The original height of the water in a pool is 5 ft , Option B is the correct answer.
What is an Equation ?An equation can be defined as a mathematical statement when two algebraic expressions are equated using an equal sign.
It is given in the question that
A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.
the height of the water is 4.75 feet.
The equation
4.75 = x + (negative 0.25)
can be used to find x, the original height of the water in a pool.
4.75 = x - 0.25
x = 5
Therefore the original height of the water in a pool is 5 ft , Option B is the correct answer.
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Answer:
B
Step-by-step explanation:
( PLEASE HELP WILL MARK BRAINLIEST PLEZ ) Calculate the area of a triangle with a base of 6 cm and a height of 12 cm. Draw and label the triangle.
Area
1/2BH1/2(6)(12)3(12)36cm²Base=6cm
Height=12cm
So,
1/2BH= 1/2×6×12
= (3×12)
= 36 cm²
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13 × (11 + 11) - (4 × 17) - 6 = X
Answer: 212
Step-by-step explanation:
13 * 22 - 68 - 6 = X
286 - 68 - 6 = X
286 - 74 = X
X = 212
he graph of the function f(x) = –(x + 6)(x + 2) is shown below.
The domain of the function is all real numbers, the range of a function is y ≤ 4
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = –(x + 6)(x + 2)
If we plot this function on the coordinate plane, we will see it is a graph of a quadratic function.
Here the no other details are given.
But we can say:
The domain of the function is all real numbers.The range of a function is y ≤ 4The x-axis intercept will be at (-6, 0) and (-2, 0).Thus, the domain of the function is all real numbers, the range of a function is y ≤ 4
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If 12,5 % discounted is offered on a R500,00 pair of shoes ,how much discount will you receive
Answer: R62,500
Step-by-step explanation:
To find the discount, simply multiply 12.5% (0.125 in decimal form) with 500,000
500,000 x 0.125 = 62,500
Answer:
₹62,50
Step-by-step explanation:
The amount of discount is found by multiplying the discount rate by the amount being discounted.
discount = 0,125 × ₹500,00 = ₹62,50
You will receive a discount of ₹62,50.
_____
Additional comment
Here, a comma is used to separate the units part of the number from the fractional part of the number. This decimal separator is an alternative to the use of a period or centered dot (·) for that purpose.
6 x (3+2) divided by 10
a puppy weighs 1 pound. what does the puppy weigh after 4 weeks
4(x-5)-(6x + 1)= 2x -19
Answer:
Step-by-step explanation:
Comment
I take it you want the value for x.
Solution
4(x-5)-(6x + 1)= 2x -19 Remove the Brackets.
4x - 20 - 6x - 1 = 2x - 19 Combine like terms
-2x - 21 = 2x - 19 Add 2x to both sides
-2x-21+2x = 2x + 2x - 19 Combine
-21 = 4x - 19 Add 19 to both sides
-21+19 = 4x -19 + 19 Combine like terms
-2 = 4x Divide by 4
-2/4 = x
x = - 1/2
Answer: x = - 1/2
or x = -0.5
Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the
following is true.
P(-C≤Z≤c)=0.9715
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Using the normal distribution, considering it's symmetry, it is found that the value of C is of 2.19.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The standard normal distribution has mean and standard deviation given, respectively, by:
[tex]\mu = 0, \sigma = 1[/tex].
Hence, considering the symmetry of the normal distribution, the value of c is Z with a p-value of (1 + 0.9715)/2 = 0.98575, hence c = Z = 2.19.
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please help me Fast!!!!! slove the question in picture
Step-by-step explanation:
A)
Class Width=8
Median= 28.1
Modal Class= 20.5-28.5
B)
Mean=31.34
find the midpoint of the line segment between the points (11, -5) and (-3, -7)
Answer:
(4, -6)
Step-by-step explanation:
(x1+x2)/2 + (y1+y2)/2 = midpoint
(11+-3)/2 = 8/2 = 4. x = 4
(-5 + -7)/2 = -12/2. y = -6
4, -6 is the midpoint
give brainliest please! hope this helps :)
A bicycle company is designing women's bicycle frames The frames can accommodate any woman taller than 54.5 inches. Given that the heights of adult American women are normally distributed, with a mean of 65 inches and a standard deviation of 3.5 inches, what percentage of American women CANNOT use the bicycles designed by this company?
Using the normal distribution, it is found that 0.13% of American women CANNOT use the bicycles designed by this company.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 65, \sigma = 3.5[/tex]
The proportion of women that cannot use the bikes(smaller than 54.5 inches) is the p-value of Z when X = 54.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{54.5 - 65}{3.5}[/tex]
Z = -3
Z = -3 has a p-value of 0.0013.
0.0013 = 0.13% of American women CANNOT use the bicycles designed by this company.
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Question 4 of 10
If ƒ(x) = 3(x+5) +−, what is f(a+2)?
[tex]f(x) = 3(x+5)\\\\f(a+2) = 3(a+2 +5) \\\\~~~~~~~~~~~~=3(a+7)\\\\~~~~~~~~~~~~=3a+21[/tex]
(07.03 MC)
Victoria used a probability simulator to pull 3 colored marbles from a bag and flip a coin 50 times. The results are shown in the tables below:
Color of
Marble Number of
Times Rolled
Blue
18
Green
20
Yellow
12
Heads Tails
20 30
Using Victoria's simulation, what is the probability of pulling a blue marble and the coin landing tails up?
48 over 50
38 over 50
540 over 2500
360 over 2500
The probability of pulling a blue marble and the coin landing tails up is 360/2500
How to determine the probability?The tables of values are given as:
Color Times
Blue 18
Green 20
Yellow 12
Heads Tails
20 30
The probability of obtaining a blue marble is:
P(Blue) = 18/50
The probability of landing tails up is:
P(Tail) = 20/50
The required probability is:
P = P(Blue) * P(Tail)
This gives
P = 18/50 * 20/50
Evaluate the product
P = 360/2500
Hence, the probability of pulling a blue marble and the coin landing tails up is 360/2500
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the mean of the data set is 18. what number is missing? 21,11,_,27,22,13,16
The missing number given the mean of the data set is 16.
What is the missing number?Mean is the average of a data set. It is determined by adding all the numbers in the data set and dividing the sum by the numbers in the data set.
Missing number = (mean x total number in the data set) - sum of numbers in the data set
(18 x 7) - ( 21 + 11 + 27 + 22 + 13 + 16)
126 - 110
= 16
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What division problem does this area model represent?
Answer:
2,160 ÷ 36 = 60
Step-by-step explanation:
The division problem that this area model represents is,
2,160 ÷ 36 = 60
Question 1: 5 pts
Bill wants to plant roses in his triangular plot. There will be 1 plant at a corner. Each row will have 6
additional plants. He wants the plot to have as many lows as possible with 150 rose plants. How many
rows will Bill's plot have?
O 7 rows
O 8 rows
O 6 rows
O 5 rows
The arrangement of the rose plants on the triangular plot is such that they
form a series or progression that is defined.
The number of rows on Bill's plot is; 8 rows
The given parameters for the triangular plot are;
Number of plants at the corner = 1 plant
Number of additional plants per row = 6 plants
Number of rose plants = 150 rose plants
The number of rows in the plot.
The difference between successive rows, d = 6
The number rose at the top vertex, a = 1
Therefore, the rose in the garden forms an arithmetic progression
The first term, a = 1
The common difference, d = 6
The number of rows Bill's plot will have, n is given by the sum of n in terms of
an arithmetic progression, Sn, is given as follows;
[tex]S_n=\frac{n}{2}[2a+(n-1)\times d[/tex]
When Sn = 150, we get;
[tex]150=\frac{n}{2} [2\times 1+(n-1)\times 6[/tex]
150 = 3·n² - 2·n
3·n² - 2·n - 150 = 0
Taking only the positive solution for n, we have;
[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-150\right)}}{2\cdot \:3}[/tex]
[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{451}}{2\cdot \:3}[/tex]
[tex]n=\frac{1+\sqrt{451}}{3},\:n=\frac{1-\sqrt{451}}{3}[/tex]
The number of rows Bill's plot has, n ≈ 7.3965
Given that the 7th row is completed, an 8th row will be present on Bill's plot
The number of rows Bill's plot will have = 8 rows
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there are 20 students 15 men and 5 women in a maths class,in how many different ways can a committee of 3 men and 2 women be choosen
[tex]\displaystyle\\\binom{15}{3}\cdot\binom{5}{2}=\dfrac{15!}{3!12!}\cdot\dfrac{5!}{2!3!}=\dfrac{13\cdot14\cdot15}{2\cdot3}\cdot\dfrac{4\cdot5}{2}=13\cdot7\cdot5\cdot2\cdot5=4550[/tex]
please help me Im almost done
Answer:
[tex]\mathsf {x = 76}[/tex]
Step-by-step explanation:
The given pair of angles lie on a line, hence they are classified as linear angles. They possess the property by which their sum is equal to 180°.
[tex]\textsf {Solving :}[/tex]
[tex]\implies \mathsf {x + 17 + 87 = 180}[/tex]
[tex]\implies \mathsf {x + 104 = 180}[/tex]
[tex]\implies \mathsf {x = 180 - 104}[/tex]
[tex]\implies \mathsf {x = 76}[/tex]
6230000 in standard form
Answer:
6.23*10^6
Step-by-step explanation:
in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so
1) write the first number and add a decimal point(.) and copy down the numbers behind the first number (DO NOT WRITE 0):
6.23
2) check how many numbers are they behind the first number
6230000
~~~~~~
in here, it's 6numbers, so 10^6
3) all in all, your answer is
6.23*10^6
Solve the system of equations
−5x−3y=−28 and x+2y=0 by combining the equations
Answer: (8, -4)
Step-by-step explanation:
-5x - 3y = -28
x + 2y = 0
1. Multiply both sides of the bottom system by 5 to cancel the x out
5(x+2y=0)
5x + 10y = 0
2. rewrite
-5x - 3y = -28
5x + 10y = 0
3. add
0x + 7y = -28
4. divide by 7
7y = -28
5. y = -4
6. plug in -4 for y in one of the original equations
x + 2(-4) = 0
7. simplify
x = 8
9. solution is
(8, -4)
If a hot air balloon pilot inflates the balloon at an average wind speed of about 5 miles per hour with an altitude of 35,000 feet, how fast will the radius of the balloon increase as it goes up higher and higher performing certain tricks? Using the differentiation formula applicable for this situation, estimate the speed of inflation and the speed of landing. Will this be able to help the pilot still perform other tricks before making a colorful landing? Give at least two comprehensible reasons and explain your answer.
The speed of landing is 15.69 ft/sec.
What is differentiation ?"Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function. In contrast to the abstract nature of the theory behind it, the practical technique of differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions.
The three basic derivatives (D) are: (1) for algebraic functions, D(xn) = nxn − 1, in which n is any real number; (2) for trigonometric functions, D(sin x) = cos x and D(cos x) = −sin x; and (3) for exponential functions, D(ex) = ex."
Let the length of the rope = r
Height of the balloon = h
we are given dr/dt = 15ft/sec
at any time t we know:
[tex]r = 125 + 15*t[/tex]
By the Pythagoras theorem we know:
[tex]h^2 + 125^2 = r^2[/tex]
We have to find dh/dt at time t = 20 sec
[tex]d/dh(h^2 + 125^2) = d/dt(r^2)[/tex]
By chain rule:
[tex]d/dh(h^2 + 125^2)*dh/dt\\ = d/dr(r^2)*dr/dt\\2h*dh/dt = 2r* dr/dt\\h*dh/dt = r*dr/dt\\dh/dt = (r/h)*dr/dt[/tex]
[tex]= [(125 + 15*20)/(425^2 - 125^2)^1/2]*15[/tex]--------------------- at time t = 2
=15.69 ft/sec
Hence dh/dt = 15.69 ft/sec
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23.4571 to the nearest 10
23.4571 to the nearest 10
asnwer: 23.5
39. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
sum the 5 exterior angles and equate to 360
5x + 3 + 4x + 8 + 5x + 5 + 6x - 1 + 3x = 360 , that is
23x + 15 = 360 ( subtract 15 from both sides )
23x = 345 ( divide both sides by 23 )
x = 15
answer asap giving max points and brainliest A projectile is launched at an angle of 30° and travels a distance of 400 meters. Gravitational acceleration equals 9.8 m/sec2 calculate the initial velocity.
answer choices:
67
87
57
Answer:
67 m/s
Step-by-step explanation:
Formula for range :
Range = u²sin2θ / gu = initial velocityθ = angle of launchg = gravitational accelerationSolving with the given values :
400 = u² x sin60° / 9.8u² x √3/2 = 3920u² = 7840/√3u² = 4526.4u = 67 m/s (approximately)Answer:
[tex]\sf u=67\:ms^{-1}[/tex]
Step-by-step explanation:
Assuming the distance traveled is the horizontal distance.
Horizontal Range Formula
[tex]\sf R=\dfrac{u^2 \sin 2\theta}{g}[/tex]
where:
R = horizontal rangeu = initial velocity[tex]\theta[/tex] = angle of initial velocityg = acceleration due to gravityGiven:
R = 400 m[tex]\theta[/tex] = 30°g = 9.8 m/s²Substituting the given values into the formula and solving for u:
[tex]\implies \sf 400=\dfrac{u^2 \sin 60^{\circ}}{9.8}[/tex]
[tex]\implies \sf 3920=u^2 \sin 60^{\circ}[/tex]
[tex]\implies \sf 3920=\left(\dfrac{\sqrt{3}}{2}\right)u^2[/tex]
[tex]\implies \sf u^2=\dfrac{7840}{\sqrt{3}}[/tex]
[tex]\implies \sf u=\sqrt{\left(\dfrac{7840}{\sqrt{3}} \right) }[/tex]
[tex]\implies \sf u=67.2787196...[/tex]
[tex]\implies \sf u=67\:ms^{-1}\:(nearest\:whole\:number)[/tex]
what the volume of the soild
Answer:
A.264
Step-by-step explanation:
((Area Of triangle*height)=Volume
Area of triangle is the base of the triangle multiplied by height of triangle divided by 2
((8*6)/2)*11=264
The measure of an exterior angle of a regular polygon is 45º. How many sides does the polygon have?
Answer:The answer is 8 sides
Step-by-step explanation:
x y
-1 -10
3 14
Complete the slope-intercept form of the linear equation that represents the relationship in the table.
to get the equation of any straight line, we simply need two points off of it, let's use the ones in the table.
[tex]\begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -1&-10\\ 3&14\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{14 +10}{3 +1}\implies \cfrac{24}{4}\implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+10=6(x+1)\implies y+10=6x+6\implies y=6x-4[/tex]
13. Figure QRSP is a rectangle.
Q.
100°
What is the measure of angle RPS?
A. 40 degrees
C. 80 degrees
B. 50 degrees]
Answer:
b 50 degrees bavaggagshdd
The area of Louisiana is approximately 4 x
104 square miles. The area of the United
States is approximately 225 times greater
than the area of Louisiana. What is the
approximate area of the United States?
Answer:
93,600
Step-by-step explanation:
4x104= 416
416x225 = 93,600
There are 10000 people living in a certain city. Suppose that the rate of population growth in the city is proportional to the number of inhabitants. Suppose that 10% of the original amount increase in 30 years, how much will the population in the city after 60 years?
Answer:
.............30000.............