Answer:
first term a=4
Step-by-step explanation:
Sum of the first 6 terms S6 = 15624
common ratio r= 5
n= 6
first term a=?
Formula: S6= a(r^n-1)/r-1
15624 = a( 5^6-1)/5-1
15624 = a(15625-1)/4
15624= a( 15624)÷4
15624= 15624a÷4
Cross multiply
15624×4 = 15624a
62496 = 15624a
divide both sides by 15624
62496÷15624 = 15624a÷15624
4 = a
a= 4
Use the identity below to complete the tasks:
23 - 63 = (a - b)(a² + ab + b2)
When using the identity for the difference of two
cubes to factor 64x8 - 27
a=
b =
Answer:
a is 2q^2r
b is 3s^2t
the expression factored is...
(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)
Step-by-step explanation:
The length of the smaller rectangle at the right is 1 inch less than twice its width. Both the dimensions of the larger rectangle are 2 inches longer than the smaller rectangle. The area of the shaded region is 86 square inches. What is the area of the larger rectangle? PLEASE its important
Answer: 464 square inches is the area of the larger rectangle.
Step-by-step explanation: Assuming that the shaded area is the part of the large rectangle outside the small rectangle, you can set up dimensions from the information given.
The small rectangle's Area = w (2w -1) which is 2w² -w
The large rectangle's Area = (w + 2)(2w + 1) which is 2w² + 5w +2
Now figure out the equation for the "shaded area" (probably outside the small rectangle) 2w² + 5w +2 -(2w² -w) = 86 (The 2w² terms cancel)
6w + 2 = 86, so 6w = 84, w=14
Substitute 14 for w in the dimensions of the large rectangle: (w + 2)(2w + 1)
(14+2)(2[14] + 1) = Area
16 × 29 = 464
(I think I deserve Brainliest for figuring this out, but I see the question has been red-flagged, so We'll see!)
Can I get the awnser to this please?
Answer:
151.320046 m^2
150 m^2
Hope it helped!!!!!
Step-by-step explanation:
Area of the circle is:
pi * r^2
Therefore:
= pi * 17^2
= 289 * pi
Now Area of the sector:
= 289 * pi * (60/360)
= 289 * pi * 1/6
= 48.1666667 * pi
= 151.320046 m^2
= 150 m^2 (rounded)
Please answer ASAP! (I'll give brainliest and no need for explanation!)
Answer:
Median=3, Mean=2.333
Step-by-step explanation:
Combine the like terms to create an equivalent expression: r+(-5r)
Answer:
-4r
Step-by-step explanation:
r + -5r
Factor out r
r( 1-5)
r(-4)
-4r
Un ciclista debe realizar una ruta a través de una carretera para ir desde una ciudad A hasta una ciudad B en varios tramos. El primer tramo mide dos tercios del tercer tramo, el segundo tramo es dos veces mayor que el tercer tramo y el cuarto tramo tiene la medida del primero más el segundo. Si el último tramo es de 80 km, ¿cuál será la distancia total recorrida de la ciudad A hasta la ciudad B?
Respuesta:
190 km
Explicación paso a paso:
Lo primero es hacer las equivalencias, sea a el primer tramo, b el segundo tramo, c el tercer tramo y el ultimo tramo, el cuarto sería d, entonces:
a = 2/3*c
b = 2*c
d = a + b
Ahora bien sabemos que d = 80, reemplazamos y nos queda:
80 = a + b
tanto a cómo b están en función del tercer tramo es decir de c, reemplazamos:
80 = 2/3*c + 2*c
80 = 8/3*c
c = 80*3/8
c = 30
ahora calculamos tanto a como b:
a = 2/3*30 = 20
b = 2*30 = 60
Ahora, el recorrido total es la suma de todos los tramos:
Total = a + b + c + d
Total = 20 + 60 + 30 + 80 = 190
Quiere decir que la distancia entre la ciudad A y la cuidad B es de 190 km
In a certain company, all employees are either beta employees or standard employees. In this company, 25% of the beta employees and 17% of the standard employees participate in the voluntary equity program. Let S be the number of standard employees. If there are 600 employees total, what is the value of S?
In addition to the question, the following conditions must be met:
(1) M > 100
(2) more than 130 employees participate in the voluntary equity program
Answer:
Value of A is 200
Step-by-step explanation:
In this scenario when we divide 100 by the percentage of each employee category we will get a proportion that the number of employees must obey.
This is illustrated below:
For Beta employees 100/25= 4
So the number of employees that are Beta must be divisible by 4
For Standard employees 100/17 = 5.882
Since fractions of employees cannot be obtained, in this case the number of employees must be a multiple of 100
Total employees are 600
The various combinations are:
1. Beta employees 500 and Standard employees 100
Survey participants= (0.25 * 500) + (0.17 * 100) = 142
Number of participants is okay as it is >130 but does not satisfy Standard employees being >100
2. Beta employees are 300 and Standard employees are 300
Survey participants = (0.25 * 300) + (0.17 * 300) = 126
This does not satisfy condition of survey participants >130
3. Beta employees 400 and Standard employees 200
Survey participants = (0.25 * 400) + (0.17 * 200) = 134
This satisfies conditions of >130 survey participants and Standard employees >100
So correct value of S is 200
Pls help ASAP! Given a polynomial f(x), if (x − 1) is a factor, what else must be true? f(0)= 1 f(1)=0 f(-1)=0 f(0)=-1
Answer:
f(1) = 0
Step-by-step explanation:
If you set x - 1 equal to 0 and solve, you get x = 1 when y is 0
Answer: x+1 plus the fator
Step-by-step explanation:
This box has the same length, width, and height as the two tennis balls. Which expression gives the volume of the empty space encircling the tennis balls inside the box?
Formala : Times bottom row with side row with the height.
Example: A box has the same length, width, and height as two tennis balls.
Times the bottom row with side row with the height.
30 Points!! Vivian is at a fair in Coachella Valley, California. Much of the valley lies below sea level. Vivian has brought along an altimeter to measure her elevation at different places in the valley. Vivian’s first ride was on the Ferris wheel. When she sat on the wheel at its lowest point, her altimeter read -9.6 feet. When she reached the top of the wheel, her altimeter read 12.3 feet.
Is the change in Vivian's elevation from the bottom of the Ferris wheel to the top a positive number or a negative number? Why?
Answer:
Its a postive number
Step-by-step explanation:
If you look it says she is at sea leveal wicth is 0 and she is going up 12.3 feet so its postive.
The change in elevation from the bottom of the Ferris wheel to the top is 21.9 feet, which is a positive number.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given that, the lowest point of the Ferris wheel is -9.6 feet, and the highest point is 12.3.
The change in elevation from the bottom of the Ferris wheel to the top of the Ferris wheel is,
12.3 - (-9.6)
=12.3 + 9.6
= 21.9
Hence, the change in elevation from the bottom of the Ferris wheel to the top is 21.9 feet, which is a positive number.
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Graph the inequality y > |x + 1| – 1. Which point is NOT part of the solution? (–1, 2) (1, −1) (–1, 0) (1, 3)
Answer:
(1,-1)
Step-by-step explanation:
If you try plugging in the numbers for x in the equation y > Ix + 1I - 1, you'll find the answer.
What is the slope of the line through (-9, 6) and (-6, -9)? A/ ⅕ B/ 5 C/ -5 D/ -⅕
Answer:
-5
Step-by-step explanation:
We can find the slope between two points by using
m = (y2-y1)/(x2-x1)
= ( -9-6)/(-6 - -9)
=(-9-6)/( -6+9)
-15/3
-5
Answer:
C
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 9, 6) and (x₂, y₂ ) = (- 6, - 9)
m = [tex]\frac{-9-6}{-6+9}[/tex] = [tex]\frac{-15}{3}[/tex] = - 5 → C
f(x)=x^2 what is g(x) PLEASE HELP FAST :)))) THANKS IN ADVANCE!!! YOU'RE THE BEST
Answer:
g(x) = -x² - 3
Step-by-step explanation:
You want to mirror f(x), hence the minus sign.
Then you want to translate it 3 down, hence the -3.
Answer:
g(x) = -x² - 3
Step-by-step explanation:
f(x) is x², so g(x) will be negative because it is on the opposite side of the plane.
g(x) will be -x², it cross the y-intercept at (0, -3)
g(x) = -x² - 3
Can any of y’all help me with this problem?
Answer:
90º clockwise rotation
Step-by-step explanation:
The rotation is a 270º counterclockwise rotation, since 270º rotation is
(x, y) → (y, -x)
F(1, 3) → (3, -1)
270º counterclockwise rotation is the same as a 90º clockwise rotation, so the answer is 90º clockwise rotation.
What is the answer of .7 of which is 3.43
Answer:
4.9
Step-by-step explanation:
3.43/0.7
34.3/7=49
3.43/0.7=4.9
The value of x is approximately 4.9 when 0.7 (70%) of x is equal to 3.43.
We are given that 0.7 (which is the same as 70%) of a certain value (x) is equal to 3.43.
We represent "0.7 of x" as 0.7x.
So, the equation becomes:
0.7x = 3.43
To find the value of x, we need to isolate it on one side of the equation. To do this, we can divide both sides of the equation by 0.7:
(0.7x) / 0.7 = 3.43 / 0.7
The 0.7 on the numerator and denominator cancel out, leaving us with just x:
x = 3.43 / 0.7
Now, we perform the division:
x = 4.9
The value of x is approximately 4.9.
Hence, when 0.7 (70%) of 4.9 is calculated, it will be approximately equal to 3.43.
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100
b)
2. Write the following decimals as common fractions in their simplest forms
a) 0,8
b) 0,03
Answer:
4/5, 3/100
Step-by-step explanation
Let's look at 0.8 first.
0.8 is 8/10, but there's some more.
Let's divide 8 / 2. It is 4.
and, 10 / 2 is 5.
so, 0.8's simplest form is 4/5.
and, 0.03's simmplest fraction is easy.
It is 3/100, cuz 3 is a prime number and 3's integer is only 1 and 3.
Hope this helps!
If α and β are the zeroes of the polynomial 2x2 + 3x – 7, then find a polynomial whose zeroes are and .
Answer:
[tex]\frac{-\sqrt{65} - 3 }{4}, \frac{\sqrt{65} + 3}{4}[/tex]
Step-by-step explanation:
Since we cannot factor the expression, we must use quadratic formula: [tex]x = \frac{-b +/-\sqrt{b^2 - 4ac} }{2a}[/tex]
Plug in a for 2, b for 3, and c for -7 and you should find your roots.
Eight people rob a bank: * By what percent does the share of three robbers increase?
Answer:
Step-by-step explanation:
It increase by 2.3
which of the following sum in simplest form (radicals)
Answer:
9√2
Step-by-step explanation:
Easiest and fastest way is to plug it into a calc and calculate. If not, you will have to simplify the expressions to have a common root in order to add.
Answer:
9√2Option C is the correct option.
Solution,
[tex] \sqrt{8} + 3 \sqrt{2} + \sqrt{32} \\ = \sqrt{2 \times 2 \times 2} + 3 \sqrt{2} + \sqrt{2 \times 2 \times 2 \times 2 \times 2} \\ = 2 \sqrt{2} + 3 \sqrt{2} + 2 \times 2 \sqrt{2} \\ = 2 \sqrt{2} + 3 \sqrt{2} + 4 \sqrt{2} \\ =( 2 + 3 + 4 )\sqrt{2 } \\ = 9 \sqrt{2} [/tex]
Hope this helps...
Good luck on your assignment..
Trig work i don’t understand. pls help
Answer: A
Step-by-step explanation:
So we know that to find the area of a triangle you have to multiply the base times the height and divide it by two or multiply it by 1/2.Looking the information given it say that theta is equal to 26 degrees and the length of a or the hypotenuse is 25 and b which in this case is the base is 32. So the information gives us the base but now we need to find the height.
To find H we need to apply trigonometry solve for h the height.
As we could see theta which is 26 degrees is opposite the height and we know the hypotenuse length. So using soh cah toh we have to know that the length of h is going to be using the sin formula opposite over hypotenuse.
[tex]sin(26)=\frac{h}{25}[/tex] solve for h by multiplying both sides by 25.
h= 25 sin(26)
h= 10.96 is being rounded to the nearest hundredth because that is essential
Now we know H is equal to 10.96 which is the Height so now we have all the information we need the height and the base.
Multiply 10.96 by 32 and divide it by 2.
10.96 * 32 = 350.72
350.72 /2 = 176.36
The best answer is A because that is the only best approximation to 175.35.
The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 57 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 50 and 57
Answer:
34%
Step-by-step explanation:
According to the empirical rule, 68% of all of the data in a normal distribution falls within one standard deviation of the mean.
Applying to this particular case, 68% of the requests fall within (50 - 7) and (50+ 7). The percentage of requests from 43 to 50 is equal to the percentage of requests from 50 to 57.
Therefore, the percentage of light bulb replacement requests numbering between 50 and 57 is 68/2 = 34%.
In your own words, tell how geometric sequences are related to exponential functions. Share your answer with the rest of the group.
Answer:
Geometric sequences are the long way to show an exponential function. The initial amount in both exponential functions and geometric sequences do the same thing, which is state the initial value and the value by which it is multiplied. What is called the common ratio in a geometric sequence is basically the second part of what the initial amount does in an exponential function. The nth term in a geometric sequence is the same as the power in an exponential function, that is to say that it shows how many times the sequence is repeated.
Step-by-step explanation:
An incomplete distribution is given below:Variable You are given that the median value is 70 and the total number of items is 200. Using the median formula fill up the frequencies.
Answer:
The missing frequencies are x = 8 and y = 43.
Step-by-step explanation:
Median Value =70
Then the median Class =60-80
Let the missing frequencies be x and y.
Given: Total Frequncy = 200 , Median = 46
[tex]\left|\begin{array}{c|ccccccc}Value&0-20&20-40&40-60&60-80&80-100&100-120&120-140\\Frequency&12&30&x&66&y&27&14\\$Cumu.Freq&12&42&42+x&108+x&108+x+y&135+x+y&149+x+y\end{array}\right|[/tex]
From the table
[tex]\sum f_i =149+x+y[/tex]
Here, n = 200
n/2 = 100
Lower Class Boundary of the median class, l=60
Frequency of the median class(f) =66
Cumulative Frequency before the median class, f=42+x
Class Width, h=10
[tex]Median = l + \dfrac{\dfrac{n}{2} - c.f }{f} \times h[/tex]
[tex]70 = 60+ \dfrac{100- 42+x }{66}\times 10\\70 = 60+ \dfrac{58+x }{66}\times 10\\70-60=\dfrac{58+x }{66}\times 10\\10*66=10(58+x)\\58+x=66\\x=66-58\\x=8[/tex]
200=149+x+y
200=149+8+y
y=200-(149+8)
y=43
Hence, the missing frequencies are x = 8 and y = 43.
which one of the following is a type of face found on a platonic solid. A,regular hexagon, B. regular octagon, C.regular nonagon, D. regular pentagon
PLEASE NEED OF AN ANSWER
Answer:
B. regular octagon
I hope this will help you
Bob goes shopping at his favorite store and finds a hat that is regularly priced at $40, but it is on sale for 20% off. The sales tax on the hat is 10% of the sale price. How much does Bob end up paying for the hat?
Answer:
$35.2
Step-by-step explanation:
Marked price of hat = $40
Sale discount = 20%
discount in $ = 20% of $40 = 20/100 * 40 = $8
Thus, sale price = marked price - sale discount = $40 - $8 = $32
Now it is given that there is sales tax of 10%
This sales tax will be applied on sale price
thus,
sales tax in dollars = 10% of sale price of hat = 10/100 * $32 = $3.2
Total price paid for hat = Sale price+ sales tax = $32 +$3.2 = $35.2
Thus, Bob ended up paying $35.2 for the hat.
Please help me find the area of this shape
Answer:
44+50 =94 in²
Step-by-step explanation:
Trapezoid
A= 1/2h(b1+b2)
A= 1/2*4(7+15)
A=1/2*4(22)
A=44
Rectangle
A=l*w
A=5*10
A=50
44+50 =94 in²
If a sample of 234 customers were taken from a population of 3620 customers, could refer to the variance of how many of the customers' ages?
If a sample of 234 customers were taken from a population of 3620 customers, s^2 could refer to the variance of how many of the customers' ages?
A. 234
B. 3620
C. Both 234 and 3620
D. Neither 234 nor
3620
Answer: 234
Step-by-step explanation:
Sample distribution = 234 customers
Population distribution = 3620 customers
S^2 which in statistics refers to the same variance utilizes the sample data in estimating the variance value of a population.
The sample variance is given by:
s^2 = (x - mean) / n - 1
where ;
n = number of observation in sample
s^2 = sample variance
mean = statistical mean of sample data
n - 1, is used to account for the bias in our estimation or inference of a population statistics from sample data.
The cross sectional area of a square shaped tunnel is 25m², the volume of the tunnel is 575m³. How long is the tunnel?
Answer:
23 mSolution,
Let the length of tunnel be 'l'
Area=25 m^2
Volume of tunnel= cross sectional area* length
[tex] or \: 575 = 25 \times l \\ or \: l = \frac{575}{25} \\ l = 23 \: m[/tex]
Hope this helps..
Good luck on your assignment..
Sean los ángulos a y B, donde la suma de la mitad de a mas la tercera parte de B es igual a 15. calcula el doble del cociente del seno de 3a y el coseno de 2B. Urgente pls a es alpha y B es beta por si acaso
Answer:
Supongo que tenemos dos ángulos A y B
"la mitad de A mas la tercera parte de B es igual a 15°" (también supongo que son grados)
A/2 + B/3 = 15°
A/2 = 15° - (B/3)
A = 30° - 2*(B/3)
Ahora queremos calcular:
2*sin(3*A)/cos(2*B)
pero podemos reemplazar A por lo que tenemos arriba:
2*sin(3*(30° - 2*(B/3)))/cos(2*B)
2*sin(90° - 2*B)/cos(2*B)
y como sabemos,
Sin( 90° - x) = Sin(90°)*cos(-x) + cos(90°)*sin(-x) = cos(-x) = cos(x)
entonces:
2*sin(90° - 2*B)/cos(2*B) = 2*cos(2*B)/cos(2*B) = 2*1 = 2.
The following box plot shows points awarded to dance teams that competed at a recent competition:
Answer:
top plot
Step-by-step explanation:
From the box and whisker plot, the smallest data point is 0 and the largest data point is 100
The median is 70
The only plot that has points at 0 and 100 is the first plot