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gulaghasi [49]
3 years ago
15

Explain algebraically using properties of logs how log(100x) is related to log(x)

Mathematics
1 answer:
DIA [1.3K]3 years ago
4 0
Log(100x)=log(100)+logx
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Tony’s deposit earned $40.80 in simple interest over 3 years in an account with an interest rate of 1.7%. How much did Tony depo
tamaranim1 [39]

Answer:

3. Tony's deposit earned $40.80 in simple interest over 3 years in an account with an interest rate of 1.7%. How much did Tony deposit?

4 0
2 years ago
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 436.0 gram setting. It
Vilka [71]

Answer:

We conclude that the machine is under filling the bags.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 436.0 gram

Sample mean, \bar{x} = 429.0 grams

Sample size, n = 40

Alpha, α = 0.05

Population standard deviation, σ = 23.0 grams

First, we design the null and the alternate hypothesis

H_{0}: \mu = 436.0\text{ grams}\\H_A: \mu < 436.0\text{ grams}

We use one-tailed(left) z test to perform this hypothesis.

Formula:

z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

Putting all the values, we have

z_{stat} = \displaystyle\frac{429 - 436}{\frac{23}{\sqrt{40}} } = -1.92

Now, z_{critical} \text{ at 0.05 level of significance } = -1.64

Since,  

z_{stat} < z_{critical}

We reject the null hypothesis and accept the alternate hypothesis. Thus, we conclude that the machine is under filling the bags.

8 0
3 years ago
How long does each phase of the moon (exactly) take long to complete?
hammer [34]
The moon takes.exactly one month. did that help?
8 0
3 years ago
LA DISTANCIA ENTRE LA TIERRA YLA LUNA ES DE 384 392 KM. LOS AUSTRONAUTAS DE LA APOLO XL SALIERON EL 16 DE JULIO DE 1969 DESDE EL
KengaRu [80]

Complete question :

la distancia entre la tierra y la luna es de 384 392 km. Los astronautas de la Apolo XL salieron el 16 de julio de 1969 desde el Centro Espacial Kennedy y al alcanzaron la orbita el 19 de julio de 1969. Suponiendo que cada dia recorrieron la misma cantidad de kilometros cuantos kilometros recorrieron por dia

Responder:

128130,66 kilometros

Explicación paso a paso:

Dado que:

Distancia entre la tierra y la luna = 384,392 km

Tiempo empleado = (19 de julio - 16 de julio) mismo año = 3 días

Velocidad = distancia / tiempo

El tiempo empleado es (3 * 24) = 72 horas

Por lo tanto,

velocidad = 384,392 / 72

= 5338,7777 kilómetros por hora

Dado que se supone que la distancia recorrida diariamente es la misma m:

El número de kilómetros recorridos por día:

5338,7777 kilómetros por hora * 24

= 128130,66 kilometros

4 0
2 years ago
If a vertical line is dropped from the x-axis to the point (12, –9) in the diagram below, what is the value of sec?
dem82 [27]

Answer:

Value of \sec \theta = \frac{5}{4}

Step-by-step explanation:

Given: A vertical line is dropped from the x-axis to the point (12, -9) as shown in the diagram below;

To find the value of \sec \theta.

By definition of secants;

\sec \theta = \frac{1}{\cos \theta}

Now, first find the cosine of angle \theta

As the point (12 , -9) lies in the IV quadrant , where \cos \theta > 0

Consider a right angle triangle;

here, Adjacent side = 12 units and Opposite side = -9 units

Using Pythagoras theorem;

(Hypotenuse side)^2= (12)^2 + (-9)^2 = 144 + 81 = 225

or

Hypotenuse = \sqrt{225} =15 units

Cosine ratio is defined as in a right angle triangle, the ratio of adjacent side to hypotenuse side.

\cos \theta = \frac{Adjacent side}{Hypotenuse side}

then;

\cos \theta = \frac{12}{15} = \frac{4}{5}

and

\sec \theta = \frac{1}{\cos \theta}= \frac{1}{\frac{4}{5}} = \frac{5}{4}

therefore, the value of \sec \theta is, \frac{5}{4}

5 0
3 years ago
Read 2 more answers
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