Answer:
(5a−3)^2
Step-by-step explanation:
25a^2 - 30a + 9
Factor the expression by grouping. First, the expression needs to be rewritten as 25a^2+pa+qa+9. To find p and q, set up a system to be solved.
p+q=−30
pq=25×9=225
Since pq is positive, p and q have the same sign. Since p+q is negative, p and q are both negative. List all such integer pairs that give product 225.
−1,−225
−3,−75
−5,−45
−9,−25
−15,−15
Calculate the sum for each pair.
−1−225=−226
−3−75=−78
−5−45=−50
−9−25=−34
−15−15=−30
The solution is the pair that gives sum −30.
p=−15
q=−15
Rewrite 25a^2 - 30a + 9 as (25a^2−15a)+(−15a+9).
(25a^2−15a)+(−15a+9)
Factor out 5a in the first and −3 in the second group.
5a(5a−3)−3(5a−3)
Factor out common term 5a−3 by using distributive property.
(5a−3)(5a−3)
Rewrite as a binomial square.
(5a−3)^2
someone please help these questions are due at 11;59 today please help urgent
1)A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 258.5-cm and a standard deviation of 2.3-cm. For shipment, 30 steel rods are bundled together.
Find the probability that the average length of a randomly selected bundle of steel rods is between 258.5-cm and 259-cm.
P(258.5-cm < M < 259-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
2)
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 127.1-cm and a standard deviation of 1.6-cm. For shipment, 6 steel rods are bundled together.
Find P17, which is the average length separating the smallest 17% bundles from the largest 83% bundles.
P17 =
-cm
Enter your answer as a number accurate to 2 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Answer:
1) P(258.5-cm < M < 259-cm) = 8.71%.
2) P17 = 125.57cm
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Question 1:
Mean of 258.5-cm and a standard deviation of 2.3-cm, which means that [tex]\mu = 258.5, \sigma = 2.3[/tex]
Find the probability that the average length of a randomly selected bundle of steel rods is between 258.5-cm and 259-cm.
This is the pvalue of Z when X = 259 subtracted by the pvalue of Z when X = 258.5.
X = 259
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{259 - 258.5}{2.3}[/tex]
[tex]Z = 0.22[/tex]
[tex]Z = 0.22[/tex] has a pvalue of 0.5871
X = 258.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{258.5 - 258.5}{2.3}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
0.5871 - 0.5 = 0.0871
0.0871*100% = 8.71%. So
P(258.5-cm < M < 259-cm) = 8.71%.
Question 2:
Mean of 127.1-cm and a standard deviation of 1.6-cm, which means that [tex]\mu = 127.1, \sigma = 1.6[/tex]
Find P17, which is the average length separating the smallest 17% bundles from the largest 83% bundles.
This is the 17th percentile, which is X when Z has a pvalue of 0.17. So X when Z = -0.954.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.954 = \frac{X - 127.1}{1.6}[/tex]
[tex]X - 127.1 = -0.954*1.6[/tex]
[tex]X = 125.57[/tex]
P17 = 125.57cm
Stewart's pencil is 4.1 centimeters more than twice the length of Nora's pencil. Nora's pencil is 5.5 cm
long.
Which equation can be used to find s, the length of Stewart's pencil in centimeters?
AS = 2(4.1) - 5.5
CS = 2(4.1) + 5.5
В
S = 2(5.5) + 4.1
DS = 2(5.5) - 4.1
Answer:
S = 2(5.5) + 4.1
Answer: s= 2(5.5) + 4.1
There are 4 classrooms for fifth grade and 4 classrooms for sixth grade at a school. Each classroom has 20 students. A teacher is planning a field trip for some fifth and sixth grade students at this school. The teacher knows the following information:
90% of fifth and sixth grade students have permission to go on the trip.
4 teachers are going on the trip.
The school requires 1 parent volunteer for every 8 students going on the trip.
Part A
How many parent volunteers are needed to go on the trip?
Answer:
18
Step-by-step explanation:
Fifth grade has 80 students and sixth grade has 80 students. so if you get 90% of both then you have 72 and 72. Add and divide by 8 and you have the answer of 18 parent volunteers going.
Answer:
18 pls give brainliest i never get them :(
Step-by-step explanation:
double the quotation of a number (x) and 6.
Hey there!
Your answer is [tex]2(\frac{x}{6} )[/tex]
"Double" represents multiplying by 2. "the quotation of a number (x) and 6" represents division. So, we can double [tex]\frac{x}{6}[/tex], which gives us [tex]2(\frac{x}{6} )[/tex].
Have a terrificly amazing day! :D
Pls Answer correctly and I’ll give you the brainliest
Answer: x=7
Step-by-step explanation:
plug y into equation...
x-(-4x+23)=12
solve...
x+-1(-4x+23)=12
x+-1(-4x)+-1(23)=12
x+4x-23=12
5x-23=12
5x=35
x=7
8. What is the area inside of the track?
Solve the inequality:
2x+10≥16
Select one:
x≥13
x≤13
x≥3
x≤3
Answer:
x≥3
Step-by-step explanation:
Answer:
3rd choice down, if you need may other help, just hit me up
A shoe box is 4 inches wide, 3 inches deep, and 12 inches long. What is the volume?
I know it's 144 but 144 what?
Answer:
144in square
Step-by-step explanation:
Is the tank filling or draining
Answer:
the tank is filling- hence the +8
Step-by-step explanation:
Simplify the following fraction: 12/8
Answer:
3/2 or 1.5
Step-by-step explanation:
have a good day
At a school, 40% of the sixth-grade students said that hip-hop is their favorite kind of music. If 68 sixth-grade students prefer hip hop music, how many sixth-grade students are at the school?
Answer:
170
Step-by-step explanation:
can someone help and show the working out please x
For the shower multiply the amount of water per minute by number of minutes:
10.6 x 7 = 74.2 liters.
Calculate volume of the tube and the amount of water in it:
35 x 40 x 120 = 168,000 cubic cm.
Convert to liters:
168,000/ 1000 = 168 liters.
Savings = 168 - 74.2 = 93.8 liters
10 cm 5 cm What is the perimeter of this rectangle?
Answer:
30 cm
Step-by-step explanation:
To find the perimeter you will have to use the formula L2 + W2 = A
1. Multiply the length (let's say 10 cm) by 2
a. 20
2. Do the same for width (5 cm)
a. 10
3. Add together
a. 20 + 10 = 30 cm
(There is another way to do it but this is easier)
Hope this helps :)
the table above represents what
Answer: exponential decay
Step-by-step explanation:
Exponential decay means that it's getting smaller and you can see that the numbers are getting smaller on the y axis.
Hope this helps :)
pleeeaassee First person get brainliest!!!!
Answer:
D. 32 inches 65-33=32 so its 32 inches
Step-by-step explanation:
This is the table answer this please
Answer:
so answer is b.42
Step-by-step explanation:
3 7
6 14
9 21
every time width increase by 3 length increase by 7 so:
12 28
15 35
18 42
The length of a rectangle is x feet more than its width. The area of the rectangle is 5x + 25. What is the width of the rectangle?
Answer:
w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]
(Anyone can correct me if I'm wrong)
Step-by-step explanation:
Before we start the solving, we can make the following statements:
Area = l x w
Area = 5x + 25
therefore,
l x w = 5x + 25
Since the question states that the length is x more than the width, so we can make the following statement:
w = l + x
With this, we can substitute it to the first statement we made, l x w = 5x + 25,
l x (l + x) = 5x + 25
[tex]l^{2}[/tex] + lx = 5x + 25
lx - 5x = 25 - [tex]l^{2}[/tex]
x(l - 5) = 25 - [tex]l^{2}[/tex]
x = [tex]\frac{25 - l^{2}}{l - 5}[/tex]
From this, we can find w by substituting it in the statement we made earlier, w = l + x,
w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]
what is the resistance of a circuit if it has a voltage of 50v and a current of 8 ? and show me the calculations
Answer:
25/4 ohm
Step-by-step explanation:
Use Ohm‘s Law: V=IR which stands for Voltage = Electric Current * Resistance.
Plug in your given values: 50 = 8R. R = 25/4 ohm.
2(T+1)=10 what does t equals ?
Type the expression that results from the following series of step
Start with Z, subtract y, then divide by x.
Answer:
z-y/x
Step-by-step explanation:
then z
then z-y
z-y/x
A quarter is tossed. How many total number of outcomes are there? total number of outcomes
Answer:
2
Step-by-step explanation:
Answer:
2 is the correct answer please mark brainliest
Step-by-step explanation:
Which probability indicates that an event will definitely occur?
1/4
1/2
3/4
1
Answer:
1
Step-by-step explanation:
because it is WHOLE where as other shows unsureness.
Does anyone know the answer to this and how to solve it? I’m completely lost-
Answer:
314
Step-by-step explanation:
Does the line cuts through the diameter of the circle?
If so just apply π * 10^2 = 314.15 radius is just 20/2 = 10
72 is what percent of 180
Answer:
.40 or 40 percent
Step-by-step explanation:
What fraction of the catapults flung a marshmallow 30 inches or less?
Answer:
1/4
Step-by-step explanation:
Each whisker represents 1/4 of data
Find the inverse of the function.
f(x) = -3x + 7
19) An airplane has 150 passengers. 48% of the passengers are traveling alone.
How many passengers are traveling alone?
Answer:
72 passengers
Step-by-step explanation:
What we know:
There are 150 passengers in total48% of the passengers are travelling aloneTo find how many passengers are travelling alone, multiply 150 by 48%.
48% ⇒ 0.48 as a decimal
150 × 0.48 = 72
Therefore, 72 passengers are travelling alone.
I hope this helps!
Answer:
72
Step-by-step explanation:
HELP PLEASE DUE IN 4 MINUTES
Answer:
8/3
Step-by-step explanation:
Answer:
C. 2/3
Step-by-step explanation:
this is the correct answer
4. Tori bought x shares of Mattel stock for m dollars per share. She sold
all of the shares months later for y dollars per share. Express her cap-
ital gain or loss algebraically.
Answer:
mx = y
or
y = mx
Step-by-step explanation:
If she pays m per share, and x represents each share, you will multiply m and x. If she sold all them for the value of y. Then you set mx equal to y.
mx = y
or
y = mx
What is the difference between a short term savings account and a long term savings account?
Answer:
takes advantage of compounding
Step-by-step explanation: