if the coordinate of p and t are -6 and 4 respectively, what it the length of segment pt?
The length of the segment [tex]pt[/tex]is [tex]10[/tex] if the coordinates of [tex]p[/tex] and [tex]t[/tex] is [tex](-6 )and( 4)[/tex]
How can find the length of the segment ?
The coordinate of [tex]p=-6[/tex]
The coordinate of [tex]t=4[/tex]
We can assume only [tex]x[/tex] coordinates given and [tex]y[/tex] coordinates is [tex]0[/tex]
so coordinate of [tex]p=(-6,0)\\[/tex]
And coordinate of [tex]t=(4,0)[/tex]
So the length of the segment
[tex]pt=x_{2} -x_{1} \\pt=4-(-6)\\pt=4+6\\pt=10[/tex]
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2. Un auto viaja a 60 km/h y se detiene a los 2 segundos. qué distancia recorrió en el
frenado? ¿qué aceleración adquirió? ¿Si la aceleración es positiva o negativa, explica
por qué?
Se calcula que la aceleración es - 8,35 m/s.
¿Qué es la aceleración?Ahora sabemos lo siguiente de la pregunta;
Velocidad inicial (u) = 60 km/h o 16,7 m/s
Tiempo empleado (t) = 2 s
Dado que;
v = tu + en
v = 0 m/s porque el carro se detenía
tu = -en
a = -(u/t)
a= -1(6,7 m/s/2 s)
a =- 8,35 m/s
La aceleración es negativa porque la velocidad disminuye con el tiempo.
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A vegetable garden is in the shape of a triangle with a base of b = 25 ft and a height of h = 9 ft. find the area of the vegetable garden.
Answer:
Step-by-step explanation:
Formula
Area = 1/2 b* h
Givens
b = 25
h = 9
Solution
Area = 1/2 * 25 * 9 Substitute givens into formula
Area = 1/2 * 225 Combine
Answer
Area = 112.5 ft^2
A music website claims the mean length of their songs is 3.75 minutes. Suppose the length of songs from this website follows a Normal distribution with standard deviation 0.5 minutes. If 7 songs from this website are randomly selected, then there is about a 90% probability that the sample mean will fall in which interval
The confidence interval is from 3.44 to 4.06 minutes.
According to the statement
we have given that the mean length of songs is 3.75 minutes and standard deviation 0.5 minutes and the sample size n is 7. and the confidence interval is 90%
and we have to find the mean interval.
So, We know that the
A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.
And A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.
We know that the z value for 90% confidence interval is 1.64.
so, The formula to calculate margin of error is
MOE = Z*standard deviation/ (n)^1/2
put the values in it
MOE = Z*standard deviation/ (n)^1/2
MOE = 1.64*0.5/ (7)^1/2
MOE = 1.64*0.189
MOE = 0.310
And to find the interval the formula is
Confidence interval = sample mean ± margin of error
Confidence interval = 3.75 ± 0.310
Confidence interval = (4.06,3.44)
So, The confidence interval is from 3.44 to 4.06 minutes.
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Sophia for the exponential function f left parenthesis x right parenthesis equals 5 times 2 to the power of x, what is the value of f left parenthesis 3 right parenthesis?
The value of f left parenthesis 3 right parenthesis is 45.
According to the statement
We have given that the F(x) = 5(x)^2
and we have to find the value when Sophia have a 3 right parenthesis.
So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.
And now we have to find the value for 3 right parenthesis
And for this purpose we have to put the value X= 3 in the f(x) then
F(x) = 5(x)^2
F(3) = 5(3)^2
F(3) = 5*9
F(3) = 45.
here the value of 3 right parenthesis is 45.
So, The value of f left parenthesis 3 right parenthesis is 45.
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If the graph of f(x) = 4 ^ x is shifted 6 units up, then what would be the equation of the new graph?
The equation of the new graph g(x) is expressed as g(x) = 4^x + 6
Exponential equationThe standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.
Translation of coordinatesTranslations is a transformation technique that changes the position of an object from one point on the plane to another.
Given the function f(x) = 4^x
If the function is shifted 6 units up, the function g(x) is derived by adding 4 to the function f(x). The resulting function is given as;
g(x) = f(x) + 6
g(x) = 4^x + 6
Hence the equation of the new graph g(x) is expressed as g(x) = 4^x + 6
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Which equation is equivalent to
f(x) = 16x4 -81 = 0?
✓(4x² +9)(4x² - 9) = 0 ✓
COMPLETE
Select all of the zeroes of the function.
O
2/3
DONE
The given equation is equivalent to (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3). And the zero of the function are: [tex]\pm \frac{3}{2}[/tex] and [tex]\pm \frac{3}{2}i[/tex].
What is a Quadratic Function?The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
For solving a quadratic function you should find the discriminant: D=b²-4ac and after that use this variable in the formula: [tex]x=\frac{-b\pm\sqrt{D} }{2a}[/tex].
FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
The question gives: [tex]16x^4-81=0[/tex], you can factor this equation. See below.
(4x²+9)*(4x²-9)
(4x²+9)*(2x-3)*(2x+3)
Therefore, you should choose one of options: (4x²+9)*(4x²-9) or (4x²+9)*(2x-3)*(2x+3).
Next step is to solve the given equation. Solving for (4x²+9)*(2x-3)*(2x+3)=0, then:
For 2x-3=0
x=3/2
For 2x+3=0
x= -3/2
For 4x²+9=0
4x²=-9
x²= -9/4
x = [tex]\pm \sqrt{\frac{-9}{4} }[/tex]
x =[tex]\pm \frac{3}{2}*\sqrt{-1 }\\ \\ \pm \frac{3}{2}*i[/tex]
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PLS HELP IM STUCK PLS
Answer:
See below
Step-by-step explanation:
Slope, m of given line = - 1/2
perpendicular slope is = -1/m = -1 / (-1/2) = +2
Point (6,9) slope form of line
y -9 = 2(x-6) expand and simplify
y - 9 = 2x -12
y = 2x -3
The figure shows secants LH and and tangent J intersecting at point L. AHIL is a right triangle. Find m/HLJ, which is
the value for x, and m I, which is the value for y.
A. x = 274
y = 86
B. x = 137
y = 43
C. x = 47
y = 86
D. x = 317
y = 43
The values of x and y from the given diagram are 47 ad 86 degrees respectively
Circle theoremFrom the given circle, the triangle HJL is a right triangle.
Determine the value of y
43 = 1/2 <y
<y = 43 * 2
<y = 86 degrees
Since the sum of angle on a straight line is 180 degrees, such that;
x+90+43 = 180
x + 133 = 180
x = 47 degrees
Hence the values of x and y from the given diagram are 47 ad 86 degrees respectively
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POSSIBLE OUTCOMES!!!
A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.
a. Find the probability of tossing a head and drawing a red marble. Explain your reasoning.
b. Find the probability of drawing two blue marbles if the first marble is not replaced. Explain your reasoning.
The probability of drawing two blue marbles if the first marble is not replaced is 1/5
How to determine the probabilities?The probability of tossing a head and drawing a red marble
The given parameters are:
White = 1
Blue =3
Red = 2
Total = 6
The probability of a head is
P(Head)= 1/2
The probability of drawing a red marble is
P(Red)= 2/6 = 1/3
The required probability is
P = P(Head) * P(Red)
This gives
P = 1/2 * 1/3
P =1/6
The probability of drawing two blue marbles if the first marble is not replaced.
Here, we have:
P(B1) = 3/6 = 1/2
P(B2) = 2/5
The required probability is
P = P(B1) * P(B2)
This gives
P = 1/2 * 2/5
P =1/5
Hence, the probability of drawing two blue marbles if the first marble is not replaced is 1/5
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See photo for problem, please help
Considering the given functions in the graph, we have that:
(f + g)(3) = 4.(f - g)(1) = -2.How to find (f + g)(3) looking at the graph?We look at the graph, and find f(3) and g(3), then add them. Hence:
g(3) = 4.f(3) = 0.Then the addition is:
(f + g)(3) = f(3) + g(3) = 0 + 4 = 4.
As for (f - g)(1):Same logic, at the graph we have that:
f(1) = -1.g(1) = 1.Hence:
(f - g)(1) = f(1) - g(1) = -1 - 1 = -2.
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f(x) = 7x
g(x) = 7x + 6
Which statement about f(x) and its translation, g(x), is true?
The domain of g(x) is {x | x > 6}, and the domain of f(x) is {x | x > 0}.
The domain of g(x) is {y | y > 0}, and the domain of f(x) is {y | y > 6}.
The asymptote of g(x) is the asymptote of f(x) shifted six units down.
The asymptote of g(x) is the asymptote of f(x) shifted six units up.
The statement which is true about the translation is; The asymptote of g(x) is the asymptote of f(x) shifted six units down.
Which statement is true about the translation?Since it follows from the task content that the function g(x) represents a 6 units vertical shift downward, it can then be concluded in the same regard that The asymptote of g(x) is the asymptote of f(x) shifted six units down.
Therefore, the true statement is; the asymptote of g(x) is the asymptote of f(x) shifted six units down.
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The fitness center held a weight loss competition in which 128 people participated. The amount of weight loss was normally distributed with a mean of 18 pounds and a standard deviation of 5.4 pounds. Approximately how many people lost at least 15 pounds?
Select one:
a. 72
b. 78
c. 84
d. 90
Answer:
d. 90
Step-by-step explanation:
z = (x - mean)/SD = (15 - 18)/5.4 = - 3/5.4 = -0.55555555... ≈
≈ -0.56
remember the z-table represents the rounded values.
the z-table at -0.56 gives us the p-value of 0.28774.
that is the probability to the left of 15 pounds, so, the probability to have lost 15 pounds or less.
to have lost at least 15 pounds, we have to get the right side of 15 pounds in the bell curve.
and that is 1 - 0.28774 = 0.71226
so, the probability to have lost at least 15 pounds is therefore 0.71226.
how many people are that ?
well, there were in total 128 people (with the total probability of 1 representing everything).
the number of people that lost at least 15 pounds are the proportionate share of 0.71226 of 1 (the whole) :
128 × 0.71226 = 91.16928...
so, the closest answer option is d. 90
Find the polynomial function in standard form that has the zeros listed. i and -i
The polynomial function in standard form that has the zeros listed. i and -i is x² +1 = 0.
What is polynomial function?A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions.
The values of x that fulfil the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.
Calculation for the polynomial function-
The general two degree/quadratic equation is given by-
ax² + bx + c = 0
Where a ≠ 0
If the two roots of the equation are x1 and x2.
Then the relation between roots and coefficients of the polynomial are -
The sum of the roots = (- coefficient of x)/(coefficient of x²)x1 + x2 = (-b)/a
The multiplication of the roots = constant/coefficient of x²x1.x2 = c/a
From the above two relation the general equation can be written as-
x² -(x1 - x2)x + x1.x2 = 0
Lets say x1 = i and x2 = -i
Substitute the values of x1 and x2 in the general equation
x² -(i - i)x + (i).(-i) = 0
x² - i ² = 0
x² + 1 = 0
Therefore, the polynomial function in standard form that has the zeros listed. i and -i is x² + 1 = 0.
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If 1 skip equals 4 hops, and 1 jump equals 3 skips, what is the total number of hops in a hop, a skip and a jump
There are 17 hops in a hop, a skip, and a jump.
How to perform changes of units?We have the relations:
1 skip = 4 hops.1 jump = 3 skips.How many hops are in a hop, a skip and a jump?
So we have:
1 hop + 1 skip + 1 jump.
First, using the second relation we rewrite:
1 hop + 1 skip + 3 skips = 1 hop + 4 skips.
Now, using the first relation:
1 hop + 4 skips = 1 hop + 4*(4 hops) = 1 hop + 16 hops = 17 hops.
There are 17 hops in a hop, a skip, and a jump.
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The average daily maximum temperature in Syracuse is 21.85°C, and the average daily minimum temperature is -4.7°C. The average daily maximum temperature is
°C higher than the average daily minimum temperature.
By applying the definition of difference, we find that the average daily maximum temperature in Syracuse is 26.55 °C higher than the average daily minimum temperature.
What is the difference between the average daily maximum temperature and the average daily minimum temperature?
Herein we must find the difference bewteen the two temperatures, defined as the subtraction of the minimum temperature from the maximum temperature:
x = 21.85 °C - (- 4.7 °C)
x = 26.55 °C
By applying the definition of difference, we find that the average daily maximum temperature in Syracuse is 26.55 °C higher than the average daily minimum temperature.
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Which expression is equivalent to?
3/2
Answer:
D
Step-by-step explanation:
simplified is 1 1/2, 1.5 or 3/2
I need help with cancelling units please
Answer:
D
Step-by-step explanation:
You are looking for what you would need to cancel the yards in 800 yards.
800 yards (1 mile/ 1760 yards). You have yards in the numerator of your original measurement. You will cross cancel out the yard on the the top and the yards on the bottom.
To play the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, paying $1 for each five-number selection. If the five numbers picked are the same as the ones drawn by the lottery, an enormous sum of money is bestowed. What is the probability that a person with one combination of five numbers will win
Using the combination formula, the probability that a person with one combination of five numbers will win is:
[tex]\frac{1}{1,221,759}[/tex]
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For this problem, 5 numbers are taken from a set of 45, hence the number of combinations is:
[tex]C_{45,5} = \frac{45!}{5!40!} = 1,221,759[/tex]
Hence the probability is:
[tex]\frac{1}{1,221,759}[/tex]
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20% of a number is 17 . find the number
Answer:
x = 85Step-by-step explanation:
20% of a number is 17 . find the number
divide 17 by 20 and you find 1%, multiply by 100 and you get 100%
x = 17 : 20 * 100
x = 0.85 * 100
x = 85
In order to avoid double counting, statisticians just count the __________________.
In order to avoid double counting, statisticians just count the final goods and services.
According to the statement
we have to find the procedure which is used by statisticians to avoid the double counting.
final goods and services are the type of way which is used to avoid the double counting.
In other words, statisticians count only the final results rather than the efforts.
So, In order to avoid double counting, statisticians just count the final goods and services.
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Solve the quadratic equation 2x2-1 = 7 x. write your answer correct to two decimal places
Answer:
Step-by-step explanation:
You have 2 x's. I think the first one is for multiplication and the second one is a variable.
2x2 -1 = 7x
4-1 = 7x (first multiple 2x2)
3=7x (second 4-1)
0.428571429 = x (Divide both sides by 7. On the left side, 3/7 is 0.428571429 and 7x/7 is just x because the 7s cancel out.
Since the answer needs to be to two decimal places, I have to decide if 0.428571429 is closer to 0.42 or 0.43 Since the digit after the 2 in the answer is 8, that makes the number closer to 0.43 than 0.42. So, the final answer is 0.43
21+21+7+7+7+7+8+8+8+8+9+9
Answer:
21+21+7+7+7+7+8+8+8+8+9+9
Step-by-step explanation:
amswer is 120
Answer:
Step-by-step explanation:
21+2=42.There are four sevens-which is 7x4=28.There are four eights meaning it is 8x4=32+28=60+42=102+(9+9)=102+18=120
what is the length and width
Answer:
Step-by-step explanation:
144,72
Answer:
If you cut the rectangle in half, you have two squares of area 144 ft², or side length 12 ft.
The length of the rectangle is 24 ft; its width is 12 ft.
A box contains 65 balls numbered from 1 to 65. If 11 balls are drawn with replacement, what is the probability that at least two of them have the same number?
Using the binomial distribution, there is a 0.265 = 26.5% probability that at least two of them have the same number.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are:
p = 1/65 = 0.0154, n = 65.
The probability that at least two of them have the same number is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which:
P(X < 2) = P(X = 0) + P(X = 1)
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{65,0}.(0.0154)^{0}.(0.9846)^{65} = 0.3647[/tex]
[tex]P(X = 1) = C_{65,1}.(0.0154)^{1}.(0.9846)^{64} = 0.3703[/tex]
So:
P(X < 2) = P(X = 0) + P(X = 1) = 0.3647 + 0.3703 = 0.735.
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.735 = 0.265[/tex]
0.265 = 26.5% probability that at least two of them have the same number.
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Marty wants to watch two fireworks shows at the same
time. The best view is from a point that is between and
equidistant from each of them. If the shows are located
at the park and the highschool shown, at which point
would Marty get the best view?
Answer:
(8 , 5)
Step-by-step explanation:
• Marty would get the best view ,if he stood at the midpoint
of the line that connect the park to the high school .
• On the coordinates plane ,the park is located at (-4 , -11)
and the high school is located at (20 , 21) .
•• Calculating the midpoint (best position) :
Let M(x , y) be the midpoint.
[tex]x=\frac{-4+20}{2} =8[/tex]
[tex]y=\frac{-11+21}{2} =5[/tex]
Answer:
(8, 5)
Step-by-step explanation:
Given points:
High School = (20, 21)Park = (-4, -11)To find the point that is between and equidistant from the High School and the park, use the formula for midpoint between two points.
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Define the endpoints:
[tex]\textsf{Let }(x_1,y_1)=(20,21)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(-4,-11)[/tex]
Substitute the endpoints into the formula:
[tex]\implies \textsf{Midpoint} =\left(\dfrac{-4+20}{2},\dfrac{-11+21}{2}\right) = (8,5)\end{aligned}[/tex]
Therefore, the point at which Marty would get the best view is (8, 5).
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Keisha devised a week-long study plan to prepare for finals. On the first day, she plans to study for 1 hour, and each successive day she will increase her study time by 30 minutes. How many hours will Keisha have studied after one week
Answer:
17.5 hours
I hope this helps and you can give a brainliest!
Step-by-step explanation:
Given: time spent per day follows the arithmetic sequence 1,1.5,2... (for 7 terms) with first term 1 and common difference 0.5 (in hours)
Concept used: the total study time is the partial sum S7of the given arithmetic series.
Calculation: As the number of terms is small, it can be calculated by hand.
S7 = 1+1.5+2+2.5+3+3.5+4
S7= 17.5 hours
Conclusion: Total time spent after one week is 17.5 hours
Answer:
17 and 1/2 hours.
Step-by-step explanation:
this is an arithmetic series with common difference 0.5 hours.
Number of hours after 7 days
= (n/2)[2a + (n -1)d]
= (7/2)(2*1 + (7-1)0.5)
= 3.5 * 5
= 17.5 hours
A state license plate consists of three letters followed by three digits. If repetition is allowed, how many different license plates are possible
A state license plate consists of three letters followed by three digits. If repetition is allowed, the number of different ways in which license plates are possible is 17,576,000.
What is a permutation?An arrangement of items in a specific order is referred to as a permutation. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection.
Calculation for the permutation -
Three letters are followed by three digits on a state license plate.
26 letters from a to z and 10 numbers from 0 to 9 make up the alphabet.
The potential of arrangements is due to the license plate's composition of three letters and three numerals.
Total ways = 26×26×26×10×10×10
= 17,576,000
Therefore, the number of different ways in which license plates are possible is 17,576,000.
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If you had worked on an externship in a prosecutor’s office, and then you moved to another state, which of these legal support positions would be best suited for?
Haven worked on an externship in a prosecutor’s office, the legal support position which you would be best suited for is: paralegal.
What is paralegal?Paralegal can be defined as a person who has been trained in subsidiary legal matters (issues), but not fully qualified to act as an attorney or lawyer.
In this context, we can infer and logically deduce that paralegal is a legal support position which you would be best suited for a person who has worked on an externship in a prosecutor’s office.
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Complete Question:
If you had worked on an externship in a prosecutor’s office, and then you moved to another state, which of these legal support positions would be best suited for?
mediator
paralegal
legal secretary
court reporter
can someone solve this for me ?
Answer: 113.1 ft^3
Step-by-step explanation:
We know the radius is 3 so substitute it in the formula like this...
V = 4/3 π (3)^3
Solve for (3)^3 which is 27.
Next multiply 4/3 by π. Which equals 4.1887....
Then multiply that answer by 27.
And your answer is 113.1 ft^3.
Answer:
[tex]V=108ft^{3}[/tex]
Step-by-step explanation:
[tex]V=\frac{4}{3}(3)(3)^{3}[/tex]
[tex]V=\frac{4}{3}(3)(27)[/tex]
[tex]V=\frac{4}{3} (81)=\frac{324}{3}[/tex]
[tex]V=108[/tex]
Hope this helps