Answer:
2x-3
Step-by-step explanation:
f(x) = 3x-1
g(x)= x+2
(f-g) (x) = 3x-1 - (x+2)
Distribute the minus sign
= 3x-1 -x-2
Combine like terms
= 3x-x -1-2
=2x -3
Find the area of'a triangle with legs that are: 12 m, 15 m, and 9 m.
M
O A. 25.5 m
OB. 38.2 m
OC. 42.4 m
OD. 54 m
Answer:
D. 54m
Step-by-step explanation:
by the side you can see that it is a right triangle with hypotenuse = 15
1/2(b)(h) = 1/2(9)(12) = 54
Answer:
D.) 54 m2
Step-by-step explanation:
I got it correct on founders edtell
7 less than the quotient of a number and 3 is 5. Find the number.
Answer:
The answer is 36
Step-by-step explanation:
Let the number be x
7 less than the quotient of a number and 3 is written as
[tex] \frac{x}{3} - 7[/tex]The result is 5
So we have
[tex] \frac{x}{3} - 7 = 5[/tex]Move - 7 to the right side of the equation
That's
[tex] \frac{x}{3} = 7 + 5[/tex][tex] \frac{x}{3} = 12[/tex]Multiply both sides by 3 to make x stand alone
We have
[tex]3 \times \frac{x}{3} = 12 \times 3[/tex]We have the final answer as
x = 36Hope this helps you
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 53.9 for a sample of size 24 and standard deviation 5.6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places.
_______ < μ < _________ please teach using calculator method
Answer:
The estimate is
[tex]52.02 < \mu < 55.78[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\ = x = 53.9[/tex]
The sample size is n = 24
The standard deviation is [tex]\sigma = 5.6[/tex]
Given that the confidence level is 90% the level of significance is mathematically represented as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table.The value is
[tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.10 }{2} } = 1.645[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because [tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval ( [tex]1 - \alpha[/tex] ) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{5.6 }{ \sqrt{24} }[/tex]
[tex]E = 1.880[/tex]
The estimate of how much the drug will lower a typical patient's systolic blood pressure(using a 90% confidence level) is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]53.9 - 1.880 < \mu < 53.9 + 1.880[/tex]
[tex]52.02 < \mu < 55.78[/tex]
what is 88.92 x 21.33
Answer:
By multiplying 88.92 from 21.33 we get 1896.6636.
Hope it's helpfulAnswer:
1896.6636
Step-by-step explanation:
Hope this helps
Give a vector parametric equation for the line through the point (−2,−4,0) that is parallel to the line ⟨−2−3t,1−4t,−5t⟩:
The tangent vector for the given line is
T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩
On its own, this vector points to a single point in space, (-3, -4, -5).
Multiply this vector by some scalar t to get a whole set of vectors, essentially stretching or contracting the vector ⟨-3, -4, -5⟩. This set is a line through the origin.
Now translate this set of vectors by adding to it the vector ⟨-2, -4, 0⟩, which correspond to the given point.
Then the equation for this new line is simply
L(t) = ⟨-3, -4, -5⟩t + ⟨-2, -4, 0⟩ = ⟨-2 - 3t, -4 - 4t, -5t⟩
The vector parametric equation for the line through the point is [tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex].
GivenGive a vector parametric equation for the line through the point (−2,−4,0) that is parallel to the line ⟨−2−3t,1−4t,−5t⟩.
What is a parametric equation vector?Parametric equations of the line segment are defined by its endpoints.
To find the vector equation of the line segment, we’ll convert its endpoints to their vector equivalents.
Two lines are parallel if they have the same direction, and in the parametric form, the direction of a line is always the vector of constants that multiply t (or the parameter).
The vector equation of a line is given by:
[tex]\rm v = r_0+tv[/tex]
Where v is the direction vector and [tex]\rm r_0[/tex] is a point of the line.
The tangent vector for the given line is
T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩
Here,
[tex]\rm r_0 = (-2,-4,0) \ and \ v=(-3, \ -4, \ -5)t\\\\[/tex]
Then,
[tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex]
x = -2-3t, y = -4-4t, and z = 0-5t
To know more about the Parametric equation click the link given below.
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4)
Write an inequality for the graph below. If necessary, use
<= for < or >= for .
9514 1404 393
Answer:
y < -1/4x -1
Step-by-step explanation:
The boundary line appears to go through the points (-4, 0) and (0, -1). This tells you it has a "rise" of -1 for a "run" of 4. The slope is ...
m = rise/run = -1/4
The y-intercept (b) is the point where the y-axis is crossed. The slope-intercept equation of the boundary line is ...
y = mx + b
y = -1/4x -1
__
The boundary line is dashed, so is not included in the solution set. The shading is below the line, so all y-values less than (but not equal to) the boundary line are in the solution set:
y < -1/4x -1
Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. 5x − 4 x(x2 + 7)2
Answer:
[tex]\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}[/tex]
Step-by-step explanation:
Given the expression [tex]\frac{5x-4}{x(x^2+7)^2}[/tex], we are to re-write the expression in form of a partial fraction.
Before we write in form of a partial fraction, we need to note the expression at the denominator. Since the expression in parenthesis is a quadratic equation, the equivalent numerator must be a linear expression.
Also the quadratic equation is a repeated form since it is squared. This means that we are to repeat the quadratic equation twice when writing as a partial fraction.
[tex]\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}[/tex]
From the above partial fraction, it can be seen that x² + 7 in parenthesis was repeated twice and their equivalent expressions at the numerator are both linear i.e Bx+E and Dx+ E where A, B, C, D and E are the unknown constant.
using complex number system Compute the three cube roots of z = −8.
Write z = -8 in polar form:
[tex]z = -8 = 8e^{i\pi}[/tex]
Then the cube roots of z are
[tex]z^{1/3} = 8^{1/3} e^{i\left(\frac{\pi+2n\pi}3\right)[/tex]
where n ∈ {0, 1, 2}, or
[tex]z^{1/3} \in \left\{8^{1/3} e^{i\pi/3}, 8^{1/3} e^{i\pi}, 8^{1/3} e^{i\,5\pi/3}\right\} \\\\ z^{1/3} \in \left\{2 \left(\dfrac12 + i\dfrac{\sqrt3}2\right), -2, 2 \left(\dfrac12-i\dfrac{\sqrt3}2\right)\right\} \\\\ \boxed{z^{1/3} \in \left\{1+i\sqrt3, -2, 1-i\sqrt3\right\}}[/tex]
Do men and women run a 5 kilometer race at the same pace? Here are boxplots of the time (in minutes) for a race recently run in Chicago. Write a brief report discussing what these data show.
Answer:
yes
Step-by-step explanation:
-36 = 6(2-8n) please
Answer:
n=1
Step-by-step explanation:
-36 = 6(2-8n)
-36=12-48n
-36-12=-48n
-48=-48n
n=1
QUE
The angle of depression of a banana from the monkey on the tree
25m high is 560. Calculate the distance of the banana from the
foot of the tree
and ton xamples of each
9514 1404 393
Answer:
16.9 m
Step-by-step explanation:
Angle BMT in the attached diagram is the complement of the angle of depression, so is 90° -56° = 34°. The distance BT is the side of the triangle opposite this angle, and the given tree height TM = 25 is the side of the triangle adjacent to the angle. Then the relevant trig relation is ...
Tan = Opposite/Adjacent
Opposite = Adjacent × Tan
BT = (25 m)·tan(34°) ≈ 16.863 m
The banana is about 16.9 meters from the tree.
ab-0.5bab−0.5ba, b, minus, 0, point, 5, b when a=1a=1a, equals, 1 and b=5b=5
Answer:
2.5
Step-by-step explanation:
Put the values in place of the corresponding variables and do the arithmetic:
ab - 0.5b = (1)(5) -0.5(5) = 5 - 2.5 = 2.5
how many pounds are in 2 tons 1,760 ounces
Answer:
4110
Step-by-step explanation:
One ton is equal to 2000 pounds and one ounce is equal to 0.0625 pounds.
2 tons*2000 lbs per ton = 4000 lbs
1760 ounces*0.0625 lebs per ounce = 110 lbs
4000+110=4110 lbs
What inequality symbol belongs in the circle: -4 _ 5
30 POINTS!
Answer:
<
Step-by-step explanation:
Inequality symbols:
< less than
> greater than
= equal to
≤ less than or equal to
≥ greater than or equal to
In this case, it is known that -4 is less than 5, or:
-4 < 5.
~
Answer:
>
Step-by-step explanation:
because 5 is bigger than -4
A^2 + 2AB +B^2
habsbsjabdhjsbfhjbsdjh
Which among the given schemes offers a monthly instalment of less than Rs 5000. ?
a) Scheme A
b) Scheme B
c) Scheme C
d) Both Scheme A and Scheme B
What is the distance between y=2x+4 and y=2x-1?
Answer:
Y=2(1)+4
Y=2+4
Y=6
Step-by-step explanation:
Please follow me
Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?
Answer:
27.73 feet
Step-by-step explanation:
Use the Pythagorean theorem. It easiest to think of the distance between the two friends as a triangle in the rectangle. One side is 12ft and the other is 25ft.
12^2+25ft^2=769
The square root of 769 is 27.73
Answer:
27.73 Ft
Step-by-step explanation:I took the test
While walking from the car into your dormitory you dropped your engagement ring somewhere in the snow. The path is 30 feet long. You are distraught because the density of its location seems to be constant along this 30-foot route. a) What is the probability that the ring is within 12 feet of your car
Answer:
0.4
Step-by-step explanation:
we are required to find the probability that the ring is within 12 meters from nthe car.
we start by defining a random variable x to be the distance from the car. the car is the starting point.
x follows a normal distribution (0,30)
[tex]f(x)=\frac{1}{30}[/tex]
[tex]0<x<30[/tex]
probabilty of x ≤ 12
= [tex]\int\limits^a_ b{\frac{1}{30} } \, dx[/tex]
a = 12
b = 0
[tex]\frac{1}{30} *(12-0)[/tex]
[tex]\frac{12}{30} = 0.4[/tex]
therefore 0.4 is the probability that the ring is within 12 feet of your car.
Each of three identical jewelry boxes has two drawers. Each drawer of the first box contains a gold coin. Each drawer of the second box contains a silver coin. In the third box, one drawer has a gold coin and the other drawer a silver coin. If a box and drawer are selected at random, and the selected drawer has a silver coin, what is the probability that the other drawer has a gold coin
Answer:
75%
Step-by-step explanation:
75% of possibility to have gold coin
The area of a square is 36cm2. What are the dimensions of the square? You must show your work. Pls tell me what the dimensions of the square are
Answer:
6 cm by 6 cm
Step-by-step explanation:
We know that the formula for area of a square is A = s² where A = area and s is the length of one side. We know that A = 36 so:
36 = s²
√36 = s
s = ±6
Note that s = -6 is an extraneous solution because you can't have a side length of -6, therefore the answer is s = 6 so the dimensions of the square are 6 cm by 6 cm.
The area of a square is found using the formula area = s^2, where s is the length of a side. ( a square has 4 equal sides).
Given the area you have:
36 = s^2
Find a by taking the square root of both sides:
S = sqrt(36)
S = 6
The square has a side length of 6 cm.
The value of 3 in 783.97
Answer:
place value of 3 in 783.97 is 3
Step-by-step explanation:
Answer:
Units
Step-by-step explanation:
The units start counting from 3 because after the point that is the 9 start counting tenth
Radicals and Exponents. Tutorial Use the properties of exponents to simplify the expression. (y 3/2 x-1/2)4 =
2. 2(x+4) -5 = 3 + 3
Step-by-step explanation:
2x + 8 - 5 = 6
2x + 3 = 6
2x = 6 - 3
2x = 3
x = 3/2
Answer:
2 ( x+4) -5 = 3+3
=) 2x +8-5=6
=) 2x+3=6
=) 2x= 6-3
=)2x = 3
=) x =3/2= 1.5
Look at the image for the question below
Answer:
348 km³
Step-by-step explanation:
Volume = base area×height
base area = 5.8×12/2 = 34.8 km²
volume = 34.8×10 = 348 km³
Question (2)
ASAP Please help.
Construct the "Square root spiral". Take a large sheet of paper and construct the "Square root spiral" in the following fashion.
Start with a point O and draw a line segment [tex]\rm{P_{1} P_{2}}[/tex] perpendicular to [tex]\rm{OP_{1}}[/tex] of unit length. Now draw a line segment [tex]\rm{P_{2} P_{3}}[/tex] perpendicular to [tex]\rm{OP_{2}}[/tex] . Then draw a line segment [tex]\rm{P_{3} P_{4}}[/tex] perpendicular to [tex]\rm{OP_{3}}[/tex]. Continuing in this matter, you get line segment of unit length perpendicular to [tex]\rm{OP_{n-1}}[/tex]. In this manner, you will have created the points [tex]\rm{P_{2}, P_{3},...... P_{n}....}[/tex], and joined them to create a beautiful spiral depicting [tex]\rm{\sqrt{2}, \sqrt{3}, \sqrt{4},...}[/tex]
Answer:
The "square root spiral," donned the "Spiral of Theodorus" was created by Theodorus to visualize a set of 17 isosceles triangles where [tex]n[/tex] is equal to a value between one and seventeen.
The central angle is attached to a central point, and the side opposite of the central angle is always equal to 1.The hypotenuse of the triangle is equivalent to [tex]\sqrt{n+1}[/tex]. The hypotenuse becomes a leg for the next triangle.I have attached an image of the Square Root spiral below.
find the slope of the line that passes through the two points (0,1) and (-8, -7)
Answer:
The slope of the line is 1Step-by-step explanation:
The slope of a line is found by using the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
where
m is the slope and
(x1 , y1) and ( x2 , y2) are the points
Substituting the above values into the above formula we have
Slope of the line that passes through
(0,1) and (-8, -7) is
[tex]m = \frac{ - 7 - 1}{ - 8 - 0} = \frac{ - 8}{ - 8} = 1[/tex]
The slope of the line is 1Hope this helps you
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 3%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that
Answer:
The probability that none of the LED light bulbs are defective is 0.7374.
Step-by-step explanation:
The complete question is:
What is the probability that none of the LED light bulbs are defective?
Solution:
Let the random variable X represent the number of defective LED light bulbs.
The probability of a LED light bulb being defective is, P (X) = p = 0.03.
A random sample of n = 10 LED light bulbs is selected.
The event of a specific LED light bulb being defective is independent of the other bulbs.
The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.03.
The probability mass function of X is:
[tex]P(X=x)={10\choose x}(0.03)^{x}(1-0.03)^{10-x};\ x=0,1,2,3...[/tex]
Compute the probability that none of the LED light bulbs are defective as follows:
[tex]P(X=0)={10\choose 0}(0.03)^{0}(1-0.03)^{10-0}[/tex]
[tex]=1\times 1\times 0.737424\\=0.737424\\\approx 0.7374[/tex]
Thus, the probability that none of the LED light bulbs are defective is 0.7374.
1. Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
Rolling a single die 53 times, keeping track of the "fives" rolled.
A) Not binomial: there are too many trials.
B) Not binomial: there are more than two outcomes for each trial.
C) Not binomial: the trials are not independent.
D) Procedure results in a binomial distribution.
2. Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
Spinning a roulette wheel 7 times, keeping track of the winning numbers.
A) Not binomial: there are more than two outcomes for each trial.
B) Procedure results in a binomial distribution.
C) Not binomial: there are too many trials.
D) Not binomial: the trials are not independent.
1. Not binomial: there are more than two outcomes for each trial.
Thus, option (B) is correct.
2. Procedure results in a binomial distribution.
Thus, option (B) is correct.
1. Not binomial: there are more than two outcomes for each trial.
In a binomial distribution, each trial can have only two outcomes (usually referred to as success and failure).
In this case, the procedure involves rolling a single die 53 times and keeping track of the "fives" rolled.
Since the outcome can be any number from 1 to 6 on each trial, it does not meet the criteria for a binomial distribution.
Thus, option (B) is correct.
2. Procedure results in a binomial distribution.
In this case, the procedure involves spinning a roulette wheel 7 times and keeping track of the winning numbers. The outcome of each trial is either a win or a loss, which satisfies the requirement for a binomial distribution.
Thus, option (B) is correct.
Learn more about Binomial Distribution here:
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is this a function {(-2, 6), (-3, 7), (-4, 8), (-3, 10)}
No, that is not a function.
To be a function, each different input (x) needs a different output (y)
In the given function there are two -3’s as inputs and they have different y values, so it can’t be a function.
Answer: no
Step-by-step explanation: To determine if a relation is a function, take a look at the x–coordinate of each ordered pair. If the x–coordinate is different in each ordered pair, then the relation is a function.
Note that the only exception to this would be that if the x-coordinate pairs up with the same y-coordinate in a relation more than once, it's still classified ad a function.
Ask yourself, do any of the ordered pairs
in this relation have the same x-coordinate?
Well by looking at this relation, we can see that two
of the ordered pairs have the same x-coordinate.
In this case, the x-coordinate of 3 appears twice.
So no, this relation is not a function.