Answer:
WX = 8 mm
Step-by-step explanation:
To be able to solve for WX, we need to first find the size of angle [tex]\angle z[/tex].
We use the law of sines in the blue triangle to do such:
[tex]\frac{sin(z)}{11} =\frac{sin(133)}{20} \\sin(z)=\frac{11\,sin(133)}{20} \\sin(z)=0.4022[/tex]
Now we can use this value in the larger right angle triangle where WX is the opposite side to angle [tex]\angle z[/tex], and the 20 mm side is the hypotenuse:
[tex]sin(z)=\frac{opposite}{hypotenuse} \\sin(z)=\frac{WX}{20}\\0.4022=\frac{WX}{20}\\WX=20\,(0.4022)\\WX=8.044\,\,mm[/tex]
which rounded to the nearest integer gives
WX = 8 mm
Suppose you place $10,000 in a retirement fund that earns a nominal interest rate of 8 percent. If you expect inflation rate to be 5 percent or lower, then calculate the real interest rate you are expecting to earn.
Answer:
Real interest rate= 3%
Step-by-step explanation:
Giving the following information:
Suppose you place $10,000 in a retirement fund that earns a nominal interest rate of 8 percent. The inflation rate is 5 percent.
The effect of the inflation rate on the interest rate is counterproductive. The inflation rate diminishes purchasing power.
Real interest rate= nominal interest rate - inflation rate
Real interest rate= 0.08 - 0.05= 0.03
What is the circumference of a circle with a diameter of 100m. A 100m B 157m C 300 m D 314m
Answer:
C = 314 m
Step-by-step explanation:
The circumference of a circle is given by
C = pi * d
Using 3.14 for pi
C = 3.14 * 100
C = 314 m
Answer:
The answer is option D.
314mStep-by-step explanation:
Circumference of a circle = πd
Where d is the diameter
From the question
d = 100m
Circumference of the circle is
100π
= 314.2
Which is 314m to the nearest whole number
Hope this helps you
Factorize: 14x^6-45x^3y^3-14y^6
Answer:
(7x^3+2y^3)(2x^3−7y^3)
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides
of this triangle?
O 5cm and 8 cm
O 6 cm and 7 cm
O 7 cm and 2 cm
8 cm and 9 cm
Answer:
Choice D - 8cm and 9cm.
Step-by-step explanation:
The other sides are not greater than 13.
A: 5 + 8 = 13
B: 6 + 7 = 13
C: 7 + 2 = 9
However, D is greater than 13 and is the correct answer.
D: 8 + 8 = 16.
Option d: 8 cm and 9 cm.
There is a theorem in mathematics stating:
" The sum of length of two sides of any triangle is greater than the rest third side"
According to that theorem, first three given options cant form the sides of the given triangle whose one side is 13 cm.
The 4th option has 8 cm and 9 cm for which we have:
8 + 9 > 13
Thus this option follows the theorem.
Hence fourth option is correct.
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Select the statements that are true for the graph of y=−(x−0.5)^2 +9 . Choose all correct statements. The vertex is (−0.5,9) . The graph has a maximum. The graph has a minimum. The vertex is (0.5,9) .
Answer:
The second and fourth statements are correct.
Step-by-step explanation:
We are given the function for the graph of:
[tex]y=-(x-0.5)^2+9[/tex]
Note that this is a quadratic function in its vertex form, given by:
[tex]y=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
Rewriting our given equation yields:
[tex]\displaystyle y = (-1)(x-(0.5))^2 + (9)[/tex]
Therefore, a = -1, h = 0.5, and k = 9.
Therefore, the vertex of the graph is at (0.5 ,9).
Because the leading coefficient is negative, the parabola opens downwards.
Therefore, the parabola has a maximum value.
In conclusion, the second and fourth statements are correct.
1. the vertex is (0.5, 9)
2. it has a maximum.
Jessica calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle was it?
E
F
G
H
Answer:
G
Step-by-step explanation:
We can find a missing length of a triangle using a Pythagorean theorem if and only the triangle is a right angled triangle.
The side of the missing length is:
a^+b^=c^
2^+4^=c^
4+16=c^
20=c^
[tex] \sqrt{20} = c ^{2} \\ 4 \sqrt{5} = c[/tex]
PLEASE HELP!! laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. find the probability that a randomly selected light bulb will last between 900 and 975 hours.
Answer:
P = 0.0215 = 2.15%
Step-by-step explanation:
First we need to convert the values of 900 and 975 to standard scores using the equation:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Where z is the standard value, x is the original value, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation. So we have that:
standard value of 900: [tex]z = \frac{900 - 750}{75} = 2[/tex]
standard value of 975: [tex]z = \frac{975 - 750}{75} = 3[/tex]
Now, we just need to look at the standard distribution table (z-table) for the values of z = 2 and z = 3:
z = 2 -> p_2 = 0.9772
z = 3 -> p_3 = 0.9987
We want the interval between 900 and 975 hours, so we need the interval between z = 2 and z = 3, so we just need to subtract their p-values:
P = p_3 - p_2 = 0.9987 - 0.9772 = 0.0215
So the probability is 0.0215 = 2.15%
Answer:
2.35 babyyyyyyyyyyy
Step-by-step explanation:
Acellus sux
simplify. Remove all perfect squares from inside the square root. V180=
Answer:
6√5
Step-by-step explanation:
We have to solve the expression [tex]\sqrt{180}[/tex]
Break 180 into its factors which are in the perfect square form.
Since, 180 = 9 × 4 × 5
= 3² × 2² × 5
Therefore, [tex]\sqrt{180}=\sqrt{3^{2}\times 2^{2}\times 5}[/tex]
= [tex]\sqrt{3^2}\times \sqrt{2^{2}}\times \sqrt{5}[/tex] [Since [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex]]
= 3 × 2 × √5
= 6√5
Therefore, solution of the given square root will be 6√5.
Which of the following is not a congruence theorem or postulate A. SSA B. SAS C. AAS D. SSS
Answer:ITS A
Step-by-step explanation:
SAS: side angle side
SSA: is not a congruence theorem
AAS:angle angle side
SSS:side side side
Answer:
The answer is A.
Step-by-step explanation:
Just took the test
A number is 30% of 20% of the number x.
Answer:
6/100x
Step-by-step explanation:
Answer:6/100x
Step-by-step explanation:
A circle has a radius of 21 inches. What is the length of the arc intercepted by a central angle that measures 4π/7 radians? Express the answer in terms of π .
Answer:
12π inches
Step-by-step explanation:
s = rθ
s = (21) (4π/7)
s = 12π
The length of the arc will be;
⇒ Arc = 37.68 inches
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The central angle = 4π/7
And, A circle has a radius of 21 inches.
Now,
We know that in circle;
⇒ Arc = Radius × Angle
Substitute all the values, we get;
⇒ Arc = 21 × 4π/7
⇒ Arc = 3 × 4 × 3.14
⇒ Arc = 37.68 inches
Thus, The length of the arc will be;
⇒ Arc = 37.68 inches
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how do i wright this as a expression? seven and the quotient of z and eight
8÷7=z and z is the answer you got when you divided,that's how I understand the question
the sum of the first term of an ap is 240 and the sum of the next 4 term is 220 find the first term of the ap
Answer:
The common difference is -5/4
T(n) = T(0) - 5n/4,
where T(0) can be any number. d = -5/4
Assuming T(0) = 0, then first term
T(1) = 0 -5/4 = -5/4
Step-by-step explanation:
T(n) = T(0) + n*d
Let
S1 = T(x) + T(x+1) + T(x+2) + T(x+3) = 4*T(0) + (x + x+1 + x+2 + x+3)d = 240
S2 = T(x+4) + T(x+5) + T(x+6) + T(x+7) = 4*T(0) + (x+5 + x+6 + x+7 + x+8)d = 220
S2 - S1
= 4*T(0) + (x+5 + x+6 + x+7 + x+8)d - (4*T(0) + (x+1 + x+2 + x+3 + x+4)d)
= (5+6+7+8 - 1 -2-3-4)d
= 4(4)d
= 16d
Since S2=220, S1 = 240
220-240 = 16d
d = -20/16 = -5/4
Since T(0) has not been defined, it could be any number.
sin theta = x , sec theta =y . find cot theta pls answer fast i need to verify my answer . you can directly write the answer no issues
Answer:
[tex]\huge\boxed{\cot\theta=\dfrac{1}{xy}}[/tex]
Step-by-step explanation:
[tex]\bold{METHOD\ 1}[/tex]
[tex]\sin\theta=x\\\\\sec\theta=y\\\\\cot\theta=?\\\\\text{We know:}\\\\\sec x=\dfrac{1}{\cos x};\ \cot x=\dfrac{\cos x}{\sin x}\\\\\sec\theta=y\to\dfrac{1}{\cos \theta}=y\to\dfrac{\cos\theta}{1}=\dfrac{1}{y}\to\cos\theta=\dfrac{1}{y}\\\\\cot \theta=\dfrac{\frac{1}{y}}{x}=\dfrac{1}{xy}[/tex]
[tex]\bold{METHOD\ 2}[/tex]
[tex]\text{We know}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\cot x=\dfrac{\cos x}{\sin x}=\dfrac{1}{\tan x}\\\\\sec x=\dfrac{1}{\cos x}\\\\\text{therefore}\\\\(sin x)(\sec x)=(\sin x)\left(\dfrac{1}{\cos x}\right)=\dfrac{\sin x}{\cos x}=\tan x\\\\\dfrac{1}{(\sin x)(\sec x)}=\dfrac{1}{\tan x}=\cot x[/tex]
[tex]\\\sin \theta=x;\ \sec\theta=y\\\\\text{substitute}\\\\\cot\theta=\dfrac{1}{xy}[/tex]
please help :) What is 7.7 x 10 to the 8 power written in standard form? A. 770,000,000 B. 77,000,000,000 C. 77,000,000 D. 7,700,000,000
Answer:
A. 770,000,000
Step-by-step explanation:
7.7x10^8 First step is to simplify
7.7x100,000,000 Then, multiply
770,000,000
Hope this helps, if it does, please consider giving me brainliest, it will help me a lot. If you still have any questions, feel free to ask.
Have a good day! :)
100 points timed Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles? 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side 5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side
Answer: A
Step-by-step explanation:
The answer is A. It accurately describes the equation shown. Negative values are represented by negative tiles and positive values are represented by positive tiles.
Hope it helps <3
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options. $8 $9 $11 $13 $14
Answer:
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options.
$8 . YES
$9 . HELL NO
$11 . DEFINITLY NOT
$13 . GET OUTTA HERE
$14 . MMM YES
Step-by-step explanation:
Answer:
A and E or 8, 14
Step-by-step explanation:
Which is the best description of the equivalency of the two expressions? Expression 1 Expression 2 5 x squared minus 2 x minus 4 + 6 x + 3 6 x squared minus 6 x + 6 minus x squared + 10 x minus 7 The two expressions are not equivalent because when x = 2, the two expressions do not have the same value. The two expressions are not equivalent because when they are simplified, they do not have the same coefficients for the x squared and x terms. They are equivalent because the sum of the constants is the same in both expressions. They are equivalent because when x = 2, the two expressions have the same value.
Answer:
The correct option is (D).
Step-by-step explanation:
The two expressions are:
[tex]\text{Exp}_{1}=5x^{2}-2x-4+6x+3\\\\\text{Exp}_{2}=6x^{2}-6x+6-x^{2}+10x-7[/tex]
On simplifying both the expressions we get:
[tex]\text{Exp}_{1}=5x^{2}+4x-1\\\\\text{Exp}_{2}=5x^{2}+4x-1[/tex]
Compute the value of both expressions for x = 2 as follows:
[tex]\text{Exp}_{1}=5(2)^{2}+4(2)-1=27\\\\\text{Exp}_{2}=5(2)^{2}+4(2)-1=27[/tex]
The value of both expressions are same for x = 2.
Thus, the correct option is:
"They are equivalent because when x = 2, the two expressions have the same value."
Answer:
d
Step-by-step explanation:
Given the coordinates for the function below, which of the following are
coordinates for its inverse?
Gallons Cost, in
of Gas Dollars
1
2
5
15
20
1.25
2.50
6.25
18.75
25.00
The coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
How to determine the inverse coordinates?The table of values is given as:
Gallons Cost
1 1.25
2 2.50
5 6.25
15 18.75
20 25.00
The inverse of the above table would have the following header
Cost Gallons
When the inverse table is populated, we have:
Cost Gallons
1.25 1
2.50 2
6.25 5
18.75 15
25.00 20
The coordinates are: (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Hence, the coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
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Chen is baking muffins and banana bread for a brunch buffet. He needs 3 and one-fifth cups of flour to make the muffins and 3 and two-thirds cups of flour to make the banana bread. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes?Chen is baking muffins and banana bread for a brunch buffet. He needs 3 and one-fifth cups of flour to make the muffins and 3 and two-thirds cups of flour to make the banana bread. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes? A. 6 cups B. 7 cups C. 8 cups D. 9 cups
Answer:
hi:) If chen needed 3 1/5 and 3 2/3, the answer should be 7. 7 cups. i hope this is right but feel free to correct me if im wrong.
B. 7 cups
The best estimate of the number of cups of flour that Chen needs to bake both recipes is 7cups.
What is the fraction?A fraction is a number which has numerator and denominator.Number of cups used to make muffins = 3 1/5
Estimation = 3 cups
Number of cups used to make banana bread = 3 2/3
Estimation = 4 cups
Number of cups of flour needs to bake both recipes = Estimated number of cups used to make muffins + Estimated number of cups used to make banana bread
= 3 + 4 cups
= 7 cups.
The best estimate of the number of cups of flour that Chen needs to bake both recipes is 7cups.
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how many cups in 34 gallons
Answer:
544 cups
Step-by-step explanation:
1 gallon consists of about 16.0047 cups, 34x16 is 544
find the value of b here
Answer:
Step-by-step explanation:
We will start with the angle that measures 57 degrees. This angle is supplementary to the one next to it coming off the straight line. 180 - 57 = 123.
The rule for quadrilaterals is that same side angles are supplementary, so the angle next to the 123-degree angle (to the immediate left of that angle 123) is 57. THAT 57-degree angle is supplementary to angle b, so angle b = 180 - 57 which is 123. So C is your answer.
Answer:
do you think you can send me the work for the program
Step-by-step explanation:
i got 1 day left and im not close to finishing it please help me out please respond with any way to contact you thanks
Aster corporation accepted a $20,000, 9 percent 120-day note dated august 25 from lee company in settlement of a past bill. On October 25, Aster Corporation decided to discount the note at a discount of 8 percent. The proceeds to Aster Corporation are (blank)
Answer:
$20, 533.33
Step-by-step explanation:
From the question, we are given the following values
Principal = $20000
Rate = 8% = 0.08
Time( in years) = 120days = 4 months = 4/12 years = 1/3 years
Interest = Principal × Rate × Time
Interest = 20,000 × 0.08× (1/4)
Interest = $533.33
Hence, the proceeds to Aster Corporation are
$20000 + $533.33
= $20,533.33
Tasha wants to find out if she is going to pass her test. She decides that she will
simulate her test by flipping a coin. This means
a) There is a 50-50 chance she will pass her test.
b) All of the questions are multiple choice.
c) She hasn't studied.
d) There is a 20% chance she will pass.
Answer:
A
Step-by-step explanation:
Since a coin only has two sides, the test must be referring to the fact that she has a 50, 50 shot at passing.
1. Which financial statement reports the amount of cash paid for acquisitions of property, plant, and equipment? In which section (operating, investing, or financing) of this statement is the information reported? 2. Indicate the amount of cash paid for acquisitions of property and equipment in the year ended September 30, 2017.
Answer:
1. Cash flow statements; the investing section
Step-by-step explanation:
The cash flow statements is a useful document that shows where the company receives funds and uses it. Thus, it shows both incoming and outgoing cash flow.
The investment section of the cash flow statement is where all the amount of cash paid for acquisitions of property and equipment is imputed. Usually the transactions are written as capital expenditure.
PLEASE HELP! I WILL GIVE BRAINIEST! Look at the figure below: A triangle ABC is drawn. D is a point on BC such that BD is equal to DC. A straight line joins points A and D. This line extend Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? a Triangle ABD and triangle ECD b Triangle ABC and triangle ECD c Triangle ABD and triangle ADC d Triangle ADC and triangle ABC
Answer:
ADB and ADC
Step-by-step explanation:
SAS is side angle side. so, which 2 triangles have same side, then angle, then side. We have to have it in that specific order.
Answer:
ABD and ECD
Step-by-step explanation:
EDC and ADB are vertical angles, so that is the angle we need for the SAS postulate. The markings on each of the corresponding sides is the same, which means we have 2 congruent sides, as well as an angle.
The graph of y = h(x) is a line segment joining the points (1, -5) and (9,1).
Drag the endpoints of the segment below to graph y = h-'(x).
Answer:
Ok, i cant drag the endpoints of the segment, but i can tell you how to do it.
First, we know that h(x) joins the points (1, -5) and (9, 1), then h(x) is a line:
h(x) = s*x + b
First, for a line that goes through the points (x1, y1) and (x2, y2), the slope will be:
s = (y2 -y1)/(x2 - x1)
Then in this case, the slope is:
s = (1 - (-5))/(9 - 1) = 0.75
Then we have
h(x) = 0.75*x + b
now, the value of b can be found as:
h(1) = -5 = 0.75*1 - b
b = - 5 - 0.75 = -5.75.
Then our equation is:
h(x) = 0.75*x - 5.75
Now, i gues you want to find the graph of:
y = h(-x)
Then our new function is:
g(x) = h(-x) = -0.75*x - 5.75.
Now to find the points, we evaluate this function in the same values of x as before.
g(1) = -0.75*1 - 5,75 = -6,5
the point is (1, -6.5)
the second point is when x = 9.
g(9) = -0.75*9 - 5.75 = -12.5
The second point is (9, -12.5)
Answer:
(−6,7) (-1,-2)
Step-by-step explanation:
Khan
Name an inscribed angle
Answer:
BHF
Step-by-step explanation:
Definition of inscribed
Please answer this in two minutes
Answer:
u = [tex]\sqrt{6}[/tex].
Step-by-step explanation:
This is a 45-45-90 triangle.
That means that there are two side lengths with lengths of x, and a hypotenuse with a length of xsqrt(2). We can then set up a proportion.
[tex]\frac{1}{\sqrt{3} } =\frac{\sqrt{2} }{u}[/tex]
1 * u = [tex]\sqrt{3} * \sqrt{2}[/tex]
u = [tex]\sqrt{6}[/tex].
Hope this helps!
three people are watching a hot air balloon travel over their town. at a certain point in time, one person stands directly below the balloon, and the others look at it at certain angles. in the following image, a,b, and c are people, and d is the balloon. person c is 384m directly below the balloon, person b is 200m away from person c, and the angle between person a, the balloon, and person b is 33 degrees. how far is person a from the hot air balloon
Answer:
Distance between balloon and a is = 383.67 m
Step-by-step explanation:
The given situation can be represented as the given diagram as attached in the answer area.
cd = 384 m
cb = 200 m
[tex]\angle adb = 33^\circ[/tex]
To find:
Distance between balloon and a i.e. side ad = ?
Solution:
First of all, let us consider the right angled [tex]\triangle bcd[/tex].
We know the trigonometric identity that:
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan\angle cbd =\dfrac{cd}{cb}\\\Rightarrowtan\angle cbd =\dfrac{384}{200}\\\Rightarrowtan\angle cbd =1.92\\\Rightarrow \angle cbd = tan^{-1}(1.92) = 62.49^\circ[/tex]
Now, using the external angle property for the external [tex]\angle cbd[/tex] for the [tex]\triangle abd[/tex]:
(External angle is equal to the sum of two opposite angles of the triangle.)
[tex]\angle cbd = \angle adb+\angle a[/tex]
[tex]\Rightarow \angle a =62.49-33 =29.49^\circ[/tex]
Now, let us consider the right angled [tex]\triangle acd[/tex].
We have the value of [tex]\angle a[/tex] and perpendicular dc.
We have to find the hypotenuse ad.
Let us use the sine identity:
[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin\angle a =\dfrac{cd}{ad}\\\Rightarrow sin(29.49^\circ) =\dfrac{384}{ad}\\\Rightarrow ad = \dfrac{384}{0.49}\\\Rightarrow \bold{ad = 783.67\ m}[/tex]
So, the answer is:
Distance between balloon and [tex]\bold{a}[/tex] is = 383.67 m