Answer
1021.41
Step-by-step explanation:
area of a circle=πr^2
r=radius=half the diameter
π*(25.5^2)=2042.82
a semi circle is half a circle so you have to half the area to get 1021.41
QUESTION 6
Find Future Value Using Compound Interest Formula:
You deposit $300 in an account earning 7% interest compounded semi-annually. How much will you have in the account in 20 years?
A. $720
B. $596.94
C. $1,187.78
D. $1,140
QUESTION 7
Find Future Value Using Compound Interest Formula:
You deposit $3,000 in an account earning 3% interest compounded monthly. How much will you have in the account in 15 years?
A. $3,091.25
B. $4,702.30
C. $4,507.25
D. $3,033.62
whats the answer yall please help me god
Answer:
C, D and E are true
Step-by-step explanation:
You know that angle 3 = 180 - ∠1 -∠2
and that angle 4 = 180 - ∠3 so
∠4 = ∠1 + ∠2 and you can deduce the C and D
Answer:
C, D, E are the correct options.
Step-by-step explanation:
[tex]C. \: \: m \angle \: 4 \: is \: greater \: than \: m \angle \: 2 \\ \\ D. \: \: m \angle \: 1 + m \angle \: 2 = m \angle \: 4 \\ \\ E. \: \: m \angle \: 4 \: is \: greater \: than \: m \angle \: 1[/tex]
The pole cast a 24 foot shadow while he cast a 4 foot shadow. Sam is 6 feet tall. What’s the height of the electricity pole
Answer:
36 ftStep-by-step explanation:
lets use proportions
6/4=x/24
cross multiply:
6*24=4x
144=4x
4x=144
x=36
The pole is 36 ft tall
4 feet tall casts a shadow of 6 feet.
36 feet tall will cast a shadow of 24 feet.
The two equations are:
4 feet tall = 6 feet
36 feet tall = 24 feet
The height of pole is 36 feet tall.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 4 is an equation.
2x + 3 = 4 is an equation.
We have,
Sam:
Height = 6 feet tall_____(1)
Shadow cast = 4 feet ______(2)
Pole:
Height = P feet tall
Shadow cast = 24 feet
Now,
From (1) and (2) we get,
6 feet tall = 4 feet
Multiply 6 on both sides.
6 x 6 feet tall = 4 x 6 feet
36 feet tall = 24 feet
This means,
The pole height is 36 feet tall.
Thus,
4 feet tall casts a shadow of 6 feet.
36 feet tall will cast a shadow of 24 feet.
The height of pole is 36 feet tall.
Learn more about equations here:
https://brainly.com/question/17194269
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darius is camping in the woods. he notices on a map that his campsite is 50 yards from the ranger station. he walks 18 yards towards the ranger station the tree forms the altitude of a right triangle that connects the top of the tree darius's campsite, and the ranger station. sketch a diagram of the situation and determine the angle of depression formed by darius sightline to the ranger station.
Answer:
The angle of depression formed by Darius's sight line to the ranger station is 53.13°.
Step-by-step explanation:
Denote Darius's camp site as C, the ranger station as R and the tree as T.
Consider the triangle CTR.
TX is the altitude of the right angled triangle TXR.
The altitude of a right angled triangle forms two triangle that similar to each other.
So, ΔTXC [tex]\sim[/tex] ΔTXR.
Compute the measure of TX as follows:
[tex]\frac{CX}{TX}=\frac{TX}{RX}\\\\TX^{2}=CX\times RX\\\\TX=\sqrt{CX\times RX}[/tex]
[tex]=\sqrt{18\times 32}\\\\=24\ \text{yd}[/tex]
The angle d represents the angle of depression formed by Darius's sight line to the ranger station.
Compute the value of d as follows:
[tex]tan\ d^{o}=\frac{RX}{TX}\\\\d^{o}=tan^{-1} [\frac{RX}{TX}][/tex]
[tex]=tan^{-1} [\frac{32}{24}]\\\\=53.13[/tex]
Thus, the angle of depression formed by Darius's sight line to the ranger station is 53.13°.
What are (a) the x component and (b) the y component of a vector in the xy plane if its direction is 250° counterclockwise from the positive direction of the x axis and its magnitude is 7.3 m?
Answer:
(-2.497, -6.860)
Step-by-step explanation:
For any magnitude r and direction θ, the translation to rectangular coordinates is ...
(r, θ) ⇒ (x, y)
(r, θ) ⇒ (r·cos(θ), r·sin(θ))
Your coordinates translate to ...
(7.3, 250°) ⇒ (7.3·cos(250°), 7.3·sin(250°)) ≈ (-2.497, -6.860)
Complete the square to rewrite y-x^2-6x+14 in vertex form. then state whether the vertex is a maximum or minimum and give its cordinates
Answer:
[tex] y= x^2 -6x +(\frac{6}{2})^2 +14 -(\frac{6}{2})^2[/tex]
And solving we have:
[tex] y= x^2 -6x +9 + 14 -9[/tex]
[tex] y= (x-3)^2 +5[/tex]
And we can write the expression like this:
[tex] y-5 = (x-3)^2[/tex]
The vertex for this case would be:
[tex] V= (3,5)[/tex]
And the minimum for the function would be 3 and there is no maximum value for the function
Step-by-step explanation:
For this case we have the following equation given:
[tex] y= x^2 -6x +14[/tex]
We can complete the square like this:
[tex] y= x^2 -6x +(\frac{6}{2})^2 +14 -(\frac{6}{2})^2[/tex]
And solving we have:
[tex] y= x^2 -6x +9 + 14 -9[/tex]
[tex] y= (x-3)^2 +5[/tex]
And we can write the expression like this:
[tex] y-5 = (x-3)^2[/tex]
The vertex for this case would be:
[tex] V= (3,5)[/tex]
And the minimum for the function would be 3 and there is no maximum value for the function
A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 559 randomly selected Americans surveyed, 370 were in favor of the initiative. Round answers to 4 decimal places where possible.
a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between and .b. If many groups of 506 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about percent will not contain the true population proportion.
Answer:
a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between 0.6290 and 0.6948.
b. If the sample size is changed, the confidence interval changes as the standard error depends on sample size.
About 90% percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10% percent will not contain the true population proportion.
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.6619.
[tex]p=X/n=370/559=0.6619[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.6619*0.3381}{559}}\\\\\\ \sigma_p=\sqrt{0.0004}=0.02[/tex]
The critical z-value for a 90% confidence interval is z=1.6449.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.6449 \cdot 0.02=0.0329[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.6619-0.0329=0.6290\\\\UL=p+z \cdot \sigma_p = 0.6619+0.0329=0.6948[/tex]
The 90% confidence interval for the population proportion is (0.6290, 0.6948).
pqrs is a rhombus with angle pqr is equals to 58 determine angle PRS
Answer: ∡PRS=61°
Step-by-step explanation:
As known the following equity is valid for the rhombus:
∡PQR+∡QRS = 180°
So ∡QRS=180°- ∡PQR
∡QRS=180°- 58°= 122°
From another hand we know that PR is bisector of ∡QRS.
So ∡PRS=∡QRS:2= 122°:2=61°
∡PRS=61°
34% of U.S. adults have very little confidence in newspapers. You randomly select eight U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly six, (b) at least four, and (c) less than five.
Please Show Work So I Can Grasp The Concept Of This Equation
Answer:
20
Step-by-step explanation:
do 9/12 = 15/?
you do 12 times 15 divided by 9
hope this helps
Sofia vai colar um pedaço de barbante no contorno de uma moldura quadrada de lado 20 cm. Qual deverá ser o comprimento desse barbante?
Answer:
A corda deve ter um comprimento mínimo de 80 cm.
The string should have a minimum length of 80 cm.
Step-by-step explanation:
Espera-se que a corda seja colada em todo o contorno da moldura quadrada.
Isso significa que a cadeia precisa cobrir pelo menos todo o perímetro da moldura quadrada pelo menos uma vez.
Perímetro de um quadrado = 4L
L = comprimento lateral do quadrado.
O comprimento lateral da moldura quadrada = 20 cm
Comprimento mínimo da corda necessária = Perímetro da moldura quadrada = 4 × 20 = 80 cm.
Espero que isto ajude!!!!
English Translation
Sofia is going to glue a piece of string to the outline of a square frame 20 cm from the side. How long should this string be?
Solution
The string is expected to be glued all around the outlne of square frame.
This means the string needs to at least cover the whole perimeter of the square frame a minimum of one time.
Perimeter of a square = 4L
L = side length of the square.
The side length of the square frame = 20 cm
Minimum length of the string required = Perimeter of the square frame = 4 × 20 = 80 cm.
Hope this Helps!!!!
What are the two shapes of cross sections we could create by slicing the pyramid
The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 4 fish is taken. What is the probability that the sample means will be more than 3.4 pounds?
Answer:
[tex]P(\bar X>3.4) = 0.385[/tex]
Step-by-step explanation:
Relevant Data provided according to the question is as follows
[tex]\mu[/tex] = 3.2
[tex]\sigma[/tex] = 0.8
n = 4
According to the given scenario the calculation of probability that the sample means will be more than 3.4 pounds is shown below:-
[tex]z = \frac{\bar X - \mu}{\frac{a}{\sqrt{n} } }[/tex]
[tex]P(\bar X>3.4) = 1 - P(\bar X\leq 3.4)[/tex]
[tex]= 1 - P \frac{\bar X - \sigma}{\frac{a}{\sqrt{n} } } \leq \frac{3.4 - \sigma}{\frac{a}\sqrt{n} }[/tex]
Now, we will solve the formula to reach the probability that is
[tex]= 1 - P \frac{\bar X - 3.2}{\frac{0.8}{\sqrt{4} } } \leq \frac{3.4 - 3.2}{\frac{0.8}\sqrt{4} }[/tex]
[tex]= 1 - P (Z \leq \frac{0.2}{0.4})[/tex]
[tex]= 1 - P (Z \leq 0.5})[/tex]
[tex]= 1 - \phi (0.5)[/tex]
= 1 - 0.6915
= 0.385
Therefore the correct answer is
[tex]P(\bar X>3.4) = 0.385[/tex]
So, for computing the probability we simply applied the above formula.
Answer:
its 21
Step-by-step explanation:
its not 21 i really dont know
Not sure what it would be
Answer:
negative
Step-by-step explanation:
The slope of the line is negative because it goes from the upper corner down to the lower corner.
I remember it as negative because a rock would roll down it, if I would have to push it, it is positive.
Which expression is equivalent to 2−35,? Choose 1 answer:
Answer:
The answer is option A.
Step-by-step explanation:
2 - 35 can be written as 2 + (-35) since in 2+( -35) when the bracket is removed it becomes 2 - 35.
Hope this helps
Answer:
Your correct answer is option a. 2 + (-35)
Step-by-step explanation:
When you are finding which equation is equivalent to the one you have, the best thing to find is what your equation's answer is.
Module 7
When you multiply a difference of two squares, why is your answer a binomial instead of a trinomial like when you multiply the sum of two squares? Create an example of multiplying a difference of two squares and show your work as you simplify the expression.
WILL GIVE BRAINLIEST
Answer:
When you multiply a difference of squares, two terms cancel each other out and result in a binomial instead of a trinomial. To understand this, you can use an example.
When you multiply (x-3) and (x+3), you can use FOIL to expand them. By doing this, you get x^2-3x+3x-9. As you can see, -3x and 3x cancel each other out, so this results in a binomial instead of a trinomial.
Answer:
when you multiply them the two terms cancel each other out which will result in a binominal
Step-by-step explanation:
2
Question Progress
Homewo
Simplify
X-9
x² – 3x
Answer:
(x - 9) is already simplified
x² - 3x simplified is x(x - 3)
Step-by-step explanation:
We need to see if we can either take out GCF or factor. Since the 1st expression we can do neither, it is in its simplest form. For the 2nd expression, we can take out an x, and we get x(x - 3) as our simplified expression.
A survey asks, "If the husband in a family wants children, but the wife decides that she does not want any children, is it all right for the wife to refuse to have children?" Of 705 subjects, 581 said yes. a. Find a 99% confidence interval for the population proportion who would say yes. (Use ascending order. Round to four decimal places as needed.) Can you conclude that the population proportion exceeds 75%? Why? in 2 A. No, we cannot conclude that the population proportion exceeds 75%, because 75% is below the lowest believable value of the confidence interval B. Yes, we can conclude that the population proportion exceeds 75% because 75% is above the lowest believable value of the confidence interval C. No, we cannot conclude that the population proportion exceeds 75% because 75% is above the lowest believable value of the confidence interval D. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval. b. Without doing any calculations, explain whether the interval in (a) would be wider or narrower than a 95% confidence interval for the population proportion who would say yes. The 99% confidence interval would be wider than a 95% confidence interval. The 99% confidence interval would be narrower than a 95% confidence interval.
Answer:
a. The 99% confidence interval for the population proportion is (0.7872, 0.8610).
D. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval.
b. The 99% confidence interval would be wider than a 95% confidence interval.
As the confidence level increases, the width interval increases, as we are requiring more confidence with the same information (there is no new sample). This means that, to be more confident, the only way is to include more values in the interval.
Step-by-step explanation:
We have to calculate a 99% confidence interval for the proportion.
The sample proportion is p=0.8241.
[tex]p=X/n=581/705=0.8241[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.8241*0.1759}{705}}\\\\\\ \sigma_p=\sqrt{0.000206}=0.0143[/tex]
The critical z-value for a 99% confidence interval is z=2.5758.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=2.5758 \cdot 0.0143=0.0369[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.8241-0.0369=0.7872\\\\UL=p+z \cdot \sigma_p = 0.8241+0.0369=0.8610[/tex]
The 99% confidence interval for the population proportion is (0.7872, 0.8610).
We can conclude that there is, at least, 99% chances that the true proportion is higher than 0.7872. So there is at least 99% chances that the population proportion is higher than 0.75.
Which vector has an x-component with a length of 4?
Answer:
vector aStep-by-step explanation:
In order to locate the vector that has an x- component with a length of 4, we need to know the position of each vector on the Cartesian plane. Each of the vectors lies on the (x, y) coordinate.
For vector a, it lies on the coordinate A(1, 4), vector b lies on the coordinate B(1,1), vector c lies on the coordinate C(4,4) while vector d lies in the coordinate D(3, 4).
It can be seen that out of this four vectors, only vector C has an x- coordinate of 4. This shows that vector a is the only vector that has an x-component with a length of 4?
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
Please answer fast!!!!
Answer:
4
Step-by-step explanation:
We are told that figure B is a scaled copy of B, which means figure A was enlarged by a certain scale factor to get a similar figure as A, now referred to as figure B.
The scale factor = ratio of any two corresponding sides of both similar figures.
Thus,
Scale factor of the similar figures given = 40/10 = 4.
This means that, figure A was scaled up by 4 times its original size to get figure B. Each side of figure B is 4 × the corresponding side in figure A.
Scale factor = 4
My friend needs help again :)
Which of the following numbers can be expressed as a decimal that terminates? 3 over 2, 2 over 3, 3 over 4, 5 over 7 3 over 2 and 2 over 3 3 over 4 and 5 over 7 3 over 2 and 3 over 4 2 over 3 and 5 over 7
Answer:
Hey there!
3/2= 1.5, which is good.
2/3=0.666666666666... no
3/4=0.75, which is good.
5/7= 0.71428... no
Answer:
3/23/53/4these sequences are limited
you can try it in a calculator
lg(3x-2) +lg(x+1) =2 –lg2
Answer:
x = 4 or x = -13/4 = -4.33
Step-by-step explanation:
log (3x - 2) + log (x + 1) = 2 - log 2
Note 2 is also equals to log 100
log (3x - 2) + log (x + 1) = log 100 - log 2
log (3x - 2)(x + 1) = log (100/2)
log 3x² + 3x - 2x - 2 = log 50
log 3x² + x - 2 = log 50
3x² + x - 2 = 50
3x² + x - 2 - 50 = 0
3x² + x - 52 = 0
find the number to multiply that will give you -52 × 3 = -156 and add to give you 1. The numbers are -12 and 13.
3x² - 12x + 13x - 52 = 0
3x(x - 4) + 13( x - 4) = 0
(3x + 13)(x - 4) = 0
x = 4 or x = -13/4 = -4.33
If you insert 4 in the logarithm equation you will see that the left side is equal to the right
log (3x - 2) + log (x + 1) = log 100 - log 2
log 10 + log 5 = log 50
log 50 = log 50
What is the difference in milligrams between a powdered headache medicine at 12 mg and a headache tablet at 0.018 g?
Answer:
6 mg
Step-by-step explanation:
12 mg
0.018 g * 1000 mg/g = 18 mg
18 mg - 12 mg = 6 mg
Write 48√3 - 15√12 + 2√75 in the form a√3 a = √3
Answer:
68√3
Step-by-step explanation:
48√3 - 15√12 + 2√75=
48√3 - 15√4*3 + 2√25*3 =
48√3 - 30√3 + 50√3= 68√3
El numeral 32012(4) representado en el sistema decimal, porfavor
Answer: El número es 902 en el sistema decimal.
Step-by-step explanation:
Supongo que tenemos el número:
32012 en base 4, y lo queremos representar en base decimal.
Entonces, usando la regla general, podemos escribir este número como:
unidades*base^0 + decenas*base^1 + centenas*base^2......
Es decir, acá tenemos:
2*4^0 + 1*4^1 + 0*4^2 + 2*4^3 + 3*4^4 = 902
El número es 902 en el sistema decimal.
The ratio of sides of 2 similar cubes is 3:4. Larger cube has a volume of 1728 cubic meters . What is the volume of the smaller cube?
Answer:
729m³
Step-by-step explanation:
To find the length of one side find the cube root of 1728m³
³√1728=12metres
To find the length of the smaller cube
ratio 3:4.
4/7=12m
3/7=?
3/7×12 = 3/7×12×7/4
4/7
=9metres
To find volume of the small cube
volume=9×9×9
=729m³
1) Suppose that a function f(x) is defined for all real values of x, except x = xo. Can anything be said about LaTeX: \displaystyle\lim\limits_{x\to x_0} f(x)lim x → x 0 f ( x )? Give reasons for your answer.
Answer:
Ok, we have that f(x) is defined for all real values of x, except for x = x0.
[tex]\lim_{x \to \ x0} f(x)[/tex]
Does it exist? why?
Remember that when we are taking the limit we are not evaluating the function in x0, instead, we are evaluating the function in values really close to x0 (values defined as x0⁺ and x0⁻, where the sign defines if we approach from above or bellow).
And because f(x) is defined in the values of x near x0, we can conclude that the limit does exist if:
[tex]\lim_{x \to \x0+} f(x) = \lim_{x \to \x0-} f(x)[/tex]
if that does not happen, like in f(x) = 1/x where x0 = 0
where the lower limit is negative and the upper limit is positive, we have that the limit does not converge.
can somebody help me with this question please
Answer:
490 J
Step-by-step explanation:
The formula is ...
PE = mgh
where g is the acceleration due to gravity: 9.8 m/s². Filling in your numbers, you find the energy to be ...
PE = (5 kg)(9.8 m/s²)(10 m) = 490 kg·m²/s² = 490 J
Two spheres have scale factor of 1:3. The smaller sphere has a surface area of 16 square feet. Find the surface area of the larger sphere
Answer:
48
Step-by-step explanation:
16*3=48
What is the area of a sector with a central angle of 5pi over 6 radians and a radius of 5.6ft
Answer:
41.0501 ft²
Step-by-step explanation:
Area of a Sector (Radians): A = 1/2r²∅
We are given r and ∅, so simply plug it into the formula:
A = 1/2(5.6)²(5π/6)
A = 1/2(31.36)(5π/6)
A = 15.68(5π/6)
A = 41.0501 ft²