Answer:
y = (3/10)x + 1/10
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. First, we need to rearrange the given equation to determine the slope of the original line.
10x + 3y = 5 <----- Original equation
3y = -10x + 5 <----- Subtract 10x from both sides
y = (-10/3)x + 5 <----- Divide both sides by 3
Now, we can tell that the slope of the original line is m = -10/3. The perpendicular line should have an opposite-signed, reciprocal slope to that of the original. Therefore, the new slope is m = 3/10.
We can find the value of "b" by plugging the new slope and values from the Point (3, 1) into slope-intercept form.
m = 3/10
x = 3
y = 1
y = mx + b <----- Slope-intercept form
1 = (3/10)(3) + b <----- Insert values
1 = 9/10 + b <----- Multiply 3/10 and 3
10/10 = 9/10 + b <----- Create common denominators
1/10 = b <----- Subtract 9/10 from both sides
Now that we know the values for "m" and "b", we can construct the equation of the perpendicular line.
y = (3/10)x + 1/10
A weather balloon is 529 meters above the ground. Two weather stations, A and B, monitor the balloon’s progress.
A weather balloon is 529 meters above the ground. Weather stations A and B are on the ground to form a triangle. A horizontal line is drawn at the top of the triangle to form angle v on the left and angle w on the right. The angle formed with A is x and the angle formed with B is y. A vertical line is drawn from the weather balloon to the ground to form a right angle and split the distance between A and B into 2 parts. The distance from A to the vertical line is 229 meters, and the distance between the vertical line and point B is 347 meters.
Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true? Check all that apply.
x > y
v > x
w = y
y < v
v = w
x < w
A, C, D are correct. In this question the options that are correct are
x > yw = y y < vHow to solve for the correct statements in the questionWe have first with legs height to be =529 m and 229 m;
second with legs height =529 m and 347 m.
Then tan x = 529/229
tan y = 529/347
We can see that tanx > tany
Hence x> y
We have alternate angles in the question. This makes x=v, y=w
For D
x > y while x = v
This tells us that v>y
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Answer:
acd
Step-by-step explanation:
Which value is not part of the five-number summary for the following data set?
35, 23, 24, 30, 28, 23, 27, 33, 27, 34, 30, 30
A. 29
B. 23
C. 31.5
D. 24
Answer:
D. 24
Step-by-step explanation:
The 5-number summary of a data set includes ...
minimum1st quartilemedian (2nd quartile)3rd quartilemaximumSummary valuesWhen the data are written in increasing order, they are ...
23 23 24 27 27 28 30 30 30 33 34 35
The minimum is the first value on the list, 23.
The first quartile is the average of the two middle values in the lower half of the data set: (24+27)/2 = 25.5.
The median is the average of the two middle values: (28+30)/2 = 29.
The third quartile is the average of the two middle values in the upper half of the data set: (30+33)/2 = 31.5.
The maximum is the last value on the list: 35.
Answer choicesA. 29 is the median
B. 23 is the minimum
C. 31.5 is the 3rd quartile
D. 24 is not part of the 5-number summary
Choose the equation that satisfies the data in the table.
Answer:
Step-by-step explanation:
the answer is D
A(n) _________is an equation satisfied by every number that is a meaningful replacement for the variable
The correct answer is identity
in order to solve the following system of equations by subtraction, which of the following could you do before subtracting the equations so that one variable will be eliminated when you subtract them?
4x-2y=7
3x-3y=15
The following system of equation can be solved by first substituting the dependent variable in the other equation . The solution yields x = -1.5 and y = 6.5 .
What is the solution of the given system of equation ?The two equations are given as -
4x-2y=7
3x-3y=15
First substituting the value of x from the first equation and then putting that value in the second equation for the following system of equation.
From first equation,
⇒ 4x = 7 + 2y
∴ x = (7 + 2y)/4
Putting this value of x in second equation,
⇒ 3*(7 + 2y)/4 - 3y = 15
⇒ 3*(7 + 2y) - 12y = 60
⇒ 21 + 6y - 12y = 60
⇒ -6y = 39
∴ y = -6.5
∴ x = (7 + 2y)/4 = -1.5
Thus x = -1.5 and y = -6.5
Therefore, the following system of equation can be solved by first substituting the dependent variable in the other equation . The solution yields x = -1.5 and y = 6.5 .
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search for research that has utilized analytical tools mentioned in the readings (i.e., single-sample ztest, t tests) and identify why that analysis was appropriate for the data.
The given analytical tools:
a. The single sample z-test analysis is appropriate for the data where the sample size is large and all data points are independent. Where the standard deviation is given(known).
b. The single sample t-test analysis is appropriate for the data where the sample size is small and the population variation or standard deviation is unknown.
What is single sample z-test analysis?This is a type of hypothesis test where the sample means and the population means are compared when the population variance or the standard deviation are given(known).
z = (X - μ)/(σ/√n)
Where X - sample mean, μ - population mean, σ - population standard deviation, and n - sample size.
Here the sample size is large and all data points are independent.
What is single sample t-test analysis?This is a type of parametric hypothesis test where the sample means and the population means are compared when the population variance or the standard deviation are not given(unknown).
t = (X - μ)/(s/√n)
Where X - sample mean, μ - population mean, s - sample standard deviation, and n - sample size.
Here the sample size is small.
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Suppose you start at the origin, move along the x-axis a distance of 6 units in the positive direction, and then move downward parallel to the z-axis a distance of 4 units. What are the coordinates of your position
The coordinates of your position are (6, 0, -4).
Porfa urgente para hoy
Si triplicamos la cantidad de cada artículo, el subtotal será de 2 940 soles, el impuesto al consumo será de 529,20 soles y el total será de 3 469,20 soles.
¿Cual es el coste total y los impuestos por cambiar la cantidad de artículos comprados?
En esta pregunta tenemos un recibo con una lista de productos, cantidades, precios unitarios y precios de compra, además de un impuesto que se aplica al consumo por concepto de los productos comprados y el total, el cual refleja tanto el subtotal como el concepto por impuestos.
En cuanto a la compra de una determinada cantidad para un artículo, el coste total respectivo es igual a producto del número de artículos por el precio unitario.
El subtotal se determina mediante la suma de los costes totales asociados a cada artículo y luego se le recarga con el impuesto al consumo. Por último, el total de compra es la suma del subtotal y los pagos tributarios.
Si triplicamos el número de cada artículo comprado, tenemos los siguientes costes para cada artículo:
Chompas de dralom
12 / 4 × 280 = 840
Chompas de Orlon
6 / 2 × 100
300
Chompas de lana de alpaca
15 / 5 × 600
1 800
El subtotal es 2 940 soles y el impuesto al consumo es 18 / 100 × 2 940 = 529,20 soles. Por tanto, el total es 3 469,20 soles.
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can someone solve this for me ?
Answer: 113.1 ft^3
Step-by-step explanation:
We know the radius is 3 so substitute it in the formula like this...
V = 4/3 π (3)^3
Solve for (3)^3 which is 27.
Next multiply 4/3 by π. Which equals 4.1887....
Then multiply that answer by 27.
And your answer is 113.1 ft^3.
Answer:
[tex]V=108ft^{3}[/tex]
Step-by-step explanation:
[tex]V=\frac{4}{3}(3)(3)^{3}[/tex]
[tex]V=\frac{4}{3}(3)(27)[/tex]
[tex]V=\frac{4}{3} (81)=\frac{324}{3}[/tex]
[tex]V=108[/tex]
Hope this helps
The angle measurements in the diagram are represented by the following expressions.
The angle measurements of angle B as represented in the diagram shown is 150°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the diagram:
∠A = ∠B (alternate interior angles)
Hence:
8x - 10 = 3x + 90
x = 20
∠B = 3(20) + 90 = 150°
The angle measurements of angle B as represented in the diagram shown is 150°
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Which is the correct equation of the line for the following graph?
Answer:
(c) y = -3x +6
Step-by-step explanation:
The equation can be written in slope-intercept form when we know the slope and the y-intercept.
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b . . . . . . where m is the slope and b is the y-intercept
Y-interceptThe y-intercept is the y-value where the line crosses the y-axis. It is 6. This eliminates choices A and D, leaving choices ...
y = 3x +6 . . . . . choice By = -3x +6 . . . . .choice CSlopeThe line goes down to the right. This is a negative slope, eliminating choice B.
The equation of the line is y = -3x +6.
__
Additional comment
The line intersects the x-axis at x=2. This means the "rise" of the line is -6 units for a "run" of 2 units. The numerical value of the slope is ...
m = rise/run = -6/2 = -3
Now, we know the parameters of the equation are m=-3, b=6, and the equation of the line is
y =-3x +6
The Drury Lane Theater has 10 seats in the first row and 38 rows in all. Each successive row contains one additional seat. How many seats are in the theater?
Answer:
Step-by-step explanation:
Given : 10 seat in first row, and the seat will increase 1 by 1 as we go above.... (as we go to the next row) - total rows - 38
Solve ; 38 rows, 10 seat in first row, 1 seat increases each row....
Extra seats - 37,
So,
37 x 10 = 370
TOTAL SEATS = 370
Answer:
1083 seats
Step-by-step explanation:
The number of seats is an arithmetic series with first term 10 and common difference 1. We want to find the sum of 38 terms of the series.
SetupThe sum of n terms of an arithmetic series with first term a1 and common difference d is given by the formula ...
Sn = (2a1 +d(n -1))(n/2)
The sum of the series of interest is ...
S38 = (2(10) +1(38 -1))(38/2)
Total seatsThe total number of seats in the theater can be found by evaluating the expression for S38:
S38 = (20 +37)(19) = 57×19 = 1083
There are 1083 seats in the theater.
Which triangles are similar to ABC? Explain.
Answer: △JKL & △ MNP
Step-by-step explanation:
△JKL is similar because:
5 x 1.6 = 8
2.5 x 1.6 = 4
3.75 x 1.6 = 6
△MNP is also similar because:
4 x 2 = 8
2 x 2 = 4
3 x 2 = 6
Select the correct answer. A linear function on a coordinate plane passes through (minus 5, minus 3), (0, minus 4), and (5, minus 5) Which equation describes the line graphed above? A. y = − 4 x − 5 B. y = − 1 5 x − 4 C. y = − 5 x − 4 D. y = − 4 x − 1 5
The linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4
Linear functionLinear function are functions that has a leading degree of 1. The equation of a linear function is expressed as y = mx + b
where
m is the slope
b is the intercept
Given the coordinates (-5, -3) and (0, -4)
Slope = -4+3/0+5
Slope = -1/5
The y-intercept of the line will be -4
Determine the equation
y = -1/5x-4
Hence the linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4
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4-5
44
Simplify.
x 43 x 166 4² = 4
응
4-5
44
1
→44x45
=
1
4[?]
Hint: When exponents with the same the
bases are multiplied, add the exponents.
Enter the value that goes in the green box.
Enter
Comparing with the original expression, the value that will go into the green box is 5
Exponents and indicesGiven the indices expression below;
[tex]\frac{4^{-5}}{4^4}[/tex]
Since 4^-5 is equivalent to 1/4^5, hence the given expression will be equivalent to;
[tex]\frac{1}{4^5\times4^4}[/tex]
Comparing with the original expression, the value that will go into the green box is 5
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Instructions: Find the missing side. Round your answer to the nearest tenth.
Using the sine ratio, the length of the missing side is: 11.8.
How to Find Missing Side Using the Sine Ratio?The sine ratio is, sin ∅ = opposite/hypotenuse.
Given the following:
∅ = 24°
Opposite = x
Hypotenuse = 29
sin 24 = x/29
x = (sin 24)(29)
x = 11.8
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Which of the following is equal to the fraction below?
(4/5)^6
A. 6(4/5)
B. 4^6/5
C. 4^6/5^6
D. 24/30
Answer:
C. 4^6 / 5^6
Step-by-step explanation:
(4/5)^6
= 4^6 / 5^6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]
[tex]\mathbf{= \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}\times \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}}[/tex]
[tex]\mathbf{= \dfrac{4\times4\times4\times4\times4\times4}{5\times5\times5\times5\times5\times5}}[/tex]
[tex]\mathbf{= \dfrac{16\times16\times16}{25\times25\times25}}[/tex]
[tex]\mathbf{= \dfrac{256 \times 16}{625\times25}}[/tex]
[tex]\mathbf{= \dfrac{4,096}{15,625}}[/tex]
[tex]\mathbf{\approx \dfrac{4^6}{5^6}}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{Option\ C. \dfrac{4^6}{5^6}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
How many different 2 digit numbers are there with the following property: the tenth digit is greater that the units digit?
Answer:
45 numbers
Step-by-step explanation:
The 10-digit numbers are from 10-99. We can manually analyze each tenth digit and see if we can find a pattern from it. First, 10-19 ~ 10 is the only number in the sequence where the tenth digit is greater than the unit digit (because 1 > 0). In every other case, 1 is less than or equal to the unit digit.
Next, 20-29 ~ 20 and 21 are the two numbers where the tenth digit is greater than the unit digit
30-39 ~ 30, 31, 32 follow the property
40-49 ~ 40, 41, 42, 43 follow the property
We can keep going, but we can see that there is a pattern. The number of numbers that correspond with the property for each set of 10 numbers is equal to the value of the tenth digit. We see that for the 40s, there are 4 numbers. For the 20s, on the other hand, there are 2 numbers. This pattern carries through:
50-59 ~ 5 numbers, 60-69 ~ 6 numbers, 70-79 ~ 7 numbers, 80-89 ~ 8 numbers, 90-99 ~ 9 numbers
We need to find how many 2-digit numbers total follow the property. We can just add our results together to get our answer:
1+2+3+4+5+6+7+8+9=45
Given the functions:
f(x) = 6x + 11 and g(x) = x + 6,
which of the following represents f[g(x)] correctly?
A. F[g(x)] = 6x + 47
B. F[g(x)] = 6x + 17
C. F[g(x)] = 6x^2 +47
D. F[g(x)] = 6x^2 + 17
Answer:
f[g(x)] = 6x + 47
Step-by-step explanation:
The expression f[g(x)] represents a composite function. You need to plug the function g(x) into the "x" value of the f(x) function. Then, you can simplify.
f(x) = 6x + 11 g(x) = x + 6
f[g(x)] <----- Composition expression
f[g(x)] = 6(x + 6) + 11 <----- Plug g(x) into x
f[g(x)] = 6x + 36 + 11 <----- Multiply terms in parentheses by 6
f[g(x)] = 6x + 47 <----- Add 36 and 11
See picture to answer!
Using the law of cosines, it is found that the length of side AB is of AB = 13.
What is the law of cosines?The law of cosines states that we can find the angle C of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
in which:
c is the length of the side opposite to angle C.a and b are the lengths of the other sides.For this problem, the parameters are:
C = 120, a = 8, b = 7.
Hence:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
[tex]c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}[/tex]
[tex]c^2 = 169[/tex]
[tex]c = \sqrt{169}[/tex]
c = 13.
Hence AB = 13.
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Twenty-three teenagers attended a church camp. This was eleven less than twice the number that attended last year. How many attended last year?
Answer: 17 campers attended last year
Step-by-step explanation:
Let x be the number that attended last year.
The number of campers this year (23) is equal to 2 times the number of last year (x), minus 11.
23 = 2x – 11
23 + 11 = 2x
34 = 2x
34/2 = x
17 = x
Cylinder A has a radius of 7 inches and a height of 5 inches. Cylinder B has a volume of 490π. What is the percentage change in volume from cylinder A to cylinder B?
50% decrease
75% increase
150% decrease
100% increase
The percentage change in volume from cylinder A to cylinder B; D: 100%
How to find the percentage change in Volume?
Formula for Volume of a Cylinder is;
V = πr²h
Thus, volume of Cylinder A is;
V_a = π * 7² * 5
V_a = 245π
Thus, percentage change in volume is;
[245π/(490π - 490π)] * 100%
Percentage change in volume = 100%
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Answer:
100% increase
Step-by-step explanation:
I got it right on the test.
find the diagonal of a rectangle solid whose dimensions are 3,4,5 (please include explanation)
The diagonal of the rectangle solid is [tex]\sqrt{50[/tex]
How to determine the diagonal of a rectangle solid?The dimensions are given as:
3,4,5
The diagonal is calculated as:
[tex]d = \sqrt{3^2 + 4^2 + 5^2[/tex]
This gives
[tex]d = \sqrt{50[/tex]
Hence, the diagonal of the rectangle solid is [tex]\sqrt{50[/tex]
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A tub contains red, green, blue and white counters. 5% of the counters are red, with an equal number of blue and white counters. The ratio of red to green counters is 3: 7. There is 20 more green than red counters. What is the probability of picking a red or blue counter?
The probability of picking a red counter is therefore; 8/25.
What is the probability of picking a red counter?Since the ratio of red to green is 2 :3 and there are 24 green counters, it follows that the number of red counters is;
x = (2/3)× 24 = 16 red.
The total of red and green is; 16 +24 = 40 which constitutes 80% of the total counters.
The total number of counters is therefore; 40/0.8 = 50 counters.
The probability of picking a red counter is therefore; 16/50 = 8/25.
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.- An employee at the local ice cream parlor asks three customers if they like chocolate ice cream. Identify the sample and the population. (circle the letter that is your answer
Sample is the 3 selected customers; And population is all customers
According to the statement
we have given that a shopkeeper asks 3 customers to taste the chocolate icecream.
And we have to identify the sample and population.
So, A definition of sample is that a
A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample.
And a Population is defines as the is a discrete group of people, animals or things that can be identified by at least one common characteristic for the purposes of data collection and analysis.
So, according to definition Sample is the 3 selected customers; And population is all customers.
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Line A is perpendicular to Line B.
If the slope of Line A is
-1/7
what is the slope of Line B?
[?]
Answer:
7
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other. For example, if line A has a slope of 2, then line B, perpendicular to line A, will have a slope of -0.5.
Find the volume of the prism. Round to the nearest tenth if necessary.
Answer:
27.2
Step-by-step explanation:
V = (1/2)(2.6)(5.1)(4.1), which is 27.2 to the nearest tenth
The angle formed by the line of sight and the horizontal line can best be described as an
the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B
What is angle of elevation?Angle of elevation can be defined as the angle formed between a horizontal line and the line of sight up to an object with the image of the object located above the horizontal line.
It is the height greater than the height of the observer.
The opposite of the angle of elevation is the angle of depression which is formed with an observer
Words associated with the angle of elevation are;
angles horizontal linesline of sightThe angle of elevation is the angle between the line of sight and the horizontal line.
Hence, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B
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Write an equation of the line point(2,-1) and parallel passing through y=3x-5 write in slope-intercept form
Answer:
y = 3x - 7
Step-by-step explanation:
Since the lines are parallel, the slopes will be the same. In this case 3. Now we have to find the y-intercept. We will use the slope (3), the x (2) and y (-1) to help us do this. We get the x and the y from the ordered pair given(2,-1).
y = mx + b
-1 = 3(2) + b Plug in what you know
-1 = 6 + b Subtract 6 from both sides
-7 = b
Now we can write the equation
y = 3x -7
Last year, during an investigation of the time spent reading e-mails on a daily basis, researchers found that on Monday the average time was 50 minutes. Office workers claim that with the increased spam and junk mail, this time has now increased. To conduct a test, a sample of 25 employees is selected with the following results: sample mean
The sample mean value is 0.26.
According to the statement we have given that the
Monday the average time was 50 minutes and we have to find the sample mean.
So, the values become
H(not):μ≤50
H(a):μ>50
Right Tail
The significance level, of the given number of employees then
α=0.05
And The value of sample mean, is
Z=x - u/i*(n)^1/2
then the value becomes
Z = 5.6 - 5/1.2*(25)^1/2.
then after calculating
Z= 1.6/1.2*5
Z= 0.26 And
Here The value of sample mean is 0.26.
So, The sample mean value is 0.26.
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