The width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200.
A rectangular garden has a length of 60 feet (ft)
a width of w ft
and a perimeter of 200 ft.
The formula of perimeter of a rectangle is 2(lenght + width)
The equation that represents the garden's perimeter is 2(60 + w) = 200
2(60 + w) = 200
120 + 2w = 200
2w = 200 - 120
2w = 80
w = 40
Therefore, width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200
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Find the missing side or angle. Round to the nearest tenth. a=4 b=5 c=7
Using the law of cosines, the missing angles are:
A = 34.1°, B = 44.4°, C = 101.5°
What is the Law of Cosines?The law of cosines is used to solve a triangle when given the lengths of the three sides of a triangle, and it is expressed by the formula:
c² = a² + b² - 2ab × Cos C.
Given the following:
a = 4 b = 5 c = 7Find C by substituting the values into the law of cosines formula:
7² = 4² + 5² - 2 × 4 × 5 × Cos C
49 = 16 + 25 - 40 × Cos C
49 = 41 - 40Cos C
49 - 41 = -40Cos C
8/-40 = Cos C
-0.2 = Cos C
C = Cos^(-1)(-0.2)
C = 101.5°
Find B using the Law of Sines:
sin B/b = sin C/c
Substitute
sin B/5 = sin 101.5/7
(sin B)(7) = (sin 101.5)(5)
sin B = (sin 101.5)(5)/7
sin B = 0.69995
B = Sin^(-1)(0.69995)
B = 44.4°
Find the measure of angle A using the triangle sum theorem:
A = 180 - 101.5 - 44.4
A = 34.1°
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Let S be any sample space, and E, F and G be any three events. Describe the event that E and G occur, but not the event F.
In the sample space, the annotation for the event where both E and G but not F occurs is given as:( E ∩ G ) ∩ Fc (Option B).
What are events in Math?An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.
Colloquially, the sample space for a given set of events is the collection of all potential values for the events. Technically, a sigma-algebra is formed by the set of probable occurrences for a given random variate, and sample space is defined as the biggest set in the sigma algebra.
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Full Question:
Let S be any sample space, and E, F, and G be any three events. Describe the event that E and G occur, but not event F.
a) ( Ec ∪ G ) ∩ Fc
b) ( E ∩ G ) ∩ Fc
c) ( E ∪ G ) ∪ Fc
d) ( Ec ∪ Gc ) ∩ F
e) ( E ∩ G ) ∩ F
f) None of the above.
The annotation for the event in the sample space when E and G both occur but F does not is given as:( E ∩ G ) ∩ Fc which is the correct answer would be an option (B).
What are events in probability?In probability theory, an event is a predetermined group of outcomes from a random experiment. Another definition of an event is any subset of a sample space, which is the collection of all possible results of a random experiment.
We are allowed to use here for the necessary notation, though one way to indicate this is the complement of E U F U G. This would be the area in the sample space S that lies outside E, F, and G in a Venn diagram.
Thus, the annotation for the event in the sample space when E and G both occur but F does not is given as:( E ∩ G ) ∩ Fc
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The question seems to be incomplete the correct question would be
Let S be any sample space, and E, F, and G be any three events. Describe the event that E and G occur, but not event F.
a) ( Ec ∪ G ) ∩ Fc
b) ( E ∩ G ) ∩ Fc
c) ( E ∪ G ) ∪ Fc
d) ( Ec ∪ Gc ) ∩ F
e) ( E ∩ G ) ∩ F
f) None of the above.
Please help me asapppppp
At 10:00 a.m., Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han runs at a pace of 12 minutes per mile. Tyler runs at a pace of 15 minutes per mile.
Do Han and Tyler meet on the path within 1 hour?
If Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han and Tyler will not meet on the path within 1 hour
Calculations to show if Han and Tyler meet on the path within 1 hourThe following information is gotten from the question
Han and Tyler both started running toward each other from opposite ends of a 10-mile path
Han runs at a pace of 12 minutes per mile
Tyler runs at a pace of 15 minutes per mile
Distance covered by Han in 1 hour
12 minutes = 1 mile
60 minutes = ? miles
cross multiplying gives
? = 60 / 12
? = 5 miles
Distance covered by Tyler in 1 hour
15 minutes = 1 mile
60 minutes = ? miles
cross multiplying gives
? = 60 / 15
? = 4 miles
This means that Han covers 5 miles in and Tyler covers 4 miles, in a 10 mile distance.
In one hour the distance covered
= 5 miles + 4 miles
= 9 miles
9 miles is less than 10 miles hence they will not meet in the path within one hour
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14. A can of vegetables has a paper label that covers the lateral surface are can, 4 in. 2.6 in. What is the lateral surface area of the can onded to the
We will have that the lateral area will be the following:
*First, we can see that if we were to cut a straight vertical line and unfold the label, we would get a rectangle, thus the surface area of the label will be given by:
[tex]S_A=h\cdot C[/tex]Here h is the height of the label and C is the circumference of the base, that is:
[tex]S_A=h\cdot2\pi r[/tex]Now, we determine the radius of the base, that is:
[tex]r=\frac{2.6}{2}\Rightarrow r=1.3[/tex]Now, we replace the values and solve for the surface area:
[tex]\Rightarrow S_A=(4)\cdot(2)\pi(1.3)\Rightarrow S_A\approx32.7[/tex]So, the surface area of the label on the can is approximately 32.7 squared inches.
A package contains 11 resistors, 2of which are defective. If 4 are selected find the probability of getting the following results.P(1 defective)=
From the given values, we know there are 2 defective resistors and 9 not defective. then, we have
[tex]P(1\text{ defective)=}\frac{C^9_3\times C^2_1}{C^{11}_4}[/tex]where
[tex]C^9_3[/tex]denote the combinations of 9 elements taking in 3, that is 3 good resistor from the 9 which are not defective. Similarly,
[tex]C^2_1[/tex]denotes the combinations of 2 elements taking in 1, that is, 1 defective resistor form the 2 defective resistors.
Then, we have
[tex]P(1\text{ defective)=}\frac{84\times2}{330}[/tex]then, the answer is
[tex]P(1\text{ defective) =}0.509[/tex]write the equation of a line through ( -3, 5), parallel to y = -x.
y= ___ x + ___
Answer:
We took it at grade 7 oh god
A man realizes he lost the detailed receipt from the store and only has the credit card receipt withthe after-tax total. If the after-tax total was $1,656.99, and the tax rate in the area is 8.396, what wasthe pre-tax subtotal?
The pre-tax subtotal was $171.00.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that:
After-tax total = $1,656.99
Tax rate in the area = 8.396%
The pre-tax price would be 100% and this tax rate is an addition.
Total percent = (100+8.396)% = 108.3%
Consider x be the pre-tax amount.
The total bill= (after-tax total) = (pre-tax subtotal) + 8.3% · (pre-tax subtotal)
(after-tax total) = (pre-tax subtotal) 108.3
Divide by the coefficient on the right;
(pre-tax subtotal) = (after-tax total)/108.3
= $1,656.99/108.3
= $171.00
Therefore, The pre-tax subtotal was $171.00.
The pre-tax amount was $130.
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The diameter D of a sphere is 12.4 m. Calculate the sphere's surface area A.
Use the value 3.14 for , and round your answer to the nearest tenth.
The sphere has a surface area of 482.8064 square meters
How to determine the surface area of the sphere?From the question, the given parameters are:
Diameter, D = 12.4 meters
π = 3.14
The surface area of the sphere is calculated using the following formula
S = 4π(D/2)²
Substitute the given parameters in the above formula
So, we have
S = 4 * 3.14 * (12.4/2)²
Evaluate the exponent
This is represented as
S = 4 * 3.14 * 38.44
Evaluate the product
This is represented as
S = 482.8064
Hence, the surface area of the sphere is 482.8064 square meters
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solve for w: x=7w-8z-4
Answer:
W=x/7+ 8z/7 + 4/7
Step-by-step explanation:
Points 1 to 6To present y=-x^3+3x^2, 9 points must be selected, point 1: Domain, 2: zeros of the function, 3: period and symmetry, 4: sign of the function, 5: going to the edge of the function, 6: asymptotes, 7: monotony and extreme values, 8: concavity and convexity, 9: to present the function graphically.
ANSWERS
1. Domain: all real values
2. Zeros: 0 (with multiplicity 2) and 3
3. Not periodic. Symmetric about the point (1, 2)
4. Positive for x < 3; negative for x > 3
5. f → ∞ as x → -∞; f → -∞ as x → ∞
6. none
EXPLANATION
1. The domain of a function is the set of all the x-values for which the function exists. In this case, we have a polynomial function and, therefore, the domain is all real values.
2. To find the zeros of the function, we have to solve,
[tex]-x^3+3x^2=0[/tex]First, factor x² and -1 out. To do so, we have to divide each term by x² and by -1 - or, in other words, divide by -x²,
[tex]\begin{gathered} -x^2\left(\frac{-x^3}{-x^2}+\frac{3x^2}{-x^2}\right)=0 \\ \\ -x^2(x^{3-2}-3x^{2-2})=0 \end{gathered}[/tex]So, we have,
[tex]-x^2(x-3)=0[/tex]In this equation, we can see that if x = 0, then the equation is true. Also, if x = 3 the equation is true. So, these are the two zeros, with the particularity that x = 0 has multiplicity 2. This is because the factor related to that zero is x squared.
Hence, the zeros are 0 and 3. 0 has multiplicity 2.
3. As mentioned before, this is a polynomial function, which means that it is not a periodic function. A cubic function is an odd function, and it is symmetric about the origin. However, this function is not the parent function, x³, but it is symmetric about the point (1, 2).
4. We know that the function is zero at x = 0 and at x = 3. For x < 0, the function is positive,
[tex]with\text{ }x=-1:\text{ }y=-(-1)^3+3(-1)^2=-(-1)+3\cdot1=1+3=4[/tex]For 0 < x < 3, the function is also positive. This is because x = 0 with multiplicity 2.
Then, since the function crosses the x-axis at x = 3 and that zero has multiplicity 1, we can conclude that the function is negative for x > 3.
Hence, is the function is positive for x < 3 and negative for x > 3.
5. As mentioned in part 4, the function is positive for all values of x less than 3, which means that the function goes to infinity as x goes to negative infinity.
Since for x > 3 the function is always negative, it goes to negative infinity as x goes to infinity.
6. A polynomial function has no restrictions in the domain and, therefore, has no asymptotes.
given circle K with diameter IJ and radius KG. GH is tangent to K at G. If GH =6 and KH =8, solve dor KG. Round your answer to the nearest tenth if necessary. If the answer cannot be determined click cannot be determined.
EXPLANATION:
We are given a circle K with radius KG. Note here that line KJ and line KG are both radii of the circle given.
Also we know that a line tangent to a circle at the point of intersecting with the radius forms a 90-degree angle with the radius.
We can now extract the following triangle from the diagram provided;
We now have a right triangle which we shall solve by use of the Pythagorean theorem;
[tex]a^2+b^2=c^2[/tex]Where we have c as the longest side (hypotenuse) and then a and b are the two other sides. Substituting into the equation above now gives us;
[tex]\begin{gathered} a^2+b^2=c^2 \\ KG^2+6^2=8^2 \\ KG^2+36=64 \end{gathered}[/tex]Subtract 36 from both sides;
[tex]\begin{gathered} KG^2+36-36=64-36 \\ KG^2=28 \end{gathered}[/tex]Take the square root of both sides;
[tex]\begin{gathered} \sqrt[]{KG^2}=\sqrt[]{28} \\ KG=5.2915 \end{gathered}[/tex]Rounded to the nearest tenth, the answer is;
ANSWER:
[tex]KG=5.3[/tex]A company's stock began the day at $ 36.77per share. That price drops by $1.69 each hour. What is the price per share after 5 hours? What would it be after 23 hours if this rate continues? Use pencil and paper. Explain what the signs of the answers mean in this context.
The price per share after 5 hours is $28.32
The price per share after 23 hours is $-2.1
Given,
A company's stock began the day at $ 36.77per share.
and, price drops be $1.69 each hour.
To find the what is the price per share after 5hours
and, also find what will be after 23 hours rate continues?
Now, According to the question:
The price of the company's stock is initially at $36.77 per share. Each hour the price drops by $1.69. This condition can be modeled by the function:
P(t) = 36.77 - 1.69t
Where t is the time in hours.
The sign means the function is decreasing as time passes.
When t=5 hours, the price will be:
P(5) = 36.77 - 1.69 × 5 = 28.32
The price per share after 5 hours is $28.32
Now find the price when t=23 hours
P(23) = 36.77 - 1.69 × 23 = - 2.1
The price per share after 23 hours is $-2.1
Hence, The price per share after 5 hours is $28.32
The price per share after 23 hours is $-2.1
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A large university accepts 70% of the students who apply. Of the students the university accepts,25% actually enroll. If 20,000 students apply, how many enroll?
The number of students that enrolled = 3,500 students.
What is enrollment?This is defined as the intake of individuals into an organism or students into an institution through adherence to specific orders given by the administrative department of the organisation.
The number of students that apply= 20,000 students
The percentage of students that are accepted= 70% of 20,000
That is, 70/100× 20,000
= 1400000/100
= 14,000 students.
The quantity of students that actually enroll = 25% of 14,000
That is, 25/100× 14000
= 350000/100
= 3,500 students.
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Each serving ofsalad dressing uses 3 tablespoons of olive oil and 1 tablespoon of vinegar. A tablespoon of olive oil costs $0.13 and a tablespoon of vinegar costs $0.04. What is the cost of x servings of dressing in dollars?
The cost of x servings of dressing in dollars will be $0.43x.
According to the question,
We have the following information:
Each serving of salad dressing uses 3 tablespoons of olive oil and 1 tablespoon of vinegar.
Cost of 1 tablespoon of olive oil = $0.13
Cost of 1 tablespoon of vinegar = $0.04
So,
The cost of each serving of salad = Cost of 3 tablespoons of olive oil + cost of 1 tablespoon of vinegar
The cost of each serving of salad = 3*0.13 + 0.04
The cost of each serving of salad = $(0.39+0.04)
The cost of each serving of salad = $0.43
Now,
The cost of x servings of salad = $0.43x
(Note that if we have to find the cost of more than 1 product than the number has to be multiplied with the cost of one product.)
Hence, the cost of x servings of salad dressing is $0.43x.
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Zach submitted the work shown below when trying to simplify the expression 3 + 2(2x - 4) what mistake did he make and what is the correct simplified expression with correct steps
Answer:
The number “2” that is a outside the brackets multiplies both of the numbers inside the brackets.
Step-by-step explanation:
3+2(2x-4)
3+4x-8
4x-5
May Someone Please Give Me The Answers To The Problems I Haven’t Done (Please Mark Which Ones They Are)Thank You!!
The simplest form of the ratios are:
(A) 3/1 = 3(B) 6/2 = 3(C) 18/6 = 3(D) 36/12 = 3What are ratios?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls).
So, the ratios in the simplest form are:
We can observe that the simplest form of all the ratios is similar which is 3.
Therefore, the simplest form of the ratios are:
(A) 3/1 = 3(B) 6/2 = 3(C) 18/6 = 3(D) 36/12 = 3Know more about ratios here:
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2/11 and 1/5 common denominator
Answer:
The answer is 55.
Step-by-step explanation:
2/11 = 2/11 × 5/5 = 10/55
1/5 = 1/5 × 11/11 = 11/55
Answer:
55
Step-by-step explanation:
2/11 and 1/5
To find the common denominator, take 11 and multiply by 5
11*5 = 55
2/11 * 5/5 = 10/55
1/5 * 11/11 = 1/55
Tom’s car has 1119 gallons of gas. If he uses 38 of the gas, how much gas does the car have left?
Answer:
1,081 gallons
Step-by-step explanation:
1,119 - 38 = 1,081
Which equation has no solution?
Answer:
1.)|4x-2|=-6
This eguation has not solution.
Answer:
the first one; absolute value cannot be negative
Step-by-step explanation:
|4x-2| = -6
add 2
|4x| = -4
divide 4 on both sides
x = -1
|4x-2| = 6
repeat the same steps
x = 2
Write an expeession equivalent to 0.4x
A. X-0.6x
B. 1-0.6x
C. X + 0.4
D. 0.4x-x
Answer:
A. X-0.6x
Step-by-step explanation:
A. X-0.6x = 0.4x YES
B. 1-0.6x = 1 - 0.6x NO
C. X + 0.4 = 1.4x NO
D. 0.4x-x = -0.6x NO
I have no clue what to do so pls include an explination
[tex]10=\frac{z}{2} +7[/tex]
The solution for the given linear equation is z = 6
How to solve the linear equation?
Here we have the following linear equation:
10 = z/2 + 7
To solve it, we need to isolate the variable in one of the sides of the equation.
First, we can subtract 7 in both sides:
10 - 7 = z/2 + 7 - 7
3 = z/2
Now we can multiply both sides by 2 to get:
2*3 = 2*(z/2)
6 = z
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I understand the answer to simplifying it, i want a mathematical expression of the method of simplifying to know how to show my work
Answer:
This is how I would approach it
Step-by-step explanation:
Write a verbal sentence to represent each equation.
9.3n-3579
10. 2(n³ + 3n²) = 4n
11.
5n
n+3
-=n-8
The expression's variables can be represented by a different symbol than the conventional x and y.
A mathematical assertion represented in English is known as a verbal expression.What does an algebraic verbal model mean?Talking Model is a formula utilizing the terms found in the problem. Labels matching variables or numerical values to the linguistic model Equational Expression Modification of the Verbal Model by the substitution of mathematical values and variables.How to Convert Algebraic Expressions to Verbal Expressions.
Step 1: Recognize the algebraic operations—such as addition, subtraction, multiplication, and division—used in the expression.Step 2: Write a statement in which a vocabulary word is combined with the numbers to represent each of these processes.Therefore, the expression's variables can be represented by a different symbol than the conventional x and y.
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Solve for the value of z.
(7z+7)°
(9z-7)°
Base on congruency of vertical angles, the value of z is 7.
What are vertically opposite angles?Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
In other words, vertically opposite angles are angles that opposed each other at one specific vertex, and are formed by two straight intersecting line.
Vertically opposite angles are congruent to each other.
Therefore,
7z + 7 = 9z - 7
subtract 9z from both sides of the equation
7z + 7 = 9z - 7
7z - 9z + 7 = 9z - 9z - 7
-2z + 7 = - 7
subtract 7 from both sides of the equation
-2z + 7 = - 7
-2z + 7 - 7 = - 7 - 7
- 2z = - 14
divide both sides by - 2
z = - 14 / -2
Therefore,
z = 7
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Determine which integer in the solution set will make the equation true.
6x − 6 = 2(2x + 5)
S: {−2, 0, 8, 11}
Answer:
8
Step-by-step explanation:
[tex]6x-6=2(2x+5) \\ \\ 6x-6=4x+10 \\ \\ 2x-6=10 \\ \\ 2x=16 \\ \\ x=8[/tex]
The cone of the volcano has a height of 414 meters and a diameter of 416 meters. Find the volume of the cone. Round your answer to the nearest hundred thousand. Use 3.14 for 1. The volume of the cone is about m3.
Volume of a cone is given by;
[tex]V=\frac{1}{3}\pi^{}r^3h[/tex]From the queston,
h = 414
diameter = 416, this implies r = d/2 = 416/2 = 208
π = 3.14
substitute the values into the formula
[tex]V=\frac{1}{3}\times3.14\text{ }\times208^2\times414[/tex][tex]=18747156.48[/tex][tex]\approx18700000m^3[/tex]Which fraction equals \dfrac{4}{7} + \dfrac{3}{8}
7
4
+
8
3
?
Answer:
[tex]$\frac{53}{56}[/tex]
Step-by-step explanation:
Hello!
Let's first convert the denominator of each fraction to the same number. Multiply the denominator by the whole number formed by the other number's denominator.
[tex]\frac{4}{7} + \frac{3}{8}[/tex][tex]\frac{4}{7}(\frac88) + \frac38(\frac77)[/tex][tex]\frac{32}{56} + \frac{21}{56}[/tex]Now we can add the numerators of the fractions and keep the denominators the same.
[tex]\frac{32}{56} + \frac{21}{56}[/tex][tex]\frac{32 + 21}{56}[/tex][tex]\frac{53}{56}[/tex]The simplified form is [tex]$\frac{53}{56}[/tex].
A recipe calls for 3 ⅜ cups of flour. How can you express that mixed number as a fraction?
4x^2+10x-4 divided by 2x-1
The division of 4 · x² + 10 · x - 4 by 2 · x - 1 is equal to (2 · x + 6) + 2 / (2 · x - 1).
How to divide a polynomial by algebra properties
In this problem we find a second grade polynomial, also known as quadratic function, being divided by a first grade polynomial, also known as linear function. The complete procedure is shown below:
4 · x² + 10 · x - 4 Given4 · x² - 2 · x + 12 · x - 4 Definition of subtraction / Distributive property(4 · x² - 2 · x) + (12 · x - 6) + 2 Existence of additive inverse / Modulative, commutative and associative property2 · x · (2 · x - 1) + 6 · (2 · x - 1) + 2 Definition of power / Definition of multiplication / Distributive property(2 · x + 6) · (2 · x - 1) + 2 Distributive and commutative properties(2 · x + 6) + 2 / (2 · x - 1) Dividing (5) by (2 · x - 1) / ResultThe resulting polynomial is (2 · x + 6) + 2 / (2 · x - 1).
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