1. Chris makes $48,000 a year. He is paid semi-monthly. What is his gross pay per pay period?
Semi-monthly means he is being paid 2 times a month.
Since there are 12 months in a year so the total number of periods will be
2×12 = 24
So the pay per period will be
[tex]\frac{\$48,000}{24}=\$2,000[/tex]Therefore, Chris's gross pay per period is $2,000
2. John earns $59,800 a year. He is paid bi-weekly. What is his annual pay?
Bi-weekly means he is being paid 2 times a week.
Since there are 52 weeks in a year so the total number of periods will be
2×52 = 104
So the annual pay is
[tex]\frac{\$59,800}{104}=\$575[/tex]Therefore, John's annual pay is $575
3. If Sondy's gross pay is $750 weekly, what is her annual salary?
Since there are 52 weeks in a year
So the annual salary is
[tex]\$750\times52=\$39,000[/tex]Therefore, Sondy's annual salary is $39,000
4. What is Jackie's monthly salary if her annual gross pay is $65,400?
Since there are 12 months in a year
Monthly salary will be
[tex]\frac{\$65,400}{12}=\$5,450[/tex]Therefore, Jackie's monthly salary is $5,450
questions A, B, C, D, E, F, G, H and I
A. The frequency is indicated in the vertical axis.
B. The horizontal axis indicates the classes, which in this case are the test scores intervals.
C. The horizontal axis has a class width of 10.
D. The frequency for the class 60-69 is 3.
E. The frequency for the class 70-79 is 9.
F. The frequency for the class 80-89 is 12.
G. The frequency for the class 90-99 is 7.
H. We can verify that 31 students took the test because we should have 31 data points (test scores) divided into the different classes.
We should obtain 31 when adding the frequency of all the classes:
[tex]3+9+12+7=31[/tex]I. The new scores are: 78, 81, 82, 85 and 88.
So the class 70-79 increases its frequency by one, while the class 80-89 increases its frequency by 4.
We can modify the histogram and obtain:
Bruce walks 3/4 mile in 1/5 hour. What is his speed in Miles per hour? Show your work.
To solve
Speed = distance / time
From the question
distance =3/4 mile time = 1/5 hour
substituting the above in the formula
Speed =
[tex]\text{speed =}\frac{\frac{3}{4}}{\frac{1}{5}}[/tex]speed = 3/4 x 5/1
[tex]\text{speed =}\frac{15}{4}\text{ miles per hour}[/tex]speed =3.75 miles per hour
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 56 N acts on a certain object, the accelerationof the object is 8 m/s?. If the acceleration of the object becomes 3 m/s?, what is the force?
STEP 1
Establish relationship between force and acceleration.
From the 1st statement, there is a direct variation between the force and the acceleration. This is put mathematically as
[tex]F\text{ }\alpha\text{ a}[/tex]We introduce a constant, m
[tex]\begin{gathered} F\text{ = ma where} \\ m\text{ is the proportionality constant creating the relationship thus } \\ Nperm/s^2\text{ as its unit} \end{gathered}[/tex]STEP 2
Derive value for the constant, m
[tex]\begin{gathered} F\text{ = ma} \\ \text{Dividing both sides by a, we have} \\ \frac{F}{a}=m \\ where\text{ }f=56N,m=8m/s^2 \\ m=\frac{56}{8}=7Nperm/s^2=7Ns^2\text{ / m} \end{gathered}[/tex]STEP 3
Apply this value of m to solve related equations.
[tex]\begin{gathered} \text{where a = 3m/s}^2\text{ and m = }7Ns^2\text{ /m} \\ \text{and F = ma = 3 x 7 = 21}N \end{gathered}[/tex]Thus, the force when acceleration becomes 3 m/sq seconds is 21 N
WHAT IS THE MEDIAN OF THE DATA BELOW: 7,7,4,6,7,4,7,6,2THE ANSWER I GOT WAS 6?
Given:
7,7,4,6,7,4,7,6, and 2.
Required:
We need to find the median of the given data set.
Explanation:
Recall that the median is the value in the middle of a data set.
The number of data in the given set is 9.
Arrange the data points in increasing order.
2,4,4,6,6,7,7,7,7.
The 5th term is the middle term of the given data set.
[tex]Median=6[/tex]Final answer:
[tex]Median=6[/tex]Findthefollowing:a) Whatis55%of262?b) Whatpercentof372is297.6?
To find 55% of 262, we just have to multiply. (55% is equivalent to 0.55)
[tex]0.55\cdot262=144.1[/tex]Therefore, 144.1 represents 55% of 262.(b)In this case, we have to divide to find the percentage 297.6 represents of 372.
[tex]\frac{297.6}{372}=0.80[/tex]Then, we multiply by 100 to express in percentage.
[tex]0.80\cdot100=80[/tex]Therefore, 297.6 represents 80% of 372.Write 25/9 as a decimal,if necessary use a bar to indicate which digit or group of digits repeats
As per given by the question,
There are given that the fraction
[tex]\frac{25}{9}[/tex]Now,
For decimal divide the numerator by the denominator.
So, the value is;
[tex]\frac{25}{9}=2.777777[/tex]Now,
According to the question, there are mention that use a bar to indicate which which digit repeats.
So,
[tex]\frac{25}{9}=2.\bar{7}[/tex]Hence, the decimal of given fraction is,
[tex]2.\bar{7}[/tex]Ariana has created a paper airplane for her physics class, the physics teacher is requiring her paper airplane to swoop down at a single point to graze the ground before it rises back into the air. Her initial attempt is modeled by the function below where h is height in feet and X is time in seconds. In how many seconds will the paper airplane crash into the ground?
Given:
[tex]h(x)=x^2-12x+35[/tex]The given function h(x) represents the height in feet and (x) is time in seconds.
We will find the time the paper airplane will crash into the ground.
When the paper airplane crashes into the ground, h(x) = 0
So, substitute h = 0
[tex]x^2-12x+35=0[/tex]Solve the equation to find (x), we will factor the equation as follows:
[tex]\begin{gathered} (x-5)(x-7)=0 \\ x-5=0\rightarrow x=5 \\ x-7=0\rightarrow x=7 \end{gathered}[/tex]So, the answer will be the time = 5 seconds and 7 seconds
Identify the part, whole, and percent in the following statement: Find 15% of 750. part = 750, whole = n, percent = 15part = 15, whole = 750. percent=ppart = n, whole = 750, percent = 15none of theseWrite a percent equation that can be used to solve the following problem: 820 is 20% of whatnumber?n=0.2 x 820820 = 0.2 xn0.2 = n < 820none of these
For the first part we have that:
[tex](750)\cdot(0.15)=112.5[/tex]Now, 112.5 is the part of the percentage, the percent is 15% and the whole is 750.
For the second part, we have that if 820 is 20% of number n, then:
[tex]\begin{gathered} n=\frac{820}{0.2}=4100 \\ \Rightarrow0.2\cdot n=820 \end{gathered}[/tex]Therefore, we can use the equation 0.2xn = 820
In circle F, what is m EA if m ZDFE - 36°?АBFEDCa54°b104°C144°d324°
Note that the measurement of arc is equal to the central angle.
A central angle is an angle whose vertex is at the center of the circle.
Since DFA is a straight line, angle DFE and angle AFE will have a sum of 180 degrees
[tex]\angle\text{DFE}+\angle\text{AFE}=180[/tex]From the given, angle DFE = 36 degrees
[tex]\begin{gathered} 36+\angle\text{AFE}=180 \\ \angle\text{AFE}=180-36 \\ \angle\text{AFE}=144 \end{gathered}[/tex]From the notes above, arc EA = angle AFE
Therefore, arc EA = 144 degrees
The answer is Choice C. 144 degrees
If you deposit $100 each month into an IRA earning 2.3% interest, how much will you have in the account after 17 years? Round your answer to the nearest cent.
Given:
The amount deposited each month, d=$100.
The rate of interest, R=2.3%.
The number of years after which the balance in the account is calculated, N=17.
The formula for the balance in the acoount after N years is,
[tex]P_N=\frac{d((1+\frac{r}{k})^{Nk}-1)}{(\frac{r}{k})}\text{ ---(1)}[/tex]Here, r is the interest rate in decimal form and k is the number of compounding periods in one year.
Since deposit is made every month, we use monthly compounding, k=12.
The rate of interest in decimal form is,
[tex]r=\frac{R}{100}=\frac{2.3}{100}=0.023[/tex]Now, substitute the known values in equation (1).
[tex]\begin{gathered} P_{17}=\frac{100((1+\frac{0.023}{12})^{17\times12}-1)}{(\frac{0.023}{12})}\text{ } \\ P_{17}=\frac{100((1+\frac{0.023}{12})^{204}-1)}{(\frac{0.023}{12})}\text{ } \\ P_{17}=24934.19 \end{gathered}[/tex]Therefore, after 17 years, the balance in the account will be $24934.19, to the nearest cent.
The rule general rule to add fractions
It is required to give a general rule for adding fractions.
The general rule is first to ensure the fractions' denominators are the same and then add the numerators.
Note that a common denominator must be found if the denominators are different.
Identify the quadratic equation with roots -2 and -1.
we know that
The roots -2 and -1.
so
The quadratic equation in factored form is equal to
[tex](x+1)(x+2)=0[/tex]Convert to standard form
[tex]\begin{gathered} x^2+2x+x+2=0 \\ x^2+3x+2=0 \end{gathered}[/tex]the answer is the third optionI’m confused pls help
Answer:
there is not enough information
Step-by-step explanation:
in this image we can see 2 sides are congruent but we can’t see if an angle is congruent
Find the slope then write an equation for the line that passes through each pair of points (5, 6), (-10, – 15)
The given points are,
x1, y1 = 5, 6
x2, y2 = -10, -15
The general line equation is,
y = mx +b
Here, m is the slope and b is the y intercept.
The slope m can be calculated as,
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-15-6}{-10-5}=\frac{21}{15}[/tex]Now, b can be calculated by taking a point and susbtituting the values in the line equation.
Let us here take, th points (5,6). Therefore we have,
[tex]\begin{gathered} 6=\frac{21}{15}\times5+b \\ 6=7+b \\ b=-1 \end{gathered}[/tex]Thus, the equation is,
[tex]y=\frac{21}{15}x-1[/tex]Which number would go outside the circles?А. 0.3В. 0C. -7D. 2
First, what are whole numbers?
They are numbers of puppies you want
1,2,3,4,5........
That eliminates 2
Integers are positive and negative numbers of puppies including having no puppies
-5,-4,-3,-2,-1,0,1,2
That eliminates -7, 0 and 2
The decimal is neither a whole number or an integer so it would go outside the circle.
A consumer research company wants to estimate the average cost of an airline ticket for a round trip within the continental United States. A random sample of 50 airfares was gathered and gave an average price of $438. Identify the variable
Answer
Option B is correct!
The variable here is the airfares that were gathered from the sample.
Explanation
In Statistics, variable is any number, quantity or characteristics that can be measured, counted or collected.
For this question, the data collected is the variable.
Hence, the variable here is the airfares that were gathered from the sample.
Hope this Helps!!!
The lines represented by the equations y + 3x = 9 and y 5x + 1 are O parallel Submit Answer O perpendicular O the same line O neither parallel nor perpendicular
To know the relation between the lines we have to calculate the slope with this expression:
[tex]y=mx+c[/tex]whre m is the slope and c the intersection with the y axis, so for the first line
[tex]\begin{gathered} y=-3x+9 \\ m=-3 \end{gathered}[/tex]and for the secon line:
[tex]\begin{gathered} y=-\frac{1}{3}x+1 \\ m=-\frac{1}{3} \end{gathered}[/tex]The slope is diferent, so they are not parallel, and they are not the same line. is they where perpendicular the slope of the second line should be the negative reciprocal of the first line. and in this case:
[tex]-3\to\frac{1}{3}[/tex]so they are not perpendicular. So the solution is numeral D) neither parallel nor perpendicular
Multiply: (5j + 3k) (5j - 3k)Multiply: (5j + 3k) (5j - 3k)
Answer:
25j^2 - 9k^2
Explanation:
Which of the following is the product of the rational expressions shown here?Х/x-2•3/x-2A. X+3/2x -4B. 3x/x^2- 4x + 4c. 3x/x^2-4
Step 1: Write out the expression
[tex]undefined[/tex]raph of y = f(x) is graphed below. What is the end behavior of f(2)?
By observing the graph we have got the following :
The graph is going down after the point (-7,0)
After the point (x,f(x)) =(-7,0) ,as x decreasing, the function f(x) is decreasing
[tex]as\text{ }x\rightarrow-\infty,\text{ f(x)}\rightarrow-\infty[/tex]The graph is going up after the point (4,0).
After the point (x,f(x)) =(4,0), as x increasing, the function f(x) is increasing
[tex]as\text{ }x\rightarrow\infty,\text{ f(x)}\rightarrow\infty[/tex]Hence we get
[tex]as\text{ }x\rightarrow\infty,\text{ f(x)}\rightarrow\infty\text{ and }as\text{ }x\rightarrow-\infty,\text{ f(x)}\rightarrow-\infty[/tex]
Hence the first option is correct.
if x, y, z are the sides of a triangle and s is the semi perimeter, then calculate the area of the triangle
the area can be calculated with the next formula
[tex]A=\sqrt[]{s(s-x)(s-y)(s-z)}[/tex]The area of a triangle can also be calculated from its semiperimeter and side lengths x,y,z sing Heron's formula
Alison Alix goes to the bank and borrows 150,000 pesos at 9.5% for 250 days. If the bank uses the ordinary interest method, how much interest will Alison have to pay?
In the ordinary interest method, interest (I) is computed as follows:
I = Prt
where P is the principal, r is the annual interest rate (as a decimal), and t is time in years. With this method, the year has 360 days instead of 365.
Substituting in the formula with P =150,000 pesos, r = 0.095 (= 9.5/100), and t = 250/360, we get:
[tex]\begin{gathered} I=150,000\cdot0.095\cdot\frac{250}{360} \\ I=9895.83\text{ pesos} \end{gathered}[/tex]
Alison will have to pay 9,895.83 pesos
Geometry midpoint If E is the midpoint of segment DF, DE = 2x + 4 and EF = 3x - 1, thenx=DE=EF=DF=
ANSWERS
x = 5
DE = 14
EF = 14
DF = 28
EXPLANATION
We have that E is the midpoint of DF.
This means that DE is the same as EF.
We have that:
DE = 2x + 4
EF = 3x - 1
=> 2x + 4 = 3x - 1
Collect like terms and solve:
3x - 2x = 4 + 1
x = 5
=> DE = 2(5) + 4 = 10 + 4
DE = 14
=> EF = 3(5) - 1 = 15 - 1
EF = 14
Since DE and EF lie on DF, we have that:
DE + EF = DF
=> DF = 14 + 14
DF = 28
X*d multiply by x*18
The point here is to remember the additive property of exponents. In general, it says that
[tex]x^b\cdot x^c=x^{b+c}[/tex]In our case, it becomes
[tex]x^d\cdot x^{18}=x^{d+18}[/tex]
The perfect square trinomial ax^2 + bx+c is equivalent to (1.2x -0.7)^2. Which of thefollowing is equivalent to a-b+c?A 0.95B 3.61С 0.25D-0.73
(1.2x -0.7)²
Applying the square:
(1.2x)² + 2(1.2x)(-0.7) + (-0.7)²
1.44x² - 1.68x + 0.49
where:
a = 1.44
b = -1.68
c = 0.49
Then, a - b + c = 1.44 - (-1.68) + 0.49 = 1.44 + 1.68 + 0.49 = 3.61
What is the midpoint of (2, 13) and (0, 11)? WHAT IS THE X VALUE? *
Given the points (2 , 13) and (0 , 11)
Let the midpoint is (x , y)
so,
[tex]x=\frac{2+0}{2}=\frac{2}{2}=1[/tex][tex]y=\frac{13+11}{2}=\frac{24}{2}=12[/tex]so, the midpoint is ( 1 , 12 )
The displacement function of a rock thrown straight up in the air is given by f(t)= -2t^2 + 15.7t meters, where t is measured in seconds find the total distance traveled by the rock when it reaches the ground a. 30.81 mb. 31.40 mc. 61.62 md. 92.43 m
As the rick is thrown straight up in the air and the function of its displacement is quadratic it means that the rock traveled a distance up to its maximum and then down to the ground. Then, the function value in the maximum is half the distance traveled by the rock.
[tex]f(t)=-2t^2+15.7t[/tex]Use the next formula to find the time (t) in the maximum point of quadratic function:
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ \\ x_{max}=-\frac{b}{2a} \end{gathered}[/tex][tex]t_{max}=-\frac{15.7}{2(-2)}=-\frac{15.7}{-4}=3.925[/tex]Evaluate the function for t=3.925 to find the maximum value:
[tex]\begin{gathered} f(3.925)=-2(3.925)^2+15.7(3.925) \\ f(3.925)\approx-2(15.4056)+61.6225 \\ f(3.925)\approx-30.8112+61.6225 \\ f(3.925)\approx30.8113 \end{gathered}[/tex]Multiply the maximum value by 2 to get the total distance traveled by the rock:
[tex]30.8113*2\approx61.62[/tex]Then, the total distance traveled by the rock when it reaches the ground is 61.62metersAnswer: CA person is on the outer edge of a carousel that is rotating counterclockwise. Using the unit circle to model the carousel, what is the exact position of the riderafter the carousel rotates pi/12 radians
To determine the location of the rider, we need to convert the polar coordinate to rectangular form.
The given polar coordinate is (1, π/12).
To convert, here are the steps.
1. To get the x-coordinate, get r cos θ.
[tex]x=rcos\theta=1cos\frac{\pi}{12}=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]2. To get the y-coordinate, get r sin θ.
[tex]y=rsin\theta=1sin\frac{\pi}{12}=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]Hence, the exact location of the rider after the carousel rotates π/12 radians is given by the coordinates found in Option D.
From the diagram below, if AC is a tangent line, and if PD = 3 and DC = 2, find the length of BC.
Explanation
From the diagram
[tex]\begin{gathered} radius\text{ of cicle =}PB=PD=3 \\ PC=PD+DC=3+2=5 \end{gathered}[/tex]Therefore;
[tex]\begin{gathered} PC^2=PB^2+BC^2 \\ 5^2=3^2+BC^2 \\ 25=9+BC^2 \\ BC^2=25-9 \\ BC^2=16 \\ BC=\sqrt{16} \\ BC=4 \end{gathered}[/tex]Answer: Option A
0 Find the perimeter of the shaded region above, Question Heln
Define the perimeter of a shape
The perimeter of any shape is the distance around the edge of a shape. That is the total length of the outline of the shape
Draw the shape given with the appropriate dimension
The shape is shaded and the perimeter is the total length of the outline
Noted that line DE is equal to BC
[tex]DE=BC=8[/tex]Therefore, the perimeter is
[tex]AB+BC+CD+DE+EA[/tex][tex]P=6+8+7+8+6[/tex][tex]P=35\text{units}[/tex]