BC/AB
This gives
tan(22) = 9/AB
Make AB the subject
AB = 9/tan(22)
Evaluate the quotient
AB = 22.3
The length DB is then calculated using:
tan(9) = DB/AB
This gives
tan(9) = DB/22.3
Make DB the subject
DB = 22.3 * tan(9)
Evaluate
DB = 3.35
The height of the flagpole is then calculated as:
Height = DB + BC
This gives
Height = 3.35 + 9
Evaluate
Height = 12.35
Approximate
Height = 12.4
Hence, the height of the flagpole is 12.4 meters
How to determine the altitude of the balloon?The diagram that illustrates the scenario is added as an attachment
Calculate the value of y using the following tangent functions
tan(57) = x/y and tan(72) = (15 + x)/y
Make y the subject in tan(57) = x/y and tan(72) = (15 + x)/y
y = x/tan(57) and y = (15 + x)/tan(72)
Substitute y = x/tan(57) in y = (15 + x)/tan(72)
x/tan(57) = (15 + x)/tan(72)
Evaluate the tangent ratios
x/1.5 = (15 + x)/3.1
Cross multiply
3.1x = 22.5 + 1.5x
Evaluate the like terms
1.6x = 22.5
Divide by 1.6
x = 14.1
The altitude of the balloon is then calculated as:
Altitude = 14.1 + 15
Altitude = 29.1
Hence, the altitude of the balloon is 29.1 meters
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Mr Lim had a bag of sweets. After giving each pupil 7 sweets, he had 4 sweets left. If he had given only 5 sweets to each pupil, he would have 4 sweets left. If he had given only 5 sweets to each pupil, he would have 80 sweets left.
i.How many pupils were there in the class?
ii. How many sweets did Mr Lim have?
Solving a system of equations we can see that there are 270 sweets and 38 pupils.
How many pupils and sweets are there?
Let's define the variables:
P = number of pupils.
S= number of sweets.
With the given information, we can write:
7*P + 4 = S
5*P + 80 = S
So we have a system of equations, now we can write:
7*P + 4 = S = 5*P + 80
Solving that for P:
7*P + 4 = 5*P + 80
7*P - 5*P = 80 - 4
2*P = 76
P = 76/2 = 38
There are 38 pupils, and the number of sweets is given by:
S = 7*P + 4 = 7*38 + 4 = 270
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is (n x (n +1)) / 2 the same as (n/2)(n+1)
Answer:
nope
Step-by-step explanation:
simplify the first equation
Answer:
yes
Step-by-step explanation:
The associative and commutative properties of multiplication allow you to rearrange the product to the form shown in the question.
Division by 2 is effectively multiplication by 1/2.
[tex](n\times(n+1))/2\qquad\text{given}\\\\=\dfrac{n(n+1)}{2}=\dfrac{n}{2}(n+1)\\\\=\boxed{(n/2)(n+1)}[/tex]
__
Additional comment
Evaluation of the expressions according to the order of operations will proceed differently for the two expressions.
For the first expression, evaluation steps are ...
add 1 to nmultiply the sum by ndivide the product by 2For the second expression, evaluation steps are ...
divide n by 2add 1 to nmultiply the results of these two operationsAs we said above, the properties of multiplication ensure the results are the same either way.
As a practical matter, for integer values of n, one of n and (n+1) will be even. It is usually convenient to divide the even number by 2. This means the evaluation might be ...
((n+1)/2)n . . . . for odd n(n+1)(n/2) . . . . for even nFor certain computer representations of the numbers, results may differ depending on the specific numbers and the order of evaluation.
Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the π button on your calculator to solve.
The volume of the figure is 1, 005. 4 mi³
Volume of a cylinderNote that the figure is a cylinder
The formula for volume of a cylinder is given as;
Volume = πr²h
Where
h = height = 5 mi
r = radius = 8mi
Substitute into the volume
Volume = 3. 142 × 8 × 8 × 5
Volume = 1,005. 4 mi³
Thus, the volume of the figure is 1, 005. 4 mi³
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evaluate 4 + 6 x 6 / 8
Answer:
8.5
Step-by-step explanation:
4 + (6)(6)/8=
17/2 = 8.5
Answer:
8.5
Step-by-step explanation:
6 x 6 = 36/8 = 4.5 + 4 = 8.5
A dealer buys oranges for 100000, he sold 60% of them for buying price, he sold 50% of the remaining for profit of 60% then he sold the remaining for a loss of 10%. Find the overall profit
Based on the amount of oranges bought, those sold at a profit and those sold at a loss, the overall profit is 14.2%
What is the overall profit?Assume that the buying price was $1 each.
The amount earned from 60% of them is:
= 60% x 100,000 x 1
= $60,000
The profit from selling 50% of the remaining is:
= (50% x 40,000) x 1.60
= $32,000
The loss from selling the other 50%:
= (50% x 40,000) x 0.90
= $22,222.22
Total selling price:
= 60,000 + 32,000 + 22,222.22
= $114,222.22
Total profit:
= (114,222.22 - 100,000) / 100,000
= 14.2%
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(6 1/7 divided by x + 3 5/9) / 4 1/6 = 1 1/3 what is x
let's firstly convert the mixed fractions to improper fractions and them proceed.
[tex]\stackrel{mixed}{6\frac{1}{7}}\implies \cfrac{6\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{43}{7}} ~\hfill \stackrel{mixed}{3\frac{5}{9}}\implies \cfrac{3\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{32}{9}} \\\\\\ \stackrel{mixed}{4\frac{1}{6}}\implies \cfrac{4\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{25}{6}} ~\hfill \stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{ ~~ \frac{6\frac{1}{7}}{x}+3\frac{5}{9} ~~ }{4\frac{1}{6}}~~ = ~~1\frac{1}{3}\implies \cfrac{ ~~ \frac{ ~~ \frac{43}{7} ~~ }{x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}\implies \cfrac{ ~~ \frac{43}{7x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}[/tex]
[tex]\cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{25}{6}\cdot \cfrac{4}{3}\implies \cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{50}{9}\implies \cfrac{43}{7x}~~ = ~~\cfrac{50}{9}-\cfrac{32}{9} \\\\\\ \cfrac{43}{7x}~~ = ~~\cfrac{18}{9}\implies \cfrac{43}{7x}=2\implies 43=14x\implies \cfrac{43}{14}=x\implies 3\frac{1}{14}=x[/tex]
Question 9 of 20:
Select the best answer for the question.
9. Select the proper order from least to greatest for 23.76.8.10 -
A. 8,3,10.76.
B.23,10.6.8.
C.8.10 6.2/3.
D.76%10.3.8.
Answer:
Please make the question clearer, but I would say B
Step-by-step explanation:
I am not sure what you mean, to me the question is unclear
A company found that an experienced surveyor can survey a roadbed in 7 hours. An apprentice surveyor needs 8 hours
to survey the same stretch of road. If the two work together, find how long it takes them to complete the job.
***
The number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.
Rate of workHours it takes the experienced surveyor = 7 hoursSurveyors rate of work = 1/7Hours it takes the apprentice = 8 hoursApprentice rate of work = 1/8If the two work together;
Time taken for both to complete the task = Surveyors rate of work + Apprentice rate of work
= 1/8 + 1/7
= (7+8) / 56
= 15/56 hours
Therefore, the number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.
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A.22
B.183
C.246
D.213
Answer:
B. 183
Step-by-step explanation:
m<L = (1/2)[m(arc)KN - m(arc)KM)]
35 = (1/2)(177x - 107x)
70 = 70x
x = 1
m(arc)KN = 177x = 177
m(arc)NMK = 360 - m(arc)KN
m(arc)MNK = 360 - 177
m(arc)MNK = 183
A ________ standard deviation represents an overall wide spread of data points while a ________ standard deviation represents a closely clustered set of points.
Answers are in bold
A larger standard deviation represents an overall wide spread of data points while a smaller standard deviation represents a closely clustered set of points.
Keep in mind the standard deviation cannot be negative. A standard deviation of 0 means that every data value is the same number; hence it is the most clustered set possible. There is no upper limit on how big the standard deviation can be.
If needed, replace "larger" with "large". And if needed, replace "smaller" with "small". I think it will depend on how your teacher wants you to word it. In all honesty, I'm not very good with grammar.
A larger standard deviation represents an overall wide spread of data points while a smaller standard deviation represents a closely clustered set of points.
What is standard deviation?The term "standard deviation refers to a measurement of the data's dispersion from the mean.
A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
The standard deviation cannot be negative, so keep that in mind. The most tightly clustered set of data is one with a standard deviation of 0, which denotes that all the data values are the same.
The size of the standard deviation has no upper bound.
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In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square yards, of ΔABC.
a = 12, b = 11, c = 7
Answer:
12 sqrt (10)
Step-by-step explanation:
S = (12 + 11 + 7) / 2 = 15
A = sqrt (s(s-a)(s-b)(s-c))
= sqrt (15(15-12)(15-11)(15-7))
= sqrt (15*3*4*8)
= sqrt (1440)
= 12 sqrt (10)
Look at the graph below.
Answer:
B. -1/3
Step-by-step explanation:
Choose 2 points. From the lower points count up until it is in line with the other point. Then count left until you reach the second point.
Rise/Run
Rise=1
Run=-3
[tex]-\frac{1}{3}[/tex]
Hope this helps!
Answer: -1/3 is the answer
Step-by-step explanation:
A 2-gallon container of laundry detergent costs $10.24. What is the price per fluid ounce?
Answer:
$0.04
Step-by-step explanation:
The cost per ounce is found by dividing the cost by the number of ounces.
SolutionIn 2 gallons, there are 2×128 fl.oz. = 256 fl.oz. Then the cost per ounce is ...
cost/ounces = $10.24/(256 fl.oz) = $0.04 /fl.oz.
The cost of the laundry detergent is $0.04 per fluid ounce.
__
Additional comment
Keeping the units with the numbers in a calculation can give you confidence that the calculated result has the units you want it to have.
Need help ASAP! This is due in an hour and this is the last question!!!
the equation with these solutions is:
0 = x^2 - 6x + 6
How to find an equation with the given solutions?
Remember that a quadratic equation with the solutions a and b is written as:
0 = (x - a)*(x - b)
Here we have the solutions:
x = 3 + √3x = 3 - √3Then we can write a quadratic equation of the form:
0 = (x - (3 + √3) )*(x - (3 - √3) )
0 = (x - 3 - √3)*(x - 3 + √3)
Expanding that, we get:
0 = x^2 - 6x + 9 - 3
0 = x^2 - 6x + 6
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Solve for x.
°x = 196
Enter your answers in the boxes. Enter the smallest answer first.
x= ____ and x= ____
4 andfirst find x by finding its smallest factor
The solution to the given system of equation is -7 and 7
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Given:
4x² = 196
4x²/4= 196/4
x² = 49
x=√49
x= ±7
Hence, the solution to the given system of equation is -7 and 7
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43% of a sample of 100 visitors to a national park believes that additional funds should be used to preserve endangered species. what is the margin of sampling error for a 95% confidence interval?
The margin of sampling error for a 95% confidence interval is 9.7%
How to find the Margin of Error?The formula for margin of error here is;
E = z√(p(1 - p)/N)
where;
n is sample size
z is the z score
p is the sample proportion
z-score for a 95% confidence interval from tables is 1.96.
We are given;
p = 43% = 0.43
n = 100
Thus;
E = 1.96√(0.43(1 - 0.43)/100)
E = 0.097 = 9.7%
Thus, we can conclude that the margin of sampling error for a 95% confidence interval is 9.7%
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A ride at a park has room for 8 children to ride at once.
How many rides are needed to allow 45 children a turn?
Answer:
6
Step-by-step explanation:
45/8=5.625
Since there are .625 children left, we need to add another ride to fill in what's left.
Louie is trying to find a rectangular canvas for his art project. its height must measure 18 inches and form a 48° angle with the diagonal at the top of the canvas. what is the length of the diagonal of the canvas? round your answer to the nearest inch. 12 inches 14 inches 24 inches 27 inches
The length of the diagonal of the canvas = 27 inches.
The correct option is D.
What is Pythagoras?A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem, or Pythagoras' theorem. The area of the square whose side is the hypotenuse is said to be equal to the total of the areas of the squares on the other two sides.
According to the given information:the Hight of the rectangle = 18 inches
the angle it form sinθ = H/P
H = 18
P =
cosθ = 48
cosθ = H/P
cosθ =18/P
P = 18/cosθ
= 29.60
= 27
The length of the diagonal of the canvas = 27 inches.
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Area=
What is the area?
Help me asap! Please!! Thanks so much:)
Answer:
area = 10
Step-by-step explanation:
Triangle BOC is a right triangle. You can see this because the slope of BO and OC are negative reciprocals (opposite sign and flipped over) You can calculate the slope, m.
m = (y-Y)/(x-X)
Slope of BO is 4/2,
slope of OC is -2/4.
see image.
So then you can use BO and OC as the base and height in an area calculation.
But first you have to calculate the length of each. Luckily they are the same length. You can use distance formula, but when you have a picture, you can just see to use Pythagorean theorem (distance formula comes from PythagThm anyway)
Both BO and OC have legs length 2 and 4. See image. They are both length sqrt20.
Use Area= 1/2bh to find the area. See image.
Pick the correct answer
Thanks so much :)
The linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have that:
Line I is decreasing, hence it has a negative slope.Line K is constant, hence it has a slope of zero.Line J is increasing, hence it has a positive slope.Hence the linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
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correct 0.34213 to three significant figures
Answer:
0.342
Step-by-step explanation:
round to the given amount of significant figures
The water usage at a car wash is modeled by the equation w(x) = 5x3 9x2 − 14x 9, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day. c(x) = 5x3 7x2 − 14x − 6 c(x) = 4x3 7x2 − 14x 6 c(x) = 4x3 7x2 − 14x − 6 c(x) = 5x3 7x2 − 14x 6
The function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].
What is a function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).To find the function to model the water used by the car wash on a shorter day:
Given that the amount of water used on normal days is given by the equation:
[tex]W(x) =5x^{3} +9x^{2} -14x+9[/tex] ......(1)The amount of decrease in water used is modeled by the equation:
[tex]D(x)=x^{3} +2x^{2} +15[/tex] ......(2)To get the function [tex]C(x)[/tex] that models the water used by the car wash on a shorter day you subtract equation (2) from equation (1).
[tex]5x^{3} +9x^{2} -14x+9-(x^{3} +2x^{2} +15)\\5x^{3} +9x^{2} -14x+9-x^{3} -2x^{2} -15\\4x^{3} +7x^{2} -14x-6[/tex]Therefore, the function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].
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The correct question is shown below:
The water usage at a car wash is modeled by the equation w(x) = 5x3 9x2 − 14x 9, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day.
(A) c(x) = 5x3 7x2 − 14x − 6
(B) c(x) = 4x3 7x2 − 14x 6
(C) c(x) = 4x3 7x2 − 14x − 6
(D) c(x) = 5x3 7x2 − 14x 6