The dimensions are Width = 7 feets ; length = 20 feets
As given,
Meadow area is 140 square feet.
Height = W (smaller dimension and 2 sides)
Height = L (longer dimension and 1 side)
Fence yards equal 34 feet;
Hence,
L + W = 34
L + 2W = 34
L = 34 - 2W - - - (1)
Recall:
Area = L * W = 140
Substitute value of L
140 = (34 - 2W) * W
140 = 34W - 2W²
2W² - 34W + 140 = 0
W² - 17W + 70 = 0
W² - 10W - 7W + 70 = 0
W(W - 10) - 7(W - 10) = 0
(W - 10) = 0 or (W - 7) =0
W = 10 or W = 7
We choose the shorter width because length should be as long as possible:
W = 7
L + 2W = 34
L = 30 - 14
L = 20 feets
Therefore, The measurements are 7 feet wide and 20 feet long.
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A and B are supplementary angles. If mA = (3x - 28)° and
m/B = (x − 4)°, then find the measure of A.
Answer:
A = 131°
Step-by-step explanation:
Supplementary angles sum 180°
A + B = 180°
(3x - 28) + (x - 4) = 180
4x - 28 - 4 = 180
4x - 32 = 180
4x = 180 + 32
4x = 212
x = 212/4
x = 53
Then:
A = 3x - 28
A = 3*53 - 28
A = 159 - 28
A = 131°
B = x - 4
B = 53 - 4
B = 49°
Check:
131° + 49° = 180°
Answer:m∠A=33
Step-by-step explanation:
What is 42/80 as a whole number ?
Answer:
it can't be in a whole number since it is a fraction and will go in decimals
an envelope contains eight bills: 22 ones, 22 fives, 22 tens, and 22 twenties. two bills are drawn at random without replacement. what is the probability that their sum is \$20$20 or more?
When two bills are drawn randomly without replacement, the probability that their sum is $20 or more is 1/2.
Given,
An envelope contains 8 bills;
Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.
When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.
Total outcomes = 2 x 2 x 2 x 2 = 16
Total possible outcomes, more than 20;
(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases
That is,
The total possible outcomes is 8.
Now,
The probability of bill to be $20 or more = Possible outcome / Total outcome
Probability = 8/16 = 1/2
That is,
When two bills are drawn randomly without replacement, the probability that their sum is $20 or more is 1/2.
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The table shows the number of cars and trucks that used a certain toll road on a particular day. The number of cars and trucks that used, and did not use, an electronic toll pass on that same day was also recorded.Toll PassCars Trucks TotalUsed537330867Did not use9046491553Total14419792420a) If one of these vehicles is selected at random, determine the probability that the vehicle is a car.b) If one of these vehicles is selected at random, determine the probability that the vehicle is a car, given that it used the toll passa) The probability that the vehicle was a car is(Round to four decimal places as needed.)
We are given a two-way probability table
Part a)
If one of the vehicles is selected at random, determine the probability that the vehicle is a car.
From the table, we see that the total number of cars are 1441
Also, the total number of vehicles is 2420
Then the probability of selecting a car is
[tex]P(car)=\frac{1441}{2420}=0.5955[/tex]Therefore, the probability that the vehicle was a car is found to be 0.5955
Part b)
If one of the vehicles is selected at random, determine the probability that it used the electronic toll pass, given that it was a car.
This is a conditional probability problem.
The conditional probability is given by
[tex]P(used\: |\: car)=\frac{n(used\: and\: car)}{n(car)}[/tex]From the table, we see that,
[tex]\begin{gathered} n(car\: and\: used)=537 \\ n(car)=1441 \end{gathered}[/tex]So, the probability is
[tex]\begin{gathered} P(used\: |\: car)=\frac{n(used\: and\: car)}{n(car)} \\ P(used\: |\: car)=\frac{537}{1441} \\ P(used\: |\: car)=0.3727 \end{gathered}[/tex]Therefore, the probability that it used the electronic toll pass, given that it was a car is found to be 0.3727
The probability that the randomly chosen vehicle is a car is 59.54 %.
The probability that the randomly chosen vehicle is a car given that it used the toll pass is 61.94%.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
The probability that the randomly chosen vehicle is a car is the total no of cars divided by the total no. of vehicles which is,
= 1441/2420.
= (1441/2420)×100%.
= 59.54 %.
The probability that the randomly chosen vehicle is a car given that it used the toll pass is the total no. of cars that used the toll pass divided by the no. of vehicles that used the toll pass which is,
= (537/867)×100%.
= 61.94%.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
The correct representation of the inequality is x > 5 or –6x + 15 < 10 – 5x.
How to solve inequality?The inequality can be best represented as follows;
–3(2x – 5) < 5(2 – x)
An inequality is a mathematical expression that has the signs <, >, ≤ and ≥.
Therefore,
–3(2x – 5) < 5(2 – x)
open the brackets
- 6x + 15 < 10 - 5x
Lets solve further by subtracting 15 from both sides of the inequality.
- 6x + 15 < 10 - 5x
- 6x + 15 - 15 < 10 - 15 - 5x
- 6x < - 5 - 5x
add 5x to both sides of the inequality.
- 6x < - 5 - 5x
- 6x + 5x < - 5 - 5x + 5x
-x < - 5
divide both sides by -1
Therefore,
x > 5
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The solution of the given inequality is x > 5 which is the correct representation of x > 5 or –6x + 15 < 10 – 5x.
The inequality is given in the question as
–3(2x – 5) < 5(2 – x)
Open the parenthesis and apply the distributive property of multiplication,
⇒ - 6x + 15 < 10 - 5x
Subtract 15 from both sides of the above inequality,
⇒ - 6x + 15 - 15 < 10 - 15 - 5x
⇒ - 6x < - 5 - 5x
Add 5x to both sides of the inequality,
⇒ - 6x + 5x < - 5 - 5x + 5x
⇒ -x < - 5
Multiply both sides by -1 and flip the sign of inequality
⇒ x > 5
Therefore, the solution of the given inequality is x > 5.
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Directions: Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.Solve for x.( + 0.5) + 5.24 = = + ( + 2.2)The value of x is
1/5 (x+0.5) +5.24 = 3/2x + 7/10 (x+2.2)
First, apply the distributive property to solve the parentheses
1/5(x)+ 1/5 (0.5) +5.24 = 3/2x + 7/10(x) + 7/10 (2.2)
1/5x +0.1 +5.24 = 3/2x + 7/10 x + 1.54
Combine like terms
1/5x +5.34 = 11/5x +1.54
Move the x terms to the left side of the equation:
1/5x-11/5x = 1.54-5.34
-2x = -3.8
Divide both sides by -2
-2x/-2 = -3.8/-2
x = 1.9
Trey's mom agreed to buy him a playstation card for $20, but it would come out of his chore money. He already has $7 in his wallet and will earn 15 for his chores. How much will he have left after paying his debt?
Answer:
2$
Step-by-step explanation:
Answer:
$2
Step-by-step explanation:
trey's mom bought him a card for $20, if he already has $7 & will get $15 for his chores, add them together & thats $22. Once he pays off the $20 he will have $2 left.
Write the sentence as an equation.
y decreased by 283 is equal to 48
Answer:
y - 283 = 48
Step-by-step explanation:
y decreased by 283 means that 283 is subtracted from y. All set equal to 48.
the angle of depression of the light to the nearest minute is
Answer
θ = 37° 30'
Explanation:
The angle of depression has the same measure as the angle of elevation, so a trigonometric function that related the sides of the triangle and the angle of elevation θ is tangent. Then:
[tex]\text{tan }\theta\text{ =}\frac{39.57}{51.56}[/tex]Therefore, the value of θ is:
[tex]\begin{gathered} \tan \text{ }\theta\text{ = 0.7674} \\ \theta=\tan ^{-1}(0.7674) \\ \theta=37.50 \end{gathered}[/tex]So, in grades and minutes, we get:
θ = 37.50 = 37° 30'
Therefore, the angle of depression is 37° 30'
Please solve for y. There should be no actual numbers besides for 9.
Answer:
y= x/(n-9)
Step-by-step explanation:
Move 9 to the right side to get n-9
Take y over to get x=y(n-9)
Then shift n-9 over to other side to get y= x/(n-9)
The length of a rectangle is 3 inches greater than the width. (Hint: draw a pictureand label itA. Write a polynomial that represents the area of the rectangle.B. Find the area of the rectangle when the width is 4 inches..
We are given that the length of a rectangle is 3 inches greater than the width.
Let us draw a rectangle and label the width and length.
Part A:
Let the width of the rectangle is x inches.
Then the length of the rectangle is (x + 3) inches.
Now recall that the area of a rectangle is given by
[tex]A=L\cdot W[/tex]Where L is the length and W is the width of the rectangle.
[tex]\begin{gathered} A=(x+3)\cdot x \\ A=x^2+3x \end{gathered}[/tex]Therefore, the above polynomial represents the area of the rectangle.
Part B:
We are given that the width is 4 inches.
Substitute the width (x = 4) into the equation of the area that we found in part A.
[tex]\begin{gathered} A=x^2+3x \\ A=(4)^2+3(4) \\ A=16+12 \\ A=28in^2 \end{gathered}[/tex]Therefore, the area of the rectangle is 28 square inches.
In today's recording, the first example was the function
f(x) = x² + 5x³ + 10x² + 20x + 24
After depressing our function twice and getting a quotient (depressed polynomial), which was the
resulting quadratic equation that we needed to solve?
O x²+4=0
O x²-4=0
O x² + 4x + 4 = 0
O x² + 4x = 0
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
How can you locate a polynomial's root?Set the equation's value to zero to get the polynomial's roots. Completely factor the polynomial expression. Then, in order to find the variable, set each factor equal to zero. The formula isx^4+5x^3-10x^2-20x+24Finding polynomial roots (zeroes) is the focus of this solution.((((x4)+(5•(x3)))-(2•5x2))-20x)+24
((((x4) + 5x3) - (2•5x2)) - 20x) + 24
Find the roots (zeroes) of F(x) = x4 + 5 x 3 x 10 x 2 x 20 + 24.The Polynomial Roots Calculator is a collection of techniques for identifying x values where F(x)=0.One of the tools discussed above is the rational roots test. Only numbers x that can be written as the quotient of two integers would be considered rational roots.According to the Rational Root Theorem, P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient if a polynomial zeroes for a rational integer P/Q.The Leading Coefficient in this situation is 1 and the Trailing Constant is 24.The element(s) are: of the Trailing Constant: 1, 1, 2, 3, 4, 6, 8, 12, and 24 of the Leading Coefficient: 1.According to the Factor Theorem, if P/Q is a polynomial's root, then q*x-p can be used to divide the polynomial. Keep in mind that q and p come from P/Q in its simplest form.In our situation, this means that 4 different polynomials, including x-2, can divide x4+5x3–10x2–20x+24.To Learn more about polynomial refer to:
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Help really need it
.........................................
Answer:
you wmekekd
Step-by-step explanation:
Find the perimeter of the polygon with the vertices J(-5, 3), K(-2, 1) and L(3, 4). Round your answer to the nearest tenth.
The perimeter of JKL is about____
units.
The perimeter of the polygon with the vertices is: 17.5 units.
How to Find the Perimeter of a Polygon?The perimeter of a polygon is the sum of all the sides of the polygon. To find the perimeter of a polygon with coordinates given for its vertices, we have to apply the distance formula to find the length between each of the vertices of the polygon.
The distance formula is d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].
Given:
J(-5, 3)
K(-2, 1)
L(3, 4)
Find JK:
JK = √[(−2−(−5))² + (1−3)²]
JK = √13
JK = 3.6 units
Find KL:
KL = √[(−2−3)² + (1−4)²]
KL = √34
KL = 5.8 units
Find JL:
JL = √[(−5−3)² + (3−4)²]
JL = √65
JL = 8.1 units
Perimeter = 3.6 + 5.8 + 8.1
Perimeter = 17.5 units.
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jim is six feet tall, and his shadow is $16$ feet long. the flagpole he is standing next to casts a shadow that is $72$ feet long. how tall is the flagpole, in feet?
The height of the flagpole is 27 feet.
Given,
If two triangles are similar, sides of these triangles will be proportional.
Height of the flagpole = h feet
Shadow castes by the flagpole = 72 feet
Height of the person = 6 feet
Shadow casted by the person = 16 feet
By using the property of similar triangles,
Hence, h/6 = 72/16
h = (6×72)/ 16
h = 27 feet
Therefore, The height of the flagpole is 27 feet.
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The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?.
Since the ages of students at a university are normally distributed with a mean of 21, the percentage of the student body that is at least 21 years old is: 50%.
What is a normal distribution?A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which indicate that all data near the mean have a higher frequency than the data that are far from the mean.
For all normal distributions, the mean is always located at the center with 50 percent (50%) or 0.5 of the distribution to either side, which is right or left of the distribution.
In this context, the percentage of student body that is at least 21 years old is represented by the percentage to the left of the normal distribution, which is 50 percent (50%):
P(x ≤ 21) = 50%
P(x ≤ 21) = 50/100
P(x ≤ 21) = 0.5.
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The sum of the angle measures of a polygon with s sides is 2,340 degrees. Find s.thank you ! :)
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The sum of interior angles of a polygon is:
[tex]\begin{gathered} (s\text{ -2 \rparen x 180}^0=\text{ 2340}^0\text{ , where s = number of sides} \\ Divide\text{ both sides by 180}^0,\text{ we have that:} \\ s\text{ - 2 = 13} \\ s\text{ = 13 + 2} \\ s\text{ = 15} \\ \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]s\text{ = 15}[/tex]Consider the function y=(x−1)2+3.(a) Give the coordinates of the vertex of the graph of the function.(b) Graph the function on a window that includes the vertex.
Given function is
[tex]y=(x-1)^2+3[/tex]The vertex of the graph is at (1,3).
Need an explanation why it’s 46.4
(Please help I need this asap)
Answer:
9 + 7 + 7.2 = 23.2
23.2 x 2 = 46.4
Step-by-step explanation:
Answer the question below
the mean cost of a five pound bag of shrimp is 40 dollars with a variance of 36. if a sample of 43 bags of shrimp is randomly selected, what is the probability that the sample mean would differ from the true mean by more than 2.5 dollars? round your answer to four decimal places.
The probability that the sample mean would differ from the true mean by more than $2.5 is 0.0062
Mean cost of the five pound shrimp bag = $40
Variance of the five pound shrimp bag = $36
The number of the shrimp bag = 43
The given mean value = $2.5
The z-score = $2.5
The probability of the sample mean differ by $2.5 from the true mean can be calculated by
P(z > 2.5) = 1 - P(z < 2.5)
From the z table , we can get the value of z < 2.5 which is 0.9938
P(z > 2.5) = 1 - 0.9938
P(z > 2.5) = 0.0062
Therefore , the probability of sample mean from the true mean by 2.5 is 0.0062
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1) Which situation could the integer -50 represent?
A) An increase of $50 in a bank account
B) The temperature on a warm fall day
C) The distance driven on the way to the beach
D) A decrease of 50 employees
Which of the following statements are true about the process and solution till the following problem 86.89-56.389?
The arithmetic says we should subtract find the difference between 86.89 and 56.389.
Notice we have to put a place holder of 0 at the ending of 86.89 to do the subtraction. Then we have to borrow 1 from the hundredth term(9) of 86.890 to make 0 ten . so ten minus 9 should be 1. Then the difference of the hundreth term(8 - 8) is 0. 8 minus 3 is 5. 6 minus 6 is zero and finally 8 minus 5 is 3.
The answers are B and D
The rectangular waiting area for a popular amusement park ride is covered by a large sun canopy. The total area of the canopy, in square feet, is 100 square feet more than twice the area where guests wait.
Which equation could you use to find the area of the place where guests wait for the ride if the area of the canopy is 7,600 square feet?
The equation which can be used to find the area of the place where guests wait for the ride if the area of the canopy is 7600 square feet is:
2a+100=7600.
Given, The rectangular waiting area for a popular amusement park ride is covered by a large sun canopy.
The total area of the canopy, in square feet, is 100 square feet more than twice the area where guests wait.
let the area of the place where guests wait be represented by 'a'.
the canopy covers the area = 2a + 100
total area of the canopy = 7600
equation used to find the area of the place where guests wait for the ride if the area of the canopy is 7,600 square feet = ?
⇒ 2a + 100 = 7600
arrange the like terms.
⇒ 2a = 7600 - 100
calculate the difference.
⇒ 2a = 7500
⇒ a = 7500/2
⇒ a = 3750
Hence the area of the place where guests wait is 3750 square feet.
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Hi Can someone help this is hard?
The domain is the set of all real numbers and the range is the set of all real numbers larger than -4, so the correct option is the third one.
How to get the domain and the range?For a function y = f(x) we define the domain as the set of the x-values (horizontal axis) and the range as the set of the y-values (vertical axis).
Here we have a parabola, in this case the domain is always the set of all real numbers, and the range is all the values above or equal to the vertex (in cases like this, where the parabola opens up).
We can see that the vertex is at y = -4
So the range is.
[-4, ∞]
So the correct option is 3.
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what isss 1+2
please help im so confused
Answer:
3
Step-by-step explanation:
1 + 2 = 3
please mark this answer brainliest if it helped you in any way:)
Answer:
3
Step-by-step explanation:
1 + 2 = 3
Let break it down.
Lets say you have 1 apple
Your friend has 2 apples
All together you have 1 + 1 + 1 = 3 apples
ickets to the zoo cost $15 for adults and $10 for children. The school has a budget of $300 for the field
trip. An equation representing the budget for the trip is 15x+10y = 300.
a. With a budget of $300, determine if 21 students and 6 adults can go to the zoo. Explain how you
know.
b. If there are four adults who need tickets, what is the maximum number of students who can go to
the zoo while staying within the school budget? Show or explain your reasoning.
c. Solve the equation15x+10y = 300 for y.
Answers: lol sorry very long answer
part a answer: Yes, because if we substitute the variables, the equation will be 15(6) + 10(21) = 300. Simplifying this will be 90 + 210 = 300. And since 90 + 210 does equal 300, 21 students and 6 adults can go to the zoo
part b answer: 24 students. Using the equation 15x + 10y = 300, we can find out the maximum number of students who can go to the zoo. First we can substitute x for 4 because that's how many adults who need the tickets. The equation will now be 15(4) + 10y = 300. Simplifying this will be 60 + 10y = 300. Now we can subtract 60 on both sides to isolate the y term. The equation will be 10y = 240. Divide each side by 10 to find out what y is and we get y = 24. So if 4 adults go the zoo, up to 24 students can go.
part c answer: y = 30 - 1.5x. To solve 15x + 10y =300, we first need to move 15x to one side of the equation. To do this we will subtract it on both sides. The equation is now 10y = 300 -15x. Then you will divide 10 on both sides to find out what y is. y = 30 - 1.5x.
Whats the Point-Slope Equation for the line that goes through
(-3, 5) and (-7, 4)
Answer the question below
A) 4/5 or 0.8
B)7
C)1/81
Simplify the following radical
√175x^5
Simplified version of the given radical expression would be...
[tex]5x^2\sqrt{7x}[/tex]
Hope this helps!
