[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em}\textit{we know that} \begin{cases} y=-4\\ x=10 \end{cases}\implies -4=k(10) \\\\\\ \cfrac{-4}{10}=k\implies -\cfrac{2}{5}=k\hspace{10em}\boxed{y=-\cfrac{2}{5}x} \\\\\\ \textit{when x = 2, what is "y"?}\qquad y=-\cfrac{2}{5}(2)\implies y=-\cfrac{4}{5}[/tex]
A bowling ball is pushed with a force of 22. 0 N and accelerates at 5. 5 m/s2. What is the mass of the bowling ball?
When a bowling ball is propelled with a force of 22. 0 N and accelerates at a rate of 5. 5 [tex]ms^{-2}[/tex], its mass is 4. 0 kg.
Newton's Second Law of Motion states that force is the result of mass times acceleration.
[tex]F=m*a[/tex]
[tex]m = F / a[/tex]
A force of 22.0 Newtons ( [tex]kgms^{-2}[/tex] ) and an acceleration of 5.5 meters per second squared were used to drive the bowling ball.
F = 22.0 [tex]kgms^{-2}[/tex] and
a = 5.5 [tex]ms^{-2}[/tex]
Put the values in the formula as replacements.
M = 22 [tex]kgms^{-2}[/tex]/ 5.5 [tex]ms^{-2}[/tex]
Meters per second squared (m/s2) units cancel each other out.
M = 22 kg / 5.5
= 4 kg
The bowling ball weighs 4 kilogram.
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Helppppp super confused !
The expression that is equivalent is 6(y + 1) and 6y + 6.
The expression that are not equivalent are 3(x + 3) and 3x + 6 and x(x + 4) and x² + 4.
How to find equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.
Now, let's check if the expression are equivalent by simplifying it.
3(x + 3) and 3x + 6
3x + 9 and 3x + 6
Therefore, the expressions are not equivalent.
6(y + 1) and 6y + 6
6y + 6 and 6y + 6
They are equivalent expression.
x(x + 4) and x² + 4
x² + 4x and x² + 4
They are not equivalent expression.
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Kelly earned 300 dollars and put 70% of it into the bank. How much did she put into the bank?
Answer:
$210 in bank
Step-by-step explanation:
Kelly earned 300 dollars and put 70% of it into the bank. How much did she put into the bank?
70% = 0.7
300 * 0.7 = $210 in bank
A bag contains 150 marbles. Some are blue the rest is white. There are 21 blue marvles for every 4 white marbles. How many blue marbles are there.
There are 126 blue marbles.
Total marbles in the bag=150
There are 21 blue marbles for every 4 white marbles then the sequence will be⇒ 4+21+4+21+4+21+4+21+4+21+4+21=150
21 blue marbles appear 6 times for every 4 blue marbles
So 21×6=126 blue marbles and 4×6=24, then 126+24=150 total marbles
∴There will be a total of 126 blue marbles along with 24 white marbles among the 150 marbles.
PLS HELP, it’s due tmrw and I need it done
a. The system of inequalities that best represent how much of the agricultural products of soybeans and corn the river barge can carry is
A. 60x + 90y ≤ 4,500,000, x ≥ 0, y ≥ 0b. option A
c. The river barge can safely ship the agricultural products
How to determine the equation the agricultural products of soybeans and corn the river barge can carryinformation gotten from the question include
Corn weighs about 60 pounds per bushel
soybeans weigh about 90 pounds per bushel
A river barge can safely carry up to 4,500,000 pounds of cargo.
Let x = bushels of corn and y = bushels of soybeans.
a. From the statement, it can be deduced that the equation is
A. 60x + 90y ≤ 4,500,000, x ≥ 0, y ≥ 0
b. some interpretation on inequality
shading above a line is greater than and below a line is less thandotted lines mean the inequality do not have equal to while solid lines mean the inequality has equal tofrom the interpretation
The inequality has "equal to" as result the graph must be a solid lineThe inequality used is less than as a result the shading must be below the linethe correct option is A (graph attached)
c. 60 * 24000 + 90 * 24000
= 3,600,000
The value is ≤ 4,500,000 hence the river barge can carry it
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Can someone at least explain this to me I’m very confused.
For given line segments RS = TR
In this question, we have been given two line segments QS and TU intersected at point R.
Also, we have been given QS = TU, QR = RU
We need to prove, RS = TR
We can observe that,
QS = QR + RS
and UT = UR + RT
QS = TU ................(Given)
QR + RS = UR + RT
QR + RS = QR + RT .............(Given QR = RU )
QR + RS - QR = QR + RT - QR .............(subtraction property of equality)
RS = TR
Hence proved.
Therefore, for given line segments RS = TR
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7. Hannah invests £750 and after 4 years has £844.13. Find the compound interest rate.
If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Hannah contributes £750 and following 4 years has £844.13. Then the compound interest rate is given as,
844.13 = 750 (1 + r)⁴
(1 + r)⁴ = 1.1255
1 + r = 1.02999
r = 0.0299
r = 2.99%
r ≈ 3%
If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.
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pls help!!!
Consider the calculation 2/3 × 5/8 .
Without calculating the product, explain how you know that 3/4 is not the answer.
(p.s. they are fractions)
Thank you for those answering!
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
a certain insecticide kills 60% of all insects in laboratory experiments. a sample of 9 insects is exposed to the insecticide in a particular experiment. what is the probability that exactly one insect will die? round your answer to four decimal places.
The probability that exactly one insect will die is 142.611.
Define probability.The subject of a random event is covered in the mathematical field of probability. For instance, if a coin is flung into the air, it could land on its Head or Tail. Probability is equal to the number of favorable outcomes (Total number of outcomes) P = n (E) / n (S) (S) E is the event, P is the probability, and S is the sample area.
Given,
P( an insect will die) = 0.60
q = 1 - p
q = 1 - 0.60
q = 0.40
Sample size,
n = 9
Binomial distribution:
P(X) = ⁿCₓ pˣ qⁿ⁻ˣ
Probability that exactly one insect will die = P(X = 1)
= ⁹C₁ × 0.6¹ × 0.4⁸
= 362880 × 0.6 × 0.000655
= 142.611
The probability that exactly one insect will die is 142.611.
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in case study 19.1, we learned that about 56% of american adults actually voted in the presidential election of 1992, whereas about 61% of a random sample claimed that they had voted. the size of the sample was not specified, but suppose it were based on 1600 american adults, a common size for such studies. (a) into what interval of values should the sample proportion fall 68%, 95%, and almost all of the time? (round your answers to three
Confidence interval for 68% confidence level = (0.548, 0.572)
Confidence interval for 95% confidence level = (0.536, 0.584)
Confidence interval for 99.99% confidence level = (0.523, 0.598)
The mean of this sample distribution is
Mean = μₓ = np = 0.61 × 1600 = 976
But the sample mean according to the population mean should have been
Sample mean = population mean = nP
= 0.56 × 1600 = 896.
To find the interval of values where the sample proportion should fall 68%, 95%, and almost all of the time, we obtain confidence intervals for those confidence levels. Because, that's basically what the definition of the confidence interval is; an interval where the true value can be obtained to a certain level. of confidence.
We will be doing the calculations in sample proportions,
We will find the confidence interval for the confidence levels of 68%, 95% and almost all of the time (99.7%).
Basically the empirical rule of 68-95-99.7 for standard deviations 1, 2, and 3 from the mean.
Confidence interval = (Sample mean) ± (Margin of error)
Sample Mean = population mean = 0.56
The margin of Error = (critical value) × (standard deviation of the distribution of sample means)
Standard deviation of the distribution of sample means = [tex]\sqrt{[p(1-p)/n]}[/tex] =
[tex]\sqrt{[(0.56\times0.44)/1600]}[/tex] = 0.0124
The critical value for 68% confidence interval = 0.999 (from the z-tables)
The critical value for 95% confidence interval = 1.960 (also from the z-tables)
Critical values for the 99.7% confidence interval = 3.000 (also from the z-tables)
Confidence interval for 68% confidence level
= 0.56 ± (0.999 × 0.0124)
= 0.56 ± 0.0124
= (0.5476, 0.5724)
Confidence interval for 95% confidence level
= 0.56 ± (1.960 × 0.0124)
= 0.56 ± 0.0243
= (0.5357, 0.5843)
Confidence interval for 99.7% confidence level
= 0.56 ± (3.000 × 0.0124)
= 0.56 ± 0.0372
= (0.5228, 0.5972)
Therefore,
Confidence interval for 68% confidence level = (0.548, 0.572)
Confidence interval for 95% confidence level = (0.536, 0.584)
Confidence interval for 99.99% confidence level = (0.523, 0.598)
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A cosine function has an amplitude of 1/3, period of π/3, horizontal shift of -2π, and vertical shift of -3, x=π, what is y
A cosine function has an amplitude of 1/3, period of π/3, horizontal shift of -2π, and vertical shift of -3, x=π, then the value y is -2.8889
The general cosine function is given by
f(x)= A cos (B x -C) +D
where A= 1/3 is the amplitude,
period = 2π /B
π/3 =2π/B
B= 2/3
C= -2π is the horizontal shift and D= -3s a downward vertical shift.
If we substitute all these values into the formula we obtain;
f(x)= 1/3 cos (2/3 x +2π ) -3
if x= π then we have to calculate y
y= 1/3*0.3333 -3
y= -2.8889
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15 ten büyük 25 den küçük tek sayılar
Answer:
Step-by-step explanation:
15 ile 25 arasında toplam 10 tam sayı var,
buna 25-15=10 şeklinde ulaşabiliriz. Ardından tek sayılar sorulduğu için ve bu 10 tam sayı içerisinde hem tek hemde çift olduğu için sayıyı ikiye böleriz
10/2=5 ve ardından en sonda bulunan 25 sayısını çıkarırız yani, 5-1=4
cevaplar: 17, 19,21,23
What is the equation of the line that passes through the points (-2, -6) and (1, 2)?
The equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.
According to the question,
We have the following information:
Points through which line is passing = (-2,-6) and (1,2)
Now, we have the following values:
x1 = -2, y1 = -6
x2 = 1 and y2 = 2
We know that the following formula is used to find the slope of the line:
m = (y2-y1)/(x2-x1)
m = (2+6)/(1+2)
m = 8/3
Now, the following formula is used to find the equation of the line:
y-y1 = m(x-x1)
y+6 = 8/3(x+2)
y+6 = 8x/3+16/3
Subtracting 6 from both sides:
y = 8x/3+16/3-6
y = 8x/3-2/3
Hence, the equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.
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Evaluate the expression.
Do not round your answer.
1/5(3+2+ 5)² =
Answer:
20
Step-by-step explanation:
do parenthesis first
1/5(3+2+ 5)² =
1/5(10)² =
then exponent
1/5(10)² =
1/5(100) =
20
the initial number of views for a reader board was 25. the number of views is growing exponentially at a rate of 18% per week. what is the number of views expected to be four weeks from now? round to the nearest whole number.
The number of views in the four weeks round to the whole number is 48.
Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.
We have to find the number of views in the fourth week.
On the first week the increase = 25 + 25× 18%
= 25 + 25 × 18/100
= 25 + 4.5
= 29.5
The second week increase = 29.5 + 29.5 × 18%
= 29.5 + 5.31
= 34.81
The third week increase = 34.81 + 34.81 × 18%
= 34.81 + 6.2658
= 41.0758
The fourth week increase = 41.0758 + 41.0758 × 18%
= 41.0758 + 7.393644
= 48.469444
Therefore the number of views in the four weeks is 48.
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Find DE, please help me
Step-by-step explanation:
ABC and CDE are similar triangles.
similar shapes means that both shapes have the same angles. and : that there is one scaling factor for all lines of one of the shapes to calculate the lengths of the lines of the other shape.
we see that all the other sides of ABC are scaled 2:1 to the corresponding sides of CDE. that means the sides of ABC are twice a long as the sides of CDE.
the same scaling factor has to apply to AB vs. DE.
therefore,
11x - 25 = 2(4x + 1) = 8x + 2
3x = 27
x = 9
DE = 4x + 1 = 4×9 + 1 = 36 + 1 = 37
Caroline can make eleven lassis out of two mangoes. How many lassis can she make out of twelve mangoes?
Answer
Step-By-Step-Explanation
2 mangoes=eleven lassis
×6 ×6
12 mangoes=66 lassis
Answer=66 lassis
When is an equation true?
Answer: when the value on each side of the equal sign is the same
Step-by-step explanation: for example, 9=9 is a true equation. 5+4 = 9 is a true equation
Make x the subject of y = 3x-2
You may use the flowchart to help you if you wish.
x 3
- 2
Answer:
x=y/3 + 2/3
Step-by-step explanation:
Is this what you wanted?
Can someone please help me
If 4x+5y=−5 is a true equation, what would be the value of 8+4x+5y?
Answer:
3
Step-by-step explanation:
[tex]4x + 5y = - 5 \\ 8 + 4x + 5y = {?} \\ 8 + - 5 \\ = 3 \\ 8 + 4x + 5y = 3[/tex]
A rectangular athletic field has an area of 40x² + 190x-50. The width of the athletic field is 8x - 2. What is the length of the athletic field?
Answer:
The length = 5x + 25
Step-by-step explanation:
A = l x w
Examine the equation below used for determining the balance on a bank account. Look through this chapter and your notes to help you write a problem that could be modeled by the equation.
The balance on the bank account at the end of the third quarter of the year is 2,630.80
How to find the compound interest?
Compound interest is defined as the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest is found using the formula
A=P(1+r/n)ⁿˣ where:
A= Amountr= interest raten= number of interest applied per period and x= number of time periodTherefore, the amount (A)=2630.80
The P=2500
interest rate is 0.17%
Number of interest applied per period is 365 periods and
number of time period is 3.
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if a peregrine falcon dove at its maximum speed for half a mile to catch prey, how many seconds would the dive take? (round your answer to the nearest second.)
The time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.
Who is peregrine falcon dove?It can be found with in Arctic tundra of North America and Greenland, and it migrates to Central and South American countries as during winter.The peregrine falcon is the world's swiftest bird, diving to acquire its prey at speeds of over 321 kph (200 mph). They are also among the most tolerant species and can flourish in populated places.For the given question;
The maximum speed of peregrine falcon dove is 200 mph.
Time of travel = 0.5 miles.
The relation of distance and speed is;
speed = distance/time
200 mph = 0.5 miles / time
Time = 0.5 miles / 200 mph
Time = 0.5 × 60 × 60 miles / 200 m/ sec
Time = 9 sec
Thus, time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.
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the degree of f(x) is ?
the end behavior is the left side is ?
and the right side is ?
The degree of the polynomial is 5, and the end behavior is:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
How to get the degree of a polynomial?
For any given polynomial, we define the degree as the largest exponent on the polynomial.
On this case we have:
f(x) = 2x^3 - 3x^5 - x^2 + 1
We can see that the largest exponent is 5, so the degree is 5.
Now, for the ending behavior.
If we have an odd degree (like in this case) we will have opposite ending behaviors in both ends of the domain.
If the leading coefficient is negative (like in this case, it is -3) then the end behavior will be:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
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Part A
The graph shows the distance in miles, , a car travels in hours.
Explain why the graph does or does not represent a proportional relationship between the variables and .
Enter your explanation in the box provided.
Part B
Two cars leave from the same city at the same time and drive in the same direction. The table shows the distances traveled by each car.
• Determine whether the relationship between the number of hours traveled and the number of miles traveled is proportional for each car.
• Use the table to explain how you determined your answers.
• Describe how the graph of the distance traveled by each car would support your answers.
Enter your answers and your explanations in the box provided.
fi r e re r er e r er e re r e r er e re
the square root of $x$ is greater than 3 and less than 4. how many integer values of $x$ satisfy this condition?
6 integers that satisfy the given condition are 10,11,12,13,14,15.
Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size
we have the number X
Of which the square root is greater than 3 and less than 4
so,
[tex]3 < \sqrt{X} < 4[/tex]
on squaring both sides
[tex]3^2 < (\sqrt{X})^{2} < 4^2[/tex]
[tex]9 < X < 16[/tex]
so the integer that satisfies the condition is 10,11,12,13,14,15.
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Answer:
6
Step-by-step explanation:
Because 4 > √x > 3, we know that 16 > x > 9. Thus, the integers from 10 to 15 inclusive satisfy this inequality, which means 6 integers satisfy the condition in the problem.
The ___ of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.
The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.
What is hyperbola?A hyperbola is a significant conic section in mathematics that is created by the intersection of a double cone with a plane surface, though not always at the center. A hyperbola is symmetric along its conjugate axis and resembles the ellipse in many ways. A hyperbola is subject to concepts like foci, directrix, latus rectus, and eccentricity. Examples of hyperbola that are frequently seen include the path taken by the tip of a sundial's shadow, the scattering trajectory of subatomic particles, etc.Here, we'll use instances that have been solved to better grasp the definition, formula, derivation, and standard forms of hyperbolas.Hence, The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.
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if
x/y=y/z=z/x
show that x=y=z
Step-by-step explanation:
x/y = y/z = z/x
x = y²/z = zy/x and y = z²/x
x = y²/z
putting this into the 3rd part of the original equation :
z/x = z/ y²/z = z²/y²
now using the y identity of the second part there :
y = z²/x
z²/y² = z² / z⁴/x² = x²/z² (= z/x per previous equation)
so,
x²/z² = z/x
x³/z³ = 1
x/z = 1
x = z
then
y/z = y/x = z/x (= 1)
and therefore,
y/x = z/x meaning
y = z (and therefore = x)
so,
x = y = z