Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.
How many bundles of steel rod does the machinist require?Given the data in the question;
Machinist needs 98 pieces of steel rodThe rods come in bundles of 8 piecesNumber of bundles of steel rods required by the mechanist = ?To determine the bundle of steel required, let y represent the bundle.
Since;
1 bundle = 8 piece
y bundle = 98 piece
We cross multiply
y bundle × 8 piece = 1 bundle × 98 piece
y = ( 1 bundle × 98 piece ) / ( bundle × 8 piece )
y = 98 pieces / 8 piece
y = 12.25 ≈ 13
Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.
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Solve for y.......
[tex]6 = 2(y + 2)[/tex]
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
y = 1[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex] \qquad❖ \: \sf \:6 = 2(y + 2)[/tex]
[tex] \qquad❖ \: \sf \:(y + 2) = \cfrac{6}{2} [/tex]
[tex] \qquad❖ \: \sf \:y + 2 = 3[/tex]
[tex] \qquad❖ \: \sf \:y = 3 - 2[/tex]
[tex] \qquad❖ \: \sf \:y = 1[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Value of y = 1The base of the following pyramid is a square. If the volume of the pyramid is 400 feet³, what is the missing length? Round the answer to the nearest hundredth. The S=11ft
The length of the missing side is 9.92 ft given that the base of the following pyramid is a square, base side length(s) is 11 ft and the volume of the square pyramid is 400 ft³. This can be obtained using the formula of finding the volume of the pyramid with base as square.
Calculate the length of the missing side:The formula of finding the volume of the pyramid with base as square is,
⇒ V = s²h/3
where V is the volume of the square pyramid, s is the side length of the base and h is the height of the square pyramid.
Here in the question it is given that,
it is a pyramid with base as squarethe side length of the base is 11 ftvolume of the square pyramid is 400 ft³that is, s = 11 ft, V = 400 ft³
By using the formula of finding the volume of the pyramid with base as square we get,
V = s²h/3
400 = (11)²h/3
By rearranging the equation we get,
h = 400 × 3/11²
h = 9.92 ft
Hence the length of the missing side is 9.92 ft given that the base of the following pyramid is a square, base side length(s) is 11 ft and the volume of the square pyramid is 400 ft³.
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what is the area of the figure bellow?
Answer:
The area of the figure is C. 48.5 cm²
find the value of x,y in the given figure with reasons.
Answer:
answer
x= 40°
Step-by-step explanation:
x= 40° [ base angle of isocles triangle]
a dust mite is 400 pm long under a microscope, it looks 100,000 pm long. what magnification scale was used
Answer: 250:1
Step-by-step explanation:
Divide the measurement of appearance by the actual measurement.
[tex]100,000/400=250[/tex]
The magnification scale is 250:1. The scale is used by a 250X magnifying lense.
Cos3A ×cos2A =cos A ×cos 2A -sin4A×sin A=prove it
Answer:
Step-by-step explanation:
cosA×cos 2A-sin4A×sinA
=cosAcos2A-2sin2Acos2A sin A
=cos 2A(cosA-2sin2AsinA)
=cos 2A(cosA-2×2sinAcosAsin A)
=cos2A×cosA(1-4sin²A)
=cos 2AcosA(1-4(1-cos²A))
=cos2A×cosA(1-4+4cos²A)
=cos 2A(-3cosA+4cos³A)
=cos 2A(4cos³A-3cosA)
=cos 2A×cos3A
The volume of a sphere is 144π. What is its Surface Area to the nearest whole number?
P=2(L+W) Solve for W
Answer:
W = (P -2L)/2
Step-by-step explanation:
P = 2(L + W) Distribute the 2
P = 2L + 2W Subtract 2L from both sides
P - 2L = 2W Divide both sides by 2
(P-2L)/2 = W
i. 749x98+749 x2 ii. 62 x 999 +4795 iii. 736 x 97 iv. 258 x 1008
solve these using distributive property
pls help if u know
Step-by-step explanation:
I= 74810
II=66733
III=71392
iv=239904
please help!!
maths functions
Answer:
The Co-ordinate of C is (4/3, -1/2)
Step-by-step explanation:
We have two equation one is of straight line equation which is:
y=2x-3 (i)
Other equation is of quadratic function which is:
y=-3x^2+5 (ii)
Put the value of y from equation (i) in equation (ii)
So, we have:
2x-3=-3x^2+5
3x^2+2x-8=0
By factorization:
3x^2+6x-4x-8=0
3x(x+2)-4x(x+2)=0
(x+2)(3x-4)=0
x+2=0 ; 3x-4=0
x=-2 ; x=4/3
Put first x=-2 in equation (i)
y=2(-2)-3
y=-4-3
y=-7
Now Put x=4/3 in equation (i)
y=2(4/3)-3
y=8/3-3
y=-1/2
So, we have two Order pair One is (-2 , -7) and Second one is (4/3 , -1/2)
Hence the Co-ordinate of C is:
C=(4/3 , -1/2)
Answer:
Point C: (3, 3)
Point D: (3, -22)
Step-by-step explanation:
If the distance between points C and D is 25 units, the y-value of point D will be 25 less than the y-value of point C. The x-values of the two points are the same.
Therefore:
[tex]\textsf{Equation 1}: \quad y=2x-3[/tex]
[tex]\textsf{Equation 2}: \quad y-25=-3x^2+5[/tex]
As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:
[tex]\implies 2x-3-25=-3x^2+5[/tex]
[tex]\implies 3x^2+2x-33=0[/tex]
[tex]\implies 3x^2-9x+11x-33=0[/tex]
[tex]\implies 3x(x-3)+11(x-3)=0[/tex]
[tex]\implies (x-3)(3x+11)=0[/tex]
[tex]\implies x=3, -\dfrac{11}{3}[/tex]
From inspection of the given graph, the x-value of points C and D is positive, therefore x = 3.
To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:
[tex]\begin{aligned} \textsf{Point C}: \quad 2x-3 & =y\\2(3)-3 & =3\\ \implies & (3, 3)\end{aligned}[/tex]
[tex]\begin{aligned} \textsf{Point D}: \quad -3x^2+5 & = y \\ -3(3)^2+5 & =-22\\ \implies & (3, -22)\end{aligned}[/tex]
Therefore, point C is (3, 3) and point D is (3, -22).
HELPPPP PLSSSSSSSSS!!!!!!!!??!
Answer:
(3+3) x (3+1)
Step-by-step explanation:
nice
We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.
Solution :» (1 + 3) × (3 + 3)
» (4) × (6)
» 24
Here's our answer..!!
Write down the answer for Q 7 and 8
The answers to the given addition operations are
7) 6 Hundredths add to 4 tenths add to 6 ones is equal to 6.46
8) 82 Hundredths add to 9 tenths add to 4 tens is equal to 41.72
Addition operationFrom the question, we are to add the given numbers
7. 6 Hundredths add to 4 tenths add to 6 ones is equal to
6 Hundredths = 0.06
4 tenths = 0.4
6 ones = 6
Thus, we get
0.06 + 0.4 + 6 = 6.46
8. 82 Hundredths add to 9 tenths add to 4 tens is equal to
82 Hundredths = 0.82
9 tenths = 0.9
4 tens = 40
Thus, we get
0.82 + 0.9 + 40 = 41.72
Hence, the answers to the given addition operations are
7) 6 Hundredths add to 4 tenths add to 6 ones is equal to 6.46
8) 82 Hundredths add to 9 tenths add to 4 tens is equal to 41.72
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An insurance provider states that their customers save at least, on average, 300 dollars per year by switching to them, with a standard deviation of 150 dollars. Before we decide to switch to the new company and go through all of the hassle, we want to test the claim. So, we go out and sample 64 individuals who switched to the new insurance company and found them to have saved an average of 255 dollars per year. Do we have enough evidence at the α = 0.05 level to state that the insurance provider is false in their claim? Discussion Prompts Answer the following questions in your initial post: What are the hypotheses based on the words given in the problem? Should we use a Z or T distribution in this case? What is our Z or T statistic? What is the P-value? Based on your p-value and alpha, what conclusion will we make? Based on your results, would you switch to this company? Explain why or why not (Note: this can go beyond the use of statistics, but statistical analysis can help our decisions)
The solution to the question is mathematically given as
1)
H0: M [tex]\geqslant[/tex] 300
H0: M [tex]\geqslant[/tex] 300
2)
Z distribution.
3)
z=-2.4
4)
P=0.0082
5)
"H0" is rejected as a hypothesis with a level of significance of 0.05.
What is the hypothesis ?Generally, the equation for is mathematically given as
Solutions
we have, [tex]$u=300$$$\begin{aligned}& \sigma=150 \text { dollars } \\N &=64 \text { individuals } \\\bar{x} &=255 \text { dollare. } \\a=& 0.05 .\end{aligned}[/tex]
(1):
H0: M [tex]\geqslant[/tex] 300 dollars; customers save at least 300 dollars per year by switching to them.
H0: M [tex]\geqslant[/tex] 300 dollars:
(This is a left-tailed test)
(2):
when [tex]\sigma[/tex] is known, we use the Z test. we use Z distribution.
(3):
[tex]\begin{gathered}z=\frac{\bar{x}-\mu}{6 / \sqrt{n}}=\frac{255-300}{150 / \sqrt{64}}=\frac{-45}{18.75}=-2.4 \\z=-2.4\end{gathered}[/tex]
(4):
[tex]Pvalue $=P(z < -2 \cdot 4)$ $=0.0082 \quad\{$ wing $z$ tables $\}$ \\\\\text { Pvalue }=0.0082[/tex]
(5):
In conclusion, Since p-value = 0·0082 <0.05
This is statistically significant at the 0.05 level.
We thus "Refect H0" using a threshold of significance of 0.05.
"H0" is rejected as a hypothesis with a level of significance of 0.05.
There is not enough data to support the assertion that consumers may save at least $300 annually by switching insurance providers.
Therefore, we would not consider making the transition to this firm.
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Find the surface area of a sphere with radius 15 in
radius -15
Surface Area of a sphere =4πr^2
=4x22/7x15x15
=19800/7
=2828.57
What is the volume of a cylinder with a radius of 3 inches and a height of 5 inches? Round to the nearest tenth if necessary.
The volume of the cylinder in discuss in which case, the radius of the cylinder is 3 inches and the height is inches is; V = 141.3in³.
What is the volume of the the described cylinder?The cylinder in discuss according to the task content has radius, 3 inches and height, 5 inches.
Since the volume of a cylinder by convention is given as; V = πr²h
Therefore, the volume of the cylinder in discuss is;
V = π (3²)×5
V = 3.14 × 45
V = 141.3in³
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Rewrite the quadratic function in vertex form (which is also called a standard form) and give the vertex.
f(x)=x^2-3x
f(x)=
Enter your answer as a point (a,b)
Vertex:
Please explain how you arrived at that answer.
The vertex form of the equation f(x) = x^2 - 3x, is f(x) = (x - 3/2)^2 - 9/5
How to rewrite the quadratic function?The quadratic function is given as:
f(x) = x^2 - 3x
Differentiate the function
f'(x) = 2x - 3
Set the function to 0
2x - 3 = 0
Add 3 to both sides
2x = 3
Divide by 2
x = 3/2
Set x = 3/2 in f(x) = x^2 - 3x
f(x) = 3/2^2 - 3 * 3/2
Evaluate
f(x) = -9/5
So, we have:
(x, f(x)) = (3/2, -9/5)
The above represents the vertex of the quadratic function.
This is properly written as:
(h, k) = (3/2, -9/5)
The vertex form of a quadratic function is
f(x) = a(x - h)^2 + k
So, we have:
f(x) = a(x - 3/2)^2 - 9/5
In f(x) = x^2 - 3x,
a = 1
So, we have:
f(x) = (x - 3/2)^2 - 9/5
Hence, the vertex form of the equation f(x) = x^2 - 3x, is f(x) = (x - 3/2)^2 - 9/5
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PLEASE HELP ASAP !!!!
Which functions have a range of {y e R-00 < y < ∞0}?
O f(x) = -4x + 11
Of(x) = x - 8
O
f(x) = 2x+3
O f(x) = -(x + 1)² - 4
O
f(x)
f(x) = x²
x² + 7x9
Answer:
Options 1 and 2
Step-by-step explanation:
Correct. The range of all linear functions without a restricted domain is the set of all real numbers.Correct. The range of all linear functions without a restricted domain is the set of all real numbers.Wrong. The exponential cannot take negative values.Wrong. Quadratics do not have a range that is the set of real numbers.Wrong. Quadratics do not have a range that is the set of real numbers.A normal population has a mean u = 31 and standard deviation = 10. What proportion of the population is less than 30?
The proportion of the population exists less than 30 then
(x< 30) = 0.986.
How to estimate the proportion of the population that exists less than 30?To estimate the z-score using the formula, z = (x - µ)/σ
Where, x be the randomly chosen values = 30
µ be the mean = 31
σ be the standard deviation = 10
Proportion of the population that exists less than 18 = P(x < 30)
Plug in the values into z = (x - µ)/σ, to get z-score.
Substitute the values in the above equation, we get
z = (30 - 31)/10
z = -1/10 = -0.1
Therefore, the value of z = - 0.1.
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Can someone help me with a step by step process of how to solve this? Calculus 2
If you fix a point on the curve in the given interval, and revolve that point about the [tex]x[/tex]-axis, it will trace out a circle with radius given by the function value [tex]y[/tex] for that point [tex]x[/tex]. The perimeter of this circle is then [tex]2\pi(8\sqrt x) = 16\pi \sqrt x[/tex].
The surface in question is essentially what you get by joining infinitely many of these circles at every point in the interval [0, 9].
So, the surface area is given by the definite integral
[tex]\displaystyle \int_0^9 16\pi \sqrt x \, dx = 16\pi\times\frac23 x^{3/2}\bigg|_{x=0}^{x=9} = \frac{32\pi}3 \left(9^{3/2} - 0^{3/2}\right) = \boxed{288\pi}[/tex]
In the diagram, is parallel to. Also, is drawn such that the length of is half the length of. If sin A = 0.5, then what is sin E?
sinE is 0.5
What are similar triangles?
Two triangles will be similar if the angles are equal (corresponding angles), and sides are in the same ratio or proportion (corresponding sides). Similar triangles may have different individual lengths of the sides of triangles, but their angles must be equal and their corresponding ratio of the length of the sides must be the same.
Clearly, given triangle AFB and triangle DFE are similar.
We know that Similar Triangles have the same corresponding angle
We can find sinE as show below:
From diagram clearly
∠A=∠E
and ∠B=∠D
Since, ∠A=∠E
Taking sin on both sides
sinA=sinE
Give, sinA=0.5
sinA=sinE=0.5
⇒ sinE=0.5
Hence, sinE is 0.5
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Which of the following options have the same value as 5\%5%5, percent of 353535?
Answer:
[tex]\frac{5}{100}\times35[/tex]
[tex]0.05\times35[/tex]
Step-by-step explanation:
Given:
Which of the following options have the same value as 5% 35, percent of 35?
Following Options:
[tex]5 \times 35[/tex]
[tex]\frac{5}{100}\times35[/tex]
[tex]0.5\times0.35[/tex]
[tex]0.05\times35[/tex]
[tex]\frac{5}{10}\times35[/tex]
Solve:
[tex]5[/tex] % [tex]= 0.05=\frac{5}{100}[/tex]
Thus the following options:
[tex]5 \times 35[/tex] [ False x ]
5 does not equal 5%
[tex]\frac{5}{100}\times35[/tex] [True √ ]
[tex]5[/tex]% [tex]=\frac{5}{100}[/tex]
[tex]0.5\times0.35[/tex] [ False x ]
[tex]0.5 = 0.50[/tex]
[tex]0.05\times35[/tex] [True √ ]
[tex]5[/tex]% [tex]= 0.05=\frac{5}{100}[/tex]
[tex]\frac{5}{10}\times35[/tex] [ False x ]
[tex]\frac{5}{10}=0.50[/tex]
Therefore, the options [B] [tex]\frac{5}{100}\times35[/tex] and [D] [tex]0.05\times35[/tex] is True.
Kavinsky
What is the solution of the inequality shown
below?
c+3>8
Answer:
c > 5
Step-by-step explanation:
The properties of equality can be used to solve inequalities. Attention needs to be paid to ordering.
ApplicationWe can subtract 3 from both sides to solve this.
c +3 > 8 . . . . . . given
c +3 -3 > 8 -3 . . . . subtract 3 from both sides
c > 5 . . . . . . . . . simplify
The solution is c > 5.
__
Additional comment
Adding or subtracting a value to a number on a number line is equivalent to shifting it right or left. It does not change ordering.
Multiplying or dividing by a positive number is equivalent to expanding or compressing the distance from zero. It does not change ordering.
Multiplying or dividing by a negative number reflects the value across the origin, in addition to expanding or compressing the distance from zero. This reflection reverses the left-right ordering. For example, -2 < -1, but 2 > 1. (Both numbers multiplied by -1.)
As long as you're aware of the effect on ordering, you can use any of the properties of equality to solve inequalities.
2. The product of two consecutive even numbers is 168. What are the numbers?
Answer:
12 and 14
Step-by-step explanation:
12 * 14 = 168
Answer:
12 & 14
Step-by-step explanation:
the work: x = first even number, (x+2) = second even number
The equation
[tex]x(x+2)=168[/tex]
[tex]x^{2} +2x=168[/tex]
[tex]x^{2} +2x-168=0[/tex]
Factoring
[tex](x-12)(x+14)=0[/tex]
first factor
[tex]x-12=0\\x=12[/tex]
Second factor
[tex]x+14=0\\x=-14[/tex]
The solution is the positive number
x = 12 is the first even number
x + 2 = 12 + 2 = 14 is the second even number
Hope this helps
There are 48 people coming to a family reunion. One fourth of them live out of state. How many live in-state?
Step-by-step explanation:
1/4×48
=12
So if 12people are out of state
48-12=36,is the number of people living in the state
Throughout this course, you have examined how real-world scenarios can be modelled using quadratic functions, exponential functions, trigonometric ratios sinusoidal functions, and sequences and series. Part A:- In this task, you will be creating unique real-world problems that can be modelled using the functions that we have learned. You may use real-world scenarios that we have examined throughout the course, but your problem should be created by you and have a unique description. Choose three (3) of the five (5) topics below and create a real-world scenario related to each of the three. 1. Exploring Quadratic Functions to Find Zeros or the Vertex; 2. Exponential Growth or Decay; 3. Using Trigonometric Ratios to Solve Three Dimensional Problems; 4. Representing Periodic Behaviour with Sinusoidal Functions: 5. Solving Financial Problems using Sequences & Series.
PLEASE SOLVE WITHOUT USING RADINAS
The exponential function is illustrated below.
How to illustrate the example?An exponential function has a growth factor or 3.76. What is the percentage growth rate?
The growth factor (b) is given as:
b = 3.76
So, the percentage growth rate (r) is calculated as:
r = b - 1
Substitute known values
r = 3.76 - 1
Evaluate the difference
r = 276%
The way to solve Financial Problems using Sequences & Series will be:
The first salary that Mr James earn is 10000 and there is a yearly increase of 2000. Find his salary in the 5th year. This will be:
= a + (n - 1)d
= 1000 + (5 - 1)2000
= 10000 + (4 × 2000)
= 10000 + 8000.
= 18000
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13. A data set has a mean of x=3905 and a standard deviation of 110. Find the z-score for each of the following.
14. A random sample of 80 tires showed that the mean mileage per tire was 41,400mi, with a standard deviation of 4700mi.
Question 13
Part (a)
[tex]\frac{3840-3905}{110}=\boxed{0.5\overline{90}}[/tex]
By similar logic, the other answers are
(b) 2.6818181....
(c) 3.5909090...
(d) 1.1363636...
Question 14
Part (a)
[tex]\frac{46800-41400}{4700} \approx \boxed{1.15}[/tex]
Part (b)
[tex]-2.57=\frac{x-41400}{4700} \\ \\ -2.57(4700)=x-41400 \\ \\ x=41400-2.57(4700) \\ \\ x \approx \boxed{29300}[/tex]
HOW MANY DIFFERENT ARRANGEMENTS CAN BE MADE WITH THE NUMBERS
28535852
Answer:
1,680
Step-by-step explanation:
8 positions with basically 8 choices.
that is 8! arrangements.
but 2 is there 2 times.
8 is there 2 times.
5 is there 3 times.
only 3 is a single digit.
so, we need to eliminate every arrangement, where the 2s trade places, where the 5s trade places, and where the 8s trade places, because they are the same numbers.
that means we have to divide the 8! by 2!, then again by 2!, and again by 3!.
8! / (2! × 2! × 3!) = 8! / 24 = 1,680
8v(v+3)(v+3) rewrite the expression factoring out (v+3)
If we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex]
Given an expression 8v(v+3)(v+3).
We are required to rewrite the given expression.
Expression is a combination of numbers, symbols, fraction , determinants,indeterminants, coefficients. They are not mostly found in equal to form. It expresses a relationship of a line or something else.
The expression is 8v(v+3)(v+3). There are three terms in which variable is v.
To rewrite the expression we have to multiply all the three terms with each other which can be done as under:
=8v(v+3)(v+3)
=[tex](8v^{2}+24v)(v+3)[/tex]
=[tex]8v^{3}+24v^{2}+24v^{2}+72v[/tex]
=[tex]8v^{3}+48v^{2} +72v[/tex]
Now divide it by 8.
=[tex]v^{3}+6v^{2} +9v[/tex]
Hence if we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex] .
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Question 8 of 10
Factor the polynomial: -5x³ - 10x² - 15x
OA. 5x(x²+2x-3)
OB. -5x(-x2 - 2x - 3)
C. -5x(x2 + 2x - 15)
OD. -5x(x2+2x+3)
(5.01 LC) A square is shown below. which expression can be used to find the area, in square units, of the Shaded triangle in the Square?
(answer options are in picture)
The expression can be used to find the area, in square units, of the Shaded triangle in the Square is 1/2 ( 4 · 4 ) .
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = side x side
where s = side length.
If a diagonal is drawn to create 2 halves, then area of each half is 8.
So, The area of a square = 1/2 ( 4 · 4 ) = 16.
If a square has a side length of 4, then the area of the square is 16.
The expression can be used to find the area, in square units, of the Shaded triangle in the Square is 1/2 ( 4 · 4 ) .
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