North Carolina = 3 * Utah
North Carolina = 2 * Oregon
Arkansas = Oregon - 1,000,000
North Carolina + Utah + Oregon + Arkansas = 27,000,000
North Carolina = 3 * Utah
Utah = 1/3 * North Carolina
Utah = 1/3 * (2 * Oregon)
(2 * Oregon) + (1/3 * (2 * Oregon)) + Oregon + (Oregon - 1,000,000) = 27,000,000
2O + (1/3 * 2O) + O + O - 1,000,000 = 27,000,000
2O + 2/3O + O + O - 1,000,000 = 27,000,000
4 2/3 O - 1,000,000 = 27,000,000
4 2/3 O = 28,000,000
O = 6,008,584
NC = 2O
NC = 2(6,008,584)
NC = 12,017,167
A = O - 1,000,000
A = 6,008,584 - 1,000,000
A = 5,008,584
NC = 3U
12,017,167 = 3U
U = 4,005,722
The populations of the four states are as follows:
- Utah has a population of 4 million.
- Oregon has a population of 6 million.
- North Carolina has a population of 12 million.
- Arkansas has a population of 5 million.
Let's denote the population of Utah, Oregon, and Arkansas as U, O, and A, respectively. According to the information given:
1. North Carolina has three times the population of Utah: [tex]\( NC = 3U \).[/tex]
2. North Carolina has twice the population of Oregon: [tex]\( NC = 2O \).[/tex]
3. Arkansas has 1 million people fewer than Oregon: [tex]\( A = O - 1 \).[/tex]
4. The total population of these four states is 27 million: [tex]\( U + O + A + NC = 27 \).[/tex]
From equations (1) and (2), we can equate the populations of Utah and Oregon since both are related to the population of North Carolina:
[tex]\( 3U = 2O \) or \( O = \frac{3}{2}U \).[/tex]
Now, substitute the value of O from equation (3) into the total population equation (4):
[tex]\( U + \frac{3}{2}U + ( \frac{3}{2}U - 1 ) + 3U = 27 \).[/tex]
Combine like terms:
[tex]\( U + \frac{3}{2}U + \frac{3}{2}U - 1 + 3U = 27 \),[/tex]
[tex]\( U + 3U + 3U - 1 = 27 \),[/tex]
[tex]\( 7U - 1 = 27 \).[/tex]
Now, solve for U:
[tex]\( 7U = 27 + 1 \),[/tex]
[tex]\( 7U = 28 \),[/tex]
[tex]\( U = \frac{28}{7} \),[/tex]
[tex]\( U = 4 \)[/tex] million.
Now that we have the population of Utah, we can find the populations of the other states:
[tex]\( O = \frac{3}{2}U = \frac{3}{2} \times 4 = 6 \)[/tex] million,
[tex]\( NC = 2O = 2 \times 6 = 12 \)[/tex] million,
[tex]\( A = O - 1 = 6 - 1 = 5 \)[/tex] million.
Write a story problem about 40 apples and 17 peat
Answer:
Lets say you have 40 apples and 17 "peats". You decide to give your friend, Timmy, 2/3's of the apple, because you know that he loves apples! You also give him 2/7 of your "peats". How many apples and peats, combined, does that leave you with?
Step-by-step explanation:
There really is none.
A princess hat for a costume is shaped like a cone. The base of the cone is 12 in across and the height is 8
in. The slant height of the outside edge, which is unknown, is the hypotenuse of the right triangle formed with
the radius and the height of the cone.
(a) Sketch the princess hat. Label the known lengths as described and label the unknown length as x.
(b) What is the slant height of the outside edge?
Answer:
Part a) The drawn in the attached figure
Part b)The slant height of the outside edge is [tex]x=10\ in[/tex]
Step-by-step explanation:
Part a) The drawn in the attached figure
Part b) What is the slant height of the outside edge?
we have that
The diameter of the base of the cone is 12 in
so
[tex]r=12/2=6\ in[/tex] ----> the radius is half the diameter
[tex]h=8\ in[/tex]
Applying the Pythagoras Theorem find the slant height x
[tex]x^{2}=r^{2}+h^{2}[/tex]
substitute the values
[tex]x^{2}=6^{2}+8^{2}\\x^{2}=100\\x=10\ in[/tex]
Which inequality represents all possible solutions of -6n < -12?
The inequality -6n < -12 has all numbers greater than 2 as its solution after isolating 'n'. We achieve this by dividing both sides by -6 and flipping the inequality sign.
Explanation:To solve this inequality, -6n < -12, you first need to isolate 'n' on one side of the inequality. We do this by dividing both sides of the inequality by -6. It's important to remember that when we divide or multiply an inequality by a negative number, we need to flip the direction of the inequality sign. So, the inequality would become n > 2. This means that all numbers greater than 2 are the solutions of the inequality.
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during a softball game kay hit a fly ball the function f(x) = -16t^2 + 64t + 4 describes the height of the softball in feet. make a table of values for the function and then graph it.
The graph is attached.
To graph a parabola we need to know the following:
- If the parabola is open upwards or downwards
- They axis intercepts (if they exist)
- The vertex position (point)
We are given the function:
[tex]f(t)=-16t^{2}+64t+4[/tex]
Where,
[tex]a=-16\\b=64\\c=4[/tex]
For this case, the coefficient of the quadratic term (a) is negative, it means that the parabola opens downwards.
Finding the axis interception points:
Making the function equal to 0, we can find the x-axis (t) intercepts, but since the equation is a function of the time, we will only consider the positive values, so:
[tex]f(t)=-16t^{2}+64t+4\\0=-16t^{2}+64t+4\\-16t^{2}+64t+4=0[/tex]
Using the quadratic equation:
[tex]\frac{-b+-\sqrt{b^{2}-4ac } }{2a}=\frac{-64+-\sqrt{64^{2}-4*-16*4} }{2*-16}\\\\\frac{-64+-\sqrt{64^{2}-4*-16*4} }{2*-16}=\frac{-64+-\sqrt{4096+256} }{-32}\\\\\frac{-64+-\sqrt{4096+256} }{-32}=\frac{-64+-(65.96) }{-32}\\\\t1=\frac{-64+(65.96) }{-32}=-0.06\\\\t2=\frac{-64-(65.96) }{-32}=4.0615[/tex]
So, at t=4.0615 the height of the softball will be 0.
Since we will work only with positive values of "x", since we are working with a function of time:
Let's start from "t" equals to 0 to "t" equals to 4.0615.
So, evaluating we have:
[tex]f(0)=-16(0)^{2}+64(0)+4=4\\\\f(1)=-16(1)^{2}+64(1)+4=52\\\\f(2)=-16(2)^{2}+64(2)+4=68\\\\f(3)=-16(3)^{2}+64(3)+4=52\\\\f(4.061)=-16(4.0615)^{2}+64(4.0615)+4=0.0034=0[/tex]
Finally, we can conclude that:
- The softball reach its maximum height at t equals to 2. (68 feet)
- The softball hits the ground at t equals to 4.0615 (0 feet)
- At t equals to 0, the height of the softball is equal to 4 feet.
See the attached image for the graphic.
Have a nice day!
Write an equation of each line that passes through the following points in slope-intercept form:
P (4, 1) and Q (3, –5)
help me please
Answer:
y = 6x - 23Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points P(4, 1) and Q(3, -5). Substitute:
[tex]m=\dfrac{-5-1}{3-4}=\dfrac{-6}{-1}=6[/tex]
The refore we have the equation:
[tex]y=6x+b[/tex]
Put the coordinates of the point P(4, 1) to the equation:
[tex]1=6(4)+b[/tex]
[tex]1=24+b[/tex] subtract 24 from both sides
[tex]-23=b\to b=-23[/tex]
Finally we have the equation:
[tex]y=6x-23[/tex]
I(5,3), j(5,-3), and L(-4,3) are three vertices of rectangles ljkL. What are the coordinates of the fourth vertex,of rectangle ljkL
Check the picture below.
The adult population of a town in 2000 was 400. The child population of the town in 2000 was 120. Both the adult and child populations increased by the same percent from 2000 to 2010. If the adult population in 2000 was 500, how many children lived in the town then?
Answer:
150
Step-by-step explanation:
500 is 125% of 400 (500/400) so you need to get what 125% of 120 is
120 x 1.25 =150
^number of children ^125% as a decimal
To find the number of children after the same percent increase in population as the adults, calculate a 25% increase based on the adult growth from 400 to 500. Applying this to the original child population (120), there were 150 children in 2010.
The question pertains to the percent increase in population and requires finding the number of children in a town given the increase in adult population. Specifically, the child population in 2000 was 120, and the adult population increased from 400 to 500 from 2000 to 2010. Assuming that the child population increased by the same percent as the adult population, we need to calculate this percentage increase and then apply it to the number of children to find the updated child population in 2010.
To find the percentage increase in the adult population:
Calculate the increase by subtracting the original number from the new number (500 - 400 = 100).Divide the increase by the original number (100 / 400 = 0.25).Convert the decimal to a percentage by multiplying by 100 (0.25 × 100 = 25%).Since the child population increased by the same percentage, we then:
Apply the 25% increase to the original child population (120).Multiply 120 by 0.25 to find the increase (120 × 0.25 = 30).Add the increase to the original child population (120 + 30 = 150).Therefore, there were 150 children in the town in 2010.
equivalent expressions 36 + 18x
Answer:
An equivalent expression is 18(2 + x)
Step-by-step explanation:
To find this, look for the greatest common factor. Since both terms are divisible by 18 equally, we take 18 out of each term. Then we divide both terms by 18 and express in a parenthesis.
18(2 + x)
The answer is there
Simplify √ 105 ..................................
Answer:
Simplify √ 105
A. 2√ 7
B. 2√ 3
C. √ 105
D. √ 42
Step-by-step explanation:
Answer:
[tex]\sqrt{105}[/tex]
Step-by-step explanation:
I'm not 100% sure why, but I looked it up on a scientific calculator.
Hope it helps, : )
.:!LightningBug!:.
HELP URGENT! WILL GIVE BRAINLIEST!!
1) What is the value of 8!?
A) 8
B) 64
C) 512
D) 40,320
2) What is the value of 5P5?
A) 5
B) 25
C) 120
D) 125
3) What is the value of 8P4?
A) 40,320
B) 1,680
C) 32
D) 24
4) What is the value of 7P7?
A) 1
B) 14
C) 49
D) 5,040
5) Four out of nine performers will be chosen to in a row on stage. How many ways can the 4 performers stand in a row?
A) 362,880
B) 347,760
C) 15,120
D) 3,024
The solutions for the given problems involving factorials and permutations are 8! = 40,320, 5P5 = 120, 8P4 = 1,680, 7P7 = 5,040 and the number of arrangement for 4 performers out of 9 is 3,024.
Explanation:The subject here is mathematics, specifically factorials and permutations. Factorials are represented by the symbol '!'. The factorial of a number n is the product of all positive integers less than or equal to n. For example, 8! = 8*7*6*5*4*3*2*1 = 40,320.
Permutations refer to the number of ways a set of objects can be arranged. 'nPn' always equals to the factorial of n, therefore 5P5 equals to 5! = 5*4*3*2*1 = 120 and 7P7 equals to 7! = 7*6*5*4*3*2*1 = 5,040.
'nPm' equals to n factorial divided by (n-m) factorial. So, 8P4 equals to 8!/(8-4)! = (8*7*6*5)/1 = 1,680.
For the last question, the number of ways 4 performers can stand in a row out of 9, is calculated as a permutation of '9P4' (because the order of performers matters). Thus, it will be 9!/(9-4)! = 9*8*7*6 = 3,024.
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which sentence is true about a ray?
A. a ray is formed by lines that do not cross each other.
B. A ray is formed by an endpoint and a line is starting at the endpoint and going to forever in one direction.
C. a ray is formed by two lines that cross at one point.
D. a ray is formed when two points on a line are labeled
Answer:
B. A ray is formed by an endpoint and a line is starting at the endpoint and going to forever in one direction.
Step-by-step explanation:
Given choices are :
A. a ray is formed by lines that do not cross each other.
B. A ray is formed by an endpoint and a line is starting at the endpoint and going to forever in one direction.
C. a ray is formed by two lines that cross at one point.
D. a ray is formed when two points on a line are labeled
Now we need to determine about which sentence is true about a ray.
We know that a ray has one fixed end point and other point moves infinitely then correct choice is :
B. A ray is formed by an endpoint and a line is starting at the endpoint and going to forever in one direction.
a drone costs 300 plus 25 for tax for each set of extra propellers. what is the cost of a drone and 4 extra set of propellers
Answer:
400
Step-by-step explanation:
The cost is arrived to by adding the initial cost of the drone to the total cost of all the extra propellers. The cost of per propeller due to tax being 25 we get the following expression.
That is: 300+ 4(25)
=400
Multiply (x^2+3x+4)(3x^2-2x+1)
Answer: option B
Step-by-step explanation:
To solve this exercise you must apply the proccedure shown below:
- Apply the Distributive property (Remember that when you multiply two powers with the same base, you must add the exponents).
[tex]b^m*b^n=b^{(m+n)}[/tex]
- Add the like terms.
Therefore, you obtain that the product is:
[tex](x^2+3x+4)(3x^2-2x+1)=3x^4-2x^3+x^2+9x^3-6x^2+3x+12x^2-8x+4\\=3x^4+7x^3+7x^2-5x+4[/tex]
Answer:
B
Step-by-step explanation:
When multiplying [tex](x^2+3x+4)(3x^2-2x+1)[/tex], we can use the distributive property of multiplication over addition:
[tex](x^2+3x+4)(3x^2-2x+1)=x^2\cdot 3x^2+x^2\cdot (-2x)+x^2\cdot 1+3x\cdot 3x^2+3x\cdot (-2x)+3x\cdot 1+4\cdot 3x^2+4\cdot (-2x)+4\cdot 1=3x^4-2x^3+x^2+9x^3-6x^2+3x+12x^2-8x+4.[/tex]
Now group the like terms:
[tex]3x^4-2x^3+x^2+9x^3-6x^2+3x+12x^2-8x+4=3x^4+(-2x^3+9x^3)+(x^2-6x^2+12x^2)+(3x-8x)+4=3x^4+7x^3+7x^2-5x+4.[/tex]
Plz, help with this! Find the area of the parallelogram.
Answer:
192 cm²
Step-by-step explanation:
The area (A) of a parallelogram is calculated using the formula
A = bh ( b is the base and h the perpendicular height )
here b = 24 and h = 8, hence
A = 24 × 8 = 192 cm²
what is the exact volume email of the cylinder
Answer:
A. V=BH
Step-by-step explanation:
The exact volume email of the cylinder in the image is 324π in³.
This is calculated using the formula for the volume of a cylinder:
Volume = πr²h
where:
π is a mathematical constant with the approximate value of 3.14
r is the radius of the cylinder
h is the height of the cylinder
In the image, the radius of the cylinder is 3 in and the height is 6 in. Therefore, the volume of the cylinder is:
Volume = π(3 in)²(6 in)
Volume = π(9 in²)(6 in)
Volume = 54π in³
However, the image also contains the text 324π in³.
This is the correct volume of the cylinder, as it takes into account the fact that the cylinder is hollow.
Therefore, the exact volume email of the cylinder in the image is 324π in³.
For similar question on exact volume.
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HELP ME PLZ AS SOON AS POSIBLE
IS THIS RIGHT
YES IT IS RIGHT.YOU ARE RIGHT
Answer:
Should be A pretty sure
Step-by-step explanation:
find the polynomial standard form of -5q^2(-q-5)
Answer:
5q^3+25q^2
Step-by-step explanation:
Dan and David win some money and share it in the ratio 5:4. Dan gets £8 more than David. How much did David get?
URGENT PLEASE ANSWER AS SOON AS POSSIBLE
Answer:
David：£32
Dan：£40
Step-by-step explanation:
A company owns rental properties and must pay for repairs and upkeep. If the monthly maintenance costs have an average of $3500.00 and a standard deviation of $257.00, give the range of costs the company can count on having to pay about 95% of the time.
Given is - the monthly maintenance costs have an average of $3500 and a standard deviation of $257. This means that around 95% of the distributed data lies within the ranges of -257 to +257 of the given standard deviation.
Hence, range becomes :
[tex]3500-257=3243[/tex] and [tex]3500+257=3757[/tex]
Thus, the range is (3243 , 3757)
Answer:
(2996.28, 4003.72)
is 95% range.
Step-by-step explanation:
Given is -
the monthly maintenance costs have an average of $3500 and a standard deviation of $257.
If X denotes the monthly maintenance costs of the company then
X is N(3500,257)
To find out 95% of the range we have Z critical = 1.96
So lower bound of range[tex]= 3500-1.96*257[/tex] and
Upper bound [tex]= 3500+1.96*257[/tex]
Hence, range becomes :
(2996.28, 4003.72)
Tristan rode his bike 3 2/3 miles on Saturday he rode 1 4/5 Mi on Sunday how many more miles did make ride on Saturday then on Sunday
Use the equation below to find y, if m=4, x = 3, and b=11.
Y = mx + b
Answer:
y = 23
Step-by-step explanation:
Assuming the equation not below is y = mx + b form...
m = 4
x = 3
b = 11
y = 4(3) + 11
y = 12+ 11
y = 23
The required value of y = 23.
Given - m = 4
x = 3
b = 11
equation is the relationship between variable and represented as is example of polynomial equation.
given equation
y = mx + b
y = 4x3 + 11
y = 12+11
y = 23
Thus, the required value of y = 23
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How can I find this answer
she can buy b and e because they are less than 50 dollars
what number of cakes sold is an outlier?
9, it’s further from the common area of plots
Answer:
9
Step-by-step explanation:
an outlier is an observation point that is distant from other observations
Determine whether the relation is a function {(8, 0), (5, 4), (9, 3), (3, 8)}
Answer: It is a function.
Step-by-step explanation:
By definition, a function is a relation in which the input value (the x value) has one and only one output value (value of y).
The first number of each ordered pair is the input value and the second number of each ordered pair is the output value.
As you can see, the inputs value of the relation given in the problem have one and only one output value. Therefore, you can conclude that the relation is a function.
Which inequality is equivalent to 3+4/x>=x+2/x
Answer:
The first alternative is correct
Step-by-step explanation:
We move all the expressions to the left hand side of the inequality then combine like terms using lcm;
[tex]\frac{3}{1}+\frac{4}{x}-\frac{x+2}{x}\geq0\\\\\frac{3x+4-(x+2)}{x}\geq0\\\frac{2x+2}{x}\geq0[/tex]
Answer:
the first one
Step-by-step explanation:
Express the left side as a single fraction
3 + [tex]\frac{4}{x}[/tex]
= [tex]\frac{3x+4}{x}[/tex], hence
[tex]\frac{3x+4}{x}[/tex] ≥ [tex]\frac{x+2}{x}[/tex]
Subtract [tex]\frac{3x+4}{x}[/tex] from both sides
0 ≥ [tex]\frac{x+2}{x}[/tex] - [tex]\frac{3x+4}{x}[/tex]
0 ≥ [tex]\frac{-2x-2}{x}[/tex]
Multiply both sides by - 1, remembering to reverse the inequality symbol as a consequence
0 ≤ [tex]\frac{2x+2}{x}[/tex], hence
[tex]\frac{2x+2}{x}[/tex] ≥ 0
I need help. what is 9x12+16-22?
Answer:
102
Step-by-step explanation:
9*12=108
108+16=124
124-22=102
I hope this helps!
Answer:
The final answer is 102
Step-by-step explanation:
It is given that, 9 x 12 + 16 - 22
It is a simple mathematics problem,
First we have to multiply 9 and 12 , then the resultant is added to 16 and 22 is subtracted from the final result.
To solve 9 x 12 + 16 - 22
9 x 12 + 16 - 22 = (9 x 12 ) + 16 - 22
= 108 + 16 - 22 = 124 - 22 = 102
Therefore the final answer is 102
Mrs. Eskew saved her money for 37 years and had $2,119,784 in the bank. She used her money to go a vacation for a month and spent $278,389. How much did she have left after her vacation?
Mrs. Eskew will have $1,841,395 left after subtracting the vacation expense of $278,389 from her initial savings of $2,119,784.
The student is asking how much money Mrs. Eskew will have left after spending part of her savings on a vacation. To find out, we simply need to subtract the amount spent on the vacation from the total amount she had saved. Mrs. Eskew started with $2,119,784 in the bank. After spending $278,389 on her vacation, we can calculate her remaining balance as follows:
$2,119,784 - $278,389 = $1,841,395.
Therefore, Mrs. Eskew will have $1,841,395 left after her vacation.
What would be the coordinates of the image if this pre-image is reflected across the x-axis?
(-2, 2), (1, 1), (3, 1), (2, 4)
(2, -2), (-1, 1), (-3, -1), (-2, -4)
(-2, 2), (1, -1), (3, 1), (2, 4)
(-2, -2), (-1, 1), (-3, -1), (-2, -4)
Answer:
The vertices of the pre-image are (-2, -2), (1, 1), (3, -1), and (2, -4).
Since the pre-image is reflected across the x-axis, leave each x-coordinate the same, and change the sign of each y-coordinate.
The vertices of the new image are (-2, 2), (1, -1), (3, 1), and (2, 4).
The width of a rectangle, in feet, is represented by (3x-1.5). The length of the rectangle, in feet, is represented by (1.25x+3). Find the perimeter of the rectangle.
Answer:
P = 8.5 x + 3 ft
Step-by-step explanation:
To find the perimeter, we use the formula
P =2(l+w) where l is the length and w is the width
P =2 (1.25x+3 + 3x-1.5)
Combine like terms
P = 2( 4.25x +1.5)
Distribute the 2
P = 8.5 x + 3 ft
The perimeter of the rectangle in terms of x is [tex]\( {\frac{17}{2}x + 3} \)[/tex].
Given the width of the rectangle is (3x - 1.5) feet and the length is (1.25x + 3) feet, we can substitute these expressions into the perimeter formula.
First, let's express the width and length in terms of xwith rational numbers to avoid dealing with decimals:
Width [tex]\( w = 3x - \frac{3}{2} \)[/tex]
Length [tex]\( l = \frac{5}{4}x + 3 \)[/tex]
Now, we can calculate the perimeter:
[tex]\( P = 2(l + w) \)\\ \( P = 2 \left( \left( \frac{5}{4}x + 3 \right) + (3x - \frac{3}{2}) \right) \)\\ \( P = 2 \left( \frac{5}{4}x + 3 + 3x - \frac{3}{2} \right) \)\\ \( P = 2 \left( \frac{5}{4}x + 3x + 3 - \frac{3}{2} \right) \)\\ \( P = 2 \left( \frac{5}{4}x + \frac{12}{4}x + \frac{6}{2} - \frac{3}{2} \right) \)\\ \( P = 2 \left( \frac{17}{4}x + \frac{3}{2} \right) \)\\ \( P = 2 \times \frac{17}{4}x + 2 \times \frac{3}{2} \)\\ \( P = \frac{34}{4}x + 3 \)\\ \( P = \frac{17}{2}x + 3 \)[/tex]
perimeter = [tex]\( {\frac{17}{2}x + 3} \)[/tex].
A house has increased in value by 36% since it was purchased. If the current value is $578,000 , what was the value when it was purchased?
I hope this helps :)