Isabella fills her pool at a rate of 18 liters per minute as per the given condition.
The slope of the volume can be used to determine how quickly it changes when given Time t in minutes and Volume V in liters. That represents a change in volume relative to a change in time.
m = (v2-v1)/(t2-t1).
selecting the first two points (2, 184) and from the provided data (7, 94).
Volume remains in the pool at what rate =
(94-184)/(7-2) = -90/5 = -18.
Therefore the rate at which Isabella fills her pool is 18 liters/minute as per the given question.
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Write an explicit formula for an,
the nth term of the sequence 3, 8, 13, .
An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 3 + 5(n - 1)..
How to write an explicit formula for the arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.From the information provided, we have the following parameters:
First term, a₁ = 3
Second term, a₂ = 8
Next, we would determine the common difference as follows:
Common difference, d = a₂ - a₁
Common difference, d = 8 - 3
Common difference, d = 5
Substituting the parameters into the mathematical expression, we have;
aₙ = 3 + (n - 1)(5)
aₙ = 3 + 5(n - 1).
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divide 1hr on the ratio 5 7
Answer:
25:35
Step-by-step explanation:
5 + 7 = 12
60 ÷ 12 = 5
5 × 5 = 25
5 ×7 = 35
ratio = 25:35
Consider kite FGHJ. What are the values of a and b? A = 14, b = 6 a = 14, b = 8 a = 17, b = 6 a = 17, b = 8
The value of a=17 cm and b=6 cm as FGHJ is a kite.
Kite has property their adjacent sides are equal. The top two sides of the kite are equal and the bottom two sides of the kite are equal.
Any quadrilateral with two sets of congruent successive sides is referred to as a kite (in contrast to a parallelogram where the opposite sides are congruent). Connecting points G and J, draw a section. Triangle GHJ and triangle GFJ are congruent. The information that GH = GF and FJ = HJ will be used.
FG=GH because of ∠F=∠H.
30=2a-4
2a=34
a=17 cm
Similarly, ∠F=∠H
FJ=HJ
3b+6=24
3b=18
b=6 cm
Hence, The value of a=17 cm and b=6 cm
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Answer:
a=17 and b=6
Step-by-step explanation:
took the test
Geometry!!! help!
Triangle DAC is isosceles with congruent sides AD and AC. Which additional given information is sufficient for showing that triangle DBC is isosceles?
Select ALL that apply
1.Line AB is an angle bisector of DAC
2.Angle BAD is congruent to angle ABC
3. Angle BDC is congruent to angle BCD
4.Angle ABD is congruent to angle ABC
5.Triangle DAB is congruent to triangle CAB
1. Line AB is an angle bisector of DAC.
4. Angle ABD is congruent to angle ABC
5. Triangle DAB is congruent to triangle CAB
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
Given, Triangle DAC is isosceles with congruent sides AD and AC.
The statements that are sufficient to for proving triangle DBC is isosceles
are, Line AB is an angle bisector of DAC.
Angle ABD is congruent to angle ABC as the opposite sides are equal.
Triangle DAB is congruent to triangle CAB as they share a common side AB and sides AD and AC are equal in length.
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what is the order these go
Answer:
see attached
Step-by-step explanation:
You want the steps in order for constructing a perpendicular to a line through an external point.
PerpendicularEssentially, the procedure identifies two points on the line (P and Q) that are equidistant from the external point (R), then proceeds to draw a perpendicular bisector of the segment between those two points. The external point is already equidistant from P and Q, so we only need to find another equidistant point (S) to complete the construction.
See the attachment for the ordering of the instruction steps. (Note the step numbers are not in order on the left.)
2. (06.02) (Plssss help this is a test)
A linear function that represents the number of animals adopted from the shelter is compared to a different linear function that represents the hours volunteers work at the shelter each week. Describe the key features of the functions
that are needed to determine if these lines intersect. (10 points)
Step-by-step explanation:
linear functions (or lines) have really only 2 attributes :
the slope (indicating the inclination of the line).
the y-intercept (the intersection with the y-axis) or the x-intercept. either way, they show the actual position of the line.
the lines intersect at one point, if they have different slopes.
they intersect at infinitely many points, if the slope and the y- or x-intercepts are equal (ultimately that means the lines are identical, so every point is an intersection point).
if they have the same slope but different y- or x-intercepts, it means they are parallel and will never intersect.
solve 1000 divided by 39 in fraction
Answer:
1000/39
Step-by-step explanation:
Which number gives the same result if it is multiplied by 999/998 or if any number is added to it?
Please give me the answer with an explanation!
Thanks in advance!
Answer:
The number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).
The property of a number being unchanged after being multiplied by a fraction and a constant is called an "Identity element". The identity element for multiplication is 1 and for addition is 0.
When any number is multiplied by 1, it stays the same. So, if we multiply any number by 999/998, which is equivalent to multiplying by 1, it stays the same.
Similarly, when any number is added to zero, it stays the same. So, if we add any number to 0, it stays the same.
Therefore, the only number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).
find the roots of each equation y^2-1/16=0
[tex]y^2 - \cfrac{1}{16}=0\implies y^2=\cfrac{1}{16}\implies y=\pm\sqrt{\cfrac{1}{16}}\implies y=\pm\cfrac{\sqrt{1}}{\sqrt{16}}\implies y=\pm \cfrac{1}{4}[/tex]
I really need helppp
Answer:
b = 8,3
Step-by-step explanation:
b + (-8,3) = 0
b - 8,3 = 0
b = 8,3
an airplane is miles north and miles east of an airport. the pilot wants to fly directly to the airport. what bearing should the pilot take?
Pilot should take reverse bearing, calculated using atan2(East,North),converted in degrees.
What is radian ?
A radian is a unit of measurement for angles. It is defined as the ratio of the length of an arc of a circle to the radius of that circle. One radian is approximately 57.3 degrees. Radians are often used in mathematics, physics, and engineering because they allow for a more natural way of measuring angles and help simplify certain calculations.
To find the bearing, we can use the formula ,
Bearing = atan2(East, North)
Where East is the number of miles east of the airport and North is the number of miles north of the airport.
The atan2 function is a variation of the arctangent function, which returns the angle (in radians) whose tangent is the quotient of its two arguments. This function is defined for all real arguments and returns a value between -π and π.
So you can convert the bearing from radians to degrees using the formula ,
degrees = bearing * (180/π)
Pilot should take reverse bearing, calculated using atan2(East,North),converted in degrees.
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solve by substitution
v+w=11
2v-w=16
Answer:
w = 3
v = 8
Step-by-step explanation:
v + w = 11 can be written
v = 11-w substitute this for v
2v - w = 16
2(11 -w) - w = 16 Distribute the 2
22 - 2w = 16 Subtract 22 from both sides
22 - 22 -2w = 16 - 22
-2w = -6 Divide both sides by -2
[tex]\frac{-2w}{-2}[/tex] = [tex]\frac{-6}{-2}[/tex]
w = 3
v = 11 - w
v = 11 -3
v =8
Check:
v + w = 11
8 + 3 = 11
11 = 11 Checks
2v - w = 16
2(8) - 3 = 16
19 - 3 = 16
16 = 16 checks
The following data give the prices of seven textbooks randomly selected from a university bookstore. $93 $172 $109 $119 $54 $164 $143 a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero
The deviations of the data values as calculated form the data given in the question is found out to be as 1698.
The formula to calculate the mean is ,
mean = fixi / n
Therefore ,
mean = 93+172+109+119+54+164+143 / 7 = 861/7 = 731.42
Now, to calculate the standard deviation,
= √∑ (fx)²/ n
he value of y² as calculated is found out to be as ,
y² = 10190.
Therefore, SD = √(10190)²/ 7= 38.1
Now , variance is equal to the square of the standard deviation ,
or variance = ∑ ( y)² / n-1
= 10190 / ( 7-1)
= 10190 /6
= 1698.
The sum of these deviation thus , is not zero.
The variance is defined as the expectation of a random variable's squared departure from its mean value, and it is used to determine how far a set of values is spread out from its mean.
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if xy + 8ey = 8e, find the value of y'' at the point where x = 0.
The value of y'' at the point where x = 0 is 8.
A derivative is a mathematical concept that measures how much a function changes as its input (or independent variable) changes. It is often represented by the symbol "dy/dx" or "f'(x)", and is used to calculate the slope of a function at a particular point.
To find the value of y'' at the point where x = 0, we first take the derivative of the equation with respect to x. This gives us y' + 8exy' = 0. Then, we take the derivative of this equation with respect to x again, which gives us y'' + 8exy'' + 8ey' = 0. Substituting x = 0 into this equation gives us y'' + 0 + 8e(0) = 0, which simplifies to y'' = 8.
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Dilate the segment with a scale factor of r=1/2
Answer:
3.5 cm long
Step-by-step explanation:
AB*1/2=7*1/2=3.5
Answer:
|AB'| = 3.5 cm
Step-by-step explanation:
Given:
|AB| = 7 cmr = ¹/₂To dilate the line segment by a scale factor r, multiply the original length of the line segment by the given scale factor:
[tex]\begin{aligned}\implies \sf |AB'|&=\sf |AB| \times r\\\\&=7 \times \dfrac{1}{2}\\\\&=\dfrac{7 \times 1}{2}\\\\&=\dfrac{7}{2}\\\\&=3.5\; \sf cm\end{aligned}[/tex]
Determine zα for the following. (Round your answers to two decimal places.)(a) α = 0.0089(b) α = 0.09(c) α = 0.707Please explain where and how you got the
The values of zα for the given significance levels are approximate:
(a) zα ≈ 2.33
(b) zα ≈ 1.34
(c) zα ≈ 0.54
To determine zα (also known as the critical value) for a given significance level α, we need to find the z-score that corresponds to the upper α percentage of the standard normal distribution. In other words, we are looking for the z-value that cuts off an area of α in the right tail of the standard normal curve.
The standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1.
To find zα, we can use a standard normal distribution table or a calculator that provides cumulative probability values for the standard normal distribution.
(a) α = 0.0089
For this case, we are looking for the z-score that corresponds to the upper 0.0089 percentage of the standard normal distribution. Using a calculator or standard normal distribution table, we find that zα ≈ 2.33.
(b) α = 0.09
In this case, we need to find the z-score that corresponds to the upper 0.09 percentage of the standard normal distribution. Again, using a calculator or standard normal distribution table, we find that zα ≈ 1.34.
(c) α = 0.707
For α = 0.707, we are interested in the z-score that corresponds to the upper 0.707 percentage of the standard normal distribution. Using a calculator or standard normal distribution table, we find that zα ≈ 0.54.
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The complete question is as follows:
Determine zα for the following. (Round your answers to two decimal places.)
(a) α = 0.0089
(b) α = 0.09
(c) α = 0.707
Please explain where and how you got the answer.
teri finds a pile of money with at least $\$600$. if she puts $\$200$ of the pile in her left pocket, gives away $\frac45$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $\$600$ of the original pile and kept the rest. what are the possible values of the number of dollars in the original pile of money? (give your answer as an interval.)
600 ≤ X < 950 are the possible values of the number of dollars in the original pile of money.
What is range?The difference between the highest and lowest values in statistics for a particular data collection is called the range. As an illustration, if the data set contains 1, 5, 8, 12, 3, the range will be 12 - 1 = 11. The difference between the greatest and lowest observation might thus also be used to determine the range.
We need to first put the data in ascending order before we can determine the range of a particular set of observations. To determine the range, calculate the difference between the highest and minimum values afterwards.
Let X be the amount in the pile.
What is left after putting $200 in the pile = X - $200
4/5 = 0.8
What she gives away = 0.8 (X - 200)
The remaining is : 0.2 (X - 200) what she puts in her right pocket.
200 + 0.2(X - 200) > X - 600
200 - 0.2X - 40 > X - 600
Solving the inequality we have :
= 160 + 0.2x > X - 600
= 760 > X - 0.2X
= 760 > 0.8X
= 950 > X
This implies : X < 950
It is said : X ≥ 600
The possible range of X is thus : 600 ≤ X < 950
thus, 600 ≤ X < 950 are the possible values of the number of dollars in the original pile of money.
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Stephen is making a map of his neighborhood. He knows the following information: His home, the bus stop, and the grocery store are all on the same street. His home, the park, and his friend's house are on the same street. A street map is shown. The streets form a triangle comprised of the locations of home, friends house, and the grocery store. The triangle is intersected by a line formed by the park and the bus stop. Stephen wants to use the Triangle Proportionality Theorem to determine the relationships on his map. He knows the angle between the park, the bus stop, and his home. Which other angle does he need to know
On solving the provided question we can say that in this triangle 6 blocks separate the bus stop from his house.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon.
The graph of the provided data is included below. 10 blocks separate his residence from the park.
His friend's home is 15 blocks away from his home. 9 blocks separate the grocery shop from his home.
The sides are in proportions according to Side-Angle-Side Similarity. Consequently, we calculate a ratio using the corresponding triangles.
= distance from home to friend's home / distance from home to park
= distance from home to grocery / distance from to bus stop
= 15/10 = 9/x
x = 6
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Answer:
His friend's house, grocery store, and his home
Step-by-step explanation:
Had this question on a test and got it right.
How do you write 1 2 on a graph?
To write the point (1, 2) on a graph, you would first locate the point on the x-axis where x = 1, and then go up 2 units on the y-axis.
The point (1, 2) is on the Cartesian plane and it represents the coordinates of a point in the 2-D space. This point is located 1 unit to the right of the y-axis and 2 units above the x-axis.
It can be represented graphically as a point on a coordinate plane where the x-coordinate is 1 and the y-coordinate is 2.
On the graph, you can plot the point by first drawing the x and y axes and their respective scales, then place a dot on the point (1,2) which represents the coordinates of the point.
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Select the parallel lines from the given pairs of lines :
Select one:
a.
y = x / 3 + 1, y = - x / 2 + 15
b.
y = 7x + 11, y = x / 2 + 11
c.
y = 3x + 21, y = − 3x - 8
d.
y = 5x / 2 + 1, y = 5x / 2 + 7
Answer:
d. y = 5x/2 + 1, y = 5x/2 + 7
Step-by-step explanation:
Both lines have the same slope (5/2) , so they are parallel.
Identify the graph of the system
Answer:Your mom
Step-by-step explanation:big
Supposed a family has a credit card balance of -300 ($300 of debt) they spend an average of $33 a day on essential items
Answer: To find out how many days it will take for the family to pay off their credit card balance, we can use the following equation:
Days = (-300) / 33
Solving for Days gives us:
Days = (-300) / 33 = -9
So it will take the family 9 days to pay off their credit card balance, assuming they only spend money on essential items and don't add any more to their debt.
Step-by-step explanation:
Nancy makes green bracelets, g, and red bracelets, r. She sells each green bracelet for $5 and each red bracelet for $3. Which expression represents the total amount of money Nancy makes selling bracelets?
Answer:
........
Step-by-step explanation:
I need help with this equation:
A line passes through the points (2,-1) and (4,-1).
I already know the slope is 0, what is the equation of the line? (In slope-intercept form)
The line which passes through the points (2,-1) and (4,-1) has the slope-intercept equation as y = -1.
What is the slope-intercept form?
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
The line passes through point (x1,y1) = (2,-1) and (x2,y2) = (4,-1)
The formula to find slope is -
m = (y2-y1)/(x2-x1)
m = (-1+1)/(4-2)
m = 0/2
m = 0
Now use the slope and point (2,-1) to find the y-intercept.
y = mx + b
-1 = 0(2) + b
-1 = 0 + b
b = -1
Write the equation in slope-intercept form as -
y = mx + b
y = 0x + (-1)
y = -1
Therefore, the equation is obtained as y = -1.
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Can a right triangle with side 6 cm 10 cm and 8cm be formed give reason?
Yes , a right triangle with the given sides 6 cm 10 cm and 8cm can be formed because the sides satisfies the Pythagoras Theorem .
According to Pythagoras Theorem , the square of the hypotnuse of triangle is equal to the square of the other two sides of triangle ;
The sides of the triangle are given as : 6cm ,10cm and 8cm ;
which means that ,
the hypotnuse is = 10 cm ;
According to Pythagoras Theorem ;
⇒ [tex]10^{2} =8^{2} +6^{2}[/tex] ;
⇒ [tex]100 = 64 + 36[/tex] ;
⇒ [tex]100= 100[/tex] ;
the side satisfies the condition to form the right triangle .
Therefore , the given sides forms a Right Triangle .
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color each of the six faces of a cube with either blue or red. note that two colorings are regarded the same if the cube looks identical after some rotation. how many different colorings can be made?
There are 8 different colorings that can be made.
Color each of the six faces of a cube with either blue or red. note that two colorings are regarded the same if the cube looks identical after some rotation.
The number of colorings can be calculated by using the equation 2^6 = 64. This is because each of the six faces of the cube can be colored either blue or red, giving two options for each face.
As there are six faces, the total number of colorings is 2^6 = 64. However, some of these colorings are the same after a rotation, so the total number of distinct colorings is 8.
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find the given median of the following data 16 14 15 18 17 20 25
Answer: 17
Step-by-step explanation:
First, change everything to ascending order.
14, 15, 16, 17, 18, 20, 25
Now, select the middle number, in this case, it is 17.
To find the median of a data set, you must put the numbers in order from least to greatest and find the middle (center) number.
The following data set: 16, 14, 15, 18, 17, 20 and 25 can be organized into the following order: 14, 15, 16, 17, 18, 20, 25.
Now, simply find out the middle number.
17 is the middle number, therefore the median.
What is the inverse of 1 2?
The inverse of a point (1, 2) on a graph would be the point (2, 1) because it's the reflection of the point (1, 2) over the line y = x.
In general, the inverse of a point (x, y) on a graph is the point (y, x). This is because when we switch the x and y coordinates of a point, we are reflecting it over the line y = x, which is the line of symmetry of the inverse function.
Inverse functions are mathematical operations that "reverse" each other. For example, if f(x) = 2x, then the inverse function f^-1(x) = x/2, when you apply f(x) and then f^-1(x) to a number you'll get the same number, so f^-1(f(x))=x, that's why they are called inverse. Inverse functions are only defined for bijective functions.
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The value of Mr. Dulaney's car x years after its purchase is
given by the function V(x) = 15, 000(0.87)^x. Approximately,
what was the value of Mr. Dulaney's car 5 years after its
purchase?
Using the given function V(x) = 15,000(0.87)^x , the value of Mr.Dulaney's car 5 years after its purchase will be approximately equal to given option $7500.
What is a function?A mathematical phrase, rule, or law that establishes the relation between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
What is the purpose of a mathematical function and how does it work?A mathematical function is a rule that assigns a unique output, also called the function value, to each input value within a certain set called the domain. The output is determined by the instructions, also called the function rule, that defines the relationship between the input and output values. It can be represented by an equation, such as y = f(x), where x is the input, y is the output, and f is the function symbol. The graph of a function is a set of points, where each input in the domain corresponds to a unique output. It helps to express the relationship between two variables and allows to make predictions and analyze patterns in mathematical problems.
Given,
V(x) = 15,000(0.87)^x where x denotes number of years after its purchase.
So, to find the value of Mr. Dulaney's car 5 years after its purchase,
let x =5
so V(x) = 15,000(0.87)^5 = $7476.31
Which is approximately equal to given option , $7,500
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Adding and subtracting mixed fractions
Answer:
what do yuo mean by adding and subtracting mixed fractions
