Answer: 80 feet
Step-by-step explanation:
We can write these as fractions and do cross multiplication with the numerator being the height of the object while the denominator being the length of the shadow:
5 * 128 = 8x
640 = 8x
80 = x
Thus, the height of the lighthouse is 80 feet tall.
La potencia que se obtiene de elevar a un mismo exponente un numero racional y su opuesto es la misma verdadero o falso?
Answer:
Falso.
Step-by-step explanation:
Sea [tex]d = \frac{a}{b}[/tex] un número racional, donde [tex]a, b \in \mathbb{R}[/tex] y [tex]b \neq 0[/tex], su opuesto es un número real [tex]c = -\left(\frac{a}{b} \right)[/tex]. En el caso de elevarse a un exponente dado, hay que comprobar cinco casos:
(a) El exponente es cero.
(b) El exponente es un negativo impar.
(c) El exponente es un negativo par.
(d) El exponente es un positivo impar.
(e) El exponente es un positivo par.
(a) El exponente es cero:
Toda potencia elevada a la cero es igual a uno. En consecuencia, [tex]c = d = 1[/tex]. La proposición es verdadera.
(b) El exponente es un negativo impar:
Considérese las siguientes expresiones:
[tex]d' = d^{-n}[/tex] y [tex]c' = c^{-n}[/tex]
Al aplicar las definiciones anteriores y las operaciones del Álgebra de los números reales tenemos el siguiente desarrollo:
[tex]d' = \left(\frac{a}{b} \right)^{-n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{-n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{(-1)\cdot n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{(-1)\cdot n}[/tex]
[tex]d' = \left[\left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]y [tex]c' = \left[(-1)^{-1}\cdot \left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c = (-1)^{n}\cdot \left(\frac{b}{a} \right)^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{b}{a} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{b}{a} \right)\right]^{n}[/tex]
Si [tex]n[/tex] es impar, entonces:
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = - \left(\frac{b}{a} \right)^{n}[/tex]
Puesto que [tex]d' \neq c'[/tex], la proposición es falsa.
(c) El exponente es un negativo par.
Si [tex]n[/tex] es par, entonces:
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left(\frac{b}{a} \right)^{n}[/tex]
Puesto que [tex]d' = c'[/tex], la proposición es verdadera.
(d) El exponente es un positivo impar.
Considérese las siguientes expresiones:
[tex]d' = d^{n}[/tex] y [tex]c' = c^{n}[/tex]
[tex]d' = \left(\frac{a}{b}\right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = (-1)^{n}\cdot \left(\frac{a}{b} \right)^{n}[/tex]
Si [tex]n[/tex] es impar, entonces:
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = - \left(\frac{a}{b} \right)^{n}[/tex]
(e) El exponente es un positivo par.
Considérese las siguientes expresiones:
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left(\frac{a}{b} \right)^{n}[/tex]
Si [tex]n[/tex] es par, entonces [tex]d' = c'[/tex] y la proposición es verdadera.
Por tanto, se concluye que es falso que toda potencia que se obtiene de elevar a un mismo exponente un número racional y su opuesto es la misma.
A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.
Answer:
[tex]Height = 12cm[/tex]
Step-by-step explanation:
Given
[tex]Volume = 1200cm^3[/tex]
The dimension of the base is:
[tex]Base =10cm[/tex]
[tex]Sides = 13cm[/tex]
See comment for complete question
Required
The height of the base
To do this, we make use of Pythagoras theorem where:
[tex]Sides^2 = (Base/2)^2 + Height^2[/tex]
So, we have:
[tex]13^2 = (10/2)^2 + Height^2[/tex]
[tex]13^2 = 5^2 + Height^2[/tex]
[tex]169 = 25 + Height^2[/tex]
Collect like terms
[tex]Height^2 = 169 - 25[/tex]
[tex]Height^2 = 144[/tex]
Take square roots of both sides
[tex]Height = 12cm[/tex]
At the beginning of year 1, Matilda invests $450 at an annual simple interest rate of 5%. She makes no deposits to or withdrawals from the account. Which explicit formula can be used to find the account's balance at the beginning of year 15? What is the balance?
Answer:
$765
Step-by-step explanation:
[tex]interest \: = \frac{prt}{100} \\ = \frac{(450)(5)(14)}{100} \\ = 315 \\ total \: money \: = 315 + 450 \\ = 765[/tex]
A(n) = 450 + (n – 1)(0.05 • 450); $765.00
People at the state fair were surveyed about which type of lemonade they preferred. The results are shown below. Pink lemonade: 156 males, 72 females Yellow lemonade: 104 males, 48 females The events "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6. P(female | pink lemonade ) = P(pink lemonade) = 0.3. P(pink lemonade | female) = 0.3 and P(pink lemonade) = 0.6. P(female | pink lemonade ) = 0.3 and P(pink lemonade) = 0.6.
Answer:
[tex]P(pink) = P(pink |\ female) = 0.6[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccc}{} & {Male} & {Female} & {Pink} & {156} & {72} \ \\ {Yellow} & {104} & {48} \ \end{array}[/tex]
Required
Why [tex]prefers\ pink\ lemonade[/tex] and [tex]female[/tex] are independent
First, calculate [tex]P(pink |\ female)[/tex]
This is calculated as:
[tex]P(pink |\ female) = \frac{n(pink\ \&\ female)}{n(female)}[/tex]
[tex]P(pink |\ female) = \frac{72}{48+72}[/tex]
[tex]P(pink |\ female) = \frac{72}{120}[/tex]
[tex]P(pink |\ female) = 0.6[/tex]
Next, calculate [tex]P(pink)[/tex]
[tex]P(pink) = \frac{n(pink)}{n(Total)}[/tex]
[tex]P(pink) = \frac{156 + 72}{156 + 72 + 104 + 48}[/tex]
[tex]P(pink) = \frac{228}{380}[/tex]
[tex]P(pink) = 0.6[/tex]
So, we have:
[tex]P(pink) = P(pink |\ female) = 0.6[/tex]
Hence, they are independent
Answer:
P(pink lemonade | female) = P(pink lemonade) = 0.6.
Step-by-step explanation:
A
Represent pictorially:
3x2/6 = 6/6 or = 1
Answer:
yes is correct 6/6 = 1 / 3*2=6 =1
Answer:
nonsense. what's the difference between 6/6 or 1 .
what is the ratio of Sin 45°?
Answer:
1/√2
Step-by-step explanation:
The value of sin 45 is 1/√2
What is (f.g)(x)?
f(x)=x^3 - 4x + 2
g(x)=x^2 + 2
Answer:
f(g(x)) =
[tex] {x}^{6} + 6 {x}^{4} + 8x^{2} + 2[/tex]
Step-by-step explanation:
put g(x) instead of any x in f(x)
[tex] {(x ^{2} + 2) }^{3} - 4( {x}^{2} + 2) + 2[/tex]
Can Someone Help Me With This ?
Answer:
its to pixelated
Step-by-step explanation:
pls help, i have class rn :(
in how many ways can alice distribute 12 apples to 3 children (a child can have no apples)
URGENTT!!!! help quick please
Factor -1.8 out of 3.6b-9
=================================================
Explanation:
Consider something like 2b+6 factoring to 2(b+3). When we distribute that outer 2 back inside the parenthesis, we're multiplying that 2 by everything inside. Factoring goes in reverse of this and we divide each term of 2b+6 by the GCF 2.
The same thing applies to this current problem as well.
Divide each term by the -1.8 we want to factor out.
(3.6b)/(-1.8) = -2b(-9)/(-1.8) = 5The results -2b and 5 will go inside the parenthesis. That's how we end up with -1.8(-2b+5)
You can use distribution to verify this
-1.8(-2b+5)
-1.8*(-2b) - 1.8*(5)
3.6b - 9
Explain what you would do first to simplify the expression below. Justify why, and then state the result of performing this step.
please help! I cant figure this out!
A 90 % confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. the interval was ($133, 306, $150, 733). To make useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?
A) Increase the sample size and increase the confidence level.
B) Decrease the sample size and increase the confidence level.
C) Decrease the sample size and decrease the confidence level.
D) Increase the sample size and decrease the confidence level.
Answer: D) Increase the sample size and decrease the confidence level.
Step-by-step explanation:
A reduced interval width means that the data is more accurate. This can only be achieved if the sample size is increased because a larger sample size is able to capture more of the characteristics of the variables being tested.
A smaller confidence interval will also lead to a reduced interval width because it means that the chances of the prediction being correct have increased.
3x + y = 10 x - y = 2 2
help with this question please
Use the quadratic formula to find both solutions to the quadratic equation
given below.
3x2 - x + 4 = 0
Answer:
[tex]x = \dfrac{1 + i\sqrt{47}}{6}[/tex] or [tex]x = \dfrac{1 - i\sqrt{47}}{6}[/tex]
Step-by-step explanation:
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
We have a = 3; b = -1; c = 4.
[tex] x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(4)}}{2(3)} [/tex]
[tex]x = \dfrac{1 \pm \sqrt{1 - 48}}{6}[/tex]
[tex]x = \dfrac{1 \pm \sqrt{-47}}{6}[/tex]
[tex]x = \dfrac{1 + i\sqrt{47}}{6}[/tex] or [tex]x = \dfrac{1 - i\sqrt{47}}{6}[/tex]
Helpppp ,I will mark you brainlist
Answer:
Okay
Step-by-step explanation:
Plss answer the bottom question
Answer:
200
Step-by-step explanation:
250/100=2.5
2.5*80=200
So the answer is 200
Which shape has the greatest number of lines of symmetry?
A. rhombus
B. square
C. rectangle
D. parallelogram
Find the perimeter of ΔJKL. Round your answer to the nearest tenth if necessary
Answer:
Step-by-step explanation:
as angles of two triangles are equal, so they are similar.
x/17 =35/14=40/16
x/17=35/14
x=35/14×17=85/2=42.5
perimeter of ΔJKL=40+35+42.5=117.5
Between 20 to 35 degrees north latitude, and also between 20 to 35 degrees south latitude are found:
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Its area includes all Sahara's locations in North Africa, South Arabia, Iran's and Iraq's larger parts, North-Western India, California throughout the United States, South Africa but most of Australia.
Half-arid temperatures include places like the Utah, Montana, and Gulf Coastal regions of sagebrush. Also, it comprises regions in Iceland, Russia, Scandinavia, Greenland, and Northeast India. Semi-arid thankless than tube called per year of rain and up to 20 inches per year at much more than arid deserts.
Regions from of the latitude of 25° to 35° usually develop desert, because air sinks and is heated under pressures in this area. The world's dry and semi-arid desert regions are between 20°C and 35°C north latitude and between 20°C and 35°C South latitude.
pls help me i’m so stuck
Answer:
Step-by-step explanation:
If a point (x, y) is reflected across y = -x, coordinates of the image point will be,
(x, y)→ (-y, -x)
Following this rule,
Vertices of the triangle will be,
(3, 1) → (-1, -3)
(3, -2) → (2, -3)
(6, -3) → (3, -6)
Therefore, image of the given triangle A will be,
(-1, -3), (2, -3) and (3, -6)
Find the area of circle Q in terms of x
Answer:
The answer is C 100πcm^3
Write each as a percent. Use proportions.
7/25
2/3
3/8
What is the product?
A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without
looking, how many ways can you get 5 apples?
Answer:
6 I think
Step-by-step explanation:
Which of the following is the constant ratio of the relation shown in the table?
Answer:
hello!
where are you from ?
Step-by-step explanation:
option 4 is correct ...there is no constant ratio.
(Algebra ll) Given the function below
Answer: B
Step-by-step explanation:
To find the values of x, we first need to write the function into an equation. We can derive 2 equations from the problem.
Equation 1: y=2|x+6|-4
Equation 2: y=6
Now, we can substitute.
2|x+6|-4=6
Let's solve for x.
2|x+6|-4=6 [add both sides by 4]
2|x+6|=10 [divide both sides by 2]
|x+6|=5 [subtract both sides by 6]
x=-1
Now that we know x=-1 is one of the solutions, we can eliminate C and D.
We know that the absolute value makes the number inside positive always. Therefore, let's solve for x with -5 instead.
|x+6|=-5 [subtract both sides by 6]
x=-11
Therefore, we know that B is the correct answer.
Determine the area of the triangle.
96.0 square units
16.9 square units
192.0 square units
97.5 square units
Answer:
A. 96.0 square units
Step-by-step explanation:
The formula for the area of a triangle when we know the side length of two sides and the measure of an included angle of a triangle is given as:
A = ½*a*b*Sin C
Where,
a = 13
b = 15
C = 80°
Plug in the values into the formula
A = ½*13*15*Sin 80
A = 96.0187559
A = 96.0 square units (nearest tenth)
Answer:A
Step-by-step explanation: I took the test
