If BD = 7x – 10, BC = 4x – 29, and CD = 5x – 9, find each value.

Answer:

55°

Step-by-step explanation:

The problem does not have a suitable diagram. Please check the attachment for the diagram.

Observing the diagram, it is evident that the triangle is isosceles, as it has two sides that are congruent (i.e., the same length). Since these sides are identical, the base angles are consequently also equal.

From the diagram, <EFG = <EGF

Since  <EFG  = 55°, it follows that  <EGF = y = 55°

Thus, the value of y is established as 55°

Answer:

The P-value ranges between 2.5% and 5% according to the t-table.

Step-by-step explanation:

A random sample of 16 students from a large university showed an average age of 25 years with a standard deviation of 2 years.

Let = true average age of all students at the university.

So, the Null Hypothesis, : 24 years {indicating the average age is less than or equal to 24 years}

Alternate Hypothesis, : > 24 years {indicating the average age is significantly greater than 24 years}

Here we employ the One-sample t-test statistics as the population's standard deviation is unknown;

                              T.S. = ~

where, = sample average age = 25 years

             s = sample standard deviation = 2 years

             n = sample size = 16

This gives us the test statistics = ~

                                     = 2

The value of the t-test statistics is 2.

Moreover, the P-value of the test-statistics can be found as follows;

P-value = P( > 2) = 0.034 {as per the t-table}

Thus, the P-value lies between 2.5% and 5% based on the t-table.

Answer:

a. 0.82%

b. 71.11%

c. 0.564 micrometer

Step-by-step explanation:

To find the z value for each measurement, we must calculate and determine the percentage they correspond to, and the difference will give us the percentage between those two statistics.

The equation for z is:

z = (x - m) / (sd)

Here, x is the value being evaluated, m denotes the mean, and sd represents the standard deviation.

a.

For 0.62 copies, we calculate:

z = (0.62 - 0.5) / (0.05)

z = 2.4

This translates to 0.9918.

Therefore, p (x > 0.62) = 1 - 0.9918

p (x > 0.62) =  0.0082 = 0.82%

b.

For 0.47 copies, we have:

z = (0.47 - 0.5) / (0.05)

z = -0.6, which equates to 0.2742.

For 0.63 copies:

z = (0.63 - 0.5) / (0.05)

z = -2.6, which yields 0.9953.

Hence, p (0.47 > x > 0.63) = 0.9953 - 0.2742

p (0.47 > x > 0.63) = 0.7211 = 72.11 %

c.

For x copies, we find:

p = 0.9 corresponds to z = 1.28.

Thus, 1.28 = (x - 0.5) / (0.05)

From which we derive:

x = 1.28*0.05 + 0.5

x = 0.564 micrometer

2G=B+3
G=B-4

2(B-4)=B+3
2B-8=B+3
B=11

Bert possesses 11 cents

1. Selected Case B. 2. 9 cm³. 3. 20 cm. 4. 4.5 m³. Explanation: In question 1, we need to fit a drum with a volume of 14,000 cm³. The volume of a cylinder can be calculated via the formula πr²h. For Case A, with r = 100 mm (10 cm) and h = 300 mm (30 cm), the total volume is approximately 9424.78 cm³, insufficient for the given drum. Case B, with r = 200 mm (20 cm) and h = 30 cm, gives a volume of approximately 37699.11 cm³. Case C with r = 32 cm and h = 250 mm (25 cm) results in a volume of about 80424.77 cm³. The smallest volume among Cases B and C is Case B at 37699.11 cm³, thus it is the correct choice. For question 2, the dimensions of the speaker are Length = 45 cm = 0.45 m, Width = 0.4 m, Height = 50 cm = 0.5 m, leading to a volume of 0.09 m³ or 9 cm³. Question 3 involves a speaker with a volume of 30,000 cm³ with Length = 30 cm = 0.45 m and Height = 500 mm = 50 cm, requiring to find its Width: 30,000 = 30 × W × 50, hence W = 20 cm. For question 4, with dimensions of Base = 2 m, Length = 3 m, Height =1.5 m, the volume of the prism is calculated as 4.5 m³.