Answer:
$499.8
Step-by-step explanation:
Principal=$580
Time=6 months=1/2 year
rate=2% p.a.
prt=580*2*1
---------------
2*100
=$499.80
Answer:
Simple Interest over the given time interval will be $5.80
Step-by-step explanation:
Principal Amount = $580
Rate of Interest = 2%
= 0.02
Time = 6 months
= 0.5 years
Now, Simple Interest is given by the formula :
Simple Interest = Principal × Rate × Time
⇒ Simple Interest = 580 × 0.02 × 0.5
⇒ Simple Interest = $5.80
Thus, Simple Interest over the given time interval will be $5.80
If a line falls on the points (8,9) and (3,8)what is its slope?enter your answer as a fraction in lowest terms. Use a slash mark (/) as a fraction bar.
Answer:
1/5
Step-by-step explanation:
it went up one on the y axis and 5 on the X and the formula is rise/run or up/left
Solve x2 − 7x + 12 = 0.
x = −3, x = −4
x = 3, x = 4
x = 2, x = 6
x = −2, x = −6
Answer:
x=4, x=3
B is correct.
Step-by-step explanation:
Given: [tex]x^2-7x+12=0[/tex]
Using middle term splitting factor the left side equation.
[tex]x^2-4x-3x+12=0[/tex]
[tex](x-4)(x-3)=0[/tex]
Equate each factor to 0 and solve for x
x-4=0 or x-3=0
x=4 and x=3
Hence, The solution of the equation is 4 or 3
Type the correct answer in each box.
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is_____ units. The point (-15, ___) lies on this circle.
Answer:
1. r=17
2. (-15,14) or (-15,-16)
Step-by-step explanation:
The radius of the circle is the distance from the center to the point on the circle, thus
[tex]r=\sqrt{(8-(-7))^2+(7-(-1))^2}=\sqrt{15^2+8^2}=\sqrt{225+64}=\sqrt{289}=17.[/tex]
The equation of the circle is
[tex](x-(-7))^2+(y-(-1))^2=r^2\\ \\(x+7)^2+(y+1)^2=289.[/tex]
If point lies on this circle, then its coordinates satisfy the circle's equation:
[tex](-15+7)^2+(y+1)^2=289\\ \\64+(y+1)^2=289\\ \\(y+1)^2=225\\ \\y+1=15\text{ or }y+1=-15\\ \\y=14\text{ or }y=-16[/tex]
the radius of the circle is 17 units.
the two possible points on the circle are (-15, 14) and (-15, -16).
The question requires calculating the radius of a circle given two points: the center of the circle and a point on the circumference. To find the radius, we will use the distance formula, which is derived from the Pythagorean theorem. The distance formula to find the distance between two points (x1, y1) and (x2, y2) is \\(
√{(x2 - x1)^2 + (y2 - y1)^2}\\).
Applying the distance formula with the center at (-7, -1) and a point on the circle being (8, 7), we get: \\(
√{(8 - (-7))^2 + (7 - (-1))^2}) = (√{(15)^2 + (8)^2}) = (√{225 + 64}) = (√{289}) = 17. Thus, the radius of the circle is 17 units.
To find the missing y-coordinate of the point (-15, ___) that lies on this circle, we use the circle's equation with its center at (-7, -1): ((x + 7)^2 + (y + 1)^2 = 17^2). Substituting x = -15, we solve for y.
((-15 + 7)^2 + (y + 1)^2 = 17^2)
((-8)^2 + (y + 1)^2 = 289)
64 + (y + 1)^2 = 289
(y + 1)^2 = 225
y + 1 = (√{225}) or y + 1 = -(√{225})
y = 14 or y = -16
Therefore, the two possible points on the circle are (-15, 14) and (-15, -16).
Factor the trinomial 6x^2+5x- 25
Answer:
x = 5/3 or x = -5/2
(3x-5) or (2x+5)
Step-by-step explanation:
Given in the question an equation
6x²+5x- 25
here a = 6
b = 5
c = -25
To solve the polynomial equation we will use quadratic equation
x = -b ±√(b²-4ac) / 2a
Plug values in the equation
-5±√(5²-4(6)(-25)) / 2(6)
-5±√(25 + 600) / 2(6)
-5±√(625) / 2(6)
-5± 25 / 2(6)
-5 + 25 / 2(6) or -5 - 25 / 2(6)
x = 5/3 or x = -5/2
Write the equation x+5y-2= 0 in normal form. Then, find the length of the normal and the length and the angle makes with the positive x-axis.
Final answer:
The normal form of x + 5y - 2 = 0 is (1/√26)x + (5/√26)y - (2/√26) = 0. The length of the normal is 1, and the angle it makes with the positive x-axis can be calculated using tan θ = 5, which gives the angle as tan-1(5).
Explanation:
To rewrite the equation x + 5y - 2 = 0 in normal form, we need to express it in the form Ax + By + C = 0, where A2 + B2 = 1. The equation is already in this form, but we must divide each term by the square root of (12 + 52) to satisfy the condition for A2 + B2. After the division, the normal form becomes (1/√26)x + (5/√26)y - (2/√26) = 0.
The length of the normal is the magnitude of the vector (A, B), which in this case, is 1 due to the normalization. To find the angle θ that the normal makes with the positive x-axis, we use the relationship tan θ = B/A. For our equation, tan θ = 5/1, so θ = tan-1(5).
The analytical method of vector addition involves identifying the x- and y-components of vectors and merging them to calculate the resultant vector's magnitude and direction.
A. Set A is an exponential function and the values increase at a faster rate than Set B.
B. Set B is a linear function and the values increase at the same rate as Set A
C. Set A is a linear function and the values increase at the same rate as Set B.
D. Set B is an exponential function and the values increase at a slower rate than Set A
Answer:
The correct answer is A.
Find all polar coordinates of point P where P = ordered pair 4 comma negative pi divided by 3.
Answer:
[tex](4,-\frac{\pi}{3}+2n\pi)[/tex] And [tex](-4,-\frac{\pi}{3}+(2n+1)\pi).[/tex]
Hope this helps you out!
Answer:
All the polar coordinates of point P are [tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex] and [tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex], where n is any integer and θ is in radian.
Step-by-step explanation:
It a polar coordinate is given as P(r,θ), then all the polar coordinates of point P are defined as
[tex]P(r,\theta)=(r,2n\pi+\theta)[/tex]
[tex]P(r,\theta)=(-r,(2n+1)\pi+\theta)[/tex]
Where, n is any integer and θ is in radian.
The given point is
[tex]P(4,-\frac{\pi}{3})[/tex]
So, all the polar coordinates of point P are defined as
[tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex]
[tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex]
Therefore all the polar coordinates of point P are [tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex] and [tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex], where n is any integer and θ is in radian.
Choose the function who’s graph isn’t given by:
Answer:
D. [tex]y=\tan (x-\pi)+2.[/tex]
Step-by-step explanation:
Consider parent function [tex]y=\tan x.[/tex] The graph of this function is the same as the graph of the function [tex]y=\tan (x-\pi),[/tex] because the tangens has period of [tex]\pi.[/tex] (See first attached diagram)
Now, you can see that the graph of the function [tex]y=\tan (x-\pi)[/tex] is translated 2 units up. This translation gives you the function [tex]y=\tan (x-\pi)+2.[/tex] (see second attached diagram)
Answer: D
Step-by-step explanation: Apex
Place the indicated product in the proper location on the grid. 3a^n(a^n + a^n-1) =
Answer:
[tex]\large\boxed{3a^n(a^n+a^{n-1})=3a^{2n}+3a^{2n-1}}[/tex]
Step-by-step explanation:
[tex]3a^n(a^n+a^{n-1})\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(3a^n)(a^n)+(3a^n)(a^{n-1})\qquad\text{use}\ x^n\cdot x^m=x^{n+m}\\\\=3a^{n+n}+3a^{n+n-1}\\\\=3a^{2n}+3a^{2n-1}[/tex]
5.The university book store sells pennants in two sizes. The pennants are similar right triangles . The small pennants is represented by triangle ABC in the largest pennants is represented by triangle XYZ. If B is 35 what is the Measure of Z?
Answer:
55 deg
Step-by-step explanation:
In triangle ABC, angle A is a right angle, so angles B and C are complementary; their measures add to 90 deg.
m<C + m<B = 90
m<C + 35 = 90
m<C = 90 - 35
m<C = 55
Angle Z corresponds to angle C, so angles Z and C are congruent.
m<Z = m<C = 55
The ratio of Sam’s height to joe’s height is 5:6. Sam is 57”tall, how tall is joe
Joe is 68.4” tall. Set the ratio of 5/6=57/x, solve using the butterfly method (multiply 57 and 6, set equal to 5x) 57•6 is 342, so at this point it would be 342=5x. 342/5 is 68.4
Please help. I need this as soon as possible
Answer:
D???
Step-by-step explanation:
D????
stand·ard de·vi·a·tion
/ˈstandərd ˌdēvēˈāSHən/
nounSTATISTICS
a quantity calculated to indicate the extent of deviation for a group as a whole.
what is the partial quotients of 43.2÷16=
43.2/16= 2.7
Answer: 2.7
Your answer would be 2.7
A sandwich shop offers a choice of 4 types of bread, 8 types of meat, and 4 types of cheese. How many different sandwiches could be made with 1 type of bread, 1 type of meat, and 1 type of cheese?
By using the counting principle in mathematics, the student can know that there are 128 possible sandwiches that can be made with one type of each ingredient.
Explanation:The question you're asking is related to the counting principle in mathematics. The counting principle suggests that if you can choose one item from 4 different types of bread, one from 8 types of meat, and one from 4 different types of cheese, the number of different sandwiches you could make is the product of these choices.
To calculate it, simply multiply the choices together like this: 4 (types of bread) * 8 (types of meat) * 4 (types of cheese) = 128. So, there are 128 different sandwiches that could be created with one type of each ingredient.
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What is tan M for this triangle? Enter your answers in the boxes.
tan M= ?/?
Answer:
Tan (M) = m/p
Step-by-step explanation:
Tan (M) = Oppo. / Adj.
Tan (M) = m/p
The required value of the tanM for the given triangle is tanM = m/p.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
here,
For the given triangle,
TanM = perpendicular / base
From the figure perpendicular = m, base = p
Now,
tanM = m/p
Thus, the required value of the tanM for the given triangle is tanM = m/p.
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What is the area of this face?
4
in.
1
Answer:
4
Step-by-step explanation:
Business services ordered a chair that cost $220.59. Upon arrival they received an invoice for $261.47. If the California sales tax rate is 7.9% what is the cost of shipping and handling
Answer:
Cost of shipping and handling = $23.453
Step-by-step explanation:
Given
Price of Chair=$220.59
Tax=7.9%
Invoice Price=$261.47
In order to find the cost of shipping and handling, we have to subtract the cost of chair and the tax from the invoice price of chair.
To find the tax,
Tax amount=220.59*0.079
=$17.42661
Now,
Cost of shipping and handling=$261.47-$220.59-$17.42661
=$23.453 ..
Answer:
The cost of shipping and handling is $23.45 .
Step-by-step explanation:
As given
Business services ordered a chair that cost $220.59.
if the California sales tax rate is 7.9%
7.9% is written in the decimal form
[tex]= \frac{7.9}{100}[/tex]
= 0.079
Thus
Sales tax price = 0.079 × Cost of the chair
= 0.079 × $220.59
= $ 17.43 (Approx)
Thus
Cost of the ordered chair with sales tax price = Cost of the chair + Sales tax price .
= $ 220.59 + $17.43
= $ 238.02
As given
Upon arrival they received an invoice for $261.47.
Thus
Cost of shipping and handling = Cost mentioned in invoice - Cost of the ordered chair with sales tax price.
Put all the values in the above
Cost of shipping and handling = $261.47 - $238.02
= $ 23.45
Therefore the cost of shipping and handling is $23.45 .
Suppose that 8% of the general population has a disease and that the test for the diesease is accurate 70% of the time. What is the probability of testing positive for the disease
Answer:
P = 0.332
Step-by-step explanation:
The probability of having the disease is 0.08
The probability that the test predicts with accuracy is 0.7.
We need to find the probability that the test positive for the disease.
Several cases may occur.
Case 1.
You have the disease and the test predicts it accurately
[tex]P_1 = 0.08(0.7) = 0.056[/tex]
Case 2
You do not have the disease and the test predicts that you have it
[tex]P_2 = 0.92(0.3) = 0.276[/tex]
Then the probability that the test predicts that you have the disease is the union of both probabilities P1 and P2
[tex]P = P_1 + P_2\\\\P = 0.056 + 0.276\\\\P = 0.332[/tex]
Suppose you select a card at random from a standard deck of cards 60 times, and 12 of those selections are hearts. How does the experimental probability compare to the theoretical probability? Include the difference between both types in your explanation.
A standard deck is composed of 52 cards, and contains 13 cards per suit. So, the theoretical probability of picking a card of any suit (and thus, in particular, a heart) is given by
[tex]P(\text{hearts}) = \dfrac{\text{\# of hearts in the deck}}{\text{\# of cards in the deck}} = \dfrac{13}{52} = \dfrac{1}{4}[/tex]
On the other hand, the experimental probability is (as the name suggests) the probability that we can deduce from our experiment: we picked 60 cards, and 12 of these were hearts. This means that it would seem to us that
[tex]P(\text{hearts}) = \dfrac{\text{\# of hearts we picked}}{\text{\# of cards we picked}} = \dfrac{12}{60} = \dfrac{1}{5}[/tex]
what is the degree of 6x^5-4x^2+2x^3-3
Answer:
5
Step-by-step explanation:
we know that
A degree in a polynomial function is the greatest exponent of that equation
In this problem the greatest exponent is x^5
therefore
the degree of the polynomial is 5
Solve the equation 6w2 – 7w – 20 = 0.
A. w = –4⁄3, w = 2⁄5
B. w = –4⁄3, w = 5⁄2
C. w = –3⁄4, w = 5⁄2
D. w = –5⁄2, w = 4⁄3
Answer:
[tex]\large\boxed{B.\ w=-\dfrac{4}{3},\ w=\dfrac{5}{2}}[/tex]
Step-by-step explanation:
[tex]6w^2-7w-20=0\\\\6w^2-15w+8w-20=0\\\\3w(2w-5)+4(2w-5)=0\\\\(2w-5)(3w+4)=0\iff2w-5=0\ \vee\ 3w+4=0\\\\2w-5=0\qquad\text{add 5 to both sides}\\2w=5\qquad\text{divide both sides by 2}\\\boxed{w=\dfrac{5}{2}}\\\\3w+4=0\qquad\text{subtract 4 from both sides}\\3w=-4\qquad\text{divide both sides by 3}\\\boxed{w=-\dfrac{4}{3}}[/tex]
Which is equivalent to 3log28 + 4log21 2 − log32?
Answer:5-log^3 2
Step-by-step explanation:
Answer:
The answer is 5-log 3 2
Step-by-step explanation:
this is the answer on edge
you're welcome
Solve the following equation. Then place the correct number in the box provided.
4(3 - 2x) = 15
Answer:
Step-by-step explanation:
4(3-2x)=15
Distribute 4:
12-8x= 15
Subtract 12:
-8x= 3
Divide
X= -3/8 or -0.375
ANSWER
[tex]x = - \frac{3}{8} [/tex]
EXPLANATION
The given equation is:
4(3 - 2x) = 15
Expand the parenthesis to obtain:
12-8x=15
Group similar terms to get;
-8x=15-12
Combine similar terms to get:
-8x=3
Divide both sides by -8
[tex]x = - \frac{3}{8} [/tex]
Find the shaded region?
trapezoid: (25+19)/2 *20 (see formula for area of a trapezoid)
and the smaller parallelogram: (10*17) (see formula for parallelogram)
and subtract the parallelogram from the trapezoid and you're done!
so we have a trapezoid with a parallelogram inside.
now, if we just get the area of the trapezoid, which includes the parallelogram, and then get the area of the parallelogram and subtract it from that of the trapezoid, what's leftover is the shaded region, because we'd be in effect making a "hole" in the trapezoid and the area leftover is the shaded part.
[tex]\bf \stackrel{\textit{area of a trapezoid}}{A=\cfrac{h(a+b)}{2}}~~ \begin{cases} a,b=\stackrel{bases}{parallel}\\ \qquad ~~ sides\\ h=height\\ \cline{1-1} a=19\\ b=25\\ h=20 \end{cases}\qquad \stackrel{\textit{area of a parallelogram}}{A=bh}~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=17\\ h=10 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{trapezoid}}{\cfrac{20(19+25)}{2}}~~-~~\stackrel{\textit{parallelogram}}{(17\cdot 10)}\implies 10(44)-170\implies 440-170\implies 270[/tex]
Round .796 to the nearest hundredth.
Answer:
The answer is .800
To round .796 to the nearest hundredth, we observe the third decimal place (6) and round up the second decimal place from 9 to 10, which effectively turns .796 into .80.
Explanation:The question asks us to round .796 to the nearest hundredth. To do this, we look at the third decimal place, which is 6. Since 6 is greater than 5, we round up the second decimal place from 9 to 10. However, since the second place cannot literally take the value of 10, it effectively rolls over and adds 1 to the first decimal place, changing .796 to .80. Therefore, the answer is .80 when rounded to the nearest hundredth.
Can someone help with this question? Thanks!
Answer:
y=15t
t is time
Two fitness clubs are adding new members. Fitness Club A currently has 450 members and adds 15 new members each month. Fitness Club B currently has 400 members and adds 25 new members each month.
After how many months will Fitness Club A and Fitness Club B have the same number of members?
Answer:4 months
Step-by-step explanation:
if you go by members for each group. group A has 450 but adds in 15 members each month. group B has 25 members each month. not take 25 and multiply it by 4 it equals to 100. and multiply 15 by 4 equals 50. which makes group B 500. and group A 500.
After 5 months, Fitness Club A and Fitness Club B will have the same number of members.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have.
We can solve this problem by setting up an equation to represent the number of members at each club after a certain number of months and then solving for the number of months that makes the number of members equal.
Let's use "m" to represent the number of months:
Number of members at Club A after m months = 450 + 15m
Number of members at Club B after m months = 400 + 25m
To find when the two clubs will have the same number of members, we can set these two expressions equal to each other and solve for m:
450 + 15m = 400 + 25m
Subtracting 400 from both sides:
50 + 15m = 25m
Subtracting 15m from both sides:
50 = 10m
Dividing both sides by 10:
m = 5
Therefore,
After 5 months, Fitness Club A and Fitness Club B will have the same number of members.
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Are two equilateral triangles similar? if one triangle has a side length of 6 cm and the other has a side length of 10 cm, what is the scale factor?
Yes, they're similar.
Step-by-step explanation:
Triangles are similar when they have the same shape but vary in sizes. This is our case here. We have two equilateral ∆s which makes them similar but what differs them is the length. One is 6 and the other is 10. Although that doesn't affect anything in the triangle. If you drew a height to any base (in either triangle) it would still be a bisector, median, and perp bisector. Their angles are alsp equal.
Carolyn wants to deposit a check into her savings account. She should _____.
Carolyn wants to deposit a check into her savings account. She should sign the back of the check , complete a deposit slip, and visit the teller at the bank.
PLEASE HELP ASAP ON THIS PROBLEM
Answer:
The ball was dropped from 150 feet.
It will take the ball 3.06 seconds to reach the ground.
Step-by-step explanation:
A story is 10 feet.
You want to find the number of seconds for the ball to reach the ground, which is a height of 0. So you can put 0 in for h(t), and then solve that. If you need more help than that, let me know.