Answer:
16.5
Step-by-step explanation:
Answer:
file cabinet = 50
chair = 90
Step-by-step explanation:
x = chair
y = file cabinet
1st year, solve for x
2x+4y = 380
2x = 380 - 4y
x = 190 - 2y
2nd year
Now substitute x = 190 - 2y in your 2nd year formula
4x+6y = 660
4(190-2y)+6y = 660
760 - 8y + 6y = 660
-2y = -100
y = 50
The cost of the filling cabinet is 50 each
Now use the value for y (50) in your first formula to get x
2x+4y=380
2x+4*50=380
2x=380-200
2x=180
x=90
According to Fidelity Investment Vision Magazine, the average weekly allowance of children varies directly as their grade level. In a recent year, the average allowance of a 9th-grade student was 9.66 dollars per week. What was the average weekly allowance of a 5 th-grade student?
The average weekly allowance of a 5th grade student as calculated using direct variation with the information provided by Fidelity Investment Vision Magazine is 5.367 dollars per week.
The question given is a direct variation problem:
Let:
• Average weekly allowance = [tex]a[/tex]
• Grade level = [tex]g[/tex]
If Average weekly allowance varies directly as grade level , then , then the direct variation between the variables can be expressed as :
[tex]a = k * g[/tex]
Where , [tex]k[/tex] = constant of proportionality
We can obtain the value of k from the given values of a and g
[tex]9.66 = k * 9\\9.66 = 9k\\k = 9.66/9[/tex]
Our equation becomes:
[tex]a = (9.66/9) * g[/tex]
[tex]a = (9.66/9) * 5\\a = 5.367[/tex] (rounded to 3 decimal places)
Hence, using proportional relationship, the average weekly allowance for a 5th grade student is [tex]5.367[/tex] per week
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please help, will give brainliest!!!!
Answer:
3
Step-by-step explanation:
3 - 3/x
----------------
1 - 1/x
Multiply the top and bottom by x
x(3 - 3/x)
----------------
x(1 - 1/x)
3x -3
------------
x-1
Factor the numerator
3(x-1)
-------
x-1
Cancel like terms
3
-----
1
3
Can someone please help me
Researchers would like to assess the overall health of white pine trees in a state park. Which of the following
methods for choosing the trees to assess would be considered a convenience sample?
O A ranger hires employees to assess every tree in the park.
O The 100 trees closest to a ranger station are assessed for damage.
O Agrid map of the park is used, and 100 random points on the grid are chosen and used to select the trees to
assess
O Each tree in the state park is tagged with a number, and 100 random numbers that represent the trees are
selected and assessed for damage.
Answer:
The 100 trees closest to a ranger station are assessed for damage.
Step-by-step explanation:
Convenience samples are samples taken from only around the focal point.
Option B is correct, The 100 trees closest to a ranger station are assessed for damage.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
A convenience sample is a non-random method of sampling that involves selecting subjects that are easy to access or readily available.
Of the methods listed, the convenience sample is the one where the trees are selected based on their proximity to a ranger station:
The 100 trees closest to a ranger station are assessed for damage.
This method is a convenience sample because it does not involve random selection of trees.
Instead, the trees are chosen based on their proximity to a specific location.
This can introduce bias into the sample, as trees near the ranger station may not be representative of the overall health of white pine trees in the state park.
Hence, Option B is correct, The 100 trees closest to a ranger station are assessed for damage.
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e/22 = 6/15, What does e equal? Please answer with work!
Answer:
e = 44/5 = 8.800
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
e/22-(6/15)=0
Step by step solution :
STEP
1
:
2
Simplify —
5
Equation at the end of step
1
:
e 2
—— - — = 0
22 5
STEP
2
:
e
Simplify ——
22
Equation at the end of step
2
:
e 2
—— - — = 0
22 5
STEP
3
:
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 22
The right denominator is : 5
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 1 0 1
11 1 0 1
5 0 1 1
Product of all
Prime Factors 22 5 110
Least Common Multiple:
110
Calculating Multipliers :
3.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 5
Right_M = L.C.M / R_Deno = 22
Making Equivalent Fractions :
3.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. e • 5
—————————————————— = —————
L.C.M 110
R. Mult. • R. Num. 2 • 22
—————————————————— = ——————
L.C.M 110
Adding fractions that have a common denominator :
3.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
e • 5 - (2 • 22) 5e - 44
———————————————— = ———————
110 110
Equation at the end of step
3
:
5e - 44
——————— = 0
110
STEP
4
:
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
5e-44
————— • 110 = 0 • 110
110
Now, on the left hand side, the 110 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
5e-44 = 0
Solving a Single Variable Equation:
4.2 Solve : 5e-44 = 0
Add 44 to both sides of the equation :
5e = 44
Divide both sides of the equation by 5:
e = 44/5 = 8.800
One solution was found :
e = 44/5 = 8.800
Answer:
e =44/5
Step-by-step explanation:
e 6
----- = --------
22 15
Using cross products
e * 15 = 6 *22
15e = 132
Divide by 15
15e/15 = 132/15
e =44/5
is f(x)=sqrt{x}+3x an exponential function?
Đạo hàm của sin(x)+ 5 bằng bao nhiêu
Answer:
cos(x).
Step-by-step explanation:
Derivative of sin(x) + 5
= cos(x).
Which of the following equations has only one solution?
Answer:
x^2 -6x+9 = 0
Step-by-step explanation:
x^2 -6x+9 = 0
Factor
(x-3)(x-3) =0
x=3
There is one solution with a multiplicity of 2
The stemplot below represents the number of bite-size snacks grabbed by 37 students in an activity for a statistics class.
A stemplot titled Number of snacks has values 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 21, 22, 23, 25, 25, 28, 32, 38, 42, 45.
Which of the following statements best describes the distribution?
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 15 to 45. There are no outliers.
The distribution of the number of snacks grabbed is symmetric with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
The distribution of the number of snacks grabbed is skewed left with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
Answer:
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
Step-by-step explanation:
First, we can see if the graph is symmetric. A symmetric graph is even on both sides of the center. As there are a lot more students that grabbed a small number of snacks, and the data is not even around the center (which is somewhere around 20 or 30 snacks). This means that the graph is not symmetric, making the second answer incorrect.
Next, we can check if the graph is skewed right or left. If the left of the graph represents a smaller amount of snacks and the right of it represents a higher number of snacks, we can see that most of the data is on the left of the graph. There are a few values to the right, but the overwhelming amount of data is on the left, making the distribution skewed to the right. This keeps the first and last answers possible
Moreover, we can find the center of the distribution. This is generally equal to the median, which is 18, so the center is around 18
After that, we can see what the values vary from. The lowest tens value is 1, and the lowest ones value in that is 2, making the lowest value 12. Similarly, the highest tens value is 4, and the highest ones value there is 5, making the range 12 to 45. This leaves the last answer, but we can check the outliers to make sure.
With the data, we can calculate the first quartile to be 15, the third quartile to be 21.5, and the interquartile range to be 21.5-15 = 6.75 . If a number is less than Q₁ - 1.5 * IQR or greater than Q₃ + 1.5 * IQR, it is a potential outlier. Applying that here, the lower bound for non-outliers is 15 - 6.5 * 1.5 = 5.25, and the upper bound if 21 + 6.5 * 1.5 = 30.75. No values are less than 5.25, but there are four values greater than 30.75 in 32, 38, 42, and 45. There are possible outliers at 38, 42, and 45, matching up with the last answer.
Step by step explanation need it
Answer:
8/17
Step-by-step explanation:
The sine of an angle is defined as the opposite side to the reference angle divided by the hypotenuse.
The side opposite the angle is always the side not connected to the reference angle. In this case the opposite side = ZY
The hypotenuse = XZ
Sin(X) = ZY/XZ
Sin(X) = 1634 = 8 / 17
Find the equation (in terms of x) of the line through the points (-2,-3) and (4,-1)
Answer:
y = 1/3x - 7/3
Step-by-step explanation:
y2 - y1 / x2 - x1
-1 - (-3) / 4 - (-2)
2/6
= 1/3
y = 1/3x + b
-1 = 1/3(4) + b
-1 = 4/3 + b
-7/3 = b
The least-squares regression equation
y = 968 – 3.34x can be used to predict the amount of monthly interest paid on a loan after x months. Suppose the amount of monthly interest after 30 months was $865.93.
What is the residual for the amount of monthly interest paid on a loan after 30 months?
–202.27
–1.87
1.87
202.27
Answer:
-1.87 (B)
865.93 - [968-3.34(30)] = -1.87
ED2021
represent -√2.3 and +√2.3 on number line
Answer:
-√2.3 on left of number line and zero and +√2.3 on right side of number line and zero
Step-by-step explanation:
solve the equation 7*2=?
Answer:
7*2=14
Step-by-step explanation:
7*2=14 because is multiplication
Answer:
14 because it is multiplication
Find an equation equivalent to r = 1 + 2 sin 0 in rectangular coordinates.
Answer:
C
Step-by-step explanation:
r=1+2sin(theta)
r^2=r+2*r*sin(theta)
x^2+y^2=±sqrt(x^2+y^2)+2y
can someone help me, please?
Answer:
0
2
-1
Step-by-step explanation:
from f(0) we find that
y = mx - 1
from f(-1) we find that the equation is
y = -3x - 1
1)
inverse f(x) :
x = -3y - 1
y = -(x + 1) / 3 x = -1
y = -(-1 + 1) / 3
y = 0
2)
y also equal to 0 since x = -1
3)
f^-1(2) = -(2+1) / 3
= -3/3
= -1
f(-1) = 2
At the beginning of a basketball season, the Spartans won 35 games out of 98 games. At this rate, how many games will they win in a normal 116 game season?
What is the perimeter of CDE?
A. 37.8 units
B. 39 units
C. 32.5 units
D. 35.6 units
This value is approximate.
=============================================================
Explanation:
To find the perimeter, we simply add up the lengths of the three external sides.
The horizontal side from D to E is 16 units long since |-10-6| = 16. I subtracted the x coordinates of the points and applied absolute value. You could also count out the spaces and you should count 16 spaces from D to E.
Unfortunately, the diagonal lengths aren't as straight forward. We have two options here: The pythagorean theorem, or the distance formula.
I'll go with the distance formula.
Let's find the distance from C to D, aka the length of side CD
[tex]C = (x1,y1) = (-1,-2)\\\\D = (x2,y2) = (-10,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-1-(-10))^2 + (-2-0)^2}\\\\d = \sqrt{(-1+10)^2 + (-2-0)^2}\\\\d = \sqrt{(9)^2 + (-2)^2}\\\\d = \sqrt{81 + 4}\\\\d = \sqrt{85}\\\\d \approx 9.2195\\\\[/tex]
Side CD is roughly 9.2195 units long.
Repeat this idea to find the length of CE
[tex]C = (x1,y1) = (-1,-2)\\\\E = (x2,y2) = (6,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-1-6)^2 + (-2-0)^2}\\\\d = \sqrt{(-7)^2 + (-2)^2}\\\\d = \sqrt{49 + 4}\\\\d = \sqrt{53}\\\\d \approx 7.2801\\\\[/tex]
Side CE is roughly 7.2801 units long
The perimeter of triangle CDE is approximately...
P = DE+CD+CE
P = 16 + 9.2195 + 7.2801
P = 32.4996
This then rounds to 32.5 units. The answer is choice C.
Solve the equation. If there is no solution, select no solution.
Answer:
no solution to the question
Answer:
4 2/3
Step-by-step explanation:
The two-step equation is solved regularly. The answer is 4 2/3.
One card is randomly selected from a deck of cards. Find the odds against drawing a black 10.
The odds against drawing a black ten are ___:___.
(Simplify your answers.)
Answer:
25/26 or 26/27 depending on free hands.
The first is if you don't use jokers/free cards
There is 13 cards in a single set, and a single 10 card.
Two sets are black and two sets a red.
Hearts, Spades, Clubs, and Diamonds
There is only 2 black tens out of 52 or 54 cards, so we can set it up as
50/52 or 52/54 which is simplified to
25/26 or 26/27 depending on free hands.
Step-by-step explanation:
I need to know the answer ASAP
Answer:
Step-by-step explanation:
ch of the following collections are w A collection of first six even number A collection of tall girls of class X. A collection of good football player A collection of wild animals. A collection of days of a week. he symbols e or €: {a, e, i, o, u}
Pls Tell question corretly
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that the first marble is white and the second marble is blue.
Answer:
3/56
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles.
The total number of marbles in the box
= 1 + 3 + 2 + 2
= 8 marbles
The probability that the first marble is white and the second marble is blue
= 3/8 * 1/7
= 3/56
Leonard made some muffins. He gave 5/8 of them to his grandmother and 10 muffins to his aunt. He then had 11 muffins left. How many muffins did he have at first?
Answer:
56
Step-by-step explanation:
x = number of muffins in total at the beginning.
x - 5/8 x - 10 = 11
x - 5/8 x = 21
8/8 x - 5/8 x = 21
3/8 x = 21
3x = 168
x = 56
Which ordered pair is a solution to the system of inequalities?
y > –x
y ≤ x + 1
A) (0,5)
B) (4,–1)
C) (1,3)
D) (–4,0)
9514 1404 393
Answer:
B) (4,–1)
Step-by-step explanation:
A graph can help you figure this out. The point (4, -1) is in the doubly-shaded area, so is a solution to this system.
==========================================================
Explanation:
Choice A can be ruled out because
[tex]y \le x+1\\\\5 \le 0+1\\\\5 \le 1\\\\[/tex]
which is false.
Choices C and D are similar, so they can be ruled out as well.
---------------------
Choice B is the answer because it makes both inequalities true.
If we plug the coordinates of (4,-1) into the first inequality, we get
[tex]y > -x\\\\-1 > -4[/tex]
which is a true statement because -1 is to the right of -4 on the number line.
Now try the other inequality
[tex]y \le x+1\\\\-1 \le 4+1\\\\-1 \le 5\\\\[/tex]
that's true also. So again, (4,-1) makes both inequalities true, and that's why choice B is the answer.
A large soda-pop manufacturer wants to introduce a new design for the label on one of its signature soda-pop drinks. The manufacturer selects a random sample of 150 customers from people who purchase the drink at a large sporting event. Each selected customer is asked whether or not he or she prefers the new design. If the manufacturer were to take a second random sample of 150 customers at the sporting event, the two samples would give somewhat different results in the proportion who prefer the new design. This variation is a source of
Answer:
This variation is a source of
response error.
Step-by-step explanation:
A response error shows the lack of accuracy in the customer responses to the survey questions. A response error can be caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements. Some responses are influenced by the answers provided to previous questions, which introduces response bias.
Compare the functions shown below:
f(x) = 7x + 3 g(x) tangent function with y intercept at 0, 2 h(x) = 2 sin(3x + π) − 1
Which of the following graphs is described by the function given below?
y = x2 - 6x-7
Answer:
A
Step-by-step explanation:
We are given the function:
[tex]\displaystyle y = x^2 - 6x - 7[/tex]
And we want to determine its graph.
One of the most important features of a quadratic is its vertex. So, we can start by finding the vertex using the formulas:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -6, and c = -7.
Find the x-coordinate of the vertex:
[tex]\displaystyle x = -\frac{(-6)}{2(1)} = 3[/tex]
Substitute this back into the equation to find the y-coordinate:
[tex]\displaystyle y(3) = -16[/tex]
Therefore, our vertex is at (3, -16).
The only graph whose quadratic's vertex is at (3, -16) is Graph A. Thus, our answer is A.
Which of the following behaviors would best describe someone who is listening and paying attention? a) Leaning toward the speaker O b) Interrupting the speaker to share their opinion c) Avoiding eye contact d) Asking questions to make sure they understand what's being said
Answer:
D
Step-by-step explanation:
If you ask questions while their speaking it shows that you are paying attention to them. Avoiding eye contact could mean your thinking about something else or you aren't interested. Interrupting them is just being disrespectful. Leaning towards them doesn't really do anything other than you moving.
needhdjdjdjdjdjdnhiskdjdjdjdjdjdjjshdjdjdjdjdjdjdjd
9514 1404 393
Answer:
-(√2)/2
Step-by-step explanation:
The expression evaluated at n=a gives the indeterminate form 0/0, so L'Hopital's rule can be used to find the limit. The second expression comes from differentiating numerator and denominator. Then the form with n=a is no longer indeterminate.
[tex]\displaystyle\lim_{n\to a}{\frac{\sqrt{2n}-\sqrt{3n-a}}{\sqrt{n}-\sqrt{a}}}=\lim_{n\to a}{\frac{\frac{2}{2\sqrt{2n}}-\frac{3}{2\sqrt{3n-a}}}{\frac{1}{2\sqrt{n}}-0}}\\\\=\sqrt{a}\left(\frac{2}{\sqrt{2a}}-\frac{3}{\sqrt{3a-a}}}\right)=\boxed{-\frac{1}{\sqrt{2}}}[/tex]
point k is between j and l. if jk = x^2 - 4x , kl = 3x - 2 and jl = 28 write and solve an equation to find the lengths of jk and kl
Answer:
JK=12
KI=16
Step-by-step explanation:
[tex]K\in\ [JI]\ \Rightarrow\ |JK|+| KI |=|KI|\\\\x^2-4x+3x-2=28\\\\\Longleftrightarrow\ x^2-x-30=0\\\\\\\Longleftrightarrow\ x^2+5x-6x-30=0\\\\\\\Longleftrightarrow\ x(x+5)-6(x+5)=0\\\\\\\Longleftrightarrow\ (x+5)(x-6)=0\\\\x=-5\ (excluded)\ or\x=6\\\\\\\Longleftrightarrow\ \\|JK|=x^2-4x=6^2-4*6=36-24=12\\|KI|=3x-2=3*6-2=18-2=16\\\\Proof: 12+16=28\\[/tex]
