a set of quiz scores is shown in the histogram below. the mean of the data set is 6.625 and the population standard deviation is 1.9 How many numbers in the data set are within 1 standard deviation of the mean? a)7 b)10 c)12 d)13
Answers
Given
Mean = 6.625
Standard Deviation = 1.9
Values within 1 standard deviation of mean, mean:
[tex]\begin{gathered} 6.625-1.9We look at the number of values at 5, 6, 7, and 8.5 = 2 people
6 = 2 people
7 = 5 people
8 = 3 people
Total = 2 + 2 + 5 + 3 = 12 people
Answer
C
Related Questions
The function shown in the graph is f(x) =
Answers
Answer:
x³-2x²-5x+6 =0
Step-by-step explanation:
x³-2x²-5x+6 =0
checking zeros
x=1 , 1-2-5+6=0, 0=0 true
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Which of these situations can be represented with an integer that, when combined with the opposite of 8, makes 0?
Answers
On the number line if you are at positive 8 and add -8 you will lose 8 and get zero! Hope this helps!
A radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t)=100(1.3)^-tWhat is the Half-Life of this substance?
Answers
Explanation:
The dunction is given below as
[tex]A(t)=100(1.3)^{-t}[/tex]To figure out the half life,
The new mass of the decayed substance will be half that of the initial substance
[tex]\begin{gathered} A(t)=100\left(1.3\right)^{-t} \\ A(t)=\frac{100}{2}=50 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A(t)=100(1.3)^{-t} \\ 50=100(1.3)^{-t} \\ \frac{50}{100}=1.3^{-t} \\ \frac{1}{2}=1.3^{-t} \end{gathered}[/tex]Apply exponent rules
[tex]\begin{gathered} \frac{1}{2}=1.3^{-t} \\ ln(\frac{1}{2})=-tln(1.3) \\ t=\frac{ln(2)}{ln(1.3)} \\ t=2.64years \end{gathered}[/tex]Hence,
The final answer is
[tex]2.64years[/tex]To the nearest tenth of a second, how much time would it take the penny to hit the ground?
Answers
In this problem, we want to approximate when a penny will hit the grownd after it has been dropped from the back of the bleachers.
Since we have been given a table, we can make a close estimate based on the y-values.
When the penny hits the ground, the value of y will be 0.
Notice on the table provided that the penny is going to reach 0 between the values of 0.6 and 0.7 seconds.
At 0.6 seconds, it has a distance of 0.236 meters from the ground.
At 0.7 seconds, supposing the penny went past hitting the ground, it was have a distance of
[tex]|-0.401|=0.401\text{ meters from the ground.}[/tex]Since the penny is closer to 0 at the 0.6 s mark than the 0.7 s mark, we can say 0.6 seconds is when the penny will hit the ground.
Here is a graphic model of the penny moving toward the ground:
CuIU/u
Rebecca is playing a video game that involves planting and cutting down trees. She
moves up an energy level for each tree she plants, and she moves down a level for
each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.
Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: tree cut
Answer the questions to find out whether Rebecca earned bonus poirlts in the next 3
turns. Use the number line to help you add.
2 3 4 5 6 7 8 9 10
1. Using only addition, write an expression that represents Rebecca's score after these
three turns. (Remember that she starts at an energy level of 4.). (2 points)
Answers
By the end of her three turns, she is level 5.
The number line is what?
A number line is a visual depiction of numbers on a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction.
If Rebecca cuts down six trees on her next round, she drops down to level four and gains six levels. Rewriting this as -6 yields 4 + (-6) = -2. her following turn, she will plant 8 trees, increasing her level by 8. -2 + 8 = 6 In her final round, she removes one tree.
6 + (-1) = 5
4 + (-6) + 8 + (-1) = 5 in total.
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h(x) is given. h(x)=f(g(x)). Give a possible combination of f(x) and g(x).
[tex]h(x)=(x-4)^3+(x-4)^\frac{3}{2} -1[/tex]
Answers
IN THEVPLACE OF x in the EQUATION OF f(x) we find that x-4 is plugged in..
THIS brings us to a result that g(x) is accompanied by x-4
[tex]g(x) = x - 4[/tex]
and For f(x) it shows
[tex]f(x) = {x}^{3} + {x}^{ \frac{3}{2} } - 1[/tex]
SINCE THE POSITION OF THE X VALUES OF WHICH x-4 was plugged in has to be reserved.
PLEASE IF YOU DON'T UNDERSTAND MESSAGE ME QUICKLY.
Write an equation and point slope for the line that passes through the giving order pairs there are two correct answers for this question Depending upon which order pair do you use for the slope for
Answers
If we label the given points to find the slope of the line, we have:
(4, 1 ) ---> x1 = 4, y1 = 1
(-2, 7) ---> x2 = -2, y2 = 7.
Then, using the formula for the slope of a line, we have:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-1}{-2-4}=\frac{6}{-6}\Rightarrow m=-1[/tex]Then, having this value of m, we can apply the formula for the Point-Slope Form of the line:
1. In the case we take the pair as ( 4, 1), the equation is:
[tex]y-y_1=m(x-x_1)=y-1=-1(x-4)=y-1=-(x-4)[/tex]2. In the case we take the pair as (-2, 7), we have:
[tex]y-7=-1(x-(-2)=y-7=-(x+2)[/tex]Then, we have two options:
[tex]y-1=-(x-4)[/tex][tex]y-7=-(x+2)[/tex]I really need help on the do you mind helping
Answers
the quation of the given graph is,
[tex]y=(x+3)^2-1[/tex]what is 1,000 / 10,000
Answers
Answer:
Step-by-step explanation:
Ok this will go into decimals:
1,000/10,000: First delete the zeros as a simple way to solve these problems
SO:
1/10=0.1 as answer
Let A = {a,b,c), B = {4,5,6), and/= {(a ,6), (b,4), (c,6)). Is f a function from A to B? Explain.
Answers
The condition for a group of paired values to be a function is that for each value of the independent variable exists one and only one value of the dependant variable.
In this case, A is the group of points that represent the independent variable, and B, the dependent variable.
As each value of A has one and only one value of B, f is a function from A to B.
The inverse is not true, as 6 would have 2 values (a and c) in the image (A).
A is the domain of the independent variable.
f is the function that transform the values present in the group A in some of the elements of the image, that is group B.
The conditions for that relation to be a function is that each of the values in the domain has one and only one value in the image.
The statements below represent some possible deposits and withdrawals from Rachel's bank account. Match each statement with the total amount that Rachel's account would change. -47.50 -22.50 22.50 She deposits $35 to her account. Then spends $12.50 from her account on lunch. She withdraws $35 from her account. Then spends $12.50 from her account on lunch. She spends $35 from her account on clothes. Then she deposits $12.50 to her account. 000 OO
Answers
merlyumanzor23, this is the solution:
A. 35 - 12.50 =
The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour plus $75 for an assistant. The committee wants to keep the total cost under $450. plssss I need stepss.
Answers
The dance committee can hire the DJ for a maximum of 3 hours keeping the cost under control
DJ charges per hour = $125
Charges for assistance = $75
Budget by the committee = $450
Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Let x represent the maximum number of hours to hire the DJ
Formulating the equation we get:
DJ charges per hour*Number of hours<= Required budget
125x + 75<=450
Solving the equation:
125x <= 375
x <=3
So, a maximum of 3 hours
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If you have a second credit card, your security deposit or spending limit prevents you from spending more than you can afford or repay
True or False?
Answers
Answer: true
Step-by-step explanation:
What is the value of 6x exponent 4 when x = 5
Answers
Answer:
6480
Step-by-step explanation:
6^4x5
Answer:
3750
Step-by-step explanation:
Hey there!
To solve this we must first make this into an equation
[tex]6x^4\\x=5\\6(5)^4\\6(625)\\3750[/tex]
Use I = PRT to solve.
(time is in years)
| = $14,400
R = 8%
T = 30 years
Find P.
Answers
Principal is $6000.
Define simple interest.Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows $5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years. Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Given Data
Using simple interest formula,
| = $14,400
R = 8%
T = 30 years
I = [tex]\frac{PRT}{100}[/tex]
14400 = [tex]\frac{P(8)(30)}{100}[/tex]
[tex]\frac{14400(100)}{8(30)}[/tex] = P
P = 6000
Principal is $6000.
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State the x and y intercepts of the given graphs.
Answers
Answer:
• x-intercept: (3, 0)
,• y-intercept: (0, -2)
Explanation:
x-intercept
The x-intercept is the point at which the graph crosses the x-axis.
From the graph, the x-intercept is at (3, 0).
y-intercept
The y-intercept is the point at which the graph crosses the y-axis.
From the graph, the y-intercept is at (0, -2).
(Please help. Will be marked brainliest) Clifford is making a really big white cake for his sister’s birthday. The recipe calls for 1.5 times as much flour as sugar. It also calls for
1
2 as much butter as sugar. All the butter, flour, and sugar together total 7.5 cups. How much butter, sugar and flour does Clifford need?
Answers
After solving the equation, Clifford need 3.75 cups of flour, 2.5 cups of sugar and 1.25 cups of butter to make the cake.
What is an equation?Equation, also referred to as a declaration of equality between two expressions that contain variable- and/or number-based components. Since equations are essentially questions, the development of mathematics has been driven by efforts to systematically find answers to those questions.
There are many different types of equations that vary in complexity, ranging from simple algebraic equations that only call for addition or multiplication to differential equations, exponential equations that employ exponential expressions, and integral equations. They serve as an expression for many physics laws.
Let flour be f, sugar be s, and butter be b
We have given that
f = 1.5s ...1
b = 1/2(s)
= 0.5s ...2
And
F + B + S = 7.5 cups
Lets substitute the vales of f and b in F + B + S, and we get
1.5s + 0.5s + S = 7.5 cups
2S + S = 7.5
3S = 7.5
S = 7.5/3
S = 2.5 cups
Flour = (1.5)2.5
= 3.75 cups
Butter = (0.5)2.5
= 1.25 cups
Thus, Clifford need 3.75 cups of flour, 2.5 cups of sugar and 1.25 cups of butter to make the cake.
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Match each equation to one of the two tape diagrams. Dragon drop each card to match the equation to the correct tape diagram. - (please use ss)
Answers
First diagram:
Sum of the three parts is equal to 9: x+x+x is 9 or three times x is 9
Equations:
[tex]\begin{gathered} 3\cdot x=9 \\ 9=3\cdot x \\ x+x+x=9 \end{gathered}[/tex]Also you can write the equation 3*x=9 as follow by solving x:
[tex]x=9\div3[/tex]Second diagram:
Sum of the two parts is equal to 9: x+3 = 9
Equations:
[tex]\begin{gathered} x+3=9 \\ 3+x=9 \end{gathered}[/tex]Solving x you can write the equation:
[tex]x=9-3[/tex]Classify the system (options: consistent, independent consistent, inconsistent) 4x + 2y = 8y = -2x + 8
Answers
Write both equations in standard form:
[tex]ax+by=c[/tex]The first one is already written in standard form:
[tex]4x+2y=8[/tex]To write the second one in standard form, add 2x to both members of the equation:
[tex]\begin{gathered} y=-2x+8 \\ \Rightarrow y+2x=-2x+8+2x \\ \Rightarrow2x+y=8 \end{gathered}[/tex]Notice that if we divide both members of the first equation by 2, we get:
[tex]\begin{gathered} \frac{4x+2y}{2}=\frac{8}{2} \\ \Rightarrow2x+y=4 \end{gathered}[/tex]Then, the system of equations is equivalent to:
[tex]\begin{gathered} 2x+y=8 \\ 2x+y=4 \end{gathered}[/tex]For the transitive property of equality, since both left members are the same, we can conclude from that system of equations that 8=4, which is false. Then, the system is inconsistent, since it leads to a contradiction.
Therefore, the answer is:
[tex]\text{Inconsistent}[/tex]Complete the truth table.
р
q
-
pЛ-4
P+
-(p+q)
F F
T
T
F
F
T
T T
F
T
T
חד
F
T
F
T
F
T
F
T
וד
F
וד
F
T
רד
F
F
Answers
given the function
[tex](-p\rightarrow q)\rightarrow(q\rightarrow-r)[/tex]option 1
P=T
Q=T
R=T
then
-P=F
-R=F
-P -> q=V
q ->-r= F
then
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=F[/tex]Option 2
P=T
Q=T
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 3
P=T
Q=F
R=T
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 4
P=T
Q=F
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 5
P=F
Q=T
R=T
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=F[/tex]Option 6
P=F
Q=T
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 7
P=F
Q=F
R=T
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 8
P=F
Q=F
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]The maximum load of a horizontal beam that is supported at both ends varies jointly as the width and the height and inversely as the length between the supports. A beam 6m long, 0.1m wide, and 0.06 m high supports a load of 360kg. What is the maximum load supported by a beam 16m long, 0.2m wide, and 0.08 m high?
Answers
Answer:
[tex]360kg[/tex]Explanation:
Here, we want to get the maximum load supported
From the first part of the question, we have it that:
The maximum load g, varies jointly with the width w and the height h, and inversely as the length l between the supports
Mathematically, we have that as:
[tex]g\text{ = k }\times\frac{wh}{l}[/tex]where k is the proportionality constant
Now, let us get the value of k
We substitute the first set of values as follows:
[tex]\begin{gathered} 360\text{ = }\frac{k\times0.1\times0.06}{6} \\ \\ k\text{ = 360,000 }\frac{kg}{m} \end{gathered}[/tex]Now, using this value of k, we want to get the value of g
Mathematically, we have that as:
[tex]g\text{ = }\frac{360,000\times0.2\times0.08}{16}\text{ = 360 }kg[/tex]1, 728 ÷ 32 what is the value of the expression
Answers
Result : 54
reminder = 0
[tex]1,728\div32[/tex]
Simplify the expression:
[tex]1,728\div32\\[/tex]
[tex]=54[/tex]
Hope this helps!
The surface areas of two similar figures are 16 in2 and 25 in2. If the volume of the larger figure is 500 in3, what is the volume of the smaller figure?
Answers
The volume of the smaller figure is 256 in³.
Given, the surface area of two figures are 16 and 25.
volume of the larger figure is 500.
volume of smaller figure =?
Similar figures have a scale factor k, (let k be >1, so k is the ratio of a distance in the larger figure to the corresponding distance in the smaller one)
First, we calculate for the ratio of the surface areas of the given figures. From the given above, the ratio is equal to 25:16
Then, we calculate for the ratio of the perimeters or sides of the figures by getting the square root of the ratio in figure 1.
ratio of perimeter or side = 5:4
The ratio of the volumes of the figures is equal to the cube of the ratio in figure 2.
ratio of volumes = (5:4)³ = 125:64
Using this ratio and the volume of the larger figure,
500 in³/x in³ = 125/64
x in³ = 500×64/125
x in³ = 256 in³
The value of x from the equation is 256. Therefore, the volume of the smaller figure is 256 in³.
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Find the volume of this cylinder. Use 3 for . V = 7r2h 12 cm 5 cm V~ [?]cm Enter
Answers
Looking at the figure, the diameter of the cylinder is 12 cm and its height is 5 cm
The radius is half the diameter, so we have r = 6 cm.
Now, using the volume formula, we have:
[tex]\begin{gathered} V=\pi r^2h \\ V=3\cdot6^2\cdot5 \\ V=3\cdot36\cdot5 \\ V=540 \end{gathered}[/tex]So the volume of the cylinder is 540 cm³.
A truck driver travels at an average speed of 65 miles per hour on a 230-mile trip to pick up a load of freight. On the return
55 miles per hour. What is the average speed for the round trip? (Round your answer to one decimal place
Answers
Answer:
60.0 miles per hour.
Step-by-step explanation:
The one-way distance is the same as the return distance, so, the average speed is obtained by averaging both speeds:
(65+55)/2 = 120/2 = 60 miles per hour
Jarrett surveyed elementary school students about their favorite animals at the zoo He displayed his results in this circle graph If 412 students chose lions as their favorite zoo animal how many total students did Jarrett survey?
Answers
Since the 40% of the students choose lion, we can use the following expression:
[tex]\begin{gathered} \text{Total of students}\cdot\frac{\text{percent}}{100}=\text{equivalent number to the percent} \\ \text{Total students}\cdot\frac{40}{100}=412 \\ \text{Isolating the variable total students:} \\ \text{Total students=}\frac{412\cdot100}{40}=\frac{41200}{40} \\ \text{Total students=1030} \end{gathered}[/tex]Jarrett survey 1030 students
Graph the line that contains the point (3,-6) and has a slipe of 1/2
Answers
to graph the line we first need to get its equation. The equation of a line is:
[tex]y-y_1=m(x-x_1)[/tex]Then, we have:
[tex]\begin{gathered} y-(-6)=\frac{1}{2}(x-3) \\ y+6=\frac{1}{2}x-\frac{3}{2} \\ y=\frac{1}{2}x-\frac{3}{2}-6 \\ y=\frac{1}{2}x-\frac{15}{2} \end{gathered}[/tex]Once we have the equation we can find another point on the line. If x=1 then y=-7, hence we have the point (1,-7).
Now we graph the points (1,-7) and (3,-6) and jo
The current temperature is 48°F. It is expected to drop 1.5°F each hour.
Answers
The current temperature is 48°F, in expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.
The current temperature is = 48°F.
It is expected to drop = 1.5°F each hour.
We can assume, temperature = 36°F
Let x hours the temperature will be 36°F.
Temperature is a measure of the average kinetic energy of the particles in an object. When the temperature increases, the motion of these particles also increases. Temperature is measured with a thermometer or a calorimeter.
Then,
48 - 1.5x = 36
It's expected to drop 1.5F per hour,
We can list the equation,
So,
We can write,
48 - 1.5x = 36
48 - 36 = 1.5x
We can sum or difference of the product,
1.5x = 12
x = 12/1.5
We can divide the products,
x = 8 hours
Therefore,
In expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.
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Answer:
The present temperature is 48°F; it is anticipated to decrease by 1.5°F every hour, reaching 36°F in 8 hours.
Step-by-step explanation:
48°F is the current temperature.
An hourly decrease of 1.5°F is anticipated.
We'll assume that it's 36°F.
The temperature will be 36°F in x hours.
The average kinetic energy of the particles in an object is measured by its temperature. The velocity of these particles likewise increases as the temperature rises. A thermometer or a calorimeter is used to determine the temperature.
Then,
48 - 1.5x = 36
It's expected to drop 1.5F per hour,
We can list the equation,
So,
We can write,
48 - 1.5x = 36
48 - 36 = 1.5x
We can sum or difference of the product,
1.5x = 12
x = 12/1.5
We can divide the products,
x = 8 hours
Therefore,
In expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.
((1/3)x^2))-((1/9)x)-(2/9)=0
Answers
The solution of the quadratic equation (1/3)x² - (1/9)x - 2/9 = 0 are x = 1, - 2/3.
Any equation that can be written in the standard form where x stands for an unknown and a, b, and c are known quantities, with a 0, is said to be quadratic.
An assignment of values to the unknown variables that establish the equality in the equation is referred to as a solution.
Consider the expression,
(1/3)x² - (1/9)x - 2/9 = 0
Multiplying each side of the quadratic equation by 9,
9 × [ (1/3)x² - (1/9)x - 2/9 = 0 ]
3x² - x - 2 = 0
Using the quadratic formula,
[tex]x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]x = \frac{1 \pm \sqrt{1+24} }{6}\\ x = \frac{1 \pm \sqrt{25} }{6}[/tex]
x = 1 and x = - 2/3
Hence, the solution of quadratic equation (1/3)x² - (1/9)x - 2/9 = 0 are x = 1, - 2/3.
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Given f(x)= -5x^5 - x^4 + 4x^3 and g(x)= -5x^5 - 3x^3 -5x^2 +8 find and simplify f(x) - g(x).
f(x) - g(x) =
degree=
leading coefficient=
Answers
The simplified function, f(x) - g(x) is - x⁴ + 7x³ + 5x² - 8.
The degree and leading coefficient are 4 and -1 respectively.
How to simplify functions?The functions to be simplified is as follows;
f(x) = - 5x⁵ - x⁴ + 4x³
g(x) = - 5x⁵ - 3x³ -5x² + 8
Therefore, let's simplify the function,
f(x) - g(x) = - 5x⁵ - x⁴ + 4x³ - (- 5x⁵ - 3x³ -5x² + 8)
open the bracket with the negative sign
f(x) - g(x) = - 5x⁵ - x⁴ + 4x³ + 5x⁵ + 3x³ + 5x² - 8
combine like terms
f(x) - g(x) = - 5x⁵ + 5x⁵ - x⁴ + 4x³ + 3x³ + 5x² - 8
f(x) - g(x) = - x⁴ + 7x³ + 5x² - 8
Therefore,
degree of the function = 4
Leading coefficient = -1
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