Answers
if
[tex]x^2+10x+21[/tex]
then
[tex]=x^2+7x+3x+21=x(x+7)+3(x+7)=(x+7)(x+3)[/tex]
Related Questions
What is the area of this composite figure? 12ft2 80 ft2 88 ft2 100 ft2
Answers
[tex]x=10ft-2ft=8tf\\\\A_1=10ft\cdot8ft=80ft^2\\\\y=10ft-6ft=4ft\\\\A_2=4ft\cdot2ft=8ft^2\\\\A_F=A_1+A_2\to A_F=80ft^2+8ft^2=88ft^2[/tex]
[tex]Answer:\ \boxed{88ft^2}[/tex]
plz help and explain thanks
Answers
for q = - 6 and x = 5 :
5⁰
------
(-6)⁻³
Apply rule : a⁰ = 1 , a≠0
5⁰ = 1 :
1
* -------
(-6)⁻³
Apply exponent rule: (-a)ⁿ = - aⁿ , if " n " is odd :
(-6)⁻³ = -6⁻³
1
* -------
-6⁻³
Apply fraction rule : a/-b = - a/b
= - 1 / -6⁻³
Apply exponent rule: a⁻ᵇ = 1 / ab
6⁻³ = 1 / 6³
=> ( - 1/1 ) / ( 6³ )
= - 6³ / 1
Apply rule a/1 = a
= - 6³
* 6 * 6 * 6 => 216
a = -216
hope this helps!
What number should be added on both sides of the equation to complete the square x2 -6x =5
Answers
Answer:
We should add 9 on the both sides of the given equation.
Step-by-step explanation:
Since, for making a perfect square on the left side of a quadratic equation,
We add the square of the half of the coefficient of x on both sides,
The given equation,
[tex]x^2-6x = 5[/tex]
Here, the coefficient of x is 6,
Half of 6 = 3
Square of 3 = 9,
Thus, we should add 9 on the both sides of the given equation.
Verification :
[tex]x^2 - 6x + 9 = 5 + 9[/tex]
[tex](x-3)^2 = 14[/tex]
What is the area of the given circle in terms of pi? Diameter 6.6. Please Help
Answers
hope this helps
r=radius
2r=d -> d/2=r
we are given d, the diameter
we need r
so
d/2=6.6/2=3.3=r
therefore
area=π*r^2
area=π*(3.3)^2
area=π*10.89
area=10.89π square units
x 13 16 18 21 23 25 26 31
p(x) .07 .21 .17 .25 .05 .04 .13 .08
the mean of the discrete random value variable x is the 20.59. What is the variance of X?
Round your answer to the nearest hundredth
a 27.89
b27.89
c33.15
d23.18
Answers
[tex]\mathbb E[X^2]=\displaystyle\sum_x x^2p(x)=13^2\cdot0.07+\cdots+31^2\cdot0.08\approx447.13[/tex]
Then the variance of [tex]X[/tex] is
[tex]\mathbb V[X]=\mathbb E[X^2]-\mathbb E[X]^2\approx447.13-20.59^2\approx23.18[/tex]
The variance of a discrete random variable calculation involves working out (x-µ)^2 * p(x) for each x value and summing them up. Using given data and mean as 20.59, variance ≈ 27.89 (options a and b).
Explanation:To calculate the variance of a discrete random variable, we use the formula: Variance = Σ[(x-µ)^2 * p(x)] where 'x' is each value of the variable, 'µ' is the mean and 'p(x)' is the probability of 'x'
Given that the mean µ is 20.59 we perform the calculation, (x-µ)^2 * p(x) for each value of 'x' and sum them all up:
(13-20.59)^2 * .07 = 14.08(16-20.59)^2 * .21 = 4.38Continuing this process for all given values of 'x' and summing them up, we find that the variance ≈ 27.89.So, the correct answer is 27.89, which corresponds to option a and b.
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Q # 13, write a rule for the linear function in the graph
Answers
[tex]m= \frac{3+1}{4-3}=4 [/tex]
Using the slope and a point (4,3) we can write the equation in slope intercept form as:
y - 3 = 4(x-4)
y = 4x -16 + 3
y = 4x - 13
So the correct answer is option A
What is 9.8 divided by 7
Answers
9.8 ÷ 7 = 1.4
So, the answer to your question is 1.4.
For either linear regression or multiple regression, the standard error of estimate can be computed as ____.
a. the square root of msresidual
b. the square root of msregression
c. msresidual/(n – 2)
d. msregression/(n – 2)
Answers
It is given by the square root of the mean square residual.
Therefore, for either linear regression or multiple regression, the standard error of estimate can be computed as the square root of msresidual.
The correct computation for the standard error of estimate in regression analysis is the square root of the residual mean square (MSresidual), which is option a. This metric represents the average distance that data points fall from the regression line.
The standard error of estimate in regression analysis, whether it's linear regression or multiple regression, provides us with a measure of the accuracy of predictions made with the regression equation. It represents the average distance that the observed values fall from the regression line.
The correct formula for computing the standard error of the estimate is the square root of the residual mean square (MSresidual), which can be denoted as the square root of MSE or RMS/RMSE. Therefore, the correct answer to the question is a. the square root of msresidual.
This is because the MSE or MSresidual is the average of the squares of the residuals (or deviations of points from the regression line), while the standard error of the estimate is its square root, providing a measure of these residuals in the original units of the dependent variable.
Milt built a prism using a 3 unit cubes. He adds two more layers of 3 unit cubes each.how many unit cubes are used for the prism?
Answers
1) Milt built a prism using a 3 unit cubes
total unit cubes is 3
2) He adds two more layers of 3 unit cubes each
total unit cubes=3+2*3----> 9 unit cubes
the answer is
9 units cubes
Milt used a total of 9 unit cubes to build his prism. This was calculated by multiplying the quantity of unit cubes in each layer (3 cubes) by the total number of layers (3).
Explanation:This is a Mathematics question about the concept of volume in prisms, specifically a cube. Milt starts by building a prism using 3 unit cubes and then adds 2 more layers of 3 unit cubes each. This means he has 3 layers of 3 cubes each.
We can calculate the total number of unit cubes used by multiplying the number of cubes in each layer by the number of layers. Here's the step-by-step calculation:
Start with quantity in a single layer: 3 unit cubes.
Multiply by the total number of layers to get the total quantity: 3 layers * 3 cubes/layer = 9 unit cubes.
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The dance committee has a budget of $125 to decorate the gym for the spring dance. They have already spent $65. Some members want to buy helium balloons that cost $0.80 each. Write and solve an inequality to show the number of balloons that the dance committee could buy
Answers
125 - 65 = 60
Now to find the amount of balloons:
0.8n = 60
Divide:
n = 75
The dance committee can buy 75 balloons
The dance committee could buy up to 75 helium balloons with their remaining budget of $60, after already spending $65 from their total budget of $125.
To determine the number of helium balloons that the dance committee could buy with their remaining budget, we first need to calculate how much money they have left after already spending $65. Since their total budget is $125, the remaining budget is calculated as $125 - $65 = $60.
Let's let b represent the number of balloons they can buy. The cost per balloon is $0.80, so the inequality representing the situation is 0.80b \<= 60. To solve for b, we divide both sides of the inequality by 0.80, which gives us b \<= 60 / 0.80, or b \<= 75.
Therefore, the dance committee could buy up to 75 helium balloons with their remaining budget, staying within their financial limitations.
What is the probability that celia is first in line and felicity is last in line?
Answers
There are 2 solutions that Celia and Felicity can be organised in:
Celia 1st in the line, Felicity last in the lane.
Felicity 1st in the line, Celia last in the line.
So, there is a 50% chance that Celia would be 1st in the line and Felicity would be last in the line.
If there is 1 other person in the line:
(The other person will be referred to as Bob)
There are 6 solutions that Bob, Celia and Felicity can be organised in:
(Correct way is in bold)
Bob 1st in line, Celia 2nd in line, Felicity last in line.
Bob 1st in line, Felicity 2nd in line, Celia last in line.
Felicity 1st in line, Bob 2nd in line, Celia last in line.
Felicity 1st in line, Celia 2nd in line, Bob last in line.
Celia 1st in line, Bob 2nd in line, Felicity last in line.
Celia 1st in line, Felicity 2nd in line, Bob last in line.
There is only 1 correct solution, so there is a 16.7% chance that Celia is first in line and Felicity is last in line.
(rounded to 1 decimal place)
If there are more people, you do what is underneath.
From the 1st section of answers (There were only Celia and Felicity in the line), there were 2 people in the line. The 2nd section of answers showed that 3 people were in the line. So, you times 2 and 3 to make 6. There were 6 solutions in the 2nd section.
From there, you get the next consecutive number of the people in the line, which is 4 (NOT 7) and times 6 by 4, which is 24. There are 24 solutions to having 4 people in the line.
Do this again and you get 24 times 5, which is 120. So there are 120 solutions to having 5 people in the line.
Keep on doing this until you get the number of people in the line you need.
Hopefully this helps!
By the way, this took around 12 minutes to type out.
Edit: Convert the number to a percentage by doing 1/120 times 100.
This gets you 0.83 (rounded to 2 decimal places)
(using the answer of 5 people in the line)
The probability of Celia being first and Felicity last in a line is found by multiplying the probabilities of each independent event. For a line of n people, it would be [tex](1/n) \(*\) (1/(n-1))[/tex]. For 10 people, this probability would be 1/90.
The scenario implies that there's a line of people, and we are interested in the probability of Celia being the first and Felicity being the last in this line. This is a combinatorial probability problem. To calculate the probability, we must first acknowledge that each person in the line is equally likely to be in any position. If we assume there are n people in total, the probability that Celia is first is 1/n, and once Celia is in place, assuming Felicity is not first, the probability that Felicity is last is 1/(n-1). Since these two events are independent (Celia being first does not affect the probability of Felicity being last), we multiply these probabilities together to find the combined probability.
Using the formula for independent events:
P(Celia first and Felicity last) = P(Celia first) * P(Felicity last given that Celia is first)P(Celia first and Felicity last) = (1/n) * (1/(n-1))If there are 10 people in the line, for example, the probability would be (1/10) * (1/9) = 1/90.
Suppose a population proportion is .40, and 80% of the time when you draw a random sample from this population you get a sample proportion of .35 or more. how large a sample were you taking?
Answers
Final answer:
To determine the sample size needed, use the formula for sample proportion: n = (z * sqrt(p * q)) / E. Plugging in the given values, the minimum sample size required is 178.
Explanation:
To determine the sample size needed, we can use the formula for sample proportion:
n = (z * sqrt(p * q)) / E
Where:
n is the sample size
z is the z-value corresponding to the desired confidence level (in this case, 80%)
p is the population proportion (0.4)
q is 1 - p
E is the maximum allowable error (0.05)
Plugging in the values, we have:
n = (z * sqrt(p * q)) / E = (0.84 * sqrt(0.4 * (1 - 0.4))) / 0.05 ≈ 177.6
Since we cannot have a fractional number of individuals, we round up to the next whole number. Therefore, we would need a minimum sample size of 178 to be 80% confident that the population proportion is estimated to within 0.05.
Annie is planning a business meeting for her company. her budget is 1,325 for renting the meeting room at the local hotel and providing lunch. she expects 26 people to attend the meeting the room cost $270 which inequality show how to find the amount × Annie can spend for lunch on each person
Answers
Annie has $1055 to spend on 26 lunches.
Let the cost of a lunch be x.
26x < 1055
x < $40.58
Answer: x < $40.58
Answer:
26x + 270 ≤ 1,325
Step-by-step explanation:
Suppose x be the amount ( in dollars ) of lunch of each person,
So, the cost of lunch for 26 people = 26x,
Also, the cost of meeting room = $ 270,
Thus, the total cost = total cost of lunch + meeting room cost
= 26x + 270,
According to the question,
The budget of meeting is $ 1,325,
That is, the total cost can not exceed to $ 1325,
[tex]\implies 26+270 \leq 1325[/tex]
Which is the required inequality that will used to find the cost of each lunch.
PLZ HELP ASAP TANGENTS OF CIRCLES PROBLEMS
Answers
Therefore the perimeter is: 12.2 + 12.1 + 5.1 + 3.3 + 3.3 + 5.2 = 41.2 units
A card is selected at random from a standard 52-card deck. (a) what is the probability that it is an ace? 4/52 (b) what is the probability that it is a heart? .25 (c) what is the probability that it is an ace or a heart
Answers
There are 4 aces in a standard 52-card deck. So the probability that AN ace is picked is just 4/52.
Part (b):
Note that there are 4 suits in a standard 52-card deck. So picking hearts will be 13/52 or 1/4.
Part (c):
The probability condition OR means we need to add the two probabilities because we do not want them simultaneously. So, we end up getting Pr(ace) + Pr(heart).
From part (a), we found that picking an ace had a probability of 4/52, which is reduced down to 1/13.
From part (b), we found that picking a heart had a probability of 1/4.
So, the probability of an ace OR a heart is 1/13 + 1/4 = 4/52 + 13/52 = 17/52.
simple interest $4000 at 7% for 8 mo.
Answers
I = (4000 x .07 x [tex] \frac{8}{12} [/tex]) + 4000
I = 186.67 + 4000
I = around $4186.67
*hope this helped!
The table shows the number of boys and girls that have black, blonde, brown, or red hair color. What is the probability that a girl has black hair?
Answers
Answer:
O.25
Step-by-step explanation:
Trust me on this one the answer was in the comments :/
The probability of a girl having black hair is determined by dividing the number of girls who have black hair by the total number of girls. Without actual numbers from the table, a specific probability cannot be calculated.
Explanation:To find the probability that a girl has black hair, we have to first know the total number of girls, and then the number of girls who have black hair. Probability is determined by dividing the number of desired outcomes by the total number of outcomes. So in this case, if we let 'G' denote the total number of girls and 'B' be the number of girls with black hair, the formula for the probability would be P(B) = B / G. Without the actual numbers from the table, we cannot calculate the specific probability.
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the sum of two numbers is 7 five times the larger number plus four times the the smaller number is 47.
Answers
x + y = 7
5x +4y = 47
You can use the first equation to write an expression for y, then substitute that into the second equation.
y = 7 - x
5x +4(7 -x) = 47 . . . . substitute for y
x + 28 = 47 . . . . . . .. simplify
x = 19 . . . . . . . . . . . . subtract 28
Using our expression for y, we have
y = 7 -19 = -12
The larger number is 19.
The smaller number is -12.
The question is about solving simultaneous equations. Two equations can be set up from the statements provided: x + y = 7 (sum of two numbers is 7) and 5x + 4y = 47 (five times the larger number plus four times the smaller number equals 47). After setting up these equations, solve for x and y.
Explanation:The subject you are asking about falls under the area of Mathematics, specifically simultaneous equations. To solve this question, we need to set up two equations based on the problem's statement and then solve these two equations together.
Given the problem that the sum of two numbers is 7 and five times the larger number plus four times the smaller number is 47, we can set it up as follows:
Let the larger number be x and the smaller number be y.The first statement gives us the equation: x + y = 7The second statement gives us the equation: 5x + 4y = 47Subtracting the first equation from the second gives 4x + 3y = 40 so y = (40 - 4x)/3. Substituting y into the first equation gives x = 7 - (40 - 4x)/3. Solve for x to find the larger number, then substitute x into the equation y = 7 - x to find the smaller number.
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PLZZZ HELP NOOOOWWW!!!
Answers
You can use the Pythagorean Theorem
[tex] a^{2} + b^{2} = c^{2} [/tex]
C is the hypotenuse which is the line across the diameter
a and b are the other sides
You have to find the bottom side of the triangle
9 - 6 = 3
Put in the values you know
[tex] 9^{2} + 3^{2} = c^{2} [/tex]
Square the numbers
[tex]81 + 9 = c^{2} [/tex]
Add
[tex]90 = c^{2} [/tex]
take the square root of both sides
[tex] \sqrt{90} = c[/tex]
The answer is [tex]C) \sqrt{90} [/tex]
Hope this helps!
line L1, L2 and L3 are in the same plane, L1 is perpendicular to L2, and L3 is parallel to L1. which of the following statement must be true?
1. L3 is parallel to L2
2.L3 is perpendicular to L2
3.L3 intersects L2
Answers
because there maybe chances that the line L1 and L3 lies above the line L2 and they can also fulfill the condition of perpendicularity so we can't be sure about statement 3 & statement 1 is clearly incorrect
The true statement will be
1. ''L3 is perpendicular to L2''
What is Parallel lines?
Parallel lines are straight lines that do not intersect at any point.
Given that;
Line L1, L2 and L3 are in the same plane,
L1 is perpendicular to L2, and L3 is parallel to L1.
Now,
Line L1 is perpendicular to L2.
And, L3 is parallel to L1.
Then, Line L3 is perpendicular to line L2
Thus, The true statements will be
1. ''L3 is perpendicular to L2'' and
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Find the distance between the points (
-
10,12) and (15,12).
Answers
[tex]d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} [/tex]
We are given two points in the form (x,y), so plug in the values to the distance formula:
[tex]d= \sqrt{(-10-15)^2-(12-12)^2} [/tex]
Next we can simplify. We know that 12-12 is 0, so we can drop it from the equation, as it will not affect our answer. Also, we know that -10-15 is -25:
[tex]d= \sqrt{(-25)^2} [/tex]
The square and square root cancel each other out leaving us with 25.
The answer is 25.
hayden delivers pizza for papa john's. His average tip is $1.50 for each pizza that he delivers. How many pizzas must he deliver to earn at least $20 in tips?
Answers
let us assume that the number of pizzas he must deliver = x
The tip obtained for one pizza = $1.50
Total tips that he must earn = 20
So, we frame the equation as shown below:
1.50*x = 20
1.50x = 20
x = 20/1.5 = 13.333
So he must deliver 13.333 pizzas
Since he cannot deliver fractional pizzas, the number of pizzas he must deliver = 14 pizzas
What are the zeros of the function f(x) =(x^2 - 3x - 10)(x + 4)
!!Please help!!!
Answers
x - 5 = 0
x = 5
x + 2 = 0
x = - 2
x + 4 = 0
x = - 4
Your zeros are at x = - 4, - 2, and 5. Or at (- 4, 0), (- 2, 0), and (5, 0).
Use synthetic division and the Remainder Theorem to find P(a)
P(x)=x^4+10x^3+8x^2+4x+10 ; a=2
2
–114
56
146
Answers
Synthetic dicision:
! 1 10 8 4 10
x=a=2 ! 2 24 64 136
----------------------------------------------
1 12 32 68 146=Remainder
P(a)=P(2)=146
Answer: Fourth option. 146
Find the magnitude and direction (in degrees) of the vector. v = ‹ - sqrt(7)/9, - sqrt(2)/3 ›
Answers
lvl = root ((- root (7) / 9) ^ 2 + (- root (2) / 3) ^ 2)
lvl = 0.555555556
The address is given by:
cos (theta) = (- root (7) / 9) / (0.555555556)
Clearing theta:
theta = acos ((- root (7) / 9) / (0.555555556))
theta = 121.95 degrees
Answer:
The magnitude and direction (in degrees) of the vector are:
lvl = 0.555555556
theta = 121.95 degrees
Bristol is analyzing positive daily customer feedback on different restaurants to find the perfect place to invest. She would like to choose a restaurant with a high median of positive mark counts and a small interquartile range. She constructed box plots shown in the diagram below. Which restaurant has a median positive mark count above 75 and the smallest interquartile range? Burrito bros, pasta pals, make your own pie, pap smurfys
Answers
Answer:
A. Burrito Bros
Two balls are drawn in succession out of a box containing 6 red and 6 white balls. find the probability that the second ball was red, given that the first ball was:
Answers
Final answer:
The probability that the second ball is red, given the color of the first ball, is 11/22.
Explanation:
To find the probability that the second ball was red, given that the first ball was either red or blue, we need to consider two cases:
If the first ball drawn was red: In this case, there are 5 red balls and 11 balls remaining. So, the probability of drawing a red ball as the second ball is 5/11.If the first ball drawn was blue: In this case, there are 6 red balls and 11 balls remaining. So, the probability of drawing a red ball as the second ball is 6/11.Since the first ball can be either red or blue with equal probability, we need to consider both cases. Thus, the total probability is (1/2) * (5/11) + (1/2) * (6/11) = 11/22.
What is the greatest common factor of 12 and 90?
Answers
Greatest Common Factors are the largest shared factors between 2 or more numbers.
The factors of 12 and 90 are...
12: 1,2,3,4,6,12
90: 1,2,3,5,6,9,10,15,18,30,45,90
Thus meaning the GCF is 6.
I hope this helps!
The graph of the function y=x^2+2 is shown. Which equation will shift the graph of the function to the right 2 units?
Answers
Find the surface area of the cylinder. Round to the nearest whole number.
•1,359 cm^2
•730 cm^2
•553 cm^2
•1,790 cm^2
Answers
Surface area = 2π(7.5)² + 2π(7.5)(8) = 730 cm² (nearest whole number)
Answer: 730 cm²