Answer:
The first term of the series is 4
Step-by-step explanation:
The sum of the first 6 terms of a geometric series is 15 , 624 and the common ratio is 5 .
To find the first term, we use the formula for the sum of terms in a geometric series.
Since the common ratio of the series is greater than 1, the sum of [tex]n^{th}[/tex] term of the geometric series is;
[tex]S = \frac{a(r^n - 1)}{r - 1}[/tex]
where r = common ratio
a = first term
When S = 15,624, r = 5 and n = 6, the first term, a, will be:
[tex]15624 = \frac{a(5^6 - 1)}{5 - 1} \\\\15624 = \frac{a(15625 - 1)}{4}\\\\15624 = \frac{a(15624)}{4}\\\\a = \frac{4 * 15624}{15624}[/tex]
a = 4
The first term of the series is 4.
The equation h(t)= -16t^2+864t models the path of a rocket shot into the air. After how many seconds does the rocket hit the ground?
Answer:
t = 54 seconds
Step-by-step explanation:
The equation that models the path of a rocket into the air is given by :
[tex]h(t)= -16t^2+864t[/tex]
It is required to find the time after which the rocket will hit the ground. When it hits the ground, the height of the rocket will becomes zero. It means,
h(t) = 0
i.e.
[tex]-16t^2+864t=0\\\\16t(-t+54)=0\\\\16t=0, -t+54=0\\\\t=0\ and\ t=54\ s[/tex]
It means after 54 seconds, the rocket will hit the ground.
Find the area of a semicircle
Answer:
18pi, or 56.52
Step-by-step explanation:
To start off, if you were to find the area of any whole circle, you would use the formula: pi x radius^2 = area of circle
However, since this is a semi-circle (half of a whole circle) you would divide the whole expression by 2, and then solve:
(pi x radius^2)/2 = area of semi-circle
(pi x 6^2)/2 = area of semi-circle
(36 x pi)/2 = area of semi-circle
18 x pi = area of semi-circle
18 x 3.14 = area of semi-circle
56.52 = area of semi-circle
The area of a circle is
[tex]\pi \: {r}^{2} [/tex]
So the area of a semicircle would be half of that, or
[tex] \frac{\pi}{2} {r}^{2} [/tex]
So just plug in the radius, six, to get this
[tex]18\pi[/tex]
In how many wages can the starting six players of a volleyball team stand in a row for a picture
A:6
B:36
C:720
Evaluate the expression 9P1
Answer :
9
Explanation :
The expression above signifies the Permutation expression
Permutation expression is given as nPr
The Permutation expression is calculated as:
nPr = P(n, r) = n! / (n - r)!
It the above question, we were asked to evaluate the expression 9P1
From the above question, we can see that:
n = 9 and r = 1
Therefore, the expression
9P1 = 9! / ( 9 - 1) !
9P1 = 9! / 8!
= 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 362880 /40320
= 9
Therefore, the evaluation of the expression 9P1 = 9
Final answer:
To evaluate the expression 9P1, we calculate the permutation for selecting 1 item from 9, which simplifies to 9/1, giving us the answer of 9.
Explanation:
The student has asked to evaluate the expression 9P1, which is a permutation problem. To find 9P1, we use the permutation formula, which is P(n, k) = n! / (n-k)!, where n is the total number of items to choose from, and k is the number of items to choose. In this case, since we want to choose 1 item from 9, the permutation is calculated as:
Identify the values of n and k (n=9, k=1).Apply the permutation formula: 9P1 = 9! / (9-1)! = 9! / 8!.Simplify the factorial expression: 9! / 8! = 9 / 1 = 9.Therefore, the value of 9P1 is 9.
In △CDE , CD=10 , DE=7 , and m∠E=62∘ . What is m∠D to the nearest tenth of a degree?
We have been given that in △CDE , CD=10 , DE=7 , and m∠E=62 degrees. We are asked to find the measure of angle D.
We will use law of sines to solve our given problem.
[tex]\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}[/tex], where, a, b and c are opposite sides to angles A, B and C respectively.
First of all we will find measure of angle C as:
[tex]\frac{7}{\sin(C)}=\frac{10}{\sin(62^{\circ})}[/tex]
[tex]\sin(C)=\frac{7\cdot \sin(62^{\circ})}{10}[/tex]
[tex]\sin(C)=\frac{7\cdot 0.882947592859}{10}[/tex]
[tex]\sin(C)=0.6180633150013[/tex]
Now we will use arcsin to solve for C as:
[tex]C=\sin^{-1}(0.6180633150013)[/tex]
[tex]C=38.174844995363^{\circ}[/tex]
[tex]C\approx 38.2^{\circ}[/tex]
Now we will use angle sum property to find measure of angle D.
[tex]\angle D+\angle C+\angle E=180^{\circ}[/tex]
[tex]\angle D+38.2^{\circ}+62^{\circ}=180^{\circ}[/tex]
[tex]\angle D+100.2^{\circ}=180^{\circ}[/tex]
[tex]\angle D+100.2^{\circ}-100.2^{\circ}=180^{\circ}-100.2^{\circ}[/tex]
[tex]\angle D=79.8^{\circ}[/tex]
Therefore, the measure of angle D is approximately [tex]79.8^{\circ}[/tex].
Measure of angle D will be 79.8°.
Sine rule in a triangle, Sine rule,[tex]\frac{c}{\text{sinC}}= \frac{d}{\text{sinD}}= \frac{e}{\text{sinE}}[/tex]
Here, c, d and e are the sides and C, D, E are the angles opposite
to these sides of the given triangle.
Given in the question,
In ΔCDE,
CD = 10 units
DE = 7 units
m∠E = 62°
By applying sine rule,
[tex]\frac{7}{\text{sinC}}= \frac{d}{\text{sinD}}= \frac{10}{\text{sin(62)}}[/tex]
[tex]\frac{7}{\text{sinC}}= \frac{10}{\text{sin(62)}}[/tex]
[tex]\text{sin(C)}=\frac{\text{sin(62)}\times 7}{10}[/tex]
[tex]=0.618063[/tex]
C = [tex]\text{sin}^{-1}(0.618063)[/tex]
C = 38.175°
≈ 38.2°
By triangle sum theorem of a triangle,
m∠C + m∠D + m∠E = 180°
38.2 + m∠D + 62° = 180°
m∠D = 79.8°
Therefore, measure of angle D will be 79.8°.
Learn more about the sine rule here,
https://brainly.com/question/13152249?referrer=searchResults
What is the radian measure of an angle of 132°?
Answer:
11/15 pi radians
Step-by-step explanation:
To convert from degrees to radians, multiply by pi/180
132 * pi/180
11/15 pi
Answer:
2.304 radians
hope this helps :)
Your math teacher asks you to help calculate the height of the gulf coast on your football field you and your partner gather the measured as shown find the height of the top of the goal post round to the nearest 10th of a foot
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image for the step by step explanation for the answer to the question
A grain silo is 56% full. At the end of the week, it is 3/4 full. What percent of the silo was filled that week?
Answer:
75 percent
Step-by-step explanation:
3/4 = 75%
75 - 56 = 19%
19%Find 3 consecutive even integers whose sum is 138.
Answer:
The integers are:
44,46,48
Step-by-step explanation:
factor the common factor 4 - 2n
Answer:
2(2-n)
Step-by-step explanation:
4 - 2n
Factor out a 2
2*2 -2n
2(2-n)
Identify the conic that is formed by the intersection of the plane described and double-napped cone.
A plane is perpendicular to m and does not intersect the vertex.
What is the conic section formed?
A. circle
B. parabola
C. ellipse
Answer:
A. Circle
Step-by-step explanation:
Perpendicular to m is parallel to the base of the cones (circular).
Therefore the cross section would be a circle (except at the vertex)
A bicycle factory produces 1505 bicycles in a week. How many bicycles will it produce in 30 days?
and
20 apples are distributed between Aaron and Ben in the ratio 2 : 3. Find, how many does each get?
Answer:
It will produce 6450 bicycles in 30 days
Aaron has 8 apples and Ben has 12 apples
Step-by-step explanation:
A)
A bicycle factory produces 1505 bicycles in a week.
No. of days in 1 week = 7
So, Number of bicycles produced in 7 days = 1505
Number of bicycles produced in 1 day =[tex]\frac{1505}{7}[/tex]
Number of bicycles produced in 30 days = [tex]\frac{1505}{7} \times 30=6450[/tex]
So, It will produce 6450 bicycles in 30 days
B)20 apples are distributed between Aaron and Ben in the ratio 2 : 3.
Let the ratio be x
So, Aaron has apples = 2x
Ben has apples = 3x
So, 2x+3x=20
5x=20
x=4
Aaron has apples = 2x =2(4)=8
Ben has apples = 3x =3(4)=12
Hence Aaron has 8 apples and Ben has 12 apples
Use the interactive graph to plot each set of points which set represents proportional relationships check all that apply
Answer:
the first and third
Step-by-step explanation:
Answer:
A and C
Step-by-step explanation:
Francesca has already knit 28 centimeters of scarf, and can knit 7 centimeters each night. How many nights will Francesca have to spend knitting in order to knit a total of 42 centimeters of scarf?
Answer:
2 nights
Step-by-step explanation:
We need to find how many nights Francesca will have to spend to knit the rest of the scarf.
First, we have to find how much she has left to knit, and then find how many nights it will take her.
She has already knit 28 centimeters of scarf.
She wants to knit a total of 42 centimeters of scarf.
Therefore, the length of scarf left to knit is:
42 - 28 = 14 centimeters
She can knit 7 centimeters each night.
Therefore, the number of nights more she needs to knit 14 centimeters is:
14 / 7 = 2 nights
She will spend 2 nights to knit a total of 42 centimeters of scarf.
PLEASE HELP I"M BAD AT MATH Use the Distributive Property to simplify the expression.
13(n+4+7m) =
Answer:
13n + 52 + 91m
Step-by-step explanation:
you multiply 13 by every number in the parenthesis
13×n=13n
13×4=52
13×7m=91m
3/10 is what number of 9
Answer:
30
Step-by-step explanation:
unknown number = x
3/10 × x = 9
3x/10 = 9
3x = 90
x = 30
Answer:
2.7 or 2 7/10.
Step-by-step explanation:
9 * 3/10
= 27 / 10
= 2.7.
Day 1: Day 2: Comparison of Day 1 and Day 2: ____ < _____ or _____ > _______ Comparison of days with absolute value: ____ < _____ or _____ > _______
Answer:
Step-by-step explanation:
Hello!
Full text:
Here are the low temperatures (in degrees Fahrenheit) for one week in Montreal, Canada:
-3.5ºF, 5ºF, 1.5ºF, -0.5ºF, -2ºF, 2.5ºF, -4ºF
Compare the weather on two different days using an inequality. Then see if their comparisons change by finding the absolute value of each.
You have to choose two days at random and compare the values of temperature registered those days and compare them, for example:
Day 1: 3rd day: 1.5ºF
Day 2: 7nth day: -4ºF
Comparison of Day 1 and Day 2:
Remember:
"<" indicates that the value from the left is less than the value from the right.
">" indicates that the value from the left is greater than the value from the right.
The temperature registered on Day 1 is 1.5ºF and the temperature registered on Day 2 is -4ºF, as you notice the second temperature is negative and therefore is less than the first temperature:
1.5ºF > -4ºF
Comparison of days with absolute value:
To compare absolute values you have to disregard the sign and consider only the number of the temperature:
|Day 1|= |1.5ºF|
|Day 2|= |4ºF|
Then the registered temperature of Day 1 is less than the registered temperature on Day 2:
|1.5ºF| < |4ºF|
I hope this helps!
Answer:
-4ºF and 1.5ºF
Step-by-step explanation:
A rectangle has a length of 7.5 inches and a width of 3 inches. This rectangle is dilated by a scale factor of 2.2 to create a new rectangle. What are the dimension of the new rectangle? Length and Width
Answer:
For this case is the rectangle is dilated a factor of 2.2 we assume that the expansion is in all the dimensions so then the new length and width are:
[tex] L_f = 2.2 L_i= 2.2* 7.5 in = 16.5 in[/tex]
[tex] W_f = 2.2 w_i = 2.2 * 3 in = 6.6 in[/tex]
Step-by-step explanation:
The area of a rectangle is given by [tex] A = L *W[/tex]
For this case is the rectangle is dilated a factor of 2.2 we assume that the expansion is in all the dimensions so then the new length and width are:
[tex] L_f = 2.2 L_i= 2.2* 7.5 in = 16.5 in[/tex]
[tex] W_f = 2.2 w_i = 2.2 * 3 in = 6.6 in[/tex]
And the area would be (2.2)^2 times the initial area since is defined as [tex]A = L_f W_f [/tex]
Answer:
The length and the width of the new rectangle are 16.5 inches and 6.6 inches respectively
Step-by-step explanation:
Given
Shape: Rectangle
[tex]Length = 7.5 inches[/tex]
[tex]Width = 3 inches[/tex]
[tex]Scale factor = 2.2[/tex]
Required
Dimension of the new rectangle
The dimensions of the new rectangle can be solved by multiplying the scale factor by the old dimensions;
This means that
New Length = Scale factor * Old Length
and
New Width = Scale factor * Old Width
Calculating the new length
New Length = Scale factor * Old Length
Substitute 2.2 for scale factor and 7.5 for old length; This gives
[tex]New Length = 2.2 * 7.5 inches[/tex]
[tex]New Length = 16.5 inches[/tex]
Calculating the new width
New Width = Scale factor * Old Width
Substitute 2.2 for scale factor and 3 for old width; This gives
[tex]New Width = 2.2 * 3 inches[/tex]
[tex]New Width= 6.6 inches[/tex]
Hence, the length and the width of the new rectangle are 16.5 inches and 6.6 inches respectively
The box plot was created by using which pieces of data?
A box-and-whisker plot. The number line goes from 0 to 130. The whiskers range from 5 to 130, and the box ranges from 10 to 105. A line divides the box at 40.
a maximum of 130 and a lower quartile of 10
a maximum of 130 and a lower quartile of 5
a maximum of 135 and a lower quartile of 10
a maximum of 135 and a lower quartile of 5
Answer:
(a) a maximum of 130 and a lower quartile of 10
Step-by-step explanation:
The whiskers of a box plot extend from the minimum to the maximum. The box ranges from the lower quartile to the upper quartile. The middle line divides the box at the median.
Your plot has ...
minimum: 5lower quartile: 10median: 40upper quartile: 105maximum: 130The maximum and lower quartile are correctly described as 130 and 10, respectively.
Answer:
A. a maximum of 130 and a lower quartile of 10
Step-by-step explanation:
Tara has a magnet collection from places she visited. She measures the length of the magnets to the nearest half inch and records the data in a line plot. Are more magnets longer than 2 1/2 inches or shorter than 2 1/2 inches? Explain
Answer:
there are more magnets that longer than 2 1/2
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
Please have a look at the attached photo.
My answer:
From the photo, we can see that:
Length of the magnet:
1 inch there is 1 magnet[tex]1\frac{1}{2}[/tex] inches there are 2 magnets2 inches there are 3 magnets 3 inches there are 4 magnets [tex]3\frac{1}{2}[/tex] there is 1 magnet4 inches there are 2 magnets=> the total number of magnets that longer than 2 1/2 are: 4+1+2 = 7
=> the total number of magnets that shorter than 2 1/2 are: 1+2+3 = 6
Hence, there are more magnets that longer than 2 1/2
Hope it will find you well.
Answer:
Step-by-step explanation:
A swimming pool in the shape of a right rectangular prism measures 24 feet by 16 feet and is 4.5 feet deep across the entire pool. What is the volume of the swimming pool, in cubic feet?
72
108
324
1,728
Answer: D- 1,728
Step-by-step explanation: I did the quiz
Answer:
d
Step-by-step explanation:
Use what you know about domain to select all of
the following functions that could be the one
graphed.
f(x) - 3
f(x) - V1
Ax) = VX+1
(x) = 3x-3
Answer:A & B
Step-by-step explanation:
The Jones family has saved a maximum of $750 for their family vacation to the beach. While planning the trip, they determine that the hotel will average $125 a night and tickets for scuba diving are $75. The inequality can be used to determine the number of nights the Jones family could spend at the hotel
750≥75 + 125h
Answer:
Value of h greater than 5.4 will make inequality false.
Step-by-step explanation:
This question is incomplete; here is the complete question.
The Jones family has saved a maximum of $750 for their family vacation to the beach. While planning the trip, they determine that the hotel will average $125 a night and tickets for scuba diving are $75. The inequality can be used to determine the number of nights the Jones family could spend at the hotel 750 ≥ 75 + 125h. What value of h does NOT make the inequality true?
From the given question,
Per night expense (expected) = $125
If Jones family stays in the hotel for 'h' days then total expenditure on stay = $125h
Charges for scuba diving = $75
Total charges for stay and scuba diving = $(125h + 75)
Since Jones family has saved $750 for the vacation trip so inequality representing the expenses will be,
125h + 75 ≤ 750
125h ≤ 675
h ≤ [tex]\frac{675}{125}[/tex]
h ≤ 5.4
That means number of days for stay should be less than equal to 5.4
and any value of h greater than 5.4 will make the inequality false.
Please help me I have been stuck on this question for ages
Answer:28 green and 35 red
Step-by-step explanation:
Given
If there are r red counter and g green counter then
Probability of drawing a green counter is [tex]P(g)=\frac{4}{9}[/tex]
and [tex]P(g)=\frac{\text{No of g counter}}{\text{Total no of counter}}[/tex]
Thus [tex]\frac{\text{No of g counter}}{\text{Total no of counter}}=\frac{4}{9}[/tex]
[tex]\frac{g}{g+r}=\frac{4}{9}[/tex]
[tex]\Rightarrow 9g=4g+4r[/tex]
[tex]\Rightarrow 5g=4r\quad \ldots(i)[/tex]
Also if 4 red and 2 green counter is added the probability of drawing a green counter is
[tex]P(g)=\frac{10}{23}=\frac{\text{No of g counter}}{\text{Total no of counter}}[/tex]
[tex]\Rightarrow \frac{10}{23}=\frac{g+2}{g+2+r+4}[/tex]
[tex]\Rightarrow \frac{10}{23}=\frac{g+2}{g+r+6}[/tex]
[tex]\Rightarrow 10g+10r+60=23g+46[/tex]
[tex]\Rightarrow 10r+14=13g\ quad \ldots(ii)[/tex]
Substitute the value of g in equation (ii)[/tex]
[tex]\Rightarrow 10\times \frac{5}{4}g+14=13g[/tex]
[tex]\Rightarrow \frac{25}{2}g+14=13g[/tex]
[tex]\Rightarrow g=28[/tex]
Therefore [tex]r=35[/tex]
Thus there 28 green counter and 35 red counter
Find lim x -2 f(x) for: a . f(x) = 9 b. f(x) = x
Answer:
Step-by-step explanation:
Given the limit function
Lim x → 2: f(x)
1. When f(x) = 9
Then,
From limit theorem
Lim x → xo: K = K
Where k is a constant. Then, the limit of a constant is that constant.
Lim x → 2: 9 = 9
So limit is 9.
2. Lim x → 2: f(x)
Lim x → 2: x
When x = 2
Lim x → 2: 2 = 2
Then, x = 2.
If the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have?
10
12
20
24
Answer:
The answer is 20
Step-by-step explanation:
Given that the smallest angle of rotation for a regular hexagon is 18°. We are to find the number of sides of the polygon. Since the polygon is regular, so all its sides and angles are equal.
Answer:
its 20
Step-by-step explanation:
got it right on my test
If the hypotenuse of a right triangle measures 15 cm and one of the legs measures 12 cm, what is the length of the other leg?
Step-by-step explanation:
12 to the 2nd power=144
15 to the 2nd power =225
225-144=81
square root of 81 is 9
Tony has a bag of 10 quarters, 12 nickels, and 8 dimes. Tony selects a coin, records it, then replaces it back in the bag before choosing again.
Find the probability he selects a quarter first, dime second, and nickel
third. Write your answer in a fraction in simplest form.
Please help me!!
Answer:
8/225
Step-by-step explanation:
The probability of each event would be the number of the type of currency that you have specified divided by the total number of coins, in this case the total amount of coins does not change as the coin returns to the bag.
The total number of coins is: 10 + 12 + 8 = 30
The probability of finding a quarter is:
10/30
The probability of finding dime is:
8/30
The probability of finding nickel is:
12/30
The final probability then is:
(10/30) * (8/30) * (12/30) = 960/27000
If we simplify this, dividing both numbers by 120, we are left with:
8/225
My living room is 6m (to the nearest m) by 5m (to the nearest m). What is the maximum and minimum area of my living room? Write your answer as an error interval.
Whoever helps I'll give a brainliest x
Answer:
24.75m ≤ 30m < 35.75m
Step-by-step explanation:
Minimum area:
5.5 (lower bound of 6m) * 4.5 (lower bound of 5m) = 24.75m
Maximum area:
6.5 (upper bound of 6m) * 5.5 (upper bound of 5m) = 35.75m
Normal area:
6*5=30m
I hope that makes some sense or helps a little!
Aubrey is selling collection of art and makes a 12% commission on all sales. What would her commission be on the sales of a $ 3250 collection of art?
Answer:
$390
Step-by-step explanation:
3250 x 0.12 = 390
Answer:
The answer is $390