The polynomial is given below as
[tex]6v^5-18v^4-168v^3[/tex]Step 1: Factor out the highest common factor which is
[tex]6v^3[/tex][tex]\begin{gathered} 6v^5-18v^4-168v^3=6v^3(\frac{6v^5}{6v^3}-\frac{18v^4}{6v^3}-\frac{168v^3}{6v^3}) \\ 6v^5-18v^4-168v^3=6v^3(v^2-3v-28) \end{gathered}[/tex]Step 2: Factorise the quadratic expression
[tex]v^2-3v-28[/tex]To factorize the quadratic expression, we will have to look for two factors that will multiply each other to give a -28, and then the same two factors will add up together to give -3
By try and error, we will have the two factors to be
[tex]\begin{gathered} -7\times+4=-28 \\ -7+4=-3 \end{gathered}[/tex]By replacing the two factors in the equation above, we will have
[tex]\begin{gathered} v^2-3v-28=v^2-7v+4v-28 \\ \text{group the factors to have} \\ (v^2-7v)+(4v-28)=v(v-7)+4(v-7) \\ v^2-3v-28=(v-7)(v+4) \end{gathered}[/tex]Hence,
[tex]6v^5-18v^4-168v^3=6v^3(v-7)(v+4)[/tex]Therefore,
The final answer is 6v³(v - 7)(v + 4)
Complete the table using the equation y = 7x +4. NO -1 0 1 2
We will have the following:
*x = -1 => y = 7(-1) + 4 = -3
*x = 0 => y = 7(0) + 4 = 4
*x = 1 => y = 7(1) + 4 = 11
*x = 2 => y = 7(2) + 4 = 18
*x = 3 => y = 7(3) + 4 = 25
Module 17 - Distribution of Sample Proportions (6 of 6 discussion 3)20 20 unread replies. 20 20 replies.Learn by DoingSome features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.ContextRecall the use of data from the National Health Survey to estimate behaviors such as alcohol consumption, cigarette smoking, and hours of sleep for all U.S. adults. In the 2005-2007 report, they estimated that 30% of all current smokers started smoking before the age of 16.PromptSuppose that we randomly select 100 U.S. adults who are smokers and find that 25% of this sample started smoking before the age of 16. In this random sample, the sample proportion (25%) differs from the estimated population proportion (30%) by 5%. In other words, there is a 5% error in the sample proportion; this sample under-estimates the population proportion by 5%.Is this much error surprising? To answer this question, find the probability that a sample proportion will over- or under-estimate the parameter by more than 5%.Show your work by checking normality conditions, calculating a z-score, explaining how the area under the normal curve is used to answer the question, and stating a conclusion in the context of this problem. Module 17 - Distribution of Sample Proportions (6 of 6 discussion 3)20 20 unread replies. 20 20 replies.Learn by DoingSome features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.ContextRecall the use of data from the National Health Survey to estimate behaviors such as alcohol consumption, cigarette smoking, and hours of sleep for all U.S. adults. In the 2005-2007 report, they estimated that 30% of all current smokers started smoking before the age of 16.PromptSuppose that we randomly select 100 U.S. adults who are smokers and find that 25% of this sample started smoking before the age of 16. In this random sample, the sample proportion (25%) differs from the estimated population proportion (30%) by 5%. In other words, there is a 5% error in the sample proportion; this sample under-estimates the population proportion by 5%.Is this much error surprising? To answer this question, find the probability that a sample proportion will over- or under-estimate the parameter by more than 5%.Show your work by checking normality conditions, calculating a z-score, explaining how the area under the normal curve is used to answer the question, and stating a conclusion in the context of this problem. m the National Health Survey to estimate behaviors such as alcohol consumption, cigarette smoking, and hours of sleep for all U.S. adults. In the 2005-2007 report, they estimated that 30% of all current smokers started smoking before the age of 16.PromptSuppose that we randomly select 100 U.S. adults who are smokers and find that 25% of this sample started smoking before the age of 16. In this random sample, the sample proportion (25%) differs from the estimated population proportion (30%) by 5%. In other words, there is a 5% error in the sample proportion; this sample under-estimates the population proportion by 5%.Is this much error surprising? To answer this question, find the probability that a sample proportion will over- or under-estimate the parameter by more than 5%.Show your work by checking normality conditions, calculating a z-score, explaining how the area under the normal curve is used to answer the question, and stating a conclusion in the context of this problem. Content by the Open Learning Initiative (Links to an external site.) and licensed under CC BY (Links to an external site.).Search entries or author
Given:
Sample size = 100
p = 30% = 0.30
p' = 25% = 0.25
Let's find the probability that a sample proportion will over- or under-estimate the parameter by more than 5%.
Here, the error is:
Errror = |p' - p| = |0.25 - 0.30| = |-0.05| = 0.05
This error is not surprising.
Now, apply the formula:
[tex]\begin{gathered} \sigma p^{\prime}=\sqrt{\frac{p(1-p)}{n}} \\ \\ \sigma p^{\prime}=\sqrt{\frac{0.3(1-0.3)}{100}} \\ \\ \sigma p^{\prime}=\sqrt{\frac{0.3(0.7)}{100}}=\sqrt{\frac{0.21}{100}}=\sqrt{0.0021}=0.0458 \end{gathered}[/tex]Now, to find the probability that a sample proportion will be over or underestimate more than 5% will be:
[tex]\begin{gathered} p(p^{\prime}<0.3-0.05)+p(p^{\prime}>0.3+0.05) \\ \\ p(p^{\prime}<0.25)+p(p^{\prime}>0.35) \\ \\ z=\frac{p^{\prime}-\mu p^{\prime}}{\sigma p} \\ \\ Where:\mu p^{\prime}=0.3 \\ \end{gathered}[/tex]Hence, we have:
[tex]\begin{gathered} p(z<\frac{0.25-0.3}{0.0458})+p(z>\frac{0.35-0.3}{0.0458}) \\ \\ p(z<\frac{-0.05}{0.0458})+p(z>\frac{0.05}{0.0458}) \\ \\ p(z<-1.09)+p(z>1.09) \end{gathered}[/tex]Using the standard normal distribution table, we have:
NORMSDIST(-1.09) =0.1379
NORMSDIST(1.09) = 0.8621
Hence, we have:
p(z<-1.09) = 0.1379
p(z>1.09) = 1 - 0.8621 = 0.1379
p(z<-1.09) + p(z>1.09) = 0.1379 + 0.1379 = 0.2758
Therefore, the probability is 0.2758.
ANSWER:
0.2758
The probably of selecting a blue pin is 18/25. The chance of selecting a blue pin is _________A.) likely B.) unlikelyC.) impossible
We have the following:
The probability is as follows
[tex]p=\frac{18}{25}=0.72[/tex]That is, we can say that the probability of selecting selecting a blue pin occurs 72% of the time or 18 times out of 25 attempts, therefore we can conclude that it is likely to happen.
The answer is A) likely
The function [tex]f(t) = 1600(0.93) ^{10t} [/tex]represents the change in a quantity over t decades. What does the constant 0.93 reveal about the rate of change of the quantity?
Given the function;
[tex]f(t)=1600\cdot(0.93)^{10t}[/tex]The function shows exponential decay with a rate of 0.93
So, the quantity will decrease each year with the rate of 0.93
consider the discrete random variable x given in the table below calculate the mean variance and standard deviation of eggs also calculate the expected value of x around solution to three decimal places if necessary
The mean and the expected value are computed as follows:
[tex]\mu=\sum ^{}_{}x_i\cdot P(x_i)[/tex]Substituting with data:
[tex]\begin{gathered} \mu=1\cdot0.07+6\cdot0.07+11\cdot0.08+15\cdot0.09+18\cdot0.69 \\ \mu=0.07+0.42+0.88+1.35+12.42 \\ \mu=15.14 \\ E(x)=15.14 \end{gathered}[/tex]The variance is calculated as follows:
[tex]\sigma^2=(x_i-\mu)^2\cdot P(x_i_{})[/tex]Substituting with data:
[tex]\begin{gathered} \sigma^2=(1-15.14)^2\cdot0.07+(6-15.14)^2\cdot0.07+(11-15.14)^2\cdot0.08+(15-15.14)^2\cdot0.09+(18-15.14)^2\cdot0.69 \\ \sigma^2=(-14.14)^2\cdot0.07+(-9.14)^2\cdot0.07+(-4.14)^2\cdot0.08+(-0.14)^2\cdot0.09+2.86^2\cdot0.69 \\ \sigma^2=199.9396\cdot0.07+83.5396\cdot0.07+17.1396\cdot0.08+0.0196\cdot0.09+8.1796\cdot0.69 \\ \sigma^2=26.860 \end{gathered}[/tex]And the standard deviation is the square root of the variance, that is:
[tex]\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{26.8604} \\ \sigma=5.183 \end{gathered}[/tex]determine if the statement is true or false if it is false explain why must be changing the statements and make it true if it's true explain why you believe to be true the common difference for a geometric sequence given 5:1 -1 negative 3 negative 5 negative 7 is 2
The common difference can be determined by subtracting the first term with the second term, second term with the third term, and so forth.
In this case we have:
[tex]1-(-1)=1+1=2[/tex][tex]-1-(-3)=-1+3=2[/tex][tex]-3-(-5)=-3+5=2[/tex]In this way we can determine that the common difference of the sequence is 2, so the statement is true.
A woman wants to measure the height of a nearby building. She places a 9ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building shadow is 117ft, and the pole casts a shadow that is 6.5 ft long. How tall is the building? Round to the nearest foot.
ANSWER
[tex]162ft[/tex]EXPLANATION
Let us make a sketch of the problem:
Let the height of the building be H.
The triangles formed by the shadows of the building and the pole are similar triangles.
In similar triangles, the ratios of the corresponding sides of the triangles are equivalent.
This implies that the ratio of the length of the shadow of the pole to the pole's height is equal to the ratio of the length of the shadow of the building to the building's height.
Hence:
[tex]\frac{6.5}{9}=\frac{117}{H}[/tex]Solve for H by cross-multiplying:
[tex]\begin{gathered} H=\frac{117\cdot9}{6.5} \\ H=162ft \end{gathered}[/tex]That is the height of the building.
Identify the quadrant in which the point (−3,2) is located.Question 19 options:Quadrant IQuadrant IIQuadrant IIIQuadrant IV
The given point is (-3,2). It is required to identify the quadrant in which the point is located.
Notice that the x-coordinate of the point is negative, while the y-coordinate is positive.
This implies that the point is located in the second quadrant.
Plot the point on the coordinate plane:
The answer is quadrant II.
(-25) + (42) + (-62) + (20) =
Answer
The answer = -25
Explanation
As long as we note that
(+) × (-) = (-)
(-) × (+) = (-)
We can easily solve this,
(-25) + (42) + (-62) + (20)
= -25 + 42 - 62 + 20
= 17 - 62 + 20
= -45 + 20
= -25
Hope this Helps!!!
asymptoteg(x) = -3*2^x+5
i need help on this question
a) Based on the naming of the triangle, the line segment WR is congruent with the line segment PL.
[tex]\bar{WR}\cong\bar{PL}[/tex]b) Based on the naming of the triangle, the third point for triangle BGT is T. The third point for the other triangle, DSN, is N. Hence, the angle for T is congruent with angle N.
[tex]\angle T\cong\angle N[/tex]c) The name of the triangle RHK is rearranged as KRH. This means that name of the triangle WVO can also be rearranged as OWV and is congruent with the triangle KRH.
[tex]\Delta KRH\cong\Delta OWV[/tex]Could you please help me with questions 36 & 37?
We have to determine if the functions are linear or not.
We can do this by rearranging the equations in this form:
[tex]y=mx+b[/tex]where m and b are constants.
NOTE: There are many ways to prove that a function is linear, but this is the easiest for this question.
36.
[tex]\begin{gathered} x+\frac{1}{y}=7 \\ \frac{1}{y}=-x+7 \end{gathered}[/tex]As this function can not be written in the form y=mx+b, then it is not linear.
37.
[tex]\begin{gathered} \frac{x}{2}=10+\frac{2y}{3} \\ \frac{x}{2}-10=\frac{2y}{3} \\ \frac{2y}{3}=\frac{1}{2}x-10 \\ y=\frac{3}{2}(\frac{1}{2}x-10) \\ y=\frac{3}{4}x-15 \end{gathered}[/tex]This function is now in the form y=mx+b, where m=3/4 and b=-15. Then, this function is a linear function.
Answer:
36. Non-linear.
37. Linear.
A skydiver jumps out of a plane form a certain height. The graph below shows their height h in meters after t seconds. What is the skydiver’s initial height?
The x-intercept and the slope Set y=0 giving 0=10x+3000 x=300010=300 seconds, or precisely 5 minutes.
How to you interpret the x-intercept and the slope?Y is described as being "above ground" in height. He will get into problems if he descends below ground!
In regard to time x, the right hand side (RHS) has negative 10x, which decreases 3000. Consequently, the starting height must be 3000 feet. Moreover, it is the y-intercept.
The number of feet that the parachutist will descend in x seconds must be the -10x. It is also the graph's gradient or slope.
The graph's intersection with the x-axis indicates that y=0 and y is the height above the earth.
The point when the item is about to strike the ground is therefore the x-intercept.
The rate of descent, or slope, remains constant as time (x) passes.
The rate of fall is actually a extremely rounded value In metric form, I believe the speed to be 9.81 meters per second per second, to two decimal places.
It is approximately 32.2 feet per second per second in imperial form.
to determine how long it will take to reach the ground.
Set y=0 giving 0=10x+3000 x=300010=300 seconds, or precisely 5 minutes.
The complete question is : A skydiver parachutes to the ground. The height y (in feet) of the skydiver after x seconds is y=−10x+3000, how do you graph and Interpret the x-intercept and the slope?
To learn more about x intercept refer to:
https://brainly.com/question/24363347
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Answer 5 mins
becasue i solved in. my phone and my teacher said its right
What Is 3×10³=3×10×10×10=
3 x 10 ^3 = 3 x 10 x 10 x10 = 3 x 100 = 300
The median for the set of six ordered data values is 28.5.7,12,23,_,41,49What is the missing value
Given data:
• 7,12,23,,X, ,41,49
• Median : 28.5
• X=?
→When we divide the data set into three equal parts , as in (7;12) (23,X) and (41;49)
→ We get that the median is (23+x )/2= 28.5
23+x = (28.5*2 )
x = 57 -23
x =34Check : 34+23 = 57/2 = 28.5 This means that x = 34 is correct.EXERCISE Carlos is jogging at a constant speed. He starts a timer when he is 12 feet from his starting position. After 3 seconds, Carlos is 21 feet from his starting position. Write a linear equation to represent the distance d of Carlos from his starting position t seconds after starting the timer.
The linear equation that represent the distance d of Carlos from his starting position is d=3t+12 where d denotes the distance and t denotes the time.
What is the meaning of speed?
The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined.
Given that when Carlos is 12 feet from his starting position, starts a timer.
He is 21 feet from his starting position after 3 s.
He covers (21 - 12) = 9 feet in 3 second.
The speed of an object is the distance that covers in unit time.
The Carlos's speed is 9/3 = 3 feet/s.
After t seconds, he covers (3×t) = 3t feet.
The distance of his from his starting position after t seconds is (3t + 12) feet.
The linear equation is d = 3t + 12.
To learn more about linear inequality, click on below link:
https://brainly.com/question/11897796
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A stick is 10 1/5 inches in length. A carpenter will cut it into shorter pieces, each 1 2/15 inches in length. How many pieces will the stick be cut into?
Answer:
9 pieces
Explanation:
From the question, we're told that the length of the stick is 10 1/5 inches, let's convert the mixed fraction into an improper fraction;
[tex]10\frac{1}{5}=\frac{51}{5}[/tex]Also, we're told that the stick was cut into shorter pieces of length 1 2/15 inches each. Converting 1 2/15 into an improper fraction, we'll have;
[tex]1\frac{2}{15}=\frac{17}{15}[/tex]To determine the number of pieces that the stick will be cut into, we'll need to divide 51/5 by 17/15;
[tex]\frac{\frac{51}{5}}{\frac{17}{15}}=\frac{51}{5}\ast\frac{15}{17}=\frac{15}{1}\ast\frac{3}{17}=\frac{153}{17}=9[/tex]If the area of a trapezoid is 46 sq. cm. and its height is 4 cm. Find the shorter base if itslonger base is 15 cm.
We are given the following information about a trapezoid.
Area = 46 sq cm
Height = 4 cm
Longer base = 15 cm
We are asked to find the shorter base of the trapezoid.
Recall that the area of a trapezoid is given by
[tex]A=\frac{a+b}{2}\cdot h[/tex]Let us substitute the given values and solve for the shorter side of the trapezoid.
[tex]\begin{gathered} 46=(\frac{a+15}{2})\cdot4 \\ 2\cdot46=(a+15)\cdot4 \\ 92=(a+15)\cdot4 \\ \frac{92}{4}=a+15 \\ 23=a+15 \\ a=23-15 \\ a=8\; cm \end{gathered}[/tex]Therefore, the shorter base of the trapezoid is 8 cm
If everyone had the same body proportion your weight in pounds would vary directly with the cube root of your height in feet according to Wikipedia the most recent statics available in 2009 indicated that the average height and weight for an adult male in the United States is 5 feet 9.4 inches in 191 pounds
Given
Height
5 ft 9.4 inches
Weight
191 pounds
Procedure
Let's calculate the equation to define the weight of a person. The structure of the equation would be as follows:
[tex]w=kh^3[/tex]Replacing the values to calculate k
[tex]\begin{gathered} 191=k(5.7833)^3 \\ k=\frac{191}{5.78^3} \\ k=0.98 \end{gathered}[/tex]The equation would be
[tex]w=0.98h^3[/tex]Hi I’m I don’t understand a variable of what this is saying.
given expression to simplify,
[tex]q^{-3}r^0s^{-1}\cdot\: q^3r^{-9}s^0[/tex][tex]\begin{gathered} q^{-3}r^0s^{-1}\cdot\: q^3r^{-9}s^0 \\ q^{-3}\cdot q^3=1 \\ \: =r^0s^{-1}r^{-9}s^0 \\ =1\cdot\frac{1}{r^9}s^{-1}s^0 \\ =1\cdot\frac{1}{r^9}\cdot\frac{1}{s} \\ =\frac{1}{r^9}\cdot\frac{1}{s} \\ =\frac{1}{r^9s} \\ =r^{-9}s^{-1} \end{gathered}[/tex]Suppose that the functions and s are defined for all real numbers x as follows r(x) = 4x; s(x) = 3x ^ 2 Write the expressions for (s + r)(x) and (sr)(x) and evaluate (s - r)(2) .
Solution
Given
[tex]\begin{gathered} r(x)=4x \\ \\ s(x)=3x^2 \end{gathered}[/tex]Then
[tex]\begin{gathered} (s+r)(x)=s(x)+r(x)=4x+3x^2 \\ \\ \Rightarrow(s+r)(x)=4x+3x^2 \end{gathered}[/tex][tex](s\cdot r)(x)=s(r(x))=s(4x)=3(4x)^2=3\times16x^2=48x^2[/tex][tex](s-r)(2)=s(2)-r(2)=3(2)^2-4(2)=12-8=4[/tex]From the diagram below, if side AB is 48 cm., side DE would be ______.
The triangle ABC is similar to the triangle DCE.
Hence, we need to find a proportion to find side DE:
If side AB = 48, it will represent the double value of the side DE.
Hence, DE = 48/2 = 24
The correct answer is option b.
find bounds on the real zeros of the polynomial functionf(x)= 17x^4 + 17x^3 - x^2 - 68x - 68
In order to identify bounds on the real zeros of this polynomial, first we need to find tendencies about the signal of f(x)
We know that the two term with highest degree is being multiplied by a positive coefficient. Therefore, we can initially conclude the f(x) tends to positive infinite as x grows either positive or negative.
We can check that, for x = -2, the first term is 272, and the remaining thermis togheter are given by:
[tex]17\cdot(-2)^3-(-2)^2-68\cdot(-2)-68=-72[/tex]Then for x < -2, and for also for x > 2, we can state for sure that f(x) remains always positive.
Then, any possible roots must lies in the intervel (-2,2)
e can also chegck that, for x = 1, f(x) = -103, and, for x = -1, f(x) = -1.
Therefore, f(x) must have a root between
Give the following numberin Base 10.1215 = [ ? ]10
To convert a number in base five to base ten, we shall use the expanded notation with the place value of each of the base five numbers.
The procedure is shown below;
[tex]\begin{gathered} 121_5 \\ \text{Assign place values starting from the right to the left} \\ \text{That is 0, 1 and 2.} \\ We\text{ now have}; \\ (1\times5^2)+(2\times5^1)+(1\times5^0) \end{gathered}[/tex]We can now simplify this as follows;
[tex]\begin{gathered} (1\times25)+(2\times5)+(1\times1) \\ =25+10+1 \\ =36 \end{gathered}[/tex]ANSWER:
[tex]121_5=36_{10}[/tex]Write the first six terms of each arithmetic sequence:a,=200d=20
Recall that the nth term of an arithmetic sequence is as follows:
[tex]\begin{gathered} a_n=a_1+d(n-1), \\ where\text{ }a_1\text{ is the first element and d is the common difference between terms.} \end{gathered}[/tex]We know that:
[tex]\begin{gathered} a_1=200, \\ d=20. \end{gathered}[/tex]Therefore:
1) The second term of the given arithmetic sequence is:
[tex]a_2=200+20(2-1),[/tex]simplifying the above result we get:
[tex]a_2=200+20(1)=220.[/tex]2) The third term of the given arithmetic sequence is:
[tex]a_3=200+20(3-1)=200+20(2)=240.[/tex]3) The fourth therm is:
[tex]a_4=200+20(4-1)=200+20(3)=260.[/tex]4) The fifth term is:
[tex]a_5=200+20(5-1)=200+20(4)=280.[/tex]5) The sixth term is:
[tex]a_6=200+20(6-1)=200+20(5)=300.[/tex]Answer: The first six terms of the given sequence are:
[tex]200,\text{ }220,\text{ }240,\text{ }260,\text{ }280,\text{ }300.[/tex]On Thursday Tyler‘s math teacher helped him write the expression T equals -2 parentheses 3+ age parentheses to represent the temperature change for that day indicate all the expressions below the equivalent to T equals negative age parentheses 3+ H parentheses
t = - 2 (3 + h )
Step 1: Expand the parenthesis so that -2 multiplies all the terms in the bracket
t = -2 x 3 - 2 x h
t = - 6 - 2h
Comparing the answer to the options provided
Option C is the best option
The points (2,-2) and (-4, 13) lie on the graph of a linear equation. What isthe linear equation? *
Answer:
[tex]y=-\frac{5}{2}x+3[/tex]Explanation:
Given the two points on the graph to be (2, -2) and (-4, 13), we can use the point-slope form of the equation of a line below to write the required linear equation;
[tex]y-y_1=m(x-x_1)[/tex]where m = slope of the line
x1 and y1 = coordinates of one of the points
Let's go ahead and determine the slope of the line;
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{13-(-2)}{-4-2}=\frac{13+2}{-6}=-\frac{15}{6}=-\frac{5}{2}[/tex]Let's go ahead and substitute the value of the slope into our point-slope equation using x1 = 2 and y1 = -2;
[tex]\begin{gathered} y-(-2)=-\frac{5}{2}(x-2) \\ y+2=-\frac{5}{2}x+5 \\ y=-\frac{5}{2}x+5-2 \\ y=-\frac{5}{2}x+3 \end{gathered}[/tex]Question 13 of 19 Use the elimination method to solve the system of equations. Choose the correct ordered pair x+y=9 x-y=7 O A. (8,1) B. (12,-3) C. (16, -7) D. (7.0) SUBMIT
The solution for the system of equations is x = 8, y = 1
Explanation:Given the pair of equations:
x + y = 9 .....................................................(1)
x - y = 7 ......................................................(2)
To solve by elimintation, add (1) and (2) to eliminate y
2x = 16
x = 16/2 = 8 ............................................(3)
Subtract (2) from (1) to eliminate x
2y = 2
y = 2/2 = 1 ................................................(4)
(3) and (4) form the solution of the equation.
x = 8, y = 1
Dominick weighs 30 pounds more than his sister. Together they weigh 330 pounds. How much does Dominick weigh?
Domik weights 30 pounds more than his sister
Together they weigh 330 pounds
Let "x" represent the weight of Dominik's sister, then his weight can be expressed as "x+30"
And their total weight can be calculated as:
[tex]x+(x+30)=330[/tex]From this expression you can calculate the value of x:
[tex]\begin{gathered} 2x+30=330 \\ 2x+30-30=330-30 \\ 2x=300 \\ \frac{2x}{2}=\frac{300}{2} \\ x=150 \end{gathered}[/tex]x=150 pounds
x+30=150+30=180 pounds
Dominik weights 180pounds and his sister 150 pounds
I think you have to create a tree diagram PLS HELP
Given a coin and spinner
We need to flip the coin once and spin the spinner once
so, the tree diagram will be as following :
So, the all possible outcomes will be :
H1 , H2 , H3 , H4 , H5 , T1 , T2 , T3 , T4 , T5