Answer:
It takes 4 seconds for the projectile to hit the ground
Step-by-step explanation:
The height of the projectile after t seconds is given by the following equation:
[tex]h(t) = -16t^{2} + 32t + 128[/tex]
How long will it take the projectile to hit the ground?
It happens when [tex]h(t) = 0[/tex]
So
[tex]h(t) = -16t^{2} + 32t + 128[/tex]
[tex]-16t^{2} + 32t + 128 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]-16t^{2} + 32t + 128 = 0[/tex]
So [tex]a = -16, b = 32, c = 128[/tex]
[tex]\bigtriangleup = 32^{2} - 4*(-16)*(128) = 9216[/tex]
[tex]t_{1} = \frac{-32 + \sqrt{9216}}{2*(-16)} = -2[/tex]
[tex]t_{2} = \frac{-32 - \sqrt{9216}}{2*(-16)} = 4[/tex]
Time is a positive measure, so:
It takes 4 seconds for the projectile to hit the ground
pls guys help me pls :c
Answer: A. [tex]x\geq21\dfrac{2}{3}[/tex] .
Step-by-step explanation:
The given inequation: [tex]81-1\dfrac{1}{5}x\leq55[/tex]
[tex]\Rightarrow\ 81-\dfrac{6}{5}x\leq55[/tex]
Multiplying 5 on both the sides, we get
[tex]5(81-\dfrac{6}{5}x)\leq5\times55\\\\\Rightarrow\ 405-6x\leq275\\\\\Rightarrow\ 6x\geq405-275\\\\\Rightarrow\ 6x\geq130\\\\\Rightarrow\ x\geq\dfrac{130}{6}\\\\\Rightarrow\ x\geq\dfrac{65}{3}\\\\\Rightarrow\ x\geq21\dfrac{2}{3}[/tex]
Hence, the inequality for x is [tex]x\geq21\dfrac{2}{3}[/tex] .
So, the correct option is A. [tex]x\geq21\dfrac{2}{3}[/tex] ..
Assuming that ten (10) candidates are presented in a random order, what is the probability that hire exactly one candidate
Answer:
The probability that only one candidate is hired is 0.10.
Step-by-step explanation:
The probability of event E occurring is the ration of the favorable number of outcomes to the total number of outcomes.
[tex]P(E)=\frac{n(E)}{N}[/tex]
It is provided that N = 10 candidates are presented in a random order.
Compute the probability that only one candidate is hired as follows:
[tex]P(\text{Only 1 Hire})=\frac{1}{10}=0.10[/tex]
Thus, the probability that only one candidate is hired is 0.10.
At a deli counter, there are sandwiches with meat and vegetarian sandwiches. Kira is at the counter buying sandwiches for a picnic. In how many ways can she choose sandwiches if fewer than must be vegetarian sandwiches
Answer:
The number ways to choose between meat and vegetarian sandwiches can be computed using computation technique.
Step-by-step explanation:
There are two types of sandwiches available at the deli counter. The possibility of combinations can be found by computation technique of statistic. It is assumed that order does not matter and sandwiches will be selected at random. The sandwiches can be arranged in any order and number ways can be found by 2Cn.
Find the number. PLEASE HELP!!!
Answer:
X=18
Step-by-step explanation:
Answer:
x = 18or x = - 20
Step-by-step explanation:
Given
x² + 2x = 360 ( subtract 360 from both sides )
x² + 2x - 360 = 0 ← quadratic in standard form
Consider the factors of the constant term (- 360) which sum to give the coefficient of the x- term (+ 2)
The factors are + 20 and - 18, since
20 × - 18 = - 360 and 20 - 18 = 2 , thus
(x + 20)(x - 18) = 0
Equate each factor to zero and solve for x
x + 20 = 0 ⇒ x = - 20
x - 18 = 0 ⇒ x = 18
Thus the number could be 18 or - 20
6th grade math help me, please:)))
Step-by-step explanation:
Hi there!!!
The answer is option A.
reason look in picture.
if you want to solve it just cross multiply it,
[tex]60x = 240000 \times 100[/tex]
or,
[tex]x = 24000000 \div 60[/tex]
and the answer would be 400000.
Hope it helps...
How does a reflection across the y-axis change the coordinates of a shape?
Answer:
When you reflect a shape avross the y-axis, the y-coordinates stay the same, but the x-coordinates turn into its opposites.
Step-by-step explanation:
EXAMPLES:
(3,6)---(reflected over y-axis)--> (-3,6)
(9,2)---(reflected over y-axis)--> (-9,2)
Hope this helped! Brainliest would be really appreciated :)
An integer is 7 more than 2 times another. If the product of the two integers is 60, then find the integers.
Answer:
15 and 4Step-by-step explanation:
Let the first integer be x and the second integer be y. If the first integer is 7 more than 2 times another, then x = 7+2y
The two integers will be y and 7+2y. If the product of both integers is 60, then;
y(7+2y) = 60
7y + 2y² = 60
2y² + 7y -60 = 0
2y²-8y+15y-60 = 0
2y(y-4)+15(y-4) = 0
(2y+15)(y-4) = 0
2y+15= 0 and y-4 = 0
2y = -15 and y = 4
y = -15/2 and 4
Taking the positive integer, y = 4
To get the other integer, we will substitute y = 4 into the equation x = 7+2y;
x = 7+2(4)
x = 7+8
x = 15
Hence the two integrs are 15 and 4
17 women and 3 men attend a family reunion. What is the percentage of men with respect to the total number of parents?
1. 3%
2. 15%
3. 16%
4. 17%
Answer:
Not enough information. (15% Men at family reunion)
Step-by-step explanation:
The question ask what percentage of men with respect to the total number of parents, who attended the family reunion; however, there is no information given on which subset of these people are parents. Therefore we cannot determine the percentage of men with respect to the total number of parents.
If we assume that all attendees of the family reunion are parents, the we can simply write:
3/20 == .15 == 15%
So there are 15% men at the family reunion. Likewise for the women we can say:
17/20 == .85 == 85%
So there are 85% women at the family reunion.
Cheers.
Answer:
[tex]\boxed{15\ \%}[/tex]
Step-by-step explanation:
Total Parents = 17+3 = 20
Men among Parents = 3
%age of men:
=> [tex]\frac{3}{20} * 100[/tex]%
=> 3 * 5 %
=> 15 %
A restaurant gat an average of 14 calls in a 2 hr time period. What is the probability that at most 2 calls in 45 min period
Answer:
0.10512
Step-by-step explanation:
Given the following :
Mean number of calls(μ) in 2 hours = 14
2 hours = 60 * 2 = 120 minutes
Average number of calls in 45 minutes :
= (45 / 120) * 14
= 0.375 * 14
= 5.25
Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)
Using the poisson probability formula:
P(x, μ) = [(e^-μ) * (μ^x)] / x!
Where :
e = euler's constant
μ = 5.25
x = 0, 1, 2
Using the online poisson probability calculator :
P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)
P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512
A process on a machine has a standard deviation of 0.04 inches. If a product with specifications of +/- 0.07 inches has to be processed on that machine, is the machine capable of performing that job? Group of answer choices
Answer:
c.) No, because Cp < 1
Step-by-step explanation:
Let us assume that there is centered in the process
and, the width is 2 times the specification
So, the width is
[tex]= 2 \times 0.07[/tex]
= 0.14
Now capability index = Cp is
[tex]= \frac{specification\ width}{6 \times standard\ deviation}\\\\= \frac{0.14}{6\times 0.04}[/tex]
= 0.58333
And the capability index should be minimum 1 for the process
And as we can see that Cp is 0.58333 which is less than 1 so the machine is not able to perform the job
Hene, the correct option is c.
solve this for me plzzz
Answer: a- steve
Step-by-step explanation:
Answer:
B Emma is correct
Step-by-step explanation:
In a class of 160 students, 90 are taking math, 78 are taking science, and 62 are taking both math and science. What is the probability of randomly choosing a student who is taking only math?
56%
39%
49%
74%
HURRY PLEASE
Answer:
56%
Step-by-step explanation:
90 ÷ 160
= 0.56
0.56 × 100
= 56%
Answer:
56%
Step-by-step explanation:
Your question is asking for students who are taking only math. Of 160 students, 90 are taking only math. This gives you the proportion of [tex]\frac{90}{160}[/tex] = 0.56. To find percents, just multiply it by 100 to get 56%.
HELPPPPPP !!!!!!!!!!!!
! 25 ~! points
15 points + brainliest if you can figure this out!
Answer:
(H1, T1)
Step-by-step explanation:
Since we know that the only number option is 1, we can cancel out the first 3 options. and obviously, there are only heads, and tails. So, using only the # 1 and heads and tails, we can conclude that the answer is (H1, T1).
Answer:
D. (H1, T1)
Step-by-step explanation:
Since all outcomes require card #1 is chosen, so any answer with 2 or 3 can be rejected, therefore the answer is
D. (H1, T1)
Solve |y + 2| > 6 im so confused
Answer:
Below
Step-by-step explanation:
● |y+2| > 6
● y+2 > 6 or y+2 < -6
Add -2 in both sides in the two inequality.
● y+2-2 > 6-2 or y+2-2 < -6-2
● y > 4 or y< -8
If x-2y=10 and y is three times the value of x, What is the value of x-y? a) -8 b) -4 c) 0 d) 2 e)4
Answer:
a) 4
Step-by-step explanation:
y = 3x
Plug it in: x - 2 (3x) = 10 --> x - 6x = 10 --> -5x = 10 --> x = -2
Therefore: y = 3(-2) --> y = -6
x - y = -2 - (-6) = 4
A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six squares will be cut from the cardboard: one square will be cut from each of the corners, and one square will be cut from the middle of each of the -5 centimeter sides . The remaining cardboard will be folded to form the box and its lid . Letting x represent the side-lengths (in centimeters) of the squares, to find the value of that maximizes the volume enclosed by this box. Then give the maximum volume. Round your responses to two decimal places.
Answer:
x = 0.53 cm
Maximum volume = 1.75 cm³
Step-by-step explanation:
Refer to the attached diagram:
The volume of the box is given by
[tex]V = Length \times Width \times Height \\\\[/tex]
Let x denote the length of the sides of the square as shown in the diagram.
The width of the shaded region is given by
[tex]Width = 3 - 2x \\\\[/tex]
The length of the shaded region is given by
[tex]Length = \frac{1}{2} (5 - 3x) \\\\[/tex]
So, the volume of the box becomes,
[tex]V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\[/tex]
In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.
[tex]\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\[/tex]
We are left with a quadratic equation.
We may solve the quadratic equation using quadratic formula.
The quadratic formula is given by
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
Where
[tex]a = 18 \\\\b = -38 \\\\c = 15 \\\\[/tex]
[tex]x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\[/tex]
Volume of the box at x= 1.59:
[tex]V = \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\[/tex]
Volume of the box at x= 0.53:
[tex]V = \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3[/tex]
The volume of the box is maximized when x = 0.53 cm
Therefore,
x = 0.53 cm
Maximum volume = 1.75 cm³
If one termite can destroy 1.2mg of wood per day, how many kilograms of wood can 10 termites destroy in 1 week? *Can someone please explain how to do this*
Answer:
10 termites will destroy 0.000084kg of wood per week
Step-by-step explanation:
Convert milligram to kilogram
1.2mg=(1.2 / 1,000,000)kg
1.2mg=0.0000012kg
1 termite destroys=0.0000012kg per day
10 termites will destroy (per day) =0.0000012×10 termites per day
10 termites in one day will destroy=0.000012kg
There are 7 days in a week
Therefore,
10 termites will destroy=destruction per day × 7 days
=0.000012×7
=0.000084kg per week
Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 56 inches long and cuts it into two pieces. Steve takes the first piece of wire and bends it into the shape of a perfect circle. He then proceeds to bend the second piece of wire into the shape of a perfect square. What should the lengths of the wires be so that the total area of the circle and square combined is as small as possible
Answer:
Step-by-step explanation:
Let the length of first piece be L .
Length of second piece = 56 - L
radius of circle made from first piece
R = L / 2π
Area of circle = π R²
= L² / 4π
side of square made fro second piece
= (56 - L) / 4
area of square = ( 56-L)² / 16
Total area
A = L² / 4π + ( 56-L)² / 16
For smallest possible combined area
dA / dL = 0
dA / dL = 2L / 4π - 2( 56-L)/16 =0
2L / 4π = 2( 56-L)/16
.159 L = 7 - .125 L
.284 L = 7
L = 24.65 inch
other part = 56 - 24.65
= 31.35 inch .
What is the slope of the line x = 4?
Answer:
slope is undefined
Step-by-step explanation:
x = 4 is the equation of a vertical line parallel to the y- axis.
The slope of a vertical line is undefined
Answer:
Undefined
Step-by-step explanation:
If the line is strait up like x = 4 that means it is undefined.
6th grade math , help me please
Answer:
a. the ratio is 1:2
b. its equivalent to the fraction 1/2
c. there would be 10 triangles
d. therw would be 45 triangles since the number of parallelograms is double the number of triangles
Answer:
See explanation.
Step-by-step explanation:
a) Simply divide the number of triangles by the number of paralellograms.
3/6
b) 3/6 is equal to 1/2.
1/2
c) Multiply 2 by 10 to get 20. Now, you also have to multiply 1 by 10.
10/20
d) There are three shapes for every instance of the ratio. Divide 90 by 3.
30
Hope this helped!
PLEASE HELP WILL GIVE BRAINLIEST PRECALC
Answer:
[tex]270^o[/tex] and [tex]450^o[/tex]
Step-by-step explanation:
Recall that [tex]\frac{\sqrt{2} }{2}[/tex] is a value of the function cosine for the special angles: [tex]135^o[/tex] and [tex]225^o[/tex], then:
[tex]\frac{x}{2} =135^o\\x=270^o\\or\\ \frac{x}{2} =225^o\\x=450^o\\[/tex]
6th grade math, help me please:)
Answer:
D. 100
Step-by-step explanation:
percents are always out of 100 because that is the maximum. if you are 100% done with your homework, you are completely finished.
A random sample of 144 observations produced a sample proportion of 0.4. An approximate 90% confidence interval for the population proportion p is between:_______
a) 0.320 and 0.480
b) 0.333 and 0.480
c) 0.333 and 0.467
d) 0.359 and 0.441
e) 0.313 and 0.487
Answer:
CI =(0.333, 0.480)
Step-by-step explanation:
The formula for calculating the confidence interval is expressed as shown;
CI = p±Z * √p(1-p)/n±0.5/n
Z is the z-score at 90% confidence
p is the sample proportion
n is the sample size
Given n = 144, p = 0.4 and z-score at 90% CI = 1.645 (from z table)
Substituting this values;
CI = p ± 1.645*√0.4(1-0.4)/144 ±0.5/n
CI = 0.4 ± 1.645*√0.4(0.6)/144 ± 0.5/144
CI = 0.4 ±1.645 * √0.24/144 ± 0.00347
CI = 0.4 ±1.645 * 0.04087± 0.00347
CI = 0.4±0.06723±0.00347
CI =(0.333, 0.480)
Exhibit 2-4A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. Undergraduate Major Graduate SchoolBusinessEngineeringOtherTotal Yes 35 42 63140 No 91104 65260 Total126146128400Among the students who plan to go to graduate school, what percentage indicated "Other" majors
Answer:
The percentage of college seniors with "Other" majors is 32%.
Step-by-step explanation:
The total number of college seniors surveyed is, N = 400.
The number of college seniors with "Other" majors is, n = 128.
The percentage of a value of x from N total is given as follows:
[tex]\text{Percentage of}\ x=\frac{x}{N}\times 100\%[/tex]
Compute the percentage of college seniors with "Other" majors as follows:
[tex]\text{Others}\%=\frac{n}{N}\times 100\%[/tex]
[tex]=\frac{128}{400}\times 100\%\\\\=32\%[/tex]
Thus, the percentage of college seniors with "Other" majors is 32%.
plzzzzz helpp j + 9 - 3 < 8
Answer:
j < 2
Step-by-step explanation:
Simplify both sides of the inequality and isolating the variable would get you the answer
need help thaanlksss
Answer:
Option (3). [tex]m(\widehat{ACB})=220[/tex]
Step-by-step explanation:
Option (1).
Since measure of an inscribed angle = [tex]\frac{1}{2}(\text{measure of the intercepted arc})[/tex]
m∠ABC = [tex]\frac{1}{2}m(\widehat{AC})[/tex]
[tex]m(\widehat{AC})[/tex] = 2(m∠ABC)
= 2(30°)
= 60°
Therefore, this option is not true.
Option (2),
Since, [tex]m(\widehat{AB})+m(\widehat{BC})+m(\widehat{AC})=360[/tex]
[tex]m(\widehat{AB})+160+60=360[/tex]
m(arc AB) = 360 - 220
= 140°
Therefore, this option is not correct.
Option (3),
[tex]m(\widehat{ACB})=m(\widehat{AC})+m(\widehat{BC})[/tex]
= 60° + 160°
= 220°
Option (3) is the correct option.
Option (4),
[tex]m(\widehat{CBA})= 360-m(\widehat{AC})[/tex]
= 360° - 60°
= 300°
Therefore, this option is not correct.
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. Please no random answers
Answer:
A
Step-by-step explanation:
A is corrects since -13 is in the the domain of g(x) and 20 is in the range of g(x):
-20 < -13 < 5-5 < 20 < 45B is also false since 4 is in the domain of g(x)) and -11 isn't in the range of g(x)
-20 < 4 < 5-11 < -5C is also false since it's mentioned that g(0) = -2
D is false since 7 isn't in the domain of g(x)
What is the length of JM in the given figure?
Answer: B. 30
Step-by-step explanation:
When given a secant and a tangent, the formula is:
exterior of secant × secant = tangent²
KM × JK = LK²
10 × (JM + 10) = 20²
10JM + 100 = 400
10JM = 300
JM = 30
Joaquin is constructing the perpendicular bisector of AB. He opens his
compass so that the distance from the two points of the compass is wider
than half the length of AB. What is his next step?
B
O A. Place the point of the compass on the midpoint of AB and draw
an arc in either direction.
O B. Place the point of the compass on point A and draw an arc acre
АВ.
O C. Place the point of the compass on point A and mark where the arc
intersects AB
O D. Place the point of the compass on the midpoint of AB and mark
the points directly above and below the midpoint.
Answer:
D. Place the point of the compass on the midpoint of AB and mark
the points directly above and below the midpoint.
Step-by-step explanation:
Below are the simple steps to follow to draw a perpendicular bisector of line AB.
First step
Set the compass at the end of one line segment and move the compass so that it would be slightly longer than half of the line AB.
Second step
Set the compass at point A and make some arcs just above line AB.
Third step
Draw an arc from point B with the same compass width.
Fourth step
Carefully set a ruler at the intersection of the arcs and draw the line segment.
Answer:place the point of the compass on point a and draw an arc across ab.
Step-by-step explanation: