Answer:
5 liters of water.
Step-by-step explanation:
Let [tex]y[/tex] be the liters of water that must be added to 15 liters of 40% sugar syrup.
Initially, we have [tex]0.4(15)=6[/tex] liters of sugar syrup, and since adding water does not add any new syrup, the amount of sugar syrup must be the same after the water has been added. After the water has been added, 30% of the solution is sugar syrup, or
[tex]Sugar\:syrup =0.3(15+y)[/tex]
And since this must equal the amount of syrup we had before:
[tex]0.3(15+y)=0.4(15)[/tex]
[tex]4.5+0.3y=6[/tex]
[tex]0.3y=1.5[/tex]
[tex]\boxed{y=5}[/tex]
Thus, 5 liters of water must be added to obtain 30% sugar syrup.
Answer:
5 liters of water
Draw the image of the figure after the given rotation about the origin
Answer:
The image would just be upside down. C would stay where it is, A would be at the point (2, -3), D would be at the point (0, -1), and B would be at the point (4, -1)
Step-by-step explanation:
the perimeter of a rectangle is 32 centimeters. The length is 1 cm more than twice the width. Find the dimensions of the rectangle.
Answer: length = 11cm , width = 5cm
Step-by-step explanation:
The formula for calculating the perimeter of a rectangle is given by :
P = 2 ( L + w )
The length is 1 cm more than twice the width implies:
L = 1 + 2w
substituting into the formula , we have
32 = 2 ( 1 + 2w + w )
32 = 2 ( 1 + 3w)
32 = 2 + 6w
32 - 2 = 6w
30 = 6w
Therefore :
w = 5
then
L = 1 + 2w
L = 1 + 2 ( 5 )
L = 1 + 10
L = 11
Therefore , the length is 11 cm and the width is 5cm
483.6 is what percent of 180
Answer:
We assume, that the number 180 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 180, so we can write it down as 100%=180.
4. We know, that x% equals 483.6 of the output value, so we can write it down as x%=483.6.
5. Now we have two simple equations:
1) 100%=180
2) x%=483.6
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=180/483.6
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for 483.6 is what percent of 180
100%/x%=180/483.6
(100/x)*x=(180/483.6)*x - we multiply both sides of the equation by x
100=0.37220843672457*x - we divide both sides of the equation by (0.37220843672457) to get x
100/0.37220843672457=x
268.66666666667=x
x=268.66666666667
now we have:
483.6 is 268.66666666667% of 180
A restaurant offers hamburgers with one, two, or three patties. Let X represent the number of patties a randomly chosen customer orders on their hamburger. Based on previous data, here's the probability distribution of X along with summary statistics:
X=# of patties 1 2 3
P(X) 0.40 0.50 0.10
Mean: μX=1.7
Standard deviation: σX≈0.67
The total price of each burger is set at $2 per patty. Let T represent the total price a randomly chosen customer pays for their burger. Find the mean of T
Answer:
The mean price a randomly chosen customer pays for her or his burger is US$ 3.40
Step-by-step explanation:
Let's find out the mean of T (total price a randomly chosen customer pays for their burger), this way:
Mean of T = 0.4 * $ 2 + 0.5 * $ 4 + 0.1 * $ 6
Mean of T = 0.8 + 2 + 0.6
Mean of T = US$ 3.40
The mean price a randomly chosen customer pays for her or his burger is US$ 3.40
In the given case, the mean of T is [tex]\[ \boxed{3.4} \text{ dollars} \][/tex]
To find the mean of T, which represents the total price a randomly chosen customer pays for their burger, we can use the relationship between T and X.
Given that the price per patty is $2, the total price T can be expressed as:
T = 2X
We are given the mean number of patties [tex]\( \mu_X = 1.7 \).[/tex]
The mean of a transformed variable can be found using the linear transformation properties of the mean.
Specifically, if [tex]\( T = aX + b \),[/tex] then:
In this case, since T = 2X , we have a = 2 and b = 0.
Therefore:
[tex]\[ \mu_T = 2\mu_X + 0 = 2 \times 1.7 = 3.4 \][/tex]
So, the mean of T is- [tex]\[ \boxed{3.4} \text{ dollars} \][/tex]
If you pass a road test, you will get your drivers license. Tamara passed her road test
Final answer:
The statement establishes the condition for obtaining a driver's license which is passing a road test. Since Tamara passed her test, according to the given logic, she will receive her driver's license. The subject matter is related to Law.
Explanation:
The question provided is related to the process of acquiring a driver's license and is rooted in understanding conditional statements, which are often associated with the field of logic, a branch of philosophy. However, the most practical context here is Law, as it involves legal criteria for obtaining a driver's license. The logic presented in the statement is straightforward: If you pass a road test, you will get your driver's license. Tamara passed her road test. Based on this information, we can deduce that Tamara will get her driver's license because she has fulfilled the condition set by the law or the driving authority responsible for issuing licenses.
2 pluse 2 what does that equal
Answer:
The answer is 4. as 2 plus 2 is equal to 4
Step-by-step explanation:
2+2=4
Together, a house and the lot it is on costs $40,000. If the house costs seven times as much as the lot, how much does the lot cost?
The lot costs 5000 dollars.
Step-by-step explanation:
The cost of a House and the lot = $40,000.
Let us assume the cost of lot as 'x'
Given that, The cost of the house is 7 times as much as the lot.
Therefore, The cost of the house= 7x
The cost of both the house and the lot= x + 7x
$40,000 = x + 7x
40,000 = 8x
x = 40,000/8
x = 5,000
The lot costs $5000.
The cost of the lot is determined by setting up an equation using the information given in which the house costs seven times as much as the lot and they total $40,000. This equation, when solved, shows the cost of the lot as $5,000.
Explanation:To solve this problem, we need to set up an equation using the information given. Let's use x to represent the cost of the lot. According to the question, the house costs seven times as much as the lot, so the house costs 7x. Together, they cost $40,000. So we have the equation:
x + 7x = $40,000
We simplify this to 8x = $40,000. Then, when we solve for x by dividing both sides of the equation by 8, we find that x, or the cost of the lot, is $5,000.
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So I need help with 8/576. I was hoping if you could
Answer:
1/72
Step-by-step explanation:
C divided by 9 is less than or equal to -4 solve the inequality and graph the solution
Answer:
Step-by-step explanation:
c/9≤-4
multiply both sides of the inequality by 9(c/9×9≤4×9) to isolate the 9 being divided by c(inverse operation):
c≤-36
that is the inequality.
to graph it, draw a number line with a closed circle on -36. then, draw an arrow on the line going toward the negative numbers, or the left side to demonstrate that c is less than or equal to -36.
The solution to the inequality is C ≤ -36, and the graph shows all values to the left of -36 on a number line.
Explanation:To solve the inequality "C divided by 9 is less than or equal to -4," you can follow these steps:
- Start with the inequality: C/9 ≤ -4.
- To isolate C, you can multiply both sides of the inequality by 9 (since dividing by 9 is the opposite of multiplying by 9). Be sure to do the same operation to both sides to maintain the inequality's balance.
C/9 * 9 ≤ -4 * 9
This simplifies to:
C ≤ -36
So, the solution to the inequality is C ≤ -36.
To graph this solution on a number line, you can:
Draw a number line.
Mark a point at -36 (you can label it as C ≤ -36).
Shade the part of the number line to the left of -36 to indicate that C is less than or equal to -36.
This graph visually represents the solution to the inequality: C is any number less than or equal to -36.
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Ethan buys a new phone. It cost 75$. He will pay for this on his 1st bill.
His phone plan charges 0.06 dollars per minute on the phone.
'He has $90 to spend on his 1st bill. How long can he be on his phone to not go over his budget?
A)80 minutes
B)250 minutes
C) 1050 minutes
D)1250 minutes
Answer:250
Step-by-step explanation: Subtract 90 from 75 which is 15 then divide 15 by .06 which is 250
Answer:a
Step-by-step explanation:
a
Which expression is equivalent to -3(4x-2)-2x
Answer:
-14x+6
Step-by-step explanation:
-3(4x-2)-2x
-12x+6-2x
-12x-2x+6
-14x+6
Which statement describes whether a right triangle can be formed using one side length from each of these squares? 3 squares have areas of 64 inches squared, 225 inches squared, and 289 inches squared.
A: Yes, a right triangle can be formed because the sum of the areas of the two smaller squares does not equal the area of the largest square.
B:Yes, a right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square.
C:No, a right triangle cannot be formed because the sum of the areas of the two smaller squares does not equal the area of the largest square.
D:No, a right triangle cannot be formed because the sum of the areas of the two smaller squares equals the area of the largest square.
Answer:
the correct answer is B
"yes, a right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square."
Step-by-step explanation:
took the test, got it right. nice day folks. amos @kay_flores575
Right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square.
What is area?
" Area is the space occupied by any two dimensional object on the flat surface."
What is right angled triangle?"Right angled triangle is a two dimensional figure with three sides and three vertices . Any one of the interior angle should be equals to 90°."
Formula applied
Pythagoras theorem
a² = b² +c²
According to the question,,
Three square with areas 64inches , 225 inches and 289 inches.
We can write this areas as
289 = 225 + 64
⇒(17)² = (15)² + (8)²
Applying formula we can say that a right triangle can be formed.
Hence, we conclude that Option B is correct.
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two positive improper fractions are multiplied. Is the product sometimes, always, or never less than 1? Explain
What is the following product? (5 square root 2-4 square root 3) (5 square root 2-4 square root 3)
Answer:
(5 square root 2-4 square root 3) (5 square root 2-4 square root 3)
= 98 - 40[tex]\sqrt{6}[/tex]
Step-by-step explanation:
i) (5[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{3}[/tex]) × (5√2 - 4√3)
=(5[tex]\sqrt{2}[/tex] × 5[tex]\sqrt{2}[/tex]) - (5[tex]\sqrt{2}[/tex] × 4[tex]\sqrt{3}[/tex]) - (4[tex]\sqrt{3}[/tex] × 5[tex]\sqrt{2}[/tex]) + (4[tex]\sqrt{3}[/tex] × 4[tex]\sqrt{3}[/tex])
= 50 - 20[tex]\sqrt{6}[/tex] - 20[tex]\sqrt{6}[/tex] + 48
= 98 - 40[tex]\sqrt{6}[/tex]
Answer:
98 - 40√6
Step-by-step explanation:
The words expression can be represented as follows:
(5√2 - 4√3) (5√2 - 4√3)
The question is to find the products .
(5√2 - 4√3) (5√2 - 4√3)
Multiply through to open the bracket
25 × 2 - 20√6- 20√6 + 16 × 3
50 - 20√6 - 20√6 + 48
50 - 40√6 + 48
50 + 48 - 40√6
98 - 40√6
Which would you use to estimate the demand for a product at various prices?
A. a demand table
B. a demand chart
C. a demand schedule
Answer:
I wanna say B. not 100% sure
sorry if wrong
Step-by-step explanation:
Answer:
Step-by-step explanation:
The correct answer is B
A circular path 3 feet wide has an inner diameter of 350 feet. How much farther is it around the outer edge of the path than around the inner edge? Round to nearest hundredth. Use 3.14 for π.
Answer:
18.84 feet farther is it around the outer edge of the path than around the inner edge.
Step-by-step explanation:
Given:
A circular path 3 feet wide has an inner diameter of 350 feet.
Use 3.14 for π.
Now, to find how much farther is it around the outer edge of the path than around the inner edge.
Width of the circular path = 3 feet.
Inner diameter of circular path = 350 feet.
So, to get the inner radius we divide the inner diameter of circular path by width of circular path:
[tex]350\div 3[/tex]
[tex]=116.67\ feet.[/tex]
r = 116.67 feet.
Now,
Thus, the outer radius is:
[tex]116.67+3[/tex]
[tex]=119.67\ feet.[/tex]
R = 119.67 feet.
Now, we get the circumference of inner edge and outer edge:
Circumference of inner edge = 2πr.
[tex]Circumference\ of\ inner\ edge=2\times 3.14\times 116.67[/tex]
[tex]=732.69\ feet.[/tex]
Circumference of outer edge = 2πR.
[tex]Circumference\ of\ outer\ edge=2\times 3.14\times 119.67[/tex]
[tex]Circumference\ of\ outer\ edge=751.53\ feet.[/tex]
Now, to get how much farther is it around the outer edge of the path than around the inner edge:
Circumference of outer edge - circumference of inner edge.
[tex]751.53-732.69[/tex]
[tex]=18.84\ feet.[/tex]
Therefore, 18.84 feet farther is it around the outer edge of the path than around the inner edge.
The difference in distance around the outer edge of the path compared to the inner edge is 18.84 feet.
To find how much farther it is around the outer edge of the circular path compared to the inner edge, we need to calculate the circumferences of both the inner and outer edges and find the difference.
1. First, calculate the inner circumference using the inner diameter of 350 feet:
Inner Circumference = π × inner diameter = 3.14 × 350 = 1099 feet.
2. Next, calculate the outer diameter by adding the width of the path to each side of the inner diameter:
Outer Diameter = inner diameter + 2 × width of the path = 350 + 2 × 3 = 356 feet.
3. Then, calculate the outer circumference using the outer diameter:
Outer Circumference = π × outer diameter = 3.14 × 356 = 1117.84 feet.
4. Finally, find the difference between the outer and inner circumferences:
Difference = Outer Circumference - Inner Circumference = 1117.84 - 1099 = 18.84 feet.
Therefore, it is 18.84 feet farther around the outer edge of the path than around the inner edge.
Maureen bought a coat. She was excited because it was on sale, so she paid $15.25 less than the original price. She paid $48.75 for the coat. Write and solve an equation to determine the original price. Let p represent the original price. It's getting cold outside! The temperature dropped steadily at a rate of about 4 degrees every hour. If the temperature dropped a total of 22 degrees, how many hours have passed? Let h represent the number of hours
Answer:
$33.50 for coat, 5.5 hours
Step-by-step explanation:
For the coat, since it was on sale, then it would be $48.75-$15.25=p=$33.50.
If the temperature drops 4 degrees every hour, if t dropped 22 degrees, then you would do 22 divided by 4, to find out how many hours it had dropped for. 22 divided by 4=h=5.5 or 5 1/2.
How do I rotate a point by 180 degrees clockwise?
180 degrees is half of a circle, and clockwise means turning in the direction a clock does - right.
So a point would be turned right halfway around.
In a two-digit number the tens digit is four less than the units digit. Seven times the tens digit plus five times the units digit is equal to 56. Find the digits.
The digits of the number are 7 and 3
Step-by-step explanation:
In a two-digit number:
The tens digit is four less than the units digitSeven times the tens digit plus five times the units digit is equal to 56We need to find the digits
Assume that the unit digit is x and the ten digit is y
∵ x represents the unit digit
∵ y represents the ten digit
∵ The ten digit is four less than the unit digit
- That means subtract 4 from the unit digit to get the ten digit
∴ y = x - 4 ⇒ (1)
∵ Seven times the tens digit plus five times the units digit is
equal to 56
- That means multiply the ten digit by 7 and the unit digit by
5 and add the two products and equate the sum by 56
∴ 7y + 5x = 56 ⇒ (2)
Now we have a system of equations to solve it
Substitute y in equation (2) by equation (1)
∵ 7(x - 4) + 5x = 56
- Simplify the left hand side
∴ 7x - 28 + 5x = 56
- Add the like terms in the left hand side
∴ 12x - 28 = 56
- Add 28 to both sides
∴ 12x = 84
- Divide both sides by 12
∴ x = 7
- Substitute the value of x in equation (1) to find y
∵ y = 7 - 4
∴ y = 3
∴ The number is 37
The digits of the number are 7 and 3
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What is the experimental probability of drawing a red marble, given the following results?
Marble Color Blue Green Red
Times Drawn 8
Answer:
7/20..i hope its correct
Step-by-step explanation:
all = 8+5+7
=20
red marbles / all = 7/20
Answer:
7/20
Step-by-step explanation:
Maria has 15 dollars that she can spend at the movies. A movie ticket costs 7 dollars. Which inequality represents the greatest amount of money, f, Maria can spend on food and drinks?
The inequality which represents the greatest amount of money, f, Maria can spend on food and drinks is f < 8.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given that,
Maria has 15 dollars that she can spend at the movies.
Total amount Maria has = $15
Cost of a movie ticket = $7
Let f be the amount that she can spend maximum on food and drinks.
f < remaining amount
f < 15 - 7
f < 8
Hence the inequality is f < 8.
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Use a calculator to find the approximate value of cos-1(0.55).
Answer:
The approximate value is [tex]56.63^o[/tex]
Step-by-step explanation:
Let
[tex]\theta[/tex] ----> the measure of angle in degrees
we have that
[tex]cos(\theta)=0.55[/tex]
Using a calculator
Find the measure of angle [tex]\theta[/tex]
[tex]\theta=cos^{-1}(0.55)[/tex]
[tex]\theta=56.63^o[/tex]
Solve x^5 - 8x^4 + 22x^3 - 26x^2 + 21x - 18 -0.
Answer:
= x^5 - 8x^4 + 22x^3 - 26x^2 + 21x - 18
Step-by-step explanation:
x^5 - 8x^4 + 22x^3 - 26x^2 + 21x - 18 - 0
Since all the exponents have different bases, the only thing we can do is subtract 18 from 0, which gives us an answer of:
= x^5 - 8x^4 + 22x^3 - 26x^2 + 21x - 18
10. Find the equation of a line with a slope of O and that passes through
the point (-2,5).
Answer:
Y=5
Step-by-step explanation:
If the slope is 0 it will be a line parallel to the x axis with a constant value of y and since we know it passes through a point with y coordinate of 5 we know that the constant value of y is 5
I need help simplifying #6
Answer:
The simplified expression is [tex]\frac{12x^8y^5}{5z^4}[/tex]
Therefore [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]
Step-by-step explanation:
Given expression is [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}[/tex]
To simplify the given expression as below :
[tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}[/tex]
[tex]=\frac{12x^5y^9z^{-8}}{5x^{-3}y^4z^{-4}}[/tex]
[tex]=\frac{12x^5y^9z^{-8}x^3y^{-4}z^4}{5}[/tex] ( by using the property [tex]a^{m}=\frac{1}{a^{-m}}[/tex] )
[tex]=\frac{12x^5.x^3.y^9.y^{-4}z^{-8}z^4}{5}[/tex]
[tex]=\frac{12}{5}x^{5+3}.y^{9-4}.z^{-8+4}[/tex] ( by using the property [tex]a^m.a^n=a^{m+n}[/tex] )
[tex]=\frac{12}{5}x^8y^5z^{-4}[/tex]
[tex]=\frac{12x^8y^5}{5z^4}[/tex] ( by using the property [tex]a^{-m}=\frac{1}{a^m}[/tex] )
[tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]
The simplified expression is [tex]\frac{12x^8y^5}{5z^4}[/tex]
Therefore [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]
Answer:
Therefore,
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]
Step-by-step explanation:
Simplify
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}[/tex]
Solution:
Using the Identities
[tex]1.\ x^{-a}=\dfrac{1}{x^{a}}[/tex]
[tex]2.\ \dfrac{1}{x^{-a}}=x^{a}[/tex]
[tex]3.\ \dfrac{x^{a}}{x^{b}}=x^{(a-b)}[/tex]
Therefore,
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{24x^{(5+3)}y^{(9-4)}z^{(-8+4)}}{10}[/tex]
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{2\times 12x^{8}y^{5}z^{-4}}{2\times 5}[/tex]
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]
Therefore,
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]
Select all of the following that are ordered pairs of the given function.
f(x)=3-2x
Answer:
(-1,5), (0,3), (2,-1)
Step-by-step explanation:
We can just test out each of the answers as follows:
Let's start with (-2,-1). We see that f(-2) = 3 - 2x(-2) = 3+4 = 7, so this is not a solution.
Now let's work out the rest:
f(-1) = 3 - 2x(-1) = 3 + 2 = 5. So yes (-1,5) is a solution
f(0) = 3-2x0 = 3 so yes, (0,3) is a solution
f(1) = 3 - 2x1 = 1 so (1,0) is not a solution
f(2) = 3 -2x2 = -1, so yes (2,-1) is a solution
Marilyn has 7/8 yard of ribbon. What is the maximum number of 1/16 yard long pieces Marilyn can cut from this ribbon
Marilyn can cut 14 equal pieces
Solution:
Given that, Marilyn has 7/8 yard of ribbon
To find: Maximum number of 1/16 yard long pieces Marilyn can cut from this ribbon
From given information,
[tex]\text{Total length of ribbon } = \frac{7}{8} \text{ yard }[/tex]
[tex]\text{Length of 1 piece } = \frac{1}{16} \text{ yard }[/tex]
Number of pieces that can be cut from total length of ribbon is found by dividing the total length of ribbon by length of 1 piece
Therefore,
[tex]\text{Number of pieces } = \frac{\text{Total length of ribbon}}{\text{Length of 1 piece }}[/tex]
Substituting the values, we get
[tex]\text{Number of pieces } = \frac{\frac{7}{8}}{\frac{1}{16}}\\\\\text{Number of pieces } = \frac{7}{8} \times \frac{16}{1}\\\\\text{Number of pieces } = 14[/tex]
Thus 14 pieces of ribbon can be cut
What is the solution for x in the equation?
9x - 20 - 4x = 40
Answer:
Step-by-step explanation:
X=12
Answer:
x= 12
Step-by-step explanation:
9x-20-4x=40
add 20 on both sides
40+20=60
combine like terms
9x-4x=5x
divide 60 by 5
=12
Maggie found the area of the irregular figure by dividing it into a triangle and a rectangle.
Answer:
33cm^2
Step-by-step explanation:
Rectangle:
5 x 6 = 30
Triangle:
1 side 6 - 3 = 3
2 side 7- 5 = 2
area of right triangle:
A = (ab) / 2
A = (3 * 2) / 2
A = 3
sum:
30 + 3 = 33
Answer:
swallla swalla swalla swalla drake swalla drake swalla swalla swalla freaky freaky gurlll
Step-by-step explanation:
what is the equation of the line that passes through (0,2) and (4,6)