Answer:
[tex]6\frac{2}{3}[/tex] ounces of mixed nuts will be in each bag.
Step-by-step explanation:
unit rate is defined as the rates are expressed as a quantity of 1, such as 3 feet per second or 6 miles per hour, they are called unit rates.
Given the statement: Candy buys 20 ounces of mixed nuts. She puts an equal amount of ounces in each of 3 bags.
Total number of mixed nuts Candy buys = 20 ounces.
As she puts an equal amount of ounces in each of the 3 bags.
Unit rate per bag = [tex]\frac{20}{3} = 6\frac{2}{3}[/tex] ounces.
therefore, [tex]6\frac{2}{3}[/tex] ounces of mixed nuts will be in each bag.
the sum of 7 2/9 and 2 7/9 in simpliest form
Answer:
10
Step-by-step explanation:
7 2/9 + 2 7/9 common denominators already the same so add
7+2=9 first start with the whole number
2/9 + 7/9= 9/9 = 1 then add the fractions
9+1=10 then add the whole number and fraction
Answer:
10
Step-by-step explanation:
Part 1
Solve 1/2 + 1/2x = x^2 − 7x+10/4x by rewriting the equation as a proportion. Which proportion is equivalent to the original equation?
Answer is C) x+1/2x = x^2-7x+10/4x
*****
Part 2
Name the true solution(s) to the equation
Answer: x = 1 and x = 8
Name the extraneous solution(s) to the equation.
Answer: x = 0
Answer:
Part 1. [tex]\dfrac{x+1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]
Part 2. Solutions: [tex]x_1=1,\ x_2=8.[/tex]
Extraneous solution: [tex]x=0.[/tex]
Step-by-step explanation:
Part 1. You are given the equation
[tex]\dfrac{1}{2}+\dfrac{1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]
Note that
[tex]\dfrac{1}{2}+\dfrac{1}{2x}=\dfrac{x+1}{2x},[/tex]
then the equation rewritten as proportion is
[tex]\dfrac{x+1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]
Part 2. Solve this equation using the main property of proportion:
[tex]4x\cdot (x+1)=2x\cdot (x^2-7x+10),\\ \\2x(2x+2-x^2+7x-10)=0,\\ \\2x(-x^2+9x-8)=0.[/tex]
x cannot be equal 0 (it is placed in the denominator of the initial equation and denominator cannot be 0), so [tex]x=0[/tex] is extraneous solution to the equation.
Thus,
[tex]-x^2+9x-8=0,\\ \\x^2-9x+8=0,\\ \\x_{1,2}=\dfrac{9\pm\sqrt{(-9)^2-4\cdot 8}}{2}=\dfrac{9\pm7}{2}=1,\ 8.[/tex]
Part A: i forgot the question but i know its the third option (c)
Part B:
Solve the original equation by solving the proportion.
The solutions are: (1,6)
Part c:
Name the extraneous solution(s) to the equation
answer: Neither
These are for edu2020
In a circle with a radius of 36.9 m, an arc is intercepted by a central angle of 8π5 radians.
Use 3.14 for π and round your final answer
Answer:
185.39 m
Step-by-step explanation:
Central angle = 8π/5 radians
Let's convert radians to degrees.
Answer:
The length of arc is 185.39 m
Step-by-step explanation:
Given that in a circle with a radius of 36.9 m, an arc is intercepted by a central angle of [tex]\frac{8\pi}{5}[/tex] radians.
we have to find the arc length.
[tex]Radius=36.9 m[/tex]
[tex]\text{Central angle=}\frac{8\pi}{5}[/tex]
The arc length can be calculated by the formula
[tex]L=r\theta[/tex]
[tex]\text{where r is radius and }\theta \text{ is central angle in radians. }[/tex]
[tex]L=36.9 \times \frac{8\pi}{5}[/tex]
[tex]L=36.9 \times \frac{8\times 3.14}{5}[/tex]
[tex]L=\frac{926.928}{5}=185.3856\sim 185.39 m[/tex]
hence, the length of arc is 185.39 m
Henry is saving money for college. He earns $210 each week working part time after school and the weekends. Henry currently has $2,240 in savings. His parents put $100 in his savings account each week and he saves one-third of his paycheck each week. Which expression represents the situation? (n represents the number of weeks) A) 2,240 + 170n B) 2,240 + 310n C) 2,240 + 210n + 100n 3 D) 2,240 + 210n + 100n 3 Eliminate
The answer is 2,240 + 170n
2,240 in savings
210n
3
Henry saves each week
100n parents put in savings each week
thus,
2,240 + 210n
3
+ 100n
2,240 + 70n + 100n
2,240 + 170n
A cyclist rode at an average speed of 15 mph for 30 miles. How long was the ride? Question 6 options: 0.5 hours 1 hour 2 hours 3 hours
Answer:
2 hours
Step-by-step explanation:
using the relationship
distance = speed × time, then
time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{30}{15}[/tex] = 2 hours
It will take 2 hours to cover 30 miles so option (C) is correct.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
A cyclist rode at an average speed of 15 mph for 30 miles.
So,
15 miles ⇒ hour
Multiply by 2
2 hours ⇒ 30 miles.
Hence "It will take 2 hours to cover 30 miles".
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Plz help me with this :)
Part A:
The range is the difference between the highest and lowest values:
Highest value = 78
Lowest value = 40
Range = 78-40 = 38
Part B:
The interquartile range is the difference between Q1 and Q3.
Q1 is the middle value of the lower half and Q3 is the middle value of the upper half.
There are 11 total numbers, 40 , 64, 66, 67,67,68,69,70, 71, 72, 78
The median would be the middle value, 68, so the lower half would be the 5 numbers below 68: 40 , 64, 66, 67,67.
The middle value of those numbers would be 66
The upper half are the 5 numbers above 68: 69,70, 71, 72, 78.
The middle value of those numbers is 71
The interquartile range would be 71 - 66 = 5
Part C:
The interquartile range is the better measure.
What is the ratio of soccer balls to footballs?
A) 1 : 3
B) 2 : 4
C) 3 : 1
D) 4 : 2
Use the Polygon tool to draw the image of the given quadrilateral under a dilation with a scale factor of 34 and center of dilation (0, 0) .
Answer:
See attached diagram
Step-by-step explanation:
Given quadrilateral has vertices at points A(-8,4), B(4,-4), C(0,-8) and D(-4,-4).
A dilation with a scale factor of [tex]\dfrac{3}{4}[/tex] and a center of dilation (0,0) has a rule
[tex](x,y)\mapsto \left(\dfrac{3}{4}x,\dfrac{3}{4}y\right).[/tex]
Then
A(-8,4)→E(-6,3);B(4,-4)→F(3,-3);C(0,-8)→G(0,-6);D(-4,-4)→H(-3,-3).See attached diagram for details.
Remark: If a scale factor is 34, then the rule is (x,y)→(34x,34y) and image vertices have coordinates (-272,136), (136,-136), (0,-272), (-136,-136).
At the city museum, child admission is $6.10 and adult admission is $9.30 . On Sunday, four times as many adult tickets as child tickets were sold, for a total sales of $909.30 . How many child tickets were sold that day?
Answer:
21 child tickets
Step-by-step explanation:
For this problem, you'd use a system of equations.
First, define your variables.
x = # of child tickets sold
y = # of adult tickets sold
There were 4 times as many adult tickets (y) as child tickets (x) sold, so:
4 x = y
4 x - y = 0
93 (4 x - y = 0)
372 x - 93 y = 0
The total revenue was $909.30, adult tickets were $9.30 each, child tickets were $6.10 each, so:
6.10 x + 9.30 y = 909.30
10 (6.10 x + 9.30 y = 909.30)
61 x + 93 y = 9093
372 x - 93 y = 0
433 x = 9093
433 x / 433 = 9093 / 433
x = 21
Jimmy is trying to factor the quadratic equation $ax^2 + bx + c = 0.$ He assumes that it will factor in the form \[ax^2 + bx + c = (Ax + B)(Cx + D),\]where $A,$ $B,$ $C,$ and $D$ are integers. If $a = 4,$ and Jimmy wants to find the value of $A,$ what are the possible values he should check, in order to find $A$?
If
[tex]ax^2+bx+c=(Ax+B)(Cx+D)[/tex]
then
[tex]ax^2+bx+c=ACx^2+(AD+BC)x+BD[/tex]
[tex]\implies a=AC[/tex]
If [tex]a[/tex] is known and Jimmy wants to find [tex]A[/tex], then he has to know the value of [tex]C[/tex].
Answer:
possible value of A are 1, 2, 4
Step-by-step explanation:
Jimmy is trying to factor the quadratic equation ax^2 + bx + c = 0.
He assumes that it will factor in the form ax^2 + bx + c = (Ax + B)(C x + D)
Given a=4
We need to find the value of A
When we do factoring we use the factors of the numbers
(Ax+B)(Cx+D) is ACx^2 + ADx + BCx + BD
[tex]ax^2 + bx + c =ACx^2 + ADx + BCx + BD[/tex]
When a=4 then AC is also 4
A* C = 4
1 * 4= 4
2 * 2= 4
4 * 1 = 4
So possible value of A are 1, 2, 4
The scale factor of a large oil container to a small oil container is 0.075. The large oil container can carry 144,000cm^3 of oil.
How much oil can the small container carry?
A.) 10,800cm3
B.) 810 cm3
C.) 60.75cm3
D.) 0.075 cm3
The correct Answer is option (A).10,800 [tex]cm^3[/tex] oil can the small container carry.
To determine how much oil the small container can carry, given the scale factor and the capacity of the large container, follow these steps:
1. Identify the given values:
- Capacity of the large container: [tex]\( 144,000 \, \text{cm}^3 \)[/tex]
- Scale factor from large to small container: [tex]\( 0.075 \)[/tex]
2. Calculate the capacity of the small container:
- Use the formula: [tex]\[ \text{Capacity of small container} = \text{Capacity of large container} \times \text{Scale factor} \][/tex]
- Substitute the given values: [tex]\[ \text{Capacity of small container} = 144,000 \, \text{cm}^3 \times 0.075 \][/tex]
3. Perform the multiplication:
[tex]\[ 144,000 \times 0.075 = 10,800 \, \text{cm}^3 \][/tex]
Therefore, the capacity of the small container is:
[tex]\[ \boxed{10,800 \, \text{cm}^3} \][/tex]
If f(x)=2x+7 and g(x)=11x-4, find (f+g)x.
Answer:
(f+g)(x) = 13x + 3
Step-by-step explanation:
Rewrite f(x)=2x+7 and g(x)=11x-4 in columns, as follows:
f(x)=2x+7
+g(x)=11x-4
----------------
Now add each column separately.
f(x)+g(x) = (f+g)(x) ("the sum of functions f and g")
2x + 11x = 13x, and, finally, 7-4 = 3.
Therefore,
f(x)=2x+7
+g(x)=11x-4
----------------
(f+g)(x) = 13x + 3
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Factor x^2 + 25 in the complex numbers.
Answer: C
Step-by-step explanation:
x² + 25
= x² - (-25)
This can now be factored using the sum & difference formula:
a² - b² = (a - b)(a + b)√x² = x
√-25 = 5i
So, x² - (-25) = (x - 5i)(x + 5i)
The lengths of two sides of a triangle are 7 and 11. Which could not be the length of the third side?
5
10
12
19
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
5, 7, 11
5 + 7 = 12 > 11 CORRECT
7, 10, 11
7 + 10 = 17 > 11 CORRECT
7, 11, 12
7 + 11 = 18 > 12 CORRECT
7, 11, 19
7 + 11 = 18 < 19 INCORRECT
Answer: 19.Using the Triangle Inequality Theorem, the third side of the triangle must be less than the sum of other two sides and more than the absolute difference of the two sides. With the sides 7 and 11 given, the third side must be more than 4 but less than 18. Therefore, 19 cannot be the length of the third side.
Explanation:In mathematics, particularly in geometry, the length of the third side of a triangle when the lengths of two sides are known, can be determined by using the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides. In this case, the lengths of the two sides are given as 7 and 11. The sum of these two lengths is 18.
So the possible length of the third side must be less than 18 but more than the absolute difference of 7 and 11 (which is 4). Hence, the third side can be more than 4 and less than 18. Therefore out of the options provided, the value 19 could not be the length of the third side of the triangle.
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Which expression is equivalent to 5x - 5x + 3x - 3x?
A) -16x
B) -4x
C) 4x
D) 0 what the answer
Answer:
5x
Step-by-step explanation:
What is your real rate of return is your savings account pays 2.5% interest and inflation is at 1%
Answer:
1.5
Step-by-step explanation:
The real rate of return is calculated as the difference between rate of interest and the inflation.
so,Interest=2.5%
Inflation=1%
=2.5-1
=1.5%
Answer:
1.485 % ( approx )
Step-by-step explanation:
We know that,
[tex]\text{Real rate of return}=\frac{1+\text{Nominal rate}}{1+\text{Inflation rate}}-1[/tex]
Given,
Nominal rate = 2.5 % = 0.025
Inflation rate = 1 % = 0.01,
[tex]\implies \text{Real rate of return}=\frac{1+0.025}{1+0.01}-1[/tex]
[tex]=\frac{1.025}{1.01}-1[/tex]
[tex]=1.01485149-1=0.01485149\approx 0.01485[/tex]
Thus, the real rate of return is 0.01485 or 1.485 %.
There are 750 spectators in the stadium of which 420 of them are woman and the rest are man what percent are men
There are 750 spectators in the stadium. 420 of these spectators are women and the rest are men. What percent of the spectators are men.
The fraction [tex]\frac{420}{750}[/tex] represents the number of women in the stadium out of all the 750 people in the stadium. We can subtract 420 from 750 and we will get a difference of 330. Now we know that there are 330 men in the stadium.
The fraction [tex]\frac{330}{750}[/tex] represents the number of men at the stadium out of everyone. To find the percent of men at the stadium, we need to turn [tex]\frac{330}{750}[/tex] into a percent. [tex]\frac{330}{750}[/tex] reduced is [tex]\frac{11}{25}[/tex] because we are dividing both the numerator and denominator by the Greatest Common Factor of 330 and 750 using 30.
11 ÷ 25 = 0.44
0.44 × 100 = 44%
Therefore, 44% of the spectators in the stadium are men.
A basketball hoop is 10 feet high. Army is 5 feet tall. How many times is the basketball hoop than army
Answer:2 times
Step-by-step explanation:
i did the assinment
A box is shaped like a cube. The box has a length of 1 foot, a width of 1 foot, and aheight of 1 foot. What is the volume of the box.
Answer:
1 cubic foot
Step-by-step explanation:
Volume = length * width * height
= 1*1*1 = 1 ft^3
The volume of the given box shaped like a cube is 1 cubic foot.
We have given that,
The box has a length of 1 foot, a width of 1 foot, and a height of 1 foot.
What is the formula of the volume?Volume = length * width * height
Volume= 1*1*1
Volume= 1 ft^3
Therefore the volume of the given box shaped like a cube is 1 cubic foot.
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Wyatt is training for a race. He will run 3/4 of a mile a day for 8 days. How far will Wyatt run altogether?
Answer:
6 miles all together in them 8 days
Step-by-step explanation:
3/4 times 8
Answer:
6 miles in all
Step-by-step explanation:
3/4 *8 duh
True or false? I'm deductive thinking, you start with a given set of rules and conditions and determine what must be true as a consequence
Which property explains why these two expressions are equal?
-5 + (x + 4) = (-5 + 4) + x
A) Associative Property
B) Commutative Property
C) Distributive Property
D) Multiplicative Identity Property what the answer
Answer:
Associative property.
Step-by-step explanation:
Associative property implies that, for instance; no matter how the numbers are grouped in the sum involving (-5, x and 4), the result is the same.
Clark buys 2 gallons of paint for $ 16.39. What is the cost per pint of paint? Round your answer to the nearest cent if necessary .
Answer:
$1.02
Step-by-step explanation:
We are told that Clark buys 2 gallons of paint for $ 16.39.
To find the cost per pint of paint let us convert amount of paint in gallons.
1 gallon = 8 pints.
2 gallons= 8*2 pints= 16 pints.
Now let us find cost per pint of paint by dividing the total cost of paint by number of pints in 2 gallons.
[tex]\text{The cost per pint of paint}=\frac{16.39}{16}[/tex]
[tex]\text{The cost per pint of paint}=1.024375[/tex]
Upon rounding our answer to nearest cent we will get,
[tex]\text{The cost per pint of paint}=1.02[/tex]
Therefore, the cost per pint of paint is $1.02.
A line that intersects a circle at exactly one point is called a ______
Chord
Tangent
Secant
A line that intersects a circle at exactly one point is called a tangent.
What is a tangent to a circle?A line segment that touches a circle specified to only one point is called a tangent to that circle.
The point where it touches the circle is called the point of tangency.
We can see that point line segment PT is the tangent of our circle and point P is the point of tangency.
Therefore, A line that intersects a circle at exactly one point is called a tangent.
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the price of a pair of shoes increases from $52 10 $64. What i the percent increase?
Answer:
Step-by-step explanation:
Step 1: Calculate the change by subtracting old cost ($52) from the new cost ($64)
Step 2: Divide that change by the old cost ($52). You will get a decimal number
Step 3: Convert the decimal number to a percentage by multiplying by 100%
Which shape best describes the object generated when the rectangle is rotated about the axis?
hollow rectangular prism
hollow cylinder
solid cylinder
solid rectangular prism
If the shape shown is rotated about the axis, a solid cylinder would be formed.
What is a cylinder?A cylinder is a three dimensional shape (has length, width and height) which has two parallel bases joined by a curved surface, at a fixed distance.
If the shape shown is rotated about the axis, a solid cylinder would be formed.
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When a rectangle is rotated about an axis, it forms a solid cylinder.
Explanation:The shape that best describes the object generated when a rectangle is rotated about an axis is a solid cylinder. When a rectangle is rotated around an axis, it forms a three-dimensional shape that is similar to a cylinder. The base of the shape is a rectangle, and the height is equal to the length of the original rectangle. The shape has a curved surface and two circular faces at the top and bottom, just like a cylinder.
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Mrs.Padre drives 2 hours at a n average speed of 35 miles per hour then she drives 3 hours at a speed of 48 miles per hour what is her average speed for the whole trip
She drove 2 hours at 35 miles per hour for a total of 35 * 2 = 70 miles.
She drove 3 hours at 48 miles per hour for a total of 48 * 3 = 144 miles.
Her total miles were: 70 + 144 = 214.
Her total driving time was 3 + 2 = 5 hours.
Divide her total miles by total time for her average speed:
214 / 5 = 42.8 miles per hour average speed.
Not sure if you need to round the answer or not.
Mrs. Padre's average speed for the entire trip is 42.8 miles per hour, which is calculated by dividing the total distance (214 miles) by the total time (5 hours).
To determine Mrs. Padre's average speed for the whole trip, we need to use the formula for average speed:
Average speed = Total distance / Total time
First, we calculate the distance traveled during each part of the trip:
For the first part: 2 hours * 35 miles/hour = 70 milesFor the second part: 3 hours * 48 miles/hour = 144 milesNext, we sum up the total distance and total time:
Total distance = 70 miles + 144 miles = 214 milesTotal time = 2 hours + 3 hours = 5 hoursNow we can calculate the average speed:
Average speed = 214 miles / 5 hours = 42.8 miles per hour
The local gym charges members a monthly fee of $50 plus an additional $2 every time you want to use the pool. Let p represent the number of times you used the pool in one month and C represent the total cost for your monthly membership. Write an equation to find the total cost of your monthly membership to the gym.
Answer:
50+2p=C
Step-by-step explanation:
Answer: Our required equation to find the total cost of his monthly membership to the gym would be [tex]C=50+2p[/tex]
Step-by-step explanation:
Let C be the total cost for your monthly membership.
Let p be the number of times you used the pool in one month.
Cost of every time he want to use the pool = $2
Monthly fee = $50
According to question, it becomes,
[tex]C=50+2p[/tex]
Hence, our required equation to find the total cost of his monthly membership to the gym would be [tex]C=50+2p[/tex]
A car travels at an average speed of 45 miles per hour for 8 miles, reduces its speed by 15 miles per hour for the next 4 miles, and then returns to a speed of 45 miles per hour. How long does the car travel at the reduced speed?
Answer:
8 minutes
Step-by-step explanation:
time = distance/speed
A decrease of 15 mph from 45 mph means the speed on the second segment is 30 mph. Filling in the given values in the above equation, we have ...
... time = (4 mi)/(30 mi/h) = 4/30 h = 8/60 h × (60 min/h) = 8 min
PLEASE HELP!!!
Write the equation of the given line in standard form.
x = 3
Step-by-step explanation:"Standard form" is the form ...
... ax + by = c
where a, b, c are mutually prime integers. The coefficients a and b cannot both be zero. The leading coefficient must be positive. If "a" is zero, then the leading coefficient is "b".
So ...
... x = 3
is in standard form already. (a=1, b=0, c=3)
_____
Further comments on Standard Form
Of course, if the line has irrational slope or intercept, the coefficients cannot all be integers.
The order of the variables may be swapped, in which case the coefficient of y is the leading coefficient and must be positive.
This is the only way a vertical line can be written, as slope-intercept form is undefined for a vertical line.