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Explanation:
First factor out the GCF 7
7x^2 + 7x - 42
7*x^2 + 7*x + 7*(-6)
7(x^2 + x - 6)
Now focus on factoring x^2+x-6
We need to find two numbers that multiply to -6 and add to 1. Those values are 3 and -2. That means x^2+x-6 factors to (x+3)(x-2).
The 7(x^2 + x - 6) then turns into 7(x+3)(x-2)
The factor out front, the "7", is the integer factor. The other factors (x+3) and (x-2) are binomial factors.
7, (x + 3), and (x - 2) are the three factors of the given expression.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
We can factor out the common factor of 7 from the given expression to get:
[tex]7(x^2 + x - 6)[/tex]
Now, we need to factor the quadratic expression x^2 + x - 6. We can do this by finding two numbers that multiply to -6 and add to 1 (the coefficient of x).
The two numbers are 3 and -2, since 3 x -2 = -6 and 3 + (-2) = 1.
So we can write [tex]x^2 + x - 6[/tex] as (x + 3)(x - 2).
Substituting this back into the expression we have:
[tex]7(x + 3)(x - 2)[/tex]
Therefore, the three factors are 7, (x + 3), and (x - 2).
Learn more about expression here:
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15 years from now Ravi's age will be four his present age what is Ravi is present age
Molly is an insurance agent. She is mailing packages filled with marketing items to a few of her clients. The items she is including are pens that weigh x ounces, notepads that weigh y ounces, and magnets that weigh z ounces: A package filled with 3 pens, 2 notepads, and 1 magnet weighs 8 ounces. A package filled with 2 pens, 1 notepad, and 2 magnets weighs 3.9 ounces. A package filled with 4 pens and 3 magnets weighs 4 ounces. Which matrix equation can be solved to find the weight of each item?
Answer:
3 2 1 x 8
2 1 2 y = 3.9
4 0 3 z 4
Step-by-step explanation:
A health magazine reported that 27% of adult males smoke cigarettes. A competing magazine thinks this claim is false. To test this claim, they select 40 adult males at random and record if they smoke cigarettes. They calculate a 95% confidence interval for the proportion of adult males who smoke and find it is 0.22 to 0.28.
(a) Interpret the confidence interval.
(b) Calculate the point estimate and margin of error used to create this confidence interval.
Point estimate:___________
Margin of error:___________
(c) Based on the confidence interval, is it plausible that the true proportion of adult males who smoke cigarettes is 27%? Explain.
Answer:
a) what is the point estimate used to create this confidence interval?
[a] 0.22
[b] 0.28
[c] 0.26
[d] 0.25 <-----------------------------
b) what is the margin of error used to create this confidence interval?
[a] .06
[b] .03 <-----------------------------
[c] .035
[d] .055
c) based on the confidence interval, it is plausible that the true proportion of adult males who smoke cigarettes is 27%?
[a] yes <-------------------------------
[b] no
Step-by-step explanation:
Based on the graph, how many distinct real number solutions does the equation x3 – 3x2 + 4 = 0 have?
Answer:
2 solutions
-1 and 2
Step-by-step explanation:
The inside diameter of a randomly selected piston ring is a normally distributed random variable with mean 12 cm and standard deviation 0.04 cm. (a) What is the diameter that is exceeded by only 5% of the piston rings
Answer:
[tex]x=12.07[/tex]
Step-by-step explanation:
From the question we are told that:
Mean [tex]\=x =12cm[/tex]
Standard deviation [tex]\sigma=0.04[/tex]
Significance level [tex]\alpha=5\%=0.05[/tex]
Therefore
Confidence level [tex]95\%=0.95[/tex]
From table [tex]P(z<1.645)=0.95[/tex]
Generally the equation for Z-score is mathematically given by
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]x=z\sigma+\mu[/tex]
[tex]x=1.645*0.04+12[/tex]
[tex]x=12.07[/tex]
A football player kicks a football into the air. The football's height, h, in meters, with respect to the amount of
time, t, in seconds, since it was kicked can be modeled by the quadratic function h= - 4.92 + 19.6.
Enter the number of seconds, t, it takes for the football to reach its maximum height.
Fifteen students were asked how many board games they played last week. The responses are summarized in the table.
Number of
Board Games
Played
Number of
Students
0
5
6
1
2.
3
3
1
Find the mean and median number of board games played by the students.
Drag numbers to the blanks to show your answer.
mean
median
0
0.5
1
1.5
2
2.5
3
Answer:
Mean - 1.5
Median - 1.5
Step-by-step explanation:
Median = middle number
Means = all numbers added up and divided by how many are there
put into algebraic expression and then Coefficient/Variable
1. 5 less than x is 20
2. the sum of x and twice y equals -6
3. the product of 5 and x squared results in 12
Answer:
1. x - 5 = 20
2. x + 2y = -6
3. 5x² = 12
Step-by-step explanation:
1. 5 less than x is 20
x - 5 = 20
2. the sum of x and twice y equals -6
x + 2y = -6
3. the product of 5 and x squared results in 12
5x² = 12
plz plz plz plz help me plz it is due in 1 hour and no links plz
Answer:
B
Step-by-step explanation:
The formula for the area of a triangle is given as:
A = ½*base*height
A = ½*b*h
A = (bh)2
If we know the area (A) and the base, to find the height, the following would be done:
Divide both sides by b
A/b = h/2
Multiply both sides by 2
[tex] \frac{A}{b} * 2 = h [/tex]
As we can see here, to find the base, we would divide the area by the vase, then multiply what we get by 2.
Is the answer yes or no?
Answer:
yes
Step-by-step explanation:
because in order to create a right triangle all of its sides must be different
Answer:
Yes
Step-by-step explanation:
Using the Pathagerum theorm (C**2 = A**2 + B**2)
The hypotinuse as always the longest side except for an equal lateral triangle. So if it is a right angle triagle so if true then,
13**2 = 5**2 + 12**2
169 = 25 + 144
169 = 169
so it is true (YES).
This is worth 30 points
Answer:
There's 3 questions which one do I answer?
Step-by-step explanation:
Jonathan's preschool class has 9 girls and 6 boys. Which properties can be used to determine the percent, p, of boys in the class?
addtion
becuase when you add the number of boys and girls together you get the overall number of the class.
Answer: properties would be multiplication and the answer would be 40%
Step-by-step explanation: You can use cross multiplication to identify the answer to this.
[tex]\frac{6}{15}[/tex] --> [tex]\frac{x}{100}[/tex]
2.
What is the equation of a hyperbola with a = 8 and c=20
Answer:
Just Assume that the transverse axis is horizontal
find the lateral area of a triangular prism with a height of 8 centimeters, and with bases having sides that measure 4 cm, 5 cm, and 6 cm
Answer:
120 cm²
Step-by-step explanation:
Applying,
A = Ph................... Equation 1
Where A = Literal Area of the triangular prism, P = Perimeter of the base, h = height.
But,
P = a+b+c............... Equation 2
Where a, b, c represent the three sides of the triangular base
Therefore,
A = h(a+b+c)............... Equation 3
From the question,
Given: h = 8 cm, a = 4 cm, b = 5 cm, c = 6 cm
Substitute these values into equation 3
A = 8(4+5+6)
A = 8(15)
A = 120 cm²
a car company uses the table below to show customers the appropriate amount of gas used when a car has been driven a certain number of miles.
if the car always uses the same amount of gas each time, how many gallons of gas would be needed to travel 480 miles?
A. 20
B. 24
C. 33
D. 39
Answer:
B. 24
Step-by-step explanation:
This is a simple ratio.If 1 mile = 0.05 gallons of gasoline, then 480 miles = 24 gallons of gasoline!Many manufacturers have quality control programs that include inspection of incoming materials for defects. Suppose a computer manufacturer receives computer boards in lots of five. Two boards are selected from each lot for inspection. We can represent possible outcomes of the selection process by pairs. For example, the pair (1, 2) represents the selection of boards 1 and 2 for inspection.
a. List the ten different possible outcomes.
b. Suppose that boards 1 and 2 are the only defective boards in a lot of five. Two boards are to be chosen at random. Define X to be the number of defective boards observed among those inspected. Find the probability distribution of X.
c. Let F(x) denote the cdf of X. First determine(0)=P( X ≤ 0), F(1), and F(2); then obtain F(x) for all other x.
Answer:
Hence, the list ten different possible outcomes are [tex](1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)[/tex], the probability distribution of X are [tex]0.3,0.6,0.1[/tex] and the cumulative distribution function is [tex]F(x)=\left\{\begin{array}{lc}0 & x<0 \\0.3 & 0 \leq x<1 \\0.9 & 1 \leq x<2 \\1 & 2 \leq x\end{array}\right.[/tex]
Step-by-step explanation:
(a)
List the ten different possible outcomes.
The number of ways that two boards are drawn from each lot of [tex]5[/tex] lots are [tex]{5 \choose 2}[/tex]
[tex]{5 \choose 2}=\frac{5!}{2!(5-2)!}[/tex]
[tex]\Rightarrow {5 \choose 2}=\frac{5\times 4\times 3!}{2!\times 3!}[/tex]
[tex]\Rightarrow {5 \choose 2}=\frac{5\times 4}{2!}[/tex]
[tex]\Rightarrow {5 \choose 2}=\frac{20}{2}[/tex]
[tex]\Rightarrow {5 \choose 2}=10[/tex]
So, the [tex]10[/tex] combinations are as follows :
[tex](1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)[/tex]
(b)
The aim is to find the probability distribution when two boards are chosen at random and board's one and two is the only defective boards.
Let X be the number of defective boards in the lot.
Therefore, select the combinations of the boards that are without 1 and 2 from 10 combinations.
Compute the [tex]P(X=0)[/tex]
[tex]P(X=0)=P\{(3,4),(3,5),(4,5)\}[/tex]
[tex]=\frac{3}{10}[/tex]
[tex]=0.3[/tex]
The probability that defectives did not occur in the lot is 0.3
Compute the [tex]P(X=1)[/tex]
Select the combinations of the boards that are with one defective either 1 and 2 from the 10 combinations.
[tex]P(X=1)=P\{(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)\}[/tex]
[tex]=\frac{6}{10}[/tex]
[tex]=0.6[/tex]
The probability that one defectives occurred in the lot is 0.6.
Compute the [tex]P(X=2)[/tex]
Select the combinations of the boards that are with two defective 1 and 2 from the 10 combinations.
[tex]P(X=2)=P\{(1,2)\}[/tex]
[tex]=\frac{1}{10}[/tex]
[tex]=0.1[/tex]
The probability that two defectives occurred in the lot is 0.1.
(c)
The cumulative distribution function (cdf)[tex]F(X=x)[/tex] is defined as,
[tex]\begin{aligned}F(X&=x)=P(X \leq x) \\F(0) &=P(X \leq 0) \\&=P(X=0) \\&=0.3 \\F(1) &=P(X \leq 1) \\&=P(X=0)+P(X=1) \\&=0.3+0.6 \\&=0.9 \\F(2) &=P(X \leq 2) \\&=P(X=0)+P(X=1)+P(X=2) \\&=0.3+0.6+0.1 \\&=1.0\end{aligned}[/tex]
Therefore, the cumulative distribution function (cdf) [tex]F(X=x)[/tex] is,
[tex]F(x)=\left\{\begin{array}{lc}0 & x<0 \\0.3 & 0 \leq x<1 \\0.9 & 1 \leq x<2 \\1 & 2 \leq x\end{array}\right.[/tex]
I NEED HELP RIGHT NOW PLS!!
Answer:
I think the answer is 2 because 2.5 x 2 = 5.
I'm sorry if this is wrong, I'm a bit unsure.
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
Answer:
2
Step-by-step explanation:
we simply divide 2 1/2 from 5
5÷2 1/2
5÷5/2
5×2/5
2(we cancel five)
WHAT IS 2/29 AS A DECIMAL
Answer:
0.068966
Step-by-step explanation:
Answer:
00.2 or 00.29 l guess sorry if it is wrong
Help me plzzzzzzzzzzzzzzzZzzzzzzZ
Answer:
8.56 x 2.1 = 17.967 or you can sum up to 18. Hope this helps!
An election ballot asks voters to select four city commissioners from a group of fourteen candidates. In how many ways can this be done ?
Mitch jarred 12 liters of jam 2 days. How many days does Mitch need to spend making jam if he want to jar 18 jam in all
Answer:
3 days
Step-by-step explanation:
well, in 2 days mitch can jar 12 liters of jam right? but 12 is divisible by 2. so let’s just do that to help us out later, 12 / 2 = 6
now that we have that, let’s make sure. in 1 day he can jar 6, in 2 he can jar 12.
that seems right! so now, can we add 6 to 12 to make 18? yep! how many more times do we need to add 6? 1 time. so 12 + 6 = 18. every 6 liters is 1 day. so 1 day + 1 day + 1 day (18 liters) is 3 days total!
hope this helped you!
plzzzzzzzz help for a brainly
Which of the following properties is shown in the question below?
Answer:
C. Associative property of multiplication
Step-by-step explanation:
The associative property of multiplication states that the way in which factors are grouped in a multiplication problem does not change the product.
Fifty seven percent (57%) of the students applying to a university are accepted. In other words, there is a 57% probability of being accepted. A sample of 12 applicants has been selected. Using Excel, answer the questions below. Please, round your solutions to 4 decimal places (if your answer has less than 4 decimals, it is okay to leave it as it is).
What is the prduct of 33 and 6925?
Answer:
228525-Look below for steps:)
Step-by-step explanation:
Step 1:
6925
* 33
______
Step 2:
5*3=15
carry the one
3*2+1=7
9*3=27
carry the 2
6*3+2=20
SO your first number is 20775 but we are NOT done yet!
add a zero below 5
5*3=15
carry the one
3*2+1=7
9*3=27 carry the 2
then 6*3+2=20
then add 207750+20775
which equals....
228525
so 228525 is your answer!!!
I really do hope this made sense!
Have a great day!
- Hailey: D
(NOTHING IS COPIED AND PASTED!!!!!)
Find the volume of the pyramid. Write your answer as a fraction or mixed number.
2 ft
1 ft
2 ft
Answer:
V=lwh /3
Step-by-step explanation:
How find the length of a hypotenuse triangle
Answer:
Step-by-step explanation:
A hypotenuse is calculated on a triangle with a right angle. The hypotenuse is the side opposite the sides with the right angle. The equation is a^2 + b^2=c^2 where the hypotenuse is the square root of c.
The perimeter of the figure below is 32.6 m. Find the length of the missing side.
Answer:
They are all equal at the sides so , the answer is 4.8m , I think the perimeter is given just to confuse you.....
Jada ran 15.25 kilometers. Han ran 8,500 meters. Who ran farther?
Answer:
15.25 km =15,250 m
so Jada ran further
Answer:
Jada ran farther
Step-by-step explanation:
First, convert 8,500 to kilometers.
8,500 ÷ 1,000 = 8.5
15.25 > 8.5
Have a wonderful day!
17. Calculate the profit and loss percent if CP is RS 480 andSP is RS420
Answer:
there is no profit there is loss because CP is greater than SP
Step-by-step explanation:
loss=CP-SP
=Rs480-Rs420
=Rs60
loss%=loss/cp*100%
=60/480*100%
=6000/480
=12.5%