Answer:
[tex] \displaystyle a_{1} = 108[/tex]
Step-by-step explanation:
we are given
the sum,common difference and nth term of a geometric sequence
we want to figure out the first term
recall geometric sequence
[tex] \displaystyle S_{ \text{n}} = \frac{ a_{1}(1 - {r}^{n} )}{1 - r} [/tex]
we are given that
[tex]S_n=189[/tex][tex]r=\dfrac{1}{2}[/tex][tex]n=3[/tex]thus substitute:
[tex] \displaystyle 189= \frac{ a_{1}(1 - {( \frac{1}{2} )}^{3} )}{1 - \frac{1}{2} } [/tex]
to figure out [tex]a_1[/tex] we need to figure out the equation
simplify denominator:
[tex] \displaystyle \frac{ a_{1}(1 - {( \frac{1}{2} )}^{3} )}{ \dfrac{1}{2} } = 189[/tex]
simplify square:
[tex] \displaystyle \frac{ a_{1}(1 - {( \frac{1}{8} )}^{} )}{ \dfrac{1}{2} } = 189[/tex]
simplify substraction:
[tex] \displaystyle \frac{ a_{1} (\frac{7}{8} )}{ \frac{1}{2} } = 189[/tex]
simplify complex fraction:
[tex] \displaystyle a_{1} (\frac{7}{8} ) \div { \frac{1}{2} } = 189[/tex]
calculate reciprocal:
[tex] \displaystyle a_{1} \frac{7}{8} \times 2 = 189[/tex]
reduce fraction:
[tex] \displaystyle a_{1} \frac{7}{4} \ = 189[/tex]
multiply both sides by 4/7:
[tex] \displaystyle a_{1} \frac{7}{4} \times \frac{4}{7} \ = 189 \times \frac{4}{7} [/tex]
reduce fraction:
[tex] \displaystyle a_{1} = 27\times 4[/tex]
simplify multiplication:
[tex] \displaystyle a_{1} = 108[/tex]
hence,
[tex] \displaystyle a_{1} = 108[/tex]
10 POINTS FOR THE CORRECT ANSWER PLEASE HELP
Step-by-step explanation:
use pythagoras theorem
a squared +b squared =c squared
4.12 squared +8 squared =x squared
16.9744+64=x squared
take the square root of 80.9744
x=9
Hi his figure is made up of unit cubes, each with a volume of 1 cubic unit.
What is the volume of the figure?
( photo is attached)
(Will give brainliest if you help)
Answer:
D. 100 cubic units
Step-by-step explanation:
There are 10 cubes in each layer (count at the top) and 10 layers (from top to bottom) in total. Multiply these to get volume.
10 x 10 =100
Answer:
B. 60 cubic units
Step-by-step explanation:
Formulas for a cube:
The volume of a cube:
V = a3
The surface area of a cube:
the area of each face (a x a) times 6 faces
S = 6a2
Face diagonal of a cube:
By the Pythagorean theorem, we know that
f2 = a2 + a2
Then f2 = 2a2
solving for f we get
f = a√2
Diagonal of the solid cube:
Again, by the Pythagorean theorem, we know that
d2 = a2 + f2
substituting f into this equation we get
d2 = a2 + (a√2)2 = a2 + 2a2 = 3a2
solving for d we get
d = a√3
Which graph represents the solution set of the following situation? Andrew is buying fruit for a fruit salad. Bananas cost $1 a pound and oranges cost $2 a pound. He plans to buy at least 10 pounds of fruit and spend no more than $20. Let x represent pounds of bananas and let y represent pounds of oranges..
Answer:
[tex]x + y \ge 10[/tex]
[tex]x + 2y \le 20[/tex]
Step-by-step explanation:
The question is incomplete as the graphs are not shown. So, I will derive the inequalities and plot the graph.
Given
[tex]Banana = \$1[/tex]
[tex]Orange = \$ 2[/tex]
[tex]Purchase = 10lb[/tex] --- At least
[tex]Spedings = \$20[/tex] --- Not more than
And we have:
[tex]x = Banana; y = Orange[/tex]
The number of purchase will be represented as:
[tex]x + y \ge Purchase[/tex] ---- (at least)
[tex]x + y \ge 10[/tex]
The amount spent will be represented as;
[tex]1 * x + 2 * y \le 20[/tex] --- (not more than)
[tex]x + 2y \le 20[/tex]
So, the inequalities are:
[tex]x + y \ge 10[/tex]
[tex]x + 2y \le 20[/tex]
See attachment for graph
Hannah decided to curl up and read a good book. She started reading at 10:00 a.m. and
finished reading at 11:43 a.m. How much time did she spend reading?
Answer:
she spend one hour and 43 minutes reading
Step-by-step explanation:
hope you have a great day kee learning
A ship left at the port at 9:00 p.m. and arrived at the next port at 5:00 a.m.
the next day. The distance between the 2 ports was 200 km.
Find the average
speed of the ship.
show solution
Answer:
25km/h
Step-by-step explanation:
It would be helpful to understand the 24 hour clock in this case so you don't get confused by the AM and PM. For reference, 5 AM is technically 17AM, since 5 + 12 = 17.
The ship departed at 9pm, subtract that from 17 and you'll get 8 hours.
17 - 9 = 8
We know that there are 8 hours total, and since the ship traveled 200km, we set up a fraction, which is 8hr/200km. Since we want the average speed, we'll go by km/hr. To do this, we need to set the hrs to 1.
8/x = 1
x = 8
200/8 = 25
Your answer is 25km/hr
What is the remainder when P(x)=2x3-3x2-5x-6 is divided by (x-3)
Answer:
remainder = 6
Step-by-step explanation:
Hope it helps.....
Ruslan's figure has a length of 5cm, a width of 3cm, and a height of 4cm. What is the volume of Ruslan's figure?
Answer:
The colume of Ruslan's figure is 60 cubic centimeters.
Step-by-step explanation:
To find the volume of something, you have to multiply the length by the width, and then multiply that to the height. So you would multiply 5 and 3 to get 15, and then you would multiply 15 and 4 to which then you would get your answer of 60 cubic centimeters.
Answer:
60cm³ is your answer
Step-by-step explanation:
volume of cuboid =l×b×h=5×3×4=60cm³
Pls help!!!! It is khan academy and I’m giving 15 points!
What is the equation of the following line written in slope-intercept form?
y = -5x
y = 5x
y = 5/x
Answer:
y=5x
Step-by-step explanation:
first, we know that a rising line's slope is always positive, so the first one is incorrect
let's figure out the slope: y-y'/x-x' is the formula.
now, -5-5/-1-1= -10/-2= 5. so the slope of this line is 5.
The graphs below have the same shape. Complete the equation of the red
graph.
Answer:
Step-by-step explanation:
F(x) = 2 - x²
Find the surface area of the figure. Round to the nearest tenth.
WILL MARK BRAINLIEST!!! PLS HELP THIS IS DUE IN 10 MIN AND PLEASE NO DROP FILES!! :)
Answer:
14 x 6.9 x 8 = 56
Step-by-step explanation:
Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 7 men employed by a medium sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 21.89 hours of personal time per year with a standard deviation of 3.29 hours. The correct 90% confidence interval for the difference between women and men in the average number of hours of personal time taken per year is ________.
Answer:
The correct 90% confidence interval for the difference between women and men in the average number of hours of personal time taken per year is
contained by the interval (0.54 , 5.18)
Step-by-step explanation:
Given that:
for women
sample size = n₁ = 16
sample mean [tex](\bar X_1)[/tex] = 24.75
standard deviation s₁ = 2.84
for men
sample size for men = n₂ = 7
sample mean [tex](\bar X_2)[/tex] = 21.89
standard deviation s₂ = 3.29
degree of freedom = [tex](n_1 + n_2 )-2[/tex]
= 16 + 7 -2
= 21
The critical value for [tex]\alpha = 0.1 \ and \ df \ of \ 21 \ is :[/tex]
[tex]t_{0.005;21}= 1.721[/tex]
The pooled standard deviation can be calculated as follows since the population variances are assumed to be equivalent.
[tex]s_p = \sqrt{\dfrac{(n_1 -1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}[/tex]
[tex]s_p = \sqrt{\dfrac{(16 -1)2.84^2+(7-1)3.29^2}{16+7-2}}[/tex]
[tex]s_p = \sqrt{\dfrac{(15)8.0656+(6)10.8241}{21}}[/tex]
[tex]s_p = 2.976[/tex]
The standard error is estimated as follow:
[tex]se = s_p\sqrt{\dfrac{1}{n_1} + \dfrac{1}{n_2}}[/tex]
[tex]se = 2.976\sqrt{\dfrac{1}{16} + \dfrac{1}{7}}[/tex]
se = 1.348
Finally, the confidence interval [tex]C.I = ( x_1 -x_2 -t_c \times se \ \ ; \ \ x_1-x_2 +t_c \times se)[/tex]
[tex]=(24.75 - 21.89 -1.721 \times 1.348 \ \ , \ \ 2475 - 21.89 + 1.721 \times 1.348) \\ \\ \mathbf{ = (0.54 \ \ , \ \ 5.18)}[/tex]
Select all that apply.
Which two rays form ∠ACB?
1. CA
2. AC
3. CB
4. CE
Answer:
The 2 rays the form ACB ARE AC and CB
What is the area of the triangle?
Answer:
30 units²
Step-by-step explanation:
a=1/2 ×length × width
a=1/2 × 12 ×5
a=6×5
a=30units squared
A high school student working a part time as a cook
Answer:
Is there supposed to be a picture???
Step-by-step explanation:
Please help! Needed ASAP!
Answer:
1 bagel $3.5
1muffin $1.25
1ticket$9
1snack$2
Step-by-step explanation:
miffin(y)
bagel(x)
x+3y=7.25
x+2y=6
since x is similar in both equations you cancel it out
subtract this
3y=7.25
2y=6
y=$1.25(price for 1 muffin)since we had 3 muffins it will be 1.25×3=7.25,where you do 7.25 to get 3.5 (price for 1 bagel)question 8:ticket(x)
snack(y)
2x+3y=24×3
3x+4y=35×2
×3 and ×2 so we can eliminate the x
6x+9y=72
6x+8y=70
eliminate x
y=2
so snack is $2
2x+(3×2)=24
24-6=18
18÷2x=9
so a ticket is $9
answer and show proof for brainliest
Answer:
The answer is A
Step-by-step explanation:
A closed circle means the number is included in the equation / solution. An open circle means it is not. The problem says greater than or equal to 36 inches tall which means that circle should be closed. And less than 48 inches. It does not say anything about being equal when it states the 48 inches so that one should be open.
Find the missing side. Round
to the nearest tenth.
17
y
44°
Х
y=[?]
Answer:
The answer is 11.8
Step-by-step explanation:
The value of x and y is 12.2 and 11.8 respectively.
What is tangent of an angle?The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
What is sine of an angle?The sine (sin) of an acute angle in a right angled triangle is the ratio between the side opposite the angle and the hypotenuse of the triangle.
According to the given question.
We have a right angled triangle.
In which one angle is 44 degrees and hypotenuse is 17 units.
Here,
With respect to angle 44 degrees the adjacent side is x and the opposite side is y.
Therefore,
Sine of 44 degrees is given by
[tex]sin44^{o} = \frac{opposite\ side }{Hypotenuse}[/tex]
[tex]\implies sin44^{o} = \frac{y }{17}[/tex]
[tex]\implies 0.6946 = \frac{y}{17}[/tex]
[tex]\implies 0.6946 \times 17 = y[/tex]
[tex]\implies y = 11.80[/tex]
[tex]\implies y = 11.8[/tex]
And, tangent of 44 degrees is give by
[tex]tan 44^{o} = \frac{opposite \ side }{adjacent \ side }[/tex]
[tex]\implies tan44^{o} = \frac{y}{x}[/tex]
[tex]\implies tan44^{o} = \frac{11.8}{x}[/tex]
[tex]\implies 0.9657 = \frac{11.8}{x}[/tex]
[tex]\implies x = \frac{11.8}{0.9657}[/tex]
[tex]\implies x = 12.22[/tex]
[tex]\implies x = 12.2[/tex]
Therefore, the value of x and y is 12.2 and 11.8 respectively.
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The hypotenuse in this 45-45-90 triangle is given. How would you find the length of a leg
of the triangle?
8 V2
45degrees
Answer:
The length of the legs of the triangle is 8 units.
Step-by-step explanation:
45-45-90 triangle
A 45-45-90 triangle is a special case of a right triangle in which both legs l have the same value and the hypothenuse is h. By the Pythagorean Theorem:
[tex]2l^2 = h^2[/tex]
Hypothenuse of 8 V2
This means that [tex]h = 8\sqrt{2}[/tex]
So
[tex]2l^2 = h^2[/tex]
[tex]2l^2 = (8\sqrt{2})^2[/tex]
[tex]2l^2 = 64*2[/tex]
[tex]l^2 = 64[/tex]
[tex]l = \sqrt{64}[/tex]
[tex]l = 8[/tex]
The length of the legs of the triangle is 8 units.
Aubrey is going to invest $160 and leave it in an account for 7 years. Assuming the interest is compounded daily, what interest rate, to the nearest tenth of a percent, would be required in order for Aubrey to end up with $220?
Answer:
4.5%
Step-by-step explanation:
compound interest formula:
[tex]PV(1+\frac{i}{n})^{t*n}[/tex]
[tex]220=160(1+\frac{x}{365})^{365*7}\\\\1.375=(1+\frac{x}{365})^{2555}\\1.0001246=1+\frac{x}{365}\\x=.0454962254126[/tex]
this rounds to
x=4.5%
Aubrey would need an interest rate of 6.3%.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
A = P [tex](1 + r/n)^{nt}[/tex]
A = the final amount (in this case, $220)
P = the initial investment (in this case, $160)
r = the interest rate (what we are trying to find)
n = the number of times the interest is compounded per year (since it's compounded daily, n = 365)
t = the time period (in years, in this case, 7)
Substituting in the given values and solving for r:
220 = 160(1 + r/365)^(3657)
220/160 = (1 + r/365)^(3657)
1.375 = (1 + r/365)^2555
ln(1.375) = 2555 ln(1 + r/365)
ln(1 + r/365) = ln(1.375)/2555
1 + r/365 = e^(ln(1.375)/2555)
r/365 = e^(ln(1.375)/2555) - 1
r = 365(e^(ln(1.375)/2555) - 1)
r ≈ 6.3%
Therefore,
Aubrey would need an interest rate of 6.3%.
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James has a mass of 32.8 kg. Ricardo's mass is 8 3/4 kg more than James's. Winthorp's mass is 3.6 kg less than Ricardo's. What is the total mass of the three boys?
Answer:79.5
Step-by-step explanation:32.8+8.75=41.55 41.55-3.6=37.95 37.95+41.55+32.8=79.5
111.94 kg is the total mass of the three boys.
What is ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. An equation with two ratios set equal to one another is called a percentage.
given, James has a mass of 32.8 kg. Ricardo's mass is 8 3/4 kg more than James's. Winthrop's mass is 3.6 kg less than Ricardo's.
Since Mass of James = 32.8 kg
thus Mass of Ricardo = [tex]8\frac{3}{4}[/tex] + 32.8 = 41.55kg
And Mass of Winthrop = 41.55 - 3.6 = 37.59kg
Sum of mass of all three boys = 32.8 + 41.55+ 37.59
Sum of the mass of all three boys = 111.94 kg
Therefore, the Total mass of the three boys is 111.94 kg.
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Linear parent function fis graphed on the grid.
Which graph best represents h(x) = -f(x) + 3?
It should be G, or the bottom left answer! I'm not sure about it but anyway I hope this helps!
Answer:option 2
Step-by-step explanation:
Please help! Answer and explanation please!
Answer:
B. 36π in²
Step-by-step explanation:
Given:
Volume = 54π in³
height (h) = 6 in.
Required:
Curved surface area of the can (area for the label needed to wrap around the can without overlapping)
Solution:
First, we need to find the radius (r) of the can.
Volume = πr²h
Plug in the given values and solve for r
54π = π*r²*6
54π = 6π*r²
54π/6π = r²
9 = r²
r = √9
r = 3 in
✔️Find the curved surface area:
Curved surface area = 2πrh
r = 3 in
h = 6 in
Plug in the values
C.S.A = 2*π*3*6
C.S.A = 36π in²
Tell whether the angles are complementary or supplementary. Then find the value of X
A circle passes through the points (3,2) and (7,2) and has radius 2√2. Find the two possible equations for this circle
Answer:
18 because of its addition
Step-by-step explanation:
πr²=3+2+7+2+2+2
=5+9+4
=18
The fuel efficiency for a new helicopter engine is given by the continuous function r(c) where r is measured in gallons per mile ....
The question is incomplete. The complete question is :
The fuel efficiency for a new helicopter engine is given by the continuous function r(c) where r is measured in gallons per mile and c is measured in miles. What are the units of [tex]$\int_0^7 r(c) \ dc$[/tex] ?
Solution :
The given continuous function is :
r(c), here c is measured in miles and the unit of r is measured in gallons per mile.
So the unit of [tex]$\int_0^7 r(c) \ dc$[/tex] is given by :
= gallons per mile x mile
= gallons
So, the final unit is gallons.
I need help please. I don’t know this
Answer:
y = 1x + 6
Step-by-step explanation:
y = mx + b is the formula we need to use. b is the y intercept which is clearly 6 on the graph. Then we need to use rise over run to find our m. We can see for every x value that increases by 1, y also increases at 1. This means our x is 1.
Answer:
(0,6) ,(4,10)
y=(10-6)/×=(4-0)
4/4= 1
Write impossible, unlikely, as likely as not, likely, or certain. Then, tell whether the probability is 0,close to 0, 1/2, close to 1, or 1 Picking a red marble from 4 white marbles and 7 green marbles
Answer:
Step-by-step explanation:
please hurry will mark brainiest
Answer:
Step-by-step explanation:
x(x+8) = 450
x² + 8x - 450 = 0
Quadratic formula:
x = [-8±√(8²-4(1)(-450))]/[2(1)]
= [-8±2√466]/2
= -4±√466
≅ 17.59, -25.59
-25.59 is an extraneous solution, so x ≅ 17.6 inches.
The dimensions of the blackboard are 17.59 inches by 25.59 inches
Plz help me I am timed! Well mark brainliest if you are correct!
Answer:
A
Step-by-step explanation:
The point Y is the center of the circle
the correct answer for point y is c