The width is 3 3/4. you just have to divide 5 5/8 by 1 1/2.
let's firstly convert those mixed fractions to improper fractions and then proceed.
[tex]\bf \stackrel{mixed}{5\frac{5}{8}}\implies \cfrac{5\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{45}{8}}~\hfill \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=length\\ w=width\\ \cline{1-1} L=\frac{3}{2}\\ A=\frac{45}{8} \end{cases}\implies \cfrac{45}{8}=\cfrac{3}{2}w\implies \cfrac{45}{8}=\cfrac{3w}{2}\implies 90=24w \\\\\\ \cfrac{90}{24}=w\implies \cfrac{15}{4}=w\implies 3\frac{3}{4}=w[/tex]
4. About 30% of the U.S. population is under 20 years old. About 17% of the population is over 60, which of the following is the probability that a person chosen at random is under 20 or over 60?
-17%
-53%
-47%
-30%
A = person is under 20
B = person is over 60
P(A or B) = P(A) + P(B) ... works because A and B are mutually exclusive
P(A or B) = 0.30 + 0.17
P(A or B) = 0.47 = 47%
The probability that a person chosen at random is under 20 or over 60 is 47% , option C is the correct answer.
What is Probability ?Probability is a topic in mathematics where the likeliness of an event is studied.
The range of probability is 0 to 1 .
0 indicates uncertainty to 1 indicating certainty.
It is given in the question that
30% of the U.S. population is under 20 years old
About 17% of the population is over 60
probability that a person chosen at random is under 20 or over 60 = ?
Let P(A) represents person under 20
Let P(B) represents person over 60
As a person is chosen at random and the events cannot happen together so they are mutually exclusive events.
The probability for mutually exclusive event is given by
P(A or B) = P(A) + P(B)
P(A) = 17% = 0.17
P(B) = 30% = 0.3
P(A or B) = 0.30 + 0.17
P(A or B) = 0.47 = 47%
Therefore , the probability that a person chosen at random is under 20 or over 60 is 47% , option C is the correct answer.
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Please answer fast!!! Will give brainliest!!!
Given: m HL =40°, m EV =130°, m VL =110°. Find: m∠EYH.
Answer:
The measure of angle EYH is [tex]25\°[/tex]
Step-by-step explanation:
step 1
Find the measure of arc EH
we know that
[tex]arc\ EV+arc\ VL+arc\ HL+arc\ EH=360\°[/tex] ----> by complete circle
substitute the given values
[tex]130\°+110\°+40\°+arc\ EH=360\°[/tex]
[tex]280\°+arc\ EH=360\°[/tex]
[tex]arc\ EH=360\°-280\°=80\°[/tex]
step 2
Find the measure of angle EYH
we know that
The measurement of the outer angle is the semi-difference of the arcs which comprises
[tex]m<EYH=\frac{1}{2}(arc\ EV-arc\ EH)[/tex]
substitute the values
[tex]m<EYH=\frac{1}{2}(130\°-80\°)=25\°[/tex]
An elevator travels 110 feet in 10 seconds. At that speed, how fac can this elevator travel in 12 seconds?
Divide 110 by 10 to get a rate if 11 feet per second. Multiply 11 by 12 seconds to get 132 feet
Using the keys above, enter an expression equivalent to (3x^2-8x-24)-(9x+6) using the fewest possible terms.
Answer:
Final answer in simplified form is [tex]3x^2-17x-30[/tex]
Step-by-step explanation:
Given expression is [tex](3x^2-8x-24)-(9x+6)[/tex]
Now we need to find an equivalent expression for [tex](3x^2-8x-24)-(9x+6)[/tex]
First we can distribute the negative sign and remove the parenthesis the combine like terms
[tex](3x^2-8x-24)-(9x+6)[/tex]
[tex]=3x^2-8x-24-9x-6[/tex]
[tex]=3x^2-17x-30[/tex]
Hence final answer in simplified form is [tex]3x^2-17x-30[/tex]
write a rational expression involving one variable for which the excluded values are -4 and -7. Please Help!!!!!!
Answer:
See below.
Step-by-step explanation:
Values are excluded if they make the denominator zero, so one rational expression could be:
(x^2 - 9) / (x + 4)(x + 7)
- when x = -4 or -7 then the denominator is zero so the values of the function is undefined for these values.
The image of point A is
A'
B'
C'
D'
Answer:
A' because it is translated to another position.
Hope this helps
Answer: A'
Step-by-step explanation:
From the given figure , it can be seen that the quadrilateral ABCD is translated to produce A'B'C'D' by some distance in a particular direction.
A translation is a kind of rigid motion used in geometry to trace a function that maps an shape a particular distance.The line segments joining a vertex in the pre-image to the corresponding vertex in the image are congruent and parallel.We can see that the point A' in the image is corresponding to the point A in the pre-image.
Hence, the image of point A is A' .
An end table costs $69.85 today. If the CPI is 194, what would an end table cost in 1983, to the nearest cent? a. $135.51 b. $124.15 c. $36.00 d. $23.76
Answer:
$36.00
Step-by-step explanation:
The cost performance index (CPI) is a measure of the financial effectiveness and efficiency of a project. As a ratio it is calculated by dividing the budgeted cost of work completed, or earned value, by the actual cost of the work performed, that is to say:
CPI = Budgeted cost of work / Actual cost of work
From the statement we know that:
CPI = 1.94
Budgeted cost of work= $69.85
Cost of work in 1983 = Budgeted cost of work / CPI
Cost of work in 1983 = $69.85 / 1.94 = $36.00
Answer:
The answer is C
Step-by-step explanation:
Thomas has a collection of CDs that he plays regularly. He has five rock CDs, three country CDs, and four movie sound track CDs. If Thomas chooses a CD at random, what are the odds that he chooses a country CD?
Answer:
The answer is 1/4.
Step-by-step explanation:
5 rock CDs, plus 3 country CDs, plus 4 movie sound track CDs, equal 12 CDs in total. To find the odds of choosing a country CD, you divide the total number of CDs, by the number of what you choose (3/12).
Answer:
The odds that he choose a country CD is 1/3
Step-by-step explanation:
12/12 ÷ 3 = 1/3
The table shows values for functions f(x) and g(x). What are the known solutions to f(x) and g(x)? Select each correct answer. 1, 3, 7, 9, 11
Answer:
3, 7
Step-by-step explanation:
Since we are asked for the known solutions to f(x) = g(x), we need to consider the values of the functions where x's are the same.
If you look at the table, you will see that f(-9) = g(-9) = 3 and f(2) = g(2) = 7.
The value of x where f(x) = g(x) is 3
Functions and valuesAccording to the given question, we are to find the value of x for which the function f(x) is equal to g(x)
From the given table, we need to find the point where the values of f(x) = g(x). The value of x at this point is the solution.
Therefore from the table, the value of x where f(x) = g(x) is 3
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POP QUIZ
First person to answer correctly gets brainliest
1. 1-1
2. (1248/56)^0
3. 2*0
Answer:
What's the question? All you posted was the potential answers.
Step-by-step explanation:
This seems really easy, but
1) 0
2) 0
3) 0
please show me how to do this, I need to show work
Answer:
x ≈ 11.68 ( to 2 dec. places )
Step-by-step explanation:
Given
[tex]6^{(x-8)}[/tex] = 730 ( take log of both sides )
log [tex]6^{(x-8)}[/tex] = log730
(x - 8)log6 = log730 ( divide both sides by log6 )
x - 8 = [tex]\frac{log730}{log6}[/tex] ≈ 3.68 ( add 8 to both sides )
x ≈ 11.68 ( to 2 dec. places )
Answer:
6^ 3.679648309
Step-by-step explanation:
Don't really have one. Went with trial and error. Set calculator to 2 d.p by the way
The Mitchells are renting a boat for the day. It costs $100, plus $20 for each hour. They have to pay for a whole hour even if they are not out there for a whole hour. For example if they boat for 3 and a half hours, they have to pay for 4 hours. They don't want to spend more than $250 for the day. How many hours can they boat? Write an inequality and solve. A)100 + 20x ? 250. They can boat for 7 hours. B)100 + 20x ? 250. They can boat for 8 hours. C)100 + 20x ? 250. They can boat for 8 hours. D)100 + 20x ? 250. They can boat for 7 hours.
Your answer would be C.
Step-by-step explanation:
250 dollars. 250-100= 150. 150/20 equls 7.5. 7.5 will round to 8. It iwll be 8 hours hey will have to pay for.
Please help me out please
Answer:
98
Step-by-step explanation:
If half the diagonal is 7 yd, then the full diagonal is 14 yd.
If we call the side length s, then using Pythagorean theorem:
c² = a² + b²
(14)² = s² + s²
196 = 2s²
s² = 98
The area of a square is s², so:
A = s²
A = 98
The area is 98 yd².
WILL GIVE BRAINLIEST
Answer:
12 m
Step-by-step explanation:
The formula for the area of a triangle is ...
A = 1/2bh . . . . . b represents the base; h represents the height
We are told that the height is 5 m less than the base, so we have ...
42 = (1/2)(b)(b -5)
84 = b(b-5) . . . . . . . . multiply by 2
We want two factors of 84 that differ by 5. The factors are ...
84 = 1·84 = 2·42 = 3·28 = 4·21 = 6·14 = 7·12
The relevant factors are 7 and 12, so now we know b-5 = 7 and b = 12.
The length of the base is 12 m.
Write an equation for a cosine function with an amplitude of 3, a period of 2, a phase shift of -2, and a vertical displacement of 5.
y=3cos2π(x+2)+5
y=3cos2π(x−5)+2
y=5cos3π(x−2)+2
y=3cos2π(x+2) / 2+5
Answer:
Last option
[tex]y = 3cos(\pi(x+2)) + 5[/tex]
Step-by-step explanation:
The general cosine function has the following form
[tex]y = Acos(b(x-\phi)) + k[/tex]
Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.
[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.
k is the vertical displacement.
[tex]\phi[/tex] is the shift phase
In this problem :
[tex]A = 3[/tex]
[tex]\frac{2\pi}{b}=2\\\\ b=\frac{2\pi}{2}\\\\ b=\pi[/tex]
[tex]\phi =-2\\\\k = 5[/tex]
So The function is:
[tex]y = 3cos(\pi(x+2)) + 5[/tex]
Two forces act on an object. The first Force has a magnitude of 400 Newtons and acts at an angle of 30 degrees as measured from the horizontal. Second Force has a magnitude of 280 Newtons in accident angle of 135 degrees is measured from the horizontal. Determine the vector v that represents the resultant Force.
a. v=(200-140rtsq2)i+(200rtsq3+140rtsq2)j
b. v=(200+140rtsq2)i+(200rtsq3+140rtsq2)j
c. v=(200rtsq3+140rtsq2)i+(200+140rtsq2)j
d. v=(200rtsq3-140rtsq2)i+(200+140rtsq2)j
ANSWER
Option D is correct
EXPLANATION
We resolve the forces into component forms.
[tex]F_1 = 400 \cos(30) i + 400 \sin(30) j[/tex]
[tex]F_1 = 200 \sqrt{3} i +200j[/tex]
Also the second is resolved to obtain,
[tex]F_2= 280 \cos(135) i + 280 \sin(135) j.[/tex]
[tex]F_2= - 140 \sqrt{2} i + 140 \sqrt{2} j[/tex]
To find the resultant vector, V, We add the corresponding components of the two forces to get:
[tex]V=F_1+F_2 [/tex]
[tex] \implies \: V = (200 \sqrt{3} - 140 \sqrt{2} )i + (200 + 140 \sqrt{2})j[/tex]
The correct answer is D.
the number line shows the record low temperatures for four states Hawaii 12 degrees Fahrenheit North Carolina -38 degrees Fahrenheit South Dakota -58 degrees Fahrenheit and Montana -70 degrees farenhight enter the difference in degrees between the record low temperatures in Hawwaii and South Dakota
Answer: -70 degrees difference
Step-by-step explanation:
Answer:
-70!!
Step-by-step explanation:hope this helped!
Sketch the following in standard position.
Determine the quadrant the angle lies in (if it is on an axis, state which axis it is on and if it is + or - axis)
Then determine the reference angle.
Answer: 1) Quadrant: I, reference angle: [tex]\dfrac{2\pi}{5}[/tex]
2) Quadrant: III, reference angle: 85°
3) Quadrant: IV, reference angle: [tex]\dfrac{\pi}{4}[/tex]
Step-by-step explanation:
Reference angle is the angle closest to the x-axis
1) The given angle is (2/5)π. The first quadrantal (π/2) would be (2.5/5)π
Since (2/5)π < (2.5/5)π then it must be in Quadrant 1.
The angle closest to the x-axis is the same as the given angle.
2) The given angle is -95°. It is measured clockwise since it is a negative angle. Since it is greater than 90°, it is greater than the 270° quadrantal. So it must be in Quadrant III.
The angle closest to the x-axis is 85°.
3) The given angle is (23/4)π. Since (8/4)π is one rotation, this is greater than one rotation. (23/4)π - (8/4)π - (8/4)π = (7/4)π. So, it rotates two complete rotations and lands at coterminal angle (7/4)π.
The angle closest to the x-axis is π/4
Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1?
a. f(x) = (x + 7)(x – i)(x + 5)(x + i)
b. f(x) = (x – 7)(x – i)(x – 5)(x + i)
c. f(x) = (x – (7 – i))(x – (5 + i))(x – (7 + i))(x – (5 – i))
d. f(x) = (x + (7 – i))(x + (5 + i))(x + (7 + i))(x + (5 – i))
Answer:
C. [tex]f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))[/tex]
Step-by-step explanation:
We want to find the equation of a polynomial the following properties;
i. Leading coefficient is 1
ii. roots (7 + i) and (5 – i) with multiplicity 1
Recall the complex conjugate properties of the roots of a polynomial.
According to this property, if
[tex]a+bi[/tex] is a root of a polynomial, then the complex conjugate, [tex]a-bi[/tex] is also a root.
This means that:
(7 - i) and (5 + i) with multiplicity 1 are also roots of this polynomial.
The complete set of roots are:
[tex]x=(7+i),x=(7-i),x=(5-i),x=(5+i)[/tex]
Therefore the polynomial is:
[tex]f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))[/tex]
The correct choice is C.
Final answer:
The correct polynomial function with roots (7 + i) and (5 – i), each with multiplicity 1 and a leading coefficient of 1, is given by (c) f(x) = (x – (7 + i))(x – (5 – i))(x – (7 - i))(x – (5 + i)).
Explanation:
The question asks which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1. For a polynomial to have these roots, its conjugates, (7 - i) and (5 + i), must also be roots because complex roots always come in conjugate pairs if the polynomial has real coefficients.
This leads us to option (c) as the correct answer. To form a polynomial with these roots, we take each root, turn it into a binomial by subtracting it from x, and then multiply these binomials together.
Doing so for the given roots, we get:
f(x) = (x – (7 + i))(x – (5 – i))(x – (7 - i))(x – (5 + i))
This polynomial matches option (c), confirming it as the correct answer.
In a bag there are 5 red marbles, 10 blue marbles, and 15 green marbles. What is the probability that you will draw a blue marble?
1/2
1/3
2/3
3/4
probability of drawing a blue marble is 1/3
One card is selected at random from a deck of cards. Determine the probability that card selected is a 5 or a 10?
Answer:
0.5
Step-by-step explanation:
because while solving a probability question you divide it by thee full number
Need help with the problem in the photo.
Answer:
B. 3x -2y = 10
Step-by-step explanation:
The given line rises three units for each two units of run to the right. Hence its slope is 3/2. A parallel line will also have a slope of 3/2.
Of the equations we can see, selection B has a slope of 3/2. It can be rewritten in slope-intercept form as ...
3x -10 = 2y . . . . . add 2y-10 to isolate the y-term; next divide by 2.
y = 3/2x -5 . . . . . the coefficient of x is the slope
Answer:
B. 3x -2y = 10
Step-by-step explanation:
The given line rises three units for each two units of run to the right. Hence its slope is 3/2. A parallel line will also have a slope of 3/2.
Of the equations we can see, selection B has a slope of 3/2. It can be rewritten in slope-intercept form as ...
3x -10 = 2y . . . . . add 2y-10 to isolate the y-term; next divide by 2.
y = 3/2x -5 . . . . . the coefficient of x is the slope
which of the following is a point on the plane curved defined by the parametric equations?
x=4t
y=12t^2+4t-1
a. (4,7)
b. (4,207)
c.(-2,4)
d.(-2,0)
Answer:
d.(-2,0)
Step-by-step explanation:
The given parametric equation is:
[tex]x=4t[/tex]
[tex]y=12t^2+4t-1[/tex]
We make t the subject in the first equation;
[tex]t=\frac{x}{4}[/tex]
We substitute into the second equation to get:
[tex]y=12(\frac{x}{4})^2+4(\frac{x}{4})-1[/tex]
[tex]y=\frac{3}{4}x^2+x-1[/tex]
When x=4 , [tex]y=\frac{3}{4}(4)^2+4-1=15[/tex]
When x=-2 , [tex]y=\frac{3}{4}(-2)^2+-2-1=0[/tex]
Therefore the point (-2,0) lies on the given parametric curve.
Which of the following correctly shows the length of each radius, the point where the circles intersect, and the equation of the tangent line at this point?
actually box 3 is correct.
because their radiuses are easy to find
but the tangent line is x=-4 or x=4
The option third radius for circle A is 4, the radius for circle B is 3 and the point of intersection is (4,3) and the tangent equation is x = 4 is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have two circles in the graph plot:
From the graph plot:
For the circle:A the radius is 4
For the circle:B the radius is 3
The point of intersection point (4, 3)
The tangent line will be:
x = 4
Thus, the option third radius for circle A is 4, the radius for circle B is 3 and the point of intersection is (4,3) and the tangent equation is x = 4 is correct.
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Kenneth brings a partially-filled beaker of red liquid into is his laboratory and uses an apparatus to add drops of blue liquid to the beaker at a constant rate. The equation y = 5x + 15 describes the relationship between the number of minutes (x) since Kenneth began adding drops of blue liquid to the beaker and the total amount of liquid in the beaker (y), in milliliters. Which statement correctly describes a solution of the equation?
there are two ways you can do
[tex]y = 5x + 15 \\ \\ 1. \: y - 15 = 5x \\ 2. \: \frac{y - 15}{5} = x \\ 3. \: x = \frac{y - 15}{5} \\ \\ \\ 1. \: 5x + 15 = y \\ 2. \: 5x + 15 + - 15 = y + - 15 \\ 5x = y - 15 \\ 3. \: \frac{5x}{5} = \frac{y - 15}{5} \\ x = \frac{1}{5} y - 3[/tex]
A solution of the equation y = 5x + 15 represents a specific moment during Kenneth's experiment, where 'x' is the time elapsed since he started adding the blue liquid, and 'y' is the total volume of the liquid mixture in the beaker.
Explanation:The equation y = 5x + 15 provided is a linear equation, which is a mathematical expression showing a constant rate of change. In this context, Kenneth's experiment in the laboratory, 'x' is the number of minutes since Kenneth began adding drops of blue liquid to the beaker, and 'y' is the total amount of liquid, in milliliters, in the beaker.
A solution to this equation refers to specific values for 'x' and 'y' which make this equation true. For instance, if we choose x = 1 minute, then we can calculate 'y' by substituting 'x' into the equation which gives y = 5*1 + 15 = 20 mL. This means that after 1 minute, Kenneth has 20 mL of liquid in his beaker. Indeed, every solution to this equation reflects a specific moment (x, or number of minutes) in Kenneth's ongoing experiment and the corresponding total volume (y) of the mixture in the beaker.
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Need help on these four and then I am done, please help, I'm slowly getting the hang of it, I've already done all the other ones!
For #11, the answer is C, I’m pretty sure.
For #12, KM = LN, and LM = KN.
I can’t help with the others though, sorry :/
Sienna wants to set up a special fund so she can save to buy presents for her friends and family throughout the year. If her gift purchases last year totalled $580, estimate how much she should save each month to have approximately the same amount available for gifts next year? a. Approximately $480 b. Approximately $58 c. Approximately $48 . d. Approximately $96
Answer:
c. $48
Step-by-step explanation:
Answer:
C. Approximately $48
Step-by-step explanation:
Given,
Total amount she have to save this year = $ 580,
The number of months in a year = 12,
So, the amount saved by her in each month
[tex]=\frac{\text{Total amount}}{\text{Number of months}}[/tex]
[tex]=\frac{580}{12}[/tex]
= $ 48.333333..
≈ $ 48
Hence, OPTION C is correct.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Choose the correct formula for the function g.
Answer: C) g(x) = 2ˣ⁻³ + 2
Step-by-step explanation:
The general form of an exponential equation is: g(x) = 2ˣ⁻ᵃ + b where
"a" is a horizontal shift to the left if positive (or right if negative)"b" is a vertical shift up if positive (or down if negative)The new function is shifted UP 2 units and RIGHT 3 units
a = 3b = 2--> g(x) = 2ˣ⁻³ + 2
Which of the following square root of -80
You can factor -80 as
[tex]-80 = (-1)\cdot 16 \cdot 5[/tex]
So, we have
[tex]\sqrt{-80} = \sqrt{(-1)\cdot 16 \cdot 5}[/tex]
The square root of a product is the product of the square roots:
[tex]\sqrt{-80} = \sqrt{(-1)}\sqrt{16}\sqrt{5}[/tex]
Since [tex]i^2=-1[/tex] and [tex]4^2=16[/tex], we have
[tex]\sqrt{-80} = 4i\sqrt{5}[/tex]
The equivalent expression of the complex expression √(-80) will be 4i√5. Then the correct option is C.
What is a complex number?A complex number is a number that is made up of both real and imaginary numbers. The complex number can be given as a + ib where a is the real part and ib is the imaginary part.
The expression is given below.
⇒ √(-80)
And we know that √(-1) = i
Then the expression can be written as
⇒ √(-1 x 16 x 5)
⇒ 4i√5
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1. Find the phase shift of the function y = 5cos(2x + pi/2).
2. Which of the following functions has a maximum y value of 4?
y = 4cosx
y = cos4x
y = cosx + 4
y = cos(x + 4)
Answer:
see explanation
Step-by-step explanation:
1
The cosine function in standard form is
y = acos(bx + c)
where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and
phase shift = - [tex]\frac{c}{b}[/tex]
here b = 2 and c = [tex]\frac{\pi }{2}[/tex], thus
phase shift = - [tex]\frac{\frac{\pi }{2} }{2}[/tex] = - [tex]\frac{\pi }{4}[/tex]
2
the amplitude = | a |
which has a maximum of a and a minimum of - a
y = 4cosx ← has a maximum value of 4
Final answer:
The phase shift of the function y = 5cos(2x + π/2) is -π/4 radians. The functions y = 4cosx and y = cosx + 4 both have a maximum y value of 4.
Explanation:
To find the phase shift of the function y = 5cos(2x + π/2), we need to look at the argument of the cosine function. The general form is y = Acos(Bx - C) where C/B is the phase shift. In this case, the argument of the cosine is 2x + π/2, thus the phase shift is -π/2 divided by the coefficient of x, which is 2, giving us a phase shift of -π/4 or -0.785 radians.
To determine which of the provided functions has a maximum y value of 4, consider the amplitude of the cosine functions. For the functions y = 4cosx, y = cos4x, and y = cos(x + 4), the amplitude is 1, and thus the maximum y value is 1 for the latter two, and 4 for the first one. However, y = cosx + 4 is a cosine function shifted upward by 4 units, and hence its maximum y value is also 5. So, the functions with a maximum y value of 4 are y = 4cosx and y = cosx + 4.