Answer: [tex]y=\frac{2}{5}x-8[/tex]
Step-by-step explanation:
By definition, the equation of the line in slope-intercept form of is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
Then, given the slope 2/5 and the point, (-10, -5), you can calculate the value of b by susbtituting and solve for it:
[tex]-10=\frac{2}{5}(-5)+b\\ -10=-2+b\\b=-8[/tex]
Substitute this value and the slope into the equation. THerefore, you obtain:
[tex]y=\frac{2}{5}x-8[/tex]
A certain volume of water contains 100,000 hydrogen atoms and 50,000 oxygen atoms.
How many hydrogen atoms are in a volume of water containing 4,000,000 oxygen atoms?
Answer:
Based off of the given information I believe the answer is 8,000,000 hydrogen atoms because it appears that the ratio between hydrogen and oxygen atoms in 2:1.
Step-by-step explanation:
Using the 2:1 ratio of hydrogen to oxygen atoms in water (H2O), a volume of water with 4,000,000 oxygen atoms would contain 8,000,000 hydrogen atoms.
We know that water, with the chemical formula H2O, consists of two hydrogen atoms for every oxygen atom. Using this information, for every oxygen atom in water, we need to account for two hydrogen atoms.
Given that a certain volume of water contains 100,000 hydrogen atoms and 50,000 oxygen atoms, we have a 2:1 ratio of hydrogen to oxygen atoms. If we want to determine how many hydrogen atoms are in a volume of water containing 4,000,000 oxygen atoms, we must apply the same 2:1 ratio.
To do so, we multiply the number of oxygen atoms by 2 (since there are two hydrogen atoms for every one oxygen atom), obtaining: 4,000,000 oxygen atoms times 2 = 8,000,000 hydrogen atoms.
email received a $50 gift card for his birthday.after buying some clothes,he had$16 left on the card.how much did he spend on the clothes?
A. 16-c=50
B. 50-c=16
C. 16c=50
D. c=16+50
The correct equation to find out how much was spent on the clothes is 50 - c = 16. Solving this, we find that c, the cost of the clothes, is $34.
The student initially had a $50 gift card and after purchasing some clothes, they were left with $16 on the card. To find out how much was spent on clothes, we need to subtract the remaining amount on the card from the initial amount. The correct equation to represent this situation is:
B. 50 - c = 16
We can then solve for c, which represents the cost of the clothes:
50 - 16 = c
34 = c
So, the amount spent on clothes is $34.
Which of the following are equivalent to the function y=3cosx + 2?
Check all that apply
Note: The ones I highlighted in blue are the answers I've chosen
Answer:
your choices are correct
Step-by-step explanation:
sin(x +π/2) is a translation of the sine function to the left by π/2 units, which makes it look exactly like the cosine function that you want.
cos(-x) is the same as cos(x), since the cosine function is an even function.
___
sin(x -π/2) will look like -cos(x), not what you want.
The third choice is a reflection across the x-axis of the function you started with. It is not equivalent.
Nate mother drives 225 miles to work each month how many miles do she drives in one year show work
Answer:
2700
Step-by-step explanation:
20 POINTS
Which equation does the graph below represent?
y = 1/4x
y = 4x
y = -1/4x
y = −4x
Answer:
Step-by-step explanation:
Line passes through (0,0) and (-1,4) .
Slope = -4
Equation of line is : y - 0 = - 4(x - 0)
y = - 4x
(9CQ) Find the distance from the balloon to the soccer fields.
Answer:
The distance from the balloon to the soccer fields = 3.6 miles ⇒ answer (b)
Step-by-step explanation:
* Let the hot air balloon at point A , the soccer fields
at point B and the football field at point C
∵ The measure of the angle of depression to the
soccer fields is 20° 15'
∴ The measure of angle B = 20° 15'
∵ The measure of the angle of depression to the
football field is 62° 30'
∴ The measure of angle C = 62° 30'
∵ The sum of measures of the interior angles of any triangle = 180°
∴ The measure of angle A = 180 - (20° 15' + 62° 30') = 97° 15'
* The distance between the balloon and the soccer field
is represented by the side AB of triangle ABC
- Use the sin Rule to find the length of side AB
∵ a/sin(A) = b/sin(B) = c/sin(C)
- a is the side opposite to angle A, b is the side opposite
to angle B and c is the side opposite to angle C
∵ AB = c ⇒ opposite to angle C
∵ The distance between the two fields = 4 miles
∴ BC = 4 miles
∵ BC = a ⇒ opposite to angle A
∴ 4/sin(97° 15') = c/sin(62° 30')
∴ c = (4 × sin(62° 30')) ÷ sin(97° 15')
∴ c = 3.6 miles
∴ The distance from the balloon to the soccer fields = 3.6 miles
answer (b)
Please help if you can!
the answer is A :)))))))))))))))))
Answer:
I am pretty sure it is Rhombus or a sideway rectangle but since they dont say more than givin I would say Rhombus
Step-by-step explanation:
15 less than twice a number g is 19. Find g.
Answer:
g = 17Step-by-step explanation:
15 less than twice a number g is 19
2g - 15 = 19 add 15 to both sides
2g - 15 + 15 = 19 + 15
2g = 34 divdie both sides by 2
2g : 2 = 34 : 2
g = 17
A number from 5 to 10 is drawn at random. What is the probability that the number is odd?
Answer:
1/2 or 0.5
Step-by-step explanation:
First think: How many numbers are there between 5 and ten that are odd?
5,7 and 9 are all odd (that makes 3 numbers)
Then you take that and divide it by the total number of numbers between 5 and 10
5,6,7,8,9,10 (that makes 6 numbers)
You then get 3/6, simplified to 1/2 or 0.5
When two six-sided dice are rolled what is the probability that the product of their scores will be greater than six?
Answer: [tex]\bold{\dfrac{11}{18}}[/tex]
Step-by-step explanation:
Think of the products row by row:
11 12 13 14 15 16 - 0 products greater than 6
21 22 23 24 25 26 - 3 products greater than 6
31 32 33 34 35 36 - 4 products greater than 6
41 42 43 44 45 46 - 5 products greater than 6
51 52 53 54 55 56 - 5 products greater than 6
61 62 63 64 65 66 - 5 products greater than 6
[tex]\dfrac{\text{number greater than 6}}{\text{total possible outcomes}}=\dfrac{22}{36}=\dfrac{11}{18}\ when\ reduced[/tex]
Answer:
11/18.
Step by.step explanation:
There are 36 possible outcomes when 2 dice are rolled.
Outcomes for a product greater than six are:
2,4 2,5 2,6 3,3 3,4 3,5 3,6 4,2 4,3 4,4 4,5 4,6 5.2 ......5.6 , 6.2 .......6.6.
= 22 ways.
required Probability is 22/36 = 11/18 (answer).
At Bud's company, bowling balls are shaped as a sphere with a diameter of 8 inches. If a store receives a shipment of 14 bowling balls, what is the total volume of the balls? 937.81 cubic inches B. 3,751.3 cubic inches C. 267.95 cubic inches D. 30,009.98 cubic inches
Answer I think it is c I hope that right I am sorry for late responds
Which is the correct formula to find the distance between two points (p,q) and (m,n)?
Answer:
The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer
Step-by-step explanation:
* The distance between any to points (x1 , y1) , (x2 , y2) is
- d = √[square the difference of x- coordinates plus
square the difference of y-coordinates]
∴ d = √[(x2 - x1)² + (y2 - y1)²] or
∴ d² = (x2 - x1)² + (y2 - y1)²
* x2 - x1 is the horizontal distance (h) and y2 - y1
is the vertical distance (v)
- By using Pythagoras theorem
∴ d = √[h² + v²]
∵ The two points are (p , q) and (m , n)
- Put x1 = m and y1 = n
- Put x2 = p and y2 = q
∴ d² = (p - m)² + (q - n)²
∴ d = √[(p - m)² + (q - n)²]
∴ The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer
Answer:
The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer
Step-by-step explanation:
The weather reporter says that there is a 14% chance that it will rain tomorrow. What is the probability that it will not rain
Since an 100% chance is all possibilities, then it must add up to 100. If we take away that 14 from 100 by subtracting, you just get 86. Therefore, there is an 86% chance that it will not rain tomorrow.
in each family of function,the____function is the most basic function in the family
A.linear
B.quadratic
C.simple
D.parent
Answer: Your answer is option D. In each family of function,the Parent function is the most basic function in the family
The family function has same highest degree, same shape for graph and consequently.
The correct option is D.
Given:
Identify the function is the most basic function in the family.
Below are the few example of family function.
[tex]y=x^2[/tex]
[tex]y=3x^2[/tex]
The graph for the both the function has same highest degree, same shape for graph and consequently. The parent function is the simplest from a family of function.
Thus, the correct option is D.
Learn more about parent function here:
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An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 136 lb and a standard deviation of 28.5 lb. a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 191 lb. The probability is approximately nothing. (Round to four decimal places as needed.) b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 130 lb and 191 lb. The probability is approximately nothing. (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? A. Part (a) because the seat performance for a sample of pilots is more important. B. Part (b) because the seat performance for a sample of pilots is more important. C. Part (b) because the seat performance for a single pilot is more important. D. Part (a) because the seat performance for a single pilot is more important.
Answer:
A) 0.5564; B) 0.8962; C) Choice D. Part (a) because the seat performance for a single pilot is more important.
Step-by-step explanation:
For part A,
We will find the z score for each value and then subtract the probabilities for each to give us the area between them. We use the z score for an individual value:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Our first X is 130 and our second X is 191. Our mean, μ, is 136 and our standard deviation, σ, is 28.5:
[tex]z=\frac{130-136}{28.5}=\frac{-6}{28.5}\approx -0.21\\\\z=\frac{191-136}{28.5}=\frac{55}{28.5}\approx 1.93[/tex]
Using a z table, we can see that the area under the curve to the left of z = -0.21 is 0.4168; the area under the curve to the left of z = 1.93 is 0.9732. This means the area between them is
0.9732-0.4168 = 0.5564.
For part B,
We will find the z score for each value again and subtract them; however, since we have a sample we will use the z score for the mean of a sample:
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
Our first X-bar is 130 and our second is 191; our mean is still 136; our standard deviation is still 28.5; and our sample size, n, is 36:
[tex]z=\frac{130-136}{28.5\div \sqrt{36}}=\frac{-6}{28.5\div 6}\approx -1.26\\\\z=\frac{191-136}{28.5\div \sqrt{36}}=\frac{55}{28.5\div 6}\approx 11.58[/tex]
The area under the curve to the left of -1.26 is 0.1038; the area under the curve to the left of 11.58 is 1.00:
1.00-0.1038 = 0.8962
For part C,
We want the probability that each individual pilot will be safe in these seats, so the value in part A is more important.
The probability that a randomly selected pilot's weight is between 130 lb and 191 lb is approximately 0.558 or 55.8%. The probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb is approximately 0.1056 or 10.56%. When redesigning the ejection seat, the probability from part (a) is more relevant.
Explanation:To find the probability that a randomly selected pilot's weight is between 130 lb and 191 lb, we need to calculate the z-scores for both weights and find the area under the curve between those two z-scores. First, we calculate the z-score for 130 lb using the formula z = (x - μ) / σ, where x is the weight of 130 lb, μ is the mean weight of 136 lb, and σ is the standard deviation of 28.5 lb. Solving for z, we get z = (130 - 136) / 28.5 = -0.21. Using a z-table or calculator, we find that the area to the left of -0.21 is approximately 0.415. Next, we calculate the z-score for 191 lb using the same formula, z = (191 - 136) / 28.5 = 1.93. Again using a z-table or calculator, we find that the area to the left of 1.93 is approximately 0.973. To find the area between the z-scores, we subtract the smaller area from the larger area: 0.973 - 0.415 = 0.558. Therefore, the probability that a randomly selected pilot's weight is between 130 lb and 191 lb is approximately 0.558 or 55.8%.
To find the probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb, we need to use the Central Limit Theorem. The sample mean follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the mean is still 136 lb and the standard deviation is 28.5 lb divided by the square root of 36, which is 4.75 lb. We can now calculate the z-scores for 130 lb and 191 lb using the same formula, z = (x - μ) / σ. The z-score for 130 lb is (130 - 136) / 4.75 = -1.26, and the z-score for 191 lb is (191 - 136) / 4.75 = 11.58. However, since the z-score for 191 lb is beyond the range of the standard normal distribution table, we can approximate it as 4. This means that we need to find the area under the curve to the left of -1.26 and subtract the area to the left of -4. Using a z-table or calculator, we find that the area to the left of -1.26 is approximately 0.1056, and the area to the left of -4 is approximately 0.000032. Subtracting the smaller area from the larger area, we get 0.1056 - 0.000032 = 0.1056. Therefore, the probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb is approximately 0.1056 or 10.56%.
When redesigning the ejection seat, the probability from part (a) is more relevant. This is because part (a) calculates the probability of a single pilot's weight falling within the given range, while part (b) calculates the probability of the mean weight of a sample of pilots falling within the given range. The ejection seat should be designed to accommodate the weight range of individual pilots, rather than the mean weight of a sample of pilots.
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It said four friends share 3 apples equally what fraction of an apple does each friend get?
Answer:
if i don't doubt then 1/4
Step-by-step explanation:
Which ordered pair is the solution set for the system of equations below? 2x + y = 18 x – y = –6
Answer:
(4,10) is the solution
Step-by-step explanation:
2x + y = 18
x – y = –6
Using elimination
2x + y = 18
x – y = –6
----------------------
3x = 12
Dividing each side by 3
3x/3 = 12/3
x =4
Now we can find y
2x+y = 18
2(4) +y =18
8+y = 18
Subtracting 8 from each side
8-8+y = 18-8
y=10
(4,10) is the solution
( please help this is the last question and i have 4 min left, thank you for the help!)
Find the difference.
Answer:
Step-by-step explanation:
-4x∧2 -1
-4x squared minus one
If Joe works eight hours per week at $10.75 an hour, how much will he make in one month?
$10.75 x 8 = $86 x 4(weeks) = $344
Multiply his hourly rate by the number of hours per week:
$10.75 x 8 hours = $86.00 per week.
An average month has 4 weeks, so in a 4 week month, multiply his weekly pay by the number of weeks in a month. ( Some months have 5 weeks, so you would need to multiply the weekly amount by 5 weeks).
$86 x 4 weeks = $344
True or false (picture provided)
Answer:
True
Step-by-step explanation:
The given inequality is
[tex]5\le x\le 8[/tex]
The boundaries of the inequality are inclusive.
We use the square brackets to indicate closed interval.
[tex]5\le x\le 8[/tex] is therefore written in interval notation as;
[5,8]
The correct choice is true
A boat traveled 27 miles in 2 hours.At this rate,how many miles will the boat in 1/2 hour?
[tex] \frac{27 \: miles \div 2}{2 \: hours \div 2} = \frac{13.5 \: miles}{1 \: hour} [/tex]
[tex] \frac{13.5 \: miles \div 2}{1 \: hour \div 2} = \frac{6.75 \: miles}{0.5 \: hour} [/tex]
The boat will travel 6.75 or
[tex]6 \frac{3}{4} [/tex]
miles in 1/2 hour.
Find the area of the trapezoid. leave your answer in simplest radical form.
Answer:
= 32√3 ft²
Step-by-step explanation:
Area of the trapezoid will be equal to the area of the square and that of the triangle.
Considering the triangle part;
Cos 60 = x/8
x = 8 × sin 60
= 4
Base of the triangle part = 4 ft
Therefore, top of the trapezoid = 6 ft
Height = 8 × sin 60
= 8 × √3/2
= 4 √3
Area of the trapezoid
Area = ((a+b)/2) × h
= ((6 + 10 )/2 )× 4√3
= 16/2 × 4√3
= 32√3 ft²
Answer:
4th option is correct
Step-by-step explanation:
Here in the triangle we have angle = 60
hypotenuse= 8
opposite and adjacent can be solved using trigonometric ratios
cos 60 = [tex]\frac{adjacent}{hupotenuse} \\\frac{adjacent}{8} \\\frac{1}{2}=\frac{adjacent}{8}[/tex]
which gives adjacent = 4 on solving
likewise using sine we can find opposite side to the angle which is height of
trapezium.
sin60[tex]\frac{opposite}{hypotenuse}=\frac{x}{8} \\\frac{\sqrt{3} }{2}=\frac{x}{8}\\x=4\sqrt{3}[/tex]
therefore height =[tex]4\sqrt{3}[/tex] and adjacent = 4 ft
therefore opposite sides of Trapezium are 10 ft and 6 ft
Formula for area of Trapezium =[tex]\frac{1}{2}[/tex](sum of parallel sides)x height
= [tex]\frac{1}{2}[/tex](10+6)x [tex]4\sqrt{3}[/tex]
on solving it ,we get [tex]32\sqrt{3}[/tex]
What is the correct way to write this fraction as a percent? A. 20% B. 25% C. 40% D. 70%
20% as a fraction is 1/5
25% is 1/4
40% is 2/5
and 70% is 7/10
Depending on what your fraction is, you can find the answer in the fraction itself-
20%, you can take 20, 5 times to get to 100. Hence 1/5.
25 can go into 100 4 times (1/4)
40 is just 20 twice, so its 2/5.
Take 10 7 times and get 7/10.
Hope this helps a bit :)
Classify the following sequence as arithmetic, geometric, neither or both: 2, 6, 18, ...
Arithmetic
Geometric
Neither
Both
Answer:
Geometric
Step-by-step explanation:
Does multiplying the same number with each term give the next term?
If so, then it is Geometric Sequence.
Does adding the same number with each term give the next term?
If so, then it is Arithmetic Sequence.
We see that multiplying by 3 gives us each successive term. 2 times 3 is 6 and 6 times 3 is 18. So it is geometric sequence.
It is NOT arithmetic sequence since we add 4 to 2 to get next number 6, but we have 12 to get next number, which is 18. So not an arithmetic sequence.
Answer is "Geometric"
Kelly has 236 feet of fence to use to enclose a rectangular space for her dog. She wants the width to be 23 feet. Draw a rectangle that could be the space for Kelley's dog. Label the length and the width
Answer:
The draw in the attached figure
Step-by-step explanation:
Let
L-----> the length of the rectangle
W----> the width of the rectangle
we know that
The perimeter of a rectangle is equal to
[tex]P=2(L+W)[/tex]
we have
[tex]W=23\ ft[/tex]
so
[tex]P=2L+46[/tex] -----> equation A
[tex]P\leq 236\ ft[/tex] ----> inequality B
substitute equation A in the inequality B and solve for L
[tex]2L+46\leq 236[/tex]
[tex]2L\leq 236-46[/tex]
[tex]2L\leq 190[/tex]
[tex]L\leq 95\ ft[/tex]
The maximum possible value of L is 95 ft
therefore
The rectangle could be
Length 95 ft
Width 23 ft
see the attached figure to see the draw
Pumping stations deliver oil at the rate modeled by the function D, given by d of t equals the quotient of 5 times t and the quantity 1 plus 3 times t with t measure in hours and and D(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 4-hour period from t = 0 to t = 4? Give 3 decimal places.
The pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.
Explanation:To find the amount of oil delivered by the pumping stations during the 4-hour period from t = 0 to t = 4, we need to evaluate the definite integral of the function D(t) over that interval. The function D(t) is given by D(t) = 5t / (1 + 3t). We can find the integral of this function using the substitution method. Let u = 1 + 3t, then du = 3dt. Rearranging this equation, we have dt = du / 3.
Substituting this in the integral, we get:
∫ D(t) dt = ∫ (5t / u) * (1/3) du = (5/3) * ∫ (t / u) du
Integrating the above expression, we get:
∫ D(t) dt = (5/3) * ∫ (t / u) du = (5/3) * ∫ (t / (1 + 3t)) du
To evaluate this integral, we can use the natural logarithm function. We know that ∫ (1/u) du = ln|u| + C, where C is the constant of integration. Substituting back for u, we have:
(5/3) * ∫ (t / (1 + 3t)) du = (5/3) * ∫ (t / u) du = (5/3) * ln|1 + 3t| + C
Now, we can use the definite integral to find the amount of oil delivered during the 4-hour period:
∫04 D(t) dt = (5/3) * ∫04 (t / (1 + 3t)) dt = (5/3) * [ln|1 + 3(4)| - ln|1 + 3(0)|] = (5/3) * [ln|13| - ln|1|] = (5/3) * ln|13| = 8.188
Therefore, the pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.
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The graph of a quadratic function has x intercepts at -3 and 5/2, and y intercept at 10. Give the function.
Answer:
f(x) = -4/3x² -2/3x +10
Step-by-step explanation:
The quadratic regression function of a graphing calculator or spreadsheet can determine the equation for you.
___
Or, you can determine it yourself.
The equation can be written in the form ...
f(x) = a(x +3)(x -5/2) . . . . . . . using the given x-intercepts
for some value of "a"
For x = 0, this must match the y-intercept.
f(0) = a(0 +3)(0 -5/2) = 10
-15/2·a = 10
a = -20/15 = -4/3
So, the function can be written as ...
f(x) = (-4/3)(x +3)(x -5/2)
or
f(x) = -4/3x² -2/3x +10
-2/3( 2x^2 + x - 15) is the answer.
From the given x-intercepts, 2 factors of the equation will be (x + 3) and
(2x - 5):- So we can write:
At the y-intercept x = 0 so we have the equation a(0+3)(2(0) - 5) = 10 where a is a constant.
a * -15 = 10
a = -2/3 so the function is (-2/3)(x + 3)(2x - 5)
= -2/3( 2x^2 + x - 15).
a taxpayer had a taxable income of 61900 and her spouse had a taxable income of 59400 if they wish to file their tax return jointly which tax bracket will they fall in to
Answer:
25%
Step-by-step explanation:
Just did test
HELP WORTH 99 POINTS IM SO CONFUSED.
A. At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge if the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate area of the larger circle (blue)
B. Find the approximate area of the smaller circle (orange)
C. Find the approximate area of the sidewalk (shaded region between the blue and orange circles.)
Use 3.14 for pi. Show your work!
(use 3.14 pi on all three problems!)
Answer:
Area of Large Circle = 380.13
Area of Small Circle = 254.47
Area of Sidewalk = 125.66
Step-by-step explanation:
The side walk is just subtracting the smaller number from the bigger one.
The area is just Pi*r^2
Answer:
A 379.94 m^2
B 254.34 m^2
C 125.6 m^2
Step-by-step explanation:
A Area of a circle is given by
A = pi r^2
We know the radius is 11
A = pi 11^2
A = 3.14 (121)
A = 379.94 m^2
B The Area of the orange circle
A = pi r^2
The radius is 9 m
A = pi 9^2
A = 3.14 (81)
A = 254.34 m^2
C The Area between the circles is the difference between the large circle and the small circle
Ablue-Aorange
379.94-254.34
125.6 m^2
Please help me out! :)