If she worked a 52 hours last week and paid [tex]1\frac{1}{2}[/tex] times her regular hourly rate for all hours over a 40 hours week, her last week pay was $840, then the hourly rate is $14.48
Total hours that she worked = 52 hours
Total payment of last week = $840
She paid [tex]1\frac{1}{2}[/tex] times her regular hourly rate for all hours over a 40 hours week.
Number of overtime hours = 52 - 40
= 12 hours
If the hourly rate is x then the over time pay is 1.5x
Then the equation will be
40x + 12×1.5x = 840
Solve the equation
40x + 18x = 840
58x = 840
x = 840/58
x = $14.48
Hence, if she worked a 52 hours work week last week and paid [tex]1\frac{1}{2}[/tex] times her regular hourly rate for all hours over a 40 hours week, her pay last week was $840, then the hourly rate is $14.48
Learn more about hourly rate here
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Can you help me, please? I don't know how to do this.
a) We were told that RS is congruent to ST. This means that triangle RST is an isosceles triangle. In an isosceles triangle, the base angles are equal. This means that
angle SRT = angle STR
Angle STR and angle STU are linear pairs. They lie on a straight line. The sum of the angles on a straight line is 180 degrees. This means that
angle STR + angle STU = 180
Given that angle STU = 8x, then
angle STR + 8x = 180
Angle STR = 180 - 8x
Given that angle SRT = 5x - 54, then
5x - 54 = 180 - 8x
5x + 8x = 180 + 54
13x = 234
x = 234/13
x = 18
Thus,
b) angle STU = 8 * 18 = 144 degrees
c) Recall, the sum of the angles in a triangle is 180 degrees. This means that
angle S + angle R + angle T = 180
angle T = angle R = 180 - 144 = 36
Thus,
36 + 36 + S = 180
72 + S = 180
S = 180 - 72
Angle S = 108 degrees
A) what is the maximum height of the ball ? B) how many seconds does it take until the ball hits the ground ?
Given:
[tex]h(t)=-16t^2+104t+56[/tex]Models the balls height height about the ground.
Required:
To find the maximum height of the ball.
Explanation:
Consider
[tex]\begin{gathered} h(t)=-16t^2+104t+56 \\ a=-16 \\ b=104 \\ c=56 \end{gathered}[/tex][tex]\begin{gathered} t=-\frac{b}{2a} \\ \\ t=-\frac{104}{2(-16)} \\ \\ t=\frac{204}{32} \\ \\ t=3.25 \end{gathered}[/tex]At t = 3.25 the maximum height is
[tex]\begin{gathered} h(3.25)=-16(3.25)^2+104(t)+56 \\ =225 \end{gathered}[/tex]Final Answer:
The maximum height of the ball is 225 feet.
how to solve this one i need help with number 5 and 8
5.
Apply the power to each number and simplify
8.anythig raised to the zero power is equal to one
6.multiply
7.substract
The area of a rectangle is 50m^2, and the length of the rectangle is 5 m less than three times the width. Find the dimensions of the rectangle.(Length= m)(Width= m)
Given:
Area of the rectangle is 50 sq. m.
The length of the rectangle is 5 m less than three times the width.
That is,
l=3w-5
To find the dimensions:
The formula for the area of the rectangle is , A=lw
Therefore,
[tex]\begin{gathered} A=(3w-5)() \\ 50=3w^2-5w \\ 3w^2-5w-50=0 \\ (3w-15)(3w+10)=0 \\ 3w=15,3w=-10 \\ w=5,w=-\frac{10}{3} \end{gathered}[/tex]Since, width can not be negative.
So, -10/3 can be neglected.
Hence, w=5
So, the length is,
[tex]\begin{gathered} l=3(5)-5_{} \\ =15-5 \\ =10 \end{gathered}[/tex]Hence, the dimensions are, l=10 m and w=5 m.
Toby eats tacos every 5 days. Toby also drinks horchata every 6 days. If Toby has horchata and tacos today how many days will he have too wait to enjoy his favorite treats on the same day again?
We are given the following information
Toby eats tacos every 5 days.
Toby also drinks horchata every 6 days.
If Toby has horchata and tacos today how many days will he have to wait to enjoy his favorite treats on the same day again?
We need to find the least common multiple (LCM) of 5 and 6 days.
Multiples of 5 = 5, 10, 15, 20, 25, 30
Multiples of 6 = 6, 12, 18, 24, 30
As you can see, the least common multiple (LCM) of 5 and 6 is 30
Therefore, Toby has to wait for 30 days to enjoy his favorite treats on the same day again.
Salma put $500 in a savings account that earns interest at a rate of 3% A. How much interest will Salma earn after 6 years? B. How much money will Salma have in the account after 6 years?
ANSWER
A. $90
B. $590
EXPLANATION
She put $500 in a savings account that earns 3% interest.
A. This is a simple interest question and for simple interest at a rate R and with a principal P (amount of money saved or deposited), after T years, the interest is given as:
[tex]I\text{ = }\frac{P\cdot\text{ R }\cdot\text{ T}}{100}[/tex]So, after 6 years, the interest is:
[tex]\begin{gathered} I\text{ = }\frac{500\cdot\text{ 3 }\cdot\text{ 6}}{100} \\ I\text{ = \$90} \end{gathered}[/tex]The interest after 6 years is $90.
B. The amount of money she will have after 6 years is the sum of the interest after 6 years and the amount of money initially deposited.
That is:
A = P + I
A = $(500 + 90)
A = $590
After 6 years, she will have $590 in the account.
how much should mary charge the customer to the nearest cent? use 3.14 for pie
step 1
Find out the area of the closet
The area is equal to the area of a right triangle plus the area of a semicircle
so
[tex]A=\frac{1}{2}(7)(6)+\frac{1}{2}^{}\cdot3.14\cdot(\frac{7}{2})^2[/tex][tex]\begin{gathered} A=21+19.2325 \\ A=40.2325\text{ ft2} \end{gathered}[/tex]step 2
Find out the total charge
40.2325*5.60+150=$375.30
therefore
the answer is $375.30Write the fraction in lowest terms. Use the method of dividing by a common factor.2/10A) 2/5B) 1/5C) 1/10D) 5/1
Given the fraction:
[tex]\frac{2}{10}[/tex]You can identify that the numerator is 2 and the denominator is 10.
Notice that the denominator and the numerator of the given fraction have this common factor in common:
[tex]Common\text{ }Factor=2[/tex]Therefore, you can reduce the fraction by dividing the numerator and the denominator by 2:
[tex]=\frac{2\div2}{10\div2}[/tex][tex]=\frac{1}{5}[/tex]Hence, the answer is: Option B.
1Let f(x) =- 6 (and g(x)9+ 6.22 – 6(fog)(x) =(gof)(x) =
Explanation
A composite function is a function that is written inside another function. Composition of a function is done by substituting one function into another function.
f [g (x)] is the composite function of f (x) and g (x). so
[tex]\begin{gathered} f(x)\text{ }=\frac{1}{x-6} \\ g(x)=\frac{9}{x}+6 \end{gathered}[/tex]hence
Step 1
[tex](f\circ g)(x)[/tex]so
[tex]\begin{gathered} f(x)\text{ }=\frac{1}{x-6} \\ (f\circ g)(x)\text{ }=\frac{1}{g(x)-6}=\frac{1}{(\frac{9}{x}+6)-6}=\frac{1}{\frac{9}{x}}=\frac{x}{9} \\ (f\circ g)(x)\text{ }=\frac{x}{9} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} (g\circ f)(x) \\ so \\ (g\circ f)(x)=\frac{9}{f(x)}+6=\frac{9}{\frac{1}{x-6}}+6=\frac{9(x-6)}{1}+6=9x-54+6=9x-48 \\ (g\circ f)(x)=9x-48 \end{gathered}[/tex]I hope this helps you
please help me solve.I have na for blank 1 and 4/3 for blank 2. but it's incorrect
Blank 1 is
[tex]\frac{4}{3}[/tex]Blank 2 is
3
I need help with this practice Since I am relatively new to this branch/topic of math, can you explain it to me step-by-step as you solve?
The values of the variables are given: a = 5 and b = 8. One of the expressions is correct, that is, the equation is true.
Let's test is one by one until we find the correct choice:
a)
8 + a + 8 + b = 104
Substitute the given values:
8 + 5 + 8 + 8 = 104
Operate:
29 = 104
This is a false equation.
b)
8 + a + 8b = 104
Substituting:
8 + 5 + 8(8) = 104
Operating:
13 + 64 = 104
77 = 104
This is false also
c)
8a + 8 + b = 104
Substituting:
8(5) + 8 = 104
40 + 8 = 104
48 = 104
This is a false i
PLEASE HELP ME I REALLY NEED HELP. THIS IS DUE IN 45 MINUTES!!! I WILL GIVE YOU BRAINLIST!!! PLEASE
EXPLANATION.
In exercise 22 you can see two different equations for two parallel lines, where a translation of two units is made at the point x towards the vertical axis at y.
By giving values to x in the equation starting with x equal to zero we obtain the first point in negative y.
Here we see a reflection at y -2 for y equal to 2 positive at y.
The equation in g is a reflection of the equation in f, we can examine the other points, they correspond exactly to the same.
NOTE:
The second equation shows us clearly how many units the points of the equation f transfer, 3 units are transferred from each point.
find the perimeter of the rectangle picture above
Okay, here we have this:
As the perimeter is the sum of all the sides, so:
Perimeter=29+29+17+17=92.
Finally we obtain that the perimeter of the rectangle is 92 units.
Here is a graph for one of the equations in a system of two equations Select all the equations thar could be the other equation in a system A: y=-3xB: y=-3/2x+6C: y=-1/6x+3D: y=2/3x-1E: y=1/2x-1F: y=4x-2
To be able to determine which equations could be the other equation in a system
A movie club surveyed 250 high school students. The students were asked how often they go to the movies and whether they prefer action movies or dramas. their responses are summarized in the following table.
a) From the given table, there are 83+17 = 100 students who prefer action movies. Since the total of people surveyed is 250, the percentage is given by
[tex]\frac{100}{205}\times100\text{ \% = 40 \%}[/tex]b) On the other hande, there are 17+48 = 65 students who go to the movies three times a month or more, then the percentage is given as
[tex]\frac{65}{250}\times100\text{ \%=26 \%}[/tex]Therefore, the answers are:
[tex]\begin{gathered} a)\text{ 40 \%} \\ b)\text{ 26 \%} \end{gathered}[/tex]The area of a circle is 50.24 square millimeters. What is the circle's radius?A = 50.24 mm2Use 3.14 for u.
The area of a circle is 50.24 square millimeters. What is the circle's radius?
A = 50.24 mm2
Use 3.14 for u.
Remember that
the area is equal to
A=pi*(r^2)
we have
A=50.24 mm2
pi=3.14
substitute given values
50.24=3.14*(r^2)
solve for r
r^2=50.24/3.14
r^2=16
square root
r=4 mmPart 2we have
C=31.4 in
Remmeber that the circumference is equal to
C=2pir
we have
C=31.4
pi=3.14
substitute
31.4=2(3.14)r
solve for r
r=31.4/(2*3.14)
r=5 inChoose the single logarithmic expression that is equivalent to the one shown.log625-log6 5
Solution
The answer is
Santa is sewing fringe to the edge of a round rug for her living room. If the rug measures 60 inches across, how many inches of fringe does Santa need?
Hello there. To solve this question, we'll have to remember how to calculate the measure of a circumference.
Given a circle with diameter d, as in the following drawing:
The measure of the circumference C can be found by the formula:
[tex]C=\pi\cdot d[/tex]In this case, knowing that the rug measures 60 inches across, to find how many inches of fringe Santa needs, we simply plug in d = 60
[tex]C=\pi\cdot60[/tex]Using an approximation for pi:
[tex]\pi\approx3.1415[/tex]We get that:
[tex]C\approx188.5\text{ in}[/tex]Write the equation of a line that is horizontal and contains the point (-4,1)
We need to find the horizontal that contain the point (-4 , 1)
The general equation of the horizontal line is :
y = c
where c is a constant
So, given the point (-4 , 1 )
so, the y-coordinates of the given point = 1
So, the equation of the required horizontal line is
[tex]y=1[/tex]
If f(x) – g(x) = 2x2 - 4x +4 and f(x) = 3.r? – 2.x + 1 , what is g(x)?
Here, we want to get the value of g(x)
We can make straight substitution here
[tex]\begin{gathered} \text{From the question;} \\ f(x)-g(x)=2x^2-4x+4 \\ g(x)=f(x)-(2x^2-4x+4) \\ g(x)=(3x^2-2x+1)-(2x^2-4x+4) \\ g(x)=3x^2-2x+1-2x^2+4x-4 \\ g(x)=3x^2-2x^2-2x+4x+1-4 \\ g(x)=x^2+2x-3 \end{gathered}[/tex]Write the equation y2 − 12y − 8x + 20 = 0 in vertex form.the quantity(y − 6)2 = 8times the quantity(x + 2) the quantity(y + 6)2 = 8times the quantity(x − 2) the quantity(x − 6)2 = 8times the quantity(y + 2) the quantity(y + 2)2 = 8times the quantity(x − 6)
ANSWER:
[tex](y-6)^2=8(x+2)[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation
[tex]y^2-12y-8x+20=0[/tex]We convert it to its vertex form like this:
[tex]\begin{gathered} 8x=y^2-12y+20 \\ \text{ we complete square} \\ 8x=y^2-12y+20+(-6)^2-(-6)^2 \\ 8x=(y-6)^2-16 \\ 8x+16=(y-6)^2 \\ (y-6)^2=8(x+2) \end{gathered}[/tex]Help me solve this hw assignment problem? Just cannot figure out the remainder. As you can see my answer was not right for remainder
Solution
Given the expression
The degree of the dividend is less than the degree of the divisor, so the polynomial division can't be performed.
However, this implies that the Quotient = 0
And the remainder will be
[tex]x^3+x^2+6[/tex]Conclusion:
[tex]\begin{gathered} Quotient=\text{ 0} \\ Remainder\text{ = x}^3+x^2+6 \end{gathered}[/tex]hello thanks for viewing my question I seem to be having some difficulty on this can you please help me thank you
ANSWER
0.306 or 30.6%
EXPLANATION
Note: Probability is the number of desired results divided by the total number of results.
Combination formula to apply:
[tex]C_{n,r}\text{ = }\frac{n!}{r!(n-r)!}[/tex]Desired Results:
3 brown worms from 7
4 red worms from 6
[tex]\begin{gathered} Desired\text{ Result = C}_{7,3}\times C_{6,4} \\ \text{ = }\frac{7!}{3!(7-3)!}\times\frac{6!}{4!(6-4)!} \\ \text{ = 35}\times15 \\ \text{ = 525} \end{gathered}[/tex]Total Result:
[tex]\begin{gathered} Total\text{ Result = C}_{13,7} \\ \text{ = }\frac{13!}{7!(13-7)!} \\ \text{ = 1716} \end{gathered}[/tex]Determine the Probability
[tex]\begin{gathered} Probability\text{ = }\frac{Desired\text{ outcome}}{total\text{ outcome}} \\ \text{ = }\frac{525}{1716} \\ \text{ = 0.3059} \\ \text{ = 0.306 or 30.6\%} \end{gathered}[/tex]Hence, the probability that she will choose 3 brown worms and 4 red worms is 0.306 or 30.6%.
2. How many rotten apples does Amber have? 1 point Jacob and Amber each buy a bag of apples. Some of the apples are rotten and some are not. Amber has the same fraction of rotten apples in her bag as Jacob has in his bag. Jacob's bag has: Amber's bag has: • A total of 4 apples • A total of 12 apples • Exactly 1 rotten apple • Exactly_rotten apple(s)
2) The number of apples in Jacob's bag is 4. If there is exactly 1 rotten apple. it means that the fraction of rotten apples in Jacob's bag is 1/4
The number of apples in Amber's bag is 12. Let x represent the exact number of rotten apples. it means that the fraction of rotten apples in Amber's bag is x/12
Since the fractions of rotten apples in both bags is the same, it means that
1/4 = x/12
By crossmultiplying, we have
4x = 12
x = 12/4
x = 3
There were 3 rotten apples in Amber's bag
the points (-4,0) and (s,-1) fall on a line with a slope of -1/8.what is the value of s?
We will use the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]m=-1/8 x₁= -4 y₁=0 x₂=s y₂=-1
[tex]-\frac{1}{8}=\frac{-1-0}{s+4}[/tex][tex]-\frac{1}{8}=\frac{-1}{s+4}[/tex]-1(s+4) = -8
multiply both-side of the equation by -1
s+4 = 8
subtract 4 from both-side of the equation
s + 4 - 4 = 8 -4
s = 4
What is the factor for the medicine remaining in a person with each passing hour?How much medicine will remain in a person after 4 hour?
Assuming Medicine remaining (in miligrams) in a person is representd by r and time is represented by t, the relationship between r and t can be determined by using two point form as,
[tex]\begin{gathered} \frac{r-50}{t-0}=\frac{50-40}{0-1} \\ r-50=t(-10) \\ r=-10t+50 \end{gathered}[/tex]use the Egyptian algorithm to multiply 16 times 113
113 x 16 = 1808
Explanations:The Egyptian algorithm uses the distributive law to perform multiplication operation
This algorithm allows us to break a single number into bits and spreading out the product on it.
Note:
16 = 1 + 2 + 3 + 10
113 x 16 = 113 x ( 1 + 2 + 3 + 10)
113 x 16 = (113 x 1) + (113 x 2) + (113 x 3) + (113 x 10)
113 x 16 = 113 + 226 + 339 + 1130
113 x 16 = 1808
Name one or more of the number set that -5 fits into
Answer:
Integers, Rational Numbers
Explanation:
When the negative sign is attached to a whole number, the number becomes a negative integer.
Thus, -5 belongs to the broad set of integers.
Furthermore, any number that can be written in the fractional form (a/b) is rational.
[tex]-5=-\frac{5}{1}[/tex]So, we can say -5 also belongs to the set of rational numbers.
Thus, -5 belongs to the set of Integers, Rational Numbers
7. Which shape(s) are possible cross sections of a right cylinder? (circle all that apply) (1pt)Trianglerectanglecircletrapezoid
Answer:
CIRCLE
Explanation
A cylinder is made of a circular base as shown;
From the diagram shown, you can see that the base is a circle, hence the possible cross-sections of a right cylinder is a CIRCLE
Number 4 Find the limit and use the x values : -0.03, -0.02,-0.01,0,0.01,0.02,0.03
EXPLANATION
First, let's represent the table with some values of x and y near to the limit:
x y
-0.03 0.66
-0.02 0.65
-0.01 0.64
0.01 0.63
0.02 0.62
0.03 0.62
Now, we need to plot the function:
[tex]\mathrm{Plug\: in\: the\: value}\: x=0[/tex][tex]=\frac{\sin\left(0+\frac{\pi}{2}\right)-\sin\left(0\right)}{\frac{\pi}{2}}[/tex][tex]\sin \mleft(0+\frac{\pi}{2}\mright)-\sin \mleft(0\mright)[/tex][tex]=\frac{1}{\frac{\pi}{2}}[/tex][tex]Applying\text{ the fraction rule:}[/tex][tex]=\frac{2}{\pi}[/tex]The limit is 2/π and it does existe because It's defined at x=0