The tennis player must consecutively land 10 more first serves in bounds to raise their success rate from 62.5% to 70%.
First, let's define the variables:
x = number of additional successful serves needed
40 + x = total number of serves after additional successful serves
25 + x = total number of successful serves after additional successful serves
We set up the equation with the desired success rate of 70%:
(25 + x) / (40 + x) = 0.70
To solve this equation, follow these steps:
Multiply both sides by (40 + x):
25 + x = 0.70 * (40 + x)
Distribute 0.70 on the right side:
25 + x = 28 + 0.70x
Isolate the variable x by subtracting 0.70x from both sides:
25 + x - 0.70x = 28
Combine like terms:
0.30x = 3
Solve for x by dividing both sides by 0.30:
x = 10
Thus, the tennis player must land 10 more consecutive first serves in bounds to increase her success rate to 70%.
Which ordered pair is the vertex of y = [x - 3]+ 2?
A.(2, –3)
B.(–3, 2)
C.(3, 2)
D.(2, 3)
What is the number of social security credits a worker needs to earn over his or her working lifetime to collect Social security benefits?
This is incredibly frustrating. PLEASE HELP ME
The graph of y=|x| is transformed as shown in the graph below. Which equation represents the transformed function?
we have that
the original function [tex]y=\left|x\right|[/tex] has the vertex at point [tex](0,0)[/tex]
The transformed function has the vertex at point [tex](-3,-2)[/tex]
so
the rule of the translation is equal to
[tex](x,y)------> (x-3,y-2)[/tex]
That means
The translation is [tex]3[/tex] units to the left and [tex]2[/tex] units down
therefore
the answer is
the transformed function is [tex]y=\left|x+3\right|-2[/tex]
Amy has 5 yards of border to put around a garden. She uses all the border to make four sections that are the same length. Which expession does not equal the length of one these sections in yards?
Answer:
4 ÷ 5
Step-by-step explanation: becuz i said so
Chloe puts 4 soaps and two bottles of lotion in each gift basket. She has 127 soaps and 85 bottles of lotion. How many gift baskets can Chloe complete?
kaelyn has 14 coins that have a vaule of $ 1.20. she only has dimes and nickles. how many nickles does kaely have
Kaelyn has 14 coins made of dimes and nickels valued at $1.20. By setting up a system of equations and solving for the number of nickels, we determine that she has 4 nickels.
The student is asking a mathematical question involving coin values and combinations. When working with combinations of coins, we typically use a system of equations or algebraic expressions. Kaelyn has 14 coins consisting of dimes and nickels with a total value of $1.20. To systematize, let's let D be the number of dimes and N be the number of nickels. The following equations represent the relationships between the coins:
D + N = 14 (since there are 14 coins in total)0.10D + 0.05N = 1.20 (representing the total value of the coins in dollars)Multiply the second equation by 100 to deal with whole numbers:
10D + 5N = 120From the first equation, we can express D as:
D = 14 - NSubstitute this into the second equation:
10(14 - N) + 5N = 120140 - 10N + 5N = 120-5N = -20N = 4So, Kaelyn has 4 nickels and the rest are dimes.
What is the area of sector GPH?
The area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\).[/tex]
To find the area of sector GPH, we use the formula for the area of a sector of a circle, which is given by [tex]\(\frac{\theta}{360^\circ} \times \pi r^2\)[/tex], where [tex]\(\theta\)[/tex] is the central angle of the sector in degrees, and [tex]\(r\)[/tex] is the radius of the circle.
Given that the central angle of sector GPH is [tex]\(90^\circ\) (or \(\frac{\pi}{2}\)[/tex] radians, since[tex]\(180^\circ\) is \(\pi\) radians)[/tex], and the radius [tex]\(r\)[/tex] is unspecified, we can express the area of the sector in terms of [tex]\(r\).[/tex]
Using the formula for the area of a sector:
[tex]\[ \text{Area of sector GPH} = \frac{\theta}{360^\circ} \times \pi r^2 \][/tex]
Substituting [tex]\(\theta = 90^\circ\):[/tex]
[tex]\[ \text{Area of sector GPH} = \frac{90^\circ}{360^\circ} \times \pi r^2 \][/tex]
Simplifying the fraction:
[tex]\[ \text{Area of sector GPH} = \frac{1}{4} \times \pi r^2 \][/tex]
So, the area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\)[/tex], which is one-fourth of the area of the entire circle. This makes sense because the sector represents a quarter of the circle's area due to its [tex]\(90^\circ\)[/tex] central angle.
ln(x+2)-ln(4x+3)=ln(1/2*x)
A right triangle has one side, s, and a hypotenuse of 12 meters. Find the area of the triangle as a function of s.
A) A(s) = 2s
144 - s2
B) A(s) = s
144 - s2
C) A(s) = 2s
12 - s2
D) A(s) = 12s
144 - s2
10)
The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)?
A) 12 ft
B) 13 ft
C) 14 ft
D) 15 ft
Answer: A(s) = [tex]\frac{s\sqrt{144-s^{2} } }{2}[/tex] ; 10) c) 14ft
Step-by-step explanation: Area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]
where:
b is base of a triangle
h is height of a triangle
For this right triangle, it is known one side, s, and hypotenuse, 12. To determine the other side, we use Pythagoras Theorem:
hypotenuse² = side² + side²
[tex]12^{2} = s^{2} + x^{2}[/tex]
[tex]x^{2} = 12^{2} - s^{2}[/tex]
[tex]x^{2} = 144 - s^{2}[/tex]
x = [tex]\sqrt{144 - s^{2} }[/tex]
To determine the Area of the right triangle as function of s:
A = [tex]\frac{b.h}{2}[/tex]
A = [tex]\frac{1}{2}[/tex](s.x)
A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])
Therefore, the area of the right triangle is:
A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])
The ladder and the wall form a right triangle. The height of it is 13 ft, the base is 5ft and the hypotenuse is the length of the ladder. So, to find the minimum length, use Pythagoras Theorem:
hypotenuse² = side² + side²
h² = 13² + 5²
h² = 169 + 25
h = [tex]\sqrt{194}[/tex]
h = 14
The minimum length the ladder has to have to reach the top is 14 ft.
which transformations are needed to change the parent some function to the sine function below?
Factor \2x^2-11x+5=0
The quadratic equation [tex]2x^2[/tex]-11x+5=0 is factored into (2x - 1)(x - 5), and it has solutions x = 0.5 and x = 5.
Explanation:The question asks us to factor the quadratic equation[tex]2x^2[/tex]-11x+5=0. To do this, we need to find two numbers that multiply to give ac (where a is the coefficient of x^2 and c is the constant term) and add to give b (the coefficient of x). Here, ac is (2)(5)=10, and b is -11. The two numbers that satisfy this are -10 and -1 because -10 * -1 = 10 and -10 + -1 = -11.
We rewrite the middle term using these two numbers and then group the terms to factor by grouping:
[tex]2x^2[/tex]- 10x - x + 5 = 0The factored form of the quadratic equation is (2x - 1)(x - 5). Therefore, the solutions to the equation are x = 0.5 and x = 5, found by setting each factor equal to zero.
what is the product of r and t if R equals 5.33 and T equals 0.5
Solve the equation 3x+5y=4
for y
Answer:
y = (4 -3x)/5
Step-by-step explanation:
Find the terms containing y. If they are all on one side of the equation (it is), then identify the terms not containing y. Subtract those. Then, divide by the coefficient of y.
3x +5y = 4
5y = 4 - 3x . . . . . non-y term subtracted
y = (4 -3x)/5 . . . . divide by the coefficient of y
_____
If you like, you can rearrange this to slope-intercept form:
... y = -3/5x +4/5
Help ASAP PLEASE!!! match the term with the appropriate definition.
Ben buys a car for $50,000. The value of the car decreases at a rate of 4% per year. How much will the car be worth in 3 years? A. $48,000 B. $44,237 C. $45,082 D. $43,270
The circle belowis centered at the point (-2 ,1) and has a radiusof length 3
Answer:
Option A, (x + 2)² + (y - 1) = 9
Explanation:
The equation form of a circle is (x - h)² + (y - k)² = r², where the center is ordered pair (h, k) and r represents the radius.
From the given information, the center is point (-2, 1) and the radius (r) is 3 units. With this, we can plug the information in and simplify:
(x - (-2))² + (y - (1))² = (3)²
(x + 2)² + (y - 1)² = 9
The equation for the given circle is (x + 2)² + (y - 1)² = 9
function that has the same domain as y=2√x
Answer:
The answer is A. y = √2x
Step-by-step explanation:
Two thirds of the families in smithville own their own homes. The total number of home owning families there is 480. How many families live in smithville?
To win at lotto in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50). the order in which the selections is made does not matter. how many different selections are possible?
We have been given that the order doesn't matter in the selection procedure. Hence, the case is of combination.
The formula for the combination is given by
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Now, in order to win at lotto, one must correctly select 6 numbers from a collection of 50 numbers. Thus, the required ways should be
[tex]^{50}C_6[/tex]
Using the above formula, the number of different selections are
[tex]^{50}C_6=\frac{50!}{6!(50-6)!}\\ \\ =\frac{50!}{6!44!}\\ \\ =\frac{44!\times 45\times 46\times 47 \times 48\times 49\times 50}{6!44!}\\ \\ =15890700[/tex]
Therefore, 15890700 different selections are possible.
Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.
What is the equivalent of pi over 3 radians in degrees?
What is the vertex of the quadratic function f(x) = (x - 8)(x - 2)
Answer: (5, -9)
What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?
hey can you please help me posted picture of question
Root plot for : y = 3x2+7x+2
Axis of Symmetry (dashed) {x}={-1.17}
Vertex at {x,y} = {-1.17,-2.08}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.00, 0.00}
Root 2 at {x,y} = {-0.33, 0.00}
on a game show that are 10 keys in the bag and three of the key start a car and contest in randomly choosing the key it doesn't not start the car she returned to the bag the host mixed up the back she randomly selects another key this key does not start the car either what is the probability of this no start no start outcome
HELP
______________________
Answer:
The answer is the third option/choice.
Which of the following functions are their own inverses? Select all that apply.
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y
d. d(p) = 1/x^2
Answer:
a,b and c.
Step-by-step explanation:
We have to find the the functions that are their own inverses.
a.t(p)=p
Then the inverse function of given function is
[tex]p=t^{-1}(p)[/tex]
Therefore, the given function is inverse function of itself.
Hence, option a is true.
b.y(j)=[tex]-\frac{1}{j}
Let y(j)=y then we get
[tex]y=-\frac{1}{j}[/tex]
[tex]j=-\frac{1}{y}[/tex]
[tex]j=-\frac{1}{y(j)}[/tex]
[tex]j=-\frac{1}{\frac{-1}{j}}[/tex]
[tex]j=j[/tex]
Hence, the function is inverse of itself.Therefore, option b is true.
c.[tex]w(y)=-\frac{2}{y}[/tex]
Suppose that w(y)=w
Then [tex]w=-\frac{2}{y}[/tex]
[tex]y=-\frac{2}{w}[/tex]
[tex]w(y)=-\frac{2}{-\frac{2}{w}}[/tex]
[tex]w(y)=w[/tex]
[tex]w(y)=-\frac{2}{y}[/tex]
Hence, the function is inverse function of itself.Therefore, option c is true.
d.[tex]d(p)=\frac{1}{x^2}[/tex]
Let d(p)=d
If we replace [tex]\frac{1}{x^2}by p then we get
[tex]d=\frac{1}{x^2}[/tex]
[tex]x^2=\frac{1}{d}[/tex]
[tex]x=\sqrt{\frac{1}{d}}[/tex]
[tex]x=\sqrt{\frac{1}{d(p)}[/tex]
Hence, the function is not self inverse function.Therefore, option d is false.
Given: KLMN is a trapezoid, KF =10 MF ║ LK AKLMF = AFMN Find: KN
In a trapezoid with parallel sides, if a pair of opposite sides are equal, then the other pair of opposite sides are also equal. Therefore, in the given trapezoid KLMN, KN is equal to AN + 10.
Explanation:In the given trapezoid KLMN, the sides KF and LM are parallel. We are given that KF = 10 and AFMN = AKLMF. We need to find KN.
Since KF and LM are parallel, KF = LM. Therefore, LM = 10.
Since AFMN = AKLMF, we can say that AN = KL. So, AN + LM = KL + KF. Substituting the given values, we get AN + 10 = KL + 10. Therefore, AN = KL.
Hence, KN = KL + LM = AN + LM = AN + 10.
Therefore, KN = AN + 10.
PLz help!
Write the equation of the line that passes through (3, −2) and has a slope of 4 in point-slope form. (2 points)
1 y + 2 = 4(x − 3)
2 y − 3 = 4(x + 2)
3 x − 3 = 4(y + 2)
4 x + 2 = 4(y − 3)
Q # 15 in the diagrams a || b a. Use the fiagrama o answer the question(diagrama not to scale.)