N zo 113° M P In the figure above, MNO is an isosceles triangle with MN = NP. What NP. What is the value of x ?
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We have an isosceles triangle.
As MN and PN are the sides that are equal to each other, the angles M and P have the same measure.
We can find the measure of P as it is the supplementary to 113 degrees.
We then can write:
[tex]\begin{gathered} m\angle P+113=180 \\ m\angle P=180-113 \\ m\angle P=67 \end{gathered}[/tex]As mP and mM are equal to 67 degrees, and the sum of the measures of the internal angles of a triangle is equal to 180 degrees, we can write:
[tex]\begin{gathered} m\angle P+m\angle M+m\angle N=180 \\ m\angle N=180-(m\angle P+m\angle M) \\ m\angle N=180-(67+67) \\ m\angle N=180-134 \\ m\angle N=46 \end{gathered}[/tex]Now, to find x, we use the information that the angle x and Nare complementary. That means that their measures add 90 degrees.
So we can write:
[tex]\begin{gathered} m\angle N+x=90 \\ 46+x=90 \\ x=90-46 \\ x=44\degree \end{gathered}[/tex]Answer: x = 44 degrees.
Related Questions
i need help with my homework PLEASE CHECK WORK WHEN DONE NUMBER 4
Answers
From the question, we have that:
1. A large company claims that the average age of their employees is 32 years. In this case, we have the mean of the population, μ = 32 years.
2. The standard deviation for the population is 4 years, that is, σ = 4 years.
3. We have the average age of employees in the sales department is 27 years, that is, x(bar) = 27 years.
4. We know that the given data is approximately normal.
From this, we can standardize the age of the employees of the company by finding the z-score as follows:
[tex]\begin{gathered} z=\frac{\bar{x}-\mu}{\sigma} \\ \text{ Therefore, we have:} \\ \\ z=\frac{27-32}{4}=-\frac{5}{4}=-1.25 \\ \\ z=-1.25 \\ \end{gathered}[/tex]As we can see, we have a z-score of z = -1.25. This value is below the mean of the population. We can use this standard value to find the cumulative probability for it using the cumulative standard normal distribution.
We need to find the corresponding cumulative probability for z = -1.25, and we have, from the table:
Therefore, we have that the area under the normal curve below the standardized employee age is:
[tex]P(z<-1.25)=0.10565[/tex]And we can represent this, graphically, as follows:
Using a graphing calculator, we have that the area under the normal curve below the standardized employee age is 0.105649773667.
Therefore, in summary, we can say that the area under the normal curve below the standardized employee age is, approximately, 0.1056 (option B).
12 cm7 cmhcm (round to the nearest tenth]
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We need to apply the Pythagorean theorem, in this case, we need to find a cathetus, then we use the formula
[tex]undefined[/tex]A lawnmower blade has a diameter of 30 inches. If the blade rotates at a speed of 126 revolutions per minute, find the linear speed of the tips of the blade in feet per second.
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The relationship between linear speed and angular speed is given by:
[tex]\begin{gathered} \omega=\frac{v}{r} \\ where\colon \\ \omega=Angular_{\text{ }}sped \\ v=Linear_{\text{ }}speed \\ r=radius \end{gathered}[/tex]so:
[tex]\begin{gathered} r=30in=0.762m \\ \omega=126rpm \\ so\colon \\ v=\omega\cdot r \\ v=126\cdot0.762 \\ v\approx\frac{10.1m}{s} \end{gathered}[/tex]therefore:
[tex]v\approx\frac{33.14ft}{s}[/tex]What is the approximate area of the shaded sector? Use 3.14 for π.
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Option A is correct
A ball is thrown from an initial height of feet with an initial upward velocity of . The ball's height (in feet) after seconds is given by the following.Find all values of for which the ball's height is feet.Round your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or" button.)
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Given the projectile motion as
[tex]\begin{equation*} 2+30t-16t^2 \end{equation*}[/tex]We can find the values of t at h=15 below.
Explanation
At height 15, we will have that;
[tex]15=2+30t-16t^2[/tex]Therefore,
[tex]\begin{gathered} 2+30t-16t^2=15 \\ \mathrm{Subtract\:}15\mathrm{\:from\:both\:sides} \\ 2+30t-16t^2-15=15-15 \\ \mathrm{Simplify} \\ -16t^2+30t-13=0 \\ \end{gathered}[/tex]We can then solve the above with quadratic formula
[tex]\begin{gathered} t_{1,\:2}=\frac{-30\pm\sqrt{30^2-4\left(-16\right)\left(-13\right)}}{2\left(-16\right)} \\ t_{1,\:2}=\frac{-30\pm \:2\sqrt{17}}{2\left(-16\right)} \\ \mathrm{Separate\:the\:solutions} \\ t_1=\frac{-30+2\sqrt{17}}{2\left(-16\right)},\:t_2=\frac{-30-2\sqrt{17}}{2\left(-16\right)} \\ \mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:} \\ t=\frac{15-\sqrt{17}}{16},\:t=\frac{15+\sqrt{17}}{16} \\ t=0.68\:t=1.20 \end{gathered}[/tex]Answer:
[tex]t=0.68;t=1.20[/tex]
A student graphed f(x)=x and g(x)= f(x)-8 on the same coordinate grid. Which statement best describes how the graph of f and g are related?
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Answer:
The correct option is D
The graph of f is shifted 8 units down to create the graph of g.
Explanation:
Given f(x) = x
If the graph of this function is shifted 8 units down, we have
x - 8
This is the function f(x) - 8
Since g(x) = f(x) - 8, we conclude that the graph of f is shifted 8 units down to create the graph of g.
Maria was going to sell all of her stampcollection to buy a video game. Afterselling half of them she changed her mind.She then bought eleven more. How manydid she start with if she now has 41?Help?
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If the graph of f(x) is:Which of the following is the graph of f(x + 2)?OA..OB..OC..D..V
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Solution:
The graph of f(x+2) is
Hence, the answer is C
Expense AmountRent payment $953.20/monthAuto payment $165.87/monthTelephone $56.98/monthAuto insurance $714.36/six monthsOnce-a-week outing $35.00/weekusing the table what are your total monthly fixed expenses $________ /month
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ANSWER
The total monthly expenses fixed is $1,316.05/month
EXPLANATION
Given that ;
The rent payment is $953.20/month
The auto payment is $165.87/month
The telephone payment is $56.98/month
The auto insurance payment is $714.36/six months
Once -a - week outing is $35.00/week
In the given data, the rent, auto, telephone are monthly expenses
since once-a-week outing is $35/week, then, we can calculate the amount spend in a month
There are 4 weeks in a month
Hence, the amount spend in a month is calculated below as
Once-a-week outing = 4 x 35
Once-a-week outing = $140/month
The next step is to find the fixed expenses per month
Fixed expenses per month = rent + auto + telephone + once-a-week outing
Fixed expenses per month = $953.20 + $165.87 + $56.98 + $140
Fixed expenses per month = $1,316.05
Hence, the total monthly expenses fixed is $1,316.05/month
Elisa won 57 lollipops playing basketball at the school fair. She gave two to every student in her math class. She has at least 7 lollipops left.
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Let:
L(x) = remaining lollipops
x = Number of students in her math class
Part A
[tex]57-2x\ge L(x)[/tex]Since she has at least 7 lollipos left:
[tex]\begin{gathered} L(x)=7 \\ 57-2x\ge7 \end{gathered}[/tex]Part B
[tex]\begin{gathered} 57-2x\ge7 \\ \text{Solving for x:} \\ \text{Subtract 57 from both sides:} \\ 57-2x-57\ge7-57 \\ -2x\ge-50 \\ \text{Divide both sides by -2:} \\ -\frac{2x}{-2}\ge-\frac{50}{2} \\ x\le25 \end{gathered}[/tex]
Part C
[tex]\begin{gathered} 57-2x\ge7 \\ \text{ Since } \\ x\le25 \\ 57-2(25)\ge7 \\ 57-50\ge7 \\ 7\ge7 \end{gathered}[/tex]
Therefore the maximum number of students Elisa has in her class is 25.
Random variable X is binomially distributed with aprobability of success p = 0. 65. After 12 trials,
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Question A
Recall
[tex]\begin{gathered} P=0.65 \\ n=12 \\ p\text{ \lparen success\rparen=0.65} \end{gathered}[/tex][tex]\begin{gathered} P(6)=\frac{12!}{(12-6)!6!}\times0.65^6\times0.35^{12-6} \\ \\ P(6)=\frac{12!}{(12-6)!6!}\times0.65^6\times0.35^6 \\ \\ P(6)=924\times0.65^6\times0.35^6 \\ \\ P(6)=0.1281 \\ \end{gathered}[/tex]The final answer
[tex]0.12810[/tex]An adult who visited a therapist during the past year is randomly selected. what is the probability this adult used non-prescription antaepressants?Round your answer to 2 decimal places.(b what is the probability that an adult visited a therapist during the past year, given that he or she used non-prescription antidepressants? Round your answer to 2 decimal places.
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We will answer the question a) using the following formula:
[tex]P(N|T)=\frac{P(N\cap T)}{P(T)}[/tex]where we have the following event:
[tex]\begin{gathered} N=\text{ Adult use non-prescription antidepressants} \\ T=Adult\text{ visit a therapist} \end{gathered}[/tex]Therefore, the probability P(N|T) is the probability of a randomly selected adult use non-prescription antidepressants given that he visited the therapist. This formula is known as conditional probability formula.
To use the formula, we have to calculate the probability :
[tex]P(N\text{ }\cap T)[/tex]This is the probability of the intersection between the events N and T, that is, the probability that a given adult visits a therapist and use non-prescription antidepressants. Thsi information was given in the question, so we have
[tex]P(N\cap T)=21\%=0.21[/tex]Therefore, we can calculate the probability required in the part a) as :
[tex]P(N|T)=\frac{P(N\cap T)}{P(T)}=\frac{21\%\text{ }}{26\%}=\frac{0.21}{0.26}\approx0.81=81\%\text{ }[/tex]Therefore, the answer for the part a) is 81%, or in decimal number 0.81.
Part b)
We are asked to calculate the probability of that a randomly selected patient who use non-prescription antidepressants visit the therapist. This can be written in symbols as (we use the notations from the solution of the part a))
[tex]P(T|N)=\frac{P(T\cap N)}{P(N)}=\frac{21\%}{43\%}=\frac{0.21}{0.43}\approx0.49=49\%\text{ }[/tex]Therefore, the answer for the part b) is 49%, or in decimal number 0.49.
Find the standard deviation of the following data set. Round to the nearest hundredth.(7.8, -3.9, 7.8, -3.5, 1.7)
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Answer:
5.75
Explanation:
Given the data set below:
[tex]7.8,-3.9,7.8,-3.5,1.7[/tex]The formula for the standard deviation of a sample is given as:
[tex]s=\sqrt{\sum\frac{(x_i-\mu)^2}{N-1}}[/tex]First, find the mean of the data set.
[tex]\begin{gathered} Mean=\frac{7.8+(-3.9)+7.8+(-3.5)+1.7}{5} \\ =\frac{9.9}{5} \\ =1.98 \end{gathered}[/tex]Next, the deviation and squares are calculated below:
Therefore:
[tex]\begin{gathered} s=\sqrt{\sum\frac{(x_i-\mu)^2}{N-1}}=\sqrt{\frac{132.428}{5-1}} \\ =\sqrt{\frac{132.428}{4}} \\ s\approx5.75 \end{gathered}[/tex]The standard deviation of the data set is 5.75 (rounded to the nearest hundredth).
Ajalia's school needs to paint their climbing wall. The wall is in the shape of square pyramid. The side length of the base is 12 feet and the height is 8 feet. If they do not paint the base of the climbing wall, how much paint will they use?
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The region to be painted is shown by the brighter coloured shapes, that is the triangles. (Note that they do not paint the base of the climbing wall, hence the square base in red is excluded).
The area of all four triangles is given as;
[tex]\begin{gathered} \text{Area}=\frac{1}{2}bh \\ \text{Area}=\frac{1}{2}\times12\times8 \\ \text{Area}=6\times8 \\ \text{Area}=48ft^2 \end{gathered}[/tex]Therefore, for 4 of such triangular shaped sides, they would need
48 times 4 square feet of paint
That means 48 x 4 = 192 ft^2
That is, they would need enough paint to cover 192 square feet of wall space
In the inequality -3>- 6, which number appears farther left on a number line and why? O A. -3 appears farther left because -3 is smaller than -6. B. -3 appears farther left because -3 is larger than -6. O c. -6 appears farther left because -6 is larger than -3. OD. -6 appears farther left because -6 is smaller than -3. SUBMIT
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the given expression is
-3 > -6
it is clear from inequality that - 3 is greater than -6
when we go left on the number line, the value decreases.
so -6 appears farther left because -6 is smaller than -3.
thus, the correct answer is option D
According to the manufacturer, each package of M&M’s should contain 21% blue, 14% brown, 18% green, 21% orange, 11% red, and 15% yellow M&M’s on averageIf you chose 2 M&M’s, what is the probability that they would both be orange?
Answers
Answer: 0.0441
Explanation:
From the information given,
Probability that a package of M&M’s contains yellow M&M’s = 21% = 21/100 = 0.21
Probability that a second package of M&M’s contains yellow M&M’s = 21% = 121/100 = 0.21
Thus, If you chose 2 M&M’s,
the probability that they would both be orange is
0.21 x 0.21 = 0.0441
What is the image of the point (1,5) after a rotation of 180 counterclockwise about the origin?
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We have the point (1,5)=(x1,y1)
In order to find the coordinate of the point after a rotation of 180°, we use the next equation
(x2,y2)=(-x1,-y1)
then the new point is
(x2,y2)=(-1,-5)
A carpenter building a shed roof places a strut from C to D, as shown, and it divides the roof asshown. How long is BC?
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We have created a set of equations to solve the problem
[tex]\begin{gathered} 28.8^2+DC^2+5^2+DC^2=33.8^2 \\ \\ 2DC^2=33.8^2-28.8^2-5^2 \\ 2DC^2=288 \\ DC^2=\frac{288}{2} \\ DC^2=144 \\ DC=12 \end{gathered}[/tex]Now with the DC value we can calculate the length of BC
[tex]\begin{gathered} BC^2=5^2+DC^2 \\ BC^2=5^2+12^2 \\ BC=\sqrt[]{25+144} \\ BC=\sqrt[]{169} \\ BC=13 \end{gathered}[/tex]The long of BC is 13
How many units must be in ending inventory if beginning inventory was 12,078 units, 48722 units were started and 37332 units were completed and transferred out?
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23,468 units must be in ending inventory if beginning inventory was 12,078 units, 48722 units were started and 37332 units were completed and transferred out.
In the given question,
We have to find how many units must be in ending inventory if beginning inventory was 12,078 units, 48722 units were started and 37332 units were completed and transferred out.
Beginning inventory was 12,078 units.
Started with 48722 units.
Completed and transferred out 37332 units.
The entire dollar amount of stock goods that are available for use or sale at the beginning of an accounting period is known as beginning inventory.
Transferring inventory between different warehouses inside a facility is commonly referred to as "transfer among warehouses," but moving inventory between factories is referred to as "transfer among factories." Inventory Transfer refers to all of them collectively.
So the Ending Inventory = Beginning Inventory + Started Inventory - Completed and transferred out
Ending Inventory = 12,078+48,722−37,332
Ending Inventory = 23,468
Hence, 23,468 units must be in ending inventory if beginning inventory was 12,078 units, 48722 units were started and 37332 units were completed and transferred out.
To learn more about inventory link is here
https://brainly.com/question/25947903
#SPJ1
Mrs. Driffel drew Circle A and wrote in it all the positiveodd numbers through 11. She drew Circle B and wrote in itall the positive multiples of 3 from 0 through 12.53163121199АBMrs. Driffel wants to determine the union of the circles, thatis, all the numbers in either Circle A or Circle B.Which of these represents the union of the two circles?
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circle A is
circle B is
the union is:
in which, each number must appears one time. Thats why 3 and 9 only appers one time in the union.
2Type the correct answer in each box.Miss Clark's farm has chickens and pigs. There are a total of 26 animal feet and 8 animal heads on her farm.If 20 feet belong to the pigs and 6 feet belong to the chickens, the ratio of the number of pigs to the number of chickens isResetNext2020 Edmentum. All rights reserved.U
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Notice that they give us the following info:
26 number of feet and 8 animal heads
20
on a map 1 inch equals 13.9 miles if two cities are 3.5 inches apart on the map how far are they actually apart? (type a decimal)
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1) Since we have a scale let's find out the distance between them
Given the relationship, since they are proportional let's cross multiply them:
1 inch = 13. 9 miles
3.5 x
2) Writing as ratios:
[tex]\begin{gathered} \frac{1}{3.5}=\frac{13.9}{x} \\ x=13.9\text{ }\times3.5 \\ x=48.65 \end{gathered}[/tex]3) If they are 3.5" according to that proportion, then those two cities are 48.65 miles apart.
the public library has volunteers shelve books after they have been returned. when Lisa arrives to volunteer, there are five nonfiction books for every 9 fiction books. if there are 117 fiction books to Shelve, how many nonfiction books need to be shelved?
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There are 5 nonfiction books for every 9 fiction books. so we understand the the rate of nonfiction to fiction is: 5 : 9
We are asked to find how many nonfiction books are there if there are 117 fiction ones.
So we use the following proportion applying the rate we know of nonfiction/fiction:
5 / 9 = x /117
where we represented with "x" the number of nonfiction books we need to find.
We solve for that "x" by multiplying both sides by 117:
5 * 117 / 9 = x
then x = 65
Then, there are 65 nonfiction books to shelve.
Consider the graph of F shown in the figure below
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Given: the graph is given.
Find: average rate of change.
Explanation: average rate of change is equals to
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]here ,
[tex]x_1=2\text{ , y}_1=3\text{ , x}_2=6\text{ and y}_2=5[/tex][tex]\frac{y_2-y_1}{x_2-x_1}=\frac{5-3}{6-2}=\frac{2}{4}=0.5[/tex]Final answer: the required answer is 0.5
5/6x - 3 - ( 2/3x + 12 )
Answers
5/6x - 3 - ( 2/3x + 12 )
[tex]\frac{5}{6}x-3-(\frac{2}{3}x+12)[/tex]step 1
REmove the parenthesis
[tex]\frac{5}{6}x-3-\frac{2}{3}x-12[/tex]step 2
Combine like terms
[tex]\begin{gathered} \frac{5}{6}x-\frac{2}{3}x-3-12 \\ \frac{1}{6}x-15 \\ rememberthat\frac{2}{3}=4/6 \end{gathered}[/tex]therefore
the answer is (1/6)x-15
Write an expression for the sequence of operations described below.triple c, then raise the result to the 10th powerDo not simplify any part of the expression.
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The given statement is,
"triple c, then raise the result to the 10th power".
Triple c is 3 times c. It means the multiplication of c by 3.
Hence, triple c can be written in mathematical form as 3c.
The result of triple c is raised to the 10th power.
3c raised to the 10th power can be written as,
[tex](3c)^{10}_{}[/tex]So, the expression for the given
Im not the best at these type of problems please help ;/
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we have that
The expected value (Ev) is equal to
EV=(1)*0.32+(2)*0.38+(3)*0.01+(4)*0.25+(5)*0.04
EV=0.32+0.76+0.03+1.00+0.20
EV=2.31
therefore
The answer is 2.31Consider this equation.sin(e)3/1010If 8 is an angle in quadrant Il, what is the value of tan(®)?
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Given,
The equation is,
[tex]sin\theta=\frac{3\sqrt{10}}{10}[/tex]Required
The value of tan theta.
The value of cos theta is,
[tex]\begin{gathered} cos\theta=\sqrt{1-(\frac{3\sqrt{10}}{10}})^2 \\ =\sqrt{1-\frac{90}{100}} \\ =\sqrt{\frac{10}{100}} \\ =-\frac{\sqrt{10}}{10} \end{gathered}[/tex]The value of tan theta is,
[tex]\begin{gathered} tan\theta=\frac{sin\theta}{cos\theta} \\ =\frac{3\sqrt{10}}{10}\times\frac{-10}{\sqrt{10}} \\ =-3 \end{gathered}[/tex]Hence, the value of tan theta is -3.
i need you to check my answers that i have and help me on the ones that i don’t have (and if the ones i’ve done are wrong, i’ll need help on those too)Question 1
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Step 1
Given;
Step 2
1) The equation of the line in slope-intercept form will be;
[tex]\begin{gathered} y=mx+b \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-5}{5-3}=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} y=5 \\ x=3 \\ 5=\frac{1}{2}(3)+b \\ 10=3+2b \\ 10-3=2b \\ b=\frac{7}{2} \\ b=3.5 \end{gathered}[/tex]Thus the equation will be;
[tex]y=\frac{1}{2}x+3.5[/tex]Answer;
[tex]y=\frac{1}{2}x+3.5[/tex]I need help please I am soo stuck
Answers
Answer:
3(4x - 4) - 7x
Explanation:
To see which expression is a simplified version of the expression given, we go through each of the choices one by one:
-3(4x - 4) - 7x
Expanding the expression in the parenthesis gives
[tex]-12x+12-7x[/tex]adding the like terms gives
[tex]-19x+12[/tex]which is not equal o 5x -12, hence it is not the correct choice.
3(4x - 4) - 7x
Expanding the expression in the parenthesis gives
[tex]12x-12-7x[/tex]adding the like terms gives
[tex]5x-12[/tex]which is equal to 5x - 12; hence, it is the correct choice.
3(-4x + 4) - 7x
Expanding the expression in the parenthesis gives
[tex]-12x+12-7x[/tex]which simplifies to
[tex]-19x+12[/tex]which is not equal o 5x -12, hence it is not the correct choice.
-3(-4x - 4) - 7x
Expanding the expression in the parenthesis gives
[tex]12x+12-7x[/tex]which simplifies to
[tex]5x+12[/tex]which s not equal to 5x - 12; therefore, this is not a correct choice!
Hence, the right answer is the second choice: 3(4x - 4) - 7x