Answer:
[tex]b=2[/tex]
Stepbystep explanation:
[tex]9+7b=8b7\\9+9+7b=8b7+9 \leftarrow \text {Addition Property of Equality} \\7b+8b=2\\7b8b+8b8b=2\leftarrow \text {Subtraction Property of Equality} \\b=2\\\frac{b}{1}=\frac{2}{1} \leftarrow \text {Division Property of Equality}\\\boxed {b=2}\\\\\huge\text {The value of 'b' should be 2}[/tex]
Simplify the expression (x^2z^3)(5yz)^2
Answer:
(5yz)^2(x^2z^3)
(25y^2z^2)(x^2z^3)
25x^2y^2z^5
Stepbystep explanation:
In ΔRST, s = 93 inches, ∠S=123° and ∠T=28°. Find the length of r, to the nearest 10th of an inch.
We have been given that in ΔRST, s = 93 inches, ∠S=123° and ∠T=28°. We are asked to find the length of r to the nearest 10th of an inch.
We will use law of sines to solve for side r.
[tex]\frac{a}{\text{Sin}(a)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are corresponding sides to angles A, B and C respectively.
Let us find measure of angle S using angle sum property of triangles.
[tex]\angle R+\angle S+\angle T=180^{\circ}[/tex]
[tex]\angle R+123^{\circ}+28^{\circ}=180^{\circ}[/tex]
[tex]\angle R+151^{\circ}=180^{\circ}[/tex]
[tex]\angle R+151^{\circ}151^{\circ}=180^{\circ}151^{\circ}[/tex]
[tex]\angle R=29^{\circ}[/tex]
[tex]\frac{r}{\text{sin}(R)}=\frac{s}{\text{sin}(S)}[/tex]
[tex]\frac{r}{\text{sin}(29^{\circ})}=\frac{93}{\text{sin}(123^{\circ})}[/tex]
[tex]\frac{r}{\text{sin}(29^{\circ})}\cdot \text{sin}(29^{\circ})=\frac{93}{\text{sin}(123^{\circ})}\cdot \text{sin}(29^{\circ})[/tex]
[tex]r=\frac{93}{0.838670567945}\cdot (0.484809620246)[/tex]
[tex]r=110.889786233799179\cdot (0.484809620246)[/tex]
[tex]r=53.7604351[/tex]
Upon rounding to nearest tenth, we will get:
[tex]r\approx 53.8[/tex]
Therefore, the length of r is approximately 53.8 inches.
Find the surface area of the prism.
Answer:
920 ft^2
Stepbystep explanation:
area of triangles: base x height / 2 (2)
8 x 15 / 2
= 60 x 2
= 120
area of rectangular base: length x width
15 x 20 = 300
area of sloped rectangle: length x width
17 x 20 = 340
area of rectangle: length x width
8 x 20 = 160
Total: 120 + 300 + 340 + 160
=920 ft^2
Answer:
920 ft²
Stepbystep explanation:
2 triangles + 3 rectangles
2(½×15×8) + 20(17+8+15)
120 + 800
920
Gabby received 6 job offers from 15 interview he did last month.Which ratio best describes the relationship between the number of jobs he was not offered and the number of jobs for which he was interviewed
Answer:
the answer is 3:5
Stepbystep explanation:
Total number of jobs for the interview = 15
number of job offers received by Gabby = 6
number of jobs not offered = 15  6 = 9
therefore, the relationship will be 9:15
3:5
i don't understand this pls help
Answer:
1
Stepbystep explanation:
Solve. Remember to follow PEMDAS.
PEMDAS is the order of operation, and =
Parenthesis
Exponent (& Roots)
Multiplication
Division
Addition
Subtraction
First, divide 54 with 6:
54/(6) = 9
Next, combine the terms.
10 + (9) = 10  9 = 1
1 is your answer.
~
here is a list of numbers: 12, 13, 19, 16 ,32, 15, 13.
a)work out the range of the numbers in the list.
b)work out the mean of the numbers in the list
Look at the attached picture
Hope it will be helpful to you ...
The range of the number given is given as (12, 32) while the mean of the given number is 17.14.
Given that,
The list of the number is given as 12, 13, 19, 16,32, 15, and 13.
The range of the number and mean of the given numbers is to be determined.
Range, it is the set of values that come out to an outcome for a certain mathematical operation.
What is mean?The mean of the values is the ratio of the total sum of values to the number of values.
Here,
Rearrange the number in ascending order,
12, 13, 13, 15, 16, 19, 32
The range of the list is given as,
Range = [12, 32]
Mean of the numbers = [12 + 13 + 13 + 15 + 16 + 19 + 32] / 7
Mean = 17.14
Thus, the range of the number given is given as (12, 32) while the mean of the given number is 17.14.
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Unit 5. 1) Please help. What is the volume of the cone?
Answer:
I think the correct answer is 27 so option c. :)
i need help thanks in advance
Answer:
36
Stepbystep explanation:
what are the first 100 hundred digits of pi?
Answer: first 1000 digest
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989
Stepbystep explanation:
Answer:
you aren't ready for this!!!!
Stepbystep explanation:
And now
AsapSCIENCE presents
100 digits of π
3.14159, this is π
Followed by 2653589
Circumference over diameter
79, then 323
OMG! Can't you see?
8462643
And now we're on a spree
38 and 32, now we're blue
Oh, who knew?
7, 950 and then a two
88 and 41, so much fun
Now a run
97169399
Then 37, 51
Half way done!
058, now don't be late
209, where's the wine?
74, it's on the floor
Then 94459
230, we gotta go
78, we can't wait
1640628
We're almost near the end, keep going
62, we're getting through
0899, on time
8628034
There's only a few more!
82, then 53
42, 11, 70 and 67
We're done! Was that fun?
Learning random digits
So that you can brag to your friends
The thickness of a protective coating applied to a conductor designed to work in corrosive conditions follows a uniform distribution over the interval [20;40] microns. Find the probability that the coating is between 24 and 38.
Answer:
[tex] P(24< X<38)= P(X<38) P(X<24)= F(38) F(24)[/tex]
And replacing we got:
[tex] P(24< X<38)=\frac{3820}{4020}\frac{2420}{4020}= 0.90.2= 0.7[/tex]
Stepbystep explanation:
We can define the random variable X as the thickness of a protective coating applied to a conductor designed to work in corrosive conditions. And the distribution for X is given by:
[tex] X \sim Unif (a = 20, b=40)[/tex]
And we want to find this probability:
[tex] P(24< X<38) [/tex]
And in order to find this probability we can use the cumulative distribution function given by:
[tex] F(x) = \frac{xa}{ba} , a\leq X \leq b[/tex]
And if we use this formula for the probability desired we have:
[tex] P(24< X<38)= P(X<38) P(X<24)= F(38) F(24)[/tex]
And replacing we got:
[tex] P(24< X<38)=\frac{3820}{4020}\frac{2420}{4020}= 0.90.2= 0.7[/tex]
What is the length c of the right triangle, rounded to the nearest
tenth?
Answer:
6.1
Stepbystep explanation:
we will name the length in front of the angle , y :
tan(71°)≅2.904= y ÷2
⇒ y= 5.8
and we know that
c = [tex]\sqrt{2^{2} + y^{2} }[/tex]
then
c = 6.14
and if we round it to the nearest tenth :
c = 6.1
Mark recently took a road trip across the country. The number of miles he drove each day was normally distributed with a mean of 450. If he drove 431.8 miles on the last day with a zscore of 0.7, what is the standard deviation?
Answer:
The (population) standard deviation is 26 miles or [tex] \\ \sigma = 26[/tex] miles.
Stepbystep explanation:
We can solve this question using the concept of zscore or standardized value, which is given by the formula:
[tex] \\ z = \frac{x  \mu}{\sigma}[/tex] [1]
Where
[tex] \\ z[/tex] is the zscore.
[tex] \\ x[/tex] is the raw score.
[tex] \\ \mu[/tex] is the population's mean.
[tex] \\ \sigma[/tex] is the population standard deviation.
Analyzing the question, we have the following data to solve this question:
The random variable number of miles driven by day is normally distributed.The population's mean is [tex] \\ \mu = 450[/tex] miles.The raw score, that is, the value we want to standardize, is [tex] \\ x = 431.8[/tex] miles.The zscore is [tex] \\ z = 0.7[/tex]. It tells us that the raw value (or raw score) is below the population mean because it is negative. It also tells us that this value is 0.7 standard deviations units (below) from [tex] \\ \mu[/tex].Therefore, using all this information, we can determine the (population) standard deviation using formula [1].
Then, substituting each value in this formula:
[tex] \\ z = \frac{x  \mu}{\sigma}[/tex]
Solving it for [tex] \\ \sigma[/tex]
Multiplying each side of the formula by [tex] \\ \sigma[/tex]
[tex] \\ \sigma*z = (x  \mu) * \frac{\sigma}{\sigma}[/tex]
[tex] \\ \sigma*z = (x  \mu) * 1[/tex]
[tex] \\ \sigma*z = x  \mu[/tex]
Multiplying each side of the formula by [tex] \\ \frac{1}{z}[/tex]
[tex] \\ \frac{1}{z}*\sigma*z = \frac{1}{z}*(x  \mu)[/tex]
[tex] \\ \frac{z}{z}*\sigma = \frac{x  \mu}{z}[/tex]
[tex] \\ 1*\sigma = \frac{x  \mu}{z}[/tex]
[tex] \\ \sigma = \frac{x  \mu}{z}[/tex]
Then, this formula, solved for [tex] \\ \sigma[/tex], will permit us to find the value for the population standard deviation asked in the question.
[tex] \\ \sigma = \frac{431.8  450}{0.7}[/tex]
[tex] \\ \sigma = \frac{18.2}{0.7}[/tex]
[tex] \\ \sigma = 26[/tex]
Thus, the (population) standard deviation is 26 miles or [tex] \\ \sigma = 26[/tex] miles.
Please help, it’s a math question
Answer:
the answer is B
Stepbystep explanation:
hope it help
On a coordinate plane, a circle has a center at (4, 5) and a radius of 3 units.
Which equation represents a circle with the same center as the circle shown but with a radius of 2 units?
(x – 4)2 + (y – 5)2 = 2
(x – 4)2 + (y – 5)2 = 4
(x – 5)2 + (y – 4)2 = 2
(x – 5)2 + (y – 4)2 = 4
Answer:
(x  4)² + (y  5)² = 4
Stepbystep explanation:
The equation of a circle in standard form is
(x  h)² + (y  k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (4, 5) and r = 2, thus
(x  4)² + (y  5)² = 2², that is
(x  4)² + (y  5)² = 4 ← second option on list
The required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x4)^2 + (y5)^2 = 4
Equation of a circleThe standard equation of a circle is expressed as:
(xa)^2 + (yb)^2 = r^2
where:
(a, b) is the centre = (4, 5)
r is the radius = 3 units
Substitute to have;
(x4)^2 + (y5)^2 = 2^2
(x4)^2 + (y5)^2 = 4
Hence the required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x4)^2 + (y5)^2 = 4
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The number y of raccoons in an area after x years can be modeled by the function y= 0.4x^2+2x+2. When were there about 45 raccoons in the area? Round your answer to the nearest year
Answer:
A timeframe of 8 years is when there were 45 raccoons in the area.
General Formulas and Concepts:
PreAlgebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityStandard Form:
[tex]\displaystyle ax^2 + bx + c = 0[/tex]
Quadratic Formula:
[tex]\displaystyle x=\frac{b \pm \sqrt{b^2  4ac}}{2a}[/tex]
Stepbystep explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \begin{aligned}y & = 0.4x^2 + 2x + 2 \\y & = 45 \ \text{raccoons} \\\end{aligned}[/tex]
Step 2: Find Specific Year
We are trying to find the year when there were 45 raccoons present in the area. From first glance, we see we probably can't factor the quadratic expression, so let's set up to use the Quadratic Formula:
[Model Equation] Substitute in y:Now that we have our variables from Standard Form, we can use the Quadratic Formula to find which years when there were 45 raccoons present in the area:
[Quadratic Formula] Substitute in variables:Since time cannot be negative, we can isolate the other root to obtain our final answer:
[tex]\displaystyle\begin{aligned}x & = 8.16536 \ \text{years} \\& \approx \boxed{ 8 \ \text{years} } \\\end{aligned}[/tex]
∴ we have found the approximate amount of years to be 8 years when there were 45 raccoons in the area.
___
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___
Topic: Algebra I
A concrete planter is formed from a squarebased pyramid that was inverted and placed inside a cube.
This question is incomplete and it lacks the attached diagram of the square based pyramid. Find attached to this answer, the square based pyramid.
Correct Question
A concrete planter is formed from a squarebased pyramid that was inverted and placed inside a cube.
A. What is the slant height of the pyramid?
B. What is the surface area of the composite figure?
HINT: The surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.
C. How many cubic yards of concrete are needed to make the planter?
Answer:
A. The slant height of the pyramid = 2.24 yards.
B. The surface area of the composite figure = 12.94 square yards.
C. The cubic yards of concrete are needed to make the planter = 2.67 cubic yards.
Stepbystep explanation:
A. What is the slant height of the pyramid?
To calculate the Slant height of a pyramid we make use of the Pythagoras Theorem which is given as:
a² + b² = c²
Where a = Height of the square pyramid represent by h
b = radius of the square pyramid represented by r
c = Slant height of the square pyramid represented by s
Therefore, we have
h² + r² = s²
Looking at the attached diagram, we are given the side length = 2 yards.
The radius of the square based pyramid = side length ÷ 2
= 2÷ 2 = 1 yard.
The height of a square based pyramid = 2 yards
Since , h² + r² = s²
The slant height of the square pyramid is calculated as :
√h² + r² = s
√(2² + 1²) = s
√5 = s
s = 2.24 yards
B. What is the surface area of the composite figure?
We were given hints in the question that the the surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.
Step 1
We find the Lateral area of the faces of the insides of the inverted pyramid
We have 4 faces, Hence,
The formula is given as
a × √( a² + 4h²
a = 2 yards
h = 2 yards
So, = 2 × √( 2² + 4 ×2²
The Lateral area of the faces = 8.94 square yards.
Step 2
Area of the 5 faces of the cube
= a²
Where a = side length = 2 yards
= 2²
= 4 square yards.
Step 3
Therefore, surface area of the composite figure = 8.94 square yards + 4 square yards
= 12.94 square yards.
C. How many cubic yards of concrete are needed to make the planter?
This is calculated by find the Volume of the Square based pyramid.
The formula is given as :
V = (1/3)a²h
Where a = side length = 2 yards
h = height of the square based pyramid = 2 yards
V = 1/3 × 2² × 2
V = 2.67 cubic yards
Mark walked 15 miles in 6 hours
Calculate his average speed
Average speed = 2.5 miles
Divide 6 from both sides.
6/6 = 1
15/6 = 2.5
So, overall Mark walks 2.5 miles per hour.
hope it helps!
It costs 31.25 for 1 box of candy and 4 large bags of popcorn at a movie theatre. For 3 boxes of candy and 5 large bags of popcorn it costs 46.50 how much does 1 bag of popcorn cost
Answer:
$6.75
Stepbystep explanation:
$31.25 = C + 4B C for box of candy and B for large bags of popcorn
$46.50 = 3C + 5B
3($31.25 = C + 4B)
$93.75 = 3C + 12B
46.50. 3C. 5B
$47.25 = 7B
÷7. ÷7
$6.75. = B
Mrs. Rodriguez bought 3 tickets for a concert. She also paid for a poster at the concert. Mrs. Rodriguez paid a total of $102 for the tickets and the poster. The equation 3t + p = 102 can be used to find p, the amount Mrs. Rodriguez paid for the poster. If Mrs. Rodriguez paid $29 for each ticket, t, then how much did she pay for the poster
Answer:
15
Stepbystep explanation:
102(29 x 3)
Answer:
p=15
Stepbyexplanation:
3t+p/102
3(29)+p=102
87+p=102
p=15
A pilot is flying a plane 20000 ft above the ground.The pilot begins a 2 descent to an airport runway.How far is the airplane from the start of the runway(in ground distance)
Answer:
381623 ft
Stepbystep explanation:
Since the airport altitude is 20000 ft and the pilot needs a 2° descent, to calculate the distance of the airplane at the start of this approach, first this is represented in the diagram attached. The distance from the runway at the start is x.
[tex]tan(3) = \frac{20000}{x} \\x=\frac{20000}{tan(3)} \\x=381623ft[/tex]
The airplane is at a distance of 381623 ft away from the airplane runaway at the start of the descent.
hey can anyone pls help me out in dis!!!!!!!!!
Answer:
Look at the attachment
someone be a real one and finish this... plz
Answer:
y + 21 =  4(x  7)
Stepbystep explanation:
The equation of a line in point slope form is
y  b = m(x  a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = [tex]\frac{y_{2}y_{1} }{x_{2}x_{1} }[/tex]
with (x₁, y₁ ) = (7,  21) and (x₂, y₂ ) = ( 4, 23)
m = [tex]\frac{23+21}{47}[/tex] = [tex]\frac{44}{11}[/tex] =  4
Using m =  4 and (a, b) = (7,  21), then
y  ( 21) =  4(x  7), that is
y + 21 =  4(x  7)
what will happen to the volume of a cylinder if the length if the height is tripled?
A. Double
B. Stay the same
C. Triple
D. 9 times as large
Answer:
Triple
Stepbystep explanation:
V = π * r^2 *h
h is directly proportional to V so when h increases V increases.
This is a linear relationship so if h is tripled the volume will be tripled as well.
if r tripled then V would be 9 times as large since r has a square relationship with V.
If you're unsure about these just plug in number r= 2, h= 4, and perform the operation they ask you to do (triple or double) and you'll always get it right.
How do you solve 15 less than or equal to
3  4s
Answer:
3 is greater than or equal to s
Stepbystep explanation:
subtract 3 on both sides
then get s by itself by dividing by 4 on both sides (bc you are dividing by a negative the sign flips)
Find the area. The figure is not drawn to scale.
1.
36 in.
40 in.
33 in.

Answer: 47,520
Stepbystep explanation: 36 times 40 times 33
What is the solution to the system of equations below? x + 3 y = 15 and 4 x + 2 y = 30
Answer:
X=6 y=3 point form (6,3)
Stepbystep explanation:
Answer:
6,3
Stepbystep explanation:
I just took the test and got 100%
ok, im failing math rn so plz help
Answer:
3/4
Stepbystep explanation:
Point A is at (4,3) and Point B is at (4,3)
The slope is at
m = (y2y1)/(x2x1)
= (3 3)/(4  4)
= (33)/(4+4)
= 6/8
= 3/4
Use Heron’s Formula, that is, the area of a triangle is , where the triangle contains sides a, b and c and to find the area of the triangle with side lengths: .a=7/2 b=4/3 c=9/4
Answer:
Area: T = 0.649
Stepbystep explanation:
Sides: a = 3.5 b = 1.333 c = 2.25
The mk family orchard has 120 apple trees and 90 pear trees. If each fruit tree produces an average of 590 pounds of fruit per year, about how many pounds of fruit can the orchard produce in one year
Answer & Stepbystep explanation:
If each fruit tree produces an average of 590 pounds of fruit, then that means we are going to multiply. For the apples, we are going to multiply 120 by 590. For the pears, we are going to multiply 90 by 590. After we multiply these numbers, we are going to add the products so we can find the total amount of pounds of fruit.
Apples:
120 × 590 = 70800
Pears:
90 × 590 = 53100
Now, we add 70800 to 53100.
70800 + 53100 = 123900
So, the orchard produces 123900 pounds of fruit in one year.
what is the slope of the line 7x+2y=5
Answer:
slope = 7/2x
Stepbystep explanation:
you can solve the equation in order to make it slopeintercept form.
7x + 2y = 5
2y = 7x + 5
divide everything by 2
it becomes y = 7/2x + 5/2
The required slope of the line is m = 7 / 2.
A line can be defined by the shortest distance between two points is called a line.
Method 1
7x + 2y = 5
Rearranging the equation in the standard form of the equation of a line
y = mx + c
where m is the slope of the line and c is the intercept of the line.
7x + 2y = 5
2y = 7x + 5
y = 7x/2 + 5      (1)
Comparing equation 1 with the standard form of the equation
m = 7/2 and c = 5
Method 2
Differentiate the given equation, with respect to x
d/dx (7x + 2 y) = d/dx (5)
7 + 2dy/dx = 0
dy/dx = 7/2
Slope = dy/dx = 7/2
Thus, the required slope of the equation is m = 7/2
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