we multiply the first parenthesis by its coefficient
[tex]\begin{gathered} ((-\frac{1}{2}\times\frac{2}{5}y)+(-\frac{1}{2}\times-2))(\frac{1}{10}y-4) \\ \\ (-\frac{2}{10}y+\frac{2}{2})(\frac{1}{10}y-4) \\ \\ (-\frac{1}{5}y+1)(\frac{1}{10}y-4) \end{gathered}[/tex]now multiply each value and add the solutions
[tex]\begin{gathered} (-\frac{1}{5}y\times\frac{1}{10}y)+(-\frac{1}{5}y\times-4)+(1\times\frac{1}{10}y)+(1\times-4) \\ \\ (-\frac{1}{50}y^2)+(\frac{4}{5}y)+(\frac{1}{10}y)+(-4) \\ \\ -\frac{1}{50}y^2+(\frac{4}{5}y+\frac{1}{10}y)-4 \\ \\ -\frac{1}{50}y^2+\frac{9}{10}y-4 \end{gathered}[/tex]5. Which of the following expressions isequivalent to the expression below?2 394Х4AC29;woltON Alw94B+D1M
A) 9 cups of berries to 12 cups of juice
Explanation
to figure out this, we need to find the original ratio and then compare
Step 1
find the ratio:
ratio cups of berries to cups of juices
[tex]\text{ratio}=\frac{3\text{ cups of berries}}{4\text{ cups of juices}}=\frac{3}{4}[/tex]hence, the rario is 3/4
Step 2
now, check the ratio of every option
a)9 cups of berries to 12 cups of juice
[tex]\begin{gathered} \text{ratio}_a=\frac{9\text{ cups of berries}}{12\text{ cups of juice}}=\frac{3}{4} \\ \text{ratio}_a=\frac{3}{4} \end{gathered}[/tex]b) 12 cups of berries to 9 cups of juice
[tex]\text{ratio}_b=\frac{12\text{ cups of berries}}{9\text{ cups of juice}}=\frac{4}{3}[/tex]c) 6 cups of berries to 15 cups of juice
[tex]\text{ratio}_c=\frac{6\text{ cups of berries }}{15\text{ cups of juice}}=\frac{6}{15}=\frac{2}{5}[/tex]d) 15 cups of berries to 10 cups of juice
[tex]\text{ratio}_d=\frac{15\text{ cups of berries }}{10\text{ cups of juice}}=\frac{15}{10}=\frac{3}{2}[/tex]therefore, the option that haas the same ratio is a) 3/4
I hope this helps you
Find the number that belongsin the green box.[?]109°13°6Round your answer to the nearest tenth.
step 1
Find the measure of the third interior angle of triangle
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
x+109+13=180
solve for x
x=180-122
x=58 degrees
step 2
Applying the law of sines
?/sin(13)=6/sin(58)
solve for ?
?=(6/sin(58))*sin(13)
?=1.6 units**Determine the x-value at which the-following function touches but does not cross the x-axis:3x^3- 182 + 27x
Okay, here we have this:
We need to identify the x-value at which the-following function touches but does not cross the x-axis in the following function: 3x^3- 18^2 + 27x. So, considering that if is a zero with even multiplicity, the graph touches the x-axis and bounces off of the axis. And if it is a zero with odd multiplicity, the graph crosses the x-axis at a zero.
According with this let's
What is theUpper Quartile (the median of 35, 38, 39, 61)?
Solution:
Given the following data below
[tex]35,38,39,61[/tex]The upper quartile, Q₂, (median) will be
[tex]\begin{gathered} Q_2=\frac{38+39}{2}=\frac{77}{2}=38.5 \\ Q_2=38.5 \end{gathered}[/tex]Hence, the answer is 38.5
which expression could be substituted for x in the second equation to find the value of y?
Substitution
We have the system of equations:
x + 2y = 20
2x - 3y = -1
To solve it with the substitution method, we need to solve the first equation for x and substitute it in the second equation.
Subtracting 2y to the first equation:
x = -2y + 20
This expression corresponds to choice B.
convert 85 degrees to radians
To convert 85 degrees to radians, consider:
[tex]\pi=180^o^{}[/tex]Let
[tex]x=85^o[/tex]Then
[tex]\begin{gathered} 180x=85\pi \\ x=\frac{85\pi}{180} \\ \\ =\frac{17}{36}\pi \end{gathered}[/tex]a recipe call for 3/4 cup of olive oil for every 1/2 cup of vinegar. how much vinigar is needed for 2 cups of olive oil? how do I solve this step by step?
The amount of vinegar needed is 1 (1/3) cups
What is Unitary method
Unitary method is a method of finding the value of 1 unit by using the value of multiple units or by the given quantity So that we can find the value of a given unknown quantity.
Here we have
A recipe requires 3/4 cup of olive oil for every 1/2 cup of vinegar
The amount of olive oil = 2 cups
Which means 3/4 cup of olive oil requires 1/2 cup of vinegar
then the vinegar required for 1 cup of Olive oil
= (vinegar Qty ÷ olive oil Qty) × 1 cup
= (1/2) ÷ (3/4) × 1
= 1/2 / 3/4 = 2/3
Therefore,
1 cup of olive oil requires 2/3 rd cup of vinegar
Then the amount of vinegar is needed for 2 cups of olive oil
= 2 × [ the amount of vinegar required for 1 cup of olive oil ]
= 2 × (2/3) = 4/3 = 1(⅓)
The amount of vinegar needed is 1 (1/3) cups
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Which of the following is a solution to the equation 16=4x-4?
Given:
[tex]16=4x-4[/tex][tex]16=4x-4[/tex][tex]20=4x[/tex][tex]\frac{20}{4}=x[/tex][tex]5=x[/tex][tex]x=5[/tex]Therefore , 5 is the answer.
Answer:5 is the answer.
Step-by-step explanation:
Determine the input value for which the statementf(x) = g(x) is true.From the graph, the input value is approximatelyf(x) = 3 and g(x) = 3x-23 = {x-25= xThe x-value at which the two functions' values areequal is
You can see from the graph, f (x) is a constant value and g (x) = -5, when x = -2, g (x) = - 2, when x = 0 and g (x) = 1, when x = 2.
3(-4+x)<-33 I need to solve for x
Simplify the inequality.
[tex]\begin{gathered} \frac{3(-4+x)}{3}<-\frac{33}{3} \\ -4+x+4<-11+4 \\ x<-7 \end{gathered}[/tex]So answer is x<-7.
how do you find the exponential equation for growth? or what is the exponential equation for growth?
Answer:
The equation f(x) = a(1 + r)x can also be used to compute exponential growth, where:
The function is represented by the word f(x).
The initial value of your data is represented by the a variable.
The growth rate is represented by the r variable.
Time is represented by the variable x.
In which quadrant is the terminal side of 115° located?+Y43-2+-XX+3 -111841.2IV3.4
ANSWER
Quadrant II
EXPLANATION
• All angles between 0° and 90° are in the first quadrant.
,• All angles between 90° and 180° are in the second quadrant.
,• All angles between 180° and 270° are in the third quadrant.
,• All angles between 270° and 360° are in the fourth quadrant.
115° is an angle measure that is between 90° and 180°. Therefore its terminal end is in the second quadrant.
how do I find the decimal value of the fraction 11/16?
You divide 11 by 16, as follow:
0.6875
16 l 110
-96
140
-128
120
-112
80
-80
0
As you can notice, the result of the division is 0.6875 (here you have used the rules for the division of a number over a greater number, which results in a decimal)
How much would you need to deposit in an account now in order to have $5000 in the account in 15years? Assume the account earns 8% interest compounded monthly.$
A(t) = amount in t years
P = Principal (original investment)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded each year
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Substitute in the given values:
[tex]5000=P(1+\frac{0.08}{12})^{12\times15}[/tex][tex]5000=P(1.0067)^{180^{}}[/tex][tex]5000=P\times3.307[/tex][tex]P=1511.94[/tex]Hence the amount need to deposit is 1511.94 dollar.
Carl is sewing a quilt. The number of yards of green fabric in the quilt is proportional to the number of yards of bluefabric in the quilt. This equation represents the proportional relationship between the number of yards of greenfabric, g, and yards of blue fabric, b, in the quilt.6 2/3 b = 5 1/3 gEnter the number of yards of green fabric used for 1 yard of blue fabric
Answer:
1 1/4 yards of green fabric.
Explanation:
The equation representing the proportional relationship between the number of yards of green fabric, g, and yards of blue fabric, b, in the quilt is:
[tex]6\frac{2}{3}b=5\frac{1}{3}g[/tex]If 1 yard of blue fabric is used: b=1
[tex]\begin{gathered} 6\frac{2}{3}\times1=5\frac{1}{3}g \\ \frac{20}{3}=\frac{16}{3}g \\ \text{ Multiply both sides by }\frac{3}{16} \\ \frac{3}{16}\times\frac{20}{3}=\frac{16}{3}\times\frac{3}{16}g \\ g=\frac{20}{16} \\ g=1\frac{1}{4}\text{ yards} \end{gathered}[/tex]If 1 yard of blue fabric is used, then 1 1/4 yards of green fabric will be used.
3. Ketin's card collection is made up of baseball cards and footbal cards. The ratio of baseball cards to football cards is 6 to 7. He has 120 baseball cards. How many cards are in Kerin's card collection? Show your work.
SOLUTION
Let the total number of cards in Ketin's card collection be k
Let the number of baseball cards be b, and
the number of football cards be f
Now, the ratio of baseball cards to football cards is 6 to 7, that is
[tex]\begin{gathered} b\colon f=6\colon7 \\ \frac{b}{f}=\frac{6}{7} \\ \text{cross multiplying, we have } \\ 7\times b=6\times f \\ 7b=6f \\ \text{dividing both sides by 7 to get b, we have } \\ \frac{7b}{7}=\frac{6f}{7} \\ b=\frac{6f}{7} \end{gathered}[/tex]Also, he has 120 baseball cards.
This means
[tex]\begin{gathered} b=120 \\ \text{but } \\ b=\frac{6f}{7} \\ \text{That means that } \\ b=\frac{6f}{7}=120 \\ So,\text{ } \\ \frac{6f}{7}=120 \\ \frac{6f}{7}=\frac{120}{1} \\ \text{cross multiplying, we have } \\ 6f=120\times7 \\ \text{dividing by 6, we have } \\ f=\frac{120\times7}{6} \\ 120\text{ divided by 6 = 20, we have } \\ f=20\times7 \\ f=140 \end{gathered}[/tex]So, the total number of cards in Ketin's card collection is
[tex]120+140=260[/tex]Hence the answer is 260
Find the missing number so that the equation has no solutions.
5x + 12 =
- 2
Submit
By solving the equation 5x + 12 = -2, the value of x in is -2.8
Solution
Bring 12 to the other side of the equation. 12 becomes -125x = -2-12
Add -2 and -12.5x = -14
We get -14
Bring 5 to the other side of the equation and divide -14 and 5x = -14 ÷ 5
Hence the value of x is -2.8x = -2.8
Hence, by solving the equation 5x + 12 = -2, the value of x in is -2.8
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You are trying to help a friend calculate their utilization rate for their study time. They can complete a maximum of 60 HW problems per hour. In the last hour, they were a little distracted but managed to complete 20 HW problems. What is their utilization rate (in %)? Calculate as a percentage (thus .05 would be entered as 5)
The utilization rate of friends' study time is 33%
In this question, we need to find the utilization rate for friends' study time.
They can complete a maximum of 60 HW problems per hour. In the last hour, they were a little distracted but managed to complete 20 HW problems.
We know that the formula for the utilization rate:
Utilization % = Actual Number of Hours Worked / the Total Available Hours.
So the utilization rate would be,
r = 20/60
r = 0.33
r = 0.33 × 100
r = 33%
Therefore, the utilization rate of friends' study time is 33%
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4 Evaluate: 2 (1) - O 1 16 2 ( ) V2 O O 1 2
To answer this question, we need to apply the following rule:
[tex]x^{-m}=\frac{1}{x^m}[/tex]This rule is known as the negative exponent rule. We also need to remember that when we have an exponent of 1/2 is the same as finding the square root for a number. Then, we have:
[tex](\frac{1}{4})^{-\frac{1}{2}}=\frac{1}{(\frac{1}{4})^{\frac{1}{2}}}=\frac{1}{\frac{\sqrt[]{1}^{}}{\sqrt[]{4}}}[/tex]Therefore, we have:
[tex]\frac{1}{\frac{1}{2}}=2[/tex]Thus, we have that:
[tex](\frac{1}{4})^{-\frac{1}{2}}=2[/tex]In summary, the correct answer is 2 (second option).
In a game, Billy must roll two dice. One die is astandard six-sided number die, and the otherdie has a different color on each side (red,blue, green, orange, yellow, and purple). Whatis the probability that Billy rolls a 3 and agreen?A 162% czB 12D1WIN
The probability of getting a 3 is:
[tex]P=\frac{1}{6}[/tex]The probability of getting green is:
[tex]P=\frac{1}{6}[/tex]Therefore the probability of getting a 3 and a green is:
[tex]P=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36}[/tex]Hence the answer is C.
Complete the proof that the point (-2, V5 ) does or does not lle on the circle centered at the origin and containing the point (0,3). Part 1 out of 4 The radius of the circle is
We will have the following:
*First: We have that the equation of the circle will be given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Here (h, k) is the coordinate of the center of the circle and r is the radius of the circle.
*Second: We will replace the center of the circle and determine the radius:
[tex]x^2+y^2=r^2[/tex]*Third: We determine the radius of the circle by using the point given:
[tex](0)^2+(3)^2=r^2\Rightarrow r^2=9\Rightarrow r=3[/tex]*Fourth: We have the following expression representing the circle:
[tex]x^2+y^2=9[/tex]So, we replace the point (-2, sqrt(5)) to determine whether or not it belongs to the circle, that is:
[tex](-2)^2+(\sqrt[]{5})^2=9\Rightarrow4+5=9\Rightarrow9=9[/tex]Thus proving that the point (-2, sqrt(5)) does lie in the circle.
Write the following number as a fraction:
0.27
Step-by-step explanation:
27/100 is the fraction of 0.27
Kayla bought 2 1/2 yards of blue cloth for 6.97 and 1 1/2 yards of yellow cloth for half as much. She used 1/4 of the blue cloth to make her mother a apron. How much cloth did it take to make the apron
She used 1/4 of the blue cloth to make her mother a apron:
[tex]\frac{5}{2}\times\frac{1}{4}=\frac{5}{8}=0.625[/tex]She used 5/8 yd or 0.625yd of blue coth to make the apron
which equation matches the graph A. y= 2x + 3 B. y= -2x + 3 C. y= -4x + 2 D. y= 4x + 2
From the given graph the line is passing through the points (-2,0) and (0,3).
Let,
[tex]\begin{gathered} (x_1,y_1)=(-1.5,0) \\ (x_2,y_2)=(0,3) \end{gathered}[/tex]From the option the equation of the line is y=2x+3
Since on subtituting (0,3) in the above expression the condition satisfys, also on substituting (-1.5,0) in the given expression the condition satisfys.
Thus, the correct option is option A.
During the last year the value of my car depreciated by 20%. If the value of my car is $19,000 today,then what was the value of my car one year ago? Round your answer to the nearest cent, if necessary .
Solution:
Given:
[tex]\begin{gathered} \text{Depreciation percentage = 20\%} \\ \text{Present value = \$19,000} \end{gathered}[/tex]Let the value of the car one year ago be represented by x.
If 20% has been depreciated, then it means the percentage left is;
100 - 20 = 80%
Hence,
[tex]80\text{ \% of x = \$19,000}[/tex][tex]\begin{gathered} \frac{80}{100}\times x=19000 \\ \frac{80x}{100}=19000 \\ 80x=100\times19000 \\ 80x=1900000 \\ x=\frac{1900000}{80} \\ x=23750 \end{gathered}[/tex]Therefore, the value of the car one year ago was $23,750
957.55x8042x6/4x6=??
6930553.9
1) Let's rewrite and solve the expression, note that since Multiplication and Division are on the same level of priority according to PEMDAS acronym for the order of operations:
[tex]\begin{gathered} 957.55\times8042\times\frac{6}{4}\times6= \\ 957.55\times8042\times\frac{3}{2}\times6= \\ 957.55\times8042\times\frac{3}{1}\times3= \\ 69305553.90= \end{gathered}[/tex]Notice that we simplified 6/4 to 3/2 and then 6 by 2. In addition to this, note that the 2 decimal places were kept, we can write 69305553.90 or simply 69305553.9
2) Hence, the answer is = 6930553.9
Show that the points (3, 6), (0, -2), (-7, -5) and (-4, 3) are thevertices of a parallelogram.
Let
A(3,6) B(0,-2) C(-7,-5) D(-4,3)
Remember that
A parallelogram has opposite sides congruent and parallel
so
step 1
Find out the length of the side AB
using the formula to calculate the distance between two points
[tex]\begin{gathered} AB=\sqrt{(-2-6)^2+(0-3)^2} \\ AB=\sqrt{73} \end{gathered}[/tex]Find out the slope of the side AB
[tex]m_{AB}=\frac{-2-6}{0-3}=\frac{8}{3}[/tex]step 2
Find out the length of the side BC
[tex]\begin{gathered} BC=\sqrt{(-5+2)^2+(-7-0)} \\ BC=\sqrt{58} \end{gathered}[/tex]Find out the slope of the side BC
[tex]m_{BC}=\frac{-5+2}{-7-0}=\frac{3}{7}[/tex]step 3
Find out the length of the side CD
[tex]\begin{gathered} CD=\sqrt{(3+5)^2+(-4+7)^2} \\ CD=\sqrt{73} \end{gathered}[/tex]Find out the slope of the side CD
[tex]m_{CD}=\frac{3+5}{-4+7}=\frac{8}{3}[/tex]step 4
Find out the length of the side AD
[tex]\begin{gathered} AD=\sqrt{(3-6)^2+(-4-3)^2} \\ AD=\sqrt{58} \end{gathered}[/tex]Find out the slope of the side AD
[tex]m_{AD}=\frac{3-6}{-4-3}=\frac{3}{7}[/tex]step 5
Compare the length of the sides
we have that
AB=CD
BC=AD
that means ----> opposite sides are congruent
Compare their slopes
mAB=mCD
mBC=mAD
that means ----> opposite sides are parallel
therefore
The given figure is a parallelogramHello, I need some assistance with this homework question please for precalculusHW Q11
A polynomial has the following form:
[tex]P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_2x^2+a_1x+a_0[/tex]Therefore, the function is a polynomial
Answer:
It is a polynomial of degree 3.
The standard form of a 3rd degree polynomial is given by:
[tex]P(x)=ax^3+bx^2+cx+d[/tex]So:
The polynomial in standard form is:
[tex]f(x)=x^3+3x[/tex]With the leading term x³ and the constant 0.
The function C(x) =17.5x-10 represents the cost (in dollars) of buying x tickets to the orchestra with a $10 coupon.
a) It represents the discount of $10 coupon
b) It repesetns the cost of each ticket
c) Five tickets cost is:
C(5) = 17.5(5) - 10 = 87.5 - 10 = 77.5
Five tickets cost $77.50
d) 130 = 17.5x - 10
130 + 10 = 17.5x
140 = 17.5x
x = 140/17.5 =8
x = 8
With $130 you can buy 8 tickets
Maria made 97% of her penalty kicks in soccer. Her teammates' percentages were uniformly distributed between 65% and 80%.Select all the statements that must be true?O A The mean would decrease by omitting Maria's score.B. The median would decrease by omitting Maria's score.O c The range would decrease by omitting Maria's score.D. The interquartile range would decrease by omitting Maria's score.E The standard deviation would decrease by omitting Maria's score,
Let's evaluate each statement to check wheter they are true or not.
A. "The mean would decrease by omitting Maria's score".
The mean is the sum of all the scores divided by the number of attempts. Since Maria had a higher score, if we omitted it then the sum would decrease and by extension the mean would decrease as well.
This option is true.
B. The median would decrease by omitting Maria's score.
The median is the value on the middle of the series, if we omit Maria's score, which was one of the highest then the middle of the series should move to the left, decreasing it.
This option is true.
C. The range would decrease by omitting Maria's score.
The range of a function are the values that said function can have as an output. If we omit Maria's score then the output of the function would be only the values scored by their team mates, which would go from 65 to 80, instead of 65 to 97. Therefore the range would decrease.
This option is true.
D. The interquartile range would decrease by omitting Maria's score.
The interquartile range are the values between the 25% values of the series and the 75% values of the series. Since Maria is the highest score between her teammates, she is not considered into the IQR and the value wouldn't change by removing her score.
This option is false.
E. The standard deviation would decrease by omitting Maria's score.
The standard deviation is the mean amount of variation in a series, since all her teammates are in the range of 65% to 80% and Maria is way above on the 97% score, by taking her score out we decrease the standard deviation, because there will be less variation in the serie.
This option is true.
