[tex]\bf \begin{array}{ll} \stackrel{term}{n}&\stackrel{-6+(n-1)\frac{1}{5}}{value}\\ \cline{1-2} 1&-6+(1-1)\frac{1}{5}\\ &-6+0\\[1em] &-6\\[1em] 4&-6+(4-1)\frac{1}{5}\\ &-6+\frac{3}{5}\\[1em] &\frac{-27}{5}\\[1em] 10&-6+(10-1)\frac{1}{5}\\ &-6+\frac{9}{5}\\[1em] &\frac{-21}{5} \end{array}[/tex]
Answer with Step-by-step explanation:
We are given a arithmetic sequence as:
[tex]A(n)=-6+(n-1)(\dfrac{1}{5})[/tex]
We have to find the first, fourth and tenth term
First term:
n=1
[tex]A(1)=-6+(1-1)(\dfrac{1}{5})[/tex]
A(1)= -6
Fourth term:
n=4
[tex]A(4)=-6+(4-1)(\dfrac{1}{5})[/tex]
[tex]A(4)=-6+\dfrac{3}{5}[/tex]
[tex]A(4)=-\dfrac{27}{5}[/tex]
Tenth term:
n=10
[tex]A(10)=-6+(10-1)(\dfrac{1}{5})[/tex]
[tex]A(10)=-6+\dfrac{9}{5}[/tex]
[tex]A(10)=-\dfrac{21}{5}[/tex]
A town’s population has increased 35% during the last 8 years and is now 50,100 people. What was the population 8 years ago?
To find the population 8 years ago, we can set up an equation and solve for the original population. The population 8 years ago was approximately 37,000 people.
Explanation:To find the population 8 years ago, we need to calculate the original population before the 35% increase. Let's assume the population 8 years ago was P.
Since the population has increased by 35% over the last 8 years, we can set up the equation: P + 0.35P = 50100
Simplifying the equation, we have: 1.35P = 50100
Divide both sides of the equation by 1.35 to solve for P: P ≈ 37000
Therefore, the population 8 years ago was approximately 37,000 people.
Which of the following statements is true concerning ABC below?
A. B is the largest angle.
B. B is the smallest angle
C. A is the largest angle
D. A is the smallest angle
Answer:
D. A is the smallest angle
Step-by-step explanation:
Angle A's lines are closest together
Answer:
D. A is the smallest angle
Step-by-step explanation:
To answer this question properly, we need to remember that the sum of the three angles, in a triangle, must result in 180º. Besides, each leg of this triangle is in the opposite direction to the angle of its vertex.
Finally, with the help of a compass we can demonstrate it even better, but in short, the larger the leg the larger the angle. So, ∠A is the smallest angle since a measures 7 units, then comes ∠B for b measures 10 units and ∠C as the largest angle for c measures 12 units.
solve the equation: x-9/10= -7. show all steps.
Answer:
-61
Step-by-step explanation:
[tex]\frac{x-9}{10} = -7[/tex]
[tex]x-9= -7(10)[/tex]
[tex]x-9= -70[/tex]
[tex]x= -70 + 9[/tex]
[tex]x= -61[/tex]
20% of the 6th graders are in the play. If
32 students are in the play, how many 6th
graders are in the play?
Answer:
6
Step-by-step explanation:
32×20%
32×.20
6.4
round it to 6
Answer:
6
Step-by-step explanation:
32×20%
32×.20
6.4
round it to 6
A new crew of painters takes two times as long to paint a small apartment as an experienced crew. together, both crews can paint the apartment in 4 hours . how many hours does it take the experience crew to paint the apartment
Answer:
Step-by-step explanation:
Let the inexperienced crew do the apartment in x hours.
Therefore it takes the experienced crew x/2 = 0.5x hours to do the same place.
x + 0.5x = 4 hours
1.5x = 4 hours
x = 4/1.5
x = 2.67 hours.
So the inexperienced crew does the job in 2.67 hours.
The experienced crew can do it 1/2 the time which is 1.335
Total time = 4 hours.
Answer:
4 hours
Step-by-step explanation:
I got it correct so...
2X + 4 = 14
what is X
Hello!
2X + 4 = 14
X = 5
2 * 5 = 10
10 + 4 = 14
I hope this helps, and have a nice day!
In order to get the answer to this question you will have to subtract four on both sides then divide ten by two to get your answer.
[tex]2x+4=14[/tex]
[tex]-4 -4[/tex]
[tex]14-4=10[/tex]
[tex]2x=10[/tex]
[tex]10\div2=5[/tex]
[tex]x=5[/tex]
Therefore the answer is "x=5."
Hope this helps
Given the fuction h (x) = x^2 + 2x -3, find the value of h (2) - h (-4)
Answer:-
0
Step-by-step explanation:
h(x) = x^2 + 2x -3
x = 2
h(2) = 2^2 + 2(2) - 3
h(2) = 4 + 4 - 3
h(2) = 8-3
h(2) = 5
x = - 4
h(-4) = (-4)^2 + 2(-4) - 3
h(-4) = 16 - 8 - 3
h(-4) = 16 - 11
h(-4) = 5
========
h(2) - h(-4)
5 - 5
0
what is 7 plus the sum of m and -17
Answer:
m - 10
Step-by-step explanation:
7 plus = 7 +
The sum of m and -17 = m + (-17)
7 + (m + -17)
We can get rid of the parentheses
7 + m + -17
Combine like terms
7 + -17 = -10
m + -10
Get rid of the addition sign
m - 10
The sale price of an item with a 33% discount on its list price L
The sale price of an item with a 33% discount is calculated by subtracting 33% of the list price from the list price itself. The equation for such a calculation is Sale Price = L - (33/100)*L.
Explanation:The question is dealing with the calculation of a discount on an item's list price. When an item has a list price 'L' and the discount rate is 33%, you would calculate the sale price by subtracting 33% of the list price (L) from the list price itself. It is given by the equation Sale Price = L - (33/100)*L. This calculation will give you the final price that needs to be paid for the item after the application of the discount.
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-9h - 15 = 93. What is “h”?
Answer:
answer is below
Step-by-step explanation:
h=-12
Divide each term in the equation –3y = –6x + 15 by –3 to solve for y. What is y?
A. y = -2x -5
B. y = -2x + 5
C. y = 2x - 5
D. y= 2x + 5
Answer:
C. y = 2x - 5
Step-by-step explanation:
–3y = –6x + 15
____ _________
–3 –3
y = 2x - 5
I am joyous to assist you anytime.
Mallie
Date
8. Travel Times Journal found that the average per person cost of a
ound that the average per person cost of a 10-day trip along the Pacific
Coast, per person, is $1,015. This includes transportation, food, lodging, and entertainment.
a. If the data is normally distributed with standard deviation $198, find
ard deviation $198, find the percent of
Vacationers who spent less than $1.200 per day. Round to the nearest hundredth of a
percent.
Answer:
82.38%
Step-by-step explanation:
Average cost = u = $ 1,015
Standard Deviation = [tex]\sigma[/tex] = $ 198
Its given that data is normally distributed. We have to find what percentage of vacationers spend less than $ 1200.
Since the data is normally distributed, we can use the concept of z score to answer this question.
We have to find:
Probability ( Spending < 1200)
In symbolic form, this can be represented as:
P(X < 1200)
The formula for the z score is:
[tex]z=\frac{x-u}{\sigma}[/tex]
Using the values in this formula, we get:
[tex]z=\frac{1200-1015}{198}=0.93[/tex]
Thus,
P(X < 1200) is equivalent to P(z < 0.93)
From the z table we can find the probability of z scores being less than 0.93 to be 0.8238
Thus,
P(z < 0.93) = 0.8238
Since,
P(X < 1200) = P(z < 0.93), we can conclude:
The percent of Vacationers who spent less than $1,200 is 0.8238 or 82.38%
find endpoint with given endpoint and midpoint
Answer:
(21, 17 )
Step-by-step explanation:
Using the midpoint formula and equating to the coordinates of the midpoint.
Let endpoint 2 have coordinates (x, y ), then
0.5(x - 3) = 9 ( multiply both sides by 2 )
x - 3 = 18 ( add 3 to both sides )
x = 21
and
0.5(y - 5) = 6 ( multiply both sides by 2 )
y - 5 = 12 ( add 5 to both sides )
y = 17
endpoint 2 = (21, 17 )
Tiffany rented a canoe at the park for a fixed charge of $2.50 plus $1.50 per hour. She wants to stay out on the
water as long as possible,
How many hours can she use the boat and spend a maximum of $7.00
2.5 hours
3 hours
4 hours
4.5 hours
Answer:
(b) 3 hours
Step-by-step explanation:
You want the amount of time Tiffany can rent a canoe if her charges are $7, calculated as $2.50 + 1.50 per hour.
EquationAn equation for the time Tiffany can rent is ...
cost = fixed charge + hourly charge × hours
7 = 2.50 + 1.50 × hours . . . . . . use the given numbers
4.50 = 1.50 × hours . . . . . . . . . subtract 2.50
3 = hours . . . . . . . . . . . . . divide by 1.50
Tiffany can use the boat for 3 hours if she can pay $7 for rental.
What would the equation be if the sum of t and 2 is equal to 5 less than t
Answer:
[tex]t=\frac{3}{2}[/tex]
Step-by-step explanation:
1.
[tex]t+2=5-t[/tex]
2.
[tex]2t+2=5[/tex]
3.
[tex]2t=3[/tex]
4.
[tex]t=\frac{3}{2}[/tex]
What is 12 divided by 3/4
The rule for division by a fraction is "change to multiplication by the reciprocal."
So you want(4/3)(12) which is 4(4) = 16
[tex]\bf 12\div \cfrac{3}{4}\implies \cfrac{12}{1}\div\cfrac{3}{4}\implies \cfrac{\stackrel{4}{~~\begin{matrix} 12 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{1}\cdot \cfrac{4}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 16[/tex]
Please help me!!!! Number 8 and 9.
The population of a city this year [2018] is 34,500. The population is expected to grow by 2% each year. What will be the population if the city in 2025?
A. 39,300
B. 23,180
C. 123,619
D. 39,630
HI I NEED HELP IVE BEEN DOING HOMEWORK FOR 6 HOURS ummmmm anyways, how do i express this (y^3•y^6 - in picture) in exponential form? i’m stupid so it would mean a lot
y^3 = y * y * y
y^6 = y * y * y * y * y * y
Answer:
Step-by-step explanation:
Kendra and her horse completed the
barrel racing course in 15.839 seconds.
What is this number rounded to
the nearest tenth? Explain how
you decided
Answer:
15.839 rounded to the nearest tenth is 15.8. This is because when we round it to the nearest hundredth it becomes 15.84 and then to the tenth it becomes 15.8, since 4 is less than 5.
Answer:
15.839 redondeado a la décima más cercana es 15.8.
Step-by-step explanation:
Esto se debe a que cuando lo redondeamos a la centésima más cercana se convierte en 15.84 y luego a la décima se convierte en 15.8, ya que 4 es menor que 5.
You are trying to decide between two job offers. You find the best option is to take the highway to work. That route is
calculated for driving at an average speed of 65 miles per hour. You would like to keep your morning commute down to less than 30
minutes. What is the farthest distance you can travel to work within the allowable time?
Answer:
32.5 miles
Step-by-step explanation:
The average speed is 65 miles per hour.
You want to keep your commute within 30 minutes, which is HALF AN HOUR.
THus, if you can go 65 miles AN HOUR, in HALF AN HOUR, you can go max, HALF OF THAT!!
So, [tex]\frac{1}{2}*65=32.5[/tex]
Thus, you can go 32.5 miles, max
Answer:
The farthest distance would be 32.5 miles
Step-by-step explanation:
Given,
Speed = 65 miles per hour,
If t represents the time ( in hours ) taken in travelling,
Since, time has to commute down less than 30 minutes,
Also, 1 hour = 60 minutes,
[tex]\implies 1\text{ minute}=\frac{1}{60}\text{ hour}[/tex]
[tex]\implies 30\text{ minutes}=\frac{30}{60}=\frac{1}{2}\text{ hour}[/tex]
Thus,
[tex]t\leq \frac{1}{2}[/tex]
i.e. the highest time taken = 1/2 hours,
We know that,
Distance = speed × time,
∵ Distance ∝ time,
⇒ Distance will farthest for largest time taken,
Hence, the farthest distance = [tex]65\times \frac{1}{2}[/tex] = 32.5 km.
Which is a better deal crayola crayons $6.97 for 120 crayons or rose art crayons $1.53 for 24?
Answer:
Crayola crayons for 6.97 dollars
Step-by-step explanation:
This is because there would only by 78 crayons in the other crayola box. I know this because you divide 120 by 1.53
Probs wrong but I tried
Answer:
6.97 for 120
Step-by-step explanation:
if you divide the number of crayons in the package by the amount of money you pay for it, they it shows you how many crayons you will get for one dollar. for the 120 for 6.97 its 17 crayons for a dollar and for the 24 for 1.53 its 12 for a dollar
CD contains the points C at 4, D at 0, and E at 2.
What is the ratio of CD to DE? Complete the
statements using the number line.
The length of CD is units
The length of DE is units
The ratio of CD to DE is
Answer:
the length of CD is 4
the length of DE is 2
the ratio of CD to DE is 2:1
Step-by-step explanation:
The length of segment CD is 4 units and segment DE is 2 units. The ratio of CD to DE is 2:1.
Explanation:To solve this problem, remember that points on a number line correspond to numbers and the lengths between the points correspond to the differences between these numbers.
The segment CD stretches from 0 to 4, hence the length of CD is 4 units.
The segment DE stretches from 2 to 0, hence the length of DE is 2 units.
However, since length cannot be negative, we take the absolute value of -2, which gives DE = 2 units.
Now, to find the ratio of CD to DE, we simply divide the length of CD by the length of DE.
The ratio of CD to DE can be found by dividing the length of CD by the length of DE. So, the ratio is 4/2 = 2.
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Use a radical sign to indicate the negative square root of 34.68. Then evaluate the expression to two decimal places using a calculator.
Answer:
-5.89
Step-by-step explanation:
we have that
The expression of the negative square root of 34.68 is equal to
[tex]-\sqrt{34.68}[/tex]
Using a calculator evaluate the expression
[tex]-\sqrt{34.68}=-5.89[/tex]
A cube has edge length s units. Use an exponent to write an expression for its volume
Answer:
s[tex]s^{3}[/tex]
Step-by-step explanation:
A cube's volume is its length * width * height. Its length, width, and height are all equal to s.
A cube's edge length is another word for its side length, which is the same for every edge in the cube.
To write the equation for the volume with s substituted for length, width, and height, we get that volume = s[tex]s^{3}[/tex].
Probably a dumb question but how can I solve this without using a calculator? The answer when using a calculator is 0.83 so how can I get that answer without using a calculator?
Answer:
[tex] \frac{25}{30} = .83[/tex]
set it up in an old-fashioned way
using the division method. 30 on the outside and 25 on the inside
Answer:
The answer is 0.833333333 but, to nearest hundredth place is it 0.83.
Step-by-step explanation:
I don't know how they call it in your school but, what we are going to do right now is called long division.
The mass would be the dividend (25) and the volume (30) would be the divisor and the density would be the quotient.
the owner of a butcher shop keeps the shop's freezer at -5°C. It is acceptable for the temperature to differ from this value by 1.5°. Write and solve an absolute-value equation to find minimum and maximum acceptable temperatures
Answer:
[tex]|x+5|=1.5[/tex]
is the equation describing minimum and maximum acceptable temperatures.
The minimum temperature could be [tex]-6.5^{\circ}[/tex]
and the maximum temperature could be [tex]-3.5^{\circ}[/tex]
Step-by-step explanation:
The owner of a butcher shop keeps the shop's freezer at -5°C. It is acceptable for the temperature to differ from this value by 1.5°. So, the minimum temperature could be
[tex]-5^{\circ}-1.5^{\circ}=-6.5^{\circ}[/tex]
and the maximum temperature could be
[tex]-5^{\circ}+1.5^{\circ}=-3.5^{\circ}[/tex]
Let [tex]x^{\circ}[/tex] be acceptable temperature of freezer. The difference between the acceptable temperature and given temperature [tex]x-(-5)=x+5[/tex] cannot be more than 1.5° and less than 1.5°, so
[tex]|x+5|\le 1.5[/tex]
Then
[tex]|x+5|=1.5[/tex]
is the equation describing minimum and maximum acceptable temperatures.
Solve it:
[tex]x+5=1.5\text{ or }x+5=-1.5\\ \\x=1.5-5\text{ or }x=-1.5-5\\ \\x=-3.5\text{ or }x=-6.5[/tex]
Line segment QR is dilated to create line segment Q'R'
using the dilation rule Dt, 1.5
What is y, the distance between points R and R?
3 units
4 units
6 units
9 units
Answer:
The distance between R and R' is 3 units ⇒ 1st answer
Step-by-step explanation:
A dilation is a transformation that produces an image that is the same
shape as the original, but in a different size.
If the image is larger than the original figure then dilation is called an
enlargement.
If the image is smaller than the original figure then the dilation
is called a reduction.
The image of a line by dilation parallel to the original line if the original
line not passes through the center of dilation.
Line segment QR is dilated to create line segment Q'R'
∴ QR is parallel to Q'R'
The factor of dilation is 1.5
∴ The length of Q'R' is 1.5 the length of QR
In Δs TRQ and TR'Q'
∵ QR // Q'R'
∴ m∠TRQ = m∠TR'Q'
∴ m∠TQR = m∠TQ'R'
∵ ∠T is common in the two triangles
∴ ΔTRQ is similar to ΔTR'Q'
∴ [tex]\frac{TR'}{TR}=\frac{R'Q'}{RQ}[/tex]
∵ [tex]\frac{Q'R'}{QR}=1.5[/tex]
∵ TR' = TR + y
∵ Tr = 6 units
∴ TR' = 6 + y units
∵ [tex]\frac{TR'}{TR}=\frac{6+y}{6}[/tex]
∴ [tex]1.5=\frac{6+y}{6}[/tex]
Multiply both sides by 6
∴ 9 = 6 + y
Subtract 6 from both sides
∴ 3 = y
* The distance between R and R' is 3 units
Answer:
3 Units on edge
Step-by-step explanation:
17_2_3_8=3 insert + - × or ÷ symbols to make each statement true
Answer:
17-2*3-8=3
Step-by-step explanation:
We have given:
17_2_3_8=3 insert + - × or ÷ symbols to make each statement true?
Solution:
We will insert multiplication sign between 2 and 3 and then subtract all the terms
17-2*3-8=3
We will solve it according to the DMAS rule:
DMAS rule is followed when multiple arithmetic operations are there in a given problem like addition, subtraction, multiplication and division. It tells they should be performed in order of Division, Multiplication, Addition and Subtraction. Without DMAS rule all mathematical equations will come up with different answers.
Lets solve the expression and check whether the L.H.S = R.H.S
17-2*3-8=3
17-6-8=3
11-8=3
3 =3
Be sure to multiply first and then subtract
⇒You can also insert addition sign in place of multiplication. It will give the same answer
Answer:
17 - 2 × 3 - 8 = 3 ⇒ (- , × , -)
Step-by-step explanation:
Lets revise the order of operation
# Multiplication and Division which comes first from left to right
# Addition and Subtraction which comes first from left to right
Lets explain how to solve the problem
17 __ 2 __ 3 __ 8 = 3
We want to use + , - , × or ÷ symbols to make the statement true
Lets try to find the correct operations
∵ The answer is smaller than all the numbers in the statement
∴ There is subtraction
∵ 17 - 2 = 15
∵ 15 - 3 = 12
∵ 12 - 8 = 4 which is not the answer
Then lets multiply 17 , 2 and multiply 3 , 8 and subtract their results
∵ 17 × 2 = 34
∵ 3 × 8 = 24
∵ 34 - 24 = 10 which is not the answer
Then lets multiply 2 , 3 and then subtract the result from 17 and then
subtract 8 from the last result
∵ 2 × 3 = 6
∵ 17 - 6 = 11
∵ 11 - 8 = 3 which is the answer
∴ 17 - 2 × 3 - 8 = 3
∴ The symbols are - , × , -
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided
Find the inverse function for f(2)= square root of 2x - 6.
Answer:
y = ( x^2 / 2 ) + 3
Step-by-step explanation:
Swap x and y, then isolate y to find a function's inverse
x = sqrt ( 2y - 6 )
x^2 = 2y - 6
x^2 + 6 = 2y
( x^2 / 2 ) + 3 = y
y = ( x^2 / 2 ) + 3 is the final answer.