Answer:
16[tex]\sqrt{5}[/tex]
Step-by-step explanation:
[tex]4\sqrt{5}[/tex]+[tex]4\sqrt{5}[/tex]+[tex]4\sqrt{5}[/tex]+[tex]4\sqrt{5}[/tex]
16[tex]\sqrt{5}[/tex]
The perimeter of the square is 16√5 units.
We have,
The concept used here is straightforward: to find the perimeter of a square, you sum the lengths of all four sides because all sides of a square are equal in length.
In this case, the side length is given as 4√5, so you multiply it by 4 to calculate the total perimeter.
To find the perimeter (P) of a square with a side length of 4√5 units, you simply add up all four sides of the square, as all sides of a square are equal in length.
So,
P = 4 * side length
P = 4 * 4√5
P = 16√5 units
Thus,
The perimeter of the square is 16√5 units.
Learn more about squares here:
https://brainly.com/question/22964077
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The number of measles cases increased 26.3% to 321 cases this year. What was the number of cases prior to the increase? Express your answer rounded correctly to the nearest whole number.
Answer:
The right answer is "[tex]x\simeq 254[/tex]".
Step-by-step explanation:
Let the number of earlier case will be "x".
Now,
⇒ [tex]x+x\times \frac{26.3}{100}=321[/tex]
or,
⇒ [tex]x+x\times 0.263=321[/tex]
By taking "x" common, we get
⇒ [tex]x(1+0.263)=321[/tex]
⇒ [tex]x=\frac{321}{1.263}[/tex]
⇒ [tex]=254.15[/tex]
or,
⇒ [tex]x\simeq 254[/tex]
Let f(x)
2x + 8, g(x) = x2 + 2x – 8, and h(x) = 3x – 6.
Perform the indicated operation. (Simplify as far as possible.)
(h · f)(3) =
Answer:
36
Step-by-step explanation:
(h · f)(x) = h(f(x))
h(f(x)) = h(2x+8)
h(f(x))= 3(2x+8) - 6
h(f(x)) = 6x + 24 - 6
h(f(x))= 6x + 18
If x = 3
h(f(x))= 6(3) + 18
h(f(x))= 18 + 18
h(f(x))= 36
Hence (h · f)(3) = 36
Which answers describe the shape below? Check all that apply.
A. Square
B. Quadrilateral
C. Rhombus
D. Trapezoid
E. Rectangle
F. Parallelogram
Answer:
b and f
Step-by-step explanation:
HELP
-5(2m-3)-4<81
I need the steps also well
Answer:
m>-7
Step-by-step explanation:
expand
-10m+15-4<81
-10m+11<81
collect like terms
-10m<81-11
-10m<70
m>-7
If the cutoff Z score on the comparison distribution is 2.33 and the sample value has a score of 2.35 on the comparison distribution, the correct decision is to:____.
A) fail to reject the null hypothesis.
B) reject the null hypothesis.
C) accept the researc hypothesis.
D) reject the research hypothesis.
Answer:
B) reject the null hypothesis.
Step-by-step explanation:
x(x-y) - y( x- y) simplify
Step-by-step explanation:
x²-xy-xy+y²
x²+2xy+y²
hope it helps
The sum of the first ten terms of an arithmetic progression consisting of
positive integer terms is equal to the sum of the 20th, 21st and 22nd term.
If the first term is less than 20, find how many terms are required to give
a sum of 960.
Answer: [tex]n=13[/tex]
Step-by-step explanation:
Given
Sum of the first 10 terms is equal to sum of 20, 21, and 22 term
[tex]\Rightarrow \dfrac{10}{2}[2a+(10-1)d]=[a+19d]+[a+20d]+[a+21d]\\\\\Rightarrow 5[2a+9d]=3a+60d\\\Rightarrow 10a+45d=3a+60d\\\Rightarrow 7a=15d[/tex]
No of terms to give a sum of 960
[tex]\Rightarrow 960=\dfrac{n}{2}[2a+(n-1)d]\\\\\Rightarrow 1920=n[2a+(n-1)\cdot \dfrac{7}{15}a]\\\\\Rightarrow 28,800=n[30a+7a(n-1)]\\\\\Rightarrow a=\dfrac{28,800}{n[30+7n-7]}\\\\\Rightarrow a=\dfrac{28,800}{n[23+7n]}[/tex]
Value of first term is less than 20
[tex]\therefore \dfrac{28,800}{n[23+7n]}<20\\\\\Rightarrow 28,800<20n[23+7n]\\\Rightarrow 0<460n+140n^2-28,800\\\Rightarrow 140n^2+460n-28,800>0\\\\\Rightarrow n>12.79\\\\\text{For integer value }\\\Rightarrow n=13[/tex]
Answer:
15
Step-by-step explanation:
In the previous answer halfway through they used the equation: 960 = (n÷2)×(2a+(n-1)×(7a÷15))
Using this equation we can substitute an number to replace n, the higher the number is the smaller a would be.
When we substitute 15 into a, then it leaves us with the answer to be a = 15 which is a positive integer and also is smaller than 20, this then let’s us know that 15 is how many terms can be summed up to make 960.
To double check this answer you can find that d = 7 by changing the a into 15 in the formula 7a/15 (found in the previous answer.
Then in the expression: (n÷2)×(2a+(n-1)×d)
substitute:
n = 14 (must be an even number for the equation to work)
a = 15
d = 7
This will give you an answer of 847, but this is only 14 terms as we changed n into 14. To add the final term you need to complete the following equation: 847+(a+(n-1)×d)
substituting:
n = 15
a = 15
d = 7
This will give you the answer of 960, again proving that it takes 15 terms to sum together to make the number 960.
I hope this has helped you.
P.S. Everything in the previous solution was right apart from the start of the last section and the answer
Last softball season, Pamela had 46 hits, a combination of singles (1 base), doubles (2 bases), and triples (3 bases). These 46 hits totaled 66 bases, and she had 4 times as many singles as doubles. How many doubles did she have?
Answer:
She had 8 doubles.
Step-by-step explanation:
This question is solved by a system of equations.
I am going to say that:
x is the number of singles.
y is the number of doubles
z is the number of triples.
46 hits
This means that [tex]x + y + z = 46[/tex]
46 hits totaled 66 bases
This means that:
[tex]x + 2y + 3z = 66[/tex]
4 times as many singles as doubles
This means that [tex]x = 4y[/tex]
So
[tex]x + 2y + 3z = 66[/tex]
[tex]4y + 2y + 3z = 66[/tex]
[tex]6y + 3z = 66[/tex]
And
[tex]x + y + z = 46[/tex]
[tex]4y + y + z = 46[/tex]
[tex]5y + z = 46 \rightarrow z = 46 - 5y[/tex]
Then
[tex]6y + 3z = 66[/tex]
[tex]6y + 3(46 - 5y) = 66[/tex]
[tex]6y + 138 - 15y = 66[/tex]
[tex]9y = 72[/tex]
[tex]y = \frac{72}{9}[/tex]
[tex]y = 8[/tex]
She had 8 doubles.
The parametric equations for the paths of two projectiles are given. At what rate is the distance between the two objects changing at the given value of t? (Round your answer to two decimal places.) x1 = 10 cos(2t), y1 = 6 sin(2t) First object x2 = 4 cos(t), y2 = 4 sin(t) Second object t = π/2
Answer:
- [tex]\frac{4}{\sqrt{29} }[/tex]
Step-by-step explanation:
The equations for the 1st object :
x₁ = 10 cos(2t), and y₁ = 6 sin(2t)
2nd object :
x₂ = 4 cos(t), y₂ = 4 sin(t)
Determine rate at which distance between objects will continue to change
solution Attached below
Distance( D ) = [tex]\sqrt{(10cos2(t) - 4cos(t))^2 + (6sin2(t) -4sin(t))^2}[/tex]
hence; dD/dt = - [tex]\frac{4}{\sqrt{29} }[/tex]
15. The area of a triangle is 72 in the base is 12 in. Find the height.
Answer:
[tex]hright =12[/tex]
Step-by-step explanation:
----------------------------------------
The formula to find the area of a triangle is [tex]A=\frac{1}{2}bh[/tex] where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.
But we already know the area and the base. So to find the height, let's substitute 72 for [tex]A[/tex] and 12 for [tex]b[/tex], and solve.
[tex]72=\frac{1}{2}(12)(h)[/tex]
[tex]72=6h[/tex]
Here, divide both sides by 6
[tex]12=h[/tex]
--------------------
Hope this is helpful.
Answer:
height = 12
Step-by-step explanation:
.............
arrange the following in descending order - 5, 0, -15, 2.5, 2.05
Answer:
2.5, 2.05, 0, -5, -15
Step-by-step explanation:
for negative numbers the bigger is worth less
Find the solution of the differential equation that satisfies the given initial condition. (dP)/(dt)
Answer:
[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]
Step-by-step explanation:
Given
[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]
[tex]P(1) = 2[/tex]
Required
The solution
We have:
[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]
[tex]\frac{dP}{dt} = (Pt)^\frac{1}{2}[/tex]
Split
[tex]\frac{dP}{dt} = P^\frac{1}{2} * t^\frac{1}{2}[/tex]
Divide both sides by [tex]P^\frac{1}{2}[/tex]
[tex]\frac{dP}{ P^\frac{1}{2}*dt} = t^\frac{1}{2}[/tex]
Multiply both sides by dt
[tex]\frac{dP}{ P^\frac{1}{2}} = t^\frac{1}{2} \cdot dt[/tex]
Integrate
[tex]\int \frac{dP}{ P^\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
Rewrite as:
[tex]\int dP \cdot P^\frac{-1}{2} = \int t^\frac{1}{2} \cdot dt[/tex]
Integrate the left hand side
[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{-1}{2}+1} = \int t^\frac{1}{2} \cdot dt[/tex]
[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
[tex]2P^{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
Integrate the right hand side
[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{1}{2} +1 }}{\frac{1}{2} +1 } + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{3}{2}}}{\frac{3}{2} } + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex] ---- (1)
To solve for c, we first make c the subject
[tex]c = 2P^{\frac{1}{2}} - \frac{2}{3}t^\frac{3}{2}[/tex]
[tex]P(1) = 2[/tex] means
[tex]t = 1; P =2[/tex]
So:
[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1^\frac{3}{2}[/tex]
[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1[/tex]
[tex]c = 2\sqrt 2 - \frac{2}{3}[/tex]
So, we have:
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + 2\sqrt 2 - \frac{2}{3}[/tex]
Divide through by 2
[tex]P^{\frac{1}{2}} = \frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3}[/tex]
Square both sides
[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]
A 27% solution ( 27mg per 100 mL of solution) is given intravenously. Suppose a total of 1,36 L of the solution is given over a 10 -hour period. Complete parts (a) through (c) below.
a. What is the flow rate in units of mL/hr?
nothing mL/hr (Type an integer or decimal rounded to the nearest thousandth as needed.)
What is the flow rate in per hour?
nothing mg/hr (Type an integer or decimal rounded to the nearest thousandth as needed.)
b. If each mL contains 13 drops (the drop factor is expressed as gtt/mL), what is the flow rate in units of 13gtt/hr?
nothing gtt/hr (Type an integer or decimal rounded to the nearest thousandth as needed.)
c. During the 10 -hour period, how much is delivered?
nothing mg (Type an integer or decimal rounded to the nearest thousandth as needed.)
Answer:
Step-by-step explanation:
a.
(1.36 L)/(10 hr) = (0.136 L)/(hr)
Flow rate = (0.136 L)/(hr) × (1000 mL)/L = (136 mL)/(hr)
136 mL × (27 mg)/(100 mL) = 36.72 mg
Delivery rate = (36.72 mg)/(hr)
b.
(136 mL)/(hr) × (13 gtt)/(mL) = (1868 gtt)/(hr)
c.
10 hr × (36.72 mg)/)hr) = 367.2 mg
How would 0.42 be shown as a percent?
A. 0.42%
B. 4%
C. 4.2%
D. 42%
Answer:
42%
Step-by-step explanation:
to find percentages, you move the decimal point twice to the right
A sample of 25 one-year-old girls had a mean weight of 24.1 pounds with a standard deviation of pounds. Assume that the population of weights is normally distributed. A pediatrician claims that the standard deviation of the weights of one-year-old girls is less than pounds. Do the data provide convincing evidence that the pediatrician's claim is true
Answer:
Paedtricians claim isn't true.
Step-by-step explanation:
The hypothesis :
H0 : σ = 7
H0 : σ > 7
The test statistic ; χ² :
χ² = [(n - 1) * s²] ÷ σ²
n = 25 ; s = 4.3, σ = 7
χ² = [(25 - 1) * 4.3²] ÷ 7²
χ² = [(24 * 4.3²] ÷ 49
χ² = 443.76 / 49
χ² = 9.056
At α = 0.01 ; critical value = 42.980
Since critical value > test statistic, we fail to reject the null, H0.
Which simplified fraction is equal to 0.53? Need answers now plz
Answer:
8/15
Step-by-step explanation:
Answer:
8/15
Step-by-step explanation:
when you divide 8/15 its 0.53
Write down 4 pairs of integers a and b such that a divided by b is -5
Drag the tiles to the correct boxes to complete the pairs.
Match each division of rational expressions with its quotient.
Answer:
Step-by-step explanation:
Um where is the diagrahm
add 10ft 3in + 3ft 9in + 8ft 10in
Please HELP!
How many pairs (A, B) are there where A and B are subsets of {1, 2, 3, 4, 5, 6, 7, 8} and A ∩ B has exactly two elements?
Answer:
There are 256 pairs in all.
Meghan sells advertisements for a radio station. Each 30 second ad costs $20 per play, and each 60 second ad
costs $35 per play. Meghan sold 12 ads for $315. She wrote the system below letting x represent the number of 30
second ads and y represent the number of 60 second ads.
X+ y = 12
20x+35y = 315
What is the solution to the system of equations?
Need answers ASAP!!!!
Answer:
usai964s46s694s4o6s64694s946649s469 opps
Answer:
[tex](x,y)=(7,5)[/tex]
Step-by-step explanation:
Megan's equation will be:
[tex]20x+35y=315[/tex]
[tex]x+y=12[/tex]
Substitute [tex]x=12-y[/tex] in the first equation:
[tex]20(12-y)+35y=315[/tex]
[tex]15y=75[/tex]
[tex]y=75/15[/tex]
[tex]y=5[/tex]
Find x:
[tex]x=12-5[/tex]
[tex]x=7[/tex]
Where x and y represent 30-second and 60-second ads sold, we find that Meghan's sales were:
[tex](x,y)=(7,5)[/tex]
hope this helps....
What does y equal in the solution of the system of equations below? 5y-3x-4z=22 2z-2x=-6 2z+3x=-6
9514 1404 393
Answer:
y = 2
Step-by-step explanation:
Subtracting the second equation from the third gives ...
(2z +3x) -(2z -2x) = (-6) -(-6)
5x = 0
x = 0
Using this in the third equation, we have ...
2z +0 = -6
z = -3
And substituting these values into the first equation, we have ...
5y -3(0) -4(-3) = 22
5y = 10 . . . . . subtract 12
y = 2
__
The solution to the system is (x, y, z) = (0, 2, -3).
What is the y-intercept of the line given by y=4x - 6
Answer:
y= -6
Step-by-step explanation:
the y-intercept is -6, which corresponds to point (0,-6)
remember that you're using the
y=mx+b format of an equation of a line where b is the y-intercept.
Also, if you make x=0, y will be -6.
Please help me >_< will give out brainliest
====================================================
Explanation:
We have an octagon because there are n = 8 sides. The diagram below shows one way to number the sides so you can count them efficiently (without missing any or double counting any).
----------------
Plug n = 8 into the formula below
S = 180(n-2)
S = 180(8-2)
S = 180(6)
S = 1080
The 8 interior angles add up to 1080 degrees.
if angle ACB = angle DCD, angle BAC = 3x-10, angle ECD= 45degrees, and angle EDC = 2x+10 wgat is x
Answer:
x = 20
Step-by-step explanation:
3x -10 = 2x +10
x = 20
A school contains 140 boys and 160 girls. what is the ratio of boys to girls?
I need full working out please
Answer:
7 : 8
Step-by-step explanation:
that is the procedure above
If 19,200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Step-by-step explanation:
√19200cm²
=138.56cm
then the highest possible volume
=(138.56)³
=2660195.926cm³
The largest possible volume of the box is; V = 25600 cm³
Let us denote the following of the square box;
Length = x
Width = y
height = h
Formula for volume of a box is;
V = length * width * height
Thus; V = xyh
but we are dealing with a square box and as such, the base sides are all equal and so; x = y. Thus;
V = x²h
The box has an open top and as such, the surface are of the box is;
S = x² + 4xh
We are given S = 19200 cm². Thus;
19200 = x² + 4xh
h = (19200 - x²)/4x
Put (19200 - x²)/4x for h in volume equation to get;
V = x²(19200 - x²)/4x
V = 4800x - 0.25x³
To get largest possible volume, it will be dimensions when dV/dx = 0. Thus;
dV/dx = 4800 - 0.75x²
At dV/dx = 0, we have;
4800 - 0.75x² = 0
0.75x² = 4800
x² = 4800/0.75
x² = 6400
x = √6400
x = 80 cm
From h = (19200 - x²)/4x;
h = (19200 - 80²)/(4 × 80)
h = (19200 - 6400)/3200
h = 4 cm
Largest possible volume = 80² × 4
Largest possible volume = 25600 cm³
Read more at; https://brainly.com/question/19053087
SOMEONE HELP ASAP PLES NO EXPLANATOIN NEEDED PLS LEAVE UR ANSWER AS TEXT (SOME TIMES I CAN'T SEE IMAGES) THANK YOU SO MUCH!!!
Answer:
i cant see the image
Step-by-step explanation:
The function f is defined by the following rule. f(x) = 5x+1 Complete the function table.
Answer:
[tex]-5 \to -24[/tex]
[tex]-1 \to -4[/tex]
[tex]2 \to 11[/tex]
[tex]3 \to 16[/tex]
[tex]4 \to 21[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x + 1[/tex]
Required
Complete the table (see attachment)
When x = -5
[tex]f(-5) = 5 * -5 + 1 = -24[/tex]
When x = -1
[tex]f(-1) = 5 * -1 + 1 = -4[/tex]
When x = 2
[tex]f(2) = 5 * 2 + 1 = 11[/tex]
When x = 3
[tex]f(3) = 5 * 3 + 1 = 16[/tex]
When x = 4
[tex]f(4) = 5 * 4 + 1 = 21[/tex]
So, the table is:
[tex]-5 \to -24[/tex]
[tex]-1 \to -4[/tex]
[tex]2 \to 11[/tex]
[tex]3 \to 16[/tex]
[tex]4 \to 21[/tex]
What is the inverse of function f?
9514 1404 393
Answer:
D. f^-1(x) = 3 -7x
Step-by-step explanation:
Solve x = f(y) for y to find the inverse function.
x = f(y)
x = (3 -y)/7 . . . . . . use the function definition
7x = 3 -y . . . . . . . .multiply by 7
y = 3 -7x . . . . . . . add y-7x to both sides
Then the inverse function is ...
[tex]\boxed{f^{-1}(x)=3-7x}[/tex]
