Answer:
[tex]P(W\ n\ F) = 43\%[/tex]
Step-by-step explanation:
Given
Represent customers that own their homes with W
Represent customers that have lived for less than 5 years with F
Such that:
[tex]P(W) = 60\%[/tex]
[tex]P(F) = 54\%[/tex]
[tex]P(W\ or\ F) = 71\%[/tex]
Required
Determine [tex]P(W\ n\ F)[/tex]
In Probability:
[tex]P(W\ or\ F) = P(W) + P(F) - P(W\ n\ F)[/tex]
Substitute values for each
[tex]71\% = 60\% + 54\% - P(W\ n\ F)[/tex]
[tex]71\% = 114\% - P(W\ n\ F)[/tex]
Solve for P(W n F)
[tex]P(W\ n\ F) = 114\% - 71\%[/tex]
[tex]P(W\ n\ F) = 43\%[/tex]
1. Given right triangle ABC with the right angle C and sin A = 1/3, which is of the following expression is also equal to 1/3?
A. cos B
B. cos(90° - A)
C. sin(90°- B)
D. Both A and B
2. The maximum slope for a hand propelled wheel chair ramp should be a 1-inch rise to every 12 inch of length. What is that maximum ramp angle recommended to the nearest degree?
Answer:
1) B
2) About 5°.
Step-by-step explanation:
1)
We can use the following co-function identity:
[tex]\sin(\theta)=\cos(90-\theta)[/tex]
Substitute A for θ:
[tex]\sin(A)=\cos(90-A)[/tex]
Since we know that sin(A) is 1/3, this means that cos(90-A) must also be 1/3.
So, our answer is B.
2)
Refer to the drawing.
Remember that 1-inch rise is a height of 1 while a 12 inch length is a length of 12.
So, to find the maximum ramp angle, we simply need to find the value of x.
We know the sides opposite and adjacent to x. So, we can use tangent:
[tex]\tan(x)=\text{opp}/\text{adj}[/tex]
Substitute 1 for the opposite side and 12 for the adjacent side:
[tex]\tan(x)=1/12[/tex]
Take the inverse tangent of both sides:
[tex]x=\tan^{-1}(1/12)[/tex]
Use a calculator. Make sure you're in Degrees mode:
[tex]x\approx4.76\textdegree\approx5\textdegree[/tex]
So, the maximum ramp angle should be about 5°
Identify the independent and dependent variables in the following situation: Julie notices that her plant grows one inch for every liter of water that it receives.
Answer:
third choice the independent variable is the amount of water given, dependent is the height of the plant
11. The first four terms of an AP, whose first term is -2 and common difference is -2 are
Answer:
- 2, - 4, - 6, -8
Step-by-step explanation:
If the first term of the arithmetic sequence is is -2 , and the common difference is -2, then we can generate the first four terms the following way:
a1 = - 2
a2 = - 2 - 2 = - 4
a3 = - 4 - 2 = - 6
a4 = - 6 - 2 = - 8
Lisa mixed 1 part of apple juice and 2 parts of vanilla yogurt to make a smoothie. How many parts of apple juice did Lisa mix with each part of vanilla yogurt?
-5 1/2 + 6 3/4 + ( -4 1/4)
Answer:
8
Step-by-step explanation:
I used a calculator
In the following diagram, it is known that EHG is a right angle, m EHF x 1 and m GHF x 5 5.
Find the value of x, the numerical values of m EHF m GHF and , and mark them on the diagram
Answer:
Step-by-step explanation:
From the diagram, it can be seen that m EHF+ m GHF = mEHG
mEHG is a right angle, then mEHG = 90°
Given
m EHF = x
m GHF = 5x
Substituting the given parameters into the formula to get x;
x+5x= 90
6x = 90
Divide both sides by 6;
6x/6 = 90/6
x = 15
Hence the value of x is 15°
Since m EHF = x, therefore the numerical value of m EHF is 15°.
Also since m GHF = 5x, the numerical value of m GHF = 5(15) = 75°
What is the difference? PLEASE HELP
You have 15 marbles in your pocket. 5 are blue, 6 are red, and 4 are green. If you reach into your pocket and pull out a marble, what is the probability that the marble will be red?
Answer:
2 out of 5 chance of being red
Step-by-step explanation:
what is the distance between -4 and 8 on a number line
Answer:
12
Step-by-step explanation:
you can hop 12 times to the right
The distance between -4 and 8 on a number line is 12.
To find the distance between -4 and 8 on a number line, you can subtract the smaller number from the larger number. In this case:
Distance = |8 - (-4)|
To subtract a negative number, you can think of it as adding the absolute value of that negative number:
Distance = |8 + 4|
Now, perform the addition:
Distance = |12|
The absolute value of 12 is 12, so the distance between -4 and 8 on a number line is 12 units.
Hence, the distance between -4 and 8 on a number line is 12.
To learn more on Distance click:
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Dmitar buys 2/3 pound of mixed nuts,1/2 pound of chocolate candies, and 1 1/4 of granola how much did dmitar spend to make the trail mix?
Answer: 11.70
Step-by-step explanation:
1/2x+ y=-7
-3x + 2y = -2
You could produce a pair of like terms with
opposite coefficients by multiplying the first equation by what number
Answer: 6
explanation: I just did it
Answer:
Step-by-step explanation:
Answer is 6
What is the answer to (7-3)^2x(5-2)^3+4^2 ?
Step-by-step explanation:
(7-3)^2*(5-2)^3+4^2
=(4)^2*(3)^3+16
=16*27+16
=432+16
=448
True or False: The distance between -7 and -13 dn a number line
Three times the sum of eight and a number is 81. Find the number.
Answer:
19
Step-by-step explanation:
81/3=27
27-8=19
19
In a certain apartment building, the ratio of tenants to cars is 3:5. If there are 30 tenants, how many cars are there?
Answer:
50 cars
Step-by-step explanation: 3x10 is 30 and 5x10 is 5
What is the answer to 18-4K=-10-4k?
Answer:
no solution
Step-by-step explanation:
add 4k to both sides of the equation and you have ...
18 = -10 . . . . false
There is no value of k that will make this statement true. There is no solution.
Put the following equation of a line into slop-intercept form, simplifying all fractions.
2y - x = -8
Answer:
y = x/2 - 4
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Write equation
2y - x = -8
Step 2: Solve for y
Add x to both sides: 2y = x - 8
Divide both sides by 2: y = x/2 - 4
6. A high school graduate works fulltime. She needs to borrow $1,500 to
attend the local junior college, but she won't be able to pay it back for
2
years. Calculate how much she will have to pay back with these two
loan plans. Which plan should she choose? Justify your answer,
Bank A: Simple interest, 18 percent per year
Bank B: Compound interest, 12 percent per year
Answer:
I think you would have to multiply 1,500 by 12 and also by 18 to figure it out.
Step-by-step explanation:
" "
6. What is the fractional equivalent of 3.15?
How to Write 3.15 or 315% as a Fraction?
Decimal Fraction Percentage
3.3 66/20 330%
3.25 65/20 325%
3.2 64/20 320%
3.15 63/20 315%
3.1 62/20 310%
3.70588 63/17 370.588%
3.5 63/18 350%
3.31579 63/19 331.579%
3 63/21 300%
A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 60.0 min at 95.0 km/h, 10.0 min at 55.0 km/h, and 35.0 min at 45.0 km/h and spends 50.0 min eating lunch and buying gas.
(a) Determine the average speed for the trip. km/h
(b) Determine the distance between the initial and final cities along the route. km
Step-by-step explanation:
(a) The average speed of a person for the trip is given by total distance traveled divided by total time taken.
[tex]V=\dfrac{d_1+d_2+d_3+d_4}{t_1+t_2+t_3+t_4}[/tex]
Since, distance = velocity × time
Also, 1 hour = 60 min
[tex]V=\dfrac{v_1t_1+v_2t_2+v_3t_3+v_4t_4}{t_1+t_2+t_3+t_4}\\\\V=\dfrac{95\times \dfrac{60}{60}+55\times \dfrac{10}{60}+45\times \dfrac{35}{60}+0\times 50}{\dfrac{60}{60}+\dfrac{10}{60}+\dfrac{35}{60}+\dfrac{50}{60}}\\\\V=50.48\ \text{km/h}[/tex]
The average speed for the trip is 50.48 km/h
(b) Total distance,
[tex]D=v_1t_1+v_2t_2+v_3t_3+v_4t_4\\\\D=95\times \dfrac{60}{60}+55\times \dfrac{10}{60}+45\times \dfrac{35}{60}+0\times 50\\\\D=130.41\ \text{km}[/tex]
The distance between the initial and final cities along the route is 130.41 km.
Last week, Jada ran 2 7/10 miles. This week, she plans to run 5 times as far as last week.
How many miles does Jada plan to run this week?
Write your answer as a fraction or as a whole or mixed number.
Answer:
13.5 miles or 27/5 miles
Step-by-step explanation:
2 7/10 is equal to 2.7 If she plans to run 5 times as much as last week, multiply 2.7 by 5.
2.7*5=13.5
simplify the ratio
2km: 3400m
Answer:
[tex]\displaystyle \frac{10}{17}[/tex]
Step-by-step explanation:
Fraction Simplifying
We are given the ratio 2 Km:3400 m. This can be written in fraction form as:
[tex]\displaystyle \frac{2\ km}{3400\ m}[/tex]
Since 2 Km = 2000 m:
[tex]\displaystyle \frac{2\ km}{3400\ m}=\frac{2000\ \not{m}}{3400\ \not{m}}[/tex]
We need to simplify the fraction:
[tex]\displaystyle \frac{2000}{3400}[/tex]
We cancel out two zeroes, which is like dividing both numbers by 100:
[tex]\displaystyle \frac{20\not{0}\not{0}}{34\not{0}\not{0}}[/tex]
The remaining fraction is:
[tex]\displaystyle \frac{20}{34}[/tex]
Dividing both by 2:
[tex]\displaystyle \frac{10}{17}[/tex]
Since the denominator is a prime number, no more simplifying is possible, thus the given ratio is equivalent to:
[tex]\boxed{\displaystyle \frac{10}{17}}[/tex]
Write an Equation using the following arithmetic sequence: 5, _____, ______, -4.
15,000 is increased by 5%. What is the new value?
Step-by-step explanation:
105% of 15000
=105/100 × 15000/1
=15,750
Bert's birthday party will cost $246 if he invites 41 guests. How many guests can there be, at most, if Bert can afford to spend a total of $534 on his birthday party? Solve using unit rates. guests
What is the value of the 8 in the number 2008277
Answer:
thousands
Step-by-step explanation:
Answer:
The answer would be the Thousands place.
Step-by-step explanation:
The order goes like this.
ones
tens
hundreds
thousands
ten-thousands
one hundred-thousands
millions
Please add me as brainliest please :)
a.
b.
c.
d.
please help me
Answer:
b
Step-by-step explanation:
the answer is - 11/12
Identify the initial value, a, and base, b, of the function f(x)=ab^x if its graph passes through the points (0, 4) and (1, 20)
Answer:
a = 4, b = 5
Step-by-step explanation:
Given the exponential function
f(x) = a[tex]b^{x}[/tex]
Use the given points to find a and b
Using (0, 4 ) , then
4 = a[tex]b^{0}[/tex] ( [tex]b^{0}[/tex] = 1 ) , thus
a = 4 , so
f(x) = 4[tex]b^{x}[/tex]
Using (1, 20 ) , then
20 = 4b ( divide both sides by 4 )
b = 5
what is the distributive property of (6+9v)6 ?
Answer:
36 + 54 v
Step-by-step explanation:
Answer:
36+54v
Step-by-step explanation:
times 6x6 and 6x9 then put in the v
If m∠2=40°, what is the measure of ∠1 + ∠6?
Answer:
180°
Step-by-step explanation:
The diagram for this question has been attached to this response.
From the diagram;
(i) ∠2 and ∠6 are equal since they are corresponding angles. This implies that the measure of angle 2 (m∠2) is equal to the measure of angle 6 (m∠6). i.e
m∠2 = m∠6 ---------(a)
But m∠2 = 40°
Substitute this into equation (a) as follows;
40° = m∠6
∴ m∠6 = 40°
(ii) ∠1 and ∠2 are supplementary. This implies that the sum of the measures of angle 1 (m∠1) and angle 2(m∠2) is equal to 180°. i.e
m∠1 + m∠2 = 180° ------------------(b)
But m∠2 = 40°
Substitute this into equation (b) as follows;
m∠1 + 40° = 180°
m∠1 = 180° - 40°
m∠1 = 140°
(iii) The measure of ∠1 + ∠6 is given by;
m∠1 + m∠6
Substitute the values of m∠1 = 140° and m∠6 = 40° into the expression to get
m∠1 + m∠6 = 140° + 40°
m∠1 + m∠6 = 180°
Therefore the measure of ∠1 + ∠6 is 180°
