Answer:
25
Step-by-step explanation:
225 divided by 9 is 25
Stretch
1. John has 15 bills in his wallet that total $145. He has a mix of five-dollar bills, ten-dollar bills, and twenty-
dollar bills. The number of ten-dollar bills is one less than twice the number of twenty-dollar bills.
a. Write a system of three linear equations in three variables to represent this situation. Be sure to
define your variables.
b. How many of each denomination does John have in his wallet? Solve this system using Gaussian
elimination.
John has 7 five-dollar bills, 5 ten-dollar bills and 3 twenty-dollar bills.
Total number of bills with John = 15
Total money with John = $145
John has a mix of $5, $10 and $20 bills
Let the number of $5 bills be x, $10 bills are y and $20 bills be z
Formulating the equations:
5x + 10y + 20z = 145-------(1)
x + y + z = 15--------(2)
As per the question, the number of ten dollar bills is one less than twice the number of twenty dollar bills:
y = 2z - 1
Putting y = 2z-1 in equating (1) and (2) we get:
5x + 10(2z-1) + 20z = 145
5x + 20z - 10 + 20z = 145
5x + 40z = 155--------(3)
x + y + z = 15
x + 2z - 1 + z = 15
x + 3z = 16--------(4)
Multiplying equation (4) with 5 and using Gaussian Elimination to equate (3) and (4)
5x + 40z = 155
5x + 15z = 80
25z = 75
z = 3
Putting z=3 in (4) we get
x = 7 and y = 5
So, John has 7 five-dollar bills, 5 ten-dollar bills and 3 twenty-dollar bills.
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Given a mean of 21 and a standard deviation of 1.2, what is the z-score of 21?
g The manager of a grocery store has selected a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is 1 minute. Refer to Exhibit 8-2. The 95% confidence interval for the average checkout time for all customers is _____. a. 2.804 to 3.196 b. 1.04 to 4.96 c. 1.36 to 4.64 d. 3 to 5
Answer:
The right solution is "0.196".
Step-by-step explanation:
The given values are:
Standard deviation,
\(\sigma=1 \ minute\)
Sample size,
\(n=100\)
Confidence level,
\(c=95\)%
\(=0.95\)
Now,
For \(\alpha=1-c\)
\(= 1-0.95\)
\(=0.05\)
then,
\(Z_{\frac{\alpha}{2} } = Z_{\frac{0.05}{2} }\)
\(=Z_{0.025}\)
\(=1.96\)
The margin or error will be:
⇒ \(E=Z_{\frac{\alpha}{2} } (\frac{\sigma}{\sqrt{n} })\)
On substituting the values, we get
= \(1.96(\frac{1}{\sqrt{100} })\)
= \(1.96\times \frac{1}{10}\)
= \(0.196\)
7p = 644. Solve the variable
Answer:
92
Step-by-step explanation:
you must first divided both sides of the equation by 7 then it will come to the answer p=92
3 (x + 7) = -12
x + 7 = ?
x = ?
Find out ? fast
Answer:
×=-11
Step-by-step explanation:
3x+21=-12
3×=-33
×=-11
Answer:
x=-11
x+7=-4
Step-by-step explanation:
3(x+7)=-12
3x+21=-12
3x=-12-21
3x=-33
x=-33/3
x=-11
-11+7=-4
When simplifying x^3 · x^2, the exponents are added together.
True
False
y
4
Solve for y.
Then, find the side lengths of the
largest triangle.
Fill in the green blank.
8
X
2
+
2
8
y
y
[?]
X
Enter
Help
Skip
Answer:
y = 4\(\sqrt{5}\) , ? = 10
Step-by-step explanation:
using Pythagoras' identity on the smallest right triangle
x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )
x = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)
using Pythagoras' identity on the middle right triangle
y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )
y = \(\sqrt{80}\) = \(\sqrt{16(5)}\) = \(\sqrt{16}\) × \(\sqrt{5}\) = 4\(\sqrt{5}\)
using Pythagoras' identity on the largest right triangle
?² = x² + y² = (2\(\sqrt{5}\) )² + (4\(\sqrt{5}\) )² = 20 + 80 = 100
Take square root of both sides
? = \(\sqrt{100}\) = 10
A physics class has students. Of these, students are physics majors and students are female. Of the physics majors, are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is nothing.\
Answer:
The probability that a randomly selected student is female or a physics major is 0.65.
Step-by-step explanation:
Note: This question is not complete. A complete is therefore provided before answering the question as follows:
A physics class has 40 students. Of these, 14 students are physics majors and 18 students are female. Of the physics majors, six are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is_______.
The Step-by-step explanation is therefore provided now as follows:
The probability that a randomly selected student is female or a physics major can be calculated using the following formula:
P(PM or F) = P(PM) + P(F) - P(PMF)
Where;
P(PM or F) = Probability of student selected is Physics Major or Female = ?
P(PM) = Probability of student selected is Physics Major = Number of Physics Major / Total number of students in the Physics class = 14 / 40 = 0.35
P(F) = Probability of student selected is Female = Number of female students in the Physics class / Total number students in the Physics class = 18 / 40 = 0.45
P(PMF) = Probability of student selected is Physics Major and Female = Number Physics Major that female in the Physics class / Total number students in the Physics class = 6 / 40 = 0.15
Substituting the values into equation (1), we have:
P(PM or F) = 0.35 + 0.45 - 0.15 = 0.65
Therefore, the probability that a randomly selected student is female or a physics major is 0.65.
Answer:
what is the physics question
Step-by-step explanation:
ab-c/d has a value of 24. write the values if :-
1- a, b, c, d are all positive.
2- a, b, c, d are all negative.
3- a, b, c, d are mixed of negative and positive.
WRITE ANSWERS FOR 1, 2 AND 3
The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24
Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.
Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9
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John had $55 He spent $3 per day for nine days. Then he was given $12 to divide equally between himself and his two cousins. John used the following expression to calculate the ar
after splitting the money with his cousins
Based on this expression, what is the amount of money John had remaining?
Answer:
$32
Step-by-step explanation:
55-(9•3)+4
Solve for 2x-3y=5 for y
Answer:
Y = -5/3 + 2/3x
Step-by-step explanation:
subtract x to the other side
Then divide the equation by -3
Solve for j ??????????????????????????
Answer:
j=24
Step-by-step explanation:
j/8 - 2 = 1
j/8 - 2 + 2 = 1 + 2
j/8 = 3
8 * j/8 = 8 * 3
j=24
. Where is the vertex of the graph that represents y=(x−2)2−8 ? Type the answers in the boxes below. ( , ) b. Where is the y -intercept? Type the answers in the boxes below.
The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.
Given equation :
y=(x−2)2−8
y = 2x - 4 - 8
= 2x - 12
The final equation is y = 2x - 12.
Compare this equation with slope and y-intercept formula :
y = mx+c
So that c = -12
The value of y-intercept according to the solution is -12.
To find the vertex. Let's assume x=0; Substitute in the equation
y = 2(0) -12
y = -12
The first vertex will be (0, -12)
If x = 1; y = 2(1) -12
y = -10
Then the second vertex will be (1, -10).
Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.
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Consider the line 4x + 7y=-1.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
1. the slop of a line perpendicular to that line is: 7/4.
2. the slope of a line parallel to that line is: - 4/7
Step-by-step explanation:
To get the perpendicular line you have to find the negative reciprocal of the slope of the original line. and lines with the same slope are parallel.
Find the surface area. please help me
Answer
248.3712
Step-by-step explanation:
2(H*W)+2(H*L)
2(5.78*6.72)+2(6.72*12.7)= 248.3712
for which values of (A) the system has at least one solution
Answer
The values of a that ensures that the system has at least one solution is
a > (21/127)
Explanation
We are told to find the values of a that ensures that the system has at least one solution. The system of equations include
3 (a - 5x) < 1 + x
2 - (x/2) > 3 + 5 (x - a)
To do this, we need to solve the expressions
3 (a - 5x) < 1 + x
3a - 15x < 1 + x
We can rewrite this as
1 + x > 3a - 15x
x + 15x > 3a - 1
16x > 3a - 1
Divide both sides 16
\(\begin{gathered} \frac{16x}{16}>\frac{3a-1}{16} \\ x>\frac{3a}{16}-\frac{1}{16} \end{gathered}\)We then solve the second one. But to do this, let's multiply through by 2
2 - (x/2) > 3 + 5 (x - a)
4 - x > 6 + 10 (x - a)
we can rewrite as
6 + 10 (x - a) < 4 - x
6 + 10x - 10a < 4 - x
10x + x < 10a - 6 + 4
11x < 10a - 2
Divide both sides by 11
\(\begin{gathered} \frac{11x}{11}<\frac{10a-2}{11} \\ x<\frac{10a}{11}-\frac{2}{11} \end{gathered}\)The two solutions are
x > (3a/16) - (1/16)
x < (10a/11) - (2/11)
To find a lasting solution, we need the inequality sign to be the same, so, we need to multiply through one of the equations by -1
x > (3a/16) - (1/16)
-x < (-3a/16) + (1/16)
So, the system of equations become
-x < (-3a/16) + (1/16)
x < (10a/11) - (2/11)
We can then add the two equations
-x + x < (-3a/16) + (1/16) + (10a/11) - (2/11)
0 < (-3a/16) + (10a/11) + (1/16) - (2/11)
0 < -0.1875a + 0.9091a + 0.0625 - 0.1818
0 < 0.7216a - 0.1193
Rewrite
0.7216a - 0.1193 > 0
0.7216a > 0.1193
Divide both sides by 0.7216
(0.7216a/0.7216) > (0.1193/0.7216)
a > 0.1653
a > (21/127)
Hope this Helps!!!
Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41
Answer:
25000
Step-by-step explanation:
Suppose that y varies directly with x
and y = 10 when x = 20. What is y
when x = 15?
Enter your answer as a simplified fraction.
?
y =
Answer:
Step-by-step explanation:
15/2
Simplify (5 to the power of 1/3) to the power of 3
Answer:
C
Step-by-step explanation:
Multiply the exponents
Reduce the gcf
Hope ghis helps! :)
Given just the graph what 3 steps are required to write the equation of a line?
Answer:
Step-by-step explanation:
step 1:
determining the values for standard form for the equation of a line,
y = mx + c
Step 2:
calculation of m, where m is the gradient or slope which determines how steep the line is.
step 3:
calculation of c, where c is the height at which the line crosses the y - axis also known as y - intercept
13) Which graph represents a non-proportional relationship?
Answer:
B
Step-by-step explanation:
Proportional relationships go through the origin (0,0) and have a constant rate of change.
Regarding proportional relationships, when graphed the line should be straight and go through the origin (0,0)
All graphs appear to have straight lines.
However graph B has a line that doesn't go through the origin, therefore B represents a non proportional relationship
What is the equation for
7x - 4/y =10
in the form y = mx + b?
Answer:
Step-by-step explanation:
assume the equation is (7x-4)/y=10
10y= 7x-4 didvide both sides by 10
y= (7/10)*x - (2/5)
m=7/10
b=-2/5
The equation for 7x - 4/y =10 in the form y = mx + b . The equation in the form
\(\(y = mx + b\) is: \[y = \frac{4}{7x - 10}\]\)
To rewrite the equation in the form we need to \(\(y = mx + b\),\) isolate the term involving y on one side of the equation. Here's the step-by-step process:
Step 1: Add \(\(\frac{4}{y}\)\) to both sides of the equation to isolate the 7x term on the left side:
\(\[7x = 10 + \frac{4}{y}\]\)
Step 2: Get rid of the fraction by multiplying both sides of the equation by y:
\(\[7xy = 10y + 4\]\)
Step 3: Now, we want to express y alone on one side. To do this, subtract 10y from both sides:
\(\[7xy = 10y + 4\]\)
Step 4: Factor out y on the left side:
\(\[y(7x - 10) = 4\]\)
Step 5: Finally, divide both sides by to solve for \(\((7x - 10)\)\)
\(\[y = \frac{4}{7x - 10}\]\)
Now, the equation is in the form where \(\(y = mx + b\), \(m\)\) is the coefficient of x and b is the constant term. In this case,\(\(m = \frac{4}{7x - 10}\) and \(b\)\) is equal to 0.
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Please look at the photo. Thank you!
The zeros with each multiplicity are given as follows:
Multiplicity one: x = 6.Multiplicity two: x = 11.Multiplicity three: x = -6 and x = -5.How to obtain the multiplicities?The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
Considering the linear factors of the function in this problem, the zeros are given as follows:
(x + 6)³ -> zero at x = -6 with multiplicity of 3.(x - 11)² -> zero at x = 11 with multiplicity of 2.x - 6 -> zero at x = 6 with multiplicity of 1.(x + 5)³ -> zero at x = -5 with multiplicity of 3.More can be learned about the Factor Theorem at brainly.com/question/24729294
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Best answer gets brain ly
The new coordinates of the image of the shape are
(3, -2) (2, -2) (2, -4)The picture of the graph showing the image is attached
How to make a 90 degrees clockwise rotationThe rule for 90 degrees clockwise rotation is
(x, y) becomes (y, -x)
The rule involves interchanging the coordinates of the ordered pair such that x takes the place of y and y tales the place of x and a change of sign
performing the rotation we have the new coordinates as below
(2, 3) becomes (3, -2)
(2, 2) becomes (2, -2)
(4, 2) becomes (2, -4)
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please help me 80% of what number is 16
What is the part?
What is the total?
What is the percent?
What is the answer?
Answer:
80 percent of 16 is 12.8 I'm sorry but that's all I know
Alvin had 30 beads more than Bobby Cathy had thrice as many beads as
Alvin. They had a total of 345 beads. How many beads did Bobby have?
Answer:
Bobby has 45 beads
Step-by-step explanation:
Let x be the number of beads Bobby has.
Then, (x + 30) is the number of beads Alvin has.
Then, 3 (x + 30) is the number of beads Cathy has.
3 (x + 30) + (x + 30) + x = 345
3x + 90 + x + 30 + x = 345
5x + 120 = 345
5x = 225
x = 45
Therefore, Bobby has 45 beads.
I need the answers for those IMMEDIATELY ! Thank you!
Answer:
Hope this helped.
Step-by-step explanation:
2:x=2y+20 y=1/2x-10
4:x=4/5y+15/5 y=5/4x-4
6:x=-2y+10 y=-1/2x+5
8:x=-7/3y+100/3 y=-3/7x+100/7
For a left-tailed test based on a sample of 18 observations with the test statistic t = 1.9, what is the associated p-value?
The associated p-value for this left-tailed t-test is 0.0359 or 3.59%.
Now, The p-value for a one-tailed t-test with a sample size of 18 and a test statistic of 1.9,
Hence, we need to look up the t-distribution table.
So, Using a one-tailed test with,
df = n - 1
= 18 - 1 = 17 degrees of freedom
We find that the area to the left of 1.9 under the curve is 0.0359.
This means that there is a 3.59% probability of observing a t-statistic less than or equal to 1.9 if the null hypothesis is true.
Therefore, the associated p-value for this left-tailed t-test is 0.0359 or 3.59%.
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What is 6.92 x 10^ -3 written in standard form ?
Answer:
6.92 x 1,000= 6,920
Step-by-step explanation: Hope this helps
Write an equation in slope-intercept form of the line that passes through the points (7, – 4) and (3, -1).
y= blank x+ blank
Answer:
Step-by-step explanation:
y2-y1/x2-x1
-1-(-4)/3-7
3/-4
y=mx+b
For the y coordinate it can be either -4,or -1
-4=3/-4x+b
b=13/4