Answer:
2(x + 3)^2 - 22
Step-by-step explanation:
2x^2 + 12x - 4
Start by making your "a" value equal to 1 by factoring the 2 from the first 2 terms in the standard form equation.
2(x^2 + 6x) - 4
Complete the square by using the formula (b/2)^2. Identify your "b" value, which is 6. Now you can complete the square.
((6)/2)^2 = 9
After completing the square, add 9 inside the parentheses and subtract 9 outside the parentheses. Since the 9 inside the parentheses is also being multiplied by 2, multiply the subtracted 9 by 2 as well.
2(x^2 + 6x + 9) - 4 - 9(2)
Factor the terms inside the parentheses by using the product/sum factoring method. This is where you find two of the same terms that multiply to "c" (9) and add to "b" (6).
In this case, positive 3 multiplies to 9 and adds to 6, so we will use the factors (x + 3)(x + 3), which is the same as (x + 3)^2.
2(x + 3)^2 - 4 - 9(2)
To finish off the problem, combine the like terms outside of the parentheses by multiplying 9 times 2 first and then subtracting -4 by 9(2).
[tex]\boxed{2(x + 3)^2 - 22 }[/tex]
In a random sample of 97 women at a company, the mean salary is $45,902 with a standard deviation of $3865. In a random sample of 75 men at the company, the mean salary is $48,454 with a standard deviation of $6677. Which interval is the 95% confidence interval for the difference between the mean salaries of all women and men at the company?
A) ($1133.20, $3970.80)
B) ($856.36, $4247.64)
C) ($1686.88, $3417.12)
D) ($319.99, $4784.01)
The 95% confidence interval for the difference between the mean salaries of all women and men at the company is (−3570.8,−1533.2), which is option C.
Identify the relevant parameters:
Sample size for women (n_w) = 97
Mean salary for women (μ_w) = $45,902
Standard deviation for women (σ_w) = $3865
Sample size for men (n_m) = 75
Mean salary for men (μ_m) = $48,454
Standard deviation for men (σ_m) = $6677
Confidence level = 95%
Calculate the pooled standard error (s_p):
s_p = √[(n_w * σ_w^2 + n_m * σ_m^2) / (n_w + n_m - 2)]
s_p = √[ (97 * 3865^2 + 75 * 6677^2) / (97 + 75 - 2)]
s_p ≈ $4973.49
Calculate the margin of error (z):
Since the sample size is large for both groups (n_w > 30 and n_m > 30), we can use the standard normal distribution (z-score) with a confidence level of 95%.
z = 1.96 (for 95% confidence level)
Calculate the confidence interval:
Lower bound = (μ_w - μ_m) - z * s_p
Lower bound = ($45,902 - $48,454) - 1.96 * $4973.49
Lower bound ≈ -$3570.80
Upper bound = (μ_w - μ_m) + z * s_p
Upper bound = ($45,902 - $48,454) + 1.96 * $4973.49
Upper bound ≈ -$1533.20
Therefore, the 95% confidence interval for the difference between the mean salaries of all women and men at the company is (-$3570.80, -$1533.20), which confirms your answer of option C.
Lines AB and CD are graphed on this coordinate plane. Which point is the intersection of lines AB and CD?
In your neighborhood, 7/25 of your neighbors have dogs. This is equivalent to what decimal?
Hi there! :)
Answer:
7/25 is equivalent to 0.28
Step-by-step explanation:
In order to go from a fraction to a decimal, you need to divide the numerator (top number) by the denominator (bottom number):
7/25 = 7 ÷ 25
7 ÷ 25 = 0.28
There you go! I really hope this helped, if there's anything just let me know! :)
Answer:0.28
Step-by-step explanation:
so you divided 7 and 25 and it gives 0.28
For a party, Maria pours 5 glasses of juice that each measure of a cup. Collin pours another 6 glasses, also with of a cup of juice each. Which mixed number is equal to the total amount of juice in all the glasses?
Final answer:
To find the total amount of juice in all the glasses, add the amounts poured by Maria and Collin. Maria pours 1 ¼ cups of juice and Collin pours 1 ½ cups of juice, so the total amount is 2 ¾ cups.
Explanation:
To find the total amount of juice in all the glasses, we need to add the amounts poured by Maria and Collin. Maria pours 5 glasses of juice, each measuring ¼ of a cup. So Maria pours a total of 5 x ¼ = 1 ¼ cups of juice. Collin pours 6 glasses, also with ¼ of a cup of juice each. So Collin pours a total of 6 x ¼ = 1 ½ cups of juice. To find the total amount of juice in all the glasses, we add 1 ¼ cups and 1 ½ cups, which gives us a total of 2 ¾ cups of juice.
The leather depot buys a coat from a supplier for $90 wholesale and marks up the price by 40%. If the retail price is $134.82 , what is the sale tax?
Answer:
$8.82 is the amount of sales tax
Step-by-step explanation:
$90 x .40 = $36.00
$90 + $36 = $126
$134.82 - $126 = $8.82 in taxes
Find the distance between the two points shown in the coordinate plane below to the nearest hundredth.
Question 16 options:
61.0
7.23
7.81
8.02
Answer:
7.81
Step-by-step explanation:
= √(5^2 + 6^2)
= √(25 + 36)
= √61
= 7.81
Answer:
7.81
Step-by-step explanation:
we have the points: (-2, -2) and (3, 4)
where i will call [tex]x_{1}=-2, y_{1}=-2,x_{2}=3,y_{2}=4[/tex]
We can find the distance using the Pythagorean theorem, considering that the distance in x between the points is: [tex]d_{x}=[/tex] [tex]x_{2}-x_{1}=3-(-2)=3+2=5[/tex]
and the distance in y between the points is: [tex]d_{y}=[/tex][tex]y_{2}-y_{1}=4-(-2)=4+2=6[/tex]
and using the Pythagorean theorem
[tex]d=\sqrt{d_{x}^2 +d_{y}^2}[/tex]
[tex]d=\sqrt{5^2+6^2}=\sqrt{25+36}=\sqrt{61} =7.81[/tex]
the distance between the two points ia 7.81
Elton hiked 16 miles each day on a 12 day hiking trip.Lola hiked 14 miles each day on her 16 day hiling trip.In all, how many more miles did Lola hike than Elton hiked
Answer:
32 miles.
Step-by-step explanation:
We have been given that Elton hiked 16 miles each day on a 12 day hiking trip.
So, the number of miles hiked by Elton in 12 days will be: [tex]16\times 12=192[/tex] miles.
Lola hiked 14 miles each day on her 16 day hiking trip.
So, the number of miles hiked by Lola in 16 days will be: [tex]14\times 16=224[/tex] miles.
Let us subtract number of miles hiked by Elton from Number of miles hiked by Lola.
[tex]\text{Number of miles that Lola hiked more than Elton}=224-192[/tex]
[tex]\text{Number of miles that Lola hiked more than Elton}=32[/tex]
Therefore, Lola hiked 32 miles more than Elton in all.
The measure of angle θ is 7pi/6 so the measure of the reference angle is what?
Answer:
[tex]\frac{\pi }{6}[/tex]
Step-by-step explanation:
Since [tex]\frac{7\pi }{6}[/tex] is in the third quadrant then
reference angle = [tex]\frac{7\pi }{6}[/tex] - π = [tex]\frac{\pi }{6}[/tex]
Total cost of job = $147.51 Duration of job = 5 hours Price of parts = $32.50 Overhead rate = 55% Hourly labor rate = _____.
Answer:
Hourly labor rate = $14.84
Step-by-step explanation:
Total cost of job = $147.51
Price of parts = $32.50
Labor cost + overhead = Total cost - parts = 147.51 - 32.5
=115.01
Overhead rate = 55%
Labor cost = 115.01/(1+55%) = 115.01/1.55
=74.2
Duration of job = 5 hours
Hourly labor rate = 74.2/5
= $14.84
Answer:
$14.84
Step-by-step explanation:
Total cost of job = $147.51=labor+overhead+parts
Price of parts = $32.50
labor+overhead =147.51-32.5=115.01
Overhead rate = 55%
labor+0.55labor= 115.01
labor=115.01/(1.55)=74.2
Duration of job = 5 hours
hourly labor=74.2/5=$14.84
Solve the inequality 4x - 6 > 6x - 20
A.) x > 7
B.) x < 7
C.) x < 2
D.) x > 2
Answer:
What the othe rguy said, also give him brainliest
Step-by-step explanation:
Find the first, fourth, and eighth terms of the sequence. A(n) = –5 • 2n–1
A. –5; –40; –640
B. –20; –160; –2,560
C. 1; –1,000; –10,000,000
D. –10; –80; –1,280
Answer:
-5; -40; -640
Step-by-step explanation:
Use this regular pentagon to answer the questions. What is the measure of one of the central angles in the regular pentagon?
Answer:
Measure of one of the central angles in the regular pentagon is 72 degree.
Step-by-step explanation:
A Central angle states that the angle made at the center of the polygon by any two adjacent vertices of the polygon.
If you draw a line from any two adjacent vertices to the center, then they would make the central angle.
Since, it is given that the polygon we use here is regular pentagon.
⇒ All the central angles are equal.
The formula to find the central angle is:
Central Angle = [tex]\frac{360^{\circ}}{n}[/tex] where n is the number of sides.
Since, the measure of the central angle thus depends only on the number of sides.
Here, side(n) = 5 (Polygon is regular pentagon)
then;
Central angle = [tex]\frac{360^{\circ}}{5} =72^{\circ}[/tex]
Therefore, the measure of one of the central angle in the regular pentagon is, [tex]72^{\circ}[/tex]
Answer:
72 and 54 are your answers
Step-by-step explanation:
A number to the 8th power divided by the same number to the 5th power is 64 what is the number?
Let the number = X
You have X^8 / X^5
When dividing two numbers with powers, Simplify the expression by subtracting the powers.
8-5=3
so X^8 / X^5 becomes x^3
Now you have x^3 = 64
To find x take the cubic root of 64:
X = ∛64
X = 4
The number is 4
You have to complete a sales record to the nearest 10 drinks. A total of 776 drinks have been sold. What number do you write in the sales record? ... Drinks?
Answer:
780 drinks
Step-by-step explanation:
round 776 to nearest more and it is 780 drinks
Answer:
The answer is 780, you round the number to the nearest 10th if it was 774 drinks answer would be 770
Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Choose the correct formula for the function g.
Answer: C
Step-by-step explanation:
g(x) has the following transformations:
1. horizontal shift to the right 3 units --> 2ˣ⁻³
2. vertical shift up 2 units --> 2ˣ⁻³ + 2
A large chess tournament starts with 1024 players. How many players will be remaining after 6 rounds
Final answer:
After 6 rounds of the chess tournament starting with 1024 players, 16 players will remain. In the story of the king and chessboard with exponential doubling of rice, the total would be [tex]2^{64[/tex] - 1 grains.
Explanation:
To determine how many players will remain after 6 rounds in a chess tournament that starts with 1024 players, we recognize this as a process of successive halving. If each round eliminates half the players, then after each round, the number of players will be:
After Round 1: 1024 / 2 = 512 playersAfter Round 2: 512 / 2 = 256 playersAfter Round 3: 256 / 2 = 128 playersAfter Round 4: 128 / 2 = 64 playersAfter Round 5: 64 / 2 = 32 playersAfter Round 6: 32 / 2 = 16 playersTherefore, 16 players will remain after 6 rounds in the tournament. Referring to the classic story of the king and the chessboard, when grains of rice are doubled on each square, the final total is one less than [tex]2^{64[/tex] grains. Without adding it all up, we can say this final number is [tex]2^{64[/tex] - 1 grains of rice.
12) Miranda wants to buy as many collectible dolls as possible, for $2.50 each. If she has $45.00 to spend, how many dolls can she buy? Which equation BEST represents this situation? A) 45x = 2.5 B) 2.5x = 45 C) x + 2.5 = 45 D) x + 45 = 2.5
Answer:
The answer would be B
2.5x = 45
(x) would be the number of dolls, multiplied by how much each doll costs ($2.50) and the product would be how much she has to spend. Hope this helps!
Sarah works as a waiter. She earns 15% in tips on meals served. This weekend, Sarah earned $172.50 in all. What is the dollar amount of the meals that Sarah served?
Answer:
$1150 amount of the meals that Sarah served.
Step-by-step explanation:
As given
Sarah works as a waiter.
She earns 15% in tips on meals served.
This weekend, Sarah earned $172.50 in all.
Let us assume that the x dollar amount of the meals that Sarah served .
15% is written in the decimal form.
[tex]= \frac{15}{100}[/tex]
= 0.15
Than the equation becomes
x × 0.15 = 172.50
Solving the above equation
[tex]x = \frac{172.50}{0.15}[/tex]
x = $1150
Therefore $1150 amount of the meals that Sarah served.
A forest covers 41,000 acres. A survey finds that 0.4?% of the forest is? old-growth trees. How many acres of? old-growth trees are? there?
Answer: A forest covers 41,000 acres. A survey finds that 0.4?% of the forest is? old-growth trees. How many acres of? old-growth trees are? there?
Alrighty, let me help you out, make things easier! The ANSWER is going to be 24,600, by this process, just take 41,000 and multiply that by 0.4. that gives you 16400, and since you are trying to find a portion of the forest, you subtract 16400 from 41,000 total acres. Hope that helps!
You Havel 48.50 in the bank and your friend has $1.00 your allowance is 9.50 per week and your friend gets twice as much. After how many weeks do u have the same amount
Answer:
4 weeks
Step-by-step explanation:
Final answer:
After 5 weeks, you and your friend will have the same amount.
Explanation:
To find out after how many weeks you and your friend will have the same amount, we need to set up an equation and solve for the number of weeks. Let's assume the number of weeks is represented by 'w'.
Your balance in the bank after 'w' weeks can be represented by the expression: 48.50 + 9.50w. Your friend's balance after 'w' weeks can be represented by the expression: 1 + 2(9.50w). We want to find out when these two balances are equal, so we set up the equation: 48.50 + 9.50w = 1 + 19w.
Solving this equation, we get:
48.50 + 9.50w = 1 + 19w
48.50 - 1 = 19w - 9.50w
47.50 = 9.50w
w = 47.50/9.50
w = 5
After 5 weeks, you and your friend will have the same amount.
What is 508 times 82 in math answer clear please and I really need help with math but thank you I will use this website more often (:
Answer:
508*82 is 41656
Step-by-step explanation:
NEED HELP !!!!!!!! ASAP PLZ
In the process of proving that opposite sides of a parallelogram are congruent, Ross drew a diagonal of the parallelogram and determined that the two triangles formed are congruent. He then concluded that opposite sides must be congruent, because corresponding parts of congruent triangles are congruent.
Using his markings in the diagram, which postulate allowed him to determine that the two triangles formed are congruent?
A) AAS
B) ASA
C) SAS
D) SSS
Answer: Congruency criteria used by Ross to prove the opposite sides are congruent is B) ASA congruence postulate
One copy of a new book by Amanda's favorite author cost $9.45. If a total of 2,740 copies of the book were sold on the first day of the book's real release, what were he total sales that day?
Answer:
25,893
Step-by-step explanation:
2.740 x 9.45=25,893
Luz drives at an average speed of 45 miles per hour. She has driven for 3 hours and has travelled a distance of 135 miles. This situation can be represented with a linear equation written in point-slope form, where x represents the number of hours and y represents the number of miles. Use this information to complete each statement about the linear equation.
Answer:
[tex](y-135)=45(x-3)[/tex]
Step-by-step explanation:
Let x represents the number of hours and y represents the number of miles.
We are told that Luz drives at an average speed of 45 miles per hour. She has driven for 3 hours and has traveled a distance of 135 miles.
We can see from our given information that slope of line is 45 as with each increase in number of hours (x), change in distance (y) is 45.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{135-0}{3-0}[/tex]
[tex]m=\frac{135}{3}[/tex]
[tex]m=45[/tex]
Since the equation of line in point-slope form is : [tex](y-y_1)=m(x-x_1)[/tex], where m represents slope of line and [tex](y_1,x_1)[/tex] represents a point the line passes through.
Upon substituting our given values in point-slope form of equation we will get,
[tex](y-135)=45(x-3)[/tex]
Therefore, the equation represented in point-slope form will be: [tex](y-135)=45(x-3)[/tex].
Answer:
The slope of the linear equation is 45.
A point on the graph of a linear equation will be (3, 135).
This linear equation can be written as (y-135)=45(x-3).
Tia and her five friends are going to the ice skating rink. Each person $5 for admission and $5 for food. Write and evaluate a numerical expression to find the total cost for admission and food
Where C = Cost and P = People
C = 2(5p)
In the context of Tia and her five friends:
C = 2(5*6) = 2(30) = 60
C = 60
The cost for Tia and her five friends to be admitted to ice skate and eat is 60$, and the equation to calculate this is C = 2(5p).
Use the slope formula to find the slope of the line passing through the given points.
(–4, 7) and (0, 8)
Answer:
Slope of the line passing through the given points are: [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Slope of a line : For any two point [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
the formula of slope is given by:
Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Given the points ( -4, 7) and (0, 8)
then, by using slope formula;
[tex]m = \frac{8-7}{0-(-4)} = \frac{1}{0+4} = \frac{1}{4}[/tex]
Therefore, the slope of the line passing through the given points are: [tex]\frac{1}{4}[/tex]
Answer:
1 / 4
Step-by-step explanation:
We are to find the slope of a line which passes through the two given points: (–4, 7) and (0, 8).
We know the formula of the slope (m):
[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
So putting in the values of the coordinates of the given points in the formula to get:
Slope = [tex]\frac{8-7}{0--4} = \frac{1}{4}[/tex]
Therefore, the slope slope of a line which passes through the two given points: (–4, 7) and (0, 8) is 1 / 4.
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 6 rows of the same length, he has 9 chairs left over. If he arranges the chairs in 4 rows of that same length, he has 13 left over. How many chairs does Liam have?
Helpppppppppppppppppp
Answer:
The answer is 6.
Step-by-step explanation:
You need to have side x + 4 equal side 3x - 8. If you plug 6 into both equations, then you get x + 4 = 910and 3x - 8 = 10. The last side of the triangle equals 6. You then add all three sides together to get 25. 10 + 10 + 5 = 25.
This is an isosceles triangle (a triangle with 2 congruent/equal sides and 2 congruent angles)
If you look at the triangle, most likely side AB and BC are congruent.
Since the sides are suppose to be the same/equal to each other, you can do this:
AB = BC
x + 4 = 3x - 8 Subtract x on both sides
4 = 2x - 8 Add 8 on both sides
12 = 2x Divide 2 on both sides
x = 6
You need to find AC.
AC = x, since you know x = 6, side AC is 6 units
At Pizza Pi 24% of the pizzas made last week had extra cheese. If 6 pizzas had extra cheese how many pizzas in all were made last week
Answer:
1.44
Step-by-step explanation:
A situation for which each member of a set, such as angles of a triangle, can be paired with one and only one member of another set. - ? Angles paired with one another in a one-to-one correspondence between geometric figures. - ? Sides paired with one another in a one-to-one correspondence between figures. - ? If a one-to-one correspondence between the parts of two figures is such that the corresponding parts are equal, then the figures are congruent. - ? The angle formed by two sides of a triangle. - ? The side of a triangle that is formed by the common side of two angles. - ?
Answer: A one-to-one correspondence between the parts of two figures is such that the corresponding parts are equal, then the figures are congruent.
The question pertains to geometric concepts of congruence, one-to-one correspondence, included side, included angle, and vector concepts in mathematics, such as orthogonal and parallel vectors, which are key concepts in solving geometry and trigonometry problems.
Explanation:The question refers to several key concepts in geometry. When each member of a set, such as angles of a triangle, can be paired with one and only one member of another set, we have a one-to-one correspondence. This correspondence can be applied to situations such as pairing angles or sides of one geometric figure with another.
For example, let's consider two triangles. If each angle of the first triangle corresponds to an angle of the second triangle, and all pairs of corresponding elements (angles or sides) are equal, then those two triangles are congruent. This is the basic principle of congruence in geometry.
The angle formed by two sides of a triangle is called an included angle. The side of a triangle that is formed by the common side of two angles is an included side. In a right triangle, like in Figure 5.17, we see the terms adjacent side, opposite side, and hypotenuse, which are used for trigonometric calculations such as sine, cosine, and tangent.
The Pythagorean Theorem plays a crucial role for right-angled triangles, stating that the square on the hypotenuse is equal to the sum of squares on the other two sides. Also, the question talks about parallel and orthogonal vectors. Two vectors are said to be parallel if they have identical directions, while orthogonal vectors are perpendicular to each other, with directions differing by exactly 90°.
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