Answer:
a₁ = 1 and r = 3Step-by-step explanation:
[tex]1+3+9+27+81\\\\a_1=1,\ a_2=3,\ a_3=9,\ a_4=27,\ a_5=81\\\\r=\dfrac{a_{n+1}}{a_n}\Rightarrow r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=\dfrac{a_5}{a_4}\\\\r=\dfrac{3}{1}=\dfrac{9}{3}=\dfrac{27}{9}=\dfrac{81}{27}=3[/tex]
Good evening ,
Answer:
a₁ = 1 r = 3Step-by-step explanation:
Since it’s a geometric series then
a₁ = 1 ( because 1 is the first term of the series)
3/1 = 9/3 = 27/9 = 81/27 = 3 then r=3.
:)
Which expression is equivalent to (7x – 5) – (3x - 2)?
A
B
C
D
10x - 7
10x - 3
4x - 7
4x - 3
Answer:D
Step-by-step explanation:
The height ,h, in feet of a baseball that is popped up into the air is a quadratic function of the time,t, in seconds, since it was hit. An equation that may model this situation is h(t)=4+60t-16t^2. Answers the following questions accurately, rounding to two decimals places when needed. How high is the ball when it strikes the bat?
Answer: [tex]4\ feet[/tex]
Step-by-step explanation:
The exercise provides you the following Quadratic function:
[tex]h(t)=4+60t-16t^2[/tex]
Then, based on the information given in the exercise, you can conclude that, when the ball strikes the bat, the time in seconds is the following:
[tex]t=0[/tex]
Therefore, in order to calculate the height in feet of the ball when it strikes the bat, you need to subsititute [tex]t=0[/tex] into the function and then evaluate.
Then, you get this result:
[tex]h(0)=4+60(0)-16(0)^2\\\\h(0)=4+0-0\\\\h(0)=4[/tex]
BRAINLEST AND POINTS PLEASE THANK U.
Answer:
P'(7, - 8 )
Step-by-step explanation:
Given the translation rule
(x, y ) → (x + 4, y - 3 )
This means add 4 to the original x- coordinate and subtract 3 from the original y- coordinate, thus
P(3, - 5 ) → P'(3 + 4, - 5 - 3 ) → P'(7, - 8 )
What is the vertex for the graph shown below?
Answer:
(5,1)
Step-by-step explanation:
A vertex is where two or more curves, lines, or edges meet
Dad bought $200,000 of term life insurance at the rate of $5.40 per thousand-dollar unit. How much is the annual premium?
Answer:
It is clear that the annual premium = $1080
Explanation:
Given:
As the total term amount for life insurance is given in the question which is $200,000
rate per $1000 unit = $5.40
Simple Calculation Procedure to get the annual premium:
First step:
Let’s assume $1000 is one unit and the mentioned rate per $1000 unit is $5.40. Now, all you need is to find total number of $1000 units in total term insurance amount ($200,000).
So,
divide $200,000 by $1000 to establish the total number of
1000 units in $200,000 = $200,000/$1000 = 200
Second step:
As 200 is found to be the total number of $1000 units in $200,000.
So, just multiply 200 with $5.40 to ultimately find the annual premium
i.e. $5.40 × 200 = $1080
Hence, it is clear that the annual premium = $1080
Keywords: life insurance, annual premium, premium term rate
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CD has endpoints C(6,-8) and D(-4,10) on a coordinate plane. What are the coordinates of the midpoint CD
Final answer:
The midpoint of the line segment with endpoints C(6,-8) and D(-4,10) is calculated to be at (1, 1) by averaging the x and y coordinates of the endpoints.
Explanation:
The midpoint of a line segment with endpoints C(6,-8) and D(-4,10) can be found by averaging the x-coordinates and the y-coordinates of the two endpoints. To do this, add together the x-coordinates, 6 and -4, and divide by 2 to find the x-coordinate of the midpoint. Add together the y-coordinates, -8 and 10, and divide by 2 to find the y-coordinate of the midpoint.
The calculations are as follows:
x-coordinate: (6 + (-4)) / 2 = 1
y-coordinate: (-8 + 10) / 2 = 1
Therefore, the midpoint of CD is (1, 1).
Given the system of inequalities, list all the points that are included in the solution to this system of inequalities:
[tex]x + y > 4[/tex]
[tex] - 2x + y < 3[/tex]
Answer:
B, C
Step-by-step explanation:
The solution space is the area to the right of the X where the lines cross. Only points B and C are in that space. Point E is on the line, but the line is not included in the solution space.
_____
The lines are drawn as though the inequality were an equation. The solution space is above the first line (which has negative slope) because y > ... indicates the solution is values of y above (>) the line.
The solution space is below the second line, which has positive slope, because y < ... indicates the solution is values of y below (<) the line.
Which of the following shows the expression −3t2−2t(4s−9t)+7st in simplest form
Answer:
15t^2-ts
Step-by-step explanation:
-3t^2-2t(4s-9t)+7ts
-3t^2-8ts+18t^2+7ts
-3t^2+18t^2-8ts+7ts
15t^2-ts
The expression −3t^2−2t(4s−9t)+7st can be simplified to 15t^2-st.
Explanation:This expression is a quadratic equation in the form of −3t^2−2t(4s−9t)+7st. To simplify, we can start by distributing the -2t across the terms inside the parentheses:
−3t^2−8st+18t^2+7st
Combining like terms, we get:
15t^2-st
So, the expression −3t^2−2t(4s−9t)+7st in simplest form is 15t^2-st.
The percentage of physicians who are women is 27.9%. In a survey of physicians employed by a large
university health system, 45 of 120 randomly selected physicians were women. Is there sufficient evidence at the 0.05
level of significance to conclude that the proportion of women physicians at the university health system exceeds
27.9%?
Answer:
Step-by-step explanation:
Given that the percentage of physicians who are women is 27.9%. In a survey of physicians employed by a large university health system,
45 of 120 randomly selected physicians were women.
Sample size n = 120
Sample proportion p = [tex]\frac{45}{120} \\=0.375[/tex]
H0: p = 0.279
Ha: p >0.279
(Two tailed test at 5% significance level)
p difference = 0.096
STd error of p assuming H0 true
= [tex]\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.279(0.721}{120} } \\=0.041[/tex]
Test statistic Z = [tex]\frac{0.096}{0.041} \\=2.345[/tex]
Z critical value one tailed is 1.645
Since Z statistic > 1.645 we reject H0
There is evidence to conclude that the proportion of women physicians at the university health system exceeds
27.9%
how can i solve thus problem help me
Answer:
Position from point A= 383.33 meters
Step-by-step explanation:
A concept to know is that the integral of velocity will give you the distance traveled.
[tex]d=\int\limits^{t_1}_{t_0}{v(t)} \, dt[/tex]
where the interval of integration are the starting time and ending time.
I let the starting time be t₀ = 0, and the ending time t₁=10 for the 10 seconds that it traveled.
I did the integration and got 383.33m traveled in 10 seconds.
So the answer is 383.33 meters.
Ignore the final answer in the image. I misread the question.
Thomas is starting a new company. He has two quotes from a computer company for the cost of computers and printers. If he buys three computers and one printer, the cost is $825. if he buys 4 computers and 2 printers, the cost is $1200. How much does each computer and printer cost?
Answer:
Cost of each Computer is $225 and Cost of each Printer is $150.
Step-by-step explanation:
Let the cost of the Computers be 'x'.
Let the cost of Printer be 'y'.
Given:
If he buys three computers and one printer, the cost is $825.
framing in equation form we get;
[tex]3x+y =825 \ \ \ \ \ equation\ 1[/tex]
Also Given:
if he buys 4 computers and 2 printers, the cost is $1200.
framing in equation form we get;
[tex]4x+2y =1200 \ \ \ \ \ equation\ 2[/tex]
Now Multiplying equation 1 by 2 we get;
[tex]2(3x+y)=825\times 2\\\\6x+2y=1650 \ \ \ \ \ equation\ 3[/tex]
Now Subtracting equation 2 from equation 3 we get;
[tex](6x+2y)- (4x+2y) = 1650-1200\\\\6x+2y-4x-2y = 450\\\\2x=450\\\\x=\frac{450}{2} =\$225[/tex]
Now Substituting the value of x in equation 1 we get;
[tex]3x+y=825\\\\3\times 225+y=825\\\\675+y =825\\\\y = 825 -675\\\\y = \$150[/tex]
Hence Cost of each Computer is $225 and Cost of each Printer is $150.
Answer:
Cost of each Computer is $225 and Cost of each Printer is $150.
If there is 1000$ in the lockbox what year will it be worth 64,000$ at 24% interest?
Hey there!
First, set up an exponential equation that represents the rate at which your original amount, 1000, gains interest:
y = 1000(1.24)^x
Y represents the value after X years. 1.24 represents the rate at which the money gains interest, 1 + 0.24 (your 24% interest rate in decimal form). 1000 is your original amount.
Now, set this equation equal to 64000, graph y = 64000 and y = 1000(1.24)^x on a graphing calculator, and see where the two equations intersect in order to solve for x.
They intersect when x is about 19.334, as seen in the graph below (it is very zoomed in so that you can see where the two functions intersect). Therefore, it will be about 19 years after the year in which you deposited the 1000 dollars before the money is worth 64000 dollars.
What is 0.800 rounded to the nearest tenth
Answer:
0.800 is the answer. If you want an explanation let me know.
Step-by-step explanation:
A drill team is raising money by holding a car wash. The team earns $6.00 for each car washed. The team's expenses include $50.00 for advertising plus $0.50 in materials for each car washed. Let f(x) represent the team's total earning for washing x cars and g(x) represent the team's total expenses for washing x cars. Describe how you can use f(x) and g(x) to obtain a function p(x) that gives the team's profit for washing x cars. Then write a rule for p(x)
The function p(x) is obtained by subtracting g(x) from f(x)
The rule of p(x) is p(x) = 5.5 x - 50
Step-by-step explanation:
A drill team is raising money by holding a car wash
The team earns $6.00 for each car washedThe team's expenses include $50.00 for advertising plus $0.50 in materials for each car washedf(x) represent the team's total earning for washing x carsg(x) represent the team's total expenses for washing x carsp(x) that gives the team's profit for washing x carsWe need to describe how can you use f(x) and g(x) to obtain a function p(x) that gives the team's profit for washing x cars, and then write a rule for p(x)
∵ The team earns $6.00 for each car washed
∵ f(x) represent the team's total earning for washing x cars
- Equate f(x) by the product of x and 6
∴ f(x) = 6 x
∵ The team's expenses include $50.00 for advertising plus $0.50
in materials for each car washed
∵ g(x) represent the team's total expenses for washing x cars
- Equate g(x) by the sum of 50 and the product of 0.5 and x
∴ g(x) = 50 + 0.5 x
The profit = total earning - total expenses
∵ f(x) is the total earning for washing x cars
∵ g(x) is the total expenses for washing x cars
∵ p(x) represents the team's profit for washing x cars
- Subtract g(x) from f(x) and equate the difference by p(x)
∴ p(x) = f(x) - g(x)
The function p(x) is obtained by subtracting g(x) from f(x)
∵ f(x) = 6 x
∵ g(x) = 50 + 0.5 x
∴ p(x) = 6 x - (50 + 0.5 x)
- Simplify the right hand side
∴ p(x) = 6 x - 50 - 0.5 x
- Add the like term
∴ p(x) = 5.5 x - 50
The rule of p(x) is p(x) = 5.5 x - 50
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How many birthdays will you have celebrated when you are one million minutes old
Answer: about 1
Step-by-step explanation:
Bc 1 mil minutes are 1.902 of a year
PLZ HELP WHY DOESNT NOONE TRY OR AT LEAST HELP ME LIKE I REALLY NEED HELP
Answer:
V'W'X'Y' are (-4, -4), (-4, 8), (8, -4) and (8, 8) respectively.Step-by-step explanation:
Dilation can be compared with zooming some image according to the given scale.
The vertices of VWXY is given by (-1, -1), (-1, 2), (2, -1), (2, 2) respectively.
Since the given scale is 4, to get the vertices of V'W'X'Y' we need to multiply the co-ordinates by 4.
The desired co-ordinates will be (-4, -4), (-4, 8), (8, -4), (8, 8) respectively.
If tan 0=11/60, what is the value of cot 0?
Answer:
Step-by-step explanation:
tan 0 = 1/ cot 0
so, tan 0=11/60,
cot 0= 1/ (11/60)
cot 0= 60/ 11
Two transformation are performed on a figure in the coordinates plane. The first transformation is a translation 8 units to the left. Which Sedona transformation will result in a image that is similar to, but not congruent to, the original figure?
A. A clockwise rotation of 90 degrees about the center
B. A clockwise rotation of 180 degrees about the center
C. A dilation by a scale factor of 1 with the origin as the center of a dilation
D. A dilation by a scale factor of 1/2 with the origin as the center of dilation
Answer:
Only option D is correct as a dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.
Step-by-step explanation:
When we transform a certain shape, we normally associate the original shape as 'object', while the transformed shape is associated as "image',
If any shape like triangle, parallelogram or any other certain quadrilateral is rotated, reflected or translated, it wold preserve the same size. Hence, the resulting transformed image would be similar and also called 'congruent' to the original object.
But, if any shape like triangle, parallelogram or any other certain quadrilateral is enlarged or resized, it would certainly change in size. Therefore, the resulting transformed image would still be considered as similar, but it would no longer congruent to the original object.
Hence, when two transformation are performed on a figure in the coordinates plane. The first transformation is a translation 8 units to the left. A dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.
In all other cases, like a clockwise rotation of 90 degrees about the center, A clockwise rotation of 180 degrees about the center and a dilation by a scale factor of 1 with the origin as the center of a dilation would not not alter the size of the shape, and the resulting transformed image would be similar as well as called 'congruent' to the original object.
Hence, only option D is correct as a dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.
Therefore, only option D is correct.
Keywords: dilation, transformation
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The Sedona transformation that will result in an image that is similar to, but not congruent to the original figure is D. A dilation by a scale factor of 1/2 with the origin as the center of dilation.
How to get an image that is similar but not congruent to the original figure?To get an image that is similar but not congruent to the original figure, we shall perform a transformation that changes the size of the figure while keeping the same shape.
This is because when a figure is translated 8 units to the left, its position changes, but its size and shape remain the same.
A dilation by a scale factor of 1/2 with the origin as the center of dilation means the image would be reduced to half of its original size while maintaining the same shape.
This transformation results in a figure that is similar but not congruent to the original figure, as it has the same shape but a different size.
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Dan pays £220 per week in rent.
His landlord decides to increase the rent by 2.5%.
How much rent does he pay now? who ever is the first person wins iPhone x
Answer:
225.5
Step-by-step explanation:
220 + (2.5% × 220) =
220 + 2.5% × 220 =
(1 + 2.5%) × 220 =
(100% + 2.5%) × 220 =
102.5% × 220 =
102.5 ÷ 100 × 220 =
102.5 × 220 ÷ 100 =
22,550 ÷ 100 =
225.5
Answer:
225.5
Step-by-step explanation:
So, you would start by doing
220 times 2.5% that would equal 5.5
Then you would add
220 + 5.5 = 225.5
Therefore your answer will be 225.5
Solve.
Cars
In the school parking lot there were 113 fewer bikes
than cars. There were 185 cars. How many cars and
bikes were in the parking lot?
Bikes
185 - 113
185
(about 190 -
Round to the nearest ten to estimate. Then
complete the chart.
(about 190)
or
-
--
= X
X=
cars and bikes.
Estimate: There were about
Actual:
- -
= X
X
=
1
Solution: There were
cars and bikes in all.
Answer:
Total bikes and cars are 260
Step-by-step explanation:
Cars: [tex]n_{cars}185[/tex]
Bikes: [tex]n_{bikes}=n_{cars}-113=72[/tex]
Total: [tex]n_{total}=n_{bikes}+n_{cars}=257[/tex]
Rounding to the nearest ten: 260
The domain of y=sqrt x-5-1 is
Answer:
The domain is the interval [5,∞)
Step-by-step explanation:
we have
[tex]y = \sqrt{x-5}-1[/tex]
we know that
The radicand (number under a radical) must be greater than or equal to zero
so
[tex]x-5\geq 0[/tex]
solve for x
Adds 5 both sides
[tex]x-5+5\geq 0+5[/tex]
[tex]x\geq 5[/tex]
therefore
The domain is the interval [5,∞)
All real numbers greater than or equal to 5
Answer:
x >= 5
Step-by-step explanation:
Edge 2021
Let $x=(0.\overline{6})(0.\overline{60})$. When $x$ is written out as a decimal, what is the sum of the first $15$ digits after the decimal point?
Answer:
32
Step-by-step explanation:
The sum of the first $15$ digits is 32.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Let $x = 0.666666.....
$x = = 6/9 = 2/3
And .606060..... = 60/99
⇒(2/3) (60/99)
⇒ (2/99)(60/3)
⇒(2/99)(20)
⇒ 40/99
⇒ .040404.........
So, the sum of the first 15 digits = 8(4) + 7(0) + 0 = 32
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15-3 as a numerical expression
Answer:
12
Step-by-step explanation:
simplify: 15 + -3
combine: 15 + -3 = 12
The numerical expression 15-3 is equal to 12.
Explanation:A numerical expression is a mathematical phrase containing only numbers and operational symbols (such as +, -, *, /) without any variables. It represents a specific value when the numbers are replaced with actual values. For example, "3 + 5 * 2" is a numerical expression that evaluates to 13.
The numerical expression 15-3 can be solved by subtracting 3 from 15. You can start with the number 15 and subtract 3 to get the result.
15 - 3 = 12
So, the numerical expression 15-3 is equal to 12.
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Richard, Henry and Gavin share some sweets in the ratio 5:4:3. Richard gets 70 sweets. How many sweets are there altogether?
There are 168 sweets altogether
Solution:Richard, Henry and Gavin share some sweets in the ratio 5 : 4 : 3
Let "5a" be the share of Richard
Let "4a" be the share of Henry
Let "3a" be the share of Gavin
Richard gets 70 sweets
share of Richard = 70
5a = 70
a = 14To find: number of sweets altogether
number of sweets altogether = share of richard + share of henry + share of gavin
number of sweets altogether = 5a + 4a + 3a
number of sweets altogether = 12a = 12(14) = 168
Thus there are 168 sweets altogether
You start at (0, 3). You move up 4 units and down 7 units. Where do you end?
Answer:
(0,0)
Step-by-step explanation:
(0, 3) + 4 = (0,7)
(0, 7) - 7 = (0,0)
If x+y=1/x+1/y and x+y≠0, what is the value of xy?
Answer:
xy = 1
Step-by-step explanation:
Given
[tex]x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y\neq 0[/tex]
Simplify the first expression:
[tex]x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y=\dfrac{y+x}{xy}\ [\text{Add fractions in the left side}]\\ \\1=\dfrac{1}{xy}\ [\text{Divide by }x+y \ (\text{it can be done since})\ x+y\neq 0]\\ \\xy=1\ [\text{Cross multiply}][/tex]
Solve the linear system of equations using the linear combination method
4x +5y=7
y=3x+9
Enter your answers in the boxes.
x=
y=
Answer:
x = -2
y = 3
Step-by-step explanation:
Write the system the following way:
4x + 5y = 7
-3x +y = 9
we need to eliminate one unknown by multiplying one equation for a suitable number in such a way that when we add the equations one unknown is eliminated.
If we multiply the second eq. by -5 the y is eliminated
4x + 5y = 7
15x -5y = -45
add the equations
19x = -38 ===> x = -38/19 ===> x = -2
Now replace this value in any equation to get y. For example, in 1st one.
4(-2) + 5y = 7 ===> -8 +5y = 7 ===> 5y = 7+8 ===> 5y = 15 ===> y = 15/5 ===>
y=3
Let f(x) be a continuous function such that f(1) = 3 and f '(x) = sqrt( x^3 + 4 ). What is the value of f(5)?
The value of f(5) is 49.1
Step-by-step explanation:
To find f(x) from f'(x) use the integration
f(x) = ∫ f'(x)
1. Find The integration of f'(x) with the constant term
2. Substitute x by 1 and f(x) by π to find the constant term
3. Write the differential function f(x) and substitute x by 5 to find f(5)
∵ f'(x) = + 6
- Change the root to fraction power
∵ =
∴ f'(x) = + 6
∴ f(x) = ∫ + 6
- In integration add the power by 1 and divide the coefficient by the
new power and insert x with the constant term
∴ f(x) = + 6x + c
- c is the constant of integration
∵
∴ f(x) = + 6x + c
- To find c substitute x by 1 and f(x) by π
∴ π = + 6(1) + c
∴ π = + 6 + c
∴ π = 6.4 + c
- Subtract 6.4 from both sides
∴ c = - 3.2584
∴ f(x) = + 6x - 3.2584
To find f(5) Substitute x by 5
∵ x = 5
∴ f(5) = + 6(5) - 3.2584
∴ f(5) = 49.1
there are 2.54 centimeters in 1 inch. there are 100 centimeters in 1 meter. to the nearest inch, how many meters are in 511 inches
12.9794 meters or 13 meters (rounded)
You can find out this answer by looking at the 2 formulas given. Then set up a ratio and cross multiply to get your answer.
Hope this helped! (Please mark me brainliest!)
Answer:
12.9794 meters or 13 meters (rounded)
Step-by-step explanation:
You can find out this answer by looking at the 2 formulas given. Then set up a ratio and cross multiply to get your answer.
Please help me. I will mark you brainliest if you get it right.
Answer:
The salesperson will earn total commission of $ 445 .
Step-by-step explanation:
The salesperson gets 5% commission for first $2500, and 8% for above that.
So, for sale of $ 6500, the salesperson will earn commission,
$ [tex](2500 \times \frac {5}{100} + (6500 - 2500) \times \frac {8}{100})[/tex]
= $ [tex](125 + (4000) \times \frac {8}{100})[/tex]
= $ (125 + 320)
= $ 445