Answer:
The common difference is the difference between any two consecutive terms in an arithmetic sequence.
The formula which is used to find the common difference in AP is
d = an - an-1
Here the common difference is
d = a2 - a1 = 8 - 2 = 6
d = a3 - a2 = 14 - 8 = 6
d = a4 - a3 = 20 - 14 = 6
d = a5 - a4 = 26 - 20 = 6
2, 8, 14, 20, 26 … = 2, (2 + 6), (8 + 6), (14 + 6), (20+ 6) …
Therefore, the common difference is 6.
Step-by-step explanation:
help me please I need it
Answer:
A
Step-by-step explanation:
The formula for a rectangular prism is length*width*height. Thus, the equation would be 6*4*16, which equals 384 cm^3.
12. Solve the following inequality.
Answer:
C. The solution set is {x|x < 6}.
Step-by-step explanation:
Given :
7x + 4 < 46Subtract 4 from both sides.
7x + 4 - 4 < 46 - 47x < 42Divide 7 from both sides.
7x/7 < 42/7x < 6C. The solution set is {x|x < 6}.
When Lillian goes bowling, her scores are normally distributed with a mean of 130
and a standard deviation of 11. Using the empirical rule, what percentage of the
games that Lillian bowls does she score between 119 and 141?
Using the Empirical Rule, it is found that she scores between 119 and 141 on 68% of the games that she bowls.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, considering that the mean is of 130 and the standard deviation is of 11, the interval between 119 and 141 is within one standard deviation of the mean, hence she scores between 119 and 141 on 68% of the games that she bowls.
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a truck tire has a diameter of 3 feet how far will the truck travel with 20 rotations of the tire?
Answer:
60 ft
Step-by-step explanation:
3 times 20 is 60 ft so there is your answer
Answer:
C
Step-by-step explanation:
Diameter is 3 feet, and the radius is half the diameter.
Radius = 3/2 = 1.5 feetCircumference
2 × π × 1.53πDistance travelled in 20 rotations
20 x 3π60π ftCIf the radius of a clock is 5 inches, what is the distance around the edge of the clock between the two and the five to the nearest hundredth of an inch
plssss help
thank you
Answer:
7.85 inches
Step-by-step explanation:
It mentions distance around the edge of the clock, which is basically another term used for arc length.
Arc Length Formula :
Arc Length = 2πr × θ/360°
Values given :
Radius (r) = 5 inches
Turning angle (θ) = 3/12 × 2π = 1/4 x 2π = π/2 = 90°
Solving :
Arc Length = 2 x 3.14 x 5 x 90/360
Arc Length = 15.7 x 0.5
Arc Length = 7.85 inches
20 points help please
How far does the unicycle move if the wheel turns once?
Pierre enters a 100m unicycle race. How many times must the wheel rotate completely in order for Pierre to travel 100m?
The unicycle would move 2.512 meters if the wheel turns once
The wheel needs to rotate completely 40 times in order for Pierre to travel 100m
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
a) The circumference of the wheel = π * diameter = 3.14 * 80 cm = 251.2 cm = 2.512 m
The unicycle would move 2.512 meters if the wheel turns once
b) For a 100m race:
Number of wheel rotation = 100 m / 2.512 m = 39.8
The wheel needs to rotate completely 40 times in order for Pierre to travel 100m
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2/2x-3
………………………………….
Answer:
(D. (-oo,0) U (0, oo )
[tex]( \infty 0)(0 \infty )[/tex]
(-oo,0) U (0, oo )
use the factored form to solve the related question, 2x^2+17x+30=0. what are the solutions
Answer: x = -6 and x = -5/2
Step-by-step explanation:
[tex]$$Solve for $x$ over the real numbers: \\ $2 x^{2}+17 x+30=0$\\\\The left hand side factors into a product with two terms:$$(x+6)(2 x+5)=0$$Split into two equations:$$x+6=0 \text { and } 2 x+5=0$$Subtract 6 from both sides:$$x=-6 \text { and } 2 x+5=0$$Subtract 5 from both sides:$$x=-6 \text { and } 2 x=-5$$Divide both sides by 2 :Answer:$$x=-6 \text { and } x=-\frac{5}{2}$$[/tex]
8.
Consider a function which takes certain values, as shown in the table below.
--
x | -2 | 0 | 3 | 8 |
y | 10 | 6 | 0 | -10 |
Find the average rate of change between x = -2 and x = 0
Step-by-step explanation:
i just answered this.
the average change rate is the change of the functional result in a given interval relative (= divided by) to the length of the interval of the input variable.
in short
( f (interval upper limit) - f (interval lower limit) ) /
(interval upper limit) - (interval lower limit)
upper limit = 0
lower limit = -2
the functional values (y) are 6 and 10 at these points.
so, we get
(6 - 10) / (0 - -2) = -4 / 2 = -2
A laptop computer is purchased for 1700 after each year the resale value decreases by 25 percent. what will the resale value be after 3 years?
José tiene una tabla de: (x² -4x + 4) cm de largo y (x+4) cm de ancho ¿Cuál es el área de la tabla?
Answer:
x³ - 12x + 16
Step-by-step explanation:
(x² -4x + 4) × (x+4) =
= x³ + 4x² - 4x² - 16x + 4x + 16
= x³ - 12x + 16
Greta is painting two different rectangular prisms. The prisms have the following dimensions.
Prism A:
Length: 1 foot
Width: 4 inches
Height: 8 inches
Prism B:
Length: 10 inches
Width: 2 inches
Height: 1.5 feet
Which prism has a greater surface area, and what is its surface area in square inches?
Answer:
prism B is greater
Step-by-step explanation:
prism A
lenght: 1×4=4
width: 4×8=32
height: 8×1=8
add them all up and multiply it by 2 = 4+32+8×2=52
prism B
lenght: 10×2=20
width: 2×1.5=3
height:1.5×10=15
add them all up and multiply it by 2= 20+3+15×2=76
PLS HELP!! I'M ON A TIME!!
Sid has a water dispenser in his refrigerator as shown in the figure.
A prism has a length of 4 inches, height of 14 inches, and width of 8 inches.
Sid would like to have three water dispensers in his refrigerator. How much cubic space will all three dispensers take up in Sid’s refrigerator?
448 in.3
896 in.3
1,200 in.3
1,344 in.3
Answer:
Its d
Step-by-step explanation:
The other person is wrong because they only solved for one water dispenser you are supposed to solve for all three :)
Using the volume of the rectangular prism, it is found that the three dispensers will take 1,344 in³ in Sid's refrigerator.
What is the volume of a rectangular prism?The volume of a rectangular prism of length l, width w and height h is given by the multiplication of these three dimensions, that is:
V = lwh.
In this problem, there are three dispensers, each with l = 4 in, h = 14 in, w = 8 in, hence the volume is given by:
V = 3 x 4 x 14 x 8 = 1,344 in³.
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I will mark branilest If a x b = 2a - 3b + ab, then 3 x 5 + 5 x 3 is equal to?
A. 20
B. 22
C. 24
D. 26
Answer:
[tex]22[/tex]
Step-by-step explanation:
Because:
[tex]a \times b = 2a - 3b + ab[/tex]
Then:
[tex]3 \times 5 + 5 \times 3[/tex]
[tex]6 - 15 + 15 + 10 - 9 + 15 \\ = 22[/tex]
Answer:
B. 22
Step-by-step explanation:
Given
a x b = 2a - 3b + ab3 x 5
2(3) - 3(5) + 3(5)65 x 3
2(5) - 3(3) + 3(5)1 + 1516⇒ 3 x 5 + 5 x 3
⇒ 6 + 16
⇒ 22 (Option B)
The number is between 500 and 510 it is an odd number its one place has the smallest 1 dugit number
Answer:
501
Step-by-step explanation:
Odd numbers between 500 and 510 are 501,503,505,507,509. Out of them the number has its one place the smallest 1 digit number is 501
What is the probability of drawing a spade from a standard deck of cards or a
7?
The probability of drawing a spade is 13/52 = 1/4
Because every hand has 13 cards and there is 52 cards in a deck
The probability of drawing a 7 is 4/52 or 1/13
Because there are seven 7 cards in a deck and 52 cards.
Evaluate the expression when a=4, b=2, and c=5. 3ab - c
Answer:
19
Step-by-step explanation:
3(4)(2) - 5
3 * 4 = 12 * 2 = 24
24 - 5 = 19
Drag the numbers into the boxes to write the number in standard form. Numbers may be used once, more than once, or not at all.
4
×
10
)
+
(
3
×
1
100
)
+
(
5
×
1
1000
)
01345
.
The written form of the expression of (4 × 10 ) + ( 3 × 1/100)+(5×1/1000) is given as 4.035.
What is standard form?A standard form of a number is known to be the used in writing the number in a way that follows a specific rules.
Therefore, The written form of the expression of (4 × 10 ) + ( 3 × 1/100)+(5×1/1000) is given as 4.035.
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How much paint is needed for the entire outside of this prism ???
SEE PICTURE ATTACHED!!!
Answer:
132
Step-by-step explanation:
surface area of a triangular prism
132 ft is needed for the entire outside
its a 3 4 5 right triangle
10 is the height
The volume of this rectangular prism is 51,615 cubic yards. What is the value of v? (will mark brainliest)
Answer:
v = 37 yards
Step-by-step explanation:
Volume of a rectangular prism = width × length × height
Given:
volume = 51,615 yd³width = vlength = 93 ydheight = 15 ydSubstituting the given values into the formula and solving for v:
⇒ 51615 = v × 93 × 15
⇒ 51615 = 1395 v
⇒ v = 51615 ÷ 1395
⇒ v = 37
Answer:
v = 37 yds
Step-by-step explanation:
Volume of a rectangular prism: length × width × height
V = L×W×H
v = 51,615 yd³l = 93 ydsw = v ydsh = 15 ydsSubstitute the values above and solve for v:
51,615 = 93 × v × 15
51,615 = 1395v
51,615/1395 = 1395v/1395
37 = v
Final answer: 37 yds
Hope this helps!
The pyramid of the sun in mexico is a square pyramid. the base edge is approximately 220 meters, and the height is approximately 70 meters. what is the approximate surface area of the sides of the pyramid to the nearest thousand square meters? the lateral surface area is about .
The lateral surface area is about 105,600 meters.
What is lateral area of a pyramid?The area of the pyramid is the measure relative to its surface and is obtained by the sum of the areas of the bases (polygonals) and of all the lateral faces (triangles). For the calculation of the lateral area of a pyramid, we will have the perimeter of the base by the inclined height of the pyramid.
In this case, the formula of the lateral surface area is:
[tex]SA=\frac{P*S}{2}+B[/tex]
Where:
P= perimeter of baseS= slant heightB= area of baseThe height informed will not be used, it will only be a parameter to perform pythagoras, that is, we will find the hypotenuse of the triangle created by the height, like this:
[tex]S=\sqrt{(B)^2/2+H^2} \\S=\sqrt{110^2+70^2}\\S=\sqrt{17,000}\\ S=130[/tex]
Returning to the formula given above, we find that:
[tex]SA= \frac{(220*4)(130)}{2}+(220*220)\\ SA= 57,200+48,400= 105,600 \ meters[/tex]
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Write a recursive formula for the explicit formula.
A(n)=5+(n− 1)(-4)
Answer:
[tex]\large\begin{cases}a_1=5 \\a_n=a_{(n-1)}-4\end{cases}[/tex]
Step-by-step explanation:
Recursive formula allows us to find the value of a specific term based on the previous term.
Explicit formula allows us to find the value of a specific term based on its position.
Given explicit formula: [tex]a(n)=5+(n-1)(-4)[/tex]
[tex]\implies a(1)=5+(1-1)(-4)=5[/tex]
[tex]\implies a(2)=5+(2-1)(-4)=1[/tex]
[tex]\implies a(3)=5+(3-1)(-4)=-3[/tex]
[tex]\implies a(4)=5+(4-1)(-4)=-7[/tex]
From inspection of the sequence, we can see that to get the next term, we need to subtract 4 from the previous term.
[tex]5 \underset{-4}{\longrightarrow} 1 \underset{-4}{\longrightarrow} -3 \underset{-4}{\longrightarrow} -7[/tex]
Therefore, the recursive formula is:
[tex]a_n=a_{(n-1)}-4[/tex]
For a recursive formula, we also need to give the value for [tex]a_1[/tex] .
Therefore, the final recursive formula for the explicit formula is:
[tex]\large\begin{cases}a_1=5 \\a_n=a_{(n-1)}-4\end{cases}[/tex]
When are two triangles similar? Select all that apply.
All three of their corresponding angles have the same measure.
Two of their corresponding angles are the same angle measure.
Only one of their angles match.
All ratios of corresponding sides are proportional.
Two of their corresponding sides are in the same ratio.
Two triangles are said to be similar when; two of their corresponding angles are the same angle measure.
What is a triangle?A triangle is a polygon with three sides and three angles.
Types of triangles
Equilateral triangleScalene triangleIsosceles triangleTwo triangles are said to be similar if two pairs of their corresponding angles are congruent. This is because if two pairs of angle are the equal, then the third pair must also be equal.
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Pick the geometric term that matches the real-world object. cylinder cube sphere triangular prism rectangular prism
Answer:
cylinder
Step-by-step explanation:
A mascara tube is a cylinder
What is the prime factorization of 120?
Answer:
2 to the power of three × 3 × 5
Step-by-step explanation:
A factory produces 1,250,000 toys each year. The number of toys is expected to increase by about 150% per year. Which model can be used to find the number of toys, n (in millions), being produced in t years? n = StartFraction 2. 5 (1. 5) Over t EndFraction, t not-equals 0 n = 1. 5 t squared 1. 25 n = 1. 5 t 1. 25 n = 1. 25 times 2. 5 Superscript t.
Answer:
see the attachment!
i hope this can help you!
5-16 find the general indefinite integral.
8. [tex]\int\left(u^{6}-2 u^{5}-u^{3}+\frac{2}{7}\right) d u[/tex]
[tex]\displaystyle\int \left( u^6 - 2u^5 - u^3 + \cfrac{2}{7} \right)du\implies \cfrac{u^7}{7}-2\cdot \cfrac{u^6}{6}-\cfrac{u^4}{4}+\cfrac{2}{7}u \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{u^7}{7}- \cfrac{u^6}{3}-\cfrac{u^4}{4}+\cfrac{2u}{7}+C~\hfill[/tex]
(x - 2)^2/36-(y+1)^2/64=1The vertices for the hyperbola are (2,5) and (2,-7) true or false
Answer: False
Step-by-step explanation:
I checked with a graphing app huhu... sorry TT
The vertices are (8, -1) , (-4, -1).
please explain every step
761680
Explanation:[tex]\sf \boxed{\sum _{n=1}^{44}\:60\left(1.2\right)^{n-2}}[/tex]
Identify the following's:
First Term [a] = 60(1.2)ⁿ⁻² = 60(1.2)¹⁻² = 50
Common ratio [r] = 1.2
Total Terms [n] = 44
===========================
[tex]\sf Geometric \ Sum \ of \ Terms = \dfrac{a(r^n - 1)}{r-1}[/tex]
===========================
Solving Steps:
[tex]\rightarrow \sf \dfrac{a(r^n - 1)}{r-1}[/tex]
[tex]\rightarrow \sf \dfrac{50(1.2^{44} - 1)}{1.2-1}[/tex]
[tex]\rightarrow \sf 761679.5808[/tex]
[tex]\rightarrow \sf 761680 \ \ \ (rounded \ to \ nearest \ integer)[/tex]
