The simplified expression is (3y-7)/(y^2-35)/3.
To simplify the given expression, we need to find the least common denominator (LCD) of the two fractions. The LCD of (y-5) and (y+7) is (y-5)(y+7).
Next, we need to multiply each fraction by the LCD in order to get the same denominator for both fractions.
(2)/(y-5) * (y+7)/(y+7) + (7)/(y+7) * (y-5)/(y-5)
= (2y+14)/(y^2-35) + (7y-35)/(y^2-35)
Now, we can combine the two fractions since they have the same denominator.
(2y+14+7y-35)/(y^2-35)
= (9y-21)/(y^2-35)
Finally, we can simplify the fraction by factoring out a 3 from the numerator.
= (3)(3y-7)/(y^2-35)
= (3y-7)/(y^2-35)/3
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(2)
Solve the inequality 2r - 5 ≤ 9 and present your answer in interval
notation.
The solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].
To solve the inequality 2r - 5 ≤ 9, we need to isolate the variable r on one side of the inequality. Here are the steps to do so:
Step 1: Add 5 to both sides of the inequality to eliminate the -5 on the left side. This gives us: 2r ≤ 14Step 2: Divide both sides of the inequality by 2 to isolate the variable r. This gives us: r ≤ 7Now, we can present our answer in interval notation. Interval notation is a way to represent an interval on the number line. It is written in the form of [a, b], where a and b are the endpoints of the interval. The square brackets mean that the endpoints are included in the interval.
Since our inequality is r ≤ 7, our interval notation would be (-∞, 7], where -∞ represents negative infinity and 7 is the endpoint. The square bracket on the 7 means that 7 is included in the interval.
Therefore, the solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].
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Find the number of permutations of the letters of the word MAKABAYAN?
Answer:
720
Step-by-step explanation:
The number of permutations of the letters of the word MAKABAYAN is 720. This is because the word MAKABAYAN has 9 letters, and the formula for calculating the number of permutations of a word with n letters is n! (n factorial). Therefore, 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 720
Chose all the asswer that describe the quadrilateral ABCD if AB // CD, AB=9 CD=9
In the quadrilateral ABCD if AB ||CD and AB=9 as well as are CD=9. Then, quadrilateral ABCD is both parallelogram and trapezium.
Explain about the features of trapezium and parallelogram? A trapezium is still a two-dimensional quadrilateral with two parallel opposed sides that is made up of four straight lines. The base and legs of the trapezium are the opposing parallel sides, which are referred as the base and indeed the non-parallel sides, respectively. It has four sides plus four corners and is a closed plane shape.Parallelogram's characteristics
The different sides are distributed uniformly and parallel.Angles on either side are equal.The following or neighboring angles are supplemental.All of the angles will end up being right angles when any of them is a right angle.In the quadrilateral ABCD:
AB ||CD AB = CD = 9.Thus, the quadrilateral ABCD is both parallelogram and trapezium.
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HI I have this project due tomorrow and I need to know what type of histogram this is
The given histogram is right skewed type.
What is a histogram?A histogram is a graphic representation of data in a grouped frequency distribution with continuous classes.
They are similar to a bar graphs, but there are no gaps between the consecutive rectangles.
Histograms are widely used for ranging data into groups. It is a highly practical graph due to its clarity and simplicity.
Histogram :-
It is a collection of rectangles next to one another, where each bar represents a different type of data.
In this context, frequency refers to the number of times a number appears in statistical data.
It is known as a frequency distribution when shown in a table.
Here, the distribution here is skewed to the left. Therefore, it is also referred to as a negatively skewed histogram graph.
Hence, the given histogram is right skewed type.
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please help me for 20 poins!!
Answer: C, 2 2/8
Step-by-step explanation: To turn a mixed number into an improper fraction, multiply the whole number by the denominator. Then, add the numerator. So in this example it would be:
4 3/8 = 35/8
2 1/8 = 17/8
Now, since the denominators are equivalent, all we need to do is subtract the numerators.
35/8 - 17/8 = 18/8
The answer needs to be changed back to a mixed number. For this problem, there is an easy way to do this.
18/8 = 8/8 + 8/8 +2/8, which as a mixed number would be 2 2/8.
So the correct choice would be (C).
A social media survey found that 75% of parents are "friends" with their children on a certain online networking site. A random sample of 160 parents was selected.
a. Calculate the standard error of the proportion.
b. What is the probability that 125 or more parents from this sample are "friends" with their children on this online networking site?
c. What is the probability that between 120 and 128 patents
The formula for standard error of proportion is √(pq/n) where p is the sample proportion, q = 1-p, and n is the sample size. Here, the sample proportion is 0.75, q is 0.25, and n is 160. Therefore, the standard error of proportion is √(0.75*0.25/160) = 0.035
The probability that between 120 and 128 patents (inclusive) are friends with their children can be calculated using the z-score formula:
z = (x - np)/√(npq)
where x is the number of parents between 120 and 128 who are friends with their children,
np = 160*0.75 = 120, and pq = 160*0.25 = 40.
Therefore,√(npq) = √(120*40) = 24.49
z = (120 - 120)/24.49 = 0
z = (121 - 120)/24.49 = 0.04
z = (122 - 120)/24.49 = 0.08
z = (123 - 120)/24.49 = 0.12
z = (124 - 120)/24.49 = 0.16
z = (125 - 120)/24.49 = 0.2
z = (126 - 120)/24.49 = 0.24
z = (127 - 120)/24.49 = 0.29
z = (128 - 120)/24.49 = 0.33
Using a z-table or a calculator, the probability that z is between 0 and 0.33 is 0.1292. Therefore, the probability that between 120 and 128 parents are friends with their children is 0.1292.
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HELP ME PLEASE THIS IS DUE TOMORROW PLEASE USE ANY STRATEGIE
Answer:
C
Step-by-step explanation:
The equation that shows the whole amount of pizza Miah ate on Saturday is 3/32 of the whole pizza
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
This word problem are interpreted to mathematical equation
The left over is calculated is 3/8
therefore 5/8 of the pizza is left for Saturday
On Saturday she ate 1/4 of the pizza
= 1/4 × 3/8
= 3/32
therefore Miah ate 3/32 of the whole pizza on Saturday.
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Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.)
The properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms ln(√z) = (1/2)ln(z)
What is the logarithms?
Logarithms are mathematical functions that help to solve exponential equations. They are used to express very large or very small numbers in a more convenient and manageable way.
We can use the property of logarithms that states:
logb (a∙c) = logb a + logb c
to expand the expression as a sum of logarithms:
ln(√z) = ln(z^(1/2))
Using the power rule of logarithms, we can simplify this as:
ln(z^(1/2)) = (1/2)ln(z)
Hence, we can write:
ln(√z) = (1/2)ln(z)
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Need help on this question
whats the answer? I have to finish this quiz since I missed it
Answer:
Step-by-step explanation:
For this triangle, we can find the angle adjacent to side length 4 using trig:
tan(theta) = 7/4
theta = tan^-1(7/4)
theta = 60.26
Now we use sine to find x:
sin(60.26) = 7/x
x = 7/sin(60.26)
x = 8.06
I don't know how far you need to round, so it can either be this or 8.1
Hope this helps!
The amount of money raised, R, varies jointly as the square root of hours worked, h, and the number of people working, p. If six people raise $72 when working 9 hours, how much would 10 people raise if they worked 16 hours?
A group of 10 people would raise a total value of $160 if they worked 16 hours.
According to the given information, the amount of money raised, R, varies jointly as the square root of hours worked, h, and the number of people working, p. This means that R = k√h * p, where k is the constant of proportionality.
We are given that six people raise $72 when working 9 hours, so we can use this information to find the value of k:
72 = k√9 * 6
72 = k * 3 * 6
72 = 18k
k = 4
Now that we know the value of k, we can use it to find the amount of money that 10 people would raise if they worked 16 hours:
R = k√h * p
R = 4√16 * 10
R = 4 * 4 * 10
R = 160
Therefore, 10 people would raise $160 if they worked 16 hours.
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There are 12 boys and 13 girls in my 3rd period class. How many pairs can I make if I choose
one boy and one girl?
#4:
Victoria is solving the equation x-3-4. Some
of her steps are shown below.
• equation 1: x-3=4 5
21
• equation 2:
2
3
X-3=
5
2
• equation 3: x-3+3=¹+3
21
5
Which statement correctly explains whether equation 3
in Victoria's work is valid in solving the equation?
It is not valid because because Victoria should subtract 3
instead of adding 3.
It is valid because -3+3=0.
It is not valid because Victoria did not also add 3 to
It is valid because because Victoria added the same amount
to each side of the equation.
The statement "It is valid because Victoria added the same amount to each side of the equation" correctly explains whether equation 3 in Victoria's work is valid in solving the equation.
What explanation is suitable?In equation 3, Victoria added 3 to both sides of the equation x-3=4/21. This operation is valid because she added the same amount (3) to both sides, which maintains the equality between the two sides of the equation. The resulting equation is x-3+3=4/21+3, which simplifies to x=4/21+63/21 or x=67/21.
Therefore, equation 3 is a valid step in solving the equation x-3=4/21.
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A jar contains 0. 85 liter of strawberry juice and 0. 50 liter of mango juice. Celina poured 0. 15 liter of watermelon juice into the jar. She then drank 0. 30 liter of the mixture
An expression to represent the total amount of juice left in the jar is "Total amount of juice left in jar = Total amount of juice in jar before Celina drinks any - Amount of juice Celina drinks"
First, let's start by labeling the quantities of juice we have. We have 0.85 liters of strawberry juice, 0.50 liters of mango juice, and 0.15 liters of watermelon juice. When we combine these three quantities, we get the total amount of juice in the jar before Celina drinks any of it. We can express this as:
Total amount of juice in jar before Celina drinks any = 0.85 + 0.50 + 0.15
Simplifying this expression, we get:
Total amount of juice in jar before Celina drinks any = 1.50 liters
Now, we know that Celina drinks 0.30 liters of the mixture. So, the total amount of juice left in the jar after she drinks some can be expressed as:
Total amount of juice left in jar = Total amount of juice in jar before Celina drinks any - Amount of juice Celina drinks
Substituting in our values, we get:
Total amount of juice left in jar = 1.50 - 0.30
Simplifying this expression, we get:
Total amount of juice left in jar = 1.20 liters
Therefore, the expression that represents the total amount of juice left in the jar after Celina drinks 0.30 liters of the mixture is:
Total amount of juice left in jar = 1.50 - 0.30 = 1.20 liters
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Complete Question:
A jar contains 0.85 liter of strawberry juice and 0.50 liter of mango juice. Celina poured 0.15 liter of watermelon juice into the jar. She then drank 0.30 liter of the mixture.
Part A: Write an expression to represent the total amount of juice left in the jar.
If M<1 = 140 what is M <4
Answer:
I think its 560
Step-by-step explanation:
Help me I don’t under stand this!
A pack of 8 collectable cards contains 1 rare card, 3 uncommon cards, and 4 common cards. If Javier has 45 packs of cards, how many more uncommon cards does he have than rare cards?
Javier has 90 more uncommon cards than rare cards.
To find out how many more uncommon cards Javier has than rare cards, we need to multiply the number of packs he has by the number of each type of card in a pack, and then subtract the number of rare cards from the number of uncommon cards. We can do this with the following equation:
Uncommon cards - Rare cards = Difference
First, we'll multiply the number of packs by the number of each type of card:
45 packs × 3 uncommon cards = 135 uncommon cards
45 packs × 1 rare card = 45 rare cards
Now we'll subtract the number of rare cards from the number of uncommon cards to find the difference:
135 uncommon cards - 45 rare cards = 90
So, the number of uncommon cards is 90 more than the rare cards.
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need help with 7 A & B? “Quadratic Functions” algebra 1
The required solutions are as follows,
(a) The parabola will open downwards and have a maximum.
(b) The axis of symmetry for this function is t = 15.
A parabola is a cross-section cut out of the cone and represented by an equation shown in the question.
Here,
(a) The function C(t) is a quadratic function with a coefficient of -0.2 in front of the t² term. Since this coefficient is negative, the parabola will open downwards and have a maximum.
(b) The axis of symmetry of a quadratic function in the form of f(x) = ax² + bx + c is given by the formula x = -b/2a.
In this case, the function is C(t) = -0.2t² + 6t + 28.5, so a = -0.2 and b = 6. Thus, the axis of symmetry is:
t = -b/2a = -6/(2*(-0.2)) = 15
Therefore, the axis of symmetry for this function is t = 15.
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Find the measure of the central angle indicated. Lines that appear to be diameters, are diameters.
The measure of the central angle indicated is 60°.
Define central angle?The central angle of a circle is the angle that an arc takes up in the centre. The radius vectors are what make up the angle's arms.
The formula for calculating a central angle is: Central Angle = Arc length (AB) / Radius (OA) = (s 360°) / 2r, where "s" stands for arc length and "r" for circle radius.
Now here in the given diagram,
Let x equal the desired angle.
The central angle that we need to find is:
Now x = 360-120-(90+90)
⇒ x = 360-300
⇒ x = 60°
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A box contains color of markers black and red the ratio of black markers to red markers is 7 : 2 if there are 144 markers the box how many markers are there of each type PLSSS HELP ANSWER ANS EXPLAIN PLSSS
Answer:
see below
Step-by-step explanation:
put paragraph of words into summarised information 1st.
ie
black : red : total
7 : 2 : 7+2 = 9 is total units
total units = 9 (which is 144 markers)
so 1 unit is .....
144 ÷ 9 = 16 markers
black = 7units
7 x 16 markers = ans
red = 2 units
2 x 16 = ans
Find the measurements of X
pt 3
Answer:
180 p
Step-by-step explanation:your welcome
write these number in standard form seventeen thousand
Answer:
17,000
Step-by-step explanation:
17000 in words is written as Seventeen-thousand. The number 17000 represents a value equivalent to it.
LetP(x)=10x7−2x6+5x5+x3−7x2−1. (a) Find the possible number of positive real zeros ofP(x). LetP(x)=10x7−2x6+5x5+x3−7x2−1. (b) Use Descartes' Rules of Signs to show that1−2cannot be a zero ofP(x)
(a) The possible number of positive real zeros of P(x) can be determined using Descartes' Rule of Signs. The Rule of Signs states that a polynomial with real coefficients can have at most as many positive real zeros as its leading coefficient has sign changes in the coefficients. This means that the polynomial has at most 3 positive real zeros.
(b) Descartes' rule of signs can also be used to prove that 1-2 cannot be a zero of P(x). According to the Rule of Signs, the number of positive real zeros of P(x) is limited to 3. However, if 1-2 is a zero of P(x), then the polynomial would have 4 sign changes, which is not possible. Therefore, 1-2 cannot be a zero of P(x).
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Please help this is he and I’m so confused
Answer: 5.25
Step-by-step explanation:
In the picture there is a smaller triangle inside a bigger triangle. You have to find the size it grows by dividing a side of the bigger triangle to the same side of the smaller triangle.
16.8/6.4 = 2.625
Then you find x by multiplying the adjacent side by the size it grows.
2*2.626 = x
2*2.626 = 5.25
Point W(-6, 7) is rotated 90° clockwise where is W
Check the picture below.
Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms?
An expression that shows the total area of five rooms is (3 × 13²) + (2 × 15²)
The correct answer is an option (A)
Let 'a' represents the side length of the square rooms measuring 13 ft each and 'b' represents the side length of the square rooms measuring 15 ft each.
We know that the formula for the area of a square is A = s²
where 's' is the side of a square.
Sides of three square rooms measure 13 feet each.
So, the area of the three rooms would be:
A₁ = 3 × a²
A₁ = 3 × 13²
And sides of two square rooms measure 15 feet each.,
So, the area of the two rooms would be:
A₂ = 2 × b²
A₂ = 2 × 15²
Total area of the five rooms A = A₁ + A₂
So, we get an expression:
A = 3 × 13² + 2 × 15²
A = 3 × 169 + 2 × 225
A = 957 ft²
Therefore the total area of the five rooms be 957 ft².
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The complete question is:
Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms?
a.(3 × 13^2) + (2 × 15^2)
b.(2 × 13^3) + (2 × 15^2)
c.(3 × 15^2) + (2 × 13^2)
d.(3 × 13^2) × (2 × 15^2)
What is the volume of a cylinder with a radius of 3 feet and a height of 4 feet? Use 3.14 for pi. Round to the nearest hundredth.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\pi (3)^2(4)\implies \stackrel{ \pi =3.14 }{V=113.04}[/tex]
In this caee there are no restricoions onb1b2, andbnso the zystern has the uniquex1=−40b1+16b2+9bj,x1=1b1−5b2−3b3+x1=5b2−2b2−bjfor all values ofb1,b2, andb3. Exercise set 1,6 7.−1x1+5x1=band using Theorm i.6. 2x1+2x2=b11.xk+x2=25x3+6x2=9 2. 4x1−5x3=−12x1−5x2=9the bri natue ike aviten 3.x1+3x2+x1=42x1+2x4+x1=−12x5+2x1+x4=4.4x3+3x2+2r5a 4 asind matrar fa tindu3xx+3xz+2xy=2xz+xn=5Q.x1−4x1=4x1+2x2+x2+x1L.B4=t1by=is.x+y+z=5 6. −x−2y−3z=0x+y−4z=10(y+x+4y+4z=7−4x+y+8=04.3x+7y+9z=4−ay−2x−4y−4tan 14. −x1+4x1+f1=x1+9x2+2x1=dx1+2r1=1r11b3=a1d2=1. Thue Iatsa Eneriaes.
It seems like the question is asking about a system of equations with no restrictions on the variables b1, b2, and b3. However, the question is filled with typos and formatting errors that make it difficult to understand the exact problem and provide an accurate answer. It would be best to ask the student to clarify the question and provide a properly formatted version of the problem before attempting to answer.
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pls help me
Let f(t) = 10 and g(t) = 65t. The distance, in miles, that a car is from a city can be modeled by f(t) + g(t), where t represents time, in hours. Riordan claims that the car is 150 miles from the city after 2 hours of driving, since (10 + 65) = 75(2) = 150. Decide if Riordan is correct. If he is correct, enter 150 below. If he is incorrect, enter the correct distance. miles
Answer: Using the given functions, we can model the distance, d(t), that the car is from the city as:
d(t) = f(t) + g(t) = 10 + 65t
So, after 2 hours of driving, the distance that the car has traveled from the city is:
d(2) = 10 + 65(2) = 10 + 130 = 140 miles
Therefore, Riordan is incorrect, and the correct distance the car is from the city after 2 hours of driving is 140 miles.
Step-by-step explanation:
A middle school basketball player makes a free throw with a probability of 0.6. Assuming each free throw is an independent event, what is the probability the player makes zero of their next three free throws? (A) 0.064 (B) 0.216 (C) 0.784 (D) 0.936 (E) None of these
A middle school basketball player makes a free throw with a probability of 0.6. Assuming each free throw is an independent event,the probability the player makes zero of their next three free throws is 0.064. The correct answer is A.
The probability that a middle school basketball player makes zero of their next three free throws can be calculated using the formula P(A) = P(A')ⁿ, where P(A) is the probability of the event occurring, P(A') is the probability of the event not occurring, and n is the number of trials.
In this case, P(A) is the probability of the player making zero free throws, P(A') is the probability of the player missing a free throw (1 - 0.6 = 0.4), and n is the number of free throws (3).
Using the formula, we can calculate the probability of the player making zero free throws as follows:
P(A) = P(A')ⁿ
P(A) = (0.4)³
P(A) = 0.064
Therefore, the correct answer is (A) 0.064.
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