9514 1404 393
Answer:
65
Step-by-step explanation:
The six numbers are sequential multiples of 10, so the mean is halfway between the middle two. Halfway between 60 and 70 is 65.
The mean of the 6 numbers is 65.
A webmaster makes $24 an hour for the first 38 hours she works during a
week and $31 an hour for each hour worked over 38 hours. Which piecewise
equation models her total weekly pay y in dollars as it relates to the number
of hours x that she has worked during the week?
24x
O A. e=1
OSXS38
x > 38
(31x+912
0
[24x
O B. y = {31(x – 38) +912 x > 38
S24x
(31x
C. y =
OSXS 38
X> 38
(24x
OSX 38
D. y = {31(x-38)
x > 38
A piecewise function is consists of different relationships between the variables over different intervals
The correct piecewise equation that models her total weekly pay is option B.
[tex]\mathbf{B.} \ y = \begin{cases} 24 \cdot x& \ 0 \leq x \leq 38 \\ 31\cdot (x - 38) + 912 & \ x > 38 \end{cases}[/tex]
The given parameters are;
The amount made by the webmaster for the first 38 hours she works = $24
The amount she makes for each hour worked after the first 38 hours = $31 an hour
Required:
To find the piecewise equation that models the total weekly pay, y, in dollars in relation to the number of hours x that she has worked during the week
Solution:
If she works for x ≤ 38 hours
The amount she makes working x less than or equal to 38 hours, y = $24/hour × x hours = $24 × x hours
The total amount the webmaster wakes by working all through the normal 38 hours is $24/hour × 38 hours = $912
If she works over 38 hours, (x > 38) we have;
The number of hours she works over 38 hours = x - 38
The amount she makes each hour after working 38 hours, y = $31/hour × (x - 38) hours
The total amount she makes y working for more than 38 hours is given as follows;
y = 31·(x - 38) + 912
The piecewise equation that models her weekly pay is therefore, presented as follow;
[tex]y = \begin{cases} 24 \cdot x& \ 0 \leq x \leq 38 \\ 31\cdot (x - 38) + 912 & \ x > 38 \end{cases}[/tex]
The above piecewise function is the same as option B
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ln the given ration 3:4 the consequent is 7,4,3
[tex]\\ \rm\longmapsto 3:4[/tex]
Convert to fraction[tex]\\ \rm\longmapsto \dfrac{3}{4}[/tex]
4 is the consequentNote.
The first term of the ratio is called consequent.
Answer:
Loading...
Step-by-step explanation:
Help Please!
Find the value of x for which ABCD must be a parallelogram.
Answer:
2
Step-by-step explanation:
We know that the opposite sides of a parallelogram are equal so:
25x+1=7x+37
18x=36
x=2
I need help question:how many questions would you need to get correct on a test that has 30 questions to get at least 70% correct?
Answer:
25
Step-by-step explanation:
Answer:
21 answers.
Step-by-step explanation:
First, change the percentage into a decimal point. Move the decimal point to the left two place values and drop the percentage sign:
70% = 70/100 = 0.70
Next, multiply 0.70 with the total amount of questions (30):
30 x 0.70 = 21
21 answers must be correct.
Check:
Divide 21 with 30:
21/30 = 0.70 = 70%
~
1/2+1/3+1/6+1/2+1/8+1/4= see problem as an addition problem
Answer:
1 7/8
Step-by-step explanation:
MaryAnne has 90 quilt squares. She plans to use 32 of them to make a quilt. What percent of her quilt square stock is she using? List your answer as a percent rounded to the nearest tenth.
Percentage = ( number used / total number) x 100
32/90 = 0.3555
0.3555 x 100 = 35.56%
Rounded to nearest tenth = 35.6%
Mary Anne is using about 35.6% of her quilt squares stock.
What is percent?A percent is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Percent FormulaPercentage = (Value/Total value) × 100.
According to the given question.
Total number of quilt squares Mary Anne have = 90
Number of quilt squares Mary Anne is using = 32
Therefore,
The percent of her quilt square she is using
= [tex]\frac{32}{90} \times 100[/tex]
[tex]= 0.3555\times 100[/tex]
[tex]= 35.6[/tex] %
Hence, Mary Anne is using about 35.6% of her quilt squares stock.
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How do I do this, is the equation 40=ksqrt(65)?
Answer:
Step-by-step explanation:
Start a little more generally. Carefully find k
distance = k * speed ^2
112 = k*40^2
112 = k * 1600 Divide by 1600
112/1600 = k
k = 0.07
Now do the question you are asked to do.
distance = k * speed^2
distance = 0.07 * 65^2
distance = 295.75
Now having done that, you can set up a proportion.
d1 / d2 = k speed1^2/kspeed2^2 Cancel the ks
112/d2 = 40^2 / 65^2 Cross multiply
112 * 65^2 = 40^2 * d2 Divide by 40^2
112 * 65^2/40^2 = d2 Expand the squares
112 * 4225 / 1600 = d2
295.75 = d2
The second way is shorter, but I suggest the long way until you get comfortable with it.
PLS HELP :( i’ve been trying to understand this but i cant. please explain this if you know how to do it pleaseee
Answer:
[tex]\huge\boxed{\sf x = 17}[/tex]
Step-by-step explanation:
Since m is a straight line, its measure is 180 degrees.
So,
2x + 5 + 8x + 5 = 180
2x + 8x + 5 + 5 = 180
10x + 10 = 180
10x = 180 - 10
10x = 170
Divide both sides by 10
x = 17
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Peace!Two cars start at the same point. One travels north at 65 km/h and the other travels east at 50 km/h. How far are they apart after 30 minutes?
Answer:
1they are 15 kilometers apart
What is the length of an edge of a cube whose total surface area is equal to 150 square feet? A. 7.5 ft B. 5 ft C. 10 ft D. 25 ft
Answer:
5 ft
Step-by-step explanation:
Using the formula,
A = 6a²
a² = A/6
a = √(A/6)
a =√(150/6)
a = √25
a = 5
The area of a 2D form is the amount of space within its perimeter. The length of the edge of the cube is 5 ft. The correct option is B.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The total surface area of a cube is 6 times the area of a face which is equal to the square of side of the cube. Therefore, the total surface area of the cube is,
Total surface area of cube = 6a²
Given that the total surface area of the cube is 150 square feet. Therefore, the length of the side of the cube can be written as,
Total surface area of cube = 6a²
150 square feet = 6a²
150 square feet / 6 = a²
25 ft² = a²
a = √(25 ft²)
a = 5 ft
Hence, the length of the edge of the cube is 5 ft.
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What is the coordinate of point A?
Answer:
The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane.
Hope it is helpfully.If ST = 3x + 8, SU = 24 and
TU = 2x – 4, what does ST = ?
Step-by-step explanation:
For TU is it -2x-4 or 2x-4 cause the question and what on your paper are different
Answer:
20
Step-by-step explanation:
ST= SU - TU
=24 - (2x-4)
=24-2x+4=28-2x
but. 2x-4+3x+8 = 5x+4 = 24
5x=24-4=20
x=20/5=4
so ST=28-2x= 28-2(4)
ST=20
The number 0,1,2,3,4 and so on are called
A straight driveway leading to a hotel is 150 feet long and 12 feet wide. It is pave with concrete 6
inches thick. At a cost of $6.25 per cubic foot, how much did the concrete cost.
How high is a tree that cast a 33ft shadow at the same time a9ft post casts a shadow w
Angles R and S are complementary. If angle R is = 4x - 20 and angle S = 6x - 7, then angle R measures ___ degrees.
Answer:
26.8°
Step-by-step explanation:
4x - 20 + 6x - 7 = 90
10x -27 =90
10x = 90+27
10x= 117
x = 11.7
so, the angle R = 4x-20 =4(11.7)-20
= 46.8-20 = 26.8°
Select all the correct answers. Which vectors are unit vectors?
Answer:
Step-by-step explanation:
[tex](-\frac{1}{3} \sqrt{\frac{7}{2} } )^2+(\frac{1}{3} \sqrt{\frac{13}{2} } )^2\\=\frac{1}{9} (\frac{7}{2} +\frac{13}{2} )\\=\frac{1}{9} (\frac{7+13}{2} )\\=\frac{1}{9} \times10\\=\frac{10}{9} \neq 1[/tex]
not a unit vector.
b.
[tex](\frac{1}{\sqrt{3} } )^2+(-\sqrt{\frac{2}{3} } )^2\\=\frac{1}{3} +\frac{2}{3} \\=\frac{1+2}{3} \\=\frac{3}{3} \\=1[/tex]
it is a unit vector.
c.
[tex](\frac{1}{2} \sqrt{\frac{5}{3} } )^2+(-\frac{1}{2} \sqrt{\frac{7}{3} } )^2\\=\frac{1}{4} (\frac{5}{3} +\frac{7}{3} )\\=\frac{1}{4} (\frac{5+7}{3} )\\=\frac{1}{4} (\frac{12}{3} )\\=\frac{1}{4} (4)\\=1[/tex]
it is a unit vector.
d.
[tex](\frac{3}{\sqrt{7} } )^2+(-\frac{2}{\sqrt{7} } )^2\\=\frac{9}{7} +\frac{4}{7} \\=\frac{9+4}{7} \\=\frac{13}{7} \neq 1[/tex]
it is not a unit vector.
Find x. Round your answer to the nearest tenth of a degree.
Answer:
41.4
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos x = 9/12
Taking the inverse cos of each side
cos ^-1 ( cos x) = cos ^-1 (9/12)
x = 41.41
To the nearest tenth
x = 41.4
A state lotto has a prize that pays $1,600 each week for 20 years.
The total value of the prize: $1,664,000
If the state can earn 9% interest on investments, how much money will they need to put into an account now to cover the weekly prize payments?
--
I'm so stuck on this question! I've tried every single formula I can remember from the textbook, but I just don't get it! Apparently the answer is "$771,396.86" but I can't for the life of me understand how! Please help!
Answer:
Step-by-step explanation:
Start by calculating the effective rate of interest:
.09/52= .0017307
(we divide by 52 because there are 52 weeks in a year)
Then just use the annuity formula
[tex]1600(\frac{1-(1+.0017307)^{-(20*52)}}{.0017307})=771396.864393[/tex]
Given a function described as the equation y = 4x - 4, what is y when x is 1, 2, and 3?
Answer:
f(1) = 0
f(2) = 4
f(3) = 8
Step-by-step explanation:
Substitute the values for the variable x.
[tex]f(1)=4(1)-4\\f(1)=4-4\\f(1)=0\\\\f(2)=4(2)-4\\f(2)=8-4\\f(2)=4\\\\f(3)=4(3)-4\\f(3)=12-4\\f(3)=8[/tex]
When x= 1
y = 4(1) - 4
y = 0
when x = 2
y = 4(2) - 4
y = 4
when x = 3
y = 4(3) - 4
y = 8
Can some one please help -18-17 simplified
Answer:
-35
Step-by-step explanation:
-(18+17)
-35
that should be the answer but don't quote me on it
Which equation is represented by the table?
Which equation is represented by the table?
Answer:
The choose A.
y= – | x+1|–4
I hope I helped you^_^
The inner dimensions of an in-ground swimming pool are: width = 13.0 ft, length = 18.0 ft, and depth = 9.0 ft. The pool walls and the bottom are uniformly 1.0 ft thick and made of concrete. What is the weight, W (in pounds) of the concrete used to construct the pool, if one cubic inch of concrete weighs 0.25 pounds? (Note: You may find it useful to draw a labeled diagram of the pool.
a. 386208
b. 32184
c. 3582
d. 2682
John is playing a game with a standard deck of playing cards. He wants to draw a jack on the first try. Which of the following statements is true?
a. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack increases.
b. The probability that John draws a jack on the first try is 3/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack stays the same.
c. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack decreases.
d. The probability that John draws a jack on the first try is 1/13. If John replaces the card, re- shuffles, and draws again, the probability that he will pull another jack stays the same.
Answer:
d
Step-by-step explanation:
It is a 1/13 chance but even if you shuffle and replace it, its still a 1/13 chance.
The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same. Hence, statement d is correct.
What do we mean by the probability of an event?The probability of an event is the ratio of the number of favorable outcomes to the event to the total number of outcomes for the experiment.
If we have an event A, the number of favorable outcomes to event A is n, and the total number of outcomes in the experiment is S, then the probability of the event A is given by,
P(A) = n/S.
How do we solve the given question?We are given that John is playing a game with a standard deck of playing cards.
We are said that he wants to try to draw a jack on the first try.
Let the event of drawing a jack be A.
The number of outcomes favorable to the event A (n) = 4 (number of jacks)
The total number of outcomes in the experiment of drawing a card (S) = 52 (the total number of cards)
∴ The probability of the event A is given by,
P(A) = n/S = 4/52 = 1/13.
∴ The probability of drawing a jack on the first try is 1/13.
When he replaces the card and re-shuffles it, the probability will be the same as the number of favorable outcomes and the total number of outcomes remains the same.
∴ The probability that John draws a jack on the first try is 1/13. If John replaces the card, re-shuffles, and draws again, the probability that he will pull another jack stays the same. Hence, statement d is correct.
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6 4/5 + 3 2/3
add and simplify
Answer:
10 3/5
Step-by-step explanation:
6 4/5 + 3 4/5
First convert to improper fraction,
34/5 + 19/5
Then add the improper fractions,
=>53/5
Then convert improper fraction to mixed fraction,
=> 53/5 = 10 3/5
Convert 3250 ml to l
3250 mL = 3.25 L
* 1 mL = 0.001 L
I hope I helped you^_^
Solve For x.
(-4x+5)-(6x+7)=0
(Pls Explain Your Answer in Simple Terms)
Answer:
[tex] - 4x + 5 - (6x + 7) = 0\\ - 4x + 5 - 6x - 7 = 0 \\ - 10x - 2 = 0 \\ 10x + 2 = 0 \\ 10x = - 2 \\ x = \frac{ - 2}{10} \\ x = - .2 \\ thank \: you[/tex]
Find the area of the triangle
Answer:
12.7 m
Step-by-step explanation:
use pythagorean theorem
[tex]13^{2} + b^{2} = 18.2^{2}[/tex]
rounds to 12.73735
not fully sure if that's right
If a cubic inch of gold weighs 316 grams, how much does a cubic centimeter of gold weigh?
9514 1404 393
Answer:
19.3 g/cm³
Step-by-step explanation:
There are 2.54 cm in one inch, so the weight of 1 cm³ is ...
(316 g/in³) ÷ (2.54 cm/in)³ = 19.3 g/cm³
Find the measure of ∠Z.
Answer:
105+105+2x=360 and x=75
Step-by-step explanation:
z=75
Answer:
Step-by-step explanation: