Data
• Total phone calls: 154
,• Second evening ( ,s ,): 10 more calls than the first evening ( ,f ,)
,• Third evening ( ,t ,): 4 times as many calls as ,f
Procedure
We have to translate the given information into algebraic expressions.
• Maria received a total of 154 phone calls at the call center:
[tex]f+s+t=154[/tex]where f represents the first evening, s the second, and t the third.
• The second evening, she received 10 more calls than the first evening:
[tex]s=10+f[/tex]• The third evening, she received 4 times as many calls as the first evening:
[tex]t=4\times f[/tex]As t and s can be used in terms of f, we will replace the second and third equations that we build in the first one:
[tex]f+s+t=154[/tex][tex]f+(10+f)+(4\times f)=154[/tex]Eliminating the parenthesis we get:
[tex]f+10+f+4f=154[/tex]Solving for f:
[tex]6f=154-10[/tex][tex]f=\frac{144}{6}[/tex][tex]f=24[/tex]Thus, the number of phone calls the first evening was 24.
Then, we have to replace this calculated value in the other equations to get s and t.
• Solving for ,s
[tex]s=10+f[/tex][tex]s=10+24[/tex][tex]s=34[/tex]• Solving for ,t
[tex]t=4f[/tex][tex]t=4\cdot24[/tex][tex]t=96[/tex]To prove our answers are correct, we can do the following:
[tex]24+34+95=154[/tex][tex]154=154[/tex]Answer
• Number of phone calls the first evening: 24
• Number of phone calls the second evening: 34
• Number of phone calls the third evening: 96
The table shows Alejandro's golf scores (relative to par) over a 4-round tournament. Round Score (strokes) 1 +2 2 –4 3 –2 4 +3 What is Alejandro's cumulative score for the tournament?
Alejandro's cumulative score for the tournament is -1.
What is cumulative score?It is important to note that cumulative score simply has to do with the total score.
From the information, the table shows Alejandro's golf scores over a 4-round tournament.
The scores for the tournament include 2, -4, -2 and 3.
Therefore, the total score will be:
= 2 - 4 - 2 + 3
= -1
The score is -1.
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Graph −4 < x < 2 on the number line. Write −4 < x < 2 in interval notation.
To graph the inequality, we need to take the following steps:
0. Draw a number line.
,1. Draw circles over -4 and 2; in this case the circles are hollow since the inequality only has exact signs.
,2. Join them with a straight line.
With this in mind the graph of the inequality is:
The inequality is written in interval notation as:
[tex](-4,2)[/tex]The speed limit on a road is 50 mph. A car drives 19 miles in 22 minutes. Is the car breaking the speed limit? You must show your workings.
Answer: Yes, the car is breaking the speed limit
Work Shown:
22 min = 22/60 = 0.36667 of an hour approximately
distance = rate*time
rate = distance/time
rate = (19 mi)/( 0.36667 hr)
rate = 51.818 mph approximately
The car is slightly over the 50 mph speed limit.
What is the equation X+y>3 in the slope interceptform (ie y=mx+b)?
Graph: y = - 4x + 2It’s just on a generic coordinate plane
The green V function is | x- 4|, so then its necessary to elevate this funtion 2 units , at y axis, to find y = | x - 4| + 2
In Exercises 1 and 2, solve the system using the elimination method.2. x + y - 2 = -22x – y += = 8-x + 2y + 2: = 10
(1,3,-7)
1) Let's write the following system of linear equations, and then solve them by the elimination method.
The first thing to do is to proceed with the elimination of one variable. In this case, let's chose to start with
x-6y+2z=5 x -2
2x-3y+z=4
3x+4y-z=-2
2x-12y+4z=10
2x-3y+z=4
3x+4y-z=-2
Adding these two equations:
2x-3y+z=4
-2x+12y-4z=-10
----------------------------------
9y -3z =-6
Now getting the other equations, let's eliminate another variable, in this case, "x"
-2x+12y-4z=-10 x 3
3x+4y-z=-2 x 2
Adding them
-6x +36y -12z=-30
6x+8y-2z=-4
----------------------------
0 44y -14z=-34
2) Now that we have a simpler system of two variables "y" and " z" let's operate them. Choosing a factor that we can multiply and cancel out the y variable, in this case, let's pick the Least Common Multiple between 9 and 44 = 396, so let's multiply them by
9y -3z = -6 x 44
44y-14z=-34 x -9
396y -132z = -264
-396y+126z=-306
----------------------------
6z =-42
z=-7
Plugging into the equation 9y -3z =-6
9y-3(-7)=-6
9y +21 =-6
9y=27
y=3
And for x
x-6y+2z=5
x-6(3)+2(-7)=5
x+18-14=5
x+4=5
x=1
3) So the solution for that system is (1, 3, -7).
These ordered pairs represent a proportional relationship. Use the interactive and the constant of proportionality to find the missing coordinates for the ordered pairs.
(3, 9), (A, 12), (5, 15), (6, B
Missing coordinates for the ordered pairs given are A= 4 and B= 18.
What are coordinates ?An integer pair used to define a point's location on a coordinate plane using the horizontal and vertical separations from the two reference axes Coordinates are two numbers (Cartesian coordinates) or, less frequently, a letter and a number that identify a specific location on a grid, also known as a coordinate plane. They are frequently represented by the x-value and y-value pair (x,y). The x (horizontal) and y (vertical) axes are the two axes of a coordinate plane with four quadrants (vertical)
Calculation12/A = 9 / 3
A = 4
Same as above
B/6 = 9/3
B = 18
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2) A recycling center was offering cash for different types of recyclables. For each pound of
paper recycled they offered $0.03, for each pound of aluminum they offered $1.32 and for
each pound of plastic they offered $0.07. Jerry took in 10 pounds of paper, 8 pounds of
aluminum and 7 pounds of plastic. How much money did he earn?
The money earned by Jerry at the recycling center is $11.35.
According to the question,
We have the following information:
For each pound of paper recycled they offered $0.03, for each pound of aluminum they offered $1.32 and for each pound of plastic they offered $0.07. Jerry took in 10 pounds of paper, 8 pounds of aluminum and 7 pounds of plastic.
Now, we have the following expression when multiplied with the cost of each pound:
10*0.03+8*1.32+7*0.07
Now, we will first use multiplication and then we will use addition:
0.3+10.56+0.49
$11.35
Hence, the money earned by Jerry at the recycling center is $11.35.
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Let f(x) = 4x² + 6.
The quadratic function g(x) is f(x) translated 3 units up.
What is the equation for g(x) in simplest form?
g(x) = ____
g (x) = 4x² + 10 is the equation for g(x) in the simplest form.
What is a function?A special relationship where each input has a single output is called a function.
Given that, f(x) = 4x² + 6, the quadratic function g(x) is f(x) translated 3 units up.
The translation of a function f (x) in the Cartesian coordinate domain can be done by following the given guidelines:
Translation guidelines ;
Horizontal shifts
Right : f (x) → f (x - a)
Left : f (x) → f (x + a)
Vertical shifts
Up : f (x) → f (x) + b
Down : f (x) → f (x) - b
General shift (Horizontal and Vertical shift) is;
f (x) → f (x ± a) ± b
We will use the guidelines for Vertical shifts, where in this case the magnitude of b = 4.
f (x) = 4x² + 6
g (x) = f (x) + 4
g (x) = 4x² + 6 + 4
g (x) = 4x² + 10
Hence, the equation for g(x) in the simplest form is g (x) = 4x² + 10
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Can someone answer this for me ill give a big reward
Answer:
carol
Step-by-step explanation:
Beth’s hair can be represented as 1 since everyone else is a fraction of her hair so we just convert the other 2 fractions to make them have the same denominator
4x3/5x3=12/15
2x5/3x5=10/15
10 is less than 12 so carol has the shortest hair
Hopes this helps please mark brainliest
To help visualize, let's say Beth's hair is 15 inches:
Beth = 15"
Abbey = 4/5 * 15" = 12"
Carol = 2/3 * 15" = 10"
Carol has the shortest hair.
write a fracción and a decimal for the part of the gris that is shaded.
The shaded part is 3 column
There are 10 columnn in total.
The number of grids are 100 and shaded grids are 30
Thus the fraction of shaded portion is:
3/10.
The decimal form is 0.3.
Anastasia needs to order liquid fertilizer for her landscaping company. She plans to keep the fertilizer in a large cylindrical storage tank, but isn’t sure how much it will hold. The tank is 10 feet tall and the circular base has a diameter of 10 feet. What is the volume of her storage tank?
785 feet² is the volume of her storage tank .
What is volume ?
Every three-dimensional item takes up space in some way. The volume of this area is what is being measured. The area contained by an object's limits in three-dimensional space is referred to as its volume. It is sometimes referred to as the object's capacity.(V = πr2h)
(V = π * (5)2 * 10)
(V = 250π)
(π) (pi) is approximately equal to (3.14)
V = 250 * 3.14 = 785
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The table below shows the changes in the value of a company's stock over the past four weeks. By how many points would the stock value need to change in Week 5 to return to its value before Week 1? Explain.
ANSWER:
+ 4 7/8
STEP-BY-STEP EXPLANATION:
Assuming that we start in week 0, with a total of 0 points, we must operate the changes in each week and the value opposite to that result must be the change necessary to return to the original value.
Just like that:
[tex]\begin{gathered} 9\frac{1}{2}+6\frac{5}{8}-12\frac{3}{4}-8\frac{1}{4}=\frac{19}{2}+\frac{53}{8}-\frac{51}{4}-\frac{33}{4}=-\frac{39}{8}=-4\frac{7}{8} \\ -4\frac{7}{8}+4\frac{7}{8}=0 \end{gathered}[/tex]Which means that to return to the initial value, 4 7/8 points must be added
Which property of addition is shown? −3+ 5 = 5 + (−3)
Associative Property
Commutative Property
Distributive Property
Identity Property.
This is the Commutative Property. It states that when addition takes place, the addends may switch positions with another addend.
The given expression −3+ 5 = 5 + (−3) is showing the commutative Property. The correct option is B.
The cumulative property states that if the position of the numbers when they are in addition is changed then it will not affect the final result of the addition. If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics.
The given expression is −3+ 5 = 5 + (−3).
From the cumulative property, the expression can be solved. The two expressions will have the same value but the frame of writing the expression is different.
This is the Commutative Property. It states that when an addition takes place, the addends may switch positions with another added.
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Lacy picks blueberries and raspberries from her garden. She has 1/5 as many pounds of blueberries as raspberries. If she picks 1 4/5 pounds more blueberries, she will have an equal weight of berries. let x represent the weight of raspberries. Which equations could be used to find the weight of the blueberries Lacey has?
Chose all correct answers.
A. [tex]\frac{1}{5} x-1\frac{1}{5}=x[/tex]
B. [tex]x-1\frac{4}{5} =\frac{1}{5}x[/tex]
C. [tex]\frac{1}{5}x=x-1\frac{4}{5}[/tex]
D. [tex]x+1\frac{4}{5}=\frac{1}{5}x-1\frac{4}{5}[/tex]
E. [tex]\frac{1}{5}x+1\frac{4}{5}=x[/tex]
F. [tex]x=1\frac{4}{5}(\frac{1}{5}+x)[/tex]
The equations that could be used to find the weight of the blueberries Lacey has are given as follows:
B. x - 1 and 4/5 = x/5.
C. x/5 = x - 1 and 4/5.
E. x/5 + 1 and 4/5 = x.
How to obtain the equations?The variable that represents the weight of the raspberries is given as follows:
x.
The variable that represents the weight of the blueberries is given as follows:
b.
She has 1/5 as many pounds of blueberries as raspberries, hence:
b = x/5.
If she picks 1 4/5 pounds more blueberries, she will have an equal weight of berries, hence:
b + 1 and 4/5 = x.
x/5 + 1 and 4/5 = x.
Thus the correct options are given as follows:
Option B, as x - 1 and 4/5 = x/5.Option C, as x/5 = x - 1 and 4/5.Option E, as x/5 + 1 and 4/5 = x.More can be learned about a system of equations at https://brainly.com/question/24342899
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Q14.
The diagram shows a solid shape.
The cone has a height of 10 cm.
The volume of the cone is 270π cm³.
The solid shape is made from a hemisphere and a cone.
The radius of the hemisphere is equal to the radius of the base of the cone.
Work out the total volume of the solid shape.
Give your answer in terms of pi.
The total volume of the solid shape is 756π cm³.
There is a solid shape. The shape is formed by joining a cone with a hemisphere. The radius of the hemisphere is equal to the radius of the base of the cone. The height of the cone is 10 cm. The volume of the cone is 270π cm³. We need to find the total volume of the solid shape. The total volume is the sum of the volumes of the cone and the hemisphere. Let the radius be "r". The volume of the cone is (1/3)πr²h. So, we can find the radius.
270π = (1/3)πr²h
810 = r²*10
r = √81 = 9
The volume of the hemisphere is (2/3)πr³ = (2/3)π9³ = 486π cm³. The total volume of the solid shape is V = 270π +486π = 756π cm³.
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Find the slope and y-intercept of the line. Graph the line.
Answer:
Graphing the equation we have;
Explanation:
Given the equation;
[tex]x+5y=40[/tex]the slope of the line can be derived by expressing the equation in slope-intercept form;
[tex]\begin{gathered} 5y=-x+40 \\ y=-\frac{1}{5}x+\frac{40}{5} \\ y=-\frac{1}{5}x+8 \end{gathered}[/tex]So, the slope and y-intercept are;
[tex]\begin{gathered} \text{slope m = -}\frac{1}{5} \\ y-\text{intercept b = 8} \end{gathered}[/tex]to graph the equation, let us find the x-intercept;
[tex]\begin{gathered} at\text{ y=0;} \\ x+5y=40 \\ x+0=40 \\ x=40 \\ (40,0) \\ at\text{ x=0;} \\ (0,8) \end{gathered}[/tex]Graphing the equation we have;
Other points on the graph includes;
[tex]\begin{gathered} at\text{ x=10}; \\ y=-\frac{1}{5}(10)+8=-2+8=6 \\ (10,6) \\ at\text{ x=20;} \\ y=-\frac{1}{5}(20)+8=-4+8=4 \\ (20,4) \end{gathered}[/tex]B. A concrete tank has an external diameter of 10 m and an internal height of 3 m. If the walls and bottom of the tank are 30 cm thick, how many cubic meters of concrete are required to make the tank? 10 m 30 cm 3 m 30 cm
The concrete required to make the tank be 27.4122 m³.
Given, a concrete tank has an external diameter of 10 m and an internal height of 3 m. If the walls and bottom of the tank are 30 cm thick.
External diameter = 10 m
Height = 3 m
Thickness = 0.3 m
External radius = 5 m
Internal radius = 5 - 0.3 = 4.7 m
Volume = πh(e.r² - i.r²)
Volume = (3.14)(3)(5² - 4.7²)
Volume = 9.42(9.7)(0.3)
Volume = 27.4122 m³
Hence, the concrete required to make the tank be 27.4122 m³.
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find the hight of a cone with a volume of 150 in 3 and a radius of 10 in.
we get that:
[tex]150=\frac{1}{3}\pi\cdot10^2\cdot h\rightarrow h=\frac{3\cdot150}{\pi\cdot100}\approx1.4323[/tex]so the height is 1.4323 in
name the polynomials pls
Answer:
1) B. quadratic trinomial
2) C. linear binomial
3) F. quadratic binomial
4) D. cubic monomial
linear (1 exponent)
quadratic (2 exponent)
cubic (3 exponent)
trinomial (3 terms), quadratic (2 terms), monomial (1 term)
1/16*1/8 in exponential form
The exponential form of 1/6 × 1/ 8 = 1/32 = 3.125 × [tex]10^{-5}[/tex]
The given numbers are 1/6 and 1/8
and exponential form means that we would have to write these numbers in such a way that the number can be expressed in the form 10 raised to the power of an integer.
When we solve 1/6
we will get 1/6 = 0.166
and when we solve 1/8 we will get
1/8 = 0.125
thus when we multiply 1/6 × 1/ 8 = 1/32
which when solved will give us
0.03125
this can be expressed as 3.125 × [tex]10^{-5}[/tex]
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(3,-1) slope= 2 what is the equation?
Slope
[tex]m=2[/tex]Potassium-42 has a half-life of 12.4 hours. How much of a 746-gram sample will be left after 62 hours?
the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)
Explanation:half life = 12.4 hours
initial amount = 746g
time elapsed = 62 hours
Using the half-life formula:
[tex]\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = amount remaining} \\ N_0\text{ = initial amount = 746g} \\ t\text{ = 62 hours} \\ t_{\frac{1}{2}\text{ }}\text{ = 12.4 hours} \end{gathered}[/tex]Substitute for the values:
[tex]\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = }746(\frac{1}{2})^{\frac{62}{12.5}} \\ N(t)\text{ = }746(\frac{1}{2})^5 \\ N(t)\text{ = }746(\frac{1}{2^5}) \end{gathered}[/tex][tex]\begin{gathered} N(t)\text{ = }(\frac{746}{32})^{} \\ N(t)\text{ = }23.3125 \end{gathered}[/tex]Hence, the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)
jack wants to buy a pair of trousers for $60.When he went to the store he found that the price was marked down by 20%. how much do they cost
Answer:
$48
no idea how working out would go
Answer: $48
Step-by-step explanation: First convert 20% to a decimal which is 0.2 or 0.20.
Then multiply 60 x 0.20 which equals 12.
Because it is a markdown then you must subtract 12 from 60 which gives you the answer $48.
I hope this helps!! Good Luck!
There are 6 mice in an attic. Their population is growing at a rate of12% per month.a. Write an exponential growth function to model this situation.
general equation of a population is
[tex]y=a(1+\frac{b}{100})^x[/tex]where a is the initial population and b the percent of growing
then replacing a=6 and b=12
[tex]y=6(1+\frac{12}{100})^x[/tex]and simplify
[tex]\begin{gathered} y=6(1+0.12)^x \\ y=6(1.12)^x \end{gathered}[/tex]write a linear function f with the values F (0) = 4 and F (3) = -8
we have the points (0,4) and (3,-8),
Hello hope all is well with you can you help me with this please number 2
Our equation is:
[tex]4(-x)-2(-x)+2=9+(-x)[/tex]Then we can operate it in the following way, I'll do it step by step
[tex]\Rightarrow4(-x)-2(-x)=(4-2)(-x)=2(-x)[/tex][tex]\begin{gathered} \Rightarrow2(-x)+2=9+(-x) \\ \Rightarrow2(-x)+2-2=9+(-x)-2 \\ \Rightarrow2(-x)=7+(-x) \end{gathered}[/tex][tex]\begin{gathered} \Rightarrow2(-x)-(-x)=7+(-x)-(-x) \\ \Rightarrow(2-1)(-x)=7+(1-1)(-x)=7 \\ \Rightarrow1(-x)=7 \\ \Rightarrow-x=7 \end{gathered}[/tex]And, if -x=7, then
[tex]\begin{gathered} 4(7)-2(7)+2=9+(7) \\ \Rightarrow28-14+2=9+7 \\ \Rightarrow16=16 \end{gathered}[/tex]The Parkview middle school football team will be playing in the state championship the coach free tickets that he would be distributing to his 52 football players to give to their friends and family if you would like to give each player at least three tickets how many total tickets Must he have?
He must have 156 total tickets.
According to the question,
We have the following information:
The Parkview middle school football team will be playing in the state championship the coach free tickets that he would be distributing to his 52 football players to give to their friends and family and you would like to give each player at least three tickets.
So, we have the following expression:
1 player = 3 tickets
Now, we will use multiplication to find total number of tickets:
52 players = 52*3 tickets
52 players = 156 tickets
Hence, he must have 156 total tickets.
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2. The volume of a 3-D shape is 13 cubic feet. The shape is scaled up and the new volume is 832 cubic
feet. What was the scale factor?
Scale factor of given equation is 64 : 1
What is scale factor ?Scale Factor is used to scale the shape in various dimensions. In Geometry you will learn about different geometric shapes in 2D and 3D. A scale factor is a measure of similar figures that look the same but have different scales or measurements. Suppose two circles are similar but may have different radii. The scale factor indicates how much larger or smaller the figure is than the original figure. Scale allows you to scale the original shape up or down and draw it. The amount by which a shape is magnified or shrunk is called the scale factor. Used when you need to increase the size of 2D shapes such as circles, triangles, squares, and rectangles. Magnification is also well understood from the basic theorem of proportionality.Calculationinitial volume = 13 cubic feet
final volume = 832 cubic feet
scale factor = 832 / 13
= 64 : 1
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Then where dose the two lines intersect needs to be (x,y) pair
Answer:
The lines are parallel, and therefore, never intersect.