32 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the pints of 60% pure fruit juice
0.60x + 0.35(40 - x) = 0.40(40)
x = 8
= 40 - 8 (pints of 35% juice)
= 32
Thus, 32 pints and 8 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.
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Solve for x. Please help me!!
Answer:
64 degrees
Step-by-step explanation:
90-32=58
180-58-58=64
Answer:
x = 64°
Step-by-step explanation:
supplementary angles is two angles whose sum is 180° (straight line)
90 + 32 = 122°
To find angle A,
A + 122 = 180
subtract 122 from both sides,
A + 122 - 122 = 180 - 122
A = 58°
This is an isosceles triangle, two angles are equal in measure (A and B). These angles lie opposite to the equal sides.
A triangles angles add up to 180°
58° + 58° + x° = 180°
116° + x = 180°
116 - 116 + x = 180 - 116
x = 64°
I need help with number 10 please
Answer:
Liz
Step-by-step explanation:
if the chart is correct only 3 people spent more than 2 1/2 hours on homework when 9 people spent less than 2 1/2 hours on homework
Solve the equation on the
interval [0, 2π).
√2 cos x - 1 = 0
Answer:
Step-by-step explanation:
[tex]\sqrt{2} cos x-1=0\\cos x=\frac{1}{\sqrt{2} } =cos (\frac{\pi }{4} ),cos (2\pi -\frac{\pi }{4} )\\cos x=cos(2n\pi +\frac{\pi }{4} ),cos(2n\pi +\frac{7\pi }{4} )\\x=2n\pi +\frac{\pi }{4} ,2n\pi +\frac{7\pi }{4} \\n=0\\x=\frac{\pi }{4} ,\frac{7\pi }{4}[/tex]
The area of a rectangle is 44m2 , and the length of the rectangle is 3m
less than double the width. Find the dimensions of the rectangle.
Answer:
width=11/2
length=8
Step-by-step explanation:
44=(2w-3) x w area for a rectangle (44) = the length (2w-3) times the width (w)
44=2w^2 - 3w distribute
2w^2-3w-44 = 0 subtract 44 from both sides
(w+4)(2w-11) factor
width=11/2
(11/2 x 2) - 3
length = 8
Consider the table that includes the input and output values of a function.
Which best describes the constant difference for the function?
a constant second difference of –6
a constant second difference of 8
a constant third difference of –6
a constant third difference of 8
The first option is correct and it best describes the constant difference for the function as a constant second difference of –6.
What is a function?A function f(x) is the relation between a set of inputs resulting and producing the desired output value of y for each input.
From the given information:
x f(x) first difference second difference third difference
-2 0 - - -
-1 -10 (-10-0)/-1--2 = -10 - -
0 -12 (-12 - 10)/0 -- 1= -2 (-2-10)/2 = -6 -
1 -12 (-12--12)/1-0 = 0 (0-2)/2 = -1 (-1+6)/2 = 5/2
2 -16 (-16--12)/2-1 = -2 (-2-0)/2 = -1 (-1+1)/2 = 0
Therefore, we can conclude that the constant difference for the function is a constant second difference of –6.
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Answer:
A
Step-by-step explanation:
Which pair represents equivalent ratios?
A.2/3,95
B.5/8,15/21
C.3/12,6/18
D.4/10,12/30
Answer:
D
Step-by-step explanation:
We can test each pair making each ratio into its simplest form.
For A 2/3 is already in its simplest form and 9/15=3/5. they are not equivalent.
For B, 5/8 is already in its simplest form and 15/21=5/7. they are not equivalent.
For C, 3/12=1/4, and 6/18=1/3. They are not equivalent.
For D, 4/10=2/5, and 12/30=2/5. They are equivalent.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Let's see which ones are equivalent}\\\huge\textbf{to each other, shall we?}\\\\\\\huge\textbf{We will convert the given fractions to}\\\huge\textbf{decimals or make the fractions on the}\\\huge\textbf{right to easier to solve or comparing it}\\\huge\textbf{to the one on the left.}[/tex]
[tex]\huge\textsf{Option A.}[/tex]
[tex]\mathsf{\dfrac{2}{3}, \dfrac{9}{15}}[/tex]
[tex]\mathsf{\dfrac{2}{3}}\\\\\mathsf{= 2\div3}\\\\\mathsf{= 0.66\overline{6}7}\\\\\\\mathsf{\dfrac{9}{15}}\\\\\mathsf{= \dfrac{9\div3}{15\div3}}\\\\\mathsf{= \dfrac{3}{5}}\\\\\\\\\mathsf{\dfrac{2}{3} \neq \dfrac{9}{15}}[/tex]
[tex]\huge\textsf{Option B.}[/tex]
[tex]\mathsf{\dfrac{5}{8}, \dfrac{15}{21}}[/tex]
[tex]\mathsf{\dfrac{5}{8}}\\\\\mathsf{= 5\div8}\\\\\mathsf{= 0.625}\\\\\\\mathsf{\dfrac{15}{21}}\\\\\mathsf{= \dfrac{15\div3}{21\div3}}\\\\\mathsf{= \dfrac{5}{7}}\\\\\mathsf{\dfrac{5}{8}\neq \dfrac{15}{21}}[/tex]
[tex]\huge\textsf{Option C.}[/tex]
[tex]\mathsf{\dfrac{3}{12}.\dfrac{6}{18}}[/tex]
[tex]\mathsf{\dfrac{3}{12}}\\\\\mathsf{= 3 \div 12}\\\\\mathsf{= 0.25}\\\\\\\\\mathsf{\dfrac{6}{18}}\\\\\\\mathsf{= \dfrac{6\div3}{18\div3}}\\\\\\\mathsf{= \dfrac{2}{6}}\\\\\\\mathsf{= \dfrac{2\div2}{6\div2}}\\\\\\\mathsf{= \dfrac{1}{3}}\\\\\\\mathsf{\dfrac{3}{12}\neq \dfrac{6}{18}}[/tex]
[tex]\huge\textsf{Option D.}[/tex]
[tex]\mathsf{\dfrac{4}{10}, \dfrac{12}{30}}[/tex]
[tex]\mathsf{\dfrac{4}{10}}\\\\\mathsf{= 4\div10}\\\\\mathsf{= 0.40}\\\\\\\mathsf{\dfrac{6}{18}}\\\\\mathsf{= \dfrac{12\div3}{30\div3}}\\\\\mathsf{= \dfrac{4}{10}}\\\\\mathsf{= \dfrac{4}{10}}\\\\\mathsf{= \dfrac{4\div2}{10\div2}}\\\\\mathsf{= \dfrac{2}{5}}\\\\\mathsf{\dfrac{4}{10} = \dfrac{12}{20}}[/tex]
[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ D. \dfrac{4}{10}, \dfrac{12}{30}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What is the range of the function y=3√x+8?
O-∞
O-8
O 0≤y<∞
O 2≤y<∞
Answer: 0 ≤ y < ∞
Step-by-step explanation:
First, let us graph the function. See attached.
-> If I graphed the formatting of the square root sign incorrectly, please let me know so I can fix the answer.
The range of the function is all of the function's output values. In this case, all of the y values.
0 ≤ y < ∞
A soccer league has 160 players. Of those players 50% are boys. How many boys are in the soccer league?
Answer:
80 boys
Step-by-step explanation:
160 total players
50% are boys
50% of 160 is 80
the model of an airplane has a wingspan of 20 inches. the model has a scale of 1 inch = 4 feet. what is the wingspan of the actual airplane? show your example
The wingspan of the actual aeroplane is 80 feet.
Given, that the model of an aeroplane has a wingspan of 20 inches and the scale factor is 1 inch = 4 feet.
We need to find what is the wingspan of the actual aeroplane.
What is a scale factor?The scale factor is a way to compare figures with commonly described but differing scales or measurements.
The wingspan of the actual aeroplane = The wingspan of the model aeroplane × Scale factor.
⇒The wingspan of the actual aeroplane = 20 × 4 feet = 80 feet.
Therefore, the wingspan of the actual aeroplane is 80 feet.
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Quadrilateral ABCD is inscribed in this circle. What is the measure of angle C?
Answer:
[tex]\boxed{\bf \angle \: C = 62^{o} }[/tex]
Step-by-step explanation:
The sum of the opposite angle of cyclic quadrilateral is 180°.
First, lets find x...
[tex]\bf \angle \: B + \angle \: D = {180}^{o} [/tex][tex]\bf (x + 20) + 3x = {180}^{o} [/tex][tex]\bf 4x + 20 = 180[/tex][tex]\bf 4x = 180 - 20[/tex][tex]\boxed{\bf x = {40}^{o}} [/tex]Now, let's find the measure of angle C....
[tex]\bf \angle \: a + \angle \: C = {180}^{o} [/tex][tex]\bf 2x + 38 + \angle \: C = {180}^{o} [/tex][tex]\bf 2(40) + 38 + \angle \: C = {180}^{o} [/tex][tex]\bf \angle \: C = 180 - 80 - 38[/tex][tex]\boxed{\bf \angle \: C = {62}^{o}}[/tex]________________________
Find the value of this expression if x = -7.
x² +5
x+1
Enter the correct answer.
Find the area (in square units) of the region under the graph of the function f on the interval [-1,5].
F(X) = 2x+8
Square units: ?
Answer:
So generally, when you're trying to find the area under the curve, you want to integrate the function within the bounds in question, which in this case is 3 and 5. As a result, you get 4e^x - x^2/2. Then you want to subtract this when you put 3 in for x from when you put 5 in for x, such as the following:
(4e^5-25/2) - (4e^3 - 9/2)
When you combine like terms, you end up with the following answer:
4e^5 - 4e^3 - 8 square units
However, you can approximate the answer to 505.31 square units
Find the reciprocal of the sum of the reciprocals of 1/-5 and -1/6
Answer:
-1/11
Step-by-step explanation:
A reciprocal means the reverse of a number. So the numerator becomes a one and the number goes in the denominator (for example 2 becomes 1/2). Or vice versa: the one becomes the denominator and the denominator becomes the numerator (for example 1/2 becomes 2/1 which is 2).
The reciprocal of -1/5 is -5.
The reciprocal of -1/6 is -6.
The sum of both reciprocals: -5 + -6 = -11
The reciprocal of the sum -11 is -1/11.
What’s the answer ?
Answer:
a ) cylinder
b) triangular pyramid
a plane intersects a sphere 5 cm away from the center of the sphere. the cross section is a circle whose diameter is 12cm. determine the radius of the sphere
Answer:
7.81 cm
Step-by-step explanation:
diameter = 12, 12/2 = 6
(r+5)(r-5) = 6 * 6
r^2 - 25 = 36
r^2 = 61
r = 7.81
radius = 7.81 cm
Answer:
26
Step-by-step explanation:
fill in the blanks with the correct form of the verb to have and the palt of the body that is numhered. (2 pls.each)
Answer:
Below
Step-by-step explanation:
1. has
2. has
3. have
4. has
5. have
6. has
7. has
8. have
9. have
10. has
11. has
12. has
13. have
14. have
ABC Bank requires a 20% down payment on all its home loans. If the house is
priced at $145,000, what is the amount of the down payment required by the
bank?
A. $18,000
B. $290,000
• C. $29,000
D. $14,500
Answer:
c. $29,000
Step-by-step explanation:
since 20% of 145,000 = 29,000
to calculate use
(20/100) * 145,000
or
(y/100) * x
y = the precentage
x = the price of the house
therefore your answer is c. $29,000
hope this helps:)
There are two colored marbles and one white marble in a box. Julie mixes the marbles and then Sam draws two marbles at random without replacement. If the two marbles match, Sam wins; otherwise, Julie wins. Does each player have an equal chance of winning? Will adding another white marble give each player an equal chance of winning? What if a game with the same rules was played using three colored marbles and one white marble?
12 times a number is decreased by 10% of the number. Write an expression.
Answer:
something like below
Step-by-step explanation:
(12n) - (n * 10/100 )
Which of the following are characteristics of the graph of the square root
parent function? Check all that apply.
Answer:
C. It is in Quadrant I
D. It starts at the origin
Step-by-step explanation:
Parent function: [tex]f(x)=\sqrt{x}[/tex]
Domain: set of all possible input values (x-values)
As the square root of a negative number does not exist in the set of Real Numbers, the domain for the parent function is:
Solution: x ≥ 0Interval notation: [0, ∞)Range: set of all possible output values (y-values)
As the domain of the parent function is x ≥ 0, the range will be:
Solution: f(x) ≥ 0Interval notation: [0, ∞)As the range and domain both begin at zero, the graph of the parent function starts at the origin (0, 0).
Quadrant: a region of the Cartesian plane formed when the x-axis and y-axis intersect each other.
Quadrant I: (x, y)
Quadrant II: (-x, y)
Quadrant III: (-x, -y)
Quadrant IV: (x, -y)
Therefore, as the range and domain of the parent function are positive, the graph is in Quadrant I.
3x2+14x=−11 solve for x
x= -.55
6x+14x=11
20x=-11
x=-11/20
Find the distance between the points (2, −3) and (−4, −7).
-------------------------------------------------------------------------------------------------------------
Answer: [tex]7.21[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{(2, -3) and (-4, -7)}[/tex]
Find: [tex]\textsf{Find the distance between the two points}[/tex]
Solution: Use the distance formula and the two points that were provided to determine the distance.
Plug in the values
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]d = \sqrt{(-4-2)^2+(-7-(-3))^2}[/tex]Simplify and expand
[tex]d = \sqrt{(-6)^2+(-7+3))^2}[/tex][tex]d = \sqrt{(-6)^2+(-4))^2}[/tex][tex]d = \sqrt{36+14}[/tex][tex]d = \sqrt{52}[/tex]If we are using square root we use the square root of 52 but if we simplify it to a decimal point we would use 7.21
In need of help in algebra, 4 questions help please
The solution to all the given equation has been determined.
What is an Intercept ?An intercept is the point at which a straight line intersects the x or y axis.
The equation given are
5x-4y = -20
x+5y = 5
x+4y = 4
x+2y = 6
All the equations are plotted on the graph and the value of the intercept are determined
For Equation 1
The solution is x = 0 , -4 , y = 4 , 0
For Equation 2
The solution is x = 0 ,5 , y=1 ,0
For Equation 3
The solution is x = 0,4 ; y = 1 ,0
For Equation 4
The solution is x =0,6 ; y = 3 ,0
The graph are attached with the answer.
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I should have payed more attention but can someone please guide me through this and build me up an answer.
Answer:
arc QM = 38°
Step-by-step explanation:
the inscribed angle NQM is half the measure of its intercepted arc NM , so
arc NM = 2 × 90° = 180°
the sum of the arcs in a circle = 360° , then
QN + NM + MQ = 360° , that is
142° + 180° + QM = 360°
322° + QM = 360° ( subtract 322° from both sides )
QM = 38°
Ms. Jerome wants to buy identical boxes of art supplies for her 25
students. If she can spend no more than $375 on art supplies,
what inequality describes the price can she afford for each
individual box of supplies, b?
The inequality describes the price $375 she can afford for 25
individual box of supplies will be $375 ≥ 25x.
What is inequality?An inequality is comparison of two values, showing if one is less than, greater than, or simply not equal to another value.
Let the price of each box is $x.
The inequality describes the price can she afford for each
individual box of supplies will be $375 ≥ 25x.
Therefore inequality is $375 ≥ 25x.
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Use the graph of the function to find its domain and range. Write the domain and range in interval notation
Answer:
Step-by-step explanation:
Point A is at (3, 2.6) and Point B is at (3, 1.4) on a coordinate grid. The distance between the two points is
Answer:
oma cursos online gratis de chino para aprender a hablar y escribir en este idioma. Aprende chino con cursos de las mejores universidades en edX.
Step-by-step explanation:
Find the volume of the sphere of 5m
A triangle has two sides of lenghts 8 and 10. what value could the length of the third sird side be?
Answer:
Step-by-step explanation:
sum of any two sides > third side
difference of any two sides < third side.
8+10=18
10-8=2
2<third side <18
please help to answer with working.
Answer:
When r=0.2, m=0.016g
When m=0.25, r=0.5cm
When r=0.7, m=0.686g
When m=11.664, r=1.8cm
Step-by-step explanation:
General outline of steps for proportionality problems:
Identify the type or proportionality.Find the proportionality constant using a known input/output pair.Use the proportionality equation to find other unknowns.Background on proportionality relationshipsThere are two main types of proportionality, "direct" and "inverse", and then there are modifications that can be made to them. Several examples are listed below:
Direct proportionality examples
y is directly proportional to x: [tex]y=kx[/tex]y is directly proportional to the square of x: [tex]y=kx^2[/tex]y is directly proportional to the cube of x: [tex]y=kx^3[/tex]Inverse proportionality examples
y is inversely proportional to x: [tex]y=\dfrac{k}{x}[/tex]y is inversely proportional to the square of x: [tex]y=\dfrac{k}{x^2}[/tex]In each case, irregardless of which type, the two quantities are related with some extra letter "k", called the proportionality constant. Either way, the proportionality constant "k" is always in the numerator, and the quantity is either multiplied to or divided from the proportionality constant "k".
Notice that for direct proportionality, in each case, the equation always ends up as "k times" the quantity.
On the other hand, notice that for inverse proportionality, in each case, the equation always ends up as "k divided by" the quantity.
Step 1. Identify the type or proportionality (Setting up our proportionality equation)The problem says "... the mass, m g, of a sphere is directly proportional to the cube of its radius, r cm...", so our equation will look like [tex]m=kr^3[/tex].
Step 2. Finding the proportionality constantTo find the proportionality constant for our situation, one must know a full input/output pair. Notice that in the 4th column, [tex]r=1.5[/tex] and [tex]m=6.75[/tex].
Substituting these values into our equation, we can find "k".
[tex](6.75)=k(1.5)^3[/tex]
[tex]6.75=k*3.375[/tex]
[tex]\dfrac{6.75}{3.375}= \dfrac{k*3.375}{3.375}[/tex]
[tex]2=k[/tex]
So, the proportionality constant for this situation is 2, and our equation for this situation becomes: [tex]m=2r^3[/tex]
Step 3. Finding the other inputs/outputsNow that we know the proportionality constant for this situation, if we have either the input OR the output, we can solve for the other unknown.
r=0.2
[tex]m=2r^3[/tex]
[tex]m=2(0.2)^3[/tex]
[tex]m=2(0.008)[/tex]
[tex]m=0.016[/tex]
Recall the the question said that the mass, m, was measured in grams, and the radius, r, was measured in centimeters. So, if the radius is 0.2cm, then the mass of the sphere would be 0.016g.
m=0.25
[tex]m=2r^3[/tex]
[tex](0.25)=2r^3[/tex]
[tex]\dfrac{0.25}{2}=\dfrac{2r^3}{2}[/tex]
[tex]0.125=r^3[/tex]
[tex]\sqrt[3]{0.125} = \sqrt[3]{r^3}[/tex]
[tex]0.5=r[/tex]
So, if the mass of the sphere were 0.25g, the radius of the sphere would be 0.5cm.
r=0.7
[tex]m=2r^3[/tex]
[tex]m=2(0.7)^3[/tex]
[tex]m=2(0.343)[/tex]
[tex]m=0.686[/tex]
So, if the radius is 0.7cm, then the mass of the sphere would be 0.686g.
m=11.664
[tex]m=2r^3[/tex]
[tex](11.664)=2r^3[/tex]
[tex]\dfrac{11.664}{2}=\dfrac{2r^3}{2}[/tex]
[tex]5.832=r^3[/tex]
[tex]\sqrt[3]{5.832} = \sqrt[3]{r^3}[/tex]
[tex]1.8=r[/tex]
So, if the mass of the sphere were 11.664g, the radius of the sphere would be 1.8cm.
