Answer:
3/4.
Step-by-step explanation:
Total number of ways to pick 3 digits from the 4 given digits = 4P3
= 4!/ 1! = 24 ways.
The odd numbers are formed when 7 is the last digit of the 3 digits and this will be in 6 numbers 247, 267, 427, 467, 647 and 627 . So there will be 24 - 6 = 18 even numbers.
So the probability of only even digits = 18/24 = 3/4.
I need help with this
What is the area of the triangle formed from (0,-1), (0.4), and (4,-1)?
Answer:
10 squared units
Step-by-step explanation:
This triangle is pretty easy since it creates a right triangle. So the base length and height length are pretty easy to identify.
The area of a triangle is .5*base*height.
The base length after drawing the points is a horizontal so just count it or do 4-0=4.
The height length after drawing the points is a vertical so just count it or do 4-(-1)=4+1=5.
So the area of the triangle is .5*4*5=.5(20)=10 units squared.
Now if you didn't fill like drawing it and you knew how to find the determinant.
You just compute
.5 times det| 0 -1 1 |
| 0 4 1 |
| 4 -1 1 |
.5[ 0 det| 4 1 | - -1 det| 0 1 | + 1 det | 0 4 | ]
| -1 1 | | 4 1 | | 4 -1 |
.5[ 0 - -1(0-4) + 1(0-16)]
.5[ 0 -4 -16]
.5[-20]
-10
And if you get a negative just take the absolute value of it giving you 10.
If (x - 5) is a factor of f(x), which of the following must be true?
O A root of f(x) is x = -5.
O A root of f(x) is x = 5.
O Both x = -5 and x = 5 are rots of f(x).
O Neither x = -5 nor x = 5 is a root of f(x).
Answer:
A root of f(x) is x=5
Step-by-step explanation:
If (x-5) is a factor of f(x), then 5 is a root.
If (x+5) is a factor of f(x), then -5 is a root.
So we are only given that (x-5) is a factor of f(x), so we only know that x=5 is a root.
This is by factor theorem. It says if (x-c) is a factor then f(c)=0 which means c is a root of f(x) because it makes the expressions equal to 0.
what’s 11/5 simplified ?
The simplified form of the fraction 11/5 is determined as 2 1/5.
What is simplification of an expression?Simplification refers to the process of reducing an expression, equation, or fraction into its simplest or most concise form.
Fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). This reduces the fraction to its simplest form.
The given fraction expression;
11/5
This expression is simplified as follows;
11/5 = 2 remainder 1
The final expression becomes;
11/5 = 2 1/5
Thus, the simplified form of the expression 11/5 is determined as 2 1/5.
Learn more about simplification here: https://brainly.com/question/28008382
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8. A patient is told to take 12 1/2 grains (gr) of aspirin qd (every day). If the
aspirin tablets contain 5 gr each, how many tablets must the patient
take qd?
Answer:
The patient must take [tex]2\frac{1}{2}\ tablets[/tex] per day
Step-by-step explanation:
we know that
12 1/2 grains (gr) of aspirin is equal to 12.5 grains
using proportion
Let
x -----> the number of aspirin tablets
[tex]\frac{1}{5} \frac{tablet}{gr} =\frac{x}{12.5} \frac{tablets}{gr} \\ \\x= 12.5/5\\ \\x=2.5\ tablets[/tex]
Convert to mixed number
[tex]2.5=2\frac{1}{2}\ tablets[/tex]
Which of the following shows the length of the third side, in inches, of the triangle below?
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=adjacent\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ \sqrt{61^1-11^2}=a\implies \implies \sqrt{3600}=a\implies 60=a[/tex]
A coffee franchise is opening a new store. The company estimates that there is a 70% chance the store will have a profit of $50,000, a 5% chance the store will break even, and a 25% chance the store will lose $3,500. Determine the expected gain or lose for this store.
Step-by-step explanation:
The expected value is the sum of each outcome times its probability.
E = (0.70)(50000) + (0.05)(0) + (0.25)(-3500)
E = 34125
The store is expected to gain $34,125.
To calculate the expected gain or loss for the new store, we multiply each possible outcome by its probability, then sum these values. This results in an expected gain of $34,125 for the store.
The problem requires calculating the expected value of the coffee franchise's new store opening. We use probability and finance to estimate the expected gains or losses.
The expected value (EV) is calculated as follows:
Multiply each outcome by its respective probability.
Sum these products to get the EV.
So, the expected value is:
EV = (0.70 imes $50,000) + (0.05 imes $0) + (0.25 imes -$3,500)
EV = $35,000 + $0 - $875
EV = $34,125
This implies an expected gain of $34,125 for the new store.
NEED HELP ASAP! The graph gx is a translation of the function fx=x2. The vertex of gx is located 5 units above and 7 units to the right of the vertex of Fx. Which equation represents gx
Answer:
g(x) is option 1 or g(x) = (x + 7)^2 + 5
A quadratic equation has the general form of:
y=ax² +bx + c
It can be
converted to the vertex form in order to determine the vertex of the parabola.
It has the standard form of:y =a(x+h)² + k
where hand k represents the vertex, h represent the point in the x axis and k is thepoint in the y axis. Therefore, from the details given in the problem, the equation that represents
g(x) is option 1 or g(x) = (x + 7)^2 + 5
The shortest side of an isosceles triangle is 26 cm less than twice as long as the other sides. The perimeter of the triangle is 70 cm. Find the lengths of the three sides and list them in ascending order.
Answer:
22 cm, 24 cm, and 24 cm.
Step-by-step explanation:
Isosceles Triangle is a type of triangle in which two of the three sides are equal in length. The perimeter is 70 cm. Therefore, in this question, since the sides are unknown, we can assume that:
Length of the shorter side = x cm.
Length of the other sides = y cm.
The relationship between x and y is given by:
x = (2y - 26) cm (because it is mentioned that the shortest side is 26 cm less than twice as long as the other sides).
Perimeter of a triangle = sum of all sides.
Since its an isosceles triangle, therefore:
Perimeter of the triangle = x + 2y.
Substituting the values in the perimeter formula gives:
Perimeter of the triangle = 2y - 26 + 2y.
70 = 4y - 26.
4y = 96.
y = 24 cm.
Substituting y = 24 in the equation x = 2y - 26 gives x = 2(24) - 26 = 22 cm.
So in the ascending order, the lengths are 22 cm, 24 cm, and 24 cm!!!
The number of users of the internet in a town increased by a factor of 1.01 every year from 2000 to 2010. The function below shows the number of internet users f(x) after x years from the year 2000:
f(x) = 3000(1.01)x
Which of the following is a reasonable domain for the function?
Answer: 3347.005 users but you cant divide people in half so its 3347 people
Answer0< x<10
Step-by-step explanation: it says reasonable so this is one of the few time it’s not all positive integers cause it’s a real world question and it’s from 2000 to 2010 so 10 years is the REASONABLE domain for this problem
on a piece of paper,graph c(x)=3X+2.00.Then determine which answer matches the graph you drew,including the correct axis labels.
Answer:
Attached
Step-by-step explanation:
The equation for the graph is
c(x)=3x+2
rewrite as
y=3x+2.............................................(1)
Then graph equation to visualize as attached.
Let the x-axis to represent minutes and the y-axis to represent cost
Answer:
The graph of required function is shown below.
Step-by-step explanation:
The given function is
[tex]c(x)=3x+2.00[/tex]
In this function c(x) is the cost for a taxi ride and x is the number of minutes.
It means, in the graph of cost function x-axis represents the time in minutes and y-axis represents the cost.
Time can not be negative. So, the function is defined for all non-negative values of x.
Table of values:
x c(x)
0 2.00
1 5.00
2 8.00
3 11.00
Plot any two points from these points on a coordinate plane and connect them by straight line.
Therefore, the graph of required function is shown below.
If .... a-b=5 Then what is 2(a-b) ??
Answer: 10
Step-by-step explanation:
if we know a-b=5, to get the answer of 2(a-b) multiply 5 by 2.
Answer:
10
Step-by-step explanation:
a-b=5
Multiply each side by 2
2(a-b) = 2*5
2 (a-b) = 10
I need help with number 2, you can use number 1 as an example. I’m confused on how to do this one as x and y are still in the equation, so I’m not sure how to get x or y alone. TYSM!!!! 20 POINTS!!!
Answer:
y = 1/2x+1/2Step-by-step explanation:
The ax+by+c=0 that is confusing you is just the standard form of a linear equation. It is supposed to help you formulate the linear equation. In this case, a = 1, b = -2, c = 1
Therefore,
1x -2y + 1 =0
Now, you said that you are confused on how to isolate and solve for one variable; in this case, you can't. But, you can switch around the places of the variables to solve for one variable. In this case, its best to solve for y, since linear equations are easier to understand written in Slope-intercept form:
y = mx+b
Now, you must be really confused, but look at the work I am about to do so you can learn how to make this easier for you!
1x -2y + 1 =0
-1x -1x --> Subtract 1x from both sides to isolate the y variable to the left side and to keep the equation balanced
-2y + 1=0 -1x
-1 -1 --> Subtract 1 from both sides to isolate the y variable further and to keep the equation balanced
-2y = -1x-1
(-2y/-2) = ((-1x-1)/-2) --> Divide by -2 on both sides to isolate the y variable even further and to keep the equation balanced
y = 1/2x+1/2
y = mx+b
This is written in slope-intercept form. It is called as such since it gives you the slope (written in front of the x variable,in this case 1/2; m = 1/2) and the y-intercept (the letter b; in this case b = +1/2). The y-intercept is where the x coordinate is equal to zero, but it is the place where the line crosses the y-axis. So your b = 1/2, which means that your y-intercept is (0, 1/2)
These are all things you use to graph a line and helps to make it easier to graph them!
Final Answer:
y = 1/2x+1/2
How do I solve this equation 4x^2-12x+29=20
[tex]4x^2-12x+29=20 \\4x^2-12x+9=0\\(2x-3)^2=0\\2x-3=0\\2x=3\\x=\dfrac{3}{2}[/tex]
With these kind of equations you want to use the quadratic formula. These problems take time, so don't fret you'll get there! :)
Quadratic formula:
-b +- √b^2-4(a)(c)
--------------------------
2(a)
Next find your a, b, and c!
a= 4
b=12
c=29
Time to plug those answers in.
12 +- √(-12)^2-4(4)(9)
-------------------------------
2(4)
Next solve everything in the radical first! Then the bottom.
12 +- √144-144
----------------------- ~ x=12/8 ~ x=3/2
8
You get: x=3/2!
Solve and graph the absolute value inequality: |2x + 4| > 8. number line with open circles on negative 6 and 2, shading in between. number line with closed circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 2 and 2, shading going in the opposite directions.
Answer:
Part 1) The solution of the absolute value is (-∞,-6)∪ (2,∞)
Number line with open circles on negative 6 and 2, shading going in the opposite directions
Part 2) The graph in the attached figure
Step-by-step explanation:
we have
[tex]\left|2x+4\right|>8[/tex]
we know that
The absolute value has two solutions
step 1
Find the positive case
[tex]+(2x+4)>8[/tex]
[tex]2x>8-4[/tex]
[tex]2x>4[/tex]
[tex]x>2[/tex]
The solution is the interval ----> (2,∞)
All real numbers greater than 2
step 2
Find the negative case
[tex]-(2x+4)>8[/tex]
Multiply by -1 both sides
[tex](2x+4)<-8[/tex]
[tex]2x<-8-4[/tex]
[tex]2x<-12[/tex]
[tex]x< -6[/tex]
The solution is the interval ----> (-∞,-6)
All real numbers less than -6
therefore
The solution of the absolute value is
(-∞,-6)∪ (2,∞)
Number line with open circles on negative 6 and 2, shading going in the opposite directions
step 3
using a graphing tool
see the attached figure
need someone to teach/explain how to do these problems: asap
Answer:
The farthest Left
Step-by-step explanation:
The second equation, y<x+1, means that every y value will be less than the x value +1. Since it is less than, and not less than or equal to, the graph is represented by the dotted line and not a solid line. Moving on to the next problem, we have to get it in slope-intercept form. We start with x-4y is less than or equal to 4. We need to separate the x and y, so we add 4u to the negative 4y, cancelling it out, but what we do to one side, we have to do to the other, so we add 4y, making our equation x is less than or equal to 4y + 4. Next, we need to get the y by itself, so we subract 4 from the y side, cancelling it out and subtract it from the other side, which leaves us with x-4 is less than or equal to 4y. 4y is just 4 times y so we divide it by four on both sides to get y is greater than or equal to 1/4x-1. Since the solution can be equal to, we make the line solid and when we plot both lines, we get the graph furthest to the left.
G-1/6=1/6. Solve for G
G -1/6= 1/6
Move -1/6 to the other side
sign changes from -1/6 to 1/6
G-1/6+1/6=1/6+1/6
G = 2/6
Reducing: divide by 2 for 2/6
2/2= 1
2/6= 3
Answer : G= 2/6= 1/3
Un triángulo tiene un área de 48 cm2 y una base de 6cm . Encuentra la longitud de la altura.
PLEASE ANSWER FAST
EASY QUESTION
50 POINTS
Complete the sentence. A secant is a
________ in the plane of a circle that
intersects the circle at exactly
________ points.
Answer:
A Secant is a line in the plane of a circle that intersects the circle at exactly two points
Step-by-step explanation:
A line intersecting in two points is called a secant line, in one point a tangent line and in no points an exterior line. A chord of a circle is the line segment that joins two distinct points of the circle. A chord is therefore contained in a unique secant line and each secant line determines a unique chord.
Please help
10 minutes!!
Find the value of x and the value of y.
A. x = 15, y = 10
B. x = 20, y = 50
C. x = 50, y = 10
D. x = 50, y = 20
For this case we have from the first quadrant that:
[tex]70 + A1 = 90[/tex]
Clearing angle 1:
[tex]A1 = 90-70[/tex]
[tex]A1 = 20\ degrees[/tex]
Ahors, the angle A3 of the third quadrant measures 70 degrees, it is observed that it is opposed by the vertex at the angle of 70 degrees of the first quadrant. So:
[tex]A3-A1 = 70-20 = 50[/tex]
Answer:
Option B
How many solutions does the following system of equations have
Answer:
D. ZeroStep-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=\dfrac{5}{2}x+2&(1)\\2y=5x+8&(2)\end{array}\right\\\\\text{substitute (1) to (2)}:\\\\2\left(\dfrac{5}{2}x+2\right)=5x+8\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(2)\left(\dfrac{5}{2}x\right)+(2)(2)=5x+8\\\\5x+4=5x+8\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\4=8\qquad\bold{FALSE}\\\\\text{The system of equations has no solution.}[/tex]
If the domain of the square root function f(x) is x<7, which statement must be true?
7 is subtracted from the x-term inside the radical.
The radical is multiplied by a negative number.
7 is added tihe radical term.
The x-term inside the radical has a negative coefficient.
Answer:
The x-term inside the radical has a negative coefficient
Step-by-step explanation:
The argument of a square root should be ALWAYS greater or equal to zero. If the domain of the function is x<7, rearranging, we have: 0<x-7
Therefore the argument is: x-7, and the function is: y = √(x-7)
The statement "The x-term inside the radical has a negative coefficient" is the right answer.
how much is 2 plus 3
Answer:
5
Step-by-step explanation:
Add
2 plus 3 equals 5
Step-by-step explanation:
so put two fingers up and then put three up then you get your answer.
Find the value of C in the picture please
Answer:
Option A. 93.5°
Step-by-step explanation:
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
so
∠C=(1/2)[83°+2(52°)]
∠C=(1/2)[83°+104°]
∠C=(1/2)[187°]
∠C=93.5°
An experiment was conducted, and it was determined that plants that received more than two hours of sunlight per day grew larger than plants that received less than two hours of sunlight per day. Which of the following best describes this situation?
A)This is an example of correlation and causation.
B)This is an example of correlation.
C)This is an example of causation.
D)This is not an example of causation or correlation.
Answer:
C). This is an example of causation
Step-by-step explanation:
Causation : It can be defined as the one event is the result of the other event. It is simply the cause and its effect. There is a causal relation between the two events.
Correlation : It can described the direction of the relation between two or more events or variables.
The conclusion of the experiment is that the plant that received more than two hours of sunlight in each day grew more than the plants that received less than two hours of sunlight in each day.
This is the cause of one event and its effect on the other event.
So option C is correct because sunlight causes plants to grow.
So option C). This is an example of causation.
Answer:
C( This is an example of causation
What is the maximum number of turns for the graph of f(x)=x^4+3x^2?
Answer:
The turns of a graph is represented by the number of maximum or minimum that the function has.
If we differenciate f(x) we get:
f'(x)=4x^3+6x
f'(x)=2x(2x^2 + 3)
Therefore f'(x) =0, when x=0. Given that negative roots are not defined.
Therefore, the number of turns will be given by the number of solutions of f'(x) which is 1.
Attached you find the graph of the function which confirms the number of turns.
If the function had other solutions, the maximum number of turns it could have is 3! because f'(x) is a third degree polynomial, therefore it can't have more than 3 solutions!
3x-2y=-1 Y=-x+3 is (1,2) a solution of the system
Answer:
Yes
Step-by-step explanation:
To be a solution of the system, it has to satisfy both the equations.
Let's check first one:
3x - 2y = -1
3 (1) - 2(2) = 3 - 4 = -1
So correct (satisfies).
Now, 2nd one:
y = -x + 3
y = -(1) + 3
y = -1 +3
y = 2
Yes, this is satisfied.
Hence, (1,2) IS A SOLUTION OF THE SYSTEM
On three rolls of a single die, you will lose $19 if a 3 turns up at least once, and you will win $5 otherwise. What is the expected value of the game?
Let X be the random variable for the amount won on a single play of this game.
Answer:
-16 cents
Step-by-step explanation:
We are given that on three rolls of a single die, you will lose $19 if a 3 turns up at least once, and you will win $5 otherwise.
We are to find the expected value of the game.
P (at least one 5 in three rolls) = 1 - P (no. of 3 in three) = [tex]1-(\frac{3}{6} )^2[/tex] = 0.875
P (other results) = 1 - 0.875 = 0.125
Random game value = -19, +5
Probabilities: 0.875, 0.125
Expected game value (X) = 0.875 × (-19) + 0.125 × (5) = -16 cents
Therefore, every time you play the game, you can expect to lose 16 cents
Answer:
It is expected to lose 5.10 dollars
Step-by-step explanation:
The probability of getting a 3 by throwing a die once is 1/6.
By throwing it 3 times the probability of not getting a 3 is:
[tex]P=(\frac{5}{6}) ^ 3 =0.5787[/tex]
Then the probability of obtaining a three at least once in the 3 attempts is:
[tex]P'=(1-0.5787)=0.421[/tex]
So if X is the discrete random variable that represents the amount gained in a single move of this game, the expected gain E(X) is:
[tex]E(X)=P'*(X') + P*(X)[/tex]
[tex]E(X) =0.421'*(-19) + 0.5787*(5)\\\\E(X) =-\$5.10[/tex]
Ali read 5 pages of her book in 7 minutes. At this rate, how long will it take Ali to read 15 pages of her book? A. 21 minutes. B. 17 minutes. C. 14 minutes. D. 12 minutes.
What’s the slope of a line perpendicular to a line through points,
E(5,7), F(3,1)
Answer:
-1/3 is the slope perpendicular
Step-by-step explanation:
When we have 2 points, we can use the formula
m = (y2-y1)/(x2-x1) to find the slope
m = (1-7)/(3-5)
=-6/-2
=3
The slope is 3
We want a slope perpendicular
Remember that is the negative reciprocal
- (1/3)
-1/3
Two lines are perpendicular when,
[tex]a_1=-a_2^{-1}[/tex]
Now solve for [tex]a_2[/tex] to get [tex]a_2=-a_1^{-1}[/tex]
First we calculate the slope [tex]a_1[/tex] from the given points [tex]E(x_1,y_1),F(x_2,y_2)\longrightarrow E(5,7),F(3,1)[/tex].
[tex]a_1=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-7}{3-5}=\dfrac{-6}{-2}=3[/tex]
Now use the first formula and insert the data in it to find the value of the second slope [tex]a_2[/tex],
[tex]a_2=-3^{-1}=\boxed{-\dfrac{1}{3}}[/tex]
And that's it.
Hope this helps.
r3t40