The number of members in the tennis club at the beginning is 1500.
How to calculate the number?Let's call the original number of members "x". Since 80% of the members were male, we know that 0.8x members were male. Similarly, since 20% of the members were female, we know that 0.2x members were female.
Next, we can use the information about the number of members that left to find the new number of male and female members. We know that the number of male members decreased by 25%, so the new number of male members is 0.8x - 0.25(0.8x) = 0.8x - 0.2x = 0.6x.
Similarly, we know that the number of female members decreased by 50%, so the new number of female members is 0.2x - 0.5(0.2x)
= 0.2x - 0.1x
= 0.1x.
Now we know that the number of members left is 450, so we can set up the equation:
x = 0.6x + 0.1x + 450
Solving for x, we get:
x = 450 / (1 - 0.7) = 450 / 0.3 = 1500
Therefore, the number of members was 1500.
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use vieta's therom to solve each problem. the difference of two solutions of x^2-17x+c=0 is 1. find c
Using Vieta's Theorem the value of c = 72.
What is the Vieta Theorem?Suppose we have a quadratic equation, in the following format:
ax² + bx + c, were a, b, and c are constant.
The roots are p and q.
As, The Theorem states that:
p + q= -b/a
pq= c/a
We have given the polynomial x²-17x+c=0
So, a= 1, b= -17
Since the difference of the solutions is 1, we have that:
p -q= 1
p = 1+ q
Now, using p + q= -b/a
1 + q + q= -(-17)/1
2q +1 = 17
2q= 16
q= 16/2
q= 8
and, p = 1+ q= 9
Again pq = c/a
8 x 9 = c/1
c= 72
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Determine whether the following statement is always, sometimes, or never true
The statement is always true that if |a| > 0, then the graph of f(x) = a∛x rises as x increases. The solution is obtained by graphing the function.
What is graphing of a function?
Drawing the graph of an applicable function is the process of graphing a function. While graphing simple functions like direct, quadratic,etc. is fairly easy, complex functions like rational, logarithmic,etc. bear some complexity and an understanding of certain fine ideas. Every point on the curve will satisfy the function equation if the curve represents the function.
We are given a function f(x) = a∛x.
We know that |a| will always be greater than or equal to 0 irrespective of "a" being positive or negative.
If |a| > 0, then the graph of f(x) = a∛x is a vertical stretch of the graph of g(x) = ∛x.
The graph for g(x) = ∛x is shown below.
Since, g(x) = ∛x rises as x increases, the same must be true for f(x) = a∛x.
Hence, if |a| > 0, then the graph of f(x) = a∛x rises as x increases.
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A train does a journey without stopping in 8 hours. if it had traveled 5 km an hour faster, it would have done the journey in 6 hours 40 min. what is its slower speed?
The train which is travelled same distance with two different speeds, the slower speed of a train is 25.075 km/hr
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
Given that,
A train does a journey without stopping in 8 hours
it had traveled 5 km/hr faster , Time taken = 6 hours 40 min = 6.67hr
slower speed = ?
Suppose total distance covered = X
⇒ X = V × 8 _____(i)
If he travelled 5 km/hr faster
⇒ X = (V+5) × 6.67 _____(ii)
For i and ii distance is same so we can equate both the values,
⇒ V × 8 = (V+5) × 6.67
⇒ 8V = 6.67V + 33.35
⇒ 1.33V = 33.35
⇒ V = 25.075
Hence, the slower speed is 25.075 km/hr
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SURVEYING How far is it across the pond?
On solving the provided question, we can say that to across the pond he ha to cover equation 2x +3x = 325 - 156 + 1 => x = 34cm/sec
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
here,
to across the pond
we can form an equation 2x +3x = 325 - 156 + 1
5x = 170
x = 34
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Given: ABCD is a parallelogram, AC is perpendicular to BD and AC is congruent to BD
Prove: ABCD is a square.
It is a rhombus since the parallelogram's sides are all equal. ABCD is a square because the diagonals of the rhombus ABCD are equal.
what is parallelogram ?A simple quadrilateral with two sets of parallel sides is known as a parallelogram in Euclidean geometry. Both sets of opposite sides are parallel and equal in a particular type of quadrilateral known as a parallelogram. Parallelograms come in four varieties, three of which are exclusive. The four different shapes are rhombuses, parallelograms, squares, and rectangles. A quadrilateral is a parallelogram if it has two sets of parallel sides. In a parallelogram, the cross-sectional lengths of the opposing sides and angles are equal. The inner angles add additional angles to the horizontal line on the same side. There are a total of 360 interior angles.
Given:
The diagonals AC and BD in the parallelogram ABCD are equal and perpendicular to one another.
∠DOC=∠COB=∠BOA=∠AOD=90
We are aware that a parallelogram's diagonals are divided in half.
OA=OC=OB=OD, thus...
(1) In OA=OA [Common side] in AOD&AOB, AOD=BOA=90
[Given]
[from (1)] OD=OB
Consequently, AODAOB [By SAS Rule of Congruency]
Thus, AD = AB.
Thus, AB=BC=CD=DA.
(2) ABCD is a parallelogram, therefore
It is a rhombus since the parallelogram's sides are all equal. ABCD is a square because the diagonals of the rhombus ABCD are equal.
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An ice chest contains 4 cans of apple juice, 8 cans of
grape juice, 8 cans of orange juice, and 5 cans of mango
juice. Suppose that you reach into the container and
randomly select three cans in succession. Find the
probability of selecting three cans of mango juice.
The probability of selecting from the ice chest three cans of
mango juice is.
(Type an integer or a simplified fraction.)
The probability of selecting 3 cans (mango juice) is found as 1/230.
Define the term probability?The subject of a random event is covered in the mathematical field of probability. For instance, if a coin is flung into the air, it could land on its Head or Tail.For the stated question:
Apple juice : 4 cansgrape juice : 8 cansorange juice : 8 cans mango juice : 5 cansTotal cans : 25 cansAs the can had been taken without replacement.
Thus,
Probability that 1st can is of mango = Total mango cans / Total cans
= 5 / 25
= 1/5
Probability that 2nd can is of mango = Mango cans left/ Total left cans
= 4 / 24
= 1/6
Probability that 3rd can is of mango = Total mango cans / Total cans
= 3 / 23
Thus,
probability of selecting 3 cans (mango juice) = 1/5 * 1/6 * 3/ 23
= 3/690
= 1 /230
Therefore, the probability of selecting 3 cans (mango juice) is found as 1/230.
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how many is 10 +10
and how many is 1+1
Answer: 10+ 10 = 20
1+1= 2
Step-by-step explanation:
Leila has a rectangle poster. The poster is 1.8 meters long and 1.25 meters wide. What is the area of the poster in square centimeters?
Answer:
22500 square centimeters
Step-by-step explanation:
1.8 meters= 180 cm
1.25 meters= 125 cm
180 times 125 = 22500
Complete the statements below about the area of the red rectangle.
Area of a rectangle equals Length ×Breadth The rectangle's size in red is equal to 0.5833 square units .
What is a formula of area of rectangle?The size of a rectangle. A = l × b. Once the length and breadth are known for any rectangle, the area may be determined. The area of the rectangle is calculated as a square-unit dimension by multiplying length and width.
length (a) = 7/8
Width (b) = 2/3
Area (A) = 0.5833 square units
P = 3.0833 for the perimeter.
Parallel (d) equals 1.1
A shape's surface area is measured by its area. By multiplying the length and breadth of a rectangle or square, you can get its area. Area A is equal to x times y. Side x Side equals the area of a square. So, Side2 square units = the area of the square. therefore a square's perimeter is equal to four units of its sides.
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I am the largest 5 digit even number that you can make that has a 3 in the thousands place
what number am i?
Answer:
Largest even number is 99998
So when its thousands place is to be 3 then the number is 93998.
Step-by-step explanation.
i think this is it
The Kim family must drive 5 hours to reach their destination. They drive 2 4/8 hours before stopping for the first time. Then they drive 1 1/3 hours before stopping again. How many more hours will it take for the Kim family to reach their destination. Show all of your work.
The number of hours that it will take more for the Kim family to reach their destination would be = 1.2 hours
How to calculate the number of hours?The total number of hours it will take for the Kim family to travel = 5 hours.
The first drive = 2 4/8 hours
The second drive = 1 ⅓ hours
The number of hours that they need to travel more will be = X
That is 5 = X + 2 4/8 + 1⅓
Make X the subject of formula:
X = 5- ( 2 4/8 + 1⅓)
X = 5 - ( 2.5 + 1.3)
X = 5 - ( 3.8)
X = 5 - 3.8
X = 1.2 hours.
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Find an equation in vertex form for the parabola with focus(1,4)
and
directrix x=5
.
The parabola equation is x = (-1/2)y2 - 4y - 1.5 when the focus and directrix are (1, 4) and 5 respectively.
what is equation ?An equation is a mathematical formula that joins two statements and uses the equal symbol (=) to indicate equivalence. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign divides the variables 3x + 5 and 14. The relationship between the two sentences on either side of a letter is explained by a mathematical formula. There is frequently only one variable, which also serves as the symbol. for instance, 2x - 4 = 2.
given
The equation's fundamental form is:
4p(x-h) = (y-k) (y-k)
The vertex is at 2 (h,k).
P is the separation between the vertex and the directrix or focus. Between the two is where the vertex is located.
Directrix: x=2, focus: (1, -4).
Vertex at the perpendicular midpoint of (1.5, -4)
Parabola opens left because it faces the focus and moves away from the directrix. This implies that p will be negative. P would be positive if the parabola opened to the right. p = -0.5
Putting this together:
4(-0.5)(x-1.5) = (y-(-4))2
-2(x-1.5) = (y+4)2
-2(x-1.5) = y2 + 8y + 16
x - 1.5 = (-1/2)(y2 + 8y + 16)
x = (-1/2)y2 - 4y - 8 + 1.5
The parabola equation is x = (-1/2)y2 - 4y - 1.5 when the focus and directrix are (1, 4) and 5 respectively.
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Graph the first two inequalities you solved in question 2
Change the inequality symbol to “=”. Graph the equation. Use a dashed line for < or >. Use a solid line for ≤ or ≥.
How do you visualize inequalities?To graph an inequality, consider the,, >, or sign to be a = sign and graph the equation. If the inequality is or >, draw a dotted line to represent the equation. Graph the equation as a solid line if the inequality is or.
-5x=15
-5x-3.5
5(-5x/5-3.5/5)
5(-x-3)
And second one is
9>13+2x
92x+13
9+(-13)> (2x+13) + (-13)
9-132x13-13
-4 > 2x
2x< -4
2x/2<-4/2
X<-2
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Consider the system.
6x-3y = 66
x + 3y = -10
Complete the description for three different substitution methods that can be used to solve the system.
Solve the second equation for x (x = - 3y) and then substitute the value into the first equation.
Solve the first equation for y (y = 2x - ) and then substitute that value into the second equation.
Solve either equation for 3y (3y = - x or 3y = 6x - ) and then substitute that value into the other equation.
The points of solution that are obtained for the system of linear equations 6x - 3y = 66 and x + 3y = -10 are (8,6).
The substitution methods given are incomplete and incorrect.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The system of linear equations are -
6x - 3y = 66....(1)
x + 3y = -10....(2)
Simplify the equation (1) and (2) by adding -
6x + x - 3y + 3y = 66 - 10
7x = 56
x = 8
Substituting the value of x = 8 in equation (1) -
6x - 3y = 66
6(8) - 3y = 66
48 - 3y = 66
-3y = 66 - 48
-3y = 18
y = -6
Therefore, the final value is obtained as (8,6).
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Question 100p+brain
What is the value of x?
Enter your answer in the box.
x =
2x-4 & 5y
Because all sides are congruent, it is an equilateral triangle. You can see this based on the lines on the sides of the triangle. Because of this, all angles are equal to each other. In a triangle, the sum of angles is 180 degrees with each angle being equal to 60 degrees.
Because both angles are equal, you get. Since you're solving for x, set 5y equal to 60 then solve for x.
5y = 2x - 4
60 = 2x - 4
60 +4 = 2x
64 = 2x
32 = x
x = 32
To confirm if this is correct, plug in 32 for x in 2x -4
2(32)-4 = 64 -4 = 60 degrees
x = 32
Answer: x=45?
Step-by-step explanation:45*2=90-4=86
A physiologist believes he has discovered a new steroid hormone that can control the blood glucose in mammals. In an experiment he injects laboratory rats with a small amount of this steroid hormone and, after a suitable waiting period measures the blood glucose level of the rats. In his twelve experimental rats he obtains the following levels of blood glucose {35,36,21,33,34,35,33,35,37,36,38,35}. From previous studies of thousands of normal, un-manipulated rats he knows that the mean (mu) blood glucose level in this species of rat (his laboratory population) is 32 and that the standard deviation is 1.15. Evaluate the hypothesis that this new steroid hormone decreases blood glucose levels. Use an alpha-level of 0.05 for this analysis.
Calculate the obtained statistic:
Answer:
Step-by-step explanation:
John has a part-time job delivering pizza. He earns a base salary of $7.15 per hour and his average
tip for delivering pizza is 18% of the price of the pizza. How much will he earn if he delivers $452
worth of pizza during a 6-hour shift?
Which of the following is the correct solution to the linear inequality shown
below?
y<2/3x+1
-
The line of the inequality will be dotted and the origin is the solution to the inequality. Hence option A is the correct option.
What is inequality?Inequalities are mathematical expressions in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is replaced by a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given the equation of the inequality is y <2/3 x +1.
The inequality contains a less than symbol.
If an inequality contains less than or equal/ greater than or equal sign, then the line of the inequality will be solid.
If an inequality contains less than or greater than, then the line of the inequality will be dotted.
The line of the given inequality will be dotted.
Now putting x = 0, y = 0 in the inequality:
0< (2/3×0) + 1
0 < 1 true.
Thus (0,0) is a solution to the inequality.
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Anything helps thanks!
Answer:
it's B
Step-by-step explanation:
9wcbux2v9wcuuv9w9uve2cu92cveu02x0v2xuv2uh wce
Find dy/dx if y = e^sin√x
dy/dx = (1/2)e^(sin√x) * cos√x , when y = e^sin√x
To find dy/dx, we can use the chain rule. The chain rule states that if y = f(g(x)), then dy/dx = dy/dg × dg/dx. In this case, we have:
y = e^(sin√x)So, f(x) = e^x and g(x) = sin√x. Therefore, dy/dx = dy/dg × dg/dx = e^(sin√x) × (cos√x) × (1/2√x)Simplifying, we get: dy/dx = (1/2)e^(sin√x) × (cos√x) × x^(-1/2)To learn more about Differentiation,
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1.3 X 2.1 = Explain your answer.
2.73
1.3x2.1=2.73
1.3
x2.1
13
+26
2.73
Answer:
To multiply 1.3 by 2.1, we need to use the distributive property of multiplication, which states that:
a × (b + c) = a × b + a × c
Using this property, we can break down 2.1 as the sum of 2 and 0.1:
1.3 × 2.1 = 1.3 × (2 + 0.1)
= 1.3 × 2 + 1.3 × 0.1
= 2.6 + 0.13
= 2.73
Therefore, 1.3 multiplied by 2.1 equals 2.73.
You get $50 to spend at an arcade. You buy food with $20
and want to use the rest for games. Each game is $2. How
many games can you play?
Answer:
15
Step-by-step explanation:
You start with $50, and if $20 is spent on food then you have 50-20= $30 remaining for games.
Games are $2 each, and you have $30 for games, so we can divide the amount of money you have by the amount of money required for each game to find out how many games you can play:
30/2 = 15
Therefore after spending $20 on food, you are able to play 15 games with the remaining money.
what is the vertex form of fx- { x }^{ 2 } +6x+5
Answer:
The answer is f(x)=(x+3)2−4 .
Step-by-step explanation:
To convert to vertex form, you must complete the square. We add k to complete the square inside the brackets, but whatever we add inside, we must subtract outside the brackets to keep the equation balanced.
3. The towers used by radio
broadcasters are tall and slender.
Using the term centre of gravity,
describe three ways you could
make a radio tower more stable
without decreasing its height.
These towers are tall, slender structures, and they work best with broad-range signals, including broadcast radio and similar outputs.
what are the towers used by ratio?
Tower Ratio means the quotient (multiplied by 100 to express such quotient as a percentage) obtained by dividing the Average Closing Price by the Starting Date Price.Lattice Towers. Lattice towers are freestanding and segmentally designed with rectangular or triangular base steel lattices. ...Guyed Towers. ...Monopole Towers. ...Camouflage Towers. ...Self-Support Towers. ...Mobile Cell Towers.A monopole tower is a simple single pole. Its elementary design reduces visual impact and is relatively simple to build, which is why this tower is favored by tower developers. A lattice tower is a freestanding vertical tower designed with rectangular or triangular bases.To learn more about radio refers to:
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15 and 3/4 divided by 7 as a fraction
15 and 3/4 divided by 7 as a fraction, the value is 2 1/4.
What is a fraction?A topic in mathematics that involves an expression having two parts called numerator and denominator is known as fraction. Types of fraction are mixed fraction, improper fraction and a proper fraction.
A mixed fraction is a type of fraction which is expressed by a whole number and a fractional part.
Considering the expression in the given question 15 and 3/4 divided by 7 as a fraction, we have;
(15 3/4) / 7 = (63/ 4)/ 7
= (63/ 4) * 1/ 7
= 63/28
= 2 1/4
So that, 15 and 3/4 divided by 7 as a fraction is 2 1/4.
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PLEASE HELP!!
Thirteen coins add up to $1.00. If the coins are all nickels and dimes, how many of each are there?
The number of Nickels and Dimes out of the 13 coins are respectively; 4 Nickels and 9 Dimes
How to solve Linear Equation Problems?We are told that we have 13 coins and they are all nickels and dimes and they sum up to $1.00.
Let N represent nickels.
Let D represent dimes
Thus;
N + D = 13
D = 13 - N
From conversion tables of nickels and dime to dollars, we can generate the equation;
$0.05N + $0.10D = $1.00
Plug in 13 - N for D to get;
$0.05N + $0.10(13 - N) = $1.00
$0.05N + $1.30 - $0.10N = $1.10
0.20 = 0.05N
N = 0.20/0.05
N = 4
D = 13 - 4
D = 9
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The area of the circular base of a cone is 25π cm², and the slant height of the cone is four times the radius of the cone.
What is the approximate lateral area of the cone?
Use π≈3.14.
Enter your answer rounded to the nearest whole number
The approximate lateral area of the cone is solved to be 314 cm²
How to find the approximate lateral area of the coneFrom the question we get that:
The area of the circular base of a cone is 25π cm²
25π cm² = πr²
the slant height of the cone is four times the radius of the cone
L = 4r
Lateral area of the cone
= πrl square units.
solving for r
25π cm² = πr²
r² = 25
r = 5
solving for the lateral area of the cone
= πrl square units.
= π * 5 * 4r
= π * 5 * 4 * 5
= 100π
= 100 * 3.14
= 314 cm²
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Solve
Plsss helpppppp
Answer:
∠L = 51°
Hope this helps!
Step-by-step explanation:
Alternate exterior angles theorem
Can anyone tell me What is 95% of 75
Answer:
Also could you mark my answer as brainliest? It helps and doesnt hurt
A commercial popcorn machine makes 12 pounds of popcorn, which can fill __ 4-ounce bags.
A) 24
B) 36
C) 40
D) 48
Show work please
Answer: 48
Step-by-step explanation: 1 pound is 16 ounces therefore each pound will have 4 bags since 16 divided by 4 is 4, 12 times 4 is 48