Final answer:
To make a 40-ounce mixture that is 60% fruit juice, equal amounts (20 ounces each) of 20% fruit juice and 100% fruit juice should be used.
Explanation:
Calculating the Fruit Juice Mixture
To solve this problem, we'll use a system of equations. Let's assume that the amount of 20% fruit juice used is x ounces, and the amount of 100% fruit juice used is y ounces. We are trying to make 40 ounces of a mixture that is 60% fruit juice.
First, the total amount of the mixture should be 40 ounces:
x + y = 40
Second, the total percentage of fruit juice in the mixture should be 60%:
0.20x + 1.00y = 0.60 * 40
Now, let's solve these equations step-by-step:
From the first equation, we can say y = 40 - x.
Substitute y in the second equation: 0.20x + 1.00(40 - x) = 24.
Simplify: 0.20x + 40 - x = 24.
Combine like terms: 40 - 0.80x = 24.
Subtract 40 from both sides: -0.80x = -16.
Divide both sides by -0.80 to find x: x = 20.
Substitute x back into y = 40 - x to find y: y = 20.
Therefore, to achieve a 60% fruit juice mixture, 20 ounces of the 20% fruit juice and 20 ounces of the 100% fruit juice should be combined.
Which expression does the fraction 3/8 represent?
1.8/3 2.3-8 3. 3/8 4. 3*8
Answer:
Im gonna guess and say it is answer 3.
Step-by-step explanation:
Jayla buys and sales
Answer:
There is no question
Step-by-step explanation:
The graph represents function 1, and the equation represents function 2: Function 1 A coordinate plane graph is shown. A horizontal line is graphed passing through the y-axis at y = 3. Function 2 y = 5x + 4 How much more is the rate of change of function 2 than the rate of change of function 1? 2 3 4 5
Answer its 5
Step-by-step explanation:
look it up theirs others with this question :)
Answer:
D. 5
Step-by-step explanation:
got it right n the test
PLS HELP!!
A circle is centered at point (-7,-1) and passes through the point (8,7).
The radius of the circle is _____ units. The point (-15,___) lies on this circle.
Answer:
Part 1) The radius of the circle is [tex]17\ units[/tex]
Part 2) The points (15,14) and (-15,-16) lies on this circle
Step-by-step explanation:
Part 1
we know that
The distance between the center of the circle at point (-7,-1) and the point (8,7) is equal to the radius of the circle
so
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]r=\sqrt{(7+1)^{2}+(8+7)^{2}}[/tex]
[tex]r=\sqrt{(8)^{2}+(15)^{2}}[/tex]
[tex]r=\sqrt{289}}[/tex]
[tex]r=17\ units[/tex]
Part 2
we know that
If the point (-15,y) lies on the circle, then the ordered pair must be satisfy the equation of the circle
The equation of the circle is equal to
[tex](x+7)^{2}+(y+1)^{2}=17^{2}[/tex] -----> equation of the circle in center radius form
substitute the value of x=-15 in the equation and solve for y
[tex](-15+7)^{2}+(y+1)^{2}=289[/tex]
[tex]64+(y+1)^{2}=289[/tex]
[tex](y+1)^{2}=289-64[/tex]
[tex](y+1)^{2}=225[/tex]
[tex]y+1=(+/-)15[/tex]
[tex]y=-1(+/-)15[/tex]
so
[tex]y=14[/tex]
[tex]y=-16[/tex]
therefore
The points (15,14) and (-15,-16) lies on this circle
see the attached figure to better understand the problem
Answer:
Part 1) The radius of the circle is
Part 2) The points (15,14) and (-15,-16) lies on this circle
Step-by-step explanation:
Would you use more centimeters or meters to measure the length of a car? Explain.
Answer:
Meters
Step-by-step explanation:
Because centimeters are to small to be a reasonable measurement for a car so you would have to use meters
The members of a track team ran laps around their school. They ran a total of 6 3/4, each lap was 7/8 miles long. How many laps did they run?
Answer:
[tex]7\frac{5}{7}\ laps[/tex]
Step-by-step explanation:
we know that
To find out how many laps they ran, divide the total distance by the distance of one lap
step 1
Convert the total distance from mixed number to an improper fraction
[tex]6\frac{3}{4}\ mi=\frac{6*4+3}{4}=\frac{27}{4}\ mi[/tex]
step 2
Find the number of laps
[tex]\frac{(27/4)}{(7/8)}=\frac{54}{7}\ laps[/tex]
step 3
Convert the number of laps to mixed number
[tex]\frac{54}{7}=\frac{49}{7}+\frac{5}{7}=7\frac{5}{7}\ laps[/tex]
Factor completely.
x2−8x+15
Do not include any spaces in your answer. Use parentheses to separate your factors. A sample answer might be (x+1)(x-4).
Question 5 options:
The answer is :
(x+5)(x+3)
In order to solve x 2 + 12 x = 2 by completing the square, what value must be added to both sides?
Answer:
36
Step-by-step explanation:
x^2 + 12 x = 2
In order to complete the square we need to add ( b/2)^2 to each side where b is the coefficient of the x term
b=12
12/2 = 6
6^2 = 36
We need to add 36 to each side
m∠A=(x+45)°,
mKE =(x+20)°,
mEW=(3x)° ,
Find: mKW.
Answer:
The measure of the arc KW is [tex]160\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<A=\frac{1}{2}(arc\ KE+arc\ EW)[/tex]
substitute the values and solve for x
[tex](x+45)\°=\frac{1}{2}(x+20+3x)\°[/tex]
[tex](2x+90)\°=(4x+20)\°[/tex]
[tex]4x-2x=90\°-20\°[/tex]
[tex]2x=70\°[/tex]
[tex]x=70\°/2=35\°[/tex]
Find the measure of the arc KW
[tex]arc\ KW=(arc\ KE+arc\ EW)=(4x+20)\°[/tex]
substitute the value of x
[tex]arc\ KW=4(35\°)+20\°=160\°[/tex]
What is the answer????
ANSWER
f(x) is an odd function.
EXPLANATION
The given function is symmetric with respect to the origin.
Hence it is an odd function.
We can also see from the graph that,
[tex]f(1) = 2[/tex]
and
[tex]f( - 1) = - 2[/tex]
This implies that,
[tex]f( - 1) = - f(1)[/tex]
Since
[tex]f( - x) = - f(x)[/tex]
the function is odd.
The correct answer is A.
A cafeteria used 5 gallon of milk in preparing lunch. How many 1-quart containers of milk did the cafeteria use?
Answer:
20 quarts of milk used
Step-by-step explanation:
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷since there are 4 quarts in a gallon, you have 20 quarts.
There are four quarts in a gallon, so you times 4 and 5. The result you get is 20 quarts.
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
DOGE
What is 3/5+3/10 as a fraction
Answer:
9/10
Step-by-step explanation:
convert 3/5 to 6/10
6/10+3/10=9/10
The value of fraction will be;
⇒ 9/10
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The fraction is,
⇒ 3/5 + 3/10
Now,
Since, The fraction is,
⇒ 3/5 + 3/10
Solve as;
⇒ 3/5 + 3/10
⇒ 6/10 + 3/10
⇒ (6 + 3) / 10
⇒ 9 / 10
Thus, The value of fraction = 9/10
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Someone help me please
Answer:
Look at the picture
Step-by-step explanation:
[tex]\log_ab=c\iff a^c=b\\\\\text{Therefore}\\\\f(x)=b^x\to y=b^x\\\\\text{find}\ f^{-1}(x).\ \text{Exchange}\ x\ \text{and}\ y\ \text{and solve for}\ y:\\\\b^y=x\qquad\text{logarithm iwth base b of both sides}\\\\\log_bb^y=\log_b(x)\qquad\text{use}\ \log_ab^m=m\log_ab\\\\y\log_bb=\log_b(x)\qquad\text{use}\ \log_aa=1\\\\y=\log_b(x)\\\\f^{-1}(x)=\log_b(x)\to g(x)=f^{-1}(x)\\\\\text{Then:}\ f(a)=b\to g(b)=a[/tex]
Last week byron bought 5 containers of yogurt and spent 12.88 on other groceries this week Cassandra bought 3 containers if the same yogurt and spent 11.50 on the other groceries how much more money did byron spent than Cassandra?
Answer:1.33
Step-by-step explanation:
Byron spent $1.38 more than Cassandra on other groceries, as we subtracted Cassandra's spending ($11.50) from Byron's ($12.88) to determine the difference.
The question asks us to determine how much more money Byron spent compared to Cassandra on their grocery shopping. To find this out, we need to compare the total amount of money each person spent. We have the cost of other groceries for each person, but the cost of yogurt is not given. To solve this problem, we just need to compare the cost of other groceries since that is the only information provided.
Byron spent $12.88 on other groceries.
Cassandra spent $11.50 on other groceries.
To find out how much more Byron spent, we subtract Cassandra's total from Byron's total:
$12.88 - $11.50 = $1.38
Therefore, Byron spent $1.38 more than Cassandra on other groceries.
Angle 1 and angle 2 are complementary the measure of angle 2 is 15 degrees less than twice the measure of angle 1 what is the measure of each angle plz help me
The measure of Angle 1 is 35 degrees and the measure of Angle 2 is 55 degrees.
Explanation:When two angles are complementary, their measures add up to 90 degrees. Let's define these two angles as follows: Angle 1 = x and Angle 2 = 2x - 15 (since it is 15 degrees less than twice the measure of Angle 1). You set up an equation based on the fact that the two angles add up to 90 degrees: x + 2x - 15 = 90. Solving this equation, you get 3x = 105, so x = 35. Thus, Angle 1 = 35° and Angle 2 = 2(35) - 15 = 55°.
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The sum of three numbers is 83. The second number is 5 less than the first. The third number is 2 times the first. what are the numbers
Answer:
22, 17, and 44.
Step-by-step explanation:
So what you do is you will have three equations that we will put together.
1. x. The first number is x because they don't give us anything about it.
2. x-5. It says that the second number is 5 less than the first number.
3. 2x. It says that the third number is 2 times the first number.
x+x-5+2x=83.
4x-5=83.
4x=88.
x=22.
That is the first number. To find the second and third, you will plug 22 into the x.
2. 22-5=17.
3. 2(22)=44.
22, 17, 44 are your answers.
Final answer:
By setting up equations based on the information provided, we solved for x as the first number and then used it to determine the other two numbers. The three numbers are 22, 17, and 44.
Explanation:
The sum of three numbers is 83. This is the first equation we'll use to solve the problem. Let's denote the first number as x. According to the question, the second number is 5 less than the first, which gives us the second equation y = x - 5. For the third number, it is given as 2 times the first, hence the third equation is z = 2x.
Now, we'll combine all three equations to express the sum:
x + (x - 5) + 2x = 83
Simplifying, we combine like terms:
4x - 5 = 83
Adding 5 to both sides gives us:
4x = 88
Dividing by 4, we find the first number:
x = 22
Now we'll use x to find the other two numbers:
y = 22 - 5 = 17
z = 2 × 22 = 44
Therefore, the three numbers are 22, 17, and 44.
2. The two figures are similar.
a) Write the similarity statement.
b) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
c) What is the scale factor? Explain.
Answer:
Part a) [tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]
Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure.(the scale factor is greater than 1)
Part c) The scale factor is [tex]3[/tex]
Step-by-step explanation:
Part a) Write the similarity statement
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
so
[tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]
substitute the values
[tex]\frac{9}{27}=\frac{12}{36} =\frac{15}{45'}[/tex]
[tex]\frac{1}{3}=\frac{1}{3} =\frac{1}{3'}[/tex] ----> is true
therefore
the figures are similar
Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure. (the scale factor is greater than 1)
Part c) we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z------> the scale factor
x-----> corresponding side of the image
y------> corresponding side of the original figure
so
[tex]z=\frac{x}{y}[/tex]
we have
[tex]x=A'B'=27\ units[/tex]
[tex]y=AB=9\ units[/tex]
substitute
[tex]z=\frac{27}{9}=3[/tex]
The scale factor is greater than 1
therefore
Is an enlargement
Answer:(A) ab/a’b’=bc/b’c’=ac/a’c’ (B) Figure a’b’c’ is an enlargement because it increase it’s sides larger than 1. (C) So we have to divide to get the scale factor for both of these figures 18/6=3 then you found the scale factor 3.
Step-by-step explanation:
Ty is painting a rectangle that is 10 inches long and 7 inches high. What attributes of a rectangle can you share with Ty to help him paint his rectangle?
A rectangle is a quadrilateral with four 90-degree angles. The opposite sides are equal, with two sides being the length (10 inches) and the other two being the width (7 inches).
Explanation:Ty, when painting a rectangle, it's important to understand its attributes. A rectangle is a quadrilateral, meaning it has four sides. Two of these sides will be 10 inches long, and the other two will be 7 inches high - these are referred to as the 'length' and 'width'. Additionally, all interior angles of a rectangle are 90 degrees, which is a right angle. So when you are painting, make sure each corner forms a 90-degree angle. Also, the opposite sides of a rectangle are always equal. If any of these attributes are not followed, the figure will not be a rectangle.
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Mary has rehearsed her ballet solo for five and a half hours. A week from now, she wants to have rehearsed at least a total of nineteen and a half hours. If she rehearses for the same amount of time each day for the next 7 days, at least how many hours must she rehearse per day?
Answer:
2 hours per day
Step-by-step explanation:
19.5 - 5.5 = 14
14 / 7 = 2 hours per day
Mary needs to rehearse 2 hours per day for the next 7 days to meet her total rehearsal goal.
To calculate the total rehearsal time for Mary:
She has rehearsed for 5.5 hours.
She wants to rehearse a total of 19.5 hours.
Therefore, 19.5 - 5.5 = 14 hours
She needs to rehearse an additional 14 hours in the upcoming week.
To find out how many hours Mary must rehearse per day in the next 7 days:
14 / 7 = 2 hours/day
What is 20 % of 275
Answer:
55
Step-by-step explanation:
So first of all I would convert the 20% to a decimal by dividing by 100 and you get 0.2
Then multiply 0.2 and 275 together and you get 55
If you are unsure on an answer, a way to quickcheck is setting the answer over your total
55
-------- = 0.2 ⇒ which equals 20%
275
Answer: 55
Step-by-step explanation:
First, find 10% of 275 (move the decimal place back once).
We now have 27.5.
Now, multiply 27.5 by 2 because we are finding 20%
So, 27.5 x 2= 55
x+y=70
65x+15y=2400
solve by substitution
please show work very important thank you so much
The solution is
x = 27 and y = 43
Step-by-step explanation:See the image
I don’t know how to start it.
Answer:
36°
Step-by-step explanation:
∠A + ∠B + ∠C = 180°
∠A:∠B:∠C = 8:10:12 = 8x:10x:12x
8x + 10x + 12x = 180
20x = 180
x = 9
∠A = 8x = 8 × 9 = 72°
∠B = 10x = 10 × 9 = 90°
∠C = 12x = 12 × 9 = 108°
∠C - ∠A = 108 -72 = 36 °
The difference between the largest and the smallest angle is 36°.
Your friend pulls out a huge home baked pizza from the oven and tells you the area is a=625(pi)cm2. What is the diameter of this pizza
Answer:
Diameter = 50 cm
Step-by-step explanation:
We are given that the area of a home bakes pizza is [tex] 6 2 5 \pi cm ^ 2[/tex].
Here, we are assuming that the pizza is circular and we know that the area of a circle is given by: [tex]\pi r^2[/tex]
So equating the given value to find the value of the diameter.
[tex]\pi r^2[/tex] [tex]=625\pi[/tex]
[tex]r^2=625[/tex]
[tex]r=\sqrt{625}[/tex]
[tex]r=25[/tex]
If the radius is 25 cm, then diameter = 25 × 2 = 50 cm
Answer:
The diameter of the pizza= 50 cm
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where r is the radius of circle
It is given that, area of pizza is 625π cm²
A pizza is like a circle.
Find the radius of pizza
Area = πr²= 625π cm²
r² = 625π/π = 625
r = √625 = ±25
radius r = 25cm
To find the diameter of pizza
Diameter = 2r = 2 * 25 = 50 cm
What is the approximate circumference of a circle with the diameter of 6
Circumference= [tex]2\pi r[/tex]
If the diameter is 6 the radius will be 3
[tex]2\pi (3)[/tex]
Circumference= 18.85
Hey there!
The formula for circumference is πd, where d is diameter.
We are given that the diameter is 6, so the circumference is 6π.
However, we are asked for the approximate circumference, not the exact.
So, let's use 3.14 as π and simplify.
6 x 3.14 = 18.84
The approximate circumference of a circle with the diameter of 6 is 18.84.
Hope this helps!
Can anyone help me please?
Which expression can be used to find the area of a circle with a diameter of 30 cm?
a. π • 30
b. 2 • π • 15
c. π • 30^2
d. π • 15^2
Answer:
its b
Step-by-step explanation:
Answer:
2 × pi or (π) × 15 = 30 cm
Step-by-step explanation:
Hodaya is drawing a map of the trials in the canyon near her house. She knows that the distance from the first creek crossing to the second creek crossing is 1.8 miles. If every 3 inches on the map represents 0.75 of a mile, how far apart will the two creek crossing be on the map, to the nearest tenth of an inch.
Answer:
It would roughly be 7 inches and 1/5 of an inch.
I hope this answer helped you! If you have any further questions or concerns, feel free to ask! :)
Step-by-step explanation:
Two creek crossings are separated by distance A = 7.2 inches on the map.
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
The information is ,
Let's say the equation looks like this: A
Right now, A is valued at
The two stream crossings' separation is indicated on the map as A.
And on the chart, 3 inches equals 0.75 miles, therefore the distance between the two stream crossings is 1.8 miles.
hence, 3 / 0.75 inches Equals 1 mile.
In the map, 1 mile equals 4 inches after simplifying the calculation.
The two creek crossing's distance on the map is therefore equal to 1.8 x 4.
The two stream crossings will be separated by 7.2 inches on map A.
Hence, the distance on the map is 7.2 inches.
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The area of a circular trampoline is 112.07 square feet. What is the radius
Answer: The correct answer is B. 5.97 feet
Step-by-step explanation:
Formula⇒A=π r2
* Hopefully the work helps:) Mark me the brainliest;)!!!
Answer:
5.97 feet
Step-by-step explanation:
Set up your equation as 112.07 = Pi*r^2
To simplify, divide 112.07 by Pi or an approximation of it and then find the square root of your answer.
112.07 = Pi*r^2
112.07/Pi = r^2
(112.07/Pi)^0.5=r
Three years ago, Sherman was twice as old as Clive. If Clive’s present age is c, which expression represents Sherman’s present age in terms of Clive’s age?
A.
2c − 3
B.
2c + 6
C.
2(c − 3)
D.
2c + 3
URGENT!!! Write the product as a sum or difference.
6cos(21t)sin(20t)
Select the correct answer below:
3cos(t)−3cos(41t)
3sin(41t)−3sin(t)
3sin(t)−3cos(41t)
3cos(41t)−3sin(t)
3cos(41t)+3cos(t)
3sin(41t)+3sin(t)
Answer:
3 sin(41t) - 3 sin(t)
Step-by-step explanation:
The general formula to convert the product of the form cos(a)sin(b) into sum is:
cos(a) sin(b) = 0.5 [ sin(a+b) - sin (a-b) ]
The given product is:
6 cos(21t) sin(20t) = 6 [ cos(21t) sin(20t) ]
Comparing the given product with general product mentioned above, we get:
a = 21t and b = 20t
Using these values in the formula we get:
6 cos(21t) sin(20t) = 6 x 0.5 [ sin(21t+20t) - sin(21t-20t)]
= 3 [sin(41t) - sin(t)]
= 3 sin(41t) - 3 sin(t)
Therefore, second option gives the correct answer
What is the product?
Answer:
So option B is the correct answer .
Step-by-step explanation:
Since it is the multiplication of 1 X 3 matrix to 3 X 3 order matrix,
so the resultant product should be 1 X 3 because when we multiply two matrices it is the condition that if A is of order p X q and B is of order q X r,
the product matrix (suppose C ) will be of order p X r.
so the product will be
= [-1*3+2*2+4*0 -1*6+2*4+4*6 -1*1+2*0+4*2]
= [ 1 26 7] .