a = amount given to the 1st share, ratio of 5.
a + 122 = amount given to the 2nd share, ratio of 7.
T = total amount
so the total amount is really "T", and we'll be splitting that into a 7 : 5 ratio, that is, we'll be dividing "T" by (7 + 5) and distribute accordingly.
[tex]\stackrel{\textit{total split by 7 + 5}}{\cfrac{T}{7+5}\implies \cfrac{T}{12}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{we know the 1st share is}}{a= 5\cdot \cfrac{T}{12}}\implies a=\cfrac{5T}{12} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know the 2nd share is}}{a+122= 7\cdot \cfrac{T}{12}}\implies a+122=\cfrac{7T}{12}\implies \stackrel{\textit{substituting from above}}{\left( \cfrac{5T}{12} \right)+122=\cfrac{7T}{12}} \\\\\\ 122=\cfrac{7T}{12}-\cfrac{5T}{12}\implies 122=\cfrac{2T}{12}\implies 122=\cfrac{T}{6}\implies \boxed{732=T}[/tex]
two cards are selected from a standard deck of 52 playing cards. the first card is not replaced before the second card is selected. find the probability of selecting a black card and then selecting a red card.
The probability of selecting a black card first and a red card second from a standard deck of 52 playing cards without replacement is 13/51.
The probability of selecting a black card on the first draw is 26/52, or 1/2, since there are 26 black cards in a standard deck of 52 playing cards.
After the first card is drawn, there are 51 cards remaining, of which 26 are red. Therefore, the probability of selecting a red card on the second draw, given that a black card was selected on the first draw, is 26/51.
To find the probability of both events happening (selecting a black card followed by a red card), we multiply the probabilities of each event:
P(black card first, red card second) = P(black card first) × P(red card second | black card first)
P(black card first, red card second) = (1/2) × (26/51)
P(black card first, red card second) = 13/51
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What is 36 + 45 rewritten as the product of a whole number and the sum of two whole numbers with no common factor
By using the distributive property the sum "36 + 45" can be expressed as product and sum of 2 numbers as 9 × (4 + 5) .
The Distributive Property states that a × (b + c) = a×b + a×c, where a, b, and c are any real numbers.
Using this property, we can rewrite the sum 36 + 45 as:
⇒ 36 + 45 = 9 × 4 + 9 × 5
Factoring out the common factor of 9,
we get ;
⇒ 36 + 45 = 9 × (4 + 5) ;
Therefore, the sum 36 + 45 as the product of a whole number (9) and a sum of two whole numbers (4 and 5) is 9×(4 + 5) .
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The given question is incomplete , the complete question is
What is 36+45 by using the distributive property to rewrite the sum as the product of a whole number other than 1 and a sum of two whole numbers ?
Zainab runs her own business where she leads guided day-long tours for small groups of tourists
in her city. Each tour has a maximum of 3 guests. Let X represent the number of customers
Zainab gets on a randomly chosen day. Based on previous data, here is the probability
distribution of X along with summary statistics:
X = # of customers
P(X)
Hy =
What are the mean and standard deviation of Y?
σy ≈
1
0.20 0.10
It costs Zainab $5 each day to pay for her own transportation to her business, and then each
customer she gets pays her $60. Let Y represent Zainab's net gain on a randomly chosen day.
dollars
dollars
2
0.40
Mean:
Standard deviation:
3
0.30
4x = 1.8
x 1.08
The mean of Y is 103 dollars. The standard deviation of X is 64.8 dollars
How to solve for the mean and the standard deviationThe mathematical expression that we would have to use i the representation of Y is Y = 60X - 5.
How to solve for the mean of Y
Y = exp(Y)
= 60 * EXP(X) - 5
the expected value of x is 1.8
= 60 * 1.8 - 5
= 103 dollars
then we have to solve for the standard deviation of Y
standard deviation of x = 1.08
= 60 * 1.08
= 64.8 dollars
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three pieces of wood measuring 70m, 105m and 175m long have to be divided to planks of equal length what is the greatest possible length of each plank
Answer:
35 m
Step-by-step explanation:
I will assume the goal is not to waste any wood. We need to find a common length that will allow each piece of wood to be divided into whole pieces with nothing left over. The shortest plank is 70 m, but that length will cause a loss of 35 m on the 105m plank, and also 35m on the 175m plank after two 70m sections have been cut off (175 - 140 = 35).
Looking at the actual lengths, one might spot that they are all evenly divisible by 35. See the table below. The numbers under "35" are the result of the length divided by 35. They are all whole numbers. We can cut each plank into 35m sections and have none left over.
Length (m) 35 (factor)
70 2 planks
105 3 planks
175 5 planks
This will result in 10 35m planks.
No need to plank me.
Compare 3/10 and 25/100 which one is greater
Answer:
The answer to your question is 3/10
How do you compare fractions?
First lets find similar fractions
2.5/10 = 25/100 We know that.
Since 3/10 is bigger that 2.5/10 by .5 it would basically conclude that 3/10 is greater/bigger the the fraction 25/100.
A line is drawn tangent to a circle of radius 8 with the origin as its center, passing through the paint (12,0). Find the point where the line touches the circle. NOTE: the tangent line will be perpendicular to the radical line from the origin to the tangent point. Use the relation between the slopes to find the point
The radius line intersects the circle at (4, 8) because the tangent line's slope, which is -1/3, is perpendicular to the radius line's slope of (0, 8), which is 0.
1. Use m = 0 to calculate the slope of the line through point (12, 0).
2. Calculate the radical line's angle between the origin and the tangent point: m = ∞
3. To determine the location where the line touches the circle, use the relationship between the slopes: M2 = -1/M1 = -1/0 = - since M1 M2 = -1
4. To determine a point's coordinates, use the equation for a circle: (x - 8)2 + (y - 8)2 = 82, so (4, 8) (4, 8)
We can use the relationship between the slopes of the tangent line and the radical line from the origin to the tangent point to determine the location where the line contacts the circle. Since the tangent line crosses through point (12,0), its slope is equal to zero. Since the radical line slopes at m2 =, m1 m2 = -1. Accordingly, m2 = -1/m1 = -1/0 = -∞.The coordinates of the spot where the line touches the circle can then be determined using the equation for a circle. (x - 8)2 + (y - 8)2 = 82 is the equation for a circle having the origin as its center and a radius of 8. The coordinates of the place where the line intersects the circle are (4, 8), which can be obtained by substituting in the values for m1 and m2.
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What is the area of the compound figure?
Answer:
42 mi²
Step-by-step explanation:
Break it up into 2 shapes, top and bottom, then add the areas together.
Area 1 (top rectangle) = 12 x 3 = 36
Area 2 (bottom rectangle) = 2 x 3 = 6
Total area = 36 + 6 = 42 mi²
Using the omission strategy, what value would be placed in the missing observation in x1?
x1x2
76
22
82
91
32
41
88
Options:
84
No value because excluded
83
90
The values in the missing observation are:
X1 X2
76 22
82 25
91 32
101 41
88 28
What is an expression?An expression contains terms with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
x1 x2
76 22
82 __
91 32
__ 41
88 28
The difference between each row are:
76 - 22 = 54
82 - 25 = 57
91 - 32 = 59
101 - 41 = 60
88 - 28 = 60
We see that,
57 - 54 = 3
59 - 57 = 2
60 - 59 = 1
60 - 60 = 0
So,
The difference between the numbers is consecutive as 3, 2, 1, 0.
Thus,
The missing values of X1 and X2 are 101 and 25.
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whats the middle product of (-2x+1)(-3x-5)
Answer:
7x
Step-by-step explanation:
That would be ( -2x )(-5) + -3x(1) = 10x - 3x = 7x
Sara can read 19 pages an hour. How many pages can Sara read in 95 min? Round to the nearest whole number.
Answer:
Step-by-step explanation:
Convers 95 min into hours
95/60 = 1.58 Hours
Sara can read 19 pages per hour
Total pages in 95 min or 1.58 hours =
19 * 1.58 = 30.02
Rounding off to nearest whole number- 30
Hope it helps
Which of the following is NOT a characteristic of a plane?
The answer option which is not a characteristic of a plane include the following: C. thickness.
What is a plane?In Mathematics, a plane is sometimes referred to as a two-dimensional surface and it can be defined as a flat, two-dimensional surface with zero curvature and zero thickness, that extends indefinitely (infinitely). Additionally, two (2) planes intersect at a line.
What are the characteristics of a plane?Generally speaking, there are different characteristics of a plane and these include the following:
LengthFlat surface.Width.In this context, we can reasonably infer and logically deduce that thickness is not a characteristic of a plane.
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Complete Question:
Which of the following is NOT a characteristic of a plane?
A. length
B. flat surface
C. thickness
D. width
The stemplot shows the years of experience for several teachers at Sycamore High School.
A stemplot titled Teaching Experience. The values are 2, 4, 5, 5, 5, 7, 9, 10, 12, 14, 15, 15, 18, 20, 24.
What is the IQR of the data?
6 years
10 years
12 years
22 years
The IQR of the data is 10 years and option B is the correct answer.
What is IQR?The dispersion of the middle 50% of the sample is measured by the interquartile range, or IQR, which is the difference between the top and lower quartiles.
The given data is: 2, 4, 5, 5, 5, 7, 9, 10, 12, 14, 15, 15, 18, 20, 24.
The median of the data is:
M = 15 + 1 /2 = 16/2 = 8th value.
M = 10
Ignoring the median divide the data into two parts.
The lower quartile median is 4th term:
Q1 = 5
The upper quartile median is 12th term:
Q2 = 15
IQR = Q2 - Q1
IQR = 15 - 5 = 10 years.
Hence, the IQR of the data is 10 years and option B is the correct answer.
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Find the area of an isosceles triangle whose one side is 10 cm greater than each of its equal sides and perimeter is 100 cm.
Answer:
the area of the isosceles triangle is approximately 104.49 cm^2.
Step-by-step explanation:
The perimeter of the triangle is 100 cm, so we can write an equation using the lengths of the sides:
x + x + (x + 10) = 100
3x + 10 = 100
3x = 90
x = 30
So the equal sides of the triangle have length 30 cm and the side that is 10 cm greater has length 40 cm.
To find the area of the triangle, we can use the formula for the area of an equilateral triangle:
Area = (sqrt(3) / 4) * (side length)^2
Area = (sqrt(3) / 4) * 30^2
Area = (sqrt(3) / 4) * 900
Area = (sqrt(3) / 4) * 30 * 30
Area = (sqrt(3) / 4) * 900
Area = (30 * sqrt(3)) / 2
Area = 45 sqrt(3)
Find an Angle Measure T ✓ The optimal tilt for Keenan's solar panelis between 58° and 60° to the horizontal. Has Keenan placed his solar panel at an optimal angle? SOLUTION COMMON ERROR 18 ft
Keenan has placed his solar panel at an optimal angle.
How determine if Keenan has placed his solar panel at an optimal angle?The cosine law is a mathematical relationship between the sides and angles of a triangle. The cosine law states that:
cos(C) = (a² + b² - c²) / 2ab
where a, b, and c are the lengths of the sides of the triangle and C is the measure of one of the angles. This law can be used to find unknown side lengths or angle measures in a triangle when given the other values.
Check the attached image for labelling.
The angle we are trying to calculate is labelled C.
cos (C) = (20² + 18² - 19²) / (2*20*18)
cos (C) = 363/720
C = cos⁻¹(363/720)
C = 59.72°
Since the angle obtained is between 58° and 60°. Thus, Keenan has placed his solar panel at an optimal angle.
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Every week at the Cougar Scouts meeting, Jamal is in charge of the craft activity. This week, he decides to make pinecone bird feeders. At the meeting, Jamal divides a bag of birdseed evenly among 12 Cougar Scouts, and each scout gets 1/2 of a cup of birdseed. Use an equation to find the amount of birdseed in the bag.
To write a fraction, use a slash (/) to separate the numerator and denominator.
Use the following expression to answer the following questions.
I
t+0.24t
The decimal in the expression represents what value as a percent? (No % sign.)
Is the expression representing an increase or a decrease? Percent Increa: V
Create the simplified version of the expression.
The percentage increase is given by the equation A = t + 0.24t = 1.24t
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the percentage increase be represented as A
Now , the equation will be
The initial quantity be represented as t
Now , the increased quantity be represented as p = 24 %
So , the increased quantity = 24 % x initial quantity
Substituting the values in the equation , we get
The increased quantity = ( 24/100)t
The increased quantity = 0.24t
So , the final quantity = initial quantity + increased quantity
On simplifying the equation , we get
The final quantity = t + 0.24t
The final quantity = 1.24t
Hence , the equation is A = 1.24t
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A quadrilateral has two angles that measure 100° and 90°. The other two angles are in a ratio of 7:10. What are the measures of those two angles?
The measures of angles C and D are 70° and 100°, respectively.
Understanding angles is a fundamental concept in geometry. A quadrilateral is a polygon with four sides, and its angles are essential to determining its properties.
Let's start by labeling the angles in the quadrilateral. We know that two angles measure 100° and 90°, so let's label them as A and B, respectively. The other two angles, which we are trying to find, can be labeled as C and D.
Now, we are given that the ratio of angles C and D is 7:10. This means that we can write the following equation:
C/D = 7/10
We can use this equation to solve for one of the angles. Let's choose angle C. We can rewrite the equation as:
C = (7/10)D
We also know that the sum of the angles in a quadrilateral is 360°. Therefore, we can write another equation:
A + B + C + D = 360°
We can substitute the values we know into this equation and solve for angle D:
100° + 90° + (7/10)D + D = 360°
Simplifying the equation:
(17/10)D = 170°
D = 100°
Now that we know the value of angle D, we can use the equation we derived earlier to find the value of angle C:
C = (7/10)D = (7/10) x 100° = 70°
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superior segway tours gives sightseeing tours around chicago, illinois. it charges a one-time fee of $45, plus $25 per hour. what is the slope of this situation?
If they charges a one-time fee of $45, plus $25 per hour, then the the slope of this situation is $25 per hour.
The situation described can be represented by the linear equation
Cost = $45 + $25 × hours
where "Cost" is the total cost of the tour and "hours" is the number of hours for which the tour is taken.
The slope of this equation represents the rate of change in the cost of the tour with respect to the number of hours.
In other words, it tells us how much the cost increases for each additional hour of the tour.
The slope of this equation is simply the coefficient of the "hours" variable, which is $25.
Therefore, the slope of this situation is $25 per hour.
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Answer:
$25 per hour.
Step-by-step explanation:
The height of a cone is 10 centimeters. The radius is 4 centimeters. What is the volume of this cone? Around your answer to the nearest hundredth. Do not include units in your answer
Answer: 167.55 cm.
Step-by-step explanation:
Cone volume formula is V=1/3hπr².
Substitute...
V= 1/3 (10) (π) (4)^2
V= 53 1/3 π
V= 167.55 cm
Hope this helps!
MM
Mario has a box. He wants to determine how much the box can hold. Which measurement should he calculate?
O area
O length
O perimeter
O volume
which of the following approaches to building a multiple linear regression model involves taking all of the possible independent variables, and then systematically eliminating insignificant ones until only significant ones remain? forward selection. stepwise regression. backward elimination. back-checking for aic
The approaches to building a multiple linear regression model is option (C) Backward elimination
Here the multiple linear regression model involves taking all of the possible independent variables, and then systematically eliminating insignificant ones until only significant ones remain
We know the independent variable is the variable that does not depends on any other variables
Here the given elimination methods is eliminating insignificant ones until only significant ones remain
In the backward elimination method starts with explanatory variables in the regression model then starts to eliminates the least significant ones will eliminates one by one
Therefore, the suitable approach is backward elimination method
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.
What is the coefficient in this expression?
-17+(-b)+(-25)
Answer:
In the expression -17 + (-b) + (-25), the coefficient is a number that multiplies a variable. In this case, the coefficients are -17, -1 (which multiplies the variable "b"), and -25.
Step-by-step explanation:
3=2x+y
4x+6=10y
Find what is x and what is y
Answer:
x=1 , y=1
Step-by-step explanation:
2x+y=3 - - (1)
4x+6=10y
=> 4x-10y=-6 - - (2)
Multiply eq (1) by 2, and we get ;
4x+2y=6 - -(3)
Now subtract eq (3) by eg (2)
4x+2y=6
-4x+10y=+6
12y=12
y=1
Sub value of y in eq (1)
2x+1=3
2x=2
x=1
double d, then subtract 6 from the result
Do not simplify any part of the expression.
Answer:
2d-6
Step-by-step explanation:
Since the d is doubled you are multipling then subtracting 6 from the result
Is y=5 and x=-1 parallel
Answer:
y=5 and x=-1 are parallel
Step-by-step explanation:
Let's do a quick review on some things:
Parallel lines are the lines that never intersect and perpendicular lines are the lines that intersect at 90°.
Lines with the same slope are parallel and if the slope of one line is the negative reciprocal of the second line, then they are perpendicular.
So, this answers to your question that it's parallel!
Hopefully this helps :)
Look at the table of values. What is the vertex of the graph? How do you know?
The vertex of the given graph is (5, 0)
What is vertex:A vertex is a point on a polygon where two rays or line segments meet, and the sides or edges of the object come together. Vertex is the plural form of vertices.
A straight line that can be extended endlessly is known as a ray. An angle is created when two line segments or rays cross one another. A vertex is created by definition whenever two lines come together to produce an angle.
Thus, we can state that a vertex is formed when two line segments or rays intersect.
Here we have a graph
The equation of the graph is y = |x - 5| + 1
As we can see that two lines are intersected at a point (5, 0)
Therefore,
The vertex of the given graph is (5, 0)
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question which of the following must be true for an estimator of a population parameter to be unbiased? responses the sampling distribution of the estimator is normal. the sampling distribution of the estimator is normal. the expected value of the estimator is equal to the population parameter. the expected value of the estimator is equal to the population parameter. the sampling distribution of the estimator is the same shape as the distribution of the population parameter. the sampling distribution of the estimator is the same shape as the distribution of the population parameter. the variability of the sampling distribution of the estimator is equal to the variability of the population parameter. the variability of the sampling distribution of the estimator is equal to the variability of the population parameter. the variability of the sampling distribution of the estimator is less than the variability of the population parameter.
The second statement in your question is the correct response.
What is the sampling distribution?
A sampling distribution is the probability distribution of a statistic (such as the sample mean or sample proportion) based on all possible random samples of a fixed size from a population.
The following statement must be true for an estimator of a population parameter to be unbiased:
The expected value of the estimator is equal to the population parameter.
Hence, the second statement in your question is the correct response.
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a card is drawn from a standard deck of 52 playing cards. what is the probability that the card will be a diamond or a seven? express your answer as a fraction or a decimal number rounded to four decimal places.
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
Total cards = 52
Total diamond cards = 13
So, probability of getting a card of diamond,
P(diamond) = 13/52 = 1/4
Now,
Total cards with number seven = 4
So, probability of getting a seven,
P(seven) = 4/52 = 1/13
Hope it helps~
Joseph runs 212 miles on Monday. Each day after that, he runs the same 113 mile route every morning. His goal is to run at least 6 miles by the end of the week. Which inequality represents the least number of days after Monday that Joseph needs to run to reach his goal?
The inequality that represents the least number of days after Monday that Joseph needs to run to reach his goal is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
Number of miles that Joseph run on Monday = [tex]2\frac{1}{2}[/tex] miles
Number of miles that Joseph run each day after that = [tex]1\frac{1}{3}[/tex] miles
The inequality is the mathematical statement that shows the relationship between two expression using an inequality symbol. The inequality symbols are less than, greater than, less than or equal and greater than or equal.
Then the inequality will be
[tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
Where x is the number of days after Monday that Joseph needs to run to reach his goal
Therefore, the inequality is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
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Rhetta started a typing program in hopes to speed up her typing skills. She started the program typing 40 words per minute. After two weeks, she can now type 56 words per minute. What was her percent of increase for typing?
Her percentage difference in programming in accordance with the statement is 40%.
What is the straightforward meaning of speed?It is discussing speed. the velocity at which the position of an object shifts in any direction. Speed is defined as the ratio of the distance traveled to the time required to cover that distance. Speed can be stated as a number since it just has to have 1 element and no magnitude.
You may use the following format to get Rhetta's increased typing speed in percentages:
(New Values - Originally Value) / (Original Value x 100) = Percent Increase
Calculating the percentage increase is as follows: Percentage Point Equals (56 - 40) / 40 x 100 Equals 40% in this instance, where the previous value was 40 words every minute and the new number was 56.
Rhetta was now 40% faster at typing.
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