By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.
How many tonnes are a given quantity of bushels?
In this question we have an application of direct proportionality model, whose form is shown below:
y = k · x (1)
Where:
x - Quantity of bushelsk - Conversion rate, in tonnes per bushel.y - Quantity of tonnesIf we know that x = 45 bu and k = 1/36.744, then the soybean quantity in tonnes is:
y = (1/36.744 t/bu) · (45 bu)
y = 1.225 t
By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.
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Find the inverse of f(x)=5x^2-3
[tex]\large\boxed{y=\pm\sqrt{\frac{x+3}{5}}}[/tex]
To find the inverse, swap the [tex]y[/tex] (or [tex]f(x)[/tex] in this case) and the [tex]x[/tex], then solve for [tex]y[/tex].
[tex]\begin{aligned}y&=5x^2-3\\x&=5y^2-3\\x+3&=5y^2-3+3\\x+3&=5y^2\\\frac{x+3}{5}&=\frac{5y^2}{5}\\\frac{x+3}{5}&=y^2\\\pm\sqrt{\frac{x+3}{5}}&=\sqrt{y^2}\\\pm\sqrt{\frac{x+3}{5}}&=y\end{aligned}[/tex]
Radio station WILM broadcast 4 minutes of news of every 25 minutes of music. Which radio station broadcasts more news each hour?
The radio station that broadcasts more news each hour based on the ratio is radio WMTH.
How to depict the ratio?From the information, radio WMTH schedules 2 minutes of news for every 20 minutes or music. Radio station WILM broadcast 4 minutes of news of every 25 minutes of music.
Therefore, the ratio of radio WMTH will be:
= 10/1 = 10:1
The ratio of Radio station WILM will be:
= 25/4 = 25:4
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Find the indicated probability.
In one town, 39% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. Round to the nearest thousandth if necessary.
Using it's concept, it is found that there is a 0.152 = 15.2% probability that they are both Democrats.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Two voters are selected, each with 39% probability of being Democrats, hence the probability of both being Democrats is given by:
p = (0.39)² = 0.152.
0.152 = 15.2% probability that they are both Democrats.
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Answer: 0.152
Step-by-step explanation:
What is the relationship between the angles?
Another answer is none of the above.
Quick algebra 1 question for 15 points!
Given the point with integral coordinates, (a, b), explain how to write the equation of the:
a) vertical line that contains (a, b):
b) horizontal line that contains (a, b):
The desired linear functions are given as follows:
a) x = a.
b) y = b.
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.A vertical line has undetermined slope, hence it is defined by x = a, containing point (a,b).
A horizontal line has slope of 0, hence it is defined by y = b, containing point (a,b).
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A rectangular shaped desk has a length of 30 inches and a width of 24 inches. A desk with a similar shape has a length of 48 inches. What is the width of this desk? ((solve fast!!))
The width of the desk will be 38.4inches
Similar shapesA rectangle is a quadrilateral that has 4 sides and angles.
If a rectangular shaped desk has a length of 30 inches and a width of 24 inches and a desk with a similar shape has a length of 48 inches, the width of the desk will be calculated using this expression;
l/w = L/W
30/24 =48/W
Cross multiply
30W = 24 * 48
W = 38.4inches
Hence the width of the desk will be 38.4inches
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Calculate measure 20
Answer:
measure of
since
Step-by-step explanation:
[tex] < 20 = 180 - (5x - 14) = 180 - 5x + 14 = 194 - 5x[/tex]
since m
[tex] < 6 = < 20[/tex]
194-5x = 5x-2
194+2=5x+5x
196=10x
x=19.6
so
[tex] < 20 = 194 - (5 \times 19.6)[/tex]
so it's= 96
[tex] \\ [/tex]
Question 3 of 6
Drag the tiles to the correct boxes to complete the pairs.
Match each equation with its solution set.
H
5 = 81
FOL
625
125
256
+243
= 32
Submit
64
Step-by-step explanation:
HOPE THIS HELPS!.....
ATTACHED IS THE SOLUTION!Answer: i hope this helps
Step-by-step explanation:
The area of triangle ABC is 84 square units. If AC= 14 units, what is the length of BD, in units ?
Answer:
70
Step-by-step explanation:
For the following exercises, graph the given functions by hand.
41. y = −| x |
Using translation concepts, the graph of the function y = -|x| is given at the end of this answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Graph y = -|x| is a reflection over the x-axis of the function y = |x|, and both functions(|x| in red, -|x| in blue) are given in the graph at the end of this answer.
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V
E
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Which of the following inequalities are correct?
Some of the numbers involved are shown on the number line below.
Choose all answers that apply:
12-18
-20
-18-12
-12 < 18
-12
←||||*|||||
-10
0
10
18
20
Answer:
I think -10 is the answer
Determine the inverse of g(x)
of g(x) = (x - 3)²
Answer:
The inverse of g(x) should be [tex]\sqrt{(x-3)}[/tex].
Step-by-step explanation:
The inverse means the opposite. The opposite of a term or expression squared will be the terms or expression square rooted.
The inverse of (x-3)² will be [tex]\sqrt{x-3}[/tex]
Hope this helps!
Please mark brainliest! Thanks!
Answer:
g(x)⁻¹ = √x + 3
Step-by-step explanation:
To find the inverse of an expression is to reverse the expression. This can be done by swapping the input and output variables. In other words, in g(x), you want to swap the places of the "x" variable the "y" variable.
Remember, g(x) = y.
y = (x - 3)² <----- Original function
x = (y - 3)² <----- Swap the variables
Now, you want to set the equation equal to "y" again. This can be done by rearranging/simplifying the expression.
x = (y - 3)² <----- Swapped variables
√x = √(y - 3)² <----- Take the square root of both sides
√x = y - 3 <----- Eliminate parentheses from previous step
√x + 3 = y <----- Add 3 to both sides
If g(x)⁻¹ represents the inverse of g(x), the new function is:
g(x)⁻¹ = √x + 3
Circle C is centered at the origin. If the radius of circle C is 5, which of the following statements is TRUE?
If the distance from the origin to a given point is greater than 5, then that point lies on circle C.
If the distance from the origin to a given point is less than 5, then that point lies outside circle C.
If the distance from the origin to a given point is 5, then that point lies on circle C.
If the distance from the origin to a given point is greater than 5, then that point lies inside circle C.
Answer:
If the distance from the origin to a given point is 5, then that point lies on circle C is true.
Step-by-step explanation:
The correct statement about given circle is "If the distance from the origin to a given point is 5, then that point lies on circle C"
What is a circle?In mathematics, the circle is a two dimensional rounded figure which has no corner edges.
Standard form = (x - a)² + (y - b)² = r²
Given that,
The center of a circle is on origin and the radius is 5 unit.
And point p lies on the circle,
So, according to definition of circle the distance between center and any point on the circle is always constant and which is known as radius.
Therefore, the distance between center end given point will be equal to 5 then it will lies on a circle.
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what would be this answer for the algebra thing
Answer:
c. 4x + 20 = 140
Step-by-step explanation:
Perimeter = 140 feet
Width = L + 10
P = 2w + 2L
P = 2(L + 10) + 2L
P = 2L + 20 + 2L
P = 4L + 20
When f = 12, the value on the left side of the equation is
Answer:
12
Step-by-step explanation:
In an equation left side = right side.
The table below shows the number of pages Ilana read during summer vacation. Is the relationship between the number of pages and the number of days a proportional relationship? Why or why not?
Days: Pages:
1////////// 85
2 //////////170
3 //////////249
4 ////////////340
5 /////////////435
Answer Choices:
1.) The relationship is proportional because the ratio of pages to days is 85.
2.) The relationship is proportional because the ratio of pages to days is 87.
3.) The relationship is not proportional because the number of pages is not constant.
4.) The relationship is not proportional because the ratio of pages to days is not constant.
No links; only answer if you know
The correct option is D, The relationship is not proportional because the ratio of pages to days is not constant.
What is a linear relationship?A linear relationship is a relationship in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c.
A linear relationship with two variables, when graphed on the cartesian plane with axes of those variables, gives a straight line.
For the given relationship to be proportional, the number of pages read should be the same every day. Therefore, the ratio of the number of pages to the number of days should be equal.
85/1 = 85
170/2 = 85
249/3 = 83
340/4 = 85
435/5 = 87
Hence, the correct option is D, The relationship is not proportional because the ratio of pages to days is not constant.
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Solve the following using the distributive property:
8x+12=2(x-3)
Answer:
x = - 3
Step-by-step explanation:
8x + 12 = 2(x - 3) ← distribute the parenthesis by 2
8x + 12 = 2x - 6 ( subtract 2x from both sides )
6x + 12 = - 6 ( subtract 12 from both sides )
6x = - 18 ( divide both sides by 6 )
x = - 3
Answer:
x = -3
Step-by-step explanation:
you first distribute 2(x-3) which gives you 2x-6 so 8x+12=2x-6.
next you move the terms to the correct side so you subtract 12 from the left side and subtract 2x from the right side then move them to the other side so you end up with 8x-2x=-6-12.
then you combine like terms so you will have 6x=-18.
then divide both sides by 6 which gives you x = -3.
8x+12=2(x-3)
8x+12 = 2x-6
8x-2x = 6-12
6x = -18
x = -3
For what values of the variable are the following expressions defined?
7a/3+a
**The equation is given below**
**Please Help, include an explanation, and a equation/answer that can be entered on learning websites to answer the question**
Answer:
The Expression will be defined if the denominator is not equal to 0 since any number divided by 0 is undefined.Therfore our main priority here is to check the denominator only because it's the only part that can make the expression undefined the expression will be defined for all real numbers (a) BUT 3+a must not equal to 0 therfore (a) can be all real numbers but must never be equal to -3Step-by-step explanation:
[tex]a \: is \: an \: element \: of \: all \: real \: numbers \: but \: not \: not \: equal \: to \: -3[/tex]HOPE THIS HELPS!John is throwing a dart at a dartboard. There are 4 rings that surround the bull's-eye ring,
which is located at the center of the dartboard.
The radius of the bulleyes region is 1 cm. The
radius of the first ring surrounding the bulleyes
is 2 cm more than that of the bulleyes and
the radius of every ring after that is 1 cm
more than that of the preceding ring. What is
the probability of John getting a dart on the
bulleyes if he cannot miss the darboard but is
randomly aiming at it?
Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): 560, 468, 685, 534, 658, 593. Find a 95% confidence interval for the mean sale price in San Luis Obispo County.
The interval for mean sale price is $582
According to statement
The given rates are 560, 468, 685, 534, 658, 593
Now,
Sample mean = X / n
Put the values in it and then
(560+ 468+ 685+ 534+ 658+ 593) / 6 = 582.1667
and use this formula S = sqrt [ X2 - n 2 / (n-1) ]
and put the values in these and
S = sqrt [ X2 - n 2 / (n-1) ] = 95.97179
So, The interval for mean sale price is $582
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The relation C= -31 t² - 80 t + 310 describes the cockroach population at
MCVI, where C is the number of cockroaches in thousands, and t is the time
in days. How many cockroaches are there at the start?
Answer:
310,000
Step-by-step explanation:
Since t represents time, the start would represent when no time has passed or in other words, when t=0, which is the y-intercept. You can plug in t as 0, but it's a bit redundant, since the y-intercept of a quadratic equation in the form: [tex]f(x)=ax^2+bx+c[/tex] will have a y-intercept at (0, c) where c is the constant, since whenever you plug in 0 as x, the ax^2 becomes 0 (since 0^2 = 0, and a * 0 = 0 since anything multiplied by 0... is 0) and the same thing goes for the bx, leaving the c alone. This means the y-intercept of the function is (0, 310) and since it's in the thousands there is 310,000 at the start
Answer:
310,000
Step-by-step explanation:
hope it helps!!!
Y=
Help me please thanks
The value of y will be equal to 4.61.
What is trigonometry?
Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.
The value of y will be calculated by using the Pythagorean theorem:-
a² + a² = (9√2)²
a = 9
Applying angle property in the triangle:-
[tex]tan26 = \dfrac{MK}{9}[/tex]
9tan26 = MK
LM = 9 - 9tan26
LM = 9 - 4.38
LM = 4.62
Therefore the value of y will be equal to 4.61.
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solve this mathematical equation 3x=5+7
Answer:
x=4
Step-by-step explanation:
3x=5+7
7+5=12
12/3=4
x=4
Hope this helps!!
Answer:
x=4
Step-by-step explanation:
add like terms
3x =5+7
3x=12
divide both sides by 3
3x=12
3 3
x=4
10 points
please help me now!!!!
Answer:
Can't do much without a direct question or embedded image.
Identify the axis of symmetry of the parabola. Kind of urgent lol
Answer: x = 4
Step-by-step explanation:
The axis of symmetry is the middle of the parabola that cuts it into two equal pieces.
Here it is fairly easy to spot, and the middle, or axis of symmetry, is x = 4.
In the triangle below, what is the cosine of 62 degrees?
Answer:
A. 8/17
Step-by-step explanation:
Cosine = adjacent over hypotenuse
Adjacent to angle 62 is 8 (The two angles are said to be adjacent angles when they share the common vertex and side).
The hypotenuse is 17 (opposite of right angle)
Suppose a batch of steel rods produced at a steel plant have a mean length of 176 millimeters, and a variance of 100. If 446 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 millimeters
The probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 mm is 0.1698 or 16.98%.
Mean length of the population (μ) = 176 mm.
Variance of the population (σ²) = 100.
Therefore, the standard deviation of the population (σ) = √100 = 10.
The sample size (n) = 446.
The mean of the sample = the mean of the population = μ = 176 mm.
The standard deviation of the sample (s) = σ/√n = 0.4735137.
We are asked to find the probability that the sample rods would differ the population mean by greater than 0.65 mm, that is,
either the length of the sample rods is less than (176 - 0.65) =175.35
or the length of the sample rods is more than (176 + 0.65) = 176.65.
This can be shown as P(X < 175.35 or X > 176.65) = 1 - P(175.35 < X < 176.65) = 1 - Normalcdf(175.35,176.65,176,0.4735137) = 1 - 0.8302 = 0.1698 or 16.98%.
Thus, the probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 mm is 0.1698 or 16.98%.
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Samual has a collection of toy cars his favorites are the 27 red ones which makes up 60% of his collection how many toy cars dose he have??
Answer:
45
Step-by-step explanation:
Use khan acedaemy
please help its timed i will give brainlyest
Answer:
20
Step-by-step explanation:
Long Division, cancel the zeroes, then 80/4 which is 20
Answer:
20
Step-by-step explanation:
8000/400= 20
Plot the points on a graph.A(0,0);B(0,2);C(2,2);D(2,0). Join AB, BC,CD and AD. What is the figure formed? Find the area of the figure.
[tex]\large \green{ \underline{ \blue{ \boxed{\bf{ \red{Given -}}}}}}[/tex]
Four points which lie at (0,0) ; (0,2) ; (2,2) ; (2,0)
[tex]\large \green{ \underline{ \blue{ \boxed{\bf{ \red{To \: Find-}}}}}}[/tex]
What is the figure formed?What is the area of the figure?
[tex]\large \green{ \underline{ \blue{ \boxed{\bf{ \red{Solution-}}}}}}[/tex]
The given points lie on graph as per the order given in the attachment.
Which shape?
As the points lie 2 units apart from their adjacent sides. It can be a square or rhombus.
The opposite pairs of sides are also parallel to each other. The adjacent sides of the figure formed are also perpendicular to each other.
Hence! the figure formed is a square.
What is the area?
[tex]\large{\sf{ \longmapsto Area_{(square)} = s \times s}}[/tex]
[tex]\large{\sf{ \longmapsto Area_{(square)} = {s}^{2} }}[/tex]
[tex]\large{\sf{ \longmapsto Area_{(square)} = {(2)}^{2} }}[/tex]
[tex]\large{\sf{ \longmapsto Area_{(square)} = 4 \: sq. \: units}}[/tex]