Answer:
50
Step-by-step explanation:
So we know that 42/3=14.
3 years before was:
14-3=11
42-3=39
The sum of 11+39 is 50
A ladder leans against the side of the a house. The ladder is 19 feet long and forms an angle of elevation of 75 degree when leaned against the house. How far away from the house is the ladder? Round your answer to the nearest tenth.
=============================================================
Explanation:
Focus entirely on the triangle on the right side. The other parts of the drawing are not necessary. In my opinion, they are distracting filler.
Refer to the diagram below.
We have an unknown adjacent side, let's call it x, that's along the horizontal part of the triangle.
The hypotenuse however is known and it is 19 ft
We use the cosine ratio to tie the two sides together
cos(angle) = adjacent/hypotenuse
cos(75) = x/19
19*cos(75) = x
x = 19*cos(75)
x = 4.9175618569479 which is approximate
x = 4.9
The base of the ladder is roughly 4.9 feet away from the base of the house.
Side note: make sure your calculator is in degree mode.
What is the solution to the equation x^2 + 10x + 75 = 0?
In this problem, y = 1/(1 + c1e−x) is a one-parameter family of solutions of the first-order DE y' = y − y2. Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. y(0)=-1/3
If y (0) = -1/3, then
-1/3 = 1 / (1 + C e ⁻⁰)
Solve for C :
-1/3 = 1 / (1 + C )
-3 = 1 + C
C = -4
So the particular solution to the DE that satisfies the given initial condition is
[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]
9. Which is a true statement about the denominator in a fraction?
(Select one answer)
It is always a negative number
It cannot be 0
It has to be an even number
It is always smaller than the numerator
Answer:
It cannot be 0
Step-by-step explanation:
it can also be positive number :2/4
it can be odd number too:3/9
it is bigger than numerator bcoz we have to divide it for numerator
So, 0 number cannot be put as denominator in fraction is true statement
Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and values of the rate at two hour time intervals are shown in the table. Find lower and upper estimates for the total amount of oil that leaked out.
t (h) 0 2 4 6 8 10
r(t) (L/h) 8.8 7.6 6.8 6.2 5.7 5.3
V=_____ upper estimate
V= ______lower estimate
The exact amount of oil that leaks out for 0 ≤ t ≤ 10 is given by the integral,
[tex]\displaystyle\int_0^{10}r(t)\,\mathrm dt[/tex]
Then the upper and lower estimates of this integral correspond to the upper and lower Riemann/Darboux sums. Since r(t) is said to be decreasing, this means that the upper estimate corresponds to the left-endpoint Riemann sum, while the lower estimate would correspond to the right-endpoint sum.
So you have
• upper estimate:
(8.8 L/h) (2 h - 0 h) + (7.6 L/h) (4 h - 2h) + (6.8 L/h) (6 h - 4h) + (6.2 L/h) (8 h - 6h) + (5.7 L/h) (10 h - 8 h)
= (2 h) (8.8 + 7.6 + 6.8 + 6.2 + 5.7) L/h)
= 70.2 L
• lower estimate:
(7.6 L/h) (2 h - 0 h) + (6.8 L/h) (4 h - 2h) + (6.2 L/h) (6 h - 4h) + (5.7 L/h) (8 h - 6h) + (5.3 L/h) (10 h - 8 h)
= (2 h) (7.6 + 6.8 + 6.2 + 5.7 + 5.3) L/h)
= 63.2 L
A satellite orbits earth at a speed of 22100 feet per second (ft/s). Use the following facts to convert this speed to miles per hour (mph). 1 mile = 5280 ft 1 min = 60 sec 1 hour = 60 min
15,068 mi/hr
Step-by-step explanation:
[tex]22100\:\frac{\text{ft}}{\text{s}}×\frac{1\:\text{mi}}{5280\:\text{ft}}×\frac{60\:\text{s}}{1\:\text{min}}×\frac{60\:\text{min}}{1\:\text{hr}}[/tex]
[tex]=15,068\:\text{mi/hr}[/tex]
The speed of 22100 feet per second will be 15068.18 miles per hour.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Unit conversion is the expression of the same property in a different unit of measurement. Time, for example, can be expressed in minutes rather than hours, and distance can be converted from miles to kilometres, feet, or any other length measurement.
Given that the speed of the satellite is 22100 feet per second. The speed in miles per hour will be calculated as,
22100 ft /s = ( 22100 x 3600 ) / 5280
22100 ft/s = 79560000 / 5280
22100 ft/s = 15068.18 miles per hour
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Find the domain of fg. f(x) = x2 +1 g(x) = 1/x a. all real numbers c. all real numbers, except -1 b. all real numbers, except 0 d. all real numbers, except 1
(12 1/3 * 2) + (10 3/4 * 2)
Answer:
[tex](12\frac{1}{3} *2)+(10\frac{3}{4} *2)\\\\=(\frac{12(3)+1}{3} *2)+(\frac{10(4)+3}{4} *2)\\\\=\frac{37*2}{3} +\frac{43*2}{4} \\\\=\frac{74}{3} +\frac{86}{4} \\\\=\frac{74(4)+86(3)}{3*4} \\\\=\frac{296+258}{12} \\\\=\frac{554}{12}[/tex]
What is the surface area of the composite figure?
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Answer:
382 cm²
Step-by-step explanation:
The side facing is a trapezoid with bases 8 and 14 cm, and height 7 cm. Its area is ...
A = 1/2(b1 +b2)h
A = (1/2)(8 +14)(7) = 77 . . . . cm²
The perimeter of the face is ...
7 cm + 8 cm + 9 cm + 14 cm = 38 cm
The total surface area is the sum of the lateral area and the base area.
SA = LA + BA
SA = (38 cm)(6 cm) + 2×(77 cm²) = 228 cm² + 154 cm²
SA = 382 cm²
The surface area of the composite figure is 382 square centimeters.
_____
Additional comment
The lateral area is the width of a rectangular face (6 cm) times the total of all of the lengths of those faces. That total is the perimeter of the trapezoidal base (38 cm).
There are two trapezoidal bases that contribute area. The first calculation figured the area of one of them.
Does the point (0, 0) satisfy the equation y = x2?
Answer:
The point is a solution
Step-by-step explanation:
y = x^2
Substitute the point into the equation and see if it is true
0 = 0^2
0=0
True
help
The points (63, 121), (71, 180), (67, 140), (65, 108), and (72, 165) give the weight in pounds as a function of height in inches for 5 students in
a class. Give the points for these students that represent height as a function of weight
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
{(121, 140), (180, 71), (140, 67), (108, 65), (165, 72);
{(121, 71), (180, 63), (140, 67), (108, 65), (165, 72)}
{(63, 121), (71, 180), (67, 140), 65, 108), (72, 165))
Answer:
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
Step-by-step explanation:
We have:
Weight as a function of height.
Give the points for these students that represent height as a function of weight:
Inverse of the input, that is, in the (x,y) format, (x,y) -> (y,x), the coordinates are exchanged, and thus, the correct option is:
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
Find the slope, if it exists, of the line containing the points (10,-3) and (10,-8).
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
m=
Answer:
The slope is undefined.
Step-by-step explanation:
The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.
Question 1
The perfect square among the following options is
8
Say
27
216
256
Answer:
217 is the perfect swuare i think
Need Help this is due in 30 minutes!
Answer:
E
Step-by-step explanation:
Since all the numbers are hundredths decimals, let multiply by the power of 2 of the base 10. So let multiply the equation by
[tex]10 {}^{2} [/tex]
So our new equation is
[tex]3 3{x}^{2} + 71x - 14 = 0[/tex]
Solve by AC method
[tex]ac = - 462[/tex]
[tex]b = 71[/tex]
We must think of two numbers that
Multiply to -462 and Add to 71. Set up equation
The numbers are 77 and -6.
So our new equation is
[tex] {33x}^{2} + 77x - 6x - 14 = 0[/tex]
Solve by factoring by grouping
[tex](33 {x}^{2} + 77x) - (6x - 14)[/tex]
Factor out 11 for the first equation
[tex]11x(3x + 7) - 2(3x + 7)[/tex]
So our factors are
[tex](11x - 2)(3x + 7)[/tex]
Set each equal to zero
[tex]11x - 2 = 0[/tex]
[tex]11x = 2[/tex]
[tex]x = \frac{2}{11} [/tex]
[tex]3x + 7 = [/tex]
[tex]3x = - 7[/tex]
[tex]x = \frac{ - 7}{3} [/tex]
35. Graph the following system of equations and find the x-coordinate of the solution.
3x+ 3y=3
Y=-1/2x+2
x=2
x= -2
X = 3
x=0
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Answer:
(b) x = -2
Step-by-step explanation:
The graph shows the lines intersect at (x, y) = (-2, 3).
The x-coordinate of the solution is x = -2.
Which expression is equivalent to 27 + 45?
Answer:
8 x 9
Have a nice day!
Given the flag ABCDE, determine the single rule (x,y) that creates the
transformed figure A'B'C'D'E'. Fill in your answer below in the format (x,y)--
>
WILL GIVE BRAINLIEST
Answer:
(y, -x)
Step-by-step explanation:
Rotation of 90°
(Clockwise)
(x, y) ---> (y, -x)
Rotation of 90°
(CounterClockwise)
(x, y) --> (-y, x)
Rotation of 180°
(Both Clockwise and Counterclockwise)
(x, y) ---> (-x, -y)
Rotation of 270°
(Clockwise)
(x, y) ---> (-y, x)
Rotation of 270°
(CounterClockwise)
(x, y) ---> (y, -x)
HELP. Need help on this
Answer:
what are the answers
Step-by-step explanation:
A biologist is researching a newly discovered species of bacteria. At time t = 0 hours, she puts 100 bacteria into what she has determined to be a favourable growth medium. The population of bacteria doubles every 3 hours. How many bacteria are there in 6 hours? a)200 b)100 c)400 d)600
Answer:
I'm sorry but I don't know this one
The table below represents average food costs broken down by meal. If you
were planning a trip, how much should you budget for food costs per day?
Breakfast
Lunch
Dinner
$12.98
$18.95
$26.58
A. $20.00
B. $60.00
C. $80.00
D. $45.00
By taking the addition of the values in the table and overestimating a little bit, the correct option is B: $60.00
How much should you budget for food costs per day?Here we have the following table of average costs:
Breakfast $12.98Lunch $18.95Dinner $26.58Assuming you eat these 3 per day, the total cost in food per day is the sum of all the values in the table.
It gives:
Total cost: $12.98 + $18.95 + $26.58 = $48.51
Notice that these are average costs, so you should budget a little bit over that just in case, then the correct option is $60, which is the first option over the average total cost.
Learn more about additions:
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Answer:
45
Step-by-step explanation:
1. In 2020, the populations of City A and City B were equal. From 2015 to 2020, the population of City A increased by 20% and the population of City B decreased by 10%. If the population of City A was 120,000 in 2015, what is the population of City B in 2015?
2. A chef is preparing a sauce for a steak she offers as a key dish in her menu. To prepare the sauce she needs to prepare a mix with 40% butter, with the rest being egg yolk. In the kitchen right now, she only has a sauce that has 20% butter (rest is egg yolk) and a sauce that has 50% butter (rest is egg yolk) in stock. In what ratio should she mix the 20% sauce with the 50% sauce in order to obtain the 40% sauce that she needs to prepare her famous recipe?
3. A book was on sale for 30% off its original price. If the sale price of the book was $28, what was the original price of the book? (Assuming there is no sales tax)
4. At a retail store, they needed to do surveys of 32 stores which equals 40% of all their stores. How many stores does the retailer have in total?*
Answer:
180000 people
1 : 2
$40
80 stores
Step-by-step explanation:
1.)
Population in 2020 are equal : Let population =
City A increased by 20% From 120,000 in 2015
(1 + 0.2) * 120,000 = (1.2 * 120,000) = 144,000
Hence, city A = 144,000.
Since, city A and B have equal population ; city B also has a population of 144000 in 2020.
Let population in 2015 = x
(1 - 0.2) * x = 144000
0.8x = 144000
x = 144000/0.8
x = 180,000
2.)
Let proportion of 20% butter = x and proportion of 50% butter = 1 - x
0.2x + 0.5(1 - x) = 0.4
0.2x + 0.5 - 0.5x = 0.4
-0.3x + 0.5 = 0.4
-0.3x = 0.4 - 0.5
-0.3x = - 0.1
x = 0.1/0.3
x = 0.3333
(1-x) = 1 - 0.33333 = 0.6666%
0.3333% of 20% butter
0.6666% of 50% butter
Hence ;
0.3333 : 0.6666
1 : 2
3.)
Let original price of book = x
Discount on sale = 30%
Sale price = $28
Sale price = original price * (1 - discount)
$28 = (1 - 0.3) * x
$28 = 0.7x
x = $28/0.7
x = $40
4.)
Let total number of stores = x
Store surveys needed = 32
40% of total stores = 32 stores
0.4x = 32
x = 32 / 0.4
x = 80
The average monthly salary of a worker is ₹8200. If there are 45 workers in a factory, then total expenditureincurred on expenditure is:
Answer: [tex]Rs.3,69,000[/tex]
Step-by-step explanation:
Given
average monthly salary of a worker is [tex]Rs.8200[/tex]
If there are 45 workers in a factory
Total expenditure is calculated by taking the product of Average monthly salary and no of workers in the factory
[tex]\Rightarrow 8200\times 45\\\Rightarrow Rs.3,69,000[/tex]
Please help me thank you
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Answer:
y = 32.1x +779.91165 cases in 2010Step-by-step explanation:
A suitable statistics calculator can tell you the coefficients of the linear regression equation. In the attached, we put the given x- and y-values into a table and asked for the best fit equation. Rounded to tenths, the equation is ...
y = 32.1x +779.9
The year 2010 is 12 years after 1998, so we can find the desired projection using x=12.
y = 32.1×12 +779.9 = 385.2 +779.9 = 1165.1
The number of cases is projected to be 1165 in 2010.
_____
We wonder if using the button "Open Statistics Calculator" will let you solve this question yourself.
write √3 x √6 in the form b√2 where b is an integer
Answer:
[tex]3 \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \sqrt{(9 \times 2)} [/tex]
Take the square root of 9 out of the square root and leave the 2 in.
Answer:
3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the rules of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{3}[/tex] × [tex]\sqrt{6}[/tex]
= [tex]\sqrt{3(6)}[/tex]
= [tex]\sqrt{18}[/tex]
= [tex]\sqrt{9(2)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex]
= 3[tex]\sqrt{2}[/tex]
Any help would be very appreciated
Answer:
21
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 60 = x / 7 sqrt(3)
7 sqrt(3) tan 60 = x
7 sqrt(3) sqrt(3) = x
7*3 = x
21 = x
What is the value of cot ø= 2/3 what is the value of csc ø
Answer:
Step-by-step explanation:
cotθ = cosθ/sinθ = 2/3
sinθ = 3/√(2²+3²) = 3/√13
cscθ = 1/sinθ = √13/3
Rectangle QRST with vertices Q(-3,2), R(-1,4), S(2,1), and T(0,-1)) in the x-axis
Answer:
D
Step-by-step explanation:
The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The reflection does not change the shape and size of the geometry. But flipped the image.
Rectangle QRST with vertices Q(-3, 2), R(-1, 4), S(2, 1), and T(0, -1).
The coordinate of the new rectangle after the reflection across is given as,
Q' = (-3, -2)
R' = (-1, -4)
S' = (2, -1)
T' = (0, 1)
The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.
More about the transformation of a point link is given below.
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Which equation could represent a linear combination of the systems?
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Answer:
(b) 0 = -78
Step-by-step explanation:
Subtracting 6 times the first equation from the second will give ...
(4x +15y) -6(2/3x +5/2y) = (12) -6(15)
0 = -78
Answer:
the answer is b
Step-by-step explanation:
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week. a. Give a 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week. b. In the general population, 30% have 5 or more servings of soft drinks a week. Is there evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population
Answer:
a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.
This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]
The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
Question b:
30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
Simplify to the extent possible:
(logx16)(log2 x)
Answer:
Step-by-step explanation:
Use the change-of-base rule.
