Answer:
ACT Score performed better.
Step-by-step explanation:
Given :
ACT :
Mean score, μ = 21.2
Standard deviation, σ = 5.1
Score, x = 26
SAT :
Mean score, μ = 1498
Standard deviation, σ = 347
Score, x = 1800
To know which score is better, we obtain the standardized, Z score of the two examination :
Zscore = (x - μ) / σ
ACT Zscore :
(26 - 21.2) / 5.1
Zscore = 4.8 / 5.1 = 0.941
ACT Zscore = 0.941
SAT Zscore :
(1800 - 1498) / 347
Zscore = 302 / 347 = 0.870
SAT Zscore = 0.870
The student with the higher Zscore performed better :
ACT Zscore > SAT Zscore
Sam's monthly bills are normally distributed with mean 2700 and standard deviation 230.9. He receives two paychecks of $1500 each in a month, post taxes and withholdings. What is the probability that his expenses will exceed his income in the following month?Ð) 10%. B) 16%.C) 21%.D) 29%.E) 37%.
Answer:
A) 10%
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Sam's monthly bills are normally distributed with mean 2700 and standard deviation 230.9.
This means that [tex]\mu = 2700, \sigma = 230.9[/tex]
What is the probability that his expenses will exceed his income in the following month?
Expenses above 2*1500 = $3000, which is 1 subtracted by the p-value of Z when X = 3000.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3000 - 2700}{230.9}[/tex]
[tex]Z = 1.3[/tex]
[tex]Z = 1.3[/tex] has a p-value of 0.9032.
1 - 0.9032 = 0.0968 that is, close to 10%, and thus the correct answer is given by option A.
find the missing length indicated.
Answer:
192
Step-by-step explanation:
x is the altitude of the right triangle. Thus, we would apply the geometric mean theorem to find the value of x. Thus, the formula is given as:
h = √(ab)
Where,
h = altitude = x
a = 144
b = 400 - 144 = 256
Plug in the given values into the formula
x = √(144*256)
x = √(36,864)
x = 192
Find the equation of the line passing through (4,1) and perpendicular to the line whose equation is 1x-3y-4=0
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Answer:
3x +y -13 = 0
Step-by-step explanation:
The perpendicular line will have the variable coefficients swapped and one of them negated. The new constant will be appropriate to the given point.
3(x -4) +1(y -1) = -0
3x +y -13 = 0
_____
Additional comment
The given equation is in "general form", so that is the form of the equation we have given as the answer. This form is convenient in that the general form equation for a line through the origin, ax+by=0, is easily translated to make it pass through a point (h, k): a(x -h) +b(y -k) = 0. Eliminating parentheses puts the equation back into general form.
I need help with this ASAP!!!
Answer:
y=-4x-6
Step-by-step explanation:
It jwust is mwannn
Helen is constructing a room. She is preparing a scale drawing of her room as 1 cm = 2.5 feet. Find the actual dimensions with the given model dimensions of 8 cm×5 cm.
20 feet×12.5 feet
15 feet×5.5 feet
10 feet×8 feet
8 feet×6.5 feet
Answer: 20 ft × 12.5 ft
Step-by-step explanation:
Since 1 cm = 2.5 ft,
8 cm = 8 · 2.5 = 20 ft5 cm = 5 · 2.5 = 12.5 ftTherefore, 8 cm × 5 cm = 20 ft × 12.5 ft
Write the phrase "the product of 19 and a number" as a mathematical expression.
A) 19 + x
B) 19 - X
C) 19x
OD) 19/x
Answer:
c
Step-by-step explanation:
product is the answer to a multiplication problem.
Could someone possibly help me with this
Answer:
40
Step-by-step explanation:
The shape has 6 sides a,b,c,d,e,f
The perimeter is the sum of the sides
P = a+b+c+d+e +f
4 of the sides add to 195 a+b+c+d = 195 Replace in the equation
P = 195 +e+f
We know that e and f are equal
P = 195+f+f
P = 195+2f
The perimeter is 275
275=195+2f
Subtract 195 from each side
275 -195 = 195+2f-195
80 = 2f
Divide by 2
80/2 = 2f/2
40 =f
The other 2 sides are 40 ft each
what's the difference between -1/2 and 1/6
Answer: -4/6 or -2/3
Step-by-step explanation:
First, you find a common denominator among the fractions, which would be 6.
Convert -1/2 to have 6 as its denominator.
-1/2* 3/3 = -3/6
And then subtract them.
-3/6 - 1/6 = -4/6
-4/6 simplified is -2/3
When you subtract a positive number from a negative number, you are adding their absolute values.
Use implicit differentiation to solve that the derivative
Given
e ˣʸ = sec(x ²)
take the derivative of both sides:
d/dx [e ˣʸ] = d/dx [sec(x ²)]
Use the chain rule:
e ˣʸ d/dx [xy] = sec(x ²) tan(x ²) d/dx [x ²]
Use the product rule on the left, and the power rule on the right:
e ˣʸ (x dy/dx + y) = sec(x ²) tan(x ²) (2x)
Solve for dy/dx :
e ˣʸ (x dy/dx + y) = 2x sec(x ²) tan(x ²)
x dy/dx + y = 2x e ⁻ˣʸ sec(x ²) tan(x ²)
x dy/dx = 2x e ⁻ˣʸ sec(x ²) tan(x ²) - y
dy/dx = 2e ⁻ˣʸ sec(x ²) tan(x ²) - y/x
Since e ˣʸ = sec(x ²), we simplify further to get
dy/dx = 2 tan(x ²) - y/x
What is the slope of the line?
-3
-1/3
1/3
3
Answer:
D) 3
Step-by-step explanation:
Rise/run, rise is 3, run is 1
Answer:
3
Step-by-step explanation:
Pick two points on the line
(0,0) and ( 1,3)
The slope is found by
m = ( y2-y1)/(x2-x1)
= ( 3-0)/(1-0)
= 3/1
= 3
can you please answer this????
Answer:
x = 5
Step-by-step explanation:
I'm taking all bases as b so not typing it
2/3 log 125 = log (125^2/3) = log 25
1/2 log 9 = log (9^1/2) = log 3
So we can rewrite the equation as,
log x = log 25 + log 3 - log 15
or, log x = log (25×3) - log 15
or, log x = log 75 - log 15
or, log x = log (75/15)
or, log x = log 5
or, x = 5
Answered by GAUTHMATH
Y
X
Pls help me you’ll get 29 points
Answer:
x = 60
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+x+x = 180
3x = 180
Divide by 3
3x/3 =180/3
x = 60
A car travels 60 kilometers in one hour before a piston breaks, then travels at 30 kilometers per hour for the remaining 60 kilometers to its destination. What is its average speed in kilometers per hour for the entire trip?
Answer:
Total Distance : 1*60 +60=120
Total time taken = 1+ 60/30= 1+2=3
Hence average speed for the trip = 120/3= 40 kmph
Hence Answer is 40
Step-by-step explanation:
The average speed is 40 km/h.
What is Average speed?The average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as:
Average Speed Formula:Average Speed = Total distance covered ÷ Total time taken
Example:
sing the average speed formula, find the average speed of Sam, who covers the first 200 kilometers in 4 hours and the next 160 kilometers in another 4 hours.
Solution:
To find the average speed we need the total distance and the total time.
Total distance covered by Sam = 200Km + 160 km = 360 km
Total time taken by Sam = 4 hour + 4 hour = 8 hour
Average Speed = Total distance covered ÷ Total time taken
Average Speed = 360 ÷ 8 = 45km/hr
Given:
d1= 60 km
d2= 30
d3 = 60
Total Distance : 1*60 +60=120
Total time taken = 1+ 60/30= 1+2=3
Now,
average speed = total distance/ total time taken
= 120/3
= 40 kmph
Learn more about average speed here;
https://brainly.com/question/12322912
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A class of 24 students is planning a field trip to a science museum. A nonrefundable deposit of $50 is required for the day-long program, plus a charge of $4.50 per student.
Determine a linear function that models the cost, c, and the number of students, s.
Answer:
c = 4.50s + 50
Step-by-step explanation:
50 is a flat rate so it is a constant. 4.50 is the charge per student so it would be multiplied by the total number of students s.
Answer:
This is the linear function: c = 4.5s + 50
This is the cost if all 24 students came along: $158.00
Step-by-step explanation:
C is the total cost, it is $4.50 per student coming, and there is a $50 non refundable deposit for the program. So, if all 24 students came along for the trip, you would do 24 times $4.50 which is $108 and then add the additional $50 for the nonrefundable deposit, making the total $158.
Suppose that the functions and g are defined for all real numbers x as follows.
f(x)=x+6
g(x) = 2x + 6
Write the expressions for (f-g)(x) and (fg)(x) and evaluate (f+g)(1).
Answer:
Step-by-step explanation:
Given functions are,
f(x) = x + 6
g(x) = 2x + 6
(f - g)(x) = (x + 6) - (2x + 6)
= -x
(f . g)(x) = f(x) × g(x)
= (x + 6)(2x + 6)
= 2x² + 6x + 12x + 36
= 2x² + 18x + 36
(f + g)(x) = (x + 6) + (2x + 6)
= 3x + 12
(f + g)(1) = 3(1) + 12
= 15
5. Sam wrote the expression below.
10 +15k
Rami said that this expression is equivalent to 5(3k + a)
Kenneth said this expression is equivalent toyk+6+8k+4.
Who is correct and why? Explain your thinking clearly,
Answer:
see below
Step-by-step explanation:
10 + 15k
Factor out the greatest common factor 5
5( 2+3k)
Rewriting
5(3k+2)
Rami is correct if a=2 then his expression is 5(3k+2)
Kenneth
yk+6+8k+4
Add the terms together
k(y+8) + 10
If y =7 then Kenneth is correct otherwise he is incorrect
Answer plssssssss!!!!!!
Answer:
the answer is 40.27
Step-by-step explanation:
37.99 × 6%= 2.28
37.99+2.28= 40.27
A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 9 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 8.5.(a) Is it appropriate to use a Student's t distribution? Explain.Yes, because the x distribution is mound-shaped and symmetric and Ï is unknown.No, the x distribution is skewed left. No, the x distribution is skewed right.No, the x distribution is not symmetric.No, Ï is known.How many degrees of freedom do we use?(b) What are the hypotheses?H0: μ = 8.5; H1: μ > 8.5H0: μ = 8.5; H1: μ â 8.5 H0: μ = 8.5; H1: μ < 8.5H0: μ < 8.5; H1: μ = 8.5H0: μ > 8.5; H1: μ = 8.5(c) Compute the t value of the sample test statistic. (Round your answer to three decimal places.)t =(d) Estimate the P-value for the test.P-value > 0.2500.100 < P-value < 0.250 0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010(e) Do we reject or fail to reject H0?At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.(f) Interpret the results.There is sufficient evidence at the 0.05 level to reject the null hypothesis.There is insufficient evidence at the 0.05 level to reject the null hypothesis.
Answer:
1.) Yes, because the x distribution is mound-shaped and symmetric and σ is unknown. ;
df = 24 ;
H0 : μ = 8.5
H1 : μ ≠ 8.5 ;
1.250 ;
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
There is insufficient evidence at the 0.05 level to reject the null hypothesis.
Step-by-step explanation:
Given :
Sample size, n = 25
xbar = 9 ; Standard deviation, s = 2
α = 0.05 ;
The degree of freedom, df = n - 1 ; 25 - 1 = 24
The hypothesis (two tailed)
H0 : μ = 8.5
H1 : μ ≠ 8.5
The test statistic :
(xbar - μ) ÷ (s/√(n))
(9 - 8.5) ÷ (2/√(25))
0.5 / 0.4
Test statistic = 1.250
The Pvalue from Tscore ;
Pvalue(1.250, 24) = 0.2234
Pvalue > α ; We fail to reject H0 ;
Suppose you want to have $400,000 for retirement in 35 years. Your account earns 9% interest. a) How much would you need to deposit in the account each month? b) How much interest will you earn? $
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Answer:
a) $135.97
b) $342,892.60
Step-by-step explanation:
a) The attached spreadsheet shows the use of the "payment" function for determining the amount of a payment that will give the desired future value. It shows the deposit needs to be $135.97 per month.
__
b) The interest earned is the difference between 420 payments and the account balance. The interest amount is $342,892.60.
Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with z arbitrary
Write each equation in standard form:
3x + y + 3z = 11
x + 2y + z = 7
-x + y + z = 0
In matrix form, this is
[tex]\begin{bmatrix}3&1&3\\1&2&1\\-1&1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}11\\7\\0\end{bmatrix}[/tex]
and in augmented matrix form,
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\1&2&1&7\\-1&1&1&0\end{bmatrix}\right][/tex]
Now for the row operations:
• Add row 1 to -3 (row 2), and add row 1 to 3 (row 3):
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&-5&0&-10\\0&4&6&11\end{bmatrix}\right][/tex]
• Multiply row 2 by -1/5:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&4&6&11\end{bmatrix}\right][/tex]
• Add -4 (row 2) to row 3:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&6&3\end{bmatrix}\right][/tex]
• Multiply row 3 by 1/6:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
• Add -1 (row 2) and -3 (row 3) to row 1:
[tex]\left[\begin{array}{ccc|c}3&0&0&\frac{15}2\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
• Mutiply row 1 by 1/3:
[tex]\left[\begin{array}{ccc|c}1&0&0&\frac52\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
Then the solution to the system is (x, y, z) = (5/2, 2, 1/2).
Help on #9 thank you
Find the product of these complex numbers.
(8 + 5)(6 + 3) =
Identify the first 4 terms in the arithmetic sequence given by the explicit formula ƒ(n) = 8 + 3(n – 1).
Answer:
Step-by-step explanation:
f(n) = 8 + 3(n) - 3
f(n) = 5 + 3n
f(1) = 5 + 3(1)
f(1) = 8
f(2) = 5 + 3(2)
f(2) = 5 + 6
f(2) = 11
f(3) = 5 + 3*3
f(3) = 14
f(4) = 5 + 3*4
f(4) = 17
In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.
Graph of two intersecting lines. The line g of x is solid and goes through the points 0, 2, negative 2, 0 and is shaded in below the line. The other line f of x is dashed, and goes through the points 0, 6, 3, 0 and is shaded in below the line.
The graph represents which system of inequalities?
y < −2x + 6
y ≤ x + 2
y ≤ −2x + 6
y < x + 2
y < 2 over 3x − 2
y ≥ 2x + 2
None of the above
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Answer:
y < −2x + 6y ≤ x + 2Step-by-step explanation:
The line with the y-intercept of 2 is solid, so the corresponding inequality will be of the form ...
y ≤ mx +2
The line with the y-intercept of 6 is dashed, so the corresponding inequality will be of the form ...
y < mx +6
The answer choice showing inequalities with these forms is ...
y < −2x + 6y ≤ x + 2Answer:
None of the above I think
Step-by-step explanation:
Suppose that the value of a stock varies each day from $12.82 to $28.17 with a uniform distribution.
Find the third quartile; 75% of all days the stock is below what value? (Enter your answer to the nearest cent.)
Answer: 24.33
======================================================
Explanation:
The range is
range = max - min
range = 28.17 - 12.82
range = 15.35
This is the width of this particular uniform distribution.
Apply 75% to this value
75% of 15.35 = 0.75*15.35 = 11.5125
Then finally, add that to the min
12.82 + 11.5125 = 24.3325 which rounds to 24.33
We can see that 75% of the values are below 24.33 which makes it the 3rd quartile (Q3).
round 11 7/16 to the nearest whole number
Answer:
11
Step-by-step explanation:
Step 1: Round [tex]11 \frac{7}{16}[/tex] to the nearest whole number
In order to round up, the fraction must be greater or equal to 1/2. However, in our problem, it is less than half which means that we do not round up. Therefore, the answer is 11.
Answer: 11
Simplify.
2 x (3-1) + 3
07
8
O 10
O 11
Answer:
7
Step-by-step explanation:
2 x (3-1) + 3
Evaluate using PEMDAS
Parenthesis
Exponents
Math and Division ( left to right )
Addition and Subtraction ( left to right )
2 x (3-1) + 3
According to PEMDAS we do the operations inside of the parenthesis first
3 - 1 = 2
We now have: 2 x 2 + 3
Next we do exponents
There are no exponents so let's move on to multiplication and division
There is indeed multiplication so we do it
2 x 2 = 4
We now have: 4 + 3
Finally we do the addition
4 + 3 = 7
The answer is 7
Complete factorization x^3-2x^2+x-2
Answer:
[tex]{ \tt{ {x}^{3} - 2 {x}^{2} + x - 2 }} \\ = { \tt{(x - 2)(x - i)(x + i)}}[/tex]
in a box of stones,the ratio of red marbles to total marbles 2:5. The ratio of green stone to total stones is 3:10. If the stones that are neither red nor green is blue,how many blue stones are the box if there are 40marbles in the box?
Answer:
12 blue marbles
Step-by-step explanation:
multiply 2:5 by 8 to get 16:40
multiply 3:10 by 4 to get 12:40
add 16 to 12 to get 28
Subtract 28 from 40 to get 12
Ultimately, you have 12 blue marbles
The given ratios can be expressed as fractions, from which the number of
each colored marble can be found.
The number of blue marbles in the box are 12 blue marbles.Reasons:
Red : Total = 2:5
Green : Total = 3:10
Stones that are neither red nor green is blue
Number of marbles (stones) in the box = 40 marbles
Required:
The number of blue stones in the box.
Solution:
Let x represent the b in the box, let R = red stones, G = green stones, and B = blue stones, we have;
x = 40
Expressing the ratios as fractions gives;
[tex]\dfrac{R}{x} = \dfrac{2}{5}[/tex]Therefore;
[tex]R= \dfrac{2}{5} \times x[/tex]
[tex]R= \dfrac{2}{5} \times 40 = 16[/tex]
The number of red stones, R = 16
Similarly, we have
[tex]\dfrac{G}{x} = \dfrac{3}{10}[/tex][tex]G = \dfrac{3}{10} \times x[/tex]
Therefore;
[tex]G = \dfrac{3}{10} \times 40 = 12[/tex]
The number of green stones, G = 12
B = x - (R + G)
Therefore;
B = 40 - (16 + 12) = 12
The number of blue marbles, B = 12 marbles.Learn more here:
https://brainly.com/question/3957420
What is the value of the expression 10(n-6) when 4=14
Answer:
it's going to be 4n so its going to be 4...
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
Assuming you meant when n=14
10(n-6)
plug in 14 for n
10(14-6)
work out parenthesis first
10(8)=
80
