Answer:
Justin spends $14.24 on gas to travel to work.
Step-by-step explanation:
Given:
Average speed at which Justin goes to work = 65 miles/hour
Time taken by Justin to arrive at work = 1 hour and 30 minutes = 1.5 hours [As 30 minutes =0.5 hours]
Distance he can travel per gallon of gas = 25 miles.
Cost of per gallon of gas = $3.65
Solution:
We first determine the distance Justin travels to work.
Distance = [tex]Speed\times time[/tex]
Distance = [tex]65\times 1.5 = 97.5\ miles[/tex]
Using unitary method to find the amount of gas required to cover the distance.
If 25 miles is covered in 1 gallon of gas
Then 1 mile will be covered in = [tex]\frac{1}{25}[/tex] gallons of gas
So, to cover 97.5 miles gas required = [tex]\frac{1}{25}\times 97.5=3.9[/tex] gallons of gas.
Using unitary method to find the cost of 3.9 gallons of gas.
Cost of 1 gallon of gas = $3.65
So, cost of 3.9 gallons of gas will be = [tex]\$3.65\times 3.9=\$14.235\approx\$14.24[/tex] (Answer)
As a prize a contest winner get to draw out one bill at a time from a box containing 10 five dollar bills 10 ten dollar bills and 10 twenty dollar bill the drawing end when 3 bill of the same denomination are drawn and of course the contest winner keeps whatever he was drawn. What is the largest sum of money that can be won under these condition?
The largest sum of money that can be won under these condition is $90.
To start finding the maximum able to be drawn, they contest winner would draw 3 [tex]\times[/tex] $20 bills = $60.
Prior to drawing the 3rd $20 bill, the contest winner could draw 2 of the $5 bills and 2 of the $10 bills.
This added to the $20 bills they had drawn would give:
(2 [tex]\times[/tex] $5) = $10
(2 [tex]\times[/tex] $10) = $20
Add all the ability to win the contest.
$10 + $20 + $60 = $90
Thus, the largest sum of money that can be won under these condition is $90.
For her birthday, Kendra received a gift card in the mail from her grandparents. The gift card was worth $50. Kendra thought, since she had just received other gifts for her birthday, she would wait a while to spend the gift card. Unfortunately, Kendra forgot all about the gift card, and the card loses $5 every month after its date of purchase if it has not been used.
If Kendra forgot the card for three months, she lost $______.
a) 9 b) 10 c) 15 d) 12
Answer:
She lost $15 on her 50 dollar credit card.
Step-by-step explanation:
Kendra received a gift card in the mail from her grandparents. The gift card was worth $50.
Kendra forgot all about the gift card, and the card loses $5 every month after its date of purchase if it has not been used.
Kendra loses $5 each month,
She forget the card for 3 months.
So, Multiply the $5 by 3 months
$5×3=$15
Hence, she lost $15.
Lisa is interested in how well people are able to detect whether another person is a "Cooperator", a "Competitor", or an "Individualist" simply by looking at a picture of the person’s face. She wants to know what kind of face can be identified most easily, and whether this varies by the race of the person in the picture. She designs a 2 x 3 within-group design where she has participants in her study look at faces from African-American and Caucasian people who are "Cooperators", "Competitors", or "Individualists." The participants identify the personality of the person in each picture and Lisa keeps track of the number of pictures accurately identified for each picture type. How many cells was each participant in?
Answer:
The answer is 6.
Step-by-step explanation:
In the question it is stated that Lisa has designed a "within-group" or "within-subject" experiment using three categories with 2 subject in each category.
Within-group / within-subject experiments mean that every participant is tested for each condition of the experiment, so everyone goes through the same process.
Considering these informations, we can calculate that each participant was in 6 cells because there are 3 categories and 2 subjects for each of the categories.
I hope this answer helps.
In an obtuse isosceles triangle the angle measurements are, x∘, x∘, and (10x−2)=128∘. Find the measurement of one of the acute angles.
Answer:
26°
Step-by-step explanation:
An obtuse triangle is a triangle that has one obtuse angle. Obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees.
An isosceles triangle is a triangle that has two equal sides and angles.
Therefore, an obtuse isosceles triangle is a triangle with an obtuse angle and two equal sides that have two equal acute angles (angle less than 90° ).
Given:
The three angles of the triangle are given to be x°, x° and (10x−2) = 128°. The obtuse angle is 128°, the two x° are acute angles. We are not using equation 10x − 2 since the value of the obtuse angle has been given as 128°
The sum of angles in a triangle is 180°
∴ x° + x° + 128° = 180°
2x° = 180° - 128°
2x° = 52°
x° = 52° / 2
x° = 26°
The measurement of one of the acute angles is 26°
the x-intercepts of y=tanx are the same as the x-coordinates of the center points of y=tanx
Answer:
It is true that the x-intercepts of y=tanx are the same as the x-coordinates of the center points of y=tanx
Step-by-step explanation:
Given function is a trignometric one
y = tanx
we have tanx has values 0 for all multiples of pi.
i.e. tan x =0 whenever [tex]x = 2n\pi[/tex] for all integers n.
Also tanx has a period of pi.
It is a discontinuous graph extending in one period from -pi/2 to pi/2.
Hence the mid point of each period is the x intercept.
It is true that the x-intercepts of y=tanx are the same as the x-coordinates of the center points of y=tanx
Final answer:
The x-intercepts of the function y=tan(x) are at integer multiples of π. The concept of 'center points' for y=tan(x) is not well-defined due to the nature of the function having no central axis and being periodic.
Explanation:
The student is inquiring about the x-intercepts and center points of the function y=tan(x). The x-intercepts of the tangent function occur wherever y=0, which happens at values of x that are integer multiples of π, as the tangent function has a period of π.
On the other hand, the concept of center points is not well-defined for the tangent function since it does not have a central axis like an ellipse or a bounded pattern. The tangent function is periodic and continuous between its vertical asymptotes, which occur at odd multiples of π/2.
If AB is the diameter of the circle with center X and C is a point on the circle such that AC = AX = 3, what is the perimeter of triangle ABC ?
Answer:
Step-by-step explanation:
The perimeter of a shape or plane figure is the distance round the shape. The diagram of the circle and the triangle ABC formed is shown in the attached photo.
To determine the length of AC, we would apply the Pythagoras theorem which is expressed as follows
Hypotenuse^2 = opposite ^2 + adjacent ^2
AC = hypotenuse
Opposite = 3
Adjacent = 3
AC^2 = 3^2 + 3^2 = 9 + 9 = 18
AC = √18 = 4.24
BX = AX = 3(they are both radii)
BC = AC = 4.24
The perimeter of triangle ABC would be
3 + 3 + 4.24 + 4.24 = 14.48
Clare said that (4/3) ÷ (5/2) is (10/3). She reasoned: (4/3) ⋅ 5 = (20/3) and (20/3) ÷ 2 = (10/3). Explain why Clare's answer and reasoning are incorrect. Find the correct quotient.
Answer:
Correct quotient =
[tex]\dfrac{8}{15}[/tex]
Step-by-step explanation:
We are given he following in the question:
[tex]\text{Clare's calculation:}\\\\\dfrac{4}{3}\div \dfrac{5}{2} = \dfrac{10}{3}\\\\\text{Clare's reason:}\\\\\dfrac{4}{3}\times 5 = \dfrac{20}{3}, \dfrac{20}{3} \div 2 = \dfrac{10}{3}[/tex]
Clare's, reason is incorrect.
The correct quotient can be calculated in the following manner:
[tex]\dfrac{4}{3}\div \dfrac{5}{2}\\\\= \dfrac{4}{3}\times \dfrac{2}{5} = \dfrac{8}{15}[/tex]
Clare simply multiplied the fraction with 5 and divided the product with 2 which is incorrect. We have to multiply the fraction with the reciprocal of divisor.
Answer:
The answer is 8/15
Step-by-step explanation:
4/3 divided by 5/2 is the same as 4/3 times 2/5
4/3 times 2/5= 8/15
8/15 is the answer
She is wrong because if you want to do it you have to multiply the fraction with 5 and then MULTIPLY it by 2 not divide it by 2.
Determine whether the function below is an even function, an odd function, both, or neither.
f(x)=(x+5)^2
A.
neither even nor odd
B.
even function
C.
both even and odd
D.
odd function
Answer:
A. neither even nor odd
Step-by-step explanation:
The equation is that of a parabola whose line of symmetry is x=-5. Even functions are symmetrical about the line x=0, so this is not an even function. It has terms of even degree, so is not an odd function.
The function is neither even nor odd.
Answer:
Option A - neither even nor odd
Step-by-step explanation:
Given : [tex]f(x)=(x+5)^2[/tex]
To find : Determine whether the function below is an even function, an odd function, both, or neither ?
Solution :
We know that,
1) If f(-x)=f(x) it is an even function.
2) If f(-x)=-f(x) it is a odd function.
[tex]f(x)=(x+5)^2[/tex]
[tex]f(x)=x^2+10x+25[/tex]
Substitute x with -x in the function,
[tex]f(-x)=(-x+5)^2[/tex]
[tex]f(-x)=x^2-10x+25[/tex]
The function does not comply with the definitions.
The function is neither even nor odd.
Therefore, option A is correct.
In June, Susie buys a dozen of cans of Dog's Dinner dog food at $1.89 per can. She also buys two bags of 'Dem Bones dental chews that each cost $12.69, and a new toy for $10.25. She pays sales tax at a rate of 7.25%. What is her total cost for the month of June?
Answer:
$62.54
Step-by-step explanation:
12 cans dog food = 12 × 1.89 = $22.68
2 bags dental chews = 2 × 12.69 = 25.38
1 toy = 10.25
Subtotal = 58.31
Sales tax = 0.0725 × 58.31 = 4.23
TOTAL = $62.54
Suzie's total cost for June was $62.54.
For the following inequality, indicate whether the boundary line should be dashed or solid. x ≤ 5 dashed solid.
Answer:
Solid
Step-by-step explanation:
Rewriting for the sake of clarity:
1) For the following inequality, indicate whether the boundary line should be dashed or solid. x ≤ 5
2) Since it is a closed interval which includes the number 5 then this can also be written as:
[tex](-\infty,5][/tex]
3) Hence, we can graph it as a solid line crossing the point (5,0). For the x coordinate 5, is within the interval.
8. When starting your credit history, a low-credit-limit, high-interest-rate credit card should be paid ____.
in full, on time, every time
in even payments each time
at least the minimum due
as much as you can when due
9. APY means ____.
annual percentage yield
annual percentage yearly
apportioned percentage yield
applied percentage yield
Answer:
8. When starting your credit history, a low-credit-limit, high-interest-rate credit card should be paid in full, on time, every time.
9. APY means annual percentage yield.
Explanation:
8. A person's credit history tells about the ability of a person to pay and repay his debts. This is very important especially when you want to avail of a credit card from a company because it reflects on how responsible you are when it comes to repaying your debts. However, when you are just starting your credit history, it is important to give a good impression, so you'd have an easier approval in the future.
Usually, for starters with low salary, a low-credit-limit with a high-interest-rate credit card is common. It is very important to pay your debts in full, on time and every time in order to avoid incurring a balance that you will be carrying from one month to the other. If you do this, you will be ending up paying lots of interest charge.
Paying in full, on time and every time will also give you the chance to have an increased credit limit in the future.
9. APY is also known as "Annual Percentage Yield." This is the actual amount (rate of return) that a person could earn while his money is being deposited in the bank in one year. Other than the deposited money, investment that earns a rate of return could also refer to bonds and stock share. APY considers the compounding interest in its computation. This means that the higher your balance, the higher the APY. The value of the asset also increases.
On a farm A 4/5 of the number of sheep are equal to 1/2 of the number of sheep on farm B. The total number of sheep on farm A and farm B is 845. How many sheep are there on farm B
Answer:
There are 520 sheep on Farm B.
Step-by-step explanation:
Let the Number of sheep on farm B be x
Given:
On a farm A 4/5 of the number of sheep are equal to 1/2 of the number of sheep on farm B.
It means Number of sheep on farm A multiplied by 4/5 is equal to 1/2 multiplied by Number of sheep on farm B.
framing the equation we get;
[tex]\frac{4}{5}\times \textrm{Number of sheep on Farm A} = \frac{1}{2} \times x[/tex]
Number of sheep on Farm A = [tex]\frac{x}{2}\times\frac{5}{4} = \frac{5x}{8}[/tex]
Now Given:
Total Number of sheep =845.
We know that Total Number of sheep is equal to sum of sheep at farm A and sheep at farm B.
Framing equation we get;
[tex]\frac{5x}{8}+x=845[/tex]
Taking L.C.M we get;
[tex]\frac{5x\times 1}{8\times1}+\frac{x\times8}{8} =845\\\\\frac{5x}{8}+\frac{x}{8} =845\\\\\frac{5x+8x}{8}=845\\\\\frac{13x}{8}= 845\\\\13x=845\times8\\\\x=\frac{845\times8}{13} = 520[/tex]
Number of sheep on Farm B = 520 sheep
Number of sheep on Farm A = [tex]\frac{5}{8}\times 520 = 325\ sheep[/tex]
Hence There are 520 sheep on Farm B.
David made a scale drawing of a mural he is going to paint. He used a scale of 1 cm=4ft. If the actual mural will be 16 feet long, how long is the mural in David's drawing
Answer:
4 cm
Step-by-step explanation:
we know that
The scale drawing is
[tex]\frac{1}{4}\ \frac{cm}{ft}[/tex]
That means ----> 1 cm in the drawing represent 4 ft in the mural
so
To find out the dimensions in the drawing, multiply the actual dimension by the scale drawing factor
so
[tex](16\ ft)(\frac{1}{4}\ \frac{cm}{ft})=4\ cm[/tex]
1. Frank Choi bought a rechargeable lantern that regularly sells for $29.99. The markdown rate was 30% and there is no sales tax on the item. Find the final price of the item.
Answer:20.993
Step-by-step explanation:
The real price "r" is
100% and =29.99
The price after discount "d" is
100% - 30% = 70% and =?
So:
"r" is 100% =29.99
"d" is 70% =?
Do a cross multiplication so :
"d"= (29.99 * 70) / 100 = 20.993
The final price of the item is 20.993.
Frank Choi bought a rechargeable lantern that regularly sells for $29.99.
The markdown rate was 30% and there is no sales tax on the item.
The real price "r" is
100% =29.99
The markdown rate was 30%
29.99 * (30/100)
8.997
The price after discount
29.99 - 8.997 = 20.993.
Therefore, the final price of the item is 20.993.
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A chemist currently has a solution of 30% hydrochloric acid and a solution of 15% hydrochloric acid. He mixes the two solutions together to create 24 oz of a 25% hydrochloric acid solution. How many ounces of the 30% hydrochloric acid solution did he use in order to obtain the 25% solution
Answer:
16 ounces of the 30% hydrochloric acid solution is used in order to obtain the 25% solution.
Step-by-step explanation:
Let amount of 30% ounces be 'x' and that of 15% ounces by 'y'.
Given:
Total amount on mixing both the solution = 24 oz
∴ [tex]x+y=24\\x=24-y------------ 1[/tex]
Also, the total acid content in the resulting 25% solution is equal to the sum of the acid contents in 30% and 15% solutions.
∴ [tex]0.30x+0.15y=0.25(24)\\0.30x+0.15y=6-------2[/tex]
Now, plug in 'x' from equation (1) into equation (2). This gives,
[tex]0.30(24-y)+0.15y=6[/tex]
[tex]7.2-0.3y+0.15y=6[/tex]
[tex]-0.3y-0.15y=6-7.2[/tex]
[tex]-0.15y=-1.2[/tex]
[tex]y=\frac{1.2}{0.15}=8[/tex] ounces
Therefore, [tex]x=24-8=16[/tex] ounces
Hence, 16 ounces of the 30% hydrochloric acid solution is used in order to obtain the 25% solution
Mr. Nordman gets a commission of $2.30 on each pair of women's shoes he sells, and a commission of $3 on each pair of men's shoes he sells. To meet his sales targets, he must sell at least 10 pairs of women's shoes and at least 5 pairs of men's shoes. He also wants to make at least a $60 a week in commissions. Define the variables, write a system of inequalities to represent this situation, and name one possible solution.
Answer:
x ≥ 5
y ≥ 10
3x + 2.3y ≥ 60
Step-by-step explanation:
Lets the number of men's shoes he sells be x and women's shoes be y.
For each men's shoes , he gets a commission of $3 and for each women's shoe, he gets a commission of $2.30 .
He needs to sell atleast 10 women's shoes and 5 men's shoes.
Also he needs to make atleast $60 per week.
x ≥ 5
y ≥ 10
3x + 2.3y ≥ 60
These are are the 3 required inequalities.
Now we will see an example.
If he sells 20 womens shoes and 10 mens shoes , he will meet the requirements.
He will make a total profit = [tex]2.3\times 20 + 3\times 10[/tex] =$76
Need help doing this question! Thanks . = )
Answer:the boat will travel about 20.62 miles
Step-by-step explanation:
Since the boat travelled from dock A to dock B without passing and stopping at dock C along the way. The number of miles travelled would be the hypotenuse of the right angle triangle shown. To determine the number of miles travelled, we would apply Pythagoras theorem which is expressed as
Hypotenuse^2 = opposite side^2 + adjacent side^2
Looking at the triangle,
Opposite side = 13 miles
Adjacent side = 16 miles
Hypotenuse^2 = 13^2 + 16^2 = 425
Hypotenuse = √425 = 20.62 miles
Rewrite with only sin x and cos x.
sin 2x - cos x
2 sin x cos2x
sin x
cos x (2 sin x - 1)
2 sin x
Answer:
cos x (2 sin x − 1)
Step-by-step explanation:
sin(2x) − cos x
Use double angle formula.
2 sin x cos x − cos x
Factor.
cos x (2 sin x − 1)
Final answer:
The expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).
Explanation:
Given the expression sin 2x - cos x, we can rewrite it using only sin x and cos x. Using the trigonometric identity sin 2x = 2 sin x cos x, we can substitute it into the expression:
sin 2x - cos x = 2 sin x cos x - cos x
Factoring out the common factor cos x, we get:
sin 2x - cos x = cos x (2 sin x - 1)
So, the expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).
The sum of the first three terms of a geometric progression is 126. If 14, 36, and 4 are added to each of these terms, respectively, then the new numbers form an arithmetic progression. Find the sixth term of the geometric progression
Answer:
if r=4:
[tex]\displaystyle a_6=6144[/tex]
if r=1/4:
[tex]\displaystyle a_6=\frac{3}{32}[/tex]
Step-by-step explanation:
Geometric and Arithmetic Progressions
We define a geometric progression when each term [tex]a_n[/tex] is defined as the previous term [tex]a_{n-1}[/tex] times a constant called the common ratio. The iterative formula is
[tex]\displaystyle a_n=a_1.r^{n-1}[/tex]
In an arithmetic progression, each term is found by adding a constant called common difference, to the previous term
[tex]\displaystyle a_n=a_1+(n-1).r[/tex]
We are given the condition that the sum of the three first terms of a geometric progression is 126
[tex]\displaystyle a_1+a_2+a_3=126[/tex]
Using the iterative formula, we have
[tex]\displaystyle a_1+a_1.r+a_1.r^2=126[/tex]
Taking a common factor
[tex]\displaystyle a_1(1+r+r^2)=126....[eq\ 1][/tex]
We also know that if 14, 36, and 4 are added to each term, respectively, the new numbers form an arithmetic progression. It means they will have a common difference. The new numbers will be
[tex]\displaystyle a_1'=a_1+14[/tex]
[tex]\displaystyle a_2'=a_2+36[/tex]
[tex]\displaystyle a_3'=a_3+4[/tex]
The common difference between term 2 and term 1 is
[tex]\displaystyle a_2'-a_1'=a_2+36-a_1-14[/tex]
Using the iterative formula again
[tex]\displaystyle a_2'-a_1'=a_1.r-a_1+22[/tex]
The common difference between term 3 and term 2 is
[tex]\displaystyle a_3'-a_2'=a_3+4-a_2-36[/tex]
Using the iterative formula again
[tex]\displaystyle a_3'-a_1'=a.r^2-a.r-32[/tex]
Both common differences must be equal
[tex]\displaystyle a_1.r-a_1+22=a_1.r^2-a_1.r-32[/tex]
Rearranging
[tex]\displaystyle 2a_1r-a_1r^2-a_1=-54[/tex]
Solving for [tex]a_1[/tex]
[tex]\displaystyle a_1=\frac{54}{1-2r+r^2}......[eq\ 2][/tex]
Replacing in eq 1
[tex]\displaystyle \frac{54(1+r+r^2)}{1-2r+r^2}=127[/tex]
Dividing by 18 and cross-multiplying
[tex]\displaystyle 3+3r+3r^2=7-14r+7r^2[/tex]
Rearranging we have a second-degree equation
[tex]\displaystyle 4r^2-17r+4=0[/tex]
Factoring
[tex]\displaystyle (r-4)(4r-1)=0[/tex]
The solutions are
[tex]\displaystyle r=4\ ,\ r=\frac{1}{4}[/tex]
If r=4, and using eq 2
[tex]\displaystyle a_1=\frac{54}{1-8+16}=6[/tex]
Having [tex]a_1[/tex] and r, we compute [tex]a_6[/tex]
[tex]\displaystyle a_6=a_1.r^5=6.(4)^5[/tex]
[tex]\displaystyle a_6=6144[/tex]
If we use the other solution r=1/4
[tex]\displaystyle a_1=\frac{54}{1-\frac{1}{2}+\frac{1}{16}}=\frac{54}{\frac{9}{16}}[/tex]
[tex]\displaystyle a_1=96[/tex]
The sixth term is
[tex]\displaystyle a_6=96(\frac{1}{4})^5=\frac{96}{1024}[/tex]
[tex]\displaystyle a_6=\frac{3}{32}[/tex]
Both solutions are feasible
Final answer:
In this question, we explore geometric and arithmetic progressions to find the 6th term of a geometric progression given specific conditions.
Explanation:
Geometric Progression (GP): In a GP, the sum of the first three terms is 126. Let the first term be a and the common ratio be r. The sum of the first three terms can be represented as a + ar + ar^2 = 126.
Arithmetic Progression (AP): Adding 14, 36, and 4 to the terms of the GP forms an AP. The common difference of this AP is 36 - 14 = 22.
Finding the 6th Term: Using the formula for the nth term of a GP, the 6th term can be calculated as a * r^5.
If 375y=x2 and x and y are positive integers,
then which of the following must be an integer?
I. y/15
II. y/30
III. (y2)/25
a) I only
b) III only
c) I and II
d) I and III
e) I, II and III
Answer:
Option d - I and III.
Step-by-step explanation:
Given : If [tex]375y=x^2[/tex] and x and y are positive integers.
To find : Which of the following must be an integer?
Solution :
As we see all option there is a multiple of y.
So, we factoring the number 375
i.e. [tex]375=3\times 5\times 5\times 5[/tex]
[tex]375=15\times 5^2[/tex]
[tex]375=15\times 25[/tex]
In order for 375y to be a perfect square,
The prime factorization of y must contain at least one 3 and one 5.
or y must be a multiple of 15.
If y is a multiple of 15, then [tex]\frac{y}{15}[/tex] must be an integer.
and [tex]\frac{y^2}{25}[/tex] must be an integer.
Therefore, I and III will be correct i.e. option d.
A boy thinks he has discovered a way to drink extra orange juice without alerting his parents. For every cup of orange juice he takes from a container of orange juice, he pours one cup of water back into the container. If he completes this process three times on the same container of juice, the resulting mixture will be exactly 50% water and 50% juice. How many cups of orange juice were originally in the container. (P.S ITS NOT 6)
Answer:
4.847 cups
Step-by-step explanation:
Let's say x is number of cups of orange juice originally in the container.
The boy takes 1 cup of orange juice out, so there is x−1 cups left out of a total volume of x cups. So the new concentration in the container is:
(x − 1) / x
Next, he takes another cup out, but this time, it isn't 100% orange juice any more. So the number of cups of orange juice left in the container is x − 1 − (x − 1) / x. The total volume is still x cups, so the new concentration is:
[x − 1 − (x − 1) / x] / x
Repeating this logic, after he replaces the third cup with water, the final concentration is:
{x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x
This final concentration is equal to 1/2.
1/2 = {x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x
1/2 x = x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x
1/2 x² = x (x − 1) − (x − 1) − [x − 1 − (x − 1) / x]
1/2 x² = x (x − 1) − (x − 1) − (x − 1) + (x − 1) / x
1/2 x² = x (x − 1) − 2 (x − 1) + (x − 1) / x
1/2 x³ = x² (x − 1) − 2x (x − 1) + (x − 1)
1/2 x³ = x³ − x² − 2x² + 2x + x − 1
0 = 1/2 x³ − 3x² + 3x − 1
0 = x³ − 6x² + 6x − 2
Using a calculator to solve this:
x = 4.847
There are originally 4.847 cups in the container.
Suppose the newspaper states that the probability of rain today is 65%.
What is the complement of the event "rain today"?
rain yesterday
rain tomorrow
no rain today
no rain tomorrow
What is the probability of the complement?
The complement of 'rain today' is 'no rain today'. Its probability is 1 - the probability of 'rain today', which calculates to 35%.
Explanation:In probability theory, the complement of any event A represents 'not A'. In this context, the event is 'rain today', therefore the complement of the event would be 'no rain today'.
Probability of an event and its complement always add up to 1. Therefore, you can calculate the probability of the complement by subtracting the probability of the event from 1. So, the probability of the complement of the event 'rain today' is 1 - 0.65 which equals 0.35 or 35%.
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Solve for x in the equation x squared + 2 x + 1 = 17.
A) x = negative 1 plus-or-minus StartRoot 15 EndRoot
B) x = negative 1 plus-or-minus StartRoot 17 EndRoot
C) x = negative 2 plus-or-minus 2 StartRoot 5 EndRoot
D) x = negative 1 plus-or-minus StartRoot 13 EndRoot
Answer: B) x = negative 1 plus-or-minus StartRoot 17 EndRoot
Step-by-step explanation:
The given equation is x squared + 2 x + 1 = 17. It is written as
x^2 + 2x + 1 = 17
It is a quadratic equation. The general form of a quadratic equation is ax^2 + bx + c
Rearranging the given equation, it becomes
x^2 + 2x + 1 - 17 = 0
x^2 + 2x - 16 = 0
We will apply the general formula for quadratic equation. It is expressed as
x = [-b ± √(b^2 - 4ac)]/2a
From the equation,
a = 1
b = 2
c = -16
x = [-2 ± √(2^2 - 4×1×-16)]/2×1
x = [-2 ± √(4 + 64)]/2
x = (-2 ± √68)/2
x = (-2 ± 2√17)/2
x = (-2 + 2√17)/2 or x = (-2 - 2√17)/2
x = -1 + √17 or x = -1 - √17
Answer:
B) x = negative 1 plus-or-minus StartRoot 17 EndRoot i hope this was help
Step-by-step explanation:
Charles Stickley's gross weekly pay is $925. His earnings to date for the year total $21,045. What amount is deducted weekly for Social Security taxes, if the tax rate is 6.2%?
Final answer:
The amount deducted weekly for Social Security taxes for Charles Stickley is $57.35.
Explanation:
The student's question is regarding the calculation of Social Security taxes based on a given gross weekly pay and applying the current tax rate.
Charles Stickley's weekly Social Security tax deduction can be calculated by multiplying his gross weekly pay by the Social Security tax rate of 6.2%.
Here's how to calculate it:
Identify the gross weekly pay, which is $925 in this case.Calculate the Social Security tax deduction by multiplying $925 by the tax rate of 6.2% (or 0.062).Perform the calculation: 925 x 0.062 = $57.35.Therefore, the amount deducted weekly for Social Security taxes is $57.35.
A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm. A solid oblique pyramid has a square base with edges measuring x centimeters. The height is (x + 2) centimeters. Which expression represents the volume of the pyramid?
The expression to represent the volume of solid oblique pyramid is (x³+2x²)/3.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, a solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x+2) cm.
We know that, the volume of square base pyramid is a²h/3
Now, x²(x+2)/3
= (x³+2x²)/3
Therefore, the volume of solid oblique pyramid is (x³+2x²)/3.
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The volume of the given solid oblique pyramid with a square base of edge length x cm and height (x+2) cm can be calculated using the formula for the volume of a pyramid, 1/3 * (base area) * (height). The volume can thus be represented by the expression 1/3 * x^3 + 2/3 * x^2 cm^3.
Explanation:The question refers to a solid oblique pyramid with a square base, where the edge length of the base is x, and the height is (x+2) cm. To calculate the volume of the pyramid, you can use the formula for the volume of a pyramid: 1/3 * (base area) * (height). For the given pyramid, the base is a square with side length x, so the area of the base is x*x or x^2. Because the height of the pyramid is (x + 2), we substitute into the formula to get: 1/3 * x^2 * (x + 2). Multiplying it out, the expression representing the volume of the pyramid is: 1/3 * x^3 + 2/3 * x^2 cm^3.
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Each day valerie charges her lunch account for her lunch. If the cost of lunch is $3 then by how much has her lunch account been impacted over a period of 15 days?
Answer: the amount by which her lunch account would have been impacted is $45
Step-by-step explanation:
Each day Valerie charges her lunch account for her lunch. If the cost of lunch is $3 then, it means that Valerie charges the lunch account with $3 daily. It means that in x days, she would have charged her lunch account with 3×x = $3x
If she charged her account for a period of 15 days, it means that x = 15. Therefore, the amount by which her lunch account would have been impacted is 3×15 = $45
The amount of turn between two straight lines that have a common end point is called __________.
Answer:
Angle
Step-by-step explanation:
In the image I added you can observe that the common endpoint is called a vertex, and the "turn" or aperture formed between the two straight lines (or arms) that converge in the vertex, is the angle and it can be measured on degrees.
I hope you find this information usefun and interesting! Good luck!
Final answer:
The amount of turn between two straight lines that have a common end point is referred to as an angle. This concept is central to the study of geometry and aids in measuring the difference in direction where two lines meet. Angles are typically measured in degrees as a part of spherical trigonometry and other geometric calculations.
Explanation:
The amount of turn between two straight lines that have a common end point is called an angle. An angle measures the difference in direction between two lines that extend from the same point. The concept of angle is found in the principles of geometry, where it is foundational to understanding shapes and their properties.
In more mathematical terms, the angle between two intersecting lines can also be seen as the distance between their poles when conceptualized on a sphere, a concept from advanced geometry and spherical trigonometry. The measurement of this angle is generally given in degrees, where a full circle is 360 degrees, and this system of measurement allows us to apply the angle measure to various geometric constructions and theorems, such as determining the sum of the angles of a triangle.
Which statements about triangle JKL are true? Select two options.
M is the midpoint of line segment KJ.
N is the midpoint of line segment JL.
MN = One-halfKJ
MN = 4.4m
MN = ML
Answer: 2nd and 3rd statement
Step-by-step explanation:
From the diagram, the 1st statement is wrong, the 2nd statement is correct
To know which of the rest of the statement is correct we have to find the value of MN
So we use the cosine rule to find the angle inside the triangle at point L
c2 = a2+b2-2abcosC
For our triangle
c= 12.8
b= 5.9+5.9=11.8
a= 3.7+3.7=7.4
C = ?
(12.8)2 = (7.4)2 + (11.8)2 - 2x11.8x7.4cosC
163.84 = 54.76+739.24 - 174.64cosC
163.84 = 194 - 174.64cosC
163.84-194 = -174.64cosC
-30.16 = -174.64cosC
-30.16/-174.64 =cosC
cosC = 0.1727
cos-1(0.1727) = 80.06
C = 80.06 degrees
So we use this value to find length MN with also cosine rule from the triangle NML
c2 = a2+b2-2abcosC
c = ?
a = 5.9
b = 3.7
C = 80.06
c2 = (5.9)2 + (3.7)2 - 2x5.9x3.7cosC
c2 = 34.81 + 13.69 - 43.66x0.1727
c2 = 48.5 - 7.54
c2 = 40.96
c = root(40.96)
c = 6.4
Which is half of KJ
So therefore, the third statement is correct
Answer:
b,c
Step-by-step explanation:
i did the test:)
Please Help! Will give Brainliest for the correct answer. Given the function f(x) = x2 and k = -3, which of the following represents a vertical shift? (An explanation would be very helpful.)
1) f(x) + k
2) f(x + k)
3) f(kx)
4) kf(x)
Answer:
1) f(x) + k
Step-by-step explanation:
1) that would result in a vertical shift as the -3, would put parabola down 3
2) that would result in horizontal shift
3) That would change the original function
4) "kf" is not a function
Answer:
1) [tex]f(x)+k[/tex]Step-by-step explanation:
Givens
[tex]f(x)=x^{2}[/tex]
[tex]k=-3[/tex]
A vertical shift of this function is represeted by the first choice: [tex]f(x)+k[/tex].
Remember, when add or subtract units to the whole function, or the dependent variable (vertical axis), we are actually shifting the function vertically. So, the first option is adding units to the dependent variable because [tex]f(x)=y[/tex].
Therefore, the right answer is 1) [tex]f(x)+k[/tex]
Simplify √192
√83
√106
√643
√824
Answer:
[tex]\displaystyle 8\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\displaystyle \sqrt{3 \times 64} = 8\sqrt{3}[/tex]
I am joyous to assist you anytime.
Answer:
the answer is: [tex]8\sqrt{3}[/tex]
good luck