Answer:
8192
Step-by-step explanation:
2 ¹²= 4096
4096 x 2 = 8192
What is an example of force causing a change in the size of the body (P.S. what is the difference between shape and size?)
Answer:
shape is how it looks like Square is a shape and size is how big something in like my size of my foot is 6 inches
Step-by-step explanation:
well idk your real question i think it is that your shape and size can change
Find the common difference of the arithmetic sequence. 4, 10, 16, 22, . . .
Answer:
6
Step-by-step explanation:
10 - 4 = 6
16 - 10 = 6
22 - 16 = 6
Answer:6
Step-by-step explanation:
1) 10-4=6
2) 16-10=6
3) 22-16=6
Find the slope of the line that passes through (1, 14) and (4,9)
Which two numbers in the points represent y values? Select both in the
list
Answer:
14 and 9
Step-by-step explanation:
Y values are always the second number in the parenthesis. The X value is the first one. I like to think of Y being dependent on X, so X goes first, then Y.
-2x(x+3)-(x+1)(x-2)=
Answer:
-3x^2 -5x +2
Step-by-step explanation:
-2x(x+3)-(x+1)(x-2)=
Distribute
-2x^2 -6x -(x+1)(x-2)
Foil
-2x^2 -6x -(x^2 -2x +x -2)
Combine like terms
-2x^2 -6x -(x^2 -x -2)
Distribute the minus sign
-2x^2 -6x -x^2 +x +2
Combine like terms
-2x^2 -x^2 -6x +x +2
-3x^2 -5x +2
Answer:
[tex]\huge\boxed{-2x(x+3)-(x+1)(x-2)=-3x^2-5x+2}[/tex]
Step-by-step explanation:
[tex]-2x(x+3)-(x+1)(x-2)[/tex]
Use the distributive property: a(b + c) = ab + ac
and FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex]=(-2x)(x)+(-2x)(3)-\bigg[(x)(x)+(x)(-2)+(1)(x)+(1)(-2)\bigg]\\\\=-2x^2-6x-\bigg(x^2-2x+x-2\bigg)=-2x^2-6x-x^2-(-2x)-x-(-2)\\\\=-2x^2-6x-x^2+2x-x+2[/tex]
Combine like terms:
[tex]=(-2x^2-x^2)+(-6x+2x-x)+2=-3x^2+(-5x)+2\\\\=-3x^2-5x+2[/tex]
Find the length of BC
Answer:
The answer is option AStep-by-step explanation:
To find the length of BC we use tan
tan ∅ = opposite / adjacent
From the question
AC is the opposite
BC is the adjacent
So we have
tan 61 = AC / BC
tan 61 = 47/BC
BC = 47/tan 61
BC = 26.05Hope this helps you
PLZ HELPpppP! A lawn is in the shape of a trapezoid with a height of 50 feet and bases of 70 feet and 130 feet. How many bags of fertilizer must be purchased to cover the lawn if each bag covers 3000 square feet? Remember that only whole bags of fertilizer can be purchased. [tex](A=\frac{1}{2}h(B+b))[/tex]
Hi,
Lawn area:[tex]A=\frac{base_{1} +base_{2} }{2} *h\\\\A=(base_{1} +base_{2} ) *h *\frac{1}{2} \\\\A=(70ft + 130ft) * 50ft *\frac{1}{2} \\\\A=5000ft^{2}[/tex]
how many bags of fertilizer we need?each bag covers 3000 ft²
[tex]N_{number of bags} = 5000ft^{2} / 3000ft^{2} \\\\N_{number of bags} = 1.6[/tex]
We need to purchase two bags fertilizer, but will use one and a half of them.
Have a good day.
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5 36 − x2 , y = 0, x = 2, x = 4; about the x-axis
Answer: V = 193.25π
Step-by-step explanation: The method to calculate volume of a solid of revolution is given by an integral of the form:
V = [tex]\pi\int\limits^a_b {[f(x)]^{2}} \, dx[/tex]
f(x) is the area is the function that rotated forms the solid.
For f(x)=y= [tex]\frac{5}{36}-x^{2}[/tex] and solid delimited by x = 2 and x = 4:
V = [tex]\pi\int\limits^4_2 {(\frac{5}{36}-x^{2} )^{2}} \, dx[/tex]
V = [tex]\pi\int\limits^4_2 {(\frac{25}{1296}-\frac{10x^{2}}{36}+x^{4}) } \, dx[/tex]
V = [tex]\pi(\frac{25.4}{1296}-\frac{10.4^{3}}{108}+\frac{4^{5}}{5}-\frac{25.2}{1296}+\frac{10.2^{3}}{108}-\frac{2^{5}}{5} )[/tex]
V = [tex]\pi(\frac{50}{1296}-\frac{560}{1296}+\frac{992}{1296} )[/tex]
V = 193.25π
The volume of a solid formed by y = [tex]\frac{5}{36} - x^{2}[/tex] and delimited by x = 2 and x = 4
is 193.25π cubic units.
what is 99/00+44(55)99
Answer:
undefined! one cannot divide by 0
Step-by-step explanation:
Answer:
undefined!
Step-by-step explanation:
A disc has a diameter of centimeters while a mini disc has a diameter of centimeters. Write the ratio of the mini disc diameter to the disc diameter.
Answer:
2 : 3
Step-by-step explanation:
A disc has a diameter of 21 cm while a mini disc has a diameter of 14cm. Write the ratio of the mini disc diameter to the disc diameter.
Answer: Let the diameter of the mini disc be [tex]d_1[/tex] while the diameter of the disc be [tex]d_2[/tex]. To get the ratio of the mini disc diameter to the disc diameter, we just simply have to divide the diameter of the mini disc by the diameter of the disc and then represent the fraction in ratio form. The ratio of the disc diameters is given by:
Ratio of the mini disc diameter to the disc diameter = Diameter of mini disc / diameter of disc
Ratio of the mini disc diameter to the disc diameter = [tex]\frac{14}{21}=\frac{2}{3}[/tex]
Ratio of the mini disc diameter to the disc diameter = 2 : 3
a sample of bacteria is growing at an hourly rate of 14% according to the exponential growth function.the sa
Answer:
pleasse elaborate more
Step-by-step explanation:
PLEASE HELP!! Write the proportion. 120 feet is to 150 feet as 8 feet is to 10 feet. (18 points!!)
Answer:
4 : 5
Step-by-step explanation:
you can divide 120 and 150 by 30 and 8 and 10 by 2.
120/30 = 4
150/30 = 5
8/2 = 4
10/2=5
Answer: 4:5
Step-by-step explanation:
if a drawing of a tree is 5 inches tall and the radio is 1:7 (inches:feet) ,how tall is the tree?
If the drawing is 5 inches tall and the ratio is 1:7, that means that 1 inch will be equal to 7 feet.
Height = 5 x 7 = 35 feet
Use Green's Theorem to evaluate F · dr. C (Check the orientation of the curve before applying the theorem.)F(x, y) = y cos(x) − xy sin(x), xy + x cos(x) , C is the triangle from (0, 0) to (0, 8) to (2, 0) to (0, 0)
Notice that C has a clockwise orientation. By Green's theorem, we have
[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\iint_D\left(\frac{\partial(xy+x\cos x)}{\partial x}-\frac{\partial(y\cos x-xy)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
where D is the triangule region with C as its boundary, given by the set
[tex]D=\{(x,y)\mid0\le x\le2\land0\le y\le8-4x\}[/tex]
So we have
[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}((y+\cos x-x\sin x)-(\cos x-x\sin x))\,\mathrm dy\,\mathrm dx[/tex]
[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}y\,\mathrm dy\,\mathrm dx=\boxed{-\dfrac{64}3}[/tex]
use the substitution method to solve the system of equation.s choose the correct ordered pair y=6x-4 y=x -7
Answer:
x=-3/5 and y=-38/5
Step-by-step explanation:
y=6x-4
y= x -7 substitute y=6x-4
6x-4=x-7
6x-x=-7+4
5x=-3
x=-3/5 ( substitute for x in y=6x-4)
y=6(-3/5)-4
y=-18/5-4
y=(-18-20)/5= -38/5
Which equation is the inverse of y = 16x2 + 1? y = plus-or-minus StartRoot StartFraction x Over 16 EndFraction minus 1 EndRoot y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 16 EndFraction y = StartFraction plus-or-minus StartRoot x EndRoot Over 4 EndFraction minus one-fourth y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 4 EndFraction
Answer:
The inverse is ±sqrt((x-1))/ 4
Step-by-step explanation:
y = 16x^2 + 1
To find the inverse, exchange x and y
x = 16 y^2 +1
Then solve for y
Subtract 1
x-1 = 16 y^2
Divide by 16
(x-1)/16 = y^2
Take the square root of each side
±sqrt((x-1)/16) = sqrt(y^2)
±sqrt((x-1))/ sqrt(16) = y
±sqrt((x-1))/ 4 = y
The inverse is ±sqrt((x-1))/ 4
Answer:
D
Step-by-step explanation:
Imagine working in a freelance developer earning 80 USD per hour how many weeks you will have to take a 12 hour flight on a weekday you can either book a flight for ticket for 11 AM for 900 USD or 11 PM flight or 11 USD there is no Internet boards if you take the day off like you will lose a day of work what would you do
Answer:
pay the 11 AM ticket
Step-by-step explanation:
Note that the flight last for 12 hours, and assuming the freelance developer can still work (have access to the internet) on the airplane throughout the flight, he stand to earn $960 ($80*12), which will still cover the cost of the flight with a profit of $60 ($960-900).
However, if he decides to pay the $11 flight ticket and there is no Internet on boards; there by losing a day of work, he stand to have lost working time which would earn with $900.
Therefore, the best choice is to pay the 11 AM ticket.
what is the 20th term of the arithmetic sequence a(n)=-5+(n-1)3
Answer:
52
Step-by-step explanation:
a(n)=-5+(n-1)3
a(20)=-5+(20-1)3
a(20)=52
The 20th term of the arithmetic sequence is 52.
What is Arithmetic sequence?An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
For example,
In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 ... is arithmetic because the difference between consecutive terms is always two.
The nth term of an arithmetic sequence is given by an = a + (n – 1)d.
Given:
a(n)=-5+(n-1)3
First term,
a(1)= -5 + 0
a(1)= -5
second, a(2)= -5 + 1*3
a(2)= -2
Third, a(3)= -5+6
a(3)= 1
d= 3
So, the 20th term
a(20)= -5+ (20-1)3
a(20)= -5 + 57
a(20)= 52
Hence, the 20th term is 52.
Learn more about Arithmetic Sequence here:
https://brainly.com/question/10396151
#SPJ2
Which expression is equivalent to 2m^2 - m^2(7-m)+6m^2?
Answer:
[tex]m^3+m^2[/tex]
Step-by-step explanation:
=> [tex]2m^2-m^2(7-m)+6m^2[/tex]
Collecting like terms and expanding the brackets
=> [tex]2m^2+6m^2-7m^2+m^3[/tex]
=> [tex]8m^2-7m^2+m^3[/tex]
=> [tex]m^2+m^3[/tex]
=> [tex]m^3+m^2[/tex]
Find x round to the nearest tenth
Answer:
83.0
Step-by-step explanation:
We have all three sides and the only thing we're missing is the X angle. And that's okay!
All you have to do is plug in the numbers into each variable. In this case if you are going to solve for X, you should use this equation.
[tex]x^2=y^2+z^2-2yzcosX[/tex]
x = 17ft
y = 8ft
x = 16fi
Then you can algebraically solve for cosX, and then use the inverse of cosx to get the angle.
When a survey was conducted among 100 students to find their favorite pizza topping, 45 students voted for pepperoni, 25 for mushrooms, and 30 voted for cheese. If a pie chart were made showing the number of votes for each topping, the central angle for the cheese sector would be __________.
Answer:
The central angle for the cheese sector would be 108 degrees.
Step-by-step explanation:
We know that a pi chart takes the form of a circle so the total angle measure is 360 degrees.
Now we want to find out what ratio of the pie chart that cheese takes up and apply it to the total degree measure.
30 of 100 students voted for cheese:
so the ratio would be 30/100 or 3/10
Now apply that to the total angle measure:
3/10*360 degrees= 108 degrees.
Use identities to find values of the sine and cosine functions of the function for the angle measure
a. theta, given that cos2theta=28/53 and 0theta < theta < 90degrees
b. 2theta, given sin theta= - sqrt 7 over 5 and cos theta > 0
c. 2x, given tan x=2 and cos x<0
Answer:
Step-by-step explanation:
a) Given cos2theta=28/53 and 0degrees< theta < 90degrees
From cos2theta=28/53
[tex]2\theta = cos^{-1}\frac{28}{53}[/tex]
[tex]2\theta = cos^{-1}0.5283\\ \\2\theta = 58.12\\\\Dividing\ both \ sides\ by \ 2\\\\\frac{2\theta}{2} = \frac{58.12}{2}\\ \\\theta = 29.06^0[/tex]
b) Given
[tex]sin\theta = \frac{-\sqrt{7} }{5} \\\\\theta = sin^{-1} \frac{-\sqrt{7} }{5}\\\\\\\theta = sin^{-1} \frac{-2.6458}{5}\\\\\theta = sin^{-1} -0.5292\\\\\theta = -31.95^0[/tex]
If cos theta [tex]\gneq[/tex] 0, this means we need to look for the quadrant where sin is negative and cos is positive. That will be the fourth quadrant. In the fourth quadrant, theta = 360 - 31.95° = 328.05°
2theta = 2 * 328.05
2theta = 656.1°
c) Given tan x=2 and cos x<0, lets find the angle of x first.
If tan x = 2
x = tan^-1 2
x = 63.4°
Sine cos is less than 0, then we need to find the angle of x where tan is positive and cos is negative. That will be the third quadrant. In the third quadrant, ew value of x = 180+63.4
x = 243.4°
Since we are to find 2x,
2x = 2(243.4)
2x = 486.8°
Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Round all answers using one decimal place.
Answer:
The missing side is [tex]B = 6.0\ cm[/tex]
The missing angles are [tex]\alpha = 56.2[/tex] and [tex]\theta = 93.8[/tex]
Step-by-step explanation:
Given
[tex]A = 10\ cm[/tex]
[tex]C = 12\ cm[/tex]
[tex]\beta = 30[/tex]
The implication of this question is to solve for the missing side and the two missing angles
Represent
Angle A with [tex]\alpha[/tex]
Angle B with [tex]\beta[/tex]
Angle C with [tex]\theta[/tex]
Calculating B
This will be calculated using cosine formula as thus;
[tex]B^2 = A^2 + C^2 - 2ACCos\beta[/tex]
Substitute values for A, C and [tex]\beta[/tex]
[tex]B^2 = 10^2 + 12^2 - 2 * 10 * 12 * Cos30[/tex]
[tex]B^2 = 100 + 144 - 240 * 0.8660[/tex]
[tex]B^2 = 100 + 144 - 207.8[/tex]
[tex]B^2 = 36.2[/tex]
Take Square root of both sides
[tex]B = \sqrt{36.2}[/tex]
[tex]B = 6.0[/tex] (Approximated)
Calculating [tex]\alpha[/tex]
This will be calculated using cosine formula as thus;
[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]
Substitute values for A, B and C
[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]
[tex]10^2 = 6^2 + 12^2 - 2 * 6 * 12 * Cos\alpha[/tex]
[tex]100 = 36 + 144 - 144Cos\alpha[/tex]
Collect Like Terms
[tex]100 - 36 - 144 = -144Cos\alpha[/tex]
[tex]-80 = -144Cos\alpha[/tex]
Divide both sides by -144
[tex]\frac{-80}{-144} = Cos\alpha[/tex]
[tex]0.5556 = Cos\alpha[/tex]
[tex]\alpha = cos^{-1}(0.5556)[/tex]
[tex]\alpha = 56.2[/tex] (Approximated)
Calculating [tex]\theta[/tex]
This will be calculated using cosine formula as thus;
[tex]C^2 = B^2 + A^2 - 2BACos\theta[/tex]
Substitute values for A, B and C
[tex]12^2 = 6^2 + 10^2 - 2 * 6 * 10Cos\theta[/tex]
[tex]144 = 36 + 100 - 120Cos\theta[/tex]
Collect Like Terms
[tex]144 - 36 - 100 = -120Cos\theta[/tex]
[tex]8 = -120Cos\theta[/tex]
Divide both sides by -120
[tex]\frac{8}{-120} = Cos\theta[/tex]
[tex]-0.0667= Cos\theta[/tex]
[tex]\theta = cos^{-1}(-0.0667)[/tex]
[tex]\theta = 93.8[/tex] (Approximated)
evaluate sin^-1(sin5)
−π2≤sin−1x≤π2
3π2≤5≤2π
−π2≤5−2π≤0≤π2
sin(5–2π)=sin5
Thus, sin−1(sin5)=5−2π
Please do either 40 or 39
Answer:
y = 1.8
Step-by-step explanation:
Question 39).
Let the operation which defines the relation between a and b is O.
Relation between a and b has been given as,
a O b = [tex]\frac{(a+b)}{(a-b)}[/tex]
Following the same operation, relation between 3 and y will be,
3 O y = [tex]\frac{3+y}{3-y}[/tex]
Since 3 O y = 4,
[tex]\frac{3+y}{3-y}=4[/tex]
3 + y = 12 - 4y
3 + y + 4y = 12 - 4y + 4y
3 + 5y = 12
3 + 5y - 3 = 12 - 3
5y = 9
[tex]\frac{5y}{5}=\frac{9}{5}[/tex]
y = 1.8
Therefore, y = 1.8 will be the answer.
Listed below are the measured radiation absorption rates (in W/kg) corresponding to 11 cell phones. Use the given data to construct a boxplot and identify the 5-number summary.
1.26 0.98 1.07 0.97 1.28 0.89 1.14 0.58 1.42 0.59 0.96
Answer:
Five-number summary in ascending order: [tex] 0.58, 0.89, 0.98, 1.26, 1.42 [/tex]
Step-by-step Explanation:
The number summary, in ascending order, includes the minimum value, maximum value, median value, upper quartile and lower quartile.
To find each of the above values, first, order the data set in ascending order. Our values given, when ordered, would be:
0.58, 0.59, 0.89, 0.96, 0.97,| 0.98|, 1.07, 1.14, 1.26, 1.28, 1.42
1.The minimum value (the least value or lower value in the given data set).
From the ordered data set, minimum value = 0.58
2. The maximum value is the highest value in the data set = 1.42
3. Median value is the middle value of the data set. The middle value is the 6th value = 0.98.
The median value divides the data set into lower and upper region, as shown below.
0.58, 0.59, 0.89, 0.96, 0.97,|0.98|, 1.07, 1.14, 1.26, 1.28, 1.42
4. Lower Quartile (Q2) is the middle value of the lower region = 0.89, as shown below,
0.58, 0.59, [0.89], 0.96, 0.97,|0.98|, 1.07, 1.14, 1.26, 1.28, 1.42
5. Upper Quartile (Q3) is the middle value of the upper region = 1.26, as shown below.
0.58, 0.59, 0.89, 0.96, 0.97,|0.98|, 1.07, 1.14, [1.26], 1.28, 1.42
: this is the middle value of lower region, after our median divides the data set into two.
0.58, 0.59, 0.89, 0.96, 0.97,|0.98|, 1.07, 1.14, 1.26, 1.28, 1.42
Therefore, the five-number summary in ascending order is as follows: [tex] 0.58, 0.89, 0.98, 1.26, 1.42 [/tex]
Min = 0.58
Q1 = 0.89
Median = 0.98
Q3 = 1.26
Max = 1.42
A box plot has been constructed using the five-number summary. Check the attachment below.
The min value is represented by the whisker that starts from your left and connects to the rectangular box.
The max value is indicated at the extreme end of the other whisker that you have from the end of the rectangular box to your far right.
The median value is indicated by the vertical line that divides the rectangular box into 2.
The lower quartile is indicated at the beginning of the rectangular box, while the upper quartile is located at the end of the rectangular box.
Bernard works for a business that sells and repairs tires. He can repair 24 tires in an 8 hour work day. What is Bernard's unit rate for the number of tires repaired in one hour?
Step-by-step explanation:
Unit rate = 24 ÷ 8 = 3 tires
Answer:
Step-by-step explanation:
24 tires/8hours
Gena wants to estimate the quotient of –21.87 divided by 4.79. Which expression shows the best expression to estimate the quotient using front-end estimation? Negative 21 divided by 4 Negative 21 divided by 5 Negative 20 divided by 4 Negative 20 divided by 5
Answer:
-21/5 = -4.2
Step-by-step explanation:
-21.87 / 4.79 = -4.5657.....
So, the quotients is -4
Now, Let's see who's quotient is equal to think one:
-21/4 = -5.25
-21/5 = -4.2
-40/4 = -5
-20/5 = 4
Answer:
-21/5 = -4.2
Step-by-step explanation:
Suppose you are climbing a hill whose shape is given by the equation z = 1600 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (120, 80, 1464). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend?
Answer:
you will start to ascend at the rate of 1.6
Step-by-step explanation:
Walking south, it's the negative part of a coordinate, so the unit vector at this point is; u = (0,-1)
We are told that the equation z = 1600 − 0.005x² − 0.01y²
Therefore, we have;
∇z = ((δ/δx)i + (δ/δx)j)(1600 − 0.005x² − 0.01y²)
This gives;
∇z = -0.005(2x)i - 0.01(2y)j
∇z = <-0.01x - 0.02y>
coordinates are (120, 80, 1464).
Thus;
∇z(120, 80, 1464) = <-0.01(120), - 0.02(80)> = <-1.20, -1.60>
D_uf = <-1.20, -1.60> × <0, - 1>
D_uf = 0 + 1.6
D_uf = 1.6
So, you will start to ascend at the rate of 1.6
When a force of 36 Newtons is applied to springs S1 and S2, the displacement of the springs is 6 centimeters and 9 cm, respectively. What is the difference between the spring constants of the two springs?
Answer:
200 N/m
Step-by-step explanation:
Rearranging the formula F = kx, you find that k = F/x. For the first spring,
F = 36 N and x = 0.06 m (6 cm). So the spring constant, F/x, is 36N/0.06m = 600 N/m
For the second spring, F = 36 N and x = 0.09 m. F/x = 36N/0.09m = 400 N/m
The difference between these values is 200 N/m, and that's the answer.
Please help. I’ll mark you as brainliest if correct!
Answer:
Step-by-step explanation:
children=c
adults=a
c+a=359
a=359-c
2.75c+6a=1621
2.75 c+6(359-c)=1621
2.75 c+2154-6c=1621
-3.25 c=1621-2154
-3.25 c=-533
[tex]-\frac{325}{100} c=-533\\-\frac{13}{4} c=-533\\c=-533 \times \frac{-4}{13} =41 \times 4=164 \\children=164\\adults=359-164=195[/tex]