Use proportions to solve the following problem.
A 30-pound bag of topsoil will cover a surface area of 9 ft^2.
a) How many pounds of topsoil are needed to cover a surface area of 270 ft^2?
b) How many bags of topsoil must be purchased to cover a surface area of 270 ft^2?
It would take 16 days for the number of magical coins to exceed 50,000.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that:
30 pound = 1 bag
30 pound = 9 ft²
a) For a surface area of 270 ft²:
Number of pounds = 270 ft² * 30 pound per 9 ft² = 900 pounds
b) For a surface area of 270 ft²:
Number of bags = 900 pounds * 1 bag per 30 pound = 30 bags
900 pounds is needed to cover a surface area of 270 ft² and 30 bags would be needed to be purchased
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The longer diagonal is 4 more than the shorter diagonal of a kite. The area is 5 times the shorter diagonal. If the shorter side is 6m find the longer diagonal and the area.
If the longer diagonal is 4 more than the shorter diagonal of a kite. The area is 5 times the shorter diagonal. If the shorter side is 6m. The longer diagonal is 10m and the area is 30m².
Longer diagonalThe longer diagonal is calculated as:
Longer diagonal=6+4
Longer diagonal=10m
The area is calculated as:
Area of kite=5m×6m
Area of kite=30m²
Therefore If the longer diagonal is 4 more than the shorter diagonal of a kite. The area is 5 times the shorter diagonal. If the shorter side is 6m. The longer diagonal is 10m and the area is 30m².
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Look at the figure. If <1 = <2 , describe the relationship between lines a and b.
Answer:
Without seeing the picture. I think that the answer might be parallel lines. The two angles pictures might be corresponding angles which means that the lines would be parallel.
Step-by-step explanation:
What's 9+10
Please don't be stoopid
Answer: 19
Step-by-step explanation: 10
+ 9
19
Answer:
9+10=19
Step-by-step explanation:
Remember treat others as you want to be treated. That being said we are not stoopid.
(6,1)+(8,9)
What’s the slope
The slope of the line with the given coordinates (6,1) and (8,9) is 4.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 6,1 )
x₁ = 6y₁ = 1Point 2( 8,9 )
x₂ = 8y₂ = 9Plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 9 - 1 )/( 8 - 6 )
Slope m = ( 8 )/( 2 )
Slope m = 8/2
Slope m = 4
Therefore, the slope of the line with the given coordinates (6,1) and (8,9) is 4.
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Two concentric circles are of radii 5 cm and 3 cm. Determine the length of the chord of the larger circle which touches the smaller circle.
The length of the chord of the larger circle which touches the smaller circle.
The chord of the larger circle which is touches the smaller circle having the length of 8cm.
Given that
Two concentric circles are of radii 5 cm and 3 cm.To find
The length of the chord of the larger circle which touches the smaller circle.So, according to the question
we have,
The radius of larger circle = 5cm.The radius of smaller circle = 3cm.From attached figure of that problem,
BC = 5cm
CD = 3cm
AB = ........? (have to find) or from geometry
AB = 2 BD ---------(1)
Now, we have to find BD,
So, from right angle triangle BDC.
BD² = BC²-CD² ( by Pythagoras theorem )
BD = [tex]\sqrt{(BC)^2-(CD)^2}[/tex]
Putting the given values,
BD = [tex]\sqrt{(5)^2-(3)^2}[/tex]
BD = [tex]\sqrt{25-9}[/tex]
BD = [tex]\sqrt{16}[/tex]
BD = 4 (∵[tex]\sqrt{16} = 4[/tex])
Now, putting the value of BD in equation (1)
AB = 2 BD ---------(1)
= 2×4
AB = 8
Answer:
The length of the chord of the larger circle which touches the smaller circle is 8cm.To learn more about Pythagoras theorem, please click on the link:
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What is the inverse of this function?
f(x)=√x
+ 3, x ≥ − 3
f-¹(x) =
x²-
-
for x ≤
Answer:
4, 3, 0
Step-by-step explanation:
Let f(y)=x.
[tex]x=-\frac{1}{2}\sqrt{y+3} \\ \\ -2x=\sqrt{y+3} \\ \\ 4x^2=y+3 \\ \\ y=f^{-1}(x)=\boxed{4}x^2-\boxed{3}[/tex]
The domain of the inverse is the same as the range of the original function. For the original function, we know that it is decreasing, so the range is
[tex]y\leq -\frac{1}{2}\sqrt{-3+3}=0[/tex]
and hence the domain of our inverse is
[tex]x \leq 0[/tex]
What are the positive and negative square roots of 256?
Answer:
16 and -16
Hope this helps! :)
Determine ratio of A to B. Round as indicated.
A = 24.7% is the divorce rate in City A
B = 28.7% is the divorce rate in City B
(Round to the nearest hundredth when necessary.)
Select one:
O a. 0.09
O b. 8.61
OC. 0.86
O d. 1.16
Ratio of A to B is option c 0.86
Given,
Divorce rate in City A = 24.7%
Divorce rate in City B = 28.7%
We have to find the ratio of A to B
First we have to change the percentage to fraction form.
That is,
Divorce rate in City A = 24.7% = 24.7/100
Divorce rate in City B = 28.7% = 28.7/100
Now, ratio of A to B
(24.7/100) : (28.7/100)
Equate this into fraction form.
That is, A : B = A/B
Therefore,
(24.7/100) : (28.7/100)
= (24.7/100) / (28.7/100)
= 24.7 × 100 / 28.7 × 100
= 2470 / 2870
= 0.86 approximately.
That is the ratio of A to B is 0.86.
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{ x − 10 ≤ x ≤ 15 }
it also needs to be graphed please help its due in 20 minutes
The graph is attached below:
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Given:
x − 10 ≤ x ≤ 15
as, the given inequality we have to break the inequality is
x − 10 ≤ x and x ≤ 15
The graph to the inequality is attached below.
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HELP FAST AGAIN PLEASE I BEG U
Answer:
[tex]\frac{72}9[/tex]
Step-by-step explanation:
We're asked to find out how many pages we will need to use if each paper can hold up to 9 cards. To find this, we would have to divide our total amount of cards by 9.
help me, i need to learn the Pythagorean theorem. ill pick brainliest!
Answer: The definition/meaning of it is a theorem attributed to Pythagoras that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Step-by-step explanation: If you need the equation solved, I can try just type under this.
A producer of printed circuit boards (PCBs) wishes to estimate the scoring depth of their circuits. To this end, they have collected 45 samples of measured depths. The mean and standard deviations of these samples is 0.165 mm and 0.022 mm respectively.
1. Create a plot showing the dependence of the size of the confidence interval (ρ) on the confidence level (γ) ranging from 0 to 1. Keep the sample size fixed at 45
2. Create a plot showing the dependence of the size of the confidence interval on the
sample size ranging from 1 to 100. Keep the confidence level fixed at 0.95. (Here you
can assume normality even where N <30)
3. Create a plot showing the pdf of the sample mean and with the area computed above shaded in. Hint: plt.fill between.
The mean and the standard deviations of the samples is 0.165 mm and 0.022 mm.
n = 45
[tex]\overline{X} = 0.165{~}mm[/tex]
s = 0.022 mm
Now, 95% of the confidence interval.
[tex]CI=\overline x {~}\pm t_{\frac{\alpha}{2}, n-1 }\frac{s}{\sqrt{n} }[/tex]
The critical values are:
α = 1 - 0.95 = 0.05
n - 1 = 45 - 1 = 44
[tex]t_{\frac{\alpha}{2} , n-1=t_{0.025,44}=2.0154[/tex]
So, 95% of CI = 0.165 ± 2.0154 × ( 0.022 ÷ √45 )
95% CI = ( 0.158, 0.172 )
1. The plot for the dependence of the size of the confidence interval on the confidence value ranging from 0 to 1.
2. A plot showing the dependence of the size of the confidence interval on the sample size ranging from 1 to 100.
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1. The data set shows the fuel efficiencies, in miles per gallon, of the vehicles featured in a car-buying guide.
27 30 41 27 20 22 36 37 44 45 29 29
(a) What is the five-number summary of the data set? Show your work.
(b) What is the range of the data set? Show your work.
(c) What is the interquartile range (IQR) of the data set? Show your work
1. The five-number summary of the data set is: 20, 27, 29.5, 39, 45.
b. Range = 25
c. Interquartile range (IQR) = 12
How to Find the Five-Number Summary?Given the data set for fuel efficiencies for vehicles featured in a car-buying guide as: 27, 30, 41, 27, 20, 22, 36, 37, 44, 45, 29, 29, we have five-number summary solved as shown below.
a. Minimum: 20 (smallest data point.)
First Quartile: 27 (center of the first part/half of the data set when ordered)
Median: 29.5 (center of the data set when ordered)
Third Quartile: 39 (center of the 2nd half of the data set when ordered)
Maximum: 45 (largest data point.)
Thus, the five-number summary of the data set is: 20, 27, 29.5, 39, 45.
b. Range = max - min
Range = 45 - 20
Range = 25
c. Interquartile range (IQR) = Third Quartile - First Quartile
Interquartile range (IQR) = 39 - 27
Interquartile range (IQR) = 12
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A cash register must have at least $27 in change consisting of d dimes and q quarters.
(a) Write a linear inequality that represents the different numbers of dimes and quarters that can satisfy the requirement.
(b) Graph the inequality.
The inequality 106q + 5d ≥ $27 represents the different number of dimes and quarters in the cash register.
When two numbers or other mathematical expressions are compared in an unequal way, this is known as an inequality. The number line, it is most frequently used to compare the sizes of two numbers.
The least amount a cash register have is $27.
The cash register has d dimes and q quarters.
We know a dime is worth 10 cents and a quarter is worth 25 cents.
Let x be the number of quarters and y be the number of dimes
So, the inequality that shows that the cash register has at least 27 dollars is:
xq + yd ≥ $27
106q + 5d ≥ $27
The graph of the inequality,
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Help please it’s 8th grade math
Answer:
The answer is D
Step-by-step explanation:
[tex]9^{16}[/tex] is the exponential form of the number which the expression shows. The expression is a fraction though, so it is [tex]\frac{1}{9^{16} }[/tex]
I have 3 questions the first one is What is an algebraic expression for “10 more than the product of 9 and a number y”? And the second one is Evaluate the following expression: (10 - 3y) - 1 , if y = 3. last one is Find the Quotient: 55 -211
From these problems, we have that:
The algebraic expression is: 10 + 9y.When y = 3, the expression has a value of 0.The quotient between two numbers is the division between them(it is not clear which numbers are in the quotient).What is the equivalent algebraic expression?The product of 9 and y is given by 9y.10 more than the expression is 10 added to the expression, hence 10 + 9y.Hence the algebraic expression is: 10 + 9y.
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
For this problem, the expression is:
(10 - 3y) - 1.
When y = 3:
(10 - 3 x 3) - 1 = 1 - 1 = 0.
What is the quotient between two amounts?The quotient between two amounts a and b is given by a divided by b. For example, the quotient between 10 and 2 is:
10/2 = 5.
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AB : BC = 3:2
Point B ∈ AC . Find the lengths of segments AB and BC if AC = 20 cm
The length of the segments AB and BC if AC = 20 then:
AB = 12cm
BC = 8cm
What is the simplest definition of a line segment?In geometry, a line segment is defined as two different points on a line. In contrast, a line segment is a piece of a line that connects two points. A line has no endpoints and runs indefinitely in both directions, whereas a line segment has two fixed as well as definite endpoints.
Is there a distinction between a line segment as well as a ray?Yes. A ray is not the same as a line segment. A ray has one endpoint, but a line segment has two. The ray's one end extends indefinitely, whereas the endpoints of a line segment are always specified and fixed.
According to the given data:We know that:
a:b=c:d as a/b=c/d
AB:BC = 3:2
is AB/BC=3/2
AB=3/2*BC
AC=20=AB+BC
So,
20=3/2*BC+BC
13/2BC=20
BC=8cm
AB=20-8=12cm
The length of the segments AB and BC if AC = 20 then:
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K
A rectangular garden bed measures 16 feet by 12 feet. A water faucet is located at one corner of the garden bed. A
hose will be connected to the water faucet. The hose must be long enough to reach the opposite corner of the garden
bed when stretched straight. Find the required length of hose.
The required length of the hose is in.
(Type an exact answer using radicals as needed.)
The required length of the hose is 20 feet.
Given,
a = 16 feet
b = 12 feet
c = ? (the required length of hose)
we can use the formula
c = √(a²+b²)
⇒ c = √(16²+12²) feet
= 20 feet.
The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle. Some examples of rectangular shapes are the flat surfaces of laptop monitors, blackboards, painting canvas, etc. You can use the formula of the area of a rectangle to find the space occupied by these objects. For example, let us consider a rectangle of length 4 inches and width 3 inches.
The area occupied by a rectangle within its boundary is called the area of the rectangle.
Area is measured in square units such as square inches, square feet or square meters. To find the area of a rectangle, multiply the length by the width. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply.
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Multiply the number by 4. Add 6 to the product. Divide this sum by 2. Subtract 3 from the quotient.
Answer:
-1.5
Step-by-step explanation:
Let x be the number
(4x+6)÷2 =-3
2(2x+6)÷2=3
2x+6=3
2x=3-6
2x=-3
x=-3÷2
x=--1.5
One week, the music store sold 2 trumpets, 3 clarinets, and 5 violins for $1,240. The next
week, they sold 3 trumpets, 1 clarinet, and 4 violins for $1,027. The following week, they sold
5 7 trumpets, 7 clarinets, and 2 violins for $2,091. Find the cost of a trumpet, clarinet, and
violin
what’s the answer????
Domain and range of the graphs are as follows:
1. D: [-4,4] and R: [1,3]
2. D: [-3,5] and R: [0,6]
3. D: [-2 ∝] and R: [-2,4]
Given:
In the first graph:
The graph's domain is its left-to-right travel distance.
Start by examining the leftmost point on this graph.
At the farthest left point, the x-value is at x=-4 Trace the graph once more until you reach the location that is the furthest to the right.
At this point, the x-value is 4. The graph is continuous from -4 to 4 since there are no breaks running from left to right.
Domain is as [-4,4] also written as -4 ≤x≤4
The graph's range is its vertical range from down to up.
Look at the graph's lowest or most distant point. At this point, the y-value is equal to 1. Now examine the graph's top or how high it rises.
This is when x=-4 or x=4, but since we're determining the range right now, we need to take a look at the point's y-value, which is at y=3. Since the graph is continuous from top to bottom, there are no breaks in it.
Range : [1,3] also written as 1 ≤ y ≤ 3
similarly we find the rest of the domain and range of the graphs.
Hence we don't get any line of symmetry in the graph.
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In the quation below all the asteriks stand for the same number.
What Is the number?
Please answer this correctly my grade depends on it, also i have other questions like this so feel free to answer them.
The domain and range of of the graph in interval notation are [-4,3) and (-5,5).
Domain and range of a graph.The domain are the independent variables for which an expression or equation exists while the range are the dependent variables for which an expression or equation exists.
The given graph is a piecewise function since there are several lines that make up the graph.
Te domain are values of the function lying along the x-axis of the line graph while the range are values of the function along the y-axis of the line graph.
Based on the explanation, we can conclude that the domain of the graph in interval notation will be [-4,3) and the range of the graph will be (-5,5).
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The graph of the quadratic function x2−4x−5=0 crosses the x-axis at x=−1 and x=5. What are the zeros of this function?
Answer:
x = 5, -1
find the roots and the x
HELPPPPP pictures will be shown
The perimeter of quadrilateral B is 12 units.
The sides of the quadrilateral are given as:
6, 9, 9, and 12.
Shortest side = 6
Shortest side of the scaled quadrilateral = 2
So, it is reduced by a factor of 3.
So, the sides of the scaled quadrilateral will be given by:
2, 3, 3 and 4.
Perimeter will be adding all the sides.
So, we get that:
The perimeter = (2 + 3 + 3 + 4)
P = 12 units
Hence, the perimeter of quadrilateral B is 12 units.
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help me with this
pls help
i love you <3
Answer:
Step by step evaluation
Formula
T = 4B + 10C
Please help!!
Create a polynomial with 3 terms, written in standard form.
how do you know it’s in standard form?
if you can explain it as well that would be great :)
In mathematics, a polynomial is a mathematical expression that is the sum of a number of terms that contain the same variable raised to different powers. These come up all the time in the study of mathematics, so it is important to be familiar with them and the different forms we can write them in.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To write a polynomial in standard form, we make sure that any like terms are combined, and then we arrange the terms so that the exponents of each term go in descending order.
For example, consider the following polynomial:
8x - x⁵ + 2x + 3x² - 7x⁴ + 3To write this polynomial in standard form, we first look for any like terms that need to be combined, where like terms are terms that have the same variable raised to the same power. We see that 8x and 2x are like terms, so we add these together to turn our polynomial into the following:
10x - x⁵+ 3x² - 7x⁴ + 3Now, we just rearrange the polynomial so that the term with the highest degree goes first, the term with the second highest degree goes second, and so on until the polynomial is arranged so that the exponents go in descending order from highest to lowest.
-x⁵ - 7x⁴+ 3x² + 10x + 3This gives us our polynomial in standard form.
A polynomial with 3 terms : x² + 3x³ + 27 - x
___________________________________________
To start a mobile dog-grooming service, a woman borrowed $2000. If the loan was for 2 years and the amount of interest was $168, what simple interest rate was she charged?
Step-by-step explanation:
and his did u use adding if it's adding or
anything I can help!
Please answer as soon as possible correctly
Answer: The answer will be in the explanation
Step-by-step explanation:
In step 2 she made the mistake of not dividing the 12/2 and replacing 5 with -13. In step 4 she made the mistake of removing the coefficient. The correct way to do it is this way. Look below on how to do it correctly!
(\sqrt[3]{125}-12/2)(4-6)^2
(5-12/2)(4-6)
(5-6)(4-6)^2
-1(4-6)^2
-1+4
3
Hope this helps owo