For the following diagrams find the measure for all the Missing angles

Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:

Sample mean of  [tex]x = 12.7[/tex]

Population standard deviation of  [tex]\sigma = 6.37[/tex]

Sample size of .n = 50

The margin of error is:

[tex]M = z \frac{\sigma }{\sqrt{n} }[/tex]

In which z is the critical value.

We have to find the critical value, which is z with a p-value of  [tex]\frac{1+\alpha }{2}[/tex] , in which  [tex]\alpha[/tex] is the confidence level.

In this problem, , thus, z with a p-value of , which means that it is z = 1.96.

Then:

[tex]M= 1.96\frac{6.37}{\sqrt{50} } = 1.77[/tex]

The confidence interval is the sample mean plus/minutes the margin of error, hence:

x- M = 12.17 - 1.77 =10.4

x+M = 12.17 + 1.77 = 13.94

The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

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Answer:

3x-4=2x+7 thus: (D)

x = 11

Step-by-step explanation:

Solve for x:

3 x - 4 = 2 x + 7

Subtract 2 x from both sides:

(3 x - 2 x) - 4 = (2 x - 2 x) + 7

3 x - 2 x = x:

x - 4 = (2 x - 2 x) + 7

2 x - 2 x = 0:

x - 4 = 7

Add 4 to both sides:

x + (4 - 4) = 4 + 7

4 - 4 = 0:

x = 7 + 4

7 + 4 = 11:

Answer: x = 11

___________________________

Solve for x:

4 - 2 (x - 5) = x - 19

-2 (x - 5) = -2 x + 10:

(-2 x + 10) + 4 = x - 19

Add like terms. 4 + 10 = 14:

-2 x + 14 = x - 19

Subtract x from both sides:

(-2 x - x) + 14 = (x - x) - 19

-2 x - x = -3 x:

-3 x + 14 = (x - x) - 19

x - x = 0:

-3 x + 14 = -19

Subtract 14 from both sides:

(14 - 14) - 3 x = -14 - 19

14 - 14 = 0:

-3 x = -14 - 19

-14 - 19 = -33:

-3 x = -33

Divide both sides of -3 x = -33 by -3:

(-3 x)/(-3) = (-33)/(-3)

(-3)/(-3) = 1:

x = (-33)/(-3)

The gcd of -33 and -3 is -3, so (-33)/(-3) = (-3×11)/(-3×1) = (-3)/(-3)×11 = 11:

Answer: x = 11

Answer:3x-4=2x+7

Step-by-step explanation:

first,  4-2x+10=x-19

        14+19 =x+2x

           33=3x

               x=11

A. 2x+10=8

    2x= -18

      x=-9

B. 3x-9=9

       3x=18

         x=6

C. x+2=2x-3

      3x = 5

         x = 5/3

D. 3x-4 = 2x+7

    3x-2x=7+4

          x=11

The solution of the given equation is:

[tex]\frac{log 9}{Log 2} - 1[/tex]  = 2.16992500144

Logarithm:

Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8. Similarly, 2 = log10 100 because 102 = 100. The latter kind of logarithm (that is, the base 10 logarithm) is called the ordinary logarithm or the Briggs logarithm and simply write log n.

Invented in the 17th century to speed up calculations, logarithms greatly reduced the time required to multiply large numbers. These were the basis of numerical computation for over 300 years until the mechanical calculator of the late 19th century and his 20th century computer sophistication made it obsolete for large-scale calculations. However, the natural logarithm (with base e ≅ 2.71828 and written ln n) continues to be one of the most useful functions in mathematics, being applied to mathematical models in the physical and biological sciences.

According to the question:

2ˣ=4.5

Take the logarithm of both sides of the equation

log2ˣ = log9 / 2

x . log2 = log9 − log2

divide both sides of the equation by log 2:

          [tex]\frac{x Log 2}{Log 2} = \frac{Log 9 - Log 2}{Log 2}[/tex]

⇒  x = [tex]\frac{log 9}{Log 2} - 1[/tex]

⇒ x = 2.16992500144.

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Answer:There are no choices but i do this type of work on edge so i could proably do it without the choices.

Step-by-step explanation:Answer would be (3x-2)(2x+3)

3x times 2x would be 6x squared  3x times 3 is 9x -2 times 2x is -4x

9x-4x is 5x and -2 times 3 is -6

Hope this helps:)

HAPPY NEW YEARS

Answer:

80+60+3x+4=180

140+3x+4=180

144+3x=180

3x=180-144

3x=36

x=12

Answer:

x = 12

Step-by-step explanation:

All triangles equal to 180 degrees so, we can set up this expression:

180 = (3x + 4) + 80 + 60

All we have to do is solve:

180 = (3x + 4) + 80 + 60

180 = 3x + 4 + 140

180 = 3x + 144

-144        -144

36 = 3x

/3     /3

12 = x

Answer: 25 cars

Step-by-step explanation:

Take 10 divided by 8 = 1.25 car per men

Then take 1.25 times 20 = 25 cars

Answer:

1. 45*4 = 180
2. 65*5= 325
3. 77*6=462
4. 89*7= 623

5. 52*3= 156

Answer:

5.8

13.25

22.62

34.23

16.56

Step-by-step explanation:

The test statistic is less than - 1.796

Hypothesisi test

H0: μ = 46

Ha: μ < 46

This is a lower tailed test

mean = 42

standard deviation = 11.9

sample size n = 12

The level of significance α = 0.05

degree of freedom df = n - 1 = 12 - 1 = 11

Test statistic = (x - mean)/(standard deviation / √n) = (42 - 46)/(11.9 / √12) = - 1.164

Test statistic = - 1.164

Using t- table, we can observe that the p - value is between 0.10 and 0.15

Using excel we find p - value = P(t < - 1.796)

p value = 0.1344

H0: μ < 46, rejection rule is

Reject H0 if test statistic < - 1. 796

Therefore, we reject the hypothesis as the test statistic is less than - 1.796

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Domain is the set of values under which a function is defined.

Range is the outcome of all the values of the domain when put in a function.

graphically, the domain is the set of values under which we get some value in the y-axis for a particular function graph .

while the range is the y-coordinate of all the points lying on the graph .

As the graph is not posted by you.

see this graph of the modulus function for instance:

        so,  R is the domain.

        but the range is only positive values of R in y.

        and,

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Particular solution for the equation a. Y" – 6y + 5y = 5x2 + 3x – 16 – 9223 is

5y = -15e²⁷ - 23/5

Particular solution for b. y" – 6y' + 5y = -10x2 - 6x + 32 +622 is 5y = 8x+ 218

Given:

y= 3e²⁷ (Solution 1)

Y = x² + 3x (Solution 2)

y" - 6y' + 5y = -9222 (Equation 1)

y" - 6y' + 5y = 5x² + 3x – 16  (Equation 2)

Where [tex]y^{"}[/tex] represents the double derivative(d²y) of y and [tex]y^{'}[/tex] represents the first derivative(dy) of the equation y.

Find Solutions for:

a. Y" – 6y + 5y = 5x² + 3x – 16 – 9223

b. y" – 6y' + 5y = -10x² - 6x + 32 +622

y= 3e²⁷ (Solution 1)(Given in the question)

Taking derivative on both sides

by = 3 de²⁷

∵ e²⁷  is constant in comparison to dy the derivative will be 0. Thus, d²y of y is also equal to zero

Then, putting values in the equation 1

- 6y' + 5y + y" = -9222 (Equation 1)

(0) - 6(0) +5(3e²⁷) = -9222

Thus, 15e²⁷ = -9222

5e²⁷ = -3074

e²⁷ = -614.8

Y = x² + 3x (Solution 2)(Given in the question)

Taking derivative on both sides

dY/dx= 2x + 3 -(iii)

taking derivative of y'

d²Y/dx² = 2

∵ 3 is a constant in dy/dx.

Then, putting values in the equation 2

y" -+ 5y - 6y'  = 5x² + 3x - 16

(2) - 6(2x + 3) +5y = 5x² + 3x - 16 + 12x - 12x

2 - 12 + 18x + 5y = 5x² +15x - 16 -12x

-10 + 18x - 15x + 5y = 5y -16 -12x

3x + 12x =10 - 16

15x = -6

x= -2/5

Putting values of x, y, dy and  d²y in equations (i) & (ii)

a. Y" – 6y + 5y = 5x² + 3x - 16 – 9223

(2)  -6(2x+3) + 5y = 5x² + 3x - 16 - 9223 + 12x - 12x

2 - 12x -18 + 5y = 5y - 9223 - 16 - 12x

2 + - 18 + 5y -6/5 -(9222 + 1)

2 + 24-6/5 + 5y + 15e²⁷ - 1 = 0

5y + 15e²⁷ + 18/5 + 1= 0

5y + 15e²⁷ + 23/5= 0

5y = -15e²⁷ - 23/5

b. y" – 6y' + 5y = -10x² - 6x + 32 +622

(0) -6(0) + 5y = -10x² - 6x +654

5y = -10x² - 6x -24x + 24x + 654

5y = -10(x² + 3x) +24x + 654

5y = -10y + 24x + 654

5y +10y = 24x + 654

15y=24x+654

5y = 8x+ 218

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Answer:

Write in standard form.

2x+7y=−49

Step-by-step explanation:

Each right triangle has a missing value of 1.9096 where = angle, O = opposing side, A = adjacent side, and H = hypotenuse.

A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangle triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.

given,

1.9096 is what's lacking.

SOH CAH TOA's identification would appear to be:

The opposite or hypotenuse of sin

Sinθ = O/H

the following being spoken

H = 11 \sin θ = 0.1736

To replace having, use:

0.1736 = O/11

O = 11 * 0.1736

O = 1.9096

the missing value is 1.9096.

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Store B is offering the best unit rate for bananas.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Grocery Store A is selling bananas for $0.75 for 12 pounds.

The unit rate will be = 0.75/12 = 0.06

Grocery Store B is selling 5 pounds of bananas for $3.75.

The unit rate will be = 3.75/5 = 0.75

Hence, Store B is offering the best unit rate for bananas.

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Answer: The first pair of equations, i.e., −3.2x=0.64 and x/4 =−0.05, have exactly the same solution. In both of these equations, the value of x comes out as -0.2.

Step-by-step explanation: Simplifying the first set of equations, we get:[tex]-3.2x=0.64[/tex]

[tex]x=0.64/-3.2[/tex]

x=-0.2

 [tex]x/4=-0.05[/tex]

[tex]x=-0.05*4[/tex]

x=-0.2

Simplifying the second set of equations, we get:

[tex]3/8x=1[/tex]

[tex]x=8/3[/tex]

x=2.66

[tex]1/3x=1/8[/tex]

[tex]x=1/8*3[/tex]

x=0.375

Simplifying the third set of equations, we get:

[tex]x/3.2=1.8[/tex]

[tex]x=1.8*3.2[/tex]

x=5.76

[tex]1.8x=3.2[/tex]

[tex]x=3.2/1.8[/tex]

x=1.77

Simplifying the fourth set of equations, we get:

[tex]-3/4x=5/2[/tex]

[tex]x=5/2*-4/3[/tex]

x=-3.33

[tex]5/2x=-3/4[/tex]

[tex]x=-3/4*2/5[/tex]

x=-0.3

Therefore, the first pair of equations, i.e., −3.2x=0.64 and x/4 =−0.05 have exactly the same solution.

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Probability of getting head = 0.45

Probability of getting tail = 1- 0.45

                                         = 0.55

No of flip flops = 10

You can select numerous impressions with the Tableau Lasso Selection tool by tracing a freehand shape around them.

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By using the tabular data given , the complete relative frequency table has been shown below

What is tabular data?

Data given in the form of rows and columns is known as tabular data.

The relative frequency table has been shown below

Frequency of students who like to like to fly and can drive = 0.32

Total frequency of students who like to fly = 0.70

Frequency of students who like to like to fly cannot drive = 0.70 - 0.32 = 0.38

Frequency of students who can drive = 0.45

Frequency of students who cannot drive = 0.55

Frequency of students who do not like to fly can drive = 0.45 - 0.32 = 0.13

Frequency of students who do not like to fly cannot drive = 0.55 - 0.38 = 0.17

Total frequency of students who do not like to fly = 0.13 + 0.17 = 0.30

The complete relative frequency table is

                                 Can drive       Cannot drive     Row totals

Like to fly                    0.32                  0.38                 0.70

Do not like to fly          0.13                  0.17                  0.30

Column totals              0.45                 0.55                   1

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The average acceleration is - 1.24 m/s². The result is calculated by using calculator. See the picture in the attachment!

Average acceleration is the rate of change in velocity per unit time. The formula can be expressed as

[tex]\overline{a} = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex]

Where

Calculate this average acceleration using calculator!

[tex]\overline{a} = \frac{-3.7 \: m/s \: - 13.9 \: m/s}{21.4 \: s- 7.2 \: s}[/tex]

See the picture in the attachment!

The average acceleration after rounding is

[tex]\overline{a} = -1.23943661972 \: m/s \: /s[/tex]

[tex]\overline{a} = -1.24 \: m/s^{2}[/tex]

Hence, the average acceleration from the data is - 1.24 m/s².

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if (x+2)² = k , making x the subject is x = √k - 2

The subject of a formula is the variable that is being worked out. It can be recognised as the letter on its own on one side of the equals sign.

For example, if V = πr²h and we want to make r the subject of the formula, we make r in place of V.

Therefore r² = V/πh

r = √ (V/πh)

Similarly

(x+2)² = k

when we square root both sides

x+2 = √k

Collecting like terms

x = √k - 2

therefore making x the subject in the formula (x+2)² = k in terms of k is x = √k - 2

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Answer:

8

Step-by-step explanation:

x=-4 perfectly suits x<=-1 since -4<=-1

Hence, when calculating g(-4), you need to apply the expression -x+4

Hence:

g(-4)=

-x+4=

-(-4)+4= ==>   plug in -4 for x

4 + 4 = 8   ==> Negating a negative number is equaled to taking the

                       positive number.

II and III only distributions has a mean that varies

The mean of a distribution is a measure of the central tendency of the data, and it can vary depending on the sample being analyzed.

For the population distribution, the mean is a fixed value that is calculated using all of the data in the population. The mean of the population distribution does not vary.

For the distribution of sample data, the mean is calculated using the data in the sample. If you take different samples from the same population, the mean of each sample will be different, so the mean of the distribution of sample data varies.

For the sampling distribution of the sample mean, the mean is calculated using the means of multiple samples. The mean of the sampling distribution is known as the population mean. As with the distribution of sample data, the mean of the sampling distribution varies depending on the samples that are used to calculate it.

Therefore, the mean of the distribution of sample data and the sampling distribution of the sample mean both vary, while the mean of the population distribution does not vary.

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On solving the provided question we can say that - the answer is 552 and 558, as consecutive integers.

Consecutive integers are those integers in a computation formula that follow one another. No number is lost in a sequence when enumerating successive numbers, hence their spacing is always consistent. Consecutive integers are the next numbers in ascending order. The consecutive integers formula may be used to discover consecutive integers for any number or to determine if a set of numbers is consecutive or not.

First set the 3 numbers to be x-2, x, and x+2. So:

x-2+x+x+2=554

3x=554

There is no solution to this issue since three cannot split equally into 554. In reality

182+184+186=552

184+186+188=558

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Answer: 1/7

Step-by-step explanation:

There are total of 7 gloves

There is 1 black glove

So take 1 divided by 7

The Fraction is 1/7

The probability that the number of lost-time accidents occurring over a period of 7 days will be exactly 3 is 0.7295

Binomial Distribution

The binomial distribution is the sum of a series of multiple independent and identically distributed Bernoulli trials. In a Bernoulli trial, the experiment is said to be random and can only have two possible outcomes- success or failure.

In a binomial distribution the probability of getting success must remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is ½ or 0.5 for every trial we conduct, since there are only two possible outcomes.

Mean rate of lost time accident = 0.3 per day

probability that the number of lost-time accidents occurring over a period of 7 days will be no more than 3.

n = 7

Using binomial distribution formula :

P(x ≤3)

Probability of success (p) = 0.3

1 - p = 1- 0.3 = 0.7

nCx * p^x * (1 - p)^(n-x)

Using the binomial probability distribution calculator to save computation time :

P(x ≤3) = P(x = 0) + p(x = 1) + p(x = 2) + p(x = 3)

P(x ≤3) = 0.0403 + 0.1556 + 0.2668 + 0.2668

P(x ≤3) = 0.7295

0.7295

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Step-by-step explanation:

when you look at that right-angled triangle that is created by the plank as Hypotenuse (the side opposite of the 90° angle), and the distance on the ground from the wall and the height on the wall (from ground to the plank) as the legs, we know that the Hypotenuse (the plank) is the radius of the trigonometric circle we can draw there, and the 15 m ground distance from the wall is

cos(our angle) × radius

15×sqrt(3) × cos(our angle) = 15

cos(our angle) = 1/ sqrt(3) = 0.577350269...

our angle = 54.73561032...°