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2 years ago

Let logba=3 logbc=2 logbd=5 what is the value of logba^3d^4/c^2

1 answer:

8 0

$Use:\\\log_ax+\log_ay=\log_a(xy)\\\\\log_ax-\log_ay=\log_a\dfrac{x}{y}\\\\\log_ax^n=n\cdot\log_ax$

$\log_ba=3;\ \log_bc=2;\ \log_bd=5$

$\log_b\dfrac{a^3d^4}{c^2}=\log_b(a^3d^4)-\log_bc^2=\log_ba^3+\log_bd^4-\log_bc^2\\\\=3\log_ba+4\log_bd-2\log_bc=3\cdot3+4\cdot5-2\cdot2=9+20-4=25$

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A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line. He must recalibrate his machines

storchak [24]

Answer:

The null hypothesis is $H_o: \mu = 4$ .

The alternate hypothesis is $H_a: \mu \neq 4$

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

Step-by-step explanation:

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line.

This means that the null hypothesis is that they are 4.00 cm long, that is:

$H_o: \mu = 4$

At the alternate hypothesis we test if it is different. So

$H_a: \mu \neq 4$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

4 is tested at the null hypothesis:

This means that $\mu = 4$

After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm.

This means that $n = 196, X = 4.14$

He knows that the population standard deviation is 0.83 cm.

This means that $\sigma = 0.83$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{4.14 - 4}{\frac{0.83}{\sqrt{196}}}$

$z = 2.36$

Pvalue of the test and decision:

The pvalue of the test is the probability that the sample mean is different by at least 4.14 - 4 = 0.14 from the target value, which is P(|z| > 2.36), which is 2 multiplied by the pvalue of z = -2.36.

Looking at the z-table, z = -2.36 has a pvalue of 0.0091

2*0.0091 = 0.0182

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

5 0

2 years ago

Muhammad owns 8 fewer swim suits than Charlie. Let k represent the number of Charlie's swim suits. Identify the expression that

andre [41]

Answer:

Number of Muhammad's swim suits = k - 8

Step-by-step explanation:

Given:

Number of Charlie's swim suits = K

Number of Muhammad's swim suits = 8 less than Charlie

Find:

Expression [Number of Muhammad's swim suits]

Computation:

Number of Muhammad's swim suits = 8 less than Charlie

Number of Muhammad's swim suits = k - 8

6 0

2 years ago

one pound of swordfish costs as much as 1.5 pounds of salmon. Mrs. O pays $39 for 2 pounds of salmon and 3 pounds of swordfish.

Alex73 [517]

Answer:

Not sure which ratio you need, but 6/9 = 2/3

Step-by-step explanation:

1.5xsalmon=swordfish

$39 = 2lb salmon and 3lb swordfish

1lb salmon=$6 6+6 = 12

1lb swordfish=$9 9+9+9 = 27

12+27 = 39

6 0

2 years ago

Simplify each expression 1. 2x + (x - 4) + (2y - 5) 2. 3(x - 2) + 4(x + 3)

Shtirlitz [24]

Answer:

1. 3x-9+2y

2. 7x+6

Step-by-step explanation:

1. 2x + (x - 4) + (2y - 5)

2x+x-4+2y-5

3x-9+2y

2. 3(x - 2) + 4(x + 3)

3x+4x-6+12

7x+6

3 0

2 years ago

Read 2 more answers

Plz help 2-5!!! its already missing I WILL GIVE BRAINLIST!!!!!!!

lisabon 2012 [21]

Answer:

#2: 26 #3: 68 #4) 19 #5) 23

Step-by-step explanation:

#2) So, 208 divided by 8 = 26

#3) 92 - 24 = 68

#4) 76(.75) = 57, 76-57 = 19

#5) 31 - 8 = 23

Hope i helped.

7 0

2 years ago