Answer: 18
Step-by-step explanation:
The important thing to remember here is order of operations. In this equation, you must remember that multiplication must be solved before addition. Afterward, it is a straightforward problem.
6+3x4
Multiplication
6+12
Addition
18
Hope it helps <3
(If it does, please mark brainliest, only need 1 more for rank up :) )
Pilar is playing with a motorized toy boat. She puts the boat in a lake and it travels 400m at a constant speed. On the way back to Pilar, the boat travels the same route at the same speed for 2 minutes, and then Pilar uses the remote control to increase the boat's speed by 10 m/min. So the return trip is 60 seconds faster. How long does the return trip take?
Answer:
The trip normally takes 8 minutes
Step-by-step explanation:
The given information states that the away distance the boat traveled = 400 m
The time traveled at the same initial speed , v₁, by the boat on the way back = 2 minutes
The increase in speed of the boat by Pilar = 10 m/min
The new speed, v₂ = v₁ + 10
The time for the return trip, t₂ = 60 seconds (1 minute) faster than time for the trip, t₁
t₂ = t₁ - 1
Therefore we have;
v₁ × t₁ = v₁×2 + v₂×(t₂-2) = 400
v₁×2 + (v₁ + 10)×(t₂-2) = 400
(v₁ + 10)×t₂ - 20 = 400
But v₁ = 400/t₁ = 400/(t₂ + 1)
Which gives;
(400/(t₂ + 1) + 10)×t₂ - 20 = 400
10×(t₂²+ 36·t₂-2)/(t₂+1) = 400
10·t₂²+ 10·t₂-420 = 0
t₂²+ t₂-42 = 0
(t₂ - 7)(t₂ + 6) = 0
t₂ = 7 minutes or -6 minutes
Given that t₂ is a natural number, we have, t₂ = 7 minutes
Whereby, t₂ = t₁ - 1, we have;
7 = t₁ - 1
t₁ = 1 + 7 = 8 Minutes
The trip normally takes 8 minutes
Answer:
actually, it is 7
Step-by-step explanation:
the previous guy's explanation was all correct, but the question is asking for the return trip, which is one minute less, so the answer is 7. Hope this helped, also, i go to rsm as well and i got this one correct
PLEASE HELP, I WILL MARK YOU BRANIEST, PLEASE EXPLAIN AND GIVE AN ACCURATE ANSWER 1) Each letter of the word "MATHEMATICS" is written on a separate slip of paper and placed in a hat. A letter is chosen at random from the hat. What is the probability of choosing "M" on your first try? 2) Suppose you choose an “M” on your first try. You keep the slip of paper (do not replace it in the hat) and go for another letter. What is the probability of getting another “M”?
Step-by-step explanation:
Total letters = 11
Probability of letter M = 2/11
Probability of second M = 1/10
One pump can drain a pool in 8 minutes. when a second pump is also used, the pool only takes 4 minutes to drain. how long would it take the second pump to drain the pool if it were the only pump in use
Answer:
8 minutes
Step-by-step explanation:
The first pump can drain in 8 minutes, therefore:
Rate of the first pump = 1/8
Working together, they can drain the pool in 4 minutes, therefore:
Rate of both pumps = 1/4
Let the time taken by the second pump =t
Rate of the second pump = 1/t.
We then have:
[tex]\dfrac{1}{8}+ \dfrac{1}{t}=\dfrac{1}{4}\\$Collect like terms$\\\dfrac{1}{t}=\dfrac{1}{4}-\dfrac{1}{8}\\\dfrac{1}{t}=\dfrac{2-1}{8}\\\dfrac{1}{t}=\dfrac{1}{8}\\$Therefore:\\t = 8 minutes[/tex]
It would take the second pump 8 minutes to drain the pool alone.
What is the amplitude of y = 4 sin 3x ?
Answer:
4
Step-by-step explanation:
y = 4 sin (3x)
The amplitude is the coefficient in front of sin
4 is the amplitude
Point S is located on RT so that RS/ST = 1/4. What are the coordinates of Point S? (4 , 4 ) (2.4, 2.4) (8 , 8 ) (4.4, 4.4)
Answer:
(4.4, 4.4)
Step-by-step explanation:
The point S can be found as the weighted average of the end points. The relative weights are the reverse of the distances to the end points:
RS : ST = 1 : 4
S = (4R +1T)/5
S = (4(2, 2) +(14, 14))/5 = (22, 22)/5
S = (4.4, 4.4)
Helppp!!!! please!!!
Answer:
A. 336 ft²
Step-by-step explanation:
Add the sides: 6*8 + 6*12 + 12*8 + 10*12 = 336
One little trick: the area of the triangle sides is base times half height, i.e., 6*8/2, but since we have two of them you can just use 6*8!
PLEASE. NEED HELP. Find the sum.
Distribute the sum:
[tex]\displaystyle\sum_{i=1}^{24}(3i-2)=3\sum_{i=1}^{24}i-2\sum_{i=1}^{24}1[/tex]
Use the following formulas:
[tex]\displaystyle\sum_{i=1}^n1=n[/tex]
[tex]\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2[/tex]
[tex]\implies\displaystyle\sum_{i=1}^{24}(3i-2)=3\cdot\frac{24\cdot25}2-2\cdot24=\boxed{852}[/tex]
In case you don't know where those formulas came from:
The first one is obvious; you're just adding n copies of 1, so 1 + 1 + ... + 1 = n.
The second can be proved in this way: let S be the sum 1 + 2 + 3 + ... + n. Rearrange it as S = n + (n - 1) + (n - 2) + ... + 1. Then 2S = (n + 1) + (n + 1) + (n + 1) + ... + (n + 1), or n copies of n + 1. So 2S = n(n + 1). Divide both sides by 2 and we're done.
$800 and paid 14% tax what was final bill
Answer:
$912
Step-by-step explanation:
First, find the tax.
Multiply the tax rate by the price.
tax rate * price
The tax rate is 14% and the price is $800.
14% * 800
Convert 14% to a decimal. Divide 14 by 100 or move the decimal places 2 spaces to the left.
14/100=0.14
14.0–> 1.4 —> 0.14
0.14 * 800
Multiply
112
The tax is $112.
Now find the total bill.
Add the tax and the price.
tax + price
The tax is $112 and the price is $800.
$112 + $800
Add
$912
The final bill is $912.
Rachel rides her bicycle due east at 12 kilometers per hour. Amos rides his
bicycle due north at 16 kilometers per hour. If they left from the same point at
the same time, how far apart will they be after 2 hours?
Answer:
40 km away.
Step-by-step explanation:
a^2 + b^2 = c^2
In this case, a = 16 * 2 = 32 km, since he travels 16 km per hour for 2 hours.
b = 12 * 2 = 24 km, since she travels 12 km per hour for 2 hours.
32^2 + 24^2 = c^2
1,024 + 576 = c^2
1600 = c^2
c^2 = 1600
c = plus or minus 40
Since distance cannot be negative, they will be 40 km away.
Hope this helps!
The required, after 2 hours, Rachel and Amos will be 40 kilometers apart.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
We can use the Pythagorean theorem to solve this problem. After 2 hours, Rachel will have traveled 24 kilometers (12 km/hour x 2 hours) due east, and Amos will have traveled 32 kilometers (16 km/hour x 2 hours) due north. Let's call the distance between them after 2 hours "d".
Using the Pythagorean theorem, we can write:
d² = (24 km)²+ (32 km)²
Simplifying this expression:
d² = 576 km² + 1024 km²
d² = 1600 km²
Taking the square root of both sides,
d = 40 km
Therefore, after 2 hours, Rachel and Amos will be 40 kilometers apart.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
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What decimal represents the shaded part in the picture?
Answer:
40/100 = 0.4
your welcome
On a very cold morning, it was -8°F. As the day went on, the temperature rose 2 degrees each hour. Which equation shows the temperature over time? CLEAR CHECK y = -2x + 8 y = -2x – 8 y = 2x + 8 y = 2x – 8
Answer:
y=2x-8
Step-by-step explanation:
Every hour, temperatures INCREASE by two degrees, so 2x.
At the beginning (x=0), the temperature was -8 degrees, so -8.
So temperature as a function of time is y=2x-8
Answer:
y = 2x-8
Step-by-step explanation:
At the beginning = -8 F
Let y be the temperature and x be the no. of hours
So, the equation becomes
=> y = -8 + 2x
Writing it in proper form
=> y = 2x-8
The graph of the function f(x) = –(x + 6)(x + 2) is shown below. On a coordinate plane, a parabola opens down. It goes through (negative 6, 0), has a vertex at (negative 4, 4), and goes through (negative 2, 0). Which statement about the function is true? The function is increasing for all real values of x where x –2. The function is decreasing for all real values of x where x < –4.
Answer:
see below
Step-by-step explanation:
f(x) = –(x + 6)(x + 2)
The function is increasing until it reaches the vertex, so it will increase until x=-4. The function will decrease after the vertex, so after x = -4
increasing: -∞ < x < -4
decreasing : -4 < x < ∞
Answer:
The function is increasing for all real values of x where x is -2
Step-by-step explanation:
You can put your work in a graphing calculator
I need help ASAP jsnsnsbdbsbsnsnsnd
Answer:
(i) 9
(ii) 12
Step-by-step explanation:
Comedy is 90 degrees out of 360 degrees or 1/4 of the circle.
36 students took the survey.
1/4 × 36 = 9
Horror is 120 degrees out of 360 degrees or 1/3 of the circle.
1/3 × 36 = 12
Answer:
9 comedy
12 horror
Step-by-step explanation:
First, there are 360 degrees in a circle.
Comedy = 90 degrees
Action and romance = 90 degrees combined
Horror = 120 degree
Science fiction = 60 degrees
To find sci fi : 90 +90 +120 = 300 - 360 = 60 degrees
36 students took the survey.
1/4 × 36 = 9
Horror is 120 degrees out of 360 degrees or 1/3 of the circle.
1/3 × 36 = 12
Need help on this math problem!!!
Answer:
[tex](fof^{-1})(x)=x[/tex]
Step-by-step explanation:
Composition of two functions f(x) and g(x) is represented by,
(fog)(x) = f[g(x)]
If a function is,
f(x) = (-6x - 8)² [where x ≤ [tex]-\frac{8}{6}[/tex]]
Another function is the inverse of f(x),
[tex]f^{-1}(x)=-\frac{\sqrt{x}+8}{6}[/tex]
Now composite function of these functions will be,
[tex](fof^{-1})(x)=f[f^{-1}(x)][/tex]
= [tex][-6(\frac{\sqrt{x}+8}{6})-8]^{2}[/tex]
= [tex][-\sqrt{x}+8-8]^2[/tex]
= [tex](-\sqrt{x})^2[/tex]
= x
Therefore, [tex](fof^{-1})(x)=x[/tex]
HELP ASAP!!!
Identify the volume and surface area of a sphere with great circle area 9 pi m^2 in terms of pi. Give your answer in terms of pi.
Step-by-step explanation:
great circle = 9[tex]\pi[/tex] = r^2.[tex]\pi[/tex] --> r = 3 m
Surface area S = 4[tex]\pi[/tex].r^2 = 36[tex]\pi[/tex] m^2
Volume V = 4/3[tex]\pi[/tex].r^3 = 36[tex]\pi[/tex] m^3
The volume of a sphere is 36π m³ and the Surface area of sphere 36π m². Therefore, option A is the correct answer.
What is the volume of a sphere?The volume of sphere is the measure of space that can be occupied by a sphere. If the radius of the sphere formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by: Volume of Sphere, V = (4/3)πr³
Given that, sphere with great circle area 9π m².
We know that, area of a circle = πr²
Now, πr²=9π m²
r=3 m
Here, volume of a sphere = 4/3 ×π×3³
= 36π m³
Surface area of sphere = A = 4πr²
= 4×π×3²
= 36π m²
Therefore, option A is the correct answer.
To learn more about the volume of a sphere visit:
https://brainly.com/question/9994313.
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You have a prepaid bus pass that has $10 on it. Every time you ride the bus it costs you 50 cents. Assume that you cannot put anymore money on the card after it is used. Create an equation for the situation above.
Answer:
y = 10 - 0.5x for 0 ≤ x ≤ 20
Step-by-step explanation:
Initial value = (0,10)
final value = (20,0)
Cost per trip = debit of 0.50 = slope
equation : y = 10 - 0.5x for 0 <= x <= 20
Write an equation (a) in slope intercept form and (b) in standard form for the line passing through (2,7) and perpendicular to 3x + 5y = 1
Answer:
Step-by-step explanation:
Solve 3x + 5y = 1 for y to obtain the slope of the given line:
5y = -3x + 1, or y = (-3/5)x + 1.
Any line perpendicular to this one has the slope which is the negative reciprocal of (-3/5): That would be 5/3.
The desired line has slope 5/3 and passes through (2, 7);
Adapt y = mx + b by substituting the known values, to find b:
7 = (5/3)(2) + b. The LCD is 3, so multiply each term by 3 to eliminate the fractional coefficient:
21 = 10 + 3b, or 11 = 3b. Then b = 11/3, and the desired equation in slope intercept form is
y = (5/3)x + 11/3
To obtain the standard form, multiply all three terms by 3 again:
3y = 5x + 11, or
5x + 11 - 3y = 0, or
5x - 3y + 11 = 0
5. i. Which of the following is an example of a chemical property?
A. color
C. the ability to rust
B. density
D. phase
ii. Why?
The answer is C. Ability to rust. This is because rusting is a chemical property of a substance, which is caused by environmental factors causing said substance to tarnish.
Which relationship in the triangle must be true?
A
c
b
C
B
а
sin(B) = sin(A)
sin(B) = cos(90 - B)
COS(B) = sin(180 - B)
cos(B) = (A)
Answer:
sin(B) = cos(90 - B).
Step-by-step explanation:
To answer this question, you must understand SOH CAH TOA.
SOH = Sine; Opposite divided by Hypotenuse
CAH = Cosine; Adjacent divided by Hypotenuse
TOA = Tangent; Opposite divided by Adjacent
I roughly drew a triangle for reference. Let's say we have a 3-4-5 triangle.
As you can see, sin(b) does not equal sin(a). To get the sine of an angle, you would do opposite over hypotenuse. For angle B, that would be 3/5, while for angle A, that would be 4/5.
As stated above, sin(B) is 3/5. Now, if you did cos(90 - B), it would be the same thing as cos(A). This is because the triangle is a right triangle. Since a triangle has 180 degrees, and one angle is a right triangle, the other two angles will add up to be 90 degrees. So, 90 - B = A. cos(A) is the same thing as adjacent over hypotenuse, which is 3/5. So, sin(B) = cos(90 - B) must be true.
Let's just check the others to make sure they are false.
cos(B) = 4/5.
sin(180 - B) is basically the same thing as sin(A + C), which is definitely NOT 4/5.
cos(B) = 4/5, which is NOT the same as A.
So, your answer is sin(B) = cos(90 - B).
Hope this helps!
In an isosceles right triangle, the length of the hypotenuse is 8 units. Which measurement is NOT associated with the triangle? * A. 4√2 units B. 8√2 units C. 45° D. 90°
Answer:
B. 8sqrt(2)
Step-by-step explanation:
The legs of an isosceles right triangle are congruent and measure 45 deg. The right angle measures 90 deg. The ratio of the lengths of the sides of a 45-45-90 deg triangle is 1 : 1 : sqrt(2).
Since the hypotenuse measures 8, then the legs measure 8/sqrt(2)
8/sqrt(2) * sqrt(2)/sqrt(2) = 8sqrt(2)/2 = 4sqrt(2)
Answer: B. 8sqrt(2)
calcula la suma de los ángulos internos de los siguientes polígonos:
a)pentágono - b)heptágono - c)octágono - d)nonágona
Porfavorr, graciasss
Answer: a)pentágono 540° = 108×5
b)heptágono 900°≈128.57 ×7
- c)octágono 1080° = 135 × 8
- d)nonágona 1260 = 140 × 9
Step-by-step explanation:
360 ÷ number of sides = x Subtract x from 180 =y measure of interior∠
Multiply y × number of sides == sum of interior angles
Find angle x, giving your answer to 1 decimal place.
Answer:
57.8 degrees and 122.2 degrees (to one decimal place)
Step-by-step explanation:
Since there are two pairs of angle/side involved, we can use the sine rule.
sin(A)/a = sin(B)/b
where
A = angle x
a = 11cm
B = 38 degrees
b = 8 cm
substitute in the sine rule equation,
sin(A) = sin(x) = sin(38)/8 * 11 = 0.61566 * 11/8 = 0.84653
Now there are two solutions for x where sin(x) = 0.84653, they are supplement angles, namely 57.8367 degrees and 122.1633 degrees.
The reason for the two solutions is because the 8cm side can swing in two positions, one that makes x acute, and the other one obtuse.
13 points, please answer!
Which shows the dilation with a possible scale factor of 1/2?
Answer:
Option B
Step-by-step explanation:
With a scale factor of 1/2, the dilated shape should be smaller because of the scale factor, So in Option B the dilated shape is smaller than the real one.
1) Option A is an enlargement
2) Option B is reduction
3) Option C is equality
Write these five numbers in order of size. Start with the smallest number. 2.5 0.5 0.52 2.2 0.25
Answer:
0.52,0.25,0.5,2.2
Step-by-step explanation:
. Write an example problem that includes a compound event. b. List all of the outcomes of the sample space of the compound event.
Answer:
living organism
Step-by-step explanation:
soil particals and decad crops living organism
Use the given degree of confidence and sample data to construct interval for the population proportion. Of 369 randomly selected medical students, 23 said that they planned to work in a rural community. Construct a 95% confidence interval for the percentage of all medical students who plan to work in a rural community. (4.16%, 8.30%) (3.77%, 9.47%) (3.30%, 9.17%) (2.99%, 9.47%) (3.77%, 8.70%) In a poll of registered voters nationwide, 43% of those polled blamed of companies the most for the recent increase in gasoline prices. The margin of error at the 96% confidence level for this point estimate is 2.4%. Construct a 95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices. (0.382, 0.478) (0.368, 0.492) (0.406, 0.477) (0.383, 0.477) Cannot be determined from the information given.
Answer:
e) (3.77%, 8.70%)
95% confidence interval for the percentage of all medical students who plan to work in a rural community
(3.83% , 8.69%)
95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices
(0.406 , 0.454)
Step-by-step explanation:
Step(i):-
Given random sample size 'n' = 369
Sample proportion
[tex]p = \frac{x}{n} = \frac{23}{369} = 0.0623[/tex]
95% confidence intervals are determined by
[tex](p^{-} - Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.0623 - 1.96 \sqrt{\frac{0.0623(1-0.0623)}{369} } , 0.0623 + 1.96\sqrt{\frac{0.0623(1-0.0623)}{369} })[/tex]
(0.0623 - 0.0246 , 0.0623 + 0.0246)
(0.0383 , 0.0869)
(3.83% , 8.69%)
95% confidence interval for the percentage of all medical students who plan to work in a rural community
(3.83% , 8.69%)
Step(ii):-
Given 43% of those polled blamed of companies the most for the recent increase in gasoline prices
sample proportion 'p' = 0.43
Given Margin of error (M.E) = 0.024
95% confidence intervals are determined by
[tex](p^{-} - Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.43 - 0.024 } , 0.43 +0.024 )[/tex]
(0.406 , 0.454)
Final answer:-
95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices
(0.406 , 0.454)
Nash's Trading Post, LLC took a physical inventory on December 31 and determined that goods costing $208,000 were on hand. Not included in the physical count were $30,000 of goods purchased from Swifty Corporation, FOB, shipping point, and $23,500 of goods sold to Marigold Corp. For $30,000, FOB destination. Both the Swifty purchase and the Marigold sale were in transit at year-end.
Answer:
$261,500
Step-by-step explanation:
What amount should Nash report as its December 31 inventory?
Item Amount
Goods on hand as per physical count $208,000
(+) Goods purchased from Swifty $30,000
Corporation FOB shipping point
(+) Goods sold to Marigold Corp $23,500
FOB destination (at cost value)
Ending inventory $261,500
Notes:
1) In case of FOB shipping point, the ownership of goods is transferred to the buyer when the goods are shipped and hence in the case of purchases from Swifty corporation, the goods should be included in the inventory of Nash's Trading Post as the goods are shipped and are in transit.
2) In case of FOB destination, the ownership of goods is transferred to the buyer when the goods reaches to the buyer, hence in the case of sales made to Marigold Corp, the goods are still in transit and the ownership is not transferred to Marigold Corp, hence Nash's Trading Post should included that goods in its inventory.
quadrilateral ghjk is a rectangle. find measure <2 and <7 if m<3 = 37. image attached
Answer:
[tex]m\angle 2=53^{\circ}[/tex]
[tex]m\angle 7=74^{\circ}[/tex]
Step-by-step explanation:
It is given that quadrilateral GHJK is a rectangle and [tex]n\angle 3=37^{\circ}[/tex].
All interior angles of a rectangle are right angles. Diagonals are equal and bisect each other.
Now,
[tex]m\angle HKJ+m\angle HKG=90^{\circ}[/tex] (Interior angles of a rectangle are right angles)
[tex]m\angle 3+m\angle HKG=90^{\circ}[/tex]
[tex]37^{\circ}+m\angle HKG=90^{\circ}[/tex]
[tex]m\angle HKG=90^{\circ}-37^{\circ}[/tex]
[tex]m\angle HKG=53^{\circ}[/tex]
In an isosceles triangle, angle with equal sides are equal.
[tex]m\angle JGK=m\angle HKG[/tex]
[tex]m\angle 2=53^{\circ}[/tex]
Therefore, measure of angle 2 is 53 degrees.
Let the diagonals intersect each other at point O.
In triangle OGK,
[tex]m\angle OGK+m\angle OKG+m\angle GOK=180^{\circ}[/tex] (Angle su property)
[tex]53^{\circ}+53^{\circ}+m\angle GOK=180^{\circ}[/tex]
[tex]106^{\circ}+m\angle GOK=180^{\circ}[/tex]
[tex]m\angle GOK=180^{\circ}-106^{\circ}=74^{\circ}[/tex]
Vertical opposite angles are equal. So,
[tex]m\angle 7=74^{\circ}[/tex]
Therefore, measure of angle 7 is 74 degrees.
HELP IF YOU KNOW THIS PLEASEEEE
Answer:
63m
Step-by-step explanation:
What is the area, in square units, of triangle $ABC$ in the figure shown if points $A$, $B$, $C$ and $D$ are coplanar, angle $D$ is a right angle, $AC = 13$, $AB = 15$ and $DC = 5$?
Answer:
The answer is 24.
Answer:
24
Step-by-step explanation:
Seeing that triangle ACD is a 5-12-13 right triangle, AD=12. Then using Pythagorean Theorem, we can calculate BD to be BD=[tex]\sqrt{15^2-12^2}=\sqrt{3^2(5^2-4^2)}=3\sqrt{25-16}=3\sqrt{9}=3 \cdot 3 = 9$[/tex]. Thus, the area of triangle ABD is [tex]$\frac{1}{2} \cdot 12 \cdot 9=6 \cdot 9=54 \text{ sq units}$[/tex] and the area of triangle ACD is [tex]$\frac{1}{2} \cdot 12 \cdot 5=6 \cdot 5=30 \text{ sq units}$[/tex]. The area of triangle ABC is the difference between the two areas: [tex]$54 \text{sq units} - 30 \text{sq units} = \boxed{24} \text{sq units}$.[/tex]