Using proportions, her gross pay is given as follows:
d. $779.10.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Her gross pay is divided as follows:
$14.70 for 33 hours.2 x $14.70 for 10 hours.Hence the total pay is:
33 x 14.70 + 2 x 10 x 14.70 = $779.10.
Which means that option d is correct.
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The data in the tables below were collected from first year students at a community college. The variable is “number of credit cards.” Two of the probabilities are missing.
Number of credit cards 0 1 2 3 4 5
Number of students 122 40 28 2 2 6
Based on this data, we can estimate the probability that a randomly selected student has X number of credit cards using relative frequencies to create a probability distribution. Note: There are 200 students.
Number of credit cards 0 1 2 3 4 5
Probability 0.14 0.01 0.01 0.03
Use this information to answer the first two questions below.
What is P(0)? (Hint: Find the relative frequency for this outcome. There are 200 students in the data set.)
The probability that number of credit cards is 0 is 0.61
What is Probability ?Probability is the likeliness of an event to happen ,
It has a range from 0 to 1 , where 0 indicates uncertainty while 1 indicates certainty
The data for the college students is given and it has been asked to determine P(0)
The total students are 200
and the students that have no credit card from the data is 122
Therefore
P(0) = 122/200 = 0.61
Therefore the probability that number of credit cards is 0 is 0.61
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Which numbers are perfect squares? Check all that apply. 02 016 018 032 0 044 094 100
Answer:
16, 100
Step-by-step explanation:
A perfect square is a number that can be achieved by multiplying a number by itself.
Example: 100 = 10 x 10, so it is a perfect square
2 is not a perfect square because it has no factors that can be multiplied with each other to equal 2. An easy way to check is to use the square root function on your calculator.
If the result is a whole number then it's a perfect square.
Perform the operation. 3/a^2b + 2/ab^2
The simplified form of the expression is 3b+2a/(ab)²
Sum of fractionsFractions are written as a ratio of two integers. Given the expression below;
3/a^2b + 2/ab^2
Find the LCM
3/a^2b + 2/ab^2 = 3b+2a/a²b²
3/a^2b + 2/ab^2 = 3b+2a/(ab)²
Hence the simplified form of the expression is 3b+2a/(ab)²
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How do you compute -3+9-7
Answer:
-1
Step-by-step explanation:
-3 + 9 = 6, 6 - 7 = -1
Given the quadratic equation: x^(2)+6=0, find all solutions for x
Answer:
[tex]x=i\sqrt6[/tex]
[tex]x=-i\sqrt6[/tex]
Step-by-step explanation:
x^2=-6
x=[tex]\sqrt-6[/tex]
Suzanne is looking at taking out a personal loan. Opportunity Loans is offering her $1600 at 3.45% for 1 year, with interest compounding monthly. General Loans is offering her $1600 at 4.2% for 1 year, with interest compounding quarterly. Assuming she makes no payments until the 1 year is up, how much interest will have accrued on each loan? On which loan will she earn the least amount of interest?
Step-by-step explanation:
So the general formula for compound interest is [tex]A = P(1+\frac{r}{n})^{nt}[/tex] where r is the interest rate, t is the time in years, and n is the amount of compounds per year. So plugging in the values for both equations you'll get
Opportunity Loans:
[tex]A = 1600(1+\frac{0.0345}{12})^{(12)(1)}[/tex]
[tex]A = 1600(1.002875)^{12}[/tex]
[tex]A \approx 1600(1.035)[/tex]
[tex]A = \$1,656.08[/tex]
Now to find the interest accrued on this loan you simply subtract 1600 from the A or final amount
[tex]Interest=1656.08-1600\\Interest=56.08[/tex]
General Loans:
[tex]A = 1600(1+\frac{0.042}{4})^{(4)(1)}[/tex]
[tex]A = 1600(1.0105)^4[/tex]
[tex]A \approx 1600(1.042)[/tex]
[tex]A = 1,668.27[/tex]
To find the interest we do the same thing we did in the previous problem
[tex]interest = 1668.27-1600\\interest=68.27[/tex]
Opportunity loans has the least amount of interest after a year
Use finite differences to determine whether each relationship is linear, quadratic, or
neither.
x y
-5 17
-4 7
-3 1
-2 -1
-1 1
The function relationship is a quadratic function
How to determine the function type?The function is given as:
x y
-5 17
-4 7
-3 1
-2 -1
-1 1
Remove the x values:
y: 17 7 1 -1 1
Calculate the difference between the consecutive y values
Difference: 10 6 2 -2
Because the first difference are not equal, it means that the function is not a linear function.
Calculate the difference between the above differences
Difference: 4 4 4
Because the second differences are equal, it means that the function is a quadratic function.
Hence, the function relationship is a quadratic function
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Jason has exactly four wooden toy blocks with digits on them. Two of the blocks have the digit 0, one of the blocks has the digit 1, and one of the blocks has the digit 2. How many distinct positive integers can he form using one or more of the blocks, without using each block more than once?
The number of positive integers is 24
How to determine the number of positive integers?The digits of the wooden toys are:
0, 0, 1, 2
Since each block cannot be used more than once, and there are four blocks in total;
The number of positive integers is;
Integers = 4!
Expand
Integers = 4 * 3 * 2 * 1
Evaluate
Integers = 24
Hence, the number of positive integers is 24
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In the diagram of AABC shown below, DE || BC.
B
A
3) 3
4) 15
E
If AB= 10, AD = 8, and AE = 12, what is the
length of EC?
1) 6
2) 2
C
dd or create
k as done
nments
As
to Susan Guha
Answer:
3
Step-by-step explanation:
AD/AB = AE/AC
8/10 = 12/AC
AC = 12(10/8) = 15
EC = 15 - 12 = 3
By visual inspection, determine the best-fitting regression model for the
scatterplot,
Answer:
Linear
Step-by-step explanation:
The line is relatively straight.
{(4z-7,z-4,z) |z is any real number} z=-5
The set when z = -5 is {-27, -9, -5}
How to determine the set elements?The set is given as:
{(4z-7,z-4,z) |z is any real number}
When z=-5, we have:
4z - 7 = 4(-5) - 7 = -27
z - 4 = -5 - 4 = -9
z = -5
So, we have:
{(4z-7,z-4,z) |z is any real number} ⇒ {-27, -9, -5}
Hence, the set when z = -5 is {-27, -9, -5}
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Let g be the piecewise defined function shown.
g(x)=
x + 4, −5 ≤ x ≤ −1
2 − x, −1 < x ≤ 5
Evaluate g at different values in its domain.
g(−4) =
g(−2) =
g(0) =
g(3) =
g(4) =
Work is attached. Hope it helps!
your heart beats 86 times per minute proportional or non proportional
The lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years. What proportion of crocodiles live between 17.5 and 20.5 years?
Find the z-table here.
0.3147
0.4068
0.5932
0.6853
Picture posted below
Option B) is correct 0.4068 portion of crocodiles live between 17.5 and 20.5
The lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years.
Z-table is tabulated data that gives the information of value of percentage of data.
standard deviation = 2.6 ; mean (μ)= 18
lives between 17.5 and 20.5
x= (20.5+17.5)/2=19
Z = (X - μ) / σ
z=-(19-18)/2.6
z= 0.38
While compare it with the z table is gives 0.4068.
Thus the required value of Z = 0.4068
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........................
Answer:
???????
Step-by-step explanation:
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Ethan ran 3/4 miles. Megan ran 7/8 miles. How much further did Megan run? Answer in simplest form.
Answer:
2/16 or 0.625
Step-by-step explanation:
Find a common denominator for the two fractions. It will be 16. 3/4=12/16
7/8=14/16 or you can do it in decimal form. 3/4=.25 and 7/8= .875
.875-.25=.0.625
[tex]\large\boxed{\frac{1}{8}\ \text{miles}}[/tex]
We need to subtract Ethan's distance from Megan's. First, we need to have a common denominator in the fractions.
Multiply both the numerator and the denominator in [tex]\frac{3}{4}[/tex] by [tex]2[/tex] to get [tex]\frac{6}{8}[/tex], which is equivalent. Now, both numbers have a denominator of [tex]8[/tex] and can be subtracted.
Now, simply subtract the numerators, leaving the denominator alone.
[tex]\frac{7}{8}-\frac{6}{8}=\frac{7-6}{8}=\boxed{\frac{1}{8}}[/tex]
The scale in the drawing is 2 cm : 5 m. Select from the drop down the correct numbers into the boxes to give the length, width, and area of the actual room.
The length, width, and area will be 25m, 15m, and 375m².
How to calculate the area?From the information given, the scale in the drawing is 2cm : 5m and the length and width are given as 10cm and 6cm respectively.
Length = 10cm = 10 × 2.5 = 25m
Width = 6cm = 6 × 2.5m = 15m
Area = Length × Width
Area = 25 × 15
Area = 375m²
Therefore, the area is 375m².
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Bernice received the following scores on five science tests: 96, 77, 86, 97, and 89.
Which of the following statements is true?
O The mean of the set is less than the median.
O The mode of the set of scores is 96.
O The median of the set of scores is 86.
o The mean and the median of the set of scores are the same.
Answer:
the mean and the median of the set of scores are the same.
Step-by-step explanation:
median = 89
mean = 96+77+86+97+89 = 445 / 5
= 89
mode = none
The mean and the median of the set of scores are the same.
What is mean and median?Introduction to Mean, Median, and Mode: In statistics, we frequently choose a representative value to roughly characterise the entire collection of data. The name "measure of central tendency" denotes that this representative value is one around which the data is centred. The mean, median, and mode are these central tendencies. The most typical way to measure central tendency is with the mean. In actuality, it represents the mean of the specified set of data. Both continuous and discrete data can be used with it. In most cases, the median shows the midpoint of the given set of data when it is arranged in a specific order.
Mean: - Average value
Median: - Middle term (after arranging in either accending or descending order)
Mean = 445/5 = 89
Median = Middle term = 3rd term = 89
Mean and median are equal.
Hence, option D is correct
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The scores on a psychology exam were normally distributed with a mean of 61 and a standard deviation of 5. A failing grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing score? Approximately what percentage of the students failed ?
The cutoff for a failing score is 51 and about 2.28% of the students failed the psychology exams.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Z score is given by the equation:
z = (raw score - mean) / standard deviation
Given mean of 61 and a standard deviation of 5.
The z score that corresponds to 2 or more standard deviations below the mean is -2. Hence:
-2 = (x - 61) / 5
x = 51
P(z < -2) = 0.0228
The cutoff for a failing score is 51 and about 2.28% of the students failed the psychology exams.
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Write an equation to match the verbal statement.
one-half is equal to the product of a number, c, and eight
Answer:
1/2 = c*8 or c*8=1/2
Step-by-step explanation:
It says 1/2 is equal to which means 1/2 is on the side for one of the equations. It doesn't really matter. It says is equal to a number, c and eight. Its implying that you multiply c and 8 together because if it meant for another number to be multiplied then a third symbol would be in the operation.
Consider functions f and g. What is the value of x when (g x f)(x) = 4
By applying the definition of functions and composition between two functions, we find that (g ° f) (x) = 4 when x is equal to 6. (Correct choice: B)
How to find the result of composition between two functionsLet be f and g functions, there is a composition of f in terms of g when the input of the former is output of the latter. Hence, we have the following relationships:
g(x):
- 2 → 4
f(x):
6 → - 2
By applying the definition of functions and composition between two functions, we find that (g ° f) (x) = 4 when x is equal to 6. (Correct choice: B)
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Question 22 of 25 Which inequality matches the verbal description? Marc is saving up for a computer. He has $250 saved already. To earn more, he works part-time at a job that pays $16 per hour. Let y represent the price of the computer he chooses, and let x represent the number of hours he works. To purchase the computer, he will need to save at least y dollars.
A. y≤ 250+ 16x
B. y≤ 16x-250
C. yz 250-16x
D. yz 250x + 16
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.
The required distance AB is given by .[tex]\sqrt{17}[/tex]
What is transformation?Transformation, is process which is used to change the position of the bor shapes.
Since, coordinate of A(0,0) B(1,4)
After transformation T: (x, y) (x + 2, y + 1) of A, B it become A'(2, 1), B '(3,5)
Now,
Distance = √(x2-x1)^2+(y2-y1)^2
AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] ; A'B' = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] ;
A(0,0) B(1,4) A'(2, 1), B '(3,5)
AB= [tex]\sqrt{(1-0)^2+(4-0)^2}[/tex] A'B'= [tex]\sqrt{(3-2)^2+(5-1)^2}[/tex]
AB= √17 A'B' = √17
Thus, the required distance AB and A'B' = √17.
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Juan owns 7 pairs of pants, 3 shirts, 5 ties, and 6 jackets. How many different outfits can he wear to school if he must wear one of each item?
To solve this problem, just use multiplication.
[tex]7\text{ pairs of pants}*3\text{ shirts}*5\text{ ties}*6\text{ jackets}=\large\boxed{630\text{ outfits}}[/tex]
You can somewhat think of this situation as a sort of tree. You start with 7 large branches representing the pants, then for every one of those you have 3 medium-sized branches to represent the pairs of pants. Each one of those has 5 sticks for the ties, which in turn each have 6 leaves to represent the jackets and therefore a complete outfit. The solution is found by getting the total number of leaves on the tree.
cuantos parque solares hay en china
The translation of the question is:
What are solar parks?The solar park is a concentrated zone of development of solar power generation projects and provides developers an area that is well characterized, with proper infrastructure and access to amenities and where the risk of the projects can be minimized.
How many solar parks are there in China?
Huanghe Hydropower Hainan Solar Park – 2.2GWTengger Desert Solar Park – 1.55GW Datong Solar Power Top Runner Base – 1.1GWYanchi Ningxia Solar Park – 1GWLongyangxia Dam Solar Park – 850MWLearn more about solar energy here:
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A square has a perimeter of 24cm. What is the length of each side?
Quick process:
⇒ Square has 4 sides
⇒ We have been given that the perimeter is 24 centimeters
⇒ Each side is equal in value and each side added up together must equal 24.
⇒ So to finish this out we need to divide the given perimeter which is 2 4 by the amount of side a square has which is 4.
⇒ So 24/4 = 6
Check the answer:
6 + 6 = 12
12 + 12 = 24 √
Perimeter of a square =24cm
Formula=4s
So 4s=24
s=24/4
s=6
Therefore side of the square is 6cm.
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Pls Help! Geometry
Find the area of the shaded region
Answer: 112.5 square cm
Step-by-step explanation:
The area of the rectangle is [tex](20)(9)=180[/tex] square cm.
The area of the white triangle is [tex]\frac{1}{2}(9)(20-3-2)=67.5[/tex] square cm.
So, the area of the shaded region is [tex]180-67.5=112.5[/tex] square cm.
The town of pratt has a population of about 8,260,000. express this number in scientific notation
Answer:
8.26 x 10^6
Step-by-step explanation:
Scientific notation mean multiply by 10 power
Which description best compares the graphs given by the equations:
x - 5y = -5 and -5x - 25y = 25
a. parallel
b. perpendicular
c. intersecting but not perpendicular
d. None of the above.
x - 5y = -5, -5x - 25y = 25
First, you'll need to get the x variable by itself.
x - 5y = -5
+5 +5
x = 0
So x is plotted on the 0.
For the second part of the first equation, you'll be looking for what the y variable represents.
x - 5y = -5
-x -x
-5y = -5
5 5
y = 1
So y is plotted on the 1 on the vertical line above the 0.
For the first part of the second equation, you'll do the same thing as in the first equation.
-5x - 25y = 25
+25 +25
-5x = 50
5 5
x = 10
So the x for this equation is plotted on 10 on the horizontal line.
For the second part of the second equation, you will do the same thing as in the first equation.
-5x - 25y = 25
+5 +5
-25y = 30
25 25
y = 1.2
So the y for the second half of the second question is plotted on 1.2 on the vertical line.
Perpendicular means the lines may or may not be of equal length and they will not be perfectly in line with each other.
Parallel means the lines may or may not be of equal length but will be perfectly in line with each other.
Intersecting means the lines may or may not be of equal length but will touch each other.
Work out the area of this triangle.
6 cm
11 cm
12 cm
Step-by-step explanation:
there is a right angle formed in this question
this leads us to Pythagoras theorem
Hyp²=opp²+Adj²
Hyp²=11²+6²
Hyp²=121+36
Hyp²=157
Hyp=√157
Hyp=12.529964086
Hyp=12.5
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