Answer:-
[tex]11.4 + 0.5y = 9.9 + 0.6y[/tex] , then the two states have the same population.
Step-by-step explanation:
Let y represents the number of years
As per the statement:
In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.
⇒ [tex]11.4 + 0.5y[/tex]
and
also, it is given that: Michigan's population was 9.9 million, increasing by 0.6 million each year.
⇒ [tex]9.9 + 0.6y[/tex]
When two states have the same population.
then the equation : [tex]11.4 + 0.5y = 9.9 + 0.6y[/tex].
Answer:
In 15 years the population will be same.
Step-by-step explanation:
Let y represent the number of years.
In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.
[tex]x=11.4+0.5y[/tex]
Michigan's population was 9.9 million, increasing by 0.6 million each year.
[tex]x=9.9+0.6y[/tex]
We have to tell that when will the two years have the same population, so we will put both equations equal.
[tex]11.4+0.5y=9.9+0.6y[/tex]
=> [tex]11.4-9.9=0.6y-0.5y[/tex]
=> [tex]0.1y=1.5[/tex]
So, y = 15
Therefore, in 15 years the population will be same.
LOTS OF POINTS!!!!!!!!
Please help asap!!!!! I need to solve for x
Answer:
x = 1 11/15
Step-by-step explanation:
Using ratios of similar triangles
3 5.2
-------- = ----------
4 (5.2 + x)
Using cross products
3 * (5.2 + x) = 5.2 * 4
Distribute
15.6 + 3x = 20.8
Subtract 15.6 from each side
15.6-15.6 + 3x = 20.8 -15.6
3x =5.2
Divide each side by 3
3x/3 = 5.2/3
x = 5.2/3
x=52/30
x = 26/15
x = 1 11/15
Which equation represents the sentence? Four more than a number is half the number.
A.n+4=n/2
B.n-4=n/2
C.4+n/2=n
D.n/2-4=n
Elton hiked 16 miles each day on a 12 day hiking trip.Lola hiked 14 miles each day on her 16 day hiling trip.In all, how many more miles did Lola hike than Elton hiked
Answer:
32 miles.
Step-by-step explanation:
We have been given that Elton hiked 16 miles each day on a 12 day hiking trip.
So, the number of miles hiked by Elton in 12 days will be: [tex]16\times 12=192[/tex] miles.
Lola hiked 14 miles each day on her 16 day hiking trip.
So, the number of miles hiked by Lola in 16 days will be: [tex]14\times 16=224[/tex] miles.
Let us subtract number of miles hiked by Elton from Number of miles hiked by Lola.
[tex]\text{Number of miles that Lola hiked more than Elton}=224-192[/tex]
[tex]\text{Number of miles that Lola hiked more than Elton}=32[/tex]
Therefore, Lola hiked 32 miles more than Elton in all.
Use the slope formula to find the slope of the line passing through the given points.
(–4, 7) and (0, 8)
Answer:
Slope of the line passing through the given points are: [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Slope of a line : For any two point [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
the formula of slope is given by:
Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Given the points ( -4, 7) and (0, 8)
then, by using slope formula;
[tex]m = \frac{8-7}{0-(-4)} = \frac{1}{0+4} = \frac{1}{4}[/tex]
Therefore, the slope of the line passing through the given points are: [tex]\frac{1}{4}[/tex]
Answer:
1 / 4
Step-by-step explanation:
We are to find the slope of a line which passes through the two given points: (–4, 7) and (0, 8).
We know the formula of the slope (m):
[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
So putting in the values of the coordinates of the given points in the formula to get:
Slope = [tex]\frac{8-7}{0--4} = \frac{1}{4}[/tex]
Therefore, the slope slope of a line which passes through the two given points: (–4, 7) and (0, 8) is 1 / 4.
What is the third quartile of this data set 21,24,25,28,29,35,37,43,44
Answer:
40
Step-by-step explanation:
The data is
21,24,25,28,29,35,37,43,44
To find the third quartile we have to arrange the data in increasing order
so the data in increasing order is
21,24,25,28,29,35,37,43,44
total number of values = 9
Median value = (n + 1 )/ 2
=(9+1)/2
=5th value
so the median is 29
Lower half of the data is the values before the median and upper half of the data is values after the median
so lower half = {21,24,25,28}
Upper half = {35,37,43,44}
so to find the third quartile we will use the upper half of the values
Third quartile means that the median of the values of upper half of the data
As the total No of value in upper half is 4 which is an even no
we will take the middle values of the upper half and take their mean
so
Third Quartile = [tex]\frac{37+43}{2}[/tex]
=[tex]\frac{80}{2}[/tex]
=40
so the value of third quartile is 40
Final answer:
The third quartile (Q3) of the data set is 40, calculated by finding the average of the two middle numbers of the upper half of the data after excluding the median.
Explanation:
To find the third quartile of a data set, which is also referred to as Q3 or the 75th percentile, one must identify the median of the upper half of the data. For the provided data set (21, 24, 25, 28, 29, 35, 37, 43, 44), with nine values, the median is 29, which is the fifth value. To calculate Q3, we take the upper half of the data set which does not include the median itself. The upper half includes (35, 37, 43, 44), and the median of this half is the third quartile. Since we have an even number of data points in the upper half, we must find the average of the two middle numbers, 37 and 43, which is (37+43)/2 or 40. Therefore, the third quartile of the provided data set is 40.
One copy of a new book by Amanda's favorite author cost $9.45. If a total of 2,740 copies of the book were sold on the first day of the book's real release, what were he total sales that day?
Answer:
25,893
Step-by-step explanation:
2.740 x 9.45=25,893
12) Miranda wants to buy as many collectible dolls as possible, for $2.50 each. If she has $45.00 to spend, how many dolls can she buy? Which equation BEST represents this situation? A) 45x = 2.5 B) 2.5x = 45 C) x + 2.5 = 45 D) x + 45 = 2.5
Answer:
The answer would be B
2.5x = 45
(x) would be the number of dolls, multiplied by how much each doll costs ($2.50) and the product would be how much she has to spend. Hope this helps!
Given:
Triangle WXY, 1 an exterior .
Prove:
1 > 2
Answer:
<1 = <2+< 3.Step-by-step explanation:
Given triangle WXY and <1 is an exterior angle.
We need to prove <1 is greater than <2.
First statement is:
Triangle WXY and <1 is an exterior angle.
Reason : Given
Note: An exterior angle of a triangle is the sum of two angles side the triangle those don't makes the linear pair with exterior angle.
We can see that <2 and < 3 are the angles of triangle those are not making a linear pair.
Therefore, <1 = <2+< 3.
So, the second statement should be first option <1 = <2+< 3.
Find the first, fourth, and eighth terms of the sequence. A(n) = –5 • 2n–1
A. –5; –40; –640
B. –20; –160; –2,560
C. 1; –1,000; –10,000,000
D. –10; –80; –1,280
Answer:
-5; -40; -640
Step-by-step explanation:
Tia and her five friends are going to the ice skating rink. Each person $5 for admission and $5 for food. Write and evaluate a numerical expression to find the total cost for admission and food
Where C = Cost and P = People
C = 2(5p)
In the context of Tia and her five friends:
C = 2(5*6) = 2(30) = 60
C = 60
The cost for Tia and her five friends to be admitted to ice skate and eat is 60$, and the equation to calculate this is C = 2(5p).
Total cost of job = $147.51 Duration of job = 5 hours Price of parts = $32.50 Overhead rate = 55% Hourly labor rate = _____.
Answer:
Hourly labor rate = $14.84
Step-by-step explanation:
Total cost of job = $147.51
Price of parts = $32.50
Labor cost + overhead = Total cost - parts = 147.51 - 32.5
=115.01
Overhead rate = 55%
Labor cost = 115.01/(1+55%) = 115.01/1.55
=74.2
Duration of job = 5 hours
Hourly labor rate = 74.2/5
= $14.84
Answer:
$14.84
Step-by-step explanation:
Total cost of job = $147.51=labor+overhead+parts
Price of parts = $32.50
labor+overhead =147.51-32.5=115.01
Overhead rate = 55%
labor+0.55labor= 115.01
labor=115.01/(1.55)=74.2
Duration of job = 5 hours
hourly labor=74.2/5=$14.84
which of the following sequences are convergent
Answer:
option A and E
Step-by-step explanation:
Arithmetic sequence converge, only in the case only when r=0
otherwise , arithmetic sequence goes increasing or decreasing at a constant rate.
So we ignore second and fourth option
If |r|<1 then geometric sequence converge
if |r|>1 then geometric sequence diverge
In option A, r= 1/5 that is less than 1 so it converge
In option C, r= -2 , |r| > 1 so geometric sequence diverge
In option E, r= 2/3 that is less than 1 so it converges
Answer is option A and E
How many solutions do these have?? PLEASE HELP!!
y=4x+3; 2y-8x=3
1
2
infinitely many
none
x-4y=12; 5x-20y=60
1
2
infinite
none
y-7x=-14; 7y-49x=-2
1
2
infinitely m
The length of a rectangle it twice it's within. If the perimeter of the rectangle is 30 cm, find its area.
w - width
2w - length (l)
30 cm - perimeter
w + w + 2w + 2w = 6w - perimeter
The equation:
6w = 30 divide both sides by 6
w = 5 cm
2w = 2(5) = 10
l = 10 cm
The area of a rectangle: A = lw.
Substitute:
A = (5)(10) = 50
Answer: The area is 50cm²A regulation soccer field has an area of 59,400 square feet. If the length is 330 feet, what is the width in feet
To find the width of a rectangle when given the area and length, divide the area by the length:
Width = 59,400 / 330 = 180 feet
In a random sample of 97 women at a company, the mean salary is $45,902 with a standard deviation of $3865. In a random sample of 75 men at the company, the mean salary is $48,454 with a standard deviation of $6677. Which interval is the 95% confidence interval for the difference between the mean salaries of all women and men at the company?
A) ($1133.20, $3970.80)
B) ($856.36, $4247.64)
C) ($1686.88, $3417.12)
D) ($319.99, $4784.01)
The 95% confidence interval for the difference between the mean salaries of all women and men at the company is (−3570.8,−1533.2), which is option C.
Identify the relevant parameters:
Sample size for women (n_w) = 97
Mean salary for women (μ_w) = $45,902
Standard deviation for women (σ_w) = $3865
Sample size for men (n_m) = 75
Mean salary for men (μ_m) = $48,454
Standard deviation for men (σ_m) = $6677
Confidence level = 95%
Calculate the pooled standard error (s_p):
s_p = √[(n_w * σ_w^2 + n_m * σ_m^2) / (n_w + n_m - 2)]
s_p = √[ (97 * 3865^2 + 75 * 6677^2) / (97 + 75 - 2)]
s_p ≈ $4973.49
Calculate the margin of error (z):
Since the sample size is large for both groups (n_w > 30 and n_m > 30), we can use the standard normal distribution (z-score) with a confidence level of 95%.
z = 1.96 (for 95% confidence level)
Calculate the confidence interval:
Lower bound = (μ_w - μ_m) - z * s_p
Lower bound = ($45,902 - $48,454) - 1.96 * $4973.49
Lower bound ≈ -$3570.80
Upper bound = (μ_w - μ_m) + z * s_p
Upper bound = ($45,902 - $48,454) + 1.96 * $4973.49
Upper bound ≈ -$1533.20
Therefore, the 95% confidence interval for the difference between the mean salaries of all women and men at the company is (-$3570.80, -$1533.20), which confirms your answer of option C.
NEED HELP !!!!!!!! ASAP PLZ
In the process of proving that opposite sides of a parallelogram are congruent, Ross drew a diagonal of the parallelogram and determined that the two triangles formed are congruent. He then concluded that opposite sides must be congruent, because corresponding parts of congruent triangles are congruent.
Using his markings in the diagram, which postulate allowed him to determine that the two triangles formed are congruent?
A) AAS
B) ASA
C) SAS
D) SSS
Answer: Congruency criteria used by Ross to prove the opposite sides are congruent is B) ASA congruence postulate
A number to the 8th power divided by the same number to the 5th power is 64 what is the number?
Let the number = X
You have X^8 / X^5
When dividing two numbers with powers, Simplify the expression by subtracting the powers.
8-5=3
so X^8 / X^5 becomes x^3
Now you have x^3 = 64
To find x take the cubic root of 64:
X = ∛64
X = 4
The number is 4
An object is thrown upward at a speed of 171 feet per second by a machine from a height of 17 feet off the ground. The height h of the object after t seconds can be found using the equation h = − 16t^2 + 171t + 17
When will the height be 307 feet?
When will the object reach the ground?
Answer:
Step-by-step explanation:
a) When will the height be 307 feet?
h = − 16t^2 + 171t + 17
307 = − 16t^2 + 171t + 17
Solving the quadratic equation by the general formula (find the plot attached). It reaches 307' twice as it is a parabolic shot.
t=2.1141s
t=8,5734s
b) When will the object reach the ground?
h = − 16t^2 + 171t + 17
0 = − 16t^2 + 171t + 17
t=-0.0985s (not real as there exists no negative time)
t=10.786s
The object will be at a height of 307 feet approximately 9.54 seconds after it was thrown. The object will reach the ground approximately 0.21 seconds after it was thrown.
To find when the height will be 307 feet, you can set the equation for the height h to 307 and solve for t:
h = -16t² + 171t + 17
307 = -16t² + 171t + 17
Now, let's rearrange the equation and set it equal to zero:
-16t² + 171t + 17 - 307 = 0
Combine like terms:
-16t² + 171t - 290 = 0
Now, you can solve this quadratic equation for t. You can use the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
In this case, a = -16, b = 171, and c = -290. Plug these values into the quadratic formula:
t = (-171 ± √(171² - 4 * (-16) * (-290))) / (2 * (-16))
Now, calculate the values for t:
t₁ = (-171 + √(171² - 4 * (-16) * (-290))) / (2 * (-16))
t₂ = (-171 - √(171² - 4 * (-16) * (-290))) / (2 * (-16))
Calculate t₁ and t₂ separately:
t₁ ≈ 9.54 seconds
t₂ ≈ -9.69 seconds
Since time cannot be negative in this context, we discard the negative solution. Therefore, the object will be at a height of 307 feet approximately 9.54 seconds after it was thrown.
To find when the object will reach the ground, you can set h equal to 0 and solve for t:
h = -16t² + 171t + 17
0 = -16t² + 171t + 17
Rearrange the equation:
-16t² + 171t + 17 = 0
Now, solve for t using the quadratic formula as we did before:
t = (-171 ± √(171² - 4 * (-16) * 17)) / (2 * (-16))
Calculate t₁ and t₂:
t₁ ≈ 0.21 seconds
t₂ ≈ 10.30 seconds
Again, you discard the negative solution. So, the object will reach the ground approximately 0.21 seconds after it was thrown.
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Helpppppppppppppppppp
Answer:
The answer is 6.
Step-by-step explanation:
You need to have side x + 4 equal side 3x - 8. If you plug 6 into both equations, then you get x + 4 = 910and 3x - 8 = 10. The last side of the triangle equals 6. You then add all three sides together to get 25. 10 + 10 + 5 = 25.
This is an isosceles triangle (a triangle with 2 congruent/equal sides and 2 congruent angles)
If you look at the triangle, most likely side AB and BC are congruent.
Since the sides are suppose to be the same/equal to each other, you can do this:
AB = BC
x + 4 = 3x - 8 Subtract x on both sides
4 = 2x - 8 Add 8 on both sides
12 = 2x Divide 2 on both sides
x = 6
You need to find AC.
AC = x, since you know x = 6, side AC is 6 units
The leather depot buys a coat from a supplier for $90 wholesale and marks up the price by 40%. If the retail price is $134.82 , what is the sale tax?
Answer:
$8.82 is the amount of sales tax
Step-by-step explanation:
$90 x .40 = $36.00
$90 + $36 = $126
$134.82 - $126 = $8.82 in taxes
Lines AB and CD are graphed on this coordinate plane. Which point is the intersection of lines AB and CD?
According to the table listing average daily expenses for a tourist by country based on high and medium categories, Brazil has a range from $12.25 to $18.33, and Greece has a range from $9.48 to $16.55. Which of the two countries has the larger difference between categories?
a.Greece
b.Brazil
Answer:
Option a. Greece.
Step-by-step explanation:
According to the table listing average daily expenses for a tourist by country based on high and medium categories,
Brazil has a range from = $12.25 to $18.33
Greece has a range from = $9.48 to $16.55
To find out the difference in range, first we get range of both the countries.
by subtracting lowest from highest
Brazil = $18.33 - $12.25 = 6.08
Greece = $16.55 - $9.48 = 7.07
= 7.07 > 6.08
Therefore, Greece has the larger difference between categories.
Option a. Greece is the correct answer.
40 copies of a popular paper book fit perfectly on a 5ft shelf. How many copies would fit perfectly on an 8ft shelf
In your neighborhood, 7/25 of your neighbors have dogs. This is equivalent to what decimal?
Hi there! :)
Answer:
7/25 is equivalent to 0.28
Step-by-step explanation:
In order to go from a fraction to a decimal, you need to divide the numerator (top number) by the denominator (bottom number):
7/25 = 7 ÷ 25
7 ÷ 25 = 0.28
There you go! I really hope this helped, if there's anything just let me know! :)
Answer:0.28
Step-by-step explanation:
so you divided 7 and 25 and it gives 0.28
Can someone please help me with this question? Thank you!
Answer:
The arcs are not congruent which makes the statement false.
Step-by-step explanation: Congruent means equal to my understanding.
Lisa went on a 52 \text { km}52 km hike. She divided the distance traveled evenly over 44 days. How many meters did Lisa walk each day?
Answer:
13,000 meters.
Step-by-step explanation:
We have been given that Lisa went on a 52 km hike. She divided the distance traveled evenly over 4 days.
Let us convert our given distance in meters.
1 km = 1,000 meters.
52 km= 52*1,000 meters = 52,000 meters.
Let us divide total distance traveled by total number of days to find the distance traveled per day.
[tex]\text{Lisa walked each day}=\frac{52000\text{ meters}}{\text{ 4 days}}[/tex]
[tex]\text{Lisa walked each day}=13,000\frac{\text{ meters}}{\text{ day}}[/tex]
Therefore, Lisa walked 13,000 meters each day.
Lisa hiked 52 km in 4 days, equaling to 13 km per day. However, this must be converted to meters, so Lisa hiked 13,000 meters each day.
Explanation:This problem is an exercise in unit conversion and division. Since Lisa divided the total distance of 52 kilometers evenly over 4 days, she hiked 13 kilometers each day (52 km / 4 = 13 km/day). However, the question asks for the answer in meters, not kilometers. Therefore, we must convert kilometers to meters. We know that 1 kilometer is equivalent to 1000 meters, so Lisa hiked 13,000 meters each day (13 km * 1000 = 13,000 m/day).
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An Electrician charges $30 for a service call plus $75 per hour of service. If he charged 210 how many hours did he work?
Answer:
2.4 hours Electrician works.
Step-by-step explanation:
Let us assume that the number of hours Electrician works be x.
As given
An Electrician charges $30 for a service call plus $75 per hour of service.
If Electrician charged $210.
Than the equation becomes
30 + 75x = 210
75x = 210 - 30
75x = 180
[tex]x =\frac{180}{75}[/tex]
x =2.4 hours
Therefore 2.4 hours Electrician works.
What are the coordinates of the midpoint of the line segment with endpoints A (-12,3) and B (8,-4)?
10, -0.5)
(10, 4.5)
(-2,4.5)
(-2, -0.5)
Answer:
D.
Step-by-step explanation:
Add the x values and divide by the amount of x's and same with the y's
what should the following equation be multiplied by in order to eliminate the fractions? x over 2 + x over 3 = 25 over 3
A. 5 B. 9 C. 25 D. 6
Final answer:
To eliminate the fractions in the equation x/2 + x/3 = 25/3, we need to multiply the entire equation by 6.
Explanation:
To eliminate the fractions in the equation x/2 + x/3 = 25/3, we need to find a common denominator for both fractions. The common denominator for 2 and 3 is 6. Therefore, we need to multiply the entire equation by 6 to eliminate the fractions.
Multiplying the equation by 6 gives us: 6(x/2) + 6(x/3) = 6(25/3)
Simplifying further, we get: 3x + 2x = 50
Combining like terms, we have: 5x = 50
Finally, dividing both sides of the equation by 5 gives us: x = 10
Final answer:
To eliminate the fractions in the equation x/2 + x/3 = 25/3, one must multiply each term by 6, which is the least common multiple of the denominators 2 and 3, making option D correct.
Explanation:
The equation x/2 + x/3 = 25/3 should be multiplied by a number that is a common multiple of the denominators 2 and 3 to eliminate the fractions. To find the least common multiple (LCM) of 2 and 3, we can list out the multiples of these numbers (2,4,6,8,... for 2 and 3,6,9,12,... for 3) and identify the smallest multiple they have in common, which is 6. Therefore, multiplying the entire equation by 6 will eliminate the fractions and give us an equation with whole numbers.
Multiplying each term of the equation by 6 gives us: 6(x/2) + 6(x/3) = 6(25/3). Simplifying each term results in: 3x + 2x = 50 which is an equation without fractions.
The correct answer to the question is D. 6.