By setting the given height (6 feet) in the height equation and using the quadratic formula to solve for time 't', we get two solutions. Since the ball reaches 6 feet twice in its ascension and decension, the latter value of t = 3.79 seconds would be the time it is caught.
Explanation:The question is regarding the time at which a baseball, hit with an initial upward velocity and caught at 6 feet above the ground, is caught. Firstly, input the given height of 6 feet into the height equation h= -16t^2 + 70t + 4 and solve for
t
. Based on the quadratic formula, we receive two solutions: t = 3.79 s and t = 0.54 s. Since the ball has two points at which it reaches the height of 6 feet during its trajectory - once while going up and once while coming down - the time when it is caught would be the larger value,
t = 3.79 s
. Therefore, approximately 3.79 seconds after being hit, the ball is caught.
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Given that x has a Poisson distribution with
mu
μ
equals
=
13
13, what is the probability that x
equals
=
5
5?
P(
5
5)
almost equals
≈
0.9930
0.9930 (Round to four decimal places as needed.)
You have a 20-foot ladder that you are using as you paint your house. You place the ladder so that it forms an angle of 30 at the point of contact between the ladder and the ground. How high will the top of the ladder be above the ground
Answer:
The Ladder is 10 ft high.
Step-by-step explanation
According to the question we have a 20 ft ladder inclined against a wall at a 30° angle, and are asked to find how high the top of the ladder is from the ground. I have added a visual representation to help you better understand the situation. As you can see we need to solve for x. Since we are given one angle and the hypotenuse we can solve for x using the SIN operator.
[tex]sin(a) = \frac{opposite}{hypotenuse}[/tex]
Since we have the angle (a) and the hypotenuse we can just plug the information into the sin equation and solve for the opposite (x).
[tex]sin(30) = \frac{x}{20ft}[/tex]
[tex]sin(30)*20ft = x[/tex]
[tex]0.5*20ft = x[/tex]
[tex]10ft = x[/tex]
So now we can see that the height of the top of the ladder to the ground is 10 ft
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The total interest paid on a 3-year loan at 9% interest compounded monthly is $1505.82 determine the monthly payment for the loan.
EASY 5 POINTS!! Which expression gives the correct volume of the figure?
Answer:
(3×2×1)+(3×1×1)
Step-by-step explanation:
AS you can se ein the figure, the figure is not a solid full rectangula prism, it is made out of two prisms the first one is the 3x2x1 rectangular prism, and the second is the 3x1x1 square prism, so by adding the volume of those two you can figure out the volume of the whole figure that is why the answer to the problem is (3×2×1)+(3×1×1)
If it takes 0.20 dollars to buy a mexican peso and 0.60 dollars to buy a brazilian real, then it takes _____ pesos to buy one brazilian real.
It will takes 3 mexican pesos to buy one brazilian real .
According to the given condition
It takes 0.20 dollars to buy a mexican peso and 0.60 dollars to buy a brazilian real,
We have to determine that it takes how many mexican pesos to buy one brazilian real.
This question can be solved by applying the principles of unitary method
One peso will be bought in $ 0.20
One real will be bought in $ 0.60
1 dollar is equivalent to
[tex]\rm 1 \; dollar = \dfrac{1}{0.2} peso \\\\\rm 1 \; dollar = \dfrac{1}{0.6 } \; real[/tex]
[tex]\rm 1/0.2\; peso = 1/0.6 \; real \\1 \; real = 0.6/0.2 = 3 \; peso[/tex]
So it will take 3 pesos to buy one real
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The CEO of a corporation has $10,000 to give as bonuses. The amount of each employee receives depends on how many employees receive a bonus. This can be modeled as
y = 10000/x
What example is this variation?
The given model of the equation y = 10000/x represents inversely proportional variation.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.
The model of the equation is given in the question, as follows:
y = 10000/x
A corporation's CEO has $10,000 available for bonuses. The amount each employee earns is determined by the number of employees that receive a bonus.
We can see that the given equation characterizes inversely proportional variation.
Hence, this variation is an example of inversely proportional.
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Find x. Round your answer to the nearest tenth of a degree.
Answer: [tex]x=49.6^{\circ}[/tex]
Step-by-step explanation:
In the given figure , we have right triangle with hypotenuse 21 units and the side opposite to angle x is 16 units.
According to the trigonometry,
[tex]\sin \theta = \dfrac{\text{side opposite of }\theta}{\text{Hypotenuse}}[/tex]
So for , the given figure , we have
[tex]\sin x = \dfrac{16}{21}\\\\\Rightarrow\ \sin x\approx0.7619\\\\\Rightarrow\ x=\sin^{-1}(0.7619)=0.8662\text{ radian}[/tex] (using sine calculation)
Convert radian into degrees , we have
[tex]x=0.8662\times\dfrac{180^{\circ}}{\pi}\\\\=0.8662\times\dfrac{180^{\circ}}{3.14159}=49.6319852107\approx49.6^{\circ}[/tex] [Round to the nearest tenth.]
Hence, [tex]x=49.6^{\circ}[/tex]
In the given right triangle, x = 49.6°
Missing angles of right trianglesThe triangle shown is a right triangle
The angle, θ = x
The opposite = 16
The hypotenuse = 21
Using the formula:
[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]
Substitute opposite = 16, hypotenuse = 21, and θ = x into the formula above to solve for x
[tex]sin x = \frac{16}{21} \\\\sin x = 0.7619\\\\x = sin^{-1}0.7619\\\\x=49.6^0[/tex]
Therefore, in the given right triangle, x = 49.6°
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A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.
What are the measures of the angles in triangle ABC?
Answer:
90, 74, 16 degrees
Step-by-step explanation:
Given that a right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.
We find that
AC square + BC square = AC square
[tex]7^2 +24^2 =625 = 25^2[/tex]
So angle C = 90 degrees.
sin A = 24/25
So A = 74 degrees and B = 16 degrees
h=7 + 29t-16t^2 find all values of t for which the balls height is 19ft
g(x) = x2 + 2, find g(3).
Answer:
Plug in 3 for x on the right side
3^2+2,
3 squared equals 9 plus 2 equals 11
Final answer: 11
Step-by-step explanation:
.
Which pairs of triangles are similar? Check all that apply.
Answer:
option (2) and (5) are correct.
ΔABC ≅ ΔJLK
ΔDEF ≅ ΔGHI
Step-by-step explanation:
Given four right angled triangle with measure of sides.
We have to check for the pairs of triangle to be similar.
Two triangles are said to be similar if their corresponding angles are equal or their corresponding sides are same ratio.
Consider, ΔABC and ΔJLK.
∠C = ∠L = 90° (given)
Also ratio of corresponding sides are same ratio, that is
[tex]\frac{AC}{LJ}=\frac{14}{7}=\frac{2}{1}[/tex]
Also, [tex]\frac{CB}{KL}=\frac{20}{10}=\frac{2}{1}[/tex]
Thus, ΔABC ≅ ΔJLK.
Option (5) is correct.
Consider, ΔDEF and ΔGHI.
∠I = ∠F = 90° (given)
Also ratio of corresponding sides are same, that is
[tex]\frac{DF}{GI}=\frac{8}{12}=\frac{2}{3}[/tex]
Also, [tex]\frac{EF}{HI}=\frac{10}{15}=\frac{2}{3}[/tex]
Thus, ΔDEF ≅ ΔGHI.
Option (2) is correct.
Thus, option (2) and (5) are correct.
The coordinates of △ABC△ABC are A(12,8), B(10,18), C(4,16)A(12,8), B(10,18), C(4,16). After a dilation, the coordinates are A'(6,4), B'(5,9), C'(2,8)A′(6,4), B′(5,9), C′(2,8). Find the scale factor.
Answer: [tex]\dfrac{1}{2}[/tex]
Step-by-step explanation:
The dilation is a transformation which makes similar shapes.
We know that In two similar geometric figures, the ratio of their corresponding corresponding x-coordinate is known as the scale factor.
For the given situation, the x-coordinate of A in pre-image = 12
The x-coordinate of A' in image = 6
Then , the scale factor for the dilation is given by :-
[tex]k=\dfrac{6}{12}=\dfrac{1}{2}[/tex]
Hence, the scale factor = [tex]\dfrac{1}{2}[/tex]
7/2x-2=28-4x solve for x
105,159 rounded to the nearest ten thousand
What is the value of -2 (7-15) over 4
On September 30, picture perfect physicians invested$100,000 in new medical equipment. What is the new assets, liabilities and equity
Suppose a basketball player has made 184 out of 329 free throws. If the player make the next two free throws, I will pay you $24. Otherwise you pay me $12. Find the expected value of the proposition
Final answer:
Expected value of proposition will be 20.134.
Explanation:
Given that the player made 184 out of 329 throws, the probability of making the next throw will be:
P(x)=[Number of shots made]/[Total number of throws]
=184/329
=0.559
Thus the expected value of proposition will be:
0.599 x 24+0.559 x 12
=20.134
Which of the following expressions is equal the expression of 4x - 2(3x - 9)
The following expressions 4x - 2(3x - 9) is equal the expression of
-2x + 18.
What is an expression?An expression is a set of terms combined using the operations +, -, x or ÷.
Given that:
4x - 2 (3x-9)
= 4x - 6x +18
= -2x +18
Hence, the expression 4x - 2 (3x-9) is equal to -2x+18.
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A triangular lake-front lot has a perimeter of 1300 feet. One side is 300 feet longer than the shortest side, while the third side is 400 feet longer than the shortest side. Find the lengths of all three sides.
A) 200 ft, 500 ft, 600 ft
B) 300 ft, 300 ft, 300 ft
C) 100 ft, 200 ft, 300 ft
D) 300 ft, 600 ft, 700 ft
Consider a company that selects employees for random drug tests. The company uses a computer to randomly select employee numbers that range from 1 to
6857
6857. Find the probability of selecting a number divisible by 1000. Find the probability of selecting a number that is not divisible by 1000.
The probability of selecting a number divisible by 1000 from the range of 1 to 6857 is approximately 0.0008763. The probability of selecting a number that is not divisible by 1000 is approximately 0.9991237.
Explanation:To find the probability of selecting a number divisible by 1000, we need to determine the total number of possible outcomes and the number of favorable outcomes. There are a total of 6857 possible outcomes since the company selects employee numbers ranging from 1 to 6857. For a number to be divisible by 1000, it must end with three zeros, so we need to find how many numbers satisfy this condition between 1 and 6857.
Since 1000 is the smallest number divisible by 1000, we can calculate the number of favorable outcomes by finding the largest integer that satisfies the condition. In this case, it is 6000. Therefore, there are 6 favorable outcomes.
The probability of selecting a number divisible by 1000 is calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes = 6 / 6857 ≈ 0.0008763.
The probability of selecting a number that is not divisible by 1000 can be calculated as the complement of the probability of selecting a number divisible by 1000:
Probability(not divisible by 1000) = 1 - Probability(divisible by 1000) ≈ 1 - 0.0008763 ≈ 0.9991237.
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James deposits $600 in an account that pays 4% simple interest, and $1200 in a second account which has a higher interest rate but is more risky. What interest rate must he get on the second account in order to earn at least $132 in interest for the year?
Can the polynomial below be factored into a perfect square? If not, select the answer that best describes why not.
64x^2+49x+8
A.
The x^2 coefficient does not permit the factoring.
B.
The x^2 coefficient does permit the factoring, but the x coefficient does not permit the factoring.
C.
The constant value does not permit the factoring.
D.
The polynomial may be factored into a perfect square.
Answer:
Option B is correct.
Step-by-step explanation:
We will work with the formula : [tex](a+b)^{2}[/tex]
= [tex]a^{2}+2ab+b^{2}[/tex]
Given polynomial is :
[tex]64x^{2} +49x+8[/tex]
here a = [tex]\sqrt{64x^{2} } =8x[/tex]
b = [tex]\sqrt{8}= 2\sqrt{2}[/tex]
2ab = [tex]2*8x*2\sqrt{2} =32\sqrt{2}x[/tex]
Now, we can see that the middle term should be [tex]32\sqrt{2} x[/tex] but in the question, it is given 49x
So, option B is true that - The x^2 coefficient does permit the factoring, but the x coefficient does not permit the factoring.
Information about movie ticket sales was printed in a movie magazine. in a sample of of fifty pg-rated movies, 36% had ticket sales in excess of $30,000,000. in a sample of thirty-five r-rated movies, 23% grossed over $30,000,000. suppose that this data is used to test the claim that the proportion of movies with ticket sales in excess of $30,000,000 is the same for pg movies as it is for r-rated movies. what would be the test statistic for this test? z = 1.29 z = 2.07 z = 4.005 z = 2.58
Let us say that the samples for fifty movies is 1 and samples for thirty five is 2. To solve the test statistic z, we can use the formula:
z = (p1 – p2) / sqrt [p (1 – p) (1 / n1 + 1 / n2)]
Where,
p1 = is the proportion for sample 1 = 0.36
p2 = is the proportion for sample 2 = 0.23
n1 = number of samples = 50
n2 = number of samples = 35
while p can be calculated using the formula:
p = [p1 * n1 / (n1 + n2)] + [p2 * n2 / (n1 + n2)]
p = [0.36 * 50 / (50 + 35)] + [0.23 * 35 / (50 + 35)]
p = 0.211764705 + 0.094705882
p = 0.306470587
Going back for the calculation of z:
z = (0.36 – 0.23) / sqrt [0.306 (1 – 0.306) (1 / 50 + 1 / 35)]
z = 1.279
Therefore the nearest answer is:
z = 1.29
A rectangular floor is 21 ft long and 12ft wide. Reuben wants to carpet the floor with carpet tiles sold by the square yard. Use the facts to find the area in square yards.
Conversion facts for length:
1 foot (ft) = 12 inches
1 yard (yd) =3 feet
1 yard (yd) = 36 inches
1 yard = 3 feet:
21 feet / 3 ft = 7 yards
12 feet / 3 feet = 4 yards
7 x 4 = 28 square yards
he will need 28 tiles
The area of the rectangular floor will be 28 square yards.
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L × W square units
A rectangular floor is 21 ft long and 12 ft wide.
We know that 1 foot = 1/3 yards.
Then the dimension of the rectangle in yards will be
L = 21 x 1/3 = 7 yards
W = 12 x 1/3 = 4 yards
Then the area of the rectangle will be
A = 7 x 4
A = 28 square yards
The area of the rectangular floor will be 28 square yards.
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The sum of three consecutive integers is −261−261. Find the three integers.
-261 / 3 =-87
-87 + -86 + -88 = -261
What is the sum of the arithmetic series? ∑[i=1,15,Fn=5i-1]
a local charity held a crafts fair selling donated,handmade items. Total proceeds from the sale were $1,875. A total of 95 items were sold,some at $15 each and the rest at $25 each. Let x be the number of $15 items and y the number of $25 items. How many items sold at $25?
Answer:
It’s 30
Step-by-step explanation:
6x2=(3×2)×___=___
6×4=2×(6×___)=___
2×(6×4)=____×8=____
100 meter long Christmas train needs 30 seconds to cross a 400nmetrr long bridge assuming the train goes at a steady speed how fast is it
2w+2l=24 what is the value of l