Angle BAC is equal to 72 degrees, which is calculated by subtracting 2 times the angle of intersection between lines p and q (34 degrees) from 180 degrees.
Given that two lines p and q intersect at X at an angle of 34 degrees
Let A be a point inside the 34 degree angle formed by p and q
Then, let B be the reflection of A through line p, and let C be the reflection of A through line q
To find angle BAC,
we must first understand that a reflection of a point across a line results in an angle equal in measure to its original angle, but on opposite sides of the line of reflection.
In this case, because A is inside the 34 degree angle formed by lines p and q,
angle AXB must be equal to 34 degrees
angle AXC must also be equal to 34 degrees
Therefore, angle BAC must be equal to 180 degrees minus 2 times 34 degrees, or 72 degrees.
In conclusion, the angle BAC is equal to 72 degrees.
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guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).
The value of the limit that exists at the given numbers is approximately 0.5.
First of all at x = 3.1, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 3.1} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]\frac{(3.1)^2-3(3.1)}{(3.1)^2-9}[/tex] = [tex]\frac{0.31}{0.61}[/tex] ≅ 0.508197
At x = 3.05, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 3.05} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(3.05)^2-3(3.05)}{(3.05)^2-9}=\frac{0.1525}{0.3025}$[/tex] ≅ 0.504132
At x = 3.01, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 3.01} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(3.01)^2-3(3.01)}{(3.01)^2-9}=\frac{0.0301}{0.0601}$[/tex] ≅ 0.500832
At x = 3.001, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 3.001} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(3.001)^2-3(3.001)}{(3.001)^2-9} $[/tex]= [tex]$\frac{3.001 \times 10^{-3}}{6.001 \times 10^{-3}}$[/tex] ≅0.500083
At x = 3.0001, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 3.0001} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(3.0001)^2-3(3.0001)}{(3.0001)^2-9} $[/tex]= [tex]$\frac{3.001 \times 10^{-4}}{6.001 \times 10^{-4}}$[/tex] ≅ 0.500008
At x = 2.9, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 2.9} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(2.9)^2-3(2.9)}{(2.9)^2-9} $[/tex]= [tex]$\frac{-0.29}{-0.59}$[/tex] = 0.491525
At x = 2.95, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 2.95} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(2.95)^2-3(2.95)}{(2.95)^2-9} $[/tex]= [tex]$\frac{-0.1475}{-0.2975}$[/tex] = 0.495798
At x = 2.99, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 2.99} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(2.99)^2-3(2.99)}{(2.99)^2-9} $[/tex]= [tex]$\frac{-0.0299}{-0.0599}$[/tex] = 0.499165
At x = 2.999, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 2.999} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(2.999)^2-3(2.999)}{(2.999)^2-9} $[/tex]= [tex]$\frac{-2.999 \times 10^{-3}}{-5.999 \times 10^{-3}}$[/tex] = 0.499917
At x = 2.9999, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 2.9999} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(2.9999)^2-3(2.9999)}{(2.9999)^2-9} $[/tex]= [tex]$\frac{-2.999 \times 10^{-4}}{-5.999 \times 10^{-4}}$[/tex] = 0.499992
From above all, we can see that the limit is approximately equal to and tends towards 0.5. So 0.5 will be our answer.
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Your question was incomplete, your most probable question was:
Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).
[tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9}[/tex], x = 3.1, 3.05, 3.01, 3.001, 3.0001, 2.9, 2.95, 2.99, 2.999, 2.9999
A cart wheel is to be made out of a circular disk of wood surrounded by a strip of rubber. The wood costs $2.50 per square foot and the rubber costs $3.60 per foot. If the wheel has a 1.5-foot radius, what is the total cost of the materials needed to construct the wheel? Show or explain how you got your answer.
The total cost of the materials used to construct the wheel is $51.57
What is the total cost?The total cost of the materials used to construct the wheel is the sum of the total cost of the wood and the rubber.
Total cost = total cost of the wood + total cost of the rubber
Total cost of the wood = (area of the wood used x cost per square foot) + (circumference of the wheel x cost of the rubber)
Area of the wood = πr²
Where :
π = pi = 3.14
R = radius
3.14 x 1.5² = 7.065 ft²
Total cost of the wood = $17.66
Circumference of the wood = 2πr
2 x 3.14 x 1.5 = 9.42 feet
Total cost of the rubber = 9.42 x 3.60 = $33.91
Total cost of the materials = $33.91 + $17.66 = $51.57
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Round to 2 decimal places. 8 of the company’s trucks from their pool of 37 trucks needed brake maintenance. What percent of the truck pool needed brake maintenance?
The percent of the truck pool that needed brake maintenance is 21.62%.
What percent of the truck pool needed brake maintenance?Percentage can be described as a fraction of an amount that is expressed as a number out of hundred. The sign that represents percentage is %. In order to convert a number to percentage, multiply the number by 100.
Percent of trucks that need maintenance = (number of trucks that need maintenance / total number of trucks) x 100
= (8/37) x 100 = 21.62%
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Consider the following table.
Defects in batchProbability
2. 0.35
3. 0.23
4. 0.20
5. 0.09
6. 0.07
7. 0.06
Find the standard deviation of this variable.
2.27
3.48
1.51
4.50
The standard deviation of the variable "Defects in batch" is approximately 0.47.
The closest answer in the options is (C) 1.51.
What is standard deviation?The standard deviation is described as a measure of the amount of variation or dispersion of a set of values.
Standard Deviation is given as = √(sum(p(x - μ)^2) / n)
Where μ = sum(xp)
= 2 * 0.35 + 3 * 0.23 + 4 * 0.20 + 5 * 0.09 + 6 * 0.07 + 7 * 0.06
= 2.49
substituting the values into the standard deviation formula, we have :
SD = √(sum(p(x - μ)^2) / n)
= √((0.35 * (2 - 2.49)^2 + 0.23 * (3 - 2.49)^2 + 0.20 * (4 - 2.49)^2 + 0.09 * (5 - 2.49)^2 + 0.07 * (6 - 2.49)^2 + 0.06 * (7 - 2.49)^2) / 6)
= √(1.32 / 6)
= √(0.22)
= 0.47
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The standard deviation of this variable is given as follows:
1.51.
How to obtain the standard deviation?Before obtaining the standard deviation, we must obtain the expected value, which is given by the sum of each value multiplied by it's respective probability, hence:
E(X) = 2 x 0.35 + 3 x 0.23 + 4 x 0.20 + 5 x 0.09 + 6 x 0.07 + 7 x 0.06
E(X) = 3.48.
Then we obtain the sum of the differences squared between each observation and the mean, multiplied by it's respective probabilities, hence:
(2-3.48)² x 0.35 + (3-3.48)² x 0.23 + (4-3.48)² x 0.20 + (5-3.48)² x 0.09 + (6-3.48)² x 0.07 + (7-3.48)² x 0.06 = 2.2696.
The standard deviation is the square root of this sum, hence:
S(X) = sqrt(2.2696)
S(X) = 1.51.
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3(2x+11) and (3c+15)(2) equivalent
Step-by-step explanation:
3(2x+11)=(3c+15)(2)
6x+33=6c+30
6c-6x=30-33
6c-6x=3
6c=3-6x
3(3-6x)+33=6(3-6x)+30
9-18x+33=18-36x+30
24-18x=12-36x
-18x=-12
x=4/6
6(4/6)+33=(3c+15)(2)
4+33=6c+30
37-30=6c
7/6=c
The expressions 3(2x + 11) and (3c + 15)(2) are not equivalent, as they are different when they are simplified the most.
What are equivalent expressions?Equivalent expressions are expressions that are simplified to the same expression.
The first expression is simplified applying the distributive property as follows:
3(2x + 11) = 6x + 33.
The second expression is also simplified applying the distributive property as follows:
(3c + 15) x 2 = 2(3c + 15) = 6c + 30.
Different expressions, due to different variables (x and c) and constants (33 and 30), hence they are not equivalent.
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What will be congruence criterion
Yes, By SAS congruency criteria both ΔDEF and ΔHIG are congruent.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
In the given figure,
⇒ DE = IH
⇒ EG = FI
⇒ ∠E = ∠I
Now, In ΔDEF and ΔHIG;
⇒ DE = IH (Given)
⇒ ∠E = ∠I (Given)
Since, EG = FI
Hence, We get;
⇒ GF + FI = FG + EG
⇒ GI = FE
So, In ΔDEF and ΔHIG;
⇒ EF = GI (Common side)
Thus, By SAS congruency criteria both ΔDEF and ΔHIG are congruent.
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6) Jack jogged 2- 5/10 miles on a path in the park. What is this distance written as a decimal?
The distance covered by the jack is 1.5 miles.
What are arithmetic operations?The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.
Given Jack jogged 2 - 5/10 miles on a path in the park.
2 - 5/10 miles
convert 5/10 in decimal form,
5/10 = 0.5
subtract 0.5 from the equation,
so 2 - 5/10 miles = 2 - 0.5 = 1.5 miles
2 - 5/10 miles = 1.5 miles
Hence distance in decimal is 1.5 miles.
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A movie rental company charges a monthly fixed membership fee of $12 plus $6 per movie that the user rents in that month. If M represents the number of movies that the user rents, and C represents the user's total charge for the month, find the relationship between M and C.
The relationship between M and C can be given by the equation C= 6M + 12
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: A movie rental company charges a monthly fixed membership fee of $12 plus $6 per movie that the user rents in that month.
Now M represents the number of movies and C represents the user's total charge for the month
Thus C= 6M + 12
where 6M is the total cost due to renting some number of movies M
Hence, The relationship between M and C can be given by the equation C= 6M + 12
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At a berry farm, Clayton picks 1
1/4cups of blackberries and twice as many raspberries. He takes the berries home and uses them to make mixed-berry muffins. If Clayton needs
3/4of a cup of mixed berries for each batch of muffins, how many batches can he make?
The number of batches of muffins she can make will be 5.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other features.
Clayton picks two times as many raspberries and 11/4 cups of blackberries at a berry farm. He brings the berries home and makes mixed-berry muffins with them.
The number of the batches of muffins can be calculated as:-
Number = ( 1¹/₄ + 2 x 1 ¹/₄ ) / ( 3 / 4 )
Number = [ ( 5 / 4 ) + ( 5 / 2 ) ] / ( 3 / 4 )
Number = [ ( 15 / 4 ) / ( 3 / 4 ) ]
Number = 5
Therefore, the number of batches of muffins will be 5.
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Let f(x)=−|x−2|+2 and g(x)=1/2x−2. Graph the functions in the same coordinate plane. What are the solutions to f(x)=g(x)? Enter your answers in the boxes from smallest to largest. x = and x =
The solutions to the equation are x = -4 and x = 4
How to determine the solutions to the equationFrom the question, we have the following parameters that can be used in our computation:
f(x)=−|x−2|+2 and g(x)=1/2x−2.
next, we graph the functions in the same coordinate plane
See attachment for the graph
The point of intersections represent the solutions
These points are x = -4 and x = 4
Hence, the solutions are x = -4 and x = 4
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juanita is evaluating four television brands using four criteria: price, quality, screen size, and features. Juanita assigns 20% importance to price, 30% importance to quality, 30% importance to screen size, and 20% importance to features. She rates the TV brands as follows:Samsung:Price (20%): 5Quality (30%): 8Screen Size (30%): 8Features (20%):9Sony: Price (20%): 4Quality (30%): 8Screen Size (30%): 8Features (20%): 9LG:Price (20%): 8Quality (30%): 6Screen Size (30%): 6Features (20%): 5Vizio:Price (20%): 9Quality (30%): 5Screen Size (30%): 4Features (20%): 4Based on the multi-attribute model, which television brand does Juanita prefer?
Junita prefers Samsung Television brand with score of 7.6. A multi-attribute model is a way of evaluating products or services based on multiple attributes or characteristics.
In this scenario, Juanita is evaluating four television brands based on four criteria: price, quality, screen size, and features. She assigns a weight to each criteria, indicating its importance to her, with price having 20% importance, quality having 30% importance, screen size having 30% importance, and features having 20% importance. She then rates each brand on each criteria and calculates an overall score for each brand using the weights and ratings. Based on her evaluations, Juanita prefers the Samsung brand as it has the highest overall score.
Based on the multi-attribute model, Juanita prefers the Samsung television brand. Here's the calculation:
Samsung: [tex]5 *0.20 + 8 * 0.30 + 8 *0.30 + 9 * 0.20 = 1 + 2.4 + 2.4 + 1.8 = 7.6[/tex]
Sony: [tex]4 * 0.20 + 8 * 0.30 + 8 * 0.30 + 9 * 0.20 = 0.8 + 2.4 + 2.4 + 1.8 = 7.4[/tex]
LG: [tex]8 *0.20 + 6 *0.30 + 6 * 0.30 + 5 * 0.20 = 1.6 + 1.8 + 1.8 + 1 = 6.2[/tex]
Vizio: [tex]9 * 0.20 + 5 * 0.30 + 4 * 0.30 + 4 * 0.20 = 1.8 + 1.5 + 1.2 + 0.8 = 5.3[/tex]
Juanita prefers the Samsung television brand with a score of 7.6 compared to the other brands.
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F(–5, 5) and G(–7, –7) are the endpoints of a line segment. What is the midpoint M of that line segment?
Answer:
-6, -1
Step-by-step explanation:
midpoint M of the line segment
M = (x1 + x2) / 2 , (y1 + y2) / 2
= (-5-7) / 2, (5-7) / 2
= -12 / 2, -2 / 2
= -6 , -1
One popular model had a front wheel with a 52 in. diameter and one spoke on the back wheel measuring 9 in
Determine the diameter of the back wheel.
The diameter of the back wheel is 18 in.
What is a diameter?A diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle.
Given that, a model had a front wheel with a 52 in. diameter and one spoke on the back wheel measuring 9 in, we need to find the diameter of the back wheel.
Since, the spoke in a wheel will act as a radius of the wheel,
Radius = diameter / 2
Also, it is given that, the one spoke on the back wheel measuring 9 in,
Therefore, the diameter of the back wheel = 9 × 2
= 18 in
Hence, the diameter of the back wheel is 18 in.
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1) The original price of a radio is $78.50 and was discounted 12% off. What is the sale price? not in college don't know why it says I am lol
Answer:$69.08
Step-by-step explanation:
You will work with the passenger Titanic data found on this [link](
The nature of the disaster and the factors that contributed to the survival of the passengers.
The formula used to calculate the survival rate of the passengers on the Titanic is as follows:
Number of Surviving Passengers/Total Number of Passengers * 100
For example, if there were 500 passengers on the Titanic and 100 of them survived, then the survival rate would be calculated as follows:
100/500 * 100 = 20%
This formula is useful for determining the survival rate of passengers on the Titanic, as well as any other disaster. By understanding the survival rate of the Titanic, we can better understand the nature of the disaster and the factors that contributed to the survival of the passengers.
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Complete question: What was the survival rate of passengers on the Titanic?
Idil invested $150 in an account paying an interest rate of 5.785% compounded annually. Sophie invested $150 in an account paying an interest rate of 5.625% compounded continuously. To the nearest hundredth of a year, how much longer would it take for Sophie's money to triple than for Idil's money to triple?
there is no difference in the values of Time for Idil or Sophie in that their amount will be tripled.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
Given, Idil invested $150 in an account paying an interest rate of 5.785% compounded annually. Sophie invested $150 in an account paying an interest rate of 5.625% compounded continuously.
From the general formula of compound interest:
Final value A = (1 + r/n)^nt,
where P is the principal balance
r is the interest rate
n is the number of times interest is compounded annually
t is the number of years,
For Idil,
P = 150, r = 5.782, A = 3*p = 450, and n = 1
Thus,
450 = 150 (1 + 5.785%)^t
3 = (1.05785)^t
t = 19.535 years
The time required to get a total amount of $450.00 with compounded interest on a principal of $150.00 at an interest rate of 5.785% per year and compounded 1 time per year is 19.535 years.
(about 19 years 6 months)
For Sophie,
P = 150, r = 5.625, A = 3*p = 450
First, convert R as a percent to r as a decimal
r = R/100
r = 5.625/100
r = 0.05625 per year,
Then, solve the equation for t
t = ln(A/P) / r
t = ln(450.00/150.00) / 0.05625
t = 19.531 years
The time required to get a total amount of $450.00 with compounded interest on a principal of $150.00 at an interest rate of 5.625% per year and compounded continuously is 19.531 years.
(about 19 years 6 months)
therefore, there is no difference in the values of Time for Idil or Sophie.
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7/22 as a decimal rounded to the nearest tenth
Answer:0.3
Step-by-step explanation:
9. If the arc measure of MN = 87°, what is the measure of
The complete question:
If the arc measure of MN = 87°, what is the measure of angle ∠MON ?
Solution:
In the given circle, the required measure of the angle ∠MON is given as 87°.
What is an angle ?
An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
Here,
For the given circle, the measure of arc MN is given in the form of an angle of 87° which consists of an angle MNO,
So the measure of the section is equal to MON i.e. ∠MON = 87°
Thus, the required measure of the angle ∠MON is given as 87°.
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There are 6 onion bagels and 18 plain bagels in a box of 24 bagels. What is the ratio of the number of onion bagels to the number of plain bagels in the box?
Un rectángulo está inscrito en un círculo de radio igual a 3 centímetros. Exprese el área A del rectángu- lo como una función de la longitud de uno de sus lados.
Therefore , the solution of the given problem of rectangle comes out to be A= b* √6²-b².
Describe the rectangle.In the Euclidean plane, a rectangle is merely a cube with four right angles. It is sometimes referred to as an equiangular quadrilateral or a quadrant that seems to have equal angles. The parallelogram also has the option of a straight angle. Four of a square's sides are all the same length. Rectangular quadrilaterals have four equal sides and four 90° vertices. It is sometimes referred as an "equirectangular square" as a result. A rectangle is also referred to as a parallelogram due to the identical and parallel lengths of its opposite sides.
Here,
radio= 3 cm
Al estar un rectángulo inscrito en un círculo, el diámetro del círculo corresponderá a la diagonal del rectángulo
Siendo b la base del rectángulo y a la altura, se tiene que:
6²= a²+b²
a²= √6²-b²
Nota: Se empleó el teorema de Pitágoras
El área del rectángulo está dado por:
A= base* altura
A= b*a
Reemplazando a:
A= b* √6²-b²
Therefore , the solution of the given problem of rectangle comes out to be A= b* √6²-b².
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Please HELP ASAP
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 20 N acts on a certain object, the acceleration of the object is 5 /ms2. If the force is changed to 16 N, what will be the acceleration of the object? /ms2
Step-by-step explanation:
Since force doesn't depend on mass and varies directly, you can set up a proportion. group the F's together and the acceleration together, as so
[tex] \frac{20}{16} = \frac{5}{x} [/tex]
Next, cross m multiply
[tex]20x = (16)(5)[/tex]
[tex]20x = 80[/tex]
Lastly, divide by 20
[tex]x = 4m {s}^{2} [/tex]
The acceleration of the object when force is 16N is 4m/s².
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, The force acting on the object varies directly with the object's acceleration.
Therefore, F ∝ a.
F = ka.
20 = 5k.
k = 4.
Now,
16 = 4a.
a = 4.
So, The acceleration is 4m/s²
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How much money should be invested at 8% compounded quarterly so that it will be worth $5000 in 5 years?
Answer: $25,000
Step-by-step explanation:
You invest $10,000 annually. If you divide 10,000 by 4, you get 25,000. It's $25,000 quarterly.
пер 15. If it took Lex from 10:00 a.m. to 11:45 a.m. to walk 14 blocks, what was his average speed in blocks per hour? Enter your answer with numbers and decimals only
His average speed in blocks per hour is 18.66 blocks per hour
What was his average speed in blocks per hour?From the question, we have the following parameters that can be used in our computation:
It took Lex from 10:00 a.m. to 11:45 a.m. to walk 14 blocks
This means that
Blocks = 14
Time = 45 minutes = 3/4 hour
The speed is then calculated as
Speed = 14/(3/4)
Evaluate
Speed = 18.66
Hence, the speed is 18.66 blocks per hour
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There are a total of 39 students in fourth grade at school this year. Today, some of the fourth graders have gone on a field trip to be exact 3/4 of the women went and 2/3 of the men went. This leaves 11 fourth graders at the school. How many women and how many men are in fourth grade at your school this year?
Solving a system of equations we wll see that there are are 24 women, and the other 15 students are men in foruth grade.
How many women and men are in fourth grade?We know that there are 39 students in fourth grade, we know that:
3/4 of the women went
2/3 of the men went
And this leaves 11 students at the school, then we can write the equation:
(3/4)*W + (2/3)*M + 11 = 39
Where W and M are the number of women and men respectively.
(3/4)*W + (2/3)*M = 39 - 11 = 28
(3/4)*W + (2/3)*M = 28
And we also know that the total number is 39, then:
M + W = 39
So we can write the system of equations:
(3/4)*W + (2/3)*M = 28
M + W = 39
M = 39 - W
REplacing that on the other equation we get:
(3/4)*W + (2/3)*(39 - W) = 28
(3/4)*W - (2/3)*w + 26 = 28
(3/4)*W - (2/3)*W = 28 - 26 = 2
(9/12)*W - (8/12)*W = 2
(1/12)*W = 2
W = 2*12 = 24
There are 24 women, and the other 15 students are men.
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What is the measure of 2HPL?
H
(12x - 15)"
(8x + 33)
The measure of <HPL is 129 degrees
How to determine the measure of <HPL?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
(12x - 15) = (8x + 33)
This is so because they are alternate angles
So, we have
12x - 15 = 8x + 33
Evaluate the like terms
4x = 48
Divide by 4
x = 12
Recall that
HPL = 12x - 15
So, we have
HPL = 12 * 12 - 15
Evaluate
HPL = 129
Hence, the angle is 129 degrees
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i need help with question 23 please i need it quick
The measure of the angle ∠FEB will be 70°.
An infinitely long row of evenly spaced dots that extends in both directions makes up a line. Its length is the only dimension it has. An illustration of a line is a horizontal mark made on a piece of paper. A figure made by two rays that intersect at the same endpoint is referred to as an angle.\
Given that the angle ∠EFB is 35° and BD is the angle bisector of ∠EFD. The measure of the angle ∠FEB will be;-
∠FEB = 2 x ∠EFB
∠FEB = 2 x 35
∠FEB = 70°
Therefore, the value of the angle ∠FEB will be 70°.
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2
In order to calculate marginal cost, producers must compare the difference in the cost of producing orie unit to the cost
of
O purchasing a unit.
O distributing that unit.
31:27
O producing the next unit.
O producing a different unit.
The solution is Marginal cost is (1200 - 1000) / (30 - 20) = 12.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
In order to calculate marginal cost, producers must compare the difference of producing one unit to the cost of producing the next unit
Marginal cost is the change in total cost as a result of increasing output produced by one unit.
For example, if the total cost of producing 20 units of a good is 1000 and the total cost of producing 30units is 1200.
Marginal cost is (1200 - 1000) / (30 - 20) = 12
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listed below are blood platelet counts (1000 cells/l) randomly selected from adults in the united states. why does it not make sense to construct a histogram for this data set?
In order to simply construct a histogram, we require additional data and the range is excessive here.
The lowest and highest valleys for this set of data are 191 and 646, respectively. Therefore, the range is excessive here. However, the total number of data, in this case, is only 2468, or ten numbers. Therefore, only N is 10 is provided. That indicates that the question contains 10 data. Therefore, we are unable to create a histogram for this data.
In the given number of data, which is too little and too close to causing a disaster. He still possesses him. Therefore, in order to simply construct a histogram, we require additional data. But with these 10 pieces of data, this is impossible. Additionally, the range is extremely wide, allowing us to construct a histogram for this question.
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Complete Question:
Listed below are blood platelet counts (1000 cells/ uL ) randomly selected from adults in the United States. Why does it not make sense to construct a histogram for this data set?
191 286 263 193 193 215 162 646 250 386
The HR manager at a large company wents to estimate the percentage of employees who would support a change to the promotion policies at the company. In this company, 30% of the employees are relatively new (have been with the company less than 4 years) while 70% are experienced (have worked at least 4 years at the company). The HR menager rendomly samples 17 new employees and 41 experienced employees. (a) Which sempling design is being used by the HR manager? • Stratified random sample O Cluster sample O Simple random sample O Systematic sample
The HR manager is using a stratified random sample, which is a technique of dividing the population into multiple strata (groups) and then randomly selecting from each stratum.
The HR manager is using a stratified random sample, which is a technique of dividing the population into multiple strata (groups) and then randomly selecting from each stratum. In this case, the population is divided into two strata, new employees (30%) and experienced employees (70%). The HR manager then randomly selects 17 new employees and 41 experienced employees. This technique ensures that each stratum is represented in the sample, making it more representative of the population. Furthermore, it increases the precision of the sample by focusing on the subgroups that may have different characteristics and opinions on the matter, rather than relying on a simple random sample. The advantage of this sampling design is that it allows the HR manager to make more accurate estimates of the population's opinion on the change in promotion policies.
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Examine the figure below, what is a = ?
The value of a in the circle is 6.
How to solve for variable in a circle?Using circle theorem, angles on the circumference from opposite end of a diameter are 90 degrees.
Therefore, the value of angle L is 90 degrees.
Recall the diameter of the circle is MK.
Hence, let's find the value of a as follows:
15a = 90
divide both sides of the equation by 15
15a / 15 = 90 / 15
a = 6
Therefore, the value of a is 6
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