Answer:
D) 56 inches to 74 inches
Step-by-step explanation:
By the Empirical Rule, 99.7% of data in a normal distribution spread across ±3σ standard deviations from the mean μ.
Hence, the range maximum is μ+3σ = 65+3(3) = 65+9 = 74 inches, and the range minimum is μ-3σ = 65-3(3) = 65-9 = 56 inches
Thus, 99.7% of the population will have a height within the range of 56 inches to 74 inches
find the answer to this question: 205.04/4
What is the slope of the line that passes through the points (-4,210) and
(-7, -19)?
My sister and I each brought a bottle of sunblock to the beach.My bottle had 89ml and my sister’s had 147 ml.How much more sunblock did my sister have?
Answer:
58 more
Step-by-step explanation:
Simmons earned a gross pay for the week of $694. If 8% was withheld for social security, 4% for Medicare taxes, 18% for income taxes, and $45 for insurance premiums, what was his net pay?
The net pay of Simmons will be $494 after the deductions.
What is net pay?The net pay is defined as the actual amount earned after the deductions of taxes and loan emi etc.
here simmon's total earning is $694
After the deductions the simmon will left with:
694x0.92x0.96x0.88=539.38
Now the insurance premiums are of $45
So the final amount will be
=539.38-45=494.38
Hence net pay of Simmons will be $494 after the deductions.
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2. 47 in = ? ft ? in
a .3ft 11in
b. 3ft 9in
c. 4ft 0in
564 ft 0 in
Answer:
a
Step-by-step explanation:
3 feet 11 inches
hope this helps
A soup can has a diameter of 9.8 cm and a height of 13.2 cm. What is the approximate volume of 12 soup cans?
Answer:
about 11,948.05 cubic cm
Step-by-step explanation:
[tex]12 \times \pi( {4.9}^{2} )(13.2) = 11948.05[/tex]
the ratio of boys:girls in a class is 4:5
A: what is the fraction of boys in the class
B: what is the fraction of girls in the class
Answer:
Answer: 4/9 of the class are boys and 5/9 of the class are girls.
Step-by-step explanation:
There are 9 nine students in total in the class since 4 + 5 = 9.
Input the amount of boys and girls there are in the class in the numerator and have 9 as the denominator. 4/9 of the class are boys and 5/9 of the class are girls.
--~Hope this helped~--
Find the area. Answer without units. *
The area of the composite figure composed of two rectangles is 217 centimetres squared
How to find the area of the composite figure?
The area of the composite figure can be found as follows:
The area of the composite figure can be found by adding up the individual area of each shape in the figure.
Therefore,
area of the figure = area of rectangle + area of rectangle
area of a rectangle = lw
where
l = lengthw = widthTherefore,
area of the figure = (14 × 11) + (7 × 9)
area of the figure = 154 + 63
area of the figure = 217 cm²
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Giving 16 points, give the right answer because I keep getting different results. Find the value of x
Answer:
38.7
Step-by-step explanation:
Use cosine
cos = adj / hyp
adj = cos x hyp
adj = cos(49) x 59
adj = 38.7
You purchased a new car for $32,000. The value
of the car decreases by 12% each year. Which
function could be used to model the value of the
car V after years?
a. V(t)=32,000(1+0.12)'
b. V()=32,000(1 -0.12)'
c. V(t)=32,000(0.12)'
d. V(t)=32,000 - 0.12r
The function that could be used to model the value of the car V after years is V(t) = 32000(1 - 0.12)^t
How to determine the function?The given parameters are:
Initial value, a = 32000
Rate, r = 12% --- depreciation rate
Since the value of the function decreases with time, the equation of the exponential function would be:
V(t) = a(1 - r)^t
So, we have:
V(t) = 32000(1 - 12%)^t
Express as decimal
V(t) = 32000(1 - 0.12)^t
Hence, the function that could be used to model the value of the car V after years is V(t) = 32000(1 - 0.12)^t
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a cylinder has a diameter or 4 ft and height of 7 ft use 3.14 for pi
Answer:
87.92ft^3
Step-by-step explanation:
Formula:
V= π*r^2 *h
V=π*2^2*7V=π*4*7V=12.56 *7V=87.92ft^3Help pls I don't understand
A radioactive compound with mass 470 grams decays at a rate of 3% per hour. Which
equation represents how many grams of the compound will remain after 6 hours?
Submit Answer
O C = 470(0.03)
O C = 470(0.7)
O C = 470(1 + 0.03)
C = 470(1 – 0.03)
After 6 hours the radioactive compound with mass 470 grams becomes 391.49 grams and the equation will be C is equal to 470(1-0.03)^6.
What is exponential decay?During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.
We know the decay can be as:
[tex]\rm C = a(1-r)^t[/tex]
We have:
a = 470 grams
r = 3% = 0.03
t = 6 hours
[tex]\rm C = 470(1-0.03)^6[/tex]
C = 391.49 grams
Thus, after 6 hours the radioactive compound with mass 470 grams becomes 391.49 grams and the equation will be C is equal to 470(1-0.03)^6.
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Find the length of the arc of the circle.
Answer:
25.12 in
Step-by-step explanation:
In the given circle
radius (r) = 12 incentral angle [tex](\theta) = 120\degree[/tex]Formula for length of arc is given as: [tex] l=\frac{\theta}{360\degree}\times 2\pi r[/tex]Plugging the values of r and [tex]\theta[/tex] in the above equation, we find:[tex] l=\frac{120\degree}{360\degree}\times 2(3.14) (12)[/tex][tex]\implies l=\frac{1}{3}\times 2(3.14) (12)[/tex][tex]\implies\huge\red{ l=25.12\:in}[/tex]A cylinder, cone, and sphere are show below. The three figures have the same radius. If the radius is 3, what is each volume?
Answer:
cylinder = 27π
cone = 9π
sphere = 36π
Step-by-step explanation:
volume of a cylinder = πr²h where r = radius and h = height
height of cylinder (h) = 3 and radius (r) = 3
so volume = π(3)²3
==> simplify exponent
volume = π9(3)
==> multiply 9 and 3
volume of cylinder = 27π
Volume of a cone = πr²(h/3) where r = radius and h = height
height of cone (h) = 3 and radius (r) = 3
so volume = π(3)²(3/3)
==> simplify exponent
volume = π9(3/3)
==> divide 3 by 3
volume = π9(1)
==> multiply 9 and 1
volume of cone = 9π
volume of a sphere = 4/3πr³ where r = radius
radius = 3
so volume = 4/3π(3)³
==> simplify exponent
volume = 4/3π27
==> multiply 4/3 and 27
volume of sphere = 36π
34) Find the inverse of y = 5x
Review the steps of the proof of the identity
At which step was an error made?
sin (A-3) - COSA.
= A.
step 1
step 2
3п
sin
step 3
step 4
Step 1: = sinAcos
3 п
2
-
COSAsin
n ()
Step 2: = (sinA)(0) + COSA( - 1)
Step 3: = (sinA)(0) + (1) (COSA)
Step 4: = 0 + COSA
Step 5: Cos A
Answer:
step 2
and then also in step 3 compensating the error in step 2
Step-by-step explanation:
I think I just answered this for another post.
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
so, step 1 is correct :
sin(A - 3pi/2) = sin(A)cos(3pi/2) - cos(A)sin(3pi/2)
but step 2 suddenly and incorrectly switched that central "-" to a "+".
yes, sin(3pi/2) = -1, but that is still an explicit factor in step 2. so it was not used to flip the central operation from subtraction to addition, and therefore this change was a mistake.
then, in step 3, another error was made by just ignoring the "-" sign of "-1" and still keeping the central "+" operation. this error compensated for the error in step 2 bringing us back by pure chance to the right result.
The perimeter of a triangle is 84 meters. The longest side of the triangle is 7 meters less than twice the length of the shortest side ,x. The middle side is 7 meters longer than the shortest side. What is the length of each side of the triangle.
Hey ! there
Answer:
Smallest side = 21 mMiddle side = 28 mLongest side = 35 mStep-by-step explanation:
In this question we are given that perimeter of a triangle is 84 m , longest side of triangle is 7 meters less than twice the length of shortest side that is x and middle side is 7 meters longer than the shortest side .
And we're asked to find the length of each side of triangle.
So ,
Shortest side = x m Middle side = ( x + 7 ) m ( Because in question it is given that middle side is 7 metres longer than the shorter side )Longest side = ( 2x -7 ) m ( Because in question it is given that longest side is 7 m less than twice the length of shortest side )We know that ,
[tex]\underline{\boxed{\frak{Perimeter_{(Triangle)} = Sum \:of\: three\: sides}}}[/tex]
Solution : -
[tex] \longmapsto \qquad x +( x + 7) + (2x - 7) = 84[/tex]
Step 1 : Removing parenthesis and cancelling 7 with -7 :
[tex] \longmapsto \qquad x + x + \cancel{7} + 2x - \cancel{ 7 }= 84[/tex]
Step 2 : Adding like terms on left side :
[tex] \longmapsto \qquad 4x = 84[/tex]
Step 3 : Dividing with 4 on both sides :
[tex] \longmapsto \qquad \dfrac{ \cancel{4}x}{ \cancel{4}} = \cancel{\dfrac{ 84}{4} }[/tex]
On calculating further, We get :
[tex] \longmapsto \qquad \red{\underline{\boxed{\frak{ x = 21 \: m}}}}\quad \bigstar[/tex]
According to question ,
x = smallest sideHenceforth , smallest side of triangle is 21 meters .▬▬▬▬▬▬▬▬▬▬▬▬▬▬
x + 7 = middle side21 + 7 = 28Henceforth , middle side of triangle is 13 meters .▬▬▬▬▬▬▬▬▬▬▬▬▬▬
2x - 7 = longest side2(21) - 742 - 735Henceforth , longest side of triangle is 35 meters .Verifying : -
Now we are checking our answer by adding all the sides and equating it with given perimeter that is 84 metres .
21 + 28 + 35 = 8449 + 35 = 8484 = 84L.H.S = R.H.SHence , Verified .Therefore , our answer is correct.
#KeepLearningWhat is the area, in square centimeters, of the trapezoid below?
8.5 cm
7.5 cm
15.7 cm
Answer:
90.75 cm^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 ( b1+b2) *h
where b1 and b2 are the lengths of the bases and h is the height
A = 1/2(8.5+ 15.7) * 7.5
1/2 (24.2) 7.5
90.75 cm^2
1. Solve.
: 1/2 divided by 2/1
Answer:
The answer to this one is 0.25
Are these ratios equivalent?
12 cards to 72 animals, 11 marbles to 66 marbles
Which type of function is shown in the table
below?
Answer:
Not a function
Step-by-step explanation:
Since 2 different points have the same x-coordinte, the relation is not a function.
find the difference 2/3-2/4
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
1. You need the same denominator to subtract
2. You can do this by picking the least common multiple of both denominators or multiplying the denominators by each other. In this case, the LCM (least common multiple) and multiply 4*3 or 3*4 is the same thing: 12.
3. But, what you do to the denominator, you do to the numerator:
[tex]\frac{2*4=8}{3*4=12} \\\\\frac{2*3=6}{4*3=12}[/tex] This leaves the fractions as [tex]\frac{8}{12} -\frac{6}{12} =\frac{2}{12}[/tex].
4. When you subtract fractions, you don't subtract the denominator.
5. You can simplify this fraction by dividing the numerator and denominator by 6: [tex]\frac{2/2}{12/2} =\frac{1}{6}[/tex]
Select the fraction that is equivalent to one fifth. (2 points)
a
1/10
b
2/1
c
2/5
d
3/5
Answer:
none
Step-by-step explanation:
[tex]one \: fifth = \frac{1}{5} \\ from \: the \: options \: no \: fraction \: is \: equivalent \: to \: one \: fifth \: and \: non \: of \: the \: fracrions \: can \: be \: reduced \: to \: give \: one \: fifth \\ so \: the \: answer \: is \: none[/tex]
The sum of three consecutive numbers is 357.
a.
Use an equation to find the smallest of the three numbers
Answer: The smallest number is 118.
Step-by-step explanation:
Let's say that the consecutive numbers are x-1, x, x+1
The sum of the three consecutive numbers is 357
(x-1) + x + (x+1) = 357
So, 3x = 357
x = 357 ÷ 3
x = 119
The 3 consecutive numbers are: 118, 119 and 120
The smallest out of the 3 is clearly 118.
Hope this helps!
Suppose a rocket is launched from a platform. The function h(t) - 4.96 + 200€ + 25gives the rocket's
height, h, in meters, in terms of time, t, in seconds. The function h(t) is equivalent to -4.9(t- 20. 41) + 2,065.82
Answer:
See below
Step-by-step explanation:
Opens Downward ( due to the - coefficient of t^2 )
when t = 0 the height is = 25 meters
initial velocity = 200 m/s
Vertex = 20.41, 2065.82
56+86/5? what is the anwser
Hurry and answer this please. Find the volume of the sphere use 3.14 for pi
Answer:
44.6cm³
Step-by-step explanation:
V=3/4×3.14×2.2³=44.6cm³
Answer:
Option 2) 44.6 cm³ os the correct answer.
Step-by-step explanation:
SOLUTION :
Here we have given that the radius of the sphere is 2.2 cm. We have to find the volume of sphere.
Finding the volume of sphere by substituting all the given values in the formula :
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3}\pi{r}^{3}}}}[/tex]
V = volume π = 3.14 r = radius[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3}\pi{r}^{3}}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times {(2.2)}^{3}}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times 10.65}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{\cancel{3}} \times 3.14 \times \cancel{10.65}}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = 4 \times 3.14 \times 3.55}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = 12.56 \times 3.55}}}[/tex]
[tex]\quad{\longrightarrow{\sf{V_{(Sphere)} = 44.58 \: {cm}^{3}}}}[/tex]
[tex]\quad{\longrightarrow{\sf{\underline{\underline{\pink{V_{(Sphere)} \approx 44.6 \: {cm}^{3}}}}}}}[/tex]
Hence, the volume of sphere is 44.6 cm³.
————————————————Enter an equation for the line of symmetry for the function f(x) = 2(x-5)^2 + 8.
so let's notice that, the equation is f(x) in x-terms, meaning the variable "x" is the independent and thus the parabola is a vertical parabola. Also let's notice that the equation is already in vertex form, keeping in mind that the axis of symmetry occurs for a vertical parabola at the x-coordinate.
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(x)=2(x-\stackrel{h}{5})^2+\stackrel{k}{8}~\hfill \stackrel{vertex}{(5,8)}~\hfill \stackrel{\textit{equation for axis of symmetry}}{x=5}[/tex]
which has more mass: a solid cylinder of gold with a height of 5 cm and a diameter of 6 cm or a solid cone of platinum with a height of 21 cm and a diameter of 8 cm
The mass of platinum cone is more than the mass of the gold cylinder which is 7529.76 grams.
What is density?It is defined as the ratio of mass and volume. The density gives an idea of how dense the object is, and it is denoted by the symbol ρ. The unit of the density is kilogram per cubic meter.
The volume for the cylinder = π(6/2)²(5) = 141.37 cubic cm
The density for gold = 19.3 gram/cm³
Mass of gold cylinder = 19.3×141.37 = 2728.44 grams
The volume of the cone = (π(8/2)²×21)/3 = 351.85 cubic cm
The density for platinum = 21.4 gram/cm³
Mass of platinum cone = 21.4×351.85 = 7529.76 grams
Thus, the mass of platinum cone is more than the mass of the gold cylinder which is 7529.76 grams.
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