Answer:
f(- 5) = 13
Step-by-step explanation:
To evaluate f(- 5) substitute x = - 5 into f(x)
f(- 5) = - 3 × - 5 - 2 = 15 - 2 = 13
A local restaurant has 20 tables all together with the most popular tables by the window and the salad bar. 5 of the tables are next to the window and another 5 of the tables are next to the salad bar. All of the customers are allowed to seat themselves. If all of the window tables are open, what is the probability that the next two customers will choose to sit at the window?
A. 50%
B. 5.2%
C. 52%
D. 6.2%
Answer:
B. 5.2%
Step-by-step explanation:
Total number of tables = 20
Number of tables next to window = 5
Number of tables next to salad bar = 5
Probability that the first customer chooses the window table = 5 out of 20 = [tex]\frac{5}{20}[/tex]
When this table is chosen, the total remaining tables are 19 out of which 4 tables are next to windows.
So, now the probability that a customer will choose a window table = 4 out of 19 = [tex]\frac{4}{19}[/tex]
Since the selection of two customers is independent of each other, the probability that two customers will chose the window table will be the product of probabilities of their individual selections.
Therefore, the probability that the next two customers will choose to sit at the window = [tex]\frac{5}{20} \times \frac{4}{19} = 0.052[/tex]
Thus, the probability that the next two customers will choose to sit at the window is 0.052 or 5.2%
Madison represented the sentence
"The product of 3 and the difference of -4 and the quotient of a number and -2 is at most 5"
by using the inequality 3 (-4 - n/-2) < 5
What is madison's error?
Answer:
The mistake is that it can be 5. They forget to include the equals in the less than or equals
Step-by-step explanation:
Start at the inside and work out
quotient of a number and -2
n/-2
difference of -4 and the quotient of a number and -2
-4 - n/-2
product of 3 and the difference of -4 and the quotient of a number and -2
3* (-4 - n/-2)
is at most 5
3* (-4 - n/-2)≤5
The mistake is that it can be 5. They forget to include the equals in the less than or equals
Answer: C
Step-by-step explanation:
Solve the exponential equation for x. 625 = 5 (7x-3)
A. x = 1
B. x = -1
C. x = 2
D. x = -2
Answer:
A. x = 1Step-by-step explanation:
[tex]5^{7x-3}=625\\\\5^{7x-3}=5^4\iff7x-3=4\qquad\text{add 3 to both sides}\\\\7x=7\qquad\text{divide both sides by 7}\\\\x=1[/tex]
Answer:
X = 1
Step-by-step explanation:
what is the input if the output is 0 ?
In other words, what is y if x is 0.
Look on the graph, a line passes through point, [tex]A(x,y)\longrightarrow A(0,-3)[/tex]
So we can conclude that at that very point the input x was 0 and the output y was -3 therefore,
[tex]\boxed{f(-3)=0}[/tex]
Hope this helps.
r3t40
The perimeter of a square is equal to four times the length of its side write the direct variation equation that represents this situation let y be the dependent variable and let x be the independent variable
Answer:
y = 4x
Step-by-step explanation:
Let x = length of the side = independent variable
Let y = perimeter of the square = dependent variable
y = 4x
2(5x+3)=4x+18 how would i solve this problem
Answer:
x=2
Step-by-step explanation:
2(5x+3)=4x+18 Remove the brackets
10x + 6 = 4x + 18 Subtract 4x from both sides.
10x - 4x + 6 = 4x-4x + 18 Combine
6x + 6 = 18 Subtract 6 from both sides
6x + 6 - 6 = 18 - 6 Combine
6x = 12 Divide by 6
6x/6 = 12/6 Do the division
x = 2
What is the scale factor of LMN to OPQ?
Answer:
The scale factor is 1 because it has not increased or decreased and therefore are congruent
The equation y=mx+b is the slope-intercept form of a linear equation.
Solve y=mx+b for m
Answer: [tex]m=\frac{y-b}{x}[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
To solve for the slope "m", you can follow these steps:
- Subtract "b" from both sides of the equation:
[tex]y-b=mx+b-b\\\\y-b=mx[/tex]
- Divide both sides of the equation by "x". Then:
[tex]\frac{y-b}{x}=\frac{mx}{x}\\\\m=\frac{y-b}{x}[/tex]
Money in a savings account is compounded continuously over time, t, and is modeled by the function
f(t) = 1000e0.017. What is the rate at which the balance grows?
Answer:
1.7% compounded continuously
Step-by-step explanation:
The model used for continuous compounding is ...
f(t) = Pe^(rt)
where P is the principal amount, and r is the interest rate being compounded. Assuming a typo in your given equation, you have ...
f(t) = 1000·e^(0.017t)
Matching the various parts of the equation, we see that P = 1000 and r = 0.017 = 1.7%.
The balance grows at a continuous rate of 1.7%.
To find the growth rate of the account balance in the given function, we differentiate it to obtain [tex]f'(t) = 1000 × 0.017e^(0.017t)[/tex], which shows that the balance grows at a continuous compound rate of 1.7% per year.
The student's question refers to a savings account where the money is compounded continuously. We are given the function [tex]f(t) = 1000e^{0.017t,[/tex]that models the account balance over time t. To find the rate at which the balance grows, we can differentiate this function concerning time.
The derivative of the function[tex]f(t) = 1000e^{0.017t[/tex] concerning t gives us [tex]f'(t) = 1000 × 0.017e^{0.017t[/tex]. This represents the rate of change of the account balance at any time t, which is also the growth rate. Therefore, the rate at which the balance grows is 0.017 or 1.7% per year.
Which of the following is the simplified fraction that's equivalent to 9.315?
A. 9315⁄999
B. 931⁄99
C. 9105⁄333
D. 935⁄111
For this case we must indicate a fraction equivalent to 9,315.
We evaluate the fractions:
[tex]\frac {9315} {999} = 9.32432432432\\\frac {931} {99} = 9,40404040404\\\frac {9105} {333} = 27,3423423423\\\frac {935} {111} = 8,42342342342[/tex]
It is observed that the fraction closest to 9,315 is[tex]\frac {9315} {999}[/tex]
If we round 9.315 we have 9.32
If we round[tex]\frac {9315} {999}[/tex] we have 9.32
Answer:
Option A
A student stands on a bathroom scale that uses the U.S. system of units. Which
of the following is most likely to be the weight shown on the scale?
A. 85 grams
B. 85 ounces
C. 85 pounds
D. 85 kilograms
Answer: 85 pounds,
Step-by-step explanation: Americans don't use the other things to measure weight.
What is the slope of the line shown below?
Answer:
1/6
Step-by-step explanation:
To find slope here, I'm going to use that slope is rise/run.
I'm going to start at the left dot. How much would I need to go to be on same level as the right point? Up 3.
Now that we are on the same level, how many units right would I need to travel to get to the right point? Right 18.
The slope is 3/18.
You can reduce this to 1/6.
Answer:
A. 1/6
The slope is 1/6.
Step-by-step explanation:
The slope formula is [tex]\Rightarrow\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex].
[tex]y_2=6\\y_1=3\\x_2=12\\x_1=(-6)\\[/tex]
[tex]\displaystyle\frac{6-3}{12-(-6)}=\frac{3}{18}=\frac{3\div3}{18\div3}=\frac{1}{6}[/tex]
[tex]\large\textnormal{Therefore, the slope is 1/6.}[/tex]
Determine if the function is a polynomial function. If the function is a polynomial function, state the degree and the leading coefficient. If the function is not a polynomial, state why. f(x)=(2x+3)^2(3x+5)^2
This is not a polynomial function because there is no leading coefficient.
This is a polynomial function of degree 4 with a leading coefficient of 36.
This is a polynomial function of degree 4 with a leading coefficient of −36.
This is not a polynomial function as the factors are not all linear.
The given function [tex]f(x)=(2x+3)^2(3x+5)^2[/tex] is a polynomial function of degree 4, with a leading coefficient of 36 determined by multiplying the squares of the leading terms of the binomials.
The function[tex]f(x)=(2x+3)^2(3x+5)^2[/tex] is indeed polynomial. To determine the degree and the leading coefficient of a polynomial, we need to expand the given expression. However, without full expansion, we can deduce the degree by adding the exponents of the individual factors since the bases are polynomials of degree 1 (2x+3 and 3x+5).
Each factor is squared, so [tex](2x+3)^2[/tex] has degree 2 and ([tex]3x+5)^2[/tex]also has degree 2. By adding these, we find that the polynomial's degree is 2+2=4. To find the leading coefficient, we consider the leading terms of each binomial which are 2x and 3x. Squaring these and then multiplying them together [tex](2x)^2 * (3x)^2 = 4x^2 * 9x^2,[/tex]we get 36 as the leading coefficient when x is raised to the 4th power. Therefore, the correct answer is: This is a polynomial function of degree 4 with a leading coefficient of 36.
The length of an edge of a cube is 4 ft.
What is the volume of the cube?
Enter the answer.
[1] ft3
Answer:
V = 64 ft^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length of the cube
V = (4)^3
V = 64 ft^3
Answer:
64 ft
Step-by-step explanation:
Volume=Height*Length*Base
=4*4*4
=16*4
=64 ft
Find the value of x using the laws of sine.
Answer:
Rounded to nearest hundredths is 8.75.
Rounded to nearest tenths is 8.7.
Step-by-step explanation:
Law of sines:
[tex]\frac{\sin(A)}{\text{ side opposite to }A}=\frac{\sin(B)}{ \text{ side opposite to }B}[/tex]
Measure of angle [tex]A[/tex] is 28 and the side opposite to it is [tex]x[/tex].
Measure of angle [tex]B[/tex] is 105 and the side opposite to it is 18.
Plug in to the formula giving:
[tex]\frac{\sin(28)}{x}=\frac{\sin(105)}{18}[/tex]
Cross multiply:
[tex]18 \sin(28)=x \sin(105)[/tex]
Divide both sides by sin(105):
[tex]\frac{18 \sin(28)}{\sin(105)}=x[/tex] is the exact answer.
I'm going to type it in my calculator now:
18*sin(28) / sin(105) is what is going in there.
The output is 8.748589074.
Rounded to nearest hundredths is 8.75.
Rounded to nearest tenths is 8.7.
Find the x-intercept of the line whose equation is 8x+2y=4
Answer:
x = 1/2
Step-by-step explanation:
Plug in 0 for y
8x + 2(0) = 4
Simplify
8x + 0 = 4
8x = 4
Divide both sides
8x/8 = x
4/8 = 1/2
Simplify
x = 1/2
Answer
x = 1/2
Answer:
X=1/2
Step-by-step explanation:
Find the measure of stv in the figure
Answer:
STV = 153 degrees
Step-by-step explanation:
180 - 18 = 162 (angles on a straight line equal 180 degrees)
3q + 15q = 162
18q = 162
q = 162 / 18
q = 9
STV = 15q + 18
= 135 + 18
= 153
Hope this helps!
UTV is a straight line, which equals 180 degrees.
This means both angles UTS and STV when added together must equal 180.
3q + 15q +18 = 180
Simplify:
18q +18 = 180
Subtract 18 from both sides:
18q = 162
Divide both sides by 18:
q = 162 / 18
q = 9
Now you have a value for q to solve the angle.
STV = 15q +18
Replace q with 9:
STV = 15(9) +18
Simplify:
STV = 135 + 18 = 153 degrees.
BRAINLIST ADDED?ANSWER THIS QUESTION I WILL UPVOTE YOUR ANSWER!!✔:)
Answer:
-10 4/64, -.3125, 1/16, 10 51/80, 10 45/48
Step-by-step explanation:
negatives, the larger the number the smaller it is, opposite for positives. 10 45/48 is closer to 11 than 10 51/80
For each geometric sequence, write a recusive rule by finding the commom ratio by calculating the ration of consecutive terms. Write an exlicit rule for the sequence by writing each term as the product of the first tern and a power of the common ratio.
n- 1, 2, 3, 4, 5
An- 2, 6, 18, 54, 162
Answer:
[tex]a_n=2.(3)^{n-1}[/tex]
Step-by-step explanation:
Given sequence is:
2,6,18,54,162
So the common ratio can be found by dividing the second term by first term:
r = 6/2 = 3
The standard formula for geometric sequence is:
[tex]a_n=a_1r^{n-1}[/tex]
Putting the value of r
[tex]a_n=2.(3)^{n-1}[/tex]
So,
[tex]a_1=2.(3)^{1-1} => 2.3^0 = 2*1 = 2\\a_2=2.(3)^{2-1} => 2.3^1 = 2*3 = 6\\a_3=2.(3)^{3-1} => 2.3^2 = 2*9 = 18\\a_4=2.(3)^{4-1} => 2.3^3 = 2*27 = 54\\a_5=2.(3)^{5-1} => 2.3^4 = 2*81 = 162[/tex]
The Amboy Kennel Club has held an annual dog show for the last 42 years. During this time he winner of "Best of Show" has been an Alaskan Malamute 21 times, a Great Pyrenees 3 times, and an Siberian Husky 18 times. Determine the empirical probability that the next winner of "Best of Show" will be a Great Pyrenees.
The empirical probability of a Great Pyrenees winning the 'Best of Show' at Amboy Kennel Club based on past performances is about 7.143%
Explanation:The subject at hand is empirical probability, which is calculated by dividing the number of times an event has happened by the total number of outcomes. In this case, the event is a Great Pyrenees winning 'Best of Show' and the total number of outcomes is the total number of dog shows.
According to the data provided, the Great Pyrenees has won 3 times out of a total of 42 dog shows. Therefore, the empirical probability can be calculated as follows:
Number of wins by Great Pyrenees = 3Total number of dog shows = 42
The empirical probability is then calculated by dividing the number of wins by Great Pyrenees by the total number of dog shows.
Therefore, the empirical probability of a Great Pyrenees winning is 3/42 = 0.07143. So, we could say that there is a 7.143% chance of a Great Pyrenees winning the 'Best of Show' in the future, based purely on historical data.
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The empirical probability that the next "Best of Show" winner will be a Great Pyrenees is calculated to be 0.0714 or 7.14%.
Empirical probability is calculated based on observed data. In this case, we want to determine the probability that the next winner of "Best of Show" at the Amboy Kennel Club will be a Great Pyrenees.
Here's the breakdown:
The total number of dog shows held: 42.The number of times a Great Pyrenees has won: 3.The empirical probability (P) is calculated as:
P(Event) = Number of favorable outcomes / Total number of outcomes.
So, the empirical probability that the next winner will be a Great Pyrenees is:
P(Great Pyrenees) = 3 / 42 = 1 / 14 ≈ 0.0714.
Thus, the empirical probability is approximately 0.0714 or 7.14%.
identify an equation in point-slope form for the line perpendicular to y=-1/2x+11 that passes through (4,-8).
A. y+8=2(x-4)
B. y+8+1/2(x-4)
C.y-8=1/2(x+4)
D.y-4=2(x+8)
Answer:
A. y+8=2(x-4)
Step-by-step explanation:
A line perpendicular to y=-1/2x+11 would have slope +2, which is the negative reciprocal of -1/2.
Starting with the slope-intercept form of the equation of a straight line, find the y-intercept based upon this new line's passing through (4, -8):
y = mx + b becomes -8 = 2(4) + b. Then b = -16, and the desired new line is
y = 2x - 16.
Eliminate answer choices B and C, because 1/2 is not the correct slope.
Choice A is correct. Note that the result of subbing 4 for x and -8 for y into A: y + 8 = 2(x - 4) is a true equation: -8 + 8 = 2(4 - 4)
Also note that y + 8 = 2(x - 4) can be written in slope-intercept form:
y = -8 + 2x - 8, or y = 2x - 16 (same as obtained earlier)
Answer:Y+8=2(x-4)
Step-by-step explanation:
it’s correct I promise
Please help on this pythagorean question, find x.
Answer:
x = 4
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to solve for x
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
(x + 3)² + (4(x + 2))² = 25² ← expand parenthesis on left side
x² + 6x + 9 + 16(x+ 2)² = 625
x² + 6x + 9 + 16(x² + 4x + 4) = 625
x² + 6x + 9 + 16x² + 64x + 64 = 625 ← simplify left side
17x² + 70x + 73 = 625 ( subtract 625 from both sides )
17x² + 70x - 552 = 0 ← in standard form
with a = 17, b = 70, c = - 552
Using the quadratic formula to solve for x
x = ( - 70 ± [tex]\sqrt{70^2-(4(17)(-552)}[/tex] ) / 34
= ( - 70 ± [tex]\sqrt{4900+37536}[/tex] ) / 34
= - 70 ± [tex]\sqrt{42436}[/tex] ) / 34
= - 70 ± 206 ) / 34
x = [tex]\frac{-70-206}{34}[/tex] = - 8.1176....
or x = [tex]\frac{-70+206}{34}[/tex] = 4
However, x > 0 ⇒ x = 4
Hence
x + 3 = 4 + 3 = 7 and
4(4 + 2) = 24
The triangle is a 7- 24- 25 right triangle
A mystery number is greater than 50 and less than 100. You can make exactly five different rectangles with the mystery number of tiles. (Hint: This means the mystery number is a square number). Its prime factorization consists of only one prime number. What is the mystery number?
Answer:
81
Step-by-step explanation:
We know the number is between 50 and 100. The prime factorization consists of only one prime number, so the number must be a perfect square. The possible numbers are 64 and 81.
The rectangles that can be made with 64 tiles are:
1×64, 2×32, 4×16, 8×8, 16×4, 32×2, 64×1
The rectangles that can be made with 81 tiles are:
1×81, 3×27, 9×9, 27×3, 81×1
There are 7 rectangles that can be made with 64 tiles. There are only 5 rectangles that can be made with 81 tiles. Therefore, the mystery number is 81.
Step-by-step explanation:
The mystery number is 64, sqare number of 8 , the only prime number contributing to it being 2
Being x the mystery number
[tex]50 < x < 100[/tex]
The only two sqare numbers that meet this request are 64 and 81.
Not knowing much about the above mentioned rectangles, 81 being the perfect square number of a perfect square number we would consider 64 the only posible answer
in survey 17/25 of the people surveyed have a cat. what percent of the people surveyed have a cat?
Answer:
The percentage of the people surveyed that have a cat is 68%
Step-by-step explanation:
we know that
To find the percentage of the people surveyed that have a cat, multiply the given fraction by 100
so
[tex]\frac{17}{25}*100=17*4=68\%[/tex]
Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers?
x+x+x=-21
x+2x+3x=-21
x+(x+1)+(x+2)=-21
x+(x+2)+(x+4)=-21
Answer:
The third one, x+(x+1)+(x+2)=-21 because x, x+1 and x+2 are three consecutive numbers.
The function f(x) = -(x - 20)(x - 100) represents a company's monthly profit as a function of x, the number of purchase
orders received. Which number of purchase orders will generate the greatest profit?
20
O 60
O 80
O 100
Answer:
The correct option is B
Step-by-step explanation:
Lets put the values in the given function one by one: You will get the answer
f(x)=-(x - 20)(x - 100)
The first option is 20. Substitute the value in the function:
f(x)=-(20-20)(20-100)
f(x)=(- 0)(-80)
f(x)= 0
Second option is 60.
Substitute the value in the function
f(x)=-(x - 20)(x - 100)
f(x)=-(60 - 20)(60 - 100)
f(x)=(-40)(-40)
f(x)=160
Third option is 80:
Substitute the value in the function
f(x)=-(x - 20)(x - 100)
f(x)=-(80 - 20)(80 - 100)
f(x)=(-60)(-20)
f(x)=120
Fourth option is 100:
Substitute the value in the function
f(x)=-(x - 20)(x - 100)
f(x)=-(100 - 20)(100 - 100)
f(x)=(-80)(0)
f(x)= 0
Therefore the values we got are 0, 160, 120, 0
The greatest value is 160.
Thus the correct option is B....
Answer:
B.) 60
Step-by-step explanation:
Which choice shows the coordinates of C’ if the trapezoid is reflected across the y-axis?
A) (-5,3)
B) (3,-5)
C) (5,-3)
D) (-3,5)
Answer:
A
Step-by-step explanation:
C is located at (5,3).
If you want to reflect this over the y-axis, you need to have the same distance that (5,3) is to the y-axis on both sides.
If you look at your graph you should see that (5,3) is 5 units a way from the y-axis so when you put it on the other side it should be 5 units a way also.
So the reflection will give you (-5,3)
Answer:
C) (5,-3)
See attached image for explanation.
the probability of picking rotten apple in a box is 1/100 .if there are 6 boxes containing 1200 apples each how many rotten apple may be picked
[tex]\huge{\boxed{72}}[/tex]
Explanation:First, find the total number of apples. [tex]6*1200=7200[/tex]
Now, multiply this by the probability of picking a rotten apple, which is [tex]\frac{1}{100}[/tex]. This is also the same as dividing by [tex]100[/tex], or moving the decimal point two places to the left. [tex]7200*\frac{1}{100}=72[/tex]
This means that based on the probability given, [tex]72[/tex] rotten apples will be picked.
Number of rotten apple may be picked are 72.
What is probability?Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.
Given
Probability of picking rotten apple in a box is [tex]\frac{1}{100}[/tex].
There are 6 boxes containing 1200 apples each
Number of rotten apple may be picked to be find.
Total number of apples = [tex]6 \times 1200 = 7200[/tex]
Number of rotten apple may be picked = [tex]7200 \times \frac{1}{100}[/tex]
= 72
Number of rotten apple may be picked are 72.
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What is the product of the expressions? Assume y ≠ 0. (2y-1/y2)(3y2/7)
Answer:
(2y-1/y_2)(3y_2/7)
= 2y*(3y_2/7) - (1/y_2)(3y_2/7)
= 6y*y_2/7 - 3/7 = (6y*y_2 - 3)/7
Note: I'm not sure if the 2y-1 was written correctly. If it were intended as the entire thing being a numerator or as 2y_1, this answer is inaccurate.
Answer:
(6y-3)/7
please give me brainliest
Step-by-step explanation:
(2y-1/y²)(3y²/7) first simplify 3y²/y² =3
(2y-1)(3/7) =
(6y-3)/7
cos x cos (-x) -sin x sin (-x) = 1. Verify the Identity. Please Show All Steps.
Answer:
cos x cos (-x) -sin x sin (-x) = 1 ⇒ proved down
Step-by-step explanation:
* Lets revise the angles in the four quadrants
- If angle x is in the first quadrant, then the equivalent angles to it are
# 180 - x ⇒ second quadrant (sin (180 - x) = sin x , cos (180 - x) = -cos x
tan (180 - x) = -tan x)
# 180 + x ⇒ third quadrant (sin (180 - x) = -sin x , cos (180 - x) = -cos x
tan (180 - x) = tan x)
# 360 - x ⇒ fourth quadrant (sin (180 - x) = -sin x , cos (180 - x) = cos x
tan (180 - x) = -tan x)
# -x ⇒fourth quadrant (sin (- x) = -sin x , cos (- x) = cos x
tan (- x) = -tan x)
* Lets solve the problem
∵ L. H .S is ⇒ cos x cos (-x) - sin (x) sin (-x)
- From the rules above cos x = cos(-x)
∴ cos x cos (-x) = cos x cos x
∴ cos x cos (-x) = cos² x
- From the rule above sin (-x) = - sin x
∴ sin x sin (-x) = sin x [- sin x]
∴ sin x sin (-x) = - sin² x
∴ cos x cos (-x) - sin (x) sin (-x) = cos² x - (- sin² x)
∴ cos x cos (-x) - sin (x) sin (-x) = cos² x + sin² x
∵ cos² x + sin² x = 1
∴ R.H.S = 1
∴ L.H.S = R.H.S
∴ cos x cos (-x) -sin x sin (-x) = 1