Answer:
17 mm
Step-by-step explanation:
P = 50 mm
2x + 1 + x = 25
x = 8
2(8) + 1 = 17 mm
The length of the longest side is 17 mm
A function, f(x), represents the distance a car travels over time. The line tangent to the function at x=1 is y=0.6x+0.9. The line tangent to the function at x=4 is y=2.1x-3.2. The line tangent to the function at x=6 is y=4.6x-16.3.
9514 1404 393
Answer:
0.6
Step-by-step explanation:
The instantaneous rate of change at any point on a curve is the slope of the tangent line at that point.
At x=1, the tangent line is given as ...
y = 0.6x +0.9
The slope of that line is the coefficient of x, 0.6.
The instantaneous rate of change of f(x) at x=1 is 0.6.
Based on 20 samples, the average resistance is 25 ohms and the sample standard deviation is 0.5 ohm. Determine the 90% confidence interval of the standard deviation of the batch. (10 points)
Answer:
90% Confidence Interval = [24.81, 25.19]
Step-by-step explanation:
From the question, our number of samples is 20, it is small because it is less than 30. Hence we use the t score confidence interval formula
= Mean ± t score × Standard deviation/√n
Mean = 25 ohms
Standard deviation = 0.5 ohms
n = 20
We find the degrees of freedom = n - 1
= 20 - 1 = 19
Using the T score table
T score for 90% confidence interval with degrees of freedom 19
= 1.729
Hence:
Confidence Interval =
= 25 ± 1.729 × 0.5/√20
= 25 ± 0.1933080767
=
Confidence Interval
25 - 0.1933080767
= 24.806691923
≈ 24.81
25 + 0.1933080767
= 25.1933080767
≈ 25.19
90% Confidence Interval = [24.81, 25.19]
the residents of a city voted on whether to raise property taxes. the ratio of yes votes to no votes was 7 to 4. if there were 9339 total votes, how many no votes where there?
9514 1404 393
Answer:
3396
Step-by-step explanation:
The ratio tells you that out of every 7+4 = 11 votes, 4 of them were 'no' votes. Then the number of no votes is ...
(4/11)(9339) = 3396 . . . no votes
3.f(-4)-3.g(-2) please help me with this problem
please answer correctly see image bellow
4⁸
alternative form:
65536,6.5536×10⁴
(-8, -8), slope is 3
Answer:
ok wdym by that is that a question ?
simpifly 24/36
...........................
Answer: 2/3 would be the simplified form
Step-by-step explanation: Hoped this helped!!!
Answer: 2/3
Step-by-step explanation:
Determine what type of number the solutions are and how many exist for the equation 3x^2+7x+5=0
Answer:
Two complex (imaginary) solutions.
Step-by-step explanation:
To determine the number/type of solutions for a quadratic, we can evaluate its discriminant.
The discriminant formula for a quadratic in standard form is:
[tex]\Delta=b^2-4ac[/tex]
We have:
[tex]3x^2+7x+5[/tex]
Hence, a=3; b=7; and c=5.
Substitute the values into our formula and evaluate. Therefore:
[tex]\Delta=(7)^2-4(3)(5) \\ =49-60\\=-11[/tex]
Hence, the result is a negative value.
If:
The discriminant is negative, there are two, complex (imaginary) roots. The discriminant is 0, there is exactly one real root. The discriminant is positive, there are two, real roots.Since our discriminant is negative, this means that for our equation, there exists two complex (imaginary) solutions.
Joanne is planning her spring garden. Plants cost an average of $4.95. She will be
buying 10 plants. Which is the best estimate of how much she will spend altogether?
Answer:
49.50
Step-by-step explanation:
Answer:
Estimate: $50.00
Step-by-step explanation:
Estimate: round both numbers
$4.95 rounds up to $5.00
10 plants is rounded to 10 plants
Set up equation
$5.00 × 10 plants
Solve
$50.00 total
Each function below is a translation of the graph of the function f(x) = x^2. Match the function with the description of its relationship to the parent function.
Answer: h(x)=x^2-1: down 1
k(x)=x^2+1: up 1
m(x)=(x-1)^2: right 1
g(x)=(x+1)^2: left 1
Step-by-step explanation: just answered this question on edge 2020.
If 1/2 cup of white sugar is needed for one batch of oatmeal raisin cookies, how much white sugar is needed for 8 batches of cookies?
Answer:
4 cups
Step-by-step explanation:
For one batch of cookies you'll need 1/2 cup of sugar. 8 batches of cookies is 8 times the amount of batches of one batch of cookies. So, if the amount of batches is multiplied by 8, then we need to multiply the amount of sugar by 8 as well:
1/2 * 8 = 8/2 = 4/1 = 4
4 cups of white sugar are needed for 8 batches of cookies.
Bradly can earn extra money by mowing lawns. His neighbors will pay him 3.00 for each lawn that takes him 3/4 of an hour. What is the amount of time in extra hours, that Bradley would have to spend mowing lawns to be able to buy a second $48 ticket for his brother.
Time for which Bradly has to mow lawns to get $48:
We know that Bradly earn $3 every 3/4 hours of mowing lawns
Time taken by Bradly to get $1:
time taken by Bradly to get $1 = time taken to get $3 / $3
time taken = (3/4) / 3
time taken = 1/4 hours / dollar
Time taken by Bradly to get $48:
Time taken to get $48 = time taken to get $1 * 48
Time taken to get $48 = 1/4 * 48
Time taken = 12 hours
Therefore, after 12 hours of Mowing lawns, Bradly will have $48
Part 1) Which rate is NOT a unit rate? (Circle)
a) 1/4 inch/1 year
b) $5/3 pounds
c) $13.50/1 hour
d) 15 drops/1 liter
The answer is
B ($5/3 pounds)
Answer:
it is B
Step-by-step explanation:
it is B $5/3 pounds
the area of a face of a cube is 144cm^2 . find its volume
Step-by-step explanation:
1 face area = length x width (aka length x length since cube)
therefore 1 side = ±√144 cm = 12 cm or - 12cm (rej as length > 0cm)
volume = length x width x height = 12 x 12 x 12 = 1728cm^3
Topic: Mensuration
If you would like to venture further into mathematics, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!
Employees of the store in the example Wear shirts with the logo on the back
Answer:
the logo could be kate spade
Brandon opened a credit card at a department store with an APR of 14.99% compounded monthly. What is the APY on this credit card? A. 1.25% B. 29.98% C. 16.06% D. 19.55%
Answer:
real annual rate= 0.1606 = 16.06%
Step-by-step explanation:
Giving the following information:
APR= 14.99% = 0.1499
First, we will determine the nominal monthly rate:
Nominal monthly rate= 0.1499/12
Nominal monthly rate= 0.01249
Now, to calculate the real annual rate, we need to use the following formula:
real annual rate= [(1 + Nominal monthly rate)^n] - 1
real annual rate= [(1.01249^12) - 1]
real annual rate= 0.1606 = 16.06%
PLEASE HELP! Find the cosine of angle G. Write your answer in simplified, rationalized form. Do not round. (see attached image)
Answer:
2/5
Step-by-step explanation:
4+19=25
square root of 25 is 5 so
adjacent over hypotenuse is 2/5
this might be wrong but I think this is how u do it
Answer:
just follow this formula
cos=adjacent over (divided by) hypothenuse
Step-by-step explanation:
answer 2 over √19
A charter airline finds that on its Saturday flights from Philadelphia to London all 180 seats will be sold if the ticket price is $200. However, for each $3 increase in ticket price, the number of seats sold decreases by one. (a) Find a formula for the number of seats sold S if the ticket price is P dollars.
Answer:
[tex]S = -\dfrac{1}{3}P+\dfrac{740}{3}[/tex]
Step-by-step explanation:
Given that:
Number of seats sold is 180 with ticket price $200.
Number of seats decreases by one when the ticket price is increased by $3.
To find:
The formula for the number of seats sold (S) when the ticket price is P dollars.
Solution:
It is linear dependency of number of seats sold, S on ticket price, P.
[tex]S\propto P[/tex]
It can be written as:
[tex]S = kP+C[/tex]
Where [tex]k[/tex] is the constant of proportionality and
[tex]C[/tex] is a constant.
Now, putting the given values:
[tex]180 = 200k +C ..... (1)[/tex]
[tex]179 = 203k+C[/tex] ...... (2)
Subtracting (1) from (2):
[tex]3k = -1\\\Rightarrow k =-\dfrac{1}{3}[/tex]
Putting the value in (1):
[tex]\Rightarrow C = 180+\dfrac{200}{3} = \dfrac{740}{3}[/tex]
Therefore the equation becomes:
[tex]S = -\dfrac{1}{3}P+\dfrac{740}{3}[/tex]
Derermine the intercepts of the line x-intercept(____,___)
Y-intercept(____,____)
Answer:
x intercept(3, 0) y intercept(0, -10)
Doris traveled 153 miles on Tuesday. She traveled 270 miles on Wednesday. How many more miles did she travel on Wednesday than she did on Tuesday?
Answer:
117
Step-by-step explanation:
270 -153=117
Describe each of the following values as (A) a discrete random variable, (B) a continuous random variable, or (C) not a random variable: 1. Exact weight of quarters now in circulation in the United States 2. Shoe sizes of humans 3. Political party affiliations of adults in the United States A.
Answer:
1. Is a continuous random variable
2. Is a discrete random variable
3. Is not a random variable
Step-by-step explanation:
1. The exact Weight of quarters in circulation in the united states is a continuous random variable. This is because a random variable such as this can take uncountable and infinite number of values.
2. The shoe sizes if humans is an example of discrete random variable. This is a discrete random variable because it has countable number of values.
3. Political party affiliation is not a random variable.
Thank you!
please help properties of exponents
Answer:
Step-by-step explanation:
3. [tex]c^{11}[/tex] add exponents
4.[tex]m^{60}[/tex] multiply exponents
5.[tex]x^{6} y^{18}[/tex] distribute and multiply exponents
6. [tex]-21 a^{47} *b[/tex] multiply and then add exponents
7.[tex]100 a^{14} b^{4} c^{12}[/tex] distribute and multiply exponents
8.[tex]n^{22}[/tex] multiply and then add exponents
write the expanded form of 4(3+4x-2), please help.
i need help. Somebody help me out
Answer:
6.31 thats what I think
Answer:D
Step-by-step explanation:
The points (-1,-6) and (-3,t)fall on a line with a slope of -5 . what is the value of t?
Answer:
t = -4
Step-by-step explanation:
[tex]\frac{6 - t}{-1 - (-3)}[/tex] = -5
[tex]\frac{6 - t}{2}[/tex] = -5
6 - t = 10
-t = 4
t = -4
Ronna needs 20.5 pints of blueberries to make jam. She picked 7.75 pints on Friday and 4,25 pints on Saturday, Hon
many more pints does she need to pick?
Answer:
8.5 I believe
Step-by-step explanation:
7 + 4 = 11
.75 + .25 = 1
11 + 1 = 12
20.5
- 12 .0
8 . 5
Determine if the triangles are congruent. If so, write a congruence statement. Explain your reasoning in a short paragraph proof.
PLS Help I'M IN A RUSH
BRAINLIEST WILL BE MARKE FOR THE BEST ANSWER GIVEN
Answer: Yes
Step-by-step explanation:
The Vertical angle would show that 2 of the angles are exactly the same. Its also given 2 lines that are marked as congurent. Since we know that angle and the lines are congruent we can also say that angle IFJ is congruent to angle IHG meaning that they are congruent because of ASA (Angle Side Angle Theorem)
Congruent triangles have equal corresponding sides lengths and angle measures.
The triangles are congruent by ASA
From the attached figure, we have:
[tex]\mathbf{HI \cong IF}[/tex]
Lines HG and JF are parallel lines.
It means that:
Angles G and F are corresponding, and also angles at I in both triangles are vertical angles.
So, we can conclude that both triangles are congruent by ASA
Read more about congruent triangles at:
https://brainly.com/question/12413243
A 7676 foot guy wire is attached to the top of an antenna. The angle between the guy wire and the ground is 68o68o. How tall (in feet) is the antenna
Answer:
70.47feet
Step-by-step explanation:
CHECK THE ATTACHMENT FOR THE INTERPRETATION OF THE QUESTION USING A FIQURE
From the attachment we can see that a triangle was formed, where the
OPPOSITE SIDE= X
HYPOTENUSE=76feet
From trigonometry,
Sin(θ)=opposite/Hypotenuse
Sin(68)= X/76
Cross multiply, we have,
X= Sin(68) × 76
X= 0.9272 × 76
X= 70.47feet
Therefore, the antenna is 70.47feet tall.
Which of the following is equivalent to (2a+1)(2a+1)?
O (2a + 1)2
O 4a + 2
O 2(2a + 1)
O4a²+1
The equivalent expression is (2a + 1)².
Option (A) is correct.
What is a Polynomial?Polynomial, a mathematical expression made comprised of numbers and variables arranged in specific patterns. They serve as the foundation for solving algebraic equations.
As per the given data in the question:
We are given an expression, and we have to find out the equivalent expression from the given options in the question.
The expression is (2a + 1)(2a + 1)
For option (A). (2a + 1)²
In (2a + 1)(2a + 1) using associative multiplication.
= 2a.2a + 2a + 2a + 1
= 4a² + 4a + 1
Using the identity: a² + 2ab + b² = (a + b)²
4a² + 4a + 1 = (2a + 1)²
The equivalent expression is (2a + 1)².
Hence, The equivalent expression is (2a + 1)².
To learn more about Polynomial, click:
brainly.com/question/11536910
#SPJ7
Let Y1 and Y2 denote the proportion of time during which employees I and II actually performed their assigned tasks during a workday, The joint density of Y1 and Y2 is given by
f(y1,y2) = { y1+y2, 0<=y1<=1, 0<=y2<=1, 0, elsewhere
Required:
a. Find the marginal density function of Y1 and Y2
b. Find P(Y1 >= 1/2 | Y2 >= 1/2).
c. If employee II spends exactly 50% of the dayworking on assigned duties, find the probability that employee I spends more than 75% of the day working on similarduties.
Answer:
Step-by-step explanation:
From the information given:
The joint density of [tex]y_1[/tex] and [tex]y_2[/tex] is given by:
[tex]f_{(y_1,y_2)} \left \{ {{y_1+y_2, \ \ 0\ \le \ y_1 \ \le 1 , \ \ 0 \ \ \le y_2 \ \ \le 1} \atop {0, \ \ \ elsewhere \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \right.[/tex]
a)To find the marginal density of [tex]y_1[/tex].
[tex]f_{y_1} (y_1) = \int \limits ^{\infty}_{-\infty} f_{y_1,y_2} (y_1 >y_2) \ dy_2[/tex]
[tex]=\int \limits ^{1}_{0}(y_1+y_2)\ dy_2[/tex]
[tex]=\int \limits ^{1}_{0} \ \ y_1dy_2+ \int \limits ^{1}_{0} \ y_2 dy_2[/tex]
[tex]= y_1 \ \int \limits ^{1}_{0} dy_2+ \int \limits ^{1}_{0} \ y_2 dy_2[/tex]
[tex]= y_1[y_2]^1_0 + \bigg [ \dfrac{y_2^2}{2}\bigg]^1_0[/tex]
[tex]= y_1 [1] + [\dfrac{1}{2}][/tex]
[tex]= y_1 + \dfrac{1}{2}[/tex]
i.e.
[tex]f_{(y_1}(y_1)}= \left \{ {{y_1+\dfrac{1}{2}, \ \ 0\ \ \le \ y_1 \ \le , \ 1} \atop {0, \ \ \ elsewhere \ \\ \ \ \ \ \ \ \ \ } \right.[/tex]
The marginal density of [tex]y_2[/tex] is:
[tex]f_{y_1} (y_2) = \int \limits ^{\infty}_{-\infty} fy_1y_1(y_1-y_2) dy_1[/tex]
[tex]= \int \limits ^1_0 \ y_1 dy_1 + y_2 \int \limits ^1_0 dy_1[/tex]
[tex]=\bigg[ \dfrac{y_1^2}{2} \bigg]^1_0 + y_2 [y_1]^1_0[/tex]
[tex]= [ \dfrac{1}{2}] + y_2 [1][/tex]
[tex]= y_2 + \dfrac{1}{2}[/tex]
i.e.
[tex]f_{(y_1}(y_2)}= \left \{ {{y_2+\dfrac{1}{2}, \ \ 0\ \ \le \ y_1 \ \le , \ 1} \atop {0, \ \ \ elsewhere \ \\ \ \ \ \ \ \ \ \ } \right.[/tex]
b)
[tex]P\bigg[y_1 \ge \dfrac{1}{2}\bigg |y_2 \ge \dfrac{1}{2} \bigg] = \dfrac{P\bigg [y_1 \ge \dfrac{1}{2} . y_2 \ge\dfrac{1}{2} \bigg]}{P\bigg[ y_2 \ge \dfrac{1}{2}\bigg]}[/tex]
[tex]= \dfrac{\int \limits ^1_{\frac{1}{2}} \int \limits ^1_{\frac{1}{2}} f_{y_1,y_1(y_1-y_2) dy_1dy_2}}{\int \limits ^1_{\frac{1}{2}} fy_1 (y_2) \ dy_2}[/tex]
[tex]= \dfrac{\int \limits ^1_{\frac{1}{2}} \int \limits ^1_{\frac{1}{2}} (y_1+y_2) \ dy_1 dy_2}{\int \limits ^1_{\frac{1}{2}} (y_2 + \dfrac{1}{2}) \ dy_2}[/tex]
[tex]= \dfrac{\dfrac{3}{8}}{\dfrac{5}{8}}[/tex]
[tex]= \dfrac{3}{8}}\times {\dfrac{8}{5}}[/tex]
[tex]= \dfrac{3}{5}}[/tex]
= 0.6
(c) The required probability is:
[tex]P(y_2 \ge 0.75 \ y_1 = 0.50) = \dfrac{P(y_2 \ge 0.75 . y_1 =0.50)}{P(y_1 = 0.50)}[/tex]
[tex]= \dfrac{\int \limits ^1_{0.75} (y_2 +0.50) \ dy_2}{(0.50 + \dfrac{1}{2})}[/tex]
[tex]= \dfrac{0.34375}{1}[/tex]
= 0.34375