The sum of the ages of the children would be 3x - 94 years.
We have the total sum of the ages of pam ,dion and their children
as 5x - 99
here , x is the age of Dion .
we see , pam is five years younger than Dion , so
age of Pam = x - 5
Now as the sum of all the ages = 5x - 99
therefore ,
Age of Dion + Age of Pan + Age of children = 5x - 99
x + x - 5 + Age of children = 5x - 99
2x - 5 + Age of children = 5x - 99
therefore ,
Age of children = 3x - 94
So the age of their children would be 3x - 94 years
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two trains leave a station at the same time and travel in opposite directions. one train travels 20 kph faster than the other train. after 3 hours, they are 810 miles apart. what is the speed of each train?
The speed of each train is 125kph and 145kph.
Here it is given that the distance between the two trains is 810 miles after traveling for 3 hours.
The difference in their speed is 20 kph.
Let x be the speed of one train. So by this, we get the speed of the second train that is x + 20.
Formula to calculate speed is:
Speed = Distance / Time
Distance = Speed × Time
Distance covered by first train = x × 3
Distance covered by second train = (x + 20) × 3
Total distance = 810
So we get;
3x + (x + 20)3 = 810
3x + 3x + 60 = 810
6x = 750
x = 125
x + 20 = 125 + 20 = 145
Therefore we get the speed of both trains which is 125kpp and 145 kph.
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PLEASE HELP ASAP WILL MARK BRAINLIST
Answer:
what is your problem
Question
Graph x=−6.
A graph of the given mathematical expression (x = -6) is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
In this scenario, a number line would be used to graph the given mathematical expression because it only contains one (1) variable.
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find an equation for the perpendicular bisector of the line segment whose endpoints are (9,-5) and (-5,-1)
The equation y = (13 / 4) · x - 19 / 2 represents the perpendicular bisector of the line segment.
How to find the equation for the perpendicular bisector of a line segmentIn this problem we need to determine the equation of the line perpendicular to a line segment whose endpoints are known. The equation of the line is represented by a first grade polynomial of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.And the relationship between the slopes of two perpendicular lines:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.And the slope of the original line can be found by the secant line formula:
m = Δy / Δx
And the midpoint of a line segment between two endpoints is defined below, necessary for the location of the bisector:
M(x, y) = 0.5 · A(x, y) + B(x, y)
Where:
M(x, y) - MidpointA(x, y), B(x, y) - EndpointsFirst, find the slope of the line segment by secant line formula:
m = [- 1 - (- 5)] / (- 5 - 9)
m = - 4 / 13
Second, find the slope of the perpendicular bisector by the slope relationship between two perpendicular lines:
m' = - 1 / m
m' = - 1 / (- 4 / 13)
m' = 13 / 4
Third, determine the midpoint of the line segment by the midpoint formula:
M(x, y) = 0.5 · (9, - 5) + 0.5 · (- 5, - 1)
M(x, y) = (4.5, - 2.5) + (- 2.5, - 0.5)
M(x, y) = (2, - 3)
Fourth, find the intercept of the perpendicular bisector by means of the equation of the line:
b = y - m' · x
b = - 3 - (13 / 4) · 2
b = - 3 - 26 / 4
b = - 3 - 13 / 2
b = - 19 / 2
The equation for the perpendicular bisector is y = (13 / 4) · x - 19 / 2.
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an inverted pyramid is being filled with water at a constant rate of 40 cubic centimeters per second. the pyramid, at the top, has the shape of a square with sides of length 5 cm, and the height is 9 cm. find the rate at which the water level is rising when the water level is 2 cm.
The rate at which the water level is rising when the water level is 5 cm is;
dh/dt = 1.6 cm/s
What is a PYRAMID?A structure with triangle outside surfaces that converge to a single step at the summit is referred to as a pyramid (from Greek: pyrams)]. This shape is roughly a pyramid in the geometric sense. A pyramid foundation might be triangular, quadrilateral, or any other type of polygon. A pyramid therefore has at least three triangular exterior surfaces (at least four faces including the base). A typical variation is the square pyramid, which has a square base and four triangular exterior surfaces.Because a pyramid is built with the pyramidion at the top and the remainder of the weight closer to the ground[3], less material will be pressing down from above. Early civilizations could build stable structures thanks to this weight distribution.Acc to our question-
length of square side; s = 4 cmheight of pyramid; h = 8 cmvolumetric rate; dV/dt = 30 cm³/sSince the base is square shaped and we know that area of a square = s², then we can say that;Volume of pyramid = ¹/₃s²hThe pyramid has a height of 8 cm and length of its' square base side is 8 cm.Now, regardless of the water height, the surface of the water will always be square shaped. This implies that the ratio of the height to the top side of square will always be the same. Thus, we can say that; s = 4/8 h = h/2Thus, Volume is;V = ¹/₃ × (h/2)² × hV = ¹/₃ × h³/4V = h³/12dV/dt = (3h²/4) dh/dtPlugging in the relevant values gives;30 = (3 × 5²/4) dh/d120 = 75 dh/dtdh/dt = 120/75dh/dt = 1.6 cm/sHence,The rate at which the water level is rising when the water level is 5 cm is; dh/dt = 1.6 cm/s
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The slope of a ramp leading from the door to the ground is 5/3. the first point has a height of 27 inches; the second point has a height of 12 inches. what is the horizontal distance,x, in inches that is between these two markers?
x=12in
Slope of ramp= SecФ =5/3
Let the height of first point be H1
Let the height of second point be H2
Then, H1=27in (Provided in the question)
H2=12in (Provided in the question)
The base of the right angled triangle then = H1-H2
Let the perpendicular be denoted as p
Let the base be denoted as b
Let the hypotenuse be denoted as h
then, b=H1-H2
b=27-12
b=15
The Formula of SecФ=1/CosФ
Since, CosФ= Base/Hypotenuse
SecФ=/Hypotenuse/Base
SecФ= h/b
SecФ= 5/3 (Provided in the question)
then,
5/3=15/b
cross multiplying
5b=15x3
b=15x3/5
cancelling out 15 by 5
b=3x3
b=9
From Pythagoras theorem
[tex]h^{2}[/tex]=[tex]p^{2}[/tex]+ [tex]b^{2}[/tex]
putting values in the equation above:
[tex]15^{2}[/tex]=[tex]p^{2}[/tex] +[tex]9^{2}[/tex]
15x15=[tex]p^{2}[/tex]+81
225-81=[tex]p^{2}[/tex]
[tex]\sqrt{225-81}[/tex]=p
[tex]\sqrt{144}[/tex]=p
12=p
Since slope of ramp is equivalent to angle of depression
thus, p=x
x=12in
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A rectangle container with a base area of 200cm2 is filled with water to a height of 15cm. If the container has a height of 20cm, how much water ( in litres) should be added to it to fill it completely?
If the container's height is 20 cm , the amount of water that should be added to fill it completely is 1 liter .
In the question ,
it is given that
the base area of the rectangular container is = 200 cm²
the total height of the container = 20 cm
the height at which the water if filled = 15 cm
the height of water that is needed to be filled = 20 - 15 = 5cm
So , the volume of water to be added is = base area × height
= 200 × 5
= 1000 cm³
= 1 Liter .... because 1000cm³ = 1 Liter
Therefore , If the container's height is 20 cm , the amount of water that should be added to fill it completely is 1 liter .
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What is the image of (1, 0) after a counterclockwise rotation of 60°?
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There are some sweets in a jar
The sweets are red or orange or blue or yellow.
Hannah is going to take at random a counter from the bag.
The table shows cach of the probabilities that the counter will be blue or will be yellow.
Colour
Probability
red
orange
blue
0.5
yellow
0.2
There are 20 blue sweets in the jar.
The probability that the sweet Hannah takes will be red is twice the probability that the
sweet will be orange.
(a) Work out the number of red sweets in the jar.
the mom
the number of Red sweets=14
Let the probability of getting a red sweet be = P(R)
Let the probability of getting a Blue sweet be = P(B)
Let the probability of getting an orange sweet be = P(O)
Let the probability of getting a yellow sweet be = P(Y)
Let the number of Red sweets be represented as = n(R)
Let the number of Yellow sweets be represented as = n(Y)
Let the number of Orange sweets be represented as = n(O)
Let the number of Blue sweets be represented as = n(B)
Let the total number of sweets in the jar be represented as = n(T)
P(B) = 0.5
P(E) = 0.2
P(R) = 2 x P(O)
The formula of probability =
Number of the Sweets of a color/Total number of sweets in the jar
then,
P(B)=n(B)/ n(T)
P(B)=0.5 (Given in question)
n(B)=20 (Given in question)
So,
0.5 = 20/n(T)
5/10 = 20/n(T)
5/10 x 1/20 = 1/n(T)
cross multiplying
n(T)=10/5 x 20
dividing 10 by 5 =2
n(T) = 2 x 20
n(T) = 40
P(Y)=0.2 (Given in question)
Applying the formula of probability
P(Y) = n(Y)/n(T)
putting values
0.2=n(Y)/40
2/10=n(Y)/40
2/10 x 40 =n(Y)
Dividing 40 by 10 = 4
n(Y)= 2 x 4
n(Y)= 8
P(R)=2P(O)
Applying the formula of probability
n(R)/n(T)=2n(O)/n(T)
Cancelling out n(T) with n(T)
So,
n(R)=2 x n(O) -(i)
n(T) = n(O)+n(R)+n(B)+n(Y)
putting values
40=n(O)+n(R)+20+8
40=n(O)+n(R)+28
40-18=n(O)+n(R)
From -(i)
22=2n(O)+n(O)
22=3n(O)
n(O)=22/3
Since,
n(R)=2xn(O)
n(R)=2x22/3
n(R)=44/3
n(R)=14.6
the number of Red sweets=14.6
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You go to the store to buy supplies for class. You want to buy a new notebook for $3 and 5
folders. The most you can spend is $10. If you buy all the same type of folders, what are the
individual folder prices you can afford?
(Algebra)
If we buy all the same type of folders, the maximum amount we can afford for an individual folder is $ 3.3
To buy : A notebook for = $ 3
number of folders required = 5
The amount of money we can spend is $ 10
The above mentioned problem is a problem of algebra because we would have to use a variable to find out the unknown value.
The individual folders price can be calculated by the equation
3x = 10
divide both sides by 3 and we will get
x = 3.3
Thus the individual folder prices we can afford is $ 3.3
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3x - 2 when x=4
please be quickkkkkkkk
Answer:
10
Step-by-step explanation:
substitute x = 4 into the expression
3x - 2 = 3(4) - 2 = 12 - 2 = 10
Answer: 10
Step-by-step explanation:
4 × 3 = 12
12 - 2= 19
Hope it helps
in a region where we have had big earthquakes (magnitude 7 and above) roughly every 200 years, what is the probability that we will not have a big earthquake in this region in the next two years?
There is a 0.990025 probability that this area won't experience a major earthquake in the next two years.
Define probability.In the field of mathematics called probability theory, random occurrences are studied. The outcome of a random event can take any number of distinct shapes, but it cannot be anticipated before it occurs. The outcome is believed to have been decided by chance.
Given,
In a region where large earthquakes of magnitude 7 or higher have occurred about once every 200 years,
First, the likelihood of an earthquake with a magnitude of 7 or higher is 1/200 = 0.005.
The likelihood of there not being an earthquake is then requested, and it is 1-0.005 = 0.995.
The likelihood that there won't be an earthquake in two years is then
0.995 x 0.995, or.0990025.
The probability that we will not have a big earthquake in this region in the next two years is 0.990025.
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In the translation T of the graph below, use the figure to describe the following transformation.
The translation T due to the transformation is (5,3)
How to describe the transformation using the figure?Translation can be defined as movement in a straight line
Given the rule: (x,y) → (x + 3, y + 1) as seen in the image. That means (x,y) translated to (x + 3, y + 1). This is what we use to solve this problem.
From the figure, the value of (x, y) can be read i.e. (x, y) = (2,2)
Thus the translation will be:
(x,y) → (x + 3, y + 1)
(2,2) → (2 + 3, 2 + 1) = (5, 3)
Therefore, the translation T of the transformation shown in the graph is (5, 3)
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Consider the system of equations : 2a + 3b - 4c = 7,
a - b + 2c = 6
(a) Find an ordered tripe of numbers (a,b,c) that satisfies both equations.
(b) Can you find a second ordered triple that satisfies both equations.
(c) Solve for b in terms of a, and solve for c in terms of a. How many solutions does this system have?
Answer:
a. 87 b. 9 c. 4
Step-by-step explanation:
a veterinarian visits a cat shelter housing 432 cats. of 42 randomly selected cats that she studies, she finds that 14 cats suffer from separation anxiety. of those, 10 cats were orphaned as kittens. what proportion of cats in the sample suffer from separation anxiety? round your answer to the nearest percent. responses 3% 3% 24% 24% 33% 33% 71%
The proportion of cats in the sample suffers from separation anxiety is 33%
Given 432 cats, a sample of 42 cats is taken.
Out of these 42, cats 14 are suffering from separation anxiety.
The proportion of cats suffering from separation anxiety is: 14/42
The percentage of Cats suffering from separation anxiety is:[tex]\frac{14}{42}*100[/tex]%
This is equal to 33%, rounding off to the nearest percentage value.
Therefore, The proportion of cats in the sample who suffers from separation anxiety is 33%.
The sample proportion (p^hat) describes the proportion of people in a sample who have a particular attribute or trait. Divide the number of persons (or items) who have the characteristic of interest by the total number of people (or items) in the sample to get the sample proportion.
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The proportion of cats in the sample suffers from separation anxiety is 33%
Given 432 cats, a sample of 42 cats is taken.
Out of these 42, cats 14 are suffering from separation anxiety.
The proportion of cats suffering from separation anxiety is: 14/42
The percentage of Cats suffering from separation anxiety is:(14/42)*100%
This is equal to 33%, rounding off to the nearest percentage value.
Therefore, The proportion of cats in the sample who suffers from separation anxiety is 33%.
The sample proportion (p^hat) describes the proportion of people in a sample who have a particular attribute or trait. Divide the number of persons (or items) who have the characteristic of interest by the total number of people (or items) in the sample to get the sample proportion.
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A 7-pound box of strawberries costs $12.32. What is the price per ounce?
Step-by-step explanation:
Answer: 9.090909090909091
Step-by-step explanation: Knowing this we can solve. We have 7 pounds, and there are 16oz in 1 pound so we multiply the number of pounds by the number of ounces in 1 pound. 7 x 16 = 112 ounces. So there are 112oz total, which costs $12.32. Now we divide $12.32 by 112oz to find the price per ounce which would be roughly 9.09
Find where the line 2y - 3x - 7=0 intersects the:
i y-axis
ii x-axis
Answer:
i = 7/2
ii = -7/3
Step-by-step explanation:
The line intersects one of the two axis when the vale of the other axis is 0
When x=0:
2y - 7 = 0
2y = 7
y = 7/2
When y = 0
-3x - 7 = 0
-3x = 7
x= -7/3
The probability that a male’s foot is between 10 and 12. 5 inches is ___%
P(10
The probability of a foot of male being between 10 and 12. 5 inches is 59%.
Define the term normal distribution?The normal distribution approximates any real-valued random distribution which clusters around one single mean value. A cumulative frequency is a procedure that determines if the total amount of information in such a data set is less than and equal to a specific value.The z score of the distribution is found as-
z = (x - μ)/σ
In which,
μ = mean = (11)
σ = standard distribution (1.5)
The likelihood that a male's foot measures between 10 and 12. 5 inches.
P(10 < x < 12.5)
For x = 10
z = (10 - 11) / 1.5
z = -0.67
check the p-value fro z score table.
p (z = -0.67) = 0.2514
For x = 12.5
z = (1.5 - 11)/1.5
z = 1
p (z = 1) = 0.8413
P(10 < x < 12.5) = 0.8413 - 0.2514
P(10 < x < 12.5) = 0.5899
P(10 < x < 12.5) = 58.99%
P(10 < x < 12.5) = 59%.
Thus, the likelihood of a male's foot being between 10 and 12. 5 inches is 59%.
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The complete question is attached in figure.
Darius ran a total distance of 52 1/4 mile last month. Each day he went for * 1 pc
a run, he ran 2 3/4 miles. How many days did Darius run last
month?
Answer:
82 and 2/4 (if it was 30 days)
Step-by-step explanation:
you turn the fraction into a decimal and multiply it by the certain number of what you need to figure out.
n?
8) 2y = 6x²-x+3
2y=6x
8
sy=-15
linear or nonlinear
Answer: I would say non linear. I have done problems like these before and anytime there is an exponent in the equation it always ends up being non linear. Also remember for it to be linear it most form a straight line that passes through the origin.
Step-by-step explanation:
PLEASE ANSWER
there are no choises
The relation between angle 1 and angle 2 is they are equal and corresponding angle.
What are parallel lines?
Two lines are said to be parallel when they do not intersect each other. We can also say that two lines that run along and meet at infinity are called parallel lines.
What are corresponding angles?
Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines and the transversal.
Given, m and l are parallel line.
Hence, m and l satisfy the condition of parallel lines.
Therefore, the angle 1 and angle 3 are equal.
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how many license plate combinations are there with either three letters then three numbers or three numbers then three letters
The license plate combinations with either three letters then three numbers or three numbers then three letters are 35152000.
The license plate combinations to be made are either three number followed by three letter or three letter followed by three number. we are here assuming that the repetition of the number and letter are allowed.
The number can be any three from 0-9. So, the total choices of number are 10.
The letter can be from A-Z. So, the total choices for letter are 26.
The total choices of the numbers possible are,
ΟΟΟ ΟΟΟ
1 2 3 4 5 6
The first three are the choices of letter and the last three are the choice of number. Two combinations are also possible by interchanging the position of the set of numbers and letters.
So, the possible combinations are,
2 x [26x26x26x10x10x10]
Hence,
The possible combinations for the license plate number are 35152000.
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I need help I am very confused on this Thank you for your guys help!!
The measure of the side MK of the triangle is 109.6.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.
For the triangles, the scale factor will be calculated as,
Scale factor = 57 /13
The measure of the side MK will be calculated as,
57 / 13 = MK / 25
MK = ( 57 x 25 ) / 13
MK = 1425 / 13
MK = 109.61
Therefore, the measure of the side MK of the triangle is 109.6.
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in rocky mountain national park, many mature pine trees along highway 34 are dying due to infestation by pine beetles. scientists would like to use a sample of size 200 to estimate the proportion of the approximately 5000 pine trees along the highway that have been infested. describe how to select a systematic random sample of 200 pine trees along highway 34.
The given alternate possible way given in the question is not good as the sample does not follow the conditions of the definition of SRS in the study.
SRS is a group or sample size of "n" objects in a population of "n" objects in which all the possible samples would have equal chances to occur or happen.
In the alternate case, There 200 trees sample is taken from near the highway, that can have fewer chances to be infected or can have more infected.
The fact that the sample was not taken randomly and has not been selected in such a way that each tree has equal chances to happen.
The SRS is not possible to obtain as it does not follow the term and conditions of SRS.It creates a bias in the study.Hence we get the required answer.
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the graph shows the relationship between the amount of peaches in pounds xand the cost of peaches in dollars y
PLEASE HELP
The proportional relationship between the amount of peaches in pounds x and the cost of peaches in dollars y is given as follows:
y = 2.5x.
Direct proportional relationshipA direct proportional relationship is a special case of a linear function, with an intercept of zero, hence the output variable symbolized by y is given by the multiplication of the input variable symbolized by x and the constant of proportionality symbolized by k, as follows:
y = kx.
In this problem, we have to find the constant k taking a point of the graph.
The point taken is:
(2,5).
Meaning that when x = 2, y = 5.
Hence the constant is calculated as follows:
5 = 2k
k = 5/2
k = 2.5.
Then the equation is:
y = 2.5x.
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What is 36.9 rounded to the nearest percent
Answer: 37%
Step-by-step explanation:
36.9 rounds up into 37%
Greta sells advertising space for her school yearbook. Last year, a quarter-page ad cost $110.
This year, Greta's teacher asks her to mark down the price by 15% to attract more sponsors.
Greta wants to know the price after the markdown.
☐ Let q equal the price of a quarter-page ad after the markdown.
Which equation can you use to find q?
q=110-0.15(15)
q=110 +0.15(110)
q=110 - 0.15(110)
q=110 +0.15(15)
The equation that could be used to find q is q = 110-0.15(110) where q equal the price of a quarter-page ad after the markdown.
According to the question,
We have the following information:
Cost of a quarter-page ad cost = $110
Mark down in the price = 15%
Now, q represents the price of a quarter-page ad after the markdown.
(Note that when we remove the sign of % means that the number has to be divided by 100.)
So, the equation will be the difference of the markdown price from the original price:
q = 110-(15/100)110
q = 110-0.15*110
q = 110-0.15(110)
Hence, the correct option is the third one.
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CORE
SKILL
ADVANCED
If a is inversely related to the square of b, and a = 3 when bis
8, which of the following is another possible value for a and b?
(A) a = 4, b = 12
(B) a = 12, b = 4
(C) a = 8, b = 3
(D) a = 2, b = 4
(E) a = 6, b = 4
Another possible values for a and b are a = 12 and b = 4
How to find another possible value for a and b?
A variation is a relation between a set of values of one variable and a set of values of other variables
Given that: a is inversely related to the square of b, and a = 3 when bis
8.
This can be written as:
a α 1/b²
a = k/b² (where k is a constant)
k = ab²
since a = 3 and b = 8.
Thus, k = 3 × 8² = 3 × 64 = 192
For a value to be another possible value for a and b, they must give k = 192 when substituted into the equation k = ab²:
a = 4, b = 12: k = 4 × 12² = 576
a = 12, b = 4: k = 12 × 4² = 192
a = 8, b = 3: k = 8 × 3² = 72
a = 2, b = 4: k = 2 × 4² = 32
a = 6, b = 4: k = 6 × 4² = 96
The values that produce k = 192 are a = 12 and b = 4. Therefore, another possible value for a and b is a = 12 and b = 4. So option B is the answer
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola from the vertex is f(x) = 7(x - 3)² + 5
How to determine the equation of the parabola?The equation of the function is given as
f(x) = 7x²
Also, we have
Vertex = (3, 5)
The form of the equation is given as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
This means that
Vertex = (h, k) = (3, 5)
Substitute (h, k) = (3, 5) in the equation f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 3)² + 5
This also means that
f(x) = 7(x - 3)² + 5
The 7 is gotten from f(x) = 7x²
Hence, the equation of the parabola is f(x) = 7(x - 3)² + 5
Read more about parabola at
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Can write the equation of the graph?
