Answer:
first H(8)= 2×8+1=16+1=17
and G(17)= 4×17-5=68-5=63
Lenny bought x shares of stock for Sy per share last month. He paid
his broker a flat fee of $20. He sold the stock this month for Sp per
share, and paid his broker a 2% commission. Express Lenny's net
proceeds algebraically.
Lenny's net proceeds algebraically are found as;[tex]\rm |xy + 20 - \frac{98}{100} |[/tex]
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Let the bought share will be $ x, and $y is the price per share
Paid fees to the broker = $ 20
The total amount spent = $(xy+20)
The price at which each share sells = $ A
Broker commission = 2 %
The total amount obtained after selling the shares;
⇒ ax - 2% of ax
⇒ 98 % of ax
Hence, Lenny's net proceeds algebraically are found as;[tex]\rm |xy + 20 - \frac{98}{100} |[/tex]
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Answer:
Step-by-step explanation:
what were Laura net proceeds
Which point is a solution to the system?
A. (0, -1)
B.(2, 3) C.(4,0)
D. (6,-6)
Answer:
(0;-1)
Step-by-step explanation:
for more details see the attachment.
2x+15
4x + 5
x = [?]
X
O
Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course.
a. Use your knowledge of triangles to figure out if the two bikers will be able to meet up if each biker travels the distance given.
b. If they do not meet up, how much farther would one of the bikers have to travel to meet the other?
c. What is the measure of the angle between the bikers?
d. What is the relationship between the measure of the angles and the paths the bikers took?
e. Classify the triangle the paths created.
f. How many miles did they travel together?
The bikers will meet at point N, all the questions have been answered below.
What is a Triangle?A triangle is a polygon with three sides, angles, and vertices.
The triangle MNO is formed on the basis of the data given in the question
If the triangle satisfies the sine-rule then the biker meets the other biker at point N
According to the sine rule
In a Triangle ABC of side length a,b and c respectively
a/ sin A = b/ sin B = c/sin C
NM/sin NOM =21/ sin 61°
NM/sin NOM = 24.01
NO/sin OMN =24/sin 89°
NO/sin OMN = 24.003
∠ONM = ( 180-61-89) = 30°
OM / sin ONM = 12/ sin 30 = 24
The ratio of the side and angles of the triangle are almost equal, therefore they satisfy the sine ruleand so, the bikers will meet at point N.
As they are meeting the distance between them will be zero.The measure of the angle between the bikers is as calculated above = 30°.The largest angle is opposite to the longer path.The triangle formed is an acute angle triangle.Total miles they travelled = 24+12+21 = 57 miles.To know more about Triangle
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What is the slope of a line parallel to the line whose equation is3x−4y=8?
−43
−34
34
43
The slope of the parallel line is 3/4
How to determine the slope?The equation is given as:
3x - 4y = 8
Rewrite as:
4y = 3x - 8
Divide through by 4
y = 3x/4 - 2
A linear equation is represented as:
y = mx + b
Where m represents the slope
By comparison:
m = 3/4
Parallel lines have equal slope
Hence, the slope of the parallel line is 3/4
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Factor the trinomial below.
x2 - 14x + 45
Answer:
(x-9) (x-5)
x = 9 x = 5
Step-by-step explanation:
find out which 2 numbers when multiplied give 45 and
when added give -14
they are -9 and -5
(x-9) (x-5)
x = 9 x = 5
Answer:
[tex]x_{1}=9, x_2=5[/tex]
Step-by-step explanation:
Recall a quadratic formula for quadratic equation [tex]ax^2+bx+c=0[/tex]: [tex]x_{1/2}=\frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]
Notice the constant in the given equation [tex]x^2-14x+45[/tex]:
[tex]a=1, b=-14, c=45[/tex]
Substitute the values into the formula:
[tex]x_{1/2}=\frac{-(-14)\pm \sqrt{(-14)^2 -4\cdot 1\cdot 45}}{2\cdot 1}[/tex]
Calculate the values:
[tex]x_{1/2}=\frac{14\pm \sqrt{196 -180}}{2}=\frac{14\pm\sqrt{16}}{2}=\frac{14\pm 4}{2}[/tex]
It follows that there are two solutions:
[tex]x_1=\frac{14+4}{2}=\frac{18}{2}=9[/tex] and [tex]x_2=\frac{14-4}{2}=\frac{10}{2}=5[/tex].
Select one of the factors of 3x² + 4x - 4.
O (x + 4)
O (3x + 2)
O (3x - 2)
O(x - 2)
Answer:
(3x-2)
Step-by-step explanation:
3x² + 4x - 4
look for two factors whose product is (3)(-4)=-12 and sum is +4
The factors will be +6 and -2
substitute these factors inplace of 4x to get:
3x² - 2x + 6x - 4
then factorize:
x(3x-2)+2(3x-2)
finally we get factors: (3x-2)(x+2)
Find the area of a rectangle with
side lengths of in. and in.
2|3
in.
415
in.
Simplify your answer completely.
in.2
Answer:
Area = length * width
= 4/5 * 2/3
= 8/15
Answer:
[tex]area = \frac{8}{15} {in}^{2} [/tex]
Step-by-step explanation:
The solution is in the attached file
To access his bank’s ATM, Tom must choose a four-digit PIN. Any digit from 0 through 9 can be used in the PIN, but digits may not be repeated. How many possible PIN numbers are there?
Answer:
Try using the permutations formulae - nPr
n = 10
r = 4
you should get the answer. I don't have calculator on me and I'm lazy searching an online calculator. cheers
Which rules define the function graphed below? (-2,2) (0,6) (4,6)
Answer:
y = 2x + 3; y = -1/3 x + 3
Step-by-step explanation:
Both lines have y-intercept 3.
The slopes are 2 and -1/3.
The equations are: y = 2x + 3; y = -1/3 x + 3
What is the area of a sector when r = 2 and 0 = 1.75 radians? [?] sq units Round your answer to the nearest tenth. Enter
Answer:
Step-by-step explanation:
The area of a sector in terms of radians as opposed to degrees is
[tex]A=\frac{\theta}{2\pi }*\pi r^2[/tex]
Filling in the formula accordingly gives us
[tex]A=\frac{1.75rad}{2\pi rad}*\pi (2)^2[/tex]
The radians cancel out, the pi's cancel out, the 2 in the denominator cancels out (divides into 2-squared once), leaving us with
A = 1.75(2) so
A = 3.5 units squared
Solve the system using substitution.
5x + 3y = -4
y - 2x = 6
([?], [? ])
Answer:
(-2,2)
Step-by-step explanation:
i tried sorry if it's wrong
At a recent chess tournament, all 15 of the participants had to fill out a form that gave their names, address and age. The ages of the participants were recorded as follows: 36, 48, 54, 92, 57, 63, 66, 76, 66, 80, 82, 65, 39, 77, and 45. Use the data to construct a frequency table and histogram with 3 classes.(15 points) Classes Class Boundaries
The frequency table and histogram are shown in the attached picture.
What is a histogram?It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.
We have:
The ages of the participants were recorded as follows:
36, 48, 54, 92, 57, 63, 66, 76, 66, 80, 82, 65, 39, 77, 45
The classes can be made:
30-42, 43-55, 56-68, 69-81, and 82-94
The histogram is shown in the picture.
Thus, the frequency table and histogram are shown in the attached picture.
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1. Simplify (7y²)
(3y³)
Answer:
21 y power 5
Step-by-step explanation:
The sum of two numbers is 32. One number is 3 times as large as the other. What are the numbers?
Answer: 8, 24
Step-by-step explanation:
Since the sum of two numbers is 32 and one number is 3 times as large as the other, the first number can be defined as x and the second number is 3x.
Divide 32 by (3+1) = 4 and you get 8, which is x.
The second number is 3(8) = 24.
Can someone please tell me the answer to this question?
Answer:
D) 12pm
Step-by-step explanation:
8 pm = 20:00
20:00 + 16:00*4 = 20:00 + 64:00 = 84:00
subtract the 24 hours in 84:00
84:00 - 3 X 24:00 = 12:00
12:00 = 12pm
3 A bag contains red and blue marbles, such that the probability of drawing a blue marble is 8 An experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. What is the probability that both of the marbles drawn are blue? a. b. $ 24% * 39% C. d 0 14% 3 A bag contains red and blue marbles , such that the probability of drawing a blue marble is 8 An experiment consists of drawing a marble , replacing it , and drawing another marble . The two draws are independent . What is the probability that both of the marbles drawn are blue ? a . b . $ 24 % * 39 % C. d 0 14 %
Answer:
My answer: B
Step-by-step explanation:
The probability mass function of random variable X which represents the number of blue marbles drawn in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
The probability of drawing exactly one blue marble = 0.46875
Complete Question
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. an experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome.
To write the Probabilty mass function, we have to establish that in two draws with replacement, the possible number of blue marbles that can be drawn is 0, 1 and 2.
Probability of drawing a blue marble = P(B) = (3/8)
Probability of not drawing a blue marble = P(B') = 1 - (3/8) = (5/8)
- Probability of drawing 0 blue marbles in 2 draws with replacement = P(B') × P(B') = (5/8) × (5/8) = (25/64) = 0.390625
- Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
- Probability of drawing two blue marble in 2 draws with replacement = P(B) × P(B)
= (3/8) × (3/8) = (9/64) = 0.140625
The probability mass function of random variable X which represents the number of blue marbles draan in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
b) Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
So, B is the answer.
A support cable for a 56-foot tower forms a 67° angle with the ground.
What is the length of the cable to the nearest foot?
56 ft.
61 ft.
60 ft.
75 ft.
Which expression is equivalent to sin?
O sin-
sin
O sin 5
O sin 5
11
sin-
Answer: Option 4
Step-by-step explanation:
[tex]\sin \frac{7\pi}{6}=\sin \left(-\frac{\pi}{6} \right)=\sin \frac{11\pi}{6}[/tex]
Using equivalent angles, the equivalent expression to [tex]\sin{\left(\frac{7\pi}{6}\right)}[/tex] is:
[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]
What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
In this problem, we have that [tex]\frac{7\pi}{6}[/tex] is on the third quadrant, as [tex]\pi < \frac{7\pi}{6} < \frac{3\pi}{2}[/tex]. Hence the equivalent angle on the first quadrant is:
[tex]\frac{7\pi}{6} - \pi = \frac{7\pi}{6} - \frac{6\pi}{6} = \frac{\pi}{6}[/tex]
The sine is negative on the third and fourth quadrants, hence the equivalent angle on the fourth quadrant is:
[tex]2\pi - \frac{\pi}{6} = \frac{11\pi}{6}[/tex]
Thus, the equivalent expression is:
[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]
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y is directly proportional to x and inversely proportional to the square of w. Give the equation:
Answer: y=kx/w^2
Step-by-step explanation:
y is directly proportional to x
y∝x
y=kx
y inversely proportional to the square of w.
y ∝ (1/(w)^2)
y=k/w^2
y=kx/w^2
The function ()=2f(x)=x2is transformed to
()=0.4(+1)2f(x)=0.4(x+1)2
Which statement describes the effect(s) of the transformation on the graph of the original function?
The parabola is narrower and shifted 1 unit to the right.
The parabola is narrower and shifted 1 unit to the left.
The parabola is wider and shifted 1 unit to the right.
The parabola is wider and shifted 1 unit to the left.
Answer:
StepWhat is the measure of z? Z X y 4 9 z = [ ? ]VI-by-step explanation:
32y+54x+56=y what is y
System A
x−4y=1
5x+6y=−5
System B
x=1+4y
5x+6y=−5
1) How can we get System B from System A?
CORRECT (SELECTED)
Replace one equation with itself where the same quantity is added to both sides
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
CORRECT (SELECTED)
Yes
1. System B from System A by replacing one equation with itself where the same quantity is added to both sides
2. Yes, both system A and system B are equivalent and therefore has the same solution
How to prove the statementsSystem A
x − 4y= 1
5x + 6y= −5
System B
x = 1+4y
5x + 6y= −5
1. System B can be gotten from system A by
from the first equation of A
x − 4y= 1
Make 'x' subject of formula
x = 1 + 4y
This makes it equal to tat of system B
Thus, replacing one equation with itself where the same quantity is added to both sides
2. System A
x = 1 + 4y
5x + 6y= −5
System B
x = 1 + 4y
5x + 6y= −5
From the above equations, we can see that both system A and system B are equivalent and therefore has the same solution.
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Find the slope of the straight line that passes through (–2, –4) and (3, –5).
A. m= -1/5
B. m = –1
C. m = 1/5
D. m = 1
[tex]\large\boxed{\textsf{A.}\ m=-\frac{1}{5}}[/tex]
We can use the slope formula, where our points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]:
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
This is also known as "rise over run" because it represents the change in vertical ([tex]y[/tex]) position divided by the change in horizontal ([tex]x[/tex]) position.
Substitute the values from the points given:
[tex]\dfrac{(-5)-(-4)}{3-(-2)}[/tex]
Subtract:
[tex]\boxed{\dfrac{-1}{5}}[/tex]
what is the average rate of change if this function interval x = -3 to x = 0
The average rate of change of the function, over the given interval is 2.
This question is incomplete, the complete question is:
What is the average rate of change of f(x) = 2x+10, if this function interval are x = -3 to x = 0.
What is the average rate of change over the interval?The average rate of change of f(x) over the interval [a,b] is expressed as;
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Given that;
f(x) = 2x + 10Interval: [ -3, 0 ], a = -3 and b = 0We substitute our values into the expression above.
[tex]\frac{f(b)-f(a)}{b-a}\\\\\frac{f(0)-f(-3)}{0-(-3)}\\\\\frac{[2(0)+10]-[2(-3)+10]}{0-(-3)}\\\\\frac{[10]-[-6+10]}{3}\\\\\frac{[10]-[4]}{3}=\frac{6}{3}=2[/tex]
Therefore, the average rate of change of the function, over the given interval is 2.
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If ∠ 1 = 26 o , find the measure of ∠ 4 .
The angle ∠4 of the given transversal shown in the diagram is gotten as; 26°.
How to find alternate angles?The alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
Now, we are told that ∠1 = 26° as seen in the attached diagram. However, it is clear that ∠2 is an alternate angle to ∠1. Thus, we can say that ∠2 = 26°.
Now, Corresponding angles are the pairs of angles that are found in the same relative position on different intersections.
From the diagram we see that ∠4 is a corresponding angle to ∠2. Thus;
∠4 = 26°.
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2. Employed Women If 60% of all women are employed
outside the home, find the probability that in a sample
of 20 women,
aid sel
Mil
2
a. Exactly 15 are employed
b. At least 10 are employed
c. At most 5 are not employed outside the home
Using the binomial distribution, the probabilities are given as follows:
a) 0.0747 = 7.47%.
b) 0.8725 = 87.25%.
c) 0.1256 = 12.56%.
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.The values of the parameters are:
n = 20, p = 0.6.
Item a:
The probability is P(X = 15), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 15) = C_{20,15}.(0.6)^{15}.(0.4)^{5} = 0.0747[/tex]
Item b:
The probability is:
[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + \cdots + P(X = 20)[/tex]
Finding each value with the equation we used in item a, we have that:
[tex]P(X \geq 10) = 0.8725[/tex]
Item c:
At least 20 - 5 = 15 on the road, hence the probability is:
[tex]P(X \geq 15) = P(X = 15) + P(X = 16) + \cdots + P(X = 20)[/tex]
Then, using the same procedure as item b, we have that:
[tex]P(X \geq 15) = 0.1256[/tex]
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Evaluate a=5 and y= -7 for y-2a
Answer: -17
Step-by-step explanation:
y - 2a
= -7 - 2(5)
= -7 - 10
= -17
Write 13.13.13.13.13 in exponential form?
13.13.13.13.13 in exponential form is 13^5
How to rewrite the expression?The expression is given as:
13.13.13.13.13
The factors of the above expression are 13.
And each factor is grouped by product
There are five 13s in the expression.
So, we have:
13.13.13.13.13 = 13^5
Hence, 13.13.13.13.13 in exponential form is 13^5
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In one lottery game, contestants pick five numbers from 1 through 23 and have to match all five for the big prize (in any order). You'll get twice your money back if you match three out of five numbers. If you buy four tickets, what's the probability of matching three out of five numbers?
(Enter your answer as a fraction in lowest terms.)
The probability of matching three out of five numbers is 153/33649
How to determine the probability?The numbers are given as:
1 to 23
There are five matching numbers
The probability of getting a match is:
p = 5-k/n where k = 0, 1, 2
While the complement probability is
q = (n - 2)/n
Using the above formulas, the probability of getting from 5 is:
P = 5/23 * 4/22 * 3/21 * 18/20 * 17/19
Evaluate the product
P = 153/33649
Hence, the probability of matching three out of five numbers is 153/33649
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