Answer:
log = cylinder
board = rectangular prism
Step-by-step explanation:
The log has a radius of 5 in and a length of 30 in.
This implies that the cross-section is a circle, and so it can be modeled as a cylinder.
The board has a width of 5.5 in, a height of 1.5 in and a length of 3ft.
Therefore, it can be modeled as a rectangular prism.
Suppose you deposit $2,000 in a saving account that pays interest at an annual rate of 4% with interest compounded monthly. Answer the
following questions:
(a)Write a function that represents the amount of money in the account after t years
(b) How much money is going to be in the account after 5 years.
(c) How many years will it take for the account to go over $2,500?
The function that represents the amount of money in the account after t years is f(t) = $2000(1.0033^12t).
The money in his account in five years would be $2442.
The number of years it would take to have a value over $2500 is 6 years.
What is the future value of the account?The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsf(t) = $2000(1.0033^60) = $2442
f(6) = $2000(1.0033^72) = 2535.41
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Angelica says the tangent is the ratio of the length of the leg opposite angle A ∠ A over the length of the leg adjacent to angle A This means B C must have a length of 3 3 units A C must have a length of: 4 4 units. They can find the length of Latex A B using the Pythagorean Theorem and then use it to find the sine and cosine ratios. Graciella says that they cannot find the length of any side of the triangle and, therefore, cannot find the ratios for sine and cosine. Both students have errors in their reasoning. Identify the mistake Angelica made in her reasoning. Provide an example that shows why she is incorrect. Identify the mistake that Graciella made in her reasoning. Explain why she is incorrect. Find the ratios for the sine and cosine of angle A Explain your process.
Based on the trigonometry ratios and the Pythagorean theorem both of them were incorrect.
Cos A = 4/5; Sin A = 3/5
What is the Trigonometry Ratios?The Trigonometry ratios relates the length of the sides of a right triangles. They are given as:
Sine ratio, sin ∅ = opp/hypCosine ratio, cos ∅ = adj/hypTangent ratio, tan ∅ = opp/adj.What is the Pythagroean Theorem?If two sides of a right triangle are known the third side can be determined using the Pythagorean theorem, which is given as, c² = a² + b², where and b are legs, and c is the hypotenuse of the right triangle.
1. Given that tan A = 3/4, it is not necessarily true that BC MUST have a length of 3 units, and AC MUST have a length of 4 units, because:
If BC = 9 units and AC = 12 units, the it will give us the same tangent ratio as:
tan A = 9/12 = 3/4.
Therefore, Angelica's mistake is stating that BC MUST be 3 units, and AC MUST be 4 units.
2. Knowing two length of the sides of a right triangle is enough information needed to find the length of the third side using the Pythagorean theorem, so Graceilla is incorrect.
3. Find AC using the Pythagorean theorem:
AB = √(3² + 4²)
AB = 5 units.
Cos A = adj/hyp = AC/AB
Cos A = 4/5
Sin A = opp/hyp = BC/AB
Sin A = 3/5
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Explanation and answer please
Answer:
$41.96
Step-by-step explanation:
30% of 59.95 is 17.99 (rounding to the nearest hundredth place since it was 17.985)
subtract 17.99 since it is the sale (30%)
59.95 - 17.99 = 41.96
the cd is worth $41.96 on sale for 30% off.
what is 3/8 - 1/4 = in simplest form
Answer:
1/8
Step-by-step explanation:
The lowest common multiple of 4 and 8 is 8.
1/4 = 2/8
3/8 - 1/4 = 3/8 - 2/8 = (3 - 2)/8 = 1/8
1/8 cannot be simplified further.
what is the quotient of 4 ÷ 1/4?
Answer:
16
Step-by-step explanation:
4 divided by 1/4 =
4/.25
16
What’s the volume for this shape?
Answer:
60 m^3
Step-by-step explanation:
3 x 4 x 5 = 60
The others are self explanatory
find the missing side of this triangle 6 x 10
Answer:
√136 units
Step-by-step explanation:
We are given that;
The provided triangle is a right triangle.The measure of the legs are 6 and 10 units.The hypotenuse of the right triangle is x units.Since the provided triangle is a right triangle, we can use pythogoras theorem to determine the missing side length of the triangle.
What is the pythogoras theorem and it's formula?Pythogoras theorem is a formula that is used to determine the missing side length of a right triangle, with the following given;
Two side lengths (Legs)A hypotenuse (Longest side)Pythogoras theorem is denoted as;
(c)² = (b)² + (a)²Where, "c" is the hypotenuse; "b" and "a" are the legs.
When we substitute the measure of the two legs and the hypotenuse of the triangle, we get;
(x)² = (10)² + (6)²Now, let's simplify the equation to determine the value of "x".
⇒ (x)² = 100 + 36 [Evaluating the squares]⇒ (x)² = 136 [Simplifying the right-hand-side]⇒ √(x)² = √136 [Taking square root both sides]⇒ x = √136 ≈ 11.66 units (2 d.p) [Taking square root both sides]The measure of the missing side is √136 units.
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Answer:
136
Step-by-step explanation:
Help 111111111111111
Answer:
6/11
Step-by-step explanation:
[tex]p(number \: less \: than \: 4) = \frac{3}{11} [/tex]
[tex]p(odd \: number) = \frac{5}{11} [/tex]
[tex]p(number \: \: less \: than \: 4 \: and \: odd) = \frac{2}{11} [/tex]
Now we know that
[tex]p(aUb) = p(a) + p(b) - p(anb)[/tex]
[tex]p(getting \: number \: less \: than\: 4 \: or \: odd \: number) = [/tex]
[tex] = \frac{3}{11} + \frac{5}{11} - \frac{2}{11} [/tex]
[tex] = \frac{6}{11} [/tex]
I hope it helped you
Find the surface area of the square pyramid?
Answer:
C) 224 square centimeters.
Step-by-step explanation:
Consider the following null and alternative hypotheses.
H zero: m < 67
Ha: m > 67
These hypotheses _______________.
Select one:
a. are established incorrectly
b. indicate a two-tailed test
c. indicate a one-tailed test with a rejection area in the right tail
d. indicate a one-tailed test with a rejection area in the left tail
1 dozen roses for $29.75 how much does one rose cost
Answer:
$2.48
Step-by-step explanation:
29.75/12 =2.479
x/9 times 15-47=28
help pls
Answer:
x=45
Step-by-step explanation:
Then,
x/5(15)-47=28
Step 1: Simplify the equation on both sides
x/9(15)-47=28
5/3x-47=28
Step 2: Add 47 to both sides
5/3x-47+47=28+47
5/3x=75
Step 3: Multiply both sides by 3/5
(3/5)*(5/3x)=(3/5)*(75)
x=45
In the figure below, find x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth.
Check the picture below.
Which choice is equivalent to the expression below?
7x2 - 42 + x2
O A. 3x12
O5x22
O C. 8x^2 - 4-15
O D. 6x1/2 -3-2
Answer:
the answer to your problem is c
Answer:
Did you copy C correctly?
If not, then C should equal 8x^2 - 16
Step-by-step explanation:
Simplify 7x^2 - 4^2 + x^2
I hope this helps!
Solve by factoring:
a² = 25
Answer:
[tex]a=[/tex] ±[tex]5[/tex]
Step-by-step explanation:
[tex]a^{2} =25[/tex]
equal to zero
[tex]a^{2} -25=0[/tex]
factor: difference of squares
[tex](a+5)(a-5)=0[/tex]
first factor:
[tex]a+5=0\\a_{1} =-5[/tex]
second factor:
[tex]a-5=0\\a_{2} =5[/tex]
Hope this helps
Find the area of this figure. Round your
answer to the nearest hundredth. Use
3.14 to approximate 7.
12.2 ft.
10 ft.
6 ft.
14 ft.
A = [?] ft.2
Notice that only half of the circle is included in the figure!
Enter
Answer:
209.25 ft²
Step-by-step explanation:
The area of the composite figure is the sum of the areas of its parts. Those parts are a triangle, rectangle, and semicircle.
__
triangleThe area formula is ...
A = 1/2bh
A = 1/2(6 ft)(10 ft) = 30 ft²
rectangleThe area formula is ...
A = bh
A = (14 ft)(10 ft) = 140 ft²
semicircleThe area formula is ...
A = 1/2πr² . . . . where radius r is half the diameter
A = 1/2(3.14)(5 ft)² = 39.25 ft²
total areaThe sum of the areas of the parts is ...
total area = (30 +140 +39.25) ft² = 209.25 ft²
Please help me I need help asap
Answer:
AB = 23 , BC = 13
Step-by-step explanation:
Isosceles mean two side angle is equal to each other.
AB and AC are the same. So we can solve for x.
[tex]AB=AC\\5x-7=23\\5x=30\\x=6\\\\AB = 5x-7\\AB = 5*6-7\\AB=30-7\\AB = 23\\\\BC = 3x-5\\BC = 3*6-5 = 18 - 5 = 13\\BC = 13[/tex]
Answer:
Step-by-step explanation:
Because they tell us it's an isosceles triangle we know two sides are the same length. since AB and AC look like they are similar we can assume that those sides are the exact same length. Since we know , now, that AB and AC are equal in length, set them equal
AB = AC
now plug in given info
5x-7 = 23
nice, now use your super hero algebra skillz to solve for X. My calculus prof. always says that students are bad at algebra, i'll help you do the algebra.
5x-7=23 ( add 7 to both sides)
5x=23+7 (add 7 to 23 )
5x=30 (divide both sides by 5 )
x=6
yay, we have X now.
we know AB =23 , because of the isosceles triangle thing.
BC = 3x-5
plug in for X :)
3*6-5=BC
18-5=BC
13=BC
Yay, all the answers, and way to get the answers are above :P
could someone help me super super quick?
Answer:
Vertex form of a quadratic equation is y=a(x-h)2+k, where (h,k) is the vertex of the parabola
The vertex of a parabola is the point at the top or bottom of the parabola
Step-by-step explanation:
Different textbooks have different interpretations of the reference "standard form" of a quadratic function. Some say f (x) = ax2 + bx + c is "standard form", while others say that f (x) = a(x - h)2 + k is "standard form". To avoid confusion, this site will not refer to either as "standard form", but will reference f (x) = a(x - h)2 + k as "vertex form" and will reference f(x) = ax2 + bx + c by its full statement.
#1
y=a(x-h)²+ky=a(x²)+3Put (2,-5)
-5=2²a+3-5=4a+34a=-8a=-2Equation
y=-2(x-0)²+3#2
y=a(x-2)²Put (5,9)
9=a(5-2)²3²a=99=9a=1Equation
y=(x-2)²+0#3
y=a(x+3)²+2put (-1,14)
14=a(2)²+214=4a+24a=12a=3Equation
y=3(x+3)²+2#4
y=a(x-5)²-3Put (1,-8)
-8=a(-4)²-3-8=16a-316a=-5a=-5/16Equation
y=-5/16(x-5)²-3
solve for x～
[tex]x {}^{2} - 5x + 6 = 0[/tex]
thankyou! :)
Estimate the amount of the tip by rounding the bill to the nearest ten dollars before calculating.
15% tip on a bill of $551.60
The amount of the tip is approximately $
Answer:
$82.50
Step-by-step explanation:
This problem requires you round the given bill value, then compute a fraction of that rounded value.
__
RoundingWe want to round the bill value to the nearest $10. The digit to the right of the tens digit is 1, so we simply replace that and all digits to the right with zeros. (Had the ones digit been 5 or more, we would increment the tens digit before zeroing digits to its right.)
$551.60 rounded to nearest $10 is $550.00
__
Tip AmountThe amount of the tip is found by multiplying the bill by the tip rate.
$550 × 15% = $550 × 0.15 = $82.50
The amount of the tip is approximately $82.50.
_____
Additional comment
It is often relatively easy to compute a tenth or half of something in your head. We know that 15% = 10% + (1/2)(10%), and that 10% of $550 is $55.
Half of $55 is $27.50, so the tip amount will be $55.00 +27.50 = 82.50, a calculation you can do mentally.
What is9.3 to a fraction?
Answer:
9.3 = 93 / 10
Step-by-step explanation:
Write the equation in slope-intercept form, and detemine the slope and y-intercept. Write the y- intercept as an ordered pair.
−x + 5y = −5
The slope is .
The y-intercept is .
The equation written in slope-intercept form is ____________ .
Answer:
slope= 0.2; intercept=-1; slope-interception form: y=0.2x-1.
Step-by-step explanation:
1) if to re-write the given equation, then
[tex]y=\frac{1}{5}x-1;[/tex]
or y=0.2x-1;
this equation is slope-interception form;
2) according to the new view of the equation,
the required slope is 1/5;
the required y-intercept is -1.
Solve the equation 9(k-2)=- 6. ( slove for k
Answer:
k=4/3
Step-by-step explanation:
9(k-2)=-6
-expand the bracket
9k-18=-6
-keep "k" on one side
9k=12
-divide both sides by 9 to get k
k=4/3
After several days of camping and long-distance bicycle riding, you decide to right straight home, riding at a constant rate. After 2 hours of riding you
kilometers from home and after 4 hours of riding youare 5 kilometers from home. Once you begin to ride home, how many hours will it take you to arrive at home?
Answer:
I just need points.
Step-by-step explanation:
If a number cube is rolled, how many times would we expect to get a number less than four out of 200 trials? Answer is 100
100
25
50
75
The expected outcomes less than 4 is the average of the outcomes
We would expect to get a number less than four out of 200 trials 100 times
How to determine the expected number of rolls?The sample space of a number cube is:
S = {1,2,3,4,5,6}
There are 3 outcomes less than 4.
So, the probability of obtaining a number less than 4 is:
p = 3/6
This gives
p = 0.5
In a roll of 200, the expected outcomes less than 4 is:
E(x) = 0.5 * 200
This gives
E(x) = 100
Hence, we would expect to get a number less than four out of 200 trials 100 times
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Answer:
100
Step-by-step explanation:
What is value of 5 in 2 500.7
Answer:
500
Step-by-step explanation:
Since the 5 is in the hundreds place in the number 2500.7, its value is 5 * 100 = 500.
Answer:
hundreds
Step-by-step explanation:
A system of equations is given below. To solve this system using substitution, which of the following equations could be used?
A. 2x-4x-6=8
B. 2x- (4x-6)=8
C. 2x+3(4x-6)=8
D. 2x-3(4x-6)=8
x^2+x-20=0
please help me otu
Answer x=2.7
Step-by-step explantion
x^2 +x-20=0
combine like terms.. so x^2 AND X TURN INTO X^3
X^3-20=0
THE SUBTRACT 20 FROM EACH SIDE
X^3=20
x=2.7
:)
solve this sum plsss
Step-by-step explanation:
the answer is in the attachment.
hope this helps you.
show that (3*8*x)^7= 6^7*8^7*x^7
Answer:
(3*8*) ^*7*8*
Step-by-step explanation:
IM DONE TO SHOW YOU