Given
David drank 10 fluid ounces of juice.
Find
how much is this in cups?
Explanation
As we know
1 cup = 8 ounces
so , 8 ounces = 1 cup
then
12 ounces =
[tex]\frac{1}{8}\times12=\frac{3}{2}=1\frac{1}{2}cups[/tex]Final Answer
hence , the required answer is
[tex]1\frac{1}{2}cups[/tex]The Elimination MethodTry These BSolve each system using elimination.a. 7x+5y=-14x - y=-16
Elimination Method : In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
The given system of equation:
7x + 5y = -1 (1)
4x - y = -16 (2)
Multiply the equation (2) by 5 :
5(4x -y ) = 5(-16)
20x - 5y = -80 (3)
Add equation (3) & (1)
(7x + 5y) + (20x -5y ) =(-1) + (-80)
7x + 5y + 20x - 5y = -1 - 80
27x = -81
x = -81/ 27
x = -3
Substitute the value of x =3 in the equation (1)
7x + 5y = -1
7(-3) + 5y = -1
-21 + 5y = -1
5y = -1 +21
5y = 20
y =20/5
y = 4
Thus, the solution of system is (x, y) = (-3, 4)
Answer : x =-3, y = 4
If the m angle3 is 112 then find the value of the missing angle measure
Question:
Solution:
According to the diagram, we get the following equations:
Equation 1:
[tex]m\angle1\text{ + m}\angle2=180^{\circ}[/tex]Equation 2:
[tex]m\angle4\text{ + m}\angle3=180^{\circ}[/tex]the angle 3 is 112 degrees, so replacing this value into the previous equation, we get:
[tex]m\angle4+112^{\circ}=180^{\circ}[/tex]solving for angle 4, we get:
[tex]m\angle4\text{ }=180^{\circ}-112^{\circ}=68^{\circ}[/tex]now, note that
Equation 3:
[tex]m\angle4\text{ + m}\angle1=180^{\circ}[/tex]but the angle 4 is 68 degrees, so replacing this into the above equation, we get:
[tex]68^{\circ}\text{ + m}\angle1=180^{\circ}[/tex]solving for angle 1, we get :
[tex]\text{ m}\angle1=180^{\circ}-68^{\circ}=112^{\circ}[/tex]Finally, from equation 1, we get:
[tex]112^{\circ}\text{ + m}\angle2=180^{\circ}[/tex]then,
[tex]\text{ m}\angle2=180^{\circ}-112^{\circ}=68^{\circ}[/tex]we can conclude that the correct answer is:
[tex]\text{ m}\angle1=112^{\circ}[/tex][tex]\text{ m}\angle2=68^{\circ}[/tex][tex]\text{ m}\angle3=112^{\circ}[/tex][tex]m\angle4\text{ =}68^{\circ}[/tex]
Over the past 6 seasons, one baseball player's batting averages were 0.248, 0.302, 0.248, 0.307, 0.295, and 0.369. A second player's batting averages were 0.349, 0.231, 0.272,0.263, 0.275, and 0.384. What are the range and mean of each player's batting averages? Use your results to compare the players' batting skills.Find the range and mean of the first player's batting averages.The range is (Type an integer or a decimal.)(Round to the nearest thousandth as needed.)The mean is
First let's write down the batting averages of the first player in ascending order:-
0.248, 0.248, 0.295, 0.302, 0,307, 0,369
The difference between the largest value and the minimum value will give us the range:-
So range for the first player will be = 0.369 - 0.248 = 0.121
Now let;s calculate the mean of the first palyer's batting averages
[tex]\begin{gathered} \text{Mean}_1=\frac{0.248+0.248+0.295+0.302+0.307+0.369}{6} \\ =\frac{1.769}{6} \\ =0.295\text{ (approx)} \end{gathered}[/tex]Now let's write down the batting averages of the second player in ascending order
0.231, 0.263, 0.272, 0.275, 0.349, 0.384
So the range for second player will be:-
0.384-0.231= 0.153
Now let;s calculate the mean of the second palyer's batting averages
[tex]\begin{gathered} \operatorname{mean}=\frac{0.231+0.263+0.272+0.275+0.349+0.384}{6} \\ =\frac{1.774}{6} \\ =0.296(approx) \end{gathered}[/tex]The mean for second player is 0.296 (approx)
And the mean for the first player is 0.295 (approx)
Since the mean avarage of both the players is almost same but the range of second player is more than that of first player, so the second player has good batting skills as compared to the first player.
a random sample of 82 statistics student were asked about their latest test score pass or fail and rather they study for the test or not the following contingency table gives a two-way classification of their response
Given:
Sample size, n = 82
We have the repsonses on the table.
Suppose a student is randomly selected, let's determine the following probabilities.
Number that studied and pass = 22
Number of students that paased = 22 + 26 = 48
a) P(Did Study and Pass) =
[tex]P=\frac{\text{Number that studied and pass}}{\text{Total number of students}}=\frac{22}{82}=0.268[/tex]b) P(Did not Study and Fail):
Total number that failed = 10 + 24 = 34
Number that did not study and fail = 24
[tex]P=\frac{Number\text{ that did not study and fail}}{Total\text{ number of students}}=\frac{24}{82}=0.293[/tex]c) P(Pass or Did not Study):
[tex]P=\frac{26+22+24}{82}=\frac{72}{82}=0.878[/tex]d) P(Fail or did study):
[tex]P=\frac{10+24+22}{82}=0.683[/tex]e) P(Fail and Pass) = 0
This is zero since there is no inetrsection for students who fail and students who pass
ANSWER:
• P(Did Study and Pass) = 0.268
,• P(Did not Study and Fail) = 0.293
,• P(Pass or Did not Study) = 0.878
,• P(Fail or did Study) = 0.683
,• P(Fail and Pass) = 0
What is an equation of the line that passes through the points (4,7) and (2,-1)? Answer in fully reduced form.
The eqaution of a line between two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Plugging our points we have:
[tex]\begin{gathered} y-(-7)=\frac{-1-(-7)}{2-4}(x-4) \\ y+7=\frac{6}{-2}(x-4) \\ y+7=-3(x-4) \\ y+7=-3x+12 \\ y=-3x+12-7 \\ y=-3x+5 \end{gathered}[/tex]Therefore the equation is:
[tex]y=-3x+5[/tex]if angle 4 equals 140 what do the other angles equal to.
Hello! Please check the image attached to see the question!
To solve this question, we must break down the question into different scenarios.
The speed expression for the first rider is:
[tex]\begin{gathered} s=\frac{d}{t} \\ \text{let us make the distance the first rider covers as y.} \\ d=y\text{ miles} \\ t=3\text{ hours.} \\ s_1=\frac{y}{3} \end{gathered}[/tex]The speed expression for the second cyclist:
[tex]\begin{gathered} s=\frac{d}{t} \\ the\text{ first rider covered a distance of y miles, the remaining distance } \\ \text{left for the second cyclist to cover is:} \\ (108-y)\text{miles at the same time of 3 hours.} \\ s_2=\frac{108-y}{3} \end{gathered}[/tex]Since one cyclist cycles 3 times as fast as the other:
It is expressed thus:
[tex]\begin{gathered} s_1=3\times s_2 \\ s_1=3s_2 \end{gathered}[/tex]Now substitute the values for the speed expression into the expression above, we will have:
[tex]\frac{y}{3}=3\times(\frac{108-y}{3})[/tex]By solving the above expression, we will get the value of y (part of the distance travelled) and we can get the speed of the faster cyclist.
[tex]\begin{gathered} \frac{y}{3}=\frac{324-3y}{3} \\ y=324-3y \\ y+3y=324 \\ \end{gathered}[/tex][tex]\begin{gathered} 4y=324 \\ y=\frac{324}{4} \\ y=81\text{ miles.} \\ \\ So\text{ the speed of the faster cyclist will be:} \\ _{}=\frac{y}{3} \\ =\frac{81\text{ miles}}{3\text{ hours}} \\ =27mi\text{/h} \end{gathered}[/tex]The speed of the faster cyclist is 27 mi/h.
y = 43 - 9Complete the missing value in the solution to theequation.(3,
We have the following:
[tex]y=4x-9[/tex]We have a solution pair is (x, y), in this case then x = 3, replacing we have
[tex]\begin{gathered} y=4\cdot3-9 \\ y=12-9 \\ y=3 \end{gathered}[/tex]The answer is: (3, 3)
Determine the volume of the rectangular prism.3 cm3 cm5 1/4cm
Answer:
47.25 cubic centimetres
Explanation:
The volume of the prism is the product of its dimensions.
[tex]3\operatorname{cm}\times5\frac{1}{4}cm\times3\operatorname{cm}[/tex]Now,
[tex]5\frac{1}{4}=5+\frac{1}{4}[/tex]multiplying 5 by 4/4 gives
[tex]\frac{4\cdot5}{4}+\frac{1}{4}[/tex][tex]=\frac{21}{4}[/tex]Therefore,
[tex]3\operatorname{cm}\times5\frac{1}{4}cm\times3\operatorname{cm}=3\operatorname{cm}\times\frac{21}{4}cm\times3\operatorname{cm}[/tex][tex]=3\cdot\frac{21}{4}\cdot3\operatorname{cm}^3[/tex][tex]=\frac{3\cdot21\cdot3}{4}cm^3[/tex][tex]=\frac{189}{4}cm^3[/tex][tex]=47.25\operatorname{cm}^3[/tex]1/8, 2/7, 1/2, 4/5 what are the next two numbers?
ANSWER:
5/4 and 2
STEP-BY-STEP EXPLANATION:
If we look closely, we notice that the pattern is that 1 is added to the numerator and one is subtracted from the denominator, as follows:
[tex]\begin{gathered} \frac{1}{8} \\ \frac{1+1}{8-1}=\frac{2}{7} \\ \frac{2+1}{7-1}=\frac{3}{6}=\frac{1}{2} \\ \frac{3+1}{6-1}=\frac{4}{5} \\ \text{therefore, the next two numbers are:} \\ \frac{4+1}{5-1}=\frac{5}{4} \\ \frac{5+1}{4-1}=\frac{6}{3}=2 \end{gathered}[/tex]What is 57.629 in expanded form?
To write a number in expanded form, we have to separate it to see the math value of individual digits.
In this case, for the number 57.629, the expanded form is:
[tex]57.629=50+7+0.6+0.02+0.009[/tex]If m Angle EOF=26 and m Angle FOG=38, then what is the measure of Angle EOG? The diagram is not to scale.
Answer:
[tex]m\angle\text{EOG}=64^0[/tex]Explanation:
From the given statement.
[tex]\begin{gathered} m\angle\text{EOF}=26^0 \\ m\angle FOG=38^0 \end{gathered}[/tex]Now:
[tex]\begin{gathered} m\angle\text{EOG}=m\angle\text{EOF}+m\angle F\text{OG} \\ =26^0+38^0 \\ =64^0 \\ \text{Therefore:} \\ m\angle\text{EOG}=64^0 \end{gathered}[/tex]Find square root of 49 Find square root of 100
We are asked to determine the square root of 49, this is written mathematically as:
[tex]\sqrt[]{49}[/tex]This means that we need to determine a number that when multiplied twice yields 49, that is:
[tex]7\times7=49[/tex]Therefore:
[tex]\sqrt[]{49}=7[/tex]paper: 100 sheets for $.99, 500 sheets for $4.29. Which is a better buy?
Answer:
the second option/ 500 sheets for 4.29
Step-by-step explanation:
Answer:
sheets for 4.29 is better buy
Helaine graphed the equation 12x-4y=3 . what was the slope of Helaines line
The slope of Helaine's line is 3
Explanations:Note that:
The slope - Intercept form of the equation of a line is:
y = mx + c
Where m = the slope
c = the intercept
The given equation is:
12x - 4y = 3
Rewrite the above equation in the form y = mx + c
4y = 12x - 3
Divide through by 4
[tex]\begin{gathered} \frac{4y}{4}=\frac{12x}{4}-\frac{3}{4} \\ \\ y\text{ = 3x - }\frac{3}{4} \end{gathered}[/tex]The slope, m = 3
The intercept, c = -3/4
Therefore, the slope of Helaines line is 3
Which linear function has the greater rate of change, the one described by the equation y = 3x + 4 or the one described by the table? 1 WN X у 3 10 17 24 4 Choose the correct answer below. O A. The function for the table has the greater rate of change. OB. The function y = 3x + 4 has the greater rate of change.Table:x y1 32 103 174 24
The rate of change is equivalent to the slope in linear functions.
So, the bigger the slope, the greater the rate of change.
In the case of the linear function y=3x+4, the slope is m=3.
In the case of the table, we have to select two points in order to calculate the slope m.
We will pick the points (1,3) and (2,10).
Then, we can calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{10-3}{2-1}=\frac{7}{1}=7[/tex]As the slope of the function in the table is bigger than the slope of the function y=3x+4, the function from the table has a greater rate of change.
[tex]\begin{gathered} m_t>m_f \\ 7>3 \end{gathered}[/tex]Answer: Option A (The function for the table has the greater rate of change)
Ramblin Roy is a dirt bike boy. One day he drives his dirt bike over to a big race. There were 178 vehicles at the race, a mix of cars and dirt bikes. Altogether there were 602 wheels on the vechicles. How many cars were there ( x) ? How many dirt bikes were there ( y ) ? A. ( 55, 123 ) B. ( 123, 55 ) C. ( 178 , 602 ) D. None of the above
There are x cars and y bikes.
The equation for the total number of vechiles is,
[tex]\begin{gathered} x+y=178 \\ y=178-x \end{gathered}[/tex]In a car, there are 4 vechiles and in a bike there are two wheels. So the equation for the wheels,
[tex]\begin{gathered} 4x+2y=602 \\ 2x+y=301 \end{gathered}[/tex]Substitute (178 - x) for y in the equation 2x + y = 301 to obtain the value of x.
[tex]\begin{gathered} 2x+178-x=301 \\ x=301-178 \\ =123 \end{gathered}[/tex]Substitute 123 for x in the equation y = 178 - x to obtain the value of y.
[tex]\begin{gathered} y=178-123 \\ =55 \end{gathered}[/tex]So number of cars are 123 and number of bikes are 55. So correct option is
B. ( 123, 55 )
Can I please get help with question 1 practice questions
Given:
Line pass through ( 3, 4)
Parallel to the,
[tex]y=-\frac{2}{3}x+1[/tex]Find-:
The equation of a line.
Explanation-:
The slope of the parallel line is also the same.
[tex]m_1=m_2[/tex]Where
m is the slope of a parallel line
The general equation of a line is:
[tex]y=mx+c[/tex]So the equation become is:
[tex]\begin{gathered} y=mx+c \\ \\ y=-\frac{2}{3}x+c \end{gathered}[/tex]The line pass ( 3,4)
That mean,
[tex](x,y)=(3,4)[/tex][tex]\begin{gathered} y=-\frac{2}{3}x+c \\ \\ (x,y)=(3,4) \\ \\ 4=-\frac{2}{3}(3)+c \\ \\ 4=-2+c \\ \\ c=4+2 \\ \\ c=6 \end{gathered}[/tex]So the equation of a line is:
[tex]\begin{gathered} y=-\frac{2}{3}x+6 \\ \\ y=\frac{-2x}{3}+\frac{18}{3} \\ \\ y=\frac{-2x+18}{3} \\ \\ 3y=-2x+18 \\ \\ 2x+3y=18 \end{gathered}[/tex]
There are 12 inches in 1 foot How many inches are in 2 feet? Enter your answer in the box There are inches in 2 feet.
24 "
1) Since there are 12 inches in 1 foot we can set a proportion, and find the missing measure:
inches feet
12 1
x 2
x = 12 * 2
x= 24
2) So there are 24 inches in 2 feet.
the product of a number of -9
If we have a number x, if we take the product of this number by -9:
[tex]-9\cdot x[/tex]The perimeter of triangle XYZ is 24 units.
What is the area of triangle XYZ? Round to the nearest
tenth of a square unit.
Trigonometric area formula: Area=1/2absin(C)
o 14.7
square units
14.9 square units
15.0 square units
15.3 square units
To the nearest tenth, the area of triangle XYZ is approximately 14.7 units².
What is a triangle?A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon.
There are three sides and three angles in every triangle, some of which may be the same.
Triangles can be divided into three groups based on the lengths of their sides, and these groups are as follows: Scalene, Isosceles, and Equilateral.
So, the area of the triangle is:
We know that:
<YXZ = 102°
Length of XY = z = 3
Length of YZ = x = 11
Length of XZ = y = ?
The perimeter of the triangle:
x+y+z = 24 units
Length XZ = y:
11+y+3 = 24
14+y = 24
y = 24 - 14
Therefore, y = 0.
Area of triangle XYZ:
The formula for trigonometric area is area of XYZ = 12(yz)sin X.
Putting values of x, y, and z as follows:
Area of ∆ XYZ = ½×10×3×sin 102
= ½×30×0.9782
= 15 × 0.9782
= 14.673
Therefore, to the nearest tenth, the area of triangle XYZ is approximately 14.7 units².
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Correct question:
What is the area of triangle XYZ? Round to the nearest tenth of a square unit. Trigonometric area formula: Area 14.7 square units 14.9 square units 15.0 square units 15.3 square units
The regular price of an item is $350. The store is having a 25% off sale,plus an additional 20% off discount. What is the price, before tax, you would pay for this item?
the price before taxes is:
[tex]350\cdot0.75\cdot0.8=210[/tex]$210 is the price before taxes
Question Sally, an investor, purchases 3,000 shares in company X at $1.75 per share. After purchasing the shares the share price increases to $2.25 per share, after which Sally decides to sell her shares. Sally is required to pay 25% tax on all profits that she makes from the sale of the shares (called Capital Gains tax). Calculate the amount of tax that Sally must pay. Give your answer to the nearest dollar. Give your answer in dollars without the dollar sign or commas.
We are given the following information
Number of shares = 3,000
Buying price of a share = $1.75
Selling price of a share = $2.25
Capital Gains tax = 25% = 0.25
We are asked to calculate the amount of tax that Sally must pay.
Let us first calculate the profit.
Profit is given by
Profit = Selling price - Buying price
The buying price is given by
Buying price = (Number of shares)×(Buying price of a share)
Buying price = 3,000×1.75
Buying price = $5,250
The selling price is given by
Selling price = (Number of shares)×(Selling price of a share)
Selling price = 3,000×2.25
Selling price = $6,750
Profit = Selling price - Buying price
Profit = $6,750 - $5,250
Profit = $1,500
Finally, the amount of tax is given by
Amount of tax = profit × Capital Gains tax
Amount of tax = 1500 × 0.25
Amount of tax = $375
Therefore, Sally is required to pay a tax of $375
Can someone please help me with this ? I just need the answer
SOLUTION:
The graph of g(x) is the graph of f(x) translated 5 units to the left.
Thus, the equation is;
[tex]g(x)=(x+5)^2[/tex]Lincoln went into a movie theater and bought 2 bags of popcorn and 4 candies, costing a total of $34. Zoey went into the same movie theater and bought 6 bags of popcorn and 5 candies, costing a total of $74. Determine the price of each bag of popcorn and the price of each candy.
12 each bags
Step-by-step explanation:
2x +4y =34
6x +5y =74
x =34- 4y ÷2
y = $3
x= $ 11
bag each price is $11
The price of one bag of popcorn is $9 and the price of one candy is $4.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Let the price of 1 bag of popcorn = x
And price of 1 candy = y
Given that,
Lincoln buys 2 bags of popcorn and 4 candies for $34
implies that,
2x + 4y = 34 (1)
Also, Zoey buys 6 bags of popcorn and 5 candies for $74
implies that,
6x + 5y = 74 (2)
By solving equation (1) and (2),
x = 9 and y = 4
The price of one bag of popcorn is $9 and the price of one candy is $4.
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12. Which of the following is a function?(A)(B)(C)(D) {(-5,9), (-2,-5),(1,-5),(5,-2)} (E){(-5,9),(-2,-5),(1,-5).(-5,-2)}
Explanation:
A relation is a function if and only if there is one value of x for different values of y.
This means that if we see repeated x-values then it's not a function. We can see this clearly in the graphs by drawing a vertical line for the values of x. Of the line crosses the graph more than once, then it's not a function.
In every graph the line crosses the graph more than once, so none of these options are functions.
Then, for a set of points we have to check the x-coordinate of each pair. If one repeats in the set, then it's not a function.
In the relation E x = -5 is repeated, so it's not a function. On the other hand, for relation D none of the x-coordinates are repeated. Therefore relation D IS a function
Answer:
Option D is a function
Is the expression below quadratic?3x + 5y - 2A. TrueB.False
A quadratic expression is given by the following form:
[tex]Ax^2+Bx+C[/tex]Therefore:
[tex]3x+5y-2[/tex]Is not a quadratic expression
i need help woth this asap i cant get it wrong
The given equation is a quadratic equation. Recall, the standard form of a quadratic equation is expressed as
ax^2 + bx + c = 0
The given equation is
x^2 - 8x = - 128
By adding 128 to both sides of the equation, we have
x^2 - 8x + 128 = - 128 + 128
x^2 - 8x + 128 = 0
By comparing this equation with the standard form equation,
a = 1, b = - 8, c = 128
The formula for solving quadratic equations is expressed as
[tex]\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2-4ac}}{2a} \\ By\text{ substituting the given values, it becomes} \\ x\text{ = }\frac{-\text{ - 8 }\pm\sqrt[]{-8^2-4(1\times128)}}{2\times1} \\ x\text{ = }\frac{8\pm\sqrt[]{64-512}}{2}\text{ = }\frac{8\pm\sqrt[]{-\text{ 448}}}{2}\text{ = }\frac{8\pm\sqrt[]{-64\text{ }\times\text{ 7}}}{2} \\ x\text{ }=\frac{8\pm(\sqrt[]{-64)}\times\sqrt[]{7}}{2} \\ \text{Note, }\sqrt[]{-\text{ 1}}\text{ = i} \\ \sqrt[]{-64}\text{ = 8i} \\ x\text{ = }\frac{8\pm8i\sqrt[]{7}}{2} \\ \text{Factoring out 2 in the numerator, we have} \\ x\text{ = }\frac{2(4\text{ }\pm4i\sqrt[]{7})}{2} \\ x\text{ = 4 }\pm4i\sqrt[]{7} \end{gathered}[/tex]Option A is correct
Name the type of angle relationship. If no relationship exists, write "none. a. <1 and < 8 b. < 2 and < 3 C. < 5 and <7 d. < 2 and < 7 e. <1 and < 3 f. < 5 and <8
Answers:
a. ∠1 and ∠8: Alternate exterior Angles.
b. ∠2 and ∠3: None
c. ∠5 and ∠7: Corresponding angles.
d. ∠2 and ∠7: Alternate interior angles.
e. ∠1 and ∠3: Corresponding angles
f. ∠5 and ∠8: None
Explanation:
a. ∠1 and ∠8: Alternate exterior Angles. They are externals, on opposite sides, and they are formed by the transversal of two lines.
b. ∠2 and ∠3: None
c. ∠5 and ∠7: Corresponding angles. One is internal and the other is external and they are on the same side of the transversal.
d. ∠2 and ∠7: Alternate interior angles. They are interior, on opposite sides, and they are formed by the transversal of two lines.
e. ∠1 and ∠3: Corresponding angles. One is internal and the other is external and they are on the same side of the transversal.
f. ∠5 and ∠8: None
(3m + n )(3m − n )solve by using foil
Given: The expression below
[tex](3m+n)(3m-n)[/tex]To: Solve using foil
Solution
foil means
F---- FIRST
O- OUTER
I ---- INNER
L ----- LAST
Let us apply the foil method
Therefore,
[tex]\begin{gathered} (3m+n)(3m-n) \\ =3m\times3m+3m\times-n+n\times3m+n\times-n \\ =9m^2-3mn+3mn-n^2 \\ -3mn+3mn=0 \\ Therefore \\ (3m+n)(3m-n)=9m^2-n^2 \end{gathered}[/tex]Hence, the solution is
9m² - n²